diff --git a/05DWB1NzozM.txt b/05DWB1NzozM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4f94b197c7d3bafd97cbf2e55d4217c9ce369b5d
--- /dev/null
+++ b/05DWB1NzozM.txt
@@ -0,0 +1,827 @@
+align:start position:0%
+ 
+one of the most powerful properties of
+
+ align:start position:0%
+one of the most powerful properties of
+ 
+
+ align:start position:0%
+one of the most powerful properties of
+integer optimization is the ability to
+
+ align:start position:0%
+integer optimization is the ability to
+ 
+
+ align:start position:0%
+integer optimization is the ability to
+add what we call logical constraints
+
+ align:start position:0%
+add what we call logical constraints
+ 
+
+ align:start position:0%
+add what we call logical constraints
+these use binary variables to implement
+
+ align:start position:0%
+these use binary variables to implement
+ 
+
+ align:start position:0%
+these use binary variables to implement
+different restrictions let's look at a
+
+ align:start position:0%
+different restrictions let's look at a
+ 
+
+ align:start position:0%
+different restrictions let's look at a
+few examples suppose we want to add the
+
+ align:start position:0%
+few examples suppose we want to add the
+ 
+
+ align:start position:0%
+few examples suppose we want to add the
+constraint that a and B can't play in
+
+ align:start position:0%
+constraint that a and B can't play in
+ 
+
+ align:start position:0%
+constraint that a and B can't play in
+both weeks 3 & 4 we can do this by
+
+ align:start position:0%
+both weeks 3 & 4 we can do this by
+ 
+
+ align:start position:0%
+both weeks 3 & 4 we can do this by
+adding the constraint X a B 3 plus X a B
+
+ align:start position:0%
+adding the constraint X a B 3 plus X a B
+ 
+
+ align:start position:0%
+adding the constraint X a B 3 plus X a B
+4 less than or equal to 1 what our
+
+ align:start position:0%
+4 less than or equal to 1 what our
+ 
+
+ align:start position:0%
+4 less than or equal to 1 what our
+feasible values for these two variables
+
+ align:start position:0%
+feasible values for these two variables
+ 
+
+ align:start position:0%
+feasible values for these two variables
+given this constraint both variables can
+
+ align:start position:0%
+given this constraint both variables can
+ 
+
+ align:start position:0%
+given this constraint both variables can
+be 0 or 1 or the other can be 1 a
+
+ align:start position:0%
+be 0 or 1 or the other can be 1 a
+ 
+
+ align:start position:0%
+be 0 or 1 or the other can be 1 a
+solution with both variables equal to 1
+
+ align:start position:0%
+solution with both variables equal to 1
+ 
+
+ align:start position:0%
+solution with both variables equal to 1
+would be infeasible so this constraint
+
+ align:start position:0%
+would be infeasible so this constraint
+ 
+
+ align:start position:0%
+would be infeasible so this constraint
+models the restriction that teams a and
+
+ align:start position:0%
+models the restriction that teams a and
+ 
+
+ align:start position:0%
+models the restriction that teams a and
+B can't play in both weeks 3 & 4 note
+
+ align:start position:0%
+B can't play in both weeks 3 & 4 note
+ 
+
+ align:start position:0%
+B can't play in both weeks 3 & 4 note
+that this only works because the
+
+ align:start position:0%
+that this only works because the
+ 
+
+ align:start position:0%
+that this only works because the
+variables only take values 0 or 1 let's
+
+ align:start position:0%
+variables only take values 0 or 1 let's
+ 
+
+ align:start position:0%
+variables only take values 0 or 1 let's
+look at another example suppose we want
+
+ align:start position:0%
+look at another example suppose we want
+ 
+
+ align:start position:0%
+look at another example suppose we want
+to add the restriction that if a and B
+
+ align:start position:0%
+to add the restriction that if a and B
+ 
+
+ align:start position:0%
+to add the restriction that if a and B
+play in week 4 then they must also play
+
+ align:start position:0%
+play in week 4 then they must also play
+ 
+
+ align:start position:0%
+play in week 4 then they must also play
+in week 2 we can do this by adding the
+
+ align:start position:0%
+in week 2 we can do this by adding the
+ 
+
+ align:start position:0%
+in week 2 we can do this by adding the
+constraint X a B 2 greater than or equal
+
+ align:start position:0%
+constraint X a B 2 greater than or equal
+ 
+
+ align:start position:0%
+constraint X a B 2 greater than or equal
+to X a B 4 let's consider feasible
+
+ align:start position:0%
+to X a B 4 let's consider feasible
+ 
+
+ align:start position:0%
+to X a B 4 let's consider feasible
+solutions to this constraint if X a B 4
+
+ align:start position:0%
+solutions to this constraint if X a B 4
+ 
+
+ align:start position:0%
+solutions to this constraint if X a B 4
+equals 1 then X a B 2 must also equal 1
+
+ align:start position:0%
+equals 1 then X a B 2 must also equal 1
+ 
+
+ align:start position:0%
+equals 1 then X a B 2 must also equal 1
+but if X a B 4 equals 0 then X a B 2 can
+
+ align:start position:0%
+but if X a B 4 equals 0 then X a B 2 can
+ 
+
+ align:start position:0%
+but if X a B 4 equals 0 then X a B 2 can
+be equal to either 0 or 1
+
+ align:start position:0%
+be equal to either 0 or 1
+ 
+
+ align:start position:0%
+be equal to either 0 or 1
+so this constraint exactly models the
+
+ align:start position:0%
+so this constraint exactly models the
+ 
+
+ align:start position:0%
+so this constraint exactly models the
+restriction we wanted lastly suppose
+
+ align:start position:0%
+restriction we wanted lastly suppose
+ 
+
+ align:start position:0%
+restriction we wanted lastly suppose
+that Team C and D must play in week 1 or
+
+ align:start position:0%
+that Team C and D must play in week 1 or
+ 
+
+ align:start position:0%
+that Team C and D must play in week 1 or
+2 they can't play both games in weeks 3
+
+ align:start position:0%
+2 they can't play both games in weeks 3
+ 
+
+ align:start position:0%
+2 they can't play both games in weeks 3
+& 4 we can model this constraint with X
+
+ align:start position:0%
+& 4 we can model this constraint with X
+ 
+
+ align:start position:0%
+& 4 we can model this constraint with X
+CD 1 plus X CD 2 greater than or equal
+
+ align:start position:0%
+CD 1 plus X CD 2 greater than or equal
+ 
+
+ align:start position:0%
+CD 1 plus X CD 2 greater than or equal
+to 1 feasible solutions are both
+
+ align:start position:0%
+to 1 feasible solutions are both
+ 
+
+ align:start position:0%
+to 1 feasible solutions are both
+variables equal to 1 or one variable
+
+ align:start position:0%
+variables equal to 1 or one variable
+ 
+
+ align:start position:0%
+variables equal to 1 or one variable
+equal to 1 both variables can't equal 0
+
+ align:start position:0%
+equal to 1 both variables can't equal 0
+ 
+
+ align:start position:0%
+equal to 1 both variables can't equal 0
+these are just a few example
+
+ align:start position:0%
+these are just a few example
+ 
+
+ align:start position:0%
+these are just a few example
+of logical constraints that we can
+
+ align:start position:0%
+of logical constraints that we can
+ 
+
+ align:start position:0%
+of logical constraints that we can
+implement using binary variables let's
+
+ align:start position:0%
+implement using binary variables let's
+ 
+
+ align:start position:0%
+implement using binary variables let's
+go into libreoffice now and add these
+
+ align:start position:0%
+go into libreoffice now and add these
+ 
+
+ align:start position:0%
+go into libreoffice now and add these
+constraints to our model in our
+
+ align:start position:0%
+constraints to our model in our
+ 
+
+ align:start position:0%
+constraints to our model in our
+spreadsheet let's scroll down to the
+
+ align:start position:0%
+spreadsheet let's scroll down to the
+ 
+
+ align:start position:0%
+spreadsheet let's scroll down to the
+bottom of our constraints list we want
+
+ align:start position:0%
+bottom of our constraints list we want
+ 
+
+ align:start position:0%
+bottom of our constraints list we want
+to add in three new constraints the
+
+ align:start position:0%
+to add in three new constraints the
+ 
+
+ align:start position:0%
+to add in three new constraints the
+first is that teams a and B can't play
+
+ align:start position:0%
+first is that teams a and B can't play
+ 
+
+ align:start position:0%
+first is that teams a and B can't play
+in both weeks three and four the second
+
+ align:start position:0%
+in both weeks three and four the second
+ 
+
+ align:start position:0%
+in both weeks three and four the second
+is that if teams a and B play in week
+
+ align:start position:0%
+is that if teams a and B play in week
+ 
+
+ align:start position:0%
+is that if teams a and B play in week
+four then they have to play a week two
+
+ align:start position:0%
+four then they have to play a week two
+ 
+
+ align:start position:0%
+four then they have to play a week two
+and the third is that team C and D have
+
+ align:start position:0%
+and the third is that team C and D have
+ 
+
+ align:start position:0%
+and the third is that team C and D have
+to play in weeks one and/or two so to
+
+ align:start position:0%
+to play in weeks one and/or two so to
+ 
+
+ align:start position:0%
+to play in weeks one and/or two so to
+add the first constraint our left-hand
+
+ align:start position:0%
+add the first constraint our left-hand
+ 
+
+ align:start position:0%
+add the first constraint our left-hand
+side should be equal to the sum of the
+
+ align:start position:0%
+side should be equal to the sum of the
+ 
+
+ align:start position:0%
+side should be equal to the sum of the
+variables for a and B in weeks three and
+
+ align:start position:0%
+variables for a and B in weeks three and
+ 
+
+ align:start position:0%
+variables for a and B in weeks three and
+four our sign is less than or equal to
+
+ align:start position:0%
+four our sign is less than or equal to
+ 
+
+ align:start position:0%
+four our sign is less than or equal to
+and our right-hand side is 1 our second
+
+ align:start position:0%
+and our right-hand side is 1 our second
+ 
+
+ align:start position:0%
+and our right-hand side is 1 our second
+constraint the left-hand side is equal
+
+ align:start position:0%
+constraint the left-hand side is equal
+ 
+
+ align:start position:0%
+constraint the left-hand side is equal
+to the decision variable for teams a and
+
+ align:start position:0%
+to the decision variable for teams a and
+ 
+
+ align:start position:0%
+to the decision variable for teams a and
+B in week 2
+
+ align:start position:0%
+B in week 2
+ 
+
+ align:start position:0%
+B in week 2
+the sign is greater than or equal to and
+
+ align:start position:0%
+the sign is greater than or equal to and
+ 
+
+ align:start position:0%
+the sign is greater than or equal to and
+the right-hand side is equal to the
+
+ align:start position:0%
+the right-hand side is equal to the
+ 
+
+ align:start position:0%
+the right-hand side is equal to the
+decision variable for teams a and B in
+
+ align:start position:0%
+decision variable for teams a and B in
+ 
+
+ align:start position:0%
+decision variable for teams a and B in
+week 4 for our third constraint the
+
+ align:start position:0%
+week 4 for our third constraint the
+ 
+
+ align:start position:0%
+week 4 for our third constraint the
+left-hand side is equal to the decision
+
+ align:start position:0%
+left-hand side is equal to the decision
+ 
+
+ align:start position:0%
+left-hand side is equal to the decision
+variables for Team C and D in weeks one
+
+ align:start position:0%
+variables for Team C and D in weeks one
+ 
+
+ align:start position:0%
+variables for Team C and D in weeks one
+and two the sine is greater than or
+
+ align:start position:0%
+and two the sine is greater than or
+ 
+
+ align:start position:0%
+and two the sine is greater than or
+equal to and the right-hand side is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can see here that our current optimal
+
+ align:start position:0%
+we can see here that our current optimal
+ 
+
+ align:start position:0%
+we can see here that our current optimal
+solution violates every single one of
+
+ align:start position:0%
+solution violates every single one of
+ 
+
+ align:start position:0%
+solution violates every single one of
+these constraints so let's go ahead and
+
+ align:start position:0%
+these constraints so let's go ahead and
+ 
+
+ align:start position:0%
+these constraints so let's go ahead and
+Reese all var model to get a new
+
+ align:start position:0%
+Reese all var model to get a new
+ 
+
+ align:start position:0%
+Reese all var model to get a new
+solution so go to the Tools menu and
+
+ align:start position:0%
+solution so go to the Tools menu and
+ 
+
+ align:start position:0%
+solution so go to the Tools menu and
+select solver now let's add in our new
+
+ align:start position:0%
+select solver now let's add in our new
+ 
+
+ align:start position:0%
+select solver now let's add in our new
+constraints so in the third cell
+
+ align:start position:0%
+constraints so in the third cell
+ 
+
+ align:start position:0%
+constraints so in the third cell
+reference box go in and select the
+
+ align:start position:0%
+reference box go in and select the
+ 
+
+ align:start position:0%
+reference box go in and select the
+left-hand side for the first constraint
+
+ align:start position:0%
+left-hand side for the first constraint
+ 
+
+ align:start position:0%
+left-hand side for the first constraint
+make sure the operator is less than or
+
+ align:start position:0%
+make sure the operator is less than or
+ 
+
+ align:start position:0%
+make sure the operator is less than or
+equal to and select the right-hand side
+
+ align:start position:0%
+equal to and select the right-hand side
+ 
+
+ align:start position:0%
+equal to and select the right-hand side
+for the value then in the fourth cell
+
+ align:start position:0%
+for the value then in the fourth cell
+ 
+
+ align:start position:0%
+for the value then in the fourth cell
+reference box select both of the
+
+ align:start position:0%
+reference box select both of the
+ 
+
+ align:start position:0%
+reference box select both of the
+left-hand sides for the
+
+ align:start position:0%
+left-hand sides for the
+ 
+
+ align:start position:0%
+left-hand sides for the
+other constraints because they're both
+
+ align:start position:0%
+other constraints because they're both
+ 
+
+ align:start position:0%
+other constraints because they're both
+greater than or equal to constraints
+
+ align:start position:0%
+greater than or equal to constraints
+ 
+
+ align:start position:0%
+greater than or equal to constraints
+change the operator to greater than or
+
+ align:start position:0%
+change the operator to greater than or
+ 
+
+ align:start position:0%
+change the operator to greater than or
+equal to and for the value select the
+
+ align:start position:0%
+equal to and for the value select the
+ 
+
+ align:start position:0%
+equal to and for the value select the
+two right-hand sides and go ahead and
+
+ align:start position:0%
+two right-hand sides and go ahead and
+ 
+
+ align:start position:0%
+two right-hand sides and go ahead and
+click solve the solving result says
+
+ align:start position:0%
+click solve the solving result says
+ 
+
+ align:start position:0%
+click solve the solving result says
+solving successfully finished result 20
+
+ align:start position:0%
+solving successfully finished result 20
+ 
+
+ align:start position:0%
+solving successfully finished result 20
+select keep result let's look at our new
+
+ align:start position:0%
+select keep result let's look at our new
+ 
+
+ align:start position:0%
+select keep result let's look at our new
+solution the objective value is now 20
+
+ align:start position:0%
+solution the objective value is now 20
+ 
+
+ align:start position:0%
+solution the objective value is now 20
+which is less than it was before but now
+
+ align:start position:0%
+which is less than it was before but now
+ 
+
+ align:start position:0%
+which is less than it was before but now
+we have teams a and B plane in weeks two
+
+ align:start position:0%
+we have teams a and B plane in weeks two
+ 
+
+ align:start position:0%
+we have teams a and B plane in weeks two
+and four and team C and D plane in weeks
+
+ align:start position:0%
+and four and team C and D plane in weeks
+ 
+
+ align:start position:0%
+and four and team C and D plane in weeks
+two and four so depending on your
+
+ align:start position:0%
+two and four so depending on your
+ 
+
+ align:start position:0%
+two and four so depending on your
+preferences as a decision maker you
+
+ align:start position:0%
+preferences as a decision maker you
+ 
+
+ align:start position:0%
+preferences as a decision maker you
+might prefer the previous solution which
+
+ align:start position:0%
+might prefer the previous solution which
+ 
+
+ align:start position:0%
+might prefer the previous solution which
+had a slightly higher objective or this
+
+ align:start position:0%
+had a slightly higher objective or this
+ 
+
+ align:start position:0%
+had a slightly higher objective or this
+solution which is a little more balanced
+
+ align:start position:0%
+solution which is a little more balanced
+ 
+
+ align:start position:0%
+solution which is a little more balanced
+in the next video we'll discuss how
+
+ align:start position:0%
+in the next video we'll discuss how
+ 
+
+ align:start position:0%
+in the next video we'll discuss how
+additional constraints often make the
+
+ align:start position:0%
+additional constraints often make the
+ 
+
+ align:start position:0%
+additional constraints often make the
+problems harder to solve and how large
+
+ align:start position:0%
+problems harder to solve and how large
+ 
+
+ align:start position:0%
+problems harder to solve and how large
+integer optimization problems are solved
+
+ align:start position:0%
+integer optimization problems are solved
+ 
+
+ align:start position:0%
+integer optimization problems are solved
+in practice
\ No newline at end of file
diff --git a/0egP7_kq23E.txt b/0egP7_kq23E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..56762eff59e09ab962792e660e88bfdf7151314b
--- /dev/null
+++ b/0egP7_kq23E.txt
@@ -0,0 +1,8376 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so this is a review session
+
+ align:start position:0%
+ocw.mit.edu so this is a review session
+ 
+
+ align:start position:0%
+ocw.mit.edu so this is a review session
+number five I guess it is uh and it
+
+ align:start position:0%
+number five I guess it is uh and it
+ 
+
+ align:start position:0%
+number five I guess it is uh and it
+comes uh before an exam next Tuesday and
+
+ align:start position:0%
+comes uh before an exam next Tuesday and
+ 
+
+ align:start position:0%
+comes uh before an exam next Tuesday and
+actually there'll be a further review
+
+ align:start position:0%
+actually there'll be a further review
+ 
+
+ align:start position:0%
+actually there'll be a further review
+session number six uh on Monday uh right
+
+ align:start position:0%
+session number six uh on Monday uh right
+ 
+
+ align:start position:0%
+session number six uh on Monday uh right
+before the exam so
+
+ align:start position:0%
+before the exam so
+ 
+
+ align:start position:0%
+before the exam so
+uh so maybe today we would there's a
+
+ align:start position:0%
+uh so maybe today we would there's a
+ 
+
+ align:start position:0%
+uh so maybe today we would there's a
+homework uh problem set on sections on
+
+ align:start position:0%
+homework uh problem set on sections on
+ 
+
+ align:start position:0%
+homework uh problem set on sections on
+chapter two SEC the uh the mostly the
+
+ align:start position:0%
+chapter two SEC the uh the mostly the
+ 
+
+ align:start position:0%
+chapter two SEC the uh the mostly the
+oscillating masses and springs and the
+
+ align:start position:0%
+oscillating masses and springs and the
+ 
+
+ align:start position:0%
+oscillating masses and springs and the
+uh today's uh lecture that you see
+
+ align:start position:0%
+uh today's uh lecture that you see
+ 
+
+ align:start position:0%
+uh today's uh lecture that you see
+traces of of U
+
+ align:start position:0%
+traces of of U
+ 
+
+ align:start position:0%
+traces of of U
+networks
+
+ align:start position:0%
+networks
+ 
+
+ align:start position:0%
+networks
+um and masses and springs also the
+
+ align:start position:0%
+um and masses and springs also the
+ 
+
+ align:start position:0%
+um and masses and springs also the
+static case so I I'm open as always to
+
+ align:start position:0%
+static case so I I'm open as always to
+ 
+
+ align:start position:0%
+static case so I I'm open as always to
+questions yes please thank you 2.2
+
+ align:start position:0%
+questions yes please thank you 2.2
+ 
+
+ align:start position:0%
+questions yes please thank you 2.2
+number 2.2 number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six okay yeah so this is uh and of
+
+ align:start position:0%
+six okay yeah so this is uh and of
+ 
+
+ align:start position:0%
+six okay yeah so this is uh and of
+course you understand so I'm happy
+
+ align:start position:0%
+course you understand so I'm happy
+ 
+
+ align:start position:0%
+course you understand so I'm happy
+that's a good question to discuss and
+
+ align:start position:0%
+that's a good question to discuss and
+ 
+
+ align:start position:0%
+that's a good question to discuss and
+and maybe number seven people will have
+
+ align:start position:0%
+and maybe number seven people will have
+ 
+
+ align:start position:0%
+and maybe number seven people will have
+some thing to say about uh good uh yeah
+
+ align:start position:0%
+some thing to say about uh good uh yeah
+ 
+
+ align:start position:0%
+some thing to say about uh good uh yeah
+so that that's just fine so so let me
+
+ align:start position:0%
+so that that's just fine so so let me
+ 
+
+ align:start position:0%
+so that that's just fine so so let me
+start right in on
+
+ align:start position:0%
+start right in on
+ 
+
+ align:start position:0%
+start right in on
+those so number six is the fact
+
+ align:start position:0%
+those so number six is the fact
+ 
+
+ align:start position:0%
+those so number six is the fact
+uh I mean everybody understands that
+
+ align:start position:0%
+uh I mean everybody understands that
+ 
+
+ align:start position:0%
+uh I mean everybody understands that
+when energy is conserved that's an
+
+ align:start position:0%
+when energy is conserved that's an
+ 
+
+ align:start position:0%
+when energy is conserved that's an
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+thing and the so the question is first
+
+ align:start position:0%
+thing and the so the question is first
+ 
+
+ align:start position:0%
+thing and the so the question is first
+first when is energy conserved in the
+
+ align:start position:0%
+first when is energy conserved in the
+ 
+
+ align:start position:0%
+first when is energy conserved in the
+differential equation in the equation
+
+ align:start position:0%
+differential equation in the equation
+ 
+
+ align:start position:0%
+differential equation in the equation
+we're trying to solve and if it is then
+
+ align:start position:0%
+we're trying to solve and if it is then
+ 
+
+ align:start position:0%
+we're trying to solve and if it is then
+we want to know we would like to choose
+
+ align:start position:0%
+we want to know we would like to choose
+ 
+
+ align:start position:0%
+we want to know we would like to choose
+difference methods that also conserve
+
+ align:start position:0%
+difference methods that also conserve
+ 
+
+ align:start position:0%
+difference methods that also conserve
+energy uh that may they may not be
+
+ align:start position:0%
+energy uh that may they may not be
+ 
+
+ align:start position:0%
+energy uh that may they may not be
+exactly right they may not be exactly at
+
+ align:start position:0%
+exactly right they may not be exactly at
+ 
+
+ align:start position:0%
+exactly right they may not be exactly at
+the right point on this circle if we're
+
+ align:start position:0%
+the right point on this circle if we're
+ 
+
+ align:start position:0%
+the right point on this circle if we're
+in that model problem but still on the
+
+ align:start position:0%
+in that model problem but still on the
+ 
+
+ align:start position:0%
+in that model problem but still on the
+circle so and the point is that the
+
+ align:start position:0%
+circle so and the point is that the
+ 
+
+ align:start position:0%
+circle so and the point is that the
+trapezoidal method does stay on the
+
+ align:start position:0%
+trapezoidal method does stay on the
+ 
+
+ align:start position:0%
+trapezoidal method does stay on the
+circle and of course the differential
+
+ align:start position:0%
+circle and of course the differential
+ 
+
+ align:start position:0%
+circle and of course the differential
+equation stays on the circle can I uh so
+
+ align:start position:0%
+equation stays on the circle can I uh so
+ 
+
+ align:start position:0%
+equation stays on the circle can I uh so
+and I tried I put quite a bit into this
+
+ align:start position:0%
+and I tried I put quite a bit into this
+ 
+
+ align:start position:0%
+and I tried I put quite a bit into this
+problem six so this is
+
+ align:start position:0%
+problem six so this is
+ 
+
+ align:start position:0%
+problem six so this is
+2.2.6 and
+
+ align:start position:0%
+2.2.6 and
+ 
+
+ align:start position:0%
+2.2.6 and
+uh and let me try to say say something
+
+ align:start position:0%
+uh and let me try to say say something
+ 
+
+ align:start position:0%
+uh and let me try to say say something
+about that okay so first of all it
+
+ align:start position:0%
+about that okay so first of all it
+ 
+
+ align:start position:0%
+about that okay so first of all it
+there's the continuous problem DT equal
+
+ align:start position:0%
+there's the continuous problem DT equal
+ 
+
+ align:start position:0%
+there's the continuous problem DT equal
+Au when does does that conserve energy
+
+ align:start position:0%
+Au when does does that conserve energy
+ 
+
+ align:start position:0%
+Au when does does that conserve energy
+and then there's the discret problem
+
+ align:start position:0%
+and then there's the discret problem
+ 
+
+ align:start position:0%
+and then there's the discret problem
+which uh we know that uh Oiler doesn't
+
+ align:start position:0%
+which uh we know that uh Oiler doesn't
+ 
+
+ align:start position:0%
+which uh we know that uh Oiler doesn't
+conserve energy because we just we've
+
+ align:start position:0%
+conserve energy because we just we've
+ 
+
+ align:start position:0%
+conserve energy because we just we've
+seen it the the computer shows you right
+
+ align:start position:0%
+seen it the the computer shows you right
+ 
+
+ align:start position:0%
+seen it the the computer shows you right
+away it goes it it spirals out from the
+
+ align:start position:0%
+away it goes it it spirals out from the
+ 
+
+ align:start position:0%
+away it goes it it spirals out from the
+circle it spirals in for forward and
+
+ align:start position:0%
+circle it spirals in for forward and
+ 
+
+ align:start position:0%
+circle it spirals in for forward and
+backward Oiler but trapezoidal method is
+
+ align:start position:0%
+backward Oiler but trapezoidal method is
+ 
+
+ align:start position:0%
+backward Oiler but trapezoidal method is
+that the one that turns out to be well
+
+ align:start position:0%
+that the one that turns out to be well
+ 
+
+ align:start position:0%
+that the one that turns out to be well
+okay so it says it refers to equation 24
+
+ align:start position:0%
+okay so it says it refers to equation 24
+ 
+
+ align:start position:0%
+okay so it says it refers to equation 24
+as the trapezoidal method and let me try
+
+ align:start position:0%
+as the trapezoidal method and let me try
+ 
+
+ align:start position:0%
+as the trapezoidal method and let me try
+to follow that notation yeah uh so this
+
+ align:start position:0%
+to follow that notation yeah uh so this
+ 
+
+ align:start position:0%
+to follow that notation yeah uh so this
+is the trapezoidal method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is uh this one did we get music there
+
+ align:start position:0%
+is is uh this one did we get music there
+ 
+
+ align:start position:0%
+is is uh this one did we get music there
+for the trapezoidal method okay n + 1
+
+ align:start position:0%
+for the trapezoidal method okay n + 1
+ 
+
+ align:start position:0%
+for the trapezoidal method okay n + 1
+equal I + a Delta t/ 2 unu N okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so that uh and actually
+
+ align:start position:0%
+right okay so that uh and actually
+ 
+
+ align:start position:0%
+right okay so that uh and actually
+problem seven that you may be want to
+
+ align:start position:0%
+problem seven that you may be want to
+ 
+
+ align:start position:0%
+problem seven that you may be want to
+discuss too is the question of how
+
+ align:start position:0%
+discuss too is the question of how
+ 
+
+ align:start position:0%
+discuss too is the question of how
+accurate this is compared to the
+
+ align:start position:0%
+accurate this is compared to the
+ 
+
+ align:start position:0%
+accurate this is compared to the
+differential equation everybody should
+
+ align:start position:0%
+differential equation everybody should
+ 
+
+ align:start position:0%
+differential equation everybody should
+see that this really came
+
+ align:start position:0%
+see that this really came
+ 
+
+ align:start position:0%
+see that this really came
+from the original way to look at this
+
+ align:start position:0%
+from the original way to look at this
+ 
+
+ align:start position:0%
+from the original way to look at this
+was UN n + 1us un n/ delta T that
+
+ align:start position:0%
+was UN n + 1us un n/ delta T that
+ 
+
+ align:start position:0%
+was UN n + 1us un n/ delta T that
+approximated the D itive equals a and
+
+ align:start position:0%
+approximated the D itive equals a and
+ 
+
+ align:start position:0%
+approximated the D itive equals a and
+then I'm taking half of I'm taking half
+
+ align:start position:0%
+then I'm taking half of I'm taking half
+ 
+
+ align:start position:0%
+then I'm taking half of I'm taking half
+at U and at the new time and half at the
+
+ align:start position:0%
+at U and at the new time and half at the
+ 
+
+ align:start position:0%
+at U and at the new time and half at the
+old time so it's got that
+
+ align:start position:0%
+old time so it's got that
+ 
+
+ align:start position:0%
+old time so it's got that
+centering that that we suspect will give
+
+ align:start position:0%
+centering that that we suspect will give
+ 
+
+ align:start position:0%
+centering that that we suspect will give
+us a little extra accuracy okay so so
+
+ align:start position:0%
+us a little extra accuracy okay so so
+ 
+
+ align:start position:0%
+us a little extra accuracy okay so so
+two questions then one was the
+
+ align:start position:0%
+two questions then one was the
+ 
+
+ align:start position:0%
+two questions then one was the
+stability so so question problem six was
+
+ align:start position:0%
+stability so so question problem six was
+ 
+
+ align:start position:0%
+stability so so question problem six was
+the energy conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+problem 2.2.7 if I anticipated is the
+
+ align:start position:0%
+problem 2.2.7 if I anticipated is the
+ 
+
+ align:start position:0%
+problem 2.2.7 if I anticipated is the
+order of
+
+ align:start position:0%
+order of
+ 
+
+ align:start position:0%
+order of
+accuracy so these are both
+
+ align:start position:0%
+accuracy so these are both
+ 
+
+ align:start position:0%
+accuracy so these are both
+topics that uh are extremely important
+
+ align:start position:0%
+topics that uh are extremely important
+ 
+
+ align:start position:0%
+topics that uh are extremely important
+in choosing a difference method we're
+
+ align:start position:0%
+in choosing a difference method we're
+ 
+
+ align:start position:0%
+in choosing a difference method we're
+very happy to know that this conser well
+
+ align:start position:0%
+very happy to know that this conser well
+ 
+
+ align:start position:0%
+very happy to know that this conser well
+we would like to know first when does
+
+ align:start position:0%
+we would like to know first when does
+ 
+
+ align:start position:0%
+we would like to know first when does
+when is energy conserved there in the
+
+ align:start position:0%
+when is energy conserved there in the
+ 
+
+ align:start position:0%
+when is energy conserved there in the
+what differential equation have
+
+ align:start position:0%
+what differential equation have
+ 
+
+ align:start position:0%
+what differential equation have
+conserved energy physically we kind of
+
+ align:start position:0%
+conserved energy physically we kind of
+ 
+
+ align:start position:0%
+conserved energy physically we kind of
+can see them coming you know if the
+
+ align:start position:0%
+can see them coming you know if the
+ 
+
+ align:start position:0%
+can see them coming you know if the
+physical uh universe is not being uh you
+
+ align:start position:0%
+physical uh universe is not being uh you
+ 
+
+ align:start position:0%
+physical uh universe is not being uh you
+know it's somehow lot lots of physical
+
+ align:start position:0%
+know it's somehow lot lots of physical
+ 
+
+ align:start position:0%
+know it's somehow lot lots of physical
+problems we see those masses and springs
+
+ align:start position:0%
+problems we see those masses and springs
+ 
+
+ align:start position:0%
+problems we see those masses and springs
+oscillating and and we say Okay
+
+ align:start position:0%
+oscillating and and we say Okay
+ 
+
+ align:start position:0%
+oscillating and and we say Okay
+nothing's coming in from outside how
+
+ align:start position:0%
+nothing's coming in from outside how
+ 
+
+ align:start position:0%
+nothing's coming in from outside how
+could energy there would be the sum of
+
+ align:start position:0%
+could energy there would be the sum of
+ 
+
+ align:start position:0%
+could energy there would be the sum of
+the kinetic energy of the
+
+ align:start position:0%
+the kinetic energy of the
+ 
+
+ align:start position:0%
+the kinetic energy of the
+masses and the potential energy in the
+
+ align:start position:0%
+masses and the potential energy in the
+ 
+
+ align:start position:0%
+masses and the potential energy in the
+springs so so energy passes
+
+ align:start position:0%
+springs so so energy passes
+ 
+
+ align:start position:0%
+springs so so energy passes
+between kinetic when the mass is zooming
+
+ align:start position:0%
+between kinetic when the mass is zooming
+ 
+
+ align:start position:0%
+between kinetic when the mass is zooming
+past equilibrium
+
+ align:start position:0%
+past equilibrium
+ 
+
+ align:start position:0%
+past equilibrium
+and and potential energy when the mass
+
+ align:start position:0%
+and and potential energy when the mass
+ 
+
+ align:start position:0%
+and and potential energy when the mass
+is stretching the spring so that we've
+
+ align:start position:0%
+is stretching the spring so that we've
+ 
+
+ align:start position:0%
+is stretching the spring so that we've
+got two cases so and we would hope and
+
+ align:start position:0%
+got two cases so and we would hope and
+ 
+
+ align:start position:0%
+got two cases so and we would hope and
+this trapezoidal method comes through
+
+ align:start position:0%
+this trapezoidal method comes through
+ 
+
+ align:start position:0%
+this trapezoidal method comes through
+that energy is conserved so can I just
+
+ align:start position:0%
+that energy is conserved so can I just
+ 
+
+ align:start position:0%
+that energy is conserved so can I just
+begin with this
+
+ align:start position:0%
+begin with this
+ 
+
+ align:start position:0%
+begin with this
+one maybe I always ought to say cuz you
+
+ align:start position:0%
+one maybe I always ought to say cuz you
+ 
+
+ align:start position:0%
+one maybe I always ought to say cuz you
+guys are also thinking about the
+
+ align:start position:0%
+guys are also thinking about the
+ 
+
+ align:start position:0%
+guys are also thinking about the
+quiz and
+
+ align:start position:0%
+quiz and
+ 
+
+ align:start position:0%
+quiz and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um so this this for example this
+
+ align:start position:0%
+um so this this for example this
+ 
+
+ align:start position:0%
+um so this this for example this
+question about how to find the order of
+
+ align:start position:0%
+question about how to find the order of
+ 
+
+ align:start position:0%
+question about how to find the order of
+accuracy that's uh I I'll speak about
+
+ align:start position:0%
+accuracy that's uh I I'll speak about
+ 
+
+ align:start position:0%
+accuracy that's uh I I'll speak about
+that but let me just say I I that's not
+
+ align:start position:0%
+that but let me just say I I that's not
+ 
+
+ align:start position:0%
+that but let me just say I I that's not
+something that we've done in enough
+
+ align:start position:0%
+something that we've done in enough
+ 
+
+ align:start position:0%
+something that we've done in enough
+detail that I would expect you to be
+
+ align:start position:0%
+detail that I would expect you to be
+ 
+
+ align:start position:0%
+detail that I would expect you to be
+quick on the quiz and just be able to do
+
+ align:start position:0%
+quick on the quiz and just be able to do
+ 
+
+ align:start position:0%
+quick on the quiz and just be able to do
+it out uh you know I I'll try to
+
+ align:start position:0%
+it out uh you know I I'll try to
+ 
+
+ align:start position:0%
+it out uh you know I I'll try to
+choose ex questions on the exam that you
+
+ align:start position:0%
+choose ex questions on the exam that you
+ 
+
+ align:start position:0%
+choose ex questions on the exam that you
+really have had more practice with but
+
+ align:start position:0%
+really have had more practice with but
+ 
+
+ align:start position:0%
+really have had more practice with but
+this is certainly important so it's was
+
+ align:start position:0%
+this is certainly important so it's was
+ 
+
+ align:start position:0%
+this is certainly important so it's was
+definitely right to put on the homework
+
+ align:start position:0%
+definitely right to put on the homework
+ 
+
+ align:start position:0%
+definitely right to put on the homework
+and this is important okay uh so let me
+
+ align:start position:0%
+and this is important okay uh so let me
+ 
+
+ align:start position:0%
+and this is important okay uh so let me
+let me tackle this
+
+ align:start position:0%
+let me tackle this
+ 
+
+ align:start position:0%
+let me tackle this
+one first the differential equation so
+
+ align:start position:0%
+one first the differential equation so
+ 
+
+ align:start position:0%
+one first the differential equation so
+by energy here I'm meaning just the
+
+ align:start position:0%
+by energy here I'm meaning just the
+ 
+
+ align:start position:0%
+by energy here I'm meaning just the
+length of U squared
+
+ align:start position:0%
+length of U squared
+ 
+
+ align:start position:0%
+length of U squared
+so let me uh so now I'm looking at
+
+ align:start position:0%
+so let me uh so now I'm looking at
+ 
+
+ align:start position:0%
+so let me uh so now I'm looking at
+energy conserved okay so I'm hoping
+
+ align:start position:0%
+energy conserved okay so I'm hoping
+ 
+
+ align:start position:0%
+energy conserved okay so I'm hoping
+energy conserved would mean that the
+
+ align:start position:0%
+energy conserved would mean that the
+ 
+
+ align:start position:0%
+energy conserved would mean that the
+derivative of
+
+ align:start position:0%
+derivative of
+ 
+
+ align:start position:0%
+derivative of
+u^2 was Zero that that's what energy
+
+ align:start position:0%
+u^2 was Zero that that's what energy
+ 
+
+ align:start position:0%
+u^2 was Zero that that's what energy
+conserving energy would mean and my
+
+ align:start position:0%
+conserving energy would mean and my
+ 
+
+ align:start position:0%
+conserving energy would mean and my
+question is which differential equations
+
+ align:start position:0%
+question is which differential equations
+ 
+
+ align:start position:0%
+question is which differential equations
+what what's the condition on a in other
+
+ align:start position:0%
+what what's the condition on a in other
+ 
+
+ align:start position:0%
+what what's the condition on a in other
+words that that I should what how would
+
+ align:start position:0%
+words that that I should what how would
+ 
+
+ align:start position:0%
+words that that I should what how would
+I recognize from this m Matrix a that I
+
+ align:start position:0%
+I recognize from this m Matrix a that I
+ 
+
+ align:start position:0%
+I recognize from this m Matrix a that I
+have this interesting property okay so
+
+ align:start position:0%
+have this interesting property okay so
+ 
+
+ align:start position:0%
+have this interesting property okay so
+let me just show you what I would do
+
+ align:start position:0%
+let me just show you what I would do
+ 
+
+ align:start position:0%
+let me just show you what I would do
+okay another way to write u^2 is U
+
+ align:start position:0%
+okay another way to write u^2 is U
+ 
+
+ align:start position:0%
+okay another way to write u^2 is U
+transpose U these These are vectors of
+
+ align:start position:0%
+transpose U these These are vectors of
+ 
+
+ align:start position:0%
+transpose U these These are vectors of
+course okay okay so what's the
+
+ align:start position:0%
+course okay okay so what's the
+ 
+
+ align:start position:0%
+course okay okay so what's the
+derivative of U transpose U see I've got
+
+ align:start position:0%
+derivative of U transpose U see I've got
+ 
+
+ align:start position:0%
+derivative of U transpose U see I've got
+my equation is telling me what the
+
+ align:start position:0%
+my equation is telling me what the
+ 
+
+ align:start position:0%
+my equation is telling me what the
+derivative of U is here I've got the
+
+ align:start position:0%
+derivative of U is here I've got the
+ 
+
+ align:start position:0%
+derivative of U is here I've got the
+thing squared okay
+
+ align:start position:0%
+thing squared okay
+ 
+
+ align:start position:0%
+thing squared okay
+it's I mean I have a product here right
+
+ align:start position:0%
+it's I mean I have a product here right
+ 
+
+ align:start position:0%
+it's I mean I have a product here right
+I've Ed times use so I'm going to use
+
+ align:start position:0%
+I've Ed times use so I'm going to use
+ 
+
+ align:start position:0%
+I've Ed times use so I'm going to use
+this the standard they happen to be
+
+ align:start position:0%
+this the standard they happen to be
+ 
+
+ align:start position:0%
+this the standard they happen to be
+vectors so I'd have if I want to use
+
+ align:start position:0%
+vectors so I'd have if I want to use
+ 
+
+ align:start position:0%
+vectors so I'd have if I want to use
+like freshman calculus I'd have to get
+
+ align:start position:0%
+like freshman calculus I'd have to get
+ 
+
+ align:start position:0%
+like freshman calculus I'd have to get
+down to the scaler to get down to the
+
+ align:start position:0%
+down to the scaler to get down to the
+ 
+
+ align:start position:0%
+down to the scaler to get down to the
+numbers but I absolutely could do that
+
+ align:start position:0%
+numbers but I absolutely could do that
+ 
+
+ align:start position:0%
+numbers but I absolutely could do that
+and just follow them along component by
+
+ align:start position:0%
+and just follow them along component by
+ 
+
+ align:start position:0%
+and just follow them along component by
+component or I could try to do it a v
+
+ align:start position:0%
+component or I could try to do it a v
+ 
+
+ align:start position:0%
+component or I could try to do it a v
+the whole column at a time and and let
+
+ align:start position:0%
+the whole column at a time and and let
+ 
+
+ align:start position:0%
+the whole column at a time and and let
+me try that that it's going to be the
+
+ align:start position:0%
+me try that that it's going to be the
+ 
+
+ align:start position:0%
+me try that that it's going to be the
+product rule right it's some in some
+
+ align:start position:0%
+product rule right it's some in some
+ 
+
+ align:start position:0%
+product rule right it's some in some
+form that I'll have this guy times the
+
+ align:start position:0%
+form that I'll have this guy times the
+ 
+
+ align:start position:0%
+form that I'll have this guy times the
+derivative of
+
+ align:start position:0%
+derivative of
+ 
+
+ align:start position:0%
+derivative of
+this plus the derivative I'll keep them
+
+ align:start position:0%
+this plus the derivative I'll keep them
+ 
+
+ align:start position:0%
+this plus the derivative I'll keep them
+in order the derivative of this
+
+ align:start position:0%
+in order the derivative of this
+ 
+
+ align:start position:0%
+in order the derivative of this
+thing times this guy right that that
+
+ align:start position:0%
+thing times this guy right that that
+ 
+
+ align:start position:0%
+thing times this guy right that that
+should be that's the product rule okay
+
+ align:start position:0%
+should be that's the product rule okay
+ 
+
+ align:start position:0%
+should be that's the product rule okay
+now what do I know here I know that the
+
+ align:start position:0%
+now what do I know here I know that the
+ 
+
+ align:start position:0%
+now what do I know here I know that the
+dudt is au right so this is U transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Au and I
+
+ align:start position:0%
+Au and I
+ 
+
+ align:start position:0%
+Au and I
+know du is that DT meant to be
+
+ align:start position:0%
+know du is that DT meant to be
+ 
+
+ align:start position:0%
+know du is that DT meant to be
+DT so what's so du DT is au again look
+
+ align:start position:0%
+DT so what's so du DT is au again look
+ 
+
+ align:start position:0%
+DT so what's so du DT is au again look
+it's this isn't difficult it's
+
+ align:start position:0%
+it's this isn't difficult it's
+ 
+
+ align:start position:0%
+it's this isn't difficult it's
+Au transpose U and the question is when
+
+ align:start position:0%
+Au transpose U and the question is when
+ 
+
+ align:start position:0%
+Au transpose U and the question is when
+is this zero okay so U so this was those
+
+ align:start position:0%
+is this zero okay so U so this was those
+ 
+
+ align:start position:0%
+is this zero okay so U so this was those
+were the two terms from the product rule
+
+ align:start position:0%
+were the two terms from the product rule
+ 
+
+ align:start position:0%
+were the two terms from the product rule
+and notice they're not exactly the same
+
+ align:start position:0%
+and notice they're not exactly the same
+ 
+
+ align:start position:0%
+and notice they're not exactly the same
+this is U transpose a u and what's this
+
+ align:start position:0%
+this is U transpose a u and what's this
+ 
+
+ align:start position:0%
+this is U transpose a u and what's this
+guy you transpose a transpose U so if I
+
+ align:start position:0%
+guy you transpose a transpose U so if I
+ 
+
+ align:start position:0%
+guy you transpose a transpose U so if I
+put them together I have U transpose
+
+ align:start position:0%
+put them together I have U transpose
+ 
+
+ align:start position:0%
+put them together I have U transpose
+times the A and the a
+
+ align:start position:0%
+times the A and the a
+ 
+
+ align:start position:0%
+times the A and the a
+transpose times U and I'm want I'm
+
+ align:start position:0%
+transpose times U and I'm want I'm
+ 
+
+ align:start position:0%
+transpose times U and I'm want I'm
+hoping that this will be zero for all
+
+ align:start position:0%
+hoping that this will be zero for all
+ 
+
+ align:start position:0%
+hoping that this will be zero for all
+these all the solutions that I've come
+
+ align:start position:0%
+these all the solutions that I've come
+ 
+
+ align:start position:0%
+these all the solutions that I've come
+up with so the condition is simply
+
+ align:start position:0%
+up with so the condition is simply
+ 
+
+ align:start position:0%
+up with so the condition is simply
+that that a plus a we want that to be
+
+ align:start position:0%
+that that a plus a we want that to be
+ 
+
+ align:start position:0%
+that that a plus a we want that to be
+the zero Matrix a plus a transpose if
+
+ align:start position:0%
+the zero Matrix a plus a transpose if
+ 
+
+ align:start position:0%
+the zero Matrix a plus a transpose if
+that's if if in other words if a
+
+ align:start position:0%
+that's if if in other words if a
+ 
+
+ align:start position:0%
+that's if if in other words if a
+transpose is minus a that that's the
+
+ align:start position:0%
+transpose is minus a that that's the
+ 
+
+ align:start position:0%
+transpose is minus a that that's the
+that's the good one if a transposes
+
+ align:start position:0%
+that's the good one if a transposes
+ 
+
+ align:start position:0%
+that's the good one if a transposes
+minus a this is zero that's zero that's
+
+ align:start position:0%
+minus a this is zero that's zero that's
+ 
+
+ align:start position:0%
+minus a this is zero that's zero that's
+zero that's zero energy is conserved so
+
+ align:start position:0%
+zero that's zero energy is conserved so
+ 
+
+ align:start position:0%
+zero that's zero energy is conserved so
+the energy is conserved when a transpose
+
+ align:start position:0%
+the energy is conserved when a transpose
+ 
+
+ align:start position:0%
+the energy is conserved when a transpose
+is minus
+
+ align:start position:0%
+is minus
+ 
+
+ align:start position:0%
+is minus
+a it's for the anti-symmetric A's that
+
+ align:start position:0%
+a it's for the anti-symmetric A's that
+ 
+
+ align:start position:0%
+a it's for the anti-symmetric A's that
+energy conserved and of course this all
+
+ align:start position:0%
+energy conserved and of course this all
+ 
+
+ align:start position:0%
+energy conserved and of course this all
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+uh what are the special solutions to
+
+ align:start position:0%
+uh what are the special solutions to
+ 
+
+ align:start position:0%
+uh what are the special solutions to
+that differential equation the special
+
+ align:start position:0%
+that differential equation the special
+ 
+
+ align:start position:0%
+that differential equation the special
+solutions to this equation are e to the
+
+ align:start position:0%
+solutions to this equation are e to the
+ 
+
+ align:start position:0%
+solutions to this equation are e to the
+just just this
+
+ align:start position:0%
+just just this
+ 
+
+ align:start position:0%
+just just this
+is connecting now with with things that
+
+ align:start position:0%
+is connecting now with with things that
+ 
+
+ align:start position:0%
+is connecting now with with things that
+really are basic the special Solutions
+
+ align:start position:0%
+really are basic the special Solutions
+ 
+
+ align:start position:0%
+really are basic the special Solutions
+the the Pure igen Solutions the one the
+
+ align:start position:0%
+the the Pure igen Solutions the one the
+ 
+
+ align:start position:0%
+the the Pure igen Solutions the one the
+ones that follow their own paths are the
+
+ align:start position:0%
+ones that follow their own paths are the
+ 
+
+ align:start position:0%
+ones that follow their own paths are the
+e to the Lambda T X's right where X is
+
+ align:start position:0%
+e to the Lambda T X's right where X is
+ 
+
+ align:start position:0%
+e to the Lambda T X's right where X is
+an IG Vector of a and Lambda is an igen
+
+ align:start position:0%
+an IG Vector of a and Lambda is an igen
+ 
+
+ align:start position:0%
+an IG Vector of a and Lambda is an igen
+value those are the guys and we expect
+
+ align:start position:0%
+value those are the guys and we expect
+ 
+
+ align:start position:0%
+value those are the guys and we expect
+to have n of them and we expect a
+
+ align:start position:0%
+to have n of them and we expect a
+ 
+
+ align:start position:0%
+to have n of them and we expect a
+combination of those to give us the
+
+ align:start position:0%
+combination of those to give us the
+ 
+
+ align:start position:0%
+combination of those to give us the
+general solution and to match the
+
+ align:start position:0%
+general solution and to match the
+ 
+
+ align:start position:0%
+general solution and to match the
+boundary condition so these are the
+
+ align:start position:0%
+boundary condition so these are the
+ 
+
+ align:start position:0%
+boundary condition so these are the
+these these n of these guys with n
+
+ align:start position:0%
+these these n of these guys with n
+ 
+
+ align:start position:0%
+these these n of these guys with n
+different IG vectors and their igen
+
+ align:start position:0%
+different IG vectors and their igen
+ 
+
+ align:start position:0%
+different IG vectors and their igen
+values are the heart of
+
+ align:start position:0%
+values are the heart of
+ 
+
+ align:start position:0%
+values are the heart of
+uh problems like this and and of course
+
+ align:start position:0%
+uh problems like this and and of course
+ 
+
+ align:start position:0%
+uh problems like this and and of course
+that's um you know the the additional
+
+ align:start position:0%
+that's um you know the the additional
+ 
+
+ align:start position:0%
+that's um you know the the additional
+homework problem that I that wasn't in
+
+ align:start position:0%
+homework problem that I that wasn't in
+ 
+
+ align:start position:0%
+homework problem that I that wasn't in
+the book but I added as an additional
+
+ align:start position:0%
+the book but I added as an additional
+ 
+
+ align:start position:0%
+the book but I added as an additional
+problem was exactly that to get you to
+
+ align:start position:0%
+problem was exactly that to get you to
+ 
+
+ align:start position:0%
+problem was exactly that to get you to
+practice with these Z vectors and I
+
+ align:start position:0%
+practice with these Z vectors and I
+ 
+
+ align:start position:0%
+practice with these Z vectors and I
+values Okay now what's the deal I want
+
+ align:start position:0%
+values Okay now what's the deal I want
+ 
+
+ align:start position:0%
+values Okay now what's the deal I want
+to connect this energy conserving with
+
+ align:start position:0%
+to connect this energy conserving with
+ 
+
+ align:start position:0%
+to connect this energy conserving with
+with this picture of solutions when
+
+ align:start position:0%
+with this picture of solutions when
+ 
+
+ align:start position:0%
+with this picture of solutions when
+would this keep the same energy when
+
+ align:start position:0%
+would this keep the same energy when
+ 
+
+ align:start position:0%
+would this keep the same energy when
+would the energy of these of of that
+
+ align:start position:0%
+would the energy of these of of that
+ 
+
+ align:start position:0%
+would the energy of these of of that
+when when would this have constant
+
+ align:start position:0%
+when when would this have constant
+ 
+
+ align:start position:0%
+when when would this have constant
+energy constant
+
+ align:start position:0%
+energy constant
+ 
+
+ align:start position:0%
+energy constant
+length the length would be constant
+
+ align:start position:0%
+length the length would be constant
+ 
+
+ align:start position:0%
+length the length would be constant
+since X is certainly that's a igen
+
+ align:start position:0%
+since X is certainly that's a igen
+ 
+
+ align:start position:0%
+since X is certainly that's a igen
+vector whatever it is this is what's
+
+ align:start position:0%
+vector whatever it is this is what's
+ 
+
+ align:start position:0%
+vector whatever it is this is what's
+changing and now I want to know when
+
+ align:start position:0%
+changing and now I want to know when
+ 
+
+ align:start position:0%
+changing and now I want to know when
+does the length not change well the test
+
+ align:start position:0%
+does the length not change well the test
+ 
+
+ align:start position:0%
+does the length not change well the test
+would be that this number should have
+
+ align:start position:0%
+would be that this number should have
+ 
+
+ align:start position:0%
+would be that this number should have
+absolute
+
+ align:start position:0%
+absolute
+ 
+
+ align:start position:0%
+absolute
+value one right if this has if this
+
+ align:start position:0%
+value one right if this has if this
+ 
+
+ align:start position:0%
+value one right if this has if this
+keeps absolute value one then then in
+
+ align:start position:0%
+keeps absolute value one then then in
+ 
+
+ align:start position:0%
+keeps absolute value one then then in
+the igen value picture I have energy
+
+ align:start position:0%
+the igen value picture I have energy
+ 
+
+ align:start position:0%
+the igen value picture I have energy
+staying the same okay now when will this
+
+ align:start position:0%
+staying the same okay now when will this
+ 
+
+ align:start position:0%
+staying the same okay now when will this
+have when will this have magnitude one
+
+ align:start position:0%
+have when will this have magnitude one
+ 
+
+ align:start position:0%
+have when will this have magnitude one
+time is running along this is e to the
+
+ align:start position:0%
+time is running along this is e to the
+ 
+
+ align:start position:0%
+time is running along this is e to the
+Lambda T so which
+
+ align:start position:0%
+Lambda T so which
+ 
+
+ align:start position:0%
+Lambda T so which
+lambdas zero certainly but now there's
+
+ align:start position:0%
+lambdas zero certainly but now there's
+ 
+
+ align:start position:0%
+lambdas zero certainly but now there's
+more you got to know the others what
+
+ align:start position:0%
+more you got to know the others what
+ 
+
+ align:start position:0%
+more you got to know the others what
+other lambdas will have what other
+
+ align:start position:0%
+other lambdas will have what other
+ 
+
+ align:start position:0%
+other lambdas will have what other
+lambdas give me this thing stays on the
+
+ align:start position:0%
+lambdas give me this thing stays on the
+ 
+
+ align:start position:0%
+lambdas give me this thing stays on the
+unit circle absolute value one key key
+
+ align:start position:0%
+unit circle absolute value one key key
+ 
+
+ align:start position:0%
+unit circle absolute value one key key
+question you you must know Lambda could
+
+ align:start position:0%
+question you you must know Lambda could
+ 
+
+ align:start position:0%
+question you you must know Lambda could
+be imaginary Lambda could be imaginary
+
+ align:start position:0%
+be imaginary Lambda could be imaginary
+ 
+
+ align:start position:0%
+be imaginary Lambda could be imaginary
+right Lambda could be imaginary e to the
+
+ align:start position:0%
+right Lambda could be imaginary e to the
+ 
+
+ align:start position:0%
+right Lambda could be imaginary e to the
+I Omega T those you know we don't you
+
+ align:start position:0%
+I Omega T those you know we don't you
+ 
+
+ align:start position:0%
+I Omega T those you know we don't you
+know those that that's just like basic
+
+ align:start position:0%
+know those that that's just like basic
+ 
+
+ align:start position:0%
+know those that that's just like basic
+fact about complex numbers that if
+
+ align:start position:0%
+fact about complex numbers that if
+ 
+
+ align:start position:0%
+fact about complex numbers that if
+Lambda is imaginary we have we would
+
+ align:start position:0%
+Lambda is imaginary we have we would
+ 
+
+ align:start position:0%
+Lambda is imaginary we have we would
+have the cosine of something t plus I *
+
+ align:start position:0%
+have the cosine of something t plus I *
+ 
+
+ align:start position:0%
+have the cosine of something t plus I *
+the S of something T cos square plus sin
+
+ align:start position:0%
+the S of something T cos square plus sin
+ 
+
+ align:start position:0%
+the S of something T cos square plus sin
+Square being 1 we'd be on the unit
+
+ align:start position:0%
+Square being 1 we'd be on the unit
+ 
+
+ align:start position:0%
+Square being 1 we'd be on the unit
+circle so we want from this picture we
+
+ align:start position:0%
+circle so we want from this picture we
+ 
+
+ align:start position:0%
+circle so we want from this picture we
+would want the lambdas to be pure
+
+ align:start position:0%
+would want the lambdas to be pure
+ 
+
+ align:start position:0%
+would want the lambdas to be pure
+imaginary and now a little Next
+
+ align:start position:0%
+imaginary and now a little Next
+ 
+
+ align:start position:0%
+imaginary and now a little Next
+Step what we'd like for the igen
+
+ align:start position:0%
+Step what we'd like for the igen
+ 
+
+ align:start position:0%
+Step what we'd like for the igen
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+let me because the real solution will
+
+ align:start position:0%
+let me because the real solution will
+ 
+
+ align:start position:0%
+let me because the real solution will
+not be just one of these
+
+ align:start position:0%
+not be just one of these
+ 
+
+ align:start position:0%
+not be just one of these
+guys but a
+
+ align:start position:0%
+guys but a
+ 
+
+ align:start position:0%
+guys but a
+combination so when we have a
+
+ align:start position:0%
+combination so when we have a
+ 
+
+ align:start position:0%
+combination so when we have a
+combination each one is doing its thing
+
+ align:start position:0%
+combination each one is doing its thing
+ 
+
+ align:start position:0%
+combination each one is doing its thing
+each one better have Lambda imaginary
+
+ align:start position:0%
+each one better have Lambda imaginary
+ 
+
+ align:start position:0%
+each one better have Lambda imaginary
+but more than
+
+ align:start position:0%
+but more than
+ 
+
+ align:start position:0%
+but more than
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if the we would want the X's to be
+
+ align:start position:0%
+if the we would want the X's to be
+ 
+
+ align:start position:0%
+if the we would want the X's to be
+perpendicular because if the X's
+
+ align:start position:0%
+perpendicular because if the X's
+ 
+
+ align:start position:0%
+perpendicular because if the X's
+interact then this guy one of
+
+ align:start position:0%
+interact then this guy one of
+ 
+
+ align:start position:0%
+interact then this guy one of
+these you will say there's 's only one
+
+ align:start position:0%
+these you will say there's 's only one
+ 
+
+ align:start position:0%
+these you will say there's 's only one
+there but I'm thinking of n of them
+
+ align:start position:0%
+there but I'm thinking of n of them
+ 
+
+ align:start position:0%
+there but I'm thinking of n of them
+there a combination say two of them
+
+ align:start position:0%
+there a combination say two of them
+ 
+
+ align:start position:0%
+there a combination say two of them
+suppose I have an e to the Lambda 1 tx1
+
+ align:start position:0%
+suppose I have an e to the Lambda 1 tx1
+ 
+
+ align:start position:0%
+suppose I have an e to the Lambda 1 tx1
+and an e to the Lambda 2 tx2 when does
+
+ align:start position:0%
+and an e to the Lambda 2 tx2 when does
+ 
+
+ align:start position:0%
+and an e to the Lambda 2 tx2 when does
+that conserve energy well the each one
+
+ align:start position:0%
+that conserve energy well the each one
+ 
+
+ align:start position:0%
+that conserve energy well the each one
+will but the
+
+ align:start position:0%
+will but the
+ 
+
+ align:start position:0%
+will but the
+combination will be fine if the X's are
+
+ align:start position:0%
+combination will be fine if the X's are
+ 
+
+ align:start position:0%
+combination will be fine if the X's are
+perpendicular because if I have
+
+ align:start position:0%
+perpendicular because if I have
+ 
+
+ align:start position:0%
+perpendicular because if I have
+perpendicular vectors then the length of
+
+ align:start position:0%
+perpendicular vectors then the length of
+ 
+
+ align:start position:0%
+perpendicular vectors then the length of
+the whole combination is by pagas is
+
+ align:start position:0%
+the whole combination is by pagas is
+ 
+
+ align:start position:0%
+the whole combination is by pagas is
+just one squar and the other squared and
+
+ align:start position:0%
+just one squar and the other squared and
+ 
+
+ align:start position:0%
+just one squar and the other squared and
+each of those pieces is
+
+ align:start position:0%
+each of those pieces is
+ 
+
+ align:start position:0%
+each of those pieces is
+constant let me say what I'm trying to
+
+ align:start position:0%
+constant let me say what I'm trying to
+ 
+
+ align:start position:0%
+constant let me say what I'm trying to
+say that the igen value igen function
+
+ align:start position:0%
+say that the igen value igen function
+ 
+
+ align:start position:0%
+say that the igen value igen function
+picture also tells us that we would like
+
+ align:start position:0%
+picture also tells us that we would like
+ 
+
+ align:start position:0%
+picture also tells us that we would like
+imaginary igen values and perpendicular
+
+ align:start position:0%
+imaginary igen values and perpendicular
+ 
+
+ align:start position:0%
+imaginary igen values and perpendicular
+IG vectors and that is exactly what you
+
+ align:start position:0%
+IG vectors and that is exactly what you
+ 
+
+ align:start position:0%
+IG vectors and that is exactly what you
+get from a transpose equal minus a so a
+
+ align:start position:0%
+get from a transpose equal minus a so a
+ 
+
+ align:start position:0%
+get from a transpose equal minus a so a
+transpose equal minus a is exactly get
+
+ align:start position:0%
+transpose equal minus a is exactly get
+ 
+
+ align:start position:0%
+transpose equal minus a is exactly get
+you those matrices anti-symmetric
+
+ align:start position:0%
+you those matrices anti-symmetric
+ 
+
+ align:start position:0%
+you those matrices anti-symmetric
+matrices have perpendicular IG vectors
+
+ align:start position:0%
+matrices have perpendicular IG vectors
+ 
+
+ align:start position:0%
+matrices have perpendicular IG vectors
+just like symmetric but the igen values
+
+ align:start position:0%
+just like symmetric but the igen values
+ 
+
+ align:start position:0%
+just like symmetric but the igen values
+are pure imaginary instead of all being
+
+ align:start position:0%
+are pure imaginary instead of all being
+ 
+
+ align:start position:0%
+are pure imaginary instead of all being
+real they're all pure imaginary in other
+
+ align:start position:0%
+real they're all pure imaginary in other
+ 
+
+ align:start position:0%
+real they're all pure imaginary in other
+words that answer and the discussion
+
+ align:start position:0%
+words that answer and the discussion
+ 
+
+ align:start position:0%
+words that answer and the discussion
+here came to the same conclusion okay
+
+ align:start position:0%
+here came to the same conclusion okay
+ 
+
+ align:start position:0%
+here came to the same conclusion okay
+that a should be anti-symmetric okay now
+
+ align:start position:0%
+that a should be anti-symmetric okay now
+ 
+
+ align:start position:0%
+that a should be anti-symmetric okay now
+let's now let me look at ready is that
+
+ align:start position:0%
+let's now let me look at ready is that
+ 
+
+ align:start position:0%
+let's now let me look at ready is that
+okay that so that's a discussion which
+
+ align:start position:0%
+okay that so that's a discussion which
+ 
+
+ align:start position:0%
+okay that so that's a discussion which
+is worth knowing about differential
+
+ align:start position:0%
+is worth knowing about differential
+ 
+
+ align:start position:0%
+is worth knowing about differential
+equations when are when is energy
+
+ align:start position:0%
+equations when are when is energy
+ 
+
+ align:start position:0%
+equations when are when is energy
+conserved now I want to do or the
+
+ align:start position:0%
+conserved now I want to do or the
+ 
+
+ align:start position:0%
+conserved now I want to do or the
+problem asked me to do what about this
+
+ align:start position:0%
+problem asked me to do what about this
+ 
+
+ align:start position:0%
+problem asked me to do what about this
+difference equation when is energy
+
+ align:start position:0%
+difference equation when is energy
+ 
+
+ align:start position:0%
+difference equation when is energy
+conserved there and I
+
+ align:start position:0%
+conserved there and I
+ 
+
+ align:start position:0%
+conserved there and I
+guess uh I believe it will be I if it's
+
+ align:start position:0%
+guess uh I believe it will be I if it's
+ 
+
+ align:start position:0%
+guess uh I believe it will be I if it's
+this is the requirement for the
+
+ align:start position:0%
+this is the requirement for the
+ 
+
+ align:start position:0%
+this is the requirement for the
+differential equation to be okay to
+
+ align:start position:0%
+differential equation to be okay to
+ 
+
+ align:start position:0%
+differential equation to be okay to
+conserve energy and so I'm going to
+
+ align:start position:0%
+conserve energy and so I'm going to
+ 
+
+ align:start position:0%
+conserve energy and so I'm going to
+expect I'm going to need that in this
+
+ align:start position:0%
+expect I'm going to need that in this
+ 
+
+ align:start position:0%
+expect I'm going to need that in this
+one and is that enough I if I have this
+
+ align:start position:0%
+one and is that enough I if I have this
+ 
+
+ align:start position:0%
+one and is that enough I if I have this
+a transpose equal minus a
+
+ align:start position:0%
+a transpose equal minus a
+ 
+
+ align:start position:0%
+a transpose equal minus a
+anti-symmetric it was good for this is
+
+ align:start position:0%
+anti-symmetric it was good for this is
+ 
+
+ align:start position:0%
+anti-symmetric it was good for this is
+it also does it also do the job here is
+
+ align:start position:0%
+it also does it also do the job here is
+ 
+
+ align:start position:0%
+it also does it also do the job here is
+the is this trapezoidal method just cool
+
+ align:start position:0%
+the is this trapezoidal method just cool
+ 
+
+ align:start position:0%
+the is this trapezoidal method just cool
+so that it will conserve energy too and
+
+ align:start position:0%
+so that it will conserve energy too and
+ 
+
+ align:start position:0%
+so that it will conserve energy too and
+the answer I think is yes and the
+
+ align:start position:0%
+the answer I think is yes and the
+ 
+
+ align:start position:0%
+the answer I think is yes and the
+problem was to prove it or to see why
+
+ align:start position:0%
+problem was to prove it or to see why
+ 
+
+ align:start position:0%
+problem was to prove it or to see why
+why is so I I what do I now
+
+ align:start position:0%
+why is so I I what do I now
+ 
+
+ align:start position:0%
+why is so I I what do I now
+want if if you don't mind my erasing I'm
+
+ align:start position:0%
+want if if you don't mind my erasing I'm
+ 
+
+ align:start position:0%
+want if if you don't mind my erasing I'm
+now going to look at the at the uh
+
+ align:start position:0%
+now going to look at the at the uh
+ 
+
+ align:start position:0%
+now going to look at the at the uh
+discreet guy so now I'm looking at when
+
+ align:start position:0%
+discreet guy so now I'm looking at when
+ 
+
+ align:start position:0%
+discreet guy so now I'm looking at when
+is UN n + 1^ 2 equal un^
+
+ align:start position:0%
+is UN n + 1^ 2 equal un^
+ 
+
+ align:start position:0%
+is UN n + 1^ 2 equal un^
+2 that's what I mean by conserving
+
+ align:start position:0%
+2 that's what I mean by conserving
+ 
+
+ align:start position:0%
+2 that's what I mean by conserving
+energy in the discret case at every step
+
+ align:start position:0%
+energy in the discret case at every step
+ 
+
+ align:start position:0%
+energy in the discret case at every step
+same energy so now I want to look at the
+
+ align:start position:0%
+same energy so now I want to look at the
+ 
+
+ align:start position:0%
+same energy so now I want to look at the
+energy in un n + one compared to the
+
+ align:start position:0%
+energy in un n + one compared to the
+ 
+
+ align:start position:0%
+energy in un n + one compared to the
+energy in un and I want to see that this
+
+ align:start position:0%
+energy in un and I want to see that this
+ 
+
+ align:start position:0%
+energy in un and I want to see that this
+is the this holds
+
+ align:start position:0%
+is the this holds
+ 
+
+ align:start position:0%
+is the this holds
+uh probably there's some smart way to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it's now we're now we're down to
+
+ align:start position:0%
+that it's now we're now we're down to
+ 
+
+ align:start position:0%
+that it's now we're now we're down to
+just like the math question you know
+
+ align:start position:0%
+just like the math question you know
+ 
+
+ align:start position:0%
+just like the math question you know
+math is always looking for some you just
+
+ align:start position:0%
+math is always looking for some you just
+ 
+
+ align:start position:0%
+math is always looking for some you just
+sort of do the right thing and stand
+
+ align:start position:0%
+sort of do the right thing and stand
+ 
+
+ align:start position:0%
+sort of do the right thing and stand
+back and poof it it it it works okay so
+
+ align:start position:0%
+back and poof it it it it works okay so
+ 
+
+ align:start position:0%
+back and poof it it it it works okay so
+what's the right thing hopefully I have
+
+ align:start position:0%
+what's the right thing hopefully I have
+ 
+
+ align:start position:0%
+what's the right thing hopefully I have
+helped you and me by saying what what
+
+ align:start position:0%
+helped you and me by saying what what
+ 
+
+ align:start position:0%
+helped you and me by saying what what
+would be a good idea to do here can I
+
+ align:start position:0%
+would be a good idea to do here can I
+ 
+
+ align:start position:0%
+would be a good idea to do here can I
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look okay it
+
+ align:start position:0%
+look okay it
+ 
+
+ align:start position:0%
+look okay it
+says oh does it say what to
+
+ align:start position:0%
+says oh does it say what to
+ 
+
+ align:start position:0%
+says oh does it say what to
+do yeah it says
+
+ align:start position:0%
+do yeah it says
+ 
+
+ align:start position:0%
+do yeah it says
+multiply by un n + 1 minus plus un n
+
+ align:start position:0%
+multiply by un n + 1 minus plus un n
+ 
+
+ align:start position:0%
+multiply by un n + 1 minus plus un n
+take the take the dotproduct is that
+
+ align:start position:0%
+take the take the dotproduct is that
+ 
+
+ align:start position:0%
+take the take the dotproduct is that
+that's interesting take the dot product
+
+ align:start position:0%
+that's interesting take the dot product
+ 
+
+ align:start position:0%
+that's interesting take the dot product
+so why did that work take the dot
+
+ align:start position:0%
+so why did that work take the dot
+ 
+
+ align:start position:0%
+so why did that work take the dot
+product of both sides with with un n +
+
+ align:start position:0%
+product of both sides with with un n +
+ 
+
+ align:start position:0%
+product of both sides with with un n +
+1us u n is that did anybody succeed with
+
+ align:start position:0%
+1us u n is that did anybody succeed with
+ 
+
+ align:start position:0%
+1us u n is that did anybody succeed with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+idea but that's the idea is and and and
+
+ align:start position:0%
+idea but that's the idea is and and and
+ 
+
+ align:start position:0%
+idea but that's the idea is and and and
+hopefully uh we'll get it to work that
+
+ align:start position:0%
+hopefully uh we'll get it to work that
+ 
+
+ align:start position:0%
+hopefully uh we'll get it to work that
+if I multiply both sides by un + 1 oh no
+
+ align:start position:0%
+if I multiply both sides by un + 1 oh no
+ 
+
+ align:start position:0%
+if I multiply both sides by un + 1 oh no
+plus un maybe better if I look at it
+
+ align:start position:0%
+plus un maybe better if I look at it
+ 
+
+ align:start position:0%
+plus un maybe better if I look at it
+this way I'm yeah I'm sort of okay to do
+
+ align:start position:0%
+this way I'm yeah I'm sort of okay to do
+ 
+
+ align:start position:0%
+this way I'm yeah I'm sort of okay to do
+it that way suppose I multiply both
+
+ align:start position:0%
+it that way suppose I multiply both
+ 
+
+ align:start position:0%
+it that way suppose I multiply both
+sides so now I'm following on this idea
+
+ align:start position:0%
+sides so now I'm following on this idea
+ 
+
+ align:start position:0%
+sides so now I'm following on this idea
+I've that equation I've Rewritten here
+
+ align:start position:0%
+I've that equation I've Rewritten here
+ 
+
+ align:start position:0%
+I've that equation I've Rewritten here
+and without practice I don't know which
+
+ align:start position:0%
+and without practice I don't know which
+ 
+
+ align:start position:0%
+and without practice I don't know which
+one is the good one to start with but I
+
+ align:start position:0%
+one is the good one to start with but I
+ 
+
+ align:start position:0%
+one is the good one to start with but I
+I'm pretty okay with starting with this
+
+ align:start position:0%
+I'm pretty okay with starting with this
+ 
+
+ align:start position:0%
+I'm pretty okay with starting with this
+one suppose I so what what's my idea
+
+ align:start position:0%
+one suppose I so what what's my idea
+ 
+
+ align:start position:0%
+one suppose I so what what's my idea
+that's my equation now I'm going to
+
+ align:start position:0%
+that's my equation now I'm going to
+ 
+
+ align:start position:0%
+that's my equation now I'm going to
+multiply both sides
+
+ align:start position:0%
+multiply both sides
+ 
+
+ align:start position:0%
+multiply both sides
+by un n + 1 plus un transpose now I
+
+ align:start position:0%
+by un n + 1 plus un transpose now I
+ 
+
+ align:start position:0%
+by un n + 1 plus un transpose now I
+don't have room to do it unfortunately I
+
+ align:start position:0%
+don't have room to do it unfortunately I
+ 
+
+ align:start position:0%
+don't have room to do it unfortunately I
+want to stick in here un plus with a
+
+ align:start position:0%
+want to stick in here un plus with a
+ 
+
+ align:start position:0%
+want to stick in here un plus with a
+plus sign in there and of course I have
+
+ align:start position:0%
+plus sign in there and of course I have
+ 
+
+ align:start position:0%
+plus sign in there and of course I have
+to do the same thing here okay are you
+
+ align:start position:0%
+to do the same thing here okay are you
+ 
+
+ align:start position:0%
+to do the same thing here okay are you
+okay do you see what I'm
+
+ align:start position:0%
+okay do you see what I'm
+ 
+
+ align:start position:0%
+okay do you see what I'm
+doing I I I want to show that this
+
+ align:start position:0%
+doing I I I want to show that this
+ 
+
+ align:start position:0%
+doing I I I want to show that this
+equation which is the same as this
+
+ align:start position:0%
+equation which is the same as this
+ 
+
+ align:start position:0%
+equation which is the same as this
+equation has this
+
+ align:start position:0%
+equation has this
+ 
+
+ align:start position:0%
+equation has this
+property which is a copy of this
+
+ align:start position:0%
+property which is a copy of this
+ 
+
+ align:start position:0%
+property which is a copy of this
+property here here would be another way
+
+ align:start position:0%
+property here here would be another way
+ 
+
+ align:start position:0%
+property here here would be another way
+to do it I mean just we could do it
+
+ align:start position:0%
+to do it I mean just we could do it
+ 
+
+ align:start position:0%
+to do it I mean just we could do it
+the the the way we're going to do it now
+
+ align:start position:0%
+the the the way we're going to do it now
+ 
+
+ align:start position:0%
+the the the way we're going to do it now
+is sort of compare Compares with the way
+
+ align:start position:0%
+is sort of compare Compares with the way
+ 
+
+ align:start position:0%
+is sort of compare Compares with the way
+we started with the derivative of the
+
+ align:start position:0%
+we started with the derivative of the
+ 
+
+ align:start position:0%
+we started with the derivative of the
+norm squar I could also ask the same
+
+ align:start position:0%
+norm squar I could also ask the same
+ 
+
+ align:start position:0%
+norm squar I could also ask the same
+question by following igen
+
+ align:start position:0%
+question by following igen
+ 
+
+ align:start position:0%
+question by following igen
+vectors I could also ask the same
+
+ align:start position:0%
+vectors I could also ask the same
+ 
+
+ align:start position:0%
+vectors I could also ask the same
+question by following igen vectors I I
+
+ align:start position:0%
+question by following igen vectors I I
+ 
+
+ align:start position:0%
+question by following igen vectors I I
+get I'm guessing that here the igen
+
+ align:start position:0%
+get I'm guessing that here the igen
+ 
+
+ align:start position:0%
+get I'm guessing that here the igen
+values un + one is yeah uh yeah you see
+
+ align:start position:0%
+values un + one is yeah uh yeah you see
+ 
+
+ align:start position:0%
+values un + one is yeah uh yeah you see
+I could could do it both ways I maybe
+
+ align:start position:0%
+I could could do it both ways I maybe
+ 
+
+ align:start position:0%
+I could could do it both ways I maybe
+having just done igen vectors let me do
+
+ align:start position:0%
+having just done igen vectors let me do
+ 
+
+ align:start position:0%
+having just done igen vectors let me do
+this one by igen vectors so what are the
+
+ align:start position:0%
+this one by igen vectors so what are the
+ 
+
+ align:start position:0%
+this one by igen vectors so what are the
+an igen Vector of
+
+ align:start position:0%
+an igen Vector of
+ 
+
+ align:start position:0%
+an igen Vector of
+a one of X itself is what happens to
+
+ align:start position:0%
+a one of X itself is what happens to
+ 
+
+ align:start position:0%
+a one of X itself is what happens to
+anigen Vector suppose U is an igen
+
+ align:start position:0%
+anigen Vector suppose U is an igen
+ 
+
+ align:start position:0%
+anigen Vector suppose U is an igen
+Vector X of a what's U1 yeah you really
+
+ align:start position:0%
+Vector X of a what's U1 yeah you really
+ 
+
+ align:start position:0%
+Vector X of a what's U1 yeah you really
+should see this question so if if u0 is
+
+ align:start position:0%
+should see this question so if if u0 is
+ 
+
+ align:start position:0%
+should see this question so if if u0 is
+the IG Vector
+
+ align:start position:0%
+the IG Vector
+ 
+
+ align:start position:0%
+the IG Vector
+X then what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U1 let me just write here a X equaling
+
+ align:start position:0%
+U1 let me just write here a X equaling
+ 
+
+ align:start position:0%
+U1 let me just write here a X equaling
+Lambda X so these are the igen values of
+
+ align:start position:0%
+Lambda X so these are the igen values of
+ 
+
+ align:start position:0%
+Lambda X so these are the igen values of
+a and now I want to and we've learned
+
+ align:start position:0%
+a and now I want to and we've learned
+ 
+
+ align:start position:0%
+a and now I want to and we've learned
+that they're pure imaginary in this case
+
+ align:start position:0%
+that they're pure imaginary in this case
+ 
+
+ align:start position:0%
+that they're pure imaginary in this case
+when we're ready to go and now I'd like
+
+ align:start position:0%
+when we're ready to go and now I'd like
+ 
+
+ align:start position:0%
+when we're ready to go and now I'd like
+to know that
+
+ align:start position:0%
+to know that
+ 
+
+ align:start position:0%
+to know that
+there that we get the good thing here
+
+ align:start position:0%
+there that we get the good thing here
+ 
+
+ align:start position:0%
+there that we get the good thing here
+okay so what if un is the is an igen
+
+ align:start position:0%
+okay so what if un is the is an igen
+ 
+
+ align:start position:0%
+okay so what if un is the is an igen
+Vector what is UN n +
+
+ align:start position:0%
+Vector what is UN n +
+ 
+
+ align:start position:0%
+Vector what is UN n +
+one okay so can I just do that that un n
+
+ align:start position:0%
+one okay so can I just do that that un n
+ 
+
+ align:start position:0%
+one okay so can I just do that that un n
++ 1
+
+ align:start position:0%
++ 1
+ 
+
+ align:start position:0%
++ 1
+is what do I have on that right hand
+
+ align:start position:0%
+is what do I have on that right hand
+ 
+
+ align:start position:0%
+is what do I have on that right hand
+side x and what is
+
+ align:start position:0%
+side x and what is
+ 
+
+ align:start position:0%
+side x and what is
+ax it's Lambda right it's Lambda X so so
+
+ align:start position:0%
+ax it's Lambda right it's Lambda X so so
+ 
+
+ align:start position:0%
+ax it's Lambda right it's Lambda X so so
+all this is 1 + Lambda delta T on 2
+
+ align:start position:0%
+all this is 1 + Lambda delta T on 2
+ 
+
+ align:start position:0%
+all this is 1 + Lambda delta T on 2
+x but now I've also got to hit it bring
+
+ align:start position:0%
+x but now I've also got to hit it bring
+ 
+
+ align:start position:0%
+x but now I've also got to hit it bring
+this guy over here here it's
+
+ align:start position:0%
+this guy over here here it's
+ 
+
+ align:start position:0%
+this guy over here here it's
+inverse and see what that does now it's
+
+ align:start position:0%
+inverse and see what that does now it's
+ 
+
+ align:start position:0%
+inverse and see what that does now it's
+the inverse so it's it's going to have
+
+ align:start position:0%
+the inverse so it's it's going to have
+ 
+
+ align:start position:0%
+the inverse so it's it's going to have
+the same igen vector and the igen value
+
+ align:start position:0%
+the same igen vector and the igen value
+ 
+
+ align:start position:0%
+the same igen vector and the igen value
+is going to go in the denominator and
+
+ align:start position:0%
+is going to go in the denominator and
+ 
+
+ align:start position:0%
+is going to go in the denominator and
+it'll be one minus delta T Lambda delta
+
+ align:start position:0%
+it'll be one minus delta T Lambda delta
+ 
+
+ align:start position:0%
+it'll be one minus delta T Lambda delta
+T /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay so that's un + one is do you see
+
+ align:start position:0%
+2 okay so that's un + one is do you see
+ 
+
+ align:start position:0%
+2 okay so that's un + one is do you see
+what's happening
+
+ align:start position:0%
+what's happening
+ 
+
+ align:start position:0%
+what's happening
+here the igen vector
+
+ align:start position:0%
+here the igen vector
+ 
+
+ align:start position:0%
+here the igen vector
+X if if we start with that ion Vector X
+
+ align:start position:0%
+X if if we start with that ion Vector X
+ 
+
+ align:start position:0%
+X if if we start with that ion Vector X
+we come out with a multiple of X and
+
+ align:start position:0%
+we come out with a multiple of X and
+ 
+
+ align:start position:0%
+we come out with a multiple of X and
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+multiple so each each finite difference
+
+ align:start position:0%
+multiple so each each finite difference
+ 
+
+ align:start position:0%
+multiple so each each finite difference
+step multiplies by a number just the way
+
+ align:start position:0%
+step multiplies by a number just the way
+ 
+
+ align:start position:0%
+step multiplies by a number just the way
+each in the continuous case we were
+
+ align:start position:0%
+each in the continuous case we were
+ 
+
+ align:start position:0%
+each in the continuous case we were
+multiplying by e to the Lambda T and in
+
+ align:start position:0%
+multiplying by e to the Lambda T and in
+ 
+
+ align:start position:0%
+multiplying by e to the Lambda T and in
+the continuous in the discrete
+
+ align:start position:0%
+the continuous in the discrete
+ 
+
+ align:start position:0%
+the continuous in the discrete
+stepbystep case we're multiplying by
+
+ align:start position:0%
+stepbystep case we're multiplying by
+ 
+
+ align:start position:0%
+stepbystep case we're multiplying by
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+number actually this is why problem
+
+ align:start position:0%
+number actually this is why problem
+ 
+
+ align:start position:0%
+number actually this is why problem
+seven is important
+
+ align:start position:0%
+seven is important
+ 
+
+ align:start position:0%
+seven is important
+because if we want to know how accurate
+
+ align:start position:0%
+because if we want to know how accurate
+ 
+
+ align:start position:0%
+because if we want to know how accurate
+the comparison is I want to compare e to
+
+ align:start position:0%
+the comparison is I want to compare e to
+ 
+
+ align:start position:0%
+the comparison is I want to compare e to
+the Lambda t with that
+
+ align:start position:0%
+the Lambda t with that
+ 
+
+ align:start position:0%
+the Lambda t with that
+number but so i' problem six is is is
+
+ align:start position:0%
+number but so i' problem six is is is
+ 
+
+ align:start position:0%
+number but so i' problem six is is is
+asking about a question about that ratio
+
+ align:start position:0%
+asking about a question about that ratio
+ 
+
+ align:start position:0%
+asking about a question about that ratio
+and problem seven is asking another
+
+ align:start position:0%
+and problem seven is asking another
+ 
+
+ align:start position:0%
+and problem seven is asking another
+question about that very same ratio now
+
+ align:start position:0%
+question about that very same ratio now
+ 
+
+ align:start position:0%
+question about that very same ratio now
+what's the question for problem six when
+
+ align:start position:0%
+what's the question for problem six when
+ 
+
+ align:start position:0%
+what's the question for problem six when
+will this vector have the same length as
+
+ align:start position:0%
+will this vector have the same length as
+ 
+
+ align:start position:0%
+will this vector have the same length as
+as this x was UN
+
+ align:start position:0%
+as this x was UN
+ 
+
+ align:start position:0%
+as this x was UN
+n what what am
+
+ align:start position:0%
+n what what am
+ 
+
+ align:start position:0%
+n what what am
+I so I started with a
+
+ align:start position:0%
+I so I started with a
+ 
+
+ align:start position:0%
+I so I started with a
+un I multiplied by this number to get un
+
+ align:start position:0%
+un I multiplied by this number to get un
+ 
+
+ align:start position:0%
+un I multiplied by this number to get un
+n + one when do they have the same
+
+ align:start position:0%
+n + one when do they have the same
+ 
+
+ align:start position:0%
+n + one when do they have the same
+length when that number has absolute
+
+ align:start position:0%
+length when that number has absolute
+ 
+
+ align:start position:0%
+length when that number has absolute
+value one so that's my if I watching
+
+ align:start position:0%
+value one so that's my if I watching
+ 
+
+ align:start position:0%
+value one so that's my if I watching
+igen
+
+ align:start position:0%
+igen
+ 
+
+ align:start position:0%
+igen
+vectors this guy had absolute value one
+
+ align:start position:0%
+vectors this guy had absolute value one
+ 
+
+ align:start position:0%
+vectors this guy had absolute value one
+cuz Lambda was
+
+ align:start position:0%
+cuz Lambda was
+ 
+
+ align:start position:0%
+cuz Lambda was
+imaginary now what about this guy
+
+ align:start position:0%
+imaginary now what about this guy
+ 
+
+ align:start position:0%
+imaginary now what about this guy
+lambda's still that same Lambda
+
+ align:start position:0%
+lambda's still that same Lambda
+ 
+
+ align:start position:0%
+lambda's still that same Lambda
+imaginary what what can you tell me
+
+ align:start position:0%
+imaginary what what can you tell me
+ 
+
+ align:start position:0%
+imaginary what what can you tell me
+about one plus so Lambda is some I Omega
+
+ align:start position:0%
+about one plus so Lambda is some I Omega
+ 
+
+ align:start position:0%
+about one plus so Lambda is some I Omega
+delta T / 2 and down here I have 1 minus
+
+ align:start position:0%
+delta T / 2 and down here I have 1 minus
+ 
+
+ align:start position:0%
+delta T / 2 and down here I have 1 minus
+I Omega that's the Lambda Delta t/ 2 I I
+
+ align:start position:0%
+I Omega that's the Lambda Delta t/ 2 I I
+ 
+
+ align:start position:0%
+I Omega that's the Lambda Delta t/ 2 I I
+believe that that does have absolute
+
+ align:start position:0%
+believe that that does have absolute
+ 
+
+ align:start position:0%
+believe that that does have absolute
+value one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody tell me why so that this is
+
+ align:start position:0%
+anybody tell me why so that this is
+ 
+
+ align:start position:0%
+anybody tell me why so that this is
+checking that uh um energy is conserved
+
+ align:start position:0%
+checking that uh um energy is conserved
+ 
+
+ align:start position:0%
+checking that uh um energy is conserved
+for each igen
+
+ align:start position:0%
+for each igen
+ 
+
+ align:start position:0%
+for each igen
+Vector the energy because the because
+
+ align:start position:0%
+Vector the energy because the because
+ 
+
+ align:start position:0%
+Vector the energy because the because
+the I Vector is multiplied by that
+
+ align:start position:0%
+the I Vector is multiplied by that
+ 
+
+ align:start position:0%
+the I Vector is multiplied by that
+number and and that's some number it's
+
+ align:start position:0%
+number and and that's some number it's
+ 
+
+ align:start position:0%
+number and and that's some number it's
+some complex number but I believe it has
+
+ align:start position:0%
+some complex number but I believe it has
+ 
+
+ align:start position:0%
+some complex number but I believe it has
+absolute value one and I believe you can
+
+ align:start position:0%
+absolute value one and I believe you can
+ 
+
+ align:start position:0%
+absolute value one and I believe you can
+tell me why yeah comp because they're
+
+ align:start position:0%
+tell me why yeah comp because they're
+ 
+
+ align:start position:0%
+tell me why yeah comp because they're
+complex conjugates
+
+ align:start position:0%
+complex conjugates
+ 
+
+ align:start position:0%
+complex conjugates
+this numerator and the denominator are
+
+ align:start position:0%
+this numerator and the denominator are
+ 
+
+ align:start position:0%
+this numerator and the denominator are
+complex conjugates in the in the in the
+
+ align:start position:0%
+complex conjugates in the in the in the
+ 
+
+ align:start position:0%
+complex conjugates in the in the in the
+complex plane here's the one and I go up
+
+ align:start position:0%
+complex plane here's the one and I go up
+ 
+
+ align:start position:0%
+complex plane here's the one and I go up
+an e to the I go up I I Omega delta T
+
+ align:start position:0%
+an e to the I go up I I Omega delta T
+ 
+
+ align:start position:0%
+an e to the I go up I I Omega delta T
+over2 or in this one I go down by either
+
+ align:start position:0%
+over2 or in this one I go down by either
+ 
+
+ align:start position:0%
+over2 or in this one I go down by either
+I but those lengths are the same that
+
+ align:start position:0%
+I but those lengths are the same that
+ 
+
+ align:start position:0%
+I but those lengths are the same that
+numerator the length of the numerator is
+
+ align:start position:0%
+numerator the length of the numerator is
+ 
+
+ align:start position:0%
+numerator the length of the numerator is
+that guy the length of the denominator
+
+ align:start position:0%
+that guy the length of the denominator
+ 
+
+ align:start position:0%
+that guy the length of the denominator
+is this guy and their ratio is one
+
+ align:start position:0%
+is this guy and their ratio is one
+ 
+
+ align:start position:0%
+is this guy and their ratio is one
+so I think that this gives us the the
+
+ align:start position:0%
+so I think that this gives us the the
+ 
+
+ align:start position:0%
+so I think that this gives us the the
+point about complex numbers that that a
+
+ align:start position:0%
+point about complex numbers that that a
+ 
+
+ align:start position:0%
+point about complex numbers that that a
+complex number and its
+
+ align:start position:0%
+complex number and its
+ 
+
+ align:start position:0%
+complex number and its
+conjugate automatically have ratio of
+
+ align:start position:0%
+conjugate automatically have ratio of
+ 
+
+ align:start position:0%
+conjugate automatically have ratio of
+magnitude one you you see the difference
+
+ align:start position:0%
+magnitude one you you see the difference
+ 
+
+ align:start position:0%
+magnitude one you you see the difference
+between Oilers method so Oilers method
+
+ align:start position:0%
+between Oilers method so Oilers method
+ 
+
+ align:start position:0%
+between Oilers method so Oilers method
+for so forward Oiler forward forward
+
+ align:start position:0%
+for so forward Oiler forward forward
+ 
+
+ align:start position:0%
+for so forward Oiler forward forward
+Oiler would not have had
+
+ align:start position:0%
+Oiler would not have had
+ 
+
+ align:start position:0%
+Oiler would not have had
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+implicit this stuff on the left side it
+
+ align:start position:0%
+implicit this stuff on the left side it
+ 
+
+ align:start position:0%
+implicit this stuff on the left side it
+would all have been on the right hand
+
+ align:start position:0%
+would all have been on the right hand
+ 
+
+ align:start position:0%
+would all have been on the right hand
+side forward Oiler would have been about
+
+ align:start position:0%
+side forward Oiler would have been about
+ 
+
+ align:start position:0%
+side forward Oiler would have been about
+I + a delta T delta T A and what are its
+
+ align:start position:0%
+I + a delta T delta T A and what are its
+ 
+
+ align:start position:0%
+I + a delta T delta T A and what are its
+igen values 1 + I Omega delta
+
+ align:start position:0%
+igen values 1 + I Omega delta
+ 
+
+ align:start position:0%
+igen values 1 + I Omega delta
+T right with no no we're not dividing by
+
+ align:start position:0%
+T right with no no we're not dividing by
+ 
+
+ align:start position:0%
+T right with no no we're not dividing by
+anybody it's this part is is up top too
+
+ align:start position:0%
+anybody it's this part is is up top too
+ 
+
+ align:start position:0%
+anybody it's this part is is up top too
+so it's 1 plus I Omega delta T now does
+
+ align:start position:0%
+so it's 1 plus I Omega delta T now does
+ 
+
+ align:start position:0%
+so it's 1 plus I Omega delta T now does
+that have absolute value
+
+ align:start position:0%
+that have absolute value
+ 
+
+ align:start position:0%
+that have absolute value
+one well you know from the way I'm
+
+ align:start position:0%
+one well you know from the way I'm
+ 
+
+ align:start position:0%
+one well you know from the way I'm
+asking the question what can you tell me
+
+ align:start position:0%
+asking the question what can you tell me
+ 
+
+ align:start position:0%
+asking the question what can you tell me
+about the absolute value of that of the
+
+ align:start position:0%
+about the absolute value of that of the
+ 
+
+ align:start position:0%
+about the absolute value of that of the
+forward Oiler growth factor greater than
+
+ align:start position:0%
+forward Oiler growth factor greater than
+ 
+
+ align:start position:0%
+forward Oiler growth factor greater than
+one because this is the one and this is
+
+ align:start position:0%
+one because this is the one and this is
+ 
+
+ align:start position:0%
+one because this is the one and this is
+the I Omega delta T maybe went up twice
+
+ align:start position:0%
+the I Omega delta T maybe went up twice
+ 
+
+ align:start position:0%
+the I Omega delta T maybe went up twice
+as far and there was nobody divide by
+
+ align:start position:0%
+as far and there was nobody divide by
+ 
+
+ align:start position:0%
+as far and there was nobody divide by
+it's bigger than one so it blows up and
+
+ align:start position:0%
+it's bigger than one so it blows up and
+ 
+
+ align:start position:0%
+it's bigger than one so it blows up and
+the backward Oiler had only the only the
+
+ align:start position:0%
+the backward Oiler had only the only the
+ 
+
+ align:start position:0%
+the backward Oiler had only the only the
+1 over 1 minus I Omega delta T so the
+
+ align:start position:0%
+1 over 1 minus I Omega delta T so the
+ 
+
+ align:start position:0%
+1 over 1 minus I Omega delta T so the
+backward was was like this like one over
+
+ align:start position:0%
+backward was was like this like one over
+ 
+
+ align:start position:0%
+backward was was like this like one over
+it and less than one but this balance
+
+ align:start position:0%
+it and less than one but this balance
+ 
+
+ align:start position:0%
+it and less than one but this balance
+has absolute value equal one so okay
+
+ align:start position:0%
+has absolute value equal one so okay
+ 
+
+ align:start position:0%
+has absolute value equal one so okay
+that's that's the sort of Heart of
+
+ align:start position:0%
+that's that's the sort of Heart of
+ 
+
+ align:start position:0%
+that's that's the sort of Heart of
+what's going on can I before I tackle
+
+ align:start position:0%
+what's going on can I before I tackle
+ 
+
+ align:start position:0%
+what's going on can I before I tackle
+the question using the hint there uh
+
+ align:start position:0%
+the question using the hint there uh
+ 
+
+ align:start position:0%
+the question using the hint there uh
+which will take me on another Blackboard
+
+ align:start position:0%
+which will take me on another Blackboard
+ 
+
+ align:start position:0%
+which will take me on another Blackboard
+can I I discuss question seven were you
+
+ align:start position:0%
+can I I discuss question seven were you
+ 
+
+ align:start position:0%
+can I I discuss question seven were you
+going to ask me about number seven yeah
+
+ align:start position:0%
+going to ask me about number seven yeah
+ 
+
+ align:start position:0%
+going to ask me about number seven yeah
+I you were okay all right we get to
+
+ align:start position:0%
+I you were okay all right we get to
+ 
+
+ align:start position:0%
+I you were okay all right we get to
+answer okay so question seven is about
+
+ align:start position:0%
+answer okay so question seven is about
+ 
+
+ align:start position:0%
+answer okay so question seven is about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+accuracy so here's the correct number
+
+ align:start position:0%
+accuracy so here's the correct number
+ 
+
+ align:start position:0%
+accuracy so here's the correct number
+this this is my e to the I Omega T
+
+ align:start position:0%
+this this is my e to the I Omega T
+ 
+
+ align:start position:0%
+this this is my e to the I Omega T
+that's the correct number that I should
+
+ align:start position:0%
+that's the correct number that I should
+ 
+
+ align:start position:0%
+that's the correct number that I should
+be multiplying by and the actual number
+
+ align:start position:0%
+be multiplying by and the actual number
+ 
+
+ align:start position:0%
+be multiplying by and the actual number
+that I'm multiplying by is that
+
+ align:start position:0%
+that I'm multiplying by is that
+ 
+
+ align:start position:0%
+that I'm multiplying by is that
+one or in the forward Oiler case it's
+
+ align:start position:0%
+one or in the forward Oiler case it's
+ 
+
+ align:start position:0%
+one or in the forward Oiler case it's
+that one and so I'm comparing the
+
+ align:start position:0%
+that one and so I'm comparing the
+ 
+
+ align:start position:0%
+that one and so I'm comparing the
+onestep accuracy so let me compare
+
+ align:start position:0%
+onestep accuracy so let me compare
+ 
+
+ align:start position:0%
+onestep accuracy so let me compare
+one-step
+
+ align:start position:0%
+one-step
+ 
+
+ align:start position:0%
+one-step
+accuracy yeah so this is this is the
+
+ align:start position:0%
+accuracy yeah so this is this is the
+ 
+
+ align:start position:0%
+accuracy yeah so this is this is the
+topic now of order of accuracy this is
+
+ align:start position:0%
+topic now of order of accuracy this is
+ 
+
+ align:start position:0%
+topic now of order of accuracy this is
+the question
+
+ align:start position:0%
+the question
+ 
+
+ align:start position:0%
+the question
+seven and it amounts to
+
+ align:start position:0%
+seven and it amounts to
+ 
+
+ align:start position:0%
+seven and it amounts to
+comparing the so what
+
+ align:start position:0%
+comparing the so what
+ 
+
+ align:start position:0%
+comparing the so what
+yeah what is one delta T Step In The
+
+ align:start position:0%
+yeah what is one delta T Step In The
+ 
+
+ align:start position:0%
+yeah what is one delta T Step In The
+Continuous case so so how much does the
+
+ align:start position:0%
+Continuous case so so how much does the
+ 
+
+ align:start position:0%
+Continuous case so so how much does the
+I Vector x what does it get multiplied
+
+ align:start position:0%
+I Vector x what does it get multiplied
+ 
+
+ align:start position:0%
+I Vector x what does it get multiplied
+by if I take a delta T step in the
+
+ align:start position:0%
+by if I take a delta T step in the
+ 
+
+ align:start position:0%
+by if I take a delta T step in the
+differential equation if I if I so this
+
+ align:start position:0%
+differential equation if I if I so this
+ 
+
+ align:start position:0%
+differential equation if I if I so this
+is the exact delta T step the the what
+
+ align:start position:0%
+is the exact delta T step the the what
+ 
+
+ align:start position:0%
+is the exact delta T step the the what
+the finite difference won't get exactly
+
+ align:start position:0%
+the finite difference won't get exactly
+ 
+
+ align:start position:0%
+the finite difference won't get exactly
+right what so the exact so step delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T the uh
+
+ align:start position:0%
+T the uh
+ 
+
+ align:start position:0%
+T the uh
+differential differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation of course I always I'm looking
+
+ align:start position:0%
+equation of course I always I'm looking
+ 
+
+ align:start position:0%
+equation of course I always I'm looking
+at axal Lambda X the differential
+
+ align:start position:0%
+at axal Lambda X the differential
+ 
+
+ align:start position:0%
+at axal Lambda X the differential
+equation multiplies X by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what what's the the exact growth
+
+ align:start position:0%
+what what what's the the exact growth
+ 
+
+ align:start position:0%
+what what what's the the exact growth
+factor you could say if I if if if my
+
+ align:start position:0%
+factor you could say if I if if if my
+ 
+
+ align:start position:0%
+factor you could say if I if if if my
+equation is Du dtal Au that's the
+
+ align:start position:0%
+equation is Du dtal Au that's the
+ 
+
+ align:start position:0%
+equation is Du dtal Au that's the
+differential equation and I'm supposing
+
+ align:start position:0%
+differential equation and I'm supposing
+ 
+
+ align:start position:0%
+differential equation and I'm supposing
+that I'm on an igen Vector
+
+ align:start position:0%
+that I'm on an igen Vector
+ 
+
+ align:start position:0%
+that I'm on an igen Vector
+X so that the solution is is e to the I
+
+ align:start position:0%
+X so that the solution is is e to the I
+ 
+
+ align:start position:0%
+X so that the solution is is e to the I
+Omega t or e to the I Lambda X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what happened over a delta T step
+
+ align:start position:0%
+now what happened over a delta T step
+ 
+
+ align:start position:0%
+now what happened over a delta T step
+this this is the answer like running
+
+ align:start position:0%
+this this is the answer like running
+ 
+
+ align:start position:0%
+this this is the answer like running
+along for all time all I'm asking you to
+
+ align:start position:0%
+along for all time all I'm asking you to
+ 
+
+ align:start position:0%
+along for all time all I'm asking you to
+do is if the step is delta T
+
+ align:start position:0%
+do is if the step is delta T
+ 
+
+ align:start position:0%
+do is if the step is delta T
+what's that
+
+ align:start position:0%
+what's that
+ 
+
+ align:start position:0%
+what's that
+number I mean that number is telling us
+
+ align:start position:0%
+number I mean that number is telling us
+ 
+
+ align:start position:0%
+number I mean that number is telling us
+how much how much it grew in that delta
+
+ align:start position:0%
+how much how much it grew in that delta
+ 
+
+ align:start position:0%
+how much how much it grew in that delta
+T step and of course it's e to the I
+
+ align:start position:0%
+T step and of course it's e to the I
+ 
+
+ align:start position:0%
+T step and of course it's e to the I
+Omega delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T that's the exact growth factor that's
+
+ align:start position:0%
+T that's the exact growth factor that's
+ 
+
+ align:start position:0%
+T that's the exact growth factor that's
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exact in one time step the I Vector gets
+
+ align:start position:0%
+exact in one time step the I Vector gets
+ 
+
+ align:start position:0%
+exact in one time step the I Vector gets
+multiplied by that because that's the
+
+ align:start position:0%
+multiplied by that because that's the
+ 
+
+ align:start position:0%
+multiplied by that because that's the
+amount of time that elapsed and what's
+
+ align:start position:0%
+amount of time that elapsed and what's
+ 
+
+ align:start position:0%
+amount of time that elapsed and what's
+the approximate growth the
+
+ align:start position:0%
+the approximate growth the
+ 
+
+ align:start position:0%
+the approximate growth the
+approximate the growth factor from
+
+ align:start position:0%
+approximate the growth factor from
+ 
+
+ align:start position:0%
+approximate the growth factor from
+trapezoidal is just what we wrote down
+
+ align:start position:0%
+trapezoidal is just what we wrote down
+ 
+
+ align:start position:0%
+trapezoidal is just what we wrote down
+here 1+ delta
+
+ align:start position:0%
+here 1+ delta
+ 
+
+ align:start position:0%
+here 1+ delta
+T or Lambda delta T yeah maybe I'll stay
+
+ align:start position:0%
+T or Lambda delta T yeah maybe I'll stay
+ 
+
+ align:start position:0%
+T or Lambda delta T yeah maybe I'll stay
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+Lambda uh rather than I
+
+ align:start position:0%
+Lambda uh rather than I
+ 
+
+ align:start position:0%
+Lambda uh rather than I
+Omega just e to the Lambda delta T and
+
+ align:start position:0%
+Omega just e to the Lambda delta T and
+ 
+
+ align:start position:0%
+Omega just e to the Lambda delta T and
+this was 1 + delta T / 2 Lambda / 1 us
+
+ align:start position:0%
+this was 1 + delta T / 2 Lambda / 1 us
+ 
+
+ align:start position:0%
+this was 1 + delta T / 2 Lambda / 1 us
+delta T / 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda so question s just says compare
+
+ align:start position:0%
+Lambda so question s just says compare
+ 
+
+ align:start position:0%
+Lambda so question s just says compare
+that with
+
+ align:start position:0%
+that with
+ 
+
+ align:start position:0%
+that with
+that if if thinking of delta T is a
+
+ align:start position:0%
+that if if thinking of delta T is a
+ 
+
+ align:start position:0%
+that if if thinking of delta T is a
+small time step if delta T is
+
+ align:start position:0%
+small time step if delta T is
+ 
+
+ align:start position:0%
+small time step if delta T is
+zero then of course the e to the 0 is
+
+ align:start position:0%
+zero then of course the e to the 0 is
+ 
+
+ align:start position:0%
+zero then of course the e to the 0 is
+one if delta T is zero I get one here
+
+ align:start position:0%
+one if delta T is zero I get one here
+ 
+
+ align:start position:0%
+one if delta T is zero I get one here
+they're correct if delta T is zero
+
+ align:start position:0%
+they're correct if delta T is zero
+ 
+
+ align:start position:0%
+they're correct if delta T is zero
+that's no big deal what what do I how do
+
+ align:start position:0%
+that's no big deal what what do I how do
+ 
+
+ align:start position:0%
+that's no big deal what what do I how do
+I study how do I understand what happens
+
+ align:start position:0%
+I study how do I understand what happens
+ 
+
+ align:start position:0%
+I study how do I understand what happens
+for small delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T this is like comparing I'm comparing
+
+ align:start position:0%
+T this is like comparing I'm comparing
+ 
+
+ align:start position:0%
+T this is like comparing I'm comparing
+this this this exponential for small
+
+ align:start position:0%
+this this this exponential for small
+ 
+
+ align:start position:0%
+this this this exponential for small
+delta T with this guy for small delta T
+
+ align:start position:0%
+delta T with this guy for small delta T
+ 
+
+ align:start position:0%
+delta T with this guy for small delta T
+how how do you make comparisons for
+
+ align:start position:0%
+how how do you make comparisons for
+ 
+
+ align:start position:0%
+how how do you make comparisons for
+small delta T well that's what Taylor
+
+ align:start position:0%
+small delta T well that's what Taylor
+ 
+
+ align:start position:0%
+small delta T well that's what Taylor
+series is all about let's do the tailor
+
+ align:start position:0%
+series is all about let's do the tailor
+ 
+
+ align:start position:0%
+series is all about let's do the tailor
+series what's the series for the
+
+ align:start position:0%
+series what's the series for the
+ 
+
+ align:start position:0%
+series what's the series for the
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+if if if delta T is small I have e to
+
+ align:start position:0%
+if if if delta T is small I have e to
+ 
+
+ align:start position:0%
+if if if delta T is small I have e to
+some little number tell me start me out
+
+ align:start position:0%
+some little number tell me start me out
+ 
+
+ align:start position:0%
+some little number tell me start me out
+on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential one thanks one plus uh right
+
+ align:start position:0%
+exponential one thanks one plus uh right
+ 
+
+ align:start position:0%
+exponential one thanks one plus uh right
+right h plus Lambda delta
+
+ align:start position:0%
+right h plus Lambda delta
+ 
+
+ align:start position:0%
+right h plus Lambda delta
+T plus this is the exponential series
+
+ align:start position:0%
+T plus this is the exponential series
+ 
+
+ align:start position:0%
+T plus this is the exponential series
+there only two Series in this world that
+
+ align:start position:0%
+there only two Series in this world that
+ 
+
+ align:start position:0%
+there only two Series in this world that
+are worth knowing really that's
+
+ align:start position:0%
+are worth knowing really that's
+ 
+
+ align:start position:0%
+are worth knowing really that's
+literally true you you calculus you
+
+ align:start position:0%
+literally true you you calculus you
+ 
+
+ align:start position:0%
+literally true you you calculus you
+study all these infinite series there
+
+ align:start position:0%
+study all these infinite series there
+ 
+
+ align:start position:0%
+study all these infinite series there
+are two that are important that are
+
+ align:start position:0%
+are two that are important that are
+ 
+
+ align:start position:0%
+are two that are important that are
+worth remembering long after calculus
+
+ align:start position:0%
+worth remembering long after calculus
+ 
+
+ align:start position:0%
+worth remembering long after calculus
+and x e to the e to the x e to the
+
+ align:start position:0%
+and x e to the e to the x e to the
+ 
+
+ align:start position:0%
+and x e to the e to the x e to the
+whatever is one of them okay what's the
+
+ align:start position:0%
+whatever is one of them okay what's the
+ 
+
+ align:start position:0%
+whatever is one of them okay what's the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+term over two Lambda delta T squar over
+
+ align:start position:0%
+term over two Lambda delta T squar over
+ 
+
+ align:start position:0%
+term over two Lambda delta T squar over
+two and then there's a cube guy and and
+
+ align:start position:0%
+two and then there's a cube guy and and
+ 
+
+ align:start position:0%
+two and then there's a cube guy and and
+if you don't mind telling me what's the
+
+ align:start position:0%
+if you don't mind telling me what's the
+ 
+
+ align:start position:0%
+if you don't mind telling me what's the
+denominator in that
+
+ align:start position:0%
+denominator in that
+ 
+
+ align:start position:0%
+denominator in that
+one it's 3 factorial 6 good and onwards
+
+ align:start position:0%
+one it's 3 factorial 6 good and onwards
+ 
+
+ align:start position:0%
+one it's 3 factorial 6 good and onwards
+okay so that's one of the series that
+
+ align:start position:0%
+okay so that's one of the series that
+ 
+
+ align:start position:0%
+okay so that's one of the series that
+everybody should know okay how are we
+
+ align:start position:0%
+everybody should know okay how are we
+ 
+
+ align:start position:0%
+everybody should know okay how are we
+going to deal with this
+
+ align:start position:0%
+going to deal with this
+ 
+
+ align:start position:0%
+going to deal with this
+guy how how we want to expand that so
+
+ align:start position:0%
+guy how how we want to expand that so
+ 
+
+ align:start position:0%
+guy how how we want to expand that so
+what am I what's my goal I want you to
+
+ align:start position:0%
+what am I what's my goal I want you to
+ 
+
+ align:start position:0%
+what am I what's my goal I want you to
+expand that in powers of Lambda delta T
+
+ align:start position:0%
+expand that in powers of Lambda delta T
+ 
+
+ align:start position:0%
+expand that in powers of Lambda delta T
+and compare with this and see how how
+
+ align:start position:0%
+and compare with this and see how how
+ 
+
+ align:start position:0%
+and compare with this and see how how
+you know where do they they aren't going
+
+ align:start position:0%
+you know where do they they aren't going
+ 
+
+ align:start position:0%
+you know where do they they aren't going
+to be equal right at some point they're
+
+ align:start position:0%
+to be equal right at some point they're
+ 
+
+ align:start position:0%
+to be equal right at some point they're
+going to be different but at least they
+
+ align:start position:0%
+going to be different but at least they
+ 
+
+ align:start position:0%
+going to be different but at least they
+should start out equal so how do you can
+
+ align:start position:0%
+should start out equal so how do you can
+ 
+
+ align:start position:0%
+should start out equal so how do you can
+you do this so here's the heart of
+
+ align:start position:0%
+you do this so here's the heart of
+ 
+
+ align:start position:0%
+you do this so here's the heart of
+problem seven what do I do how do I
+
+ align:start position:0%
+problem seven what do I do how do I
+ 
+
+ align:start position:0%
+problem seven what do I do how do I
+expand this in powers of delta
+
+ align:start position:0%
+expand this in powers of delta
+ 
+
+ align:start position:0%
+expand this in powers of delta
+T can I do you mind if I just this is
+
+ align:start position:0%
+T can I do you mind if I just this is
+ 
+
+ align:start position:0%
+T can I do you mind if I just this is
+just a number let me put it times times
+
+ align:start position:0%
+just a number let me put it times times
+ 
+
+ align:start position:0%
+just a number let me put it times times
+one over it so this is times 1 minus
+
+ align:start position:0%
+one over it so this is times 1 minus
+ 
+
+ align:start position:0%
+one over it so this is times 1 minus
+delta T / 2 Lambda inverse right I just
+
+ align:start position:0%
+delta T / 2 Lambda inverse right I just
+ 
+
+ align:start position:0%
+delta T / 2 Lambda inverse right I just
+bring that up as a number so it's it's
+
+ align:start position:0%
+bring that up as a number so it's it's
+ 
+
+ align:start position:0%
+bring that up as a number so it's it's
+this guy times one over this
+
+ align:start position:0%
+this guy times one over this
+ 
+
+ align:start position:0%
+this guy times one over this
+guy what do I do this is you know here's
+
+ align:start position:0%
+guy what do I do this is you know here's
+ 
+
+ align:start position:0%
+guy what do I do this is you know here's
+here's the moment when uh you know the
+
+ align:start position:0%
+here's the moment when uh you know the
+ 
+
+ align:start position:0%
+here's the moment when uh you know the
+math tools get
+
+ align:start position:0%
+math tools get
+ 
+
+ align:start position:0%
+math tools get
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+and I'm I'm well aware that you know
+
+ align:start position:0%
+and I'm I'm well aware that you know
+ 
+
+ align:start position:0%
+and I'm I'm well aware that you know
+it's like years since you did calculus
+
+ align:start position:0%
+it's like years since you did calculus
+ 
+
+ align:start position:0%
+it's like years since you did calculus
+or series or whatever and uh those tools
+
+ align:start position:0%
+or series or whatever and uh those tools
+ 
+
+ align:start position:0%
+or series or whatever and uh those tools
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+rusty and the point is that they are
+
+ align:start position:0%
+rusty and the point is that they are
+ 
+
+ align:start position:0%
+rusty and the point is that they are
+really genuine tools that that we can
+
+ align:start position:0%
+really genuine tools that that we can
+ 
+
+ align:start position:0%
+really genuine tools that that we can
+now use so what do you
+
+ align:start position:0%
+now use so what do you
+ 
+
+ align:start position:0%
+now use so what do you
+think what shall I this is the sort of
+
+ align:start position:0%
+think what shall I this is the sort of
+ 
+
+ align:start position:0%
+think what shall I this is the sort of
+like problem one this is the one coming
+
+ align:start position:0%
+like problem one this is the one coming
+ 
+
+ align:start position:0%
+like problem one this is the one coming
+from the denominator this is 1 over 1 -
+
+ align:start position:0%
+from the denominator this is 1 over 1 -
+ 
+
+ align:start position:0%
+from the denominator this is 1 over 1 -
+x you should so I have a 1 over 1 - x
+
+ align:start position:0%
+x you should so I have a 1 over 1 - x
+ 
+
+ align:start position:0%
+x you should so I have a 1 over 1 - x
+deal and what's the series for that I
+
+ align:start position:0%
+deal and what's the series for that I
+ 
+
+ align:start position:0%
+deal and what's the series for that I
+you know I said there were two series
+
+ align:start position:0%
+you know I said there were two series
+ 
+
+ align:start position:0%
+you know I said there were two series
+worth remembering and sure enough the
+
+ align:start position:0%
+worth remembering and sure enough the
+ 
+
+ align:start position:0%
+worth remembering and sure enough the
+exponential was one of them and now
+
+ align:start position:0%
+exponential was one of them and now
+ 
+
+ align:start position:0%
+exponential was one of them and now
+we're ready for the other one what's the
+
+ align:start position:0%
+we're ready for the other one what's the
+ 
+
+ align:start position:0%
+we're ready for the other one what's the
+series for that
+
+ align:start position:0%
+series for that
+ 
+
+ align:start position:0%
+series for that
+guy 1 + x Good
+
+ align:start position:0%
+guy 1 + x Good
+ 
+
+ align:start position:0%
+guy 1 + x Good
+Start
+
+ align:start position:0%
+Start
+ 
+
+ align:start position:0%
+Start
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus x s right X2
+
+ align:start position:0%
+plus x s right X2
+ 
+
+ align:start position:0%
+plus x s right X2
+plus X cub and so on real simple it's
+
+ align:start position:0%
+plus X cub and so on real simple it's
+ 
+
+ align:start position:0%
+plus X cub and so on real simple it's
+all the same stuff with no factorials
+
+ align:start position:0%
+all the same stuff with no factorials
+ 
+
+ align:start position:0%
+all the same stuff with no factorials
+those are the two series to to know
+
+ align:start position:0%
+those are the two series to to know
+ 
+
+ align:start position:0%
+those are the two series to to know
+the exponential series and the geometric
+
+ align:start position:0%
+the exponential series and the geometric
+ 
+
+ align:start position:0%
+the exponential series and the geometric
+Series right that's the geometric series
+
+ align:start position:0%
+Series right that's the geometric series
+ 
+
+ align:start position:0%
+Series right that's the geometric series
+okay so that's what I've got out of this
+
+ align:start position:0%
+okay so that's what I've got out of this
+ 
+
+ align:start position:0%
+okay so that's what I've got out of this
+stuff can I write it below I have 1 +
+
+ align:start position:0%
+stuff can I write it below I have 1 +
+ 
+
+ align:start position:0%
+stuff can I write it below I have 1 +
+Delta t/ 2 Lambda can I get I let me
+
+ align:start position:0%
+Delta t/ 2 Lambda can I get I let me
+ 
+
+ align:start position:0%
+Delta t/ 2 Lambda can I get I let me
+just call that X for the moment Delta t/
+
+ align:start position:0%
+just call that X for the moment Delta t/
+ 
+
+ align:start position:0%
+just call that X for the moment Delta t/
+2 Lambda is my x 1 + x and this is 1
+
+ align:start position:0%
+2 Lambda is my x 1 + x and this is 1
+ 
+
+ align:start position:0%
+2 Lambda is my x 1 + x and this is 1
+over 1 - x which you just told me is 1 +
+
+ align:start position:0%
+over 1 - x which you just told me is 1 +
+ 
+
+ align:start position:0%
+over 1 - x which you just told me is 1 +
+x + x^2 plus X cub and so
+
+ align:start position:0%
+x + x^2 plus X cub and so
+ 
+
+ align:start position:0%
+x + x^2 plus X cub and so
+on and now I I got to do that
+
+ align:start position:0%
+on and now I I got to do that
+ 
+
+ align:start position:0%
+on and now I I got to do that
+multiplication okay X is remember this
+
+ align:start position:0%
+multiplication okay X is remember this
+ 
+
+ align:start position:0%
+multiplication okay X is remember this
+is X this is this is my X I'm just to
+
+ align:start position:0%
+is X this is this is my X I'm just to
+ 
+
+ align:start position:0%
+is X this is this is my X I'm just to
+save space can you multiply those
+
+ align:start position:0%
+save space can you multiply those
+ 
+
+ align:start position:0%
+save space can you multiply those
+guys so that's 1+ x times this lot of
+
+ align:start position:0%
+guys so that's 1+ x times this lot of
+ 
+
+ align:start position:0%
+guys so that's 1+ x times this lot of
+stuff here what do I have all together
+
+ align:start position:0%
+stuff here what do I have all together
+ 
+
+ align:start position:0%
+stuff here what do I have all together
+well the one what's the next
+
+ align:start position:0%
+well the one what's the next
+ 
+
+ align:start position:0%
+well the one what's the next
+term 2 X's everybody spots the two x's
+
+ align:start position:0%
+term 2 X's everybody spots the two x's
+ 
+
+ align:start position:0%
+term 2 X's everybody spots the two x's
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and then the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term you have to get these terms right
+
+ align:start position:0%
+term you have to get these terms right
+ 
+
+ align:start position:0%
+term you have to get these terms right
+because we plan to compare with this guy
+
+ align:start position:0%
+because we plan to compare with this guy
+ 
+
+ align:start position:0%
+because we plan to compare with this guy
+and see how many we get how many X squs
+
+ align:start position:0%
+and see how many we get how many X squs
+ 
+
+ align:start position:0%
+and see how many we get how many X squs
+are in there is it two looks like two 2
+
+ align:start position:0%
+are in there is it two looks like two 2
+ 
+
+ align:start position:0%
+are in there is it two looks like two 2
+X2 and 2 x cubes and so on yeah that
+
+ align:start position:0%
+X2 and 2 x cubes and so on yeah that
+ 
+
+ align:start position:0%
+X2 and 2 x cubes and so on yeah that
+that looks right okay now I'm I'm ready
+
+ align:start position:0%
+that looks right okay now I'm I'm ready
+ 
+
+ align:start position:0%
+that looks right okay now I'm I'm ready
+what am I ready
+
+ align:start position:0%
+what am I ready
+ 
+
+ align:start position:0%
+what am I ready
+for I'm ready to say what x is X is this
+
+ align:start position:0%
+for I'm ready to say what x is X is this
+ 
+
+ align:start position:0%
+for I'm ready to say what x is X is this
+delta T over 2 Lambda so what is it what
+
+ align:start position:0%
+delta T over 2 Lambda so what is it what
+ 
+
+ align:start position:0%
+delta T over 2 Lambda so what is it what
+have I got here one what is this guy now
+
+ align:start position:0%
+have I got here one what is this guy now
+ 
+
+ align:start position:0%
+have I got here one what is this guy now
+2 X's
+
+ align:start position:0%
+2 X's
+ 
+
+ align:start position:0%
+2 X's
+is delta T
+
+ align:start position:0%
+is delta T
+ 
+
+ align:start position:0%
+is delta T
+Lambda is this good yes right we're
+
+ align:start position:0%
+Lambda is this good yes right we're
+ 
+
+ align:start position:0%
+Lambda is this good yes right we're
+pleased because the 2x is the two of
+
+ align:start position:0%
+pleased because the 2x is the two of
+ 
+
+ align:start position:0%
+pleased because the 2x is the two of
+these is delta T Lambda and that's what
+
+ align:start position:0%
+these is delta T Lambda and that's what
+ 
+
+ align:start position:0%
+these is delta T Lambda and that's what
+we wanted to match absolutely delta T
+
+ align:start position:0%
+we wanted to match absolutely delta T
+ 
+
+ align:start position:0%
+we wanted to match absolutely delta T
+Lambda or Lambda delta T now let's keep
+
+ align:start position:0%
+Lambda or Lambda delta T now let's keep
+ 
+
+ align:start position:0%
+Lambda or Lambda delta T now let's keep
+going by the way if this first term
+
+ align:start position:0%
+going by the way if this first term
+ 
+
+ align:start position:0%
+going by the way if this first term
+hadn't matched we would be extremely
+
+ align:start position:0%
+hadn't matched we would be extremely
+ 
+
+ align:start position:0%
+hadn't matched we would be extremely
+surprised right because the the that
+
+ align:start position:0%
+surprised right because the the that
+ 
+
+ align:start position:0%
+surprised right because the the that
+first matching is only saying that my
+
+ align:start position:0%
+first matching is only saying that my
+ 
+
+ align:start position:0%
+first matching is only saying that my
+difference equation is like consistent
+
+ align:start position:0%
+difference equation is like consistent
+ 
+
+ align:start position:0%
+difference equation is like consistent
+it's a reasonable
+
+ align:start position:0%
+it's a reasonable
+ 
+
+ align:start position:0%
+it's a reasonable
+reasonable creation out out of the
+
+ align:start position:0%
+reasonable creation out out of the
+ 
+
+ align:start position:0%
+reasonable creation out out of the
+differential equation and we knew that
+
+ align:start position:0%
+differential equation and we knew that
+ 
+
+ align:start position:0%
+differential equation and we knew that
+the question is how much further we
+
+ align:start position:0%
+the question is how much further we
+ 
+
+ align:start position:0%
+the question is how much further we
+going to get Oiler will not get any
+
+ align:start position:0%
+going to get Oiler will not get any
+ 
+
+ align:start position:0%
+going to get Oiler will not get any
+further with Oiler the next ones will
+
+ align:start position:0%
+further with Oiler the next ones will
+ 
+
+ align:start position:0%
+further with Oiler the next ones will
+fail but I think with trapezoid the next
+
+ align:start position:0%
+fail but I think with trapezoid the next
+ 
+
+ align:start position:0%
+fail but I think with trapezoid the next
+ones are going to work does it
+
+ align:start position:0%
+ones are going to work does it
+ 
+
+ align:start position:0%
+ones are going to work does it
+work you're all you're like we're
+
+ align:start position:0%
+work you're all you're like we're
+ 
+
+ align:start position:0%
+work you're all you're like we're
+holding our Breath Right two now I'm
+
+ align:start position:0%
+holding our Breath Right two now I'm
+ 
+
+ align:start position:0%
+holding our Breath Right two now I'm
+going to put in X squar and see about
+
+ align:start position:0%
+going to put in X squar and see about
+ 
+
+ align:start position:0%
+going to put in X squar and see about
+this term X is
+
+ align:start position:0%
+this term X is
+ 
+
+ align:start position:0%
+this term X is
+what x is this guy Delta t/ 2
+
+ align:start position:0%
+what x is this guy Delta t/ 2
+ 
+
+ align:start position:0%
+what x is this guy Delta t/ 2
+Lambda delta T Lambda over 2^ 2ar and
+
+ align:start position:0%
+Lambda delta T Lambda over 2^ 2ar and
+ 
+
+ align:start position:0%
+Lambda delta T Lambda over 2^ 2ar and
+now you get the the
+
+ align:start position:0%
+now you get the the
+ 
+
+ align:start position:0%
+now you get the the
+fun because you're going to compare this
+
+ align:start position:0%
+fun because you're going to compare this
+ 
+
+ align:start position:0%
+fun because you're going to compare this
+term with
+
+ align:start position:0%
+term with
+ 
+
+ align:start position:0%
+term with
+what with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term and are they the
+
+ align:start position:0%
+term and are they the
+ 
+
+ align:start position:0%
+term and are they the
+same yes yes so that's that's the way
+
+ align:start position:0%
+same yes yes so that's that's the way
+ 
+
+ align:start position:0%
+same yes yes so that's that's the way
+you see that you got the extra accuracy
+
+ align:start position:0%
+you see that you got the extra accuracy
+ 
+
+ align:start position:0%
+you see that you got the extra accuracy
+which Oiler did not give you but so that
+
+ align:start position:0%
+which Oiler did not give you but so that
+ 
+
+ align:start position:0%
+which Oiler did not give you but so that
+that's why the trapezoidal rule is a
+
+ align:start position:0%
+that's why the trapezoidal rule is a
+ 
+
+ align:start position:0%
+that's why the trapezoidal rule is a
+second order accurate method okay that
+
+ align:start position:0%
+second order accurate method okay that
+ 
+
+ align:start position:0%
+second order accurate method okay that
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh you may say like that I went
+
+ align:start position:0%
+uh you may say like that I went
+ 
+
+ align:start position:0%
+uh you may say like that I went
+overboard to say all that you know you
+
+ align:start position:0%
+overboard to say all that you know you
+ 
+
+ align:start position:0%
+overboard to say all that you know you
+you may say I didn't ask that question
+
+ align:start position:0%
+you may say I didn't ask that question
+ 
+
+ align:start position:0%
+you may say I didn't ask that question
+but it's the right question to ask about
+
+ align:start position:0%
+but it's the right question to ask about
+ 
+
+ align:start position:0%
+but it's the right question to ask about
+order of accuracy and it's what problem
+
+ align:start position:0%
+order of accuracy and it's what problem
+ 
+
+ align:start position:0%
+order of accuracy and it's what problem
+seven was intending to bring to to maybe
+
+ align:start position:0%
+seven was intending to bring to to maybe
+ 
+
+ align:start position:0%
+seven was intending to bring to to maybe
+I called it h in problem 7 rather than
+
+ align:start position:0%
+I called it h in problem 7 rather than
+ 
+
+ align:start position:0%
+I called it h in problem 7 rather than
+uh X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+well oh gosh I realize I've still have
+
+ align:start position:0%
+well oh gosh I realize I've still have
+ 
+
+ align:start position:0%
+well oh gosh I realize I've still have
+you I'm supposed to come back to this
+
+ align:start position:0%
+you I'm supposed to come back to this
+ 
+
+ align:start position:0%
+you I'm supposed to come back to this
+this one but some people might have
+
+ align:start position:0%
+this one but some people might have
+ 
+
+ align:start position:0%
+this one but some people might have
+other problems that they're interested
+
+ align:start position:0%
+other problems that they're interested
+ 
+
+ align:start position:0%
+other problems that they're interested
+in let let me because time is pushing
+
+ align:start position:0%
+in let let me because time is pushing
+ 
+
+ align:start position:0%
+in let let me because time is pushing
+along uh and the solution of this one
+
+ align:start position:0%
+along uh and the solution of this one
+ 
+
+ align:start position:0%
+along uh and the solution of this one
+will post let me at least offer the
+
+ align:start position:0%
+will post let me at least offer the
+ 
+
+ align:start position:0%
+will post let me at least offer the
+possibility to ask me about something
+
+ align:start position:0%
+possibility to ask me about something
+ 
+
+ align:start position:0%
+possibility to ask me about something
+completely not six or seven here but
+
+ align:start position:0%
+completely not six or seven here but
+ 
+
+ align:start position:0%
+completely not six or seven here but
+something entirely different like what's
+
+ align:start position:0%
+something entirely different like what's
+ 
+
+ align:start position:0%
+something entirely different like what's
+the first question on the quiz or
+
+ align:start position:0%
+the first question on the quiz or
+ 
+
+ align:start position:0%
+the first question on the quiz or
+anything and that let me say I'm a
+
+ align:start position:0%
+anything and that let me say I'm a
+ 
+
+ align:start position:0%
+anything and that let me say I'm a
+uh I'll hope to know by Tuesday
+
+ align:start position:0%
+uh I'll hope to know by Tuesday
+ 
+
+ align:start position:0%
+uh I'll hope to know by Tuesday
+uh I I it's it's I love to to teach and
+
+ align:start position:0%
+uh I I it's it's I love to to teach and
+ 
+
+ align:start position:0%
+uh I I it's it's I love to to teach and
+but making up exams is serious work
+
+ align:start position:0%
+but making up exams is serious work
+ 
+
+ align:start position:0%
+but making up exams is serious work
+anyway uh uh let me move up open a board
+
+ align:start position:0%
+anyway uh uh let me move up open a board
+ 
+
+ align:start position:0%
+anyway uh uh let me move up open a board
+and O open to another question of of any
+
+ align:start position:0%
+and O open to another question of of any
+ 
+
+ align:start position:0%
+and O open to another question of of any
+sort any place chapter one chapter two
+
+ align:start position:0%
+sort any place chapter one chapter two
+ 
+
+ align:start position:0%
+sort any place chapter one chapter two
+whatever is there
+
+ align:start position:0%
+whatever is there
+ 
+
+ align:start position:0%
+whatever is there
+anything so you I know that you're in
+
+ align:start position:0%
+anything so you I know that you're in
+ 
+
+ align:start position:0%
+anything so you I know that you're in
+the middle of this homework uh so I can
+
+ align:start position:0%
+the middle of this homework uh so I can
+ 
+
+ align:start position:0%
+the middle of this homework uh so I can
+say a little more here about the about
+
+ align:start position:0%
+say a little more here about the about
+ 
+
+ align:start position:0%
+say a little more here about the about
+the uh that number six if you if you
+
+ align:start position:0%
+the uh that number six if you if you
+ 
+
+ align:start position:0%
+the uh that number six if you if you
+want but I wanted to allow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+on uh the A and the from today from
+
+ align:start position:0%
+on uh the A and the from today from
+ 
+
+ align:start position:0%
+on uh the A and the from today from
+today's lecture this was the incidence
+
+ align:start position:0%
+today's lecture this was the incidence
+ 
+
+ align:start position:0%
+today's lecture this was the incidence
+Matrix okay and this was the a transpose
+
+ align:start position:0%
+Matrix okay and this was the a transpose
+ 
+
+ align:start position:0%
+Matrix okay and this was the a transpose
+a that's probably still on the board
+
+ align:start position:0%
+a that's probably still on the board
+ 
+
+ align:start position:0%
+a that's probably still on the board
+somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so this is what uh so this is
+
+ align:start position:0%
+yeah yeah so this is what uh so this is
+ 
+
+ align:start position:0%
+yeah yeah so this is what uh so this is
+the a which you should take in and and
+
+ align:start position:0%
+the a which you should take in and and
+ 
+
+ align:start position:0%
+the a which you should take in and and
+be able to create if I gave you the
+
+ align:start position:0%
+be able to create if I gave you the
+ 
+
+ align:start position:0%
+be able to create if I gave you the
+graph and this is the a transpose a so
+
+ align:start position:0%
+graph and this is the a transpose a so
+ 
+
+ align:start position:0%
+graph and this is the a transpose a so
+so it's through today's lecture right
+
+ align:start position:0%
+so it's through today's lecture right
+ 
+
+ align:start position:0%
+so it's through today's lecture right
+yeah next next lecture I'll be talking
+
+ align:start position:0%
+yeah next next lecture I'll be talking
+ 
+
+ align:start position:0%
+yeah next next lecture I'll be talking
+about the a transpose by itself which
+
+ align:start position:0%
+about the a transpose by itself which
+ 
+
+ align:start position:0%
+about the a transpose by itself which
+involves kof's current law it's
+
+ align:start position:0%
+involves kof's current law it's
+ 
+
+ align:start position:0%
+involves kof's current law it's
+beautiful beautiful a transpose W equals
+
+ align:start position:0%
+beautiful beautiful a transpose W equals
+ 
+
+ align:start position:0%
+beautiful beautiful a transpose W equals
+z but
+
+ align:start position:0%
+z but
+ 
+
+ align:start position:0%
+z but
+I think this part was straightforward
+
+ align:start position:0%
+I think this part was straightforward
+ 
+
+ align:start position:0%
+I think this part was straightforward
+enough to to be able to add this to our
+
+ align:start position:0%
+enough to to be able to add this to our
+ 
+
+ align:start position:0%
+enough to to be able to add this to our
+list
+
+ align:start position:0%
+list
+ 
+
+ align:start position:0%
+list
+of uh problems where which fit the
+
+ align:start position:0%
+of uh problems where which fit the
+ 
+
+ align:start position:0%
+of uh problems where which fit the
+framework yeah yeah so that's that's
+
+ align:start position:0%
+framework yeah yeah so that's that's
+ 
+
+ align:start position:0%
+framework yeah yeah so that's that's
+what that was about that doesn't mean
+
+ align:start position:0%
+what that was about that doesn't mean
+ 
+
+ align:start position:0%
+what that was about that doesn't mean
+that this will be on but it could be
+
+ align:start position:0%
+that this will be on but it could be
+ 
+
+ align:start position:0%
+that this will be on but it could be
+right okay what else you guys are
+
+ align:start position:0%
+right okay what else you guys are
+ 
+
+ align:start position:0%
+right okay what else you guys are
+patient to come on yeah thanks that gec
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+it's only valid when X is less than one
+
+ align:start position:0%
+it's only valid when X is less than one
+ 
+
+ align:start position:0%
+it's only valid when X is less than one
+yeah that's uh so that's now the math
+
+ align:start position:0%
+yeah that's uh so that's now the math
+ 
+
+ align:start position:0%
+yeah that's uh so that's now the math
+point that this expansion for e to the x
+
+ align:start position:0%
+point that this expansion for e to the x
+ 
+
+ align:start position:0%
+point that this expansion for e to the x
+is valid all X's because you're dividing
+
+ align:start position:0%
+is valid all X's because you're dividing
+ 
+
+ align:start position:0%
+is valid all X's because you're dividing
+by these bigger and bigger numbers but
+
+ align:start position:0%
+by these bigger and bigger numbers but
+ 
+
+ align:start position:0%
+by these bigger and bigger numbers but
+this one is only valid up to xal 1 at
+
+ align:start position:0%
+this one is only valid up to xal 1 at
+ 
+
+ align:start position:0%
+this one is only valid up to xal 1 at
+xal 1 we're getting 1 + 1 + 1 and we're
+
+ align:start position:0%
+xal 1 we're getting 1 + 1 + 1 and we're
+ 
+
+ align:start position:0%
+xal 1 we're getting 1 + 1 + 1 and we're
+getting 1 over 1 - one sort of infinity
+
+ align:start position:0%
+getting 1 over 1 - one sort of infinity
+ 
+
+ align:start position:0%
+getting 1 over 1 - one sort of infinity
+matches Infinity but then if x goes up
+
+ align:start position:0%
+matches Infinity but then if x goes up
+ 
+
+ align:start position:0%
+matches Infinity but then if x goes up
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+two yeah what happens if x is
+
+ align:start position:0%
+two yeah what happens if x is
+ 
+
+ align:start position:0%
+two yeah what happens if x is
+two it's it's sort of not good but you
+
+ align:start position:0%
+two it's it's sort of not good but you
+ 
+
+ align:start position:0%
+two it's it's sort of not good but you
+know mathematics is it's never
+
+ align:start position:0%
+know mathematics is it's never
+ 
+
+ align:start position:0%
+know mathematics is it's never
+completely crazy right if x is two what
+
+ align:start position:0%
+completely crazy right if x is two what
+ 
+
+ align:start position:0%
+completely crazy right if x is two what
+does this say what have I got on the
+
+ align:start position:0%
+does this say what have I got on the
+ 
+
+ align:start position:0%
+does this say what have I got on the
+left hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side-1 and what have I got on the right
+
+ align:start position:0%
+side-1 and what have I got on the right
+ 
+
+ align:start position:0%
+side-1 and what have I got on the right
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+side 1 + 2 + 4 +
+
+ align:start position:0%
+side 1 + 2 + 4 +
+ 
+
+ align:start position:0%
+side 1 + 2 + 4 +
+8 I should not allow this to be
+
+ align:start position:0%
+8 I should not allow this to be
+ 
+
+ align:start position:0%
+8 I should not allow this to be
+videotaped but uh that that actually not
+
+ align:start position:0%
+videotaped but uh that that actually not
+ 
+
+ align:start position:0%
+videotaped but uh that that actually not
+so completely crazy in some in some
+
+ align:start position:0%
+so completely crazy in some in some
+ 
+
+ align:start position:0%
+so completely crazy in some in some
+nutty way you know that could still make
+
+ align:start position:0%
+nutty way you know that could still make
+ 
+
+ align:start position:0%
+nutty way you know that could still make
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+sense I won't that certainly will not be
+
+ align:start position:0%
+sense I won't that certainly will not be
+ 
+
+ align:start position:0%
+sense I won't that certainly will not be
+on the so you're right that X should be
+
+ align:start position:0%
+on the so you're right that X should be
+ 
+
+ align:start position:0%
+on the so you're right that X should be
+less than one and of course uh it will
+
+ align:start position:0%
+less than one and of course uh it will
+ 
+
+ align:start position:0%
+less than one and of course uh it will
+be here because I'm looking at little
+
+ align:start position:0%
+be here because I'm looking at little
+ 
+
+ align:start position:0%
+be here because I'm looking at little
+Delta T's little so my delta T my X was
+
+ align:start position:0%
+Delta T's little so my delta T my X was
+ 
+
+ align:start position:0%
+Delta T's little so my delta T my X was
+this thing and my delta T the time step
+
+ align:start position:0%
+this thing and my delta T the time step
+ 
+
+ align:start position:0%
+this thing and my delta T the time step
+was small and and somehow that tells me
+
+ align:start position:0%
+was small and and somehow that tells me
+ 
+
+ align:start position:0%
+was small and and somehow that tells me
+actually this this is a a good
+
+ align:start position:0%
+actually this this is a a good
+ 
+
+ align:start position:0%
+actually this this is a a good
+indication it gives me the units that
+
+ align:start position:0%
+indication it gives me the units that
+ 
+
+ align:start position:0%
+indication it gives me the units that
+stability and things going right will
+
+ align:start position:0%
+stability and things going right will
+ 
+
+ align:start position:0%
+stability and things going right will
+depend on Lambda delta T will depend on
+
+ align:start position:0%
+depend on Lambda delta T will depend on
+ 
+
+ align:start position:0%
+depend on Lambda delta T will depend on
+Lambda delta T that's the key parameter
+
+ align:start position:0%
+Lambda delta T that's the key parameter
+ 
+
+ align:start position:0%
+Lambda delta T that's the key parameter
+there that's that's like the
+
+ align:start position:0%
+there that's that's like the
+ 
+
+ align:start position:0%
+there that's that's like the
+dimensionless parameter uh that that we
+
+ align:start position:0%
+dimensionless parameter uh that that we
+ 
+
+ align:start position:0%
+dimensionless parameter uh that that we
+or Lambda delta T over 2 or whatever but
+
+ align:start position:0%
+or Lambda delta T over 2 or whatever but
+ 
+
+ align:start position:0%
+or Lambda delta T over 2 or whatever but
+Lambda delta T is the key and and and
+
+ align:start position:0%
+Lambda delta T is the key and and and
+ 
+
+ align:start position:0%
+Lambda delta T is the key and and and
+highly important key it tells us that as
+
+ align:start position:0%
+highly important key it tells us that as
+ 
+
+ align:start position:0%
+highly important key it tells us that as
+Lambda gets bigger as the Matrix has
+
+ align:start position:0%
+Lambda gets bigger as the Matrix has
+ 
+
+ align:start position:0%
+Lambda gets bigger as the Matrix has
+bigger igen values delta T has got to
+
+ align:start position:0%
+bigger igen values delta T has got to
+ 
+
+ align:start position:0%
+bigger igen values delta T has got to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+smaller and and I mentioned stiff
+
+ align:start position:0%
+smaller and and I mentioned stiff
+ 
+
+ align:start position:0%
+smaller and and I mentioned stiff
+equations stiff equations are equations
+
+ align:start position:0%
+equations stiff equations are equations
+ 
+
+ align:start position:0%
+equations stiff equations are equations
+where the I values Lambda are are are
+
+ align:start position:0%
+where the I values Lambda are are are
+ 
+
+ align:start position:0%
+where the I values Lambda are are are
+out of scale you know you might have two
+
+ align:start position:0%
+out of scale you know you might have two
+ 
+
+ align:start position:0%
+out of scale you know you might have two
+IG values one of size one and the other
+
+ align:start position:0%
+IG values one of size one and the other
+ 
+
+ align:start position:0%
+IG values one of size one and the other
+of size 10 the 4th because you've got
+
+ align:start position:0%
+of size 10 the 4th because you've got
+ 
+
+ align:start position:0%
+of size 10 the 4th because you've got
+two physical processes going on at the
+
+ align:start position:0%
+two physical processes going on at the
+ 
+
+ align:start position:0%
+two physical processes going on at the
+same time
+
+ align:start position:0%
+same time
+ 
+
+ align:start position:0%
+same time
+time and those equations are tough
+
+ align:start position:0%
+time and those equations are tough
+ 
+
+ align:start position:0%
+time and those equations are tough
+because that 10 the fourth guy is
+
+ align:start position:0%
+because that 10 the fourth guy is
+ 
+
+ align:start position:0%
+because that 10 the fourth guy is
+forcing your your delta T to be really
+
+ align:start position:0%
+forcing your your delta T to be really
+ 
+
+ align:start position:0%
+forcing your your delta T to be really
+small whereas the the action might the
+
+ align:start position:0%
+small whereas the the action might the
+ 
+
+ align:start position:0%
+small whereas the the action might the
+true real solution might be controlled
+
+ align:start position:0%
+true real solution might be controlled
+ 
+
+ align:start position:0%
+true real solution might be controlled
+by the Lambda equal one guy so to follow
+
+ align:start position:0%
+by the Lambda equal one guy so to follow
+ 
+
+ align:start position:0%
+by the Lambda equal one guy so to follow
+this slow Evolution you're having to
+
+ align:start position:0%
+this slow Evolution you're having to
+ 
+
+ align:start position:0%
+this slow Evolution you're having to
+take very small steps because on top of
+
+ align:start position:0%
+take very small steps because on top of
+ 
+
+ align:start position:0%
+take very small steps because on top of
+that slow Evolution with the Lambda
+
+ align:start position:0%
+that slow Evolution with the Lambda
+ 
+
+ align:start position:0%
+that slow Evolution with the Lambda
+equal 1 there's some very fast Evolution
+
+ align:start position:0%
+equal 1 there's some very fast Evolution
+ 
+
+ align:start position:0%
+equal 1 there's some very fast Evolution
+maybe with Lambda equal minus 10 th000
+
+ align:start position:0%
+maybe with Lambda equal minus 10 th000
+ 
+
+ align:start position:0%
+maybe with Lambda equal minus 10 th000
+yeah so that uh there's there's a lot uh
+
+ align:start position:0%
+yeah so that uh there's there's a lot uh
+ 
+
+ align:start position:0%
+yeah so that uh there's there's a lot uh
+happened here and and you always you
+
+ align:start position:0%
+happened here and and you always you
+ 
+
+ align:start position:0%
+happened here and and you always you
+have to think okay is there some way
+
+ align:start position:0%
+have to think okay is there some way
+ 
+
+ align:start position:0%
+have to think okay is there some way
+around that box and uh because forward
+
+ align:start position:0%
+around that box and uh because forward
+ 
+
+ align:start position:0%
+around that box and uh because forward
+Oiler would not get you through yeah
+
+ align:start position:0%
+Oiler would not get you through yeah
+ 
+
+ align:start position:0%
+Oiler would not get you through yeah
+okay thanks for that question you got
+
+ align:start position:0%
+okay thanks for that question you got
+ 
+
+ align:start position:0%
+okay thanks for that question you got
+another one okay so then if you're you
+
+ align:start position:0%
+another one okay so then if you're you
+ 
+
+ align:start position:0%
+another one okay so then if you're you
+weren using
+
+ align:start position:0%
+weren using
+ 
+
+ align:start position:0%
+weren using
+would uh if you weren't using small
+
+ align:start position:0%
+would uh if you weren't using small
+ 
+
+ align:start position:0%
+would uh if you weren't using small
+enough time steps okay
+
+ align:start position:0%
+enough time steps okay
+ 
+
+ align:start position:0%
+enough time steps okay
+for trapezoidal let's say I mean that
+
+ align:start position:0%
+for trapezoidal let's say I mean that
+ 
+
+ align:start position:0%
+for trapezoidal let's say I mean that
+expansion wouldn't hold if you were
+
+ align:start position:0%
+expansion wouldn't hold if you were
+ 
+
+ align:start position:0%
+expansion wouldn't hold if you were
+using a land well the expansion is
+
+ align:start position:0%
+using a land well the expansion is
+ 
+
+ align:start position:0%
+using a land well the expansion is
+really intended for small delta T yeah
+
+ align:start position:0%
+really intended for small delta T yeah
+ 
+
+ align:start position:0%
+really intended for small delta T yeah
+it's not intended I'm not you you see I
+
+ align:start position:0%
+it's not intended I'm not you you see I
+ 
+
+ align:start position:0%
+it's not intended I'm not you you see I
+never added up the whole series I just
+
+ align:start position:0%
+never added up the whole series I just
+ 
+
+ align:start position:0%
+never added up the whole series I just
+compared a couple of terms to see how
+
+ align:start position:0%
+compared a couple of terms to see how
+ 
+
+ align:start position:0%
+compared a couple of terms to see how
+how am I doing and they I got the extra
+
+ align:start position:0%
+how am I doing and they I got the extra
+ 
+
+ align:start position:0%
+how am I doing and they I got the extra
+term to match from trapezoidal that I
+
+ align:start position:0%
+term to match from trapezoidal that I
+ 
+
+ align:start position:0%
+term to match from trapezoidal that I
+didn't get from Oiler uh yeah so what
+
+ align:start position:0%
+didn't get from Oiler uh yeah so what
+ 
+
+ align:start position:0%
+didn't get from Oiler uh yeah so what
+what's to say if if you took Del Del to
+
+ align:start position:0%
+what's to say if if you took Del Del to
+ 
+
+ align:start position:0%
+what's to say if if you took Del Del to
+T too big what would happen in the
+
+ align:start position:0%
+T too big what would happen in the
+ 
+
+ align:start position:0%
+T too big what would happen in the
+trapezoidal
+
+ align:start position:0%
+trapezoidal
+ 
+
+ align:start position:0%
+trapezoidal
+method well you would stay on the circle
+
+ align:start position:0%
+method well you would stay on the circle
+ 
+
+ align:start position:0%
+method well you would stay on the circle
+cuz because the absolute value of this
+
+ align:start position:0%
+cuz because the absolute value of this
+ 
+
+ align:start position:0%
+cuz because the absolute value of this
+thing is truly one even if Lambda is
+
+ align:start position:0%
+thing is truly one even if Lambda is
+ 
+
+ align:start position:0%
+thing is truly one even if Lambda is
+enormous and delta T is way too big we
+
+ align:start position:0%
+enormous and delta T is way too big we
+ 
+
+ align:start position:0%
+enormous and delta T is way too big we
+still had we still had complex
+
+ align:start position:0%
+still had we still had complex
+ 
+
+ align:start position:0%
+still had we still had complex
+conjugates and their ratio was one so we
+
+ align:start position:0%
+conjugates and their ratio was one so we
+ 
+
+ align:start position:0%
+conjugates and their ratio was one so we
+would not leave The Circle at least in
+
+ align:start position:0%
+would not leave The Circle at least in
+ 
+
+ align:start position:0%
+would not leave The Circle at least in
+perfect arithmetic as everybody says you
+
+ align:start position:0%
+perfect arithmetic as everybody says you
+ 
+
+ align:start position:0%
+perfect arithmetic as everybody says you
+know if we didn't make any round off air
+
+ align:start position:0%
+know if we didn't make any round off air
+ 
+
+ align:start position:0%
+know if we didn't make any round off air
+we would not leave the circle but boy
+
+ align:start position:0%
+we would not leave the circle but boy
+ 
+
+ align:start position:0%
+we would not leave the circle but boy
+would we skip all over the place on that
+
+ align:start position:0%
+would we skip all over the place on that
+ 
+
+ align:start position:0%
+would we skip all over the place on that
+Circle so if we took delta T too big we
+
+ align:start position:0%
+Circle so if we took delta T too big we
+ 
+
+ align:start position:0%
+Circle so if we took delta T too big we
+would be completely inaccurate we
+
+ align:start position:0%
+would be completely inaccurate we
+ 
+
+ align:start position:0%
+would be completely inaccurate we
+wouldn't be unstable for trapezoidal
+
+ align:start position:0%
+wouldn't be unstable for trapezoidal
+ 
+
+ align:start position:0%
+wouldn't be unstable for trapezoidal
+because it would stay on the circle but
+
+ align:start position:0%
+because it would stay on the circle but
+ 
+
+ align:start position:0%
+because it would stay on the circle but
+it would be way the phase would be
+
+ align:start position:0%
+it would be way the phase would be
+ 
+
+ align:start position:0%
+it would be way the phase would be
+completely wrong yeah yeah so it' be a
+
+ align:start position:0%
+completely wrong yeah yeah so it' be a
+ 
+
+ align:start position:0%
+completely wrong yeah yeah so it' be a
+complex number of absolute value one but
+
+ align:start position:0%
+complex number of absolute value one but
+ 
+
+ align:start position:0%
+complex number of absolute value one but
+it would not be close to the
+
+ align:start position:0%
+it would not be close to the
+ 
+
+ align:start position:0%
+it would not be close to the
+exact uh growth factor
+
+ align:start position:0%
+exact uh growth factor
+ 
+
+ align:start position:0%
+exact uh growth factor
+yeah well so many things to to say you
+
+ align:start position:0%
+yeah well so many things to to say you
+ 
+
+ align:start position:0%
+yeah well so many things to to say you
+know I realize that uh the course moves
+
+ align:start position:0%
+know I realize that uh the course moves
+ 
+
+ align:start position:0%
+know I realize that uh the course moves
+along pretty quickly but uh this topic
+
+ align:start position:0%
+along pretty quickly but uh this topic
+ 
+
+ align:start position:0%
+along pretty quickly but uh this topic
+of numerical methods for differential
+
+ align:start position:0%
+of numerical methods for differential
+ 
+
+ align:start position:0%
+of numerical methods for differential
+equations that that's a core part of
+
+ align:start position:0%
+equations that that's a core part of
+ 
+
+ align:start position:0%
+equations that that's a core part of
+18086 so I'm like anticipating here in
+
+ align:start position:0%
+18086 so I'm like anticipating here in
+ 
+
+ align:start position:0%
+18086 so I'm like anticipating here in
+just two a couple of days what really
+
+ align:start position:0%
+just two a couple of days what really
+ 
+
+ align:start position:0%
+just two a couple of days what really
+takes longer is the stability and the
+
+ align:start position:0%
+takes longer is the stability and the
+ 
+
+ align:start position:0%
+takes longer is the stability and the
+accuracy and the and the best choices
+
+ align:start position:0%
+accuracy and the and the best choices
+ 
+
+ align:start position:0%
+accuracy and the and the best choices
+for time dep time dependent problems
+
+ align:start position:0%
+for time dep time dependent problems
+ 
+
+ align:start position:0%
+for time dep time dependent problems
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah okay always good questions anything
+
+ align:start position:0%
+yeah okay always good questions anything
+ 
+
+ align:start position:0%
+yeah okay always good questions anything
+else just on your mind of any sort yes
+
+ align:start position:0%
+else just on your mind of any sort yes
+ 
+
+ align:start position:0%
+else just on your mind of any sort yes
+thanks the textbook page 114 114 yeah
+
+ align:start position:0%
+thanks the textbook page 114 114 yeah
+ 
+
+ align:start position:0%
+thanks the textbook page 114 114 yeah
+there is a
+
+ align:start position:0%
+there is a
+ 
+
+ align:start position:0%
+there is a
+2.7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay 114 figure
+
+ align:start position:0%
+okay 114 figure
+ 
+
+ align:start position:0%
+okay 114 figure
+2.7 oh yes okay
+
+ align:start position:0%
+2.7 oh yes okay
+ 
+
+ align:start position:0%
+2.7 oh yes okay
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+this so let's see which so that that has
+
+ align:start position:0%
+this so let's see which so that that has
+ 
+
+ align:start position:0%
+this so let's see which so that that has
+a bunch of figures uh so that in order
+
+ align:start position:0%
+a bunch of figures uh so that in order
+ 
+
+ align:start position:0%
+a bunch of figures uh so that in order
+to say for everybody who's not looking
+
+ align:start position:0%
+to say for everybody who's not looking
+ 
+
+ align:start position:0%
+to say for everybody who's not looking
+at the book those figures are about the
+
+ align:start position:0%
+at the book those figures are about the
+ 
+
+ align:start position:0%
+at the book those figures are about the
+problem we've discussed here or the
+
+ align:start position:0%
+problem we've discussed here or the
+ 
+
+ align:start position:0%
+problem we've discussed here or the
+model problem where uh we're on a circle
+
+ align:start position:0%
+model problem where uh we're on a circle
+ 
+
+ align:start position:0%
+model problem where uh we're on a circle
+so do I have space to draw a circle well
+
+ align:start position:0%
+so do I have space to draw a circle well
+ 
+
+ align:start position:0%
+so do I have space to draw a circle well
+let me just make space here
+
+ align:start position:0%
+let me just make space here
+ 
+
+ align:start position:0%
+let me just make space here
+okay so page 114 has that model problem
+
+ align:start position:0%
+okay so page 114 has that model problem
+ 
+
+ align:start position:0%
+okay so page 114 has that model problem
+that we've drawn before this the exact
+
+ align:start position:0%
+that we've drawn before this the exact
+ 
+
+ align:start position:0%
+that we've drawn before this the exact
+solution here's the it's the phase plane
+
+ align:start position:0%
+solution here's the it's the phase plane
+ 
+
+ align:start position:0%
+solution here's the it's the phase plane
+there's U and there's U Prime and the U
+
+ align:start position:0%
+there's U and there's U Prime and the U
+ 
+
+ align:start position:0%
+there's U and there's U Prime and the U
+was cost T so the U Prime was minus sin
+
+ align:start position:0%
+was cost T so the U Prime was minus sin
+ 
+
+ align:start position:0%
+was cost T so the U Prime was minus sin
+T and we travel around the circle on the
+
+ align:start position:0%
+T and we travel around the circle on the
+ 
+
+ align:start position:0%
+T and we travel around the circle on the
+exact solution energy constant U ^2
+
+ align:start position:0%
+exact solution energy constant U ^2
+ 
+
+ align:start position:0%
+exact solution energy constant U ^2
+stays one U ^2 plus u Prime squ stay 1
+
+ align:start position:0%
+stays one U ^2 plus u Prime squ stay 1
+ 
+
+ align:start position:0%
+stays one U ^2 plus u Prime squ stay 1
+now which figure was it you wanted me
+
+ align:start position:0%
+now which figure was it you wanted me
+ 
+
+ align:start position:0%
+now which figure was it you wanted me
+to look at
+
+ align:start position:0%
+to look at
+ 
+
+ align:start position:0%
+to look at
+so of any of them um yeah okay that's
+
+ align:start position:0%
+so of any of them um yeah okay that's
+ 
+
+ align:start position:0%
+so of any of them um yeah okay that's
+fine uh let's see is trapezoidal on that
+
+ align:start position:0%
+fine uh let's see is trapezoidal on that
+ 
+
+ align:start position:0%
+fine uh let's see is trapezoidal on that
+one yeah trapezoidal was the first one
+
+ align:start position:0%
+one yeah trapezoidal was the first one
+ 
+
+ align:start position:0%
+one yeah trapezoidal was the first one
+okay so figure 26 shows the trapezoidal
+
+ align:start position:0%
+okay so figure 26 shows the trapezoidal
+ 
+
+ align:start position:0%
+okay so figure 26 shows the trapezoidal
+method moving around the circle so what
+
+ align:start position:0%
+method moving around the circle so what
+ 
+
+ align:start position:0%
+method moving around the circle so what
+happens yeah thanks it's a very suitable
+
+ align:start position:0%
+happens yeah thanks it's a very suitable
+ 
+
+ align:start position:0%
+happens yeah thanks it's a very suitable
+question okay
+
+ align:start position:0%
+question okay
+ 
+
+ align:start position:0%
+question okay
+and I took uh the in that figure I took
+
+ align:start position:0%
+and I took uh the in that figure I took
+ 
+
+ align:start position:0%
+and I took uh the in that figure I took
+the how long does it take for the exact
+
+ align:start position:0%
+the how long does it take for the exact
+ 
+
+ align:start position:0%
+the how long does it take for the exact
+solution to get exactly back where it
+
+ align:start position:0%
+solution to get exactly back where it
+ 
+
+ align:start position:0%
+solution to get exactly back where it
+started at t equal what do I come
+
+ align:start position:0%
+started at t equal what do I come
+ 
+
+ align:start position:0%
+started at t equal what do I come
+back 2 pi t equal to 2 pi I'm right back
+
+ align:start position:0%
+back 2 pi t equal to 2 pi I'm right back
+ 
+
+ align:start position:0%
+back 2 pi t equal to 2 pi I'm right back
+where I was right cosine has Period 2 pi
+
+ align:start position:0%
+where I was right cosine has Period 2 pi
+ 
+
+ align:start position:0%
+where I was right cosine has Period 2 pi
+okay now suppose I take two suppose a
+
+ align:start position:0%
+okay now suppose I take two suppose a
+ 
+
+ align:start position:0%
+okay now suppose I take two suppose a
+single step of size two Pi would be
+
+ align:start position:0%
+single step of size two Pi would be
+ 
+
+ align:start position:0%
+single step of size two Pi would be
+really uh ridiculous right I mean delta
+
+ align:start position:0%
+really uh ridiculous right I mean delta
+ 
+
+ align:start position:0%
+really uh ridiculous right I mean delta
+T I want to now delta T so let me take
+
+ align:start position:0%
+T I want to now delta T so let me take
+ 
+
+ align:start position:0%
+T I want to now delta T so let me take
+in that figure I took delta T to be 2 pi
+
+ align:start position:0%
+in that figure I took delta T to be 2 pi
+ 
+
+ align:start position:0%
+in that figure I took delta T to be 2 pi
+ided
+
+ align:start position:0%
+ided
+ 
+
+ align:start position:0%
+ided
+32 so I'm taking delta T to be the 2 pi
+
+ align:start position:0%
+32 so I'm taking delta T to be the 2 pi
+ 
+
+ align:start position:0%
+32 so I'm taking delta T to be the 2 pi
+that that would bring me all the way
+
+ align:start position:0%
+that that would bring me all the way
+ 
+
+ align:start position:0%
+that that would bring me all the way
+around but I'm taking dividing by 32 so
+
+ align:start position:0%
+around but I'm taking dividing by 32 so
+ 
+
+ align:start position:0%
+around but I'm taking dividing by 32 so
+what does that mean what what does the
+
+ align:start position:0%
+what does that mean what what does the
+ 
+
+ align:start position:0%
+what does that mean what what does the
+exact solution do at those steps 32
+
+ align:start position:0%
+exact solution do at those steps 32
+ 
+
+ align:start position:0%
+exact solution do at those steps 32
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+it goes on the Circle 32 equal steps 3
+
+ align:start position:0%
+it goes on the Circle 32 equal steps 3
+ 
+
+ align:start position:0%
+it goes on the Circle 32 equal steps 3
+360 or 2 pi ID 32 radians every time
+
+ align:start position:0%
+360 or 2 pi ID 32 radians every time
+ 
+
+ align:start position:0%
+360 or 2 pi ID 32 radians every time
+comes back exactly there the exact
+
+ align:start position:0%
+comes back exactly there the exact
+ 
+
+ align:start position:0%
+comes back exactly there the exact
+solution and uh right where I
+
+ align:start position:0%
+solution and uh right where I
+ 
+
+ align:start position:0%
+solution and uh right where I
+started so it's like following the the a
+
+ align:start position:0%
+started so it's like following the the a
+ 
+
+ align:start position:0%
+started so it's like following the the a
+planet now I do it by finite
+
+ align:start position:0%
+planet now I do it by finite
+ 
+
+ align:start position:0%
+planet now I do it by finite
+differences and so now I'm going to
+
+ align:start position:0%
+differences and so now I'm going to
+ 
+
+ align:start position:0%
+differences and so now I'm going to
+follow the trapezoidal rule just what
+
+ align:start position:0%
+follow the trapezoidal rule just what
+ 
+
+ align:start position:0%
+follow the trapezoidal rule just what
+we've been talking about with that time
+
+ align:start position:0%
+we've been talking about with that time
+ 
+
+ align:start position:0%
+we've been talking about with that time
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+and with the equation everybody
+
+ align:start position:0%
+and with the equation everybody
+ 
+
+ align:start position:0%
+and with the equation everybody
+remembers the the equation was uu Prime
+
+ align:start position:0%
+remembers the the equation was uu Prime
+ 
+
+ align:start position:0%
+remembers the the equation was uu Prime
+equals do you remember what the Matrix
+
+ align:start position:0%
+equals do you remember what the Matrix
+ 
+
+ align:start position:0%
+equals do you remember what the Matrix
+was in that
+
+ align:start position:0%
+was in that
+ 
+
+ align:start position:0%
+was in that
+equation oh this is the derivative of it
+
+ align:start position:0%
+equation oh this is the derivative of it
+ 
+
+ align:start position:0%
+equation oh this is the derivative of it
+and this is u u Prime sorry to squeeze
+
+ align:start position:0%
+and this is u u Prime sorry to squeeze
+ 
+
+ align:start position:0%
+and this is u u Prime sorry to squeeze
+this in but what I'm U Prime is U
+
+ align:start position:0%
+this in but what I'm U Prime is U
+ 
+
+ align:start position:0%
+this in but what I'm U Prime is U
+prime uble prime is minus
+
+ align:start position:0%
+prime uble prime is minus
+ 
+
+ align:start position:0%
+prime uble prime is minus
+U now now we know why that Matrix was
+
+ align:start position:0%
+U now now we know why that Matrix was
+ 
+
+ align:start position:0%
+U now now we know why that Matrix was
+good right wh why is that that that's my
+
+ align:start position:0%
+good right wh why is that that that's my
+ 
+
+ align:start position:0%
+good right wh why is that that that's my
+Matrix a why is it
+
+ align:start position:0%
+Matrix a why is it
+ 
+
+ align:start position:0%
+Matrix a why is it
+good because it's exactly it
+
+ align:start position:0%
+good because it's exactly it
+ 
+
+ align:start position:0%
+good because it's exactly it
+fits a transposes minus a it's anti-
+
+ align:start position:0%
+fits a transposes minus a it's anti-
+ 
+
+ align:start position:0%
+fits a transposes minus a it's anti-
+symmetric keeps me right on the circle
+
+ align:start position:0%
+symmetric keeps me right on the circle
+ 
+
+ align:start position:0%
+symmetric keeps me right on the circle
+okay now trapezoidal method keeps me
+
+ align:start position:0%
+okay now trapezoidal method keeps me
+ 
+
+ align:start position:0%
+okay now trapezoidal method keeps me
+right on the Circle 32 steps and so the
+
+ align:start position:0%
+right on the Circle 32 steps and so the
+ 
+
+ align:start position:0%
+right on the Circle 32 steps and so the
+picture just shows where it goes after
+
+ align:start position:0%
+picture just shows where it goes after
+ 
+
+ align:start position:0%
+picture just shows where it goes after
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+steps and 32 32 does it come back
+
+ align:start position:0%
+steps and 32 32 does it come back
+ 
+
+ align:start position:0%
+steps and 32 32 does it come back
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+well not exactly right we don't expect
+
+ align:start position:0%
+well not exactly right we don't expect
+ 
+
+ align:start position:0%
+well not exactly right we don't expect
+the exact the finite difference solution
+
+ align:start position:0%
+the exact the finite difference solution
+ 
+
+ align:start position:0%
+the exact the finite difference solution
+to be exactly in sync with the cosine T
+
+ align:start position:0%
+to be exactly in sync with the cosine T
+ 
+
+ align:start position:0%
+to be exactly in sync with the cosine T
+the real one but it's really close I
+
+ align:start position:0%
+the real one but it's really close I
+ 
+
+ align:start position:0%
+the real one but it's really close I
+think in that figure you can your eye
+
+ align:start position:0%
+think in that figure you can your eye
+ 
+
+ align:start position:0%
+think in that figure you can your eye
+can see that that's sort of a double
+
+ align:start position:0%
+can see that that's sort of a double
+ 
+
+ align:start position:0%
+can see that that's sort of a double
+point there at 2 pi I I put a little
+
+ align:start position:0%
+point there at 2 pi I I put a little
+ 
+
+ align:start position:0%
+point there at 2 pi I I put a little
+arrow indicating small phase error it it
+
+ align:start position:0%
+arrow indicating small phase error it it
+ 
+
+ align:start position:0%
+arrow indicating small phase error it it
+misses by a little bit right it misses
+
+ align:start position:0%
+misses by a little bit right it misses
+ 
+
+ align:start position:0%
+misses by a little bit right it misses
+by a little bit and
+
+ align:start position:0%
+by a little bit and
+ 
+
+ align:start position:0%
+by a little bit and
+actually roughly what does it Miss
+
+ align:start position:0%
+actually roughly what does it Miss
+ 
+
+ align:start position:0%
+actually roughly what does it Miss
+by this is this was the point of the
+
+ align:start position:0%
+by this is this was the point of the
+ 
+
+ align:start position:0%
+by this is this was the point of the
+order of accuracy stuff what what
+
+ align:start position:0%
+order of accuracy stuff what what
+ 
+
+ align:start position:0%
+order of accuracy stuff what what
+roughly what size is the is that little
+
+ align:start position:0%
+roughly what size is the is that little
+ 
+
+ align:start position:0%
+roughly what size is the is that little
+error that's what we did over here the
+
+ align:start position:0%
+error that's what we did over here the
+ 
+
+ align:start position:0%
+error that's what we did over here the
+the the term that we got wrong was a
+
+ align:start position:0%
+the the term that we got wrong was a
+ 
+
+ align:start position:0%
+the the term that we got wrong was a
+delta T
+
+ align:start position:0%
+delta T
+ 
+
+ align:start position:0%
+delta T
+cubed at each
+
+ align:start position:0%
+cubed at each
+ 
+
+ align:start position:0%
+cubed at each
+step can I just tell you the answer the
+
+ align:start position:0%
+step can I just tell you the answer the
+ 
+
+ align:start position:0%
+step can I just tell you the answer the
+the error here is of size Delta Del T
+
+ align:start position:0%
+the error here is of size Delta Del T
+ 
+
+ align:start position:0%
+the error here is of size Delta Del T
+squar cuz over here we matched those
+
+ align:start position:0%
+squar cuz over here we matched those
+ 
+
+ align:start position:0%
+squar cuz over here we matched those
+series and we found the error was delta
+
+ align:start position:0%
+series and we found the error was delta
+ 
+
+ align:start position:0%
+series and we found the error was delta
+T cubed that's in a single step but now
+
+ align:start position:0%
+T cubed that's in a single step but now
+ 
+
+ align:start position:0%
+T cubed that's in a single step but now
+we've got like one over delta T steps
+
+ align:start position:0%
+we've got like one over delta T steps
+ 
+
+ align:start position:0%
+we've got like one over delta T steps
+you you see what I'm saying that if it
+
+ align:start position:0%
+you you see what I'm saying that if it
+ 
+
+ align:start position:0%
+you you see what I'm saying that if it
+was delt if the local if the error was
+
+ align:start position:0%
+was delt if the local if the error was
+ 
+
+ align:start position:0%
+was delt if the local if the error was
+delta T Cub per step and I have one over
+
+ align:start position:0%
+delta T Cub per step and I have one over
+ 
+
+ align:start position:0%
+delta T Cub per step and I have one over
+delta T
+
+ align:start position:0%
+delta T
+ 
+
+ align:start position:0%
+delta T
+steps to get somewhere or 2 pi over
+
+ align:start position:0%
+steps to get somewhere or 2 pi over
+ 
+
+ align:start position:0%
+steps to get somewhere or 2 pi over
+delta T or whatever uh then that gives
+
+ align:start position:0%
+delta T or whatever uh then that gives
+ 
+
+ align:start position:0%
+delta T or whatever uh then that gives
+me delta T so that that little error
+
+ align:start position:0%
+me delta T so that that little error
+ 
+
+ align:start position:0%
+me delta T so that that little error
+there is is my error of size delta T
+
+ align:start position:0%
+there is is my error of size delta T
+ 
+
+ align:start position:0%
+there is is my error of size delta T
+squar and that square tells me I've got
+
+ align:start position:0%
+squar and that square tells me I've got
+ 
+
+ align:start position:0%
+squar and that square tells me I've got
+a good method at least decent second
+
+ align:start position:0%
+a good method at least decent second
+ 
+
+ align:start position:0%
+a good method at least decent second
+order accurate and the trapezoidal rule
+
+ align:start position:0%
+order accurate and the trapezoidal rule
+ 
+
+ align:start position:0%
+order accurate and the trapezoidal rule
+is uh sort of the natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one well okay so that's a full hour
+
+ align:start position:0%
+one well okay so that's a full hour
+ 
+
+ align:start position:0%
+one well okay so that's a full hour
+mostly devoted to two or three things
+
+ align:start position:0%
+mostly devoted to two or three things
+ 
+
+ align:start position:0%
+mostly devoted to two or three things
+actually the I vectors came in into it
+
+ align:start position:0%
+actually the I vectors came in into it
+ 
+
+ align:start position:0%
+actually the I vectors came in into it
+and the the energy conservation came
+
+ align:start position:0%
+and the the energy conservation came
+ 
+
+ align:start position:0%
+and the the energy conservation came
+into it the stability matching series
+
+ align:start position:0%
+into it the stability matching series
+ 
+
+ align:start position:0%
+into it the stability matching series
+came into it and the
+
+ align:start position:0%
+came into it and the
+ 
+
+ align:start position:0%
+came into it and the
+picture okay so I'll see you Friday for
+
+ align:start position:0%
+picture okay so I'll see you Friday for
+ 
+
+ align:start position:0%
+picture okay so I'll see you Friday for
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+about uh these guys and then Monday
+
+ align:start position:0%
+about uh these guys and then Monday
+ 
+
+ align:start position:0%
+about uh these guys and then Monday
+evening
+
+ align:start position:0%
+evening
+ 
+
+ align:start position:0%
+evening
+please ask me everything you want to on
+
+ align:start position:0%
+please ask me everything you want to on
+ 
+
+ align:start position:0%
+please ask me everything you want to on
+Monday evening
+
+ align:start position:0%
+Monday evening
+ 
+
+ align:start position:0%
+Monday evening
+okay thank you
\ No newline at end of file
diff --git a/0kA91PvS3sk.txt b/0kA91PvS3sk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..502a446e5ef835c32319ea89b566c9985ae61503
--- /dev/null
+++ b/0kA91PvS3sk.txt
@@ -0,0 +1,8291 @@
+align:start position:0%
+ 
+all right why don't we get started today
+
+ align:start position:0%
+all right why don't we get started today
+ 
+
+ align:start position:0%
+all right why don't we get started today
+we're going to move on to finally the
+
+ align:start position:0%
+we're going to move on to finally the
+ 
+
+ align:start position:0%
+we're going to move on to finally the
+most realistic market structure we
+
+ align:start position:0%
+most realistic market structure we
+ 
+
+ align:start position:0%
+most realistic market structure we
+talked about perfectly competitive
+
+ align:start position:0%
+talked about perfectly competitive
+ 
+
+ align:start position:0%
+talked about perfectly competitive
+market so now that was a very useful
+
+ align:start position:0%
+market so now that was a very useful
+ 
+
+ align:start position:0%
+market so now that was a very useful
+extreme example to help us think about
+
+ align:start position:0%
+extreme example to help us think about
+ 
+
+ align:start position:0%
+extreme example to help us think about
+economic efficiency we then flipped over
+
+ align:start position:0%
+economic efficiency we then flipped over
+ 
+
+ align:start position:0%
+economic efficiency we then flipped over
+to talk about the somewhat more
+
+ align:start position:0%
+to talk about the somewhat more
+ 
+
+ align:start position:0%
+to talk about the somewhat more
+realistic case of monopoly but still
+
+ align:start position:0%
+realistic case of monopoly but still
+ 
+
+ align:start position:0%
+realistic case of monopoly but still
+very few markets have only one
+
+ align:start position:0%
+very few markets have only one
+ 
+
+ align:start position:0%
+very few markets have only one
+participant a true monopoly is rare in
+
+ align:start position:0%
+participant a true monopoly is rare in
+ 
+
+ align:start position:0%
+participant a true monopoly is rare in
+the private market what most markets are
+
+ align:start position:0%
+the private market what most markets are
+ 
+
+ align:start position:0%
+the private market what most markets are
+marked are by are probably more features
+
+ align:start position:0%
+marked are by are probably more features
+ 
+
+ align:start position:0%
+marked are by are probably more features
+of oligopoly which is a market with a
+
+ align:start position:0%
+of oligopoly which is a market with a
+ 
+
+ align:start position:0%
+of oligopoly which is a market with a
+small group of firms competing with each
+
+ align:start position:0%
+small group of firms competing with each
+ 
+
+ align:start position:0%
+small group of firms competing with each
+other but with barriers to entry that
+
+ align:start position:0%
+other but with barriers to entry that
+ 
+
+ align:start position:0%
+other but with barriers to entry that
+keep out an unlimited number of firms
+
+ align:start position:0%
+keep out an unlimited number of firms
+ 
+
+ align:start position:0%
+keep out an unlimited number of firms
+say about these as markets where there
+
+ align:start position:0%
+say about these as markets where there
+ 
+
+ align:start position:0%
+say about these as markets where there
+are some barriers to entry so firms just
+
+ align:start position:0%
+are some barriers to entry so firms just
+ 
+
+ align:start position:0%
+are some barriers to entry so firms just
+can't cautiously enter an exit like they
+
+ align:start position:0%
+can't cautiously enter an exit like they
+ 
+
+ align:start position:0%
+can't cautiously enter an exit like they
+could in our IBM Dell example but where
+
+ align:start position:0%
+could in our IBM Dell example but where
+ 
+
+ align:start position:0%
+could in our IBM Dell example but where
+there's small enough eros entry that a
+
+ align:start position:0%
+there's small enough eros entry that a
+ 
+
+ align:start position:0%
+there's small enough eros entry that a
+few firms have gotten in not just one so
+
+ align:start position:0%
+few firms have gotten in not just one so
+ 
+
+ align:start position:0%
+few firms have gotten in not just one so
+it's not a natural monopoly it's not
+
+ align:start position:0%
+it's not a natural monopoly it's not
+ 
+
+ align:start position:0%
+it's not a natural monopoly it's not
+like one the only one forum can be in
+
+ align:start position:0%
+like one the only one forum can be in
+ 
+
+ align:start position:0%
+like one the only one forum can be in
+there multiple firms are in there but
+
+ align:start position:0%
+there multiple firms are in there but
+ 
+
+ align:start position:0%
+there multiple firms are in there but
+they only know that to compete with each
+
+ align:start position:0%
+they only know that to compete with each
+ 
+
+ align:start position:0%
+they only know that to compete with each
+other not with the big wide world okay
+
+ align:start position:0%
+other not with the big wide world okay
+ 
+
+ align:start position:0%
+other not with the big wide world okay
+so for example the classic example an
+
+ align:start position:0%
+so for example the classic example an
+ 
+
+ align:start position:0%
+so for example the classic example an
+oligopoly is should be the auto industry
+
+ align:start position:0%
+oligopoly is should be the auto industry
+ 
+
+ align:start position:0%
+oligopoly is should be the auto industry
+it's a auto manufacturers clearly
+
+ align:start position:0%
+it's a auto manufacturers clearly
+ 
+
+ align:start position:0%
+it's a auto manufacturers clearly
+compete clearly if you watch any
+
+ align:start position:0%
+compete clearly if you watch any
+ 
+
+ align:start position:0%
+compete clearly if you watch any
+sporting event and watch how much
+
+ align:start position:0%
+sporting event and watch how much
+ 
+
+ align:start position:0%
+sporting event and watch how much
+advertising that goes on they clearly
+
+ align:start position:0%
+advertising that goes on they clearly
+ 
+
+ align:start position:0%
+advertising that goes on they clearly
+are competing with each other that can
+
+ align:start position:0%
+are competing with each other that can
+ 
+
+ align:start position:0%
+are competing with each other that can
+prank each other all the time
+
+ align:start position:0%
+prank each other all the time
+ 
+
+ align:start position:0%
+prank each other all the time
+but there's only all on most of the cars
+
+ align:start position:0%
+but there's only all on most of the cars
+ 
+
+ align:start position:0%
+but there's only all on most of the cars
+in the world are produced by fewer than
+
+ align:start position:0%
+in the world are produced by fewer than
+ 
+
+ align:start position:0%
+in the world are produced by fewer than
+ten auto manufacturers the notion that
+
+ align:start position:0%
+ten auto manufacturers the notion that
+ 
+
+ align:start position:0%
+ten auto manufacturers the notion that
+we have but a perfectly competitive
+
+ align:start position:0%
+we have but a perfectly competitive
+ 
+
+ align:start position:0%
+we have but a perfectly competitive
+market of thousands of sellers selling
+
+ align:start position:0%
+market of thousands of sellers selling
+ 
+
+ align:start position:0%
+market of thousands of sellers selling
+identical goods it's clearly not right
+
+ align:start position:0%
+identical goods it's clearly not right
+ 
+
+ align:start position:0%
+identical goods it's clearly not right
+when it comes to buying a car so that's
+
+ align:start position:0%
+when it comes to buying a car so that's
+ 
+
+ align:start position:0%
+when it comes to buying a car so that's
+sort of the model we're gonna want to
+
+ align:start position:0%
+sort of the model we're gonna want to
+ 
+
+ align:start position:0%
+sort of the model we're gonna want to
+focus on for the next few lectures
+
+ align:start position:0%
+focus on for the next few lectures
+ 
+
+ align:start position:0%
+focus on for the next few lectures
+now within Oh within an oligopoly market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whenever we think about this market we
+
+ align:start position:0%
+whenever we think about this market we
+ 
+
+ align:start position:0%
+whenever we think about this market we
+want to start by noting that within this
+
+ align:start position:0%
+want to start by noting that within this
+ 
+
+ align:start position:0%
+want to start by noting that within this
+market the limited set of competitors
+
+ align:start position:0%
+market the limited set of competitors
+ 
+
+ align:start position:0%
+market the limited set of competitors
+can behave in two ways then we can
+
+ align:start position:0%
+can behave in two ways then we can
+ 
+
+ align:start position:0%
+can behave in two ways then we can
+behave cooperatively cooperatively or
+
+ align:start position:0%
+behave cooperatively cooperatively or
+ 
+
+ align:start position:0%
+behave cooperatively cooperatively or
+non cooperatively okay cooperative means
+
+ align:start position:0%
+non cooperatively okay cooperative means
+ 
+
+ align:start position:0%
+non cooperatively okay cooperative means
+they can form what's called a cartel so
+
+ align:start position:0%
+they can form what's called a cartel so
+ 
+
+ align:start position:0%
+they can form what's called a cartel so
+when there's an oligopoly market and the
+
+ align:start position:0%
+when there's an oligopoly market and the
+ 
+
+ align:start position:0%
+when there's an oligopoly market and the
+firm's cooperatively get together and
+
+ align:start position:0%
+firm's cooperatively get together and
+ 
+
+ align:start position:0%
+firm's cooperatively get together and
+make decisions that's called the cartel
+
+ align:start position:0%
+make decisions that's called the cartel
+ 
+
+ align:start position:0%
+make decisions that's called the cartel
+the most famous example of which is OPEC
+
+ align:start position:0%
+the most famous example of which is OPEC
+ 
+
+ align:start position:0%
+the most famous example of which is OPEC
+the Organization of Petroleum Exporting
+
+ align:start position:0%
+the Organization of Petroleum Exporting
+ 
+
+ align:start position:0%
+the Organization of Petroleum Exporting
+Countries which are the set of countries
+
+ align:start position:0%
+Countries which are the set of countries
+ 
+
+ align:start position:0%
+Countries which are the set of countries
+that control about two-thirds of the
+
+ align:start position:0%
+that control about two-thirds of the
+ 
+
+ align:start position:0%
+that control about two-thirds of the
+words world's oil led by Saudi Arabia is
+
+ align:start position:0%
+words world's oil led by Saudi Arabia is
+ 
+
+ align:start position:0%
+words world's oil led by Saudi Arabia is
+the major player in in OPEC it's a
+
+ align:start position:0%
+the major player in in OPEC it's a
+ 
+
+ align:start position:0%
+the major player in in OPEC it's a
+cartel about a dozen nations and what
+
+ align:start position:0%
+cartel about a dozen nations and what
+ 
+
+ align:start position:0%
+cartel about a dozen nations and what
+they do is they control the vast
+
+ align:start position:0%
+they do is they control the vast
+ 
+
+ align:start position:0%
+they do is they control the vast
+majority of the world's oil reserves and
+
+ align:start position:0%
+majority of the world's oil reserves and
+ 
+
+ align:start position:0%
+majority of the world's oil reserves and
+by behaving cooperatively they
+
+ align:start position:0%
+by behaving cooperatively they
+ 
+
+ align:start position:0%
+by behaving cooperatively they
+essentially turn themselves into a
+
+ align:start position:0%
+essentially turn themselves into a
+ 
+
+ align:start position:0%
+essentially turn themselves into a
+monopoly OPEC acts as if they've got
+
+ align:start position:0%
+monopoly OPEC acts as if they've got
+ 
+
+ align:start position:0%
+monopoly OPEC acts as if they've got
+sort of got the monopoly on oil
+
+ align:start position:0%
+sort of got the monopoly on oil
+ 
+
+ align:start position:0%
+sort of got the monopoly on oil
+certainly they they used to now it's
+
+ align:start position:0%
+certainly they they used to now it's
+ 
+
+ align:start position:0%
+certainly they they used to now it's
+getting harder other Kanaan OPEC
+
+ align:start position:0%
+getting harder other Kanaan OPEC
+ 
+
+ align:start position:0%
+getting harder other Kanaan OPEC
+countries are started producing more oil
+
+ align:start position:0%
+countries are started producing more oil
+ 
+
+ align:start position:0%
+countries are started producing more oil
+and breaking down but for a long time
+
+ align:start position:0%
+and breaking down but for a long time
+ 
+
+ align:start position:0%
+and breaking down but for a long time
+they were essentially the co-operative
+
+ align:start position:0%
+they were essentially the co-operative
+ 
+
+ align:start position:0%
+they were essentially the co-operative
+Peru savoia land act essentially like a
+
+ align:start position:0%
+Peru savoia land act essentially like a
+ 
+
+ align:start position:0%
+Peru savoia land act essentially like a
+monopoly and they made lots of profits
+
+ align:start position:0%
+monopoly and they made lots of profits
+ 
+
+ align:start position:0%
+monopoly and they made lots of profits
+like a monopoly they kept prices high
+
+ align:start position:0%
+like a monopoly they kept prices high
+ 
+
+ align:start position:0%
+like a monopoly they kept prices high
+they kept production inefficiently low
+
+ align:start position:0%
+they kept production inefficiently low
+ 
+
+ align:start position:0%
+they kept production inefficiently low
+and they made lots of money okay however
+
+ align:start position:0%
+and they made lots of money okay however
+ 
+
+ align:start position:0%
+and they made lots of money okay however
+um that's a great outcome for producers
+
+ align:start position:0%
+um that's a great outcome for producers
+ 
+
+ align:start position:0%
+um that's a great outcome for producers
+but as we'll talk about next time it's
+
+ align:start position:0%
+but as we'll talk about next time it's
+ 
+
+ align:start position:0%
+but as we'll talk about next time it's
+actually a hard outcome to enforce
+
+ align:start position:0%
+actually a hard outcome to enforce
+ 
+
+ align:start position:0%
+actually a hard outcome to enforce
+turned out to be hard to keep cartels
+
+ align:start position:0%
+turned out to be hard to keep cartels
+ 
+
+ align:start position:0%
+turned out to be hard to keep cartels
+together and so typically oligopoly
+
+ align:start position:0%
+together and so typically oligopoly
+ 
+
+ align:start position:0%
+together and so typically oligopoly
+markets behave in a non cooperative way
+
+ align:start position:0%
+markets behave in a non cooperative way
+ 
+
+ align:start position:0%
+markets behave in a non cooperative way
+with the participants competing with
+
+ align:start position:0%
+with the participants competing with
+ 
+
+ align:start position:0%
+with the participants competing with
+each other not cooperating with each
+
+ align:start position:0%
+each other not cooperating with each
+ 
+
+ align:start position:0%
+each other not cooperating with each
+other and in this case you can actually
+
+ align:start position:0%
+other and in this case you can actually
+ 
+
+ align:start position:0%
+other and in this case you can actually
+get them driving their profits down far
+
+ align:start position:0%
+get them driving their profits down far
+ 
+
+ align:start position:0%
+get them driving their profits down far
+below the monopoly level and indeed
+
+ align:start position:0%
+below the monopoly level and indeed
+ 
+
+ align:start position:0%
+below the monopoly level and indeed
+perhaps even all the way to the
+
+ align:start position:0%
+perhaps even all the way to the
+ 
+
+ align:start position:0%
+perhaps even all the way to the
+competitive level so you think about
+
+ align:start position:0%
+competitive level so you think about
+ 
+
+ align:start position:0%
+competitive level so you think about
+markets as a competitive is one extreme
+
+ align:start position:0%
+markets as a competitive is one extreme
+ 
+
+ align:start position:0%
+markets as a competitive is one extreme
+and the monopolies the other extreme
+
+ align:start position:0%
+and the monopolies the other extreme
+ 
+
+ align:start position:0%
+and the monopolies the other extreme
+oligopoly in between a cooperative
+
+ align:start position:0%
+oligopoly in between a cooperative
+ 
+
+ align:start position:0%
+oligopoly in between a cooperative
+oligopoly market like cartel will end up
+
+ align:start position:0%
+oligopoly market like cartel will end up
+ 
+
+ align:start position:0%
+oligopoly market like cartel will end up
+close to the monopoly outcome a non
+
+ align:start position:0%
+close to the monopoly outcome a non
+ 
+
+ align:start position:0%
+close to the monopoly outcome a non
+cooperative market well it's somewhere
+
+ align:start position:0%
+cooperative market well it's somewhere
+ 
+
+ align:start position:0%
+cooperative market well it's somewhere
+in between and we're gonna model today
+
+ align:start position:0%
+in between and we're gonna model today
+ 
+
+ align:start position:0%
+in between and we're gonna model today
+is we're in between do they end up okay
+
+ align:start position:0%
+is we're in between do they end up okay
+ 
+
+ align:start position:0%
+is we're in between do they end up okay
+now to think about this we're gonna have
+
+ align:start position:0%
+now to think about this we're gonna have
+ 
+
+ align:start position:0%
+now to think about this we're gonna have
+to turn to a tool which has really
+
+ align:start position:0%
+to turn to a tool which has really
+ 
+
+ align:start position:0%
+to turn to a tool which has really
+become a dominant tool in economics over
+
+ align:start position:0%
+become a dominant tool in economics over
+ 
+
+ align:start position:0%
+become a dominant tool in economics over
+the last 40 years which is the tool of
+
+ align:start position:0%
+the last 40 years which is the tool of
+ 
+
+ align:start position:0%
+the last 40 years which is the tool of
+game theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game theory so basically we could think
+
+ align:start position:0%
+game theory so basically we could think
+ 
+
+ align:start position:0%
+game theory so basically we could think
+of all look up we're gonna think of
+
+ align:start position:0%
+of all look up we're gonna think of
+ 
+
+ align:start position:0%
+of all look up we're gonna think of
+oligopoly firms as engaging in a game
+
+ align:start position:0%
+oligopoly firms as engaging in a game
+ 
+
+ align:start position:0%
+oligopoly firms as engaging in a game
+okay and as with any game you need to
+
+ align:start position:0%
+okay and as with any game you need to
+ 
+
+ align:start position:0%
+okay and as with any game you need to
+sort of know two things one is you need
+
+ align:start position:0%
+sort of know two things one is you need
+ 
+
+ align:start position:0%
+sort of know two things one is you need
+to know what's the strategy and the
+
+ align:start position:0%
+to know what's the strategy and the
+ 
+
+ align:start position:0%
+to know what's the strategy and the
+second is you need to know when is the
+
+ align:start position:0%
+second is you need to know when is the
+ 
+
+ align:start position:0%
+second is you need to know when is the
+game over kind of what's the equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's sort of essentially what you
+
+ align:start position:0%
+and that's sort of essentially what you
+ 
+
+ align:start position:0%
+and that's sort of essentially what you
+tell with any game and so basically what
+
+ align:start position:0%
+tell with any game and so basically what
+ 
+
+ align:start position:0%
+tell with any game and so basically what
+we're gonna do the key with game theory
+
+ align:start position:0%
+we're gonna do the key with game theory
+ 
+
+ align:start position:0%
+we're gonna do the key with game theory
+is that we are going to define the
+
+ align:start position:0%
+is that we are going to define the
+ 
+
+ align:start position:0%
+is that we are going to define the
+equilibrium and that's going to yield
+
+ align:start position:0%
+equilibrium and that's going to yield
+ 
+
+ align:start position:0%
+equilibrium and that's going to yield
+for us the strategy that players are
+
+ align:start position:0%
+for us the strategy that players are
+ 
+
+ align:start position:0%
+for us the strategy that players are
+going to use however equilibrium in a
+
+ align:start position:0%
+going to use however equilibrium in a
+ 
+
+ align:start position:0%
+going to use however equilibrium in a
+game is not well-defined it's like a set
+
+ align:start position:0%
+game is not well-defined it's like a set
+ 
+
+ align:start position:0%
+game is not well-defined it's like a set
+of rules that are printed out like
+
+ align:start position:0%
+of rules that are printed out like
+ 
+
+ align:start position:0%
+of rules that are printed out like
+monopoly in a non cooperative oligopoly
+
+ align:start position:0%
+monopoly in a non cooperative oligopoly
+ 
+
+ align:start position:0%
+monopoly in a non cooperative oligopoly
+market the equilibrium you have to
+
+ align:start position:0%
+market the equilibrium you have to
+ 
+
+ align:start position:0%
+market the equilibrium you have to
+actually come up with different concepts
+
+ align:start position:0%
+actually come up with different concepts
+ 
+
+ align:start position:0%
+actually come up with different concepts
+of what equilibrium is there's not a
+
+ align:start position:0%
+of what equilibrium is there's not a
+ 
+
+ align:start position:0%
+of what equilibrium is there's not a
+hard-and-fast scientific rule and the
+
+ align:start position:0%
+hard-and-fast scientific rule and the
+ 
+
+ align:start position:0%
+hard-and-fast scientific rule and the
+typical one that's used is called the
+
+ align:start position:0%
+typical one that's used is called the
+ 
+
+ align:start position:0%
+typical one that's used is called the
+Nash equilibrium the Nash equilibrium
+
+ align:start position:0%
+Nash equilibrium the Nash equilibrium
+ 
+
+ align:start position:0%
+Nash equilibrium the Nash equilibrium
+named for the John Nash the famous
+
+ align:start position:0%
+named for the John Nash the famous
+ 
+
+ align:start position:0%
+named for the John Nash the famous
+mathematician who economists have
+
+ align:start position:0%
+mathematician who economists have
+ 
+
+ align:start position:0%
+mathematician who economists have
+claimed as their own even though it's
+
+ align:start position:0%
+claimed as their own even though it's
+ 
+
+ align:start position:0%
+claimed as their own even though it's
+really a mathematician but we get in the
+
+ align:start position:0%
+really a mathematician but we get in the
+ 
+
+ align:start position:0%
+really a mathematician but we get in the
+Nobel Prize anyway and you know if you
+
+ align:start position:0%
+Nobel Prize anyway and you know if you
+ 
+
+ align:start position:0%
+Nobel Prize anyway and you know if you
+think of this in comments probably one
+
+ align:start position:0%
+think of this in comments probably one
+ 
+
+ align:start position:0%
+think of this in comments probably one
+of most famous you know you all know
+
+ align:start position:0%
+of most famous you know you all know
+ 
+
+ align:start position:0%
+of most famous you know you all know
+about the movie and book Beautiful Mind
+
+ align:start position:0%
+about the movie and book Beautiful Mind
+ 
+
+ align:start position:0%
+about the movie and book Beautiful Mind
+he is basically the father of of game
+
+ align:start position:0%
+he is basically the father of of game
+ 
+
+ align:start position:0%
+he is basically the father of of game
+theory okay so basically what is the
+
+ align:start position:0%
+theory okay so basically what is the
+ 
+
+ align:start position:0%
+theory okay so basically what is the
+Nash equilibrium the Nash equilibria is
+
+ align:start position:0%
+Nash equilibrium the Nash equilibria is
+ 
+
+ align:start position:0%
+Nash equilibrium the Nash equilibria is
+defined as the point at which no player
+
+ align:start position:0%
+defined as the point at which no player
+ 
+
+ align:start position:0%
+defined as the point at which no player
+wants to change their strategy given
+
+ align:start position:0%
+wants to change their strategy given
+ 
+
+ align:start position:0%
+wants to change their strategy given
+what the other players are doing so the
+
+ align:start position:0%
+what the other players are doing so the
+ 
+
+ align:start position:0%
+what the other players are doing so the
+point at which no player wants to change
+
+ align:start position:0%
+point at which no player wants to change
+ 
+
+ align:start position:0%
+point at which no player wants to change
+its strategy given what the other
+
+ align:start position:0%
+its strategy given what the other
+ 
+
+ align:start position:0%
+its strategy given what the other
+players are doing so in lodz every
+
+ align:start position:0%
+players are doing so in lodz every
+ 
+
+ align:start position:0%
+players are doing so in lodz every
+player is happy with where they are
+
+ align:start position:0%
+player is happy with where they are
+ 
+
+ align:start position:0%
+player is happy with where they are
+given what every other players decided
+
+ align:start position:0%
+given what every other players decided
+ 
+
+ align:start position:0%
+given what every other players decided
+I'm happy to do what I've decided so
+
+ align:start position:0%
+I'm happy to do what I've decided so
+ 
+
+ align:start position:0%
+I'm happy to do what I've decided so
+I've got a strategy and given the
+
+ align:start position:0%
+I've got a strategy and given the
+ 
+
+ align:start position:0%
+I've got a strategy and given the
+strategy other players are using if I'm
+
+ align:start position:0%
+strategy other players are using if I'm
+ 
+
+ align:start position:0%
+strategy other players are using if I'm
+happy with my strategy then that's an
+
+ align:start position:0%
+happy with my strategy then that's an
+ 
+
+ align:start position:0%
+happy with my strategy then that's an
+equilibrium okay so this is a super
+
+ align:start position:0%
+equilibrium okay so this is a super
+ 
+
+ align:start position:0%
+equilibrium okay so this is a super
+abstract concept so let's illustrate it
+
+ align:start position:0%
+abstract concept so let's illustrate it
+ 
+
+ align:start position:0%
+abstract concept so let's illustrate it
+with an example and the classic example
+
+ align:start position:0%
+with an example and the classic example
+ 
+
+ align:start position:0%
+with an example and the classic example
+of game theory is the prisoner's dilemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which many of you I'm sure know about
+
+ align:start position:0%
+which many of you I'm sure know about
+ 
+
+ align:start position:0%
+which many of you I'm sure know about
+maybe than most of you but let's just go
+
+ align:start position:0%
+maybe than most of you but let's just go
+ 
+
+ align:start position:0%
+maybe than most of you but let's just go
+through it this is the thing from the
+
+ align:start position:0%
+through it this is the thing from the
+ 
+
+ align:start position:0%
+through it this is the thing from the
+old cop movies you see where they arrest
+
+ align:start position:0%
+old cop movies you see where they arrest
+ 
+
+ align:start position:0%
+old cop movies you see where they arrest
+two guys and they put them in separate
+
+ align:start position:0%
+two guys and they put them in separate
+ 
+
+ align:start position:0%
+two guys and they put them in separate
+rooms and they basically interrogate
+
+ align:start position:0%
+rooms and they basically interrogate
+ 
+
+ align:start position:0%
+rooms and they basically interrogate
+them separately ok and what they say is
+
+ align:start position:0%
+them separately ok and what they say is
+ 
+
+ align:start position:0%
+them separately ok and what they say is
+um they're put in separate rooms and
+
+ align:start position:0%
+um they're put in separate rooms and
+ 
+
+ align:start position:0%
+um they're put in separate rooms and
+let's say that these guys get told to
+
+ align:start position:0%
+let's say that these guys get told to
+ 
+
+ align:start position:0%
+let's say that these guys get told to
+follow and they each get told separately
+
+ align:start position:0%
+follow and they each get told separately
+ 
+
+ align:start position:0%
+follow and they each get told separately
+the following thing they get told that
+
+ align:start position:0%
+the following thing they get told that
+ 
+
+ align:start position:0%
+the following thing they get told that
+right now if nothing else happens
+
+ align:start position:0%
+right now if nothing else happens
+ 
+
+ align:start position:0%
+right now if nothing else happens
+there's enough evidence to send them
+
+ align:start position:0%
+there's enough evidence to send them
+ 
+
+ align:start position:0%
+there's enough evidence to send them
+each away for one year however they're
+
+ align:start position:0%
+each away for one year however they're
+ 
+
+ align:start position:0%
+each away for one year however they're
+told if they turn on their friend and
+
+ align:start position:0%
+told if they turn on their friend and
+ 
+
+ align:start position:0%
+told if they turn on their friend and
+say and say their friends guilty then
+
+ align:start position:0%
+say and say their friends guilty then
+ 
+
+ align:start position:0%
+say and say their friends guilty then
+they go free and their friend gets five
+
+ align:start position:0%
+they go free and their friend gets five
+ 
+
+ align:start position:0%
+they go free and their friend gets five
+years if their friend turns on them then
+
+ align:start position:0%
+years if their friend turns on them then
+ 
+
+ align:start position:0%
+years if their friend turns on them then
+the friend goes free and they get five
+
+ align:start position:0%
+the friend goes free and they get five
+ 
+
+ align:start position:0%
+the friend goes free and they get five
+years but if they both turn on each
+
+ align:start position:0%
+years but if they both turn on each
+ 
+
+ align:start position:0%
+years but if they both turn on each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+they both get two years okay set up as
+
+ align:start position:0%
+they both get two years okay set up as
+ 
+
+ align:start position:0%
+they both get two years okay set up as
+if they both stay silent they both get
+
+ align:start position:0%
+if they both stay silent they both get
+ 
+
+ align:start position:0%
+if they both stay silent they both get
+one year if one turns then that person
+
+ align:start position:0%
+one year if one turns then that person
+ 
+
+ align:start position:0%
+one year if one turns then that person
+gets to leave in the other person gets
+
+ align:start position:0%
+gets to leave in the other person gets
+ 
+
+ align:start position:0%
+gets to leave in the other person gets
+five years but if they both turn then
+
+ align:start position:0%
+five years but if they both turn then
+ 
+
+ align:start position:0%
+five years but if they both turn then
+these get two years so how do we think
+
+ align:start position:0%
+these get two years so how do we think
+ 
+
+ align:start position:0%
+these get two years so how do we think
+about decision making that context the
+
+ align:start position:0%
+about decision making that context the
+ 
+
+ align:start position:0%
+about decision making that context the
+way we do that is we write down we call
+
+ align:start position:0%
+way we do that is we write down we call
+ 
+
+ align:start position:0%
+way we do that is we write down we call
+a payoff matrix we sort of write down a
+
+ align:start position:0%
+a payoff matrix we sort of write down a
+ 
+
+ align:start position:0%
+a payoff matrix we sort of write down a
+matrix form this decision so let's think
+
+ align:start position:0%
+matrix form this decision so let's think
+ 
+
+ align:start position:0%
+matrix form this decision so let's think
+about it what a playoff matrix look like
+
+ align:start position:0%
+about it what a playoff matrix look like
+ 
+
+ align:start position:0%
+about it what a playoff matrix look like
+up here a prisoner B and here you have
+
+ align:start position:0%
+up here a prisoner B and here you have
+ 
+
+ align:start position:0%
+up here a prisoner B and here you have
+prisoner a for centre a and prisoner a
+
+ align:start position:0%
+prisoner a for centre a and prisoner a
+ 
+
+ align:start position:0%
+prisoner a for centre a and prisoner a
+can remain silent or they can talk and
+
+ align:start position:0%
+can remain silent or they can talk and
+ 
+
+ align:start position:0%
+can remain silent or they can talk and
+prisoner B can remain silent
+
+ align:start position:0%
+prisoner B can remain silent
+ 
+
+ align:start position:0%
+prisoner B can remain silent
+or they can talk okay
+
+ align:start position:0%
+or they can talk okay
+ 
+
+ align:start position:0%
+or they can talk okay
+and then we just write down what are the
+
+ align:start position:0%
+and then we just write down what are the
+ 
+
+ align:start position:0%
+and then we just write down what are the
+outcomes or the payoffs from these
+
+ align:start position:0%
+outcomes or the payoffs from these
+ 
+
+ align:start position:0%
+outcomes or the payoffs from these
+different strategies so prisoner a says
+
+ align:start position:0%
+different strategies so prisoner a says
+ 
+
+ align:start position:0%
+different strategies so prisoner a says
+nothing and prisoner B says nothing then
+
+ align:start position:0%
+nothing and prisoner B says nothing then
+ 
+
+ align:start position:0%
+nothing and prisoner B says nothing then
+a gets one year and B gets one year if
+
+ align:start position:0%
+a gets one year and B gets one year if
+ 
+
+ align:start position:0%
+a gets one year and B gets one year if
+prisoner a says nothing and prisoner B
+
+ align:start position:0%
+prisoner a says nothing and prisoner B
+ 
+
+ align:start position:0%
+prisoner a says nothing and prisoner B
+says oh yeah prisoner a he's definitely
+
+ align:start position:0%
+says oh yeah prisoner a he's definitely
+ 
+
+ align:start position:0%
+says oh yeah prisoner a he's definitely
+guilty then prisoner a gets five years
+
+ align:start position:0%
+guilty then prisoner a gets five years
+ 
+
+ align:start position:0%
+guilty then prisoner a gets five years
+and prisoner being at zero years if the
+
+ align:start position:0%
+and prisoner being at zero years if the
+ 
+
+ align:start position:0%
+and prisoner being at zero years if the
+opposite happens if prisoner he says
+
+ align:start position:0%
+opposite happens if prisoner he says
+ 
+
+ align:start position:0%
+opposite happens if prisoner he says
+yeah B's guilty and B doesn't say
+
+ align:start position:0%
+yeah B's guilty and B doesn't say
+ 
+
+ align:start position:0%
+yeah B's guilty and B doesn't say
+anything about a then a gets zero years
+
+ align:start position:0%
+anything about a then a gets zero years
+ 
+
+ align:start position:0%
+anything about a then a gets zero years
+and B gets five years but if they both
+
+ align:start position:0%
+and B gets five years but if they both
+ 
+
+ align:start position:0%
+and B gets five years but if they both
+say the other ones guilty then they each
+
+ align:start position:0%
+say the other ones guilty then they each
+ 
+
+ align:start position:0%
+say the other ones guilty then they each
+get two years okay that's the payoff
+
+ align:start position:0%
+get two years okay that's the payoff
+ 
+
+ align:start position:0%
+get two years okay that's the payoff
+matrix okay and now we want to ask given
+
+ align:start position:0%
+matrix okay and now we want to ask given
+ 
+
+ align:start position:0%
+matrix okay and now we want to ask given
+this payoff matrix what is the right
+
+ align:start position:0%
+this payoff matrix what is the right
+ 
+
+ align:start position:0%
+this payoff matrix what is the right
+strategy for each prisoner to pursue and
+
+ align:start position:0%
+strategy for each prisoner to pursue and
+ 
+
+ align:start position:0%
+strategy for each prisoner to pursue and
+the way we do this in the Nash
+
+ align:start position:0%
+the way we do this in the Nash
+ 
+
+ align:start position:0%
+the way we do this in the Nash
+equilibria makaan cept is we look for a
+
+ align:start position:0%
+equilibria makaan cept is we look for a
+ 
+
+ align:start position:0%
+equilibria makaan cept is we look for a
+dominant strategy it's very strategy
+
+ align:start position:0%
+dominant strategy it's very strategy
+ 
+
+ align:start position:0%
+dominant strategy it's very strategy
+that I would pursue regardless of what
+
+ align:start position:0%
+that I would pursue regardless of what
+ 
+
+ align:start position:0%
+that I would pursue regardless of what
+the other person does and if there is
+
+ align:start position:0%
+the other person does and if there is
+ 
+
+ align:start position:0%
+the other person does and if there is
+I'll pursue that because remember the
+
+ align:start position:0%
+I'll pursue that because remember the
+ 
+
+ align:start position:0%
+I'll pursue that because remember the
+national Calibri concept is what do I
+
+ align:start position:0%
+national Calibri concept is what do I
+ 
+
+ align:start position:0%
+national Calibri concept is what do I
+want to do given what the other person's
+
+ align:start position:0%
+want to do given what the other person's
+ 
+
+ align:start position:0%
+want to do given what the other person's
+doing if I have a strategy I want to do
+
+ align:start position:0%
+doing if I have a strategy I want to do
+ 
+
+ align:start position:0%
+doing if I have a strategy I want to do
+no matter what the other person is doing
+
+ align:start position:0%
+no matter what the other person is doing
+ 
+
+ align:start position:0%
+no matter what the other person is doing
+then I'll do it so and ask is there a
+
+ align:start position:0%
+then I'll do it so and ask is there a
+ 
+
+ align:start position:0%
+then I'll do it so and ask is there a
+dominant strategy is there a strategy
+
+ align:start position:0%
+dominant strategy is there a strategy
+ 
+
+ align:start position:0%
+dominant strategy is there a strategy
+there's the best thing to do no matter
+
+ align:start position:0%
+there's the best thing to do no matter
+ 
+
+ align:start position:0%
+there's the best thing to do no matter
+what the other guy does okay well
+
+ align:start position:0%
+what the other guy does okay well
+ 
+
+ align:start position:0%
+what the other guy does okay well
+clearly if they're cooperating if these
+
+ align:start position:0%
+clearly if they're cooperating if these
+ 
+
+ align:start position:0%
+clearly if they're cooperating if these
+were these were stupid police and they
+
+ align:start position:0%
+were these were stupid police and they
+ 
+
+ align:start position:0%
+were these were stupid police and they
+sat in the same room told us then left
+
+ align:start position:0%
+sat in the same room told us then left
+ 
+
+ align:start position:0%
+sat in the same room told us then left
+the two guys cooperating said well
+
+ align:start position:0%
+the two guys cooperating said well
+ 
+
+ align:start position:0%
+the two guys cooperating said well
+clearly the dominant cooperative
+
+ align:start position:0%
+clearly the dominant cooperative
+ 
+
+ align:start position:0%
+clearly the dominant cooperative
+strategy is for all of us to remain
+
+ align:start position:0%
+strategy is for all of us to remain
+ 
+
+ align:start position:0%
+strategy is for all of us to remain
+silent that's the dominant coopera
+
+ align:start position:0%
+silent that's the dominant coopera
+ 
+
+ align:start position:0%
+silent that's the dominant coopera
+strategy then as a team we only get two
+
+ align:start position:0%
+strategy then as a team we only get two
+ 
+
+ align:start position:0%
+strategy then as a team we only get two
+total years in jail where everything
+
+ align:start position:0%
+total years in jail where everything
+ 
+
+ align:start position:0%
+total years in jail where everything
+gives much more many more years in jail
+
+ align:start position:0%
+gives much more many more years in jail
+ 
+
+ align:start position:0%
+gives much more many more years in jail
+so they're buddies and they trust each
+
+ align:start position:0%
+so they're buddies and they trust each
+ 
+
+ align:start position:0%
+so they're buddies and they trust each
+other and they cooperate then that's the
+
+ align:start position:0%
+other and they cooperate then that's the
+ 
+
+ align:start position:0%
+other and they cooperate then that's the
+closest right strategy well let's say
+
+ align:start position:0%
+closest right strategy well let's say
+ 
+
+ align:start position:0%
+closest right strategy well let's say
+the police are smart and put them in
+
+ align:start position:0%
+the police are smart and put them in
+ 
+
+ align:start position:0%
+the police are smart and put them in
+separate rooms
+
+ align:start position:0%
+separate rooms
+ 
+
+ align:start position:0%
+separate rooms
+okay well what's the dominant
+
+ align:start position:0%
+okay well what's the dominant
+ 
+
+ align:start position:0%
+okay well what's the dominant
+non-cooperative strategy what is the
+
+ align:start position:0%
+non-cooperative strategy what is the
+ 
+
+ align:start position:0%
+non-cooperative strategy what is the
+strategy that a or b that aides say a
+
+ align:start position:0%
+strategy that a or b that aides say a
+ 
+
+ align:start position:0%
+strategy that a or b that aides say a
+should produce yeah why
+
+ align:start position:0%
+should produce yeah why
+ 
+
+ align:start position:0%
+should produce yeah why
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in silence you talk you get zero and if
+
+ align:start position:0%
+in silence you talk you get zero and if
+ 
+
+ align:start position:0%
+in silence you talk you get zero and if
+they're talking they talking you talk as
+
+ align:start position:0%
+they're talking they talking you talk as
+ 
+
+ align:start position:0%
+they're talking they talking you talk as
+well you get 2 vs. 5 exactly 4 person or
+
+ align:start position:0%
+well you get 2 vs. 5 exactly 4 person or
+ 
+
+ align:start position:0%
+well you get 2 vs. 5 exactly 4 person or
+a in this first row compared the first
+
+ align:start position:0%
+a in this first row compared the first
+ 
+
+ align:start position:0%
+a in this first row compared the first
+row left first column will say prisoner
+
+ align:start position:0%
+row left first column will say prisoner
+ 
+
+ align:start position:0%
+row left first column will say prisoner
+be silent then clearly you're better off
+
+ align:start position:0%
+be silent then clearly you're better off
+ 
+
+ align:start position:0%
+be silent then clearly you're better off
+talking than not talking 0 rather than 1
+
+ align:start position:0%
+talking than not talking 0 rather than 1
+ 
+
+ align:start position:0%
+talking than not talking 0 rather than 1
+let's say prisoner B talks then you're
+
+ align:start position:0%
+let's say prisoner B talks then you're
+ 
+
+ align:start position:0%
+let's say prisoner B talks then you're
+still better off talking than not
+
+ align:start position:0%
+still better off talking than not
+ 
+
+ align:start position:0%
+still better off talking than not
+talking so no matter what B does you
+
+ align:start position:0%
+talking so no matter what B does you
+ 
+
+ align:start position:0%
+talking so no matter what B does you
+should talk
+
+ align:start position:0%
+should talk
+ 
+
+ align:start position:0%
+should talk
+likewise prisoner B no matter what a
+
+ align:start position:0%
+likewise prisoner B no matter what a
+ 
+
+ align:start position:0%
+likewise prisoner B no matter what a
+does B should talk so the
+
+ align:start position:0%
+does B should talk so the
+ 
+
+ align:start position:0%
+does B should talk so the
+non-cooperative room is actually this
+
+ align:start position:0%
+non-cooperative room is actually this
+ 
+
+ align:start position:0%
+non-cooperative room is actually this
+outcome they both end up talking you get
+
+ align:start position:0%
+outcome they both end up talking you get
+ 
+
+ align:start position:0%
+outcome they both end up talking you get
+sort of a race to the bottom
+
+ align:start position:0%
+sort of a race to the bottom
+ 
+
+ align:start position:0%
+sort of a race to the bottom
+the non-cooperative outcome is much
+
+ align:start position:0%
+the non-cooperative outcome is much
+ 
+
+ align:start position:0%
+the non-cooperative outcome is much
+worse than if they could have cooperated
+
+ align:start position:0%
+worse than if they could have cooperated
+ 
+
+ align:start position:0%
+worse than if they could have cooperated
+ok so basically what you get is that the
+
+ align:start position:0%
+ok so basically what you get is that the
+ 
+
+ align:start position:0%
+ok so basically what you get is that the
+non-cooperative equilibrium is always
+
+ align:start position:0%
+non-cooperative equilibrium is always
+ 
+
+ align:start position:0%
+non-cooperative equilibrium is always
+worse for the players than the
+
+ align:start position:0%
+worse for the players than the
+ 
+
+ align:start position:0%
+worse for the players than the
+co-operative equilibria and this was
+
+ align:start position:0%
+co-operative equilibria and this was
+ 
+
+ align:start position:0%
+co-operative equilibria and this was
+like an unbelievable insight of Nash
+
+ align:start position:0%
+like an unbelievable insight of Nash
+ 
+
+ align:start position:0%
+like an unbelievable insight of Nash
+before Nash we always thought
+
+ align:start position:0%
+before Nash we always thought
+ 
+
+ align:start position:0%
+before Nash we always thought
+competition was always than ever we're
+
+ align:start position:0%
+competition was always than ever we're
+ 
+
+ align:start position:0%
+competition was always than ever we're
+good with some more competitions better
+
+ align:start position:0%
+good with some more competitions better
+ 
+
+ align:start position:0%
+good with some more competitions better
+for the reasons we taught you in the
+
+ align:start position:0%
+for the reasons we taught you in the
+ 
+
+ align:start position:0%
+for the reasons we taught you in the
+first 10 or 10 or 12 lectures of this
+
+ align:start position:0%
+first 10 or 10 or 12 lectures of this
+ 
+
+ align:start position:0%
+first 10 or 10 or 12 lectures of this
+class Nash was the first one to say no
+
+ align:start position:0%
+class Nash was the first one to say no
+ 
+
+ align:start position:0%
+class Nash was the first one to say no
+actually competition can be bad
+
+ align:start position:0%
+actually competition can be bad
+ 
+
+ align:start position:0%
+actually competition can be bad
+cooperation can be better as you
+
+ align:start position:0%
+cooperation can be better as you
+ 
+
+ align:start position:0%
+cooperation can be better as you
+remember the scene in a beautiful mind
+
+ align:start position:0%
+remember the scene in a beautiful mind
+ 
+
+ align:start position:0%
+remember the scene in a beautiful mind
+where they're picking up girls in the
+
+ align:start position:0%
+where they're picking up girls in the
+ 
+
+ align:start position:0%
+where they're picking up girls in the
+bar and he describes sort of basically a
+
+ align:start position:0%
+bar and he describes sort of basically a
+ 
+
+ align:start position:0%
+bar and he describes sort of basically a
+Nash strategy ok how competition lead to
+
+ align:start position:0%
+Nash strategy ok how competition lead to
+ 
+
+ align:start position:0%
+Nash strategy ok how competition lead to
+the worst outcome ok and basically
+
+ align:start position:0%
+the worst outcome ok and basically
+ 
+
+ align:start position:0%
+the worst outcome ok and basically
+that's what you see here that
+
+ align:start position:0%
+that's what you see here that
+ 
+
+ align:start position:0%
+that's what you see here that
+competition can actually lead to a worse
+
+ align:start position:0%
+competition can actually lead to a worse
+ 
+
+ align:start position:0%
+competition can actually lead to a worse
+outcome than cooperation and that was
+
+ align:start position:0%
+outcome than cooperation and that was
+ 
+
+ align:start position:0%
+outcome than cooperation and that was
+really sort of Nash's sort of brilliant
+
+ align:start position:0%
+really sort of Nash's sort of brilliant
+ 
+
+ align:start position:0%
+really sort of Nash's sort of brilliant
+insight now um this is a sort of a cute
+
+ align:start position:0%
+insight now um this is a sort of a cute
+ 
+
+ align:start position:0%
+insight now um this is a sort of a cute
+example of prisoners but actually but
+
+ align:start position:0%
+example of prisoners but actually but
+ 
+
+ align:start position:0%
+example of prisoners but actually but
+well for two points first of all this
+
+ align:start position:0%
+well for two points first of all this
+ 
+
+ align:start position:0%
+well for two points first of all this
+generally shows you how you do gain fear
+
+ align:start position:0%
+generally shows you how you do gain fear
+ 
+
+ align:start position:0%
+generally shows you how you do gain fear
+with Nash with Nash equilibria basically
+
+ align:start position:0%
+with Nash with Nash equilibria basically
+ 
+
+ align:start position:0%
+with Nash with Nash equilibria basically
+you look at the payoff matrix you find
+
+ align:start position:0%
+you look at the payoff matrix you find
+ 
+
+ align:start position:0%
+you look at the payoff matrix you find
+the dominant strategy and then you find
+
+ align:start position:0%
+the dominant strategy and then you find
+ 
+
+ align:start position:0%
+the dominant strategy and then you find
+where those dominant strategies
+
+ align:start position:0%
+where those dominant strategies
+ 
+
+ align:start position:0%
+where those dominant strategies
+intersect and here the dominant
+
+ align:start position:0%
+intersect and here the dominant
+ 
+
+ align:start position:0%
+intersect and here the dominant
+strategies intersect at this cell
+
+ align:start position:0%
+strategies intersect at this cell
+ 
+
+ align:start position:0%
+strategies intersect at this cell
+therefore that's the equilibrium okay so
+
+ align:start position:0%
+therefore that's the equilibrium okay so
+ 
+
+ align:start position:0%
+therefore that's the equilibrium okay so
+that's basically how you do game theory
+
+ align:start position:0%
+that's basically how you do game theory
+ 
+
+ align:start position:0%
+that's basically how you do game theory
+you know you know
+
+ align:start position:0%
+you know you know
+ 
+
+ align:start position:0%
+you know you know
+getting through kindergarten level okay
+
+ align:start position:0%
+getting through kindergarten level okay
+ 
+
+ align:start position:0%
+getting through kindergarten level okay
+you look at the matrix you find each
+
+ align:start position:0%
+you look at the matrix you find each
+ 
+
+ align:start position:0%
+you look at the matrix you find each
+player's dominus strategy and you find
+
+ align:start position:0%
+player's dominus strategy and you find
+ 
+
+ align:start position:0%
+player's dominus strategy and you find
+the point at which those dominant
+
+ align:start position:0%
+the point at which those dominant
+ 
+
+ align:start position:0%
+the point at which those dominant
+strategies intersect and at that point
+
+ align:start position:0%
+strategies intersect and at that point
+ 
+
+ align:start position:0%
+strategies intersect and at that point
+that's the equilibrium now that's all
+
+ align:start position:0%
+that's the equilibrium now that's all
+ 
+
+ align:start position:0%
+that's the equilibrium now that's all
+well and good for sort of a simple
+
+ align:start position:0%
+well and good for sort of a simple
+ 
+
+ align:start position:0%
+well and good for sort of a simple
+example like this but let's actually
+
+ align:start position:0%
+example like this but let's actually
+ 
+
+ align:start position:0%
+example like this but let's actually
+apply to an economics example let's
+
+ align:start position:0%
+apply to an economics example let's
+ 
+
+ align:start position:0%
+apply to an economics example let's
+think about advertising
+
+ align:start position:0%
+think about advertising
+ 
+
+ align:start position:0%
+think about advertising
+so think about Coke and Pepsi okay um
+
+ align:start position:0%
+so think about Coke and Pepsi okay um
+ 
+
+ align:start position:0%
+so think about Coke and Pepsi okay um
+now right now let's think about their
+
+ align:start position:0%
+now right now let's think about their
+ 
+
+ align:start position:0%
+now right now let's think about their
+decision advertise now obviously this is
+
+ align:start position:0%
+decision advertise now obviously this is
+ 
+
+ align:start position:0%
+decision advertise now obviously this is
+a simple problem obviously Pepsi should
+
+ align:start position:0%
+a simple problem obviously Pepsi should
+ 
+
+ align:start position:0%
+a simple problem obviously Pepsi should
+just be illegal because cokes just way
+
+ align:start position:0%
+just be illegal because cokes just way
+ 
+
+ align:start position:0%
+just be illegal because cokes just way
+better but sadly it's not and sometimes
+
+ align:start position:0%
+better but sadly it's not and sometimes
+ 
+
+ align:start position:0%
+better but sadly it's not and sometimes
+I have to drink Pepsi and I'm very sad
+
+ align:start position:0%
+I have to drink Pepsi and I'm very sad
+ 
+
+ align:start position:0%
+I have to drink Pepsi and I'm very sad
+but nonetheless in the real world we
+
+ align:start position:0%
+but nonetheless in the real world we
+ 
+
+ align:start position:0%
+but nonetheless in the real world we
+have Coke impacts they have to decide
+
+ align:start position:0%
+have Coke impacts they have to decide
+ 
+
+ align:start position:0%
+have Coke impacts they have to decide
+how much to advertise now the dominant
+
+ align:start position:0%
+how much to advertise now the dominant
+ 
+
+ align:start position:0%
+how much to advertise now the dominant
+cooperative strategy would be to say
+
+ align:start position:0%
+cooperative strategy would be to say
+ 
+
+ align:start position:0%
+cooperative strategy would be to say
+look advertising cost us a ton of money
+
+ align:start position:0%
+look advertising cost us a ton of money
+ 
+
+ align:start position:0%
+look advertising cost us a ton of money
+let's just split the market
+
+ align:start position:0%
+let's just split the market
+ 
+
+ align:start position:0%
+let's just split the market
+let's have monopoly market and just
+
+ align:start position:0%
+let's have monopoly market and just
+ 
+
+ align:start position:0%
+let's have monopoly market and just
+split it we're close to splitting it
+
+ align:start position:0%
+split it we're close to splitting it
+ 
+
+ align:start position:0%
+split it we're close to splitting it
+anyway cokes got some more of it we're
+
+ align:start position:0%
+anyway cokes got some more of it we're
+ 
+
+ align:start position:0%
+anyway cokes got some more of it we're
+close to splitting let's just split it
+
+ align:start position:0%
+close to splitting let's just split it
+ 
+
+ align:start position:0%
+close to splitting let's just split it
+yeah why different than the
+
+ align:start position:0%
+yeah why different than the
+ 
+
+ align:start position:0%
+yeah why different than the
+cooperative's that's that's imposed not
+
+ align:start position:0%
+cooperative's that's that's imposed not
+ 
+
+ align:start position:0%
+cooperative's that's that's imposed not
+by Coke and Pepsi jointly that's opposed
+
+ align:start position:0%
+by Coke and Pepsi jointly that's opposed
+ 
+
+ align:start position:0%
+by Coke and Pepsi jointly that's opposed
+by Pepsi saying to a university campus
+
+ align:start position:0%
+by Pepsi saying to a university campus
+ 
+
+ align:start position:0%
+by Pepsi saying to a university campus
+for example we will only we will cut you
+
+ align:start position:0%
+for example we will only we will cut you
+ 
+
+ align:start position:0%
+for example we will only we will cut you
+a better deal if you'll agree not to
+
+ align:start position:0%
+a better deal if you'll agree not to
+ 
+
+ align:start position:0%
+a better deal if you'll agree not to
+sell coke that's not cooperation that's
+
+ align:start position:0%
+sell coke that's not cooperation that's
+ 
+
+ align:start position:0%
+sell coke that's not cooperation that's
+competition okay so the quad there's a
+
+ align:start position:0%
+competition okay so the quad there's a
+ 
+
+ align:start position:0%
+competition okay so the quad there's a
+proper strategy what if they don't
+
+ align:start position:0%
+proper strategy what if they don't
+ 
+
+ align:start position:0%
+proper strategy what if they don't
+cooperate okay
+
+ align:start position:0%
+cooperate okay
+ 
+
+ align:start position:0%
+cooperate okay
+well let's imagine we are the following
+
+ align:start position:0%
+well let's imagine we are the following
+ 
+
+ align:start position:0%
+well let's imagine we are the following
+payoff matrix okay you've got Pepsi up
+
+ align:start position:0%
+payoff matrix okay you've got Pepsi up
+ 
+
+ align:start position:0%
+payoff matrix okay you've got Pepsi up
+here and they can advertise or not
+
+ align:start position:0%
+here and they can advertise or not
+ 
+
+ align:start position:0%
+here and they can advertise or not
+advertise and you've got Coke here and
+
+ align:start position:0%
+advertise and you've got Coke here and
+ 
+
+ align:start position:0%
+advertise and you've got Coke here and
+they can advertise or not advertise and
+
+ align:start position:0%
+they can advertise or not advertise and
+ 
+
+ align:start position:0%
+they can advertise or not advertise and
+let's say the payoff matrix is the
+
+ align:start position:0%
+let's say the payoff matrix is the
+ 
+
+ align:start position:0%
+let's say the payoff matrix is the
+following let's say if both Pepsi and
+
+ align:start position:0%
+following let's say if both Pepsi and
+ 
+
+ align:start position:0%
+following let's say if both Pepsi and
+Coke let's say that the total um let's
+
+ align:start position:0%
+Coke let's say that the total um let's
+ 
+
+ align:start position:0%
+Coke let's say that the total um let's
+say the total amount of profit to be
+
+ align:start position:0%
+say the total amount of profit to be
+ 
+
+ align:start position:0%
+say the total amount of profit to be
+made is 16 whatever a billion whatever
+
+ align:start position:0%
+made is 16 whatever a billion whatever
+ 
+
+ align:start position:0%
+made is 16 whatever a billion whatever
+units want to make it 16 billion okay
+
+ align:start position:0%
+units want to make it 16 billion okay
+ 
+
+ align:start position:0%
+units want to make it 16 billion okay
+and let's say if there's no advertising
+
+ align:start position:0%
+and let's say if there's no advertising
+ 
+
+ align:start position:0%
+and let's say if there's no advertising
+Coke gets 8m Pepsi gets eight okay
+
+ align:start position:0%
+Coke gets 8m Pepsi gets eight okay
+ 
+
+ align:start position:0%
+Coke gets 8m Pepsi gets eight okay
+but let's say but let's say advertising
+
+ align:start position:0%
+but let's say but let's say advertising
+ 
+
+ align:start position:0%
+but let's say but let's say advertising
+cost money it costs five five billion so
+
+ align:start position:0%
+cost money it costs five five billion so
+ 
+
+ align:start position:0%
+cost money it costs five five billion so
+let's say if they both advertise then
+
+ align:start position:0%
+let's say if they both advertise then
+ 
+
+ align:start position:0%
+let's say if they both advertise then
+they still end up splitting the market
+
+ align:start position:0%
+they still end up splitting the market
+ 
+
+ align:start position:0%
+they still end up splitting the market
+but they only make three C equals three
+
+ align:start position:0%
+but they only make three C equals three
+ 
+
+ align:start position:0%
+but they only make three C equals three
+P equals three so it's a I'm sorry it's
+
+ align:start position:0%
+P equals three so it's a I'm sorry it's
+ 
+
+ align:start position:0%
+P equals three so it's a I'm sorry it's
+the obviou advertising yes you're right
+
+ align:start position:0%
+the obviou advertising yes you're right
+ 
+
+ align:start position:0%
+the obviou advertising yes you're right
+C equals three P equals three and here C
+
+ align:start position:0%
+C equals three P equals three and here C
+ 
+
+ align:start position:0%
+C equals three P equals three and here C
+equals eight P equals eight okay so
+
+ align:start position:0%
+equals eight P equals eight okay so
+ 
+
+ align:start position:0%
+equals eight P equals eight okay so
+basically they are so basically of a
+
+ align:start position:0%
+basically they are so basically of a
+ 
+
+ align:start position:0%
+basically they are so basically of a
+situation where they both end up
+
+ align:start position:0%
+situation where they both end up
+ 
+
+ align:start position:0%
+situation where they both end up
+splitting the market either way but they
+
+ align:start position:0%
+splitting the market either way but they
+ 
+
+ align:start position:0%
+splitting the market either way but they
+just split a smaller net profit if they
+
+ align:start position:0%
+just split a smaller net profit if they
+ 
+
+ align:start position:0%
+just split a smaller net profit if they
+advertise so clearly they'd rather be
+
+ align:start position:0%
+advertise so clearly they'd rather be
+ 
+
+ align:start position:0%
+advertise so clearly they'd rather be
+here than here but what happens in the
+
+ align:start position:0%
+here than here but what happens in the
+ 
+
+ align:start position:0%
+here than here but what happens in the
+off-diagonal elements well let's say
+
+ align:start position:0%
+off-diagonal elements well let's say
+ 
+
+ align:start position:0%
+off-diagonal elements well let's say
+also that if coke advertises but Pepsi
+
+ align:start position:0%
+also that if coke advertises but Pepsi
+ 
+
+ align:start position:0%
+also that if coke advertises but Pepsi
+does not then let's say Coke ends up
+
+ align:start position:0%
+does not then let's say Coke ends up
+ 
+
+ align:start position:0%
+does not then let's say Coke ends up
+making 13 billion and Pepsi ends up
+
+ align:start position:0%
+making 13 billion and Pepsi ends up
+ 
+
+ align:start position:0%
+making 13 billion and Pepsi ends up
+making - I'm sorry if Coke advertises
+
+ align:start position:0%
+making - I'm sorry if Coke advertises
+ 
+
+ align:start position:0%
+making - I'm sorry if Coke advertises
+and if Coke advertises and Pepsi does
+
+ align:start position:0%
+and if Coke advertises and Pepsi does
+ 
+
+ align:start position:0%
+and if Coke advertises and Pepsi does
+not adjust what my teen and Pepsi makes
+
+ align:start position:0%
+not adjust what my teen and Pepsi makes
+ 
+
+ align:start position:0%
+not adjust what my teen and Pepsi makes
+negative - they actually lose money
+
+ align:start position:0%
+negative - they actually lose money
+ 
+
+ align:start position:0%
+negative - they actually lose money
+because a fixed cost then don't sell
+
+ align:start position:0%
+because a fixed cost then don't sell
+ 
+
+ align:start position:0%
+because a fixed cost then don't sell
+anything nobody buys perhaps their to
+
+ align:start position:0%
+anything nobody buys perhaps their to
+ 
+
+ align:start position:0%
+anything nobody buys perhaps their to
+lose money and let's say if Pepsi
+
+ align:start position:0%
+lose money and let's say if Pepsi
+ 
+
+ align:start position:0%
+lose money and let's say if Pepsi
+advertises and coke doesn't then coke
+
+ align:start position:0%
+advertises and coke doesn't then coke
+ 
+
+ align:start position:0%
+advertises and coke doesn't then coke
+makes negative - and Pepsi makes 13 okay
+
+ align:start position:0%
+makes negative - and Pepsi makes 13 okay
+ 
+
+ align:start position:0%
+makes negative - and Pepsi makes 13 okay
+so actually if you don't advertise
+
+ align:start position:0%
+so actually if you don't advertise
+ 
+
+ align:start position:0%
+so actually if you don't advertise
+you're really screwed and the other guys
+
+ align:start position:0%
+you're really screwed and the other guys
+ 
+
+ align:start position:0%
+you're really screwed and the other guys
+really screwed yeah this doesn't move
+
+ align:start position:0%
+really screwed yeah this doesn't move
+ 
+
+ align:start position:0%
+really screwed yeah this doesn't move
+the cost of advertising but it's just
+
+ align:start position:0%
+the cost of advertising but it's just
+ 
+
+ align:start position:0%
+the cost of advertising but it's just
+coke you know gets gets a huge market
+
+ align:start position:0%
+coke you know gets gets a huge market
+ 
+
+ align:start position:0%
+coke you know gets gets a huge market
+expands its market okay so now let's
+
+ align:start position:0%
+expands its market okay so now let's
+ 
+
+ align:start position:0%
+expands its market okay so now let's
+play the game
+
+ align:start position:0%
+play the game
+ 
+
+ align:start position:0%
+play the game
+well now let's say your coke you say
+
+ align:start position:0%
+well now let's say your coke you say
+ 
+
+ align:start position:0%
+well now let's say your coke you say
+well if I advertise if I advertise and
+
+ align:start position:0%
+well if I advertise if I advertise and
+ 
+
+ align:start position:0%
+well if I advertise if I advertise and
+Pepsi advertises I make three but if I
+
+ align:start position:0%
+Pepsi advertises I make three but if I
+ 
+
+ align:start position:0%
+Pepsi advertises I make three but if I
+don't advertising Pepsi advertises I
+
+ align:start position:0%
+don't advertising Pepsi advertises I
+ 
+
+ align:start position:0%
+don't advertising Pepsi advertises I
+make negative - so I should advertise if
+
+ align:start position:0%
+make negative - so I should advertise if
+ 
+
+ align:start position:0%
+make negative - so I should advertise if
+I advertise Pepsi doesn't advertise that
+
+ align:start position:0%
+I advertise Pepsi doesn't advertise that
+ 
+
+ align:start position:0%
+I advertise Pepsi doesn't advertise that
+make 13 if I if I don't advertise and
+
+ align:start position:0%
+make 13 if I if I don't advertise and
+ 
+
+ align:start position:0%
+make 13 if I if I don't advertise and
+Pepsi doesn't advertise I make eight so
+
+ align:start position:0%
+Pepsi doesn't advertise I make eight so
+ 
+
+ align:start position:0%
+Pepsi doesn't advertise I make eight so
+either way my dominant strategies to
+
+ align:start position:0%
+either way my dominant strategies to
+ 
+
+ align:start position:0%
+either way my dominant strategies to
+advertise and likewise Pepsi does the
+
+ align:start position:0%
+advertise and likewise Pepsi does the
+ 
+
+ align:start position:0%
+advertise and likewise Pepsi does the
+same thing it's actually I screwed up
+
+ align:start position:0%
+same thing it's actually I screwed up
+ 
+
+ align:start position:0%
+same thing it's actually I screwed up
+writing this compared to my notes but
+
+ align:start position:0%
+writing this compared to my notes but
+ 
+
+ align:start position:0%
+writing this compared to my notes but
+it's good because it shows
+
+ align:start position:0%
+it's good because it shows
+ 
+
+ align:start position:0%
+it's good because it shows
+you flip the matrix but the logic is the
+
+ align:start position:0%
+you flip the matrix but the logic is the
+ 
+
+ align:start position:0%
+you flip the matrix but the logic is the
+same it hopes you sort of not just
+
+ align:start position:0%
+same it hopes you sort of not just
+ 
+
+ align:start position:0%
+same it hopes you sort of not just
+memorize cells little a matrix but learn
+
+ align:start position:0%
+memorize cells little a matrix but learn
+ 
+
+ align:start position:0%
+memorize cells little a matrix but learn
+the logic the point is either way the
+
+ align:start position:0%
+the logic the point is either way the
+ 
+
+ align:start position:0%
+the logic the point is either way the
+dominant strategist to advertise so they
+
+ align:start position:0%
+dominant strategist to advertise so they
+ 
+
+ align:start position:0%
+dominant strategist to advertise so they
+both advertise so real-world example of
+
+ align:start position:0%
+both advertise so real-world example of
+ 
+
+ align:start position:0%
+both advertise so real-world example of
+how you can end up now so much Oh pepsin
+
+ align:start position:0%
+how you can end up now so much Oh pepsin
+ 
+
+ align:start position:0%
+how you can end up now so much Oh pepsin
+coke do this
+
+ align:start position:0%
+coke do this
+ 
+
+ align:start position:0%
+coke do this
+actually there was industry that did
+
+ align:start position:0%
+actually there was industry that did
+ 
+
+ align:start position:0%
+actually there was industry that did
+this so when I was a kid you never ever
+
+ align:start position:0%
+this so when I was a kid you never ever
+ 
+
+ align:start position:0%
+this so when I was a kid you never ever
+saw ads for liquor on TV
+
+ align:start position:0%
+saw ads for liquor on TV
+ 
+
+ align:start position:0%
+saw ads for liquor on TV
+there were beer ads and wine ads but no
+
+ align:start position:0%
+there were beer ads and wine ads but no
+ 
+
+ align:start position:0%
+there were beer ads and wine ads but no
+hard alcohol that no bourbon no whiskey
+
+ align:start position:0%
+hard alcohol that no bourbon no whiskey
+ 
+
+ align:start position:0%
+hard alcohol that no bourbon no whiskey
+no nothing gin all this always you know
+
+ align:start position:0%
+no nothing gin all this always you know
+ 
+
+ align:start position:0%
+no nothing gin all this always you know
+captain Morgan's ads we see now they
+
+ align:start position:0%
+captain Morgan's ads we see now they
+ 
+
+ align:start position:0%
+captain Morgan's ads we see now they
+didn't exist when I was a kid but it
+
+ align:start position:0%
+didn't exist when I was a kid but it
+ 
+
+ align:start position:0%
+didn't exist when I was a kid but it
+wasn't because the law it was because
+
+ align:start position:0%
+wasn't because the law it was because
+ 
+
+ align:start position:0%
+wasn't because the law it was because
+the hard liquor industry cooperatively
+
+ align:start position:0%
+the hard liquor industry cooperatively
+ 
+
+ align:start position:0%
+the hard liquor industry cooperatively
+agreed none that would advertise this
+
+ align:start position:0%
+agreed none that would advertise this
+ 
+
+ align:start position:0%
+agreed none that would advertise this
+actually imposed a cooperative Librium
+
+ align:start position:0%
+actually imposed a cooperative Librium
+ 
+
+ align:start position:0%
+actually imposed a cooperative Librium
+and then that broke down I don't know
+
+ align:start position:0%
+and then that broke down I don't know
+ 
+
+ align:start position:0%
+and then that broke down I don't know
+the story of how it broke down but
+
+ align:start position:0%
+the story of how it broke down but
+ 
+
+ align:start position:0%
+the story of how it broke down but
+something broke down now they all
+
+ align:start position:0%
+something broke down now they all
+ 
+
+ align:start position:0%
+something broke down now they all
+advertise and they're probably all worse
+
+ align:start position:0%
+advertise and they're probably all worse
+ 
+
+ align:start position:0%
+advertise and they're probably all worse
+off than they were when they just didn't
+
+ align:start position:0%
+off than they were when they just didn't
+ 
+
+ align:start position:0%
+off than they were when they just didn't
+advertise okay we'll talk next time
+
+ align:start position:0%
+advertise okay we'll talk next time
+ 
+
+ align:start position:0%
+advertise okay we'll talk next time
+about why it probably broke down I don't
+
+ align:start position:0%
+about why it probably broke down I don't
+ 
+
+ align:start position:0%
+about why it probably broke down I don't
+know the stories well I have a rough
+
+ align:start position:0%
+know the stories well I have a rough
+ 
+
+ align:start position:0%
+know the stories well I have a rough
+sense and I'll talk about that next time
+
+ align:start position:0%
+sense and I'll talk about that next time
+ 
+
+ align:start position:0%
+sense and I'll talk about that next time
+but this is the point of how a
+
+ align:start position:0%
+but this is the point of how a
+ 
+
+ align:start position:0%
+but this is the point of how a
+non-cooperative living can drive you to
+
+ align:start position:0%
+non-cooperative living can drive you to
+ 
+
+ align:start position:0%
+non-cooperative living can drive you to
+a bad outcome okay now basically this
+
+ align:start position:0%
+a bad outcome okay now basically this
+ 
+
+ align:start position:0%
+a bad outcome okay now basically this
+doesn't just apply to prisoners or
+
+ align:start position:0%
+doesn't just apply to prisoners or
+ 
+
+ align:start position:0%
+doesn't just apply to prisoners or
+business that applies to people too so
+
+ align:start position:0%
+business that applies to people too so
+ 
+
+ align:start position:0%
+business that applies to people too so
+let's say poor Hector back there is had
+
+ align:start position:0%
+let's say poor Hector back there is had
+ 
+
+ align:start position:0%
+let's say poor Hector back there is had
+a fight with his girlfriend okay and
+
+ align:start position:0%
+a fight with his girlfriend okay and
+ 
+
+ align:start position:0%
+a fight with his girlfriend okay and
+they've had a big fight they've been
+
+ align:start position:0%
+they've had a big fight they've been
+ 
+
+ align:start position:0%
+they've had a big fight they've been
+gone a little while they've had a big
+
+ align:start position:0%
+gone a little while they've had a big
+ 
+
+ align:start position:0%
+gone a little while they've had a big
+fight and Hector's got to decide do I
+
+ align:start position:0%
+fight and Hector's got to decide do I
+ 
+
+ align:start position:0%
+fight and Hector's got to decide do I
+apologize so don't wait for her to
+
+ align:start position:0%
+apologize so don't wait for her to
+ 
+
+ align:start position:0%
+apologize so don't wait for her to
+apologize okay
+
+ align:start position:0%
+apologize okay
+ 
+
+ align:start position:0%
+apologize okay
+well the last thing Hector wants is to
+
+ align:start position:0%
+well the last thing Hector wants is to
+ 
+
+ align:start position:0%
+well the last thing Hector wants is to
+go up there and apologize have mercy
+
+ align:start position:0%
+go up there and apologize have mercy
+ 
+
+ align:start position:0%
+go up there and apologize have mercy
+forget it I'm breaking up with you
+
+ align:start position:0%
+forget it I'm breaking up with you
+ 
+
+ align:start position:0%
+forget it I'm breaking up with you
+that'd be the worst okay if he knows
+
+ align:start position:0%
+that'd be the worst okay if he knows
+ 
+
+ align:start position:0%
+that'd be the worst okay if he knows
+she's gonna be like oh I'm sorry too
+
+ align:start position:0%
+she's gonna be like oh I'm sorry too
+ 
+
+ align:start position:0%
+she's gonna be like oh I'm sorry too
+then he'd be happy to do it but what if
+
+ align:start position:0%
+then he'd be happy to do it but what if
+ 
+
+ align:start position:0%
+then he'd be happy to do it but what if
+he goes she has no I'm breaking up with
+
+ align:start position:0%
+he goes she has no I'm breaking up with
+ 
+
+ align:start position:0%
+he goes she has no I'm breaking up with
+you will then and she's thinking the
+
+ align:start position:0%
+you will then and she's thinking the
+ 
+
+ align:start position:0%
+you will then and she's thinking the
+same thing so what happens they break up
+
+ align:start position:0%
+same thing so what happens they break up
+ 
+
+ align:start position:0%
+same thing so what happens they break up
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we've been through this many times in
+
+ align:start position:0%
+we've been through this many times in
+ 
+
+ align:start position:0%
+we've been through this many times in
+our lives this is the non-cooperative
+
+ align:start position:0%
+our lives this is the non-cooperative
+ 
+
+ align:start position:0%
+our lives this is the non-cooperative
+strategy okay basically if you don't the
+
+ align:start position:0%
+strategy okay basically if you don't the
+ 
+
+ align:start position:0%
+strategy okay basically if you don't the
+other person is gonna do your dominant
+
+ align:start position:0%
+other person is gonna do your dominant
+ 
+
+ align:start position:0%
+other person is gonna do your dominant
+strategies to be an okay and
+
+ align:start position:0%
+strategies to be an okay and
+ 
+
+ align:start position:0%
+strategies to be an okay and
+basically that happens a lot in the
+
+ align:start position:0%
+basically that happens a lot in the
+ 
+
+ align:start position:0%
+basically that happens a lot in the
+context of the real world okay
+
+ align:start position:0%
+context of the real world okay
+ 
+
+ align:start position:0%
+context of the real world okay
+so now we have this sort of sad sounding
+
+ align:start position:0%
+so now we have this sort of sad sounding
+ 
+
+ align:start position:0%
+so now we have this sort of sad sounding
+outcome that basically game theory leads
+
+ align:start position:0%
+outcome that basically game theory leads
+ 
+
+ align:start position:0%
+outcome that basically game theory leads
+to bad outcomes for producers at least
+
+ align:start position:0%
+to bad outcomes for producers at least
+ 
+
+ align:start position:0%
+to bad outcomes for producers at least
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this is what's exciting about game
+
+ align:start position:0%
+this is what's exciting about game
+ 
+
+ align:start position:0%
+this is what's exciting about game
+theory so when I went to grad school
+
+ align:start position:0%
+theory so when I went to grad school
+ 
+
+ align:start position:0%
+theory so when I went to grad school
+back you know when dinosaurs roamed the
+
+ align:start position:0%
+back you know when dinosaurs roamed the
+ 
+
+ align:start position:0%
+back you know when dinosaurs roamed the
+earth game theory was sort of taught
+
+ align:start position:0%
+earth game theory was sort of taught
+ 
+
+ align:start position:0%
+earth game theory was sort of taught
+barely in the sequence it was sort of
+
+ align:start position:0%
+barely in the sequence it was sort of
+ 
+
+ align:start position:0%
+barely in the sequence it was sort of
+like an extra course taught a little bit
+
+ align:start position:0%
+like an extra course taught a little bit
+ 
+
+ align:start position:0%
+like an extra course taught a little bit
+now it sort of dominates the teaching of
+
+ align:start position:0%
+now it sort of dominates the teaching of
+ 
+
+ align:start position:0%
+now it sort of dominates the teaching of
+microeconomics in economics and it
+
+ align:start position:0%
+microeconomics in economics and it
+ 
+
+ align:start position:0%
+microeconomics in economics and it
+doesn't dominate but it's a whole like
+
+ align:start position:0%
+doesn't dominate but it's a whole like
+ 
+
+ align:start position:0%
+doesn't dominate but it's a whole like
+component of our core microeconomics
+
+ align:start position:0%
+component of our core microeconomics
+ 
+
+ align:start position:0%
+component of our core microeconomics
+education because it's given such a cool
+
+ align:start position:0%
+education because it's given such a cool
+ 
+
+ align:start position:0%
+education because it's given such a cool
+set of tools to think about these
+
+ align:start position:0%
+set of tools to think about these
+ 
+
+ align:start position:0%
+set of tools to think about these
+decisions now I can't give you even 1%
+
+ align:start position:0%
+decisions now I can't give you even 1%
+ 
+
+ align:start position:0%
+decisions now I can't give you even 1%
+of the flavor of game theory if you want
+
+ align:start position:0%
+of the flavor of game theory if you want
+ 
+
+ align:start position:0%
+of the flavor of game theory if you want
+to learn more I highly suggest you take
+
+ align:start position:0%
+to learn more I highly suggest you take
+ 
+
+ align:start position:0%
+to learn more I highly suggest you take
+1412 which is our game theory class and
+
+ align:start position:0%
+1412 which is our game theory class and
+ 
+
+ align:start position:0%
+1412 which is our game theory class and
+you can learn a ton but let me use sort
+
+ align:start position:0%
+you can learn a ton but let me use sort
+ 
+
+ align:start position:0%
+you can learn a ton but let me use sort
+of one interesting wrinkle of the kind
+
+ align:start position:0%
+of one interesting wrinkle of the kind
+ 
+
+ align:start position:0%
+of one interesting wrinkle of the kind
+of things game theory can do to go
+
+ align:start position:0%
+of things game theory can do to go
+ 
+
+ align:start position:0%
+of things game theory can do to go
+beyond this and that's to imagine that
+
+ align:start position:0%
+beyond this and that's to imagine that
+ 
+
+ align:start position:0%
+beyond this and that's to imagine that
+Coke and Pepsi are not playing a
+
+ align:start position:0%
+Coke and Pepsi are not playing a
+ 
+
+ align:start position:0%
+Coke and Pepsi are not playing a
+one-shot game but a repeated game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repeated game ok so now imagine that um
+
+ align:start position:0%
+repeated game ok so now imagine that um
+ 
+
+ align:start position:0%
+repeated game ok so now imagine that um
+coke says to Pepsi the following I
+
+ align:start position:0%
+coke says to Pepsi the following I
+ 
+
+ align:start position:0%
+coke says to Pepsi the following I
+promise to not advertise as long as you
+
+ align:start position:0%
+promise to not advertise as long as you
+ 
+
+ align:start position:0%
+promise to not advertise as long as you
+don't advertise but if you ever
+
+ align:start position:0%
+don't advertise but if you ever
+ 
+
+ align:start position:0%
+don't advertise but if you ever
+advertise I will advertise forever ok
+
+ align:start position:0%
+advertise I will advertise forever ok
+ 
+
+ align:start position:0%
+advertise I will advertise forever ok
+coke system FC I promise not to
+
+ align:start position:0%
+coke system FC I promise not to
+ 
+
+ align:start position:0%
+coke system FC I promise not to
+advertise as long as you don't advertise
+
+ align:start position:0%
+advertise as long as you don't advertise
+ 
+
+ align:start position:0%
+advertise as long as you don't advertise
+but if I ever catch you advertising I'm
+
+ align:start position:0%
+but if I ever catch you advertising I'm
+ 
+
+ align:start position:0%
+but if I ever catch you advertising I'm
+gonna advertise forever ok so now a
+
+ align:start position:0%
+gonna advertise forever ok so now a
+ 
+
+ align:start position:0%
+gonna advertise forever ok so now a
+match think about Pepsi's choice in
+
+ align:start position:0%
+match think about Pepsi's choice in
+ 
+
+ align:start position:0%
+match think about Pepsi's choice in
+period one Pepsi is choice in period 1
+
+ align:start position:0%
+period one Pepsi is choice in period 1
+ 
+
+ align:start position:0%
+period one Pepsi is choice in period 1
+impaired 1 they could say ha stupid coke
+
+ align:start position:0%
+impaired 1 they could say ha stupid coke
+ 
+
+ align:start position:0%
+impaired 1 they could say ha stupid coke
+I'm gonna jump on them and advertise
+
+ align:start position:0%
+I'm gonna jump on them and advertise
+ 
+
+ align:start position:0%
+I'm gonna jump on them and advertise
+they promised me I could advertise I'm
+
+ align:start position:0%
+they promised me I could advertise I'm
+ 
+
+ align:start position:0%
+they promised me I could advertise I'm
+gonna make so Pepsi advertises they're
+
+ align:start position:0%
+gonna make so Pepsi advertises they're
+ 
+
+ align:start position:0%
+gonna make so Pepsi advertises they're
+gonna make 13 in period 1 right because
+
+ align:start position:0%
+gonna make 13 in period 1 right because
+ 
+
+ align:start position:0%
+gonna make 13 in period 1 right because
+cokes taking themselves off to the side
+
+ align:start position:0%
+cokes taking themselves off to the side
+ 
+
+ align:start position:0%
+cokes taking themselves off to the side
+but after period 1 they're gonna make 8
+
+ align:start position:0%
+but after period 1 they're gonna make 8
+ 
+
+ align:start position:0%
+but after period 1 they're gonna make 8
+forever
+
+ align:start position:0%
+forever
+ 
+
+ align:start position:0%
+forever
+no they're gonna sorry they're gonna
+
+ align:start position:0%
+no they're gonna sorry they're gonna
+ 
+
+ align:start position:0%
+no they're gonna sorry they're gonna
+make three forever because cokes can
+
+ align:start position:0%
+make three forever because cokes can
+ 
+
+ align:start position:0%
+make three forever because cokes can
+advertise they're gonna advertise they
+
+ align:start position:0%
+advertise they're gonna advertise they
+ 
+
+ align:start position:0%
+advertise they're gonna advertise they
+break down to the non-cooperative
+
+ align:start position:0%
+break down to the non-cooperative
+ 
+
+ align:start position:0%
+break down to the non-cooperative
+equilibrium ok
+
+ align:start position:0%
+equilibrium ok
+ 
+
+ align:start position:0%
+equilibrium ok
+if Pepsi advertise now what if Pepsi
+
+ align:start position:0%
+if Pepsi advertise now what if Pepsi
+ 
+
+ align:start position:0%
+if Pepsi advertise now what if Pepsi
+doesn't advertise as well as it doesn't
+
+ align:start position:0%
+doesn't advertise as well as it doesn't
+ 
+
+ align:start position:0%
+doesn't advertise as well as it doesn't
+advertise then it gets to deal with Coke
+
+ align:start position:0%
+advertise then it gets to deal with Coke
+ 
+
+ align:start position:0%
+advertise then it gets to deal with Coke
+so it makes eight forever so now we'll
+
+ align:start position:0%
+so it makes eight forever so now we'll
+ 
+
+ align:start position:0%
+so it makes eight forever so now we'll
+talk later in the course about how you
+
+ align:start position:0%
+talk later in the course about how you
+ 
+
+ align:start position:0%
+talk later in the course about how you
+my numbers that happen different times
+
+ align:start position:0%
+my numbers that happen different times
+ 
+
+ align:start position:0%
+my numbers that happen different times
+to trust me a forever is a way better
+
+ align:start position:0%
+to trust me a forever is a way better
+ 
+
+ align:start position:0%
+to trust me a forever is a way better
+deal Don thirteen and three forever okay
+
+ align:start position:0%
+deal Don thirteen and three forever okay
+ 
+
+ align:start position:0%
+deal Don thirteen and three forever okay
+so actually by having this be a repeated
+
+ align:start position:0%
+so actually by having this be a repeated
+ 
+
+ align:start position:0%
+so actually by having this be a repeated
+game coke has solved the prisoner's
+
+ align:start position:0%
+game coke has solved the prisoner's
+ 
+
+ align:start position:0%
+game coke has solved the prisoner's
+dilemma it's essentially imposed a
+
+ align:start position:0%
+dilemma it's essentially imposed a
+ 
+
+ align:start position:0%
+dilemma it's essentially imposed a
+cooperative equilibrium on the problem
+
+ align:start position:0%
+cooperative equilibrium on the problem
+ 
+
+ align:start position:0%
+cooperative equilibrium on the problem
+okay so that's how a repeated game can
+
+ align:start position:0%
+okay so that's how a repeated game can
+ 
+
+ align:start position:0%
+okay so that's how a repeated game can
+fix this but as we're getting through it
+
+ align:start position:0%
+fix this but as we're getting through it
+ 
+
+ align:start position:0%
+fix this but as we're getting through it
+gets really exciting that only works if
+
+ align:start position:0%
+gets really exciting that only works if
+ 
+
+ align:start position:0%
+gets really exciting that only works if
+this game never ends because once Coke
+
+ align:start position:0%
+this game never ends because once Coke
+ 
+
+ align:start position:0%
+this game never ends because once Coke
+or Pepsi thinks there's an end to the
+
+ align:start position:0%
+or Pepsi thinks there's an end to the
+ 
+
+ align:start position:0%
+or Pepsi thinks there's an end to the
+game the entire thing breaks down okay
+
+ align:start position:0%
+game the entire thing breaks down okay
+ 
+
+ align:start position:0%
+game the entire thing breaks down okay
+so imagine for example the coke makes
+
+ align:start position:0%
+so imagine for example the coke makes
+ 
+
+ align:start position:0%
+so imagine for example the coke makes
+the offer to Pepsi but Pepsi's worried
+
+ align:start position:0%
+the offer to Pepsi but Pepsi's worried
+ 
+
+ align:start position:0%
+the offer to Pepsi but Pepsi's worried
+that in 10 years the government's going
+
+ align:start position:0%
+that in 10 years the government's going
+ 
+
+ align:start position:0%
+that in 10 years the government's going
+to outlaw soda okay
+
+ align:start position:0%
+to outlaw soda okay
+ 
+
+ align:start position:0%
+to outlaw soda okay
+the government you know has said look
+
+ align:start position:0%
+the government you know has said look
+ 
+
+ align:start position:0%
+the government you know has said look
+we're heading that direction so does
+
+ align:start position:0%
+we're heading that direction so does
+ 
+
+ align:start position:0%
+we're heading that direction so does
+gonna be legal in 10 years so I don't
+
+ align:start position:0%
+gonna be legal in 10 years so I don't
+ 
+
+ align:start position:0%
+gonna be legal in 10 years so I don't
+want to do this
+
+ align:start position:0%
+want to do this
+ 
+
+ align:start position:0%
+want to do this
+so in that case know that I'm sorry not
+
+ align:start position:0%
+so in that case know that I'm sorry not
+ 
+
+ align:start position:0%
+so in that case know that I'm sorry not
+that I want to I so I have that in my
+
+ align:start position:0%
+that I want to I so I have that in my
+ 
+
+ align:start position:0%
+that I want to I so I have that in my
+mind so Coke offers the deal now what do
+
+ align:start position:0%
+mind so Coke offers the deal now what do
+ 
+
+ align:start position:0%
+mind so Coke offers the deal now what do
+I think well let's think about Pepsi's
+
+ align:start position:0%
+I think well let's think about Pepsi's
+ 
+
+ align:start position:0%
+I think well let's think about Pepsi's
+decision in the ninth year they've made
+
+ align:start position:0%
+decision in the ninth year they've made
+ 
+
+ align:start position:0%
+decision in the ninth year they've made
+eight eight eight eight eight and they
+
+ align:start position:0%
+eight eight eight eight eight and they
+ 
+
+ align:start position:0%
+eight eight eight eight eight and they
+get to your nine now in year nine they
+
+ align:start position:0%
+get to your nine now in year nine they
+ 
+
+ align:start position:0%
+get to your nine now in year nine they
+know that next year there's no more game
+
+ align:start position:0%
+know that next year there's no more game
+ 
+
+ align:start position:0%
+know that next year there's no more game
+so what should they do advertise grab
+
+ align:start position:0%
+so what should they do advertise grab
+ 
+
+ align:start position:0%
+so what should they do advertise grab
+the thirteen in the last period because
+
+ align:start position:0%
+the thirteen in the last period because
+ 
+
+ align:start position:0%
+the thirteen in the last period because
+Coke can't punish them because the
+
+ align:start position:0%
+Coke can't punish them because the
+ 
+
+ align:start position:0%
+Coke can't punish them because the
+game's over
+
+ align:start position:0%
+game's over
+ 
+
+ align:start position:0%
+game's over
+but Coke knows this so it's Coke gonna
+
+ align:start position:0%
+but Coke knows this so it's Coke gonna
+ 
+
+ align:start position:0%
+but Coke knows this so it's Coke gonna
+do in the ninth year advertise its can
+
+ align:start position:0%
+do in the ninth year advertise its can
+ 
+
+ align:start position:0%
+do in the ninth year advertise its can
+advertise so they're both gonna make so
+
+ align:start position:0%
+advertise so they're both gonna make so
+ 
+
+ align:start position:0%
+advertise so they're both gonna make so
+so they're both gonna make a three
+
+ align:start position:0%
+so they're both gonna make a three
+ 
+
+ align:start position:0%
+so they're both gonna make a three
+well if Pepsi knows cokes can advertise
+
+ align:start position:0%
+well if Pepsi knows cokes can advertise
+ 
+
+ align:start position:0%
+well if Pepsi knows cokes can advertise
+than that ninth year no matter what
+
+ align:start position:0%
+than that ninth year no matter what
+ 
+
+ align:start position:0%
+than that ninth year no matter what
+what's your pet's you in the eighth year
+
+ align:start position:0%
+what's your pet's you in the eighth year
+ 
+
+ align:start position:0%
+what's your pet's you in the eighth year
+advertise and if Coke knows pets can
+
+ align:start position:0%
+advertise and if Coke knows pets can
+ 
+
+ align:start position:0%
+advertise and if Coke knows pets can
+advertise an eighth year bunch of coke
+
+ align:start position:0%
+advertise an eighth year bunch of coke
+ 
+
+ align:start position:0%
+advertise an eighth year bunch of coke
+do and so on and ends up that they both
+
+ align:start position:0%
+do and so on and ends up that they both
+ 
+
+ align:start position:0%
+do and so on and ends up that they both
+advertise all the way through so the
+
+ align:start position:0%
+advertise all the way through so the
+ 
+
+ align:start position:0%
+advertise all the way through so the
+game breaks down if it's an end this is
+
+ align:start position:0%
+game breaks down if it's an end this is
+ 
+
+ align:start position:0%
+game breaks down if it's an end this is
+really kind of neat and this is what
+
+ align:start position:0%
+really kind of neat and this is what
+ 
+
+ align:start position:0%
+really kind of neat and this is what
+game through is all about is how do you
+
+ align:start position:0%
+game through is all about is how do you
+ 
+
+ align:start position:0%
+game through is all about is how do you
+think through these more complicated
+
+ align:start position:0%
+think through these more complicated
+ 
+
+ align:start position:0%
+think through these more complicated
+scenarios that are much more complicated
+
+ align:start position:0%
+scenarios that are much more complicated
+ 
+
+ align:start position:0%
+scenarios that are much more complicated
+the prisoner's dilemma and actually
+
+ align:start position:0%
+the prisoner's dilemma and actually
+ 
+
+ align:start position:0%
+the prisoner's dilemma and actually
+think about how firms and individuals
+
+ align:start position:0%
+think about how firms and individuals
+ 
+
+ align:start position:0%
+think about how firms and individuals
+might actually behave yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these contracts
+
+ align:start position:0%
+these contracts
+ 
+
+ align:start position:0%
+these contracts
+earlier sure that's much and once again
+
+ align:start position:0%
+earlier sure that's much and once again
+ 
+
+ align:start position:0%
+earlier sure that's much and once again
+that's exact that's what you cover in a
+
+ align:start position:0%
+that's exact that's what you cover in a
+ 
+
+ align:start position:0%
+that's exact that's what you cover in a
+field of course like game theories what
+
+ align:start position:0%
+field of course like game theories what
+ 
+
+ align:start position:0%
+field of course like game theories what
+about alternative forms of contracting
+
+ align:start position:0%
+about alternative forms of contracting
+ 
+
+ align:start position:0%
+about alternative forms of contracting
+with exclusionary contractor what we
+
+ align:start position:0%
+with exclusionary contractor what we
+ 
+
+ align:start position:0%
+with exclusionary contractor what we
+call tying in contracting that's great
+
+ align:start position:0%
+call tying in contracting that's great
+ 
+
+ align:start position:0%
+call tying in contracting that's great
+and they would but that's that's why you
+
+ align:start position:0%
+and they would but that's that's why you
+ 
+
+ align:start position:0%
+and they would but that's that's why you
+got to take 1412 okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the way I've set this problem up if
+
+ align:start position:0%
+yeah the way I've set this problem up if
+ 
+
+ align:start position:0%
+yeah the way I've set this problem up if
+they could commit to that that'd be
+
+ align:start position:0%
+they could commit to that that'd be
+ 
+
+ align:start position:0%
+they could commit to that that'd be
+right but you'd have to commit to it
+
+ align:start position:0%
+right but you'd have to commit to it
+ 
+
+ align:start position:0%
+right but you'd have to commit to it
+because then the funds the period the
+
+ align:start position:0%
+because then the funds the period the
+ 
+
+ align:start position:0%
+because then the funds the period the
+period the Pepsi promised to take off if
+
+ align:start position:0%
+period the Pepsi promised to take off if
+ 
+
+ align:start position:0%
+period the Pepsi promised to take off if
+they actually advertised that period
+
+ align:start position:0%
+they actually advertised that period
+ 
+
+ align:start position:0%
+they actually advertised that period
+then cokes screwed so that would work as
+
+ align:start position:0%
+then cokes screwed so that would work as
+ 
+
+ align:start position:0%
+then cokes screwed so that would work as
+a repeated game solution but it wouldn't
+
+ align:start position:0%
+a repeated game solution but it wouldn't
+ 
+
+ align:start position:0%
+a repeated game solution but it wouldn't
+work as a as a non repeated game so as
+
+ align:start position:0%
+work as a as a non repeated game so as
+ 
+
+ align:start position:0%
+work as a as a non repeated game so as
+again as the work is an infinite
+
+ align:start position:0%
+again as the work is an infinite
+ 
+
+ align:start position:0%
+again as the work is an infinite
+repeated game but not a non infinite
+
+ align:start position:0%
+repeated game but not a non infinite
+ 
+
+ align:start position:0%
+repeated game but not a non infinite
+repeated game okay
+
+ align:start position:0%
+repeated game okay
+ 
+
+ align:start position:0%
+repeated game okay
+good question okay other questions all
+
+ align:start position:0%
+good question okay other questions all
+ 
+
+ align:start position:0%
+good question okay other questions all
+right so that's the basic game theory
+
+ align:start position:0%
+right so that's the basic game theory
+ 
+
+ align:start position:0%
+right so that's the basic game theory
+that's just a taste for the excitement
+
+ align:start position:0%
+that's just a taste for the excitement
+ 
+
+ align:start position:0%
+that's just a taste for the excitement
+that you can live with game theory but
+
+ align:start position:0%
+that you can live with game theory but
+ 
+
+ align:start position:0%
+that you can live with game theory but
+in fact in economics we like to write
+
+ align:start position:0%
+in fact in economics we like to write
+ 
+
+ align:start position:0%
+in fact in economics we like to write
+that these fun examples but we really
+
+ align:start position:0%
+that these fun examples but we really
+ 
+
+ align:start position:0%
+that these fun examples but we really
+prefer to do math so let's actually
+
+ align:start position:0%
+prefer to do math so let's actually
+ 
+
+ align:start position:0%
+prefer to do math so let's actually
+think about the math of how we take game
+
+ align:start position:0%
+think about the math of how we take game
+ 
+
+ align:start position:0%
+think about the math of how we take game
+theory concepts and put them in practice
+
+ align:start position:0%
+theory concepts and put them in practice
+ 
+
+ align:start position:0%
+theory concepts and put them in practice
+and that's we that the way we do that is
+
+ align:start position:0%
+and that's we that the way we do that is
+ 
+
+ align:start position:0%
+and that's we that the way we do that is
+through the concept of the cournot model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the cournot model of non cooperative
+
+ align:start position:0%
+the cournot model of non cooperative
+ 
+
+ align:start position:0%
+the cournot model of non cooperative
+oligopolies okay so it's the cournot
+
+ align:start position:0%
+oligopolies okay so it's the cournot
+ 
+
+ align:start position:0%
+oligopolies okay so it's the cournot
+model of non cooperative oligopoly is
+
+ align:start position:0%
+model of non cooperative oligopoly is
+ 
+
+ align:start position:0%
+model of non cooperative oligopoly is
+the standard workhorse model takes this
+
+ align:start position:0%
+the standard workhorse model takes this
+ 
+
+ align:start position:0%
+the standard workhorse model takes this
+intuition and puts it into the kind of
+
+ align:start position:0%
+intuition and puts it into the kind of
+ 
+
+ align:start position:0%
+intuition and puts it into the kind of
+optimizing math we've been doing this so
+
+ align:start position:0%
+optimizing math we've been doing this so
+ 
+
+ align:start position:0%
+optimizing math we've been doing this so
+far this class okay so let's now let's
+
+ align:start position:0%
+far this class okay so let's now let's
+ 
+
+ align:start position:0%
+far this class okay so let's now let's
+imagine non cooperative case but now
+
+ align:start position:0%
+imagine non cooperative case but now
+ 
+
+ align:start position:0%
+imagine non cooperative case but now
+let's imagine there's not just two
+
+ align:start position:0%
+let's imagine there's not just two
+ 
+
+ align:start position:0%
+let's imagine there's not just two
+choices but realistically there's a
+
+ align:start position:0%
+choices but realistically there's a
+ 
+
+ align:start position:0%
+choices but realistically there's a
+whole set of choices okay then how would
+
+ align:start position:0%
+whole set of choices okay then how would
+ 
+
+ align:start position:0%
+whole set of choices okay then how would
+you behave in the in that case so let's
+
+ align:start position:0%
+you behave in the in that case so let's
+ 
+
+ align:start position:0%
+you behave in the in that case so let's
+imagine that there's two airlines United
+
+ align:start position:0%
+imagine that there's two airlines United
+ 
+
+ align:start position:0%
+imagine that there's two airlines United
+in American United America two so we're
+
+ align:start position:0%
+in American United America two so we're
+ 
+
+ align:start position:0%
+in American United America two so we're
+gonna have a oligopolistic to firm
+
+ align:start position:0%
+gonna have a oligopolistic to firm
+ 
+
+ align:start position:0%
+gonna have a oligopolistic to firm
+airline industry obviously the math can
+
+ align:start position:0%
+airline industry obviously the math can
+ 
+
+ align:start position:0%
+airline industry obviously the math can
+extend to more firms but just to start
+
+ align:start position:0%
+extend to more firms but just to start
+ 
+
+ align:start position:0%
+extend to more firms but just to start
+now and I'll talk about that next
+
+ align:start position:0%
+now and I'll talk about that next
+ 
+
+ align:start position:0%
+now and I'll talk about that next
+lecture but for now imagine a two firm
+
+ align:start position:0%
+lecture but for now imagine a two firm
+ 
+
+ align:start position:0%
+lecture but for now imagine a two firm
+industry United an American and because
+
+ align:start position:0%
+industry United an American and because
+ 
+
+ align:start position:0%
+industry United an American and because
+the hub-and-spoke system we discussed
+
+ align:start position:0%
+the hub-and-spoke system we discussed
+ 
+
+ align:start position:0%
+the hub-and-spoke system we discussed
+last time let's imagine of the only two
+
+ align:start position:0%
+last time let's imagine of the only two
+ 
+
+ align:start position:0%
+last time let's imagine of the only two
+folks that go from Boston Chicago okay
+
+ align:start position:0%
+folks that go from Boston Chicago okay
+ 
+
+ align:start position:0%
+folks that go from Boston Chicago okay
+because this hub-and-spoke system the
+
+ align:start position:0%
+because this hub-and-spoke system the
+ 
+
+ align:start position:0%
+because this hub-and-spoke system the
+only folks to go from Boston Chicago at
+
+ align:start position:0%
+only folks to go from Boston Chicago at
+ 
+
+ align:start position:0%
+only folks to go from Boston Chicago at
+night in America and they do in fact
+
+ align:start position:0%
+night in America and they do in fact
+ 
+
+ align:start position:0%
+night in America and they do in fact
+dominate that line so let's imagine the
+
+ align:start position:0%
+dominate that line so let's imagine the
+ 
+
+ align:start position:0%
+dominate that line so let's imagine the
+only folks and say no other firms could
+
+ align:start position:0%
+only folks and say no other firms could
+ 
+
+ align:start position:0%
+only folks and say no other firms could
+get peed in this and this on this route
+
+ align:start position:0%
+get peed in this and this on this route
+ 
+
+ align:start position:0%
+get peed in this and this on this route
+because they can't get slots at the
+
+ align:start position:0%
+because they can't get slots at the
+ 
+
+ align:start position:0%
+because they can't get slots at the
+airport so the question is how do these
+
+ align:start position:0%
+airport so the question is how do these
+ 
+
+ align:start position:0%
+airport so the question is how do these
+firms decide how many flights to run
+
+ align:start position:0%
+firms decide how many flights to run
+ 
+
+ align:start position:0%
+firms decide how many flights to run
+it's not just advertised don't it's
+
+ align:start position:0%
+it's not just advertised don't it's
+ 
+
+ align:start position:0%
+it's not just advertised don't it's
+literally a continuous decision of how
+
+ align:start position:0%
+literally a continuous decision of how
+ 
+
+ align:start position:0%
+literally a continuous decision of how
+many flights to run every day and how
+
+ align:start position:0%
+many flights to run every day and how
+ 
+
+ align:start position:0%
+many flights to run every day and how
+much to charge
+
+ align:start position:0%
+much to charge
+ 
+
+ align:start position:0%
+much to charge
+okay they've got to make that decision
+
+ align:start position:0%
+okay they've got to make that decision
+ 
+
+ align:start position:0%
+okay they've got to make that decision
+and the Nash equilibrium here we call a
+
+ align:start position:0%
+and the Nash equilibrium here we call a
+ 
+
+ align:start position:0%
+and the Nash equilibrium here we call a
+core know the sort of subset of Nash for
+
+ align:start position:0%
+core know the sort of subset of Nash for
+ 
+
+ align:start position:0%
+core know the sort of subset of Nash for
+this examples called the cournot
+
+ align:start position:0%
+this examples called the cournot
+ 
+
+ align:start position:0%
+this examples called the cournot
+equilibrium and the cournot equilibrium
+
+ align:start position:0%
+equilibrium and the cournot equilibrium
+ 
+
+ align:start position:0%
+equilibrium and the cournot equilibrium
+exists when a firm chooses a quantity
+
+ align:start position:0%
+exists when a firm chooses a quantity
+ 
+
+ align:start position:0%
+exists when a firm chooses a quantity
+such that given the quantity chosen by
+
+ align:start position:0%
+such that given the quantity chosen by
+ 
+
+ align:start position:0%
+such that given the quantity chosen by
+the other firm they don't want to change
+
+ align:start position:0%
+the other firm they don't want to change
+ 
+
+ align:start position:0%
+the other firm they don't want to change
+so a firm chooses essentially the profit
+
+ align:start position:0%
+so a firm chooses essentially the profit
+ 
+
+ align:start position:0%
+so a firm chooses essentially the profit
+maximizing quantity given the quantity
+
+ align:start position:0%
+maximizing quantity given the quantity
+ 
+
+ align:start position:0%
+maximizing quantity given the quantity
+chosen by the other firm okay and if
+
+ align:start position:0%
+chosen by the other firm okay and if
+ 
+
+ align:start position:0%
+chosen by the other firm okay and if
+that profit maximizing quantity okay
+
+ align:start position:0%
+that profit maximizing quantity okay
+ 
+
+ align:start position:0%
+that profit maximizing quantity okay
+then that you're in cournot equilibrium
+
+ align:start position:0%
+then that you're in cournot equilibrium
+ 
+
+ align:start position:0%
+then that you're in cournot equilibrium
+if you have chosen a quantity that is
+
+ align:start position:0%
+if you have chosen a quantity that is
+ 
+
+ align:start position:0%
+if you have chosen a quantity that is
+profit maximizing given what the other
+
+ align:start position:0%
+profit maximizing given what the other
+ 
+
+ align:start position:0%
+profit maximizing given what the other
+firm is doing okay so basically how do
+
+ align:start position:0%
+firm is doing okay so basically how do
+ 
+
+ align:start position:0%
+firm is doing okay so basically how do
+we how do we actually carry this out
+
+ align:start position:0%
+we how do we actually carry this out
+ 
+
+ align:start position:0%
+we how do we actually carry this out
+okay let's talk about the steps okay so
+
+ align:start position:0%
+okay let's talk about the steps okay so
+ 
+
+ align:start position:0%
+okay let's talk about the steps okay so
+the first step here's I'm going to talk
+
+ align:start position:0%
+the first step here's I'm going to talk
+ 
+
+ align:start position:0%
+the first step here's I'm going to talk
+intuitively about the math what we're
+
+ align:start position:0%
+intuitively about the math what we're
+ 
+
+ align:start position:0%
+intuitively about the math what we're
+gonna do and I'm gonna talk
+
+ align:start position:0%
+gonna do and I'm gonna talk
+ 
+
+ align:start position:0%
+gonna do and I'm gonna talk
+mathematically and graphically we
+
+ align:start position:0%
+mathematically and graphically we
+ 
+
+ align:start position:0%
+mathematically and graphically we
+actually do they're essentially three
+
+ align:start position:0%
+actually do they're essentially three
+ 
+
+ align:start position:0%
+actually do they're essentially three
+steps in solving for the cournot
+
+ align:start position:0%
+steps in solving for the cournot
+ 
+
+ align:start position:0%
+steps in solving for the cournot
+equilibrium the first is ask how your
+
+ align:start position:0%
+equilibrium the first is ask how your
+ 
+
+ align:start position:0%
+equilibrium the first is ask how your
+demand changes when some of its absorbed
+
+ align:start position:0%
+demand changes when some of its absorbed
+ 
+
+ align:start position:0%
+demand changes when some of its absorbed
+by other firms so the first is solve for
+
+ align:start position:0%
+by other firms so the first is solve for
+ 
+
+ align:start position:0%
+by other firms so the first is solve for
+your residual demand function what does
+
+ align:start position:0%
+your residual demand function what does
+ 
+
+ align:start position:0%
+your residual demand function what does
+your demand curve look like given what
+
+ align:start position:0%
+your demand curve look like given what
+ 
+
+ align:start position:0%
+your demand curve look like given what
+the other firm does that's step one step
+
+ align:start position:0%
+the other firm does that's step one step
+ 
+
+ align:start position:0%
+the other firm does that's step one step
+two is that you develop a marginal
+
+ align:start position:0%
+two is that you develop a marginal
+ 
+
+ align:start position:0%
+two is that you develop a marginal
+revenue which is a function of the other
+
+ align:start position:0%
+revenue which is a function of the other
+ 
+
+ align:start position:0%
+revenue which is a function of the other
+firms quantity little Q it's multiple
+
+ align:start position:0%
+firms quantity little Q it's multiple
+ 
+
+ align:start position:0%
+firms quantity little Q it's multiple
+firms okay the other firms that's really
+
+ align:start position:0%
+firms okay the other firms that's really
+ 
+
+ align:start position:0%
+firms okay the other firms that's really
+bad hard to read the other firm's
+
+ align:start position:0%
+bad hard to read the other firm's
+ 
+
+ align:start position:0%
+bad hard to read the other firm's
+quantity so it's your marginal revenue
+
+ align:start position:0%
+quantity so it's your marginal revenue
+ 
+
+ align:start position:0%
+quantity so it's your marginal revenue
+function typically it's a function I'm
+
+ align:start position:0%
+function typically it's a function I'm
+ 
+
+ align:start position:0%
+function typically it's a function I'm
+sorry of both your quantity and the
+
+ align:start position:0%
+sorry of both your quantity and the
+ 
+
+ align:start position:0%
+sorry of both your quantity and the
+other firm's quantity a function of both
+
+ align:start position:0%
+other firm's quantity a function of both
+ 
+
+ align:start position:0%
+other firm's quantity a function of both
+your quantity and the other firm's
+
+ align:start position:0%
+your quantity and the other firm's
+ 
+
+ align:start position:0%
+your quantity and the other firm's
+quantity we developed marginal revenues
+
+ align:start position:0%
+quantity we developed marginal revenues
+ 
+
+ align:start position:0%
+quantity we developed marginal revenues
+as a function of your own quantity we
+
+ align:start position:0%
+as a function of your own quantity we
+ 
+
+ align:start position:0%
+as a function of your own quantity we
+know how to do that now we're developing
+
+ align:start position:0%
+know how to do that now we're developing
+ 
+
+ align:start position:0%
+know how to do that now we're developing
+our job as a function of your quantity
+
+ align:start position:0%
+our job as a function of your quantity
+ 
+
+ align:start position:0%
+our job as a function of your quantity
+and the other firm's quantity then you
+
+ align:start position:0%
+and the other firm's quantity then you
+ 
+
+ align:start position:0%
+and the other firm's quantity then you
+simply set this marginal revenue equal
+
+ align:start position:0%
+simply set this marginal revenue equal
+ 
+
+ align:start position:0%
+simply set this marginal revenue equal
+to marginal cost and that delivers you a
+
+ align:start position:0%
+to marginal cost and that delivers you a
+ 
+
+ align:start position:0%
+to marginal cost and that delivers you a
+conditional answer that delivers you
+
+ align:start position:0%
+conditional answer that delivers you
+ 
+
+ align:start position:0%
+conditional answer that delivers you
+your optimal quantity as a function of
+
+ align:start position:0%
+your optimal quantity as a function of
+ 
+
+ align:start position:0%
+your optimal quantity as a function of
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+firms quanti okay
+
+ align:start position:0%
+firms quanti okay
+ 
+
+ align:start position:0%
+firms quanti okay
+well that doesn't do it's a whole lot of
+
+ align:start position:0%
+well that doesn't do it's a whole lot of
+ 
+
+ align:start position:0%
+well that doesn't do it's a whole lot of
+good except there's two firms so the
+
+ align:start position:0%
+good except there's two firms so the
+ 
+
+ align:start position:0%
+good except there's two firms so the
+fourth step is we do the same thing for
+
+ align:start position:0%
+fourth step is we do the same thing for
+ 
+
+ align:start position:0%
+fourth step is we do the same thing for
+the other firm and get the same kind of
+
+ align:start position:0%
+the other firm and get the same kind of
+ 
+
+ align:start position:0%
+the other firm and get the same kind of
+equation then what do we have two
+
+ align:start position:0%
+equation then what do we have two
+ 
+
+ align:start position:0%
+equation then what do we have two
+equations and two unknowns so we solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what we do here is essentially
+
+ align:start position:0%
+okay so what we do here is essentially
+ 
+
+ align:start position:0%
+okay so what we do here is essentially
+the same thing we did before but now
+
+ align:start position:0%
+the same thing we did before but now
+ 
+
+ align:start position:0%
+the same thing we did before but now
+your marginal revenue is not just a
+
+ align:start position:0%
+your marginal revenue is not just a
+ 
+
+ align:start position:0%
+your marginal revenue is not just a
+function of your own clients a function
+
+ align:start position:0%
+function of your own clients a function
+ 
+
+ align:start position:0%
+function of your own clients a function
+the other guy's quantity same with the
+
+ align:start position:0%
+the other guy's quantity same with the
+ 
+
+ align:start position:0%
+the other guy's quantity same with the
+other guy that gives you two equations
+
+ align:start position:0%
+other guy that gives you two equations
+ 
+
+ align:start position:0%
+other guy that gives you two equations
+two unknowns we solve and the point at
+
+ align:start position:0%
+two unknowns we solve and the point at
+ 
+
+ align:start position:0%
+two unknowns we solve and the point at
+which both firms are happy is the
+
+ align:start position:0%
+which both firms are happy is the
+ 
+
+ align:start position:0%
+which both firms are happy is the
+cournot equilibrium okay
+
+ align:start position:0%
+cournot equilibrium okay
+ 
+
+ align:start position:0%
+cournot equilibrium okay
+so let's actually that's confusing so
+
+ align:start position:0%
+so let's actually that's confusing so
+ 
+
+ align:start position:0%
+so let's actually that's confusing so
+let's actually look at that let's start
+
+ align:start position:0%
+let's actually look at that let's start
+ 
+
+ align:start position:0%
+let's actually look at that let's start
+we'll do suppose graphically and
+
+ align:start position:0%
+we'll do suppose graphically and
+ 
+
+ align:start position:0%
+we'll do suppose graphically and
+mathematically let's start with figure
+
+ align:start position:0%
+mathematically let's start with figure
+ 
+
+ align:start position:0%
+mathematically let's start with figure
+thirteen one okay to make things easy
+
+ align:start position:0%
+thirteen one okay to make things easy
+ 
+
+ align:start position:0%
+thirteen one okay to make things easy
+let's start by imagining then American
+
+ align:start position:0%
+let's start by imagining then American
+ 
+
+ align:start position:0%
+let's start by imagining then American
+Airlines is a monopoly let's start with
+
+ align:start position:0%
+Airlines is a monopoly let's start with
+ 
+
+ align:start position:0%
+Airlines is a monopoly let's start with
+the world with them American Airlines
+
+ align:start position:0%
+the world with them American Airlines
+ 
+
+ align:start position:0%
+the world with them American Airlines
+monopoly okay and let's say that the
+
+ align:start position:0%
+monopoly okay and let's say that the
+ 
+
+ align:start position:0%
+monopoly okay and let's say that the
+demand function is P equals 339 minus Q
+
+ align:start position:0%
+demand function is P equals 339 minus Q
+ 
+
+ align:start position:0%
+demand function is P equals 339 minus Q
+that's an Amman for flights from Boston
+
+ align:start position:0%
+that's an Amman for flights from Boston
+ 
+
+ align:start position:0%
+that's an Amman for flights from Boston
+to Chicago okay and let's say that the
+
+ align:start position:0%
+to Chicago okay and let's say that the
+ 
+
+ align:start position:0%
+to Chicago okay and let's say that the
+marginal cost to make life easy I could
+
+ align:start position:0%
+marginal cost to make life easy I could
+ 
+
+ align:start position:0%
+marginal cost to make life easy I could
+have a cost function make your life
+
+ align:start position:0%
+have a cost function make your life
+ 
+
+ align:start position:0%
+have a cost function make your life
+difficult but maybe someday I'll do that
+
+ align:start position:0%
+difficult but maybe someday I'll do that
+ 
+
+ align:start position:0%
+difficult but maybe someday I'll do that
+but for now to make your life easy
+
+ align:start position:0%
+but for now to make your life easy
+ 
+
+ align:start position:0%
+but for now to make your life easy
+let's just say there's a flat marginal
+
+ align:start position:0%
+let's just say there's a flat marginal
+ 
+
+ align:start position:0%
+let's just say there's a flat marginal
+cost of 147 dollars okay I'm not gonna
+
+ align:start position:0%
+cost of 147 dollars okay I'm not gonna
+ 
+
+ align:start position:0%
+cost of 147 dollars okay I'm not gonna
+laugh or not gonna make life difficult
+
+ align:start position:0%
+laugh or not gonna make life difficult
+ 
+
+ align:start position:0%
+laugh or not gonna make life difficult
+with solving for marginal cost functions
+
+ align:start position:0%
+with solving for marginal cost functions
+ 
+
+ align:start position:0%
+with solving for marginal cost functions
+for now it's just him a flat marginal
+
+ align:start position:0%
+for now it's just him a flat marginal
+ 
+
+ align:start position:0%
+for now it's just him a flat marginal
+cost of 147 no matter how many flights
+
+ align:start position:0%
+cost of 147 no matter how many flights
+ 
+
+ align:start position:0%
+cost of 147 no matter how many flights
+they do its $147 per passenger so if
+
+ align:start position:0%
+they do its $147 per passenger so if
+ 
+
+ align:start position:0%
+they do its $147 per passenger so if
+your monopolist how do you solve this
+
+ align:start position:0%
+your monopolist how do you solve this
+ 
+
+ align:start position:0%
+your monopolist how do you solve this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+well first you derive your marginal
+
+ align:start position:0%
+well first you derive your marginal
+ 
+
+ align:start position:0%
+well first you derive your marginal
+revenue function
+
+ align:start position:0%
+revenue function
+ 
+
+ align:start position:0%
+revenue function
+well what's marginal revenue function
+
+ align:start position:0%
+well what's marginal revenue function
+ 
+
+ align:start position:0%
+well what's marginal revenue function
+well revenues is P times Q which is 339
+
+ align:start position:0%
+well revenues is P times Q which is 339
+ 
+
+ align:start position:0%
+well revenues is P times Q which is 339
+Q minus Q squared so your marginal
+
+ align:start position:0%
+Q minus Q squared so your marginal
+ 
+
+ align:start position:0%
+Q minus Q squared so your marginal
+revenue function is 339 minus 2q
+
+ align:start position:0%
+revenue function is 339 minus 2q
+ 
+
+ align:start position:0%
+revenue function is 339 minus 2q
+that's your marver to reginal function
+
+ align:start position:0%
+that's your marver to reginal function
+ 
+
+ align:start position:0%
+that's your marver to reginal function
+if you're the monopolist what's your
+
+ align:start position:0%
+if you're the monopolist what's your
+ 
+
+ align:start position:0%
+if you're the monopolist what's your
+marginal cost well already said it's 147
+
+ align:start position:0%
+marginal cost well already said it's 147
+ 
+
+ align:start position:0%
+marginal cost well already said it's 147
+and then you just solve and when you
+
+ align:start position:0%
+and then you just solve and when you
+ 
+
+ align:start position:0%
+and then you just solve and when you
+solve that you get the Q the optimal
+
+ align:start position:0%
+solve that you get the Q the optimal
+ 
+
+ align:start position:0%
+solve that you get the Q the optimal
+quantity is 96 flights and then how do
+
+ align:start position:0%
+quantity is 96 flights and then how do
+ 
+
+ align:start position:0%
+quantity is 96 flights and then how do
+you get the price how do you get the
+
+ align:start position:0%
+you get the price how do you get the
+ 
+
+ align:start position:0%
+you get the price how do you get the
+price of an awfully problem how do we
+
+ align:start position:0%
+price of an awfully problem how do we
+ 
+
+ align:start position:0%
+price of an awfully problem how do we
+know what the what the price is
+
+ align:start position:0%
+know what the what the price is
+ 
+
+ align:start position:0%
+know what the what the price is
+yeah you're gonna plug it back into the
+
+ align:start position:0%
+yeah you're gonna plug it back into the
+ 
+
+ align:start position:0%
+yeah you're gonna plug it back into the
+demand curve you got to take that
+
+ align:start position:0%
+demand curve you got to take that
+ 
+
+ align:start position:0%
+demand curve you got to take that
+quantity plug it back to the main curve
+
+ align:start position:0%
+quantity plug it back to the main curve
+ 
+
+ align:start position:0%
+quantity plug it back to the main curve
+so the price is 339 minus 96 or 243 okay
+
+ align:start position:0%
+so the price is 339 minus 96 or 243 okay
+ 
+
+ align:start position:0%
+so the price is 339 minus 96 or 243 okay
+so I just solved the monopoly problem
+
+ align:start position:0%
+so I just solved the monopoly problem
+ 
+
+ align:start position:0%
+so I just solved the monopoly problem
+quickly but that's um but that's what we
+
+ align:start position:0%
+quickly but that's um but that's what we
+ 
+
+ align:start position:0%
+quickly but that's um but that's what we
+did what we've done already in this
+
+ align:start position:0%
+did what we've done already in this
+ 
+
+ align:start position:0%
+did what we've done already in this
+class and you could see that in the
+
+ align:start position:0%
+class and you could see that in the
+ 
+
+ align:start position:0%
+class and you could see that in the
+graph here okay in Figure 13 1 you've
+
+ align:start position:0%
+graph here okay in Figure 13 1 you've
+ 
+
+ align:start position:0%
+graph here okay in Figure 13 1 you've
+got demand curve which is 3 P equals 339
+
+ align:start position:0%
+got demand curve which is 3 P equals 339
+ 
+
+ align:start position:0%
+got demand curve which is 3 P equals 339
+minus Q you've got a supply curve which
+
+ align:start position:0%
+minus Q you've got a supply curve which
+ 
+
+ align:start position:0%
+minus Q you've got a supply curve which
+is a flat marginal cost at 147 you
+
+ align:start position:0%
+is a flat marginal cost at 147 you
+ 
+
+ align:start position:0%
+is a flat marginal cost at 147 you
+develop a marginal revenue function
+
+ align:start position:0%
+develop a marginal revenue function
+ 
+
+ align:start position:0%
+develop a marginal revenue function
+which is 339 minus 2q as in our previous
+
+ align:start position:0%
+which is 339 minus 2q as in our previous
+ 
+
+ align:start position:0%
+which is 339 minus 2q as in our previous
+example that's just basically an inward
+
+ align:start position:0%
+example that's just basically an inward
+ 
+
+ align:start position:0%
+example that's just basically an inward
+shift of the demand function that
+
+ align:start position:0%
+shift of the demand function that
+ 
+
+ align:start position:0%
+shift of the demand function that
+intersects marginal cost at 96 flights
+
+ align:start position:0%
+intersects marginal cost at 96 flights
+ 
+
+ align:start position:0%
+intersects marginal cost at 96 flights
+okay we have this a thousand passengers
+
+ align:start position:0%
+okay we have this a thousand passengers
+ 
+
+ align:start position:0%
+okay we have this a thousand passengers
+per quarter doesn't really matter the
+
+ align:start position:0%
+per quarter doesn't really matter the
+ 
+
+ align:start position:0%
+per quarter doesn't really matter the
+unit's ignore the you know it's just all
+
+ align:start position:0%
+unit's ignore the you know it's just all
+ 
+
+ align:start position:0%
+unit's ignore the you know it's just all
+standardization okay and then to get the
+
+ align:start position:0%
+standardization okay and then to get the
+ 
+
+ align:start position:0%
+standardization okay and then to get the
+price you read it off the demand curve
+
+ align:start position:0%
+price you read it off the demand curve
+ 
+
+ align:start position:0%
+price you read it off the demand curve
+you say ninety six flights means a price
+
+ align:start position:0%
+you say ninety six flights means a price
+ 
+
+ align:start position:0%
+you say ninety six flights means a price
+of 243 first flight okay that's what we
+
+ align:start position:0%
+of 243 first flight okay that's what we
+ 
+
+ align:start position:0%
+of 243 first flight okay that's what we
+do if American was a monopolist now
+
+ align:start position:0%
+do if American was a monopolist now
+ 
+
+ align:start position:0%
+do if American was a monopolist now
+however Americans not a monopolist
+
+ align:start position:0%
+however Americans not a monopolist
+ 
+
+ align:start position:0%
+however Americans not a monopolist
+American deals with United and American
+
+ align:start position:0%
+American deals with United and American
+ 
+
+ align:start position:0%
+American deals with United and American
+doesn't know what United's going to do
+
+ align:start position:0%
+doesn't know what United's going to do
+ 
+
+ align:start position:0%
+doesn't know what United's going to do
+so what does American do well let's say
+
+ align:start position:0%
+so what does American do well let's say
+ 
+
+ align:start position:0%
+so what does American do well let's say
+America now has to deal with the fact
+
+ align:start position:0%
+America now has to deal with the fact
+ 
+
+ align:start position:0%
+America now has to deal with the fact
+that the evening has to recognize that
+
+ align:start position:0%
+that the evening has to recognize that
+ 
+
+ align:start position:0%
+that the evening has to recognize that
+the demand it's got its own demand
+
+ align:start position:0%
+the demand it's got its own demand
+ 
+
+ align:start position:0%
+the demand it's got its own demand
+function Q a which is the total quantity
+
+ align:start position:0%
+function Q a which is the total quantity
+ 
+
+ align:start position:0%
+function Q a which is the total quantity
+in the market minus Q you okay
+
+ align:start position:0%
+in the market minus Q you okay
+ 
+
+ align:start position:0%
+in the market minus Q you okay
+so it has a residual demand function
+
+ align:start position:0%
+so it has a residual demand function
+ 
+
+ align:start position:0%
+so it has a residual demand function
+which is the total demand in the market
+
+ align:start position:0%
+which is the total demand in the market
+ 
+
+ align:start position:0%
+which is the total demand in the market
+- what United sells
+
+ align:start position:0%
+- what United sells
+ 
+
+ align:start position:0%
+- what United sells
+okay so suppose for example American
+
+ align:start position:0%
+okay so suppose for example American
+ 
+
+ align:start position:0%
+okay so suppose for example American
+thinks Americans got a spy inside United
+
+ align:start position:0%
+thinks Americans got a spy inside United
+ 
+
+ align:start position:0%
+thinks Americans got a spy inside United
+an American says ha
+
+ align:start position:0%
+an American says ha
+ 
+
+ align:start position:0%
+an American says ha
+I think United's gonna fly 64 flights ok
+
+ align:start position:0%
+I think United's gonna fly 64 flights ok
+ 
+
+ align:start position:0%
+I think United's gonna fly 64 flights ok
+so imagine America thinks United's gonna
+
+ align:start position:0%
+so imagine America thinks United's gonna
+ 
+
+ align:start position:0%
+so imagine America thinks United's gonna
+fly 64 64 flights well in that case it
+
+ align:start position:0%
+fly 64 64 flights well in that case it
+ 
+
+ align:start position:0%
+fly 64 64 flights well in that case it
+would say well in that case my arm if
+
+ align:start position:0%
+would say well in that case my arm if
+ 
+
+ align:start position:0%
+would say well in that case my arm if
+they're gonna fight 64 flights then my
+
+ align:start position:0%
+they're gonna fight 64 flights then my
+ 
+
+ align:start position:0%
+they're gonna fight 64 flights then my
+demand function is P sub a equals 339
+
+ align:start position:0%
+demand function is P sub a equals 339
+ 
+
+ align:start position:0%
+demand function is P sub a equals 339
+minus Q sub a minus 64 right because the
+
+ align:start position:0%
+minus Q sub a minus 64 right because the
+ 
+
+ align:start position:0%
+minus Q sub a minus 64 right because the
+big quantity okay the big quantity is is
+
+ align:start position:0%
+big quantity okay the big quantity is is
+ 
+
+ align:start position:0%
+big quantity okay the big quantity is is
+little Q a plus little Q U so my demand
+
+ align:start position:0%
+little Q a plus little Q U so my demand
+ 
+
+ align:start position:0%
+little Q a plus little Q U so my demand
+function is 339 minus Q sub a minus 64
+
+ align:start position:0%
+function is 339 minus Q sub a minus 64
+ 
+
+ align:start position:0%
+function is 339 minus Q sub a minus 64
+okay or in other words my residual
+
+ align:start position:0%
+okay or in other words my residual
+ 
+
+ align:start position:0%
+okay or in other words my residual
+demand function is that P sub a equals
+
+ align:start position:0%
+demand function is that P sub a equals
+ 
+
+ align:start position:0%
+demand function is that P sub a equals
+339 equals
+
+ align:start position:0%
+339 equals
+ 
+
+ align:start position:0%
+339 equals
+275 275 minus QA so if I think United's
+
+ align:start position:0%
+275 275 minus QA so if I think United's
+ 
+
+ align:start position:0%
+275 275 minus QA so if I think United's
+gonna fly 64 flights then my effective
+
+ align:start position:0%
+gonna fly 64 flights then my effective
+ 
+
+ align:start position:0%
+gonna fly 64 flights then my effective
+demand function is 275 minus Q and then
+
+ align:start position:0%
+demand function is 275 minus Q and then
+ 
+
+ align:start position:0%
+demand function is 275 minus Q and then
+I'm done then I just solve for what
+
+ align:start position:0%
+I'm done then I just solve for what
+ 
+
+ align:start position:0%
+I'm done then I just solve for what
+would I do as a monopolist given the
+
+ align:start position:0%
+would I do as a monopolist given the
+ 
+
+ align:start position:0%
+would I do as a monopolist given the
+other guys flying 64 flights so you can
+
+ align:start position:0%
+other guys flying 64 flights so you can
+ 
+
+ align:start position:0%
+other guys flying 64 flights so you can
+see that in Figure 13 - okay so I have a
+
+ align:start position:0%
+see that in Figure 13 - okay so I have a
+ 
+
+ align:start position:0%
+see that in Figure 13 - okay so I have a
+demand function I say well if United's
+
+ align:start position:0%
+demand function I say well if United's
+ 
+
+ align:start position:0%
+demand function I say well if United's
+gonna fly 64 flights that demand
+
+ align:start position:0%
+gonna fly 64 flights that demand
+ 
+
+ align:start position:0%
+gonna fly 64 flights that demand
+function gets shifted in by 64 and then
+
+ align:start position:0%
+function gets shifted in by 64 and then
+ 
+
+ align:start position:0%
+function gets shifted in by 64 and then
+the same thing I did before I solve for
+
+ align:start position:0%
+the same thing I did before I solve for
+ 
+
+ align:start position:0%
+the same thing I did before I solve for
+marginal revenue okay I solve for
+
+ align:start position:0%
+marginal revenue okay I solve for
+ 
+
+ align:start position:0%
+marginal revenue okay I solve for
+marginal revenue and I intersect that
+
+ align:start position:0%
+marginal revenue and I intersect that
+ 
+
+ align:start position:0%
+marginal revenue and I intersect that
+with marginal cost that's gonna happen
+
+ align:start position:0%
+with marginal cost that's gonna happen
+ 
+
+ align:start position:0%
+with marginal cost that's gonna happen
+at 64 flights and a price of 211 okay so
+
+ align:start position:0%
+at 64 flights and a price of 211 okay so
+ 
+
+ align:start position:0%
+at 64 flights and a price of 211 okay so
+basically it's the same exercise it's
+
+ align:start position:0%
+basically it's the same exercise it's
+ 
+
+ align:start position:0%
+basically it's the same exercise it's
+not that hard you just first take out
+
+ align:start position:0%
+not that hard you just first take out
+ 
+
+ align:start position:0%
+not that hard you just first take out
+what United's gonna do the problem is
+
+ align:start position:0%
+what United's gonna do the problem is
+ 
+
+ align:start position:0%
+what United's gonna do the problem is
+American doesn't have a spy they don't
+
+ align:start position:0%
+American doesn't have a spy they don't
+ 
+
+ align:start position:0%
+American doesn't have a spy they don't
+really know what United's gonna do they
+
+ align:start position:0%
+really know what United's gonna do they
+ 
+
+ align:start position:0%
+really know what United's gonna do they
+have to essentially up a strategy given
+
+ align:start position:0%
+have to essentially up a strategy given
+ 
+
+ align:start position:0%
+have to essentially up a strategy given
+the possibilities of what United might
+
+ align:start position:0%
+the possibilities of what United might
+ 
+
+ align:start position:0%
+the possibilities of what United might
+do they have to say look I don't know
+
+ align:start position:0%
+do they have to say look I don't know
+ 
+
+ align:start position:0%
+do they have to say look I don't know
+what Q sub u is so I have to devise my
+
+ align:start position:0%
+what Q sub u is so I have to devise my
+ 
+
+ align:start position:0%
+what Q sub u is so I have to devise my
+optimal strategy given Q sub u
+
+ align:start position:0%
+optimal strategy given Q sub u
+ 
+
+ align:start position:0%
+optimal strategy given Q sub u
+okay in the Lord's I have to
+
+ align:start position:0%
+okay in the Lord's I have to
+ 
+
+ align:start position:0%
+okay in the Lord's I have to
+simultaneously solve for what I would do
+
+ align:start position:0%
+simultaneously solve for what I would do
+ 
+
+ align:start position:0%
+simultaneously solve for what I would do
+at every possible quantity United would
+
+ align:start position:0%
+at every possible quantity United would
+ 
+
+ align:start position:0%
+at every possible quantity United would
+sell if to solve what I would do for
+
+ align:start position:0%
+sell if to solve what I would do for
+ 
+
+ align:start position:0%
+sell if to solve what I would do for
+every possible quantity I would sell and
+
+ align:start position:0%
+every possible quantity I would sell and
+ 
+
+ align:start position:0%
+every possible quantity I would sell and
+we call this developing your reaction or
+
+ align:start position:0%
+we call this developing your reaction or
+ 
+
+ align:start position:0%
+we call this developing your reaction or
+best response curve your reaction curve
+
+ align:start position:0%
+best response curve your reaction curve
+ 
+
+ align:start position:0%
+best response curve your reaction curve
+or your best response curve which is
+
+ align:start position:0%
+or your best response curve which is
+ 
+
+ align:start position:0%
+or your best response curve which is
+what is the best thing to do given what
+
+ align:start position:0%
+what is the best thing to do given what
+ 
+
+ align:start position:0%
+what is the best thing to do given what
+the other guy is doing what is the best
+
+ align:start position:0%
+the other guy is doing what is the best
+ 
+
+ align:start position:0%
+the other guy is doing what is the best
+thing to do given what the other guys
+
+ align:start position:0%
+thing to do given what the other guys
+ 
+
+ align:start position:0%
+thing to do given what the other guys
+doing okay you can see that in Figure 13
+
+ align:start position:0%
+doing okay you can see that in Figure 13
+ 
+
+ align:start position:0%
+doing okay you can see that in Figure 13
+3 we show how that works okay
+
+ align:start position:0%
+3 we show how that works okay
+ 
+
+ align:start position:0%
+3 we show how that works okay
+that shows best response curves so for
+
+ align:start position:0%
+that shows best response curves so for
+ 
+
+ align:start position:0%
+that shows best response curves so for
+example look at the intersection on the
+
+ align:start position:0%
+example look at the intersection on the
+ 
+
+ align:start position:0%
+example look at the intersection on the
+y-axis where the red line hits the
+
+ align:start position:0%
+y-axis where the red line hits the
+ 
+
+ align:start position:0%
+y-axis where the red line hits the
+vertical hits the y-axis
+
+ align:start position:0%
+vertical hits the y-axis
+ 
+
+ align:start position:0%
+vertical hits the y-axis
+that was our monopoly equilibrium I'm
+
+ align:start position:0%
+that was our monopoly equilibrium I'm
+ 
+
+ align:start position:0%
+that was our monopoly equilibrium I'm
+sorry where the where the I'm sorry
+
+ align:start position:0%
+sorry where the where the I'm sorry
+ 
+
+ align:start position:0%
+sorry where the where the I'm sorry
+where the blue line it's the x-axis my
+
+ align:start position:0%
+where the blue line it's the x-axis my
+ 
+
+ align:start position:0%
+where the blue line it's the x-axis my
+bad we're doing American look at where
+
+ align:start position:0%
+bad we're doing American look at where
+ 
+
+ align:start position:0%
+bad we're doing American look at where
+the blue line hits the x-axis that is
+
+ align:start position:0%
+the blue line hits the x-axis that is
+ 
+
+ align:start position:0%
+the blue line hits the x-axis that is
+assuming zero united flights right where
+
+ align:start position:0%
+assuming zero united flights right where
+ 
+
+ align:start position:0%
+assuming zero united flights right where
+the blue line it's the x-axis is where
+
+ align:start position:0%
+the blue line it's the x-axis is where
+ 
+
+ align:start position:0%
+the blue line it's the x-axis is where
+the zero united flights
+
+ align:start position:0%
+the zero united flights
+ 
+
+ align:start position:0%
+the zero united flights
+well we know what american would do
+
+ align:start position:0%
+well we know what american would do
+ 
+
+ align:start position:0%
+well we know what american would do
+there they would fly 96 flights we
+
+ align:start position:0%
+there they would fly 96 flights we
+ 
+
+ align:start position:0%
+there they would fly 96 flights we
+already solve that now look at the point
+
+ align:start position:0%
+already solve that now look at the point
+ 
+
+ align:start position:0%
+already solve that now look at the point
+the point where United is flying 64
+
+ align:start position:0%
+the point where United is flying 64
+ 
+
+ align:start position:0%
+the point where United is flying 64
+flights
+
+ align:start position:0%
+flights
+ 
+
+ align:start position:0%
+flights
+well we also know what American would do
+
+ align:start position:0%
+well we also know what American would do
+ 
+
+ align:start position:0%
+well we also know what American would do
+then we read off the wheat we know that
+
+ align:start position:0%
+then we read off the wheat we know that
+ 
+
+ align:start position:0%
+then we read off the wheat we know that
+we solved in the previous figure they
+
+ align:start position:0%
+we solved in the previous figure they
+ 
+
+ align:start position:0%
+we solved in the previous figure they
+would then do 64 flights and in general
+
+ align:start position:0%
+would then do 64 flights and in general
+ 
+
+ align:start position:0%
+would then do 64 flights and in general
+what that blue line is is for every
+
+ align:start position:0%
+what that blue line is is for every
+ 
+
+ align:start position:0%
+what that blue line is is for every
+quantity that United flies what does
+
+ align:start position:0%
+quantity that United flies what does
+ 
+
+ align:start position:0%
+quantity that United flies what does
+American want to fly okay now let's
+
+ align:start position:0%
+American want to fly okay now let's
+ 
+
+ align:start position:0%
+American want to fly okay now let's
+actually do and so meanwhile United is
+
+ align:start position:0%
+actually do and so meanwhile United is
+ 
+
+ align:start position:0%
+actually do and so meanwhile United is
+doing the same mathematics imagine to
+
+ align:start position:0%
+doing the same mathematics imagine to
+ 
+
+ align:start position:0%
+doing the same mathematics imagine to
+make life easy will almost always do
+
+ align:start position:0%
+make life easy will almost always do
+ 
+
+ align:start position:0%
+make life easy will almost always do
+this to make life easy
+
+ align:start position:0%
+this to make life easy
+ 
+
+ align:start position:0%
+this to make life easy
+imagine United has the same marginal
+
+ align:start position:0%
+imagine United has the same marginal
+ 
+
+ align:start position:0%
+imagine United has the same marginal
+cost American and obviously faces the
+
+ align:start position:0%
+cost American and obviously faces the
+ 
+
+ align:start position:0%
+cost American and obviously faces the
+same market demand curve
+
+ align:start position:0%
+same market demand curve
+ 
+
+ align:start position:0%
+same market demand curve
+well then literally their math is
+
+ align:start position:0%
+well then literally their math is
+ 
+
+ align:start position:0%
+well then literally their math is
+totally symmetric if American was it in
+
+ align:start position:0%
+totally symmetric if American was it in
+ 
+
+ align:start position:0%
+totally symmetric if American was it in
+the market you'd have with the red line
+
+ align:start position:0%
+the market you'd have with the red line
+ 
+
+ align:start position:0%
+the market you'd have with the red line
+intersects the vertical axis if American
+
+ align:start position:0%
+intersects the vertical axis if American
+ 
+
+ align:start position:0%
+intersects the vertical axis if American
+was flying 0 united with fly 96 light
+
+ align:start position:0%
+was flying 0 united with fly 96 light
+ 
+
+ align:start position:0%
+was flying 0 united with fly 96 light
+because their problem is identical to
+
+ align:start position:0%
+because their problem is identical to
+ 
+
+ align:start position:0%
+because their problem is identical to
+Americans monopoly problem likewise so
+
+ align:start position:0%
+Americans monopoly problem likewise so
+ 
+
+ align:start position:0%
+Americans monopoly problem likewise so
+that red the red line is united best
+
+ align:start position:0%
+that red the red line is united best
+ 
+
+ align:start position:0%
+that red the red line is united best
+response curve so we've graphed for
+
+ align:start position:0%
+response curve so we've graphed for
+ 
+
+ align:start position:0%
+response curve so we've graphed for
+every possible amount of flights that
+
+ align:start position:0%
+every possible amount of flights that
+ 
+
+ align:start position:0%
+every possible amount of flights that
+United does what's Americans optimal
+
+ align:start position:0%
+United does what's Americans optimal
+ 
+
+ align:start position:0%
+United does what's Americans optimal
+amount of flights we've solved for every
+
+ align:start position:0%
+amount of flights we've solved for every
+ 
+
+ align:start position:0%
+amount of flights we've solved for every
+amount of flights that American does
+
+ align:start position:0%
+amount of flights that American does
+ 
+
+ align:start position:0%
+amount of flights that American does
+which United off the amount of flights
+
+ align:start position:0%
+which United off the amount of flights
+ 
+
+ align:start position:0%
+which United off the amount of flights
+where those lines intersect is the
+
+ align:start position:0%
+where those lines intersect is the
+ 
+
+ align:start position:0%
+where those lines intersect is the
+cournot equilibrium why is that the
+
+ align:start position:0%
+cournot equilibrium why is that the
+ 
+
+ align:start position:0%
+cournot equilibrium why is that the
+konoka Librium because at that point
+
+ align:start position:0%
+konoka Librium because at that point
+ 
+
+ align:start position:0%
+konoka Librium because at that point
+both firms are doing the best they can
+
+ align:start position:0%
+both firms are doing the best they can
+ 
+
+ align:start position:0%
+both firms are doing the best they can
+give them what the other firms chosen in
+
+ align:start position:0%
+give them what the other firms chosen in
+ 
+
+ align:start position:0%
+give them what the other firms chosen in
+other words to say this is given what
+
+ align:start position:0%
+other words to say this is given what
+ 
+
+ align:start position:0%
+other words to say this is given what
+the other firms doing neither firm wants
+
+ align:start position:0%
+the other firms doing neither firm wants
+ 
+
+ align:start position:0%
+the other firms doing neither firm wants
+to deviate the profit maximizing choice
+
+ align:start position:0%
+to deviate the profit maximizing choice
+ 
+
+ align:start position:0%
+to deviate the profit maximizing choice
+is to be where they are given the other
+
+ align:start position:0%
+is to be where they are given the other
+ 
+
+ align:start position:0%
+is to be where they are given the other
+firms behavior okay so basically the
+
+ align:start position:0%
+firms behavior okay so basically the
+ 
+
+ align:start position:0%
+firms behavior okay so basically the
+cournot equilibrium is the only
+
+ align:start position:0%
+cournot equilibrium is the only
+ 
+
+ align:start position:0%
+cournot equilibrium is the only
+equilibrium that's possible
+
+ align:start position:0%
+equilibrium that's possible
+ 
+
+ align:start position:0%
+equilibrium that's possible
+in this market okay so and why is that
+
+ align:start position:0%
+in this market okay so and why is that
+ 
+
+ align:start position:0%
+in this market okay so and why is that
+so for example imagine that American
+
+ align:start position:0%
+so for example imagine that American
+ 
+
+ align:start position:0%
+so for example imagine that American
+came in and said look I like doing 96
+
+ align:start position:0%
+came in and said look I like doing 96
+ 
+
+ align:start position:0%
+came in and said look I like doing 96
+flights
+
+ align:start position:0%
+flights
+ 
+
+ align:start position:0%
+flights
+I love being monopolist I'm just dude 96
+
+ align:start position:0%
+I love being monopolist I'm just dude 96
+ 
+
+ align:start position:0%
+I love being monopolist I'm just dude 96
+flights and I'm gonna charge vomited
+
+ align:start position:0%
+flights and I'm gonna charge vomited
+ 
+
+ align:start position:0%
+flights and I'm gonna charge vomited
+nine six flights I'm in charge of $43
+
+ align:start position:0%
+nine six flights I'm in charge of $43
+ 
+
+ align:start position:0%
+nine six flights I'm in charge of $43
+well in that case American United I'm
+
+ align:start position:0%
+well in that case American United I'm
+ 
+
+ align:start position:0%
+well in that case American United I'm
+sorry would happily come in at two
+
+ align:start position:0%
+sorry would happily come in at two
+ 
+
+ align:start position:0%
+sorry would happily come in at two
+hundred and forty two dollars and
+
+ align:start position:0%
+hundred and forty two dollars and
+ 
+
+ align:start position:0%
+hundred and forty two dollars and
+undercut them and sell lots of flights
+
+ align:start position:0%
+undercut them and sell lots of flights
+ 
+
+ align:start position:0%
+undercut them and sell lots of flights
+because that's still well above marginal
+
+ align:start position:0%
+because that's still well above marginal
+ 
+
+ align:start position:0%
+because that's still well above marginal
+cost so that's not an equilibrium
+
+ align:start position:0%
+cost so that's not an equilibrium
+ 
+
+ align:start position:0%
+cost so that's not an equilibrium
+because because United and American are
+
+ align:start position:0%
+because because United and American are
+ 
+
+ align:start position:0%
+because because United and American are
+choosing different outcomes it's only I
+
+ align:start position:0%
+choosing different outcomes it's only I
+ 
+
+ align:start position:0%
+choosing different outcomes it's only I
+could have they both it's they're both
+
+ align:start position:0%
+could have they both it's they're both
+ 
+
+ align:start position:0%
+could have they both it's they're both
+to the point where the same outcome
+
+ align:start position:0%
+to the point where the same outcome
+ 
+
+ align:start position:0%
+to the point where the same outcome
+makes them both happy okay so that's the
+
+ align:start position:0%
+makes them both happy okay so that's the
+ 
+
+ align:start position:0%
+makes them both happy okay so that's the
+graphics let's actually do the let's do
+
+ align:start position:0%
+graphics let's actually do the let's do
+ 
+
+ align:start position:0%
+graphics let's actually do the let's do
+the math here let's do the cournot math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in general the residual demand for
+
+ align:start position:0%
+okay in general the residual demand for
+ 
+
+ align:start position:0%
+okay in general the residual demand for
+American is that P equals 339 minus Q a
+
+ align:start position:0%
+American is that P equals 339 minus Q a
+ 
+
+ align:start position:0%
+American is that P equals 339 minus Q a
+minus Q you okay remember big Q is Q a
+
+ align:start position:0%
+minus Q you okay remember big Q is Q a
+ 
+
+ align:start position:0%
+minus Q you okay remember big Q is Q a
+plus Q you so since big Q since the
+
+ align:start position:0%
+plus Q you so since big Q since the
+ 
+
+ align:start position:0%
+plus Q you so since big Q since the
+demand function is 339 minus big Q I
+
+ align:start position:0%
+demand function is 339 minus big Q I
+ 
+
+ align:start position:0%
+demand function is 339 minus big Q I
+simply broke big Q into Q a and Q you
+
+ align:start position:0%
+simply broke big Q into Q a and Q you
+ 
+
+ align:start position:0%
+simply broke big Q into Q a and Q you
+okay it's not meat this all unclear
+
+ align:start position:0%
+okay it's not meat this all unclear
+ 
+
+ align:start position:0%
+okay it's not meat this all unclear
+simply broke up the big Q into those two
+
+ align:start position:0%
+simply broke up the big Q into those two
+ 
+
+ align:start position:0%
+simply broke up the big Q into those two
+components so that means that Americans
+
+ align:start position:0%
+components so that means that Americans
+ 
+
+ align:start position:0%
+components so that means that Americans
+revenue function that's called revenue a
+
+ align:start position:0%
+revenue function that's called revenue a
+ 
+
+ align:start position:0%
+revenue function that's called revenue a
+revenue for American is 339 times Q a
+
+ align:start position:0%
+revenue for American is 339 times Q a
+ 
+
+ align:start position:0%
+revenue for American is 339 times Q a
+minus Q a squared minus Q aqu this is a
+
+ align:start position:0%
+minus Q a squared minus Q aqu this is a
+ 
+
+ align:start position:0%
+minus Q a squared minus Q aqu this is a
+new term this was the old this was the
+
+ align:start position:0%
+new term this was the old this was the
+ 
+
+ align:start position:0%
+new term this was the old this was the
+old revenue function we had when they
+
+ align:start position:0%
+old revenue function we had when they
+ 
+
+ align:start position:0%
+old revenue function we had when they
+were innopolis now I've got this new
+
+ align:start position:0%
+were innopolis now I've got this new
+ 
+
+ align:start position:0%
+were innopolis now I've got this new
+term that didn't exist before
+
+ align:start position:0%
+term that didn't exist before
+ 
+
+ align:start position:0%
+term that didn't exist before
+so that means their marginal revenue for
+
+ align:start position:0%
+so that means their marginal revenue for
+ 
+
+ align:start position:0%
+so that means their marginal revenue for
+American is now 339 minus 2q a minus Q U
+
+ align:start position:0%
+American is now 339 minus 2q a minus Q U
+ 
+
+ align:start position:0%
+American is now 339 minus 2q a minus Q U
+so now their marginal revenue is
+
+ align:start position:0%
+so now their marginal revenue is
+ 
+
+ align:start position:0%
+so now their marginal revenue is
+actually a function of their own
+
+ align:start position:0%
+actually a function of their own
+ 
+
+ align:start position:0%
+actually a function of their own
+behavior but their competitors behavior
+
+ align:start position:0%
+behavior but their competitors behavior
+ 
+
+ align:start position:0%
+behavior but their competitors behavior
+that's the new marginal revenue function
+
+ align:start position:0%
+that's the new marginal revenue function
+ 
+
+ align:start position:0%
+that's the new marginal revenue function
+okay now but the profit maximization
+
+ align:start position:0%
+okay now but the profit maximization
+ 
+
+ align:start position:0%
+okay now but the profit maximization
+rules the same you just set that equal
+
+ align:start position:0%
+rules the same you just set that equal
+ 
+
+ align:start position:0%
+rules the same you just set that equal
+to marginal cost
+
+ align:start position:0%
+to marginal cost
+ 
+
+ align:start position:0%
+to marginal cost
+she said equal to 147 and you solve and
+
+ align:start position:0%
+she said equal to 147 and you solve and
+ 
+
+ align:start position:0%
+she said equal to 147 and you solve and
+what you end up getting is the Q sub a
+
+ align:start position:0%
+what you end up getting is the Q sub a
+ 
+
+ align:start position:0%
+what you end up getting is the Q sub a
+star the outcome Q sub a is 96 minus
+
+ align:start position:0%
+star the outcome Q sub a is 96 minus
+ 
+
+ align:start position:0%
+star the outcome Q sub a is 96 minus
+one-half Q U star or qu q a star is 96
+
+ align:start position:0%
+one-half Q U star or qu q a star is 96
+ 
+
+ align:start position:0%
+one-half Q U star or qu q a star is 96
+minus one-half qu if you solve this
+
+ align:start position:0%
+minus one-half qu if you solve this
+ 
+
+ align:start position:0%
+minus one-half qu if you solve this
+equation that's what you get that's
+
+ align:start position:0%
+equation that's what you get that's
+ 
+
+ align:start position:0%
+equation that's what you get that's
+one-half one-half qu so now we have the
+
+ align:start position:0%
+one-half one-half qu so now we have the
+ 
+
+ align:start position:0%
+one-half one-half qu so now we have the
+optimal quantity but it's a function
+
+ align:start position:0%
+optimal quantity but it's a function
+ 
+
+ align:start position:0%
+optimal quantity but it's a function
+what the other guy does that's a problem
+
+ align:start position:0%
+what the other guy does that's a problem
+ 
+
+ align:start position:0%
+what the other guy does that's a problem
+except that we use the same math for
+
+ align:start position:0%
+except that we use the same math for
+ 
+
+ align:start position:0%
+except that we use the same math for
+United now if the problem symmetric you
+
+ align:start position:0%
+United now if the problem symmetric you
+ 
+
+ align:start position:0%
+United now if the problem symmetric you
+don't have to do the math again you know
+
+ align:start position:0%
+don't have to do the math again you know
+ 
+
+ align:start position:0%
+don't have to do the math again you know
+the best response function will be
+
+ align:start position:0%
+the best response function will be
+ 
+
+ align:start position:0%
+the best response function will be
+symmetric but that won't always be the
+
+ align:start position:0%
+symmetric but that won't always be the
+ 
+
+ align:start position:0%
+symmetric but that won't always be the
+case so I'm gonna do a shortcut here of
+
+ align:start position:0%
+case so I'm gonna do a shortcut here of
+ 
+
+ align:start position:0%
+case so I'm gonna do a shortcut here of
+saying the best response function for Q
+
+ align:start position:0%
+saying the best response function for Q
+ 
+
+ align:start position:0%
+saying the best response function for Q
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+is Q star u equals 96 minus 1/2 QA okay
+
+ align:start position:0%
+is Q star u equals 96 minus 1/2 QA okay
+ 
+
+ align:start position:0%
+is Q star u equals 96 minus 1/2 QA okay
+so I've just written down their best
+
+ align:start position:0%
+so I've just written down their best
+ 
+
+ align:start position:0%
+so I've just written down their best
+response functions correspond to the
+
+ align:start position:0%
+response functions correspond to the
+ 
+
+ align:start position:0%
+response functions correspond to the
+graph look at the so Q star a that's the
+
+ align:start position:0%
+graph look at the so Q star a that's the
+ 
+
+ align:start position:0%
+graph look at the so Q star a that's the
+blue line it's 96 minus one-half Q you
+
+ align:start position:0%
+blue line it's 96 minus one-half Q you
+ 
+
+ align:start position:0%
+blue line it's 96 minus one-half Q you
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+choose star u that's a red line 96 minus
+
+ align:start position:0%
+choose star u that's a red line 96 minus
+ 
+
+ align:start position:0%
+choose star u that's a red line 96 minus
+1/2 QA that's the best france function
+
+ align:start position:0%
+1/2 QA that's the best france function
+ 
+
+ align:start position:0%
+1/2 QA that's the best france function
+now once again to remind you i could
+
+ align:start position:0%
+now once again to remind you i could
+ 
+
+ align:start position:0%
+now once again to remind you i could
+simply skip to this step but normally
+
+ align:start position:0%
+simply skip to this step but normally
+ 
+
+ align:start position:0%
+simply skip to this step but normally
+you have to solve through for both firms
+
+ align:start position:0%
+you have to solve through for both firms
+ 
+
+ align:start position:0%
+you have to solve through for both firms
+they might not have identical best
+
+ align:start position:0%
+they might not have identical best
+ 
+
+ align:start position:0%
+they might not have identical best
+response functions or symmetrical best
+
+ align:start position:0%
+response functions or symmetrical best
+ 
+
+ align:start position:0%
+response functions or symmetrical best
+response function well now we're golden
+
+ align:start position:0%
+response function well now we're golden
+ 
+
+ align:start position:0%
+response function well now we're golden
+we have two equations and two unknowns
+
+ align:start position:0%
+we have two equations and two unknowns
+ 
+
+ align:start position:0%
+we have two equations and two unknowns
+we know how to deal with that and you
+
+ align:start position:0%
+we know how to deal with that and you
+ 
+
+ align:start position:0%
+we know how to deal with that and you
+solve them and you get the Q a star
+
+ align:start position:0%
+solve them and you get the Q a star
+ 
+
+ align:start position:0%
+solve them and you get the Q a star
+equals Q u star equals 64 you solve
+
+ align:start position:0%
+equals Q u star equals 64 you solve
+ 
+
+ align:start position:0%
+equals Q u star equals 64 you solve
+those two equations two unknowns okay so
+
+ align:start position:0%
+those two equations two unknowns okay so
+ 
+
+ align:start position:0%
+those two equations two unknowns okay so
+64 it's a solution to that system what's
+
+ align:start position:0%
+64 it's a solution to that system what's
+ 
+
+ align:start position:0%
+64 it's a solution to that system what's
+the price
+
+ align:start position:0%
+the price
+ 
+
+ align:start position:0%
+the price
+so in raise their hand and tell me
+
+ align:start position:0%
+so in raise their hand and tell me
+ 
+
+ align:start position:0%
+so in raise their hand and tell me
+what's the price without looking at the
+
+ align:start position:0%
+what's the price without looking at the
+ 
+
+ align:start position:0%
+what's the price without looking at the
+graph yeah and how did you get that you
+
+ align:start position:0%
+graph yeah and how did you get that you
+ 
+
+ align:start position:0%
+graph yeah and how did you get that you
+gotta plug in 64 twice a lot of you'll
+
+ align:start position:0%
+gotta plug in 64 twice a lot of you'll
+ 
+
+ align:start position:0%
+gotta plug in 64 twice a lot of you'll
+get this wrong you'll say Oh 339 minus
+
+ align:start position:0%
+get this wrong you'll say Oh 339 minus
+ 
+
+ align:start position:0%
+get this wrong you'll say Oh 339 minus
+64 but no its 339 minus 128 because
+
+ align:start position:0%
+64 but no its 339 minus 128 because
+ 
+
+ align:start position:0%
+64 but no its 339 minus 128 because
+they're each flying 64 and the price
+
+ align:start position:0%
+they're each flying 64 and the price
+ 
+
+ align:start position:0%
+they're each flying 64 and the price
+comes from the total demand in the
+
+ align:start position:0%
+comes from the total demand in the
+ 
+
+ align:start position:0%
+comes from the total demand in the
+market so the price is 211 okay that's
+
+ align:start position:0%
+market so the price is 211 okay that's
+ 
+
+ align:start position:0%
+market so the price is 211 okay that's
+an important mistake to avoid a lot of
+
+ align:start position:0%
+an important mistake to avoid a lot of
+ 
+
+ align:start position:0%
+an important mistake to avoid a lot of
+people get here they'll be super excited
+
+ align:start position:0%
+people get here they'll be super excited
+ 
+
+ align:start position:0%
+people get here they'll be super excited
+they're tired they throw the 64 back of
+
+ align:start position:0%
+they're tired they throw the 64 back of
+ 
+
+ align:start position:0%
+they're tired they throw the 64 back of
+the main equation but remember demands a
+
+ align:start position:0%
+the main equation but remember demands a
+ 
+
+ align:start position:0%
+the main equation but remember demands a
+function of the total market if Symetra
+
+ align:start position:0%
+function of the total market if Symetra
+ 
+
+ align:start position:0%
+function of the total market if Symetra
+gluts doing 64 then the price is gonna
+
+ align:start position:0%
+gluts doing 64 then the price is gonna
+ 
+
+ align:start position:0%
+gluts doing 64 then the price is gonna
+be 211 and that is the Nash or cournot
+
+ align:start position:0%
+be 211 and that is the Nash or cournot
+ 
+
+ align:start position:0%
+be 211 and that is the Nash or cournot
+equilibrium both firms are happy to fly
+
+ align:start position:0%
+equilibrium both firms are happy to fly
+ 
+
+ align:start position:0%
+equilibrium both firms are happy to fly
+64 flights at a price of 2 11 neither
+
+ align:start position:0%
+64 flights at a price of 2 11 neither
+ 
+
+ align:start position:0%
+64 flights at a price of 2 11 neither
+firm wants to deviate and you know that
+
+ align:start position:0%
+firm wants to deviate and you know that
+ 
+
+ align:start position:0%
+firm wants to deviate and you know that
+because you've maximized their profits
+
+ align:start position:0%
+because you've maximized their profits
+ 
+
+ align:start position:0%
+because you've maximized their profits
+and the profits for American are
+
+ align:start position:0%
+and the profits for American are
+ 
+
+ align:start position:0%
+and the profits for American are
+maximized when United's lying 64 the
+
+ align:start position:0%
+maximized when United's lying 64 the
+ 
+
+ align:start position:0%
+maximized when United's lying 64 the
+profits to American are maximized at
+
+ align:start position:0%
+profits to American are maximized at
+ 
+
+ align:start position:0%
+profits to American are maximized at
+flying 64 when Americans flying 64 the
+
+ align:start position:0%
+flying 64 when Americans flying 64 the
+ 
+
+ align:start position:0%
+flying 64 when Americans flying 64 the
+profits for United are maximized at
+
+ align:start position:0%
+profits for United are maximized at
+ 
+
+ align:start position:0%
+profits for United are maximized at
+flying 64 therefore that is the national
+
+ align:start position:0%
+flying 64 therefore that is the national
+ 
+
+ align:start position:0%
+flying 64 therefore that is the national
+equilibrium okay now when we get to
+
+ align:start position:0%
+equilibrium okay now when we get to
+ 
+
+ align:start position:0%
+equilibrium okay now when we get to
+reality things might not always work out
+
+ align:start position:0%
+reality things might not always work out
+ 
+
+ align:start position:0%
+reality things might not always work out
+so neatly things might not be symmetric
+
+ align:start position:0%
+so neatly things might not be symmetric
+ 
+
+ align:start position:0%
+so neatly things might not be symmetric
+you might also not have an equilibrium
+
+ align:start position:0%
+you might also not have an equilibrium
+ 
+
+ align:start position:0%
+you might also not have an equilibrium
+how could you not have an equilibrium
+
+ align:start position:0%
+how could you not have an equilibrium
+ 
+
+ align:start position:0%
+how could you not have an equilibrium
+here how could that happen
+
+ align:start position:0%
+here how could that happen
+ 
+
+ align:start position:0%
+here how could that happen
+graphically what would that mean yeah
+
+ align:start position:0%
+graphically what would that mean yeah
+ 
+
+ align:start position:0%
+graphically what would that mean yeah
+yeah the best response occurs might not
+
+ align:start position:0%
+yeah the best response occurs might not
+ 
+
+ align:start position:0%
+yeah the best response occurs might not
+intersect you might not get an
+
+ align:start position:0%
+intersect you might not get an
+ 
+
+ align:start position:0%
+intersect you might not get an
+equilibrium we don't know what the hell
+
+ align:start position:0%
+equilibrium we don't know what the hell
+ 
+
+ align:start position:0%
+equilibrium we don't know what the hell
+to do then all chaos breaks loose okay
+
+ align:start position:0%
+to do then all chaos breaks loose okay
+ 
+
+ align:start position:0%
+to do then all chaos breaks loose okay
+but you might not get a knuckle Librium
+
+ align:start position:0%
+but you might not get a knuckle Librium
+ 
+
+ align:start position:0%
+but you might not get a knuckle Librium
+okay in this market because the best
+
+ align:start position:0%
+okay in this market because the best
+ 
+
+ align:start position:0%
+okay in this market because the best
+response curves might uh might not
+
+ align:start position:0%
+response curves might uh might not
+ 
+
+ align:start position:0%
+response curves might uh might not
+intersect okay
+
+ align:start position:0%
+intersect okay
+ 
+
+ align:start position:0%
+intersect okay
+in reality in life you could have funky
+
+ align:start position:0%
+in reality in life you could have funky
+ 
+
+ align:start position:0%
+in reality in life you could have funky
+best response curves that are nonlinear
+
+ align:start position:0%
+best response curves that are nonlinear
+ 
+
+ align:start position:0%
+best response curves that are nonlinear
+you can have multiple intersections you
+
+ align:start position:0%
+you can have multiple intersections you
+ 
+
+ align:start position:0%
+you can have multiple intersections you
+could have multiple we call multiple
+
+ align:start position:0%
+could have multiple we call multiple
+ 
+
+ align:start position:0%
+could have multiple we call multiple
+equilibria and then it becomes an
+
+ align:start position:0%
+equilibria and then it becomes an
+ 
+
+ align:start position:0%
+equilibria and then it becomes an
+indeterminant problem and you have to
+
+ align:start position:0%
+indeterminant problem and you have to
+ 
+
+ align:start position:0%
+indeterminant problem and you have to
+figure out which equlibrium they settle
+
+ align:start position:0%
+figure out which equlibrium they settle
+ 
+
+ align:start position:0%
+figure out which equlibrium they settle
+at and that involves higher-order
+
+ align:start position:0%
+at and that involves higher-order
+ 
+
+ align:start position:0%
+at and that involves higher-order
+mathematics that you talked about in
+
+ align:start position:0%
+mathematics that you talked about in
+ 
+
+ align:start position:0%
+mathematics that you talked about in
+more advanced classes so this is sort of
+
+ align:start position:0%
+more advanced classes so this is sort of
+ 
+
+ align:start position:0%
+more advanced classes so this is sort of
+the simplest easiest cases symmetric
+
+ align:start position:0%
+the simplest easiest cases symmetric
+ 
+
+ align:start position:0%
+the simplest easiest cases symmetric
+case with linear best response functions
+
+ align:start position:0%
+case with linear best response functions
+ 
+
+ align:start position:0%
+case with linear best response functions
+intersect is your easiest case but in
+
+ align:start position:0%
+intersect is your easiest case but in
+ 
+
+ align:start position:0%
+intersect is your easiest case but in
+general the general way to solve this is
+
+ align:start position:0%
+general the general way to solve this is
+ 
+
+ align:start position:0%
+general the general way to solve this is
+the same which is to look is to use the
+
+ align:start position:0%
+the same which is to look is to use the
+ 
+
+ align:start position:0%
+the same which is to look is to use the
+principle of game theory look go back to
+
+ align:start position:0%
+principle of game theory look go back to
+ 
+
+ align:start position:0%
+principle of game theory look go back to
+the prisoner's dilemma okay all we're
+
+ align:start position:0%
+the prisoner's dilemma okay all we're
+ 
+
+ align:start position:0%
+the prisoner's dilemma okay all we're
+doing here was creating best response
+
+ align:start position:0%
+doing here was creating best response
+ 
+
+ align:start position:0%
+doing here was creating best response
+functions it's just there wasn't a line
+
+ align:start position:0%
+functions it's just there wasn't a line
+ 
+
+ align:start position:0%
+functions it's just there wasn't a line
+it was just a point the best response
+
+ align:start position:0%
+it was just a point the best response
+ 
+
+ align:start position:0%
+it was just a point the best response
+function was what we laid out here all
+
+ align:start position:0%
+function was what we laid out here all
+ 
+
+ align:start position:0%
+function was what we laid out here all
+we do is see United American examples go
+
+ align:start position:0%
+we do is see United American examples go
+ 
+
+ align:start position:0%
+we do is see United American examples go
+to a continuum and about best response
+
+ align:start position:0%
+to a continuum and about best response
+ 
+
+ align:start position:0%
+to a continuum and about best response
+functions is the best response point
+
+ align:start position:0%
+functions is the best response point
+ 
+
+ align:start position:0%
+functions is the best response point
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions okay let's stop there
+
+ align:start position:0%
+other questions okay let's stop there
+ 
+
+ align:start position:0%
+other questions okay let's stop there
+we'll come back next time we'll talk
+
+ align:start position:0%
+we'll come back next time we'll talk
+ 
+
+ align:start position:0%
+we'll come back next time we'll talk
+about why don't we why don't we all just
+
+ align:start position:0%
+about why don't we why don't we all just
+ 
+
+ align:start position:0%
+about why don't we why don't we all just
+get along like mr. Rogers wants
\ No newline at end of file
diff --git a/0x4Jf6hBr-k.txt b/0x4Jf6hBr-k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..394a8a08b1b58c37c6ae1eb8c2a2b7a845d97072
--- /dev/null
+++ b/0x4Jf6hBr-k.txt
@@ -0,0 +1,16699 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a creative common license. Your support
+
+ align:start position:0%
+a creative common license. Your support
+ 
+
+ align:start position:0%
+a creative common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+Courseware at ocw.mmit.edu.
+ 
+
+ align:start position:0%
+Courseware at ocw.mmit.edu.
+>> Before we move on to the rest of the
+
+ align:start position:0%
+>> Before we move on to the rest of the
+ 
+
+ align:start position:0%
+>> Before we move on to the rest of the
+topics, uh maybe just a some
+
+ align:start position:0%
+topics, uh maybe just a some
+ 
+
+ align:start position:0%
+topics, uh maybe just a some
+administrative stuff about the next
+
+ align:start position:0%
+administrative stuff about the next
+ 
+
+ align:start position:0%
+administrative stuff about the next
+assignment. Uh so the idea is to model a
+
+ align:start position:0%
+assignment. Uh so the idea is to model a
+ 
+
+ align:start position:0%
+assignment. Uh so the idea is to model a
+system right? Uh so the idea is to pick
+
+ align:start position:0%
+system right? Uh so the idea is to pick
+ 
+
+ align:start position:0%
+system right? Uh so the idea is to pick
+some sort of the old system. Um
+
+ align:start position:0%
+some sort of the old system. Um
+ 
+
+ align:start position:0%
+some sort of the old system. Um
+in the past people have picked stuff
+
+ align:start position:0%
+in the past people have picked stuff
+ 
+
+ align:start position:0%
+in the past people have picked stuff
+like applying for college because they
+
+ align:start position:0%
+like applying for college because they
+ 
+
+ align:start position:0%
+like applying for college because they
+knew all about that. Uh they you know
+
+ align:start position:0%
+knew all about that. Uh they you know
+ 
+
+ align:start position:0%
+knew all about that. Uh they you know
+people have talked about uh an example I
+
+ align:start position:0%
+people have talked about uh an example I
+ 
+
+ align:start position:0%
+people have talked about uh an example I
+give is you know running a nuclear
+
+ align:start position:0%
+give is you know running a nuclear
+ 
+
+ align:start position:0%
+give is you know running a nuclear
+reactor or something. That's basically
+
+ align:start position:0%
+reactor or something. That's basically
+ 
+
+ align:start position:0%
+reactor or something. That's basically
+there's a there's a uh but hey, you
+
+ align:start position:0%
+there's a there's a uh but hey, you
+ 
+
+ align:start position:0%
+there's a there's a uh but hey, you
+know, if if any of you are new to
+
+ align:start position:0%
+know, if if any of you are new to
+ 
+
+ align:start position:0%
+know, if if any of you are new to
+science majors, you know,
+
+ align:start position:0%
+science majors, you know,
+ 
+
+ align:start position:0%
+science majors, you know,
+>> Oh, perfect. Okay. All right. Well, one
+
+ align:start position:0%
+>> Oh, perfect. Okay. All right. Well, one
+ 
+
+ align:start position:0%
+>> Oh, perfect. Okay. All right. Well, one
+of one of my favorite 2 games was was
+
+ align:start position:0%
+of one of my favorite 2 games was was
+ 
+
+ align:start position:0%
+of one of my favorite 2 games was was
+actually uh nuclear reactor simulation.
+
+ align:start position:0%
+actually uh nuclear reactor simulation.
+ 
+
+ align:start position:0%
+actually uh nuclear reactor simulation.
+It always melted down. That's why it was
+
+ align:start position:0%
+It always melted down. That's why it was
+ 
+
+ align:start position:0%
+It always melted down. That's why it was
+fun. Awesome. Um but yeah, you know,
+
+ align:start position:0%
+fun. Awesome. Um but yeah, you know,
+ 
+
+ align:start position:0%
+fun. Awesome. Um but yeah, you know,
+pick pick a real world system to model
+
+ align:start position:0%
+pick pick a real world system to model
+ 
+
+ align:start position:0%
+pick pick a real world system to model
+um to start uh modeling. Obviously,
+
+ align:start position:0%
+um to start uh modeling. Obviously,
+ 
+
+ align:start position:0%
+um to start uh modeling. Obviously,
+you're trying to find a fun. Obviously,
+
+ align:start position:0%
+you're trying to find a fun. Obviously,
+ 
+
+ align:start position:0%
+you're trying to find a fun. Obviously,
+you're trying to make something that
+
+ align:start position:0%
+you're trying to make something that
+ 
+
+ align:start position:0%
+you're trying to make something that
+people are going to enjoy playing. Uh uh
+
+ align:start position:0%
+people are going to enjoy playing. Uh uh
+ 
+
+ align:start position:0%
+people are going to enjoy playing. Uh uh
+but the the idea is to start from a
+
+ align:start position:0%
+but the the idea is to start from a
+ 
+
+ align:start position:0%
+but the the idea is to start from a
+slightly different place from where we
+
+ align:start position:0%
+slightly different place from where we
+ 
+
+ align:start position:0%
+slightly different place from where we
+had uh uh um in the first assignment.
+
+ align:start position:0%
+had uh uh um in the first assignment.
+ 
+
+ align:start position:0%
+had uh uh um in the first assignment.
+Now, a couple of you guys already did
+
+ align:start position:0%
+Now, a couple of you guys already did
+ 
+
+ align:start position:0%
+Now, a couple of you guys already did
+that for the first assignment though. I
+
+ align:start position:0%
+that for the first assignment though. I
+ 
+
+ align:start position:0%
+that for the first assignment though. I
+mean, things like picking up girls at a
+
+ align:start position:0%
+mean, things like picking up girls at a
+ 
+
+ align:start position:0%
+mean, things like picking up girls at a
+party. I mean, you're modeling real
+
+ align:start position:0%
+party. I mean, you're modeling real
+ 
+
+ align:start position:0%
+party. I mean, you're modeling real
+system in a sense. Uh still haven't
+
+ align:start position:0%
+system in a sense. Uh still haven't
+ 
+
+ align:start position:0%
+system in a sense. Uh still haven't
+played the genealogy game yet. So So, so
+
+ align:start position:0%
+played the genealogy game yet. So So, so
+ 
+
+ align:start position:0%
+played the genealogy game yet. So So, so
+we're going to play that tomorrow. So,
+
+ align:start position:0%
+we're going to play that tomorrow. So,
+ 
+
+ align:start position:0%
+we're going to play that tomorrow. So,
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we'll see that. Um the the survival
+
+ align:start position:0%
+we'll see that. Um the the survival
+ 
+
+ align:start position:0%
+we'll see that. Um the the survival
+horror game I would say is not a real
+
+ align:start position:0%
+horror game I would say is not a real
+ 
+
+ align:start position:0%
+horror game I would say is not a real
+world system.
+
+ align:start position:0%
+world system.
+ 
+
+ align:start position:0%
+world system.
+>> It was a system.
+
+ align:start position:0%
+>> It was a system.
+ 
+
+ align:start position:0%
+>> It was a system.
+>> Tasers.
+
+ align:start position:0%
+>> Tasers.
+ 
+
+ align:start position:0%
+>> Tasers.
+>> Yeah. Or wizards enemies.
+
+ align:start position:0%
+>> Yeah. Or wizards enemies.
+ 
+
+ align:start position:0%
+>> Yeah. Or wizards enemies.
+>> But uh so so yeah, pick pick something.
+
+ align:start position:0%
+>> But uh so so yeah, pick pick something.
+ 
+
+ align:start position:0%
+>> But uh so so yeah, pick pick something.
+Um uh we've seen games um uh negotiating
+
+ align:start position:0%
+Um uh we've seen games um uh negotiating
+ 
+
+ align:start position:0%
+Um uh we've seen games um uh negotiating
+around like negotiating uh greenhouse
+
+ align:start position:0%
+around like negotiating uh greenhouse
+ 
+
+ align:start position:0%
+around like negotiating uh greenhouse
+gas emissions. There was there was one
+
+ align:start position:0%
+gas emissions. There was there was one
+ 
+
+ align:start position:0%
+gas emissions. There was there was one
+uh which was really really cutthroat as
+
+ align:start position:0%
+uh which was really really cutthroat as
+ 
+
+ align:start position:0%
+uh which was really really cutthroat as
+you'll probably imagine.
+
+ align:start position:0%
+you'll probably imagine.
+ 
+
+ align:start position:0%
+you'll probably imagine.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Um actually I'll try to I'll try to get
+
+ align:start position:0%
+>> Um actually I'll try to I'll try to get
+ 
+
+ align:start position:0%
+>> Um actually I'll try to I'll try to get
+the team to come in late in the semester
+
+ align:start position:0%
+the team to come in late in the semester
+ 
+
+ align:start position:0%
+the team to come in late in the semester
+to talk about the card game. Uh this was
+
+ align:start position:0%
+to talk about the card game. Uh this was
+ 
+
+ align:start position:0%
+to talk about the card game. Uh this was
+a freshman team on Periscope.
+
+ align:start position:0%
+a freshman team on Periscope.
+ 
+
+ align:start position:0%
+a freshman team on Periscope.
+Um let's see. Uh you on Wednesday we're
+
+ align:start position:0%
+Um let's see. Uh you on Wednesday we're
+ 
+
+ align:start position:0%
+Um let's see. Uh you on Wednesday we're
+going to do the usual brainstorming
+
+ align:start position:0%
+going to do the usual brainstorming
+ 
+
+ align:start position:0%
+going to do the usual brainstorming
+exercise in the second half of the of
+
+ align:start position:0%
+exercise in the second half of the of
+ 
+
+ align:start position:0%
+exercise in the second half of the of
+the class. You know everybody throw out
+
+ align:start position:0%
+the class. You know everybody throw out
+ 
+
+ align:start position:0%
+the class. You know everybody throw out
+your ideas come in with a bunch of
+
+ align:start position:0%
+your ideas come in with a bunch of
+ 
+
+ align:start position:0%
+your ideas come in with a bunch of
+ideas. We'll try to build on that. Um
+
+ align:start position:0%
+ideas. We'll try to build on that. Um
+ 
+
+ align:start position:0%
+ideas. We'll try to build on that. Um
+but uh this time around you're allowed
+
+ align:start position:0%
+but uh this time around you're allowed
+ 
+
+ align:start position:0%
+but uh this time around you're allowed
+to actually pre-build your team. You
+
+ align:start position:0%
+to actually pre-build your team. You
+ 
+
+ align:start position:0%
+to actually pre-build your team. You
+you're allowed to to to ask people, you
+
+ align:start position:0%
+you're allowed to to to ask people, you
+ 
+
+ align:start position:0%
+you're allowed to to to ask people, you
+know, hey, you guys want to work
+
+ align:start position:0%
+know, hey, you guys want to work
+ 
+
+ align:start position:0%
+know, hey, you guys want to work
+together? Um you don't actually have to
+
+ align:start position:0%
+together? Um you don't actually have to
+ 
+
+ align:start position:0%
+together? Um you don't actually have to
+like figure it out on the spot if you
+
+ align:start position:0%
+like figure it out on the spot if you
+ 
+
+ align:start position:0%
+like figure it out on the spot if you
+don't want to. Um I don't really care
+
+ align:start position:0%
+don't want to. Um I don't really care
+ 
+
+ align:start position:0%
+don't want to. Um I don't really care
+how you do it as long as by Friday you
+
+ align:start position:0%
+how you do it as long as by Friday you
+ 
+
+ align:start position:0%
+how you do it as long as by Friday you
+know who your team is. Um and and who's
+
+ align:start position:0%
+know who your team is. Um and and who's
+ 
+
+ align:start position:0%
+know who your team is. Um and and who's
+on team sizes are are the same.
+
+ align:start position:0%
+on team sizes are are the same.
+ 
+
+ align:start position:0%
+on team sizes are are the same.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+any questions? Are we able to simulate
+
+ align:start position:0%
+any questions? Are we able to simulate
+ 
+
+ align:start position:0%
+any questions? Are we able to simulate
+things that aren't from like this era?
+
+ align:start position:0%
+things that aren't from like this era?
+ 
+
+ align:start position:0%
+things that aren't from like this era?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Okay.
+
+ align:start position:0%
+>> Okay.
+ 
+
+ align:start position:0%
+>> Okay.
+>> Like like from history?
+
+ align:start position:0%
+>> Like like from history?
+ 
+
+ align:start position:0%
+>> Like like from history?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Okay. Not from like the future.
+
+ align:start position:0%
+>> Okay. Not from like the future.
+ 
+
+ align:start position:0%
+>> Okay. Not from like the future.
+>> Oh,
+
+ align:start position:0%
+>> Oh,
+ 
+
+ align:start position:0%
+>> Oh,
+>> no.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Future.
+
+ align:start position:0%
+Future.
+ 
+
+ align:start position:0%
+Future.
+>> Yeah. Yeah. Sure. It's like this is how
+
+ align:start position:0%
+>> Yeah. Yeah. Sure. It's like this is how
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Sure. It's like this is how
+things are going to work.
+
+ align:start position:0%
+things are going to work.
+ 
+
+ align:start position:0%
+things are going to work.
+>> Well, well, I mean I mean Okay. So, so
+
+ align:start position:0%
+>> Well, well, I mean I mean Okay. So, so
+ 
+
+ align:start position:0%
+>> Well, well, I mean I mean Okay. So, so
+yes. Yes. Absolutely. Historical stuff.
+
+ align:start position:0%
+yes. Yes. Absolutely. Historical stuff.
+ 
+
+ align:start position:0%
+yes. Yes. Absolutely. Historical stuff.
+Uh um and but you do have some
+
+ align:start position:0%
+Uh um and but you do have some
+ 
+
+ align:start position:0%
+Uh um and but you do have some
+liberties. Uh I'm not saying that your
+
+ align:start position:0%
+liberties. Uh I'm not saying that your
+ 
+
+ align:start position:0%
+liberties. Uh I'm not saying that your
+game has to be a faithful simulation. Am
+
+ align:start position:0%
+game has to be a faithful simulation. Am
+ 
+
+ align:start position:0%
+game has to be a faithful simulation. Am
+I getting a little bit more into
+
+ align:start position:0%
+I getting a little bit more into
+ 
+
+ align:start position:0%
+I getting a little bit more into
+simulation? say um but it doesn't have
+
+ align:start position:0%
+simulation? say um but it doesn't have
+ 
+
+ align:start position:0%
+simulation? say um but it doesn't have
+to be a faithful simulation necessarily
+
+ align:start position:0%
+to be a faithful simulation necessarily
+ 
+
+ align:start position:0%
+to be a faithful simulation necessarily
+of what you're talking but you know in a
+
+ align:start position:0%
+of what you're talking but you know in a
+ 
+
+ align:start position:0%
+of what you're talking but you know in a
+sense you're trying to like capture the
+
+ align:start position:0%
+sense you're trying to like capture the
+ 
+
+ align:start position:0%
+sense you're trying to like capture the
+spirit of it um you know if if if the
+
+ align:start position:0%
+spirit of it um you know if if if the
+ 
+
+ align:start position:0%
+spirit of it um you know if if if the
+point is I'm running a nuclear reactor
+
+ align:start position:0%
+point is I'm running a nuclear reactor
+ 
+
+ align:start position:0%
+point is I'm running a nuclear reactor
+and you can sort of capture the oh my
+
+ align:start position:0%
+and you can sort of capture the oh my
+ 
+
+ align:start position:0%
+and you can sort of capture the oh my
+god it's so dangerous or the oh my god
+
+ align:start position:0%
+god it's so dangerous or the oh my god
+ 
+
+ align:start position:0%
+god it's so dangerous or the oh my god
+it's so boring aspect of it uh have you
+
+ align:start position:0%
+it's so boring aspect of it uh have you
+ 
+
+ align:start position:0%
+it's so boring aspect of it uh have you
+actually worked on nuclear reactor
+
+ align:start position:0%
+actually worked on nuclear reactor
+ 
+
+ align:start position:0%
+actually worked on nuclear reactor
+>> well there
+
+ align:start position:0%
+>> well there
+ 
+
+ align:start position:0%
+>> well there
+>> and I know like the mechanics of it but
+
+ align:start position:0%
+>> and I know like the mechanics of it but
+ 
+
+ align:start position:0%
+>> and I know like the mechanics of it but
+I think there I I've been told it's not
+
+ align:start position:0%
+I think there I I've been told it's not
+ 
+
+ align:start position:0%
+I think there I I've been told it's not
+necessarily the most exciting job in the
+
+ align:start position:0%
+necessarily the most exciting job in the
+ 
+
+ align:start position:0%
+necessarily the most exciting job in the
+No. Yeah, you just sit there and do your
+
+ align:start position:0%
+No. Yeah, you just sit there and do your
+ 
+
+ align:start position:0%
+No. Yeah, you just sit there and do your
+homework and every once in a while you
+
+ align:start position:0%
+homework and every once in a while you
+ 
+
+ align:start position:0%
+homework and every once in a while you
+look up
+
+ align:start position:0%
+look up
+ 
+
+ align:start position:0%
+look up
+very reasonable
+
+ align:start position:0%
+very reasonable
+ 
+
+ align:start position:0%
+very reasonable
+>> and they get paid for like I know 12 or
+
+ align:start position:0%
+>> and they get paid for like I know 12 or
+ 
+
+ align:start position:0%
+>> and they get paid for like I know 12 or
+13 bucks an hour or something.
+
+ align:start position:0%
+13 bucks an hour or something.
+ 
+
+ align:start position:0%
+13 bucks an hour or something.
+>> Yeah. So, so you know if the whole idea
+
+ align:start position:0%
+>> Yeah. So, so you know if the whole idea
+ 
+
+ align:start position:0%
+>> Yeah. So, so you know if the whole idea
+of the game is let's try try try to get
+
+ align:start position:0%
+of the game is let's try try try to get
+ 
+
+ align:start position:0%
+of the game is let's try try try to get
+as much homework done without
+
+ align:start position:0%
+as much homework done without
+ 
+
+ align:start position:0%
+as much homework done without
+>> that might be more entertaining than
+
+ align:start position:0%
+>> that might be more entertaining than
+ 
+
+ align:start position:0%
+>> that might be more entertaining than
+just like
+
+ align:start position:0%
+just like
+ 
+
+ align:start position:0%
+just like
+>> cool
+
+ align:start position:0%
+>> cool
+ 
+
+ align:start position:0%
+>> cool
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+>> um
+
+ align:start position:0%
+>> um
+ 
+
+ align:start position:0%
+>> um
+but I got my problems then
+
+ align:start position:0%
+but I got my problems then
+ 
+
+ align:start position:0%
+but I got my problems then
+>> just plus one points you have to do
+
+ align:start position:0%
+>> just plus one points you have to do
+ 
+
+ align:start position:0%
+>> just plus one points you have to do
+homework while you play
+
+ align:start position:0%
+homework while you play
+ 
+
+ align:start position:0%
+homework while you play
+>> Wow
+
+ align:start position:0%
+>> Wow
+ 
+
+ align:start position:0%
+>> Wow
+Terrible be the worst game Whatever.
+
+ align:start position:0%
+Terrible be the worst game Whatever.
+ 
+
+ align:start position:0%
+Terrible be the worst game Whatever.
+What happens if you
+
+ align:start position:0%
+What happens if you
+ 
+
+ align:start position:0%
+What happens if you
+>> guys
+
+ align:start position:0%
+>> guys
+ 
+
+ align:start position:0%
+>> guys
+may be too meta at that point?
+
+ align:start position:0%
+may be too meta at that point?
+ 
+
+ align:start position:0%
+may be too meta at that point?
+>> And besides, but I think we still have a
+
+ align:start position:0%
+>> And besides, but I think we still have a
+ 
+
+ align:start position:0%
+>> And besides, but I think we still have a
+time limit like half an hour or
+
+ align:start position:0%
+time limit like half an hour or
+ 
+
+ align:start position:0%
+time limit like half an hour or
+something like that. You know, it's like
+
+ align:start position:0%
+something like that. You know, it's like
+ 
+
+ align:start position:0%
+something like that. You know, it's like
+homework.
+
+ align:start position:0%
+homework.
+ 
+
+ align:start position:0%
+homework.
+>> We have really easy homework.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um, let's see. Just a reminder for
+
+ align:start position:0%
+>> Um, let's see. Just a reminder for
+ 
+
+ align:start position:0%
+>> Um, let's see. Just a reminder for
+everyone who hasn't uh who's been
+
+ align:start position:0%
+everyone who hasn't uh who's been
+ 
+
+ align:start position:0%
+everyone who hasn't uh who's been
+falling off on the forum post, please
+
+ align:start position:0%
+falling off on the forum post, please
+ 
+
+ align:start position:0%
+falling off on the forum post, please
+make sure that you keep up on your forum
+
+ align:start position:0%
+make sure that you keep up on your forum
+ 
+
+ align:start position:0%
+make sure that you keep up on your forum
+post. Those things actually do affect
+
+ align:start position:0%
+post. Those things actually do affect
+ 
+
+ align:start position:0%
+post. Those things actually do affect
+your grade. Uh so um again we're
+
+ align:start position:0%
+your grade. Uh so um again we're
+ 
+
+ align:start position:0%
+your grade. Uh so um again we're
+expecting one in person not one team. Uh
+
+ align:start position:0%
+expecting one in person not one team. Uh
+ 
+
+ align:start position:0%
+expecting one in person not one team. Uh
+so if you have any uh opinions since
+
+ align:start position:0%
+so if you have any uh opinions since
+ 
+
+ align:start position:0%
+so if you have any uh opinions since
+we're in between reading uh assignments
+
+ align:start position:0%
+we're in between reading uh assignments
+ 
+
+ align:start position:0%
+we're in between reading uh assignments
+right right now you can write about the
+
+ align:start position:0%
+right right now you can write about the
+ 
+
+ align:start position:0%
+right right now you can write about the
+assignment but if you wrote up something
+
+ align:start position:0%
+assignment but if you wrote up something
+ 
+
+ align:start position:0%
+assignment but if you wrote up something
+let's say a reflection on how the past
+
+ align:start position:0%
+let's say a reflection on how the past
+ 
+
+ align:start position:0%
+let's say a reflection on how the past
+assignment went. You know that that's
+
+ align:start position:0%
+assignment went. You know that that's
+ 
+
+ align:start position:0%
+assignment went. You know that that's
+fine. We're not expecting more than one
+
+ align:start position:0%
+fine. We're not expecting more than one
+ 
+
+ align:start position:0%
+fine. We're not expecting more than one
+forum post a week. Of course, feel free
+
+ align:start position:0%
+forum post a week. Of course, feel free
+ 
+
+ align:start position:0%
+forum post a week. Of course, feel free
+to comment on other people's forum posts
+
+ align:start position:0%
+to comment on other people's forum posts
+ 
+
+ align:start position:0%
+to comment on other people's forum posts
+as well. And those if you want to like
+
+ align:start position:0%
+as well. And those if you want to like
+ 
+
+ align:start position:0%
+as well. And those if you want to like
+if you if there's a discussion or a
+
+ align:start position:0%
+if you if there's a discussion or a
+ 
+
+ align:start position:0%
+if you if there's a discussion or a
+point that's been raised that's kind of
+
+ align:start position:0%
+point that's been raised that's kind of
+ 
+
+ align:start position:0%
+point that's been raised that's kind of
+interesting and you want to kind of
+
+ align:start position:0%
+interesting and you want to kind of
+ 
+
+ align:start position:0%
+interesting and you want to kind of
+develop on that, you know, put some
+
+ align:start position:0%
+develop on that, you know, put some
+ 
+
+ align:start position:0%
+develop on that, you know, put some
+thought into it. Write something
+
+ align:start position:0%
+thought into it. Write something
+ 
+
+ align:start position:0%
+thought into it. Write something
+interesting that's going to keep on the
+
+ align:start position:0%
+interesting that's going to keep on the
+ 
+
+ align:start position:0%
+interesting that's going to keep on the
+conversation that that counts too. Um
+
+ align:start position:0%
+conversation that that counts too. Um
+ 
+
+ align:start position:0%
+conversation that that counts too. Um
+and and that's fine.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, puddles. Um
+
+ align:start position:0%
+Okay. So, puddles. Um
+ 
+
+ align:start position:0%
+Okay. So, puddles. Um
+so, Brenda's Okay. So actually before I
+
+ align:start position:0%
+so, Brenda's Okay. So actually before I
+ 
+
+ align:start position:0%
+so, Brenda's Okay. So actually before I
+start the renders, let's let's start
+
+ align:start position:0%
+start the renders, let's let's start
+ 
+
+ align:start position:0%
+start the renders, let's let's start
+with Scott's Scott. What what what were
+
+ align:start position:0%
+with Scott's Scott. What what what were
+ 
+
+ align:start position:0%
+with Scott's Scott. What what what were
+some of the definitions or some of the
+
+ align:start position:0%
+some of the definitions or some of the
+ 
+
+ align:start position:0%
+some of the definitions or some of the
+things that Scott King was mentioning
+
+ align:start position:0%
+things that Scott King was mentioning
+ 
+
+ align:start position:0%
+things that Scott King was mentioning
+that were good for puzzle design?
+
+ align:start position:0%
+that were good for puzzle design?
+ 
+
+ align:start position:0%
+that were good for puzzle design?
+>> I was reading
+
+ align:start position:0%
+>> I was reading
+ 
+
+ align:start position:0%
+>> I was reading
+>> that was in the book or not in the book.
+
+ align:start position:0%
+>> that was in the book or not in the book.
+ 
+
+ align:start position:0%
+>> that was in the book or not in the book.
+>> Uh this was the the the web page
+
+ align:start position:0%
+>> Uh this was the the the web page
+ 
+
+ align:start position:0%
+>> Uh this was the the the web page
+>> web page
+
+ align:start position:0%
+>> web page
+ 
+
+ align:start position:0%
+>> web page
+difficulty
+
+ align:start position:0%
+difficulty
+ 
+
+ align:start position:0%
+difficulty
+>> fun and has the right answer.
+
+ align:start position:0%
+>> fun and has the right answer.
+ 
+
+ align:start position:0%
+>> fun and has the right answer.
+>> Yeah,
+
+ align:start position:0%
+>> Yeah,
+ 
+
+ align:start position:0%
+>> Yeah,
+>> that's actually a solution. Yeah. could
+
+ align:start position:0%
+>> that's actually a solution. Yeah. could
+ 
+
+ align:start position:0%
+>> that's actually a solution. Yeah. could
+actually create.
+
+ align:start position:0%
+actually create.
+ 
+
+ align:start position:0%
+actually create.
+>> He he he he didn't really differentiate
+
+ align:start position:0%
+>> He he he he didn't really differentiate
+ 
+
+ align:start position:0%
+>> He he he he didn't really differentiate
+between like kind of like puzzles that
+
+ align:start position:0%
+between like kind of like puzzles that
+ 
+
+ align:start position:0%
+between like kind of like puzzles that
+could be generated uh you know like a
+
+ align:start position:0%
+could be generated uh you know like a
+ 
+
+ align:start position:0%
+could be generated uh you know like a
+sudoku or something where you have you
+
+ align:start position:0%
+sudoku or something where you have you
+ 
+
+ align:start position:0%
+sudoku or something where you have you
+kind of have an algorithm that lets you
+
+ align:start position:0%
+kind of have an algorithm that lets you
+ 
+
+ align:start position:0%
+kind of have an algorithm that lets you
+create multiple puzzles and but as long
+
+ align:start position:0%
+create multiple puzzles and but as long
+ 
+
+ align:start position:0%
+create multiple puzzles and but as long
+as that that particular iteration had
+
+ align:start position:0%
+as that that particular iteration had
+ 
+
+ align:start position:0%
+as that that particular iteration had
+right answer. Uh so that was really
+
+ align:start position:0%
+right answer. Uh so that was really
+ 
+
+ align:start position:0%
+right answer. Uh so that was really
+fair. Um anything else you remember
+
+ align:start position:0%
+fair. Um anything else you remember
+ 
+
+ align:start position:0%
+fair. Um anything else you remember
+talked a lot about difficulty.
+
+ align:start position:0%
+talked a lot about difficulty.
+ 
+
+ align:start position:0%
+talked a lot about difficulty.
+>> Mhm. make it accessible but not super
+
+ align:start position:0%
+>> Mhm. make it accessible but not super
+ 
+
+ align:start position:0%
+>> Mhm. make it accessible but not super
+easy,
+
+ align:start position:0%
+easy,
+ 
+
+ align:start position:0%
+easy,
+>> right?
+
+ align:start position:0%
+>> right?
+ 
+
+ align:start position:0%
+>> right?
+>> And targeting a specific audience.
+
+ align:start position:0%
+>> And targeting a specific audience.
+ 
+
+ align:start position:0%
+>> And targeting a specific audience.
+>> There's also the ability to uh change
+
+ align:start position:0%
+>> There's also the ability to uh change
+ 
+
+ align:start position:0%
+>> There's also the ability to uh change
+the difficulty. Was it dynamic
+
+ align:start position:0%
+the difficulty. Was it dynamic
+ 
+
+ align:start position:0%
+the difficulty. Was it dynamic
+difficulty?
+
+ align:start position:0%
+difficulty?
+ 
+
+ align:start position:0%
+difficulty?
+>> Uh so some areas may actually be easier
+
+ align:start position:0%
+>> Uh so some areas may actually be easier
+ 
+
+ align:start position:0%
+>> Uh so some areas may actually be easier
+easier settings and then actually what
+
+ align:start position:0%
+easier settings and then actually what
+ 
+
+ align:start position:0%
+easier settings and then actually what
+they want it to be in harder settings.
+
+ align:start position:0%
+they want it to be in harder settings.
+ 
+
+ align:start position:0%
+they want it to be in harder settings.
+>> I think that was Brenda's but yeah.
+
+ align:start position:0%
+>> I think that was Brenda's but yeah.
+ 
+
+ align:start position:0%
+>> I think that was Brenda's but yeah.
+There's there's also the distinction
+
+ align:start position:0%
+There's there's also the distinction
+ 
+
+ align:start position:0%
+There's there's also the distinction
+between sort of like type of difficulty
+
+ align:start position:0%
+between sort of like type of difficulty
+ 
+
+ align:start position:0%
+between sort of like type of difficulty
+like you know things where
+
+ align:start position:0%
+like you know things where
+ 
+
+ align:start position:0%
+like you know things where
+>> you know the letter puzzle that he has
+
+ align:start position:0%
+>> you know the letter puzzle that he has
+ 
+
+ align:start position:0%
+>> you know the letter puzzle that he has
+at the beginning where it requires
+
+ align:start position:0%
+at the beginning where it requires
+ 
+
+ align:start position:0%
+at the beginning where it requires
+>> sort of like thinking about it figuring
+
+ align:start position:0%
+>> sort of like thinking about it figuring
+ 
+
+ align:start position:0%
+>> sort of like thinking about it figuring
+out how
+
+ align:start position:0%
+out how
+ 
+
+ align:start position:0%
+out how
+>> yeah it's it's it was patience versus
+
+ align:start position:0%
+>> yeah it's it's it was patience versus
+ 
+
+ align:start position:0%
+>> yeah it's it's it was patience versus
+something else I can remember
+
+ align:start position:0%
+something else I can remember
+ 
+
+ align:start position:0%
+something else I can remember
+>> but then you have things like mazes
+
+ align:start position:0%
+>> but then you have things like mazes
+ 
+
+ align:start position:0%
+>> but then you have things like mazes
+where it's all patience where you have
+
+ align:start position:0%
+where it's all patience where you have
+ 
+
+ align:start position:0%
+where it's all patience where you have
+to like be very like careful and and
+
+ align:start position:0%
+to like be very like careful and and
+ 
+
+ align:start position:0%
+to like be very like careful and and
+your way through
+
+ align:start position:0%
+your way through
+ 
+
+ align:start position:0%
+your way through
+>> and sometimes they're like bringing in
+
+ align:start position:0%
+>> and sometimes they're like bringing in
+ 
+
+ align:start position:0%
+>> and sometimes they're like bringing in
+information from from other domains from
+
+ align:start position:0%
+information from from other domains from
+ 
+
+ align:start position:0%
+information from from other domains from
+outside from outside of the console it's
+
+ align:start position:0%
+outside from outside of the console it's
+ 
+
+ align:start position:0%
+outside from outside of the console it's
+just like all the information that is
+
+ align:start position:0%
+just like all the information that is
+ 
+
+ align:start position:0%
+just like all the information that is
+currently in the puzzle. Um
+
+ align:start position:0%
+currently in the puzzle. Um
+ 
+
+ align:start position:0%
+currently in the puzzle. Um
+uh but but the interesting thing about
+
+ align:start position:0%
+uh but but the interesting thing about
+ 
+
+ align:start position:0%
+uh but but the interesting thing about
+the puzzle that he particularly shows is
+
+ align:start position:0%
+the puzzle that he particularly shows is
+ 
+
+ align:start position:0%
+the puzzle that he particularly shows is
+that he shows a range of different ways
+
+ align:start position:0%
+that he shows a range of different ways
+ 
+
+ align:start position:0%
+that he shows a range of different ways
+to actually solve it. None of which are
+
+ align:start position:0%
+to actually solve it. None of which are
+ 
+
+ align:start position:0%
+to actually solve it. None of which are
+actually satisfying except for that
+
+ align:start position:0%
+actually satisfying except for that
+ 
+
+ align:start position:0%
+actually satisfying except for that
+final answer which which he irritatedly
+
+ align:start position:0%
+final answer which which he irritatedly
+ 
+
+ align:start position:0%
+final answer which which he irritatedly
+does not tell you like gives you another
+
+ align:start position:0%
+does not tell you like gives you another
+ 
+
+ align:start position:0%
+does not tell you like gives you another
+puzzle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um but um you know it's kind of
+
+ align:start position:0%
+Um but um you know it's kind of
+ 
+
+ align:start position:0%
+Um but um you know it's kind of
+interesting to think about actually
+
+ align:start position:0%
+interesting to think about actually
+ 
+
+ align:start position:0%
+interesting to think about actually
+what's the audience for those kinds of
+
+ align:start position:0%
+what's the audience for those kinds of
+ 
+
+ align:start position:0%
+what's the audience for those kinds of
+specific puzzles. I mean there there are
+
+ align:start position:0%
+specific puzzles. I mean there there are
+ 
+
+ align:start position:0%
+specific puzzles. I mean there there are
+magazines out there like games magazine
+
+ align:start position:0%
+magazines out there like games magazine
+ 
+
+ align:start position:0%
+magazines out there like games magazine
+in particular but um sometimes you see
+
+ align:start position:0%
+in particular but um sometimes you see
+ 
+
+ align:start position:0%
+in particular but um sometimes you see
+um stuff nestled into magazines um uh
+
+ align:start position:0%
+um stuff nestled into magazines um uh
+ 
+
+ align:start position:0%
+um stuff nestled into magazines um uh
+that are not just about games. you see
+
+ align:start position:0%
+that are not just about games. you see
+ 
+
+ align:start position:0%
+that are not just about games. you see
+stuff like cross word puzzles and
+
+ align:start position:0%
+stuff like cross word puzzles and
+ 
+
+ align:start position:0%
+stuff like cross word puzzles and
+newspapers and everything like that and
+
+ align:start position:0%
+newspapers and everything like that and
+ 
+
+ align:start position:0%
+newspapers and everything like that and
+now things like Sudoku and all that are
+
+ align:start position:0%
+now things like Sudoku and all that are
+ 
+
+ align:start position:0%
+now things like Sudoku and all that are
+becoming way more popular um that are
+
+ align:start position:0%
+becoming way more popular um that are
+ 
+
+ align:start position:0%
+becoming way more popular um that are
+you know that are meant to be really
+
+ align:start position:0%
+you know that are meant to be really
+ 
+
+ align:start position:0%
+you know that are meant to be really
+really mass audience whereas a magazine
+
+ align:start position:0%
+really mass audience whereas a magazine
+ 
+
+ align:start position:0%
+really mass audience whereas a magazine
+that is specifically targeted at puzzle
+
+ align:start position:0%
+that is specifically targeted at puzzle
+ 
+
+ align:start position:0%
+that is specifically targeted at puzzle
+enthusiasts can be like super hardcore
+
+ align:start position:0%
+enthusiasts can be like super hardcore
+ 
+
+ align:start position:0%
+enthusiasts can be like super hardcore
+but of course if the whole magazine then
+
+ align:start position:0%
+but of course if the whole magazine then
+ 
+
+ align:start position:0%
+but of course if the whole magazine then
+you can have like a whole range of
+
+ align:start position:0%
+you can have like a whole range of
+ 
+
+ align:start position:0%
+you can have like a whole range of
+different difficulties in there you know
+
+ align:start position:0%
+different difficulties in there you know
+ 
+
+ align:start position:0%
+different difficulties in there you know
+the the assumption that you can solve
+
+ align:start position:0%
+the the assumption that you can solve
+ 
+
+ align:start position:0%
+the the assumption that you can solve
+something not so
+
+ align:start position:0%
+something not so
+ 
+
+ align:start position:0%
+something not so
+>> out of interest does anybody know like
+
+ align:start position:0%
+>> out of interest does anybody know like
+ 
+
+ align:start position:0%
+>> out of interest does anybody know like
+really actually know how people in
+
+ align:start position:0%
+really actually know how people in
+ 
+
+ align:start position:0%
+really actually know how people in
+newspapers generate cross word puzzles
+
+ align:start position:0%
+newspapers generate cross word puzzles
+ 
+
+ align:start position:0%
+newspapers generate cross word puzzles
+and pseudo puzzles? Like does anybody
+
+ align:start position:0%
+and pseudo puzzles? Like does anybody
+ 
+
+ align:start position:0%
+and pseudo puzzles? Like does anybody
+know what the actual process behind that
+
+ align:start position:0%
+know what the actual process behind that
+ 
+
+ align:start position:0%
+know what the actual process behind that
+is? Cuz I don't know, right?
+
+ align:start position:0%
+is? Cuz I don't know, right?
+ 
+
+ align:start position:0%
+is? Cuz I don't know, right?
+>> I think
+
+ align:start position:0%
+>> I think
+ 
+
+ align:start position:0%
+>> I think
+>> I mean I imagine how you might do it.
+
+ align:start position:0%
+>> I mean I imagine how you might do it.
+ 
+
+ align:start position:0%
+>> I mean I imagine how you might do it.
+You might start with the filled out
+
+ align:start position:0%
+You might start with the filled out
+ 
+
+ align:start position:0%
+You might start with the filled out
+thing and then like remove bits to get
+
+ align:start position:0%
+thing and then like remove bits to get
+ 
+
+ align:start position:0%
+thing and then like remove bits to get
+your sudoku
+
+ align:start position:0%
+your sudoku
+ 
+
+ align:start position:0%
+your sudoku
+>> or you might brute force dictionary
+
+ align:start position:0%
+>> or you might brute force dictionary
+ 
+
+ align:start position:0%
+>> or you might brute force dictionary
+search to come up with words which fit
+
+ align:start position:0%
+search to come up with words which fit
+ 
+
+ align:start position:0%
+search to come up with words which fit
+together in order for
+
+ align:start position:0%
+together in order for
+ 
+
+ align:start position:0%
+together in order for
+>> what they do with sudoku now is they
+
+ align:start position:0%
+>> what they do with sudoku now is they
+ 
+
+ align:start position:0%
+>> what they do with sudoku now is they
+have some like computer algorithm to and
+
+ align:start position:0%
+have some like computer algorithm to and
+ 
+
+ align:start position:0%
+have some like computer algorithm to and
+has scales difficulty and it generates a
+
+ align:start position:0%
+has scales difficulty and it generates a
+ 
+
+ align:start position:0%
+has scales difficulty and it generates a
+random sudoku puzzle from your input
+
+ align:start position:0%
+random sudoku puzzle from your input
+ 
+
+ align:start position:0%
+random sudoku puzzle from your input
+powerful
+
+ align:start position:0%
+powerful
+ 
+
+ align:start position:0%
+powerful
+>> sudoku is solved enough that you can
+
+ align:start position:0%
+>> sudoku is solved enough that you can
+ 
+
+ align:start position:0%
+>> sudoku is solved enough that you can
+actually just algorithmically generate
+
+ align:start position:0%
+actually just algorithmically generate
+ 
+
+ align:start position:0%
+actually just algorithmically generate
+for like
+
+ align:start position:0%
+for like
+ 
+
+ align:start position:0%
+for like
+>> a an actual ual, you know, numerical
+
+ align:start position:0%
+>> a an actual ual, you know, numerical
+ 
+
+ align:start position:0%
+>> a an actual ual, you know, numerical
+difficulty.
+
+ align:start position:0%
+difficulty.
+ 
+
+ align:start position:0%
+difficulty.
+>> You scale it from, you know, like 1 to
+
+ align:start position:0%
+>> You scale it from, you know, like 1 to
+ 
+
+ align:start position:0%
+>> You scale it from, you know, like 1 to
+10. 10 being where
+
+ align:start position:0%
+10. 10 being where
+ 
+
+ align:start position:0%
+10. 10 being where
+>> where there's like literally only one
+
+ align:start position:0%
+>> where there's like literally only one
+ 
+
+ align:start position:0%
+>> where there's like literally only one
+step to take at each point.
+
+ align:start position:0%
+step to take at each point.
+ 
+
+ align:start position:0%
+step to take at each point.
+>> Oh, the one the one that takes three
+
+ align:start position:0%
+>> Oh, the one the one that takes three
+ 
+
+ align:start position:0%
+>> Oh, the one the one that takes three
+months that took him three months to
+
+ align:start position:0%
+months that took him three months to
+ 
+
+ align:start position:0%
+months that took him three months to
+solve or something.
+
+ align:start position:0%
+solve or something.
+ 
+
+ align:start position:0%
+solve or something.
+>> But but like cross there's there's
+
+ align:start position:0%
+>> But but like cross there's there's
+ 
+
+ align:start position:0%
+>> But but like cross there's there's
+people actually just get paid to sit
+
+ align:start position:0%
+people actually just get paid to sit
+ 
+
+ align:start position:0%
+people actually just get paid to sit
+down and generate those.
+
+ align:start position:0%
+down and generate those.
+ 
+
+ align:start position:0%
+down and generate those.
+>> Will shorts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times takes submissions from other
+
+ align:start position:0%
+times takes submissions from other
+ 
+
+ align:start position:0%
+times takes submissions from other
+people. That's why it says edited by
+
+ align:start position:0%
+people. That's why it says edited by
+ 
+
+ align:start position:0%
+people. That's why it says edited by
+Will Schwarz because people submit stuff
+
+ align:start position:0%
+Will Schwarz because people submit stuff
+ 
+
+ align:start position:0%
+Will Schwarz because people submit stuff
+and then he kind of like just touches it
+
+ align:start position:0%
+and then he kind of like just touches it
+ 
+
+ align:start position:0%
+and then he kind of like just touches it
+up.
+
+ align:start position:0%
+up.
+ 
+
+ align:start position:0%
+up.
+>> So he he kind of crowdsources cross word
+
+ align:start position:0%
+>> So he he kind of crowdsources cross word
+ 
+
+ align:start position:0%
+>> So he he kind of crowdsources cross word
+puzzle
+
+ align:start position:0%
+puzzle
+ 
+
+ align:start position:0%
+puzzle
+>> generation. I'm sure I'm sure
+
+ align:start position:0%
+>> generation. I'm sure I'm sure
+ 
+
+ align:start position:0%
+>> generation. I'm sure I'm sure
+>> in the past you had to created it own.
+
+ align:start position:0%
+>> in the past you had to created it own.
+ 
+
+ align:start position:0%
+>> in the past you had to created it own.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> But I mean so the difficulty in a cross
+
+ align:start position:0%
+>> But I mean so the difficulty in a cross
+ 
+
+ align:start position:0%
+>> But I mean so the difficulty in a cross
+word puzzle isn't just like in the sort
+
+ align:start position:0%
+word puzzle isn't just like in the sort
+ 
+
+ align:start position:0%
+word puzzle isn't just like in the sort
+of geometric layout of how the words the
+
+ align:start position:0%
+of geometric layout of how the words the
+ 
+
+ align:start position:0%
+of geometric layout of how the words the
+words go is the the specific clues that
+
+ align:start position:0%
+words go is the the specific clues that
+ 
+
+ align:start position:0%
+words go is the the specific clues that
+they give you can be more or less
+
+ align:start position:0%
+they give you can be more or less
+ 
+
+ align:start position:0%
+they give you can be more or less
+obuscated in some ways. And New York
+
+ align:start position:0%
+obuscated in some ways. And New York
+ 
+
+ align:start position:0%
+obuscated in some ways. And New York
+Times in particular with this is, you
+
+ align:start position:0%
+Times in particular with this is, you
+ 
+
+ align:start position:0%
+Times in particular with this is, you
+know, they they'll give you like two
+
+ align:start position:0%
+know, they they'll give you like two
+ 
+
+ align:start position:0%
+know, they they'll give you like two
+words that don't that that with with no
+
+ align:start position:0%
+words that don't that that with with no
+ 
+
+ align:start position:0%
+words that don't that that with with no
+grammatical context about how that's
+
+ align:start position:0%
+grammatical context about how that's
+ 
+
+ align:start position:0%
+grammatical context about how that's
+supposed to fit in.
+
+ align:start position:0%
+supposed to fit in.
+ 
+
+ align:start position:0%
+supposed to fit in.
+>> Well, it gets harder during the week.
+
+ align:start position:0%
+>> Well, it gets harder during the week.
+ 
+
+ align:start position:0%
+>> Well, it gets harder during the week.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+>> yeah.
+
+ align:start position:0%
+>> yeah.
+ 
+
+ align:start position:0%
+>> yeah.
+>> Yeah. So, so so and and and so you you
+
+ align:start position:0%
+>> Yeah. So, so so and and and so you you
+ 
+
+ align:start position:0%
+>> Yeah. So, so so and and and so you you
+you can actually compare and see how
+
+ align:start position:0%
+you can actually compare and see how
+ 
+
+ align:start position:0%
+you can actually compare and see how
+that difficulty scaling is just by
+
+ align:start position:0%
+that difficulty scaling is just by
+ 
+
+ align:start position:0%
+that difficulty scaling is just by
+looking at the clues, not even looking
+
+ align:start position:0%
+looking at the clues, not even looking
+ 
+
+ align:start position:0%
+looking at the clues, not even looking
+at the puzzle itself. Um and of course
+
+ align:start position:0%
+at the puzzle itself. Um and of course
+ 
+
+ align:start position:0%
+at the puzzle itself. Um and of course
+the other thing about crosswords is uh
+
+ align:start position:0%
+the other thing about crosswords is uh
+ 
+
+ align:start position:0%
+the other thing about crosswords is uh
+you know just just to bring up a point
+
+ align:start position:0%
+you know just just to bring up a point
+ 
+
+ align:start position:0%
+you know just just to bring up a point
+that we talked about in earlier class
+
+ align:start position:0%
+that we talked about in earlier class
+ 
+
+ align:start position:0%
+that we talked about in earlier class
+you know it's that the cross words that
+
+ align:start position:0%
+you know it's that the cross words that
+ 
+
+ align:start position:0%
+you know it's that the cross words that
+we're familiar with at least are
+
+ align:start position:0%
+we're familiar with at least are
+ 
+
+ align:start position:0%
+we're familiar with at least are
+dependent on the redundancy of the
+
+ align:start position:0%
+dependent on the redundancy of the
+ 
+
+ align:start position:0%
+dependent on the redundancy of the
+English language right you know there
+
+ align:start position:0%
+English language right you know there
+ 
+
+ align:start position:0%
+English language right you know there
+you don't need every single letter in a
+
+ align:start position:0%
+you don't need every single letter in a
+ 
+
+ align:start position:0%
+you don't need every single letter in a
+in of a word in order to figure out what
+
+ align:start position:0%
+in of a word in order to figure out what
+ 
+
+ align:start position:0%
+in of a word in order to figure out what
+that word is so that if there's a word
+
+ align:start position:0%
+that word is so that if there's a word
+ 
+
+ align:start position:0%
+that word is so that if there's a word
+that you couldn't otherwise have gotten
+
+ align:start position:0%
+that you couldn't otherwise have gotten
+ 
+
+ align:start position:0%
+that you couldn't otherwise have gotten
+from the clue you can still get it just
+
+ align:start position:0%
+from the clue you can still get it just
+ 
+
+ align:start position:0%
+from the clue you can still get it just
+by seeing the letters that are available
+
+ align:start position:0%
+by seeing the letters that are available
+ 
+
+ align:start position:0%
+by seeing the letters that are available
+that's because English language is kind
+
+ align:start position:0%
+that's because English language is kind
+ 
+
+ align:start position:0%
+that's because English language is kind
+of about 50% redundant information. If
+
+ align:start position:0%
+of about 50% redundant information. If
+ 
+
+ align:start position:0%
+of about 50% redundant information. If
+you dropped every single vowel in in in
+
+ align:start position:0%
+you dropped every single vowel in in in
+ 
+
+ align:start position:0%
+you dropped every single vowel in in in
+in a sentence, you could probably still
+
+ align:start position:0%
+in a sentence, you could probably still
+ 
+
+ align:start position:0%
+in a sentence, you could probably still
+make out what that sentence said. And
+
+ align:start position:0%
+make out what that sentence said. And
+ 
+
+ align:start position:0%
+make out what that sentence said. And
+you don't necessarily get that with
+
+ align:start position:0%
+you don't necessarily get that with
+ 
+
+ align:start position:0%
+you don't necessarily get that with
+Chinese, for instance.
+
+ align:start position:0%
+Chinese, for instance.
+ 
+
+ align:start position:0%
+Chinese, for instance.
+How many folks here have like some or
+
+ align:start position:0%
+How many folks here have like some or
+ 
+
+ align:start position:0%
+How many folks here have like some or
+there probably are other languages here
+
+ align:start position:0%
+there probably are other languages here
+ 
+
+ align:start position:0%
+there probably are other languages here
+where like every single character can
+
+ align:start position:0%
+where like every single character can
+ 
+
+ align:start position:0%
+where like every single character can
+mean means a word or something like
+
+ align:start position:0%
+mean means a word or something like
+ 
+
+ align:start position:0%
+mean means a word or something like
+that?
+
+ align:start position:0%
+that?
+ 
+
+ align:start position:0%
+that?
+>> Hebrew has no vows, right?
+
+ align:start position:0%
+>> Hebrew has no vows, right?
+ 
+
+ align:start position:0%
+>> Hebrew has no vows, right?
+>> Well, they do like third grade and they
+
+ align:start position:0%
+>> Well, they do like third grade and they
+ 
+
+ align:start position:0%
+>> Well, they do like third grade and they
+start dropping them after that. So it's
+
+ align:start position:0%
+start dropping them after that. So it's
+ 
+
+ align:start position:0%
+start dropping them after that. So it's
+basically because it is understandable
+
+ align:start position:0%
+basically because it is understandable
+ 
+
+ align:start position:0%
+basically because it is understandable
+without vowels, you eventually just stop
+
+ align:start position:0%
+without vowels, you eventually just stop
+ 
+
+ align:start position:0%
+without vowels, you eventually just stop
+using them.
+
+ align:start position:0%
+using them.
+ 
+
+ align:start position:0%
+using them.
+>> Oh yeah. So that's interesting. If you
+
+ align:start position:0%
+>> Oh yeah. So that's interesting. If you
+ 
+
+ align:start position:0%
+>> Oh yeah. So that's interesting. If you
+had a cross word in Hebrew that where
+
+ align:start position:0%
+had a cross word in Hebrew that where
+ 
+
+ align:start position:0%
+had a cross word in Hebrew that where
+you expected to write in the words with
+
+ align:start position:0%
+you expected to write in the words with
+ 
+
+ align:start position:0%
+you expected to write in the words with
+vowels, you probably could actually uh
+
+ align:start position:0%
+vowels, you probably could actually uh
+ 
+
+ align:start position:0%
+vowels, you probably could actually uh
+do it one very similar to to an English
+
+ align:start position:0%
+do it one very similar to to an English
+ 
+
+ align:start position:0%
+do it one very similar to to an English
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+>> It's difficult because the vowels in
+
+ align:start position:0%
+>> It's difficult because the vowels in
+ 
+
+ align:start position:0%
+>> It's difficult because the vowels in
+Hebrew are attached to a letter, not a
+
+ align:start position:0%
+Hebrew are attached to a letter, not a
+ 
+
+ align:start position:0%
+Hebrew are attached to a letter, not a
+separate character.
+
+ align:start position:0%
+separate character.
+ 
+
+ align:start position:0%
+separate character.
+>> Below letters or barow.
+
+ align:start position:0%
+>> Below letters or barow.
+ 
+
+ align:start position:0%
+>> Below letters or barow.
+>> No.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But you wonder if in the in a cross word
+
+ align:start position:0%
+But you wonder if in the in a cross word
+ 
+
+ align:start position:0%
+But you wonder if in the in a cross word
+in a letter can make a different sound
+
+ align:start position:0%
+in a letter can make a different sound
+ 
+
+ align:start position:0%
+in a letter can make a different sound
+with both.
+
+ align:start position:0%
+with both.
+ 
+
+ align:start position:0%
+with both.
+>> Mhm.
+
+ align:start position:0%
+>> Mhm.
+ 
+
+ align:start position:0%
+>> Mhm.
+>> Soft C or hard C
+
+ align:start position:0%
+>> Soft C or hard C
+ 
+
+ align:start position:0%
+>> Soft C or hard C
+>> because a V can be vo or va or they you
+
+ align:start position:0%
+>> because a V can be vo or va or they you
+ 
+
+ align:start position:0%
+>> because a V can be vo or va or they you
+don't know. You only know by context.
+
+ align:start position:0%
+don't know. You only know by context.
+ 
+
+ align:start position:0%
+don't know. You only know by context.
+>> English like C could be a hard soft
+
+ align:start position:0%
+>> English like C could be a hard soft
+ 
+
+ align:start position:0%
+>> English like C could be a hard soft
+>> or G could be J.
+
+ align:start position:0%
+>> or G could be J.
+ 
+
+ align:start position:0%
+>> or G could be J.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah. It's true. that although in
+
+ align:start position:0%
+>> Yeah. It's true. that although in
+ 
+
+ align:start position:0%
+>> Yeah. It's true. that although in
+English in particular the phonetic
+
+ align:start position:0%
+English in particular the phonetic
+ 
+
+ align:start position:0%
+English in particular the phonetic
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+the the way how a certain word is
+
+ align:start position:0%
+the the way how a certain word is
+ 
+
+ align:start position:0%
+the the way how a certain word is
+pronounced isn't necessarily uh isn't
+
+ align:start position:0%
+pronounced isn't necessarily uh isn't
+ 
+
+ align:start position:0%
+pronounced isn't necessarily uh isn't
+necessarily essential for solving a
+
+ align:start position:0%
+necessarily essential for solving a
+ 
+
+ align:start position:0%
+necessarily essential for solving a
+puzzle puzzle unless the clues happen to
+
+ align:start position:0%
+puzzle puzzle unless the clues happen to
+ 
+
+ align:start position:0%
+puzzle puzzle unless the clues happen to
+be phonetic clues you know sounds like a
+
+ align:start position:0%
+be phonetic clues you know sounds like a
+ 
+
+ align:start position:0%
+be phonetic clues you know sounds like a
+fish uh so so so
+
+ align:start position:0%
+fish uh so so so
+ 
+
+ align:start position:0%
+fish uh so so so
+that may not come in so much play when
+
+ align:start position:0%
+that may not come in so much play when
+ 
+
+ align:start position:0%
+that may not come in so much play when
+it comes to English in particular
+
+ align:start position:0%
+it comes to English in particular
+ 
+
+ align:start position:0%
+it comes to English in particular
+>> um Jason you had your hand up earlier
+
+ align:start position:0%
+>> um Jason you had your hand up earlier
+ 
+
+ align:start position:0%
+>> um Jason you had your hand up earlier
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+>> it There's going to be count
+
+ align:start position:0%
+>> it There's going to be count
+ 
+
+ align:start position:0%
+>> it There's going to be count
+algorithmically generated.
+
+ align:start position:0%
+algorithmically generated.
+ 
+
+ align:start position:0%
+algorithmically generated.
+>> Well, also one thing about algorithmic
+
+ align:start position:0%
+>> Well, also one thing about algorithmic
+ 
+
+ align:start position:0%
+>> Well, also one thing about algorithmic
+about Sudoku difficulty, a lot of it
+
+ align:start position:0%
+about Sudoku difficulty, a lot of it
+ 
+
+ align:start position:0%
+about Sudoku difficulty, a lot of it
+comes on the selective removal of
+
+ align:start position:0%
+comes on the selective removal of
+ 
+
+ align:start position:0%
+comes on the selective removal of
+numbers. It's not what is the final
+
+ align:start position:0%
+numbers. It's not what is the final
+ 
+
+ align:start position:0%
+numbers. It's not what is the final
+number, the final pattern going to look
+
+ align:start position:0%
+number, the final pattern going to look
+ 
+
+ align:start position:0%
+number, the final pattern going to look
+like. That's actually the difficulty.
+
+ align:start position:0%
+like. That's actually the difficulty.
+ 
+
+ align:start position:0%
+like. That's actually the difficulty.
+It's how do we remove the numbers in a
+
+ align:start position:0%
+It's how do we remove the numbers in a
+ 
+
+ align:start position:0%
+It's how do we remove the numbers in a
+way that gives multiple possible answers
+
+ align:start position:0%
+way that gives multiple possible answers
+ 
+
+ align:start position:0%
+way that gives multiple possible answers
+uh or multiple possible dead ends uh
+
+ align:start position:0%
+uh or multiple possible dead ends uh
+ 
+
+ align:start position:0%
+uh or multiple possible dead ends uh
+because really there's only one solution
+
+ align:start position:0%
+because really there's only one solution
+ 
+
+ align:start position:0%
+because really there's only one solution
+at the end of it. Um I'm not actually
+
+ align:start position:0%
+at the end of it. Um I'm not actually
+ 
+
+ align:start position:0%
+at the end of it. Um I'm not actually
+familiar with the algorithm which does
+
+ align:start position:0%
+familiar with the algorithm which does
+ 
+
+ align:start position:0%
+familiar with the algorithm which does
+so but it seems to be very clear that
+
+ align:start position:0%
+so but it seems to be very clear that
+ 
+
+ align:start position:0%
+so but it seems to be very clear that
+there are at least two algorithms. One
+
+ align:start position:0%
+there are at least two algorithms. One
+ 
+
+ align:start position:0%
+there are at least two algorithms. One
+of which is very easy which is just
+
+ align:start position:0%
+of which is very easy which is just
+ 
+
+ align:start position:0%
+of which is very easy which is just
+provide a a legitimate pseudogu solution
+
+ align:start position:0%
+provide a a legitimate pseudogu solution
+ 
+
+ align:start position:0%
+provide a a legitimate pseudogu solution
+and then one slightly harder is which
+
+ align:start position:0%
+and then one slightly harder is which
+ 
+
+ align:start position:0%
+and then one slightly harder is which
+now which numbers to be removed so that
+
+ align:start position:0%
+now which numbers to be removed so that
+ 
+
+ align:start position:0%
+now which numbers to be removed so that
+it's still solvable.
+
+ align:start position:0%
+it's still solvable.
+ 
+
+ align:start position:0%
+it's still solvable.
+Um can people take picross? Um yeah,
+
+ align:start position:0%
+Um can people take picross? Um yeah,
+ 
+
+ align:start position:0%
+Um can people take picross? Um yeah,
+>> some someone want to describe it for the
+
+ align:start position:0%
+>> some someone want to describe it for the
+ 
+
+ align:start position:0%
+>> some someone want to describe it for the
+folks who haven't aren't familiar with
+
+ align:start position:0%
+folks who haven't aren't familiar with
+ 
+
+ align:start position:0%
+folks who haven't aren't familiar with
+with with it. We can use the whiteboard.
+
+ align:start position:0%
+with with it. We can use the whiteboard.
+ 
+
+ align:start position:0%
+with with it. We can use the whiteboard.
+>> Sure.
+
+ align:start position:0%
+>> Sure.
+ 
+
+ align:start position:0%
+>> Sure.
+>> Um I think on the
+
+ align:start position:0%
+>> Um I think on the
+ 
+
+ align:start position:0%
+>> Um I think on the
+>> I think the green one works better.
+
+ align:start position:0%
+>> I think the green one works better.
+ 
+
+ align:start position:0%
+>> I think the green one works better.
+>> Yeah, I remember read
+
+ align:start position:0%
+>> Yeah, I remember read
+ 
+
+ align:start position:0%
+>> Yeah, I remember read
+only familiar across 3D.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, that's the best way.
+
+ align:start position:0%
+Yeah, that's the best way.
+ 
+
+ align:start position:0%
+Yeah, that's the best way.
+>> Sorry to put you on the spot.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> The idea is that you'll have words and
+
+ align:start position:0%
+>> The idea is that you'll have words and
+ 
+
+ align:start position:0%
+>> The idea is that you'll have words and
+poems
+
+ align:start position:0%
+poems
+ 
+
+ align:start position:0%
+poems
+>> and then they'll have some number.
+
+ align:start position:0%
+>> and then they'll have some number.
+ 
+
+ align:start position:0%
+>> and then they'll have some number.
+>> Oh, this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> this one you fill in the blocks.
+
+ align:start position:0%
+>> this one you fill in the blocks.
+ 
+
+ align:start position:0%
+>> this one you fill in the blocks.
+>> Okay. And then and then given this
+
+ align:start position:0%
+>> Okay. And then and then given this
+ 
+
+ align:start position:0%
+>> Okay. And then and then given this
+information we have to work out which of
+
+ align:start position:0%
+information we have to work out which of
+ 
+
+ align:start position:0%
+information we have to work out which of
+these blocks is filled and which can be
+
+ align:start position:0%
+these blocks is filled and which can be
+ 
+
+ align:start position:0%
+these blocks is filled and which can be
+removed.
+
+ align:start position:0%
+removed.
+ 
+
+ align:start position:0%
+removed.
+>> And the idea is that
+
+ align:start position:0%
+>> And the idea is that
+ 
+
+ align:start position:0%
+>> And the idea is that
+>> the numbers
+
+ align:start position:0%
+>> the numbers
+ 
+
+ align:start position:0%
+>> the numbers
+>> the number tells you the number of
+
+ align:start position:0%
+>> the number tells you the number of
+ 
+
+ align:start position:0%
+>> the number tells you the number of
+blocks in that row or column which has a
+
+ align:start position:0%
+blocks in that row or column which has a
+ 
+
+ align:start position:0%
+blocks in that row or column which has a
+filled block in it.
+
+ align:start position:0%
+filled block in it.
+ 
+
+ align:start position:0%
+filled block in it.
+>> So it's like
+
+ align:start position:0%
+>> So it's like
+ 
+
+ align:start position:0%
+>> So it's like
+>> so in this case like
+
+ align:start position:0%
+>> so in this case like
+ 
+
+ align:start position:0%
+>> so in this case like
+>> they're also given
+
+ align:start position:0%
+>> they're also given
+ 
+
+ align:start position:0%
+>> they're also given
+>> nothing in this column
+
+ align:start position:0%
+>> nothing in this column
+ 
+
+ align:start position:0%
+>> nothing in this column
+this column and that column can have
+
+ align:start position:0%
+this column and that column can have
+ 
+
+ align:start position:0%
+this column and that column can have
+anything in it. Um and this is probably
+
+ align:start position:0%
+anything in it. Um and this is probably
+ 
+
+ align:start position:0%
+anything in it. Um and this is probably
+not actually example because it's
+
+ align:start position:0%
+not actually example because it's
+ 
+
+ align:start position:0%
+not actually example because it's
+probably the numbers are
+
+ align:start position:0%
+probably the numbers are
+ 
+
+ align:start position:0%
+probably the numbers are
+>> the subs are not the same.
+
+ align:start position:0%
+>> the subs are not the same.
+ 
+
+ align:start position:0%
+>> the subs are not the same.
+>> But yeah,
+
+ align:start position:0%
+>> But yeah,
+ 
+
+ align:start position:0%
+>> But yeah,
+>> so
+
+ align:start position:0%
+>> so
+ 
+
+ align:start position:0%
+>> so
+you get the idea.
+
+ align:start position:0%
+you get the idea.
+ 
+
+ align:start position:0%
+you get the idea.
+>> It's not going to work, but you get the
+
+ align:start position:0%
+>> It's not going to work, but you get the
+ 
+
+ align:start position:0%
+>> It's not going to work, but you get the
+idea. And then things can get more
+
+ align:start position:0%
+idea. And then things can get more
+ 
+
+ align:start position:0%
+idea. And then things can get more
+complicated. So the
+
+ align:start position:0%
+complicated. So the
+ 
+
+ align:start position:0%
+complicated. So the
+>> additionally, if there's just I think a
+
+ align:start position:0%
+>> additionally, if there's just I think a
+ 
+
+ align:start position:0%
+>> additionally, if there's just I think a
+three, then it means that there's a
+
+ align:start position:0%
+three, then it means that there's a
+ 
+
+ align:start position:0%
+three, then it means that there's a
+connected block of three. So for
+
+ align:start position:0%
+connected block of three. So for
+ 
+
+ align:start position:0%
+connected block of three. So for
+instance, this that and that might all
+
+ align:start position:0%
+instance, this that and that might all
+ 
+
+ align:start position:0%
+instance, this that and that might all
+have to be. Um, but if there's a three,
+
+ align:start position:0%
+have to be. Um, but if there's a three,
+ 
+
+ align:start position:0%
+have to be. Um, but if there's a three,
+which I think is in like a square or
+
+ align:start position:0%
+which I think is in like a square or
+ 
+
+ align:start position:0%
+which I think is in like a square or
+something along these lines, that means
+
+ align:start position:0%
+something along these lines, that means
+ 
+
+ align:start position:0%
+something along these lines, that means
+that there are three in that column, but
+
+ align:start position:0%
+that there are three in that column, but
+ 
+
+ align:start position:0%
+that there are three in that column, but
+there's a gap in there somewhere. And
+
+ align:start position:0%
+there's a gap in there somewhere. And
+ 
+
+ align:start position:0%
+there's a gap in there somewhere. And
+then if it's like a three in a circle or
+
+ align:start position:0%
+then if it's like a three in a circle or
+ 
+
+ align:start position:0%
+then if it's like a three in a circle or
+something else complicated like that,
+
+ align:start position:0%
+something else complicated like that,
+ 
+
+ align:start position:0%
+something else complicated like that,
+then it means that there are three, but
+
+ align:start position:0%
+then it means that there are three, but
+ 
+
+ align:start position:0%
+then it means that there are three, but
+they all have gaps between
+
+ align:start position:0%
+they all have gaps between
+ 
+
+ align:start position:0%
+they all have gaps between
+where they have a list of numbers and
+
+ align:start position:0%
+where they have a list of numbers and
+ 
+
+ align:start position:0%
+where they have a list of numbers and
+those are the
+
+ align:start position:0%
+those are the
+ 
+
+ align:start position:0%
+those are the
+>> there are consecutive blocks of that
+
+ align:start position:0%
+>> there are consecutive blocks of that
+ 
+
+ align:start position:0%
+>> there are consecutive blocks of that
+length. Yeah.
+
+ align:start position:0%
+length. Yeah.
+ 
+
+ align:start position:0%
+length. Yeah.
+>> So, so, so, so for one column you might
+
+ align:start position:0%
+>> So, so, so, so for one column you might
+ 
+
+ align:start position:0%
+>> So, so, so, so for one column you might
+say like 2 three five which means there
+
+ align:start position:0%
+say like 2 three five which means there
+ 
+
+ align:start position:0%
+say like 2 three five which means there
+is a block of two followed by a block of
+
+ align:start position:0%
+is a block of two followed by a block of
+ 
+
+ align:start position:0%
+is a block of two followed by a block of
+three followed by a block of five
+
+ align:start position:0%
+three followed by a block of five
+ 
+
+ align:start position:0%
+three followed by a block of five
+>> and they have to have a gap between them
+
+ align:start position:0%
+>> and they have to have a gap between them
+ 
+
+ align:start position:0%
+>> and they have to have a gap between them
+>> and they will have a gap in between
+
+ align:start position:0%
+>> and they will have a gap in between
+ 
+
+ align:start position:0%
+>> and they will have a gap in between
+them. So, it's not like if there's
+
+ align:start position:0%
+them. So, it's not like if there's
+ 
+
+ align:start position:0%
+them. So, it's not like if there's
+actually a block of eight in there
+
+ align:start position:0%
+actually a block of eight in there
+ 
+
+ align:start position:0%
+actually a block of eight in there
+somewhere.
+
+ align:start position:0%
+somewhere.
+ 
+
+ align:start position:0%
+somewhere.
+>> But but that's the but the whole idea is
+
+ align:start position:0%
+>> But but that's the but the whole idea is
+ 
+
+ align:start position:0%
+>> But but that's the but the whole idea is
+that you know you've got this um
+
+ align:start position:0%
+that you know you've got this um
+ 
+
+ align:start position:0%
+that you know you've got this um
+information that that is actually
+
+ align:start position:0%
+information that that is actually
+ 
+
+ align:start position:0%
+information that that is actually
+redundant. you know, you've got more
+
+ align:start position:0%
+redundant. you know, you've got more
+ 
+
+ align:start position:0%
+redundant. you know, you've got more
+information in there than you
+
+ align:start position:0%
+information in there than you
+ 
+
+ align:start position:0%
+information in there than you
+necessarily need to be able to figure
+
+ align:start position:0%
+necessarily need to be able to figure
+ 
+
+ align:start position:0%
+necessarily need to be able to figure
+out which blocks in the solution should
+
+ align:start position:0%
+out which blocks in the solution should
+ 
+
+ align:start position:0%
+out which blocks in the solution should
+be filled and when it should be empty,
+
+ align:start position:0%
+be filled and when it should be empty,
+ 
+
+ align:start position:0%
+be filled and when it should be empty,
+but you know, it's presented to you in
+
+ align:start position:0%
+but you know, it's presented to you in
+ 
+
+ align:start position:0%
+but you know, it's presented to you in
+this opuscated way. The the evidence the
+
+ align:start position:0%
+this opuscated way. The the evidence the
+ 
+
+ align:start position:0%
+this opuscated way. The the evidence the
+the clues that are given to you in a way
+
+ align:start position:0%
+the clues that are given to you in a way
+ 
+
+ align:start position:0%
+the clues that are given to you in a way
+that you know that requires you to
+
+ align:start position:0%
+that you know that requires you to
+ 
+
+ align:start position:0%
+that you know that requires you to
+perform these algorithms in order to
+
+ align:start position:0%
+perform these algorithms in order to
+ 
+
+ align:start position:0%
+perform these algorithms in order to
+figure out which one is created and
+
+ align:start position:0%
+figure out which one is created and
+ 
+
+ align:start position:0%
+figure out which one is created and
+usually that's an algorithm that you can
+
+ align:start position:0%
+usually that's an algorithm that you can
+ 
+
+ align:start position:0%
+usually that's an algorithm that you can
+use yourself. Uh although you know like
+
+ align:start position:0%
+use yourself. Uh although you know like
+ 
+
+ align:start position:0%
+use yourself. Uh although you know like
+um I think Kim was the one who was
+
+ align:start position:0%
+um I think Kim was the one who was
+ 
+
+ align:start position:0%
+um I think Kim was the one who was
+talking about pattern matching although
+
+ align:start position:0%
+talking about pattern matching although
+ 
+
+ align:start position:0%
+talking about pattern matching although
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+uh but you know eventually as you get
+
+ align:start position:0%
+uh but you know eventually as you get
+ 
+
+ align:start position:0%
+uh but you know eventually as you get
+good at these things you start to you
+
+ align:start position:0%
+good at these things you start to you
+ 
+
+ align:start position:0%
+good at these things you start to you
+you start to recognize patterns right
+
+ align:start position:0%
+you start to recognize patterns right
+ 
+
+ align:start position:0%
+you start to recognize patterns right
+off the bat right like that's a zero oh
+
+ align:start position:0%
+off the bat right like that's a zero oh
+ 
+
+ align:start position:0%
+off the bat right like that's a zero oh
+wow okay so that entire row is empty
+
+ align:start position:0%
+wow okay so that entire row is empty
+ 
+
+ align:start position:0%
+wow okay so that entire row is empty
+that that that's that's that's the sort
+
+ align:start position:0%
+that that that's that's that's the sort
+ 
+
+ align:start position:0%
+that that that's that's that's the sort
+of thing that you that becomes automatic
+
+ align:start position:0%
+of thing that you that becomes automatic
+ 
+
+ align:start position:0%
+of thing that you that becomes automatic
+after you you you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> um so let's see I'm not sure if I much
+
+ align:start position:0%
+>> um so let's see I'm not sure if I much
+ 
+
+ align:start position:0%
+>> um so let's see I'm not sure if I much
+more to talk about Scott Kim, but you
+
+ align:start position:0%
+more to talk about Scott Kim, but you
+ 
+
+ align:start position:0%
+more to talk about Scott Kim, but you
+know these are these are more like
+
+ align:start position:0%
+know these are these are more like
+ 
+
+ align:start position:0%
+know these are these are more like
+generated stuff. Tip over has
+
+ align:start position:0%
+generated stuff. Tip over has
+ 
+
+ align:start position:0%
+generated stuff. Tip over has
+so this is this basically is um it's
+
+ align:start position:0%
+so this is this basically is um it's
+ 
+
+ align:start position:0%
+so this is this basically is um it's
+along the lines of what uh Scott Pin uh
+
+ align:start position:0%
+along the lines of what uh Scott Pin uh
+ 
+
+ align:start position:0%
+along the lines of what uh Scott Pin uh
+is talking about, but obviously this is
+
+ align:start position:0%
+is talking about, but obviously this is
+ 
+
+ align:start position:0%
+is talking about, but obviously this is
+more physical, not a pen and paper kind
+
+ align:start position:0%
+more physical, not a pen and paper kind
+ 
+
+ align:start position:0%
+more physical, not a pen and paper kind
+of thing.
+
+ align:start position:0%
+of thing.
+ 
+
+ align:start position:0%
+of thing.
+>> Can you move for the coffee yet?
+
+ align:start position:0%
+>> Can you move for the coffee yet?
+ 
+
+ align:start position:0%
+>> Can you move for the coffee yet?
+>> Oh, move the coffee.
+
+ align:start position:0%
+>> Oh, move the coffee.
+ 
+
+ align:start position:0%
+>> Oh, move the coffee.
+>> No, I just want you to look at this.
+
+ align:start position:0%
+>> No, I just want you to look at this.
+ 
+
+ align:start position:0%
+>> No, I just want you to look at this.
+>> Okay, good.
+
+ align:start position:0%
+>> Okay, good.
+ 
+
+ align:start position:0%
+>> Okay, good.
+Look at this first. Don't look at that.
+
+ align:start position:0%
+Look at this first. Don't look at that.
+ 
+
+ align:start position:0%
+Look at this first. Don't look at that.
+Uh don't look at that. Um so the basic
+
+ align:start position:0%
+Uh don't look at that. Um so the basic
+ 
+
+ align:start position:0%
+Uh don't look at that. Um so the basic
+idea is let me just start with one. Um
+
+ align:start position:0%
+idea is let me just start with one. Um
+ 
+
+ align:start position:0%
+idea is let me just start with one. Um
+you get a card that's actually a a
+
+ align:start position:0%
+you get a card that's actually a a
+ 
+
+ align:start position:0%
+you get a card that's actually a a
+puzzle. Um I wish we were doing this
+
+ align:start position:0%
+puzzle. Um I wish we were doing this
+ 
+
+ align:start position:0%
+puzzle. Um I wish we were doing this
+outside now because I could have zoomed
+
+ align:start position:0%
+outside now because I could have zoomed
+ 
+
+ align:start position:0%
+outside now because I could have zoomed
+this out. Um but the puzzle basically
+
+ align:start position:0%
+this out. Um but the puzzle basically
+ 
+
+ align:start position:0%
+this out. Um but the puzzle basically
+just tells you how you're supposed to
+
+ align:start position:0%
+just tells you how you're supposed to
+ 
+
+ align:start position:0%
+just tells you how you're supposed to
+set up your board initially. So there's
+
+ align:start position:0%
+set up your board initially. So there's
+ 
+
+ align:start position:0%
+set up your board initially. So there's
+a Oops, wrong.
+
+ align:start position:0%
+a Oops, wrong.
+ 
+
+ align:start position:0%
+a Oops, wrong.
+There's a green guy there. There's a
+
+ align:start position:0%
+There's a green guy there. There's a
+ 
+
+ align:start position:0%
+There's a green guy there. There's a
+green guy there. This is supposed to be
+
+ align:start position:0%
+green guy there. This is supposed to be
+ 
+
+ align:start position:0%
+green guy there. This is supposed to be
+an easy puzzle. I hope it is because I'm
+
+ align:start position:0%
+an easy puzzle. I hope it is because I'm
+ 
+
+ align:start position:0%
+an easy puzzle. I hope it is because I'm
+really bad at this.
+
+ align:start position:0%
+really bad at this.
+ 
+
+ align:start position:0%
+really bad at this.
+Red guy goes there, I think. Yeah. And
+
+ align:start position:0%
+Red guy goes there, I think. Yeah. And
+ 
+
+ align:start position:0%
+Red guy goes there, I think. Yeah. And
+that's the puzzle.
+
+ align:start position:0%
+that's the puzzle.
+ 
+
+ align:start position:0%
+that's the puzzle.
+And then and there's one with a little
+
+ align:start position:0%
+And then and there's one with a little
+ 
+
+ align:start position:0%
+And then and there's one with a little
+square on it and then you have this
+
+ align:start position:0%
+square on it and then you have this
+ 
+
+ align:start position:0%
+square on it and then you have this
+chat. What?
+
+ align:start position:0%
+chat. What?
+ 
+
+ align:start position:0%
+chat. What?
+>> That's cool.
+
+ align:start position:0%
+>> That's cool.
+ 
+
+ align:start position:0%
+>> That's cool.
+>> That's awesome. So the basic idea is you
+
+ align:start position:0%
+>> That's awesome. So the basic idea is you
+ 
+
+ align:start position:0%
+>> That's awesome. So the basic idea is you
+tip over the pieces so that um so that
+
+ align:start position:0%
+tip over the pieces so that um so that
+ 
+
+ align:start position:0%
+tip over the pieces so that um so that
+the guy moves um and you don't want to
+
+ align:start position:0%
+the guy moves um and you don't want to
+ 
+
+ align:start position:0%
+the guy moves um and you don't want to
+be tipping over the pieces in a way
+
+ align:start position:0%
+be tipping over the pieces in a way
+ 
+
+ align:start position:0%
+be tipping over the pieces in a way
+where uh the um where the guy can't move
+
+ align:start position:0%
+where uh the um where the guy can't move
+ 
+
+ align:start position:0%
+where uh the um where the guy can't move
+anymore.
+
+ align:start position:0%
+anymore.
+ 
+
+ align:start position:0%
+anymore.
+>> Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> yeah. So you're you're tipping over
+
+ align:start position:0%
+>> yeah. So you're you're tipping over
+ 
+
+ align:start position:0%
+>> yeah. So you're you're tipping over
+things to make a path that he can walk
+
+ align:start position:0%
+things to make a path that he can walk
+ 
+
+ align:start position:0%
+things to make a path that he can walk
+along, right?
+
+ align:start position:0%
+along, right?
+ 
+
+ align:start position:0%
+along, right?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> And then make a closed loop
+
+ align:start position:0%
+>> And then make a closed loop
+ 
+
+ align:start position:0%
+>> And then make a closed loop
+>> and he has to touch every piece.
+
+ align:start position:0%
+>> and he has to touch every piece.
+ 
+
+ align:start position:0%
+>> and he has to touch every piece.
+>> I think he just has to get to this one
+
+ align:start position:0%
+>> I think he just has to get to this one
+ 
+
+ align:start position:0%
+>> I think he just has to get to this one
+get to the red one. Um,
+
+ align:start position:0%
+get to the red one. Um,
+ 
+
+ align:start position:0%
+get to the red one. Um,
+>> there's a plus mark.
+
+ align:start position:0%
+>> there's a plus mark.
+ 
+
+ align:start position:0%
+>> there's a plus mark.
+>> So, knock it that way and then green
+
+ align:start position:0%
+>> So, knock it that way and then green
+ 
+
+ align:start position:0%
+>> So, knock it that way and then green
+this way.
+
+ align:start position:0%
+this way.
+ 
+
+ align:start position:0%
+this way.
+>> Yeah. Yes, I agree.
+
+ align:start position:0%
+>> Yeah. Yes, I agree.
+ 
+
+ align:start position:0%
+>> Yeah. Yes, I agree.
+>> Yeah. I'm not exactly sure how to solve
+
+ align:start position:0%
+>> Yeah. I'm not exactly sure how to solve
+ 
+
+ align:start position:0%
+>> Yeah. I'm not exactly sure how to solve
+this one.
+
+ align:start position:0%
+this one.
+ 
+
+ align:start position:0%
+this one.
+>> So, yellow that way, green.
+
+ align:start position:0%
+>> So, yellow that way, green.
+ 
+
+ align:start position:0%
+>> So, yellow that way, green.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yellow that way.
+
+ align:start position:0%
+>> Yellow that way.
+ 
+
+ align:start position:0%
+>> Yellow that way.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Wait, you're allowed to tip him over?
+
+ align:start position:0%
+>> Wait, you're allowed to tip him over?
+ 
+
+ align:start position:0%
+>> Wait, you're allowed to tip him over?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Did he die?
+
+ align:start position:0%
+>> Did he die?
+ 
+
+ align:start position:0%
+>> Did he die?
+>> My understanding is that he needs to
+
+ align:start position:0%
+>> My understanding is that he needs to
+ 
+
+ align:start position:0%
+>> My understanding is that he needs to
+fall onto another piece actually.
+
+ align:start position:0%
+fall onto another piece actually.
+ 
+
+ align:start position:0%
+fall onto another piece actually.
+>> Oh, so let let me just confirm I set
+
+ align:start position:0%
+>> Oh, so let let me just confirm I set
+ 
+
+ align:start position:0%
+>> Oh, so let let me just confirm I set
+this up right actually. Yeah, I did.
+
+ align:start position:0%
+this up right actually. Yeah, I did.
+ 
+
+ align:start position:0%
+this up right actually. Yeah, I did.
+>> No. So, you push the yellow that way and
+
+ align:start position:0%
+>> No. So, you push the yellow that way and
+ 
+
+ align:start position:0%
+>> No. So, you push the yellow that way and
+then the green that way and the other
+
+ align:start position:0%
+then the green that way and the other
+ 
+
+ align:start position:0%
+then the green that way and the other
+green that way.
+
+ align:start position:0%
+green that way.
+ 
+
+ align:start position:0%
+green that way.
+So with the yellow one goes.
+
+ align:start position:0%
+So with the yellow one goes.
+ 
+
+ align:start position:0%
+So with the yellow one goes.
+>> So do the green ones first.
+
+ align:start position:0%
+>> So do the green ones first.
+ 
+
+ align:start position:0%
+>> So do the green ones first.
+>> Yeah. I don't understand the rules for
+
+ align:start position:0%
+>> Yeah. I don't understand the rules for
+ 
+
+ align:start position:0%
+>> Yeah. I don't understand the rules for
+yellow.
+
+ align:start position:0%
+yellow.
+ 
+
+ align:start position:0%
+yellow.
+>> Exactly. And then
+
+ align:start position:0%
+>> Exactly. And then
+ 
+
+ align:start position:0%
+>> Exactly. And then
+>> there.
+
+ align:start position:0%
+>> there.
+ 
+
+ align:start position:0%
+>> there.
+>> No, it doesn't.
+
+ align:start position:0%
+>> No, it doesn't.
+ 
+
+ align:start position:0%
+>> No, it doesn't.
+>> Yeah. I I
+
+ align:start position:0%
+>> Yeah. I I
+ 
+
+ align:start position:0%
+>> Yeah. I I
+>> How does he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, he he's he's actually allowed to
+
+ align:start position:0%
+Yeah, he he's he's actually allowed to
+ 
+
+ align:start position:0%
+Yeah, he he's he's actually allowed to
+move on anything that that's
+
+ align:start position:0%
+move on anything that that's
+ 
+
+ align:start position:0%
+move on anything that that's
+continuously connected. So as long as
+
+ align:start position:0%
+continuously connected. So as long as
+ 
+
+ align:start position:0%
+continuously connected. So as long as
+you can continuously
+
+ align:start position:0%
+you can continuously
+ 
+
+ align:start position:0%
+you can continuously
+connect up to this, you're fine. So tip
+
+ align:start position:0%
+connect up to this, you're fine. So tip
+ 
+
+ align:start position:0%
+connect up to this, you're fine. So tip
+tip the second green over.
+
+ align:start position:0%
+tip the second green over.
+ 
+
+ align:start position:0%
+tip the second green over.
+>> So tip that first green.
+
+ align:start position:0%
+>> So tip that first green.
+ 
+
+ align:start position:0%
+>> So tip that first green.
+>> No other way.
+
+ align:start position:0%
+>> No other way.
+ 
+
+ align:start position:0%
+>> No other way.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Doesn't that wrong path right now? If
+
+ align:start position:0%
+>> Doesn't that wrong path right now? If
+ 
+
+ align:start position:0%
+>> Doesn't that wrong path right now? If
+you tip that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Are you sure tipping over means move on
+
+ align:start position:0%
+>> Are you sure tipping over means move on
+ 
+
+ align:start position:0%
+>> Are you sure tipping over means move on
+spot or not?
+
+ align:start position:0%
+spot or not?
+ 
+
+ align:start position:0%
+spot or not?
+>> Well, if it doesn't then you can't reach
+
+ align:start position:0%
+>> Well, if it doesn't then you can't reach
+ 
+
+ align:start position:0%
+>> Well, if it doesn't then you can't reach
+the red effort. Yeah, I am absolutely
+
+ align:start position:0%
+the red effort. Yeah, I am absolutely
+ 
+
+ align:start position:0%
+the red effort. Yeah, I am absolutely
+sure it means that you're supposed to
+
+ align:start position:0%
+sure it means that you're supposed to
+ 
+
+ align:start position:0%
+sure it means that you're supposed to
+tip it over in a way that might be a
+
+ align:start position:0%
+tip it over in a way that might be a
+ 
+
+ align:start position:0%
+tip it over in a way that might be a
+>> screw. Tip the yellow over first and
+
+ align:start position:0%
+>> screw. Tip the yellow over first and
+ 
+
+ align:start position:0%
+>> screw. Tip the yellow over first and
+move the move the guy onto the green,
+
+ align:start position:0%
+move the move the guy onto the green,
+ 
+
+ align:start position:0%
+move the move the guy onto the green,
+then tip over the green.
+
+ align:start position:0%
+then tip over the green.
+ 
+
+ align:start position:0%
+then tip over the green.
+>> Oh, right.
+
+ align:start position:0%
+>> Oh, right.
+ 
+
+ align:start position:0%
+>> Oh, right.
+>> You think you are? I think you are.
+
+ align:start position:0%
+>> You think you are? I think you are.
+ 
+
+ align:start position:0%
+>> You think you are? I think you are.
+>> What? Why?
+
+ align:start position:0%
+>> What? Why?
+ 
+
+ align:start position:0%
+>> What? Why?
+>> That was crazy.
+
+ align:start position:0%
+>> That was crazy.
+ 
+
+ align:start position:0%
+>> That was crazy.
+>> That was why That is why it's supposed
+
+ align:start position:0%
+>> That was why That is why it's supposed
+ 
+
+ align:start position:0%
+>> That was why That is why it's supposed
+to be a beginner puzzle. You can
+
+ align:start position:0%
+to be a beginner puzzle. You can
+ 
+
+ align:start position:0%
+to be a beginner puzzle. You can
+actually do it. You can actually do it.
+
+ align:start position:0%
+actually do it. You can actually do it.
+ 
+
+ align:start position:0%
+actually do it. You can actually do it.
+This is This is why this is puzzle one.
+
+ align:start position:0%
+This is This is why this is puzzle one.
+ 
+
+ align:start position:0%
+This is This is why this is puzzle one.
+>> Uh you don't have to fall on top of
+
+ align:start position:0%
+>> Uh you don't have to fall on top of
+ 
+
+ align:start position:0%
+>> Uh you don't have to fall on top of
+anything.
+
+ align:start position:0%
+anything.
+ 
+
+ align:start position:0%
+anything.
+>> It's bizarre.
+
+ align:start position:0%
+>> It's bizarre.
+ 
+
+ align:start position:0%
+>> It's bizarre.
+>> Yeah. Like the instinct is you know you
+
+ align:start position:0%
+>> Yeah. Like the instinct is you know you
+ 
+
+ align:start position:0%
+>> Yeah. Like the instinct is you know you
+want to build a path that you can walk
+
+ align:start position:0%
+want to build a path that you can walk
+ 
+
+ align:start position:0%
+want to build a path that you can walk
+makes no sense.
+
+ align:start position:0%
+makes no sense.
+ 
+
+ align:start position:0%
+makes no sense.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> The guy does not make any
+
+ align:start position:0%
+>> The guy does not make any
+ 
+
+ align:start position:0%
+>> The guy does not make any
+>> but you know this is not entirely unlike
+
+ align:start position:0%
+>> but you know this is not entirely unlike
+ 
+
+ align:start position:0%
+>> but you know this is not entirely unlike
+the kind of puzzle that Scott does. I
+
+ align:start position:0%
+the kind of puzzle that Scott does. I
+ 
+
+ align:start position:0%
+the kind of puzzle that Scott does. I
+mean, sure, this is there's this one
+
+ align:start position:0%
+mean, sure, this is there's this one
+ 
+
+ align:start position:0%
+mean, sure, this is there's this one
+particular uh uh piece of plastic that
+
+ align:start position:0%
+particular uh uh piece of plastic that
+ 
+
+ align:start position:0%
+particular uh uh piece of plastic that
+uh that the game is designed to work
+
+ align:start position:0%
+uh that the game is designed to work
+ 
+
+ align:start position:0%
+uh that the game is designed to work
+with, but basically it's just, you know,
+
+ align:start position:0%
+with, but basically it's just, you know,
+ 
+
+ align:start position:0%
+with, but basically it's just, you know,
+it's like a book, right? It's like a
+
+ align:start position:0%
+it's like a book, right? It's like a
+ 
+
+ align:start position:0%
+it's like a book, right? It's like a
+book of puzzles. Um
+
+ align:start position:0%
+book of puzzles. Um
+ 
+
+ align:start position:0%
+book of puzzles. Um
+so there there are also solutions in
+
+ align:start position:0%
+so there there are also solutions in
+ 
+
+ align:start position:0%
+so there there are also solutions in
+here, but I I find the solutions harder
+
+ align:start position:0%
+here, but I I find the solutions harder
+ 
+
+ align:start position:0%
+here, but I I find the solutions harder
+to read than others.
+
+ align:start position:0%
+to read than others.
+ 
+
+ align:start position:0%
+to read than others.
+>> Pad recognition was in the book.
+
+ align:start position:0%
+>> Pad recognition was in the book.
+ 
+
+ align:start position:0%
+>> Pad recognition was in the book.
+>> Was it brand book?
+
+ align:start position:0%
+>> Was it brand book?
+ 
+
+ align:start position:0%
+>> Was it brand book?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah. Yeah. So, actually that's um
+
+ align:start position:0%
+>> Yeah. Yeah. So, actually that's um
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. So, actually that's um
+that's probably a good a good excuse to
+
+ align:start position:0%
+that's probably a good a good excuse to
+ 
+
+ align:start position:0%
+that's probably a good a good excuse to
+switch over to Brenda's. Uh well,
+
+ align:start position:0%
+switch over to Brenda's. Uh well,
+ 
+
+ align:start position:0%
+switch over to Brenda's. Uh well,
+actually before that I want to talk a
+
+ align:start position:0%
+actually before that I want to talk a
+ 
+
+ align:start position:0%
+actually before that I want to talk a
+little bit about tangs. I mean everyone
+
+ align:start position:0%
+little bit about tangs. I mean everyone
+ 
+
+ align:start position:0%
+little bit about tangs. I mean everyone
+play the tangs.
+
+ align:start position:0%
+play the tangs.
+ 
+
+ align:start position:0%
+play the tangs.
+>> No. Okay. So, you know the basic idea is
+
+ align:start position:0%
+>> No. Okay. So, you know the basic idea is
+ 
+
+ align:start position:0%
+>> No. Okay. So, you know the basic idea is
+you got these shapes. Um is this
+
+ align:start position:0%
+you got these shapes. Um is this
+ 
+
+ align:start position:0%
+you got these shapes. Um is this
+magnetic? Yeah, it is.
+
+ align:start position:0%
+magnetic? Yeah, it is.
+ 
+
+ align:start position:0%
+magnetic? Yeah, it is.
+>> Cool. Um, you've got these shapes and if
+
+ align:start position:0%
+>> Cool. Um, you've got these shapes and if
+ 
+
+ align:start position:0%
+>> Cool. Um, you've got these shapes and if
+you assemble them right, as the box,
+
+ align:start position:0%
+you assemble them right, as the box,
+ 
+
+ align:start position:0%
+you assemble them right, as the box,
+this is usually displayed on the side of
+
+ align:start position:0%
+this is usually displayed on the side of
+ 
+
+ align:start position:0%
+this is usually displayed on the side of
+a box somewhere. Where the heck are we
+
+ align:start position:0%
+a box somewhere. Where the heck are we
+ 
+
+ align:start position:0%
+a box somewhere. Where the heck are we
+on the inside?
+
+ align:start position:0%
+on the inside?
+ 
+
+ align:start position:0%
+on the inside?
+>> I I've got a big P picture on the side
+
+ align:start position:0%
+>> I I've got a big P picture on the side
+ 
+
+ align:start position:0%
+>> I I've got a big P picture on the side
+is that um you can actually fit all of
+
+ align:start position:0%
+is that um you can actually fit all of
+ 
+
+ align:start position:0%
+is that um you can actually fit all of
+these uh shapes inside that square. So,
+
+ align:start position:0%
+these uh shapes inside that square. So,
+ 
+
+ align:start position:0%
+these uh shapes inside that square. So,
+these are basically just a square that's
+
+ align:start position:0%
+these are basically just a square that's
+ 
+
+ align:start position:0%
+these are basically just a square that's
+been divided in in in a specific way.
+
+ align:start position:0%
+been divided in in in a specific way.
+ 
+
+ align:start position:0%
+been divided in in in a specific way.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+once I got this assembled, everyone can
+
+ align:start position:0%
+once I got this assembled, everyone can
+ 
+
+ align:start position:0%
+once I got this assembled, everyone can
+just like pass this around. Anyone who's
+
+ align:start position:0%
+just like pass this around. Anyone who's
+ 
+
+ align:start position:0%
+just like pass this around. Anyone who's
+already seen it can pass it on. That one
+
+ align:start position:0%
+already seen it can pass it on. That one
+ 
+
+ align:start position:0%
+already seen it can pass it on. That one
+doesn't fit very well, but I think it's
+
+ align:start position:0%
+doesn't fit very well, but I think it's
+ 
+
+ align:start position:0%
+doesn't fit very well, but I think it's
+cool now. Hey, that's tada. Hey, so this
+
+ align:start position:0%
+cool now. Hey, that's tada. Hey, so this
+ 
+
+ align:start position:0%
+cool now. Hey, that's tada. Hey, so this
+is the basic set. This is No.
+
+ align:start position:0%
+is the basic set. This is No.
+ 
+
+ align:start position:0%
+is the basic set. This is No.
+Um, this is now this is how it's been
+
+ align:start position:0%
+Um, this is now this is how it's been
+ 
+
+ align:start position:0%
+Um, this is now this is how it's been
+sold at least is that this is actually a
+
+ align:start position:0%
+sold at least is that this is actually a
+ 
+
+ align:start position:0%
+sold at least is that this is actually a
+calendar. So every day you get a
+
+ align:start position:0%
+calendar. So every day you get a
+ 
+
+ align:start position:0%
+calendar. So every day you get a
+different shape.
+
+ align:start position:0%
+different shape.
+ 
+
+ align:start position:0%
+different shape.
+>> It's a cute little thing. You know, some
+
+ align:start position:0%
+>> It's a cute little thing. You know, some
+ 
+
+ align:start position:0%
+>> It's a cute little thing. You know, some
+of them have pretty rudimentary like
+
+ align:start position:0%
+of them have pretty rudimentary like
+ 
+
+ align:start position:0%
+of them have pretty rudimentary like
+geometric shape. Some of them have like
+
+ align:start position:0%
+geometric shape. Some of them have like
+ 
+
+ align:start position:0%
+geometric shape. Some of them have like
+I think this is supposed to be a sphinx
+
+ align:start position:0%
+I think this is supposed to be a sphinx
+ 
+
+ align:start position:0%
+I think this is supposed to be a sphinx
+or some kind. Yeah, it looks like a
+
+ align:start position:0%
+or some kind. Yeah, it looks like a
+ 
+
+ align:start position:0%
+or some kind. Yeah, it looks like a
+frog.
+
+ align:start position:0%
+frog.
+ 
+
+ align:start position:0%
+frog.
+>> But this looks like a Pac-Man.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+you know and you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so the idea is that uh you know you
+
+ align:start position:0%
+um so the idea is that uh you know you
+ 
+
+ align:start position:0%
+um so the idea is that uh you know you
+rearrange those particular shapes into
+
+ align:start position:0%
+rearrange those particular shapes into
+ 
+
+ align:start position:0%
+rearrange those particular shapes into
+all of these different shapes and uh you
+
+ align:start position:0%
+all of these different shapes and uh you
+ 
+
+ align:start position:0%
+all of these different shapes and uh you
+know it's it's you could play the game
+
+ align:start position:0%
+know it's it's you could play the game
+ 
+
+ align:start position:0%
+know it's it's you could play the game
+without getting these puzzle solutions,
+
+ align:start position:0%
+without getting these puzzle solutions,
+ 
+
+ align:start position:0%
+without getting these puzzle solutions,
+right? And Scott Ken talks about a lot
+
+ align:start position:0%
+right? And Scott Ken talks about a lot
+ 
+
+ align:start position:0%
+right? And Scott Ken talks about a lot
+about like first if you've got a toy
+
+ align:start position:0%
+about like first if you've got a toy
+ 
+
+ align:start position:0%
+about like first if you've got a toy
+that's worth playing with, now you've
+
+ align:start position:0%
+that's worth playing with, now you've
+ 
+
+ align:start position:0%
+that's worth playing with, now you've
+got the beginning of something that
+
+ align:start position:0%
+got the beginning of something that
+ 
+
+ align:start position:0%
+got the beginning of something that
+would be a good thing. The nice thing
+
+ align:start position:0%
+would be a good thing. The nice thing
+ 
+
+ align:start position:0%
+would be a good thing. The nice thing
+about tipover is that it's kind of fun
+
+ align:start position:0%
+about tipover is that it's kind of fun
+ 
+
+ align:start position:0%
+about tipover is that it's kind of fun
+to tip over things.
+
+ align:start position:0%
+to tip over things.
+ 
+
+ align:start position:0%
+to tip over things.
+And the thing about tangs is that I
+
+ align:start position:0%
+And the thing about tangs is that I
+ 
+
+ align:start position:0%
+And the thing about tangs is that I
+actually had more fun playing with tangs
+
+ align:start position:0%
+actually had more fun playing with tangs
+ 
+
+ align:start position:0%
+actually had more fun playing with tangs
+than trying to solve specific problem
+
+ align:start position:0%
+than trying to solve specific problem
+ 
+
+ align:start position:0%
+than trying to solve specific problem
+just like just trying to rearrange
+
+ align:start position:0%
+just like just trying to rearrange
+ 
+
+ align:start position:0%
+just like just trying to rearrange
+these. Who hasn't seen these before?
+
+ align:start position:0%
+these. Who hasn't seen these before?
+ 
+
+ align:start position:0%
+these. Who hasn't seen these before?
+Get a sense of
+
+ align:start position:0%
+Get a sense of
+ 
+
+ align:start position:0%
+Get a sense of
+>> wow.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be ashamed to yourself
+
+ align:start position:0%
+be ashamed to yourself
+ 
+
+ align:start position:0%
+be ashamed to yourself
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+>> and all the work that you did is gone.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> But that's the thing is that you know as
+
+ align:start position:0%
+>> But that's the thing is that you know as
+ 
+
+ align:start position:0%
+>> But that's the thing is that you know as
+a toy you know it doesn't really matter
+
+ align:start position:0%
+a toy you know it doesn't really matter
+ 
+
+ align:start position:0%
+a toy you know it doesn't really matter
+right because it's just it's just a it's
+
+ align:start position:0%
+right because it's just it's just a it's
+ 
+
+ align:start position:0%
+right because it's just it's just a it's
+just a piece a set of pieces that can be
+
+ align:start position:0%
+just a piece a set of pieces that can be
+ 
+
+ align:start position:0%
+just a piece a set of pieces that can be
+configuring anything and you kind of
+
+ align:start position:0%
+configuring anything and you kind of
+ 
+
+ align:start position:0%
+configuring anything and you kind of
+want to take it apart and you know make
+
+ align:start position:0%
+want to take it apart and you know make
+ 
+
+ align:start position:0%
+want to take it apart and you know make
+new shapes with it like little house.
+
+ align:start position:0%
+new shapes with it like little house.
+ 
+
+ align:start position:0%
+new shapes with it like little house.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so you know, if you've got something
+
+ align:start position:0%
+so you know, if you've got something
+ 
+
+ align:start position:0%
+so you know, if you've got something
+that's kind of fun to fiddle with to
+
+ align:start position:0%
+that's kind of fun to fiddle with to
+ 
+
+ align:start position:0%
+that's kind of fun to fiddle with to
+begin with, you've got possibly the
+
+ align:start position:0%
+begin with, you've got possibly the
+ 
+
+ align:start position:0%
+begin with, you've got possibly the
+beginning of a game in general, uh, but,
+
+ align:start position:0%
+beginning of a game in general, uh, but,
+ 
+
+ align:start position:0%
+beginning of a game in general, uh, but,
+uh, the way how Scott was talking about
+
+ align:start position:0%
+uh, the way how Scott was talking about
+ 
+
+ align:start position:0%
+uh, the way how Scott was talking about
+it, there's this intermediate step where
+
+ align:start position:0%
+it, there's this intermediate step where
+ 
+
+ align:start position:0%
+it, there's this intermediate step where
+it's a puzzle, you know, it's this it's
+
+ align:start position:0%
+it's a puzzle, you know, it's this it's
+ 
+
+ align:start position:0%
+it's a puzzle, you know, it's this it's
+a toy with a specific solution that
+
+ align:start position:0%
+a toy with a specific solution that
+ 
+
+ align:start position:0%
+a toy with a specific solution that
+you're trying to get to. And then gaming
+
+ align:start position:0%
+you're trying to get to. And then gaming
+ 
+
+ align:start position:0%
+you're trying to get to. And then gaming
+is kind of like one step beyond that
+
+ align:start position:0%
+is kind of like one step beyond that
+ 
+
+ align:start position:0%
+is kind of like one step beyond that
+where now there's like multiple
+
+ align:start position:0%
+where now there's like multiple
+ 
+
+ align:start position:0%
+where now there's like multiple
+solutions and competitive uh at least
+
+ align:start position:0%
+solutions and competitive uh at least
+ 
+
+ align:start position:0%
+solutions and competitive uh at least
+that's that's how he was constructing
+
+ align:start position:0%
+that's that's how he was constructing
+ 
+
+ align:start position:0%
+that's that's how he was constructing
+it. He's not really a game theorist. He
+
+ align:start position:0%
+it. He's not really a game theorist. He
+ 
+
+ align:start position:0%
+it. He's not really a game theorist. He
+just puzzles.
+
+ align:start position:0%
+just puzzles.
+ 
+
+ align:start position:0%
+just puzzles.
+>> He talks about in terms of a goal,
+
+ align:start position:0%
+>> He talks about in terms of a goal,
+ 
+
+ align:start position:0%
+>> He talks about in terms of a goal,
+right? So that with a toy that you don't
+
+ align:start position:0%
+right? So that with a toy that you don't
+ 
+
+ align:start position:0%
+right? So that with a toy that you don't
+have a goal but then with a puzzle you
+
+ align:start position:0%
+have a goal but then with a puzzle you
+ 
+
+ align:start position:0%
+have a goal but then with a puzzle you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+>> you have you have one goal with no
+
+ align:start position:0%
+>> you have you have one goal with no
+ 
+
+ align:start position:0%
+>> you have you have one goal with no
+interaction and then a game is many with
+
+ align:start position:0%
+interaction and then a game is many with
+ 
+
+ align:start position:0%
+interaction and then a game is many with
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+>> and possibly multiple goals as well. I
+
+ align:start position:0%
+>> and possibly multiple goals as well. I
+ 
+
+ align:start position:0%
+>> and possibly multiple goals as well. I
+don't know but but again it becomes more
+
+ align:start position:0%
+don't know but but again it becomes more
+ 
+
+ align:start position:0%
+don't know but but again it becomes more
+and more directed whereas toy is very
+
+ align:start position:0%
+and more directed whereas toy is very
+ 
+
+ align:start position:0%
+and more directed whereas toy is very
+free form. So, so there are people who
+
+ align:start position:0%
+free form. So, so there are people who
+ 
+
+ align:start position:0%
+free form. So, so there are people who
+describe games uh like the Sims for
+
+ align:start position:0%
+describe games uh like the Sims for
+ 
+
+ align:start position:0%
+describe games uh like the Sims for
+instance as actually toys, you know, and
+
+ align:start position:0%
+instance as actually toys, you know, and
+ 
+
+ align:start position:0%
+instance as actually toys, you know, and
+in the same way that you describe a
+
+ align:start position:0%
+in the same way that you describe a
+ 
+
+ align:start position:0%
+in the same way that you describe a
+dollhouse as a toy, the Sims is kind of
+
+ align:start position:0%
+dollhouse as a toy, the Sims is kind of
+ 
+
+ align:start position:0%
+dollhouse as a toy, the Sims is kind of
+like the digital uh digital dollhouse.
+
+ align:start position:0%
+like the digital uh digital dollhouse.
+ 
+
+ align:start position:0%
+like the digital uh digital dollhouse.
+But later versions of the Sims kind of
+
+ align:start position:0%
+But later versions of the Sims kind of
+ 
+
+ align:start position:0%
+But later versions of the Sims kind of
+like added more and more specific roles
+
+ align:start position:0%
+like added more and more specific roles
+ 
+
+ align:start position:0%
+like added more and more specific roles
+like you know and now you have to throw
+
+ align:start position:0%
+like you know and now you have to throw
+ 
+
+ align:start position:0%
+like you know and now you have to throw
+a party with at least five people in it
+
+ align:start position:0%
+a party with at least five people in it
+ 
+
+ align:start position:0%
+a party with at least five people in it
+uh or you have to attain career level
+
+ align:start position:0%
+uh or you have to attain career level
+ 
+
+ align:start position:0%
+uh or you have to attain career level
+you know five or something like that. Um
+
+ align:start position:0%
+you know five or something like that. Um
+ 
+
+ align:start position:0%
+you know five or something like that. Um
+I can't remember exactly how you how you
+
+ align:start position:0%
+I can't remember exactly how you how you
+ 
+
+ align:start position:0%
+I can't remember exactly how you how you
+mentioned it but then that kind of like
+
+ align:start position:0%
+mentioned it but then that kind of like
+ 
+
+ align:start position:0%
+mentioned it but then that kind of like
+has that whole we are going to give more
+
+ align:start position:0%
+has that whole we are going to give more
+ 
+
+ align:start position:0%
+has that whole we are going to give more
+and more specific things for you to work
+
+ align:start position:0%
+and more specific things for you to work
+ 
+
+ align:start position:0%
+and more specific things for you to work
+towards but it but the Sims is very
+
+ align:start position:0%
+towards but it but the Sims is very
+ 
+
+ align:start position:0%
+towards but it but the Sims is very
+careful not to lose its toy sense the
+
+ align:start position:0%
+careful not to lose its toy sense the
+ 
+
+ align:start position:0%
+careful not to lose its toy sense the
+sense of you can if you really wanted to
+
+ align:start position:0%
+sense of you can if you really wanted to
+ 
+
+ align:start position:0%
+sense of you can if you really wanted to
+just dig around with these guys just go
+
+ align:start position:0%
+just dig around with these guys just go
+ 
+
+ align:start position:0%
+just dig around with these guys just go
+right ahead just just just uh just uh uh
+
+ align:start position:0%
+right ahead just just just uh just uh uh
+ 
+
+ align:start position:0%
+right ahead just just just uh just uh uh
+just play around with them and see what
+
+ align:start position:0%
+just play around with them and see what
+ 
+
+ align:start position:0%
+just play around with them and see what
+happens. Um, so yeah.
+
+ align:start position:0%
+happens. Um, so yeah.
+ 
+
+ align:start position:0%
+happens. Um, so yeah.
+>> Why is there a distinction for physical
+
+ align:start position:0%
+>> Why is there a distinction for physical
+ 
+
+ align:start position:0%
+>> Why is there a distinction for physical
+objects between toys and games? But for
+
+ align:start position:0%
+objects between toys and games? But for
+ 
+
+ align:start position:0%
+objects between toys and games? But for
+like video games like Minecraft is
+
+ align:start position:0%
+like video games like Minecraft is
+ 
+
+ align:start position:0%
+like video games like Minecraft is
+technically still a game, but it's
+
+ align:start position:0%
+technically still a game, but it's
+ 
+
+ align:start position:0%
+technically still a game, but it's
+different modes. Yeah,
+
+ align:start position:0%
+different modes. Yeah,
+ 
+
+ align:start position:0%
+different modes. Yeah,
+>> I guess it has different modes, but it's
+
+ align:start position:0%
+>> I guess it has different modes, but it's
+ 
+
+ align:start position:0%
+>> I guess it has different modes, but it's
+more of a toy. I think
+
+ align:start position:0%
+more of a toy. I think
+ 
+
+ align:start position:0%
+more of a toy. I think
+>> I would say that that's entirely
+
+ align:start position:0%
+>> I would say that that's entirely
+ 
+
+ align:start position:0%
+>> I would say that that's entirely
+marketing. That's the only reason is um
+
+ align:start position:0%
+marketing. That's the only reason is um
+ 
+
+ align:start position:0%
+marketing. That's the only reason is um
+people haven't figured out how to sell
+
+ align:start position:0%
+people haven't figured out how to sell
+ 
+
+ align:start position:0%
+people haven't figured out how to sell
+digital toys and there are games idolis
+
+ align:start position:0%
+digital toys and there are games idolis
+ 
+
+ align:start position:0%
+digital toys and there are games idolis
+in like Best Buy and and so well there's
+
+ align:start position:0%
+in like Best Buy and and so well there's
+ 
+
+ align:start position:0%
+in like Best Buy and and so well there's
+this fun thing I'm going to put in the
+
+ align:start position:0%
+this fun thing I'm going to put in the
+ 
+
+ align:start position:0%
+this fun thing I'm going to put in the
+game section. Everyone starts calling it
+
+ align:start position:0%
+game section. Everyone starts calling it
+ 
+
+ align:start position:0%
+game section. Everyone starts calling it
+games and that's kind of the same the
+
+ align:start position:0%
+games and that's kind of the same the
+ 
+
+ align:start position:0%
+games and that's kind of the same the
+same thing with the Sims is like really
+
+ align:start position:0%
+same thing with the Sims is like really
+ 
+
+ align:start position:0%
+same thing with the Sims is like really
+the Sims should be its own genre but you
+
+ align:start position:0%
+the Sims should be its own genre but you
+ 
+
+ align:start position:0%
+the Sims should be its own genre but you
+can't sell its own genre that well. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was there a hand over here?
+
+ align:start position:0%
+was there a hand over here?
+ 
+
+ align:start position:0%
+was there a hand over here?
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+okay. So, so that's um that's some of
+
+ align:start position:0%
+okay. So, so that's um that's some of
+ 
+
+ align:start position:0%
+okay. So, so that's um that's some of
+the stuff with Brenda's uh uh with it
+
+ align:start position:0%
+the stuff with Brenda's uh uh with it
+ 
+
+ align:start position:0%
+the stuff with Brenda's uh uh with it
+starts reading. First, let's move on to
+
+ align:start position:0%
+starts reading. First, let's move on to
+ 
+
+ align:start position:0%
+starts reading. First, let's move on to
+Brenda's. Um, and she's very specific
+
+ align:start position:0%
+Brenda's. Um, and she's very specific
+ 
+
+ align:start position:0%
+Brenda's. Um, and she's very specific
+about the kinds of puzzles that she's
+
+ align:start position:0%
+about the kinds of puzzles that she's
+ 
+
+ align:start position:0%
+about the kinds of puzzles that she's
+talking about. There's these things that
+
+ align:start position:0%
+talking about. There's these things that
+ 
+
+ align:start position:0%
+talking about. There's these things that
+get in the way of a very specific
+
+ align:start position:0%
+get in the way of a very specific
+ 
+
+ align:start position:0%
+get in the way of a very specific
+narrative experience that a game wants
+
+ align:start position:0%
+narrative experience that a game wants
+ 
+
+ align:start position:0%
+narrative experience that a game wants
+to you to to guide you through. She she
+
+ align:start position:0%
+to you to to guide you through. She she
+ 
+
+ align:start position:0%
+to you to to guide you through. She she
+describes them more as roadblocks than
+
+ align:start position:0%
+describes them more as roadblocks than
+ 
+
+ align:start position:0%
+describes them more as roadblocks than
+anything else. um but you know things to
+
+ align:start position:0%
+anything else. um but you know things to
+ 
+
+ align:start position:0%
+anything else. um but you know things to
+sort of like make the challenge higher
+
+ align:start position:0%
+sort of like make the challenge higher
+ 
+
+ align:start position:0%
+sort of like make the challenge higher
+but possibly so high that no one's going
+
+ align:start position:0%
+but possibly so high that no one's going
+ 
+
+ align:start position:0%
+but possibly so high that no one's going
+to be able to get past it. Um, some of
+
+ align:start position:0%
+to be able to get past it. Um, some of
+ 
+
+ align:start position:0%
+to be able to get past it. Um, some of
+her examples are things that come up as
+
+ align:start position:0%
+her examples are things that come up as
+ 
+
+ align:start position:0%
+her examples are things that come up as
+sort of intermittent but optional
+
+ align:start position:0%
+sort of intermittent but optional
+ 
+
+ align:start position:0%
+sort of intermittent but optional
+mechanics like hacking in bio in in in
+
+ align:start position:0%
+mechanics like hacking in bio in in in
+ 
+
+ align:start position:0%
+mechanics like hacking in bio in in in
+Bioshock. And sometimes there are like
+
+ align:start position:0%
+Bioshock. And sometimes there are like
+ 
+
+ align:start position:0%
+Bioshock. And sometimes there are like
+things that you have to solve. Uh,
+
+ align:start position:0%
+things that you have to solve. Uh,
+ 
+
+ align:start position:0%
+things that you have to solve. Uh,
+especially in adventure games, there's
+
+ align:start position:0%
+especially in adventure games, there's
+ 
+
+ align:start position:0%
+especially in adventure games, there's
+this you have to combine this object
+
+ align:start position:0%
+this you have to combine this object
+ 
+
+ align:start position:0%
+this you have to combine this object
+with that object and bring it to a
+
+ align:start position:0%
+with that object and bring it to a
+ 
+
+ align:start position:0%
+with that object and bring it to a
+specific location and then now you have
+
+ align:start position:0%
+specific location and then now you have
+ 
+
+ align:start position:0%
+specific location and then now you have
+to, you know, uh, and now you you you
+
+ align:start position:0%
+to, you know, uh, and now you you you
+ 
+
+ align:start position:0%
+to, you know, uh, and now you you you
+can proceed with whatever narrative
+
+ align:start position:0%
+can proceed with whatever narrative
+ 
+
+ align:start position:0%
+can proceed with whatever narrative
+you've got. She had this spec this
+
+ align:start position:0%
+you've got. She had this spec this
+ 
+
+ align:start position:0%
+you've got. She had this spec this
+specific axe to grind against.
+
+ align:start position:0%
+specific axe to grind against.
+ 
+
+ align:start position:0%
+specific axe to grind against.
+puzzles having meaningful rewards or not
+
+ align:start position:0%
+puzzles having meaningful rewards or not
+ 
+
+ align:start position:0%
+puzzles having meaningful rewards or not
+being completely blocking. So for
+
+ align:start position:0%
+being completely blocking. So for
+ 
+
+ align:start position:0%
+being completely blocking. So for
+instance, she says you should never have
+
+ align:start position:0%
+instance, she says you should never have
+ 
+
+ align:start position:0%
+instance, she says you should never have
+a a puzzle being required to open a
+
+ align:start position:0%
+a a puzzle being required to open a
+ 
+
+ align:start position:0%
+a a puzzle being required to open a
+door. She said solve a puzzle and then
+
+ align:start position:0%
+door. She said solve a puzzle and then
+ 
+
+ align:start position:0%
+door. She said solve a puzzle and then
+get some kind of tangible reward like or
+
+ align:start position:0%
+get some kind of tangible reward like or
+ 
+
+ align:start position:0%
+get some kind of tangible reward like or
+something. This is after I spent like
+
+ align:start position:0%
+something. This is after I spent like
+ 
+
+ align:start position:0%
+something. This is after I spent like
+the bus ride to New York City playing
+
+ align:start position:0%
+the bus ride to New York City playing
+ 
+
+ align:start position:0%
+the bus ride to New York City playing
+Professor Leon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which was like nonstop. We found a door.
+
+ align:start position:0%
+which was like nonstop. We found a door.
+ 
+
+ align:start position:0%
+which was like nonstop. We found a door.
+It's got a lock on it. looks like a
+
+ align:start position:0%
+It's got a lock on it. looks like a
+ 
+
+ align:start position:0%
+It's got a lock on it. looks like a
+puzzle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I wasn't entirely sure what to make
+
+ align:start position:0%
+So, I wasn't entirely sure what to make
+ 
+
+ align:start position:0%
+So, I wasn't entirely sure what to make
+of that. I thought that like my
+
+ align:start position:0%
+of that. I thought that like my
+ 
+
+ align:start position:0%
+of that. I thought that like my
+professor Leighton experience was fine
+
+ align:start position:0%
+professor Leighton experience was fine
+ 
+
+ align:start position:0%
+professor Leighton experience was fine
+and I didn't need to get fat laton loot
+
+ align:start position:0%
+and I didn't need to get fat laton loot
+ 
+
+ align:start position:0%
+and I didn't need to get fat laton loot
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+>> that's that's actually something. Yeah.
+
+ align:start position:0%
+>> that's that's actually something. Yeah.
+ 
+
+ align:start position:0%
+>> that's that's actually something. Yeah.
+And and uh there's a really good article
+
+ align:start position:0%
+And and uh there's a really good article
+ 
+
+ align:start position:0%
+And and uh there's a really good article
+actually written by Clara over in our
+
+ align:start position:0%
+actually written by Clara over in our
+ 
+
+ align:start position:0%
+actually written by Clara over in our
+lab that actually was an article. It was
+
+ align:start position:0%
+lab that actually was an article. It was
+ 
+
+ align:start position:0%
+lab that actually was an article. It was
+a it was a transcript of the talk that
+
+ align:start position:0%
+a it was a transcript of the talk that
+ 
+
+ align:start position:0%
+a it was a transcript of the talk that
+she gave at Austin GDC. I I'll send out
+
+ align:start position:0%
+she gave at Austin GDC. I I'll send out
+ 
+
+ align:start position:0%
+she gave at Austin GDC. I I'll send out
+the link to everyone about how you can
+
+ align:start position:0%
+the link to everyone about how you can
+ 
+
+ align:start position:0%
+the link to everyone about how you can
+integrate and why you should integrate
+
+ align:start position:0%
+integrate and why you should integrate
+ 
+
+ align:start position:0%
+integrate and why you should integrate
+puzzles really really well in the
+
+ align:start position:0%
+puzzles really really well in the
+ 
+
+ align:start position:0%
+puzzles really really well in the
+narrative. It's like really why is there
+
+ align:start position:0%
+narrative. It's like really why is there
+ 
+
+ align:start position:0%
+narrative. It's like really why is there
+a puzzle in your game at all unless it's
+
+ align:start position:0%
+a puzzle in your game at all unless it's
+ 
+
+ align:start position:0%
+a puzzle in your game at all unless it's
+been integrated into narrative. Um and
+
+ align:start position:0%
+been integrated into narrative. Um and
+ 
+
+ align:start position:0%
+been integrated into narrative. Um and
+Brenda seems to be sort of providing a
+
+ align:start position:0%
+Brenda seems to be sort of providing a
+ 
+
+ align:start position:0%
+Brenda seems to be sort of providing a
+cautionary
+
+ align:start position:0%
+cautionary
+ 
+
+ align:start position:0%
+cautionary
+uh you know tale of the but if you do it
+
+ align:start position:0%
+uh you know tale of the but if you do it
+ 
+
+ align:start position:0%
+uh you know tale of the but if you do it
+badly no one can get on with the story.
+
+ align:start position:0%
+badly no one can get on with the story.
+ 
+
+ align:start position:0%
+badly no one can get on with the story.
+No one can enjoy the rest of the game.
+
+ align:start position:0%
+No one can enjoy the rest of the game.
+ 
+
+ align:start position:0%
+No one can enjoy the rest of the game.
+Becomes this one thing that prevents you
+
+ align:start position:0%
+Becomes this one thing that prevents you
+ 
+
+ align:start position:0%
+Becomes this one thing that prevents you
+from proceeding. Is there anyone who
+
+ align:start position:0%
+from proceeding. Is there anyone who
+ 
+
+ align:start position:0%
+from proceeding. Is there anyone who
+kind of had that moment and then
+
+ align:start position:0%
+kind of had that moment and then
+ 
+
+ align:start position:0%
+kind of had that moment and then
+>> about 5 minutes into mist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I think three
+
+ align:start position:0%
+>> I think three
+ 
+
+ align:start position:0%
+>> I think three
+>> I don't know they had sort of some cool
+
+ align:start position:0%
+>> I don't know they had sort of some cool
+ 
+
+ align:start position:0%
+>> I don't know they had sort of some cool
+like live action video and stuff and it
+
+ align:start position:0%
+like live action video and stuff and it
+ 
+
+ align:start position:0%
+like live action video and stuff and it
+looked like it could be like an
+
+ align:start position:0%
+looked like it could be like an
+ 
+
+ align:start position:0%
+looked like it could be like an
+interesting story and I was kind of
+
+ align:start position:0%
+interesting story and I was kind of
+ 
+
+ align:start position:0%
+interesting story and I was kind of
+amused by the technological prowess of
+
+ align:start position:0%
+amused by the technological prowess of
+ 
+
+ align:start position:0%
+amused by the technological prowess of
+integrating like video into 3D and then
+
+ align:start position:0%
+integrating like video into 3D and then
+ 
+
+ align:start position:0%
+integrating like video into 3D and then
+suddenly I like looked into the picture
+
+ align:start position:0%
+suddenly I like looked into the picture
+ 
+
+ align:start position:0%
+suddenly I like looked into the picture
+and I was on an island and and then
+
+ align:start position:0%
+and I was on an island and and then
+ 
+
+ align:start position:0%
+and I was on an island and and then
+there was nothing happening and I had to
+
+ align:start position:0%
+there was nothing happening and I had to
+ 
+
+ align:start position:0%
+there was nothing happening and I had to
+turn things to face each other and I
+
+ align:start position:0%
+turn things to face each other and I
+ 
+
+ align:start position:0%
+turn things to face each other and I
+couldn't figure it out.
+
+ align:start position:0%
+couldn't figure it out.
+ 
+
+ align:start position:0%
+couldn't figure it out.
+>> I definitely had that when I originally
+
+ align:start position:0%
+>> I definitely had that when I originally
+ 
+
+ align:start position:0%
+>> I definitely had that when I originally
+played The Legend of Zelda the original
+
+ align:start position:0%
+played The Legend of Zelda the original
+ 
+
+ align:start position:0%
+played The Legend of Zelda the original
+one where so I don't know if you don't
+
+ align:start position:0%
+one where so I don't know if you don't
+ 
+
+ align:start position:0%
+one where so I don't know if you don't
+so they didn't tell you anything pretty
+
+ align:start position:0%
+so they didn't tell you anything pretty
+ 
+
+ align:start position:0%
+so they didn't tell you anything pretty
+much. And so the temples you have, you
+
+ align:start position:0%
+much. And so the temples you have, you
+ 
+
+ align:start position:0%
+much. And so the temples you have, you
+just walk around. There's something
+
+ align:start position:0%
+just walk around. There's something
+ 
+
+ align:start position:0%
+just walk around. There's something
+that's like, okay, there's a tree in a
+
+ align:start position:0%
+that's like, okay, there's a tree in a
+ 
+
+ align:start position:0%
+that's like, okay, there's a tree in a
+forest. You're supposed to cut, you're
+
+ align:start position:0%
+forest. You're supposed to cut, you're
+ 
+
+ align:start position:0%
+forest. You're supposed to cut, you're
+supposed to burn this particular one.
+
+ align:start position:0%
+supposed to burn this particular one.
+ 
+
+ align:start position:0%
+supposed to burn this particular one.
+And and there's the entrance to the to
+
+ align:start position:0%
+And and there's the entrance to the to
+ 
+
+ align:start position:0%
+And and there's the entrance to the to
+this temple that you can't perceive
+
+ align:start position:0%
+this temple that you can't perceive
+ 
+
+ align:start position:0%
+this temple that you can't perceive
+until you do this thing. And so it's
+
+ align:start position:0%
+until you do this thing. And so it's
+ 
+
+ align:start position:0%
+until you do this thing. And so it's
+just like, how am I supposed to know
+
+ align:start position:0%
+just like, how am I supposed to know
+ 
+
+ align:start position:0%
+just like, how am I supposed to know
+that I'm supposed to burn this
+
+ align:start position:0%
+that I'm supposed to burn this
+ 
+
+ align:start position:0%
+that I'm supposed to burn this
+particular tree in the middle of this
+
+ align:start position:0%
+particular tree in the middle of this
+ 
+
+ align:start position:0%
+particular tree in the middle of this
+huge map?
+
+ align:start position:0%
+huge map?
+ 
+
+ align:start position:0%
+huge map?
+>> Did you beat any of the other
+
+ align:start position:0%
+>> Did you beat any of the other
+ 
+
+ align:start position:0%
+>> Did you beat any of the other
+>> Yeah. And they didn't say anything. No,
+
+ align:start position:0%
+>> Yeah. And they didn't say anything. No,
+ 
+
+ align:start position:0%
+>> Yeah. And they didn't say anything. No,
+I mean the others.
+
+ align:start position:0%
+I mean the others.
+ 
+
+ align:start position:0%
+I mean the others.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Actually, yesterday we are time again.
+
+ align:start position:0%
+>> Actually, yesterday we are time again.
+ 
+
+ align:start position:0%
+>> Actually, yesterday we are time again.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+>> I mean that tells you
+
+ align:start position:0%
+>> I mean that tells you
+ 
+
+ align:start position:0%
+>> I mean that tells you
+>> I was just saying so the interesting
+
+ align:start position:0%
+>> I was just saying so the interesting
+ 
+
+ align:start position:0%
+>> I was just saying so the interesting
+thing is so most people nowadays they
+
+ align:start position:0%
+thing is so most people nowadays they
+ 
+
+ align:start position:0%
+thing is so most people nowadays they
+end up playing like the Ocarina of Time
+
+ align:start position:0%
+end up playing like the Ocarina of Time
+ 
+
+ align:start position:0%
+end up playing like the Ocarina of Time
+and George Mass and start moving
+
+ align:start position:0%
+and George Mass and start moving
+ 
+
+ align:start position:0%
+and George Mass and start moving
+backwards. So then end up playing Zelda
+
+ align:start position:0%
+backwards. So then end up playing Zelda
+ 
+
+ align:start position:0%
+backwards. So then end up playing Zelda
+the first Zelda after having played
+
+ align:start position:0%
+the first Zelda after having played
+ 
+
+ align:start position:0%
+the first Zelda after having played
+these old ones.
+
+ align:start position:0%
+these old ones.
+ 
+
+ align:start position:0%
+these old ones.
+>> So you sort of know that you're expected
+
+ align:start position:0%
+>> So you sort of know that you're expected
+ 
+
+ align:start position:0%
+>> So you sort of know that you're expected
+to do these random things to get like
+
+ align:start position:0%
+to do these random things to get like
+ 
+
+ align:start position:0%
+to do these random things to get like
+across. So I feel like it's easier for
+
+ align:start position:0%
+across. So I feel like it's easier for
+ 
+
+ align:start position:0%
+across. So I feel like it's easier for
+people. But then,
+
+ align:start position:0%
+people. But then,
+ 
+
+ align:start position:0%
+people. But then,
+>> but with the original Zelda, the you
+
+ align:start position:0%
+>> but with the original Zelda, the you
+ 
+
+ align:start position:0%
+>> but with the original Zelda, the you
+know how in new ones they have like it's
+
+ align:start position:0%
+know how in new ones they have like it's
+ 
+
+ align:start position:0%
+know how in new ones they have like it's
+like let's say a wall you can blow up.
+
+ align:start position:0%
+like let's say a wall you can blow up.
+ 
+
+ align:start position:0%
+like let's say a wall you can blow up.
+It's discolored or something. And the in
+
+ align:start position:0%
+It's discolored or something. And the in
+ 
+
+ align:start position:0%
+It's discolored or something. And the in
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+>> every tree looks exactly the same. They
+
+ align:start position:0%
+>> every tree looks exactly the same. They
+ 
+
+ align:start position:0%
+>> every tree looks exactly the same. They
+use the same sprites.
+
+ align:start position:0%
+use the same sprites.
+ 
+
+ align:start position:0%
+use the same sprites.
+>> If I remember correctly though, it's
+
+ align:start position:0%
+>> If I remember correctly though, it's
+ 
+
+ align:start position:0%
+>> If I remember correctly though, it's
+placed such that it's like in the center
+
+ align:start position:0%
+placed such that it's like in the center
+ 
+
+ align:start position:0%
+placed such that it's like in the center
+of your screen, right? So it does look a
+
+ align:start position:0%
+of your screen, right? So it does look a
+ 
+
+ align:start position:0%
+of your screen, right? So it does look a
+little bit different.
+
+ align:start position:0%
+little bit different.
+ 
+
+ align:start position:0%
+little bit different.
+>> No, no,
+
+ align:start position:0%
+>> No, no,
+ 
+
+ align:start position:0%
+>> No, no,
+>> it was like
+
+ align:start position:0%
+>> it was like
+ 
+
+ align:start position:0%
+>> it was like
+>> it was just a random tree.
+
+ align:start position:0%
+>> it was just a random tree.
+ 
+
+ align:start position:0%
+>> it was just a random tree.
+>> Band of trees.
+
+ align:start position:0%
+>> Band of trees.
+ 
+
+ align:start position:0%
+>> Band of trees.
+>> Yeah, it was just a whole bunch of
+
+ align:start position:0%
+>> Yeah, it was just a whole bunch of
+ 
+
+ align:start position:0%
+>> Yeah, it was just a whole bunch of
+trees.
+
+ align:start position:0%
+trees.
+ 
+
+ align:start position:0%
+trees.
+And so you just you really just have to
+
+ align:start position:0%
+And so you just you really just have to
+ 
+
+ align:start position:0%
+And so you just you really just have to
+get a whatever like a type of thing to
+
+ align:start position:0%
+get a whatever like a type of thing to
+ 
+
+ align:start position:0%
+get a whatever like a type of thing to
+burn it and a specific one
+
+ align:start position:0%
+burn it and a specific one
+ 
+
+ align:start position:0%
+burn it and a specific one
+>> and burn it. Usually that place is a
+
+ align:start position:0%
+>> and burn it. Usually that place is a
+ 
+
+ align:start position:0%
+>> and burn it. Usually that place is a
+little suspicious. So I think there was
+
+ align:start position:0%
+little suspicious. So I think there was
+ 
+
+ align:start position:0%
+little suspicious. So I think there was
+like a one tile column like you could
+
+ align:start position:0%
+like a one tile column like you could
+ 
+
+ align:start position:0%
+like a one tile column like you could
+like navigate around just like this like
+
+ align:start position:0%
+like navigate around just like this like
+ 
+
+ align:start position:0%
+like navigate around just like this like
+loop you just entered and was
+
+ align:start position:0%
+loop you just entered and was
+ 
+
+ align:start position:0%
+loop you just entered and was
+suspicious.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I feel very frustrated by games that
+
+ align:start position:0%
+>> I feel very frustrated by games that
+ 
+
+ align:start position:0%
+>> I feel very frustrated by games that
+like require walkthroughs in order to
+
+ align:start position:0%
+like require walkthroughs in order to
+ 
+
+ align:start position:0%
+like require walkthroughs in order to
+play them. Sure. And that was the other
+
+ align:start position:0%
+play them. Sure. And that was the other
+ 
+
+ align:start position:0%
+play them. Sure. And that was the other
+thing that she said that she suggested
+
+ align:start position:0%
+thing that she said that she suggested
+ 
+
+ align:start position:0%
+thing that she said that she suggested
+some game designers do. They put the
+
+ align:start position:0%
+some game designers do. They put the
+ 
+
+ align:start position:0%
+some game designers do. They put the
+solution in the the the Prima guide so
+
+ align:start position:0%
+solution in the the the Prima guide so
+ 
+
+ align:start position:0%
+solution in the the the Prima guide so
+that you have to buy the Prima guide in
+
+ align:start position:0%
+that you have to buy the Prima guide in
+ 
+
+ align:start position:0%
+that you have to buy the Prima guide in
+order to otherwise.
+
+ align:start position:0%
+order to otherwise.
+ 
+
+ align:start position:0%
+order to otherwise.
+>> But it's also
+
+ align:start position:0%
+>> But it's also
+ 
+
+ align:start position:0%
+>> But it's also
+deal with the
+
+ align:start position:0%
+deal with the
+ 
+
+ align:start position:0%
+deal with the
+>> Well, you must have Oh,
+
+ align:start position:0%
+>> Well, you must have Oh,
+ 
+
+ align:start position:0%
+>> Well, you must have Oh,
+>> yeah.
+
+ align:start position:0%
+>> yeah.
+ 
+
+ align:start position:0%
+>> yeah.
+>> There's actually say official on the top
+
+ align:start position:0%
+>> There's actually say official on the top
+ 
+
+ align:start position:0%
+>> There's actually say official on the top
+for a reason.
+
+ align:start position:0%
+for a reason.
+ 
+
+ align:start position:0%
+for a reason.
+See, it's also ironic because modern
+
+ align:start position:0%
+See, it's also ironic because modern
+ 
+
+ align:start position:0%
+See, it's also ironic because modern
+Zelda games like they they hold it's
+
+ align:start position:0%
+Zelda games like they they hold it's
+ 
+
+ align:start position:0%
+Zelda games like they they hold it's
+very obvious that you have to use this
+
+ align:start position:0%
+very obvious that you have to use this
+ 
+
+ align:start position:0%
+very obvious that you have to use this
+or that item.
+
+ align:start position:0%
+or that item.
+ 
+
+ align:start position:0%
+or that item.
+>> You got a key. Use this key to open.
+
+ align:start position:0%
+>> You got a key. Use this key to open.
+ 
+
+ align:start position:0%
+>> You got a key. Use this key to open.
+>> Oh, you got this item in the dungeon.
+
+ align:start position:0%
+>> Oh, you got this item in the dungeon.
+ 
+
+ align:start position:0%
+>> Oh, you got this item in the dungeon.
+You had to use this item to kill the
+
+ align:start position:0%
+You had to use this item to kill the
+ 
+
+ align:start position:0%
+You had to use this item to kill the
+boss. That sort of thing. Like it's
+
+ align:start position:0%
+boss. That sort of thing. Like it's
+ 
+
+ align:start position:0%
+boss. That sort of thing. Like it's
+blatant.
+
+ align:start position:0%
+blatant.
+ 
+
+ align:start position:0%
+blatant.
+>> Well, for people who are really really
+
+ align:start position:0%
+>> Well, for people who are really really
+ 
+
+ align:start position:0%
+>> Well, for people who are really really
+hopeless, there's the little fairy.
+
+ align:start position:0%
+hopeless, there's the little fairy.
+ 
+
+ align:start position:0%
+hopeless, there's the little fairy.
+>> Hey, listen. Listen. is usually less
+
+ align:start position:0%
+>> Hey, listen. Listen. is usually less
+ 
+
+ align:start position:0%
+>> Hey, listen. Listen. is usually less
+less useful than
+
+ align:start position:0%
+less useful than
+ 
+
+ align:start position:0%
+less useful than
+>> but I mean I mean so one big difference
+
+ align:start position:0%
+>> but I mean I mean so one big difference
+ 
+
+ align:start position:0%
+>> but I mean I mean so one big difference
+between the old Zelda games and the new
+
+ align:start position:0%
+between the old Zelda games and the new
+ 
+
+ align:start position:0%
+between the old Zelda games and the new
+Zelda games it's just this continual
+
+ align:start position:0%
+Zelda games it's just this continual
+ 
+
+ align:start position:0%
+Zelda games it's just this continual
+refinement in the user interface um and
+
+ align:start position:0%
+refinement in the user interface um and
+ 
+
+ align:start position:0%
+refinement in the user interface um and
+you know in it goes all the way from
+
+ align:start position:0%
+you know in it goes all the way from
+ 
+
+ align:start position:0%
+you know in it goes all the way from
+like little things like um like the like
+
+ align:start position:0%
+like little things like um like the like
+ 
+
+ align:start position:0%
+like little things like um like the like
+the notes that you hear when you find a
+
+ align:start position:0%
+the notes that you hear when you find a
+ 
+
+ align:start position:0%
+the notes that you hear when you find a
+new dungeon you know and when you hear
+
+ align:start position:0%
+new dungeon you know and when you hear
+ 
+
+ align:start position:0%
+new dungeon you know and when you hear
+exactly when precisely you hear the
+
+ align:start position:0%
+exactly when precisely you hear the
+ 
+
+ align:start position:0%
+exactly when precisely you hear the
+sound of you know
+
+ align:start position:0%
+sound of you know
+ 
+
+ align:start position:0%
+sound of you know
+if I think
+
+ align:start position:0%
+if I think
+ 
+
+ align:start position:0%
+if I think
+um you know as a clue that now you have
+
+ align:start position:0%
+um you know as a clue that now you have
+ 
+
+ align:start position:0%
+um you know as a clue that now you have
+opened a door um that that that's one of
+
+ align:start position:0%
+opened a door um that that that's one of
+ 
+
+ align:start position:0%
+opened a door um that that that's one of
+those things that if you if you look at
+
+ align:start position:0%
+those things that if you if you look at
+ 
+
+ align:start position:0%
+those things that if you if you look at
+postmodms of ocarina time I think
+
+ align:start position:0%
+postmodms of ocarina time I think
+ 
+
+ align:start position:0%
+postmodms of ocarina time I think
+there's a couple on gamma sudra exactly
+
+ align:start position:0%
+there's a couple on gamma sudra exactly
+ 
+
+ align:start position:0%
+there's a couple on gamma sudra exactly
+when that sound plays is a decision that
+
+ align:start position:0%
+when that sound plays is a decision that
+ 
+
+ align:start position:0%
+when that sound plays is a decision that
+was very carefully designed um and uh it
+
+ align:start position:0%
+was very carefully designed um and uh it
+ 
+
+ align:start position:0%
+was very carefully designed um and uh it
+seems to me that in digital puzzles in
+
+ align:start position:0%
+seems to me that in digital puzzles in
+ 
+
+ align:start position:0%
+seems to me that in digital puzzles in
+those kinds of like especially in some
+
+ align:start position:0%
+those kinds of like especially in some
+ 
+
+ align:start position:0%
+those kinds of like especially in some
+sort of narrative structure like in
+
+ align:start position:0%
+sort of narrative structure like in
+ 
+
+ align:start position:0%
+sort of narrative structure like in
+opera um that's the big problem that you
+
+ align:start position:0%
+opera um that's the big problem that you
+ 
+
+ align:start position:0%
+opera um that's the big problem that you
+have to solve you have to give enough
+
+ align:start position:0%
+have to solve you have to give enough
+ 
+
+ align:start position:0%
+have to solve you have to give enough
+clues you have to give enough UI
+
+ align:start position:0%
+clues you have to give enough UI
+ 
+
+ align:start position:0%
+clues you have to give enough UI
+feedback and you have to think about
+
+ align:start position:0%
+feedback and you have to think about
+ 
+
+ align:start position:0%
+feedback and you have to think about
+your UI so hard um in a way that is
+
+ align:start position:0%
+your UI so hard um in a way that is
+ 
+
+ align:start position:0%
+your UI so hard um in a way that is
+going to make it possible for people to
+
+ align:start position:0%
+going to make it possible for people to
+ 
+
+ align:start position:0%
+going to make it possible for people to
+get all the information they need. So
+
+ align:start position:0%
+get all the information they need. So
+ 
+
+ align:start position:0%
+get all the information they need. So
+say that burning fire tree situation if
+
+ align:start position:0%
+say that burning fire tree situation if
+ 
+
+ align:start position:0%
+say that burning fire tree situation if
+there's nowhere else in the world for
+
+ align:start position:0%
+there's nowhere else in the world for
+ 
+
+ align:start position:0%
+there's nowhere else in the world for
+you to get that information that's bad
+
+ align:start position:0%
+you to get that information that's bad
+ 
+
+ align:start position:0%
+you to get that information that's bad
+design puzzle. If there is a guy in I I
+
+ align:start position:0%
+design puzzle. If there is a guy in I I
+ 
+
+ align:start position:0%
+design puzzle. If there is a guy in I I
+can't remember the Zelda one, but if
+
+ align:start position:0%
+can't remember the Zelda one, but if
+ 
+
+ align:start position:0%
+can't remember the Zelda one, but if
+there is a guy who actually tells you
+
+ align:start position:0%
+there is a guy who actually tells you
+ 
+
+ align:start position:0%
+there is a guy who actually tells you
+that that's the tree that you need to
+
+ align:start position:0%
+that that's the tree that you need to
+ 
+
+ align:start position:0%
+that that's the tree that you need to
+burn, but it's not obvious, especially
+
+ align:start position:0%
+burn, but it's not obvious, especially
+ 
+
+ align:start position:0%
+burn, but it's not obvious, especially
+for someone who hasn't encountered that
+
+ align:start position:0%
+for someone who hasn't encountered that
+ 
+
+ align:start position:0%
+for someone who hasn't encountered that
+guy, that that's where you get the
+
+ align:start position:0%
+guy, that that's where you get the
+ 
+
+ align:start position:0%
+guy, that that's where you get the
+information. It's still a bad design
+
+ align:start position:0%
+information. It's still a bad design
+ 
+
+ align:start position:0%
+information. It's still a bad design
+puzzle, even though now that's the
+
+ align:start position:0%
+puzzle, even though now that's the
+ 
+
+ align:start position:0%
+puzzle, even though now that's the
+solution. Um but thinking about and some
+
+ align:start position:0%
+solution. Um but thinking about and some
+ 
+
+ align:start position:0%
+solution. Um but thinking about and some
+examples will be u in a lot of textbased
+
+ align:start position:0%
+examples will be u in a lot of textbased
+ 
+
+ align:start position:0%
+examples will be u in a lot of textbased
+adventures as well as graphical text
+
+ align:start position:0%
+adventures as well as graphical text
+ 
+
+ align:start position:0%
+adventures as well as graphical text
+heavy graphical adventures you have a I
+
+ align:start position:0%
+heavy graphical adventures you have a I
+ 
+
+ align:start position:0%
+heavy graphical adventures you have a I
+can't solve this puzzle but what my
+
+ align:start position:0%
+can't solve this puzzle but what my
+ 
+
+ align:start position:0%
+can't solve this puzzle but what my
+character says to the player about why
+
+ align:start position:0%
+character says to the player about why
+ 
+
+ align:start position:0%
+character says to the player about why
+you can't solve the puzzle itself a clue
+
+ align:start position:0%
+you can't solve the puzzle itself a clue
+ 
+
+ align:start position:0%
+you can't solve the puzzle itself a clue
+it's like I must not have had I I must
+
+ align:start position:0%
+it's like I must not have had I I must
+ 
+
+ align:start position:0%
+it's like I must not have had I I must
+not have the right item like you know
+
+ align:start position:0%
+not have the right item like you know
+ 
+
+ align:start position:0%
+not have the right item like you know
+maybe there's something else I can use.
+
+ align:start position:0%
+maybe there's something else I can use.
+ 
+
+ align:start position:0%
+maybe there's something else I can use.
+That's a huge clue. I feel like digital
+
+ align:start position:0%
+That's a huge clue. I feel like digital
+ 
+
+ align:start position:0%
+That's a huge clue. I feel like digital
+puzzle games have gotten really good at
+
+ align:start position:0%
+puzzle games have gotten really good at
+ 
+
+ align:start position:0%
+puzzle games have gotten really good at
+integrating hint systems
+
+ align:start position:0%
+integrating hint systems
+ 
+
+ align:start position:0%
+integrating hint systems
+um in recent years,
+
+ align:start position:0%
+um in recent years,
+ 
+
+ align:start position:0%
+um in recent years,
+but I can't think of any physical
+
+ align:start position:0%
+but I can't think of any physical
+ 
+
+ align:start position:0%
+but I can't think of any physical
+puzzles that I've come across, though I
+
+ align:start position:0%
+puzzles that I've come across, though I
+ 
+
+ align:start position:0%
+puzzles that I've come across, though I
+may just not have caught it like been up
+
+ align:start position:0%
+may just not have caught it like been up
+ 
+
+ align:start position:0%
+may just not have caught it like been up
+to speed with physical puzzles that have
+
+ align:start position:0%
+to speed with physical puzzles that have
+ 
+
+ align:start position:0%
+to speed with physical puzzles that have
+that kind of
+
+ align:start position:0%
+that kind of
+ 
+
+ align:start position:0%
+that kind of
+not totally revealing the solution, but
+
+ align:start position:0%
+not totally revealing the solution, but
+ 
+
+ align:start position:0%
+not totally revealing the solution, but
+giving you a gradual hint which can help
+
+ align:start position:0%
+giving you a gradual hint which can help
+ 
+
+ align:start position:0%
+giving you a gradual hint which can help
+you figure it out. Well, mystery hunt
+
+ align:start position:0%
+you figure it out. Well, mystery hunt
+ 
+
+ align:start position:0%
+you figure it out. Well, mystery hunt
+puzzle is kind of
+
+ align:start position:0%
+puzzle is kind of
+ 
+
+ align:start position:0%
+puzzle is kind of
+>> Oh,
+
+ align:start position:0%
+>> Oh,
+ 
+
+ align:start position:0%
+>> Oh,
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+describe the mystery hunt for folks who
+
+ align:start position:0%
+describe the mystery hunt for folks who
+ 
+
+ align:start position:0%
+describe the mystery hunt for folks who
+don't who
+
+ align:start position:0%
+don't who
+ 
+
+ align:start position:0%
+don't who
+>> uh it's basically it's a competition run
+
+ align:start position:0%
+>> uh it's basically it's a competition run
+ 
+
+ align:start position:0%
+>> uh it's basically it's a competition run
+at MIT over AP where uh teams of people
+
+ align:start position:0%
+at MIT over AP where uh teams of people
+ 
+
+ align:start position:0%
+at MIT over AP where uh teams of people
+compete to solve a bunch of puzzles like
+
+ align:start position:0%
+compete to solve a bunch of puzzles like
+ 
+
+ align:start position:0%
+compete to solve a bunch of puzzles like
+70 puzzles that kind of build on each
+
+ align:start position:0%
+70 puzzles that kind of build on each
+ 
+
+ align:start position:0%
+70 puzzles that kind of build on each
+other. So you have, you know, say 20
+
+ align:start position:0%
+other. So you have, you know, say 20
+ 
+
+ align:start position:0%
+other. So you have, you know, say 20
+base puzzles and you solve those 20
+
+ align:start position:0%
+base puzzles and you solve those 20
+ 
+
+ align:start position:0%
+base puzzles and you solve those 20
+puzzles, you get 20 words as solutions
+
+ align:start position:0%
+puzzles, you get 20 words as solutions
+ 
+
+ align:start position:0%
+puzzles, you get 20 words as solutions
+and then those 20 words become a new
+
+ align:start position:0%
+and then those 20 words become a new
+ 
+
+ align:start position:0%
+and then those 20 words become a new
+puzzle and it's a meta puzzle and it
+
+ align:start position:0%
+puzzle and it's a meta puzzle and it
+ 
+
+ align:start position:0%
+puzzle and it's a meta puzzle and it
+keep kind of keeps going like that for a
+
+ align:start position:0%
+keep kind of keeps going like that for a
+ 
+
+ align:start position:0%
+keep kind of keeps going like that for a
+couple layers. But the point is the
+
+ align:start position:0%
+couple layers. But the point is the
+ 
+
+ align:start position:0%
+couple layers. But the point is the
+winning team from the previous year
+
+ align:start position:0%
+winning team from the previous year
+ 
+
+ align:start position:0%
+winning team from the previous year
+writes the next year's mystery hunt. So
+
+ align:start position:0%
+writes the next year's mystery hunt. So
+ 
+
+ align:start position:0%
+writes the next year's mystery hunt. So
+like you get all kinds of varying
+
+ align:start position:0%
+like you get all kinds of varying
+ 
+
+ align:start position:0%
+like you get all kinds of varying
+puzzles of varying difficulties and
+
+ align:start position:0%
+puzzles of varying difficulties and
+ 
+
+ align:start position:0%
+puzzles of varying difficulties and
+styles and a very well-designed puzzle
+
+ align:start position:0%
+styles and a very well-designed puzzle
+ 
+
+ align:start position:0%
+styles and a very well-designed puzzle
+actually does that because you have this
+
+ align:start position:0%
+actually does that because you have this
+ 
+
+ align:start position:0%
+actually does that because you have this
+thing called flavor. Oh, I guess I
+
+ align:start position:0%
+thing called flavor. Oh, I guess I
+ 
+
+ align:start position:0%
+thing called flavor. Oh, I guess I
+should say that the puzzles aren't like
+
+ align:start position:0%
+should say that the puzzles aren't like
+ 
+
+ align:start position:0%
+should say that the puzzles aren't like
+sudoku or crosswords. You literally just
+
+ align:start position:0%
+sudoku or crosswords. You literally just
+ 
+
+ align:start position:0%
+sudoku or crosswords. You literally just
+get, you know, something on a screen or
+
+ align:start position:0%
+get, you know, something on a screen or
+ 
+
+ align:start position:0%
+get, you know, something on a screen or
+something on a piece of paper and you
+
+ align:start position:0%
+something on a piece of paper and you
+ 
+
+ align:start position:0%
+something on a piece of paper and you
+have to figure out what to do with it.
+
+ align:start position:0%
+have to figure out what to do with it.
+ 
+
+ align:start position:0%
+have to figure out what to do with it.
+You're not given any instructions for
+
+ align:start position:0%
+You're not given any instructions for
+ 
+
+ align:start position:0%
+You're not given any instructions for
+how to solve it whatsoever. And the the
+
+ align:start position:0%
+how to solve it whatsoever. And the the
+ 
+
+ align:start position:0%
+how to solve it whatsoever. And the the
+only clues you get are either by the
+
+ align:start position:0%
+only clues you get are either by the
+ 
+
+ align:start position:0%
+only clues you get are either by the
+title of the puzzle, by like the group
+
+ align:start position:0%
+title of the puzzle, by like the group
+ 
+
+ align:start position:0%
+title of the puzzle, by like the group
+of puzzles that it's in, or by this
+
+ align:start position:0%
+of puzzles that it's in, or by this
+ 
+
+ align:start position:0%
+of puzzles that it's in, or by this
+thing called flavor text, which is like
+
+ align:start position:0%
+thing called flavor text, which is like
+ 
+
+ align:start position:0%
+thing called flavor text, which is like
+they say some kind of random phrase that
+
+ align:start position:0%
+they say some kind of random phrase that
+ 
+
+ align:start position:0%
+they say some kind of random phrase that
+seems to not have anything to do with
+
+ align:start position:0%
+seems to not have anything to do with
+ 
+
+ align:start position:0%
+seems to not have anything to do with
+anything, but that kind of gives you a
+
+ align:start position:0%
+anything, but that kind of gives you a
+ 
+
+ align:start position:0%
+anything, but that kind of gives you a
+clue about what to do in the first
+
+ align:start position:0%
+clue about what to do in the first
+ 
+
+ align:start position:0%
+clue about what to do in the first
+puzzle.
+
+ align:start position:0%
+puzzle.
+ 
+
+ align:start position:0%
+puzzle.
+>> So that's it's kind of like what you're
+
+ align:start position:0%
+>> So that's it's kind of like what you're
+ 
+
+ align:start position:0%
+>> So that's it's kind of like what you're
+describing. That's interesting because I
+
+ align:start position:0%
+describing. That's interesting because I
+ 
+
+ align:start position:0%
+describing. That's interesting because I
+mean it's really challenging when you
+
+ align:start position:0%
+mean it's really challenging when you
+ 
+
+ align:start position:0%
+mean it's really challenging when you
+don't have any mechanism for like giving
+
+ align:start position:0%
+don't have any mechanism for like giving
+ 
+
+ align:start position:0%
+don't have any mechanism for like giving
+feedback to the person who's working on
+
+ align:start position:0%
+feedback to the person who's working on
+ 
+
+ align:start position:0%
+feedback to the person who's working on
+a puzzle. It in Zelda or what have you.
+
+ align:start position:0%
+a puzzle. It in Zelda or what have you.
+ 
+
+ align:start position:0%
+a puzzle. It in Zelda or what have you.
+You can see that they've spent a long
+
+ align:start position:0%
+You can see that they've spent a long
+ 
+
+ align:start position:0%
+You can see that they've spent a long
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+ around.
+
+ align:start position:0%
+ around.
+ 
+
+ align:start position:0%
+ around.
+It's kind of a double-edged sword in
+
+ align:start position:0%
+It's kind of a double-edged sword in
+ 
+
+ align:start position:0%
+It's kind of a double-edged sword in
+that particular case because you had so
+
+ align:start position:0%
+that particular case because you had so
+ 
+
+ align:start position:0%
+that particular case because you had so
+many mechanisms and now you're expected
+
+ align:start position:0%
+many mechanisms and now you're expected
+ 
+
+ align:start position:0%
+many mechanisms and now you're expected
+to use all of them. Uh in in in in a
+
+ align:start position:0%
+to use all of them. Uh in in in in a
+ 
+
+ align:start position:0%
+to use all of them. Uh in in in in a
+game like like you have to use sound,
+
+ align:start position:0%
+game like like you have to use sound,
+ 
+
+ align:start position:0%
+game like like you have to use sound,
+you have to use contextual buttons, you
+
+ align:start position:0%
+you have to use contextual buttons, you
+ 
+
+ align:start position:0%
+you have to use contextual buttons, you
+have to use the inventory, uh the
+
+ align:start position:0%
+have to use the inventory, uh the
+ 
+
+ align:start position:0%
+have to use the inventory, uh the
+position of the player matters, you
+
+ align:start position:0%
+position of the player matters, you
+ 
+
+ align:start position:0%
+position of the player matters, you
+know, sometimes I've seen games where
+
+ align:start position:0%
+know, sometimes I've seen games where
+ 
+
+ align:start position:0%
+know, sometimes I've seen games where
+the the main clue is what is the the
+
+ align:start position:0%
+the the main clue is what is the the
+ 
+
+ align:start position:0%
+the the main clue is what is the the
+character looking at for instance, you
+
+ align:start position:0%
+character looking at for instance, you
+ 
+
+ align:start position:0%
+character looking at for instance, you
+know, and if you walk around, why does
+
+ align:start position:0%
+know, and if you walk around, why does
+ 
+
+ align:start position:0%
+know, and if you walk around, why does
+my character keep looking that way every
+
+ align:start position:0%
+my character keep looking that way every
+ 
+
+ align:start position:0%
+my character keep looking that way every
+time I look at it? Oh, that's the clue,
+
+ align:start position:0%
+time I look at it? Oh, that's the clue,
+ 
+
+ align:start position:0%
+time I look at it? Oh, that's the clue,
+you know. Um so so yeah for us in a lot
+
+ align:start position:0%
+you know. Um so so yeah for us in a lot
+ 
+
+ align:start position:0%
+you know. Um so so yeah for us in a lot
+of like um physical stuff um I would say
+
+ align:start position:0%
+of like um physical stuff um I would say
+ 
+
+ align:start position:0%
+of like um physical stuff um I would say
+that one of the reasons is if you're
+
+ align:start position:0%
+that one of the reasons is if you're
+ 
+
+ align:start position:0%
+that one of the reasons is if you're
+starting if you're starting to build
+
+ align:start position:0%
+starting if you're starting to build
+ 
+
+ align:start position:0%
+starting if you're starting to build
+these physical games from toys um you a
+
+ align:start position:0%
+these physical games from toys um you a
+ 
+
+ align:start position:0%
+these physical games from toys um you a
+lot of the affordances
+
+ align:start position:0%
+lot of the affordances
+ 
+
+ align:start position:0%
+lot of the affordances
+a a lot of things you could possibly do
+
+ align:start position:0%
+a a lot of things you could possibly do
+ 
+
+ align:start position:0%
+a a lot of things you could possibly do
+are kind of built into the physical
+
+ align:start position:0%
+are kind of built into the physical
+ 
+
+ align:start position:0%
+are kind of built into the physical
+object. Uh, and if you're building a
+
+ align:start position:0%
+object. Uh, and if you're building a
+ 
+
+ align:start position:0%
+object. Uh, and if you're building a
+puzzle based on what you could do as
+
+ align:start position:0%
+puzzle based on what you could do as
+ 
+
+ align:start position:0%
+puzzle based on what you could do as
+with these things as a toy, um, then
+
+ align:start position:0%
+with these things as a toy, um, then
+ 
+
+ align:start position:0%
+with these things as a toy, um, then
+you're necessarily already using the
+
+ align:start position:0%
+you're necessarily already using the
+ 
+
+ align:start position:0%
+you're necessarily already using the
+constraints of what you can do it do
+
+ align:start position:0%
+constraints of what you can do it do
+ 
+
+ align:start position:0%
+constraints of what you can do it do
+with it as a toy in order to try to to
+
+ align:start position:0%
+with it as a toy in order to try to to
+ 
+
+ align:start position:0%
+with it as a toy in order to try to to
+to create a puzzle.
+
+ align:start position:0%
+to create a puzzle.
+ 
+
+ align:start position:0%
+to create a puzzle.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+this might be a good exercise actually.
+
+ align:start position:0%
+this might be a good exercise actually.
+ 
+
+ align:start position:0%
+this might be a good exercise actually.
+We have time we we we we could take a
+
+ align:start position:0%
+We have time we we we we could take a
+ 
+
+ align:start position:0%
+We have time we we we we could take a
+shot at this and just like you know
+
+ align:start position:0%
+shot at this and just like you know
+ 
+
+ align:start position:0%
+shot at this and just like you know
+trying to come up with a puzzle and see
+
+ align:start position:0%
+trying to come up with a puzzle and see
+ 
+
+ align:start position:0%
+trying to come up with a puzzle and see
+but instead of doing of imagining one in
+
+ align:start position:0%
+but instead of doing of imagining one in
+ 
+
+ align:start position:0%
+but instead of doing of imagining one in
+a digital space trying to imagine one in
+
+ align:start position:0%
+a digital space trying to imagine one in
+ 
+
+ align:start position:0%
+a digital space trying to imagine one in
+physical space and because I suspect
+
+ align:start position:0%
+physical space and because I suspect
+ 
+
+ align:start position:0%
+physical space and because I suspect
+what you actually get is that you get a
+
+ align:start position:0%
+what you actually get is that you get a
+ 
+
+ align:start position:0%
+what you actually get is that you get a
+lot of free you get a free ride with
+
+ align:start position:0%
+lot of free you get a free ride with
+ 
+
+ align:start position:0%
+lot of free you get a free ride with
+physical puzzles because things
+
+ align:start position:0%
+physical puzzles because things
+ 
+
+ align:start position:0%
+physical puzzles because things
+physically
+
+ align:start position:0%
+physically
+ 
+
+ align:start position:0%
+physically
+have interactions that puzzle
+
+ align:start position:0%
+have interactions that puzzle
+ 
+
+ align:start position:0%
+have interactions that puzzle
+I feel like uh played Portal recently
+
+ align:start position:0%
+I feel like uh played Portal recently
+ 
+
+ align:start position:0%
+I feel like uh played Portal recently
+and that's a game where like
+
+ align:start position:0%
+and that's a game where like
+ 
+
+ align:start position:0%
+and that's a game where like
+the the puzzles are it's not in a I mean
+
+ align:start position:0%
+the the puzzles are it's not in a I mean
+ 
+
+ align:start position:0%
+the the puzzles are it's not in a I mean
+obviously it's still a digital game but
+
+ align:start position:0%
+obviously it's still a digital game but
+ 
+
+ align:start position:0%
+obviously it's still a digital game but
+the puzzles are very much physical
+
+ align:start position:0%
+the puzzles are very much physical
+ 
+
+ align:start position:0%
+the puzzles are very much physical
+puzzles like you kind of have an idea
+
+ align:start position:0%
+puzzles like you kind of have an idea
+ 
+
+ align:start position:0%
+puzzles like you kind of have an idea
+about what has have people played Portal
+
+ align:start position:0%
+about what has have people played Portal
+ 
+
+ align:start position:0%
+about what has have people played Portal
+of course or know the idea
+
+ align:start position:0%
+of course or know the idea
+ 
+
+ align:start position:0%
+of course or know the idea
+okay um I mean you have these two
+
+ align:start position:0%
+okay um I mean you have these two
+ 
+
+ align:start position:0%
+okay um I mean you have these two
+portals and you like do you understand
+
+ align:start position:0%
+portals and you like do you understand
+ 
+
+ align:start position:0%
+portals and you like do you understand
+what the physics is going to be like so
+
+ align:start position:0%
+what the physics is going to be like so
+ 
+
+ align:start position:0%
+what the physics is going to be like so
+the puzzles aren't frustrating in the
+
+ align:start position:0%
+the puzzles aren't frustrating in the
+ 
+
+ align:start position:0%
+the puzzles aren't frustrating in the
+sense that it's like oh you pull you
+
+ align:start position:0%
+sense that it's like oh you pull you
+ 
+
+ align:start position:0%
+sense that it's like oh you pull you
+realize there's like this random statue
+
+ align:start position:0%
+realize there's like this random statue
+ 
+
+ align:start position:0%
+realize there's like this random statue
+here and if you like pull a lever it
+
+ align:start position:0%
+here and if you like pull a lever it
+ 
+
+ align:start position:0%
+here and if you like pull a lever it
+like raises the water level or something
+
+ align:start position:0%
+like raises the water level or something
+ 
+
+ align:start position:0%
+like raises the water level or something
+like that like it I don't know what it
+
+ align:start position:0%
+like that like it I don't know what it
+ 
+
+ align:start position:0%
+like that like it I don't know what it
+but it's like it's very intuitive and
+
+ align:start position:0%
+but it's like it's very intuitive and
+ 
+
+ align:start position:0%
+but it's like it's very intuitive and
+it's it feels like a physical puzzle in
+
+ align:start position:0%
+it's it feels like a physical puzzle in
+ 
+
+ align:start position:0%
+it's it feels like a physical puzzle in
+the sense that I know what will happen
+
+ align:start position:0%
+the sense that I know what will happen
+ 
+
+ align:start position:0%
+the sense that I know what will happen
+if I do this and I just figure out have
+
+ align:start position:0%
+if I do this and I just figure out have
+ 
+
+ align:start position:0%
+if I do this and I just figure out have
+to how to put the pieces together and
+
+ align:start position:0%
+to how to put the pieces together and
+ 
+
+ align:start position:0%
+to how to put the pieces together and
+also in portal what I think does a
+
+ align:start position:0%
+also in portal what I think does a
+ 
+
+ align:start position:0%
+also in portal what I think does a
+really good job of as well as what some
+
+ align:start position:0%
+really good job of as well as what some
+ 
+
+ align:start position:0%
+really good job of as well as what some
+physical puzzles do is having a learning
+
+ align:start position:0%
+physical puzzles do is having a learning
+ 
+
+ align:start position:0%
+physical puzzles do is having a learning
+curve like tanagram will have some basic
+
+ align:start position:0%
+curve like tanagram will have some basic
+ 
+
+ align:start position:0%
+curve like tanagram will have some basic
+puzzles or I'm sure the following thing
+
+ align:start position:0%
+puzzles or I'm sure the following thing
+ 
+
+ align:start position:0%
+puzzles or I'm sure the following thing
+a lot of them we can do physical puzzle
+
+ align:start position:0%
+a lot of them we can do physical puzzle
+ 
+
+ align:start position:0%
+a lot of them we can do physical puzzle
+things we like I don't know have to jump
+
+ align:start position:0%
+things we like I don't know have to jump
+ 
+
+ align:start position:0%
+things we like I don't know have to jump
+over pieces or whatever basic levels,
+
+ align:start position:0%
+over pieces or whatever basic levels,
+ 
+
+ align:start position:0%
+over pieces or whatever basic levels,
+basic uh boards where they show you
+
+ align:start position:0%
+basic uh boards where they show you
+ 
+
+ align:start position:0%
+basic uh boards where they show you
+various techniques and you only have to
+
+ align:start position:0%
+various techniques and you only have to
+ 
+
+ align:start position:0%
+various techniques and you only have to
+figure out one technique and it's very
+
+ align:start position:0%
+figure out one technique and it's very
+ 
+
+ align:start position:0%
+figure out one technique and it's very
+obvious what you have to do and then
+
+ align:start position:0%
+obvious what you have to do and then
+ 
+
+ align:start position:0%
+obvious what you have to do and then
+later on you have to use those
+
+ align:start position:0%
+later on you have to use those
+ 
+
+ align:start position:0%
+later on you have to use those
+techniques.
+
+ align:start position:0%
+techniques.
+ 
+
+ align:start position:0%
+techniques.
+>> Well, I mean in zippover this particular
+
+ align:start position:0%
+>> Well, I mean in zippover this particular
+ 
+
+ align:start position:0%
+>> Well, I mean in zippover this particular
+example does something that portal also
+
+ align:start position:0%
+example does something that portal also
+ 
+
+ align:start position:0%
+example does something that portal also
+does really well is that the very first
+
+ align:start position:0%
+does really well is that the very first
+ 
+
+ align:start position:0%
+does really well is that the very first
+puzzle that we did earlier only has one
+
+ align:start position:0%
+puzzle that we did earlier only has one
+ 
+
+ align:start position:0%
+puzzle that we did earlier only has one
+solution and you do not you do not get
+
+ align:start position:0%
+solution and you do not you do not get
+ 
+
+ align:start position:0%
+solution and you do not you do not get
+that solution unless you understand all
+
+ align:start position:0%
+that solution unless you understand all
+ 
+
+ align:start position:0%
+that solution unless you understand all
+the mechanics. Yeah. like we like we
+
+ align:start position:0%
+the mechanics. Yeah. like we like we
+ 
+
+ align:start position:0%
+the mechanics. Yeah. like we like we
+tried to solve it a bunch of different
+
+ align:start position:0%
+tried to solve it a bunch of different
+ 
+
+ align:start position:0%
+tried to solve it a bunch of different
+times and it's like because we didn't
+
+ align:start position:0%
+times and it's like because we didn't
+ 
+
+ align:start position:0%
+times and it's like because we didn't
+quite understand the rules, we couldn't
+
+ align:start position:0%
+quite understand the rules, we couldn't
+ 
+
+ align:start position:0%
+quite understand the rules, we couldn't
+get it until we understood the mechanics
+
+ align:start position:0%
+get it until we understood the mechanics
+ 
+
+ align:start position:0%
+get it until we understood the mechanics
+of the game. Now we can sly solve it. So
+
+ align:start position:0%
+of the game. Now we can sly solve it. So
+ 
+
+ align:start position:0%
+of the game. Now we can sly solve it. So
+from level from puzzle level two
+
+ align:start position:0%
+from level from puzzle level two
+ 
+
+ align:start position:0%
+from level from puzzle level two
+onwards, we can be confident that we
+
+ align:start position:0%
+onwards, we can be confident that we
+ 
+
+ align:start position:0%
+onwards, we can be confident that we
+actually know like Portal and even
+
+ align:start position:0%
+actually know like Portal and even
+ 
+
+ align:start position:0%
+actually know like Portal and even
+actually just about any well-designed
+
+ align:start position:0%
+actually just about any well-designed
+ 
+
+ align:start position:0%
+actually just about any well-designed
+game, but I'm going to say Portal is a
+
+ align:start position:0%
+game, but I'm going to say Portal is a
+ 
+
+ align:start position:0%
+game, but I'm going to say Portal is a
+fine example. you've beaten the game,
+
+ align:start position:0%
+fine example. you've beaten the game,
+ 
+
+ align:start position:0%
+fine example. you've beaten the game,
+you can play through the game again with
+
+ align:start position:0%
+you can play through the game again with
+ 
+
+ align:start position:0%
+you can play through the game again with
+developer commentary. And you will and
+
+ align:start position:0%
+developer commentary. And you will and
+ 
+
+ align:start position:0%
+developer commentary. And you will and
+when you hear that, you will actually
+
+ align:start position:0%
+when you hear that, you will actually
+ 
+
+ align:start position:0%
+when you hear that, you will actually
+realize that um every single fairly
+
+ align:start position:0%
+realize that um every single fairly
+ 
+
+ align:start position:0%
+realize that um every single fairly
+intuitive physical thing that that that
+
+ align:start position:0%
+intuitive physical thing that that that
+ 
+
+ align:start position:0%
+intuitive physical thing that that that
+you pick up in the game had to be taught
+
+ align:start position:0%
+you pick up in the game had to be taught
+ 
+
+ align:start position:0%
+you pick up in the game had to be taught
+to you. And they've designed the level
+
+ align:start position:0%
+to you. And they've designed the level
+ 
+
+ align:start position:0%
+to you. And they've designed the level
+very clearly. So, right at the beginning
+
+ align:start position:0%
+very clearly. So, right at the beginning
+ 
+
+ align:start position:0%
+very clearly. So, right at the beginning
+of the game, if uh folks can remember,
+
+ align:start position:0%
+of the game, if uh folks can remember,
+ 
+
+ align:start position:0%
+of the game, if uh folks can remember,
+um you're trapped in a little cell,
+
+ align:start position:0%
+um you're trapped in a little cell,
+ 
+
+ align:start position:0%
+um you're trapped in a little cell,
+right? and uh the the uh GLaDOS talks to
+
+ align:start position:0%
+right? and uh the the uh GLaDOS talks to
+ 
+
+ align:start position:0%
+right? and uh the the uh GLaDOS talks to
+you and a portal opens and you can walk
+
+ align:start position:0%
+you and a portal opens and you can walk
+ 
+
+ align:start position:0%
+you and a portal opens and you can walk
+through it. What do you see out of the
+
+ align:start position:0%
+through it. What do you see out of the
+ 
+
+ align:start position:0%
+through it. What do you see out of the
+first portal that opens?
+
+ align:start position:0%
+first portal that opens?
+ 
+
+ align:start position:0%
+first portal that opens?
+>> You see yourself going into the other
+
+ align:start position:0%
+>> You see yourself going into the other
+ 
+
+ align:start position:0%
+>> You see yourself going into the other
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+>> You see yourself going through the other
+
+ align:start position:0%
+>> You see yourself going through the other
+ 
+
+ align:start position:0%
+>> You see yourself going through the other
+portal. It is like they force you to
+
+ align:start position:0%
+portal. It is like they force you to
+ 
+
+ align:start position:0%
+portal. It is like they force you to
+have to look at what the basic game
+
+ align:start position:0%
+have to look at what the basic game
+ 
+
+ align:start position:0%
+have to look at what the basic game
+mechanic is going to be before you can
+
+ align:start position:0%
+mechanic is going to be before you can
+ 
+
+ align:start position:0%
+mechanic is going to be before you can
+do anything else in game that's
+
+ align:start position:0%
+do anything else in game that's
+ 
+
+ align:start position:0%
+do anything else in game that's
+productive in game. uh you know you can
+
+ align:start position:0%
+productive in game. uh you know you can
+ 
+
+ align:start position:0%
+productive in game. uh you know you can
+pick up the radio but yeah
+
+ align:start position:0%
+pick up the radio but yeah
+ 
+
+ align:start position:0%
+pick up the radio but yeah
+so so you know u so you know that's that
+
+ align:start position:0%
+so so you know u so you know that's that
+ 
+
+ align:start position:0%
+so so you know u so you know that's that
+that was a design decision they could
+
+ align:start position:0%
+that was a design decision they could
+ 
+
+ align:start position:0%
+that was a design decision they could
+have made that they they could have
+
+ align:start position:0%
+have made that they they could have
+ 
+
+ align:start position:0%
+have made that they they could have
+decided not to make it they could have
+
+ align:start position:0%
+decided not to make it they could have
+ 
+
+ align:start position:0%
+decided not to make it they could have
+made you just go through that into a
+
+ align:start position:0%
+made you just go through that into a
+ 
+
+ align:start position:0%
+made you just go through that into a
+different room and you and and and a
+
+ align:start position:0%
+different room and you and and and a
+ 
+
+ align:start position:0%
+different room and you and and and a
+learning opportunity would have been
+
+ align:start position:0%
+learning opportunity would have been
+ 
+
+ align:start position:0%
+learning opportunity would have been
+lost right there um so if you got a copy
+
+ align:start position:0%
+lost right there um so if you got a copy
+ 
+
+ align:start position:0%
+lost right there um so if you got a copy
+of portal I would suggest go back and
+
+ align:start position:0%
+of portal I would suggest go back and
+ 
+
+ align:start position:0%
+of portal I would suggest go back and
+play through the the developer comment
+
+ align:start position:0%
+play through the the developer comment
+ 
+
+ align:start position:0%
+play through the the developer comment
+tries because they're they're hilarious
+
+ align:start position:0%
+tries because they're they're hilarious
+ 
+
+ align:start position:0%
+tries because they're they're hilarious
+and they're also really really good for
+
+ align:start position:0%
+and they're also really really good for
+ 
+
+ align:start position:0%
+and they're also really really good for
+demonstrating
+
+ align:start position:0%
+demonstrating
+ 
+
+ align:start position:0%
+demonstrating
+in this room. This is what we had to do
+
+ align:start position:0%
+in this room. This is what we had to do
+ 
+
+ align:start position:0%
+in this room. This is what we had to do
+in order to make people get it. Um, I'm
+
+ align:start position:0%
+in order to make people get it. Um, I'm
+ 
+
+ align:start position:0%
+in order to make people get it. Um, I'm
+also thinking of things like Mario World
+
+ align:start position:0%
+also thinking of things like Mario World
+ 
+
+ align:start position:0%
+also thinking of things like Mario World
+one where like you don't get to you
+
+ align:start position:0%
+one where like you don't get to you
+ 
+
+ align:start position:0%
+one where like you don't get to you
+don't get very far unless you get the
+
+ align:start position:0%
+don't get very far unless you get the
+ 
+
+ align:start position:0%
+don't get very far unless you get the
+basic game mechanics down and but they
+
+ align:start position:0%
+basic game mechanics down and but they
+ 
+
+ align:start position:0%
+basic game mechanics down and but they
+make it really gentle in that I don't
+
+ align:start position:0%
+make it really gentle in that I don't
+ 
+
+ align:start position:0%
+make it really gentle in that I don't
+think there are any pits that instant
+
+ align:start position:0%
+think there are any pits that instant
+ 
+
+ align:start position:0%
+think there are any pits that instant
+instantly choke you.
+
+ align:start position:0%
+instantly choke you.
+ 
+
+ align:start position:0%
+instantly choke you.
+>> Yeah, that's exactly what I was
+
+ align:start position:0%
+>> Yeah, that's exactly what I was
+ 
+
+ align:start position:0%
+>> Yeah, that's exactly what I was
+thinking. Mario World, the first Gamma
+
+ align:start position:0%
+thinking. Mario World, the first Gamma
+ 
+
+ align:start position:0%
+thinking. Mario World, the first Gamma
+Suture article we read on uh like game
+
+ align:start position:0%
+Suture article we read on uh like game
+ 
+
+ align:start position:0%
+Suture article we read on uh like game
+distractions from Rich Mario World that
+
+ align:start position:0%
+distractions from Rich Mario World that
+ 
+
+ align:start position:0%
+distractions from Rich Mario World that
+he's like you expect the same kind of
+
+ align:start position:0%
+he's like you expect the same kind of
+ 
+
+ align:start position:0%
+he's like you expect the same kind of
+actions to be consistent all the time
+
+ align:start position:0%
+actions to be consistent all the time
+ 
+
+ align:start position:0%
+actions to be consistent all the time
+jumping and I guess you kind of look at
+
+ align:start position:0%
+jumping and I guess you kind of look at
+ 
+
+ align:start position:0%
+jumping and I guess you kind of look at
+like different things there like double
+
+ align:start position:0%
+like different things there like double
+ 
+
+ align:start position:0%
+like different things there like double
+jumping like that specific puzzle
+
+ align:start position:0%
+jumping like that specific puzzle
+ 
+
+ align:start position:0%
+jumping like that specific puzzle
+also. I mean a lot of Mario's things uh
+
+ align:start position:0%
+also. I mean a lot of Mario's things uh
+ 
+
+ align:start position:0%
+also. I mean a lot of Mario's things uh
+uh worlds are made up basically as
+
+ align:start position:0%
+uh worlds are made up basically as
+ 
+
+ align:start position:0%
+uh worlds are made up basically as
+spatial puzzles, right? and it's like
+
+ align:start position:0%
+spatial puzzles, right? and it's like
+ 
+
+ align:start position:0%
+spatial puzzles, right? and it's like
+you know you have to get there but you
+
+ align:start position:0%
+you know you have to get there but you
+ 
+
+ align:start position:0%
+you know you have to get there but you
+don't know exactly how you're going to
+
+ align:start position:0%
+don't know exactly how you're going to
+ 
+
+ align:start position:0%
+don't know exactly how you're going to
+use all the mechanics that you got.
+
+ align:start position:0%
+use all the mechanics that you got.
+ 
+
+ align:start position:0%
+use all the mechanics that you got.
+>> Um in Mario 64
+
+ align:start position:0%
+>> Um in Mario 64
+ 
+
+ align:start position:0%
+>> Um in Mario 64
+I think their way of solving the the
+
+ align:start position:0%
+I think their way of solving the the
+ 
+
+ align:start position:0%
+I think their way of solving the the
+impass problem of not locking off all
+
+ align:start position:0%
+impass problem of not locking off all
+ 
+
+ align:start position:0%
+impass problem of not locking off all
+the content from the game because of one
+
+ align:start position:0%
+the content from the game because of one
+ 
+
+ align:start position:0%
+the content from the game because of one
+puzzle you can't get giving you so much
+
+ align:start position:0%
+puzzle you can't get giving you so much
+ 
+
+ align:start position:0%
+puzzle you can't get giving you so much
+to do that even if they don't really
+
+ align:start position:0%
+to do that even if they don't really
+ 
+
+ align:start position:0%
+to do that even if they don't really
+tell you and even if a good 30 40% are
+
+ align:start position:0%
+tell you and even if a good 30 40% are
+ 
+
+ align:start position:0%
+tell you and even if a good 30 40% are
+going to remain mysterious to you and
+
+ align:start position:0%
+going to remain mysterious to you and
+ 
+
+ align:start position:0%
+going to remain mysterious to you and
+you're not able to figure them out
+
+ align:start position:0%
+you're not able to figure them out
+ 
+
+ align:start position:0%
+you're not able to figure them out
+there's so much to jump around between
+
+ align:start position:0%
+there's so much to jump around between
+ 
+
+ align:start position:0%
+there's so much to jump around between
+that you're never locked off from a
+
+ align:start position:0%
+that you're never locked off from a
+ 
+
+ align:start position:0%
+that you're never locked off from a
+significant amount of content. So you
+
+ align:start position:0%
+significant amount of content. So you
+ 
+
+ align:start position:0%
+significant amount of content. So you
+you you've got the hublike structure of
+
+ align:start position:0%
+you you've got the hublike structure of
+ 
+
+ align:start position:0%
+you you've got the hublike structure of
+like you can do any one of five
+
+ align:start position:0%
+like you can do any one of five
+ 
+
+ align:start position:0%
+like you can do any one of five
+different things at any given time plus
+
+ align:start position:0%
+different things at any given time plus
+ 
+
+ align:start position:0%
+different things at any given time plus
+all plus you have sort of secondary
+
+ align:start position:0%
+all plus you have sort of secondary
+ 
+
+ align:start position:0%
+all plus you have sort of secondary
+solutions like you can always go back to
+
+ align:start position:0%
+solutions like you can always go back to
+ 
+
+ align:start position:0%
+solutions like you can always go back to
+a world that you've been before and try
+
+ align:start position:0%
+a world that you've been before and try
+ 
+
+ align:start position:0%
+a world that you've been before and try
+to put all the stars.
+
+ align:start position:0%
+to put all the stars.
+ 
+
+ align:start position:0%
+to put all the stars.
+Um I think that's kind of what Brenda
+
+ align:start position:0%
+Um I think that's kind of what Brenda
+ 
+
+ align:start position:0%
+Um I think that's kind of what Brenda
+was kind of indicating of the you don't
+
+ align:start position:0%
+was kind of indicating of the you don't
+ 
+
+ align:start position:0%
+was kind of indicating of the you don't
+necessarily want if you're putting
+
+ align:start position:0%
+necessarily want if you're putting
+ 
+
+ align:start position:0%
+necessarily want if you're putting
+puzzles in your game. she was advocating
+
+ align:start position:0%
+puzzles in your game. she was advocating
+ 
+
+ align:start position:0%
+puzzles in your game. she was advocating
+for Brenda and Ian were were advocating
+
+ align:start position:0%
+for Brenda and Ian were were advocating
+ 
+
+ align:start position:0%
+for Brenda and Ian were were advocating
+for something that wouldn't that that
+
+ align:start position:0%
+for something that wouldn't that that
+ 
+
+ align:start position:0%
+for something that wouldn't that that
+wasn't necessary to progress on on to
+
+ align:start position:0%
+wasn't necessary to progress on on to
+ 
+
+ align:start position:0%
+wasn't necessary to progress on on to
+the next one. But I think that's
+
+ align:start position:0%
+the next one. But I think that's
+ 
+
+ align:start position:0%
+the next one. But I think that's
+I think that's not a requirement. I
+
+ align:start position:0%
+I think that's not a requirement. I
+ 
+
+ align:start position:0%
+I think that's not a requirement. I
+think that's a if you want to make your
+
+ align:start position:0%
+think that's a if you want to make your
+ 
+
+ align:start position:0%
+think that's a if you want to make your
+life easier, this is what you do. If you
+
+ align:start position:0%
+life easier, this is what you do. If you
+ 
+
+ align:start position:0%
+life easier, this is what you do. If you
+decide that you're up to the task, you
+
+ align:start position:0%
+decide that you're up to the task, you
+ 
+
+ align:start position:0%
+decide that you're up to the task, you
+can achieve some really amazing effects
+
+ align:start position:0%
+can achieve some really amazing effects
+ 
+
+ align:start position:0%
+can achieve some really amazing effects
+by having your puzzles narratively
+
+ align:start position:0%
+by having your puzzles narratively
+ 
+
+ align:start position:0%
+by having your puzzles narratively
+important. Um, so there's um,
+
+ align:start position:0%
+important. Um, so there's um,
+ 
+
+ align:start position:0%
+important. Um, so there's um,
+uh, has anyone heard of the game called
+
+ align:start position:0%
+uh, has anyone heard of the game called
+ 
+
+ align:start position:0%
+uh, has anyone heard of the game called
+Eternal Darkness? It's, uh, sort of the
+
+ align:start position:0%
+Eternal Darkness? It's, uh, sort of the
+ 
+
+ align:start position:0%
+Eternal Darkness? It's, uh, sort of the
+craftian horror game on the Gamecube?
+
+ align:start position:0%
+craftian horror game on the Gamecube?
+ 
+
+ align:start position:0%
+craftian horror game on the Gamecube?
+Uh, I'll sort of describe it, but
+
+ align:start position:0%
+Uh, I'll sort of describe it, but
+ 
+
+ align:start position:0%
+Uh, I'll sort of describe it, but
+basically the whole basic idea is that
+
+ align:start position:0%
+basically the whole basic idea is that
+ 
+
+ align:start position:0%
+basically the whole basic idea is that
+you have four gods all waring, all
+
+ align:start position:0%
+you have four gods all waring, all
+ 
+
+ align:start position:0%
+you have four gods all waring, all
+waring against each other. Three of them
+
+ align:start position:0%
+waring against each other. Three of them
+ 
+
+ align:start position:0%
+waring against each other. Three of them
+hate one of them, but then those three
+
+ align:start position:0%
+hate one of them, but then those three
+ 
+
+ align:start position:0%
+hate one of them, but then those three
+of them hate each other. and and most of
+
+ align:start position:0%
+of them hate each other. and and most of
+ 
+
+ align:start position:0%
+of them hate each other. and and most of
+the puzzles are just sort of
+
+ align:start position:0%
+the puzzles are just sort of
+ 
+
+ align:start position:0%
+the puzzles are just sort of
+understanding that there is this there's
+
+ align:start position:0%
+understanding that there is this there's
+ 
+
+ align:start position:0%
+understanding that there is this there's
+this mystical logic you know one god
+
+ align:start position:0%
+this mystical logic you know one god
+ 
+
+ align:start position:0%
+this mystical logic you know one god
+defeats another god defeats another god
+
+ align:start position:0%
+defeats another god defeats another god
+ 
+
+ align:start position:0%
+defeats another god defeats another god
+in a rock paper scissor circle and all
+
+ align:start position:0%
+in a rock paper scissor circle and all
+ 
+
+ align:start position:0%
+in a rock paper scissor circle and all
+of them hate this one other thing um so
+
+ align:start position:0%
+of them hate this one other thing um so
+ 
+
+ align:start position:0%
+of them hate this one other thing um so
+um early on in the game there's actually
+
+ align:start position:0%
+um early on in the game there's actually
+ 
+
+ align:start position:0%
+um early on in the game there's actually
+a puzzle there are actually a number of
+
+ align:start position:0%
+a puzzle there are actually a number of
+ 
+
+ align:start position:0%
+a puzzle there are actually a number of
+different p uh p puzzles where you see
+
+ align:start position:0%
+different p uh p puzzles where you see
+ 
+
+ align:start position:0%
+different p uh p puzzles where you see
+the symbols of these gods and you have
+
+ align:start position:0%
+the symbols of these gods and you have
+ 
+
+ align:start position:0%
+the symbols of these gods and you have
+to kind of rearrange them in the correct
+
+ align:start position:0%
+to kind of rearrange them in the correct
+ 
+
+ align:start position:0%
+to kind of rearrange them in the correct
+order and the rest of the game is all
+
+ align:start position:0%
+order and the rest of the game is all
+ 
+
+ align:start position:0%
+order and the rest of the game is all
+going to be like variations on sort of
+
+ align:start position:0%
+going to be like variations on sort of
+ 
+
+ align:start position:0%
+going to be like variations on sort of
+understanding what these gods do to each
+
+ align:start position:0%
+understanding what these gods do to each
+ 
+
+ align:start position:0%
+understanding what these gods do to each
+other. So those those are all puzzles
+
+ align:start position:0%
+other. So those those are all puzzles
+ 
+
+ align:start position:0%
+other. So those those are all puzzles
+that inform you about how the world
+
+ align:start position:0%
+that inform you about how the world
+ 
+
+ align:start position:0%
+that inform you about how the world
+works. Um that and that's that kind of
+
+ align:start position:0%
+works. Um that and that's that kind of
+ 
+
+ align:start position:0%
+works. Um that and that's that kind of
+works in two ways. One information that
+
+ align:start position:0%
+works in two ways. One information that
+ 
+
+ align:start position:0%
+works in two ways. One information that
+you've already gathered about the world
+
+ align:start position:0%
+you've already gathered about the world
+ 
+
+ align:start position:0%
+you've already gathered about the world
+about how this world works gives you
+
+ align:start position:0%
+about how this world works gives you
+ 
+
+ align:start position:0%
+about how this world works gives you
+clues on how to beat the puzzles.
+
+ align:start position:0%
+clues on how to beat the puzzles.
+ 
+
+ align:start position:0%
+clues on how to beat the puzzles.
+Beating the puzzles, finding the
+
+ align:start position:0%
+Beating the puzzles, finding the
+ 
+
+ align:start position:0%
+Beating the puzzles, finding the
+solutions for the clues gives you
+
+ align:start position:0%
+solutions for the clues gives you
+ 
+
+ align:start position:0%
+solutions for the clues gives you
+information about how the world works.
+
+ align:start position:0%
+information about how the world works.
+ 
+
+ align:start position:0%
+information about how the world works.
+And that's that's kind of like the holy
+
+ align:start position:0%
+And that's that's kind of like the holy
+ 
+
+ align:start position:0%
+And that's that's kind of like the holy
+grail of a puzzle designer in a digital
+
+ align:start position:0%
+grail of a puzzle designer in a digital
+ 
+
+ align:start position:0%
+grail of a puzzle designer in a digital
+game is that you're going to design a
+
+ align:start position:0%
+game is that you're going to design a
+ 
+
+ align:start position:0%
+game is that you're going to design a
+puzzle that's going to reinforce how the
+
+ align:start position:0%
+puzzle that's going to reinforce how the
+ 
+
+ align:start position:0%
+puzzle that's going to reinforce how the
+world works. Um we there's a chap um who
+
+ align:start position:0%
+world works. Um we there's a chap um who
+ 
+
+ align:start position:0%
+world works. Um we there's a chap um who
+gave a talk and I believe his name is
+
+ align:start position:0%
+gave a talk and I believe his name is
+ 
+
+ align:start position:0%
+gave a talk and I believe his name is
+Jeff Howard. He came to um he came to
+
+ align:start position:0%
+Jeff Howard. He came to um he came to
+ 
+
+ align:start position:0%
+Jeff Howard. He came to um he came to
+camp and gave a talk last
+
+ align:start position:0%
+camp and gave a talk last
+ 
+
+ align:start position:0%
+camp and gave a talk last
+>> last year and um and he makes this case
+
+ align:start position:0%
+>> last year and um and he makes this case
+ 
+
+ align:start position:0%
+>> last year and um and he makes this case
+that games and the logic in that that
+
+ align:start position:0%
+that games and the logic in that that
+ 
+
+ align:start position:0%
+that games and the logic in that that
+you present in games uh do basically uh
+
+ align:start position:0%
+you present in games uh do basically uh
+ 
+
+ align:start position:0%
+you present in games uh do basically uh
+the equivalent of what magic does in of
+
+ align:start position:0%
+the equivalent of what magic does in of
+ 
+
+ align:start position:0%
+the equivalent of what magic does in of
+what magic systems actually do in the
+
+ align:start position:0%
+what magic systems actually do in the
+ 
+
+ align:start position:0%
+what magic systems actually do in the
+real world. you know, um what people
+
+ align:start position:0%
+real world. you know, um what people
+ 
+
+ align:start position:0%
+real world. you know, um what people
+like like like
+
+ align:start position:0%
+like like like
+ 
+
+ align:start position:0%
+like like like
+oultists or astrologers or they
+
+ align:start position:0%
+oultists or astrologers or they
+ 
+
+ align:start position:0%
+oultists or astrologers or they
+basically give you logics on, you know,
+
+ align:start position:0%
+basically give you logics on, you know,
+ 
+
+ align:start position:0%
+basically give you logics on, you know,
+uh that that that explain how the world
+
+ align:start position:0%
+uh that that that explain how the world
+ 
+
+ align:start position:0%
+uh that that that explain how the world
+is going to work. One that may not
+
+ align:start position:0%
+is going to work. One that may not
+ 
+
+ align:start position:0%
+is going to work. One that may not
+necessarily be obvious, but if you knew
+
+ align:start position:0%
+necessarily be obvious, but if you knew
+ 
+
+ align:start position:0%
+necessarily be obvious, but if you knew
+this knowledge, you'd be able to
+
+ align:start position:0%
+this knowledge, you'd be able to
+ 
+
+ align:start position:0%
+this knowledge, you'd be able to
+understand how this will work in you.
+
+ align:start position:0%
+understand how this will work in you.
+ 
+
+ align:start position:0%
+understand how this will work in you.
+But more importantly, you'll be able to
+
+ align:start position:0%
+But more importantly, you'll be able to
+ 
+
+ align:start position:0%
+But more importantly, you'll be able to
+do things in the world that you know
+
+ align:start position:0%
+do things in the world that you know
+ 
+
+ align:start position:0%
+do things in the world that you know
+that that allow you to accomplish things
+
+ align:start position:0%
+that that allow you to accomplish things
+ 
+
+ align:start position:0%
+that that allow you to accomplish things
+uh uh that you wouldn't otherwise do.
+
+ align:start position:0%
+uh uh that you wouldn't otherwise do.
+ 
+
+ align:start position:0%
+uh uh that you wouldn't otherwise do.
+Learning a game is very much like like
+
+ align:start position:0%
+Learning a game is very much like like
+ 
+
+ align:start position:0%
+Learning a game is very much like like
+like like that. You know, it's like I
+
+ align:start position:0%
+like like that. You know, it's like I
+ 
+
+ align:start position:0%
+like like that. You know, it's like I
+don't know how this world works, but if
+
+ align:start position:0%
+don't know how this world works, but if
+ 
+
+ align:start position:0%
+don't know how this world works, but if
+I understood these particular rules, I
+
+ align:start position:0%
+I understood these particular rules, I
+ 
+
+ align:start position:0%
+I understood these particular rules, I
+could be able to accomplish greater
+
+ align:start position:0%
+could be able to accomplish greater
+ 
+
+ align:start position:0%
+could be able to accomplish greater
+things. Um and puzzles can be one of
+
+ align:start position:0%
+things. Um and puzzles can be one of
+ 
+
+ align:start position:0%
+things. Um and puzzles can be one of
+those things where where it becomes a
+
+ align:start position:0%
+those things where where it becomes a
+ 
+
+ align:start position:0%
+those things where where it becomes a
+test, right? It becomes a test of just
+
+ align:start position:0%
+test, right? It becomes a test of just
+ 
+
+ align:start position:0%
+test, right? It becomes a test of just
+exactly how well do you understand this?
+
+ align:start position:0%
+exactly how well do you understand this?
+ 
+
+ align:start position:0%
+exactly how well do you understand this?
+uh even if it's like in a combat game
+
+ align:start position:0%
+uh even if it's like in a combat game
+ 
+
+ align:start position:0%
+uh even if it's like in a combat game
+like uh Quick or God of War or
+
+ align:start position:0%
+like uh Quick or God of War or
+ 
+
+ align:start position:0%
+like uh Quick or God of War or
+something, you know, I can understand
+
+ align:start position:0%
+something, you know, I can understand
+ 
+
+ align:start position:0%
+something, you know, I can understand
+how the combat system basically works if
+
+ align:start position:0%
+how the combat system basically works if
+ 
+
+ align:start position:0%
+how the combat system basically works if
+I just keep mashing the X button or
+
+ align:start position:0%
+I just keep mashing the X button or
+ 
+
+ align:start position:0%
+I just keep mashing the X button or
+something or just like shoot everything
+
+ align:start position:0%
+something or just like shoot everything
+ 
+
+ align:start position:0%
+something or just like shoot everything
+with rockets. Um but if I really really
+
+ align:start position:0%
+with rockets. Um but if I really really
+ 
+
+ align:start position:0%
+with rockets. Um but if I really really
+understand the combat system, I might be
+
+ align:start position:0%
+understand the combat system, I might be
+ 
+
+ align:start position:0%
+understand the combat system, I might be
+able to hit something that I wouldn't
+
+ align:start position:0%
+able to hit something that I wouldn't
+ 
+
+ align:start position:0%
+able to hit something that I wouldn't
+necessarily be able to hit. I might be
+
+ align:start position:0%
+necessarily be able to hit. I might be
+ 
+
+ align:start position:0%
+necessarily be able to hit. I might be
+able to um I might be able to take down
+
+ align:start position:0%
+able to um I might be able to take down
+ 
+
+ align:start position:0%
+able to um I might be able to take down
+a a horde of enemies instead of like
+
+ align:start position:0%
+a a horde of enemies instead of like
+ 
+
+ align:start position:0%
+a a horde of enemies instead of like
+taking them down one at a time. Um I
+
+ align:start position:0%
+taking them down one at a time. Um I
+ 
+
+ align:start position:0%
+taking them down one at a time. Um I
+might be able to beat a boss. And
+
+ align:start position:0%
+might be able to beat a boss. And
+ 
+
+ align:start position:0%
+might be able to beat a boss. And
+actually a lot of boss boss battles in
+
+ align:start position:0%
+actually a lot of boss boss battles in
+ 
+
+ align:start position:0%
+actually a lot of boss boss battles in
+digital games are actually puzzles.
+
+ align:start position:0%
+digital games are actually puzzles.
+ 
+
+ align:start position:0%
+digital games are actually puzzles.
+There's not it's not how well do you
+
+ align:start position:0%
+There's not it's not how well do you
+ 
+
+ align:start position:0%
+There's not it's not how well do you
+generally react, it's can you figure out
+
+ align:start position:0%
+generally react, it's can you figure out
+ 
+
+ align:start position:0%
+generally react, it's can you figure out
+the pattern. Um but that pattern makes
+
+ align:start position:0%
+the pattern. Um but that pattern makes
+ 
+
+ align:start position:0%
+the pattern. Um but that pattern makes
+no doesn't mean anything unless you've
+
+ align:start position:0%
+no doesn't mean anything unless you've
+ 
+
+ align:start position:0%
+no doesn't mean anything unless you've
+already figured out how all your other
+
+ align:start position:0%
+already figured out how all your other
+ 
+
+ align:start position:0%
+already figured out how all your other
+combat skills work. So, a boss battle in
+
+ align:start position:0%
+combat skills work. So, a boss battle in
+ 
+
+ align:start position:0%
+combat skills work. So, a boss battle in
+Zelda only makes sense if you figured
+
+ align:start position:0%
+Zelda only makes sense if you figured
+ 
+
+ align:start position:0%
+Zelda only makes sense if you figured
+out how that one item that you picked up
+
+ align:start position:0%
+out how that one item that you picked up
+ 
+
+ align:start position:0%
+out how that one item that you picked up
+in the dungeon works really, really
+
+ align:start position:0%
+in the dungeon works really, really
+ 
+
+ align:start position:0%
+in the dungeon works really, really
+well. You know, okay, it shoots fire.
+
+ align:start position:0%
+well. You know, okay, it shoots fire.
+ 
+
+ align:start position:0%
+well. You know, okay, it shoots fire.
+That means not only does it hurt things
+
+ align:start position:0%
+That means not only does it hurt things
+ 
+
+ align:start position:0%
+That means not only does it hurt things
+from distance, it also lights certain
+
+ align:start position:0%
+from distance, it also lights certain
+ 
+
+ align:start position:0%
+from distance, it also lights certain
+things on fire. And that's what a Zelda
+
+ align:start position:0%
+things on fire. And that's what a Zelda
+ 
+
+ align:start position:0%
+things on fire. And that's what a Zelda
+boss battle basically is. Combining this
+
+ align:start position:0%
+boss battle basically is. Combining this
+ 
+
+ align:start position:0%
+boss battle basically is. Combining this
+latest ability that I got with
+
+ align:start position:0%
+latest ability that I got with
+ 
+
+ align:start position:0%
+latest ability that I got with
+everything else that you've done before
+
+ align:start position:0%
+everything else that you've done before
+ 
+
+ align:start position:0%
+everything else that you've done before
+into taking it down. That's why boss
+
+ align:start position:0%
+into taking it down. That's why boss
+ 
+
+ align:start position:0%
+into taking it down. That's why boss
+puzzle battle is kind of like a puzzle.
+
+ align:start position:0%
+puzzle battle is kind of like a puzzle.
+ 
+
+ align:start position:0%
+puzzle battle is kind of like a puzzle.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+one thing I wanted to say before I go
+
+ align:start position:0%
+one thing I wanted to say before I go
+ 
+
+ align:start position:0%
+one thing I wanted to say before I go
+on, you're asking about like hints in a
+
+ align:start position:0%
+on, you're asking about like hints in a
+ 
+
+ align:start position:0%
+on, you're asking about like hints in a
+physical puzzle. And the one thing that
+
+ align:start position:0%
+physical puzzle. And the one thing that
+ 
+
+ align:start position:0%
+physical puzzle. And the one thing that
+jumped to my mind was um, a couple years
+
+ align:start position:0%
+jumped to my mind was um, a couple years
+ 
+
+ align:start position:0%
+jumped to my mind was um, a couple years
+ago, the weekly dig, I don't know if
+
+ align:start position:0%
+ago, the weekly dig, I don't know if
+ 
+
+ align:start position:0%
+ago, the weekly dig, I don't know if
+anyone reads it, it's like a free Boston
+
+ align:start position:0%
+anyone reads it, it's like a free Boston
+ 
+
+ align:start position:0%
+anyone reads it, it's like a free Boston
+newspaper. And there was a cross word
+
+ align:start position:0%
+newspaper. And there was a cross word
+ 
+
+ align:start position:0%
+newspaper. And there was a cross word
+puzzles for the longest time. They were
+
+ align:start position:0%
+puzzles for the longest time. They were
+ 
+
+ align:start position:0%
+puzzles for the longest time. They were
+thematic. And so you would have a guest
+
+ align:start position:0%
+thematic. And so you would have a guest
+ 
+
+ align:start position:0%
+thematic. And so you would have a guest
+cross lord and uh, like the first one I
+
+ align:start position:0%
+cross lord and uh, like the first one I
+ 
+
+ align:start position:0%
+cross lord and uh, like the first one I
+ever did was Hulk Hogan. So all of all
+
+ align:start position:0%
+ever did was Hulk Hogan. So all of all
+ 
+
+ align:start position:0%
+ever did was Hulk Hogan. So all of all
+of the hints in the cross word puzzle
+
+ align:start position:0%
+of the hints in the cross word puzzle
+ 
+
+ align:start position:0%
+of the hints in the cross word puzzle
+are related to Hulk Hogan. So it's a
+
+ align:start position:0%
+are related to Hulk Hogan. So it's a
+ 
+
+ align:start position:0%
+are related to Hulk Hogan. So it's a
+question of like not what does this mean
+
+ align:start position:0%
+question of like not what does this mean
+ 
+
+ align:start position:0%
+question of like not what does this mean
+to me, but what would it mean to Hulk
+
+ align:start position:0%
+to me, but what would it mean to Hulk
+ 
+
+ align:start position:0%
+to me, but what would it mean to Hulk
+Hogan? And um and they don't do it
+
+ align:start position:0%
+Hogan? And um and they don't do it
+ 
+
+ align:start position:0%
+Hogan? And um and they don't do it
+anymore, which is really depressing
+
+ align:start position:0%
+anymore, which is really depressing
+ 
+
+ align:start position:0%
+anymore, which is really depressing
+because every week it was somewhat
+
+ align:start position:0%
+because every week it was somewhat
+ 
+
+ align:start position:0%
+because every week it was somewhat
+different. And it kind of it was like a
+
+ align:start position:0%
+different. And it kind of it was like a
+ 
+
+ align:start position:0%
+different. And it kind of it was like a
+built-in hint, right? As you weren't,
+
+ align:start position:0%
+built-in hint, right? As you weren't,
+ 
+
+ align:start position:0%
+built-in hint, right? As you weren't,
+you didn't just think about it
+
+ align:start position:0%
+you didn't just think about it
+ 
+
+ align:start position:0%
+you didn't just think about it
+literally. You have to kind of
+
+ align:start position:0%
+literally. You have to kind of
+ 
+
+ align:start position:0%
+literally. You have to kind of
+contextualize it. You can think about
+
+ align:start position:0%
+contextualize it. You can think about
+ 
+
+ align:start position:0%
+contextualize it. You can think about
+all the things that come with the puzzle
+
+ align:start position:0%
+all the things that come with the puzzle
+ 
+
+ align:start position:0%
+all the things that come with the puzzle
+as potential in players introduced sense
+
+ align:start position:0%
+as potential in players introduced sense
+ 
+
+ align:start position:0%
+as potential in players introduced sense
+like the title like the play the text as
+
+ align:start position:0%
+like the title like the play the text as
+ 
+
+ align:start position:0%
+like the title like the play the text as
+you were describing the fact that it's
+
+ align:start position:0%
+you were describing the fact that it's
+ 
+
+ align:start position:0%
+you were describing the fact that it's
+in the like like the fact that you get a
+
+ align:start position:0%
+in the like like the fact that you get a
+ 
+
+ align:start position:0%
+in the like like the fact that you get a
+puzzle and mystery hunts immediately
+
+ align:start position:0%
+puzzle and mystery hunts immediately
+ 
+
+ align:start position:0%
+puzzle and mystery hunts immediately
+clues you in that maybe the solution for
+
+ align:start position:0%
+clues you in that maybe the solution for
+ 
+
+ align:start position:0%
+clues you in that maybe the solution for
+this lies in a different puzzle that not
+
+ align:start position:0%
+this lies in a different puzzle that not
+ 
+
+ align:start position:0%
+this lies in a different puzzle that not
+the one that I'm currently looking at
+
+ align:start position:0%
+the one that I'm currently looking at
+ 
+
+ align:start position:0%
+the one that I'm currently looking at
+right now because that's how mystery
+
+ align:start position:0%
+right now because that's how mystery
+ 
+
+ align:start position:0%
+right now because that's how mystery
+hunt things are. Um,
+
+ align:start position:0%
+hunt things are. Um,
+ 
+
+ align:start position:0%
+hunt things are. Um,
+uh,
+
+ align:start position:0%
+uh,
+ 
+
+ align:start position:0%
+uh,
+Metal Gear Solid is, uh, has a really,
+
+ align:start position:0%
+Metal Gear Solid is, uh, has a really,
+ 
+
+ align:start position:0%
+Metal Gear Solid is, uh, has a really,
+really bizarre one where, uh,
+
+ align:start position:0%
+really bizarre one where, uh,
+ 
+
+ align:start position:0%
+really bizarre one where, uh,
+>> look in the back case.
+
+ align:start position:0%
+>> look in the back case.
+ 
+
+ align:start position:0%
+>> look in the back case.
+>> Yes. Where they tell you, oh, there's a
+
+ align:start position:0%
+>> Yes. Where they tell you, oh, there's a
+ 
+
+ align:start position:0%
+>> Yes. Where they tell you, oh, there's a
+specific radio frequency that you need.
+
+ align:start position:0%
+specific radio frequency that you need.
+ 
+
+ align:start position:0%
+specific radio frequency that you need.
+It's written in the back of the box and
+
+ align:start position:0%
+It's written in the back of the box and
+ 
+
+ align:start position:0%
+It's written in the back of the box and
+it's like the back of the box
+
+ align:start position:0%
+it's like the back of the box
+ 
+
+ align:start position:0%
+it's like the back of the box
+or antipiriracy.
+
+ align:start position:0%
+or antipiriracy.
+ 
+
+ align:start position:0%
+or antipiriracy.
+>> Yeah. I mean, yes, but it's still a
+
+ align:start position:0%
+>> Yeah. I mean, yes, but it's still a
+ 
+
+ align:start position:0%
+>> Yeah. I mean, yes, but it's still a
+puzzle, you know. It's like, you know,
+
+ align:start position:0%
+puzzle, you know. It's like, you know,
+ 
+
+ align:start position:0%
+puzzle, you know. It's like, you know,
+to solve that. I mean, they were pretty
+
+ align:start position:0%
+to solve that. I mean, they were pretty
+ 
+
+ align:start position:0%
+to solve that. I mean, they were pretty
+obvious because uh or maybe it's just me
+
+ align:start position:0%
+obvious because uh or maybe it's just me
+ 
+
+ align:start position:0%
+obvious because uh or maybe it's just me
+because it took me about half an hour to
+
+ align:start position:0%
+because it took me about half an hour to
+ 
+
+ align:start position:0%
+because it took me about half an hour to
+figure that one out.
+
+ align:start position:0%
+figure that one out.
+ 
+
+ align:start position:0%
+figure that one out.
+>> Took me some hours.
+
+ align:start position:0%
+>> Took me some hours.
+ 
+
+ align:start position:0%
+>> Took me some hours.
+>> I mean, Middle Gear Hell did a lot of
+
+ align:start position:0%
+>> I mean, Middle Gear Hell did a lot of
+ 
+
+ align:start position:0%
+>> I mean, Middle Gear Hell did a lot of
+like meta puzzles like that. Like when
+
+ align:start position:0%
+like meta puzzles like that. Like when
+ 
+
+ align:start position:0%
+like meta puzzles like that. Like when
+when you fought Psycho Mantis the first
+
+ align:start position:0%
+when you fought Psycho Mantis the first
+ 
+
+ align:start position:0%
+when you fought Psycho Mantis the first
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+>> Well, so the thing you had to do is you
+
+ align:start position:0%
+>> Well, so the thing you had to do is you
+ 
+
+ align:start position:0%
+>> Well, so the thing you had to do is you
+had to unplug your controller and plug
+
+ align:start position:0%
+had to unplug your controller and plug
+ 
+
+ align:start position:0%
+had to unplug your controller and plug
+it into the second port because he would
+
+ align:start position:0%
+it into the second port because he would
+ 
+
+ align:start position:0%
+it into the second port because he would
+read your movements
+
+ align:start position:0%
+read your movements
+ 
+
+ align:start position:0%
+read your movements
+>> and it it was just like it was this cool
+
+ align:start position:0%
+>> and it it was just like it was this cool
+ 
+
+ align:start position:0%
+>> and it it was just like it was this cool
+like physical layer of it where like
+
+ align:start position:0%
+like physical layer of it where like
+ 
+
+ align:start position:0%
+like physical layer of it where like
+you're playing the game, you realize I
+
+ align:start position:0%
+you're playing the game, you realize I
+ 
+
+ align:start position:0%
+you're playing the game, you realize I
+have to interact with the physical
+
+ align:start position:0%
+have to interact with the physical
+ 
+
+ align:start position:0%
+have to interact with the physical
+world. so that he can't see what I'm
+
+ align:start position:0%
+world. so that he can't see what I'm
+ 
+
+ align:start position:0%
+world. so that he can't see what I'm
+doing.
+
+ align:start position:0%
+doing.
+ 
+
+ align:start position:0%
+doing.
+>> But but actually that one had a clue
+
+ align:start position:0%
+>> But but actually that one had a clue
+ 
+
+ align:start position:0%
+>> But but actually that one had a clue
+because if you had a in that particular
+
+ align:start position:0%
+because if you had a in that particular
+ 
+
+ align:start position:0%
+because if you had a in that particular
+example, that one gave you a very big
+
+ align:start position:0%
+example, that one gave you a very big
+ 
+
+ align:start position:0%
+example, that one gave you a very big
+clue because right at the beginning of
+
+ align:start position:0%
+clue because right at the beginning of
+ 
+
+ align:start position:0%
+clue because right at the beginning of
+that match, uh that boss tells you to
+
+ align:start position:0%
+that match, uh that boss tells you to
+ 
+
+ align:start position:0%
+that match, uh that boss tells you to
+put your controller on the ground and he
+
+ align:start position:0%
+put your controller on the ground and he
+ 
+
+ align:start position:0%
+put your controller on the ground and he
+said that I'm going to control this this
+
+ align:start position:0%
+said that I'm going to control this this
+ 
+
+ align:start position:0%
+said that I'm going to control this this
+controller with my mind and actually
+
+ align:start position:0%
+controller with my mind and actually
+ 
+
+ align:start position:0%
+controller with my mind and actually
+just right.
+
+ align:start position:0%
+just right.
+ 
+
+ align:start position:0%
+just right.
+>> That's only if you have DualS. So since
+
+ align:start position:0%
+>> That's only if you have DualS. So since
+ 
+
+ align:start position:0%
+>> That's only if you have DualS. So since
+it was on PlayStation,
+
+ align:start position:0%
+it was on PlayStation,
+ 
+
+ align:start position:0%
+it was on PlayStation,
+>> uh if you didn't, he just ignored that
+
+ align:start position:0%
+>> uh if you didn't, he just ignored that
+ 
+
+ align:start position:0%
+>> uh if you didn't, he just ignored that
+part and you didn't you didn't get that
+
+ align:start position:0%
+part and you didn't you didn't get that
+ 
+
+ align:start position:0%
+part and you didn't you didn't get that
+clue at all. Yeah, that and that's a
+
+ align:start position:0%
+clue at all. Yeah, that and that's a
+ 
+
+ align:start position:0%
+clue at all. Yeah, that and that's a
+problem. But but it's still it's still
+
+ align:start position:0%
+problem. But but it's still it's still
+ 
+
+ align:start position:0%
+problem. But but it's still it's still
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+>> there were other clues.
+
+ align:start position:0%
+>> there were other clues.
+ 
+
+ align:start position:0%
+>> there were other clues.
+>> There were also other clues like you
+
+ align:start position:0%
+>> There were also other clues like you
+ 
+
+ align:start position:0%
+>> There were also other clues like you
+would talk about how you had been
+
+ align:start position:0%
+would talk about how you had been
+ 
+
+ align:start position:0%
+would talk about how you had been
+playing certain games by reading saves
+
+ align:start position:0%
+playing certain games by reading saves
+ 
+
+ align:start position:0%
+playing certain games by reading saves
+on your
+
+ align:start position:0%
+on your
+ 
+
+ align:start position:0%
+on your
+>> I think it was on your notion
+
+ align:start position:0%
+>> I think it was on your notion
+ 
+
+ align:start position:0%
+>> I think it was on your notion
+of the night.
+
+ align:start position:0%
+of the night.
+ 
+
+ align:start position:0%
+of the night.
+>> Those are the ones.
+
+ align:start position:0%
+>> Those are the ones.
+ 
+
+ align:start position:0%
+>> Those are the ones.
+>> So So basically it's it's telling you
+
+ align:start position:0%
+>> So So basically it's it's telling you
+ 
+
+ align:start position:0%
+>> So So basically it's it's telling you
+it's giving you a clue that there
+
+ align:start position:0%
+it's giving you a clue that there
+ 
+
+ align:start position:0%
+it's giving you a clue that there
+there's going to be something better
+
+ align:start position:0%
+there's going to be something better
+ 
+
+ align:start position:0%
+there's going to be something better
+about the way that you're currently
+
+ align:start position:0%
+about the way that you're currently
+ 
+
+ align:start position:0%
+about the way that you're currently
+playing. Uh, the funny thing about the
+
+ align:start position:0%
+playing. Uh, the funny thing about the
+ 
+
+ align:start position:0%
+playing. Uh, the funny thing about the
+radio channel one is that that one
+
+ align:start position:0%
+radio channel one is that that one
+ 
+
+ align:start position:0%
+radio channel one is that that one
+really did not give you any clues that
+
+ align:start position:0%
+really did not give you any clues that
+ 
+
+ align:start position:0%
+really did not give you any clues that
+it was something better. It just told
+
+ align:start position:0%
+it was something better. It just told
+ 
+
+ align:start position:0%
+it was something better. It just told
+you about it at the back at the back of
+
+ align:start position:0%
+you about it at the back at the back of
+ 
+
+ align:start position:0%
+you about it at the back at the back of
+the box. It is like and it didn't tell
+
+ align:start position:0%
+the box. It is like and it didn't tell
+ 
+
+ align:start position:0%
+the box. It is like and it didn't tell
+you the back of the case, the the video
+
+ align:start position:0%
+you the back of the case, the the video
+ 
+
+ align:start position:0%
+you the back of the case, the the video
+game case, right? It's not going to be
+
+ align:start position:0%
+game case, right? It's not going to be
+ 
+
+ align:start position:0%
+game case, right? It's not going to be
+that explicit. It's a CD case
+
+ align:start position:0%
+that explicit. It's a CD case
+ 
+
+ align:start position:0%
+that explicit. It's a CD case
+specifically.
+
+ align:start position:0%
+specifically.
+ 
+
+ align:start position:0%
+specifically.
+>> Oh, CD case.
+
+ align:start position:0%
+>> Oh, CD case.
+ 
+
+ align:start position:0%
+>> Oh, CD case.
+>> Yeah, I appreciate I I was really
+
+ align:start position:0%
+>> Yeah, I appreciate I I was really
+ 
+
+ align:start position:0%
+>> Yeah, I appreciate I I was really
+confused cuz I think mine came in like a
+
+ align:start position:0%
+confused cuz I think mine came in like a
+ 
+
+ align:start position:0%
+confused cuz I think mine came in like a
+slip of paper or something.
+
+ align:start position:0%
+slip of paper or something.
+ 
+
+ align:start position:0%
+slip of paper or something.
+>> Oh, yeah.
+
+ align:start position:0%
+>> Oh, yeah.
+ 
+
+ align:start position:0%
+>> Oh, yeah.
+>> Yeah, if you buy it used or something.
+
+ align:start position:0%
+>> Yeah, if you buy it used or something.
+ 
+
+ align:start position:0%
+>> Yeah, if you buy it used or something.
+>> Wow. So, it's anti-use game protection
+
+ align:start position:0%
+>> Wow. So, it's anti-use game protection
+ 
+
+ align:start position:0%
+>> Wow. So, it's anti-use game protection
+as well. But uh yeah, mine was Yeah, I
+
+ align:start position:0%
+as well. But uh yeah, mine was Yeah, I
+ 
+
+ align:start position:0%
+as well. But uh yeah, mine was Yeah, I
+think mine actually said at the back of
+
+ align:start position:0%
+think mine actually said at the back of
+ 
+
+ align:start position:0%
+think mine actually said at the back of
+the CD case, but I was playing like a
+
+ align:start position:0%
+the CD case, but I was playing like a
+ 
+
+ align:start position:0%
+the CD case, but I was playing like a
+re-release or something and that came in
+
+ align:start position:0%
+re-release or something and that came in
+ 
+
+ align:start position:0%
+re-release or something and that came in
+the the DVD case. So, I didn't make that
+
+ align:start position:0%
+the the DVD case. So, I didn't make that
+ 
+
+ align:start position:0%
+the the DVD case. So, I didn't make that
+connection, but you know, if you look at
+
+ align:start position:0%
+connection, but you know, if you look at
+ 
+
+ align:start position:0%
+connection, but you know, if you look at
+the back of it, you see the you you
+
+ align:start position:0%
+the back of it, you see the you you
+ 
+
+ align:start position:0%
+the back of it, you see the you you
+you'll see what the radio frequency is
+
+ align:start position:0%
+you'll see what the radio frequency is
+ 
+
+ align:start position:0%
+you'll see what the radio frequency is
+in a um in the screenshot. What one of
+
+ align:start position:0%
+in a um in the screenshot. What one of
+ 
+
+ align:start position:0%
+in a um in the screenshot. What one of
+the the eight screenshots that they show
+
+ align:start position:0%
+the the eight screenshots that they show
+ 
+
+ align:start position:0%
+the the eight screenshots that they show
+to demonstrate this is what the game is
+
+ align:start position:0%
+to demonstrate this is what the game is
+ 
+
+ align:start position:0%
+to demonstrate this is what the game is
+all about. There's a number just right
+
+ align:start position:0%
+all about. There's a number just right
+ 
+
+ align:start position:0%
+all about. There's a number just right
+in there and then you keep
+
+ align:start position:0%
+in there and then you keep
+ 
+
+ align:start position:0%
+in there and then you keep
+>> behind our
+
+ align:start position:0%
+>> behind our
+ 
+
+ align:start position:0%
+>> behind our
+play of those like breakout games where
+
+ align:start position:0%
+play of those like breakout games where
+ 
+
+ align:start position:0%
+play of those like breakout games where
+you just lock in a room you have to
+
+ align:start position:0%
+you just lock in a room you have to
+ 
+
+ align:start position:0%
+you just lock in a room you have to
+>> escape the room
+
+ align:start position:0%
+>> escape the room
+ 
+
+ align:start position:0%
+>> escape the room
+and you find you like find a paper.
+
+ align:start position:0%
+and you find you like find a paper.
+ 
+
+ align:start position:0%
+and you find you like find a paper.
+>> So um actually who who doesn't know what
+
+ align:start position:0%
+>> So um actually who who doesn't know what
+ 
+
+ align:start position:0%
+>> So um actually who who doesn't know what
+these are about escape the room.
+
+ align:start position:0%
+these are about escape the room.
+ 
+
+ align:start position:0%
+these are about escape the room.
+>> Okay. So, escape the room. Actually,
+
+ align:start position:0%
+>> Okay. So, escape the room. Actually,
+ 
+
+ align:start position:0%
+>> Okay. So, escape the room. Actually,
+could we bring up something on the
+
+ align:start position:0%
+could we bring up something on the
+ 
+
+ align:start position:0%
+could we bring up something on the
+computer? Let's do that. Grab the video.
+
+ align:start position:0%
+computer? Let's do that. Grab the video.
+ 
+
+ align:start position:0%
+computer? Let's do that. Grab the video.
+Well, the video cable. I mean, the after
+
+ align:start position:0%
+Well, the video cable. I mean, the after
+ 
+
+ align:start position:0%
+Well, the video cable. I mean, the after
+my office. Oh, okay. Cool. Um, well,
+
+ align:start position:0%
+my office. Oh, okay. Cool. Um, well,
+ 
+
+ align:start position:0%
+my office. Oh, okay. Cool. Um, well,
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um escape the room games are typically
+
+ align:start position:0%
+um escape the room games are typically
+ 
+
+ align:start position:0%
+um escape the room games are typically
+flash games. Uh, and and they're kind of
+
+ align:start position:0%
+flash games. Uh, and and they're kind of
+ 
+
+ align:start position:0%
+flash games. Uh, and and they're kind of
+like adventure games. You um only
+
+ align:start position:0%
+like adventure games. You um only
+ 
+
+ align:start position:0%
+like adventure games. You um only
+because there's usually only one room,
+
+ align:start position:0%
+because there's usually only one room,
+ 
+
+ align:start position:0%
+because there's usually only one room,
+although sometimes they have multiple
+
+ align:start position:0%
+although sometimes they have multiple
+ 
+
+ align:start position:0%
+although sometimes they have multiple
+rooms. It's a much smaller world than
+
+ align:start position:0%
+rooms. It's a much smaller world than
+ 
+
+ align:start position:0%
+rooms. It's a much smaller world than
+most adventure games, but the basic idea
+
+ align:start position:0%
+most adventure games, but the basic idea
+ 
+
+ align:start position:0%
+most adventure games, but the basic idea
+is the same. you pick up objects, you
+
+ align:start position:0%
+is the same. you pick up objects, you
+ 
+
+ align:start position:0%
+is the same. you pick up objects, you
+use objects in in in in in in a room and
+
+ align:start position:0%
+use objects in in in in in in a room and
+ 
+
+ align:start position:0%
+use objects in in in in in in a room and
+you try to make things happen, you know.
+
+ align:start position:0%
+you try to make things happen, you know.
+ 
+
+ align:start position:0%
+you try to make things happen, you know.
+Um, if you haven't made anything happen,
+
+ align:start position:0%
+Um, if you haven't made anything happen,
+ 
+
+ align:start position:0%
+Um, if you haven't made anything happen,
+you are not progressing in the game. If
+
+ align:start position:0%
+you are not progressing in the game. If
+ 
+
+ align:start position:0%
+you are not progressing in the game. If
+you made something happen, you're almost
+
+ align:start position:0%
+you made something happen, you're almost
+ 
+
+ align:start position:0%
+you made something happen, you're almost
+certainly making forward progress in the
+
+ align:start position:0%
+certainly making forward progress in the
+ 
+
+ align:start position:0%
+certainly making forward progress in the
+game. Um, and and there is actually a a
+
+ align:start position:0%
+game. Um, and and there is actually a a
+ 
+
+ align:start position:0%
+game. Um, and and there is actually a a
+guide for playing adventure games
+
+ align:start position:0%
+guide for playing adventure games
+ 
+
+ align:start position:0%
+guide for playing adventure games
+written by Rob Roberto Williams within
+
+ align:start position:0%
+written by Rob Roberto Williams within
+ 
+
+ align:start position:0%
+written by Rob Roberto Williams within
+the original series. and her guide is
+
+ align:start position:0%
+the original series. and her guide is
+ 
+
+ align:start position:0%
+the original series. and her guide is
+like, "Pick up everything, go
+
+ align:start position:0%
+like, "Pick up everything, go
+ 
+
+ align:start position:0%
+like, "Pick up everything, go
+everywhere, use everything on
+
+ align:start position:0%
+everywhere, use everything on
+ 
+
+ align:start position:0%
+everywhere, use everything on
+everything." It's like, that's actually
+
+ align:start position:0%
+everything." It's like, that's actually
+ 
+
+ align:start position:0%
+everything." It's like, that's actually
+what the escape room game is, but
+
+ align:start position:0%
+what the escape room game is, but
+ 
+
+ align:start position:0%
+what the escape room game is, but
+there's a little bit more humane escape
+
+ align:start position:0%
+there's a little bit more humane escape
+ 
+
+ align:start position:0%
+there's a little bit more humane escape
+to room game because there just not that
+
+ align:start position:0%
+to room game because there just not that
+ 
+
+ align:start position:0%
+to room game because there just not that
+many places that you can explore because
+
+ align:start position:0%
+many places that you can explore because
+ 
+
+ align:start position:0%
+many places that you can explore because
+the idea is that you're stuck in a room.
+
+ align:start position:0%
+the idea is that you're stuck in a room.
+ 
+
+ align:start position:0%
+the idea is that you're stuck in a room.
+Um, and uh, and basically it comes down
+
+ align:start position:0%
+Um, and uh, and basically it comes down
+ 
+
+ align:start position:0%
+Um, and uh, and basically it comes down
+to just use everything on everything
+
+ align:start position:0%
+to just use everything on everything
+ 
+
+ align:start position:0%
+to just use everything on everything
+until you figure out what what turns
+
+ align:start position:0%
+until you figure out what what turns
+ 
+
+ align:start position:0%
+until you figure out what what turns
+out. Rarely isn't logical. Often it
+
+ align:start position:0%
+out. Rarely isn't logical. Often it
+ 
+
+ align:start position:0%
+out. Rarely isn't logical. Often it
+often pretty entertaining because
+
+ align:start position:0%
+often pretty entertaining because
+ 
+
+ align:start position:0%
+often pretty entertaining because
+they're animation heavy. So every time
+
+ align:start position:0%
+they're animation heavy. So every time
+ 
+
+ align:start position:0%
+they're animation heavy. So every time
+you do something right, you get some
+
+ align:start position:0%
+you do something right, you get some
+ 
+
+ align:start position:0%
+you do something right, you get some
+crazy animation. I put the fish into the
+
+ align:start position:0%
+crazy animation. I put the fish into the
+ 
+
+ align:start position:0%
+crazy animation. I put the fish into the
+male slot and then out appears an
+
+ align:start position:0%
+male slot and then out appears an
+ 
+
+ align:start position:0%
+male slot and then out appears an
+octopus.
+
+ align:start position:0%
+octopus.
+ 
+
+ align:start position:0%
+octopus.
+It's like it's fun to watch. Um whereas
+
+ align:start position:0%
+It's like it's fun to watch. Um whereas
+ 
+
+ align:start position:0%
+It's like it's fun to watch. Um whereas
+the kind of combinatorily
+
+ align:start position:0%
+the kind of combinatorily
+ 
+
+ align:start position:0%
+the kind of combinatorily
+opposite of those are the grow games.
+
+ align:start position:0%
+opposite of those are the grow games.
+ 
+
+ align:start position:0%
+opposite of those are the grow games.
+>> Oh yeah.
+
+ align:start position:0%
+>> Oh yeah.
+ 
+
+ align:start position:0%
+>> Oh yeah.
+>> Um and there there is a series of games
+
+ align:start position:0%
+>> Um and there there is a series of games
+ 
+
+ align:start position:0%
+>> Um and there there is a series of games
+called Grow. Um I think the guy who does
+
+ align:start position:0%
+called Grow. Um I think the guy who does
+ 
+
+ align:start position:0%
+called Grow. Um I think the guy who does
+them called eyes maze and that's like Z.
+
+ align:start position:0%
+them called eyes maze and that's like Z.
+ 
+
+ align:start position:0%
+them called eyes maze and that's like Z.
+Um and and um and the whole basic idea
+
+ align:start position:0%
+Um and and um and the whole basic idea
+ 
+
+ align:start position:0%
+Um and and um and the whole basic idea
+is that um imagine that you have a
+
+ align:start position:0%
+is that um imagine that you have a
+ 
+
+ align:start position:0%
+is that um imagine that you have a
+flower pot and every time you add
+
+ align:start position:0%
+flower pot and every time you add
+ 
+
+ align:start position:0%
+flower pot and every time you add
+something to it, something happens. But
+
+ align:start position:0%
+something to it, something happens. But
+ 
+
+ align:start position:0%
+something to it, something happens. But
+the order in which you're adding things
+
+ align:start position:0%
+the order in which you're adding things
+ 
+
+ align:start position:0%
+the order in which you're adding things
+to it makes different things happen.
+
+ align:start position:0%
+to it makes different things happen.
+ 
+
+ align:start position:0%
+to it makes different things happen.
+>> And there are solutions basically in
+
+ align:start position:0%
+>> And there are solutions basically in
+ 
+
+ align:start position:0%
+>> And there are solutions basically in
+making the optimal number of things h
+
+ align:start position:0%
+making the optimal number of things h
+ 
+
+ align:start position:0%
+making the optimal number of things h
+happen if you if you if you do it if you
+
+ align:start position:0%
+happen if you if you if you do it if you
+ 
+
+ align:start position:0%
+happen if you if you if you do it if you
+do it right. So what you can do is not a
+
+ align:start position:0%
+do it right. So what you can do is not a
+ 
+
+ align:start position:0%
+do it right. So what you can do is not a
+mystery at all. You know, you you have I
+
+ align:start position:0%
+mystery at all. You know, you you have I
+ 
+
+ align:start position:0%
+mystery at all. You know, you you have I
+have these six things that I could add
+
+ align:start position:0%
+have these six things that I could add
+ 
+
+ align:start position:0%
+have these six things that I could add
+to my part and it doesn't and and I know
+
+ align:start position:0%
+to my part and it doesn't and and I know
+ 
+
+ align:start position:0%
+to my part and it doesn't and and I know
+that's those are the only six things I
+
+ align:start position:0%
+that's those are the only six things I
+ 
+
+ align:start position:0%
+that's those are the only six things I
+could add. The question is what order do
+
+ align:start position:0%
+could add. The question is what order do
+ 
+
+ align:start position:0%
+could add. The question is what order do
+I do them? Um and doing them in
+
+ align:start position:0%
+I do them? Um and doing them in
+ 
+
+ align:start position:0%
+I do them? Um and doing them in
+different orders gives you different
+
+ align:start position:0%
+different orders gives you different
+ 
+
+ align:start position:0%
+different orders gives you different
+different results. I feel that
+
+ align:start position:0%
+different results. I feel that
+ 
+
+ align:start position:0%
+different results. I feel that
+these these two genres are kind of
+
+ align:start position:0%
+these these two genres are kind of
+ 
+
+ align:start position:0%
+these these two genres are kind of
+linked, but they're not uh but they're
+
+ align:start position:0%
+linked, but they're not uh but they're
+ 
+
+ align:start position:0%
+linked, but they're not uh but they're
+playing off very different things. One
+
+ align:start position:0%
+playing off very different things. One
+ 
+
+ align:start position:0%
+playing off very different things. One
+of them is I don't know what I'm going
+
+ align:start position:0%
+of them is I don't know what I'm going
+ 
+
+ align:start position:0%
+of them is I don't know what I'm going
+to do. Uh, but I know that whatever I do
+
+ align:start position:0%
+to do. Uh, but I know that whatever I do
+ 
+
+ align:start position:0%
+to do. Uh, but I know that whatever I do
+is got to be in the space. And the other
+
+ align:start position:0%
+is got to be in the space. And the other
+ 
+
+ align:start position:0%
+is got to be in the space. And the other
+one is very much I know exactly what I
+
+ align:start position:0%
+one is very much I know exactly what I
+ 
+
+ align:start position:0%
+one is very much I know exactly what I
+can possibly do. I just don't know what
+
+ align:start position:0%
+can possibly do. I just don't know what
+ 
+
+ align:start position:0%
+can possibly do. I just don't know what
+order to do them. So couple of puzzles
+
+ align:start position:0%
+order to do them. So couple of puzzles
+ 
+
+ align:start position:0%
+order to do them. So couple of puzzles
+that you see online. These are fairly
+
+ align:start position:0%
+that you see online. These are fairly
+ 
+
+ align:start position:0%
+that you see online. These are fairly
+encapsulated things. One one game is one
+
+ align:start position:0%
+encapsulated things. One one game is one
+ 
+
+ align:start position:0%
+encapsulated things. One one game is one
+series of puzzles. There's no it's not
+
+ align:start position:0%
+series of puzzles. There's no it's not
+ 
+
+ align:start position:0%
+series of puzzles. There's no it's not
+like a professor kind of encyclopedia
+
+ align:start position:0%
+like a professor kind of encyclopedia
+ 
+
+ align:start position:0%
+like a professor kind of encyclopedia
+puzzles kind of thing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um, let's see. I I think I'm
+
+ align:start position:0%
+Okay. Um, let's see. I I think I'm
+ 
+
+ align:start position:0%
+Okay. Um, let's see. I I think I'm
+actually going going to grab a few more
+
+ align:start position:0%
+actually going going to grab a few more
+ 
+
+ align:start position:0%
+actually going going to grab a few more
+puzzles and bring them in. But, uh, I do
+
+ align:start position:0%
+puzzles and bring them in. But, uh, I do
+ 
+
+ align:start position:0%
+puzzles and bring them in. But, uh, I do
+actually want uh, uh, to try to see
+
+ align:start position:0%
+actually want uh, uh, to try to see
+ 
+
+ align:start position:0%
+actually want uh, uh, to try to see
+whether we can put together a list of
+
+ align:start position:0%
+whether we can put together a list of
+ 
+
+ align:start position:0%
+whether we can put together a list of
+the kinds of puzzles that we haven't
+
+ align:start position:0%
+the kinds of puzzles that we haven't
+ 
+
+ align:start position:0%
+the kinds of puzzles that we haven't
+talked about today. Uh, these could be
+
+ align:start position:0%
+talked about today. Uh, these could be
+ 
+
+ align:start position:0%
+talked about today. Uh, these could be
+physical puzzles. These could be puzzles
+
+ align:start position:0%
+physical puzzles. These could be puzzles
+ 
+
+ align:start position:0%
+physical puzzles. These could be puzzles
+that you've seen in the book, but like a
+
+ align:start position:0%
+that you've seen in the book, but like a
+ 
+
+ align:start position:0%
+that you've seen in the book, but like a
+genre. Um, logic puzzles, you know, of a
+
+ align:start position:0%
+genre. Um, logic puzzles, you know, of a
+ 
+
+ align:start position:0%
+genre. Um, logic puzzles, you know, of a
+certain kind that you either really
+
+ align:start position:0%
+certain kind that you either really
+ 
+
+ align:start position:0%
+certain kind that you either really
+really like or you really really love.
+
+ align:start position:0%
+really like or you really really love.
+ 
+
+ align:start position:0%
+really like or you really really love.
+Um, and just just break up in groups of
+
+ align:start position:0%
+Um, and just just break up in groups of
+ 
+
+ align:start position:0%
+Um, and just just break up in groups of
+three, four, six, seven, eight, nine.
+
+ align:start position:0%
+three, four, six, seven, eight, nine.
+ 
+
+ align:start position:0%
+three, four, six, seven, eight, nine.
+I'm going to bring you guys to do this.
+
+ align:start position:0%
+I'm going to bring you guys to do this.
+ 
+
+ align:start position:0%
+I'm going to bring you guys to do this.
+10 12 13 15 16 17 people. 17 people.
+
+ align:start position:0%
+10 12 13 15 16 17 people. 17 people.
+ 
+
+ align:start position:0%
+10 12 13 15 16 17 people. 17 people.
+That doesn't divide at all.
+
+ align:start position:0%
+That doesn't divide at all.
+ 
+
+ align:start position:0%
+That doesn't divide at all.
+>> One group.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Okay. Two or three. Groups of two or
+
+ align:start position:0%
+>> Okay. Two or three. Groups of two or
+ 
+
+ align:start position:0%
+>> Okay. Two or three. Groups of two or
+three. And just like
+
+ align:start position:0%
+three. And just like
+ 
+
+ align:start position:0%
+three. And just like
+>> uh Jason should be back.
+
+ align:start position:0%
+>> uh Jason should be back.
+ 
+
+ align:start position:0%
+>> uh Jason should be back.
+>> Okay. Then groups then groups of three.
+
+ align:start position:0%
+>> Okay. Then groups then groups of three.
+ 
+
+ align:start position:0%
+>> Okay. Then groups then groups of three.
+Um and uh right
+
+ align:start position:0%
+Um and uh right
+ 
+
+ align:start position:0%
+Um and uh right
+>> and
+
+ align:start position:0%
+>> and
+ 
+
+ align:start position:0%
+>> and
+come up with yeah just like
+
+ align:start position:0%
+come up with yeah just like
+ 
+
+ align:start position:0%
+come up with yeah just like
+>> you know just a couple of puzzles that
+
+ align:start position:0%
+>> you know just a couple of puzzles that
+ 
+
+ align:start position:0%
+>> you know just a couple of puzzles that
+we haven't discussed and you know and a
+
+ align:start position:0%
+we haven't discussed and you know and a
+ 
+
+ align:start position:0%
+we haven't discussed and you know and a
+description about what they're like and
+
+ align:start position:0%
+description about what they're like and
+ 
+
+ align:start position:0%
+description about what they're like and
+we'll just quickly run through the class
+
+ align:start position:0%
+we'll just quickly run through the class
+ 
+
+ align:start position:0%
+we'll just quickly run through the class
+to sort of like give everyone an idea of
+
+ align:start position:0%
+to sort of like give everyone an idea of
+ 
+
+ align:start position:0%
+to sort of like give everyone an idea of
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+>> a as a toy playing with a Rubik's cube
+
+ align:start position:0%
+>> a as a toy playing with a Rubik's cube
+ 
+
+ align:start position:0%
+>> a as a toy playing with a Rubik's cube
+is more fun than the algorithm to solve
+
+ align:start position:0%
+is more fun than the algorithm to solve
+ 
+
+ align:start position:0%
+is more fun than the algorithm to solve
+it. That's not fun at all in my opinion.
+
+ align:start position:0%
+it. That's not fun at all in my opinion.
+ 
+
+ align:start position:0%
+it. That's not fun at all in my opinion.
+>> Yeah. Like it's probably you can also
+
+ align:start position:0%
+>> Yeah. Like it's probably you can also
+ 
+
+ align:start position:0%
+>> Yeah. Like it's probably you can also
+solve it but there's algorithms there
+
+ align:start position:0%
+solve it but there's algorithms there
+ 
+
+ align:start position:0%
+solve it but there's algorithms there
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> yeah one of the things you're talking
+
+ align:start position:0%
+>> yeah one of the things you're talking
+ 
+
+ align:start position:0%
+>> yeah one of the things you're talking
+about was interactive fiction
+
+ align:start position:0%
+about was interactive fiction
+ 
+
+ align:start position:0%
+about was interactive fiction
+>> and uh
+
+ align:start position:0%
+>> and uh
+ 
+
+ align:start position:0%
+>> and uh
+>> like text
+
+ align:start position:0%
+>> like text
+ 
+
+ align:start position:0%
+>> like text
+>> yeah text text adventures and how um
+
+ align:start position:0%
+>> yeah text text adventures and how um
+ 
+
+ align:start position:0%
+>> yeah text text adventures and how um
+sometimes it could be considered just
+
+ align:start position:0%
+sometimes it could be considered just
+ 
+
+ align:start position:0%
+sometimes it could be considered just
+like if you're playing a regular
+
+ align:start position:0%
+like if you're playing a regular
+ 
+
+ align:start position:0%
+like if you're playing a regular
+adventure game but just with text
+
+ align:start position:0%
+adventure game but just with text
+ 
+
+ align:start position:0%
+adventure game but just with text
+instead. And so um the puzzle could be
+
+ align:start position:0%
+instead. And so um the puzzle could be
+ 
+
+ align:start position:0%
+instead. And so um the puzzle could be
+how you interact with the world or it
+
+ align:start position:0%
+how you interact with the world or it
+ 
+
+ align:start position:0%
+how you interact with the world or it
+could be trying to figure out what
+
+ align:start position:0%
+could be trying to figure out what
+ 
+
+ align:start position:0%
+could be trying to figure out what
+actions are available to the user. Like
+
+ align:start position:0%
+actions are available to the user. Like
+ 
+
+ align:start position:0%
+actions are available to the user. Like
+sometimes not all actions are there but
+
+ align:start position:0%
+sometimes not all actions are there but
+ 
+
+ align:start position:0%
+sometimes not all actions are there but
+also um in some games the nature of text
+
+ align:start position:0%
+also um in some games the nature of text
+ 
+
+ align:start position:0%
+also um in some games the nature of text
+gives you different ways to have a
+
+ align:start position:0%
+gives you different ways to have a
+ 
+
+ align:start position:0%
+gives you different ways to have a
+puzzle like in a lost pig because you're
+
+ align:start position:0%
+puzzle like in a lost pig because you're
+ 
+
+ align:start position:0%
+puzzle like in a lost pig because you're
+playing in fork. He doesn't know English
+
+ align:start position:0%
+playing in fork. He doesn't know English
+ 
+
+ align:start position:0%
+playing in fork. He doesn't know English
+very well or like doesn't doesn't have
+
+ align:start position:0%
+very well or like doesn't doesn't have
+ 
+
+ align:start position:0%
+very well or like doesn't doesn't have
+full control of language. So you're
+
+ align:start position:0%
+full control of language. So you're
+ 
+
+ align:start position:0%
+full control of language. So you're
+trying to decipher his words to figure
+
+ align:start position:0%
+trying to decipher his words to figure
+ 
+
+ align:start position:0%
+trying to decipher his words to figure
+out what he's actually saying.
+
+ align:start position:0%
+out what he's actually saying.
+ 
+
+ align:start position:0%
+out what he's actually saying.
+>> An example they can do give that to make
+
+ align:start position:0%
+>> An example they can do give that to make
+ 
+
+ align:start position:0%
+>> An example they can do give that to make
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+>> um I haven't played
+
+ align:start position:0%
+>> um I haven't played
+ 
+
+ align:start position:0%
+>> um I haven't played
+>> in that game. There's uh one part where
+
+ align:start position:0%
+>> in that game. There's uh one part where
+ 
+
+ align:start position:0%
+>> in that game. There's uh one part where
+he's describing a box and it has a slot
+
+ align:start position:0%
+he's describing a box and it has a slot
+ 
+
+ align:start position:0%
+he's describing a box and it has a slot
+and you you you put something in it and
+
+ align:start position:0%
+and you you you put something in it and
+ 
+
+ align:start position:0%
+and you you you put something in it and
+then it gives you something out. But
+
+ align:start position:0%
+then it gives you something out. But
+ 
+
+ align:start position:0%
+then it gives you something out. But
+like the way he's describing it, you
+
+ align:start position:0%
+like the way he's describing it, you
+ 
+
+ align:start position:0%
+like the way he's describing it, you
+don't really know what he's describing
+
+ align:start position:0%
+don't really know what he's describing
+ 
+
+ align:start position:0%
+don't really know what he's describing
+until you realize he's talking about a
+
+ align:start position:0%
+until you realize he's talking about a
+ 
+
+ align:start position:0%
+until you realize he's talking about a
+vending machine.
+
+ align:start position:0%
+vending machine.
+ 
+
+ align:start position:0%
+vending machine.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+>> He describes it as like a tall box with
+
+ align:start position:0%
+>> He describes it as like a tall box with
+ 
+
+ align:start position:0%
+>> He describes it as like a tall box with
+that slot in it.
+
+ align:start position:0%
+that slot in it.
+ 
+
+ align:start position:0%
+that slot in it.
+>> Um, and another example we were talking
+
+ align:start position:0%
+>> Um, and another example we were talking
+ 
+
+ align:start position:0%
+>> Um, and another example we were talking
+about was the game Isle, uh, which is
+
+ align:start position:0%
+about was the game Isle, uh, which is
+ 
+
+ align:start position:0%
+about was the game Isle, uh, which is
+you're you're this guy in like a grocery
+
+ align:start position:0%
+you're you're this guy in like a grocery
+ 
+
+ align:start position:0%
+you're you're this guy in like a grocery
+store and you you have it gives you like
+
+ align:start position:0%
+store and you you have it gives you like
+ 
+
+ align:start position:0%
+store and you you have it gives you like
+this big, uh, prologue and you have one
+
+ align:start position:0%
+this big, uh, prologue and you have one
+ 
+
+ align:start position:0%
+this big, uh, prologue and you have one
+action that you can do. So after you
+
+ align:start position:0%
+action that you can do. So after you
+ 
+
+ align:start position:0%
+action that you can do. So after you
+type in your one action, it tells you
+
+ align:start position:0%
+type in your one action, it tells you
+ 
+
+ align:start position:0%
+type in your one action, it tells you
+what happens and gives you an epilog
+
+ align:start position:0%
+what happens and gives you an epilog
+ 
+
+ align:start position:0%
+what happens and gives you an epilog
+and then the and then the game starts
+
+ align:start position:0%
+and then the and then the game starts
+ 
+
+ align:start position:0%
+and then the and then the game starts
+over. But then using using the
+
+ align:start position:0%
+over. But then using using the
+ 
+
+ align:start position:0%
+over. But then using using the
+information from that epilog, you you
+
+ align:start position:0%
+information from that epilog, you you
+ 
+
+ align:start position:0%
+information from that epilog, you you
+have a different choice of actions that
+
+ align:start position:0%
+have a different choice of actions that
+ 
+
+ align:start position:0%
+have a different choice of actions that
+you can take and different keywords to
+
+ align:start position:0%
+you can take and different keywords to
+ 
+
+ align:start position:0%
+you can take and different keywords to
+use. And so by playing it over and over,
+
+ align:start position:0%
+use. And so by playing it over and over,
+ 
+
+ align:start position:0%
+use. And so by playing it over and over,
+you're like uncovering more of the story
+
+ align:start position:0%
+you're like uncovering more of the story
+ 
+
+ align:start position:0%
+you're like uncovering more of the story
+until you get somewhere.
+
+ align:start position:0%
+until you get somewhere.
+ 
+
+ align:start position:0%
+until you get somewhere.
+>> So the puzzle solution.
+
+ align:start position:0%
+>> So the puzzle solution.
+ 
+
+ align:start position:0%
+>> So the puzzle solution.
+>> Yeah. Isle A.
+
+ align:start position:0%
+>> Yeah. Isle A.
+ 
+
+ align:start position:0%
+>> Yeah. Isle A.
+>> Yeah. I want to play
+
+ align:start position:0%
+>> Yeah. I want to play
+ 
+
+ align:start position:0%
+>> Yeah. I want to play
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+game.
+
+ align:start position:0%
+game.
+ 
+
+ align:start position:0%
+game.
+Um, we also thought about puzzles that
+
+ align:start position:0%
+Um, we also thought about puzzles that
+ 
+
+ align:start position:0%
+Um, we also thought about puzzles that
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+games and put into a very contrived
+
+ align:start position:0%
+games and put into a very contrived
+ 
+
+ align:start position:0%
+games and put into a very contrived
+scenario like bridge puzzles or chess
+
+ align:start position:0%
+scenario like bridge puzzles or chess
+ 
+
+ align:start position:0%
+scenario like bridge puzzles or chess
+puzzles or back when the duelist
+
+ align:start position:0%
+puzzles or back when the duelist
+ 
+
+ align:start position:0%
+puzzles or back when the duelist
+magazines still existed there. Magic the
+
+ align:start position:0%
+magazines still existed there. Magic the
+ 
+
+ align:start position:0%
+magazines still existed there. Magic the
+Gathering puzzles.
+
+ align:start position:0%
+Gathering puzzles.
+ 
+
+ align:start position:0%
+Gathering puzzles.
+>> So, so like like chess puzzles are like
+
+ align:start position:0%
+>> So, so like like chess puzzles are like
+ 
+
+ align:start position:0%
+>> So, so like like chess puzzles are like
+here's this board. What was the move
+
+ align:start position:0%
+here's this board. What was the move
+ 
+
+ align:start position:0%
+here's this board. What was the move
+that that that
+
+ align:start position:0%
+that that that
+ 
+
+ align:start position:0%
+that that that
+black to win in three moves?
+
+ align:start position:0%
+black to win in three moves?
+ 
+
+ align:start position:0%
+black to win in three moves?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Something like that. So that's like you
+
+ align:start position:0%
+>> Something like that. So that's like you
+ 
+
+ align:start position:0%
+>> Something like that. So that's like you
+you are now placing additional
+
+ align:start position:0%
+you are now placing additional
+ 
+
+ align:start position:0%
+you are now placing additional
+constraints on the game.
+
+ align:start position:0%
+constraints on the game.
+ 
+
+ align:start position:0%
+constraints on the game.
+>> Yeah, exactly. It already puts you in a
+
+ align:start position:0%
+>> Yeah, exactly. It already puts you in a
+ 
+
+ align:start position:0%
+>> Yeah, exactly. It already puts you in a
+situation like pretend you're in this
+
+ align:start position:0%
+situation like pretend you're in this
+ 
+
+ align:start position:0%
+situation like pretend you're in this
+game now. We promise you there's a way
+
+ align:start position:0%
+game now. We promise you there's a way
+ 
+
+ align:start position:0%
+game now. We promise you there's a way
+you can automatically win. You have to
+
+ align:start position:0%
+you can automatically win. You have to
+ 
+
+ align:start position:0%
+you can automatically win. You have to
+find it.
+
+ align:start position:0%
+find it.
+ 
+
+ align:start position:0%
+find it.
+>> Yeah. There's a number of uh sort of
+
+ align:start position:0%
+>> Yeah. There's a number of uh sort of
+ 
+
+ align:start position:0%
+>> Yeah. There's a number of uh sort of
+computer games like Choo Choo Rocket and
+
+ align:start position:0%
+computer games like Choo Choo Rocket and
+ 
+
+ align:start position:0%
+computer games like Choo Choo Rocket and
+everything where that's like just a
+
+ align:start position:0%
+everything where that's like just a
+ 
+
+ align:start position:0%
+everything where that's like just a
+completely second.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Chuchu Rocket. Chuchu Rocket. Too rocket
+
+ align:start position:0%
+>> Chuchu Rocket. Chuchu Rocket. Too rocket
+ 
+
+ align:start position:0%
+>> Chuchu Rocket. Chuchu Rocket. Too rocket
+is a frenetic fourplayer. Um like uh
+
+ align:start position:0%
+is a frenetic fourplayer. Um like uh
+ 
+
+ align:start position:0%
+is a frenetic fourplayer. Um like uh
+>> it's it's a mice hurting game.
+
+ align:start position:0%
+>> it's it's a mice hurting game.
+ 
+
+ align:start position:0%
+>> it's it's a mice hurting game.
+>> Mice mice hurting game.
+
+ align:start position:0%
+>> Mice mice hurting game.
+ 
+
+ align:start position:0%
+>> Mice mice hurting game.
+>> Get them into rocket ships.
+
+ align:start position:0%
+>> Get them into rocket ships.
+ 
+
+ align:start position:0%
+>> Get them into rocket ships.
+>> Yeah. So they can go into space.
+
+ align:start position:0%
+>> Yeah. So they can go into space.
+ 
+
+ align:start position:0%
+>> Yeah. So they can go into space.
+>> It is
+
+ align:start position:0%
+>> It is
+ 
+
+ align:start position:0%
+>> It is
+for the dream. It's so good.
+
+ align:start position:0%
+for the dream. It's so good.
+ 
+
+ align:start position:0%
+for the dream. It's so good.
+>> Oh really?
+
+ align:start position:0%
+>> Oh really?
+ 
+
+ align:start position:0%
+>> Oh really?
+>> Really?
+
+ align:start position:0%
+>> Really?
+ 
+
+ align:start position:0%
+>> Really?
+>> The idea is just a whole bunch of mice
+
+ align:start position:0%
+>> The idea is just a whole bunch of mice
+ 
+
+ align:start position:0%
+>> The idea is just a whole bunch of mice
+wandering around the screen and each
+
+ align:start position:0%
+wandering around the screen and each
+ 
+
+ align:start position:0%
+wandering around the screen and each
+player gets to place like three arrows
+
+ align:start position:0%
+player gets to place like three arrows
+ 
+
+ align:start position:0%
+player gets to place like three arrows
+and whenever the mice run the arrow they
+
+ align:start position:0%
+and whenever the mice run the arrow they
+ 
+
+ align:start position:0%
+and whenever the mice run the arrow they
+follow the arrow. So you want to get all
+
+ align:start position:0%
+follow the arrow. So you want to get all
+ 
+
+ align:start position:0%
+follow the arrow. So you want to get all
+you like want to get the cats and the
+
+ align:start position:0%
+you like want to get the cats and the
+ 
+
+ align:start position:0%
+you like want to get the cats and the
+other chips and they eat their mice.
+
+ align:start position:0%
+other chips and they eat their mice.
+ 
+
+ align:start position:0%
+other chips and they eat their mice.
+>> And puzzle mode says you have three
+
+ align:start position:0%
+>> And puzzle mode says you have three
+ 
+
+ align:start position:0%
+>> And puzzle mode says you have three
+arrows in these particular directions.
+
+ align:start position:0%
+arrows in these particular directions.
+ 
+
+ align:start position:0%
+arrows in these particular directions.
+Figure out where to place them. As much
+
+ align:start position:0%
+Figure out where to place them. As much
+ 
+
+ align:start position:0%
+Figure out where to place them. As much
+time as you want, but there's only one
+
+ align:start position:0%
+time as you want, but there's only one
+ 
+
+ align:start position:0%
+time as you want, but there's only one
+one right answer. And that immediately
+
+ align:start position:0%
+one right answer. And that immediately
+ 
+
+ align:start position:0%
+one right answer. And that immediately
+shows you the difference between game
+
+ align:start position:0%
+shows you the difference between game
+ 
+
+ align:start position:0%
+shows you the difference between game
+and puzzle where they all
+
+ align:start position:0%
+and puzzle where they all
+ 
+
+ align:start position:0%
+and puzzle where they all
+>> cool.
+
+ align:start position:0%
+>> cool.
+ 
+
+ align:start position:0%
+>> cool.
+So uh first off, I don't like jigsaw
+
+ align:start position:0%
+So uh first off, I don't like jigsaw
+ 
+
+ align:start position:0%
+So uh first off, I don't like jigsaw
+puzzles, but Michelle loves them. And
+
+ align:start position:0%
+puzzles, but Michelle loves them. And
+ 
+
+ align:start position:0%
+puzzles, but Michelle loves them. And
+then we also talked about who donuts.
+
+ align:start position:0%
+then we also talked about who donuts.
+ 
+
+ align:start position:0%
+then we also talked about who donuts.
+And I really love redemptance because
+
+ align:start position:0%
+And I really love redemptance because
+ 
+
+ align:start position:0%
+And I really love redemptance because
+it's like what you have to pay attention
+
+ align:start position:0%
+it's like what you have to pay attention
+ 
+
+ align:start position:0%
+it's like what you have to pay attention
+to detail in the story is like the one
+
+ align:start position:0%
+to detail in the story is like the one
+ 
+
+ align:start position:0%
+to detail in the story is like the one
+thing that like I guess the example that
+
+ align:start position:0%
+thing that like I guess the example that
+ 
+
+ align:start position:0%
+thing that like I guess the example that
+we were talking about is if there's a
+
+ align:start position:0%
+we were talking about is if there's a
+ 
+
+ align:start position:0%
+we were talking about is if there's a
+mailman it happens to be on a Sunday he
+
+ align:start position:0%
+mailman it happens to be on a Sunday he
+ 
+
+ align:start position:0%
+mailman it happens to be on a Sunday he
+probably committed the crime because
+
+ align:start position:0%
+probably committed the crime because
+ 
+
+ align:start position:0%
+probably committed the crime because
+they don't have mail on Sundays like
+
+ align:start position:0%
+they don't have mail on Sundays like
+ 
+
+ align:start position:0%
+they don't have mail on Sundays like
+small details like that.
+
+ align:start position:0%
+small details like that.
+ 
+
+ align:start position:0%
+small details like that.
+>> Are you talking about mystery books or
+
+ align:start position:0%
+>> Are you talking about mystery books or
+ 
+
+ align:start position:0%
+>> Are you talking about mystery books or
+just like little paragraphs?
+
+ align:start position:0%
+just like little paragraphs?
+ 
+
+ align:start position:0%
+just like little paragraphs?
+>> Well, it's usually like a story and they
+
+ align:start position:0%
+>> Well, it's usually like a story and they
+ 
+
+ align:start position:0%
+>> Well, it's usually like a story and they
+say like, "Oh, here's the scenario.
+
+ align:start position:0%
+say like, "Oh, here's the scenario.
+ 
+
+ align:start position:0%
+say like, "Oh, here's the scenario.
+Here's the background story. Who is the
+
+ align:start position:0%
+Here's the background story. Who is the
+ 
+
+ align:start position:0%
+Here's the background story. Who is the
+who is the murder? Who's the murderer?"
+
+ align:start position:0%
+who is the murder? Who's the murderer?"
+ 
+
+ align:start position:0%
+who is the murder? Who's the murderer?"
+>> They compiled it though to you. Yeah.
+
+ align:start position:0%
+>> They compiled it though to you. Yeah.
+ 
+
+ align:start position:0%
+>> They compiled it though to you. Yeah.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> Feels like you told us at parties like
+
+ align:start position:0%
+>> Feels like you told us at parties like
+ 
+
+ align:start position:0%
+>> Feels like you told us at parties like
+that like for at parties, right?
+
+ align:start position:0%
+that like for at parties, right?
+ 
+
+ align:start position:0%
+that like for at parties, right?
+>> That's very true.
+
+ align:start position:0%
+>> That's very true.
+ 
+
+ align:start position:0%
+>> That's very true.
+>> Yeah. How
+
+ align:start position:0%
+>> Yeah. How
+ 
+
+ align:start position:0%
+>> Yeah. How
+>> I didn't see you was talking for a
+
+ align:start position:0%
+>> I didn't see you was talking for a
+ 
+
+ align:start position:0%
+>> I didn't see you was talking for a
+second. That was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Did we actually
+
+ align:start position:0%
+>> Did we actually
+ 
+
+ align:start position:0%
+>> Did we actually
+you guys?
+
+ align:start position:0%
+you guys?
+ 
+
+ align:start position:0%
+you guys?
+>> Okay. All right. Uh, another puzzle we
+
+ align:start position:0%
+>> Okay. All right. Uh, another puzzle we
+ 
+
+ align:start position:0%
+>> Okay. All right. Uh, another puzzle we
+came up with was uh the the ones that
+
+ align:start position:0%
+came up with was uh the the ones that
+ 
+
+ align:start position:0%
+came up with was uh the the ones that
+you did in elementary school with like
+
+ align:start position:0%
+you did in elementary school with like
+ 
+
+ align:start position:0%
+you did in elementary school with like
+the the big grid and you would have, you
+
+ align:start position:0%
+the the big grid and you would have, you
+ 
+
+ align:start position:0%
+the the big grid and you would have, you
+know, like someone's name and maybe
+
+ align:start position:0%
+know, like someone's name and maybe
+ 
+
+ align:start position:0%
+know, like someone's name and maybe
+their favorite food and you'd be given a
+
+ align:start position:0%
+their favorite food and you'd be given a
+ 
+
+ align:start position:0%
+their favorite food and you'd be given a
+bunch of clues and you have to match
+
+ align:start position:0%
+bunch of clues and you have to match
+ 
+
+ align:start position:0%
+bunch of clues and you have to match
+them.
+
+ align:start position:0%
+them.
+ 
+
+ align:start position:0%
+them.
+>> Yeah. With like the checks and the exits
+
+ align:start position:0%
+>> Yeah. With like the checks and the exits
+ 
+
+ align:start position:0%
+>> Yeah. With like the checks and the exits
+and stuff.
+
+ align:start position:0%
+and stuff.
+ 
+
+ align:start position:0%
+and stuff.
+>> So,
+
+ align:start position:0%
+>> So,
+ 
+
+ align:start position:0%
+>> So,
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+>> they're just generally called logic
+
+ align:start position:0%
+>> they're just generally called logic
+ 
+
+ align:start position:0%
+>> they're just generally called logic
+puzzles, I believe. And it's just you're
+
+ align:start position:0%
+puzzles, I believe. And it's just you're
+ 
+
+ align:start position:0%
+puzzles, I believe. And it's just you're
+given the the incomplete set of
+
+ align:start position:0%
+given the the incomplete set of
+ 
+
+ align:start position:0%
+given the the incomplete set of
+information, but enough constraints that
+
+ align:start position:0%
+information, but enough constraints that
+ 
+
+ align:start position:0%
+information, but enough constraints that
+you can figure out the rest of the
+
+ align:start position:0%
+you can figure out the rest of the
+ 
+
+ align:start position:0%
+you can figure out the rest of the
+information. And really the the way to
+
+ align:start position:0%
+information. And really the the way to
+ 
+
+ align:start position:0%
+information. And really the the way to
+solve it is just like write everybody's
+
+ align:start position:0%
+solve it is just like write everybody's
+ 
+
+ align:start position:0%
+solve it is just like write everybody's
+name, all all the characters that you're
+
+ align:start position:0%
+name, all all the characters that you're
+ 
+
+ align:start position:0%
+name, all all the characters that you're
+given in a piece of pros. Write down all
+
+ align:start position:0%
+given in a piece of pros. Write down all
+ 
+
+ align:start position:0%
+given in a piece of pros. Write down all
+the characters on one column. Write down
+
+ align:start position:0%
+the characters on one column. Write down
+ 
+
+ align:start position:0%
+the characters on one column. Write down
+all the things that you're trying to
+
+ align:start position:0%
+all the things that you're trying to
+ 
+
+ align:start position:0%
+all the things that you're trying to
+figure out like who's wearing what
+
+ align:start position:0%
+figure out like who's wearing what
+ 
+
+ align:start position:0%
+figure out like who's wearing what
+colored shirt for instance. So just
+
+ align:start position:0%
+colored shirt for instance. So just
+ 
+
+ align:start position:0%
+colored shirt for instance. So just
+write out all the colors on the other
+
+ align:start position:0%
+write out all the colors on the other
+ 
+
+ align:start position:0%
+write out all the colors on the other
+column. And just by the process of of
+
+ align:start position:0%
+column. And just by the process of of
+ 
+
+ align:start position:0%
+column. And just by the process of of
+elimination, just figuring out um
+
+ align:start position:0%
+elimination, just figuring out um
+ 
+
+ align:start position:0%
+elimination, just figuring out um
+usually these the answers are usually
+
+ align:start position:0%
+usually these the answers are usually
+ 
+
+ align:start position:0%
+usually these the answers are usually
+exclusive, right? So like if somebody's
+
+ align:start position:0%
+exclusive, right? So like if somebody's
+ 
+
+ align:start position:0%
+exclusive, right? So like if somebody's
+wearing a red shirt, the person cannot
+
+ align:start position:0%
+wearing a red shirt, the person cannot
+ 
+
+ align:start position:0%
+wearing a red shirt, the person cannot
+be wearing a green shirt. Um, you know,
+
+ align:start position:0%
+be wearing a green shirt. Um, you know,
+ 
+
+ align:start position:0%
+be wearing a green shirt. Um, you know,
+uh, so yeah,
+
+ align:start position:0%
+uh, so yeah,
+ 
+
+ align:start position:0%
+uh, so yeah,
+>> like they're like much harder on like
+
+ align:start position:0%
+>> like they're like much harder on like
+ 
+
+ align:start position:0%
+>> like they're like much harder on like
+every fourth statement is fault. Like
+
+ align:start position:0%
+every fourth statement is fault. Like
+ 
+
+ align:start position:0%
+every fourth statement is fault. Like
+you don't know one state is definitely
+
+ align:start position:0%
+you don't know one state is definitely
+ 
+
+ align:start position:0%
+you don't know one state is definitely
+false. I've seen ones where every
+
+ align:start position:0%
+false. I've seen ones where every
+ 
+
+ align:start position:0%
+false. I've seen ones where every
+statement is false except for one. They
+
+ align:start position:0%
+statement is false except for one. They
+ 
+
+ align:start position:0%
+statement is false except for one. They
+like I can bring in my book and they're
+
+ align:start position:0%
+like I can bring in my book and they're
+ 
+
+ align:start position:0%
+like I can bring in my book and they're
+just like hideous.
+
+ align:start position:0%
+just like hideous.
+ 
+
+ align:start position:0%
+just like hideous.
+>> Uh you the worst version of that is
+
+ align:start position:0%
+>> Uh you the worst version of that is
+ 
+
+ align:start position:0%
+>> Uh you the worst version of that is
+figuring out how how to see people in
+
+ align:start position:0%
+figuring out how how to see people in
+ 
+
+ align:start position:0%
+figuring out how how to see people in
+the wedding.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Is that in 6034? Did that last week?
+
+ align:start position:0%
+>> Is that in 6034? Did that last week?
+ 
+
+ align:start position:0%
+>> Is that in 6034? Did that last week?
+>> Oh, cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> You guys want to throw any?
+
+ align:start position:0%
+>> You guys want to throw any?
+ 
+
+ align:start position:0%
+>> You guys want to throw any?
+>> Sure. Um, we started by trying to think
+
+ align:start position:0%
+>> Sure. Um, we started by trying to think
+ 
+
+ align:start position:0%
+>> Sure. Um, we started by trying to think
+of all the puzzles that we really
+
+ align:start position:0%
+of all the puzzles that we really
+ 
+
+ align:start position:0%
+of all the puzzles that we really
+dislike and uh we came up with a couple
+
+ align:start position:0%
+dislike and uh we came up with a couple
+ 
+
+ align:start position:0%
+dislike and uh we came up with a couple
+here. The sliding square puzzles. You
+
+ align:start position:0%
+here. The sliding square puzzles. You
+ 
+
+ align:start position:0%
+here. The sliding square puzzles. You
+have like a
+
+ align:start position:0%
+have like a
+ 
+
+ align:start position:0%
+have like a
+they're basically just a variation on a
+
+ align:start position:0%
+they're basically just a variation on a
+ 
+
+ align:start position:0%
+they're basically just a variation on a
+jigsaw puzzle where the rules are more
+
+ align:start position:0%
+jigsaw puzzle where the rules are more
+ 
+
+ align:start position:0%
+jigsaw puzzle where the rules are more
+constrained. Um, I don't like jigsaw
+
+ align:start position:0%
+constrained. Um, I don't like jigsaw
+ 
+
+ align:start position:0%
+constrained. Um, I don't like jigsaw
+puzzles either.
+
+ align:start position:0%
+puzzles either.
+ 
+
+ align:start position:0%
+puzzles either.
+Like mine did there. And then John had a
+
+ align:start position:0%
+Like mine did there. And then John had a
+ 
+
+ align:start position:0%
+Like mine did there. And then John had a
+couple like lights out. I guess there's
+
+ align:start position:0%
+couple like lights out. I guess there's
+ 
+
+ align:start position:0%
+couple like lights out. I guess there's
+a lights out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certain areas and you have to like flip
+
+ align:start position:0%
+certain areas and you have to like flip
+ 
+
+ align:start position:0%
+certain areas and you have to like flip
+them.
+
+ align:start position:0%
+them.
+ 
+
+ align:start position:0%
+them.
+So, so you got a like like a grid of
+
+ align:start position:0%
+So, so you got a like like a grid of
+ 
+
+ align:start position:0%
+So, so you got a like like a grid of
+buttons and every button you push will
+
+ align:start position:0%
+buttons and every button you push will
+ 
+
+ align:start position:0%
+buttons and every button you push will
+invert the all the neighboring buttons
+
+ align:start position:0%
+invert the all the neighboring buttons
+ 
+
+ align:start position:0%
+invert the all the neighboring buttons
+like in I think the top bottom left and
+
+ align:start position:0%
+like in I think the top bottom left and
+ 
+
+ align:start position:0%
+like in I think the top bottom left and
+right will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> yeah and then I guess a similar well
+
+ align:start position:0%
+>> yeah and then I guess a similar well
+ 
+
+ align:start position:0%
+>> yeah and then I guess a similar well
+maybe not similar but there's why don't
+
+ align:start position:0%
+maybe not similar but there's why don't
+ 
+
+ align:start position:0%
+maybe not similar but there's why don't
+you describe the concentric circles
+
+ align:start position:0%
+you describe the concentric circles
+ 
+
+ align:start position:0%
+you describe the concentric circles
+>> yeah their puzzles are similar that
+
+ align:start position:0%
+>> yeah their puzzles are similar that
+ 
+
+ align:start position:0%
+>> yeah their puzzles are similar that
+we're um taking an action on um one item
+
+ align:start position:0%
+we're um taking an action on um one item
+ 
+
+ align:start position:0%
+we're um taking an action on um one item
+in the scene will um these are going to
+
+ align:start position:0%
+in the scene will um these are going to
+ 
+
+ align:start position:0%
+in the scene will um these are going to
+be dual puzzles the concentric circle
+
+ align:start position:0%
+be dual puzzles the concentric circle
+ 
+
+ align:start position:0%
+be dual puzzles the concentric circle
+ones um will uh have effects on other
+
+ align:start position:0%
+ones um will uh have effects on other
+ 
+
+ align:start position:0%
+ones um will uh have effects on other
+things in the system. And um uh
+
+ align:start position:0%
+things in the system. And um uh
+ 
+
+ align:start position:0%
+things in the system. And um uh
+typically these are used in games where
+
+ align:start position:0%
+typically these are used in games where
+ 
+
+ align:start position:0%
+typically these are used in games where
+there'll be like a center podium with a
+
+ align:start position:0%
+there'll be like a center podium with a
+ 
+
+ align:start position:0%
+there'll be like a center podium with a
+pathway leading off of um the center one
+
+ align:start position:0%
+pathway leading off of um the center one
+ 
+
+ align:start position:0%
+pathway leading off of um the center one
+side of the podium. Then there'll be a
+
+ align:start position:0%
+side of the podium. Then there'll be a
+ 
+
+ align:start position:0%
+side of the podium. Then there'll be a
+concentric circle around that a
+
+ align:start position:0%
+concentric circle around that a
+ 
+
+ align:start position:0%
+concentric circle around that a
+concentric ring with a pathway off of
+
+ align:start position:0%
+concentric ring with a pathway off of
+ 
+
+ align:start position:0%
+concentric ring with a pathway off of
+that ring and another angle and then you
+
+ align:start position:0%
+that ring and another angle and then you
+ 
+
+ align:start position:0%
+that ring and another angle and then you
+know more and more circles um to each
+
+ align:start position:0%
+know more and more circles um to each
+ 
+
+ align:start position:0%
+know more and more circles um to each
+side and uh you get to uh rotate
+
+ align:start position:0%
+side and uh you get to uh rotate
+ 
+
+ align:start position:0%
+side and uh you get to uh rotate
+individual circles and that will rotate
+
+ align:start position:0%
+individual circles and that will rotate
+ 
+
+ align:start position:0%
+individual circles and that will rotate
+the other circles in different ways.
+
+ align:start position:0%
+the other circles in different ways.
+ 
+
+ align:start position:0%
+the other circles in different ways.
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+>> create every time I rotate one something
+
+ align:start position:0%
+>> create every time I rotate one something
+ 
+
+ align:start position:0%
+>> create every time I rotate one something
+else is going to rotate.
+
+ align:start position:0%
+else is going to rotate.
+ 
+
+ align:start position:0%
+else is going to rotate.
+>> Yeah. And there's always like it's
+
+ align:start position:0%
+>> Yeah. And there's always like it's
+ 
+
+ align:start position:0%
+>> Yeah. And there's always like it's
+always thrown like right before like a
+
+ align:start position:0%
+always thrown like right before like a
+ 
+
+ align:start position:0%
+always thrown like right before like a
+boss battle game is like, "Oh, damn it."
+
+ align:start position:0%
+boss battle game is like, "Oh, damn it."
+ 
+
+ align:start position:0%
+boss battle game is like, "Oh, damn it."
+>> I guess three of those are examples of
+
+ align:start position:0%
+>> I guess three of those are examples of
+ 
+
+ align:start position:0%
+>> I guess three of those are examples of
+games where like you have to take action
+
+ align:start position:0%
+games where like you have to take action
+ 
+
+ align:start position:0%
+games where like you have to take action
+on an environment, but your action has
+
+ align:start position:0%
+on an environment, but your action has
+ 
+
+ align:start position:0%
+on an environment, but your action has
+indirect effects,
+
+ align:start position:0%
+indirect effects,
+ 
+
+ align:start position:0%
+indirect effects,
+>> you know, throughout the environment and
+
+ align:start position:0%
+>> you know, throughout the environment and
+ 
+
+ align:start position:0%
+>> you know, throughout the environment and
+it's just really annoying figuring out
+
+ align:start position:0%
+it's just really annoying figuring out
+ 
+
+ align:start position:0%
+it's just really annoying figuring out
+how to optimize that.
+
+ align:start position:0%
+how to optimize that.
+ 
+
+ align:start position:0%
+how to optimize that.
+>> But they are predictable effects. It's
+
+ align:start position:0%
+>> But they are predictable effects. It's
+ 
+
+ align:start position:0%
+>> But they are predictable effects. It's
+like every time I rotate this one left,
+
+ align:start position:0%
+like every time I rotate this one left,
+ 
+
+ align:start position:0%
+like every time I rotate this one left,
+that one's going to rotate right.
+
+ align:start position:0%
+that one's going to rotate right.
+ 
+
+ align:start position:0%
+that one's going to rotate right.
+I think it's kind of funny how like the
+
+ align:start position:0%
+I think it's kind of funny how like the
+ 
+
+ align:start position:0%
+I think it's kind of funny how like the
+context has a lot to do with whether
+
+ align:start position:0%
+context has a lot to do with whether
+ 
+
+ align:start position:0%
+context has a lot to do with whether
+these puzzles are employed or not
+
+ align:start position:0%
+these puzzles are employed or not
+ 
+
+ align:start position:0%
+these puzzles are employed or not
+because like I do enjoy Professor
+
+ align:start position:0%
+because like I do enjoy Professor
+ 
+
+ align:start position:0%
+because like I do enjoy Professor
+Leighton quite a bit.
+
+ align:start position:0%
+Leighton quite a bit.
+ 
+
+ align:start position:0%
+Leighton quite a bit.
+>> Um it's like it's the most uh you know
+
+ align:start position:0%
+>> Um it's like it's the most uh you know
+ 
+
+ align:start position:0%
+>> Um it's like it's the most uh you know
+arbitrary narrative like justifying that
+
+ align:start position:0%
+arbitrary narrative like justifying that
+ 
+
+ align:start position:0%
+arbitrary narrative like justifying that
+there's puzzles in the world but like
+
+ align:start position:0%
+there's puzzles in the world but like
+ 
+
+ align:start position:0%
+there's puzzles in the world but like
+it's just fun like your intentionality
+
+ align:start position:0%
+it's just fun like your intentionality
+ 
+
+ align:start position:0%
+it's just fun like your intentionality
+when playing the game is that you're
+
+ align:start position:0%
+when playing the game is that you're
+ 
+
+ align:start position:0%
+when playing the game is that you're
+going to be solving puzzles and that has
+
+ align:start position:0%
+going to be solving puzzles and that has
+ 
+
+ align:start position:0%
+going to be solving puzzles and that has
+something as well. like in the middle.
+
+ align:start position:0%
+something as well. like in the middle.
+ 
+
+ align:start position:0%
+something as well. like in the middle.
+>> Yeah. The way that also the way that
+
+ align:start position:0%
+>> Yeah. The way that also the way that
+ 
+
+ align:start position:0%
+>> Yeah. The way that also the way that
+that is presented kind of makes it funny
+
+ align:start position:0%
+that is presented kind of makes it funny
+ 
+
+ align:start position:0%
+that is presented kind of makes it funny
+in math as well, right? So like the
+
+ align:start position:0%
+in math as well, right? So like the
+ 
+
+ align:start position:0%
+in math as well, right? So like the
+mafia goons come up to you and say,
+
+ align:start position:0%
+mafia goons come up to you and say,
+ 
+
+ align:start position:0%
+mafia goons come up to you and say,
+"We're going to stop you from coming in
+
+ align:start position:0%
+"We're going to stop you from coming in
+ 
+
+ align:start position:0%
+"We're going to stop you from coming in
+here unless you can solve this puzzle.
+
+ align:start position:0%
+here unless you can solve this puzzle.
+ 
+
+ align:start position:0%
+here unless you can solve this puzzle.
+Shouldn't you just shoot me?
+
+ align:start position:0%
+Shouldn't you just shoot me?
+ 
+
+ align:start position:0%
+Shouldn't you just shoot me?
+Solve all your problems." No. No. Solve
+
+ align:start position:0%
+Solve all your problems." No. No. Solve
+ 
+
+ align:start position:0%
+Solve all your problems." No. No. Solve
+this puzzle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They're making fun of themselves even.
+
+ align:start position:0%
+They're making fun of themselves even.
+ 
+
+ align:start position:0%
+They're making fun of themselves even.
+>> All right. Cool.
+
+ align:start position:0%
+>> All right. Cool.
+ 
+
+ align:start position:0%
+>> All right. Cool.
+Uh, okay. I'm not sure if we really
+
+ align:start position:0%
+Uh, okay. I'm not sure if we really
+ 
+
+ align:start position:0%
+Uh, okay. I'm not sure if we really
+commented on what we liked or didn't
+
+ align:start position:0%
+commented on what we liked or didn't
+ 
+
+ align:start position:0%
+commented on what we liked or didn't
+like, but the some things that we came
+
+ align:start position:0%
+like, but the some things that we came
+ 
+
+ align:start position:0%
+like, but the some things that we came
+up that haven't been brought up yet are,
+
+ align:start position:0%
+up that haven't been brought up yet are,
+ 
+
+ align:start position:0%
+up that haven't been brought up yet are,
+uh, cryptics, which are kind of a
+
+ align:start position:0%
+uh, cryptics, which are kind of a
+ 
+
+ align:start position:0%
+uh, cryptics, which are kind of a
+combination between like crossword and
+
+ align:start position:0%
+combination between like crossword and
+ 
+
+ align:start position:0%
+combination between like crossword and
+riddles, uh, riddles, um, comatorial
+
+ align:start position:0%
+riddles, uh, riddles, um, comatorial
+ 
+
+ align:start position:0%
+riddles, uh, riddles, um, comatorial
+games as a puzzle genre,
+
+ align:start position:0%
+games as a puzzle genre,
+ 
+
+ align:start position:0%
+games as a puzzle genre,
+um, logic puzzles in general, not just
+
+ align:start position:0%
+um, logic puzzles in general, not just
+ 
+
+ align:start position:0%
+um, logic puzzles in general, not just
+like typical logic puzzles like that.
+
+ align:start position:0%
+like typical logic puzzles like that.
+ 
+
+ align:start position:0%
+like typical logic puzzles like that.
+you can have like
+
+ align:start position:0%
+you can have like
+ 
+
+ align:start position:0%
+you can have like
+state machines or pseudohoo or any type
+
+ align:start position:0%
+state machines or pseudohoo or any type
+ 
+
+ align:start position:0%
+state machines or pseudohoo or any type
+of numerical puzzle. We also wanted to
+
+ align:start position:0%
+of numerical puzzle. We also wanted to
+ 
+
+ align:start position:0%
+of numerical puzzle. We also wanted to
+differentiate that uh a lot of those
+
+ align:start position:0%
+differentiate that uh a lot of those
+ 
+
+ align:start position:0%
+differentiate that uh a lot of those
+games or some of those games are
+
+ align:start position:0%
+games or some of those games are
+ 
+
+ align:start position:0%
+games or some of those games are
+spatially oriented and some aren't
+
+ align:start position:0%
+spatially oriented and some aren't
+ 
+
+ align:start position:0%
+spatially oriented and some aren't
+>> which we thought was an important aspect
+
+ align:start position:0%
+>> which we thought was an important aspect
+ 
+
+ align:start position:0%
+>> which we thought was an important aspect
+but not necessarily definitive of a
+
+ align:start position:0%
+but not necessarily definitive of a
+ 
+
+ align:start position:0%
+but not necessarily definitive of a
+completely different genre.
+
+ align:start position:0%
+completely different genre.
+ 
+
+ align:start position:0%
+completely different genre.
+>> I'm not sure if seen escape machine
+
+ align:start position:0%
+>> I'm not sure if seen escape machine
+ 
+
+ align:start position:0%
+>> I'm not sure if seen escape machine
+puzzle actually outside of like computer
+
+ align:start position:0%
+puzzle actually outside of like computer
+ 
+
+ align:start position:0%
+puzzle actually outside of like computer
+science text. I know some
+
+ align:start position:0%
+science text. I know some
+ 
+
+ align:start position:0%
+science text. I know some
+>> I really like
+
+ align:start position:0%
+>> I really like
+ 
+
+ align:start position:0%
+>> I really like
+>> I'll have to ask you suspect it's gonna
+
+ align:start position:0%
+>> I'll have to ask you suspect it's gonna
+ 
+
+ align:start position:0%
+>> I'll have to ask you suspect it's gonna
+be more involved than we have time for.
+
+ align:start position:0%
+be more involved than we have time for.
+ 
+
+ align:start position:0%
+be more involved than we have time for.
+>> By by combinatorial puzzles you mean
+
+ align:start position:0%
+>> By by combinatorial puzzles you mean
+ 
+
+ align:start position:0%
+>> By by combinatorial puzzles you mean
+stuff like like you have
+
+ align:start position:0%
+stuff like like you have
+ 
+
+ align:start position:0%
+stuff like like you have
+>> comtorial games like
+
+ align:start position:0%
+>> comtorial games like
+ 
+
+ align:start position:0%
+>> comtorial games like
+>> all the games that fall under comtorial
+
+ align:start position:0%
+>> all the games that fall under comtorial
+ 
+
+ align:start position:0%
+>> all the games that fall under comtorial
+game theory.
+
+ align:start position:0%
+game theory.
+ 
+
+ align:start position:0%
+game theory.
+>> Okay theoretically puzzles
+
+ align:start position:0%
+>> Okay theoretically puzzles
+ 
+
+ align:start position:0%
+>> Okay theoretically puzzles
+>> like everything.
+
+ align:start position:0%
+>> like everything.
+ 
+
+ align:start position:0%
+>> like everything.
+>> Cool. That's a lot of games.
+
+ align:start position:0%
+>> Cool. That's a lot of games.
+ 
+
+ align:start position:0%
+>> Cool. That's a lot of games.
+>> See we also have exploration. So games
+
+ align:start position:0%
+>> See we also have exploration. So games
+ 
+
+ align:start position:0%
+>> See we also have exploration. So games
+where you have to see everything around
+
+ align:start position:0%
+where you have to see everything around
+ 
+
+ align:start position:0%
+where you have to see everything around
+you to know what is available for use.
+
+ align:start position:0%
+you to know what is available for use.
+ 
+
+ align:start position:0%
+you to know what is available for use.
+Now on the the braith in the book they
+
+ align:start position:0%
+Now on the the braith in the book they
+ 
+
+ align:start position:0%
+Now on the the braith in the book they
+talked about exit Zelda.
+
+ align:start position:0%
+talked about exit Zelda.
+ 
+
+ align:start position:0%
+talked about exit Zelda.
+>> Okay. and just other so a game like
+
+ align:start position:0%
+>> Okay. and just other so a game like
+ 
+
+ align:start position:0%
+>> Okay. and just other so a game like
+situation in game that I didn't like is
+
+ align:start position:0%
+situation in game that I didn't like is
+ 
+
+ align:start position:0%
+situation in game that I didn't like is
+you're playing a game and something
+
+ align:start position:0%
+you're playing a game and something
+ 
+
+ align:start position:0%
+you're playing a game and something
+happens you don't step too fast or
+
+ align:start position:0%
+happens you don't step too fast or
+ 
+
+ align:start position:0%
+happens you don't step too fast or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+>> and because of that you get to an
+
+ align:start position:0%
+>> and because of that you get to an
+ 
+
+ align:start position:0%
+>> and because of that you get to an
+irreversible spot where you don't have
+
+ align:start position:0%
+irreversible spot where you don't have
+ 
+
+ align:start position:0%
+irreversible spot where you don't have
+the tools necessary to beat the enemy
+
+ align:start position:0%
+the tools necessary to beat the enemy
+ 
+
+ align:start position:0%
+the tools necessary to beat the enemy
+right in front of you but you also are
+
+ align:start position:0%
+right in front of you but you also are
+ 
+
+ align:start position:0%
+right in front of you but you also are
+trapped and can't go back it happened to
+
+ align:start position:0%
+trapped and can't go back it happened to
+ 
+
+ align:start position:0%
+trapped and can't go back it happened to
+me one time it was a Star Wars night of
+
+ align:start position:0%
+me one time it was a Star Wars night of
+ 
+
+ align:start position:0%
+me one time it was a Star Wars night of
+the old republic and there's an enemy
+
+ align:start position:0%
+the old republic and there's an enemy
+ 
+
+ align:start position:0%
+the old republic and there's an enemy
+there's an enemy I couldn't go forward
+
+ align:start position:0%
+there's an enemy I couldn't go forward
+ 
+
+ align:start position:0%
+there's an enemy I couldn't go forward
+>> there was the enemy you couldn't go
+
+ align:start position:0%
+>> there was the enemy you couldn't go
+ 
+
+ align:start position:0%
+>> there was the enemy you couldn't go
+forward and the door or like there was a
+
+ align:start position:0%
+forward and the door or like there was a
+ 
+
+ align:start position:0%
+forward and the door or like there was a
+cliff so you couldn't get back up
+
+ align:start position:0%
+cliff so you couldn't get back up
+ 
+
+ align:start position:0%
+cliff so you couldn't get back up
+>> and so since I couldn't do anything I
+
+ align:start position:0%
+>> and so since I couldn't do anything I
+ 
+
+ align:start position:0%
+>> and so since I couldn't do anything I
+was forced to just completely go back to
+
+ align:start position:0%
+was forced to just completely go back to
+ 
+
+ align:start position:0%
+was forced to just completely go back to
+like the last save.
+
+ align:start position:0%
+like the last save.
+ 
+
+ align:start position:0%
+like the last save.
+>> But is that a puzzle or is that just a
+
+ align:start position:0%
+>> But is that a puzzle or is that just a
+ 
+
+ align:start position:0%
+>> But is that a puzzle or is that just a
+bug?
+
+ align:start position:0%
+bug?
+ 
+
+ align:start position:0%
+bug?
+>> I mean it was like it's it's the type
+
+ align:start position:0%
+>> I mean it was like it's it's the type
+ 
+
+ align:start position:0%
+>> I mean it was like it's it's the type
+where it's exploration and item is an
+
+ align:start position:0%
+where it's exploration and item is an
+ 
+
+ align:start position:0%
+where it's exploration and item is an
+item use. So, you need to get an item to
+
+ align:start position:0%
+item use. So, you need to get an item to
+ 
+
+ align:start position:0%
+item use. So, you need to get an item to
+go ahead and like if you had this item,
+
+ align:start position:0%
+go ahead and like if you had this item,
+ 
+
+ align:start position:0%
+go ahead and like if you had this item,
+then the enemy that you
+
+ align:start position:0%
+then the enemy that you
+ 
+
+ align:start position:0%
+then the enemy that you
+>> I think it was like a rancor or
+
+ align:start position:0%
+>> I think it was like a rancor or
+ 
+
+ align:start position:0%
+>> I think it was like a rancor or
+something.
+
+ align:start position:0%
+something.
+ 
+
+ align:start position:0%
+something.
+>> You could beat the rancor or at least
+
+ align:start position:0%
+>> You could beat the rancor or at least
+ 
+
+ align:start position:0%
+>> You could beat the rancor or at least
+put it to sleep and walk by it. But
+
+ align:start position:0%
+put it to sleep and walk by it. But
+ 
+
+ align:start position:0%
+put it to sleep and walk by it. But
+without it, you had to try and just beat
+
+ align:start position:0%
+without it, you had to try and just beat
+ 
+
+ align:start position:0%
+without it, you had to try and just beat
+it or it would kill you.
+
+ align:start position:0%
+it or it would kill you.
+ 
+
+ align:start position:0%
+it or it would kill you.
+>> Okay.
+
+ align:start position:0%
+>> Okay.
+ 
+
+ align:start position:0%
+>> Okay.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Okay. So, so it was an item that would
+
+ align:start position:0%
+>> Okay. So, so it was an item that would
+ 
+
+ align:start position:0%
+>> Okay. So, so it was an item that would
+have made combat easier basically, but
+
+ align:start position:0%
+have made combat easier basically, but
+ 
+
+ align:start position:0%
+have made combat easier basically, but
+then it was kind they kind of made made
+
+ align:start position:0%
+then it was kind they kind of made made
+ 
+
+ align:start position:0%
+then it was kind they kind of made made
+it this one way.
+
+ align:start position:0%
+it this one way.
+ 
+
+ align:start position:0%
+it this one way.
+>> It's like Yeah. So, so yeah. So, you see
+
+ align:start position:0%
+>> It's like Yeah. So, so yeah. So, you see
+ 
+
+ align:start position:0%
+>> It's like Yeah. So, so yeah. So, you see
+a lot of puzzle games where they have
+
+ align:start position:0%
+a lot of puzzle games where they have
+ 
+
+ align:start position:0%
+a lot of puzzle games where they have
+like easy reset, right? It's like, you
+
+ align:start position:0%
+like easy reset, right? It's like, you
+ 
+
+ align:start position:0%
+like easy reset, right? It's like, you
+know, you you you can try start trying
+
+ align:start position:0%
+know, you you you can try start trying
+ 
+
+ align:start position:0%
+know, you you you can try start trying
+to solve it and you realize you screw up
+
+ align:start position:0%
+to solve it and you realize you screw up
+ 
+
+ align:start position:0%
+to solve it and you realize you screw up
+something along the way, you hit reset
+
+ align:start position:0%
+something along the way, you hit reset
+ 
+
+ align:start position:0%
+something along the way, you hit reset
+and go back right back to the beginning.
+
+ align:start position:0%
+and go back right back to the beginning.
+ 
+
+ align:start position:0%
+and go back right back to the beginning.
+Nice of the public has no easy reset. Uh
+
+ align:start position:0%
+Nice of the public has no easy reset. Uh
+ 
+
+ align:start position:0%
+Nice of the public has no easy reset. Uh
+you live with the consequences. I guess
+
+ align:start position:0%
+you live with the consequences. I guess
+ 
+
+ align:start position:0%
+you live with the consequences. I guess
+that's what they were trying to go for.
+
+ align:start position:0%
+that's what they were trying to go for.
+ 
+
+ align:start position:0%
+that's what they were trying to go for.
+But,
+
+ align:start position:0%
+But,
+ 
+
+ align:start position:0%
+But,
+>> all right. So, we also had a loading of
+
+ align:start position:0%
+>> all right. So, we also had a loading of
+ 
+
+ align:start position:0%
+>> all right. So, we also had a loading of
+sliding puzzles either either with
+
+ align:start position:0%
+sliding puzzles either either with
+ 
+
+ align:start position:0%
+sliding puzzles either either with
+numbers or with pictures. Both of them
+
+ align:start position:0%
+numbers or with pictures. Both of them
+ 
+
+ align:start position:0%
+numbers or with pictures. Both of them
+are equally annoying.
+
+ align:start position:0%
+are equally annoying.
+ 
+
+ align:start position:0%
+are equally annoying.
+It's easy.
+
+ align:start position:0%
+It's easy.
+ 
+
+ align:start position:0%
+It's easy.
+>> But but on the other hand, Alec loves
+
+ align:start position:0%
+>> But but on the other hand, Alec loves
+ 
+
+ align:start position:0%
+>> But but on the other hand, Alec loves
+rush hour and and
+
+ align:start position:0%
+rush hour and and
+ 
+
+ align:start position:0%
+rush hour and and
+>> it's the travel.
+
+ align:start position:0%
+>> it's the travel.
+ 
+
+ align:start position:0%
+>> it's the travel.
+>> You have to slide cars out of the way to
+
+ align:start position:0%
+>> You have to slide cars out of the way to
+ 
+
+ align:start position:0%
+>> You have to slide cars out of the way to
+form a path.
+
+ align:start position:0%
+form a path.
+ 
+
+ align:start position:0%
+form a path.
+>> In Professor Leighton, there are an
+
+ align:start position:0%
+>> In Professor Leighton, there are an
+ 
+
+ align:start position:0%
+>> In Professor Leighton, there are an
+awful lot of sliding puzzles that have
+
+ align:start position:0%
+awful lot of sliding puzzles that have
+ 
+
+ align:start position:0%
+awful lot of sliding puzzles that have
+like differently shaped pieces or oddly
+
+ align:start position:0%
+like differently shaped pieces or oddly
+ 
+
+ align:start position:0%
+like differently shaped pieces or oddly
+shaped pieces,
+
+ align:start position:0%
+shaped pieces,
+ 
+
+ align:start position:0%
+shaped pieces,
+>> which is slightly more interesting or
+
+ align:start position:0%
+>> which is slightly more interesting or
+ 
+
+ align:start position:0%
+>> which is slightly more interesting or
+less annoying than sliding puzzles, but
+
+ align:start position:0%
+less annoying than sliding puzzles, but
+ 
+
+ align:start position:0%
+less annoying than sliding puzzles, but
+like regular sliding puzzles, but it's
+
+ align:start position:0%
+like regular sliding puzzles, but it's
+ 
+
+ align:start position:0%
+like regular sliding puzzles, but it's
+still incredibly frustrating. Well, I
+
+ align:start position:0%
+still incredibly frustrating. Well, I
+ 
+
+ align:start position:0%
+still incredibly frustrating. Well, I
+think the difference there is that when
+
+ align:start position:0%
+think the difference there is that when
+ 
+
+ align:start position:0%
+think the difference there is that when
+you have differently sized pieces, like
+
+ align:start position:0%
+you have differently sized pieces, like
+ 
+
+ align:start position:0%
+you have differently sized pieces, like
+when when you're doing just like a
+
+ align:start position:0%
+when when you're doing just like a
+ 
+
+ align:start position:0%
+when when you're doing just like a
+sliding puzzle where you're trying to
+
+ align:start position:0%
+sliding puzzle where you're trying to
+ 
+
+ align:start position:0%
+sliding puzzle where you're trying to
+recreate an image, there's definite
+
+ align:start position:0%
+recreate an image, there's definite
+ 
+
+ align:start position:0%
+recreate an image, there's definite
+patterns that you keep using over and
+
+ align:start position:0%
+patterns that you keep using over and
+ 
+
+ align:start position:0%
+patterns that you keep using over and
+over again because you're just like
+
+ align:start position:0%
+over again because you're just like
+ 
+
+ align:start position:0%
+over again because you're just like
+rotating spacesh
+
+ align:start position:0%
+rotating spacesh
+ 
+
+ align:start position:0%
+rotating spacesh
+>> um so it's not actually interesting.
+
+ align:start position:0%
+>> um so it's not actually interesting.
+ 
+
+ align:start position:0%
+>> um so it's not actually interesting.
+Whereas rush hour, you actually have to
+
+ align:start position:0%
+Whereas rush hour, you actually have to
+ 
+
+ align:start position:0%
+Whereas rush hour, you actually have to
+like think about how things fit
+
+ align:start position:0%
+like think about how things fit
+ 
+
+ align:start position:0%
+like think about how things fit
+together. So, one other puzzle type that
+
+ align:start position:0%
+together. So, one other puzzle type that
+ 
+
+ align:start position:0%
+together. So, one other puzzle type that
+we haven't really mentioned that I
+
+ align:start position:0%
+we haven't really mentioned that I
+ 
+
+ align:start position:0%
+we haven't really mentioned that I
+actually really enjoy is like uh
+
+ align:start position:0%
+actually really enjoy is like uh
+ 
+
+ align:start position:0%
+actually really enjoy is like uh
+pictographic puzzles where it relies on
+
+ align:start position:0%
+pictographic puzzles where it relies on
+ 
+
+ align:start position:0%
+pictographic puzzles where it relies on
+on sort of your association with visual
+
+ align:start position:0%
+on sort of your association with visual
+ 
+
+ align:start position:0%
+on sort of your association with visual
+images and like word play and stuff.
+
+ align:start position:0%
+images and like word play and stuff.
+ 
+
+ align:start position:0%
+images and like word play and stuff.
+Like for example, you'll have a puzzle
+
+ align:start position:0%
+Like for example, you'll have a puzzle
+ 
+
+ align:start position:0%
+Like for example, you'll have a puzzle
+that's just, you know, an image of an
+
+ align:start position:0%
+that's just, you know, an image of an
+ 
+
+ align:start position:0%
+that's just, you know, an image of an
+eyeball uh a bumblebee and a screenshot
+
+ align:start position:0%
+eyeball uh a bumblebee and a screenshot
+ 
+
+ align:start position:0%
+eyeball uh a bumblebee and a screenshot
+of Jiggy Dench in like in a James Bond
+
+ align:start position:0%
+of Jiggy Dench in like in a James Bond
+ 
+
+ align:start position:0%
+of Jiggy Dench in like in a James Bond
+movie. And the idea is it's IBM.
+
+ align:start position:0%
+movie. And the idea is it's IBM.
+ 
+
+ align:start position:0%
+movie. And the idea is it's IBM.
+So like I I love puzzles like that.
+
+ align:start position:0%
+So like I I love puzzles like that.
+ 
+
+ align:start position:0%
+So like I I love puzzles like that.
+>> Puzzles.
+
+ align:start position:0%
+>> Puzzles.
+ 
+
+ align:start position:0%
+>> Puzzles.
+>> Yeah. So stuff like that where where it
+
+ align:start position:0%
+>> Yeah. So stuff like that where where it
+ 
+
+ align:start position:0%
+>> Yeah. So stuff like that where where it
+relies on on someone like a human being
+
+ align:start position:0%
+relies on on someone like a human being
+ 
+
+ align:start position:0%
+relies on on someone like a human being
+actually associating information with
+
+ align:start position:0%
+actually associating information with
+ 
+
+ align:start position:0%
+actually associating information with
+something visual rather than it being
+
+ align:start position:0%
+something visual rather than it being
+ 
+
+ align:start position:0%
+something visual rather than it being
+just like a straight logic puzzle where
+
+ align:start position:0%
+just like a straight logic puzzle where
+ 
+
+ align:start position:0%
+just like a straight logic puzzle where
+you have this this you know this
+
+ align:start position:0%
+you have this this you know this
+ 
+
+ align:start position:0%
+you have this this you know this
+information and we use this to derive
+
+ align:start position:0%
+information and we use this to derive
+ 
+
+ align:start position:0%
+information and we use this to derive
+the rest of the information.
+
+ align:start position:0%
+the rest of the information.
+ 
+
+ align:start position:0%
+the rest of the information.
+>> Yeah. Re rebu
+
+ align:start position:0%
+>> Yeah. Re rebu
+ 
+
+ align:start position:0%
+>> Yeah. Re rebu
+and of course those are very language
+
+ align:start position:0%
+and of course those are very language
+ 
+
+ align:start position:0%
+and of course those are very language
+focused even though they're image based.
+
+ align:start position:0%
+focused even though they're image based.
+ 
+
+ align:start position:0%
+focused even though they're image based.
+So, uh, but like the one that has the
+
+ align:start position:0%
+So, uh, but like the one that has the
+ 
+
+ align:start position:0%
+So, uh, but like the one that has the
+two lines and then read in the middle.
+
+ align:start position:0%
+two lines and then read in the middle.
+ 
+
+ align:start position:0%
+two lines and then read in the middle.
+>> Well, you
+
+ align:start position:0%
+>> Well, you
+ 
+
+ align:start position:0%
+>> Well, you
+>> Well, things like that. Yeah.
+
+ align:start position:0%
+>> Well, things like that. Yeah.
+ 
+
+ align:start position:0%
+>> Well, things like that. Yeah.
+>> Yeah. you have reverbs where you're
+
+ align:start position:0%
+>> Yeah. you have reverbs where you're
+ 
+
+ align:start position:0%
+>> Yeah. you have reverbs where you're
+trying to like basically reconstruct
+
+ align:start position:0%
+trying to like basically reconstruct
+ 
+
+ align:start position:0%
+trying to like basically reconstruct
+something and then um I forget what uh
+
+ align:start position:0%
+something and then um I forget what uh
+ 
+
+ align:start position:0%
+something and then um I forget what uh
+the what's the classification of puzzles
+
+ align:start position:0%
+the what's the classification of puzzles
+ 
+
+ align:start position:0%
+the what's the classification of puzzles
+where you're given some assembly of
+
+ align:start position:0%
+where you're given some assembly of
+ 
+
+ align:start position:0%
+where you're given some assembly of
+images and you're trying to like you
+
+ align:start position:0%
+images and you're trying to like you
+ 
+
+ align:start position:0%
+images and you're trying to like you
+know um god uh uh if if if I if I wrote
+
+ align:start position:0%
+know um god uh uh if if if I if I wrote
+ 
+
+ align:start position:0%
+know um god uh uh if if if I if I wrote
+in what's
+
+ align:start position:0%
+in what's
+ 
+
+ align:start position:0%
+in what's
+this this is not a good puzzle but just
+
+ align:start position:0%
+this this is not a good puzzle but just
+ 
+
+ align:start position:0%
+this this is not a good puzzle but just
+to give an example if I put you know
+
+ align:start position:0%
+to give an example if I put you know
+ 
+
+ align:start position:0%
+to give an example if I put you know
+feels.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, this is kind of fun. I think there
+
+ align:start position:0%
+>> Yeah, this is kind of fun. I think there
+ 
+
+ align:start position:0%
+>> Yeah, this is kind of fun. I think there
+is a a specific word for these kind of
+
+ align:start position:0%
+is a a specific word for these kind of
+ 
+
+ align:start position:0%
+is a a specific word for these kind of
+things, but the whole idea they're
+
+ align:start position:0%
+things, but the whole idea they're
+ 
+
+ align:start position:0%
+things, but the whole idea they're
+trying to reconstruct this reconstruct
+
+ align:start position:0%
+trying to reconstruct this reconstruct
+ 
+
+ align:start position:0%
+trying to reconstruct this reconstruct
+sentence from from the so um so um
+
+ align:start position:0%
+sentence from from the so um so um
+ 
+
+ align:start position:0%
+sentence from from the so um so um
+so uh yeah, I mean the these are they're
+
+ align:start position:0%
+so uh yeah, I mean the these are they're
+ 
+
+ align:start position:0%
+so uh yeah, I mean the these are they're
+usually spatial to to to to begin with,
+
+ align:start position:0%
+usually spatial to to to to begin with,
+ 
+
+ align:start position:0%
+usually spatial to to to to begin with,
+but uh I think there was a whole game
+
+ align:start position:0%
+but uh I think there was a whole game
+ 
+
+ align:start position:0%
+but uh I think there was a whole game
+show in the 80s that was just all Yeah,
+
+ align:start position:0%
+show in the 80s that was just all Yeah,
+ 
+
+ align:start position:0%
+show in the 80s that was just all Yeah,
+that's awesome. That's that's great. Um,
+
+ align:start position:0%
+that's awesome. That's that's great. Um,
+ 
+
+ align:start position:0%
+that's awesome. That's that's great. Um,
+in Australia they had a triple
+
+ align:start position:0%
+in Australia they had a triple
+ 
+
+ align:start position:0%
+in Australia they had a triple
+catchphrase which was
+
+ align:start position:0%
+catchphrase which was
+ 
+
+ align:start position:0%
+catchphrase which was
+>> I think catchphrase was the short
+
+ align:start position:0%
+>> I think catchphrase was the short
+ 
+
+ align:start position:0%
+>> I think catchphrase was the short
+>> so we we wrote a big list of different
+
+ align:start position:0%
+>> so we we wrote a big list of different
+ 
+
+ align:start position:0%
+>> so we we wrote a big list of different
+types of puzzles. So we've got let's
+
+ align:start position:0%
+types of puzzles. So we've got let's
+ 
+
+ align:start position:0%
+types of puzzles. So we've got let's
+just run through right we got lots of
+
+ align:start position:0%
+just run through right we got lots of
+ 
+
+ align:start position:0%
+just run through right we got lots of
+different sliding puzzle variants. We've
+
+ align:start position:0%
+different sliding puzzle variants. We've
+ 
+
+ align:start position:0%
+different sliding puzzle variants. We've
+got hidden object finding. If anyone's
+
+ align:start position:0%
+got hidden object finding. If anyone's
+ 
+
+ align:start position:0%
+got hidden object finding. If anyone's
+done the words wallow then it's kind of
+
+ align:start position:0%
+done the words wallow then it's kind of
+ 
+
+ align:start position:0%
+done the words wallow then it's kind of
+a similar deal. Um we have riddles
+
+ align:start position:0%
+a similar deal. Um we have riddles
+ 
+
+ align:start position:0%
+a similar deal. Um we have riddles
+various kinds of logic puzzles
+
+ align:start position:0%
+various kinds of logic puzzles
+ 
+
+ align:start position:0%
+various kinds of logic puzzles
+particularly two which we've mentioned
+
+ align:start position:0%
+particularly two which we've mentioned
+ 
+
+ align:start position:0%
+particularly two which we've mentioned
+before somebody who is has several
+
+ align:start position:0%
+before somebody who is has several
+ 
+
+ align:start position:0%
+before somebody who is has several
+people witnesses give statements one of
+
+ align:start position:0%
+people witnesses give statements one of
+ 
+
+ align:start position:0%
+people witnesses give statements one of
+them's a liar which one's a liar so find
+
+ align:start position:0%
+them's a liar which one's a liar so find
+ 
+
+ align:start position:0%
+them's a liar which one's a liar so find
+an inconsistent person and there's the
+
+ align:start position:0%
+an inconsistent person and there's the
+ 
+
+ align:start position:0%
+an inconsistent person and there's the
+um thing with property X is next to
+
+ align:start position:0%
+um thing with property X is next to
+ 
+
+ align:start position:0%
+um thing with property X is next to
+thing with property Y what order are
+
+ align:start position:0%
+thing with property Y what order are
+ 
+
+ align:start position:0%
+thing with property Y what order are
+they sitting in that kind of puzzle
+
+ align:start position:0%
+they sitting in that kind of puzzle
+ 
+
+ align:start position:0%
+they sitting in that kind of puzzle
+there's a million of them in professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's um these kinds of
+
+ align:start position:0%
+there's um these kinds of
+ 
+
+ align:start position:0%
+there's um these kinds of
+um unraveling or reverse engineering
+
+ align:start position:0%
+um unraveling or reverse engineering
+ 
+
+ align:start position:0%
+um unraveling or reverse engineering
+type puzzles where some system has been
+
+ align:start position:0%
+type puzzles where some system has been
+ 
+
+ align:start position:0%
+type puzzles where some system has been
+permuted and you have to restore it to
+
+ align:start position:0%
+permuted and you have to restore it to
+ 
+
+ align:start position:0%
+permuted and you have to restore it to
+its original state of which Rubik's cube
+
+ align:start position:0%
+its original state of which Rubik's cube
+ 
+
+ align:start position:0%
+its original state of which Rubik's cube
+is like the canonical example I guess
+
+ align:start position:0%
+is like the canonical example I guess
+ 
+
+ align:start position:0%
+is like the canonical example I guess
+but then there's a bunch of other
+
+ align:start position:0%
+but then there's a bunch of other
+ 
+
+ align:start position:0%
+but then there's a bunch of other
+different work on how chess games can
+
+ align:start position:0%
+different work on how chess games can
+ 
+
+ align:start position:0%
+different work on how chess games can
+fit in that can
+
+ align:start position:0%
+fit in that can
+ 
+
+ align:start position:0%
+fit in that can
+>> there's like tile rotation and swapping
+
+ align:start position:0%
+>> there's like tile rotation and swapping
+ 
+
+ align:start position:0%
+>> there's like tile rotation and swapping
+puzzles like one example of this is
+
+ align:start position:0%
+puzzles like one example of this is
+ 
+
+ align:start position:0%
+puzzles like one example of this is
+hacking but then there are a million
+
+ align:start position:0%
+hacking but then there are a million
+ 
+
+ align:start position:0%
+hacking but then there are a million
+other variations on exchanging tiles or
+
+ align:start position:0%
+other variations on exchanging tiles or
+ 
+
+ align:start position:0%
+other variations on exchanging tiles or
+swapping them around or this kind of
+
+ align:start position:0%
+swapping them around or this kind of
+ 
+
+ align:start position:0%
+swapping them around or this kind of
+thing. Lots of different kinds of math
+
+ align:start position:0%
+thing. Lots of different kinds of math
+ 
+
+ align:start position:0%
+thing. Lots of different kinds of math
+puzzles. Um, this particular word
+
+ align:start position:0%
+puzzles. Um, this particular word
+ 
+
+ align:start position:0%
+puzzles. Um, this particular word
+transformation puzzle type that I that I
+
+ align:start position:0%
+transformation puzzle type that I that I
+ 
+
+ align:start position:0%
+transformation puzzle type that I that I
+used to see all the time when I was a
+
+ align:start position:0%
+used to see all the time when I was a
+ 
+
+ align:start position:0%
+used to see all the time when I was a
+kid where you by changing one letter of
+
+ align:start position:0%
+kid where you by changing one letter of
+ 
+
+ align:start position:0%
+kid where you by changing one letter of
+a word per step, you have to transform
+
+ align:start position:0%
+a word per step, you have to transform
+ 
+
+ align:start position:0%
+a word per step, you have to transform
+one word into another. Um, mazes,
+
+ align:start position:0%
+one word into another. Um, mazes,
+ 
+
+ align:start position:0%
+one word into another. Um, mazes,
+jigsaw puzzles,
+
+ align:start position:0%
+jigsaw puzzles,
+ 
+
+ align:start position:0%
+jigsaw puzzles,
+>> code breaking, nobody even mentioned
+
+ align:start position:0%
+>> code breaking, nobody even mentioned
+ 
+
+ align:start position:0%
+>> code breaking, nobody even mentioned
+yet. Um, and then also these kind of
+
+ align:start position:0%
+yet. Um, and then also these kind of
+ 
+
+ align:start position:0%
+yet. Um, and then also these kind of
+thought experimenty type puzzles. I
+
+ align:start position:0%
+thought experimenty type puzzles. I
+ 
+
+ align:start position:0%
+thought experimenty type puzzles. I
+don't know how else to categorize them.
+
+ align:start position:0%
+don't know how else to categorize them.
+ 
+
+ align:start position:0%
+don't know how else to categorize them.
+Give us an example.
+
+ align:start position:0%
+Give us an example.
+ 
+
+ align:start position:0%
+Give us an example.
+>> All right. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm trying to remember
+
+ align:start position:0%
+I'm trying to remember
+ 
+
+ align:start position:0%
+I'm trying to remember
+how this works, but I think it is. Does
+
+ align:start position:0%
+how this works, but I think it is. Does
+ 
+
+ align:start position:0%
+how this works, but I think it is. Does
+this one This one popped on up on Day
+
+ align:start position:0%
+this one This one popped on up on Day
+ 
+
+ align:start position:0%
+this one This one popped on up on Day
+Nine's podcast the other day. I don't
+
+ align:start position:0%
+Nine's podcast the other day. I don't
+ 
+
+ align:start position:0%
+Nine's podcast the other day. I don't
+want to give it because otherwise
+
+ align:start position:0%
+want to give it because otherwise
+ 
+
+ align:start position:0%
+want to give it because otherwise
+>> if I get it wrong, then people will go,
+
+ align:start position:0%
+>> if I get it wrong, then people will go,
+ 
+
+ align:start position:0%
+>> if I get it wrong, then people will go,
+"Oh my god." and try and puzzle it out.
+
+ align:start position:0%
+"Oh my god." and try and puzzle it out.
+ 
+
+ align:start position:0%
+"Oh my god." and try and puzzle it out.
+>> Let me see if I can.
+
+ align:start position:0%
+>> Let me see if I can.
+ 
+
+ align:start position:0%
+>> Let me see if I can.
+>> So, it has to do with a piece of string
+
+ align:start position:0%
+>> So, it has to do with a piece of string
+ 
+
+ align:start position:0%
+>> So, it has to do with a piece of string
+and burning.
+
+ align:start position:0%
+and burning.
+ 
+
+ align:start position:0%
+and burning.
+>> Oh, the 15 minutes.
+
+ align:start position:0%
+>> Oh, the 15 minutes.
+ 
+
+ align:start position:0%
+>> Oh, the 15 minutes.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Do you remember Do you remember exactly
+
+ align:start position:0%
+>> Do you remember Do you remember exactly
+ 
+
+ align:start position:0%
+>> Do you remember Do you remember exactly
+how?
+
+ align:start position:0%
+how?
+ 
+
+ align:start position:0%
+how?
+>> Yeah. You okay? You have two pieces of
+
+ align:start position:0%
+>> Yeah. You okay? You have two pieces of
+ 
+
+ align:start position:0%
+>> Yeah. You okay? You have two pieces of
+string. Uh you know that the whole
+
+ align:start position:0%
+string. Uh you know that the whole
+ 
+
+ align:start position:0%
+string. Uh you know that the whole
+string takes an hour to burn. Uh but
+
+ align:start position:0%
+string takes an hour to burn. Uh but
+ 
+
+ align:start position:0%
+string takes an hour to burn. Uh but
+it's not linear. So like you don't it's
+
+ align:start position:0%
+it's not linear. So like you don't it's
+ 
+
+ align:start position:0%
+it's not linear. So like you don't it's
+not linear. Uh you have an infinite
+
+ align:start position:0%
+not linear. Uh you have an infinite
+ 
+
+ align:start position:0%
+not linear. Uh you have an infinite
+supply of matches. How can you measure
+
+ align:start position:0%
+supply of matches. How can you measure
+ 
+
+ align:start position:0%
+supply of matches. How can you measure
+15 minutes with the strength?
+
+ align:start position:0%
+15 minutes with the strength?
+ 
+
+ align:start position:0%
+15 minutes with the strength?
+>> Those are lateral thinking puzzles.
+
+ align:start position:0%
+>> Those are lateral thinking puzzles.
+ 
+
+ align:start position:0%
+>> Those are lateral thinking puzzles.
+Yeah, they're all thinking puzzles. I
+
+ align:start position:0%
+Yeah, they're all thinking puzzles. I
+ 
+
+ align:start position:0%
+Yeah, they're all thinking puzzles. I
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+>> I think they're I I would classify this
+
+ align:start position:0%
+>> I think they're I I would classify this
+ 
+
+ align:start position:0%
+>> I think they're I I would classify this
+under riddles, but we have two identic
+
+ align:start position:0%
+under riddles, but we have two identic
+ 
+
+ align:start position:0%
+under riddles, but we have two identic
+>> identical identical pieces.
+
+ align:start position:0%
+>> identical identical pieces.
+ 
+
+ align:start position:0%
+>> identical identical pieces.
+>> They both No, they're identical, but
+
+ align:start position:0%
+>> They both No, they're identical, but
+ 
+
+ align:start position:0%
+>> They both No, they're identical, but
+they both take an hour.
+
+ align:start position:0%
+they both take an hour.
+ 
+
+ align:start position:0%
+they both take an hour.
+>> They don't have to.
+
+ align:start position:0%
+>> They don't have to.
+ 
+
+ align:start position:0%
+>> They don't have to.
+>> They don't have to be, but they both
+
+ align:start position:0%
+>> They don't have to be, but they both
+ 
+
+ align:start position:0%
+>> They don't have to be, but they both
+take an hour to burn. Nonidently,
+
+ align:start position:0%
+take an hour to burn. Nonidently,
+ 
+
+ align:start position:0%
+take an hour to burn. Nonidently,
+>> couldn't you just be lighting matches
+
+ align:start position:0%
+>> couldn't you just be lighting matches
+ 
+
+ align:start position:0%
+>> couldn't you just be lighting matches
+the entire time and see how many matches
+
+ align:start position:0%
+the entire time and see how many matches
+ 
+
+ align:start position:0%
+the entire time and see how many matches
+you can burn an hour and after that just
+
+ align:start position:0%
+you can burn an hour and after that just
+ 
+
+ align:start position:0%
+you can burn an hour and after that just
+take that number? No, but like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> but then how are you going to measure
+
+ align:start position:0%
+>> but then how are you going to measure
+ 
+
+ align:start position:0%
+>> but then how are you going to measure
+that original hour?
+
+ align:start position:0%
+that original hour?
+ 
+
+ align:start position:0%
+that original hour?
+>> This this assume you want to measure.
+
+ align:start position:0%
+>> This this assume you want to measure.
+ 
+
+ align:start position:0%
+>> This this assume you want to measure.
+>> But you know that thing takes an hour to
+
+ align:start position:0%
+>> But you know that thing takes an hour to
+ 
+
+ align:start position:0%
+>> But you know that thing takes an hour to
+burn. Yeah,
+
+ align:start position:0%
+burn. Yeah,
+ 
+
+ align:start position:0%
+burn. Yeah,
+>> the whole thing.
+
+ align:start position:0%
+>> the whole thing.
+ 
+
+ align:start position:0%
+>> the whole thing.
+>> It takes slightly longer than the amount
+
+ align:start position:0%
+>> It takes slightly longer than the amount
+ 
+
+ align:start position:0%
+>> It takes slightly longer than the amount
+of time.
+
+ align:start position:0%
+of time.
+ 
+
+ align:start position:0%
+of time.
+Well, we could, but then it would be
+
+ align:start position:0%
+Well, we could, but then it would be
+ 
+
+ align:start position:0%
+Well, we could, but then it would be
+nice to give people time to think about
+
+ align:start position:0%
+nice to give people time to think about
+ 
+
+ align:start position:0%
+nice to give people time to think about
+it, too. So, so
+
+ align:start position:0%
+it, too. So, so
+ 
+
+ align:start position:0%
+it, too. So, so
+answer on Wednesday.
\ No newline at end of file
diff --git a/15HVevXRsBA.txt b/15HVevXRsBA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..98e42e906c81825f8f34d56ff67a8041a177b9dd
--- /dev/null
+++ b/15HVevXRsBA.txt
@@ -0,0 +1,1743 @@
+Last time we saw things about
+gradients and directional
+
+derivatives.
+Before that we studied how to
+
+look for minima and maxima of
+functions of several variables.
+
+And today we are going to look
+again at min/max problems but in
+
+a different setting,
+namely, one for variables that
+
+are not independent.
+And so what we will see is you
+
+may have heard of Lagrange
+multipliers.
+
+And this is the one point in
+the term when I can shine with
+
+my French accent and say
+Lagrange's name properly.
+
+OK.
+What are Lagrange multipliers
+
+about?
+Well, the goal is to minimize
+
+or maximize a function of
+several variables.
+
+Let's say, for example,
+f of x, y, z,
+
+but where these variables are
+no longer independent.
+
+They are not independent.
+That means that there is a
+
+relation between them.
+The relation is maybe some
+
+equation of the form g of x,
+y, z equals some constant.
+
+You take the relation between
+x, y, z, you call that g and
+
+that gives you the constraint.
+And your goal is to minimize f
+
+only of those values of x,
+y, z that satisfy the
+
+constraint.
+What is one way to do that?
+
+Well, one to do that,
+if the constraint is very
+
+simple, we can maybe solve for
+one of the variables.
+
+Maybe we can solve this
+equation for one of the
+
+variables, plug it back into f,
+and then we have a usual
+
+min/max problem that we have
+seen how to do.
+
+The problem is sometimes you
+cannot actually solve for x,
+
+y, z in here because this
+condition is too complicated and
+
+then we need a new method.
+That is what we are going to do.
+
+Why would we care about that?
+Well, one example is actually
+
+in physics.
+Maybe you have seen in
+
+thermodynamics that you study
+quantities about gases,
+
+and those quantities that
+involve pressure,
+
+volume and temperature.
+And pressure,
+
+volume and temperature are not
+independent of each other.
+
+I mean you know probably the
+equation PV = NRT.
+
+And, of course,
+there you could actually solve
+
+to express things in terms of
+one or the other.
+
+But sometimes it is more
+convenient to keep all three
+
+variables but treat them as
+constrained.
+
+It is just an example of a
+situation where you might want
+
+to do this.
+Anyway, we will look mostly at
+
+particular examples,
+but just to point out that this
+
+is useful when you study guesses
+in physics.
+
+The first observation is we
+cannot use our usual method of
+
+looking for critical points of
+f.
+
+Because critical points of f
+typically will not satisfy this
+
+condition and so won't be good
+solutions.
+
+We need something else.
+Let's look at an example,
+
+and we will see how that leads
+us to the method.
+
+For example,
+let's say that I want to find
+
+the point closest to the origin
+-- -- on the hyperbola xy equals
+
+3 in the plane.
+That means I have this
+
+hyperbola, and I am asking
+myself what is the point on it
+
+that is the closest to the
+origin?
+
+I mean we can solve this by
+elementary geometry,
+
+we don't need actually Lagrange
+multipliers,
+
+but we are going to do it with
+Lagrange multipliers because it
+
+is a pretty good example.
+What does it mean?
+
+Well, it means that we want to
+minimize distance to the origin.
+
+What is the distance to the
+origin?
+
+If I have a point,
+at coordinates (x,
+
+y) and then the distance to the
+origin is square root of x
+
+squared plus y squared.
+Well, do we really want to
+
+minimize that or can we minimize
+something easier?
+
+Yeah.
+Maybe we can minimize the
+
+square of a distance.
+Let's forget this guy and
+
+instead -- Actually,
+we will minimize f of x,
+
+y equals x squared plus y
+squared,
+
+that looks better, 
+subject to the constraint xy =
+
+3.
+And so we will call this thing
+
+g of x, y to illustrate the
+general method.
+
+Let's look at a picture.
+Here you can see in yellow the
+
+hyperbola xy equals three.
+And we are going to look for
+
+the points that are the closest
+to the origin.
+
+What can we do?
+Well, for example,
+
+we can plot the function x
+squared plus y squared,
+
+function f.
+That is the contour plot of f
+
+with a hyperbola on top of it.
+Now let's see what we can do
+
+with that.
+Well, let's ask ourselves,
+
+for example,
+if I look at points where f
+
+equals 20 now.
+I think I am at 20 but you
+
+cannot really see it.
+That is a circle with a point
+
+whose distant square is 20.
+Well, can I find a solution if
+
+I am on the hyperbola?
+Yes, there are four points at
+
+this distance.
+Can I do better?
+
+Well, let's decrease for
+distance.
+
+Yes, we can still find points
+on the hyperbola and so on.
+
+Except if we go too low then
+there are no points on this
+
+circle anymore in the hyperbola.
+If we decrease the value of f
+
+that we want to look at that
+will somehow limit value beyond
+
+which we cannot go,
+and that is the minimum of f.
+
+We are trying to look for the
+smallest value of f that will
+
+actually be realized on the
+hyperbola.
+
+When does that happen?
+Well, I have to backtrack a
+
+little bit.
+It seems like the limiting case
+
+is basically here.
+It is when the circle is
+
+tangent to the hyperbola.
+That is the smallest circle
+
+that will hit the hyperbola.
+If I take a larger value of f,
+
+I will have solutions.
+If I take a smaller value of f,
+
+I will not have any solutions
+anymore.
+
+So, that is the situation that
+we want to solve for.
+
+How do we find that minimum?
+Well, a key observation that is
+
+valid on this picture,
+and that actually remain true
+
+in the completely general case,
+is that when we have a minimum
+
+the level curve of f is actually
+tangent to our hyperbola.
+
+It is tangent to the set of
+points where x,
+
+y equals three,
+to the hyperbola.
+
+Let's write that down.
+We observe that at the minimum
+
+the level curve of f is tangent
+to the hyperbola.
+
+Remember, the hyperbola is
+given by the equal g equals
+
+three, so it is a level curve of
+g.
+
+We have a level curve of f and
+a level curve of g that are
+
+tangent to each other.
+And I claim that is going to be
+
+the general situation that we
+are interested in.
+
+How do we try to solve for
+points where this happens?
+
+How do we find x,
+y where the level curves of f
+
+and g are tangent to each other?
+Let's think for a second.
+
+If the two level curves are
+tangent to each other that means
+
+they have the same tangent line.
+That means that the normal
+
+vectors should be parallel.
+Let me maybe draw a picture
+
+here.
+This is the level curve maybe f
+
+equals something.
+And this is the level curve g
+
+equals constant.
+Here my constant is three.
+
+Well, if I look for gradient
+vectors, the gradient of f will
+
+be perpendicular to the level
+curve of f.
+
+The gradient of g will be
+perpendicular to the level curve
+
+of g.
+They don't have any reason to
+
+be of the same size,
+but they have to be parallel to
+
+each other.
+Of course, they could also be
+
+parallel pointing in opposite
+directions.
+
+But the key point is that when
+this happens the gradient of f
+
+is parallel to the gradient of
+g.
+
+Well, let's check that.
+Here is a point.
+
+And I can plot the gradient of
+f in blue.
+
+The gradient of g in yellow.
+And you see,
+
+in most of these places,
+somehow the two gradients are
+
+not really parallel.
+Actually, I should not be
+
+looking at random points.
+I should be looking only on the
+
+hyperbola.
+I want points on the hyperbola
+
+where the two gradients are
+parallel.
+
+Well, when does that happen?
+Well, it looks like it will
+
+happen here.
+When I am at a minimum,
+
+the two gradient vectors are
+parallel.
+
+It is not really proof.
+It is an example that seems to
+
+be convincing.
+So far things work pretty well.
+
+How do we decide if two vectors
+are parallel?
+
+Well, they are parallel when
+they are proportional to each
+
+other.
+You can write one of them as a
+
+constant times the other one,
+and that constant usually one
+
+uses the Greek letter lambda.
+I don't know if you have seen
+
+it before.
+It is the Greek letter for L.
+
+And probably,
+I am sure, it is somebody's
+
+idea of paying tribute to
+Lagrange by putting an L in
+
+there.
+Lambda is just a constant.
+
+And we are looking for a scalar
+lambda and points x and y where
+
+this holds.
+In fact, 
+
+what we are doing is replacing
+min/max problems in two
+
+variables with a constraint
+between them by a set of
+
+equations involving,
+you will see, three variables.
+
+We had min/max with two
+variables x, y,
+
+but no independent.
+We had a constraint g of x,
+
+y equals constant.
+And that becomes something new.
+
+That becomes a system of
+equations where we have to
+
+solve, well, let's write down
+what it means for gradient f to
+
+be proportional to gradient g.
+That means that f sub x should
+
+be lambda times g sub x,
+and f sub y should be lambda
+
+times g sub y.
+Because the gradient vectors
+
+here are f sub x,
+f sub y and g sub x,
+
+g sub y.
+If you have a third variable z
+
+then you have also an equation f
+sub z equals lambda g sub z.
+
+Now, let's see.
+How many unknowns do we have in
+
+these equations?
+Well, there is x,
+
+there is y and there is lambda.
+We have three unknowns and have
+
+only two equations.
+Something is missing.
+
+Well, I mean x and y are not
+actually independent.
+
+They are related by the
+equation g of x,
+
+y equals c, so we need to add
+the constraint g equals c.
+
+And now we have three equations
+involving three variables.
+
+Let's see how that works.
+Here remember we have f equals
+
+x squared y squared and g = xy.
+What is f sub x?
+
+It is going to be 2x equals
+lambda times,
+
+what is g sub x,
+y.
+
+Maybe I should write here f sub
+x equals lambda g sub x just to
+
+remind you.
+Then we have f sub y equals
+
+lambda g sub y.
+F sub y is 2y equals lambda
+
+times g sub y is x.
+And then our third equation g
+
+equals c becomes xy equals
+three.
+
+So, that is what you would have
+to solve.
+
+Any questions at this point?
+No.
+
+Yes?
+How do I know the direction of
+
+a gradient?
+Do you mean how do I know that
+
+it is perpendicular to a level
+curve?
+
+Oh, how do I know if it points
+in that direction on the
+
+opposite one?
+Well, that depends.
+
+I mean we'd seen in last time,
+but the gradient is
+
+perpendicular to the level and
+points towards higher values of
+
+a function.
+So it could be -- Wait.
+
+What did I have?
+It could be that my gradient
+
+vectors up there actually point
+in opposite directions.
+
+It doesn't matter to me because
+it will still look the same in
+
+terms of the equation,
+just lambda will be positive or
+
+negative, depending on the case.
+I can handle both situations.
+
+It's not a problem.
+I can allow lambda to be
+
+positive or negative.
+Well, in this example,
+
+it looks like lambda will be
+positive.
+
+If you look at the picture on
+the plot.
+
+Yes?
+Well, because actually they are
+
+not equal to each other.
+If you look at this point where
+
+the hyperbola and the circle
+touch each other,
+
+first of all,
+I don't know which circle I am
+
+going to look at.
+I am trying to solve,
+
+actually, for the radius of the
+circle.
+
+I am trying to find what the
+minimum value of f is.
+
+And, second,
+at that point,
+
+the value of f and the value of
+g are not equal.
+
+g is equal to three because I
+want the hyperbola x equals
+
+three.
+The value of f will be the
+
+square of a distance,
+whatever that is.
+
+I think it will end up being 6,
+but we will see.
+
+So, you cannot really set them
+equal because you don't know
+
+what f is equal to in advance.
+Yes?
+
+Not quite.
+Actually, here I am just using
+
+this idea of finding a point
+closest to the origin to
+
+illustrate an example of a
+min/max problem.
+
+The general problem we are
+trying to solve is minimize f
+
+subject to g equals constant.
+And what we are going to do for
+
+that is we are really going to
+say instead let's look at places
+
+where gradient f and gradient g
+are parallel to each other and
+
+solve for equations of that.
+I think we completely lose the
+
+notion of closest point if we
+just look at these equations.
+
+We don't really say anything
+about closest points anymore.
+
+Of course, that is what they
+mean in the end.
+
+But, in the general setting,
+there is no closest point
+
+involved anymore.
+OK.
+
+Yes?
+Yes.
+
+It is always going to be the
+case that,
+
+at the minimum, 
+or at the maximum of a function
+
+subject to a constraint,
+the level curves of f and the
+
+level curves of g will be
+tangent to each other.
+
+That is the basis for this
+method.
+
+I am going to justify that soon.
+It could be minimum or maximum.
+
+In three-dimensions it could
+even be a saddle point.
+
+And, in fact,
+I should say in advance,
+
+this method will not tell us
+whether it is a minimum or a
+
+maximum.
+We do not have any way of
+
+knowing, except for testing
+values.
+
+We cannot use second derivative
+tests or anything like that.
+
+I will get back to that.
+Yes?
+
+Yes.
+Here you can set y equals to
+
+favor x.
+Then you can minimize x squared
+
+plus nine over x squared.
+In general, if I am trying to
+
+solve a more complicated
+problem, I might not be able to
+
+solve.
+I am doing an example where,
+
+indeed, here you could solve
+and remove one variable,
+
+but you cannot always do that.
+And this method will still work.
+
+The other one won't.
+OK.
+
+I don't see any other questions.
+Are there any other questions?
+
+No.
+OK.
+
+I see a lot of students
+stretching and so on,
+
+so it is very confusing for me.
+How do we solve these equations?
+
+Well, the answer is in general
+we might be in deep trouble.
+
+There is no general method for
+solving the equations that you
+
+get from this method.
+You just have to think about
+
+them.
+Sometimes it will be very easy.
+
+Sometimes it will be so hard
+that you cannot actually do it
+
+without the computer.
+Sometimes it will be just hard
+
+enough to be on Part B of this
+week's problem set.
+
+I claim in this case we can
+actually do it without so much
+
+trouble, because actually we can
+think of this as a two by two
+
+linear system in x and y.
+Well, let me do something.
+
+Let me rewrite the first two
+equations as 2x - lambda y = 0.
+
+And lambda x - 2y = 0.
+And xy = 3.
+
+That is what we want to solve.
+Well, I can put this into
+
+matrix form.
+Two minus lambda,
+
+lambda minus two times x,
+y equals 0,0.
+
+Now, how do I solve a linear
+system matrix times x,
+
+y equals zero?
+Well, I always have an obvious
+
+solution.
+X and y both equal to zero.
+
+Is that a good solution?
+No, because zero times zero is
+
+not three.
+We want another solution,
+
+the trivial solution.
+0,0 does not solve the
+
+constraint equation xy equals
+three, so we want another
+
+solution.
+When do we have another
+
+solution?
+Well, when the determinant of a
+
+matrix is zero.
+We have other solutions that
+
+exist only if determinant of a
+matrix is zero.
+
+M is this guy.
+Let's compute the determinant.
+
+Well, that seems to be negative
+four plus lambda squared.
+
+That is zero exactly when
+lambda squared equals four,
+
+which is lambda is plus or
+minus two.
+
+Already you see here it is a
+the level of difficulty that is
+
+a little bit much for an exam
+but perfectly fine for a problem
+
+set or for a beautiful lecture
+like this one.
+
+How do we deal with -- Well,
+we have two cases to look at.
+
+Lambda equals two or lambda
+equals minus two.
+
+Let's start with lambda equals
+two.
+
+If I set lambda equals two,
+what does this equation become?
+
+Well, it becomes x equals y.
+This one becomes y equals x.
+
+Well, they seem to be the same.
+x equals y.
+
+And then the equation xy equals
+three becomes,
+
+well, x squared equals three.
+I have two solutions.
+
+One is x equals root three and,
+therefore, y equals root three
+
+as well, or negative root three
+and negative root three.
+
+Let's look at the other case.
+If I set lambda equal to
+
+negative two then I get 2x
+equals negative 2y.
+
+That means x equals negative y.
+The second one,
+
+2y equals negative 2x.
+That is y equals negative x.
+
+Well, that is the same thing.
+And xy equals three becomes
+
+negative x squared equals three.
+Can we solve that?
+
+No.
+There are no solutions here.
+
+Now we have two candidate
+points which are these two
+
+points, root three,
+root three or negative root
+
+three, negative root three.
+OK.
+
+Let's actually look at what we
+have here.
+
+Maybe you cannot read the
+coordinates, but the point that
+
+I have here is indeed root
+three, root three.
+
+How do we see that lambda
+equals two?
+
+Well, if you look at this
+picture, the gradient of f,
+
+that is the blue vector,
+is indeed twice the yellow
+
+vector, gradient g.
+That is where you read the
+
+value of lambda.
+And we have the other solution
+
+which is somewhere here.
+Negative root three,
+
+negative root there.
+And there, again,
+
+lambda equals two.
+The two vectors are
+
+proportional by a factor of two.
+Yes?
+
+No, solutions are not quite
+guaranteed to be absolute minima
+
+or maxima.
+They are guaranteed to be
+
+somehow critical points end of a
+constraint.
+
+That means if you were able to
+solve and eliminate the variable
+
+that would be a critical point.
+When you have the same problem,
+
+as we have critical points,
+are they maxima or minima?
+
+And the answer is,
+well, we won't know until we
+
+check.
+More questions?
+
+No.
+Yes?
+
+What is a Lagrange multiplier?
+Well, it is this number lambda
+
+that is called the multiplier
+here.
+
+It is a multiplier because it
+is what you have to multiply
+
+gradient of g by to get gradient
+of f.
+
+It multiplies.
+
+Let's try to see why is this
+method valid?
+
+Because so far I have shown you
+pictures and have said see they
+
+are tangent.
+But why is it that they have to
+
+be tangent in general?
+Let's think about it.
+
+Let's say that we are at
+constrained min or max.
+
+What that means is that if I
+move on the level g equals
+
+constant then the value of f
+should only increase or only
+
+decrease.
+But it means,
+
+in particular,
+to first order it will not
+
+change.
+At an unconstrained min or max,
+
+partial derivatives are zero.
+In this case,
+
+derivatives are zero only in
+the allowed directions.
+
+And the allowed directions are
+those that stay on the levels of
+
+this g equals constant.
+In any direction along the
+
+level set g = c the rate of
+change of f must be zero.
+
+That is what happens at minima
+or maxima.
+
+Except here,
+of course, we look only at the
+
+allowed directions.
+Let's say the same thing in
+
+terms of directional
+derivatives.
+
+That means for any direction
+that is tangent to the
+
+constraint level g equal c,
+we must have df over ds in the
+
+direction of u equals zero.
+I will draw a picture.
+
+Let's say now I am in three
+variables just to give you
+
+different examples.
+Here I have a level surface g
+
+equals c.
+I am at my point.
+
+And if I move in any direction
+that is on the level surface,
+
+so I move in the direction u
+tangent to the level surface,
+
+then the rate of change of f in
+that direction should be zero.
+
+Now, remember what the formula
+is for this guy.
+
+Well, we have seen that this
+guy is actually radiant f dot u.
+
+That means any such vector u
+must be perpendicular to the
+
+gradient of f.
+That means that the gradient of
+
+f should be perpendicular to
+anything that is tangent to this
+
+level.
+That means the gradient of f
+
+should be perpendicular to the
+level set.
+
+That is what we have shown.
+
+But we know another vector that
+is also perpendicular to the
+
+level set of g.
+That is the gradient of g.
+
+We conclude that the gradient
+of f must be parallel to the
+
+gradient of g because both are
+perpendicular to the level set
+
+of g.
+I see confused faces,
+
+so let me try to tell you again
+where that comes from.
+
+We said if we had a constrained
+minimum or maximum,
+
+if we move in the level set of
+g, f doesn't change.
+
+Well, it doesn't change to
+first order.
+
+It is the same idea as when you
+are looking for a minimum you
+
+set the derivative equal to
+zero.
+
+So the derivative in any
+direction, tangent to g equals
+
+c, should be the directional
+derivative of f,
+
+in any such direction,
+should be zero.
+
+That is what we mean by
+critical point of f.
+
+And so that means that any
+vector u, any unit vector
+
+tangent to the level set of g is
+going to be perpendicular to the
+
+gradient of f.
+That means that the gradient of
+
+f is perpendicular to the level
+set of g.
+
+If you want,
+that means the level sets of f
+
+and g are tangent to each other.
+That is justifying what we have
+
+observed in the picture that the
+two level sets have to be
+
+tangent to each other at the
+prime minimum or maximum.
+
+Does that make a little bit of
+sense?
+
+Kind of.
+I see at least a few faces
+
+nodding so I take that to be a
+positive answer.
+
+Since I have been asked by
+several of you,
+
+how do I know if it is a
+maximum or a minimum?
+
+Well, warning,
+the method doesn't tell whether
+
+a solution is a minimum or a
+maximum.
+
+How do we do it?
+Well, more bad news.
+
+We cannot use the second
+derivative test.
+
+And the reason for that is that
+we care actually only about
+
+these specific directions that
+are tangent to variable of g.
+
+And we don't want to bother to
+try to define directional second
+
+derivatives.
+Not to mention that actually it
+
+wouldn't work.
+There is a criterion but it is
+
+much more complicated than that.
+Basically, the answer for us is
+
+that we don't have a second
+derivative test in this
+
+situation.
+What are we left with?
+
+Well, we are just left with
+comparing values.
+
+Say that in this problem you
+found a point where f equals
+
+three, a point where f equals
+nine, a point where f equals 15.
+
+Well, then probably the minimum
+is the point where f equals
+
+three and the maximum is 15.
+Actually, in this case,
+
+where we found minima,
+these two points are tied for
+
+minimum.
+What about the maximum?
+
+What is the maximum of f on the
+hyperbola?
+
+Well, it is infinity because
+the point can go as far as you
+
+want from the origin.
+But the general idea is if we
+
+have a good reason to believe
+that there should be a minimum,
+
+and it's not like at infinity
+or something weird like that,
+
+then the minimum will be a
+solution of the Lagrange
+
+multiplier equations.
+We just look for all the
+
+solutions and then we choose the
+one that gives us the lowest
+
+value.
+Is that good enough?
+
+Let me actually write that down.
+
+To find the minimum or the
+maximum, we compare values of f
+
+at the various solutions -- --
+to Lagrange multiplier
+
+equations.
+
+I should say also that
+sometimes you can just conclude
+
+by thinking geometrically.
+In this case,
+
+when it is asking you which
+point is closest to the origin
+
+you can just see that your
+answer is the correct one.
+
+Let's do an advanced example.
+Advanced means that -- Well,
+
+this one I didn't actually dare
+to put on top of the other
+
+problem sets.
+Instead, I am going to do it.
+
+What is this going to be about?
+We are going to look for a
+
+surface minimizing pyramid.
+Let's say that we want to build
+
+a pyramid with a given
+triangular base -- -- and a
+
+given volume.
+Say that I have maybe in the x,
+
+y plane I am giving you some
+triangle.
+
+And I am going to try to build
+a pyramid.
+
+Of course, I can choose where
+to put the top of a pyramid.
+
+This guy will end up being
+behind now.
+
+And the constraint and the goal
+is to minimize the total surface
+
+area.
+The first time I taught this
+
+class, it was a few years ago,
+was just before they built the
+
+Stata Center.
+And then I used to motivate
+
+this problem by saying Frank
+Gehry has gone crazy and has
+
+been given a triangular plot of
+land he wants to put a pyramid.
+
+There needs to be the right
+amount of volume so that you can
+
+put all the offices in there.
+And he wants it to be,
+
+actually, covered in solid
+gold.
+
+And because that is expensive,
+the administration wants him to
+
+cut the costs a bit.
+And so you have to minimize the
+
+total size so that it doesn't
+cost too much.
+
+We will see if MIT comes up
+with a triangular pyramid
+
+building.
+Hopefully not.
+
+It could be our next dorm,
+you never know.
+
+Anyway, it is a fine geometry
+problem.
+
+Let's try to think about how we
+can do this.
+
+The natural way to think about
+it would be -- Well,
+
+what do we have to look for
+first?
+
+We have to look for the
+position of that top point.
+
+Remember we know that the
+volume of a pyramid is one-third
+
+the area of base times height.
+In fact, fixing the volume,
+
+knowing that we have fixed the
+area of a base,
+
+means that we are fixing the
+height of the pyramid.
+
+The height is completely fixed.
+What we have to choose just is
+
+where do we put that top point?
+Do we put it smack in the
+
+middle of a triangle or to a
+side or even anywhere we want?
+
+Its z coordinate is fixed.
+Let's call h the height.
+
+What we could do is something
+like this.
+
+We say we have three points of
+a base.
+
+Let's call them p1 at (x1,
+y1,0); p2 at (x2,
+
+y2,0); p3 at (x3,
+y3,0).
+
+This point p is the unknown
+point at (x, y,
+
+h).
+We know the height.
+
+And then we want to minimize
+the sum of the areas of these
+
+three triangles.
+One here, one here and one at
+
+the back.
+And areas of triangles we know
+
+how to express by using length
+of cross-product.
+
+It becomes a function of x and
+y.
+
+And you can try to minimize it.
+Actually, it doesn't quite work.
+
+The formulas are just too
+complicated.
+
+You will never get there.
+What happens is actually maybe
+
+we need better coordinates.
+Why do we need better
+
+coordinates?
+That is because the geometry is
+
+kind of difficult to do if you
+use x, y coordinates.
+
+I mean formula for
+cross-product is fine,
+
+but then the length of the
+vector will be annoying and just
+
+doesn't look good.
+Instead, let's think about it
+
+differently.
+
+I claim if we do it this way
+and we express the area as a
+
+function of x,
+y, well, actually we can't
+
+solve for a minimum.
+Here is another way to do it.
+
+Well, what has worked pretty
+well for us so far is this
+
+geometric idea of base times
+height.
+
+So let's think in terms of the
+heights of side triangles.
+
+I am going to use the height of
+these things.
+
+And I am going to say that the
+area will be the sum of three
+
+terms, which are three bases
+times three heights.
+
+Let's give names to these
+quantities.
+
+Actually, for that it is going
+to be good to have the point in
+
+the xy plane that lives directly
+below p.
+
+Let's call it q.
+P is the point that coordinates
+
+x, y, h.
+And let's call q the point that
+
+is just below it and so it'
+coordinates are x,
+
+y, 0.
+Let's see.
+
+Let me draw a map of this thing.
+p1, p2, p3 and I have my point
+
+q in the middle.
+Let's see.
+
+To know these areas,
+I need to know the base.
+
+Well, the base I can decide
+that I know it because it is
+
+part of my given data.
+I know the sides of this
+
+triangle.
+Let me call the lengths a1,
+
+a2, a3.
+I also need to know the height,
+
+so I need to know these
+lengths.
+
+How do I know these lengths?
+Well, its distance in space,
+
+but it is a little bit
+annoying.
+
+But maybe I can reduce it to a
+distance in the plane by looking
+
+instead at this distance here.
+Let me give names to the
+
+distances from q to the sides.
+Let's call u1,
+
+u2, u3 the distances from q to
+the sides.
+
+Well, now I can claim I can
+find, actually,
+
+sorry.
+I need to draw one more thing.
+
+I claim I have a nice formula
+for the area,
+
+because this is vertical and
+this is horizontal so this
+
+length here is u3,
+this length here is h.
+
+So what is this length here?
+It is the square root of u3
+
+squared plus h squared.
+And similarly for these other
+
+guys.
+They are square roots of a u
+
+squared plus h squared.
+The heights of the faces are
+
+square root of u1 squared times
+h squared.
+
+And similarly with u2 and u3.
+So the total side area is going
+
+to be the area of the first
+faces,
+
+one-half of base times height, 
+plus one-half of a base times a
+
+height plus one-half of the
+third one.
+
+It doesn't look so much better.
+But, trust me,
+
+it will get better.
+Now, that is a function of
+
+three variables,
+u1, u2, u3.
+
+And how do we relate u1,
+u2, u3 to each other?
+
+They are probably not
+independent.
+
+Well, let's cut this triangle
+here into three pieces like
+
+that.
+Then each piece has side --
+
+Well, let's look at it the piece
+of the bottom.
+
+It has base a3, height u3.
+Cutting base into three tells
+
+you that the area of a base is
+one-half of a1,
+
+u1 plus one-half of a2,
+u2 plus one-half of a3,
+
+u3.
+And that is our constraint.
+
+My three variables,
+u1, u2, u3, are constrained in
+
+this way.
+The sum of this figure must be
+
+the area of a base.
+And I want to minimize that guy.
+
+So that is my g and that guy
+here is my f.
+
+Now we try to apply our
+Lagrange multiplier equations.
+
+Well, partial f of a partial u1
+is -- Well,
+
+if you do the calculation, 
+you will see it is one-half a1, 
+
+u1 over square root of u1^2
+plus h^2 equals lambda,
+
+what is partial g, 
+partial a1?
+
+That one you can do, I am sure.
+It is one-half a1.
+
+Oh, these guys simplify.
+If you do the same with the
+
+second one -- -- things simplify
+again.
+
+And the same with the third one.
+Well, you will get,
+
+after simplifying,
+u3 over square root of u3
+
+squared plus h squared equals
+lambda.
+
+Now, that means this guy equals
+this guy equals this guy.
+
+They are all equal to lambda.
+And, if you think about it,
+
+that means that u1 = u2 = u3.
+See, it looked like scary
+
+equations but the solution is
+very simple.
+
+What does it mean?
+It means that our point q
+
+should be equidistant from all
+three sides.
+
+That is called the incenter.
+Q should be in the incenter.
+
+The next time you have to build
+a golden pyramid and don't want
+
+to go broke, well,
+you know where to put the top.
+
+If that was a bit fast, sorry.
+Anyway, it is not completely
+
+crucial.
+But go over it and you will see
+
+it works.
+Have a nice weekend.
\ No newline at end of file
diff --git a/1El4znkRH0g.txt b/1El4znkRH0g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..303fbec86a2fc68e22778cf63578e50c36242712
--- /dev/null
+++ b/1El4znkRH0g.txt
@@ -0,0 +1,7131 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so hello and welcome as I mentioned last
+
+ align:start position:0%
+so hello and welcome as I mentioned last
+ 
+
+ align:start position:0%
+so hello and welcome as I mentioned last
+time we're essentially done with the
+
+ align:start position:0%
+time we're essentially done with the
+ 
+
+ align:start position:0%
+time we're essentially done with the
+course we've done all the theoretical
+
+ align:start position:0%
+course we've done all the theoretical
+ 
+
+ align:start position:0%
+course we've done all the theoretical
+underpinnings what remains is to talk
+
+ align:start position:0%
+underpinnings what remains is to talk
+ 
+
+ align:start position:0%
+underpinnings what remains is to talk
+about two important applications of four
+
+ align:start position:0%
+about two important applications of four
+ 
+
+ align:start position:0%
+about two important applications of four
+yang in fact some some applications that
+
+ align:start position:0%
+yang in fact some some applications that
+ 
+
+ align:start position:0%
+yang in fact some some applications that
+are very difficult to do if we didn't
+
+ align:start position:0%
+are very difficult to do if we didn't
+ 
+
+ align:start position:0%
+are very difficult to do if we didn't
+have Fourier analysis and in fact quite
+
+ align:start position:0%
+have Fourier analysis and in fact quite
+ 
+
+ align:start position:0%
+have Fourier analysis and in fact quite
+simple to think about once we have
+
+ align:start position:0%
+simple to think about once we have
+ 
+
+ align:start position:0%
+simple to think about once we have
+Fourier analysis so today I'm going to
+
+ align:start position:0%
+Fourier analysis so today I'm going to
+ 
+
+ align:start position:0%
+Fourier analysis so today I'm going to
+talk about sampling we'll spend this
+
+ align:start position:0%
+talk about sampling we'll spend this
+ 
+
+ align:start position:0%
+talk about sampling we'll spend this
+lecture and the next lecture on sampling
+
+ align:start position:0%
+lecture and the next lecture on sampling
+ 
+
+ align:start position:0%
+lecture and the next lecture on sampling
+and then the following two lectures will
+
+ align:start position:0%
+and then the following two lectures will
+ 
+
+ align:start position:0%
+and then the following two lectures will
+be on modulation and we're done so we're
+
+ align:start position:0%
+be on modulation and we're done so we're
+ 
+
+ align:start position:0%
+be on modulation and we're done so we're
+almost done so we've talked about
+
+ align:start position:0%
+almost done so we've talked about
+ 
+
+ align:start position:0%
+almost done so we've talked about
+sampling lots in the past in fact it was
+
+ align:start position:0%
+sampling lots in the past in fact it was
+ 
+
+ align:start position:0%
+sampling lots in the past in fact it was
+on the very first homework that's in
+
+ align:start position:0%
+on the very first homework that's in
+ 
+
+ align:start position:0%
+on the very first homework that's in
+fact I think one of the strong points of
+
+ align:start position:0%
+fact I think one of the strong points of
+ 
+
+ align:start position:0%
+fact I think one of the strong points of
+this course is that we regard
+
+ align:start position:0%
+this course is that we regard
+ 
+
+ align:start position:0%
+this course is that we regard
+continuous-time signals and
+
+ align:start position:0%
+continuous-time signals and
+ 
+
+ align:start position:0%
+continuous-time signals and
+discrete-time signals on equal footing
+
+ align:start position:0%
+discrete-time signals on equal footing
+ 
+
+ align:start position:0%
+discrete-time signals on equal footing
+and part of the goal is to be very
+
+ align:start position:0%
+and part of the goal is to be very
+ 
+
+ align:start position:0%
+and part of the goal is to be very
+comfortable to convert back and forth
+
+ align:start position:0%
+comfortable to convert back and forth
+ 
+
+ align:start position:0%
+comfortable to convert back and forth
+because both representations are so
+
+ align:start position:0%
+because both representations are so
+ 
+
+ align:start position:0%
+because both representations are so
+important we see sig we see CT coming up
+
+ align:start position:0%
+important we see sig we see CT coming up
+ 
+
+ align:start position:0%
+important we see sig we see CT coming up
+in fundamental ways because a lot of the
+
+ align:start position:0%
+in fundamental ways because a lot of the
+ 
+
+ align:start position:0%
+in fundamental ways because a lot of the
+things that we're interested in our
+
+ align:start position:0%
+things that we're interested in our
+ 
+
+ align:start position:0%
+things that we're interested in our
+systems based on physics and that's just
+
+ align:start position:0%
+systems based on physics and that's just
+ 
+
+ align:start position:0%
+systems based on physics and that's just
+the way it is physics works in
+
+ align:start position:0%
+the way it is physics works in
+ 
+
+ align:start position:0%
+the way it is physics works in
+continuous time by and large
+
+ align:start position:0%
+continuous time by and large
+ 
+
+ align:start position:0%
+continuous time by and large
+however because of digital electronics
+
+ align:start position:0%
+however because of digital electronics
+ 
+
+ align:start position:0%
+however because of digital electronics
+we like to process things with elect
+
+ align:start position:0%
+we like to process things with elect
+ 
+
+ align:start position:0%
+we like to process things with elect
+with digital electronics because it's so
+
+ align:start position:0%
+with digital electronics because it's so
+ 
+
+ align:start position:0%
+with digital electronics because it's so
+inexpensive so for that reason we want
+
+ align:start position:0%
+inexpensive so for that reason we want
+ 
+
+ align:start position:0%
+inexpensive so for that reason we want
+to go back and forth and what we'll see
+
+ align:start position:0%
+to go back and forth and what we'll see
+ 
+
+ align:start position:0%
+to go back and forth and what we'll see
+today is that when we think about system
+
+ align:start position:0%
+today is that when we think about system
+ 
+
+ align:start position:0%
+today is that when we think about system
+levels when we think about signal level
+
+ align:start position:0%
+levels when we think about signal level
+ 
+
+ align:start position:0%
+levels when we think about signal level
+conversion Fourier transforms the keys
+
+ align:start position:0%
+conversion Fourier transforms the keys
+ 
+
+ align:start position:0%
+conversion Fourier transforms the keys
+so keep in mind we've already thought
+
+ align:start position:0%
+so keep in mind we've already thought
+ 
+
+ align:start position:0%
+so keep in mind we've already thought
+about how you would convert a CT system
+
+ align:start position:0%
+about how you would convert a CT system
+ 
+
+ align:start position:0%
+about how you would convert a CT system
+into a DT representation we did that
+
+ align:start position:0%
+into a DT representation we did that
+ 
+
+ align:start position:0%
+into a DT representation we did that
+back in about homework three or so so
+
+ align:start position:0%
+back in about homework three or so so
+ 
+
+ align:start position:0%
+back in about homework three or so so
+what's special today is thinking about
+
+ align:start position:0%
+what's special today is thinking about
+ 
+
+ align:start position:0%
+what's special today is thinking about
+rather than thinking about systems
+
+ align:start position:0%
+rather than thinking about systems
+ 
+
+ align:start position:0%
+rather than thinking about systems
+thinking about signals and there's as
+
+ align:start position:0%
+thinking about signals and there's as
+ 
+
+ align:start position:0%
+thinking about signals and there's as
+you can imagine there's enormous reasons
+
+ align:start position:0%
+you can imagine there's enormous reasons
+ 
+
+ align:start position:0%
+you can imagine there's enormous reasons
+why you would want to think about
+
+ align:start position:0%
+why you would want to think about
+ 
+
+ align:start position:0%
+why you would want to think about
+signals from a digital point of view
+
+ align:start position:0%
+signals from a digital point of view
+ 
+
+ align:start position:0%
+signals from a digital point of view
+virtually all the things that you play
+
+ align:start position:0%
+virtually all the things that you play
+ 
+
+ align:start position:0%
+virtually all the things that you play
+with all the time are digital so you
+
+ align:start position:0%
+with all the time are digital so you
+ 
+
+ align:start position:0%
+with all the time are digital so you
+think about audio signals they're now
+
+ align:start position:0%
+think about audio signals they're now
+ 
+
+ align:start position:0%
+think about audio signals they're now
+stored digitally
+
+ align:start position:0%
+stored digitally
+ 
+
+ align:start position:0%
+stored digitally
+I think about pictures digital video
+
+ align:start position:0%
+I think about pictures digital video
+ 
+
+ align:start position:0%
+I think about pictures digital video
+digital everything on the web because
+
+ align:start position:0%
+digital everything on the web because
+ 
+
+ align:start position:0%
+digital everything on the web because
+there's no other way the web can work if
+
+ align:start position:0%
+there's no other way the web can work if
+ 
+
+ align:start position:0%
+there's no other way the web can work if
+it's on the web it's digital so there's
+
+ align:start position:0%
+it's on the web it's digital so there's
+ 
+
+ align:start position:0%
+it's on the web it's digital so there's
+just an enormous reason why we would
+
+ align:start position:0%
+just an enormous reason why we would
+ 
+
+ align:start position:0%
+just an enormous reason why we would
+like to understand how to take a
+
+ align:start position:0%
+like to understand how to take a
+ 
+
+ align:start position:0%
+like to understand how to take a
+continuous time signal and turn it into
+
+ align:start position:0%
+continuous time signal and turn it into
+ 
+
+ align:start position:0%
+continuous time signal and turn it into
+a discrete representation this is just
+
+ align:start position:0%
+a discrete representation this is just
+ 
+
+ align:start position:0%
+a discrete representation this is just
+motivation we tend to think about common
+
+ align:start position:0%
+motivation we tend to think about common
+ 
+
+ align:start position:0%
+motivation we tend to think about common
+signals that we deal with every day as
+
+ align:start position:0%
+signals that we deal with every day as
+ 
+
+ align:start position:0%
+signals that we deal with every day as
+though they were in continuous time
+
+ align:start position:0%
+though they were in continuous time
+ 
+
+ align:start position:0%
+though they were in continuous time
+continuous space same thing we think
+
+ align:start position:0%
+continuous space same thing we think
+ 
+
+ align:start position:0%
+continuous space same thing we think
+about things like pictures as though
+
+ align:start position:0%
+about things like pictures as though
+ 
+
+ align:start position:0%
+about things like pictures as though
+they were continuous they aren't anybody
+
+ align:start position:0%
+they were continuous they aren't anybody
+ 
+
+ align:start position:0%
+they were continuous they aren't anybody
+who has a digital camera knows that if
+
+ align:start position:0%
+who has a digital camera knows that if
+ 
+
+ align:start position:0%
+who has a digital camera knows that if
+you zoom in enough you see individual
+
+ align:start position:0%
+you zoom in enough you see individual
+ 
+
+ align:start position:0%
+you zoom in enough you see individual
+pixels they are not continuous
+
+ align:start position:0%
+pixels they are not continuous
+ 
+
+ align:start position:0%
+pixels they are not continuous
+representations or discrete
+
+ align:start position:0%
+representations or discrete
+ 
+
+ align:start position:0%
+representations or discrete
+representations even some kinds of
+
+ align:start position:0%
+representations even some kinds of
+ 
+
+ align:start position:0%
+representations even some kinds of
+pictures that are ancient while ancient
+
+ align:start position:0%
+pictures that are ancient while ancient
+ 
+
+ align:start position:0%
+pictures that are ancient while ancient
+from Europe by your standards at least
+
+ align:start position:0%
+from Europe by your standards at least
+ 
+
+ align:start position:0%
+from Europe by your standards at least
+even well-known kinds of pictures like
+
+ align:start position:0%
+even well-known kinds of pictures like
+ 
+
+ align:start position:0%
+even well-known kinds of pictures like
+newsprint are in an underlying sense
+
+ align:start position:0%
+newsprint are in an underlying sense
+ 
+
+ align:start position:0%
+newsprint are in an underlying sense
+they are a discrete representation so
+
+ align:start position:0%
+they are a discrete representation so
+ 
+
+ align:start position:0%
+they are a discrete representation so
+what's showed here is a picture of a
+
+ align:start position:0%
+what's showed here is a picture of a
+ 
+
+ align:start position:0%
+what's showed here is a picture of a
+rose and a halftone image of the type
+
+ align:start position:0%
+rose and a halftone image of the type
+ 
+
+ align:start position:0%
+rose and a halftone image of the type
+that would be printed in a newspaper and
+
+ align:start position:0%
+that would be printed in a newspaper and
+ 
+
+ align:start position:0%
+that would be printed in a newspaper and
+if you zoom in you can see that this so
+
+ align:start position:0%
+if you zoom in you can see that this so
+ 
+
+ align:start position:0%
+if you zoom in you can see that this so
+if you zoom into this square so that you
+
+ align:start position:0%
+if you zoom into this square so that you
+ 
+
+ align:start position:0%
+if you zoom into this square so that you
+can see this better this which is not
+
+ align:start position:0%
+can see this better this which is not
+ 
+
+ align:start position:0%
+can see this better this which is not
+really continuous right I'm showing it
+
+ align:start position:0%
+really continuous right I'm showing it
+ 
+
+ align:start position:0%
+really continuous right I'm showing it
+on a digital projector it's actually got
+
+ align:start position:0%
+on a digital projector it's actually got
+ 
+
+ align:start position:0%
+on a digital projector it's actually got
+pixels too but the pixels are small
+
+ align:start position:0%
+pixels too but the pixels are small
+ 
+
+ align:start position:0%
+pixels too but the pixels are small
+enough for the time being I'm going to
+
+ align:start position:0%
+enough for the time being I'm going to
+ 
+
+ align:start position:0%
+enough for the time being I'm going to
+ignore that so consider this continuous
+
+ align:start position:0%
+ignore that so consider this continuous
+ 
+
+ align:start position:0%
+ignore that so consider this continuous
+even though it isn't and you can see the
+
+ align:start position:0%
+even though it isn't and you can see the
+ 
+
+ align:start position:0%
+even though it isn't and you can see the
+discrete nature of this one much more
+
+ align:start position:0%
+discrete nature of this one much more
+ 
+
+ align:start position:0%
+discrete nature of this one much more
+clearly in fact the halftone pictures
+
+ align:start position:0%
+clearly in fact the halftone pictures
+ 
+
+ align:start position:0%
+clearly in fact the halftone pictures
+that you see at a newspaper are not only
+
+ align:start position:0%
+that you see at a newspaper are not only
+ 
+
+ align:start position:0%
+that you see at a newspaper are not only
+discrete in time in space but they're
+
+ align:start position:0%
+discrete in time in space but they're
+ 
+
+ align:start position:0%
+discrete in time in space but they're
+discrete in amplitude because they're
+
+ align:start position:0%
+discrete in amplitude because they're
+ 
+
+ align:start position:0%
+discrete in amplitude because they're
+printed with ink ink comes in two
+
+ align:start position:0%
+printed with ink ink comes in two
+ 
+
+ align:start position:0%
+printed with ink ink comes in two
+flavors ink or knowing so they are a
+
+ align:start position:0%
+flavors ink or knowing so they are a
+ 
+
+ align:start position:0%
+flavors ink or knowing so they are a
+binary representation in intensity as
+
+ align:start position:0%
+binary representation in intensity as
+ 
+
+ align:start position:0%
+binary representation in intensity as
+well and we'll talk about that a little
+
+ align:start position:0%
+well and we'll talk about that a little
+ 
+
+ align:start position:0%
+well and we'll talk about that a little
+bit more in the next time so in order to
+
+ align:start position:0%
+bit more in the next time so in order to
+ 
+
+ align:start position:0%
+bit more in the next time so in order to
+have a complete digital representation
+
+ align:start position:0%
+have a complete digital representation
+ 
+
+ align:start position:0%
+have a complete digital representation
+you need to think about not only
+
+ align:start position:0%
+you need to think about not only
+ 
+
+ align:start position:0%
+you need to think about not only
+sampling in the time or here the space
+
+ align:start position:0%
+sampling in the time or here the space
+ 
+
+ align:start position:0%
+sampling in the time or here the space
+dimension but also sampling in the
+
+ align:start position:0%
+dimension but also sampling in the
+ 
+
+ align:start position:0%
+dimension but also sampling in the
+voltage or the amplitude dimensional
+
+ align:start position:0%
+voltage or the amplitude dimensional
+ 
+
+ align:start position:0%
+voltage or the amplitude dimensional
+even the highest resolution picture you
+
+ align:start position:0%
+even the highest resolution picture you
+ 
+
+ align:start position:0%
+even the highest resolution picture you
+have ever seen is digital so this refers
+
+ align:start position:0%
+have ever seen is digital so this refers
+ 
+
+ align:start position:0%
+have ever seen is digital so this refers
+to the completely ancient technology of
+
+ align:start position:0%
+to the completely ancient technology of
+ 
+
+ align:start position:0%
+to the completely ancient technology of
+how do you make a digital print so a
+
+ align:start position:0%
+how do you make a digital print so a
+ 
+
+ align:start position:0%
+how do you make a digital print so a
+very high quality picture is made from
+
+ align:start position:0%
+very high quality picture is made from
+ 
+
+ align:start position:0%
+very high quality picture is made from
+an emulsion of some sort of a chemical
+
+ align:start position:0%
+an emulsion of some sort of a chemical
+ 
+
+ align:start position:0%
+an emulsion of some sort of a chemical
+and originally silver bromide the idea
+
+ align:start position:0%
+and originally silver bromide the idea
+ 
+
+ align:start position:0%
+and originally silver bromide the idea
+was that you had very small crystals of
+
+ align:start position:0%
+was that you had very small crystals of
+ 
+
+ align:start position:0%
+was that you had very small crystals of
+silver bromide that could be reduced by
+
+ align:start position:0%
+silver bromide that could be reduced by
+ 
+
+ align:start position:0%
+silver bromide that could be reduced by
+a photon to turn them into silver metal
+
+ align:start position:0%
+a photon to turn them into silver metal
+ 
+
+ align:start position:0%
+a photon to turn them into silver metal
+and the idea was that exposure to light
+
+ align:start position:0%
+and the idea was that exposure to light
+ 
+
+ align:start position:0%
+and the idea was that exposure to light
+would therefore convert silver bromide
+
+ align:start position:0%
+would therefore convert silver bromide
+ 
+
+ align:start position:0%
+would therefore convert silver bromide
+the silver and then developing meant
+
+ align:start position:0%
+the silver and then developing meant
+ 
+
+ align:start position:0%
+the silver and then developing meant
+washing away the silver bromide salt
+
+ align:start position:0%
+washing away the silver bromide salt
+ 
+
+ align:start position:0%
+washing away the silver bromide salt
+that remained that was not converted
+
+ align:start position:0%
+that remained that was not converted
+ 
+
+ align:start position:0%
+that remained that was not converted
+leaving behind the silver that had and
+
+ align:start position:0%
+leaving behind the silver that had and
+ 
+
+ align:start position:0%
+leaving behind the silver that had and
+that was the basis for the chemical
+
+ align:start position:0%
+that was the basis for the chemical
+ 
+
+ align:start position:0%
+that was the basis for the chemical
+reaction that gave rise to pictures the
+
+ align:start position:0%
+reaction that gave rise to pictures the
+ 
+
+ align:start position:0%
+reaction that gave rise to pictures the
+point being that even there these
+
+ align:start position:0%
+point being that even there these
+ 
+
+ align:start position:0%
+point being that even there these
+crystals are on the order of a micron in
+
+ align:start position:0%
+crystals are on the order of a micron in
+ 
+
+ align:start position:0%
+crystals are on the order of a micron in
+size and they're either on or off so
+
+ align:start position:0%
+size and they're either on or off so
+ 
+
+ align:start position:0%
+size and they're either on or off so
+even there it was a sampled version and
+
+ align:start position:0%
+even there it was a sampled version and
+ 
+
+ align:start position:0%
+even there it was a sampled version and
+if it weren't enough everything you've
+
+ align:start position:0%
+if it weren't enough everything you've
+ 
+
+ align:start position:0%
+if it weren't enough everything you've
+ever seen is sampled because that's the
+
+ align:start position:0%
+ever seen is sampled because that's the
+ 
+
+ align:start position:0%
+ever seen is sampled because that's the
+way your eye works your eye has
+
+ align:start position:0%
+way your eye works your eye has
+ 
+
+ align:start position:0%
+way your eye works your eye has
+individual cells that either respond to
+
+ align:start position:0%
+individual cells that either respond to
+ 
+
+ align:start position:0%
+individual cells that either respond to
+light or don't there's about 100 million
+
+ align:start position:0%
+light or don't there's about 100 million
+ 
+
+ align:start position:0%
+light or don't there's about 100 million
+rods about 6 million cones so every
+
+ align:start position:0%
+rods about 6 million cones so every
+ 
+
+ align:start position:0%
+rods about 6 million cones so every
+image you have ever seen is sampled so
+
+ align:start position:0%
+image you have ever seen is sampled so
+ 
+
+ align:start position:0%
+image you have ever seen is sampled so
+one question is and you know it's such a
+
+ align:start position:0%
+one question is and you know it's such a
+ 
+
+ align:start position:0%
+one question is and you know it's such a
+good sampling that you don't even notice
+
+ align:start position:0%
+good sampling that you don't even notice
+ 
+
+ align:start position:0%
+good sampling that you don't even notice
+but maybe that's because you're well
+
+ align:start position:0%
+but maybe that's because you're well
+ 
+
+ align:start position:0%
+but maybe that's because you're well
+unaware to be polite so that so so the
+
+ align:start position:0%
+unaware to be polite so that so so the
+ 
+
+ align:start position:0%
+unaware to be polite so that so so the
+thing about how well sampled is it so I
+
+ align:start position:0%
+thing about how well sampled is it so I
+ 
+
+ align:start position:0%
+thing about how well sampled is it so I
+know that this picture is sampled
+
+ align:start position:0%
+know that this picture is sampled
+ 
+
+ align:start position:0%
+know that this picture is sampled
+because I can come up and I can see the
+
+ align:start position:0%
+because I can come up and I can see the
+ 
+
+ align:start position:0%
+because I can come up and I can see the
+individual pixels I can see a little
+
+ align:start position:0%
+individual pixels I can see a little
+ 
+
+ align:start position:0%
+individual pixels I can see a little
+grid of pixels
+
+ align:start position:0%
+grid of pixels
+ 
+
+ align:start position:0%
+grid of pixels
+there's 1024 by 768 I want you to think
+
+ align:start position:0%
+there's 1024 by 768 I want you to think
+ 
+
+ align:start position:0%
+there's 1024 by 768 I want you to think
+about how well your eye is sampling that
+
+ align:start position:0%
+about how well your eye is sampling that
+ 
+
+ align:start position:0%
+about how well your eye is sampling that
+by thinking about whether or not you
+
+ align:start position:0%
+by thinking about whether or not you
+ 
+
+ align:start position:0%
+by thinking about whether or not you
+should be able to see the pixels from
+
+ align:start position:0%
+should be able to see the pixels from
+ 
+
+ align:start position:0%
+should be able to see the pixels from
+where you're sitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+based on the sampling this in your
+
+ align:start position:0%
+based on the sampling this in your
+ 
+
+ align:start position:0%
+based on the sampling this in your
+retina okay so look at your neighbor say
+
+ align:start position:0%
+retina okay so look at your neighbor say
+ 
+
+ align:start position:0%
+retina okay so look at your neighbor say
+hi figure out whether you have enough
+
+ align:start position:0%
+hi figure out whether you have enough
+ 
+
+ align:start position:0%
+hi figure out whether you have enough
+rods and cones to see individual pixels
+
+ align:start position:0%
+rods and cones to see individual pixels
+ 
+
+ align:start position:0%
+rods and cones to see individual pixels
+or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay does anybody have a cow who can
+
+ align:start position:0%
+okay does anybody have a cow who can
+ 
+
+ align:start position:0%
+okay does anybody have a cow who can
+tell me a way to think about this or who
+
+ align:start position:0%
+tell me a way to think about this or who
+ 
+
+ align:start position:0%
+tell me a way to think about this or who
+can help me the answer do you have
+
+ align:start position:0%
+can help me the answer do you have
+ 
+
+ align:start position:0%
+can help me the answer do you have
+enough rods and cones to sample the
+
+ align:start position:0%
+enough rods and cones to sample the
+ 
+
+ align:start position:0%
+enough rods and cones to sample the
+pixels on the screen yes no but you
+
+ align:start position:0%
+pixels on the screen yes no but you
+ 
+
+ align:start position:0%
+pixels on the screen yes no but you
+can't you cannot okay well that could be
+
+ align:start position:0%
+can't you cannot okay well that could be
+ 
+
+ align:start position:0%
+can't you cannot okay well that could be
+because you don't have enough rods and
+
+ align:start position:0%
+because you don't have enough rods and
+ 
+
+ align:start position:0%
+because you don't have enough rods and
+cones a class astigmatism is that a rod
+
+ align:start position:0%
+cones a class astigmatism is that a rod
+ 
+
+ align:start position:0%
+cones a class astigmatism is that a rod
+and cone problem that's a lens problem
+
+ align:start position:0%
+and cone problem that's a lens problem
+ 
+
+ align:start position:0%
+and cone problem that's a lens problem
+so maybe you have enough rods and cones
+
+ align:start position:0%
+so maybe you have enough rods and cones
+ 
+
+ align:start position:0%
+so maybe you have enough rods and cones
+and not enough lens there's actually
+
+ align:start position:0%
+and not enough lens there's actually
+ 
+
+ align:start position:0%
+and not enough lens there's actually
+another reason you might not be able to
+
+ align:start position:0%
+another reason you might not be able to
+ 
+
+ align:start position:0%
+another reason you might not be able to
+do it besides rods cones and lenses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain there's even another one okay
+
+ align:start position:0%
+brain there's even another one okay
+ 
+
+ align:start position:0%
+brain there's even another one okay
+we're up there another reason why you
+
+ align:start position:0%
+we're up there another reason why you
+ 
+
+ align:start position:0%
+we're up there another reason why you
+might let me not be able to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rods cones lenses brains photons that's
+
+ align:start position:0%
+rods cones lenses brains photons that's
+ 
+
+ align:start position:0%
+rods cones lenses brains photons that's
+an interesting thought I think you could
+
+ align:start position:0%
+an interesting thought I think you could
+ 
+
+ align:start position:0%
+an interesting thought I think you could
+probably pull that off yeah the number
+
+ align:start position:0%
+probably pull that off yeah the number
+ 
+
+ align:start position:0%
+probably pull that off yeah the number
+of photons if the lighting were low
+
+ align:start position:0%
+of photons if the lighting were low
+ 
+
+ align:start position:0%
+of photons if the lighting were low
+enough your eyes are very sensitive you
+
+ align:start position:0%
+enough your eyes are very sensitive you
+ 
+
+ align:start position:0%
+enough your eyes are very sensitive you
+can see you can see you can report a
+
+ align:start position:0%
+can see you can see you can report a
+ 
+
+ align:start position:0%
+can see you can see you can report a
+difference with one photon one it's
+
+ align:start position:0%
+difference with one photon one it's
+ 
+
+ align:start position:0%
+difference with one photon one it's
+pretty little it's kind of a limit right
+
+ align:start position:0%
+pretty little it's kind of a limit right
+ 
+
+ align:start position:0%
+pretty little it's kind of a limit right
+yeah it's so far away that you can't see
+
+ align:start position:0%
+yeah it's so far away that you can't see
+ 
+
+ align:start position:0%
+yeah it's so far away that you can't see
+the pixels but why is it because you
+
+ align:start position:0%
+the pixels but why is it because you
+ 
+
+ align:start position:0%
+the pixels but why is it because you
+don't have enough rosin cones because
+
+ align:start position:0%
+don't have enough rosin cones because
+ 
+
+ align:start position:0%
+don't have enough rosin cones because
+your lenses are screwed up so you might
+
+ align:start position:0%
+your lenses are screwed up so you might
+ 
+
+ align:start position:0%
+your lenses are screwed up so you might
+be using your rods and cones for
+
+ align:start position:0%
+be using your rods and cones for
+ 
+
+ align:start position:0%
+be using your rods and cones for
+different things you're right your cones
+
+ align:start position:0%
+different things you're right your cones
+ 
+
+ align:start position:0%
+different things you're right your cones
+are focused in an area called the fovea
+
+ align:start position:0%
+are focused in an area called the fovea
+ 
+
+ align:start position:0%
+are focused in an area called the fovea
+right so one way you could improve that
+
+ align:start position:0%
+right so one way you could improve that
+ 
+
+ align:start position:0%
+right so one way you could improve that
+would be to look at it can somebody
+
+ align:start position:0%
+would be to look at it can somebody
+ 
+
+ align:start position:0%
+would be to look at it can somebody
+think of something besides rods cones
+
+ align:start position:0%
+think of something besides rods cones
+ 
+
+ align:start position:0%
+think of something besides rods cones
+lenses and brains can somebody think of
+
+ align:start position:0%
+lenses and brains can somebody think of
+ 
+
+ align:start position:0%
+lenses and brains can somebody think of
+convolution lecturer with some sort of
+
+ align:start position:0%
+convolution lecturer with some sort of
+ 
+
+ align:start position:0%
+convolution lecturer with some sort of
+application that we did in convolution
+
+ align:start position:0%
+application that we did in convolution
+ 
+
+ align:start position:0%
+application that we did in convolution
+no of course not that was more than ten
+
+ align:start position:0%
+no of course not that was more than ten
+ 
+
+ align:start position:0%
+no of course not that was more than ten
+lectures ago in convolution we looked at
+
+ align:start position:0%
+lectures ago in convolution we looked at
+ 
+
+ align:start position:0%
+lectures ago in convolution we looked at
+the Hubble Space Telescope
+
+ align:start position:0%
+the Hubble Space Telescope
+ 
+
+ align:start position:0%
+the Hubble Space Telescope
+and we looked at a microscope yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles in the air that was something
+
+ align:start position:0%
+particles in the air that was something
+ 
+
+ align:start position:0%
+particles in the air that was something
+that happened in in Hubble so
+
+ align:start position:0%
+that happened in in Hubble so
+ 
+
+ align:start position:0%
+that happened in in Hubble so
+smoke-filled rooms that's bad there's
+
+ align:start position:0%
+smoke-filled rooms that's bad there's
+ 
+
+ align:start position:0%
+smoke-filled rooms that's bad there's
+something from the Hubble experiment
+
+ align:start position:0%
+something from the Hubble experiment
+ 
+
+ align:start position:0%
+something from the Hubble experiment
+from the Hubble lecture we talked about
+
+ align:start position:0%
+from the Hubble lecture we talked about
+ 
+
+ align:start position:0%
+from the Hubble lecture we talked about
+how there was a point spread function
+
+ align:start position:0%
+how there was a point spread function
+ 
+
+ align:start position:0%
+how there was a point spread function
+associated with diffraction and there's
+
+ align:start position:0%
+associated with diffraction and there's
+ 
+
+ align:start position:0%
+associated with diffraction and there's
+also a diffraction limit besides because
+
+ align:start position:0%
+also a diffraction limit besides because
+ 
+
+ align:start position:0%
+also a diffraction limit besides because
+of the size of you poop pupil okay
+
+ align:start position:0%
+of the size of you poop pupil okay
+ 
+
+ align:start position:0%
+of the size of you poop pupil okay
+because you're looking through a narrow
+
+ align:start position:0%
+because you're looking through a narrow
+ 
+
+ align:start position:0%
+because you're looking through a narrow
+aperture that limits the resolution as
+
+ align:start position:0%
+aperture that limits the resolution as
+ 
+
+ align:start position:0%
+aperture that limits the resolution as
+well but let's get back to this Ronson
+
+ align:start position:0%
+well but let's get back to this Ronson
+ 
+
+ align:start position:0%
+well but let's get back to this Ronson
+coat you have enough rods and cones how
+
+ align:start position:0%
+coat you have enough rods and cones how
+ 
+
+ align:start position:0%
+coat you have enough rods and cones how
+do you do that how do you think about
+
+ align:start position:0%
+do you do that how do you think about
+ 
+
+ align:start position:0%
+do you do that how do you think about
+whether you have enough rods and cones
+
+ align:start position:0%
+whether you have enough rods and cones
+ 
+
+ align:start position:0%
+whether you have enough rods and cones
+okay step one look at the previous slide
+
+ align:start position:0%
+okay step one look at the previous slide
+ 
+
+ align:start position:0%
+okay step one look at the previous slide
+what was the important thing on the
+
+ align:start position:0%
+what was the important thing on the
+ 
+
+ align:start position:0%
+what was the important thing on the
+previous slide three microns per rod and
+
+ align:start position:0%
+previous slide three microns per rod and
+ 
+
+ align:start position:0%
+previous slide three microns per rod and
+cone right so rising cones are separated
+
+ align:start position:0%
+cone right so rising cones are separated
+ 
+
+ align:start position:0%
+cone right so rising cones are separated
+by three microns so how what do I do
+
+ align:start position:0%
+by three microns so how what do I do
+ 
+
+ align:start position:0%
+by three microns so how what do I do
+with that how do I compare rods and
+
+ align:start position:0%
+with that how do I compare rods and
+ 
+
+ align:start position:0%
+with that how do I compare rods and
+cones three microns to this anybody
+
+ align:start position:0%
+cones three microns to this anybody
+ 
+
+ align:start position:0%
+cones three microns to this anybody
+remember anything about optics so I have
+
+ align:start position:0%
+remember anything about optics so I have
+ 
+
+ align:start position:0%
+remember anything about optics so I have
+this big lens right and we have the eye
+
+ align:start position:0%
+this big lens right and we have the eye
+ 
+
+ align:start position:0%
+this big lens right and we have the eye
+on one side and we have the object on
+
+ align:start position:0%
+on one side and we have the object on
+ 
+
+ align:start position:0%
+on one side and we have the object on
+the other side and we need to map some
+
+ align:start position:0%
+the other side and we need to map some
+ 
+
+ align:start position:0%
+the other side and we need to map some
+retina over here to some screen over
+
+ align:start position:0%
+retina over here to some screen over
+ 
+
+ align:start position:0%
+retina over here to some screen over
+here what's the important to do what's
+
+ align:start position:0%
+here what's the important to do what's
+ 
+
+ align:start position:0%
+here what's the important to do what's
+the important thing to do in the Mac oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come on Joe remember going to high
+
+ align:start position:0%
+come on Joe remember going to high
+ 
+
+ align:start position:0%
+come on Joe remember going to high
+school No
+
+ align:start position:0%
+school No
+ 
+
+ align:start position:0%
+school No
+okay so if you have a lens right rays go
+
+ align:start position:0%
+okay so if you have a lens right rays go
+ 
+
+ align:start position:0%
+okay so if you have a lens right rays go
+straight through the lens without being
+
+ align:start position:0%
+straight through the lens without being
+ 
+
+ align:start position:0%
+straight through the lens without being
+bent right that's why the rules for
+
+ align:start position:0%
+bent right that's why the rules for
+ 
+
+ align:start position:0%
+bent right that's why the rules for
+lenses so that is enough information
+
+ align:start position:0%
+lenses so that is enough information
+ 
+
+ align:start position:0%
+lenses so that is enough information
+actually to tell us the map the map
+
+ align:start position:0%
+actually to tell us the map the map
+ 
+
+ align:start position:0%
+actually to tell us the map the map
+three lenses so as to preserve angles so
+
+ align:start position:0%
+three lenses so as to preserve angles so
+ 
+
+ align:start position:0%
+three lenses so as to preserve angles so
+if we figure out how closely spaced are
+
+ align:start position:0%
+if we figure out how closely spaced are
+ 
+
+ align:start position:0%
+if we figure out how closely spaced are
+the rods and cones on this side that'll
+
+ align:start position:0%
+the rods and cones on this side that'll
+ 
+
+ align:start position:0%
+the rods and cones on this side that'll
+give me some angle that I can resolve
+
+ align:start position:0%
+give me some angle that I can resolve
+ 
+
+ align:start position:0%
+give me some angle that I can resolve
+and the question is whether that's angle
+
+ align:start position:0%
+and the question is whether that's angle
+ 
+
+ align:start position:0%
+and the question is whether that's angle
+is bigger or smaller than the angle
+
+ align:start position:0%
+is bigger or smaller than the angle
+ 
+
+ align:start position:0%
+is bigger or smaller than the angle
+that's required to resolve pixels okay
+
+ align:start position:0%
+that's required to resolve pixels okay
+ 
+
+ align:start position:0%
+that's required to resolve pixels okay
+so the angle so if we make a small angle
+
+ align:start position:0%
+so the angle so if we make a small angle
+ 
+
+ align:start position:0%
+so the angle so if we make a small angle
+approximation say that theta is on the
+
+ align:start position:0%
+approximation say that theta is on the
+ 
+
+ align:start position:0%
+approximation say that theta is on the
+order of sine theta right then the
+
+ align:start position:0%
+order of sine theta right then the
+ 
+
+ align:start position:0%
+order of sine theta right then the
+spacing between these is like three
+
+ align:start position:0%
+spacing between these is like three
+ 
+
+ align:start position:0%
+spacing between these is like three
+micrometers the distance between the
+
+ align:start position:0%
+micrometers the distance between the
+ 
+
+ align:start position:0%
+micrometers the distance between the
+lens in your eye and the retina is on
+
+ align:start position:0%
+lens in your eye and the retina is on
+ 
+
+ align:start position:0%
+lens in your eye and the retina is on
+the order of say three centimeters
+
+ align:start position:0%
+the order of say three centimeters
+ 
+
+ align:start position:0%
+the order of say three centimeters
+something like that so that's the angle
+
+ align:start position:0%
+something like that so that's the angle
+ 
+
+ align:start position:0%
+something like that so that's the angle
+at your eye and the question is how does
+
+ align:start position:0%
+at your eye and the question is how does
+ 
+
+ align:start position:0%
+at your eye and the question is how does
+that compare to the angle at the screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and so the screen this is like
+
+ align:start position:0%
+right and so the screen this is like
+ 
+
+ align:start position:0%
+right and so the screen this is like
+three meters but the pixels there's 1024
+
+ align:start position:0%
+three meters but the pixels there's 1024
+ 
+
+ align:start position:0%
+three meters but the pixels there's 1024
+pixels in that range and this distance
+
+ align:start position:0%
+pixels in that range and this distance
+ 
+
+ align:start position:0%
+pixels in that range and this distance
+is like 10 meters something like that
+
+ align:start position:0%
+is like 10 meters something like that
+ 
+
+ align:start position:0%
+is like 10 meters something like that
+so the question is whether or not the
+
+ align:start position:0%
+so the question is whether or not the
+ 
+
+ align:start position:0%
+so the question is whether or not the
+angle subtended by the pixels is bigger
+
+ align:start position:0%
+angle subtended by the pixels is bigger
+ 
+
+ align:start position:0%
+angle subtended by the pixels is bigger
+or smaller than the angle subtended by
+
+ align:start position:0%
+or smaller than the angle subtended by
+ 
+
+ align:start position:0%
+or smaller than the angle subtended by
+the rods and cones right that's the
+
+ align:start position:0%
+the rods and cones right that's the
+ 
+
+ align:start position:0%
+the rods and cones right that's the
+issue and so if you work that out the
+
+ align:start position:0%
+issue and so if you work that out the
+ 
+
+ align:start position:0%
+issue and so if you work that out the
+angle between the rods and cones is on
+
+ align:start position:0%
+angle between the rods and cones is on
+ 
+
+ align:start position:0%
+angle between the rods and cones is on
+the order of 10 to the minus 4 Radian
+
+ align:start position:0%
+the order of 10 to the minus 4 Radian
+ 
+
+ align:start position:0%
+the order of 10 to the minus 4 Radian
+and the angle between pixels is on the
+
+ align:start position:0%
+and the angle between pixels is on the
+ 
+
+ align:start position:0%
+and the angle between pixels is on the
+order of 3 times that so got a couple of
+
+ align:start position:0%
+order of 3 times that so got a couple of
+ 
+
+ align:start position:0%
+order of 3 times that so got a couple of
+interesting things you have enough rods
+
+ align:start position:0%
+interesting things you have enough rods
+ 
+
+ align:start position:0%
+interesting things you have enough rods
+and cones to see it but only barely okay
+
+ align:start position:0%
+and cones to see it but only barely okay
+ 
+
+ align:start position:0%
+and cones to see it but only barely okay
+by a factor of 3 roughly I'm not
+
+ align:start position:0%
+by a factor of 3 roughly I'm not
+ 
+
+ align:start position:0%
+by a factor of 3 roughly I'm not
+worrying about the fovea right the fovea
+
+ align:start position:0%
+worrying about the fovea right the fovea
+ 
+
+ align:start position:0%
+worrying about the fovea right the fovea
+has more right so this is just a crude
+
+ align:start position:0%
+has more right so this is just a crude
+ 
+
+ align:start position:0%
+has more right so this is just a crude
+approximation I'm not worried about your
+
+ align:start position:0%
+approximation I'm not worried about your
+ 
+
+ align:start position:0%
+approximation I'm not worried about your
+eyeglasses
+
+ align:start position:0%
+eyeglasses
+ 
+
+ align:start position:0%
+eyeglasses
+but crudely speaking you have enough
+
+ align:start position:0%
+but crudely speaking you have enough
+ 
+
+ align:start position:0%
+but crudely speaking you have enough
+rods and cones to resolve the pixels and
+
+ align:start position:0%
+rods and cones to resolve the pixels and
+ 
+
+ align:start position:0%
+rods and cones to resolve the pixels and
+another factor of 3 or so which means
+
+ align:start position:0%
+another factor of 3 or so which means
+ 
+
+ align:start position:0%
+another factor of 3 or so which means
+for example that making a projector with
+
+ align:start position:0%
+for example that making a projector with
+ 
+
+ align:start position:0%
+for example that making a projector with
+3 by 3 times more pixels makes sense
+
+ align:start position:0%
+3 by 3 times more pixels makes sense
+ 
+
+ align:start position:0%
+3 by 3 times more pixels makes sense
+and making one that's got a hundred
+
+ align:start position:0%
+and making one that's got a hundred
+ 
+
+ align:start position:0%
+and making one that's got a hundred
+times 100 times more pixels doesn't ok
+
+ align:start position:0%
+times 100 times more pixels doesn't ok
+ 
+
+ align:start position:0%
+times 100 times more pixels doesn't ok
+and that's the kind of thing we'd like
+
+ align:start position:0%
+and that's the kind of thing we'd like
+ 
+
+ align:start position:0%
+and that's the kind of thing we'd like
+to work out when we're thinking about
+
+ align:start position:0%
+to work out when we're thinking about
+ 
+
+ align:start position:0%
+to work out when we're thinking about
+discrete representations for signals
+
+ align:start position:0%
+discrete representations for signals
+ 
+
+ align:start position:0%
+discrete representations for signals
+right how many samples do you need ok so
+
+ align:start position:0%
+right how many samples do you need ok so
+ 
+
+ align:start position:0%
+right how many samples do you need ok so
+what we'd like to do today is figure out
+
+ align:start position:0%
+what we'd like to do today is figure out
+ 
+
+ align:start position:0%
+what we'd like to do today is figure out
+how sampling affects the info
+
+ align:start position:0%
+how sampling affects the info
+ 
+
+ align:start position:0%
+how sampling affects the info
+that's contained in a signal we'd like
+
+ align:start position:0%
+that's contained in a signal we'd like
+ 
+
+ align:start position:0%
+that's contained in a signal we'd like
+to sample a signal so think about the
+
+ align:start position:0%
+to sample a signal so think about the
+ 
+
+ align:start position:0%
+to sample a signal so think about the
+blue signal here and think about the red
+
+ align:start position:0%
+blue signal here and think about the red
+ 
+
+ align:start position:0%
+blue signal here and think about the red
+samples
+
+ align:start position:0%
+samples
+ 
+
+ align:start position:0%
+samples
+we'd like to sample a signal in a way
+
+ align:start position:0%
+we'd like to sample a signal in a way
+ 
+
+ align:start position:0%
+we'd like to sample a signal in a way
+that we preserve all of the information
+
+ align:start position:0%
+that we preserve all of the information
+ 
+
+ align:start position:0%
+that we preserve all of the information
+about that signal and as you can see
+
+ align:start position:0%
+about that signal and as you can see
+ 
+
+ align:start position:0%
+about that signal and as you can see
+from the example that I picked it's not
+
+ align:start position:0%
+from the example that I picked it's not
+ 
+
+ align:start position:0%
+from the example that I picked it's not
+at all clear that you can do that in
+
+ align:start position:0%
+at all clear that you can do that in
+ 
+
+ align:start position:0%
+at all clear that you can do that in
+fact if you look at the bottom picture
+
+ align:start position:0%
+fact if you look at the bottom picture
+ 
+
+ align:start position:0%
+fact if you look at the bottom picture
+I've coerced two signals to follow on
+
+ align:start position:0%
+I've coerced two signals to follow on
+ 
+
+ align:start position:0%
+I've coerced two signals to follow on
+the same samples so the green signal is
+
+ align:start position:0%
+the same samples so the green signal is
+ 
+
+ align:start position:0%
+the same samples so the green signal is
+the co 7 pi n over 3 and the red signal
+
+ align:start position:0%
+the co 7 pi n over 3 and the red signal
+ 
+
+ align:start position:0%
+the co 7 pi n over 3 and the red signal
+is the co spy n over 3 and they go they
+
+ align:start position:0%
+is the co spy n over 3 and they go they
+ 
+
+ align:start position:0%
+is the co spy n over 3 and they go they
+all go through the same blue samples the
+
+ align:start position:0%
+all go through the same blue samples the
+ 
+
+ align:start position:0%
+all go through the same blue samples the
+same blue samples is shared by both of
+
+ align:start position:0%
+same blue samples is shared by both of
+ 
+
+ align:start position:0%
+same blue samples is shared by both of
+those signals so is patently obvious
+
+ align:start position:0%
+those signals so is patently obvious
+ 
+
+ align:start position:0%
+those signals so is patently obvious
+that I cannot uniquely reconstruct the
+
+ align:start position:0%
+that I cannot uniquely reconstruct the
+ 
+
+ align:start position:0%
+that I cannot uniquely reconstruct the
+signal from the samples that's
+
+ align:start position:0%
+signal from the samples that's
+ 
+
+ align:start position:0%
+signal from the samples that's
+absolutely clear right it's also clear
+
+ align:start position:0%
+absolutely clear right it's also clear
+ 
+
+ align:start position:0%
+absolutely clear right it's also clear
+by just thinking about the the the basic
+
+ align:start position:0%
+by just thinking about the the the basic
+ 
+
+ align:start position:0%
+by just thinking about the the the basic
+mathematics of signals a CT signal could
+
+ align:start position:0%
+mathematics of signals a CT signal could
+ 
+
+ align:start position:0%
+mathematics of signals a CT signal could
+move up and down arbitrarily between two
+
+ align:start position:0%
+move up and down arbitrarily between two
+ 
+
+ align:start position:0%
+move up and down arbitrarily between two
+samples how could you possibly learn
+
+ align:start position:0%
+samples how could you possibly learn
+ 
+
+ align:start position:0%
+samples how could you possibly learn
+information about what happened between
+
+ align:start position:0%
+information about what happened between
+ 
+
+ align:start position:0%
+information about what happened between
+the samples by looking just at the
+
+ align:start position:0%
+the samples by looking just at the
+ 
+
+ align:start position:0%
+the samples by looking just at the
+samples right so it's not at all clear
+
+ align:start position:0%
+samples right so it's not at all clear
+ 
+
+ align:start position:0%
+samples right so it's not at all clear
+that you're going to be able to do this
+
+ align:start position:0%
+that you're going to be able to do this
+ 
+
+ align:start position:0%
+that you're going to be able to do this
+so let's take the opposite tact which is
+
+ align:start position:0%
+so let's take the opposite tact which is
+ 
+
+ align:start position:0%
+so let's take the opposite tact which is
+to say let's assume I only have the
+
+ align:start position:0%
+to say let's assume I only have the
+ 
+
+ align:start position:0%
+to say let's assume I only have the
+samples what can I tell you about what
+
+ align:start position:0%
+samples what can I tell you about what
+ 
+
+ align:start position:0%
+samples what can I tell you about what
+the signal might have been what's the
+
+ align:start position:0%
+the signal might have been what's the
+ 
+
+ align:start position:0%
+the signal might have been what's the
+relationship between the samples and the
+
+ align:start position:0%
+relationship between the samples and the
+ 
+
+ align:start position:0%
+relationship between the samples and the
+signal and the way to think about that
+
+ align:start position:0%
+signal and the way to think about that
+ 
+
+ align:start position:0%
+signal and the way to think about that
+one way is the thing about something
+
+ align:start position:0%
+one way is the thing about something
+ 
+
+ align:start position:0%
+one way is the thing about something
+that we will call impulse reconstruction
+
+ align:start position:0%
+that we will call impulse reconstruction
+ 
+
+ align:start position:0%
+that we will call impulse reconstruction
+if I only had the samples what could I
+
+ align:start position:0%
+if I only had the samples what could I
+ 
+
+ align:start position:0%
+if I only had the samples what could I
+do to reproduce a CT signal the simplest
+
+ align:start position:0%
+do to reproduce a CT signal the simplest
+ 
+
+ align:start position:0%
+do to reproduce a CT signal the simplest
+thing I might conceive of doing is
+
+ align:start position:0%
+thing I might conceive of doing is
+ 
+
+ align:start position:0%
+thing I might conceive of doing is
+replace every sample with some nonzero
+
+ align:start position:0%
+replace every sample with some nonzero
+ 
+
+ align:start position:0%
+replace every sample with some nonzero
+component of the CT representation so I
+
+ align:start position:0%
+component of the CT representation so I
+ 
+
+ align:start position:0%
+component of the CT representation so I
+only have samples up here at n T so
+
+ align:start position:0%
+only have samples up here at n T so
+ 
+
+ align:start position:0%
+only have samples up here at n T so
+generate a new CT signal that contains
+
+ align:start position:0%
+generate a new CT signal that contains
+ 
+
+ align:start position:0%
+generate a new CT signal that contains
+the information in the samples that is
+
+ align:start position:0%
+the information in the samples that is
+ 
+
+ align:start position:0%
+the information in the samples that is
+to say X of N
+
+ align:start position:0%
+to say X of N
+ 
+
+ align:start position:0%
+to say X of N
+which means I only have an integer
+
+ align:start position:0%
+which means I only have an integer
+ 
+
+ align:start position:0%
+which means I only have an integer
+number of non zero elements in the CT
+
+ align:start position:0%
+number of non zero elements in the CT
+ 
+
+ align:start position:0%
+number of non zero elements in the CT
+representation so in order to make that
+
+ align:start position:0%
+representation so in order to make that
+ 
+
+ align:start position:0%
+representation so in order to make that
+signal have a nonzero integral the
+
+ align:start position:0%
+signal have a nonzero integral the
+ 
+
+ align:start position:0%
+signal have a nonzero integral the
+things I represent each sample with
+
+ align:start position:0%
+things I represent each sample with
+ 
+
+ align:start position:0%
+things I represent each sample with
+better be an impulse right otherwise I
+
+ align:start position:0%
+better be an impulse right otherwise I
+ 
+
+ align:start position:0%
+better be an impulse right otherwise I
+would have finitely many nonzero points
+
+ align:start position:0%
+would have finitely many nonzero points
+ 
+
+ align:start position:0%
+would have finitely many nonzero points
+in a finite time interval in the
+
+ align:start position:0%
+in a finite time interval in the
+ 
+
+ align:start position:0%
+in a finite time interval in the
+interval and the integral over the
+
+ align:start position:0%
+interval and the integral over the
+ 
+
+ align:start position:0%
+interval and the integral over the
+interval would be zero always right so I
+
+ align:start position:0%
+interval would be zero always right so I
+ 
+
+ align:start position:0%
+interval would be zero always right so I
+have to use impulses so the simplest
+
+ align:start position:0%
+have to use impulses so the simplest
+ 
+
+ align:start position:0%
+have to use impulses so the simplest
+thing I could do would be take every one
+
+ align:start position:0%
+thing I could do would be take every one
+ 
+
+ align:start position:0%
+thing I could do would be take every one
+of these samples and replace it by an
+
+ align:start position:0%
+of these samples and replace it by an
+ 
+
+ align:start position:0%
+of these samples and replace it by an
+impulse located at the right time so put
+
+ align:start position:0%
+impulse located at the right time so put
+ 
+
+ align:start position:0%
+impulse located at the right time so put
+the nth one at time T equals n cap T put
+
+ align:start position:0%
+the nth one at time T equals n cap T put
+ 
+
+ align:start position:0%
+the nth one at time T equals n cap T put
+it where the sample came from and scale
+
+ align:start position:0%
+it where the sample came from and scale
+ 
+
+ align:start position:0%
+it where the sample came from and scale
+the weight to be in proportion to the
+
+ align:start position:0%
+the weight to be in proportion to the
+ 
+
+ align:start position:0%
+the weight to be in proportion to the
+amplitude of X of n that's kind of the
+
+ align:start position:0%
+amplitude of X of n that's kind of the
+ 
+
+ align:start position:0%
+amplitude of X of n that's kind of the
+simplest thing I could possibly do
+
+ align:start position:0%
+simplest thing I could possibly do
+ 
+
+ align:start position:0%
+simplest thing I could possibly do
+that's called impulse reconstruction and
+
+ align:start position:0%
+that's called impulse reconstruction and
+ 
+
+ align:start position:0%
+that's called impulse reconstruction and
+then let's ask the question how does the
+
+ align:start position:0%
+then let's ask the question how does the
+ 
+
+ align:start position:0%
+then let's ask the question how does the
+X that I started with relate to this X P
+
+ align:start position:0%
+X that I started with relate to this X P
+ 
+
+ align:start position:0%
+X that I started with relate to this X P
+this impulse reconstruction thing that I
+
+ align:start position:0%
+this impulse reconstruction thing that I
+ 
+
+ align:start position:0%
+this impulse reconstruction thing that I
+just made and as you might imagine from
+
+ align:start position:0%
+just made and as you might imagine from
+ 
+
+ align:start position:0%
+just made and as you might imagine from
+the theory of lectures that relationship
+
+ align:start position:0%
+the theory of lectures that relationship
+ 
+
+ align:start position:0%
+the theory of lectures that relationship
+is going to be simple right so think
+
+ align:start position:0%
+is going to be simple right so think
+ 
+
+ align:start position:0%
+is going to be simple right so think
+about what what am i doing I'm trying to
+
+ align:start position:0%
+about what what am i doing I'm trying to
+ 
+
+ align:start position:0%
+about what what am i doing I'm trying to
+think about I started with X event I
+
+ align:start position:0%
+think about I started with X event I
+ 
+
+ align:start position:0%
+think about I started with X event I
+started with X of T sorry I turned that
+
+ align:start position:0%
+started with X of T sorry I turned that
+ 
+
+ align:start position:0%
+started with X of T sorry I turned that
+into samples I turned that into X P of T
+
+ align:start position:0%
+into samples I turned that into X P of T
+ 
+
+ align:start position:0%
+into samples I turned that into X P of T
+and now I'm trying to compare those two
+
+ align:start position:0%
+and now I'm trying to compare those two
+ 
+
+ align:start position:0%
+and now I'm trying to compare those two
+signals that's the game plan
+
+ align:start position:0%
+signals that's the game plan
+ 
+
+ align:start position:0%
+signals that's the game plan
+so think about X of P from the previous
+
+ align:start position:0%
+so think about X of P from the previous
+ 
+
+ align:start position:0%
+so think about X of P from the previous
+slide it's weighted impulses shifted in
+
+ align:start position:0%
+slide it's weighted impulses shifted in
+ 
+
+ align:start position:0%
+slide it's weighted impulses shifted in
+time to the appropriate place this X of
+
+ align:start position:0%
+time to the appropriate place this X of
+ 
+
+ align:start position:0%
+time to the appropriate place this X of
+n was was derived by uniform sampling of
+
+ align:start position:0%
+n was was derived by uniform sampling of
+ 
+
+ align:start position:0%
+n was was derived by uniform sampling of
+X of T so X of n was X of n T and since
+
+ align:start position:0%
+X of T so X of n was X of n T and since
+ 
+
+ align:start position:0%
+X of T so X of n was X of n T and since
+this impulse is 0 everywhere except
+
+ align:start position:0%
+this impulse is 0 everywhere except
+ 
+
+ align:start position:0%
+this impulse is 0 everywhere except
+where the argument is 0 it doesn't
+
+ align:start position:0%
+where the argument is 0 it doesn't
+ 
+
+ align:start position:0%
+where the argument is 0 it doesn't
+matter whether I call this thing NT or T
+
+ align:start position:0%
+matter whether I call this thing NT or T
+ 
+
+ align:start position:0%
+matter whether I call this thing NT or T
+the same thing because the impulse only
+
+ align:start position:0%
+the same thing because the impulse only
+ 
+
+ align:start position:0%
+the same thing because the impulse only
+looks at T equals NT so whether I call
+
+ align:start position:0%
+looks at T equals NT so whether I call
+ 
+
+ align:start position:0%
+looks at T equals NT so whether I call
+it n T or T is irrelevant if I call it T
+
+ align:start position:0%
+it n T or T is irrelevant if I call it T
+ 
+
+ align:start position:0%
+it n T or T is irrelevant if I call it T
+then this part has no N in it and I can
+
+ align:start position:0%
+then this part has no N in it and I can
+ 
+
+ align:start position:0%
+then this part has no N in it and I can
+factor it outside and I just get an
+
+ align:start position:0%
+factor it outside and I just get an
+ 
+
+ align:start position:0%
+factor it outside and I just get an
+impulse train and not too surprisingly X
+
+ align:start position:0%
+impulse train and not too surprisingly X
+ 
+
+ align:start position:0%
+impulse train and not too surprisingly X
+P is just the product this signal is
+
+ align:start position:0%
+P is just the product this signal is
+ 
+
+ align:start position:0%
+P is just the product this signal is
+just this signal multiplied by an
+
+ align:start position:0%
+just this signal multiplied by an
+ 
+
+ align:start position:0%
+just this signal multiplied by an
+impulse train okay so if I derive X P by
+
+ align:start position:0%
+impulse train okay so if I derive X P by
+ 
+
+ align:start position:0%
+impulse train okay so if I derive X P by
+multiplying by an impulse train your
+
+ align:start position:0%
+multiplying by an impulse train your
+ 
+
+ align:start position:0%
+multiplying by an impulse train your
+knee-jerk reaction is to say multiply by
+
+ align:start position:0%
+knee-jerk reaction is to say multiply by
+ 
+
+ align:start position:0%
+knee-jerk reaction is to say multiply by
+an impulse train
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sounds like a Fourier transform
+
+ align:start position:0%
+sounds like a Fourier transform
+ 
+
+ align:start position:0%
+sounds like a Fourier transform
+somewhere on if I multiply in time by an
+
+ align:start position:0%
+somewhere on if I multiply in time by an
+ 
+
+ align:start position:0%
+somewhere on if I multiply in time by an
+impulse train what do I do in Fourier
+
+ align:start position:0%
+impulse train what do I do in Fourier
+ 
+
+ align:start position:0%
+impulse train what do I do in Fourier
+transform land convolve right multiply
+
+ align:start position:0%
+transform land convolve right multiply
+ 
+
+ align:start position:0%
+transform land convolve right multiply
+in time convolve in frequency so if this
+
+ align:start position:0%
+in time convolve in frequency so if this
+ 
+
+ align:start position:0%
+in time convolve in frequency so if this
+was my original ax this thing if this is
+
+ align:start position:0%
+was my original ax this thing if this is
+ 
+
+ align:start position:0%
+was my original ax this thing if this is
+the transform of that thing and if this
+
+ align:start position:0%
+the transform of that thing and if this
+ 
+
+ align:start position:0%
+the transform of that thing and if this
+is the transform of my impulse train
+
+ align:start position:0%
+is the transform of my impulse train
+ 
+
+ align:start position:0%
+is the transform of my impulse train
+transform of an impulse train in time is
+
+ align:start position:0%
+transform of an impulse train in time is
+ 
+
+ align:start position:0%
+transform of an impulse train in time is
+an impulse train in frequency the the
+
+ align:start position:0%
+an impulse train in frequency the the
+ 
+
+ align:start position:0%
+an impulse train in frequency the the
+impulses in frequency are separated by
+
+ align:start position:0%
+impulses in frequency are separated by
+ 
+
+ align:start position:0%
+impulses in frequency are separated by
+Omega s equal to 2pi over T and the
+
+ align:start position:0%
+Omega s equal to 2pi over T and the
+ 
+
+ align:start position:0%
+Omega s equal to 2pi over T and the
+amplitude is equal to Omega s 2 PI over
+
+ align:start position:0%
+amplitude is equal to Omega s 2 PI over
+ 
+
+ align:start position:0%
+amplitude is equal to Omega s 2 PI over
+T so they're spaced and have an
+
+ align:start position:0%
+T so they're spaced and have an
+ 
+
+ align:start position:0%
+T so they're spaced and have an
+amplitude both the spacing and the
+
+ align:start position:0%
+amplitude both the spacing and the
+ 
+
+ align:start position:0%
+amplitude both the spacing and the
+amplitude or 2pi over T right and if I'm
+
+ align:start position:0%
+amplitude or 2pi over T right and if I'm
+ 
+
+ align:start position:0%
+amplitude or 2pi over T right and if I'm
+multiplying in time x times P I can
+
+ align:start position:0%
+multiplying in time x times P I can
+ 
+
+ align:start position:0%
+multiplying in time x times P I can
+volve in frequency so this is my answer
+
+ align:start position:0%
+volve in frequency so this is my answer
+ 
+
+ align:start position:0%
+volve in frequency so this is my answer
+what's the relationship between X and XP
+
+ align:start position:0%
+what's the relationship between X and XP
+ 
+
+ align:start position:0%
+what's the relationship between X and XP
+it's multiplied in time by an impulse
+
+ align:start position:0%
+it's multiplied in time by an impulse
+ 
+
+ align:start position:0%
+it's multiplied in time by an impulse
+train or its convolve din frequency with
+
+ align:start position:0%
+train or its convolve din frequency with
+ 
+
+ align:start position:0%
+train or its convolve din frequency with
+an impulse train so the answer how does
+
+ align:start position:0%
+an impulse train so the answer how does
+ 
+
+ align:start position:0%
+an impulse train so the answer how does
+XP relate to ax it looks very similar
+
+ align:start position:0%
+XP relate to ax it looks very similar
+ 
+
+ align:start position:0%
+XP relate to ax it looks very similar
+for some frequencies but there's a lot
+
+ align:start position:0%
+for some frequencies but there's a lot
+ 
+
+ align:start position:0%
+for some frequencies but there's a lot
+more frequencies okay not too surprising
+
+ align:start position:0%
+more frequencies okay not too surprising
+ 
+
+ align:start position:0%
+more frequencies okay not too surprising
+I multiplied by impulses impulses have
+
+ align:start position:0%
+I multiplied by impulses impulses have
+ 
+
+ align:start position:0%
+I multiplied by impulses impulses have
+all frequencies right so what I've done
+
+ align:start position:0%
+all frequencies right so what I've done
+ 
+
+ align:start position:0%
+all frequencies right so what I've done
+when I've sampled it if I think about
+
+ align:start position:0%
+when I've sampled it if I think about
+ 
+
+ align:start position:0%
+when I've sampled it if I think about
+the sampled signal being represented in
+
+ align:start position:0%
+the sampled signal being represented in
+ 
+
+ align:start position:0%
+the sampled signal being represented in
+CT as the multiplication by an infinite
+
+ align:start position:0%
+CT as the multiplication by an infinite
+ 
+
+ align:start position:0%
+CT as the multiplication by an infinite
+impulse train I've introduced new
+
+ align:start position:0%
+impulse train I've introduced new
+ 
+
+ align:start position:0%
+impulse train I've introduced new
+frequency components to the Fourier
+
+ align:start position:0%
+frequency components to the Fourier
+ 
+
+ align:start position:0%
+frequency components to the Fourier
+representation that's the main message
+
+ align:start position:0%
+representation that's the main message
+ 
+
+ align:start position:0%
+representation that's the main message
+this slide is today's lecture the way we
+
+ align:start position:0%
+this slide is today's lecture the way we
+ 
+
+ align:start position:0%
+this slide is today's lecture the way we
+can think about sampling in time is as
+
+ align:start position:0%
+can think about sampling in time is as
+ 
+
+ align:start position:0%
+can think about sampling in time is as
+convolution and frequency okay
+
+ align:start position:0%
+convolution and frequency okay
+ 
+
+ align:start position:0%
+convolution and frequency okay
+so let's think about that a little more
+
+ align:start position:0%
+so let's think about that a little more
+ 
+
+ align:start position:0%
+so let's think about that a little more
+what I just talked about was the
+
+ align:start position:0%
+what I just talked about was the
+ 
+
+ align:start position:0%
+what I just talked about was the
+relationship between the Fourier
+
+ align:start position:0%
+relationship between the Fourier
+ 
+
+ align:start position:0%
+relationship between the Fourier
+transforms of X and XP but the goal is
+
+ align:start position:0%
+transforms of X and XP but the goal is
+ 
+
+ align:start position:0%
+transforms of X and XP but the goal is
+to think about the samples so what's the
+
+ align:start position:0%
+to think about the samples so what's the
+ 
+
+ align:start position:0%
+to think about the samples so what's the
+relationship between the DT the
+
+ align:start position:0%
+relationship between the DT the
+ 
+
+ align:start position:0%
+relationship between the DT the
+discrete-time fourier transform of the
+
+ align:start position:0%
+discrete-time fourier transform of the
+ 
+
+ align:start position:0%
+discrete-time fourier transform of the
+sampled signal and the continuous-time
+
+ align:start position:0%
+sampled signal and the continuous-time
+ 
+
+ align:start position:0%
+sampled signal and the continuous-time
+fourier transform of this impulse
+
+ align:start position:0%
+fourier transform of this impulse
+ 
+
+ align:start position:0%
+fourier transform of this impulse
+reconstruction right so I is already for
+
+ align:start position:0%
+reconstruction right so I is already for
+ 
+
+ align:start position:0%
+reconstruction right so I is already for
+you I've compared the frequency risk the
+
+ align:start position:0%
+you I've compared the frequency risk the
+ 
+
+ align:start position:0%
+you I've compared the frequency risk the
+Fourier representations of these two as
+
+ align:start position:0%
+Fourier representations of these two as
+ 
+
+ align:start position:0%
+Fourier representations of these two as
+an exercise you compare the frequency
+
+ align:start position:0%
+an exercise you compare the frequency
+ 
+
+ align:start position:0%
+an exercise you compare the frequency
+representations of those two and figure
+
+ align:start position:0%
+representations of those two and figure
+ 
+
+ align:start position:0%
+representations of those two and figure
+out if any of these are the right way to
+
+ align:start position:0%
+out if any of these are the right way to
+ 
+
+ align:start position:0%
+out if any of these are the right way to
+look at it so look at your neighbor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so which one best describes the
+
+ align:start position:0%
+so which one best describes the
+ 
+
+ align:start position:0%
+so which one best describes the
+relationship between those fourier
+
+ align:start position:0%
+relationship between those fourier
+ 
+
+ align:start position:0%
+relationship between those fourier
+representations number 1 2 3 or none of
+
+ align:start position:0%
+representations number 1 2 3 or none of
+ 
+
+ align:start position:0%
+representations number 1 2 3 or none of
+the above ok so a hundred percent I
+
+ align:start position:0%
+the above ok so a hundred percent I
+ 
+
+ align:start position:0%
+the above ok so a hundred percent I
+think so easier question is X of e to
+
+ align:start position:0%
+think so easier question is X of e to
+ 
+
+ align:start position:0%
+think so easier question is X of e to
+the J Omega X of e to the J Omega so
+
+ align:start position:0%
+the J Omega X of e to the J Omega so
+ 
+
+ align:start position:0%
+the J Omega X of e to the J Omega so
+this way X of e to the J Omega is that a
+
+ align:start position:0%
+this way X of e to the J Omega is that a
+ 
+
+ align:start position:0%
+this way X of e to the J Omega is that a
+periodic or a periodic function of Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+periodic what's the period go to the
+
+ align:start position:0%
+periodic what's the period go to the
+ 
+
+ align:start position:0%
+periodic what's the period go to the
+period of X of e to the J Omega what's
+
+ align:start position:0%
+period of X of e to the J Omega what's
+ 
+
+ align:start position:0%
+period of X of e to the J Omega what's
+the period of e to the J Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm hearing about the three not quite
+
+ align:start position:0%
+so I'm hearing about the three not quite
+ 
+
+ align:start position:0%
+so I'm hearing about the three not quite
+correct answers they all kind of have
+
+ align:start position:0%
+correct answers they all kind of have
+ 
+
+ align:start position:0%
+correct answers they all kind of have
+the right stuff in them what's the
+
+ align:start position:0%
+the right stuff in them what's the
+ 
+
+ align:start position:0%
+the right stuff in them what's the
+period of e to the J Omega what's the
+
+ align:start position:0%
+period of e to the J Omega what's the
+ 
+
+ align:start position:0%
+period of e to the J Omega what's the
+period of cosine what's the period of
+
+ align:start position:0%
+period of cosine what's the period of
+ 
+
+ align:start position:0%
+period of cosine what's the period of
+cosine 2pi thank you okay so this one's
+
+ align:start position:0%
+cosine 2pi thank you okay so this one's
+ 
+
+ align:start position:0%
+cosine 2pi thank you okay so this one's
+periodic in 2pi so X of e to the J Omega
+
+ align:start position:0%
+periodic in 2pi so X of e to the J Omega
+ 
+
+ align:start position:0%
+periodic in 2pi so X of e to the J Omega
+is periodic and jus pi because e to the
+
+ align:start position:0%
+is periodic and jus pi because e to the
+ 
+
+ align:start position:0%
+is periodic and jus pi because e to the
+J Omega is periodic and do pi right
+
+ align:start position:0%
+J Omega is periodic and do pi right
+ 
+
+ align:start position:0%
+J Omega is periodic and do pi right
+how about XP of J Omega is that periodic
+
+ align:start position:0%
+how about XP of J Omega is that periodic
+ 
+
+ align:start position:0%
+how about XP of J Omega is that periodic
+or a periodic XP of J Omega XP is the
+
+ align:start position:0%
+or a periodic XP of J Omega XP is the
+ 
+
+ align:start position:0%
+or a periodic XP of J Omega XP is the
+signal that I got when I multiplied in
+
+ align:start position:0%
+signal that I got when I multiplied in
+ 
+
+ align:start position:0%
+signal that I got when I multiplied in
+the time domain X of T times P of T P of
+
+ align:start position:0%
+the time domain X of T times P of T P of
+ 
+
+ align:start position:0%
+the time domain X of T times P of T P of
+T being an impulse train okay an impulse
+
+ align:start position:0%
+T being an impulse train okay an impulse
+ 
+
+ align:start position:0%
+T being an impulse train okay an impulse
+train times a time domain signal and
+
+ align:start position:0%
+train times a time domain signal and
+ 
+
+ align:start position:0%
+train times a time domain signal and
+that's how I got XP and then XP is the
+
+ align:start position:0%
+that's how I got XP and then XP is the
+ 
+
+ align:start position:0%
+that's how I got XP and then XP is the
+transform of that is the transform of XP
+
+ align:start position:0%
+transform of that is the transform of XP
+ 
+
+ align:start position:0%
+transform of that is the transform of XP
+periodic or a periodic periodic what's
+
+ align:start position:0%
+periodic or a periodic periodic what's
+ 
+
+ align:start position:0%
+periodic or a periodic periodic what's
+the period of XP two PI over T precisely
+
+ align:start position:0%
+the period of XP two PI over T precisely
+ 
+
+ align:start position:0%
+the period of XP two PI over T precisely
+so this one is periodic in Omega is two
+
+ align:start position:0%
+so this one is periodic in Omega is two
+ 
+
+ align:start position:0%
+so this one is periodic in Omega is two
+pi I shouldn't write it that way I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should say that the period is 2 pi and
+
+ align:start position:0%
+should say that the period is 2 pi and
+ 
+
+ align:start position:0%
+should say that the period is 2 pi and
+here the period of Omega is 2 PI over T
+
+ align:start position:0%
+here the period of Omega is 2 PI over T
+ 
+
+ align:start position:0%
+here the period of Omega is 2 PI over T
+so what's relationship between Omega and
+
+ align:start position:0%
+so what's relationship between Omega and
+ 
+
+ align:start position:0%
+so what's relationship between Omega and
+Omega in order to make a function so in
+
+ align:start position:0%
+Omega in order to make a function so in
+ 
+
+ align:start position:0%
+Omega in order to make a function so in
+order to make a function that is similar
+
+ align:start position:0%
+order to make a function that is similar
+ 
+
+ align:start position:0%
+order to make a function that is similar
+we're going to have to have Omega is
+
+ align:start position:0%
+we're going to have to have Omega is
+ 
+
+ align:start position:0%
+we're going to have to have Omega is
+omega over T ok we're going to have to
+
+ align:start position:0%
+omega over T ok we're going to have to
+ 
+
+ align:start position:0%
+omega over T ok we're going to have to
+convert the units of capital Omega which
+
+ align:start position:0%
+convert the units of capital Omega which
+ 
+
+ align:start position:0%
+convert the units of capital Omega which
+are radians into the units of literal
+
+ align:start position:0%
+are radians into the units of literal
+ 
+
+ align:start position:0%
+are radians into the units of literal
+Omega which is radians per second so we
+
+ align:start position:0%
+Omega which is radians per second so we
+ 
+
+ align:start position:0%
+Omega which is radians per second so we
+need a time in the bottom okay and if
+
+ align:start position:0%
+need a time in the bottom okay and if
+ 
+
+ align:start position:0%
+need a time in the bottom okay and if
+you want to be a little bit more formal
+
+ align:start position:0%
+you want to be a little bit more formal
+ 
+
+ align:start position:0%
+you want to be a little bit more formal
+on it you can just write out the
+
+ align:start position:0%
+on it you can just write out the
+ 
+
+ align:start position:0%
+on it you can just write out the
+definitions right I did this last time
+
+ align:start position:0%
+definitions right I did this last time
+ 
+
+ align:start position:0%
+definitions right I did this last time
+this was from last like two lectures ago
+
+ align:start position:0%
+this was from last like two lectures ago
+ 
+
+ align:start position:0%
+this was from last like two lectures ago
+so here's the definition of the
+
+ align:start position:0%
+so here's the definition of the
+ 
+
+ align:start position:0%
+so here's the definition of the
+discrete-time fourier transform right
+
+ align:start position:0%
+discrete-time fourier transform right
+ 
+
+ align:start position:0%
+discrete-time fourier transform right
+you take the samples and weight them by
+
+ align:start position:0%
+you take the samples and weight them by
+ 
+
+ align:start position:0%
+you take the samples and weight them by
+e to the minus J Omega n here's the
+
+ align:start position:0%
+e to the minus J Omega n here's the
+ 
+
+ align:start position:0%
+e to the minus J Omega n here's the
+definition of the CT Fourier transform
+
+ align:start position:0%
+definition of the CT Fourier transform
+ 
+
+ align:start position:0%
+definition of the CT Fourier transform
+where I've substituted X P of T is this
+
+ align:start position:0%
+where I've substituted X P of T is this
+ 
+
+ align:start position:0%
+where I've substituted X P of T is this
+thing right isn't it it's a string of
+
+ align:start position:0%
+thing right isn't it it's a string of
+ 
+
+ align:start position:0%
+thing right isn't it it's a string of
+impulses each weighted by X van and then
+
+ align:start position:0%
+impulses each weighted by X van and then
+ 
+
+ align:start position:0%
+impulses each weighted by X van and then
+I interchange the integral in the
+
+ align:start position:0%
+I interchange the integral in the
+ 
+
+ align:start position:0%
+I interchange the integral in the
+summation and I don't worry about
+
+ align:start position:0%
+summation and I don't worry about
+ 
+
+ align:start position:0%
+summation and I don't worry about
+whether it's going to work or not you
+
+ align:start position:0%
+whether it's going to work or not you
+ 
+
+ align:start position:0%
+whether it's going to work or not you
+have to take a follow-on course and of
+
+ align:start position:0%
+have to take a follow-on course and of
+ 
+
+ align:start position:0%
+have to take a follow-on course and of
+course 18 in order to figure out whether
+
+ align:start position:0%
+course 18 in order to figure out whether
+ 
+
+ align:start position:0%
+course 18 in order to figure out whether
+that makes sense or not but it does so I
+
+ align:start position:0%
+that makes sense or not but it does so I
+ 
+
+ align:start position:0%
+that makes sense or not but it does so I
+interchange the order and then the end
+
+ align:start position:0%
+interchange the order and then the end
+ 
+
+ align:start position:0%
+interchange the order and then the end
+part factors out and this just sifts out
+
+ align:start position:0%
+part factors out and this just sifts out
+ 
+
+ align:start position:0%
+part factors out and this just sifts out
+the value of Omega at t at the value of
+
+ align:start position:0%
+the value of Omega at t at the value of
+ 
+
+ align:start position:0%
+the value of Omega at t at the value of
+T at NT so I replace then this T with NT
+
+ align:start position:0%
+T at NT so I replace then this T with NT
+ 
+
+ align:start position:0%
+T at NT so I replace then this T with NT
+the integral goes away and I end up with
+
+ align:start position:0%
+the integral goes away and I end up with
+ 
+
+ align:start position:0%
+the integral goes away and I end up with
+something that looks almost exactly like
+
+ align:start position:0%
+something that looks almost exactly like
+ 
+
+ align:start position:0%
+something that looks almost exactly like
+that except that capital Omega has
+
+ align:start position:0%
+that except that capital Omega has
+ 
+
+ align:start position:0%
+that except that capital Omega has
+turned into a little Omega times T okay
+
+ align:start position:0%
+turned into a little Omega times T okay
+ 
+
+ align:start position:0%
+turned into a little Omega times T okay
+so the discrete-time fourier transform
+
+ align:start position:0%
+so the discrete-time fourier transform
+ 
+
+ align:start position:0%
+so the discrete-time fourier transform
+is just a scaled in frequency version of
+
+ align:start position:0%
+is just a scaled in frequency version of
+ 
+
+ align:start position:0%
+is just a scaled in frequency version of
+this impulse sampled original signal
+
+ align:start position:0%
+this impulse sampled original signal
+ 
+
+ align:start position:0%
+this impulse sampled original signal
+that okay so the impulse reconstruction
+
+ align:start position:0%
+that okay so the impulse reconstruction
+ 
+
+ align:start position:0%
+that okay so the impulse reconstruction
+is related to the Fourier transform of
+
+ align:start position:0%
+is related to the Fourier transform of
+ 
+
+ align:start position:0%
+is related to the Fourier transform of
+the impulse reconstruction is related to
+
+ align:start position:0%
+the impulse reconstruction is related to
+ 
+
+ align:start position:0%
+the impulse reconstruction is related to
+the Fourier transform of samples by
+
+ align:start position:0%
+the Fourier transform of samples by
+ 
+
+ align:start position:0%
+the Fourier transform of samples by
+scaling frequencies that way so they so
+
+ align:start position:0%
+scaling frequencies that way so they so
+ 
+
+ align:start position:0%
+scaling frequencies that way so they so
+those representations have the same
+
+ align:start position:0%
+those representations have the same
+ 
+
+ align:start position:0%
+those representations have the same
+information precisely except for the
+
+ align:start position:0%
+information precisely except for the
+ 
+
+ align:start position:0%
+information precisely except for the
+scaling of frequency right the period in
+
+ align:start position:0%
+scaling of frequency right the period in
+ 
+
+ align:start position:0%
+scaling of frequency right the period in
+the bottom waveform is 2pi the period
+
+ align:start position:0%
+the bottom waveform is 2pi the period
+ 
+
+ align:start position:0%
+the bottom waveform is 2pi the period
+and this one is 2pi over capital T okay
+
+ align:start position:0%
+and this one is 2pi over capital T okay
+ 
+
+ align:start position:0%
+and this one is 2pi over capital T okay
+so the answer to the question then is
+
+ align:start position:0%
+so the answer to the question then is
+ 
+
+ align:start position:0%
+so the answer to the question then is
+easy under what conditions does the
+
+ align:start position:0%
+easy under what conditions does the
+ 
+
+ align:start position:0%
+easy under what conditions does the
+original question was under what
+
+ align:start position:0%
+original question was under what
+ 
+
+ align:start position:0%
+original question was under what
+conditions can i sample in a way that
+
+ align:start position:0%
+conditions can i sample in a way that
+ 
+
+ align:start position:0%
+conditions can i sample in a way that
+preserves the information in the
+
+ align:start position:0%
+preserves the information in the
+ 
+
+ align:start position:0%
+preserves the information in the
+original signal
+
+ align:start position:0%
+original signal
+ 
+
+ align:start position:0%
+original signal
+well this diagram makes it relatively
+
+ align:start position:0%
+well this diagram makes it relatively
+ 
+
+ align:start position:0%
+well this diagram makes it relatively
+clear if I have if the original X was
+
+ align:start position:0%
+clear if I have if the original X was
+ 
+
+ align:start position:0%
+clear if I have if the original X was
+just one of these triangles
+
+ align:start position:0%
+just one of these triangles
+ 
+
+ align:start position:0%
+just one of these triangles
+and as XP is the periodic extension of
+
+ align:start position:0%
+and as XP is the periodic extension of
+ 
+
+ align:start position:0%
+and as XP is the periodic extension of
+that then so long as the periodic
+
+ align:start position:0%
+that then so long as the periodic
+ 
+
+ align:start position:0%
+that then so long as the periodic
+extensions don't overlap with each other
+
+ align:start position:0%
+extensions don't overlap with each other
+ 
+
+ align:start position:0%
+extensions don't overlap with each other
+I can derive X from XP by simply
+
+ align:start position:0%
+I can derive X from XP by simply
+ 
+
+ align:start position:0%
+I can derive X from XP by simply
+low-pass filtering throw away the
+
+ align:start position:0%
+low-pass filtering throw away the
+ 
+
+ align:start position:0%
+low-pass filtering throw away the
+frequencies that got introduced by the
+
+ align:start position:0%
+frequencies that got introduced by the
+ 
+
+ align:start position:0%
+frequencies that got introduced by the
+convolution with an impulse train so as
+
+ align:start position:0%
+convolution with an impulse train so as
+ 
+
+ align:start position:0%
+convolution with an impulse train so as
+long as the frequencies don't overlap as
+
+ align:start position:0%
+long as the frequencies don't overlap as
+ 
+
+ align:start position:0%
+long as the frequencies don't overlap as
+long as there's a clean spot here where
+
+ align:start position:0%
+long as there's a clean spot here where
+ 
+
+ align:start position:0%
+long as there's a clean spot here where
+there's nothing happening as long as the
+
+ align:start position:0%
+there's nothing happening as long as the
+ 
+
+ align:start position:0%
+there's nothing happening as long as the
+frequencies of the periodic extensions
+
+ align:start position:0%
+frequencies of the periodic extensions
+ 
+
+ align:start position:0%
+frequencies of the periodic extensions
+don't overlap then I can sample in a way
+
+ align:start position:0%
+don't overlap then I can sample in a way
+ 
+
+ align:start position:0%
+don't overlap then I can sample in a way
+that is that contains all of the
+
+ align:start position:0%
+that is that contains all of the
+ 
+
+ align:start position:0%
+that is that contains all of the
+information of the original so long as
+
+ align:start position:0%
+information of the original so long as
+ 
+
+ align:start position:0%
+information of the original so long as
+when I'm all done I low pass filter
+
+ align:start position:0%
+when I'm all done I low pass filter
+ 
+
+ align:start position:0%
+when I'm all done I low pass filter
+that's called the sampling theorem so
+
+ align:start position:0%
+that's called the sampling theorem so
+ 
+
+ align:start position:0%
+that's called the sampling theorem so
+the sampling theorem which is not at all
+
+ align:start position:0%
+the sampling theorem which is not at all
+ 
+
+ align:start position:0%
+the sampling theorem which is not at all
+obvious if you don't think about the
+
+ align:start position:0%
+obvious if you don't think about the
+ 
+
+ align:start position:0%
+obvious if you don't think about the
+Fourier space if you only started with
+
+ align:start position:0%
+Fourier space if you only started with
+ 
+
+ align:start position:0%
+Fourier space if you only started with
+the time domain representations that I
+
+ align:start position:0%
+the time domain representations that I
+ 
+
+ align:start position:0%
+the time domain representations that I
+showed in the first few slides it's not
+
+ align:start position:0%
+showed in the first few slides it's not
+ 
+
+ align:start position:0%
+showed in the first few slides it's not
+at all obvious that there even is a way
+
+ align:start position:0%
+at all obvious that there even is a way
+ 
+
+ align:start position:0%
+at all obvious that there even is a way
+to sample in an information preserving
+
+ align:start position:0%
+to sample in an information preserving
+ 
+
+ align:start position:0%
+to sample in an information preserving
+fashion but what we've just seen is that
+
+ align:start position:0%
+fashion but what we've just seen is that
+ 
+
+ align:start position:0%
+fashion but what we've just seen is that
+it's really simple to think about it in
+
+ align:start position:0%
+it's really simple to think about it in
+ 
+
+ align:start position:0%
+it's really simple to think about it in
+the Fourier domain thinking about in the
+
+ align:start position:0%
+the Fourier domain thinking about in the
+ 
+
+ align:start position:0%
+the Fourier domain thinking about in the
+Fourier domain gives rise to what we
+
+ align:start position:0%
+Fourier domain gives rise to what we
+ 
+
+ align:start position:0%
+Fourier domain gives rise to what we
+call the sampling theorem which says
+
+ align:start position:0%
+call the sampling theorem which says
+ 
+
+ align:start position:0%
+call the sampling theorem which says
+that if a signal is band limited that
+
+ align:start position:0%
+that if a signal is band limited that
+ 
+
+ align:start position:0%
+that if a signal is band limited that
+has to do with this overlap part if the
+
+ align:start position:0%
+has to do with this overlap part if the
+ 
+
+ align:start position:0%
+has to do with this overlap part if the
+signal is band limited that means that
+
+ align:start position:0%
+signal is band limited that means that
+ 
+
+ align:start position:0%
+signal is band limited that means that
+all of the non zero frequency elements
+
+ align:start position:0%
+all of the non zero frequency elements
+ 
+
+ align:start position:0%
+all of the non zero frequency elements
+are in some band of frequencies nothing
+
+ align:start position:0%
+are in some band of frequencies nothing
+ 
+
+ align:start position:0%
+are in some band of frequencies nothing
+outside that band outside some band I
+
+ align:start position:0%
+outside that band outside some band I
+ 
+
+ align:start position:0%
+outside that band outside some band I
+don't care what the band is but outside
+
+ align:start position:0%
+don't care what the band is but outside
+ 
+
+ align:start position:0%
+don't care what the band is but outside
+that band the Fourier transform has to
+
+ align:start position:0%
+that band the Fourier transform has to
+ 
+
+ align:start position:0%
+that band the Fourier transform has to
+be 0 if the Fourier transform is 0
+
+ align:start position:0%
+be 0 if the Fourier transform is 0
+ 
+
+ align:start position:0%
+be 0 if the Fourier transform is 0
+outside some band then it's possible to
+
+ align:start position:0%
+outside some band then it's possible to
+ 
+
+ align:start position:0%
+outside some band then it's possible to
+sample in a way that doesn't that
+
+ align:start position:0%
+sample in a way that doesn't that
+ 
+
+ align:start position:0%
+sample in a way that doesn't that
+preserves all the information so long as
+
+ align:start position:0%
+preserves all the information so long as
+ 
+
+ align:start position:0%
+preserves all the information so long as
+I sample fast enough so if it's if the
+
+ align:start position:0%
+I sample fast enough so if it's if the
+ 
+
+ align:start position:0%
+I sample fast enough so if it's if the
+original signal is band limited so the
+
+ align:start position:0%
+original signal is band limited so the
+ 
+
+ align:start position:0%
+original signal is band limited so the
+Fourier transform is 0 for frequencies
+
+ align:start position:0%
+Fourier transform is 0 for frequencies
+ 
+
+ align:start position:0%
+Fourier transform is 0 for frequencies
+above some frequency Omega M then X is
+
+ align:start position:0%
+above some frequency Omega M then X is
+ 
+
+ align:start position:0%
+above some frequency Omega M then X is
+uniquely determined by its samples
+
+ align:start position:0%
+uniquely determined by its samples
+ 
+
+ align:start position:0%
+uniquely determined by its samples
+uniquely means that I can do an inverse
+
+ align:start position:0%
+uniquely means that I can do an inverse
+ 
+
+ align:start position:0%
+uniquely means that I can do an inverse
+so it's uniquely determined by the
+
+ align:start position:0%
+so it's uniquely determined by the
+ 
+
+ align:start position:0%
+so it's uniquely determined by the
+samples
+
+ align:start position:0%
+samples
+ 
+
+ align:start position:0%
+samples
+only if Omega asks this sampling
+
+ align:start position:0%
+only if Omega asks this sampling
+ 
+
+ align:start position:0%
+only if Omega asks this sampling
+frequency which is two PI over T that's
+
+ align:start position:0%
+frequency which is two PI over T that's
+ 
+
+ align:start position:0%
+frequency which is two PI over T that's
+the period of the impulse train so if
+
+ align:start position:0%
+the period of the impulse train so if
+ 
+
+ align:start position:0%
+the period of the impulse train so if
+two PI over T exceeds twice the
+
+ align:start position:0%
+two PI over T exceeds twice the
+ 
+
+ align:start position:0%
+two PI over T exceeds twice the
+frequency of the band limit we'll see in
+
+ align:start position:0%
+frequency of the band limit we'll see in
+ 
+
+ align:start position:0%
+frequency of the band limit we'll see in
+a minute where the factor of two comes
+
+ align:start position:0%
+a minute where the factor of two comes
+ 
+
+ align:start position:0%
+a minute where the factor of two comes
+from the factor of two comes from
+
+ align:start position:0%
+from the factor of two comes from
+ 
+
+ align:start position:0%
+from the factor of two comes from
+negative frequencies so the sampling
+
+ align:start position:0%
+negative frequencies so the sampling
+ 
+
+ align:start position:0%
+negative frequencies so the sampling
+theorem says that there is a way for a
+
+ align:start position:0%
+theorem says that there is a way for a
+ 
+
+ align:start position:0%
+theorem says that there is a way for a
+certain kind of signal signals that are
+
+ align:start position:0%
+certain kind of signal signals that are
+ 
+
+ align:start position:0%
+certain kind of signal signals that are
+band-limited can be sampled in a way
+
+ align:start position:0%
+band-limited can be sampled in a way
+ 
+
+ align:start position:0%
+band-limited can be sampled in a way
+that preserves all the information so
+
+ align:start position:0%
+that preserves all the information so
+ 
+
+ align:start position:0%
+that preserves all the information so
+here's a summary if you sample uniformly
+
+ align:start position:0%
+here's a summary if you sample uniformly
+ 
+
+ align:start position:0%
+here's a summary if you sample uniformly
+that's not the only kind of sampling we
+
+ align:start position:0%
+that's not the only kind of sampling we
+ 
+
+ align:start position:0%
+that's not the only kind of sampling we
+do in practice but it's the basis of all
+
+ align:start position:0%
+do in practice but it's the basis of all
+ 
+
+ align:start position:0%
+do in practice but it's the basis of all
+of our theories for the way sampling
+
+ align:start position:0%
+of our theories for the way sampling
+ 
+
+ align:start position:0%
+of our theories for the way sampling
+works so that's the only one we'll do in
+
+ align:start position:0%
+works so that's the only one we'll do in
+ 
+
+ align:start position:0%
+works so that's the only one we'll do in
+double O 3 but just for your
+
+ align:start position:0%
+double O 3 but just for your
+ 
+
+ align:start position:0%
+double O 3 but just for your
+intellectual area fication there are
+
+ align:start position:0%
+intellectual area fication there are
+ 
+
+ align:start position:0%
+intellectual area fication there are
+more sophisticated ways to sample and in
+
+ align:start position:0%
+more sophisticated ways to sample and in
+ 
+
+ align:start position:0%
+more sophisticated ways to sample and in
+fact that's a topic of current research
+
+ align:start position:0%
+fact that's a topic of current research
+ 
+
+ align:start position:0%
+fact that's a topic of current research
+but for the time being we're only going
+
+ align:start position:0%
+but for the time being we're only going
+ 
+
+ align:start position:0%
+but for the time being we're only going
+to worry about uniform sampling if you
+
+ align:start position:0%
+to worry about uniform sampling if you
+ 
+
+ align:start position:0%
+to worry about uniform sampling if you
+sample a signal uniformly in time that
+
+ align:start position:0%
+sample a signal uniformly in time that
+ 
+
+ align:start position:0%
+sample a signal uniformly in time that
+is every T set capital T seconds then
+
+ align:start position:0%
+is every T set capital T seconds then
+ 
+
+ align:start position:0%
+is every T set capital T seconds then
+you can do band-limited reconstruction
+
+ align:start position:0%
+you can do band-limited reconstruction
+ 
+
+ align:start position:0%
+you can do band-limited reconstruction
+which means that replace every sample
+
+ align:start position:0%
+which means that replace every sample
+ 
+
+ align:start position:0%
+which means that replace every sample
+with an impulse weighted by the sample
+
+ align:start position:0%
+with an impulse weighted by the sample
+ 
+
+ align:start position:0%
+with an impulse weighted by the sample
+weight and spaced in time where it would
+
+ align:start position:0%
+weight and spaced in time where it would
+ 
+
+ align:start position:0%
+weight and spaced in time where it would
+have come from then run it through an
+
+ align:start position:0%
+have come from then run it through an
+ 
+
+ align:start position:0%
+have come from then run it through an
+ideal low-pass filter to get rid of the
+
+ align:start position:0%
+ideal low-pass filter to get rid of the
+ 
+
+ align:start position:0%
+ideal low-pass filter to get rid of the
+stuff that the high frequency copies and
+
+ align:start position:0%
+stuff that the high frequency copies and
+ 
+
+ align:start position:0%
+stuff that the high frequency copies and
+what comes out will be equal to that as
+
+ align:start position:0%
+what comes out will be equal to that as
+ 
+
+ align:start position:0%
+what comes out will be equal to that as
+long as you've satisfied this
+
+ align:start position:0%
+long as you've satisfied this
+ 
+
+ align:start position:0%
+long as you've satisfied this
+relationship that the frequencies that
+
+ align:start position:0%
+relationship that the frequencies that
+ 
+
+ align:start position:0%
+relationship that the frequencies that
+are contained in the signal must be less
+
+ align:start position:0%
+are contained in the signal must be less
+ 
+
+ align:start position:0%
+are contained in the signal must be less
+than the sampling frequency over to okay
+
+ align:start position:0%
+than the sampling frequency over to okay
+ 
+
+ align:start position:0%
+than the sampling frequency over to okay
+okay so what's the implication of the
+
+ align:start position:0%
+okay so what's the implication of the
+ 
+
+ align:start position:0%
+okay so what's the implication of the
+sampling theorem think about a
+
+ align:start position:0%
+sampling theorem think about a
+ 
+
+ align:start position:0%
+sampling theorem think about a
+particular problem we can hear sounds
+
+ align:start position:0%
+particular problem we can hear sounds
+ 
+
+ align:start position:0%
+particular problem we can hear sounds
+with frequency components that range
+
+ align:start position:0%
+with frequency components that range
+ 
+
+ align:start position:0%
+with frequency components that range
+from 20 Hertz to 20 kilohertz what's the
+
+ align:start position:0%
+from 20 Hertz to 20 kilohertz what's the
+ 
+
+ align:start position:0%
+from 20 Hertz to 20 kilohertz what's the
+minimum what's the biggest sampling
+
+ align:start position:0%
+minimum what's the biggest sampling
+ 
+
+ align:start position:0%
+minimum what's the biggest sampling
+interval T that we can use to retain all
+
+ align:start position:0%
+interval T that we can use to retain all
+ 
+
+ align:start position:0%
+interval T that we can use to retain all
+of the information in a signal that we
+
+ align:start position:0%
+of the information in a signal that we
+ 
+
+ align:start position:0%
+of the information in a signal that we
+can hear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the answer one two three four
+
+ align:start position:0%
+so what's the answer one two three four
+ 
+
+ align:start position:0%
+so what's the answer one two three four
+five six okay sort of shrinking number
+
+ align:start position:0%
+five six okay sort of shrinking number
+ 
+
+ align:start position:0%
+five six okay sort of shrinking number
+of votes and sort of a shrinking number
+
+ align:start position:0%
+of votes and sort of a shrinking number
+ 
+
+ align:start position:0%
+of votes and sort of a shrinking number
+of correct votes so it's about seventy
+
+ align:start position:0%
+of correct votes so it's about seventy
+ 
+
+ align:start position:0%
+of correct votes so it's about seventy
+five percent the only tricky part really
+
+ align:start position:0%
+five percent the only tricky part really
+ 
+
+ align:start position:0%
+five percent the only tricky part really
+is thinking about frequencies so I told
+
+ align:start position:0%
+is thinking about frequencies so I told
+ 
+
+ align:start position:0%
+is thinking about frequencies so I told
+you frequencies in the commonly used
+
+ align:start position:0%
+you frequencies in the commonly used
+ 
+
+ align:start position:0%
+you frequencies in the commonly used
+engineering terms I told you that we
+
+ align:start position:0%
+engineering terms I told you that we
+ 
+
+ align:start position:0%
+engineering terms I told you that we
+hear frequencies from 20 to 20,000 Hertz
+
+ align:start position:0%
+hear frequencies from 20 to 20,000 Hertz
+ 
+
+ align:start position:0%
+hear frequencies from 20 to 20,000 Hertz
+in this course we usually think about
+
+ align:start position:0%
+in this course we usually think about
+ 
+
+ align:start position:0%
+in this course we usually think about
+frequencies as Omega Radian frequency
+
+ align:start position:0%
+frequencies as Omega Radian frequency
+ 
+
+ align:start position:0%
+frequencies as Omega Radian frequency
+Hertz are cycles per second there's two
+
+ align:start position:0%
+Hertz are cycles per second there's two
+ 
+
+ align:start position:0%
+Hertz are cycles per second there's two
+PI radians cycles Hertz or cycles per
+
+ align:start position:0%
+PI radians cycles Hertz or cycles per
+ 
+
+ align:start position:0%
+PI radians cycles Hertz or cycles per
+second Radian frequency is cycles per
+
+ align:start position:0%
+second Radian frequency is cycles per
+ 
+
+ align:start position:0%
+second Radian frequency is cycles per
+second radians per second there's two PI
+
+ align:start position:0%
+second radians per second there's two PI
+ 
+
+ align:start position:0%
+second radians per second there's two PI
+radians per cycle okay sorry I screwed
+
+ align:start position:0%
+radians per cycle okay sorry I screwed
+ 
+
+ align:start position:0%
+radians per cycle okay sorry I screwed
+that up Hertz is cycles per second Omega
+
+ align:start position:0%
+that up Hertz is cycles per second Omega
+ 
+
+ align:start position:0%
+that up Hertz is cycles per second Omega
+is radians per second the conversion is
+
+ align:start position:0%
+is radians per second the conversion is
+ 
+
+ align:start position:0%
+is radians per second the conversion is
+two pi radians per cycle okay so we need
+
+ align:start position:0%
+two pi radians per cycle okay so we need
+ 
+
+ align:start position:0%
+two pi radians per cycle okay so we need
+to have the highest frequency in the
+
+ align:start position:0%
+to have the highest frequency in the
+ 
+
+ align:start position:0%
+to have the highest frequency in the
+signal has to be smaller than the
+
+ align:start position:0%
+signal has to be smaller than the
+ 
+
+ align:start position:0%
+signal has to be smaller than the
+sampling frequency divided by two the
+
+ align:start position:0%
+sampling frequency divided by two the
+ 
+
+ align:start position:0%
+sampling frequency divided by two the
+highest frequency in the signal is 2 pi
+
+ align:start position:0%
+highest frequency in the signal is 2 pi
+ 
+
+ align:start position:0%
+highest frequency in the signal is 2 pi
+fm if F is frequencies 20 to 20
+
+ align:start position:0%
+fm if F is frequencies 20 to 20
+ 
+
+ align:start position:0%
+fm if F is frequencies 20 to 20
+kilohertz and the sampling frequency is
+
+ align:start position:0%
+kilohertz and the sampling frequency is
+ 
+
+ align:start position:0%
+kilohertz and the sampling frequency is
+2 PI over capital T so you clear the
+
+ align:start position:0%
+2 PI over capital T so you clear the
+ 
+
+ align:start position:0%
+2 PI over capital T so you clear the
+fraction and figure out the T has to be
+
+ align:start position:0%
+fraction and figure out the T has to be
+ 
+
+ align:start position:0%
+fraction and figure out the T has to be
+smaller than 25 microseconds okay okay
+
+ align:start position:0%
+smaller than 25 microseconds okay okay
+ 
+
+ align:start position:0%
+smaller than 25 microseconds okay okay
+so the idea then is that there's a way
+
+ align:start position:0%
+so the idea then is that there's a way
+ 
+
+ align:start position:0%
+so the idea then is that there's a way
+of thinking about any signal with a
+
+ align:start position:0%
+of thinking about any signal with a
+ 
+
+ align:start position:0%
+of thinking about any signal with a
+finite bandwidth there's a way of
+
+ align:start position:0%
+finite bandwidth there's a way of
+ 
+
+ align:start position:0%
+finite bandwidth there's a way of
+sampling using uniform sampling so that
+
+ align:start position:0%
+sampling using uniform sampling so that
+ 
+
+ align:start position:0%
+sampling using uniform sampling so that
+you can sample that signal without loss
+
+ align:start position:0%
+you can sample that signal without loss
+ 
+
+ align:start position:0%
+you can sample that signal without loss
+of information all you need to do is
+
+ align:start position:0%
+of information all you need to do is
+ 
+
+ align:start position:0%
+of information all you need to do is
+figure out how frequently you need the
+
+ align:start position:0%
+figure out how frequently you need the
+ 
+
+ align:start position:0%
+figure out how frequently you need the
+Sandpoint yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a signal is not band-limited you have
+
+ align:start position:0%
+if a signal is not band-limited you have
+ 
+
+ align:start position:0%
+if a signal is not band-limited you have
+a problem so the question is what is to
+
+ align:start position:0%
+a problem so the question is what is to
+ 
+
+ align:start position:0%
+a problem so the question is what is to
+what extent is it possible to sample a
+
+ align:start position:0%
+what extent is it possible to sample a
+ 
+
+ align:start position:0%
+what extent is it possible to sample a
+signal that is not band-limited so
+
+ align:start position:0%
+signal that is not band-limited so
+ 
+
+ align:start position:0%
+signal that is not band-limited so
+that's the next topic so the question is
+
+ align:start position:0%
+that's the next topic so the question is
+ 
+
+ align:start position:0%
+that's the next topic so the question is
+the the question I'm going to address
+
+ align:start position:0%
+the the question I'm going to address
+ 
+
+ align:start position:0%
+the the question I'm going to address
+now is well what happens if you don't
+
+ align:start position:0%
+now is well what happens if you don't
+ 
+
+ align:start position:0%
+now is well what happens if you don't
+satisfy the sampling theorem what if
+
+ align:start position:0%
+satisfy the sampling theorem what if
+ 
+
+ align:start position:0%
+satisfy the sampling theorem what if
+there are frequency components that are
+
+ align:start position:0%
+there are frequency components that are
+ 
+
+ align:start position:0%
+there are frequency components that are
+outside the admissible band the the
+
+ align:start position:0%
+outside the admissible band the the
+ 
+
+ align:start position:0%
+outside the admissible band the the
+Missal the admissible region of
+
+ align:start position:0%
+Missal the admissible region of
+ 
+
+ align:start position:0%
+Missal the admissible region of
+frequencies okay so to think about that
+
+ align:start position:0%
+frequencies okay so to think about that
+ 
+
+ align:start position:0%
+frequencies okay so to think about that
+I'm going to think about this as a model
+
+ align:start position:0%
+I'm going to think about this as a model
+ 
+
+ align:start position:0%
+I'm going to think about this as a model
+of sampling so I think about and the
+
+ align:start position:0%
+of sampling so I think about and the
+ 
+
+ align:start position:0%
+of sampling so I think about and the
+value of the model is it is entirely in
+
+ align:start position:0%
+value of the model is it is entirely in
+ 
+
+ align:start position:0%
+value of the model is it is entirely in
+CT it gets confusing when you mix
+
+ align:start position:0%
+CT it gets confusing when you mix
+ 
+
+ align:start position:0%
+CT it gets confusing when you mix
+domains and you have to compare this
+
+ align:start position:0%
+domains and you have to compare this
+ 
+
+ align:start position:0%
+domains and you have to compare this
+kind of a frequency to that kind of a
+
+ align:start position:0%
+kind of a frequency to that kind of a
+ 
+
+ align:start position:0%
+kind of a frequency to that kind of a
+frequency so what I'm going to do is
+
+ align:start position:0%
+frequency so what I'm going to do is
+ 
+
+ align:start position:0%
+frequency so what I'm going to do is
+think about it entirely in CT by making
+
+ align:start position:0%
+think about it entirely in CT by making
+ 
+
+ align:start position:0%
+think about it entirely in CT by making
+a model of how sampling works sampling
+
+ align:start position:0%
+a model of how sampling works sampling
+ 
+
+ align:start position:0%
+a model of how sampling works sampling
+is equivalent to take the original
+
+ align:start position:0%
+is equivalent to take the original
+ 
+
+ align:start position:0%
+is equivalent to take the original
+signal that you're trying to sample
+
+ align:start position:0%
+signal that you're trying to sample
+ 
+
+ align:start position:0%
+signal that you're trying to sample
+multiplied by an impulse train showed
+
+ align:start position:0%
+multiplied by an impulse train showed
+ 
+
+ align:start position:0%
+multiplied by an impulse train showed
+here you get out this XP thing that
+
+ align:start position:0%
+here you get out this XP thing that
+ 
+
+ align:start position:0%
+here you get out this XP thing that
+we've been talking about and then run
+
+ align:start position:0%
+we've been talking about and then run
+ 
+
+ align:start position:0%
+we've been talking about and then run
+that through an ideal low-pass filter
+
+ align:start position:0%
+that through an ideal low-pass filter
+ 
+
+ align:start position:0%
+that through an ideal low-pass filter
+and if this comes out looking like that
+
+ align:start position:0%
+and if this comes out looking like that
+ 
+
+ align:start position:0%
+and if this comes out looking like that
+then it was the it can be sampling
+
+ align:start position:0%
+then it was the it can be sampling
+ 
+
+ align:start position:0%
+then it was the it can be sampling
+preserves all of the information now
+
+ align:start position:0%
+preserves all of the information now
+ 
+
+ align:start position:0%
+preserves all of the information now
+what I want to do is think about what
+
+ align:start position:0%
+what I want to do is think about what
+ 
+
+ align:start position:0%
+what I want to do is think about what
+happens when I put in a signal for which
+
+ align:start position:0%
+happens when I put in a signal for which
+ 
+
+ align:start position:0%
+happens when I put in a signal for which
+that doesn't hold so let's start with
+
+ align:start position:0%
+that doesn't hold so let's start with
+ 
+
+ align:start position:0%
+that doesn't hold so let's start with
+the simplest possible case let's think
+
+ align:start position:0%
+the simplest possible case let's think
+ 
+
+ align:start position:0%
+the simplest possible case let's think
+about a tone so a signal that contains a
+
+ align:start position:0%
+about a tone so a signal that contains a
+ 
+
+ align:start position:0%
+about a tone so a signal that contains a
+single frequency component so I'm
+
+ align:start position:0%
+single frequency component so I'm
+ 
+
+ align:start position:0%
+single frequency component so I'm
+representing that by so say a cosine
+
+ align:start position:0%
+representing that by so say a cosine
+ 
+
+ align:start position:0%
+representing that by so say a cosine
+wave cosine Omega naught T so I'm
+
+ align:start position:0%
+wave cosine Omega naught T so I'm
+ 
+
+ align:start position:0%
+wave cosine Omega naught T so I'm
+representing that by two impulses
+
+ align:start position:0%
+representing that by two impulses
+ 
+
+ align:start position:0%
+representing that by two impulses
+Euler's equation and I'm thinking about
+
+ align:start position:0%
+Euler's equation and I'm thinking about
+ 
+
+ align:start position:0%
+Euler's equation and I'm thinking about
+some sampling waveform where I'm looking
+
+ align:start position:0%
+some sampling waveform where I'm looking
+ 
+
+ align:start position:0%
+some sampling waveform where I'm looking
+at it here in frequency so the spacing
+
+ align:start position:0%
+at it here in frequency so the spacing
+ 
+
+ align:start position:0%
+at it here in frequency so the spacing
+is 2 pi over T and if the frequencies in
+
+ align:start position:0%
+is 2 pi over T and if the frequencies in
+ 
+
+ align:start position:0%
+is 2 pi over T and if the frequencies in
+the signal are smaller than half of the
+
+ align:start position:0%
+the signal are smaller than half of the
+ 
+
+ align:start position:0%
+the signal are smaller than half of the
+maximum frequency Omega s everything
+
+ align:start position:0%
+maximum frequency Omega s everything
+ 
+
+ align:start position:0%
+maximum frequency Omega s everything
+should work and you can sort of see in
+
+ align:start position:0%
+should work and you can sort of see in
+ 
+
+ align:start position:0%
+should work and you can sort of see in
+the Fourier picture what's happening
+
+ align:start position:0%
+the Fourier picture what's happening
+ 
+
+ align:start position:0%
+the Fourier picture what's happening
+when I convolve these two signals I'm
+
+ align:start position:0%
+when I convolve these two signals I'm
+ 
+
+ align:start position:0%
+when I convolve these two signals I'm
+multiplying in time so I'm convulsing in
+
+ align:start position:0%
+multiplying in time so I'm convulsing in
+ 
+
+ align:start position:0%
+multiplying in time so I'm convulsing in
+frequency when I convolve this with the
+
+ align:start position:0%
+frequency when I convolve this with the
+ 
+
+ align:start position:0%
+frequency when I convolve this with the
+impulse train this impulse brings this
+
+ align:start position:0%
+impulse train this impulse brings this
+ 
+
+ align:start position:0%
+impulse train this impulse brings this
+pair of frequencies here but this
+
+ align:start position:0%
+pair of frequencies here but this
+ 
+
+ align:start position:0%
+pair of frequencies here but this
+impulse brings this pair up here and
+
+ align:start position:0%
+impulse brings this pair up here and
+ 
+
+ align:start position:0%
+impulse brings this pair up here and
+then this one brings this pair up here
+
+ align:start position:0%
+then this one brings this pair up here
+ 
+
+ align:start position:0%
+then this one brings this pair up here
+so I repeat so I get a repetition then
+
+ align:start position:0%
+so I repeat so I get a repetition then
+ 
+
+ align:start position:0%
+so I repeat so I get a repetition then
+of the original two at integer multiples
+
+ align:start position:0%
+of the original two at integer multiples
+ 
+
+ align:start position:0%
+of the original two at integer multiples
+of Omega s ok so if I low pass filter
+
+ align:start position:0%
+of Omega s ok so if I low pass filter
+ 
+
+ align:start position:0%
+of Omega s ok so if I low pass filter
+then with the red line everything's fine
+
+ align:start position:0%
+then with the red line everything's fine
+ 
+
+ align:start position:0%
+then with the red line everything's fine
+I end up with a signal at the output the
+
+ align:start position:0%
+I end up with a signal at the output the
+ 
+
+ align:start position:0%
+I end up with a signal at the output the
+same as signals the input no problem
+
+ align:start position:0%
+same as signals the input no problem
+ 
+
+ align:start position:0%
+same as signals the input no problem
+what happens however as I increase
+
+ align:start position:0%
+what happens however as I increase
+ 
+
+ align:start position:0%
+what happens however as I increase
+frequency same thing the originals are
+
+ align:start position:0%
+frequency same thing the originals are
+ 
+
+ align:start position:0%
+frequency same thing the originals are
+reproduced here the modulation by this
+
+ align:start position:0%
+reproduced here the modulation by this
+ 
+
+ align:start position:0%
+reproduced here the modulation by this
+brings this up to here the low pass
+
+ align:start position:0%
+brings this up to here the low pass
+ 
+
+ align:start position:0%
+brings this up to here the low pass
+filter still separates it out the
+
+ align:start position:0%
+filter still separates it out the
+ 
+
+ align:start position:0%
+filter still separates it out the
+problem is here now I'm running into
+
+ align:start position:0%
+problem is here now I'm running into
+ 
+
+ align:start position:0%
+problem is here now I'm running into
+trouble because the the original signal
+
+ align:start position:0%
+trouble because the the original signal
+ 
+
+ align:start position:0%
+trouble because the the original signal
+fell right on the edge of my limit Omega
+
+ align:start position:0%
+fell right on the edge of my limit Omega
+ 
+
+ align:start position:0%
+fell right on the edge of my limit Omega
+s over 2 and the problem is even more
+
+ align:start position:0%
+s over 2 and the problem is even more
+ 
+
+ align:start position:0%
+s over 2 and the problem is even more
+clear if I go to an even higher
+
+ align:start position:0%
+clear if I go to an even higher
+ 
+
+ align:start position:0%
+clear if I go to an even higher
+frequency so now this component is
+
+ align:start position:0%
+frequency so now this component is
+ 
+
+ align:start position:0%
+frequency so now this component is
+coming out here which is outside the
+
+ align:start position:0%
+coming out here which is outside the
+ 
+
+ align:start position:0%
+coming out here which is outside the
+bought the box the thing that's
+
+ align:start position:0%
+bought the box the thing that's
+ 
+
+ align:start position:0%
+bought the box the thing that's
+happening though is that convolution
+
+ align:start position:0%
+happening though is that convolution
+ 
+
+ align:start position:0%
+happening though is that convolution
+with this guy is bringing in an element
+
+ align:start position:0%
+with this guy is bringing in an element
+ 
+
+ align:start position:0%
+with this guy is bringing in an element
+that is spaced by Omega s and it's now
+
+ align:start position:0%
+that is spaced by Omega s and it's now
+ 
+
+ align:start position:0%
+that is spaced by Omega s and it's now
+inside the box that's bad everybody see
+
+ align:start position:0%
+inside the box that's bad everybody see
+ 
+
+ align:start position:0%
+inside the box that's bad everybody see
+what's happening so I'm just studying
+
+ align:start position:0%
+what's happening so I'm just studying
+ 
+
+ align:start position:0%
+what's happening so I'm just studying
+what happens as I have one frequency and
+
+ align:start position:0%
+what happens as I have one frequency and
+ 
+
+ align:start position:0%
+what happens as I have one frequency and
+vary the frequency if I have a tone at a
+
+ align:start position:0%
+vary the frequency if I have a tone at a
+ 
+
+ align:start position:0%
+vary the frequency if I have a tone at a
+single frequency and I vary the
+
+ align:start position:0%
+single frequency and I vary the
+ 
+
+ align:start position:0%
+single frequency and I vary the
+frequency of the tone as long as the
+
+ align:start position:0%
+frequency of the tone as long as the
+ 
+
+ align:start position:0%
+frequency of the tone as long as the
+frequency is inside my limit Omega s
+
+ align:start position:0%
+frequency is inside my limit Omega s
+ 
+
+ align:start position:0%
+frequency is inside my limit Omega s
+over 2 I'm fine
+
+ align:start position:0%
+over 2 I'm fine
+ 
+
+ align:start position:0%
+over 2 I'm fine
+the low pass filter reconstructs the
+
+ align:start position:0%
+the low pass filter reconstructs the
+ 
+
+ align:start position:0%
+the low pass filter reconstructs the
+original but something bizarre happens
+
+ align:start position:0%
+original but something bizarre happens
+ 
+
+ align:start position:0%
+original but something bizarre happens
+whenever I'm outside and to see what's
+
+ align:start position:0%
+whenever I'm outside and to see what's
+ 
+
+ align:start position:0%
+whenever I'm outside and to see what's
+going on it's easy it's easiest to see
+
+ align:start position:0%
+going on it's easy it's easiest to see
+ 
+
+ align:start position:0%
+going on it's easy it's easiest to see
+what's going on by making a map between
+
+ align:start position:0%
+what's going on by making a map between
+ 
+
+ align:start position:0%
+what's going on by making a map between
+the input frequency and the apparent
+
+ align:start position:0%
+the input frequency and the apparent
+ 
+
+ align:start position:0%
+the input frequency and the apparent
+frequency the apparent frequency at the
+
+ align:start position:0%
+frequency the apparent frequency at the
+ 
+
+ align:start position:0%
+frequency the apparent frequency at the
+output so what happens if I'm at a low
+
+ align:start position:0%
+output so what happens if I'm at a low
+ 
+
+ align:start position:0%
+output so what happens if I'm at a low
+frequency I'm on a linear relationship
+
+ align:start position:0%
+frequency I'm on a linear relationship
+ 
+
+ align:start position:0%
+frequency I'm on a linear relationship
+between the
+
+ align:start position:0%
+between the
+ 
+
+ align:start position:0%
+between the
+put frequency output the output
+
+ align:start position:0%
+put frequency output the output
+ 
+
+ align:start position:0%
+put frequency output the output
+reproduces the input exactly and you can
+
+ align:start position:0%
+reproduces the input exactly and you can
+ 
+
+ align:start position:0%
+reproduces the input exactly and you can
+see as I'm increasing the frequency I'm
+
+ align:start position:0%
+see as I'm increasing the frequency I'm
+ 
+
+ align:start position:0%
+see as I'm increasing the frequency I'm
+just sampling this function at a
+
+ align:start position:0%
+just sampling this function at a
+ 
+
+ align:start position:0%
+just sampling this function at a
+different place but when I go higher it
+
+ align:start position:0%
+different place but when I go higher it
+ 
+
+ align:start position:0%
+different place but when I go higher it
+appears as though the frequency got
+
+ align:start position:0%
+appears as though the frequency got
+ 
+
+ align:start position:0%
+appears as though the frequency got
+smaller okay
+
+ align:start position:0%
+smaller okay
+ 
+
+ align:start position:0%
+smaller okay
+we call that aliasing this is a question
+
+ align:start position:0%
+we call that aliasing this is a question
+ 
+
+ align:start position:0%
+we call that aliasing this is a question
+to get you to think through alias angle
+
+ align:start position:0%
+to get you to think through alias angle
+ 
+
+ align:start position:0%
+to get you to think through alias angle
+but in the interest of time because I
+
+ align:start position:0%
+but in the interest of time because I
+ 
+
+ align:start position:0%
+but in the interest of time because I
+have a demo I'll leave this for you to
+
+ align:start position:0%
+have a demo I'll leave this for you to
+ 
+
+ align:start position:0%
+have a demo I'll leave this for you to
+think about so the question is thinking
+
+ align:start position:0%
+think about so the question is thinking
+ 
+
+ align:start position:0%
+think about so the question is thinking
+about what's the effect of aliasing and
+
+ align:start position:0%
+about what's the effect of aliasing and
+ 
+
+ align:start position:0%
+about what's the effect of aliasing and
+where do the new frequencies land
+
+ align:start position:0%
+where do the new frequencies land
+ 
+
+ align:start position:0%
+where do the new frequencies land
+relative to the input frequency right
+
+ align:start position:0%
+relative to the input frequency right
+ 
+
+ align:start position:0%
+relative to the input frequency right
+they have this funny folding property
+
+ align:start position:0%
+they have this funny folding property
+ 
+
+ align:start position:0%
+they have this funny folding property
+and the effect of the folding property
+
+ align:start position:0%
+and the effect of the folding property
+ 
+
+ align:start position:0%
+and the effect of the folding property
+kind of wreaks havoc so I'll skip this
+
+ align:start position:0%
+kind of wreaks havoc so I'll skip this
+ 
+
+ align:start position:0%
+kind of wreaks havoc so I'll skip this
+for now and just jump to the idea that
+
+ align:start position:0%
+for now and just jump to the idea that
+ 
+
+ align:start position:0%
+for now and just jump to the idea that
+the intuition that we get by thinking
+
+ align:start position:0%
+the intuition that we get by thinking
+ 
+
+ align:start position:0%
+the intuition that we get by thinking
+about single frequencies carries over to
+
+ align:start position:0%
+about single frequencies carries over to
+ 
+
+ align:start position:0%
+about single frequencies carries over to
+complex frequency representations so now
+
+ align:start position:0%
+complex frequency representations so now
+ 
+
+ align:start position:0%
+complex frequency representations so now
+what if my message what if my input had
+
+ align:start position:0%
+what if my message what if my input had
+ 
+
+ align:start position:0%
+what if my message what if my input had
+this triangular frequency Fourier
+
+ align:start position:0%
+this triangular frequency Fourier
+ 
+
+ align:start position:0%
+this triangular frequency Fourier
+transform rather than just a single
+
+ align:start position:0%
+transform rather than just a single
+ 
+
+ align:start position:0%
+transform rather than just a single
+spike and so I'm sampling it as showed
+
+ align:start position:0%
+spike and so I'm sampling it as showed
+ 
+
+ align:start position:0%
+spike and so I'm sampling it as showed
+here so this is my impulse training
+
+ align:start position:0%
+here so this is my impulse training
+ 
+
+ align:start position:0%
+here so this is my impulse training
+frequency and as before the message gets
+
+ align:start position:0%
+frequency and as before the message gets
+ 
+
+ align:start position:0%
+frequency and as before the message gets
+reproduced at integer multiples of Omega
+
+ align:start position:0%
+reproduced at integer multiples of Omega
+ 
+
+ align:start position:0%
+reproduced at integer multiples of Omega
+s and as long as the bandwidth of the
+
+ align:start position:0%
+s and as long as the bandwidth of the
+ 
+
+ align:start position:0%
+s and as long as the bandwidth of the
+message is small enough I can put the
+
+ align:start position:0%
+message is small enough I can put the
+ 
+
+ align:start position:0%
+message is small enough I can put the
+read low pass filter to sample to
+
+ align:start position:0%
+read low pass filter to sample to
+ 
+
+ align:start position:0%
+read low pass filter to sample to
+eliminate the copies from the periodic
+
+ align:start position:0%
+eliminate the copies from the periodic
+ 
+
+ align:start position:0%
+eliminate the copies from the periodic
+extension and I get an output that's
+
+ align:start position:0%
+extension and I get an output that's
+ 
+
+ align:start position:0%
+extension and I get an output that's
+equal to the input the problem is that
+
+ align:start position:0%
+equal to the input the problem is that
+ 
+
+ align:start position:0%
+equal to the input the problem is that
+if I increase the bandwidth of the
+
+ align:start position:0%
+if I increase the bandwidth of the
+ 
+
+ align:start position:0%
+if I increase the bandwidth of the
+implant as I increase the bandwidth of
+
+ align:start position:0%
+implant as I increase the bandwidth of
+ 
+
+ align:start position:0%
+implant as I increase the bandwidth of
+the input the margin between the base
+
+ align:start position:0%
+the input the margin between the base
+ 
+
+ align:start position:0%
+the input the margin between the base
+signal and the periodic extension gets
+
+ align:start position:0%
+signal and the periodic extension gets
+ 
+
+ align:start position:0%
+signal and the periodic extension gets
+smaller and if the free and if the
+
+ align:start position:0%
+smaller and if the free and if the
+ 
+
+ align:start position:0%
+smaller and if the free and if the
+bandwidth gets too great they begin to
+
+ align:start position:0%
+bandwidth gets too great they begin to
+ 
+
+ align:start position:0%
+bandwidth gets too great they begin to
+overlap so now if I low-pass filter this
+
+ align:start position:0%
+overlap so now if I low-pass filter this
+ 
+
+ align:start position:0%
+overlap so now if I low-pass filter this
+signal I pick up the desired blue part
+
+ align:start position:0%
+signal I pick up the desired blue part
+ 
+
+ align:start position:0%
+signal I pick up the desired blue part
+of this but the undesired green part
+
+ align:start position:0%
+of this but the undesired green part
+ 
+
+ align:start position:0%
+of this but the undesired green part
+that okay and the result is that the
+
+ align:start position:0%
+that okay and the result is that the
+ 
+
+ align:start position:0%
+that okay and the result is that the
+signal is not a faithful reproduction of
+
+ align:start position:0%
+signal is not a faithful reproduction of
+ 
+
+ align:start position:0%
+signal is not a faithful reproduction of
+what I started with same sort of thing
+
+ align:start position:0%
+what I started with same sort of thing
+ 
+
+ align:start position:0%
+what I started with same sort of thing
+happens if I hold the message of
+
+ align:start position:0%
+happens if I hold the message of
+ 
+
+ align:start position:0%
+happens if I hold the message of
+constant and change the frequency space
+
+ align:start position:0%
+constant and change the frequency space
+ 
+
+ align:start position:0%
+constant and change the frequency space
+angle as long as I sample with big
+
+ align:start position:0%
+angle as long as I sample with big
+ 
+
+ align:start position:0%
+angle as long as I sample with big
+enough frequencies that is small enough
+
+ align:start position:0%
+enough frequencies that is small enough
+ 
+
+ align:start position:0%
+enough frequencies that is small enough
+times there's an inverse relationship
+
+ align:start position:0%
+times there's an inverse relationship
+ 
+
+ align:start position:0%
+times there's an inverse relationship
+between frequency and time if the
+
+ align:start position:0%
+between frequency and time if the
+ 
+
+ align:start position:0%
+between frequency and time if the
+frequency is big enough so the times are
+
+ align:start position:0%
+frequency is big enough so the times are
+ 
+
+ align:start position:0%
+frequency is big enough so the times are
+short enough I can reproduce what the
+
+ align:start position:0%
+short enough I can reproduce what the
+ 
+
+ align:start position:0%
+short enough I can reproduce what the
+out what the signal looked like but now
+
+ align:start position:0%
+out what the signal looked like but now
+ 
+
+ align:start position:0%
+out what the signal looked like but now
+if I change the sampling to happen
+
+ align:start position:0%
+if I change the sampling to happen
+ 
+
+ align:start position:0%
+if I change the sampling to happen
+slower I start to get aliasing so it's
+
+ align:start position:0%
+slower I start to get aliasing so it's
+ 
+
+ align:start position:0%
+slower I start to get aliasing so it's
+exactly analogous so that means that if
+
+ align:start position:0%
+exactly analogous so that means that if
+ 
+
+ align:start position:0%
+exactly analogous so that means that if
+you have a fixed signal there's some
+
+ align:start position:0%
+you have a fixed signal there's some
+ 
+
+ align:start position:0%
+you have a fixed signal there's some
+minimum rate at which you have to sample
+
+ align:start position:0%
+minimum rate at which you have to sample
+ 
+
+ align:start position:0%
+minimum rate at which you have to sample
+it in order to not lose information so
+
+ align:start position:0%
+it in order to not lose information so
+ 
+
+ align:start position:0%
+it in order to not lose information so
+what I want to do now is demonstrate
+
+ align:start position:0%
+what I want to do now is demonstrate
+ 
+
+ align:start position:0%
+what I want to do now is demonstrate
+that by thinking about music so I have a
+
+ align:start position:0%
+that by thinking about music so I have a
+ 
+
+ align:start position:0%
+that by thinking about music so I have a
+cut of music that I have that was
+
+ align:start position:0%
+cut of music that I have that was
+ 
+
+ align:start position:0%
+cut of music that I have that was
+originally taken from a CD so it was
+
+ align:start position:0%
+originally taken from a CD so it was
+ 
+
+ align:start position:0%
+originally taken from a CD so it was
+sampled at forty four point one
+
+ align:start position:0%
+sampled at forty four point one
+ 
+
+ align:start position:0%
+sampled at forty four point one
+kilohertz that's standard CD frequency
+
+ align:start position:0%
+kilohertz that's standard CD frequency
+ 
+
+ align:start position:0%
+kilohertz that's standard CD frequency
+sampling and ivory sampled it at 1/2 1/4
+
+ align:start position:0%
+sampling and ivory sampled it at 1/2 1/4
+ 
+
+ align:start position:0%
+sampling and ivory sampled it at 1/2 1/4
+1/8 1/16 and I'm going to play what
+
+ align:start position:0%
+1/8 1/16 and I'm going to play what
+ 
+
+ align:start position:0%
+1/8 1/16 and I'm going to play what
+happens when I do these various
+
+ align:start position:0%
+happens when I do these various
+ 
+
+ align:start position:0%
+happens when I do these various
+resampling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some of you may have been able to
+
+ align:start position:0%
+okay some of you may have been able to
+ 
+
+ align:start position:0%
+okay some of you may have been able to
+tell the difference so the idea is that
+
+ align:start position:0%
+tell the difference so the idea is that
+ 
+
+ align:start position:0%
+tell the difference so the idea is that
+by decreasing the rate at which I'm
+
+ align:start position:0%
+by decreasing the rate at which I'm
+ 
+
+ align:start position:0%
+by decreasing the rate at which I'm
+sampling it in time I get fewer samples
+
+ align:start position:0%
+sampling it in time I get fewer samples
+ 
+
+ align:start position:0%
+sampling it in time I get fewer samples
+in the total signal which makes it
+
+ align:start position:0%
+in the total signal which makes it
+ 
+
+ align:start position:0%
+in the total signal which makes it
+easier to store and increases the amount
+
+ align:start position:0%
+easier to store and increases the amount
+ 
+
+ align:start position:0%
+easier to store and increases the amount
+of stuff that I could put on a given
+
+ align:start position:0%
+of stuff that I could put on a given
+ 
+
+ align:start position:0%
+of stuff that I could put on a given
+medium that's good problem is it doesn't
+
+ align:start position:0%
+medium that's good problem is it doesn't
+ 
+
+ align:start position:0%
+medium that's good problem is it doesn't
+sound this good right so every step down
+
+ align:start position:0%
+sound this good right so every step down
+ 
+
+ align:start position:0%
+sound this good right so every step down
+this path resulted in half the
+
+ align:start position:0%
+this path resulted in half the
+ 
+
+ align:start position:0%
+this path resulted in half the
+information of the previous one which
+
+ align:start position:0%
+information of the previous one which
+ 
+
+ align:start position:0%
+information of the previous one which
+means that I could double the capacity
+
+ align:start position:0%
+means that I could double the capacity
+ 
+
+ align:start position:0%
+means that I could double the capacity
+of your mp3 player okay but there was
+
+ align:start position:0%
+of your mp3 player okay but there was
+ 
+
+ align:start position:0%
+of your mp3 player okay but there was
+distortions added because of this
+
+ align:start position:0%
+distortions added because of this
+ 
+
+ align:start position:0%
+distortions added because of this
+aliasing problem right because some of
+
+ align:start position:0%
+aliasing problem right because some of
+ 
+
+ align:start position:0%
+aliasing problem right because some of
+the frequencies at the lower sampling
+
+ align:start position:0%
+the frequencies at the lower sampling
+ 
+
+ align:start position:0%
+the frequencies at the lower sampling
+rates were too large to be faithfully
+
+ align:start position:0%
+rates were too large to be faithfully
+ 
+
+ align:start position:0%
+rates were too large to be faithfully
+reproduced by the sampling right they
+
+ align:start position:0%
+reproduced by the sampling right they
+ 
+
+ align:start position:0%
+reproduced by the sampling right they
+got moved they got alias to the wrong
+
+ align:start position:0%
+got moved they got alias to the wrong
+ 
+
+ align:start position:0%
+got moved they got alias to the wrong
+place that gives rise to sounds that are
+
+ align:start position:0%
+place that gives rise to sounds that are
+ 
+
+ align:start position:0%
+place that gives rise to sounds that are
+in harmonic and they sound bad
+
+ align:start position:0%
+in harmonic and they sound bad
+ 
+
+ align:start position:0%
+in harmonic and they sound bad
+okay so so yeah so this just
+
+ align:start position:0%
+okay so so yeah so this just
+ 
+
+ align:start position:0%
+okay so so yeah so this just
+recapitulates what we what we were
+
+ align:start position:0%
+recapitulates what we what we were
+ 
+
+ align:start position:0%
+recapitulates what we what we were
+seeing in the demo I started out barely
+
+ align:start position:0%
+seeing in the demo I started out barely
+ 
+
+ align:start position:0%
+seeing in the demo I started out barely
+having enough bandwidth to represent the
+
+ align:start position:0%
+having enough bandwidth to represent the
+ 
+
+ align:start position:0%
+having enough bandwidth to represent the
+original signal and as I made the
+
+ align:start position:0%
+original signal and as I made the
+ 
+
+ align:start position:0%
+original signal and as I made the
+sampling frequency smaller making the
+
+ align:start position:0%
+sampling frequency smaller making the
+ 
+
+ align:start position:0%
+sampling frequency smaller making the
+the distance between samples bigger as I
+
+ align:start position:0%
+the distance between samples bigger as I
+ 
+
+ align:start position:0%
+the distance between samples bigger as I
+made the frequency of the sampling
+
+ align:start position:0%
+made the frequency of the sampling
+ 
+
+ align:start position:0%
+made the frequency of the sampling
+smaller I started to get overlap and
+
+ align:start position:0%
+smaller I started to get overlap and
+ 
+
+ align:start position:0%
+smaller I started to get overlap and
+that's what sounded funny so the more
+
+ align:start position:0%
+that's what sounded funny so the more
+ 
+
+ align:start position:0%
+that's what sounded funny so the more
+the slower I sampled the more overlap
+
+ align:start position:0%
+the slower I sampled the more overlap
+ 
+
+ align:start position:0%
+the slower I sampled the more overlap
+and the funnier it sounded so the
+
+ align:start position:0%
+and the funnier it sounded so the
+ 
+
+ align:start position:0%
+and the funnier it sounded so the
+question is what can you do well how can
+
+ align:start position:0%
+question is what can you do well how can
+ 
+
+ align:start position:0%
+question is what can you do well how can
+you deal with that one way you can deal
+
+ align:start position:0%
+you deal with that one way you can deal
+ 
+
+ align:start position:0%
+you deal with that one way you can deal
+with that is what we call anti aliasing
+
+ align:start position:0%
+with that is what we call anti aliasing
+ 
+
+ align:start position:0%
+with that is what we call anti aliasing
+okay so it's very bad if you put a
+
+ align:start position:0%
+okay so it's very bad if you put a
+ 
+
+ align:start position:0%
+okay so it's very bad if you put a
+frequency into a sampling system where
+
+ align:start position:0%
+frequency into a sampling system where
+ 
+
+ align:start position:0%
+frequency into a sampling system where
+the frequency is too big to be
+
+ align:start position:0%
+the frequency is too big to be
+ 
+
+ align:start position:0%
+the frequency is too big to be
+faithfully reproduced because it comes
+
+ align:start position:0%
+faithfully reproduced because it comes
+ 
+
+ align:start position:0%
+faithfully reproduced because it comes
+out at a different frequency that cannot
+
+ align:start position:0%
+out at a different frequency that cannot
+ 
+
+ align:start position:0%
+out at a different frequency that cannot
+be determined from the output alone so
+
+ align:start position:0%
+be determined from the output alone so
+ 
+
+ align:start position:0%
+be determined from the output alone so
+how can you deal with that one way you
+
+ align:start position:0%
+how can you deal with that one way you
+ 
+
+ align:start position:0%
+how can you deal with that one way you
+can deal with it is to prease pre-filter
+
+ align:start position:0%
+can deal with it is to prease pre-filter
+ 
+
+ align:start position:0%
+can deal with it is to prease pre-filter
+take out everything that could be
+
+ align:start position:0%
+take out everything that could be
+ 
+
+ align:start position:0%
+take out everything that could be
+offensive
+
+ align:start position:0%
+offensive
+ 
+
+ align:start position:0%
+offensive
+before you sample that's called
+
+ align:start position:0%
+before you sample that's called
+ 
+
+ align:start position:0%
+before you sample that's called
+anti-aliasing and the result is not
+
+ align:start position:0%
+anti-aliasing and the result is not
+ 
+
+ align:start position:0%
+anti-aliasing and the result is not
+faithful reproduction of the original
+
+ align:start position:0%
+faithful reproduction of the original
+ 
+
+ align:start position:0%
+faithful reproduction of the original
+but it's at least faithful reproduction
+
+ align:start position:0%
+but it's at least faithful reproduction
+ 
+
+ align:start position:0%
+but it's at least faithful reproduction
+of the part of the band that is
+
+ align:start position:0%
+of the part of the band that is
+ 
+
+ align:start position:0%
+of the part of the band that is
+reproduced okay so it's not distortion
+
+ align:start position:0%
+reproduced okay so it's not distortion
+ 
+
+ align:start position:0%
+reproduced okay so it's not distortion
+free the transformation from the very
+
+ align:start position:0%
+free the transformation from the very
+ 
+
+ align:start position:0%
+free the transformation from the very
+input to the very output is not this
+
+ align:start position:0%
+input to the very output is not this
+ 
+
+ align:start position:0%
+input to the very output is not this
+there's not a unity transformation
+
+ align:start position:0%
+there's not a unity transformation
+ 
+
+ align:start position:0%
+there's not a unity transformation
+because you violated the sampling
+
+ align:start position:0%
+because you violated the sampling
+ 
+
+ align:start position:0%
+because you violated the sampling
+theorem but at least you don't elias
+
+ align:start position:0%
+theorem but at least you don't elias
+ 
+
+ align:start position:0%
+theorem but at least you don't elias
+frequencies - they're wrong place so the
+
+ align:start position:0%
+frequencies - they're wrong place so the
+ 
+
+ align:start position:0%
+frequencies - they're wrong place so the
+result I'll play so without
+
+ align:start position:0%
+result I'll play so without
+ 
+
+ align:start position:0%
+result I'll play so without
+anti-aliasing without anti-aliasing
+
+ align:start position:0%
+anti-aliasing without anti-aliasing
+ 
+
+ align:start position:0%
+anti-aliasing without anti-aliasing
+without with without with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the final one didn't sound
+
+ align:start position:0%
+okay so the final one didn't sound
+ 
+
+ align:start position:0%
+okay so the final one didn't sound
+exactly like the original but at least
+
+ align:start position:0%
+exactly like the original but at least
+ 
+
+ align:start position:0%
+exactly like the original but at least
+it wasn't grating so the idea then is
+
+ align:start position:0%
+it wasn't grating so the idea then is
+ 
+
+ align:start position:0%
+it wasn't grating so the idea then is
+just that sampling is very important and
+
+ align:start position:0%
+just that sampling is very important and
+ 
+
+ align:start position:0%
+just that sampling is very important and
+by thinking about in the Fourier domain
+
+ align:start position:0%
+by thinking about in the Fourier domain
+ 
+
+ align:start position:0%
+by thinking about in the Fourier domain
+we get a lot of insights that we
+
+ align:start position:0%
+we get a lot of insights that we
+ 
+
+ align:start position:0%
+we get a lot of insights that we
+wouldn't have got otherwise see you
+
+ align:start position:0%
+wouldn't have got otherwise see you
+ 
+
+ align:start position:0%
+wouldn't have got otherwise see you
+tomorrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/1eIFnKOZ-oY.txt b/1eIFnKOZ-oY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9fe8177d77a03f2965c94cd18959a50fc29599ed
--- /dev/null
+++ b/1eIFnKOZ-oY.txt
@@ -0,0 +1,340 @@
+In this lecture you'll learn various techniques
+for creating combinational logic circuits
+
+that implement a particular functional specification.
+
+A functional specification is part of the
+static discipline we use to create the combinational
+
+logic abstraction of a circuit.
+
+One approach is to use natural language to
+describe the operation of a device.
+
+This approach has its pros and cons.
+
+In its favor, natural language can convey
+complicated concepts in surprisingly compact
+
+form and it is a notation that most of us
+know how to read and understand.
+
+But, unless the words are very carefully crafted,
+there may be ambiguities introduced by words
+
+with multiple interpretations or by lack of
+completeness since it's not always obvious
+
+whether all eventualities have been dealt
+with.
+
+There are good alternatives that address the
+shortcomings mentioned above.
+
+Truth tables are a straightforward tabular
+representation that specifies the values of
+
+the outputs for each possible combination
+of the digital inputs.
+
+If a device has N digital inputs, its truth
+table will have 2^N rows.
+
+In the example shown here, the device has
+3 inputs, each of which can have the value
+
+0 or the value 1.
+
+There are 2*2*2 = 2^3 = 8 combinations of
+the three input values, so there are 8 rows
+
+in the truth table.
+
+It's straightforward to systematically enumerate
+the 8 combinations, which makes it easy to
+
+ensure that no combination is omitted when
+building the specification.
+
+And since the output values are specified
+explicitly, there isn't much room for misinterpreting
+
+the desired functionality!
+
+Truth tables are an excellent choice for devices
+with small numbers of inputs and outputs.
+
+Sadly, they aren't really practical when the
+devices have many inputs.
+
+If, for example, we were describing the functionality
+of a circuit to add two 32-bit numbers, there
+
+would be 64 inputs altogether and the truth
+table would need 2^64 rows.
+
+Hmm, not sure how practical that is!
+
+If we entered the correct output value for
+a row once per second, it would take 584 billion
+
+years to fill in the table!
+
+Another alternative specification is to use
+Boolean equations to describe how to compute
+
+the output values from the input values using
+Boolean algebra.
+
+The operations we use are the logical operations
+AND, OR, and XOR, each of which takes two
+
+Boolean operands, and NOT which takes a single
+Boolean operand.
+
+Using the truth tables that describe these
+logical operations, it's straightforward to
+
+compute an output value from a particular
+combination of input values using the sequence
+
+of operations laid out in the equation.
+
+Let me say a quick word about the notation
+used for Boolean equations.
+
+Input values are represented by the name of
+the input, in this example one of "A", "B",
+
+or "C".
+
+The digital input value 0 is equivalent to
+the Boolean value FALSE and the digital input
+
+value 1 is equivalent to the Boolean value
+TRUE.
+
+The Boolean operation NOT is indicated by
+a horizontal line drawn above a Boolean expression.
+
+In this example, the first symbol following
+the equal sign is a "C" with line above it,
+
+indicating that the value of C should be inverted
+before it's used in evaluating the rest of
+
+the expression.
+
+The Boolean operation AND is represented by
+the multiplication operation using standard
+
+mathematical notation.
+
+Sometimes we'll use an explicit multiplication
+operator - usually written as a dot between
+
+two Boolean expressions - as shown in the
+first term of the example equation.
+
+Sometimes the AND operator is implicit as
+shown in the remaining three terms of the
+
+example equation.
+
+The Boolean operation OR is represented by
+the addition operation, always shown as a
+
+"+" sign.
+
+Boolean equations are useful when the device
+has many inputs.
+
+And, as we'll see, it's easy to convert a
+Boolean equation into a circuit schematic.
+
+Truth tables and Boolean equations are interchangeable.
+
+If we have a Boolean equation for each output,
+we can fill in the output columns for a row
+
+of the truth table by evaluating the Boolean
+equations using the particular combination
+
+of input values for that row.
+
+For example, to determine the value for Y
+in the first row of the truth table, we'd
+
+substitute the Boolean value FALSE for the
+symbols A, B, and C in the equation and then
+
+use Boolean algebra to compute the result.
+
+We can go the other way too.
+
+We can always convert a truth table into a
+particular form of Boolean equation called
+
+a sum-of-products.
+
+Let's see how…
+
+Start by looking at the truth table and answering
+the question "When does Y have the value 1?"
+
+Or, in the language of Boolean algebra: "When
+is Y TRUE?".
+
+Well, Y is TRUE when the inputs correspond
+to row 2 of the truth table, OR to row 4,
+
+OR to rows 7 OR 8.
+
+Altogether there are 4 combinations of inputs
+for which Y is TRUE.
+
+The corresponding Boolean equation thus is
+the OR for four terms, where each term is
+
+a boolean expression which evaluates to TRUE
+for a particular combination of inputs.
+
+Row 2 of the truth table corresponds to C=0,
+B=0, and A=1.
+
+The corresponding Boolean expression is (NOT
+C) AND (NOT B)
+
+AND A, an expression that evaluates to TRUE
+if and only if C is 0, B is 0, and A is 1.
+
+The boolean expression corresponding to row
+4 is (NOT C) AND B AND A.
+
+And so on for rows 7 and 8.
+
+The approach will always give us an expression
+in the form of a sum-of-products.
+
+"Sum" refers to the OR operations and "products"
+refers to the groups of AND operations.
+
+In this example we have the sum of four product
+terms.
+
+Our next step is to use the Boolean expression
+as a recipe for constructing a circuit implementation
+
+using combinational logic gates.
+
+As circuit designers we'll be working with
+a library of combinational logic gates, which
+
+either is given to us by the integrated circuit
+manufacturer, or which we've designed ourselves
+
+as CMOS gates using NFET and PFET switches.
+
+One of the simplest gates is the inverter,
+which has the schematic symbol shown here.
+
+The small circle on the output wire indicates
+an inversion, a common convention used in
+
+schematics.
+
+We can see from its truth table that the inverter
+implements the Boolean NOT function.
+
+The AND gate outputs 1 if and only if the
+A input is 1 *and* the B input is 1, hence
+
+the name "AND".
+
+The library will usually include AND gates
+with 3 inputs, 4 inputs, etc., which produce
+
+a 1 output if and only if all of their inputs
+are 1.
+
+The OR gate outputs 1 if the A input is 1
+*or* if the B input is 1, hence the name "OR".
+
+Again, the library will usually include OR
+gates with 3 inputs, 4 inputs, etc., which
+
+produce a 1 output when at least one of their
+inputs is 1.
+
+These are the standard schematic symbols for
+AND and OR gates.
+
+Note that the AND symbol is straight on the
+input side, while the OR symbol is curved.
+
+With a little practice, you'll find it easy
+to remember which schematic symbols are which.
+
+Now let's use these building blocks to build
+a circuit that implements a sum-of-products
+
+equation.
+
+The structure of the circuit exactly follows
+the structure of the Boolean equation.
+
+We use inverters to perform the necessary
+Boolean NOT operations.
+
+In a sum-of-products equation the inverters
+are operating on particular input values,
+
+in this case A, B and C.
+To keep the schematic easy to read we've used
+
+a separate inverter for each of the four NOT
+operations in the Boolean equation, but in
+
+real life we might invert the C input once
+to produce a NOT-C signal, then use that signal
+
+whenever a NOT-C value is needed.
+
+Each of the four product terms is built using
+a 3-input AND gate.
+
+And the product terms are ORed together using
+a 4-input OR gate.
+
+The final circuit has a layer of inverters,
+a layer of AND gates and final OR gate.
+
+In the next section we'll talk about how to
+build AND or OR gates with many inputs from
+
+library components with fewer inputs.
+
+The propagation delay for a sum-of-products
+circuit looks pretty short: the longest path
+
+from inputs to outputs includes an inverter,
+an AND gate and an OR gate.
+
+Can we really implement any Boolean equation
+in a circuit with a tPD of three gate delays?
+
+Actually not, since building ANDs and ORs
+with many inputs will require additional layers
+
+of components, which will increase the propagation
+delay.
+
+We'll learn about this in the next section.
+
+The good news is that we now have straightforward
+techniques for converting a truth table to
+
+its corresponding sum-of-products Boolean
+equation, and for building a circuit that
+
+implements that equation.
\ No newline at end of file
diff --git a/41ee6EsHchA.txt b/41ee6EsHchA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14d9d6378895ed05345c379cb3e9323c80252417
--- /dev/null
+++ b/41ee6EsHchA.txt
@@ -0,0 +1,2787 @@
+align:start position:0%
+ 
+okay so that's our introduction to the
+
+ align:start position:0%
+okay so that's our introduction to the
+ 
+
+ align:start position:0%
+okay so that's our introduction to the
+subject now we have to get going with to
+
+ align:start position:0%
+subject now we have to get going with to
+ 
+
+ align:start position:0%
+subject now we have to get going with to
+explore how to set up the scattering
+
+ align:start position:0%
+explore how to set up the scattering
+ 
+
+ align:start position:0%
+explore how to set up the scattering
+problem so equations that we need to
+
+ align:start position:0%
+problem so equations that we need to
+ 
+
+ align:start position:0%
+problem so equations that we need to
+solve well what are the equations we
+
+ align:start position:0%
+solve well what are the equations we
+ 
+
+ align:start position:0%
+solve well what are the equations we
+will have a Hamiltonian just P squared
+
+ align:start position:0%
+will have a Hamiltonian just P squared
+ 
+
+ align:start position:0%
+will have a Hamiltonian just P squared
+over 2m plus a potential V of R need not
+
+ align:start position:0%
+over 2m plus a potential V of R need not
+ 
+
+ align:start position:0%
+over 2m plus a potential V of R need not
+be yet a central potential as usual we
+
+ align:start position:0%
+be yet a central potential as usual we
+ 
+
+ align:start position:0%
+be yet a central potential as usual we
+will think of a wave function that
+
+ align:start position:0%
+will think of a wave function that
+ 
+
+ align:start position:0%
+will think of a wave function that
+depends on R and T that will be written
+
+ align:start position:0%
+depends on R and T that will be written
+ 
+
+ align:start position:0%
+depends on R and T that will be written
+a subside that depends on R times e to
+
+ align:start position:0%
+a subside that depends on R times e to
+ 
+
+ align:start position:0%
+a subside that depends on R times e to
+the minus I R an energy eigenstate and
+
+ align:start position:0%
+the minus I R an energy eigenstate and
+ 
+
+ align:start position:0%
+the minus I R an energy eigenstate and
+then the equation that you have to solve
+
+ align:start position:0%
+then the equation that you have to solve
+ 
+
+ align:start position:0%
+then the equation that you have to solve
+the time independent independent
+
+ align:start position:0%
+the time independent independent
+ 
+
+ align:start position:0%
+the time independent independent
+Schrodinger equation becomes minus H
+
+ align:start position:0%
+Schrodinger equation becomes minus H
+ 
+
+ align:start position:0%
+Schrodinger equation becomes minus H
+squared over 2m laplacian plus VF are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acting on so far is equal to e Phi of R
+
+ align:start position:0%
+acting on so far is equal to e Phi of R
+ 
+
+ align:start position:0%
+acting on so far is equal to e Phi of R
+so these are the equations that you have
+
+ align:start position:0%
+so these are the equations that you have
+ 
+
+ align:start position:0%
+so these are the equations that you have
+seen already endlessly in quantum
+
+ align:start position:0%
+seen already endlessly in quantum
+ 
+
+ align:start position:0%
+seen already endlessly in quantum
+mechanics these are equations we write
+
+ align:start position:0%
+mechanics these are equations we write
+ 
+
+ align:start position:0%
+mechanics these are equations we write
+to get warmed up and we just repeat for
+
+ align:start position:0%
+to get warmed up and we just repeat for
+ 
+
+ align:start position:0%
+to get warmed up and we just repeat for
+ourselves that we have a Hamiltonian in
+
+ align:start position:0%
+ourselves that we have a Hamiltonian in
+ 
+
+ align:start position:0%
+ourselves that we have a Hamiltonian in
+the picture where the particles are
+
+ align:start position:0%
+the picture where the particles are
+ 
+
+ align:start position:0%
+the picture where the particles are
+scattering off of a central potential
+
+ align:start position:0%
+scattering off of a central potential
+ 
+
+ align:start position:0%
+scattering off of a central potential
+not a potential a central potential in
+
+ align:start position:0%
+not a potential a central potential in
+ 
+
+ align:start position:0%
+not a potential a central potential in
+fact just off of a potential work with
+
+ align:start position:0%
+fact just off of a potential work with
+ 
+
+ align:start position:0%
+fact just off of a potential work with
+energy eigenstates and these are going
+
+ align:start position:0%
+energy eigenstates and these are going
+ 
+
+ align:start position:0%
+energy eigenstates and these are going
+to be the equation for the energy
+
+ align:start position:0%
+to be the equation for the energy
+ 
+
+ align:start position:0%
+to be the equation for the energy
+eigenstates now let's write the first
+
+ align:start position:0%
+eigenstates now let's write the first
+ 
+
+ align:start position:0%
+eigenstates now let's write the first
+picture of our picture of the scattering
+
+ align:start position:0%
+picture of our picture of the scattering
+ 
+
+ align:start position:0%
+picture of our picture of the scattering
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+is some sort of target here or potential
+
+ align:start position:0%
+is some sort of target here or potential
+ 
+
+ align:start position:0%
+is some sort of target here or potential
+and particles that come in and scatter
+
+ align:start position:0%
+and particles that come in and scatter
+ 
+
+ align:start position:0%
+and particles that come in and scatter
+off of this potential so we're looking
+
+ align:start position:0%
+off of this potential so we're looking
+ 
+
+ align:start position:0%
+off of this potential so we're looking
+for energy eigenstates and we will try
+
+ align:start position:0%
+for energy eigenstates and we will try
+ 
+
+ align:start position:0%
+for energy eigenstates and we will try
+to identify our energy eigenstates and
+
+ align:start position:0%
+to identify our energy eigenstates and
+ 
+
+ align:start position:0%
+to identify our energy eigenstates and
+what we're gonna see is that this
+
+ align:start position:0%
+what we're gonna see is that this
+ 
+
+ align:start position:0%
+what we're gonna see is that this
+potential is finite range as well range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite range we can deal with potentials
+
+ align:start position:0%
+finite range we can deal with potentials
+ 
+
+ align:start position:0%
+finite range we can deal with potentials
+that fall off relatively fast already
+
+ align:start position:0%
+that fall off relatively fast already
+ 
+
+ align:start position:0%
+that fall off relatively fast already
+the Coulomb potential doesn't fall off
+
+ align:start position:0%
+the Coulomb potential doesn't fall off
+ 
+
+ align:start position:0%
+the Coulomb potential doesn't fall off
+that fast but potentials that fall
+
+ align:start position:0%
+that fast but potentials that fall
+ 
+
+ align:start position:0%
+that fast but potentials that fall
+faster than the Coulomb potential
+
+ align:start position:0%
+faster than the Coulomb potential
+ 
+
+ align:start position:0%
+faster than the Coulomb potential
+potentially they're just localized which
+
+ align:start position:0%
+potentially they're just localized which
+ 
+
+ align:start position:0%
+potentially they're just localized which
+is it's pretty common if you have an
+
+ align:start position:0%
+is it's pretty common if you have an
+ 
+
+ align:start position:0%
+is it's pretty common if you have an
+atom and you scatter things off of it if
+
+ align:start position:0%
+atom and you scatter things off of it if
+ 
+
+ align:start position:0%
+atom and you scatter things off of it if
+it's a neutral atom the potential due to
+
+ align:start position:0%
+it's a neutral atom the potential due to
+ 
+
+ align:start position:0%
+it's a neutral atom the potential due to
+the atom is zero outside the atom but as
+
+ align:start position:0%
+the atom is zero outside the atom but as
+ 
+
+ align:start position:0%
+the atom is zero outside the atom but as
+soon as you go inside the atom you start
+
+ align:start position:0%
+soon as you go inside the atom you start
+ 
+
+ align:start position:0%
+soon as you go inside the atom you start
+experiences all the electric forces that
+
+ align:start position:0%
+experiences all the electric forces that
+ 
+
+ align:start position:0%
+experiences all the electric forces that
+are due to the nucleus and the electrons
+
+ align:start position:0%
+are due to the nucleus and the electrons
+ 
+
+ align:start position:0%
+are due to the nucleus and the electrons
+so a finite range potential and we're
+
+ align:start position:0%
+so a finite range potential and we're
+ 
+
+ align:start position:0%
+so a finite range potential and we're
+going to think of solutions that okay
+
+ align:start position:0%
+going to think of solutions that okay
+ 
+
+ align:start position:0%
+going to think of solutions that okay
+away from the finite range are plane
+
+ align:start position:0%
+away from the finite range are plane
+ 
+
+ align:start position:0%
+away from the finite range are plane
+waves solutions of constant energy
+
+ align:start position:0%
+waves solutions of constant energy
+ 
+
+ align:start position:0%
+waves solutions of constant energy
+specified with perhaps some momentum so
+
+ align:start position:0%
+specified with perhaps some momentum so
+ 
+
+ align:start position:0%
+specified with perhaps some momentum so
+we will think of E as H squared K
+
+ align:start position:0%
+we will think of E as H squared K
+ 
+
+ align:start position:0%
+we will think of E as H squared K
+squared over 2m this is a way of
+
+ align:start position:0%
+squared over 2m this is a way of
+ 
+
+ align:start position:0%
+squared over 2m this is a way of
+thinking of the energy of a given energy
+
+ align:start position:0%
+thinking of the energy of a given energy
+ 
+
+ align:start position:0%
+thinking of the energy of a given energy
+eigenstate so it's another label for the
+
+ align:start position:0%
+eigenstate so it's another label for the
+ 
+
+ align:start position:0%
+eigenstate so it's another label for the
+energy this one it looks like I've done
+
+ align:start position:0%
+energy this one it looks like I've done
+ 
+
+ align:start position:0%
+energy this one it looks like I've done
+something but I haven't done much except
+
+ align:start position:0%
+something but I haven't done much except
+ 
+
+ align:start position:0%
+something but I haven't done much except
+to begin an in equation process in your
+
+ align:start position:0%
+to begin an in equation process in your
+ 
+
+ align:start position:0%
+to begin an in equation process in your
+head in which somehow these are going to
+
+ align:start position:0%
+head in which somehow these are going to
+ 
+
+ align:start position:0%
+head in which somehow these are going to
+be related to energy eigenstates that
+
+ align:start position:0%
+be related to energy eigenstates that
+ 
+
+ align:start position:0%
+be related to energy eigenstates that
+have some momentum as they propagate all
+
+ align:start position:0%
+have some momentum as they propagate all
+ 
+
+ align:start position:0%
+have some momentum as they propagate all
+over space so if I ride that I can just
+
+ align:start position:0%
+over space so if I ride that I can just
+ 
+
+ align:start position:0%
+over space so if I ride that I can just
+simply put this on the left-hand side
+
+ align:start position:0%
+simply put this on the left-hand side
+ 
+
+ align:start position:0%
+simply put this on the left-hand side
+and get an equation that it's kind of
+
+ align:start position:0%
+and get an equation that it's kind of
+ 
+
+ align:start position:0%
+and get an equation that it's kind of
+nicer minus H squared over 2m laplacian
+
+ align:start position:0%
+nicer minus H squared over 2m laplacian
+ 
+
+ align:start position:0%
+nicer minus H squared over 2m laplacian
+square plus K squared plus VFR sIFR
+
+ align:start position:0%
+square plus K squared plus VFR sIFR
+ 
+
+ align:start position:0%
+square plus K squared plus VFR sIFR
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's not really a matter scattering
+
+ align:start position:0%
+okay it's not really a matter scattering
+ 
+
+ align:start position:0%
+okay it's not really a matter scattering
+up of solving this equation at this
+
+ align:start position:0%
+up of solving this equation at this
+ 
+
+ align:start position:0%
+up of solving this equation at this
+moment infinitely many solutions of this
+
+ align:start position:0%
+moment infinitely many solutions of this
+ 
+
+ align:start position:0%
+moment infinitely many solutions of this
+equation and most of them may not be
+
+ align:start position:0%
+equation and most of them may not be
+ 
+
+ align:start position:0%
+equation and most of them may not be
+relevant for us we're not trying to find
+
+ align:start position:0%
+relevant for us we're not trying to find
+ 
+
+ align:start position:0%
+relevant for us we're not trying to find
+every solution of this equation we're
+
+ align:start position:0%
+every solution of this equation we're
+ 
+
+ align:start position:0%
+every solution of this equation we're
+trying to find solutions that have
+
+ align:start position:0%
+trying to find solutions that have
+ 
+
+ align:start position:0%
+trying to find solutions that have
+something to do with the physics and
+
+ align:start position:0%
+something to do with the physics and
+ 
+
+ align:start position:0%
+something to do with the physics and
+you've done that when you had potentials
+
+ align:start position:0%
+you've done that when you had potentials
+ 
+
+ align:start position:0%
+you've done that when you had potentials
+in one dimension and that inclusion is
+
+ align:start position:0%
+in one dimension and that inclusion is
+ 
+
+ align:start position:0%
+in one dimension and that inclusion is
+going to prove invaluable so when you
+
+ align:start position:0%
+going to prove invaluable so when you
+ 
+
+ align:start position:0%
+going to prove invaluable so when you
+have a potential in one dimension you
+
+ align:start position:0%
+have a potential in one dimension you
+ 
+
+ align:start position:0%
+have a potential in one dimension you
+didn't say okay I'm gonna find all the
+
+ align:start position:0%
+didn't say okay I'm gonna find all the
+ 
+
+ align:start position:0%
+didn't say okay I'm gonna find all the
+energy eigenstates you you said let's
+
+ align:start position:0%
+energy eigenstates you you said let's
+ 
+
+ align:start position:0%
+energy eigenstates you you said let's
+search for things that are reasonable
+
+ align:start position:0%
+search for things that are reasonable
+ 
+
+ align:start position:0%
+search for things that are reasonable
+and physically motivated so you put in a
+
+ align:start position:0%
+and physically motivated so you put in a
+ 
+
+ align:start position:0%
+and physically motivated so you put in a
+wave that was moving in and you said
+
+ align:start position:0%
+wave that was moving in and you said
+ 
+
+ align:start position:0%
+wave that was moving in and you said
+okay this wave is a solution until it
+
+ align:start position:0%
+okay this wave is a solution until it
+ 
+
+ align:start position:0%
+okay this wave is a solution until it
+reaches this point where it just stops
+
+ align:start position:0%
+reaches this point where it just stops
+ 
+
+ align:start position:0%
+reaches this point where it just stops
+being a solution you need more if you
+
+ align:start position:0%
+being a solution you need more if you
+ 
+
+ align:start position:0%
+being a solution you need more if you
+put in this wave you will generate a
+
+ align:start position:0%
+put in this wave you will generate a
+ 
+
+ align:start position:0%
+put in this wave you will generate a
+reflected wave and a transmitted wave
+
+ align:start position:0%
+reflected wave and a transmitted wave
+ 
+
+ align:start position:0%
+reflected wave and a transmitted wave
+those two waves are gonna be generated
+
+ align:start position:0%
+those two waves are gonna be generated
+ 
+
+ align:start position:0%
+those two waves are gonna be generated
+and then you write and
+
+ align:start position:0%
+and then you write and
+ 
+
+ align:start position:0%
+and then you write and
+SATs for this wave sub coefficient a e
+
+ align:start position:0%
+SATs for this wave sub coefficient a e
+ 
+
+ align:start position:0%
+SATs for this wave sub coefficient a e
+to the ikx b e to the minus ikx e e to
+
+ align:start position:0%
+to the ikx b e to the minus ikx e e to
+ 
+
+ align:start position:0%
+to the ikx b e to the minus ikx e e to
+the other and then you solve your
+
+ align:start position:0%
+the other and then you solve your
+ 
+
+ align:start position:0%
+the other and then you solve your
+equation so we need to do the same thing
+
+ align:start position:0%
+equation so we need to do the same thing
+ 
+
+ align:start position:0%
+equation so we need to do the same thing
+with this kind of equation and this kind
+
+ align:start position:0%
+with this kind of equation and this kind
+ 
+
+ align:start position:0%
+with this kind of equation and this kind
+of potential we have to set up some sort
+
+ align:start position:0%
+of potential we have to set up some sort
+ 
+
+ align:start position:0%
+of potential we have to set up some sort
+of situation where we have the physics
+
+ align:start position:0%
+of situation where we have the physics
+ 
+
+ align:start position:0%
+of situation where we have the physics
+intuition of a wave that is coming in
+
+ align:start position:0%
+intuition of a wave that is coming in
+ 
+
+ align:start position:0%
+intuition of a wave that is coming in
+and then whatever the system will do to
+
+ align:start position:0%
+and then whatever the system will do to
+ 
+
+ align:start position:0%
+and then whatever the system will do to
+that wave to upgrade it into a full
+
+ align:start position:0%
+that wave to upgrade it into a full
+ 
+
+ align:start position:0%
+that wave to upgrade it into a full
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+so that's wouldn't want to do here in
+
+ align:start position:0%
+so that's wouldn't want to do here in
+ 
+
+ align:start position:0%
+so that's wouldn't want to do here in
+analogy to that thing this could be
+
+ align:start position:0%
+analogy to that thing this could be
+ 
+
+ align:start position:0%
+analogy to that thing this could be
+called incoming wave and this whole
+
+ align:start position:0%
+called incoming wave and this whole
+ 
+
+ align:start position:0%
+called incoming wave and this whole
+thing the reflected and the transmitted
+
+ align:start position:0%
+thing the reflected and the transmitted
+ 
+
+ align:start position:0%
+thing the reflected and the transmitted
+could be called the scattered wave the
+
+ align:start position:0%
+could be called the scattered wave the
+ 
+
+ align:start position:0%
+could be called the scattered wave the
+thing that gets produced by the
+
+ align:start position:0%
+thing that gets produced by the
+ 
+
+ align:start position:0%
+thing that gets produced by the
+scattering process so if you had there's
+
+ align:start position:0%
+scattering process so if you had there's
+ 
+
+ align:start position:0%
+scattering process so if you had there's
+a lot of solutions of that equation if B
+
+ align:start position:0%
+a lot of solutions of that equation if B
+ 
+
+ align:start position:0%
+a lot of solutions of that equation if B
+was identically 0 if you had no
+
+ align:start position:0%
+was identically 0 if you had no
+ 
+
+ align:start position:0%
+was identically 0 if you had no
+potential you could have lots of
+
+ align:start position:0%
+potential you could have lots of
+ 
+
+ align:start position:0%
+potential you could have lots of
+solutions because in fact if the
+
+ align:start position:0%
+solutions because in fact if the
+ 
+
+ align:start position:0%
+solutions because in fact if the
+potential is not zero plane waves are
+
+ align:start position:0%
+potential is not zero plane waves are
+ 
+
+ align:start position:0%
+potential is not zero plane waves are
+always solutions without any potential
+
+ align:start position:0%
+always solutions without any potential
+ 
+
+ align:start position:0%
+always solutions without any potential
+particles that move as plane wave so if
+
+ align:start position:0%
+particles that move as plane wave so if
+ 
+
+ align:start position:0%
+particles that move as plane wave so if
+we equals zero plane waves of the farm
+
+ align:start position:0%
+we equals zero plane waves of the farm
+ 
+
+ align:start position:0%
+we equals zero plane waves of the farm
+side equal e to the I K X are solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with k equal the square root of K dot k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or with K squared equal K dot K plane
+
+ align:start position:0%
+or with K squared equal K dot K plane
+ 
+
+ align:start position:0%
+or with K squared equal K dot K plane
+waves are always solutions of these
+
+ align:start position:0%
+waves are always solutions of these
+ 
+
+ align:start position:0%
+waves are always solutions of these
+equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if plane waves are solutions of this
+
+ align:start position:0%
+so if plane waves are solutions of this
+ 
+
+ align:start position:0%
+so if plane waves are solutions of this
+equation for V equal to zero this is the
+
+ align:start position:0%
+equation for V equal to zero this is the
+ 
+
+ align:start position:0%
+equation for V equal to zero this is the
+same thing as saying here that a e to
+
+ align:start position:0%
+same thing as saying here that a e to
+ 
+
+ align:start position:0%
+same thing as saying here that a e to
+the ikx
+
+ align:start position:0%
+the ikx
+ 
+
+ align:start position:0%
+the ikx
+is a solution of this equation as long
+
+ align:start position:0%
+is a solution of this equation as long
+ 
+
+ align:start position:0%
+is a solution of this equation as long
+as you don't hit the potential so here
+
+ align:start position:0%
+as you don't hit the potential so here
+ 
+
+ align:start position:0%
+as you don't hit the potential so here
+we're gonna do something quite similar
+
+ align:start position:0%
+we're gonna do something quite similar
+ 
+
+ align:start position:0%
+we're gonna do something quite similar
+we're gonna say that we we're going to
+
+ align:start position:0%
+we're gonna say that we we're going to
+ 
+
+ align:start position:0%
+we're gonna say that we we're going to
+put in an incident wave function wave
+
+ align:start position:0%
+put in an incident wave function wave
+ 
+
+ align:start position:0%
+put in an incident wave function wave
+function and I will instead of writing
+
+ align:start position:0%
+function and I will instead of writing
+ 
+
+ align:start position:0%
+function and I will instead of writing
+psy I will call it Phi of X the incident
+
+ align:start position:0%
+psy I will call it Phi of X the incident
+ 
+
+ align:start position:0%
+psy I will call it Phi of X the incident
+wave function Phi of X it's going to be
+
+ align:start position:0%
+wave function Phi of X it's going to be
+ 
+
+ align:start position:0%
+wave function Phi of X it's going to be
+just e to the I K Z so it's a wave
+
+ align:start position:0%
+just e to the I K Z so it's a wave
+ 
+
+ align:start position:0%
+just e to the I K Z so it's a wave
+function I call it Phi to distinguish it
+
+ align:start position:0%
+function I call it Phi to distinguish it
+ 
+
+ align:start position:0%
+function I call it Phi to distinguish it
+from psy psy in general it's a full
+
+ align:start position:0%
+from psy psy in general it's a full
+ 
+
+ align:start position:0%
+from psy psy in general it's a full
+solution of the Schrodinger equation
+
+ align:start position:0%
+solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+solution of the Schrodinger equation
+that's our understanding of psy so Phi
+
+ align:start position:0%
+that's our understanding of psy so Phi
+ 
+
+ align:start position:0%
+that's our understanding of psy so Phi
+it reminds you that well it's it's some
+
+ align:start position:0%
+it reminds you that well it's it's some
+ 
+
+ align:start position:0%
+it reminds you that well it's it's some
+wave function I'm not sure it's a
+
+ align:start position:0%
+wave function I'm not sure it's a
+ 
+
+ align:start position:0%
+wave function I'm not sure it's a
+solution in fact it probably is not a
+
+ align:start position:0%
+solution in fact it probably is not a
+ 
+
+ align:start position:0%
+solution in fact it probably is not a
+solution as soon as you have the
+
+ align:start position:0%
+solution as soon as you have the
+ 
+
+ align:start position:0%
+solution as soon as you have the
+potential different from zero so this is
+
+ align:start position:0%
+potential different from zero so this is
+ 
+
+ align:start position:0%
+potential different from zero so this is
+this common we forget the case v equals
+
+ align:start position:0%
+this common we forget the case v equals
+ 
+
+ align:start position:0%
+this common we forget the case v equals
+zero and now we put an incident wave
+
+ align:start position:0%
+zero and now we put an incident wave
+ 
+
+ align:start position:0%
+zero and now we put an incident wave
+function which is of this form the
+
+ align:start position:0%
+function which is of this form the
+ 
+
+ align:start position:0%
+function which is of this form the
+solves the equation as long as you're
+
+ align:start position:0%
+solves the equation as long as you're
+ 
+
+ align:start position:0%
+solves the equation as long as you're
+away from the potential this is true
+
+ align:start position:0%
+away from the potential this is true
+ 
+
+ align:start position:0%
+away from the potential this is true
+good it's a solution of the Schrodinger
+
+ align:start position:0%
+good it's a solution of the Schrodinger
+ 
+
+ align:start position:0%
+good it's a solution of the Schrodinger
+equation away from V of R away from B
+
+ align:start position:0%
+equation away from V of R away from B
+ 
+
+ align:start position:0%
+equation away from V of R away from B
+afar means wherever V of R is equal to
+
+ align:start position:0%
+afar means wherever V of R is equal to
+ 
+
+ align:start position:0%
+afar means wherever V of R is equal to
+zero you have a solution nevertheless so
+
+ align:start position:0%
+zero you have a solution nevertheless so
+ 
+
+ align:start position:0%
+zero you have a solution nevertheless so
+if we call the range of the potential
+
+ align:start position:0%
+if we call the range of the potential
+ 
+
+ align:start position:0%
+if we call the range of the potential
+let's call the range of the potential
+
+ align:start position:0%
+let's call the range of the potential
+ 
+
+ align:start position:0%
+let's call the range of the potential
+finite range a that is to take that if
+
+ align:start position:0%
+finite range a that is to take that if
+ 
+
+ align:start position:0%
+finite range a that is to take that if
+there's an origin here up to a radius a
+
+ align:start position:0%
+there's an origin here up to a radius a
+ 
+
+ align:start position:0%
+there's an origin here up to a radius a
+there is some potential and beyond the
+
+ align:start position:0%
+there is some potential and beyond the
+ 
+
+ align:start position:0%
+there is some potential and beyond the
+radius a the potential vanishes so this
+
+ align:start position:0%
+radius a the potential vanishes so this
+ 
+
+ align:start position:0%
+radius a the potential vanishes so this
+definitely works it's all case away from
+
+ align:start position:0%
+definitely works it's all case away from
+ 
+
+ align:start position:0%
+definitely works it's all case away from
+the R or as long as or as long as R is
+
+ align:start position:0%
+the R or as long as or as long as R is
+ 
+
+ align:start position:0%
+the R or as long as or as long as R is
+greater than a for whatever value of Z
+
+ align:start position:0%
+greater than a for whatever value of Z
+ 
+
+ align:start position:0%
+greater than a for whatever value of Z
+you take this is fine so here is our
+
+ align:start position:0%
+you take this is fine so here is our
+ 
+
+ align:start position:0%
+you take this is fine so here is our
+wave and now this is just the incident
+
+ align:start position:0%
+wave and now this is just the incident
+ 
+
+ align:start position:0%
+wave and now this is just the incident
+wave this is not gonna be the whole
+
+ align:start position:0%
+wave this is not gonna be the whole
+ 
+
+ align:start position:0%
+wave this is not gonna be the whole
+solution just like if live
+
+ align:start position:0%
+solution just like if live
+ 
+
+ align:start position:0%
+solution just like if live
+one-dimensional case there must be more
+
+ align:start position:0%
+one-dimensional case there must be more
+ 
+
+ align:start position:0%
+one-dimensional case there must be more
+so what is there more and our challenge
+
+ align:start position:0%
+so what is there more and our challenge
+ 
+
+ align:start position:0%
+so what is there more and our challenge
+to begin with this problem is to set up
+
+ align:start position:0%
+to begin with this problem is to set up
+ 
+
+ align:start position:0%
+to begin with this problem is to set up
+what else could there be
+
+ align:start position:0%
+what else could there be
+ 
+
+ align:start position:0%
+what else could there be
+so looking at it you'd say alright so
+
+ align:start position:0%
+so looking at it you'd say alright so
+ 
+
+ align:start position:0%
+so looking at it you'd say alright so
+thing comes in if they're scattering is
+
+ align:start position:0%
+thing comes in if they're scattering is
+ 
+
+ align:start position:0%
+thing comes in if they're scattering is
+going to particle sometimes I'm going to
+
+ align:start position:0%
+going to particle sometimes I'm going to
+ 
+
+ align:start position:0%
+going to particle sometimes I'm going to
+go off in various directions so the
+
+ align:start position:0%
+go off in various directions so the
+ 
+
+ align:start position:0%
+go off in various directions so the
+outgoing wave here there were outgoing
+
+ align:start position:0%
+outgoing wave here there were outgoing
+ 
+
+ align:start position:0%
+outgoing wave here there were outgoing
+waves reflected and transmitted the
+
+ align:start position:0%
+waves reflected and transmitted the
+ 
+
+ align:start position:0%
+waves reflected and transmitted the
+outgoing wave in the three-dimensional
+
+ align:start position:0%
+outgoing wave in the three-dimensional
+ 
+
+ align:start position:0%
+outgoing wave in the three-dimensional
+scaring problem should be some sort of
+
+ align:start position:0%
+scaring problem should be some sort of
+ 
+
+ align:start position:0%
+scaring problem should be some sort of
+spherical wave
+
+ align:start position:0%
+spherical wave
+ 
+
+ align:start position:0%
+spherical wave
+being away from our equal 0 which is the
+
+ align:start position:0%
+being away from our equal 0 which is the
+ 
+
+ align:start position:0%
+being away from our equal 0 which is the
+origin that should be the other way that
+
+ align:start position:0%
+origin that should be the other way that
+ 
+
+ align:start position:0%
+origin that should be the other way that
+I would write so my answers should be
+
+ align:start position:0%
+I would write so my answers should be
+ 
+
+ align:start position:0%
+I would write so my answers should be
+that there's some sort of spherical wave
+
+ align:start position:0%
+that there's some sort of spherical wave
+ 
+
+ align:start position:0%
+that there's some sort of spherical wave
+that is moving away so to complete this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a spherical outgoing wave so while
+
+ align:start position:0%
+with a spherical outgoing wave so while
+ 
+
+ align:start position:0%
+with a spherical outgoing wave so while
+here this is a plane wave moving in the
+
+ align:start position:0%
+here this is a plane wave moving in the
+ 
+
+ align:start position:0%
+here this is a plane wave moving in the
+direction of the vector K if I want to
+
+ align:start position:0%
+direction of the vector K if I want to
+ 
+
+ align:start position:0%
+direction of the vector K if I want to
+write the spherical wave I would write e
+
+ align:start position:0%
+write the spherical wave I would write e
+ 
+
+ align:start position:0%
+write the spherical wave I would write e
+to the I just K R e to the IKr is
+
+ align:start position:0%
+to the I just K R e to the IKr is
+ 
+
+ align:start position:0%
+to the I just K R e to the IKr is
+spherically symmetric and it propagates
+
+ align:start position:0%
+spherically symmetric and it propagates
+ 
+
+ align:start position:0%
+spherically symmetric and it propagates
+radially out if you remember as usual
+
+ align:start position:0%
+radially out if you remember as usual
+ 
+
+ align:start position:0%
+radially out if you remember as usual
+that you have e to the minus I in T over
+
+ align:start position:0%
+that you have e to the minus I in T over
+ 
+
+ align:start position:0%
+that you have e to the minus I in T over
+H bar so you have km R minus ET that is
+
+ align:start position:0%
+H bar so you have km R minus ET that is
+ 
+
+ align:start position:0%
+H bar so you have km R minus ET that is
+a wave that propagates radially out so
+
+ align:start position:0%
+a wave that propagates radially out so
+ 
+
+ align:start position:0%
+a wave that propagates radially out so
+maybe this is kind of this scattered
+
+ align:start position:0%
+maybe this is kind of this scattered
+ 
+
+ align:start position:0%
+maybe this is kind of this scattered
+wave this e to the IKr moving out
+
+ align:start position:0%
+wave this e to the IKr moving out
+ 
+
+ align:start position:0%
+wave this e to the IKr moving out
+everywhere would be your scattered wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if that is a scattered wave remember we
+
+ align:start position:0%
+if that is a scattered wave remember we
+ 
+
+ align:start position:0%
+if that is a scattered wave remember we
+should the scattered wave should solve
+
+ align:start position:0%
+should the scattered wave should solve
+ 
+
+ align:start position:0%
+should the scattered wave should solve
+the Schrodinger equation in fact the sum
+
+ align:start position:0%
+the Schrodinger equation in fact the sum
+ 
+
+ align:start position:0%
+the Schrodinger equation in fact the sum
+of these two should solve the scattering
+
+ align:start position:0%
+of these two should solve the scattering
+ 
+
+ align:start position:0%
+of these two should solve the scattering
+equation on the other hand we've seen
+
+ align:start position:0%
+equation on the other hand we've seen
+ 
+
+ align:start position:0%
+equation on the other hand we've seen
+that this solves it as long as you're
+
+ align:start position:0%
+that this solves it as long as you're
+ 
+
+ align:start position:0%
+that this solves it as long as you're
+away from the potential and therefore
+
+ align:start position:0%
+away from the potential and therefore
+ 
+
+ align:start position:0%
+away from the potential and therefore
+this should also solve it if you're away
+
+ align:start position:0%
+this should also solve it if you're away
+ 
+
+ align:start position:0%
+this should also solve it if you're away
+from the potential so I ask you do you
+
+ align:start position:0%
+from the potential so I ask you do you
+ 
+
+ align:start position:0%
+from the potential so I ask you do you
+think this solve the Schrodinger
+
+ align:start position:0%
+think this solve the Schrodinger
+ 
+
+ align:start position:0%
+think this solve the Schrodinger
+equation when you're away from the
+
+ align:start position:0%
+equation when you're away from the
+ 
+
+ align:start position:0%
+equation when you're away from the
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would eat to the IKr solve the equation
+
+ align:start position:0%
+would eat to the IKr solve the equation
+ 
+
+ align:start position:0%
+would eat to the IKr solve the equation
+but for that you would need that if
+
+ align:start position:0%
+but for that you would need that if
+ 
+
+ align:start position:0%
+but for that you would need that if
+you're away from the potential do you
+
+ align:start position:0%
+you're away from the potential do you
+ 
+
+ align:start position:0%
+you're away from the potential do you
+have laplacian of e to the IKr roughly
+
+ align:start position:0%
+have laplacian of e to the IKr roughly
+ 
+
+ align:start position:0%
+have laplacian of e to the IKr roughly
+equals zero is that true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will it solve it no it doesn't solve it
+
+ align:start position:0%
+will it solve it no it doesn't solve it
+ 
+
+ align:start position:0%
+will it solve it no it doesn't solve it
+doesn't even come close to solving it
+
+ align:start position:0%
+doesn't even come close to solving it
+ 
+
+ align:start position:0%
+doesn't even come close to solving it
+it's pretty bad but the reason it's bad
+
+ align:start position:0%
+it's pretty bad but the reason it's bad
+ 
+
+ align:start position:0%
+it's pretty bad but the reason it's bad
+is physically clear this wave as it
+
+ align:start position:0%
+is physically clear this wave as it
+ 
+
+ align:start position:0%
+is physically clear this wave as it
+expands out must become weaker and
+
+ align:start position:0%
+expands out must become weaker and
+ 
+
+ align:start position:0%
+expands out must become weaker and
+weaker so that the probability flux
+
+ align:start position:0%
+weaker so that the probability flux
+ 
+
+ align:start position:0%
+weaker so that the probability flux
+remains constant you know you don't want
+
+ align:start position:0%
+remains constant you know you don't want
+ 
+
+ align:start position:0%
+remains constant you know you don't want
+an accumulation of probability between a
+
+ align:start position:0%
+an accumulation of probability between a
+ 
+
+ align:start position:0%
+an accumulation of probability between a
+shell at 1 kilometer and a shell at 2
+
+ align:start position:0%
+shell at 1 kilometer and a shell at 2
+ 
+
+ align:start position:0%
+shell at 1 kilometer and a shell at 2
+kilometer so whatever flux is going out
+
+ align:start position:0%
+kilometer so whatever flux is going out
+ 
+
+ align:start position:0%
+kilometer so whatever flux is going out
+from the shell in one kilometer should
+
+ align:start position:0%
+from the shell in one kilometer should
+ 
+
+ align:start position:0%
+from the shell in one kilometer should
+be going out of the bigger shell so
+
+ align:start position:0%
+be going out of the bigger shell so
+ 
+
+ align:start position:0%
+be going out of the bigger shell so
+therefore it should fall off with our oh
+
+ align:start position:0%
+therefore it should fall off with our oh
+ 
+
+ align:start position:0%
+therefore it should fall off with our oh
+I'm sorry I I didn't write this well so
+
+ align:start position:0%
+I'm sorry I I didn't write this well so
+ 
+
+ align:start position:0%
+I'm sorry I I didn't write this well so
+if you are gonna have this to be a
+
+ align:start position:0%
+if you are gonna have this to be a
+ 
+
+ align:start position:0%
+if you are gonna have this to be a
+solution of the Schrodinger equation
+
+ align:start position:0%
+solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+solution of the Schrodinger equation
+outside of VR equals 0 you should have
+
+ align:start position:0%
+outside of VR equals 0 you should have
+ 
+
+ align:start position:0%
+outside of VR equals 0 you should have
+laplacian plus K squared of this thing
+
+ align:start position:0%
+laplacian plus K squared of this thing
+ 
+
+ align:start position:0%
+laplacian plus K squared of this thing
+equal to 0 so if this is equal to 0 and
+
+ align:start position:0%
+equal to 0 so if this is equal to 0 and
+ 
+
+ align:start position:0%
+equal to 0 so if this is equal to 0 and
+the potential is equal to 0 the whole
+
+ align:start position:0%
+the potential is equal to 0 the whole
+ 
+
+ align:start position:0%
+the potential is equal to 0 the whole
+thing is equal to 0 so we need this to
+
+ align:start position:0%
+thing is equal to 0 so we need this to
+ 
+
+ align:start position:0%
+thing is equal to 0 so we need this to
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+but even this one of course is not true
+
+ align:start position:0%
+but even this one of course is not true
+ 
+
+ align:start position:0%
+but even this one of course is not true
+it's just absolutely not true the one
+
+ align:start position:0%
+it's just absolutely not true the one
+ 
+
+ align:start position:0%
+it's just absolutely not true the one
+that works is the following laplacian
+
+ align:start position:0%
+that works is the following laplacian
+ 
+
+ align:start position:0%
+that works is the following laplacian
+plus K squared of e to the IKr over R is
+
+ align:start position:0%
+plus K squared of e to the IKr over R is
+ 
+
+ align:start position:0%
+plus K squared of e to the IKr over R is
+equal to 0 for our different from 0 this
+
+ align:start position:0%
+equal to 0 for our different from 0 this
+ 
+
+ align:start position:0%
+equal to 0 for our different from 0 this
+is a computation I think you guys have
+
+ align:start position:0%
+is a computation I think you guys have
+ 
+
+ align:start position:0%
+is a computation I think you guys have
+done before when you were studying the
+
+ align:start position:0%
+done before when you were studying the
+ 
+
+ align:start position:0%
+done before when you were studying the
+hermeticity of P squared you ended up
+
+ align:start position:0%
+hermeticity of P squared you ended up
+ 
+
+ align:start position:0%
+hermeticity of P squared you ended up
+doing this kind of things this laplacian
+
+ align:start position:0%
+doing this kind of things this laplacian
+ 
+
+ align:start position:0%
+doing this kind of things this laplacian
+produces a delta function at R equals 0
+
+ align:start position:0%
+produces a delta function at R equals 0
+ 
+
+ align:start position:0%
+produces a delta function at R equals 0
+but R equals 0 is not the place we're
+
+ align:start position:0%
+but R equals 0 is not the place we're
+ 
+
+ align:start position:0%
+but R equals 0 is not the place we're
+interested in we're trying to find how
+
+ align:start position:0%
+interested in we're trying to find how
+ 
+
+ align:start position:0%
+interested in we're trying to find how
+the waves look away from the scattering
+
+ align:start position:0%
+the waves look away from the scattering
+ 
+
+ align:start position:0%
+the waves look away from the scattering
+Center
+
+ align:start position:0%
+Center
+ 
+
+ align:start position:0%
+Center
+so we need this to hold away from our
+
+ align:start position:0%
+so we need this to hold away from our
+ 
+
+ align:start position:0%
+so we need this to hold away from our
+equals zero in fact bigger for our
+
+ align:start position:0%
+equals zero in fact bigger for our
+ 
+
+ align:start position:0%
+equals zero in fact bigger for our
+bigger than a and one way of checking
+
+ align:start position:0%
+bigger than a and one way of checking
+ 
+
+ align:start position:0%
+bigger than a and one way of checking
+this kind of thing is to remember that
+
+ align:start position:0%
+this kind of thing is to remember that
+ 
+
+ align:start position:0%
+this kind of thing is to remember that
+the laplacian of a function of r is in
+
+ align:start position:0%
+the laplacian of a function of r is in
+ 
+
+ align:start position:0%
+the laplacian of a function of r is in
+fact 1 over r v ii we r squared r times
+
+ align:start position:0%
+fact 1 over r v ii we r squared r times
+ 
+
+ align:start position:0%
+fact 1 over r v ii we r squared r times
+F that's a neat formula for the
+
+ align:start position:0%
+F that's a neat formula for the
+ 
+
+ align:start position:0%
+F that's a neat formula for the
+laplacian of a function that just
+
+ align:start position:0%
+laplacian of a function that just
+ 
+
+ align:start position:0%
+laplacian of a function that just
+depends on R if it depends on theta and
+
+ align:start position:0%
+depends on R if it depends on theta and
+ 
+
+ align:start position:0%
+depends on R if it depends on theta and
+Phi is more complicated but with this
+
+ align:start position:0%
+Phi is more complicated but with this
+ 
+
+ align:start position:0%
+Phi is more complicated but with this
+function it becomes a one-line
+
+ align:start position:0%
+function it becomes a one-line
+ 
+
+ align:start position:0%
+function it becomes a one-line
+calculation to do this and the R here is
+
+ align:start position:0%
+calculation to do this and the R here is
+ 
+
+ align:start position:0%
+calculation to do this and the R here is
+just fantastic because by the time you
+
+ align:start position:0%
+just fantastic because by the time you
+ 
+
+ align:start position:0%
+just fantastic because by the time you
+multiplied by R this function is just
+
+ align:start position:0%
+multiplied by R this function is just
+ 
+
+ align:start position:0%
+multiplied by R this function is just
+exponential you take two derivatives you
+
+ align:start position:0%
+exponential you take two derivatives you
+ 
+
+ align:start position:0%
+exponential you take two derivatives you
+get minus K squared and then the R gets
+
+ align:start position:0%
+get minus K squared and then the R gets
+ 
+
+ align:start position:0%
+get minus K squared and then the R gets
+cancelled as well and everything works
+
+ align:start position:0%
+cancelled as well and everything works
+ 
+
+ align:start position:0%
+cancelled as well and everything works
+beautifully here and so this equation
+
+ align:start position:0%
+beautifully here and so this equation
+ 
+
+ align:start position:0%
+beautifully here and so this equation
+holds ok and then we do have a possible
+
+ align:start position:0%
+holds ok and then we do have a possible
+ 
+
+ align:start position:0%
+holds ok and then we do have a possible
+scattered wave so we are almost there
+
+ align:start position:0%
+scattered wave so we are almost there
+ 
+
+ align:start position:0%
+scattered wave so we are almost there
+we can write the scattering wave size
+
+ align:start position:0%
+we can write the scattering wave size
+ 
+
+ align:start position:0%
+we can write the scattering wave size
+scattering scattering of X could be e to
+
+ align:start position:0%
+scattering scattering of X could be e to
+ 
+
+ align:start position:0%
+scattering scattering of X could be e to
+the I K R over R and then leave it at
+
+ align:start position:0%
+the I K R over R and then leave it at
+ 
+
+ align:start position:0%
+the I K R over R and then leave it at
+that but this would not be general
+
+ align:start position:0%
+that but this would not be general
+ 
+
+ align:start position:0%
+that but this would not be general
+enough there's no reason why this wave
+
+ align:start position:0%
+enough there's no reason why this wave
+ 
+
+ align:start position:0%
+enough there's no reason why this wave
+would not depend also on theta and Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is the Z direction and there's
+
+ align:start position:0%
+here is the Z direction and there's
+ 
+
+ align:start position:0%
+here is the Z direction and there's
+points with angle theta and if you
+
+ align:start position:0%
+points with angle theta and if you
+ 
+
+ align:start position:0%
+points with angle theta and if you
+rotate it with some angle Phi here
+
+ align:start position:0%
+rotate it with some angle Phi here
+ 
+
+ align:start position:0%
+rotate it with some angle Phi here
+and therefore this function could as
+
+ align:start position:0%
+and therefore this function could as
+ 
+
+ align:start position:0%
+and therefore this function could as
+well depend on theta and Phi so we'll
+
+ align:start position:0%
+well depend on theta and Phi so we'll
+ 
+
+ align:start position:0%
+well depend on theta and Phi so we'll
+include that factor f of theta and Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you would say look you have a nice
+
+ align:start position:0%
+now you would say look you have a nice
+ 
+
+ align:start position:0%
+now you would say look you have a nice
+solution of the Schrodinger equation
+
+ align:start position:0%
+solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+solution of the Schrodinger equation
+already here and and what what should
+
+ align:start position:0%
+already here and and what what should
+ 
+
+ align:start position:0%
+already here and and what what should
+you be doing why do you add this factor
+
+ align:start position:0%
+you be doing why do you add this factor
+ 
+
+ align:start position:0%
+you be doing why do you add this factor
+with this factor it may not be any more
+
+ align:start position:0%
+with this factor it may not be any more
+ 
+
+ align:start position:0%
+with this factor it may not be any more
+a solution of the Schrodinger equation
+
+ align:start position:0%
+a solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+a solution of the Schrodinger equation
+it's changing the equation and I have a
+
+ align:start position:0%
+it's changing the equation and I have a
+ 
+
+ align:start position:0%
+it's changing the equation and I have a
+laplacian and it's gonna be more
+
+ align:start position:0%
+laplacian and it's gonna be more
+ 
+
+ align:start position:0%
+laplacian and it's gonna be more
+complicated well this is true and we
+
+ align:start position:0%
+complicated well this is true and we
+ 
+
+ align:start position:0%
+complicated well this is true and we
+will see that better soon but this will
+
+ align:start position:0%
+will see that better soon but this will
+ 
+
+ align:start position:0%
+will see that better soon but this will
+remain an approximate solution for are
+
+ align:start position:0%
+remain an approximate solution for are
+ 
+
+ align:start position:0%
+remain an approximate solution for are
+much bigger than a is the leading term
+
+ align:start position:0%
+much bigger than a is the leading term
+ 
+
+ align:start position:0%
+much bigger than a is the leading term
+of a solution leaving term solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you have a leading in terms of a
+
+ align:start position:0%
+so if you have a leading in terms of a
+ 
+
+ align:start position:0%
+so if you have a leading in terms of a
+solution here this is all you want you
+
+ align:start position:0%
+solution here this is all you want you
+ 
+
+ align:start position:0%
+solution here this is all you want you
+are working at are much bigger than a
+
+ align:start position:0%
+are working at are much bigger than a
+ 
+
+ align:start position:0%
+are working at are much bigger than a
+and your whole wave and finally be
+
+ align:start position:0%
+and your whole wave and finally be
+ 
+
+ align:start position:0%
+and your whole wave and finally be
+written so your full wave sigh of or
+
+ align:start position:0%
+written so your full wave sigh of or
+ 
+
+ align:start position:0%
+written so your full wave sigh of or
+your full energy eigenstate sigh of aren
+
+ align:start position:0%
+your full energy eigenstate sigh of aren
+ 
+
+ align:start position:0%
+your full energy eigenstate sigh of aren
+t is going to be equal approximately
+
+ align:start position:0%
+t is going to be equal approximately
+ 
+
+ align:start position:0%
+t is going to be equal approximately
+equal to e to the I K well I'll write it
+
+ align:start position:0%
+equal to e to the I K well I'll write it
+ 
+
+ align:start position:0%
+equal to e to the I K well I'll write it
+this way Phi of R that incident wave
+
+ align:start position:0%
+this way Phi of R that incident wave
+ 
+
+ align:start position:0%
+this way Phi of R that incident wave
+will wrote I wrote if X there I'm sorry
+
+ align:start position:0%
+will wrote I wrote if X there I'm sorry
+ 
+
+ align:start position:0%
+will wrote I wrote if X there I'm sorry
+a plus size gathering of I should beside
+
+ align:start position:0%
+a plus size gathering of I should beside
+ 
+
+ align:start position:0%
+a plus size gathering of I should beside
+X or R let's call this R and I should
+
+ align:start position:0%
+X or R let's call this R and I should
+ 
+
+ align:start position:0%
+X or R let's call this R and I should
+call this R tie our precise scattering
+
+ align:start position:0%
+call this R tie our precise scattering
+ 
+
+ align:start position:0%
+call this R tie our precise scattering
+of our and it's therefore equal to e to
+
+ align:start position:0%
+of our and it's therefore equal to e to
+ 
+
+ align:start position:0%
+of our and it's therefore equal to e to
+the I K Z plus F of theta phi e to the I
+
+ align:start position:0%
+the I K Z plus F of theta phi e to the I
+ 
+
+ align:start position:0%
+the I K Z plus F of theta phi e to the I
+K R over R and this is only valid for
+
+ align:start position:0%
+K R over R and this is only valid for
+ 
+
+ align:start position:0%
+K R over R and this is only valid for
+our much bigger than a far away this had
+
+ align:start position:0%
+our much bigger than a far away this had
+ 
+
+ align:start position:0%
+our much bigger than a far away this had
+an analog in our problem in one
+
+ align:start position:0%
+an analog in our problem in one
+ 
+
+ align:start position:0%
+an analog in our problem in one
+dimension in one dimension you set up a
+
+ align:start position:0%
+dimension in one dimension you set up a
+ 
+
+ align:start position:0%
+dimension in one dimension you set up a
+wave and you put here the wave and
+
+ align:start position:0%
+wave and you put here the wave and
+ 
+
+ align:start position:0%
+wave and you put here the wave and
+there's a reflected wave and there's a
+
+ align:start position:0%
+there's a reflected wave and there's a
+ 
+
+ align:start position:0%
+there's a reflected wave and there's a
+transmitted wave and in setting the
+
+ align:start position:0%
+transmitted wave and in setting the
+ 
+
+ align:start position:0%
+transmitted wave and in setting the
+promised a this is valid far to the left
+
+ align:start position:0%
+promised a this is valid far to the left
+ 
+
+ align:start position:0%
+promised a this is valid far to the left
+far to the left meanings at least to the
+
+ align:start position:0%
+far to the left meanings at least to the
+ 
+
+ align:start position:0%
+far to the left meanings at least to the
+left of the barrier this is valid to the
+
+ align:start position:0%
+left of the barrier this is valid to the
+ 
+
+ align:start position:0%
+left of the barrier this is valid to the
+right and this were exact solutions in
+
+ align:start position:0%
+right and this were exact solutions in
+ 
+
+ align:start position:0%
+right and this were exact solutions in
+this region here you can't do that well
+
+ align:start position:0%
+this region here you can't do that well
+ 
+
+ align:start position:0%
+this region here you can't do that well
+but you can do reasonably well you can
+
+ align:start position:0%
+but you can do reasonably well you can
+ 
+
+ align:start position:0%
+but you can do reasonably well you can
+write solutions that are
+
+ align:start position:0%
+write solutions that are
+ 
+
+ align:start position:0%
+write solutions that are
+leading term accurate as long as you are
+
+ align:start position:0%
+leading term accurate as long as you are
+ 
+
+ align:start position:0%
+leading term accurate as long as you are
+far away so this is the first step in
+
+ align:start position:0%
+far away so this is the first step in
+ 
+
+ align:start position:0%
+far away so this is the first step in
+this whole process in which we are
+
+ align:start position:0%
+this whole process in which we are
+ 
+
+ align:start position:0%
+this whole process in which we are
+setting up the wave functions it is the
+
+ align:start position:0%
+setting up the wave functions it is the
+ 
+
+ align:start position:0%
+setting up the wave functions it is the
+most important equation this is the way
+
+ align:start position:0%
+most important equation this is the way
+ 
+
+ align:start position:0%
+most important equation this is the way
+we're going to try to find solutions now
+
+ align:start position:0%
+we're going to try to find solutions now
+ 
+
+ align:start position:0%
+we're going to try to find solutions now
+when you try to find solutions at the
+
+ align:start position:0%
+when you try to find solutions at the
+ 
+
+ align:start position:0%
+when you try to find solutions at the
+end of the day you will have to work in
+
+ align:start position:0%
+end of the day you will have to work in
+ 
+
+ align:start position:0%
+end of the day you will have to work in
+the region and are going to zero so
+
+ align:start position:0%
+the region and are going to zero so
+ 
+
+ align:start position:0%
+the region and are going to zero so
+sooner or later we'll get there but from
+
+ align:start position:0%
+sooner or later we'll get there but from
+ 
+
+ align:start position:0%
+sooner or later we'll get there but from
+the time being we we have all the
+
+ align:start position:0%
+the time being we we have all the
+ 
+
+ align:start position:0%
+the time being we we have all the
+information about what's going on far
+
+ align:start position:0%
+information about what's going on far
+ 
+
+ align:start position:0%
+information about what's going on far
+away and from there we can get most of
+
+ align:start position:0%
+away and from there we can get most of
+ 
+
+ align:start position:0%
+away and from there we can get most of
+what we need in particular this F of
+
+ align:start position:0%
+what we need in particular this F of
+ 
+
+ align:start position:0%
+what we need in particular this F of
+theta and Phi is the quantity we need to
+
+ align:start position:0%
+theta and Phi is the quantity we need to
+ 
+
+ align:start position:0%
+theta and Phi is the quantity we need to
+figure out this is all this f of theta
+
+ align:start position:0%
+figure out this is all this f of theta
+ 
+
+ align:start position:0%
+figure out this is all this f of theta
+and Phi R is called the scattering
+
+ align:start position:0%
+and Phi R is called the scattering
+ 
+
+ align:start position:0%
+and Phi R is called the scattering
+amplitude F theta and Phi or scattering
+
+ align:start position:0%
+amplitude F theta and Phi or scattering
+ 
+
+ align:start position:0%
+amplitude F theta and Phi or scattering
+and it
\ No newline at end of file
diff --git a/4aiTCDvlUeI.txt b/4aiTCDvlUeI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9f5db597b9469526a76ffb7602dea4be401512cd
--- /dev/null
+++ b/4aiTCDvlUeI.txt
@@ -0,0 +1,3219 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+sful
+
+ align:start position:0%
+sful
+ 
+
+ align:start position:0%
+sful
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+the was
+
+ align:start position:0%
+the was
+ 
+
+ align:start position:0%
+the was
+oh father was
+
+ align:start position:0%
+oh father was
+ 
+
+ align:start position:0%
+oh father was
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there the night was W with
+
+ align:start position:0%
+there the night was W with
+ 
+
+ align:start position:0%
+there the night was W with
+de
+
+ align:start position:0%
+de
+ 
+
+ align:start position:0%
+de
+the was deep and the child
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did and
+
+ align:start position:0%
+did and
+ 
+
+ align:start position:0%
+did and
+the of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay it's a little bit more coordinated
+
+ align:start position:0%
+okay it's a little bit more coordinated
+ 
+
+ align:start position:0%
+okay it's a little bit more coordinated
+from me I still interestingly missed the
+
+ align:start position:0%
+from me I still interestingly missed the
+ 
+
+ align:start position:0%
+from me I still interestingly missed the
+interval uh going from the end of 27 to
+
+ align:start position:0%
+interval uh going from the end of 27 to
+ 
+
+ align:start position:0%
+interval uh going from the end of 27 to
+the beginning of 28 uh ordinarily I'm
+
+ align:start position:0%
+the beginning of 28 uh ordinarily I'm
+ 
+
+ align:start position:0%
+the beginning of 28 uh ordinarily I'm
+not in such a good hurry to dolge all my
+
+ align:start position:0%
+not in such a good hurry to dolge all my
+ 
+
+ align:start position:0%
+not in such a good hurry to dolge all my
+mistakes to people who me perform
+
+ align:start position:0%
+mistakes to people who me perform
+ 
+
+ align:start position:0%
+mistakes to people who me perform
+however I think in this case it's it's
+
+ align:start position:0%
+however I think in this case it's it's
+ 
+
+ align:start position:0%
+however I think in this case it's it's
+Germain um there was a wonderful comment
+
+ align:start position:0%
+Germain um there was a wonderful comment
+ 
+
+ align:start position:0%
+Germain um there was a wonderful comment
+that a colleague of yours whose name
+
+ align:start position:0%
+that a colleague of yours whose name
+ 
+
+ align:start position:0%
+that a colleague of yours whose name
+forgive me I can't remember the very
+
+ align:start position:0%
+forgive me I can't remember the very
+ 
+
+ align:start position:0%
+forgive me I can't remember the very
+first time I ever did this class with
+
+ align:start position:0%
+first time I ever did this class with
+ 
+
+ align:start position:0%
+first time I ever did this class with
+you um there were I think only three
+
+ align:start position:0%
+you um there were I think only three
+ 
+
+ align:start position:0%
+you um there were I think only three
+people or something it was anyway it was
+
+ align:start position:0%
+people or something it was anyway it was
+ 
+
+ align:start position:0%
+people or something it was anyway it was
+another composition uh professor and I
+
+ align:start position:0%
+another composition uh professor and I
+ 
+
+ align:start position:0%
+another composition uh professor and I
+was having trouble parsing out what
+
+ align:start position:0%
+was having trouble parsing out what
+ 
+
+ align:start position:0%
+was having trouble parsing out what
+looked on paper to be a very simple
+
+ align:start position:0%
+looked on paper to be a very simple
+ 
+
+ align:start position:0%
+looked on paper to be a very simple
+Melody but it was awkwardly written it
+
+ align:start position:0%
+Melody but it was awkwardly written it
+ 
+
+ align:start position:0%
+Melody but it was awkwardly written it
+was a uh they were funny intervals and
+
+ align:start position:0%
+was a uh they were funny intervals and
+ 
+
+ align:start position:0%
+was a uh they were funny intervals and
+and strange jumps on unusual syllables
+
+ align:start position:0%
+and strange jumps on unusual syllables
+ 
+
+ align:start position:0%
+and strange jumps on unusual syllables
+and the student composer it should be
+
+ align:start position:0%
+and the student composer it should be
+ 
+
+ align:start position:0%
+and the student composer it should be
+said was becoming annoyed with me for
+
+ align:start position:0%
+said was becoming annoyed with me for
+ 
+
+ align:start position:0%
+said was becoming annoyed with me for
+missing it repeatedly and then her
+
+ align:start position:0%
+missing it repeatedly and then her
+ 
+
+ align:start position:0%
+missing it repeatedly and then her
+professor raised his hand and very tly
+
+ align:start position:0%
+professor raised his hand and very tly
+ 
+
+ align:start position:0%
+professor raised his hand and very tly
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+well take an experienced musician in an
+
+ align:start position:0%
+well take an experienced musician in an
+ 
+
+ align:start position:0%
+well take an experienced musician in an
+awkward line of music and you can't
+
+ align:start position:0%
+awkward line of music and you can't
+ 
+
+ align:start position:0%
+awkward line of music and you can't
+expect it to be much smoother than that
+
+ align:start position:0%
+expect it to be much smoother than that
+ 
+
+ align:start position:0%
+expect it to be much smoother than that
+at first gloss and it was a very telling
+
+ align:start position:0%
+at first gloss and it was a very telling
+ 
+
+ align:start position:0%
+at first gloss and it was a very telling
+comment um and it's incredibly ephemeral
+
+ align:start position:0%
+comment um and it's incredibly ephemeral
+ 
+
+ align:start position:0%
+comment um and it's incredibly ephemeral
+Concept in in that you know what what
+
+ align:start position:0%
+Concept in in that you know what what
+ 
+
+ align:start position:0%
+Concept in in that you know what what
+does a smooth or logical or organic
+
+ align:start position:0%
+does a smooth or logical or organic
+ 
+
+ align:start position:0%
+does a smooth or logical or organic
+melody mean to each of us and it depends
+
+ align:start position:0%
+melody mean to each of us and it depends
+ 
+
+ align:start position:0%
+melody mean to each of us and it depends
+also on what compositional idiom you're
+
+ align:start position:0%
+also on what compositional idiom you're
+ 
+
+ align:start position:0%
+also on what compositional idiom you're
+working in you know something like this
+
+ align:start position:0%
+working in you know something like this
+ 
+
+ align:start position:0%
+working in you know something like this
+that owes so much to the tradition of uh
+
+ align:start position:0%
+that owes so much to the tradition of uh
+ 
+
+ align:start position:0%
+that owes so much to the tradition of uh
+say German art song or let's say uh
+
+ align:start position:0%
+say German art song or let's say uh
+ 
+
+ align:start position:0%
+say German art song or let's say uh
+basically art song from the mid mid 19th
+
+ align:start position:0%
+basically art song from the mid mid 19th
+ 
+
+ align:start position:0%
+basically art song from the mid mid 19th
+century um there are certain standards
+
+ align:start position:0%
+century um there are certain standards
+ 
+
+ align:start position:0%
+century um there are certain standards
+of of um excuse me standards isn't the
+
+ align:start position:0%
+of of um excuse me standards isn't the
+ 
+
+ align:start position:0%
+of of um excuse me standards isn't the
+word I want there are certain uh
+
+ align:start position:0%
+word I want there are certain uh
+ 
+
+ align:start position:0%
+word I want there are certain uh
+convention in the way Melodies will
+
+ align:start position:0%
+convention in the way Melodies will
+ 
+
+ align:start position:0%
+convention in the way Melodies will
+unfold that we all kind of accept and
+
+ align:start position:0%
+unfold that we all kind of accept and
+ 
+
+ align:start position:0%
+unfold that we all kind of accept and
+listen for and for some reason I I think
+
+ align:start position:0%
+listen for and for some reason I I think
+ 
+
+ align:start position:0%
+listen for and for some reason I I think
+it has largely to do with where you're
+
+ align:start position:0%
+it has largely to do with where you're
+ 
+
+ align:start position:0%
+it has largely to do with where you're
+going harmonically that interval is hard
+
+ align:start position:0%
+going harmonically that interval is hard
+ 
+
+ align:start position:0%
+going harmonically that interval is hard
+for me to hear the C to F it's only it's
+
+ align:start position:0%
+for me to hear the C to F it's only it's
+ 
+
+ align:start position:0%
+for me to hear the C to F it's only it's
+an open fifth it's the easiest interval
+
+ align:start position:0%
+an open fifth it's the easiest interval
+ 
+
+ align:start position:0%
+an open fifth it's the easiest interval
+you can possibly sing nonetheless
+
+ align:start position:0%
+you can possibly sing nonetheless
+ 
+
+ align:start position:0%
+you can possibly sing nonetheless
+because harmonically it's heading in a
+
+ align:start position:0%
+because harmonically it's heading in a
+ 
+
+ align:start position:0%
+because harmonically it's heading in a
+direction that doesn't necessarily make
+
+ align:start position:0%
+direction that doesn't necessarily make
+ 
+
+ align:start position:0%
+direction that doesn't necessarily make
+that much
+
+ align:start position:0%
+that much
+ 
+
+ align:start position:0%
+that much
+sense uh in regard to what has preceded
+
+ align:start position:0%
+sense uh in regard to what has preceded
+ 
+
+ align:start position:0%
+sense uh in regard to what has preceded
+it it feels a little bit awkward um now
+
+ align:start position:0%
+it it feels a little bit awkward um now
+ 
+
+ align:start position:0%
+it it feels a little bit awkward um now
+I understand where you're where you're
+
+ align:start position:0%
+I understand where you're where you're
+ 
+
+ align:start position:0%
+I understand where you're where you're
+wanting to wind up and that does make
+
+ align:start position:0%
+wanting to wind up and that does make
+ 
+
+ align:start position:0%
+wanting to wind up and that does make
+sense sort of on paper but at the same
+
+ align:start position:0%
+sense sort of on paper but at the same
+ 
+
+ align:start position:0%
+sense sort of on paper but at the same
+time you've embedded us so so deeply in
+
+ align:start position:0%
+time you've embedded us so so deeply in
+ 
+
+ align:start position:0%
+time you've embedded us so so deeply in
+this new harmonic
+
+ align:start position:0%
+this new harmonic
+ 
+
+ align:start position:0%
+this new harmonic
+area if you really want to get back to
+
+ align:start position:0%
+area if you really want to get back to
+ 
+
+ align:start position:0%
+area if you really want to get back to
+the home key it seems to me that the
+
+ align:start position:0%
+the home key it seems to me that the
+ 
+
+ align:start position:0%
+the home key it seems to me that the
+song should happen in three episodes one
+
+ align:start position:0%
+song should happen in three episodes one
+ 
+
+ align:start position:0%
+song should happen in three episodes one
+being the ultimate the uh initial
+
+ align:start position:0%
+being the ultimate the uh initial
+ 
+
+ align:start position:0%
+being the ultimate the uh initial
+statement rather in the home key area
+
+ align:start position:0%
+statement rather in the home key area
+ 
+
+ align:start position:0%
+statement rather in the home key area
+then your trip to whatever relative key
+
+ align:start position:0%
+then your trip to whatever relative key
+ 
+
+ align:start position:0%
+then your trip to whatever relative key
+area you wish to go and then some sort
+
+ align:start position:0%
+area you wish to go and then some sort
+ 
+
+ align:start position:0%
+area you wish to go and then some sort
+of vocal resolution that brings us back
+
+ align:start position:0%
+of vocal resolution that brings us back
+ 
+
+ align:start position:0%
+of vocal resolution that brings us back
+to the home area now again this the this
+
+ align:start position:0%
+to the home area now again this the this
+ 
+
+ align:start position:0%
+to the home area now again this the this
+is I'm talking strictly in terms of that
+
+ align:start position:0%
+is I'm talking strictly in terms of that
+ 
+
+ align:start position:0%
+is I'm talking strictly in terms of that
+kind of Convention of 19th century art
+
+ align:start position:0%
+kind of Convention of 19th century art
+ 
+
+ align:start position:0%
+kind of Convention of 19th century art
+song um this whole idea uh of symmetry
+
+ align:start position:0%
+song um this whole idea uh of symmetry
+ 
+
+ align:start position:0%
+song um this whole idea uh of symmetry
+which of course you know has been in
+
+ align:start position:0%
+which of course you know has been in
+ 
+
+ align:start position:0%
+which of course you know has been in
+existence long before that period but I
+
+ align:start position:0%
+existence long before that period but I
+ 
+
+ align:start position:0%
+existence long before that period but I
+think just for the sense
+
+ align:start position:0%
+think just for the sense
+ 
+
+ align:start position:0%
+think just for the sense
+of going back to the home key area you
+
+ align:start position:0%
+of going back to the home key area you
+ 
+
+ align:start position:0%
+of going back to the home key area you
+need to give the singer a little bit
+
+ align:start position:0%
+need to give the singer a little bit
+ 
+
+ align:start position:0%
+need to give the singer a little bit
+more and not just sort of let the piano
+
+ align:start position:0%
+more and not just sort of let the piano
+ 
+
+ align:start position:0%
+more and not just sort of let the piano
+take care of it there is of course I
+
+ align:start position:0%
+take care of it there is of course I
+ 
+
+ align:start position:0%
+take care of it there is of course I
+don't know how much Schuman you've
+
+ align:start position:0%
+don't know how much Schuman you've
+ 
+
+ align:start position:0%
+don't know how much Schuman you've
+listened to the art song of of Robert
+
+ align:start position:0%
+listened to the art song of of Robert
+ 
+
+ align:start position:0%
+listened to the art song of of Robert
+Schuman obviously right and left he does
+
+ align:start position:0%
+Schuman obviously right and left he does
+ 
+
+ align:start position:0%
+Schuman obviously right and left he does
+this very odd thing for those of you who
+
+ align:start position:0%
+this very odd thing for those of you who
+ 
+
+ align:start position:0%
+this very odd thing for those of you who
+have not listened to a lot of Schuman
+
+ align:start position:0%
+have not listened to a lot of Schuman
+ 
+
+ align:start position:0%
+have not listened to a lot of Schuman
+Shan is famous for writing these
+
+ align:start position:0%
+Shan is famous for writing these
+ 
+
+ align:start position:0%
+Shan is famous for writing these
+magnificent songs and then tacking on
+
+ align:start position:0%
+magnificent songs and then tacking on
+ 
+
+ align:start position:0%
+magnificent songs and then tacking on
+these seemingly like unrelated postludes
+
+ align:start position:0%
+these seemingly like unrelated postludes
+ 
+
+ align:start position:0%
+these seemingly like unrelated postludes
+that go on sometimes for a minute
+
+ align:start position:0%
+that go on sometimes for a minute
+ 
+
+ align:start position:0%
+that go on sometimes for a minute
+there's a famous song cycle of his where
+
+ align:start position:0%
+there's a famous song cycle of his where
+ 
+
+ align:start position:0%
+there's a famous song cycle of his where
+the last song the singer has just poured
+
+ align:start position:0%
+the last song the singer has just poured
+ 
+
+ align:start position:0%
+the last song the singer has just poured
+out her heart in this you know terribly
+
+ align:start position:0%
+out her heart in this you know terribly
+ 
+
+ align:start position:0%
+out her heart in this you know terribly
+wrenching way you know that her husband
+
+ align:start position:0%
+wrenching way you know that her husband
+ 
+
+ align:start position:0%
+wrenching way you know that her husband
+has died in her she will bury herself
+
+ align:start position:0%
+has died in her she will bury herself
+ 
+
+ align:start position:0%
+has died in her she will bury herself
+you know within her own heart and never
+
+ align:start position:0%
+you know within her own heart and never
+ 
+
+ align:start position:0%
+you know within her own heart and never
+never be revealed again very dark ending
+
+ align:start position:0%
+never be revealed again very dark ending
+ 
+
+ align:start position:0%
+never be revealed again very dark ending
+she finishes the song and then he sort
+
+ align:start position:0%
+she finishes the song and then he sort
+ 
+
+ align:start position:0%
+she finishes the song and then he sort
+of gives us a little leading chord and
+
+ align:start position:0%
+of gives us a little leading chord and
+ 
+
+ align:start position:0%
+of gives us a little leading chord and
+then goes off on this like gorgeous
+
+ align:start position:0%
+then goes off on this like gorgeous
+ 
+
+ align:start position:0%
+then goes off on this like gorgeous
+Little Piano Sonata all by himself and
+
+ align:start position:0%
+Little Piano Sonata all by himself and
+ 
+
+ align:start position:0%
+Little Piano Sonata all by himself and
+the singer just sort of stands there and
+
+ align:start position:0%
+the singer just sort of stands there and
+ 
+
+ align:start position:0%
+the singer just sort of stands there and
+the first time I saw that I was like oh
+
+ align:start position:0%
+the first time I saw that I was like oh
+ 
+
+ align:start position:0%
+the first time I saw that I was like oh
+thanks thanks a lot that's really handy
+
+ align:start position:0%
+thanks thanks a lot that's really handy
+ 
+
+ align:start position:0%
+thanks thanks a lot that's really handy
+so I think it can work in very specific
+
+ align:start position:0%
+so I think it can work in very specific
+ 
+
+ align:start position:0%
+so I think it can work in very specific
+context I mean I it's hard not to stand
+
+ align:start position:0%
+context I mean I it's hard not to stand
+ 
+
+ align:start position:0%
+context I mean I it's hard not to stand
+there and feel like you have egg on your
+
+ align:start position:0%
+there and feel like you have egg on your
+ 
+
+ align:start position:0%
+there and feel like you have egg on your
+face but unless you parse out the idea
+
+ align:start position:0%
+face but unless you parse out the idea
+ 
+
+ align:start position:0%
+face but unless you parse out the idea
+of of the the key that you want to end
+
+ align:start position:0%
+of of the the key that you want to end
+ 
+
+ align:start position:0%
+of of the the key that you want to end
+up in more thoroughly I say either
+
+ align:start position:0%
+up in more thoroughly I say either
+ 
+
+ align:start position:0%
+up in more thoroughly I say either
+elongate your
+
+ align:start position:0%
+elongate your
+ 
+
+ align:start position:0%
+elongate your
+postlude have it make more of a
+
+ align:start position:0%
+postlude have it make more of a
+ 
+
+ align:start position:0%
+postlude have it make more of a
+statement about what has preceded so it
+
+ align:start position:0%
+statement about what has preceded so it
+ 
+
+ align:start position:0%
+statement about what has preceded so it
+gives balance at the end of the song to
+
+ align:start position:0%
+gives balance at the end of the song to
+ 
+
+ align:start position:0%
+gives balance at the end of the song to
+what has happened at the front end
+
+ align:start position:0%
+what has happened at the front end
+ 
+
+ align:start position:0%
+what has happened at the front end
+because the front end is very strong you
+
+ align:start position:0%
+because the front end is very strong you
+ 
+
+ align:start position:0%
+because the front end is very strong you
+have this very emotional I mean it
+
+ align:start position:0%
+have this very emotional I mean it
+ 
+
+ align:start position:0%
+have this very emotional I mean it
+reminds me a little bit of um Al of of
+
+ align:start position:0%
+reminds me a little bit of um Al of of
+ 
+
+ align:start position:0%
+reminds me a little bit of um Al of of
+shat which I'm sure you've listen to uh
+
+ align:start position:0%
+shat which I'm sure you've listen to uh
+ 
+
+ align:start position:0%
+shat which I'm sure you've listen to uh
+where we have a distinct voice of a
+
+ align:start position:0%
+where we have a distinct voice of a
+ 
+
+ align:start position:0%
+where we have a distinct voice of a
+character and then a distinct voice of
+
+ align:start position:0%
+character and then a distinct voice of
+ 
+
+ align:start position:0%
+character and then a distinct voice of
+uh a narrator so you've given us this
+
+ align:start position:0%
+uh a narrator so you've given us this
+ 
+
+ align:start position:0%
+uh a narrator so you've given us this
+nice thing but then we're sort of
+
+ align:start position:0%
+nice thing but then we're sort of
+ 
+
+ align:start position:0%
+nice thing but then we're sort of
+missing the day new mall sort of missing
+
+ align:start position:0%
+missing the day new mall sort of missing
+ 
+
+ align:start position:0%
+missing the day new mall sort of missing
+the last step now obviously there's no
+
+ align:start position:0%
+the last step now obviously there's no
+ 
+
+ align:start position:0%
+the last step now obviously there's no
+more text in the poem you're all fresh
+
+ align:start position:0%
+more text in the poem you're all fresh
+ 
+
+ align:start position:0%
+more text in the poem you're all fresh
+out but I guess uh that's the one thing
+
+ align:start position:0%
+out but I guess uh that's the one thing
+ 
+
+ align:start position:0%
+out but I guess uh that's the one thing
+that is sort of missing to me an overall
+
+ align:start position:0%
+that is sort of missing to me an overall
+ 
+
+ align:start position:0%
+that is sort of missing to me an overall
+sense of balance uh to the song in terms
+
+ align:start position:0%
+sense of balance uh to the song in terms
+ 
+
+ align:start position:0%
+sense of balance uh to the song in terms
+of how it sings in terms of how it feels
+
+ align:start position:0%
+of how it sings in terms of how it feels
+ 
+
+ align:start position:0%
+of how it sings in terms of how it feels
+in the voice it's very nicely written in
+
+ align:start position:0%
+in the voice it's very nicely written in
+ 
+
+ align:start position:0%
+in the voice it's very nicely written in
+terms of uh vocal line um a typical trap
+
+ align:start position:0%
+terms of uh vocal line um a typical trap
+ 
+
+ align:start position:0%
+terms of uh vocal line um a typical trap
+that young composers often fall into
+
+ align:start position:0%
+that young composers often fall into
+ 
+
+ align:start position:0%
+that young composers often fall into
+including ones who really should know
+
+ align:start position:0%
+including ones who really should know
+ 
+
+ align:start position:0%
+including ones who really should know
+better because they're earning their
+
+ align:start position:0%
+better because they're earning their
+ 
+
+ align:start position:0%
+better because they're earning their
+money being composers um is to either be
+
+ align:start position:0%
+money being composers um is to either be
+ 
+
+ align:start position:0%
+money being composers um is to either be
+far too conservative with the voice and
+
+ align:start position:0%
+far too conservative with the voice and
+ 
+
+ align:start position:0%
+far too conservative with the voice and
+just sort of out of out of fear of of
+
+ align:start position:0%
+just sort of out of out of fear of of
+ 
+
+ align:start position:0%
+just sort of out of out of fear of of
+demanding too much or just going
+
+ align:start position:0%
+demanding too much or just going
+ 
+
+ align:start position:0%
+demanding too much or just going
+completely off the deep end and having
+
+ align:start position:0%
+completely off the deep end and having
+ 
+
+ align:start position:0%
+completely off the deep end and having
+you know making demands of this of the
+
+ align:start position:0%
+you know making demands of this of the
+ 
+
+ align:start position:0%
+you know making demands of this of the
+singer that are just not vocally
+
+ align:start position:0%
+singer that are just not vocally
+ 
+
+ align:start position:0%
+singer that are just not vocally
+appropriate for the person's uh fa or
+
+ align:start position:0%
+appropriate for the person's uh fa or
+ 
+
+ align:start position:0%
+appropriate for the person's uh fa or
+voice cat organization uh and you've
+
+ align:start position:0%
+voice cat organization uh and you've
+ 
+
+ align:start position:0%
+voice cat organization uh and you've
+done a good job of sort of having one
+
+ align:start position:0%
+done a good job of sort of having one
+ 
+
+ align:start position:0%
+done a good job of sort of having one
+foot in each Camp having the bulk of the
+
+ align:start position:0%
+foot in each Camp having the bulk of the
+ 
+
+ align:start position:0%
+foot in each Camp having the bulk of the
+melody sitting in a very comfortable
+
+ align:start position:0%
+melody sitting in a very comfortable
+ 
+
+ align:start position:0%
+melody sitting in a very comfortable
+sort of middle range and allowing it to
+
+ align:start position:0%
+sort of middle range and allowing it to
+ 
+
+ align:start position:0%
+sort of middle range and allowing it to
+Arc up and down
+
+ align:start position:0%
+Arc up and down
+ 
+
+ align:start position:0%
+Arc up and down
+um to make certain dramatic statements
+
+ align:start position:0%
+um to make certain dramatic statements
+ 
+
+ align:start position:0%
+um to make certain dramatic statements
+which I think is really clever um and
+
+ align:start position:0%
+which I think is really clever um and
+ 
+
+ align:start position:0%
+which I think is really clever um and
+difficult to do as well so cros to you
+
+ align:start position:0%
+difficult to do as well so cros to you
+ 
+
+ align:start position:0%
+difficult to do as well so cros to you
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that um Daniel you forgive me if i n on
+
+ align:start position:0%
+that um Daniel you forgive me if i n on
+ 
+
+ align:start position:0%
+that um Daniel you forgive me if i n on
+for a couple seconds longer um with
+
+ align:start position:0%
+for a couple seconds longer um with
+ 
+
+ align:start position:0%
+for a couple seconds longer um with
+regard to the score itself there's one
+
+ align:start position:0%
+regard to the score itself there's one
+ 
+
+ align:start position:0%
+regard to the score itself there's one
+particularly strange thing and Peter you
+
+ align:start position:0%
+particularly strange thing and Peter you
+ 
+
+ align:start position:0%
+particularly strange thing and Peter you
+need to put in your two cents here but
+
+ align:start position:0%
+need to put in your two cents here but
+ 
+
+ align:start position:0%
+need to put in your two cents here but
+it's measure 20 it's a very awkward way
+
+ align:start position:0%
+it's measure 20 it's a very awkward way
+ 
+
+ align:start position:0%
+it's measure 20 it's a very awkward way
+of notating that Rhythm if that's indeed
+
+ align:start position:0%
+of notating that Rhythm if that's indeed
+ 
+
+ align:start position:0%
+of notating that Rhythm if that's indeed
+the Rhythm that you
+
+ align:start position:0%
+the Rhythm that you
+ 
+
+ align:start position:0%
+the Rhythm that you
+intended it comes out is the night was
+
+ align:start position:0%
+intended it comes out is the night was
+ 
+
+ align:start position:0%
+intended it comes out is the night was
+dark no father was there it was kind of
+
+ align:start position:0%
+dark no father was there it was kind of
+ 
+
+ align:start position:0%
+dark no father was there it was kind of
+a if I were
+
+ align:start position:0%
+a if I were
+ 
+
+ align:start position:0%
+a if I were
+to recite it with a rhythm that made the
+
+ align:start position:0%
+to recite it with a rhythm that made the
+ 
+
+ align:start position:0%
+to recite it with a rhythm that made the
+most sense to me with in context of the
+
+ align:start position:0%
+most sense to me with in context of the
+ 
+
+ align:start position:0%
+most sense to me with in context of the
+speech I would have probably said the
+
+ align:start position:0%
+speech I would have probably said the
+ 
+
+ align:start position:0%
+speech I would have probably said the
+night was dark no father was there in
+
+ align:start position:0%
+night was dark no father was there in
+ 
+
+ align:start position:0%
+night was dark no father was there in
+other words back the whole thing up by
+
+ align:start position:0%
+other words back the whole thing up by
+ 
+
+ align:start position:0%
+other words back the whole thing up by
+an E
+
+ align:start position:0%
+an E
+ 
+
+ align:start position:0%
+an E
+note the way it's written there in uh in
+
+ align:start position:0%
+note the way it's written there in uh in
+ 
+
+ align:start position:0%
+note the way it's written there in uh in
+68 we're looking for certain visual
+
+ align:start position:0%
+68 we're looking for certain visual
+ 
+
+ align:start position:0%
+68 we're looking for certain visual
+groupings on the page and to give us you
+
+ align:start position:0%
+groupings on the page and to give us you
+ 
+
+ align:start position:0%
+groupings on the page and to give us you
+know the qu note makes sense I mean it's
+
+ align:start position:0%
+know the qu note makes sense I mean it's
+ 
+
+ align:start position:0%
+know the qu note makes sense I mean it's
+nothing fancy but what trips up the eye
+
+ align:start position:0%
+nothing fancy but what trips up the eye
+ 
+
+ align:start position:0%
+nothing fancy but what trips up the eye
+is the dotted e tied to the 16th tied to
+
+ align:start position:0%
+is the dotted e tied to the 16th tied to
+ 
+
+ align:start position:0%
+is the dotted e tied to the 16th tied to
+the two additional eights if you see
+
+ align:start position:0%
+the two additional eights if you see
+ 
+
+ align:start position:0%
+the two additional eights if you see
+what I mean that's a that looks odd on
+
+ align:start position:0%
+what I mean that's a that looks odd on
+ 
+
+ align:start position:0%
+what I mean that's a that looks odd on
+the page and it makes if we're thinking
+
+ align:start position:0%
+the page and it makes if we're thinking
+ 
+
+ align:start position:0%
+the page and it makes if we're thinking
+in 68 we're not necessarily going to
+
+ align:start position:0%
+in 68 we're not necessarily going to
+ 
+
+ align:start position:0%
+in 68 we're not necessarily going to
+parse that out as a sudden feel of 34
+
+ align:start position:0%
+parse that out as a sudden feel of 34
+ 
+
+ align:start position:0%
+parse that out as a sudden feel of 34
+because that's not a 34 pulse is not
+
+ align:start position:0%
+because that's not a 34 pulse is not
+ 
+
+ align:start position:0%
+because that's not a 34 pulse is not
+something that we're feeling uniformly
+
+ align:start position:0%
+something that we're feeling uniformly
+ 
+
+ align:start position:0%
+something that we're feeling uniformly
+throughout this section you see what I'm
+
+ align:start position:0%
+throughout this section you see what I'm
+ 
+
+ align:start position:0%
+throughout this section you see what I'm
+talking about I'm not sure I'm
+
+ align:start position:0%
+talking about I'm not sure I'm
+ 
+
+ align:start position:0%
+talking about I'm not sure I'm
+articulating it as clearly as as a
+
+ align:start position:0%
+articulating it as clearly as as a
+ 
+
+ align:start position:0%
+articulating it as clearly as as a
+composer would but um I say either if
+
+ align:start position:0%
+composer would but um I say either if
+ 
+
+ align:start position:0%
+composer would but um I say either if
+you want to stick to that Rhythm then
+
+ align:start position:0%
+you want to stick to that Rhythm then
+ 
+
+ align:start position:0%
+you want to stick to that Rhythm then
+see if you can find a different way of
+
+ align:start position:0%
+see if you can find a different way of
+ 
+
+ align:start position:0%
+see if you can find a different way of
+notating it with Tide notes tide notes
+
+ align:start position:0%
+notating it with Tide notes tide notes
+ 
+
+ align:start position:0%
+notating it with Tide notes tide notes
+seem fussy and weird but actually
+
+ align:start position:0%
+seem fussy and weird but actually
+ 
+
+ align:start position:0%
+seem fussy and weird but actually
+visually they can make the language much
+
+ align:start position:0%
+visually they can make the language much
+ 
+
+ align:start position:0%
+visually they can make the language much
+clearer to the eye when looking at
+
+ align:start position:0%
+clearer to the eye when looking at
+ 
+
+ align:start position:0%
+clearer to the eye when looking at
+it my only suggestion uh in my
+
+ align:start position:0%
+it my only suggestion uh in my
+ 
+
+ align:start position:0%
+it my only suggestion uh in my
+own uh what am I trying to
+
+ align:start position:0%
+own uh what am I trying to
+ 
+
+ align:start position:0%
+own uh what am I trying to
+say in support of my other suggestion
+
+ align:start position:0%
+say in support of my other suggestion
+ 
+
+ align:start position:0%
+say in support of my other suggestion
+which is shifting up slightly like
+
+ align:start position:0%
+which is shifting up slightly like
+ 
+
+ align:start position:0%
+which is shifting up slightly like
+moving it back by an eighth note would
+
+ align:start position:0%
+moving it back by an eighth note would
+ 
+
+ align:start position:0%
+moving it back by an eighth note would
+be to give a truer sense of the shape of
+
+ align:start position:0%
+be to give a truer sense of the shape of
+ 
+
+ align:start position:0%
+be to give a truer sense of the shape of
+the text this comes out feel like no
+
+ align:start position:0%
+the text this comes out feel like no
+ 
+
+ align:start position:0%
+the text this comes out feel like no
+father was there I'm not sure if you
+
+ align:start position:0%
+father was there I'm not sure if you
+ 
+
+ align:start position:0%
+father was there I'm not sure if you
+mean no father was there or no father
+
+ align:start position:0%
+mean no father was there or no father
+ 
+
+ align:start position:0%
+mean no father was there or no father
+was there you need to make up your mind
+
+ align:start position:0%
+was there you need to make up your mind
+ 
+
+ align:start position:0%
+was there you need to make up your mind
+which is the important word in there
+
+ align:start position:0%
+which is the important word in there
+ 
+
+ align:start position:0%
+which is the important word in there
+because the way you said it it's it's it
+
+ align:start position:0%
+because the way you said it it's it's it
+ 
+
+ align:start position:0%
+because the way you said it it's it's it
+falls in neither Camp you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I'm trying to think if I had any
+
+ align:start position:0%
+see I'm trying to think if I had any
+ 
+
+ align:start position:0%
+see I'm trying to think if I had any
+other ideas with regard to the score I
+
+ align:start position:0%
+other ideas with regard to the score I
+ 
+
+ align:start position:0%
+other ideas with regard to the score I
+didn't Daniel would you please feel
+
+ align:start position:0%
+didn't Daniel would you please feel
+ 
+
+ align:start position:0%
+didn't Daniel would you please feel
+through that I'll say a couple of things
+
+ align:start position:0%
+through that I'll say a couple of things
+ 
+
+ align:start position:0%
+through that I'll say a couple of things
+um first that I appreciate a lot of the
+
+ align:start position:0%
+um first that I appreciate a lot of the
+ 
+
+ align:start position:0%
+um first that I appreciate a lot of the
+articulation that you've given this
+
+ align:start position:0%
+articulation that you've given this
+ 
+
+ align:start position:0%
+articulation that you've given this
+piano part um and but one one difficult
+
+ align:start position:0%
+piano part um and but one one difficult
+ 
+
+ align:start position:0%
+piano part um and but one one difficult
+thing about this piece is when there are
+
+ align:start position:0%
+thing about this piece is when there are
+ 
+
+ align:start position:0%
+thing about this piece is when there are
+different articulations in each hand and
+
+ align:start position:0%
+different articulations in each hand and
+ 
+
+ align:start position:0%
+different articulations in each hand and
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+something that certainly as a Pianist
+
+ align:start position:0%
+something that certainly as a Pianist
+ 
+
+ align:start position:0%
+something that certainly as a Pianist
+you come across but but it's always a
+
+ align:start position:0%
+you come across but but it's always a
+ 
+
+ align:start position:0%
+you come across but but it's always a
+very uh specific thing that a composer
+
+ align:start position:0%
+very uh specific thing that a composer
+ 
+
+ align:start position:0%
+very uh specific thing that a composer
+is going for when when a Pianist is
+
+ align:start position:0%
+is going for when when a Pianist is
+ 
+
+ align:start position:0%
+is going for when when a Pianist is
+asked to do such separate articulations
+
+ align:start position:0%
+asked to do such separate articulations
+ 
+
+ align:start position:0%
+asked to do such separate articulations
+in the hands um and even I don't know if
+
+ align:start position:0%
+in the hands um and even I don't know if
+ 
+
+ align:start position:0%
+in the hands um and even I don't know if
+you noticed in 24 I think the second
+
+ align:start position:0%
+you noticed in 24 I think the second
+ 
+
+ align:start position:0%
+you noticed in 24 I think the second
+time we did it I played the right hand
+
+ align:start position:0%
+time we did it I played the right hand
+ 
+
+ align:start position:0%
+time we did it I played the right hand
+Legato and I played the left hand
+
+ align:start position:0%
+Legato and I played the left hand
+ 
+
+ align:start position:0%
+Legato and I played the left hand
+staccato I you know I revers the
+
+ align:start position:0%
+staccato I you know I revers the
+ 
+
+ align:start position:0%
+staccato I you know I revers the
+articulations um and I guess I'm only
+
+ align:start position:0%
+articulations um and I guess I'm only
+ 
+
+ align:start position:0%
+articulations um and I guess I'm only
+mentioning this to
+
+ align:start position:0%
+mentioning this to
+ 
+
+ align:start position:0%
+mentioning this to
+say be be careful when you do that um
+
+ align:start position:0%
+say be be careful when you do that um
+ 
+
+ align:start position:0%
+say be be careful when you do that um
+because it it makes such a strong
+
+ align:start position:0%
+because it it makes such a strong
+ 
+
+ align:start position:0%
+because it it makes such a strong
+impression on me to see that on the page
+
+ align:start position:0%
+impression on me to see that on the page
+ 
+
+ align:start position:0%
+impression on me to see that on the page
+um but I agree that the
+
+ align:start position:0%
+um but I agree that the
+ 
+
+ align:start position:0%
+um but I agree that the
+end feels it feels a little lopsided in
+
+ align:start position:0%
+end feels it feels a little lopsided in
+ 
+
+ align:start position:0%
+end feels it feels a little lopsided in
+favor of of the front of the piece and
+
+ align:start position:0%
+favor of of the front of the piece and
+ 
+
+ align:start position:0%
+favor of of the front of the piece and
+that if if you do get a chance to expand
+
+ align:start position:0%
+that if if you do get a chance to expand
+ 
+
+ align:start position:0%
+that if if you do get a chance to expand
+on the end I was I love measure eight
+
+ align:start position:0%
+on the end I was I love measure eight
+ 
+
+ align:start position:0%
+on the end I was I love measure eight
+when that Chola Rhythm comes in uh in my
+
+ align:start position:0%
+when that Chola Rhythm comes in uh in my
+ 
+
+ align:start position:0%
+when that Chola Rhythm comes in uh in my
+part this
+
+ align:start position:0%
+part this
+ 
+
+ align:start position:0%
+part this
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I was kind of waiting for that to
+
+ align:start position:0%
+and I was kind of waiting for that to
+ 
+
+ align:start position:0%
+and I was kind of waiting for that to
+come back at the end um and I know you
+
+ align:start position:0%
+come back at the end um and I know you
+ 
+
+ align:start position:0%
+come back at the end um and I know you
+don't have the same text to work with
+
+ align:start position:0%
+don't have the same text to work with
+ 
+
+ align:start position:0%
+don't have the same text to work with
+but it's such a memorable moment that if
+
+ align:start position:0%
+but it's such a memorable moment that if
+ 
+
+ align:start position:0%
+but it's such a memorable moment that if
+that kind of gesture were to come back
+
+ align:start position:0%
+that kind of gesture were to come back
+ 
+
+ align:start position:0%
+that kind of gesture were to come back
+at the end it would give us that sense
+
+ align:start position:0%
+at the end it would give us that sense
+ 
+
+ align:start position:0%
+at the end it would give us that sense
+of return and solidifying you know the
+
+ align:start position:0%
+of return and solidifying you know the
+ 
+
+ align:start position:0%
+of return and solidifying you know the
+home key and all of
+
+ align:start position:0%
+home key and all of
+ 
+
+ align:start position:0%
+home key and all of
+that no very very nice part to play I
+
+ align:start position:0%
+that no very very nice part to play I
+ 
+
+ align:start position:0%
+that no very very nice part to play I
+wanted to extract
+
+ align:start position:0%
+wanted to extract
+ 
+
+ align:start position:0%
+wanted to extract
+briefly on the points Danel made about
+
+ align:start position:0%
+briefly on the points Danel made about
+ 
+
+ align:start position:0%
+briefly on the points Danel made about
+articulation which are really really
+
+ align:start position:0%
+articulation which are really really
+ 
+
+ align:start position:0%
+articulation which are really really
+really well put one thing that I find I
+
+ align:start position:0%
+really well put one thing that I find I
+ 
+
+ align:start position:0%
+really well put one thing that I find I
+have found I should say uh frequently is
+
+ align:start position:0%
+have found I should say uh frequently is
+ 
+
+ align:start position:0%
+have found I should say uh frequently is
+often what makes differences in
+
+ align:start position:0%
+often what makes differences in
+ 
+
+ align:start position:0%
+often what makes differences in
+articulation really work or what
+
+ align:start position:0%
+articulation really work or what
+ 
+
+ align:start position:0%
+articulation really work or what
+gives tension to a piece is if the
+
+ align:start position:0%
+gives tension to a piece is if the
+ 
+
+ align:start position:0%
+gives tension to a piece is if the
+entire piano part has one texture and
+
+ align:start position:0%
+entire piano part has one texture and
+ 
+
+ align:start position:0%
+entire piano part has one texture and
+the voice is asked to use a different
+
+ align:start position:0%
+the voice is asked to use a different
+ 
+
+ align:start position:0%
+the voice is asked to use a different
+texture um I can think of aund different
+
+ align:start position:0%
+texture um I can think of aund different
+ 
+
+ align:start position:0%
+texture um I can think of aund different
+examples um of course now I can't oh
+
+ align:start position:0%
+examples um of course now I can't oh
+ 
+
+ align:start position:0%
+examples um of course now I can't oh
+there there's a a piece probably one of
+
+ align:start position:0%
+there there's a a piece probably one of
+ 
+
+ align:start position:0%
+there there's a a piece probably one of
+many called of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shat where the piano is really imitating
+
+ align:start position:0%
+shat where the piano is really imitating
+ 
+
+ align:start position:0%
+shat where the piano is really imitating
+the plucking of a mandolin it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and the voice has this sort of
+
+ align:start position:0%
+like and the voice has this sort of
+ 
+
+ align:start position:0%
+like and the voice has this sort of
+fabulous sort of honeyed soaring
+
+ align:start position:0%
+fabulous sort of honeyed soaring
+ 
+
+ align:start position:0%
+fabulous sort of honeyed soaring
+gorgeous thing but it's the contrast
+
+ align:start position:0%
+gorgeous thing but it's the contrast
+ 
+
+ align:start position:0%
+gorgeous thing but it's the contrast
+between you know if the piano was
+
+ align:start position:0%
+between you know if the piano was
+ 
+
+ align:start position:0%
+between you know if the piano was
+all and the voice was doing that it
+
+ align:start position:0%
+all and the voice was doing that it
+ 
+
+ align:start position:0%
+all and the voice was doing that it
+would sound like a big muddy mess but
+
+ align:start position:0%
+would sound like a big muddy mess but
+ 
+
+ align:start position:0%
+would sound like a big muddy mess but
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+juxtaposed dry against wet pretty good
+
+ align:start position:0%
+juxtaposed dry against wet pretty good
+ 
+
+ align:start position:0%
+juxtaposed dry against wet pretty good
+way of putting it um somehow it just
+
+ align:start position:0%
+way of putting it um somehow it just
+ 
+
+ align:start position:0%
+way of putting it um somehow it just
+makes the song Come to Life it makes it
+
+ align:start position:0%
+makes the song Come to Life it makes it
+ 
+
+ align:start position:0%
+makes the song Come to Life it makes it
+so romantic and so evocative suddenly
+
+ align:start position:0%
+so romantic and so evocative suddenly
+ 
+
+ align:start position:0%
+so romantic and so evocative suddenly
+you hear precisely what is intended
+
+ align:start position:0%
+you hear precisely what is intended
+ 
+
+ align:start position:0%
+you hear precisely what is intended
+you've got such a good a sense of the
+
+ align:start position:0%
+you've got such a good a sense of the
+ 
+
+ align:start position:0%
+you've got such a good a sense of the
+sort of like
+
+ align:start position:0%
+sort of like
+ 
+
+ align:start position:0%
+sort of like
+brooding uh picture that the poem uh
+
+ align:start position:0%
+brooding uh picture that the poem uh
+ 
+
+ align:start position:0%
+brooding uh picture that the poem uh
+delineates I think that you can work
+
+ align:start position:0%
+delineates I think that you can work
+ 
+
+ align:start position:0%
+delineates I think that you can work
+using articulation specifically between
+
+ align:start position:0%
+using articulation specifically between
+ 
+
+ align:start position:0%
+using articulation specifically between
+the voice partner piano part um or
+
+ align:start position:0%
+the voice partner piano part um or
+ 
+
+ align:start position:0%
+the voice partner piano part um or
+Dynamics or whatever it may be to
+
+ align:start position:0%
+Dynamics or whatever it may be to
+ 
+
+ align:start position:0%
+Dynamics or whatever it may be to
+heighten that and make it more specific
+
+ align:start position:0%
+heighten that and make it more specific
+ 
+
+ align:start position:0%
+heighten that and make it more specific
+I also thought of one other thing that I
+
+ align:start position:0%
+I also thought of one other thing that I
+ 
+
+ align:start position:0%
+I also thought of one other thing that I
+wanted to mention which
+
+ align:start position:0%
+wanted to mention which
+ 
+
+ align:start position:0%
+wanted to mention which
+is uh and again this has a lot to do
+
+ align:start position:0%
+is uh and again this has a lot to do
+ 
+
+ align:start position:0%
+is uh and again this has a lot to do
+with the convention of 19th century song
+
+ align:start position:0%
+with the convention of 19th century song
+ 
+
+ align:start position:0%
+with the convention of 19th century song
+which this which your composition seems
+
+ align:start position:0%
+which this which your composition seems
+ 
+
+ align:start position:0%
+which this which your composition seems
+to owe uh a good deal to and that is a a
+
+ align:start position:0%
+to owe uh a good deal to and that is a a
+ 
+
+ align:start position:0%
+to owe uh a good deal to and that is a a
+not a terribly strong feeling of cadence
+
+ align:start position:0%
+not a terribly strong feeling of cadence
+ 
+
+ align:start position:0%
+not a terribly strong feeling of cadence
+at the end and I'm not saying that it
+
+ align:start position:0%
+at the end and I'm not saying that it
+ 
+
+ align:start position:0%
+at the end and I'm not saying that it
+has to be that way of course it doesn't
+
+ align:start position:0%
+has to be that way of course it doesn't
+ 
+
+ align:start position:0%
+has to be that way of course it doesn't
+it's always one's individual choice but
+
+ align:start position:0%
+it's always one's individual choice but
+ 
+
+ align:start position:0%
+it's always one's individual choice but
+if you're working within this harmonic
+
+ align:start position:0%
+if you're working within this harmonic
+ 
+
+ align:start position:0%
+if you're working within this harmonic
+language uh unless you're going to do
+
+ align:start position:0%
+language uh unless you're going to do
+ 
+
+ align:start position:0%
+language uh unless you're going to do
+something that
+
+ align:start position:0%
+something that
+ 
+
+ align:start position:0%
+something that
+is very specifically moving away from
+
+ align:start position:0%
+is very specifically moving away from
+ 
+
+ align:start position:0%
+is very specifically moving away from
+that tradition in other words paying uh
+
+ align:start position:0%
+that tradition in other words paying uh
+ 
+
+ align:start position:0%
+that tradition in other words paying uh
+tribute to that tradition of of vocal
+
+ align:start position:0%
+tribute to that tradition of of vocal
+ 
+
+ align:start position:0%
+tribute to that tradition of of vocal
+and piano writing yet putting your own
+
+ align:start position:0%
+and piano writing yet putting your own
+ 
+
+ align:start position:0%
+and piano writing yet putting your own
+impr prematur on it I think it needs to
+
+ align:start position:0%
+impr prematur on it I think it needs to
+ 
+
+ align:start position:0%
+impr prematur on it I think it needs to
+be more specific and clearly articulated
+
+ align:start position:0%
+be more specific and clearly articulated
+ 
+
+ align:start position:0%
+be more specific and clearly articulated
+then sort of a a Cadence that kind of
+
+ align:start position:0%
+then sort of a a Cadence that kind of
+ 
+
+ align:start position:0%
+then sort of a a Cadence that kind of
+hints at something a little bit more
+
+ align:start position:0%
+hints at something a little bit more
+ 
+
+ align:start position:0%
+hints at something a little bit more
+abstract but doesn't really deliver bit
+
+ align:start position:0%
+abstract but doesn't really deliver bit
+ 
+
+ align:start position:0%
+abstract but doesn't really deliver bit
+of goods so again it all gets back to
+
+ align:start position:0%
+of goods so again it all gets back to
+ 
+
+ align:start position:0%
+of goods so again it all gets back to
+the idea of giving the piece more
+
+ align:start position:0%
+the idea of giving the piece more
+ 
+
+ align:start position:0%
+the idea of giving the piece more
+balance giving it a little something on
+
+ align:start position:0%
+balance giving it a little something on
+ 
+
+ align:start position:0%
+balance giving it a little something on
+the end to weigh it down if that makes
+
+ align:start position:0%
+the end to weigh it down if that makes
+ 
+
+ align:start position:0%
+the end to weigh it down if that makes
+sense um for the piano part purposely
+
+ align:start position:0%
+sense um for the piano part purposely
+ 
+
+ align:start position:0%
+sense um for the piano part purposely
+didn't want to have strong Cadence
+
+ align:start position:0%
+didn't want to have strong Cadence
+ 
+
+ align:start position:0%
+didn't want to have strong Cadence
+because I wanted to go back to text
+
+ align:start position:0%
+because I wanted to go back to text
+ 
+
+ align:start position:0%
+because I wanted to go back to text
+painting for the vapor flu um
+
+ align:start position:0%
+painting for the vapor flu um
+ 
+
+ align:start position:0%
+painting for the vapor flu um
+part but yeah I agree I should expand
+
+ align:start position:0%
+part but yeah I agree I should expand
+ 
+
+ align:start position:0%
+part but yeah I agree I should expand
+more upon if that's the intent then
+
+ align:start position:0%
+more upon if that's the intent then
+ 
+
+ align:start position:0%
+more upon if that's the intent then
+there's a good deal more you can do to
+
+ align:start position:0%
+there's a good deal more you can do to
+ 
+
+ align:start position:0%
+there's a good deal more you can do to
+help push your pianist in that Direction
+
+ align:start position:0%
+help push your pianist in that Direction
+ 
+
+ align:start position:0%
+help push your pianist in that Direction
+and again you could feel free to
+
+ align:start position:0%
+and again you could feel free to
+ 
+
+ align:start position:0%
+and again you could feel free to
+interrup me but I would suggest marking
+
+ align:start position:0%
+interrup me but I would suggest marking
+ 
+
+ align:start position:0%
+interrup me but I would suggest marking
+your ritardando earlier and marking
+
+ align:start position:0%
+your ritardando earlier and marking
+ 
+
+ align:start position:0%
+your ritardando earlier and marking
+Dynamics for sure uh with actual words
+
+ align:start position:0%
+Dynamics for sure uh with actual words
+ 
+
+ align:start position:0%
+Dynamics for sure uh with actual words
+or like uh morendo or
+
+ align:start position:0%
+or like uh morendo or
+ 
+
+ align:start position:0%
+or like uh morendo or
+uh I don't know just find find find the
+
+ align:start position:0%
+uh I don't know just find find find the
+ 
+
+ align:start position:0%
+uh I don't know just find find find the
+right combination of of words and
+
+ align:start position:0%
+right combination of of words and
+ 
+
+ align:start position:0%
+right combination of of words and
+diacritical markings to indicate that
+
+ align:start position:0%
+diacritical markings to indicate that
+ 
+
+ align:start position:0%
+diacritical markings to indicate that
+you're looking for a very specific sort
+
+ align:start position:0%
+you're looking for a very specific sort
+ 
+
+ align:start position:0%
+you're looking for a very specific sort
+of ephemeral Vanishing vaporous effect
+
+ align:start position:0%
+of ephemeral Vanishing vaporous effect
+ 
+
+ align:start position:0%
+of ephemeral Vanishing vaporous effect
+because here looking at it it looks like
+
+ align:start position:0%
+because here looking at it it looks like
+ 
+
+ align:start position:0%
+because here looking at it it looks like
+you want the same in all four measures
+
+ align:start position:0%
+you want the same in all four measures
+ 
+
+ align:start position:0%
+you want the same in all four measures
+and a little bit of slowing down and a
+
+ align:start position:0%
+and a little bit of slowing down and a
+ 
+
+ align:start position:0%
+and a little bit of slowing down and a
+little bit quiet in the last measure
+
+ align:start position:0%
+little bit quiet in the last measure
+ 
+
+ align:start position:0%
+little bit quiet in the last measure
+when in fact the effect you're going for
+
+ align:start position:0%
+when in fact the effect you're going for
+ 
+
+ align:start position:0%
+when in fact the effect you're going for
+will demand a lot
+
+ align:start position:0%
+will demand a lot
+ 
+
+ align:start position:0%
+will demand a lot
+more uh a lot more of something of De
+
+ align:start position:0%
+more uh a lot more of something of De
+ 
+
+ align:start position:0%
+more uh a lot more of something of De
+Crescendo or lightness of touch or more
+
+ align:start position:0%
+Crescendo or lightness of touch or more
+ 
+
+ align:start position:0%
+Crescendo or lightness of touch or more
+pedal or less pedal or something but
+
+ align:start position:0%
+pedal or less pedal or something but
+ 
+
+ align:start position:0%
+pedal or less pedal or something but
+whatever it is don't be afraid to be
+
+ align:start position:0%
+whatever it is don't be afraid to be
+ 
+
+ align:start position:0%
+whatever it is don't be afraid to be
+specific Daniel made a great comment at
+
+ align:start position:0%
+specific Daniel made a great comment at
+ 
+
+ align:start position:0%
+specific Daniel made a great comment at
+the beginning which is that a
+
+ align:start position:0%
+the beginning which is that a
+ 
+
+ align:start position:0%
+the beginning which is that a
+well-marked piece I mean it may seem
+
+ align:start position:0%
+well-marked piece I mean it may seem
+ 
+
+ align:start position:0%
+well-marked piece I mean it may seem
+fiddly and fussy to go in you know
+
+ align:start position:0%
+fiddly and fussy to go in you know
+ 
+
+ align:start position:0%
+fiddly and fussy to go in you know
+finale or whatever put in all those
+
+ align:start position:0%
+finale or whatever put in all those
+ 
+
+ align:start position:0%
+finale or whatever put in all those
+stupid Within These pedal articulations
+
+ align:start position:0%
+stupid Within These pedal articulations
+ 
+
+ align:start position:0%
+stupid Within These pedal articulations
+we love that kind of thing that's that's
+
+ align:start position:0%
+we love that kind of thing that's that's
+ 
+
+ align:start position:0%
+we love that kind of thing that's that's
+where we we sort of live and die as
+
+ align:start position:0%
+where we we sort of live and die as
+ 
+
+ align:start position:0%
+where we we sort of live and die as
+performers I mean I love having you know
+
+ align:start position:0%
+performers I mean I love having you know
+ 
+
+ align:start position:0%
+performers I mean I love having you know
+a piece by I know name name your
+
+ align:start position:0%
+a piece by I know name name your
+ 
+
+ align:start position:0%
+a piece by I know name name your
+favorite 17th Century composer you know
+
+ align:start position:0%
+favorite 17th Century composer you know
+ 
+
+ align:start position:0%
+favorite 17th Century composer you know
+where there are no diacritical markings
+
+ align:start position:0%
+where there are no diacritical markings
+ 
+
+ align:start position:0%
+where there are no diacritical markings
+at all because you know you get to make
+
+ align:start position:0%
+at all because you know you get to make
+ 
+
+ align:start position:0%
+at all because you know you get to make
+up your own mind about things but what I
+
+ align:start position:0%
+up your own mind about things but what I
+ 
+
+ align:start position:0%
+up your own mind about things but what I
+particularly love is a composer like
+
+ align:start position:0%
+particularly love is a composer like
+ 
+
+ align:start position:0%
+particularly love is a composer like
+Benjamin Brittain where everything was
+
+ align:start position:0%
+Benjamin Brittain where everything was
+ 
+
+ align:start position:0%
+Benjamin Brittain where everything was
+incredibly specific and he was Notorious
+
+ align:start position:0%
+incredibly specific and he was Notorious
+ 
+
+ align:start position:0%
+incredibly specific and he was Notorious
+for being so dactic and really
+
+ align:start position:0%
+for being so dactic and really
+ 
+
+ align:start position:0%
+for being so dactic and really
+irritating with his publisher be like he
+
+ align:start position:0%
+irritating with his publisher be like he
+ 
+
+ align:start position:0%
+irritating with his publisher be like he
+you left the rest out throw them away
+
+ align:start position:0%
+you left the rest out throw them away
+ 
+
+ align:start position:0%
+you left the rest out throw them away
+print it again so the more specific you
+
+ align:start position:0%
+print it again so the more specific you
+ 
+
+ align:start position:0%
+print it again so the more specific you
+can be the stronger impression you give
+
+ align:start position:0%
+can be the stronger impression you give
+ 
+
+ align:start position:0%
+can be the stronger impression you give
+us of what you intend so in other words
+
+ align:start position:0%
+us of what you intend so in other words
+ 
+
+ align:start position:0%
+us of what you intend so in other words
+if there aren't enough di critical
+
+ align:start position:0%
+if there aren't enough di critical
+ 
+
+ align:start position:0%
+if there aren't enough di critical
+markings it seems to us like you have it
+
+ align:start position:0%
+markings it seems to us like you have it
+ 
+
+ align:start position:0%
+markings it seems to us like you have it
+made up your mind and yet you're telling
+
+ align:start position:0%
+made up your mind and yet you're telling
+ 
+
+ align:start position:0%
+made up your mind and yet you're telling
+me that you have a very specific thing
+
+ align:start position:0%
+me that you have a very specific thing
+ 
+
+ align:start position:0%
+me that you have a very specific thing
+in mind so let that be expressed on the
+
+ align:start position:0%
+in mind so let that be expressed on the
+ 
+
+ align:start position:0%
+in mind so let that be expressed on the
+page Peter what would you like to do
+
+ align:start position:0%
+page Peter what would you like to do
+ 
+
+ align:start position:0%
+page Peter what would you like to do
+shall we move on yeah all right good
+
+ align:start position:0%
+shall we move on yeah all right good
+ 
+
+ align:start position:0%
+shall we move on yeah all right good
+that's very beautiful Stephanie nice job
+
+ align:start position:0%
+that's very beautiful Stephanie nice job
+ 
+
+ align:start position:0%
+that's very beautiful Stephanie nice job
+Round of Applause for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+composer
\ No newline at end of file
diff --git a/4lUVayy53V4.txt b/4lUVayy53V4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09d51489d2a8dd05803fdf779fbdf323f5d58996
--- /dev/null
+++ b/4lUVayy53V4.txt
@@ -0,0 +1,1843 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+so in this lecture we have a very brief
+
+ align:start position:0%
+so in this lecture we have a very brief
+ 
+
+ align:start position:0%
+so in this lecture we have a very brief
+view at the current status of higgs
+
+ align:start position:0%
+view at the current status of higgs
+ 
+
+ align:start position:0%
+view at the current status of higgs
+boson research
+
+ align:start position:0%
+boson research
+ 
+
+ align:start position:0%
+boson research
+and i have to tell you that we could
+
+ align:start position:0%
+and i have to tell you that we could
+ 
+
+ align:start position:0%
+and i have to tell you that we could
+spend an entire week
+
+ align:start position:0%
+spend an entire week
+ 
+
+ align:start position:0%
+spend an entire week
+discussing this i just give you the high
+
+ align:start position:0%
+discussing this i just give you the high
+ 
+
+ align:start position:0%
+discussing this i just give you the high
+level overview maybe the you know 30 000
+
+ align:start position:0%
+level overview maybe the you know 30 000
+ 
+
+ align:start position:0%
+level overview maybe the you know 30 000
+feet kind of overview of what we know
+
+ align:start position:0%
+feet kind of overview of what we know
+ 
+
+ align:start position:0%
+feet kind of overview of what we know
+about the exposure
+
+ align:start position:0%
+about the exposure
+ 
+
+ align:start position:0%
+about the exposure
+on the canvas page you'll find a
+
+ align:start position:0%
+on the canvas page you'll find a
+ 
+
+ align:start position:0%
+on the canvas page you'll find a
+reference to a summary report which
+
+ align:start position:0%
+reference to a summary report which
+ 
+
+ align:start position:0%
+reference to a summary report which
+gives you a little bit more information
+
+ align:start position:0%
+gives you a little bit more information
+ 
+
+ align:start position:0%
+gives you a little bit more information
+than i give you here
+
+ align:start position:0%
+than i give you here
+ 
+
+ align:start position:0%
+than i give you here
+but i do think that there's a few things
+
+ align:start position:0%
+but i do think that there's a few things
+ 
+
+ align:start position:0%
+but i do think that there's a few things
+to highlight and those are the ones
+
+ align:start position:0%
+to highlight and those are the ones
+ 
+
+ align:start position:0%
+to highlight and those are the ones
+which i'm going to talk about
+
+ align:start position:0%
+which i'm going to talk about
+ 
+
+ align:start position:0%
+which i'm going to talk about
+the first part is that we have
+
+ align:start position:0%
+the first part is that we have
+ 
+
+ align:start position:0%
+the first part is that we have
+discovered the higgs boson in the case
+
+ align:start position:0%
+discovered the higgs boson in the case
+ 
+
+ align:start position:0%
+discovered the higgs boson in the case
+to photons and also indicates to z
+
+ align:start position:0%
+to photons and also indicates to z
+ 
+
+ align:start position:0%
+to photons and also indicates to z
+bosons where the zebras and itself
+
+ align:start position:0%
+bosons where the zebras and itself
+ 
+
+ align:start position:0%
+bosons where the zebras and itself
+decays into a pair of
+
+ align:start position:0%
+decays into a pair of
+ 
+
+ align:start position:0%
+decays into a pair of
+leptons electrons and neurons and the
+
+ align:start position:0%
+leptons electrons and neurons and the
+ 
+
+ align:start position:0%
+leptons electrons and neurons and the
+detectors we have available
+
+ align:start position:0%
+detectors we have available
+ 
+
+ align:start position:0%
+detectors we have available
+and here this is an example for atlas
+
+ align:start position:0%
+and here this is an example for atlas
+ 
+
+ align:start position:0%
+and here this is an example for atlas
+and for cms
+
+ align:start position:0%
+and for cms
+ 
+
+ align:start position:0%
+and for cms
+they are very good in measuring with
+
+ align:start position:0%
+they are very good in measuring with
+ 
+
+ align:start position:0%
+they are very good in measuring with
+precision the
+
+ align:start position:0%
+precision the
+ 
+
+ align:start position:0%
+precision the
+the energy or momentum of photons
+
+ align:start position:0%
+the energy or momentum of photons
+ 
+
+ align:start position:0%
+the energy or momentum of photons
+electrons and neurons so this allows us
+
+ align:start position:0%
+electrons and neurons so this allows us
+ 
+
+ align:start position:0%
+electrons and neurons so this allows us
+to then reconstruct
+
+ align:start position:0%
+to then reconstruct
+ 
+
+ align:start position:0%
+to then reconstruct
+the mass of the higgs boson as it goes
+
+ align:start position:0%
+the mass of the higgs boson as it goes
+ 
+
+ align:start position:0%
+the mass of the higgs boson as it goes
+through the decay
+
+ align:start position:0%
+through the decay
+ 
+
+ align:start position:0%
+through the decay
+and you can see this here this is 125 gb
+
+ align:start position:0%
+and you can see this here this is 125 gb
+ 
+
+ align:start position:0%
+and you can see this here this is 125 gb
+we construct the two photon final state
+
+ align:start position:0%
+we construct the two photon final state
+ 
+
+ align:start position:0%
+we construct the two photon final state
+so we have fixed to
+
+ align:start position:0%
+so we have fixed to
+ 
+
+ align:start position:0%
+so we have fixed to
+two photons from atlas you see that
+
+ align:start position:0%
+two photons from atlas you see that
+ 
+
+ align:start position:0%
+two photons from atlas you see that
+there is a slight bump
+
+ align:start position:0%
+there is a slight bump
+ 
+
+ align:start position:0%
+there is a slight bump
+over an enormous background so those are
+
+ align:start position:0%
+over an enormous background so those are
+ 
+
+ align:start position:0%
+over an enormous background so those are
+other sources of diphoton events
+
+ align:start position:0%
+other sources of diphoton events
+ 
+
+ align:start position:0%
+other sources of diphoton events
+which are produced in the hydrogen
+
+ align:start position:0%
+which are produced in the hydrogen
+ 
+
+ align:start position:0%
+which are produced in the hydrogen
+collider but when you subtract those two
+
+ align:start position:0%
+collider but when you subtract those two
+ 
+
+ align:start position:0%
+collider but when you subtract those two
+spectra which is shown here data minus
+
+ align:start position:0%
+spectra which is shown here data minus
+ 
+
+ align:start position:0%
+spectra which is shown here data minus
+background
+
+ align:start position:0%
+background
+ 
+
+ align:start position:0%
+background
+you see this beautiful peak of x to
+
+ align:start position:0%
+you see this beautiful peak of x to
+ 
+
+ align:start position:0%
+you see this beautiful peak of x to
+gamma commandments
+
+ align:start position:0%
+gamma commandments
+ 
+
+ align:start position:0%
+gamma commandments
+similarly x to z z
+
+ align:start position:0%
+similarly x to z z
+ 
+
+ align:start position:0%
+similarly x to z z
+and i put a little star here because one
+
+ align:start position:0%
+and i put a little star here because one
+ 
+
+ align:start position:0%
+and i put a little star here because one
+of the zebras has to be off shell
+
+ align:start position:0%
+of the zebras has to be off shell
+ 
+
+ align:start position:0%
+of the zebras has to be off shell
+the zebra mass is 91 gb the mass of the
+
+ align:start position:0%
+the zebra mass is 91 gb the mass of the
+ 
+
+ align:start position:0%
+the zebra mass is 91 gb the mass of the
+exposure 125 gb
+
+ align:start position:0%
+exposure 125 gb
+ 
+
+ align:start position:0%
+exposure 125 gb
+so 90 plus 91 plus 91 is 928 so one has
+
+ align:start position:0%
+so 90 plus 91 plus 91 is 928 so one has
+ 
+
+ align:start position:0%
+so 90 plus 91 plus 91 is 928 so one has
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+a little off its mass peak
+
+ align:start position:0%
+a little off its mass peak
+ 
+
+ align:start position:0%
+a little off its mass peak
+and then we look at the case into e plus
+
+ align:start position:0%
+and then we look at the case into e plus
+ 
+
+ align:start position:0%
+and then we look at the case into e plus
+and minus
+
+ align:start position:0%
+and minus
+ 
+
+ align:start position:0%
+and minus
+and mu plus mu minus and combination
+
+ align:start position:0%
+and mu plus mu minus and combination
+ 
+
+ align:start position:0%
+and mu plus mu minus and combination
+also so for example for muon events or
+
+ align:start position:0%
+also so for example for muon events or
+ 
+
+ align:start position:0%
+also so for example for muon events or
+for electron events as well
+
+ align:start position:0%
+for electron events as well
+ 
+
+ align:start position:0%
+for electron events as well
+those are shown here and again you have
+
+ align:start position:0%
+those are shown here and again you have
+ 
+
+ align:start position:0%
+those are shown here and again you have
+this beautiful peak
+
+ align:start position:0%
+this beautiful peak
+ 
+
+ align:start position:0%
+this beautiful peak
+consistent with higgs boson at a mass of
+
+ align:start position:0%
+consistent with higgs boson at a mass of
+ 
+
+ align:start position:0%
+consistent with higgs boson at a mass of
+125 gv
+
+ align:start position:0%
+125 gv
+ 
+
+ align:start position:0%
+125 gv
+and again you have other processes which
+
+ align:start position:0%
+and again you have other processes which
+ 
+
+ align:start position:0%
+and again you have other processes which
+contribute to this final state
+
+ align:start position:0%
+contribute to this final state
+ 
+
+ align:start position:0%
+contribute to this final state
+namely the one where you have the four
+
+ align:start position:0%
+namely the one where you have the four
+ 
+
+ align:start position:0%
+namely the one where you have the four
+leptons coming
+
+ align:start position:0%
+leptons coming
+ 
+
+ align:start position:0%
+leptons coming
+from the zebra then itself and or
+
+ align:start position:0%
+from the zebra then itself and or
+ 
+
+ align:start position:0%
+from the zebra then itself and or
+um from a pair of the bosons is shown
+
+ align:start position:0%
+um from a pair of the bosons is shown
+ 
+
+ align:start position:0%
+um from a pair of the bosons is shown
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+there's also processes which mimic the
+
+ align:start position:0%
+there's also processes which mimic the
+ 
+
+ align:start position:0%
+there's also processes which mimic the
+leptons
+
+ align:start position:0%
+leptons
+ 
+
+ align:start position:0%
+leptons
+in the detector those have to be
+
+ align:start position:0%
+in the detector those have to be
+ 
+
+ align:start position:0%
+in the detector those have to be
+evaluated as well and they're typically
+
+ align:start position:0%
+evaluated as well and they're typically
+ 
+
+ align:start position:0%
+evaluated as well and they're typically
+shown here in this plot in green
+
+ align:start position:0%
+shown here in this plot in green
+ 
+
+ align:start position:0%
+shown here in this plot in green
+okay so as you can imagine we can
+
+ align:start position:0%
+okay so as you can imagine we can
+ 
+
+ align:start position:0%
+okay so as you can imagine we can
+measure the cross-section very precisely
+
+ align:start position:0%
+measure the cross-section very precisely
+ 
+
+ align:start position:0%
+measure the cross-section very precisely
+because we can identify those particles
+
+ align:start position:0%
+because we can identify those particles
+ 
+
+ align:start position:0%
+because we can identify those particles
+well but we can also measure the mass
+
+ align:start position:0%
+well but we can also measure the mass
+ 
+
+ align:start position:0%
+well but we can also measure the mass
+and this is shown here
+
+ align:start position:0%
+and this is shown here
+ 
+
+ align:start position:0%
+and this is shown here
+the summary of measurements from atlas
+
+ align:start position:0%
+the summary of measurements from atlas
+ 
+
+ align:start position:0%
+the summary of measurements from atlas
+and cms using
+
+ align:start position:0%
+and cms using
+ 
+
+ align:start position:0%
+and cms using
+those two final states the one with two
+
+ align:start position:0%
+those two final states the one with two
+ 
+
+ align:start position:0%
+those two final states the one with two
+photons or the one with four leptons
+
+ align:start position:0%
+photons or the one with four leptons
+ 
+
+ align:start position:0%
+photons or the one with four leptons
+and you see that measurements are
+
+ align:start position:0%
+and you see that measurements are
+ 
+
+ align:start position:0%
+and you see that measurements are
+generally in agreement
+
+ align:start position:0%
+generally in agreement
+ 
+
+ align:start position:0%
+generally in agreement
+and they can be combined to this
+
+ align:start position:0%
+and they can be combined to this
+ 
+
+ align:start position:0%
+and they can be combined to this
+measurement of 125 gv
+
+ align:start position:0%
+measurement of 125 gv
+ 
+
+ align:start position:0%
+measurement of 125 gv
+and the best the combined value is shown
+
+ align:start position:0%
+and the best the combined value is shown
+ 
+
+ align:start position:0%
+and the best the combined value is shown
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so this is a precision measurement and
+
+ align:start position:0%
+so this is a precision measurement and
+ 
+
+ align:start position:0%
+so this is a precision measurement and
+since the exposure mass now is the only
+
+ align:start position:0%
+since the exposure mass now is the only
+ 
+
+ align:start position:0%
+since the exposure mass now is the only
+unknown
+
+ align:start position:0%
+unknown
+ 
+
+ align:start position:0%
+unknown
+parameter of the higgs in the standard
+
+ align:start position:0%
+parameter of the higgs in the standard
+ 
+
+ align:start position:0%
+parameter of the higgs in the standard
+model we we know
+
+ align:start position:0%
+model we we know
+ 
+
+ align:start position:0%
+model we we know
+and can check all other properties
+
+ align:start position:0%
+and can check all other properties
+ 
+
+ align:start position:0%
+and can check all other properties
+and one is you know the coupling
+
+ align:start position:0%
+and one is you know the coupling
+ 
+
+ align:start position:0%
+and one is you know the coupling
+strengths to the both on which we just
+
+ align:start position:0%
+strengths to the both on which we just
+ 
+
+ align:start position:0%
+strengths to the both on which we just
+looked at already
+
+ align:start position:0%
+looked at already
+ 
+
+ align:start position:0%
+looked at already
+or the coupling strength to the fermions
+
+ align:start position:0%
+or the coupling strength to the fermions
+ 
+
+ align:start position:0%
+or the coupling strength to the fermions
+so this is two examples one
+
+ align:start position:0%
+so this is two examples one
+ 
+
+ align:start position:0%
+so this is two examples one
+it's showing hicks to taut events
+
+ align:start position:0%
+it's showing hicks to taut events
+ 
+
+ align:start position:0%
+it's showing hicks to taut events
+top last minus and you see again there's
+
+ align:start position:0%
+top last minus and you see again there's
+ 
+
+ align:start position:0%
+top last minus and you see again there's
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+background processes which mimic have
+
+ align:start position:0%
+background processes which mimic have
+ 
+
+ align:start position:0%
+background processes which mimic have
+the same signature the signal
+
+ align:start position:0%
+the same signature the signal
+ 
+
+ align:start position:0%
+the same signature the signal
+but we can find when we subtract the
+
+ align:start position:0%
+but we can find when we subtract the
+ 
+
+ align:start position:0%
+but we can find when we subtract the
+background from the data
+
+ align:start position:0%
+background from the data
+ 
+
+ align:start position:0%
+background from the data
+the nexus of event again at 125 gb
+
+ align:start position:0%
+the nexus of event again at 125 gb
+ 
+
+ align:start position:0%
+the nexus of event again at 125 gb
+so towers themselves decay and the decay
+
+ align:start position:0%
+so towers themselves decay and the decay
+ 
+
+ align:start position:0%
+so towers themselves decay and the decay
+into neutrinos which cannot be measured
+
+ align:start position:0%
+into neutrinos which cannot be measured
+ 
+
+ align:start position:0%
+into neutrinos which cannot be measured
+at this detectors
+
+ align:start position:0%
+at this detectors
+ 
+
+ align:start position:0%
+at this detectors
+are therefore the mass reconstruction is
+
+ align:start position:0%
+are therefore the mass reconstruction is
+ 
+
+ align:start position:0%
+are therefore the mass reconstruction is
+much harder than in the final stage we
+
+ align:start position:0%
+much harder than in the final stage we
+ 
+
+ align:start position:0%
+much harder than in the final stage we
+discussed before
+
+ align:start position:0%
+discussed before
+ 
+
+ align:start position:0%
+discussed before
+that is easier in this final stage here
+
+ align:start position:0%
+that is easier in this final stage here
+ 
+
+ align:start position:0%
+that is easier in this final stage here
+where we have a higgs into two moons
+
+ align:start position:0%
+where we have a higgs into two moons
+ 
+
+ align:start position:0%
+where we have a higgs into two moons
+in the plus c minus the issue here is
+
+ align:start position:0%
+in the plus c minus the issue here is
+ 
+
+ align:start position:0%
+in the plus c minus the issue here is
+that the rate
+
+ align:start position:0%
+that the rate
+ 
+
+ align:start position:0%
+that the rate
+is very small the number of fixed bosons
+
+ align:start position:0%
+is very small the number of fixed bosons
+ 
+
+ align:start position:0%
+is very small the number of fixed bosons
+decaying to be
+
+ align:start position:0%
+decaying to be
+ 
+
+ align:start position:0%
+decaying to be
+very small but there's also a large
+
+ align:start position:0%
+very small but there's also a large
+ 
+
+ align:start position:0%
+very small but there's also a large
+amount of background so again very
+
+ align:start position:0%
+amount of background so again very
+ 
+
+ align:start position:0%
+amount of background so again very
+similar to the hicks to gamma gamma
+
+ align:start position:0%
+similar to the hicks to gamma gamma
+ 
+
+ align:start position:0%
+similar to the hicks to gamma gamma
+finance that we looked before we have a
+
+ align:start position:0%
+finance that we looked before we have a
+ 
+
+ align:start position:0%
+finance that we looked before we have a
+huge amount of background
+
+ align:start position:0%
+huge amount of background
+ 
+
+ align:start position:0%
+huge amount of background
+and here by eyes you don't even see the
+
+ align:start position:0%
+and here by eyes you don't even see the
+ 
+
+ align:start position:0%
+and here by eyes you don't even see the
+bump you see the bump a little bit
+
+ align:start position:0%
+bump you see the bump a little bit
+ 
+
+ align:start position:0%
+bump you see the bump a little bit
+uh when you do data minus background
+
+ align:start position:0%
+uh when you do data minus background
+ 
+
+ align:start position:0%
+uh when you do data minus background
+subtraction
+
+ align:start position:0%
+subtraction
+ 
+
+ align:start position:0%
+subtraction
+so you see this small axis here which is
+
+ align:start position:0%
+so you see this small axis here which is
+ 
+
+ align:start position:0%
+so you see this small axis here which is
+consistent with redundant standard
+
+ align:start position:0%
+consistent with redundant standard
+ 
+
+ align:start position:0%
+consistent with redundant standard
+deviation so
+
+ align:start position:0%
+deviation so
+ 
+
+ align:start position:0%
+deviation so
+the likelihood of the background to
+
+ align:start position:0%
+the likelihood of the background to
+ 
+
+ align:start position:0%
+the likelihood of the background to
+fluctuate without the presence of the
+
+ align:start position:0%
+fluctuate without the presence of the
+ 
+
+ align:start position:0%
+fluctuate without the presence of the
+hex signal
+
+ align:start position:0%
+hex signal
+ 
+
+ align:start position:0%
+hex signal
+is about three standard deviation all
+
+ align:start position:0%
+is about three standard deviation all
+ 
+
+ align:start position:0%
+is about three standard deviation all
+right this information then can be used
+
+ align:start position:0%
+right this information then can be used
+ 
+
+ align:start position:0%
+right this information then can be used
+to interact information about the
+
+ align:start position:0%
+to interact information about the
+ 
+
+ align:start position:0%
+to interact information about the
+couplings itself and this is a beautiful
+
+ align:start position:0%
+couplings itself and this is a beautiful
+ 
+
+ align:start position:0%
+couplings itself and this is a beautiful
+plot here
+
+ align:start position:0%
+plot here
+ 
+
+ align:start position:0%
+plot here
+which shows the x coupling on one axis
+
+ align:start position:0%
+which shows the x coupling on one axis
+ 
+
+ align:start position:0%
+which shows the x coupling on one axis
+either to the fermions or the bodon
+
+ align:start position:0%
+either to the fermions or the bodon
+ 
+
+ align:start position:0%
+either to the fermions or the bodon
+versus the mass of the particle
+
+ align:start position:0%
+versus the mass of the particle
+ 
+
+ align:start position:0%
+versus the mass of the particle
+and so you find your favorite particles
+
+ align:start position:0%
+and so you find your favorite particles
+ 
+
+ align:start position:0%
+and so you find your favorite particles
+the top the w
+
+ align:start position:0%
+the top the w
+ 
+
+ align:start position:0%
+the top the w
+z the bottom the tower and the muon
+
+ align:start position:0%
+z the bottom the tower and the muon
+ 
+
+ align:start position:0%
+z the bottom the tower and the muon
+those are the ones where we can actually
+
+ align:start position:0%
+those are the ones where we can actually
+ 
+
+ align:start position:0%
+those are the ones where we can actually
+measure the coupling um and you see
+
+ align:start position:0%
+measure the coupling um and you see
+ 
+
+ align:start position:0%
+measure the coupling um and you see
+whether or not this is an agreement with
+
+ align:start position:0%
+whether or not this is an agreement with
+ 
+
+ align:start position:0%
+whether or not this is an agreement with
+a standard model which is this
+
+ align:start position:0%
+a standard model which is this
+ 
+
+ align:start position:0%
+a standard model which is this
+blue dotted line here and you see it is
+
+ align:start position:0%
+blue dotted line here and you see it is
+ 
+
+ align:start position:0%
+blue dotted line here and you see it is
+and that plot here tells me that the
+
+ align:start position:0%
+and that plot here tells me that the
+ 
+
+ align:start position:0%
+and that plot here tells me that the
+higgs mechanism
+
+ align:start position:0%
+higgs mechanism
+ 
+
+ align:start position:0%
+higgs mechanism
+is responsible responsible for the mass
+
+ align:start position:0%
+is responsible responsible for the mass
+ 
+
+ align:start position:0%
+is responsible responsible for the mass
+generation of this particle
+
+ align:start position:0%
+generation of this particle
+ 
+
+ align:start position:0%
+generation of this particle
+so it might be that there is a mechanism
+
+ align:start position:0%
+so it might be that there is a mechanism
+ 
+
+ align:start position:0%
+so it might be that there is a mechanism
+which is very similar to the higgs boson
+
+ align:start position:0%
+which is very similar to the higgs boson
+ 
+
+ align:start position:0%
+which is very similar to the higgs boson
+which results in the very same
+
+ align:start position:0%
+which results in the very same
+ 
+
+ align:start position:0%
+which results in the very same
+observations in nature
+
+ align:start position:0%
+observations in nature
+ 
+
+ align:start position:0%
+observations in nature
+um but it's not quite what we have in
+
+ align:start position:0%
+um but it's not quite what we have in
+ 
+
+ align:start position:0%
+um but it's not quite what we have in
+the standard model in order to make
+
+ align:start position:0%
+the standard model in order to make
+ 
+
+ align:start position:0%
+the standard model in order to make
+those statements
+
+ align:start position:0%
+those statements
+ 
+
+ align:start position:0%
+those statements
+one has to improve the size
+
+ align:start position:0%
+one has to improve the size
+ 
+
+ align:start position:0%
+one has to improve the size
+of the error bars here or the
+
+ align:start position:0%
+of the error bars here or the
+ 
+
+ align:start position:0%
+of the error bars here or the
+statistical significance or the
+
+ align:start position:0%
+statistical significance or the
+ 
+
+ align:start position:0%
+statistical significance or the
+significance of the measurements
+
+ align:start position:0%
+significance of the measurements
+ 
+
+ align:start position:0%
+significance of the measurements
+that is part of our program that's what
+
+ align:start position:0%
+that is part of our program that's what
+ 
+
+ align:start position:0%
+that is part of our program that's what
+we're trying to do
+
+ align:start position:0%
+we're trying to do
+ 
+
+ align:start position:0%
+we're trying to do
+all right in summary again this is a
+
+ align:start position:0%
+all right in summary again this is a
+ 
+
+ align:start position:0%
+all right in summary again this is a
+very high level summary so we measured
+
+ align:start position:0%
+very high level summary so we measured
+ 
+
+ align:start position:0%
+very high level summary so we measured
+the mass
+
+ align:start position:0%
+the mass
+ 
+
+ align:start position:0%
+the mass
+we measured the spin and cp of exposure
+
+ align:start position:0%
+we measured the spin and cp of exposure
+ 
+
+ align:start position:0%
+we measured the spin and cp of exposure
+we measured the coupling to the z the w
+
+ align:start position:0%
+we measured the coupling to the z the w
+ 
+
+ align:start position:0%
+we measured the coupling to the z the w
+the top the bottom the tau and the muon
+
+ align:start position:0%
+the top the bottom the tau and the muon
+ 
+
+ align:start position:0%
+the top the bottom the tau and the muon
+we have not been able to measure the
+
+ align:start position:0%
+we have not been able to measure the
+ 
+
+ align:start position:0%
+we have not been able to measure the
+coupling to lighter quark masses
+
+ align:start position:0%
+coupling to lighter quark masses
+ 
+
+ align:start position:0%
+coupling to lighter quark masses
+strange charm up and down
+
+ align:start position:0%
+strange charm up and down
+ 
+
+ align:start position:0%
+strange charm up and down
+we have not been able to measure the
+
+ align:start position:0%
+we have not been able to measure the
+ 
+
+ align:start position:0%
+we have not been able to measure the
+coupling to the lx one
+
+ align:start position:0%
+coupling to the lx one
+ 
+
+ align:start position:0%
+coupling to the lx one
+that would be spectacular and we have
+
+ align:start position:0%
+that would be spectacular and we have
+ 
+
+ align:start position:0%
+that would be spectacular and we have
+not measured the coupling to itself so
+
+ align:start position:0%
+not measured the coupling to itself so
+ 
+
+ align:start position:0%
+not measured the coupling to itself so
+in the standard model the higgs boson
+
+ align:start position:0%
+in the standard model the higgs boson
+ 
+
+ align:start position:0%
+in the standard model the higgs boson
+can couple to itself
+
+ align:start position:0%
+can couple to itself
+ 
+
+ align:start position:0%
+can couple to itself
+so we have diagrams which look like this
+
+ align:start position:0%
+so we have diagrams which look like this
+ 
+
+ align:start position:0%
+so we have diagrams which look like this
+x x x and we have not been able to
+
+ align:start position:0%
+x x x and we have not been able to
+ 
+
+ align:start position:0%
+x x x and we have not been able to
+measure this
+
+ align:start position:0%
+measure this
+ 
+
+ align:start position:0%
+measure this
+this is not free in the standard model
+
+ align:start position:0%
+this is not free in the standard model
+ 
+
+ align:start position:0%
+this is not free in the standard model
+and this would be you know
+
+ align:start position:0%
+and this would be you know
+ 
+
+ align:start position:0%
+and this would be you know
+closing the argument that the higgs
+
+ align:start position:0%
+closing the argument that the higgs
+ 
+
+ align:start position:0%
+closing the argument that the higgs
+boson requires mass
+
+ align:start position:0%
+boson requires mass
+ 
+
+ align:start position:0%
+boson requires mass
+or the higgs boson is the particle
+
+ align:start position:0%
+or the higgs boson is the particle
+ 
+
+ align:start position:0%
+or the higgs boson is the particle
+predicted in the standard model
+
+ align:start position:0%
+predicted in the standard model
+ 
+
+ align:start position:0%
+predicted in the standard model
+giving mass to w and z goes on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you want you can the strength of the
+
+ align:start position:0%
+if you want you can the strength of the
+ 
+
+ align:start position:0%
+if you want you can the strength of the
+coupling here is this lambda
+
+ align:start position:0%
+coupling here is this lambda
+ 
+
+ align:start position:0%
+coupling here is this lambda
+this is the lambda term in our potential
+
+ align:start position:0%
+this is the lambda term in our potential
+ 
+
+ align:start position:0%
+this is the lambda term in our potential
+so that's what we are trying to measure
+
+ align:start position:0%
+so that's what we are trying to measure
+ 
+
+ align:start position:0%
+so that's what we are trying to measure
+in the future
+
+ align:start position:0%
+in the future
+ 
+
+ align:start position:0%
+in the future
+but there's more open questions um maybe
+
+ align:start position:0%
+but there's more open questions um maybe
+ 
+
+ align:start position:0%
+but there's more open questions um maybe
+there's more than
+
+ align:start position:0%
+there's more than
+ 
+
+ align:start position:0%
+there's more than
+one exposure on the higgs adding one
+
+ align:start position:0%
+one exposure on the higgs adding one
+ 
+
+ align:start position:0%
+one exposure on the higgs adding one
+duplet to the standard model with this
+
+ align:start position:0%
+duplet to the standard model with this
+ 
+
+ align:start position:0%
+duplet to the standard model with this
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+is one possible solution to the problem
+
+ align:start position:0%
+is one possible solution to the problem
+ 
+
+ align:start position:0%
+is one possible solution to the problem
+of generating mars
+
+ align:start position:0%
+of generating mars
+ 
+
+ align:start position:0%
+of generating mars
+but you could have very well added two
+
+ align:start position:0%
+but you could have very well added two
+ 
+
+ align:start position:0%
+but you could have very well added two
+or n
+
+ align:start position:0%
+or n
+ 
+
+ align:start position:0%
+or n
+or triplets or more complicated things
+
+ align:start position:0%
+or triplets or more complicated things
+ 
+
+ align:start position:0%
+or triplets or more complicated things
+and so the question is
+
+ align:start position:0%
+and so the question is
+ 
+
+ align:start position:0%
+and so the question is
+are those maybe realized in nature or
+
+ align:start position:0%
+are those maybe realized in nature or
+ 
+
+ align:start position:0%
+are those maybe realized in nature or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will more precision tell us something
+
+ align:start position:0%
+will more precision tell us something
+ 
+
+ align:start position:0%
+will more precision tell us something
+about the higgs boson
+
+ align:start position:0%
+about the higgs boson
+ 
+
+ align:start position:0%
+about the higgs boson
+are there the case of the higgs bosons
+
+ align:start position:0%
+are there the case of the higgs bosons
+ 
+
+ align:start position:0%
+are there the case of the higgs bosons
+of non-standard model particles for
+
+ align:start position:0%
+of non-standard model particles for
+ 
+
+ align:start position:0%
+of non-standard model particles for
+example the higgs boson decaying into
+
+ align:start position:0%
+example the higgs boson decaying into
+ 
+
+ align:start position:0%
+example the higgs boson decaying into
+those guys here which could be evidence
+
+ align:start position:0%
+those guys here which could be evidence
+ 
+
+ align:start position:0%
+those guys here which could be evidence
+for dark matter
+
+ align:start position:0%
+for dark matter
+ 
+
+ align:start position:0%
+for dark matter
+we have looks we have not seen this but
+
+ align:start position:0%
+we have looks we have not seen this but
+ 
+
+ align:start position:0%
+we have looks we have not seen this but
+more precision might give us a different
+
+ align:start position:0%
+more precision might give us a different
+ 
+
+ align:start position:0%
+more precision might give us a different
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+so that's basically the status or the
+
+ align:start position:0%
+so that's basically the status or the
+ 
+
+ align:start position:0%
+so that's basically the status or the
+summary of where we are with the higgs
+
+ align:start position:0%
+summary of where we are with the higgs
+ 
+
+ align:start position:0%
+summary of where we are with the higgs
+boson again much more can be said about
+
+ align:start position:0%
+boson again much more can be said about
+ 
+
+ align:start position:0%
+boson again much more can be said about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and you will see this every now and then
+
+ align:start position:0%
+and you will see this every now and then
+ 
+
+ align:start position:0%
+and you will see this every now and then
+in seminars at mit
+
+ align:start position:0%
+in seminars at mit
+ 
+
+ align:start position:0%
+in seminars at mit
+or other places
+
+ align:start position:0%
+or other places
+ 
+
+ align:start position:0%
+or other places
+you
\ No newline at end of file
diff --git a/56vQ0S2eAjw.txt b/56vQ0S2eAjw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d197300451ad1ea4433a43b548d3466b930b921a
--- /dev/null
+++ b/56vQ0S2eAjw.txt
@@ -0,0 +1,4235 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+today what I want to do is in the within
+
+ align:start position:0%
+today what I want to do is in the within
+ 
+
+ align:start position:0%
+today what I want to do is in the within
+the lexicon is tell you about nature's
+
+ align:start position:0%
+the lexicon is tell you about nature's
+ 
+
+ align:start position:0%
+the lexicon is tell you about nature's
+most spectacularly beautiful cofactors
+
+ align:start position:0%
+most spectacularly beautiful cofactors
+ 
+
+ align:start position:0%
+most spectacularly beautiful cofactors
+and these are formed from vitamin b12
+
+ align:start position:0%
+and these are formed from vitamin b12
+ 
+
+ align:start position:0%
+and these are formed from vitamin b12
+which you find in your vitamin bottle ok
+
+ align:start position:0%
+which you find in your vitamin bottle ok
+ 
+
+ align:start position:0%
+which you find in your vitamin bottle ok
+so what is the structure of vitamin b12
+
+ align:start position:0%
+so what is the structure of vitamin b12
+ 
+
+ align:start position:0%
+so what is the structure of vitamin b12
+and why do I say there it's
+
+ align:start position:0%
+and why do I say there it's
+ 
+
+ align:start position:0%
+and why do I say there it's
+spectacularly beautiful so it's very
+
+ align:start position:0%
+spectacularly beautiful so it's very
+ 
+
+ align:start position:0%
+spectacularly beautiful so it's very
+hard to see you but if you look at the
+
+ align:start position:0%
+hard to see you but if you look at the
+ 
+
+ align:start position:0%
+hard to see you but if you look at the
+structure of this where have you seen a
+
+ align:start position:0%
+structure of this where have you seen a
+ 
+
+ align:start position:0%
+structure of this where have you seen a
+molecule this complicated with five
+
+ align:start position:0%
+molecule this complicated with five
+ 
+
+ align:start position:0%
+molecule this complicated with five
+membered rings each of which has a
+
+ align:start position:0%
+membered rings each of which has a
+ 
+
+ align:start position:0%
+membered rings each of which has a
+nitrogen in this you've seen this when
+
+ align:start position:0%
+nitrogen in this you've seen this when
+ 
+
+ align:start position:0%
+nitrogen in this you've seen this when
+you studied hemoglobin and you think
+
+ align:start position:0%
+you studied hemoglobin and you think
+ 
+
+ align:start position:0%
+you studied hemoglobin and you think
+about heme and protoporphyrin 9 if you
+
+ align:start position:0%
+about heme and protoporphyrin 9 if you
+ 
+
+ align:start position:0%
+about heme and protoporphyrin 9 if you
+look at the biosynthetic pathway of heme
+
+ align:start position:0%
+look at the biosynthetic pathway of heme
+ 
+
+ align:start position:0%
+look at the biosynthetic pathway of heme
+or branch point of that pathway is to
+
+ align:start position:0%
+or branch point of that pathway is to
+ 
+
+ align:start position:0%
+or branch point of that pathway is to
+make this ring which is found in
+
+ align:start position:0%
+make this ring which is found in
+ 
+
+ align:start position:0%
+make this ring which is found in
+adenosylcobalamin and methylcobalamin
+
+ align:start position:0%
+adenosylcobalamin and methylcobalamin
+ 
+
+ align:start position:0%
+adenosylcobalamin and methylcobalamin
+which is what we're going to be focusing
+
+ align:start position:0%
+which is what we're going to be focusing
+ 
+
+ align:start position:0%
+which is what we're going to be focusing
+on today and this ring is called the
+
+ align:start position:0%
+on today and this ring is called the
+ 
+
+ align:start position:0%
+on today and this ring is called the
+Koren ring so what I want to do is
+
+ align:start position:0%
+Koren ring so what I want to do is
+ 
+
+ align:start position:0%
+Koren ring so what I want to do is
+introduce you a little bit to this Koren
+
+ align:start position:0%
+introduce you a little bit to this Koren
+ 
+
+ align:start position:0%
+introduce you a little bit to this Koren
+ring and what's unusual about it
+
+ align:start position:0%
+ring and what's unusual about it
+ 
+
+ align:start position:0%
+ring and what's unusual about it
+compared to pro tempore for nine that
+
+ align:start position:0%
+compared to pro tempore for nine that
+ 
+
+ align:start position:0%
+compared to pro tempore for nine that
+you've been seen before you've seen
+
+ align:start position:0%
+you've been seen before you've seen
+ 
+
+ align:start position:0%
+you've been seen before you've seen
+before so the vitamin as in the case of
+
+ align:start position:0%
+before so the vitamin as in the case of
+ 
+
+ align:start position:0%
+before so the vitamin as in the case of
+all vitamins that we've talked about
+
+ align:start position:0%
+all vitamins that we've talked about
+ 
+
+ align:start position:0%
+all vitamins that we've talked about
+over the course of the semester is not
+
+ align:start position:0%
+over the course of the semester is not
+ 
+
+ align:start position:0%
+over the course of the semester is not
+the actual cofactor used in the
+
+ align:start position:0%
+the actual cofactor used in the
+ 
+
+ align:start position:0%
+the actual cofactor used in the
+enzymatic transformation the vitamin
+
+ align:start position:0%
+enzymatic transformation the vitamin
+ 
+
+ align:start position:0%
+enzymatic transformation the vitamin
+which in this case would have this group
+
+ align:start position:0%
+which in this case would have this group
+ 
+
+ align:start position:0%
+which in this case would have this group
+replaced with cyanide is vitamin b12 the
+
+ align:start position:0%
+replaced with cyanide is vitamin b12 the
+ 
+
+ align:start position:0%
+replaced with cyanide is vitamin b12 the
+actual cofactors that bind to the enzyme
+
+ align:start position:0%
+actual cofactors that bind to the enzyme
+ 
+
+ align:start position:0%
+actual cofactors that bind to the enzyme
+have that cyanide replaced with either a
+
+ align:start position:0%
+have that cyanide replaced with either a
+ 
+
+ align:start position:0%
+have that cyanide replaced with either a
+methyl group and that's called
+
+ align:start position:0%
+methyl group and that's called
+ 
+
+ align:start position:0%
+methyl group and that's called
+methylcobalamin or they have it replaced
+
+ align:start position:0%
+methylcobalamin or they have it replaced
+ 
+
+ align:start position:0%
+methylcobalamin or they have it replaced
+with five prime deoxyadenosine and
+
+ align:start position:0%
+with five prime deoxyadenosine and
+ 
+
+ align:start position:0%
+with five prime deoxyadenosine and
+that's called adenosylcobalamin and so
+
+ align:start position:0%
+that's called adenosylcobalamin and so
+ 
+
+ align:start position:0%
+that's called adenosylcobalamin and so
+the rest of the molecule is exactly the
+
+ align:start position:0%
+the rest of the molecule is exactly the
+ 
+
+ align:start position:0%
+the rest of the molecule is exactly the
+same the
+
+ align:start position:0%
+same the
+ 
+
+ align:start position:0%
+same the
+only thing that's distinct is the axial
+
+ align:start position:0%
+only thing that's distinct is the axial
+ 
+
+ align:start position:0%
+only thing that's distinct is the axial
+again so you remember from your
+
+ align:start position:0%
+again so you remember from your
+ 
+
+ align:start position:0%
+again so you remember from your
+transition metal chemistry you had when
+
+ align:start position:0%
+transition metal chemistry you had when
+ 
+
+ align:start position:0%
+transition metal chemistry you had when
+you were freshmen that here you have a
+
+ align:start position:0%
+you were freshmen that here you have a
+ 
+
+ align:start position:0%
+you were freshmen that here you have a
+cobalt 3 and it's coordinated to foreign
+
+ align:start position:0%
+cobalt 3 and it's coordinated to foreign
+ 
+
+ align:start position:0%
+cobalt 3 and it's coordinated to foreign
+nitrogen's okay so this would be the
+
+ align:start position:0%
+nitrogen's okay so this would be the
+ 
+
+ align:start position:0%
+nitrogen's okay so this would be the
+equatorial plane and we're going to draw
+
+ align:start position:0%
+equatorial plane and we're going to draw
+ 
+
+ align:start position:0%
+equatorial plane and we're going to draw
+it like this
+
+ align:start position:0%
+it like this
+ 
+
+ align:start position:0%
+it like this
+subsequently because you can see how
+
+ align:start position:0%
+subsequently because you can see how
+ 
+
+ align:start position:0%
+subsequently because you can see how
+complicated this molecule is in the
+
+ align:start position:0%
+complicated this molecule is in the
+ 
+
+ align:start position:0%
+complicated this molecule is in the
+metal sits right and this mitt this
+
+ align:start position:0%
+metal sits right and this mitt this
+ 
+
+ align:start position:0%
+metal sits right and this mitt this
+plane but you can see that you don't
+
+ align:start position:0%
+plane but you can see that you don't
+ 
+
+ align:start position:0%
+plane but you can see that you don't
+have complete saturation of these parol
+
+ align:start position:0%
+have complete saturation of these parol
+ 
+
+ align:start position:0%
+have complete saturation of these parol
+type rings so there's some pucker and
+
+ align:start position:0%
+type rings so there's some pucker and
+ 
+
+ align:start position:0%
+type rings so there's some pucker and
+contrast with hymns which are very flat
+
+ align:start position:0%
+contrast with hymns which are very flat
+ 
+
+ align:start position:0%
+contrast with hymns which are very flat
+and then these are called equatorial
+
+ align:start position:0%
+and then these are called equatorial
+ 
+
+ align:start position:0%
+and then these are called equatorial
+ligands and then you have axial ligands
+
+ align:start position:0%
+ligands and then you have axial ligands
+ 
+
+ align:start position:0%
+ligands and then you have axial ligands
+and so there are a number of things that
+
+ align:start position:0%
+and so there are a number of things that
+ 
+
+ align:start position:0%
+and so there are a number of things that
+again that I wanted to point out that
+
+ align:start position:0%
+again that I wanted to point out that
+ 
+
+ align:start position:0%
+again that I wanted to point out that
+are unusual about b12 one is the fact
+
+ align:start position:0%
+are unusual about b12 one is the fact
+ 
+
+ align:start position:0%
+are unusual about b12 one is the fact
+that the Corrin ring again is much more
+
+ align:start position:0%
+that the Corrin ring again is much more
+ 
+
+ align:start position:0%
+that the Corrin ring again is much more
+reduced than a parole ring and so it's
+
+ align:start position:0%
+reduced than a parole ring and so it's
+ 
+
+ align:start position:0%
+reduced than a parole ring and so it's
+puckered and if you look at the
+
+ align:start position:0%
+puckered and if you look at the
+ 
+
+ align:start position:0%
+puckered and if you look at the
+structure of I mean the visible spectrum
+
+ align:start position:0%
+structure of I mean the visible spectrum
+ 
+
+ align:start position:0%
+structure of I mean the visible spectrum
+are you use your eye and use your
+
+ align:start position:0%
+are you use your eye and use your
+ 
+
+ align:start position:0%
+are you use your eye and use your
+eyeball method you see that
+
+ align:start position:0%
+eyeball method you see that
+ 
+
+ align:start position:0%
+eyeball method you see that
+cyanocobalamin is bright purple if you
+
+ align:start position:0%
+cyanocobalamin is bright purple if you
+ 
+
+ align:start position:0%
+cyanocobalamin is bright purple if you
+replace this our group with a methyl
+
+ align:start position:0%
+replace this our group with a methyl
+ 
+
+ align:start position:0%
+replace this our group with a methyl
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+this color turns out to be sort of
+
+ align:start position:0%
+this color turns out to be sort of
+ 
+
+ align:start position:0%
+this color turns out to be sort of
+yellow orange and if you replace this
+
+ align:start position:0%
+yellow orange and if you replace this
+ 
+
+ align:start position:0%
+yellow orange and if you replace this
+with fiber mt.gox adenosine it turns out
+
+ align:start position:0%
+with fiber mt.gox adenosine it turns out
+ 
+
+ align:start position:0%
+with fiber mt.gox adenosine it turns out
+to be pink so that's why I say that this
+
+ align:start position:0%
+to be pink so that's why I say that this
+ 
+
+ align:start position:0%
+to be pink so that's why I say that this
+is nature's most spectacular beautiful
+
+ align:start position:0%
+is nature's most spectacular beautiful
+ 
+
+ align:start position:0%
+is nature's most spectacular beautiful
+cofactor so the other thing is you have
+
+ align:start position:0%
+cofactor so the other thing is you have
+ 
+
+ align:start position:0%
+cofactor so the other thing is you have
+two axial ligands I just introduced you
+
+ align:start position:0%
+two axial ligands I just introduced you
+ 
+
+ align:start position:0%
+two axial ligands I just introduced you
+to these guys on the top face but what
+
+ align:start position:0%
+to these guys on the top face but what
+ 
+
+ align:start position:0%
+to these guys on the top face but what
+you also see on the bottom face the
+
+ align:start position:0%
+you also see on the bottom face the
+ 
+
+ align:start position:0%
+you also see on the bottom face the
+bottom axial ligand is this unusual
+
+ align:start position:0%
+bottom axial ligand is this unusual
+ 
+
+ align:start position:0%
+bottom axial ligand is this unusual
+structure which is called dimethyl
+
+ align:start position:0%
+structure which is called dimethyl
+ 
+
+ align:start position:0%
+structure which is called dimethyl
+benzene midazolam and it's attached to a
+
+ align:start position:0%
+benzene midazolam and it's attached to a
+ 
+
+ align:start position:0%
+benzene midazolam and it's attached to a
+ribose but the unusual thing is in most
+
+ align:start position:0%
+ribose but the unusual thing is in most
+ 
+
+ align:start position:0%
+ribose but the unusual thing is in most
+nucleus IDEs that you've encountered
+
+ align:start position:0%
+nucleus IDEs that you've encountered
+ 
+
+ align:start position:0%
+nucleus IDEs that you've encountered
+like ATP this configuration is in the
+
+ align:start position:0%
+like ATP this configuration is in the
+ 
+
+ align:start position:0%
+like ATP this configuration is in the
+beta position it's on the top face of
+
+ align:start position:0%
+beta position it's on the top face of
+ 
+
+ align:start position:0%
+beta position it's on the top face of
+the sugar in here it's in the Alpha
+
+ align:start position:0%
+the sugar in here it's in the Alpha
+ 
+
+ align:start position:0%
+the sugar in here it's in the Alpha
+position so that's distinct and the
+
+ align:start position:0%
+position so that's distinct and the
+ 
+
+ align:start position:0%
+position so that's distinct and the
+other thing that's distinct is the
+
+ align:start position:0%
+other thing that's distinct is the
+ 
+
+ align:start position:0%
+other thing that's distinct is the
+decorations around the sidechain
+
+ align:start position:0%
+decorations around the sidechain
+ 
+
+ align:start position:0%
+decorations around the sidechain
+compared to what you see in porphyrins
+
+ align:start position:0%
+compared to what you see in porphyrins
+ 
+
+ align:start position:0%
+compared to what you see in porphyrins
+so this is a cofactor we're going to be
+
+ align:start position:0%
+so this is a cofactor we're going to be
+ 
+
+ align:start position:0%
+so this is a cofactor we're going to be
+talking about and one of the questions
+
+ align:start position:0%
+talking about and one of the questions
+ 
+
+ align:start position:0%
+talking about and one of the questions
+that that you're interested in is where
+
+ align:start position:0%
+that that you're interested in is where
+ 
+
+ align:start position:0%
+that that you're interested in is where
+do we find these cofactors and
+
+ align:start position:0%
+do we find these cofactors and
+ 
+
+ align:start position:0%
+do we find these cofactors and
+metabolism in a mammalian metabolism
+
+ align:start position:0%
+metabolism in a mammalian metabolism
+ 
+
+ align:start position:0%
+metabolism in a mammalian metabolism
+they're very the appearance of these
+
+ align:start position:0%
+they're very the appearance of these
+ 
+
+ align:start position:0%
+they're very the appearance of these
+cofactors is quite limited so the only
+
+ align:start position:0%
+cofactors is quite limited so the only
+ 
+
+ align:start position:0%
+cofactors is quite limited so the only
+place you see it in metabolism in
+
+ align:start position:0%
+place you see it in metabolism in
+ 
+
+ align:start position:0%
+place you see it in metabolism in
+mammalian systems is you see
+
+ align:start position:0%
+mammalian systems is you see
+ 
+
+ align:start position:0%
+mammalian systems is you see
+methylcobalamin ok where this is a
+
+ align:start position:0%
+methylcobalamin ok where this is a
+ 
+
+ align:start position:0%
+methylcobalamin ok where this is a
+methyl group in formation of the amino
+
+ align:start position:0%
+methyl group in formation of the amino
+ 
+
+ align:start position:0%
+methyl group in formation of the amino
+acid Matheny and so the methyl group
+
+ align:start position:0%
+acid Matheny and so the methyl group
+ 
+
+ align:start position:0%
+acid Matheny and so the methyl group
+from methionine I'll show you briefly at
+
+ align:start position:0%
+from methionine I'll show you briefly at
+ 
+
+ align:start position:0%
+from methionine I'll show you briefly at
+the very end of this little presentation
+
+ align:start position:0%
+the very end of this little presentation
+ 
+
+ align:start position:0%
+the very end of this little presentation
+comes from this methyl group you use
+
+ align:start position:0%
+comes from this methyl group you use
+ 
+
+ align:start position:0%
+comes from this methyl group you use
+Dennis O cobalamin in odd chain fatty
+
+ align:start position:0%
+Dennis O cobalamin in odd chain fatty
+ 
+
+ align:start position:0%
+Dennis O cobalamin in odd chain fatty
+acid metabolism so you have fatty acids
+
+ align:start position:0%
+acid metabolism so you have fatty acids
+ 
+
+ align:start position:0%
+acid metabolism so you have fatty acids
+that are either either at our odds a
+
+ align:start position:0%
+that are either either at our odds a
+ 
+
+ align:start position:0%
+that are either either at our odds a
+no-brain ones down you get proprio Co
+
+ align:start position:0%
+no-brain ones down you get proprio Co
+ 
+
+ align:start position:0%
+no-brain ones down you get proprio Co
+way the proprio Co way through a series
+
+ align:start position:0%
+way the proprio Co way through a series
+ 
+
+ align:start position:0%
+way the proprio Co way through a series
+of steps is converted into Melanie Ocoee
+
+ align:start position:0%
+of steps is converted into Melanie Ocoee
+ 
+
+ align:start position:0%
+of steps is converted into Melanie Ocoee
+which then gets converted to
+
+ align:start position:0%
+which then gets converted to
+ 
+
+ align:start position:0%
+which then gets converted to
+succinylcholine
+
+ align:start position:0%
+succinylcholine
+ 
+
+ align:start position:0%
+succinylcholine
+in to the TCA cycle and in that pathway
+
+ align:start position:0%
+in to the TCA cycle and in that pathway
+ 
+
+ align:start position:0%
+in to the TCA cycle and in that pathway
+you use an enzyme a mutase that uses
+
+ align:start position:0%
+you use an enzyme a mutase that uses
+ 
+
+ align:start position:0%
+you use an enzyme a mutase that uses
+adenosylcobalamin we'll talk briefly
+
+ align:start position:0%
+adenosylcobalamin we'll talk briefly
+ 
+
+ align:start position:0%
+adenosylcobalamin we'll talk briefly
+about the chemistry of adenosylcobalamin
+
+ align:start position:0%
+about the chemistry of adenosylcobalamin
+ 
+
+ align:start position:0%
+about the chemistry of adenosylcobalamin
+also methylcobalamin ok so there were a
+
+ align:start position:0%
+also methylcobalamin ok so there were a
+ 
+
+ align:start position:0%
+also methylcobalamin ok so there were a
+few things that i wanted to say about
+
+ align:start position:0%
+few things that i wanted to say about
+ 
+
+ align:start position:0%
+few things that i wanted to say about
+some generalizations that i wanted to
+
+ align:start position:0%
+some generalizations that i wanted to
+ 
+
+ align:start position:0%
+some generalizations that i wanted to
+make about these cofactors and the first
+
+ align:start position:0%
+make about these cofactors and the first
+ 
+
+ align:start position:0%
+make about these cofactors and the first
+one is that again the Corrin ring is
+
+ align:start position:0%
+one is that again the Corrin ring is
+ 
+
+ align:start position:0%
+one is that again the Corrin ring is
+much more reduced than the parol ring
+
+ align:start position:0%
+much more reduced than the parol ring
+ 
+
+ align:start position:0%
+much more reduced than the parol ring
+that you see in protoporphyrin 9 which
+
+ align:start position:0%
+that you see in protoporphyrin 9 which
+ 
+
+ align:start position:0%
+that you see in protoporphyrin 9 which
+you've seen in hemoglobin before the
+
+ align:start position:0%
+you've seen in hemoglobin before the
+ 
+
+ align:start position:0%
+you've seen in hemoglobin before the
+second thing is that you have this
+
+ align:start position:0%
+second thing is that you have this
+ 
+
+ align:start position:0%
+second thing is that you have this
+unusual dimethyl benzyl midazolam in
+
+ align:start position:0%
+unusual dimethyl benzyl midazolam in
+ 
+
+ align:start position:0%
+unusual dimethyl benzyl midazolam in
+which you see nowhere else in cofactor
+
+ align:start position:0%
+which you see nowhere else in cofactor
+ 
+
+ align:start position:0%
+which you see nowhere else in cofactor
+chemistry it's only found in this
+
+ align:start position:0%
+chemistry it's only found in this
+ 
+
+ align:start position:0%
+chemistry it's only found in this
+particular cofactor the second thing
+
+ align:start position:0%
+particular cofactor the second thing
+ 
+
+ align:start position:0%
+particular cofactor the second thing
+which I think is the most amazing is
+
+ align:start position:0%
+which I think is the most amazing is
+ 
+
+ align:start position:0%
+which I think is the most amazing is
+that what you see if you
+
+ align:start position:0%
+that what you see if you
+ 
+
+ align:start position:0%
+that what you see if you
+look back here is that you have if this
+
+ align:start position:0%
+look back here is that you have if this
+ 
+
+ align:start position:0%
+look back here is that you have if this
+is a methyl group or this is this
+
+ align:start position:0%
+is a methyl group or this is this
+ 
+
+ align:start position:0%
+is a methyl group or this is this
+five-prime deoxyadenosine you have a
+
+ align:start position:0%
+five-prime deoxyadenosine you have a
+ 
+
+ align:start position:0%
+five-prime deoxyadenosine you have a
+carbon cobalt bond well this was
+
+ align:start position:0%
+carbon cobalt bond well this was
+ 
+
+ align:start position:0%
+carbon cobalt bond well this was
+discovered in the 1950s and the first
+
+ align:start position:0%
+discovered in the 1950s and the first
+ 
+
+ align:start position:0%
+discovered in the 1950s and the first
+structure was solved of this molecule by
+
+ align:start position:0%
+structure was solved of this molecule by
+ 
+
+ align:start position:0%
+structure was solved of this molecule by
+Dorothy crow for Hodgkin in 1964 and she
+
+ align:start position:0%
+Dorothy crow for Hodgkin in 1964 and she
+ 
+
+ align:start position:0%
+Dorothy crow for Hodgkin in 1964 and she
+won the Nobel Prize did this work no
+
+ align:start position:0%
+won the Nobel Prize did this work no
+ 
+
+ align:start position:0%
+won the Nobel Prize did this work no
+chemists had ever seen a carbon cobalt
+
+ align:start position:0%
+chemists had ever seen a carbon cobalt
+ 
+
+ align:start position:0%
+chemists had ever seen a carbon cobalt
+bond and they thought in fact
+
+ align:start position:0%
+bond and they thought in fact
+ 
+
+ align:start position:0%
+bond and they thought in fact
+biochemists were crazy that they even
+
+ align:start position:0%
+biochemists were crazy that they even
+ 
+
+ align:start position:0%
+biochemists were crazy that they even
+proposed such a structure so this
+
+ align:start position:0%
+proposed such a structure so this
+ 
+
+ align:start position:0%
+proposed such a structure so this
+structure and we'll see that this this
+
+ align:start position:0%
+structure and we'll see that this this
+ 
+
+ align:start position:0%
+structure and we'll see that this this
+is where all the chemistry happens is
+
+ align:start position:0%
+is where all the chemistry happens is
+ 
+
+ align:start position:0%
+is where all the chemistry happens is
+completely unique and people spent 25
+
+ align:start position:0%
+completely unique and people spent 25
+ 
+
+ align:start position:0%
+completely unique and people spent 25
+years figuring out how this cofactor it
+
+ align:start position:0%
+years figuring out how this cofactor it
+ 
+
+ align:start position:0%
+years figuring out how this cofactor it
+actually work to do the transformations
+
+ align:start position:0%
+actually work to do the transformations
+ 
+
+ align:start position:0%
+actually work to do the transformations
+that I'll very briefly introduce you to
+
+ align:start position:0%
+that I'll very briefly introduce you to
+ 
+
+ align:start position:0%
+that I'll very briefly introduce you to
+so this is the first example of a carbon
+
+ align:start position:0%
+so this is the first example of a carbon
+ 
+
+ align:start position:0%
+so this is the first example of a carbon
+cobalt and we'll see that cobalt is in
+
+ align:start position:0%
+cobalt and we'll see that cobalt is in
+ 
+
+ align:start position:0%
+cobalt and we'll see that cobalt is in
+the plus 3 oxidation state bond so it's
+
+ align:start position:0%
+the plus 3 oxidation state bond so it's
+ 
+
+ align:start position:0%
+the plus 3 oxidation state bond so it's
+the first organo metallic cofactor and
+
+ align:start position:0%
+the first organo metallic cofactor and
+ 
+
+ align:start position:0%
+the first organo metallic cofactor and
+what people also found by studying this
+
+ align:start position:0%
+what people also found by studying this
+ 
+
+ align:start position:0%
+what people also found by studying this
+molecule is that the cobalt can actually
+
+ align:start position:0%
+molecule is that the cobalt can actually
+ 
+
+ align:start position:0%
+molecule is that the cobalt can actually
+exist in 3 oxidation state it can exist
+
+ align:start position:0%
+exist in 3 oxidation state it can exist
+ 
+
+ align:start position:0%
+exist in 3 oxidation state it can exist
+in the Cobell one state we're in the DZ
+
+ align:start position:0%
+in the Cobell one state we're in the DZ
+ 
+
+ align:start position:0%
+in the Cobell one state we're in the DZ
+squared orbital if you don't remember
+
+ align:start position:0%
+squared orbital if you don't remember
+ 
+
+ align:start position:0%
+squared orbital if you don't remember
+what a DZ squared orbital is you need to
+
+ align:start position:0%
+what a DZ squared orbital is you need to
+ 
+
+ align:start position:0%
+what a DZ squared orbital is you need to
+go back and look at your freshman
+
+ align:start position:0%
+go back and look at your freshman
+ 
+
+ align:start position:0%
+go back and look at your freshman
+chemistry you have two electrons and it
+
+ align:start position:0%
+chemistry you have two electrons and it
+ 
+
+ align:start position:0%
+chemistry you have two electrons and it
+turns out that cobalt 1 is a super
+
+ align:start position:0%
+turns out that cobalt 1 is a super
+ 
+
+ align:start position:0%
+turns out that cobalt 1 is a super
+nucleophile and we'll see that that
+
+ align:start position:0%
+nucleophile and we'll see that that
+ 
+
+ align:start position:0%
+nucleophile and we'll see that that
+plays a key role in the chemistry and so
+
+ align:start position:0%
+plays a key role in the chemistry and so
+ 
+
+ align:start position:0%
+plays a key role in the chemistry and so
+again this is the cobalt the D we're
+
+ align:start position:0%
+again this is the cobalt the D we're
+ 
+
+ align:start position:0%
+again this is the cobalt the D we're
+only looking at one of the orbit
+
+ align:start position:0%
+only looking at one of the orbit
+ 
+
+ align:start position:0%
+only looking at one of the orbit
+orbitals of the cobalt on the other hand
+
+ align:start position:0%
+orbitals of the cobalt on the other hand
+ 
+
+ align:start position:0%
+orbitals of the cobalt on the other hand
+in adenosine and this is found in methyl
+
+ align:start position:0%
+in adenosine and this is found in methyl
+ 
+
+ align:start position:0%
+in adenosine and this is found in methyl
+this is going to be used in
+
+ align:start position:0%
+this is going to be used in
+ 
+
+ align:start position:0%
+this is going to be used in
+methylcobalamin so when you have a
+
+ align:start position:0%
+methylcobalamin so when you have a
+ 
+
+ align:start position:0%
+methylcobalamin so when you have a
+methyl group as the axial again you're
+
+ align:start position:0%
+methyl group as the axial again you're
+ 
+
+ align:start position:0%
+methyl group as the axial again you're
+going to use cobalt in this oxidation
+
+ align:start position:0%
+going to use cobalt in this oxidation
+ 
+
+ align:start position:0%
+going to use cobalt in this oxidation
+state which is the plus 1 state for
+
+ align:start position:0%
+state which is the plus 1 state for
+ 
+
+ align:start position:0%
+state which is the plus 1 state for
+almost all other b12 dependent reactions
+
+ align:start position:0%
+almost all other b12 dependent reactions
+ 
+
+ align:start position:0%
+almost all other b12 dependent reactions
+you have cobalt 2 which has you
+
+ align:start position:0%
+you have cobalt 2 which has you
+ 
+
+ align:start position:0%
+you have cobalt 2 which has you
+lausanne electrons he have one only one
+
+ align:start position:0%
+lausanne electrons he have one only one
+ 
+
+ align:start position:0%
+lausanne electrons he have one only one
+electron by itself in its DZ squared
+
+ align:start position:0%
+electron by itself in its DZ squared
+ 
+
+ align:start position:0%
+electron by itself in its DZ squared
+orbital and this really dictates the
+
+ align:start position:0%
+orbital and this really dictates the
+ 
+
+ align:start position:0%
+orbital and this really dictates the
+chemistry and so this is found in
+
+ align:start position:0%
+chemistry and so this is found in
+ 
+
+ align:start position:0%
+chemistry and so this is found in
+adenosylcobalamin chemistry and then in
+
+ align:start position:0%
+adenosylcobalamin chemistry and then in
+ 
+
+ align:start position:0%
+adenosylcobalamin chemistry and then in
+the resting state you have cobalt 3 and
+
+ align:start position:0%
+the resting state you have cobalt 3 and
+ 
+
+ align:start position:0%
+the resting state you have cobalt 3 and
+cobalt 3 has none of the electrons in
+
+ align:start position:0%
+cobalt 3 has none of the electrons in
+ 
+
+ align:start position:0%
+cobalt 3 has none of the electrons in
+the DZ squared orbital and this is
+
+ align:start position:0%
+the DZ squared orbital and this is
+ 
+
+ align:start position:0%
+the DZ squared orbital and this is
+basically the resting state this most
+
+ align:start position:0%
+basically the resting state this most
+ 
+
+ align:start position:0%
+basically the resting state this most
+stable state where you find this
+
+ align:start position:0%
+stable state where you find this
+ 
+
+ align:start position:0%
+stable state where you find this
+cofactor
+
+ align:start position:0%
+cofactor
+ 
+
+ align:start position:0%
+cofactor
+so in cyano cobalamin which is vitamin
+
+ align:start position:0%
+so in cyano cobalamin which is vitamin
+ 
+
+ align:start position:0%
+so in cyano cobalamin which is vitamin
+b12 the cobalt is in the plus 3
+
+ align:start position:0%
+b12 the cobalt is in the plus 3
+ 
+
+ align:start position:0%
+b12 the cobalt is in the plus 3
+oxidation state ok so what we're gonna
+
+ align:start position:0%
+oxidation state ok so what we're gonna
+ 
+
+ align:start position:0%
+oxidation state ok so what we're gonna
+see very briefly we're not spending much
+
+ align:start position:0%
+see very briefly we're not spending much
+ 
+
+ align:start position:0%
+see very briefly we're not spending much
+time on this is the cobalt 1 state it's
+
+ align:start position:0%
+time on this is the cobalt 1 state it's
+ 
+
+ align:start position:0%
+time on this is the cobalt 1 state it's
+a super good nucleophile that affects
+
+ align:start position:0%
+a super good nucleophile that affects
+ 
+
+ align:start position:0%
+a super good nucleophile that affects
+the chemistry the cobalt 2 state has one
+
+ align:start position:0%
+the chemistry the cobalt 2 state has one
+ 
+
+ align:start position:0%
+the chemistry the cobalt 2 state has one
+unpaired electron
+
+ align:start position:0%
+unpaired electron
+ 
+
+ align:start position:0%
+unpaired electron
+you haven't been introduced to chemistry
+
+ align:start position:0%
+you haven't been introduced to chemistry
+ 
+
+ align:start position:0%
+you haven't been introduced to chemistry
+with one unpaired electron which is
+
+ align:start position:0%
+with one unpaired electron which is
+ 
+
+ align:start position:0%
+with one unpaired electron which is
+radical chemistry that most people don't
+
+ align:start position:0%
+radical chemistry that most people don't
+ 
+
+ align:start position:0%
+radical chemistry that most people don't
+spend a lot of time talking about
+
+ align:start position:0%
+spend a lot of time talking about
+ 
+
+ align:start position:0%
+spend a lot of time talking about
+adenosylcobalamin because it's radicals
+
+ align:start position:0%
+adenosylcobalamin because it's radicals
+ 
+
+ align:start position:0%
+adenosylcobalamin because it's radicals
+and they don't learn much about radicals
+
+ align:start position:0%
+and they don't learn much about radicals
+ 
+
+ align:start position:0%
+and they don't learn much about radicals
+in introductory organic chemistry but
+
+ align:start position:0%
+in introductory organic chemistry but
+ 
+
+ align:start position:0%
+in introductory organic chemistry but
+i'll show you briefly how the enzymes
+
+ align:start position:0%
+i'll show you briefly how the enzymes
+ 
+
+ align:start position:0%
+i'll show you briefly how the enzymes
+work they use this cobalt to state the
+
+ align:start position:0%
+work they use this cobalt to state the
+ 
+
+ align:start position:0%
+work they use this cobalt to state the
+other thing I wanted to mention was that
+
+ align:start position:0%
+other thing I wanted to mention was that
+ 
+
+ align:start position:0%
+other thing I wanted to mention was that
+the colors and so if you try want to
+
+ align:start position:0%
+the colors and so if you try want to
+ 
+
+ align:start position:0%
+the colors and so if you try want to
+understand how these cofactors work the
+
+ align:start position:0%
+understand how these cofactors work the
+ 
+
+ align:start position:0%
+understand how these cofactors work the
+different number of electrons govern
+
+ align:start position:0%
+different number of electrons govern
+ 
+
+ align:start position:0%
+different number of electrons govern
+what colors you can end up seeing and
+
+ align:start position:0%
+what colors you can end up seeing and
+ 
+
+ align:start position:0%
+what colors you can end up seeing and
+again I always use this as an example on
+
+ align:start position:0%
+again I always use this as an example on
+ 
+
+ align:start position:0%
+again I always use this as an example on
+mi t--'s campus in the spring cobalt 2
+
+ align:start position:0%
+mi t--'s campus in the spring cobalt 2
+ 
+
+ align:start position:0%
+mi t--'s campus in the spring cobalt 2
+has spectacular orange color like the
+
+ align:start position:0%
+has spectacular orange color like the
+ 
+
+ align:start position:0%
+has spectacular orange color like the
+orange azaleas and cobalt 3 is like the
+
+ align:start position:0%
+orange azaleas and cobalt 3 is like the
+ 
+
+ align:start position:0%
+orange azaleas and cobalt 3 is like the
+pink azaleas and so they're really
+
+ align:start position:0%
+pink azaleas and so they're really
+ 
+
+ align:start position:0%
+pink azaleas and so they're really
+dramatically different this is why I say
+
+ align:start position:0%
+dramatically different this is why I say
+ 
+
+ align:start position:0%
+dramatically different this is why I say
+this is nature's most beautiful
+
+ align:start position:0%
+this is nature's most beautiful
+ 
+
+ align:start position:0%
+this is nature's most beautiful
+cofactors okay so what I want to do now
+
+ align:start position:0%
+cofactors okay so what I want to do now
+ 
+
+ align:start position:0%
+cofactors okay so what I want to do now
+is briefly talk about mechanism and I'm
+
+ align:start position:0%
+is briefly talk about mechanism and I'm
+ 
+
+ align:start position:0%
+is briefly talk about mechanism and I'm
+going to suppose mostly talk about
+
+ align:start position:0%
+going to suppose mostly talk about
+ 
+
+ align:start position:0%
+going to suppose mostly talk about
+mechanism of the cobalt 2 state and how
+
+ align:start position:0%
+mechanism of the cobalt 2 state and how
+ 
+
+ align:start position:0%
+mechanism of the cobalt 2 state and how
+adenosylcobalamin works since that's the
+
+ align:start position:0%
+adenosylcobalamin works since that's the
+ 
+
+ align:start position:0%
+adenosylcobalamin works since that's the
+one that's most complicated so what I'm
+
+ align:start position:0%
+one that's most complicated so what I'm
+ 
+
+ align:start position:0%
+one that's most complicated so what I'm
+drawing here is if we look at the
+
+ align:start position:0%
+drawing here is if we look at the
+ 
+
+ align:start position:0%
+drawing here is if we look at the
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+if we look at the structure of
+
+ align:start position:0%
+if we look at the structure of
+ 
+
+ align:start position:0%
+if we look at the structure of
+adenosylcobalamin
+
+ align:start position:0%
+adenosylcobalamin
+ 
+
+ align:start position:0%
+adenosylcobalamin
+you see you have a cobalt with four
+
+ align:start position:0%
+you see you have a cobalt with four
+ 
+
+ align:start position:0%
+you see you have a cobalt with four
+nitrogens these are the four nitrogen's
+
+ align:start position:0%
+nitrogens these are the four nitrogen's
+ 
+
+ align:start position:0%
+nitrogens these are the four nitrogen's
+and these are the two axial ligands so
+
+ align:start position:0%
+and these are the two axial ligands so
+ 
+
+ align:start position:0%
+and these are the two axial ligands so
+this is abbreviated I'm going to be
+
+ align:start position:0%
+this is abbreviated I'm going to be
+ 
+
+ align:start position:0%
+this is abbreviated I'm going to be
+using in all the subsequent chemical
+
+ align:start position:0%
+using in all the subsequent chemical
+ 
+
+ align:start position:0%
+using in all the subsequent chemical
+descriptions of what I'm talking about
+
+ align:start position:0%
+descriptions of what I'm talking about
+ 
+
+ align:start position:0%
+descriptions of what I'm talking about
+okay so I'm not going to draw this
+
+ align:start position:0%
+okay so I'm not going to draw this
+ 
+
+ align:start position:0%
+okay so I'm not going to draw this
+structure I would over and over again
+
+ align:start position:0%
+structure I would over and over again
+ 
+
+ align:start position:0%
+structure I would over and over again
+okay so here's our adenosylcobalamin
+
+ align:start position:0%
+okay so here's our adenosylcobalamin
+ 
+
+ align:start position:0%
+okay so here's our adenosylcobalamin
+that we just talked about and there's
+
+ align:start position:0%
+that we just talked about and there's
+ 
+
+ align:start position:0%
+that we just talked about and there's
+DMB is the dimethyl benzyl midazolam and
+
+ align:start position:0%
+DMB is the dimethyl benzyl midazolam and
+ 
+
+ align:start position:0%
+DMB is the dimethyl benzyl midazolam and
+and then you have the 5-prime
+
+ align:start position:0%
+and then you have the 5-prime
+ 
+
+ align:start position:0%
+and then you have the 5-prime
+deoxyadenosine and the top face which is
+
+ align:start position:0%
+deoxyadenosine and the top face which is
+ 
+
+ align:start position:0%
+deoxyadenosine and the top face which is
+where all the chemistry is going to
+
+ align:start position:0%
+where all the chemistry is going to
+ 
+
+ align:start position:0%
+where all the chemistry is going to
+happen so the business end of the
+
+ align:start position:0%
+happen so the business end of the
+ 
+
+ align:start position:0%
+happen so the business end of the
+molecule is going to be this part of the
+
+ align:start position:0%
+molecule is going to be this part of the
+ 
+
+ align:start position:0%
+molecule is going to be this part of the
+molecule and the key to everything is
+
+ align:start position:0%
+molecule and the key to everything is
+ 
+
+ align:start position:0%
+molecule and the key to everything is
+this carbon cobalt bond now what's
+
+ align:start position:0%
+this carbon cobalt bond now what's
+ 
+
+ align:start position:0%
+this carbon cobalt bond now what's
+unusual about a carbon cobalt bond it's
+
+ align:start position:0%
+unusual about a carbon cobalt bond it's
+ 
+
+ align:start position:0%
+unusual about a carbon cobalt bond it's
+very weak if you if you go to 240
+
+ align:start position:0%
+very weak if you if you go to 240
+ 
+
+ align:start position:0%
+very weak if you if you go to 240
+degrees the bond breaks most things you
+
+ align:start position:0%
+degrees the bond breaks most things you
+ 
+
+ align:start position:0%
+degrees the bond breaks most things you
+can go to hundreds of degrees and the
+
+ align:start position:0%
+can go to hundreds of degrees and the
+ 
+
+ align:start position:0%
+can go to hundreds of degrees and the
+bond is stable so it's thermally labile
+
+ align:start position:0%
+bond is stable so it's thermally labile
+ 
+
+ align:start position:0%
+bond is stable so it's thermally labile
+and then the other thing that's unique
+
+ align:start position:0%
+and then the other thing that's unique
+ 
+
+ align:start position:0%
+and then the other thing that's unique
+about this cofactor is that it's
+
+ align:start position:0%
+about this cofactor is that it's
+ 
+
+ align:start position:0%
+about this cofactor is that it's
+light-sensitive so if you put
+
+ align:start position:0%
+light-sensitive so if you put
+ 
+
+ align:start position:0%
+light-sensitive so if you put
+adenosylcobalamin out on the benchtop
+
+ align:start position:0%
+adenosylcobalamin out on the benchtop
+ 
+
+ align:start position:0%
+adenosylcobalamin out on the benchtop
+here within two minutes the whole thing
+
+ align:start position:0%
+here within two minutes the whole thing
+ 
+
+ align:start position:0%
+here within two minutes the whole thing
+would be destroyed because you would
+
+ align:start position:0%
+would be destroyed because you would
+ 
+
+ align:start position:0%
+would be destroyed because you would
+break this carbon cobalt bond okay and
+
+ align:start position:0%
+break this carbon cobalt bond okay and
+ 
+
+ align:start position:0%
+break this carbon cobalt bond okay and
+that's the key to the chemistry of how
+
+ align:start position:0%
+that's the key to the chemistry of how
+ 
+
+ align:start position:0%
+that's the key to the chemistry of how
+this cofactor works okay so I'm gonna
+
+ align:start position:0%
+this cofactor works okay so I'm gonna
+ 
+
+ align:start position:0%
+this cofactor works okay so I'm gonna
+give you a generic mechanism and then
+
+ align:start position:0%
+give you a generic mechanism and then
+ 
+
+ align:start position:0%
+give you a generic mechanism and then
+I'm gonna focus on the mechanism of
+
+ align:start position:0%
+I'm gonna focus on the mechanism of
+ 
+
+ align:start position:0%
+I'm gonna focus on the mechanism of
+methyl Melanie okay a mutase which you
+
+ align:start position:0%
+methyl Melanie okay a mutase which you
+ 
+
+ align:start position:0%
+methyl Melanie okay a mutase which you
+find in human metabolism um before I get
+
+ align:start position:0%
+find in human metabolism um before I get
+ 
+
+ align:start position:0%
+find in human metabolism um before I get
+started let me just show you what the
+
+ align:start position:0%
+started let me just show you what the
+ 
+
+ align:start position:0%
+started let me just show you what the
+reaction is and show you why it's
+
+ align:start position:0%
+reaction is and show you why it's
+ 
+
+ align:start position:0%
+reaction is and show you why it's
+unusual and then we'll go back to the
+
+ align:start position:0%
+unusual and then we'll go back to the
+ 
+
+ align:start position:0%
+unusual and then we'll go back to the
+actual mechanism okay so what does
+
+ align:start position:0%
+actual mechanism okay so what does
+ 
+
+ align:start position:0%
+actual mechanism okay so what does
+methyl Melanie OCO a mutase do again it
+
+ align:start position:0%
+methyl Melanie OCO a mutase do again it
+ 
+
+ align:start position:0%
+methyl Melanie OCO a mutase do again it
+plays a central role in odd chain fatty
+
+ align:start position:0%
+plays a central role in odd chain fatty
+ 
+
+ align:start position:0%
+plays a central role in odd chain fatty
+acid metabolism okay so this is Kawai
+
+ align:start position:0%
+acid metabolism okay so this is Kawai
+ 
+
+ align:start position:0%
+acid metabolism okay so this is Kawai
+you need to go back and look at your
+
+ align:start position:0%
+you need to go back and look at your
+ 
+
+ align:start position:0%
+you need to go back and look at your
+lexicon if you can't remember the
+
+ align:start position:0%
+lexicon if you can't remember the
+ 
+
+ align:start position:0%
+lexicon if you can't remember the
+structure of Kawai but just remember
+
+ align:start position:0%
+structure of Kawai but just remember
+ 
+
+ align:start position:0%
+structure of Kawai but just remember
+it's a thio Wester that's all you need
+
+ align:start position:0%
+it's a thio Wester that's all you need
+ 
+
+ align:start position:0%
+it's a thio Wester that's all you need
+to know okay so this is the substrate
+
+ align:start position:0%
+to know okay so this is the substrate
+ 
+
+ align:start position:0%
+to know okay so this is the substrate
+and this is called methyl
+
+ align:start position:0%
+and this is called methyl
+ 
+
+ align:start position:0%
+and this is called methyl
+one'll go away okay so
+
+ align:start position:0%
+one'll go away okay so
+ 
+
+ align:start position:0%
+one'll go away okay so
+adenosylcobalamin catalyzes
+
+ align:start position:0%
+adenosylcobalamin catalyzes
+ 
+
+ align:start position:0%
+adenosylcobalamin catalyzes
+rearrangements and this reaction has
+
+ align:start position:0%
+rearrangements and this reaction has
+ 
+
+ align:start position:0%
+rearrangements and this reaction has
+fascinated chemists for 30 years because
+
+ align:start position:0%
+fascinated chemists for 30 years because
+ 
+
+ align:start position:0%
+fascinated chemists for 30 years because
+it was a no chemical precedent just like
+
+ align:start position:0%
+it was a no chemical precedent just like
+ 
+
+ align:start position:0%
+it was a no chemical precedent just like
+there was no chemical precedent for
+
+ align:start position:0%
+there was no chemical precedent for
+ 
+
+ align:start position:0%
+there was no chemical precedent for
+carbon cobalt bonds when biochemists
+
+ align:start position:0%
+carbon cobalt bonds when biochemists
+ 
+
+ align:start position:0%
+carbon cobalt bonds when biochemists
+discovered this there was no precedent
+
+ align:start position:0%
+discovered this there was no precedent
+ 
+
+ align:start position:0%
+discovered this there was no precedent
+for the reaction I'm going to show you
+
+ align:start position:0%
+for the reaction I'm going to show you
+ 
+
+ align:start position:0%
+for the reaction I'm going to show you
+so what is the reaction it's a
+
+ align:start position:0%
+so what is the reaction it's a
+ 
+
+ align:start position:0%
+so what is the reaction it's a
+rearrangement and it's rearrangement
+
+ align:start position:0%
+rearrangement and it's rearrangement
+ 
+
+ align:start position:0%
+rearrangement and it's rearrangement
+because this hydrogen moves from this
+
+ align:start position:0%
+because this hydrogen moves from this
+ 
+
+ align:start position:0%
+because this hydrogen moves from this
+carbon to this carbon and this whole
+
+ align:start position:0%
+carbon to this carbon and this whole
+ 
+
+ align:start position:0%
+carbon to this carbon and this whole
+group the SIA West earth moves from this
+
+ align:start position:0%
+group the SIA West earth moves from this
+ 
+
+ align:start position:0%
+group the SIA West earth moves from this
+carbon to this carbon so that's the
+
+ align:start position:0%
+carbon to this carbon so that's the
+ 
+
+ align:start position:0%
+carbon to this carbon so that's the
+actual reaction it's reversible and so
+
+ align:start position:0%
+actual reaction it's reversible and so
+ 
+
+ align:start position:0%
+actual reaction it's reversible and so
+what you do is you generate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+succinylcholine is moved over here and
+
+ align:start position:0%
+succinylcholine is moved over here and
+ 
+
+ align:start position:0%
+succinylcholine is moved over here and
+this is succinylcholine and we haven't
+
+ align:start position:0%
+this is succinylcholine and we haven't
+ 
+
+ align:start position:0%
+this is succinylcholine and we haven't
+talked about it yet but succinylcholine
+
+ align:start position:0%
+talked about it yet but succinylcholine
+ 
+
+ align:start position:0%
+talked about it yet but succinylcholine
+Tirol metabolism in the TCA cycle okay
+
+ align:start position:0%
+Tirol metabolism in the TCA cycle okay
+ 
+
+ align:start position:0%
+Tirol metabolism in the TCA cycle okay
+so the question that we want to focus on
+
+ align:start position:0%
+so the question that we want to focus on
+ 
+
+ align:start position:0%
+so the question that we want to focus on
+now is how do you catalyze this weird
+
+ align:start position:0%
+now is how do you catalyze this weird
+ 
+
+ align:start position:0%
+now is how do you catalyze this weird
+rearrangement what is this cofactor this
+
+ align:start position:0%
+rearrangement what is this cofactor this
+ 
+
+ align:start position:0%
+rearrangement what is this cofactor this
+big huge molecule with this carbon weak
+
+ align:start position:0%
+big huge molecule with this carbon weak
+ 
+
+ align:start position:0%
+big huge molecule with this carbon weak
+carbon cobalt by not what does it do
+
+ align:start position:0%
+carbon cobalt by not what does it do
+ 
+
+ align:start position:0%
+carbon cobalt by not what does it do
+okay so I'm going to come back to this
+
+ align:start position:0%
+okay so I'm going to come back to this
+ 
+
+ align:start position:0%
+okay so I'm going to come back to this
+in a minute but this let me show you
+
+ align:start position:0%
+in a minute but this let me show you
+ 
+
+ align:start position:0%
+in a minute but this let me show you
+what it does okay so this is a generic
+
+ align:start position:0%
+what it does okay so this is a generic
+ 
+
+ align:start position:0%
+what it does okay so this is a generic
+mechanism because while I said there's
+
+ align:start position:0%
+mechanism because while I said there's
+ 
+
+ align:start position:0%
+mechanism because while I said there's
+only one enzyme in humans that uses that
+
+ align:start position:0%
+only one enzyme in humans that uses that
+ 
+
+ align:start position:0%
+only one enzyme in humans that uses that
+Denis of CO Baumann if you move in to
+
+ align:start position:0%
+Denis of CO Baumann if you move in to
+ 
+
+ align:start position:0%
+Denis of CO Baumann if you move in to
+fungi or you move into our key or
+
+ align:start position:0%
+fungi or you move into our key or
+ 
+
+ align:start position:0%
+fungi or you move into our key or
+bacteria you find there are many b12
+
+ align:start position:0%
+bacteria you find there are many b12
+ 
+
+ align:start position:0%
+bacteria you find there are many b12
+dependent reactions that also do
+
+ align:start position:0%
+dependent reactions that also do
+ 
+
+ align:start position:0%
+dependent reactions that also do
+rearrangements but different kinds of
+
+ align:start position:0%
+rearrangements but different kinds of
+ 
+
+ align:start position:0%
+rearrangements but different kinds of
+rearrangements okay so what's the
+
+ align:start position:0%
+rearrangements okay so what's the
+ 
+
+ align:start position:0%
+rearrangements okay so what's the
+generic mechanism okay so the generic
+
+ align:start position:0%
+generic mechanism okay so the generic
+ 
+
+ align:start position:0%
+generic mechanism okay so the generic
+mechanism is the following so here we
+
+ align:start position:0%
+mechanism is the following so here we
+ 
+
+ align:start position:0%
+mechanism is the following so here we
+have our adenosylcobalamin here's our
+
+ align:start position:0%
+have our adenosylcobalamin here's our
+ 
+
+ align:start position:0%
+have our adenosylcobalamin here's our
+substrate okay and the idea is and this
+
+ align:start position:0%
+substrate okay and the idea is and this
+ 
+
+ align:start position:0%
+substrate okay and the idea is and this
+is we need to move the hydrogen from
+
+ align:start position:0%
+is we need to move the hydrogen from
+ 
+
+ align:start position:0%
+is we need to move the hydrogen from
+here to here okay
+
+ align:start position:0%
+here to here okay
+ 
+
+ align:start position:0%
+here to here okay
+does it just jump through space and the
+
+ align:start position:0%
+does it just jump through space and the
+ 
+
+ align:start position:0%
+does it just jump through space and the
+answer is no the cofactor
+
+ align:start position:0%
+answer is no the cofactor
+ 
+
+ align:start position:0%
+answer is no the cofactor
+adenosylcobalamin is going to
+
+ align:start position:0%
+adenosylcobalamin is going to
+ 
+
+ align:start position:0%
+adenosylcobalamin is going to
+the hydrogen and then it's gonna
+
+ align:start position:0%
+the hydrogen and then it's gonna
+ 
+
+ align:start position:0%
+the hydrogen and then it's gonna
+transfer it you're going to generate a
+
+ align:start position:0%
+transfer it you're going to generate a
+ 
+
+ align:start position:0%
+transfer it you're going to generate a
+reactive species and then it's gonna
+
+ align:start position:0%
+reactive species and then it's gonna
+ 
+
+ align:start position:0%
+reactive species and then it's gonna
+transfer it back to form a new product
+
+ align:start position:0%
+transfer it back to form a new product
+ 
+
+ align:start position:0%
+transfer it back to form a new product
+so the cofactor and this took people a
+
+ align:start position:0%
+so the cofactor and this took people a
+ 
+
+ align:start position:0%
+so the cofactor and this took people a
+long time to figure out because it was
+
+ align:start position:0%
+long time to figure out because it was
+ 
+
+ align:start position:0%
+long time to figure out because it was
+no chemical precedent for this is
+
+ align:start position:0%
+no chemical precedent for this is
+ 
+
+ align:start position:0%
+no chemical precedent for this is
+mediating the hydrogen transfer so
+
+ align:start position:0%
+mediating the hydrogen transfer so
+ 
+
+ align:start position:0%
+mediating the hydrogen transfer so
+that's what I'm going to show you how
+
+ align:start position:0%
+that's what I'm going to show you how
+ 
+
+ align:start position:0%
+that's what I'm going to show you how
+that actually works so here what happens
+
+ align:start position:0%
+that actually works so here what happens
+ 
+
+ align:start position:0%
+that actually works so here what happens
+is the coal key to the chemistry of
+
+ align:start position:0%
+is the coal key to the chemistry of
+ 
+
+ align:start position:0%
+is the coal key to the chemistry of
+adenosylcobalamin which again is is most
+
+ align:start position:0%
+adenosylcobalamin which again is is most
+ 
+
+ align:start position:0%
+adenosylcobalamin which again is is most
+of you haven't seen something like this
+
+ align:start position:0%
+of you haven't seen something like this
+ 
+
+ align:start position:0%
+of you haven't seen something like this
+before because of the you haven't seen
+
+ align:start position:0%
+before because of the you haven't seen
+ 
+
+ align:start position:0%
+before because of the you haven't seen
+something like this before because
+
+ align:start position:0%
+something like this before because
+ 
+
+ align:start position:0%
+something like this before because
+you're not exposed to radical chemistry
+
+ align:start position:0%
+you're not exposed to radical chemistry
+ 
+
+ align:start position:0%
+you're not exposed to radical chemistry
+is that you have hemolysis of the carbon
+
+ align:start position:0%
+is that you have hemolysis of the carbon
+ 
+
+ align:start position:0%
+is that you have hemolysis of the carbon
+cobalt bond so what does that mean it
+
+ align:start position:0%
+cobalt bond so what does that mean it
+ 
+
+ align:start position:0%
+cobalt bond so what does that mean it
+means one electron goes to the axial
+
+ align:start position:0%
+means one electron goes to the axial
+ 
+
+ align:start position:0%
+means one electron goes to the axial
+ligand and one electron goes to the
+
+ align:start position:0%
+ligand and one electron goes to the
+ 
+
+ align:start position:0%
+ligand and one electron goes to the
+Cobalt so the cobalt 3 is reduced from
+
+ align:start position:0%
+Cobalt so the cobalt 3 is reduced from
+ 
+
+ align:start position:0%
+Cobalt so the cobalt 3 is reduced from
+cobalt 3 to cobalt 2 and what you're
+
+ align:start position:0%
+cobalt 3 to cobalt 2 and what you're
+ 
+
+ align:start position:0%
+cobalt 3 to cobalt 2 and what you're
+left with is this radical species of
+
+ align:start position:0%
+left with is this radical species of
+ 
+
+ align:start position:0%
+left with is this radical species of
+five prime deoxy adenosyl radical okay
+
+ align:start position:0%
+five prime deoxy adenosyl radical okay
+ 
+
+ align:start position:0%
+five prime deoxy adenosyl radical okay
+so this is the reactive species because
+
+ align:start position:0%
+so this is the reactive species because
+ 
+
+ align:start position:0%
+so this is the reactive species because
+what you're doing and these in these
+
+ align:start position:0%
+what you're doing and these in these
+ 
+
+ align:start position:0%
+what you're doing and these in these
+transformations is pulling off an
+
+ align:start position:0%
+transformations is pulling off an
+ 
+
+ align:start position:0%
+transformations is pulling off an
+amazingly non acidic hydrogen and normal
+
+ align:start position:0%
+amazingly non acidic hydrogen and normal
+ 
+
+ align:start position:0%
+amazingly non acidic hydrogen and normal
+amino acid side chains cannot do that
+
+ align:start position:0%
+amino acid side chains cannot do that
+ 
+
+ align:start position:0%
+amino acid side chains cannot do that
+kind of chemistry you have to go to
+
+ align:start position:0%
+kind of chemistry you have to go to
+ 
+
+ align:start position:0%
+kind of chemistry you have to go to
+these reactive radical species to be
+
+ align:start position:0%
+these reactive radical species to be
+ 
+
+ align:start position:0%
+these reactive radical species to be
+able to do this
+
+ align:start position:0%
+able to do this
+ 
+
+ align:start position:0%
+able to do this
+tough chemistry so here we've generated
+
+ align:start position:0%
+tough chemistry so here we've generated
+ 
+
+ align:start position:0%
+tough chemistry so here we've generated
+a radical species it is sitting right
+
+ align:start position:0%
+a radical species it is sitting right
+ 
+
+ align:start position:0%
+a radical species it is sitting right
+next to the substrate in the active site
+
+ align:start position:0%
+next to the substrate in the active site
+ 
+
+ align:start position:0%
+next to the substrate in the active site
+of the enzyme and so what does it do it
+
+ align:start position:0%
+of the enzyme and so what does it do it
+ 
+
+ align:start position:0%
+of the enzyme and so what does it do it
+removes a hydrogen atom a hydrogen with
+
+ align:start position:0%
+removes a hydrogen atom a hydrogen with
+ 
+
+ align:start position:0%
+removes a hydrogen atom a hydrogen with
+one electron okay and so again this is
+
+ align:start position:0%
+one electron okay and so again this is
+ 
+
+ align:start position:0%
+one electron okay and so again this is
+free radical chemistry that most of you
+
+ align:start position:0%
+free radical chemistry that most of you
+ 
+
+ align:start position:0%
+free radical chemistry that most of you
+don't think about that much but what you
+
+ align:start position:0%
+don't think about that much but what you
+ 
+
+ align:start position:0%
+don't think about that much but what you
+do is the hydrogen from the substrate is
+
+ align:start position:0%
+do is the hydrogen from the substrate is
+ 
+
+ align:start position:0%
+do is the hydrogen from the substrate is
+now transferred to this axial ligand
+
+ align:start position:0%
+now transferred to this axial ligand
+ 
+
+ align:start position:0%
+now transferred to this axial ligand
+that stays stuck in the active site so
+
+ align:start position:0%
+that stays stuck in the active site so
+ 
+
+ align:start position:0%
+that stays stuck in the active site so
+we've seen this guy move over here and
+
+ align:start position:0%
+we've seen this guy move over here and
+ 
+
+ align:start position:0%
+we've seen this guy move over here and
+now what you've done is transferred one
+
+ align:start position:0%
+now what you've done is transferred one
+ 
+
+ align:start position:0%
+now what you've done is transferred one
+radical from the cofactor into a second
+
+ align:start position:0%
+radical from the cofactor into a second
+ 
+
+ align:start position:0%
+radical from the cofactor into a second
+radical that substrate okay so that's
+
+ align:start position:0%
+radical that substrate okay so that's
+ 
+
+ align:start position:0%
+radical that substrate okay so that's
+the key now it's carrying this hydrogen
+
+ align:start position:0%
+the key now it's carrying this hydrogen
+ 
+
+ align:start position:0%
+the key now it's carrying this hydrogen
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+eventually it wants to put the hydrogen
+
+ align:start position:0%
+eventually it wants to put the hydrogen
+ 
+
+ align:start position:0%
+eventually it wants to put the hydrogen
+back on to form the product okay that's
+
+ align:start position:0%
+back on to form the product okay that's
+ 
+
+ align:start position:0%
+back on to form the product okay that's
+part of the rearrangement reaction so
+
+ align:start position:0%
+part of the rearrangement reaction so
+ 
+
+ align:start position:0%
+part of the rearrangement reaction so
+what happens now is and this looks like
+
+ align:start position:0%
+what happens now is and this looks like
+ 
+
+ align:start position:0%
+what happens now is and this looks like
+magic
+
+ align:start position:0%
+magic
+ 
+
+ align:start position:0%
+magic
+I'm just showing that a substrate
+
+ align:start position:0%
+I'm just showing that a substrate
+ 
+
+ align:start position:0%
+I'm just showing that a substrate
+radical goes to product radical and I
+
+ align:start position:0%
+radical goes to product radical and I
+ 
+
+ align:start position:0%
+radical goes to product radical and I
+will show you how this works in the case
+
+ align:start position:0%
+will show you how this works in the case
+ 
+
+ align:start position:0%
+will show you how this works in the case
+of methyl Melanie lock away mute is in a
+
+ align:start position:0%
+of methyl Melanie lock away mute is in a
+ 
+
+ align:start position:0%
+of methyl Melanie lock away mute is in a
+minute okay so there's some kind of
+
+ align:start position:0%
+minute okay so there's some kind of
+ 
+
+ align:start position:0%
+minute okay so there's some kind of
+rearrangement remember we had two things
+
+ align:start position:0%
+rearrangement remember we had two things
+ 
+
+ align:start position:0%
+rearrangement remember we had two things
+rearranging the hydrogen but we also had
+
+ align:start position:0%
+rearranging the hydrogen but we also had
+ 
+
+ align:start position:0%
+rearranging the hydrogen but we also had
+a second a thioester rearranging so we
+
+ align:start position:0%
+a second a thioester rearranging so we
+ 
+
+ align:start position:0%
+a second a thioester rearranging so we
+have a rearrangement reaction and this
+
+ align:start position:0%
+have a rearrangement reaction and this
+ 
+
+ align:start position:0%
+have a rearrangement reaction and this
+is reversible and in the reaction I'm
+
+ align:start position:0%
+is reversible and in the reaction I'm
+ 
+
+ align:start position:0%
+is reversible and in the reaction I'm
+going to be talking about today and so
+
+ align:start position:0%
+going to be talking about today and so
+ 
+
+ align:start position:0%
+going to be talking about today and so
+this is the same as this structurally
+
+ align:start position:0%
+this is the same as this structurally
+ 
+
+ align:start position:0%
+this is the same as this structurally
+these are the same I've just written out
+
+ align:start position:0%
+these are the same I've just written out
+ 
+
+ align:start position:0%
+these are the same I've just written out
+the methyl group and so we have a
+
+ align:start position:0%
+the methyl group and so we have a
+ 
+
+ align:start position:0%
+the methyl group and so we have a
+substrate radical converting into a
+
+ align:start position:0%
+substrate radical converting into a
+ 
+
+ align:start position:0%
+substrate radical converting into a
+product radical okay and now what we
+
+ align:start position:0%
+product radical okay and now what we
+ 
+
+ align:start position:0%
+product radical okay and now what we
+want to do is generate the product and
+
+ align:start position:0%
+want to do is generate the product and
+ 
+
+ align:start position:0%
+want to do is generate the product and
+so the hydrogen from this carrier your
+
+ align:start position:0%
+so the hydrogen from this carrier your
+ 
+
+ align:start position:0%
+so the hydrogen from this carrier your
+axial again is now going to be
+
+ align:start position:0%
+axial again is now going to be
+ 
+
+ align:start position:0%
+axial again is now going to be
+transferred by hydrogen atom transfer
+
+ align:start position:0%
+transferred by hydrogen atom transfer
+ 
+
+ align:start position:0%
+transferred by hydrogen atom transfer
+back to P dot to form the product so
+
+ align:start position:0%
+back to P dot to form the product so
+ 
+
+ align:start position:0%
+back to P dot to form the product so
+again it's one electron chemistry and
+
+ align:start position:0%
+again it's one electron chemistry and
+ 
+
+ align:start position:0%
+again it's one electron chemistry and
+doing one electron chemistry the
+
+ align:start position:0%
+doing one electron chemistry the
+ 
+
+ align:start position:0%
+doing one electron chemistry the
+hydrogen is transferred back to P and
+
+ align:start position:0%
+hydrogen is transferred back to P and
+ 
+
+ align:start position:0%
+hydrogen is transferred back to P and
+then what do you do you lose one radical
+
+ align:start position:0%
+then what do you do you lose one radical
+ 
+
+ align:start position:0%
+then what do you do you lose one radical
+and you generate another radical you
+
+ align:start position:0%
+and you generate another radical you
+ 
+
+ align:start position:0%
+and you generate another radical you
+regenerate the radical we started with
+
+ align:start position:0%
+regenerate the radical we started with
+ 
+
+ align:start position:0%
+regenerate the radical we started with
+the five prime deoxyadenosine radical on
+
+ align:start position:0%
+the five prime deoxyadenosine radical on
+ 
+
+ align:start position:0%
+the five prime deoxyadenosine radical on
+the axial again now I have written here
+
+ align:start position:0%
+the axial again now I have written here
+ 
+
+ align:start position:0%
+the axial again now I have written here
+hydrogen in black and in red why is that
+
+ align:start position:0%
+hydrogen in black and in red why is that
+ 
+
+ align:start position:0%
+hydrogen in black and in red why is that
+true because here's a methyl group and
+
+ align:start position:0%
+true because here's a methyl group and
+ 
+
+ align:start position:0%
+true because here's a methyl group and
+if you have free complete freedom of
+
+ align:start position:0%
+if you have free complete freedom of
+ 
+
+ align:start position:0%
+if you have free complete freedom of
+rotation around that carbon-carbon bond
+
+ align:start position:0%
+rotation around that carbon-carbon bond
+ 
+
+ align:start position:0%
+rotation around that carbon-carbon bond
+you can pull off either the methyl
+
+ align:start position:0%
+you can pull off either the methyl
+ 
+
+ align:start position:0%
+you can pull off either the methyl
+hydrogen's become equivalent so it can
+
+ align:start position:0%
+hydrogen's become equivalent so it can
+ 
+
+ align:start position:0%
+hydrogen's become equivalent so it can
+pull off a hydrogen red or a hydrogen
+
+ align:start position:0%
+pull off a hydrogen red or a hydrogen
+ 
+
+ align:start position:0%
+pull off a hydrogen red or a hydrogen
+black okay can't distinguish in the
+
+ align:start position:0%
+black okay can't distinguish in the
+ 
+
+ align:start position:0%
+black okay can't distinguish in the
+active site of the enzyme so what you
+
+ align:start position:0%
+active site of the enzyme so what you
+ 
+
+ align:start position:0%
+active site of the enzyme so what you
+now generate is the same thing we
+
+ align:start position:0%
+now generate is the same thing we
+ 
+
+ align:start position:0%
+now generate is the same thing we
+started with but except we have a
+
+ align:start position:0%
+started with but except we have a
+ 
+
+ align:start position:0%
+started with but except we have a
+product but we have five prime
+
+ align:start position:0%
+product but we have five prime
+ 
+
+ align:start position:0%
+product but we have five prime
+deoxyadenosine cobalt do here we have
+
+ align:start position:0%
+deoxyadenosine cobalt do here we have
+ 
+
+ align:start position:0%
+deoxyadenosine cobalt do here we have
+five prime deoxyadenosine radical cobalt
+
+ align:start position:0%
+five prime deoxyadenosine radical cobalt
+ 
+
+ align:start position:0%
+five prime deoxyadenosine radical cobalt
+two and what you do is you reform the
+
+ align:start position:0%
+two and what you do is you reform the
+ 
+
+ align:start position:0%
+two and what you do is you reform the
+carbon cobalt bond at the end of every
+
+ align:start position:0%
+carbon cobalt bond at the end of every
+ 
+
+ align:start position:0%
+carbon cobalt bond at the end of every
+turnover and now you're ready to start
+
+ align:start position:0%
+turnover and now you're ready to start
+ 
+
+ align:start position:0%
+turnover and now you're ready to start
+all over again
+
+ align:start position:0%
+all over again
+ 
+
+ align:start position:0%
+all over again
+so that's the reaction this five prime
+
+ align:start position:0%
+so that's the reaction this five prime
+ 
+
+ align:start position:0%
+so that's the reaction this five prime
+deoxyadenosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alig in this axial ligand sitting over
+
+ align:start position:0%
+alig in this axial ligand sitting over
+ 
+
+ align:start position:0%
+alig in this axial ligand sitting over
+here acts as a hydrogen atom
+
+ align:start position:0%
+here acts as a hydrogen atom
+ 
+
+ align:start position:0%
+here acts as a hydrogen atom
+transferring agent to remove a hydrogen
+
+ align:start position:0%
+transferring agent to remove a hydrogen
+ 
+
+ align:start position:0%
+transferring agent to remove a hydrogen
+from the substrate and to transfer it
+
+ align:start position:0%
+from the substrate and to transfer it
+ 
+
+ align:start position:0%
+from the substrate and to transfer it
+back to the product okay I'm going to
+
+ align:start position:0%
+back to the product okay I'm going to
+ 
+
+ align:start position:0%
+back to the product okay I'm going to
+show you how this works now in the case
+
+ align:start position:0%
+show you how this works now in the case
+ 
+
+ align:start position:0%
+show you how this works now in the case
+of methyl Melanie Alcoa mutase so here's
+
+ align:start position:0%
+of methyl Melanie Alcoa mutase so here's
+ 
+
+ align:start position:0%
+of methyl Melanie Alcoa mutase so here's
+our methyl Melanie Ocoee and we're going
+
+ align:start position:0%
+our methyl Melanie Ocoee and we're going
+ 
+
+ align:start position:0%
+our methyl Melanie Ocoee and we're going
+to be converted into succinate Ocoee so
+
+ align:start position:0%
+to be converted into succinate Ocoee so
+ 
+
+ align:start position:0%
+to be converted into succinate Ocoee so
+this again is migrating and this guy is
+
+ align:start position:0%
+this again is migrating and this guy is
+ 
+
+ align:start position:0%
+this again is migrating and this guy is
+migrating there that's the goal and so
+
+ align:start position:0%
+migrating there that's the goal and so
+ 
+
+ align:start position:0%
+migrating there that's the goal and so
+what happens here is you cleave the
+
+ align:start position:0%
+what happens here is you cleave the
+ 
+
+ align:start position:0%
+what happens here is you cleave the
+carbon cobalt bond to form cobalt 2 & 5
+
+ align:start position:0%
+carbon cobalt bond to form cobalt 2 & 5
+ 
+
+ align:start position:0%
+carbon cobalt bond to form cobalt 2 & 5
+Prime deoxy adenosyl radical and now
+
+ align:start position:0%
+Prime deoxy adenosyl radical and now
+ 
+
+ align:start position:0%
+Prime deoxy adenosyl radical and now
+this five prime deoxyadenosine
+
+ align:start position:0%
+this five prime deoxyadenosine
+ 
+
+ align:start position:0%
+this five prime deoxyadenosine
+can remove a hydrogen atom from the
+
+ align:start position:0%
+can remove a hydrogen atom from the
+ 
+
+ align:start position:0%
+can remove a hydrogen atom from the
+substrate so it leaves you with another
+
+ align:start position:0%
+substrate so it leaves you with another
+ 
+
+ align:start position:0%
+substrate so it leaves you with another
+radical this radical goes away you
+
+ align:start position:0%
+radical this radical goes away you
+ 
+
+ align:start position:0%
+radical this radical goes away you
+generate another radical and now this
+
+ align:start position:0%
+generate another radical and now this
+ 
+
+ align:start position:0%
+generate another radical and now this
+hydrogen from the substrate is
+
+ align:start position:0%
+hydrogen from the substrate is
+ 
+
+ align:start position:0%
+hydrogen from the substrate is
+transferred to our cofactor so it's the
+
+ align:start position:0%
+transferred to our cofactor so it's the
+ 
+
+ align:start position:0%
+transferred to our cofactor so it's the
+hydrogen transferring agent so now the
+
+ align:start position:0%
+hydrogen transferring agent so now the
+ 
+
+ align:start position:0%
+hydrogen transferring agent so now the
+question is how does this weird
+
+ align:start position:0%
+question is how does this weird
+ 
+
+ align:start position:0%
+question is how does this weird
+rearrangement reaction it how does this
+
+ align:start position:0%
+rearrangement reaction it how does this
+ 
+
+ align:start position:0%
+rearrangement reaction it how does this
+co a migrate from one place to another
+
+ align:start position:0%
+co a migrate from one place to another
+ 
+
+ align:start position:0%
+co a migrate from one place to another
+again there was no chemical precedent
+
+ align:start position:0%
+again there was no chemical precedent
+ 
+
+ align:start position:0%
+again there was no chemical precedent
+and a literature for this and when the
+
+ align:start position:0%
+and a literature for this and when the
+ 
+
+ align:start position:0%
+and a literature for this and when the
+answer is we still don't know the answer
+
+ align:start position:0%
+answer is we still don't know the answer
+ 
+
+ align:start position:0%
+answer is we still don't know the answer
+so there are two mechanistic
+
+ align:start position:0%
+so there are two mechanistic
+ 
+
+ align:start position:0%
+so there are two mechanistic
+possibilities one is that you go through
+
+ align:start position:0%
+possibilities one is that you go through
+ 
+
+ align:start position:0%
+possibilities one is that you go through
+a three membered ring cyclopropane ring
+
+ align:start position:0%
+a three membered ring cyclopropane ring
+ 
+
+ align:start position:0%
+a three membered ring cyclopropane ring
+intermediate so what you can picture
+
+ align:start position:0%
+intermediate so what you can picture
+ 
+
+ align:start position:0%
+intermediate so what you can picture
+happening is that one of the electrons
+
+ align:start position:0%
+happening is that one of the electrons
+ 
+
+ align:start position:0%
+happening is that one of the electrons
+from the carbonyl forms a bond with the
+
+ align:start position:0%
+from the carbonyl forms a bond with the
+ 
+
+ align:start position:0%
+from the carbonyl forms a bond with the
+unpaired electron on this carbon and you
+
+ align:start position:0%
+unpaired electron on this carbon and you
+ 
+
+ align:start position:0%
+unpaired electron on this carbon and you
+generate this cyclopropane intermediate
+
+ align:start position:0%
+generate this cyclopropane intermediate
+ 
+
+ align:start position:0%
+generate this cyclopropane intermediate
+so you've gone from this radical to
+
+ align:start position:0%
+so you've gone from this radical to
+ 
+
+ align:start position:0%
+so you've gone from this radical to
+another radical we haven't lost any
+
+ align:start position:0%
+another radical we haven't lost any
+ 
+
+ align:start position:0%
+another radical we haven't lost any
+radicals but now what we want to do is
+
+ align:start position:0%
+radicals but now what we want to do is
+ 
+
+ align:start position:0%
+radicals but now what we want to do is
+we want this group to migrate so now
+
+ align:start position:0%
+we want this group to migrate so now
+ 
+
+ align:start position:0%
+we want this group to migrate so now
+what happens this intermediate can
+
+ align:start position:0%
+what happens this intermediate can
+ 
+
+ align:start position:0%
+what happens this intermediate can
+collapse it can collapse back to form
+
+ align:start position:0%
+collapse it can collapse back to form
+ 
+
+ align:start position:0%
+collapse it can collapse back to form
+starting material and the 5-prime
+
+ align:start position:0%
+starting material and the 5-prime
+ 
+
+ align:start position:0%
+starting material and the 5-prime
+deoxyadenosine radical or you can break
+
+ align:start position:0%
+deoxyadenosine radical or you can break
+ 
+
+ align:start position:0%
+deoxyadenosine radical or you can break
+this bond in which case you collapse to
+
+ align:start position:0%
+this bond in which case you collapse to
+ 
+
+ align:start position:0%
+this bond in which case you collapse to
+form the direct precursor to the product
+
+ align:start position:0%
+form the direct precursor to the product
+ 
+
+ align:start position:0%
+form the direct precursor to the product
+so it can break down in either direction
+
+ align:start position:0%
+so it can break down in either direction
+ 
+
+ align:start position:0%
+so it can break down in either direction
+and the reaction is reversible and if it
+
+ align:start position:0%
+and the reaction is reversible and if it
+ 
+
+ align:start position:0%
+and the reaction is reversible and if it
+breaks down in this direction you form a
+
+ align:start position:0%
+breaks down in this direction you form a
+ 
+
+ align:start position:0%
+breaks down in this direction you form a
+new router
+
+ align:start position:0%
+new router
+ 
+
+ align:start position:0%
+new router
+this radical is distinct from this
+
+ align:start position:0%
+this radical is distinct from this
+ 
+
+ align:start position:0%
+this radical is distinct from this
+radical and now what happens is that the
+
+ align:start position:0%
+radical and now what happens is that the
+ 
+
+ align:start position:0%
+radical and now what happens is that the
+hydrogen that you removed from your
+
+ align:start position:0%
+hydrogen that you removed from your
+ 
+
+ align:start position:0%
+hydrogen that you removed from your
+starting material can be returned back
+
+ align:start position:0%
+starting material can be returned back
+ 
+
+ align:start position:0%
+starting material can be returned back
+to the product and what you generate
+
+ align:start position:0%
+to the product and what you generate
+ 
+
+ align:start position:0%
+to the product and what you generate
+then is five prime deoxyadenosine
+
+ align:start position:0%
+then is five prime deoxyadenosine
+ 
+
+ align:start position:0%
+then is five prime deoxyadenosine
+radical and cobalt two and now you've
+
+ align:start position:0%
+radical and cobalt two and now you've
+ 
+
+ align:start position:0%
+radical and cobalt two and now you've
+when you transfer the hydrogen back you
+
+ align:start position:0%
+when you transfer the hydrogen back you
+ 
+
+ align:start position:0%
+when you transfer the hydrogen back you
+form your product like I showed you in
+
+ align:start position:0%
+form your product like I showed you in
+ 
+
+ align:start position:0%
+form your product like I showed you in
+the previous slide and now you reform
+
+ align:start position:0%
+the previous slide and now you reform
+ 
+
+ align:start position:0%
+the previous slide and now you reform
+the carbon cobalt bond to form reform
+
+ align:start position:0%
+the carbon cobalt bond to form reform
+ 
+
+ align:start position:0%
+the carbon cobalt bond to form reform
+that active form of the cofactor so
+
+ align:start position:0%
+that active form of the cofactor so
+ 
+
+ align:start position:0%
+that active form of the cofactor so
+alternatively you can make this
+
+ align:start position:0%
+alternatively you can make this
+ 
+
+ align:start position:0%
+alternatively you can make this
+rearrangement happen by another
+
+ align:start position:0%
+rearrangement happen by another
+ 
+
+ align:start position:0%
+rearrangement happen by another
+mechanism which is called a
+
+ align:start position:0%
+mechanism which is called a
+ 
+
+ align:start position:0%
+mechanism which is called a
+fragmentation mechanism and I won't go
+
+ align:start position:0%
+fragmentation mechanism and I won't go
+ 
+
+ align:start position:0%
+fragmentation mechanism and I won't go
+through the details in this but you can
+
+ align:start position:0%
+through the details in this but you can
+ 
+
+ align:start position:0%
+through the details in this but you can
+sit and look at this for those of you
+
+ align:start position:0%
+sit and look at this for those of you
+ 
+
+ align:start position:0%
+sit and look at this for those of you
+are really interested in sophisticated
+
+ align:start position:0%
+are really interested in sophisticated
+ 
+
+ align:start position:0%
+are really interested in sophisticated
+proposals for the chemical mechanisms of
+
+ align:start position:0%
+proposals for the chemical mechanisms of
+ 
+
+ align:start position:0%
+proposals for the chemical mechanisms of
+the rearrangement so adenosylcobalamin
+
+ align:start position:0%
+the rearrangement so adenosylcobalamin
+ 
+
+ align:start position:0%
+the rearrangement so adenosylcobalamin
+chemistry is unprecedented every step in
+
+ align:start position:0%
+chemistry is unprecedented every step in
+ 
+
+ align:start position:0%
+chemistry is unprecedented every step in
+the way every step along the way and
+
+ align:start position:0%
+the way every step along the way and
+ 
+
+ align:start position:0%
+the way every step along the way and
+it's now known to be widely used but not
+
+ align:start position:0%
+it's now known to be widely used but not
+ 
+
+ align:start position:0%
+it's now known to be widely used but not
+so much so in humans but you know really
+
+ align:start position:0%
+so much so in humans but you know really
+ 
+
+ align:start position:0%
+so much so in humans but you know really
+humans are only a small part of the
+
+ align:start position:0%
+humans are only a small part of the
+ 
+
+ align:start position:0%
+humans are only a small part of the
+world we have many many more bacteria in
+
+ align:start position:0%
+world we have many many more bacteria in
+ 
+
+ align:start position:0%
+world we have many many more bacteria in
+our ki then we have humans so this is a
+
+ align:start position:0%
+our ki then we have humans so this is a
+ 
+
+ align:start position:0%
+our ki then we have humans so this is a
+pretty important transformation so
+
+ align:start position:0%
+pretty important transformation so
+ 
+
+ align:start position:0%
+pretty important transformation so
+hopefully now when you see this again it
+
+ align:start position:0%
+hopefully now when you see this again it
+ 
+
+ align:start position:0%
+hopefully now when you see this again it
+won't be completely magic but this is a
+
+ align:start position:0%
+won't be completely magic but this is a
+ 
+
+ align:start position:0%
+won't be completely magic but this is a
+challenging reaction that most of you
+
+ align:start position:0%
+challenging reaction that most of you
+ 
+
+ align:start position:0%
+challenging reaction that most of you
+haven't been exposed to before but
+
+ align:start position:0%
+haven't been exposed to before but
+ 
+
+ align:start position:0%
+haven't been exposed to before but
+hopefully some of you get excited about
+
+ align:start position:0%
+hopefully some of you get excited about
+ 
+
+ align:start position:0%
+hopefully some of you get excited about
+radical mediated transformations I just
+
+ align:start position:0%
+radical mediated transformations I just
+ 
+
+ align:start position:0%
+radical mediated transformations I just
+let me close by saying from
+
+ align:start position:0%
+let me close by saying from
+ 
+
+ align:start position:0%
+let me close by saying from
+bioinformatics studies in the last five
+
+ align:start position:0%
+bioinformatics studies in the last five
+ 
+
+ align:start position:0%
+bioinformatics studies in the last five
+years or so we now know there are over
+
+ align:start position:0%
+years or so we now know there are over
+ 
+
+ align:start position:0%
+years or so we now know there are over
+50,000 reactions that use free radical
+
+ align:start position:0%
+50,000 reactions that use free radical
+ 
+
+ align:start position:0%
+50,000 reactions that use free radical
+chemistry yet we don't talk about
+
+ align:start position:0%
+chemistry yet we don't talk about
+ 
+
+ align:start position:0%
+chemistry yet we don't talk about
+radical chemistry in 507 so hopefully
+
+ align:start position:0%
+radical chemistry in 507 so hopefully
+ 
+
+ align:start position:0%
+radical chemistry in 507 so hopefully
+some of you will get interested enough
+
+ align:start position:0%
+some of you will get interested enough
+ 
+
+ align:start position:0%
+some of you will get interested enough
+in biochemistry to come in and start
+
+ align:start position:0%
+in biochemistry to come in and start
+ 
+
+ align:start position:0%
+in biochemistry to come in and start
+figuring out how all these radical
+
+ align:start position:0%
+figuring out how all these radical
+ 
+
+ align:start position:0%
+figuring out how all these radical
+dependent reactions occur not in primary
+
+ align:start position:0%
+dependent reactions occur not in primary
+ 
+
+ align:start position:0%
+dependent reactions occur not in primary
+metabolism but in many secondary
+
+ align:start position:0%
+metabolism but in many secondary
+ 
+
+ align:start position:0%
+metabolism but in many secondary
+metabolic pathways okay thank you
\ No newline at end of file
diff --git a/6xaaeop7gJ8.txt b/6xaaeop7gJ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..316f6ab0d6fe9232df9919db06c9bb99403963f0
--- /dev/null
+++ b/6xaaeop7gJ8.txt
@@ -0,0 +1,1794 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: In the last lecture,
+I introduced and
+
+illustrated the kinds of signals
+and systems that we'll
+
+be dealing with throughout
+this course.
+
+In today's lecture I'd like to
+be a little more specific, and
+
+in particular, talk about some
+of the basic signals, both
+
+continuous-time and
+discrete-time that will form
+
+important building blocks as
+the course progresses.
+
+Let's begin with one signal, the
+continuous-time sinusoidal
+
+signal, which perhaps
+you're already
+
+somewhat familiar with.
+
+Mathematically, the
+continuous-time sinusoidal
+
+signal is expressed as
+I've indicated here.
+
+There are three parameters,
+A, omega_0 and phi.
+
+The parameter A is referred
+to as the amplitude, the
+
+parameter omega 0 as the
+frequency, and the parameter
+
+phi as the phase.
+
+And graphically, the
+continuous-time sinusoidal
+
+signal has the form
+shown here.
+
+Now, the sinusoidal signal
+has a number of important
+
+properties that we'll find it
+convenient to exploit as the
+
+course goes along, one of which
+is the fact that the
+
+sinusoidal signal is what is
+referred to as periodic.
+
+What I mean by periodic is that
+under an appropriate time
+
+shift, which I indicate here as
+T_0, the signal replicates
+
+or repeats itself.
+
+Or said another way, if we shift
+the time origin by an
+
+appropriate amount T_0, the
+smallest value T_0 being
+
+referred to as the period,
+then x(t) is
+
+equal to itself, shifted.
+
+And we can demonstrate it
+mathematically by simply
+
+substituting into the
+mathematical expression for
+
+the sinusoidal signal t
++ T_0, in place of t.
+
+When we carry out the expansion
+we then have, for
+
+the argument of the sinusoid,
+omega_0 t + omega_0 T_0 + phi.
+
+Now, one of the things that
+we know about sinusoidal
+
+functions is that if you change
+the argument by any
+
+integer multiple of 2 pi,
+then the function
+
+has the same value.
+
+And so we can exploit that
+here, in particular with
+
+omega_0 T_0 and integer
+multiple of 2 pi.
+
+Then the right-hand side of this
+equation is equal to the
+
+left-hand side of
+the equation.
+
+So with omega_0 T_0 equal to 2
+pi times an integer, or T_0
+
+equal to 2 pi times an
+integer divided by
+
+omega_0, the signal repeats.
+
+The period is defined as the
+smallest value of T_0.
+
+And so the period is 2 pi
+divided by omega_0.
+
+And going back to
+our sinusoidal
+
+signal, we can see that--
+
+and I've indicated here, then,
+the period as 2 pi / omega_0.
+
+And that's the value under
+which the signal repeats.
+
+Now in addition, a useful
+property of the sinusoidal
+
+signal is the fact that a time
+shift of a sinusoid is
+
+equivalent to a phase change.
+
+And we can demonstrate that
+again mathematically, in
+
+particular if we put the
+sinusoidal signal
+
+under a time shift--
+
+I've indicated the time
+shift that I'm
+
+talking about by t_0--
+
+and expand this out, then we see
+that that is equivalent to
+
+a change in phase.
+
+And an important thing to
+recognize about this statement
+
+is that not only is a time
+shift generating a phase
+
+change, but, in fact, if we
+inserted a phase change, there
+
+is always a value of t_0 which
+would correspond to an
+
+equivalent time shift.
+
+Said another way, if we take
+omega_0 t_0 and think of that
+
+as our change in phase, for any
+change in phase, we can
+
+solve this equation for a time
+shift, or conversely for any
+
+value of time shift,
+that represents
+
+an appropriate phase.
+
+So a time shift corresponds to
+a phase change, and a phase
+
+change, likewise, corresponds
+to time shift.
+
+And so for example, if we look
+at the general sinusoidal
+
+signal that we saw previously,
+in effect, changing the phase
+
+corresponds to moving
+this signal in time
+
+one way or the other.
+
+For example, if we look at the
+sinusoidal signal with a phase
+
+equal to 0 that corresponds
+to locating the time
+
+origin at this peak.
+
+And I've indicated that on
+the following graph.
+
+So here we have illustrated a
+sinusoid with 0 phase, or a
+
+cosine with 0 phase,
+corresponding to taking our
+
+general picture and
+shifting it.
+
+Shifting it appropriately
+as I've indicated here.
+
+This, of course, still has the
+property that it's a periodic
+
+function, since we simply
+displaced it in time.
+
+And by looking at the graph,
+what we see is that it has
+
+another very important property,
+a property referred
+
+to as even.
+
+And that's a property that we'll
+find useful, in general,
+
+to refer to in relation
+to signals.
+
+A signal is said to be even if,
+when we reflect it about
+
+the origin, it looks
+exactly the same.
+
+So it's symmetric about
+the origin.
+
+And looking at this
+sinusoid, that, in
+
+fact, has that property.
+
+And mathematically, the
+statement that it's even is
+
+equivalent to the statement that
+if we replace the time
+
+argument by its negative,
+the function
+
+itself doesn't change.
+
+Now this corresponded to a
+phase shift of 0 in our
+
+original cosine expression.
+
+If instead, we had chosen a
+phase shift of, let's say,
+
+-pi/2, then instead of a
+cosinusoidal signal, what we
+
+would regenerate is a sinusoid
+with the appropriate phase.
+
+Or, said another way, if we take
+our original cosine and
+
+substitute in for the phase
+-pi/2, then of course we have
+
+this mathematical expression.
+
+Using just straightforward
+trigonometric identities, we
+
+can express that alternately
+as sin(omega_0*t).
+
+The frequency and amplitude,
+of course, haven't changed.
+
+And that, you can convince
+yourself, also is equivalent
+
+to shifting the cosine by an
+amount in time that I've
+
+indicated here, namely a
+quarter of a period.
+
+So illustrated below is the
+graph now, when we have a
+
+phase of -pi/2 in our cosine,
+which is a sinusoidal signal.
+
+Of course, it's still
+periodic.
+
+It's periodic with a period of
+2 pi / omega_0 again, because
+
+all that we've done by
+introducing a phase change is
+
+introduced the time shift.
+
+Now, when we look at the
+sinusoid in comparison with
+
+the cosine, namely with this
+particular choice of phase,
+
+this has a different symmetry,
+and that symmetry
+
+is referred to odd.
+
+What odd symmetry means,
+graphically, is that when we
+
+flip the signal about the time
+origin, we also multiply it by
+
+a minus sign.
+
+So that's, in effect,
+anti-symmetric.
+
+It's not the mirror image,
+but it's the mirror
+
+image flipped over.
+
+And we'll find many occasions,
+not only to refer to signals
+
+more general than sinusoidal
+signals, as even in some cases
+
+and odd in other cases.
+
+And in general, mathematically,
+an odd signal
+
+is one which satisfies the
+algebraic expression, x(t).
+
+When you replace t by its
+negative, is equal to -x(-t).
+
+So replacing the argument by its
+negative corresponds to an
+
+algebraic sign reversal.
+
+OK.
+
+So this is the class of
+continuous-time sinusoids.
+
+We'll have a little more
+to say about it later.
+
+But I'd now like to turn to
+discrete-time sinusoids.
+
+What we'll see is that
+discrete-time sinusoids are
+
+very much like continuous-time
+ones, but also with some very
+
+important differences.
+
+And we want to focus, not only
+on the similarities, but also
+
+on the differences.
+
+Well, let's begin with the
+mathematical expression.
+
+A discrete-time sinusoidal
+signal, mathematically, is as
+
+I've indicated here, A
+cos(omega_0 n + phi).
+
+And just as in the
+continuous-time case, the
+
+parameter A is what we'll refer
+to as the amplitude,
+
+omega_0 as the frequency,
+and phi as the phase.
+
+And I've illustrated here
+several discrete-time
+
+sinusoidal signals.
+
+And they kind of look similar.
+
+In fact, if you track what
+you might think of as the
+
+envelope, it looks very much
+like what a continuous-time
+
+sinusoid might look like.
+
+But keep in mind that the
+independent variable, in this
+
+case, is an integer variable.
+
+And so the sequence only takes
+on values at integer values of
+
+the argument.
+
+And we'll see that has a very
+important implication, and
+
+we'll see that shortly.
+
+Now, one of the issues that
+we addressed in the
+
+continuous-time case
+was periodicity.
+
+And I want to return to that
+shortly, because that is one
+
+of the areas where there is
+an important distinction.
+
+Let's first, though, examine the
+statement similar to the
+
+one that we examined for
+continuous time, namely the
+
+relationship between a time
+shift and a phase change.
+
+Now, in continuous time, of
+course, we saw that a time
+
+shift corresponds to a phase
+change, and vice versa.
+
+Let's first look at the
+relationship between shifting
+
+time and generating
+a change in phase.
+
+In particular for discrete time,
+if I implement a time
+
+shift that generates
+a phase change--
+
+and we can see that easily
+by simply inserting a
+
+time shift, n + n_0.
+
+And if we expand out this
+argument, we have omega_0 n +
+
+omega_0 n_0.
+
+And so I've done that on the
+right-hand side of the
+
+equation here.
+
+And the omega_0 n_0, then,
+simply corresponds
+
+to a change in phase.
+
+So clearly, a shift in time
+generates a change in phase.
+
+And for example, if we take a
+particular sinusoidal signal,
+
+let's say we take the cosine
+signal at a particular
+
+frequency, and with a phase
+equal to 0, a sequence that we
+
+might generate is one that
+I've illustrated here.
+
+So what I'm illustrating
+here is the cosine
+
+signal with 0 phase.
+
+And it has a particular behavior
+to it, which will
+
+depend somewhat on
+the frequency.
+
+If I now take this same sequence
+and shift it so that
+
+the time origin is shifted a
+quarter of a period away, then
+
+you can convince yourself--
+
+and it's straightforward to
+work out-- that that time
+
+shift corresponds to a
+phase shift of pi/2.
+
+So in that case, with the cosine
+with a phase of -pi/2,
+
+that will correspond to the
+expression that I have here.
+
+We could alternately write
+that, using again a
+
+trigonometric identity,
+as a sine function.
+
+And that, I've stated, is
+equivalent to a time shift.
+
+Namely, this shift of pi/2 is
+equal to a certain time shift,
+
+and the time shift for this
+particular example is a
+
+quarter of a period.
+
+So here, we have the sinusoid.
+
+Previously we had the cosine.
+
+The cosine was exactly the same
+sequence, but with the
+
+origin located here.
+
+And in fact, that's exactly the
+way we drew this graph.
+
+Namely, we just simply took the
+same values and changed
+
+the time origin.
+
+Now, looking at this sequence,
+which is the sinusoidal
+
+sequence, the phase of -pi/2,
+that has a certain symmetry.
+
+And in fact, what we see is that
+it has an odd symmetry,
+
+just as in the continuous-time
+case.
+
+Namely, if we take that
+sequence, flip it about the
+
+axis, and flip it over in sign,
+that we get the same
+
+sequence back again.
+
+Whereas with 0 phase
+corresponding to the cosine
+
+that I showed previously, that
+has an even symmetry.
+
+Namely, if I flip it about the
+time origin and don't do a
+
+sign reversal, then the sequence
+is maintained.
+
+So here, we have an odd
+symmetry, expressed
+
+mathematically as
+I've indicated.
+
+Namely, replacing the
+independent variable by its
+
+negative attaches a negative
+sign to the whole sequence.
+
+Whereas in the previous case,
+what we have is 0 phase and an
+
+even symmetry.
+
+And that's expressed
+mathematically as x[n]
+
+= x[-n].
+
+Now, one of the things I've
+said so far about
+
+discrete-time sinusoids is that
+a time shift corresponds
+
+to a phase change.
+
+And we can then ask whether the
+reverse statement is also
+
+true, and we knew that the
+reverse statement was true in
+
+continuous time.
+
+Specifically, is it true that
+a phase change always
+
+corresponds to a time shift?
+
+Now, we know that that is
+true, namely, that this
+
+statement works both ways
+in continuous time.
+
+Does it in discrete time?
+
+Well, the answer, somewhat
+interestingly or surprisingly
+
+until you sit down and think
+about it, is no.
+
+It is not necessarily true in
+discrete time that any phase
+
+change can be interpreted
+as a simple time
+
+shift of the sequence.
+
+And let me just indicate
+what the problem is.
+
+If we look at the relationship
+between the left side and the
+
+right side of this equation,
+expanding this out as we did
+
+previously, we have that omega_0
+n + omega_0 n_0 must
+
+correspond to omega_0 n + phi.
+
+And so omega_0 n_0
+must correspond
+
+to the phase change.
+
+Now, what you can see pretty
+clearly is that depending on
+
+the relationship between phi
+and omega_0, n_0 may or may
+
+not come out to be an integer.
+
+Now, in continuous time, the
+amount of time shift did not
+
+have to be an integer amount.
+
+In discrete time, when we talk
+about a time shift, the amount
+
+of time shift-- obviously,
+because of the nature of
+
+discrete time signals--
+
+must be an integer.
+
+So the phase changes related
+to time shifts must satisfy
+
+this particular relationship.
+
+Namely, that omega_0 n_0, where
+n_0 is an integer, is
+
+equal to the change in phase.
+
+OK.
+
+Now, that's one distinction
+between continuous time and
+
+discrete time.
+
+Let's now focus on another
+one, namely the issue of
+
+periodicity.
+
+And what we'll see is that
+again, whereas in continuous
+
+time, all continuous-time
+sinusoids are periodic, in the
+
+discrete-time case that is
+not necessarily true.
+
+To explore that a little more
+carefully, let's look at the
+
+expression, again, for a general
+sinusoidal signal with
+
+an arbitrary amplitude,
+frequency, and phase.
+
+And for this to be periodic,
+what we require is that there
+
+be some value, N, under which,
+when we shift the sequence by
+
+that amount, we get the same
+sequence back again.
+
+And the smallest-value
+N is what we've
+
+defined as the period.
+
+Now, when we try that on a
+sinusoid, we of course
+
+substitute in for n, n + N.
+And when we expand out the
+
+argument here, we'll get the
+argument that I have on the
+
+right-hand side.
+
+And in order for this to repeat,
+in other words, in
+
+order for us to discard this
+term, omega_0 N, where N is
+
+the period, must be an integer
+multiple of 2 pi.
+
+And in that case, it's periodic
+as long as omega_0 N,
+
+N being the period, is 2
+pi times an integer.
+
+Just simply dividing this out,
+we have N, the period, is 2 pi
+
+m / omega_0.
+
+Well, you could say, OK
+what's the big deal?
+
+Whatever N happens to come out
+to be when we do that little
+
+bit of algebra, that's
+the period.
+
+But in fact, N, or 2 pi m /
+omega_0, may not ever come out
+
+to be an integer.
+
+Or it may not come out
+to be the one that
+
+you thought it might.
+
+For example, let's look at some
+
+particular sinusoidal signals.
+
+Let's see.
+
+We have the first one
+here, which is a
+
+sinusoid, as I've shown.
+
+And it has a frequency, what
+I've referred to as the
+
+frequency, omega_0
+= 2 pi / 12.
+
+And what we'd like to look at
+is 2 pi / omega_0, then find
+
+an integer to multiply
+that by in order
+
+to get another integer.
+
+Let's just try that here.
+
+If we look at 2 pi / omega_0, 2
+pi / omega_0, for this case,
+
+is equal to 12.
+
+Well, that's fine.
+
+12 is an integer.
+
+So what that says is that this
+sinusoidal signal is periodic.
+
+And in fact, it's periodic
+with a period of 12.
+
+Let's look at the next one.
+
+The next one, we would have
+2 pi / omega_0 again.
+
+And that's equal to 31/4.
+
+So what that says is that
+the period is 31/4.
+
+But wait a minute.
+
+31/4 isn't an integer.
+
+We have to multiply
+that by an integer
+
+to get another integer.
+
+Well, we'd multiply that by 4,
+so (2 pi / omega_0) times 4 is
+
+31, 31 is an integer.
+
+And so what that says is this is
+periodic, not with a period
+
+of 2 pi / omega_0, but with a
+period of (2 pi / omega_0)
+
+times 4, namely with
+a period of 31.
+
+Finally, let's take the example
+where omega_0 is equal
+
+to 1/6, as I've shown here.
+
+That actually looks, if you
+track it with your eye, like
+
+it's periodic.
+
+2 pi / omega_0, in that case,
+is equal to 12 pi.
+
+Well, what integer can I
+multiply 12 pi by and get
+
+another integer?
+
+The answer is none, because pi
+is an irrational number.
+
+So in fact, what that says is
+that if you look at this
+
+sinusoidal signal, it's not
+periodic at all, even though
+
+you might fool yourself into
+thinking it is simply because
+
+the envelope looks periodic.
+
+Namely, the continuous-time
+equivalent of this is
+
+periodic, the discrete-time
+sequence is not.
+
+OK.
+
+Well, we've seen, then, some
+important distinctions between
+
+continuous-time sinusoidal
+signals and discrete-time
+
+sinusoidal signals.
+
+The first one is the fact that
+in the continuous-time case, a
+
+time shift and phase change
+are always equivalent.
+
+Whereas in the discrete-time
+case, in effect, it works one
+
+way but not the other way.
+
+We've also seen that for a
+continuous-time signal, the
+
+continuous-time signal is always
+periodic, whereas the
+
+discrete-time signal
+is not necessarily.
+
+In particular, for the
+continuous-time case, if we
+
+have a general expression for
+the sinusoidal signal that
+
+I've indicated here,
+that's periodic for
+
+any choice of omega_0.
+
+Whereas in the discrete-time
+case, it's periodic only if 2
+
+pi / omega_0 can be multiplied
+by an integer
+
+to get another integer.
+
+Now, another important and,
+as it turns out, useful
+
+distinction between the
+continuous-time and
+
+discrete-time case is the fact
+that in the discrete-time
+
+case, as we vary what I've
+called the frequency omega_0,
+
+we only see distinct
+signals as omega_0
+
+varies over a 2 pi interval.
+
+And if we let omega_0 vary
+outside the range of, let's
+
+say, -pi to pi, or 0 to 2 pi,
+we'll see the same sequences
+
+all over again, even though at
+first glance, the mathematical
+
+expression might
+look different.
+
+So in the discrete-time case,
+this class of signals is
+
+identical for values of omega_0
+separated by 2 pi,
+
+whereas in the continuous-time
+case, that is not true.
+
+In particular, if I consider
+these sinusoidal
+
+continuous-time signals, as I
+vary omega_0, what will happen
+
+is that I will always see
+different sinusoidal signals.
+
+Namely, these won't be equal.
+
+And in effect, we can justify
+that statement algebraically.
+
+And I won't take the time
+to do it carefully.
+
+But let's look, first of all,
+at the discrete-time case.
+
+And the statement that I'm
+making is that if I have two
+
+discrete-time sinusoidal signals
+at two different
+
+frequencies, and if these
+frequencies are separated by
+
+an integer multiple of 2 pi--
+namely if omega_2 is equal to
+
+omega_1 + 2 pi times
+an integer m--
+
+when I substitute this into this
+expression, because of
+
+the fact that n is also an
+integer, I'll have m * n as an
+
+integer multiple of 2 pi.
+
+And that term, of course, will
+disappear because of the
+
+periodicity of the sinusoid,
+and these two
+
+sequences will be equal.
+
+On the other hand in the
+continuous-time case, since t
+
+is not restricted to be an
+integer variable, for
+
+different values of omega_1 and
+omega_2, these sinusoidal
+
+signals will always
+be different.
+
+OK.
+
+Now, many of the issues that
+I've raised so far, in
+
+relation to sinusoidal signals,
+are elaborated on in
+
+more detail in the text.
+
+And of course, you'll have an
+opportunity to exercise some
+
+of this as you work through
+the video course manual.
+
+Let me stress that sinusoidal
+signals will play an extremely
+
+important role for us as
+building blocks for general
+
+signals and descriptions of
+systems, and leads to the
+
+whole concept Fourier analysis,
+which is very
+
+heavily exploited throughout
+the course.
+
+What I'd now like to turn to is
+another class of important
+
+building blocks.
+
+And in fact, we'll see that
+under certain conditions,
+
+these relate strongly to
+sinusoidal signals, namely the
+
+class of real and complex
+exponentials.
+
+Let me begin, first of all, with
+the real exponential, and
+
+in particular, in the
+continuous-time case.
+
+A real continuous-time
+exponential is mathematically
+
+expressed, as I indicate here,
+x(t) = C e ^ (a t), where for
+
+the real exponential, C and
+a are real numbers.
+
+And that's what we mean by
+the real exponential.
+
+Shortly, we'll also consider
+complex exponentials, where
+
+these numbers can then
+become complex.
+
+So this is an exponential
+function.
+
+And for example, if the
+parameter a is positive, that
+
+means that we have a growing
+exponential function.
+
+If the parameter a is negative,
+then that means that
+
+we have a decaying exponential
+function.
+
+Now, somewhat as an aside, it's
+kind of interesting to
+
+note that for exponentials, a
+time shift corresponds to a
+
+scale change, which is somewhat
+different than what
+
+happens with sinusoids.
+
+In the sinusoidal case, we saw
+that a time shift corresponded
+
+to a phase change.
+
+With the real exponential, a
+time shift, as it turns out,
+
+corresponds to simply
+changing the scale.
+
+There's nothing particularly
+crucial or
+
+exciting about that.
+
+And in fact, perhaps stressing
+it is a little misleading.
+
+For general functions, of
+course, about all that you can
+
+say about what happens when you
+implement a time shift is
+
+that it implements
+a time shift.
+
+OK.
+
+So here's the real
+exponential.
+
+Just C e ^ (a t).
+
+Let's look at the real
+exponential, now, in the
+
+discrete-time case.
+
+And in the discrete-time case,
+we have several alternate ways
+
+of expressing it.
+
+We can express the real
+exponential in the form C e ^
+
+(beta n), or as we'll find more
+convenient, in part for a
+
+reason at I'll indicate shortly,
+we can rewrite this
+
+as C alpha ^ n, where of course,
+alpha = e ^ beta.
+
+More typically in the
+discrete-time case, we'll
+
+express the exponential
+as C alpha ^ n.
+
+So for example, this becomes,
+essentially, a geometric
+
+series or progression
+as n continues for
+
+certain values of alpha.
+
+Here for example, we have for
+alpha greater than 0, first of
+
+all on the top, the case where
+the magnitude of alpha is
+
+greater than 1, so that the
+sequence is exponentially or
+
+geometrically growing.
+
+On the bottom, again with alpha
+positive, but now with
+
+its magnitude less than 1, we
+have a geometric progression
+
+that is exponentially or
+geometrically decaying.
+
+OK.
+
+So this, in both of these
+cases, is with alpha
+
+greater than 0.
+
+Now the function that we're
+talking about is alpha ^ n.
+
+And of course, what you can
+see is that if alpha is
+
+negative instead of positive,
+then when n is even, that
+
+minus sign is going
+to disappear.
+
+When n is odd, there will
+be a minus sign.
+
+And so for alpha negative, the
+sequence is going to alternate
+
+positive and negative values.
+
+So for example, here we have
+alpha negative, with its
+
+magnitude less than 1.
+
+And you can see that, again,
+its envelope decays
+
+geometrically, and the values
+alternate in sign.
+
+And here we have the magnitude
+of alpha greater than 1, with
+
+alpha negative.
+
+Again, they alternate in sign,
+and of course it's growing
+
+geometrically.
+
+Now, if you think about alpha
+positive and go back to the
+
+expression that I have at the
+top, namely C alpha ^ n.
+
+With alpha positive, you can
+see a straightforward
+
+relationship between
+alpha and beta.
+
+Namely, beta is the natural
+logarithm of alpha.
+
+Something to think
+about is what
+
+happens if alpha is negative?
+
+Which is, of course, a very
+important and useful class of
+
+real discrete-time exponentials
+also.
+
+Well, it turns out that with
+alpha negative, if you try to
+
+express it as C e ^ (beta n),
+then beta comes out to be an
+
+imaginary number.
+
+And that is one, but not the
+only reason why, in the
+
+discrete-time case, it's often
+most convenient to phrase real
+
+exponentials in the form alpha ^
+n, rather than e ^ (beta n).
+
+In other words, to express them
+in this form rather than
+
+in this form.
+
+Those are real exponentials,
+continuous-time and
+
+discrete-time.
+
+Now let's look at the
+continuous-time complex
+
+exponential.
+
+And what I mean by a complex
+exponential, again, is an
+
+exponential of the
+form C e ^ (a t).
+
+But in this case, we allow the
+parameters C and a to be
+
+complex numbers.
+
+And let's just track this
+through algebraically.
+
+If C and a are complex numbers,
+let's write C in
+
+polar form, so it has a
+magnitude and an angle.
+
+Let's write a in rectangular
+form, so it has a real part
+
+and an imaginary part.
+
+And when we substitute these
+two in here, combine some
+
+things together--
+
+well actually, I haven't
+combined yet.
+
+I have this for the amplitude
+factor, and this for the
+
+exponential factor.
+
+I can now pull out of this the
+term corresponding to e ^ (r
+
+t), and combine the imaginary
+parts together.
+
+And I come down to the
+expression that I have here.
+
+So following this further, an
+exponential of this form, e ^
+
+(j omega) or e ^ (j phi), using
+Euler's relation, can be
+
+expressed as the sum of a cosine
+plus j times a sine.
+
+And so that corresponds
+to this factor.
+
+And then there is this
+time-varying amplitude factor
+
+on top of it.
+
+Finally putting those together,
+we end up with the
+
+expression that I show
+on the bottom.
+
+And what this corresponds to are
+two sinusoidal signals, 90
+
+degrees out of phase, as
+indicated by the fact that
+
+there's a cosine and a sine.
+
+So there's a real part and
+an imaginary part, with
+
+sinusoidal components 90 degrees
+out of phase, and a
+
+time-varying amplitude factor,
+which is a real exponential.
+
+So it's a sinusoid multiplied by
+a real exponential in both
+
+the real part and the
+imaginary part.
+
+And let's just see what one of
+those terms might look like.
+
+What I've indicated at the top
+is a sinusoidal signal with a
+
+time-varying exponential
+envelope, or an envelope which
+
+is a real exponential, and in
+particular which is growing,
+
+namely with r greater than 0.
+
+And on the bottom, I've
+indicated the same thing with
+
+r less than 0.
+
+And this kind of sinusoidal
+signal, by the way, is
+
+typically referred to as
+a damped sinusoid.
+
+So with r negative, what we have
+in the real and imaginary
+
+parts are damped sinusoids.
+
+And the sinusoidal components of
+that are 90 degrees out of
+
+phase, in the real part and
+in the imaginary part.
+
+OK.
+
+Now, in the discrete-time case,
+we have more or less the
+
+same kind of outcome.
+
+In particular we'll make
+reference to our complex
+
+exponentials in the
+discrete-time case.
+
+The expression for the complex
+exponential looks very much
+
+like the expression for the real
+exponential, except that
+
+now we have complex factors.
+
+So C and alpha are
+complex numbers.
+
+And again, if we track through
+the algebra, and get to a
+
+point where we have a real
+exponential multiplied by a
+
+factor which is a purely
+imaginary exponential, apply
+
+Euler's relationship to this, we
+then finally come down to a
+
+sequence, which has a real
+exponential amplitude
+
+multiplying one sinusoid
+in the real part.
+
+And in the imaginary part,
+exactly the same kind of
+
+exponential multiplying a
+sinusoid that's 90 degrees out
+
+of phase from that.
+
+And so if we look at what one
+of these factors might look
+
+like, it's what we would expect
+given the analogy with
+
+the continuous-time case.
+
+Namely, it's a sinusoidal
+sequence with a real
+
+exponential envelope.
+
+In the case where alpha
+is positive, then
+
+it's a growing envelope.
+
+In the case where alpha
+is negative--
+
+I'm sorry--
+
+where the magnitude of alpha
+is greater than 1, it's a
+
+growing exponential envelope.
+
+Where the magnitude of alpha
+is less than 1, it's a
+
+decaying exponential envelope.
+
+And so I've illustrated
+that here.
+
+Here we have the magnitude
+of alpha greater than 1.
+
+And here we have the magnitude
+of alpha less than 1.
+
+In both cases, sinusoidal
+sequences underneath the
+
+envelope, and then an envelope
+that is dictated by what the
+
+magnitude of alpha is.
+
+OK.
+
+Now, in the discrete-time case,
+then, we have results
+
+similar to the continuous-time
+case.
+
+Namely, components in a real and
+imaginary part that have a
+
+real exponential factor
+times a sinusoid.
+
+Of course, if the magnitude of
+alpha is equal to 1, then this
+
+factor disappears,
+or is equal to 1.
+
+And this factor is equal to 1.
+
+And so we have sinusoids
+in both the real
+
+and imaginary parts.
+
+Now, one can ask whether,
+in general, the complex
+
+exponential with the magnitude
+of alpha equal to 1 is
+
+periodic or not periodic.
+
+And the clue to that can be
+inferred by examining this
+
+expression.
+
+In particular, in the
+discrete-time case with the
+
+magnitude of alpha equal to 1,
+we have pure sinusoids in the
+
+real part and the
+imaginary part.
+
+And in fact, in a
+continuous-time case with r
+
+equal to 0, we have sinusoids
+in the real part and the
+
+imaginary part.
+
+In a continuous-time case when
+we have a pure complex
+
+exponential, so that the terms
+aren't exponentially growing
+
+or decaying, those
+
+exponentials are always periodic.
+
+Because, of course, the real
+and imaginary sinusoidal
+
+components are periodic.
+
+In the discrete-time case, we
+know that the sinusoids may or
+
+may not be periodic, depending
+on the value of omega_0.
+
+And so in fact, in the
+discrete-time case, the
+
+exponential e ^ (j omega_0 n),
+that I've indicated here, may
+
+or may not be periodic depending
+on what the value of
+
+omega_0 is.
+
+OK.
+
+Now, to summarize, in this
+lecture I've introduced and
+
+discussed a number of important
+basic signals.
+
+In particular, sinusoids and
+real and complex exponentials.
+
+One of the important outcomes of
+the discussion, emphasized
+
+further in the text, is that
+there are some very important
+
+similarities between them.
+
+But there are also some very
+important differences.
+
+And these differences will
+surface when we exploit
+
+sinusoids and complex
+exponentials as basic building
+
+blocks for more general
+continuous-time and
+
+discrete-time signals.
+
+In the next lecture, what I'll
+discuss are some other very
+
+important building blocks,
+namely, what are referred to
+
+as step signals and
+impulse signals.
+
+And those, together with the
+sinusoidal signals and
+
+exponentials as we've talked
+about today, will really form
+
+the cornerstone for,
+essentially, all of the signal
+
+and system analysis that we'll
+be dealing with for the
+
+remainder of course.
+
+Thank you.
\ No newline at end of file
diff --git a/7_hOHxaaxGE.txt b/7_hOHxaaxGE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b66d976c5eb1fdb4da9e72f7ce4873b40c74bcee
--- /dev/null
+++ b/7_hOHxaaxGE.txt
@@ -0,0 +1,507 @@
+align:start position:0%
+ 
+and finally to end this piece of the
+
+ align:start position:0%
+and finally to end this piece of the
+ 
+
+ align:start position:0%
+and finally to end this piece of the
+tutorial I'd like to encourage you to
+
+ align:start position:0%
+tutorial I'd like to encourage you to
+ 
+
+ align:start position:0%
+tutorial I'd like to encourage you to
+use your imagination think of lighting
+
+ align:start position:0%
+use your imagination think of lighting
+ 
+
+ align:start position:0%
+use your imagination think of lighting
+that's not necessarily in the textbooks
+
+ align:start position:0%
+that's not necessarily in the textbooks
+ 
+
+ align:start position:0%
+that's not necessarily in the textbooks
+look at this for example it's a device
+
+ align:start position:0%
+look at this for example it's a device
+ 
+
+ align:start position:0%
+look at this for example it's a device
+that you'll be seeing a great deal of in
+
+ align:start position:0%
+that you'll be seeing a great deal of in
+ 
+
+ align:start position:0%
+that you'll be seeing a great deal of in
+our virtual tool of lighting which
+
+ align:start position:0%
+our virtual tool of lighting which
+ 
+
+ align:start position:0%
+our virtual tool of lighting which
+you'll get to later I do not place it on
+
+ align:start position:0%
+you'll get to later I do not place it on
+ 
+
+ align:start position:0%
+you'll get to later I do not place it on
+the light box I use the light box as a
+
+ align:start position:0%
+the light box I use the light box as a
+ 
+
+ align:start position:0%
+the light box I use the light box as a
+light source as you see in this image
+
+ align:start position:0%
+light source as you see in this image
+ 
+
+ align:start position:0%
+light source as you see in this image
+because of its transparency and it's
+
+ align:start position:0%
+because of its transparency and it's
+ 
+
+ align:start position:0%
+because of its transparency and it's
+actually quite beautiful just as
+
+ align:start position:0%
+actually quite beautiful just as
+ 
+
+ align:start position:0%
+actually quite beautiful just as
+something itself I put it on my flatbed
+
+ align:start position:0%
+something itself I put it on my flatbed
+ 
+
+ align:start position:0%
+something itself I put it on my flatbed
+scanner but this is not a scanned image
+
+ align:start position:0%
+scanner but this is not a scanned image
+ 
+
+ align:start position:0%
+scanner but this is not a scanned image
+I'm actually using the light from the
+
+ align:start position:0%
+I'm actually using the light from the
+ 
+
+ align:start position:0%
+I'm actually using the light from the
+flatbed scanner as you can see in this
+
+ align:start position:0%
+flatbed scanner as you can see in this
+ 
+
+ align:start position:0%
+flatbed scanner as you can see in this
+image sometimes it could work when you
+
+ align:start position:0%
+image sometimes it could work when you
+ 
+
+ align:start position:0%
+image sometimes it could work when you
+get light from the side as it is in this
+
+ align:start position:0%
+get light from the side as it is in this
+ 
+
+ align:start position:0%
+get light from the side as it is in this
+case and another idea that perhaps you
+
+ align:start position:0%
+case and another idea that perhaps you
+ 
+
+ align:start position:0%
+case and another idea that perhaps you
+haven't thought about is to use a small
+
+ align:start position:0%
+haven't thought about is to use a small
+ 
+
+ align:start position:0%
+haven't thought about is to use a small
+LED flashlight if you want to image a
+
+ align:start position:0%
+LED flashlight if you want to image a
+ 
+
+ align:start position:0%
+LED flashlight if you want to image a
+very small area of your device here
+
+ align:start position:0%
+very small area of your device here
+ 
+
+ align:start position:0%
+very small area of your device here
+we're just photographing the spiral
+
+ align:start position:0%
+we're just photographing the spiral
+ 
+
+ align:start position:0%
+we're just photographing the spiral
+which measures about two and a half
+
+ align:start position:0%
+which measures about two and a half
+ 
+
+ align:start position:0%
+which measures about two and a half
+centimeters across all I did was shined
+
+ align:start position:0%
+centimeters across all I did was shined
+ 
+
+ align:start position:0%
+centimeters across all I did was shined
+an LED flashlight on to that area around
+
+ align:start position:0%
+an LED flashlight on to that area around
+ 
+
+ align:start position:0%
+an LED flashlight on to that area around
+the area it we get lighting fall off so
+
+ align:start position:0%
+the area it we get lighting fall off so
+ 
+
+ align:start position:0%
+the area it we get lighting fall off so
+we decided only to image this particular
+
+ align:start position:0%
+we decided only to image this particular
+ 
+
+ align:start position:0%
+we decided only to image this particular
+piece in the device this is a image i
+
+ align:start position:0%
+piece in the device this is a image i
+ 
+
+ align:start position:0%
+piece in the device this is a image i
+started making a material called
+
+ align:start position:0%
+started making a material called
+ 
+
+ align:start position:0%
+started making a material called
+ferrofluid and just seeing actually is a
+
+ align:start position:0%
+ferrofluid and just seeing actually is a
+ 
+
+ align:start position:0%
+ferrofluid and just seeing actually is a
+close shot of this material it is oil
+
+ align:start position:0%
+close shot of this material it is oil
+ 
+
+ align:start position:0%
+close shot of this material it is oil
+that has suspended iron filings I put it
+
+ align:start position:0%
+that has suspended iron filings I put it
+ 
+
+ align:start position:0%
+that has suspended iron filings I put it
+on a glass slide under the glass slide
+
+ align:start position:0%
+on a glass slide under the glass slide
+ 
+
+ align:start position:0%
+on a glass slide under the glass slide
+is a yellow post-it and under the yellow
+
+ align:start position:0%
+is a yellow post-it and under the yellow
+ 
+
+ align:start position:0%
+is a yellow post-it and under the yellow
+posted are seven circular magnets and
+
+ align:start position:0%
+posted are seven circular magnets and
+ 
+
+ align:start position:0%
+posted are seven circular magnets and
+you're seeing the small iron particles
+
+ align:start position:0%
+you're seeing the small iron particles
+ 
+
+ align:start position:0%
+you're seeing the small iron particles
+respond to the magnets it's basically
+
+ align:start position:0%
+respond to the magnets it's basically
+ 
+
+ align:start position:0%
+respond to the magnets it's basically
+too tight a shot to see anything of
+
+ align:start position:0%
+too tight a shot to see anything of
+ 
+
+ align:start position:0%
+too tight a shot to see anything of
+value in this image I pulled away a bit
+
+ align:start position:0%
+value in this image I pulled away a bit
+ 
+
+ align:start position:0%
+value in this image I pulled away a bit
+and I see a little more of what's going
+
+ align:start position:0%
+and I see a little more of what's going
+ 
+
+ align:start position:0%
+and I see a little more of what's going
+on but basically the window panes become
+
+ align:start position:0%
+on but basically the window panes become
+ 
+
+ align:start position:0%
+on but basically the window panes become
+may
+
+ align:start position:0%
+may
+ 
+
+ align:start position:0%
+may
+too much of a distraction and it's not
+
+ align:start position:0%
+too much of a distraction and it's not
+ 
+
+ align:start position:0%
+too much of a distraction and it's not
+quite right and so I decided seeing how
+
+ align:start position:0%
+quite right and so I decided seeing how
+ 
+
+ align:start position:0%
+quite right and so I decided seeing how
+reflective the whole image could be to
+
+ align:start position:0%
+reflective the whole image could be to
+ 
+
+ align:start position:0%
+reflective the whole image could be to
+put a green card above it so now we're
+
+ align:start position:0%
+put a green card above it so now we're
+ 
+
+ align:start position:0%
+put a green card above it so now we're
+seeing a little bit of green reflecting
+
+ align:start position:0%
+seeing a little bit of green reflecting
+ 
+
+ align:start position:0%
+seeing a little bit of green reflecting
+off of the material it's just purely an
+
+ align:start position:0%
+off of the material it's just purely an
+ 
+
+ align:start position:0%
+off of the material it's just purely an
+aesthetic decision it's not clarifying
+
+ align:start position:0%
+aesthetic decision it's not clarifying
+ 
+
+ align:start position:0%
+aesthetic decision it's not clarifying
+anything but I'm starting to think that
+
+ align:start position:0%
+anything but I'm starting to think that
+ 
+
+ align:start position:0%
+anything but I'm starting to think that
+I might have an interesting image here
+
+ align:start position:0%
+I might have an interesting image here
+ 
+
+ align:start position:0%
+I might have an interesting image here
+and eventually I did wind up with this
+
+ align:start position:0%
+and eventually I did wind up with this
+ 
+
+ align:start position:0%
+and eventually I did wind up with this
+final image with the windowpane with the
+
+ align:start position:0%
+final image with the windowpane with the
+ 
+
+ align:start position:0%
+final image with the windowpane with the
+green card reflecting and if you really
+
+ align:start position:0%
+green card reflecting and if you really
+ 
+
+ align:start position:0%
+green card reflecting and if you really
+look carefully you see the mistake of a
+
+ align:start position:0%
+look carefully you see the mistake of a
+ 
+
+ align:start position:0%
+look carefully you see the mistake of a
+bad photographer because you see me
+
+ align:start position:0%
+bad photographer because you see me
+ 
+
+ align:start position:0%
+bad photographer because you see me
+although it's fun to play around with
+
+ align:start position:0%
+although it's fun to play around with
+ 
+
+ align:start position:0%
+although it's fun to play around with
+the children and asking them to find
+
+ align:start position:0%
+the children and asking them to find
+ 
+
+ align:start position:0%
+the children and asking them to find
+Feliz but this is an image that got a
+
+ align:start position:0%
+Feliz but this is an image that got a
+ 
+
+ align:start position:0%
+Feliz but this is an image that got a
+lot of notice when I made it a while ago
+
+ align:start position:0%
+lot of notice when I made it a while ago
+ 
+
+ align:start position:0%
+lot of notice when I made it a while ago
+and I was using my imagination in terms
+
+ align:start position:0%
+and I was using my imagination in terms
+ 
+
+ align:start position:0%
+and I was using my imagination in terms
+of trying to find a way of using light
+
+ align:start position:0%
+of trying to find a way of using light
+ 
+
+ align:start position:0%
+of trying to find a way of using light
+in perhaps a different way
\ No newline at end of file
diff --git a/7afYLl70cO0.txt b/7afYLl70cO0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91e25965a5c81a3eb8aaa4d5f75ef7a8474bc7a1
--- /dev/null
+++ b/7afYLl70cO0.txt
@@ -0,0 +1,7579 @@
+align:start position:0%
+ 
+alright let's get started so I'm
+
+ align:start position:0%
+alright let's get started so I'm
+ 
+
+ align:start position:0%
+alright let's get started so I'm
+starting with this video here what's
+
+ align:start position:0%
+starting with this video here what's
+ 
+
+ align:start position:0%
+starting with this video here what's
+happening here is there's this mouse and
+
+ align:start position:0%
+happening here is there's this mouse and
+ 
+
+ align:start position:0%
+happening here is there's this mouse and
+you see there's like this fiber-optic
+
+ align:start position:0%
+you see there's like this fiber-optic
+ 
+
+ align:start position:0%
+you see there's like this fiber-optic
+cable going into its brain and the mouse
+
+ align:start position:0%
+cable going into its brain and the mouse
+ 
+
+ align:start position:0%
+cable going into its brain and the mouse
+is asleep right now
+
+ align:start position:0%
+is asleep right now
+ 
+
+ align:start position:0%
+is asleep right now
+and now the researchers are shining
+
+ align:start position:0%
+and now the researchers are shining
+ 
+
+ align:start position:0%
+and now the researchers are shining
+light into its brain a specific region
+
+ align:start position:0%
+light into its brain a specific region
+ 
+
+ align:start position:0%
+light into its brain a specific region
+of the brain to activate specific
+
+ align:start position:0%
+of the brain to activate specific
+ 
+
+ align:start position:0%
+of the brain to activate specific
+neurons in order to test whether they
+
+ align:start position:0%
+neurons in order to test whether they
+ 
+
+ align:start position:0%
+neurons in order to test whether they
+function and arousal and here you see
+
+ align:start position:0%
+function and arousal and here you see
+ 
+
+ align:start position:0%
+function and arousal and here you see
+the mouse is going to wake up there it
+
+ align:start position:0%
+the mouse is going to wake up there it
+ 
+
+ align:start position:0%
+the mouse is going to wake up there it
+goes it's awake now okay so for today's
+
+ align:start position:0%
+goes it's awake now okay so for today's
+ 
+
+ align:start position:0%
+goes it's awake now okay so for today's
+lecture we're gonna sort work towards
+
+ align:start position:0%
+lecture we're gonna sort work towards
+ 
+
+ align:start position:0%
+lecture we're gonna sort work towards
+understanding how this experiment works
+
+ align:start position:0%
+understanding how this experiment works
+ 
+
+ align:start position:0%
+understanding how this experiment works
+and we're gonna talk about how neurons
+
+ align:start position:0%
+and we're gonna talk about how neurons
+ 
+
+ align:start position:0%
+and we're gonna talk about how neurons
+function and how researchers are able to
+
+ align:start position:0%
+function and how researchers are able to
+ 
+
+ align:start position:0%
+function and how researchers are able to
+control that function in order to modify
+
+ align:start position:0%
+control that function in order to modify
+ 
+
+ align:start position:0%
+control that function in order to modify
+behavior in this case the arousal of
+
+ align:start position:0%
+behavior in this case the arousal of
+ 
+
+ align:start position:0%
+behavior in this case the arousal of
+this mouse okay so this is going to
+
+ align:start position:0%
+this mouse okay so this is going to
+ 
+
+ align:start position:0%
+this mouse okay so this is going to
+involved a particular type of cell in
+
+ align:start position:0%
+involved a particular type of cell in
+ 
+
+ align:start position:0%
+involved a particular type of cell in
+our body which is the neuron and neurons
+
+ align:start position:0%
+our body which is the neuron and neurons
+ 
+
+ align:start position:0%
+our body which is the neuron and neurons
+are highly specialized cells that have a
+
+ align:start position:0%
+are highly specialized cells that have a
+ 
+
+ align:start position:0%
+are highly specialized cells that have a
+function to transmit information from
+
+ align:start position:0%
+function to transmit information from
+ 
+
+ align:start position:0%
+function to transmit information from
+one part of the body to another okay and
+
+ align:start position:0%
+one part of the body to another okay and
+ 
+
+ align:start position:0%
+one part of the body to another okay and
+so neurons are highly polarized cells
+
+ align:start position:0%
+so neurons are highly polarized cells
+ 
+
+ align:start position:0%
+so neurons are highly polarized cells
+which you can see here on the left of
+
+ align:start position:0%
+which you can see here on the left of
+ 
+
+ align:start position:0%
+which you can see here on the left of
+this neuron you see this Arbor of
+
+ align:start position:0%
+this neuron you see this Arbor of
+ 
+
+ align:start position:0%
+this neuron you see this Arbor of
+protrusions which are called dendrites
+
+ align:start position:0%
+protrusions which are called dendrites
+ 
+
+ align:start position:0%
+protrusions which are called dendrites
+and then on this side of the cell body
+
+ align:start position:0%
+and then on this side of the cell body
+ 
+
+ align:start position:0%
+and then on this side of the cell body
+you see a single extension which is an
+
+ align:start position:0%
+you see a single extension which is an
+ 
+
+ align:start position:0%
+you see a single extension which is an
+axon and then the terminus of the axon
+
+ align:start position:0%
+axon and then the terminus of the axon
+ 
+
+ align:start position:0%
+axon and then the terminus of the axon
+over here and this nerve cell transmits
+
+ align:start position:0%
+over here and this nerve cell transmits
+ 
+
+ align:start position:0%
+over here and this nerve cell transmits
+information in a single direction it'll
+
+ align:start position:0%
+information in a single direction it'll
+ 
+
+ align:start position:0%
+information in a single direction it'll
+transmit information from this side to
+
+ align:start position:0%
+transmit information from this side to
+ 
+
+ align:start position:0%
+transmit information from this side to
+this side okay and these neurons are
+
+ align:start position:0%
+this side okay and these neurons are
+ 
+
+ align:start position:0%
+this side okay and these neurons are
+able to communicate with the each other
+
+ align:start position:0%
+able to communicate with the each other
+ 
+
+ align:start position:0%
+able to communicate with the each other
+and they communicate at the ends of the
+
+ align:start position:0%
+and they communicate at the ends of the
+ 
+
+ align:start position:0%
+and they communicate at the ends of the
+neuron which are known as synapses which
+
+ align:start position:0%
+neuron which are known as synapses which
+ 
+
+ align:start position:0%
+neuron which are known as synapses which
+I'll come back to and talk about later
+
+ align:start position:0%
+I'll come back to and talk about later
+ 
+
+ align:start position:0%
+I'll come back to and talk about later
+on in the lecture ok so neurons could be
+
+ align:start position:0%
+on in the lecture ok so neurons could be
+ 
+
+ align:start position:0%
+on in the lecture ok so neurons could be
+making synapses on this side and also
+
+ align:start position:0%
+making synapses on this side and also
+ 
+
+ align:start position:0%
+making synapses on this side and also
+making synapses on this side with other
+
+ align:start position:0%
+making synapses on this side with other
+ 
+
+ align:start position:0%
+making synapses on this side with other
+neurons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so to start to unpack the function
+
+ align:start position:0%
+okay so to start to unpack the function
+ 
+
+ align:start position:0%
+okay so to start to unpack the function
+of this neuron and I should highlight
+
+ align:start position:0%
+of this neuron and I should highlight
+ 
+
+ align:start position:0%
+of this neuron and I should highlight
+that this this flow of information can
+
+ align:start position:0%
+that this this flow of information can
+ 
+
+ align:start position:0%
+that this this flow of information can
+occur over very long distances right
+
+ align:start position:0%
+occur over very long distances right
+ 
+
+ align:start position:0%
+occur over very long distances right
+your sciatic nerve extends from the base
+
+ align:start position:0%
+your sciatic nerve extends from the base
+ 
+
+ align:start position:0%
+your sciatic nerve extends from the base
+of your spine all the way down into your
+
+ align:start position:0%
+of your spine all the way down into your
+ 
+
+ align:start position:0%
+of your spine all the way down into your
+foot okay so that axon is a 1 meter in
+
+ align:start position:0%
+foot okay so that axon is a 1 meter in
+ 
+
+ align:start position:0%
+foot okay so that axon is a 1 meter in
+length so that's an extremely long
+
+ align:start position:0%
+length so that's an extremely long
+ 
+
+ align:start position:0%
+length so that's an extremely long
+distance to transmit information along a
+
+ align:start position:0%
+distance to transmit information along a
+ 
+
+ align:start position:0%
+distance to transmit information along a
+single cell and so we're gonna go from
+
+ align:start position:0%
+single cell and so we're gonna go from
+ 
+
+ align:start position:0%
+single cell and so we're gonna go from
+thinking about how signals are
+
+ align:start position:0%
+thinking about how signals are
+ 
+
+ align:start position:0%
+thinking about how signals are
+transmitted in single cells and this
+
+ align:start position:0%
+transmitted in single cells and this
+ 
+
+ align:start position:0%
+transmitted in single cells and this
+will evolve electrical sing signaling
+
+ align:start position:0%
+will evolve electrical sing signaling
+ 
+
+ align:start position:0%
+will evolve electrical sing signaling
+then we'll talk about synapses and how
+
+ align:start position:0%
+then we'll talk about synapses and how
+ 
+
+ align:start position:0%
+then we'll talk about synapses and how
+synapses function to communicate between
+
+ align:start position:0%
+synapses function to communicate between
+ 
+
+ align:start position:0%
+synapses function to communicate between
+neurons and this is going to involve
+
+ align:start position:0%
+neurons and this is going to involve
+ 
+
+ align:start position:0%
+neurons and this is going to involve
+also sort of understanding how certain
+
+ align:start position:0%
+also sort of understanding how certain
+ 
+
+ align:start position:0%
+also sort of understanding how certain
+antidepressants like prozac work and
+
+ align:start position:0%
+antidepressants like prozac work and
+ 
+
+ align:start position:0%
+antidepressants like prozac work and
+then we'll end by talking about how
+
+ align:start position:0%
+then we'll end by talking about how
+ 
+
+ align:start position:0%
+then we'll end by talking about how
+researchers did this experiment to wake
+
+ align:start position:0%
+researchers did this experiment to wake
+ 
+
+ align:start position:0%
+researchers did this experiment to wake
+up the mouse and it all starts with
+
+ align:start position:0%
+up the mouse and it all starts with
+ 
+
+ align:start position:0%
+up the mouse and it all starts with
+something that I told you about at the
+
+ align:start position:0%
+something that I told you about at the
+ 
+
+ align:start position:0%
+something that I told you about at the
+beginning of the semester which is that
+
+ align:start position:0%
+beginning of the semester which is that
+ 
+
+ align:start position:0%
+beginning of the semester which is that
+there the plasma membrane separates
+
+ align:start position:0%
+there the plasma membrane separates
+ 
+
+ align:start position:0%
+there the plasma membrane separates
+distinct compartments the outside of the
+
+ align:start position:0%
+distinct compartments the outside of the
+ 
+
+ align:start position:0%
+distinct compartments the outside of the
+cell from the cytoplasm and there are
+
+ align:start position:0%
+cell from the cytoplasm and there are
+ 
+
+ align:start position:0%
+cell from the cytoplasm and there are
+distinct ion concentrations on either
+
+ align:start position:0%
+distinct ion concentrations on either
+ 
+
+ align:start position:0%
+distinct ion concentrations on either
+side of this boundary okay so we're
+
+ align:start position:0%
+side of this boundary okay so we're
+ 
+
+ align:start position:0%
+side of this boundary okay so we're
+starting now talking about a single
+
+ align:start position:0%
+starting now talking about a single
+ 
+
+ align:start position:0%
+starting now talking about a single
+neuron cell and we're going to talk
+
+ align:start position:0%
+neuron cell and we're going to talk
+ 
+
+ align:start position:0%
+neuron cell and we're going to talk
+about a type of signal known as an
+
+ align:start position:0%
+about a type of signal known as an
+ 
+
+ align:start position:0%
+about a type of signal known as an
+electrical passion potential so we're
+
+ align:start position:0%
+electrical passion potential so we're
+ 
+
+ align:start position:0%
+electrical passion potential so we're
+going to talk about an action potential
+
+ align:start position:0%
+going to talk about an action potential
+ 
+
+ align:start position:0%
+going to talk about an action potential
+and what an action potential is is this
+
+ align:start position:0%
+and what an action potential is is this
+ 
+
+ align:start position:0%
+and what an action potential is is this
+an electrical signal that travels the
+
+ align:start position:0%
+an electrical signal that travels the
+ 
+
+ align:start position:0%
+an electrical signal that travels the
+length of the neuron okay so this action
+
+ align:start position:0%
+length of the neuron okay so this action
+ 
+
+ align:start position:0%
+length of the neuron okay so this action
+potential I'll abbreviate this ap so
+
+ align:start position:0%
+potential I'll abbreviate this ap so
+ 
+
+ align:start position:0%
+potential I'll abbreviate this ap so
+when I refer to AP I'm not referring to
+
+ align:start position:0%
+when I refer to AP I'm not referring to
+ 
+
+ align:start position:0%
+when I refer to AP I'm not referring to
+Advanced Placement but action potential
+
+ align:start position:0%
+Advanced Placement but action potential
+ 
+
+ align:start position:0%
+Advanced Placement but action potential
+okay so this is an electrical signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that travels the length of the axon in
+
+ align:start position:0%
+that travels the length of the axon in
+ 
+
+ align:start position:0%
+that travels the length of the axon in
+the neuron and so in order to have an
+
+ align:start position:0%
+the neuron and so in order to have an
+ 
+
+ align:start position:0%
+the neuron and so in order to have an
+electrical signal propagate we need some
+
+ align:start position:0%
+electrical signal propagate we need some
+ 
+
+ align:start position:0%
+electrical signal propagate we need some
+sort of electrical property that the
+
+ align:start position:0%
+sort of electrical property that the
+ 
+
+ align:start position:0%
+sort of electrical property that the
+cell has that enables this and so I
+
+ align:start position:0%
+cell has that enables this and so I
+ 
+
+ align:start position:0%
+cell has that enables this and so I
+showed you or I told you earlier in this
+
+ align:start position:0%
+showed you or I told you earlier in this
+ 
+
+ align:start position:0%
+showed you or I told you earlier in this
+aster how sodium ions are concentrated
+
+ align:start position:0%
+aster how sodium ions are concentrated
+ 
+
+ align:start position:0%
+aster how sodium ions are concentrated
+on the outside of the cell and potassium
+
+ align:start position:0%
+on the outside of the cell and potassium
+ 
+
+ align:start position:0%
+on the outside of the cell and potassium
+ions are concentrated on the inside you
+
+ align:start position:0%
+ions are concentrated on the inside you
+ 
+
+ align:start position:0%
+ions are concentrated on the inside you
+see here's the sodium gradient here
+
+ align:start position:0%
+see here's the sodium gradient here
+ 
+
+ align:start position:0%
+see here's the sodium gradient here
+potassium gradient here and now I'm
+
+ align:start position:0%
+potassium gradient here and now I'm
+ 
+
+ align:start position:0%
+potassium gradient here and now I'm
+gonna tell you how it is that this
+
+ align:start position:0%
+gonna tell you how it is that this
+ 
+
+ align:start position:0%
+gonna tell you how it is that this
+happens because this is
+
+ align:start position:0%
+happens because this is
+ 
+
+ align:start position:0%
+happens because this is
+thermodynamically not favored right
+
+ align:start position:0%
+thermodynamically not favored right
+ 
+
+ align:start position:0%
+thermodynamically not favored right
+these these ions would prefer by
+
+ align:start position:0%
+these these ions would prefer by
+ 
+
+ align:start position:0%
+these these ions would prefer by
+diffusion to be equal concentrations on
+
+ align:start position:0%
+diffusion to be equal concentrations on
+ 
+
+ align:start position:0%
+diffusion to be equal concentrations on
+both sides of this plasma membrane which
+
+ align:start position:0%
+both sides of this plasma membrane which
+ 
+
+ align:start position:0%
+both sides of this plasma membrane which
+means that the cell to shift this from
+
+ align:start position:0%
+means that the cell to shift this from
+ 
+
+ align:start position:0%
+means that the cell to shift this from
+equilibrium has to expend energy to set
+
+ align:start position:0%
+equilibrium has to expend energy to set
+ 
+
+ align:start position:0%
+equilibrium has to expend energy to set
+up this situation and so in the plasma
+
+ align:start position:0%
+up this situation and so in the plasma
+ 
+
+ align:start position:0%
+up this situation and so in the plasma
+membrane of the cell there is a protein
+
+ align:start position:0%
+membrane of the cell there is a protein
+ 
+
+ align:start position:0%
+membrane of the cell there is a protein
+it's an integral membrane protein and
+
+ align:start position:0%
+it's an integral membrane protein and
+ 
+
+ align:start position:0%
+it's an integral membrane protein and
+sits inside the plasma membrane so this
+
+ align:start position:0%
+sits inside the plasma membrane so this
+ 
+
+ align:start position:0%
+sits inside the plasma membrane so this
+here is the plasma membrane and this
+
+ align:start position:0%
+here is the plasma membrane and this
+ 
+
+ align:start position:0%
+here is the plasma membrane and this
+integral membrane protein is called a
+
+ align:start position:0%
+integral membrane protein is called a
+ 
+
+ align:start position:0%
+integral membrane protein is called a
+sodium potassium ATPase so it's going to
+
+ align:start position:0%
+sodium potassium ATPase so it's going to
+ 
+
+ align:start position:0%
+sodium potassium ATPase so it's going to
+have a subunit that hydrolyzes ATP to
+
+ align:start position:0%
+have a subunit that hydrolyzes ATP to
+ 
+
+ align:start position:0%
+have a subunit that hydrolyzes ATP to
+adp and the protein uses the energy of
+
+ align:start position:0%
+adp and the protein uses the energy of
+ 
+
+ align:start position:0%
+adp and the protein uses the energy of
+ATP hydrolysis to pump sodium ions up
+
+ align:start position:0%
+ATP hydrolysis to pump sodium ions up
+ 
+
+ align:start position:0%
+ATP hydrolysis to pump sodium ions up
+their concentration gradient so the
+
+ align:start position:0%
+their concentration gradient so the
+ 
+
+ align:start position:0%
+their concentration gradient so the
+sodium ions are going out of the cell
+
+ align:start position:0%
+sodium ions are going out of the cell
+ 
+
+ align:start position:0%
+sodium ions are going out of the cell
+and this is going against the flow that
+
+ align:start position:0%
+and this is going against the flow that
+ 
+
+ align:start position:0%
+and this is going against the flow that
+sodium would normally like to take which
+
+ align:start position:0%
+sodium would normally like to take which
+ 
+
+ align:start position:0%
+sodium would normally like to take which
+would be going downstream and it pumps
+
+ align:start position:0%
+would be going downstream and it pumps
+ 
+
+ align:start position:0%
+would be going downstream and it pumps
+potassium ions into the cytoplasm such
+
+ align:start position:0%
+potassium ions into the cytoplasm such
+ 
+
+ align:start position:0%
+potassium ions into the cytoplasm such
+that there's a higher concentration of
+
+ align:start position:0%
+that there's a higher concentration of
+ 
+
+ align:start position:0%
+that there's a higher concentration of
+potassium ions in the cytoplasm okay so
+
+ align:start position:0%
+potassium ions in the cytoplasm okay so
+ 
+
+ align:start position:0%
+potassium ions in the cytoplasm okay so
+these neurons expend a huge about a
+
+ align:start position:0%
+these neurons expend a huge about a
+ 
+
+ align:start position:0%
+these neurons expend a huge about a
+quarter amount a quarter of their ATP is
+
+ align:start position:0%
+quarter amount a quarter of their ATP is
+ 
+
+ align:start position:0%
+quarter amount a quarter of their ATP is
+used by pumping ions like this such that
+
+ align:start position:0%
+used by pumping ions like this such that
+ 
+
+ align:start position:0%
+used by pumping ions like this such that
+there is gradients of ions across the
+
+ align:start position:0%
+there is gradients of ions across the
+ 
+
+ align:start position:0%
+there is gradients of ions across the
+plasma membrane okay
+
+ align:start position:0%
+plasma membrane okay
+ 
+
+ align:start position:0%
+plasma membrane okay
+now if if one sodium ion was pumped out
+
+ align:start position:0%
+now if if one sodium ion was pumped out
+ 
+
+ align:start position:0%
+now if if one sodium ion was pumped out
+for every potassium ion pumped in
+
+ align:start position:0%
+for every potassium ion pumped in
+ 
+
+ align:start position:0%
+for every potassium ion pumped in
+there'd be no charge difference between
+
+ align:start position:0%
+there'd be no charge difference between
+ 
+
+ align:start position:0%
+there'd be no charge difference between
+the exterior and the cytoplasm but what
+
+ align:start position:0%
+the exterior and the cytoplasm but what
+ 
+
+ align:start position:0%
+the exterior and the cytoplasm but what
+happens in the plasma membrane is that
+
+ align:start position:0%
+happens in the plasma membrane is that
+ 
+
+ align:start position:0%
+happens in the plasma membrane is that
+in addition to the sodium potassium
+
+ align:start position:0%
+in addition to the sodium potassium
+ 
+
+ align:start position:0%
+in addition to the sodium potassium
+ATPase there are other channels that are
+
+ align:start position:0%
+ATPase there are other channels that are
+ 
+
+ align:start position:0%
+ATPase there are other channels that are
+present there are sodium channels these
+
+ align:start position:0%
+present there are sodium channels these
+ 
+
+ align:start position:0%
+present there are sodium channels these
+are mostly closed but there are some
+
+ align:start position:0%
+are mostly closed but there are some
+ 
+
+ align:start position:0%
+are mostly closed but there are some
+potassium channels that are leaky and
+
+ align:start position:0%
+potassium channels that are leaky and
+ 
+
+ align:start position:0%
+potassium channels that are leaky and
+they're basically leaking potassium from
+
+ align:start position:0%
+they're basically leaking potassium from
+ 
+
+ align:start position:0%
+they're basically leaking potassium from
+the cytoplasm out into the ectoplasm
+
+ align:start position:0%
+the cytoplasm out into the ectoplasm
+ 
+
+ align:start position:0%
+the cytoplasm out into the ectoplasm
+okay and if you have positive charges
+
+ align:start position:0%
+okay and if you have positive charges
+ 
+
+ align:start position:0%
+okay and if you have positive charges
+going out the cell then the inside of
+
+ align:start position:0%
+going out the cell then the inside of
+ 
+
+ align:start position:0%
+going out the cell then the inside of
+the membrane is going to have a net
+
+ align:start position:0%
+the membrane is going to have a net
+ 
+
+ align:start position:0%
+the membrane is going to have a net
+negative charge and the outside of the
+
+ align:start position:0%
+negative charge and the outside of the
+ 
+
+ align:start position:0%
+negative charge and the outside of the
+membrane is going to have a net positive
+
+ align:start position:0%
+membrane is going to have a net positive
+ 
+
+ align:start position:0%
+membrane is going to have a net positive
+charge okay and this charge across the
+
+ align:start position:0%
+charge okay and this charge across the
+ 
+
+ align:start position:0%
+charge okay and this charge across the
+membrane where you have positive on the
+
+ align:start position:0%
+membrane where you have positive on the
+ 
+
+ align:start position:0%
+membrane where you have positive on the
+outside and minus on the inside I should
+
+ align:start position:0%
+outside and minus on the inside I should
+ 
+
+ align:start position:0%
+outside and minus on the inside I should
+label this exterior and this is
+
+ align:start position:0%
+label this exterior and this is
+ 
+
+ align:start position:0%
+label this exterior and this is
+cytoplasm this voltage difference is
+
+ align:start position:0%
+cytoplasm this voltage difference is
+ 
+
+ align:start position:0%
+cytoplasm this voltage difference is
+known as the membrane potential okay so
+
+ align:start position:0%
+known as the membrane potential okay so
+ 
+
+ align:start position:0%
+known as the membrane potential okay so
+this is a membrane potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's an electrical potential across
+
+ align:start position:0%
+and it's an electrical potential across
+ 
+
+ align:start position:0%
+and it's an electrical potential across
+the membrane if you're an electrical
+
+ align:start position:0%
+the membrane if you're an electrical
+ 
+
+ align:start position:0%
+the membrane if you're an electrical
+engineer you can think of the plasma
+
+ align:start position:0%
+engineer you can think of the plasma
+ 
+
+ align:start position:0%
+engineer you can think of the plasma
+membrane as a capacitor okay so this
+
+ align:start position:0%
+membrane as a capacitor okay so this
+ 
+
+ align:start position:0%
+membrane as a capacitor okay so this
+plasma membrane is holding this charge
+
+ align:start position:0%
+plasma membrane is holding this charge
+ 
+
+ align:start position:0%
+plasma membrane is holding this charge
+difference across it okay and so there's
+
+ align:start position:0%
+difference across it okay and so there's
+ 
+
+ align:start position:0%
+difference across it okay and so there's
+a voltage across the membrane and in an
+
+ align:start position:0%
+a voltage across the membrane and in an
+ 
+
+ align:start position:0%
+a voltage across the membrane and in an
+arresting state the cell's resting
+
+ align:start position:0%
+arresting state the cell's resting
+ 
+
+ align:start position:0%
+arresting state the cell's resting
+potential is negative 70 millivolts okay
+
+ align:start position:0%
+potential is negative 70 millivolts okay
+ 
+
+ align:start position:0%
+potential is negative 70 millivolts okay
+so if the cell is not getting stimulated
+
+ align:start position:0%
+so if the cell is not getting stimulated
+ 
+
+ align:start position:0%
+so if the cell is not getting stimulated
+by something like a neurotransmitter the
+
+ align:start position:0%
+by something like a neurotransmitter the
+ 
+
+ align:start position:0%
+by something like a neurotransmitter the
+resting potential is negative 70
+
+ align:start position:0%
+resting potential is negative 70
+ 
+
+ align:start position:0%
+resting potential is negative 70
+millivolts where the inside is negative
+
+ align:start position:0%
+millivolts where the inside is negative
+ 
+
+ align:start position:0%
+millivolts where the inside is negative
+and outside is positive okay
+
+ align:start position:0%
+and outside is positive okay
+ 
+
+ align:start position:0%
+and outside is positive okay
+so now I just wanted to find some terms
+
+ align:start position:0%
+so now I just wanted to find some terms
+ 
+
+ align:start position:0%
+so now I just wanted to find some terms
+that are gonna be useful for us when we
+
+ align:start position:0%
+that are gonna be useful for us when we
+ 
+
+ align:start position:0%
+that are gonna be useful for us when we
+talk about action potentials so when
+
+ align:start position:0%
+talk about action potentials so when
+ 
+
+ align:start position:0%
+talk about action potentials so when
+there's this negative inside potential a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative inside potential is referred to
+
+ align:start position:0%
+negative inside potential is referred to
+ 
+
+ align:start position:0%
+negative inside potential is referred to
+as polarized so it's polarized because
+
+ align:start position:0%
+as polarized so it's polarized because
+ 
+
+ align:start position:0%
+as polarized so it's polarized because
+there's a polarity across this membrane
+
+ align:start position:0%
+there's a polarity across this membrane
+ 
+
+ align:start position:0%
+there's a polarity across this membrane
+where one side is positive and the other
+
+ align:start position:0%
+where one side is positive and the other
+ 
+
+ align:start position:0%
+where one side is positive and the other
+side is negative okay
+
+ align:start position:0%
+side is negative okay
+ 
+
+ align:start position:0%
+side is negative okay
+so polarized refers to if there's a
+
+ align:start position:0%
+so polarized refers to if there's a
+ 
+
+ align:start position:0%
+so polarized refers to if there's a
+negative inside potential so the resting
+
+ align:start position:0%
+negative inside potential so the resting
+ 
+
+ align:start position:0%
+negative inside potential so the resting
+state of the side is there's a polarized
+
+ align:start position:0%
+state of the side is there's a polarized
+ 
+
+ align:start position:0%
+state of the side is there's a polarized
+it's polarized however the cell can lose
+
+ align:start position:0%
+it's polarized however the cell can lose
+ 
+
+ align:start position:0%
+it's polarized however the cell can lose
+this polarity and not have a charge
+
+ align:start position:0%
+this polarity and not have a charge
+ 
+
+ align:start position:0%
+this polarity and not have a charge
+differential or it can flip and be
+
+ align:start position:0%
+differential or it can flip and be
+ 
+
+ align:start position:0%
+differential or it can flip and be
+positive on the inside and when that
+
+ align:start position:0%
+positive on the inside and when that
+ 
+
+ align:start position:0%
+positive on the inside and when that
+happens if there's either zero or
+
+ align:start position:0%
+happens if there's either zero or
+ 
+
+ align:start position:0%
+happens if there's either zero or
+positive inside potential this is
+
+ align:start position:0%
+positive inside potential this is
+ 
+
+ align:start position:0%
+positive inside potential this is
+referred to as depolarized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay anyone have an idea as to how the
+
+ align:start position:0%
+okay anyone have an idea as to how the
+ 
+
+ align:start position:0%
+okay anyone have an idea as to how the
+cell would flip the potential what would
+
+ align:start position:0%
+cell would flip the potential what would
+ 
+
+ align:start position:0%
+cell would flip the potential what would
+have to happen in the plasma membrane to
+
+ align:start position:0%
+have to happen in the plasma membrane to
+ 
+
+ align:start position:0%
+have to happen in the plasma membrane to
+flip this potential and depolarize the
+
+ align:start position:0%
+flip this potential and depolarize the
+ 
+
+ align:start position:0%
+flip this potential and depolarize the
+cell yes Steven so Steven suggested
+
+ align:start position:0%
+cell yes Steven so Steven suggested
+ 
+
+ align:start position:0%
+cell yes Steven so Steven suggested
+opening ion channels which ion channels
+
+ align:start position:0%
+opening ion channels which ion channels
+ 
+
+ align:start position:0%
+opening ion channels which ion channels
+would you open yeah so Steven suggested
+
+ align:start position:0%
+would you open yeah so Steven suggested
+ 
+
+ align:start position:0%
+would you open yeah so Steven suggested
+if you open these is going to depolarize
+
+ align:start position:0%
+if you open these is going to depolarize
+ 
+
+ align:start position:0%
+if you open these is going to depolarize
+the cell because remember sodium is high
+
+ align:start position:0%
+the cell because remember sodium is high
+ 
+
+ align:start position:0%
+the cell because remember sodium is high
+on the outside out here and so if you
+
+ align:start position:0%
+on the outside out here and so if you
+ 
+
+ align:start position:0%
+on the outside out here and so if you
+open these channels positive ions are
+
+ align:start position:0%
+open these channels positive ions are
+ 
+
+ align:start position:0%
+open these channels positive ions are
+gonna flow in and that's going to make
+
+ align:start position:0%
+gonna flow in and that's going to make
+ 
+
+ align:start position:0%
+gonna flow in and that's going to make
+this less negative and this less
+
+ align:start position:0%
+this less negative and this less
+ 
+
+ align:start position:0%
+this less negative and this less
+positive okay so this is the situation
+
+ align:start position:0%
+positive okay so this is the situation
+ 
+
+ align:start position:0%
+positive okay so this is the situation
+here right where these sodium channels
+
+ align:start position:0%
+here right where these sodium channels
+ 
+
+ align:start position:0%
+here right where these sodium channels
+open and the sodium channels are the
+
+ align:start position:0%
+open and the sodium channels are the
+ 
+
+ align:start position:0%
+open and the sodium channels are the
+sodium ions rushing in is going to
+
+ align:start position:0%
+sodium ions rushing in is going to
+ 
+
+ align:start position:0%
+sodium ions rushing in is going to
+create a depolarization where you now
+
+ align:start position:0%
+create a depolarization where you now
+ 
+
+ align:start position:0%
+create a depolarization where you now
+flip the potential and there's a greater
+
+ align:start position:0%
+flip the potential and there's a greater
+ 
+
+ align:start position:0%
+flip the potential and there's a greater
+positive charge on the inside of the
+
+ align:start position:0%
+positive charge on the inside of the
+ 
+
+ align:start position:0%
+positive charge on the inside of the
+plasma membrane
+
+ align:start position:0%
+plasma membrane
+ 
+
+ align:start position:0%
+plasma membrane
+okay everyone see how because the sodium
+
+ align:start position:0%
+okay everyone see how because the sodium
+ 
+
+ align:start position:0%
+okay everyone see how because the sodium
+ions are going to just go downstream
+
+ align:start position:0%
+ions are going to just go downstream
+ 
+
+ align:start position:0%
+ions are going to just go downstream
+their higher concentration out here so
+
+ align:start position:0%
+their higher concentration out here so
+ 
+
+ align:start position:0%
+their higher concentration out here so
+just by opening these channels the cell
+
+ align:start position:0%
+just by opening these channels the cell
+ 
+
+ align:start position:0%
+just by opening these channels the cell
+doesn't have to do any work to do this
+
+ align:start position:0%
+doesn't have to do any work to do this
+ 
+
+ align:start position:0%
+doesn't have to do any work to do this
+sodium is just going to flow down its
+
+ align:start position:0%
+sodium is just going to flow down its
+ 
+
+ align:start position:0%
+sodium is just going to flow down its
+gradient into the cytoplasm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what an action potential is is
+
+ align:start position:0%
+okay so what an action potential is is
+ 
+
+ align:start position:0%
+okay so what an action potential is is
+it's a transient dope depolarization of
+
+ align:start position:0%
+it's a transient dope depolarization of
+ 
+
+ align:start position:0%
+it's a transient dope depolarization of
+the nerve cell okay so the action
+
+ align:start position:0%
+the nerve cell okay so the action
+ 
+
+ align:start position:0%
+the nerve cell okay so the action
+potential or ap is a transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depolarization of the neuron which means
+
+ align:start position:0%
+depolarization of the neuron which means
+ 
+
+ align:start position:0%
+depolarization of the neuron which means
+it doesn't just depolarize and stay
+
+ align:start position:0%
+it doesn't just depolarize and stay
+ 
+
+ align:start position:0%
+it doesn't just depolarize and stay
+depolarized
+
+ align:start position:0%
+depolarized
+ 
+
+ align:start position:0%
+depolarized
+but it depolarizes and then restores
+
+ align:start position:0%
+but it depolarizes and then restores
+ 
+
+ align:start position:0%
+but it depolarizes and then restores
+itself back to the resting polarity and
+
+ align:start position:0%
+itself back to the resting polarity and
+ 
+
+ align:start position:0%
+itself back to the resting polarity and
+so what you see when you measure the
+
+ align:start position:0%
+so what you see when you measure the
+ 
+
+ align:start position:0%
+so what you see when you measure the
+voltage across the plasma membrane in
+
+ align:start position:0%
+voltage across the plasma membrane in
+ 
+
+ align:start position:0%
+voltage across the plasma membrane in
+the neuron you see that it can spike and
+
+ align:start position:0%
+the neuron you see that it can spike and
+ 
+
+ align:start position:0%
+the neuron you see that it can spike and
+depolarize but then it's rapidly
+
+ align:start position:0%
+depolarize but then it's rapidly
+ 
+
+ align:start position:0%
+depolarize but then it's rapidly
+restored to its resting state okay so
+
+ align:start position:0%
+restored to its resting state okay so
+ 
+
+ align:start position:0%
+restored to its resting state okay so
+it's a transient process and when we
+
+ align:start position:0%
+it's a transient process and when we
+ 
+
+ align:start position:0%
+it's a transient process and when we
+think about the neuron at higher
+
+ align:start position:0%
+think about the neuron at higher
+ 
+
+ align:start position:0%
+think about the neuron at higher
+resolution what you're going to see is
+
+ align:start position:0%
+resolution what you're going to see is
+ 
+
+ align:start position:0%
+resolution what you're going to see is
+not only is it transient but it's also a
+
+ align:start position:0%
+not only is it transient but it's also a
+ 
+
+ align:start position:0%
+not only is it transient but it's also a
+traveling wave that propagates along the
+
+ align:start position:0%
+traveling wave that propagates along the
+ 
+
+ align:start position:0%
+traveling wave that propagates along the
+entire length of the cell okay so this
+
+ align:start position:0%
+entire length of the cell okay so this
+ 
+
+ align:start position:0%
+entire length of the cell okay so this
+is also a traveling wave and one thing
+
+ align:start position:0%
+is also a traveling wave and one thing
+ 
+
+ align:start position:0%
+is also a traveling wave and one thing
+that you can notice about these neurons
+
+ align:start position:0%
+that you can notice about these neurons
+ 
+
+ align:start position:0%
+that you can notice about these neurons
+or the action potentials here is that
+
+ align:start position:0%
+or the action potentials here is that
+ 
+
+ align:start position:0%
+or the action potentials here is that
+they all depolarize to the same extent
+
+ align:start position:0%
+they all depolarize to the same extent
+ 
+
+ align:start position:0%
+they all depolarize to the same extent
+so they all depolarize to this positive
+
+ align:start position:0%
+so they all depolarize to this positive
+ 
+
+ align:start position:0%
+so they all depolarize to this positive
+50 millivolts and so this illustrates a
+
+ align:start position:0%
+50 millivolts and so this illustrates a
+ 
+
+ align:start position:0%
+50 millivolts and so this illustrates a
+key property of neurons and that the the
+
+ align:start position:0%
+key property of neurons and that the the
+ 
+
+ align:start position:0%
+key property of neurons and that the the
+level of activity of a neuron is not
+
+ align:start position:0%
+level of activity of a neuron is not
+ 
+
+ align:start position:0%
+level of activity of a neuron is not
+determined by the size of this action
+
+ align:start position:0%
+determined by the size of this action
+ 
+
+ align:start position:0%
+determined by the size of this action
+potential this action potential is an
+
+ align:start position:0%
+potential this action potential is an
+ 
+
+ align:start position:0%
+potential this action potential is an
+all-or-nothing event it either happens
+
+ align:start position:0%
+all-or-nothing event it either happens
+ 
+
+ align:start position:0%
+all-or-nothing event it either happens
+or it doesn't and when it happens it
+
+ align:start position:0%
+or it doesn't and when it happens it
+ 
+
+ align:start position:0%
+or it doesn't and when it happens it
+depolarizes to the same level okay so
+
+ align:start position:0%
+depolarizes to the same level okay so
+ 
+
+ align:start position:0%
+depolarizes to the same level okay so
+the action potential is all or nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can think of it as a binary signal
+
+ align:start position:0%
+you can think of it as a binary signal
+ 
+
+ align:start position:0%
+you can think of it as a binary signal
+and therefore the way that neurons
+
+ align:start position:0%
+and therefore the way that neurons
+ 
+
+ align:start position:0%
+and therefore the way that neurons
+encode sort of the magnitude of
+
+ align:start position:0%
+encode sort of the magnitude of
+ 
+
+ align:start position:0%
+encode sort of the magnitude of
+activation is not through the level of
+
+ align:start position:0%
+activation is not through the level of
+ 
+
+ align:start position:0%
+activation is not through the level of
+depolarization of a single action
+
+ align:start position:0%
+depolarization of a single action
+ 
+
+ align:start position:0%
+depolarization of a single action
+potential but it is able to distinguish
+
+ align:start position:0%
+potential but it is able to distinguish
+ 
+
+ align:start position:0%
+potential but it is able to distinguish
+between different frequencies of action
+
+ align:start position:0%
+between different frequencies of action
+ 
+
+ align:start position:0%
+between different frequencies of action
+potentials that are propagating along
+
+ align:start position:0%
+potentials that are propagating along
+ 
+
+ align:start position:0%
+potentials that are propagating along
+the neuron
+
+ align:start position:0%
+the neuron
+ 
+
+ align:start position:0%
+the neuron
+okay so signal strength in this case is
+
+ align:start position:0%
+okay so signal strength in this case is
+ 
+
+ align:start position:0%
+okay so signal strength in this case is
+related to the frequency of action
+
+ align:start position:0%
+related to the frequency of action
+ 
+
+ align:start position:0%
+related to the frequency of action
+potentials firing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we're gonna unpack how it is
+
+ align:start position:0%
+okay so now we're gonna unpack how it is
+ 
+
+ align:start position:0%
+okay so now we're gonna unpack how it is
+a nerve cell fires in action potential
+
+ align:start position:0%
+a nerve cell fires in action potential
+ 
+
+ align:start position:0%
+a nerve cell fires in action potential
+and how it propagates along the entire
+
+ align:start position:0%
+and how it propagates along the entire
+ 
+
+ align:start position:0%
+and how it propagates along the entire
+cell length right in the case of the
+
+ align:start position:0%
+cell length right in the case of the
+ 
+
+ align:start position:0%
+cell length right in the case of the
+sciatic nerve this has to happen across
+
+ align:start position:0%
+sciatic nerve this has to happen across
+ 
+
+ align:start position:0%
+sciatic nerve this has to happen across
+an entire meter okay that's a very long
+
+ align:start position:0%
+an entire meter okay that's a very long
+ 
+
+ align:start position:0%
+an entire meter okay that's a very long
+distance to propagate this change in
+
+ align:start position:0%
+distance to propagate this change in
+ 
+
+ align:start position:0%
+distance to propagate this change in
+electrical signal at least for a cell
+
+ align:start position:0%
+electrical signal at least for a cell
+ 
+
+ align:start position:0%
+electrical signal at least for a cell
+and so we're going to talk about the
+
+ align:start position:0%
+and so we're going to talk about the
+ 
+
+ align:start position:0%
+and so we're going to talk about the
+mechanism and I'm going to start at the
+
+ align:start position:0%
+mechanism and I'm going to start at the
+ 
+
+ align:start position:0%
+mechanism and I'm going to start at the
+beginning when this action potential
+
+ align:start position:0%
+beginning when this action potential
+ 
+
+ align:start position:0%
+beginning when this action potential
+initiates so we'll start at the
+
+ align:start position:0%
+initiates so we'll start at the
+ 
+
+ align:start position:0%
+initiates so we'll start at the
+initiation of the action potential so
+
+ align:start position:0%
+initiation of the action potential so
+ 
+
+ align:start position:0%
+initiation of the action potential so
+how is it that this nerve cell is told
+
+ align:start position:0%
+how is it that this nerve cell is told
+ 
+
+ align:start position:0%
+how is it that this nerve cell is told
+to start depolarizing at the dendrites
+
+ align:start position:0%
+to start depolarizing at the dendrites
+ 
+
+ align:start position:0%
+to start depolarizing at the dendrites
+okay because there's gonna be another
+
+ align:start position:0%
+okay because there's gonna be another
+ 
+
+ align:start position:0%
+okay because there's gonna be another
+neuron here which is going to
+
+ align:start position:0%
+neuron here which is going to
+ 
+
+ align:start position:0%
+neuron here which is going to
+communicate to this neuron over here to
+
+ align:start position:0%
+communicate to this neuron over here to
+ 
+
+ align:start position:0%
+communicate to this neuron over here to
+tell it to start depolarizing okay it
+
+ align:start position:0%
+tell it to start depolarizing okay it
+ 
+
+ align:start position:0%
+tell it to start depolarizing okay it
+does this at the location known as the
+
+ align:start position:0%
+does this at the location known as the
+ 
+
+ align:start position:0%
+does this at the location known as the
+synapse which is basically the sort of
+
+ align:start position:0%
+synapse which is basically the sort of
+ 
+
+ align:start position:0%
+synapse which is basically the sort of
+the connection between the two neurons
+
+ align:start position:0%
+the connection between the two neurons
+ 
+
+ align:start position:0%
+the connection between the two neurons
+and the way this process is initiated is
+
+ align:start position:0%
+and the way this process is initiated is
+ 
+
+ align:start position:0%
+and the way this process is initiated is
+similar to the type of signaling that
+
+ align:start position:0%
+similar to the type of signaling that
+ 
+
+ align:start position:0%
+similar to the type of signaling that
+you saw in the past few lectures where
+
+ align:start position:0%
+you saw in the past few lectures where
+ 
+
+ align:start position:0%
+you saw in the past few lectures where
+you have a ligand and a receptor okay in
+
+ align:start position:0%
+you have a ligand and a receptor okay in
+ 
+
+ align:start position:0%
+you have a ligand and a receptor okay in
+this case the ligand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ligand is going to be what's known
+
+ align:start position:0%
+the ligand is going to be what's known
+ 
+
+ align:start position:0%
+the ligand is going to be what's known
+as a neurotransmitter which is a small
+
+ align:start position:0%
+as a neurotransmitter which is a small
+ 
+
+ align:start position:0%
+as a neurotransmitter which is a small
+molecule and I'll show you some later on
+
+ align:start position:0%
+molecule and I'll show you some later on
+ 
+
+ align:start position:0%
+molecule and I'll show you some later on
+and the receptor is going to be a
+
+ align:start position:0%
+and the receptor is going to be a
+ 
+
+ align:start position:0%
+and the receptor is going to be a
+receptor the binds to this log and but
+
+ align:start position:0%
+receptor the binds to this log and but
+ 
+
+ align:start position:0%
+receptor the binds to this log and but
+in this case rather than being something
+
+ align:start position:0%
+in this case rather than being something
+ 
+
+ align:start position:0%
+in this case rather than being something
+like a g-protein coupled receptor or a
+
+ align:start position:0%
+like a g-protein coupled receptor or a
+ 
+
+ align:start position:0%
+like a g-protein coupled receptor or a
+receptor tyrosine kinase the receptor is
+
+ align:start position:0%
+receptor tyrosine kinase the receptor is
+ 
+
+ align:start position:0%
+receptor tyrosine kinase the receptor is
+going to be an ion channel okay so the
+
+ align:start position:0%
+going to be an ion channel okay so the
+ 
+
+ align:start position:0%
+going to be an ion channel okay so the
+receptor is going to be an ion channel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so you see one example on the
+
+ align:start position:0%
+okay and so you see one example on the
+ 
+
+ align:start position:0%
+okay and so you see one example on the
+slide up here where here's a receptor
+
+ align:start position:0%
+slide up here where here's a receptor
+ 
+
+ align:start position:0%
+slide up here where here's a receptor
+and these receptors are what are known
+
+ align:start position:0%
+and these receptors are what are known
+ 
+
+ align:start position:0%
+and these receptors are what are known
+as ligand gated sodium or ion channels
+
+ align:start position:0%
+as ligand gated sodium or ion channels
+ 
+
+ align:start position:0%
+as ligand gated sodium or ion channels
+in this case it's a sodium channel so
+
+ align:start position:0%
+in this case it's a sodium channel so
+ 
+
+ align:start position:0%
+in this case it's a sodium channel so
+it's going to be whether or not it's
+
+ align:start position:0%
+it's going to be whether or not it's
+ 
+
+ align:start position:0%
+it's going to be whether or not it's
+open depends on the presence of the
+
+ align:start position:0%
+open depends on the presence of the
+ 
+
+ align:start position:0%
+open depends on the presence of the
+ligand so if we take a neurotransmitter
+
+ align:start position:0%
+ligand so if we take a neurotransmitter
+ 
+
+ align:start position:0%
+ligand so if we take a neurotransmitter
+like serotonin if it's not bound to the
+
+ align:start position:0%
+like serotonin if it's not bound to the
+ 
+
+ align:start position:0%
+like serotonin if it's not bound to the
+receptor the receptor is closed but if
+
+ align:start position:0%
+receptor the receptor is closed but if
+ 
+
+ align:start position:0%
+receptor the receptor is closed but if
+serotonin binds to this receptor it
+
+ align:start position:0%
+serotonin binds to this receptor it
+ 
+
+ align:start position:0%
+serotonin binds to this receptor it
+opens up the channel which can
+
+ align:start position:0%
+opens up the channel which can
+ 
+
+ align:start position:0%
+opens up the channel which can
+selectively let in a type of ion in this
+
+ align:start position:0%
+selectively let in a type of ion in this
+ 
+
+ align:start position:0%
+selectively let in a type of ion in this
+case sodium right in this case this is
+
+ align:start position:0%
+case sodium right in this case this is
+ 
+
+ align:start position:0%
+case sodium right in this case this is
+an activating channel because letting in
+
+ align:start position:0%
+an activating channel because letting in
+ 
+
+ align:start position:0%
+an activating channel because letting in
+sodium is going to depolarize the cell
+
+ align:start position:0%
+sodium is going to depolarize the cell
+ 
+
+ align:start position:0%
+sodium is going to depolarize the cell
+okay so this ligand receptor binding
+
+ align:start position:0%
+okay so this ligand receptor binding
+ 
+
+ align:start position:0%
+okay so this ligand receptor binding
+uses a ligand gated there's a ligand
+
+ align:start position:0%
+uses a ligand gated there's a ligand
+ 
+
+ align:start position:0%
+uses a ligand gated there's a ligand
+gated sodium channel and it's this
+
+ align:start position:0%
+gated sodium channel and it's this
+ 
+
+ align:start position:0%
+gated sodium channel and it's this
+ligand gated sodium channel which starts
+
+ align:start position:0%
+ligand gated sodium channel which starts
+ 
+
+ align:start position:0%
+ligand gated sodium channel which starts
+the depolarization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's how that's how you sort
+
+ align:start position:0%
+okay so that's how that's how you sort
+ 
+
+ align:start position:0%
+okay so that's how that's how you sort
+of like knock over the first domino
+
+ align:start position:0%
+of like knock over the first domino
+ 
+
+ align:start position:0%
+of like knock over the first domino
+right but then there has to be some
+
+ align:start position:0%
+right but then there has to be some
+ 
+
+ align:start position:0%
+right but then there has to be some
+mechanism to propagate this along the
+
+ align:start position:0%
+mechanism to propagate this along the
+ 
+
+ align:start position:0%
+mechanism to propagate this along the
+length of a very long cell and so I'll
+
+ align:start position:0%
+length of a very long cell and so I'll
+ 
+
+ align:start position:0%
+length of a very long cell and so I'll
+tell you this involves a different type
+
+ align:start position:0%
+tell you this involves a different type
+ 
+
+ align:start position:0%
+tell you this involves a different type
+of sort of signaling mechanism from what
+
+ align:start position:0%
+of sort of signaling mechanism from what
+ 
+
+ align:start position:0%
+of sort of signaling mechanism from what
+you're used to thinking about because
+
+ align:start position:0%
+you're used to thinking about because
+ 
+
+ align:start position:0%
+you're used to thinking about because
+this involves a different type of an ion
+
+ align:start position:0%
+this involves a different type of an ion
+ 
+
+ align:start position:0%
+this involves a different type of an ion
+channel and it's called a voltage-gated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll breve eh
+
+ align:start position:0%
+and I'll breve eh
+ 
+
+ align:start position:0%
+and I'll breve eh
+voltage-gated just VG and in this case
+
+ align:start position:0%
+voltage-gated just VG and in this case
+ 
+
+ align:start position:0%
+voltage-gated just VG and in this case
+it'll be a sodium channel okay so what's
+
+ align:start position:0%
+it'll be a sodium channel okay so what's
+ 
+
+ align:start position:0%
+it'll be a sodium channel okay so what's
+a voltage-gated sodium channel this is a
+
+ align:start position:0%
+a voltage-gated sodium channel this is a
+ 
+
+ align:start position:0%
+a voltage-gated sodium channel this is a
+voltage-gated sodium channel here and
+
+ align:start position:0%
+voltage-gated sodium channel here and
+ 
+
+ align:start position:0%
+voltage-gated sodium channel here and
+you can see in the resting state of the
+
+ align:start position:0%
+you can see in the resting state of the
+ 
+
+ align:start position:0%
+you can see in the resting state of the
+cell this channel is closed and it's
+
+ align:start position:0%
+cell this channel is closed and it's
+ 
+
+ align:start position:0%
+cell this channel is closed and it's
+closed because of this red rod structure
+
+ align:start position:0%
+closed because of this red rod structure
+ 
+
+ align:start position:0%
+closed because of this red rod structure
+that's positively charged
+
+ align:start position:0%
+that's positively charged
+ 
+
+ align:start position:0%
+that's positively charged
+that's a positively charged alpha helix
+
+ align:start position:0%
+that's a positively charged alpha helix
+ 
+
+ align:start position:0%
+that's a positively charged alpha helix
+that is a part of this protein is and is
+
+ align:start position:0%
+that is a part of this protein is and is
+ 
+
+ align:start position:0%
+that is a part of this protein is and is
+embedded in the membrane but this alpha
+
+ align:start position:0%
+embedded in the membrane but this alpha
+ 
+
+ align:start position:0%
+embedded in the membrane but this alpha
+helix is is positioned down towards the
+
+ align:start position:0%
+helix is is positioned down towards the
+ 
+
+ align:start position:0%
+helix is is positioned down towards the
+cytoplasm because it's positively
+
+ align:start position:0%
+cytoplasm because it's positively
+ 
+
+ align:start position:0%
+cytoplasm because it's positively
+charged and the cytosolic face of the
+
+ align:start position:0%
+charged and the cytosolic face of the
+ 
+
+ align:start position:0%
+charged and the cytosolic face of the
+plasma membrane is negatively charged
+
+ align:start position:0%
+plasma membrane is negatively charged
+ 
+
+ align:start position:0%
+plasma membrane is negatively charged
+okay and the confirmation of this
+
+ align:start position:0%
+okay and the confirmation of this
+ 
+
+ align:start position:0%
+okay and the confirmation of this
+protein then depends on the charge
+
+ align:start position:0%
+protein then depends on the charge
+ 
+
+ align:start position:0%
+protein then depends on the charge
+across this membrane because when
+
+ align:start position:0%
+across this membrane because when
+ 
+
+ align:start position:0%
+across this membrane because when
+there's depolarization that shifts the
+
+ align:start position:0%
+there's depolarization that shifts the
+ 
+
+ align:start position:0%
+there's depolarization that shifts the
+position of this alpha helix such that
+
+ align:start position:0%
+position of this alpha helix such that
+ 
+
+ align:start position:0%
+position of this alpha helix such that
+now it shifts up towards the exterior
+
+ align:start position:0%
+now it shifts up towards the exterior
+ 
+
+ align:start position:0%
+now it shifts up towards the exterior
+face of the plasma membrane and that
+
+ align:start position:0%
+face of the plasma membrane and that
+ 
+
+ align:start position:0%
+face of the plasma membrane and that
+opens the channel which lets sodium ions
+
+ align:start position:0%
+opens the channel which lets sodium ions
+ 
+
+ align:start position:0%
+opens the channel which lets sodium ions
+rush in okay okay again sodium ions here
+
+ align:start position:0%
+rush in okay okay again sodium ions here
+ 
+
+ align:start position:0%
+rush in okay okay again sodium ions here
+they're always rushing downstream
+
+ align:start position:0%
+they're always rushing downstream
+ 
+
+ align:start position:0%
+they're always rushing downstream
+they're on their concentration gradient
+
+ align:start position:0%
+they're on their concentration gradient
+ 
+
+ align:start position:0%
+they're on their concentration gradient
+okay so in this case whether or not this
+
+ align:start position:0%
+okay so in this case whether or not this
+ 
+
+ align:start position:0%
+okay so in this case whether or not this
+channel is open or closed depends not on
+
+ align:start position:0%
+channel is open or closed depends not on
+ 
+
+ align:start position:0%
+channel is open or closed depends not on
+the presence of a ligand but on the
+
+ align:start position:0%
+the presence of a ligand but on the
+ 
+
+ align:start position:0%
+the presence of a ligand but on the
+membrane potential across the plasma
+
+ align:start position:0%
+membrane potential across the plasma
+ 
+
+ align:start position:0%
+membrane potential across the plasma
+membrane okay so these voltage-gated
+
+ align:start position:0%
+membrane okay so these voltage-gated
+ 
+
+ align:start position:0%
+membrane okay so these voltage-gated
+sodium channels they're opened
+
+ align:start position:0%
+sodium channels they're opened
+ 
+
+ align:start position:0%
+sodium channels they're opened
+by depolarization okay and then the
+
+ align:start position:0%
+by depolarization okay and then the
+ 
+
+ align:start position:0%
+by depolarization okay and then the
+question becomes if you open these
+
+ align:start position:0%
+question becomes if you open these
+ 
+
+ align:start position:0%
+question becomes if you open these
+channels at the very end of the neuron
+
+ align:start position:0%
+channels at the very end of the neuron
+ 
+
+ align:start position:0%
+channels at the very end of the neuron
+how do you get it such that this
+
+ align:start position:0%
+how do you get it such that this
+ 
+
+ align:start position:0%
+how do you get it such that this
+electrical signal moves uni-directional
+
+ align:start position:0%
+electrical signal moves uni-directional
+ 
+
+ align:start position:0%
+electrical signal moves uni-directional
+II along the neuron okay so what leads
+
+ align:start position:0%
+II along the neuron okay so what leads
+ 
+
+ align:start position:0%
+II along the neuron okay so what leads
+to you need directionality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay who's been to a sporting event
+
+ align:start position:0%
+okay who's been to a sporting event
+ 
+
+ align:start position:0%
+okay who's been to a sporting event
+light lately okay good you guys know the
+
+ align:start position:0%
+light lately okay good you guys know the
+ 
+
+ align:start position:0%
+light lately okay good you guys know the
+wave okay so we're gonna do the wave
+
+ align:start position:0%
+wave okay so we're gonna do the wave
+ 
+
+ align:start position:0%
+wave okay so we're gonna do the wave
+once you stand up you're gonna be tired
+
+ align:start position:0%
+once you stand up you're gonna be tired
+ 
+
+ align:start position:0%
+once you stand up you're gonna be tired
+and you're gonna have to sit down for a
+
+ align:start position:0%
+and you're gonna have to sit down for a
+ 
+
+ align:start position:0%
+and you're gonna have to sit down for a
+while okay I'm going to be a ligand volt
+
+ align:start position:0%
+while okay I'm going to be a ligand volt
+ 
+
+ align:start position:0%
+while okay I'm going to be a ligand volt
+I'm the ligand gated sodium channel so
+
+ align:start position:0%
+I'm the ligand gated sodium channel so
+ 
+
+ align:start position:0%
+I'm the ligand gated sodium channel so
+I'm gonna start things off okay you
+
+ align:start position:0%
+I'm gonna start things off okay you
+ 
+
+ align:start position:0%
+I'm gonna start things off okay you
+ready
+
+ align:start position:0%
+ready
+ 
+
+ align:start position:0%
+ready
+alright here we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's basically an action
+
+ align:start position:0%
+okay that's basically an action
+ 
+
+ align:start position:0%
+okay that's basically an action
+potential okay so the way that this
+
+ align:start position:0%
+potential okay so the way that this
+ 
+
+ align:start position:0%
+potential okay so the way that this
+happened that this was uni-directional
+
+ align:start position:0%
+happened that this was uni-directional
+ 
+
+ align:start position:0%
+happened that this was uni-directional
+right is once you once you stood up and
+
+ align:start position:0%
+right is once you once you stood up and
+ 
+
+ align:start position:0%
+right is once you once you stood up and
+did the wave right you then sat down and
+
+ align:start position:0%
+did the wave right you then sat down and
+ 
+
+ align:start position:0%
+did the wave right you then sat down and
+you stopped doing anything okay
+
+ align:start position:0%
+you stopped doing anything okay
+ 
+
+ align:start position:0%
+you stopped doing anything okay
+and so these voltage-gated sodium
+
+ align:start position:0%
+and so these voltage-gated sodium
+ 
+
+ align:start position:0%
+and so these voltage-gated sodium
+channels have a similar property okay if
+
+ align:start position:0%
+channels have a similar property okay if
+ 
+
+ align:start position:0%
+channels have a similar property okay if
+we look at the next step in this the
+
+ align:start position:0%
+we look at the next step in this the
+ 
+
+ align:start position:0%
+we look at the next step in this the
+sodium channel is opened by
+
+ align:start position:0%
+sodium channel is opened by
+ 
+
+ align:start position:0%
+sodium channel is opened by
+depolarization and you see there's this
+
+ align:start position:0%
+depolarization and you see there's this
+ 
+
+ align:start position:0%
+depolarization and you see there's this
+ball of chain segment of the protein
+
+ align:start position:0%
+ball of chain segment of the protein
+ 
+
+ align:start position:0%
+ball of chain segment of the protein
+whether you see that yellow ball and
+
+ align:start position:0%
+whether you see that yellow ball and
+ 
+
+ align:start position:0%
+whether you see that yellow ball and
+once the sodium channel opens after
+
+ align:start position:0%
+once the sodium channel opens after
+ 
+
+ align:start position:0%
+once the sodium channel opens after
+about a millisecond that ball sticks in
+
+ align:start position:0%
+about a millisecond that ball sticks in
+ 
+
+ align:start position:0%
+about a millisecond that ball sticks in
+the channel pore and blocks it okay so
+
+ align:start position:0%
+the channel pore and blocks it okay so
+ 
+
+ align:start position:0%
+the channel pore and blocks it okay so
+these sodium channels open to let in
+
+ align:start position:0%
+these sodium channels open to let in
+ 
+
+ align:start position:0%
+these sodium channels open to let in
+sodium ions but then they're immediately
+
+ align:start position:0%
+sodium ions but then they're immediately
+ 
+
+ align:start position:0%
+sodium ions but then they're immediately
+inactivated after about a millisecond
+
+ align:start position:0%
+inactivated after about a millisecond
+ 
+
+ align:start position:0%
+inactivated after about a millisecond
+okay and so that enables uni-directional
+
+ align:start position:0%
+okay and so that enables uni-directional
+ 
+
+ align:start position:0%
+okay and so that enables uni-directional
+'ti okay so this is what I'll call
+
+ align:start position:0%
+'ti okay so this is what I'll call
+ 
+
+ align:start position:0%
+'ti okay so this is what I'll call
+voltage-gated sodium channel
+
+ align:start position:0%
+voltage-gated sodium channel
+ 
+
+ align:start position:0%
+voltage-gated sodium channel
+inactivation okay and how this promotes
+
+ align:start position:0%
+inactivation okay and how this promotes
+ 
+
+ align:start position:0%
+inactivation okay and how this promotes
+a travelling wave of depolarization is
+
+ align:start position:0%
+a travelling wave of depolarization is
+ 
+
+ align:start position:0%
+a travelling wave of depolarization is
+that if we consider an action potential
+
+ align:start position:0%
+that if we consider an action potential
+ 
+
+ align:start position:0%
+that if we consider an action potential
+moving along this axon from left to
+
+ align:start position:0%
+moving along this axon from left to
+ 
+
+ align:start position:0%
+moving along this axon from left to
+right and if the sodium channels in the
+
+ align:start position:0%
+right and if the sodium channels in the
+ 
+
+ align:start position:0%
+right and if the sodium channels in the
+green zone are currently open it came
+
+ align:start position:0%
+green zone are currently open it came
+ 
+
+ align:start position:0%
+green zone are currently open it came
+from the left which means that all the
+
+ align:start position:0%
+from the left which means that all the
+ 
+
+ align:start position:0%
+from the left which means that all the
+sodium channels to the left of this
+
+ align:start position:0%
+sodium channels to the left of this
+ 
+
+ align:start position:0%
+sodium channels to the left of this
+green zone are going to be inactivated
+
+ align:start position:0%
+green zone are going to be inactivated
+ 
+
+ align:start position:0%
+green zone are going to be inactivated
+okay so because they're inactivated here
+
+ align:start position:0%
+okay so because they're inactivated here
+ 
+
+ align:start position:0%
+okay so because they're inactivated here
+there won't be further deep polarization
+
+ align:start position:0%
+there won't be further deep polarization
+ 
+
+ align:start position:0%
+there won't be further deep polarization
+going to the left but depolarization
+
+ align:start position:0%
+going to the left but depolarization
+ 
+
+ align:start position:0%
+going to the left but depolarization
+will have to move to the right and you
+
+ align:start position:0%
+will have to move to the right and you
+ 
+
+ align:start position:0%
+will have to move to the right and you
+basically get this traveling wave and it
+
+ align:start position:0%
+basically get this traveling wave and it
+ 
+
+ align:start position:0%
+basically get this traveling wave and it
+goes one direction because if it came
+
+ align:start position:0%
+goes one direction because if it came
+ 
+
+ align:start position:0%
+goes one direction because if it came
+from somewhere which it always does then
+
+ align:start position:0%
+from somewhere which it always does then
+ 
+
+ align:start position:0%
+from somewhere which it always does then
+where it just was coming from all those
+
+ align:start position:0%
+where it just was coming from all those
+ 
+
+ align:start position:0%
+where it just was coming from all those
+sodium channels the voltage-gated sodium
+
+ align:start position:0%
+sodium channels the voltage-gated sodium
+ 
+
+ align:start position:0%
+sodium channels the voltage-gated sodium
+channels are going to be closed okay so
+
+ align:start position:0%
+channels are going to be closed okay so
+ 
+
+ align:start position:0%
+channels are going to be closed okay so
+this allows it to move in a
+
+ align:start position:0%
+this allows it to move in a
+ 
+
+ align:start position:0%
+this allows it to move in a
+single direction along the neuron also
+
+ align:start position:0%
+single direction along the neuron also
+ 
+
+ align:start position:0%
+single direction along the neuron also
+once the action potential gets to the
+
+ align:start position:0%
+once the action potential gets to the
+ 
+
+ align:start position:0%
+once the action potential gets to the
+end of the neuron it doesn't reflect
+
+ align:start position:0%
+end of the neuron it doesn't reflect
+ 
+
+ align:start position:0%
+end of the neuron it doesn't reflect
+back the other way in the neuron this
+
+ align:start position:0%
+back the other way in the neuron this
+ 
+
+ align:start position:0%
+back the other way in the neuron this
+can only go one direction okay so this
+
+ align:start position:0%
+can only go one direction okay so this
+ 
+
+ align:start position:0%
+can only go one direction okay so this
+provides you need directionality okay so
+
+ align:start position:0%
+provides you need directionality okay so
+ 
+
+ align:start position:0%
+provides you need directionality okay so
+it's this inactive or refractory period
+
+ align:start position:0%
+it's this inactive or refractory period
+ 
+
+ align:start position:0%
+it's this inactive or refractory period
+of the voltage-gated sodium channel
+
+ align:start position:0%
+of the voltage-gated sodium channel
+ 
+
+ align:start position:0%
+of the voltage-gated sodium channel
+which prevents the action potential from
+
+ align:start position:0%
+which prevents the action potential from
+ 
+
+ align:start position:0%
+which prevents the action potential from
+moving backwards okay now if you look at
+
+ align:start position:0%
+moving backwards okay now if you look at
+ 
+
+ align:start position:0%
+moving backwards okay now if you look at
+these action potentials in this cell you
+
+ align:start position:0%
+these action potentials in this cell you
+ 
+
+ align:start position:0%
+these action potentials in this cell you
+see that they happen but you don't just
+
+ align:start position:0%
+see that they happen but you don't just
+ 
+
+ align:start position:0%
+see that they happen but you don't just
+depolarize and stay depolarized the cell
+
+ align:start position:0%
+depolarize and stay depolarized the cell
+ 
+
+ align:start position:0%
+depolarize and stay depolarized the cell
+depolarizes and then repolarizes very
+
+ align:start position:0%
+depolarizes and then repolarizes very
+ 
+
+ align:start position:0%
+depolarizes and then repolarizes very
+rapidly
+
+ align:start position:0%
+rapidly
+ 
+
+ align:start position:0%
+rapidly
+okay so there's an oscillation okay so
+
+ align:start position:0%
+okay so there's an oscillation okay so
+ 
+
+ align:start position:0%
+okay so there's an oscillation okay so
+there has to be some way to terminate
+
+ align:start position:0%
+there has to be some way to terminate
+ 
+
+ align:start position:0%
+there has to be some way to terminate
+the action potential so there's a t
+
+ align:start position:0%
+the action potential so there's a t
+ 
+
+ align:start position:0%
+the action potential so there's a t
+termination or repolarization of the
+
+ align:start position:0%
+termination or repolarization of the
+ 
+
+ align:start position:0%
+termination or repolarization of the
+cell so there has to be a way for this
+
+ align:start position:0%
+cell so there has to be a way for this
+ 
+
+ align:start position:0%
+cell so there has to be a way for this
+nerve cell to rapidly restore membrane
+
+ align:start position:0%
+nerve cell to rapidly restore membrane
+ 
+
+ align:start position:0%
+nerve cell to rapidly restore membrane
+potential and I want you to think for
+
+ align:start position:0%
+potential and I want you to think for
+ 
+
+ align:start position:0%
+potential and I want you to think for
+just a couple seconds about what type of
+
+ align:start position:0%
+just a couple seconds about what type of
+ 
+
+ align:start position:0%
+just a couple seconds about what type of
+channel will might you open to
+
+ align:start position:0%
+channel will might you open to
+ 
+
+ align:start position:0%
+channel will might you open to
+reestablish this polarity what ion do
+
+ align:start position:0%
+reestablish this polarity what ion do
+ 
+
+ align:start position:0%
+reestablish this polarity what ion do
+you need to flow from where to where in
+
+ align:start position:0%
+you need to flow from where to where in
+ 
+
+ align:start position:0%
+you need to flow from where to where in
+order to get a net negative charge on
+
+ align:start position:0%
+order to get a net negative charge on
+ 
+
+ align:start position:0%
+order to get a net negative charge on
+the inside who don't
+
+ align:start position:0%
+the inside who don't
+ 
+
+ align:start position:0%
+the inside who don't
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay you could pump the sodium ions out
+
+ align:start position:0%
+okay you could pump the sodium ions out
+ 
+
+ align:start position:0%
+okay you could pump the sodium ions out
+and that's totally accurate so that's
+
+ align:start position:0%
+and that's totally accurate so that's
+ 
+
+ align:start position:0%
+and that's totally accurate so that's
+going to require moving sodium ions up a
+
+ align:start position:0%
+going to require moving sodium ions up a
+ 
+
+ align:start position:0%
+going to require moving sodium ions up a
+concentration gradient which is going to
+
+ align:start position:0%
+concentration gradient which is going to
+ 
+
+ align:start position:0%
+concentration gradient which is going to
+take energy and is going to be slow so
+
+ align:start position:0%
+take energy and is going to be slow so
+ 
+
+ align:start position:0%
+take energy and is going to be slow so
+is there another option we could take
+
+ align:start position:0%
+is there another option we could take
+ 
+
+ align:start position:0%
+is there another option we could take
+advantage of here to repolarize Rachel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Rachel is suggested to moving the
+
+ align:start position:0%
+so Rachel is suggested to moving the
+ 
+
+ align:start position:0%
+so Rachel is suggested to moving the
+potassium ions to the outside which is
+
+ align:start position:0%
+potassium ions to the outside which is
+ 
+
+ align:start position:0%
+potassium ions to the outside which is
+how this is done
+
+ align:start position:0%
+how this is done
+ 
+
+ align:start position:0%
+how this is done
+so remember potassium is high on the in
+
+ align:start position:0%
+so remember potassium is high on the in
+ 
+
+ align:start position:0%
+so remember potassium is high on the in
+the cytoplasm low on the exo plasm and
+
+ align:start position:0%
+the cytoplasm low on the exo plasm and
+ 
+
+ align:start position:0%
+the cytoplasm low on the exo plasm and
+therefore if you have a voltage-gated
+
+ align:start position:0%
+therefore if you have a voltage-gated
+ 
+
+ align:start position:0%
+therefore if you have a voltage-gated
+potassium channel that's going to cause
+
+ align:start position:0%
+potassium channel that's going to cause
+ 
+
+ align:start position:0%
+potassium channel that's going to cause
+a rush of positive ions out of the cell
+
+ align:start position:0%
+a rush of positive ions out of the cell
+ 
+
+ align:start position:0%
+a rush of positive ions out of the cell
+and that will be able to restore the net
+
+ align:start position:0%
+and that will be able to restore the net
+ 
+
+ align:start position:0%
+and that will be able to restore the net
+negative potential on the inside of the
+
+ align:start position:0%
+negative potential on the inside of the
+ 
+
+ align:start position:0%
+negative potential on the inside of the
+cell okay so this termination or
+
+ align:start position:0%
+cell okay so this termination or
+ 
+
+ align:start position:0%
+cell okay so this termination or
+repolarization Leeds is the result of
+
+ align:start position:0%
+repolarization Leeds is the result of
+ 
+
+ align:start position:0%
+repolarization Leeds is the result of
+the opening of voltage-gated in this
+
+ align:start position:0%
+the opening of voltage-gated in this
+ 
+
+ align:start position:0%
+the opening of voltage-gated in this
+case not sodium channels but potassium
+
+ align:start position:0%
+case not sodium channels but potassium
+ 
+
+ align:start position:0%
+case not sodium channels but potassium
+channels when do you think these have to
+
+ align:start position:0%
+channels when do you think these have to
+ 
+
+ align:start position:0%
+channels when do you think these have to
+open relative to the sodium channel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should they open right with the sodium
+
+ align:start position:0%
+should they open right with the sodium
+ 
+
+ align:start position:0%
+should they open right with the sodium
+channel
+
+ align:start position:0%
+channel
+ 
+
+ align:start position:0%
+channel
+karmen shaking your head no do you want
+
+ align:start position:0%
+karmen shaking your head no do you want
+ 
+
+ align:start position:0%
+karmen shaking your head no do you want
+to explain your logic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly mm-hmm so a Carmen said is if
+
+ align:start position:0%
+exactly mm-hmm so a Carmen said is if
+ 
+
+ align:start position:0%
+exactly mm-hmm so a Carmen said is if
+they open simultaneously you have sodium
+
+ align:start position:0%
+they open simultaneously you have sodium
+ 
+
+ align:start position:0%
+they open simultaneously you have sodium
+flowing in your potassium flowing out
+
+ align:start position:0%
+flowing in your potassium flowing out
+ 
+
+ align:start position:0%
+flowing in your potassium flowing out
+and that's not going to necessarily
+
+ align:start position:0%
+and that's not going to necessarily
+ 
+
+ align:start position:0%
+and that's not going to necessarily
+change their charge okay so when would
+
+ align:start position:0%
+change their charge okay so when would
+ 
+
+ align:start position:0%
+change their charge okay so when would
+these have to open relative to sodium
+
+ align:start position:0%
+these have to open relative to sodium
+ 
+
+ align:start position:0%
+these have to open relative to sodium
+channels yeah Carmen so after it's
+
+ align:start position:0%
+channels yeah Carmen so after it's
+ 
+
+ align:start position:0%
+channels yeah Carmen so after it's
+depolarized yeah so this has to be
+
+ align:start position:0%
+depolarized yeah so this has to be
+ 
+
+ align:start position:0%
+depolarized yeah so this has to be
+delayed relative to the sodium channels
+
+ align:start position:0%
+delayed relative to the sodium channels
+ 
+
+ align:start position:0%
+delayed relative to the sodium channels
+okay so this has to be delayed relative
+
+ align:start position:0%
+okay so this has to be delayed relative
+ 
+
+ align:start position:0%
+okay so this has to be delayed relative
+to the voltage-gated sodium channels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because if you're thinking about
+
+ align:start position:0%
+right because if you're thinking about
+ 
+
+ align:start position:0%
+right because if you're thinking about
+this traveling wave of depolarization
+
+ align:start position:0%
+this traveling wave of depolarization
+ 
+
+ align:start position:0%
+this traveling wave of depolarization
+the depolarization is going to be high
+
+ align:start position:0%
+the depolarization is going to be high
+ 
+
+ align:start position:0%
+the depolarization is going to be high
+where the sodium channels are only
+
+ align:start position:0%
+where the sodium channels are only
+ 
+
+ align:start position:0%
+where the sodium channels are only
+entering and then following that you
+
+ align:start position:0%
+entering and then following that you
+ 
+
+ align:start position:0%
+entering and then following that you
+would have potassium ions getting pumped
+
+ align:start position:0%
+would have potassium ions getting pumped
+ 
+
+ align:start position:0%
+would have potassium ions getting pumped
+out and basically repolarizing the cell
+
+ align:start position:0%
+out and basically repolarizing the cell
+ 
+
+ align:start position:0%
+out and basically repolarizing the cell
+okay everyone see how you sort of you
+
+ align:start position:0%
+okay everyone see how you sort of you
+ 
+
+ align:start position:0%
+okay everyone see how you sort of you
+get depolarization with sodium rushing
+
+ align:start position:0%
+get depolarization with sodium rushing
+ 
+
+ align:start position:0%
+get depolarization with sodium rushing
+in and then after that you repolarize
+
+ align:start position:0%
+in and then after that you repolarize
+ 
+
+ align:start position:0%
+in and then after that you repolarize
+with the potassium getting pumped out
+
+ align:start position:0%
+with the potassium getting pumped out
+ 
+
+ align:start position:0%
+with the potassium getting pumped out
+right so here you have a spike and you
+
+ align:start position:0%
+right so here you have a spike and you
+ 
+
+ align:start position:0%
+right so here you have a spike and you
+complete the cycle it can even get
+
+ align:start position:0%
+complete the cycle it can even get
+ 
+
+ align:start position:0%
+complete the cycle it can even get
+hyperpolarized where it gets even more
+
+ align:start position:0%
+hyperpolarized where it gets even more
+ 
+
+ align:start position:0%
+hyperpolarized where it gets even more
+negative than it normally does and then
+
+ align:start position:0%
+negative than it normally does and then
+ 
+
+ align:start position:0%
+negative than it normally does and then
+it eventually gets back to this resting
+
+ align:start position:0%
+it eventually gets back to this resting
+ 
+
+ align:start position:0%
+it eventually gets back to this resting
+potential of around negative 60 or
+
+ align:start position:0%
+potential of around negative 60 or
+ 
+
+ align:start position:0%
+potential of around negative 60 or
+negative 70 millivolts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this has to happen fast and I
+
+ align:start position:0%
+okay so this has to happen fast and I
+ 
+
+ align:start position:0%
+okay so this has to happen fast and I
+want to tell you about one process or
+
+ align:start position:0%
+want to tell you about one process or
+ 
+
+ align:start position:0%
+want to tell you about one process or
+property of neurons and another helpful
+
+ align:start position:0%
+property of neurons and another helpful
+ 
+
+ align:start position:0%
+property of neurons and another helpful
+cell that enables this to go extremely
+
+ align:start position:0%
+cell that enables this to go extremely
+ 
+
+ align:start position:0%
+cell that enables this to go extremely
+fast and that is that there are these
+
+ align:start position:0%
+fast and that is that there are these
+ 
+
+ align:start position:0%
+fast and that is that there are these
+glial cells in your body and your brain
+
+ align:start position:0%
+glial cells in your body and your brain
+ 
+
+ align:start position:0%
+glial cells in your body and your brain
+that wrap around the axons of the
+
+ align:start position:0%
+that wrap around the axons of the
+ 
+
+ align:start position:0%
+that wrap around the axons of the
+neurons and basically function like
+
+ align:start position:0%
+neurons and basically function like
+ 
+
+ align:start position:0%
+neurons and basically function like
+electrical tape for neurons okay so they
+
+ align:start position:0%
+electrical tape for neurons okay so they
+ 
+
+ align:start position:0%
+electrical tape for neurons okay so they
+are these there's electrical insulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around the axons of these neurons and
+
+ align:start position:0%
+around the axons of these neurons and
+ 
+
+ align:start position:0%
+around the axons of these neurons and
+this is provided by another specialized
+
+ align:start position:0%
+this is provided by another specialized
+ 
+
+ align:start position:0%
+this is provided by another specialized
+cell type called a glial cell so this is
+
+ align:start position:0%
+cell type called a glial cell so this is
+ 
+
+ align:start position:0%
+cell type called a glial cell so this is
+by a glial cell okay and here are two
+
+ align:start position:0%
+by a glial cell okay and here are two
+ 
+
+ align:start position:0%
+by a glial cell okay and here are two
+examples of glial cells there are Lego
+
+ align:start position:0%
+examples of glial cells there are Lego
+ 
+
+ align:start position:0%
+examples of glial cells there are Lego
+oligodendrocytes and you can see how
+
+ align:start position:0%
+oligodendrocytes and you can see how
+ 
+
+ align:start position:0%
+oligodendrocytes and you can see how
+this cells extending processes that wrap
+
+ align:start position:0%
+this cells extending processes that wrap
+ 
+
+ align:start position:0%
+this cells extending processes that wrap
+around the axons of these two neurons
+
+ align:start position:0%
+around the axons of these two neurons
+ 
+
+ align:start position:0%
+around the axons of these two neurons
+here's a Schwann cell over here which
+
+ align:start position:0%
+here's a Schwann cell over here which
+ 
+
+ align:start position:0%
+here's a Schwann cell over here which
+again wraps around the axon and these
+
+ align:start position:0%
+again wraps around the axon and these
+ 
+
+ align:start position:0%
+again wraps around the axon and these
+cells basically form what's called a
+
+ align:start position:0%
+cells basically form what's called a
+ 
+
+ align:start position:0%
+cells basically form what's called a
+myelin sheath so they form a myelin
+
+ align:start position:0%
+myelin sheath so they form a myelin
+ 
+
+ align:start position:0%
+myelin sheath so they form a myelin
+sheath around the axons and that
+
+ align:start position:0%
+sheath around the axons and that
+ 
+
+ align:start position:0%
+sheath around the axons and that
+insulates the plasma membrane of the
+
+ align:start position:0%
+insulates the plasma membrane of the
+ 
+
+ align:start position:0%
+insulates the plasma membrane of the
+axon such that so here's a an axon you
+
+ align:start position:0%
+axon such that so here's a an axon you
+ 
+
+ align:start position:0%
+axon such that so here's a an axon you
+have glial cells or wrapped around and
+
+ align:start position:0%
+have glial cells or wrapped around and
+ 
+
+ align:start position:0%
+have glial cells or wrapped around and
+it sort of forms like beads on a string
+
+ align:start position:0%
+it sort of forms like beads on a string
+ 
+
+ align:start position:0%
+it sort of forms like beads on a string
+and so there are these gaps between the
+
+ align:start position:0%
+and so there are these gaps between the
+ 
+
+ align:start position:0%
+and so there are these gaps between the
+myelin sheath that are known as the note
+
+ align:start position:0%
+myelin sheath that are known as the note
+ 
+
+ align:start position:0%
+myelin sheath that are known as the note
+nodes of ranvier okay so there are these
+
+ align:start position:0%
+nodes of ranvier okay so there are these
+ 
+
+ align:start position:0%
+nodes of ranvier okay so there are these
+nodes of ranvier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which are gaps in the myelin sheath and
+
+ align:start position:0%
+which are gaps in the myelin sheath and
+ 
+
+ align:start position:0%
+which are gaps in the myelin sheath and
+these nodes perform an important
+
+ align:start position:0%
+these nodes perform an important
+ 
+
+ align:start position:0%
+these nodes perform an important
+function for the neuron because where
+
+ align:start position:0%
+function for the neuron because where
+ 
+
+ align:start position:0%
+function for the neuron because where
+the axon is wrapped the the membrane is
+
+ align:start position:0%
+the axon is wrapped the the membrane is
+ 
+
+ align:start position:0%
+the axon is wrapped the the membrane is
+electrically insulated and so the sodium
+
+ align:start position:0%
+electrically insulated and so the sodium
+ 
+
+ align:start position:0%
+electrically insulated and so the sodium
+ions are the sodium channels and
+
+ align:start position:0%
+ions are the sodium channels and
+ 
+
+ align:start position:0%
+ions are the sodium channels and
+potassium channels the voltage-gated
+
+ align:start position:0%
+potassium channels the voltage-gated
+ 
+
+ align:start position:0%
+potassium channels the voltage-gated
+ones localized to these nodes and when
+
+ align:start position:0%
+ones localized to these nodes and when
+ 
+
+ align:start position:0%
+ones localized to these nodes and when
+the action potential is traveling along
+
+ align:start position:0%
+the action potential is traveling along
+ 
+
+ align:start position:0%
+the action potential is traveling along
+the axon because these regions where the
+
+ align:start position:0%
+the axon because these regions where the
+ 
+
+ align:start position:0%
+the axon because these regions where the
+myelin sheath is are electrically
+
+ align:start position:0%
+myelin sheath is are electrically
+ 
+
+ align:start position:0%
+myelin sheath is are electrically
+insulated the axon potential doesn't
+
+ align:start position:0%
+insulated the axon potential doesn't
+ 
+
+ align:start position:0%
+insulated the axon potential doesn't
+just move continuously but jumps from
+
+ align:start position:0%
+just move continuously but jumps from
+ 
+
+ align:start position:0%
+just move continuously but jumps from
+node to node such that you're just
+
+ align:start position:0%
+node to node such that you're just
+ 
+
+ align:start position:0%
+node to node such that you're just
+opening the sodium channels at these
+
+ align:start position:0%
+opening the sodium channels at these
+ 
+
+ align:start position:0%
+opening the sodium channels at these
+nodes and that allows the action
+
+ align:start position:0%
+nodes and that allows the action
+ 
+
+ align:start position:0%
+nodes and that allows the action
+potential to travel about a hundredfold
+
+ align:start position:0%
+potential to travel about a hundredfold
+ 
+
+ align:start position:0%
+potential to travel about a hundredfold
+faster along the axon and that's what
+
+ align:start position:0%
+faster along the axon and that's what
+ 
+
+ align:start position:0%
+faster along the axon and that's what
+allows your neurons to transmit these
+
+ align:start position:0%
+allows your neurons to transmit these
+ 
+
+ align:start position:0%
+allows your neurons to transmit these
+electrical signals from the base of your
+
+ align:start position:0%
+electrical signals from the base of your
+ 
+
+ align:start position:0%
+electrical signals from the base of your
+spine to your foot so rapidly okay so
+
+ align:start position:0%
+spine to your foot so rapidly okay so
+ 
+
+ align:start position:0%
+spine to your foot so rapidly okay so
+you get an increase in speed because the
+
+ align:start position:0%
+you get an increase in speed because the
+ 
+
+ align:start position:0%
+you get an increase in speed because the
+action potential is jumping from node to
+
+ align:start position:0%
+action potential is jumping from node to
+ 
+
+ align:start position:0%
+action potential is jumping from node to
+node and one important reason to bring
+
+ align:start position:0%
+node and one important reason to bring
+ 
+
+ align:start position:0%
+node and one important reason to bring
+this up is because there is a an
+
+ align:start position:0%
+this up is because there is a an
+ 
+
+ align:start position:0%
+this up is because there is a an
+important human disease that affects the
+
+ align:start position:0%
+important human disease that affects the
+ 
+
+ align:start position:0%
+important human disease that affects the
+electrical insulation in the myelin
+
+ align:start position:0%
+electrical insulation in the myelin
+ 
+
+ align:start position:0%
+electrical insulation in the myelin
+sheath here and that's multiple
+
+ align:start position:0%
+sheath here and that's multiple
+ 
+
+ align:start position:0%
+sheath here and that's multiple
+sclerosis so we're gonna unpack multiple
+
+ align:start position:0%
+sclerosis so we're gonna unpack multiple
+ 
+
+ align:start position:0%
+sclerosis so we're gonna unpack multiple
+sclerosis in a couple lectures this is
+
+ align:start position:0%
+sclerosis in a couple lectures this is
+ 
+
+ align:start position:0%
+sclerosis in a couple lectures this is
+an autoimmune disorder and so we're
+
+ align:start position:0%
+an autoimmune disorder and so we're
+ 
+
+ align:start position:0%
+an autoimmune disorder and so we're
+going to talk about immunity later in
+
+ align:start position:0%
+going to talk about immunity later in
+ 
+
+ align:start position:0%
+going to talk about immunity later in
+the semester and we'll talk about how
+
+ align:start position:0%
+the semester and we'll talk about how
+ 
+
+ align:start position:0%
+the semester and we'll talk about how
+that happens but for now I just want to
+
+ align:start position:0%
+that happens but for now I just want to
+ 
+
+ align:start position:0%
+that happens but for now I just want to
+point out that multiple sclerosis
+
+ align:start position:0%
+point out that multiple sclerosis
+ 
+
+ align:start position:0%
+point out that multiple sclerosis
+happens when the immune system attacks
+
+ align:start position:0%
+happens when the immune system attacks
+ 
+
+ align:start position:0%
+happens when the immune system attacks
+this myelin sheath so in multiple
+
+ align:start position:0%
+this myelin sheath so in multiple
+ 
+
+ align:start position:0%
+this myelin sheath so in multiple
+sclerosis the myelin sheath is damaged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if you damage this electrical
+
+ align:start position:0%
+okay and if you damage this electrical
+ 
+
+ align:start position:0%
+okay and if you damage this electrical
+insulation
+
+ align:start position:0%
+insulation
+ 
+
+ align:start position:0%
+insulation
+you greatly slow down these action
+
+ align:start position:0%
+you greatly slow down these action
+ 
+
+ align:start position:0%
+you greatly slow down these action
+potentials and that has a significant
+
+ align:start position:0%
+potentials and that has a significant
+ 
+
+ align:start position:0%
+potentials and that has a significant
+impact on nerve
+
+ align:start position:0%
+impact on nerve
+ 
+
+ align:start position:0%
+impact on nerve
+pulses in the brain and throughout the
+
+ align:start position:0%
+pulses in the brain and throughout the
+ 
+
+ align:start position:0%
+pulses in the brain and throughout the
+entire body and that's why multiple
+
+ align:start position:0%
+entire body and that's why multiple
+ 
+
+ align:start position:0%
+entire body and that's why multiple
+sclerosis is such a devastating disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right I'm gonna start moving now to
+
+ align:start position:0%
+all right I'm gonna start moving now to
+ 
+
+ align:start position:0%
+all right I'm gonna start moving now to
+consider one more than one neuron so
+
+ align:start position:0%
+consider one more than one neuron so
+ 
+
+ align:start position:0%
+consider one more than one neuron so
+until now we've just talked about how an
+
+ align:start position:0%
+until now we've just talked about how an
+ 
+
+ align:start position:0%
+until now we've just talked about how an
+electrical signal is sent along the
+
+ align:start position:0%
+electrical signal is sent along the
+ 
+
+ align:start position:0%
+electrical signal is sent along the
+length of one cell and now we're gonna
+
+ align:start position:0%
+length of one cell and now we're gonna
+ 
+
+ align:start position:0%
+length of one cell and now we're gonna
+start thinking about multiple neurons
+
+ align:start position:0%
+start thinking about multiple neurons
+ 
+
+ align:start position:0%
+start thinking about multiple neurons
+and how they connect and how neurons
+
+ align:start position:0%
+and how they connect and how neurons
+ 
+
+ align:start position:0%
+and how they connect and how neurons
+integrate information from multiple
+
+ align:start position:0%
+integrate information from multiple
+ 
+
+ align:start position:0%
+integrate information from multiple
+other neurons to decide whether or not
+
+ align:start position:0%
+other neurons to decide whether or not
+ 
+
+ align:start position:0%
+other neurons to decide whether or not
+to send an action potential okay and so
+
+ align:start position:0%
+to send an action potential okay and so
+ 
+
+ align:start position:0%
+to send an action potential okay and so
+if we consider this connection right
+
+ align:start position:0%
+if we consider this connection right
+ 
+
+ align:start position:0%
+if we consider this connection right
+here there's a synapse right here here's
+
+ align:start position:0%
+here there's a synapse right here here's
+ 
+
+ align:start position:0%
+here there's a synapse right here here's
+a sending a cell that's sending
+
+ align:start position:0%
+a sending a cell that's sending
+ 
+
+ align:start position:0%
+a sending a cell that's sending
+information in the cell that is
+
+ align:start position:0%
+information in the cell that is
+ 
+
+ align:start position:0%
+information in the cell that is
+receiving that information when we're
+
+ align:start position:0%
+receiving that information when we're
+ 
+
+ align:start position:0%
+receiving that information when we're
+considering a synapse so if we consider
+
+ align:start position:0%
+considering a synapse so if we consider
+ 
+
+ align:start position:0%
+considering a synapse so if we consider
+a synapse there's a cell that is sending
+
+ align:start position:0%
+a synapse there's a cell that is sending
+ 
+
+ align:start position:0%
+a synapse there's a cell that is sending
+the signal which is called the pre
+
+ align:start position:0%
+the signal which is called the pre
+ 
+
+ align:start position:0%
+the signal which is called the pre
+synapse this is the sender cell and
+
+ align:start position:0%
+synapse this is the sender cell and
+ 
+
+ align:start position:0%
+synapse this is the sender cell and
+there's a postsynaptic cell okay but you
+
+ align:start position:0%
+there's a postsynaptic cell okay but you
+ 
+
+ align:start position:0%
+there's a postsynaptic cell okay but you
+can have more than one neuron sending a
+
+ align:start position:0%
+can have more than one neuron sending a
+ 
+
+ align:start position:0%
+can have more than one neuron sending a
+signal to a neuron at this at a given
+
+ align:start position:0%
+signal to a neuron at this at a given
+ 
+
+ align:start position:0%
+signal to a neuron at this at a given
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+right so here you have one neuron there
+
+ align:start position:0%
+right so here you have one neuron there
+ 
+
+ align:start position:0%
+right so here you have one neuron there
+it's sending a signal at this synapse
+
+ align:start position:0%
+it's sending a signal at this synapse
+ 
+
+ align:start position:0%
+it's sending a signal at this synapse
+but you might have another neuron
+
+ align:start position:0%
+but you might have another neuron
+ 
+
+ align:start position:0%
+but you might have another neuron
+sending a signal to a synapse on this
+
+ align:start position:0%
+sending a signal to a synapse on this
+ 
+
+ align:start position:0%
+sending a signal to a synapse on this
+part of the cell and you could have
+
+ align:start position:0%
+part of the cell and you could have
+ 
+
+ align:start position:0%
+part of the cell and you could have
+another signal coming in here and so
+
+ align:start position:0%
+another signal coming in here and so
+ 
+
+ align:start position:0%
+another signal coming in here and so
+this this neuron will then have to
+
+ align:start position:0%
+this this neuron will then have to
+ 
+
+ align:start position:0%
+this this neuron will then have to
+decide whether or not to fire an action
+
+ align:start position:0%
+decide whether or not to fire an action
+ 
+
+ align:start position:0%
+decide whether or not to fire an action
+potential down its axon okay and the way
+
+ align:start position:0%
+potential down its axon okay and the way
+ 
+
+ align:start position:0%
+potential down its axon okay and the way
+that the neuron decides this is to
+
+ align:start position:0%
+that the neuron decides this is to
+ 
+
+ align:start position:0%
+that the neuron decides this is to
+integrate the signals so there's a
+
+ align:start position:0%
+integrate the signals so there's a
+ 
+
+ align:start position:0%
+integrate the signals so there's a
+signal integration process and what's
+
+ align:start position:0%
+signal integration process and what's
+ 
+
+ align:start position:0%
+signal integration process and what's
+important for signal integration in a
+
+ align:start position:0%
+important for signal integration in a
+ 
+
+ align:start position:0%
+important for signal integration in a
+neuron is whether or not the cell body
+
+ align:start position:0%
+neuron is whether or not the cell body
+ 
+
+ align:start position:0%
+neuron is whether or not the cell body
+whether the voltage increases above a
+
+ align:start position:0%
+whether the voltage increases above a
+ 
+
+ align:start position:0%
+whether the voltage increases above a
+certain threshold potential so if the
+
+ align:start position:0%
+certain threshold potential so if the
+ 
+
+ align:start position:0%
+certain threshold potential so if the
+cell body doesn't increase if the
+
+ align:start position:0%
+cell body doesn't increase if the
+ 
+
+ align:start position:0%
+cell body doesn't increase if the
+voltage doesn't increase
+
+ align:start position:0%
+voltage doesn't increase
+ 
+
+ align:start position:0%
+voltage doesn't increase
+above this potential there will be no
+
+ align:start position:0%
+above this potential there will be no
+ 
+
+ align:start position:0%
+above this potential there will be no
+action potential fired but if the action
+
+ align:start position:0%
+action potential fired but if the action
+ 
+
+ align:start position:0%
+action potential fired but if the action
+if the voltage increases above the
+
+ align:start position:0%
+if the voltage increases above the
+ 
+
+ align:start position:0%
+if the voltage increases above the
+threshold potential then it fires the
+
+ align:start position:0%
+threshold potential then it fires the
+ 
+
+ align:start position:0%
+threshold potential then it fires the
+action potential and signals to a
+
+ align:start position:0%
+action potential and signals to a
+ 
+
+ align:start position:0%
+action potential and signals to a
+downstream neuron or muscle or another
+
+ align:start position:0%
+downstream neuron or muscle or another
+ 
+
+ align:start position:0%
+downstream neuron or muscle or another
+cell okay so here it is the threshold
+
+ align:start position:0%
+cell okay so here it is the threshold
+ 
+
+ align:start position:0%
+cell okay so here it is the threshold
+potential in the cell body that
+
+ align:start position:0%
+potential in the cell body that
+ 
+
+ align:start position:0%
+potential in the cell body that
+determines whether or not an action
+
+ align:start position:0%
+determines whether or not an action
+ 
+
+ align:start position:0%
+determines whether or not an action
+potential is sent down the axon okay and
+
+ align:start position:0%
+potential is sent down the axon okay and
+ 
+
+ align:start position:0%
+potential is sent down the axon okay and
+there are different types of signals
+
+ align:start position:0%
+there are different types of signals
+ 
+
+ align:start position:0%
+there are different types of signals
+that nerve cells can send so there are
+
+ align:start position:0%
+that nerve cells can send so there are
+ 
+
+ align:start position:0%
+that nerve cells can send so there are
+different types of signals signals can
+
+ align:start position:0%
+different types of signals signals can
+ 
+
+ align:start position:0%
+different types of signals signals can
+be excitatory meaning it deep will tend
+
+ align:start position:0%
+be excitatory meaning it deep will tend
+ 
+
+ align:start position:0%
+be excitatory meaning it deep will tend
+to depolarize the neuron so there are
+
+ align:start position:0%
+to depolarize the neuron so there are
+ 
+
+ align:start position:0%
+to depolarize the neuron so there are
+excitatory signals which results in
+
+ align:start position:0%
+excitatory signals which results in
+ 
+
+ align:start position:0%
+excitatory signals which results in
+depolarization for example with
+
+ align:start position:0%
+depolarization for example with
+ 
+
+ align:start position:0%
+depolarization for example with
+serotonin that opens a sodium channel
+
+ align:start position:0%
+serotonin that opens a sodium channel
+ 
+
+ align:start position:0%
+serotonin that opens a sodium channel
+and that results in depolarization so
+
+ align:start position:0%
+and that results in depolarization so
+ 
+
+ align:start position:0%
+and that results in depolarization so
+that's an excitatory signal but there
+
+ align:start position:0%
+that's an excitatory signal but there
+ 
+
+ align:start position:0%
+that's an excitatory signal but there
+are other types of signals that bind to
+
+ align:start position:0%
+are other types of signals that bind to
+ 
+
+ align:start position:0%
+are other types of signals that bind to
+different types of receptors that are
+
+ align:start position:0%
+different types of receptors that are
+ 
+
+ align:start position:0%
+different types of receptors that are
+inhibitory what might be a type of
+
+ align:start position:0%
+inhibitory what might be a type of
+ 
+
+ align:start position:0%
+inhibitory what might be a type of
+receptor that would inhibit this process
+
+ align:start position:0%
+receptor that would inhibit this process
+ 
+
+ align:start position:0%
+receptor that would inhibit this process
+of sending an action potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what might an inhibitory receptor be to
+
+ align:start position:0%
+what might an inhibitory receptor be to
+ 
+
+ align:start position:0%
+what might an inhibitory receptor be to
+make sure to lower the chance that this
+
+ align:start position:0%
+make sure to lower the chance that this
+ 
+
+ align:start position:0%
+make sure to lower the chance that this
+action potential will be fired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what if I told you it's it's an ion
+
+ align:start position:0%
+what if I told you it's it's an ion
+ 
+
+ align:start position:0%
+what if I told you it's it's an ion
+channel what ion would you expect it
+
+ align:start position:0%
+channel what ion would you expect it
+ 
+
+ align:start position:0%
+channel what ion would you expect it
+might pass pseudo
+
+ align:start position:0%
+might pass pseudo
+ 
+
+ align:start position:0%
+might pass pseudo
+potassium Uno is exactly right right if
+
+ align:start position:0%
+potassium Uno is exactly right right if
+ 
+
+ align:start position:0%
+potassium Uno is exactly right right if
+you test if it passes potassium then
+
+ align:start position:0%
+you test if it passes potassium then
+ 
+
+ align:start position:0%
+you test if it passes potassium then
+it's gonna it's gonna make the inside
+
+ align:start position:0%
+it's gonna it's gonna make the inside
+ 
+
+ align:start position:0%
+it's gonna it's gonna make the inside
+more negative and that's what's known as
+
+ align:start position:0%
+more negative and that's what's known as
+ 
+
+ align:start position:0%
+more negative and that's what's known as
+hyperpolarization so receptors that
+
+ align:start position:0%
+hyperpolarization so receptors that
+ 
+
+ align:start position:0%
+hyperpolarization so receptors that
+result in hyperpolarization would have
+
+ align:start position:0%
+result in hyperpolarization would have
+ 
+
+ align:start position:0%
+result in hyperpolarization would have
+an inhibitory effect on this process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right and remember if your
+
+ align:start position:0%
+okay right and remember if your
+ 
+
+ align:start position:0%
+okay right and remember if your
+hyperpolarizing then you're gonna you
+
+ align:start position:0%
+hyperpolarizing then you're gonna you
+ 
+
+ align:start position:0%
+hyperpolarizing then you're gonna you
+could cause this to actually go down and
+
+ align:start position:0%
+could cause this to actually go down and
+ 
+
+ align:start position:0%
+could cause this to actually go down and
+get even farther away from this
+
+ align:start position:0%
+get even farther away from this
+ 
+
+ align:start position:0%
+get even farther away from this
+threshold potential right and if you
+
+ align:start position:0%
+threshold potential right and if you
+ 
+
+ align:start position:0%
+threshold potential right and if you
+have an activating signal and an
+
+ align:start position:0%
+have an activating signal and an
+ 
+
+ align:start position:0%
+have an activating signal and an
+inhibitory signal they might cancel out
+
+ align:start position:0%
+inhibitory signal they might cancel out
+ 
+
+ align:start position:0%
+inhibitory signal they might cancel out
+because one will depolarize in the other
+
+ align:start position:0%
+because one will depolarize in the other
+ 
+
+ align:start position:0%
+because one will depolarize in the other
+will hyperpolarize so it's in this way
+
+ align:start position:0%
+will hyperpolarize so it's in this way
+ 
+
+ align:start position:0%
+will hyperpolarize so it's in this way
+and neuron is able to integrate signals
+
+ align:start position:0%
+and neuron is able to integrate signals
+ 
+
+ align:start position:0%
+and neuron is able to integrate signals
+coming from different neurons and that
+
+ align:start position:0%
+coming from different neurons and that
+ 
+
+ align:start position:0%
+coming from different neurons and that
+influences whether or not it will send
+
+ align:start position:0%
+influences whether or not it will send
+ 
+
+ align:start position:0%
+influences whether or not it will send
+the signal to a downstream a cell okay
+
+ align:start position:0%
+the signal to a downstream a cell okay
+ 
+
+ align:start position:0%
+the signal to a downstream a cell okay
+so now we're focusing on what is the
+
+ align:start position:0%
+so now we're focusing on what is the
+ 
+
+ align:start position:0%
+so now we're focusing on what is the
+communication between one neuron and
+
+ align:start position:0%
+communication between one neuron and
+ 
+
+ align:start position:0%
+communication between one neuron and
+another and this revolves around this
+
+ align:start position:0%
+another and this revolves around this
+ 
+
+ align:start position:0%
+another and this revolves around this
+thing that's called the synapse which is
+
+ align:start position:0%
+thing that's called the synapse which is
+ 
+
+ align:start position:0%
+thing that's called the synapse which is
+basically the gap between the axon
+
+ align:start position:0%
+basically the gap between the axon
+ 
+
+ align:start position:0%
+basically the gap between the axon
+terminal of one neuron and the dendrites
+
+ align:start position:0%
+terminal of one neuron and the dendrites
+ 
+
+ align:start position:0%
+terminal of one neuron and the dendrites
+of a postsynaptic neuron okay and so the
+
+ align:start position:0%
+of a postsynaptic neuron okay and so the
+ 
+
+ align:start position:0%
+of a postsynaptic neuron okay and so the
+way that multiple neurons communicate
+
+ align:start position:0%
+way that multiple neurons communicate
+ 
+
+ align:start position:0%
+way that multiple neurons communicate
+with each other are through a type of
+
+ align:start position:0%
+with each other are through a type of
+ 
+
+ align:start position:0%
+with each other are through a type of
+signal known as a neurotransmitter okay
+
+ align:start position:0%
+signal known as a neurotransmitter okay
+ 
+
+ align:start position:0%
+signal known as a neurotransmitter okay
+and this is what initiates the signal so
+
+ align:start position:0%
+and this is what initiates the signal so
+ 
+
+ align:start position:0%
+and this is what initiates the signal so
+there's a signal initiation process at
+
+ align:start position:0%
+there's a signal initiation process at
+ 
+
+ align:start position:0%
+there's a signal initiation process at
+the synapse initiation and then this
+
+ align:start position:0%
+the synapse initiation and then this
+ 
+
+ align:start position:0%
+the synapse initiation and then this
+involves the presynaptic neuron
+
+ align:start position:0%
+involves the presynaptic neuron
+ 
+
+ align:start position:0%
+involves the presynaptic neuron
+secreting a neurotransmitter so the
+
+ align:start position:0%
+secreting a neurotransmitter so the
+ 
+
+ align:start position:0%
+secreting a neurotransmitter so the
+signal in this case signals between
+
+ align:start position:0%
+signal in this case signals between
+ 
+
+ align:start position:0%
+signal in this case signals between
+neurons are called neurotransmitters and
+
+ align:start position:0%
+neurons are called neurotransmitters and
+ 
+
+ align:start position:0%
+neurons are called neurotransmitters and
+as you see on the slide these are
+
+ align:start position:0%
+as you see on the slide these are
+ 
+
+ align:start position:0%
+as you see on the slide these are
+examples of neurotransmitters they're
+
+ align:start position:0%
+examples of neurotransmitters they're
+ 
+
+ align:start position:0%
+examples of neurotransmitters they're
+often derived from amino acids and so
+
+ align:start position:0%
+often derived from amino acids and so
+ 
+
+ align:start position:0%
+often derived from amino acids and so
+there's small molecules they're not the
+
+ align:start position:0%
+there's small molecules they're not the
+ 
+
+ align:start position:0%
+there's small molecules they're not the
+proteins that you often see with
+
+ align:start position:0%
+proteins that you often see with
+ 
+
+ align:start position:0%
+proteins that you often see with
+receptor tyrosine kinase ligands this is
+
+ align:start position:0%
+receptor tyrosine kinase ligands this is
+ 
+
+ align:start position:0%
+receptor tyrosine kinase ligands this is
+a different class of signal
+
+ align:start position:0%
+a different class of signal
+ 
+
+ align:start position:0%
+a different class of signal
+so one example is serotonin and if you
+
+ align:start position:0%
+so one example is serotonin and if you
+ 
+
+ align:start position:0%
+so one example is serotonin and if you
+look up at those will find serotonin
+
+ align:start position:0%
+look up at those will find serotonin
+ 
+
+ align:start position:0%
+look up at those will find serotonin
+here there it is here you can see it's a
+
+ align:start position:0%
+here there it is here you can see it's a
+ 
+
+ align:start position:0%
+here there it is here you can see it's a
+derivative of tryptophan okay so it's a
+
+ align:start position:0%
+derivative of tryptophan okay so it's a
+ 
+
+ align:start position:0%
+derivative of tryptophan okay so it's a
+small molecule and it's able to bind to
+
+ align:start position:0%
+small molecule and it's able to bind to
+ 
+
+ align:start position:0%
+small molecule and it's able to bind to
+a receptor on the postsynaptic cell and
+
+ align:start position:0%
+a receptor on the postsynaptic cell and
+ 
+
+ align:start position:0%
+a receptor on the postsynaptic cell and
+induce depolarization okay and so
+
+ align:start position:0%
+induce depolarization okay and so
+ 
+
+ align:start position:0%
+induce depolarization okay and so
+neurons are the way that they
+
+ align:start position:0%
+neurons are the way that they
+ 
+
+ align:start position:0%
+neurons are the way that they
+communicate as neurons are a case of
+
+ align:start position:0%
+communicate as neurons are a case of
+ 
+
+ align:start position:0%
+communicate as neurons are a case of
+where luck favors the prepared
+
+ align:start position:0%
+where luck favors the prepared
+ 
+
+ align:start position:0%
+where luck favors the prepared
+neurons are totally prepared to send
+
+ align:start position:0%
+neurons are totally prepared to send
+ 
+
+ align:start position:0%
+neurons are totally prepared to send
+signals to each other they have
+
+ align:start position:0%
+signals to each other they have
+ 
+
+ align:start position:0%
+signals to each other they have
+everything ready to go when they get
+
+ align:start position:0%
+everything ready to go when they get
+ 
+
+ align:start position:0%
+everything ready to go when they get
+word from from upstream and they're
+
+ align:start position:0%
+word from from upstream and they're
+ 
+
+ align:start position:0%
+word from from upstream and they're
+ready to send signals to their next cell
+
+ align:start position:0%
+ready to send signals to their next cell
+ 
+
+ align:start position:0%
+ready to send signals to their next cell
+okay and that's because if we look at
+
+ align:start position:0%
+okay and that's because if we look at
+ 
+
+ align:start position:0%
+okay and that's because if we look at
+the synapse prior to an action potential
+
+ align:start position:0%
+the synapse prior to an action potential
+ 
+
+ align:start position:0%
+the synapse prior to an action potential
+everything is ready to go
+
+ align:start position:0%
+everything is ready to go
+ 
+
+ align:start position:0%
+everything is ready to go
+the cell has neurotransmitter and it's
+
+ align:start position:0%
+the cell has neurotransmitter and it's
+ 
+
+ align:start position:0%
+the cell has neurotransmitter and it's
+packaged in these vesicles and it's
+
+ align:start position:0%
+packaged in these vesicles and it's
+ 
+
+ align:start position:0%
+packaged in these vesicles and it's
+tethered to the plasma membrane ready to
+
+ align:start position:0%
+tethered to the plasma membrane ready to
+ 
+
+ align:start position:0%
+tethered to the plasma membrane ready to
+be released
+
+ align:start position:0%
+be released
+ 
+
+ align:start position:0%
+be released
+okay so prior to the action potential
+
+ align:start position:0%
+okay so prior to the action potential
+ 
+
+ align:start position:0%
+okay so prior to the action potential
+there are vesicles filled with
+
+ align:start position:0%
+there are vesicles filled with
+ 
+
+ align:start position:0%
+there are vesicles filled with
+neurotransmitter that are docked at the
+
+ align:start position:0%
+neurotransmitter that are docked at the
+ 
+
+ align:start position:0%
+neurotransmitter that are docked at the
+plasma membrane I abbreviate plasma
+
+ align:start position:0%
+plasma membrane I abbreviate plasma
+ 
+
+ align:start position:0%
+plasma membrane I abbreviate plasma
+membrane p.m. just so I don't have to
+
+ align:start position:0%
+membrane p.m. just so I don't have to
+ 
+
+ align:start position:0%
+membrane p.m. just so I don't have to
+write it out okay so these contain
+
+ align:start position:0%
+write it out okay so these contain
+ 
+
+ align:start position:0%
+write it out okay so these contain
+neurotransmitter right but you see in
+
+ align:start position:0%
+neurotransmitter right but you see in
+ 
+
+ align:start position:0%
+neurotransmitter right but you see in
+this dock vesicle the neurotransmitter
+
+ align:start position:0%
+this dock vesicle the neurotransmitter
+ 
+
+ align:start position:0%
+this dock vesicle the neurotransmitter
+is in red and it can't get out if that
+
+ align:start position:0%
+is in red and it can't get out if that
+ 
+
+ align:start position:0%
+is in red and it can't get out if that
+vesicle does not fuse with the plasma
+
+ align:start position:0%
+vesicle does not fuse with the plasma
+ 
+
+ align:start position:0%
+vesicle does not fuse with the plasma
+membrane okay so these contain
+
+ align:start position:0%
+membrane okay so these contain
+ 
+
+ align:start position:0%
+membrane okay so these contain
+neurotransmitter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but at this point the vesicles have
+
+ align:start position:0%
+but at this point the vesicles have
+ 
+
+ align:start position:0%
+but at this point the vesicles have
+infused but the vesicles not fused okay
+
+ align:start position:0%
+infused but the vesicles not fused okay
+ 
+
+ align:start position:0%
+infused but the vesicles not fused okay
+when should they fuse in this system of
+
+ align:start position:0%
+when should they fuse in this system of
+ 
+
+ align:start position:0%
+when should they fuse in this system of
+neurons signaling to each other when
+
+ align:start position:0%
+neurons signaling to each other when
+ 
+
+ align:start position:0%
+neurons signaling to each other when
+should these the vesicle fused with the
+
+ align:start position:0%
+should these the vesicle fused with the
+ 
+
+ align:start position:0%
+should these the vesicle fused with the
+plasma membrane
+
+ align:start position:0%
+plasma membrane
+ 
+
+ align:start position:0%
+plasma membrane
+what should trigger the fusion process
+
+ align:start position:0%
+what should trigger the fusion process
+ 
+
+ align:start position:0%
+what should trigger the fusion process
+yes miles yeah so miles is exactly right
+
+ align:start position:0%
+yes miles yeah so miles is exactly right
+ 
+
+ align:start position:0%
+yes miles yeah so miles is exactly right
+right if we consider my diagram here
+
+ align:start position:0%
+right if we consider my diagram here
+ 
+
+ align:start position:0%
+right if we consider my diagram here
+right there's an action potential
+
+ align:start position:0%
+right there's an action potential
+ 
+
+ align:start position:0%
+right there's an action potential
+traveling along this axon when it gets
+
+ align:start position:0%
+traveling along this axon when it gets
+ 
+
+ align:start position:0%
+traveling along this axon when it gets
+to the axon terminus that should be that
+
+ align:start position:0%
+to the axon terminus that should be that
+ 
+
+ align:start position:0%
+to the axon terminus that should be that
+fits the signal for these vesicles
+
+ align:start position:0%
+fits the signal for these vesicles
+ 
+
+ align:start position:0%
+fits the signal for these vesicles
+diffuse to the plasma membrane and to
+
+ align:start position:0%
+diffuse to the plasma membrane and to
+ 
+
+ align:start position:0%
+diffuse to the plasma membrane and to
+release neurotransmitter okay so the
+
+ align:start position:0%
+release neurotransmitter okay so the
+ 
+
+ align:start position:0%
+release neurotransmitter okay so the
+arrival of the action potential right so
+
+ align:start position:0%
+arrival of the action potential right so
+ 
+
+ align:start position:0%
+arrival of the action potential right so
+remember so in this case serotonin is
+
+ align:start position:0%
+remember so in this case serotonin is
+ 
+
+ align:start position:0%
+remember so in this case serotonin is
+going to be in blue right if serotonin
+
+ align:start position:0%
+going to be in blue right if serotonin
+ 
+
+ align:start position:0%
+going to be in blue right if serotonin
+is inside my vesicle here is going to
+
+ align:start position:0%
+is inside my vesicle here is going to
+ 
+
+ align:start position:0%
+is inside my vesicle here is going to
+need to exocytosis and now the serotonin
+
+ align:start position:0%
+need to exocytosis and now the serotonin
+ 
+
+ align:start position:0%
+need to exocytosis and now the serotonin
+is going to be outside the cell ready to
+
+ align:start position:0%
+is going to be outside the cell ready to
+ 
+
+ align:start position:0%
+is going to be outside the cell ready to
+bind to the receptor okay all right so
+
+ align:start position:0%
+bind to the receptor okay all right so
+ 
+
+ align:start position:0%
+bind to the receptor okay all right so
+as Miles pointed out you have an action
+
+ align:start position:0%
+as Miles pointed out you have an action
+ 
+
+ align:start position:0%
+as Miles pointed out you have an action
+potential the fusion should be triggered
+
+ align:start position:0%
+potential the fusion should be triggered
+ 
+
+ align:start position:0%
+potential the fusion should be triggered
+by the action potential in order to fuse
+
+ align:start position:0%
+by the action potential in order to fuse
+ 
+
+ align:start position:0%
+by the action potential in order to fuse
+there needs to be some signal inside the
+
+ align:start position:0%
+there needs to be some signal inside the
+ 
+
+ align:start position:0%
+there needs to be some signal inside the
+cytoplasm to tell the vesicle to fuse
+
+ align:start position:0%
+cytoplasm to tell the vesicle to fuse
+ 
+
+ align:start position:0%
+cytoplasm to tell the vesicle to fuse
+that signal is increased calcium ion
+
+ align:start position:0%
+that signal is increased calcium ion
+ 
+
+ align:start position:0%
+that signal is increased calcium ion
+concentration and then when calcium
+
+ align:start position:0%
+concentration and then when calcium
+ 
+
+ align:start position:0%
+concentration and then when calcium
+concentration increases in the cytoplasm
+
+ align:start position:0%
+concentration increases in the cytoplasm
+ 
+
+ align:start position:0%
+concentration increases in the cytoplasm
+that triggers the fusion of these
+
+ align:start position:0%
+that triggers the fusion of these
+ 
+
+ align:start position:0%
+that triggers the fusion of these
+vesicles and when you get fusion there's
+
+ align:start position:0%
+vesicles and when you get fusion there's
+ 
+
+ align:start position:0%
+vesicles and when you get fusion there's
+that's exocytosis and the serotonin is
+
+ align:start position:0%
+that's exocytosis and the serotonin is
+ 
+
+ align:start position:0%
+that's exocytosis and the serotonin is
+now on the outside of the cell where it
+
+ align:start position:0%
+now on the outside of the cell where it
+ 
+
+ align:start position:0%
+now on the outside of the cell where it
+can travel across the synaptic
+
+ align:start position:0%
+can travel across the synaptic
+ 
+
+ align:start position:0%
+can travel across the synaptic
+and bind to a receptor on the
+
+ align:start position:0%
+and bind to a receptor on the
+ 
+
+ align:start position:0%
+and bind to a receptor on the
+postsynaptic neuron okay so this fusion
+
+ align:start position:0%
+postsynaptic neuron okay so this fusion
+ 
+
+ align:start position:0%
+postsynaptic neuron okay so this fusion
+is when neurotransmitter is released
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neurotransmitter is released here okay
+
+ align:start position:0%
+neurotransmitter is released here okay
+ 
+
+ align:start position:0%
+neurotransmitter is released here okay
+in the way that this increasing calcium
+
+ align:start position:0%
+in the way that this increasing calcium
+ 
+
+ align:start position:0%
+in the way that this increasing calcium
+has to happen when the action potential
+
+ align:start position:0%
+has to happen when the action potential
+ 
+
+ align:start position:0%
+has to happen when the action potential
+arrives at the axon terminus so when it
+
+ align:start position:0%
+arrives at the axon terminus so when it
+ 
+
+ align:start position:0%
+arrives at the axon terminus so when it
+arrives in the axon terminus there's
+
+ align:start position:0%
+arrives in the axon terminus there's
+ 
+
+ align:start position:0%
+arrives in the axon terminus there's
+depolarization of that part of the cell
+
+ align:start position:0%
+depolarization of that part of the cell
+ 
+
+ align:start position:0%
+depolarization of that part of the cell
+and so there's a special type of protein
+
+ align:start position:0%
+and so there's a special type of protein
+ 
+
+ align:start position:0%
+and so there's a special type of protein
+called a voltage-gated calcium channel
+
+ align:start position:0%
+called a voltage-gated calcium channel
+ 
+
+ align:start position:0%
+called a voltage-gated calcium channel
+right these all these channels are very
+
+ align:start position:0%
+right these all these channels are very
+ 
+
+ align:start position:0%
+right these all these channels are very
+selective for different ions so a
+
+ align:start position:0%
+selective for different ions so a
+ 
+
+ align:start position:0%
+selective for different ions so a
+voltage-gated sodium channel isn't
+
+ align:start position:0%
+voltage-gated sodium channel isn't
+ 
+
+ align:start position:0%
+voltage-gated sodium channel isn't
+letting in all the ions outside the cell
+
+ align:start position:0%
+letting in all the ions outside the cell
+ 
+
+ align:start position:0%
+letting in all the ions outside the cell
+it's selective to sodium and this case
+
+ align:start position:0%
+it's selective to sodium and this case
+ 
+
+ align:start position:0%
+it's selective to sodium and this case
+this voltage-gated calcium channel is
+
+ align:start position:0%
+this voltage-gated calcium channel is
+ 
+
+ align:start position:0%
+this voltage-gated calcium channel is
+just gonna let in calcium and then
+
+ align:start position:0%
+just gonna let in calcium and then
+ 
+
+ align:start position:0%
+just gonna let in calcium and then
+there's a mechanism that links calcium
+
+ align:start position:0%
+there's a mechanism that links calcium
+ 
+
+ align:start position:0%
+there's a mechanism that links calcium
+entry to vesicle fusion and that's going
+
+ align:start position:0%
+entry to vesicle fusion and that's going
+ 
+
+ align:start position:0%
+entry to vesicle fusion and that's going
+to be shown here what you see on this
+
+ align:start position:0%
+to be shown here what you see on this
+ 
+
+ align:start position:0%
+to be shown here what you see on this
+docked synaptic vesicle is this calcium
+
+ align:start position:0%
+docked synaptic vesicle is this calcium
+ 
+
+ align:start position:0%
+docked synaptic vesicle is this calcium
+binding protein called sanic
+
+ align:start position:0%
+binding protein called sanic
+ 
+
+ align:start position:0%
+binding protein called sanic
+synaptotagmin that's present on the
+
+ align:start position:0%
+synaptotagmin that's present on the
+ 
+
+ align:start position:0%
+synaptotagmin that's present on the
+vesicle and so when calcium goes into
+
+ align:start position:0%
+vesicle and so when calcium goes into
+ 
+
+ align:start position:0%
+vesicle and so when calcium goes into
+the cytoplasm that protein binds to
+
+ align:start position:0%
+the cytoplasm that protein binds to
+ 
+
+ align:start position:0%
+the cytoplasm that protein binds to
+calcium and it activates the fusion
+
+ align:start position:0%
+calcium and it activates the fusion
+ 
+
+ align:start position:0%
+calcium and it activates the fusion
+machinery such that the plasma membrane
+
+ align:start position:0%
+machinery such that the plasma membrane
+ 
+
+ align:start position:0%
+machinery such that the plasma membrane
+of the vesicle fuses or the membrane of
+
+ align:start position:0%
+of the vesicle fuses or the membrane of
+ 
+
+ align:start position:0%
+of the vesicle fuses or the membrane of
+the vesicle fuses with the plasma
+
+ align:start position:0%
+the vesicle fuses with the plasma
+ 
+
+ align:start position:0%
+the vesicle fuses with the plasma
+membrane of the cell thus releasing the
+
+ align:start position:0%
+membrane of the cell thus releasing the
+ 
+
+ align:start position:0%
+membrane of the cell thus releasing the
+neurotransmitter into the synaptic cleft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is this is what starts the
+
+ align:start position:0%
+okay so this is this is what starts the
+ 
+
+ align:start position:0%
+okay so this is this is what starts the
+signal now you probably know that you're
+
+ align:start position:0%
+signal now you probably know that you're
+ 
+
+ align:start position:0%
+signal now you probably know that you're
+you're these neurons are not active or
+
+ align:start position:0%
+you're these neurons are not active or
+ 
+
+ align:start position:0%
+you're these neurons are not active or
+on all the time so something has to
+
+ align:start position:0%
+on all the time so something has to
+ 
+
+ align:start position:0%
+on all the time so something has to
+terminate the signal usually quite
+
+ align:start position:0%
+terminate the signal usually quite
+ 
+
+ align:start position:0%
+terminate the signal usually quite
+rapidly okay so now I want to talk about
+
+ align:start position:0%
+rapidly okay so now I want to talk about
+ 
+
+ align:start position:0%
+rapidly okay so now I want to talk about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so like all signaling pathways signaling
+
+ align:start position:0%
+so like all signaling pathways signaling
+ 
+
+ align:start position:0%
+so like all signaling pathways signaling
+is useless if you can just turn it on
+
+ align:start position:0%
+is useless if you can just turn it on
+ 
+
+ align:start position:0%
+is useless if you can just turn it on
+you have to be able to toggle it on and
+
+ align:start position:0%
+you have to be able to toggle it on and
+ 
+
+ align:start position:0%
+you have to be able to toggle it on and
+off in order for biological systems to
+
+ align:start position:0%
+off in order for biological systems to
+ 
+
+ align:start position:0%
+off in order for biological systems to
+function properly right and that's the
+
+ align:start position:0%
+function properly right and that's the
+ 
+
+ align:start position:0%
+function properly right and that's the
+case with neurons if you just turn on a
+
+ align:start position:0%
+case with neurons if you just turn on a
+ 
+
+ align:start position:0%
+case with neurons if you just turn on a
+neuron and you don't have a way to turn
+
+ align:start position:0%
+neuron and you don't have a way to turn
+ 
+
+ align:start position:0%
+neuron and you don't have a way to turn
+it back off again then that's pretty
+
+ align:start position:0%
+it back off again then that's pretty
+ 
+
+ align:start position:0%
+it back off again then that's pretty
+useless okay and so we have to have a
+
+ align:start position:0%
+useless okay and so we have to have a
+ 
+
+ align:start position:0%
+useless okay and so we have to have a
+way to turn off the signal and if we
+
+ align:start position:0%
+way to turn off the signal and if we
+ 
+
+ align:start position:0%
+way to turn off the signal and if we
+consider the synapse this is the
+
+ align:start position:0%
+consider the synapse this is the
+ 
+
+ align:start position:0%
+consider the synapse this is the
+presynaptic neuron here I'm going to
+
+ align:start position:0%
+presynaptic neuron here I'm going to
+ 
+
+ align:start position:0%
+presynaptic neuron here I'm going to
+draw a postsynaptic neuron here and
+
+ align:start position:0%
+draw a postsynaptic neuron here and
+ 
+
+ align:start position:0%
+draw a postsynaptic neuron here and
+neurotransmitter is released by the
+
+ align:start position:0%
+neurotransmitter is released by the
+ 
+
+ align:start position:0%
+neurotransmitter is released by the
+presynaptic neuron this is the
+
+ align:start position:0%
+presynaptic neuron this is the
+ 
+
+ align:start position:0%
+presynaptic neuron this is the
+postsynaptic neuron here
+
+ align:start position:0%
+postsynaptic neuron here
+ 
+
+ align:start position:0%
+postsynaptic neuron here
+neurotransmitter is released into the
+
+ align:start position:0%
+neurotransmitter is released into the
+ 
+
+ align:start position:0%
+neurotransmitter is released into the
+synaptic cleft okay so this the region
+
+ align:start position:0%
+synaptic cleft okay so this the region
+ 
+
+ align:start position:0%
+synaptic cleft okay so this the region
+the sort of extracellular region between
+
+ align:start position:0%
+the sort of extracellular region between
+ 
+
+ align:start position:0%
+the sort of extracellular region between
+these two neurons is called the synaptic
+
+ align:start position:0%
+these two neurons is called the synaptic
+ 
+
+ align:start position:0%
+these two neurons is called the synaptic
+cleft so now the cell just dumped a
+
+ align:start position:0%
+cleft so now the cell just dumped a
+ 
+
+ align:start position:0%
+cleft so now the cell just dumped a
+whole buttload of neurotransmitter into
+
+ align:start position:0%
+whole buttload of neurotransmitter into
+ 
+
+ align:start position:0%
+whole buttload of neurotransmitter into
+the synaptic cleft right how is it going
+
+ align:start position:0%
+the synaptic cleft right how is it going
+ 
+
+ align:start position:0%
+the synaptic cleft right how is it going
+to turn this off what does it have to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah Stephen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so Stevens exactly right what Steven
+
+ align:start position:0%
+so Stevens exactly right what Steven
+ 
+
+ align:start position:0%
+so Stevens exactly right what Steven
+suggested is is there a way for the
+
+ align:start position:0%
+suggested is is there a way for the
+ 
+
+ align:start position:0%
+suggested is is there a way for the
+presynaptic neuron to reabsorb this
+
+ align:start position:0%
+presynaptic neuron to reabsorb this
+ 
+
+ align:start position:0%
+presynaptic neuron to reabsorb this
+neurotransmitter and thus recycle it
+
+ align:start position:0%
+neurotransmitter and thus recycle it
+ 
+
+ align:start position:0%
+neurotransmitter and thus recycle it
+okay and so there's so I could either
+
+ align:start position:0%
+okay and so there's so I could either
+ 
+
+ align:start position:0%
+okay and so there's so I could either
+reabsorb it or degrade the
+
+ align:start position:0%
+reabsorb it or degrade the
+ 
+
+ align:start position:0%
+reabsorb it or degrade the
+neurotransmitter it's a different
+
+ align:start position:0%
+neurotransmitter it's a different
+ 
+
+ align:start position:0%
+neurotransmitter it's a different
+process for different neurotransmitters
+
+ align:start position:0%
+process for different neurotransmitters
+ 
+
+ align:start position:0%
+process for different neurotransmitters
+for serotonin there are channels that
+
+ align:start position:0%
+for serotonin there are channels that
+ 
+
+ align:start position:0%
+for serotonin there are channels that
+are present in the plasma membrane and
+
+ align:start position:0%
+are present in the plasma membrane and
+ 
+
+ align:start position:0%
+are present in the plasma membrane and
+these mediate reuptake of the serotonin
+
+ align:start position:0%
+these mediate reuptake of the serotonin
+ 
+
+ align:start position:0%
+these mediate reuptake of the serotonin
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you have channels that are basically
+
+ align:start position:0%
+so you have channels that are basically
+ 
+
+ align:start position:0%
+so you have channels that are basically
+after the neurotransmitter is released
+
+ align:start position:0%
+after the neurotransmitter is released
+ 
+
+ align:start position:0%
+after the neurotransmitter is released
+it sucks the neurotransmitter back into
+
+ align:start position:0%
+it sucks the neurotransmitter back into
+ 
+
+ align:start position:0%
+it sucks the neurotransmitter back into
+the presynaptic cell such that it can
+
+ align:start position:0%
+the presynaptic cell such that it can
+ 
+
+ align:start position:0%
+the presynaptic cell such that it can
+then sort of reuse the neurotransmitter
+
+ align:start position:0%
+then sort of reuse the neurotransmitter
+ 
+
+ align:start position:0%
+then sort of reuse the neurotransmitter
+later on okay and so this process of
+
+ align:start position:0%
+later on okay and so this process of
+ 
+
+ align:start position:0%
+later on okay and so this process of
+reuptake highlights a very important or
+
+ align:start position:0%
+reuptake highlights a very important or
+ 
+
+ align:start position:0%
+reuptake highlights a very important or
+an important process that's been
+
+ align:start position:0%
+an important process that's been
+ 
+
+ align:start position:0%
+an important process that's been
+utilized by drug companies to create
+
+ align:start position:0%
+utilized by drug companies to create
+ 
+
+ align:start position:0%
+utilized by drug companies to create
+antidepressants so antidepressants like
+
+ align:start position:0%
+antidepressants so antidepressants like
+ 
+
+ align:start position:0%
+antidepressants so antidepressants like
+prozac and zoloft effect this reuptake
+
+ align:start position:0%
+prozac and zoloft effect this reuptake
+ 
+
+ align:start position:0%
+prozac and zoloft effect this reuptake
+process and what that does is it keeps
+
+ align:start position:0%
+process and what that does is it keeps
+ 
+
+ align:start position:0%
+process and what that does is it keeps
+the neurotransmitter in the synaptic
+
+ align:start position:0%
+the neurotransmitter in the synaptic
+ 
+
+ align:start position:0%
+the neurotransmitter in the synaptic
+cleft for longer such as it enhances the
+
+ align:start position:0%
+cleft for longer such as it enhances the
+ 
+
+ align:start position:0%
+cleft for longer such as it enhances the
+signaling and so the idea behind these
+
+ align:start position:0%
+signaling and so the idea behind these
+ 
+
+ align:start position:0%
+signaling and so the idea behind these
+drugs is that if you are suffering
+
+ align:start position:0%
+drugs is that if you are suffering
+ 
+
+ align:start position:0%
+drugs is that if you are suffering
+depression from a lack of serotonin then
+
+ align:start position:0%
+depression from a lack of serotonin then
+ 
+
+ align:start position:0%
+depression from a lack of serotonin then
+you can rescue that by preventing the
+
+ align:start position:0%
+you can rescue that by preventing the
+ 
+
+ align:start position:0%
+you can rescue that by preventing the
+rapid real take of the neurotransmitter
+
+ align:start position:0%
+rapid real take of the neurotransmitter
+ 
+
+ align:start position:0%
+rapid real take of the neurotransmitter
+into the cell after the synapse is
+
+ align:start position:0%
+into the cell after the synapse is
+ 
+
+ align:start position:0%
+into the cell after the synapse is
+stimulated and the neurotransmitter is
+
+ align:start position:0%
+stimulated and the neurotransmitter is
+ 
+
+ align:start position:0%
+stimulated and the neurotransmitter is
+released okay and so prozac Zoloft these
+
+ align:start position:0%
+released okay and so prozac Zoloft these
+ 
+
+ align:start position:0%
+released okay and so prozac Zoloft these
+are a class of drugs that are known as
+
+ align:start position:0%
+are a class of drugs that are known as
+ 
+
+ align:start position:0%
+are a class of drugs that are known as
+selective serotonin reuptake inhibitors
+
+ align:start position:0%
+selective serotonin reuptake inhibitors
+ 
+
+ align:start position:0%
+selective serotonin reuptake inhibitors
+serotonin reuptake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inhibitors it's kind of a mouthful
+
+ align:start position:0%
+inhibitors it's kind of a mouthful
+ 
+
+ align:start position:0%
+inhibitors it's kind of a mouthful
+this is abbreviated SSRIs okay but the
+
+ align:start position:0%
+this is abbreviated SSRIs okay but the
+ 
+
+ align:start position:0%
+this is abbreviated SSRIs okay but the
+way they function is to leave the
+
+ align:start position:0%
+way they function is to leave the
+ 
+
+ align:start position:0%
+way they function is to leave the
+neurotransmitter in the synaptic cleft
+
+ align:start position:0%
+neurotransmitter in the synaptic cleft
+ 
+
+ align:start position:0%
+neurotransmitter in the synaptic cleft
+for longer so that you enhance signaling
+
+ align:start position:0%
+for longer so that you enhance signaling
+ 
+
+ align:start position:0%
+for longer so that you enhance signaling
+even if you have low levels of the
+
+ align:start position:0%
+even if you have low levels of the
+ 
+
+ align:start position:0%
+even if you have low levels of the
+neurotransmitter to begin with I also
+
+ align:start position:0%
+neurotransmitter to begin with I also
+ 
+
+ align:start position:0%
+neurotransmitter to begin with I also
+want to point out that if we look at
+
+ align:start position:0%
+want to point out that if we look at
+ 
+
+ align:start position:0%
+want to point out that if we look at
+this diagram here the synaptic vesicle
+
+ align:start position:0%
+this diagram here the synaptic vesicle
+ 
+
+ align:start position:0%
+this diagram here the synaptic vesicle
+fuses and then this releases the
+
+ align:start position:0%
+fuses and then this releases the
+ 
+
+ align:start position:0%
+fuses and then this releases the
+neurotransmitter but all the machinery
+
+ align:start position:0%
+neurotransmitter but all the machinery
+ 
+
+ align:start position:0%
+neurotransmitter but all the machinery
+on this vesicle is recycled by
+
+ align:start position:0%
+on this vesicle is recycled by
+ 
+
+ align:start position:0%
+on this vesicle is recycled by
+endocytosis such that it can be reused
+
+ align:start position:0%
+endocytosis such that it can be reused
+ 
+
+ align:start position:0%
+endocytosis such that it can be reused
+again okay
+
+ align:start position:0%
+again okay
+ 
+
+ align:start position:0%
+again okay
+so cells are really good at recycling
+
+ align:start position:0%
+so cells are really good at recycling
+ 
+
+ align:start position:0%
+so cells are really good at recycling
+stuff right if this is sort of the
+
+ align:start position:0%
+stuff right if this is sort of the
+ 
+
+ align:start position:0%
+stuff right if this is sort of the
+membrane to you endocytosis and then you
+
+ align:start position:0%
+membrane to you endocytosis and then you
+ 
+
+ align:start position:0%
+membrane to you endocytosis and then you
+can use it again later on okay and so
+
+ align:start position:0%
+can use it again later on okay and so
+ 
+
+ align:start position:0%
+can use it again later on okay and so
+there's recycling not only of the
+
+ align:start position:0%
+there's recycling not only of the
+ 
+
+ align:start position:0%
+there's recycling not only of the
+neurotransmitter but also all of the
+
+ align:start position:0%
+neurotransmitter but also all of the
+ 
+
+ align:start position:0%
+neurotransmitter but also all of the
+machinery on these synaptic vesicles
+
+ align:start position:0%
+machinery on these synaptic vesicles
+ 
+
+ align:start position:0%
+machinery on these synaptic vesicles
+that are responsible for the fusion
+
+ align:start position:0%
+that are responsible for the fusion
+ 
+
+ align:start position:0%
+that are responsible for the fusion
+event all right now I want to end by
+
+ align:start position:0%
+event all right now I want to end by
+ 
+
+ align:start position:0%
+event all right now I want to end by
+just telling you how this experiment
+
+ align:start position:0%
+just telling you how this experiment
+ 
+
+ align:start position:0%
+just telling you how this experiment
+works where we're able to activate
+
+ align:start position:0%
+works where we're able to activate
+ 
+
+ align:start position:0%
+works where we're able to activate
+specific neurons in a brain and that
+
+ align:start position:0%
+specific neurons in a brain and that
+ 
+
+ align:start position:0%
+specific neurons in a brain and that
+leads to the animal sort of waking up
+
+ align:start position:0%
+leads to the animal sort of waking up
+ 
+
+ align:start position:0%
+leads to the animal sort of waking up
+okay so in a normal neuron so this is
+
+ align:start position:0%
+okay so in a normal neuron so this is
+ 
+
+ align:start position:0%
+okay so in a normal neuron so this is
+the last part optogenetics and I'm gonna
+
+ align:start position:0%
+the last part optogenetics and I'm gonna
+ 
+
+ align:start position:0%
+the last part optogenetics and I'm gonna
+go through this very fast but normally
+
+ align:start position:0%
+go through this very fast but normally
+ 
+
+ align:start position:0%
+go through this very fast but normally
+you need a neurotransmitter to induce
+
+ align:start position:0%
+you need a neurotransmitter to induce
+ 
+
+ align:start position:0%
+you need a neurotransmitter to induce
+depolarization but what optogenetics is
+
+ align:start position:0%
+depolarization but what optogenetics is
+ 
+
+ align:start position:0%
+depolarization but what optogenetics is
+is an approach to control the activity
+
+ align:start position:0%
+is an approach to control the activity
+ 
+
+ align:start position:0%
+is an approach to control the activity
+of a cell with light okay so in this
+
+ align:start position:0%
+of a cell with light okay so in this
+ 
+
+ align:start position:0%
+of a cell with light okay so in this
+case we're gonna have light inducing
+
+ align:start position:0%
+case we're gonna have light inducing
+ 
+
+ align:start position:0%
+case we're gonna have light inducing
+depolarization and the way this is done
+
+ align:start position:0%
+depolarization and the way this is done
+ 
+
+ align:start position:0%
+depolarization and the way this is done
+is there's a protein discovered from
+
+ align:start position:0%
+is there's a protein discovered from
+ 
+
+ align:start position:0%
+is there's a protein discovered from
+from photosynthetic algae that's
+
+ align:start position:0%
+from photosynthetic algae that's
+ 
+
+ align:start position:0%
+from photosynthetic algae that's
+responsive to light and it is a sodium
+
+ align:start position:0%
+responsive to light and it is a sodium
+ 
+
+ align:start position:0%
+responsive to light and it is a sodium
+channel and this protein is called
+
+ align:start position:0%
+channel and this protein is called
+ 
+
+ align:start position:0%
+channel and this protein is called
+channelrhodopsin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifically CHR - and this is a
+
+ align:start position:0%
+specifically CHR - and this is a
+ 
+
+ align:start position:0%
+specifically CHR - and this is a
+light-sensitive protein where light
+
+ align:start position:0%
+light-sensitive protein where light
+ 
+
+ align:start position:0%
+light-sensitive protein where light
+induces sodium channel opening okay so
+
+ align:start position:0%
+induces sodium channel opening okay so
+ 
+
+ align:start position:0%
+induces sodium channel opening okay so
+that's gonna depolarize the cell and
+
+ align:start position:0%
+that's gonna depolarize the cell and
+ 
+
+ align:start position:0%
+that's gonna depolarize the cell and
+what you can do is if you have a gene
+
+ align:start position:0%
+what you can do is if you have a gene
+ 
+
+ align:start position:0%
+what you can do is if you have a gene
+that you know is specifically expressed
+
+ align:start position:0%
+that you know is specifically expressed
+ 
+
+ align:start position:0%
+that you know is specifically expressed
+in a certain type of neuron you can take
+
+ align:start position:0%
+in a certain type of neuron you can take
+ 
+
+ align:start position:0%
+in a certain type of neuron you can take
+the promoter and enhancer region of that
+
+ align:start position:0%
+the promoter and enhancer region of that
+ 
+
+ align:start position:0%
+the promoter and enhancer region of that
+gene and hook it up to this single
+
+ align:start position:0%
+gene and hook it up to this single
+ 
+
+ align:start position:0%
+gene and hook it up to this single
+component channelrhodopsin that open
+
+ align:start position:0%
+component channelrhodopsin that open
+ 
+
+ align:start position:0%
+component channelrhodopsin that open
+reading frame using recombinant DNA
+
+ align:start position:0%
+reading frame using recombinant DNA
+ 
+
+ align:start position:0%
+reading frame using recombinant DNA
+technology and if that's expressed
+
+ align:start position:0%
+technology and if that's expressed
+ 
+
+ align:start position:0%
+technology and if that's expressed
+specifically in the neurons that you're
+
+ align:start position:0%
+specifically in the neurons that you're
+ 
+
+ align:start position:0%
+specifically in the neurons that you're
+trying to test you can then shine a
+
+ align:start position:0%
+trying to test you can then shine a
+ 
+
+ align:start position:0%
+trying to test you can then shine a
+light into the brain of the organism and
+
+ align:start position:0%
+light into the brain of the organism and
+ 
+
+ align:start position:0%
+light into the brain of the organism and
+activate specifically this type of
+
+ align:start position:0%
+activate specifically this type of
+ 
+
+ align:start position:0%
+activate specifically this type of
+neuron and that allows you to test the
+
+ align:start position:0%
+neuron and that allows you to test the
+ 
+
+ align:start position:0%
+neuron and that allows you to test the
+function of the neuron in the behavior
+
+ align:start position:0%
+function of the neuron in the behavior
+ 
+
+ align:start position:0%
+function of the neuron in the behavior
+of an organism so in this case this
+
+ align:start position:0%
+of an organism so in this case this
+ 
+
+ align:start position:0%
+of an organism so in this case this
+mouse the light is shined into its brain
+
+ align:start position:0%
+mouse the light is shined into its brain
+ 
+
+ align:start position:0%
+mouse the light is shined into its brain
+and they're testing a specific type of
+
+ align:start position:0%
+and they're testing a specific type of
+ 
+
+ align:start position:0%
+and they're testing a specific type of
+neuron that is involved in arousal of
+
+ align:start position:0%
+neuron that is involved in arousal of
+ 
+
+ align:start position:0%
+neuron that is involved in arousal of
+the mouse and it wakes up oh it's not
+
+ align:start position:0%
+the mouse and it wakes up oh it's not
+ 
+
+ align:start position:0%
+the mouse and it wakes up oh it's not
+playing so here this is the this is a no
+
+ align:start position:0%
+playing so here this is the this is a no
+ 
+
+ align:start position:0%
+playing so here this is the this is a no
+this is the brain activity on the top
+
+ align:start position:0%
+this is the brain activity on the top
+ 
+
+ align:start position:0%
+this is the brain activity on the top
+and the muscle activity on the bottom so
+
+ align:start position:0%
+and the muscle activity on the bottom so
+ 
+
+ align:start position:0%
+and the muscle activity on the bottom so
+you're gonna see light there's the light
+
+ align:start position:0%
+you're gonna see light there's the light
+ 
+
+ align:start position:0%
+you're gonna see light there's the light
+you see it light going into the brain
+
+ align:start position:0%
+you see it light going into the brain
+ 
+
+ align:start position:0%
+you see it light going into the brain
+there they induce light at that
+
+ align:start position:0%
+there they induce light at that
+ 
+
+ align:start position:0%
+there they induce light at that
+frequency for a while and then they're
+
+ align:start position:0%
+frequency for a while and then they're
+ 
+
+ align:start position:0%
+frequency for a while and then they're
+gonna wait and see the mouse see if when
+
+ align:start position:0%
+gonna wait and see the mouse see if when
+ 
+
+ align:start position:0%
+gonna wait and see the mouse see if when
+the mouse wakes up and it's gonna wake
+
+ align:start position:0%
+the mouse wakes up and it's gonna wake
+ 
+
+ align:start position:0%
+the mouse wakes up and it's gonna wake
+up right now there it goes
+
+ align:start position:0%
+up right now there it goes
+ 
+
+ align:start position:0%
+up right now there it goes
+woke up you see now it's muscle activity
+
+ align:start position:0%
+woke up you see now it's muscle activity
+ 
+
+ align:start position:0%
+woke up you see now it's muscle activity
+is going okay so you can test the
+
+ align:start position:0%
+is going okay so you can test the
+ 
+
+ align:start position:0%
+is going okay so you can test the
+function of specific nerve cells using
+
+ align:start position:0%
+function of specific nerve cells using
+ 
+
+ align:start position:0%
+function of specific nerve cells using
+this approach and it's because you have
+
+ align:start position:0%
+this approach and it's because you have
+ 
+
+ align:start position:0%
+this approach and it's because you have
+a light-sensitive sodium channel so I'm
+
+ align:start position:0%
+a light-sensitive sodium channel so I'm
+ 
+
+ align:start position:0%
+a light-sensitive sodium channel so I'm
+done for today have a great weekend I
+
+ align:start position:0%
+done for today have a great weekend I
+ 
+
+ align:start position:0%
+done for today have a great weekend I
+will see you on Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/9mYYNtaZJp8.txt b/9mYYNtaZJp8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aeebbaf88db29faf1d8d02557af52d1902d61687
--- /dev/null
+++ b/9mYYNtaZJp8.txt
@@ -0,0 +1,8338 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay uh we we want to I want
+
+ align:start position:0%
+ocw.mit.edu okay uh we we want to I want
+ 
+
+ align:start position:0%
+ocw.mit.edu okay uh we we want to I want
+to talk about the last Topic in the
+
+ align:start position:0%
+to talk about the last Topic in the
+ 
+
+ align:start position:0%
+to talk about the last Topic in the
+Scott book and then on Friday we'll
+
+ align:start position:0%
+Scott book and then on Friday we'll
+ 
+
+ align:start position:0%
+Scott book and then on Friday we'll
+start talking about
+
+ align:start position:0%
+start talking about
+ 
+
+ align:start position:0%
+start talking about
+sociobiology uh so you'll need to be
+
+ align:start position:0%
+sociobiology uh so you'll need to be
+ 
+
+ align:start position:0%
+sociobiology uh so you'll need to be
+reading the
+
+ align:start position:0%
+reading the
+ 
+
+ align:start position:0%
+reading the
+uh the book by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elcock the mating and reproduction is
+
+ align:start position:0%
+elcock the mating and reproduction is
+ 
+
+ align:start position:0%
+elcock the mating and reproduction is
+very important for sociobiology
+
+ align:start position:0%
+very important for sociobiology
+ 
+
+ align:start position:0%
+very important for sociobiology
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+is and of course it's inter it's
+
+ align:start position:0%
+is and of course it's inter it's
+ 
+
+ align:start position:0%
+is and of course it's inter it's
+important in ethology and other
+
+ align:start position:0%
+important in ethology and other
+ 
+
+ align:start position:0%
+important in ethology and other
+approaches to study of animal behavior
+
+ align:start position:0%
+approaches to study of animal behavior
+ 
+
+ align:start position:0%
+approaches to study of animal behavior
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+uh so Scott is using mainly data of
+
+ align:start position:0%
+uh so Scott is using mainly data of
+ 
+
+ align:start position:0%
+uh so Scott is using mainly data of
+experimental ethology and as well as
+
+ align:start position:0%
+experimental ethology and as well as
+ 
+
+ align:start position:0%
+experimental ethology and as well as
+various observations by ethologists but
+
+ align:start position:0%
+various observations by ethologists but
+ 
+
+ align:start position:0%
+various observations by ethologists but
+then you'll see it's closely related to
+
+ align:start position:0%
+then you'll see it's closely related to
+ 
+
+ align:start position:0%
+then you'll see it's closely related to
+some of the studies of socio biology
+
+ align:start position:0%
+some of the studies of socio biology
+ 
+
+ align:start position:0%
+some of the studies of socio biology
+that we'll be talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about so when we talk about Evolution we
+
+ align:start position:0%
+about so when we talk about Evolution we
+ 
+
+ align:start position:0%
+about so when we talk about Evolution we
+we talk about both natural selection and
+
+ align:start position:0%
+we talk about both natural selection and
+ 
+
+ align:start position:0%
+we talk about both natural selection and
+sex sexual selection that were both
+
+ align:start position:0%
+sex sexual selection that were both
+ 
+
+ align:start position:0%
+sex sexual selection that were both
+discussing by Charles
+
+ align:start position:0%
+discussing by Charles
+ 
+
+ align:start position:0%
+discussing by Charles
+Darwin and you should have a clear
+
+ align:start position:0%
+Darwin and you should have a clear
+ 
+
+ align:start position:0%
+Darwin and you should have a clear
+understanding of the difference in the
+
+ align:start position:0%
+understanding of the difference in the
+ 
+
+ align:start position:0%
+understanding of the difference in the
+meaning uh we've talked about both of
+
+ align:start position:0%
+meaning uh we've talked about both of
+ 
+
+ align:start position:0%
+meaning uh we've talked about both of
+them in the
+
+ align:start position:0%
+them in the
+ 
+
+ align:start position:0%
+them in the
+class you should be able to give ad uh
+
+ align:start position:0%
+class you should be able to give ad uh
+ 
+
+ align:start position:0%
+class you should be able to give ad uh
+examples of each of them and for every
+
+ align:start position:0%
+examples of each of them and for every
+ 
+
+ align:start position:0%
+examples of each of them and for every
+time you discuss a
+
+ align:start position:0%
+time you discuss a
+ 
+
+ align:start position:0%
+time you discuss a
+trait
+
+ align:start position:0%
+trait
+ 
+
+ align:start position:0%
+trait
+uh besides understanding whether it
+
+ align:start position:0%
+uh besides understanding whether it
+ 
+
+ align:start position:0%
+uh besides understanding whether it
+arose from natural selection or sex
+
+ align:start position:0%
+arose from natural selection or sex
+ 
+
+ align:start position:0%
+arose from natural selection or sex
+sexual selection or some combination you
+
+ align:start position:0%
+sexual selection or some combination you
+ 
+
+ align:start position:0%
+sexual selection or some combination you
+have to consider the likely costs and
+
+ align:start position:0%
+have to consider the likely costs and
+ 
+
+ align:start position:0%
+have to consider the likely costs and
+benefits uh
+
+ align:start position:0%
+benefits uh
+ 
+
+ align:start position:0%
+benefits uh
+and what do we mean by costs and
+
+ align:start position:0%
+and what do we mean by costs and
+ 
+
+ align:start position:0%
+and what do we mean by costs and
+benefits we always will take the
+
+ align:start position:0%
+benefits we always will take the
+ 
+
+ align:start position:0%
+benefits we always will take the
+sociobiological view that we're talking
+
+ align:start position:0%
+sociobiological view that we're talking
+ 
+
+ align:start position:0%
+sociobiological view that we're talking
+about not benefits for individual
+
+ align:start position:0%
+about not benefits for individual
+ 
+
+ align:start position:0%
+about not benefits for individual
+survival
+
+ align:start position:0%
+survival
+ 
+
+ align:start position:0%
+survival
+necessarily but for increasing the
+
+ align:start position:0%
+necessarily but for increasing the
+ 
+
+ align:start position:0%
+necessarily but for increasing the
+likelihood of passing on the genes
+
+ align:start position:0%
+likelihood of passing on the genes
+ 
+
+ align:start position:0%
+likelihood of passing on the genes
+this is the way it's used in
+
+ align:start position:0%
+this is the way it's used in
+ 
+
+ align:start position:0%
+this is the way it's used in
+sociobiology
+
+ align:start position:0%
+sociobiology
+ 
+
+ align:start position:0%
+sociobiology
+uh and obviously traits in order to
+
+ align:start position:0%
+uh and obviously traits in order to
+ 
+
+ align:start position:0%
+uh and obviously traits in order to
+evolve uh the benefits have to exceed
+
+ align:start position:0%
+evolve uh the benefits have to exceed
+ 
+
+ align:start position:0%
+evolve uh the benefits have to exceed
+the cost it doesn't mean there aren't
+
+ align:start position:0%
+the cost it doesn't mean there aren't
+ 
+
+ align:start position:0%
+the cost it doesn't mean there aren't
+costs and sometimes it's a puzzle
+
+ align:start position:0%
+costs and sometimes it's a puzzle
+ 
+
+ align:start position:0%
+costs and sometimes it's a puzzle
+just they see because it seems the cost
+
+ align:start position:0%
+just they see because it seems the cost
+ 
+
+ align:start position:0%
+just they see because it seems the cost
+is so drastic like if the female eats
+
+ align:start position:0%
+is so drastic like if the female eats
+ 
+
+ align:start position:0%
+is so drastic like if the female eats
+the male after mating that do seems to
+
+ align:start position:0%
+the male after mating that do seems to
+ 
+
+ align:start position:0%
+the male after mating that do seems to
+be a rather high cost to the mail so
+
+ align:start position:0%
+be a rather high cost to the mail so
+ 
+
+ align:start position:0%
+be a rather high cost to the mail so
+we'll bring that up uh later in the
+
+ align:start position:0%
+we'll bring that up uh later in the
+ 
+
+ align:start position:0%
+we'll bring that up uh later in the
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+because that's a typical darwinian
+
+ align:start position:0%
+because that's a typical darwinian
+ 
+
+ align:start position:0%
+because that's a typical darwinian
+puzzle when first when you first look at
+
+ align:start position:0%
+puzzle when first when you first look at
+ 
+
+ align:start position:0%
+puzzle when first when you first look at
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+data so when we're talking it's easiest
+
+ align:start position:0%
+data so when we're talking it's easiest
+ 
+
+ align:start position:0%
+data so when we're talking it's easiest
+when just trying to contrast natural and
+
+ align:start position:0%
+when just trying to contrast natural and
+ 
+
+ align:start position:0%
+when just trying to contrast natural and
+sexual sexual selection to First
+
+ align:start position:0%
+sexual sexual selection to First
+ 
+
+ align:start position:0%
+sexual sexual selection to First
+consider is it sexual
+
+ align:start position:0%
+consider is it sexual
+ 
+
+ align:start position:0%
+consider is it sexual
+selection and we we've given examples of
+
+ align:start position:0%
+selection and we we've given examples of
+ 
+
+ align:start position:0%
+selection and we we've given examples of
+that already like your tail feathers of
+
+ align:start position:0%
+that already like your tail feathers of
+ 
+
+ align:start position:0%
+that already like your tail feathers of
+the female
+
+ align:start position:0%
+the female
+ 
+
+ align:start position:0%
+the female
+peacocks or or a
+
+ align:start position:0%
+peacocks or or a
+ 
+
+ align:start position:0%
+peacocks or or a
+peasant the red color the bright red
+
+ align:start position:0%
+peasant the red color the bright red
+ 
+
+ align:start position:0%
+peasant the red color the bright red
+color of the male cardinal it makes him
+
+ align:start position:0%
+color of the male cardinal it makes him
+ 
+
+ align:start position:0%
+color of the male cardinal it makes him
+stand out particularly in against the
+
+ align:start position:0%
+stand out particularly in against the
+ 
+
+ align:start position:0%
+stand out particularly in against the
+snow and winter it makes him very
+
+ align:start position:0%
+snow and winter it makes him very
+ 
+
+ align:start position:0%
+snow and winter it makes him very
+conspicuous to
+
+ align:start position:0%
+conspicuous to
+ 
+
+ align:start position:0%
+conspicuous to
+Predators as well as to the female we
+
+ align:start position:0%
+Predators as well as to the female we
+ 
+
+ align:start position:0%
+Predators as well as to the female we
+talked about the long tail the sword
+
+ align:start position:0%
+talked about the long tail the sword
+ 
+
+ align:start position:0%
+talked about the long tail the sword
+tail fish the Lion's man of course is a
+
+ align:start position:0%
+tail fish the Lion's man of course is a
+ 
+
+ align:start position:0%
+tail fish the Lion's man of course is a
+common one a Stags
+
+ align:start position:0%
+common one a Stags
+ 
+
+ align:start position:0%
+common one a Stags
+antlers why do we say they evolve by
+
+ align:start position:0%
+antlers why do we say they evolve by
+ 
+
+ align:start position:0%
+antlers why do we say they evolve by
+sexual selection because they evolve
+
+ align:start position:0%
+sexual selection because they evolve
+ 
+
+ align:start position:0%
+sexual selection because they evolve
+because the female pre ERS males with
+
+ align:start position:0%
+because the female pre ERS males with
+ 
+
+ align:start position:0%
+because the female pre ERS males with
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traits so they benefit
+
+ align:start position:0%
+traits so they benefit
+ 
+
+ align:start position:0%
+traits so they benefit
+reproduction for the male because it
+
+ align:start position:0%
+reproduction for the male because it
+ 
+
+ align:start position:0%
+reproduction for the male because it
+makes him more attractive if you can't
+
+ align:start position:0%
+makes him more attractive if you can't
+ 
+
+ align:start position:0%
+makes him more attractive if you can't
+attract females to mate with and he
+
+ align:start position:0%
+attract females to mate with and he
+ 
+
+ align:start position:0%
+attract females to mate with and he
+won't pass on so many genes if
+
+ align:start position:0%
+won't pass on so many genes if
+ 
+
+ align:start position:0%
+won't pass on so many genes if
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+now usually you're talking about the
+
+ align:start position:0%
+now usually you're talking about the
+ 
+
+ align:start position:0%
+now usually you're talking about the
+appearance of the male when you're
+
+ align:start position:0%
+appearance of the male when you're
+ 
+
+ align:start position:0%
+appearance of the male when you're
+talking about sexual selection but it
+
+ align:start position:0%
+talking about sexual selection but it
+ 
+
+ align:start position:0%
+talking about sexual selection but it
+does happen it affects the
+
+ align:start position:0%
+does happen it affects the
+ 
+
+ align:start position:0%
+does happen it affects the
+characteristics of female too especially
+
+ align:start position:0%
+characteristics of female too especially
+ 
+
+ align:start position:0%
+characteristics of female too especially
+if males exercise
+
+ align:start position:0%
+if males exercise
+ 
+
+ align:start position:0%
+if males exercise
+Choice okay and so we'll talk about that
+
+ align:start position:0%
+Choice okay and so we'll talk about that
+ 
+
+ align:start position:0%
+Choice okay and so we'll talk about that
+too well if it didn't evolve by sexual
+
+ align:start position:0%
+too well if it didn't evolve by sexual
+ 
+
+ align:start position:0%
+too well if it didn't evolve by sexual
+selection
+
+ align:start position:0%
+selection
+ 
+
+ align:start position:0%
+selection
+then the traits evolv still by natural
+
+ align:start position:0%
+then the traits evolv still by natural
+ 
+
+ align:start position:0%
+then the traits evolv still by natural
+selection the factors that enable
+
+ align:start position:0%
+selection the factors that enable
+ 
+
+ align:start position:0%
+selection the factors that enable
+survival at least through the age of
+
+ align:start position:0%
+survival at least through the age of
+ 
+
+ align:start position:0%
+survival at least through the age of
+reproduction and in many cases the age
+
+ align:start position:0%
+reproduction and in many cases the age
+ 
+
+ align:start position:0%
+reproduction and in many cases the age
+of reproduction includes
+
+ align:start position:0%
+of reproduction includes
+ 
+
+ align:start position:0%
+of reproduction includes
+rude tending care of
+
+ align:start position:0%
+rude tending care of
+ 
+
+ align:start position:0%
+rude tending care of
+young and maybe in our species uh care
+
+ align:start position:0%
+young and maybe in our species uh care
+ 
+
+ align:start position:0%
+young and maybe in our species uh care
+of the young of our
+
+ align:start position:0%
+of the young of our
+ 
+
+ align:start position:0%
+of the young of our
+young okay
+
+ align:start position:0%
+young okay
+ 
+
+ align:start position:0%
+young okay
+so we talked remember about the birds of
+
+ align:start position:0%
+so we talked remember about the birds of
+ 
+
+ align:start position:0%
+so we talked remember about the birds of
+paradise we saw the example of
+
+ align:start position:0%
+paradise we saw the example of
+ 
+
+ align:start position:0%
+paradise we saw the example of
+the uh this is
+
+ align:start position:0%
+the uh this is
+ 
+
+ align:start position:0%
+the uh this is
+the a bird of one of the birds of
+
+ align:start position:0%
+the a bird of one of the birds of
+ 
+
+ align:start position:0%
+the a bird of one of the birds of
+paradise Goldie bird of
+
+ align:start position:0%
+paradise Goldie bird of
+ 
+
+ align:start position:0%
+paradise Goldie bird of
+paradise uh in the video that we saw
+
+ align:start position:0%
+paradise uh in the video that we saw
+ 
+
+ align:start position:0%
+paradise uh in the video that we saw
+with the the dancing bird of paradise it
+
+ align:start position:0%
+with the the dancing bird of paradise it
+ 
+
+ align:start position:0%
+with the the dancing bird of paradise it
+was a paradise rifle bird from
+
+ align:start position:0%
+was a paradise rifle bird from
+ 
+
+ align:start position:0%
+was a paradise rifle bird from
+Australia these animal these birds occur
+
+ align:start position:0%
+Australia these animal these birds occur
+ 
+
+ align:start position:0%
+Australia these animal these birds occur
+in the within Indonesia and also in
+
+ align:start position:0%
+in the within Indonesia and also in
+ 
+
+ align:start position:0%
+in the within Indonesia and also in
+eastern Australia we were the I believe
+
+ align:start position:0%
+eastern Australia we were the I believe
+ 
+
+ align:start position:0%
+eastern Australia we were the I believe
+the video we saw was all of
+
+ align:start position:0%
+the video we saw was all of
+ 
+
+ align:start position:0%
+the video we saw was all of
+the Australian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+birds why do you think the elaboration
+
+ align:start position:0%
+birds why do you think the elaboration
+ 
+
+ align:start position:0%
+birds why do you think the elaboration
+of these feathers has gone to such
+
+ align:start position:0%
+of these feathers has gone to such
+ 
+
+ align:start position:0%
+of these feathers has gone to such
+extremes
+
+ align:start position:0%
+extremes
+ 
+
+ align:start position:0%
+extremes
+doesn't it have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+costs I mean a male that's having to
+
+ align:start position:0%
+costs I mean a male that's having to
+ 
+
+ align:start position:0%
+costs I mean a male that's having to
+care around carry around these feathers
+
+ align:start position:0%
+care around carry around these feathers
+ 
+
+ align:start position:0%
+care around carry around these feathers
+or look at
+
+ align:start position:0%
+or look at
+ 
+
+ align:start position:0%
+or look at
+this the peacock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it seems to be somewhat of a burden
+
+ align:start position:0%
+here it seems to be somewhat of a burden
+ 
+
+ align:start position:0%
+here it seems to be somewhat of a burden
+to have feathers that long and yet the
+
+ align:start position:0%
+to have feathers that long and yet the
+ 
+
+ align:start position:0%
+to have feathers that long and yet the
+females prefer
+
+ align:start position:0%
+females prefer
+ 
+
+ align:start position:0%
+females prefer
+it you know if you give a
+
+ align:start position:0%
+it you know if you give a
+ 
+
+ align:start position:0%
+it you know if you give a
+female uh peacock a choice between males
+
+ align:start position:0%
+female uh peacock a choice between males
+ 
+
+ align:start position:0%
+female uh peacock a choice between males
+with areas here's a I took this picture
+
+ align:start position:0%
+with areas here's a I took this picture
+ 
+
+ align:start position:0%
+with areas here's a I took this picture
+myself at the Boston Zoological Society
+
+ align:start position:0%
+myself at the Boston Zoological Society
+ 
+
+ align:start position:0%
+myself at the Boston Zoological Society
+Park and uh it shows the string male
+
+ align:start position:0%
+Park and uh it shows the string male
+ 
+
+ align:start position:0%
+Park and uh it shows the string male
+he's displaying his tail feathers
+
+ align:start position:0%
+he's displaying his tail feathers
+ 
+
+ align:start position:0%
+he's displaying his tail feathers
+there's the pan in
+
+ align:start position:0%
+there's the pan in
+ 
+
+ align:start position:0%
+there's the pan in
+front
+
+ align:start position:0%
+front
+ 
+
+ align:start position:0%
+front
+uh with feathers like that I mean how
+
+ align:start position:0%
+uh with feathers like that I mean how
+ 
+
+ align:start position:0%
+uh with feathers like that I mean how
+does he get away from predators you see
+
+ align:start position:0%
+does he get away from predators you see
+ 
+
+ align:start position:0%
+does he get away from predators you see
+now in the case of these birds it's it's
+
+ align:start position:0%
+now in the case of these birds it's it's
+ 
+
+ align:start position:0%
+now in the case of these birds it's it's
+fairly easy to understand because they
+
+ align:start position:0%
+fairly easy to understand because they
+ 
+
+ align:start position:0%
+fairly easy to understand because they
+don't have many in the environments
+
+ align:start position:0%
+don't have many in the environments
+ 
+
+ align:start position:0%
+don't have many in the environments
+where these birds are found they don't
+
+ align:start position:0%
+where these birds are found they don't
+ 
+
+ align:start position:0%
+where these birds are found they don't
+have many
+
+ align:start position:0%
+have many
+ 
+
+ align:start position:0%
+have many
+predators okay
+
+ align:start position:0%
+predators okay
+ 
+
+ align:start position:0%
+predators okay
+so are there still costs well if it went
+
+ align:start position:0%
+so are there still costs well if it went
+ 
+
+ align:start position:0%
+so are there still costs well if it went
+too far what would the cost be it would
+
+ align:start position:0%
+too far what would the cost be it would
+ 
+
+ align:start position:0%
+too far what would the cost be it would
+start interfering with its ability to
+
+ align:start position:0%
+start interfering with its ability to
+ 
+
+ align:start position:0%
+start interfering with its ability to
+forage just to locomote get
+
+ align:start position:0%
+forage just to locomote get
+ 
+
+ align:start position:0%
+forage just to locomote get
+around okay so these are there's
+
+ align:start position:0%
+around okay so these are there's
+ 
+
+ align:start position:0%
+around okay so these are there's
+certainly limits to how far sexual
+
+ align:start position:0%
+certainly limits to how far sexual
+ 
+
+ align:start position:0%
+certainly limits to how far sexual
+selection can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+here's the MC Darwin was of course had
+
+ align:start position:0%
+here's the MC Darwin was of course had
+ 
+
+ align:start position:0%
+here's the MC Darwin was of course had
+introduced this idea of sexual
+
+ align:start position:0%
+introduced this idea of sexual
+ 
+
+ align:start position:0%
+introduced this idea of sexual
+selection and he was made fun of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in among other ways by
+
+ align:start position:0%
+in among other ways by
+ 
+
+ align:start position:0%
+in among other ways by
+cartoonists and here it shows the
+
+ align:start position:0%
+cartoonists and here it shows the
+ 
+
+ align:start position:0%
+cartoonists and here it shows the
+Victorian cartoonists uh made fun of
+
+ align:start position:0%
+Victorian cartoonists uh made fun of
+ 
+
+ align:start position:0%
+Victorian cartoonists uh made fun of
+Darwin's ideas about sexual
+
+ align:start position:0%
+Darwin's ideas about sexual
+ 
+
+ align:start position:0%
+Darwin's ideas about sexual
+selection uh and the importance of
+
+ align:start position:0%
+selection uh and the importance of
+ 
+
+ align:start position:0%
+selection uh and the importance of
+visual displays is uh it shows him here
+
+ align:start position:0%
+visual displays is uh it shows him here
+ 
+
+ align:start position:0%
+visual displays is uh it shows him here
+in inspecting the mimicking of stop
+
+ align:start position:0%
+in inspecting the mimicking of stop
+ 
+
+ align:start position:0%
+in inspecting the mimicking of stop
+pisia what is
+
+ align:start position:0%
+pisia what is
+ 
+
+ align:start position:0%
+pisia what is
+that the very large buts in females of
+
+ align:start position:0%
+that the very large buts in females of
+ 
+
+ align:start position:0%
+that the very large buts in females of
+certain groups of
+
+ align:start position:0%
+certain groups of
+ 
+
+ align:start position:0%
+certain groups of
+humans and it
+
+ align:start position:0%
+humans and it
+ 
+
+ align:start position:0%
+humans and it
+became a Victorian style to wear
+
+ align:start position:0%
+became a Victorian style to wear
+ 
+
+ align:start position:0%
+became a Victorian style to wear
+Buffet so Darwin of course had a ready
+
+ align:start position:0%
+Buffet so Darwin of course had a ready
+ 
+
+ align:start position:0%
+Buffet so Darwin of course had a ready
+interpretation of that
+
+ align:start position:0%
+interpretation of that
+ 
+
+ align:start position:0%
+interpretation of that
+they wouldn't do it if males didn't like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it if you want to know more about stopa
+
+ align:start position:0%
+it if you want to know more about stopa
+ 
+
+ align:start position:0%
+it if you want to know more about stopa
+just go to Google don't go to Google
+
+ align:start position:0%
+just go to Google don't go to Google
+ 
+
+ align:start position:0%
+just go to Google don't go to Google
+Scholar although you can go there too
+
+ align:start position:0%
+Scholar although you can go there too
+ 
+
+ align:start position:0%
+Scholar although you can go there too
+and you will find the scholarly papers
+
+ align:start position:0%
+and you will find the scholarly papers
+ 
+
+ align:start position:0%
+and you will find the scholarly papers
+but if you just go to the regular Google
+
+ align:start position:0%
+but if you just go to the regular Google
+ 
+
+ align:start position:0%
+but if you just go to the regular Google
+you'll find all kinds of information
+
+ align:start position:0%
+you'll find all kinds of information
+ 
+
+ align:start position:0%
+you'll find all kinds of information
+photographs comments some of them with
+
+ align:start position:0%
+photographs comments some of them with
+ 
+
+ align:start position:0%
+photographs comments some of them with
+tongue and cheek some of them claiming
+
+ align:start position:0%
+tongue and cheek some of them claiming
+ 
+
+ align:start position:0%
+tongue and cheek some of them claiming
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+racism and and others really most of
+
+ align:start position:0%
+racism and and others really most of
+ 
+
+ align:start position:0%
+racism and and others really most of
+it's just very interesting and it
+
+ align:start position:0%
+it's just very interesting and it
+ 
+
+ align:start position:0%
+it's just very interesting and it
+illustrates Variety in human
+
+ align:start position:0%
+illustrates Variety in human
+ 
+
+ align:start position:0%
+illustrates Variety in human
+evolution I think when we talk about
+
+ align:start position:0%
+evolution I think when we talk about
+ 
+
+ align:start position:0%
+evolution I think when we talk about
+socio biology this will come up
+
+ align:start position:0%
+socio biology this will come up
+ 
+
+ align:start position:0%
+socio biology this will come up
+again this a particular
+
+ align:start position:0%
+again this a particular
+ 
+
+ align:start position:0%
+again this a particular
+illustration not in cartoons but in real
+
+ align:start position:0%
+illustration not in cartoons but in real
+ 
+
+ align:start position:0%
+illustration not in cartoons but in real
+people okay and now this is the next
+
+ align:start position:0%
+people okay and now this is the next
+ 
+
+ align:start position:0%
+people okay and now this is the next
+concept that Scott brings up the very
+
+ align:start position:0%
+concept that Scott brings up the very
+ 
+
+ align:start position:0%
+concept that Scott brings up the very
+ations and reproductive
+
+ align:start position:0%
+ations and reproductive
+ 
+
+ align:start position:0%
+ations and reproductive
+investment uh by the male and the female
+
+ align:start position:0%
+investment uh by the male and the female
+ 
+
+ align:start position:0%
+investment uh by the male and the female
+of a species because often they differ
+
+ align:start position:0%
+of a species because often they differ
+ 
+
+ align:start position:0%
+of a species because often they differ
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+considerably we saw when we talked about
+
+ align:start position:0%
+considerably we saw when we talked about
+ 
+
+ align:start position:0%
+considerably we saw when we talked about
+sticklebacks early in the class that the
+
+ align:start position:0%
+sticklebacks early in the class that the
+ 
+
+ align:start position:0%
+sticklebacks early in the class that the
+male does all the nesting and care of
+
+ align:start position:0%
+male does all the nesting and care of
+ 
+
+ align:start position:0%
+male does all the nesting and care of
+the eggs so the male is making a big
+
+ align:start position:0%
+the eggs so the male is making a big
+ 
+
+ align:start position:0%
+the eggs so the male is making a big
+investment a reproductive investment the
+
+ align:start position:0%
+investment a reproductive investment the
+ 
+
+ align:start position:0%
+investment a reproductive investment the
+female doesn't make so many so much
+
+ align:start position:0%
+female doesn't make so many so much
+ 
+
+ align:start position:0%
+female doesn't make so many so much
+reproductive investment
+
+ align:start position:0%
+reproductive investment
+ 
+
+ align:start position:0%
+reproductive investment
+in other species of fish the male just
+
+ align:start position:0%
+in other species of fish the male just
+ 
+
+ align:start position:0%
+in other species of fish the male just
+leaves after fertilizing the eggs he
+
+ align:start position:0%
+leaves after fertilizing the eggs he
+ 
+
+ align:start position:0%
+leaves after fertilizing the eggs he
+seems to make heat in that those species
+
+ align:start position:0%
+seems to make heat in that those species
+ 
+
+ align:start position:0%
+seems to make heat in that those species
+it's the male it's not making any
+
+ align:start position:0%
+it's the male it's not making any
+ 
+
+ align:start position:0%
+it's the male it's not making any
+reproductive
+
+ align:start position:0%
+reproductive
+ 
+
+ align:start position:0%
+reproductive
+investment so of course then their
+
+ align:start position:0%
+investment so of course then their
+ 
+
+ align:start position:0%
+investment so of course then their
+strategies are going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differ and you'll can predict difference
+
+ align:start position:0%
+differ and you'll can predict difference
+ 
+
+ align:start position:0%
+differ and you'll can predict difference
+very great differences in behavior and
+
+ align:start position:0%
+very great differences in behavior and
+ 
+
+ align:start position:0%
+very great differences in behavior and
+choices of those the male and the
+
+ align:start position:0%
+choices of those the male and the
+ 
+
+ align:start position:0%
+choices of those the male and the
+female in Lions the female has to invest
+
+ align:start position:0%
+female in Lions the female has to invest
+ 
+
+ align:start position:0%
+female in Lions the female has to invest
+more in two years that includes
+
+ align:start position:0%
+more in two years that includes
+ 
+
+ align:start position:0%
+more in two years that includes
+gestation and nearly two years of care
+
+ align:start position:0%
+gestation and nearly two years of care
+ 
+
+ align:start position:0%
+gestation and nearly two years of care
+of the young the males do comparatively
+
+ align:start position:0%
+of the young the males do comparatively
+ 
+
+ align:start position:0%
+of the young the males do comparatively
+little because even when the female is
+
+ align:start position:0%
+little because even when the female is
+ 
+
+ align:start position:0%
+little because even when the female is
+Dre and young she often is still doing
+
+ align:start position:0%
+Dre and young she often is still doing
+ 
+
+ align:start position:0%
+Dre and young she often is still doing
+much of the hunting though the male will
+
+ align:start position:0%
+much of the hunting though the male will
+ 
+
+ align:start position:0%
+much of the hunting though the male will
+hunt as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the spotted sandpipers an example
+
+ align:start position:0%
+well the spotted sandpipers an example
+ 
+
+ align:start position:0%
+well the spotted sandpipers an example
+where the males do most of the brood
+
+ align:start position:0%
+where the males do most of the brood
+ 
+
+ align:start position:0%
+where the males do most of the brood
+tending and the female she will help
+
+ align:start position:0%
+tending and the female she will help
+ 
+
+ align:start position:0%
+tending and the female she will help
+sometimes for a while and then she just
+
+ align:start position:0%
+sometimes for a while and then she just
+ 
+
+ align:start position:0%
+sometimes for a while and then she just
+leaves she goes off and lays another
+
+ align:start position:0%
+leaves she goes off and lays another
+ 
+
+ align:start position:0%
+leaves she goes off and lays another
+clutch of eggs of four she L LS four
+
+ align:start position:0%
+clutch of eggs of four she L LS four
+ 
+
+ align:start position:0%
+clutch of eggs of four she L LS four
+eggs at a time in each Nest she goes off
+
+ align:start position:0%
+eggs at a time in each Nest she goes off
+ 
+
+ align:start position:0%
+eggs at a time in each Nest she goes off
+to lay another clutch of for eggs with a
+
+ align:start position:0%
+to lay another clutch of for eggs with a
+ 
+
+ align:start position:0%
+to lay another clutch of for eggs with a
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nail so again it's the male making the
+
+ align:start position:0%
+nail so again it's the male making the
+ 
+
+ align:start position:0%
+nail so again it's the male making the
+reproductive investment and I mean what
+
+ align:start position:0%
+reproductive investment and I mean what
+ 
+
+ align:start position:0%
+reproductive investment and I mean what
+would happen so he leaves what about the
+
+ align:start position:0%
+would happen so he leaves what about the
+ 
+
+ align:start position:0%
+would happen so he leaves what about the
+male well if he leaves then his
+
+ align:start position:0%
+male well if he leaves then his
+ 
+
+ align:start position:0%
+male well if he leaves then his
+reproductive investment goes to zero for
+
+ align:start position:0%
+reproductive investment goes to zero for
+ 
+
+ align:start position:0%
+reproductive investment goes to zero for
+that span of time he's already put time
+
+ align:start position:0%
+that span of time he's already put time
+ 
+
+ align:start position:0%
+that span of time he's already put time
+into it if he
+
+ align:start position:0%
+into it if he
+ 
+
+ align:start position:0%
+into it if he
+wants his jeans to be passed on he's got
+
+ align:start position:0%
+wants his jeans to be passed on he's got
+ 
+
+ align:start position:0%
+wants his jeans to be passed on he's got
+to stay and take care of those
+
+ align:start position:0%
+to stay and take care of those
+ 
+
+ align:start position:0%
+to stay and take care of those
+chicks whereas the
+
+ align:start position:0%
+chicks whereas the
+ 
+
+ align:start position:0%
+chicks whereas the
+female she gets it for free or not for
+
+ align:start position:0%
+female she gets it for free or not for
+ 
+
+ align:start position:0%
+female she gets it for free or not for
+free she still had to lay the eggs and
+
+ align:start position:0%
+free she still had to lay the eggs and
+ 
+
+ align:start position:0%
+free she still had to lay the eggs and
+that takes a lot of energy and a lot of
+
+ align:start position:0%
+that takes a lot of energy and a lot of
+ 
+
+ align:start position:0%
+that takes a lot of energy and a lot of
+foraging but she can increase her
+
+ align:start position:0%
+foraging but she can increase her
+ 
+
+ align:start position:0%
+foraging but she can increase her
+reproductive uh output simply by laying
+
+ align:start position:0%
+reproductive uh output simply by laying
+ 
+
+ align:start position:0%
+reproductive uh output simply by laying
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+eggs getting another egg male to bring
+
+ align:start position:0%
+eggs getting another egg male to bring
+ 
+
+ align:start position:0%
+eggs getting another egg male to bring
+the food
+
+ align:start position:0%
+the food
+ 
+
+ align:start position:0%
+the food
+and help rear the
+
+ align:start position:0%
+and help rear the
+ 
+
+ align:start position:0%
+and help rear the
+eggs we'll come back to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sandpipers so let's talk a little more
+
+ align:start position:0%
+sandpipers so let's talk a little more
+ 
+
+ align:start position:0%
+sandpipers so let's talk a little more
+about how the male and female
+
+ align:start position:0%
+about how the male and female
+ 
+
+ align:start position:0%
+about how the male and female
+uh can use very different ways to
+
+ align:start position:0%
+uh can use very different ways to
+ 
+
+ align:start position:0%
+uh can use very different ways to
+maximize their reproductive output in
+
+ align:start position:0%
+maximize their reproductive output in
+ 
+
+ align:start position:0%
+maximize their reproductive output in
+most cases in many cases certainly we
+
+ align:start position:0%
+most cases in many cases certainly we
+ 
+
+ align:start position:0%
+most cases in many cases certainly we
+just saw examples where that's not true
+
+ align:start position:0%
+just saw examples where that's not true
+ 
+
+ align:start position:0%
+just saw examples where that's not true
+but the the male can increase his number
+
+ align:start position:0%
+but the the male can increase his number
+ 
+
+ align:start position:0%
+but the the male can increase his number
+of Offspring uh just by mating
+
+ align:start position:0%
+of Offspring uh just by mating
+ 
+
+ align:start position:0%
+of Offspring uh just by mating
+indiscriminately mate with as many
+
+ align:start position:0%
+indiscriminately mate with as many
+ 
+
+ align:start position:0%
+indiscriminately mate with as many
+females as
+
+ align:start position:0%
+females as
+ 
+
+ align:start position:0%
+females as
+possible if the female is doing the
+
+ align:start position:0%
+possible if the female is doing the
+ 
+
+ align:start position:0%
+possible if the female is doing the
+brute tending and he doesn't have to do
+
+ align:start position:0%
+brute tending and he doesn't have to do
+ 
+
+ align:start position:0%
+brute tending and he doesn't have to do
+it that would be his best best strategy
+
+ align:start position:0%
+it that would be his best best strategy
+ 
+
+ align:start position:0%
+it that would be his best best strategy
+if he wants to maximize reproductive
+
+ align:start position:0%
+if he wants to maximize reproductive
+ 
+
+ align:start position:0%
+if he wants to maximize reproductive
+output and you see that
+
+ align:start position:0%
+output and you see that
+ 
+
+ align:start position:0%
+output and you see that
+okay the female has limited egg
+
+ align:start position:0%
+okay the female has limited egg
+ 
+
+ align:start position:0%
+okay the female has limited egg
+production so she is more interested in
+
+ align:start position:0%
+production so she is more interested in
+ 
+
+ align:start position:0%
+production so she is more interested in
+the male that in just maximizing the
+
+ align:start position:0%
+the male that in just maximizing the
+ 
+
+ align:start position:0%
+the male that in just maximizing the
+quality of The Offspring that is given
+
+ align:start position:0%
+quality of The Offspring that is given
+ 
+
+ align:start position:0%
+quality of The Offspring that is given
+the best
+
+ align:start position:0%
+the best
+ 
+
+ align:start position:0%
+the best
+chance of of surviving and reproducing
+
+ align:start position:0%
+chance of of surviving and reproducing
+ 
+
+ align:start position:0%
+chance of of surviving and reproducing
+themselves so she's going to have a
+
+ align:start position:0%
+themselves so she's going to have a
+ 
+
+ align:start position:0%
+themselves so she's going to have a
+great interest in finding good
+
+ align:start position:0%
+great interest in finding good
+ 
+
+ align:start position:0%
+great interest in finding good
+genes and her
+
+ align:start position:0%
+genes and her
+ 
+
+ align:start position:0%
+genes and her
+mating or good
+
+ align:start position:0%
+mating or good
+ 
+
+ align:start position:0%
+mating or good
+resources from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+male so because of these different
+
+ align:start position:0%
+male so because of these different
+ 
+
+ align:start position:0%
+male so because of these different
+interests of the male and female that
+
+ align:start position:0%
+interests of the male and female that
+ 
+
+ align:start position:0%
+interests of the male and female that
+that offer often are considerably
+
+ align:start position:0%
+that offer often are considerably
+ 
+
+ align:start position:0%
+that offer often are considerably
+different though it varies just how in
+
+ align:start position:0%
+different though it varies just how in
+ 
+
+ align:start position:0%
+different though it varies just how in
+different species but you always have
+
+ align:start position:0%
+different species but you always have
+ 
+
+ align:start position:0%
+different species but you always have
+this male female difference in in
+
+ align:start position:0%
+this male female difference in in
+ 
+
+ align:start position:0%
+this male female difference in in
+uh their production of the gamet so um
+
+ align:start position:0%
+uh their production of the gamet so um
+ 
+
+ align:start position:0%
+uh their production of the gamet so um
+the result is various you can call them
+
+ align:start position:0%
+the result is various you can call them
+ 
+
+ align:start position:0%
+the result is various you can call them
+compromises between the interests of the
+
+ align:start position:0%
+compromises between the interests of the
+ 
+
+ align:start position:0%
+compromises between the interests of the
+male and interests of the
+
+ align:start position:0%
+male and interests of the
+ 
+
+ align:start position:0%
+male and interests of the
+female and when we say this and talking
+
+ align:start position:0%
+female and when we say this and talking
+ 
+
+ align:start position:0%
+female and when we say this and talking
+about compromises I don't mean these
+
+ align:start position:0%
+about compromises I don't mean these
+ 
+
+ align:start position:0%
+about compromises I don't mean these
+animals are aware of it okay but looked
+
+ align:start position:0%
+animals are aware of it okay but looked
+ 
+
+ align:start position:0%
+animals are aware of it okay but looked
+at from as an evolutionary biologist or
+
+ align:start position:0%
+at from as an evolutionary biologist or
+ 
+
+ align:start position:0%
+at from as an evolutionary biologist or
+sociobiologist
+
+ align:start position:0%
+sociobiologist
+ 
+
+ align:start position:0%
+sociobiologist
+uh you interpret it in terms of
+
+ align:start position:0%
+uh you interpret it in terms of
+ 
+
+ align:start position:0%
+uh you interpret it in terms of
+evolution not in terms of what they're
+
+ align:start position:0%
+evolution not in terms of what they're
+ 
+
+ align:start position:0%
+evolution not in terms of what they're
+aware of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and of course we know the
+
+ align:start position:0%
+okay and of course we know the
+ 
+
+ align:start position:0%
+okay and of course we know the
+reproductive investment varies we've
+
+ align:start position:0%
+reproductive investment varies we've
+ 
+
+ align:start position:0%
+reproductive investment varies we've
+already talked about that and so now we
+
+ align:start position:0%
+already talked about that and so now we
+ 
+
+ align:start position:0%
+already talked about that and so now we
+have to talk about mate Choice which
+
+ align:start position:0%
+have to talk about mate Choice which
+ 
+
+ align:start position:0%
+have to talk about mate Choice which
+varies a lot and there's a lot of
+
+ align:start position:0%
+varies a lot and there's a lot of
+ 
+
+ align:start position:0%
+varies a lot and there's a lot of
+studies of it and by sociobiologists and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+others made Choice by
+
+ align:start position:0%
+others made Choice by
+ 
+
+ align:start position:0%
+others made Choice by
+females appears
+
+ align:start position:0%
+females appears
+ 
+
+ align:start position:0%
+females appears
+in most cases in almost all cases to be
+
+ align:start position:0%
+in most cases in almost all cases to be
+ 
+
+ align:start position:0%
+in most cases in almost all cases to be
+based on one of two properties of the
+
+ align:start position:0%
+based on one of two properties of the
+ 
+
+ align:start position:0%
+based on one of two properties of the
+male so we want to know what those are
+
+ align:start position:0%
+male so we want to know what those are
+ 
+
+ align:start position:0%
+male so we want to know what those are
+and we want
+
+ align:start position:0%
+and we want
+ 
+
+ align:start position:0%
+and we want
+examples and
+
+ align:start position:0%
+examples and
+ 
+
+ align:start position:0%
+examples and
+uh of each type of uh Choice first of
+
+ align:start position:0%
+uh of each type of uh Choice first of
+ 
+
+ align:start position:0%
+uh of each type of uh Choice first of
+all material
+
+ align:start position:0%
+all material
+ 
+
+ align:start position:0%
+all material
+benefits you know what kind of resources
+
+ align:start position:0%
+benefits you know what kind of resources
+ 
+
+ align:start position:0%
+benefits you know what kind of resources
+does that male is that male capable of
+
+ align:start position:0%
+does that male is that male capable of
+ 
+
+ align:start position:0%
+does that male is that male capable of
+providing why should I choose him so for
+
+ align:start position:0%
+providing why should I choose him so for
+ 
+
+ align:start position:0%
+providing why should I choose him so for
+example in the turn the common
+
+ align:start position:0%
+example in the turn the common
+ 
+
+ align:start position:0%
+example in the turn the common
+turn uh if he wants to mate he better
+
+ align:start position:0%
+turn uh if he wants to mate he better
+ 
+
+ align:start position:0%
+turn uh if he wants to mate he better
+bring her something good to
+
+ align:start position:0%
+bring her something good to
+ 
+
+ align:start position:0%
+bring her something good to
+eat and he brings freshly caught fish to
+
+ align:start position:0%
+eat and he brings freshly caught fish to
+ 
+
+ align:start position:0%
+eat and he brings freshly caught fish to
+the female the bigger the fish the
+
+ align:start position:0%
+the female the bigger the fish the
+ 
+
+ align:start position:0%
+the female the bigger the fish the
+better if he's not such a good forger
+
+ align:start position:0%
+better if he's not such a good forger
+ 
+
+ align:start position:0%
+better if he's not such a good forger
+and doesn't bring her enough she may not
+
+ align:start position:0%
+and doesn't bring her enough she may not
+ 
+
+ align:start position:0%
+and doesn't bring her enough she may not
+mate with
+
+ align:start position:0%
+mate with
+ 
+
+ align:start position:0%
+mate with
+it the black tip hanging
+
+ align:start position:0%
+it the black tip hanging
+ 
+
+ align:start position:0%
+it the black tip hanging
+ply we're going to talk about that
+
+ align:start position:0%
+ply we're going to talk about that
+ 
+
+ align:start position:0%
+ply we're going to talk about that
+next but he always brings food to the
+
+ align:start position:0%
+next but he always brings food to the
+ 
+
+ align:start position:0%
+next but he always brings food to the
+female
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also the difference there is that he
+
+ align:start position:0%
+also the difference there is that he
+ 
+
+ align:start position:0%
+also the difference there is that he
+makes with her well she's eating the
+
+ align:start position:0%
+makes with her well she's eating the
+ 
+
+ align:start position:0%
+makes with her well she's eating the
+food there's other material benefits
+
+ align:start position:0%
+food there's other material benefits
+ 
+
+ align:start position:0%
+food there's other material benefits
+that a female can look for let me just
+
+ align:start position:0%
+that a female can look for let me just
+ 
+
+ align:start position:0%
+that a female can look for let me just
+jump to the gold page we can talk about
+
+ align:start position:0%
+jump to the gold page we can talk about
+ 
+
+ align:start position:0%
+jump to the gold page we can talk about
+that now but when he's got more brightly
+
+ align:start position:0%
+that now but when he's got more brightly
+ 
+
+ align:start position:0%
+that now but when he's got more brightly
+colored
+
+ align:start position:0%
+colored
+ 
+
+ align:start position:0%
+colored
+plumage it means he's got more eroids in
+
+ align:start position:0%
+plumage it means he's got more eroids in
+ 
+
+ align:start position:0%
+plumage it means he's got more eroids in
+his body and there have been studies of
+
+ align:start position:0%
+his body and there have been studies of
+ 
+
+ align:start position:0%
+his body and there have been studies of
+that that Scott does review in the
+
+ align:start position:0%
+that that Scott does review in the
+ 
+
+ align:start position:0%
+that that Scott does review in the
+reading
+
+ align:start position:0%
+reading
+ 
+
+ align:start position:0%
+reading
+uh that show that carotenoids high
+
+ align:start position:0%
+uh that show that carotenoids high
+ 
+
+ align:start position:0%
+uh that show that carotenoids high
+levels are cor correlated with strong
+
+ align:start position:0%
+levels are cor correlated with strong
+ 
+
+ align:start position:0%
+levels are cor correlated with strong
+immune systems but it indicates Better
+
+ align:start position:0%
+immune systems but it indicates Better
+ 
+
+ align:start position:0%
+immune systems but it indicates Better
+Health and that has to be because he's
+
+ align:start position:0%
+Health and that has to be because he's
+ 
+
+ align:start position:0%
+Health and that has to be because he's
+getting the carotenoids from his diet so
+
+ align:start position:0%
+getting the carotenoids from his diet so
+ 
+
+ align:start position:0%
+getting the carotenoids from his diet so
+he's a good forager and he's less also
+
+ align:start position:0%
+he's a good forager and he's less also
+ 
+
+ align:start position:0%
+he's a good forager and he's less also
+the studies indicate he's less likely to
+
+ align:start position:0%
+the studies indicate he's less likely to
+ 
+
+ align:start position:0%
+the studies indicate he's less likely to
+have parasites all important if that uh
+
+ align:start position:0%
+have parasites all important if that uh
+ 
+
+ align:start position:0%
+have parasites all important if that uh
+if he's going to be helping the
+
+ align:start position:0%
+if he's going to be helping the
+ 
+
+ align:start position:0%
+if he's going to be helping the
+female let's just show that picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here there's the gold p and there's a
+
+ align:start position:0%
+here there's the gold p and there's a
+ 
+
+ align:start position:0%
+here there's the gold p and there's a
+the female on the right and the a pretty
+
+ align:start position:0%
+the female on the right and the a pretty
+ 
+
+ align:start position:0%
+the female on the right and the a pretty
+brightly colored gold pinch on the left
+
+ align:start position:0%
+brightly colored gold pinch on the left
+ 
+
+ align:start position:0%
+brightly colored gold pinch on the left
+so he's got quite he's been taking in
+
+ align:start position:0%
+so he's got quite he's been taking in
+ 
+
+ align:start position:0%
+so he's got quite he's been taking in
+carotenoid he's a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forager
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what other than things other than
+
+ align:start position:0%
+well what other than things other than
+ 
+
+ align:start position:0%
+well what other than things other than
+material benefits well how handsome male
+
+ align:start position:0%
+material benefits well how handsome male
+ 
+
+ align:start position:0%
+material benefits well how handsome male
+is how attractive as he is just by
+
+ align:start position:0%
+is how attractive as he is just by
+ 
+
+ align:start position:0%
+is how attractive as he is just by
+himself I mean if the females let's say
+
+ align:start position:0%
+himself I mean if the females let's say
+ 
+
+ align:start position:0%
+himself I mean if the females let's say
+you let's just take humans the female is
+
+ align:start position:0%
+you let's just take humans the female is
+ 
+
+ align:start position:0%
+you let's just take humans the female is
+wealthy she's already got all the
+
+ align:start position:0%
+wealthy she's already got all the
+ 
+
+ align:start position:0%
+wealthy she's already got all the
+material benefits she's need maybe he
+
+ align:start position:0%
+material benefits she's need maybe he
+ 
+
+ align:start position:0%
+material benefits she's need maybe he
+has servants well then just
+
+ align:start position:0%
+has servants well then just
+ 
+
+ align:start position:0%
+has servants well then just
+choose the best looking strongest male
+
+ align:start position:0%
+choose the best looking strongest male
+ 
+
+ align:start position:0%
+choose the best looking strongest male
+get good jeans just focus on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can might not work so well because
+
+ align:start position:0%
+that can might not work so well because
+ 
+
+ align:start position:0%
+that can might not work so well because
+she's her Offspring is going to inherit
+
+ align:start position:0%
+she's her Offspring is going to inherit
+ 
+
+ align:start position:0%
+she's her Offspring is going to inherit
+her genes and his so if he's not good at
+
+ align:start position:0%
+her genes and his so if he's not good at
+ 
+
+ align:start position:0%
+her genes and his so if he's not good at
+resource provision her Offspring might
+
+ align:start position:0%
+resource provision her Offspring might
+ 
+
+ align:start position:0%
+resource provision her Offspring might
+not be as well off as she
+
+ align:start position:0%
+not be as well off as she
+ 
+
+ align:start position:0%
+not be as well off as she
+is but both of these things are invol in
+
+ align:start position:0%
+is but both of these things are invol in
+ 
+
+ align:start position:0%
+is but both of these things are invol in
+some species it seems to be totally am
+
+ align:start position:0%
+some species it seems to be totally am
+ 
+
+ align:start position:0%
+some species it seems to be totally am
+Mount material benefits but in most in
+
+ align:start position:0%
+Mount material benefits but in most in
+ 
+
+ align:start position:0%
+Mount material benefits but in most in
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+species other factors of how attractive
+
+ align:start position:0%
+species other factors of how attractive
+ 
+
+ align:start position:0%
+species other factors of how attractive
+the male is will affect the female on
+
+ align:start position:0%
+the male is will affect the female on
+ 
+
+ align:start position:0%
+the male is will affect the female on
+her
+
+ align:start position:0%
+her
+ 
+
+ align:start position:0%
+her
+choice let's go back to the hanging
+
+ align:start position:0%
+choice let's go back to the hanging
+ 
+
+ align:start position:0%
+choice let's go back to the hanging
+flies now
+
+ align:start position:0%
+flies now
+ 
+
+ align:start position:0%
+flies now
+this he I said he brings food to the
+
+ align:start position:0%
+this he I said he brings food to the
+ 
+
+ align:start position:0%
+this he I said he brings food to the
+female and he copulates whether well
+
+ align:start position:0%
+female and he copulates whether well
+ 
+
+ align:start position:0%
+female and he copulates whether well
+she's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eating and if he bring they found in
+
+ align:start position:0%
+eating and if he bring they found in
+ 
+
+ align:start position:0%
+eating and if he bring they found in
+studies that if he brings a larger gift
+
+ align:start position:0%
+studies that if he brings a larger gift
+ 
+
+ align:start position:0%
+studies that if he brings a larger gift
+of food that is a larger
+
+ align:start position:0%
+of food that is a larger
+ 
+
+ align:start position:0%
+of food that is a larger
+insect that she copulates longer with
+
+ align:start position:0%
+insect that she copulates longer with
+ 
+
+ align:start position:0%
+insect that she copulates longer with
+him why because it takes her longer to
+
+ align:start position:0%
+him why because it takes her longer to
+ 
+
+ align:start position:0%
+him why because it takes her longer to
+eat
+
+ align:start position:0%
+eat
+ 
+
+ align:start position:0%
+eat
+it and the longer she copulates the more
+
+ align:start position:0%
+it and the longer she copulates the more
+ 
+
+ align:start position:0%
+it and the longer she copulates the more
+sperm he transfers because it turns out
+
+ align:start position:0%
+sperm he transfers because it turns out
+ 
+
+ align:start position:0%
+sperm he transfers because it turns out
+and this is what the study show we show
+
+ align:start position:0%
+and this is what the study show we show
+ 
+
+ align:start position:0%
+and this is what the study show we show
+you a few graphs here this one was done
+
+ align:start position:0%
+you a few graphs here this one was done
+ 
+
+ align:start position:0%
+you a few graphs here this one was done
+in nature this is done in the lab okay
+
+ align:start position:0%
+in nature this is done in the lab okay
+ 
+
+ align:start position:0%
+in nature this is done in the lab okay
+and so they've plotted there on the
+
+ align:start position:0%
+and so they've plotted there on the
+ 
+
+ align:start position:0%
+and so they've plotted there on the
+ordinate uh in this case the duration of
+
+ align:start position:0%
+ordinate uh in this case the duration of
+ 
+
+ align:start position:0%
+ordinate uh in this case the duration of
+culation
+
+ align:start position:0%
+culation
+ 
+
+ align:start position:0%
+culation
+which is correlated with the amount of
+
+ align:start position:0%
+which is correlated with the amount of
+ 
+
+ align:start position:0%
+which is correlated with the amount of
+sperm being transferred and the the body
+
+ align:start position:0%
+sperm being transferred and the the body
+ 
+
+ align:start position:0%
+sperm being transferred and the the body
+size of the prey that he brings for her
+
+ align:start position:0%
+size of the prey that he brings for her
+ 
+
+ align:start position:0%
+size of the prey that he brings for her
+to eat and look at it the as the prey
+
+ align:start position:0%
+to eat and look at it the as the prey
+ 
+
+ align:start position:0%
+to eat and look at it the as the prey
+gets bigger and bigger up to a certain
+
+ align:start position:0%
+gets bigger and bigger up to a certain
+ 
+
+ align:start position:0%
+gets bigger and bigger up to a certain
+point he mates with him longer and
+
+ align:start position:0%
+point he mates with him longer and
+ 
+
+ align:start position:0%
+point he mates with him longer and
+longer but then it seems to level up and
+
+ align:start position:0%
+longer but then it seems to level up and
+ 
+
+ align:start position:0%
+longer but then it seems to level up and
+it's even clearer in the laboratory
+
+ align:start position:0%
+it's even clearer in the laboratory
+ 
+
+ align:start position:0%
+it's even clearer in the laboratory
+studies
+
+ align:start position:0%
+studies
+ 
+
+ align:start position:0%
+studies
+so the payoff to the male if he brings
+
+ align:start position:0%
+so the payoff to the male if he brings
+ 
+
+ align:start position:0%
+so the payoff to the male if he brings
+larger insects is increased quantity of
+
+ align:start position:0%
+larger insects is increased quantity of
+ 
+
+ align:start position:0%
+larger insects is increased quantity of
+sperm
+
+ align:start position:0%
+sperm
+ 
+
+ align:start position:0%
+sperm
+transferred I mean the ejaculation takes
+
+ align:start position:0%
+transferred I mean the ejaculation takes
+ 
+
+ align:start position:0%
+transferred I mean the ejaculation takes
+it turns out about 20 minutes in this
+
+ align:start position:0%
+it turns out about 20 minutes in this
+ 
+
+ align:start position:0%
+it turns out about 20 minutes in this
+animal so if he finish if she finishes
+
+ align:start position:0%
+animal so if he finish if she finishes
+ 
+
+ align:start position:0%
+animal so if he finish if she finishes
+eating before 20 minutes because he
+
+ align:start position:0%
+eating before 20 minutes because he
+ 
+
+ align:start position:0%
+eating before 20 minutes because he
+didn't bring a large enough insect he
+
+ align:start position:0%
+didn't bring a large enough insect he
+ 
+
+ align:start position:0%
+didn't bring a large enough insect he
+flies off finds another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+male so he may not end up being the
+
+ align:start position:0%
+male so he may not end up being the
+ 
+
+ align:start position:0%
+male so he may not end up being the
+father at least not of all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eggs if there's food left after 20
+
+ align:start position:0%
+eggs if there's food left after 20
+ 
+
+ align:start position:0%
+eggs if there's food left after 20
+minutes well the male gets a doggy bag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's the
+
+ align:start position:0%
+okay there's the
+ 
+
+ align:start position:0%
+okay there's the
+gold okay now I brought this up in the
+
+ align:start position:0%
+gold okay now I brought this up in the
+ 
+
+ align:start position:0%
+gold okay now I brought this up in the
+introduction we talk about Evolution as
+
+ align:start position:0%
+introduction we talk about Evolution as
+ 
+
+ align:start position:0%
+introduction we talk about Evolution as
+survival of the
+
+ align:start position:0%
+survival of the
+ 
+
+ align:start position:0%
+survival of the
+fittest okay question is what do we mean
+
+ align:start position:0%
+fittest okay question is what do we mean
+ 
+
+ align:start position:0%
+fittest okay question is what do we mean
+by by that it's survival of the fittest
+
+ align:start position:0%
+by by that it's survival of the fittest
+ 
+
+ align:start position:0%
+by by that it's survival of the fittest
+then why is it that certain species of
+
+ align:start position:0%
+then why is it that certain species of
+ 
+
+ align:start position:0%
+then why is it that certain species of
+spiders and also occurs in certain
+
+ align:start position:0%
+spiders and also occurs in certain
+ 
+
+ align:start position:0%
+spiders and also occurs in certain
+insects the male is eaten by the female
+
+ align:start position:0%
+insects the male is eaten by the female
+ 
+
+ align:start position:0%
+insects the male is eaten by the female
+in the active population it happens in
+
+ align:start position:0%
+in the active population it happens in
+ 
+
+ align:start position:0%
+in the active population it happens in
+the Australian redback
+
+ align:start position:0%
+the Australian redback
+ 
+
+ align:start position:0%
+the Australian redback
+spider uh and there are some reasons we
+
+ align:start position:0%
+spider uh and there are some reasons we
+ 
+
+ align:start position:0%
+spider uh and there are some reasons we
+can discern for how it's still
+
+ align:start position:0%
+can discern for how it's still
+ 
+
+ align:start position:0%
+can discern for how it's still
+benefiting him but there are other
+
+ align:start position:0%
+benefiting him but there are other
+ 
+
+ align:start position:0%
+benefiting him but there are other
+species too that do that the praying
+
+ align:start position:0%
+species too that do that the praying
+ 
+
+ align:start position:0%
+species too that do that the praying
+mantis is the best
+
+ align:start position:0%
+mantis is the best
+ 
+
+ align:start position:0%
+mantis is the best
+known uh the female tarantula commonly
+
+ align:start position:0%
+known uh the female tarantula commonly
+ 
+
+ align:start position:0%
+known uh the female tarantula commonly
+eats that's the burrowing spider in the
+
+ align:start position:0%
+eats that's the burrowing spider in the
+ 
+
+ align:start position:0%
+eats that's the burrowing spider in the
+American southwest for example they
+
+ align:start position:0%
+American southwest for example they
+ 
+
+ align:start position:0%
+American southwest for example they
+often eat males but it's not always
+
+ align:start position:0%
+often eat males but it's not always
+ 
+
+ align:start position:0%
+often eat males but it's not always
+their mate but it might
+
+ align:start position:0%
+their mate but it might
+ 
+
+ align:start position:0%
+their mate but it might
+be okay so here's the Australian redback
+
+ align:start position:0%
+be okay so here's the Australian redback
+ 
+
+ align:start position:0%
+be okay so here's the Australian redback
+spider see what they look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like these are the reasons why it can
+
+ align:start position:0%
+like these are the reasons why it can
+ 
+
+ align:start position:0%
+like these are the reasons why it can
+still benefit the male in terms of his
+
+ align:start position:0%
+still benefit the male in terms of his
+ 
+
+ align:start position:0%
+still benefit the male in terms of his
+passing on his being first of all he's
+
+ align:start position:0%
+passing on his being first of all he's
+ 
+
+ align:start position:0%
+passing on his being first of all he's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+likely to survive long enough to find a
+
+ align:start position:0%
+likely to survive long enough to find a
+ 
+
+ align:start position:0%
+likely to survive long enough to find a
+second mid they're shortlived
+
+ align:start position:0%
+second mid they're shortlived
+ 
+
+ align:start position:0%
+second mid they're shortlived
+animal and
+
+ align:start position:0%
+animal and
+ 
+
+ align:start position:0%
+animal and
+again if she eats
+
+ align:start position:0%
+again if she eats
+ 
+
+ align:start position:0%
+again if she eats
+him she's less likely to made again if
+
+ align:start position:0%
+him she's less likely to made again if
+ 
+
+ align:start position:0%
+him she's less likely to made again if
+she's well
+
+ align:start position:0%
+she's well
+ 
+
+ align:start position:0%
+she's well
+fed and more
+
+ align:start position:0%
+fed and more
+ 
+
+ align:start position:0%
+fed and more
+nutrition it can benefit her she's more
+
+ align:start position:0%
+nutrition it can benefit her she's more
+ 
+
+ align:start position:0%
+nutrition it can benefit her she's more
+likely than to have his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+offspring you know so what the hell go
+
+ align:start position:0%
+offspring you know so what the hell go
+ 
+
+ align:start position:0%
+offspring you know so what the hell go
+ahead okay here's the praying mantis
+
+ align:start position:0%
+ahead okay here's the praying mantis
+ 
+
+ align:start position:0%
+ahead okay here's the praying mantis
+there you see in the center I put the
+
+ align:start position:0%
+there you see in the center I put the
+ 
+
+ align:start position:0%
+there you see in the center I put the
+center picture of the male and a female
+
+ align:start position:0%
+center picture of the male and a female
+ 
+
+ align:start position:0%
+center picture of the male and a female
+the female is the bigger
+
+ align:start position:0%
+the female is the bigger
+ 
+
+ align:start position:0%
+the female is the bigger
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and in the low right there she's eating
+
+ align:start position:0%
+and in the low right there she's eating
+ 
+
+ align:start position:0%
+and in the low right there she's eating
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mail okay uh this is a study I found uh
+
+ align:start position:0%
+mail okay uh this is a study I found uh
+ 
+
+ align:start position:0%
+mail okay uh this is a study I found uh
+in the literature sexual cannibalism in
+
+ align:start position:0%
+in the literature sexual cannibalism in
+ 
+
+ align:start position:0%
+in the literature sexual cannibalism in
+the praying mansis this particular
+
+ align:start position:0%
+the praying mansis this particular
+ 
+
+ align:start position:0%
+the praying mansis this particular
+praying
+
+ align:start position:0%
+praying
+ 
+
+ align:start position:0%
+praying
+Manis
+
+ align:start position:0%
+Manis
+ 
+
+ align:start position:0%
+Manis
+uh they found that if you the females
+
+ align:start position:0%
+uh they found that if you the females
+ 
+
+ align:start position:0%
+uh they found that if you the females
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+wellfed they usually don't eat the male
+
+ align:start position:0%
+wellfed they usually don't eat the male
+ 
+
+ align:start position:0%
+wellfed they usually don't eat the male
+okay females that are fed more are
+
+ align:start position:0%
+okay females that are fed more are
+ 
+
+ align:start position:0%
+okay females that are fed more are
+heavier and they produce heavier eggs
+
+ align:start position:0%
+heavier and they produce heavier eggs
+ 
+
+ align:start position:0%
+heavier and they produce heavier eggs
+feel more likely to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survive if you feed the females less
+
+ align:start position:0%
+survive if you feed the females less
+ 
+
+ align:start position:0%
+survive if you feed the females less
+these are experiments where they can f
+
+ align:start position:0%
+these are experiments where they can f
+ 
+
+ align:start position:0%
+these are experiments where they can f
+that then the females are much more
+
+ align:start position:0%
+that then the females are much more
+ 
+
+ align:start position:0%
+that then the females are much more
+likely to eat the
+
+ align:start position:0%
+likely to eat the
+ 
+
+ align:start position:0%
+likely to eat the
+male so they did an experiment where
+
+ align:start position:0%
+male so they did an experiment where
+ 
+
+ align:start position:0%
+male so they did an experiment where
+some females were prevented from eating
+
+ align:start position:0%
+some females were prevented from eating
+ 
+
+ align:start position:0%
+some females were prevented from eating
+the male others were not prevented those
+
+ align:start position:0%
+the male others were not prevented those
+ 
+
+ align:start position:0%
+the male others were not prevented those
+that ate the male produced heavier
+
+ align:start position:0%
+that ate the male produced heavier
+ 
+
+ align:start position:0%
+that ate the male produced heavier
+eggs indicating that the cannibalism was
+
+ align:start position:0%
+eggs indicating that the cannibalism was
+ 
+
+ align:start position:0%
+eggs indicating that the cannibalism was
+adaptive for the
+
+ align:start position:0%
+adaptive for the
+ 
+
+ align:start position:0%
+adaptive for the
+female but the
+
+ align:start position:0%
+female but the
+ 
+
+ align:start position:0%
+female but the
+males unlike those spiders we talked
+
+ align:start position:0%
+males unlike those spiders we talked
+ 
+
+ align:start position:0%
+males unlike those spiders we talked
+about the males do try to avoid being
+
+ align:start position:0%
+about the males do try to avoid being
+ 
+
+ align:start position:0%
+about the males do try to avoid being
+eaten indicating from that behavior
+
+ align:start position:0%
+eaten indicating from that behavior
+ 
+
+ align:start position:0%
+eaten indicating from that behavior
+that's probably less adaptive to the
+
+ align:start position:0%
+that's probably less adaptive to the
+ 
+
+ align:start position:0%
+that's probably less adaptive to the
+males that may mean that if he was not
+
+ align:start position:0%
+males that may mean that if he was not
+ 
+
+ align:start position:0%
+males that may mean that if he was not
+eaten maybe he would have a chance to
+
+ align:start position:0%
+eaten maybe he would have a chance to
+ 
+
+ align:start position:0%
+eaten maybe he would have a chance to
+meet with another female that's not
+
+ align:start position:0%
+meet with another female that's not
+ 
+
+ align:start position:0%
+meet with another female that's not
+certain but that's what the study
+
+ align:start position:0%
+certain but that's what the study
+ 
+
+ align:start position:0%
+certain but that's what the study
+indicates
+
+ align:start position:0%
+indicates
+ 
+
+ align:start position:0%
+indicates
+so how adaptive the behavior is can be
+
+ align:start position:0%
+so how adaptive the behavior is can be
+ 
+
+ align:start position:0%
+so how adaptive the behavior is can be
+different for the female and for the
+
+ align:start position:0%
+different for the female and for the
+ 
+
+ align:start position:0%
+different for the female and for the
+male it's clearly adapted for the
+
+ align:start position:0%
+male it's clearly adapted for the
+ 
+
+ align:start position:0%
+male it's clearly adapted for the
+female for the males of some species
+
+ align:start position:0%
+female for the males of some species
+ 
+
+ align:start position:0%
+female for the males of some species
+as we said for the spider probably
+
+ align:start position:0%
+as we said for the spider probably
+ 
+
+ align:start position:0%
+as we said for the spider probably
+benefits him more than hurts him because
+
+ align:start position:0%
+benefits him more than hurts him because
+ 
+
+ align:start position:0%
+benefits him more than hurts him because
+he's not going to live long enough to
+
+ align:start position:0%
+he's not going to live long enough to
+ 
+
+ align:start position:0%
+he's not going to live long enough to
+made again anyway but maybe for some
+
+ align:start position:0%
+made again anyway but maybe for some
+ 
+
+ align:start position:0%
+made again anyway but maybe for some
+like the praying mantis it may not be
+
+ align:start position:0%
+like the praying mantis it may not be
+ 
+
+ align:start position:0%
+like the praying mantis it may not be
+the most adaptive for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+him okay so what are the conditions that
+
+ align:start position:0%
+him okay so what are the conditions that
+ 
+
+ align:start position:0%
+him okay so what are the conditions that
+make the female more likely to be the
+
+ align:start position:0%
+make the female more likely to be the
+ 
+
+ align:start position:0%
+make the female more likely to be the
+one that is making the choice of
+
+ align:start position:0%
+one that is making the choice of
+ 
+
+ align:start position:0%
+one that is making the choice of
+mates the studies have tended to focus
+
+ align:start position:0%
+mates the studies have tended to focus
+ 
+
+ align:start position:0%
+mates the studies have tended to focus
+on species with sex Ro reversal that is
+
+ align:start position:0%
+on species with sex Ro reversal that is
+ 
+
+ align:start position:0%
+on species with sex Ro reversal that is
+the males doing all the brood tending
+
+ align:start position:0%
+the males doing all the brood tending
+ 
+
+ align:start position:0%
+the males doing all the brood tending
+and so forth but there are
+
+ align:start position:0%
+and so forth but there are
+ 
+
+ align:start position:0%
+and so forth but there are
+exceptions uh so they look into the
+
+ align:start position:0%
+exceptions uh so they look into the
+ 
+
+ align:start position:0%
+exceptions uh so they look into the
+conditions that seem to facilitate the
+
+ align:start position:0%
+conditions that seem to facilitate the
+ 
+
+ align:start position:0%
+conditions that seem to facilitate the
+evolution of selective mate Choice
+
+ align:start position:0%
+evolution of selective mate Choice
+ 
+
+ align:start position:0%
+evolution of selective mate Choice
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+uh by the male instead of the
+
+ align:start position:0%
+uh by the male instead of the
+ 
+
+ align:start position:0%
+uh by the male instead of the
+female first of all if the male defends
+
+ align:start position:0%
+female first of all if the male defends
+ 
+
+ align:start position:0%
+female first of all if the male defends
+The
+
+ align:start position:0%
+The
+ 
+
+ align:start position:0%
+The
+Nest there's a limit like like in the
+
+ align:start position:0%
+Nest there's a limit like like in the
+ 
+
+ align:start position:0%
+Nest there's a limit like like in the
+stickle backs there there's a limited
+
+ align:start position:0%
+stickle backs there there's a limited
+ 
+
+ align:start position:0%
+stickle backs there there's a limited
+number of eggs he can
+
+ align:start position:0%
+number of eggs he can
+ 
+
+ align:start position:0%
+number of eggs he can
+defend uh he certainly would have a lot
+
+ align:start position:0%
+defend uh he certainly would have a lot
+ 
+
+ align:start position:0%
+defend uh he certainly would have a lot
+of difficulty defending more than one
+
+ align:start position:0%
+of difficulty defending more than one
+ 
+
+ align:start position:0%
+of difficulty defending more than one
+Nest
+
+ align:start position:0%
+Nest
+ 
+
+ align:start position:0%
+Nest
+uh so he can't maximize reproduction
+
+ align:start position:0%
+uh so he can't maximize reproduction
+ 
+
+ align:start position:0%
+uh so he can't maximize reproduction
+just by indiscriminate mating
+
+ align:start position:0%
+just by indiscriminate mating
+ 
+
+ align:start position:0%
+just by indiscriminate mating
+okay so it's in his best interest to
+
+ align:start position:0%
+okay so it's in his best interest to
+ 
+
+ align:start position:0%
+okay so it's in his best interest to
+choose the best female either with the
+
+ align:start position:0%
+choose the best female either with the
+ 
+
+ align:start position:0%
+choose the best female either with the
+most most eggs for that one nest and
+
+ align:start position:0%
+most most eggs for that one nest and
+ 
+
+ align:start position:0%
+most most eggs for that one nest and
+that seems to be true for the stickle
+
+ align:start position:0%
+that seems to be true for the stickle
+ 
+
+ align:start position:0%
+that seems to be true for the stickle
+bags uh or other signs that it's a male
+
+ align:start position:0%
+bags uh or other signs that it's a male
+ 
+
+ align:start position:0%
+bags uh or other signs that it's a male
+a female that's producing perhaps
+
+ align:start position:0%
+a female that's producing perhaps
+ 
+
+ align:start position:0%
+a female that's producing perhaps
+heavier eggs and so forth they'd have a
+
+ align:start position:0%
+heavier eggs and so forth they'd have a
+ 
+
+ align:start position:0%
+heavier eggs and so forth they'd have a
+better chance of
+
+ align:start position:0%
+better chance of
+ 
+
+ align:start position:0%
+better chance of
+survival and if there's many more
+
+ align:start position:0%
+survival and if there's many more
+ 
+
+ align:start position:0%
+survival and if there's many more
+females than males and that's true of
+
+ align:start position:0%
+females than males and that's true of
+ 
+
+ align:start position:0%
+females than males and that's true of
+some species then mate choice is more
+
+ align:start position:0%
+some species then mate choice is more
+ 
+
+ align:start position:0%
+some species then mate choice is more
+likely male male males making the choice
+
+ align:start position:0%
+likely male male males making the choice
+ 
+
+ align:start position:0%
+likely male male males making the choice
+is more likely
+
+ align:start position:0%
+is more likely
+ 
+
+ align:start position:0%
+is more likely
+especially if the male's also in charge
+
+ align:start position:0%
+especially if the male's also in charge
+ 
+
+ align:start position:0%
+especially if the male's also in charge
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now you also have variations in
+
+ align:start position:0%
+okay now you also have variations in
+ 
+
+ align:start position:0%
+okay now you also have variations in
+mating strategies even within a species
+
+ align:start position:0%
+mating strategies even within a species
+ 
+
+ align:start position:0%
+mating strategies even within a species
+so that's what I want to talk about here
+
+ align:start position:0%
+so that's what I want to talk about here
+ 
+
+ align:start position:0%
+so that's what I want to talk about here
+the different male mating
+
+ align:start position:0%
+the different male mating
+ 
+
+ align:start position:0%
+the different male mating
+strategies I ask for example of how in
+
+ align:start position:0%
+strategies I ask for example of how in
+ 
+
+ align:start position:0%
+strategies I ask for example of how in
+some species different individual males
+
+ align:start position:0%
+some species different individual males
+ 
+
+ align:start position:0%
+some species different individual males
+adopt very different mating Str strategy
+
+ align:start position:0%
+adopt very different mating Str strategy
+ 
+
+ align:start position:0%
+adopt very different mating Str strategy
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+uh these males may all have the same
+
+ align:start position:0%
+uh these males may all have the same
+ 
+
+ align:start position:0%
+uh these males may all have the same
+genes okay and these are the examples
+
+ align:start position:0%
+genes okay and these are the examples
+ 
+
+ align:start position:0%
+genes okay and these are the examples
+we'll talk about the scar of beetles
+
+ align:start position:0%
+we'll talk about the scar of beetles
+ 
+
+ align:start position:0%
+we'll talk about the scar of beetles
+some of which are very big and they have
+
+ align:start position:0%
+some of which are very big and they have
+ 
+
+ align:start position:0%
+some of which are very big and they have
+horns some of them are smaller and don't
+
+ align:start position:0%
+horns some of them are smaller and don't
+ 
+
+ align:start position:0%
+horns some of them are smaller and don't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+horns so it looks like those big ones
+
+ align:start position:0%
+horns so it looks like those big ones
+ 
+
+ align:start position:0%
+horns so it looks like those big ones
+are a lot more
+
+ align:start position:0%
+are a lot more
+ 
+
+ align:start position:0%
+are a lot more
+fit we want to know you know what do the
+
+ align:start position:0%
+fit we want to know you know what do the
+ 
+
+ align:start position:0%
+fit we want to know you know what do the
+smaller ones do you find the same
+
+ align:start position:0%
+smaller ones do you find the same
+ 
+
+ align:start position:0%
+smaller ones do you find the same
+problem in toads because some of them
+
+ align:start position:0%
+problem in toads because some of them
+ 
+
+ align:start position:0%
+problem in toads because some of them
+are very big and can croak loudly and
+
+ align:start position:0%
+are very big and can croak loudly and
+ 
+
+ align:start position:0%
+are very big and can croak loudly and
+attract females some are not so much
+
+ align:start position:0%
+attract females some are not so much
+ 
+
+ align:start position:0%
+attract females some are not so much
+smaller same is true of iguanas we saw
+
+ align:start position:0%
+smaller same is true of iguanas we saw
+ 
+
+ align:start position:0%
+smaller same is true of iguanas we saw
+in the picture earlier we were talking
+
+ align:start position:0%
+in the picture earlier we were talking
+ 
+
+ align:start position:0%
+in the picture earlier we were talking
+about foraging strategies you found out
+
+ align:start position:0%
+about foraging strategies you found out
+ 
+
+ align:start position:0%
+about foraging strategies you found out
+the foraging strategies were quite
+
+ align:start position:0%
+the foraging strategies were quite
+ 
+
+ align:start position:0%
+the foraging strategies were quite
+different in the large iguanas and the
+
+ align:start position:0%
+different in the large iguanas and the
+ 
+
+ align:start position:0%
+different in the large iguanas and the
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+ones they have a more unusual mating
+
+ align:start position:0%
+ones they have a more unusual mating
+ 
+
+ align:start position:0%
+ones they have a more unusual mating
+strategy so first of all the scarab
+
+ align:start position:0%
+strategy so first of all the scarab
+ 
+
+ align:start position:0%
+strategy so first of all the scarab
+beetles they've evolved two distinct
+
+ align:start position:0%
+beetles they've evolved two distinct
+ 
+
+ align:start position:0%
+beetles they've evolved two distinct
+morphologies as I mentioned the smaller
+
+ align:start position:0%
+morphologies as I mentioned the smaller
+ 
+
+ align:start position:0%
+morphologies as I mentioned the smaller
+ones have no harms but they're more
+
+ align:start position:0%
+ones have no harms but they're more
+ 
+
+ align:start position:0%
+ones have no harms but they're more
+agile they're
+
+ align:start position:0%
+agile they're
+ 
+
+ align:start position:0%
+agile they're
+quicker so they can some very often
+
+ align:start position:0%
+quicker so they can some very often
+ 
+
+ align:start position:0%
+quicker so they can some very often
+they're able the male is defending they
+
+ align:start position:0%
+they're able the male is defending they
+ 
+
+ align:start position:0%
+they're able the male is defending they
+have underground nest and the male will
+
+ align:start position:0%
+have underground nest and the male will
+ 
+
+ align:start position:0%
+have underground nest and the male will
+defend Nest he will try to keep other
+
+ align:start position:0%
+defend Nest he will try to keep other
+ 
+
+ align:start position:0%
+defend Nest he will try to keep other
+Mal from getting it his eggs okay or to
+
+ align:start position:0%
+Mal from getting it his eggs okay or to
+ 
+
+ align:start position:0%
+Mal from getting it his eggs okay or to
+getting at the female who is there in
+
+ align:start position:0%
+getting at the female who is there in
+ 
+
+ align:start position:0%
+getting at the female who is there in
+the tunnel
+
+ align:start position:0%
+the tunnel
+ 
+
+ align:start position:0%
+the tunnel
+but those small males are often able to
+
+ align:start position:0%
+but those small males are often able to
+ 
+
+ align:start position:0%
+but those small males are often able to
+get past the male the big male avoid his
+
+ align:start position:0%
+get past the male the big male avoid his
+ 
+
+ align:start position:0%
+get past the male the big male avoid his
+horns and get to the female now he's got
+
+ align:start position:0%
+horns and get to the female now he's got
+ 
+
+ align:start position:0%
+horns and get to the female now he's got
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+quick because why does m just turn
+
+ align:start position:0%
+quick because why does m just turn
+ 
+
+ align:start position:0%
+quick because why does m just turn
+around and get him well he's so he's so
+
+ align:start position:0%
+around and get him well he's so he's so
+ 
+
+ align:start position:0%
+around and get him well he's so he's so
+big with these big wide horns he he
+
+ align:start position:0%
+big with these big wide horns he he
+ 
+
+ align:start position:0%
+big with these big wide horns he he
+usually has to come clear out of the
+
+ align:start position:0%
+usually has to come clear out of the
+ 
+
+ align:start position:0%
+usually has to come clear out of the
+tunnel and turn
+
+ align:start position:0%
+tunnel and turn
+ 
+
+ align:start position:0%
+tunnel and turn
+around well that gives that small male
+
+ align:start position:0%
+around well that gives that small male
+ 
+
+ align:start position:0%
+around well that gives that small male
+just time
+
+ align:start position:0%
+just time
+ 
+
+ align:start position:0%
+just time
+okay so sneak a quick one with the
+
+ align:start position:0%
+okay so sneak a quick one with the
+ 
+
+ align:start position:0%
+okay so sneak a quick one with the
+female before he can
+
+ align:start position:0%
+female before he can
+ 
+
+ align:start position:0%
+female before he can
+attack and then he just has the problem
+
+ align:start position:0%
+attack and then he just has the problem
+ 
+
+ align:start position:0%
+attack and then he just has the problem
+of getting past him because he will come
+
+ align:start position:0%
+of getting past him because he will come
+ 
+
+ align:start position:0%
+of getting past him because he will come
+in now with a small Marine iguana it's
+
+ align:start position:0%
+in now with a small Marine iguana it's
+ 
+
+ align:start position:0%
+in now with a small Marine iguana it's
+even more
+
+ align:start position:0%
+even more
+ 
+
+ align:start position:0%
+even more
+interesting the copulation normally
+
+ align:start position:0%
+interesting the copulation normally
+ 
+
+ align:start position:0%
+interesting the copulation normally
+requires several minutes for the male to
+
+ align:start position:0%
+requires several minutes for the male to
+ 
+
+ align:start position:0%
+requires several minutes for the male to
+ejaculate uh but these small iguanas
+
+ align:start position:0%
+ejaculate uh but these small iguanas
+ 
+
+ align:start position:0%
+ejaculate uh but these small iguanas
+have the ability to ejaculate in advance
+
+ align:start position:0%
+have the ability to ejaculate in advance
+ 
+
+ align:start position:0%
+have the ability to ejaculate in advance
+and store the sperm in a Groove in their
+
+ align:start position:0%
+and store the sperm in a Groove in their
+ 
+
+ align:start position:0%
+and store the sperm in a Groove in their
+penis so he only needs a very brief
+
+ align:start position:0%
+penis so he only needs a very brief
+ 
+
+ align:start position:0%
+penis so he only needs a very brief
+population deposits the sperm and gets
+
+ align:start position:0%
+population deposits the sperm and gets
+ 
+
+ align:start position:0%
+population deposits the sperm and gets
+out of
+
+ align:start position:0%
+out of
+ 
+
+ align:start position:0%
+out of
+it okay and of course the male the
+
+ align:start position:0%
+it okay and of course the male the
+ 
+
+ align:start position:0%
+it okay and of course the male the
+bigger male will be trying to prevent
+
+ align:start position:0%
+bigger male will be trying to prevent
+ 
+
+ align:start position:0%
+bigger male will be trying to prevent
+him from mating so but so they've
+
+ align:start position:0%
+him from mating so but so they've
+ 
+
+ align:start position:0%
+him from mating so but so they've
+evolved with trategy they don't need so
+
+ align:start position:0%
+evolved with trategy they don't need so
+ 
+
+ align:start position:0%
+evolved with trategy they don't need so
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+time so both the large and the small
+
+ align:start position:0%
+time so both the large and the small
+ 
+
+ align:start position:0%
+time so both the large and the small
+them males are able to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+okay let's talk about the various mating
+
+ align:start position:0%
+okay let's talk about the various mating
+ 
+
+ align:start position:0%
+okay let's talk about the various mating
+systems and why there are so many
+
+ align:start position:0%
+systems and why there are so many
+ 
+
+ align:start position:0%
+systems and why there are so many
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones and here we mean bigy polyandry
+
+ align:start position:0%
+ones and here we mean bigy polyandry
+ 
+
+ align:start position:0%
+ones and here we mean bigy polyandry
+bandry U this this was studied
+
+ align:start position:0%
+bandry U this this was studied
+ 
+
+ align:start position:0%
+bandry U this this was studied
+extensively in Birds by Nick Davies
+
+ align:start position:0%
+extensively in Birds by Nick Davies
+ 
+
+ align:start position:0%
+extensively in Birds by Nick Davies
+uh most of his studies were done on the
+
+ align:start position:0%
+uh most of his studies were done on the
+ 
+
+ align:start position:0%
+uh most of his studies were done on the
+reproductive behavior of the dunck it's
+
+ align:start position:0%
+reproductive behavior of the dunck it's
+ 
+
+ align:start position:0%
+reproductive behavior of the dunck it's
+a small European song bird the Hedge
+
+ align:start position:0%
+a small European song bird the Hedge
+ 
+
+ align:start position:0%
+a small European song bird the Hedge
+Sparrow is its common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+name and they found all the different
+
+ align:start position:0%
+name and they found all the different
+ 
+
+ align:start position:0%
+name and they found all the different
+varieties of mating strategy in this
+
+ align:start position:0%
+varieties of mating strategy in this
+ 
+
+ align:start position:0%
+varieties of mating strategy in this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+one species of bird and this is the way
+
+ align:start position:0%
+one species of bird and this is the way
+ 
+
+ align:start position:0%
+one species of bird and this is the way
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+summarized uh that issue he said we
+
+ align:start position:0%
+summarized uh that issue he said we
+ 
+
+ align:start position:0%
+summarized uh that issue he said we
+should view The Mating Game not as a
+
+ align:start position:0%
+should view The Mating Game not as a
+ 
+
+ align:start position:0%
+should view The Mating Game not as a
+Cooper operation between the Sexes but
+
+ align:start position:0%
+Cooper operation between the Sexes but
+ 
+
+ align:start position:0%
+Cooper operation between the Sexes but
+as a conflict resulting in a compromise
+
+ align:start position:0%
+as a conflict resulting in a compromise
+ 
+
+ align:start position:0%
+as a conflict resulting in a compromise
+in the interests of one or both of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them it doesn't sound
+
+ align:start position:0%
+them it doesn't sound
+ 
+
+ align:start position:0%
+them it doesn't sound
+like a lyric love poetry does
+
+ align:start position:0%
+like a lyric love poetry does
+ 
+
+ align:start position:0%
+like a lyric love poetry does
+it no we're talking about
+
+ align:start position:0%
+it no we're talking about
+ 
+
+ align:start position:0%
+it no we're talking about
+Evolution okay and yes it has affected
+
+ align:start position:0%
+Evolution okay and yes it has affected
+ 
+
+ align:start position:0%
+Evolution okay and yes it has affected
+humans very
+
+ align:start position:0%
+humans very
+ 
+
+ align:start position:0%
+humans very
+strongly here's the basic mating systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monogamy you all know what monogamy is
+
+ align:start position:0%
+monogamy you all know what monogamy is
+ 
+
+ align:start position:0%
+monogamy you all know what monogamy is
+but we have to distinguish between
+
+ align:start position:0%
+but we have to distinguish between
+ 
+
+ align:start position:0%
+but we have to distinguish between
+social monogamy and genetic
+
+ align:start position:0%
+social monogamy and genetic
+ 
+
+ align:start position:0%
+social monogamy and genetic
+monogamy what's the
+
+ align:start position:0%
+monogamy what's the
+ 
+
+ align:start position:0%
+monogamy what's the
+difference social monogamy means one the
+
+ align:start position:0%
+difference social monogamy means one the
+ 
+
+ align:start position:0%
+difference social monogamy means one the
+female lives with the same
+
+ align:start position:0%
+female lives with the same
+ 
+
+ align:start position:0%
+female lives with the same
+male all the time the same male these
+
+ align:start position:0%
+male all the time the same male these
+ 
+
+ align:start position:0%
+male all the time the same male these
+monogamy genetic monogamy
+
+ align:start position:0%
+monogamy genetic monogamy
+ 
+
+ align:start position:0%
+monogamy genetic monogamy
+as who fathers are children and
+
+ align:start position:0%
+as who fathers are children and
+ 
+
+ align:start position:0%
+as who fathers are children and
+here in many cases they thought social
+
+ align:start position:0%
+here in many cases they thought social
+ 
+
+ align:start position:0%
+here in many cases they thought social
+monogamy always meant genetic monogamy
+
+ align:start position:0%
+monogamy always meant genetic monogamy
+ 
+
+ align:start position:0%
+monogamy always meant genetic monogamy
+but now we have the ability to look at
+
+ align:start position:0%
+but now we have the ability to look at
+ 
+
+ align:start position:0%
+but now we have the ability to look at
+the DNA and we found out we find out
+
+ align:start position:0%
+the DNA and we found out we find out
+ 
+
+ align:start position:0%
+the DNA and we found out we find out
+that that's often not true not for
+
+ align:start position:0%
+that that's often not true not for
+ 
+
+ align:start position:0%
+that that's often not true not for
+humans not for Birds but these are the
+
+ align:start position:0%
+humans not for Birds but these are the
+ 
+
+ align:start position:0%
+humans not for Birds but these are the
+where most of the studies have been done
+
+ align:start position:0%
+where most of the studies have been done
+ 
+
+ align:start position:0%
+where most of the studies have been done
+especially
+
+ align:start position:0%
+especially
+ 
+
+ align:start position:0%
+especially
+Birds
+
+ align:start position:0%
+Birds
+ 
+
+ align:start position:0%
+Birds
+okay polygyny that's when you
+
+ align:start position:0%
+okay polygyny that's when you
+ 
+
+ align:start position:0%
+okay polygyny that's when you
+have one male mating with more than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+female and
+
+ align:start position:0%
+female and
+ 
+
+ align:start position:0%
+female and
+uh you have the resource-based polygyny
+
+ align:start position:0%
+uh you have the resource-based polygyny
+ 
+
+ align:start position:0%
+uh you have the resource-based polygyny
+WHERE females
+
+ align:start position:0%
+WHERE females
+ 
+
+ align:start position:0%
+WHERE females
+chose by the value of the territory
+
+ align:start position:0%
+chose by the value of the territory
+ 
+
+ align:start position:0%
+chose by the value of the territory
+that's done in the
+
+ align:start position:0%
+that's done in the
+ 
+
+ align:start position:0%
+that's done in the
+Iguana the pl P fly
+
+ align:start position:0%
+Iguana the pl P fly
+ 
+
+ align:start position:0%
+Iguana the pl P fly
+catcher
+
+ align:start position:0%
+catcher
+ 
+
+ align:start position:0%
+catcher
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and there you find interesting choices a
+
+ align:start position:0%
+and there you find interesting choices a
+ 
+
+ align:start position:0%
+and there you find interesting choices a
+female faced with a choice between a
+
+ align:start position:0%
+female faced with a choice between a
+ 
+
+ align:start position:0%
+female faced with a choice between a
+single male and a male that already has
+
+ align:start position:0%
+single male and a male that already has
+ 
+
+ align:start position:0%
+single male and a male that already has
+one female will often choose the male
+
+ align:start position:0%
+one female will often choose the male
+ 
+
+ align:start position:0%
+one female will often choose the male
+that already has another
+
+ align:start position:0%
+that already has another
+ 
+
+ align:start position:0%
+that already has another
+female
+
+ align:start position:0%
+female
+ 
+
+ align:start position:0%
+female
+why better
+
+ align:start position:0%
+why better
+ 
+
+ align:start position:0%
+why better
+territory he's looking at the whole
+
+ align:start position:0%
+territory he's looking at the whole
+ 
+
+ align:start position:0%
+territory he's looking at the whole
+picture if that male is capable because
+
+ align:start position:0%
+picture if that male is capable because
+ 
+
+ align:start position:0%
+picture if that male is capable because
+of his territory the value of his
+
+ align:start position:0%
+of his territory the value of his
+ 
+
+ align:start position:0%
+of his territory the value of his
+territory of the mating with more than
+
+ align:start position:0%
+territory of the mating with more than
+ 
+
+ align:start position:0%
+territory of the mating with more than
+one female he's happy to join the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+family female defense
+
+ align:start position:0%
+family female defense
+ 
+
+ align:start position:0%
+family female defense
+polygyny well you know what that is the
+
+ align:start position:0%
+polygyny well you know what that is the
+ 
+
+ align:start position:0%
+polygyny well you know what that is the
+Harum if a male can defend more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+females as you know some sea
+
+ align:start position:0%
+females as you know some sea
+ 
+
+ align:start position:0%
+females as you know some sea
+mammal marine mammals do that sea
+
+ align:start position:0%
+mammal marine mammals do that sea
+ 
+
+ align:start position:0%
+mammal marine mammals do that sea
+lions seals they will have a large
+
+ align:start position:0%
+lions seals they will have a large
+ 
+
+ align:start position:0%
+lions seals they will have a large
+number of the the male will the large
+
+ align:start position:0%
+number of the the male will the large
+ 
+
+ align:start position:0%
+number of the the male will the large
+male will have a herum but they have to
+
+ align:start position:0%
+male will have a herum but they have to
+ 
+
+ align:start position:0%
+male will have a herum but they have to
+be strong enough and quick enough to
+
+ align:start position:0%
+be strong enough and quick enough to
+ 
+
+ align:start position:0%
+be strong enough and quick enough to
+defend that those females and that will
+
+ align:start position:0%
+defend that those females and that will
+ 
+
+ align:start position:0%
+defend that those females and that will
+limit the
+
+ align:start position:0%
+limit the
+ 
+
+ align:start position:0%
+limit the
+size of their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh their
+
+ align:start position:0%
+uh their
+ 
+
+ align:start position:0%
+uh their
+group but that's female defense poig and
+
+ align:start position:0%
+group but that's female defense poig and
+ 
+
+ align:start position:0%
+group but that's female defense poig and
+then Le based poyy we'll bring that up
+
+ align:start position:0%
+then Le based poyy we'll bring that up
+ 
+
+ align:start position:0%
+then Le based poyy we'll bring that up
+again at the end there's about 200
+
+ align:start position:0%
+again at the end there's about 200
+ 
+
+ align:start position:0%
+again at the end there's about 200
+species that have Lex that's occurs in
+
+ align:start position:0%
+species that have Lex that's occurs in
+ 
+
+ align:start position:0%
+species that have Lex that's occurs in
+the snipe it conerts in fruit fruit
+
+ align:start position:0%
+the snipe it conerts in fruit fruit
+ 
+
+ align:start position:0%
+the snipe it conerts in fruit fruit
+flies and various Birds this is when the
+
+ align:start position:0%
+flies and various Birds this is when the
+ 
+
+ align:start position:0%
+flies and various Birds this is when the
+female chooses among males that are
+
+ align:start position:0%
+female chooses among males that are
+ 
+
+ align:start position:0%
+female chooses among males that are
+lined up in front of her that's the Leck
+
+ align:start position:0%
+lined up in front of her that's the Leck
+ 
+
+ align:start position:0%
+lined up in front of her that's the Leck
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+like Nature's single bar you know or the
+
+ align:start position:0%
+like Nature's single bar you know or the
+ 
+
+ align:start position:0%
+like Nature's single bar you know or the
+female comes in and she can get
+
+ align:start position:0%
+female comes in and she can get
+ 
+
+ align:start position:0%
+female comes in and she can get
+everything done a whole all the whole
+
+ align:start position:0%
+everything done a whole all the whole
+ 
+
+ align:start position:0%
+everything done a whole all the whole
+group of females can deal with it at
+
+ align:start position:0%
+group of females can deal with it at
+ 
+
+ align:start position:0%
+group of females can deal with it at
+once because the males are all there and
+
+ align:start position:0%
+once because the males are all there and
+ 
+
+ align:start position:0%
+once because the males are all there and
+there's various reasons why Lex form
+
+ align:start position:0%
+there's various reasons why Lex form
+ 
+
+ align:start position:0%
+there's various reasons why Lex form
+we'll bring that up in the end but
+
+ align:start position:0%
+we'll bring that up in the end but
+ 
+
+ align:start position:0%
+we'll bring that up in the end but
+that's another kind of polyandry because
+
+ align:start position:0%
+that's another kind of polyandry because
+ 
+
+ align:start position:0%
+that's another kind of polyandry because
+uh oh
+
+ align:start position:0%
+uh oh
+ 
+
+ align:start position:0%
+uh oh
+sorry polygyny because the male of and
+
+ align:start position:0%
+sorry polygyny because the male of and
+ 
+
+ align:start position:0%
+sorry polygyny because the male of and
+only one male doing almost all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ma you know the the Hot Shot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+male and then polyandry where we
+
+ align:start position:0%
+male and then polyandry where we
+ 
+
+ align:start position:0%
+male and then polyandry where we
+mentioned the sand Piper where the
+
+ align:start position:0%
+mentioned the sand Piper where the
+ 
+
+ align:start position:0%
+mentioned the sand Piper where the
+female will leave the first male and
+
+ align:start position:0%
+female will leave the first male and
+ 
+
+ align:start position:0%
+female will leave the first male and
+have a second brood of eggs so he's
+
+ align:start position:0%
+have a second brood of eggs so he's
+ 
+
+ align:start position:0%
+have a second brood of eggs so he's
+mating with at least two
+
+ align:start position:0%
+mating with at least two
+ 
+
+ align:start position:0%
+mating with at least two
+males
+
+ align:start position:0%
+males
+ 
+
+ align:start position:0%
+males
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh but this occurs in various other
+
+ align:start position:0%
+uh but this occurs in various other
+ 
+
+ align:start position:0%
+uh but this occurs in various other
+birds as
+
+ align:start position:0%
+birds as
+ 
+
+ align:start position:0%
+birds as
+well and it occurs in some
+
+ align:start position:0%
+well and it occurs in some
+ 
+
+ align:start position:0%
+well and it occurs in some
+uh it occurs in some human
+
+ align:start position:0%
+uh it occurs in some human
+ 
+
+ align:start position:0%
+uh it occurs in some human
+groups and then pigan andry where you
+
+ align:start position:0%
+groups and then pigan andry where you
+ 
+
+ align:start position:0%
+groups and then pigan andry where you
+have more than one male and one more
+
+ align:start position:0%
+have more than one male and one more
+ 
+
+ align:start position:0%
+have more than one male and one more
+than one female
+
+ align:start position:0%
+than one female
+ 
+
+ align:start position:0%
+than one female
+okay and you have all of these mating
+
+ align:start position:0%
+okay and you have all of these mating
+ 
+
+ align:start position:0%
+okay and you have all of these mating
+systems in the dunck and I would like
+
+ align:start position:0%
+systems in the dunck and I would like
+ 
+
+ align:start position:0%
+systems in the dunck and I would like
+you to I underlined here figure 83
+
+ align:start position:0%
+you to I underlined here figure 83
+ 
+
+ align:start position:0%
+you to I underlined here figure 83
+because I want you to study that um I
+
+ align:start position:0%
+because I want you to study that um I
+ 
+
+ align:start position:0%
+because I want you to study that um I
+didn't get a copy of it I'm sorry I
+
+ align:start position:0%
+didn't get a copy of it I'm sorry I
+ 
+
+ align:start position:0%
+didn't get a copy of it I'm sorry I
+actually have a disc I think that has
+
+ align:start position:0%
+actually have a disc I think that has
+ 
+
+ align:start position:0%
+actually have a disc I think that has
+these but it's an interesting
+
+ align:start position:0%
+these but it's an interesting
+ 
+
+ align:start position:0%
+these but it's an interesting
+figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and in it he shows the four kinds of
+
+ align:start position:0%
+uh and in it he shows the four kinds of
+ 
+
+ align:start position:0%
+uh and in it he shows the four kinds of
+mating and and he shows you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how what
+
+ align:start position:0%
+how what
+ 
+
+ align:start position:0%
+how what
+happens if the
+
+ align:start position:0%
+happens if the
+ 
+
+ align:start position:0%
+happens if the
+female you know leaves the monogamous
+
+ align:start position:0%
+female you know leaves the monogamous
+ 
+
+ align:start position:0%
+female you know leaves the monogamous
+situation how can she benefit and what
+
+ align:start position:0%
+situation how can she benefit and what
+ 
+
+ align:start position:0%
+situation how can she benefit and what
+happens if the male leaves how can they
+
+ align:start position:0%
+happens if the male leaves how can they
+ 
+
+ align:start position:0%
+happens if the male leaves how can they
+benefit and they've collected data on
+
+ align:start position:0%
+benefit and they've collected data on
+ 
+
+ align:start position:0%
+benefit and they've collected data on
+this and then those groups uh what are
+
+ align:start position:0%
+this and then those groups uh what are
+ 
+
+ align:start position:0%
+this and then those groups uh what are
+the selective factors that make them
+
+ align:start position:0%
+the selective factors that make them
+ 
+
+ align:start position:0%
+the selective factors that make them
+make them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh become p danders in the last one and
+
+ align:start position:0%
+uh become p danders in the last one and
+ 
+
+ align:start position:0%
+uh become p danders in the last one and
+the data as I read it there I think
+
+ align:start position:0%
+the data as I read it there I think
+ 
+
+ align:start position:0%
+the data as I read it there I think
+there's a mistake in the figure it
+
+ align:start position:0%
+there's a mistake in the figure it
+ 
+
+ align:start position:0%
+there's a mistake in the figure it
+doesn't fully make sense but most of it
+
+ align:start position:0%
+doesn't fully make sense but most of it
+ 
+
+ align:start position:0%
+doesn't fully make sense but most of it
+makes very good sense and these Studies
+
+ align:start position:0%
+makes very good sense and these Studies
+ 
+
+ align:start position:0%
+makes very good sense and these Studies
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+Davies uh I believe it was his group
+
+ align:start position:0%
+Davies uh I believe it was his group
+ 
+
+ align:start position:0%
+Davies uh I believe it was his group
+that collected that data but I want you
+
+ align:start position:0%
+that collected that data but I want you
+ 
+
+ align:start position:0%
+that collected that data but I want you
+to look at that because it shows
+
+ align:start position:0%
+to look at that because it shows
+ 
+
+ align:start position:0%
+to look at that because it shows
+how the counts of mating of genetic
+
+ align:start position:0%
+how the counts of mating of genetic
+ 
+
+ align:start position:0%
+how the counts of mating of genetic
+success can vary just depending on the
+
+ align:start position:0%
+success can vary just depending on the
+ 
+
+ align:start position:0%
+success can vary just depending on the
+mating system and sometimes moving to
+
+ align:start position:0%
+mating system and sometimes moving to
+ 
+
+ align:start position:0%
+mating system and sometimes moving to
+another mating system affects one sex
+
+ align:start position:0%
+another mating system affects one sex
+ 
+
+ align:start position:0%
+another mating system affects one sex
+more than
+
+ align:start position:0%
+more than
+ 
+
+ align:start position:0%
+more than
+another and that's what's LED because
+
+ align:start position:0%
+another and that's what's LED because
+ 
+
+ align:start position:0%
+another and that's what's LED because
+all of these occur in the dunck it it
+
+ align:start position:0%
+all of these occur in the dunck it it
+ 
+
+ align:start position:0%
+all of these occur in the dunck it it
+was a good species to study for
+
+ align:start position:0%
+was a good species to study for
+ 
+
+ align:start position:0%
+was a good species to study for
+that and he certainly did find different
+
+ align:start position:0%
+that and he certainly did find different
+ 
+
+ align:start position:0%
+that and he certainly did find different
+benefits to male and to female if they
+
+ align:start position:0%
+benefits to male and to female if they
+ 
+
+ align:start position:0%
+benefits to male and to female if they
+move to another mating
+
+ align:start position:0%
+move to another mating
+ 
+
+ align:start position:0%
+move to another mating
+system okay so what makes monogamy
+
+ align:start position:0%
+system okay so what makes monogamy
+ 
+
+ align:start position:0%
+system okay so what makes monogamy
+happen there must be some situations
+
+ align:start position:0%
+happen there must be some situations
+ 
+
+ align:start position:0%
+happen there must be some situations
+that favor
+
+ align:start position:0%
+that favor
+ 
+
+ align:start position:0%
+that favor
+monogamy and uh these are specific
+
+ align:start position:0%
+monogamy and uh these are specific
+ 
+
+ align:start position:0%
+monogamy and uh these are specific
+examples of monogamous animals the
+
+ align:start position:0%
+examples of monogamous animals the
+ 
+
+ align:start position:0%
+examples of monogamous animals the
+Siberian hamster the jarian hamster
+
+ align:start position:0%
+Siberian hamster the jarian hamster
+ 
+
+ align:start position:0%
+Siberian hamster the jarian hamster
+bopus uh um it lives in nature in under
+
+ align:start position:0%
+bopus uh um it lives in nature in under
+ 
+
+ align:start position:0%
+bopus uh um it lives in nature in under
+very harsh conditions it's very cold
+
+ align:start position:0%
+very harsh conditions it's very cold
+ 
+
+ align:start position:0%
+very harsh conditions it's very cold
+food is limited uh foraging is
+
+ align:start position:0%
+food is limited uh foraging is
+ 
+
+ align:start position:0%
+food is limited uh foraging is
+difficult it makes it unlikely that pups
+
+ align:start position:0%
+difficult it makes it unlikely that pups
+ 
+
+ align:start position:0%
+difficult it makes it unlikely that pups
+could survive unless they have at least
+
+ align:start position:0%
+could survive unless they have at least
+ 
+
+ align:start position:0%
+could survive unless they have at least
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+caregivers so that's a very good
+
+ align:start position:0%
+caregivers so that's a very good
+ 
+
+ align:start position:0%
+caregivers so that's a very good
+reason if neither of them can
+
+ align:start position:0%
+reason if neither of them can
+ 
+
+ align:start position:0%
+reason if neither of them can
+make if they have only there's only one
+
+ align:start position:0%
+make if they have only there's only one
+ 
+
+ align:start position:0%
+make if they have only there's only one
+uh just if there's only one of them
+
+ align:start position:0%
+uh just if there's only one of them
+ 
+
+ align:start position:0%
+uh just if there's only one of them
+female can't do it by herself so it's
+
+ align:start position:0%
+female can't do it by herself so it's
+ 
+
+ align:start position:0%
+female can't do it by herself so it's
+not good for the male either because he
+
+ align:start position:0%
+not good for the male either because he
+ 
+
+ align:start position:0%
+not good for the male either because he
+can M with her but if he doesn't stay to
+
+ align:start position:0%
+can M with her but if he doesn't stay to
+ 
+
+ align:start position:0%
+can M with her but if he doesn't stay to
+take care of the young they won't
+
+ align:start position:0%
+take care of the young they won't
+ 
+
+ align:start position:0%
+take care of the young they won't
+survive you know and they've collected
+
+ align:start position:0%
+survive you know and they've collected
+ 
+
+ align:start position:0%
+survive you know and they've collected
+data on this and this appears to be the
+
+ align:start position:0%
+data on this and this appears to be the
+ 
+
+ align:start position:0%
+data on this and this appears to be the
+case with Siberian hamsters the deep sea
+
+ align:start position:0%
+case with Siberian hamsters the deep sea
+ 
+
+ align:start position:0%
+case with Siberian hamsters the deep sea
+anglerfish that's a different problem
+
+ align:start position:0%
+anglerfish that's a different problem
+ 
+
+ align:start position:0%
+anglerfish that's a different problem
+he's one of these sit and weight
+
+ align:start position:0%
+he's one of these sit and weight
+ 
+
+ align:start position:0%
+he's one of these sit and weight
+Predators he sits in one place until you
+
+ align:start position:0%
+Predators he sits in one place until you
+ 
+
+ align:start position:0%
+Predators he sits in one place until you
+know uh something he can eat comes along
+
+ align:start position:0%
+know uh something he can eat comes along
+ 
+
+ align:start position:0%
+know uh something he can eat comes along
+and he hardly ever sees another
+
+ align:start position:0%
+and he hardly ever sees another
+ 
+
+ align:start position:0%
+and he hardly ever sees another
+anglerfish so when he does the male
+
+ align:start position:0%
+anglerfish so when he does the male
+ 
+
+ align:start position:0%
+anglerfish so when he does the male
+attaches himself to the female as a kind
+
+ align:start position:0%
+attaches himself to the female as a kind
+ 
+
+ align:start position:0%
+attaches himself to the female as a kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+parasite otherwise you know he's not
+
+ align:start position:0%
+parasite otherwise you know he's not
+ 
+
+ align:start position:0%
+parasite otherwise you know he's not
+likely to see another female might too
+
+ align:start position:0%
+likely to see another female might too
+ 
+
+ align:start position:0%
+likely to see another female might too
+much time may go by you may never have
+
+ align:start position:0%
+much time may go by you may never have
+ 
+
+ align:start position:0%
+much time may go by you may never have
+another chance so it's a good reason to
+
+ align:start position:0%
+another chance so it's a good reason to
+ 
+
+ align:start position:0%
+another chance so it's a good reason to
+for a peculiar kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monogamy but monogamy isn't as common as
+
+ align:start position:0%
+monogamy but monogamy isn't as common as
+ 
+
+ align:start position:0%
+monogamy but monogamy isn't as common as
+other mating
+
+ align:start position:0%
+other mating
+ 
+
+ align:start position:0%
+other mating
+strategies in many species they have a
+
+ align:start position:0%
+strategies in many species they have a
+ 
+
+ align:start position:0%
+strategies in many species they have a
+kind of monogamy but it's not that the
+
+ align:start position:0%
+kind of monogamy but it's not that the
+ 
+
+ align:start position:0%
+kind of monogamy but it's not that the
+female wouldn't go off and mate with
+
+ align:start position:0%
+female wouldn't go off and mate with
+ 
+
+ align:start position:0%
+female wouldn't go off and mate with
+another male so the male simply
+
+ align:start position:0%
+another male so the male simply
+ 
+
+ align:start position:0%
+another male so the male simply
+practices mate
+
+ align:start position:0%
+practices mate
+ 
+
+ align:start position:0%
+practices mate
+guarding he drives away he watches her
+
+ align:start position:0%
+guarding he drives away he watches her
+ 
+
+ align:start position:0%
+guarding he drives away he watches her
+and drives away other males if they try
+
+ align:start position:0%
+and drives away other males if they try
+ 
+
+ align:start position:0%
+and drives away other males if they try
+to mate with her he watches her he
+
+ align:start position:0%
+to mate with her he watches her he
+ 
+
+ align:start position:0%
+to mate with her he watches her he
+guards her until she lays the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eggs he wants to make make sure that
+
+ align:start position:0%
+eggs he wants to make make sure that
+ 
+
+ align:start position:0%
+eggs he wants to make make sure that
+it's his sperm the only sperm that
+
+ align:start position:0%
+it's his sperm the only sperm that
+ 
+
+ align:start position:0%
+it's his sperm the only sperm that
+inseminate those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eggs so that reduces the chance of
+
+ align:start position:0%
+eggs so that reduces the chance of
+ 
+
+ align:start position:0%
+eggs so that reduces the chance of
+extrair copulations and it occurs in
+
+ align:start position:0%
+extrair copulations and it occurs in
+ 
+
+ align:start position:0%
+extrair copulations and it occurs in
+many species as we will see when we
+
+ align:start position:0%
+many species as we will see when we
+ 
+
+ align:start position:0%
+many species as we will see when we
+study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sociobiology so what strategies do you
+
+ align:start position:0%
+sociobiology so what strategies do you
+ 
+
+ align:start position:0%
+sociobiology so what strategies do you
+have other than mate guarding to enforce
+
+ align:start position:0%
+have other than mate guarding to enforce
+ 
+
+ align:start position:0%
+have other than mate guarding to enforce
+a a kind of
+
+ align:start position:0%
+a a kind of
+ 
+
+ align:start position:0%
+a a kind of
+monogamy so in other words it may not
+
+ align:start position:0%
+monogamy so in other words it may not
+ 
+
+ align:start position:0%
+monogamy so in other words it may not
+always be the natural
+
+ align:start position:0%
+always be the natural
+ 
+
+ align:start position:0%
+always be the natural
+preference especially of the female she
+
+ align:start position:0%
+preference especially of the female she
+ 
+
+ align:start position:0%
+preference especially of the female she
+might readily mate with another male so
+
+ align:start position:0%
+might readily mate with another male so
+ 
+
+ align:start position:0%
+might readily mate with another male so
+the males have evolved strategies other
+
+ align:start position:0%
+the males have evolved strategies other
+ 
+
+ align:start position:0%
+the males have evolved strategies other
+than mateu guarding for example in there
+
+ align:start position:0%
+than mateu guarding for example in there
+ 
+
+ align:start position:0%
+than mateu guarding for example in there
+are crabs in which the male's ejaculate
+
+ align:start position:0%
+are crabs in which the male's ejaculate
+ 
+
+ align:start position:0%
+are crabs in which the male's ejaculate
+forms a
+
+ align:start position:0%
+forms a
+ 
+
+ align:start position:0%
+forms a
+plug that makes it almost impossible for
+
+ align:start position:0%
+plug that makes it almost impossible for
+ 
+
+ align:start position:0%
+plug that makes it almost impossible for
+another male to get any sperm in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you know it
+
+ align:start position:0%
+there you know it
+ 
+
+ align:start position:0%
+there you know it
+works and of course you what would you
+
+ align:start position:0%
+works and of course you what would you
+ 
+
+ align:start position:0%
+works and of course you what would you
+expect an evolution if that goes on too
+
+ align:start position:0%
+expect an evolution if that goes on too
+ 
+
+ align:start position:0%
+expect an evolution if that goes on too
+long you'd expect other males perhaps
+
+ align:start position:0%
+long you'd expect other males perhaps
+ 
+
+ align:start position:0%
+long you'd expect other males perhaps
+will evolve a strategy to overcome that
+
+ align:start position:0%
+will evolve a strategy to overcome that
+ 
+
+ align:start position:0%
+will evolve a strategy to overcome that
+or the female will evolve the strategy
+
+ align:start position:0%
+or the female will evolve the strategy
+ 
+
+ align:start position:0%
+or the female will evolve the strategy
+if it's to her
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+benefit in dunx you have the phenomenon
+
+ align:start position:0%
+benefit in dunx you have the phenomenon
+ 
+
+ align:start position:0%
+benefit in dunx you have the phenomenon
+of last sperm
+
+ align:start position:0%
+of last sperm
+ 
+
+ align:start position:0%
+of last sperm
+precedence that means the last male that
+
+ align:start position:0%
+precedence that means the last male that
+ 
+
+ align:start position:0%
+precedence that means the last male that
+Ma with
+
+ align:start position:0%
+Ma with
+ 
+
+ align:start position:0%
+Ma with
+her it is his sperm that are the most
+
+ align:start position:0%
+her it is his sperm that are the most
+ 
+
+ align:start position:0%
+her it is his sperm that are the most
+likely to be successful ful in
+
+ align:start position:0%
+likely to be successful ful in
+ 
+
+ align:start position:0%
+likely to be successful ful in
+fertilizing her
+
+ align:start position:0%
+fertilizing her
+ 
+
+ align:start position:0%
+fertilizing her
+eggs so the males before they mate with
+
+ align:start position:0%
+eggs so the males before they mate with
+ 
+
+ align:start position:0%
+eggs so the males before they mate with
+a female will peck at her cloa region
+
+ align:start position:0%
+a female will peck at her cloa region
+ 
+
+ align:start position:0%
+a female will peck at her cloa region
+and they've observed they first didn't
+
+ align:start position:0%
+and they've observed they first didn't
+ 
+
+ align:start position:0%
+and they've observed they first didn't
+weren't sure about why he does that it
+
+ align:start position:0%
+weren't sure about why he does that it
+ 
+
+ align:start position:0%
+weren't sure about why he does that it
+seem to be part of the mating ritual but
+
+ align:start position:0%
+seem to be part of the mating ritual but
+ 
+
+ align:start position:0%
+seem to be part of the mating ritual but
+then they observe that if he does that
+
+ align:start position:0%
+then they observe that if he does that
+ 
+
+ align:start position:0%
+then they observe that if he does that
+for a while she
+
+ align:start position:0%
+for a while she
+ 
+
+ align:start position:0%
+for a while she
+excretes a fluid and if they look at
+
+ align:start position:0%
+excretes a fluid and if they look at
+ 
+
+ align:start position:0%
+excretes a fluid and if they look at
+that fluid under the microscope they
+
+ align:start position:0%
+that fluid under the microscope they
+ 
+
+ align:start position:0%
+that fluid under the microscope they
+find out there she's actually getting
+
+ align:start position:0%
+find out there she's actually getting
+ 
+
+ align:start position:0%
+find out there she's actually getting
+rid of sperm put there by an earlier
+
+ align:start position:0%
+rid of sperm put there by an earlier
+ 
+
+ align:start position:0%
+rid of sperm put there by an earlier
+male in other words that male wants to
+
+ align:start position:0%
+male in other words that male wants to
+ 
+
+ align:start position:0%
+male in other words that male wants to
+be not only the last one to make but he
+
+ align:start position:0%
+be not only the last one to make but he
+ 
+
+ align:start position:0%
+be not only the last one to make but he
+wants to reduce the chances that
+
+ align:start position:0%
+wants to reduce the chances that
+ 
+
+ align:start position:0%
+wants to reduce the chances that
+previous
+
+ align:start position:0%
+previous
+ 
+
+ align:start position:0%
+previous
+mes sperm will be able to fertilize any
+
+ align:start position:0%
+mes sperm will be able to fertilize any
+ 
+
+ align:start position:0%
+mes sperm will be able to fertilize any
+of her
+
+ align:start position:0%
+of her
+ 
+
+ align:start position:0%
+of her
+eggs the male invertebrates are even
+
+ align:start position:0%
+eggs the male invertebrates are even
+ 
+
+ align:start position:0%
+eggs the male invertebrates are even
+more interesting because they've evolved
+
+ align:start position:0%
+more interesting because they've evolved
+ 
+
+ align:start position:0%
+more interesting because they've evolved
+special methods to get rid of the sperm
+
+ align:start position:0%
+special methods to get rid of the sperm
+ 
+
+ align:start position:0%
+special methods to get rid of the sperm
+of the female some of them have penises
+
+ align:start position:0%
+of the female some of them have penises
+ 
+
+ align:start position:0%
+of the female some of them have penises
+that looks like a bottle brush they can
+
+ align:start position:0%
+that looks like a bottle brush they can
+ 
+
+ align:start position:0%
+that looks like a bottle brush they can
+put it in and scrub her out get rid of
+
+ align:start position:0%
+put it in and scrub her out get rid of
+ 
+
+ align:start position:0%
+put it in and scrub her out get rid of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spr and you can read about that on page
+
+ align:start position:0%
+spr and you can read about that on page
+ 
+
+ align:start position:0%
+spr and you can read about that on page
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay now we're still not there's
+
+ align:start position:0%
+there okay now we're still not there's
+ 
+
+ align:start position:0%
+there okay now we're still not there's
+still more to this story uh in polyandry
+
+ align:start position:0%
+still more to this story uh in polyandry
+ 
+
+ align:start position:0%
+still more to this story uh in polyandry
+situations in some
+
+ align:start position:0%
+situations in some
+ 
+
+ align:start position:0%
+situations in some
+species last sperm precedence doesn't
+
+ align:start position:0%
+species last sperm precedence doesn't
+ 
+
+ align:start position:0%
+species last sperm precedence doesn't
+predict paternity the way it in the the
+
+ align:start position:0%
+predict paternity the way it in the the
+ 
+
+ align:start position:0%
+predict paternity the way it in the the
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+dunck uh and if it doesn't predict
+
+ align:start position:0%
+dunck uh and if it doesn't predict
+ 
+
+ align:start position:0%
+dunck uh and if it doesn't predict
+paternity then it raises the possibility
+
+ align:start position:0%
+paternity then it raises the possibility
+ 
+
+ align:start position:0%
+paternity then it raises the possibility
+that somehow the
+
+ align:start position:0%
+that somehow the
+ 
+
+ align:start position:0%
+that somehow the
+female is able to control the
+
+ align:start position:0%
+female is able to control the
+ 
+
+ align:start position:0%
+female is able to control the
+situation maybe she can decide which
+
+ align:start position:0%
+situation maybe she can decide which
+ 
+
+ align:start position:0%
+situation maybe she can decide which
+male which sperm going to fertilize her
+
+ align:start position:0%
+male which sperm going to fertilize her
+ 
+
+ align:start position:0%
+male which sperm going to fertilize her
+Offspring so that will certainly come up
+
+ align:start position:0%
+Offspring so that will certainly come up
+ 
+
+ align:start position:0%
+Offspring so that will certainly come up
+again uh
+
+ align:start position:0%
+again uh
+ 
+
+ align:start position:0%
+again uh
+and then you have really more
+
+ align:start position:0%
+and then you have really more
+ 
+
+ align:start position:0%
+and then you have really more
+straightforward things because the more
+
+ align:start position:0%
+straightforward things because the more
+ 
+
+ align:start position:0%
+straightforward things because the more
+sperm there is the more likely it's
+
+ align:start position:0%
+sperm there is the more likely it's
+ 
+
+ align:start position:0%
+sperm there is the more likely it's
+going to be contain those the ones that
+
+ align:start position:0%
+going to be contain those the ones that
+ 
+
+ align:start position:0%
+going to be contain those the ones that
+fertilize the eggs
+
+ align:start position:0%
+fertilize the eggs
+ 
+
+ align:start position:0%
+fertilize the eggs
+so in the dragon lizard if they see
+
+ align:start position:0%
+so in the dragon lizard if they see
+ 
+
+ align:start position:0%
+so in the dragon lizard if they see
+their female with another
+
+ align:start position:0%
+their female with another
+ 
+
+ align:start position:0%
+their female with another
+male they will mate longer with her to
+
+ align:start position:0%
+male they will mate longer with her to
+ 
+
+ align:start position:0%
+male they will mate longer with her to
+increase the quantity of the ejaculate
+
+ align:start position:0%
+increase the quantity of the ejaculate
+ 
+
+ align:start position:0%
+increase the quantity of the ejaculate
+that increases the probability it's
+
+ align:start position:0%
+that increases the probability it's
+ 
+
+ align:start position:0%
+that increases the probability it's
+similar to L firm precedence okay it may
+
+ align:start position:0%
+similar to L firm precedence okay it may
+ 
+
+ align:start position:0%
+similar to L firm precedence okay it may
+be a ma major reason why less firm
+
+ align:start position:0%
+be a ma major reason why less firm
+ 
+
+ align:start position:0%
+be a ma major reason why less firm
+precedence works
+
+ align:start position:0%
+precedence works
+ 
+
+ align:start position:0%
+precedence works
+okay and there are many species that do
+
+ align:start position:0%
+okay and there are many species that do
+ 
+
+ align:start position:0%
+okay and there are many species that do
+that they simp if the the female is
+
+ align:start position:0%
+that they simp if the the female is
+ 
+
+ align:start position:0%
+that they simp if the the female is
+encountering other males a lot they'll
+
+ align:start position:0%
+encountering other males a lot they'll
+ 
+
+ align:start position:0%
+encountering other males a lot they'll
+just mate for longer periods they
+
+ align:start position:0%
+just mate for longer periods they
+ 
+
+ align:start position:0%
+just mate for longer periods they
+produce more sperm and also when they do
+
+ align:start position:0%
+produce more sperm and also when they do
+ 
+
+ align:start position:0%
+produce more sperm and also when they do
+that they occupy the female for a long
+
+ align:start position:0%
+that they occupy the female for a long
+ 
+
+ align:start position:0%
+that they occupy the female for a long
+longer period of time and the more they
+
+ align:start position:0%
+longer period of time and the more they
+ 
+
+ align:start position:0%
+longer period of time and the more they
+can occupy her the less chance she's
+
+ align:start position:0%
+can occupy her the less chance she's
+ 
+
+ align:start position:0%
+can occupy her the less chance she's
+going to get to calculate with another
+
+ align:start position:0%
+going to get to calculate with another
+ 
+
+ align:start position:0%
+going to get to calculate with another
+male and of course they can also evolve
+
+ align:start position:0%
+male and of course they can also evolve
+ 
+
+ align:start position:0%
+male and of course they can also evolve
+production of more energetic
+
+ align:start position:0%
+production of more energetic
+ 
+
+ align:start position:0%
+production of more energetic
+sperms that can beat the competition it
+
+ align:start position:0%
+sperms that can beat the competition it
+ 
+
+ align:start position:0%
+sperms that can beat the competition it
+takes a while in the reproductive tra
+
+ align:start position:0%
+takes a while in the reproductive tra
+ 
+
+ align:start position:0%
+takes a while in the reproductive tra
+for the sperm to even find the EG so
+
+ align:start position:0%
+for the sperm to even find the EG so
+ 
+
+ align:start position:0%
+for the sperm to even find the EG so
+that's another
+
+ align:start position:0%
+that's another
+ 
+
+ align:start position:0%
+that's another
+strategy and
+
+ align:start position:0%
+strategy and
+ 
+
+ align:start position:0%
+strategy and
+sociobiology science sociobiologists
+
+ align:start position:0%
+sociobiology science sociobiologists
+ 
+
+ align:start position:0%
+sociobiology science sociobiologists
+have found evidence for these various
+
+ align:start position:0%
+have found evidence for these various
+ 
+
+ align:start position:0%
+have found evidence for these various
+things as we will be discussing
+
+ align:start position:0%
+things as we will be discussing
+ 
+
+ align:start position:0%
+things as we will be discussing
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+okay I mentioned DNA analysis it's done
+
+ align:start position:0%
+okay I mentioned DNA analysis it's done
+ 
+
+ align:start position:0%
+okay I mentioned DNA analysis it's done
+on the sandpipers remember they they lay
+
+ align:start position:0%
+on the sandpipers remember they they lay
+ 
+
+ align:start position:0%
+on the sandpipers remember they they lay
+one clutch of eggs four eggs they stay
+
+ align:start position:0%
+one clutch of eggs four eggs they stay
+ 
+
+ align:start position:0%
+one clutch of eggs four eggs they stay
+for a little while and they fly off and
+
+ align:start position:0%
+for a little while and they fly off and
+ 
+
+ align:start position:0%
+for a little while and they fly off and
+they lay another clutch of eggs the
+
+ align:start position:0%
+they lay another clutch of eggs the
+ 
+
+ align:start position:0%
+they lay another clutch of eggs the
+first male has to stay with the first
+
+ align:start position:0%
+first male has to stay with the first
+ 
+
+ align:start position:0%
+first male has to stay with the first
+four so she gets another male take care
+
+ align:start position:0%
+four so she gets another male take care
+ 
+
+ align:start position:0%
+four so she gets another male take care
+of her second group what have they
+
+ align:start position:0%
+of her second group what have they
+ 
+
+ align:start position:0%
+of her second group what have they
+found the second clutch of eggs may have
+
+ align:start position:0%
+found the second clutch of eggs may have
+ 
+
+ align:start position:0%
+found the second clutch of eggs may have
+been fed by the first mate and not the
+
+ align:start position:0%
+been fed by the first mate and not the
+ 
+
+ align:start position:0%
+been fed by the first mate and not the
+second so in that case there's only one
+
+ align:start position:0%
+second so in that case there's only one
+ 
+
+ align:start position:0%
+second so in that case there's only one
+way this could happen he stored sperm
+
+ align:start position:0%
+way this could happen he stored sperm
+ 
+
+ align:start position:0%
+way this could happen he stored sperm
+from the first mate
+
+ align:start position:0%
+from the first mate
+ 
+
+ align:start position:0%
+from the first mate
+and simply delayed its use we made a we
+
+ align:start position:0%
+and simply delayed its use we made a we
+ 
+
+ align:start position:0%
+and simply delayed its use we made a we
+call it a covert choice because it's not
+
+ align:start position:0%
+call it a covert choice because it's not
+ 
+
+ align:start position:0%
+call it a covert choice because it's not
+overt
+
+ align:start position:0%
+overt
+ 
+
+ align:start position:0%
+overt
+Behavior so she's
+
+ align:start position:0%
+Behavior so she's
+ 
+
+ align:start position:0%
+Behavior so she's
+simply enslaving the second
+
+ align:start position:0%
+simply enslaving the second
+ 
+
+ align:start position:0%
+simply enslaving the second
+male you know getting him to raise her
+
+ align:start position:0%
+male you know getting him to raise her
+ 
+
+ align:start position:0%
+male you know getting him to raise her
+eggs you see she's made a choice in the
+
+ align:start position:0%
+eggs you see she's made a choice in the
+ 
+
+ align:start position:0%
+eggs you see she's made a choice in the
+quality of the genes by assessing you
+
+ align:start position:0%
+quality of the genes by assessing you
+ 
+
+ align:start position:0%
+quality of the genes by assessing you
+know the two males and so when she meets
+
+ align:start position:0%
+know the two males and so when she meets
+ 
+
+ align:start position:0%
+know the two males and so when she meets
+the second male he might be perfectly
+
+ align:start position:0%
+the second male he might be perfectly
+ 
+
+ align:start position:0%
+the second male he might be perfectly
+capable of
+
+ align:start position:0%
+capable of
+ 
+
+ align:start position:0%
+capable of
+nesting and brood pending but maybe not
+
+ align:start position:0%
+nesting and brood pending but maybe not
+ 
+
+ align:start position:0%
+nesting and brood pending but maybe not
+as attracted to her in other ways as
+
+ align:start position:0%
+as attracted to her in other ways as
+ 
+
+ align:start position:0%
+as attracted to her in other ways as
+that first male so then she'll she
+
+ align:start position:0%
+that first male so then she'll she
+ 
+
+ align:start position:0%
+that first male so then she'll she
+stored up sperm from the first male so
+
+ align:start position:0%
+stored up sperm from the first male so
+ 
+
+ align:start position:0%
+stored up sperm from the first male so
+she can make that
+
+ align:start position:0%
+she can make that
+ 
+
+ align:start position:0%
+she can make that
+choice very it's comparable to us what I
+
+ align:start position:0%
+choice very it's comparable to us what I
+ 
+
+ align:start position:0%
+choice very it's comparable to us what I
+know about
+
+ align:start position:0%
+know about
+ 
+
+ align:start position:0%
+know about
+kangaroos kangaroos will generally carry
+
+ align:start position:0%
+kangaroos kangaroos will generally carry
+ 
+
+ align:start position:0%
+kangaroos kangaroos will generally carry
+two fetuses but only one one of them
+
+ align:start position:0%
+two fetuses but only one one of them
+ 
+
+ align:start position:0%
+two fetuses but only one one of them
+will mature the other one will be held
+
+ align:start position:0%
+will mature the other one will be held
+ 
+
+ align:start position:0%
+will mature the other one will be held
+in a kind of suspended animation okay
+
+ align:start position:0%
+in a kind of suspended animation okay
+ 
+
+ align:start position:0%
+in a kind of suspended animation okay
+and then if something happens to her
+
+ align:start position:0%
+and then if something happens to her
+ 
+
+ align:start position:0%
+and then if something happens to her
+first little
+
+ align:start position:0%
+first little
+ 
+
+ align:start position:0%
+first little
+Joey he
+
+ align:start position:0%
+Joey he
+ 
+
+ align:start position:0%
+Joey he
+dies then the second one will start
+
+ align:start position:0%
+dies then the second one will start
+ 
+
+ align:start position:0%
+dies then the second one will start
+drawing in her so she's got a spare
+
+ align:start position:0%
+drawing in her so she's got a spare
+ 
+
+ align:start position:0%
+drawing in her so she's got a spare
+similar to this and it's the same father
+
+ align:start position:0%
+similar to this and it's the same father
+ 
+
+ align:start position:0%
+similar to this and it's the same father
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+now at a later
+
+ align:start position:0%
+now at a later
+ 
+
+ align:start position:0%
+now at a later
+time she's got a backup fetus
+
+ align:start position:0%
+time she's got a backup fetus
+ 
+
+ align:start position:0%
+time she's got a backup fetus
+okay the last topic here the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Leck how can a male in a Leck who never
+
+ align:start position:0%
+Leck how can a male in a Leck who never
+ 
+
+ align:start position:0%
+Leck how can a male in a Leck who never
+seems to succeed in mating with a female
+
+ align:start position:0%
+seems to succeed in mating with a female
+ 
+
+ align:start position:0%
+seems to succeed in mating with a female
+never nevertheless
+
+ align:start position:0%
+never nevertheless
+ 
+
+ align:start position:0%
+never nevertheless
+benefit by participating in that like
+
+ align:start position:0%
+benefit by participating in that like
+ 
+
+ align:start position:0%
+benefit by participating in that like
+why does he
+
+ align:start position:0%
+why does he
+ 
+
+ align:start position:0%
+why does he
+participate he's obviously not the Hot
+
+ align:start position:0%
+participate he's obviously not the Hot
+ 
+
+ align:start position:0%
+participate he's obviously not the Hot
+Shot okay well there's various models to
+
+ align:start position:0%
+Shot okay well there's various models to
+ 
+
+ align:start position:0%
+Shot okay well there's various models to
+deal with that whole issue of the leg
+
+ align:start position:0%
+deal with that whole issue of the leg
+ 
+
+ align:start position:0%
+deal with that whole issue of the leg
+hot the hot spot model this is the
+
+ align:start position:0%
+hot the hot spot model this is the
+ 
+
+ align:start position:0%
+hot the hot spot model this is the
+advantage that let's say the females are
+
+ align:start position:0%
+advantage that let's say the females are
+ 
+
+ align:start position:0%
+advantage that let's say the females are
+not going to mate for very long then
+
+ align:start position:0%
+not going to mate for very long then
+ 
+
+ align:start position:0%
+not going to mate for very long then
+you've got a position yourself where all
+
+ align:start position:0%
+you've got a position yourself where all
+ 
+
+ align:start position:0%
+you've got a position yourself where all
+the females aren coming so they go to a
+
+ align:start position:0%
+the females aren coming so they go to a
+ 
+
+ align:start position:0%
+the females aren coming so they go to a
+place where all the females come that's
+
+ align:start position:0%
+place where all the females come that's
+ 
+
+ align:start position:0%
+place where all the females come that's
+called The Hot Spot model Hot Spot model
+
+ align:start position:0%
+called The Hot Spot model Hot Spot model
+ 
+
+ align:start position:0%
+called The Hot Spot model Hot Spot model
+well you can benefit by being near a hot
+
+ align:start position:0%
+well you can benefit by being near a hot
+ 
+
+ align:start position:0%
+well you can benefit by being near a hot
+shot because he will attract the females
+
+ align:start position:0%
+shot because he will attract the females
+ 
+
+ align:start position:0%
+shot because he will attract the females
+and maybe you'll get it to
+
+ align:start position:0%
+and maybe you'll get it to
+ 
+
+ align:start position:0%
+and maybe you'll get it to
+him there's some evidence for
+
+ align:start position:0%
+him there's some evidence for
+ 
+
+ align:start position:0%
+him there's some evidence for
+that another the female preference model
+
+ align:start position:0%
+that another the female preference model
+ 
+
+ align:start position:0%
+that another the female preference model
+is simply that females because of their
+
+ align:start position:0%
+is simply that females because of their
+ 
+
+ align:start position:0%
+is simply that females because of their
+they're facing predators and Lex groups
+
+ align:start position:0%
+they're facing predators and Lex groups
+ 
+
+ align:start position:0%
+they're facing predators and Lex groups
+of animals making mate choices are going
+
+ align:start position:0%
+of animals making mate choices are going
+ 
+
+ align:start position:0%
+of animals making mate choices are going
+to attract Predators too so he wants
+
+ align:start position:0%
+to attract Predators too so he wants
+ 
+
+ align:start position:0%
+to attract Predators too so he wants
+this to be over with very quickly so
+
+ align:start position:0%
+this to be over with very quickly so
+ 
+
+ align:start position:0%
+this to be over with very quickly so
+this maybe Lex have evolved in those
+
+ align:start position:0%
+this maybe Lex have evolved in those
+ 
+
+ align:start position:0%
+this maybe Lex have evolved in those
+species just to speed it up get the
+
+ align:start position:0%
+species just to speed it up get the
+ 
+
+ align:start position:0%
+species just to speed it up get the
+whole thing done in very brief period of
+
+ align:start position:0%
+whole thing done in very brief period of
+ 
+
+ align:start position:0%
+whole thing done in very brief period of
+time the model that is preferred by
+
+ align:start position:0%
+time the model that is preferred by
+ 
+
+ align:start position:0%
+time the model that is preferred by
+Scott and it doesn't mean these other
+
+ align:start position:0%
+Scott and it doesn't mean these other
+ 
+
+ align:start position:0%
+Scott and it doesn't mean these other
+things aren't factors in the evolution
+
+ align:start position:0%
+things aren't factors in the evolution
+ 
+
+ align:start position:0%
+things aren't factors in the evolution
+the and since it occurs in over 200
+
+ align:start position:0%
+the and since it occurs in over 200
+ 
+
+ align:start position:0%
+the and since it occurs in over 200
+species it's likely that more than one
+
+ align:start position:0%
+species it's likely that more than one
+ 
+
+ align:start position:0%
+species it's likely that more than one
+factor has influenced its Evolution but
+
+ align:start position:0%
+factor has influenced its Evolution but
+ 
+
+ align:start position:0%
+factor has influenced its Evolution but
+K selection simply means that in many
+
+ align:start position:0%
+K selection simply means that in many
+ 
+
+ align:start position:0%
+K selection simply means that in many
+lexs most of those males are related to
+
+ align:start position:0%
+lexs most of those males are related to
+ 
+
+ align:start position:0%
+lexs most of those males are related to
+each other so even if some of many those
+
+ align:start position:0%
+each other so even if some of many those
+ 
+
+ align:start position:0%
+each other so even if some of many those
+males don't get a chance to M at all
+
+ align:start position:0%
+males don't get a chance to M at all
+ 
+
+ align:start position:0%
+males don't get a chance to M at all
+maybe they're still benefiting because
+
+ align:start position:0%
+maybe they're still benefiting because
+ 
+
+ align:start position:0%
+maybe they're still benefiting because
+they sell jeans with that hot shot
+
+ align:start position:0%
+they sell jeans with that hot shot
+ 
+
+ align:start position:0%
+they sell jeans with that hot shot
+okay big brother can
+
+ align:start position:0%
+okay big brother can
+ 
+
+ align:start position:0%
+okay big brother can
+make but he carries a lot of same de
+
+ align:start position:0%
+make but he carries a lot of same de
+ 
+
+ align:start position:0%
+make but he carries a lot of same de
+diety okay so you see it because when
+
+ align:start position:0%
+diety okay so you see it because when
+ 
+
+ align:start position:0%
+diety okay so you see it because when
+you look
+
+ align:start position:0%
+you look
+ 
+
+ align:start position:0%
+you look
+at genetic fitness you have to
+
+ align:start position:0%
+at genetic fitness you have to
+ 
+
+ align:start position:0%
+at genetic fitness you have to
+consider how many copies of your genes
+
+ align:start position:0%
+consider how many copies of your genes
+ 
+
+ align:start position:0%
+consider how many copies of your genes
+are getting passed
+
+ align:start position:0%
+are getting passed
+ 
+
+ align:start position:0%
+are getting passed
+on and you are you increase your Fitness
+
+ align:start position:0%
+on and you are you increase your Fitness
+ 
+
+ align:start position:0%
+on and you are you increase your Fitness
+by helping your
+
+ align:start position:0%
+by helping your
+ 
+
+ align:start position:0%
+by helping your
+brother so the females are more
+
+ align:start position:0%
+brother so the females are more
+ 
+
+ align:start position:0%
+brother so the females are more
+attracted to the Le okay only your
+
+ align:start position:0%
+attracted to the Le okay only your
+ 
+
+ align:start position:0%
+attracted to the Le okay only your
+brother gets to mate but you're still
+
+ align:start position:0%
+brother gets to mate but you're still
+ 
+
+ align:start position:0%
+brother gets to mate but you're still
+getting passing on jeans okay that's the
+
+ align:start position:0%
+getting passing on jeans okay that's the
+ 
+
+ align:start position:0%
+getting passing on jeans okay that's the
+kin selection
+
+ align:start position:0%
+kin selection
+ 
+
+ align:start position:0%
+kin selection
+model and I'm just pointing out they're
+
+ align:start position:0%
+model and I'm just pointing out they're
+ 
+
+ align:start position:0%
+model and I'm just pointing out they're
+not mutually exclusive these
+
+ align:start position:0%
+not mutually exclusive these
+ 
+
+ align:start position:0%
+not mutually exclusive these
+models and yet we know there should be
+
+ align:start position:0%
+models and yet we know there should be
+ 
+
+ align:start position:0%
+models and yet we know there should be
+it seems like it's a setup for reducing
+
+ align:start position:0%
+it seems like it's a setup for reducing
+ 
+
+ align:start position:0%
+it seems like it's a setup for reducing
+genetic variation and yet the genetic
+
+ align:start position:0%
+genetic variation and yet the genetic
+ 
+
+ align:start position:0%
+genetic variation and yet the genetic
+studies indicate that somehow the
+
+ align:start position:0%
+studies indicate that somehow the
+ 
+
+ align:start position:0%
+studies indicate that somehow the
+females do manage to preserve a lot of
+
+ align:start position:0%
+females do manage to preserve a lot of
+ 
+
+ align:start position:0%
+females do manage to preserve a lot of
+variability indicating that even though
+
+ align:start position:0%
+variability indicating that even though
+ 
+
+ align:start position:0%
+variability indicating that even though
+the Behavioral Studies by scientists
+
+ align:start position:0%
+the Behavioral Studies by scientists
+ 
+
+ align:start position:0%
+the Behavioral Studies by scientists
+haven't seen many of those other males
+
+ align:start position:0%
+haven't seen many of those other males
+ 
+
+ align:start position:0%
+haven't seen many of those other males
+mating uh it's clear that a lot of them
+
+ align:start position:0%
+mating uh it's clear that a lot of them
+ 
+
+ align:start position:0%
+mating uh it's clear that a lot of them
+do so my guess is that the females are
+
+ align:start position:0%
+do so my guess is that the females are
+ 
+
+ align:start position:0%
+do so my guess is that the females are
+in fact in addition to mating with that
+
+ align:start position:0%
+in fact in addition to mating with that
+ 
+
+ align:start position:0%
+in fact in addition to mating with that
+the Hot Shot male they're probably
+
+ align:start position:0%
+the Hot Shot male they're probably
+ 
+
+ align:start position:0%
+the Hot Shot male they're probably
+mating additional times with the males
+
+ align:start position:0%
+mating additional times with the males
+ 
+
+ align:start position:0%
+mating additional times with the males
+before they they
+
+ align:start position:0%
+before they they
+ 
+
+ align:start position:0%
+before they they
+leave okay but this is unclear from the
+
+ align:start position:0%
+leave okay but this is unclear from the
+ 
+
+ align:start position:0%
+leave okay but this is unclear from the
+studies all
+
+ align:start position:0%
+studies all
+ 
+
+ align:start position:0%
+studies all
+right sorry I went over little bit
\ No newline at end of file
diff --git a/Av9sFr_NsBU.txt b/Av9sFr_NsBU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f299acc29160377500875fc52ee345be3dc6cdf
--- /dev/null
+++ b/Av9sFr_NsBU.txt
@@ -0,0 +1,8875 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay um most everyone's here
+
+ align:start position:0%
+ocw.mit.edu okay um most everyone's here
+ 
+
+ align:start position:0%
+ocw.mit.edu okay um most everyone's here
+um we're still going to take a few
+
+ align:start position:0%
+um we're still going to take a few
+ 
+
+ align:start position:0%
+um we're still going to take a few
+minutes to wait for the last um few
+
+ align:start position:0%
+minutes to wait for the last um few
+ 
+
+ align:start position:0%
+minutes to wait for the last um few
+people to show up um I don't have a ton
+
+ align:start position:0%
+people to show up um I don't have a ton
+ 
+
+ align:start position:0%
+people to show up um I don't have a ton
+of announcements
+
+ align:start position:0%
+of announcements
+ 
+
+ align:start position:0%
+of announcements
+but if you looked at the syllabus you
+
+ align:start position:0%
+but if you looked at the syllabus you
+ 
+
+ align:start position:0%
+but if you looked at the syllabus you
+might notice that there are a couple
+
+ align:start position:0%
+might notice that there are a couple
+ 
+
+ align:start position:0%
+might notice that there are a couple
+days where we have I think we've got TBD
+
+ align:start position:0%
+days where we have I think we've got TBD
+ 
+
+ align:start position:0%
+days where we have I think we've got TBD
+as the topic like to be determined um
+
+ align:start position:0%
+as the topic like to be determined um
+ 
+
+ align:start position:0%
+as the topic like to be determined um
+what I'd like to do is just take a quick
+
+ align:start position:0%
+what I'd like to do is just take a quick
+ 
+
+ align:start position:0%
+what I'd like to do is just take a quick
+poll um from you all is there anything
+
+ align:start position:0%
+poll um from you all is there anything
+ 
+
+ align:start position:0%
+poll um from you all is there anything
+that you are interested in learning
+
+ align:start position:0%
+that you are interested in learning
+ 
+
+ align:start position:0%
+that you are interested in learning
+about in the creation of video games
+
+ align:start position:0%
+about in the creation of video games
+ 
+
+ align:start position:0%
+about in the creation of video games
+that you either we haven't talked about
+
+ align:start position:0%
+that you either we haven't talked about
+ 
+
+ align:start position:0%
+that you either we haven't talked about
+it in class yet maybe we've talked about
+
+ align:start position:0%
+it in class yet maybe we've talked about
+ 
+
+ align:start position:0%
+it in class yet maybe we've talked about
+it but not fully um you've looked at the
+
+ align:start position:0%
+it but not fully um you've looked at the
+ 
+
+ align:start position:0%
+it but not fully um you've looked at the
+syllabus and it and it's not there on
+
+ align:start position:0%
+syllabus and it and it's not there on
+ 
+
+ align:start position:0%
+syllabus and it and it's not there on
+the syllabus um so any spe and it and or
+
+ align:start position:0%
+the syllabus um so any spe and it and or
+ 
+
+ align:start position:0%
+the syllabus um so any spe and it and or
+it's something that you think is going
+
+ align:start position:0%
+it's something that you think is going
+ 
+
+ align:start position:0%
+it's something that you think is going
+to be directly useful for the games that
+
+ align:start position:0%
+to be directly useful for the games that
+ 
+
+ align:start position:0%
+to be directly useful for the games that
+you're working on right
+
+ align:start position:0%
+you're working on right
+ 
+
+ align:start position:0%
+you're working on right
+now so just putting that out there if
+
+ align:start position:0%
+now so just putting that out there if
+ 
+
+ align:start position:0%
+now so just putting that out there if
+there any topics you might want to talk
+
+ align:start position:0%
+there any topics you might want to talk
+ 
+
+ align:start position:0%
+there any topics you might want to talk
+about learn
+
+ align:start position:0%
+about learn
+ 
+
+ align:start position:0%
+about learn
+about let me
+
+ align:start position:0%
+about let me
+ 
+
+ align:start position:0%
+about let me
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+yes other classes us like the last last
+
+ align:start position:0%
+yes other classes us like the last last
+ 
+
+ align:start position:0%
+yes other classes us like the last last
+class of the last two classes us like
+
+ align:start position:0%
+class of the last two classes us like
+ 
+
+ align:start position:0%
+class of the last two classes us like
+what people actually do in Industry okay
+
+ align:start position:0%
+what people actually do in Industry okay
+ 
+
+ align:start position:0%
+what people actually do in Industry okay
+so yeah cool so what people do in the
+
+ align:start position:0%
+so yeah cool so what people do in the
+ 
+
+ align:start position:0%
+so yeah cool so what people do in the
+industry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool you are in luck on
+
+ align:start position:0%
+cool you are in luck on
+ 
+
+ align:start position:0%
+cool you are in luck on
+December 1st and 3D on the 1 we're
+
+ align:start position:0%
+December 1st and 3D on the 1 we're
+ 
+
+ align:start position:0%
+December 1st and 3D on the 1 we're
+having a business and games um panel so
+
+ align:start position:0%
+having a business and games um panel so
+ 
+
+ align:start position:0%
+having a business and games um panel so
+two um two independent developers in the
+
+ align:start position:0%
+two um two independent developers in the
+ 
+
+ align:start position:0%
+two um two independent developers in the
+area are going to come by and talk about
+
+ align:start position:0%
+area are going to come by and talk about
+ 
+
+ align:start position:0%
+area are going to come by and talk about
+um how they started their companies what
+
+ align:start position:0%
+um how they started their companies what
+ 
+
+ align:start position:0%
+um how they started their companies what
+do they do what's their daily life
+
+ align:start position:0%
+do they do what's their daily life
+ 
+
+ align:start position:0%
+do they do what's their daily life
+things like that and then another one
+
+ align:start position:0%
+things like that and then another one
+ 
+
+ align:start position:0%
+things like that and then another one
+following that is um the community
+
+ align:start position:0%
+following that is um the community
+ 
+
+ align:start position:0%
+following that is um the community
+manager for fire hose games um Sean
+
+ align:start position:0%
+manager for fire hose games um Sean
+ 
+
+ align:start position:0%
+manager for fire hose games um Sean
+Baptist is going to talk to us about how
+
+ align:start position:0%
+Baptist is going to talk to us about how
+ 
+
+ align:start position:0%
+Baptist is going to talk to us about how
+does he get how do they get their games
+
+ align:start position:0%
+does he get how do they get their games
+ 
+
+ align:start position:0%
+does he get how do they get their games
+out in the world and how do they get
+
+ align:start position:0%
+out in the world and how do they get
+ 
+
+ align:start position:0%
+out in the world and how do they get
+people to play their games um and how do
+
+ align:start position:0%
+people to play their games um and how do
+ 
+
+ align:start position:0%
+people to play their games um and how do
+they engage their their their fan base
+
+ align:start position:0%
+they engage their their their fan base
+ 
+
+ align:start position:0%
+they engage their their their fan base
+and how do they even just create a fan
+
+ align:start position:0%
+and how do they even just create a fan
+ 
+
+ align:start position:0%
+and how do they even just create a fan
+base in general um so that's not on the
+
+ align:start position:0%
+base in general um so that's not on the
+ 
+
+ align:start position:0%
+base in general um so that's not on the
+syllabus but that will be we will be
+
+ align:start position:0%
+syllabus but that will be we will be
+ 
+
+ align:start position:0%
+syllabus but that will be we will be
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+that any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topics okay I want to ask this again in
+
+ align:start position:0%
+topics okay I want to ask this again in
+ 
+
+ align:start position:0%
+topics okay I want to ask this again in
+a couple weeks um in case something pops
+
+ align:start position:0%
+a couple weeks um in case something pops
+ 
+
+ align:start position:0%
+a couple weeks um in case something pops
+up because you probably haven't done a
+
+ align:start position:0%
+up because you probably haven't done a
+ 
+
+ align:start position:0%
+up because you probably haven't done a
+lot of technical things with your um
+
+ align:start position:0%
+lot of technical things with your um
+ 
+
+ align:start position:0%
+lot of technical things with your um
+with your game engine yet um so if
+
+ align:start position:0%
+with your game engine yet um so if
+ 
+
+ align:start position:0%
+with your game engine yet um so if
+there's anything gaming specific that
+
+ align:start position:0%
+there's anything gaming specific that
+ 
+
+ align:start position:0%
+there's anything gaming specific that
+you might want to know about um either
+
+ align:start position:0%
+you might want to know about um either
+ 
+
+ align:start position:0%
+you might want to know about um either
+let us know through the mail through the
+
+ align:start position:0%
+let us know through the mail through the
+ 
+
+ align:start position:0%
+let us know through the mail through the
+video game boss's um email address or
+
+ align:start position:0%
+video game boss's um email address or
+ 
+
+ align:start position:0%
+video game boss's um email address or
+let us know a class yeah who would be
+
+ align:start position:0%
+let us know a class yeah who would be
+ 
+
+ align:start position:0%
+let us know a class yeah who would be
+giving these lectures like is this open
+
+ align:start position:0%
+giving these lectures like is this open
+ 
+
+ align:start position:0%
+giving these lectures like is this open
+to can you get I can get people so I can
+
+ align:start position:0%
+to can you get I can get people so I can
+ 
+
+ align:start position:0%
+to can you get I can get people so I can
+I can get people who are um local um
+
+ align:start position:0%
+I can get people who are um local um
+ 
+
+ align:start position:0%
+I can get people who are um local um
+we've got connections to local industry
+
+ align:start position:0%
+we've got connections to local industry
+ 
+
+ align:start position:0%
+we've got connections to local industry
+um we've got connections to the people
+
+ align:start position:0%
+um we've got connections to the people
+ 
+
+ align:start position:0%
+um we've got connections to the people
+who make the tools in some cases
+
+ align:start position:0%
+who make the tools in some cases
+ 
+
+ align:start position:0%
+who make the tools in some cases
+depending on the tool that's kind of why
+
+ align:start position:0%
+depending on the tool that's kind of why
+ 
+
+ align:start position:0%
+depending on the tool that's kind of why
+I'm asking now because it gives me time
+
+ align:start position:0%
+I'm asking now because it gives me time
+ 
+
+ align:start position:0%
+I'm asking now because it gives me time
+to to to find new to to fill new gaps uh
+
+ align:start position:0%
+to to to find new to to fill new gaps uh
+ 
+
+ align:start position:0%
+to to to find new to to fill new gaps uh
+also so it might be something that we
+
+ align:start position:0%
+also so it might be something that we
+ 
+
+ align:start position:0%
+also so it might be something that we
+can talk to um so if there's anything
+
+ align:start position:0%
+can talk to um so if there's anything
+ 
+
+ align:start position:0%
+can talk to um so if there's anything
+design related that you think is useful
+
+ align:start position:0%
+design related that you think is useful
+ 
+
+ align:start position:0%
+design related that you think is useful
+for your for your games that we haven't
+
+ align:start position:0%
+for your for your games that we haven't
+ 
+
+ align:start position:0%
+for your for your games that we haven't
+talked about yet um and you don't see it
+
+ align:start position:0%
+talked about yet um and you don't see it
+ 
+
+ align:start position:0%
+talked about yet um and you don't see it
+on the schedule let us know um if
+
+ align:start position:0%
+on the schedule let us know um if
+ 
+
+ align:start position:0%
+on the schedule let us know um if
+there's anything technical related um
+
+ align:start position:0%
+there's anything technical related um
+ 
+
+ align:start position:0%
+there's anything technical related um
+Drew can can can come up and and say
+
+ align:start position:0%
+Drew can can can come up and and say
+ 
+
+ align:start position:0%
+Drew can can can come up and and say
+something the other thing we can do is
+
+ align:start position:0%
+something the other thing we can do is
+ 
+
+ align:start position:0%
+something the other thing we can do is
+if there's anything that you want to do
+
+ align:start position:0%
+if there's anything that you want to do
+ 
+
+ align:start position:0%
+if there's anything that you want to do
+or if you want to set up office hours in
+
+ align:start position:0%
+or if you want to set up office hours in
+ 
+
+ align:start position:0%
+or if you want to set up office hours in
+class um to talk about a certain topic
+
+ align:start position:0%
+class um to talk about a certain topic
+ 
+
+ align:start position:0%
+class um to talk about a certain topic
+for your for your um for your games
+
+ align:start position:0%
+for your for your um for your games
+ 
+
+ align:start position:0%
+for your for your um for your games
+specifically technical issues technical
+
+ align:start position:0%
+specifically technical issues technical
+ 
+
+ align:start position:0%
+specifically technical issues technical
+questions um that's what Drew is here
+
+ align:start position:0%
+questions um that's what Drew is here
+ 
+
+ align:start position:0%
+questions um that's what Drew is here
+for to to come and talk to you to talk
+
+ align:start position:0%
+for to to come and talk to you to talk
+ 
+
+ align:start position:0%
+for to to come and talk to you to talk
+with your group as a whole or just
+
+ align:start position:0%
+with your group as a whole or just
+ 
+
+ align:start position:0%
+with your group as a whole or just
+individual members of your group to talk
+
+ align:start position:0%
+individual members of your group to talk
+ 
+
+ align:start position:0%
+individual members of your group to talk
+about the issues that you have so we can
+
+ align:start position:0%
+about the issues that you have so we can
+ 
+
+ align:start position:0%
+about the issues that you have so we can
+do that during class during our
+
+ align:start position:0%
+do that during class during our
+ 
+
+ align:start position:0%
+do that during class during our
+scheduled one and a half to two hour um
+
+ align:start position:0%
+scheduled one and a half to two hour um
+ 
+
+ align:start position:0%
+scheduled one and a half to two hour um
+working class periods or um you can set
+
+ align:start position:0%
+working class periods or um you can set
+ 
+
+ align:start position:0%
+working class periods or um you can set
+up work office hours with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+him okay um just give people a couple
+
+ align:start position:0%
+him okay um just give people a couple
+ 
+
+ align:start position:0%
+him okay um just give people a couple
+more minutes the attendance sheet is
+
+ align:start position:0%
+more minutes the attendance sheet is
+ 
+
+ align:start position:0%
+more minutes the attendance sheet is
+moving around um
+
+ align:start position:0%
+moving around um
+ 
+
+ align:start position:0%
+moving around um
+so is everybody sitting with their teams
+
+ align:start position:0%
+so is everybody sitting with their teams
+ 
+
+ align:start position:0%
+so is everybody sitting with their teams
+right now does it look like
+
+ align:start position:0%
+right now does it look like
+ 
+
+ align:start position:0%
+right now does it look like
+can we just show I'm going to go across
+
+ align:start position:0%
+can we just show I'm going to go across
+ 
+
+ align:start position:0%
+can we just show I'm going to go across
+and just kind of try to figure out which
+
+ align:start position:0%
+and just kind of try to figure out which
+ 
+
+ align:start position:0%
+and just kind of try to figure out which
+of these teams are so this is the snap
+
+ align:start position:0%
+of these teams are so this is the snap
+ 
+
+ align:start position:0%
+of these teams are so this is the snap
+team is everyone
+
+ align:start position:0%
+team is everyone
+ 
+
+ align:start position:0%
+team is everyone
+here two okay uh which team this is
+
+ align:start position:0%
+here two okay uh which team this is
+ 
+
+ align:start position:0%
+here two okay uh which team this is
+forecast based Futures over here right
+
+ align:start position:0%
+forecast based Futures over here right
+ 
+
+ align:start position:0%
+forecast based Futures over here right
+how far do you go John are you in this
+
+ align:start position:0%
+how far do you go John are you in this
+ 
+
+ align:start position:0%
+how far do you go John are you in this
+team or you in the next team cool all
+
+ align:start position:0%
+team or you in the next team cool all
+ 
+
+ align:start position:0%
+team or you in the next team cool all
+right next team over which team are you
+
+ align:start position:0%
+right next team over which team are you
+ 
+
+ align:start position:0%
+right next team over which team are you
+Kera
+
+ align:start position:0%
+Kera
+ 
+
+ align:start position:0%
+Kera
+no you're a Col team were you the um
+
+ align:start position:0%
+no you're a Col team were you the um
+ 
+
+ align:start position:0%
+no you're a Col team were you the um
+island group Animal Crossing one cool um
+
+ align:start position:0%
+island group Animal Crossing one cool um
+ 
+
+ align:start position:0%
+island group Animal Crossing one cool um
+and then in the front here we've got
+
+ align:start position:0%
+and then in the front here we've got
+ 
+
+ align:start position:0%
+and then in the front here we've got
+Heatwave and in the back it's the other
+
+ align:start position:0%
+Heatwave and in the back it's the other
+ 
+
+ align:start position:0%
+Heatwave and in the back it's the other
+call group okay um I did not get a
+
+ align:start position:0%
+call group okay um I did not get a
+ 
+
+ align:start position:0%
+call group okay um I did not get a
+chance to play your game so but I will
+
+ align:start position:0%
+chance to play your game so but I will
+ 
+
+ align:start position:0%
+chance to play your game so but I will
+eventually um cool so there's G to be a
+
+ align:start position:0%
+eventually um cool so there's G to be a
+ 
+
+ align:start position:0%
+eventually um cool so there's G to be a
+little bit of interactivity in the talk
+
+ align:start position:0%
+little bit of interactivity in the talk
+ 
+
+ align:start position:0%
+little bit of interactivity in the talk
+um I've given this talk before um I
+
+ align:start position:0%
+um I've given this talk before um I
+ 
+
+ align:start position:0%
+um I've given this talk before um I
+rewrote the lectures and I haven't given
+
+ align:start position:0%
+rewrote the lectures and I haven't given
+ 
+
+ align:start position:0%
+rewrote the lectures and I haven't given
+it since I rewrote the lecture so we'll
+
+ align:start position:0%
+it since I rewrote the lecture so we'll
+ 
+
+ align:start position:0%
+it since I rewrote the lecture so we'll
+see how it goes they're my backup to let
+
+ align:start position:0%
+see how it goes they're my backup to let
+ 
+
+ align:start position:0%
+see how it goes they're my backup to let
+me know if I forgot
+
+ align:start position:0%
+me know if I forgot
+ 
+
+ align:start position:0%
+me know if I forgot
+anything um there will be some reading
+
+ align:start position:0%
+anything um there will be some reading
+ 
+
+ align:start position:0%
+anything um there will be some reading
+on this that I'm going to put into
+
+ align:start position:0%
+on this that I'm going to put into
+ 
+
+ align:start position:0%
+on this that I'm going to put into
+Stellar so if you are um interested in
+
+ align:start position:0%
+Stellar so if you are um interested in
+ 
+
+ align:start position:0%
+Stellar so if you are um interested in
+the topic if you're if you have more the
+
+ align:start position:0%
+the topic if you're if you have more the
+ 
+
+ align:start position:0%
+the topic if you're if you have more the
+topic and you want to read the reading I
+
+ align:start position:0%
+topic and you want to read the reading I
+ 
+
+ align:start position:0%
+topic and you want to read the reading I
+highly recommend it especially if you
+
+ align:start position:0%
+highly recommend it especially if you
+ 
+
+ align:start position:0%
+highly recommend it especially if you
+think you're going to be in a leadership
+
+ align:start position:0%
+think you're going to be in a leadership
+ 
+
+ align:start position:0%
+think you're going to be in a leadership
+position in the future or any kind of
+
+ align:start position:0%
+position in the future or any kind of
+ 
+
+ align:start position:0%
+position in the future or any kind of
+managerial position or you're interested
+
+ align:start position:0%
+managerial position or you're interested
+ 
+
+ align:start position:0%
+managerial position or you're interested
+in just psychology and how people talk
+
+ align:start position:0%
+in just psychology and how people talk
+ 
+
+ align:start position:0%
+in just psychology and how people talk
+to each other and work together um so
+
+ align:start position:0%
+to each other and work together um so
+ 
+
+ align:start position:0%
+to each other and work together um so
+our three main topics um this will
+
+ align:start position:0%
+our three main topics um this will
+ 
+
+ align:start position:0%
+our three main topics um this will
+actually be pretty quick on this lecture
+
+ align:start position:0%
+actually be pretty quick on this lecture
+ 
+
+ align:start position:0%
+actually be pretty quick on this lecture
+um we're going to talk about we're going
+
+ align:start position:0%
+um we're going to talk about we're going
+ 
+
+ align:start position:0%
+um we're going to talk about we're going
+to do a really quick review of agile um
+
+ align:start position:0%
+to do a really quick review of agile um
+ 
+
+ align:start position:0%
+to do a really quick review of agile um
+we're going to talk about Team Dynamics
+
+ align:start position:0%
+we're going to talk about Team Dynamics
+ 
+
+ align:start position:0%
+we're going to talk about Team Dynamics
+and then we're going to talk about how
+
+ align:start position:0%
+and then we're going to talk about how
+ 
+
+ align:start position:0%
+and then we're going to talk about how
+do distributed agile teams perform so
+
+ align:start position:0%
+do distributed agile teams perform so
+ 
+
+ align:start position:0%
+do distributed agile teams perform so
+what are some of the the best practices
+
+ align:start position:0%
+what are some of the the best practices
+ 
+
+ align:start position:0%
+what are some of the the best practices
+they have uh for performing and then
+
+ align:start position:0%
+they have uh for performing and then
+ 
+
+ align:start position:0%
+they have uh for performing and then
+you're going to work in class um you'll
+
+ align:start position:0%
+you're going to work in class um you'll
+ 
+
+ align:start position:0%
+you're going to work in class um you'll
+have at least two hours to work in class
+
+ align:start position:0%
+have at least two hours to work in class
+ 
+
+ align:start position:0%
+have at least two hours to work in class
+today if not a little bit more than
+
+ align:start position:0%
+today if not a little bit more than
+ 
+
+ align:start position:0%
+today if not a little bit more than
+that so agile processes if you forget
+
+ align:start position:0%
+that so agile processes if you forget
+ 
+
+ align:start position:0%
+that so agile processes if you forget
+everything in this class you end the
+
+ align:start position:0%
+everything in this class you end the
+ 
+
+ align:start position:0%
+everything in this class you end the
+class you go into the into the real
+
+ align:start position:0%
+class you go into the into the real
+ 
+
+ align:start position:0%
+class you go into the into the real
+world you and somebody asks you what is
+
+ align:start position:0%
+world you and somebody asks you what is
+ 
+
+ align:start position:0%
+world you and somebody asks you what is
+agile um I hope you remember this part
+
+ align:start position:0%
+agile um I hope you remember this part
+ 
+
+ align:start position:0%
+agile um I hope you remember this part
+um iterative development is anybody
+
+ align:start position:0%
+um iterative development is anybody
+ 
+
+ align:start position:0%
+um iterative development is anybody
+doing does anybody consider what they're
+
+ align:start position:0%
+doing does anybody consider what they're
+ 
+
+ align:start position:0%
+doing does anybody consider what they're
+doing iterated development on their
+
+ align:start position:0%
+doing iterated development on their
+ 
+
+ align:start position:0%
+doing iterated development on their
+projects right
+
+ align:start position:0%
+projects right
+ 
+
+ align:start position:0%
+projects right
+now are you working in short periods of
+
+ align:start position:0%
+now are you working in short periods of
+ 
+
+ align:start position:0%
+now are you working in short periods of
+time so you've broken up your time into
+
+ align:start position:0%
+time so you've broken up your time into
+ 
+
+ align:start position:0%
+time so you've broken up your time into
+small Sprints are you doing all you
+
+ align:start position:0%
+small Sprints are you doing all you
+ 
+
+ align:start position:0%
+small Sprints are you doing all you
+can't really read it that well in the
+
+ align:start position:0%
+can't really read it that well in the
+ 
+
+ align:start position:0%
+can't really read it that well in the
+slide um but are you within that short
+
+ align:start position:0%
+slide um but are you within that short
+ 
+
+ align:start position:0%
+slide um but are you within that short
+period of time designing what you're
+
+ align:start position:0%
+period of time designing what you're
+ 
+
+ align:start position:0%
+period of time designing what you're
+going to work on planning how how it's
+
+ align:start position:0%
+going to work on planning how how it's
+ 
+
+ align:start position:0%
+going to work on planning how how it's
+going to work doing it and then testing
+
+ align:start position:0%
+going to work doing it and then testing
+ 
+
+ align:start position:0%
+going to work doing it and then testing
+it evaluating the test and changing are
+
+ align:start position:0%
+it evaluating the test and changing are
+ 
+
+ align:start position:0%
+it evaluating the test and changing are
+you doing all of that within one week or
+
+ align:start position:0%
+you doing all of that within one week or
+ 
+
+ align:start position:0%
+you doing all of that within one week or
+or two week
+
+ align:start position:0%
+or two week
+ 
+
+ align:start position:0%
+or two week
+cycle raise your hands yay raise your
+
+ align:start position:0%
+cycle raise your hands yay raise your
+ 
+
+ align:start position:0%
+cycle raise your hands yay raise your
+hand so yes raise your
+
+ align:start position:0%
+hand so yes raise your
+ 
+
+ align:start position:0%
+hand so yes raise your
+hands no raise your hands it's okay if
+
+ align:start position:0%
+hands no raise your hands it's okay if
+ 
+
+ align:start position:0%
+hands no raise your hands it's okay if
+you say
+
+ align:start position:0%
+you say
+ 
+
+ align:start position:0%
+you say
+now okay um if you if you're doing
+
+ align:start position:0%
+now okay um if you if you're doing
+ 
+
+ align:start position:0%
+now okay um if you if you're doing
+something that looks like this then
+
+ align:start position:0%
+something that looks like this then
+ 
+
+ align:start position:0%
+something that looks like this then
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+um and as as remember um agile in
+
+ align:start position:0%
+um and as as remember um agile in
+ 
+
+ align:start position:0%
+um and as as remember um agile in
+particular scrum processes um they're
+
+ align:start position:0%
+particular scrum processes um they're
+ 
+
+ align:start position:0%
+particular scrum processes um they're
+based on these three pillars that um
+
+ align:start position:0%
+based on these three pillars that um
+ 
+
+ align:start position:0%
+based on these three pillars that um
+that Sarah talked about when we first
+
+ align:start position:0%
+that Sarah talked about when we first
+ 
+
+ align:start position:0%
+that Sarah talked about when we first
+brought this up um so the pillar of
+
+ align:start position:0%
+brought this up um so the pillar of
+ 
+
+ align:start position:0%
+brought this up um so the pillar of
+transparency um and what we mean by
+
+ align:start position:0%
+transparency um and what we mean by
+ 
+
+ align:start position:0%
+transparency um and what we mean by
+transparency there we really just mean a
+
+ align:start position:0%
+transparency there we really just mean a
+ 
+
+ align:start position:0%
+transparency there we really just mean a
+common nomenclature I to be honest I
+
+ align:start position:0%
+common nomenclature I to be honest I
+ 
+
+ align:start position:0%
+common nomenclature I to be honest I
+don't care what you call the things that
+
+ align:start position:0%
+don't care what you call the things that
+ 
+
+ align:start position:0%
+don't care what you call the things that
+you that you that you use as part of
+
+ align:start position:0%
+you that you that you use as part of
+ 
+
+ align:start position:0%
+you that you that you use as part of
+your process in your in your team so
+
+ align:start position:0%
+your process in your in your team so
+ 
+
+ align:start position:0%
+your process in your in your team so
+long as everyone within the team knows
+
+ align:start position:0%
+long as everyone within the team knows
+ 
+
+ align:start position:0%
+long as everyone within the team knows
+what it is so so long as whoever you're
+
+ align:start position:0%
+what it is so so long as whoever you're
+ 
+
+ align:start position:0%
+what it is so so long as whoever you're
+submitting those those um processes to
+
+ align:start position:0%
+submitting those those um processes to
+ 
+
+ align:start position:0%
+submitting those those um processes to
+also know it know who it is so we're not
+
+ align:start position:0%
+also know it know who it is so we're not
+ 
+
+ align:start position:0%
+also know it know who it is so we're not
+acting as your product owners in the
+
+ align:start position:0%
+acting as your product owners in the
+ 
+
+ align:start position:0%
+acting as your product owners in the
+class but if you had a product owner
+
+ align:start position:0%
+class but if you had a product owner
+ 
+
+ align:start position:0%
+class but if you had a product owner
+they should also know what you're
+
+ align:start position:0%
+they should also know what you're
+ 
+
+ align:start position:0%
+they should also know what you're
+calling things what you're calling your
+
+ align:start position:0%
+calling things what you're calling your
+ 
+
+ align:start position:0%
+calling things what you're calling your
+product backlog what you're calling a
+
+ align:start position:0%
+product backlog what you're calling a
+ 
+
+ align:start position:0%
+product backlog what you're calling a
+task um how you're estimating and how
+
+ align:start position:0%
+task um how you're estimating and how
+ 
+
+ align:start position:0%
+task um how you're estimating and how
+you're doing your processes so everyone
+
+ align:start position:0%
+you're doing your processes so everyone
+ 
+
+ align:start position:0%
+you're doing your processes so everyone
+on the team should know it not just in a
+
+ align:start position:0%
+on the team should know it not just in a
+ 
+
+ align:start position:0%
+on the team should know it not just in a
+more traditional manner a project
+
+ align:start position:0%
+more traditional manner a project
+ 
+
+ align:start position:0%
+more traditional manner a project
+manager knowing what what all the
+
+ align:start position:0%
+manager knowing what what all the
+ 
+
+ align:start position:0%
+manager knowing what what all the
+processes are uh there's a number of
+
+ align:start position:0%
+processes are uh there's a number of
+ 
+
+ align:start position:0%
+processes are uh there's a number of
+inspection that's going on on so um
+
+ align:start position:0%
+inspection that's going on on so um
+ 
+
+ align:start position:0%
+inspection that's going on on so um
+through the process you are taking a
+
+ align:start position:0%
+through the process you are taking a
+ 
+
+ align:start position:0%
+through the process you are taking a
+look at all the artifacts that you
+
+ align:start position:0%
+look at all the artifacts that you
+ 
+
+ align:start position:0%
+look at all the artifacts that you
+created so those backlog items um task
+
+ align:start position:0%
+created so those backlog items um task
+ 
+
+ align:start position:0%
+created so those backlog items um task
+lists things like that that you're
+
+ align:start position:0%
+lists things like that that you're
+ 
+
+ align:start position:0%
+lists things like that that you're
+creating during the process um you're
+
+ align:start position:0%
+creating during the process um you're
+ 
+
+ align:start position:0%
+creating during the process um you're
+inspecting it in particular you're
+
+ align:start position:0%
+inspecting it in particular you're
+ 
+
+ align:start position:0%
+inspecting it in particular you're
+inspecting it during meetings so you're
+
+ align:start position:0%
+inspecting it during meetings so you're
+ 
+
+ align:start position:0%
+inspecting it during meetings so you're
+taking a look at what you've done in a
+
+ align:start position:0%
+taking a look at what you've done in a
+ 
+
+ align:start position:0%
+taking a look at what you've done in a
+meeting and talking about it so you're
+
+ align:start position:0%
+meeting and talking about it so you're
+ 
+
+ align:start position:0%
+meeting and talking about it so you're
+not just doing a process you're doing a
+
+ align:start position:0%
+not just doing a process you're doing a
+ 
+
+ align:start position:0%
+not just doing a process you're doing a
+process and you're talking about it and
+
+ align:start position:0%
+process and you're talking about it and
+ 
+
+ align:start position:0%
+process and you're talking about it and
+you're actively thinking about the
+
+ align:start position:0%
+you're actively thinking about the
+ 
+
+ align:start position:0%
+you're actively thinking about the
+process and then you're adapting So
+
+ align:start position:0%
+process and then you're adapting So
+ 
+
+ align:start position:0%
+process and then you're adapting So
+based on evidence um based on um need
+
+ align:start position:0%
+based on evidence um based on um need
+ 
+
+ align:start position:0%
+based on evidence um based on um need
+changes in needs you are changing that
+
+ align:start position:0%
+changes in needs you are changing that
+ 
+
+ align:start position:0%
+changes in needs you are changing that
+process again if you're doing any one of
+
+ align:start position:0%
+process again if you're doing any one of
+ 
+
+ align:start position:0%
+process again if you're doing any one of
+these three things you're doing process
+
+ align:start position:0%
+these three things you're doing process
+ 
+
+ align:start position:0%
+these three things you're doing process
+as well and you're doing agile you're
+
+ align:start position:0%
+as well and you're doing agile you're
+ 
+
+ align:start position:0%
+as well and you're doing agile you're
+you're doing some form of agile like
+
+ align:start position:0%
+you're doing some form of agile like
+ 
+
+ align:start position:0%
+you're doing some form of agile like
+process that's another thing I hope you
+
+ align:start position:0%
+process that's another thing I hope you
+ 
+
+ align:start position:0%
+process that's another thing I hope you
+hope you take from the
+
+ align:start position:0%
+hope you take from the
+ 
+
+ align:start position:0%
+hope you take from the
+class um the agile Manifesto and it's
+
+ align:start position:0%
+class um the agile Manifesto and it's
+ 
+
+ align:start position:0%
+class um the agile Manifesto and it's
+kind of a it is a Manifesto it is an
+
+ align:start position:0%
+kind of a it is a Manifesto it is an
+ 
+
+ align:start position:0%
+kind of a it is a Manifesto it is an
+idea it is a um it is something that has
+
+ align:start position:0%
+idea it is a um it is something that has
+ 
+
+ align:start position:0%
+idea it is a um it is something that has
+some political weight behind it is
+
+ align:start position:0%
+some political weight behind it is
+ 
+
+ align:start position:0%
+some political weight behind it is
+saying this is the way to do things this
+
+ align:start position:0%
+saying this is the way to do things this
+ 
+
+ align:start position:0%
+saying this is the way to do things this
+is the right way to do things um but
+
+ align:start position:0%
+is the right way to do things um but
+ 
+
+ align:start position:0%
+is the right way to do things um but
+it's actually more vague than that it's
+
+ align:start position:0%
+it's actually more vague than that it's
+ 
+
+ align:start position:0%
+it's actually more vague than that it's
+really just saying
+
+ align:start position:0%
+really just saying
+ 
+
+ align:start position:0%
+really just saying
+here are some four key things that we
+
+ align:start position:0%
+here are some four key things that we
+ 
+
+ align:start position:0%
+here are some four key things that we
+feel are more important than other four
+
+ align:start position:0%
+feel are more important than other four
+ 
+
+ align:start position:0%
+feel are more important than other four
+key things um and today we're going to
+
+ align:start position:0%
+key things um and today we're going to
+ 
+
+ align:start position:0%
+key things um and today we're going to
+focus so the first the first item is
+
+ align:start position:0%
+focus so the first the first item is
+ 
+
+ align:start position:0%
+focus so the first the first item is
+individuals and interactions over
+
+ align:start position:0%
+individuals and interactions over
+ 
+
+ align:start position:0%
+individuals and interactions over
+processes and tools so we've been
+
+ align:start position:0%
+processes and tools so we've been
+ 
+
+ align:start position:0%
+processes and tools so we've been
+talking to you a lot about process and
+
+ align:start position:0%
+talking to you a lot about process and
+ 
+
+ align:start position:0%
+talking to you a lot about process and
+tools uh for the first part of the
+
+ align:start position:0%
+tools uh for the first part of the
+ 
+
+ align:start position:0%
+tools uh for the first part of the
+semester now we're going to talk about
+
+ align:start position:0%
+semester now we're going to talk about
+ 
+
+ align:start position:0%
+semester now we're going to talk about
+individuals and and interactions between
+
+ align:start position:0%
+individuals and and interactions between
+ 
+
+ align:start position:0%
+individuals and and interactions between
+individuals so your team
+
+ align:start position:0%
+individuals so your team
+ 
+
+ align:start position:0%
+individuals so your team
+members all right what's a
+
+ align:start position:0%
+members all right what's a
+ 
+
+ align:start position:0%
+members all right what's a
+team anybody give me a working
+
+ align:start position:0%
+team anybody give me a working
+ 
+
+ align:start position:0%
+team anybody give me a working
+definition for what you'd call a te
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+team what' you
+
+ align:start position:0%
+team what' you
+ 
+
+ align:start position:0%
+team what' you
+say a bunch of puppies is it a group of
+
+ align:start position:0%
+say a bunch of puppies is it a group of
+ 
+
+ align:start position:0%
+say a bunch of puppies is it a group of
+people is it just a group of people
+
+ align:start position:0%
+people is it just a group of people
+ 
+
+ align:start position:0%
+people is it just a group of people
+group of people work
+
+ align:start position:0%
+group of people work
+ 
+
+ align:start position:0%
+group of people work
+towards yes anything
+
+ align:start position:0%
+towards yes anything
+ 
+
+ align:start position:0%
+towards yes anything
+else so it's a collection of individuals
+
+ align:start position:0%
+else so it's a collection of individuals
+ 
+
+ align:start position:0%
+else so it's a collection of individuals
+so it's a group of people they're
+
+ align:start position:0%
+so it's a group of people they're
+ 
+
+ align:start position:0%
+so it's a group of people they're
+working toward a common purpose they
+
+ align:start position:0%
+working toward a common purpose they
+ 
+
+ align:start position:0%
+working toward a common purpose they
+have shared responsibility for common
+
+ align:start position:0%
+have shared responsibility for common
+ 
+
+ align:start position:0%
+have shared responsibility for common
+outcomes if one of those puppies trips
+
+ align:start position:0%
+outcomes if one of those puppies trips
+ 
+
+ align:start position:0%
+outcomes if one of those puppies trips
+that stick goes in another puppy's mouth
+
+ align:start position:0%
+that stick goes in another puppy's mouth
+ 
+
+ align:start position:0%
+that stick goes in another puppy's mouth
+and it hurts a lot um
+
+ align:start position:0%
+and it hurts a lot um
+ 
+
+ align:start position:0%
+and it hurts a lot um
+um so that and and I want you to to to
+
+ align:start position:0%
+um so that and and I want you to to to
+ 
+
+ align:start position:0%
+um so that and and I want you to to to
+keep that in mind shared responsibility
+
+ align:start position:0%
+keep that in mind shared responsibility
+ 
+
+ align:start position:0%
+keep that in mind shared responsibility
+common purpose common
+
+ align:start position:0%
+common purpose common
+ 
+
+ align:start position:0%
+common purpose common
+outcomes all right so um teams evolve
+
+ align:start position:0%
+outcomes all right so um teams evolve
+ 
+
+ align:start position:0%
+outcomes all right so um teams evolve
+over time and um the the little bit of
+
+ align:start position:0%
+over time and um the the little bit of
+ 
+
+ align:start position:0%
+over time and um the the little bit of
+research I'm going to talk about
+
+ align:start position:0%
+research I'm going to talk about
+ 
+
+ align:start position:0%
+research I'm going to talk about
+actually comes from um uh studying group
+
+ align:start position:0%
+actually comes from um uh studying group
+ 
+
+ align:start position:0%
+actually comes from um uh studying group
+behaviors but in the and this is all
+
+ align:start position:0%
+behaviors but in the and this is all
+ 
+
+ align:start position:0%
+behaviors but in the and this is all
+from about the 1960s and on up um in
+
+ align:start position:0%
+from about the 1960s and on up um in
+ 
+
+ align:start position:0%
+from about the 1960s and on up um in
+around the 2000s and I'll post this
+
+ align:start position:0%
+around the 2000s and I'll post this
+ 
+
+ align:start position:0%
+around the 2000s and I'll post this
+reading up um it was proven or was there
+
+ align:start position:0%
+reading up um it was proven or was there
+ 
+
+ align:start position:0%
+reading up um it was proven or was there
+was some study shown that this actually
+
+ align:start position:0%
+was some study shown that this actually
+ 
+
+ align:start position:0%
+was some study shown that this actually
+works for teams this does work for for
+
+ align:start position:0%
+works for teams this does work for for
+ 
+
+ align:start position:0%
+works for teams this does work for for
+people who have a common goal but as you
+
+ align:start position:0%
+people who have a common goal but as you
+ 
+
+ align:start position:0%
+people who have a common goal but as you
+get a bunch of people together and you
+
+ align:start position:0%
+get a bunch of people together and you
+ 
+
+ align:start position:0%
+get a bunch of people together and you
+get a small group of people together and
+
+ align:start position:0%
+get a small group of people together and
+ 
+
+ align:start position:0%
+get a small group of people together and
+in our terms we're talking a small group
+
+ align:start position:0%
+in our terms we're talking a small group
+ 
+
+ align:start position:0%
+in our terms we're talking a small group
+of people um 8 to 10 people um maybe a
+
+ align:start position:0%
+of people um 8 to 10 people um maybe a
+ 
+
+ align:start position:0%
+of people um 8 to 10 people um maybe a
+little bit bigger but about 10 people
+
+ align:start position:0%
+little bit bigger but about 10 people
+ 
+
+ align:start position:0%
+little bit bigger but about 10 people
+total um they're going to evolve based
+
+ align:start position:0%
+total um they're going to evolve based
+ 
+
+ align:start position:0%
+total um they're going to evolve based
+on those interpersonal relationships so
+
+ align:start position:0%
+on those interpersonal relationships so
+ 
+
+ align:start position:0%
+on those interpersonal relationships so
+how they know each other what they talk
+
+ align:start position:0%
+how they know each other what they talk
+ 
+
+ align:start position:0%
+how they know each other what they talk
+about how they talk about and their task
+
+ align:start position:0%
+about how they talk about and their task
+ 
+
+ align:start position:0%
+about how they talk about and their task
+behaviors so we're going to be talking
+
+ align:start position:0%
+behaviors so we're going to be talking
+ 
+
+ align:start position:0%
+behaviors so we're going to be talking
+about not the tasks that are do you are
+
+ align:start position:0%
+about not the tasks that are do you are
+ 
+
+ align:start position:0%
+about not the tasks that are do you are
+doing in your teams but the behaviors
+
+ align:start position:0%
+doing in your teams but the behaviors
+ 
+
+ align:start position:0%
+doing in your teams but the behaviors
+surrounding the tasks that you're doing
+
+ align:start position:0%
+surrounding the tasks that you're doing
+ 
+
+ align:start position:0%
+surrounding the tasks that you're doing
+it so um if you are working on a task if
+
+ align:start position:0%
+it so um if you are working on a task if
+ 
+
+ align:start position:0%
+it so um if you are working on a task if
+you are doing some coding how are you
+
+ align:start position:0%
+you are doing some coding how are you
+ 
+
+ align:start position:0%
+you are doing some coding how are you
+coding or who are you coding with how
+
+ align:start position:0%
+coding or who are you coding with how
+ 
+
+ align:start position:0%
+coding or who are you coding with how
+are you talking to other people about
+
+ align:start position:0%
+are you talking to other people about
+ 
+
+ align:start position:0%
+are you talking to other people about
+what you're coding and you can apply
+
+ align:start position:0%
+what you're coding and you can apply
+ 
+
+ align:start position:0%
+what you're coding and you can apply
+that to any other T any any task that
+
+ align:start position:0%
+that to any other T any any task that
+ 
+
+ align:start position:0%
+that to any other T any any task that
+you're doing in your teams there's a lot
+
+ align:start position:0%
+you're doing in your teams there's a lot
+ 
+
+ align:start position:0%
+you're doing in your teams there's a lot
+of different theories um actually
+
+ align:start position:0%
+of different theories um actually
+ 
+
+ align:start position:0%
+of different theories um actually
+Wikipedia is a pretty good um just a
+
+ align:start position:0%
+Wikipedia is a pretty good um just a
+ 
+
+ align:start position:0%
+Wikipedia is a pretty good um just a
+good nutshell of of what are all the
+
+ align:start position:0%
+good nutshell of of what are all the
+ 
+
+ align:start position:0%
+good nutshell of of what are all the
+different kinds of theories um and how
+
+ align:start position:0%
+different kinds of theories um and how
+ 
+
+ align:start position:0%
+different kinds of theories um and how
+different kind of models we can use to
+
+ align:start position:0%
+different kind of models we can use to
+ 
+
+ align:start position:0%
+different kind of models we can use to
+describe how groups talk to each other
+
+ align:start position:0%
+describe how groups talk to each other
+ 
+
+ align:start position:0%
+describe how groups talk to each other
+and how groups evolve um but they all
+
+ align:start position:0%
+and how groups evolve um but they all
+ 
+
+ align:start position:0%
+and how groups evolve um but they all
+come down to these things there's a
+
+ align:start position:0%
+come down to these things there's a
+ 
+
+ align:start position:0%
+come down to these things there's a
+period of getting to know each other um
+
+ align:start position:0%
+period of getting to know each other um
+ 
+
+ align:start position:0%
+period of getting to know each other um
+there's a period of experiencing
+
+ align:start position:0%
+there's a period of experiencing
+ 
+
+ align:start position:0%
+there's a period of experiencing
+conflict and there's both positive and
+
+ align:start position:0%
+conflict and there's both positive and
+ 
+
+ align:start position:0%
+conflict and there's both positive and
+negative conflict when you're talking
+
+ align:start position:0%
+negative conflict when you're talking
+ 
+
+ align:start position:0%
+negative conflict when you're talking
+with each other your roles shift based
+
+ align:start position:0%
+with each other your roles shift based
+ 
+
+ align:start position:0%
+with each other your roles shift based
+on changing knowledge and changing
+
+ align:start position:0%
+on changing knowledge and changing
+ 
+
+ align:start position:0%
+on changing knowledge and changing
+experience and hopefully at some point
+
+ align:start position:0%
+experience and hopefully at some point
+ 
+
+ align:start position:0%
+experience and hopefully at some point
+there's some kind of consensus there's
+
+ align:start position:0%
+there's some kind of consensus there's
+ 
+
+ align:start position:0%
+there's some kind of consensus there's
+some kind of moving forward decisions
+
+ align:start position:0%
+some kind of moving forward decisions
+ 
+
+ align:start position:0%
+some kind of moving forward decisions
+happen here uh the point is though what
+
+ align:start position:0%
+happen here uh the point is though what
+ 
+
+ align:start position:0%
+happen here uh the point is though what
+kind of decisions get made are they
+
+ align:start position:0%
+kind of decisions get made are they
+ 
+
+ align:start position:0%
+kind of decisions get made are they
+effective decisions um or they
+
+ align:start position:0%
+effective decisions um or they
+ 
+
+ align:start position:0%
+effective decisions um or they
+ineffective
+
+ align:start position:0%
+ineffective
+ 
+
+ align:start position:0%
+ineffective
+unproven they get made because you just
+
+ align:start position:0%
+unproven they get made because you just
+ 
+
+ align:start position:0%
+unproven they get made because you just
+have to make them and you have to move
+
+ align:start position:0%
+have to make them and you have to move
+ 
+
+ align:start position:0%
+have to make them and you have to move
+move on um we're hoping is that by
+
+ align:start position:0%
+move on um we're hoping is that by
+ 
+
+ align:start position:0%
+move on um we're hoping is that by
+analyzing how your teams work you can
+
+ align:start position:0%
+analyzing how your teams work you can
+ 
+
+ align:start position:0%
+analyzing how your teams work you can
+then move towards having some effective
+
+ align:start position:0%
+then move towards having some effective
+ 
+
+ align:start position:0%
+then move towards having some effective
+decision decision
+
+ align:start position:0%
+decision decision
+ 
+
+ align:start position:0%
+decision decision
+making um so one so the model that we're
+
+ align:start position:0%
+making um so one so the model that we're
+ 
+
+ align:start position:0%
+making um so one so the model that we're
+going to talk about um is tuckman's
+
+ align:start position:0%
+going to talk about um is tuckman's
+ 
+
+ align:start position:0%
+going to talk about um is tuckman's
+model from 65 it's got four phases um
+
+ align:start position:0%
+model from 65 it's got four phases um
+ 
+
+ align:start position:0%
+model from 65 it's got four phases um
+forming norming storming performing it's
+
+ align:start position:0%
+forming norming storming performing it's
+ 
+
+ align:start position:0%
+forming norming storming performing it's
+very cutesy you get it's gets used in
+
+ align:start position:0%
+very cutesy you get it's gets used in
+ 
+
+ align:start position:0%
+very cutesy you get it's gets used in
+training sessions a lot um it can just
+
+ align:start position:0%
+training sessions a lot um it can just
+ 
+
+ align:start position:0%
+training sessions a lot um it can just
+be something that you can just spit out
+
+ align:start position:0%
+be something that you can just spit out
+ 
+
+ align:start position:0%
+be something that you can just spit out
+and say and someone says oh you're smart
+
+ align:start position:0%
+and say and someone says oh you're smart
+ 
+
+ align:start position:0%
+and say and someone says oh you're smart
+you know that that that model but maybe
+
+ align:start position:0%
+you know that that that model but maybe
+ 
+
+ align:start position:0%
+you know that that that model but maybe
+you don't know everything behind it um I
+
+ align:start position:0%
+you don't know everything behind it um I
+ 
+
+ align:start position:0%
+you don't know everything behind it um I
+might be more the you're smart but maybe
+
+ align:start position:0%
+might be more the you're smart but maybe
+ 
+
+ align:start position:0%
+might be more the you're smart but maybe
+you don't know more everything behind it
+
+ align:start position:0%
+you don't know more everything behind it
+ 
+
+ align:start position:0%
+you don't know more everything behind it
+I'm still learning about how this works
+
+ align:start position:0%
+I'm still learning about how this works
+ 
+
+ align:start position:0%
+I'm still learning about how this works
+um but each phase has items you you can
+
+ align:start position:0%
+um but each phase has items you you can
+ 
+
+ align:start position:0%
+um but each phase has items you you can
+identify and more useful for us is this
+
+ align:start position:0%
+identify and more useful for us is this
+ 
+
+ align:start position:0%
+identify and more useful for us is this
+is a model you can use to figure out
+
+ align:start position:0%
+is a model you can use to figure out
+ 
+
+ align:start position:0%
+is a model you can use to figure out
+where your team is right now um what
+
+ align:start position:0%
+where your team is right now um what
+ 
+
+ align:start position:0%
+where your team is right now um what
+phase are you in so you can then make
+
+ align:start position:0%
+phase are you in so you can then make
+ 
+
+ align:start position:0%
+phase are you in so you can then make
+decisions about where you need to go and
+
+ align:start position:0%
+decisions about where you need to go and
+ 
+
+ align:start position:0%
+decisions about where you need to go and
+how you need to work together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better so um the forming uh phase of it
+
+ align:start position:0%
+better so um the forming uh phase of it
+ 
+
+ align:start position:0%
+better so um the forming uh phase of it
+this is when you first start getting
+
+ align:start position:0%
+this is when you first start getting
+ 
+
+ align:start position:0%
+this is when you first start getting
+together everyone wants to be friendly
+
+ align:start position:0%
+together everyone wants to be friendly
+ 
+
+ align:start position:0%
+together everyone wants to be friendly
+um everyone wants to get along and to be
+
+ align:start position:0%
+um everyone wants to get along and to be
+ 
+
+ align:start position:0%
+um everyone wants to get along and to be
+accepted with each other um there might
+
+ align:start position:0%
+accepted with each other um there might
+ 
+
+ align:start position:0%
+accepted with each other um there might
+be some serious problems from the get-go
+
+ align:start position:0%
+be some serious problems from the get-go
+ 
+
+ align:start position:0%
+be some serious problems from the get-go
+but they're usually avoided um and the
+
+ align:start position:0%
+but they're usually avoided um and the
+ 
+
+ align:start position:0%
+but they're usually avoided um and the
+team learns about challenges and goals
+
+ align:start position:0%
+team learns about challenges and goals
+ 
+
+ align:start position:0%
+team learns about challenges and goals
+but not much gets done um there's no
+
+ align:start position:0%
+but not much gets done um there's no
+ 
+
+ align:start position:0%
+but not much gets done um there's no
+real task completion going on in this
+
+ align:start position:0%
+real task completion going on in this
+ 
+
+ align:start position:0%
+real task completion going on in this
+stage um has everybody seen this can
+
+ align:start position:0%
+stage um has everybody seen this can
+ 
+
+ align:start position:0%
+stage um has everybody seen this can
+when you think about your previous teams
+
+ align:start position:0%
+when you think about your previous teams
+ 
+
+ align:start position:0%
+when you think about your previous teams
+you've been in this stage right when you
+
+ align:start position:0%
+you've been in this stage right when you
+ 
+
+ align:start position:0%
+you've been in this stage right when you
+first got
+
+ align:start position:0%
+first got
+ 
+
+ align:start position:0%
+first got
+together so project two project three
+
+ align:start position:0%
+together so project two project three
+ 
+
+ align:start position:0%
+together so project two project three
+I'm going to talk I want to ask you some
+
+ align:start position:0%
+I'm going to talk I want to ask you some
+ 
+
+ align:start position:0%
+I'm going to talk I want to ask you some
+questions about projects two and three
+
+ align:start position:0%
+questions about projects two and three
+ 
+
+ align:start position:0%
+questions about projects two and three
+as we go forward all
+
+ align:start position:0%
+as we go forward all
+ 
+
+ align:start position:0%
+as we go forward all
+right that's a happy stage then storming
+
+ align:start position:0%
+right that's a happy stage then storming
+ 
+
+ align:start position:0%
+right that's a happy stage then storming
+happens people are able to express
+
+ align:start position:0%
+happens people are able to express
+ 
+
+ align:start position:0%
+happens people are able to express
+discontent there actually might have
+
+ align:start position:0%
+discontent there actually might have
+ 
+
+ align:start position:0%
+discontent there actually might have
+been discontent in phase one but it
+
+ align:start position:0%
+been discontent in phase one but it
+ 
+
+ align:start position:0%
+been discontent in phase one but it
+actually wasn't being it wasn't being
+
+ align:start position:0%
+actually wasn't being it wasn't being
+ 
+
+ align:start position:0%
+actually wasn't being it wasn't being
+expressed in some form in phase two it's
+
+ align:start position:0%
+expressed in some form in phase two it's
+ 
+
+ align:start position:0%
+expressed in some form in phase two it's
+being expressed but how it's being
+
+ align:start position:0%
+being expressed but how it's being
+ 
+
+ align:start position:0%
+being expressed but how it's being
+Express can be kind of different so it
+
+ align:start position:0%
+Express can be kind of different so it
+ 
+
+ align:start position:0%
+Express can be kind of different so it
+could be someone actively saying no
+
+ align:start position:0%
+could be someone actively saying no
+ 
+
+ align:start position:0%
+could be someone actively saying no
+you're wrong that's stupid um it could
+
+ align:start position:0%
+you're wrong that's stupid um it could
+ 
+
+ align:start position:0%
+you're wrong that's stupid um it could
+be someone not talking but they're
+
+ align:start position:0%
+be someone not talking but they're
+ 
+
+ align:start position:0%
+be someone not talking but they're
+feeling the same thing and they're
+
+ align:start position:0%
+feeling the same thing and they're
+ 
+
+ align:start position:0%
+feeling the same thing and they're
+thinking about the same thing it's the
+
+ align:start position:0%
+thinking about the same thing it's the
+ 
+
+ align:start position:0%
+thinking about the same thing it's the
+same kind of discon happen umin opinions
+
+ align:start position:0%
+same kind of discon happen umin opinions
+ 
+
+ align:start position:0%
+same kind of discon happen umin opinions
+tend to get challenged um it can be
+
+ align:start position:0%
+tend to get challenged um it can be
+ 
+
+ align:start position:0%
+tend to get challenged um it can be
+contentious it can be
+
+ align:start position:0%
+contentious it can be
+ 
+
+ align:start position:0%
+contentious it can be
+unpleasant um in order to advance past
+
+ align:start position:0%
+unpleasant um in order to advance past
+ 
+
+ align:start position:0%
+unpleasant um in order to advance past
+this stage what your team really needs
+
+ align:start position:0%
+this stage what your team really needs
+ 
+
+ align:start position:0%
+this stage what your team really needs
+is tolerance and patience I'm just to
+
+ align:start position:0%
+is tolerance and patience I'm just to
+ 
+
+ align:start position:0%
+is tolerance and patience I'm just to
+kind of get through it but even more
+
+ align:start position:0%
+kind of get through it but even more
+ 
+
+ align:start position:0%
+kind of get through it but even more
+important you need to establish lines of
+
+ align:start position:0%
+important you need to establish lines of
+ 
+
+ align:start position:0%
+important you need to establish lines of
+trust and open communication to get
+
+ align:start position:0%
+trust and open communication to get
+ 
+
+ align:start position:0%
+trust and open communication to get
+through the stage and this is where this
+
+ align:start position:0%
+through the stage and this is where this
+ 
+
+ align:start position:0%
+through the stage and this is where this
+is what we've been doing for the past
+
+ align:start position:0%
+is what we've been doing for the past
+ 
+
+ align:start position:0%
+is what we've been doing for the past
+first of the semester is creating
+
+ align:start position:0%
+first of the semester is creating
+ 
+
+ align:start position:0%
+first of the semester is creating
+processes we've been giving you some
+
+ align:start position:0%
+processes we've been giving you some
+ 
+
+ align:start position:0%
+processes we've been giving you some
+tools that you can use so then you can
+
+ align:start position:0%
+tools that you can use so then you can
+ 
+
+ align:start position:0%
+tools that you can use so then you can
+then create those processes in your
+
+ align:start position:0%
+then create those processes in your
+ 
+
+ align:start position:0%
+then create those processes in your
+teams so just a quick hand raise from
+
+ align:start position:0%
+teams so just a quick hand raise from
+ 
+
+ align:start position:0%
+teams so just a quick hand raise from
+teams
+
+ align:start position:0%
+teams
+ 
+
+ align:start position:0%
+teams
+um does anybody think that they are in
+
+ align:start position:0%
+um does anybody think that they are in
+ 
+
+ align:start position:0%
+um does anybody think that they are in
+this stage right
+
+ align:start position:0%
+this stage right
+ 
+
+ align:start position:0%
+this stage right
+now do you think in your team you are
+
+ align:start position:0%
+now do you think in your team you are
+ 
+
+ align:start position:0%
+now do you think in your team you are
+currently you're expressing discontent
+
+ align:start position:0%
+currently you're expressing discontent
+ 
+
+ align:start position:0%
+currently you're expressing discontent
+you are creating processes you don't
+
+ align:start position:0%
+you are creating processes you don't
+ 
+
+ align:start position:0%
+you are creating processes you don't
+have processes yet but you're figuring
+
+ align:start position:0%
+have processes yet but you're figuring
+ 
+
+ align:start position:0%
+have processes yet but you're figuring
+out what your processes might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be maybe what do you say you're not sure
+
+ align:start position:0%
+be maybe what do you say you're not sure
+ 
+
+ align:start position:0%
+be maybe what do you say you're not sure
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+um next up norming so this is where have
+
+ align:start position:0%
+um next up norming so this is where have
+ 
+
+ align:start position:0%
+um next up norming so this is where have
+those processes um individuals start
+
+ align:start position:0%
+those processes um individuals start
+ 
+
+ align:start position:0%
+those processes um individuals start
+giving up their own ideas and goals
+
+ align:start position:0%
+giving up their own ideas and goals
+ 
+
+ align:start position:0%
+giving up their own ideas and goals
+you're moving you're actually moving
+
+ align:start position:0%
+you're moving you're actually moving
+ 
+
+ align:start position:0%
+you're moving you're actually moving
+towards a team goal right now and people
+
+ align:start position:0%
+towards a team goal right now and people
+ 
+
+ align:start position:0%
+towards a team goal right now and people
+are starting to take responsibility and
+
+ align:start position:0%
+are starting to take responsibility and
+ 
+
+ align:start position:0%
+are starting to take responsibility and
+rules are established okay comparing
+
+ align:start position:0%
+rules are established okay comparing
+ 
+
+ align:start position:0%
+rules are established okay comparing
+storming to norming raise your hands if
+
+ align:start position:0%
+storming to norming raise your hands if
+ 
+
+ align:start position:0%
+storming to norming raise your hands if
+you think you're in norming your team is
+
+ align:start position:0%
+you think you're in norming your team is
+ 
+
+ align:start position:0%
+you think you're in norming your team is
+in norming right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now okay yeah all right now raise your
+
+ align:start position:0%
+now okay yeah all right now raise your
+ 
+
+ align:start position:0%
+now okay yeah all right now raise your
+hands if you think your team is in
+
+ align:start position:0%
+hands if you think your team is in
+ 
+
+ align:start position:0%
+hands if you think your team is in
+storming right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so is anybody performing are
+
+ align:start position:0%
+all right so is anybody performing are
+ 
+
+ align:start position:0%
+all right so is anybody performing are
+you functioning as a unit efficiently
+
+ align:start position:0%
+you functioning as a unit efficiently
+ 
+
+ align:start position:0%
+you functioning as a unit efficiently
+are your team members already
+
+ align:start position:0%
+are your team members already
+ 
+
+ align:start position:0%
+are your team members already
+autonomous is descent expected and
+
+ align:start position:0%
+autonomous is descent expected and
+ 
+
+ align:start position:0%
+autonomous is descent expected and
+addressed right now this is where you
+
+ align:start position:0%
+addressed right now this is where you
+ 
+
+ align:start position:0%
+addressed right now this is where you
+want to get
+
+ align:start position:0%
+want to get
+ 
+
+ align:start position:0%
+want to get
+to you probably aren't this far yet my
+
+ align:start position:0%
+to you probably aren't this far yet my
+ 
+
+ align:start position:0%
+to you probably aren't this far yet my
+bets you're probably somewhere in the in
+
+ align:start position:0%
+bets you're probably somewhere in the in
+ 
+
+ align:start position:0%
+bets you're probably somewhere in the in
+the storming area of things maybe
+
+ align:start position:0%
+the storming area of things maybe
+ 
+
+ align:start position:0%
+the storming area of things maybe
+getting close to the norming area of
+
+ align:start position:0%
+getting close to the norming area of
+ 
+
+ align:start position:0%
+getting close to the norming area of
+things basically you're still trying to
+
+ align:start position:0%
+things basically you're still trying to
+ 
+
+ align:start position:0%
+things basically you're still trying to
+you're still talking to each other
+
+ align:start position:0%
+you're still talking to each other
+ 
+
+ align:start position:0%
+you're still talking to each other
+you're still trying to figure out what
+
+ align:start position:0%
+you're still trying to figure out what
+ 
+
+ align:start position:0%
+you're still trying to figure out what
+are the the different ways of
+
+ align:start position:0%
+are the the different ways of
+ 
+
+ align:start position:0%
+are the the different ways of
+communicating with each other um what
+
+ align:start position:0%
+communicating with each other um what
+ 
+
+ align:start position:0%
+communicating with each other um what
+are the the different um processes and
+
+ align:start position:0%
+are the the different um processes and
+ 
+
+ align:start position:0%
+are the the different um processes and
+rules you might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have and you might not get this far uh
+
+ align:start position:0%
+have and you might not get this far uh
+ 
+
+ align:start position:0%
+have and you might not get this far uh
+in class in class by the end of the
+
+ align:start position:0%
+in class in class by the end of the
+ 
+
+ align:start position:0%
+in class in class by the end of the
+semester you might not be uh fully
+
+ align:start position:0%
+semester you might not be uh fully
+ 
+
+ align:start position:0%
+semester you might not be uh fully
+efficient by the end of the the end of
+
+ align:start position:0%
+efficient by the end of the the end of
+ 
+
+ align:start position:0%
+efficient by the end of the the end of
+the class and that's
+
+ align:start position:0%
+the class and that's
+ 
+
+ align:start position:0%
+the class and that's
+okay but if you are it's kind of
+
+ align:start position:0%
+okay but if you are it's kind of
+ 
+
+ align:start position:0%
+okay but if you are it's kind of
+cool so um the model in practice tends
+
+ align:start position:0%
+cool so um the model in practice tends
+ 
+
+ align:start position:0%
+cool so um the model in practice tends
+to be it's nonlinear it's it gets talked
+
+ align:start position:0%
+to be it's nonlinear it's it gets talked
+ 
+
+ align:start position:0%
+to be it's nonlinear it's it gets talked
+about and it was originally um
+
+ align:start position:0%
+about and it was originally um
+ 
+
+ align:start position:0%
+about and it was originally um
+established as a you go from here to
+
+ align:start position:0%
+established as a you go from here to
+ 
+
+ align:start position:0%
+established as a you go from here to
+here to here to here you go through the
+
+ align:start position:0%
+here to here to here you go through the
+ 
+
+ align:start position:0%
+here to here to here you go through the
+phases at the end of the thing you're
+
+ align:start position:0%
+phases at the end of the thing you're
+ 
+
+ align:start position:0%
+phases at the end of the thing you're
+done your team's awesome go you um what
+
+ align:start position:0%
+done your team's awesome go you um what
+ 
+
+ align:start position:0%
+done your team's awesome go you um what
+we actually see in process is that teams
+
+ align:start position:0%
+we actually see in process is that teams
+ 
+
+ align:start position:0%
+we actually see in process is that teams
+tend to they get in the forming they go
+
+ align:start position:0%
+tend to they get in the forming they go
+ 
+
+ align:start position:0%
+tend to they get in the forming they go
+in this circle where they go from from
+
+ align:start position:0%
+in this circle where they go from from
+ 
+
+ align:start position:0%
+in this circle where they go from from
+having some issues figuring out how to
+
+ align:start position:0%
+having some issues figuring out how to
+ 
+
+ align:start position:0%
+having some issues figuring out how to
+how to deal with those issues establish
+
+ align:start position:0%
+how to deal with those issues establish
+ 
+
+ align:start position:0%
+how to deal with those issues establish
+some rules all right we're do really
+
+ align:start position:0%
+some rules all right we're do really
+ 
+
+ align:start position:0%
+some rules all right we're do really
+well again new challenge comes up we're
+
+ align:start position:0%
+well again new challenge comes up we're
+ 
+
+ align:start position:0%
+well again new challenge comes up we're
+back into we're back into storming we're
+
+ align:start position:0%
+back into we're back into storming we're
+ 
+
+ align:start position:0%
+back into we're back into storming we're
+we we are we've put ourselves in a
+
+ align:start position:0%
+we we are we've put ourselves in a
+ 
+
+ align:start position:0%
+we we are we've put ourselves in a
+position where we don't know how to talk
+
+ align:start position:0%
+position where we don't know how to talk
+ 
+
+ align:start position:0%
+position where we don't know how to talk
+to each other or we don't know how to
+
+ align:start position:0%
+to each other or we don't know how to
+ 
+
+ align:start position:0%
+to each other or we don't know how to
+communicate with each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's some problems with the with
+
+ align:start position:0%
+so there's some problems with the with
+ 
+
+ align:start position:0%
+so there's some problems with the with
+the model this is really a descriptive
+
+ align:start position:0%
+the model this is really a descriptive
+ 
+
+ align:start position:0%
+the model this is really a descriptive
+model it's a way it's a tool for us to
+
+ align:start position:0%
+model it's a way it's a tool for us to
+ 
+
+ align:start position:0%
+model it's a way it's a tool for us to
+use to see how things are going it's
+
+ align:start position:0%
+use to see how things are going it's
+ 
+
+ align:start position:0%
+use to see how things are going it's
+basically a way to evaluate symptoms
+
+ align:start position:0%
+basically a way to evaluate symptoms
+ 
+
+ align:start position:0%
+basically a way to evaluate symptoms
+um but there's no triggers in the model
+
+ align:start position:0%
+um but there's no triggers in the model
+ 
+
+ align:start position:0%
+um but there's no triggers in the model
+we don't know when those things happen
+
+ align:start position:0%
+we don't know when those things happen
+ 
+
+ align:start position:0%
+we don't know when those things happen
+when does it when does your team switch
+
+ align:start position:0%
+when does it when does your team switch
+ 
+
+ align:start position:0%
+when does it when does your team switch
+from storming to norming so this is what
+
+ align:start position:0%
+from storming to norming so this is what
+ 
+
+ align:start position:0%
+from storming to norming so this is what
+I'd like you to do in your in your teams
+
+ align:start position:0%
+I'd like you to do in your in your teams
+ 
+
+ align:start position:0%
+I'd like you to do in your in your teams
+just take a couple minutes talk about um
+
+ align:start position:0%
+just take a couple minutes talk about um
+ 
+
+ align:start position:0%
+just take a couple minutes talk about um
+talk about your previous teams you've
+
+ align:start position:0%
+talk about your previous teams you've
+ 
+
+ align:start position:0%
+talk about your previous teams you've
+been on talk about the team you're on
+
+ align:start position:0%
+been on talk about the team you're on
+ 
+
+ align:start position:0%
+been on talk about the team you're on
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+when do you think your team would move
+
+ align:start position:0%
+when do you think your team would move
+ 
+
+ align:start position:0%
+when do you think your team would move
+from stage to stage and how could a team
+
+ align:start position:0%
+from stage to stage and how could a team
+ 
+
+ align:start position:0%
+from stage to stage and how could a team
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+intentionally so and in particular think
+
+ align:start position:0%
+intentionally so and in particular think
+ 
+
+ align:start position:0%
+intentionally so and in particular think
+about that storming dorming part of it
+
+ align:start position:0%
+about that storming dorming part of it
+ 
+
+ align:start position:0%
+about that storming dorming part of it
+so what is it going to take for your
+
+ align:start position:0%
+so what is it going to take for your
+ 
+
+ align:start position:0%
+so what is it going to take for your
+team right now or what happened in your
+
+ align:start position:0%
+team right now or what happened in your
+ 
+
+ align:start position:0%
+team right now or what happened in your
+team right now to go from we are having
+
+ align:start position:0%
+team right now to go from we are having
+ 
+
+ align:start position:0%
+team right now to go from we are having
+some some difficulty talking with each
+
+ align:start position:0%
+some some difficulty talking with each
+ 
+
+ align:start position:0%
+some some difficulty talking with each
+other we're we're we have a bunch of
+
+ align:start position:0%
+other we're we're we have a bunch of
+ 
+
+ align:start position:0%
+other we're we're we have a bunch of
+opinions two we're on on the same page
+
+ align:start position:0%
+opinions two we're on on the same page
+ 
+
+ align:start position:0%
+opinions two we're on on the same page
+take three minutes just just one thing I
+
+ align:start position:0%
+take three minutes just just one thing I
+ 
+
+ align:start position:0%
+take three minutes just just one thing I
+want to chime in there's a very very
+
+ align:start position:0%
+want to chime in there's a very very
+ 
+
+ align:start position:0%
+want to chime in there's a very very
+good chance that your team actually is
+
+ align:start position:0%
+good chance that your team actually is
+ 
+
+ align:start position:0%
+good chance that your team actually is
+still in forming stage and one of the
+
+ align:start position:0%
+still in forming stage and one of the
+ 
+
+ align:start position:0%
+still in forming stage and one of the
+reasons why no one like very few of you
+
+ align:start position:0%
+reasons why no one like very few of you
+ 
+
+ align:start position:0%
+reasons why no one like very few of you
+might have put up your hands that you
+
+ align:start position:0%
+might have put up your hands that you
+ 
+
+ align:start position:0%
+might have put up your hands that you
+don't actually want to express dissent
+
+ align:start position:0%
+don't actually want to express dissent
+ 
+
+ align:start position:0%
+don't actually want to express dissent
+which is exactly the situation that you
+
+ align:start position:0%
+which is exactly the situation that you
+ 
+
+ align:start position:0%
+which is exactly the situation that you
+get in forming stage um you know it's it
+
+ align:start position:0%
+get in forming stage um you know it's it
+ 
+
+ align:start position:0%
+get in forming stage um you know it's it
+is uncomfortable but hopefully there you
+
+ align:start position:0%
+is uncomfortable but hopefully there you
+ 
+
+ align:start position:0%
+is uncomfortable but hopefully there you
+can logically see the benefits of being
+
+ align:start position:0%
+can logically see the benefits of being
+ 
+
+ align:start position:0%
+can logically see the benefits of being
+in a team where you can talk about the
+
+ align:start position:0%
+in a team where you can talk about the
+ 
+
+ align:start position:0%
+in a team where you can talk about the
+things that you disagree with right so
+
+ align:start position:0%
+things that you disagree with right so
+ 
+
+ align:start position:0%
+things that you disagree with right so
+um so it's possible that you are still
+
+ align:start position:0%
+um so it's possible that you are still
+ 
+
+ align:start position:0%
+um so it's possible that you are still
+informing and you know it's good to
+
+ align:start position:0%
+informing and you know it's good to
+ 
+
+ align:start position:0%
+informing and you know it's good to
+identify your teams as okay this is
+
+ align:start position:0%
+identify your teams as okay this is
+ 
+
+ align:start position:0%
+identify your teams as okay this is
+normal evolution of a team and that's
+
+ align:start position:0%
+normal evolution of a team and that's
+ 
+
+ align:start position:0%
+normal evolution of a team and that's
+where our team is at right now so talk
+
+ align:start position:0%
+where our team is at right now so talk
+ 
+
+ align:start position:0%
+where our team is at right now so talk
+about it among your team so take three
+
+ align:start position:0%
+about it among your team so take three
+ 
+
+ align:start position:0%
+about it among your team so take three
+minutes just talking your teams and I'm
+
+ align:start position:0%
+minutes just talking your teams and I'm
+ 
+
+ align:start position:0%
+minutes just talking your teams and I'm
+gonna ask you some questions when we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so each group give me a
+
+ align:start position:0%
+so each group give me a
+ 
+
+ align:start position:0%
+so each group give me a
+something you talked about about what
+
+ align:start position:0%
+something you talked about about what
+ 
+
+ align:start position:0%
+something you talked about about what
+are the what are the triggers what are
+
+ align:start position:0%
+are the what are the triggers what are
+ 
+
+ align:start position:0%
+are the what are the triggers what are
+the things you saw as you moved just let
+
+ align:start position:0%
+the things you saw as you moved just let
+ 
+
+ align:start position:0%
+the things you saw as you moved just let
+me know which phases you're talking
+
+ align:start position:0%
+me know which phases you're talking
+ 
+
+ align:start position:0%
+me know which phases you're talking
+about so go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead how do you know or what's the what
+
+ align:start position:0%
+ahead how do you know or what's the what
+ 
+
+ align:start position:0%
+ahead how do you know or what's the what
+caused that
+
+ align:start position:0%
+caused that
+ 
+
+ align:start position:0%
+caused that
+what caused you to get there do you
+
+ align:start position:0%
+what caused you to get there do you
+ 
+
+ align:start position:0%
+what caused you to get there do you
+think we got a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theame we
+
+ align:start position:0%
+theame we
+ 
+
+ align:start position:0%
+theame we
+had the
+
+ align:start position:0%
+had the
+ 
+
+ align:start position:0%
+had the
+reason closer to because we just
+
+ align:start position:0%
+reason closer to because we just
+ 
+
+ align:start position:0%
+reason closer to because we just
+and Pi off and Mar
+
+ align:start position:0%
+and Pi off and Mar
+ 
+
+ align:start position:0%
+and Pi off and Mar
+done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anding because still working
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lision all right so it's big
+
+ align:start position:0%
+lision all right so it's big
+ 
+
+ align:start position:0%
+lision all right so it's big
+decisions how big are those two
+
+ align:start position:0%
+decisions how big are those two
+ 
+
+ align:start position:0%
+decisions how big are those two
+teams four and four okay so somebody
+
+ align:start position:0%
+teams four and four okay so somebody
+ 
+
+ align:start position:0%
+teams four and four okay so somebody
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+next a trigger that you saw that that
+
+ align:start position:0%
+next a trigger that you saw that that
+ 
+
+ align:start position:0%
+next a trigger that you saw that that
+made you go from one stage to the
+
+ align:start position:0%
+made you go from one stage to the
+ 
+
+ align:start position:0%
+made you go from one stage to the
+other um I think we're also in the place
+
+ align:start position:0%
+other um I think we're also in the place
+ 
+
+ align:start position:0%
+other um I think we're also in the place
+as a team we're moving from storming to
+
+ align:start position:0%
+as a team we're moving from storming to
+ 
+
+ align:start position:0%
+as a team we're moving from storming to
+norming and part of that a trigger was
+
+ align:start position:0%
+norming and part of that a trigger was
+ 
+
+ align:start position:0%
+norming and part of that a trigger was
+solidifying our game or working on
+
+ align:start position:0%
+solidifying our game or working on
+ 
+
+ align:start position:0%
+solidifying our game or working on
+solidifying our game idea because at
+
+ align:start position:0%
+solidifying our game idea because at
+ 
+
+ align:start position:0%
+solidifying our game idea because at
+this point while we all recognize one of
+
+ align:start position:0%
+this point while we all recognize one of
+ 
+
+ align:start position:0%
+this point while we all recognize one of
+build get of team we all have different
+
+ align:start position:0%
+build get of team we all have different
+ 
+
+ align:start position:0%
+build get of team we all have different
+ideas of like what this game should be
+
+ align:start position:0%
+ideas of like what this game should be
+ 
+
+ align:start position:0%
+ideas of like what this game should be
+and as we solidifying our game we're
+
+ align:start position:0%
+and as we solidifying our game we're
+ 
+
+ align:start position:0%
+and as we solidifying our game we're
+also getting ourselves in line with like
+
+ align:start position:0%
+also getting ourselves in line with like
+ 
+
+ align:start position:0%
+also getting ourselves in line with like
+what we're actually doing and how we're
+
+ align:start position:0%
+what we're actually doing and how we're
+ 
+
+ align:start position:0%
+what we're actually doing and how we're
+going to make it happen Okay so do you
+
+ align:start position:0%
+going to make it happen Okay so do you
+ 
+
+ align:start position:0%
+going to make it happen Okay so do you
+think that the task of solidifying the
+
+ align:start position:0%
+think that the task of solidifying the
+ 
+
+ align:start position:0%
+think that the task of solidifying the
+game ID is helping you because there's
+
+ align:start position:0%
+game ID is helping you because there's
+ 
+
+ align:start position:0%
+game ID is helping you because there's
+this big decision you have to make is
+
+ align:start position:0%
+this big decision you have to make is
+ 
+
+ align:start position:0%
+this big decision you have to make is
+that helping
+
+ align:start position:0%
+that helping
+ 
+
+ align:start position:0%
+that helping
+you move like work as a team it's not
+
+ align:start position:0%
+you move like work as a team it's not
+ 
+
+ align:start position:0%
+you move like work as a team it's not
+getting in your way I think it's the
+
+ align:start position:0%
+getting in your way I think it's the
+ 
+
+ align:start position:0%
+getting in your way I think it's the
+fact that like as we're doing this we
+
+ align:start position:0%
+fact that like as we're doing this we
+ 
+
+ align:start position:0%
+fact that like as we're doing this we
+have a lot of we defitely have to s for
+
+ align:start position:0%
+have a lot of we defitely have to s for
+ 
+
+ align:start position:0%
+have a lot of we defitely have to s for
+like you know conflict in our team where
+
+ align:start position:0%
+like you know conflict in our team where
+ 
+
+ align:start position:0%
+like you know conflict in our team where
+people were shatting out different ideas
+
+ align:start position:0%
+people were shatting out different ideas
+ 
+
+ align:start position:0%
+people were shatting out different ideas
+and like trying to work through it and
+
+ align:start position:0%
+and like trying to work through it and
+ 
+
+ align:start position:0%
+and like trying to work through it and
+at first we weren't doing the best job
+
+ align:start position:0%
+at first we weren't doing the best job
+ 
+
+ align:start position:0%
+at first we weren't doing the best job
+of like getting those ideas and working
+
+ align:start position:0%
+of like getting those ideas and working
+ 
+
+ align:start position:0%
+of like getting those ideas and working
+through them but I see that now we're
+
+ align:start position:0%
+through them but I see that now we're
+ 
+
+ align:start position:0%
+through them but I see that now we're
+doing a much better job of understanding
+
+ align:start position:0%
+doing a much better job of understanding
+ 
+
+ align:start position:0%
+doing a much better job of understanding
+each other and like seeing how it fits
+
+ align:start position:0%
+each other and like seeing how it fits
+ 
+
+ align:start position:0%
+each other and like seeing how it fits
+into the bigger picture okay cool next
+
+ align:start position:0%
+into the bigger picture okay cool next
+ 
+
+ align:start position:0%
+into the bigger picture okay cool next
+team a triggering moment that you saw in
+
+ align:start position:0%
+team a triggering moment that you saw in
+ 
+
+ align:start position:0%
+team a triggering moment that you saw in
+this team or previous teams so we had a
+
+ align:start position:0%
+this team or previous teams so we had a
+ 
+
+ align:start position:0%
+this team or previous teams so we had a
+bigger callar team at first and I think
+
+ align:start position:0%
+bigger callar team at first and I think
+ 
+
+ align:start position:0%
+bigger callar team at first and I think
+that decid split up um was a way that
+
+ align:start position:0%
+that decid split up um was a way that
+ 
+
+ align:start position:0%
+that decid split up um was a way that
+helped us jump from foring to storming
+
+ align:start position:0%
+helped us jump from foring to storming
+ 
+
+ align:start position:0%
+helped us jump from foring to storming
+um because we needed to sort of storm to
+
+ align:start position:0%
+um because we needed to sort of storm to
+ 
+
+ align:start position:0%
+um because we needed to sort of storm to
+get our team to get two different ideas
+
+ align:start position:0%
+get our team to get two different ideas
+ 
+
+ align:start position:0%
+get our team to get two different ideas
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh ideas in terms of where our gam go in
+
+ align:start position:0%
+uh ideas in terms of where our gam go in
+ 
+
+ align:start position:0%
+uh ideas in terms of where our gam go in
+theor session so it's basically just
+
+ align:start position:0%
+theor session so it's basically just
+ 
+
+ align:start position:0%
+theor session so it's basically just
+it's reducing the number of opinions
+
+ align:start position:0%
+it's reducing the number of opinions
+ 
+
+ align:start position:0%
+it's reducing the number of opinions
+really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right on that is share with your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people so with our game I think getting
+
+ align:start position:0%
+people so with our game I think getting
+ 
+
+ align:start position:0%
+people so with our game I think getting
+us to norming was really they talked
+
+ align:start position:0%
+us to norming was really they talked
+ 
+
+ align:start position:0%
+us to norming was really they talked
+about assigning uh tasks but also just
+
+ align:start position:0%
+about assigning uh tasks but also just
+ 
+
+ align:start position:0%
+about assigning uh tasks but also just
+the accountability aspect because
+
+ align:start position:0%
+the accountability aspect because
+ 
+
+ align:start position:0%
+the accountability aspect because
+instead of spending time arguing we
+
+ align:start position:0%
+instead of spending time arguing we
+ 
+
+ align:start position:0%
+instead of spending time arguing we
+already kind of have a designated person
+
+ align:start position:0%
+already kind of have a designated person
+ 
+
+ align:start position:0%
+already kind of have a designated person
+or a couple of people who are
+
+ align:start position:0%
+or a couple of people who are
+ 
+
+ align:start position:0%
+or a couple of people who are
+accountable for different things which
+
+ align:start position:0%
+accountable for different things which
+ 
+
+ align:start position:0%
+accountable for different things which
+allows us to just kind of not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arguing so that's like certain people
+
+ align:start position:0%
+arguing so that's like certain people
+ 
+
+ align:start position:0%
+arguing so that's like certain people
+have different like they own some
+
+ align:start position:0%
+have different like they own some
+ 
+
+ align:start position:0%
+have different like they own some
+subtask or own sub roles yes okay cool
+
+ align:start position:0%
+subtask or own sub roles yes okay cool
+ 
+
+ align:start position:0%
+subtask or own sub roles yes okay cool
+in the back what do you think so I guess
+
+ align:start position:0%
+in the back what do you think so I guess
+ 
+
+ align:start position:0%
+in the back what do you think so I guess
+what got us over to storming was meeting
+
+ align:start position:0%
+what got us over to storming was meeting
+ 
+
+ align:start position:0%
+what got us over to storming was meeting
+together as a team to make design
+
+ align:start position:0%
+together as a team to make design
+ 
+
+ align:start position:0%
+together as a team to make design
+decisions are sort of like what has been
+
+ align:start position:0%
+decisions are sort of like what has been
+ 
+
+ align:start position:0%
+decisions are sort of like what has been
+said there and I think that the next
+
+ align:start position:0%
+said there and I think that the next
+ 
+
+ align:start position:0%
+said there and I think that the next
+step for bringing us over to norming
+
+ align:start position:0%
+step for bringing us over to norming
+ 
+
+ align:start position:0%
+step for bringing us over to norming
+would be like actually getting everyone
+
+ align:start position:0%
+would be like actually getting everyone
+ 
+
+ align:start position:0%
+would be like actually getting everyone
+to participate in design decisions cuz
+
+ align:start position:0%
+to participate in design decisions cuz
+ 
+
+ align:start position:0%
+to participate in design decisions cuz
+like people have both not shown up and
+
+ align:start position:0%
+like people have both not shown up and
+ 
+
+ align:start position:0%
+like people have both not shown up and
+not particularly shown interest in
+
+ align:start position:0%
+not particularly shown interest in
+ 
+
+ align:start position:0%
+not particularly shown interest in
+getting things going so getting everyone
+
+ align:start position:0%
+getting things going so getting everyone
+ 
+
+ align:start position:0%
+getting things going so getting everyone
+on board even is all right that's a so
+
+ align:start position:0%
+on board even is all right that's a so
+ 
+
+ align:start position:0%
+on board even is all right that's a so
+that's a big one that's a that's a huge
+
+ align:start position:0%
+that's a big one that's a that's a huge
+ 
+
+ align:start position:0%
+that's a big one that's a that's a huge
+difficulty with um especially with
+
+ align:start position:0%
+difficulty with um especially with
+ 
+
+ align:start position:0%
+difficulty with um especially with
+student projects you've got all these
+
+ align:start position:0%
+student projects you've got all these
+ 
+
+ align:start position:0%
+student projects you've got all these
+other things going on around you um do
+
+ align:start position:0%
+other things going on around you um do
+ 
+
+ align:start position:0%
+other things going on around you um do
+you think you need everyone to
+
+ align:start position:0%
+you think you need everyone to
+ 
+
+ align:start position:0%
+you think you need everyone to
+contribute to the design or do you need
+
+ align:start position:0%
+contribute to the design or do you need
+ 
+
+ align:start position:0%
+contribute to the design or do you need
+everyone to be on board with the
+
+ align:start position:0%
+everyone to be on board with the
+ 
+
+ align:start position:0%
+everyone to be on board with the
+design uh
+
+ align:start position:0%
+design uh
+ 
+
+ align:start position:0%
+design uh
+so I understand like some people just
+
+ align:start position:0%
+so I understand like some people just
+ 
+
+ align:start position:0%
+so I understand like some people just
+are are less interested in having deep
+
+ align:start position:0%
+are are less interested in having deep
+ 
+
+ align:start position:0%
+are are less interested in having deep
+discussions about the design of the game
+
+ align:start position:0%
+discussions about the design of the game
+ 
+
+ align:start position:0%
+discussions about the design of the game
+but getting everyone to both be aware
+
+ align:start position:0%
+but getting everyone to both be aware
+ 
+
+ align:start position:0%
+but getting everyone to both be aware
+and willing to participate when they
+
+ align:start position:0%
+and willing to participate when they
+ 
+
+ align:start position:0%
+and willing to participate when they
+need to okay CU yeah there's there's
+
+ align:start position:0%
+need to okay CU yeah there's there's
+ 
+
+ align:start position:0%
+need to okay CU yeah there's there's
+important conversations being done that
+
+ align:start position:0%
+important conversations being done that
+ 
+
+ align:start position:0%
+important conversations being done that
+if they're not there when it happens
+
+ align:start position:0%
+if they're not there when it happens
+ 
+
+ align:start position:0%
+if they're not there when it happens
+they're not going to know where the
+
+ align:start position:0%
+they're not going to know where the
+ 
+
+ align:start position:0%
+they're not going to know where the
+status of the game is yeah and they just
+
+ align:start position:0%
+status of the game is yeah and they just
+ 
+
+ align:start position:0%
+status of the game is yeah and they just
+need to be like willing to participate
+
+ align:start position:0%
+need to be like willing to participate
+ 
+
+ align:start position:0%
+need to be like willing to participate
+like if they're not there take the step
+
+ align:start position:0%
+like if they're not there take the step
+ 
+
+ align:start position:0%
+like if they're not there take the step
+of oh what' you guys talk about I'm
+
+ align:start position:0%
+of oh what' you guys talk about I'm
+ 
+
+ align:start position:0%
+of oh what' you guys talk about I'm
+interested in knowing I want to okay
+
+ align:start position:0%
+interested in knowing I want to okay
+ 
+
+ align:start position:0%
+interested in knowing I want to okay
+cool thank you for that lead because
+
+ align:start position:0%
+cool thank you for that lead because
+ 
+
+ align:start position:0%
+cool thank you for that lead because
+that gets us to our next stage so um
+
+ align:start position:0%
+that gets us to our next stage so um
+ 
+
+ align:start position:0%
+that gets us to our next stage so um
+we're talking like we're talking kind of
+
+ align:start position:0%
+we're talking like we're talking kind of
+ 
+
+ align:start position:0%
+we're talking like we're talking kind of
+I think we find ourselves talking a lot
+
+ align:start position:0%
+I think we find ourselves talking a lot
+ 
+
+ align:start position:0%
+I think we find ourselves talking a lot
+about the um the product that we're
+
+ align:start position:0%
+about the um the product that we're
+ 
+
+ align:start position:0%
+about the um the product that we're
+making it's just easier it's the thing
+
+ align:start position:0%
+making it's just easier it's the thing
+ 
+
+ align:start position:0%
+making it's just easier it's the thing
+it's that it's that hard evident like
+
+ align:start position:0%
+it's that it's that hard evident like
+ 
+
+ align:start position:0%
+it's that it's that hard evident like
+that hard thing you can see like it's
+
+ align:start position:0%
+that hard thing you can see like it's
+ 
+
+ align:start position:0%
+that hard thing you can see like it's
+being made it's being done um it's we
+
+ align:start position:0%
+being made it's being done um it's we
+ 
+
+ align:start position:0%
+being made it's being done um it's we
+can play it it means we're probably
+
+ align:start position:0%
+can play it it means we're probably
+ 
+
+ align:start position:0%
+can play it it means we're probably
+doing something right um but it's still
+
+ align:start position:0%
+doing something right um but it's still
+ 
+
+ align:start position:0%
+doing something right um but it's still
+very difficult still to talk about the
+
+ align:start position:0%
+very difficult still to talk about the
+ 
+
+ align:start position:0%
+very difficult still to talk about the
+people although I saw being talking
+
+ align:start position:0%
+people although I saw being talking
+ 
+
+ align:start position:0%
+people although I saw being talking
+about the people a little bit here
+
+ align:start position:0%
+about the people a little bit here
+ 
+
+ align:start position:0%
+about the people a little bit here
+especially with accountability um and in
+
+ align:start position:0%
+especially with accountability um and in
+ 
+
+ align:start position:0%
+especially with accountability um and in
+this one was good cool
+
+ align:start position:0%
+this one was good cool
+ 
+
+ align:start position:0%
+this one was good cool
+um so that that g brings me to the next
+
+ align:start position:0%
+um so that that g brings me to the next
+ 
+
+ align:start position:0%
+um so that that g brings me to the next
+topic teams are composed of individuals
+
+ align:start position:0%
+topic teams are composed of individuals
+ 
+
+ align:start position:0%
+topic teams are composed of individuals
+and each person on your team is going to
+
+ align:start position:0%
+and each person on your team is going to
+ 
+
+ align:start position:0%
+and each person on your team is going to
+have a lot of different factors
+
+ align:start position:0%
+have a lot of different factors
+ 
+
+ align:start position:0%
+have a lot of different factors
+affecting what they do how they do it
+
+ align:start position:0%
+affecting what they do how they do it
+ 
+
+ align:start position:0%
+affecting what they do how they do it
+when they do it um I can't give you the
+
+ align:start position:0%
+when they do it um I can't give you the
+ 
+
+ align:start position:0%
+when they do it um I can't give you the
+magic formula to to get them motivated U
+
+ align:start position:0%
+magic formula to to get them motivated U
+ 
+
+ align:start position:0%
+magic formula to to get them motivated U
+what I can do is show you some of the
+
+ align:start position:0%
+what I can do is show you some of the
+ 
+
+ align:start position:0%
+what I can do is show you some of the
+different ways that you can then try to
+
+ align:start position:0%
+different ways that you can then try to
+ 
+
+ align:start position:0%
+different ways that you can then try to
+to to either understand the people
+
+ align:start position:0%
+to to either understand the people
+ 
+
+ align:start position:0%
+to to either understand the people
+you're with understand the people on
+
+ align:start position:0%
+you're with understand the people on
+ 
+
+ align:start position:0%
+you're with understand the people on
+your team or talk or find things to talk
+
+ align:start position:0%
+your team or talk or find things to talk
+ 
+
+ align:start position:0%
+your team or talk or find things to talk
+to them about you might notice a number
+
+ align:start position:0%
+to them about you might notice a number
+ 
+
+ align:start position:0%
+to them about you might notice a number
+of these things so to get someone who's
+
+ align:start position:0%
+of these things so to get someone who's
+ 
+
+ align:start position:0%
+of these things so to get someone who's
+motivated someone who's going to be able
+
+ align:start position:0%
+motivated someone who's going to be able
+ 
+
+ align:start position:0%
+motivated someone who's going to be able
+to participate um think about all these
+
+ align:start position:0%
+to participate um think about all these
+ 
+
+ align:start position:0%
+to participate um think about all these
+things think about personal
+
+ align:start position:0%
+things think about personal
+ 
+
+ align:start position:0%
+things think about personal
+development um so you were in a class
+
+ align:start position:0%
+development um so you were in a class
+ 
+
+ align:start position:0%
+development um so you were in a class
+you were here hopefully because you want
+
+ align:start position:0%
+you were here hopefully because you want
+ 
+
+ align:start position:0%
+you were here hopefully because you want
+to learn um you want to learn a new
+
+ align:start position:0%
+to learn um you want to learn a new
+ 
+
+ align:start position:0%
+to learn um you want to learn a new
+skill you want to try a new skill
+
+ align:start position:0%
+skill you want to try a new skill
+ 
+
+ align:start position:0%
+skill you want to try a new skill
+everyone wants to learn a new skill
+
+ align:start position:0%
+everyone wants to learn a new skill
+ 
+
+ align:start position:0%
+everyone wants to learn a new skill
+there might be a skill that they want to
+
+ align:start position:0%
+there might be a skill that they want to
+ 
+
+ align:start position:0%
+there might be a skill that they want to
+work on on your team and I think we've
+
+ align:start position:0%
+work on on your team and I think we've
+ 
+
+ align:start position:0%
+work on on your team and I think we've
+talked about that in the past when we're
+
+ align:start position:0%
+talked about that in the past when we're
+ 
+
+ align:start position:0%
+talked about that in the past when we're
+talking about the vision statement and
+
+ align:start position:0%
+talking about the vision statement and
+ 
+
+ align:start position:0%
+talking about the vision statement and
+people putting down why they're involved
+
+ align:start position:0%
+people putting down why they're involved
+ 
+
+ align:start position:0%
+people putting down why they're involved
+on the team and why they're involved on
+
+ align:start position:0%
+on the team and why they're involved on
+ 
+
+ align:start position:0%
+on the team and why they're involved on
+this project so being aware of that and
+
+ align:start position:0%
+this project so being aware of that and
+ 
+
+ align:start position:0%
+this project so being aware of that and
+constantly coming back to that for each
+
+ align:start position:0%
+constantly coming back to that for each
+ 
+
+ align:start position:0%
+constantly coming back to that for each
+person especially if you if you have
+
+ align:start position:0%
+person especially if you if you have
+ 
+
+ align:start position:0%
+person especially if you if you have
+someone on your team who's who is just
+
+ align:start position:0%
+someone on your team who's who is just
+ 
+
+ align:start position:0%
+someone on your team who's who is just
+not participating and you need to figure
+
+ align:start position:0%
+not participating and you need to figure
+ 
+
+ align:start position:0%
+not participating and you need to figure
+out um how to engage them think about
+
+ align:start position:0%
+out um how to engage them think about
+ 
+
+ align:start position:0%
+out um how to engage them think about
+the skills that they want to bring to
+
+ align:start position:0%
+the skills that they want to bring to
+ 
+
+ align:start position:0%
+the skills that they want to bring to
+the table the skills are trying to
+
+ align:start position:0%
+the table the skills are trying to
+ 
+
+ align:start position:0%
+the table the skills are trying to
+practice uh when it comes to motivation
+
+ align:start position:0%
+practice uh when it comes to motivation
+ 
+
+ align:start position:0%
+practice uh when it comes to motivation
+um it largely comes down to Intrinsic or
+
+ align:start position:0%
+um it largely comes down to Intrinsic or
+ 
+
+ align:start position:0%
+um it largely comes down to Intrinsic or
+extrinsic on the the the externs it
+
+ align:start position:0%
+extrinsic on the the the externs it
+ 
+
+ align:start position:0%
+extrinsic on the the the externs it
+might be the grade that they're going to
+
+ align:start position:0%
+might be the grade that they're going to
+ 
+
+ align:start position:0%
+might be the grade that they're going to
+get um but it's really difficult to um
+
+ align:start position:0%
+get um but it's really difficult to um
+ 
+
+ align:start position:0%
+get um but it's really difficult to um
+to really hone in on that because the
+
+ align:start position:0%
+to really hone in on that because the
+ 
+
+ align:start position:0%
+to really hone in on that because the
+grades shared between your group so that
+
+ align:start position:0%
+grades shared between your group so that
+ 
+
+ align:start position:0%
+grades shared between your group so that
+might be not be the place to look at um
+
+ align:start position:0%
+might be not be the place to look at um
+ 
+
+ align:start position:0%
+might be not be the place to look at um
+try to take a look at the intrinsic
+
+ align:start position:0%
+try to take a look at the intrinsic
+ 
+
+ align:start position:0%
+try to take a look at the intrinsic
+things what are the things that if they
+
+ align:start position:0%
+things what are the things that if they
+ 
+
+ align:start position:0%
+things what are the things that if they
+were enthusi en if they had enthusiasms
+
+ align:start position:0%
+were enthusi en if they had enthusiasms
+ 
+
+ align:start position:0%
+were enthusi en if they had enthusiasms
+about the project at some point um try
+
+ align:start position:0%
+about the project at some point um try
+ 
+
+ align:start position:0%
+about the project at some point um try
+to remember what that was um ask
+
+ align:start position:0%
+to remember what that was um ask
+ 
+
+ align:start position:0%
+to remember what that was um ask
+somebody else on your team what what
+
+ align:start position:0%
+somebody else on your team what what
+ 
+
+ align:start position:0%
+somebody else on your team what what
+that might have been see if you can
+
+ align:start position:0%
+that might have been see if you can
+ 
+
+ align:start position:0%
+that might have been see if you can
+bring those that enthusiasm back into
+
+ align:start position:0%
+bring those that enthusiasm back into
+ 
+
+ align:start position:0%
+bring those that enthusiasm back into
+the project um or selfworth and there's
+
+ align:start position:0%
+the project um or selfworth and there's
+ 
+
+ align:start position:0%
+the project um or selfworth and there's
+been some research that shows that the
+
+ align:start position:0%
+been some research that shows that the
+ 
+
+ align:start position:0%
+been some research that shows that the
+reason why people work well on teams and
+
+ align:start position:0%
+reason why people work well on teams and
+ 
+
+ align:start position:0%
+reason why people work well on teams and
+the reason why we want to work on teams
+
+ align:start position:0%
+the reason why we want to work on teams
+ 
+
+ align:start position:0%
+the reason why we want to work on teams
+is because it brings self it brings us
+
+ align:start position:0%
+is because it brings self it brings us
+ 
+
+ align:start position:0%
+is because it brings self it brings us
+selfworth um there is and in particular
+
+ align:start position:0%
+selfworth um there is and in particular
+ 
+
+ align:start position:0%
+selfworth um there is and in particular
+some self-awareness that can happen um
+
+ align:start position:0%
+some self-awareness that can happen um
+ 
+
+ align:start position:0%
+some self-awareness that can happen um
+by being on a team and getting um and it
+
+ align:start position:0%
+by being on a team and getting um and it
+ 
+
+ align:start position:0%
+by being on a team and getting um and it
+actually kind of links a little bit to
+
+ align:start position:0%
+actually kind of links a little bit to
+ 
+
+ align:start position:0%
+actually kind of links a little bit to
+to extrinsic rewards by getting rewarded
+
+ align:start position:0%
+to extrinsic rewards by getting rewarded
+ 
+
+ align:start position:0%
+to extrinsic rewards by getting rewarded
+getting feedback um on my performance is
+
+ align:start position:0%
+getting feedback um on my performance is
+ 
+
+ align:start position:0%
+getting feedback um on my performance is
+going to help me do better um
+
+ align:start position:0%
+going to help me do better um
+ 
+
+ align:start position:0%
+going to help me do better um
+empowerment um giving ownership so raise
+
+ align:start position:0%
+empowerment um giving ownership so raise
+ 
+
+ align:start position:0%
+empowerment um giving ownership so raise
+your hand if your team uses assigning
+
+ align:start position:0%
+your hand if your team uses assigning
+ 
+
+ align:start position:0%
+your hand if your team uses assigning
+tasks or taking tasks so assigning tasks
+
+ align:start position:0%
+tasks or taking tasks so assigning tasks
+ 
+
+ align:start position:0%
+tasks or taking tasks so assigning tasks
+raise your hand if your team assigns
+
+ align:start position:0%
+raise your hand if your team assigns
+ 
+
+ align:start position:0%
+raise your hand if your team assigns
+tasks to individuals that team kind of
+
+ align:start position:0%
+tasks to individuals that team kind of
+ 
+
+ align:start position:0%
+tasks to individuals that team kind of
+yeah you assign so there's one person on
+
+ align:start position:0%
+yeah you assign so there's one person on
+ 
+
+ align:start position:0%
+yeah you assign so there's one person on
+your team that says you are going to do
+
+ align:start position:0%
+your team that says you are going to do
+ 
+
+ align:start position:0%
+your team that says you are going to do
+this all right has anybody tried
+
+ align:start position:0%
+this all right has anybody tried
+ 
+
+ align:start position:0%
+this all right has anybody tried
+ownership where someone takes a task
+
+ align:start position:0%
+ownership where someone takes a task
+ 
+
+ align:start position:0%
+ownership where someone takes a task
+from a set of tasks that are
+
+ align:start position:0%
+from a set of tasks that are
+ 
+
+ align:start position:0%
+from a set of tasks that are
+available little little
+
+ align:start position:0%
+available little little
+ 
+
+ align:start position:0%
+available little little
+when does that work when does ownership
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work what's that people interested so
+
+ align:start position:0%
+work what's that people interested so
+ 
+
+ align:start position:0%
+work what's that people interested so
+there's there's some there's some of
+
+ align:start position:0%
+there's there's some there's some of
+ 
+
+ align:start position:0%
+there's there's some there's some of
+those other things that there's some
+
+ align:start position:0%
+those other things that there's some
+ 
+
+ align:start position:0%
+those other things that there's some
+enthusiasms over over it yeah it's
+
+ align:start position:0%
+enthusiasms over over it yeah it's
+ 
+
+ align:start position:0%
+enthusiasms over over it yeah it's
+usually like a while before the
+
+ align:start position:0%
+usually like a while before the
+ 
+
+ align:start position:0%
+usually like a while before the
+deadine Okay cool so yeah yeah you can
+
+ align:start position:0%
+deadine Okay cool so yeah yeah you can
+ 
+
+ align:start position:0%
+deadine Okay cool so yeah yeah you can
+problem you say's do this andbody
+
+ align:start position:0%
+problem you say's do this andbody
+ 
+
+ align:start position:0%
+problem you say's do this andbody
+volunteers my experience has been kind
+
+ align:start position:0%
+volunteers my experience has been kind
+ 
+
+ align:start position:0%
+volunteers my experience has been kind
+of it's good if people volunteer for
+
+ align:start position:0%
+of it's good if people volunteer for
+ 
+
+ align:start position:0%
+of it's good if people volunteer for
+tasks enas about but then nobody will to
+
+ align:start position:0%
+tasks enas about but then nobody will to
+ 
+
+ align:start position:0%
+tasks enas about but then nobody will to
+do something that needs to
+
+ align:start position:0%
+do something that needs to
+ 
+
+ align:start position:0%
+do something that needs to
+beone this absolutely H okay so where
+
+ align:start position:0%
+beone this absolutely H okay so where
+ 
+
+ align:start position:0%
+beone this absolutely H okay so where
+does yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead absolutely so there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some I think something that's kind of at
+
+ align:start position:0%
+some I think something that's kind of at
+ 
+
+ align:start position:0%
+some I think something that's kind of at
+the beginning
+
+ align:start position:0%
+the beginning
+ 
+
+ align:start position:0%
+the beginning
+and then like Tas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are okay so so at the beginning um
+
+ align:start position:0%
+are okay so so at the beginning um
+ 
+
+ align:start position:0%
+are okay so so at the beginning um
+everybody takes on tasks and at the end
+
+ align:start position:0%
+everybody takes on tasks and at the end
+ 
+
+ align:start position:0%
+everybody takes on tasks and at the end
+when you have the leftovers um they get
+
+ align:start position:0%
+when you have the leftovers um they get
+ 
+
+ align:start position:0%
+when you have the leftovers um they get
+assigned yeah Matt one of the biggest
+
+ align:start position:0%
+assigned yeah Matt one of the biggest
+ 
+
+ align:start position:0%
+assigned yeah Matt one of the biggest
+problems I've seen this is that
+
+ align:start position:0%
+problems I've seen this is that
+ 
+
+ align:start position:0%
+problems I've seen this is that
+you're espe this is easy we have a lot
+
+ align:start position:0%
+you're espe this is easy we have a lot
+ 
+
+ align:start position:0%
+you're espe this is easy we have a lot
+of other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so it might not you yeah so you
+
+ align:start position:0%
+then so it might not you yeah so you
+ 
+
+ align:start position:0%
+then so it might not you yeah so you
+might not actually have ownership it
+
+ align:start position:0%
+might not actually have ownership it
+ 
+
+ align:start position:0%
+might not actually have ownership it
+might look like you had ownership there
+
+ align:start position:0%
+might look like you had ownership there
+ 
+
+ align:start position:0%
+might look like you had ownership there
+is the evidence of ownership in that
+
+ align:start position:0%
+is the evidence of ownership in that
+ 
+
+ align:start position:0%
+is the evidence of ownership in that
+someone said okay I'll take that task
+
+ align:start position:0%
+someone said okay I'll take that task
+ 
+
+ align:start position:0%
+someone said okay I'll take that task
+but there's no there's no follow-through
+
+ align:start position:0%
+but there's no there's no follow-through
+ 
+
+ align:start position:0%
+but there's no there's no follow-through
+there's no commitment and that gets to
+
+ align:start position:0%
+there's no commitment and that gets to
+ 
+
+ align:start position:0%
+there's no commitment and that gets to
+the next one commitment um the best way
+
+ align:start position:0%
+the next one commitment um the best way
+ 
+
+ align:start position:0%
+the next one commitment um the best way
+to have commitment on your team is for
+
+ align:start position:0%
+to have commitment on your team is for
+ 
+
+ align:start position:0%
+to have commitment on your team is for
+one person to be committed to express
+
+ align:start position:0%
+one person to be committed to express
+ 
+
+ align:start position:0%
+one person to be committed to express
+that commitment to express that loyalty
+
+ align:start position:0%
+that commitment to express that loyalty
+ 
+
+ align:start position:0%
+that commitment to express that loyalty
+for everyone else to see that loyalty
+
+ align:start position:0%
+for everyone else to see that loyalty
+ 
+
+ align:start position:0%
+for everyone else to see that loyalty
+and see that commitment and then
+
+ align:start position:0%
+and see that commitment and then
+ 
+
+ align:start position:0%
+and see that commitment and then
+hopefully they pick up the ball and
+
+ align:start position:0%
+hopefully they pick up the ball and
+ 
+
+ align:start position:0%
+hopefully they pick up the ball and
+they're like okay I'm going to be
+
+ align:start position:0%
+they're like okay I'm going to be
+ 
+
+ align:start position:0%
+they're like okay I'm going to be
+committed to if that second person
+
+ align:start position:0%
+committed to if that second person
+ 
+
+ align:start position:0%
+committed to if that second person
+doesn't do that pick it up then the
+
+ align:start position:0%
+doesn't do that pick it up then the
+ 
+
+ align:start position:0%
+doesn't do that pick it up then the
+chain it doesn't travel through the
+
+ align:start position:0%
+chain it doesn't travel through the
+ 
+
+ align:start position:0%
+chain it doesn't travel through the
+chain it just doesn't happen even though
+
+ align:start position:0%
+chain it just doesn't happen even though
+ 
+
+ align:start position:0%
+chain it just doesn't happen even though
+that one person went out of the way to
+
+ align:start position:0%
+that one person went out of the way to
+ 
+
+ align:start position:0%
+that one person went out of the way to
+to show that kind of sacrifice it just
+
+ align:start position:0%
+to show that kind of sacrifice it just
+ 
+
+ align:start position:0%
+to show that kind of sacrifice it just
+didn't get picked up um so maybe think
+
+ align:start position:0%
+didn't get picked up um so maybe think
+ 
+
+ align:start position:0%
+didn't get picked up um so maybe think
+about is that do do you see that chain
+
+ align:start position:0%
+about is that do do you see that chain
+ 
+
+ align:start position:0%
+about is that do do you see that chain
+happening on your on your teams do you
+
+ align:start position:0%
+happening on your on your teams do you
+ 
+
+ align:start position:0%
+happening on your on your teams do you
+see it breaking can you identify where
+
+ align:start position:0%
+see it breaking can you identify where
+ 
+
+ align:start position:0%
+see it breaking can you identify where
+that breaking point is and can you think
+
+ align:start position:0%
+that breaking point is and can you think
+ 
+
+ align:start position:0%
+that breaking point is and can you think
+about ways to to to fix
+
+ align:start position:0%
+about ways to to to fix
+ 
+
+ align:start position:0%
+about ways to to to fix
+that um trust is a big one um how many
+
+ align:start position:0%
+that um trust is a big one um how many
+ 
+
+ align:start position:0%
+that um trust is a big one um how many
+so raise your hands if you have worked
+
+ align:start position:0%
+so raise your hands if you have worked
+ 
+
+ align:start position:0%
+so raise your hands if you have worked
+with the majority of the people on your
+
+ align:start position:0%
+with the majority of the people on your
+ 
+
+ align:start position:0%
+with the majority of the people on your
+team before in some fashion this class
+
+ align:start position:0%
+team before in some fashion this class
+ 
+
+ align:start position:0%
+team before in some fashion this class
+or other classes you you feel like you
+
+ align:start position:0%
+or other classes you you feel like you
+ 
+
+ align:start position:0%
+or other classes you you feel like you
+know your teammates like raise your
+
+ align:start position:0%
+know your teammates like raise your
+ 
+
+ align:start position:0%
+know your teammates like raise your
+hands if you feel like you really know
+
+ align:start position:0%
+hands if you feel like you really know
+ 
+
+ align:start position:0%
+hands if you feel like you really know
+your teammates you've worked with them
+
+ align:start position:0%
+your teammates you've worked with them
+ 
+
+ align:start position:0%
+your teammates you've worked with them
+before hi if you really think so so one
+
+ align:start position:0%
+before hi if you really think so so one
+ 
+
+ align:start position:0%
+before hi if you really think so so one
+two maybe one two
+
+ align:start position:0%
+two maybe one two
+ 
+
+ align:start position:0%
+two maybe one two
+three so think about how well you know
+
+ align:start position:0%
+three so think about how well you know
+ 
+
+ align:start position:0%
+three so think about how well you know
+each other think about ways you can
+
+ align:start position:0%
+each other think about ways you can
+ 
+
+ align:start position:0%
+each other think about ways you can
+figure out how you can know each other
+
+ align:start position:0%
+figure out how you can know each other
+ 
+
+ align:start position:0%
+figure out how you can know each other
+better um social
+
+ align:start position:0%
+better um social
+ 
+
+ align:start position:0%
+better um social
+interactions going up to coffee going up
+
+ align:start position:0%
+interactions going up to coffee going up
+ 
+
+ align:start position:0%
+interactions going up to coffee going up
+for lunch things like that is there
+
+ align:start position:0%
+for lunch things like that is there
+ 
+
+ align:start position:0%
+for lunch things like that is there
+something that you can do that will help
+
+ align:start position:0%
+something that you can do that will help
+ 
+
+ align:start position:0%
+something that you can do that will help
+that kind of that kind of thing H happen
+
+ align:start position:0%
+that kind of that kind of thing H happen
+ 
+
+ align:start position:0%
+that kind of that kind of thing H happen
+and then here's the big one this is the
+
+ align:start position:0%
+and then here's the big one this is the
+ 
+
+ align:start position:0%
+and then here's the big one this is the
+mit1 stress and stress tends to be the
+
+ align:start position:0%
+mit1 stress and stress tends to be the
+ 
+
+ align:start position:0%
+mit1 stress and stress tends to be the
+the negative it can be positive in that
+
+ align:start position:0%
+the negative it can be positive in that
+ 
+
+ align:start position:0%
+the negative it can be positive in that
+it's the end of the project and it's due
+
+ align:start position:0%
+it's the end of the project and it's due
+ 
+
+ align:start position:0%
+it's the end of the project and it's due
+and you just need to get things done and
+
+ align:start position:0%
+and you just need to get things done and
+ 
+
+ align:start position:0%
+and you just need to get things done and
+that can be that can lead to crunch but
+
+ align:start position:0%
+that can be that can lead to crunch but
+ 
+
+ align:start position:0%
+that can be that can lead to crunch but
+then there's also the huge negative
+
+ align:start position:0%
+then there's also the huge negative
+ 
+
+ align:start position:0%
+then there's also the huge negative
+aspect of stress and it's a very that's
+
+ align:start position:0%
+aspect of stress and it's a very that's
+ 
+
+ align:start position:0%
+aspect of stress and it's a very that's
+very much an external factor for the
+
+ align:start position:0%
+very much an external factor for the
+ 
+
+ align:start position:0%
+very much an external factor for the
+most part um it could be an internal
+
+ align:start position:0%
+most part um it could be an internal
+ 
+
+ align:start position:0%
+most part um it could be an internal
+Factor if if stress isn't if there's
+
+ align:start position:0%
+Factor if if stress isn't if there's
+ 
+
+ align:start position:0%
+Factor if if stress isn't if there's
+some stress being caused by internal um
+
+ align:start position:0%
+some stress being caused by internal um
+ 
+
+ align:start position:0%
+some stress being caused by internal um
+things going on with your team it's
+
+ align:start position:0%
+things going on with your team it's
+ 
+
+ align:start position:0%
+things going on with your team it's
+likely related to one of the ones above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it um so so one way to think about um
+
+ align:start position:0%
+it um so so one way to think about um
+ 
+
+ align:start position:0%
+it um so so one way to think about um
+these these three uh one two three seven
+
+ align:start position:0%
+these these three uh one two three seven
+ 
+
+ align:start position:0%
+these these three uh one two three seven
+things um you can think of them as in
+
+ align:start position:0%
+things um you can think of them as in
+ 
+
+ align:start position:0%
+things um you can think of them as in
+terms of the desire ability to learn new
+
+ align:start position:0%
+terms of the desire ability to learn new
+ 
+
+ align:start position:0%
+terms of the desire ability to learn new
+skills or the desire ability to take on
+
+ align:start position:0%
+skills or the desire ability to take on
+ 
+
+ align:start position:0%
+skills or the desire ability to take on
+a task um so if you're trying to come up
+
+ align:start position:0%
+a task um so if you're trying to come up
+ 
+
+ align:start position:0%
+a task um so if you're trying to come up
+with strategies within your team on how
+
+ align:start position:0%
+with strategies within your team on how
+ 
+
+ align:start position:0%
+with strategies within your team on how
+to how to solve some of these problems
+
+ align:start position:0%
+to how to solve some of these problems
+ 
+
+ align:start position:0%
+to how to solve some of these problems
+think of it in those two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms all right so how do distributed
+
+ align:start position:0%
+terms all right so how do distributed
+ 
+
+ align:start position:0%
+terms all right so how do distributed
+teams perform um so what do I mean by
+
+ align:start position:0%
+teams perform um so what do I mean by
+ 
+
+ align:start position:0%
+teams perform um so what do I mean by
+distributed what is a distributed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+team
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah or just everyone's all over
+
+ align:start position:0%
+yeah yeah or just everyone's all over
+ 
+
+ align:start position:0%
+yeah yeah or just everyone's all over
+the place it could mean that you are in
+
+ align:start position:0%
+the place it could mean that you are in
+ 
+
+ align:start position:0%
+the place it could mean that you are in
+Singapore and someone else is in Ohio um
+
+ align:start position:0%
+Singapore and someone else is in Ohio um
+ 
+
+ align:start position:0%
+Singapore and someone else is in Ohio um
+you could be separated by time zones by
+
+ align:start position:0%
+you could be separated by time zones by
+ 
+
+ align:start position:0%
+you could be separated by time zones by
+oceans um by and really I think that
+
+ align:start position:0%
+oceans um by and really I think that
+ 
+
+ align:start position:0%
+oceans um by and really I think that
+might be East Campus and McGregor maybe
+
+ align:start position:0%
+might be East Campus and McGregor maybe
+ 
+
+ align:start position:0%
+might be East Campus and McGregor maybe
+um it could just be through distance it
+
+ align:start position:0%
+um it could just be through distance it
+ 
+
+ align:start position:0%
+um it could just be through distance it
+could be through your schools it could
+
+ align:start position:0%
+could be through your schools it could
+ 
+
+ align:start position:0%
+could be through your schools it could
+be through your departments your Majors
+
+ align:start position:0%
+be through your departments your Majors
+ 
+
+ align:start position:0%
+be through your departments your Majors
+whatnot um there's some kind of
+
+ align:start position:0%
+whatnot um there's some kind of
+ 
+
+ align:start position:0%
+whatnot um there's some kind of
+boundaries going on between people um in
+
+ align:start position:0%
+boundaries going on between people um in
+ 
+
+ align:start position:0%
+boundaries going on between people um in
+this case it's it's largely time um it's
+
+ align:start position:0%
+this case it's it's largely time um it's
+ 
+
+ align:start position:0%
+this case it's it's largely time um it's
+basically some people can work during
+
+ align:start position:0%
+basically some people can work during
+ 
+
+ align:start position:0%
+basically some people can work during
+some hours some people can't can't work
+
+ align:start position:0%
+some hours some people can't can't work
+ 
+
+ align:start position:0%
+some hours some people can't can't work
+during those hour those other hours so
+
+ align:start position:0%
+during those hour those other hours so
+ 
+
+ align:start position:0%
+during those hour those other hours so
+what have you done so far to to to fix
+
+ align:start position:0%
+what have you done so far to to to fix
+ 
+
+ align:start position:0%
+what have you done so far to to to fix
+that you think back on some of the
+
+ align:start position:0%
+that you think back on some of the
+ 
+
+ align:start position:0%
+that you think back on some of the
+postmortem you've given us what are some
+
+ align:start position:0%
+postmortem you've given us what are some
+ 
+
+ align:start position:0%
+postmortem you've given us what are some
+of the strategies you've already used
+
+ align:start position:0%
+of the strategies you've already used
+ 
+
+ align:start position:0%
+of the strategies you've already used
+and seen used to to figure out how to
+
+ align:start position:0%
+and seen used to to figure out how to
+ 
+
+ align:start position:0%
+and seen used to to figure out how to
+work in across different time time
+
+ align:start position:0%
+work in across different time time
+ 
+
+ align:start position:0%
+work in across different time time
+periods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what's it
+
+ align:start position:0%
+yeah what's it
+ 
+
+ align:start position:0%
+yeah what's it
+called it's like
+
+ align:start position:0%
+called it's like
+ 
+
+ align:start position:0%
+called it's like
+what what's that it's group instant M
+
+ align:start position:0%
+what what's that it's group instant M
+ 
+
+ align:start position:0%
+what what's that it's group instant M
+yay and it keeps of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allas cool anybody else using a group I
+
+ align:start position:0%
+allas cool anybody else using a group I
+ 
+
+ align:start position:0%
+allas cool anybody else using a group I
+or an IRC chat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool cool okay it's great when it have
+
+ align:start position:0%
+cool cool okay it's great when it have
+ 
+
+ align:start position:0%
+cool cool okay it's great when it have
+when it can hook up to things and it
+
+ align:start position:0%
+when it can hook up to things and it
+ 
+
+ align:start position:0%
+when it can hook up to things and it
+works with your workflow it's also just
+
+ align:start position:0%
+works with your workflow it's also just
+ 
+
+ align:start position:0%
+works with your workflow it's also just
+great to have just period if you don't
+
+ align:start position:0%
+great to have just period if you don't
+ 
+
+ align:start position:0%
+great to have just period if you don't
+use any of those maybe think about Skype
+
+ align:start position:0%
+use any of those maybe think about Skype
+ 
+
+ align:start position:0%
+use any of those maybe think about Skype
+any other things people use
+
+ align:start position:0%
+any other things people use
+ 
+
+ align:start position:0%
+any other things people use
+yeah in my experience
+
+ align:start position:0%
+yeah in my experience
+ 
+
+ align:start position:0%
+yeah in my experience
+like let's say we walking on something
+
+ align:start position:0%
+like let's say we walking on something
+ 
+
+ align:start position:0%
+like let's say we walking on something
+and all of at that point be good to like
+
+ align:start position:0%
+and all of at that point be good to like
+ 
+
+ align:start position:0%
+and all of at that point be good to like
+keep the whole team informed about your
+
+ align:start position:0%
+keep the whole team informed about your
+ 
+
+ align:start position:0%
+keep the whole team informed about your
+progress what Isen on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reporting I remember some people had
+
+ align:start position:0%
+reporting I remember some people had
+ 
+
+ align:start position:0%
+reporting I remember some people had
+issues with email on previous teams is
+
+ align:start position:0%
+issues with email on previous teams is
+ 
+
+ align:start position:0%
+issues with email on previous teams is
+anybody still using email as a primary
+
+ align:start position:0%
+anybody still using email as a primary
+ 
+
+ align:start position:0%
+anybody still using email as a primary
+means of communication on your
+
+ align:start position:0%
+means of communication on your
+ 
+
+ align:start position:0%
+means of communication on your
+team how's it working for you all so far
+
+ align:start position:0%
+team how's it working for you all so far
+ 
+
+ align:start position:0%
+team how's it working for you all so far
+has it got to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yep um are those emails going to be
+
+ align:start position:0%
+yeah yep um are those emails going to be
+ 
+
+ align:start position:0%
+yeah yep um are those emails going to be
+archived and viewable by everyone at a
+
+ align:start position:0%
+archived and viewable by everyone at a
+ 
+
+ align:start position:0%
+archived and viewable by everyone at a
+later date be a good idea yeah
+
+ align:start position:0%
+later date be a good idea yeah
+ 
+
+ align:start position:0%
+later date be a good idea yeah
+um and I think that's why we tend to to
+
+ align:start position:0%
+um and I think that's why we tend to to
+ 
+
+ align:start position:0%
+um and I think that's why we tend to to
+think about um group IMS and
+
+ align:start position:0%
+think about um group IMS and
+ 
+
+ align:start position:0%
+think about um group IMS and
+particularly um Philip likes IRC for
+
+ align:start position:0%
+particularly um Philip likes IRC for
+ 
+
+ align:start position:0%
+particularly um Philip likes IRC for
+that very reason certain IRC servers we
+
+ align:start position:0%
+that very reason certain IRC servers we
+ 
+
+ align:start position:0%
+that very reason certain IRC servers we
+we'll keep an archive for you um other
+
+ align:start position:0%
+we'll keep an archive for you um other
+ 
+
+ align:start position:0%
+we'll keep an archive for you um other
+kinds of groupware we'll do that too but
+
+ align:start position:0%
+kinds of groupware we'll do that too but
+ 
+
+ align:start position:0%
+kinds of groupware we'll do that too but
+they tend to be pricey um um is anybody
+
+ align:start position:0%
+they tend to be pricey um um is anybody
+ 
+
+ align:start position:0%
+they tend to be pricey um um is anybody
+still using has anybody started using
+
+ align:start position:0%
+still using has anybody started using
+ 
+
+ align:start position:0%
+still using has anybody started using
+Trello on your teams
+
+ align:start position:0%
+Trello on your teams
+ 
+
+ align:start position:0%
+Trello on your teams
+yet yeah are you using it as a
+
+ align:start position:0%
+yet yeah are you using it as a
+ 
+
+ align:start position:0%
+yet yeah are you using it as a
+communication method or as a recording
+
+ align:start position:0%
+communication method or as a recording
+ 
+
+ align:start position:0%
+communication method or as a recording
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+things okay anybody using that as a
+
+ align:start position:0%
+things okay anybody using that as a
+ 
+
+ align:start position:0%
+things okay anybody using that as a
+communication method at all trying that
+
+ align:start position:0%
+communication method at all trying that
+ 
+
+ align:start position:0%
+communication method at all trying that
+out okay because I think it do it can do
+
+ align:start position:0%
+out okay because I think it do it can do
+ 
+
+ align:start position:0%
+out okay because I think it do it can do
+email notifications and things like that
+
+ align:start position:0%
+email notifications and things like that
+ 
+
+ align:start position:0%
+email notifications and things like that
+when things change assigning members to
+
+ align:start position:0%
+when things change assigning members to
+ 
+
+ align:start position:0%
+when things change assigning members to
+tasks stuff like
+
+ align:start position:0%
+tasks stuff like
+ 
+
+ align:start position:0%
+tasks stuff like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+cool all right so again we got talking
+
+ align:start position:0%
+cool all right so again we got talking
+ 
+
+ align:start position:0%
+cool all right so again we got talking
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+tools um what other things can we do so
+
+ align:start position:0%
+tools um what other things can we do so
+ 
+
+ align:start position:0%
+tools um what other things can we do so
+um another another paper that it's going
+
+ align:start position:0%
+um another another paper that it's going
+ 
+
+ align:start position:0%
+um another another paper that it's going
+to be on Stellar if you want to look at
+
+ align:start position:0%
+to be on Stellar if you want to look at
+ 
+
+ align:start position:0%
+to be on Stellar if you want to look at
+it was basically a survey of distributed
+
+ align:start position:0%
+it was basically a survey of distributed
+ 
+
+ align:start position:0%
+it was basically a survey of distributed
+teams using angel processes and giving
+
+ align:start position:0%
+teams using angel processes and giving
+ 
+
+ align:start position:0%
+teams using angel processes and giving
+up some best practices of what worked
+
+ align:start position:0%
+up some best practices of what worked
+ 
+
+ align:start position:0%
+up some best practices of what worked
+best for them and I was nice and I'm
+
+ align:start position:0%
+best for them and I was nice and I'm
+ 
+
+ align:start position:0%
+best for them and I was nice and I'm
+just giving you the uh summary of that
+
+ align:start position:0%
+just giving you the uh summary of that
+ 
+
+ align:start position:0%
+just giving you the uh summary of that
+um so one thing they noticed is having a
+
+ align:start position:0%
+um so one thing they noticed is having a
+ 
+
+ align:start position:0%
+um so one thing they noticed is having a
+one team mindset was the thing that got
+
+ align:start position:0%
+one team mindset was the thing that got
+ 
+
+ align:start position:0%
+one team mindset was the thing that got
+them through um working together as a
+
+ align:start position:0%
+them through um working together as a
+ 
+
+ align:start position:0%
+them through um working together as a
+group um what do we mean by one team
+
+ align:start position:0%
+group um what do we mean by one team
+ 
+
+ align:start position:0%
+group um what do we mean by one team
+that the the group identifies well first
+
+ align:start position:0%
+that the the group identifies well first
+ 
+
+ align:start position:0%
+that the the group identifies well first
+it identifies as a team like what we
+
+ align:start position:0%
+it identifies as a team like what we
+ 
+
+ align:start position:0%
+it identifies as a team like what we
+talked about before they all have a of a
+
+ align:start position:0%
+talked about before they all have a of a
+ 
+
+ align:start position:0%
+talked about before they all have a of a
+a goal that they're going towards they
+
+ align:start position:0%
+a goal that they're going towards they
+ 
+
+ align:start position:0%
+a goal that they're going towards they
+all identify as going towards that goal
+
+ align:start position:0%
+all identify as going towards that goal
+ 
+
+ align:start position:0%
+all identify as going towards that goal
+um they don't identify as as just a as
+
+ align:start position:0%
+um they don't identify as as just a as
+ 
+
+ align:start position:0%
+um they don't identify as as just a as
+an individual
+
+ align:start position:0%
+an individual
+ 
+
+ align:start position:0%
+an individual
+group but that's a that's actually a
+
+ align:start position:0%
+group but that's a that's actually a
+ 
+
+ align:start position:0%
+group but that's a that's actually a
+major part of their identity um and for
+
+ align:start position:0%
+major part of their identity um and for
+ 
+
+ align:start position:0%
+major part of their identity um and for
+them it's because that's their 40h hour
+
+ align:start position:0%
+them it's because that's their 40h hour
+ 
+
+ align:start position:0%
+them it's because that's their 40h hour
+80 hour 12 hour work days uh or work
+
+ align:start position:0%
+80 hour 12 hour work days uh or work
+ 
+
+ align:start position:0%
+80 hour 12 hour work days uh or work
+weeks um something I think you you going
+
+ align:start position:0%
+weeks um something I think you you going
+ 
+
+ align:start position:0%
+weeks um something I think you you going
+to have issue with because you're only
+
+ align:start position:0%
+to have issue with because you're only
+ 
+
+ align:start position:0%
+to have issue with because you're only
+because you're working smaller periods
+
+ align:start position:0%
+because you're working smaller periods
+ 
+
+ align:start position:0%
+because you're working smaller periods
+of time um but what they're able to do
+
+ align:start position:0%
+of time um but what they're able to do
+ 
+
+ align:start position:0%
+of time um but what they're able to do
+the way they're able to do that is
+
+ align:start position:0%
+the way they're able to do that is
+ 
+
+ align:start position:0%
+the way they're able to do that is
+they've got these frequent team
+
+ align:start position:0%
+they've got these frequent team
+ 
+
+ align:start position:0%
+they've got these frequent team
+interactions and actually when they're
+
+ align:start position:0%
+interactions and actually when they're
+ 
+
+ align:start position:0%
+interactions and actually when they're
+working for a long period of time
+
+ align:start position:0%
+working for a long period of time
+ 
+
+ align:start position:0%
+working for a long period of time
+they're still there are people who are
+
+ align:start position:0%
+they're still there are people who are
+ 
+
+ align:start position:0%
+they're still there are people who are
+working on their own in their home or
+
+ align:start position:0%
+working on their own in their home or
+ 
+
+ align:start position:0%
+working on their own in their home or
+their home office with another team
+
+ align:start position:0%
+their home office with another team
+ 
+
+ align:start position:0%
+their home office with another team
+that's that's very far away and yet
+
+ align:start position:0%
+that's that's very far away and yet
+ 
+
+ align:start position:0%
+that's that's very far away and yet
+these these teams still do a daily
+
+ align:start position:0%
+these these teams still do a daily
+ 
+
+ align:start position:0%
+these these teams still do a daily
+standup does anybody here do a daily
+
+ align:start position:0%
+standup does anybody here do a daily
+ 
+
+ align:start position:0%
+standup does anybody here do a daily
+standup on their on their teams right
+
+ align:start position:0%
+standup on their on their teams right
+ 
+
+ align:start position:0%
+standup on their on their teams right
+now so what they're doing is they're
+
+ align:start position:0%
+now so what they're doing is they're
+ 
+
+ align:start position:0%
+now so what they're doing is they're
+going on video they're talking to each
+
+ align:start position:0%
+going on video they're talking to each
+ 
+
+ align:start position:0%
+going on video they're talking to each
+other for a very short period of time
+
+ align:start position:0%
+other for a very short period of time
+ 
+
+ align:start position:0%
+other for a very short period of time
+about what they've done what they're
+
+ align:start position:0%
+about what they've done what they're
+ 
+
+ align:start position:0%
+about what they've done what they're
+going to do what's in their way um the
+
+ align:start position:0%
+going to do what's in their way um the
+ 
+
+ align:start position:0%
+going to do what's in their way um the
+cool thing with daily standups and why
+
+ align:start position:0%
+cool thing with daily standups and why
+ 
+
+ align:start position:0%
+cool thing with daily standups and why
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+it goes back to those those um seven
+ 
+
+ align:start position:0%
+it goes back to those those um seven
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+
+ align:start position:0%
+items I listed about how do you get
+ 
+
+ align:start position:0%
+items I listed about how do you get
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+
+ align:start position:0%
+people engaged on a team it shows
+ 
+
+ align:start position:0%
+people engaged on a team it shows
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+
+ align:start position:0%
+commitment um the fact that there are
+ 
+
+ align:start position:0%
+commitment um the fact that there are
+some people that there are people who
+
+ align:start position:0%
+some people that there are people who
+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+hour of the day that they're not
+ 
+
+ align:start position:0%
+hour of the day that they're not
+normally going to meet um and they're
+
+ align:start position:0%
+normally going to meet um and they're
+ 
+
+ align:start position:0%
+normally going to meet um and they're
+doing that because of the team they're
+
+ align:start position:0%
+doing that because of the team they're
+ 
+
+ align:start position:0%
+doing that because of the team they're
+sacrificing something personal for the
+
+ align:start position:0%
+sacrificing something personal for the
+ 
+
+ align:start position:0%
+sacrificing something personal for the
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+
+ align:start position:0%
+team everyone else on the team sees that
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+they see that kind of commitment they
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+feel they feel like they need to reflect
+ 
+
+ align:start position:0%
+feel they feel like they need to reflect
+that back themselves also trust and in
+
+ align:start position:0%
+that back themselves also trust and in
+ 
+
+ align:start position:0%
+that back themselves also trust and in
+this particular case it's the trust of
+
+ align:start position:0%
+this particular case it's the trust of
+ 
+
+ align:start position:0%
+this particular case it's the trust of
+not letting meetings take too long these
+
+ align:start position:0%
+not letting meetings take too long these
+ 
+
+ align:start position:0%
+not letting meetings take too long these
+daily standups really should only take
+
+ align:start position:0%
+daily standups really should only take
+ 
+
+ align:start position:0%
+daily standups really should only take
+10 minutes um an effective team can do
+
+ align:start position:0%
+10 minutes um an effective team can do
+ 
+
+ align:start position:0%
+10 minutes um an effective team can do
+it in five um an effective 10 person
+
+ align:start position:0%
+it in five um an effective 10 person
+ 
+
+ align:start position:0%
+it in five um an effective 10 person
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+
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+team 30 seconds each go everyone says
+ 
+
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+what they've done everyone sees each
+
+ align:start position:0%
+what they've done everyone sees each
+ 
+
+ align:start position:0%
+what they've done everyone sees each
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+
+ align:start position:0%
+other's faces the great thing about
+ 
+
+ align:start position:0%
+other's faces the great thing about
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+
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+ 
+
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+seeing each other's faces is you can see
+what stage of fear and anxiety they're
+
+ align:start position:0%
+what stage of fear and anxiety they're
+ 
+
+ align:start position:0%
+what stage of fear and anxiety they're
+in then you can then talk to them later
+
+ align:start position:0%
+in then you can then talk to them later
+ 
+
+ align:start position:0%
+in then you can then talk to them later
+and have some other personal
+
+ align:start position:0%
+and have some other personal
+ 
+
+ align:start position:0%
+and have some other personal
+interactions with
+
+ align:start position:0%
+interactions with
+ 
+
+ align:start position:0%
+interactions with
+them um other thing they do is they they
+
+ align:start position:0%
+them um other thing they do is they they
+ 
+
+ align:start position:0%
+them um other thing they do is they they
+do collocated work um they've got money
+
+ align:start position:0%
+do collocated work um they've got money
+ 
+
+ align:start position:0%
+do collocated work um they've got money
+sometimes so they're flying people back
+
+ align:start position:0%
+sometimes so they're flying people back
+ 
+
+ align:start position:0%
+sometimes so they're flying people back
+and forth um but again they're also
+
+ align:start position:0%
+and forth um but again they're also
+ 
+
+ align:start position:0%
+and forth um but again they're also
+doing collocated work by doing things
+
+ align:start position:0%
+doing collocated work by doing things
+ 
+
+ align:start position:0%
+doing collocated work by doing things
+using having Skype always on in the
+
+ align:start position:0%
+using having Skype always on in the
+ 
+
+ align:start position:0%
+using having Skype always on in the
+background while they're working
+
+ align:start position:0%
+background while they're working
+ 
+
+ align:start position:0%
+background while they're working
+together but they're not doing it the
+
+ align:start position:0%
+together but they're not doing it the
+ 
+
+ align:start position:0%
+together but they're not doing it the
+entire time they can't afford that so
+
+ align:start position:0%
+entire time they can't afford that so
+ 
+
+ align:start position:0%
+entire time they can't afford that so
+one thing you can do is to schedule your
+
+ align:start position:0%
+one thing you can do is to schedule your
+ 
+
+ align:start position:0%
+one thing you can do is to schedule your
+collocated time at the beginning of the
+
+ align:start position:0%
+collocated time at the beginning of the
+ 
+
+ align:start position:0%
+collocated time at the beginning of the
+project which I which is basically what
+
+ align:start position:0%
+project which I which is basically what
+ 
+
+ align:start position:0%
+project which I which is basically what
+we've been doing in class for the past
+
+ align:start position:0%
+we've been doing in class for the past
+ 
+
+ align:start position:0%
+we've been doing in class for the past
+few weeks at identifying important
+
+ align:start position:0%
+few weeks at identifying important
+ 
+
+ align:start position:0%
+few weeks at identifying important
+milestones and making sure you've
+
+ align:start position:0%
+milestones and making sure you've
+ 
+
+ align:start position:0%
+milestones and making sure you've
+scheduled a collocated period during
+
+ align:start position:0%
+scheduled a collocated period during
+ 
+
+ align:start position:0%
+scheduled a collocated period during
+that Milestone right before that
+
+ align:start position:0%
+that Milestone right before that
+ 
+
+ align:start position:0%
+that Milestone right before that
+Milestone is going to help you greatly
+
+ align:start position:0%
+Milestone is going to help you greatly
+ 
+
+ align:start position:0%
+Milestone is going to help you greatly
+doing instrict teams and doing video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chat and here's a big one we haven't
+
+ align:start position:0%
+chat and here's a big one we haven't
+ 
+
+ align:start position:0%
+chat and here's a big one we haven't
+talked about in class so much um but I
+
+ align:start position:0%
+talked about in class so much um but I
+ 
+
+ align:start position:0%
+talked about in class so much um but I
+get the impression that some of you
+
+ align:start position:0%
+get the impression that some of you
+ 
+
+ align:start position:0%
+get the impression that some of you
+might be interested in this kind of
+
+ align:start position:0%
+might be interested in this kind of
+ 
+
+ align:start position:0%
+might be interested in this kind of
+thing um having coaches so we've already
+
+ align:start position:0%
+thing um having coaches so we've already
+ 
+
+ align:start position:0%
+thing um having coaches so we've already
+we've already seen some of the teams um
+
+ align:start position:0%
+we've already seen some of the teams um
+ 
+
+ align:start position:0%
+we've already seen some of the teams um
+have dedicated scrum master or producer
+
+ align:start position:0%
+have dedicated scrum master or producer
+ 
+
+ align:start position:0%
+have dedicated scrum master or producer
+think about having a dedicated coach so
+
+ align:start position:0%
+think about having a dedicated coach so
+ 
+
+ align:start position:0%
+think about having a dedicated coach so
+someone who's on your team who is there
+
+ align:start position:0%
+someone who's on your team who is there
+ 
+
+ align:start position:0%
+someone who's on your team who is there
+to cultivate team spirit um they're
+
+ align:start position:0%
+to cultivate team spirit um they're
+ 
+
+ align:start position:0%
+to cultivate team spirit um they're
+going to emphasize the importance of one
+
+ align:start position:0%
+going to emphasize the importance of one
+ 
+
+ align:start position:0%
+going to emphasize the importance of one
+team they could be your scrum master or
+
+ align:start position:0%
+team they could be your scrum master or
+ 
+
+ align:start position:0%
+team they could be your scrum master or
+producer but they don't actually should
+
+ align:start position:0%
+producer but they don't actually should
+ 
+
+ align:start position:0%
+producer but they don't actually should
+they they're not actually the same role
+
+ align:start position:0%
+they they're not actually the same role
+ 
+
+ align:start position:0%
+they they're not actually the same role
+the scrum Master the producer is
+
+ align:start position:0%
+the scrum Master the producer is
+ 
+
+ align:start position:0%
+the scrum Master the producer is
+measuring productivity they're measuring
+
+ align:start position:0%
+measuring productivity they're measuring
+ 
+
+ align:start position:0%
+measuring productivity they're measuring
+tasks um how will things get done um the
+
+ align:start position:0%
+tasks um how will things get done um the
+ 
+
+ align:start position:0%
+tasks um how will things get done um the
+coaches a very different they're looking
+
+ align:start position:0%
+coaches a very different they're looking
+ 
+
+ align:start position:0%
+coaches a very different they're looking
+at how people interact with each other
+
+ align:start position:0%
+at how people interact with each other
+ 
+
+ align:start position:0%
+at how people interact with each other
+how people talk to each other how people
+
+ align:start position:0%
+how people talk to each other how people
+ 
+
+ align:start position:0%
+how people talk to each other how people
+work with each other often times people
+
+ align:start position:0%
+work with each other often times people
+ 
+
+ align:start position:0%
+work with each other often times people
+who are naturally inclined to do one can
+
+ align:start position:0%
+who are naturally inclined to do one can
+ 
+
+ align:start position:0%
+who are naturally inclined to do one can
+be inclined to do the other but that's
+
+ align:start position:0%
+be inclined to do the other but that's
+ 
+
+ align:start position:0%
+be inclined to do the other but that's
+not always the case um so if you have
+
+ align:start position:0%
+not always the case um so if you have
+ 
+
+ align:start position:0%
+not always the case um so if you have
+someone on your team who is one of those
+
+ align:start position:0%
+someone on your team who is one of those
+ 
+
+ align:start position:0%
+someone on your team who is one of those
+extroverted outgoing or even introverted
+
+ align:start position:0%
+extroverted outgoing or even introverted
+ 
+
+ align:start position:0%
+extroverted outgoing or even introverted
+but really interested in what
+
+ align:start position:0%
+but really interested in what
+ 
+
+ align:start position:0%
+but really interested in what
+individuals do oneon-one and how
+
+ align:start position:0%
+individuals do oneon-one and how
+ 
+
+ align:start position:0%
+individuals do oneon-one and how
+individuals work um see if you can um
+
+ align:start position:0%
+individuals work um see if you can um
+ 
+
+ align:start position:0%
+individuals work um see if you can um
+incorporate some coaching strategies uh
+
+ align:start position:0%
+incorporate some coaching strategies uh
+ 
+
+ align:start position:0%
+incorporate some coaching strategies uh
+with with your teammates and again you
+
+ align:start position:0%
+with with your teammates and again you
+ 
+
+ align:start position:0%
+with with your teammates and again you
+can do one-on-one meetings um and we can
+
+ align:start position:0%
+can do one-on-one meetings um and we can
+ 
+
+ align:start position:0%
+can do one-on-one meetings um and we can
+talk about this in the future if you're
+
+ align:start position:0%
+talk about this in the future if you're
+ 
+
+ align:start position:0%
+talk about this in the future if you're
+interested in this kind of stuff we can
+
+ align:start position:0%
+interested in this kind of stuff we can
+ 
+
+ align:start position:0%
+interested in this kind of stuff we can
+we can unpack on this topic and talk
+
+ align:start position:0%
+we can unpack on this topic and talk
+ 
+
+ align:start position:0%
+we can unpack on this topic and talk
+about it further um but I highly
+
+ align:start position:0%
+about it further um but I highly
+ 
+
+ align:start position:0%
+about it further um but I highly
+recommend
+
+ align:start position:0%
+recommend
+ 
+
+ align:start position:0%
+recommend
+it all right so um I did mention
+
+ align:start position:0%
+it all right so um I did mention
+ 
+
+ align:start position:0%
+it all right so um I did mention
+meetings um you do have agile meetings
+
+ align:start position:0%
+meetings um you do have agile meetings
+ 
+
+ align:start position:0%
+meetings um you do have agile meetings
+these people have agile meetings um
+
+ align:start position:0%
+these people have agile meetings um
+ 
+
+ align:start position:0%
+these people have agile meetings um
+these are what they are hopefully you're
+
+ align:start position:0%
+these are what they are hopefully you're
+ 
+
+ align:start position:0%
+these are what they are hopefully you're
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+so who has a formal Sprint process where
+
+ align:start position:0%
+so who has a formal Sprint process where
+ 
+
+ align:start position:0%
+so who has a formal Sprint process where
+you plan your Sprint before you start so
+
+ align:start position:0%
+you plan your Sprint before you start so
+ 
+
+ align:start position:0%
+you plan your Sprint before you start so
+you create a task you basically you
+
+ align:start position:0%
+you create a task you basically you
+ 
+
+ align:start position:0%
+you create a task you basically you
+create your Sprint task list at a at a
+
+ align:start position:0%
+create your Sprint task list at a at a
+ 
+
+ align:start position:0%
+create your Sprint task list at a at a
+meeting is everyone there or that's when
+
+ align:start position:0%
+meeting is everyone there or that's when
+ 
+
+ align:start position:0%
+meeting is everyone there or that's when
+you're saying not everyone's there
+
+ align:start position:0%
+you're saying not everyone's there
+ 
+
+ align:start position:0%
+you're saying not everyone's there
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tasks okay we have a week by what we
+
+ align:start position:0%
+tasks okay we have a week by what we
+ 
+
+ align:start position:0%
+tasks okay we have a week by what we
+want to get okay cool um and you had a
+
+ align:start position:0%
+want to get okay cool um and you had a
+ 
+
+ align:start position:0%
+want to get okay cool um and you had a
+meeting to do to create that okay U so
+
+ align:start position:0%
+meeting to do to create that okay U so
+ 
+
+ align:start position:0%
+meeting to do to create that okay U so
+then you have your daily standups at the
+
+ align:start position:0%
+then you have your daily standups at the
+ 
+
+ align:start position:0%
+then you have your daily standups at the
+end of the Sprint um you want to have a
+
+ align:start position:0%
+end of the Sprint um you want to have a
+ 
+
+ align:start position:0%
+end of the Sprint um you want to have a
+Sprint review which is basically the
+
+ align:start position:0%
+Sprint review which is basically the
+ 
+
+ align:start position:0%
+Sprint review which is basically the
+inverse of the Sprint planning meeting
+
+ align:start position:0%
+inverse of the Sprint planning meeting
+ 
+
+ align:start position:0%
+inverse of the Sprint planning meeting
+you go back and see what you made um
+
+ align:start position:0%
+you go back and see what you made um
+ 
+
+ align:start position:0%
+you go back and see what you made um
+hopefully you have a build and you just
+
+ align:start position:0%
+hopefully you have a build and you just
+ 
+
+ align:start position:0%
+hopefully you have a build and you just
+basically look at the build compare the
+
+ align:start position:0%
+basically look at the build compare the
+ 
+
+ align:start position:0%
+basically look at the build compare the
+build to the completed tasks and make
+
+ align:start position:0%
+build to the completed tasks and make
+ 
+
+ align:start position:0%
+build to the completed tasks and make
+sure it matches the other meeting um
+
+ align:start position:0%
+sure it matches the other meeting um
+ 
+
+ align:start position:0%
+sure it matches the other meeting um
+that you may or may not be doing is the
+
+ align:start position:0%
+that you may or may not be doing is the
+ 
+
+ align:start position:0%
+that you may or may not be doing is the
+agile retrospective and that's how did
+
+ align:start position:0%
+agile retrospective and that's how did
+ 
+
+ align:start position:0%
+agile retrospective and that's how did
+you work this week is anybody doing that
+
+ align:start position:0%
+you work this week is anybody doing that
+ 
+
+ align:start position:0%
+you work this week is anybody doing that
+is anybody at the end of their Sprint
+
+ align:start position:0%
+is anybody at the end of their Sprint
+ 
+
+ align:start position:0%
+is anybody at the end of their Sprint
+talking about basically talking about
+
+ align:start position:0%
+talking about basically talking about
+ 
+
+ align:start position:0%
+talking about basically talking about
+the processes of what you did and how
+
+ align:start position:0%
+the processes of what you did and how
+ 
+
+ align:start position:0%
+the processes of what you did and how
+you did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay it's kind of what I expect
+
+ align:start position:0%
+it okay it's kind of what I expect
+ 
+
+ align:start position:0%
+it okay it's kind of what I expect
+um I think you're doing yourself a
+
+ align:start position:0%
+um I think you're doing yourself a
+ 
+
+ align:start position:0%
+um I think you're doing yourself a
+disservice if you're not doing that and
+
+ align:start position:0%
+disservice if you're not doing that and
+ 
+
+ align:start position:0%
+disservice if you're not doing that and
+in particular if you are doing that and
+
+ align:start position:0%
+in particular if you are doing that and
+ 
+
+ align:start position:0%
+in particular if you are doing that and
+you're making that a face-to-face
+
+ align:start position:0%
+you're making that a face-to-face
+ 
+
+ align:start position:0%
+you're making that a face-to-face
+meeting that's the time when you can
+
+ align:start position:0%
+meeting that's the time when you can
+ 
+
+ align:start position:0%
+meeting that's the time when you can
+talk about some of these interpersonal
+
+ align:start position:0%
+talk about some of these interpersonal
+ 
+
+ align:start position:0%
+talk about some of these interpersonal
+issues that's the time when you can talk
+
+ align:start position:0%
+issues that's the time when you can talk
+ 
+
+ align:start position:0%
+issues that's the time when you can talk
+about your feelings uh that's the time
+
+ align:start position:0%
+about your feelings uh that's the time
+ 
+
+ align:start position:0%
+about your feelings uh that's the time
+when you can can open up and and try to
+
+ align:start position:0%
+when you can can open up and and try to
+ 
+
+ align:start position:0%
+when you can can open up and and try to
+figure out what is about like why are
+
+ align:start position:0%
+figure out what is about like why are
+ 
+
+ align:start position:0%
+figure out what is about like why are
+some of these tasks not getting um taken
+
+ align:start position:0%
+some of these tasks not getting um taken
+ 
+
+ align:start position:0%
+some of these tasks not getting um taken
+on um who's not doing them and what's in
+
+ align:start position:0%
+on um who's not doing them and what's in
+ 
+
+ align:start position:0%
+on um who's not doing them and what's in
+their way uh from doing them but really
+
+ align:start position:0%
+their way uh from doing them but really
+ 
+
+ align:start position:0%
+their way uh from doing them but really
+it's not it's not about the it's not
+
+ align:start position:0%
+it's not it's not about the it's not
+ 
+
+ align:start position:0%
+it's not it's not about the it's not
+really about what's in their way it's
+
+ align:start position:0%
+really about what's in their way it's
+ 
+
+ align:start position:0%
+really about what's in their way it's
+difficult to talk about it's not about
+
+ align:start position:0%
+difficult to talk about it's not about
+ 
+
+ align:start position:0%
+difficult to talk about it's not about
+what's in their way but it might be
+
+ align:start position:0%
+what's in their way but it might be
+ 
+
+ align:start position:0%
+what's in their way but it might be
+about what outside of the project and
+
+ align:start position:0%
+about what outside of the project and
+ 
+
+ align:start position:0%
+about what outside of the project and
+outside of the team could be in their
+
+ align:start position:0%
+outside of the team could be in their
+ 
+
+ align:start position:0%
+outside of the team could be in their
+way and you can can work through some of
+
+ align:start position:0%
+way and you can can work through some of
+ 
+
+ align:start position:0%
+way and you can can work through some of
+those kind of issues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm done what I'd like you to do
+
+ align:start position:0%
+so I'm done what I'd like you to do
+ 
+
+ align:start position:0%
+so I'm done what I'd like you to do
+before you go and work in your teams is
+
+ align:start position:0%
+before you go and work in your teams is
+ 
+
+ align:start position:0%
+before you go and work in your teams is
+schedule a Sprint retrospective so think
+
+ align:start position:0%
+schedule a Sprint retrospective so think
+ 
+
+ align:start position:0%
+schedule a Sprint retrospective so think
+a look take a look at your Sprint at
+
+ align:start position:0%
+a look take a look at your Sprint at
+ 
+
+ align:start position:0%
+a look take a look at your Sprint at
+your Sprint process how long is your
+
+ align:start position:0%
+your Sprint process how long is your
+ 
+
+ align:start position:0%
+your Sprint process how long is your
+Sprint is it one week or two weeks um
+
+ align:start position:0%
+Sprint is it one week or two weeks um
+ 
+
+ align:start position:0%
+Sprint is it one week or two weeks um
+we've been assuming it's a one week week
+
+ align:start position:0%
+we've been assuming it's a one week week
+ 
+
+ align:start position:0%
+we've been assuming it's a one week week
+process onee Sprints um schedule a time
+
+ align:start position:0%
+process onee Sprints um schedule a time
+ 
+
+ align:start position:0%
+process onee Sprints um schedule a time
+period that everyone can attend and a
+
+ align:start position:0%
+period that everyone can attend and a
+ 
+
+ align:start position:0%
+period that everyone can attend and a
+Time an amount of time that they can
+
+ align:start position:0%
+Time an amount of time that they can
+ 
+
+ align:start position:0%
+Time an amount of time that they can
+attend that they can see each other face
+
+ align:start position:0%
+attend that they can see each other face
+ 
+
+ align:start position:0%
+attend that they can see each other face
+to face but not as NE are in the same
+
+ align:start position:0%
+to face but not as NE are in the same
+ 
+
+ align:start position:0%
+to face but not as NE are in the same
+room if you can be in the same room
+
+ align:start position:0%
+room if you can be in the same room
+ 
+
+ align:start position:0%
+room if you can be in the same room
+awesome if you can't try to figure out a
+
+ align:start position:0%
+awesome if you can't try to figure out a
+ 
+
+ align:start position:0%
+awesome if you can't try to figure out a
+time that you can chat using Google
+
+ align:start position:0%
+time that you can chat using Google
+ 
+
+ align:start position:0%
+time that you can chat using Google
+hangout or some other kind of video chat
+
+ align:start position:0%
+hangout or some other kind of video chat
+ 
+
+ align:start position:0%
+hangout or some other kind of video chat
+some other kind of face to-face video
+
+ align:start position:0%
+some other kind of face to-face video
+ 
+
+ align:start position:0%
+some other kind of face to-face video
+chat um make sure the meeting is focused
+
+ align:start position:0%
+chat um make sure the meeting is focused
+ 
+
+ align:start position:0%
+chat um make sure the meeting is focused
+on talking about your processes so don't
+
+ align:start position:0%
+on talking about your processes so don't
+ 
+
+ align:start position:0%
+on talking about your processes so don't
+talk about your game don't talk about
+
+ align:start position:0%
+talk about your game don't talk about
+ 
+
+ align:start position:0%
+talk about your game don't talk about
+the work that you've done talk about how
+
+ align:start position:0%
+the work that you've done talk about how
+ 
+
+ align:start position:0%
+the work that you've done talk about how
+you organize yourself um and in
+
+ align:start position:0%
+you organize yourself um and in
+ 
+
+ align:start position:0%
+you organize yourself um and in
+particular talk about your interpersonal
+
+ align:start position:0%
+particular talk about your interpersonal
+ 
+
+ align:start position:0%
+particular talk about your interpersonal
+matters talk about um basically
+
+ align:start position:0%
+matters talk about um basically
+ 
+
+ align:start position:0%
+matters talk about um basically
+communicate about communicating so talk
+
+ align:start position:0%
+communicate about communicating so talk
+ 
+
+ align:start position:0%
+communicate about communicating so talk
+about how you are talking to each other
+
+ align:start position:0%
+about how you are talking to each other
+ 
+
+ align:start position:0%
+about how you are talking to each other
+um and yeah I'm going to talk to you
+
+ align:start position:0%
+um and yeah I'm going to talk to you
+ 
+
+ align:start position:0%
+um and yeah I'm going to talk to you
+about this again in a couple weeks and
+
+ align:start position:0%
+about this again in a couple weeks and
+ 
+
+ align:start position:0%
+about this again in a couple weeks and
+in a couple weeks I'm going to give you
+
+ align:start position:0%
+in a couple weeks I'm going to give you
+ 
+
+ align:start position:0%
+in a couple weeks I'm going to give you
+some more um act once you're actually in
+
+ align:start position:0%
+some more um act once you're actually in
+ 
+
+ align:start position:0%
+some more um act once you're actually in
+the process of I think most of you right
+
+ align:start position:0%
+the process of I think most of you right
+ 
+
+ align:start position:0%
+the process of I think most of you right
+now are probably in the concepting phase
+
+ align:start position:0%
+now are probably in the concepting phase
+ 
+
+ align:start position:0%
+now are probably in the concepting phase
+pre-production phase right now you're
+
+ align:start position:0%
+pre-production phase right now you're
+ 
+
+ align:start position:0%
+pre-production phase right now you're
+still kind of figuring out your game you
+
+ align:start position:0%
+still kind of figuring out your game you
+ 
+
+ align:start position:0%
+still kind of figuring out your game you
+haven't quite like I guess you you guys
+
+ align:start position:0%
+haven't quite like I guess you you guys
+ 
+
+ align:start position:0%
+haven't quite like I guess you you guys
+are actually working on your back end
+
+ align:start position:0%
+are actually working on your back end
+ 
+
+ align:start position:0%
+are actually working on your back end
+because someone did the initial design
+
+ align:start position:0%
+because someone did the initial design
+ 
+
+ align:start position:0%
+because someone did the initial design
+for you uh the rest are probably still
+
+ align:start position:0%
+for you uh the rest are probably still
+ 
+
+ align:start position:0%
+for you uh the rest are probably still
+working out that design phase uh when I
+
+ align:start position:0%
+working out that design phase uh when I
+ 
+
+ align:start position:0%
+working out that design phase uh when I
+talk about this again you'll likely be
+
+ align:start position:0%
+talk about this again you'll likely be
+ 
+
+ align:start position:0%
+talk about this again you'll likely be
+in fullon um production mode and so some
+
+ align:start position:0%
+in fullon um production mode and so some
+ 
+
+ align:start position:0%
+in fullon um production mode and so some
+of the the activities I'm going to show
+
+ align:start position:0%
+of the the activities I'm going to show
+ 
+
+ align:start position:0%
+of the the activities I'm going to show
+you might hopefully help when you're
+
+ align:start position:0%
+you might hopefully help when you're
+ 
+
+ align:start position:0%
+you might hopefully help when you're
+doing these
+
+ align:start position:0%
+doing these
+ 
+
+ align:start position:0%
+doing these
+meetings any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so it's 150 go ahead and
+
+ align:start position:0%
+questions okay so it's 150 go ahead and
+ 
+
+ align:start position:0%
+questions okay so it's 150 go ahead and
+take a few minutes to uh break and then
+
+ align:start position:0%
+take a few minutes to uh break and then
+ 
+
+ align:start position:0%
+take a few minutes to uh break and then
+the rest of the class is yours to work
+
+ align:start position:0%
+the rest of the class is yours to work
+ 
+
+ align:start position:0%
+the rest of the class is yours to work
+in your teams but still do
+
+ align:start position:0%
+in your teams but still do
+ 
+
+ align:start position:0%
+in your teams but still do
+this you can leave it you can leave it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/B4xIxr3fB7c.txt b/B4xIxr3fB7c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..052ced21d233366122ab51900377e75e3cb23796
--- /dev/null
+++ b/B4xIxr3fB7c.txt
@@ -0,0 +1,1941 @@
+PROFESSOR: We are thundering
+rapidly to the
+
+midpoint of the term.
+
+I think a week from this
+coming Thursday will be
+
+exactly halfway, and the
+halfway point is when I
+
+usually try, give or take a
+day, to change gears very
+
+abruptly and start looking at
+the symmetry of physical
+
+properties and tensors and
+actual discussion of physical
+
+properties that are
+anisotropic.
+
+So we'll be finishing
+up our discussion of
+
+symmetry fairly quickly.
+
+We still have, however, some
+major derivations to perform,
+
+and we'll get into one
+of these today.
+
+Last time we had begun the
+process of deriving what are
+
+called the point groups as
+opposed to the plane groups.
+
+The plane groups were
+combinations of symmetry with
+
+a lattice that extended
+throughout a plane in space.
+
+A point group we've seen in the
+form of two-dimensional
+
+point groups.
+
+We're now going to today derive
+the three-dimensional
+
+point groups.
+
+And, again, the name stems from
+the fact that these are
+
+clusters of symmetry about a
+common point so that at very
+
+least that one point
+in space stays put.
+
+So, hence, point groups--
+
+these are symmetries
+about a point.
+
+And to put some embellishing
+adjectives on here, these will
+
+be the three-dimensional
+crystallographic point groups.
+
+Because there are an infinite
+number of point groups, we're
+
+considering just those
+symmetries that can be
+
+combined with a lattice
+and therefore are
+
+permissible to crystals.
+
+I'd like to point out in case
+you've not been making much
+
+use of Buerger's book that we
+actually are getting back to
+
+Buerger's treatment.
+
+We'll do some of the derivations
+over the next few
+
+days with a little bit more
+detail and with a slightly
+
+different procedure
+than Buerger.
+
+But the bases covered
+are the same.
+
+So let me just point out where
+some of this material is in
+
+Buerger's book.
+
+Buerger does Euler's
+Construction, and he does this
+
+in a once over lightly.
+
+I think this is not the
+best part of the book.
+
+This is on pages 35 to 43.
+
+In particular, he sort of leaps
+ahead quickly and just
+
+looks for one angle between
+rotation axes and doesn't get
+
+the-- do specifically the ones
+that are 90 degrees and are
+
+not as interesting.
+
+Some of the combination theorems
+are in Chapter 6, and
+
+there you'll find the statement
+that two reflections
+
+at an angle mu is equivalent
+to a net rotation of mu,
+
+except Buerger doesn't
+call them sigmas.
+
+He calls them m's.
+
+He uses the same symbol for
+individual operations and for
+
+the symmetry of them, and I
+think that's a little untidy.
+
+Also, the theorem that says that
+if we have a mirror plane
+
+that's perpendicular to a
+twofold rotation axis, that
+
+gives rise to inversion center
+at the point of intersection.
+
+And then he launches into a
+rather condensed version of
+
+the derivation of the point
+groups on pages 59 to 68.
+
+Then, in Chapter 7, derives the
+two dimensional lattices
+
+or the plane nets.
+
+This is on page 69 to 83.
+
+We've done that differently and
+much more exhaustively by
+
+deriving the two-dimensional
+plane groups and the lattices
+
+are part of the plane groups,
+and we've gotten them
+
+automatically.
+
+There is a place where in the
+derivation of the space
+
+lattices, he's a little bit
+incomplete and actually does
+
+something that's wrong A-ha--
+
+I showed Buerger was wrong
+at one place in his book.
+
+But anyway, this is where the
+material that we're covering
+
+now is mentioned in
+Buerger's book.
+
+Last time, we had hit
+a new surprise.
+
+We had asked if we take the
+basic rotational symmetries
+
+and add an inversion to
+something like three--
+
+so, three is a subgroup,
+the operation of
+
+inversion is an extender.
+
+We found that there was a new
+operation that came up, and
+
+this was a rotoinversion
+operation.
+
+And then the resulting point
+group, which we called 3-bar--
+
+the symbol itself, 3-bar, is
+a threefold rotoinversion.
+
+And if we were not clever
+enough to invent a
+
+rotoinversion operation, we
+would have stumbled headlong
+
+over it in adding inversion
+as an extender
+
+to a threefold axis.
+
+And a rotoinversion axis is
+something that involves in
+
+general rotating through some
+angle alpha to get from a
+
+first object to a second object
+of the same handedness
+
+and then not yet putting it
+down, first inverting it
+
+through axis--
+
+through a point on the axis--
+
+to get a second object.
+
+I shouldn't call this second
+because this is not rotation
+
+with inversion simultaneously
+but a two step operation.
+
+So we rotate from 1 to this
+virtual object also of same
+
+handedness and then before
+putting it down, we invert it
+
+to get number two, which
+is left handed.
+
+And the operation of getting
+there in two steps but in one
+
+repetition is the operation
+of rotoinversion.
+
+That operation was one of the
+members of the group that
+
+results when you add inversion
+as an extender to 3.
+
+But, really, this was not
+something that was a new sort
+
+of symmetry element.
+
+It was an operation that came
+up, but we could regard the
+
+point down that we've labeled
+3-bar as simply a threefold
+
+axis with an inversion
+center sitting on it.
+
+But then we looked
+at another one.
+
+And by anticipation, I said
+we ought to look at these.
+
+And we looked at what happened
+when we took a fourfold
+
+rotoinversion operation where we
+would take the first object
+
+number one, rotate it through
+90 degrees, and
+
+not yet put it down.
+
+We'd first invert it through a
+point on an axis, and we got
+
+one that was 90 degrees away
+but pointing down in of
+
+opposite handedness.
+
+If we repeated that operation
+several times, we found that
+
+we got two objects up above a
+plane normal to the rotation
+
+part of the operation and
+passing through the point,
+
+which we inverted.
+
+So there's one right handed one
+up here, a second right
+
+handed one up here, and then two
+down below, which were of
+
+opposite chirality,
+number 3 and 4.
+
+And that is an entirely
+new beast.
+
+We have no way of describing
+the relation between these
+
+four objects other than saying
+rotate, don't put it down,
+
+first invert.
+
+Rotate, don't put it down,
+first invert again.
+
+So this is something
+entirely new.
+
+It's a two step operation.
+
+You cannot describe it any more
+simply than saying take
+
+two steps to do the repetition
+in the same sense that the
+
+glide plane that we discovered
+in the plane groups had a step
+
+of translation followed
+immediately by reflection, and
+
+that was a new sort
+of operation.
+
+So here's another example
+of a two-step operation.
+
+The symbol for this point group
+is 4-bar, and the symbol
+
+for it-- if you want to indicate
+its locus, is, it's
+
+got a squareness to it because
+these objects as mutually are
+
+separated by 90 degrees, but it
+really has only a twofold
+
+symmetry, so the symmetry
+for a 4-bar axis.
+
+It's not really an
+axis at all.
+
+It's a 4-bar point,
+because only a
+
+point is left invariant.
+
+But the symbol for a 4-bar
+"axis" is this square with a
+
+little twofold axis
+inscribed in it.
+
+Alright.
+
+We ought to really, then, step
+back and ask how many
+
+different rotoinversion axes
+there might be, and add these
+
+to our bags of tricks.
+
+And what I'm going to invite you
+to do is to examine this
+
+systematically on a problem set
+which I will pass around,
+
+along with several other
+problems for your
+
+consideration, as well.
+
+And having stumbled onto that
+combination, another thing we
+
+might ask to broaden our bag of
+tricks still further is to
+
+say is there such a thing as
+a rotoreflection axis?
+
+And we called n-bar
+a rotoinversion.
+
+I wrote a reflection axis is
+indicated by an n with this
+
+little squiggle on top.
+
+Anyone who has studied Spanish
+realizes that the proper name
+
+for the squiggle is a
+tilde, T-I-L-D-E.
+
+And this would be an operation
+where there's a locus in which
+
+we'll perform the reflection
+part of the operation, so this
+
+would be a 2 step operation that
+involves taking a first
+
+one and rotating it to a virtual
+object number two but
+
+not putting it down.
+
+Before putting it down, we will
+
+reflect in a planar locus.
+
+So this is number two, and it
+will be of opposite chirality.
+
+So that's another operation that
+involves rotation coupled
+
+as one part of a step that
+involves R, the second of our
+
+three translation free
+operations, namely reflection
+
+and inversion.
+
+So are these something
+we should consider?
+
+What I've invited you to do is
+to draw out for n equals 1 to
+
+8 the patterns produced by
+rotoinversion and the patterns
+
+created by rotoreflection, and
+then see if you regard these
+
+as new operations or whether
+they can be broken down into
+
+the simultaneous presence of
+more than one of our old
+
+friends such as 3-bar being a
+plain old threefold axis with
+
+an inversion sitting on it.
+
+The fact that I'm asking you
+take your time to do this
+
+suggests that yes, you are
+going to find some
+
+rotoinversion and rotoreflection
+axes, which are
+
+inherently 2 step operations
+and can't be decomposed.
+
+What I'd like to do now, then,
+is to systematically look at
+
+the axial combinations.
+
+These are of the form n one,
+two, three, four, and six and
+
+the dihedral symmetries.
+
+These are of the form n22, or
+just 32 in the case of the one
+
+with the threefold axis.
+
+And then the two cubic
+arrangements 23, twofold axis
+
+out of the face normal to a
+cube, threefold axes out of
+
+all of the body diagonals,
+and 432.
+
+And what I'm going to do with
+you is to use these as
+
+worksheets to guide the logic
+of what we're doing, and we
+
+won't do every single
+one of them.
+
+I think once we do a few, the
+general principle is clear and
+
+the results there
+are before you.
+
+But what we'll take, then, is
+the axes n, the axes n22, and
+
+then the two cubic symmetries
+23 and 432.
+
+Then, finally, we found 4-bar
+as a different rotation
+
+axis-like symmetry element, so
+I'll add that to the list.
+
+Then consider what we can add
+to these symmetries as
+
+extenders, and these are an
+additional element that we can
+
+add to what is already a
+
+self-contained nice little group.
+
+We muck things up by introducing
+another operation,
+
+and then we'll have to take
+combinations of that operation
+
+with all the symmetry elements
+that are there in the parent
+
+subgroup and see what new
+symmetry elements arise.
+
+The ground rules in these
+additions are fairly simple
+
+but nevertheless profound.
+
+The addition of the extender
+cannot create any new symmetry
+
+axes by its operation, and the
+reason for that should be
+
+quite clear.
+
+We obtained these combinations
+of rotation axes using Euler's
+
+principle, and that was
+thorough and orderly,
+
+systematic and complete.
+
+These are the only
+arrangements of
+
+crystallographic rotation
+axes that are possible.
+
+So if we add an extender that
+creates, for example, a new
+
+twofold axis in n22, it's either
+going to be something
+
+that we already have in this
+list, and therefore not
+
+interesting, or something
+that just cannot
+
+constitute a group.
+
+We'll take combinations of
+operations and we will never
+
+find a closed finite set.
+
+So if we add a mirror operation,
+a reflection
+
+operation as an extender, the
+addition of the reflection
+
+operation sigma must be either
+perpendicular to the axis.
+
+And what that's going to do is
+just flip the top part of the
+
+rotation axis and reflect it
+down to the bottom axis.
+
+Nothing new was created.
+
+And it could alternatively be
+parallel to the axis and
+
+passing through it.
+
+In that case, we've already seen
+the consequences of this
+
+addition in deriving the
+two-dimensional point groups,
+
+namely to 2mm, 3m,
+4mm, and 6mm.
+
+No new axis is created.
+
+One of the additions that is
+something we mentioned last
+
+time is that in the case of the
+dihedral groups where we
+
+have an n-fold axis and
+then twofold axes
+
+arranged in some fashion--
+
+not in some arbitrary fashion.
+
+It's going to be 2 pi over n
+times 1/2, depending on the
+
+n-fold axis--
+
+we could pass the
+mirror operation
+
+through the twofold axis.
+
+And that's what we'll call
+a vertical mirror plane.
+
+But when there's more than one
+axis present, we could also
+
+put the reflection operation
+diagonally in between the
+
+twofold axes.
+
+So we're going to refer to this
+as a diagonal mirror.
+
+It's snaked in between the
+axes that are present.
+
+So, perpendicular reflection
+operation as an extender, one
+
+parallel to the axis and passing
+through it, or one
+
+that is diagonal passing
+in between them.
+
+And finally, that exhausts
+what we can do with
+
+reflection, but we could
+add inversion.
+
+And if we're not going create
+new axes, and we're going to
+
+get a point group-- a finite
+set of objects--
+
+the inversion center has to be
+on one of the single axis,
+
+namely these groups n, or at the
+point of intersection, if
+
+there's more than one.
+
+So there's the job
+laid out for us.
+
+And we've got two theorems to
+aid us in quickly finding the
+
+new operations that arise--
+
+in effect, taking a shortcut
+to establish the group
+
+multiplication table, and the
+two theorems are as follows.
+
+We saw that if you take a
+rotation operation A pi, that
+
+takes a first object that's
+right handed and rotates it to
+
+a second object that is
+also right handed.
+
+Then follow that by reflection
+in a mirror plane that is
+
+perpendicular to the axis.
+
+The net effect of going from 1
+to number 3, which is left
+
+handed, is to create an
+inversion center at the point
+
+of intersection.
+
+So there's a theorem that we
+can write down once and for
+
+all and say that A pi followed
+by reflection in a mirror
+
+plane that's perpendicular to
+axis A has, as a net effect,
+
+the operation of inversion.
+
+And if this is not a twofold
+axis, it's something like a
+
+fourfold axis or a sixfold
+axis, that contains the
+
+operation A pi as part of the
+operations contained in that
+
+axis, and that's going
+to create an
+
+inversion center as well.
+
+So for any evenfold axis, add a
+perpendicular mirror plane,
+
+and automatically the inversion
+center comes up.
+
+And we can permute the order
+of these operations if we
+
+rotate by 180 degrees and then
+invert the net effect is
+
+reflection in the perpendicular
+mirror plane.
+
+So this is something that you
+permute around into three
+
+different combinations.
+
+Does the order of the operation
+make a difference?
+
+And the answer is no, the
+order is not important.
+
+For example, rotating and then
+reflecting is the same as
+
+reflecting and then
+rotating it.
+
+It went up at the same
+point, number 3.
+
+Remember a fancy word for this
+when we define what's meant by
+
+a group, that these groups are
+going to be what's called
+
+Abelian, and an Abelian group
+is where any combination of
+
+operations a followed by b is
+identical to b followed by a.
+
+I told you that great joke among
+mathematicians, what is
+
+purple and commutes?
+
+And the answer is an
+Abelian grape.
+
+Ha, ha, ha--
+
+I think that's stupid, but it
+drives mathematicians into
+
+guffaws of laughter.
+
+A second theorem, and this is
+one that we've already seen in
+
+two dimensions, is that if you
+take an operation A alpha,
+
+pass a reflection operation
+sigma 1 through it, that to
+
+the effect of that is going to
+be another mirror plane that
+
+is alpha over 2 away
+from the first.
+
+Notice I'm a little bit sloppy
+in talking about reflection
+
+operation and mirror plane
+because if a reflection
+
+operation is there, that's all
+I need to have to say that
+
+this is the locus of a symmetry
+
+point, a mirror plane.
+
+So this is another one.
+
+Do you think that this an
+Abelian combination to say
+
+that A alpha followed by sigma
+1 is equal to sigma 2.
+
+Is this Abelian?
+
+AUDIENCE: No.
+
+PROFESSOR: No, it's not.
+
+And how do you answer that?
+
+Not through any means more
+profound than just drawing it
+
+out and seeing what you get.
+
+Let's take 3n as an example.
+
+So let's do the operation.
+
+In this order, do the rotation
+A 2 pi over 3 to go from this
+
+one up to this one, and then
+let's reflect across this
+
+horizontal mirror plane.
+
+So this is 1 right handed,
+this is 2 right handed
+
+reflect, here's number three
+and it's left handed.
+
+So that's A 2 pi over
+3 followed by
+
+reflection in sigma 1.
+
+And if we do the operations in
+reverse order, reflect in
+
+sigma 1 to go up to here, so
+this would be 2 prime and then
+
+rotate by 120 degrees.
+
+We would go to here to here,
+and that is not the same
+
+location as this one.
+
+So this is not equal to sigma
+1 followed by A 2 pi over 3.
+
+How can you tell when is the
+combination of operations is
+
+going to be Abelian and
+when is it not?
+
+It sounds rather clumsy to
+state it in words, but
+
+whenever the two symmetry
+operations leave each other
+
+unmoved, then you can
+permute the order.
+
+For example, in this combination
+here the rotation
+
+leaves the mirror
+plane unchanged.
+
+It just spins around
+in its own plane.
+
+The mirror plane leaves the
+rotation unchanged, it just
+
+reflects it end to end.
+
+Here this rotation axis and
+these mirror planes obviously
+
+do not leave each other
+unchanged because the
+
+threefold axis rotates
+the mirror plane to
+
+two other new locations.
+
+So whenever that's the case, if
+the operations do not leave
+
+each other unchanged, the order
+makes a difference.
+
+So that's a useful thing
+to keep in mind.
+
+Let's now turn to these sheets
+that I passed out, and you
+
+might want to unstaple them
+because they're designed to go
+
+side by side, and there
+are three pages.
+
+What I've done across the top
+of the pages is to give the
+
+different combinations of
+crystallographic rotation axes
+
+that are possible.
+
+So going from the first sheet
+across to the last, there's
+
+the rotation axes
+by themselves--
+
+one, two, three,
+four, and six.
+
+Then there are the groups of
+the form n22, 222, 32, 422,
+
+622, and then the two cubic
+combinations 23 and 432.
+
+So there are the 11 possible
+combination of
+
+crystallographic rotation axes,
+and stuck off by itself
+
+at the end is the
+oddball 4-bar.
+
+For the axes by themselves, the
+diagonal mirror addition
+
+is not defined.
+
+The diagonal mirror position
+by definition snakes in
+
+between axes that are there
+in the axial combination.
+
+If there's only one axis,
+that's not defined.
+
+But you could add a horizontal
+mirror plane.
+
+A horizontal mirror planes
+adds a onefold axis.
+
+It's just a mirror plane.
+
+So that's called m in
+the international
+
+notation for mirror.
+
+And it's called C sub S, C
+because it's a cyclic group,
+
+and the S stands for Spiegel.
+
+That's the Schoenflies
+notation.
+
+If we add a--
+
+take two and add a horizontal
+mirror plane--
+
+this is the thing that we
+sketched out here--
+
+this gives a pattern of four
+objects, two that are up above
+
+the mirror plane of one
+chirality, two down below the
+
+mirror plane of opposite
+chirality.
+
+These projections of the
+patterns are down along the
+
+rotation axis, and when you
+see a dot in a circle, the
+
+circle represents the point that
+is down and the dot is
+
+one that's up on top.
+
+So there are two pairs
+of objects--
+
+two right handed ones that are
+up and two left-handed ones
+
+that are down.
+
+And that, in international
+notation, is 2/m the twofold
+
+axis is over a mirror plane.
+
+So that's the way to make
+sense of the symbol and
+
+remember what it means.
+
+In the Schoenflies
+notation at C2.
+
+You've added a horizontal mirror
+plane as an extender.
+
+Going down the remaining ones
+in that list because they're
+
+all very, very similar--
+
+add a mirror plane to a
+threefold axis, the triangle
+
+is reflected down to a triangle
+of motifs of opposite
+
+chirality, so that's 3 over m.
+
+For sure, it's called 6-bar, but
+let's forget about that.
+
+The Schoenflies notation C3H,
+and similarly there's a 4 over
+
+m, a square above, and a square
+of opposite handedness
+
+below the mirror plane.
+
+The horizontal mirror plane in
+all of these cases is shown as
+
+a bold line.
+
+They've added fainter vertical
+lines to give
+
+you an angular reference.
+
+Don't be confused by that
+in the Xerox copy--
+
+the weight of the lines
+is not distinguished.
+
+So the only symmetry element
+in 4 over m, for example,
+
+should be shown by this solid
+bold circle that is in the
+
+plane of the paper.
+
+The two crossed lines are
+lighter and those are just as
+
+mutual orientations.
+
+And finally, there's another
+one of this form
+
+which is 6 over m.
+
+On all of the evenfold
+additions-- that is, to say
+
+everything but 3m--
+
+if you add that horizontal
+mirror plane, it's going to be
+
+perpendicular to an
+operation A pi.
+
+Therefore, inversion pops up
+as one of the operations in
+
+the group, and 2 over m, 4
+over m, 6 over m, those
+
+regular polyhedra of objects--
+
+can be inverted through the
+point of intersection of the
+
+axis in the mirror plane, and
+that leaves the set unchanged.
+
+So if we go down to the bottom
+of the list and say, can we
+
+add inversion to these axial
+arrangements, in the case of
+
+2, 4, and 6--
+
+no, adding inversion doesn't
+give you anything new, because
+
+that's already there in the
+groups of the form CNH, or
+
+2/m, 4/m, 6/m.
+
+Diagonal is not defined, so the
+only additional one that
+
+we could pick up by adding
+inversion is adding inversion
+
+to a threefold axis,
+and that's one we
+
+did the other day.
+
+Adding inversion to a threefold
+axis gives us three
+
+that are up of one handedness,
+three that are down of
+
+opposite handedness, and
+the orientation of
+
+the triangle is skewed.
+
+That is called 3-bar.
+
+But it's just nothing more than
+a threefold axis with an
+
+inversion center
+sitting on it.
+
+Schoenflies' notation is C3i.
+
+Then the only other additions to
+the single axes are adding
+
+the mirror plane in a vertical
+fashion passing through the
+
+axis, and these we've already
+seen in two dimensions so we
+
+don't have to spend
+much time on them.
+
+There's 2 mm, which is C2V.
+
+3m--
+
+all the mirror planes result
+upon adding a single mirror
+
+plane to the threefold axis--
+
+4 mm, and 6 mm.
+
+These are just three-dimensional
+extensions
+
+parallel to the axis of the
+symmetry that we already
+
+derived for a plane
+in space in the
+
+two-dimensional point groups.
+
+So we're almost half done.
+
+It's easy, isn't it?
+
+Any questions at this point?
+
+So the only ones that are really
+new that we haven't
+
+seen already in two dimensions
+are the rotation axis
+
+perpendicular to the
+mirrored plane.
+
+That brings us to roughly the
+middle of the second sheet,
+
+and the arrangement of axes 222
+represents three mutually
+
+orthogonal twofold axes.
+
+If we add a horizontal mirror
+plane, that's going to put an
+
+inversion center at the point
+of intersection because that
+
+horizontal reflection is going
+to be sitting normal to a
+
+twofold axis.
+
+And then since the other twofold
+axes see an inversion
+
+center sitting on it, there's
+a mirror plane perpendicular
+
+to those other twofold axes.
+
+So adding again to go through
+that again, adding inversion
+
+to the point of intersection of
+the twofold axes creates a
+
+mirror plane perpendicular to
+each of those twofold axes.
+
+So it becomes 2/m 2/m 2/m--
+
+each of the twofold axes
+acquires a different sort of
+
+mirror plane perpendicular
+to its orientation.
+
+And 2/m 2/m 2/m, even though
+I love saying it,
+
+is kind of a mouthful.
+
+So that's very often abbreviated
+to just mmm, which
+
+really is a nice exclamation
+when you see what a lovely
+
+symmetry it is.
+
+The pattern shown in the diagram
+to the left is just
+
+the pattern of 222 with the
+objects reflected up or
+
+reflected down, and you
+get a total of 8.
+
+That means that there are eight
+operations in the group,
+
+and you can add up quickly
+what they are.
+
+They are the three operations
+of rotating by pi, the
+
+operation of identity, then
+three mirror planes because
+
+the mirror planes all
+indistinct, and then the
+
+operation of inversion.
+
+So there are the eight
+operations that are present
+
+that generate the objects
+from a single one.
+
+Add a horizontal mirror plane to
+32 and you get a threefold
+
+axis perpendicular to the
+threefold axis, so you write
+
+that as 3m.
+
+That mirror plane now passes
+through the horizontal twofold
+
+axes, and a twofold axis with a
+mirror plane passing through
+
+it wants another mirror plane
+90 degrees away, so a new
+
+mirror plane pops up passing
+through each of the twofold
+
+axes and perpendicular to the
+horizontal mirror plane.
+
+Those mirror planes are
+in the same direction
+
+as the twofold axis.
+
+They're not perpendicular to it,
+and when symmetry elements
+
+are parallel to a common
+direction you write them out
+
+on the same line, so here's a
+case of a mixed metaphor.
+
+One mirror plane that's
+perpendicular to an axis, the
+
+threefold axis, so you write
+that as 3 over m.
+
+The other twofold axes have
+mirror points passing through
+
+them, so you write that as 2m
+and the threefold axes makes
+
+all of those 2m symmetries
+equivalent to one another.
+
+Pattern, and this is true for
+all of these symmetries, is
+
+nothing more than the pattern
+of the subgroup repeated by
+
+the one operation that you've
+added as an extender .
+
+So if you look at the pattern of
+32, object all of the same
+
+chirality, all apparently
+up and down, and add the
+
+horizontal mirror plane.
+
+The one that is up goes down,
+the one that's down goes up,
+
+and you get a set of
+four around each
+
+of the twofold axes.
+
+422 behaves very similarly.
+
+The pattern is just the pattern
+of 422 reflected in a
+
+plane, so you have a
+set of 16 objects--
+
+eight of them up of one
+chirality, those are the solid
+
+dots, if you will, and then
+another two, four, six, eight
+
+that are down of opposite
+chirality.
+
+You have a mirror plane that
+you added as the horizontal
+
+mirror plane perpendicular
+to the fourfold axis.
+
+All of the horizontal twofold
+axes see a mirror plane
+
+passing through them.
+
+So they've got to have a mirror
+plane that's 90 degrees
+
+away, and those are the vertical
+mirror planes.
+
+Either the point is obvious now
+or you're not following me
+
+at all, so I'll simply say on
+the left-hand column of the
+
+final sheet, 622 with a
+horizontal mirror plane goes
+
+to 6/m, 2/m, 2/m, called
+D6h in Schoenflies.
+
+I'll leave the cubic
+ones until last.
+
+They're not nearly as
+bad as they seem.
+
+But obviously they have a lot
+of symmetry all over the
+
+place, and we'll want to take a
+closer look at the patterns.
+
+The next extender is a vertical
+mirror plane, and
+
+we've already got the groups of
+the form cnv, because they
+
+are just extensions in a third
+dimension of one set we've
+
+seen in two dimensions.
+
+If we try adding the vertical
+mirror plane, which is defined
+
+as passing through the principal
+axis of high
+
+symmetry and perpendicular to
+the twofold axes, we've
+
+already encountered those in
+every group except 32.
+
+2/m, 2/m, 2/m already has the
+vertical mirror plane.
+
+The same is true of 3/mm2.
+
+The same is true of 4/m, 2/m,
+2/m and 6/m, 2/m, 2/m.
+
+The vertical mirror plane comes
+in automatically when we
+
+add the horizontal mirror plane
+as the extender, So
+
+nothing new there at all.
+
+And now we come to one
+that is interesting.
+
+This is the diagonal
+mirror plane.
+
+And I'll do this one slowly
+and then in some detail
+
+because it's another example
+of how we would trip over
+
+something if we were not clever
+enough to think of it.
+
+Let me begin by drawing the
+three orthogonal axes of 222.
+
+So we have one object that's up
+and one object that's down.
+
+The twofold axis perpendicular
+to the board will take this
+
+one that's down and rotate it
+to here and take this one
+
+that's up and rotate
+it to here.
+
+So that is the pattern of 222.
+
+We can snake a mirror plane in
+between the twofold axes, and
+
+a mirror plane passing through
+the vertical twofold axis has
+
+to be accompanied by one that's
+90 degrees away, half
+
+the throw of the axis, which
+comes from our theorem that
+
+says A pi dot sigma vertical
+has to be equal to a sigma
+
+prime that's vertical and pi/2
+away from the first.
+
+In terms of the pattern, this
+second mirror plane that comes
+
+up is going to reflect this one
+across to here, it's going
+
+to reflect this one across to
+here, it's going to take this
+
+one and reflect it over to here,
+and take this one and
+
+reflect it to the
+right, as well.
+
+So now we've got a total
+of eight objects.
+
+This one is right handed, and
+this one is also right handed
+
+because we repeated
+it by rotation.
+
+Then we reflected that pair, so
+these two are left handed,
+
+and reflect it across the other
+diagonal mirror plane.
+
+They're back to right handed
+again, and these have to be
+
+left handed as well, so
+there's the pattern.
+
+Is there an inversion center
+in this pattern?
+
+The answer is no, because there
+is no mirror plane that
+
+is perpendicular to a twofold
+axis, so this point group has
+
+no inversion in it.
+
+It's said to be acentric,
+without a inversion center.
+
+Do we know how everything is
+related to everything else?
+
+We know how this one
+is related to this
+
+one by twofold rotation.
+
+We know how this one is related
+to this one, and
+
+that's by reflection across
+the mirror plane.
+
+How is the first one related
+to this one?
+
+How do you get it through 90
+degrees and then pop it down
+
+and change the chirality?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: You can't do
+that in one step.
+
+You've got to do just what
+I said in words.
+
+Rotate it 90 degrees, don't put
+it down yet, and reflect
+
+it down in a horizontal
+mirror plane.
+
+This horizontal mirror plane
+is not a symmetry element,
+
+it's part of the operation
+that's necessary to get us
+
+from this guy over to this guy
+of opposite chirality.
+
+So this is an example
+a new type of
+
+operation, a 2 step operation.
+
+This is a 90-degree
+rotoreflection axis.
+
+And again, I feel compelled to
+put the axis in quotation
+
+marks, because really it's a
+pair of operations that leaves
+
+only a point unmoved,
+so it's really a
+
+point symmetry element.
+
+There's another way of
+describing the same thing, and
+
+that would be rotoinversion.
+
+We could rotate by 90 degrees in
+the reverse sense, not yet
+
+put it down, and invert,
+and we get, again,
+
+the relation between--
+
+what did I do?
+
+Rotate it here, yes--
+
+rotate to here and then invert,
+and we got that one.
+
+So that's another way of
+defining the relation.
+
+A 90-degree rotoreflection
+is a minus 90-degree
+
+rotoinversion.
+
+So you pays your money and you
+takes your choice, and what
+
+the groundbreakers who went
+before us did was to take
+
+rotoinversion.
+
+as the operation to survive.
+
+So here is, if we were not smart
+enough to invent it, our
+
+4-bar rotoinversion axis.
+
+So if we hadn't been clever
+enough-- and it would take a
+
+pretty clever, devious mind to
+invent a 2 step rotoinversion
+
+operation--
+
+as soon as we added this sort of
+extender, a diagonal mirror
+
+plane to a group of the form
+n22, we would have found that
+
+there was a new sort of
+transformation that could not
+
+be described any more simply
+than to say take
+
+two steps to do it.
+
+Rotate 90 degrees
+and then invert.
+
+So we have to add the operation
+of A pi over 2-bar
+
+to our basic bag of tricks
+for generating patterns.
+
+The group 32 is also a group to
+which we can add a diagonal
+
+mirror plane.
+
+And if you do that, again, the
+bold lines that are mirror
+
+planes in that group and the
+axes that are faint lines are
+
+easy to mix up.
+
+But if we examine that group
+without the confusing lines,
+
+here are the twofold axes.
+
+And remember that they are all
+equivalent to one another by
+
+the threefold axis.
+
+So this axial group
+is the group 32.
+
+If we put down a mirror plane
+interleaved between the
+
+twofold axes, notice that
+each of those mirror is
+
+perpendicular to
+a twofold axis.
+
+So we can write this as 2/m.
+
+2/m means there's an inversion
+center at the intersection of
+
+the twofold axes with
+the mirror planes.
+
+And a inversion center sitting
+on a threefold axis makes it a
+
+3-bar axis, so this group
+is called 3-bar 2/m.
+
+And the pattern is what a
+twofold axis would do.
+
+These would be up-down-right
+ones.
+
+Reflect those and you get an
+up-down pair of left ones.
+
+Reflect again and you get
+an up-down pair of
+
+right-handed ones.
+
+Reflect yet again, and you
+get an up-down pair
+
+of left-handed ones.
+
+Reflect still once more, and
+you get a down-up pair of
+
+right-handed ones.
+
+One more time, up-down
+left-handed ones.
+
+So you get a total of 2,
+4, 6, 8, 10, 12 points.
+
+So this is 3-bar 2/m in
+Schoenflies notation D3--
+
+that's the symbol 32--
+
+with a diagonal mirror
+plane added.
+
+You indicate that by a
+d in the subscript.
+
+OK.
+
+I think that's probably a point
+where you're more than
+
+ready for a break.
+
+We've got very few yet to do.
+
+One surprise is that if you add
+diagonal mirror planes to
+
+422 and 622, you get perfectly
+lovely exquisite groups but
+
+they're not crystallographic,
+so we don't
+
+include them in our list.
+
+But we'll discuss them when we
+come back, and then take a
+
+look also at the cubic
+symmetries.
+
+Impossible to draw, but really
+not all that difficult to
+
+understand.
+
+So let's stop at this point
+and take a stretch.
+
+People are stretching already.
+
+They need it.
+
+We'll resume in 10
+minutes' time.
\ No newline at end of file
diff --git a/BKo57m-uU1k.txt b/BKo57m-uU1k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1cfed89a9f75ab26e6e920031b9964fb1f222634
--- /dev/null
+++ b/BKo57m-uU1k.txt
@@ -0,0 +1,10443 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a quick problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might want to grab a pen and paper
+
+ align:start position:0%
+you might want to grab a pen and paper
+ 
+
+ align:start position:0%
+you might want to grab a pen and paper
+and it I think it's not that hard but
+
+ align:start position:0%
+and it I think it's not that hard but
+ 
+
+ align:start position:0%
+and it I think it's not that hard but
+let's just ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say we have this function which is
+
+ align:start position:0%
+let's say we have this function which is
+ 
+
+ align:start position:0%
+let's say we have this function which is
+just the two Norm of x
+
+ align:start position:0%
+just the two Norm of x
+ 
+
+ align:start position:0%
+just the two Norm of x
+from RN to R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so everybody knows this function
+
+ align:start position:0%
+right so everybody knows this function
+ 
+
+ align:start position:0%
+right so everybody knows this function
+of course it's the square root of X1
+
+ align:start position:0%
+of course it's the square root of X1
+ 
+
+ align:start position:0%
+of course it's the square root of X1
+squared up to X N squared
+
+ align:start position:0%
+squared up to X N squared
+ 
+
+ align:start position:0%
+squared up to X N squared
+right so a vector goes in the scalar
+
+ align:start position:0%
+right so a vector goes in the scalar
+ 
+
+ align:start position:0%
+right so a vector goes in the scalar
+comes out and my simple question is what
+
+ align:start position:0%
+comes out and my simple question is what
+ 
+
+ align:start position:0%
+comes out and my simple question is what
+is the gradient
+
+ align:start position:0%
+is the gradient
+ 
+
+ align:start position:0%
+is the gradient
+of this function
+
+ align:start position:0%
+of this function
+ 
+
+ align:start position:0%
+of this function
+and the reason why I'm putting this up
+
+ align:start position:0%
+and the reason why I'm putting this up
+ 
+
+ align:start position:0%
+and the reason why I'm putting this up
+in part is because I suspect everybody
+
+ align:start position:0%
+in part is because I suspect everybody
+ 
+
+ align:start position:0%
+in part is because I suspect everybody
+in the room can do this the 1802 way
+
+ align:start position:0%
+in the room can do this the 1802 way
+ 
+
+ align:start position:0%
+in the room can do this the 1802 way
+with indices and if you'd like to do it
+
+ align:start position:0%
+with indices and if you'd like to do it
+ 
+
+ align:start position:0%
+with indices and if you'd like to do it
+that way because that's where your
+
+ align:start position:0%
+that way because that's where your
+ 
+
+ align:start position:0%
+that way because that's where your
+comfort is that's fine
+
+ align:start position:0%
+comfort is that's fine
+ 
+
+ align:start position:0%
+comfort is that's fine
+but I think the real challenge is if you
+
+ align:start position:0%
+but I think the real challenge is if you
+ 
+
+ align:start position:0%
+but I think the real challenge is if you
+to kind of exercise what you've learned
+
+ align:start position:0%
+to kind of exercise what you've learned
+ 
+
+ align:start position:0%
+to kind of exercise what you've learned
+so far is to see if you can do this
+
+ align:start position:0%
+so far is to see if you can do this
+ 
+
+ align:start position:0%
+so far is to see if you can do this
+without indices that what I call the
+
+ align:start position:0%
+without indices that what I call the
+ 
+
+ align:start position:0%
+without indices that what I call the
+grown-up way right there's no right and
+
+ align:start position:0%
+grown-up way right there's no right and
+ 
+
+ align:start position:0%
+grown-up way right there's no right and
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+um if you get the right answer that's
+
+ align:start position:0%
+um if you get the right answer that's
+ 
+
+ align:start position:0%
+um if you get the right answer that's
+fine but of course I think that that I
+
+ align:start position:0%
+fine but of course I think that that I
+ 
+
+ align:start position:0%
+fine but of course I think that that I
+think that the the comfortable way is is
+
+ align:start position:0%
+think that the the comfortable way is is
+ 
+
+ align:start position:0%
+think that the the comfortable way is is
+well comfortable for everybody and the
+
+ align:start position:0%
+well comfortable for everybody and the
+ 
+
+ align:start position:0%
+well comfortable for everybody and the
+grown-up way takes some practice so let
+
+ align:start position:0%
+grown-up way takes some practice so let
+ 
+
+ align:start position:0%
+grown-up way takes some practice so let
+me put this up and I'll go through it in
+
+ align:start position:0%
+me put this up and I'll go through it in
+ 
+
+ align:start position:0%
+me put this up and I'll go through it in
+a moment so
+
+ align:start position:0%
+a moment so
+ 
+
+ align:start position:0%
+a moment so
+a simple question the gradient of this
+
+ align:start position:0%
+a simple question the gradient of this
+ 
+
+ align:start position:0%
+a simple question the gradient of this
+of this function and
+
+ align:start position:0%
+of this function and
+ 
+
+ align:start position:0%
+of this function and
+I think the 1802 way might be to start
+
+ align:start position:0%
+I think the 1802 way might be to start
+ 
+
+ align:start position:0%
+I think the 1802 way might be to start
+with the first component but pretty
+
+ align:start position:0%
+with the first component but pretty
+ 
+
+ align:start position:0%
+with the first component but pretty
+quickly you realize that every
+
+ align:start position:0%
+quickly you realize that every
+ 
+
+ align:start position:0%
+quickly you realize that every
+component's the same right so you you
+
+ align:start position:0%
+component's the same right so you you
+ 
+
+ align:start position:0%
+component's the same right so you you
+might start calculating for example d
+
+ align:start position:0%
+might start calculating for example d
+ 
+
+ align:start position:0%
+might start calculating for example d
+dx1
+
+ align:start position:0%
+dx1
+ 
+
+ align:start position:0%
+dx1
+of the square root of X1 squared plus X
+
+ align:start position:0%
+of the square root of X1 squared plus X
+ 
+
+ align:start position:0%
+of the square root of X1 squared plus X
+N squared
+
+ align:start position:0%
+N squared
+ 
+
+ align:start position:0%
+N squared
+right and
+
+ align:start position:0%
+right and
+ 
+
+ align:start position:0%
+right and
+you know using all the calculus you
+
+ align:start position:0%
+you know using all the calculus you
+ 
+
+ align:start position:0%
+you know using all the calculus you
+remember the derivative of something to
+
+ align:start position:0%
+remember the derivative of something to
+ 
+
+ align:start position:0%
+remember the derivative of something to
+the one-half is the same thing to the
+
+ align:start position:0%
+the one-half is the same thing to the
+ 
+
+ align:start position:0%
+the one-half is the same thing to the
+negative one-half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then you would
+
+ align:start position:0%
+right and then you would
+ 
+
+ align:start position:0%
+right and then you would
+you would get 2x1 so this would be one
+
+ align:start position:0%
+you would get 2x1 so this would be one
+ 
+
+ align:start position:0%
+you would get 2x1 so this would be one
+times two x one
+
+ align:start position:0%
+times two x one
+ 
+
+ align:start position:0%
+times two x one
+right and you would have X1 over the
+
+ align:start position:0%
+right and you would have X1 over the
+ 
+
+ align:start position:0%
+right and you would have X1 over the
+square root of X1 squared plus xn
+
+ align:start position:0%
+square root of X1 squared plus xn
+ 
+
+ align:start position:0%
+square root of X1 squared plus xn
+squared okay and it wouldn't take you
+
+ align:start position:0%
+squared okay and it wouldn't take you
+ 
+
+ align:start position:0%
+squared okay and it wouldn't take you
+long to realize that if you did X2
+
+ align:start position:0%
+long to realize that if you did X2
+ 
+
+ align:start position:0%
+long to realize that if you did X2
+there's no real difference and before
+
+ align:start position:0%
+there's no real difference and before
+ 
+
+ align:start position:0%
+there's no real difference and before
+you knew it you would find out that
+
+ align:start position:0%
+you knew it you would find out that
+ 
+
+ align:start position:0%
+you knew it you would find out that
+the gradient of course would be the
+
+ align:start position:0%
+the gradient of course would be the
+ 
+
+ align:start position:0%
+the gradient of course would be the
+vector x divided by its length that
+
+ align:start position:0%
+vector x divided by its length that
+ 
+
+ align:start position:0%
+vector x divided by its length that
+gives you every com right and that would
+
+ align:start position:0%
+gives you every com right and that would
+ 
+
+ align:start position:0%
+gives you every com right and that would
+be the what I would call the 1802 way
+
+ align:start position:0%
+be the what I would call the 1802 way
+ 
+
+ align:start position:0%
+be the what I would call the 1802 way
+and it's not so bad okay but in this
+
+ align:start position:0%
+and it's not so bad okay but in this
+ 
+
+ align:start position:0%
+and it's not so bad okay but in this
+class we're trying to see if we can
+
+ align:start position:0%
+class we're trying to see if we can
+ 
+
+ align:start position:0%
+class we're trying to see if we can
+avoid using indices sometimes you can't
+
+ align:start position:0%
+avoid using indices sometimes you can't
+ 
+
+ align:start position:0%
+avoid using indices sometimes you can't
+many times you can right and so we want
+
+ align:start position:0%
+many times you can right and so we want
+ 
+
+ align:start position:0%
+many times you can right and so we want
+to emphasize the ability to not use
+
+ align:start position:0%
+to emphasize the ability to not use
+ 
+
+ align:start position:0%
+to emphasize the ability to not use
+indices
+
+ align:start position:0%
+indices
+ 
+
+ align:start position:0%
+indices
+okay and so I don't know has anyone
+
+ align:start position:0%
+okay and so I don't know has anyone
+ 
+
+ align:start position:0%
+okay and so I don't know has anyone
+already written it out for the or
+
+ align:start position:0%
+already written it out for the or
+ 
+
+ align:start position:0%
+already written it out for the or
+convince themselves they could do it
+
+ align:start position:0%
+convince themselves they could do it
+ 
+
+ align:start position:0%
+convince themselves they could do it
+without indices yet
+
+ align:start position:0%
+without indices yet
+ 
+
+ align:start position:0%
+without indices yet
+has anyone done it yet
+
+ align:start position:0%
+has anyone done it yet
+ 
+
+ align:start position:0%
+has anyone done it yet
+but you think you can do it
+
+ align:start position:0%
+but you think you can do it
+ 
+
+ align:start position:0%
+but you think you can do it
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+I'm going to write down
+
+ align:start position:0%
+I'm going to write down
+ 
+
+ align:start position:0%
+I'm going to write down
+R is equal to the length of x
+
+ align:start position:0%
+R is equal to the length of x
+ 
+
+ align:start position:0%
+R is equal to the length of x
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+and therefore our our squared is X
+
+ align:start position:0%
+and therefore our our squared is X
+ 
+
+ align:start position:0%
+and therefore our our squared is X
+transpose X right this is sort of the
+
+ align:start position:0%
+transpose X right this is sort of the
+ 
+
+ align:start position:0%
+transpose X right this is sort of the
+the linear algebra way to set things up
+
+ align:start position:0%
+the linear algebra way to set things up
+ 
+
+ align:start position:0%
+the linear algebra way to set things up
+right and then I'm just going to take
+
+ align:start position:0%
+right and then I'm just going to take
+ 
+
+ align:start position:0%
+right and then I'm just going to take
+the differential of both sides and get 2
+
+ align:start position:0%
+the differential of both sides and get 2
+ 
+
+ align:start position:0%
+the differential of both sides and get 2
+r d r
+
+ align:start position:0%
+r d r
+ 
+
+ align:start position:0%
+r d r
+equals and we we know this differential
+
+ align:start position:0%
+equals and we we know this differential
+ 
+
+ align:start position:0%
+equals and we we know this differential
+so I can just write it down but if you
+
+ align:start position:0%
+so I can just write it down but if you
+ 
+
+ align:start position:0%
+so I can just write it down but if you
+forgot it you can get it yourself
+
+ align:start position:0%
+forgot it you can get it yourself
+ 
+
+ align:start position:0%
+forgot it you can get it yourself
+right so um two oh sorry this is Dr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is two x transpose DX
+
+ align:start position:0%
+is two x transpose DX
+ 
+
+ align:start position:0%
+is two x transpose DX
+right and so therefore
+
+ align:start position:0%
+right and so therefore
+ 
+
+ align:start position:0%
+right and so therefore
+Dr is equal to X transpose over RDX and
+
+ align:start position:0%
+Dr is equal to X transpose over RDX and
+ 
+
+ align:start position:0%
+Dr is equal to X transpose over RDX and
+then the gradient
+
+ align:start position:0%
+then the gradient
+ 
+
+ align:start position:0%
+then the gradient
+is the transpose of this which is X over
+
+ align:start position:0%
+is the transpose of this which is X over
+ 
+
+ align:start position:0%
+is the transpose of this which is X over
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+okay so no indices that that was kind of
+
+ align:start position:0%
+okay so no indices that that was kind of
+ 
+
+ align:start position:0%
+okay so no indices that that was kind of
+the trick here just to be able to do
+
+ align:start position:0%
+the trick here just to be able to do
+ 
+
+ align:start position:0%
+the trick here just to be able to do
+this sort of thing without any indices
+
+ align:start position:0%
+this sort of thing without any indices
+ 
+
+ align:start position:0%
+this sort of thing without any indices
+okay kind of like
+
+ align:start position:0%
+okay kind of like
+ 
+
+ align:start position:0%
+okay kind of like
+super powers for vectors and matrices to
+
+ align:start position:0%
+super powers for vectors and matrices to
+ 
+
+ align:start position:0%
+super powers for vectors and matrices to
+like I said this isn't hard
+
+ align:start position:0%
+like I said this isn't hard
+ 
+
+ align:start position:0%
+like I said this isn't hard
+what happens though is as things get a
+
+ align:start position:0%
+what happens though is as things get a
+ 
+
+ align:start position:0%
+what happens though is as things get a
+little more complicated have been good
+
+ align:start position:0%
+little more complicated have been good
+ 
+
+ align:start position:0%
+little more complicated have been good
+at this sort of the non-index approach
+
+ align:start position:0%
+at this sort of the non-index approach
+ 
+
+ align:start position:0%
+at this sort of the non-index approach
+gets more and more valuable
+
+ align:start position:0%
+gets more and more valuable
+ 
+
+ align:start position:0%
+gets more and more valuable
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+again there's no one right way to do it
+
+ align:start position:0%
+again there's no one right way to do it
+ 
+
+ align:start position:0%
+again there's no one right way to do it
+you could you could grind it through no
+
+ align:start position:0%
+you could you could grind it through no
+ 
+
+ align:start position:0%
+you could you could grind it through no
+matter how complicated I bet you all can
+
+ align:start position:0%
+matter how complicated I bet you all can
+ 
+
+ align:start position:0%
+matter how complicated I bet you all can
+do it but this is the fun way to do it
+
+ align:start position:0%
+do it but this is the fun way to do it
+ 
+
+ align:start position:0%
+do it but this is the fun way to do it
+all right lose this thing over here any
+
+ align:start position:0%
+all right lose this thing over here any
+ 
+
+ align:start position:0%
+all right lose this thing over here any
+questions about that
+
+ align:start position:0%
+questions about that
+ 
+
+ align:start position:0%
+questions about that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I don't know if you've looked at the
+
+ align:start position:0%
+so I don't know if you've looked at the
+ 
+
+ align:start position:0%
+so I don't know if you've looked at the
+homework yet but uh the first problem
+
+ align:start position:0%
+homework yet but uh the first problem
+ 
+
+ align:start position:0%
+homework yet but uh the first problem
+has the transformations of the plane
+
+ align:start position:0%
+has the transformations of the plane
+ 
+
+ align:start position:0%
+has the transformations of the plane
+with the corgis and we're looking for
+
+ align:start position:0%
+with the corgis and we're looking for
+ 
+
+ align:start position:0%
+with the corgis and we're looking for
+two by two Jacobian matrices and in one
+
+ align:start position:0%
+two by two Jacobian matrices and in one
+ 
+
+ align:start position:0%
+two by two Jacobian matrices and in one
+case there's a there there's
+
+ align:start position:0%
+case there's a there there's
+ 
+
+ align:start position:0%
+case there's a there there's
+in in part D where there where where
+
+ align:start position:0%
+in in part D where there where where
+ 
+
+ align:start position:0%
+in in part D where there where where
+there's the warp there's a a matrix
+
+ align:start position:0%
+there's the warp there's a a matrix
+ 
+
+ align:start position:0%
+there's the warp there's a a matrix
+function of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's multiplied by X
+
+ align:start position:0%
+that's multiplied by X
+ 
+
+ align:start position:0%
+that's multiplied by X
+right if the Matrix didn't depend on X
+
+ align:start position:0%
+right if the Matrix didn't depend on X
+ 
+
+ align:start position:0%
+right if the Matrix didn't depend on X
+the Jacobian would just be the Matrix
+
+ align:start position:0%
+the Jacobian would just be the Matrix
+ 
+
+ align:start position:0%
+the Jacobian would just be the Matrix
+right but because the Matrix depends on
+
+ align:start position:0%
+right but because the Matrix depends on
+ 
+
+ align:start position:0%
+right but because the Matrix depends on
+X there's going to be two terms right
+
+ align:start position:0%
+X there's going to be two terms right
+ 
+
+ align:start position:0%
+X there's going to be two terms right
+there's going to be
+
+ align:start position:0%
+there's going to be
+ 
+
+ align:start position:0%
+there's going to be
+roughly D Matrix
+
+ align:start position:0%
+roughly D Matrix
+ 
+
+ align:start position:0%
+roughly D Matrix
+of of x times X plus this is kind of the
+
+ align:start position:0%
+of of x times X plus this is kind of the
+ 
+
+ align:start position:0%
+of of x times X plus this is kind of the
+the template
+
+ align:start position:0%
+the template
+ 
+
+ align:start position:0%
+the template
+right and somehow a DX is going to come
+
+ align:start position:0%
+right and somehow a DX is going to come
+ 
+
+ align:start position:0%
+right and somehow a DX is going to come
+out of this term as well and so this
+
+ align:start position:0%
+out of this term as well and so this
+ 
+
+ align:start position:0%
+out of this term as well and so this
+term is the easy one that that would if
+
+ align:start position:0%
+term is the easy one that that would if
+ 
+
+ align:start position:0%
+term is the easy one that that would if
+if the Matrix is constant right and this
+
+ align:start position:0%
+if the Matrix is constant right and this
+ 
+
+ align:start position:0%
+if the Matrix is constant right and this
+one takes a little bit more work right
+
+ align:start position:0%
+one takes a little bit more work right
+ 
+
+ align:start position:0%
+one takes a little bit more work right
+so that's problem D on your homework in
+
+ align:start position:0%
+so that's problem D on your homework in
+ 
+
+ align:start position:0%
+so that's problem D on your homework in
+the first part
+
+ align:start position:0%
+the first part
+ 
+
+ align:start position:0%
+the first part
+all right good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay well then I'm going to go back
+
+ align:start position:0%
+um okay well then I'm going to go back
+ 
+
+ align:start position:0%
+um okay well then I'm going to go back
+and do what I was starting to do
+
+ align:start position:0%
+and do what I was starting to do
+ 
+
+ align:start position:0%
+and do what I was starting to do
+less time and I think it just makes
+
+ align:start position:0%
+less time and I think it just makes
+ 
+
+ align:start position:0%
+less time and I think it just makes
+sense to go back to the beginning since
+
+ align:start position:0%
+sense to go back to the beginning since
+ 
+
+ align:start position:0%
+sense to go back to the beginning since
+we've had a whole weekend since
+
+ align:start position:0%
+we've had a whole weekend since
+ 
+
+ align:start position:0%
+we've had a whole weekend since
+last time okay and so uh Matrix Jacobian
+
+ align:start position:0%
+last time okay and so uh Matrix Jacobian
+ 
+
+ align:start position:0%
+last time okay and so uh Matrix Jacobian
+so in this this this Julia notebook here
+
+ align:start position:0%
+so in this this this Julia notebook here
+ 
+
+ align:start position:0%
+so in this this this Julia notebook here
+and by the way if anybody has questions
+
+ align:start position:0%
+and by the way if anybody has questions
+ 
+
+ align:start position:0%
+and by the way if anybody has questions
+about Julia if you feel free to ask
+
+ align:start position:0%
+about Julia if you feel free to ask
+ 
+
+ align:start position:0%
+about Julia if you feel free to ask
+about that as well but the the goal here
+
+ align:start position:0%
+about that as well but the the goal here
+ 
+
+ align:start position:0%
+about that as well but the the goal here
+this is a this Blackboard example is a
+
+ align:start position:0%
+this is a this Blackboard example is a
+ 
+
+ align:start position:0%
+this is a this Blackboard example is a
+scalar function of a vector
+
+ align:start position:0%
+scalar function of a vector
+ 
+
+ align:start position:0%
+scalar function of a vector
+and I'm really excited about functions
+
+ align:start position:0%
+and I'm really excited about functions
+ 
+
+ align:start position:0%
+and I'm really excited about functions
+where the input and output are actually
+
+ align:start position:0%
+where the input and output are actually
+ 
+
+ align:start position:0%
+where the input and output are actually
+matrices themselves right so you know
+
+ align:start position:0%
+matrices themselves right so you know
+ 
+
+ align:start position:0%
+matrices themselves right so you know
+Matrix Square Matrix inverse we've seen
+
+ align:start position:0%
+Matrix Square Matrix inverse we've seen
+ 
+
+ align:start position:0%
+Matrix Square Matrix inverse we've seen
+Matrix Cube I like to think of the Lu
+
+ align:start position:0%
+Matrix Cube I like to think of the Lu
+ 
+
+ align:start position:0%
+Matrix Cube I like to think of the Lu
+decomposition as a as a function of
+
+ align:start position:0%
+decomposition as a as a function of
+ 
+
+ align:start position:0%
+decomposition as a as a function of
+matrices I don't know if you've ever
+
+ align:start position:0%
+matrices I don't know if you've ever
+ 
+
+ align:start position:0%
+matrices I don't know if you've ever
+thought about it but the Lu
+
+ align:start position:0%
+thought about it but the Lu
+ 
+
+ align:start position:0%
+thought about it but the Lu
+decomposition or even the eigen Dig
+
+ align:start position:0%
+decomposition or even the eigen Dig
+ 
+
+ align:start position:0%
+decomposition or even the eigen Dig
+composition of a matrix is is a function
+
+ align:start position:0%
+composition of a matrix is is a function
+ 
+
+ align:start position:0%
+composition of a matrix is is a function
+from matrices to
+
+ align:start position:0%
+from matrices to
+ 
+
+ align:start position:0%
+from matrices to
+pieces of matrices in effect
+
+ align:start position:0%
+pieces of matrices in effect
+ 
+
+ align:start position:0%
+pieces of matrices in effect
+so uh we'll we'll see how that goes
+
+ align:start position:0%
+so uh we'll we'll see how that goes
+ 
+
+ align:start position:0%
+so uh we'll we'll see how that goes
+through all right so
+
+ align:start position:0%
+through all right so
+ 
+
+ align:start position:0%
+through all right so
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+go back to the beginning here just very
+
+ align:start position:0%
+go back to the beginning here just very
+ 
+
+ align:start position:0%
+go back to the beginning here just very
+quickly we're using Julia's symbolics
+
+ align:start position:0%
+quickly we're using Julia's symbolics
+ 
+
+ align:start position:0%
+quickly we're using Julia's symbolics
+which is kind of fun to do
+
+ align:start position:0%
+which is kind of fun to do
+ 
+
+ align:start position:0%
+which is kind of fun to do
+okay and this shows up later I don't
+
+ align:start position:0%
+okay and this shows up later I don't
+ 
+
+ align:start position:0%
+okay and this shows up later I don't
+know why it's at the beginning so we'll
+
+ align:start position:0%
+know why it's at the beginning so we'll
+ 
+
+ align:start position:0%
+know why it's at the beginning so we'll
+just get right past it but here's the
+
+ align:start position:0%
+just get right past it but here's the
+ 
+
+ align:start position:0%
+just get right past it but here's the
+Matrix that will work with a lot this is
+
+ align:start position:0%
+Matrix that will work with a lot this is
+ 
+
+ align:start position:0%
+Matrix that will work with a lot this is
+the symbolic Matrix that has pqrs going
+
+ align:start position:0%
+the symbolic Matrix that has pqrs going
+ 
+
+ align:start position:0%
+the symbolic Matrix that has pqrs going
+in the column major order
+
+ align:start position:0%
+in the column major order
+ 
+
+ align:start position:0%
+in the column major order
+okay and so I just declared PQ and R and
+
+ align:start position:0%
+okay and so I just declared PQ and R and
+ 
+
+ align:start position:0%
+okay and so I just declared PQ and R and
+S to be variables as well as Theta so
+
+ align:start position:0%
+S to be variables as well as Theta so
+ 
+
+ align:start position:0%
+S to be variables as well as Theta so
+Julia lets me put them in as elements of
+
+ align:start position:0%
+Julia lets me put them in as elements of
+ 
+
+ align:start position:0%
+Julia lets me put them in as elements of
+matrices okay so simple thing and last
+
+ align:start position:0%
+matrices okay so simple thing and last
+ 
+
+ align:start position:0%
+matrices okay so simple thing and last
+time I introduced the VEC command which
+
+ align:start position:0%
+time I introduced the VEC command which
+ 
+
+ align:start position:0%
+time I introduced the VEC command which
+basically squashes a two by two Matrix
+
+ align:start position:0%
+basically squashes a two by two Matrix
+ 
+
+ align:start position:0%
+basically squashes a two by two Matrix
+or any in fact any Matrix down to a
+
+ align:start position:0%
+or any in fact any Matrix down to a
+ 
+
+ align:start position:0%
+or any in fact any Matrix down to a
+vector it's just all you do with VEC in
+
+ align:start position:0%
+vector it's just all you do with VEC in
+ 
+
+ align:start position:0%
+vector it's just all you do with VEC in
+case you missed it last time is you take
+
+ align:start position:0%
+case you missed it last time is you take
+ 
+
+ align:start position:0%
+case you missed it last time is you take
+the First Column and stack it on the
+
+ align:start position:0%
+the First Column and stack it on the
+ 
+
+ align:start position:0%
+the First Column and stack it on the
+second column stack it on the third
+
+ align:start position:0%
+second column stack it on the third
+ 
+
+ align:start position:0%
+second column stack it on the third
+column and so forth okay and this is
+
+ align:start position:0%
+column and so forth okay and this is
+ 
+
+ align:start position:0%
+column and so forth okay and this is
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+what we show students because it's
+
+ align:start position:0%
+what we show students because it's
+ 
+
+ align:start position:0%
+what we show students because it's
+concrete
+
+ align:start position:0%
+concrete
+ 
+
+ align:start position:0%
+concrete
+but as far as I can tell you never
+
+ align:start position:0%
+but as far as I can tell you never
+ 
+
+ align:start position:0%
+but as far as I can tell you never
+really need to vect things other than
+
+ align:start position:0%
+really need to vect things other than
+ 
+
+ align:start position:0%
+really need to vect things other than
+maybe in your mind right but I mean it
+
+ align:start position:0%
+maybe in your mind right but I mean it
+ 
+
+ align:start position:0%
+maybe in your mind right but I mean it
+it's another one of these Comfort things
+
+ align:start position:0%
+it's another one of these Comfort things
+ 
+
+ align:start position:0%
+it's another one of these Comfort things
+that I don't think you really have to do
+
+ align:start position:0%
+that I don't think you really have to do
+ 
+
+ align:start position:0%
+that I don't think you really have to do
+in practice okay but it does have a way
+
+ align:start position:0%
+in practice okay but it does have a way
+ 
+
+ align:start position:0%
+in practice okay but it does have a way
+of of of allowing you to use one
+
+ align:start position:0%
+of of of allowing you to use one
+ 
+
+ align:start position:0%
+of of of allowing you to use one
+notation for many many things so there's
+
+ align:start position:0%
+notation for many many things so there's
+ 
+
+ align:start position:0%
+notation for many many things so there's
+the vet command it just squashes a
+
+ align:start position:0%
+the vet command it just squashes a
+ 
+
+ align:start position:0%
+the vet command it just squashes a
+matrix okay and
+
+ align:start position:0%
+matrix okay and
+ 
+
+ align:start position:0%
+matrix okay and
+and here's the Matrix square of a two by
+
+ align:start position:0%
+and here's the Matrix square of a two by
+ 
+
+ align:start position:0%
+and here's the Matrix square of a two by
+two Matrix all of you can do this just
+
+ align:start position:0%
+two Matrix all of you can do this just
+ 
+
+ align:start position:0%
+two Matrix all of you can do this just
+take that pqrs Matrix and do that dot
+
+ align:start position:0%
+take that pqrs Matrix and do that dot
+ 
+
+ align:start position:0%
+take that pqrs Matrix and do that dot
+product the thing and you get the Matrix
+
+ align:start position:0%
+product the thing and you get the Matrix
+ 
+
+ align:start position:0%
+product the thing and you get the Matrix
+Square which we convex
+
+ align:start position:0%
+Square which we convex
+ 
+
+ align:start position:0%
+Square which we convex
+right and maybe I'll make this just a
+
+ align:start position:0%
+right and maybe I'll make this just a
+ 
+
+ align:start position:0%
+right and maybe I'll make this just a
+little bit smaller so it can get a
+
+ align:start position:0%
+little bit smaller so it can get a
+ 
+
+ align:start position:0%
+little bit smaller so it can get a
+little more real estate
+
+ align:start position:0%
+little more real estate
+ 
+
+ align:start position:0%
+little more real estate
+yeah so uh okay good
+
+ align:start position:0%
+yeah so uh okay good
+ 
+
+ align:start position:0%
+yeah so uh okay good
+so this this is this is the VEC of the
+
+ align:start position:0%
+so this this is this is the VEC of the
+ 
+
+ align:start position:0%
+so this this is this is the VEC of the
+The Matrix square and so uh one way to
+
+ align:start position:0%
+The Matrix square and so uh one way to
+ 
+
+ align:start position:0%
+The Matrix square and so uh one way to
+think of Matrix square is a function
+
+ align:start position:0%
+think of Matrix square is a function
+ 
+
+ align:start position:0%
+think of Matrix square is a function
+from R4 to R4 it's the input of the
+
+ align:start position:0%
+from R4 to R4 it's the input of the
+ 
+
+ align:start position:0%
+from R4 to R4 it's the input of the
+variables P Q R and S and the output are
+
+ align:start position:0%
+variables P Q R and S and the output are
+ 
+
+ align:start position:0%
+variables P Q R and S and the output are
+these four functions of pqr and S you
+
+ align:start position:0%
+these four functions of pqr and S you
+ 
+
+ align:start position:0%
+these four functions of pqr and S you
+know p squared plus q r all the way down
+
+ align:start position:0%
+know p squared plus q r all the way down
+ 
+
+ align:start position:0%
+know p squared plus q r all the way down
+to q r plus s squared
+
+ align:start position:0%
+to q r plus s squared
+ 
+
+ align:start position:0%
+to q r plus s squared
+right so that that's a function that
+
+ align:start position:0%
+right so that that's a function that
+ 
+
+ align:start position:0%
+right so that that's a function that
+takes R4 to R4 but really we all know
+
+ align:start position:0%
+takes R4 to R4 but really we all know
+ 
+
+ align:start position:0%
+takes R4 to R4 but really we all know
+it's a function from two by two matrices
+
+ align:start position:0%
+it's a function from two by two matrices
+ 
+
+ align:start position:0%
+it's a function from two by two matrices
+to two by two matrices right R4 tar4 is
+
+ align:start position:0%
+to two by two matrices right R4 tar4 is
+ 
+
+ align:start position:0%
+to two by two matrices right R4 tar4 is
+just a crutch right it's really two by
+
+ align:start position:0%
+just a crutch right it's really two by
+ 
+
+ align:start position:0%
+just a crutch right it's really two by
+two matrices to two by two matrices
+
+ align:start position:0%
+two matrices to two by two matrices
+ 
+
+ align:start position:0%
+two matrices to two by two matrices
+okay and so we can calculate the
+
+ align:start position:0%
+okay and so we can calculate the
+ 
+
+ align:start position:0%
+okay and so we can calculate the
+Jacobian of this thing
+
+ align:start position:0%
+Jacobian of this thing
+ 
+
+ align:start position:0%
+Jacobian of this thing
+okay and I'll just remind you that the
+
+ align:start position:0%
+okay and I'll just remind you that the
+ 
+
+ align:start position:0%
+okay and I'll just remind you that the
+Jacobian is nothing other than all the
+
+ align:start position:0%
+Jacobian is nothing other than all the
+ 
+
+ align:start position:0%
+Jacobian is nothing other than all the
+derivatives of each of these four
+
+ align:start position:0%
+derivatives of each of these four
+ 
+
+ align:start position:0%
+derivatives of each of these four
+expressions with respect to all of the
+
+ align:start position:0%
+expressions with respect to all of the
+ 
+
+ align:start position:0%
+expressions with respect to all of the
+four input variables P Q R and S right
+
+ align:start position:0%
+four input variables P Q R and S right
+ 
+
+ align:start position:0%
+four input variables P Q R and S right
+so so this output p squared plus QR
+
+ align:start position:0%
+so so this output p squared plus QR
+ 
+
+ align:start position:0%
+so so this output p squared plus QR
+belongs to the first row and we'll take
+
+ align:start position:0%
+belongs to the first row and we'll take
+ 
+
+ align:start position:0%
+belongs to the first row and we'll take
+the derivative respect to p and then q
+
+ align:start position:0%
+the derivative respect to p and then q
+ 
+
+ align:start position:0%
+the derivative respect to p and then q
+and then R and then s and if you do that
+
+ align:start position:0%
+and then R and then s and if you do that
+ 
+
+ align:start position:0%
+and then R and then s and if you do that
+you'll get this first row okay and so
+
+ align:start position:0%
+you'll get this first row okay and so
+ 
+
+ align:start position:0%
+you'll get this first row okay and so
+forth so the the inputs the are the
+
+ align:start position:0%
+forth so the the inputs the are the
+ 
+
+ align:start position:0%
+forth so the the inputs the are the
+columns the outputs are the rows okay
+
+ align:start position:0%
+columns the outputs are the rows okay
+ 
+
+ align:start position:0%
+columns the outputs are the rows okay
+and that's the Jacobian matrix okay and
+
+ align:start position:0%
+and that's the Jacobian matrix okay and
+ 
+
+ align:start position:0%
+and that's the Jacobian matrix okay and
+Julia's happy to compute it for you but
+
+ align:start position:0%
+Julia's happy to compute it for you but
+ 
+
+ align:start position:0%
+Julia's happy to compute it for you but
+you could have all done this yourself as
+
+ align:start position:0%
+you could have all done this yourself as
+ 
+
+ align:start position:0%
+you could have all done this yourself as
+well okay so there's the Jacobian and
+
+ align:start position:0%
+well okay so there's the Jacobian and
+ 
+
+ align:start position:0%
+well okay so there's the Jacobian and
+our goal
+
+ align:start position:0%
+our goal
+ 
+
+ align:start position:0%
+our goal
+is to our goal is really to find the
+
+ align:start position:0%
+is to our goal is really to find the
+ 
+
+ align:start position:0%
+is to our goal is really to find the
+notation that lets you write this Matrix
+
+ align:start position:0%
+notation that lets you write this Matrix
+ 
+
+ align:start position:0%
+notation that lets you write this Matrix
+without writing the Matrix that's what
+
+ align:start position:0%
+without writing the Matrix that's what
+ 
+
+ align:start position:0%
+without writing the Matrix that's what
+we're trying to do here we'd like to
+
+ align:start position:0%
+we're trying to do here we'd like to
+ 
+
+ align:start position:0%
+we're trying to do here we'd like to
+write this Matrix but without writing
+
+ align:start position:0%
+write this Matrix but without writing
+ 
+
+ align:start position:0%
+write this Matrix but without writing
+the Matrix that's what we're heading for
+
+ align:start position:0%
+the Matrix that's what we're heading for
+ 
+
+ align:start position:0%
+the Matrix that's what we're heading for
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+I love to check things over I like to do
+
+ align:start position:0%
+I love to check things over I like to do
+ 
+
+ align:start position:0%
+I love to check things over I like to do
+things with symbols if I can I like to
+
+ align:start position:0%
+things with symbols if I can I like to
+ 
+
+ align:start position:0%
+things with symbols if I can I like to
+do things with numbers if I can it makes
+
+ align:start position:0%
+do things with numbers if I can it makes
+ 
+
+ align:start position:0%
+do things with numbers if I can it makes
+me happy when things come out equal so
+
+ align:start position:0%
+me happy when things come out equal so
+ 
+
+ align:start position:0%
+me happy when things come out equal so
+let's do this numerically right so
+
+ align:start position:0%
+let's do this numerically right so
+ 
+
+ align:start position:0%
+let's do this numerically right so
+here's my inputs are going to be one two
+
+ align:start position:0%
+here's my inputs are going to be one two
+ 
+
+ align:start position:0%
+here's my inputs are going to be one two
+three four
+
+ align:start position:0%
+three four
+ 
+
+ align:start position:0%
+three four
+okay and the
+
+ align:start position:0%
+okay and the
+ 
+
+ align:start position:0%
+okay and the
+I'm going to make some perturbations of
+
+ align:start position:0%
+I'm going to make some perturbations of
+ 
+
+ align:start position:0%
+I'm going to make some perturbations of
+the one two three four by just taking
+
+ align:start position:0%
+the one two three four by just taking
+ 
+
+ align:start position:0%
+the one two three four by just taking
+one two three four divided by ten
+
+ align:start position:0%
+one two three four divided by ten
+ 
+
+ align:start position:0%
+one two three four divided by ten
+thousand and I'm going to put into this
+
+ align:start position:0%
+thousand and I'm going to put into this
+ 
+
+ align:start position:0%
+thousand and I'm going to put into this
+Jacobian I'm just going to put in these
+
+ align:start position:0%
+Jacobian I'm just going to put in these
+ 
+
+ align:start position:0%
+Jacobian I'm just going to put in these
+numbers this Jacobian so this is the
+
+ align:start position:0%
+numbers this Jacobian so this is the
+ 
+
+ align:start position:0%
+numbers this Jacobian so this is the
+this is the this is the Jacobian of the
+
+ align:start position:0%
+this is the this is the Jacobian of the
+ 
+
+ align:start position:0%
+this is the this is the Jacobian of the
+square function at the Matrix one two
+
+ align:start position:0%
+square function at the Matrix one two
+ 
+
+ align:start position:0%
+square function at the Matrix one two
+three four right so if I perturb The
+
+ align:start position:0%
+three four right so if I perturb The
+ 
+
+ align:start position:0%
+three four right so if I perturb The
+Matrix a little bit like this e here I
+
+ align:start position:0%
+Matrix a little bit like this e here I
+ 
+
+ align:start position:0%
+Matrix a little bit like this e here I
+should know how the Matrix perturbs
+
+ align:start position:0%
+should know how the Matrix perturbs
+ 
+
+ align:start position:0%
+should know how the Matrix perturbs
+okay and and so all I should have to do
+
+ align:start position:0%
+okay and and so all I should have to do
+ 
+
+ align:start position:0%
+okay and and so all I should have to do
+is take this Jacobian which is
+
+ align:start position:0%
+is take this Jacobian which is
+ 
+
+ align:start position:0%
+is take this Jacobian which is
+this this is the same expression as here
+
+ align:start position:0%
+this this is the same expression as here
+ 
+
+ align:start position:0%
+this this is the same expression as here
+and multiply that by the VEC of my
+
+ align:start position:0%
+and multiply that by the VEC of my
+ 
+
+ align:start position:0%
+and multiply that by the VEC of my
+perturbation okay and uh of course here
+
+ align:start position:0%
+perturbation okay and uh of course here
+ 
+
+ align:start position:0%
+perturbation okay and uh of course here
+here's what we get as the answer and we
+
+ align:start position:0%
+here's what we get as the answer and we
+ 
+
+ align:start position:0%
+here's what we get as the answer and we
+can check that with by just doing a
+
+ align:start position:0%
+can check that with by just doing a
+ 
+
+ align:start position:0%
+can check that with by just doing a
+finite difference with the matrices and
+
+ align:start position:0%
+finite difference with the matrices and
+ 
+
+ align:start position:0%
+finite difference with the matrices and
+you could see the first order it just
+
+ align:start position:0%
+you could see the first order it just
+ 
+
+ align:start position:0%
+you could see the first order it just
+works okay so when I see this I'm happy
+
+ align:start position:0%
+works okay so when I see this I'm happy
+ 
+
+ align:start position:0%
+works okay so when I see this I'm happy
+all right other people trust mathematics
+
+ align:start position:0%
+all right other people trust mathematics
+ 
+
+ align:start position:0%
+all right other people trust mathematics
+me I make too many errors I gotta I have
+
+ align:start position:0%
+me I make too many errors I gotta I have
+ 
+
+ align:start position:0%
+me I make too many errors I gotta I have
+to double check it and you know just
+
+ align:start position:0%
+to double check it and you know just
+ 
+
+ align:start position:0%
+to double check it and you know just
+just to see these numbers you know this
+
+ align:start position:0%
+just to see these numbers you know this
+ 
+
+ align:start position:0%
+just to see these numbers you know this
+0.0014 and the 0030 and the
+
+ align:start position:0%
+0.0014 and the 0030 and the
+ 
+
+ align:start position:0%
+0.0014 and the 0030 and the
+0020 and the 0044 just matching up with
+
+ align:start position:0%
+0020 and the 0044 just matching up with
+ 
+
+ align:start position:0%
+0020 and the 0044 just matching up with
+the numbers above again this is just the
+
+ align:start position:0%
+the numbers above again this is just the
+ 
+
+ align:start position:0%
+the numbers above again this is just the
+finite differences this is what the
+
+ align:start position:0%
+finite differences this is what the
+ 
+
+ align:start position:0%
+finite differences this is what the
+theory tells you right and it I don't
+
+ align:start position:0%
+theory tells you right and it I don't
+ 
+
+ align:start position:0%
+theory tells you right and it I don't
+know if you guys need to check your work
+
+ align:start position:0%
+know if you guys need to check your work
+ 
+
+ align:start position:0%
+know if you guys need to check your work
+but I love checking my work invariably I
+
+ align:start position:0%
+but I love checking my work invariably I
+ 
+
+ align:start position:0%
+but I love checking my work invariably I
+lose factors of 2 where pi
+
+ align:start position:0%
+lose factors of 2 where pi
+ 
+
+ align:start position:0%
+lose factors of 2 where pi
+so this is the best way to find them
+
+ align:start position:0%
+so this is the best way to find them
+ 
+
+ align:start position:0%
+so this is the best way to find them
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+so uh uh so so so
+
+ align:start position:0%
+so uh uh so so so
+ 
+
+ align:start position:0%
+so uh uh so so so
+rather than vexing and flattening
+
+ align:start position:0%
+rather than vexing and flattening
+ 
+
+ align:start position:0%
+rather than vexing and flattening
+another way to basically uh to basically
+
+ align:start position:0%
+another way to basically uh to basically
+ 
+
+ align:start position:0%
+another way to basically uh to basically
+Express the Jacobian of a square and
+
+ align:start position:0%
+Express the Jacobian of a square and
+ 
+
+ align:start position:0%
+Express the Jacobian of a square and
+you'll see why it works in a minute is
+
+ align:start position:0%
+you'll see why it works in a minute is
+ 
+
+ align:start position:0%
+you'll see why it works in a minute is
+to express it as a linear transformation
+
+ align:start position:0%
+to express it as a linear transformation
+ 
+
+ align:start position:0%
+to express it as a linear transformation
+okay and one of the things that if it
+
+ align:start position:0%
+okay and one of the things that if it
+ 
+
+ align:start position:0%
+okay and one of the things that if it
+didn't if you weren't if you weren't hit
+
+ align:start position:0%
+didn't if you weren't if you weren't hit
+ 
+
+ align:start position:0%
+didn't if you weren't if you weren't hit
+with this with your linear algebra class
+
+ align:start position:0%
+with this with your linear algebra class
+ 
+
+ align:start position:0%
+with this with your linear algebra class
+when you first took linear algebra then
+
+ align:start position:0%
+when you first took linear algebra then
+ 
+
+ align:start position:0%
+when you first took linear algebra then
+this is a good time to recognize that
+
+ align:start position:0%
+this is a good time to recognize that
+ 
+
+ align:start position:0%
+this is a good time to recognize that
+being you know
+
+ align:start position:0%
+being you know
+ 
+
+ align:start position:0%
+being you know
+being able to write down a linear
+
+ align:start position:0%
+being able to write down a linear
+ 
+
+ align:start position:0%
+being able to write down a linear
+transformation doesn't mean you have to
+
+ align:start position:0%
+transformation doesn't mean you have to
+ 
+
+ align:start position:0%
+transformation doesn't mean you have to
+write down a matrix right you could
+
+ align:start position:0%
+write down a matrix right you could
+ 
+
+ align:start position:0%
+write down a matrix right you could
+write down linear Transformations
+
+ align:start position:0%
+write down linear Transformations
+ 
+
+ align:start position:0%
+write down linear Transformations
+without writing down a matrix for
+
+ align:start position:0%
+without writing down a matrix for
+ 
+
+ align:start position:0%
+without writing down a matrix for
+example uh you think of M as a constant
+
+ align:start position:0%
+example uh you think of M as a constant
+ 
+
+ align:start position:0%
+example uh you think of M as a constant
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right so m is going to be our position
+
+ align:start position:0%
+right so m is going to be our position
+ 
+
+ align:start position:0%
+right so m is going to be our position
+where we're taking derivative or
+
+ align:start position:0%
+where we're taking derivative or
+ 
+
+ align:start position:0%
+where we're taking derivative or
+whatever it is it's a constant okay and
+
+ align:start position:0%
+whatever it is it's a constant okay and
+ 
+
+ align:start position:0%
+whatever it is it's a constant okay and
+I just want to point out that this is a
+
+ align:start position:0%
+I just want to point out that this is a
+ 
+
+ align:start position:0%
+I just want to point out that this is a
+linear transformation of matrices right
+
+ align:start position:0%
+linear transformation of matrices right
+ 
+
+ align:start position:0%
+linear transformation of matrices right
+so if m is a two by two Matrix and e is
+
+ align:start position:0%
+so if m is a two by two Matrix and e is
+ 
+
+ align:start position:0%
+so if m is a two by two Matrix and e is
+a two by two Matrix
+
+ align:start position:0%
+a two by two Matrix
+ 
+
+ align:start position:0%
+a two by two Matrix
+uh this expression without writing down
+
+ align:start position:0%
+uh this expression without writing down
+ 
+
+ align:start position:0%
+uh this expression without writing down
+the Matrix is a linear transformation
+
+ align:start position:0%
+the Matrix is a linear transformation
+ 
+
+ align:start position:0%
+the Matrix is a linear transformation
+what do you have to check if it's a
+
+ align:start position:0%
+what do you have to check if it's a
+ 
+
+ align:start position:0%
+what do you have to check if it's a
+linear transformation well let's see if
+
+ align:start position:0%
+linear transformation well let's see if
+ 
+
+ align:start position:0%
+linear transformation well let's see if
+I multiply e by a number like 2 or Pi
+
+ align:start position:0%
+I multiply e by a number like 2 or Pi
+ 
+
+ align:start position:0%
+I multiply e by a number like 2 or Pi
+does the output get multiplied by by the
+
+ align:start position:0%
+does the output get multiplied by by the
+ 
+
+ align:start position:0%
+does the output get multiplied by by the
+same number like 2 or Pi yep the scalar
+
+ align:start position:0%
+same number like 2 or Pi yep the scalar
+ 
+
+ align:start position:0%
+same number like 2 or Pi yep the scalar
+would pull right out and if I input E1
+
+ align:start position:0%
+would pull right out and if I input E1
+ 
+
+ align:start position:0%
+would pull right out and if I input E1
+plus E2 with the output be the output of
+
+ align:start position:0%
+plus E2 with the output be the output of
+ 
+
+ align:start position:0%
+plus E2 with the output be the output of
+the 1 plus the output of the two right
+
+ align:start position:0%
+the 1 plus the output of the two right
+ 
+
+ align:start position:0%
+the 1 plus the output of the two right
+you know you check those two things and
+
+ align:start position:0%
+you know you check those two things and
+ 
+
+ align:start position:0%
+you know you check those two things and
+that's what you need to check that the
+
+ align:start position:0%
+that's what you need to check that the
+ 
+
+ align:start position:0%
+that's what you need to check that the
+function is linear you don't need a
+
+ align:start position:0%
+function is linear you don't need a
+ 
+
+ align:start position:0%
+function is linear you don't need a
+matrix right okay matrices are very
+
+ align:start position:0%
+matrix right okay matrices are very
+ 
+
+ align:start position:0%
+matrix right okay matrices are very
+concrete but you don't need them when
+
+ align:start position:0%
+concrete but you don't need them when
+ 
+
+ align:start position:0%
+concrete but you don't need them when
+you're grown up right so this is a
+
+ align:start position:0%
+you're grown up right so this is a
+ 
+
+ align:start position:0%
+you're grown up right so this is a
+linear transformation on E
+
+ align:start position:0%
+linear transformation on E
+ 
+
+ align:start position:0%
+linear transformation on E
+okay and it's going to turn out to be
+
+ align:start position:0%
+okay and it's going to turn out to be
+ 
+
+ align:start position:0%
+okay and it's going to turn out to be
+exactly the right linear transformation
+
+ align:start position:0%
+exactly the right linear transformation
+ 
+
+ align:start position:0%
+exactly the right linear transformation
+for the very Matrix we have at hand and
+
+ align:start position:0%
+for the very Matrix we have at hand and
+ 
+
+ align:start position:0%
+for the very Matrix we have at hand and
+so with M being the Matrix one two three
+
+ align:start position:0%
+so with M being the Matrix one two three
+ 
+
+ align:start position:0%
+so with M being the Matrix one two three
+four and E here let's remind you what
+
+ align:start position:0%
+four and E here let's remind you what
+ 
+
+ align:start position:0%
+four and E here let's remind you what
+these matrices are if you've already
+
+ align:start position:0%
+these matrices are if you've already
+ 
+
+ align:start position:0%
+these matrices are if you've already
+forgotten but if m is the Matrix one two
+
+ align:start position:0%
+forgotten but if m is the Matrix one two
+ 
+
+ align:start position:0%
+forgotten but if m is the Matrix one two
+three four and E is the perturbation
+
+ align:start position:0%
+three four and E is the perturbation
+ 
+
+ align:start position:0%
+three four and E is the perturbation
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+the same numbers divided by ten thousand
+
+ align:start position:0%
+the same numbers divided by ten thousand
+ 
+
+ align:start position:0%
+the same numbers divided by ten thousand
+this linear transformation applied to e
+
+ align:start position:0%
+this linear transformation applied to e
+ 
+
+ align:start position:0%
+this linear transformation applied to e
+gives you the derivative without right
+
+ align:start position:0%
+gives you the derivative without right
+ 
+
+ align:start position:0%
+gives you the derivative without right
+somehow the information in here is the
+
+ align:start position:0%
+somehow the information in here is the
+ 
+
+ align:start position:0%
+somehow the information in here is the
+same as the information of the Jacobian
+
+ align:start position:0%
+same as the information of the Jacobian
+ 
+
+ align:start position:0%
+same as the information of the Jacobian
+and yet I never formed the Jacobian okay
+
+ align:start position:0%
+and yet I never formed the Jacobian okay
+ 
+
+ align:start position:0%
+and yet I never formed the Jacobian okay
+that's a key key Point never form the
+
+ align:start position:0%
+that's a key key Point never form the
+ 
+
+ align:start position:0%
+that's a key key Point never form the
+Jacobian but the information of get to
+
+ align:start position:0%
+Jacobian but the information of get to
+ 
+
+ align:start position:0%
+Jacobian but the information of get to
+get the answer is embodied in this
+
+ align:start position:0%
+get the answer is embodied in this
+ 
+
+ align:start position:0%
+get the answer is embodied in this
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+right so who needs who needs to build
+
+ align:start position:0%
+right so who needs who needs to build
+ 
+
+ align:start position:0%
+right so who needs who needs to build
+the 4x4 Matrix if you can just have this
+
+ align:start position:0%
+the 4x4 Matrix if you can just have this
+ 
+
+ align:start position:0%
+the 4x4 Matrix if you can just have this
+expression questions
+
+ align:start position:0%
+expression questions
+ 
+
+ align:start position:0%
+expression questions
+anything does it make sense doesn't make
+
+ align:start position:0%
+anything does it make sense doesn't make
+ 
+
+ align:start position:0%
+anything does it make sense doesn't make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+you want to see why that works
+
+ align:start position:0%
+you want to see why that works
+ 
+
+ align:start position:0%
+you want to see why that works
+all right so I find the chronicle
+
+ align:start position:0%
+all right so I find the chronicle
+ 
+
+ align:start position:0%
+all right so I find the chronicle
+product notation is a good way to kind
+
+ align:start position:0%
+product notation is a good way to kind
+ 
+
+ align:start position:0%
+product notation is a good way to kind
+of to sort of be ready to to set the
+
+ align:start position:0%
+of to sort of be ready to to set the
+ 
+
+ align:start position:0%
+of to sort of be ready to to set the
+sort of thing up right and so let me
+
+ align:start position:0%
+sort of thing up right and so let me
+ 
+
+ align:start position:0%
+sort of thing up right and so let me
+tell you about the chronicle product
+
+ align:start position:0%
+tell you about the chronicle product
+ 
+
+ align:start position:0%
+tell you about the chronicle product
+notation and I'm going to set up these
+
+ align:start position:0%
+notation and I'm going to set up these
+ 
+
+ align:start position:0%
+notation and I'm going to set up these
+variables a b c and d okay and here's
+
+ align:start position:0%
+variables a b c and d okay and here's
+ 
+
+ align:start position:0%
+variables a b c and d okay and here's
+just a pair of matrices
+
+ align:start position:0%
+just a pair of matrices
+ 
+
+ align:start position:0%
+just a pair of matrices
+okay and what I want you to notice is
+
+ align:start position:0%
+okay and what I want you to notice is
+ 
+
+ align:start position:0%
+okay and what I want you to notice is
+that we have oh am I sharing my screen
+
+ align:start position:0%
+that we have oh am I sharing my screen
+ 
+
+ align:start position:0%
+that we have oh am I sharing my screen
+just occurred to me that I'm not even
+
+ align:start position:0%
+just occurred to me that I'm not even
+ 
+
+ align:start position:0%
+just occurred to me that I'm not even
+sure I'm sharing my screen
+
+ align:start position:0%
+sure I'm sharing my screen
+ 
+
+ align:start position:0%
+sure I'm sharing my screen
+yeah sorry about that
+
+ align:start position:0%
+yeah sorry about that
+ 
+
+ align:start position:0%
+yeah sorry about that
+just hit me that you don't see what I'm
+
+ align:start position:0%
+just hit me that you don't see what I'm
+ 
+
+ align:start position:0%
+just hit me that you don't see what I'm
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+all right there we go
+
+ align:start position:0%
+all right there we go
+ 
+
+ align:start position:0%
+all right there we go
+and the reason I realized that is
+
+ align:start position:0%
+and the reason I realized that is
+ 
+
+ align:start position:0%
+and the reason I realized that is
+because I wanted to use this pen here
+
+ align:start position:0%
+because I wanted to use this pen here
+ 
+
+ align:start position:0%
+because I wanted to use this pen here
+anyway so uh so I want everybody to see
+
+ align:start position:0%
+anyway so uh so I want everybody to see
+ 
+
+ align:start position:0%
+anyway so uh so I want everybody to see
+the top half versus the bottom half of
+
+ align:start position:0%
+the top half versus the bottom half of
+ 
+
+ align:start position:0%
+the top half versus the bottom half of
+this Matrix right so uh here what I'm
+
+ align:start position:0%
+this Matrix right so uh here what I'm
+ 
+
+ align:start position:0%
+this Matrix right so uh here what I'm
+doing is I'm taking the chronicle
+
+ align:start position:0%
+doing is I'm taking the chronicle
+ 
+
+ align:start position:0%
+doing is I'm taking the chronicle
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+of this two by one Matrix
+
+ align:start position:0%
+of this two by one Matrix
+ 
+
+ align:start position:0%
+of this two by one Matrix
+Chron occur the
+
+ align:start position:0%
+Chron occur the
+ 
+
+ align:start position:0%
+Chron occur the
+let's see if I can do this it's hard to
+
+ align:start position:0%
+let's see if I can do this it's hard to
+ 
+
+ align:start position:0%
+let's see if I can do this it's hard to
+I'm using just the mouse
+
+ align:start position:0%
+I'm using just the mouse
+ 
+
+ align:start position:0%
+I'm using just the mouse
+so P Q R and S is this coming out on the
+
+ align:start position:0%
+so P Q R and S is this coming out on the
+ 
+
+ align:start position:0%
+so P Q R and S is this coming out on the
+screen can you see the green
+
+ align:start position:0%
+screen can you see the green
+ 
+
+ align:start position:0%
+screen can you see the green
+so P Q R and S and I just want you to
+
+ align:start position:0%
+so P Q R and S and I just want you to
+ 
+
+ align:start position:0%
+so P Q R and S and I just want you to
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+whoops
+
+ align:start position:0%
+whoops
+ 
+
+ align:start position:0%
+whoops
+it's not doing it now
+
+ align:start position:0%
+it's not doing it now
+ 
+
+ align:start position:0%
+it's not doing it now
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we go
+
+ align:start position:0%
+there we go
+ 
+
+ align:start position:0%
+there we go
+okay so I want you all to see that
+
+ align:start position:0%
+okay so I want you all to see that
+ 
+
+ align:start position:0%
+okay so I want you all to see that
+that it's taking the the whole second
+
+ align:start position:0%
+that it's taking the the whole second
+ 
+
+ align:start position:0%
+that it's taking the the whole second
+Matrix pqrs and multiplying it by a on
+
+ align:start position:0%
+Matrix pqrs and multiplying it by a on
+ 
+
+ align:start position:0%
+Matrix pqrs and multiplying it by a on
+top and it's oh and then this is taking
+
+ align:start position:0%
+top and it's oh and then this is taking
+ 
+
+ align:start position:0%
+top and it's oh and then this is taking
+the whole second Matrix pqrs and
+
+ align:start position:0%
+the whole second Matrix pqrs and
+ 
+
+ align:start position:0%
+the whole second Matrix pqrs and
+multiplying by B on the bottom right and
+
+ align:start position:0%
+multiplying by B on the bottom right and
+ 
+
+ align:start position:0%
+multiplying by B on the bottom right and
+so what it does is in effect it takes
+
+ align:start position:0%
+so what it does is in effect it takes
+ 
+
+ align:start position:0%
+so what it does is in effect it takes
+you'll see that every possible product
+
+ align:start position:0%
+you'll see that every possible product
+ 
+
+ align:start position:0%
+you'll see that every possible product
+of something over here on the left and
+
+ align:start position:0%
+of something over here on the left and
+ 
+
+ align:start position:0%
+of something over here on the left and
+something over here on the right shows
+
+ align:start position:0%
+something over here on the right shows
+ 
+
+ align:start position:0%
+something over here on the right shows
+up and it shows up in a very consistent
+
+ align:start position:0%
+up and it shows up in a very consistent
+ 
+
+ align:start position:0%
+up and it shows up in a very consistent
+order once you see a couple more
+
+ align:start position:0%
+order once you see a couple more
+ 
+
+ align:start position:0%
+order once you see a couple more
+examples you'll see how the pattern goes
+
+ align:start position:0%
+examples you'll see how the pattern goes
+ 
+
+ align:start position:0%
+examples you'll see how the pattern goes
+so this is the chronicle product so
+
+ align:start position:0%
+so this is the chronicle product so
+ 
+
+ align:start position:0%
+so this is the chronicle product so
+let's see so
+
+ align:start position:0%
+let's see so
+ 
+
+ align:start position:0%
+let's see so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so here's an example where we take a
+
+ align:start position:0%
+so here's an example where we take a
+ 
+
+ align:start position:0%
+so here's an example where we take a
+ABCD with pqrs and I'm sure you can all
+
+ align:start position:0%
+ABCD with pqrs and I'm sure you can all
+ 
+
+ align:start position:0%
+ABCD with pqrs and I'm sure you can all
+see that there's a pqrs times the a pqrs
+
+ align:start position:0%
+see that there's a pqrs times the a pqrs
+ 
+
+ align:start position:0%
+see that there's a pqrs times the a pqrs
+now in the bottom left times the b in
+
+ align:start position:0%
+now in the bottom left times the b in
+ 
+
+ align:start position:0%
+now in the bottom left times the b in
+the upper right the pqrs is times the C
+
+ align:start position:0%
+the upper right the pqrs is times the C
+ 
+
+ align:start position:0%
+the upper right the pqrs is times the C
+and times the D right so the the pattern
+
+ align:start position:0%
+and times the D right so the the pattern
+ 
+
+ align:start position:0%
+and times the D right so the the pattern
+is one way to look at it is you take
+
+ align:start position:0%
+is one way to look at it is you take
+ 
+
+ align:start position:0%
+is one way to look at it is you take
+every element on the left and uh
+
+ align:start position:0%
+every element on the left and uh
+ 
+
+ align:start position:0%
+every element on the left and uh
+multiply it by the entire Matrix on the
+
+ align:start position:0%
+multiply it by the entire Matrix on the
+ 
+
+ align:start position:0%
+multiply it by the entire Matrix on the
+right and then put it in the same order
+
+ align:start position:0%
+right and then put it in the same order
+ 
+
+ align:start position:0%
+right and then put it in the same order
+right and so sometimes it's easier to
+
+ align:start position:0%
+right and so sometimes it's easier to
+ 
+
+ align:start position:0%
+right and so sometimes it's easier to
+see it with with these sort of pictures
+
+ align:start position:0%
+see it with with these sort of pictures
+ 
+
+ align:start position:0%
+see it with with these sort of pictures
+and so here what we have is this two by
+
+ align:start position:0%
+and so here what we have is this two by
+ 
+
+ align:start position:0%
+and so here what we have is this two by
+two two by three Matrix which is a b c d
+
+ align:start position:0%
+two two by three Matrix which is a b c d
+ 
+
+ align:start position:0%
+two two by three Matrix which is a b c d
+e e f so I can
+
+ align:start position:0%
+e e f so I can
+ 
+
+ align:start position:0%
+e e f so I can
+put it over here if you want to see it
+
+ align:start position:0%
+put it over here if you want to see it
+ 
+
+ align:start position:0%
+put it over here if you want to see it
+so I'm taking the chronicle product of a
+
+ align:start position:0%
+so I'm taking the chronicle product of a
+ 
+
+ align:start position:0%
+so I'm taking the chronicle product of a
+b c d e f this way
+
+ align:start position:0%
+b c d e f this way
+ 
+
+ align:start position:0%
+b c d e f this way
+and I'm taking the chronicle product
+
+ align:start position:0%
+and I'm taking the chronicle product
+ 
+
+ align:start position:0%
+and I'm taking the chronicle product
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+uh there's the pizza
+
+ align:start position:0%
+uh there's the pizza
+ 
+
+ align:start position:0%
+uh there's the pizza
+what do we have the alien
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pizza the alien uh the smiley cat
+
+ align:start position:0%
+the pizza the alien uh the smiley cat
+ 
+
+ align:start position:0%
+the pizza the alien uh the smiley cat
+and what do we have here the panda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so uh you know Julia is perfectly
+
+ align:start position:0%
+right so uh you know Julia is perfectly
+ 
+
+ align:start position:0%
+right so uh you know Julia is perfectly
+comfortable with doing that sort of
+
+ align:start position:0%
+comfortable with doing that sort of
+ 
+
+ align:start position:0%
+comfortable with doing that sort of
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+right and you could see that we have a
+
+ align:start position:0%
+right and you could see that we have a
+ 
+
+ align:start position:0%
+right and you could see that we have a
+times the pizza the
+
+ align:start position:0%
+times the pizza the
+ 
+
+ align:start position:0%
+times the pizza the
+did I put the alien on the wrong order
+
+ align:start position:0%
+did I put the alien on the wrong order
+ 
+
+ align:start position:0%
+did I put the alien on the wrong order
+yep the aliens over here
+
+ align:start position:0%
+yep the aliens over here
+ 
+
+ align:start position:0%
+yep the aliens over here
+but you you get the idea
+
+ align:start position:0%
+but you you get the idea
+ 
+
+ align:start position:0%
+but you you get the idea
+right so you have a times Pizza alien
+
+ align:start position:0%
+right so you have a times Pizza alien
+ 
+
+ align:start position:0%
+right so you have a times Pizza alien
+panther cat B times Pizza alien Panda
+
+ align:start position:0%
+panther cat B times Pizza alien Panda
+ 
+
+ align:start position:0%
+panther cat B times Pizza alien Panda
+cat c times Pizza alien Panda cat D
+
+ align:start position:0%
+cat c times Pizza alien Panda cat D
+ 
+
+ align:start position:0%
+cat c times Pizza alien Panda cat D
+times those e times those F times those
+
+ align:start position:0%
+times those e times those F times those
+ 
+
+ align:start position:0%
+times those e times those F times those
+right I think you get the pattern you
+
+ align:start position:0%
+right I think you get the pattern you
+ 
+
+ align:start position:0%
+right I think you get the pattern you
+could do it in the other order oh let's
+
+ align:start position:0%
+could do it in the other order oh let's
+ 
+
+ align:start position:0%
+could do it in the other order oh let's
+see what else did we do
+
+ align:start position:0%
+see what else did we do
+ 
+
+ align:start position:0%
+see what else did we do
+uh oh here it is with the identity
+
+ align:start position:0%
+uh oh here it is with the identity
+ 
+
+ align:start position:0%
+uh oh here it is with the identity
+right so so it's this one is
+
+ align:start position:0%
+right so so it's this one is
+ 
+
+ align:start position:0%
+right so so it's this one is
+Pizza times one pizza times zero
+
+ align:start position:0%
+Pizza times one pizza times zero
+ 
+
+ align:start position:0%
+Pizza times one pizza times zero
+Pizza Time Zero Pizza times one alien
+
+ align:start position:0%
+Pizza Time Zero Pizza times one alien
+ 
+
+ align:start position:0%
+Pizza Time Zero Pizza times one alien
+times one alien times zero alien times
+
+ align:start position:0%
+times one alien times zero alien times
+ 
+
+ align:start position:0%
+times one alien times zero alien times
+zero alien yeah I think you all get it
+
+ align:start position:0%
+zero alien yeah I think you all get it
+ 
+
+ align:start position:0%
+zero alien yeah I think you all get it
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but still fun to watch
+
+ align:start position:0%
+but still fun to watch
+ 
+
+ align:start position:0%
+but still fun to watch
+okay here it is in the other order
+
+ align:start position:0%
+okay here it is in the other order
+ 
+
+ align:start position:0%
+okay here it is in the other order
+so uh so this is one times Pizza alien
+
+ align:start position:0%
+so uh so this is one times Pizza alien
+ 
+
+ align:start position:0%
+so uh so this is one times Pizza alien
+Panda cat zero times Pizza alien right
+
+ align:start position:0%
+Panda cat zero times Pizza alien right
+ 
+
+ align:start position:0%
+Panda cat zero times Pizza alien right
+zero times the two and then again one
+
+ align:start position:0%
+zero times the two and then again one
+ 
+
+ align:start position:0%
+zero times the two and then again one
+times all of these funny symbols okay
+
+ align:start position:0%
+times all of these funny symbols okay
+ 
+
+ align:start position:0%
+times all of these funny symbols okay
+you get it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so the chronicle product with the
+
+ align:start position:0%
+yeah so the chronicle product with the
+ 
+
+ align:start position:0%
+yeah so the chronicle product with the
+identity is is a rather important
+
+ align:start position:0%
+identity is is a rather important
+ 
+
+ align:start position:0%
+identity is is a rather important
+special case right so here here it is
+
+ align:start position:0%
+special case right so here here it is
+ 
+
+ align:start position:0%
+special case right so here here it is
+with just the pqrs
+
+ align:start position:0%
+with just the pqrs
+ 
+
+ align:start position:0%
+with just the pqrs
+so here's the chronicle product of the
+
+ align:start position:0%
+so here's the chronicle product of the
+ 
+
+ align:start position:0%
+so here's the chronicle product of the
+transpose with the identity just putting
+
+ align:start position:0%
+transpose with the identity just putting
+ 
+
+ align:start position:0%
+transpose with the identity just putting
+everything in the other order and
+
+ align:start position:0%
+everything in the other order and
+ 
+
+ align:start position:0%
+everything in the other order and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and and what I want to demonstrate
+
+ align:start position:0%
+and and what I want to demonstrate
+ 
+
+ align:start position:0%
+and and what I want to demonstrate
+is that if you
+
+ align:start position:0%
+is that if you
+ 
+
+ align:start position:0%
+is that if you
+if you form the sum of these two
+
+ align:start position:0%
+if you form the sum of these two
+ 
+
+ align:start position:0%
+if you form the sum of these two
+Chronicle products as matrices
+
+ align:start position:0%
+Chronicle products as matrices
+ 
+
+ align:start position:0%
+Chronicle products as matrices
+and compare it with the Jacobian that
+
+ align:start position:0%
+and compare it with the Jacobian that
+ 
+
+ align:start position:0%
+and compare it with the Jacobian that
+you've already seen for the square
+
+ align:start position:0%
+you've already seen for the square
+ 
+
+ align:start position:0%
+you've already seen for the square
+function you'll notice that you get
+
+ align:start position:0%
+function you'll notice that you get
+ 
+
+ align:start position:0%
+function you'll notice that you get
+exactly the same expression
+
+ align:start position:0%
+exactly the same expression
+ 
+
+ align:start position:0%
+exactly the same expression
+okay so one way to write the Jacobian
+
+ align:start position:0%
+okay so one way to write the Jacobian
+ 
+
+ align:start position:0%
+okay so one way to write the Jacobian
+without writing the Jacobian is to just
+
+ align:start position:0%
+without writing the Jacobian is to just
+ 
+
+ align:start position:0%
+without writing the Jacobian is to just
+write these Chronicle products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you don't just because you write down
+
+ align:start position:0%
+so you don't just because you write down
+ 
+
+ align:start position:0%
+so you don't just because you write down
+the chronicle product it doesn't mean
+
+ align:start position:0%
+the chronicle product it doesn't mean
+ 
+
+ align:start position:0%
+the chronicle product it doesn't mean
+you actually have to multiply it all out
+
+ align:start position:0%
+you actually have to multiply it all out
+ 
+
+ align:start position:0%
+you actually have to multiply it all out
+though right you could write it as an
+
+ align:start position:0%
+though right you could write it as an
+ 
+
+ align:start position:0%
+though right you could write it as an
+expression okay and the what underlies
+
+ align:start position:0%
+expression okay and the what underlies
+ 
+
+ align:start position:0%
+expression okay and the what underlies
+everything and an identity that years
+
+ align:start position:0%
+everything and an identity that years
+ 
+
+ align:start position:0%
+everything and an identity that years
+ago I I remember I wrote this in big
+
+ align:start position:0%
+ago I I remember I wrote this in big
+ 
+
+ align:start position:0%
+ago I I remember I wrote this in big
+thick letters on an index card and I
+
+ align:start position:0%
+thick letters on an index card and I
+ 
+
+ align:start position:0%
+thick letters on an index card and I
+placed it on my bookshelf above my desk
+
+ align:start position:0%
+placed it on my bookshelf above my desk
+ 
+
+ align:start position:0%
+placed it on my bookshelf above my desk
+to make sure that I would never forget
+
+ align:start position:0%
+to make sure that I would never forget
+ 
+
+ align:start position:0%
+to make sure that I would never forget
+it so this is absolutely worth
+
+ align:start position:0%
+it so this is absolutely worth
+ 
+
+ align:start position:0%
+it so this is absolutely worth
+memorizing that if you have the right
+
+ align:start position:0%
+memorizing that if you have the right
+ 
+
+ align:start position:0%
+memorizing that if you have the right
+compatibility so that you know you can
+
+ align:start position:0%
+compatibility so that you know you can
+ 
+
+ align:start position:0%
+compatibility so that you know you can
+multiply B times c times a transpose
+
+ align:start position:0%
+multiply B times c times a transpose
+ 
+
+ align:start position:0%
+multiply B times c times a transpose
+right so the the number of columns of B
+
+ align:start position:0%
+right so the the number of columns of B
+ 
+
+ align:start position:0%
+right so the the number of columns of B
+has to be the number of rows of C Etc
+
+ align:start position:0%
+has to be the number of rows of C Etc
+ 
+
+ align:start position:0%
+has to be the number of rows of C Etc
+that the chronicle product of A and B
+
+ align:start position:0%
+that the chronicle product of A and B
+ 
+
+ align:start position:0%
+that the chronicle product of A and B
+when multiplied by the VEC of C
+
+ align:start position:0%
+when multiplied by the VEC of C
+ 
+
+ align:start position:0%
+when multiplied by the VEC of C
+always is identically equal to the VEC
+
+ align:start position:0%
+always is identically equal to the VEC
+ 
+
+ align:start position:0%
+always is identically equal to the VEC
+of BC a transpose okay so I would
+
+ align:start position:0%
+of BC a transpose okay so I would
+ 
+
+ align:start position:0%
+of BC a transpose okay so I would
+recommend memorizing that because it's
+
+ align:start position:0%
+recommend memorizing that because it's
+ 
+
+ align:start position:0%
+recommend memorizing that because it's
+just so handy to always know that
+
+ align:start position:0%
+just so handy to always know that
+ 
+
+ align:start position:0%
+just so handy to always know that
+okay and the the kind of mnemonic that I
+
+ align:start position:0%
+okay and the the kind of mnemonic that I
+ 
+
+ align:start position:0%
+okay and the the kind of mnemonic that I
+still have in my mind
+
+ align:start position:0%
+still have in my mind
+ 
+
+ align:start position:0%
+still have in my mind
+I mean you could just say to yourself
+
+ align:start position:0%
+I mean you could just say to yourself
+ 
+
+ align:start position:0%
+I mean you could just say to yourself
+BCA transpose but the way I kind of look
+
+ align:start position:0%
+BCA transpose but the way I kind of look
+ 
+
+ align:start position:0%
+BCA transpose but the way I kind of look
+at it and if this works for you that's
+
+ align:start position:0%
+at it and if this works for you that's
+ 
+
+ align:start position:0%
+at it and if this works for you that's
+fine and if it doesn't work you could
+
+ align:start position:0%
+fine and if it doesn't work you could
+ 
+
+ align:start position:0%
+fine and if it doesn't work you could
+have your own way but the way I look at
+
+ align:start position:0%
+have your own way but the way I look at
+ 
+
+ align:start position:0%
+have your own way but the way I look at
+this is I see I see the B is is is
+
+ align:start position:0%
+this is I see I see the B is is is
+ 
+
+ align:start position:0%
+this is I see I see the B is is is
+closest to the C on the left so I say BC
+
+ align:start position:0%
+closest to the C on the left so I say BC
+ 
+
+ align:start position:0%
+closest to the C on the left so I say BC
+and then I say ah the H then should go
+
+ align:start position:0%
+and then I say ah the H then should go
+ 
+
+ align:start position:0%
+and then I say ah the H then should go
+this is again a little memory thing it
+
+ align:start position:0%
+this is again a little memory thing it
+ 
+
+ align:start position:0%
+this is again a little memory thing it
+doesn't mean anything but the a should
+
+ align:start position:0%
+doesn't mean anything but the a should
+ 
+
+ align:start position:0%
+doesn't mean anything but the a should
+go around the other way and since it
+
+ align:start position:0%
+go around the other way and since it
+ 
+
+ align:start position:0%
+go around the other way and since it
+since it went around it deserves to be
+
+ align:start position:0%
+since it went around it deserves to be
+ 
+
+ align:start position:0%
+since it went around it deserves to be
+transposed
+
+ align:start position:0%
+transposed
+ 
+
+ align:start position:0%
+transposed
+so if that works for you that's fine the
+
+ align:start position:0%
+so if that works for you that's fine the
+ 
+
+ align:start position:0%
+so if that works for you that's fine the
+B is just to the left of the C the a has
+
+ align:start position:0%
+B is just to the left of the C the a has
+ 
+
+ align:start position:0%
+B is just to the left of the C the a has
+to come around so it gets transposed
+
+ align:start position:0%
+to come around so it gets transposed
+ 
+
+ align:start position:0%
+to come around so it gets transposed
+okay that somehow and that always works
+
+ align:start position:0%
+okay that somehow and that always works
+ 
+
+ align:start position:0%
+okay that somehow and that always works
+okay and so you can
+
+ align:start position:0%
+okay and so you can
+ 
+
+ align:start position:0%
+okay and so you can
+you know you can
+
+ align:start position:0%
+you know you can
+ 
+
+ align:start position:0%
+you know you can
+in fact here is some random here you can
+
+ align:start position:0%
+in fact here is some random here you can
+ 
+
+ align:start position:0%
+in fact here is some random here you can
+see with some random numbers right
+
+ align:start position:0%
+see with some random numbers right
+ 
+
+ align:start position:0%
+see with some random numbers right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where in fact I could I could type this
+
+ align:start position:0%
+where in fact I could I could type this
+ 
+
+ align:start position:0%
+where in fact I could I could type this
+till the cows come home it'll always
+
+ align:start position:0%
+till the cows come home it'll always
+ 
+
+ align:start position:0%
+till the cows come home it'll always
+come out to be a true identity so here
+
+ align:start position:0%
+come out to be a true identity so here
+ 
+
+ align:start position:0%
+come out to be a true identity so here
+we can I could hit it again but it'll
+
+ align:start position:0%
+we can I could hit it again but it'll
+ 
+
+ align:start position:0%
+we can I could hit it again but it'll
+always be true
+
+ align:start position:0%
+always be true
+ 
+
+ align:start position:0%
+always be true
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um you see it's b c a transpose okay
+
+ align:start position:0%
+um you see it's b c a transpose okay
+ 
+
+ align:start position:0%
+um you see it's b c a transpose okay
+everybody convinced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the chronicle product of two five by
+
+ align:start position:0%
+so the chronicle product of two five by
+ 
+
+ align:start position:0%
+so the chronicle product of two five by
+five matrices would be 25 by 25 just to
+
+ align:start position:0%
+five matrices would be 25 by 25 just to
+ 
+
+ align:start position:0%
+five matrices would be 25 by 25 just to
+show you and here are some useful
+
+ align:start position:0%
+show you and here are some useful
+ 
+
+ align:start position:0%
+show you and here are some useful
+identities uh worth knowing about so if
+
+ align:start position:0%
+identities uh worth knowing about so if
+ 
+
+ align:start position:0%
+identities uh worth knowing about so if
+you take the transpose of a Chronicle
+
+ align:start position:0%
+you take the transpose of a Chronicle
+ 
+
+ align:start position:0%
+you take the transpose of a Chronicle
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+it's the chronicle product of the
+
+ align:start position:0%
+it's the chronicle product of the
+ 
+
+ align:start position:0%
+it's the chronicle product of the
+transposes and it's not in the other
+
+ align:start position:0%
+transposes and it's not in the other
+ 
+
+ align:start position:0%
+transposes and it's not in the other
+order right like if this was if you were
+
+ align:start position:0%
+order right like if this was if you were
+ 
+
+ align:start position:0%
+order right like if this was if you were
+thinking of ordinary Matrix multiply
+
+ align:start position:0%
+thinking of ordinary Matrix multiply
+ 
+
+ align:start position:0%
+thinking of ordinary Matrix multiply
+you'd have a b transpose you know that
+
+ align:start position:0%
+you'd have a b transpose you know that
+ 
+
+ align:start position:0%
+you'd have a b transpose you know that
+would be B transpose a transpose but
+
+ align:start position:0%
+would be B transpose a transpose but
+ 
+
+ align:start position:0%
+would be B transpose a transpose but
+um when you do the chronicle product the
+
+ align:start position:0%
+um when you do the chronicle product the
+ 
+
+ align:start position:0%
+um when you do the chronicle product the
+order Remains the Same okay so don't get
+
+ align:start position:0%
+order Remains the Same okay so don't get
+ 
+
+ align:start position:0%
+order Remains the Same okay so don't get
+confused with Matrix multiplation
+
+ align:start position:0%
+confused with Matrix multiplation
+ 
+
+ align:start position:0%
+confused with Matrix multiplation
+again with inverse inverse if this
+
+ align:start position:0%
+again with inverse inverse if this
+ 
+
+ align:start position:0%
+again with inverse inverse if this
+wasn't a Chronicle product if it was a
+
+ align:start position:0%
+wasn't a Chronicle product if it was a
+ 
+
+ align:start position:0%
+wasn't a Chronicle product if it was a
+matrix multiply product again you would
+
+ align:start position:0%
+matrix multiply product again you would
+ 
+
+ align:start position:0%
+matrix multiply product again you would
+you would put this in the other order
+
+ align:start position:0%
+you would put this in the other order
+ 
+
+ align:start position:0%
+you would put this in the other order
+but with Chronicle product it stays in
+
+ align:start position:0%
+but with Chronicle product it stays in
+ 
+
+ align:start position:0%
+but with Chronicle product it stays in
+that order
+
+ align:start position:0%
+that order
+ 
+
+ align:start position:0%
+that order
+another useful thing to know is if a and
+
+ align:start position:0%
+another useful thing to know is if a and
+ 
+
+ align:start position:0%
+another useful thing to know is if a and
+b are square matrices if a is n by n and
+
+ align:start position:0%
+b are square matrices if a is n by n and
+ 
+
+ align:start position:0%
+b are square matrices if a is n by n and
+B is M by m
+
+ align:start position:0%
+B is M by m
+ 
+
+ align:start position:0%
+B is M by m
+then the determinant is the determinant
+
+ align:start position:0%
+then the determinant is the determinant
+ 
+
+ align:start position:0%
+then the determinant is the determinant
+of a to the m so so a is the n by N1 it
+
+ align:start position:0%
+of a to the m so so a is the n by N1 it
+ 
+
+ align:start position:0%
+of a to the m so so a is the n by N1 it
+picks up the M from the B and then B is
+
+ align:start position:0%
+picks up the M from the B and then B is
+ 
+
+ align:start position:0%
+picks up the M from the B and then B is
+the m by M1 it takes picks up the N from
+
+ align:start position:0%
+the m by M1 it takes picks up the N from
+ 
+
+ align:start position:0%
+the m by M1 it takes picks up the N from
+the a right so there's a formula
+
+ align:start position:0%
+the a right so there's a formula
+ 
+
+ align:start position:0%
+the a right so there's a formula
+um the trace of a Chronicle product is
+
+ align:start position:0%
+um the trace of a Chronicle product is
+ 
+
+ align:start position:0%
+um the trace of a Chronicle product is
+the product of the traces
+
+ align:start position:0%
+the product of the traces
+ 
+
+ align:start position:0%
+the product of the traces
+um a chronic or B is orthogonal if a and
+
+ align:start position:0%
+um a chronic or B is orthogonal if a and
+ 
+
+ align:start position:0%
+um a chronic or B is orthogonal if a and
+b are both orthogonal
+
+ align:start position:0%
+b are both orthogonal
+ 
+
+ align:start position:0%
+b are both orthogonal
+The Matrix multiply of A chronography
+
+ align:start position:0%
+The Matrix multiply of A chronography
+ 
+
+ align:start position:0%
+The Matrix multiply of A chronography
+and C chronic or D is the Matrix
+
+ align:start position:0%
+and C chronic or D is the Matrix
+ 
+
+ align:start position:0%
+and C chronic or D is the Matrix
+multiply of A and C with that of B and D
+
+ align:start position:0%
+multiply of A and C with that of B and D
+ 
+
+ align:start position:0%
+multiply of A and C with that of B and D
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah so so a chronic or B and B
+
+ align:start position:0%
+yeah so so a chronic or B and B
+ 
+
+ align:start position:0%
+yeah so so a chronic or B and B
+Chronicle a have the same eigenvalues
+
+ align:start position:0%
+Chronicle a have the same eigenvalues
+ 
+
+ align:start position:0%
+Chronicle a have the same eigenvalues
+which are actually the products of the
+
+ align:start position:0%
+which are actually the products of the
+ 
+
+ align:start position:0%
+which are actually the products of the
+eigenvalues of A and B separately and
+
+ align:start position:0%
+eigenvalues of A and B separately and
+ 
+
+ align:start position:0%
+eigenvalues of A and B separately and
+the eigenvectors are just transposed of
+
+ align:start position:0%
+the eigenvectors are just transposed of
+ 
+
+ align:start position:0%
+the eigenvectors are just transposed of
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+okay and so uh
+
+ align:start position:0%
+okay and so uh
+ 
+
+ align:start position:0%
+okay and so uh
+so so maybe this is worth writing out on
+
+ align:start position:0%
+so so maybe this is worth writing out on
+ 
+
+ align:start position:0%
+so so maybe this is worth writing out on
+the board just to see it but this is
+
+ align:start position:0%
+the board just to see it but this is
+ 
+
+ align:start position:0%
+the board just to see it but this is
+kind of how I like to do this so
+
+ align:start position:0%
+kind of how I like to do this so
+ 
+
+ align:start position:0%
+kind of how I like to do this so
+if somebody tells me to talk about the
+
+ align:start position:0%
+if somebody tells me to talk about the
+ 
+
+ align:start position:0%
+if somebody tells me to talk about the
+derivative this this is my favorite way
+
+ align:start position:0%
+derivative this this is my favorite way
+ 
+
+ align:start position:0%
+derivative this this is my favorite way
+of seeing the derivative of x squared
+
+ align:start position:0%
+of seeing the derivative of x squared
+ 
+
+ align:start position:0%
+of seeing the derivative of x squared
+okay so I'm going to go over here and
+
+ align:start position:0%
+okay so I'm going to go over here and
+ 
+
+ align:start position:0%
+okay so I'm going to go over here and
+I'm going to say
+
+ align:start position:0%
+I'm going to say
+ 
+
+ align:start position:0%
+I'm going to say
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+the derivative of x squared
+
+ align:start position:0%
+the derivative of x squared
+ 
+
+ align:start position:0%
+the derivative of x squared
+which we've all known to we've seen this
+
+ align:start position:0%
+which we've all known to we've seen this
+ 
+
+ align:start position:0%
+which we've all known to we've seen this
+now a few times I'm going to use this
+
+ align:start position:0%
+now a few times I'm going to use this
+ 
+
+ align:start position:0%
+now a few times I'm going to use this
+white truck the derivative of x squared
+
+ align:start position:0%
+white truck the derivative of x squared
+ 
+
+ align:start position:0%
+white truck the derivative of x squared
+of course is going to be the Matrix x
+
+ align:start position:0%
+of course is going to be the Matrix x
+ 
+
+ align:start position:0%
+of course is going to be the Matrix x
+times DX plus DX
+
+ align:start position:0%
+times DX plus DX
+ 
+
+ align:start position:0%
+times DX plus DX
+X from the product rule okay
+
+ align:start position:0%
+X from the product rule okay
+ 
+
+ align:start position:0%
+X from the product rule okay
+but I'm going to look at this and I'm
+
+ align:start position:0%
+but I'm going to look at this and I'm
+ 
+
+ align:start position:0%
+but I'm going to look at this and I'm
+going to say in my mind this is x t x i
+
+ align:start position:0%
+going to say in my mind this is x t x i
+ 
+
+ align:start position:0%
+going to say in my mind this is x t x i
+right and this is i d x x
+
+ align:start position:0%
+right and this is i d x x
+ 
+
+ align:start position:0%
+right and this is i d x x
+I normally wouldn't write that out but
+
+ align:start position:0%
+I normally wouldn't write that out but
+ 
+
+ align:start position:0%
+I normally wouldn't write that out but
+just for purposes of showing you folks
+
+ align:start position:0%
+just for purposes of showing you folks
+ 
+
+ align:start position:0%
+just for purposes of showing you folks
+I'll put the identity Matrix in okay and
+
+ align:start position:0%
+I'll put the identity Matrix in okay and
+ 
+
+ align:start position:0%
+I'll put the identity Matrix in okay and
+then I would say that
+
+ align:start position:0%
+then I would say that
+ 
+
+ align:start position:0%
+then I would say that
+that uh what do which chronic or product
+
+ align:start position:0%
+that uh what do which chronic or product
+ 
+
+ align:start position:0%
+that uh what do which chronic or product
+do I need well let's see
+
+ align:start position:0%
+do I need well let's see
+ 
+
+ align:start position:0%
+do I need well let's see
+the thing that's on the left is going to
+
+ align:start position:0%
+the thing that's on the left is going to
+ 
+
+ align:start position:0%
+the thing that's on the left is going to
+be closest to the DX so I'll put the X
+
+ align:start position:0%
+be closest to the DX so I'll put the X
+ 
+
+ align:start position:0%
+be closest to the DX so I'll put the X
+here right and then this I would be
+
+ align:start position:0%
+here right and then this I would be
+ 
+
+ align:start position:0%
+here right and then this I would be
+transposed but since it's the identity I
+
+ align:start position:0%
+transposed but since it's the identity I
+ 
+
+ align:start position:0%
+transposed but since it's the identity I
+don't have to write that out okay and
+
+ align:start position:0%
+don't have to write that out okay and
+ 
+
+ align:start position:0%
+don't have to write that out okay and
+then here
+
+ align:start position:0%
+then here
+ 
+
+ align:start position:0%
+then here
+you see the same game the thing that's
+
+ align:start position:0%
+you see the same game the thing that's
+ 
+
+ align:start position:0%
+you see the same game the thing that's
+to the left of the DX is the I this
+
+ align:start position:0%
+to the left of the DX is the I this
+ 
+
+ align:start position:0%
+to the left of the DX is the I this
+thing then has to be X transpose
+
+ align:start position:0%
+thing then has to be X transpose
+ 
+
+ align:start position:0%
+thing then has to be X transpose
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+one one thing you could write is the VEC
+
+ align:start position:0%
+one one thing you could write is the VEC
+ 
+
+ align:start position:0%
+one one thing you could write is the VEC
+but I don't really like this but this
+
+ align:start position:0%
+but I don't really like this but this
+ 
+
+ align:start position:0%
+but I don't really like this but this
+would be reasonable to write the VEC of
+
+ align:start position:0%
+would be reasonable to write the VEC of
+ 
+
+ align:start position:0%
+would be reasonable to write the VEC of
+DX squared
+
+ align:start position:0%
+DX squared
+ 
+
+ align:start position:0%
+DX squared
+is this times the vector of x
+
+ align:start position:0%
+is this times the vector of x
+ 
+
+ align:start position:0%
+is this times the vector of x
+okay and this is expressing it's just
+
+ align:start position:0%
+okay and this is expressing it's just
+ 
+
+ align:start position:0%
+okay and this is expressing it's just
+another notation for what's over there
+
+ align:start position:0%
+another notation for what's over there
+ 
+
+ align:start position:0%
+another notation for what's over there
+okay but what I really like to write is
+
+ align:start position:0%
+okay but what I really like to write is
+ 
+
+ align:start position:0%
+okay but what I really like to write is
+I like to think of this as a linear
+
+ align:start position:0%
+I like to think of this as a linear
+ 
+
+ align:start position:0%
+I like to think of this as a linear
+operator and maybe I'll use the square
+
+ align:start position:0%
+operator and maybe I'll use the square
+ 
+
+ align:start position:0%
+operator and maybe I'll use the square
+brackets that Stephen likes to use and I
+
+ align:start position:0%
+brackets that Stephen likes to use and I
+ 
+
+ align:start position:0%
+brackets that Stephen likes to use and I
+think I would the one I would enjoy the
+
+ align:start position:0%
+think I would the one I would enjoy the
+ 
+
+ align:start position:0%
+think I would the one I would enjoy the
+most to write if I have to put
+
+ align:start position:0%
+most to write if I have to put
+ 
+
+ align:start position:0%
+most to write if I have to put
+everything on the you see there's
+
+ align:start position:0%
+everything on the you see there's
+ 
+
+ align:start position:0%
+everything on the you see there's
+something nice about putting the DX on
+
+ align:start position:0%
+something nice about putting the DX on
+ 
+
+ align:start position:0%
+something nice about putting the DX on
+the on the right so I think this is the
+
+ align:start position:0%
+the on the right so I think this is the
+ 
+
+ align:start position:0%
+the on the right so I think this is the
+notation that I would like the best this
+
+ align:start position:0%
+notation that I would like the best this
+ 
+
+ align:start position:0%
+notation that I would like the best this
+is equal to this as an operator acting
+
+ align:start position:0%
+is equal to this as an operator acting
+ 
+
+ align:start position:0%
+is equal to this as an operator acting
+on the X and
+
+ align:start position:0%
+on the X and
+ 
+
+ align:start position:0%
+on the X and
+okay and by that what I mean by that is
+
+ align:start position:0%
+okay and by that what I mean by that is
+ 
+
+ align:start position:0%
+okay and by that what I mean by that is
+if I ever have a chronic or B
+
+ align:start position:0%
+if I ever have a chronic or B
+ 
+
+ align:start position:0%
+if I ever have a chronic or B
+acting on anything
+
+ align:start position:0%
+acting on anything
+ 
+
+ align:start position:0%
+acting on anything
+I'll just call it m
+
+ align:start position:0%
+I'll just call it m
+ 
+
+ align:start position:0%
+I'll just call it m
+I'm going to have that mean
+
+ align:start position:0%
+I'm going to have that mean
+ 
+
+ align:start position:0%
+I'm going to have that mean
+a m sorry BM a transpose
+
+ align:start position:0%
+a m sorry BM a transpose
+ 
+
+ align:start position:0%
+a m sorry BM a transpose
+right so that would be my definition of
+
+ align:start position:0%
+right so that would be my definition of
+ 
+
+ align:start position:0%
+right so that would be my definition of
+a chronic or bracket with square with a
+
+ align:start position:0%
+a chronic or bracket with square with a
+ 
+
+ align:start position:0%
+a chronic or bracket with square with a
+square input
+
+ align:start position:0%
+square input
+ 
+
+ align:start position:0%
+square input
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you want to have the DX all on one
+
+ align:start position:0%
+if you want to have the DX all on one
+ 
+
+ align:start position:0%
+if you want to have the DX all on one
+side this is how I would do it yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effective DX thank you you are quite
+
+ align:start position:0%
+effective DX thank you you are quite
+ 
+
+ align:start position:0%
+effective DX thank you you are quite
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+good thanks for the catch perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so that's basically what I'm writing
+
+ align:start position:0%
+so that's basically what I'm writing
+ 
+
+ align:start position:0%
+so that's basically what I'm writing
+here in this part of the notes over here
+
+ align:start position:0%
+here in this part of the notes over here
+ 
+
+ align:start position:0%
+here in this part of the notes over here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and again this is I I often don't even
+
+ align:start position:0%
+and again this is I I often don't even
+ 
+
+ align:start position:0%
+and again this is I I often don't even
+put the square bracket so what I maybe
+
+ align:start position:0%
+put the square bracket so what I maybe
+ 
+
+ align:start position:0%
+put the square bracket so what I maybe
+it's not a bad idea to avoid confusion
+
+ align:start position:0%
+it's not a bad idea to avoid confusion
+ 
+
+ align:start position:0%
+it's not a bad idea to avoid confusion
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+kind of following Stephen's notation it
+
+ align:start position:0%
+kind of following Stephen's notation it
+ 
+
+ align:start position:0%
+kind of following Stephen's notation it
+would be sort of like this would be the
+
+ align:start position:0%
+would be sort of like this would be the
+ 
+
+ align:start position:0%
+would be sort of like this would be the
+way to do it as this chronic or operator
+
+ align:start position:0%
+way to do it as this chronic or operator
+ 
+
+ align:start position:0%
+way to do it as this chronic or operator
+acting on DX
+
+ align:start position:0%
+acting on DX
+ 
+
+ align:start position:0%
+acting on DX
+I find that there's never any real
+
+ align:start position:0%
+I find that there's never any real
+ 
+
+ align:start position:0%
+I find that there's never any real
+confusion and so I don't I don't write
+
+ align:start position:0%
+confusion and so I don't I don't write
+ 
+
+ align:start position:0%
+confusion and so I don't I don't write
+the VEC I don't put a square bracket I
+
+ align:start position:0%
+the VEC I don't put a square bracket I
+ 
+
+ align:start position:0%
+the VEC I don't put a square bracket I
+just do this I think I'm the only one
+
+ align:start position:0%
+just do this I think I'm the only one
+ 
+
+ align:start position:0%
+just do this I think I'm the only one
+who does this so there's no reason why
+
+ align:start position:0%
+who does this so there's no reason why
+ 
+
+ align:start position:0%
+who does this so there's no reason why
+you should follow me but I find it quite
+
+ align:start position:0%
+you should follow me but I find it quite
+ 
+
+ align:start position:0%
+you should follow me but I find it quite
+nice to just write it this way and drop
+
+ align:start position:0%
+nice to just write it this way and drop
+ 
+
+ align:start position:0%
+nice to just write it this way and drop
+the back I I think there's never any
+
+ align:start position:0%
+the back I I think there's never any
+ 
+
+ align:start position:0%
+the back I I think there's never any
+confusion this is an operator acting on
+
+ align:start position:0%
+confusion this is an operator acting on
+ 
+
+ align:start position:0%
+confusion this is an operator acting on
+the DX in just the way we say
+
+ align:start position:0%
+the DX in just the way we say
+ 
+
+ align:start position:0%
+the DX in just the way we say
+okay so you get to make your own choice
+
+ align:start position:0%
+okay so you get to make your own choice
+ 
+
+ align:start position:0%
+okay so you get to make your own choice
+that's how I like to do it
+
+ align:start position:0%
+that's how I like to do it
+ 
+
+ align:start position:0%
+that's how I like to do it
+all right uh
+
+ align:start position:0%
+all right uh
+ 
+
+ align:start position:0%
+all right uh
+okay so just to show off
+
+ align:start position:0%
+okay so just to show off
+ 
+
+ align:start position:0%
+okay so just to show off
+um a little bit in in Julia
+
+ align:start position:0%
+um a little bit in in Julia
+ 
+
+ align:start position:0%
+um a little bit in in Julia
+um so we can get these jacobians and
+
+ align:start position:0%
+um so we can get these jacobians and
+ 
+
+ align:start position:0%
+um so we can get these jacobians and
+Trulia using the automatic
+
+ align:start position:0%
+Trulia using the automatic
+ 
+
+ align:start position:0%
+Trulia using the automatic
+differentiation okay and we're going to
+
+ align:start position:0%
+differentiation okay and we're going to
+ 
+
+ align:start position:0%
+differentiation okay and we're going to
+talk about automatic differentiation I
+
+ align:start position:0%
+talk about automatic differentiation I
+ 
+
+ align:start position:0%
+talk about automatic differentiation I
+would imagine I don't know if it's later
+
+ align:start position:0%
+would imagine I don't know if it's later
+ 
+
+ align:start position:0%
+would imagine I don't know if it's later
+this week or or when are we talking
+
+ align:start position:0%
+this week or or when are we talking
+ 
+
+ align:start position:0%
+this week or or when are we talking
+about A.D Steven do we do we know later
+
+ align:start position:0%
+about A.D Steven do we do we know later
+ 
+
+ align:start position:0%
+about A.D Steven do we do we know later
+this week or maybe next week yeah I
+
+ align:start position:0%
+this week or maybe next week yeah I
+ 
+
+ align:start position:0%
+this week or maybe next week yeah I
+think probably like by Friday or
+
+ align:start position:0%
+think probably like by Friday or
+ 
+
+ align:start position:0%
+think probably like by Friday or
+something like that all right maybe by
+
+ align:start position:0%
+something like that all right maybe by
+ 
+
+ align:start position:0%
+something like that all right maybe by
+Friday we'll talk about automatic
+
+ align:start position:0%
+Friday we'll talk about automatic
+ 
+
+ align:start position:0%
+Friday we'll talk about automatic
+differentiation uh so the the key
+
+ align:start position:0%
+differentiation uh so the the key
+ 
+
+ align:start position:0%
+differentiation uh so the the key
+introduction for those of you who've
+
+ align:start position:0%
+introduction for those of you who've
+ 
+
+ align:start position:0%
+introduction for those of you who've
+never seen ad is that it's not symbolic
+
+ align:start position:0%
+never seen ad is that it's not symbolic
+ 
+
+ align:start position:0%
+never seen ad is that it's not symbolic
+like Mathematica and it's not numerical
+
+ align:start position:0%
+like Mathematica and it's not numerical
+ 
+
+ align:start position:0%
+like Mathematica and it's not numerical
+finite differences right it's it's none
+
+ align:start position:0%
+finite differences right it's it's none
+ 
+
+ align:start position:0%
+finite differences right it's it's none
+of those things it's something
+
+ align:start position:0%
+of those things it's something
+ 
+
+ align:start position:0%
+of those things it's something
+I mean of course it's mathematically
+
+ align:start position:0%
+I mean of course it's mathematically
+ 
+
+ align:start position:0%
+I mean of course it's mathematically
+equivalent and but it's it's when I
+
+ align:start position:0%
+equivalent and but it's it's when I
+ 
+
+ align:start position:0%
+equivalent and but it's it's when I
+first saw it I was kind of surprised as
+
+ align:start position:0%
+first saw it I was kind of surprised as
+ 
+
+ align:start position:0%
+first saw it I was kind of surprised as
+to exactly how it works
+
+ align:start position:0%
+to exactly how it works
+ 
+
+ align:start position:0%
+to exactly how it works
+so uh you might be surprised too but
+
+ align:start position:0%
+so uh you might be surprised too but
+ 
+
+ align:start position:0%
+so uh you might be surprised too but
+right now we're just going to be users
+
+ align:start position:0%
+right now we're just going to be users
+ 
+
+ align:start position:0%
+right now we're just going to be users
+I'm just going to grab here's that J
+
+ align:start position:0%
+I'm just going to grab here's that J
+ 
+
+ align:start position:0%
+I'm just going to grab here's that J
+Matrix and I'm just going to point out
+
+ align:start position:0%
+Matrix and I'm just going to point out
+ 
+
+ align:start position:0%
+Matrix and I'm just going to point out
+that if it'll compute the Jacobian of
+
+ align:start position:0%
+that if it'll compute the Jacobian of
+ 
+
+ align:start position:0%
+that if it'll compute the Jacobian of
+the square function at the point M right
+
+ align:start position:0%
+the square function at the point M right
+ 
+
+ align:start position:0%
+the square function at the point M right
+and we could check that it gives the
+
+ align:start position:0%
+and we could check that it gives the
+ 
+
+ align:start position:0%
+and we could check that it gives the
+right answer
+
+ align:start position:0%
+right answer
+ 
+
+ align:start position:0%
+right answer
+okay and in fact it'll work with symbols
+
+ align:start position:0%
+okay and in fact it'll work with symbols
+ 
+
+ align:start position:0%
+okay and in fact it'll work with symbols
+as well as at right so in some sense
+
+ align:start position:0%
+as well as at right so in some sense
+ 
+
+ align:start position:0%
+as well as at right so in some sense
+here we're getting the Jacobian at every
+
+ align:start position:0%
+here we're getting the Jacobian at every
+ 
+
+ align:start position:0%
+here we're getting the Jacobian at every
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+right because the you know the the
+
+ align:start position:0%
+right because the you know the the
+ 
+
+ align:start position:0%
+right because the you know the the
+elements are variables
+
+ align:start position:0%
+elements are variables
+ 
+
+ align:start position:0%
+elements are variables
+all right let's do everything we just
+
+ align:start position:0%
+all right let's do everything we just
+ 
+
+ align:start position:0%
+all right let's do everything we just
+did but let's let's kind of move up to
+
+ align:start position:0%
+did but let's let's kind of move up to
+ 
+
+ align:start position:0%
+did but let's let's kind of move up to
+the Matrix Cube function
+
+ align:start position:0%
+the Matrix Cube function
+ 
+
+ align:start position:0%
+the Matrix Cube function
+so here's the Matrix Cube function for
+
+ align:start position:0%
+so here's the Matrix Cube function for
+ 
+
+ align:start position:0%
+so here's the Matrix Cube function for
+two by two matrices written out in all
+
+ align:start position:0%
+two by two matrices written out in all
+ 
+
+ align:start position:0%
+two by two matrices written out in all
+of its Glory
+
+ align:start position:0%
+of its Glory
+ 
+
+ align:start position:0%
+of its Glory
+this is the sort of thing that if I did
+
+ align:start position:0%
+this is the sort of thing that if I did
+ 
+
+ align:start position:0%
+this is the sort of thing that if I did
+it on the Blackboard
+
+ align:start position:0%
+it on the Blackboard
+ 
+
+ align:start position:0%
+it on the Blackboard
+just writing it out would take a little
+
+ align:start position:0%
+just writing it out would take a little
+ 
+
+ align:start position:0%
+just writing it out would take a little
+too long but the computer doesn't mind
+
+ align:start position:0%
+too long but the computer doesn't mind
+ 
+
+ align:start position:0%
+too long but the computer doesn't mind
+right so there's the there's the Matrix
+
+ align:start position:0%
+right so there's the there's the Matrix
+ 
+
+ align:start position:0%
+right so there's the there's the Matrix
+Cube function right I mean the computer
+
+ align:start position:0%
+Cube function right I mean the computer
+ 
+
+ align:start position:0%
+Cube function right I mean the computer
+wouldn't care if I did x to the fourth
+
+ align:start position:0%
+wouldn't care if I did x to the fourth
+ 
+
+ align:start position:0%
+wouldn't care if I did x to the fourth
+I assume let's see what point does it
+
+ align:start position:0%
+I assume let's see what point does it
+ 
+
+ align:start position:0%
+I assume let's see what point does it
+get hairy maybe at the fifth it's kind
+
+ align:start position:0%
+get hairy maybe at the fifth it's kind
+ 
+
+ align:start position:0%
+get hairy maybe at the fifth it's kind
+of well you'd have to scroll but there
+
+ align:start position:0%
+of well you'd have to scroll but there
+ 
+
+ align:start position:0%
+of well you'd have to scroll but there
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+okay so let's do the cube
+
+ align:start position:0%
+okay so let's do the cube
+ 
+
+ align:start position:0%
+okay so let's do the cube
+all right so there's the Matrix Cube
+
+ align:start position:0%
+all right so there's the Matrix Cube
+ 
+
+ align:start position:0%
+all right so there's the Matrix Cube
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay and uh
+
+ align:start position:0%
+okay and uh
+ 
+
+ align:start position:0%
+okay and uh
+we can we we can get the Jacobian again
+
+ align:start position:0%
+we can we we can get the Jacobian again
+ 
+
+ align:start position:0%
+we can we we can get the Jacobian again
+it's just a matter of just to remind you
+
+ align:start position:0%
+it's just a matter of just to remind you
+ 
+
+ align:start position:0%
+it's just a matter of just to remind you
+that there's nothing I'm just laying the
+
+ align:start position:0%
+that there's nothing I'm just laying the
+ 
+
+ align:start position:0%
+that there's nothing I'm just laying the
+computer do the work but you all could
+
+ align:start position:0%
+computer do the work but you all could
+ 
+
+ align:start position:0%
+computer do the work but you all could
+do it if I took the derivative of this
+
+ align:start position:0%
+do it if I took the derivative of this
+ 
+
+ align:start position:0%
+do it if I took the derivative of this
+respect to P you get this expression
+
+ align:start position:0%
+respect to P you get this expression
+ 
+
+ align:start position:0%
+respect to P you get this expression
+there is with respect to Q you'd get RS
+
+ align:start position:0%
+there is with respect to Q you'd get RS
+ 
+
+ align:start position:0%
+there is with respect to Q you'd get RS
+plus two two PR right you can all do
+
+ align:start position:0%
+plus two two PR right you can all do
+ 
+
+ align:start position:0%
+plus two two PR right you can all do
+this derivative with respect to S and
+
+ align:start position:0%
+this derivative with respect to S and
+ 
+
+ align:start position:0%
+this derivative with respect to S and
+the derivative with respect to T and
+
+ align:start position:0%
+the derivative with respect to T and
+ 
+
+ align:start position:0%
+the derivative with respect to T and
+then you move down and do the same for
+
+ align:start position:0%
+then you move down and do the same for
+ 
+
+ align:start position:0%
+then you move down and do the same for
+this one and then this one then this one
+
+ align:start position:0%
+this one and then this one then this one
+ 
+
+ align:start position:0%
+this one and then this one then this one
+right but let the computer do the work
+
+ align:start position:0%
+right but let the computer do the work
+ 
+
+ align:start position:0%
+right but let the computer do the work
+and so here's all the 16 derivatives you
+
+ align:start position:0%
+and so here's all the 16 derivatives you
+ 
+
+ align:start position:0%
+and so here's all the 16 derivatives you
+know right here in our faces
+
+ align:start position:0%
+know right here in our faces
+ 
+
+ align:start position:0%
+know right here in our faces
+um and uh
+
+ align:start position:0%
+um and uh
+ 
+
+ align:start position:0%
+um and uh
+uh here let's see um so these are just
+
+ align:start position:0%
+uh here let's see um so these are just
+ 
+
+ align:start position:0%
+uh here let's see um so these are just
+two different ways to basically I guess
+
+ align:start position:0%
+two different ways to basically I guess
+ 
+
+ align:start position:0%
+two different ways to basically I guess
+write the same thing
+
+ align:start position:0%
+write the same thing
+ 
+
+ align:start position:0%
+write the same thing
+um so but of course we would you we
+
+ align:start position:0%
+um so but of course we would you we
+ 
+
+ align:start position:0%
+um so but of course we would you we
+would like to use the product rule so it
+
+ align:start position:0%
+would like to use the product rule so it
+ 
+
+ align:start position:0%
+would like to use the product rule so it
+would be DX times x squared plus X dxx
+
+ align:start position:0%
+would be DX times x squared plus X dxx
+ 
+
+ align:start position:0%
+would be DX times x squared plus X dxx
+Plus dxx squared right so Stephen showed
+
+ align:start position:0%
+Plus dxx squared right so Stephen showed
+ 
+
+ align:start position:0%
+Plus dxx squared right so Stephen showed
+you that I think the other day right and
+
+ align:start position:0%
+you that I think the other day right and
+ 
+
+ align:start position:0%
+you that I think the other day right and
+this cannot be simplified really I mean
+
+ align:start position:0%
+this cannot be simplified really I mean
+ 
+
+ align:start position:0%
+this cannot be simplified really I mean
+you could change notation but you can't
+
+ align:start position:0%
+you could change notation but you can't
+ 
+
+ align:start position:0%
+you could change notation but you can't
+combine any of these terms right so of
+
+ align:start position:0%
+combine any of these terms right so of
+ 
+
+ align:start position:0%
+combine any of these terms right so of
+course if it's a scalar
+
+ align:start position:0%
+course if it's a scalar
+ 
+
+ align:start position:0%
+course if it's a scalar
+if everything was a scalar this would
+
+ align:start position:0%
+if everything was a scalar this would
+ 
+
+ align:start position:0%
+if everything was a scalar this would
+this would amount to 3x squared DX which
+
+ align:start position:0%
+this would amount to 3x squared DX which
+ 
+
+ align:start position:0%
+this would amount to 3x squared DX which
+which is the ordinary 1801 kind of
+
+ align:start position:0%
+which is the ordinary 1801 kind of
+ 
+
+ align:start position:0%
+which is the ordinary 1801 kind of
+answer but for matrices this is all you
+
+ align:start position:0%
+answer but for matrices this is all you
+ 
+
+ align:start position:0%
+answer but for matrices this is all you
+get and so if you want to write this as
+
+ align:start position:0%
+get and so if you want to write this as
+ 
+
+ align:start position:0%
+get and so if you want to write this as
+a function as a linear function where e
+
+ align:start position:0%
+a function as a linear function where e
+ 
+
+ align:start position:0%
+a function as a linear function where e
+is the DX and M is the X you see that
+
+ align:start position:0%
+is the DX and M is the X you see that
+ 
+
+ align:start position:0%
+is the DX and M is the X you see that
+right so here I'm just just I guess I'm
+
+ align:start position:0%
+right so here I'm just just I guess I'm
+ 
+
+ align:start position:0%
+right so here I'm just just I guess I'm
+just using another notation where
+
+ align:start position:0%
+just using another notation where
+ 
+
+ align:start position:0%
+just using another notation where
+of E and M oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know for the X and X right so I'm
+
+ align:start position:0%
+you know for the X and X right so I'm
+ 
+
+ align:start position:0%
+you know for the X and X right so I'm
+just using these variables right this is
+
+ align:start position:0%
+just using these variables right this is
+ 
+
+ align:start position:0%
+just using these variables right this is
+the linear function right and again
+
+ align:start position:0%
+the linear function right and again
+ 
+
+ align:start position:0%
+the linear function right and again
+you know it takes sometimes it takes a
+
+ align:start position:0%
+you know it takes sometimes it takes a
+ 
+
+ align:start position:0%
+you know it takes sometimes it takes a
+little getting used to it's like you
+
+ align:start position:0%
+little getting used to it's like you
+ 
+
+ align:start position:0%
+little getting used to it's like you
+might look in this and say wait this is
+
+ align:start position:0%
+might look in this and say wait this is
+ 
+
+ align:start position:0%
+might look in this and say wait this is
+not a linear function I mean I've got an
+
+ align:start position:0%
+not a linear function I mean I've got an
+ 
+
+ align:start position:0%
+not a linear function I mean I've got an
+M squared right or M times ETA this is
+
+ align:start position:0%
+M squared right or M times ETA this is
+ 
+
+ align:start position:0%
+M squared right or M times ETA this is
+not linear but why do I get to tell you
+
+ align:start position:0%
+not linear but why do I get to tell you
+ 
+
+ align:start position:0%
+not linear but why do I get to tell you
+that this is a linear function you've
+
+ align:start position:0%
+that this is a linear function you've
+ 
+
+ align:start position:0%
+that this is a linear function you've
+got squaring of M that's not linear
+
+ align:start position:0%
+got squaring of M that's not linear
+ 
+
+ align:start position:0%
+got squaring of M that's not linear
+squaring is not linear what
+
+ align:start position:0%
+squaring is not linear what
+ 
+
+ align:start position:0%
+squaring is not linear what
+it's linear in E Bingo right so this
+
+ align:start position:0%
+it's linear in E Bingo right so this
+ 
+
+ align:start position:0%
+it's linear in E Bingo right so this
+function is linear in E and that's all
+
+ align:start position:0%
+function is linear in E and that's all
+ 
+
+ align:start position:0%
+function is linear in E and that's all
+that ever matters right and I'll even
+
+ align:start position:0%
+that ever matters right and I'll even
+ 
+
+ align:start position:0%
+that ever matters right and I'll even
+remind you in ordinary freshman calculus
+
+ align:start position:0%
+remind you in ordinary freshman calculus
+ 
+
+ align:start position:0%
+remind you in ordinary freshman calculus
+that the derivative of x cubed 3x
+
+ align:start position:0%
+that the derivative of x cubed 3x
+ 
+
+ align:start position:0%
+that the derivative of x cubed 3x
+squared is not linear in X right the
+
+ align:start position:0%
+squared is not linear in X right the
+ 
+
+ align:start position:0%
+squared is not linear in X right the
+derivative actually is very non-linear
+
+ align:start position:0%
+derivative actually is very non-linear
+ 
+
+ align:start position:0%
+derivative actually is very non-linear
+in X it's quadratic in X right but what
+
+ align:start position:0%
+in X it's quadratic in X right but what
+ 
+
+ align:start position:0%
+in X it's quadratic in X right but what
+is linear is that if that if you make a
+
+ align:start position:0%
+is linear is that if that if you make a
+ 
+
+ align:start position:0%
+is linear is that if that if you make a
+perturbation e to the X then um the the
+
+ align:start position:0%
+perturbation e to the X then um the the
+ 
+
+ align:start position:0%
+perturbation e to the X then um the the
+the output is pertured by three x
+
+ align:start position:0%
+the output is pertured by three x
+ 
+
+ align:start position:0%
+the output is pertured by three x
+squared times e right and that is linear
+
+ align:start position:0%
+squared times e right and that is linear
+ 
+
+ align:start position:0%
+squared times e right and that is linear
+right so so this is what's going on in
+
+ align:start position:0%
+right so so this is what's going on in
+ 
+
+ align:start position:0%
+right so so this is what's going on in
+Matrix land
+
+ align:start position:0%
+Matrix land
+ 
+
+ align:start position:0%
+Matrix land
+okay here's a numerical finite
+
+ align:start position:0%
+okay here's a numerical finite
+ 
+
+ align:start position:0%
+okay here's a numerical finite
+difference here is this function applied
+
+ align:start position:0%
+difference here is this function applied
+ 
+
+ align:start position:0%
+difference here is this function applied
+to e and as usual you see that to the to
+
+ align:start position:0%
+to e and as usual you see that to the to
+ 
+
+ align:start position:0%
+to e and as usual you see that to the to
+a reasonable number of digits you get
+
+ align:start position:0%
+a reasonable number of digits you get
+ 
+
+ align:start position:0%
+a reasonable number of digits you get
+the same answer all right so Julia's
+
+ align:start position:0%
+the same answer all right so Julia's
+ 
+
+ align:start position:0%
+the same answer all right so Julia's
+this is Julia's function this linear
+
+ align:start position:0%
+this is Julia's function this linear
+ 
+
+ align:start position:0%
+this is Julia's function this linear
+function right here applied to the
+
+ align:start position:0%
+function right here applied to the
+ 
+
+ align:start position:0%
+function right here applied to the
+perturbation e
+
+ align:start position:0%
+perturbation e
+ 
+
+ align:start position:0%
+perturbation e
+right so the e e here is a dummy
+
+ align:start position:0%
+right so the e e here is a dummy
+ 
+
+ align:start position:0%
+right so the e e here is a dummy
+variable it's just the dummy variable
+
+ align:start position:0%
+variable it's just the dummy variable
+ 
+
+ align:start position:0%
+variable it's just the dummy variable
+for the function and then here e is the
+
+ align:start position:0%
+for the function and then here e is the
+ 
+
+ align:start position:0%
+for the function and then here e is the
+numerical perturbation that I'm making
+
+ align:start position:0%
+numerical perturbation that I'm making
+ 
+
+ align:start position:0%
+numerical perturbation that I'm making
+okay so is play having two roles here
+
+ align:start position:0%
+okay so is play having two roles here
+ 
+
+ align:start position:0%
+okay so is play having two roles here
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+we could check against the symbolic
+
+ align:start position:0%
+we could check against the symbolic
+ 
+
+ align:start position:0%
+we could check against the symbolic
+answer and of course I don't know how
+
+ align:start position:0%
+answer and of course I don't know how
+ 
+
+ align:start position:0%
+answer and of course I don't know how
+easy it is to see it maybe I'll just
+
+ align:start position:0%
+easy it is to see it maybe I'll just
+ 
+
+ align:start position:0%
+easy it is to see it maybe I'll just
+flatten up here but you could see that
+
+ align:start position:0%
+flatten up here but you could see that
+ 
+
+ align:start position:0%
+flatten up here but you could see that
+these numbers that are about to go off
+
+ align:start position:0%
+these numbers that are about to go off
+ 
+
+ align:start position:0%
+these numbers that are about to go off
+screen here are exactly the same here so
+
+ align:start position:0%
+screen here are exactly the same here so
+ 
+
+ align:start position:0%
+screen here are exactly the same here so
+everything checks out it all works out
+
+ align:start position:0%
+everything checks out it all works out
+ 
+
+ align:start position:0%
+everything checks out it all works out
+you get the right answer so how do we do
+
+ align:start position:0%
+you get the right answer so how do we do
+ 
+
+ align:start position:0%
+you get the right answer so how do we do
+this with the chronicle notation
+
+ align:start position:0%
+this with the chronicle notation
+ 
+
+ align:start position:0%
+this with the chronicle notation
+well um I think you know here let's just
+
+ align:start position:0%
+well um I think you know here let's just
+ 
+
+ align:start position:0%
+well um I think you know here let's just
+do this one on the Blackboard as well
+
+ align:start position:0%
+do this one on the Blackboard as well
+ 
+
+ align:start position:0%
+do this one on the Blackboard as well
+just just to do it
+
+ align:start position:0%
+just just to do it
+ 
+
+ align:start position:0%
+just just to do it
+so I'm just going to do the very same
+
+ align:start position:0%
+so I'm just going to do the very same
+ 
+
+ align:start position:0%
+so I'm just going to do the very same
+thing here but I'll do it for X cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+just to get the practice right so
+
+ align:start position:0%
+just to get the practice right so
+ 
+
+ align:start position:0%
+just to get the practice right so
+the xq version of what's here is going
+
+ align:start position:0%
+the xq version of what's here is going
+ 
+
+ align:start position:0%
+the xq version of what's here is going
+to be x squared DX plus X DX X plus d x
+
+ align:start position:0%
+to be x squared DX plus X DX X plus d x
+ 
+
+ align:start position:0%
+to be x squared DX plus X DX X plus d x
+x squared right
+
+ align:start position:0%
+x squared right
+ 
+
+ align:start position:0%
+x squared right
+okay and I'm going to look at this and
+
+ align:start position:0%
+okay and I'm going to look at this and
+ 
+
+ align:start position:0%
+okay and I'm going to look at this and
+say aha I Chronicle x squared right
+
+ align:start position:0%
+say aha I Chronicle x squared right
+ 
+
+ align:start position:0%
+say aha I Chronicle x squared right
+because x squared is multiplying DX on
+
+ align:start position:0%
+because x squared is multiplying DX on
+ 
+
+ align:start position:0%
+because x squared is multiplying DX on
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+here I'm going to look at this and say
+
+ align:start position:0%
+here I'm going to look at this and say
+ 
+
+ align:start position:0%
+here I'm going to look at this and say
+there's an X and an X transpose right
+
+ align:start position:0%
+there's an X and an X transpose right
+ 
+
+ align:start position:0%
+there's an X and an X transpose right
+because X is on the left and and X is on
+
+ align:start position:0%
+because X is on the left and and X is on
+ 
+
+ align:start position:0%
+because X is on the left and and X is on
+the right but it comes around and it
+
+ align:start position:0%
+the right but it comes around and it
+ 
+
+ align:start position:0%
+the right but it comes around and it
+gets transposed right and this one I'm
+
+ align:start position:0%
+gets transposed right and this one I'm
+ 
+
+ align:start position:0%
+gets transposed right and this one I'm
+going to say is X transpose squared
+
+ align:start position:0%
+going to say is X transpose squared
+ 
+
+ align:start position:0%
+going to say is X transpose squared
+Chronicle I because it's on the right
+
+ align:start position:0%
+Chronicle I because it's on the right
+ 
+
+ align:start position:0%
+Chronicle I because it's on the right
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+whatever is on the right here goes on
+
+ align:start position:0%
+whatever is on the right here goes on
+ 
+
+ align:start position:0%
+whatever is on the right here goes on
+the left here and gets transposed right
+
+ align:start position:0%
+the left here and gets transposed right
+ 
+
+ align:start position:0%
+the left here and gets transposed right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what I would write
+
+ align:start position:0%
+what I would write
+ 
+
+ align:start position:0%
+what I would write
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if you want to put in the square
+
+ align:start position:0%
+but if you want to put in the square
+ 
+
+ align:start position:0%
+but if you want to put in the square
+brackets to emphasize this is an
+
+ align:start position:0%
+brackets to emphasize this is an
+ 
+
+ align:start position:0%
+brackets to emphasize this is an
+operator that's fine by me right or you
+
+ align:start position:0%
+operator that's fine by me right or you
+ 
+
+ align:start position:0%
+operator that's fine by me right or you
+could of course put everything with Vex
+
+ align:start position:0%
+could of course put everything with Vex
+ 
+
+ align:start position:0%
+could of course put everything with Vex
+if if you want to as well right so you
+
+ align:start position:0%
+if if you want to as well right so you
+ 
+
+ align:start position:0%
+if if you want to as well right so you
+can so your choices are you can write
+
+ align:start position:0%
+can so your choices are you can write
+ 
+
+ align:start position:0%
+can so your choices are you can write
+this this is the operator notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could just write
+
+ align:start position:0%
+you could just write
+ 
+
+ align:start position:0%
+you could just write
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the same thing over here with a DX which
+
+ align:start position:0%
+the same thing over here with a DX which
+ 
+
+ align:start position:0%
+the same thing over here with a DX which
+is that this is the this is this is sort
+
+ align:start position:0%
+is that this is the this is this is sort
+ 
+
+ align:start position:0%
+is that this is the this is this is sort
+of Steven's notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess this is Alan's notation
+
+ align:start position:0%
+I guess this is Alan's notation
+ 
+
+ align:start position:0%
+I guess this is Alan's notation
+so you get you you get to pick
+
+ align:start position:0%
+so you get you you get to pick
+ 
+
+ align:start position:0%
+so you get you you get to pick
+and then finally most people's notation
+
+ align:start position:0%
+and then finally most people's notation
+ 
+
+ align:start position:0%
+and then finally most people's notation
+which I think is horrible is that the
+
+ align:start position:0%
+which I think is horrible is that the
+ 
+
+ align:start position:0%
+which I think is horrible is that the
+VEC
+
+ align:start position:0%
+VEC
+ 
+
+ align:start position:0%
+VEC
+if the X cubed is equal to all this
+
+ align:start position:0%
+if the X cubed is equal to all this
+ 
+
+ align:start position:0%
+if the X cubed is equal to all this
+times the VEC of DX
+
+ align:start position:0%
+times the VEC of DX
+ 
+
+ align:start position:0%
+times the VEC of DX
+so this is sort of the most standard
+
+ align:start position:0%
+so this is sort of the most standard
+ 
+
+ align:start position:0%
+so this is sort of the most standard
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you get to take your pick
+
+ align:start position:0%
+okay so you get to take your pick
+ 
+
+ align:start position:0%
+okay so you get to take your pick
+there's no one right answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it just did I write it in some other
+
+ align:start position:0%
+is it just did I write it in some other
+ 
+
+ align:start position:0%
+is it just did I write it in some other
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+I mean you know one plus two is two plus
+
+ align:start position:0%
+I mean you know one plus two is two plus
+ 
+
+ align:start position:0%
+I mean you know one plus two is two plus
+one kind of thing is that what we're
+
+ align:start position:0%
+one kind of thing is that what we're
+ 
+
+ align:start position:0%
+one kind of thing is that what we're
+talking about here yeah I've got the M
+
+ align:start position:0%
+talking about here yeah I've got the M
+ 
+
+ align:start position:0%
+talking about here yeah I've got the M
+squared on the right yeah I it's if you
+
+ align:start position:0%
+squared on the right yeah I it's if you
+ 
+
+ align:start position:0%
+squared on the right yeah I it's if you
+look at this one oh yeah I
+
+ align:start position:0%
+look at this one oh yeah I
+ 
+
+ align:start position:0%
+look at this one oh yeah I
+um yeah that doesn't matter though yeah
+
+ align:start position:0%
+um yeah that doesn't matter though yeah
+ 
+
+ align:start position:0%
+um yeah that doesn't matter though yeah
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+um right or even up here
+
+ align:start position:0%
+um right or even up here
+ 
+
+ align:start position:0%
+um right or even up here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah so but of course
+
+ align:start position:0%
+yeah so but of course
+ 
+
+ align:start position:0%
+yeah so but of course
+um uh uh it looks like you have e times
+
+ align:start position:0%
+um uh uh it looks like you have e times
+ 
+
+ align:start position:0%
+um uh uh it looks like you have e times
+M twice is one of those supposed to be M
+
+ align:start position:0%
+M twice is one of those supposed to be M
+ 
+
+ align:start position:0%
+M twice is one of those supposed to be M
+times M times Z oh
+
+ align:start position:0%
+times M times Z oh
+ 
+
+ align:start position:0%
+times M times Z oh
+how did that happen oh is that what you
+
+ align:start position:0%
+how did that happen oh is that what you
+ 
+
+ align:start position:0%
+how did that happen oh is that what you
+were noticing oh that's not good news
+
+ align:start position:0%
+were noticing oh that's not good news
+ 
+
+ align:start position:0%
+were noticing oh that's not good news
+how did I get the right answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh you know I happen to pick an e that
+
+ align:start position:0%
+oh you know I happen to pick an e that
+ 
+
+ align:start position:0%
+oh you know I happen to pick an e that
+commuted with M which is probably not a
+
+ align:start position:0%
+commuted with M which is probably not a
+ 
+
+ align:start position:0%
+commuted with M which is probably not a
+good check
+
+ align:start position:0%
+good check
+ 
+
+ align:start position:0%
+good check
+you're oh my gosh that's exactly why I
+
+ align:start position:0%
+you're oh my gosh that's exactly why I
+ 
+
+ align:start position:0%
+you're oh my gosh that's exactly why I
+got the right answer don't ever tick so
+
+ align:start position:0%
+got the right answer don't ever tick so
+ 
+
+ align:start position:0%
+got the right answer don't ever tick so
+I didn't really have a good General test
+
+ align:start position:0%
+I didn't really have a good General test
+ 
+
+ align:start position:0%
+I didn't really have a good General test
+I see so let's yeah so let's another one
+
+ align:start position:0%
+I see so let's yeah so let's another one
+ 
+
+ align:start position:0%
+I see so let's yeah so let's another one
+below it looks like
+
+ align:start position:0%
+below it looks like
+ 
+
+ align:start position:0%
+below it looks like
+uh yeah I probably copied and pasted it
+
+ align:start position:0%
+uh yeah I probably copied and pasted it
+ 
+
+ align:start position:0%
+uh yeah I probably copied and pasted it
+you're right oh good catch
+
+ align:start position:0%
+you're right oh good catch
+ 
+
+ align:start position:0%
+you're right oh good catch
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+why did I do that
+
+ align:start position:0%
+why did I do that
+ 
+
+ align:start position:0%
+why did I do that
+so yeah so we should fix the thing
+
+ align:start position:0%
+so yeah so we should fix the thing
+ 
+
+ align:start position:0%
+so yeah so we should fix the thing
+online not just what I'm doing here so
+
+ align:start position:0%
+online not just what I'm doing here so
+ 
+
+ align:start position:0%
+online not just what I'm doing here so
+where did I Define e or
+
+ align:start position:0%
+where did I Define e or
+ 
+
+ align:start position:0%
+where did I Define e or
+well then I let's
+
+ align:start position:0%
+well then I let's
+ 
+
+ align:start position:0%
+well then I let's
+did he get to find earlier and earlier
+
+ align:start position:0%
+did he get to find earlier and earlier
+ 
+
+ align:start position:0%
+did he get to find earlier and earlier
+there's a way in Pluto
+
+ align:start position:0%
+there's a way in Pluto
+ 
+
+ align:start position:0%
+there's a way in Pluto
+to um
+
+ align:start position:0%
+to um
+ 
+
+ align:start position:0%
+to um
+if you you go below the E and I think
+
+ align:start position:0%
+if you you go below the E and I think
+ 
+
+ align:start position:0%
+if you you go below the E and I think
+you hit command or option oh command
+
+ align:start position:0%
+you hit command or option oh command
+ 
+
+ align:start position:0%
+you hit command or option oh command
+click to jump to the definition okay so
+
+ align:start position:0%
+click to jump to the definition okay so
+ 
+
+ align:start position:0%
+click to jump to the definition okay so
+let's see if I command click there's my
+
+ align:start position:0%
+let's see if I command click there's my
+ 
+
+ align:start position:0%
+let's see if I command click there's my
+okay so this is where yeah because it
+
+ align:start position:0%
+okay so this is where yeah because it
+ 
+
+ align:start position:0%
+okay so this is where yeah because it
+because he committed with them I got
+
+ align:start position:0%
+because he committed with them I got
+ 
+
+ align:start position:0%
+because he committed with them I got
+away with murder so let's do the
+
+ align:start position:0%
+away with murder so let's do the
+ 
+
+ align:start position:0%
+away with murder so let's do the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+let's not do that let's go round of two
+
+ align:start position:0%
+let's not do that let's go round of two
+ 
+
+ align:start position:0%
+let's not do that let's go round of two
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+divided by one ten thousand or something
+
+ align:start position:0%
+divided by one ten thousand or something
+ 
+
+ align:start position:0%
+divided by one ten thousand or something
+so here's a perturbation okay and I'll
+
+ align:start position:0%
+so here's a perturbation okay and I'll
+ 
+
+ align:start position:0%
+so here's a perturbation okay and I'll
+point out that with this one I really
+
+ align:start position:0%
+point out that with this one I really
+ 
+
+ align:start position:0%
+point out that with this one I really
+did have the wrong answer and thank you
+
+ align:start position:0%
+did have the wrong answer and thank you
+ 
+
+ align:start position:0%
+did have the wrong answer and thank you
+for catching that
+
+ align:start position:0%
+for catching that
+ 
+
+ align:start position:0%
+for catching that
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let's see so where where were we before
+
+ align:start position:0%
+let's see so where where were we before
+ 
+
+ align:start position:0%
+let's see so where where were we before
+we had all the wrong answers so here
+
+ align:start position:0%
+we had all the wrong answers so here
+ 
+
+ align:start position:0%
+we had all the wrong answers so here
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um so if I did this
+
+ align:start position:0%
+um so if I did this
+ 
+
+ align:start position:0%
+um so if I did this
+no actually it doesn't matter right here
+
+ align:start position:0%
+no actually it doesn't matter right here
+ 
+
+ align:start position:0%
+no actually it doesn't matter right here
+but if I did it over here
+
+ align:start position:0%
+but if I did it over here
+ 
+
+ align:start position:0%
+but if I did it over here
+so you see we're getting the right
+
+ align:start position:0%
+so you see we're getting the right
+ 
+
+ align:start position:0%
+so you see we're getting the right
+answer now
+
+ align:start position:0%
+answer now
+ 
+
+ align:start position:0%
+answer now
+but if I put back what I had at the
+
+ align:start position:0%
+but if I put back what I had at the
+ 
+
+ align:start position:0%
+but if I put back what I had at the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+you'd see I'd have the wrong answer
+
+ align:start position:0%
+you'd see I'd have the wrong answer
+ 
+
+ align:start position:0%
+you'd see I'd have the wrong answer
+so it really did matter and I'm glad you
+
+ align:start position:0%
+so it really did matter and I'm glad you
+ 
+
+ align:start position:0%
+so it really did matter and I'm glad you
+found it
+
+ align:start position:0%
+found it
+ 
+
+ align:start position:0%
+found it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+nobody found that last year
+
+ align:start position:0%
+nobody found that last year
+ 
+
+ align:start position:0%
+nobody found that last year
+and I think I even showed this in
+
+ align:start position:0%
+and I think I even showed this in
+ 
+
+ align:start position:0%
+and I think I even showed this in
+another class
+
+ align:start position:0%
+another class
+ 
+
+ align:start position:0%
+another class
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+but I had a notebook that I showed for
+
+ align:start position:0%
+but I had a notebook that I showed for
+ 
+
+ align:start position:0%
+but I had a notebook that I showed for
+about four or five years until somebody
+
+ align:start position:0%
+about four or five years until somebody
+ 
+
+ align:start position:0%
+about four or five years until somebody
+found the mistake so we're doing better
+
+ align:start position:0%
+found the mistake so we're doing better
+ 
+
+ align:start position:0%
+found the mistake so we're doing better
+okay good any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about so
+
+ align:start position:0%
+about so
+ 
+
+ align:start position:0%
+about so
+all right so there all right let's move
+
+ align:start position:0%
+all right so there all right let's move
+ 
+
+ align:start position:0%
+all right so there all right let's move
+on to something that might seem a little
+
+ align:start position:0%
+on to something that might seem a little
+ 
+
+ align:start position:0%
+on to something that might seem a little
+bit kind of even more interesting
+
+ align:start position:0%
+bit kind of even more interesting
+ 
+
+ align:start position:0%
+bit kind of even more interesting
+something that I like to think of as a
+
+ align:start position:0%
+something that I like to think of as a
+ 
+
+ align:start position:0%
+something that I like to think of as a
+matrix function but you know however you
+
+ align:start position:0%
+matrix function but you know however you
+ 
+
+ align:start position:0%
+matrix function but you know however you
+want to think about it is fine the Lu
+
+ align:start position:0%
+want to think about it is fine the Lu
+ 
+
+ align:start position:0%
+want to think about it is fine the Lu
+decomposition
+
+ align:start position:0%
+decomposition
+ 
+
+ align:start position:0%
+decomposition
+okay so let's think about this for a
+
+ align:start position:0%
+okay so let's think about this for a
+ 
+
+ align:start position:0%
+okay so let's think about this for a
+minute does everybody know what Lu even
+
+ align:start position:0%
+minute does everybody know what Lu even
+ 
+
+ align:start position:0%
+minute does everybody know what Lu even
+means just to make sure so uh so the OU
+
+ align:start position:0%
+means just to make sure so uh so the OU
+ 
+
+ align:start position:0%
+means just to make sure so uh so the OU
+decomposition says that
+
+ align:start position:0%
+decomposition says that
+ 
+
+ align:start position:0%
+decomposition says that
+that a matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which uh by the way it doesn't always
+
+ align:start position:0%
+which uh by the way it doesn't always
+ 
+
+ align:start position:0%
+which uh by the way it doesn't always
+exist but it kind of often exists a
+
+ align:start position:0%
+exist but it kind of often exists a
+ 
+
+ align:start position:0%
+exist but it kind of often exists a
+matrix a can be written
+
+ align:start position:0%
+matrix a can be written
+ 
+
+ align:start position:0%
+matrix a can be written
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+unit lower triangular which means once
+
+ align:start position:0%
+unit lower triangular which means once
+ 
+
+ align:start position:0%
+unit lower triangular which means once
+on the diagonal
+
+ align:start position:0%
+on the diagonal
+ 
+
+ align:start position:0%
+on the diagonal
+times an upper triangular Matrix no
+
+ align:start position:0%
+times an upper triangular Matrix no
+ 
+
+ align:start position:0%
+times an upper triangular Matrix no
+assumptions about the diagonal okay and
+
+ align:start position:0%
+assumptions about the diagonal okay and
+ 
+
+ align:start position:0%
+assumptions about the diagonal okay and
+so this is called the Lu decomposition
+
+ align:start position:0%
+so this is called the Lu decomposition
+ 
+
+ align:start position:0%
+so this is called the Lu decomposition
+of a matrix and you've all you've all
+
+ align:start position:0%
+of a matrix and you've all you've all
+ 
+
+ align:start position:0%
+of a matrix and you've all you've all
+seen it you've all heard the word Lu
+
+ align:start position:0%
+seen it you've all heard the word Lu
+ 
+
+ align:start position:0%
+seen it you've all heard the word Lu
+it's it's equivalent to gaussian
+
+ align:start position:0%
+it's it's equivalent to gaussian
+ 
+
+ align:start position:0%
+it's it's equivalent to gaussian
+elimination
+
+ align:start position:0%
+elimination
+ 
+
+ align:start position:0%
+elimination
+okay and one thing that's worth pointing
+
+ align:start position:0%
+okay and one thing that's worth pointing
+ 
+
+ align:start position:0%
+okay and one thing that's worth pointing
+out is that if a is an N by n Matrix so
+
+ align:start position:0%
+out is that if a is an N by n Matrix so
+ 
+
+ align:start position:0%
+out is that if a is an N by n Matrix so
+it has N squared elements
+
+ align:start position:0%
+it has N squared elements
+ 
+
+ align:start position:0%
+it has N squared elements
+right if you look at sort of the the
+
+ align:start position:0%
+right if you look at sort of the the
+ 
+
+ align:start position:0%
+right if you look at sort of the the
+amount of memory you need that you know
+
+ align:start position:0%
+amount of memory you need that you know
+ 
+
+ align:start position:0%
+amount of memory you need that you know
+the number of numbers that you have to
+
+ align:start position:0%
+the number of numbers that you have to
+ 
+
+ align:start position:0%
+the number of numbers that you have to
+to write out L as a matrix what you need
+
+ align:start position:0%
+to write out L as a matrix what you need
+ 
+
+ align:start position:0%
+to write out L as a matrix what you need
+is well let's see how many numbers are
+
+ align:start position:0%
+is well let's see how many numbers are
+ 
+
+ align:start position:0%
+is well let's see how many numbers are
+there sitting inside of a I mean we
+
+ align:start position:0%
+there sitting inside of a I mean we
+ 
+
+ align:start position:0%
+there sitting inside of a I mean we
+don't care about the zeros like how many
+
+ align:start position:0%
+don't care about the zeros like how many
+ 
+
+ align:start position:0%
+don't care about the zeros like how many
+like numbers with information in them
+
+ align:start position:0%
+like numbers with information in them
+ 
+
+ align:start position:0%
+like numbers with information in them
+how many numbers are in a upper
+
+ align:start position:0%
+how many numbers are in a upper
+ 
+
+ align:start position:0%
+how many numbers are in a upper
+triangular n by n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times n plus 1 over 2 exactly
+
+ align:start position:0%
+times n plus 1 over 2 exactly
+ 
+
+ align:start position:0%
+times n plus 1 over 2 exactly
+okay and then you know you don't even
+
+ align:start position:0%
+okay and then you know you don't even
+ 
+
+ align:start position:0%
+okay and then you know you don't even
+have to store the ones in fact uh uh uh
+
+ align:start position:0%
+have to store the ones in fact uh uh uh
+ 
+
+ align:start position:0%
+have to store the ones in fact uh uh uh
+all the linear algebra routines like La
+
+ align:start position:0%
+all the linear algebra routines like La
+ 
+
+ align:start position:0%
+all the linear algebra routines like La
+pack which is is what it's underneath
+
+ align:start position:0%
+pack which is is what it's underneath
+ 
+
+ align:start position:0%
+pack which is is what it's underneath
+Julia python or Matlab or whatever you
+
+ align:start position:0%
+Julia python or Matlab or whatever you
+ 
+
+ align:start position:0%
+Julia python or Matlab or whatever you
+like to use everybody's using the same
+
+ align:start position:0%
+like to use everybody's using the same
+ 
+
+ align:start position:0%
+like to use everybody's using the same
+La pack software under the hood they
+
+ align:start position:0%
+La pack software under the hood they
+ 
+
+ align:start position:0%
+La pack software under the hood they
+don't even store the ones because you
+
+ align:start position:0%
+don't even store the ones because you
+ 
+
+ align:start position:0%
+don't even store the ones because you
+don't have to right I mean why waste
+
+ align:start position:0%
+don't have to right I mean why waste
+ 
+
+ align:start position:0%
+don't have to right I mean why waste
+memory that you implicitly know it's a
+
+ align:start position:0%
+memory that you implicitly know it's a
+ 
+
+ align:start position:0%
+memory that you implicitly know it's a
+one so what are the number how many are
+
+ align:start position:0%
+one so what are the number how many are
+ 
+
+ align:start position:0%
+one so what are the number how many are
+there here that has information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many numbers on the outside
+
+ align:start position:0%
+how many numbers on the outside
+ 
+
+ align:start position:0%
+how many numbers on the outside
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+same but
+
+ align:start position:0%
+same but
+ 
+
+ align:start position:0%
+same but
+but a minus oh I like the way you said
+
+ align:start position:0%
+but a minus oh I like the way you said
+ 
+
+ align:start position:0%
+but a minus oh I like the way you said
+that the same but a minus okay n times n
+
+ align:start position:0%
+that the same but a minus okay n times n
+ 
+
+ align:start position:0%
+that the same but a minus okay n times n
+minus one over two good and if you add
+
+ align:start position:0%
+minus one over two good and if you add
+ 
+
+ align:start position:0%
+minus one over two good and if you add
+those two numbers up so if you I mean
+
+ align:start position:0%
+those two numbers up so if you I mean
+ 
+
+ align:start position:0%
+those two numbers up so if you I mean
+you can sort of do it visually if you
+
+ align:start position:0%
+you can sort of do it visually if you
+ 
+
+ align:start position:0%
+you can sort of do it visually if you
+like right you could
+
+ align:start position:0%
+like right you could
+ 
+
+ align:start position:0%
+like right you could
+add them up with you know this one's
+
+ align:start position:0%
+add them up with you know this one's
+ 
+
+ align:start position:0%
+add them up with you know this one's
+below the ones
+
+ align:start position:0%
+below the ones
+ 
+
+ align:start position:0%
+below the ones
+what do you what do you get
+
+ align:start position:0%
+what do you what do you get
+ 
+
+ align:start position:0%
+what do you what do you get
+you can visually add it visually or just
+
+ align:start position:0%
+you can visually add it visually or just
+ 
+
+ align:start position:0%
+you can visually add it visually or just
+do it algebraically whatever works for
+
+ align:start position:0%
+do it algebraically whatever works for
+ 
+
+ align:start position:0%
+do it algebraically whatever works for
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+what do you get
+
+ align:start position:0%
+what do you get
+ 
+
+ align:start position:0%
+what do you get
+N squared so
+
+ align:start position:0%
+N squared so
+ 
+
+ align:start position:0%
+N squared so
+I don't know if you ever stopped to
+
+ align:start position:0%
+I don't know if you ever stopped to
+ 
+
+ align:start position:0%
+I don't know if you ever stopped to
+think about this but the Lu
+
+ align:start position:0%
+think about this but the Lu
+ 
+
+ align:start position:0%
+think about this but the Lu
+decomposition is nothing other than a
+
+ align:start position:0%
+decomposition is nothing other than a
+ 
+
+ align:start position:0%
+decomposition is nothing other than a
+function from N squared variables to N
+
+ align:start position:0%
+function from N squared variables to N
+ 
+
+ align:start position:0%
+function from N squared variables to N
+squared variables right it's just a
+
+ align:start position:0%
+squared variables right it's just a
+ 
+
+ align:start position:0%
+squared variables right it's just a
+function from N squared variables to N
+
+ align:start position:0%
+function from N squared variables to N
+ 
+
+ align:start position:0%
+function from N squared variables to N
+squared variables and so therefore it
+
+ align:start position:0%
+squared variables and so therefore it
+ 
+
+ align:start position:0%
+squared variables and so therefore it
+has a Jacobian right it has a Jacobian
+
+ align:start position:0%
+has a Jacobian right it has a Jacobian
+ 
+
+ align:start position:0%
+has a Jacobian right it has a Jacobian
+that if you write it as a matrix will be
+
+ align:start position:0%
+that if you write it as a matrix will be
+ 
+
+ align:start position:0%
+that if you write it as a matrix will be
+N squared by N squared just as much as
+
+ align:start position:0%
+N squared by N squared just as much as
+ 
+
+ align:start position:0%
+N squared by N squared just as much as
+the Matrix square or Matrix Cube or the
+
+ align:start position:0%
+the Matrix square or Matrix Cube or the
+ 
+
+ align:start position:0%
+the Matrix square or Matrix Cube or the
+Matrix inverse function has a Jacobian
+
+ align:start position:0%
+Matrix inverse function has a Jacobian
+ 
+
+ align:start position:0%
+Matrix inverse function has a Jacobian
+that's N squared by N squared so does
+
+ align:start position:0%
+that's N squared by N squared so does
+ 
+
+ align:start position:0%
+that's N squared by N squared so does
+the Lu decomposition and in fact
+
+ align:start position:0%
+the Lu decomposition and in fact
+ 
+
+ align:start position:0%
+the Lu decomposition and in fact
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in fact here's the two by two version it
+
+ align:start position:0%
+in fact here's the two by two version it
+ 
+
+ align:start position:0%
+in fact here's the two by two version it
+gets more complicated when you go above
+
+ align:start position:0%
+gets more complicated when you go above
+ 
+
+ align:start position:0%
+gets more complicated when you go above
+two by two but here are L and U
+
+ align:start position:0%
+two by two but here are L and U
+ 
+
+ align:start position:0%
+two by two but here are L and U
+explicitly right so there's there so two
+
+ align:start position:0%
+explicitly right so there's there so two
+ 
+
+ align:start position:0%
+explicitly right so there's there so two
+by two Matrix has four elements and
+
+ align:start position:0%
+by two Matrix has four elements and
+ 
+
+ align:start position:0%
+by two Matrix has four elements and
+there's this one element in L and these
+
+ align:start position:0%
+there's this one element in L and these
+ 
+
+ align:start position:0%
+there's this one element in L and these
+three elements in U right and we could
+
+ align:start position:0%
+three elements in U right and we could
+ 
+
+ align:start position:0%
+three elements in U right and we could
+think of the Lu decomposition as
+
+ align:start position:0%
+think of the Lu decomposition as
+ 
+
+ align:start position:0%
+think of the Lu decomposition as
+the function from the four elements pqrs
+
+ align:start position:0%
+the function from the four elements pqrs
+ 
+
+ align:start position:0%
+the function from the four elements pqrs
+to these four numbers the the one in L
+
+ align:start position:0%
+to these four numbers the the one in L
+ 
+
+ align:start position:0%
+to these four numbers the the one in L
+and the three in U right so here's the
+
+ align:start position:0%
+and the three in U right so here's the
+ 
+
+ align:start position:0%
+and the three in U right so here's the
+oud composition in Julia just checking
+
+ align:start position:0%
+oud composition in Julia just checking
+ 
+
+ align:start position:0%
+oud composition in Julia just checking
+that L times U is is pqrs okay and so
+
+ align:start position:0%
+that L times U is is pqrs okay and so
+ 
+
+ align:start position:0%
+that L times U is is pqrs okay and so
+here are the four entries the the the
+
+ align:start position:0%
+here are the four entries the the the
+ 
+
+ align:start position:0%
+here are the four entries the the the
+the L entry over here and then the three
+
+ align:start position:0%
+the L entry over here and then the three
+ 
+
+ align:start position:0%
+the L entry over here and then the three
+U entries I'm just writing out and of
+
+ align:start position:0%
+U entries I'm just writing out and of
+ 
+
+ align:start position:0%
+U entries I'm just writing out and of
+course Julia would happily take the
+
+ align:start position:0%
+course Julia would happily take the
+ 
+
+ align:start position:0%
+course Julia would happily take the
+Jacobian of that function and give you
+
+ align:start position:0%
+Jacobian of that function and give you
+ 
+
+ align:start position:0%
+Jacobian of that function and give you
+the four by four Matrix Jacobian right
+
+ align:start position:0%
+the four by four Matrix Jacobian right
+ 
+
+ align:start position:0%
+the four by four Matrix Jacobian right
+and so I hope everybody remembers how
+
+ align:start position:0%
+and so I hope everybody remembers how
+ 
+
+ align:start position:0%
+and so I hope everybody remembers how
+this works I've said it a few times you
+
+ align:start position:0%
+this works I've said it a few times you
+ 
+
+ align:start position:0%
+this works I've said it a few times you
+take the first one Q over p and then
+
+ align:start position:0%
+take the first one Q over p and then
+ 
+
+ align:start position:0%
+take the first one Q over p and then
+take the respect to P that's minus Q
+
+ align:start position:0%
+take the respect to P that's minus Q
+ 
+
+ align:start position:0%
+take the respect to P that's minus Q
+over P Squared three respect to Q would
+
+ align:start position:0%
+over P Squared three respect to Q would
+ 
+
+ align:start position:0%
+over P Squared three respect to Q would
+be one over p and then there's no r or S
+
+ align:start position:0%
+be one over p and then there's no r or S
+ 
+
+ align:start position:0%
+be one over p and then there's no r or S
+here right and you can
+
+ align:start position:0%
+here right and you can
+ 
+
+ align:start position:0%
+here right and you can
+right and then you can do the same for
+
+ align:start position:0%
+right and then you can do the same for
+ 
+
+ align:start position:0%
+right and then you can do the same for
+the second third and fourth entry right
+
+ align:start position:0%
+the second third and fourth entry right
+ 
+
+ align:start position:0%
+the second third and fourth entry right
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so uh in fact I mean I'm writing this as
+
+ align:start position:0%
+so uh in fact I mean I'm writing this as
+ 
+
+ align:start position:0%
+so uh in fact I mean I'm writing this as
+an exercise but hopefully you can all
+
+ align:start position:0%
+an exercise but hopefully you can all
+ 
+
+ align:start position:0%
+an exercise but hopefully you can all
+see this this you can just do this with
+
+ align:start position:0%
+see this this you can just do this with
+ 
+
+ align:start position:0%
+see this this you can just do this with
+the product rule and get the right
+
+ align:start position:0%
+the product rule and get the right
+ 
+
+ align:start position:0%
+the product rule and get the right
+answer so dlu is going to be d o u plus
+
+ align:start position:0%
+answer so dlu is going to be d o u plus
+ 
+
+ align:start position:0%
+answer so dlu is going to be d o u plus
+ldu okay and did I write the answer here
+
+ align:start position:0%
+ldu okay and did I write the answer here
+ 
+
+ align:start position:0%
+ldu okay and did I write the answer here
+no all right I'll have you guys shout it
+
+ align:start position:0%
+no all right I'll have you guys shout it
+ 
+
+ align:start position:0%
+no all right I'll have you guys shout it
+out so let's see if you're kind of
+
+ align:start position:0%
+out so let's see if you're kind of
+ 
+
+ align:start position:0%
+out so let's see if you're kind of
+getting the hang of this chronic or
+
+ align:start position:0%
+getting the hang of this chronic or
+ 
+
+ align:start position:0%
+getting the hang of this chronic or
+product notation right and so the
+
+ align:start position:0%
+product notation right and so the
+ 
+
+ align:start position:0%
+product notation right and so the
+product rule says that dlu
+
+ align:start position:0%
+product rule says that dlu
+ 
+
+ align:start position:0%
+product rule says that dlu
+is going to equal l d u plus d l u or
+
+ align:start position:0%
+is going to equal l d u plus d l u or
+ 
+
+ align:start position:0%
+is going to equal l d u plus d l u or
+did I write it the other way not that it
+
+ align:start position:0%
+did I write it the other way not that it
+ 
+
+ align:start position:0%
+did I write it the other way not that it
+matters uh I wrote the other way it
+
+ align:start position:0%
+matters uh I wrote the other way it
+ 
+
+ align:start position:0%
+matters uh I wrote the other way it
+doesn't matter though plus d l u the
+
+ align:start position:0%
+doesn't matter though plus d l u the
+ 
+
+ align:start position:0%
+doesn't matter though plus d l u the
+thing that does matter is the L is
+
+ align:start position:0%
+thing that does matter is the L is
+ 
+
+ align:start position:0%
+thing that does matter is the L is
+always to the left of the U right it
+
+ align:start position:0%
+always to the left of the U right it
+ 
+
+ align:start position:0%
+always to the left of the U right it
+doesn't matter which term you write
+
+ align:start position:0%
+doesn't matter which term you write
+ 
+
+ align:start position:0%
+doesn't matter which term you write
+first though all right so anybody
+
+ align:start position:0%
+first though all right so anybody
+ 
+
+ align:start position:0%
+first though all right so anybody
+getting good at this what Chronicle
+
+ align:start position:0%
+getting good at this what Chronicle
+ 
+
+ align:start position:0%
+getting good at this what Chronicle
+product is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's an i and an L or something
+
+ align:start position:0%
+there's an i and an L or something
+ 
+
+ align:start position:0%
+there's an i and an L or something
+this one will have an i and a u you
+
+ align:start position:0%
+this one will have an i and a u you
+ 
+
+ align:start position:0%
+this one will have an i and a u you
+getting good at it yet
+
+ align:start position:0%
+getting good at it yet
+ 
+
+ align:start position:0%
+getting good at it yet
+this one's iconica L and then this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what what goes here what goes here
+
+ align:start position:0%
+what what what goes here what goes here
+ 
+
+ align:start position:0%
+what what what goes here what goes here
+U transverse Chronicle I exactly all
+
+ align:start position:0%
+U transverse Chronicle I exactly all
+ 
+
+ align:start position:0%
+U transverse Chronicle I exactly all
+right you guys are good right so you
+
+ align:start position:0%
+right you guys are good right so you
+ 
+
+ align:start position:0%
+right you guys are good right so you
+could write this like this and that I
+
+ align:start position:0%
+could write this like this and that I
+ 
+
+ align:start position:0%
+could write this like this and that I
+think is a perfectly good way to write
+
+ align:start position:0%
+think is a perfectly good way to write
+ 
+
+ align:start position:0%
+think is a perfectly good way to write
+down the Jacobian of course this is in
+
+ align:start position:0%
+down the Jacobian of course this is in
+ 
+
+ align:start position:0%
+down the Jacobian of course this is in
+Matrix form and it's not in separate
+
+ align:start position:0%
+Matrix form and it's not in separate
+ 
+
+ align:start position:0%
+Matrix form and it's not in separate
+form but it has all the right
+
+ align:start position:0%
+form but it has all the right
+ 
+
+ align:start position:0%
+form but it has all the right
+information yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that gets a little tricky but
+
+ align:start position:0%
+yeah that gets a little tricky but
+ 
+
+ align:start position:0%
+yeah that gets a little tricky but
+yeah that does get a little tricky so
+
+ align:start position:0%
+yeah that does get a little tricky so
+ 
+
+ align:start position:0%
+yeah that does get a little tricky so
+I'm just gonna I'm just gonna say that
+
+ align:start position:0%
+I'm just gonna I'm just gonna say that
+ 
+
+ align:start position:0%
+I'm just gonna I'm just gonna say that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+so the underlying Vector space is yeah
+
+ align:start position:0%
+so the underlying Vector space is yeah
+ 
+
+ align:start position:0%
+so the underlying Vector space is yeah
+yeah this is this is a little tricky so
+
+ align:start position:0%
+yeah this is this is a little tricky so
+ 
+
+ align:start position:0%
+yeah this is this is a little tricky so
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that I'm I like to think of the DL uh
+
+ align:start position:0%
+that I'm I like to think of the DL uh
+ 
+
+ align:start position:0%
+that I'm I like to think of the DL uh
+zero zero zero and then
+
+ align:start position:0%
+zero zero zero and then
+ 
+
+ align:start position:0%
+zero zero zero and then
+dl21 after all
+
+ align:start position:0%
+dl21 after all
+ 
+
+ align:start position:0%
+dl21 after all
+the ones the derivative of the ones on
+
+ align:start position:0%
+the ones the derivative of the ones on
+ 
+
+ align:start position:0%
+the ones the derivative of the ones on
+the diagonal zero and then everything
+
+ align:start position:0%
+the diagonal zero and then everything
+ 
+
+ align:start position:0%
+the diagonal zero and then everything
+else is zero anyway right and the D U is
+
+ align:start position:0%
+else is zero anyway right and the D U is
+ 
+
+ align:start position:0%
+else is zero anyway right and the D U is
+a zero d u one one d u one two and du22
+
+ align:start position:0%
+a zero d u one one d u one two and du22
+ 
+
+ align:start position:0%
+a zero d u one one d u one two and du22
+right so in some sense if you really
+
+ align:start position:0%
+right so in some sense if you really
+ 
+
+ align:start position:0%
+right so in some sense if you really
+wanted to do it the standard notation
+
+ align:start position:0%
+wanted to do it the standard notation
+ 
+
+ align:start position:0%
+wanted to do it the standard notation
+the way the one that would be like this
+
+ align:start position:0%
+the way the one that would be like this
+ 
+
+ align:start position:0%
+the way the one that would be like this
+you would have to write down
+
+ align:start position:0%
+you would have to write down
+ 
+
+ align:start position:0%
+you would have to write down
+you you would have to write down
+
+ align:start position:0%
+you you would have to write down
+ 
+
+ align:start position:0%
+you you would have to write down
+something that worked with the l21 and
+
+ align:start position:0%
+something that worked with the l21 and
+ 
+
+ align:start position:0%
+something that worked with the l21 and
+du11
+
+ align:start position:0%
+du11
+ 
+
+ align:start position:0%
+du11
+du12 and du22 but again I feel like
+
+ align:start position:0%
+du12 and du22 but again I feel like
+ 
+
+ align:start position:0%
+du12 and du22 but again I feel like
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+that's just like following the crowd
+
+ align:start position:0%
+that's just like following the crowd
+ 
+
+ align:start position:0%
+that's just like following the crowd
+right me I would rather just say that I
+
+ align:start position:0%
+right me I would rather just say that I
+ 
+
+ align:start position:0%
+right me I would rather just say that I
+understand that my Vector space consists
+
+ align:start position:0%
+understand that my Vector space consists
+ 
+
+ align:start position:0%
+understand that my Vector space consists
+of lower triangular perturbations to L
+
+ align:start position:0%
+of lower triangular perturbations to L
+ 
+
+ align:start position:0%
+of lower triangular perturbations to L
+and upper triangle perturbations to U
+
+ align:start position:0%
+and upper triangle perturbations to U
+ 
+
+ align:start position:0%
+and upper triangle perturbations to U
+and so let's just look at it that way
+
+ align:start position:0%
+and so let's just look at it that way
+ 
+
+ align:start position:0%
+and so let's just look at it that way
+okay and that's that's kind of how I
+
+ align:start position:0%
+okay and that's that's kind of how I
+ 
+
+ align:start position:0%
+okay and that's that's kind of how I
+like to see it but maybe that's maybe
+
+ align:start position:0%
+like to see it but maybe that's maybe
+ 
+
+ align:start position:0%
+like to see it but maybe that's maybe
+I'm pushing the notation too far maybe
+
+ align:start position:0%
+I'm pushing the notation too far maybe
+ 
+
+ align:start position:0%
+I'm pushing the notation too far maybe
+you would prefer you know maybe for the
+
+ align:start position:0%
+you would prefer you know maybe for the
+ 
+
+ align:start position:0%
+you would prefer you know maybe for the
+purposes of this class I would be better
+
+ align:start position:0%
+purposes of this class I would be better
+ 
+
+ align:start position:0%
+purposes of this class I would be better
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+doing it like this
+
+ align:start position:0%
+doing it like this
+ 
+
+ align:start position:0%
+doing it like this
+but even this is slightly yeah maybe
+
+ align:start position:0%
+but even this is slightly yeah maybe
+ 
+
+ align:start position:0%
+but even this is slightly yeah maybe
+that would be better for now
+
+ align:start position:0%
+that would be better for now
+ 
+
+ align:start position:0%
+that would be better for now
+but you see I like to put all my
+
+ align:start position:0%
+but you see I like to put all my
+ 
+
+ align:start position:0%
+but you see I like to put all my
+perturbations on the right so again
+
+ align:start position:0%
+perturbations on the right so again
+ 
+
+ align:start position:0%
+perturbations on the right so again
+there's nobody's fully standardized all
+
+ align:start position:0%
+there's nobody's fully standardized all
+ 
+
+ align:start position:0%
+there's nobody's fully standardized all
+this notation so once again you have
+
+ align:start position:0%
+this notation so once again you have
+ 
+
+ align:start position:0%
+this notation so once again you have
+your choice
+
+ align:start position:0%
+your choice
+ 
+
+ align:start position:0%
+your choice
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here I'll show you just a couple of
+
+ align:start position:0%
+so here I'll show you just a couple of
+ 
+
+ align:start position:0%
+so here I'll show you just a couple of
+more Matrix factorizations just quickly
+
+ align:start position:0%
+more Matrix factorizations just quickly
+ 
+
+ align:start position:0%
+more Matrix factorizations just quickly
+I'm not going to go into too much detail
+
+ align:start position:0%
+I'm not going to go into too much detail
+ 
+
+ align:start position:0%
+I'm not going to go into too much detail
+but I want you to just see that that you
+
+ align:start position:0%
+but I want you to just see that that you
+ 
+
+ align:start position:0%
+but I want you to just see that that you
+know you can still do this for other
+
+ align:start position:0%
+know you can still do this for other
+ 
+
+ align:start position:0%
+know you can still do this for other
+situations so one favorite of mine is a
+
+ align:start position:0%
+situations so one favorite of mine is a
+ 
+
+ align:start position:0%
+situations so one favorite of mine is a
+two parameter example
+
+ align:start position:0%
+two parameter example
+ 
+
+ align:start position:0%
+two parameter example
+um in you know two by two matrices have
+
+ align:start position:0%
+um in you know two by two matrices have
+ 
+
+ align:start position:0%
+um in you know two by two matrices have
+four parameters but but there's only two
+
+ align:start position:0%
+four parameters but but there's only two
+ 
+
+ align:start position:0%
+four parameters but but there's only two
+real parameters here which uh uh a
+
+ align:start position:0%
+real parameters here which uh uh a
+ 
+
+ align:start position:0%
+real parameters here which uh uh a
+traceless symmetric matrices so the fact
+
+ align:start position:0%
+traceless symmetric matrices so the fact
+ 
+
+ align:start position:0%
+traceless symmetric matrices so the fact
+that the Matrix two by two Matrix is
+
+ align:start position:0%
+that the Matrix two by two Matrix is
+ 
+
+ align:start position:0%
+that the Matrix two by two Matrix is
+symmetric means you have the S over here
+
+ align:start position:0%
+symmetric means you have the S over here
+ 
+
+ align:start position:0%
+symmetric means you have the S over here
+and over here and the fact that it's
+
+ align:start position:0%
+and over here and the fact that it's
+ 
+
+ align:start position:0%
+and over here and the fact that it's
+traceless is says that the trace is zero
+
+ align:start position:0%
+traceless is says that the trace is zero
+ 
+
+ align:start position:0%
+traceless is says that the trace is zero
+right so if you have a p over here you
+
+ align:start position:0%
+right so if you have a p over here you
+ 
+
+ align:start position:0%
+right so if you have a p over here you
+need a minus P to make the sum of the
+
+ align:start position:0%
+need a minus P to make the sum of the
+ 
+
+ align:start position:0%
+need a minus P to make the sum of the
+diagonal zero okay and so this is a two
+
+ align:start position:0%
+diagonal zero okay and so this is a two
+ 
+
+ align:start position:0%
+diagonal zero okay and so this is a two
+parameter family and this is by the way
+
+ align:start position:0%
+parameter family and this is by the way
+ 
+
+ align:start position:0%
+parameter family and this is by the way
+the queue that showed up on top right so
+
+ align:start position:0%
+the queue that showed up on top right so
+ 
+
+ align:start position:0%
+the queue that showed up on top right so
+uh if you if you write down you all know
+
+ align:start position:0%
+uh if you if you write down you all know
+ 
+
+ align:start position:0%
+uh if you if you write down you all know
+that symmetric matrices have orthogonal
+
+ align:start position:0%
+that symmetric matrices have orthogonal
+ 
+
+ align:start position:0%
+that symmetric matrices have orthogonal
+eigenvectors so you can write it with
+
+ align:start position:0%
+eigenvectors so you can write it with
+ 
+
+ align:start position:0%
+eigenvectors so you can write it with
+cosines and Sines and as a little bit of
+
+ align:start position:0%
+cosines and Sines and as a little bit of
+ 
+
+ align:start position:0%
+cosines and Sines and as a little bit of
+setup I'm using one half Theta as as
+
+ align:start position:0%
+setup I'm using one half Theta as as
+ 
+
+ align:start position:0%
+setup I'm using one half Theta as as
+opposed to just using Theta okay and
+
+ align:start position:0%
+opposed to just using Theta okay and
+ 
+
+ align:start position:0%
+opposed to just using Theta okay and
+and here's my eigenvalues The eigenvalue
+
+ align:start position:0%
+and here's my eigenvalues The eigenvalue
+ 
+
+ align:start position:0%
+and here's my eigenvalues The eigenvalue
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+the only thing that we know about the
+
+ align:start position:0%
+the only thing that we know about the
+ 
+
+ align:start position:0%
+the only thing that we know about the
+eigenvalue Matrix for starters is is
+
+ align:start position:0%
+eigenvalue Matrix for starters is is
+ 
+
+ align:start position:0%
+eigenvalue Matrix for starters is is
+that the sum of the eigenvalues are zero
+
+ align:start position:0%
+that the sum of the eigenvalues are zero
+ 
+
+ align:start position:0%
+that the sum of the eigenvalues are zero
+so let's call this the positive one and
+
+ align:start position:0%
+so let's call this the positive one and
+ 
+
+ align:start position:0%
+so let's call this the positive one and
+this the negative one okay and
+
+ align:start position:0%
+this the negative one okay and
+ 
+
+ align:start position:0%
+this the negative one okay and
+what what we have to equate is this is
+
+ align:start position:0%
+what what we have to equate is this is
+ 
+
+ align:start position:0%
+what what we have to equate is this is
+the eigen decomposition right so uh so
+
+ align:start position:0%
+the eigen decomposition right so uh so
+ 
+
+ align:start position:0%
+the eigen decomposition right so uh so
+so so you know these two are equal these
+
+ align:start position:0%
+so so you know these two are equal these
+ 
+
+ align:start position:0%
+so so you know these two are equal these
+two are opposite And So It all becomes
+
+ align:start position:0%
+two are opposite And So It all becomes
+ 
+
+ align:start position:0%
+two are opposite And So It all becomes
+let's see if we can get this right here
+
+ align:start position:0%
+let's see if we can get this right here
+ 
+
+ align:start position:0%
+let's see if we can get this right here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so so this is the Matrix
+
+ align:start position:0%
+yeah so so this is the Matrix
+ 
+
+ align:start position:0%
+yeah so so this is the Matrix
+okay and um this is the Matrix has two
+
+ align:start position:0%
+okay and um this is the Matrix has two
+ 
+
+ align:start position:0%
+okay and um this is the Matrix has two
+parameters P and S the eigen
+
+ align:start position:0%
+parameters P and S the eigen
+ 
+
+ align:start position:0%
+parameters P and S the eigen
+decomposition has two parameters maybe I
+
+ align:start position:0%
+decomposition has two parameters maybe I
+ 
+
+ align:start position:0%
+decomposition has two parameters maybe I
+should have emphasized that so the
+
+ align:start position:0%
+should have emphasized that so the
+ 
+
+ align:start position:0%
+should have emphasized that so the
+eigenvectors have one parameter Theta
+
+ align:start position:0%
+eigenvectors have one parameter Theta
+ 
+
+ align:start position:0%
+eigenvectors have one parameter Theta
+and the eigenvalue has one parameter R
+
+ align:start position:0%
+and the eigenvalue has one parameter R
+ 
+
+ align:start position:0%
+and the eigenvalue has one parameter R
+right so so the eigen decomposition here
+
+ align:start position:0%
+right so so the eigen decomposition here
+ 
+
+ align:start position:0%
+right so so the eigen decomposition here
+this little two by two eigen
+
+ align:start position:0%
+this little two by two eigen
+ 
+
+ align:start position:0%
+this little two by two eigen
+decomposition is a map from the two
+
+ align:start position:0%
+decomposition is a map from the two
+ 
+
+ align:start position:0%
+decomposition is a map from the two
+variables PS to the two variables R
+
+ align:start position:0%
+variables PS to the two variables R
+ 
+
+ align:start position:0%
+variables PS to the two variables R
+Theta right and Computing the
+
+ align:start position:0%
+Theta right and Computing the
+ 
+
+ align:start position:0%
+Theta right and Computing the
+eigenvalues of this two by two Matrix is
+
+ align:start position:0%
+eigenvalues of this two by two Matrix is
+ 
+
+ align:start position:0%
+eigenvalues of this two by two Matrix is
+just a map from R2 to R2
+
+ align:start position:0%
+just a map from R2 to R2
+ 
+
+ align:start position:0%
+just a map from R2 to R2
+okay and we can get the Jacobian and
+
+ align:start position:0%
+okay and we can get the Jacobian and
+ 
+
+ align:start position:0%
+okay and we can get the Jacobian and
+here's the Jacobian of that map right so
+
+ align:start position:0%
+here's the Jacobian of that map right so
+ 
+
+ align:start position:0%
+here's the Jacobian of that map right so
+this is the actual two by two Jacobian
+
+ align:start position:0%
+this is the actual two by two Jacobian
+ 
+
+ align:start position:0%
+this is the actual two by two Jacobian
+of of that and sometimes it's fun to
+
+ align:start position:0%
+of of that and sometimes it's fun to
+ 
+
+ align:start position:0%
+of of that and sometimes it's fun to
+compute the Jacobian determinant which
+
+ align:start position:0%
+compute the Jacobian determinant which
+ 
+
+ align:start position:0%
+compute the Jacobian determinant which
+is r in this case
+
+ align:start position:0%
+is r in this case
+ 
+
+ align:start position:0%
+is r in this case
+and some of you might recognize that
+
+ align:start position:0%
+and some of you might recognize that
+ 
+
+ align:start position:0%
+and some of you might recognize that
+this eigen decomposition change of
+
+ align:start position:0%
+this eigen decomposition change of
+ 
+
+ align:start position:0%
+this eigen decomposition change of
+coordinates is exactly the same
+
+ align:start position:0%
+coordinates is exactly the same
+ 
+
+ align:start position:0%
+coordinates is exactly the same
+mathematical change of coordinates of
+
+ align:start position:0%
+mathematical change of coordinates of
+ 
+
+ align:start position:0%
+mathematical change of coordinates of
+going from Cartesian to Polar
+
+ align:start position:0%
+going from Cartesian to Polar
+ 
+
+ align:start position:0%
+going from Cartesian to Polar
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+okay and this determinant R is exactly
+
+ align:start position:0%
+okay and this determinant R is exactly
+ 
+
+ align:start position:0%
+okay and this determinant R is exactly
+the so you know many of you probably
+
+ align:start position:0%
+the so you know many of you probably
+ 
+
+ align:start position:0%
+the so you know many of you probably
+memorized that that the area element in
+
+ align:start position:0%
+memorized that that the area element in
+ 
+
+ align:start position:0%
+memorized that that the area element in
+Cartesian coordinates the x d y is rdrd
+
+ align:start position:0%
+Cartesian coordinates the x d y is rdrd
+ 
+
+ align:start position:0%
+Cartesian coordinates the x d y is rdrd
+Theta well here's we just we just in
+
+ align:start position:0%
+Theta well here's we just we just in
+ 
+
+ align:start position:0%
+Theta well here's we just we just in
+effect let let Julia derive that for us
+
+ align:start position:0%
+effect let let Julia derive that for us
+ 
+
+ align:start position:0%
+effect let let Julia derive that for us
+okay but let's go further I'll do one
+
+ align:start position:0%
+okay but let's go further I'll do one
+ 
+
+ align:start position:0%
+okay but let's go further I'll do one
+more example
+
+ align:start position:0%
+more example
+ 
+
+ align:start position:0%
+more example
+the full two by two symmetric eigen
+
+ align:start position:0%
+the full two by two symmetric eigen
+ 
+
+ align:start position:0%
+the full two by two symmetric eigen
+problem but any questions about
+
+ align:start position:0%
+problem but any questions about
+ 
+
+ align:start position:0%
+problem but any questions about
+about this sort of restricted eigen
+
+ align:start position:0%
+about this sort of restricted eigen
+ 
+
+ align:start position:0%
+about this sort of restricted eigen
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+it's a map from R2 to R2 and it's
+
+ align:start position:0%
+it's a map from R2 to R2 and it's
+ 
+
+ align:start position:0%
+it's a map from R2 to R2 and it's
+exactly the map it's exactly the map
+
+ align:start position:0%
+exactly the map it's exactly the map
+ 
+
+ align:start position:0%
+exactly the map it's exactly the map
+that's why I chose the Theta over two
+
+ align:start position:0%
+that's why I chose the Theta over two
+ 
+
+ align:start position:0%
+that's why I chose the Theta over two
+it's exactly the map from Cartesian to
+
+ align:start position:0%
+it's exactly the map from Cartesian to
+ 
+
+ align:start position:0%
+it's exactly the map from Cartesian to
+corn to Polar coordinates by I don't
+
+ align:start position:0%
+corn to Polar coordinates by I don't
+ 
+
+ align:start position:0%
+corn to Polar coordinates by I don't
+know whether you call that a coincidence
+
+ align:start position:0%
+know whether you call that a coincidence
+ 
+
+ align:start position:0%
+know whether you call that a coincidence
+or what but I think it's intriguing that
+
+ align:start position:0%
+or what but I think it's intriguing that
+ 
+
+ align:start position:0%
+or what but I think it's intriguing that
+it's the same map all right let's do the
+
+ align:start position:0%
+it's the same map all right let's do the
+ 
+
+ align:start position:0%
+it's the same map all right let's do the
+full symmetric
+
+ align:start position:0%
+full symmetric
+ 
+
+ align:start position:0%
+full symmetric
+so in the so the full case a symmetric
+
+ align:start position:0%
+so in the so the full case a symmetric
+ 
+
+ align:start position:0%
+so in the so the full case a symmetric
+Matrix is a three-dimensional Vector
+
+ align:start position:0%
+Matrix is a three-dimensional Vector
+ 
+
+ align:start position:0%
+Matrix is a three-dimensional Vector
+space right so you've got three three
+
+ align:start position:0%
+space right so you've got three three
+ 
+
+ align:start position:0%
+space right so you've got three three
+parameters right the the two diagonals
+
+ align:start position:0%
+parameters right the the two diagonals
+ 
+
+ align:start position:0%
+parameters right the the two diagonals
+and then the the off diagonals are the
+
+ align:start position:0%
+and then the the off diagonals are the
+ 
+
+ align:start position:0%
+and then the the off diagonals are the
+same number so we can refer to every
+
+ align:start position:0%
+same number so we can refer to every
+ 
+
+ align:start position:0%
+same number so we can refer to every
+three two by two symmetric Matrix with
+
+ align:start position:0%
+three two by two symmetric Matrix with
+ 
+
+ align:start position:0%
+three two by two symmetric Matrix with
+the variables p r and s
+
+ align:start position:0%
+the variables p r and s
+ 
+
+ align:start position:0%
+the variables p r and s
+right and the the three variables are
+
+ align:start position:0%
+right and the the three variables are
+ 
+
+ align:start position:0%
+right and the the three variables are
+since the Matrix symmetric Matrix has
+
+ align:start position:0%
+since the Matrix symmetric Matrix has
+ 
+
+ align:start position:0%
+since the Matrix symmetric Matrix has
+has an orthogonal eigenvectors you still
+
+ align:start position:0%
+has an orthogonal eigenvectors you still
+ 
+
+ align:start position:0%
+has an orthogonal eigenvectors you still
+have one parameter Theta for the
+
+ align:start position:0%
+have one parameter Theta for the
+ 
+
+ align:start position:0%
+have one parameter Theta for the
+eigenvectors but we have two parameters
+
+ align:start position:0%
+eigenvectors but we have two parameters
+ 
+
+ align:start position:0%
+eigenvectors but we have two parameters
+Lambda one and Lambda 2 for the
+
+ align:start position:0%
+Lambda one and Lambda 2 for the
+ 
+
+ align:start position:0%
+Lambda one and Lambda 2 for the
+eigenvalues okay and so the symmetric
+
+ align:start position:0%
+eigenvalues okay and so the symmetric
+ 
+
+ align:start position:0%
+eigenvalues okay and so the symmetric
+eigenvalue problem is once again mapping
+
+ align:start position:0%
+eigenvalue problem is once again mapping
+ 
+
+ align:start position:0%
+eigenvalue problem is once again mapping
+this time from R3 to R3 right you can go
+
+ align:start position:0%
+this time from R3 to R3 right you can go
+ 
+
+ align:start position:0%
+this time from R3 to R3 right you can go
+backwards and forwards you can go from
+
+ align:start position:0%
+backwards and forwards you can go from
+ 
+
+ align:start position:0%
+backwards and forwards you can go from
+the eigenvalues and eigenvectors to The
+
+ align:start position:0%
+the eigenvalues and eigenvectors to The
+ 
+
+ align:start position:0%
+the eigenvalues and eigenvectors to The
+Matrix which by the way is the more
+
+ align:start position:0%
+Matrix which by the way is the more
+ 
+
+ align:start position:0%
+Matrix which by the way is the more
+convenient direction or you can go from
+
+ align:start position:0%
+convenient direction or you can go from
+ 
+
+ align:start position:0%
+convenient direction or you can go from
+The Matrix entries to the eigenvalues
+
+ align:start position:0%
+The Matrix entries to the eigenvalues
+ 
+
+ align:start position:0%
+The Matrix entries to the eigenvalues
+and eigenvectors right and so everybody
+
+ align:start position:0%
+and eigenvectors right and so everybody
+ 
+
+ align:start position:0%
+and eigenvectors right and so everybody
+in first year linear algebra learns how
+
+ align:start position:0%
+in first year linear algebra learns how
+ 
+
+ align:start position:0%
+in first year linear algebra learns how
+to go this way
+
+ align:start position:0%
+to go this way
+ 
+
+ align:start position:0%
+to go this way
+right you you you compute you've set up
+
+ align:start position:0%
+right you you you compute you've set up
+ 
+
+ align:start position:0%
+right you you you compute you've set up
+the characteristic polynomial you write
+
+ align:start position:0%
+the characteristic polynomial you write
+ 
+
+ align:start position:0%
+the characteristic polynomial you write
+down the quadratic you solve it right
+
+ align:start position:0%
+down the quadratic you solve it right
+ 
+
+ align:start position:0%
+down the quadratic you solve it right
+and you know in one way or another you
+
+ align:start position:0%
+and you know in one way or another you
+ 
+
+ align:start position:0%
+and you know in one way or another you
+can get the eigenvector as well
+
+ align:start position:0%
+can get the eigenvector as well
+ 
+
+ align:start position:0%
+can get the eigenvector as well
+um so you know you you look at the null
+
+ align:start position:0%
+um so you know you you look at the null
+ 
+
+ align:start position:0%
+um so you know you you look at the null
+space of a minus Lambda I or something
+
+ align:start position:0%
+space of a minus Lambda I or something
+ 
+
+ align:start position:0%
+space of a minus Lambda I or something
+right so this is this left Direction
+
+ align:start position:0%
+right so this is this left Direction
+ 
+
+ align:start position:0%
+right so this is this left Direction
+you've all done in your first year
+
+ align:start position:0%
+you've all done in your first year
+ 
+
+ align:start position:0%
+you've all done in your first year
+linear algebra class turns out it's a
+
+ align:start position:0%
+linear algebra class turns out it's a
+ 
+
+ align:start position:0%
+linear algebra class turns out it's a
+little more convenient to go the other
+
+ align:start position:0%
+little more convenient to go the other
+ 
+
+ align:start position:0%
+little more convenient to go the other
+way this is just a matrix multiply where
+
+ align:start position:0%
+way this is just a matrix multiply where
+ 
+
+ align:start position:0%
+way this is just a matrix multiply where
+I set up the eigenvalues and
+
+ align:start position:0%
+I set up the eigenvalues and
+ 
+
+ align:start position:0%
+I set up the eigenvalues and
+eigenvectors and then I compute The
+
+ align:start position:0%
+eigenvectors and then I compute The
+ 
+
+ align:start position:0%
+eigenvectors and then I compute The
+Matrix okay and so here is the Jacobian
+
+ align:start position:0%
+Matrix okay and so here is the Jacobian
+ 
+
+ align:start position:0%
+Matrix okay and so here is the Jacobian
+calculation so it's a three by three
+
+ align:start position:0%
+calculation so it's a three by three
+ 
+
+ align:start position:0%
+calculation so it's a three by three
+Jacobian there it is in all of its Glory
+
+ align:start position:0%
+Jacobian there it is in all of its Glory
+ 
+
+ align:start position:0%
+Jacobian there it is in all of its Glory
+a little bit painful to do by hand but
+
+ align:start position:0%
+a little bit painful to do by hand but
+ 
+
+ align:start position:0%
+a little bit painful to do by hand but
+completely doable Julia of course just
+
+ align:start position:0%
+completely doable Julia of course just
+ 
+
+ align:start position:0%
+completely doable Julia of course just
+happily gives you the answer without all
+
+ align:start position:0%
+happily gives you the answer without all
+ 
+
+ align:start position:0%
+happily gives you the answer without all
+the hard work
+
+ align:start position:0%
+the hard work
+ 
+
+ align:start position:0%
+the hard work
+and I'll just mention that if you
+
+ align:start position:0%
+and I'll just mention that if you
+ 
+
+ align:start position:0%
+and I'll just mention that if you
+calculate the determinants of this
+
+ align:start position:0%
+calculate the determinants of this
+ 
+
+ align:start position:0%
+calculate the determinants of this
+Matrix so you you get you sort of get
+
+ align:start position:0%
+Matrix so you you get you sort of get
+ 
+
+ align:start position:0%
+Matrix so you you get you sort of get
+the the the the volume element right so
+
+ align:start position:0%
+the the the the volume element right so
+ 
+
+ align:start position:0%
+the the the the volume element right so
+just to make sure everybody knows how
+
+ align:start position:0%
+just to make sure everybody knows how
+ 
+
+ align:start position:0%
+just to make sure everybody knows how
+that works the volume of the Jacobian is
+
+ align:start position:0%
+that works the volume of the Jacobian is
+ 
+
+ align:start position:0%
+that works the volume of the Jacobian is
+how much
+
+ align:start position:0%
+how much
+ 
+
+ align:start position:0%
+how much
+a little Cube scales right like if I go
+
+ align:start position:0%
+a little Cube scales right like if I go
+ 
+
+ align:start position:0%
+a little Cube scales right like if I go
+back to that picture of the Corgi being
+
+ align:start position:0%
+back to that picture of the Corgi being
+ 
+
+ align:start position:0%
+back to that picture of the Corgi being
+warped right I could look at his nose
+
+ align:start position:0%
+warped right I could look at his nose
+ 
+
+ align:start position:0%
+warped right I could look at his nose
+and um and then in the image you know
+
+ align:start position:0%
+and um and then in the image you know
+ 
+
+ align:start position:0%
+and um and then in the image you know
+maybe it gets squashed the the ratio is
+
+ align:start position:0%
+maybe it gets squashed the the ratio is
+ 
+
+ align:start position:0%
+maybe it gets squashed the the ratio is
+is the determinants of the
+
+ align:start position:0%
+is the determinants of the
+ 
+
+ align:start position:0%
+is the determinants of the
+transformation it's actually determined
+
+ align:start position:0%
+transformation it's actually determined
+ 
+
+ align:start position:0%
+transformation it's actually determined
+of the Jacobian right and if you do that
+
+ align:start position:0%
+of the Jacobian right and if you do that
+ 
+
+ align:start position:0%
+of the Jacobian right and if you do that
+you actually get Lambda 1 minus two
+
+ align:start position:0%
+you actually get Lambda 1 minus two
+ 
+
+ align:start position:0%
+you actually get Lambda 1 minus two
+Lambda 2 and uh people like to say that
+
+ align:start position:0%
+Lambda 2 and uh people like to say that
+ 
+
+ align:start position:0%
+Lambda 2 and uh people like to say that
+symmetric I get that eigenvalues don't
+
+ align:start position:0%
+symmetric I get that eigenvalues don't
+ 
+
+ align:start position:0%
+symmetric I get that eigenvalues don't
+wanna so so so if the determinant being
+
+ align:start position:0%
+wanna so so so if the determinant being
+ 
+
+ align:start position:0%
+wanna so so so if the determinant being
+Lambda one minus Lambda 2 is an
+
+ align:start position:0%
+Lambda one minus Lambda 2 is an
+ 
+
+ align:start position:0%
+Lambda one minus Lambda 2 is an
+indication of repulsion between
+
+ align:start position:0%
+indication of repulsion between
+ 
+
+ align:start position:0%
+indication of repulsion between
+eigenvalues but maybe that's neither
+
+ align:start position:0%
+eigenvalues but maybe that's neither
+ 
+
+ align:start position:0%
+eigenvalues but maybe that's neither
+here nor there all right well I think my
+
+ align:start position:0%
+here nor there all right well I think my
+ 
+
+ align:start position:0%
+here nor there all right well I think my
+timing is perfect I went through this
+
+ align:start position:0%
+timing is perfect I went through this
+ 
+
+ align:start position:0%
+timing is perfect I went through this
+notebook and it's 1201 exactly so should
+
+ align:start position:0%
+notebook and it's 1201 exactly so should
+ 
+
+ align:start position:0%
+notebook and it's 1201 exactly so should
+we take the five minute break and then
+
+ align:start position:0%
+we take the five minute break and then
+ 
+
+ align:start position:0%
+we take the five minute break and then
+Steven you'll be on board for the next
+
+ align:start position:0%
+Steven you'll be on board for the next
+ 
+
+ align:start position:0%
+Steven you'll be on board for the next
+certain stuff
+
+ align:start position:0%
+certain stuff
+ 
+
+ align:start position:0%
+certain stuff
+all right so 1206 come on back we'll
+
+ align:start position:0%
+all right so 1206 come on back we'll
+ 
+
+ align:start position:0%
+all right so 1206 come on back we'll
+start up again
\ No newline at end of file
diff --git a/BUnUOv_INyM.txt b/BUnUOv_INyM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5db763d17ab6df36012257727bae2ae01194fa3a
--- /dev/null
+++ b/BUnUOv_INyM.txt
@@ -0,0 +1,9419 @@
+align:start position:0%
+ 
+today what we're gonna do is continue
+
+ align:start position:0%
+today what we're gonna do is continue
+ 
+
+ align:start position:0%
+today what we're gonna do is continue
+our discussion of factor markets by
+
+ align:start position:0%
+our discussion of factor markets by
+ 
+
+ align:start position:0%
+our discussion of factor markets by
+essentially talking about how capital
+
+ align:start position:0%
+essentially talking about how capital
+ 
+
+ align:start position:0%
+essentially talking about how capital
+markets impact real-world decisions so
+
+ align:start position:0%
+markets impact real-world decisions so
+ 
+
+ align:start position:0%
+markets impact real-world decisions so
+last time we talked about the capital
+
+ align:start position:0%
+last time we talked about the capital
+ 
+
+ align:start position:0%
+last time we talked about the capital
+market we talked about essentially the
+
+ align:start position:0%
+market we talked about essentially the
+ 
+
+ align:start position:0%
+market we talked about essentially the
+way that firms finance their capital is
+
+ align:start position:0%
+way that firms finance their capital is
+ 
+
+ align:start position:0%
+way that firms finance their capital is
+by going to a pool of savings that
+
+ align:start position:0%
+by going to a pool of savings that
+ 
+
+ align:start position:0%
+by going to a pool of savings that
+individuals decide and how much to make
+
+ align:start position:0%
+individuals decide and how much to make
+ 
+
+ align:start position:0%
+individuals decide and how much to make
+individuals make an inter temporal
+
+ align:start position:0%
+individuals make an inter temporal
+ 
+
+ align:start position:0%
+individuals make an inter temporal
+choice on how much to save actually
+
+ align:start position:0%
+choice on how much to save actually
+ 
+
+ align:start position:0%
+choice on how much to save actually
+technically make an internal choice
+
+ align:start position:0%
+technically make an internal choice
+ 
+
+ align:start position:0%
+technically make an internal choice
+about how much to consume each period
+
+ align:start position:0%
+about how much to consume each period
+ 
+
+ align:start position:0%
+about how much to consume each period
+that then yields an amount of savings
+
+ align:start position:0%
+that then yields an amount of savings
+ 
+
+ align:start position:0%
+that then yields an amount of savings
+and then based on that pool of savings
+
+ align:start position:0%
+and then based on that pool of savings
+ 
+
+ align:start position:0%
+and then based on that pool of savings
+firms borrow with some interest rate I
+
+ align:start position:0%
+firms borrow with some interest rate I
+ 
+
+ align:start position:0%
+firms borrow with some interest rate I
+and they decide how much to invest now
+
+ align:start position:0%
+and they decide how much to invest now
+ 
+
+ align:start position:0%
+and they decide how much to invest now
+today we're going to talk about a number
+
+ align:start position:0%
+today we're going to talk about a number
+ 
+
+ align:start position:0%
+today we're going to talk about a number
+of interesting applications that arise
+
+ align:start position:0%
+of interesting applications that arise
+ 
+
+ align:start position:0%
+of interesting applications that arise
+from capital markets that are important
+
+ align:start position:0%
+from capital markets that are important
+ 
+
+ align:start position:0%
+from capital markets that are important
+in the real world I'm going to start by
+
+ align:start position:0%
+in the real world I'm going to start by
+ 
+
+ align:start position:0%
+in the real world I'm going to start by
+talking about the concept of present
+
+ align:start position:0%
+talking about the concept of present
+ 
+
+ align:start position:0%
+talking about the concept of present
+value present value now the key insight
+
+ align:start position:0%
+value present value now the key insight
+ 
+
+ align:start position:0%
+value present value now the key insight
+when we think about capital markets is
+
+ align:start position:0%
+when we think about capital markets is
+ 
+
+ align:start position:0%
+when we think about capital markets is
+that a dollar tomorrow is worth less
+
+ align:start position:0%
+that a dollar tomorrow is worth less
+ 
+
+ align:start position:0%
+that a dollar tomorrow is worth less
+than a dollar today a dollar tomorrow is
+
+ align:start position:0%
+than a dollar today a dollar tomorrow is
+ 
+
+ align:start position:0%
+than a dollar today a dollar tomorrow is
+worth less than dollars a that's because
+
+ align:start position:0%
+worth less than dollars a that's because
+ 
+
+ align:start position:0%
+worth less than dollars a that's because
+if you had the dollar today you could
+
+ align:start position:0%
+if you had the dollar today you could
+ 
+
+ align:start position:0%
+if you had the dollar today you could
+productively invest it and have more
+
+ align:start position:0%
+productively invest it and have more
+ 
+
+ align:start position:0%
+productively invest it and have more
+than a dollar tomorrow so in Davos a is
+
+ align:start position:0%
+than a dollar tomorrow so in Davos a is
+ 
+
+ align:start position:0%
+than a dollar tomorrow so in Davos a is
+worth more because you could do
+
+ align:start position:0%
+worth more because you could do
+ 
+
+ align:start position:0%
+worth more because you could do
+something productive with that dollar if
+
+ align:start position:0%
+something productive with that dollar if
+ 
+
+ align:start position:0%
+something productive with that dollar if
+you had it today okay what that means is
+
+ align:start position:0%
+you had it today okay what that means is
+ 
+
+ align:start position:0%
+you had it today okay what that means is
+that dollars in different periods are
+
+ align:start position:0%
+that dollars in different periods are
+ 
+
+ align:start position:0%
+that dollars in different periods are
+worth different things you can't just
+
+ align:start position:0%
+worth different things you can't just
+ 
+
+ align:start position:0%
+worth different things you can't just
+add them up
+
+ align:start position:0%
+add them up
+ 
+
+ align:start position:0%
+add them up
+okay the analogy I like is thinking
+
+ align:start position:0%
+okay the analogy I like is thinking
+ 
+
+ align:start position:0%
+okay the analogy I like is thinking
+about imagine you had a pound of apples
+
+ align:start position:0%
+about imagine you had a pound of apples
+ 
+
+ align:start position:0%
+about imagine you had a pound of apples
+a pound of steak and a pound of gold you
+
+ align:start position:0%
+a pound of steak and a pound of gold you
+ 
+
+ align:start position:0%
+a pound of steak and a pound of gold you
+wouldn't just add them up and say I have
+
+ align:start position:0%
+wouldn't just add them up and say I have
+ 
+
+ align:start position:0%
+wouldn't just add them up and say I have
+three pounds that'd be useless you'd
+
+ align:start position:0%
+three pounds that'd be useless you'd
+ 
+
+ align:start position:0%
+three pounds that'd be useless you'd
+want to know what each is worth it you
+
+ align:start position:0%
+want to know what each is worth it you
+ 
+
+ align:start position:0%
+want to know what each is worth it you
+want to add up the dollar value of them
+
+ align:start position:0%
+want to add up the dollar value of them
+ 
+
+ align:start position:0%
+want to add up the dollar value of them
+okay it's a similar thing with money
+
+ align:start position:0%
+okay it's a similar thing with money
+ 
+
+ align:start position:0%
+okay it's a similar thing with money
+received over time you can't just say
+
+ align:start position:0%
+received over time you can't just say
+ 
+
+ align:start position:0%
+received over time you can't just say
+I'm getting a dollar today a dollar next
+
+ align:start position:0%
+I'm getting a dollar today a dollar next
+ 
+
+ align:start position:0%
+I'm getting a dollar today a dollar next
+year and a dollar five years from now
+
+ align:start position:0%
+year and a dollar five years from now
+ 
+
+ align:start position:0%
+year and a dollar five years from now
+they aren't the same thing
+
+ align:start position:0%
+they aren't the same thing
+ 
+
+ align:start position:0%
+they aren't the same thing
+money received at different points of
+
+ align:start position:0%
+money received at different points of
+ 
+
+ align:start position:0%
+money received at different points of
+time or worth different amounts because
+
+ align:start position:0%
+time or worth different amounts because
+ 
+
+ align:start position:0%
+time or worth different amounts because
+money received in the future forgoes the
+
+ align:start position:0%
+money received in the future forgoes the
+ 
+
+ align:start position:0%
+money received in the future forgoes the
+possibility of investing it today okay
+
+ align:start position:0%
+possibility of investing it today okay
+ 
+
+ align:start position:0%
+possibility of investing it today okay
+so what do we do to deal with this well
+
+ align:start position:0%
+so what do we do to deal with this well
+ 
+
+ align:start position:0%
+so what do we do to deal with this well
+in economics we deal with this bike the
+
+ align:start position:0%
+in economics we deal with this bike the
+ 
+
+ align:start position:0%
+in economics we deal with this bike the
+concept of present value present value
+
+ align:start position:0%
+concept of present value present value
+ 
+
+ align:start position:0%
+concept of present value present value
+is the value of every periods payment
+
+ align:start position:0%
+is the value of every periods payment
+ 
+
+ align:start position:0%
+is the value of every periods payment
+in terms of today so the way we deal
+
+ align:start position:0%
+in terms of today so the way we deal
+ 
+
+ align:start position:0%
+in terms of today so the way we deal
+with the fact that money different
+
+ align:start position:0%
+with the fact that money different
+ 
+
+ align:start position:0%
+with the fact that money different
+parents worth different amounts is by
+
+ align:start position:0%
+parents worth different amounts is by
+ 
+
+ align:start position:0%
+parents worth different amounts is by
+what we call discounting it back to
+
+ align:start position:0%
+what we call discounting it back to
+ 
+
+ align:start position:0%
+what we call discounting it back to
+today we said so take future dollars and
+
+ align:start position:0%
+today we said so take future dollars and
+ 
+
+ align:start position:0%
+today we said so take future dollars and
+dip it discount them back to today to
+
+ align:start position:0%
+dip it discount them back to today to
+ 
+
+ align:start position:0%
+dip it discount them back to today to
+get present value we discount them
+
+ align:start position:0%
+get present value we discount them
+ 
+
+ align:start position:0%
+get present value we discount them
+because future dollars are worthless
+
+ align:start position:0%
+because future dollars are worthless
+ 
+
+ align:start position:0%
+because future dollars are worthless
+okay so let's think of it this way
+
+ align:start position:0%
+okay so let's think of it this way
+ 
+
+ align:start position:0%
+okay so let's think of it this way
+suppose that um the interest rate is 10
+
+ align:start position:0%
+suppose that um the interest rate is 10
+ 
+
+ align:start position:0%
+suppose that um the interest rate is 10
+percent let students they have imagine
+
+ align:start position:0%
+percent let students they have imagine
+ 
+
+ align:start position:0%
+percent let students they have imagine
+the interest rate I is 10 percent and
+
+ align:start position:0%
+the interest rate I is 10 percent and
+ 
+
+ align:start position:0%
+the interest rate I is 10 percent and
+let's say that you want to have 100
+
+ align:start position:0%
+let's say that you want to have 100
+ 
+
+ align:start position:0%
+let's say that you want to have 100
+dollars next year you want your you want
+
+ align:start position:0%
+dollars next year you want your you want
+ 
+
+ align:start position:0%
+dollars next year you want your you want
+next year you want to have 100 dollars
+
+ align:start position:0%
+next year you want to have 100 dollars
+ 
+
+ align:start position:0%
+next year you want to have 100 dollars
+well how much do you have to put in the
+
+ align:start position:0%
+well how much do you have to put in the
+ 
+
+ align:start position:0%
+well how much do you have to put in the
+bank today okay well we could solve the
+
+ align:start position:0%
+bank today okay well we could solve the
+ 
+
+ align:start position:0%
+bank today okay well we could solve the
+equation which is that you want the
+
+ align:start position:0%
+equation which is that you want the
+ 
+
+ align:start position:0%
+equation which is that you want the
+amount you put in the bank today let's
+
+ align:start position:0%
+amount you put in the bank today let's
+ 
+
+ align:start position:0%
+amount you put in the bank today let's
+call that Y times 1 plus the interest
+
+ align:start position:0%
+call that Y times 1 plus the interest
+ 
+
+ align:start position:0%
+call that Y times 1 plus the interest
+rate because that's what you make by
+
+ align:start position:0%
+rate because that's what you make by
+ 
+
+ align:start position:0%
+rate because that's what you make by
+having the bank equal to 100 that's
+
+ align:start position:0%
+having the bank equal to 100 that's
+ 
+
+ align:start position:0%
+having the bank equal to 100 that's
+equation we want to solve right the
+
+ align:start position:0%
+equation we want to solve right the
+ 
+
+ align:start position:0%
+equation we want to solve right the
+money you've bout you put in today y
+
+ align:start position:0%
+money you've bout you put in today y
+ 
+
+ align:start position:0%
+money you've bout you put in today y
+times 1 plus the interest rate you want
+
+ align:start position:0%
+times 1 plus the interest rate you want
+ 
+
+ align:start position:0%
+times 1 plus the interest rate you want
+that to be equal to 100 so what that
+
+ align:start position:0%
+that to be equal to 100 so what that
+ 
+
+ align:start position:0%
+that to be equal to 100 so what that
+says is that y equals 90 point nine if
+
+ align:start position:0%
+says is that y equals 90 point nine if
+ 
+
+ align:start position:0%
+says is that y equals 90 point nine if
+you put $90.90
+
+ align:start position:0%
+you put $90.90
+ 
+
+ align:start position:0%
+you put $90.90
+in the bank today at a 10 percent
+
+ align:start position:0%
+in the bank today at a 10 percent
+ 
+
+ align:start position:0%
+in the bank today at a 10 percent
+interest rate you will have $100
+
+ align:start position:0%
+interest rate you will have $100
+ 
+
+ align:start position:0%
+interest rate you will have $100
+tomorrow more generally we say that the
+
+ align:start position:0%
+tomorrow more generally we say that the
+ 
+
+ align:start position:0%
+tomorrow more generally we say that the
+present value of any future payment it's
+
+ align:start position:0%
+present value of any future payment it's
+ 
+
+ align:start position:0%
+present value of any future payment it's
+the future value the amount you get in
+
+ align:start position:0%
+the future value the amount you get in
+ 
+
+ align:start position:0%
+the future value the amount you get in
+the future over 1 plus I to the power
+
+ align:start position:0%
+the future over 1 plus I to the power
+ 
+
+ align:start position:0%
+the future over 1 plus I to the power
+little T where T is the periods in the
+
+ align:start position:0%
+little T where T is the periods in the
+ 
+
+ align:start position:0%
+little T where T is the periods in the
+future so money received t periods in
+
+ align:start position:0%
+future so money received t periods in
+ 
+
+ align:start position:0%
+future so money received t periods in
+the future today is worth the amount you
+
+ align:start position:0%
+the future today is worth the amount you
+ 
+
+ align:start position:0%
+the future today is worth the amount you
+get in the future over 1 plus I to the T
+
+ align:start position:0%
+get in the future over 1 plus I to the T
+ 
+
+ align:start position:0%
+get in the future over 1 plus I to the T
+okay so that is our general formula for
+
+ align:start position:0%
+okay so that is our general formula for
+ 
+
+ align:start position:0%
+okay so that is our general formula for
+how we think about present value take
+
+ align:start position:0%
+how we think about present value take
+ 
+
+ align:start position:0%
+how we think about present value take
+all the future payments and you discount
+
+ align:start position:0%
+all the future payments and you discount
+ 
+
+ align:start position:0%
+all the future payments and you discount
+them back today by dividing by 1 call
+
+ align:start position:0%
+them back today by dividing by 1 call
+ 
+
+ align:start position:0%
+them back today by dividing by 1 call
+side of the T now that works well if
+
+ align:start position:0%
+side of the T now that works well if
+ 
+
+ align:start position:0%
+side of the T now that works well if
+there's a future payment in one future
+
+ align:start position:0%
+there's a future payment in one future
+ 
+
+ align:start position:0%
+there's a future payment in one future
+payment coming but what if as in many
+
+ align:start position:0%
+payment coming but what if as in many
+ 
+
+ align:start position:0%
+payment coming but what if as in many
+cases is the whole stream of future
+
+ align:start position:0%
+cases is the whole stream of future
+ 
+
+ align:start position:0%
+cases is the whole stream of future
+payments coming well the logic then is
+
+ align:start position:0%
+payments coming well the logic then is
+ 
+
+ align:start position:0%
+payments coming well the logic then is
+the same you just want to take each
+
+ align:start position:0%
+the same you just want to take each
+ 
+
+ align:start position:0%
+the same you just want to take each
+future payment and discount it by how
+
+ align:start position:0%
+future payment and discount it by how
+ 
+
+ align:start position:0%
+future payment and discount it by how
+far it is in the future
+
+ align:start position:0%
+far it is in the future
+ 
+
+ align:start position:0%
+far it is in the future
+okay so suppose that you say um that you
+
+ align:start position:0%
+okay so suppose that you say um that you
+ 
+
+ align:start position:0%
+okay so suppose that you say um that you
+want me to loan you $30 and that you'll
+
+ align:start position:0%
+want me to loan you $30 and that you'll
+ 
+
+ align:start position:0%
+want me to loan you $30 and that you'll
+pay me back $10 each of the next three
+
+ align:start position:0%
+pay me back $10 each of the next three
+ 
+
+ align:start position:0%
+pay me back $10 each of the next three
+years okay
+
+ align:start position:0%
+years okay
+ 
+
+ align:start position:0%
+years okay
+and suppose the interest rates 10% well
+
+ align:start position:0%
+and suppose the interest rates 10% well
+ 
+
+ align:start position:0%
+and suppose the interest rates 10% well
+I will say no to that because I will say
+
+ align:start position:0%
+I will say no to that because I will say
+ 
+
+ align:start position:0%
+I will say no to that because I will say
+if you're gonna pay me back $10 each of
+
+ align:start position:0%
+if you're gonna pay me back $10 each of
+ 
+
+ align:start position:0%
+if you're gonna pay me back $10 each of
+the next three years then what is it
+
+ align:start position:0%
+the next three years then what is it
+ 
+
+ align:start position:0%
+the next three years then what is it
+what's the present value of that the
+
+ align:start position:0%
+what's the present value of that the
+ 
+
+ align:start position:0%
+what's the present value of that the
+present value is next year's $10 over
+
+ align:start position:0%
+present value is next year's $10 over
+ 
+
+ align:start position:0%
+present value is next year's $10 over
+1.1 because the interest rate is 10%
+
+ align:start position:0%
+1.1 because the interest rate is 10%
+ 
+
+ align:start position:0%
+1.1 because the interest rate is 10%
+plus the $10 a year after that over 1.1
+
+ align:start position:0%
+plus the $10 a year after that over 1.1
+ 
+
+ align:start position:0%
+plus the $10 a year after that over 1.1
+squared plus the $10 the year after that
+
+ align:start position:0%
+squared plus the $10 the year after that
+ 
+
+ align:start position:0%
+squared plus the $10 the year after that
+over 1.1 cubed which way if I add it up
+
+ align:start position:0%
+over 1.1 cubed which way if I add it up
+ 
+
+ align:start position:0%
+over 1.1 cubed which way if I add it up
+is 24 87 so I am losing money if I if I
+
+ align:start position:0%
+is 24 87 so I am losing money if I if I
+ 
+
+ align:start position:0%
+is 24 87 so I am losing money if I if I
+give you $30 today and if you give me
+
+ align:start position:0%
+give you $30 today and if you give me
+ 
+
+ align:start position:0%
+give you $30 today and if you give me
+$10 back each of the next three years
+
+ align:start position:0%
+$10 back each of the next three years
+ 
+
+ align:start position:0%
+$10 back each of the next three years
+I'm losing money why because if I had
+
+ align:start position:0%
+I'm losing money why because if I had
+ 
+
+ align:start position:0%
+I'm losing money why because if I had
+simply taken that money and invested in
+
+ align:start position:0%
+simply taken that money and invested in
+ 
+
+ align:start position:0%
+simply taken that money and invested in
+the bank I would have had a lot more
+
+ align:start position:0%
+the bank I would have had a lot more
+ 
+
+ align:start position:0%
+the bank I would have had a lot more
+than the $30 I'm gonna get for you after
+
+ align:start position:0%
+than the $30 I'm gonna get for you after
+ 
+
+ align:start position:0%
+than the $30 I'm gonna get for you after
+three years okay so the money that comes
+
+ align:start position:0%
+three years okay so the money that comes
+ 
+
+ align:start position:0%
+three years okay so the money that comes
+in the future must be discounted back to
+
+ align:start position:0%
+in the future must be discounted back to
+ 
+
+ align:start position:0%
+in the future must be discounted back to
+today that's the key inside of present
+
+ align:start position:0%
+today that's the key inside of present
+ 
+
+ align:start position:0%
+today that's the key inside of present
+value you can't just add it up you've
+
+ align:start position:0%
+value you can't just add it up you've
+ 
+
+ align:start position:0%
+value you can't just add it up you've
+got to put it in today's terms by
+
+ align:start position:0%
+got to put it in today's terms by
+ 
+
+ align:start position:0%
+got to put it in today's terms by
+discounting it by the interest rate and
+
+ align:start position:0%
+discounting it by the interest rate and
+ 
+
+ align:start position:0%
+discounting it by the interest rate and
+how far it for future yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're assuming now inflation zero so
+
+ align:start position:0%
+we're assuming now inflation zero so
+ 
+
+ align:start position:0%
+we're assuming now inflation zero so
+we're assuming right now we're not doing
+
+ align:start position:0%
+we're assuming right now we're not doing
+ 
+
+ align:start position:0%
+we're assuming right now we're not doing
+with inflation we're assuming a world
+
+ align:start position:0%
+with inflation we're assuming a world
+ 
+
+ align:start position:0%
+with inflation we're assuming a world
+where prices don't change we'll come
+
+ align:start position:0%
+where prices don't change we'll come
+ 
+
+ align:start position:0%
+where prices don't change we'll come
+back to inflation in a few minutes but
+
+ align:start position:0%
+back to inflation in a few minutes but
+ 
+
+ align:start position:0%
+back to inflation in a few minutes but
+for now just assume that prices don't
+
+ align:start position:0%
+for now just assume that prices don't
+ 
+
+ align:start position:0%
+for now just assume that prices don't
+change okay so basically arm essentially
+
+ align:start position:0%
+change okay so basically arm essentially
+ 
+
+ align:start position:0%
+change okay so basically arm essentially
+the formula then for the present value
+
+ align:start position:0%
+the formula then for the present value
+ 
+
+ align:start position:0%
+the formula then for the present value
+your general formula for present value
+
+ align:start position:0%
+your general formula for present value
+ 
+
+ align:start position:0%
+your general formula for present value
+you need to know is the present value
+
+ align:start position:0%
+you need to know is the present value
+ 
+
+ align:start position:0%
+you need to know is the present value
+equals present value equals if you get a
+
+ align:start position:0%
+equals present value equals if you get a
+ 
+
+ align:start position:0%
+equals present value equals if you get a
+flat stream of payment F for a number of
+
+ align:start position:0%
+flat stream of payment F for a number of
+ 
+
+ align:start position:0%
+flat stream of payment F for a number of
+periods it's f times 1 over 1 plus I to
+
+ align:start position:0%
+periods it's f times 1 over 1 plus I to
+ 
+
+ align:start position:0%
+periods it's f times 1 over 1 plus I to
+the T plus 1 I'm sorry 1 over 1 plus I
+
+ align:start position:0%
+the T plus 1 I'm sorry 1 over 1 plus I
+ 
+
+ align:start position:0%
+the T plus 1 I'm sorry 1 over 1 plus I
+to the 1 plus 1 over 1 plus I squared
+
+ align:start position:0%
+to the 1 plus 1 over 1 plus I squared
+ 
+
+ align:start position:0%
+to the 1 plus 1 over 1 plus I squared
+plus 1 over 1 plus I cubed plus not that
+
+ align:start position:0%
+plus 1 over 1 plus I cubed plus not that
+ 
+
+ align:start position:0%
+plus 1 over 1 plus I cubed plus not that
+up at the top for how many periods you
+
+ align:start position:0%
+up at the top for how many periods you
+ 
+
+ align:start position:0%
+up at the top for how many periods you
+get it so if you're getting a payment F
+
+ align:start position:0%
+get it so if you're getting a payment F
+ 
+
+ align:start position:0%
+get it so if you're getting a payment F
+over a certain number of periods
+
+ align:start position:0%
+over a certain number of periods
+ 
+
+ align:start position:0%
+over a certain number of periods
+you've got to discount it by how many
+
+ align:start position:0%
+you've got to discount it by how many
+ 
+
+ align:start position:0%
+you've got to discount it by how many
+periods you're gonna get it okay
+
+ align:start position:0%
+periods you're gonna get it okay
+ 
+
+ align:start position:0%
+periods you're gonna get it okay
+or more generally a common formula will
+
+ align:start position:0%
+or more generally a common formula will
+ 
+
+ align:start position:0%
+or more generally a common formula will
+ask you to use in this class is to think
+
+ align:start position:0%
+ask you to use in this class is to think
+ 
+
+ align:start position:0%
+ask you to use in this class is to think
+about the formula for a perpetuity a
+
+ align:start position:0%
+about the formula for a perpetuity a
+ 
+
+ align:start position:0%
+about the formula for a perpetuity a
+perpetuity is a flat payment you get
+
+ align:start position:0%
+perpetuity is a flat payment you get
+ 
+
+ align:start position:0%
+perpetuity is a flat payment you get
+forever so if we think the infinite sum
+
+ align:start position:0%
+forever so if we think the infinite sum
+ 
+
+ align:start position:0%
+forever so if we think the infinite sum
+of this equation we can summarize it as
+
+ align:start position:0%
+of this equation we can summarize it as
+ 
+
+ align:start position:0%
+of this equation we can summarize it as
+present value approximately equals F
+
+ align:start position:0%
+present value approximately equals F
+ 
+
+ align:start position:0%
+present value approximately equals F
+over the interest rate so if I promise
+
+ align:start position:0%
+over the interest rate so if I promise
+ 
+
+ align:start position:0%
+over the interest rate so if I promise
+you to pay you forever a certain amount
+
+ align:start position:0%
+you to pay you forever a certain amount
+ 
+
+ align:start position:0%
+you to pay you forever a certain amount
+F that is worth F over the interest rate
+
+ align:start position:0%
+F that is worth F over the interest rate
+ 
+
+ align:start position:0%
+F that is worth F over the interest rate
+so in other words if each rates 10% a
+
+ align:start position:0%
+so in other words if each rates 10% a
+ 
+
+ align:start position:0%
+so in other words if each rates 10% a
+promise to pay you $10 forever is worth
+
+ align:start position:0%
+promise to pay you $10 forever is worth
+ 
+
+ align:start position:0%
+promise to pay you $10 forever is worth
+about a hundred bucks that's the rough
+
+ align:start position:0%
+about a hundred bucks that's the rough
+ 
+
+ align:start position:0%
+about a hundred bucks that's the rough
+that's just the infinite sum if you read
+
+ align:start position:0%
+that's just the infinite sum if you read
+ 
+
+ align:start position:0%
+that's just the infinite sum if you read
+a beautiful mind John Nash through that
+
+ align:start position:0%
+a beautiful mind John Nash through that
+ 
+
+ align:start position:0%
+a beautiful mind John Nash through that
+in his head but I can't but that's just
+
+ align:start position:0%
+in his head but I can't but that's just
+ 
+
+ align:start position:0%
+in his head but I can't but that's just
+the formula okay so basically that is
+
+ align:start position:0%
+the formula okay so basically that is
+ 
+
+ align:start position:0%
+the formula okay so basically that is
+the general formula for perpetuity and
+
+ align:start position:0%
+the general formula for perpetuity and
+ 
+
+ align:start position:0%
+the general formula for perpetuity and
+that makes and that makes a life easy
+
+ align:start position:0%
+that makes and that makes a life easy
+ 
+
+ align:start position:0%
+that makes and that makes a life easy
+will give you a lot of examples where we
+
+ align:start position:0%
+will give you a lot of examples where we
+ 
+
+ align:start position:0%
+will give you a lot of examples where we
+you know cuz if I say I want you to pay
+
+ align:start position:0%
+you know cuz if I say I want you to pay
+ 
+
+ align:start position:0%
+you know cuz if I say I want you to pay
+them for eight years in the future you
+
+ align:start position:0%
+them for eight years in the future you
+ 
+
+ align:start position:0%
+them for eight years in the future you
+got to write out eight terms here it's a
+
+ align:start position:0%
+got to write out eight terms here it's a
+ 
+
+ align:start position:0%
+got to write out eight terms here it's a
+pain in the ass so it will say is money
+
+ align:start position:0%
+pain in the ass so it will say is money
+ 
+
+ align:start position:0%
+pain in the ass so it will say is money
+forever and they can just use this
+
+ align:start position:0%
+forever and they can just use this
+ 
+
+ align:start position:0%
+forever and they can just use this
+shortcut which is the present value for
+
+ align:start position:0%
+shortcut which is the present value for
+ 
+
+ align:start position:0%
+shortcut which is the present value for
+a perpetuity it's just F over I okay
+
+ align:start position:0%
+a perpetuity it's just F over I okay
+ 
+
+ align:start position:0%
+a perpetuity it's just F over I okay
+questions about that yeah that's a great
+
+ align:start position:0%
+questions about that yeah that's a great
+ 
+
+ align:start position:0%
+questions about that yeah that's a great
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+yes I'm assuming constant just rate over
+
+ align:start position:0%
+yes I'm assuming constant just rate over
+ 
+
+ align:start position:0%
+yes I'm assuming constant just rate over
+time now in reality you'd want to have
+
+ align:start position:0%
+time now in reality you'd want to have
+ 
+
+ align:start position:0%
+time now in reality you'd want to have
+each periods interest rate here and then
+
+ align:start position:0%
+each periods interest rate here and then
+ 
+
+ align:start position:0%
+each periods interest rate here and then
+you can't use this formula because the
+
+ align:start position:0%
+you can't use this formula because the
+ 
+
+ align:start position:0%
+you can't use this formula because the
+interest rate itself is changing very
+
+ align:start position:0%
+interest rate itself is changing very
+ 
+
+ align:start position:0%
+interest rate itself is changing very
+good point okay now the other way to
+
+ align:start position:0%
+good point okay now the other way to
+ 
+
+ align:start position:0%
+good point okay now the other way to
+think about this is instead of thinking
+
+ align:start position:0%
+think about this is instead of thinking
+ 
+
+ align:start position:0%
+think about this is instead of thinking
+just this this will be easy for most of
+
+ align:start position:0%
+just this this will be easy for most of
+ 
+
+ align:start position:0%
+just this this will be easy for most of
+you but just it's useful to think it
+
+ align:start position:0%
+you but just it's useful to think it
+ 
+
+ align:start position:0%
+you but just it's useful to think it
+through let's flip on his head not think
+
+ align:start position:0%
+through let's flip on his head not think
+ 
+
+ align:start position:0%
+through let's flip on his head not think
+about present valueless think about
+
+ align:start position:0%
+about present valueless think about
+ 
+
+ align:start position:0%
+about present valueless think about
+future value this is a useful tool as
+
+ align:start position:0%
+future value this is a useful tool as
+ 
+
+ align:start position:0%
+future value this is a useful tool as
+well as slipping on its head okay
+
+ align:start position:0%
+well as slipping on its head okay
+ 
+
+ align:start position:0%
+well as slipping on its head okay
+so let's think about the value of a
+
+ align:start position:0%
+so let's think about the value of a
+ 
+
+ align:start position:0%
+so let's think about the value of a
+future stream of payments well by the
+
+ align:start position:0%
+future stream of payments well by the
+ 
+
+ align:start position:0%
+future stream of payments well by the
+same logic we wrote before future value
+
+ align:start position:0%
+same logic we wrote before future value
+ 
+
+ align:start position:0%
+same logic we wrote before future value
+by same watch we wrote before if you're
+
+ align:start position:0%
+by same watch we wrote before if you're
+ 
+
+ align:start position:0%
+by same watch we wrote before if you're
+gonna have money that's tears in the
+
+ align:start position:0%
+gonna have money that's tears in the
+ 
+
+ align:start position:0%
+gonna have money that's tears in the
+future the future value of that money
+
+ align:start position:0%
+future the future value of that money
+ 
+
+ align:start position:0%
+future the future value of that money
+that you're gonna get okay if you're
+
+ align:start position:0%
+that you're gonna get okay if you're
+ 
+
+ align:start position:0%
+that you're gonna get okay if you're
+gonna basically take your money and
+
+ align:start position:0%
+gonna basically take your money and
+ 
+
+ align:start position:0%
+gonna basically take your money and
+invest it you're gonna have money that
+
+ align:start position:0%
+invest it you're gonna have money that
+ 
+
+ align:start position:0%
+invest it you're gonna have money that
+you're gonna invest today and put it in
+
+ align:start position:0%
+you're gonna invest today and put it in
+ 
+
+ align:start position:0%
+you're gonna invest today and put it in
+the bank and some interest rate then the
+
+ align:start position:0%
+the bank and some interest rate then the
+ 
+
+ align:start position:0%
+the bank and some interest rate then the
+future value is the amount you put in
+
+ align:start position:0%
+future value is the amount you put in
+ 
+
+ align:start position:0%
+future value is the amount you put in
+times one plus the interest rate tunity
+
+ align:start position:0%
+times one plus the interest rate tunity
+ 
+
+ align:start position:0%
+times one plus the interest rate tunity
+so I've simply reversed that formula
+
+ align:start position:0%
+so I've simply reversed that formula
+ 
+
+ align:start position:0%
+so I've simply reversed that formula
+present value future value
+
+ align:start position:0%
+present value future value
+ 
+
+ align:start position:0%
+present value future value
+so basically future value if you put
+
+ align:start position:0%
+so basically future value if you put
+ 
+
+ align:start position:0%
+so basically future value if you put
+money in the bank at some interest rate
+
+ align:start position:0%
+money in the bank at some interest rate
+ 
+
+ align:start position:0%
+money in the bank at some interest rate
+you're going to get to have over time
+
+ align:start position:0%
+you're going to get to have over time
+ 
+
+ align:start position:0%
+you're going to get to have over time
+that money times 1 plus I to the T now
+
+ align:start position:0%
+that money times 1 plus I to the T now
+ 
+
+ align:start position:0%
+that money times 1 plus I to the T now
+the reason we write this formula and
+
+ align:start position:0%
+the reason we write this formula and
+ 
+
+ align:start position:0%
+the reason we write this formula and
+sort of flip it for you is because I
+
+ align:start position:0%
+sort of flip it for you is because I
+ 
+
+ align:start position:0%
+sort of flip it for you is because I
+want to highlight the key feature here
+
+ align:start position:0%
+want to highlight the key feature here
+ 
+
+ align:start position:0%
+want to highlight the key feature here
+then I want to drill into your heads one
+
+ align:start position:0%
+then I want to drill into your heads one
+ 
+
+ align:start position:0%
+then I want to drill into your heads one
+of them I don't know I guess 10 things I
+
+ align:start position:0%
+of them I don't know I guess 10 things I
+ 
+
+ align:start position:0%
+of them I don't know I guess 10 things I
+most care you leave this course thinking
+
+ align:start position:0%
+most care you leave this course thinking
+ 
+
+ align:start position:0%
+most care you leave this course thinking
+about if you're not gonna major in
+
+ align:start position:0%
+about if you're not gonna major in
+ 
+
+ align:start position:0%
+about if you're not gonna major in
+economics but remembering is the beauty
+
+ align:start position:0%
+economics but remembering is the beauty
+ 
+
+ align:start position:0%
+economics but remembering is the beauty
+of compounding which is that with a
+
+ align:start position:0%
+of compounding which is that with a
+ 
+
+ align:start position:0%
+of compounding which is that with a
+formula like this you weren't interest
+
+ align:start position:0%
+formula like this you weren't interest
+ 
+
+ align:start position:0%
+formula like this you weren't interest
+on your interest if you leave money in
+
+ align:start position:0%
+on your interest if you leave money in
+ 
+
+ align:start position:0%
+on your interest if you leave money in
+the bank you don't just earn interest on
+
+ align:start position:0%
+the bank you don't just earn interest on
+ 
+
+ align:start position:0%
+the bank you don't just earn interest on
+the initial amount you put in your an
+
+ align:start position:0%
+the initial amount you put in your an
+ 
+
+ align:start position:0%
+the initial amount you put in your an
+interest on the interest you earn over
+
+ align:start position:0%
+interest on the interest you earn over
+ 
+
+ align:start position:0%
+interest on the interest you earn over
+time ok and this can be quite large so
+
+ align:start position:0%
+time ok and this can be quite large so
+ 
+
+ align:start position:0%
+time ok and this can be quite large so
+let's do a simple example ok just to
+
+ align:start position:0%
+let's do a simple example ok just to
+ 
+
+ align:start position:0%
+let's do a simple example ok just to
+show you how big this can be to get you
+
+ align:start position:0%
+show you how big this can be to get you
+ 
+
+ align:start position:0%
+show you how big this can be to get you
+all thinking about what you should do
+
+ align:start position:0%
+all thinking about what you should do
+ 
+
+ align:start position:0%
+all thinking about what you should do
+with your money when you get a job ok
+
+ align:start position:0%
+with your money when you get a job ok
+ 
+
+ align:start position:0%
+with your money when you get a job ok
+imagine you plan to work full time from
+
+ align:start position:0%
+imagine you plan to work full time from
+ 
+
+ align:start position:0%
+imagine you plan to work full time from
+age 22 to age 70
+
+ align:start position:0%
+age 22 to age 70
+ 
+
+ align:start position:0%
+age 22 to age 70
+well daunting to think about now
+
+ align:start position:0%
+well daunting to think about now
+ 
+
+ align:start position:0%
+well daunting to think about now
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+to retire after 70 by the time you guys
+
+ align:start position:0%
+to retire after 70 by the time you guys
+ 
+
+ align:start position:0%
+to retire after 70 by the time you guys
+retire but let's just think about 22 to
+
+ align:start position:0%
+retire but let's just think about 22 to
+ 
+
+ align:start position:0%
+retire but let's just think about 22 to
+70 okay and let's say that you can save
+
+ align:start position:0%
+70 okay and let's say that you can save
+ 
+
+ align:start position:0%
+70 okay and let's say that you can save
+at a constant 7% interest rate inflation
+
+ align:start position:0%
+at a constant 7% interest rate inflation
+ 
+
+ align:start position:0%
+at a constant 7% interest rate inflation
+zero the interest rates constant make
+
+ align:start position:0%
+zero the interest rates constant make
+ 
+
+ align:start position:0%
+zero the interest rates constant make
+life easy 7% interest rate okay and
+
+ align:start position:0%
+life easy 7% interest rate okay and
+ 
+
+ align:start position:0%
+life easy 7% interest rate okay and
+let's consider two different plans you
+
+ align:start position:0%
+let's consider two different plans you
+ 
+
+ align:start position:0%
+let's consider two different plans you
+have for savings plan one plan one is
+
+ align:start position:0%
+have for savings plan one plan one is
+ 
+
+ align:start position:0%
+have for savings plan one plan one is
+that you're gonna save $3,000 a year for
+
+ align:start position:0%
+that you're gonna save $3,000 a year for
+ 
+
+ align:start position:0%
+that you're gonna save $3,000 a year for
+the first 15 years that you work and
+
+ align:start position:0%
+the first 15 years that you work and
+ 
+
+ align:start position:0%
+the first 15 years that you work and
+then stop saving 3000 0:15 is then you
+
+ align:start position:0%
+then stop saving 3000 0:15 is then you
+ 
+
+ align:start position:0%
+then stop saving 3000 0:15 is then you
+just gonna leave that in the bank leave
+
+ align:start position:0%
+just gonna leave that in the bank leave
+ 
+
+ align:start position:0%
+just gonna leave that in the bank leave
+alone never save any more just let that
+
+ align:start position:0%
+alone never save any more just let that
+ 
+
+ align:start position:0%
+alone never save any more just let that
+money sit in the bank okay well in that
+
+ align:start position:0%
+money sit in the bank okay well in that
+ 
+
+ align:start position:0%
+money sit in the bank okay well in that
+case what will you have
+
+ align:start position:0%
+case what will you have
+ 
+
+ align:start position:0%
+case what will you have
+well after the first 15 years of putting
+
+ align:start position:0%
+well after the first 15 years of putting
+ 
+
+ align:start position:0%
+well after the first 15 years of putting
+three thousand dollars in the bank every
+
+ align:start position:0%
+three thousand dollars in the bank every
+ 
+
+ align:start position:0%
+three thousand dollars in the bank every
+year if you work out the math you will
+
+ align:start position:0%
+year if you work out the math you will
+ 
+
+ align:start position:0%
+year if you work out the math you will
+have $75,000 75387
+
+ align:start position:0%
+have $75,000 75387
+ 
+
+ align:start position:0%
+have $75,000 75387
+after 15 years okay that's now that's
+
+ align:start position:0%
+after 15 years okay that's now that's
+ 
+
+ align:start position:0%
+after 15 years okay that's now that's
+not just fifteen years times that's
+
+ align:start position:0%
+not just fifteen years times that's
+ 
+
+ align:start position:0%
+not just fifteen years times that's
+bigger than fifteen times 3,000 cuz
+
+ align:start position:0%
+bigger than fifteen times 3,000 cuz
+ 
+
+ align:start position:0%
+bigger than fifteen times 3,000 cuz
+you're earning interest along the way
+
+ align:start position:0%
+you're earning interest along the way
+ 
+
+ align:start position:0%
+you're earning interest along the way
+okay that's nice fifteen years then
+
+ align:start position:0%
+okay that's nice fifteen years then
+ 
+
+ align:start position:0%
+okay that's nice fifteen years then
+you're just gonna let that sit there and
+
+ align:start position:0%
+you're just gonna let that sit there and
+ 
+
+ align:start position:0%
+you're just gonna let that sit there and
+that's gonna sit there
+
+ align:start position:0%
+that's gonna sit there
+ 
+
+ align:start position:0%
+that's gonna sit there
+remember after 15 years you started
+
+ align:start position:0%
+remember after 15 years you started
+ 
+
+ align:start position:0%
+remember after 15 years you started
+working at 22 only 37 years old that's
+
+ align:start position:0%
+working at 22 only 37 years old that's
+ 
+
+ align:start position:0%
+working at 22 only 37 years old that's
+gonna then sit there for the next 33
+
+ align:start position:0%
+gonna then sit there for the next 33
+ 
+
+ align:start position:0%
+gonna then sit there for the next 33
+years you're not gonna touch it I could
+
+ align:start position:0%
+years you're not gonna touch it I could
+ 
+
+ align:start position:0%
+years you're not gonna touch it I could
+save anymore
+
+ align:start position:0%
+save anymore
+ 
+
+ align:start position:0%
+save anymore
+what that means is after 33 years this
+
+ align:start position:0%
+what that means is after 33 years this
+ 
+
+ align:start position:0%
+what that means is after 33 years this
+turns into 75 387 times 1.07 to the 33rd
+
+ align:start position:0%
+turns into 75 387 times 1.07 to the 33rd
+ 
+
+ align:start position:0%
+turns into 75 387 times 1.07 to the 33rd
+okay after 33 years or seven hundred and
+
+ align:start position:0%
+okay after 33 years or seven hundred and
+ 
+
+ align:start position:0%
+okay after 33 years or seven hundred and
+three thousand dollars seven oh three oh
+
+ align:start position:0%
+three thousand dollars seven oh three oh
+ 
+
+ align:start position:0%
+three thousand dollars seven oh three oh
+ten okay so you save $3,000 it's not a
+
+ align:start position:0%
+ten okay so you save $3,000 it's not a
+ 
+
+ align:start position:0%
+ten okay so you save $3,000 it's not a
+lot of money you guys gonna make a lot
+
+ align:start position:0%
+lot of money you guys gonna make a lot
+ 
+
+ align:start position:0%
+lot of money you guys gonna make a lot
+of money three thousand dollars for 15
+
+ align:start position:0%
+of money three thousand dollars for 15
+ 
+
+ align:start position:0%
+of money three thousand dollars for 15
+years and then you never had to save
+
+ align:start position:0%
+years and then you never had to save
+ 
+
+ align:start position:0%
+years and then you never had to save
+again contrast that with different
+
+ align:start position:0%
+again contrast that with different
+ 
+
+ align:start position:0%
+again contrast that with different
+approach let's say you say look that's
+
+ align:start position:0%
+approach let's say you say look that's
+ 
+
+ align:start position:0%
+approach let's say you say look that's
+stupid I'm young I'm gonna party I'll
+
+ align:start position:0%
+stupid I'm young I'm gonna party I'll
+ 
+
+ align:start position:0%
+stupid I'm young I'm gonna party I'll
+worry about retirement retirements close
+
+ align:start position:0%
+worry about retirement retirements close
+ 
+
+ align:start position:0%
+worry about retirement retirements close
+so I'm gonna save nothing the first 15
+
+ align:start position:0%
+so I'm gonna save nothing the first 15
+ 
+
+ align:start position:0%
+so I'm gonna save nothing the first 15
+years and then I'm gonna save three
+
+ align:start position:0%
+years and then I'm gonna save three
+ 
+
+ align:start position:0%
+years and then I'm gonna save three
+thousand dollars every year for 15 years
+
+ align:start position:0%
+thousand dollars every year for 15 years
+ 
+
+ align:start position:0%
+thousand dollars every year for 15 years
+I'm going to save nothing then I'll save
+
+ align:start position:0%
+I'm going to save nothing then I'll save
+ 
+
+ align:start position:0%
+I'm going to save nothing then I'll save
+$3,000 over year okay well if you do
+
+ align:start position:0%
+$3,000 over year okay well if you do
+ 
+
+ align:start position:0%
+$3,000 over year okay well if you do
+that and do the math you end up with
+
+ align:start position:0%
+that and do the math you end up with
+ 
+
+ align:start position:0%
+that and do the math you end up with
+when you retire three fifty six eight
+
+ align:start position:0%
+when you retire three fifty six eight
+ 
+
+ align:start position:0%
+when you retire three fifty six eight
+hundred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think about this for one second
+
+ align:start position:0%
+think about this for one second
+ 
+
+ align:start position:0%
+think about this for one second
+in this case you save for two more than
+
+ align:start position:0%
+in this case you save for two more than
+ 
+
+ align:start position:0%
+in this case you save for two more than
+twice as many years you say for 33 years
+
+ align:start position:0%
+twice as many years you say for 33 years
+ 
+
+ align:start position:0%
+twice as many years you say for 33 years
+and you ended up with half as much
+
+ align:start position:0%
+and you ended up with half as much
+ 
+
+ align:start position:0%
+and you ended up with half as much
+that's the miracle of compounding the
+
+ align:start position:0%
+that's the miracle of compounding the
+ 
+
+ align:start position:0%
+that's the miracle of compounding the
+earlier you save the more money you can
+
+ align:start position:0%
+earlier you save the more money you can
+ 
+
+ align:start position:0%
+earlier you save the more money you can
+make it along the way and that's why you
+
+ align:start position:0%
+make it along the way and that's why you
+ 
+
+ align:start position:0%
+make it along the way and that's why you
+guys need to start saving right away
+
+ align:start position:0%
+guys need to start saving right away
+ 
+
+ align:start position:0%
+guys need to start saving right away
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+plan 2 was I do nothing the first 15
+
+ align:start position:0%
+plan 2 was I do nothing the first 15
+ 
+
+ align:start position:0%
+plan 2 was I do nothing the first 15
+years then I save the remaining 30 I
+
+ align:start position:0%
+years then I save the remaining 30 I
+ 
+
+ align:start position:0%
+years then I save the remaining 30 I
+save $3,000 in for the mating 30 years
+
+ align:start position:0%
+save $3,000 in for the mating 30 years
+ 
+
+ align:start position:0%
+save $3,000 in for the mating 30 years
+of my career okay so literally in
+
+ align:start position:0%
+of my career okay so literally in
+ 
+
+ align:start position:0%
+of my career okay so literally in
+playing one I say for 15 years and then
+
+ align:start position:0%
+playing one I say for 15 years and then
+ 
+
+ align:start position:0%
+playing one I say for 15 years and then
+I stop here I say for 33 years but by
+
+ align:start position:0%
+I stop here I say for 33 years but by
+ 
+
+ align:start position:0%
+I stop here I say for 33 years but by
+starting early and using the miracle of
+
+ align:start position:0%
+starting early and using the miracle of
+ 
+
+ align:start position:0%
+starting early and using the miracle of
+compounding ended put twice as much
+
+ align:start position:0%
+compounding ended put twice as much
+ 
+
+ align:start position:0%
+compounding ended put twice as much
+money okay now this is actually pretty I
+
+ align:start position:0%
+money okay now this is actually pretty I
+ 
+
+ align:start position:0%
+money okay now this is actually pretty I
+can act this is one of the few things in
+
+ align:start position:0%
+can act this is one of the few things in
+ 
+
+ align:start position:0%
+can act this is one of the few things in
+this class my kids can understand when
+
+ align:start position:0%
+this class my kids can understand when
+ 
+
+ align:start position:0%
+this class my kids can understand when
+they were little
+
+ align:start position:0%
+they were little
+ 
+
+ align:start position:0%
+they were little
+because having hadn't been to Boston
+
+ align:start position:0%
+because having hadn't been to Boston
+ 
+
+ align:start position:0%
+because having hadn't been to Boston
+Science Museum and you guys been okay if
+
+ align:start position:0%
+Science Museum and you guys been okay if
+ 
+
+ align:start position:0%
+Science Museum and you guys been okay if
+there's a little kid area where they've
+
+ align:start position:0%
+there's a little kid area where they've
+ 
+
+ align:start position:0%
+there's a little kid area where they've
+got this ramp and you can essentially
+
+ align:start position:0%
+got this ramp and you can essentially
+ 
+
+ align:start position:0%
+got this ramp and you can essentially
+drop balls down a ramp and one ramp is
+
+ align:start position:0%
+drop balls down a ramp and one ramp is
+ 
+
+ align:start position:0%
+drop balls down a ramp and one ramp is
+flat and then steep and one ramp is
+
+ align:start position:0%
+flat and then steep and one ramp is
+ 
+
+ align:start position:0%
+flat and then steep and one ramp is
+steep and then flat and of course the
+
+ align:start position:0%
+steep and then flat and of course the
+ 
+
+ align:start position:0%
+steep and then flat and of course the
+one that's steeper than flat wins it's
+
+ align:start position:0%
+one that's steeper than flat wins it's
+ 
+
+ align:start position:0%
+one that's steeper than flat wins it's
+faster and that's just because of
+
+ align:start position:0%
+faster and that's just because of
+ 
+
+ align:start position:0%
+faster and that's just because of
+compounding that's because acceleration
+
+ align:start position:0%
+compounding that's because acceleration
+ 
+
+ align:start position:0%
+compounding that's because acceleration
+is compounding okay so basically the
+
+ align:start position:0%
+is compounding okay so basically the
+ 
+
+ align:start position:0%
+is compounding okay so basically the
+point is that the earlier you start
+
+ align:start position:0%
+point is that the earlier you start
+ 
+
+ align:start position:0%
+point is that the earlier you start
+saving the more money you'll have and
+
+ align:start position:0%
+saving the more money you'll have and
+ 
+
+ align:start position:0%
+saving the more money you'll have and
+that's why you guys should pay attention
+
+ align:start position:0%
+that's why you guys should pay attention
+ 
+
+ align:start position:0%
+that's why you guys should pay attention
+when you're offered a job and offer 401
+
+ align:start position:0%
+when you're offered a job and offer 401
+ 
+
+ align:start position:0%
+when you're offered a job and offer 401
+K and I think retirement I'll never
+
+ align:start position:0%
+K and I think retirement I'll never
+ 
+
+ align:start position:0%
+K and I think retirement I'll never
+retire you say no I want to save now
+
+ align:start position:0%
+retire you say no I want to save now
+ 
+
+ align:start position:0%
+retire you say no I want to save now
+because the more I saved now the more
+
+ align:start position:0%
+because the more I saved now the more
+ 
+
+ align:start position:0%
+because the more I saved now the more
+that'll compound by the time I retire
+
+ align:start position:0%
+that'll compound by the time I retire
+ 
+
+ align:start position:0%
+that'll compound by the time I retire
+okay now you can actually see this it's
+
+ align:start position:0%
+okay now you can actually see this it's
+ 
+
+ align:start position:0%
+okay now you can actually see this it's
+not just MIT students have to think
+
+ align:start position:0%
+not just MIT students have to think
+ 
+
+ align:start position:0%
+not just MIT students have to think
+about this but professional athletes so
+
+ align:start position:0%
+about this but professional athletes so
+ 
+
+ align:start position:0%
+about this but professional athletes so
+probably none of you have heard of Bobby
+
+ align:start position:0%
+probably none of you have heard of Bobby
+ 
+
+ align:start position:0%
+probably none of you have heard of Bobby
+Bonilla any of you guys heard of Bobby
+
+ align:start position:0%
+Bonilla any of you guys heard of Bobby
+ 
+
+ align:start position:0%
+Bonilla any of you guys heard of Bobby
+Benina no okay well if you were 25 years
+
+ align:start position:0%
+Benina no okay well if you were 25 years
+ 
+
+ align:start position:0%
+Benina no okay well if you were 25 years
+ago in this class if you were to support
+
+ align:start position:0%
+ago in this class if you were to support
+ 
+
+ align:start position:0%
+ago in this class if you were to support
+you order in Bobby benita he was a
+
+ align:start position:0%
+you order in Bobby benita he was a
+ 
+
+ align:start position:0%
+you order in Bobby benita he was a
+pretty good player in his time and um he
+
+ align:start position:0%
+pretty good player in his time and um he
+ 
+
+ align:start position:0%
+pretty good player in his time and um he
+retired
+
+ align:start position:0%
+retired
+ 
+
+ align:start position:0%
+retired
+um he but by the end of his career he
+
+ align:start position:0%
+um he but by the end of his career he
+ 
+
+ align:start position:0%
+um he but by the end of his career he
+was kind of a slacker he wasn't really
+
+ align:start position:0%
+was kind of a slacker he wasn't really
+ 
+
+ align:start position:0%
+was kind of a slacker he wasn't really
+worth much he was playing for the Mets
+
+ align:start position:0%
+worth much he was playing for the Mets
+ 
+
+ align:start position:0%
+worth much he was playing for the Mets
+and the Mets said look in 1999 they said
+
+ align:start position:0%
+and the Mets said look in 1999 they said
+ 
+
+ align:start position:0%
+and the Mets said look in 1999 they said
+look we basically want to pay you off to
+
+ align:start position:0%
+look we basically want to pay you off to
+ 
+
+ align:start position:0%
+look we basically want to pay you off to
+leave the team
+
+ align:start position:0%
+leave the team
+ 
+
+ align:start position:0%
+leave the team
+you have a contract we're just gonna
+
+ align:start position:0%
+you have a contract we're just gonna
+ 
+
+ align:start position:0%
+you have a contract we're just gonna
+sleep I pay the remaining 5.9 million on
+
+ align:start position:0%
+sleep I pay the remaining 5.9 million on
+ 
+
+ align:start position:0%
+sleep I pay the remaining 5.9 million on
+your contract in 1999 give me the money
+
+ align:start position:0%
+your contract in 1999 give me the money
+ 
+
+ align:start position:0%
+your contract in 1999 give me the money
+most athletes would have said great I'm
+
+ align:start position:0%
+most athletes would have said great I'm
+ 
+
+ align:start position:0%
+most athletes would have said great I'm
+off to Vegas
+
+ align:start position:0%
+off to Vegas
+ 
+
+ align:start position:0%
+off to Vegas
+Bobby buddy you didn't he said well look
+
+ align:start position:0%
+Bobby buddy you didn't he said well look
+ 
+
+ align:start position:0%
+Bobby buddy you didn't he said well look
+I've got enough money right now but I
+
+ align:start position:0%
+I've got enough money right now but I
+ 
+
+ align:start position:0%
+I've got enough money right now but I
+might need the money later
+
+ align:start position:0%
+might need the money later
+ 
+
+ align:start position:0%
+might need the money later
+so instead why don't you defer the money
+
+ align:start position:0%
+so instead why don't you defer the money
+ 
+
+ align:start position:0%
+so instead why don't you defer the money
+at an 8% interest rate and pay me
+
+ align:start position:0%
+at an 8% interest rate and pay me
+ 
+
+ align:start position:0%
+at an 8% interest rate and pay me
+starting in 2011 when I'm getting close
+
+ align:start position:0%
+starting in 2011 when I'm getting close
+ 
+
+ align:start position:0%
+starting in 2011 when I'm getting close
+to retirement need the money they were
+
+ align:start position:0%
+to retirement need the money they were
+ 
+
+ align:start position:0%
+to retirement need the money they were
+like hey that's were like great we'll
+
+ align:start position:0%
+like hey that's were like great we'll
+ 
+
+ align:start position:0%
+like hey that's were like great we'll
+have to pay you now that's great well
+
+ align:start position:0%
+have to pay you now that's great well
+ 
+
+ align:start position:0%
+have to pay you now that's great well
+Bobby Bini Lea by the time his payments
+
+ align:start position:0%
+Bobby Bini Lea by the time his payments
+ 
+
+ align:start position:0%
+Bobby Bini Lea by the time his payments
+are to 2011 they've grown to 30 million
+
+ align:start position:0%
+are to 2011 they've grown to 30 million
+ 
+
+ align:start position:0%
+are to 2011 they've grown to 30 million
+dollars and every year on a certain day
+
+ align:start position:0%
+dollars and every year on a certain day
+ 
+
+ align:start position:0%
+dollars and every year on a certain day
+just pass the reason they call Bobby
+
+ align:start position:0%
+just pass the reason they call Bobby
+ 
+
+ align:start position:0%
+just pass the reason they call Bobby
+Bonilla de Bobby who's now like 7 years
+
+ align:start position:0%
+Bonilla de Bobby who's now like 7 years
+ 
+
+ align:start position:0%
+Bonilla de Bobby who's now like 7 years
+old gets a 1 gets a million dollar check
+
+ align:start position:0%
+old gets a 1 gets a million dollar check
+ 
+
+ align:start position:0%
+old gets a 1 gets a million dollar check
+from the Mets every year okay because
+
+ align:start position:0%
+from the Mets every year okay because
+ 
+
+ align:start position:0%
+from the Mets every year okay because
+there's patient enough to put this off
+
+ align:start position:0%
+there's patient enough to put this off
+ 
+
+ align:start position:0%
+there's patient enough to put this off
+and get the virtue of compounding okay
+
+ align:start position:0%
+and get the virtue of compounding okay
+ 
+
+ align:start position:0%
+and get the virtue of compounding okay
+so this is sort of if Bobby Bonita you
+
+ align:start position:0%
+so this is sort of if Bobby Bonita you
+ 
+
+ align:start position:0%
+so this is sort of if Bobby Bonita you
+know a stupid baseball player can do it
+
+ align:start position:0%
+know a stupid baseball player can do it
+ 
+
+ align:start position:0%
+know a stupid baseball player can do it
+you guys can do it so make sure that you
+
+ align:start position:0%
+you guys can do it so make sure that you
+ 
+
+ align:start position:0%
+you guys can do it so make sure that you
+guys are saving when you start jobs okay
+
+ align:start position:0%
+guys are saving when you start jobs okay
+ 
+
+ align:start position:0%
+guys are saving when you start jobs okay
+questions about that okay now let's
+
+ align:start position:0%
+questions about that okay now let's
+ 
+
+ align:start position:0%
+questions about that okay now let's
+let's let's let's get a little bit
+
+ align:start position:0%
+let's let's let's get a little bit
+ 
+
+ align:start position:0%
+let's let's let's get a little bit
+realistic and let's recognize that in
+
+ align:start position:0%
+realistic and let's recognize that in
+ 
+
+ align:start position:0%
+realistic and let's recognize that in
+life prices aren't constant but rather
+
+ align:start position:0%
+life prices aren't constant but rather
+ 
+
+ align:start position:0%
+life prices aren't constant but rather
+we have inflation and how does that
+
+ align:start position:0%
+we have inflation and how does that
+ 
+
+ align:start position:0%
+we have inflation and how does that
+affect our thinking here how does
+
+ align:start position:0%
+affect our thinking here how does
+ 
+
+ align:start position:0%
+affect our thinking here how does
+inflation affect the way we think about
+
+ align:start position:0%
+inflation affect the way we think about
+ 
+
+ align:start position:0%
+inflation affect the way we think about
+this problem well it turns out it
+
+ align:start position:0%
+this problem well it turns out it
+ 
+
+ align:start position:0%
+this problem well it turns out it
+actually adds one step but it's actually
+
+ align:start position:0%
+actually adds one step but it's actually
+ 
+
+ align:start position:0%
+actually adds one step but it's actually
+a pretty easy step to put in extra turns
+
+ align:start position:0%
+a pretty easy step to put in extra turns
+ 
+
+ align:start position:0%
+a pretty easy step to put in extra turns
+out you can add inflation without doing
+
+ align:start position:0%
+out you can add inflation without doing
+ 
+
+ align:start position:0%
+out you can add inflation without doing
+a whole lot of work so let's talk about
+
+ align:start position:0%
+a whole lot of work so let's talk about
+ 
+
+ align:start position:0%
+a whole lot of work so let's talk about
+first what inflation is inflation is the
+
+ align:start position:0%
+first what inflation is inflation is the
+ 
+
+ align:start position:0%
+first what inflation is inflation is the
+rise in the price level year-over-year
+
+ align:start position:0%
+rise in the price level year-over-year
+ 
+
+ align:start position:0%
+rise in the price level year-over-year
+tackling the inflation rate is a
+
+ align:start position:0%
+tackling the inflation rate is a
+ 
+
+ align:start position:0%
+tackling the inflation rate is a
+percentage concept it's the percent rise
+
+ align:start position:0%
+percentage concept it's the percent rise
+ 
+
+ align:start position:0%
+percentage concept it's the percent rise
+in the price level year after year and
+
+ align:start position:0%
+in the price level year after year and
+ 
+
+ align:start position:0%
+in the price level year after year and
+you might say the price level of what of
+
+ align:start position:0%
+you might say the price level of what of
+ 
+
+ align:start position:0%
+you might say the price level of what of
+a banana of a computer of what well what
+
+ align:start position:0%
+a banana of a computer of what well what
+ 
+
+ align:start position:0%
+a banana of a computer of what well what
+the government does is they form
+
+ align:start position:0%
+the government does is they form
+ 
+
+ align:start position:0%
+the government does is they form
+something called the Consumer Price
+
+ align:start position:0%
+something called the Consumer Price
+ 
+
+ align:start position:0%
+something called the Consumer Price
+Index the CPI talked about CPI yet okay
+
+ align:start position:0%
+Index the CPI talked about CPI yet okay
+ 
+
+ align:start position:0%
+Index the CPI talked about CPI yet okay
+I'm sorry I just and I hate repeating
+
+ align:start position:0%
+I'm sorry I just and I hate repeating
+ 
+
+ align:start position:0%
+I'm sorry I just and I hate repeating
+myself okay so they form something
+
+ align:start position:0%
+myself okay so they form something
+ 
+
+ align:start position:0%
+myself okay so they form something
+called the Consumer Price Index
+
+ align:start position:0%
+called the Consumer Price Index
+ 
+
+ align:start position:0%
+called the Consumer Price Index
+what's Tim Price Index literally the
+
+ align:start position:0%
+what's Tim Price Index literally the
+ 
+
+ align:start position:0%
+what's Tim Price Index literally the
+government every quarter I believe it is
+
+ align:start position:0%
+government every quarter I believe it is
+ 
+
+ align:start position:0%
+government every quarter I believe it is
+it may be every month goes out and gets
+
+ align:start position:0%
+it may be every month goes out and gets
+ 
+
+ align:start position:0%
+it may be every month goes out and gets
+the prices of a basket of hundreds of
+
+ align:start position:0%
+the prices of a basket of hundreds of
+ 
+
+ align:start position:0%
+the prices of a basket of hundreds of
+goods they literally say what does a
+
+ align:start position:0%
+goods they literally say what does a
+ 
+
+ align:start position:0%
+goods they literally say what does a
+banana cost this month compared to last
+
+ align:start position:0%
+banana cost this month compared to last
+ 
+
+ align:start position:0%
+banana cost this month compared to last
+month what does a laptop cost this month
+
+ align:start position:0%
+month what does a laptop cost this month
+ 
+
+ align:start position:0%
+month what does a laptop cost this month
+compared to last month etc so they go
+
+ align:start position:0%
+compared to last month etc so they go
+ 
+
+ align:start position:0%
+compared to last month etc so they go
+out and they price this bundle of goods
+
+ align:start position:0%
+out and they price this bundle of goods
+ 
+
+ align:start position:0%
+out and they price this bundle of goods
+and then literally they just asked how
+
+ align:start position:0%
+and then literally they just asked how
+ 
+
+ align:start position:0%
+and then literally they just asked how
+has the price that
+
+ align:start position:0%
+has the price that
+ 
+
+ align:start position:0%
+has the price that
+take a weighted average of that bundle
+
+ align:start position:0%
+take a weighted average of that bundle
+ 
+
+ align:start position:0%
+take a weighted average of that bundle
+where the weights are consumer spending
+
+ align:start position:0%
+where the weights are consumer spending
+ 
+
+ align:start position:0%
+where the weights are consumer spending
+so consumers spend a lot more if their
+
+ align:start position:0%
+so consumers spend a lot more if their
+ 
+
+ align:start position:0%
+so consumers spend a lot more if their
+income on housing than bananas so the
+
+ align:start position:0%
+income on housing than bananas so the
+ 
+
+ align:start position:0%
+income on housing than bananas so the
+price of housing gets a lot more weight
+
+ align:start position:0%
+price of housing gets a lot more weight
+ 
+
+ align:start position:0%
+price of housing gets a lot more weight
+in the CPI than as the price of bananas
+
+ align:start position:0%
+in the CPI than as the price of bananas
+ 
+
+ align:start position:0%
+in the CPI than as the price of bananas
+essentially a weighted average of prices
+
+ align:start position:0%
+essentially a weighted average of prices
+ 
+
+ align:start position:0%
+essentially a weighted average of prices
+in society and then that they cream
+
+ align:start position:0%
+in society and then that they cream
+ 
+
+ align:start position:0%
+in society and then that they cream
+index 1982 is normalized to one and they
+
+ align:start position:0%
+index 1982 is normalized to one and they
+ 
+
+ align:start position:0%
+index 1982 is normalized to one and they
+just say how much in percentage terms
+
+ align:start position:0%
+just say how much in percentage terms
+ 
+
+ align:start position:0%
+just say how much in percentage terms
+did that weighted average bundle go up
+
+ align:start position:0%
+did that weighted average bundle go up
+ 
+
+ align:start position:0%
+did that weighted average bundle go up
+in price okay and you can see that in
+
+ align:start position:0%
+in price okay and you can see that in
+ 
+
+ align:start position:0%
+in price okay and you can see that in
+Figure 17 one here's historical CPI so
+
+ align:start position:0%
+Figure 17 one here's historical CPI so
+ 
+
+ align:start position:0%
+Figure 17 one here's historical CPI so
+basically what you see is this is the
+
+ align:start position:0%
+basically what you see is this is the
+ 
+
+ align:start position:0%
+basically what you see is this is the
+level of the CPI which is sort of
+
+ align:start position:0%
+level of the CPI which is sort of
+ 
+
+ align:start position:0%
+level of the CPI which is sort of
+meaningless we care about his inflation
+
+ align:start position:0%
+meaningless we care about his inflation
+ 
+
+ align:start position:0%
+meaningless we care about his inflation
+which is the year-to-year percentage
+
+ align:start position:0%
+which is the year-to-year percentage
+ 
+
+ align:start position:0%
+which is the year-to-year percentage
+change in the CPI and what you can see
+
+ align:start position:0%
+change in the CPI and what you can see
+ 
+
+ align:start position:0%
+change in the CPI and what you can see
+is basically it's going up prices are
+
+ align:start position:0%
+is basically it's going up prices are
+ 
+
+ align:start position:0%
+is basically it's going up prices are
+going up it went up very steeply if you
+
+ align:start position:0%
+going up it went up very steeply if you
+ 
+
+ align:start position:0%
+going up it went up very steeply if you
+look from 1970 to 1980 the slope there
+
+ align:start position:0%
+look from 1970 to 1980 the slope there
+ 
+
+ align:start position:0%
+look from 1970 to 1980 the slope there
+is much higher than the slope before
+
+ align:start position:0%
+is much higher than the slope before
+ 
+
+ align:start position:0%
+is much higher than the slope before
+after we had very rapid inflation in the
+
+ align:start position:0%
+after we had very rapid inflation in the
+ 
+
+ align:start position:0%
+after we had very rapid inflation in the
+1970s it then and then since flattened
+
+ align:start position:0%
+1970s it then and then since flattened
+ 
+
+ align:start position:0%
+1970s it then and then since flattened
+and inflation has been much slower and
+
+ align:start position:0%
+and inflation has been much slower and
+ 
+
+ align:start position:0%
+and inflation has been much slower and
+inflation averaged is about three
+
+ align:start position:0%
+inflation averaged is about three
+ 
+
+ align:start position:0%
+inflation averaged is about three
+percent a year okay
+
+ align:start position:0%
+percent a year okay
+ 
+
+ align:start position:0%
+percent a year okay
+so basically that's how we measure
+
+ align:start position:0%
+so basically that's how we measure
+ 
+
+ align:start position:0%
+so basically that's how we measure
+inflation now the question is how does
+
+ align:start position:0%
+inflation now the question is how does
+ 
+
+ align:start position:0%
+inflation now the question is how does
+that affect our thinking about present
+
+ align:start position:0%
+that affect our thinking about present
+ 
+
+ align:start position:0%
+that affect our thinking about present
+value if there's actually inflation and
+
+ align:start position:0%
+value if there's actually inflation and
+ 
+
+ align:start position:0%
+value if there's actually inflation and
+the bottom line is we don't care about
+
+ align:start position:0%
+the bottom line is we don't care about
+ 
+
+ align:start position:0%
+the bottom line is we don't care about
+dollars we care about how many goods we
+
+ align:start position:0%
+dollars we care about how many goods we
+ 
+
+ align:start position:0%
+dollars we care about how many goods we
+can buy therefore it doesn't matter
+
+ align:start position:0%
+can buy therefore it doesn't matter
+ 
+
+ align:start position:0%
+can buy therefore it doesn't matter
+what's happening to how much money we
+
+ align:start position:0%
+what's happening to how much money we
+ 
+
+ align:start position:0%
+what's happening to how much money we
+have it matters what's happened - how
+
+ align:start position:0%
+have it matters what's happened - how
+ 
+
+ align:start position:0%
+have it matters what's happened - how
+many Goods we can buy therefore what we
+
+ align:start position:0%
+many Goods we can buy therefore what we
+ 
+
+ align:start position:0%
+many Goods we can buy therefore what we
+care about is not what we call the
+
+ align:start position:0%
+care about is not what we call the
+ 
+
+ align:start position:0%
+care about is not what we call the
+nominal interest rate we care about we
+
+ align:start position:0%
+nominal interest rate we care about we
+ 
+
+ align:start position:0%
+nominal interest rate we care about we
+call the real interest rate or which we
+
+ align:start position:0%
+call the real interest rate or which we
+ 
+
+ align:start position:0%
+call the real interest rate or which we
+define as the nominal interest rate
+
+ align:start position:0%
+define as the nominal interest rate
+ 
+
+ align:start position:0%
+define as the nominal interest rate
+which is well been talking about we see
+
+ align:start position:0%
+which is well been talking about we see
+ 
+
+ align:start position:0%
+which is well been talking about we see
+advertised in a bank - the rate of
+
+ align:start position:0%
+advertised in a bank - the rate of
+ 
+
+ align:start position:0%
+advertised in a bank - the rate of
+inflation which for some reason we use
+
+ align:start position:0%
+inflation which for some reason we use
+ 
+
+ align:start position:0%
+inflation which for some reason we use
+PI even though that's also profits so
+
+ align:start position:0%
+PI even though that's also profits so
+ 
+
+ align:start position:0%
+PI even though that's also profits so
+sorry about that okay so we define the
+
+ align:start position:0%
+sorry about that okay so we define the
+ 
+
+ align:start position:0%
+sorry about that okay so we define the
+real interest rate as the nominal
+
+ align:start position:0%
+real interest rate as the nominal
+ 
+
+ align:start position:0%
+real interest rate as the nominal
+interest rate - the inflation rate okay
+
+ align:start position:0%
+interest rate - the inflation rate okay
+ 
+
+ align:start position:0%
+interest rate - the inflation rate okay
+the nominal and real estate nominal rate
+
+ align:start position:0%
+the nominal and real estate nominal rate
+ 
+
+ align:start position:0%
+the nominal and real estate nominal rate
+- the inflation rate and what the real
+
+ align:start position:0%
+- the inflation rate and what the real
+ 
+
+ align:start position:0%
+- the inflation rate and what the real
+interest rate measures is how much more
+
+ align:start position:0%
+interest rate measures is how much more
+ 
+
+ align:start position:0%
+interest rate measures is how much more
+I have in time in terms of goods I can
+
+ align:start position:0%
+I have in time in terms of goods I can
+ 
+
+ align:start position:0%
+I have in time in terms of goods I can
+consume not how much more I have in
+
+ align:start position:0%
+consume not how much more I have in
+ 
+
+ align:start position:0%
+consume not how much more I have in
+terms of dollars which actually in the
+
+ align:start position:0%
+terms of dollars which actually in the
+ 
+
+ align:start position:0%
+terms of dollars which actually in the
+end doesn't matter okay so suppose
+
+ align:start position:0%
+end doesn't matter okay so suppose
+ 
+
+ align:start position:0%
+end doesn't matter okay so suppose
+that I'm gonna save $100 at a 10%
+
+ align:start position:0%
+that I'm gonna save $100 at a 10%
+ 
+
+ align:start position:0%
+that I'm gonna save $100 at a 10%
+interest rate it's go simple example
+
+ align:start position:0%
+interest rate it's go simple example
+ 
+
+ align:start position:0%
+interest rate it's go simple example
+they have $100 or 10% interest rate okay
+
+ align:start position:0%
+they have $100 or 10% interest rate okay
+ 
+
+ align:start position:0%
+they have $100 or 10% interest rate okay
+what I then next you'll have one hundred
+
+ align:start position:0%
+what I then next you'll have one hundred
+ 
+
+ align:start position:0%
+what I then next you'll have one hundred
+and ten dollars but that's irrelevant
+
+ align:start position:0%
+and ten dollars but that's irrelevant
+ 
+
+ align:start position:0%
+and ten dollars but that's irrelevant
+what I want to know is how many Goods
+
+ align:start position:0%
+what I want to know is how many Goods
+ 
+
+ align:start position:0%
+what I want to know is how many Goods
+can I buy next year so for example let's
+
+ align:start position:0%
+can I buy next year so for example let's
+ 
+
+ align:start position:0%
+can I buy next year so for example let's
+say you spend all your money on skittles
+
+ align:start position:0%
+say you spend all your money on skittles
+ 
+
+ align:start position:0%
+say you spend all your money on skittles
+that's all you buy okay and let's say
+
+ align:start position:0%
+that's all you buy okay and let's say
+ 
+
+ align:start position:0%
+that's all you buy okay and let's say
+skittles cost $1 this year and there's
+
+ align:start position:0%
+skittles cost $1 this year and there's
+ 
+
+ align:start position:0%
+skittles cost $1 this year and there's
+no inflation those cost $1 next year
+
+ align:start position:0%
+no inflation those cost $1 next year
+ 
+
+ align:start position:0%
+no inflation those cost $1 next year
+then what that means with a 10% interest
+
+ align:start position:0%
+then what that means with a 10% interest
+ 
+
+ align:start position:0%
+then what that means with a 10% interest
+rate is you can buy ten more bags of
+
+ align:start position:0%
+rate is you can buy ten more bags of
+ 
+
+ align:start position:0%
+rate is you can buy ten more bags of
+Skittles next year this year your
+
+ align:start position:0%
+Skittles next year this year your
+ 
+
+ align:start position:0%
+Skittles next year this year your
+hundred dollars could buy you a hundred
+
+ align:start position:0%
+hundred dollars could buy you a hundred
+ 
+
+ align:start position:0%
+hundred dollars could buy you a hundred
+bags of Skittles next year your hundred
+
+ align:start position:0%
+bags of Skittles next year your hundred
+ 
+
+ align:start position:0%
+bags of Skittles next year your hundred
+ten dollars can buy 110 bags of Skittles
+
+ align:start position:0%
+ten dollars can buy 110 bags of Skittles
+ 
+
+ align:start position:0%
+ten dollars can buy 110 bags of Skittles
+so you are ten percent richer but now
+
+ align:start position:0%
+so you are ten percent richer but now
+ 
+
+ align:start position:0%
+so you are ten percent richer but now
+let's say the price of skittles goes up
+
+ align:start position:0%
+let's say the price of skittles goes up
+ 
+
+ align:start position:0%
+let's say the price of skittles goes up
+10 percent well what that means is you
+
+ align:start position:0%
+10 percent well what that means is you
+ 
+
+ align:start position:0%
+10 percent well what that means is you
+can only buy the same amount of skittles
+
+ align:start position:0%
+can only buy the same amount of skittles
+ 
+
+ align:start position:0%
+can only buy the same amount of skittles
+next year you could buy this year you
+
+ align:start position:0%
+next year you could buy this year you
+ 
+
+ align:start position:0%
+next year you could buy this year you
+could buy a hundred bags this year and
+
+ align:start position:0%
+could buy a hundred bags this year and
+ 
+
+ align:start position:0%
+could buy a hundred bags this year and
+100 bags next year so it doesn't matter
+
+ align:start position:0%
+100 bags next year so it doesn't matter
+ 
+
+ align:start position:0%
+100 bags next year so it doesn't matter
+you have a hundred and ten dollars next
+
+ align:start position:0%
+you have a hundred and ten dollars next
+ 
+
+ align:start position:0%
+you have a hundred and ten dollars next
+year who cares you can only get the same
+
+ align:start position:0%
+year who cares you can only get the same
+ 
+
+ align:start position:0%
+year who cares you can only get the same
+amount of skittles what you care about
+
+ align:start position:0%
+amount of skittles what you care about
+ 
+
+ align:start position:0%
+amount of skittles what you care about
+is the goods you can buy note on utility
+
+ align:start position:0%
+is the goods you can buy note on utility
+ 
+
+ align:start position:0%
+is the goods you can buy note on utility
+wouldn't put dollars utility function we
+
+ align:start position:0%
+wouldn't put dollars utility function we
+ 
+
+ align:start position:0%
+wouldn't put dollars utility function we
+put consumption so the interest rate you
+
+ align:start position:0%
+put consumption so the interest rate you
+ 
+
+ align:start position:0%
+put consumption so the interest rate you
+care about is the real interest rate if
+
+ align:start position:0%
+care about is the real interest rate if
+ 
+
+ align:start position:0%
+care about is the real interest rate if
+the nominal in straight is ten percent
+
+ align:start position:0%
+the nominal in straight is ten percent
+ 
+
+ align:start position:0%
+the nominal in straight is ten percent
+but inflation is ten percent then the
+
+ align:start position:0%
+but inflation is ten percent then the
+ 
+
+ align:start position:0%
+but inflation is ten percent then the
+real interest rate is zero you can't buy
+
+ align:start position:0%
+real interest rate is zero you can't buy
+ 
+
+ align:start position:0%
+real interest rate is zero you can't buy
+any more Goods next year all the money
+
+ align:start position:0%
+any more Goods next year all the money
+ 
+
+ align:start position:0%
+any more Goods next year all the money
+you made by putting the bank got eaten
+
+ align:start position:0%
+you made by putting the bank got eaten
+ 
+
+ align:start position:0%
+you made by putting the bank got eaten
+up by how much more expensive things are
+
+ align:start position:0%
+up by how much more expensive things are
+ 
+
+ align:start position:0%
+up by how much more expensive things are
+so what that means is all the math we've
+
+ align:start position:0%
+so what that means is all the math we've
+ 
+
+ align:start position:0%
+so what that means is all the math we've
+done and everything we'll talk about it
+
+ align:start position:0%
+done and everything we'll talk about it
+ 
+
+ align:start position:0%
+done and everything we'll talk about it
+all goes through you just need to be
+
+ align:start position:0%
+all goes through you just need to be
+ 
+
+ align:start position:0%
+all goes through you just need to be
+thinking about using the real interest
+
+ align:start position:0%
+thinking about using the real interest
+ 
+
+ align:start position:0%
+thinking about using the real interest
+rate not the nominal interest rate okay
+
+ align:start position:0%
+rate not the nominal interest rate okay
+ 
+
+ align:start position:0%
+rate not the nominal interest rate okay
+but otherwise everything we've done is
+
+ align:start position:0%
+but otherwise everything we've done is
+ 
+
+ align:start position:0%
+but otherwise everything we've done is
+goes through you just need to
+
+ align:start position:0%
+goes through you just need to
+ 
+
+ align:start position:0%
+goes through you just need to
+essentially think about this in terms of
+
+ align:start position:0%
+essentially think about this in terms of
+ 
+
+ align:start position:0%
+essentially think about this in terms of
+how many goods you can buy not how much
+
+ align:start position:0%
+how many goods you can buy not how much
+ 
+
+ align:start position:0%
+how many goods you can buy not how much
+money you have now this isn't quite let
+
+ align:start position:0%
+money you have now this isn't quite let
+ 
+
+ align:start position:0%
+money you have now this isn't quite let
+me just take two minutes and do a little
+
+ align:start position:0%
+me just take two minutes and do a little
+ 
+
+ align:start position:0%
+me just take two minutes and do a little
+macroeconomics this isn't quite as
+
+ align:start position:0%
+macroeconomics this isn't quite as
+ 
+
+ align:start position:0%
+macroeconomics this isn't quite as
+simple as it sounds because of course
+
+ align:start position:0%
+simple as it sounds because of course
+ 
+
+ align:start position:0%
+simple as it sounds because of course
+you see in the bank I in the bank window
+
+ align:start position:0%
+you see in the bank I in the bank window
+ 
+
+ align:start position:0%
+you see in the bank I in the bank window
+I you don't see pie you don't see
+
+ align:start position:0%
+I you don't see pie you don't see
+ 
+
+ align:start position:0%
+I you don't see pie you don't see
+inflation that's what we revealed
+
+ align:start position:0%
+inflation that's what we revealed
+ 
+
+ align:start position:0%
+inflation that's what we revealed
+ex-post
+
+ align:start position:0%
+ex-post
+ 
+
+ align:start position:0%
+ex-post
+so really technically you don't have to
+
+ align:start position:0%
+so really technically you don't have to
+ 
+
+ align:start position:0%
+so really technically you don't have to
+know this is just for those who care
+
+ align:start position:0%
+know this is just for those who care
+ 
+
+ align:start position:0%
+know this is just for those who care
+it's just the test
+
+ align:start position:0%
+it's just the test
+ 
+
+ align:start position:0%
+it's just the test
+technically what you really want is
+
+ align:start position:0%
+technically what you really want is
+ 
+
+ align:start position:0%
+technically what you really want is
+expected inflation right when you think
+
+ align:start position:0%
+expected inflation right when you think
+ 
+
+ align:start position:0%
+expected inflation right when you think
+I'm putting in the money in the bank you
+
+ align:start position:0%
+I'm putting in the money in the bank you
+ 
+
+ align:start position:0%
+I'm putting in the money in the bank you
+know you learn 3% the realist rate is
+
+ align:start position:0%
+know you learn 3% the realist rate is
+ 
+
+ align:start position:0%
+know you learn 3% the realist rate is
+that - what you think inflation is going
+
+ align:start position:0%
+that - what you think inflation is going
+ 
+
+ align:start position:0%
+that - what you think inflation is going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+right so it actually becomes complicated
+
+ align:start position:0%
+right so it actually becomes complicated
+ 
+
+ align:start position:0%
+right so it actually becomes complicated
+it's not as simple ex-post it's easy to
+
+ align:start position:0%
+it's not as simple ex-post it's easy to
+ 
+
+ align:start position:0%
+it's not as simple ex-post it's easy to
+find the real interest rate ex ante it's
+
+ align:start position:0%
+find the real interest rate ex ante it's
+ 
+
+ align:start position:0%
+find the real interest rate ex ante it's
+not so easy because depends on what you
+
+ align:start position:0%
+not so easy because depends on what you
+ 
+
+ align:start position:0%
+not so easy because depends on what you
+think inflation is going to be there's
+
+ align:start position:0%
+think inflation is going to be there's
+ 
+
+ align:start position:0%
+think inflation is going to be there's
+some tricks there there's also a bunch
+
+ align:start position:0%
+some tricks there there's also a bunch
+ 
+
+ align:start position:0%
+some tricks there there's also a bunch
+of tricks and measuring the inflation
+
+ align:start position:0%
+of tricks and measuring the inflation
+ 
+
+ align:start position:0%
+of tricks and measuring the inflation
+rate so for example like I said the
+
+ align:start position:0%
+rate so for example like I said the
+ 
+
+ align:start position:0%
+rate so for example like I said the
+Bureau of Labor Statistics goes out and
+
+ align:start position:0%
+Bureau of Labor Statistics goes out and
+ 
+
+ align:start position:0%
+Bureau of Labor Statistics goes out and
+has a bundle of 600 goods it gets their
+
+ align:start position:0%
+has a bundle of 600 goods it gets their
+ 
+
+ align:start position:0%
+has a bundle of 600 goods it gets their
+prices but what is it good I mean a
+
+ align:start position:0%
+prices but what is it good I mean a
+ 
+
+ align:start position:0%
+prices but what is it good I mean a
+bananas a banana but a laptop what the
+
+ align:start position:0%
+bananas a banana but a laptop what the
+ 
+
+ align:start position:0%
+bananas a banana but a laptop what the
+hell is a laptop how much RAM does it
+
+ align:start position:0%
+hell is a laptop how much RAM does it
+ 
+
+ align:start position:0%
+hell is a laptop how much RAM does it
+have what's the graphics card
+
+ align:start position:0%
+have what's the graphics card
+ 
+
+ align:start position:0%
+have what's the graphics card
+you know how faith is to display well
+
+ align:start position:0%
+you know how faith is to display well
+ 
+
+ align:start position:0%
+you know how faith is to display well
+the Bureau logistics doesn't go out and
+
+ align:start position:0%
+the Bureau logistics doesn't go out and
+ 
+
+ align:start position:0%
+the Bureau logistics doesn't go out and
+price literally hundreds of laptops at
+
+ align:start position:0%
+price literally hundreds of laptops at
+ 
+
+ align:start position:0%
+price literally hundreds of laptops at
+prices one or two and the problem with
+
+ align:start position:0%
+prices one or two and the problem with
+ 
+
+ align:start position:0%
+prices one or two and the problem with
+that is the following let's say you find
+
+ align:start position:0%
+that is the following let's say you find
+ 
+
+ align:start position:0%
+that is the following let's say you find
+that today a laptop is a thousand and
+
+ align:start position:0%
+that today a laptop is a thousand and
+ 
+
+ align:start position:0%
+that today a laptop is a thousand and
+tomorrow it's 1,500 but it can do let's
+
+ align:start position:0%
+tomorrow it's 1,500 but it can do let's
+ 
+
+ align:start position:0%
+tomorrow it's 1,500 but it can do let's
+say today laptops a thousand and
+
+ align:start position:0%
+say today laptops a thousand and
+ 
+
+ align:start position:0%
+say today laptops a thousand and
+tomorrow it's 1500 but it can do a ton
+
+ align:start position:0%
+tomorrow it's 1500 but it can do a ton
+ 
+
+ align:start position:0%
+tomorrow it's 1500 but it can do a ton
+more stuff well we would say inflation
+
+ align:start position:0%
+more stuff well we would say inflation
+ 
+
+ align:start position:0%
+more stuff well we would say inflation
+is 50% but that's not really right
+
+ align:start position:0%
+is 50% but that's not really right
+ 
+
+ align:start position:0%
+is 50% but that's not really right
+because the good you're consuming is not
+
+ align:start position:0%
+because the good you're consuming is not
+ 
+
+ align:start position:0%
+because the good you're consuming is not
+the laptop it's the computing ability of
+
+ align:start position:0%
+the laptop it's the computing ability of
+ 
+
+ align:start position:0%
+the laptop it's the computing ability of
+the laptop and that's gone up so to say
+
+ align:start position:0%
+the laptop and that's gone up so to say
+ 
+
+ align:start position:0%
+the laptop and that's gone up so to say
+inflation 50% is wrong inflation 50% -
+
+ align:start position:0%
+inflation 50% is wrong inflation 50% -
+ 
+
+ align:start position:0%
+inflation 50% is wrong inflation 50% -
+the quality improvement of the better
+
+ align:start position:0%
+the quality improvement of the better
+ 
+
+ align:start position:0%
+the quality improvement of the better
+laptop you got think of it another way
+
+ align:start position:0%
+laptop you got think of it another way
+ 
+
+ align:start position:0%
+laptop you got think of it another way
+imagine laptop prices didn't go up but
+
+ align:start position:0%
+imagine laptop prices didn't go up but
+ 
+
+ align:start position:0%
+imagine laptop prices didn't go up but
+RAM doubled okay would you say you're no
+
+ align:start position:0%
+RAM doubled okay would you say you're no
+ 
+
+ align:start position:0%
+RAM doubled okay would you say you're no
+better off buying a laptop with twice as
+
+ align:start position:0%
+better off buying a laptop with twice as
+ 
+
+ align:start position:0%
+better off buying a laptop with twice as
+much RAM at the same price no you're
+
+ align:start position:0%
+much RAM at the same price no you're
+ 
+
+ align:start position:0%
+much RAM at the same price no you're
+better off but about our inflation
+
+ align:start position:0%
+better off but about our inflation
+ 
+
+ align:start position:0%
+better off but about our inflation
+concept would say no you're the same
+
+ align:start position:0%
+concept would say no you're the same
+ 
+
+ align:start position:0%
+concept would say no you're the same
+often so the trick here is it simple and
+
+ align:start position:0%
+often so the trick here is it simple and
+ 
+
+ align:start position:0%
+often so the trick here is it simple and
+practice and we'll pretend as simple to
+
+ align:start position:0%
+practice and we'll pretend as simple to
+ 
+
+ align:start position:0%
+practice and we'll pretend as simple to
+say are as I - PI but two tricks a it's
+
+ align:start position:0%
+say are as I - PI but two tricks a it's
+ 
+
+ align:start position:0%
+say are as I - PI but two tricks a it's
+expected PI which is hard to guess and
+
+ align:start position:0%
+expected PI which is hard to guess and
+ 
+
+ align:start position:0%
+expected PI which is hard to guess and
+be inflation is really hard to measure
+
+ align:start position:0%
+be inflation is really hard to measure
+ 
+
+ align:start position:0%
+be inflation is really hard to measure
+because there's things like quality bias
+
+ align:start position:0%
+because there's things like quality bias
+ 
+
+ align:start position:0%
+because there's things like quality bias
+and other things there's a whole field
+
+ align:start position:0%
+and other things there's a whole field
+ 
+
+ align:start position:0%
+and other things there's a whole field
+de macroeconomics worrying about
+
+ align:start position:0%
+de macroeconomics worrying about
+ 
+
+ align:start position:0%
+de macroeconomics worrying about
+inflation measurement so let's spend a
+
+ align:start position:0%
+inflation measurement so let's spend a
+ 
+
+ align:start position:0%
+inflation measurement so let's spend a
+lot of time on it but it's just sort of
+
+ align:start position:0%
+lot of time on it but it's just sort of
+ 
+
+ align:start position:0%
+lot of time on it but it's just sort of
+the kind of interesting we tweak just to
+
+ align:start position:0%
+the kind of interesting we tweak just to
+ 
+
+ align:start position:0%
+the kind of interesting we tweak just to
+sort of talk about how sort of at high
+
+ align:start position:0%
+sort of talk about how sort of at high
+ 
+
+ align:start position:0%
+sort of talk about how sort of at high
+level we go things here like everything
+
+ align:start position:0%
+level we go things here like everything
+ 
+
+ align:start position:0%
+level we go things here like everything
+else in this class largely we get it
+
+ align:start position:0%
+else in this class largely we get it
+ 
+
+ align:start position:0%
+else in this class largely we get it
+right largely expected inflation is not
+
+ align:start position:0%
+right largely expected inflation is not
+ 
+
+ align:start position:0%
+right largely expected inflation is not
+too badly modelled by last year's
+
+ align:start position:0%
+too badly modelled by last year's
+ 
+
+ align:start position:0%
+too badly modelled by last year's
+inflation and quality bias bias we can
+
+ align:start position:0%
+inflation and quality bias bias we can
+ 
+
+ align:start position:0%
+inflation and quality bias bias we can
+model it stuff so this isn't a bad model
+
+ align:start position:0%
+model it stuff so this isn't a bad model
+ 
+
+ align:start position:0%
+model it stuff so this isn't a bad model
+but it just sort of points to some of
+
+ align:start position:0%
+but it just sort of points to some of
+ 
+
+ align:start position:0%
+but it just sort of points to some of
+the subtleties you have to deal with a
+
+ align:start position:0%
+the subtleties you have to deal with a
+ 
+
+ align:start position:0%
+the subtleties you have to deal with a
+reality when you try to implement these
+
+ align:start position:0%
+reality when you try to implement these
+ 
+
+ align:start position:0%
+reality when you try to implement these
+basic sort of formulations okay now
+
+ align:start position:0%
+basic sort of formulations okay now
+ 
+
+ align:start position:0%
+basic sort of formulations okay now
+with that in mind I'm gonna now say
+
+ align:start position:0%
+with that in mind I'm gonna now say
+ 
+
+ align:start position:0%
+with that in mind I'm gonna now say
+let's assume inflation zero again okay
+
+ align:start position:0%
+let's assume inflation zero again okay
+ 
+
+ align:start position:0%
+let's assume inflation zero again okay
+so we'll go back and use I and we'll use
+
+ align:start position:0%
+so we'll go back and use I and we'll use
+ 
+
+ align:start position:0%
+so we'll go back and use I and we'll use
+I interchangeably with our for the rest
+
+ align:start position:0%
+I interchangeably with our for the rest
+ 
+
+ align:start position:0%
+I interchangeably with our for the rest
+of this course okay unless asked
+
+ align:start position:0%
+of this course okay unless asked
+ 
+
+ align:start position:0%
+of this course okay unless asked
+differently unless told differently
+
+ align:start position:0%
+differently unless told differently
+ 
+
+ align:start position:0%
+differently unless told differently
+assume inflation zero so INR and are
+
+ align:start position:0%
+assume inflation zero so INR and are
+ 
+
+ align:start position:0%
+assume inflation zero so INR and are
+interchangeable with that in mind let's
+
+ align:start position:0%
+interchangeable with that in mind let's
+ 
+
+ align:start position:0%
+interchangeable with that in mind let's
+go to the next topic which is taking
+
+ align:start position:0%
+go to the next topic which is taking
+ 
+
+ align:start position:0%
+go to the next topic which is taking
+these tools how do we model choices over
+
+ align:start position:0%
+these tools how do we model choices over
+ 
+
+ align:start position:0%
+these tools how do we model choices over
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do people model how do people make
+
+ align:start position:0%
+how do people model how do people make
+ 
+
+ align:start position:0%
+how do people model how do people make
+decisions over time and there's a simple
+
+ align:start position:0%
+decisions over time and there's a simple
+ 
+
+ align:start position:0%
+decisions over time and there's a simple
+int so this is tricky because if I said
+
+ align:start position:0%
+int so this is tricky because if I said
+ 
+
+ align:start position:0%
+int so this is tricky because if I said
+to you hey I'm gonna give you what do
+
+ align:start position:0%
+to you hey I'm gonna give you what do
+ 
+
+ align:start position:0%
+to you hey I'm gonna give you what do
+you want $30 or $50 you'd say I want $50
+
+ align:start position:0%
+you want $30 or $50 you'd say I want $50
+ 
+
+ align:start position:0%
+you want $30 or $50 you'd say I want $50
+but actually shouldn't say that you
+
+ align:start position:0%
+but actually shouldn't say that you
+ 
+
+ align:start position:0%
+but actually shouldn't say that you
+should say over what period of time by
+
+ align:start position:0%
+should say over what period of time by
+ 
+
+ align:start position:0%
+should say over what period of time by
+getting the 30 and over what period of
+
+ align:start position:0%
+getting the 30 and over what period of
+ 
+
+ align:start position:0%
+getting the 30 and over what period of
+time by getting the 50 if it's today I
+
+ align:start position:0%
+time by getting the 50 if it's today I
+ 
+
+ align:start position:0%
+time by getting the 50 if it's today I
+want 50 but then 50 is 20 years in the
+
+ align:start position:0%
+want 50 but then 50 is 20 years in the
+ 
+
+ align:start position:0%
+want 50 but then 50 is 20 years in the
+future in the 30s today I might want the
+
+ align:start position:0%
+future in the 30s today I might want the
+ 
+
+ align:start position:0%
+future in the 30s today I might want the
+30 what that means is you have to
+
+ align:start position:0%
+30 what that means is you have to
+ 
+
+ align:start position:0%
+30 what that means is you have to
+evaluate choices in present value terms
+
+ align:start position:0%
+evaluate choices in present value terms
+ 
+
+ align:start position:0%
+evaluate choices in present value terms
+you can't just add up the money you have
+
+ align:start position:0%
+you can't just add up the money you have
+ 
+
+ align:start position:0%
+you can't just add up the money you have
+to evaluate those choices in present
+
+ align:start position:0%
+to evaluate those choices in present
+ 
+
+ align:start position:0%
+to evaluate those choices in present
+value terms and then you need to pick
+
+ align:start position:0%
+value terms and then you need to pick
+ 
+
+ align:start position:0%
+value terms and then you need to pick
+the option with the highest present
+
+ align:start position:0%
+the option with the highest present
+ 
+
+ align:start position:0%
+the option with the highest present
+value so let's see let's come back to
+
+ align:start position:0%
+value so let's see let's come back to
+ 
+
+ align:start position:0%
+value so let's see let's come back to
+athletes because I've let a contracts
+
+ align:start position:0%
+athletes because I've let a contracts
+ 
+
+ align:start position:0%
+athletes because I've let a contracts
+deal with this all the time let's
+
+ align:start position:0%
+deal with this all the time let's
+ 
+
+ align:start position:0%
+deal with this all the time let's
+imagine athlean considering two
+
+ align:start position:0%
+imagine athlean considering two
+ 
+
+ align:start position:0%
+imagine athlean considering two
+different contracts okay contract one
+
+ align:start position:0%
+different contracts okay contract one
+ 
+
+ align:start position:0%
+different contracts okay contract one
+pays contract a pays a million dollars
+
+ align:start position:0%
+pays contract a pays a million dollars
+ 
+
+ align:start position:0%
+pays contract a pays a million dollars
+today contract be okay
+
+ align:start position:0%
+today contract be okay
+ 
+
+ align:start position:0%
+today contract be okay
+pays 500,000 today and 1.5 million in
+
+ align:start position:0%
+pays 500,000 today and 1.5 million in
+ 
+
+ align:start position:0%
+pays 500,000 today and 1.5 million in
+ten years okay now when you read in the
+
+ align:start position:0%
+ten years okay now when you read in the
+ 
+
+ align:start position:0%
+ten years okay now when you read in the
+newspaper you'll see this guy got off
+
+ align:start position:0%
+newspaper you'll see this guy got off
+ 
+
+ align:start position:0%
+newspaper you'll see this guy got off
+for a million this guy got off for two
+
+ align:start position:0%
+for a million this guy got off for two
+ 
+
+ align:start position:0%
+for a million this guy got off for two
+million
+
+ align:start position:0%
+million
+ 
+
+ align:start position:0%
+million
+that's what newspaper will say but
+
+ align:start position:0%
+that's what newspaper will say but
+ 
+
+ align:start position:0%
+that's what newspaper will say but
+that's wrong because these are painted
+
+ align:start position:0%
+that's wrong because these are painted
+ 
+
+ align:start position:0%
+that's wrong because these are painted
+different periods of times that are
+
+ align:start position:0%
+different periods of times that are
+ 
+
+ align:start position:0%
+different periods of times that are
+different amounts indeed
+
+ align:start position:0%
+different amounts indeed
+ 
+
+ align:start position:0%
+different amounts indeed
+the present value the first contract is
+
+ align:start position:0%
+the present value the first contract is
+ 
+
+ align:start position:0%
+the present value the first contract is
+what 1 million dollars it's today what's
+
+ align:start position:0%
+what 1 million dollars it's today what's
+ 
+
+ align:start position:0%
+what 1 million dollars it's today what's
+the present value the second contract
+
+ align:start position:0%
+the present value the second contract
+ 
+
+ align:start position:0%
+the present value the second contract
+someone tell me how I'd write that down
+
+ align:start position:0%
+someone tell me how I'd write that down
+ 
+
+ align:start position:0%
+someone tell me how I'd write that down
+I'd write down the present value the
+
+ align:start position:0%
+I'd write down the present value the
+ 
+
+ align:start position:0%
+I'd write down the present value the
+second contract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly what you want I'll st. straight
+
+ align:start position:0%
+exactly what you want I'll st. straight
+ 
+
+ align:start position:0%
+exactly what you want I'll st. straight
+to the 10th right because we're getting
+
+ align:start position:0%
+to the 10th right because we're getting
+ 
+
+ align:start position:0%
+to the 10th right because we're getting
+in 10 years okay
+
+ align:start position:0%
+in 10 years okay
+ 
+
+ align:start position:0%
+in 10 years okay
+so essentially um that means that
+
+ align:start position:0%
+so essentially um that means that
+ 
+
+ align:start position:0%
+so essentially um that means that
+whether it's a better deal or not
+
+ align:start position:0%
+whether it's a better deal or not
+ 
+
+ align:start position:0%
+whether it's a better deal or not
+depends on the interest rate indeed if
+
+ align:start position:0%
+depends on the interest rate indeed if
+ 
+
+ align:start position:0%
+depends on the interest rate indeed if
+the interest is 7% and this rate is 7%
+
+ align:start position:0%
+the interest is 7% and this rate is 7%
+ 
+
+ align:start position:0%
+the interest is 7% and this rate is 7%
+this has a present value of 1.3 million
+
+ align:start position:0%
+this has a present value of 1.3 million
+ 
+
+ align:start position:0%
+this has a present value of 1.3 million
+so it's a good deal if the interest rate
+
+ align:start position:0%
+so it's a good deal if the interest rate
+ 
+
+ align:start position:0%
+so it's a good deal if the interest rate
+was 14% then this deal would have a
+
+ align:start position:0%
+was 14% then this deal would have a
+ 
+
+ align:start position:0%
+was 14% then this deal would have a
+present value of 0.9 million so it's a
+
+ align:start position:0%
+present value of 0.9 million so it's a
+ 
+
+ align:start position:0%
+present value of 0.9 million so it's a
+worse deal so whether or not this a
+
+ align:start position:0%
+worse deal so whether or not this a
+ 
+
+ align:start position:0%
+worse deal so whether or not this a
+better or worse deal depends on the
+
+ align:start position:0%
+better or worse deal depends on the
+ 
+
+ align:start position:0%
+better or worse deal depends on the
+interest rate why is that
+
+ align:start position:0%
+interest rate why is that
+ 
+
+ align:start position:0%
+interest rate why is that
+why is this a worse deal the higher the
+
+ align:start position:0%
+why is this a worse deal the higher the
+ 
+
+ align:start position:0%
+why is this a worse deal the higher the
+interest rate yeah exactly
+
+ align:start position:0%
+interest rate yeah exactly
+ 
+
+ align:start position:0%
+interest rate yeah exactly
+you could have invested it earlier got
+
+ align:start position:0%
+you could have invested it earlier got
+ 
+
+ align:start position:0%
+you could have invested it earlier got
+in the compounding and had way more
+
+ align:start position:0%
+in the compounding and had way more
+ 
+
+ align:start position:0%
+in the compounding and had way more
+money in 10 years so the higher the
+
+ align:start position:0%
+money in 10 years so the higher the
+ 
+
+ align:start position:0%
+money in 10 years so the higher the
+interest rate the more you want to get
+
+ align:start position:0%
+interest rate the more you want to get
+ 
+
+ align:start position:0%
+interest rate the more you want to get
+your money upfront and save it the less
+
+ align:start position:0%
+your money upfront and save it the less
+ 
+
+ align:start position:0%
+your money upfront and save it the less
+valuable is money in the future okay now
+
+ align:start position:0%
+valuable is money in the future okay now
+ 
+
+ align:start position:0%
+valuable is money in the future okay now
+so essentially what this says you have
+
+ align:start position:0%
+so essentially what this says you have
+ 
+
+ align:start position:0%
+so essentially what this says you have
+to always use present value to bring
+
+ align:start position:0%
+to always use present value to bring
+ 
+
+ align:start position:0%
+to always use present value to bring
+things into current dollars now this is
+
+ align:start position:0%
+things into current dollars now this is
+ 
+
+ align:start position:0%
+things into current dollars now this is
+not an abstract concept
+
+ align:start position:0%
+not an abstract concept
+ 
+
+ align:start position:0%
+not an abstract concept
+let's take max scherzer who's a picture
+
+ align:start position:0%
+let's take max scherzer who's a picture
+ 
+
+ align:start position:0%
+let's take max scherzer who's a picture
+with the Washington Nationals max
+
+ align:start position:0%
+with the Washington Nationals max
+ 
+
+ align:start position:0%
+with the Washington Nationals max
+scherzer um a couple years ago signed a
+
+ align:start position:0%
+scherzer um a couple years ago signed a
+ 
+
+ align:start position:0%
+scherzer um a couple years ago signed a
+seven-year two hundred a seven-year two
+
+ align:start position:0%
+seven-year two hundred a seven-year two
+ 
+
+ align:start position:0%
+seven-year two hundred a seven-year two
+hundred and ten million dollar contract
+
+ align:start position:0%
+hundred and ten million dollar contract
+ 
+
+ align:start position:0%
+hundred and ten million dollar contract
+which he was able to brag was the
+
+ align:start position:0%
+which he was able to brag was the
+ 
+
+ align:start position:0%
+which he was able to brag was the
+second-highest ever signed by a pitcher
+
+ align:start position:0%
+second-highest ever signed by a pitcher
+ 
+
+ align:start position:0%
+second-highest ever signed by a pitcher
+and the tenth highest contract ever
+
+ align:start position:0%
+and the tenth highest contract ever
+ 
+
+ align:start position:0%
+and the tenth highest contract ever
+signed by any baseball player seven
+
+ align:start position:0%
+signed by any baseball player seven
+ 
+
+ align:start position:0%
+signed by any baseball player seven
+years to ten but in fact um that
+
+ align:start position:0%
+years to ten but in fact um that
+ 
+
+ align:start position:0%
+years to ten but in fact um that
+contract was not we're gonna pay you
+
+ align:start position:0%
+contract was not we're gonna pay you
+ 
+
+ align:start position:0%
+contract was not we're gonna pay you
+thirty million dollars a year for seven
+
+ align:start position:0%
+thirty million dollars a year for seven
+ 
+
+ align:start position:0%
+thirty million dollars a year for seven
+years it was we're gonna pay you 15
+
+ align:start position:0%
+years it was we're gonna pay you 15
+ 
+
+ align:start position:0%
+years it was we're gonna pay you 15
+million dollars a year for 14 years
+
+ align:start position:0%
+million dollars a year for 14 years
+ 
+
+ align:start position:0%
+million dollars a year for 14 years
+you're gonna play him for only seven
+
+ align:start position:0%
+you're gonna play him for only seven
+ 
+
+ align:start position:0%
+you're gonna play him for only seven
+we're gonna pay over fourteen years so
+
+ align:start position:0%
+we're gonna pay over fourteen years so
+ 
+
+ align:start position:0%
+we're gonna pay over fourteen years so
+in fact in present value terms it was
+
+ align:start position:0%
+in fact in present value terms it was
+ 
+
+ align:start position:0%
+in fact in present value terms it was
+worth somewhat less if you use the
+
+ align:start position:0%
+worth somewhat less if you use the
+ 
+
+ align:start position:0%
+worth somewhat less if you use the
+current interest rate when you signed it
+
+ align:start position:0%
+current interest rate when you signed it
+ 
+
+ align:start position:0%
+current interest rate when you signed it
+which is about four point seven percent
+
+ align:start position:0%
+which is about four point seven percent
+ 
+
+ align:start position:0%
+which is about four point seven percent
+it was only worth actually 166 million
+
+ align:start position:0%
+it was only worth actually 166 million
+ 
+
+ align:start position:0%
+it was only worth actually 166 million
+not too shabby
+
+ align:start position:0%
+not too shabby
+ 
+
+ align:start position:0%
+not too shabby
+but suddenly drops the 20th most
+
+ align:start position:0%
+but suddenly drops the 20th most
+ 
+
+ align:start position:0%
+but suddenly drops the 20th most
+valuable baseball contracting about
+
+ align:start position:0%
+valuable baseball contracting about
+ 
+
+ align:start position:0%
+valuable baseball contracting about
+fourth among pitchers so Max Scherzer
+
+ align:start position:0%
+fourth among pitchers so Max Scherzer
+ 
+
+ align:start position:0%
+fourth among pitchers so Max Scherzer
+was able to feel better about himself
+
+ align:start position:0%
+was able to feel better about himself
+ 
+
+ align:start position:0%
+was able to feel better about himself
+that he signed to it you know this
+
+ align:start position:0%
+that he signed to it you know this
+ 
+
+ align:start position:0%
+that he signed to it you know this
+valuable contract but in fact it was
+
+ align:start position:0%
+valuable contract but in fact it was
+ 
+
+ align:start position:0%
+valuable contract but in fact it was
+worth less than he thought me shed no
+
+ align:start position:0%
+worth less than he thought me shed no
+ 
+
+ align:start position:0%
+worth less than he thought me shed no
+tears from Max Scherzer he's doing fine
+
+ align:start position:0%
+tears from Max Scherzer he's doing fine
+ 
+
+ align:start position:0%
+tears from Max Scherzer he's doing fine
+but it was worth less than he thought
+
+ align:start position:0%
+but it was worth less than he thought
+ 
+
+ align:start position:0%
+but it was worth less than he thought
+or maybe one example it's more in our
+
+ align:start position:0%
+or maybe one example it's more in our
+ 
+
+ align:start position:0%
+or maybe one example it's more in our
+mind with the Mega Millions think about
+
+ align:start position:0%
+mind with the Mega Millions think about
+ 
+
+ align:start position:0%
+mind with the Mega Millions think about
+a lottery winner so if a Mega Millions
+
+ align:start position:0%
+a lottery winner so if a Mega Millions
+ 
+
+ align:start position:0%
+a lottery winner so if a Mega Millions
+winner gets two hundred ninety million
+
+ align:start position:0%
+winner gets two hundred ninety million
+ 
+
+ align:start position:0%
+winner gets two hundred ninety million
+dollars hey which sounds like a great
+
+ align:start position:0%
+dollars hey which sounds like a great
+ 
+
+ align:start position:0%
+dollars hey which sounds like a great
+deal that's paid out over 20 years so
+
+ align:start position:0%
+deal that's paid out over 20 years so
+ 
+
+ align:start position:0%
+deal that's paid out over 20 years so
+it's not two hundred ninety million
+
+ align:start position:0%
+it's not two hundred ninety million
+ 
+
+ align:start position:0%
+it's not two hundred ninety million
+dollars it's fourteen and a half million
+
+ align:start position:0%
+dollars it's fourteen and a half million
+ 
+
+ align:start position:0%
+dollars it's fourteen and a half million
+for each of 20 years so in present value
+
+ align:start position:0%
+for each of 20 years so in present value
+ 
+
+ align:start position:0%
+for each of 20 years so in present value
+terms if we think about a 7% interest
+
+ align:start position:0%
+terms if we think about a 7% interest
+ 
+
+ align:start position:0%
+terms if we think about a 7% interest
+rate then that's not 290 million 164
+
+ align:start position:0%
+rate then that's not 290 million 164
+ 
+
+ align:start position:0%
+rate then that's not 290 million 164
+million once again not too shabby okay
+
+ align:start position:0%
+million once again not too shabby okay
+ 
+
+ align:start position:0%
+million once again not too shabby okay
+but a lot less than the advertised
+
+ align:start position:0%
+but a lot less than the advertised
+ 
+
+ align:start position:0%
+but a lot less than the advertised
+amount so we have to take these dollars
+
+ align:start position:0%
+amount so we have to take these dollars
+ 
+
+ align:start position:0%
+amount so we have to take these dollars
+and put them in present value okay so
+
+ align:start position:0%
+and put them in present value okay so
+ 
+
+ align:start position:0%
+and put them in present value okay so
+now now here's an interesting question
+
+ align:start position:0%
+now now here's an interesting question
+ 
+
+ align:start position:0%
+now now here's an interesting question
+for that if you look at the recent
+
+ align:start position:0%
+for that if you look at the recent
+ 
+
+ align:start position:0%
+for that if you look at the recent
+lottery okay you had a choice of the
+
+ align:start position:0%
+lottery okay you had a choice of the
+ 
+
+ align:start position:0%
+lottery okay you had a choice of the
+person one person one point six billion
+
+ align:start position:0%
+person one person one point six billion
+ 
+
+ align:start position:0%
+person one person one point six billion
+one person one down person in South
+
+ align:start position:0%
+one person one down person in South
+ 
+
+ align:start position:0%
+one person one down person in South
+Carolina on that and they were given a
+
+ align:start position:0%
+Carolina on that and they were given a
+ 
+
+ align:start position:0%
+Carolina on that and they were given a
+choice of the 1.6 billion which is paid
+
+ align:start position:0%
+choice of the 1.6 billion which is paid
+ 
+
+ align:start position:0%
+choice of the 1.6 billion which is paid
+actually over 30 years or a lump sum
+
+ align:start position:0%
+actually over 30 years or a lump sum
+ 
+
+ align:start position:0%
+actually over 30 years or a lump sum
+they can get right away how should they
+
+ align:start position:0%
+they can get right away how should they
+ 
+
+ align:start position:0%
+they can get right away how should they
+decide which of those options to take
+
+ align:start position:0%
+decide which of those options to take
+ 
+
+ align:start position:0%
+decide which of those options to take
+how should I say I wouldn't think the
+
+ align:start position:0%
+how should I say I wouldn't think the
+ 
+
+ align:start position:0%
+how should I say I wouldn't think the
+1.6 billion paid over 30 years so in
+
+ align:start position:0%
+1.6 billion paid over 30 years so in
+ 
+
+ align:start position:0%
+1.6 billion paid over 30 years so in
+physics over 30 paid in equal
+
+ align:start position:0%
+physics over 30 paid in equal
+ 
+
+ align:start position:0%
+physics over 30 paid in equal
+installments you know over time versus
+
+ align:start position:0%
+installments you know over time versus
+ 
+
+ align:start position:0%
+installments you know over time versus
+just getting a lump sum today not if one
+
+ align:start position:0%
+just getting a lump sum today not if one
+ 
+
+ align:start position:0%
+just getting a lump sum today not if one
+put six million but a less at lower
+
+ align:start position:0%
+put six million but a less at lower
+ 
+
+ align:start position:0%
+put six million but a less at lower
+amount how should they think about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first value they should say well what do
+
+ align:start position:0%
+first value they should say well what do
+ 
+
+ align:start position:0%
+first value they should say well what do
+I think Peter's rates gonna be by this
+
+ align:start position:0%
+I think Peter's rates gonna be by this
+ 
+
+ align:start position:0%
+I think Peter's rates gonna be by this
+could be really low let's say the
+
+ align:start position:0%
+could be really low let's say the
+ 
+
+ align:start position:0%
+could be really low let's say the
+gate-source rates going to be zero then
+
+ align:start position:0%
+gate-source rates going to be zero then
+ 
+
+ align:start position:0%
+gate-source rates going to be zero then
+which deal should I take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should spread it out over time because
+
+ align:start position:0%
+I should spread it out over time because
+ 
+
+ align:start position:0%
+I should spread it out over time because
+the money and the futures worth the same
+
+ align:start position:0%
+the money and the futures worth the same
+ 
+
+ align:start position:0%
+the money and the futures worth the same
+is today so miles take the 1.6 billion
+
+ align:start position:0%
+is today so miles take the 1.6 billion
+ 
+
+ align:start position:0%
+is today so miles take the 1.6 billion
+but if I think since rates couldn't be
+
+ align:start position:0%
+but if I think since rates couldn't be
+ 
+
+ align:start position:0%
+but if I think since rates couldn't be
+higher then I should take the money
+
+ align:start position:0%
+higher then I should take the money
+ 
+
+ align:start position:0%
+higher then I should take the money
+upfront and invest that money and earn
+
+ align:start position:0%
+upfront and invest that money and earn
+ 
+
+ align:start position:0%
+upfront and invest that money and earn
+my own interest
+
+ align:start position:0%
+my own interest
+ 
+
+ align:start position:0%
+my own interest
+so essentially becomes a debate of how
+
+ align:start position:0%
+so essentially becomes a debate of how
+ 
+
+ align:start position:0%
+so essentially becomes a debate of how
+what you think the straight is versus
+
+ align:start position:0%
+what you think the straight is versus
+ 
+
+ align:start position:0%
+what you think the straight is versus
+what the state thinks interest rate is
+
+ align:start position:0%
+what the state thinks interest rate is
+ 
+
+ align:start position:0%
+what the state thinks interest rate is
+they're setting those two to be equal
+
+ align:start position:0%
+they're setting those two to be equal
+ 
+
+ align:start position:0%
+they're setting those two to be equal
+under some they're some assumption of
+
+ align:start position:0%
+under some they're some assumption of
+ 
+
+ align:start position:0%
+under some they're some assumption of
+the interest rate I don't know what
+
+ align:start position:0%
+the interest rate I don't know what
+ 
+
+ align:start position:0%
+the interest rate I don't know what
+number they chose whatever number they
+
+ align:start position:0%
+number they chose whatever number they
+ 
+
+ align:start position:0%
+number they chose whatever number they
+chose it was some number they chose
+
+ align:start position:0%
+chose it was some number they chose
+ 
+
+ align:start position:0%
+chose it was some number they chose
+because this is our assumption interest
+
+ align:start position:0%
+because this is our assumption interest
+ 
+
+ align:start position:0%
+because this is our assumption interest
+rate you've gotta decide do you think
+
+ align:start position:0%
+rate you've gotta decide do you think
+ 
+
+ align:start position:0%
+rate you've gotta decide do you think
+it's rates gonna be higher or lower
+
+ align:start position:0%
+it's rates gonna be higher or lower
+ 
+
+ align:start position:0%
+it's rates gonna be higher or lower
+these could be higher than the state
+
+ align:start position:0%
+these could be higher than the state
+ 
+
+ align:start position:0%
+these could be higher than the state
+thinks it is then you want the money up
+
+ align:start position:0%
+thinks it is then you want the money up
+ 
+
+ align:start position:0%
+thinks it is then you want the money up
+front and you'll invest it if you need
+
+ align:start position:0%
+front and you'll invest it if you need
+ 
+
+ align:start position:0%
+front and you'll invest it if you need
+to be lower than you should take your
+
+ align:start position:0%
+to be lower than you should take your
+ 
+
+ align:start position:0%
+to be lower than you should take your
+money over time
+
+ align:start position:0%
+money over time
+ 
+
+ align:start position:0%
+money over time
+and because the states giving you
+
+ align:start position:0%
+and because the states giving you
+ 
+
+ align:start position:0%
+and because the states giving you
+basically a better deal okay people
+
+ align:start position:0%
+basically a better deal okay people
+ 
+
+ align:start position:0%
+basically a better deal okay people
+understand that okay so now armed with
+
+ align:start position:0%
+understand that okay so now armed with
+ 
+
+ align:start position:0%
+understand that okay so now armed with
+this let's go and think about how do
+
+ align:start position:0%
+this let's go and think about how do
+ 
+
+ align:start position:0%
+this let's go and think about how do
+firms make investment decisions how do
+
+ align:start position:0%
+firms make investment decisions how do
+ 
+
+ align:start position:0%
+firms make investment decisions how do
+firms make investment decisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember investment or investment is
+
+ align:start position:0%
+remember investment or investment is
+ 
+
+ align:start position:0%
+remember investment or investment is
+about the delay of future consumption of
+
+ align:start position:0%
+about the delay of future consumption of
+ 
+
+ align:start position:0%
+about the delay of future consumption of
+current consumption for future
+
+ align:start position:0%
+current consumption for future
+ 
+
+ align:start position:0%
+current consumption for future
+consumptions about putting some aside
+
+ align:start position:0%
+consumptions about putting some aside
+ 
+
+ align:start position:0%
+consumptions about putting some aside
+today by spending money on a machine
+
+ align:start position:0%
+today by spending money on a machine
+ 
+
+ align:start position:0%
+today by spending money on a machine
+which will deliver you benefits in the
+
+ align:start position:0%
+which will deliver you benefits in the
+ 
+
+ align:start position:0%
+which will deliver you benefits in the
+future now this adds one wrinkle to
+
+ align:start position:0%
+future now this adds one wrinkle to
+ 
+
+ align:start position:0%
+future now this adds one wrinkle to
+we've done so far which is that we've
+
+ align:start position:0%
+we've done so far which is that we've
+ 
+
+ align:start position:0%
+we've done so far which is that we've
+only talked about money that's always
+
+ align:start position:0%
+only talked about money that's always
+ 
+
+ align:start position:0%
+only talked about money that's always
+positive somehow you get in the future
+
+ align:start position:0%
+positive somehow you get in the future
+ 
+
+ align:start position:0%
+positive somehow you get in the future
+when you're making an investment
+
+ align:start position:0%
+when you're making an investment
+ 
+
+ align:start position:0%
+when you're making an investment
+decision it's a little bit more
+
+ align:start position:0%
+decision it's a little bit more
+ 
+
+ align:start position:0%
+decision it's a little bit more
+complicated because you're actually
+
+ align:start position:0%
+complicated because you're actually
+ 
+
+ align:start position:0%
+complicated because you're actually
+spending money today to make money
+
+ align:start position:0%
+spending money today to make money
+ 
+
+ align:start position:0%
+spending money today to make money
+tomorrow so in that case we talk about
+
+ align:start position:0%
+tomorrow so in that case we talk about
+ 
+
+ align:start position:0%
+tomorrow so in that case we talk about
+we call net present value which is the
+
+ align:start position:0%
+we call net present value which is the
+ 
+
+ align:start position:0%
+we call net present value which is the
+same thing it just allows for negative
+
+ align:start position:0%
+same thing it just allows for negative
+ 
+
+ align:start position:0%
+same thing it just allows for negative
+values net present value which is
+
+ align:start position:0%
+values net present value which is
+ 
+
+ align:start position:0%
+values net present value which is
+essentially saying in every period
+
+ align:start position:0%
+essentially saying in every period
+ 
+
+ align:start position:0%
+essentially saying in every period
+you want to count for the cost that
+
+ align:start position:0%
+you want to count for the cost that
+ 
+
+ align:start position:0%
+you want to count for the cost that
+period and the benefits that period and
+
+ align:start position:0%
+period and the benefits that period and
+ 
+
+ align:start position:0%
+period and the benefits that period and
+you want to invest only if the net
+
+ align:start position:0%
+you want to invest only if the net
+ 
+
+ align:start position:0%
+you want to invest only if the net
+present value is greater than zero so
+
+ align:start position:0%
+present value is greater than zero so
+ 
+
+ align:start position:0%
+present value is greater than zero so
+for example think about a project that
+
+ align:start position:0%
+for example think about a project that
+ 
+
+ align:start position:0%
+for example think about a project that
+has a stream of payments in every period
+
+ align:start position:0%
+has a stream of payments in every period
+ 
+
+ align:start position:0%
+has a stream of payments in every period
+of R sub I every period it's got stream
+
+ align:start position:0%
+of R sub I every period it's got stream
+ 
+
+ align:start position:0%
+of R sub I every period it's got stream
+of payments of R sub I and instead of
+
+ align:start position:0%
+of payments of R sub I and instead of
+ 
+
+ align:start position:0%
+of payments of R sub I and instead of
+costs of C sub I the costs are the
+
+ align:start position:0%
+costs of C sub I the costs are the
+ 
+
+ align:start position:0%
+costs of C sub I the costs are the
+upfront investment B the maintenance of
+
+ align:start position:0%
+upfront investment B the maintenance of
+ 
+
+ align:start position:0%
+upfront investment B the maintenance of
+the machine whatever it costs to run it
+
+ align:start position:0%
+the machine whatever it costs to run it
+ 
+
+ align:start position:0%
+the machine whatever it costs to run it
+okay then the net present value that
+
+ align:start position:0%
+okay then the net present value that
+ 
+
+ align:start position:0%
+okay then the net present value that
+investment
+
+ align:start position:0%
+investment
+ 
+
+ align:start position:0%
+investment
+is r0 minus C 0 comma r1 on a c1 over 1
+
+ align:start position:0%
+is r0 minus C 0 comma r1 on a c1 over 1
+ 
+
+ align:start position:0%
+is r0 minus C 0 comma r1 on a c1 over 1
+plus I I'm sorry
+
+ align:start position:0%
+plus I I'm sorry
+ 
+
+ align:start position:0%
+plus I I'm sorry
+plus over 1 plus I plus r2 minus C 2
+
+ align:start position:0%
+plus over 1 plus I plus r2 minus C 2
+ 
+
+ align:start position:0%
+plus over 1 plus I plus r2 minus C 2
+over 1 plus I squared plus 4 as many
+
+ align:start position:0%
+over 1 plus I squared plus 4 as many
+ 
+
+ align:start position:0%
+over 1 plus I squared plus 4 as many
+periods of the investment last okay
+
+ align:start position:0%
+periods of the investment last okay
+ 
+
+ align:start position:0%
+periods of the investment last okay
+that's the net present value of an
+
+ align:start position:0%
+that's the net present value of an
+ 
+
+ align:start position:0%
+that's the net present value of an
+investment so basically what you want to
+
+ align:start position:0%
+investment so basically what you want to
+ 
+
+ align:start position:0%
+investment so basically what you want to
+ask is take each parents costs and
+
+ align:start position:0%
+ask is take each parents costs and
+ 
+
+ align:start position:0%
+ask is take each parents costs and
+benefits into account on net is it
+
+ align:start position:0%
+benefits into account on net is it
+ 
+
+ align:start position:0%
+benefits into account on net is it
+greater than 0 okay so the key point is
+
+ align:start position:0%
+greater than 0 okay so the key point is
+ 
+
+ align:start position:0%
+greater than 0 okay so the key point is
+that basically sometimes investments
+
+ align:start position:0%
+that basically sometimes investments
+ 
+
+ align:start position:0%
+that basically sometimes investments
+which have upfront costs can be valuable
+
+ align:start position:0%
+which have upfront costs can be valuable
+ 
+
+ align:start position:0%
+which have upfront costs can be valuable
+as long as the long-run benefits are
+
+ align:start position:0%
+as long as the long-run benefits are
+ 
+
+ align:start position:0%
+as long as the long-run benefits are
+large enough so if you think about an
+
+ align:start position:0%
+large enough so if you think about an
+ 
+
+ align:start position:0%
+large enough so if you think about an
+investment that's got a hundred so so
+
+ align:start position:0%
+investment that's got a hundred so so
+ 
+
+ align:start position:0%
+investment that's got a hundred so so
+imagine think about a simple trivial
+
+ align:start position:0%
+imagine think about a simple trivial
+ 
+
+ align:start position:0%
+imagine think about a simple trivial
+example of the first period you buy a
+
+ align:start position:0%
+example of the first period you buy a
+ 
+
+ align:start position:0%
+example of the first period you buy a
+machine and it costs um and it cost $100
+
+ align:start position:0%
+machine and it costs um and it cost $100
+ 
+
+ align:start position:0%
+machine and it costs um and it cost $100
+so c0 is 100 and let's say for every
+
+ align:start position:0%
+so c0 is 100 and let's say for every
+ 
+
+ align:start position:0%
+so c0 is 100 and let's say for every
+period thereafter that machine will
+
+ align:start position:0%
+period thereafter that machine will
+ 
+
+ align:start position:0%
+period thereafter that machine will
+deliver your revenues revenue i revenues
+
+ align:start position:0%
+deliver your revenues revenue i revenues
+ 
+
+ align:start position:0%
+deliver your revenues revenue i revenues
+for i greater than 0 of 200 but it will
+
+ align:start position:0%
+for i greater than 0 of 200 but it will
+ 
+
+ align:start position:0%
+for i greater than 0 of 200 but it will
+have maintenance costs costs i greater
+
+ align:start position:0%
+have maintenance costs costs i greater
+ 
+
+ align:start position:0%
+have maintenance costs costs i greater
+than 0 of 50 so what's the net present
+
+ align:start position:0%
+than 0 of 50 so what's the net present
+ 
+
+ align:start position:0%
+than 0 of 50 so what's the net present
+value well the net present value is
+
+ align:start position:0%
+value well the net present value is
+ 
+
+ align:start position:0%
+value well the net present value is
+simply minus 100 and let's say machine's
+
+ align:start position:0%
+simply minus 100 and let's say machine's
+ 
+
+ align:start position:0%
+simply minus 100 and let's say machine's
+gonna last forever
+
+ align:start position:0%
+gonna last forever
+ 
+
+ align:start position:0%
+gonna last forever
+minus 100 plus 150 over I think about
+
+ align:start position:0%
+minus 100 plus 150 over I think about
+ 
+
+ align:start position:0%
+minus 100 plus 150 over I think about
+that for a second basically what we're
+
+ align:start position:0%
+that for a second basically what we're
+ 
+
+ align:start position:0%
+that for a second basically what we're
+saying is you're throwing 100 out of
+
+ align:start position:0%
+saying is you're throwing 100 out of
+ 
+
+ align:start position:0%
+saying is you're throwing 100 out of
+today that's negative but every period
+
+ align:start position:0%
+today that's negative but every period
+ 
+
+ align:start position:0%
+today that's negative but every period
+your future going to net $150 because
+
+ align:start position:0%
+your future going to net $150 because
+ 
+
+ align:start position:0%
+your future going to net $150 because
+you're gonna make $250 maintenance cost
+
+ align:start position:0%
+you're gonna make $250 maintenance cost
+ 
+
+ align:start position:0%
+you're gonna make $250 maintenance cost
+and we have per formula so we just apply
+
+ align:start position:0%
+and we have per formula so we just apply
+ 
+
+ align:start position:0%
+and we have per formula so we just apply
+the formula for perpetuity we have a set
+
+ align:start position:0%
+the formula for perpetuity we have a set
+ 
+
+ align:start position:0%
+the formula for perpetuity we have a set
+of future payments of $150 so your net
+
+ align:start position:0%
+of future payments of $150 so your net
+ 
+
+ align:start position:0%
+of future payments of $150 so your net
+net present value is minus 100 plus 150
+
+ align:start position:0%
+net present value is minus 100 plus 150
+ 
+
+ align:start position:0%
+net present value is minus 100 plus 150
+over I so let's think about
+
+ align:start position:0%
+over I so let's think about
+ 
+
+ align:start position:0%
+over I so let's think about
+look at this formula for a second what
+
+ align:start position:0%
+look at this formula for a second what
+ 
+
+ align:start position:0%
+look at this formula for a second what
+does that say what is the relationship
+
+ align:start position:0%
+does that say what is the relationship
+ 
+
+ align:start position:0%
+does that say what is the relationship
+between whether the firm's gonna want to
+
+ align:start position:0%
+between whether the firm's gonna want to
+ 
+
+ align:start position:0%
+between whether the firm's gonna want to
+invest and the interest rate what does
+
+ align:start position:0%
+invest and the interest rate what does
+ 
+
+ align:start position:0%
+invest and the interest rate what does
+this imply the relationship between
+
+ align:start position:0%
+this imply the relationship between
+ 
+
+ align:start position:0%
+this imply the relationship between
+firms desire for investment and the
+
+ align:start position:0%
+firms desire for investment and the
+ 
+
+ align:start position:0%
+firms desire for investment and the
+interest rate as the interest rate goes
+
+ align:start position:0%
+interest rate as the interest rate goes
+ 
+
+ align:start position:0%
+interest rate as the interest rate goes
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+well firms want to do more investment or
+
+ align:start position:0%
+well firms want to do more investment or
+ 
+
+ align:start position:0%
+well firms want to do more investment or
+less investment in Y well firms want to
+
+ align:start position:0%
+less investment in Y well firms want to
+ 
+
+ align:start position:0%
+less investment in Y well firms want to
+be more eager to buy machines or
+
+ align:start position:0%
+be more eager to buy machines or
+ 
+
+ align:start position:0%
+be more eager to buy machines or
+lessening to buy machines and why and
+
+ align:start position:0%
+lessening to buy machines and why and
+ 
+
+ align:start position:0%
+lessening to buy machines and why and
+straight goes up yeah let's see here
+
+ align:start position:0%
+straight goes up yeah let's see here
+ 
+
+ align:start position:0%
+straight goes up yeah let's see here
+less eager State again because why I
+
+ align:start position:0%
+less eager State again because why I
+ 
+
+ align:start position:0%
+less eager State again because why I
+think it easier thing is borrowing just
+
+ align:start position:0%
+think it easier thing is borrowing just
+ 
+
+ align:start position:0%
+think it easier thing is borrowing just
+think about they got a bunch of money
+
+ align:start position:0%
+think about they got a bunch of money
+ 
+
+ align:start position:0%
+think about they got a bunch of money
+Apple's got a bunch of money today
+
+ align:start position:0%
+Apple's got a bunch of money today
+ 
+
+ align:start position:0%
+Apple's got a bunch of money today
+they're sitting on if they buy the
+
+ align:start position:0%
+they're sitting on if they buy the
+ 
+
+ align:start position:0%
+they're sitting on if they buy the
+Machine they're going to get this return
+
+ align:start position:0%
+Machine they're going to get this return
+ 
+
+ align:start position:0%
+Machine they're going to get this return
+if they don't buy the Machine they can
+
+ align:start position:0%
+if they don't buy the Machine they can
+ 
+
+ align:start position:0%
+if they don't buy the Machine they can
+put it in the bank or invest in Apple
+
+ align:start position:0%
+put it in the bank or invest in Apple
+ 
+
+ align:start position:0%
+put it in the bank or invest in Apple
+stock and get some interest rate I the
+
+ align:start position:0%
+stock and get some interest rate I the
+ 
+
+ align:start position:0%
+stock and get some interest rate I the
+higher the alternative the higher the
+
+ align:start position:0%
+higher the alternative the higher the
+ 
+
+ align:start position:0%
+higher the alternative the higher the
+interest rate the less they want invest
+
+ align:start position:0%
+interest rate the less they want invest
+ 
+
+ align:start position:0%
+interest rate the less they want invest
+or think of it this way the interest
+
+ align:start position:0%
+or think of it this way the interest
+ 
+
+ align:start position:0%
+or think of it this way the interest
+rate is the opportunity cost of
+
+ align:start position:0%
+rate is the opportunity cost of
+ 
+
+ align:start position:0%
+rate is the opportunity cost of
+investment okay the more the firm
+
+ align:start position:0%
+investment okay the more the firm
+ 
+
+ align:start position:0%
+investment okay the more the firm
+invests in their machines the less they
+
+ align:start position:0%
+invests in their machines the less they
+ 
+
+ align:start position:0%
+invests in their machines the less they
+can earn saving through some other
+
+ align:start position:0%
+can earn saving through some other
+ 
+
+ align:start position:0%
+can earn saving through some other
+mechanism and the price that they pay by
+
+ align:start position:0%
+mechanism and the price that they pay by
+ 
+
+ align:start position:0%
+mechanism and the price that they pay by
+forgoing that other savings is I okay
+
+ align:start position:0%
+forgoing that other savings is I okay
+ 
+
+ align:start position:0%
+forgoing that other savings is I okay
+yeah basically you always want to try to
+
+ align:start position:0%
+yeah basically you always want to try to
+ 
+
+ align:start position:0%
+yeah basically you always want to try to
+make as much money as you can and make
+
+ align:start position:0%
+make as much money as you can and make
+ 
+
+ align:start position:0%
+make as much money as you can and make
+the cost as late as you can for any
+
+ align:start position:0%
+the cost as late as you can for any
+ 
+
+ align:start position:0%
+the cost as late as you can for any
+given amount you'd absolutely like to
+
+ align:start position:0%
+given amount you'd absolutely like to
+ 
+
+ align:start position:0%
+given amount you'd absolutely like to
+shift your you'd actually like
+
+ align:start position:0%
+shift your you'd actually like
+ 
+
+ align:start position:0%
+shift your you'd actually like
+absolutely like to do that
+
+ align:start position:0%
+absolutely like to do that
+ 
+
+ align:start position:0%
+absolutely like to do that
+that's why we'll talk about this in my
+
+ align:start position:0%
+that's why we'll talk about this in my
+ 
+
+ align:start position:0%
+that's why we'll talk about this in my
+in my public finance class we talked
+
+ align:start position:0%
+in my public finance class we talked
+ 
+
+ align:start position:0%
+in my public finance class we talked
+about why when you're paying taxes you
+
+ align:start position:0%
+about why when you're paying taxes you
+ 
+
+ align:start position:0%
+about why when you're paying taxes you
+always want to try to find shenanigans
+
+ align:start position:0%
+always want to try to find shenanigans
+ 
+
+ align:start position:0%
+always want to try to find shenanigans
+allow you to pay your taxes later so for
+
+ align:start position:0%
+allow you to pay your taxes later so for
+ 
+
+ align:start position:0%
+allow you to pay your taxes later so for
+any given tax until later you pay it the
+
+ align:start position:0%
+any given tax until later you pay it the
+ 
+
+ align:start position:0%
+any given tax until later you pay it the
+more cost the less it cost you because
+
+ align:start position:0%
+more cost the less it cost you because
+ 
+
+ align:start position:0%
+more cost the less it cost you because
+you get to earn the interest along the
+
+ align:start position:0%
+you get to earn the interest along the
+ 
+
+ align:start position:0%
+you get to earn the interest along the
+way and then pay it with after it and
+
+ align:start position:0%
+way and then pay it with after it and
+ 
+
+ align:start position:0%
+way and then pay it with after it and
+pay it later on this is a key
+
+ align:start position:0%
+pay it later on this is a key
+ 
+
+ align:start position:0%
+pay it later on this is a key
+macroeconomic concept you'll often hear
+
+ align:start position:0%
+macroeconomic concept you'll often hear
+ 
+
+ align:start position:0%
+macroeconomic concept you'll often hear
+in the news high interest rates are bad
+
+ align:start position:0%
+in the news high interest rates are bad
+ 
+
+ align:start position:0%
+in the news high interest rates are bad
+for business and you might have thought
+
+ align:start position:0%
+for business and you might have thought
+ 
+
+ align:start position:0%
+for business and you might have thought
+why is that this is why hunt rates are
+
+ align:start position:0%
+why is that this is why hunt rates are
+ 
+
+ align:start position:0%
+why is that this is why hunt rates are
+bad for the economy you'll hear why are
+
+ align:start position:0%
+bad for the economy you'll hear why are
+ 
+
+ align:start position:0%
+bad for the economy you'll hear why are
+high streets bad for the economy you
+
+ align:start position:0%
+high streets bad for the economy you
+ 
+
+ align:start position:0%
+high streets bad for the economy you
+might say wasted that makes no sense my
+
+ align:start position:0%
+might say wasted that makes no sense my
+ 
+
+ align:start position:0%
+might say wasted that makes no sense my
+interest rate means I earn more on my
+
+ align:start position:0%
+interest rate means I earn more on my
+ 
+
+ align:start position:0%
+interest rate means I earn more on my
+savings why is that bad for the economy
+
+ align:start position:0%
+savings why is that bad for the economy
+ 
+
+ align:start position:0%
+savings why is that bad for the economy
+it's bad for the economy because it
+
+ align:start position:0%
+it's bad for the economy because it
+ 
+
+ align:start position:0%
+it's bad for the economy because it
+lowers the demand for capital because
+
+ align:start position:0%
+lowers the demand for capital because
+ 
+
+ align:start position:0%
+lowers the demand for capital because
+the higher
+
+ align:start position:0%
+the higher
+ 
+
+ align:start position:0%
+the higher
+the interest rate the less firms
+
+ align:start position:0%
+the interest rate the less firms
+ 
+
+ align:start position:0%
+the interest rate the less firms
+actually want to invest the more they
+
+ align:start position:0%
+actually want to invest the more they
+ 
+
+ align:start position:0%
+actually want to invest the more they
+just want to stock their money away in
+
+ align:start position:0%
+just want to stock their money away in
+ 
+
+ align:start position:0%
+just want to stock their money away in
+the bank okay so that is kind of um
+
+ align:start position:0%
+the bank okay so that is kind of um
+ 
+
+ align:start position:0%
+the bank okay so that is kind of um
+that's the key that's the key question
+
+ align:start position:0%
+that's the key that's the key question
+ 
+
+ align:start position:0%
+that's the key that's the key question
+now then let me ask another question if
+
+ align:start position:0%
+now then let me ask another question if
+ 
+
+ align:start position:0%
+now then let me ask another question if
+you're a firm what's the right eye to
+
+ align:start position:0%
+you're a firm what's the right eye to
+ 
+
+ align:start position:0%
+you're a firm what's the right eye to
+use if you're a firm think about this
+
+ align:start position:0%
+use if you're a firm think about this
+ 
+
+ align:start position:0%
+use if you're a firm think about this
+investment we know the higher I is the
+
+ align:start position:0%
+investment we know the higher I is the
+ 
+
+ align:start position:0%
+investment we know the higher I is the
+less you want to invest but what is I
+
+ align:start position:0%
+less you want to invest but what is I
+ 
+
+ align:start position:0%
+less you want to invest but what is I
+once again forget inflation inflation
+
+ align:start position:0%
+once again forget inflation inflation
+ 
+
+ align:start position:0%
+once again forget inflation inflation
+zero what's the right what we call firm
+
+ align:start position:0%
+zero what's the right what we call firm
+ 
+
+ align:start position:0%
+zero what's the right what we call firm
+discount rate the discount rate is the
+
+ align:start position:0%
+discount rate the discount rate is the
+ 
+
+ align:start position:0%
+discount rate the discount rate is the
+amount by which firms are going to
+
+ align:start position:0%
+amount by which firms are going to
+ 
+
+ align:start position:0%
+amount by which firms are going to
+discount future dollars to bring them
+
+ align:start position:0%
+discount future dollars to bring them
+ 
+
+ align:start position:0%
+discount future dollars to bring them
+back today how does the firm think about
+
+ align:start position:0%
+back today how does the firm think about
+ 
+
+ align:start position:0%
+back today how does the firm think about
+what I to use what I should the firm use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your Apple yeah they don't want invest
+
+ align:start position:0%
+your Apple yeah they don't want invest
+ 
+
+ align:start position:0%
+your Apple yeah they don't want invest
+unless it's positive that's a good point
+
+ align:start position:0%
+unless it's positive that's a good point
+ 
+
+ align:start position:0%
+unless it's positive that's a good point
+but but but but the way they do is they
+
+ align:start position:0%
+but but but but the way they do is they
+ 
+
+ align:start position:0%
+but but but but the way they do is they
+write down the method may plug in and I
+
+ align:start position:0%
+write down the method may plug in and I
+ 
+
+ align:start position:0%
+write down the method may plug in and I
+what I do they plug in yeah well I might
+
+ align:start position:0%
+what I do they plug in yeah well I might
+ 
+
+ align:start position:0%
+what I do they plug in yeah well I might
+be but it's not there's not one answer
+
+ align:start position:0%
+be but it's not there's not one answer
+ 
+
+ align:start position:0%
+be but it's not there's not one answer
+what's the general answer the firm wants
+
+ align:start position:0%
+what's the general answer the firm wants
+ 
+
+ align:start position:0%
+what's the general answer the firm wants
+to use what's the general answer that
+
+ align:start position:0%
+to use what's the general answer that
+ 
+
+ align:start position:0%
+to use what's the general answer that
+the firm if you're a firm thinking about
+
+ align:start position:0%
+the firm if you're a firm thinking about
+ 
+
+ align:start position:0%
+the firm if you're a firm thinking about
+in vacant investment you want to
+
+ align:start position:0%
+in vacant investment you want to
+ 
+
+ align:start position:0%
+in vacant investment you want to
+discount that investment what do you
+
+ align:start position:0%
+discount that investment what do you
+ 
+
+ align:start position:0%
+discount that investment what do you
+want to discount it by yeah the next
+
+ align:start position:0%
+want to discount it by yeah the next
+ 
+
+ align:start position:0%
+want to discount it by yeah the next
+best thing you could do so if I'm
+
+ align:start position:0%
+best thing you could do so if I'm
+ 
+
+ align:start position:0%
+best thing you could do so if I'm
+thinking about building this machine
+
+ align:start position:0%
+thinking about building this machine
+ 
+
+ align:start position:0%
+thinking about building this machine
+when I discount I wanna think about
+
+ align:start position:0%
+when I discount I wanna think about
+ 
+
+ align:start position:0%
+when I discount I wanna think about
+what's the next best thing I could do
+
+ align:start position:0%
+what's the next best thing I could do
+ 
+
+ align:start position:0%
+what's the next best thing I could do
+with that money
+
+ align:start position:0%
+with that money
+ 
+
+ align:start position:0%
+with that money
+that's the discount rate I want to use
+
+ align:start position:0%
+that's the discount rate I want to use
+ 
+
+ align:start position:0%
+that's the discount rate I want to use
+so in a world where firms either
+
+ align:start position:0%
+so in a world where firms either
+ 
+
+ align:start position:0%
+so in a world where firms either
+couldn't buy a machine or put it in the
+
+ align:start position:0%
+couldn't buy a machine or put it in the
+ 
+
+ align:start position:0%
+couldn't buy a machine or put it in the
+bank it's easy it's the bank interest
+
+ align:start position:0%
+bank it's easy it's the bank interest
+ 
+
+ align:start position:0%
+bank it's easy it's the bank interest
+rate but life's not that easy firms have
+
+ align:start position:0%
+rate but life's not that easy firms have
+ 
+
+ align:start position:0%
+rate but life's not that easy firms have
+dozens of investments so where every
+
+ align:start position:0%
+dozens of investments so where every
+ 
+
+ align:start position:0%
+dozens of investments so where every
+investment you want to discount it by
+
+ align:start position:0%
+investment you want to discount it by
+ 
+
+ align:start position:0%
+investment you want to discount it by
+the next best thing you can do with the
+
+ align:start position:0%
+the next best thing you can do with the
+ 
+
+ align:start position:0%
+the next best thing you can do with the
+money concept of opportunity cost that's
+
+ align:start position:0%
+money concept of opportunity cost that's
+ 
+
+ align:start position:0%
+money concept of opportunity cost that's
+why it's a very first thing we taught in
+
+ align:start position:0%
+why it's a very first thing we taught in
+ 
+
+ align:start position:0%
+why it's a very first thing we taught in
+this class opportunity cost is always
+
+ align:start position:0%
+this class opportunity cost is always
+ 
+
+ align:start position:0%
+this class opportunity cost is always
+what drives things okay questions about
+
+ align:start position:0%
+what drives things okay questions about
+ 
+
+ align:start position:0%
+what drives things okay questions about
+that now this isn't just for firms this
+
+ align:start position:0%
+that now this isn't just for firms this
+ 
+
+ align:start position:0%
+that now this isn't just for firms this
+same math applies to consumers as well
+
+ align:start position:0%
+same math applies to consumers as well
+ 
+
+ align:start position:0%
+same math applies to consumers as well
+let's think about me a number of years
+
+ align:start position:0%
+let's think about me a number of years
+ 
+
+ align:start position:0%
+let's think about me a number of years
+ago I had to decide whether to insulate
+
+ align:start position:0%
+ago I had to decide whether to insulate
+ 
+
+ align:start position:0%
+ago I had to decide whether to insulate
+my ancient house
+
+ align:start position:0%
+my ancient house
+ 
+
+ align:start position:0%
+my ancient house
+okay let's write down the numbers to
+
+ align:start position:0%
+okay let's write down the numbers to
+ 
+
+ align:start position:0%
+okay let's write down the numbers to
+sort of think how this worked
+
+ align:start position:0%
+sort of think how this worked
+ 
+
+ align:start position:0%
+sort of think how this worked
+I had heating bills at that time back
+
+ align:start position:0%
+I had heating bills at that time back
+ 
+
+ align:start position:0%
+I had heating bills at that time back
+when gas was cheaper of about two
+
+ align:start position:0%
+when gas was cheaper of about two
+ 
+
+ align:start position:0%
+when gas was cheaper of about two
+thousand dollars a year
+
+ align:start position:0%
+thousand dollars a year
+ 
+
+ align:start position:0%
+thousand dollars a year
+where's my heating bills for the house
+
+ align:start position:0%
+where's my heating bills for the house
+ 
+
+ align:start position:0%
+where's my heating bills for the house
+okay the best estimate I could get was
+
+ align:start position:0%
+okay the best estimate I could get was
+ 
+
+ align:start position:0%
+okay the best estimate I could get was
+it if I insulated my house I would lower
+
+ align:start position:0%
+it if I insulated my house I would lower
+ 
+
+ align:start position:0%
+it if I insulated my house I would lower
+my heating costs by 25%
+
+ align:start position:0%
+my heating costs by 25%
+ 
+
+ align:start position:0%
+my heating costs by 25%
+so my heating costs would fall by $500
+
+ align:start position:0%
+so my heating costs would fall by $500
+ 
+
+ align:start position:0%
+so my heating costs would fall by $500
+per year if isolated my cost if isolated
+
+ align:start position:0%
+per year if isolated my cost if isolated
+ 
+
+ align:start position:0%
+per year if isolated my cost if isolated
+my house and the insulation but to
+
+ align:start position:0%
+my house and the insulation but to
+ 
+
+ align:start position:0%
+my house and the insulation but to
+inflate my house I had to pay the guy to
+
+ align:start position:0%
+inflate my house I had to pay the guy to
+ 
+
+ align:start position:0%
+inflate my house I had to pay the guy to
+insulate it and that cost the insulation
+
+ align:start position:0%
+insulate it and that cost the insulation
+ 
+
+ align:start position:0%
+insulate it and that cost the insulation
+cost $4,000 how do I think about whether
+
+ align:start position:0%
+cost $4,000 how do I think about whether
+ 
+
+ align:start position:0%
+cost $4,000 how do I think about whether
+they should insulate or not how do I
+
+ align:start position:0%
+they should insulate or not how do I
+ 
+
+ align:start position:0%
+they should insulate or not how do I
+think about that decision what equation
+
+ align:start position:0%
+think about that decision what equation
+ 
+
+ align:start position:0%
+think about that decision what equation
+should I write down yeah I should say
+
+ align:start position:0%
+should I write down yeah I should say
+ 
+
+ align:start position:0%
+should I write down yeah I should say
+I'll assume I'm gonna own the house
+
+ align:start position:0%
+I'll assume I'm gonna own the house
+ 
+
+ align:start position:0%
+I'll assume I'm gonna own the house
+forever or at least long enough that I
+
+ align:start position:0%
+forever or at least long enough that I
+ 
+
+ align:start position:0%
+forever or at least long enough that I
+can treat it as forever
+
+ align:start position:0%
+can treat it as forever
+ 
+
+ align:start position:0%
+can treat it as forever
+and I write down that formula and what
+
+ align:start position:0%
+and I write down that formula and what
+ 
+
+ align:start position:0%
+and I write down that formula and what
+that formula says is that if I think in
+
+ align:start position:0%
+that formula says is that if I think in
+ 
+
+ align:start position:0%
+that formula says is that if I think in
+shrinks less than 12.5% I should
+
+ align:start position:0%
+shrinks less than 12.5% I should
+ 
+
+ align:start position:0%
+shrinks less than 12.5% I should
+insulate if I think pH rate is more than
+
+ align:start position:0%
+insulate if I think pH rate is more than
+ 
+
+ align:start position:0%
+insulate if I think pH rate is more than
+12.5% I should just invest the money and
+
+ align:start position:0%
+12.5% I should just invest the money and
+ 
+
+ align:start position:0%
+12.5% I should just invest the money and
+use the use of returns that investment
+
+ align:start position:0%
+use the use of returns that investment
+ 
+
+ align:start position:0%
+use the use of returns that investment
+to pay my higher heating bills so it all
+
+ align:start position:0%
+to pay my higher heating bills so it all
+ 
+
+ align:start position:0%
+to pay my higher heating bills so it all
+depends on what the interest rate is
+
+ align:start position:0%
+depends on what the interest rate is
+ 
+
+ align:start position:0%
+depends on what the interest rate is
+okay now so that's why and I did it I
+
+ align:start position:0%
+okay now so that's why and I did it I
+ 
+
+ align:start position:0%
+okay now so that's why and I did it I
+insulated but that's exactly so the same
+
+ align:start position:0%
+insulated but that's exactly so the same
+ 
+
+ align:start position:0%
+insulated but that's exactly so the same
+logic we could think of is is basically
+
+ align:start position:0%
+logic we could think of is is basically
+ 
+
+ align:start position:0%
+logic we could think of is is basically
+essentially the same ideas firms you
+
+ align:start position:0%
+essentially the same ideas firms you
+ 
+
+ align:start position:0%
+essentially the same ideas firms you
+want think about the upfront costs and
+
+ align:start position:0%
+want think about the upfront costs and
+ 
+
+ align:start position:0%
+want think about the upfront costs and
+the long-run returns okay
+
+ align:start position:0%
+the long-run returns okay
+ 
+
+ align:start position:0%
+the long-run returns okay
+here's a funny economics question what
+
+ align:start position:0%
+here's a funny economics question what
+ 
+
+ align:start position:0%
+here's a funny economics question what
+if I don't intend to hold the house
+
+ align:start position:0%
+if I don't intend to hold the house
+ 
+
+ align:start position:0%
+if I don't intend to hold the house
+forever I would argue I should still use
+
+ align:start position:0%
+forever I would argue I should still use
+ 
+
+ align:start position:0%
+forever I would argue I should still use
+this formula why yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly because I'm increasing the value
+
+ align:start position:0%
+exactly because I'm increasing the value
+ 
+
+ align:start position:0%
+exactly because I'm increasing the value
+of an asset that I'll then sell so
+
+ align:start position:0%
+of an asset that I'll then sell so
+ 
+
+ align:start position:0%
+of an asset that I'll then sell so
+presume by insulating I've raised the
+
+ align:start position:0%
+presume by insulating I've raised the
+ 
+
+ align:start position:0%
+presume by insulating I've raised the
+price of my house how much I raised it
+
+ align:start position:0%
+price of my house how much I raised it
+ 
+
+ align:start position:0%
+price of my house how much I raised it
+by exactly five hundred of her eyes so
+
+ align:start position:0%
+by exactly five hundred of her eyes so
+ 
+
+ align:start position:0%
+by exactly five hundred of her eyes so
+I'm gonna insulate and sell next year I
+
+ align:start position:0%
+I'm gonna insulate and sell next year I
+ 
+
+ align:start position:0%
+I'm gonna insulate and sell next year I
+should still insulate because I should
+
+ align:start position:0%
+should still insulate because I should
+ 
+
+ align:start position:0%
+should still insulate because I should
+get five hundred of RI more dollars for
+
+ align:start position:0%
+get five hundred of RI more dollars for
+ 
+
+ align:start position:0%
+get five hundred of RI more dollars for
+my house so in fact it doesn't matter if
+
+ align:start position:0%
+my house so in fact it doesn't matter if
+ 
+
+ align:start position:0%
+my house so in fact it doesn't matter if
+you can sell an asset then actually your
+
+ align:start position:0%
+you can sell an asset then actually your
+ 
+
+ align:start position:0%
+you can sell an asset then actually your
+pur isin is always infinite it's not
+
+ align:start position:0%
+pur isin is always infinite it's not
+ 
+
+ align:start position:0%
+pur isin is always infinite it's not
+just the short horizon which is kind of
+
+ align:start position:0%
+just the short horizon which is kind of
+ 
+
+ align:start position:0%
+just the short horizon which is kind of
+interesting insight okay so the last
+
+ align:start position:0%
+interesting insight okay so the last
+ 
+
+ align:start position:0%
+interesting insight okay so the last
+thing I want to talk about is the fact
+
+ align:start position:0%
+thing I want to talk about is the fact
+ 
+
+ align:start position:0%
+thing I want to talk about is the fact
+that these decisions are not just
+
+ align:start position:0%
+that these decisions are not just
+ 
+
+ align:start position:0%
+that these decisions are not just
+relevant you guys are like retirement
+
+ align:start position:0%
+relevant you guys are like retirement
+ 
+
+ align:start position:0%
+relevant you guys are like retirement
+business machines insulation guide your
+
+ align:start position:0%
+business machines insulation guide your
+ 
+
+ align:start position:0%
+business machines insulation guide your
+old John I don't care about any of this
+
+ align:start position:0%
+old John I don't care about any of this
+ 
+
+ align:start position:0%
+old John I don't care about any of this
+stuff well let's hear what something you
+
+ align:start position:0%
+stuff well let's hear what something you
+ 
+
+ align:start position:0%
+stuff well let's hear what something you
+care about which is going to college
+
+ align:start position:0%
+care about which is going to college
+ 
+
+ align:start position:0%
+care about which is going to college
+let's talk about your decision you've
+
+ align:start position:0%
+let's talk about your decision you've
+ 
+
+ align:start position:0%
+let's talk about your decision you've
+already made it but you've got a little
+
+ align:start position:0%
+already made it but you've got a little
+ 
+
+ align:start position:0%
+already made it but you've got a little
+sibling and they're deciding whether to
+
+ align:start position:0%
+sibling and they're deciding whether to
+ 
+
+ align:start position:0%
+sibling and they're deciding whether to
+go to college
+
+ align:start position:0%
+go to college
+ 
+
+ align:start position:0%
+go to college
+okay well let's and and and they're not
+
+ align:start position:0%
+okay well let's and and and they're not
+ 
+
+ align:start position:0%
+okay well let's and and and they're not
+going to go to MIT they're gonna go to a
+
+ align:start position:0%
+going to go to MIT they're gonna go to a
+ 
+
+ align:start position:0%
+going to go to MIT they're gonna go to a
+more typical school and they've got to
+
+ align:start position:0%
+more typical school and they've got to
+ 
+
+ align:start position:0%
+more typical school and they've got to
+decide whether go to college well in
+
+ align:start position:0%
+decide whether go to college well in
+ 
+
+ align:start position:0%
+decide whether go to college well in
+fact their decision is an investment
+
+ align:start position:0%
+fact their decision is an investment
+ 
+
+ align:start position:0%
+fact their decision is an investment
+decision just like any other investment
+
+ align:start position:0%
+decision just like any other investment
+ 
+
+ align:start position:0%
+decision just like any other investment
+decision what they're investing in is
+
+ align:start position:0%
+decision what they're investing in is
+ 
+
+ align:start position:0%
+decision what they're investing in is
+what we call their human capital when
+
+ align:start position:0%
+what we call their human capital when
+ 
+
+ align:start position:0%
+what we call their human capital when
+you get education you're investing in
+
+ align:start position:0%
+you get education you're investing in
+ 
+
+ align:start position:0%
+you get education you're investing in
+yourself just like you invest in a
+
+ align:start position:0%
+yourself just like you invest in a
+ 
+
+ align:start position:0%
+yourself just like you invest in a
+machine because you are you hope raising
+
+ align:start position:0%
+machine because you are you hope raising
+ 
+
+ align:start position:0%
+machine because you are you hope raising
+the value of what you can do of what you
+
+ align:start position:0%
+the value of what you can do of what you
+ 
+
+ align:start position:0%
+the value of what you can do of what you
+can earn by investing in learning stuff
+
+ align:start position:0%
+can earn by investing in learning stuff
+ 
+
+ align:start position:0%
+can earn by investing in learning stuff
+well that human capital investment has
+
+ align:start position:0%
+well that human capital investment has
+ 
+
+ align:start position:0%
+well that human capital investment has
+the same features of any other
+
+ align:start position:0%
+the same features of any other
+ 
+
+ align:start position:0%
+the same features of any other
+investment there's an opportunity cost
+
+ align:start position:0%
+investment there's an opportunity cost
+ 
+
+ align:start position:0%
+investment there's an opportunity cost
+which is what what's the opportunity
+
+ align:start position:0%
+which is what what's the opportunity
+ 
+
+ align:start position:0%
+which is what what's the opportunity
+cost of investing your time and going to
+
+ align:start position:0%
+cost of investing your time and going to
+ 
+
+ align:start position:0%
+cost of investing your time and going to
+come what's the opportunity cost of
+
+ align:start position:0%
+come what's the opportunity cost of
+ 
+
+ align:start position:0%
+come what's the opportunity cost of
+going to college yeah you could this to
+
+ align:start position:0%
+going to college yeah you could this to
+ 
+
+ align:start position:0%
+going to college yeah you could this to
+one is you can get a job you could not
+
+ align:start position:0%
+one is you can get a job you could not
+ 
+
+ align:start position:0%
+one is you can get a job you could not
+pay tuition so if you think about going
+
+ align:start position:0%
+pay tuition so if you think about going
+ 
+
+ align:start position:0%
+pay tuition so if you think about going
+to college you're sacrificing two things
+
+ align:start position:0%
+to college you're sacrificing two things
+ 
+
+ align:start position:0%
+to college you're sacrificing two things
+you all that money you're paying you
+
+ align:start position:0%
+you all that money you're paying you
+ 
+
+ align:start position:0%
+you all that money you're paying you
+could basically invest instead of giving
+
+ align:start position:0%
+could basically invest instead of giving
+ 
+
+ align:start position:0%
+could basically invest instead of giving
+it to some college and you can be a
+
+ align:start position:0%
+it to some college and you can be a
+ 
+
+ align:start position:0%
+it to some college and you can be a
+burning money instead of sitting here
+
+ align:start position:0%
+burning money instead of sitting here
+ 
+
+ align:start position:0%
+burning money instead of sitting here
+listening to me okay so if you think
+
+ align:start position:0%
+listening to me okay so if you think
+ 
+
+ align:start position:0%
+listening to me okay so if you think
+about that um you actually it actually
+
+ align:start position:0%
+about that um you actually it actually
+ 
+
+ align:start position:0%
+about that um you actually it actually
+becomes a hard decision you might think
+
+ align:start position:0%
+becomes a hard decision you might think
+ 
+
+ align:start position:0%
+becomes a hard decision you might think
+so let's think about a simple example
+
+ align:start position:0%
+so let's think about a simple example
+ 
+
+ align:start position:0%
+so let's think about a simple example
+let's imagine that if you don't go to
+
+ align:start position:0%
+let's imagine that if you don't go to
+ 
+
+ align:start position:0%
+let's imagine that if you don't go to
+you work from age 18 to 70 and if you do
+
+ align:start position:0%
+you work from age 18 to 70 and if you do
+ 
+
+ align:start position:0%
+you work from age 18 to 70 and if you do
+go to college work from age 22 to 70
+
+ align:start position:0%
+go to college work from age 22 to 70
+ 
+
+ align:start position:0%
+go to college work from age 22 to 70
+sorry ignore grad school okay four years
+
+ align:start position:0%
+sorry ignore grad school okay four years
+ 
+
+ align:start position:0%
+sorry ignore grad school okay four years
+of college either start working in 18
+
+ align:start position:0%
+of college either start working in 18
+ 
+
+ align:start position:0%
+of college either start working in 18
+and start working at 22 and let's say
+
+ align:start position:0%
+and start working at 22 and let's say
+ 
+
+ align:start position:0%
+and start working at 22 and let's say
+college cost $35,000 a year obviously
+
+ align:start position:0%
+college cost $35,000 a year obviously
+ 
+
+ align:start position:0%
+college cost $35,000 a year obviously
+not MIT okay let's say college cost
+
+ align:start position:0%
+not MIT okay let's say college cost
+ 
+
+ align:start position:0%
+not MIT okay let's say college cost
+$35,000 a year okay and let's say that
+
+ align:start position:0%
+$35,000 a year okay and let's say that
+ 
+
+ align:start position:0%
+$35,000 a year okay and let's say that
+if you worked
+
+ align:start position:0%
+if you worked
+ 
+
+ align:start position:0%
+if you worked
+you could have let's say that if you
+
+ align:start position:0%
+you could have let's say that if you
+ 
+
+ align:start position:0%
+you could have let's say that if you
+worked while you were if you worked
+
+ align:start position:0%
+worked while you were if you worked
+ 
+
+ align:start position:0%
+worked while you were if you worked
+starting in high school you could have
+
+ align:start position:0%
+starting in high school you could have
+ 
+
+ align:start position:0%
+starting in high school you could have
+earned
+
+ align:start position:0%
+earned
+ 
+
+ align:start position:0%
+earned
+um actually Patricia we don't have the
+
+ align:start position:0%
+um actually Patricia we don't have the
+ 
+
+ align:start position:0%
+um actually Patricia we don't have the
+yeah you could have earned $20,000 you
+
+ align:start position:0%
+yeah you could have earned $20,000 you
+ 
+
+ align:start position:0%
+yeah you could have earned $20,000 you
+could have earned $20,000 if you'd if
+
+ align:start position:0%
+could have earned $20,000 if you'd if
+ 
+
+ align:start position:0%
+could have earned $20,000 if you'd if
+you you could have started at $20,000
+
+ align:start position:0%
+you you could have started at $20,000
+ 
+
+ align:start position:0%
+you you could have started at $20,000
+you've gone to work at age 18 okay well
+
+ align:start position:0%
+you've gone to work at age 18 okay well
+ 
+
+ align:start position:0%
+you've gone to work at age 18 okay well
+we can actually graph what this looks
+
+ align:start position:0%
+we can actually graph what this looks
+ 
+
+ align:start position:0%
+we can actually graph what this looks
+like in Figure 17 - 17 - if you think
+
+ align:start position:0%
+like in Figure 17 - 17 - if you think
+ 
+
+ align:start position:0%
+like in Figure 17 - 17 - if you think
+about age 18 from age 18 to age 22
+
+ align:start position:0%
+about age 18 from age 18 to age 22
+ 
+
+ align:start position:0%
+about age 18 from age 18 to age 22
+that's the green area if you go to
+
+ align:start position:0%
+that's the green area if you go to
+ 
+
+ align:start position:0%
+that's the green area if you go to
+college you give up the $35,000 in
+
+ align:start position:0%
+college you give up the $35,000 in
+ 
+
+ align:start position:0%
+college you give up the $35,000 in
+tuition and the 20k you could have
+
+ align:start position:0%
+tuition and the 20k you could have
+ 
+
+ align:start position:0%
+tuition and the 20k you could have
+earned the bottom line is basically the
+
+ align:start position:0%
+earned the bottom line is basically the
+ 
+
+ align:start position:0%
+earned the bottom line is basically the
+red line is your lifetime earnings if
+
+ align:start position:0%
+red line is your lifetime earnings if
+ 
+
+ align:start position:0%
+red line is your lifetime earnings if
+you go to high school if you if you
+
+ align:start position:0%
+you go to high school if you if you
+ 
+
+ align:start position:0%
+you go to high school if you if you
+don't go to college the great the green
+
+ align:start position:0%
+don't go to college the great the green
+ 
+
+ align:start position:0%
+don't go to college the great the green
+line is your lifetime earnings the blue
+
+ align:start position:0%
+line is your lifetime earnings the blue
+ 
+
+ align:start position:0%
+line is your lifetime earnings the blue
+line I'm sorry is your lifetime earnings
+
+ align:start position:0%
+line I'm sorry is your lifetime earnings
+ 
+
+ align:start position:0%
+line I'm sorry is your lifetime earnings
+if you go to college empirical estimates
+
+ align:start position:0%
+if you go to college empirical estimates
+ 
+
+ align:start position:0%
+if you go to college empirical estimates
+suggests at age 22 the typical college
+
+ align:start position:0%
+suggests at age 22 the typical college
+ 
+
+ align:start position:0%
+suggests at age 22 the typical college
+graduate earns $45,000 yes you're not
+
+ align:start position:0%
+graduate earns $45,000 yes you're not
+ 
+
+ align:start position:0%
+graduate earns $45,000 yes you're not
+the typical college graduate the typical
+
+ align:start position:0%
+the typical college graduate the typical
+ 
+
+ align:start position:0%
+the typical college graduate the typical
+college graduates $45,000 and the
+
+ align:start position:0%
+college graduates $45,000 and the
+ 
+
+ align:start position:0%
+college graduates $45,000 and the
+typical highschool non-college educators
+
+ align:start position:0%
+typical highschool non-college educators
+ 
+
+ align:start position:0%
+typical highschool non-college educators
+are seven it's $28,000 so at age 22 you
+
+ align:start position:0%
+are seven it's $28,000 so at age 22 you
+ 
+
+ align:start position:0%
+are seven it's $28,000 so at age 22 you
+come out of college or any 45 and if
+
+ align:start position:0%
+come out of college or any 45 and if
+ 
+
+ align:start position:0%
+come out of college or any 45 and if
+you'd not gone to college we're in 28
+
+ align:start position:0%
+you'd not gone to college we're in 28
+ 
+
+ align:start position:0%
+you'd not gone to college we're in 28
+not you but a normal person okay but
+
+ align:start position:0%
+not you but a normal person okay but
+ 
+
+ align:start position:0%
+not you but a normal person okay but
+moreover knowledge you learn more when
+
+ align:start position:0%
+moreover knowledge you learn more when
+ 
+
+ align:start position:0%
+moreover knowledge you learn more when
+you leave college your earnings grows
+
+ align:start position:0%
+you leave college your earnings grows
+ 
+
+ align:start position:0%
+you leave college your earnings grows
+faster so if you're college-educated not
+
+ align:start position:0%
+faster so if you're college-educated not
+ 
+
+ align:start position:0%
+faster so if you're college-educated not
+only means you earn 17 K more at 22 it
+
+ align:start position:0%
+only means you earn 17 K more at 22 it
+ 
+
+ align:start position:0%
+only means you earn 17 K more at 22 it
+also means your earnings grows faster so
+
+ align:start position:0%
+also means your earnings grows faster so
+ 
+
+ align:start position:0%
+also means your earnings grows faster so
+that by age 51 the
+
+ align:start position:0%
+that by age 51 the
+ 
+
+ align:start position:0%
+that by age 51 the
+average at college educated person earns
+
+ align:start position:0%
+average at college educated person earns
+ 
+
+ align:start position:0%
+average at college educated person earns
+$80,000 while the average high school
+
+ align:start position:0%
+$80,000 while the average high school
+ 
+
+ align:start position:0%
+$80,000 while the average high school
+person earns $45,000 so what you see
+
+ align:start position:0%
+person earns $45,000 so what you see
+ 
+
+ align:start position:0%
+person earns $45,000 so what you see
+here is the blue line starts above the
+
+ align:start position:0%
+here is the blue line starts above the
+ 
+
+ align:start position:0%
+here is the blue line starts above the
+red line okay and maybe I would learn to
+
+ align:start position:0%
+red line okay and maybe I would learn to
+ 
+
+ align:start position:0%
+red line okay and maybe I would learn to
+clip this on a fight and gone to college
+
+ align:start position:0%
+clip this on a fight and gone to college
+ 
+
+ align:start position:0%
+clip this on a fight and gone to college
+okay so the gap widens over time so how
+
+ align:start position:0%
+okay so the gap widens over time so how
+ 
+
+ align:start position:0%
+okay so the gap widens over time so how
+do we think about this decision well the
+
+ align:start position:0%
+do we think about this decision well the
+ 
+
+ align:start position:0%
+do we think about this decision well the
+cost is the green area the cost is over
+
+ align:start position:0%
+cost is the green area the cost is over
+ 
+
+ align:start position:0%
+cost is the green area the cost is over
+four years you could have earned money
+
+ align:start position:0%
+four years you could have earned money
+ 
+
+ align:start position:0%
+four years you could have earned money
+and you wouldn't had to pay tuition the
+
+ align:start position:0%
+and you wouldn't had to pay tuition the
+ 
+
+ align:start position:0%
+and you wouldn't had to pay tuition the
+benefit is the yellow area over that
+
+ align:start position:0%
+benefit is the yellow area over that
+ 
+
+ align:start position:0%
+benefit is the yellow area over that
+entire time after graduation you're
+
+ align:start position:0%
+entire time after graduation you're
+ 
+
+ align:start position:0%
+entire time after graduation you're
+making more money now obviously in terms
+
+ align:start position:0%
+making more money now obviously in terms
+ 
+
+ align:start position:0%
+making more money now obviously in terms
+of size the yellow area is much much
+
+ align:start position:0%
+of size the yellow area is much much
+ 
+
+ align:start position:0%
+of size the yellow area is much much
+bigger than the green area but the
+
+ align:start position:0%
+bigger than the green area but the
+ 
+
+ align:start position:0%
+bigger than the green area but the
+yellow area comes later that's the key
+
+ align:start position:0%
+yellow area comes later that's the key
+ 
+
+ align:start position:0%
+yellow area comes later that's the key
+thing she might look and say look it's
+
+ align:start position:0%
+thing she might look and say look it's
+ 
+
+ align:start position:0%
+thing she might look and say look it's
+obvious you get before this lecture you
+
+ align:start position:0%
+obvious you get before this lecture you
+ 
+
+ align:start position:0%
+obvious you get before this lecture you
+might say well it's obvious you go to
+
+ align:start position:0%
+might say well it's obvious you go to
+ 
+
+ align:start position:0%
+might say well it's obvious you go to
+college look the yellows way bigger than
+
+ align:start position:0%
+college look the yellows way bigger than
+ 
+
+ align:start position:0%
+college look the yellows way bigger than
+the green but that's not necessarily
+
+ align:start position:0%
+the green but that's not necessarily
+ 
+
+ align:start position:0%
+the green but that's not necessarily
+true cuz the green comes now and the
+
+ align:start position:0%
+true cuz the green comes now and the
+ 
+
+ align:start position:0%
+true cuz the green comes now and the
+yellow comes later indeed if you look at
+
+ align:start position:0%
+yellow comes later indeed if you look at
+ 
+
+ align:start position:0%
+yellow comes later indeed if you look at
+the table this actually shows the net
+
+ align:start position:0%
+the table this actually shows the net
+ 
+
+ align:start position:0%
+the table this actually shows the net
+present value on a college in high
+
+ align:start position:0%
+present value on a college in high
+ 
+
+ align:start position:0%
+present value on a college in high
+school and what this shows is at low
+
+ align:start position:0%
+school and what this shows is at low
+ 
+
+ align:start position:0%
+school and what this shows is at low
+interest rates you're much better off
+
+ align:start position:0%
+interest rates you're much better off
+ 
+
+ align:start position:0%
+interest rates you're much better off
+going to college so if there's no
+
+ align:start position:0%
+going to college so if there's no
+ 
+
+ align:start position:0%
+going to college so if there's no
+interest rate okay then college is a
+
+ align:start position:0%
+interest rate okay then college is a
+ 
+
+ align:start position:0%
+interest rate okay then college is a
+much much better deal your net present
+
+ align:start position:0%
+much much better deal your net present
+ 
+
+ align:start position:0%
+much much better deal your net present
+value of earnings if you go to you're
+
+ align:start position:0%
+value of earnings if you go to you're
+ 
+
+ align:start position:0%
+value of earnings if you go to you're
+never that I go to college is 2.6
+
+ align:start position:0%
+never that I go to college is 2.6
+ 
+
+ align:start position:0%
+never that I go to college is 2.6
+million we're only 1.6 million if you
+
+ align:start position:0%
+million we're only 1.6 million if you
+ 
+
+ align:start position:0%
+million we're only 1.6 million if you
+don't go to college but once the
+
+ align:start position:0%
+don't go to college but once the
+ 
+
+ align:start position:0%
+don't go to college but once the
+interest rate gets above 8% it suddenly
+
+ align:start position:0%
+interest rate gets above 8% it suddenly
+ 
+
+ align:start position:0%
+interest rate gets above 8% it suddenly
+becomes a worse deal to go to college
+
+ align:start position:0%
+becomes a worse deal to go to college
+ 
+
+ align:start position:0%
+becomes a worse deal to go to college
+that is that only a 9% interest rate
+
+ align:start position:0%
+that is that only a 9% interest rate
+ 
+
+ align:start position:0%
+that is that only a 9% interest rate
+which existed not that long ago okay in
+
+ align:start position:0%
+which existed not that long ago okay in
+ 
+
+ align:start position:0%
+which existed not that long ago okay in
+our history it was actually a worse deal
+
+ align:start position:0%
+our history it was actually a worse deal
+ 
+
+ align:start position:0%
+our history it was actually a worse deal
+for to average person to go to college
+
+ align:start position:0%
+for to average person to go to college
+ 
+
+ align:start position:0%
+for to average person to go to college
+yeah well actually it's interesting it
+
+ align:start position:0%
+yeah well actually it's interesting it
+ 
+
+ align:start position:0%
+yeah well actually it's interesting it
+depends the poor financial aid why
+
+ align:start position:0%
+depends the poor financial aid why
+ 
+
+ align:start position:0%
+depends the poor financial aid why
+someone tell me why it's depend in the
+
+ align:start position:0%
+someone tell me why it's depend in the
+ 
+
+ align:start position:0%
+someone tell me why it's depend in the
+form of financial aid it actually comes
+
+ align:start position:0%
+form of financial aid it actually comes
+ 
+
+ align:start position:0%
+form of financial aid it actually comes
+in different forms so why is it depend
+
+ align:start position:0%
+in different forms so why is it depend
+ 
+
+ align:start position:0%
+in different forms so why is it depend
+on how you get the financial aid yeah if
+
+ align:start position:0%
+on how you get the financial aid yeah if
+ 
+
+ align:start position:0%
+on how you get the financial aid yeah if
+it's a life if it's a grant then yeah
+
+ align:start position:0%
+it's a life if it's a grant then yeah
+ 
+
+ align:start position:0%
+it's a life if it's a grant then yeah
+you should just take that out of the
+
+ align:start position:0%
+you should just take that out of the
+ 
+
+ align:start position:0%
+you should just take that out of the
+cost but if it's a loan depends what it
+
+ align:start position:0%
+cost but if it's a loan depends what it
+ 
+
+ align:start position:0%
+cost but if it's a loan depends what it
+straight you get the loan act if the low
+
+ align:start position:0%
+straight you get the loan act if the low
+ 
+
+ align:start position:0%
+straight you get the loan act if the low
+is that the market interest rate then
+
+ align:start position:0%
+is that the market interest rate then
+ 
+
+ align:start position:0%
+is that the market interest rate then
+it's no different right
+
+ align:start position:0%
+it's no different right
+ 
+
+ align:start position:0%
+it's no different right
+but that's a great point which is why
+
+ align:start position:0%
+but that's a great point which is why
+ 
+
+ align:start position:0%
+but that's a great point which is why
+college financial aid comes in two forms
+
+ align:start position:0%
+college financial aid comes in two forms
+ 
+
+ align:start position:0%
+college financial aid comes in two forms
+grants for very low income people and
+
+ align:start position:0%
+grants for very low income people and
+ 
+
+ align:start position:0%
+grants for very low income people and
+low-interest loans for other people why
+
+ align:start position:0%
+low-interest loans for other people why
+ 
+
+ align:start position:0%
+low-interest loans for other people why
+do we give loan which loans for college
+
+ align:start position:0%
+do we give loan which loans for college
+ 
+
+ align:start position:0%
+do we give loan which loans for college
+because of this graph because we're
+
+ align:start position:0%
+because of this graph because we're
+ 
+
+ align:start position:0%
+because of this graph because we're
+saying we want to we think people need
+
+ align:start position:0%
+saying we want to we think people need
+ 
+
+ align:start position:0%
+saying we want to we think people need
+to invest in their education we're
+
+ align:start position:0%
+to invest in their education we're
+ 
+
+ align:start position:0%
+to invest in their education we're
+afraid that if they face the regular
+
+ align:start position:0%
+afraid that if they face the regular
+ 
+
+ align:start position:0%
+afraid that if they face the regular
+interest rate they won't be willing to
+
+ align:start position:0%
+interest rate they won't be willing to
+ 
+
+ align:start position:0%
+interest rate they won't be willing to
+do it because the green that would
+
+ align:start position:0%
+do it because the green that would
+ 
+
+ align:start position:0%
+do it because the green that would
+bigger than the yellow so actually gonna
+
+ align:start position:0%
+bigger than the yellow so actually gonna
+ 
+
+ align:start position:0%
+bigger than the yellow so actually gonna
+subsidize their loan their interest rate
+
+ align:start position:0%
+subsidize their loan their interest rate
+ 
+
+ align:start position:0%
+subsidize their loan their interest rate
+so that's you might have thought to
+
+ align:start position:0%
+so that's you might have thought to
+ 
+
+ align:start position:0%
+so that's you might have thought to
+yourself sort of a weird way to get
+
+ align:start position:0%
+yourself sort of a weird way to get
+ 
+
+ align:start position:0%
+yourself sort of a weird way to get
+people to go to college is to have a
+
+ align:start position:0%
+people to go to college is to have a
+ 
+
+ align:start position:0%
+people to go to college is to have a
+lower student loan interest rate but in
+
+ align:start position:0%
+lower student loan interest rate but in
+ 
+
+ align:start position:0%
+lower student loan interest rate but in
+fact it makes perfect sense
+
+ align:start position:0%
+fact it makes perfect sense
+ 
+
+ align:start position:0%
+fact it makes perfect sense
+by having a student loan interest rate
+
+ align:start position:0%
+by having a student loan interest rate
+ 
+
+ align:start position:0%
+by having a student loan interest rate
+that's lower than the market rate you
+
+ align:start position:0%
+that's lower than the market rate you
+ 
+
+ align:start position:0%
+that's lower than the market rate you
+encourage people to go to college
+
+ align:start position:0%
+encourage people to go to college
+ 
+
+ align:start position:0%
+encourage people to go to college
+because essentially you lower this
+
+ align:start position:0%
+because essentially you lower this
+ 
+
+ align:start position:0%
+because essentially you lower this
+discount rate for at least at least on
+
+ align:start position:0%
+discount rate for at least at least on
+ 
+
+ align:start position:0%
+discount rate for at least at least on
+the part that's tuition payments okay so
+
+ align:start position:0%
+the part that's tuition payments okay so
+ 
+
+ align:start position:0%
+the part that's tuition payments okay so
+that's actually a very exciting um we
+
+ align:start position:0%
+that's actually a very exciting um we
+ 
+
+ align:start position:0%
+that's actually a very exciting um we
+need to think about in a very important
+
+ align:start position:0%
+need to think about in a very important
+ 
+
+ align:start position:0%
+need to think about in a very important
+part of public policy it's how we set
+
+ align:start position:0%
+part of public policy it's how we set
+ 
+
+ align:start position:0%
+part of public policy it's how we set
+the interest rate on student loans for
+
+ align:start position:0%
+the interest rate on student loans for
+ 
+
+ align:start position:0%
+the interest rate on student loans for
+any of you how many you guys have a
+
+ align:start position:0%
+any of you how many you guys have a
+ 
+
+ align:start position:0%
+any of you how many you guys have a
+student loan do you know and you gather
+
+ align:start position:0%
+student loan do you know and you gather
+ 
+
+ align:start position:0%
+student loan do you know and you gather
+student loan you might not know anyway I
+
+ align:start position:0%
+student loan you might not know anyway I
+ 
+
+ align:start position:0%
+student loan you might not know anyway I
+set the interest rate in that student
+
+ align:start position:0%
+set the interest rate in that student
+ 
+
+ align:start position:0%
+set the interest rate in that student
+loan so thank you actually when I was in
+
+ align:start position:0%
+loan so thank you actually when I was in
+ 
+
+ align:start position:0%
+loan so thank you actually when I was in
+the government I wasn't gone for
+
+ align:start position:0%
+the government I wasn't gone for
+ 
+
+ align:start position:0%
+the government I wasn't gone for
+fourteen months the Clinton
+
+ align:start position:0%
+fourteen months the Clinton
+ 
+
+ align:start position:0%
+fourteen months the Clinton
+administration it was super fun but
+
+ align:start position:0%
+administration it was super fun but
+ 
+
+ align:start position:0%
+administration it was super fun but
+looking back I only got one thing done
+
+ align:start position:0%
+looking back I only got one thing done
+ 
+
+ align:start position:0%
+looking back I only got one thing done
+which I got to set things straight in
+
+ align:start position:0%
+which I got to set things straight in
+ 
+
+ align:start position:0%
+which I got to set things straight in
+student loans so that was kind of fun uh
+
+ align:start position:0%
+student loans so that was kind of fun uh
+ 
+
+ align:start position:0%
+student loans so that was kind of fun uh
+but otherwise I it was just a lot of fun
+
+ align:start position:0%
+but otherwise I it was just a lot of fun
+ 
+
+ align:start position:0%
+but otherwise I it was just a lot of fun
+being there so so anyway uh let's stop
+
+ align:start position:0%
+being there so so anyway uh let's stop
+ 
+
+ align:start position:0%
+being there so so anyway uh let's stop
+there and we will we will continue uh
+
+ align:start position:0%
+there and we will we will continue uh
+ 
+
+ align:start position:0%
+there and we will we will continue uh
+let's say with it so no class on Monday
+
+ align:start position:0%
+let's say with it so no class on Monday
+ 
+
+ align:start position:0%
+let's say with it so no class on Monday
+that's Veterans Day so we'll meet in a
+
+ align:start position:0%
+that's Veterans Day so we'll meet in a
+ 
+
+ align:start position:0%
+that's Veterans Day so we'll meet in a
+week next Wednesday
\ No newline at end of file
diff --git a/BekDicq9MdM.txt b/BekDicq9MdM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2b165e7b11607ed83a34ee67d44aac43d74a26e5
--- /dev/null
+++ b/BekDicq9MdM.txt
@@ -0,0 +1,3040 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to this
+
+lecture on nonlinear finite
+element analysis of solids and
+
+structures.
+
+In this lecture, I like to
+discuss with you solution
+
+methods that we use to solve the
+finite element equations
+
+in nonlinear static analysis.
+
+In the previous lectures, we
+derived this set of equations,
+
+where tK is a tangent
+stiffness matrix.
+
+Delta Ui is a nodal point
+vector of incremental
+
+displacements corresponding
+to iteration i.
+
+t plus delta t R is the
+externally applied load vector
+
+corresponding to time
+t plus delta t.
+
+And t plus delta t F i minus 1
+is equal to the nodal point
+
+force vector corresponding to
+the internal elements stresses
+
+at time t plus delta t,
+and at the end of
+
+iteration i minus 1.
+
+The displacements are updated
+as shown here.
+
+Delta Ui, of course,
+is calculated
+
+from this set of equations.
+
+We add delta Ui to the previous
+displacements that
+
+corresponded to iteration
+t plus delta --
+
+to time t plus delta t and
+iteration i minus 1.
+
+It's the end of iteration
+i minus 1.
+
+And this right-hand side gives
+us the new displacement vector
+
+corresponding to iteration
+i, end of iteration i.
+
+Now this is one scheme that it's
+used to solve the finite
+
+element equations.
+
+We refer to this as
+the mortified
+
+Newton-Raphson method.
+
+However, there are other
+schemes as well.
+
+And schemes that are in certain
+
+problems much more effective.
+
+Since it is so important to use
+an effective method for
+
+the solution of the finite
+element equations because the
+
+costs can otherwise be very
+high, we should be familiar
+
+with those other techniques.
+
+And I'd like to share
+those now with you.
+
+Therefore, we will look in
+this lecture at other
+
+techniques to solve the finite
+element equations.
+
+And we need, of course, to
+discuss convergence criteria.
+
+It's very important to use
+
+appropriate convergence criteria.
+
+Otherwise, you iterate too long
+and/or on the other side,
+
+you may actually stop iterating
+before you have
+
+achieved proper convergence.
+
+So let me then go over to my
+view graphs and let us start
+
+the discussion here.
+
+The basic set of equations that
+we would like to solve
+
+are given here.
+
+Notice R is the vector of
+externally applied nodal point
+
+forces at time t plus delta t.
+
+And F is the vector of nodal
+point forces corresponding to
+
+the internal element stresses
+at time t plus delta t.
+
+Of course, this vector is
+unknown, and we want to
+
+iterate somehow to find it and
+make sure, of course, that at
+
+the end of that iteration, if we
+have the proper vector F, R
+
+is equal to F, or R minus
+F is equal to 0.
+
+We assume that the loading is
+deformation-independent.
+
+If say, loading is
+deformation-dependent, we can
+
+also deal with that situation.
+
+But we will have to add
+additional terms to our
+
+iterative scheme.
+
+And I will get back to
+that a little later.
+
+Notice that F in the total
+Lagrangian formulation the way
+
+we have discussed it earlier is
+evaluated by this product
+
+here integrated over the
+original volume for a single
+
+element and for the UL
+formulation, F is calculated
+
+as shown here.
+
+Here, of course, we integrate
+over the current volume, or
+
+the volume that we actually
+want to calculate.
+
+Notice in the iteration, of
+course, this volume here would
+
+be t plus delta t V i minus 1
+as we will discuss just now.
+
+Because in the iteration, we
+always update this integral
+
+and that integral with the
+iteration counter that we are
+
+having on the right-hand side
+of the system of equations.
+
+The methods that we use are
+based on the Newton-Raphson
+
+method, which is really used
+very abundantly to find roots
+
+of an equation.
+
+A small historical note:
+
+Newton gave a first version
+of the method in 1669.
+
+Raphson then generalized and
+simplified the method
+
+actually, in 1690.
+
+Both mathematicians used
+the same concept.
+
+And both algorithms gave really,
+the same results.
+
+But it is very appropriate to
+refer to the methods that
+
+we're using as the
+Newton-Raphson method because
+
+Raphson really contributed quite
+a bit to that method.
+
+So let us now consider a single
+
+Newton-Raphson iteration.
+
+The way you may have actually
+encountered it already earlier
+
+in your studies of solution
+methods for the roots of an
+
+algebraic equation.
+
+Basically, what you're
+doing is this.
+
+You're saying if you have xi
+minus 1, you calculate
+
+f at xi minus 1.
+
+You divide this value by the
+f prime at xi minus 1.
+
+And then this right-hand side
+gives you better value, a
+
+better approximation to the
+root of the equation.
+
+Once you have xi, you repeat
+the process and
+
+you get xi plus 1.
+
+You keep on repeating the
+process until, basically f xi
+
+here is close to 0.
+
+Because then you have a root.
+
+Well, if we use that
+Newton-Raphson formula, it is
+
+quite interesting to see how
+it has been derived.
+
+We can write for any point xi,
+a neighboring point xi minus
+
+1, directly this equation here
+by a Taylor series expansion.
+
+And if we neglect the higher
+order terms, we get that f of
+
+xi is approximately equal to
+this relationship on the
+
+right-hand side.
+
+Well, since f of xi is supposed
+to be 0, because we
+
+are looking for a 0 of
+the equation, we
+
+set it equal to 0.
+
+And here you see directly
+the formula that
+
+I showed you earlier.
+
+So this is a very quick
+derivation of the
+
+Newton-Raphson procedure.
+
+Let us look at a mathematical
+example to see how the method
+
+works, and to get some insight
+into the technique.
+
+Let us choose a very simple
+example, not much to do with
+
+finite element analysis.
+
+Let us say that f of x equals
+sine x and that our starting
+
+value is equal to 2
+for the iteration.
+
+You always have to choose, of
+course, a starting value for
+
+the iteration.
+
+Then, in this column you see the
+values that are calculated
+
+in the successive iterations.
+
+And we also show
+here the error.
+
+It is interesting to observe
+that when you are close to the
+
+root, you have quadratic
+convergence.
+
+Meaning that the error here,
+epsilon becomes an error.
+
+Epsilon squared here.
+
+This is summarized on
+this view graph.
+
+Mathematically, if we have that
+the error, Ei minus 1, is
+
+given by this equation here.
+
+Of course, there's an
+approximate sign here.
+
+Then the error in the
+next iteration
+
+will be of this order.
+
+So the convergence is really
+very rapid once we are close
+
+to the root.
+
+Here we can see, however,
+that if we are not
+
+close to the root--
+
+in other words, if we are too
+far from the root, and we pick
+
+a bad value, then we don't
+get to the desired
+
+root, which is pi.
+
+But we get a value that
+is far away from pi.
+
+It is also root, but certainly
+not the root that we are
+
+interested in.
+
+So Newton-Raphson iteration
+is not always convergent
+
+directly, converging directly
+to the result that we would
+
+like to obtain.
+
+There has to be some care when
+we use that iterative scheme.
+
+And in fact, we have to be close
+enough just to basically
+
+say what has to happen.
+
+We have to be close enough to
+the root in order to have
+
+convergence to the root that
+we're looking for.
+
+And ultimately, if we do
+converge to that root, we will
+
+get quadratic convergence
+to the root.
+
+And that is, of course,
+very desirable.
+
+But the starting value is
+critical, as you can see here
+
+from this view graph.
+
+Let us look pictorially at
+the solution process.
+
+Here we have our
+sine function.
+
+And we are looking
+for this root.
+
+In iteration 1, we basically set
+up a tangent to that sine
+
+function at the starting
+value, x0.
+
+And we calculate x1 using this
+tangent as another estimate to
+
+the value that we're
+interested in.
+
+Now in the iteration 2, we lay
+a tangent to the f function.
+
+Which, of course, is sine
+x, at the new value
+
+corresponding to x1.
+
+And with this tangent,
+we get to this value.
+
+And you can see already
+that we got closer
+
+to the desired value.
+
+We were this far away
+originally.
+
+Then that far away.
+
+And now we are only
+that far away.
+
+Notice our sine function
+has this value here.
+
+And certainly, it's not 0 yet.
+
+So we lay another tangent
+at that point.
+
+And that's being done on
+this view graph here.
+
+Another tangent, and now
+we get much closer
+
+to the desired value.
+
+Right here, x3 is already
+quite close.
+
+But not close enough as
+shown by this value.
+
+It's not yet close enough
+to 0, this length here.
+
+And we lay another tangent
+to that point now.
+
+And that's shown on this
+view graph now.
+
+And we can see with the blue
+line being the tangent at this
+
+point, we get x4 very close
+to the 0 value that we are
+
+actually interested in.
+
+Certainly on this view graph,
+you can't see any difference
+
+anymore between x4 and
+the desired value.
+
+So this is basically the process
+that we are following
+
+through when we go from
+iteration 1 to iteration 2 to
+
+iteration 3 and to
+iteration 4.
+
+Beautiful convergence in this
+particular example.
+
+And the reason being that x0 is
+close enough to the desired
+
+value, the desired root.
+
+Which, itself, of course,
+is close to x4.
+
+Four
+
+Well, if however, we were to
+take a value that is not close
+
+enough and then we, as I showed
+earlier, we do not
+
+converge to the actual root.
+
+And this is shown here.
+
+For example, if we take a
+tangent at a point where f of
+
+prime is almost 0, then of
+course, this tangent throws us
+
+far away from this root.
+
+And we will converge
+to some other root.
+
+Of course, we don't want to use
+an exact 0 here because we
+
+have f of x divided
+by f prime of x.
+
+So with an exact 0, we could
+not [UNINTELLIGIBLE].
+
+But a tangent that is close to
+0, an f prime value that is
+
+close to 0, would throw us far
+away from the desired root.
+
+And that shows some of the
+difficulties using--
+
+in fact, almost all iterative
+schemes that we may not get
+
+fast enough to our root.
+
+And in fact, we may never get
+to the root that we are
+
+looking for.
+
+Well, let us then look at the
+Newton-Raphson iteration for
+
+multiple degrees of freedom.
+
+Here we have our R minus
+F that we want to
+
+be setting to 0.
+
+Or we want to rather, solve for
+the displacements t plus
+
+delta t U, which are the
+solution because this t plus
+
+delta t u displacements would
+give us this force vector.
+
+And this force vector
+equilibrates the R vector.
+
+Meaning f of U, this little
+f of U, is equal to 0.
+
+And that, of course, is what
+we want to achieve.
+
+Notice that we have here,
+of course, now
+
+n degrees of freedom.
+
+Therefore, n equations
+to solve.
+
+Previously, we only looked
+at one equation.
+
+If we apply the same principle
+as before to this little f,
+
+namely we expand f as a Taylor
+series about t plus delta t U
+
+i minus 1, then we get
+this equation on
+
+the right-hand side.
+
+And of course, on the left-hand
+side, we have f of t
+
+plus delta t Ui.
+
+Notice they are higher terms,
+which we will neglect just as
+
+we have done earlier for
+the single equation.
+
+Because we are looking for
+Taylor series expansion about
+
+t plus delta t U i minus 1.
+
+If we neglect this part here,
+we obtain directly this
+
+equation here.
+
+0 on the left-hand side, because
+once again, we are
+
+looking for the displacements
+values for which f is 0.
+
+So therefore, we set this
+deliberately equal to 0.
+
+And on the right-hand side, we
+have f t plus delta t U i
+
+minus 1 plus partial f with
+respect to U times the delta
+
+U. This delta U is unknown,
+of course,
+
+that we want to calculate.
+
+And this delta U is nothing
+else then the difference
+
+between the U value in iteration
+i and the U value in
+
+iteration i minus 1.
+
+Notice that this f is
+evaluated at t plus
+
+delta t U i minus 1.
+
+Let us look now at
+this equation.
+
+And if we write it a little bit
+more out, we find that on
+
+the left-hand side, we have,
+of course, a vector of 0's.
+
+On the right-hand side, we
+have a vector of f i
+
+components, f1 to fn.
+
+All of which are evaluated at
+t plus delta t U i minus 1.
+
+And then we have here a matrix,
+which is a square
+
+matrix in which the individual
+elements are partials of f i
+
+with respect to Uj.
+
+For example, f1, partial f1
+with respect to U1 here.
+
+Partial fn with respect to
+U n here, et cetera.
+
+This matrix here will give us
+a tangent stiffness matrix.
+
+Notice this matrix is multiplied
+by the vector of
+
+incremental nodal point
+displacements corresponding to
+
+iteration i.
+
+If we remember that f, the
+little f, at t plus delta t U
+
+i minus 1 is equal to R minus
+2 plus delta t F i minus 1.
+
+Capital F here, little
+f there, remember?
+
+Then, the partial of little f
+with respect to U at t plus
+
+delta t U i minus 1 is given
+via this equation.
+
+Now, please recognize that
+partial of R with respect to U
+
+is equal to 0 if the loads are
+deformation-independent.
+
+Of course, if the loads depend
+on the deformations, in other
+
+words, if the loads depend on
+the U displacements, then this
+
+would not be 0, and we would
+have to actually put a term in
+
+here, carry that term along
+in the solution of
+
+the nonlinear equations.
+
+But for the moment,
+we neglect this.
+
+We assume that the loads are
+deformation-independent.
+
+And then, this term
+is equal to 0.
+
+This here is now giving us the
+tangent stiffness matrix.
+
+And it is written down here.
+
+The tangent stiffness matrix
+is nothing else than the
+
+partials of capital F with
+respect to the U's, to the
+
+displacements.
+
+The final result then is given
+on this view graph.
+
+We substitute all the
+information that I shared with
+
+you into the Taylor series
+expansion around t plus delta
+
+t U i minus 1.
+
+We get directly this
+equation here.
+
+Notice tangent stiffness matrix
+corresponding to time t
+
+plus delta t and iteration
+i minus 1.
+
+Delta U i corresponding to
+iteration i we have to be very
+
+clear about this, that this is
+an increment in displacement
+
+from time t plus delta t
+iteration i minus 1 to
+
+iteration i.
+
+And of course, the nodal
+point force vector.
+
+Externally applied nodal point
+forces go in here.
+
+And this is the nodal point
+force vector corresponding to
+
+the internal element stresses at
+time t plus delta t and at
+
+the end of iteration
+i minus 1.
+
+Evaluated differently in the
+total Lagrangian formulation
+
+from the way we're evaluating
+it in the updated Lagrangian
+
+formulation.
+
+We talked about this vector
+abundantly in
+
+the previous lectures.
+
+We talked about this vector,
+of course, also in the
+
+previous lectures.
+
+We had in the previous lectures
+here at tK, a
+
+constant tangent stiffness
+matrix, which was set up at
+
+the beginning of this whole
+interactive process, and was
+
+never updated.
+
+Well, here we now update
+that stiffness matrix.
+
+And I think if you look through
+the information that I
+
+just discussed with you,
+you recognize why
+
+we're updating it.
+
+We are doing so because we are
+always starting with the new
+
+Taylor series expansion about
+the point i minus 1.
+
+This set of equations if of
+course solved for delta Ui.
+
+We add delta Ui to what we
+had already in terms of
+
+displacements to get our new
+estimate for the nodal point
+
+displacements.
+
+It is important to realize that
+the K matrix, which we
+
+are using in the solution
+process, is symmetric.
+
+Because first of all, we use
+symmetric stress and strain
+
+measures in our governing
+equation.
+
+Remember that when we apply the
+principle of virtual work,
+
+we use Cauchy stresses
+and infinitesimally
+
+small virtual strains.
+
+Now notice that both of these
+tenses are symmetric tenses.
+
+Of course, these are the tenses
+we're using in the UL,
+
+in the updated Lagrangian
+formulation.
+
+In the total Lagrangian
+formulation, we use the second
+
+Piola-Kirchhoff stress in
+Green-Lagrange strain.
+
+Both of these measures are
+again, symmetric measures.
+
+Both tenses are symmetric
+tenses.
+
+If we had introduced for a
+formulation non-symmetric
+
+tenses, for example a
+non-symmetric stress tenser,
+
+and of course, an energy
+conjugate non-symmetric strain
+
+tenser, we would have obtained
+a non-symmetric K matrix,
+
+which would be much more
+difficult to deal with.
+
+Much less cost effective in
+the solution process.
+
+Also, please recognize that
+we interpolated the real
+
+displacements and the virtual
+displacements with exactly the
+
+same functions.
+
+Whereas this point here is a
+continuum mechanics point,
+
+this is really a finite
+element point.
+
+If we had used different
+interpolation functions for
+
+the real displacements, then for
+the virtual displacements,
+
+or vice-versa, then we would
+have not necessarily obtained
+
+a symmetric K matrix.
+
+Of course, the most natural
+procedure is to use the same
+
+kind of interpolation functions
+for the virtual
+
+displacements as we used for
+the real displacements, and
+
+that's what we did.
+
+Finally, we also assumed
+that the loading was
+
+deformation-independent.
+
+If we have deformation-dependent
+loading,
+
+then if you go more back to the
+earlier view graph, then
+
+of course, this right-hand
+side vector R here would
+
+depend on the displacements.
+
+And there are basically two
+different approaches
+
+that one can take.
+
+In the first approach, one
+simply updates this vector
+
+with the iteration, or with
+taking into account the
+
+current or last calculated
+volume and surface areas for
+
+the elements.
+
+So we would simply put here
+an i minus 1 up there.
+
+The left-hand side matrix,
+we leave unchanged.
+
+And if that converges fast,
+certainly it's a very
+
+effective approach to use.
+
+We use that approach
+abundantly.
+
+However, another approach
+is to actually take the
+
+differentiation of R with
+respect to the U's, the way we
+
+have been looking at it earlier
+on an earlier view
+
+graph, and then you get some
+components that you
+
+add to the K matrix.
+
+And that K matrix may then
+out to be non-symmetric.
+
+However, if the loading is
+deformation-independent, then
+
+the differentiation of R with
+respect to the displacements U
+
+is equal to 0, and there's
+no component from that
+
+differentiation coming
+into the K matrix.
+
+And our K, of course, provided
+these are also
+
+satisfied, is symmetric.
+
+The iterative scheme that we
+just discussed is referred to
+
+as the full Newton-Raphson
+method.
+
+Full because we are setting
+up a new K matrix at the
+
+beginning of each iteration.
+
+The full Newton-Raphson method
+shows mathematically quadratic
+
+convergence the way we discussed
+it a bit earlier in
+
+the lecture.
+
+And that, of course, is always
+the case provided you are
+
+close enough to the root.
+
+This quadratic convergence only
+holds provided you are
+
+close enough to the root when
+you solve your equations.
+
+In finite element analysis, it
+is also important to recognize
+
+that a number of requirements
+must be fulfilled.
+
+For example, in elasto-plastic
+analysis, the stresses and
+
+strains must be properly--
+
+plastic strains must be
+properly updated.
+
+And similarly, the rotations
+in a shell analysis must be
+
+properly updated.
+
+So it is not necessarily the
+case that you automatically
+
+get quadratic convergence when
+you do finite element
+
+announces with a full
+Newton-Raphson method.
+
+It is very important to also,
+on the level of updating the
+
+stresses and the rotations,
+really do things properly in
+
+quotes in order to obtain the
+full quadratic convergence of
+
+the Newton-Raphson method.
+
+We can depict the iteration
+process in
+
+two equivalent ways.
+
+The first way is shown
+here, the left.
+
+And it's really the way we've
+been discussing just now the
+
+solution of f equals R minus
+capital F. Where we want to
+
+solve for the root, the
+0 of this equation.
+
+Notice here we have in red
+the little f depicted.
+
+Notice that at this point here,
+we have t plus delta t
+
+capital F i minus 1.
+
+And t plus delta t
+R is this value.
+
+Now, as we get closer to the
+root, which is of course, the
+
+point where the red curve
+crosses this U-axis, as we get
+
+closer to the root, this capital
+F will get closer and
+
+closer to the R. And that is,
+of course, when the little f
+
+is equal to 0.
+
+That's all we are
+showing here.
+
+Notice that we are setting up
+a slope f prime at the point
+
+corresponding to the i minus
+first iteration.
+
+And that slope brings us into
+this point, which will be the
+
+next point for--
+
+or the next starting point
+for the next iteration.
+
+I should say, the point
+of starting
+
+with the next iteration.
+
+Now, this is one way
+of looking at
+
+the iterative process.
+
+We can also look at
+it as shown here.
+
+Notice we have here the R
+plotted now horizontally.
+
+The displacement vertically.
+
+Notice the R at a particular
+time t plus delta t is shown
+
+by this dashed line.
+
+And we really want to find this
+particular point here and
+
+the corresponding U displacement
+of course.
+
+At this point, the little f is
+0 and the corresponding U
+
+displacement is down here.
+
+Notice that at the iteration
+i minus 1, it's the end of
+
+iteration i minus 1, we have
+obtained this point here.
+
+The U displacement corresponding
+to that point is
+
+obtained by projecting down
+on the displacement axes.
+
+And this slope here, the blue
+line, gives us a tangent
+
+stiffness matrix slope.
+
+These are two equivalent ways.
+
+This is here more like a force
+deflection curve, and we will
+
+use this representation
+now abundantly.
+
+But keep in mind, it's really
+the same thing if you look at
+
+it closely.
+
+Well, modifications
+to the iterative
+
+scheme are the following.
+
+If we leave the stiffness matrix
+constant throughout a
+
+complete solution process--
+
+in other words, tau is
+equal to 0 here.
+
+It's never updated.
+
+We talk about the initial
+stress method.
+
+If tau is equal to t, where t,
+of course, corresponds to a
+
+particular solution step and
+meaning that the K matrix is
+
+constant, but it is updated
+as the beginning
+
+of a solution step.
+
+Then we talk about the modified
+Newton method.
+
+Modified Newton-Raphson
+method.
+
+Or, we may also find it
+effective to update the K
+
+matrix only at particular
+solution steps, at certain
+
+times only.
+
+We note that the initial stress
+method and the modified
+
+Newton methods are, of course,
+much less expensive than the
+
+full Newton method per
+iteration, however.
+
+We should add that many more
+iterations are necessary to
+
+achieve the same accuracy if we
+don't set up a new K matrix
+
+in every iteration.
+
+The initial stress method and
+modified Newton iteration
+
+technique do not exhibit
+quadratic convergence because
+
+to obtain quadratic convergence,
+you need to set
+
+up a new K matrix in
+each iteration.
+
+And of course, you have to be
+close enough to the root, to
+
+the solution that you're
+looking for.
+
+Let us now look at
+a simple example.
+
+An example where we have just
+one degree of freedom.
+
+And where we deal with
+two load steps.
+
+Here we show the force
+applied to the
+
+problem, or to the structure.
+
+In the first load step,
+we apply 1R.
+
+And then in the second
+load step, 2R.
+
+Notice horizontally here, I'm
+plotting displacements.
+
+And the force displacement
+curve is
+
+shown by the red line.
+
+Now, to obtain the solution for
+this displacement, U1, and
+
+that displacement U2, we, as
+we discussed, set up a K
+
+matrix, which corresponds
+to the slope, a
+
+slope on the red curve.
+
+And we iterate towards
+the sought solutions.
+
+Here, we have the iterative
+process using the initial
+
+stress method.
+
+In other words, where tau is
+equal to 0 in our governing
+
+finite element equations.
+
+This means that we are setting
+up a K matrix initially, and
+
+that K matrix is depicted here
+by the slope, the blue slope
+
+that you're seeing.
+
+Now with this slope and this
+load applied, we get the
+
+displacement shown down here.
+
+Notice the left superscript
+means load step 1.
+
+The right superscript means
+solution after iteration 1.
+
+And this is the solution
+obtained from this triangle.
+
+Notice there's a blue line up
+there, going up there, and
+
+where that blue line crosses the
+dashed line, we pick up a
+
+vertical fine, black line.
+
+And that vertical black line
+cuts through the displacement
+
+axes at this particular value.
+
+So this is the solution of
+our first iteration.
+
+Now, having calculated this
+displacement value, we go up
+
+vertically and get to the
+red line, the red curve.
+
+And that red curve corresponds,
+of course, to the
+
+internal forces.
+
+To the internal force I should
+say, corresponding to this
+
+displacement.
+
+There's a red dot right
+on that red curve.
+
+And at that red dot now, we've
+set up a K matrix again.
+
+Now notice, in the initial
+stress method, we keep the K
+
+matrix constant.
+
+This means that the slope here
+of this blue line that goes
+
+through this red point is the
+same as the slope that we had
+
+earlier right here.
+
+With that slope and the out of
+balance load-- and let's look
+
+now very closely here--
+
+that corresponds to the distance
+between this red
+
+point and that dashed line with
+this out of balance load
+
+and this blue slope, we get an
+increment in displacement
+
+shown right here.
+
+And that increment in
+displacement added to the
+
+previous displacement gives
+us this value down here.
+
+And in fact, this value is
+very close to the correct
+
+solution, the exact solution,
+which is the solution
+
+corresponding to the dashed
+vertical line here.
+
+Notice that the dashed vertical
+line is the exact
+
+solution to that dashed
+horizontal line.
+
+And our vertical black line,
+which we are calculating, is
+
+virtually on that dashed
+black line.
+
+So we can accept now,
+convergence.
+
+Let's now go into the
+next load step.
+
+In the next load step,
+we want to, again,
+
+deal with a K matrix.
+
+And in the initial stress
+method, we use the same K
+
+matrix throughout
+the solution.
+
+Meaning that the slope now,
+which we are laying onto the
+
+red curve, that slope being this
+blue line, is the same
+
+slope that we used before in
+the first two iterations.
+
+With this slope and the out of
+balance load corresponding to
+
+the distance between this
+horizontal line, the dashed
+
+horizontal line, and that dashed
+horizontal line because
+
+we conversed in the
+first load step.
+
+With that out of balance load,
+we get an incremental
+
+displacement shown from
+here to there.
+
+And that incremental
+displacement then, added to
+
+the previous displacement,
+gives us this value in
+
+displacement.
+
+Notice time t plus delta t or
+load step t plus delta t,
+
+which is here.
+
+Load step 2 and iteration
+1, end of iteration 1.
+
+This is now our current
+displacement.
+
+With this current displacement,
+once again,
+
+which comes from this triangle
+here, with this current
+
+displacement, we go vertically
+up and get to that red point,
+
+which lies on the force
+displacement curve--
+
+internal force displacement
+curve more accurately.
+
+And now we have this red point,
+and we set up, or we
+
+use now, again, a K matrix.
+
+Of course, in the initial
+stress method we use the
+
+constant K matrix.
+
+So this slope is the
+same as that slope.
+
+And now watch closely.
+
+From this triangle here, which
+corresponds to this out of
+
+balance load, which is
+the same as that
+
+out of balance load.
+
+Out of balance load obtained
+by putting here
+
+a horizontal line.
+
+Notice and the difference
+between the dashed line up
+
+there and the horizontal line
+given by my pointer is the out
+
+of balance load.
+
+Which of course, is the same as
+the distance between this
+
+red point and that
+dashed line.
+
+This out of balance load with
+this slope gives us another
+
+increment in displacement,
+which brings us
+
+to this value here.
+
+We repeat that process and
+iteratively, we get closer and
+
+closer to the correct solution,
+the exact solution,
+
+which is the dashed vertical
+line here for the
+
+displacement.
+
+Because at that dashed vertical
+line, we are getting
+
+to that red curve.
+
+Now, this is the initial
+stress method.
+
+And once again, the point here
+is that we kept the same K
+
+matrix throughout the
+solution process.
+
+Surely, if you now were to look
+at this iterative scheme
+
+to obtain a faster solution,
+you would want to
+
+set up a new K matrix.
+
+In other words, once you have
+this displacement value
+
+calculated, you want to update
+the slope corresponding to the
+
+slope of the red curve.
+
+And if you do so--
+
+in other words, you update this
+blue slope corresponding
+
+to the red dots that you
+have obtained in
+
+your iterative scheme.
+
+These red dots, of course,
+being different from what
+
+you're seeing here now.
+
+Then you would have the full
+Newton-Raphson method.
+
+If you only update the K matrix
+or the blue tangent
+
+that we are seeing here whenever
+you have converged to
+
+an equilibrium point.
+
+Meaning when you have converged
+corresponding for
+
+the first load step in
+this particular case.
+
+If you only update the stiffness
+matrix once you have
+
+converged to this load--
+
+for this load step, then you
+would have the modified
+
+Newton-Raphson method.
+
+I think if you look at this
+picture with these
+
+possibilities, you will realize
+that surely, the full
+
+Newton-Raphson method with
+updating the slope after each
+
+iteration will converge
+fastest.
+
+And the modified Newton-Raphson
+method will
+
+converge a little slower than
+the full Newton-Raphson
+
+method, but still faster than
+the initial stress method.
+
+Well, this then brings us to the
+end of the discussion of
+
+this example.
+
+I like to now introduce you to
+another scheme that can be
+
+very important when we solve
+nonlinear equations, finite
+
+element equations.
+
+And that scheme is the scheme
+of line searches.
+
+The basic equations that we are
+looking at that we want to
+
+solve are once more
+depicted here.
+
+Tangent stiffness matrix,
+incremental displacement
+
+vector, externally applied
+loads, nodal point forces
+
+corresponding to the internal
+element stresses at time t
+
+plus delta t, and at the end
+of iteration i minus 1,
+
+beginning of iteration
+i, of course.
+
+Notice I don't have an i on
+here, I just want to denote
+
+this for the moment as an
+incremental nodal point
+
+displacement vector, which
+carries, however, a bar.
+
+Let us consider forming Fi using
+this equation where beta
+
+is an unknown.
+
+We want to choose beta
+now judiciously.
+
+We want to choose beta such
+that, in some sense, R minus
+
+Fi is small.
+
+And we have to, of course, look
+at the mechanism that we
+
+use to make R minus F
+small in some sense.
+
+Well, as a side note, we
+recognize that when this
+
+equation here is 0 for all
+possible U's, then clearly
+
+this must be 0.
+
+In other words, if we were to
+say to ourselves, let's make
+
+this equation 0 for
+all possible U's.
+
+Then really, we would have
+solved this equal to 0.
+
+The reason, of course, for it
+is that we could choose here
+
+for U a vector, which carries
+0's everywhere except a 1 in
+
+one location.
+
+And if that is a particular
+row, then corresponding to
+
+that row, surely this vector
+here, this R minus F
+
+corresponding to that row
+must be equal to 0.
+
+So if we were simply to use here
+the identity matrix, or
+
+if we were to construct the
+identity matrix by allowing n
+
+U's that are linearly
+independent, of course,
+
+because they all make up such
+vector but with a 1 in a
+
+different location.
+
+As a matter of fact, we want to
+use U1 with a 1 here, 0's
+
+everywhere.
+
+U2, 1 here, 0 here, everywhere
+else 0, and so on.
+
+To construct an identity
+matrix here.
+
+Then with that identity matrix,
+clearly R minus F
+
+would be 0 everywhere.
+
+Of course, that is not a
+viable scheme really.
+
+But what we want to do is to
+choose a particular vector
+
+here so as to make R minus
+F still 0 in some sense.
+
+And the vector that is quite
+effectively chosen is the
+
+vector that we obtain from the
+solution of K delta U bar
+
+equals R minus F.
+
+If we use that vector here,
+basically projecting the R,
+
+capital R, minus F
+onto that vector.
+
+And we look for this to be 0.
+
+Then we have so to say, searched
+in the direction of
+
+delta U bar and made delta U
+bar transposed times this
+
+vector here equal to 0.
+
+How does this scheme work?
+
+Well, we add beta times delta U
+bar to the value that we had
+
+already from the previous
+iteration.
+
+And we search along beta such
+that this top here is much
+
+smaller than the bottom.
+
+In other words, STOL shall be
+a convergence tolerance.
+
+Notice the way it works.
+
+We choose a value of beta.
+
+With beta known, we add this
+quantity to this one.
+
+We get a value here.
+
+We take this value, calculate
+Fi corresponding to that
+
+value, see whether
+the convergence
+
+tolerance is satisfied.
+
+If not, we have to choose
+a new beta.
+
+And like that, we choose new
+betas until we have satisfied
+
+this convergence tolerance.
+
+That's what we call
+line search.
+
+We are searching along the
+line given by delta U bar
+
+until this is satisfied.
+
+It's a very important scheme,
+and this scheme can be
+
+combined with modified Newton
+iteration, with the initial
+
+stress method, and with
+full Newton iteration.
+
+And it adds a lot to the
+stability of the solution, of
+
+the overall solution or the
+nonlinear equations.
+
+We will find, or discuss
+applications just now.
+
+But at this point, we need to
+stop for a minute because we
+
+need to go onto a new tape.
+
+Finally, I would like to discuss
+with you a method that
+
+we also find to be very
+effective in nonlinear finite
+
+element computations.
+
+Namely, the BFGS method.
+
+BFGS stands for Broyden-Fletcher
+
+-Goldfarb-Shanno.
+
+And in this method, we
+proceed as follows.
+
+We calculate or define
+a delta i as shown
+
+here in this equation.
+
+And we define a gamma i as
+shown in this equation.
+
+We want to calculate the
+coefficient matrix such that
+
+this equation is
+here satisfied.
+
+In other words, given delta i
+and gamma i, we want to use
+
+the coefficient matrix that
+satisfies this equation.
+
+And that's basically what's
+being done in the BFGS scheme.
+
+Pictorially then, we can show
+for a single degree of freedom
+
+system, say the F plotted
+along this axis.
+
+The U displacements plotted
+along this axis.
+
+Notice here in green
+we show delta i.
+
+And we show here in
+green gamma i.
+
+And notice that the matrix
+that we want to use is
+
+indicated by this blue slope.
+
+Which is, in other words, given
+by delta i and gamma i.
+
+Well, the BFGS method is an
+iterative algorithm, which
+
+produces successive
+approximations to efficient
+
+stiffness matrix.
+
+Actually, we actually work
+with the inverse of that
+
+stiffness matrix as I will
+elaborate upon just now.
+
+It's really a compromise
+between the full Newton
+
+iteration method and
+the modified
+
+Newton iteration method.
+
+It shows very excellent
+convergence characteristics in
+
+the solution of many
+types of problems.
+
+Let's look at the individual
+steps that we use when we
+
+apply the BFGS method.
+
+We, first of all, calculate
+the direction of the
+
+displacement increment.
+
+Here we have delta U bar i is
+equal to K inverse, the
+
+inverse of the K matrix,
+corresponding to
+
+iteration i minus 1.
+
+And here we have the out
+of balance load vector.
+
+Notice once again we do not
+calculate actually an inverse
+
+of a matrix.
+
+We calculate the LDL transpose
+factorization of a matrix, and
+
+then we, as I will just now
+show, update that inverse in
+
+the BFGS iteration by specific
+matrices of rank 2.
+
+We get to that just now.
+
+Well, having calculated this
+delta U bar i, we use that
+
+delta U bar i in the line search
+to obtain a better
+
+displacement vector, a
+displacement vector
+
+corresponding to iteration i.
+
+A better value then just adding
+the delta U bar i to it
+
+by adjusting beta.
+
+In other words, we choose beta
+in such way as to satisfy this
+
+equation here.
+
+This is, of course, the equation
+that we are now
+
+familiar with as being equation
+that shows that
+
+convergence has been reached
+in a line search.
+
+Having now calculated the t
+plus delta t Ui and the
+
+corresponding t plus delta t Fi,
+we can calculate the delta
+
+i and gamma i.
+
+And therefore, apply
+the BFGS method.
+
+And that's now step three,
+calculation of
+
+the new secant matrix.
+
+K inverse of iteration i is
+equal to Ai transposed k
+
+inverse of iteration
+i minus 1 times Ai.
+
+This A matrix is obtained
+as shown here.
+
+v wi transposed.
+
+The vi and wi's are given as a
+function of the delta i, gamma
+
+i, and K i minus 1 value.
+
+You should look at the textbook
+to see the details of
+
+actually evaluating
+the vi and wi.
+
+But once you have vi, wi, you
+can calculate A. And clearly,
+
+by this equation then, you get
+a new stiffness matrix.
+
+It is important to note that in
+this iterative scheme, only
+
+vector products are needed
+to obtain vi and wi.
+
+And it's also then important
+to note that only vector
+
+products are used to calculate
+delta U bar i.
+
+If this would not be the case,
+particularly here.
+
+Then of course, the
+iterative scheme
+
+would be very expensive.
+
+Let me show you a bit of the
+details why we only need to
+
+use vector products to
+get the solution.
+
+Here, we have one typical
+step of the iteration.
+
+Notice on the left-hand side,
+we have delta U bar i.
+
+The value of displacement
+increment
+
+that we want to calculate.
+
+On the right-hand side, we
+have i plus wi minus 1 vi
+
+minus 1 transposed.
+
+In other words, the Ai
+minus 1 transposed.
+
+And we would have such matrices
+going on here until
+
+we are coming to the A1
+transposed matrix.
+
+Then we have the inverse
+of a stiffness matrix.
+
+Here, corresponding
+to time tau.
+
+And then we have the Ai matrices
+as shown here.
+
+Now, notice that this total
+amount then is multiplied by
+
+the R minus F i minus 1, the
+out of balance load vector.
+
+Let's now go through the
+computations that are required
+
+to get delta U bar i.
+
+Here we have delta R. This delta
+R, the out of balance
+
+load vector, which I
+just call delta R,
+
+multiplies this matrix.
+
+But if you look at this
+multiplication, we find that
+
+this delta R times w i minus 1
+transposed is simply a number.
+
+So it's one vector
+multiplication
+
+that gives us a number.
+
+This number multiplied by
+v i minus 1 is just the
+
+multiplication of a number
+times a vector.
+
+It's very simple.
+
+And notice, of course, this
+delta R i minus 1 is also
+
+multiplying the identity
+matrix.
+
+So in this step here, we have
+really nothing else then a
+
+vector multiplication.
+
+The only vector multiplication
+that, in fact, is there, is
+
+this value, this vector here,
+times that vector there,
+
+transposed.
+
+That gives us a number.
+
+This number times a vector
+[UNINTELLIGIBLE]
+
+operation.
+
+And of course, this one here
+times the i matrix is just
+
+this vector by itself.
+
+So in this step, what
+we obtain is
+
+simply another vector.
+
+We take this vector and
+repeat the process.
+
+And since the repetition is
+just what we discussed
+
+already, we find that we only
+need vector multiplications to
+
+roll up all of these
+multiplications up to here.
+
+Then we have a vector multiplied
+by K inverse.
+
+Well, that involves only vector
+multiplications again,
+
+because we have already
+the LDL transposed
+
+factorization of tau k.
+
+These vector multiplications
+result again, in a vector.
+
+And that vector multiplied by
+these matrices here in the
+
+same way as we have proceeded
+here, means again, only vector
+
+multiplications.
+
+So this very important step
+here only requires vector
+
+multiplications.
+
+And that makes this whole
+process really efficient.
+
+In summary then, we have the
+following solution procedures
+
+that we feel are
+very effective.
+
+The mortified Newton-Raphson
+iteration with line searches.
+
+Here we have the basic modified
+
+Newton iteration equation.
+
+And here we have the line
+search equation.
+
+We, of course, after each such
+solution, evaluate an
+
+efficient beta.
+
+A beta that makes U--
+
+t plus delta U i a good vector
+when measured on the line
+
+search criteria the way
+I discussed it.
+
+And these two equations then,
+summarize really the modified
+
+Newton iteration with
+the line search.
+
+The BFGS method is another
+effective scheme.
+
+We use the BFGS method always
+with line searches.
+
+And then, as a third option,
+the full Newton-Raphson
+
+iteration with or without
+line searches.
+
+The full Newton-Raphson
+iteration with line searches
+
+is, of course, most powerful.
+
+But it is also most expensive
+per iteration.
+
+We should point out that these
+techniques that I discussed so
+
+far cannot be applied for
+post-buckling analysis.
+
+We will consider the solution of
+the response after buckling
+
+has been occurring, after the
+item load level has been
+
+reached in a forthcoming
+lecture.
+
+The next view graphs summarize
+these schemes: the modified
+
+Newton-Raphson, the BFGS
+method, and the full
+
+Newton-Raphson method.
+
+And I'd like to just very
+quickly go through the whole
+
+solution process for each
+of these methods.
+
+In the modified Newton iteration
+technique, we
+
+initialize our displacements
+corresponding to the beginning
+
+of the first iteration, the end
+of the 0 iteration as tU.
+
+And similarly, we initialize our
+force vector corresponding
+
+to the internal element
+stresses.
+
+We set i is equal to 1, the
+iteration counter equal to 1.
+
+We calculate a K matrix at the
+beginning of the load step,
+
+and we keep that K
+matrix constant.
+
+We then go into this step here
+where we calculate the out of
+
+balance loads.
+
+Calculate a new displacement
+vector.
+
+And in this box here, we
+measure whether we have
+
+converged already.
+
+Of course, this convergence
+would only be measured after
+
+we have gone say, at
+least twice through
+
+the iteration process.
+
+Or rather, we have calculated
+this increment in displacement
+
+vector twice.
+
+Because at the beginning
+corresponding to i equal to 1,
+
+we have now this fairly large
+out of balance load.
+
+We have just incremented
+the load vector.
+
+Therefore, this right inside
+should be non-zero.
+
+And we would get an increment
+in displacements.
+
+And to measure how large that
+increment in displacement is,
+
+we really want to go through
+this whole cycle at
+
+least one more time.
+
+We then, having calculated this
+incremental displacement
+
+vector with the bar on there,
+we perform a line search the
+
+way we discussed it to update
+our displacements
+
+corresponding to the
+iteration i.
+
+Of course, we only have come so
+far once through it, so i
+
+is equal to 1 still.
+
+And this gives us the accepted
+value of displacements
+
+corresponding to the
+first iteration.
+
+We now increment our iteration
+counter, and go in to the
+
+second iteration.
+
+Notice now in the second
+iteration, we have R minus t
+
+plus delta t F1 here.
+
+We calculate delta U bar 2.
+
+And now we would certainly
+measure convergence.
+
+And I will just now talk about
+how we measure convergence.
+
+If we have not converged yet,
+we keep on cycling through
+
+here until we do actually
+get convergence.
+
+The distinguishing feature of
+the modified Newton iteration
+
+is that we are having
+a constant K matrix.
+
+That we do not update
+the K matrix is this
+
+iterative loop here.
+
+It remains constant.
+
+Remember in the initial stress
+technique, initial stress
+
+method, we would not even update
+the K matrix ever after
+
+the first time it has
+been calculated.
+
+But in the modified Newton
+iteration, we update it at the
+
+beginning of each load step.
+
+In the BFGS method, we
+proceed as follows.
+
+We initial, again, our
+displacements and our nodal
+
+point force vector corresponding
+to the internal
+
+element stresses.
+
+We calculate tK.
+
+We calculate our incremental
+displacement vector with the
+
+bar on top.
+
+We measure convergence if i
+is greater or equal to.
+
+There's no point as I just
+mentioned, measuring
+
+convergence when you go first
+time through here.
+
+And we perform then the line
+search having calculated our
+
+actual incremental in nodal
+point displacement that we
+
+want to add to the previous
+nodal point displacements to
+
+get to this displacement
+vector.
+
+We, of course, also have
+this force vector.
+
+We now can update our inverse
+matrix, our inverse secret
+
+matrix the way we
+discussed it.
+
+And we increment our counter.
+
+And we keep on cycling through
+here until we find in this box
+
+that we have converged.
+
+In the full Newton iteration
+with line searches, we once
+
+again, initialize our
+displacement vector, our force
+
+vector, our iteration counter.
+
+We now calculate a new K matrix
+corresponding to the
+
+last conditions on displacements
+and internal
+
+forces, of course.
+
+We enter here to calculate our
+incremental displacement
+
+vector with the K matrix that
+was just evaluated.
+
+And we measure convergence
+once again only when i is
+
+greater equal to.
+
+We perform a line search to
+determine beta in here.
+
+We therefore, update our
+displacement vector to the
+
+displacements that now
+correspond to the end of
+
+iteration i.
+
+We update our iteration
+counter.
+
+Or rather, increase our
+iteration counter.
+
+And we are calculating a new
+stiffness matrix corresponding
+
+to the last calculated
+displacement.
+
+This is, of course, a
+distinguishing feature of the
+
+full Newton-Raphson method that
+we are calculating a new
+
+K matrix at the beginning
+of each iteration.
+
+Well, these view graphs then,
+summarize the full process of
+
+iteration for the modified
+Newton, the BFGS, and the full
+
+Newton method.
+
+Notice that I have included the
+line search as the option.
+
+If you don't have line
+searching, of course, it would
+
+simply mean that you set beta
+equal to 1, and skip that
+
+particular step of
+line searching.
+
+But in many cases, line
+searching is quite important.
+
+And certainly, can
+be necessary in
+
+some types of problems.
+
+Let us now look at what happens
+in this box here.
+
+How do we measure convergence?
+
+In each of these iterative
+schemes, we had such a box.
+
+And I like to look now more
+closely at how we measure
+
+convergence.
+
+The measure of convergence
+should, of course, tell us,
+
+how well do we satisfy
+equilibrium?
+
+And there are basically three
+items that can be used.
+
+Namely energy, force, or moment,
+displacement, and
+
+rotation, of course,
+correspondingly as well.
+
+But these are the items that one
+can work with to measure
+
+convergence.
+
+If you use an energy convergence
+criteria, and we
+
+are very fond of this one.
+
+You might want to use this
+equation here delta U bar i
+
+transposed times the out of
+balance load divided by delta
+
+U bar 1 transposed times t
+plus delta t R minus tF.
+
+Now notice, this is the
+increment in nodal point
+
+forces, or the out of
+balance load, at the
+
+beginning of the load step.
+
+So this here is an energy
+corresponding to the beginning
+
+of the load step.
+
+And we are comparing here
+a similar quantity, but
+
+corresponding to the
+current load.
+
+Corresponding to the
+current iteration.
+
+And if this quotient here is
+very small measured on that
+
+convergence tolerance, then
+we say we have converged.
+
+An important point is that in
+this convergence measure, we
+
+enter with displacements and
+with out of balance loads.
+
+Both enter in this convergence
+measure.
+
+And please realize also that
+if the loads don't increase
+
+from time t to t plus delta t,
+meaning that this here is
+
+equal to 0--
+
+0 vector.
+
+Then, of course, we
+get 0 down here.
+
+And we could not apply this
+convergence criteria
+
+indirectly.
+
+Therefore, we would do is
+instead of 0 here, a
+
+reasonable small number in
+the computer program.
+
+Also note that we apply
+this test here
+
+prior to line searching.
+
+In line searching, after line
+searching of course, this top
+
+part here is small.
+
+And we, therefore, do not want
+to apply this scheme here or
+
+this convergence measure
+after line searching.
+
+We should do it before
+line searching.
+
+To measure convergence on
+forces, we can use this
+
+equation here.
+
+Notice here we have the
+out of balance loads.
+
+We take the Euclidean norm on
+the out of balance loads, and
+
+we compare that with
+RNORM, input by the
+
+user, by the analyst.
+
+It is interesting, important to
+note that we introduce here
+
+only the components
+corresponding to the
+
+translational degrees
+of freedom.
+
+And here, of course, this
+RNORM is also a force
+
+corresponding, so to say, to a
+
+translational degree of freedom.
+
+If we have also rotational
+degrees of freedom, then we
+
+would take instead
+of RNORM, RMNORM.
+
+And we would extract from these
+vectors, the components
+
+corresponding to the rotational
+
+degrees of freedom only.
+
+The point is that we want to
+have the same units up
+
+here as down here.
+
+Forces, forces, moments,
+moments.
+
+And we don't want to mix
+components from these
+
+quantities.
+
+Of course, RMNORM and RNORM must
+be chosen by the analyst.
+
+The are input to the analysis as
+defined in the input to the
+
+computer program.
+
+Typically, RTOL is 0.01.
+
+RNORM is simply the maximum
+of the NORM of the
+
+loads that are applied.
+
+Notice this Euclidean norm is
+evaluated as shown down here
+
+for a vector a.
+
+The symbolism, two bars each
+side with a 2 means nothing
+
+else then taking the squares of
+all the components of the
+
+vector, adding those
+squares up.
+
+And then, taking the square
+root out of that addition.
+
+On displacements, we can also
+measure convergence.
+
+And here is the equation
+that can be used.
+
+The Euclidean norm on
+the incremental
+
+displacement vector.
+
+And that is compared
+with DNORM.
+
+Again, DNORM.
+
+Notice that this here is again,
+input by the analyst to
+
+the computer program.
+
+It is part of the input that is
+provided for the analysis.
+
+And it's a reference
+displacement.
+
+Notice then, of course, we
+should only include here the
+
+displacements, translational
+displacements in other words.
+
+If we have also, rotational
+degrees of freedom.
+
+Then we would here include only
+the rotational degrees of
+
+freedom components and
+use here DMNORM.
+
+This way again, we compare one
+quantity with certain units
+
+with a quantity that
+has the same units.
+
+Once for translations and
+once for rotations.
+
+And so when we have rotational
+degrees of freedom in the
+
+analysis, we this way make
+sure really, that the
+
+incremental displacements and
+incremental rotations are
+
+small at convergence.
+
+This then completes what I
+wanted to share with you in
+
+this lecture.
+
+Thank you very much for
+your attention.
\ No newline at end of file
diff --git a/CdrVM6MGnGo.txt b/CdrVM6MGnGo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3bc656852a287f099d1580db2bcf81bfdd188f7f
--- /dev/null
+++ b/CdrVM6MGnGo.txt
@@ -0,0 +1,779 @@
+align:start position:0%
+ 
+least mean squares estimation is
+
+ align:start position:0%
+least mean squares estimation is
+ 
+
+ align:start position:0%
+least mean squares estimation is
+remarkable because it has such a simple
+
+ align:start position:0%
+remarkable because it has such a simple
+ 
+
+ align:start position:0%
+remarkable because it has such a simple
+answer the way to come up with estimates
+
+ align:start position:0%
+answer the way to come up with estimates
+ 
+
+ align:start position:0%
+answer the way to come up with estimates
+if what you care about is to keep the
+
+ align:start position:0%
+if what you care about is to keep the
+ 
+
+ align:start position:0%
+if what you care about is to keep the
+mean squared error small the way to come
+
+ align:start position:0%
+mean squared error small the way to come
+ 
+
+ align:start position:0%
+mean squared error small the way to come
+up with estimates is to just report the
+
+ align:start position:0%
+up with estimates is to just report the
+ 
+
+ align:start position:0%
+up with estimates is to just report the
+conditional expectation which is going
+
+ align:start position:0%
+conditional expectation which is going
+ 
+
+ align:start position:0%
+conditional expectation which is going
+to be a number once you have obtained
+
+ align:start position:0%
+to be a number once you have obtained
+ 
+
+ align:start position:0%
+to be a number once you have obtained
+some values of the data or more
+
+ align:start position:0%
+some values of the data or more
+ 
+
+ align:start position:0%
+some values of the data or more
+abstractly you can think of it as a
+
+ align:start position:0%
+abstractly you can think of it as a
+ 
+
+ align:start position:0%
+abstractly you can think of it as a
+random variable if you do not know ahead
+
+ align:start position:0%
+random variable if you do not know ahead
+ 
+
+ align:start position:0%
+random variable if you do not know ahead
+of time what data you're going to obtain
+
+ align:start position:0%
+of time what data you're going to obtain
+ 
+
+ align:start position:0%
+of time what data you're going to obtain
+because this estimator is so important
+
+ align:start position:0%
+because this estimator is so important
+ 
+
+ align:start position:0%
+because this estimator is so important
+it is worth writing down what the
+
+ align:start position:0%
+it is worth writing down what the
+ 
+
+ align:start position:0%
+it is worth writing down what the
+performance of that estimator is so
+
+ align:start position:0%
+performance of that estimator is so
+ 
+
+ align:start position:0%
+performance of that estimator is so
+suppose that you have obtained a
+
+ align:start position:0%
+suppose that you have obtained a
+ 
+
+ align:start position:0%
+suppose that you have obtained a
+particular measurement a particular
+
+ align:start position:0%
+particular measurement a particular
+ 
+
+ align:start position:0%
+particular measurement a particular
+value of the observation then the
+
+ align:start position:0%
+value of the observation then the
+ 
+
+ align:start position:0%
+value of the observation then the
+resulting mean squared error within that
+
+ align:start position:0%
+resulting mean squared error within that
+ 
+
+ align:start position:0%
+resulting mean squared error within that
+conditional universe where you have
+
+ align:start position:0%
+conditional universe where you have
+ 
+
+ align:start position:0%
+conditional universe where you have
+already obtained that value is just this
+
+ align:start position:0%
+already obtained that value is just this
+ 
+
+ align:start position:0%
+already obtained that value is just this
+quantity it's the mean square of the
+
+ align:start position:0%
+quantity it's the mean square of the
+ 
+
+ align:start position:0%
+quantity it's the mean square of the
+error between the variable that you're
+
+ align:start position:0%
+error between the variable that you're
+ 
+
+ align:start position:0%
+error between the variable that you're
+trying to estimate and your estimate and
+
+ align:start position:0%
+trying to estimate and your estimate and
+ 
+
+ align:start position:0%
+trying to estimate and your estimate and
+everything gets computed within this
+
+ align:start position:0%
+everything gets computed within this
+ 
+
+ align:start position:0%
+everything gets computed within this
+conditional universe now this is a very
+
+ align:start position:0%
+conditional universe now this is a very
+ 
+
+ align:start position:0%
+conditional universe now this is a very
+familiar quantity however it's the
+
+ align:start position:0%
+familiar quantity however it's the
+ 
+
+ align:start position:0%
+familiar quantity however it's the
+expected value of a random variable
+
+ align:start position:0%
+expected value of a random variable
+ 
+
+ align:start position:0%
+expected value of a random variable
+difference from its mean squared this is
+
+ align:start position:0%
+difference from its mean squared this is
+ 
+
+ align:start position:0%
+difference from its mean squared this is
+just a variance except that because all
+
+ align:start position:0%
+just a variance except that because all
+ 
+
+ align:start position:0%
+just a variance except that because all
+quantities are calculated in a
+
+ align:start position:0%
+quantities are calculated in a
+ 
+
+ align:start position:0%
+quantities are calculated in a
+conditional universe this is the
+
+ align:start position:0%
+conditional universe this is the
+ 
+
+ align:start position:0%
+conditional universe this is the
+conditional variance so the conditional
+
+ align:start position:0%
+conditional variance so the conditional
+ 
+
+ align:start position:0%
+conditional variance so the conditional
+variance is the optimal mean squared
+
+ align:start position:0%
+variance is the optimal mean squared
+ 
+
+ align:start position:0%
+variance is the optimal mean squared
+error the mean squared error that you
+
+ align:start position:0%
+error the mean squared error that you
+ 
+
+ align:start position:0%
+error the mean squared error that you
+obtain when you use this particular
+
+ align:start position:0%
+obtain when you use this particular
+ 
+
+ align:start position:0%
+obtain when you use this particular
+estimate and it's the value that you
+
+ align:start position:0%
+estimate and it's the value that you
+ 
+
+ align:start position:0%
+estimate and it's the value that you
+would report to your boss if you were
+
+ align:start position:0%
+would report to your boss if you were
+ 
+
+ align:start position:0%
+would report to your boss if you were
+asked how good is the estimate that you
+
+ align:start position:0%
+asked how good is the estimate that you
+ 
+
+ align:start position:0%
+asked how good is the estimate that you
+are giving me but suppose that you have
+
+ align:start position:0%
+are giving me but suppose that you have
+ 
+
+ align:start position:0%
+are giving me but suppose that you have
+not yet obtained a measurement but you
+
+ align:start position:0%
+not yet obtained a measurement but you
+ 
+
+ align:start position:0%
+not yet obtained a measurement but you
+are going to your boss and you're
+
+ align:start position:0%
+are going to your boss and you're
+ 
+
+ align:start position:0%
+are going to your boss and you're
+proposing this particular estimator is
+
+ align:start position:0%
+proposing this particular estimator is
+ 
+
+ align:start position:0%
+proposing this particular estimator is
+your design what are you going to report
+
+ align:start position:0%
+your design what are you going to report
+ 
+
+ align:start position:0%
+your design what are you going to report
+to your boss is the performance of your
+
+ align:start position:0%
+to your boss is the performance of your
+ 
+
+ align:start position:0%
+to your boss is the performance of your
+design since you have not yet obtained
+
+ align:start position:0%
+design since you have not yet obtained
+ 
+
+ align:start position:0%
+design since you have not yet obtained
+the value of X X is the random variable
+
+ align:start position:0%
+the value of X X is the random variable
+ 
+
+ align:start position:0%
+the value of X X is the random variable
+you do not know what the value of this
+
+ align:start position:0%
+you do not know what the value of this
+ 
+
+ align:start position:0%
+you do not know what the value of this
+conditional expectation is going to be
+
+ align:start position:0%
+conditional expectation is going to be
+ 
+
+ align:start position:0%
+conditional expectation is going to be
+it's a random variable but no matter
+
+ align:start position:0%
+it's a random variable but no matter
+ 
+
+ align:start position:0%
+it's a random variable but no matter
+what it is this is going to be the error
+
+ align:start position:0%
+what it is this is going to be the error
+ 
+
+ align:start position:0%
+what it is this is going to be the error
+that you're going to be obtained
+
+ align:start position:0%
+that you're going to be obtained
+ 
+
+ align:start position:0%
+that you're going to be obtained
+and this is the overall value of the
+
+ align:start position:0%
+and this is the overall value of the
+ 
+
+ align:start position:0%
+and this is the overall value of the
+mean squared error so this is the
+
+ align:start position:0%
+mean squared error so this is the
+ 
+
+ align:start position:0%
+mean squared error so this is the
+quantity that you would report to your
+
+ align:start position:0%
+quantity that you would report to your
+ 
+
+ align:start position:0%
+quantity that you would report to your
+boss as your overall mean squared error
+
+ align:start position:0%
+boss as your overall mean squared error
+ 
+
+ align:start position:0%
+boss as your overall mean squared error
+the value that you report before
+
+ align:start position:0%
+the value that you report before
+ 
+
+ align:start position:0%
+the value that you report before
+obtaining any specific measurement now
+
+ align:start position:0%
+obtaining any specific measurement now
+ 
+
+ align:start position:0%
+obtaining any specific measurement now
+what is this quantity this quantity is
+
+ align:start position:0%
+what is this quantity this quantity is
+ 
+
+ align:start position:0%
+what is this quantity this quantity is
+just the average of this quantity up
+
+ align:start position:0%
+just the average of this quantity up
+ 
+
+ align:start position:0%
+just the average of this quantity up
+here averaged over all the possible
+
+ align:start position:0%
+here averaged over all the possible
+ 
+
+ align:start position:0%
+here averaged over all the possible
+values of X and in our more abstract
+
+ align:start position:0%
+values of X and in our more abstract
+ 
+
+ align:start position:0%
+values of X and in our more abstract
+notation it is just the expectation of
+
+ align:start position:0%
+notation it is just the expectation of
+ 
+
+ align:start position:0%
+notation it is just the expectation of
+the conditional variance the conditional
+
+ align:start position:0%
+the conditional variance the conditional
+ 
+
+ align:start position:0%
+the conditional variance the conditional
+variance the abstract conditional
+
+ align:start position:0%
+variance the abstract conditional
+ 
+
+ align:start position:0%
+variance the abstract conditional
+variance is a random variable that takes
+
+ align:start position:0%
+variance is a random variable that takes
+ 
+
+ align:start position:0%
+variance is a random variable that takes
+this value whenever capital X happens to
+
+ align:start position:0%
+this value whenever capital X happens to
+ 
+
+ align:start position:0%
+this value whenever capital X happens to
+be equal to little X and when we average
+
+ align:start position:0%
+be equal to little X and when we average
+ 
+
+ align:start position:0%
+be equal to little X and when we average
+it over all possible values of X we just
+
+ align:start position:0%
+it over all possible values of X we just
+ 
+
+ align:start position:0%
+it over all possible values of X we just
+have the expectation of this random
+
+ align:start position:0%
+have the expectation of this random
+ 
+
+ align:start position:0%
+have the expectation of this random
+variable let me continue now with a few
+
+ align:start position:0%
+variable let me continue now with a few
+ 
+
+ align:start position:0%
+variable let me continue now with a few
+more comments on LMS estimation first
+
+ align:start position:0%
+more comments on LMS estimation first
+ 
+
+ align:start position:0%
+more comments on LMS estimation first
+something that should be pretty clear at
+
+ align:start position:0%
+something that should be pretty clear at
+ 
+
+ align:start position:0%
+something that should be pretty clear at
+this point is that LMS estimation is
+
+ align:start position:0%
+this point is that LMS estimation is
+ 
+
+ align:start position:0%
+this point is that LMS estimation is
+only relevant to estimation problems
+
+ align:start position:0%
+only relevant to estimation problems
+ 
+
+ align:start position:0%
+only relevant to estimation problems
+this is because in hypothesis testing
+
+ align:start position:0%
+this is because in hypothesis testing
+ 
+
+ align:start position:0%
+this is because in hypothesis testing
+problems we typically care about the
+
+ align:start position:0%
+problems we typically care about the
+ 
+
+ align:start position:0%
+problems we typically care about the
+probability of error not the mean
+
+ align:start position:0%
+probability of error not the mean
+ 
+
+ align:start position:0%
+probability of error not the mean
+squared error a second important comment
+
+ align:start position:0%
+squared error a second important comment
+ 
+
+ align:start position:0%
+squared error a second important comment
+is that in some cases the LMS estimates
+
+ align:start position:0%
+is that in some cases the LMS estimates
+ 
+
+ align:start position:0%
+is that in some cases the LMS estimates
+and the map estimates turn out to be the
+
+ align:start position:0%
+and the map estimates turn out to be the
+ 
+
+ align:start position:0%
+and the map estimates turn out to be the
+same when is that the case if the
+
+ align:start position:0%
+same when is that the case if the
+ 
+
+ align:start position:0%
+same when is that the case if the
+posterior distribution of theta happens
+
+ align:start position:0%
+posterior distribution of theta happens
+ 
+
+ align:start position:0%
+posterior distribution of theta happens
+to have a single peak and it is also
+
+ align:start position:0%
+to have a single peak and it is also
+ 
+
+ align:start position:0%
+to have a single peak and it is also
+symmetric around a certain point so that
+
+ align:start position:0%
+symmetric around a certain point so that
+ 
+
+ align:start position:0%
+symmetric around a certain point so that
+the peak also occurs at that particular
+
+ align:start position:0%
+the peak also occurs at that particular
+ 
+
+ align:start position:0%
+the peak also occurs at that particular
+point then clearly the peak occurs here
+
+ align:start position:0%
+point then clearly the peak occurs here
+ 
+
+ align:start position:0%
+point then clearly the peak occurs here
+but the conditional expectation is also
+
+ align:start position:0%
+but the conditional expectation is also
+ 
+
+ align:start position:0%
+but the conditional expectation is also
+that same point because it is the center
+
+ align:start position:0%
+that same point because it is the center
+ 
+
+ align:start position:0%
+that same point because it is the center
+of symmetry so in those cases the two
+
+ align:start position:0%
+of symmetry so in those cases the two
+ 
+
+ align:start position:0%
+of symmetry so in those cases the two
+types of estimates or estimators
+
+ align:start position:0%
+types of estimates or estimators
+ 
+
+ align:start position:0%
+types of estimates or estimators
+coincide when does this happen
+
+ align:start position:0%
+coincide when does this happen
+ 
+
+ align:start position:0%
+coincide when does this happen
+this happens in one particular important
+
+ align:start position:0%
+this happens in one particular important
+ 
+
+ align:start position:0%
+this happens in one particular important
+special case we have seen that in linear
+
+ align:start position:0%
+special case we have seen that in linear
+ 
+
+ align:start position:0%
+special case we have seen that in linear
+normal models the posterior distribution
+
+ align:start position:0%
+normal models the posterior distribution
+ 
+
+ align:start position:0%
+normal models the posterior distribution
+is normal and so this is one
+
+ align:start position:0%
+is normal and so this is one
+ 
+
+ align:start position:0%
+is normal and so this is one
+is where the map estimate and the LMS
+
+ align:start position:0%
+is where the map estimate and the LMS
+ 
+
+ align:start position:0%
+is where the map estimate and the LMS
+estimates are going to coincide
\ No newline at end of file
diff --git a/DJO6ilwbWiI.txt b/DJO6ilwbWiI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..523f8d2d99fc86a5c05e885346ef5fcf3359cd03
--- /dev/null
+++ b/DJO6ilwbWiI.txt
@@ -0,0 +1,3475 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ 
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi in our lesson last time we showed
+
+ align:start position:0%
+hi in our lesson last time we showed
+ 
+
+ align:start position:0%
+hi in our lesson last time we showed
+that to find the general solution of a
+
+ align:start position:0%
+that to find the general solution of a
+ 
+
+ align:start position:0%
+that to find the general solution of a
+linear differential equation we first
+
+ align:start position:0%
+linear differential equation we first
+ 
+
+ align:start position:0%
+linear differential equation we first
+looked for the general solution of the
+
+ align:start position:0%
+looked for the general solution of the
+ 
+
+ align:start position:0%
+looked for the general solution of the
+homogeneous or reduced equation that is
+
+ align:start position:0%
+homogeneous or reduced equation that is
+ 
+
+ align:start position:0%
+homogeneous or reduced equation that is
+the equation where the right hand side
+
+ align:start position:0%
+the equation where the right hand side
+ 
+
+ align:start position:0%
+the equation where the right hand side
+was zero and then found a particular
+
+ align:start position:0%
+was zero and then found a particular
+ 
+
+ align:start position:0%
+was zero and then found a particular
+solution of the original equation and
+
+ align:start position:0%
+solution of the original equation and
+ 
+
+ align:start position:0%
+solution of the original equation and
+then the sum of these two solutions
+
+ align:start position:0%
+then the sum of these two solutions
+ 
+
+ align:start position:0%
+then the sum of these two solutions
+would be the general solution
+
+ align:start position:0%
+would be the general solution
+ 
+
+ align:start position:0%
+would be the general solution
+consequently we agreed that we would now
+
+ align:start position:0%
+consequently we agreed that we would now
+ 
+
+ align:start position:0%
+consequently we agreed that we would now
+separate our study into two parts one to
+
+ align:start position:0%
+separate our study into two parts one to
+ 
+
+ align:start position:0%
+separate our study into two parts one to
+find a general solution of the reduced
+
+ align:start position:0%
+find a general solution of the reduced
+ 
+
+ align:start position:0%
+find a general solution of the reduced
+or homogeneous equation and the other to
+
+ align:start position:0%
+or homogeneous equation and the other to
+ 
+
+ align:start position:0%
+or homogeneous equation and the other to
+find a particular solution of the given
+
+ align:start position:0%
+find a particular solution of the given
+ 
+
+ align:start position:0%
+find a particular solution of the given
+equation in today's lesson we are going
+
+ align:start position:0%
+equation in today's lesson we are going
+ 
+
+ align:start position:0%
+equation in today's lesson we are going
+to tackle the problem of finding the
+
+ align:start position:0%
+to tackle the problem of finding the
+ 
+
+ align:start position:0%
+to tackle the problem of finding the
+general solution of the homogeneous
+
+ align:start position:0%
+general solution of the homogeneous
+ 
+
+ align:start position:0%
+general solution of the homogeneous
+equation but subject to a very special
+
+ align:start position:0%
+equation but subject to a very special
+ 
+
+ align:start position:0%
+equation but subject to a very special
+case special in the sense that it's easy
+
+ align:start position:0%
+case special in the sense that it's easy
+ 
+
+ align:start position:0%
+case special in the sense that it's easy
+to handle but also special in the sense
+
+ align:start position:0%
+to handle but also special in the sense
+ 
+
+ align:start position:0%
+to handle but also special in the sense
+that many practical applications live up
+
+ align:start position:0%
+that many practical applications live up
+ 
+
+ align:start position:0%
+that many practical applications live up
+to this particular model what we're
+
+ align:start position:0%
+to this particular model what we're
+ 
+
+ align:start position:0%
+to this particular model what we're
+going to tackle today is solving the
+
+ align:start position:0%
+going to tackle today is solving the
+ 
+
+ align:start position:0%
+going to tackle today is solving the
+linear equation L of yal 0 subject to
+
+ align:start position:0%
+linear equation L of yal 0 subject to
+ 
+
+ align:start position:0%
+linear equation L of yal 0 subject to
+the condition that we have constant
+
+ align:start position:0%
+the condition that we have constant
+ 
+
+ align:start position:0%
+the condition that we have constant
+coefficients in other words we are going
+
+ align:start position:0%
+coefficients in other words we are going
+ 
+
+ align:start position:0%
+coefficients in other words we are going
+to deal with Y Prime + 2 a y Prime + b y
+
+ align:start position:0%
+to deal with Y Prime + 2 a y Prime + b y
+ 
+
+ align:start position:0%
+to deal with Y Prime + 2 a y Prime + b y
+equals z where A and B are constants the
+
+ align:start position:0%
+equals z where A and B are constants the
+ 
+
+ align:start position:0%
+equals z where A and B are constants the
+only reason I put the two in here is to
+
+ align:start position:0%
+only reason I put the two in here is to
+ 
+
+ align:start position:0%
+only reason I put the two in here is to
+simplify some algebra later on after all
+
+ align:start position:0%
+simplify some algebra later on after all
+ 
+
+ align:start position:0%
+simplify some algebra later on after all
+if a is an arbitrary constant so is 2 a
+
+ align:start position:0%
+if a is an arbitrary constant so is 2 a
+ 
+
+ align:start position:0%
+if a is an arbitrary constant so is 2 a
+we'll talk about that in more detail
+
+ align:start position:0%
+we'll talk about that in more detail
+ 
+
+ align:start position:0%
+we'll talk about that in more detail
+when where I need it the thing is that
+
+ align:start position:0%
+when where I need it the thing is that
+ 
+
+ align:start position:0%
+when where I need it the thing is that
+to solve an equation of this particular
+
+ align:start position:0%
+to solve an equation of this particular
+ 
+
+ align:start position:0%
+to solve an equation of this particular
+type where A and B are constants we
+
+ align:start position:0%
+type where A and B are constants we
+ 
+
+ align:start position:0%
+type where A and B are constants we
+essentially try for a solution in the
+
+ align:start position:0%
+essentially try for a solution in the
+ 
+
+ align:start position:0%
+essentially try for a solution in the
+form yal e to the RX recalling that when
+
+ align:start position:0%
+form yal e to the RX recalling that when
+ 
+
+ align:start position:0%
+form yal e to the RX recalling that when
+we differentiate this we get r e to the
+
+ align:start position:0%
+we differentiate this we get r e to the
+ 
+
+ align:start position:0%
+we differentiate this we get r e to the
+RX when we differentiate a second time
+
+ align:start position:0%
+RX when we differentiate a second time
+ 
+
+ align:start position:0%
+RX when we differentiate a second time
+we get R 2 e to the RX consequently
+
+ align:start position:0%
+we get R 2 e to the RX consequently
+ 
+
+ align:start position:0%
+we get R 2 e to the RX consequently
+substituting this into here we get that
+
+ align:start position:0%
+substituting this into here we get that
+ 
+
+ align:start position:0%
+substituting this into here we get that
+e to the RX is a constant factor and
+
+ align:start position:0%
+e to the RX is a constant factor and
+ 
+
+ align:start position:0%
+e to the RX is a constant factor and
+we're then left with a polinomial in r
+
+ align:start position:0%
+we're then left with a polinomial in r
+ 
+
+ align:start position:0%
+we're then left with a polinomial in r
+equal to r^ 2 + 2 a r + B in other words
+
+ align:start position:0%
+equal to r^ 2 + 2 a r + B in other words
+ 
+
+ align:start position:0%
+equal to r^ 2 + 2 a r + B in other words
+mechanically notice that the power of R
+
+ align:start position:0%
+mechanically notice that the power of R
+ 
+
+ align:start position:0%
+mechanically notice that the power of R
+replaces the given derivative R 2
+
+ align:start position:0%
+replaces the given derivative R 2
+ 
+
+ align:start position:0%
+replaces the given derivative R 2
+replaces y Prime R to the first Power
+
+ align:start position:0%
+replaces y Prime R to the first Power
+ 
+
+ align:start position:0%
+replaces y Prime R to the first Power
+replaces y Prime and this is the r to
+
+ align:start position:0%
+replaces y Prime and this is the r to
+ 
+
+ align:start position:0%
+replaces y Prime and this is the r to
+the zero term replaces the zero
+
+ align:start position:0%
+the zero term replaces the zero
+ 
+
+ align:start position:0%
+the zero term replaces the zero
+derivative term namely the zeroth
+
+ align:start position:0%
+derivative term namely the zeroth
+ 
+
+ align:start position:0%
+derivative term namely the zeroth
+derivative is y itself at any rate since
+
+ align:start position:0%
+derivative is y itself at any rate since
+ 
+
+ align:start position:0%
+derivative is y itself at any rate since
+e to the RX cannot be zero to find the
+
+ align:start position:0%
+e to the RX cannot be zero to find the
+ 
+
+ align:start position:0%
+e to the RX cannot be zero to find the
+values of r that satisfy this equation
+
+ align:start position:0%
+values of r that satisfy this equation
+ 
+
+ align:start position:0%
+values of r that satisfy this equation
+then what we have to do is set this
+
+ align:start position:0%
+then what we have to do is set this
+ 
+
+ align:start position:0%
+then what we have to do is set this
+polinomial in this case a quadratic
+
+ align:start position:0%
+polinomial in this case a quadratic
+ 
+
+ align:start position:0%
+polinomial in this case a quadratic
+equation and notice of course if I had
+
+ align:start position:0%
+equation and notice of course if I had
+ 
+
+ align:start position:0%
+equation and notice of course if I had
+order greater than two the same Theory
+
+ align:start position:0%
+order greater than two the same Theory
+ 
+
+ align:start position:0%
+order greater than two the same Theory
+would hold I have simply as usual picked
+
+ align:start position:0%
+would hold I have simply as usual picked
+ 
+
+ align:start position:0%
+would hold I have simply as usual picked
+second order equations for illustrative
+
+ align:start position:0%
+second order equations for illustrative
+ 
+
+ align:start position:0%
+second order equations for illustrative
+purposes the exercises will take care of
+
+ align:start position:0%
+purposes the exercises will take care of
+ 
+
+ align:start position:0%
+purposes the exercises will take care of
+higher orders at any rate the values of
+
+ align:start position:0%
+higher orders at any rate the values of
+ 
+
+ align:start position:0%
+higher orders at any rate the values of
+R are determined by the equation r^2 + 2
+
+ align:start position:0%
+R are determined by the equation r^2 + 2
+ 
+
+ align:start position:0%
+R are determined by the equation r^2 + 2
+a r + B = 0 now you see if I use the
+
+ align:start position:0%
+a r + B = 0 now you see if I use the
+ 
+
+ align:start position:0%
+a r + B = 0 now you see if I use the
+quadratic formula and solve this
+
+ align:start position:0%
+quadratic formula and solve this
+ 
+
+ align:start position:0%
+quadratic formula and solve this
+equation for r i find that R is minus a
+
+ align:start position:0%
+equation for r i find that R is minus a
+ 
+
+ align:start position:0%
+equation for r i find that R is minus a
+plus or minus the square < TK of a^2
+
+ align:start position:0%
+plus or minus the square < TK of a^2
+ 
+
+ align:start position:0%
+plus or minus the square < TK of a^2
+minus B that's the reason I used 2 a
+
+ align:start position:0%
+minus B that's the reason I used 2 a
+ 
+
+ align:start position:0%
+minus B that's the reason I used 2 a
+instead of a here you see if I had used
+
+ align:start position:0%
+instead of a here you see if I had used
+ 
+
+ align:start position:0%
+instead of a here you see if I had used
+a here without the two then the
+
+ align:start position:0%
+a here without the two then the
+ 
+
+ align:start position:0%
+a here without the two then the
+quadratic formula would would have said
+
+ align:start position:0%
+quadratic formula would would have said
+ 
+
+ align:start position:0%
+quadratic formula would would have said
+R is equal to - A plus or minus the sare
+
+ align:start position:0%
+R is equal to - A plus or minus the sare
+ 
+
+ align:start position:0%
+R is equal to - A plus or minus the sare
+< TK of a^ 2 - 4 B over 2 a and with
+
+ align:start position:0%
+< TK of a^ 2 - 4 B over 2 a and with
+ 
+
+ align:start position:0%
+< TK of a^ 2 - 4 B over 2 a and with
+Blackboard space at a premium I hate to
+
+ align:start position:0%
+Blackboard space at a premium I hate to
+ 
+
+ align:start position:0%
+Blackboard space at a premium I hate to
+have to keep writing in a 2A as a
+
+ align:start position:0%
+have to keep writing in a 2A as a
+ 
+
+ align:start position:0%
+have to keep writing in a 2A as a
+denominator and every time I do that I
+
+ align:start position:0%
+denominator and every time I do that I
+ 
+
+ align:start position:0%
+denominator and every time I do that I
+lose a line of space on my board so for
+
+ align:start position:0%
+lose a line of space on my board so for
+ 
+
+ align:start position:0%
+lose a line of space on my board so for
+convenience sake I chose the two in here
+
+ align:start position:0%
+convenience sake I chose the two in here
+ 
+
+ align:start position:0%
+convenience sake I chose the two in here
+so I could write R this way now notice
+
+ align:start position:0%
+so I could write R this way now notice
+ 
+
+ align:start position:0%
+so I could write R this way now notice
+that in general this determines two
+
+ align:start position:0%
+that in general this determines two
+ 
+
+ align:start position:0%
+that in general this determines two
+values of r one with the positive square
+
+ align:start position:0%
+values of r one with the positive square
+ 
+
+ align:start position:0%
+values of r one with the positive square
+root one with the negative square root
+
+ align:start position:0%
+root one with the negative square root
+ 
+
+ align:start position:0%
+root one with the negative square root
+let me call R1 the root that I get with
+
+ align:start position:0%
+let me call R1 the root that I get with
+ 
+
+ align:start position:0%
+let me call R1 the root that I get with
+a positive sign R2 the root with a
+
+ align:start position:0%
+a positive sign R2 the root with a
+ 
+
+ align:start position:0%
+a positive sign R2 the root with a
+negative sign and the point that I want
+
+ align:start position:0%
+negative sign and the point that I want
+ 
+
+ align:start position:0%
+negative sign and the point that I want
+to mention is that the nature of the
+
+ align:start position:0%
+to mention is that the nature of the
+ 
+
+ align:start position:0%
+to mention is that the nature of the
+magnitude of a^2 minus B determines what
+
+ align:start position:0%
+magnitude of a^2 minus B determines what
+ 
+
+ align:start position:0%
+magnitude of a^2 minus B determines what
+the values of R look like for example if
+
+ align:start position:0%
+the values of R look like for example if
+ 
+
+ align:start position:0%
+the values of R look like for example if
+a^2 minus B is positive then R1 and R2
+
+ align:start position:0%
+a^2 minus B is positive then R1 and R2
+ 
+
+ align:start position:0%
+a^2 minus B is positive then R1 and R2
+are unequal real Roots if A2 minus B if
+
+ align:start position:0%
+are unequal real Roots if A2 minus B if
+ 
+
+ align:start position:0%
+are unequal real Roots if A2 minus B if
+A2 minus B is zero then R1 and R2 are
+
+ align:start position:0%
+A2 minus B is zero then R1 and R2 are
+ 
+
+ align:start position:0%
+A2 minus B is zero then R1 and R2 are
+both equal toga a and if a^ 2 minus B is
+
+ align:start position:0%
+both equal toga a and if a^ 2 minus B is
+ 
+
+ align:start position:0%
+both equal toga a and if a^ 2 minus B is
+negative R1 and R2 are complex
+
+ align:start position:0%
+negative R1 and R2 are complex
+ 
+
+ align:start position:0%
+negative R1 and R2 are complex
+conjugates now the idea is simply this
+
+ align:start position:0%
+conjugates now the idea is simply this
+ 
+
+ align:start position:0%
+conjugates now the idea is simply this
+what we're going to do now is I'm going
+
+ align:start position:0%
+what we're going to do now is I'm going
+ 
+
+ align:start position:0%
+what we're going to do now is I'm going
+to summarize for you what these results
+
+ align:start position:0%
+to summarize for you what these results
+ 
+
+ align:start position:0%
+to summarize for you what these results
+are I'm going to use the cookbook
+
+ align:start position:0%
+are I'm going to use the cookbook
+ 
+
+ align:start position:0%
+are I'm going to use the cookbook
+technique first of illustrating all
+
+ align:start position:0%
+technique first of illustrating all
+ 
+
+ align:start position:0%
+technique first of illustrating all
+three cases for you giving you examples
+
+ align:start position:0%
+three cases for you giving you examples
+ 
+
+ align:start position:0%
+three cases for you giving you examples
+of each and then I will conclude today's
+
+ align:start position:0%
+of each and then I will conclude today's
+ 
+
+ align:start position:0%
+of each and then I will conclude today's
+lesson simply by showing you why the
+
+ align:start position:0%
+lesson simply by showing you why the
+ 
+
+ align:start position:0%
+lesson simply by showing you why the
+recipes work and with a little bit of
+
+ align:start position:0%
+recipes work and with a little bit of
+ 
+
+ align:start position:0%
+recipes work and with a little bit of
+luck for the first time in our course we
+
+ align:start position:0%
+luck for the first time in our course we
+ 
+
+ align:start position:0%
+luck for the first time in our course we
+may actually have a short lecture but
+
+ align:start position:0%
+may actually have a short lecture but
+ 
+
+ align:start position:0%
+may actually have a short lecture but
+let's see what actually goes on here
+
+ align:start position:0%
+let's see what actually goes on here
+ 
+
+ align:start position:0%
+let's see what actually goes on here
+let's not be too presumptuous the three
+
+ align:start position:0%
+let's not be too presumptuous the three
+ 
+
+ align:start position:0%
+let's not be too presumptuous the three
+cases are this either a s is greater
+
+ align:start position:0%
+cases are this either a s is greater
+ 
+
+ align:start position:0%
+cases are this either a s is greater
+than b case one a squ is greater than b
+
+ align:start position:0%
+than b case one a squ is greater than b
+ 
+
+ align:start position:0%
+than b case one a squ is greater than b
+so R1 is equal to R2 and they're both
+
+ align:start position:0%
+so R1 is equal to R2 and they're both
+ 
+
+ align:start position:0%
+so R1 is equal to R2 and they're both
+real and in this case the general
+
+ align:start position:0%
+real and in this case the general
+ 
+
+ align:start position:0%
+real and in this case the general
+solution of the homogeneous equation Y
+
+ align:start position:0%
+solution of the homogeneous equation Y
+ 
+
+ align:start position:0%
+solution of the homogeneous equation Y
+Prime + 2 a y Prime + B yal 0 is simply
+
+ align:start position:0%
+Prime + 2 a y Prime + B yal 0 is simply
+ 
+
+ align:start position:0%
+Prime + 2 a y Prime + B yal 0 is simply
+a linear combination of e to the r1x and
+
+ align:start position:0%
+a linear combination of e to the r1x and
+ 
+
+ align:start position:0%
+a linear combination of e to the r1x and
+e to the r2x namely C1 e to the r1x plus
+
+ align:start position:0%
+e to the r2x namely C1 e to the r1x plus
+ 
+
+ align:start position:0%
+e to the r2x namely C1 e to the r1x plus
+C2 e to the
+
+ align:start position:0%
+C2 e to the
+ 
+
+ align:start position:0%
+C2 e to the
+r2x for the second case when A2 equal B
+
+ align:start position:0%
+r2x for the second case when A2 equal B
+ 
+
+ align:start position:0%
+r2x for the second case when A2 equal B
+in that case R1 equals R2 and because
+
+ align:start position:0%
+in that case R1 equals R2 and because
+ 
+
+ align:start position:0%
+in that case R1 equals R2 and because
+they're equal let me just call both of
+
+ align:start position:0%
+they're equal let me just call both of
+ 
+
+ align:start position:0%
+they're equal let me just call both of
+them R1 notice that if I came back up
+
+ align:start position:0%
+them R1 notice that if I came back up
+ 
+
+ align:start position:0%
+them R1 notice that if I came back up
+here this would really not be a general
+
+ align:start position:0%
+here this would really not be a general
+ 
+
+ align:start position:0%
+here this would really not be a general
+solution in this case because with R1
+
+ align:start position:0%
+solution in this case because with R1
+ 
+
+ align:start position:0%
+solution in this case because with R1
+equal to R2 e to the r1x is a common
+
+ align:start position:0%
+equal to R2 e to the r1x is a common
+ 
+
+ align:start position:0%
+equal to R2 e to the r1x is a common
+factor I could then Con well amalgamate
+
+ align:start position:0%
+factor I could then Con well amalgamate
+ 
+
+ align:start position:0%
+factor I could then Con well amalgamate
+the two arbitrary constants here and
+
+ align:start position:0%
+the two arbitrary constants here and
+ 
+
+ align:start position:0%
+the two arbitrary constants here and
+write what that that y subg the general
+
+ align:start position:0%
+write what that that y subg the general
+ 
+
+ align:start position:0%
+write what that that y subg the general
+solution is just C1 + C2 * e to the r1x
+
+ align:start position:0%
+solution is just C1 + C2 * e to the r1x
+ 
+
+ align:start position:0%
+solution is just C1 + C2 * e to the r1x
+and if C1 and C2 are arbitrary constants
+
+ align:start position:0%
+and if C1 and C2 are arbitrary constants
+ 
+
+ align:start position:0%
+and if C1 and C2 are arbitrary constants
+then their sum is simply a arbitrary
+
+ align:start position:0%
+then their sum is simply a arbitrary
+ 
+
+ align:start position:0%
+then their sum is simply a arbitrary
+constant it turns out that in this
+
+ align:start position:0%
+constant it turns out that in this
+ 
+
+ align:start position:0%
+constant it turns out that in this
+particular case another solution of this
+
+ align:start position:0%
+particular case another solution of this
+ 
+
+ align:start position:0%
+particular case another solution of this
+equation meaning what another one other
+
+ align:start position:0%
+equation meaning what another one other
+ 
+
+ align:start position:0%
+equation meaning what another one other
+than e to the r1x which is not a
+
+ align:start position:0%
+than e to the r1x which is not a
+ 
+
+ align:start position:0%
+than e to the r1x which is not a
+constant multiple of e to the r1x is x e
+
+ align:start position:0%
+constant multiple of e to the r1x is x e
+ 
+
+ align:start position:0%
+constant multiple of e to the r1x is x e
+to the r1x and we'll verify that later
+
+ align:start position:0%
+to the r1x and we'll verify that later
+ 
+
+ align:start position:0%
+to the r1x and we'll verify that later
+in the lecture for now just take this
+
+ align:start position:0%
+in the lecture for now just take this
+ 
+
+ align:start position:0%
+in the lecture for now just take this
+for granted and in that case it turns
+
+ align:start position:0%
+for granted and in that case it turns
+ 
+
+ align:start position:0%
+for granted and in that case it turns
+out that the general solution is given
+
+ align:start position:0%
+out that the general solution is given
+ 
+
+ align:start position:0%
+out that the general solution is given
+by the linear combination of e to the R1
+
+ align:start position:0%
+by the linear combination of e to the R1
+ 
+
+ align:start position:0%
+by the linear combination of e to the R1
+x and x e to the r1x C1 e to the r1x
+
+ align:start position:0%
+x and x e to the r1x C1 e to the r1x
+ 
+
+ align:start position:0%
+x and x e to the r1x C1 e to the r1x
+plus C2 x e to the r1x in the third case
+
+ align:start position:0%
+plus C2 x e to the r1x in the third case
+ 
+
+ align:start position:0%
+plus C2 x e to the r1x in the third case
+we have that a s is less than B that
+
+ align:start position:0%
+we have that a s is less than B that
+ 
+
+ align:start position:0%
+we have that a s is less than B that
+means that R1 and R2 are complex complex
+
+ align:start position:0%
+means that R1 and R2 are complex complex
+ 
+
+ align:start position:0%
+means that R1 and R2 are complex complex
+conjugates which means that R has the
+
+ align:start position:0%
+conjugates which means that R has the
+ 
+
+ align:start position:0%
+conjugates which means that R has the
+form a real number plus or minus I times
+
+ align:start position:0%
+form a real number plus or minus I times
+ 
+
+ align:start position:0%
+form a real number plus or minus I times
+a real number calling the real part
+
+ align:start position:0%
+a real number calling the real part
+ 
+
+ align:start position:0%
+a real number calling the real part
+Alpha and the imaginary part beta all
+
+ align:start position:0%
+Alpha and the imaginary part beta all
+ 
+
+ align:start position:0%
+Alpha and the imaginary part beta all
+we're saying is if a^2 minus B is
+
+ align:start position:0%
+we're saying is if a^2 minus B is
+ 
+
+ align:start position:0%
+we're saying is if a^2 minus B is
+negative Alpha is playing the role of a
+
+ align:start position:0%
+negative Alpha is playing the role of a
+ 
+
+ align:start position:0%
+negative Alpha is playing the role of a
+here and beta is just the negative of
+
+ align:start position:0%
+here and beta is just the negative of
+ 
+
+ align:start position:0%
+here and beta is just the negative of
+what's under the radical sign here in
+
+ align:start position:0%
+what's under the radical sign here in
+ 
+
+ align:start position:0%
+what's under the radical sign here in
+other words if a^ minus B is negative B
+
+ align:start position:0%
+other words if a^ minus B is negative B
+ 
+
+ align:start position:0%
+other words if a^ minus B is negative B
+minus a s is positive in other words the
+
+ align:start position:0%
+minus a s is positive in other words the
+ 
+
+ align:start position:0%
+minus a s is positive in other words the
+beta part is just B the square root of B
+
+ align:start position:0%
+beta part is just B the square root of B
+ 
+
+ align:start position:0%
+beta part is just B the square root of B
+minus a 2 you see and in this case it
+
+ align:start position:0%
+minus a 2 you see and in this case it
+ 
+
+ align:start position:0%
+minus a 2 you see and in this case it
+turns out that the general solution is a
+
+ align:start position:0%
+turns out that the general solution is a
+ 
+
+ align:start position:0%
+turns out that the general solution is a
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+combination a very interesting one well
+
+ align:start position:0%
+combination a very interesting one well
+ 
+
+ align:start position:0%
+combination a very interesting one well
+let me factor out the e to the alpha x
+
+ align:start position:0%
+let me factor out the e to the alpha x
+ 
+
+ align:start position:0%
+let me factor out the e to the alpha x
+what it says is First Take e raised to
+
+ align:start position:0%
+what it says is First Take e raised to
+ 
+
+ align:start position:0%
+what it says is First Take e raised to
+the alpha x power where Alpha is the
+
+ align:start position:0%
+the alpha x power where Alpha is the
+ 
+
+ align:start position:0%
+the alpha x power where Alpha is the
+real part of our root R okay and then
+
+ align:start position:0%
+real part of our root R okay and then
+ 
+
+ align:start position:0%
+real part of our root R okay and then
+multiply that by a linear combination of
+
+ align:start position:0%
+multiply that by a linear combination of
+ 
+
+ align:start position:0%
+multiply that by a linear combination of
+sin beta X and cosine beta X where beta
+
+ align:start position:0%
+sin beta X and cosine beta X where beta
+ 
+
+ align:start position:0%
+sin beta X and cosine beta X where beta
+is the imaginary part of R by the way
+
+ align:start position:0%
+is the imaginary part of R by the way
+ 
+
+ align:start position:0%
+is the imaginary part of R by the way
+without going into this because the
+
+ align:start position:0%
+without going into this because the
+ 
+
+ align:start position:0%
+without going into this because the
+textbook does it very eloquently and
+
+ align:start position:0%
+textbook does it very eloquently and
+ 
+
+ align:start position:0%
+textbook does it very eloquently and
+we'll have enough exercises on this to
+
+ align:start position:0%
+we'll have enough exercises on this to
+ 
+
+ align:start position:0%
+we'll have enough exercises on this to
+hammer this home later notice the
+
+ align:start position:0%
+hammer this home later notice the
+ 
+
+ align:start position:0%
+hammer this home later notice the
+intrinsically different geometric nature
+
+ align:start position:0%
+intrinsically different geometric nature
+ 
+
+ align:start position:0%
+intrinsically different geometric nature
+of interpreting these various solutions
+
+ align:start position:0%
+of interpreting these various solutions
+ 
+
+ align:start position:0%
+of interpreting these various solutions
+for example in this particular case just
+
+ align:start position:0%
+for example in this particular case just
+ 
+
+ align:start position:0%
+for example in this particular case just
+speaking very quickly here we see the
+
+ align:start position:0%
+speaking very quickly here we see the
+ 
+
+ align:start position:0%
+speaking very quickly here we see the
+general solution is the sum of two
+
+ align:start position:0%
+general solution is the sum of two
+ 
+
+ align:start position:0%
+general solution is the sum of two
+exponentials coming down to here notice
+
+ align:start position:0%
+exponentials coming down to here notice
+ 
+
+ align:start position:0%
+exponentials coming down to here notice
+that if Alpha happened to be zero in
+
+ align:start position:0%
+that if Alpha happened to be zero in
+ 
+
+ align:start position:0%
+that if Alpha happened to be zero in
+other words if I were purely imaginary
+
+ align:start position:0%
+other words if I were purely imaginary
+ 
+
+ align:start position:0%
+other words if I were purely imaginary
+notice that the solution would be what
+
+ align:start position:0%
+notice that the solution would be what
+ 
+
+ align:start position:0%
+notice that the solution would be what
+we call oscillatory motion and if Alpha
+
+ align:start position:0%
+we call oscillatory motion and if Alpha
+ 
+
+ align:start position:0%
+we call oscillatory motion and if Alpha
+is not zero notice that e to the alpha x
+
+ align:start position:0%
+is not zero notice that e to the alpha x
+ 
+
+ align:start position:0%
+is not zero notice that e to the alpha x
+C1 cosine beta X Plus C2 sin beta X is
+
+ align:start position:0%
+C1 cosine beta X Plus C2 sin beta X is
+ 
+
+ align:start position:0%
+C1 cosine beta X Plus C2 sin beta X is
+an oscillation that is either blown up
+
+ align:start position:0%
+an oscillation that is either blown up
+ 
+
+ align:start position:0%
+an oscillation that is either blown up
+if Alpha is positive or shrunk if Alpha
+
+ align:start position:0%
+if Alpha is positive or shrunk if Alpha
+ 
+
+ align:start position:0%
+if Alpha is positive or shrunk if Alpha
+is negative in other words the
+
+ align:start position:0%
+is negative in other words the
+ 
+
+ align:start position:0%
+is negative in other words the
+oscillatory part stays here but if Alpha
+
+ align:start position:0%
+oscillatory part stays here but if Alpha
+ 
+
+ align:start position:0%
+oscillatory part stays here but if Alpha
+happens to be negative say as X gets
+
+ align:start position:0%
+happens to be negative say as X gets
+ 
+
+ align:start position:0%
+happens to be negative say as X gets
+very large e to the Alp X goes to zero
+
+ align:start position:0%
+very large e to the Alp X goes to zero
+ 
+
+ align:start position:0%
+very large e to the Alp X goes to zero
+that pulls this whole expression down to
+
+ align:start position:0%
+that pulls this whole expression down to
+ 
+
+ align:start position:0%
+that pulls this whole expression down to
+zero and that's the case where you get
+
+ align:start position:0%
+zero and that's the case where you get
+ 
+
+ align:start position:0%
+zero and that's the case where you get
+what's called damped oscillatory Motion
+
+ align:start position:0%
+what's called damped oscillatory Motion
+ 
+
+ align:start position:0%
+what's called damped oscillatory Motion
+in other words you get oscillation but
+
+ align:start position:0%
+in other words you get oscillation but
+ 
+
+ align:start position:0%
+in other words you get oscillation but
+the amplitude keeps shrinking you see
+
+ align:start position:0%
+the amplitude keeps shrinking you see
+ 
+
+ align:start position:0%
+the amplitude keeps shrinking you see
+physically different things start to
+
+ align:start position:0%
+physically different things start to
+ 
+
+ align:start position:0%
+physically different things start to
+happen here and this is a very
+
+ align:start position:0%
+happen here and this is a very
+ 
+
+ align:start position:0%
+happen here and this is a very
+interesting subtlety that just small
+
+ align:start position:0%
+interesting subtlety that just small
+ 
+
+ align:start position:0%
+interesting subtlety that just small
+changes change the entire solution or
+
+ align:start position:0%
+changes change the entire solution or
+ 
+
+ align:start position:0%
+changes change the entire solution or
+the meaning of the solution and maybe
+
+ align:start position:0%
+the meaning of the solution and maybe
+ 
+
+ align:start position:0%
+the meaning of the solution and maybe
+the best way to illustrate that is to
+
+ align:start position:0%
+the best way to illustrate that is to
+ 
+
+ align:start position:0%
+the best way to illustrate that is to
+show examples of all three of these
+
+ align:start position:0%
+show examples of all three of these
+ 
+
+ align:start position:0%
+show examples of all three of these
+cases where the examples almost look
+
+ align:start position:0%
+cases where the examples almost look
+ 
+
+ align:start position:0%
+cases where the examples almost look
+alike but let me show you what I mean
+
+ align:start position:0%
+alike but let me show you what I mean
+ 
+
+ align:start position:0%
+alike but let me show you what I mean
+for example we already saw last time
+
+ align:start position:0%
+for example we already saw last time
+ 
+
+ align:start position:0%
+for example we already saw last time
+that if y primeus 4 y Prime + 3 y equal
+
+ align:start position:0%
+that if y primeus 4 y Prime + 3 y equal
+ 
+
+ align:start position:0%
+that if y primeus 4 y Prime + 3 y equal
+0 then the general solution was C1 e to
+
+ align:start position:0%
+0 then the general solution was C1 e to
+ 
+
+ align:start position:0%
+0 then the general solution was C1 e to
+X Plus C2 e to 3x that's precisely this
+
+ align:start position:0%
+X Plus C2 e to 3x that's precisely this
+ 
+
+ align:start position:0%
+X Plus C2 e to 3x that's precisely this
+case here because if we look at the
+
+ align:start position:0%
+case here because if we look at the
+ 
+
+ align:start position:0%
+case here because if we look at the
+equation that determines R it's r^ 2 - 4
+
+ align:start position:0%
+equation that determines R it's r^ 2 - 4
+ 
+
+ align:start position:0%
+equation that determines R it's r^ 2 - 4
+r + 3 0 that says that R1 is 1 R2 is
+
+ align:start position:0%
+r + 3 0 that says that R1 is 1 R2 is
+ 
+
+ align:start position:0%
+r + 3 0 that says that R1 is 1 R2 is
+three the roots are 1 and three so two
+
+ align:start position:0%
+three the roots are 1 and three so two
+ 
+
+ align:start position:0%
+three the roots are 1 and three so two
+solutions are e to x e to the 3x R1 and
+
+ align:start position:0%
+solutions are e to x e to the 3x R1 and
+ 
+
+ align:start position:0%
+solutions are e to x e to the 3x R1 and
+R2 are real and unequal that's exactly
+
+ align:start position:0%
+R2 are real and unequal that's exactly
+ 
+
+ align:start position:0%
+R2 are real and unequal that's exactly
+the type that we were talking about back
+
+ align:start position:0%
+the type that we were talking about back
+ 
+
+ align:start position:0%
+the type that we were talking about back
+here when we were talking about case one
+
+ align:start position:0%
+here when we were talking about case one
+ 
+
+ align:start position:0%
+here when we were talking about case one
+as far as case 2 is concerned notice
+
+ align:start position:0%
+as far as case 2 is concerned notice
+ 
+
+ align:start position:0%
+as far as case 2 is concerned notice
+that y Prime - 4 y Prime + 4 y = 0 leads
+
+ align:start position:0%
+that y Prime - 4 y Prime + 4 y = 0 leads
+ 
+
+ align:start position:0%
+that y Prime - 4 y Prime + 4 y = 0 leads
+to the equation r^ 2 - 4 r + 4 = 0 that
+
+ align:start position:0%
+to the equation r^ 2 - 4 r + 4 = 0 that
+ 
+
+ align:start position:0%
+to the equation r^ 2 - 4 r + 4 = 0 that
+factors into r - 2 s is z and that says
+
+ align:start position:0%
+factors into r - 2 s is z and that says
+ 
+
+ align:start position:0%
+factors into r - 2 s is z and that says
+that Ral 2 is a multiple root to
+
+ align:start position:0%
+that Ral 2 is a multiple root to
+ 
+
+ align:start position:0%
+that Ral 2 is a multiple root to
+illustrate case two again the proof
+
+ align:start position:0%
+illustrate case two again the proof
+ 
+
+ align:start position:0%
+illustrate case two again the proof
+coming shortly but not now what we're
+
+ align:start position:0%
+coming shortly but not now what we're
+ 
+
+ align:start position:0%
+coming shortly but not now what we're
+saying is that in this case e to 2X and
+
+ align:start position:0%
+saying is that in this case e to 2X and
+ 
+
+ align:start position:0%
+saying is that in this case e to 2X and
+x e to 2x will be non-constant multiples
+
+ align:start position:0%
+x e to 2x will be non-constant multiples
+ 
+
+ align:start position:0%
+x e to 2x will be non-constant multiples
+of one another that are solutions and
+
+ align:start position:0%
+of one another that are solutions and
+ 
+
+ align:start position:0%
+of one another that are solutions and
+that consequently the general solution
+
+ align:start position:0%
+that consequently the general solution
+ 
+
+ align:start position:0%
+that consequently the general solution
+will be C1 e to 2x plus c2x e to
+
+ align:start position:0%
+will be C1 e to 2x plus c2x e to
+ 
+
+ align:start position:0%
+will be C1 e to 2x plus c2x e to
+2x the third case is that I'll pick is y
+
+ align:start position:0%
+2x the third case is that I'll pick is y
+ 
+
+ align:start position:0%
+2x the third case is that I'll pick is y
+Prime - 4 y Prime + + 5 y = 0 which
+
+ align:start position:0%
+Prime - 4 y Prime + + 5 y = 0 which
+ 
+
+ align:start position:0%
+Prime - 4 y Prime + + 5 y = 0 which
+leads to the equation r^2 - 4 r + 5 = 0
+
+ align:start position:0%
+leads to the equation r^2 - 4 r + 5 = 0
+ 
+
+ align:start position:0%
+leads to the equation r^2 - 4 r + 5 = 0
+and solving by the quadratic formula for
+
+ align:start position:0%
+and solving by the quadratic formula for
+ 
+
+ align:start position:0%
+and solving by the quadratic formula for
+R this leads to R = 4 + orus the < TK of
+
+ align:start position:0%
+R this leads to R = 4 + orus the < TK of
+ 
+
+ align:start position:0%
+R this leads to R = 4 + orus the < TK of
+16 - 20 /2 the < TK of 16 - 20 that's
+
+ align:start position:0%
+16 - 20 /2 the < TK of 16 - 20 that's
+ 
+
+ align:start position:0%
+16 - 20 /2 the < TK of 16 - 20 that's
+the < TK of -4 is 2 i 4 plus or - 2 I
+
+ align:start position:0%
+the < TK of -4 is 2 i 4 plus or - 2 I
+ 
+
+ align:start position:0%
+the < TK of -4 is 2 i 4 plus or - 2 I
+over 2 just leads to 2 plus or minus I
+
+ align:start position:0%
+over 2 just leads to 2 plus or minus I
+ 
+
+ align:start position:0%
+over 2 just leads to 2 plus or minus I
+since Alpha is the real part of the root
+
+ align:start position:0%
+since Alpha is the real part of the root
+ 
+
+ align:start position:0%
+since Alpha is the real part of the root
+Alpha will be two since beta is the
+
+ align:start position:0%
+Alpha will be two since beta is the
+ 
+
+ align:start position:0%
+Alpha will be two since beta is the
+magnitude of the imaginary part of the
+
+ align:start position:0%
+magnitude of the imaginary part of the
+ 
+
+ align:start position:0%
+magnitude of the imaginary part of the
+root beta will be one in this case Alpha
+
+ align:start position:0%
+root beta will be one in this case Alpha
+ 
+
+ align:start position:0%
+root beta will be one in this case Alpha
+is two beta is 1 and therefore the
+
+ align:start position:0%
+is two beta is 1 and therefore the
+ 
+
+ align:start position:0%
+is two beta is 1 and therefore the
+general solution is what e to 2x * C1
+
+ align:start position:0%
+general solution is what e to 2x * C1
+ 
+
+ align:start position:0%
+general solution is what e to 2x * C1
+cosine X Plus C2 sinx and by the way
+
+ align:start position:0%
+cosine X Plus C2 sinx and by the way
+ 
+
+ align:start position:0%
+cosine X Plus C2 sinx and by the way
+before I leave this example here's what
+
+ align:start position:0%
+before I leave this example here's what
+ 
+
+ align:start position:0%
+before I leave this example here's what
+I meant by saying how subtle this was
+
+ align:start position:0%
+I meant by saying how subtle this was
+ 
+
+ align:start position:0%
+I meant by saying how subtle this was
+notice that all three of these equations
+
+ align:start position:0%
+notice that all three of these equations
+ 
+
+ align:start position:0%
+notice that all three of these equations
+are identical except for the coefficient
+
+ align:start position:0%
+are identical except for the coefficient
+ 
+
+ align:start position:0%
+are identical except for the coefficient
+of Y in the first equation the
+
+ align:start position:0%
+of Y in the first equation the
+ 
+
+ align:start position:0%
+of Y in the first equation the
+coefficient was of Y was three in the
+
+ align:start position:0%
+coefficient was of Y was three in the
+ 
+
+ align:start position:0%
+coefficient was of Y was three in the
+second equation four and in the third
+
+ align:start position:0%
+second equation four and in the third
+ 
+
+ align:start position:0%
+second equation four and in the third
+equation five other than that they all
+
+ align:start position:0%
+equation five other than that they all
+ 
+
+ align:start position:0%
+equation five other than that they all
+looked alike the equations and yet in
+
+ align:start position:0%
+looked alike the equations and yet in
+ 
+
+ align:start position:0%
+looked alike the equations and yet in
+one case we got the two real and unequal
+
+ align:start position:0%
+one case we got the two real and unequal
+ 
+
+ align:start position:0%
+one case we got the two real and unequal
+roots in the second case we got the real
+
+ align:start position:0%
+roots in the second case we got the real
+ 
+
+ align:start position:0%
+roots in the second case we got the real
+but equal roots and in the third case
+
+ align:start position:0%
+but equal roots and in the third case
+ 
+
+ align:start position:0%
+but equal roots and in the third case
+the non-real complex conjugates all
+
+ align:start position:0%
+the non-real complex conjugates all
+ 
+
+ align:start position:0%
+the non-real complex conjugates all
+right that's all there is to this lesson
+
+ align:start position:0%
+right that's all there is to this lesson
+ 
+
+ align:start position:0%
+right that's all there is to this lesson
+except for giving you some insight as to
+
+ align:start position:0%
+except for giving you some insight as to
+ 
+
+ align:start position:0%
+except for giving you some insight as to
+why these recipes hold from this point
+
+ align:start position:0%
+why these recipes hold from this point
+ 
+
+ align:start position:0%
+why these recipes hold from this point
+on the rest is drill that does there's
+
+ align:start position:0%
+on the rest is drill that does there's
+ 
+
+ align:start position:0%
+on the rest is drill that does there's
+not much more we can do other than to
+
+ align:start position:0%
+not much more we can do other than to
+ 
+
+ align:start position:0%
+not much more we can do other than to
+have you uh look to see what's happening
+
+ align:start position:0%
+have you uh look to see what's happening
+ 
+
+ align:start position:0%
+have you uh look to see what's happening
+and work on the exercises but I thought
+
+ align:start position:0%
+and work on the exercises but I thought
+ 
+
+ align:start position:0%
+and work on the exercises but I thought
+that it might help if I give you a few
+
+ align:start position:0%
+that it might help if I give you a few
+ 
+
+ align:start position:0%
+that it might help if I give you a few
+little supplementary notes as to why
+
+ align:start position:0%
+little supplementary notes as to why
+ 
+
+ align:start position:0%
+little supplementary notes as to why
+these things work out and they work out
+
+ align:start position:0%
+these things work out and they work out
+ 
+
+ align:start position:0%
+these things work out and they work out
+easily enough so I decided to do the
+
+ align:start position:0%
+easily enough so I decided to do the
+ 
+
+ align:start position:0%
+easily enough so I decided to do the
+supplementary notes as part of the
+
+ align:start position:0%
+supplementary notes as part of the
+ 
+
+ align:start position:0%
+supplementary notes as part of the
+lecture namely first of all notice that
+
+ align:start position:0%
+lecture namely first of all notice that
+ 
+
+ align:start position:0%
+lecture namely first of all notice that
+in the case where R1 is unequal to R2
+
+ align:start position:0%
+in the case where R1 is unequal to R2
+ 
+
+ align:start position:0%
+in the case where R1 is unequal to R2
+and they're both real that e to the r1x
+
+ align:start position:0%
+and they're both real that e to the r1x
+ 
+
+ align:start position:0%
+and they're both real that e to the r1x
+and e to the r2x are both real solutions
+
+ align:start position:0%
+and e to the r2x are both real solutions
+ 
+
+ align:start position:0%
+and e to the r2x are both real solutions
+and more importantly since one cannot be
+
+ align:start position:0%
+and more importantly since one cannot be
+ 
+
+ align:start position:0%
+and more importantly since one cannot be
+a constant multiple of the other their
+
+ align:start position:0%
+a constant multiple of the other their
+ 
+
+ align:start position:0%
+a constant multiple of the other their
+linear combination must be the general
+
+ align:start position:0%
+linear combination must be the general
+ 
+
+ align:start position:0%
+linear combination must be the general
+Solution that's what we saw last time
+
+ align:start position:0%
+Solution that's what we saw last time
+ 
+
+ align:start position:0%
+Solution that's what we saw last time
+remember the only time you were in
+
+ align:start position:0%
+remember the only time you were in
+ 
+
+ align:start position:0%
+remember the only time you were in
+trouble is if one was a constant
+
+ align:start position:0%
+trouble is if one was a constant
+ 
+
+ align:start position:0%
+trouble is if one was a constant
+multiple of the other why can't e to the
+
+ align:start position:0%
+multiple of the other why can't e to the
+ 
+
+ align:start position:0%
+multiple of the other why can't e to the
+r1x and e to the r2x be constant
+
+ align:start position:0%
+r1x and e to the r2x be constant
+ 
+
+ align:start position:0%
+r1x and e to the r2x be constant
+multiples of one another the answer
+
+ align:start position:0%
+multiples of one another the answer
+ 
+
+ align:start position:0%
+multiples of one another the answer
+quite simply is this assume that they
+
+ align:start position:0%
+quite simply is this assume that they
+ 
+
+ align:start position:0%
+quite simply is this assume that they
+were divide both sides by e to the r2x
+
+ align:start position:0%
+were divide both sides by e to the r2x
+ 
+
+ align:start position:0%
+were divide both sides by e to the r2x
+we then get e to the R1 - r2x as a
+
+ align:start position:0%
+we then get e to the R1 - r2x as a
+ 
+
+ align:start position:0%
+we then get e to the R1 - r2x as a
+constant but look at this is e raised to
+
+ align:start position:0%
+constant but look at this is e raised to
+ 
+
+ align:start position:0%
+constant but look at this is e raised to
+a very power the only way that e raed to
+
+ align:start position:0%
+a very power the only way that e raed to
+ 
+
+ align:start position:0%
+a very power the only way that e raed to
+a variable power can be a constant is if
+
+ align:start position:0%
+a variable power can be a constant is if
+ 
+
+ align:start position:0%
+a variable power can be a constant is if
+the multiplier of the x is itself zero
+
+ align:start position:0%
+the multiplier of the x is itself zero
+ 
+
+ align:start position:0%
+the multiplier of the x is itself zero
+so the X doesn't appear here in other
+
+ align:start position:0%
+so the X doesn't appear here in other
+ 
+
+ align:start position:0%
+so the X doesn't appear here in other
+words in that case notice that R1 minus
+
+ align:start position:0%
+words in that case notice that R1 minus
+ 
+
+ align:start position:0%
+words in that case notice that R1 minus
+R2 must be zero and that's the same as
+
+ align:start position:0%
+R2 must be zero and that's the same as
+ 
+
+ align:start position:0%
+R2 must be zero and that's the same as
+saying that R1 equals R2 in other words
+
+ align:start position:0%
+saying that R1 equals R2 in other words
+ 
+
+ align:start position:0%
+saying that R1 equals R2 in other words
+the only way that e to the r1x can be a
+
+ align:start position:0%
+the only way that e to the r1x can be a
+ 
+
+ align:start position:0%
+the only way that e to the r1x can be a
+constant multiple of e to the r2x is if
+
+ align:start position:0%
+constant multiple of e to the r2x is if
+ 
+
+ align:start position:0%
+constant multiple of e to the r2x is if
+R1 equals R2 but we're given in case one
+
+ align:start position:0%
+R1 equals R2 but we're given in case one
+ 
+
+ align:start position:0%
+R1 equals R2 but we're given in case one
+that R1 is not equal to R2 that's why
+
+ align:start position:0%
+that R1 is not equal to R2 that's why
+ 
+
+ align:start position:0%
+that R1 is not equal to R2 that's why
+the solution works as far as case 2 is
+
+ align:start position:0%
+the solution works as far as case 2 is
+ 
+
+ align:start position:0%
+the solution works as far as case 2 is
+concerned notice that what we have to
+
+ align:start position:0%
+concerned notice that what we have to
+ 
+
+ align:start position:0%
+concerned notice that what we have to
+establish is it's obvious that x e to
+
+ align:start position:0%
+establish is it's obvious that x e to
+ 
+
+ align:start position:0%
+establish is it's obvious that x e to
+the r1x is not a constant multiple of e
+
+ align:start position:0%
+the r1x is not a constant multiple of e
+ 
+
+ align:start position:0%
+the r1x is not a constant multiple of e
+to the r1x after all their ratio is X
+
+ align:start position:0%
+to the r1x after all their ratio is X
+ 
+
+ align:start position:0%
+to the r1x after all their ratio is X
+which is not a constant the hard thing
+
+ align:start position:0%
+which is not a constant the hard thing
+ 
+
+ align:start position:0%
+which is not a constant the hard thing
+to do is to justify how we can find out
+
+ align:start position:0%
+to do is to justify how we can find out
+ 
+
+ align:start position:0%
+to do is to justify how we can find out
+that x e to the r1x is a solution in
+
+ align:start position:0%
+that x e to the r1x is a solution in
+ 
+
+ align:start position:0%
+that x e to the r1x is a solution in
+that case and the answer is look at that
+
+ align:start position:0%
+that case and the answer is look at that
+ 
+
+ align:start position:0%
+that case and the answer is look at that
+that case occurs when A2 equals B if a 2
+
+ align:start position:0%
+that case occurs when A2 equals B if a 2
+ 
+
+ align:start position:0%
+that case occurs when A2 equals B if a 2
+equals B notice that y Prime + 2 a y
+
+ align:start position:0%
+equals B notice that y Prime + 2 a y
+ 
+
+ align:start position:0%
+equals B notice that y Prime + 2 a y
+Prime + b y becomes replaced by y Prime
+
+ align:start position:0%
+Prime + b y becomes replaced by y Prime
+ 
+
+ align:start position:0%
+Prime + b y becomes replaced by y Prime
++ 2 a y Prime + a^ 2 y now we very
+
+ align:start position:0%
++ 2 a y Prime + a^ 2 y now we very
+ 
+
+ align:start position:0%
++ 2 a y Prime + a^ 2 y now we very
+cleverly invoke the trick of writing 2 a
+
+ align:start position:0%
+cleverly invoke the trick of writing 2 a
+ 
+
+ align:start position:0%
+cleverly invoke the trick of writing 2 a
+y Prime as a y prime plus a y Prime see
+
+ align:start position:0%
+y Prime as a y prime plus a y Prime see
+ 
+
+ align:start position:0%
+y Prime as a y prime plus a y Prime see
+we take this and write it like this now
+
+ align:start position:0%
+we take this and write it like this now
+ 
+
+ align:start position:0%
+we take this and write it like this now
+we factor out an a from this expression
+
+ align:start position:0%
+we factor out an a from this expression
+ 
+
+ align:start position:0%
+we factor out an a from this expression
+here we have a * y Prime + a y notice
+
+ align:start position:0%
+here we have a * y Prime + a y notice
+ 
+
+ align:start position:0%
+here we have a * y Prime + a y notice
+that these two terms are just the
+
+ align:start position:0%
+that these two terms are just the
+ 
+
+ align:start position:0%
+that these two terms are just the
+derivative of y Prime + a y in other
+
+ align:start position:0%
+derivative of y Prime + a y in other
+ 
+
+ align:start position:0%
+derivative of y Prime + a y in other
+words if I let you equal y Prime + a y
+
+ align:start position:0%
+words if I let you equal y Prime + a y
+ 
+
+ align:start position:0%
+words if I let you equal y Prime + a y
+then this being u means that with the
+
+ align:start position:0%
+then this being u means that with the
+ 
+
+ align:start position:0%
+then this being u means that with the
+Prime on this this is U Prime this just
+
+ align:start position:0%
+Prime on this this is U Prime this just
+ 
+
+ align:start position:0%
+Prime on this this is U Prime this just
+becomes U Prime + Au U equals z that's a
+
+ align:start position:0%
+becomes U Prime + Au U equals z that's a
+ 
+
+ align:start position:0%
+becomes U Prime + Au U equals z that's a
+first order differential equation in U
+
+ align:start position:0%
+first order differential equation in U
+ 
+
+ align:start position:0%
+first order differential equation in U
+in which the variables are separable see
+
+ align:start position:0%
+in which the variables are separable see
+ 
+
+ align:start position:0%
+in which the variables are separable see
+in other words this becomes this from
+
+ align:start position:0%
+in other words this becomes this from
+ 
+
+ align:start position:0%
+in other words this becomes this from
+this I can very quickly find that U is
+
+ align:start position:0%
+this I can very quickly find that U is
+ 
+
+ align:start position:0%
+this I can very quickly find that U is
+equal to c e to minus ax I didn't want C
+
+ align:start position:0%
+equal to c e to minus ax I didn't want C
+ 
+
+ align:start position:0%
+equal to c e to minus ax I didn't want C
+I wanted I didn't want U I wanted y I
+
+ align:start position:0%
+I wanted I didn't want U I wanted y I
+ 
+
+ align:start position:0%
+I wanted I didn't want U I wanted y I
+remember that by definition of my
+
+ align:start position:0%
+remember that by definition of my
+ 
+
+ align:start position:0%
+remember that by definition of my
+substitution U is y Prime + a y
+
+ align:start position:0%
+substitution U is y Prime + a y
+ 
+
+ align:start position:0%
+substitution U is y Prime + a y
+consequently this leads to Y Prime + a y
+
+ align:start position:0%
+consequently this leads to Y Prime + a y
+ 
+
+ align:start position:0%
+consequently this leads to Y Prime + a y
+is c e to the minus ax this is a first
+
+ align:start position:0%
+is c e to the minus ax this is a first
+ 
+
+ align:start position:0%
+is c e to the minus ax this is a first
+order linear differential equation we
+
+ align:start position:0%
+order linear differential equation we
+ 
+
+ align:start position:0%
+order linear differential equation we
+learned how to solve that in a previous
+
+ align:start position:0%
+learned how to solve that in a previous
+ 
+
+ align:start position:0%
+learned how to solve that in a previous
+unit leaving the details again to you it
+
+ align:start position:0%
+unit leaving the details again to you it
+ 
+
+ align:start position:0%
+unit leaving the details again to you it
+now follows that a particular solution
+
+ align:start position:0%
+now follows that a particular solution
+ 
+
+ align:start position:0%
+now follows that a particular solution
+of this equation will be Y subp is x e
+
+ align:start position:0%
+of this equation will be Y subp is x e
+ 
+
+ align:start position:0%
+of this equation will be Y subp is x e
+to the minus ax recalling that in this
+
+ align:start position:0%
+to the minus ax recalling that in this
+ 
+
+ align:start position:0%
+to the minus ax recalling that in this
+case R1 is minus a this is x e to the
+
+ align:start position:0%
+case R1 is minus a this is x e to the
+ 
+
+ align:start position:0%
+case R1 is minus a this is x e to the
+r1x this together with e to the r1x form
+
+ align:start position:0%
+r1x this together with e to the r1x form
+ 
+
+ align:start position:0%
+r1x this together with e to the r1x form
+your two linearly independent Solutions
+
+ align:start position:0%
+your two linearly independent Solutions
+ 
+
+ align:start position:0%
+your two linearly independent Solutions
+and consequently that's why the general
+
+ align:start position:0%
+and consequently that's why the general
+ 
+
+ align:start position:0%
+and consequently that's why the general
+solution in this case is C1 e to the r1x
+
+ align:start position:0%
+solution in this case is C1 e to the r1x
+ 
+
+ align:start position:0%
+solution in this case is C1 e to the r1x
+plus c2x e to the r1x the third case
+
+ align:start position:0%
+plus c2x e to the r1x the third case
+ 
+
+ align:start position:0%
+plus c2x e to the r1x the third case
+where we got the imaginary roots or the
+
+ align:start position:0%
+where we got the imaginary roots or the
+ 
+
+ align:start position:0%
+where we got the imaginary roots or the
+non-real roots hinges on a very
+
+ align:start position:0%
+non-real roots hinges on a very
+ 
+
+ align:start position:0%
+non-real roots hinges on a very
+interesting property of linearity plus
+
+ align:start position:0%
+interesting property of linearity plus
+ 
+
+ align:start position:0%
+interesting property of linearity plus
+complex functions if u and v are real
+
+ align:start position:0%
+complex functions if u and v are real
+ 
+
+ align:start position:0%
+complex functions if u and v are real
+notice that L of U plus IV by linearity
+
+ align:start position:0%
+notice that L of U plus IV by linearity
+ 
+
+ align:start position:0%
+notice that L of U plus IV by linearity
+is L of U plus I L of V because after
+
+ align:start position:0%
+is L of U plus I L of V because after
+ 
+
+ align:start position:0%
+is L of U plus I L of V because after
+all I is a constant be it imaginary or
+
+ align:start position:0%
+all I is a constant be it imaginary or
+ 
+
+ align:start position:0%
+all I is a constant be it imaginary or
+otherwise consequently by linearity
+
+ align:start position:0%
+otherwise consequently by linearity
+ 
+
+ align:start position:0%
+otherwise consequently by linearity
+since L of u+ i v is L of U plus I L of
+
+ align:start position:0%
+since L of u+ i v is L of U plus I L of
+ 
+
+ align:start position:0%
+since L of u+ i v is L of U plus I L of
+V the only way that L of U plus I V can
+
+ align:start position:0%
+V the only way that L of U plus I V can
+ 
+
+ align:start position:0%
+V the only way that L of U plus I V can
+equal zero is if L of U plus I L of V
+
+ align:start position:0%
+equal zero is if L of U plus I L of V
+ 
+
+ align:start position:0%
+equal zero is if L of U plus I L of V
+equals z and the only way a complex
+
+ align:start position:0%
+equals z and the only way a complex
+ 
+
+ align:start position:0%
+equals z and the only way a complex
+number can equal zero is if both its
+
+ align:start position:0%
+number can equal zero is if both its
+ 
+
+ align:start position:0%
+number can equal zero is if both its
+real and imaginary parts are zero in
+
+ align:start position:0%
+real and imaginary parts are zero in
+ 
+
+ align:start position:0%
+real and imaginary parts are zero in
+other words then if L of U plus IV is
+
+ align:start position:0%
+other words then if L of U plus IV is
+ 
+
+ align:start position:0%
+other words then if L of U plus IV is
+zero it means that L of U and and L of V
+
+ align:start position:0%
+zero it means that L of U and and L of V
+ 
+
+ align:start position:0%
+zero it means that L of U and and L of V
+must themselves be zero see the real
+
+ align:start position:0%
+must themselves be zero see the real
+ 
+
+ align:start position:0%
+must themselves be zero see the real
+part must be zero the imaginary part
+
+ align:start position:0%
+part must be zero the imaginary part
+ 
+
+ align:start position:0%
+part must be zero the imaginary part
+must be zero now how do we apply this to
+
+ align:start position:0%
+must be zero now how do we apply this to
+ 
+
+ align:start position:0%
+must be zero now how do we apply this to
+case three notice that in case three we
+
+ align:start position:0%
+case three notice that in case three we
+ 
+
+ align:start position:0%
+case three notice that in case three we
+solved for R and got that R was equal to
+
+ align:start position:0%
+solved for R and got that R was equal to
+ 
+
+ align:start position:0%
+solved for R and got that R was equal to
+Alpha plus or minus I beta let me pick
+
+ align:start position:0%
+Alpha plus or minus I beta let me pick
+ 
+
+ align:start position:0%
+Alpha plus or minus I beta let me pick
+the positive root and we said our
+
+ align:start position:0%
+the positive root and we said our
+ 
+
+ align:start position:0%
+the positive root and we said our
+solution was e to the alpha plus I beta
+
+ align:start position:0%
+solution was e to the alpha plus I beta
+ 
+
+ align:start position:0%
+solution was e to the alpha plus I beta
+X now the idea is this looks quite
+
+ align:start position:0%
+X now the idea is this looks quite
+ 
+
+ align:start position:0%
+X now the idea is this looks quite
+imaginary and it is in this form but
+
+ align:start position:0%
+imaginary and it is in this form but
+ 
+
+ align:start position:0%
+imaginary and it is in this form but
+what we've just seen is that since this
+
+ align:start position:0%
+what we've just seen is that since this
+ 
+
+ align:start position:0%
+what we've just seen is that since this
+is a solution of this homogeneous
+
+ align:start position:0%
+is a solution of this homogeneous
+ 
+
+ align:start position:0%
+is a solution of this homogeneous
+equation the real and the imaginary part
+
+ align:start position:0%
+equation the real and the imaginary part
+ 
+
+ align:start position:0%
+equation the real and the imaginary part
+separately must be Solutions
+
+ align:start position:0%
+separately must be Solutions
+ 
+
+ align:start position:0%
+separately must be Solutions
+consequently if I write this in the in
+
+ align:start position:0%
+consequently if I write this in the in
+ 
+
+ align:start position:0%
+consequently if I write this in the in
+the traditional U plus IV form then u
+
+ align:start position:0%
+the traditional U plus IV form then u
+ 
+
+ align:start position:0%
+the traditional U plus IV form then u
+and v separately will also be Solutions
+
+ align:start position:0%
+and v separately will also be Solutions
+ 
+
+ align:start position:0%
+and v separately will also be Solutions
+well let's see how I write e to the
+
+ align:start position:0%
+well let's see how I write e to the
+ 
+
+ align:start position:0%
+well let's see how I write e to the
+alpha plus I beta X in traditional form
+
+ align:start position:0%
+alpha plus I beta X in traditional form
+ 
+
+ align:start position:0%
+alpha plus I beta X in traditional form
+first of all this is e to the alpha
+
+ align:start position:0%
+first of all this is e to the alpha
+ 
+
+ align:start position:0%
+first of all this is e to the alpha
+x time e to the I beta X by the rules of
+
+ align:start position:0%
+x time e to the I beta X by the rules of
+ 
+
+ align:start position:0%
+x time e to the I beta X by the rules of
+exponents we recall from our lecture on
+
+ align:start position:0%
+exponents we recall from our lecture on
+ 
+
+ align:start position:0%
+exponents we recall from our lecture on
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+functions that e to the I beta X is cine
+
+ align:start position:0%
+functions that e to the I beta X is cine
+ 
+
+ align:start position:0%
+functions that e to the I beta X is cine
+beta X plus I sin beta X consequently e
+
+ align:start position:0%
+beta X plus I sin beta X consequently e
+ 
+
+ align:start position:0%
+beta X plus I sin beta X consequently e
+to the alpha plus I beta X is just e to
+
+ align:start position:0%
+to the alpha plus I beta X is just e to
+ 
+
+ align:start position:0%
+to the alpha plus I beta X is just e to
+the alpha x times this expression here
+
+ align:start position:0%
+the alpha x times this expression here
+ 
+
+ align:start position:0%
+the alpha x times this expression here
+or separating it into the form U plus i
+
+ align:start position:0%
+or separating it into the form U plus i
+ 
+
+ align:start position:0%
+or separating it into the form U plus i
+v e to the alpha plus I beta X is e to
+
+ align:start position:0%
+v e to the alpha plus I beta X is e to
+ 
+
+ align:start position:0%
+v e to the alpha plus I beta X is e to
+the alpha x cosine beta X which is a
+
+ align:start position:0%
+the alpha x cosine beta X which is a
+ 
+
+ align:start position:0%
+the alpha x cosine beta X which is a
+real number because Alpha and beta are
+
+ align:start position:0%
+real number because Alpha and beta are
+ 
+
+ align:start position:0%
+real number because Alpha and beta are
+real plus I * e to the alpha x sin beta
+
+ align:start position:0%
+real plus I * e to the alpha x sin beta
+ 
+
+ align:start position:0%
+real plus I * e to the alpha x sin beta
+X and e to the alpha x sin beta X is
+
+ align:start position:0%
+X and e to the alpha x sin beta X is
+ 
+
+ align:start position:0%
+X and e to the alpha x sin beta X is
+also a real number because Alpha and
+
+ align:start position:0%
+also a real number because Alpha and
+ 
+
+ align:start position:0%
+also a real number because Alpha and
+beta are real in other words you the
+
+ align:start position:0%
+beta are real in other words you the
+ 
+
+ align:start position:0%
+beta are real in other words you the
+alpha x cosine beta X that's the real
+
+ align:start position:0%
+alpha x cosine beta X that's the real
+ 
+
+ align:start position:0%
+alpha x cosine beta X that's the real
+part of this complex number V is e to
+
+ align:start position:0%
+part of this complex number V is e to
+ 
+
+ align:start position:0%
+part of this complex number V is e to
+the alpha x sin beta X which is the
+
+ align:start position:0%
+the alpha x sin beta X which is the
+ 
+
+ align:start position:0%
+the alpha x sin beta X which is the
+imaginary part of this since we've just
+
+ align:start position:0%
+imaginary part of this since we've just
+ 
+
+ align:start position:0%
+imaginary part of this since we've just
+seen that the real and the imaginary
+
+ align:start position:0%
+seen that the real and the imaginary
+ 
+
+ align:start position:0%
+seen that the real and the imaginary
+parts of this function must satisfy this
+
+ align:start position:0%
+parts of this function must satisfy this
+ 
+
+ align:start position:0%
+parts of this function must satisfy this
+equation also that tells us that e to
+
+ align:start position:0%
+equation also that tells us that e to
+ 
+
+ align:start position:0%
+equation also that tells us that e to
+the alpha x cosine beta X and e to the
+
+ align:start position:0%
+the alpha x cosine beta X and e to the
+ 
+
+ align:start position:0%
+the alpha x cosine beta X and e to the
+alpha x sin beta X also satisfy this
+
+ align:start position:0%
+alpha x sin beta X also satisfy this
+ 
+
+ align:start position:0%
+alpha x sin beta X also satisfy this
+equation and that by the way is exactly
+
+ align:start position:0%
+equation and that by the way is exactly
+ 
+
+ align:start position:0%
+equation and that by the way is exactly
+what we saw in case three only we
+
+ align:start position:0%
+what we saw in case three only we
+ 
+
+ align:start position:0%
+what we saw in case three only we
+factored out the e to the alpha x notice
+
+ align:start position:0%
+factored out the e to the alpha x notice
+ 
+
+ align:start position:0%
+factored out the e to the alpha x notice
+by the way that these two equations
+
+ align:start position:0%
+by the way that these two equations
+ 
+
+ align:start position:0%
+by the way that these two equations
+cannot be constant multiples of one
+
+ align:start position:0%
+cannot be constant multiples of one
+ 
+
+ align:start position:0%
+cannot be constant multiples of one
+another because if we divide say the top
+
+ align:start position:0%
+another because if we divide say the top
+ 
+
+ align:start position:0%
+another because if we divide say the top
+by the bottom the e to the alpha x
+
+ align:start position:0%
+by the bottom the e to the alpha x
+ 
+
+ align:start position:0%
+by the bottom the e to the alpha x
+cancel sin beta X over cosine beta X is
+
+ align:start position:0%
+cancel sin beta X over cosine beta X is
+ 
+
+ align:start position:0%
+cancel sin beta X over cosine beta X is
+tan beta X and for beta not equal to
+
+ align:start position:0%
+tan beta X and for beta not equal to
+ 
+
+ align:start position:0%
+tan beta X and for beta not equal to
+zero tan beta X can't be a constant so
+
+ align:start position:0%
+zero tan beta X can't be a constant so
+ 
+
+ align:start position:0%
+zero tan beta X can't be a constant so
+that these two solutions do indeed
+
+ align:start position:0%
+that these two solutions do indeed
+ 
+
+ align:start position:0%
+that these two solutions do indeed
+generate the general solution now that's
+
+ align:start position:0%
+generate the general solution now that's
+ 
+
+ align:start position:0%
+generate the general solution now that's
+all there is to this particular problem
+
+ align:start position:0%
+all there is to this particular problem
+ 
+
+ align:start position:0%
+all there is to this particular problem
+the rest as I say is left to the
+
+ align:start position:0%
+the rest as I say is left to the
+ 
+
+ align:start position:0%
+the rest as I say is left to the
+exercises what we're going to do next
+
+ align:start position:0%
+exercises what we're going to do next
+ 
+
+ align:start position:0%
+exercises what we're going to do next
+time is tackle the companion part of
+
+ align:start position:0%
+time is tackle the companion part of
+ 
+
+ align:start position:0%
+time is tackle the companion part of
+this problem and that is how do you find
+
+ align:start position:0%
+this problem and that is how do you find
+ 
+
+ align:start position:0%
+this problem and that is how do you find
+the particular solution of a linear
+
+ align:start position:0%
+the particular solution of a linear
+ 
+
+ align:start position:0%
+the particular solution of a linear
+differential equation with constant
+
+ align:start position:0%
+differential equation with constant
+ 
+
+ align:start position:0%
+differential equation with constant
+coefficients where the right hand side
+
+ align:start position:0%
+coefficients where the right hand side
+ 
+
+ align:start position:0%
+coefficients where the right hand side
+is not zero in other words the
+
+ align:start position:0%
+is not zero in other words the
+ 
+
+ align:start position:0%
+is not zero in other words the
+non-homogeneous case but more about that
+
+ align:start position:0%
+non-homogeneous case but more about that
+ 
+
+ align:start position:0%
+non-homogeneous case but more about that
+next time so until next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/DZ138JSpoxQ.txt b/DZ138JSpoxQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7299429e399c0339397a952ccccbe2a8af325f12
--- /dev/null
+++ b/DZ138JSpoxQ.txt
@@ -0,0 +1,1730 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So, now we'll start
+on the last of the main topics
+
+in the course.
+
+So we've finished most of our
+macroscopic thermodynamics,
+
+and our microscopic
+approach to it
+
+through statistical mechanics.
+
+And now, our final topic
+is kinetics.
+
+Kinetics is really a very
+different kind of topic.
+
+Because unlike thermodynamics,
+thermodynamics tells you all
+
+about equilibrium properties.
+
+A huge part of the work of this
+term has been to figure
+
+out what equilibrium is.
+
+What is the equilibrium state,
+given some situation.
+
+You've got some phases
+present.
+
+Different then, you could go
+from solid to liquid to gas.
+
+Or you've got different chemical
+constituents together
+
+that can react and go
+back and forth.
+
+What are the equilibrium
+concentrations?
+
+But we haven't worried at all
+about how long it might take
+
+to get there.
+
+And that's what kinetics does.
+
+Kinetics is concerned with rates
+of reactions, primarily.
+
+How long it takes to
+reach equilibrium.
+
+And of course it's
+super-important.
+
+Because if you look at that
+window glass, it's not in
+
+equilibrium.
+
+It's silicon dioxide,
+the equilibrium
+
+state would be a crystal.
+
+It would be crystal
+and quartz.
+
+Nevertheless, none of us is
+very worried that on the
+
+moment it's likely to suddenly,
+spontaneously turn
+
+into a crystal and be opaque and
+scatter light and do all
+
+that sort of stuff.
+
+And in lots of other situations,
+certainly if you
+
+look at any living biological
+system, including yourselves
+
+or your friends or any other
+one, it's certainly far from
+
+equilibrium.
+
+And you probably would hope
+for it to stay that way.
+
+So there's an enormous amount
+of chemistry and processes
+
+we're concerned with.
+
+Which depend intimately on
+kinetics in order to work the
+
+way they work.
+
+They also do depend on
+thermodynamics and where
+
+equilibrium states are.
+
+But that doesn't mean
+they necessarily
+
+reach equilibrium states.
+
+So we're going to go through
+kinetics, starting with the
+
+simplest examples and working
+our way up to
+
+more complex cases.
+
+And just see how we can describe
+elementary chemical
+
+reaction rates and processes.
+
+So that's our concern
+now, is dynamics.
+
+How long things take to
+get to equilibrium.
+
+And actually just like
+macroscopic thermodynamics,
+
+kinetics does take an empirical
+
+approach to the topic.
+
+In other words, it's based on
+experimental observation.
+
+Of macroscopic rates.
+
+How long it takes a collection
+of stuff, a mole of stuff to
+
+change chemically.
+
+And undergo reaction.
+
+And so forth.
+
+We often infer molecular
+mechanisms based on kinetics.
+
+And it's hugely important
+and valuable to do that.
+
+But it's also important to
+recognize that what kinetics
+
+can do is show us how we can
+formulate microscopic
+
+mechanisms that might be
+consistent with our
+
+macroscopic kinetics models.
+
+But the kinetics models
+by themselves
+
+don't prove the mechanism.
+
+And there are all sorts of
+examples where mechanisms that
+
+were proposed and accepted
+because they were consistent
+
+with macroscopic kinetics
+results turned out to fail.
+
+There are other ways to
+prove mechanisms.
+
+You might be able to design
+direct spectroscopic
+
+observations of intermediates
+and so forth.
+
+And in that case, it often
+becomes possible to
+
+distinguish between different
+mechanisms.
+
+Which might all satisfy the
+macroscopic kinetics equation.
+
+So we use kinetics to infer a
+mechanism but not necessarily
+
+to prove it.
+
+Not generally to prove it.
+
+We also use kinetics to describe
+an enormous range of
+
+time scales.
+
+So, the fastest things that
+we're sometimes concerned with
+
+that might take place on
+femtosecond time scales, 10 to
+
+the minus 13 seconds
+or so, or 10 to the
+
+minus 15 seconds, even.
+
+So, if we look at the range
+of time scales we might be
+
+concerned with, might go
+anywhere from about 10 to the
+
+minus 15 seconds at the fastest,
+and might go to
+
+enormous scales on
+the other end.
+
+All the way out to maybe 10 to
+the 10 seconds, which is on
+
+the thousands of years.
+
+Could be longer than
+that, sometimes
+
+even millions of years.
+
+And the formalism that we'll set
+up applies equally to the
+
+full range of time scales.
+
+So it can describe an enormous
+amount of chemical activity.
+
+More commonly, for stuff that
+we're going to compare to, you
+
+might measure in the lab.
+
+Common time scales range from
+roughly 10 to the minus 6
+
+seconds out to about 10
+to the 5th seconds.
+
+That is, microseconds
+to about a day.
+
+But there are plenty of examples
+of going either
+
+faster or slower, depending on
+the need and the experimental
+
+equipment available.
+
+Let's define a few terms.
+
+Let's talk about how we're
+going to just formulate
+
+chemical reaction rates.
+
+So, let's just imagine any
+simple reaction of this sort.
+
+So A plus B are going to go to
+C. There's some rate at which
+
+it happens.
+
+Note, by the way, it's an
+arrow in one direction.
+
+It's not an equals sign
+like we've seen
+
+before, or a double arrow.
+
+So the point I'm emphasizing
+here is when we talk about
+
+reaction rates, unlike
+equilibria, we're talking
+
+about a particular direction.
+
+Later on, we will talk about
+reversible reactions.
+
+But there, too, the arrow going
+this way refers only to
+
+one of the chemical reactions
+that can take place.
+
+Namely, in this case, the
+changing of what was the
+
+product now, would be the
+reactant, C, back into A plus
+
+B and it has nothing to do
+with the rate this way.
+
+Measured independently
+and so on.
+
+So the rate, we can look at the
+rate of disappearance of
+
+A. So it's just negative
+d[A]/dt, where the brackets
+
+indicate concentration.
+
+Usually in moles per liter.
+
+If it's in a gas, then it would
+be pA, of pressure.
+
+So negative d[A]/dt
+is our rate.
+
+And note that that's generally
+a positive number.
+
+We're looking at reactions
+going, if it's a reaction
+
+going in this direction.
+
+A is gradually disappearing.
+
+So we're going to define
+our rate this way.
+
+To be a positive number.
+
+The rate for C is going
+to be plus d[C]/dt.
+
+It's also going to be
+defined in a way
+
+that makes it positive.
+
+Because in this case, since the
+reaction's going this way,
+
+we're looking at the
+appearance of C.
+
+Now, by stoichiometry , in this
+case, of course whenever
+
+a molecule or a mole of A
+disappears, a molecule or a
+
+mole of C appears.
+
+So because of that, in this
+case, the stoichiometry tells
+
+us that that d[C]/dt is equal
+to negative d[A]/dt.
+
+And also equal to negative
+d[B]/dt.
+
+And any of those can be used to
+
+define the rate of reaction.
+
+Now, this is a particularly
+simple case because I've
+
+chosen the case where all
+of the stoichiometric
+
+coefficients are equal to one.
+
+So now let's just look at any
+case that's different.
+
+Let's look at 2A plus B goes to
+something else, 3C plus D.
+
+And just look at the reaction
+rates that we might see there.
+
+So here now, the appearance of
+C is going to be three times
+
+as fast as the appearance
+of D, for example.
+
+And also three times as fast as
+the disappearance of B. So
+
+if we write negative d[B]/dt,
+we expect that's going to be
+
+negative 1/2 d[A]/dt.
+
+In other words, A is going to
+disappear twice as fast as B.
+
+Every time a molecule of B
+reacts, two molecules of A do.
+
+And that's going to be plus 1/3
+d[C]/dt, and every time
+
+that happens three molecules
+of C get formed.
+
+And it's going to
+be plus d[D]/dt.
+
+One molecule of D gets formed.
+
+And so, the reaction rate could
+be defined in terms of
+
+any of these.
+
+But the important thing is to
+keep track of stoichiometry so
+
+that the rate as it pertains
+to each constituent is
+
+accounted for correctly.
+
+So to generalize, if I have
+little a of A, and little b of
+
+B, going to little c of C, and
+little d of D, then the rate
+
+of reaction can be written as
+minus one over a d[A]/dt, or
+
+minus one over b d[B]/dt, or
+one over c d[C]/dt, or one
+
+over d d[D]/dt.
+
+So, experimentally, lots of
+measurements of reaction rates
+
+have been made.
+
+And now to start on what's seen
+empirically, basically
+
+the following result is
+extremely common.
+
+The rate is equal to some
+constant times the
+
+concentration of A to some
+power alpha, times the
+
+concentration of B to some
+power beta, and so on.
+
+For all reactants.
+
+Multiplied together,
+each concentration
+
+taken to some power.
+
+Notice no products.
+
+Again, we're only looking at
+a reaction going one way.
+
+And if we look at the
+rate, this is
+
+typically what's found.
+
+Alpha is called the order of
+reaction, with respect to A.
+
+Beta order with respect
+to B. And so on.
+
+And little k is our rate
+constant which, just to make
+
+clear, since we've been using it
+extensively in the past few
+
+lectures, is completely
+not equal to
+
+the Boltzmann constant.
+
+Absolutely no connection
+between them.
+
+Now, alpha and beta, what they
+are, what they turn out to be,
+
+is typically what's determined
+as a result of kinetic
+
+measurement.
+
+Typically they're
+small integers.
+
+So, just sort of a typical
+example, if you look at the
+
+reaction of NO and O2, to make
+NO2, simple reaction, and you
+
+look at minus d[O2]/dt, use
+that as a measure of the
+
+reaction rate.
+
+What's found is that it's
+a constant times NO
+
+concentration squared,
+times O2.
+
+Simple, right?
+
+One of the exponents is
+two, the other's one.
+
+Doesn't seem so surprising
+mechanistically.
+
+But it's not always the case.
+
+Even when you have small
+integers, it's not always the
+
+case that the most obvious
+mechanism you would infer is
+
+the real mechanism.
+
+And sometimes those exponents
+don't turn
+
+out even to be integers.
+
+But here's another example.
+
+If you just look it CH3CHO going
+to methane and carbon
+
+monoxide, seems like it would
+be a pretty straightforward
+
+thing, too.
+
+So if you measure, for
+example, the rate of
+
+appearance of methane, what
+you discover is that it's
+
+equal to a constant times the
+concentration of the starting
+
+material to the 3/2 power.
+
+Not obvious mechanistically why
+that should be the case.
+
+Usually it's telling
+us something.
+
+It's telling us that the
+reaction mechanism is
+
+complicated.
+
+It's a multi-step process.
+
+Sometimes there could be chain
+reactions and so forth.
+
+So again, seeing things like
+this certainly helps us to
+
+infer molecular mechanisms.
+
+Again, they don't prove
+molecular mechanisms.
+
+But they certainly can be very
+helpful in suggesting them.
+
+And then other means can be
+used to try to prove them.
+
+Including, above all, direct
+observation of the
+
+intermediates that you would
+expect on the basis of one
+
+mechanism or another.
+
+Now let's just go through some
+elementary examples of
+
+kinetics one at a time.
+
+So let's start with the simplest
+possible case.
+
+Actually, a very rare case, but
+one that'll help us just
+
+set up the formalism
+of, and the
+
+mechanism for us to proceed.
+
+So let's talk about zero
+order reactions.
+
+Actually very rare.
+
+So, what this means is
+something like A
+
+goes over to products.
+
+Make a measurement of d[A]/dt,
+and discover that it's k time
+
+A to the power of zero,
+that is, it's just k.
+
+There's no dependence on the
+concentration of A. Or
+
+anything else.
+
+And you have some rate
+of its disappearance.
+
+So here's an example of it.
+
+You could have oxalic acid,
+and it just turns into
+
+hydrogen carbon dioxide
+and carbon dioxide.
+
+Things break apart, forms
+these products.
+
+Make a measurement of
+the disappearance.
+
+Seems to have nothing to do with
+the concentration of it.
+
+At least under certain
+conditions.
+
+Now, turns out that there's
+another element that helps
+
+understand this.
+
+Turns out that light
+is needed, it's a
+
+photochemical reaction.
+
+And then it's easy to see
+how this can happen.
+
+Let's say we have an abundance
+of the starting material, and
+
+not very much light.
+
+So every now and then photons
+bleed in, and every now and
+
+then when they're absorbed,
+it leads to dissociation.
+
+In that situation, you'll be
+limited by the photons, but
+
+not by the concentration
+of the molecules.
+
+And in fact, strictly speaking
+although this is zero order in
+
+terms of the chemical
+constituents, it's not zero
+
+order in the photons.
+
+So in some sense, in this sort
+of situation, the photons
+
+should be considered one
+of the reactants.
+
+You could write this as this
+plus h nu plus one photon,
+
+goes over to these products.
+
+And then if you measure the
+rate and things are under
+
+circumstances like I described,
+you would discover
+
+that in fact yes you'd
+be photon limited.
+
+The rate would depend
+on how many both
+
+photons are coming in.
+
+Still, ordinarily, chemical
+rate equations aren't
+
+formulated in those terms.
+
+So in the usual formulation,
+this would still have the
+
+appearance of a zero
+order reaction.
+
+Now, how do we write and
+formulate a solution?
+
+So it's simple.
+
+We've we've written a
+differential equation here.
+
+It's a pretty straightforward
+one.
+
+Minus d[A]/dt is just
+a constant.
+
+So we can solve it.
+
+And typically we'll solve it by
+rewriting in integral form
+
+and then doing the integration
+as long as we can do the
+
+integration.
+
+So from here we can write the
+integral from starting
+
+concentration [A]0 to some other
+concentration, [A], d[A]
+
+is equal to minus k integral
+from zero to t dt.
+
+So all we've done is integrate
+on both sides.
+
+And we've assumed a starting
+concentration.
+
+We've assumed an initial
+condition.
+
+And we've also assumed an
+initial time, which usually we
+
+can just call zero.
+
+And this is, of course,
+something we can solve for
+
+straight away.
+
+So we just have that [A] minus
+[A]0 is negative kt minus
+
+zero, which is minus kt.
+
+So [A] is minus kt.
+
+Plus [A]0.
+
+In other words, the
+concentration of [A] at any
+
+time is given by the initial
+concentration, minus the rate
+
+constant times time.
+
+It decays linearly in time.
+
+So we can sketch that.
+
+This is our initial
+concentration.
+
+And then it's just going to
+decline with time after that.
+
+And there's our solution.
+
+In lots of cases, it's
+useful to define
+
+what's called a half-life.
+
+It's just useful.
+
+Because it provides some
+timeframe, a single number
+
+that's a timeframe on which
+the reaction occurs.
+
+So, the half-life is just the
+time that it takes for half of
+
+the reactants to disappear.
+t 1/2 time to
+
+react half the reactants.
+
+OK, so in this case it's
+straightforward to see when
+
+that happens.
+
+In other words, that's the
+time at which this
+
+concentration of A is just
+equal to [A]0 over two.
+
+So we have [A]0 over two is
+minus kt 1/2 plus [A]0 or t
+
+1/2 is equal to [A] over 2k.
+
+[A]0 over 2k.
+
+So there's our half-life.
+
+So if we go over here,
+we can put that in.
+
+[A]0 over two, and this
+time is our half-life.
+
+So that's zero order
+reactions.
+
+And, again, zero order
+reactions are rare.
+
+But the procedure we're going to
+used to solve for kinetics
+
+is outlined in this way.
+
+And we'll use that
+again and again.
+
+Let's look at first-order
+kinetics.
+
+Let's go over here.
+
+Now, first order reactions
+are quite common.
+
+Much, much more common
+than zero order.
+
+So here, you have A
+goes to products.
+
+That's the simplest case.
+
+But this time if we measure
+d[A]/dt, we discover that it's
+
+equal to a constant times the
+concentration of A. There's an
+
+important point to note here.
+
+What are the units of
+k, in this case.
+
+What do they have to be?
+
+Yeah, reciprocal
+seconds right?
+
+The equation has to work.
+
+This is concentration
+per second.
+
+This is concentration.
+
+This better be per second.
+
+Let's just, before we move on
+completely, look at this.
+
+What are its units?
+
+Here's the equation.
+
+What are the units of k?
+
+No, not unitless, because,
+look at this.
+
+This is some concentration
+unit,
+
+typically moles per liter.
+
+So this is moles per liter
+per second, right?
+
+It's disappearance of some
+concentration for time.
+
+That's got to be here.
+
+All that is here.
+
+Moles per liter per second.
+
+So in every case, the units of
+k, the rate constant, have to
+
+be figured out on the basis of
+the specific rate equation.
+
+Doesn't have the same units.
+
+When the kinetics are
+of different order.
+
+Now, let's solve this using the
+same approach as before.
+
+Namely, this is still a
+pretty straightforward
+
+differential equation.
+
+So let's just integrate
+both sides.
+
+So that is going to tell us the
+integral from [A]0 to [A].
+
+But now we have [A]
+on this side.
+
+So here we just had
+a constant.
+
+And effectively, I didn't
+write it out.
+
+But we effectively wrote this,
+rewrote this, as d[A]
+
+equals minus k dt,
+and then went
+
+from here to the integral.
+
+We're going to do the
+same thing here,
+
+except now there's this.
+
+So really we're going
+to have d[A]
+
+over [A] is minus k dt.
+
+That's what we're going to
+integrate on both side.
+
+We need to have the variables
+distinct on each side.
+
+So we have d[A]
+
+over [A].
+
+Equal to minus k integral
+from zero to t dt.
+
+And so, of course, you know
+how to do this integral.
+
+It's going to look
+like log of [A].
+
+And again, it's taken
+at [A] or, at [A]0.
+
+So we have log of
+[A] over [A]0.
+
+We're going to have log of [A]
+minus log of [A]0 coming out.
+
+And that's equal to minus kt.
+
+So now the kinetics are
+quite different.
+
+We have [A] is equal to [A]0,
+e to the minus kt.
+
+Very important, very common
+sort of result.
+
+It's saying we start with a
+certain amount of material,
+
+and there's an exponential
+decay of it.
+
+So very different from
+kinetics here,
+
+which are just linear.
+
+And again the kinetics here, if
+you imagine that situation
+
+where you've got starting
+material and bleeding in
+
+gradually are photons,
+presumably at the same rate,
+
+then sure that material you're
+going to see the disappearance
+
+of it linearly with time.
+
+Just depending on the
+rate at which the
+
+photons are coming in.
+
+Here it's very different
+because, presumably, A is
+
+required in order to
+do this reaction.
+
+It'll depend on how much.
+
+Because of course if there's
+more of it, you'll just have
+
+more at any given time decaying
+over to products.
+
+So you have an exponential
+decay.
+
+So let's plot that.
+
+Here's [A], let's
+make that [A]0.
+
+There it is.
+
+Now, let's look at what happens
+to the product.
+
+So let's imagine that it's A
+going to B, so of course minus
+
+d[A]/dt is just equal to
+d[B]/dt, and the rate of
+
+appearance of B has to match the
+rate of disappearance of
+
+A. Let's assume that we
+don't have any of
+
+B present at first.
+
+So let's make [B]0
+equal to zero.
+
+Well then, [B] just has to equal
+[A]0 minus [A], right?
+
+All the stuff that's left, all
+of the A that has disappeared,
+
+that's given by this
+difference.
+
+Is just equal to B. So that's
+just [A]0 minus concentration
+
+of A, but that's just
+given by that.
+
+Which is [A]0 e to
+the minus kt.
+
+Or in other words, [B] is just
+equal to [A]0 times one minus
+
+e to the minus kt.
+
+So at t equals zero, this
+is zero and this is one.
+
+In other words, this is going
+to be zero at first.
+
+And then it's going to grow in
+with the same exponential form
+
+that this decayed.
+
+So, [B] is going to do
+the exact opposite.
+
+It's going to be like this.
+
+So this is [B] of t and this is
+[A] of t equals [A]0 e to
+
+the minus kt.
+
+Now, it's always useful to,
+whenever possible, to plot
+
+these things linearly.
+
+Find a way to plot these
+as straight lines.
+
+And of course in this case it's
+straightforward to do
+
+that as a log plot.
+
+So if we take the log of both
+sides, we know of course that
+
+the log of [A] is just minus kt,
+plus the log of [A]0, so
+
+now let's look at that.
+
+Make this the log of [A]0 and
+this is the log of [A]
+
+on the axis.
+
+That'll be time.
+
+So there's just some
+linear decay now.
+
+And the slope is minus k.
+
+So experimentally, of course,
+this'll be done typically as a
+
+simple way of determining it.
+
+Now, we also can usefully look
+at the half life, in this
+
+case, in the case of first
+order kinetics.
+
+So we have an expression
+in general for [A].
+
+So if we let [A] equal [A]0 over
+two, at t equals t 1/2,
+
+that tells us that log of [A]0
+over two divided by [A]0 is
+
+minus kt to the 1/2.
+
+But this is just the log of two,
+or log of two is over k
+
+is t to the 1/2.
+
+And so t to the 1/2 is
+just 0.693 over k.
+
+So we can write that just
+generally, completely
+
+independent of whatever [A] is,
+also independent of what
+
+[A]0 is, and that makes sense.
+
+So the point is, if you have
+something that just
+
+spontaneously decays into
+products, maybe it's just
+
+gradual chemical decomposition
+of something.
+
+Spontaneously, without the
+participation of other
+
+constituents.
+
+There's a general half-life
+that can be
+
+associated with that.
+
+That'll just be related
+directly to
+
+the rate of the decay.
+
+So it's knowable and measurable
+in a simple form.
+
+And again, the half-life
+is always useful.
+
+Because it just gives a simple,
+one-number measure of
+
+the rough timescale for
+things to change.
+
+So if we go back to this plot,
+and then once again here's our
+
+half concentration.
+
+And here's our t 1/2, just a
+useful way of summarizing in a
+
+simple way, what happens.
+
+Yeah?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Ooh.
+
+Well, I didn't think about it.
+
+But it isn't necessary
+that that'll happen.
+
+Sure seems like it must be.
+
+When one is half decayed, the
+other must be half formed as
+
+long as there wasn't any
+B present at first.
+
+So yeah, thank you.
+
+Well, given that, something
+needs to move.
+
+But let's pretend like I got it
+right at this intersection.
+
+Even though it doesn't
+look that good.
+
+So really it should be there.
+
+Thank you.
+
+So the single most common
+example of first order
+
+kinetics of this form is
+radioactive decay.
+
+You've got some radioactive
+isotopic that can
+
+spontaneously decay into
+some other nucleus.
+
+And of course, this is measured
+and half-lives have
+
+been tabulated for lots
+of cases of this sort.
+
+So a simple example.
+
+Let's look at carbon-14.
+
+It's got a nuclear
+charge of six.
+
+It can decay into nitrogen-14
+through
+
+the loss of an electron.
+
+Happens.
+
+First order kinetics.
+
+Now, in the atmosphere, what
+happens is this will end up,
+
+the 14C ends up getting
+replenished..
+
+Because from cosmic rays, what
+can happen is in the
+
+atmosphere, you can have your
+nitrogen plus a neutron will
+
+come and form 14C plus
+a hydrogen atom.
+
+So in fact, the overall
+concentration in the
+
+atmosphere of 14C tends to
+be constant over time.
+
+But stuff that's formed down
+here on Earth, with carbon,
+
+its content of 14C decays over
+time, and it doesn't get
+
+replenished.
+
+So, let's think back
+some long time ago.
+
+Here's a tree. we can
+make it pretty.
+
+So it's got some concentration
+of 14C that came from carbon
+
+dioxide in the atmosphere.
+
+That's what it started with.
+
+That's our starting point.
+
+At some point later, through
+natural occurrence or human
+
+intervention, that tree
+became horizontal.
+
+Then, and although we're looking
+back here, let's call
+
+this our t equals zero.
+
+And our 14C concentration
+at the time is our
+
+concentration at zero.
+
+Now let's say, shortly after
+that, either right after
+
+because of deliberate action,
+or shortly after because it
+
+was just discovered, somebody
+decides to build something
+
+using that tree.
+
+So, early human craft.
+
+And then let's say lots later,
+depending on your definition
+
+of lots, modern human, which can
+be denoted by this style
+
+of hat, makes exciting
+discovery.
+
+Terrific.
+
+And would like to know
+how old is it.
+
+How long ago did all
+that stuff happen.
+
+Let's assume this is also
+approximately t equals zero.
+
+Well, so a log of [14C]
+
+over [14C]0.
+
+So this carbon dating,
+all it's really doing
+
+is measuring that.
+
+It gives a number for it.
+
+And we know this because we're
+assuming it hasn't changed any
+
+in all those years.
+
+In the atmosphere.
+
+It's different down here,
+because the tree or the boat
+
+wasn't replenished.
+
+Not nearly as many cosmic
+rays fell on it.
+
+So that's minus log of t.
+
+And it turns out the t
+1/2 is 5,760 years.
+
+Amazing, that this can be
+known down to ten years.
+
+But it is.
+
+So that says, k his 0.693
+divided by t to the 1/2, which
+
+is one over 8,312 years.
+
+So there's our answer, then.
+
+The time, how long ago that
+happened, is just minus 8,312
+
+years times the log of [14C]
+
+in the artifact.
+
+Divided by the log
+of, by [14C]
+
+in the air.
+
+And the assumption again is that
+this is the same now as
+
+it was back then.
+
+And there's a bigger number than
+this, so it's a positive
+
+number overall.
+
+So in a fairly straightforward
+way, we'll use first order
+
+kinetics to determine
+the lifetime of
+
+something like this.
+
+Because we know the
+rate constant.
+
+And everything else follows.
+
+Let's see.
+
+Next there's going to be
+second order kinetics.
+
+But let me just stop here and
+say just a word about the exam
+
+on Wednesday.
+
+So I've handed out an
+information sheet about it.
+
+But I don't have anything very
+different to say this time
+
+than I've had to say about
+previous exams.
+
+Solve lots of problems.
+
+Go over the homework.
+
+Go over practice problems.
+
+Try last year's exam as
+a sample exam when
+
+you're ready to do it.
+
+Try it under test conditions.
+
+There's nothing on the exam that
+you're going to look at
+
+and say oh my God, how was I
+supposed to know that we ought
+
+to study that.
+
+There won't be any surprises.
+
+Most of the exam questions so
+far, not all have been easy,
+
+but I think they've been more
+or less plain vanilla in the
+
+sense that they're right more
+or less down the middle of
+
+what we're trying to teach.
+
+And not very many are taking off
+little peripheral elements
+
+of the class.
+
+And it's not going to be
+any different here.
+
+So if you can just do the
+problem solving and get
+
+familiar enough with it that
+you're just good at it, so
+
+that you can do it with a
+reasonable speed, you're going
+
+to be fine.
+
+Also try to work on just
+understanding the
+
+underpinnings.
+
+Especially of statistical
+mechanics.
+
+That's where when you have these
+true-false or multiple
+
+choice questions, these sort
+of thought exercises.
+
+Those are really hard.
+
+Because they go a little bit
+beyond problem solving.
+
+If you could do the
+problem solving,
+
+you're going to do fine.
+
+But it's always useful if you
+can also formulate things.
+
+And for that, it's never easy
+to just tell you here's what
+
+you have to do, to
+get good at this.
+
+Because you have to
+think about it.
+
+And it's always hard.
+
+But to be sure, if you can just
+try when you review the
+
+statistical mechanics,
+especially, and you review the
+
+expressions that you use and
+how you solve problems with
+
+them, the next step in studying
+is to try to think,
+
+OK, do I really understand
+where that
+
+expression came from.
+
+And why it makes sense
+physically.
+
+And if you can do that, then
+so much the better.
+
+Then you'll be in an even
+stronger position.
+
+The info sheet gives a handful
+of equations that we do expect
+
+you to come in with those
+on your fingertips.
+
+There are not very many.
+
+Mostly we'll provide expressions
+that you'll need,
+
+and the important thing is that
+you know, understand,
+
+where they apply.
+
+And how to use them.
+
+So, good luck on Wednesday.
\ No newline at end of file
diff --git a/DaHJqeTDN1M.txt b/DaHJqeTDN1M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..19628526158c5ed85e1022fc0880e550a18d5b24
--- /dev/null
+++ b/DaHJqeTDN1M.txt
@@ -0,0 +1,1946 @@
+align:start position:0%
+ 
+hi everyone uh so for this problem we're
+
+ align:start position:0%
+hi everyone uh so for this problem we're
+ 
+
+ align:start position:0%
+hi everyone uh so for this problem we're
+just going to take a look at uh
+
+ align:start position:0%
+just going to take a look at uh
+ 
+
+ align:start position:0%
+just going to take a look at uh
+Computing some igen values and igen
+
+ align:start position:0%
+Computing some igen values and igen
+ 
+
+ align:start position:0%
+Computing some igen values and igen
+vectors of uh several matrices and this
+
+ align:start position:0%
+vectors of uh several matrices and this
+ 
+
+ align:start position:0%
+vectors of uh several matrices and this
+is just a review problem for exam number
+
+ align:start position:0%
+is just a review problem for exam number
+ 
+
+ align:start position:0%
+is just a review problem for exam number
+three so specifically we're given a
+
+ align:start position:0%
+three so specifically we're given a
+ 
+
+ align:start position:0%
+three so specifically we're given a
+projection Matrix which has the form of
+
+ align:start position:0%
+projection Matrix which has the form of
+ 
+
+ align:start position:0%
+projection Matrix which has the form of
+a a transpose divided by a transpose a
+
+ align:start position:0%
+a a transpose divided by a transpose a
+ 
+
+ align:start position:0%
+a a transpose divided by a transpose a
+where a is the vector 3 and four the
+
+ align:start position:0%
+where a is the vector 3 and four the
+ 
+
+ align:start position:0%
+where a is the vector 3 and four the
+second problem is for a rotation Matrix
+
+ align:start position:0%
+second problem is for a rotation Matrix
+ 
+
+ align:start position:0%
+second problem is for a rotation Matrix
+Q uh which is the number
+
+ align:start position:0%
+Q uh which is the number
+ 
+
+ align:start position:0%
+Q uh which is the number
+0.6.8 point8
+
+ align:start position:0%
+0.6.8 point8
+ 
+
+ align:start position:0%
+0.6.8 point8
+and6 and then the third one is for a
+
+ align:start position:0%
+and6 and then the third one is for a
+ 
+
+ align:start position:0%
+and6 and then the third one is for a
+reflection Matrix uh which is 2p minus
+
+ align:start position:0%
+reflection Matrix uh which is 2p minus
+ 
+
+ align:start position:0%
+reflection Matrix uh which is 2p minus
+the identity so I'll let you uh work
+
+ align:start position:0%
+the identity so I'll let you uh work
+ 
+
+ align:start position:0%
+the identity so I'll let you uh work
+these out and then I'll come back in a
+
+ align:start position:0%
+these out and then I'll come back in a
+ 
+
+ align:start position:0%
+these out and then I'll come back in a
+second and I'll uh fill in my uh
+
+ align:start position:0%
+second and I'll uh fill in my uh
+ 
+
+ align:start position:0%
+second and I'll uh fill in my uh
+Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi everyone welcome back okay so for the
+
+ align:start position:0%
+hi everyone welcome back okay so for the
+ 
+
+ align:start position:0%
+hi everyone welcome back okay so for the
+first problem uh we're given a matrix P
+
+ align:start position:0%
+first problem uh we're given a matrix P
+ 
+
+ align:start position:0%
+first problem uh we're given a matrix P
+which is a projection Matrix and from
+
+ align:start position:0%
+which is a projection Matrix and from
+ 
+
+ align:start position:0%
+which is a projection Matrix and from
+earlier on in the course we probably
+
+ align:start position:0%
+earlier on in the course we probably
+ 
+
+ align:start position:0%
+earlier on in the course we probably
+already know that the igen values of a
+
+ align:start position:0%
+already know that the igen values of a
+ 
+
+ align:start position:0%
+already know that the igen values of a
+projection Matrix are are either zero or
+
+ align:start position:0%
+projection Matrix are are either zero or
+ 
+
+ align:start position:0%
+projection Matrix are are either zero or
+one and I'll just recall how how do you
+
+ align:start position:0%
+one and I'll just recall how how do you
+ 
+
+ align:start position:0%
+one and I'll just recall how how do you
+know that well if x is is an igen Vector
+
+ align:start position:0%
+know that well if x is is an igen Vector
+ 
+
+ align:start position:0%
+know that well if x is is an igen Vector
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+P then it satisfies uh the equation PX
+
+ align:start position:0%
+P then it satisfies uh the equation PX
+ 
+
+ align:start position:0%
+P then it satisfies uh the equation PX
+Lambda X but for projection Matrix p^2
+
+ align:start position:0%
+Lambda X but for projection Matrix p^2
+ 
+
+ align:start position:0%
+Lambda X but for projection Matrix p^2
+is equal to P so if p is a projection we
+
+ align:start position:0%
+is equal to P so if p is a projection we
+ 
+
+ align:start position:0%
+is equal to P so if p is a projection we
+have p^2 equal
+
+ align:start position:0%
+have p^2 equal
+ 
+
+ align:start position:0%
+have p^2 equal
+p and uh specifically what this means
+
+ align:start position:0%
+p and uh specifically what this means
+ 
+
+ align:start position:0%
+p and uh specifically what this means
+is uh p^2
+
+ align:start position:0%
+is uh p^2
+ 
+
+ align:start position:0%
+is uh p^2
+X is equal to
+
+ align:start position:0%
+X is equal to
+ 
+
+ align:start position:0%
+X is equal to
+uh Lambda
+
+ align:start position:0%
+uh Lambda
+ 
+
+ align:start position:0%
+uh Lambda
+x uh so we have P acting on P of
+
+ align:start position:0%
+x uh so we have P acting on P of
+ 
+
+ align:start position:0%
+x uh so we have P acting on P of
+X is equal to Lambda X
+
+ align:start position:0%
+X is equal to Lambda X
+ 
+
+ align:start position:0%
+X is equal to Lambda X
+and on the left hand side PX is going to
+
+ align:start position:0%
+and on the left hand side PX is going to
+ 
+
+ align:start position:0%
+and on the left hand side PX is going to
+give me Lambda X PX again will give me
+
+ align:start position:0%
+give me Lambda X PX again will give me
+ 
+
+ align:start position:0%
+give me Lambda X PX again will give me
+Lambda X and so we get Lambda 2
+
+ align:start position:0%
+Lambda X and so we get Lambda 2
+ 
+
+ align:start position:0%
+Lambda X and so we get Lambda 2
+x equals Lambda
+
+ align:start position:0%
+x equals Lambda
+ 
+
+ align:start position:0%
+x equals Lambda
+X and if I bring everything to the left
+
+ align:start position:0%
+X and if I bring everything to the left
+ 
+
+ align:start position:0%
+X and if I bring everything to the left
+hand side I get Lambda * Lambda minus
+
+ align:start position:0%
+hand side I get Lambda * Lambda minus
+ 
+
+ align:start position:0%
+hand side I get Lambda * Lambda minus
+one xal 0 and because X is not a zero
+
+ align:start position:0%
+one xal 0 and because X is not a zero
+ 
+
+ align:start position:0%
+one xal 0 and because X is not a zero
+Vector what that means is Lambda has to
+
+ align:start position:0%
+Vector what that means is Lambda has to
+ 
+
+ align:start position:0%
+Vector what that means is Lambda has to
+be either zero or one so this is just a
+
+ align:start position:0%
+be either zero or one so this is just a
+ 
+
+ align:start position:0%
+be either zero or one so this is just a
+quick proof that uh the a value of a
+
+ align:start position:0%
+quick proof that uh the a value of a
+ 
+
+ align:start position:0%
+quick proof that uh the a value of a
+project Matrix is either Z or one so we
+
+ align:start position:0%
+project Matrix is either Z or one so we
+ 
+
+ align:start position:0%
+project Matrix is either Z or one so we
+already know that P is going to have Aug
+
+ align:start position:0%
+already know that P is going to have Aug
+ 
+
+ align:start position:0%
+already know that P is going to have Aug
+a values of0 or
+
+ align:start position:0%
+a values of0 or
+ 
+
+ align:start position:0%
+a values of0 or
+one now specifically how do identify
+
+ align:start position:0%
+one now specifically how do identify
+ 
+
+ align:start position:0%
+one now specifically how do identify
+which a vectors uh correspond to zero
+
+ align:start position:0%
+which a vectors uh correspond to zero
+ 
+
+ align:start position:0%
+which a vectors uh correspond to zero
+and which a vectors correspond to one
+
+ align:start position:0%
+and which a vectors correspond to one
+ 
+
+ align:start position:0%
+and which a vectors correspond to one
+well in this case P has a specific form
+
+ align:start position:0%
+well in this case P has a specific form
+ 
+
+ align:start position:0%
+well in this case P has a specific form
+which is a * a transpose divid a
+
+ align:start position:0%
+which is a * a transpose divid a
+ 
+
+ align:start position:0%
+which is a * a transpose divid a
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so I'll just write out uh explicitly
+
+ align:start position:0%
+a so I'll just write out uh explicitly
+ 
+
+ align:start position:0%
+a so I'll just write out uh explicitly
+what this is so h transpose
+
+ align:start position:0%
+what this is so h transpose
+ 
+
+ align:start position:0%
+what this is so h transpose
+a 1 / a transpose a is going to be 9 +
+
+ align:start position:0%
+a 1 / a transpose a is going to be 9 +
+ 
+
+ align:start position:0%
+a 1 / a transpose a is going to be 9 +
+16 on the denominator then we're going
+
+ align:start position:0%
+16 on the denominator then we're going
+ 
+
+ align:start position:0%
+16 on the denominator then we're going
+to have three and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four and three and
+
+ align:start position:0%
+four and three and
+ 
+
+ align:start position:0%
+four and three and
+four now when we have a matrix of this
+
+ align:start position:0%
+four now when we have a matrix of this
+ 
+
+ align:start position:0%
+four now when we have a matrix of this
+form it's always going to be the case
+
+ align:start position:0%
+form it's always going to be the case
+ 
+
+ align:start position:0%
+form it's always going to be the case
+that the vector a is going to be an igen
+
+ align:start position:0%
+that the vector a is going to be an igen
+ 
+
+ align:start position:0%
+that the vector a is going to be an igen
+Vector with igen value one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check what is p acting on
+
+ align:start position:0%
+check what is p acting on
+ 
+
+ align:start position:0%
+check what is p acting on
+a well we end up
+
+ align:start position:0%
+a well we end up
+ 
+
+ align:start position:0%
+a well we end up
+with the Matrix p is 1 over
+
+ align:start position:0%
+with the Matrix p is 1 over
+ 
+
+ align:start position:0%
+with the Matrix p is 1 over
+25 3
+
+ align:start position:0%
+25 3
+ 
+
+ align:start position:0%
+25 3
+4 3
+
+ align:start position:0%
+4 3
+ 
+
+ align:start position:0%
+4 3
+4 this is the Matrix
+
+ align:start position:0%
+4 this is the Matrix
+ 
+
+ align:start position:0%
+4 this is the Matrix
+p and if we acted on the vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+34 notice how this piece right here we
+
+ align:start position:0%
+34 notice how this piece right here we
+ 
+
+ align:start position:0%
+34 notice how this piece right here we
+can multiply out this is going to be a
+
+ align:start position:0%
+can multiply out this is going to be a
+ 
+
+ align:start position:0%
+can multiply out this is going to be a
+transpose and this is going to be a and
+
+ align:start position:0%
+transpose and this is going to be a and
+ 
+
+ align:start position:0%
+transpose and this is going to be a and
+if we multiply these two pieces out we
+
+ align:start position:0%
+if we multiply these two pieces out we
+ 
+
+ align:start position:0%
+if we multiply these two pieces out we
+get one we get
+
+ align:start position:0%
+get one we get
+ 
+
+ align:start position:0%
+get one we get
+25 which is exactly the denominator a
+
+ align:start position:0%
+25 which is exactly the denominator a
+ 
+
+ align:start position:0%
+25 which is exactly the denominator a
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+a so at the end of the day we get
+
+ align:start position:0%
+a so at the end of the day we get
+ 
+
+ align:start position:0%
+a so at the end of the day we get
+34 because the 25 divides out with the
+
+ align:start position:0%
+34 because the 25 divides out with the
+ 
+
+ align:start position:0%
+34 because the 25 divides out with the
+25 now note that this is exactly what we
+
+ align:start position:0%
+25 now note that this is exactly what we
+ 
+
+ align:start position:0%
+25 now note that this is exactly what we
+started with this is exactly
+
+ align:start position:0%
+started with this is exactly
+ 
+
+ align:start position:0%
+started with this is exactly
+a so note here that the vector a
+
+ align:start position:0%
+a so note here that the vector a
+ 
+
+ align:start position:0%
+a so note here that the vector a
+uh corresponds to an igen value of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+meanwhile for an IG
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+zero well it it always turns out to be
+
+ align:start position:0%
+zero well it it always turns out to be
+ 
+
+ align:start position:0%
+zero well it it always turns out to be
+the case that if I take any Vector
+
+ align:start position:0%
+the case that if I take any Vector
+ 
+
+ align:start position:0%
+the case that if I take any Vector
+perpendicular to a p acting on that
+
+ align:start position:0%
+perpendicular to a p acting on that
+ 
+
+ align:start position:0%
+perpendicular to a p acting on that
+Vector is going to be
+
+ align:start position:0%
+Vector is going to be
+ 
+
+ align:start position:0%
+Vector is going to be
+zero so what's a vector which I'll call
+
+ align:start position:0%
+zero so what's a vector which I'll call
+ 
+
+ align:start position:0%
+zero so what's a vector which I'll call
+B that's perpendicular to a well note
+
+ align:start position:0%
+B that's perpendicular to a well note
+ 
+
+ align:start position:0%
+B that's perpendicular to a well note
+that a is just a 2 x two Vector so that
+
+ align:start position:0%
+that a is just a 2 x two Vector so that
+ 
+
+ align:start position:0%
+that a is just a 2 x two Vector so that
+means there's only going to be One
+
+ align:start position:0%
+means there's only going to be One
+ 
+
+ align:start position:0%
+means there's only going to be One
+Direction that's perpendicular to a now
+
+ align:start position:0%
+Direction that's perpendicular to a now
+ 
+
+ align:start position:0%
+Direction that's perpendicular to a now
+just by eyeballing it I can see that a
+
+ align:start position:0%
+just by eyeballing it I can see that a
+ 
+
+ align:start position:0%
+just by eyeballing it I can see that a
+vector that's going to be perpendicular
+
+ align:start position:0%
+vector that's going to be perpendicular
+ 
+
+ align:start position:0%
+vector that's going to be perpendicular
+to a is four and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three so let's quickly check that this
+
+ align:start position:0%
+three so let's quickly check that this
+ 
+
+ align:start position:0%
+three so let's quickly check that this
+is an I uh I Vector of p with I value
+
+ align:start position:0%
+is an I uh I Vector of p with I value
+ 
+
+ align:start position:0%
+is an I uh I Vector of p with I value
+zero so what we need to show is that P
+
+ align:start position:0%
+zero so what we need to show is that P
+ 
+
+ align:start position:0%
+zero so what we need to show is that P
+acting on this Vector B is
+
+ align:start position:0%
+acting on this Vector B is
+ 
+
+ align:start position:0%
+acting on this Vector B is
+zero so P acting on B
+
+ align:start position:0%
+zero so P acting on B
+ 
+
+ align:start position:0%
+zero so P acting on B
+is going to be 1 over
+
+ align:start position:0%
+is going to be 1 over
+ 
+
+ align:start position:0%
+is going to be 1 over
+25 it's going to be
+
+ align:start position:0%
+25 it's going to be
+ 
+
+ align:start position:0%
+25 it's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+34 multiplied by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+43 and note how when I multiply
+
+ align:start position:0%
+43 and note how when I multiply
+ 
+
+ align:start position:0%
+43 and note how when I multiply
+out this row on this column I get -3 * 4
+
+ align:start position:0%
+out this row on this column I get -3 * 4
+ 
+
+ align:start position:0%
+out this row on this column I get -3 * 4
++ 3 * 4 which is is going to be
+
+ align:start position:0%
++ 3 * 4 which is is going to be
+ 
+
+ align:start position:0%
++ 3 * 4 which is is going to be
+zero okay so this shows that this Vector
+
+ align:start position:0%
+zero okay so this shows that this Vector
+ 
+
+ align:start position:0%
+zero okay so this shows that this Vector
+B has an igen value of zero because note
+
+ align:start position:0%
+B has an igen value of zero because note
+ 
+
+ align:start position:0%
+B has an igen value of zero because note
+that we can write this as z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b okay for the second part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q uh what are the igen vectors and I
+
+ align:start position:0%
+Q uh what are the igen vectors and I
+ 
+
+ align:start position:0%
+Q uh what are the igen vectors and I
+values of this Matrix
+
+ align:start position:0%
+values of this Matrix
+ 
+
+ align:start position:0%
+values of this Matrix
+Q well Q uh is a rotation Matrix so I'll
+
+ align:start position:0%
+Q well Q uh is a rotation Matrix so I'll
+ 
+
+ align:start position:0%
+Q well Q uh is a rotation Matrix so I'll
+just write out Q
+
+ align:start position:0%
+just write out Q
+ 
+
+ align:start position:0%
+just write out Q
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6.88
+
+ align:start position:0%
+6.88
+ 
+
+ align:start position:0%
+6.88
+6 so note that we can identify uh the
+
+ align:start position:0%
+6 so note that we can identify uh the
+ 
+
+ align:start position:0%
+6 so note that we can identify uh the
+the diagonal elements with a cosine uh
+
+ align:start position:0%
+the diagonal elements with a cosine uh
+ 
+
+ align:start position:0%
+the diagonal elements with a cosine uh
+of some angle Theta and we can associate
+
+ align:start position:0%
+of some angle Theta and we can associate
+ 
+
+ align:start position:0%
+of some angle Theta and we can associate
+the off diagonal Parts as uh sin Theta
+
+ align:start position:0%
+the off diagonal Parts as uh sin Theta
+ 
+
+ align:start position:0%
+the off diagonal Parts as uh sin Theta
+and negative sin Theta and the reason we
+
+ align:start position:0%
+and negative sin Theta and the reason we
+ 
+
+ align:start position:0%
+and negative sin Theta and the reason we
+can do that is because 6^ 2+ 8^ 2 is 1
+
+ align:start position:0%
+can do that is because 6^ 2+ 8^ 2 is 1
+ 
+
+ align:start position:0%
+can do that is because 6^ 2+ 8^ 2 is 1
+so this is a rotation
+
+ align:start position:0%
+so this is a rotation
+ 
+
+ align:start position:0%
+so this is a rotation
+Matrix now uh to work out the a values I
+
+ align:start position:0%
+Matrix now uh to work out the a values I
+ 
+
+ align:start position:0%
+Matrix now uh to work out the a values I
+take a look at the characteristic
+
+ align:start position:0%
+take a look at the characteristic
+ 
+
+ align:start position:0%
+take a look at the characteristic
+equation so this is going to give me if
+
+ align:start position:0%
+equation so this is going to give me if
+ 
+
+ align:start position:0%
+equation so this is going to give me if
+I take a look at the characteristic
+
+ align:start position:0%
+I take a look at the characteristic
+ 
+
+ align:start position:0%
+I take a look at the characteristic
+equation it's going to be 6 minus
+
+ align:start position:0%
+equation it's going to be 6 minus
+ 
+
+ align:start position:0%
+equation it's going to be 6 minus
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+squared then we have minus * 8 * .8 so
+
+ align:start position:0%
+squared then we have minus * 8 * .8 so
+ 
+
+ align:start position:0%
+squared then we have minus * 8 * .8 so
+that's going to be
+
+ align:start position:0%
+that's going to be
+ 
+
+ align:start position:0%
+that's going to be
+plus 8^
+
+ align:start position:0%
+plus 8^
+ 
+
+ align:start position:0%
+plus 8^
+SAR and we want this to be zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I rewrite this I get Lambda is 6
+
+ align:start position:0%
+so if I rewrite this I get Lambda is 6
+ 
+
+ align:start position:0%
+so if I rewrite this I get Lambda is 6
+Plus or
+
+ align:start position:0%
+Plus or
+ 
+
+ align:start position:0%
+Plus or
+minus8 I where I is the imaginary number
+
+ align:start position:0%
+minus8 I where I is the imaginary number
+ 
+
+ align:start position:0%
+minus8 I where I is the imaginary number
+so notice how the igen values come in
+
+ align:start position:0%
+so notice how the igen values come in
+ 
+
+ align:start position:0%
+so notice how the igen values come in
+complex conjugate Pairs and this is
+
+ align:start position:0%
+complex conjugate Pairs and this is
+ 
+
+ align:start position:0%
+complex conjugate Pairs and this is
+always the case when we have a real
+
+ align:start position:0%
+always the case when we have a real
+ 
+
+ align:start position:0%
+always the case when we have a real
+Matrix so we can uh we can find first
+
+ align:start position:0%
+Matrix so we can uh we can find first
+ 
+
+ align:start position:0%
+Matrix so we can uh we can find first
+off just the igen value that corresponds
+
+ align:start position:0%
+off just the igen value that corresponds
+ 
+
+ align:start position:0%
+off just the igen value that corresponds
+to 6 +8 I and then at the end we'll be
+
+ align:start position:0%
+to 6 +8 I and then at the end we'll be
+ 
+
+ align:start position:0%
+to 6 +8 I and then at the end we'll be
+able to find the second igen vector by
+
+ align:start position:0%
+able to find the second igen vector by
+ 
+
+ align:start position:0%
+able to find the second igen vector by
+just taking the complex conjugate of the
+
+ align:start position:0%
+just taking the complex conjugate of the
+ 
+
+ align:start position:0%
+just taking the complex conjugate of the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+one so let's compute Q minus Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I and if we have this acting on some
+
+ align:start position:0%
+I and if we have this acting on some
+ 
+
+ align:start position:0%
+I and if we have this acting on some
+igen Vector U we want this to be
+
+ align:start position:0%
+igen Vector U we want this to be
+ 
+
+ align:start position:0%
+igen Vector U we want this to be
+zero now Q minus Lambda I is going to be
+
+ align:start position:0%
+zero now Q minus Lambda I is going to be
+ 
+
+ align:start position:0%
+zero now Q minus Lambda I is going to be
+for the case Lambda is 6 +8
+
+ align:start position:0%
+for the case Lambda is 6 +8
+ 
+
+ align:start position:0%
+for the case Lambda is 6 +8
+I this is going to give me a quantity
+
+ align:start position:0%
+I this is going to give me a quantity
+ 
+
+ align:start position:0%
+I this is going to give me a quantity
+of minus 8
+
+ align:start position:0%
+of minus 8
+ 
+
+ align:start position:0%
+of minus 8
+I minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+88 and minus8
+
+ align:start position:0%
+88 and minus8
+ 
+
+ align:start position:0%
+88 and minus8
+I and I'm going to write down components
+
+ align:start position:0%
+I and I'm going to write down components
+ 
+
+ align:start position:0%
+I and I'm going to write down components
+of U which are U1 and
+
+ align:start position:0%
+of U which are U1 and
+ 
+
+ align:start position:0%
+of U which are U1 and
+U2 and we want this to
+
+ align:start position:0%
+U2 and we want this to
+ 
+
+ align:start position:0%
+U2 and we want this to
+vanish and we note that the second row
+
+ align:start position:0%
+vanish and we note that the second row
+ 
+
+ align:start position:0%
+vanish and we note that the second row
+is a constant multiple of the first row
+
+ align:start position:0%
+is a constant multiple of the first row
+ 
+
+ align:start position:0%
+is a constant multiple of the first row
+specifically If I multiply this first
+
+ align:start position:0%
+specifically If I multiply this first
+ 
+
+ align:start position:0%
+specifically If I multiply this first
+row through by I we would get Negative
+
+ align:start position:0%
+row through by I we would get Negative
+ 
+
+ align:start position:0%
+row through by I we would get Negative
+i^2 which is just one
+
+ align:start position:0%
+i^2 which is just one
+ 
+
+ align:start position:0%
+i^2 which is just one
+and then the second part would be
+
+ align:start position:0%
+and then the second part would be
+ 
+
+ align:start position:0%
+and then the second part would be
+negative I so we would just get the
+
+ align:start position:0%
+negative I so we would just get the
+ 
+
+ align:start position:0%
+negative I so we would just get the
+second row back which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so we just need to find U1 U2 that
+
+ align:start position:0%
+good so we just need to find U1 U2 that
+ 
+
+ align:start position:0%
+good so we just need to find U1 U2 that
+are orthogonal to this first this first
+
+ align:start position:0%
+are orthogonal to this first this first
+ 
+
+ align:start position:0%
+are orthogonal to this first this first
+row and again just by inspection I can
+
+ align:start position:0%
+row and again just by inspection I can
+ 
+
+ align:start position:0%
+row and again just by inspection I can
+pick one and negative
+
+ align:start position:0%
+pick one and negative
+ 
+
+ align:start position:0%
+pick one and negative
+I so note that uh that would give mega8
+
+ align:start position:0%
+I so note that uh that would give mega8
+ 
+
+ align:start position:0%
+I so note that uh that would give mega8
+I Plus 8 I and this vanishes so this is
+
+ align:start position:0%
+I Plus 8 I and this vanishes so this is
+ 
+
+ align:start position:0%
+I Plus 8 I and this vanishes so this is
+one uh this is the a that corresponds to
+
+ align:start position:0%
+one uh this is the a that corresponds to
+ 
+
+ align:start position:0%
+one uh this is the a that corresponds to
+the value Lambda 6 +8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I uh in the
+
+ align:start position:0%
+I uh in the
+ 
+
+ align:start position:0%
+I uh in the
+meantime if I take the
+
+ align:start position:0%
+meantime if I take the
+ 
+
+ align:start position:0%
+meantime if I take the
+second I value which is negative point8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I can take U which is just the complex
+
+ align:start position:0%
+I I can take U which is just the complex
+ 
+
+ align:start position:0%
+I I can take U which is just the complex
+conjugate of this U up
+
+ align:start position:0%
+conjugate of this U up
+ 
+
+ align:start position:0%
+conjugate of this U up
+here so it'll be 1 plus
+
+ align:start position:0%
+here so it'll be 1 plus
+ 
+
+ align:start position:0%
+here so it'll be 1 plus
+I so this concludes the aen values uh an
+
+ align:start position:0%
+I so this concludes the aen values uh an
+ 
+
+ align:start position:0%
+I so this concludes the aen values uh an
+aen vectors of this Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q okay now lastly number three we're
+
+ align:start position:0%
+Q okay now lastly number three we're
+ 
+
+ align:start position:0%
+Q okay now lastly number three we're
+looking at uh a rotation
+
+ align:start position:0%
+looking at uh a rotation
+ 
+
+ align:start position:0%
+looking at uh a rotation
+Matrix uh sorry not a rotation Matrix
+
+ align:start position:0%
+Matrix uh sorry not a rotation Matrix
+ 
+
+ align:start position:0%
+Matrix uh sorry not a rotation Matrix
+but a reflection Matrix which has the
+
+ align:start position:0%
+but a reflection Matrix which has the
+ 
+
+ align:start position:0%
+but a reflection Matrix which has the
+form 2 p minus
+
+ align:start position:0%
+form 2 p minus
+ 
+
+ align:start position:0%
+form 2 p minus
+I where p is the same Matrix uh that we
+
+ align:start position:0%
+I where p is the same Matrix uh that we
+ 
+
+ align:start position:0%
+I where p is the same Matrix uh that we
+had in part
+
+ align:start position:0%
+had in part
+ 
+
+ align:start position:0%
+had in part
+one now it at first glance it looks like
+
+ align:start position:0%
+one now it at first glance it looks like
+ 
+
+ align:start position:0%
+one now it at first glance it looks like
+we might have to diag Alize this entire
+
+ align:start position:0%
+we might have to diag Alize this entire
+ 
+
+ align:start position:0%
+we might have to diag Alize this entire
+Matrix however note that by shifting uh
+
+ align:start position:0%
+Matrix however note that by shifting uh
+ 
+
+ align:start position:0%
+Matrix however note that by shifting uh
+2 p by I uh we only shift the a values
+
+ align:start position:0%
+2 p by I uh we only shift the a values
+ 
+
+ align:start position:0%
+2 p by I uh we only shift the a values
+and we don't actually change the aen
+
+ align:start position:0%
+and we don't actually change the aen
+ 
+
+ align:start position:0%
+and we don't actually change the aen
+vectors so note that this Matrix R which
+
+ align:start position:0%
+vectors so note that this Matrix R which
+ 
+
+ align:start position:0%
+vectors so note that this Matrix R which
+is 2 p minus I it's going to have the
+
+ align:start position:0%
+is 2 p minus I it's going to have the
+ 
+
+ align:start position:0%
+is 2 p minus I it's going to have the
+same igen vectors as P it's just going
+
+ align:start position:0%
+same igen vectors as P it's just going
+ 
+
+ align:start position:0%
+same igen vectors as P it's just going
+to have different igen
+
+ align:start position:0%
+to have different igen
+ 
+
+ align:start position:0%
+to have different igen
+values so first off we're going to have
+
+ align:start position:0%
+values so first off we're going to have
+ 
+
+ align:start position:0%
+values so first off we're going to have
+uh one IG
+
+ align:start position:0%
+uh one IG
+ 
+
+ align:start position:0%
+uh one IG
+Vector uh so the first igen Vector is
+
+ align:start position:0%
+Vector uh so the first igen Vector is
+ 
+
+ align:start position:0%
+Vector uh so the first igen Vector is
+going to be a so we have one igen vector
+
+ align:start position:0%
+going to be a so we have one igen vector
+ 
+
+ align:start position:0%
+going to be a so we have one igen vector
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+a so we have one igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector which is
+
+ align:start position:0%
+vector which is
+ 
+
+ align:start position:0%
+vector which is
+a and note that when for the vector
+
+ align:start position:0%
+a and note that when for the vector
+ 
+
+ align:start position:0%
+a and note that when for the vector
+a uh it corresponds to the igen value of
+
+ align:start position:0%
+a uh it corresponds to the igen value of
+ 
+
+ align:start position:0%
+a uh it corresponds to the igen value of
+one so what igen value does this
+
+ align:start position:0%
+one so what igen value does this
+ 
+
+ align:start position:0%
+one so what igen value does this
+correspond
+
+ align:start position:0%
+correspond
+ 
+
+ align:start position:0%
+correspond
+to this is going to give me a
+
+ align:start position:0%
+to this is going to give me a
+ 
+
+ align:start position:0%
+to this is going to give me a
+Lambda which is 2 * 1
+
+ align:start position:0%
+Lambda which is 2 * 1
+ 
+
+ align:start position:0%
+Lambda which is 2 * 1
+minus one so it's one so note that a the
+
+ align:start position:0%
+minus one so it's one so note that a the
+ 
+
+ align:start position:0%
+minus one so it's one so note that a the
+vector a not only has an Igan value of
+
+ align:start position:0%
+vector a not only has an Igan value of
+ 
+
+ align:start position:0%
+vector a not only has an Igan value of
+one for p but it has an a value of one
+
+ align:start position:0%
+one for p but it has an a value of one
+ 
+
+ align:start position:0%
+one for p but it has an a value of one
+for r as
+
+ align:start position:0%
+for r as
+ 
+
+ align:start position:0%
+for r as
+well the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case was
+
+ align:start position:0%
+case was
+ 
+
+ align:start position:0%
+case was
+B and remember that B has an igen value
+
+ align:start position:0%
+B and remember that B has an igen value
+ 
+
+ align:start position:0%
+B and remember that B has an igen value
+of zero for p so when we act our acting
+
+ align:start position:0%
+of zero for p so when we act our acting
+ 
+
+ align:start position:0%
+of zero for p so when we act our acting
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B we have 2 * 0 minus 1 B so this is
+
+ align:start position:0%
+B we have 2 * 0 minus 1 B so this is
+ 
+
+ align:start position:0%
+B we have 2 * 0 minus 1 B so this is
+going to give us negative
+
+ align:start position:0%
+going to give us negative
+ 
+
+ align:start position:0%
+going to give us negative
+B so the igen value for B is going to be
+
+ align:start position:0%
+B so the igen value for B is going to be
+ 
+
+ align:start position:0%
+B so the igen value for B is going to be
+negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 okay and this is actually a general uh
+
+ align:start position:0%
+1 okay and this is actually a general uh
+ 
+
+ align:start position:0%
+1 okay and this is actually a general uh
+case for uh reflection matrices is that
+
+ align:start position:0%
+case for uh reflection matrices is that
+ 
+
+ align:start position:0%
+case for uh reflection matrices is that
+they typically have I values of plus one
+
+ align:start position:0%
+they typically have I values of plus one
+ 
+
+ align:start position:0%
+they typically have I values of plus one
+or negative
+
+ align:start position:0%
+or negative
+ 
+
+ align:start position:0%
+or negative
+one Okay so we've just taken a look at
+
+ align:start position:0%
+one Okay so we've just taken a look at
+ 
+
+ align:start position:0%
+one Okay so we've just taken a look at
+uh several matrices that come up in
+
+ align:start position:0%
+uh several matrices that come up in
+ 
+
+ align:start position:0%
+uh several matrices that come up in
+practice uh We've looked at projection
+
+ align:start position:0%
+practice uh We've looked at projection
+ 
+
+ align:start position:0%
+practice uh We've looked at projection
+matrices reflection matrices and
+
+ align:start position:0%
+matrices reflection matrices and
+ 
+
+ align:start position:0%
+matrices reflection matrices and
+rotation matrices and we've uh seen a
+
+ align:start position:0%
+rotation matrices and we've uh seen a
+ 
+
+ align:start position:0%
+rotation matrices and we've uh seen a
+little bit of the properties of their
+
+ align:start position:0%
+little bit of the properties of their
+ 
+
+ align:start position:0%
+little bit of the properties of their
+igen values and igen vectors so I'll uh
+
+ align:start position:0%
+igen values and igen vectors so I'll uh
+ 
+
+ align:start position:0%
+igen values and igen vectors so I'll uh
+just conclude here and uh good luck on
+
+ align:start position:0%
+just conclude here and uh good luck on
+ 
+
+ align:start position:0%
+just conclude here and uh good luck on
+your test
\ No newline at end of file
diff --git a/EjXtpzysDL4.txt b/EjXtpzysDL4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..70be8b44a3578d0590a408269c77c7f04b44ba67
--- /dev/null
+++ b/EjXtpzysDL4.txt
@@ -0,0 +1,11072 @@
+align:start position:0%
+ 
+Okay. So, uh let me just recall first
+
+ align:start position:0%
+Okay. So, uh let me just recall first
+ 
+
+ align:start position:0%
+Okay. So, uh let me just recall first
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so what we were talking about so this is
+
+ align:start position:0%
+so what we were talking about so this is
+ 
+
+ align:start position:0%
+so what we were talking about so this is
+a very important concept uh of a
+
+ align:start position:0%
+a very important concept uh of a
+ 
+
+ align:start position:0%
+a very important concept uh of a
+sequence concept of a sequence.
+
+ align:start position:0%
+sequence concept of a sequence.
+ 
+
+ align:start position:0%
+sequence concept of a sequence.
+So sequence is is the formal definition
+
+ align:start position:0%
+So sequence is is the formal definition
+ 
+
+ align:start position:0%
+So sequence is is the formal definition
+is that you have a map from the natural
+
+ align:start position:0%
+is that you have a map from the natural
+ 
+
+ align:start position:0%
+is that you have a map from the natural
+number into R
+
+ align:start position:0%
+number into R
+ 
+
+ align:start position:0%
+number into R
+and then we denote so then the image of
+
+ align:start position:0%
+and then we denote so then the image of
+ 
+
+ align:start position:0%
+and then we denote so then the image of
+a particular natural number n it's
+
+ align:start position:0%
+a particular natural number n it's
+ 
+
+ align:start position:0%
+a particular natural number n it's
+usually denoted like a n like this you
+
+ align:start position:0%
+usually denoted like a n like this you
+ 
+
+ align:start position:0%
+usually denoted like a n like this you
+know it could be some other instead of a
+
+ align:start position:0%
+know it could be some other instead of a
+ 
+
+ align:start position:0%
+know it could be some other instead of a
+it could be bn potentially it could be
+
+ align:start position:0%
+it could be bn potentially it could be
+ 
+
+ align:start position:0%
+it could be bn potentially it could be
+another subscript but it's this is like
+
+ align:start position:0%
+another subscript but it's this is like
+ 
+
+ align:start position:0%
+another subscript but it's this is like
+the most common thing to denote it like
+
+ align:start position:0%
+the most common thing to denote it like
+ 
+
+ align:start position:0%
+the most common thing to denote it like
+this instead of like but it really is a
+
+ align:start position:0%
+this instead of like but it really is a
+ 
+
+ align:start position:0%
+this instead of like but it really is a
+function. Okay, so that's a sequence a
+
+ align:start position:0%
+function. Okay, so that's a sequence a
+ 
+
+ align:start position:0%
+function. Okay, so that's a sequence a
+subsequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So subsequence is that you have a
+
+ align:start position:0%
+So subsequence is that you have a
+ 
+
+ align:start position:0%
+So subsequence is that you have a
+sequence and then you have another map
+
+ align:start position:0%
+sequence and then you have another map
+ 
+
+ align:start position:0%
+sequence and then you have another map
+but this map is not just any map from
+
+ align:start position:0%
+but this map is not just any map from
+ 
+
+ align:start position:0%
+but this map is not just any map from
+the integers to the integers. It has to
+
+ align:start position:0%
+the integers to the integers. It has to
+ 
+
+ align:start position:0%
+the integers to the integers. It has to
+be strictly increasing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And why does it have to be strictly
+
+ align:start position:0%
+And why does it have to be strictly
+ 
+
+ align:start position:0%
+And why does it have to be strictly
+increasing? Because we want for the
+
+ align:start position:0%
+increasing? Because we want for the
+ 
+
+ align:start position:0%
+increasing? Because we want for the
+subsequence. If you think about the
+
+ align:start position:0%
+subsequence. If you think about the
+ 
+
+ align:start position:0%
+subsequence. If you think about the
+numbers that come out when you plug in a
+
+ align:start position:0%
+numbers that come out when you plug in a
+ 
+
+ align:start position:0%
+numbers that come out when you plug in a
+when you're looking at the a then you
+
+ align:start position:0%
+when you're looking at the a then you
+ 
+
+ align:start position:0%
+when you're looking at the a then you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+some of those numbers to be in the
+
+ align:start position:0%
+some of those numbers to be in the
+ 
+
+ align:start position:0%
+some of those numbers to be in the
+subsequence, but you want the ordering
+
+ align:start position:0%
+subsequence, but you want the ordering
+ 
+
+ align:start position:0%
+subsequence, but you want the ordering
+to be the same. So this map so that's
+
+ align:start position:0%
+to be the same. So this map so that's
+ 
+
+ align:start position:0%
+to be the same. So this map so that's
+why this map has to be strictly
+
+ align:start position:0%
+why this map has to be strictly
+ 
+
+ align:start position:0%
+why this map has to be strictly
+increasing right can't sort of I mean
+
+ align:start position:0%
+increasing right can't sort of I mean
+ 
+
+ align:start position:0%
+increasing right can't sort of I mean
+you and you can't pick the several
+
+ align:start position:0%
+you and you can't pick the several
+ 
+
+ align:start position:0%
+you and you can't pick the several
+elements many times if it wasn't picked
+
+ align:start position:0%
+elements many times if it wasn't picked
+ 
+
+ align:start position:0%
+elements many times if it wasn't picked
+many times in the original uh sequence
+
+ align:start position:0%
+many times in the original uh sequence
+ 
+
+ align:start position:0%
+many times in the original uh sequence
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this is so a subsequence is where you
+
+ align:start position:0%
+so this is so a subsequence is where you
+ 
+
+ align:start position:0%
+so this is so a subsequence is where you
+have another map from the natural number
+
+ align:start position:0%
+have another map from the natural number
+ 
+
+ align:start position:0%
+have another map from the natural number
+to the natural number that is strictly
+
+ align:start position:0%
+to the natural number that is strictly
+ 
+
+ align:start position:0%
+to the natural number that is strictly
+increasing and then you're looking at
+
+ align:start position:0%
+increasing and then you're looking at
+ 
+
+ align:start position:0%
+increasing and then you're looking at
+the composition of these two maps so
+
+ align:start position:0%
+the composition of these two maps so
+ 
+
+ align:start position:0%
+the composition of these two maps so
+you're looking at sorry uh this thing
+
+ align:start position:0%
+you're looking at sorry uh this thing
+ 
+
+ align:start position:0%
+you're looking at sorry uh this thing
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right and you call this here and then
+
+ align:start position:0%
+right and you call this here and then
+ 
+
+ align:start position:0%
+right and you call this here and then
+that's usually
+
+ align:start position:0%
+that's usually
+ 
+
+ align:start position:0%
+that's usually
+denoted something
+
+ align:start position:0%
+denoted something
+ 
+
+ align:start position:0%
+denoted something
+like this a n k a n is the original
+
+ align:start position:0%
+like this a n k a n is the original
+ 
+
+ align:start position:0%
+like this a n k a n is the original
+sequence k means that it's really that
+
+ align:start position:0%
+sequence k means that it's really that
+ 
+
+ align:start position:0%
+sequence k means that it's really that
+you take the image of k under this
+
+ align:start position:0%
+you take the image of k under this
+ 
+
+ align:start position:0%
+you take the image of k under this
+strictly increasing map and then you're
+
+ align:start position:0%
+strictly increasing map and then you're
+ 
+
+ align:start position:0%
+strictly increasing map and then you're
+looking at the element in the sequence
+
+ align:start position:0%
+looking at the element in the sequence
+ 
+
+ align:start position:0%
+looking at the element in the sequence
+right so it's sort of n k is really you
+
+ align:start position:0%
+right so it's sort of n k is really you
+ 
+
+ align:start position:0%
+right so it's sort of n k is really you
+should think about it as G of K.
+
+ align:start position:0%
+should think about it as G of K.
+ 
+
+ align:start position:0%
+should think about it as G of K.
+Okay, so that's that's what a a a
+
+ align:start position:0%
+Okay, so that's that's what a a a
+ 
+
+ align:start position:0%
+Okay, so that's that's what a a a
+subsequence is. And again, it's
+
+ align:start position:0%
+subsequence is. And again, it's
+ 
+
+ align:start position:0%
+subsequence is. And again, it's
+important that it's strictly increasing
+
+ align:start position:0%
+important that it's strictly increasing
+ 
+
+ align:start position:0%
+important that it's strictly increasing
+because you want the elements to be in
+
+ align:start position:0%
+because you want the elements to be in
+ 
+
+ align:start position:0%
+because you want the elements to be in
+the same order than it was in the
+
+ align:start position:0%
+the same order than it was in the
+ 
+
+ align:start position:0%
+the same order than it was in the
+original sequence. And you don't want
+
+ align:start position:0%
+original sequence. And you don't want
+ 
+
+ align:start position:0%
+original sequence. And you don't want
+things you don't even want things to be
+
+ align:start position:0%
+things you don't even want things to be
+ 
+
+ align:start position:0%
+things you don't even want things to be
+picked more times than it was in
+
+ align:start position:0%
+picked more times than it was in
+ 
+
+ align:start position:0%
+picked more times than it was in
+original sequence. Mhm. So that that's
+
+ align:start position:0%
+original sequence. Mhm. So that that's
+ 
+
+ align:start position:0%
+original sequence. Mhm. So that that's
+that's you know so this this whole
+
+ align:start position:0%
+that's you know so this this whole
+ 
+
+ align:start position:0%
+that's you know so this this whole
+concept of a sequence of subunits is
+
+ align:start position:0%
+concept of a sequence of subunits is
+ 
+
+ align:start position:0%
+concept of a sequence of subunits is
+really important. Then
+
+ align:start position:0%
+really important. Then
+ 
+
+ align:start position:0%
+really important. Then
+the next really important concept is
+
+ align:start position:0%
+the next really important concept is
+ 
+
+ align:start position:0%
+the next really important concept is
+uh is of convergence.
+
+ align:start position:0%
+uh is of convergence.
+ 
+
+ align:start position:0%
+uh is of convergence.
+So if you have a sequence a n then you
+
+ align:start position:0%
+So if you have a sequence a n then you
+ 
+
+ align:start position:0%
+So if you have a sequence a n then you
+say that is converging to a. So so a is
+
+ align:start position:0%
+say that is converging to a. So so a is
+ 
+
+ align:start position:0%
+say that is converging to a. So so a is
+another real number. It's not infinity.
+
+ align:start position:0%
+another real number. It's not infinity.
+ 
+
+ align:start position:0%
+another real number. It's not infinity.
+is another real number and so a n
+
+ align:start position:0%
+is another real number and so a n
+ 
+
+ align:start position:0%
+is another real number and so a n
+converts. So a n converts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to a if for all
+
+ align:start position:0%
+to a if for all
+ 
+
+ align:start position:0%
+to a if for all
+epsilon greater than zero there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n an integer n you know by capital n
+
+ align:start position:0%
+n an integer n you know by capital n
+ 
+
+ align:start position:0%
+n an integer n you know by capital n
+such that if little n is bigger equal to
+
+ align:start position:0%
+such that if little n is bigger equal to
+ 
+
+ align:start position:0%
+such that if little n is bigger equal to
+this capital n then a n minus minus a
+
+ align:start position:0%
+this capital n then a n minus minus a
+ 
+
+ align:start position:0%
+this capital n then a n minus minus a
+have to be less than epsilon. Right? of
+
+ align:start position:0%
+have to be less than epsilon. Right? of
+ 
+
+ align:start position:0%
+have to be less than epsilon. Right? of
+those. So if you are sufficiently far
+
+ align:start position:0%
+those. So if you are sufficiently far
+ 
+
+ align:start position:0%
+those. So if you are sufficiently far
+out in sequence then everything in that
+
+ align:start position:0%
+out in sequence then everything in that
+ 
+
+ align:start position:0%
+out in sequence then everything in that
+sequence is bunch epsilon close to a
+
+ align:start position:0%
+sequence is bunch epsilon close to a
+ 
+
+ align:start position:0%
+sequence is bunch epsilon close to a
+okay that's what it's saying
+
+ align:start position:0%
+okay that's what it's saying
+ 
+
+ align:start position:0%
+okay that's what it's saying
+and so as if you have a sequence
+
+ align:start position:0%
+and so as if you have a sequence
+ 
+
+ align:start position:0%
+and so as if you have a sequence
+so a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is not convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is set to be divergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um and the next thing for sequences is
+
+ align:start position:0%
+Um and the next thing for sequences is
+ 
+
+ align:start position:0%
+Um and the next thing for sequences is
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I'm just briefly reviewing this from
+
+ align:start position:0%
+I'm just briefly reviewing this from
+ 
+
+ align:start position:0%
+I'm just briefly reviewing this from
+last time. The next thing for sequences
+
+ align:start position:0%
+last time. The next thing for sequences
+ 
+
+ align:start position:0%
+last time. The next thing for sequences
+are the are the break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to break uh
+
+ align:start position:0%
+to break uh
+ 
+
+ align:start position:0%
+to break uh
+uh laws or whatever you want to call
+
+ align:start position:0%
+uh laws or whatever you want to call
+ 
+
+ align:start position:0%
+uh laws or whatever you want to call
+them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so that is that if you take a
+
+ align:start position:0%
+And so that is that if you take a
+ 
+
+ align:start position:0%
+And so that is that if you take a
+sequence, if you have a sequence a n and
+
+ align:start position:0%
+sequence, if you have a sequence a n and
+ 
+
+ align:start position:0%
+sequence, if you have a sequence a n and
+a n converts to a bn converts to b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if you form the sum of these two
+
+ align:start position:0%
+then if you form the sum of these two
+ 
+
+ align:start position:0%
+then if you form the sum of these two
+uh a
+
+ align:start position:0%
+uh a
+ 
+
+ align:start position:0%
+uh a
+n + bn.
+
+ align:start position:0%
+n + bn.
+ 
+
+ align:start position:0%
+n + bn.
+So this is a new sequence where the nth
+
+ align:start position:0%
+So this is a new sequence where the nth
+ 
+
+ align:start position:0%
+So this is a new sequence where the nth
+element is the sum of the nth element of
+
+ align:start position:0%
+element is the sum of the nth element of
+ 
+
+ align:start position:0%
+element is the sum of the nth element of
+the other two sequences. then this
+
+ align:start position:0%
+the other two sequences. then this
+ 
+
+ align:start position:0%
+the other two sequences. then this
+sequence here CN also converge and the
+
+ align:start position:0%
+sequence here CN also converge and the
+ 
+
+ align:start position:0%
+sequence here CN also converge and the
+limit here is the sum of the limits.
+
+ align:start position:0%
+limit here is the sum of the limits.
+ 
+
+ align:start position:0%
+limit here is the sum of the limits.
+Okay. And likewise if you take a if
+
+ align:start position:0%
+Okay. And likewise if you take a if
+ 
+
+ align:start position:0%
+Okay. And likewise if you take a if
+you're looking at at if you define a
+
+ align:start position:0%
+you're looking at at if you define a
+ 
+
+ align:start position:0%
+you're looking at at if you define a
+sequence so this was one
+
+ align:start position:0%
+sequence so this was one
+ 
+
+ align:start position:0%
+sequence so this was one
+two is that if you take a constant so
+
+ align:start position:0%
+two is that if you take a constant so
+ 
+
+ align:start position:0%
+two is that if you take a constant so
+this is a constant
+
+ align:start position:0%
+this is a constant
+ 
+
+ align:start position:0%
+this is a constant
+and you define cn to be c * a n then
+
+ align:start position:0%
+and you define cn to be c * a n then
+ 
+
+ align:start position:0%
+and you define cn to be c * a n then
+this cn also converge and the limit here
+
+ align:start position:0%
+this cn also converge and the limit here
+ 
+
+ align:start position:0%
+this cn also converge and the limit here
+is just c * a right that's the second
+
+ align:start position:0%
+is just c * a right that's the second
+ 
+
+ align:start position:0%
+is just c * a right that's the second
+one then uh this one I might have done
+
+ align:start position:0%
+one then uh this one I might have done
+ 
+
+ align:start position:0%
+one then uh this one I might have done
+it in the other order but there's no you
+
+ align:start position:0%
+it in the other order but there's no you
+ 
+
+ align:start position:0%
+it in the other order but there's no you
+know it's not you know there's no
+
+ align:start position:0%
+know it's not you know there's no
+ 
+
+ align:start position:0%
+know it's not you know there's no
+particular order
+
+ align:start position:0%
+particular order
+ 
+
+ align:start position:0%
+particular order
+um to have it in.
+
+ align:start position:0%
+um to have it in.
+ 
+
+ align:start position:0%
+um to have it in.
+Uh the third one is that if you are
+
+ align:start position:0%
+Uh the third one is that if you are
+ 
+
+ align:start position:0%
+Uh the third one is that if you are
+looking at the product. So if you define
+
+ align:start position:0%
+looking at the product. So if you define
+ 
+
+ align:start position:0%
+looking at the product. So if you define
+a sequence that is given by the product
+
+ align:start position:0%
+a sequence that is given by the product
+ 
+
+ align:start position:0%
+a sequence that is given by the product
+of the two then C and converge also and
+
+ align:start position:0%
+of the two then C and converge also and
+ 
+
+ align:start position:0%
+of the two then C and converge also and
+the limit is the product of the limits.
+
+ align:start position:0%
+the limit is the product of the limits.
+ 
+
+ align:start position:0%
+the limit is the product of the limits.
+And then the fourth rule is that if a n
+
+ align:start position:0%
+And then the fourth rule is that if a n
+ 
+
+ align:start position:0%
+And then the fourth rule is that if a n
+is not equal to zero for all n and the
+
+ align:start position:0%
+is not equal to zero for all n and the
+ 
+
+ align:start position:0%
+is not equal to zero for all n and the
+limit here
+
+ align:start position:0%
+limit here
+ 
+
+ align:start position:0%
+limit here
+is also not equal to zero. Then if
+
+ align:start position:0%
+is also not equal to zero. Then if
+ 
+
+ align:start position:0%
+is also not equal to zero. Then if
+you're looking at 1 / a n then those
+
+ align:start position:0%
+you're looking at 1 / a n then those
+ 
+
+ align:start position:0%
+you're looking at 1 / a n then those
+converge to one.
+
+ align:start position:0%
+converge to one.
+ 
+
+ align:start position:0%
+converge to one.
+Okay. So those are the four four the
+
+ align:start position:0%
+Okay. So those are the four four the
+ 
+
+ align:start position:0%
+Okay. So those are the four four the
+four roots.
+
+ align:start position:0%
+four roots.
+ 
+
+ align:start position:0%
+four roots.
+Just write it as four. And again, it's
+
+ align:start position:0%
+Just write it as four. And again, it's
+ 
+
+ align:start position:0%
+Just write it as four. And again, it's
+not like there's any particular
+
+ align:start position:0%
+not like there's any particular
+ 
+
+ align:start position:0%
+not like there's any particular
+convention with the ordering. And I
+
+ align:start position:0%
+convention with the ordering. And I
+ 
+
+ align:start position:0%
+convention with the ordering. And I
+think I might have done it. I might have
+
+ align:start position:0%
+think I might have done it. I might have
+ 
+
+ align:start position:0%
+think I might have done it. I might have
+exchanged the order of one and two last
+
+ align:start position:0%
+exchanged the order of one and two last
+ 
+
+ align:start position:0%
+exchanged the order of one and two last
+time. But
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. Um now, uh let's see an example of
+
+ align:start position:0%
+okay. Um now, uh let's see an example of
+ 
+
+ align:start position:0%
+okay. Um now, uh let's see an example of
+how that works.
+
+ align:start position:0%
+how that works.
+ 
+
+ align:start position:0%
+how that works.
+So let's define a sequence.
+
+ align:start position:0%
+So let's define a sequence.
+ 
+
+ align:start position:0%
+So let's define a sequence.
+Uh let's define a sequence uh n 2 + 1 n
+
+ align:start position:0%
+Uh let's define a sequence uh n 2 + 1 n
+ 
+
+ align:start position:0%
+Uh let's define a sequence uh n 2 + 1 n
+2 + uh n +
+
+ align:start position:0%
+2 + uh n +
+ 
+
+ align:start position:0%
+2 + uh n +
+uh + one. Let's look at this sequence
+
+ align:start position:0%
+uh + one. Let's look at this sequence
+ 
+
+ align:start position:0%
+uh + one. Let's look at this sequence
+here right for each n that give us uh
+
+ align:start position:0%
+here right for each n that give us uh
+ 
+
+ align:start position:0%
+here right for each n that give us uh
+actually a rational number but it's only
+
+ align:start position:0%
+actually a rational number but it's only
+ 
+
+ align:start position:0%
+actually a rational number but it's only
+real number.
+
+ align:start position:0%
+real number.
+ 
+
+ align:start position:0%
+real number.
+Now in order to understand this I can
+
+ align:start position:0%
+Now in order to understand this I can
+ 
+
+ align:start position:0%
+Now in order to understand this I can
+rewrite this one here as I can factor
+
+ align:start position:0%
+rewrite this one here as I can factor
+ 
+
+ align:start position:0%
+rewrite this one here as I can factor
+out 1 / n well I can factor out n squ
+
+ align:start position:0%
+out 1 / n well I can factor out n squ
+ 
+
+ align:start position:0%
+out 1 / n well I can factor out n squ
+here. So I can write it like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that. And then of course I can get
+
+ align:start position:0%
+like that. And then of course I can get
+ 
+
+ align:start position:0%
+like that. And then of course I can get
+rid of the n squ
+
+ align:start position:0%
+rid of the n squ
+ 
+
+ align:start position:0%
+rid of the n squ
+in both denominator and denominator. And
+
+ align:start position:0%
+in both denominator and denominator. And
+ 
+
+ align:start position:0%
+in both denominator and denominator. And
+now I can look so so this so you may as
+
+ align:start position:0%
+now I can look so so this so you may as
+ 
+
+ align:start position:0%
+now I can look so so this so you may as
+well think about the sequence as this
+
+ align:start position:0%
+well think about the sequence as this
+ 
+
+ align:start position:0%
+well think about the sequence as this
+thing here. So now if I defined um so
+
+ align:start position:0%
+thing here. So now if I defined um so
+ 
+
+ align:start position:0%
+thing here. So now if I defined um so
+now I can just look at say uh I can look
+
+ align:start position:0%
+now I can just look at say uh I can look
+ 
+
+ align:start position:0%
+now I can just look at say uh I can look
+at uh the sequence which is one I can
+
+ align:start position:0%
+at uh the sequence which is one I can
+ 
+
+ align:start position:0%
+at uh the sequence which is one I can
+just first look at the sequence which is
+
+ align:start position:0%
+just first look at the sequence which is
+ 
+
+ align:start position:0%
+just first look at the sequence which is
+1 / n. If I'm looking at this sequence
+
+ align:start position:0%
+1 / n. If I'm looking at this sequence
+ 
+
+ align:start position:0%
+1 / n. If I'm looking at this sequence
+here, right, one / n, this here converts
+
+ align:start position:0%
+here, right, one / n, this here converts
+ 
+
+ align:start position:0%
+here, right, one / n, this here converts
+to zero. This is essentially just
+
+ align:start position:0%
+to zero. This is essentially just
+ 
+
+ align:start position:0%
+to zero. This is essentially just
+followed from the ardian property,
+
+ align:start position:0%
+followed from the ardian property,
+ 
+
+ align:start position:0%
+followed from the ardian property,
+right? But we already we've already seen
+
+ align:start position:0%
+right? But we already we've already seen
+ 
+
+ align:start position:0%
+right? But we already we've already seen
+this that 1 / n converts to zero.
+
+ align:start position:0%
+this that 1 / n converts to zero.
+ 
+
+ align:start position:0%
+this that 1 / n converts to zero.
+And the same hold for 1 / n^2, right?
+
+ align:start position:0%
+And the same hold for 1 / n^2, right?
+ 
+
+ align:start position:0%
+And the same hold for 1 / n^2, right?
+This here also converts to zero, right?
+
+ align:start position:0%
+This here also converts to zero, right?
+ 
+
+ align:start position:0%
+This here also converts to zero, right?
+And so if you're looking at the
+
+ align:start position:0%
+And so if you're looking at the
+ 
+
+ align:start position:0%
+And so if you're looking at the
+sequence, you could even look at the
+
+ align:start position:0%
+sequence, you could even look at the
+ 
+
+ align:start position:0%
+sequence, you could even look at the
+sequence.
+
+ align:start position:0%
+sequence.
+ 
+
+ align:start position:0%
+sequence.
+Let's call this x n. This here is yn.
+
+ align:start position:0%
+Let's call this x n. This here is yn.
+ 
+
+ align:start position:0%
+Let's call this x n. This here is yn.
+I'm going to run out of character very
+
+ align:start position:0%
+I'm going to run out of character very
+ 
+
+ align:start position:0%
+I'm going to run out of character very
+quickly. Uh set n. This is just going to
+
+ align:start position:0%
+quickly. Uh set n. This is just going to
+ 
+
+ align:start position:0%
+quickly. Uh set n. This is just going to
+be the sequence which is constant one.
+
+ align:start position:0%
+be the sequence which is constant one.
+ 
+
+ align:start position:0%
+be the sequence which is constant one.
+Right? Well, if if it's constant one,
+
+ align:start position:0%
+Right? Well, if if it's constant one,
+ 
+
+ align:start position:0%
+Right? Well, if if it's constant one,
+then obviously it's converging to one,
+
+ align:start position:0%
+then obviously it's converging to one,
+ 
+
+ align:start position:0%
+then obviously it's converging to one,
+right? And so now I can just think about
+
+ align:start position:0%
+right? And so now I can just think about
+ 
+
+ align:start position:0%
+right? And so now I can just think about
+I can think about the sequence bn
+
+ align:start position:0%
+I can think about the sequence bn
+ 
+
+ align:start position:0%
+I can think about the sequence bn
+to be equal to x sorry equal to set
+
+ align:start position:0%
+to be equal to x sorry equal to set
+ 
+
+ align:start position:0%
+to be equal to x sorry equal to set
+plus uh y set n plus yn right this here
+
+ align:start position:0%
+plus uh y set n plus yn right this here
+ 
+
+ align:start position:0%
+plus uh y set n plus yn right this here
+is a sequence here is what yn is here's
+
+ align:start position:0%
+is a sequence here is what yn is here's
+ 
+
+ align:start position:0%
+is a sequence here is what yn is here's
+what set n is right so if you add these
+
+ align:start position:0%
+what set n is right so if you add these
+ 
+
+ align:start position:0%
+what set n is right so if you add these
+two this is converging to one this is
+
+ align:start position:0%
+two this is converging to one this is
+ 
+
+ align:start position:0%
+two this is converging to one this is
+converging to zero by the algebraic
+
+ align:start position:0%
+converging to zero by the algebraic
+ 
+
+ align:start position:0%
+converging to zero by the algebraic
+property of limits this converts also to
+
+ align:start position:0%
+property of limits this converts also to
+ 
+
+ align:start position:0%
+property of limits this converts also to
+the sum of the limit so this here
+
+ align:start position:0%
+the sum of the limit so this here
+ 
+
+ align:start position:0%
+the sum of the limit so this here
+converts to one right now I can also
+
+ align:start position:0%
+converts to one right now I can also
+ 
+
+ align:start position:0%
+converts to one right now I can also
+define a sequence where I'm just adding
+
+ align:start position:0%
+define a sequence where I'm just adding
+ 
+
+ align:start position:0%
+define a sequence where I'm just adding
+set in and then I'm adding x in and then
+
+ align:start position:0%
+set in and then I'm adding x in and then
+ 
+
+ align:start position:0%
+set in and then I'm adding x in and then
+I'm adding y in right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here converts to one this here to
+
+ align:start position:0%
+this here converts to one this here to
+ 
+
+ align:start position:0%
+this here converts to one this here to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+this here to zero. So the sum here also
+
+ align:start position:0%
+this here to zero. So the sum here also
+ 
+
+ align:start position:0%
+this here to zero. So the sum here also
+converge to the sum of the limit but the
+
+ align:start position:0%
+converge to the sum of the limit but the
+ 
+
+ align:start position:0%
+converge to the sum of the limit but the
+sum of the limits is one.
+
+ align:start position:0%
+sum of the limits is one.
+ 
+
+ align:start position:0%
+sum of the limits is one.
+Now you have that
+
+ align:start position:0%
+Now you have that
+ 
+
+ align:start position:0%
+Now you have that
+one over c sorry now you have that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put it up here and then then I will I'll
+
+ align:start position:0%
+put it up here and then then I will I'll
+ 
+
+ align:start position:0%
+put it up here and then then I will I'll
+just go over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now you have that um that CN
+
+ align:start position:0%
+So now you have that um that CN
+ 
+
+ align:start position:0%
+So now you have that um that CN
+converts to one.
+
+ align:start position:0%
+converts to one.
+ 
+
+ align:start position:0%
+converts to one.
+Um and let's call this here C. And so in
+
+ align:start position:0%
+Um and let's call this here C. And so in
+ 
+
+ align:start position:0%
+Um and let's call this here C. And so in
+in particular, I mean all of these
+
+ align:start position:0%
+in particular, I mean all of these
+ 
+
+ align:start position:0%
+in particular, I mean all of these
+numbers here, these things here are all
+
+ align:start position:0%
+numbers here, these things here are all
+ 
+
+ align:start position:0%
+numbers here, these things here are all
+strictly positive. So each of the CN are
+
+ align:start position:0%
+strictly positive. So each of the CN are
+ 
+
+ align:start position:0%
+strictly positive. So each of the CN are
+strictly positive. So they're definitely
+
+ align:start position:0%
+strictly positive. So they're definitely
+ 
+
+ align:start position:0%
+strictly positive. So they're definitely
+not zero, right? So the CN so not only
+
+ align:start position:0%
+not zero, right? So the CN so not only
+ 
+
+ align:start position:0%
+not zero, right? So the CN so not only
+do they converge to one but the CN are
+
+ align:start position:0%
+do they converge to one but the CN are
+ 
+
+ align:start position:0%
+do they converge to one but the CN are
+not equal to zero and the limit C well
+
+ align:start position:0%
+not equal to zero and the limit C well
+ 
+
+ align:start position:0%
+not equal to zero and the limit C well
+that's one so that's of course not equal
+
+ align:start position:0%
+that's one so that's of course not equal
+ 
+
+ align:start position:0%
+that's one so that's of course not equal
+to zero either right so you can apply
+
+ align:start position:0%
+to zero either right so you can apply
+ 
+
+ align:start position:0%
+to zero either right so you can apply
+the fourth rule here the fourth rule for
+
+ align:start position:0%
+the fourth rule here the fourth rule for
+ 
+
+ align:start position:0%
+the fourth rule here the fourth rule for
+the sequence not for the sequence CN not
+
+ align:start position:0%
+the sequence not for the sequence CN not
+ 
+
+ align:start position:0%
+the sequence not for the sequence CN not
+right so apply the fourth rule to the
+
+ align:start position:0%
+right so apply the fourth rule to the
+ 
+
+ align:start position:0%
+right so apply the fourth rule to the
+sequence CN and then you have that one
+
+ align:start position:0%
+sequence CN and then you have that one
+ 
+
+ align:start position:0%
+sequence CN and then you have that one
+over CN converge to one / c. But one c
+
+ align:start position:0%
+over CN converge to one / c. But one c
+ 
+
+ align:start position:0%
+over CN converge to one / c. But one c
+was one. So this is one. Right?
+
+ align:start position:0%
+was one. So this is one. Right?
+ 
+
+ align:start position:0%
+was one. So this is one. Right?
+Now you can look at at um at bn
+
+ align:start position:0%
+Now you can look at at um at bn
+ 
+
+ align:start position:0%
+Now you can look at at um at bn
+* 1 / cn. But bn * 1 / cn, right?
+
+ align:start position:0%
+* 1 / cn. But bn * 1 / cn, right?
+ 
+
+ align:start position:0%
+* 1 / cn. But bn * 1 / cn, right?
+Remember what bn was? Here's bn. And bn
+
+ align:start position:0%
+Remember what bn was? Here's bn. And bn
+ 
+
+ align:start position:0%
+Remember what bn was? Here's bn. And bn
+is really the denominator up here.
+
+ align:start position:0%
+is really the denominator up here.
+ 
+
+ align:start position:0%
+is really the denominator up here.
+Right? It's the nominator up here. when
+
+ align:start position:0%
+Right? It's the nominator up here. when
+ 
+
+ align:start position:0%
+Right? It's the nominator up here. when
+you have divided by n squ on both sides
+
+ align:start position:0%
+you have divided by n squ on both sides
+ 
+
+ align:start position:0%
+you have divided by n squ on both sides
+uh by not on both sides but both in the
+
+ align:start position:0%
+uh by not on both sides but both in the
+ 
+
+ align:start position:0%
+uh by not on both sides but both in the
+top and the denominator.
+
+ align:start position:0%
+top and the denominator.
+ 
+
+ align:start position:0%
+top and the denominator.
+So bn is the denominator and cn is the
+
+ align:start position:0%
+So bn is the denominator and cn is the
+ 
+
+ align:start position:0%
+So bn is the denominator and cn is the
+denominator. So bn divided by CN this
+
+ align:start position:0%
+denominator. So bn divided by CN this
+ 
+
+ align:start position:0%
+denominator. So bn divided by CN this
+here is a n right
+
+ align:start position:0%
+here is a n right
+ 
+
+ align:start position:0%
+here is a n right
+and now this here converge that's what
+
+ align:start position:0%
+and now this here converge that's what
+ 
+
+ align:start position:0%
+and now this here converge that's what
+we saw over there using the algebraic
+
+ align:start position:0%
+we saw over there using the algebraic
+ 
+
+ align:start position:0%
+we saw over there using the algebraic
+rule it converts to one this here also
+
+ align:start position:0%
+rule it converts to one this here also
+ 
+
+ align:start position:0%
+rule it converts to one this here also
+converts to one by the algebraic rules
+
+ align:start position:0%
+converts to one by the algebraic rules
+ 
+
+ align:start position:0%
+converts to one by the algebraic rules
+number three of the algebraic rules is
+
+ align:start position:0%
+number three of the algebraic rules is
+ 
+
+ align:start position:0%
+number three of the algebraic rules is
+that for the product it will also
+
+ align:start position:0%
+that for the product it will also
+ 
+
+ align:start position:0%
+that for the product it will also
+converge so and it converts to the
+
+ align:start position:0%
+converge so and it converts to the
+ 
+
+ align:start position:0%
+converge so and it converts to the
+product of the limits so that's one
+
+ align:start position:0%
+product of the limits so that's one
+ 
+
+ align:start position:0%
+product of the limits so that's one
+And obviously so I you know this is like
+
+ align:start position:0%
+And obviously so I you know this is like
+ 
+
+ align:start position:0%
+And obviously so I you know this is like
+when you're looking at a sequence it's
+
+ align:start position:0%
+when you're looking at a sequence it's
+ 
+
+ align:start position:0%
+when you're looking at a sequence it's
+often uh expressed in some form with
+
+ align:start position:0%
+often uh expressed in some form with
+ 
+
+ align:start position:0%
+often uh expressed in some form with
+some functions like this and you and you
+
+ align:start position:0%
+some functions like this and you and you
+ 
+
+ align:start position:0%
+some functions like this and you and you
+do this reduction and very quickly you
+
+ align:start position:0%
+do this reduction and very quickly you
+ 
+
+ align:start position:0%
+do this reduction and very quickly you
+know this would be almost automatic
+
+ align:start position:0%
+know this would be almost automatic
+ 
+
+ align:start position:0%
+know this would be almost automatic
+right I mean this is too easy almost
+
+ align:start position:0%
+right I mean this is too easy almost
+ 
+
+ align:start position:0%
+right I mean this is too easy almost
+this one I mean you know this is the
+
+ align:start position:0%
+this one I mean you know this is the
+ 
+
+ align:start position:0%
+this one I mean you know this is the
+first time you see it but you know in in
+
+ align:start position:0%
+first time you see it but you know in in
+ 
+
+ align:start position:0%
+first time you see it but you know in in
+a couple of weeks this will feel uh too
+
+ align:start position:0%
+a couple of weeks this will feel uh too
+ 
+
+ align:start position:0%
+a couple of weeks this will feel uh too
+easy uh then then there would be
+
+ align:start position:0%
+easy uh then then there would be
+ 
+
+ align:start position:0%
+easy uh then then there would be
+something more complicated.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So that's that's the algebraic rules uh
+
+ align:start position:0%
+So that's that's the algebraic rules uh
+ 
+
+ align:start position:0%
+So that's that's the algebraic rules uh
+of for sequences.
+
+ align:start position:0%
+of for sequences.
+ 
+
+ align:start position:0%
+of for sequences.
+The next thing I want to talk about is I
+
+ align:start position:0%
+The next thing I want to talk about is I
+ 
+
+ align:start position:0%
+The next thing I want to talk about is I
+want to try to make more precise
+
+ align:start position:0%
+want to try to make more precise
+ 
+
+ align:start position:0%
+want to try to make more precise
+um you know this about square. I mean,
+
+ align:start position:0%
+um you know this about square. I mean,
+ 
+
+ align:start position:0%
+um you know this about square. I mean,
+you know, we made it pretty precise, but
+
+ align:start position:0%
+you know, we made it pretty precise, but
+ 
+
+ align:start position:0%
+you know, we made it pretty precise, but
+I want to think about
+
+ align:start position:0%
+I want to think about
+ 
+
+ align:start position:0%
+I want to think about
+uh uh I don't have a very good eraser,
+
+ align:start position:0%
+uh uh I don't have a very good eraser,
+ 
+
+ align:start position:0%
+uh uh I don't have a very good eraser,
+unfortunately. Let me just see. This is
+
+ align:start position:0%
+unfortunately. Let me just see. This is
+ 
+
+ align:start position:0%
+unfortunately. Let me just see. This is
+a better one.
+
+ align:start position:0%
+a better one.
+ 
+
+ align:start position:0%
+a better one.
+This one here will make it very dirty.
+
+ align:start position:0%
+This one here will make it very dirty.
+ 
+
+ align:start position:0%
+This one here will make it very dirty.
+Okay. So, so the next thing I want to
+
+ align:start position:0%
+Okay. So, so the next thing I want to
+ 
+
+ align:start position:0%
+Okay. So, so the next thing I want to
+So, we did define square of two and we
+
+ align:start position:0%
+So, we did define square of two and we
+ 
+
+ align:start position:0%
+So, we did define square of two and we
+talked about that quite extensively. how
+
+ align:start position:0%
+talked about that quite extensively. how
+ 
+
+ align:start position:0%
+talked about that quite extensively. how
+square root two, you know, how it really
+
+ align:start position:0%
+square root two, you know, how it really
+ 
+
+ align:start position:0%
+square root two, you know, how it really
+was defined and it was a real number and
+
+ align:start position:0%
+was defined and it was a real number and
+ 
+
+ align:start position:0%
+was defined and it was a real number and
+the real numbers followed from
+
+ align:start position:0%
+the real numbers followed from
+ 
+
+ align:start position:0%
+the real numbers followed from
+that the field the reals is complete.
+
+ align:start position:0%
+that the field the reals is complete.
+ 
+
+ align:start position:0%
+that the field the reals is complete.
+But we also
+
+ align:start position:0%
+But we also
+ 
+
+ align:start position:0%
+But we also
+we also sort of in the back of our mind
+
+ align:start position:0%
+we also sort of in the back of our mind
+ 
+
+ align:start position:0%
+we also sort of in the back of our mind
+we had that we already sort of knew what
+
+ align:start position:0%
+we had that we already sort of knew what
+ 
+
+ align:start position:0%
+we had that we already sort of knew what
+square root of two were, right? Because
+
+ align:start position:0%
+square root of two were, right? Because
+ 
+
+ align:start position:0%
+square root of two were, right? Because
+when you think about square root two, I
+
+ align:start position:0%
+when you think about square root two, I
+ 
+
+ align:start position:0%
+when you think about square root two, I
+mean at least I think about square root
+
+ align:start position:0%
+mean at least I think about square root
+ 
+
+ align:start position:0%
+mean at least I think about square root
+two. I think about it as 1.4. I mean
+
+ align:start position:0%
+two. I think about it as 1.4. I mean
+ 
+
+ align:start position:0%
+two. I think about it as 1.4. I mean
+just because you can't really express it
+
+ align:start position:0%
+just because you can't really express it
+ 
+
+ align:start position:0%
+just because you can't really express it
+as a fraction. So you think about it as
+
+ align:start position:0%
+as a fraction. So you think about it as
+ 
+
+ align:start position:0%
+as a fraction. So you think about it as
+1.414
+
+ align:start position:0%
+1.414
+ 
+
+ align:start position:0%
+1.414
+etc. And then I don't remember I don't
+
+ align:start position:0%
+etc. And then I don't remember I don't
+ 
+
+ align:start position:0%
+etc. And then I don't remember I don't
+remember the second years third and
+
+ align:start position:0%
+remember the second years third and
+ 
+
+ align:start position:0%
+remember the second years third and
+fourth whatever but you know you may
+
+ align:start position:0%
+fourth whatever but you know you may
+ 
+
+ align:start position:0%
+fourth whatever but you know you may
+remember just a few of the digits fine
+
+ align:start position:0%
+remember just a few of the digits fine
+ 
+
+ align:start position:0%
+remember just a few of the digits fine
+and but so how do we make so so that's
+
+ align:start position:0%
+and but so how do we make so so that's
+ 
+
+ align:start position:0%
+and but so how do we make so so that's
+sort of our intuition
+
+ align:start position:0%
+sort of our intuition
+ 
+
+ align:start position:0%
+sort of our intuition
+uh with 1.4 four with with square two.
+
+ align:start position:0%
+uh with 1.4 four with with square two.
+ 
+
+ align:start position:0%
+uh with 1.4 four with with square two.
+Uh but how do we make this more precise?
+
+ align:start position:0%
+Uh but how do we make this more precise?
+ 
+
+ align:start position:0%
+Uh but how do we make this more precise?
+Right? And so to make this more precise,
+
+ align:start position:0%
+Right? And so to make this more precise,
+ 
+
+ align:start position:0%
+Right? And so to make this more precise,
+we want to look at particular sequences.
+
+ align:start position:0%
+we want to look at particular sequences.
+ 
+
+ align:start position:0%
+we want to look at particular sequences.
+So what's called monotone
+
+ align:start position:0%
+So what's called monotone
+ 
+
+ align:start position:0%
+So what's called monotone
+sequences?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what is a mono sequence?
+
+ align:start position:0%
+So what is a mono sequence?
+ 
+
+ align:start position:0%
+So what is a mono sequence?
+So there's two types of monotom
+
+ align:start position:0%
+So there's two types of monotom
+ 
+
+ align:start position:0%
+So there's two types of monotom
+sequence. There's one which is monot
+
+ align:start position:0%
+sequence. There's one which is monot
+ 
+
+ align:start position:0%
+sequence. There's one which is monot
+increasing sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's similarly monotum
+
+ align:start position:0%
+and then there's similarly monotum
+ 
+
+ align:start position:0%
+and then there's similarly monotum
+decreasing sequence. So a monotum
+
+ align:start position:0%
+decreasing sequence. So a monotum
+ 
+
+ align:start position:0%
+decreasing sequence. So a monotum
+increasing sequence this is just means
+
+ align:start position:0%
+increasing sequence this is just means
+ 
+
+ align:start position:0%
+increasing sequence this is just means
+that for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have that the next element is larger
+
+ align:start position:0%
+you have that the next element is larger
+ 
+
+ align:start position:0%
+you have that the next element is larger
+or equal to the previous element. That's
+
+ align:start position:0%
+or equal to the previous element. That's
+ 
+
+ align:start position:0%
+or equal to the previous element. That's
+a mono increasing sequence. Right? Some
+
+ align:start position:0%
+a mono increasing sequence. Right? Some
+ 
+
+ align:start position:0%
+a mono increasing sequence. Right? Some
+people talk about strictly monotum
+
+ align:start position:0%
+people talk about strictly monotum
+ 
+
+ align:start position:0%
+people talk about strictly monotum
+increasing and then this have to be a
+
+ align:start position:0%
+increasing and then this have to be a
+ 
+
+ align:start position:0%
+increasing and then this have to be a
+strict.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh the second thing is kind of the
+
+ align:start position:0%
+Uh the second thing is kind of the
+ 
+
+ align:start position:0%
+Uh the second thing is kind of the
+obvious parallel to this is monoton
+
+ align:start position:0%
+obvious parallel to this is monoton
+ 
+
+ align:start position:0%
+obvious parallel to this is monoton
+decreasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing sequences.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's these two types. Okay. And
+
+ align:start position:0%
+So that's these two types. Okay. And
+ 
+
+ align:start position:0%
+So that's these two types. Okay. And
+this just means that the next element so
+
+ align:start position:0%
+this just means that the next element so
+ 
+
+ align:start position:0%
+this just means that the next element so
+a n + one is less or equal to the
+
+ align:start position:0%
+a n + one is less or equal to the
+ 
+
+ align:start position:0%
+a n + one is less or equal to the
+previous one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so now there's a theorem and and
+
+ align:start position:0%
+And so now there's a theorem and and
+ 
+
+ align:start position:0%
+And so now there's a theorem and and
+I'll prove this in a in just a minute.
+
+ align:start position:0%
+I'll prove this in a in just a minute.
+ 
+
+ align:start position:0%
+I'll prove this in a in just a minute.
+But I also want to
+
+ align:start position:0%
+But I also want to
+ 
+
+ align:start position:0%
+But I also want to
+and I want to come back to square root
+
+ align:start position:0%
+and I want to come back to square root
+ 
+
+ align:start position:0%
+and I want to come back to square root
+of two and then I want to look at
+
+ align:start position:0%
+of two and then I want to look at
+ 
+
+ align:start position:0%
+of two and then I want to look at
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+classical example of a monotum sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right so this is a mono sequence and now
+
+ align:start position:0%
+right so this is a mono sequence and now
+ 
+
+ align:start position:0%
+right so this is a mono sequence and now
+let me state the mono convergence
+
+ align:start position:0%
+let me state the mono convergence
+ 
+
+ align:start position:0%
+let me state the mono convergence
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose that so this is the following
+
+ align:start position:0%
+So suppose that so this is the following
+ 
+
+ align:start position:0%
+So suppose that so this is the following
+theorem. Suppose that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and there's two versions of this.
+
+ align:start position:0%
+that and there's two versions of this.
+ 
+
+ align:start position:0%
+that and there's two versions of this.
+There's one version for monotum
+
+ align:start position:0%
+There's one version for monotum
+ 
+
+ align:start position:0%
+There's one version for monotum
+increasing sequence and then there's one
+
+ align:start position:0%
+increasing sequence and then there's one
+ 
+
+ align:start position:0%
+increasing sequence and then there's one
+version for mono decreasing sequence. I
+
+ align:start position:0%
+version for mono decreasing sequence. I
+ 
+
+ align:start position:0%
+version for mono decreasing sequence. I
+just state one of them because the other
+
+ align:start position:0%
+just state one of them because the other
+ 
+
+ align:start position:0%
+just state one of them because the other
+one's kind of obvious parallel. So
+
+ align:start position:0%
+one's kind of obvious parallel. So
+ 
+
+ align:start position:0%
+one's kind of obvious parallel. So
+suppose that a end is a monotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increasing sequence
+
+ align:start position:0%
+increasing sequence
+ 
+
+ align:start position:0%
+increasing sequence
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then it is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded. So this just means that there
+
+ align:start position:0%
+bounded. So this just means that there
+ 
+
+ align:start position:0%
+bounded. So this just means that there
+exists
+
+ align:start position:0%
+exists
+ 
+
+ align:start position:0%
+exists
+i.e.
+
+ align:start position:0%
+i.e.
+ 
+
+ align:start position:0%
+i.e.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some a real number.
+
+ align:start position:0%
+some a real number.
+ 
+
+ align:start position:0%
+some a real number.
+So that's
+
+ align:start position:0%
+So that's
+ 
+
+ align:start position:0%
+So that's
+right. You have a1 this here is that is
+
+ align:start position:0%
+right. You have a1 this here is that is
+ 
+
+ align:start position:0%
+right. You have a1 this here is that is
+monotum right this is monotum that they
+
+ align:start position:0%
+monotum right this is monotum that they
+ 
+
+ align:start position:0%
+monotum right this is monotum that they
+cannot increase but but the claim is
+
+ align:start position:0%
+cannot increase but but the claim is
+ 
+
+ align:start position:0%
+cannot increase but but the claim is
+that now the all of the a is lesser
+
+ align:start position:0%
+that now the all of the a is lesser
+ 
+
+ align:start position:0%
+that now the all of the a is lesser
+equal to this a
+
+ align:start position:0%
+equal to this a
+ 
+
+ align:start position:0%
+equal to this a
+it's any monotum increasing sequence is
+
+ align:start position:0%
+it's any monotum increasing sequence is
+ 
+
+ align:start position:0%
+it's any monotum increasing sequence is
+clearly bounded from below right because
+
+ align:start position:0%
+clearly bounded from below right because
+ 
+
+ align:start position:0%
+clearly bounded from below right because
+already the first element is a lower
+
+ align:start position:0%
+already the first element is a lower
+ 
+
+ align:start position:0%
+already the first element is a lower
+bound right so if you have a mono
+
+ align:start position:0%
+bound right so if you have a mono
+ 
+
+ align:start position:0%
+bound right so if you have a mono
+increasing sequence then Um
+
+ align:start position:0%
+increasing sequence then Um
+ 
+
+ align:start position:0%
+increasing sequence then Um
+then uh that is bounded then it's
+
+ align:start position:0%
+then uh that is bounded then it's
+ 
+
+ align:start position:0%
+then uh that is bounded then it's
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh we limit say we limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+a is the soup
+
+ align:start position:0%
+a is the soup
+ 
+
+ align:start position:0%
+a is the soup
+of the a inch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that is a mono convergence sequence.
+
+ align:start position:0%
+So that is a mono convergence sequence.
+ 
+
+ align:start position:0%
+So that is a mono convergence sequence.
+Okay. and and and that is the the kind
+
+ align:start position:0%
+Okay. and and and that is the the kind
+ 
+
+ align:start position:0%
+Okay. and and and that is the the kind
+of main theorem about mono convergent
+
+ align:start position:0%
+of main theorem about mono convergent
+ 
+
+ align:start position:0%
+of main theorem about mono convergent
+sequence is that if you have a monotum
+
+ align:start position:0%
+sequence is that if you have a monotum
+ 
+
+ align:start position:0%
+sequence is that if you have a monotum
+increasing sequence
+
+ align:start position:0%
+increasing sequence
+ 
+
+ align:start position:0%
+increasing sequence
+that is bounded then it's also
+
+ align:start position:0%
+that is bounded then it's also
+ 
+
+ align:start position:0%
+that is bounded then it's also
+convergence right and likewise if you
+
+ align:start position:0%
+convergence right and likewise if you
+ 
+
+ align:start position:0%
+convergence right and likewise if you
+have a monotum decreasing sequence that
+
+ align:start position:0%
+have a monotum decreasing sequence that
+ 
+
+ align:start position:0%
+have a monotum decreasing sequence that
+is bounded from below
+
+ align:start position:0%
+is bounded from below
+ 
+
+ align:start position:0%
+is bounded from below
+right then it is also convergent and so
+
+ align:start position:0%
+right then it is also convergent and so
+ 
+
+ align:start position:0%
+right then it is also convergent and so
+maybe maybe I will state it
+
+ align:start position:0%
+maybe maybe I will state it
+ 
+
+ align:start position:0%
+maybe maybe I will state it
+u but it's is the obvious parallel.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+so this is part one
+
+ align:start position:0%
+so this is part one
+ 
+
+ align:start position:0%
+so this is part one
+of the monome converting sequence.
+
+ align:start position:0%
+of the monome converting sequence.
+ 
+
+ align:start position:0%
+of the monome converting sequence.
+Part two of part B is that if
+
+ align:start position:0%
+Part two of part B is that if
+ 
+
+ align:start position:0%
+Part two of part B is that if
+if A is a monotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh that is bounded uh that is
+
+ align:start position:0%
+uh that is bounded uh that is
+ 
+
+ align:start position:0%
+uh that is bounded uh that is
+that is bounded from below.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh a is convergent
+
+ align:start position:0%
+uh a is convergent
+ 
+
+ align:start position:0%
+uh a is convergent
+with limit a where a is now the in
+
+ align:start position:0%
+with limit a where a is now the in
+ 
+
+ align:start position:0%
+with limit a where a is now the in
+of these numbers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+so you might say the first thing you
+
+ align:start position:0%
+so you might say the first thing you
+ 
+
+ align:start position:0%
+so you might say the first thing you
+might say, we'll come to square root two
+
+ align:start position:0%
+might say, we'll come to square root two
+ 
+
+ align:start position:0%
+might say, we'll come to square root two
+in just a minute, but you may see that
+
+ align:start position:0%
+in just a minute, but you may see that
+ 
+
+ align:start position:0%
+in just a minute, but you may see that
+this seems rather special, you know,
+
+ align:start position:0%
+this seems rather special, you know,
+ 
+
+ align:start position:0%
+this seems rather special, you know,
+like if you take a random uh sequence,
+
+ align:start position:0%
+like if you take a random uh sequence,
+ 
+
+ align:start position:0%
+like if you take a random uh sequence,
+obviously it's not going to be monitor.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um but but here's the thing that so
+
+ align:start position:0%
+Um but but here's the thing that so
+ 
+
+ align:start position:0%
+Um but but here's the thing that so
+uh let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be any bounded sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So bounded again means that it's bounded
+
+ align:start position:0%
+So bounded again means that it's bounded
+ 
+
+ align:start position:0%
+So bounded again means that it's bounded
+from above and bounded from below. So if
+
+ align:start position:0%
+from above and bounded from below. So if
+ 
+
+ align:start position:0%
+from above and bounded from below. So if
+you take any boundless sequence
+
+ align:start position:0%
+you take any boundless sequence
+ 
+
+ align:start position:0%
+you take any boundless sequence
+then we can form two other sequences.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Two other sequences
+
+ align:start position:0%
+Two other sequences
+ 
+
+ align:start position:0%
+Two other sequences
+I mean obviously form many other but
+
+ align:start position:0%
+I mean obviously form many other but
+ 
+
+ align:start position:0%
+I mean obviously form many other but
+here's two other very natural
+
+ align:start position:0%
+here's two other very natural
+ 
+
+ align:start position:0%
+here's two other very natural
+uh sequences.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The first one I call BN
+
+ align:start position:0%
+The first one I call BN
+ 
+
+ align:start position:0%
+The first one I call BN
+and BN is is the soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of where you're taking where you're
+
+ align:start position:0%
+of where you're taking where you're
+ 
+
+ align:start position:0%
+of where you're taking where you're
+starting at a end
+
+ align:start position:0%
+starting at a end
+ 
+
+ align:start position:0%
+starting at a end
+and then you take the soup of all of the
+
+ align:start position:0%
+and then you take the soup of all of the
+ 
+
+ align:start position:0%
+and then you take the soup of all of the
+ones from A in and outwards in the
+
+ align:start position:0%
+ones from A in and outwards in the
+ 
+
+ align:start position:0%
+ones from A in and outwards in the
+sequence. Right? So this is one
+
+ align:start position:0%
+sequence. Right? So this is one
+ 
+
+ align:start position:0%
+sequence. Right? So this is one
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+right we know that that you know the set
+
+ align:start position:0%
+right we know that that you know the set
+ 
+
+ align:start position:0%
+right we know that that you know the set
+of a ends is bounded right so you can
+
+ align:start position:0%
+of a ends is bounded right so you can
+ 
+
+ align:start position:0%
+of a ends is bounded right so you can
+certainly take the soup and you get a
+
+ align:start position:0%
+certainly take the soup and you get a
+ 
+
+ align:start position:0%
+certainly take the soup and you get a
+real number right that's that that gives
+
+ align:start position:0%
+real number right that's that that gives
+ 
+
+ align:start position:0%
+real number right that's that that gives
+you another sequence
+
+ align:start position:0%
+you another sequence
+ 
+
+ align:start position:0%
+you another sequence
+you can also look at cn similarly where
+
+ align:start position:0%
+you can also look at cn similarly where
+ 
+
+ align:start position:0%
+you can also look at cn similarly where
+you take instead of the soup you take
+
+ align:start position:0%
+you take instead of the soup you take
+ 
+
+ align:start position:0%
+you take instead of the soup you take
+the in of the same that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+like that. All right. So, in particular,
+
+ align:start position:0%
+like that. All right. So, in particular,
+ 
+
+ align:start position:0%
+like that. All right. So, in particular,
+right, just to make sure it's totally
+
+ align:start position:0%
+right, just to make sure it's totally
+ 
+
+ align:start position:0%
+right, just to make sure it's totally
+clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that if you were looking at
+
+ align:start position:0%
+that if you were looking at
+ 
+
+ align:start position:0%
+that if you were looking at
+say BN, so what is BN? If you're looking
+
+ align:start position:0%
+say BN, so what is BN? If you're looking
+ 
+
+ align:start position:0%
+say BN, so what is BN? If you're looking
+at say B3
+
+ align:start position:0%
+at say B3
+ 
+
+ align:start position:0%
+at say B3
+then this is the soup where you're
+
+ align:start position:0%
+then this is the soup where you're
+ 
+
+ align:start position:0%
+then this is the soup where you're
+starting at A3 A4
+
+ align:start position:0%
+starting at A3 A4
+ 
+
+ align:start position:0%
+starting at A3 A4
+etc.
+
+ align:start position:0%
+etc.
+ 
+
+ align:start position:0%
+etc.
+And so you see of course that B23 here
+
+ align:start position:0%
+And so you see of course that B23 here
+ 
+
+ align:start position:0%
+And so you see of course that B23 here
+well obviously B3 is bigger equal
+
+ align:start position:0%
+well obviously B3 is bigger equal
+ 
+
+ align:start position:0%
+well obviously B3 is bigger equal
+to B2 right because B2 here
+
+ align:start position:0%
+to B2 right because B2 here
+ 
+
+ align:start position:0%
+to B2 right because B2 here
+is sorry it's no it's not bigger equal
+
+ align:start position:0%
+is sorry it's no it's not bigger equal
+ 
+
+ align:start position:0%
+is sorry it's no it's not bigger equal
+to it's lesser equal to B2
+
+ align:start position:0%
+to it's lesser equal to B2
+ 
+
+ align:start position:0%
+to it's lesser equal to B2
+because you see in B2 the definition of
+
+ align:start position:0%
+because you see in B2 the definition of
+ 
+
+ align:start position:0%
+because you see in B2 the definition of
+B2 so let's just write B2 down
+
+ align:start position:0%
+B2 so let's just write B2 down
+ 
+
+ align:start position:0%
+B2 so let's just write B2 down
+so B2 is that you take the soup here of
+
+ align:start position:0%
+so B2 is that you take the soup here of
+ 
+
+ align:start position:0%
+so B2 is that you take the soup here of
+A2 and then A3
+
+ align:start position:0%
+A2 and then A3
+ 
+
+ align:start position:0%
+A2 and then A3
+A4 etc.
+
+ align:start position:0%
+A4 etc.
+ 
+
+ align:start position:0%
+A4 etc.
+Right? But you see that B2 here it's
+
+ align:start position:0%
+Right? But you see that B2 here it's
+ 
+
+ align:start position:0%
+Right? But you see that B2 here it's
+both of them are defined to be soup but
+
+ align:start position:0%
+both of them are defined to be soup but
+ 
+
+ align:start position:0%
+both of them are defined to be soup but
+B2 is defined as soup over a larger set
+
+ align:start position:0%
+B2 is defined as soup over a larger set
+ 
+
+ align:start position:0%
+B2 is defined as soup over a larger set
+because in addition to these elements it
+
+ align:start position:0%
+because in addition to these elements it
+ 
+
+ align:start position:0%
+because in addition to these elements it
+also includes A2 right. So clearly B2
+
+ align:start position:0%
+also includes A2 right. So clearly B2
+ 
+
+ align:start position:0%
+also includes A2 right. So clearly B2
+here is bigger equal to B3
+
+ align:start position:0%
+here is bigger equal to B3
+ 
+
+ align:start position:0%
+here is bigger equal to B3
+right and in fact the same argument
+
+ align:start position:0%
+right and in fact the same argument
+ 
+
+ align:start position:0%
+right and in fact the same argument
+tells you that if you take B
+
+ align:start position:0%
+tells you that if you take B
+ 
+
+ align:start position:0%
+tells you that if you take B
+n + one then this is or bn sorry bn is
+
+ align:start position:0%
+n + one then this is or bn sorry bn is
+ 
+
+ align:start position:0%
+n + one then this is or bn sorry bn is
+bigger equal to bn + one
+
+ align:start position:0%
+bigger equal to bn + one
+ 
+
+ align:start position:0%
+bigger equal to bn + one
+because this here is the soup over a
+
+ align:start position:0%
+because this here is the soup over a
+ 
+
+ align:start position:0%
+because this here is the soup over a
+larger set it's soup over all the ones
+
+ align:start position:0%
+larger set it's soup over all the ones
+ 
+
+ align:start position:0%
+larger set it's soup over all the ones
+you take soup in here plus a n right so
+
+ align:start position:0%
+you take soup in here plus a n right so
+ 
+
+ align:start position:0%
+you take soup in here plus a n right so
+you have this property here right and so
+
+ align:start position:0%
+you have this property here right and so
+ 
+
+ align:start position:0%
+you have this property here right and so
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+>> what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If it's a monot increasing um
+
+ align:start position:0%
+If it's a monot increasing um
+ 
+
+ align:start position:0%
+If it's a monot increasing um
+>> yeah because monotum increasing uh then
+
+ align:start position:0%
+>> yeah because monotum increasing uh then
+ 
+
+ align:start position:0%
+>> yeah because monotum increasing uh then
+this here uh right yeah then it becomes
+
+ align:start position:0%
+this here uh right yeah then it becomes
+ 
+
+ align:start position:0%
+this here uh right yeah then it becomes
+very special.
+
+ align:start position:0%
+very special.
+ 
+
+ align:start position:0%
+very special.
+Uh so it's it's if you take a mon if the
+
+ align:start position:0%
+Uh so it's it's if you take a mon if the
+ 
+
+ align:start position:0%
+Uh so it's it's if you take a mon if the
+a was monoton increasing then the all of
+
+ align:start position:0%
+a was monoton increasing then the all of
+ 
+
+ align:start position:0%
+a was monoton increasing then the all of
+these any element here would just be the
+
+ align:start position:0%
+these any element here would just be the
+ 
+
+ align:start position:0%
+these any element here would just be the
+a we talked about before it would always
+
+ align:start position:0%
+a we talked about before it would always
+ 
+
+ align:start position:0%
+a we talked about before it would always
+be the limit.
+
+ align:start position:0%
+be the limit.
+ 
+
+ align:start position:0%
+be the limit.
+So so it's um it's it somehow wouldn't
+
+ align:start position:0%
+So so it's um it's it somehow wouldn't
+ 
+
+ align:start position:0%
+So so it's um it's it somehow wouldn't
+be that interesting a sequence. It would
+
+ align:start position:0%
+be that interesting a sequence. It would
+ 
+
+ align:start position:0%
+be that interesting a sequence. It would
+be a constant sequence and and it would
+
+ align:start position:0%
+be a constant sequence and and it would
+ 
+
+ align:start position:0%
+be a constant sequence and and it would
+be just
+
+ align:start position:0%
+be just
+ 
+
+ align:start position:0%
+be just
+>> but but but that but nevertheless it's a
+
+ align:start position:0%
+>> but but but that but nevertheless it's a
+ 
+
+ align:start position:0%
+>> but but but that but nevertheless it's a
+good example you know. I guess that's
+
+ align:start position:0%
+good example you know. I guess that's
+ 
+
+ align:start position:0%
+good example you know. I guess that's
+still anybody.
+
+ align:start position:0%
+still anybody.
+ 
+
+ align:start position:0%
+still anybody.
+>> Yeah. Yeah. Definitely. Right. Because
+
+ align:start position:0%
+>> Yeah. Yeah. Definitely. Right. Because
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Definitely. Right. Because
+it's just constant. Exactly.
+
+ align:start position:0%
+it's just constant. Exactly.
+ 
+
+ align:start position:0%
+it's just constant. Exactly.
+>> It's a it's a good example, but it's
+
+ align:start position:0%
+>> It's a it's a good example, but it's
+ 
+
+ align:start position:0%
+>> It's a it's a good example, but it's
+just kind of almost like too simple
+
+ align:start position:0%
+just kind of almost like too simple
+ 
+
+ align:start position:0%
+just kind of almost like too simple
+because you get a constant sequence,
+
+ align:start position:0%
+because you get a constant sequence,
+ 
+
+ align:start position:0%
+because you get a constant sequence,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+So, okay. So, we have for this sequence
+
+ align:start position:0%
+So, okay. So, we have for this sequence
+ 
+
+ align:start position:0%
+So, okay. So, we have for this sequence
+that we defined. So we have again these
+
+ align:start position:0%
+that we defined. So we have again these
+ 
+
+ align:start position:0%
+that we defined. So we have again these
+if you take any sequence then you get
+
+ align:start position:0%
+if you take any sequence then you get
+ 
+
+ align:start position:0%
+if you take any sequence then you get
+then you have two sequences B and a CN
+
+ align:start position:0%
+then you have two sequences B and a CN
+ 
+
+ align:start position:0%
+then you have two sequences B and a CN
+and B and here is now a decreasing
+
+ align:start position:0%
+and B and here is now a decreasing
+ 
+
+ align:start position:0%
+and B and here is now a decreasing
+sequence and in instead of writing
+
+ align:start position:0%
+sequence and in instead of writing
+ 
+
+ align:start position:0%
+sequence and in instead of writing
+decreasing sequence then uh it's much
+
+ align:start position:0%
+decreasing sequence then uh it's much
+ 
+
+ align:start position:0%
+decreasing sequence then uh it's much
+easier to write it like this. This is
+
+ align:start position:0%
+easier to write it like this. This is
+ 
+
+ align:start position:0%
+easier to write it like this. This is
+pretty standard. I mean you know it's
+
+ align:start position:0%
+pretty standard. I mean you know it's
+ 
+
+ align:start position:0%
+pretty standard. I mean you know it's
+just to uh if you just look quickly at
+
+ align:start position:0%
+just to uh if you just look quickly at
+ 
+
+ align:start position:0%
+just to uh if you just look quickly at
+it uh you know what this means.
+
+ align:start position:0%
+it uh you know what this means.
+ 
+
+ align:start position:0%
+it uh you know what this means.
+going to write out but let's look at CN
+
+ align:start position:0%
+going to write out but let's look at CN
+ 
+
+ align:start position:0%
+going to write out but let's look at CN
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+remember that we assume that a n we a
+
+ align:start position:0%
+remember that we assume that a n we a
+ 
+
+ align:start position:0%
+remember that we assume that a n we a
+could be any sequence but it is supposed
+
+ align:start position:0%
+could be any sequence but it is supposed
+ 
+
+ align:start position:0%
+could be any sequence but it is supposed
+to be bounded right so this is now a
+
+ align:start position:0%
+to be bounded right so this is now a
+ 
+
+ align:start position:0%
+to be bounded right so this is now a
+monotum decreasing sequence that is
+
+ align:start position:0%
+monotum decreasing sequence that is
+ 
+
+ align:start position:0%
+monotum decreasing sequence that is
+bounded so it actually has a limit right
+
+ align:start position:0%
+bounded so it actually has a limit right
+ 
+
+ align:start position:0%
+bounded so it actually has a limit right
+the cs what about the cs so the cns
+
+ align:start position:0%
+the cs what about the cs so the cns
+ 
+
+ align:start position:0%
+the cs what about the cs so the cns
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+the CN
+
+ align:start position:0%
+the CN
+ 
+
+ align:start position:0%
+the CN
+well CN was defined to be the in
+
+ align:start position:0%
+well CN was defined to be the in
+ 
+
+ align:start position:0%
+well CN was defined to be the in
+starting at a end
+
+ align:start position:0%
+starting at a end
+ 
+
+ align:start position:0%
+starting at a end
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so it' be starting like that and so this
+
+ align:start position:0%
+so it' be starting like that and so this
+ 
+
+ align:start position:0%
+so it' be starting like that and so this
+means that if you take CN + one
+
+ align:start position:0%
+means that if you take CN + one
+ 
+
+ align:start position:0%
+means that if you take CN + one
+then you take the infom But you don't
+
+ align:start position:0%
+then you take the infom But you don't
+ 
+
+ align:start position:0%
+then you take the infom But you don't
+include this element. Right? So it's a
+
+ align:start position:0%
+include this element. Right? So it's a
+ 
+
+ align:start position:0%
+include this element. Right? So it's a
+infreum over fewer elements. But then
+
+ align:start position:0%
+infreum over fewer elements. But then
+ 
+
+ align:start position:0%
+infreum over fewer elements. But then
+this here must be larger equal
+
+ align:start position:0%
+this here must be larger equal
+ 
+
+ align:start position:0%
+this here must be larger equal
+right to that. So you see that the
+
+ align:start position:0%
+right to that. So you see that the
+ 
+
+ align:start position:0%
+right to that. So you see that the
+sequence CN
+
+ align:start position:0%
+sequence CN
+ 
+
+ align:start position:0%
+sequence CN
+is monotum. This here is monotum
+
+ align:start position:0%
+is monotum. This here is monotum
+ 
+
+ align:start position:0%
+is monotum. This here is monotum
+increasing again is bounded and and and
+
+ align:start position:0%
+increasing again is bounded and and and
+ 
+
+ align:start position:0%
+increasing again is bounded and and and
+just copying from over there. The BN was
+
+ align:start position:0%
+just copying from over there. The BN was
+ 
+
+ align:start position:0%
+just copying from over there. The BN was
+decreasing.
+
+ align:start position:0%
+decreasing.
+ 
+
+ align:start position:0%
+decreasing.
+>> Okay. This is like I mean it's also like
+
+ align:start position:0%
+>> Okay. This is like I mean it's also like
+ 
+
+ align:start position:0%
+>> Okay. This is like I mean it's also like
+I mean this is an important thing. It's
+
+ align:start position:0%
+I mean this is an important thing. It's
+ 
+
+ align:start position:0%
+I mean this is an important thing. It's
+also something that you would see in lot
+
+ align:start position:0%
+also something that you would see in lot
+ 
+
+ align:start position:0%
+also something that you would see in lot
+of different context where you define
+
+ align:start position:0%
+of different context where you define
+ 
+
+ align:start position:0%
+of different context where you define
+something some sort of sub and then you
+
+ align:start position:0%
+something some sort of sub and then you
+ 
+
+ align:start position:0%
+something some sort of sub and then you
+have these property
+
+ align:start position:0%
+have these property
+ 
+
+ align:start position:0%
+have these property
+and so now the thing is that if you're
+
+ align:start position:0%
+and so now the thing is that if you're
+ 
+
+ align:start position:0%
+and so now the thing is that if you're
+looking at so aure it might not be so
+
+ align:start position:0%
+looking at so aure it might not be so
+ 
+
+ align:start position:0%
+looking at so aure it might not be so
+clear to compare a random element in
+
+ align:start position:0%
+clear to compare a random element in
+ 
+
+ align:start position:0%
+clear to compare a random element in
+this sequence to a random element in
+
+ align:start position:0%
+this sequence to a random element in
+ 
+
+ align:start position:0%
+this sequence to a random element in
+that but what is clear is that if you
+
+ align:start position:0%
+that but what is clear is that if you
+ 
+
+ align:start position:0%
+that but what is clear is that if you
+try to compare BN with CN And
+
+ align:start position:0%
+try to compare BN with CN And
+ 
+
+ align:start position:0%
+try to compare BN with CN And
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it's the same set. It's the same set.
+
+ align:start position:0%
+it's the same set. It's the same set.
+ 
+
+ align:start position:0%
+it's the same set. It's the same set.
+And one you take the soup, the other you
+
+ align:start position:0%
+And one you take the soup, the other you
+ 
+
+ align:start position:0%
+And one you take the soup, the other you
+take the in. So of course BN is bigger
+
+ align:start position:0%
+take the in. So of course BN is bigger
+ 
+
+ align:start position:0%
+take the in. So of course BN is bigger
+equal to CN,
+
+ align:start position:0%
+equal to CN,
+ 
+
+ align:start position:0%
+equal to CN,
+right? So you have this, right? And so
+
+ align:start position:0%
+right? So you have this, right? And so
+ 
+
+ align:start position:0%
+right? So you have this, right? And so
+now you see that if you take like a
+
+ align:start position:0%
+now you see that if you take like a
+ 
+
+ align:start position:0%
+now you see that if you take like a
+random element here, if it was like
+
+ align:start position:0%
+random element here, if it was like
+ 
+
+ align:start position:0%
+random element here, if it was like
+further out, if it was N, sorry, if it
+
+ align:start position:0%
+further out, if it was N, sorry, if it
+ 
+
+ align:start position:0%
+further out, if it was N, sorry, if it
+was C N further out, I just write it as
+
+ align:start position:0%
+was C N further out, I just write it as
+ 
+
+ align:start position:0%
+was C N further out, I just write it as
+something further out. So you adding
+
+ align:start position:0%
+something further out. So you adding
+ 
+
+ align:start position:0%
+something further out. So you adding
+something else to it. So this would be
+
+ align:start position:0%
+something else to it. So this would be
+ 
+
+ align:start position:0%
+something else to it. So this would be
+like further out. We know that this
+
+ align:start position:0%
+like further out. We know that this
+ 
+
+ align:start position:0%
+like further out. We know that this
+sequence here.
+
+ align:start position:0%
+sequence here.
+ 
+
+ align:start position:0%
+sequence here.
+Yeah. Anyway, so you get Sorry, now
+
+ align:start position:0%
+Yeah. Anyway, so you get Sorry, now
+ 
+
+ align:start position:0%
+Yeah. Anyway, so you get Sorry, now
+you're getting this. I'm getting this
+
+ align:start position:0%
+you're getting this. I'm getting this
+ 
+
+ align:start position:0%
+you're getting this. I'm getting this
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and right so you have this so what you
+
+ align:start position:0%
+and right so you have this so what you
+ 
+
+ align:start position:0%
+and right so you have this so what you
+should what I should have done is that
+
+ align:start position:0%
+should what I should have done is that
+ 
+
+ align:start position:0%
+should what I should have done is that
+this sequence here so you have so let
+
+ align:start position:0%
+this sequence here so you have so let
+ 
+
+ align:start position:0%
+this sequence here so you have so let
+let me rather draw it like this so I
+
+ align:start position:0%
+let me rather draw it like this so I
+ 
+
+ align:start position:0%
+let me rather draw it like this so I
+have that this that so here is maybe C1
+
+ align:start position:0%
+have that this that so here is maybe C1
+ 
+
+ align:start position:0%
+have that this that so here is maybe C1
+here is B1
+
+ align:start position:0%
+here is B1
+ 
+
+ align:start position:0%
+here is B1
+and now the next one the next element
+
+ align:start position:0%
+and now the next one the next element
+ 
+
+ align:start position:0%
+and now the next one the next element
+the sequence C n is increasing and the
+
+ align:start position:0%
+the sequence C n is increasing and the
+ 
+
+ align:start position:0%
+the sequence C n is increasing and the
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+bn is decreasing. So then but you always
+
+ align:start position:0%
+bn is decreasing. So then but you always
+ 
+
+ align:start position:0%
+bn is decreasing. So then but you always
+have this here. So c2 have to lie to the
+
+ align:start position:0%
+have this here. So c2 have to lie to the
+ 
+
+ align:start position:0%
+have this here. So c2 have to lie to the
+right of this but it has to lie to the
+
+ align:start position:0%
+right of this but it has to lie to the
+ 
+
+ align:start position:0%
+right of this but it has to lie to the
+left of b2.
+
+ align:start position:0%
+left of b2.
+ 
+
+ align:start position:0%
+left of b2.
+So you're getting this here.
+
+ align:start position:0%
+So you're getting this here.
+ 
+
+ align:start position:0%
+So you're getting this here.
+So, so you see that this is a way to
+
+ align:start position:0%
+So, so you see that this is a way to
+ 
+
+ align:start position:0%
+So, so you see that this is a way to
+kind of you know this gives you a way to
+
+ align:start position:0%
+kind of you know this gives you a way to
+ 
+
+ align:start position:0%
+kind of you know this gives you a way to
+compare right that that the CN will
+
+ align:start position:0%
+compare right that that the CN will
+ 
+
+ align:start position:0%
+compare right that that the CN will
+always lie to the left of the BN.
+
+ align:start position:0%
+always lie to the left of the BN.
+ 
+
+ align:start position:0%
+always lie to the left of the BN.
+So you have so so now what we have done
+
+ align:start position:0%
+So you have so so now what we have done
+ 
+
+ align:start position:0%
+So you have so so now what we have done
+here is we took any boundary sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we formed two mono sequences.
+
+ align:start position:0%
+and we formed two mono sequences.
+ 
+
+ align:start position:0%
+and we formed two mono sequences.
+They're both mono
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we have so so this means that now
+
+ align:start position:0%
+And we have so so this means that now
+ 
+
+ align:start position:0%
+And we have so so this means that now
+from the monot convergence that we
+
+ align:start position:0%
+from the monot convergence that we
+ 
+
+ align:start position:0%
+from the monot convergence that we
+haven't quite proven yet but from the
+
+ align:start position:0%
+haven't quite proven yet but from the
+ 
+
+ align:start position:0%
+haven't quite proven yet but from the
+mono convergence uh convergence theorem
+
+ align:start position:0%
+mono convergence uh convergence theorem
+ 
+
+ align:start position:0%
+mono convergence uh convergence theorem
+because these are bounded we have that
+
+ align:start position:0%
+because these are bounded we have that
+ 
+
+ align:start position:0%
+because these are bounded we have that
+bm converge converging they are going uh
+
+ align:start position:0%
+bm converge converging they are going uh
+ 
+
+ align:start position:0%
+bm converge converging they are going uh
+they're going down right so they're
+
+ align:start position:0%
+they're going down right so they're
+ 
+
+ align:start position:0%
+they're going down right so they're
+converging so one often would write it
+
+ align:start position:0%
+converging so one often would write it
+ 
+
+ align:start position:0%
+converging so one often would write it
+like this more suggestively
+
+ align:start position:0%
+like this more suggestively
+ 
+
+ align:start position:0%
+like this more suggestively
+that is converging downward to a limit B
+
+ align:start position:0%
+that is converging downward to a limit B
+ 
+
+ align:start position:0%
+that is converging downward to a limit B
+and the CN
+
+ align:start position:0%
+and the CN
+ 
+
+ align:start position:0%
+and the CN
+is converging upward to a limit C.
+
+ align:start position:0%
+is converging upward to a limit C.
+ 
+
+ align:start position:0%
+is converging upward to a limit C.
+Right? And so what you get is because of
+
+ align:start position:0%
+Right? And so what you get is because of
+ 
+
+ align:start position:0%
+Right? And so what you get is because of
+all of these elements, all the C ends
+
+ align:start position:0%
+all of these elements, all the C ends
+ 
+
+ align:start position:0%
+all of these elements, all the C ends
+lie to the left of the B ends. This
+
+ align:start position:0%
+lie to the left of the B ends. This
+ 
+
+ align:start position:0%
+lie to the left of the B ends. This
+means that and we we'll prove this later
+
+ align:start position:0%
+means that and we we'll prove this later
+ 
+
+ align:start position:0%
+means that and we we'll prove this later
+but it seems probably pretty obvious
+
+ align:start position:0%
+but it seems probably pretty obvious
+ 
+
+ align:start position:0%
+but it seems probably pretty obvious
+that the limit here C is less or equal
+
+ align:start position:0%
+that the limit here C is less or equal
+ 
+
+ align:start position:0%
+that the limit here C is less or equal
+to B
+
+ align:start position:0%
+to B
+ 
+
+ align:start position:0%
+to B
+and this so we'll come back to this also
+
+ align:start position:0%
+and this so we'll come back to this also
+ 
+
+ align:start position:0%
+and this so we'll come back to this also
+next time um when we talked I if I have
+
+ align:start position:0%
+next time um when we talked I if I have
+ 
+
+ align:start position:0%
+next time um when we talked I if I have
+time I'll talk a little bit about cushy
+
+ align:start position:0%
+time I'll talk a little bit about cushy
+ 
+
+ align:start position:0%
+time I'll talk a little bit about cushy
+sequence but I won't really prove too
+
+ align:start position:0%
+sequence but I won't really prove too
+ 
+
+ align:start position:0%
+sequence but I won't really prove too
+much about it and and and but this here
+
+ align:start position:0%
+much about it and and and but this here
+ 
+
+ align:start position:0%
+much about it and and and but this here
+will play a important role
+
+ align:start position:0%
+will play a important role
+ 
+
+ align:start position:0%
+will play a important role
+uh when we prove the the basic theorem
+
+ align:start position:0%
+uh when we prove the the basic theorem
+ 
+
+ align:start position:0%
+uh when we prove the the basic theorem
+about cushy sequences.
+
+ align:start position:0%
+about cushy sequences.
+ 
+
+ align:start position:0%
+about cushy sequences.
+Okay. So so the takeaway here at the
+
+ align:start position:0%
+Okay. So so the takeaway here at the
+ 
+
+ align:start position:0%
+Okay. So so the takeaway here at the
+moment is just that uh so you have you
+
+ align:start position:0%
+moment is just that uh so you have you
+ 
+
+ align:start position:0%
+moment is just that uh so you have you
+have this concept of a monot
+
+ align:start position:0%
+have this concept of a monot
+ 
+
+ align:start position:0%
+have this concept of a monot
+uh either increasing or decreasing
+
+ align:start position:0%
+uh either increasing or decreasing
+ 
+
+ align:start position:0%
+uh either increasing or decreasing
+sequence. If such a sequence is bounded
+
+ align:start position:0%
+sequence. If such a sequence is bounded
+ 
+
+ align:start position:0%
+sequence. If such a sequence is bounded
+then it's convergent. That's a mono
+
+ align:start position:0%
+then it's convergent. That's a mono
+ 
+
+ align:start position:0%
+then it's convergent. That's a mono
+convergence theorem. And again from any
+
+ align:start position:0%
+convergence theorem. And again from any
+ 
+
+ align:start position:0%
+convergence theorem. And again from any
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+any boundary sequence you can act that's
+
+ align:start position:0%
+any boundary sequence you can act that's
+ 
+
+ align:start position:0%
+any boundary sequence you can act that's
+there that's a very natural mono
+
+ align:start position:0%
+there that's a very natural mono
+ 
+
+ align:start position:0%
+there that's a very natural mono
+increasing sequence and a very natural
+
+ align:start position:0%
+increasing sequence and a very natural
+ 
+
+ align:start position:0%
+increasing sequence and a very natural
+mono decreasing sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now let's try to prove the monotom
+
+ align:start position:0%
+Now let's try to prove the monotom
+ 
+
+ align:start position:0%
+Now let's try to prove the monotom
+convergence theorem and then let's get
+
+ align:start position:0%
+convergence theorem and then let's get
+ 
+
+ align:start position:0%
+convergence theorem and then let's get
+back to how to think about square root
+
+ align:start position:0%
+back to how to think about square root
+ 
+
+ align:start position:0%
+back to how to think about square root
+of two in a more intuitive way using
+
+ align:start position:0%
+of two in a more intuitive way using
+ 
+
+ align:start position:0%
+of two in a more intuitive way using
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now the proof of the monome.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we So now let me just remind you what
+
+ align:start position:0%
+So we So now let me just remind you what
+ 
+
+ align:start position:0%
+So we So now let me just remind you what
+we have.
+
+ align:start position:0%
+we have.
+ 
+
+ align:start position:0%
+we have.
+So I'm only going to prove one of the
+
+ align:start position:0%
+So I'm only going to prove one of the
+ 
+
+ align:start position:0%
+So I'm only going to prove one of the
+two versions of it where the sequence is
+
+ align:start position:0%
+two versions of it where the sequence is
+ 
+
+ align:start position:0%
+two versions of it where the sequence is
+monotum increasing because the other one
+
+ align:start position:0%
+monotum increasing because the other one
+ 
+
+ align:start position:0%
+monotum increasing because the other one
+is just proof is is just the same with
+
+ align:start position:0%
+is just proof is is just the same with
+ 
+
+ align:start position:0%
+is just proof is is just the same with
+obvious modification. So I'm assuming so
+
+ align:start position:0%
+obvious modification. So I'm assuming so
+ 
+
+ align:start position:0%
+obvious modification. So I'm assuming so
+this is the assumption.
+
+ align:start position:0%
+this is the assumption.
+ 
+
+ align:start position:0%
+this is the assumption.
+So this is the assumption.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so this is just that the next
+
+ align:start position:0%
+So, so this is just that the next
+ 
+
+ align:start position:0%
+So, so this is just that the next
+element is larger equal to the previous
+
+ align:start position:0%
+element is larger equal to the previous
+ 
+
+ align:start position:0%
+element is larger equal to the previous
+one and they're all bounded by this a
+
+ align:start position:0%
+one and they're all bounded by this a
+ 
+
+ align:start position:0%
+one and they're all bounded by this a
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now I take I we set
+
+ align:start position:0%
+now I take I we set
+ 
+
+ align:start position:0%
+now I take I we set
+little a equal to the soup
+
+ align:start position:0%
+little a equal to the soup
+ 
+
+ align:start position:0%
+little a equal to the soup
+uh of the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I want to show we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a converts to a.
+
+ align:start position:0%
+that a converts to a.
+ 
+
+ align:start position:0%
+that a converts to a.
+Now to do that what we need is we need
+
+ align:start position:0%
+Now to do that what we need is we need
+ 
+
+ align:start position:0%
+Now to do that what we need is we need
+this stuff about that for a given
+
+ align:start position:0%
+this stuff about that for a given
+ 
+
+ align:start position:0%
+this stuff about that for a given
+epsilon there exist a capital n.
+
+ align:start position:0%
+epsilon there exist a capital n.
+ 
+
+ align:start position:0%
+epsilon there exist a capital n.
+Okay. So now let me first make the
+
+ align:start position:0%
+Okay. So now let me first make the
+ 
+
+ align:start position:0%
+Okay. So now let me first make the
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the that the soup right so a here
+
+ align:start position:0%
+that the that the soup right so a here
+ 
+
+ align:start position:0%
+that the that the soup right so a here
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+a here is the soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. Remember that the soup of a set
+
+ align:start position:0%
+right. Remember that the soup of a set
+ 
+
+ align:start position:0%
+right. Remember that the soup of a set
+is the smallest upper bound right so but
+
+ align:start position:0%
+is the smallest upper bound right so but
+ 
+
+ align:start position:0%
+is the smallest upper bound right so but
+since it is so it's partic so a is in
+
+ align:start position:0%
+since it is so it's partic so a is in
+ 
+
+ align:start position:0%
+since it is so it's partic so a is in
+particular an upper bound so you have
+
+ align:start position:0%
+particular an upper bound so you have
+ 
+
+ align:start position:0%
+particular an upper bound so you have
+that a n is less than a for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+a is an upper bound. It's actually the
+
+ align:start position:0%
+a is an upper bound. It's actually the
+ 
+
+ align:start position:0%
+a is an upper bound. It's actually the
+smallest upper bound. But for this you
+
+ align:start position:0%
+smallest upper bound. But for this you
+ 
+
+ align:start position:0%
+smallest upper bound. But for this you
+just need it's a upper bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So I'm going to look at a n sorry I'm
+
+ align:start position:0%
+So I'm going to look at a n sorry I'm
+ 
+
+ align:start position:0%
+So I'm going to look at a n sorry I'm
+going to look at a minus a n.
+
+ align:start position:0%
+going to look at a minus a n.
+ 
+
+ align:start position:0%
+going to look at a minus a n.
+And what I want to prove is that for a
+
+ align:start position:0%
+And what I want to prove is that for a
+ 
+
+ align:start position:0%
+And what I want to prove is that for a
+given epsilon if I'm sufficiently far
+
+ align:start position:0%
+given epsilon if I'm sufficiently far
+ 
+
+ align:start position:0%
+given epsilon if I'm sufficiently far
+out if I'm bigger than some capital if
+
+ align:start position:0%
+out if I'm bigger than some capital if
+ 
+
+ align:start position:0%
+out if I'm bigger than some capital if
+little n is bigger than some capital n
+
+ align:start position:0%
+little n is bigger than some capital n
+ 
+
+ align:start position:0%
+little n is bigger than some capital n
+then this here is less than epsilon
+
+ align:start position:0%
+then this here is less than epsilon
+ 
+
+ align:start position:0%
+then this here is less than epsilon
+right that's what I want to prove but
+
+ align:start position:0%
+right that's what I want to prove but
+ 
+
+ align:start position:0%
+right that's what I want to prove but
+this thing here you see this here I
+
+ align:start position:0%
+this thing here you see this here I
+ 
+
+ align:start position:0%
+this thing here you see this here I
+don't need the absolute value because I
+
+ align:start position:0%
+don't need the absolute value because I
+ 
+
+ align:start position:0%
+don't need the absolute value because I
+already know that this is bigger than
+
+ align:start position:0%
+already know that this is bigger than
+ 
+
+ align:start position:0%
+already know that this is bigger than
+that so I don't need the absolute value
+
+ align:start position:0%
+that so I don't need the absolute value
+ 
+
+ align:start position:0%
+that so I don't need the absolute value
+so I can just so this is what I want to
+
+ align:start position:0%
+so I can just so this is what I want to
+ 
+
+ align:start position:0%
+so I can just so this is what I want to
+prove that I want to prove that for
+
+ align:start position:0%
+prove that I want to prove that for
+ 
+
+ align:start position:0%
+prove that I want to prove that for
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+given epsilon greater than zero there
+
+ align:start position:0%
+given epsilon greater than zero there
+ 
+
+ align:start position:0%
+given epsilon greater than zero there
+exist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So maybe let me just write it a little
+
+ align:start position:0%
+So maybe let me just write it a little
+ 
+
+ align:start position:0%
+So maybe let me just write it a little
+larger here. So what I want to prove is
+
+ align:start position:0%
+larger here. So what I want to prove is
+ 
+
+ align:start position:0%
+larger here. So what I want to prove is
+that given
+
+ align:start position:0%
+that given
+ 
+
+ align:start position:0%
+that given
+epsilon greater than zero there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a capital n such that
+
+ align:start position:0%
+a capital n such that
+ 
+
+ align:start position:0%
+a capital n such that
+if little n is bigger equal to this
+
+ align:start position:0%
+if little n is bigger equal to this
+ 
+
+ align:start position:0%
+if little n is bigger equal to this
+capital n then a minus a n which I know
+
+ align:start position:0%
+capital n then a minus a n which I know
+ 
+
+ align:start position:0%
+capital n then a minus a n which I know
+is positive I just need to prove that
+
+ align:start position:0%
+is positive I just need to prove that
+ 
+
+ align:start position:0%
+is positive I just need to prove that
+this is less than epsilon.
+
+ align:start position:0%
+this is less than epsilon.
+ 
+
+ align:start position:0%
+this is less than epsilon.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, so now how do you do that? Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know.
+
+ align:start position:0%
+I know.
+ 
+
+ align:start position:0%
+I know.
+So, at the moment, I just use that A was
+
+ align:start position:0%
+So, at the moment, I just use that A was
+ 
+
+ align:start position:0%
+So, at the moment, I just use that A was
+an upper bound. Now, I'm going to use
+
+ align:start position:0%
+an upper bound. Now, I'm going to use
+ 
+
+ align:start position:0%
+an upper bound. Now, I'm going to use
+that is the least upper bound.
+
+ align:start position:0%
+that is the least upper bound.
+ 
+
+ align:start position:0%
+that is the least upper bound.
+So since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is the least upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh a minus epsilon is not
+
+ align:start position:0%
+uh a minus epsilon is not
+ 
+
+ align:start position:0%
+uh a minus epsilon is not
+an upper bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? A minus epsilon is not an upper
+
+ align:start position:0%
+Right? A minus epsilon is not an upper
+ 
+
+ align:start position:0%
+Right? A minus epsilon is not an upper
+bound. So this means that there must
+
+ align:start position:0%
+bound. So this means that there must
+ 
+
+ align:start position:0%
+bound. So this means that there must
+exist so
+
+ align:start position:0%
+exist so
+ 
+
+ align:start position:0%
+exist so
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital n so that a n is bigger or
+
+ align:start position:0%
+capital n so that a n is bigger or
+ 
+
+ align:start position:0%
+capital n so that a n is bigger or
+equal. So a capital n just this one here
+
+ align:start position:0%
+equal. So a capital n just this one here
+ 
+
+ align:start position:0%
+equal. So a capital n just this one here
+is bigger than a minus epsilon. Right?
+
+ align:start position:0%
+is bigger than a minus epsilon. Right?
+ 
+
+ align:start position:0%
+is bigger than a minus epsilon. Right?
+because otherwise it would have been an
+
+ align:start position:0%
+because otherwise it would have been an
+ 
+
+ align:start position:0%
+because otherwise it would have been an
+upper box but it's actually strictly but
+
+ align:start position:0%
+upper box but it's actually strictly but
+ 
+
+ align:start position:0%
+upper box but it's actually strictly but
+maybe I should strictly because I'll put
+
+ align:start position:0%
+maybe I should strictly because I'll put
+ 
+
+ align:start position:0%
+maybe I should strictly because I'll put
+it up.
+
+ align:start position:0%
+it up.
+ 
+
+ align:start position:0%
+it up.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+but I already know that this thing here
+
+ align:start position:0%
+but I already know that this thing here
+ 
+
+ align:start position:0%
+but I already know that this thing here
+is less than a
+
+ align:start position:0%
+is less than a
+ 
+
+ align:start position:0%
+is less than a
+so but and I also know in fact I know
+
+ align:start position:0%
+so but and I also know in fact I know
+ 
+
+ align:start position:0%
+so but and I also know in fact I know
+more than this. I know that this thing
+
+ align:start position:0%
+more than this. I know that this thing
+ 
+
+ align:start position:0%
+more than this. I know that this thing
+here is less or equal to a little n as
+
+ align:start position:0%
+here is less or equal to a little n as
+ 
+
+ align:start position:0%
+here is less or equal to a little n as
+long as little n is bigger than capital
+
+ align:start position:0%
+long as little n is bigger than capital
+ 
+
+ align:start position:0%
+long as little n is bigger than capital
+n. That was just because the sequence
+
+ align:start position:0%
+n. That was just because the sequence
+ 
+
+ align:start position:0%
+n. That was just because the sequence
+was increasing and all of them is
+
+ align:start position:0%
+was increasing and all of them is
+ 
+
+ align:start position:0%
+was increasing and all of them is
+smaller than this upper bound. So now
+
+ align:start position:0%
+smaller than this upper bound. So now
+ 
+
+ align:start position:0%
+smaller than this upper bound. So now
+you see that so here you have a all the
+
+ align:start position:0%
+you see that so here you have a all the
+ 
+
+ align:start position:0%
+you see that so here you have a all the
+elements a in lie to the left and if
+
+ align:start position:0%
+elements a in lie to the left and if
+ 
+
+ align:start position:0%
+elements a in lie to the left and if
+you're looking at just the one from a
+
+ align:start position:0%
+you're looking at just the one from a
+ 
+
+ align:start position:0%
+you're looking at just the one from a
+capital N outwards then here you have a
+
+ align:start position:0%
+capital N outwards then here you have a
+ 
+
+ align:start position:0%
+capital N outwards then here you have a
+minus epsilon and then they lie between
+
+ align:start position:0%
+minus epsilon and then they lie between
+ 
+
+ align:start position:0%
+minus epsilon and then they lie between
+this one here and that in particular
+
+ align:start position:0%
+this one here and that in particular
+ 
+
+ align:start position:0%
+this one here and that in particular
+they lie to the right of this and to the
+
+ align:start position:0%
+they lie to the right of this and to the
+ 
+
+ align:start position:0%
+they lie to the right of this and to the
+left of that. So this means that they're
+
+ align:start position:0%
+left of that. So this means that they're
+ 
+
+ align:start position:0%
+left of that. So this means that they're
+squeezed in this little interval and
+
+ align:start position:0%
+squeezed in this little interval and
+ 
+
+ align:start position:0%
+squeezed in this little interval and
+it's so this difference here this
+
+ align:start position:0%
+it's so this difference here this
+ 
+
+ align:start position:0%
+it's so this difference here this
+difference from here to here is
+
+ align:start position:0%
+difference from here to here is
+ 
+
+ align:start position:0%
+difference from here to here is
+certainly bounded by the distance to
+
+ align:start position:0%
+certainly bounded by the distance to
+ 
+
+ align:start position:0%
+certainly bounded by the distance to
+here which was epsilon
+
+ align:start position:0%
+here which was epsilon
+ 
+
+ align:start position:0%
+here which was epsilon
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+So this proved that this in here is less
+
+ align:start position:0%
+So this proved that this in here is less
+ 
+
+ align:start position:0%
+So this proved that this in here is less
+than.
+
+ align:start position:0%
+than.
+ 
+
+ align:start position:0%
+than.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And with obvious modification
+
+ align:start position:0%
+And with obvious modification
+ 
+
+ align:start position:0%
+And with obvious modification
+uh the proof of that if you take so this
+
+ align:start position:0%
+uh the proof of that if you take so this
+ 
+
+ align:start position:0%
+uh the proof of that if you take so this
+was an increasing sequence. The proof uh
+
+ align:start position:0%
+was an increasing sequence. The proof uh
+ 
+
+ align:start position:0%
+was an increasing sequence. The proof uh
+that if you have a decreasing sequence
+
+ align:start position:0%
+that if you have a decreasing sequence
+ 
+
+ align:start position:0%
+that if you have a decreasing sequence
+that is bounded right that that that the
+
+ align:start position:0%
+that is bounded right that that that the
+ 
+
+ align:start position:0%
+that is bounded right that that that the
+limit of that is the in proof with
+
+ align:start position:0%
+limit of that is the in proof with
+ 
+
+ align:start position:0%
+limit of that is the in proof with
+obvious changes is is know the same.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now let's come back to square root of
+
+ align:start position:0%
+So now let's come back to square root of
+ 
+
+ align:start position:0%
+So now let's come back to square root of
+two. Right. And so we have this idea
+
+ align:start position:0%
+two. Right. And so we have this idea
+ 
+
+ align:start position:0%
+two. Right. And so we have this idea
+that square<unk> two in a way the way
+
+ align:start position:0%
+that square<unk> two in a way the way
+ 
+
+ align:start position:0%
+that square<unk> two in a way the way
+you know to just get an idea about how
+
+ align:start position:0%
+you know to just get an idea about how
+ 
+
+ align:start position:0%
+you know to just get an idea about how
+large it is you think about it as uh you
+
+ align:start position:0%
+large it is you think about it as uh you
+ 
+
+ align:start position:0%
+large it is you think about it as uh you
+know you think about it as one and then
+
+ align:start position:0%
+know you think about it as one and then
+ 
+
+ align:start position:0%
+know you think about it as one and then
+a number of digits afterwards right
+
+ align:start position:0%
+a number of digits afterwards right
+ 
+
+ align:start position:0%
+a number of digits afterwards right
+that's a kind of approximation
+
+ align:start position:0%
+that's a kind of approximation
+ 
+
+ align:start position:0%
+that's a kind of approximation
+so so let's try to make this more
+
+ align:start position:0%
+so so let's try to make this more
+ 
+
+ align:start position:0%
+so so let's try to make this more
+precise
+
+ align:start position:0%
+precise
+ 
+
+ align:start position:0%
+precise
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+I'm going to look at a I'm going to
+
+ align:start position:0%
+I'm going to look at a I'm going to
+ 
+
+ align:start position:0%
+I'm going to look at a I'm going to
+define
+
+ align:start position:0%
+define
+ 
+
+ align:start position:0%
+define
+uh two sequence uh two sequences
+
+ align:start position:0%
+uh two sequence uh two sequences
+ 
+
+ align:start position:0%
+uh two sequence uh two sequences
+uh a n and bn sorry two. So we'll define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a n and bn
+
+ align:start position:0%
+a n and bn
+ 
+
+ align:start position:0%
+a n and bn
+and a n will really be a n where
+
+ align:start position:0%
+and a n will really be a n where
+ 
+
+ align:start position:0%
+and a n will really be a n where
+where a n
+
+ align:start position:0%
+where a n
+ 
+
+ align:start position:0%
+where a n
+is going to be bn
+
+ align:start position:0%
+is going to be bn
+ 
+
+ align:start position:0%
+is going to be bn
+/ 10 to ^ nus one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Remember that anything to you know if
+
+ align:start position:0%
+Remember that anything to you know if
+ 
+
+ align:start position:0%
+Remember that anything to you know if
+it's 10 to the power zero by definition
+
+ align:start position:0%
+it's 10 to the power zero by definition
+ 
+
+ align:start position:0%
+it's 10 to the power zero by definition
+that's one. Okay. So this here in
+
+ align:start position:0%
+that's one. Okay. So this here in
+ 
+
+ align:start position:0%
+that's one. Okay. So this here in
+particular means that a
+
+ align:start position:0%
+particular means that a
+ 
+
+ align:start position:0%
+particular means that a
+a1 should be equal to b1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we're going to define it like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we are
+
+ align:start position:0%
+And we are
+ 
+
+ align:start position:0%
+And we are
+going to define the BN.
+
+ align:start position:0%
+going to define the BN.
+ 
+
+ align:start position:0%
+going to define the BN.
+So and the sequences here the the so
+
+ align:start position:0%
+So and the sequences here the the so
+ 
+
+ align:start position:0%
+So and the sequences here the the so
+there would be some properties here is
+
+ align:start position:0%
+there would be some properties here is
+ 
+
+ align:start position:0%
+there would be some properties here is
+that the sequence
+
+ align:start position:0%
+that the sequence
+ 
+
+ align:start position:0%
+that the sequence
+uh sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh a is monotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a just real numbers that it's monot
+
+ align:start position:0%
+a just real numbers that it's monot
+ 
+
+ align:start position:0%
+a just real numbers that it's monot
+increasing
+
+ align:start position:0%
+increasing
+ 
+
+ align:start position:0%
+increasing
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+and uh and the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is going to be defined to right so
+
+ align:start position:0%
+um is going to be defined to right so
+ 
+
+ align:start position:0%
+um is going to be defined to right so
+and and and a is defined like that sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and the bn
+
+ align:start position:0%
+um and the bn
+ 
+
+ align:start position:0%
+um and the bn
+and the bn are just
+
+ align:start position:0%
+and the bn are just
+ 
+
+ align:start position:0%
+and the bn are just
+natural numbers Okay.
+
+ align:start position:0%
+natural numbers Okay.
+ 
+
+ align:start position:0%
+natural numbers Okay.
+So, so a n is defined from bn. It's
+
+ align:start position:0%
+So, so a n is defined from bn. It's
+ 
+
+ align:start position:0%
+So, so a n is defined from bn. It's
+really a n that we are interested in,
+
+ align:start position:0%
+really a n that we are interested in,
+ 
+
+ align:start position:0%
+really a n that we are interested in,
+but bn is going to be a useful tool
+
+ align:start position:0%
+but bn is going to be a useful tool
+ 
+
+ align:start position:0%
+but bn is going to be a useful tool
+here. And so,
+
+ align:start position:0%
+here. And so,
+ 
+
+ align:start position:0%
+here. And so,
+and it's going to be and the bn to some
+
+ align:start position:0%
+and it's going to be and the bn to some
+ 
+
+ align:start position:0%
+and it's going to be and the bn to some
+extent is very simple because they're
+
+ align:start position:0%
+extent is very simple because they're
+ 
+
+ align:start position:0%
+extent is very simple because they're
+just natural numbers.
+
+ align:start position:0%
+just natural numbers.
+ 
+
+ align:start position:0%
+just natural numbers.
+So, now um so now we define
+
+ align:start position:0%
+So, now um so now we define
+ 
+
+ align:start position:0%
+So, now um so now we define
+bn.
+
+ align:start position:0%
+bn.
+ 
+
+ align:start position:0%
+bn.
+So bn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+b²
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bigger and less or equal to 2 uh * uh
+
+ align:start position:0%
+is bigger and less or equal to 2 uh * uh
+ 
+
+ align:start position:0%
+is bigger and less or equal to 2 uh * uh
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+to the power 2 n - 2.
+
+ align:start position:0%
+to the power 2 n - 2.
+ 
+
+ align:start position:0%
+to the power 2 n - 2.
+So that's how right so this here so this
+
+ align:start position:0%
+So that's how right so this here so this
+ 
+
+ align:start position:0%
+So that's how right so this here so this
+so the sets of natural number that is
+
+ align:start position:0%
+so the sets of natural number that is
+ 
+
+ align:start position:0%
+so the sets of natural number that is
+bounded by that right that's like a
+
+ align:start position:0%
+bounded by that right that's like a
+ 
+
+ align:start position:0%
+bounded by that right that's like a
+finite set so you just take the max of
+
+ align:start position:0%
+finite set so you just take the max of
+ 
+
+ align:start position:0%
+finite set so you just take the max of
+soup or whatever the max of that's it
+
+ align:start position:0%
+soup or whatever the max of that's it
+ 
+
+ align:start position:0%
+soup or whatever the max of that's it
+right it's just the max of that's it so
+
+ align:start position:0%
+right it's just the max of that's it so
+ 
+
+ align:start position:0%
+right it's just the max of that's it so
+that's a natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+and now again we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then we define. So now we have
+
+ align:start position:0%
+right and then we define. So now we have
+ 
+
+ align:start position:0%
+right and then we define. So now we have
+the bs
+
+ align:start position:0%
+the bs
+ 
+
+ align:start position:0%
+the bs
+and then again a ends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the a
+
+ align:start position:0%
+the a
+ 
+
+ align:start position:0%
+the a
+n are defined to be bn divided by 10 to
+
+ align:start position:0%
+n are defined to be bn divided by 10 to
+ 
+
+ align:start position:0%
+n are defined to be bn divided by 10 to
+the n minus one. Right? Right. And so
+
+ align:start position:0%
+the n minus one. Right? Right. And so
+ 
+
+ align:start position:0%
+the n minus one. Right? Right. And so
+again you see that and so right. So now
+
+ align:start position:0%
+again you see that and so right. So now
+ 
+
+ align:start position:0%
+again you see that and so right. So now
+the first thing you observe is that if n
+
+ align:start position:0%
+the first thing you observe is that if n
+ 
+
+ align:start position:0%
+the first thing you observe is that if n
+is equal to one
+
+ align:start position:0%
+is equal to one
+ 
+
+ align:start position:0%
+is equal to one
+if n is equal to one then this thing
+
+ align:start position:0%
+if n is equal to one then this thing
+ 
+
+ align:start position:0%
+if n is equal to one then this thing
+here is zero so this means this has one
+
+ align:start position:0%
+here is zero so this means this has one
+ 
+
+ align:start position:0%
+here is zero so this means this has one
+so it's the largest natural number so
+
+ align:start position:0%
+so it's the largest natural number so
+ 
+
+ align:start position:0%
+so it's the largest natural number so
+that the square is less than two so this
+
+ align:start position:0%
+that the square is less than two so this
+ 
+
+ align:start position:0%
+that the square is less than two so this
+means that bn
+
+ align:start position:0%
+means that bn
+ 
+
+ align:start position:0%
+means that bn
+so n= to one bn is equal to one and
+
+ align:start position:0%
+so n= to one bn is equal to one and
+ 
+
+ align:start position:0%
+so n= to one bn is equal to one and
+because this thing here is also
+
+ align:start position:0%
+because this thing here is also
+ 
+
+ align:start position:0%
+because this thing here is also
+zero. So this the denominator is is one.
+
+ align:start position:0%
+zero. So this the denominator is is one.
+ 
+
+ align:start position:0%
+zero. So this the denominator is is one.
+So a n a1 sorry a1 is one. b1 is one and
+
+ align:start position:0%
+So a n a1 sorry a1 is one. b1 is one and
+ 
+
+ align:start position:0%
+So a n a1 sorry a1 is one. b1 is one and
+a1 has to be the same as b1. And so
+
+ align:start position:0%
+a1 has to be the same as b1. And so
+ 
+
+ align:start position:0%
+a1 has to be the same as b1. And so
+that's also one.
+
+ align:start position:0%
+that's also one.
+ 
+
+ align:start position:0%
+that's also one.
+Okay. So that's how it starts.
+
+ align:start position:0%
+Okay. So that's how it starts.
+ 
+
+ align:start position:0%
+Okay. So that's how it starts.
+And now what we want to prove is that um
+
+ align:start position:0%
+And now what we want to prove is that um
+ 
+
+ align:start position:0%
+And now what we want to prove is that um
+we want to prove that the sequence a n
+
+ align:start position:0%
+we want to prove that the sequence a n
+ 
+
+ align:start position:0%
+we want to prove that the sequence a n
+is monotm increasing right we want to
+
+ align:start position:0%
+is monotm increasing right we want to
+ 
+
+ align:start position:0%
+is monotm increasing right we want to
+prove that a end is monotum increasing
+
+ align:start position:0%
+prove that a end is monotum increasing
+ 
+
+ align:start position:0%
+prove that a end is monotum increasing
+so let's just try to understand that
+
+ align:start position:0%
+so let's just try to understand that
+ 
+
+ align:start position:0%
+so let's just try to understand that
+right and so again for mono increasing
+
+ align:start position:0%
+right and so again for mono increasing
+ 
+
+ align:start position:0%
+right and so again for mono increasing
+you just need to compare two consecutive
+
+ align:start position:0%
+you just need to compare two consecutive
+ 
+
+ align:start position:0%
+you just need to compare two consecutive
+elements right so so we want to show
+
+ align:start position:0%
+elements right so so we want to show
+ 
+
+ align:start position:0%
+elements right so so we want to show
+so so this here remember that there's a
+
+ align:start position:0%
+so so this here remember that there's a
+ 
+
+ align:start position:0%
+so so this here remember that there's a
+kind of you know there's ways to write a
+
+ align:start position:0%
+kind of you know there's ways to write a
+ 
+
+ align:start position:0%
+kind of you know there's ways to write a
+formal proof and then there's like
+
+ align:start position:0%
+formal proof and then there's like
+ 
+
+ align:start position:0%
+formal proof and then there's like
+things you have on the scrap paper to
+
+ align:start position:0%
+things you have on the scrap paper to
+ 
+
+ align:start position:0%
+things you have on the scrap paper to
+get the idea. So this is would be what
+
+ align:start position:0%
+get the idea. So this is would be what
+ 
+
+ align:start position:0%
+get the idea. So this is would be what
+we're going on may maybe the first
+
+ align:start position:0%
+we're going on may maybe the first
+ 
+
+ align:start position:0%
+we're going on may maybe the first
+statement is so we want to show this you
+
+ align:start position:0%
+statement is so we want to show this you
+ 
+
+ align:start position:0%
+statement is so we want to show this you
+could certainly put as part of the proof
+
+ align:start position:0%
+could certainly put as part of the proof
+ 
+
+ align:start position:0%
+could certainly put as part of the proof
+want to show
+
+ align:start position:0%
+want to show
+ 
+
+ align:start position:0%
+want to show
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+a n is less or equal to a n + one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right? So a n since a n here is
+
+ align:start position:0%
+that right? So a n since a n here is
+ 
+
+ align:start position:0%
+that right? So a n since a n here is
+equal to bn / 10 ^ n minus 2. You want
+
+ align:start position:0%
+equal to bn / 10 ^ n minus 2. You want
+ 
+
+ align:start position:0%
+equal to bn / 10 ^ n minus 2. You want
+to prove that this thing here is less
+
+ align:start position:0%
+to prove that this thing here is less
+ 
+
+ align:start position:0%
+to prove that this thing here is less
+than a n + 1 which is b n + 1
+
+ align:start position:0%
+than a n + 1 which is b n + 1
+ 
+
+ align:start position:0%
+than a n + 1 which is b n + 1
+over 10 to the n + 1 - one. So this here
+
+ align:start position:0%
+over 10 to the n + 1 - one. So this here
+ 
+
+ align:start position:0%
+over 10 to the n + 1 - one. So this here
+is b n + 1 over 10 uh to the power n.
+
+ align:start position:0%
+is b n + 1 over 10 uh to the power n.
+ 
+
+ align:start position:0%
+is b n + 1 over 10 uh to the power n.
+That's what you want to prove.
+
+ align:start position:0%
+That's what you want to prove.
+ 
+
+ align:start position:0%
+That's what you want to prove.
+So we want to show so so you see that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to show so this is what we want
+
+ align:start position:0%
+we want to show so this is what we want
+ 
+
+ align:start position:0%
+we want to show so this is what we want
+to prove that this thing here is less
+
+ align:start position:0%
+to prove that this thing here is less
+ 
+
+ align:start position:0%
+to prove that this thing here is less
+than this. If you multiply by 10 to the^
+
+ align:start position:0%
+than this. If you multiply by 10 to the^
+ 
+
+ align:start position:0%
+than this. If you multiply by 10 to the^
+n on both sides then you get over here
+
+ align:start position:0%
+n on both sides then you get over here
+ 
+
+ align:start position:0%
+n on both sides then you get over here
+and after you reduce it you get 10. So
+
+ align:start position:0%
+and after you reduce it you get 10. So
+ 
+
+ align:start position:0%
+and after you reduce it you get 10. So
+en so need to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+needs to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that 10
+
+ align:start position:0%
+that 10
+ 
+
+ align:start position:0%
+that 10
+bn
+
+ align:start position:0%
+bn
+ 
+
+ align:start position:0%
+bn
+is less or equal to bn + one
+
+ align:start position:0%
+is less or equal to bn + one
+ 
+
+ align:start position:0%
+is less or equal to bn + one
+right that's what we need to prove right
+
+ align:start position:0%
+right that's what we need to prove right
+ 
+
+ align:start position:0%
+right that's what we need to prove right
+and again this just comes from that you
+
+ align:start position:0%
+and again this just comes from that you
+ 
+
+ align:start position:0%
+and again this just comes from that you
+we want to prove forget about the a now
+
+ align:start position:0%
+we want to prove forget about the a now
+ 
+
+ align:start position:0%
+we want to prove forget about the a now
+you can just think about that we need to
+
+ align:start position:0%
+you can just think about that we need to
+ 
+
+ align:start position:0%
+you can just think about that we need to
+prove that this in here is less than
+
+ align:start position:0%
+prove that this in here is less than
+ 
+
+ align:start position:0%
+prove that this in here is less than
+this multiply over by 10 to the n on
+
+ align:start position:0%
+this multiply over by 10 to the n on
+ 
+
+ align:start position:0%
+this multiply over by 10 to the n on
+both sides then there's still 10 * bn
+
+ align:start position:0%
+both sides then there's still 10 * bn
+ 
+
+ align:start position:0%
+both sides then there's still 10 * bn
+left and here it's just b
+
+ align:start position:0%
+left and here it's just b
+ 
+
+ align:start position:0%
+left and here it's just b
+okay so we need to show this one here
+
+ align:start position:0%
+okay so we need to show this one here
+ 
+
+ align:start position:0%
+okay so we need to show this one here
+right and so if I was to write it down I
+
+ align:start position:0%
+right and so if I was to write it down I
+ 
+
+ align:start position:0%
+right and so if I was to write it down I
+would probably have some of this on
+
+ align:start position:0%
+would probably have some of this on
+ 
+
+ align:start position:0%
+would probably have some of this on
+scrap paper and then I would instead
+
+ align:start position:0%
+scrap paper and then I would instead
+ 
+
+ align:start position:0%
+scrap paper and then I would instead
+sort of establish this here first and
+
+ align:start position:0%
+sort of establish this here first and
+ 
+
+ align:start position:0%
+sort of establish this here first and
+then say therefore you know and then
+
+ align:start position:0%
+then say therefore you know and then
+ 
+
+ align:start position:0%
+then say therefore you know and then
+I'll conclude why you So you but but of
+
+ align:start position:0%
+I'll conclude why you So you but but of
+ 
+
+ align:start position:0%
+I'll conclude why you So you but but of
+course that's not the way you're
+
+ align:start position:0%
+course that's not the way you're
+ 
+
+ align:start position:0%
+course that's not the way you're
+thinking about it right I mean you first
+
+ align:start position:0%
+thinking about it right I mean you first
+ 
+
+ align:start position:0%
+thinking about it right I mean you first
+try to analyze what you have to prove
+
+ align:start position:0%
+try to analyze what you have to prove
+ 
+
+ align:start position:0%
+try to analyze what you have to prove
+and then once you know that then you try
+
+ align:start position:0%
+and then once you know that then you try
+ 
+
+ align:start position:0%
+and then once you know that then you try
+to write it down nicely
+
+ align:start position:0%
+to write it down nicely
+ 
+
+ align:start position:0%
+to write it down nicely
+okay so so we need to prove this here
+
+ align:start position:0%
+okay so so we need to prove this here
+ 
+
+ align:start position:0%
+okay so so we need to prove this here
+and so now
+
+ align:start position:0%
+and so now
+ 
+
+ align:start position:0%
+and so now
+uh right so now the thing is that we
+
+ align:start position:0%
+uh right so now the thing is that we
+ 
+
+ align:start position:0%
+uh right so now the thing is that we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+we have that so The definition of bn
+
+ align:start position:0%
+we have that so The definition of bn
+ 
+
+ align:start position:0%
+we have that so The definition of bn
+which is right here that's the
+
+ align:start position:0%
+which is right here that's the
+ 
+
+ align:start position:0%
+which is right here that's the
+definition of bn but let me copy it over
+
+ align:start position:0%
+definition of bn but let me copy it over
+ 
+
+ align:start position:0%
+definition of bn but let me copy it over
+here. So we know that bn squared is less
+
+ align:start position:0%
+here. So we know that bn squared is less
+ 
+
+ align:start position:0%
+here. So we know that bn squared is less
+or equal to it's the largest integer. So
+
+ align:start position:0%
+or equal to it's the largest integer. So
+ 
+
+ align:start position:0%
+or equal to it's the largest integer. So
+that you have this in here,
+
+ align:start position:0%
+that you have this in here,
+ 
+
+ align:start position:0%
+that you have this in here,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+But this means that if you're looking at
+
+ align:start position:0%
+But this means that if you're looking at
+ 
+
+ align:start position:0%
+But this means that if you're looking at
+10 bn, that's still an integer. And if
+
+ align:start position:0%
+10 bn, that's still an integer. And if
+ 
+
+ align:start position:0%
+10 bn, that's still an integer. And if
+you square this here, right? Then this
+
+ align:start position:0%
+you square this here, right? Then this
+ 
+
+ align:start position:0%
+you square this here, right? Then this
+is the same as 100
+
+ align:start position:0%
+is the same as 100
+ 
+
+ align:start position:0%
+is the same as 100
+times bn squared. And so that's that
+
+ align:start position:0%
+times bn squared. And so that's that
+ 
+
+ align:start position:0%
+times bn squared. And so that's that
+actually has to be less than 100 * this.
+
+ align:start position:0%
+actually has to be less than 100 * this.
+ 
+
+ align:start position:0%
+actually has to be less than 100 * this.
+So this kills those uh I mean so it just
+
+ align:start position:0%
+So this kills those uh I mean so it just
+ 
+
+ align:start position:0%
+So this kills those uh I mean so it just
+becomes less or equal to two 10 to the
+
+ align:start position:0%
+becomes less or equal to two 10 to the
+ 
+
+ align:start position:0%
+becomes less or equal to two 10 to the
+2n
+
+ align:start position:0%
+2n
+ 
+
+ align:start position:0%
+2n
+right like that
+
+ align:start position:0%
+right like that
+ 
+
+ align:start position:0%
+right like that
+and this here you can also write as 2
+
+ align:start position:0%
+and this here you can also write as 2
+ 
+
+ align:start position:0%
+and this here you can also write as 2
+to the 10 * 10 to ^ 2 n + 1 - 2 right
+
+ align:start position:0%
+to the 10 * 10 to ^ 2 n + 1 - 2 right
+ 
+
+ align:start position:0%
+to the 10 * 10 to ^ 2 n + 1 - 2 right
+but now you see that bn so this so this
+
+ align:start position:0%
+but now you see that bn so this so this
+ 
+
+ align:start position:0%
+but now you see that bn so this so this
+so 10 bn is an integer and it has this
+
+ align:start position:0%
+so 10 bn is an integer and it has this
+ 
+
+ align:start position:0%
+so 10 bn is an integer and it has this
+property but bn + one was supposed to be
+
+ align:start position:0%
+property but bn + one was supposed to be
+ 
+
+ align:start position:0%
+property but bn + one was supposed to be
+the largest integer so that the square
+
+ align:start position:0%
+the largest integer so that the square
+ 
+
+ align:start position:0%
+the largest integer so that the square
+here is less than 2 * 10 to to 2 n + 1 -
+
+ align:start position:0%
+here is less than 2 * 10 to to 2 n + 1 -
+ 
+
+ align:start position:0%
+here is less than 2 * 10 to to 2 n + 1 -
+2 you see that bn + one is a is the
+
+ align:start position:0%
+2 you see that bn + one is a is the
+ 
+
+ align:start position:0%
+2 you see that bn + one is a is the
+largest one with this property so you
+
+ align:start position:0%
+largest one with this property so you
+ 
+
+ align:start position:0%
+largest one with this property so you
+conclude that so since
+
+ align:start position:0%
+conclude that so since
+ 
+
+ align:start position:0%
+conclude that so since
+bn + one is the largest such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and both are integers
+
+ align:start position:0%
+and both are integers
+ 
+
+ align:start position:0%
+and both are integers
+and and bn is is an integer
+
+ align:start position:0%
+and and bn is is an integer
+ 
+
+ align:start position:0%
+and and bn is is an integer
+then uh bn + one must be bigger equal to
+
+ align:start position:0%
+then uh bn + one must be bigger equal to
+ 
+
+ align:start position:0%
+then uh bn + one must be bigger equal to
+bn
+
+ align:start position:0%
+bn
+ 
+
+ align:start position:0%
+bn
+uh must be bigger than 10 * bn right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's exactly what we want to prove
+
+ align:start position:0%
+and that's exactly what we want to prove
+ 
+
+ align:start position:0%
+and that's exactly what we want to prove
+right that that uh bn + one was bigger
+
+ align:start position:0%
+right that that uh bn + one was bigger
+ 
+
+ align:start position:0%
+right that that uh bn + one was bigger
+than bn.
+
+ align:start position:0%
+than bn.
+ 
+
+ align:start position:0%
+than bn.
+So we now have that the sequence a
+
+ align:start position:0%
+So we now have that the sequence a
+ 
+
+ align:start position:0%
+So we now have that the sequence a
+defined this slightly cryptical way but
+
+ align:start position:0%
+defined this slightly cryptical way but
+ 
+
+ align:start position:0%
+defined this slightly cryptical way but
+really it's not I mean it sounds maybe
+
+ align:start position:0%
+really it's not I mean it sounds maybe
+ 
+
+ align:start position:0%
+really it's not I mean it sounds maybe
+cryptical but it's just to instead of
+
+ align:start position:0%
+cryptical but it's just to instead of
+ 
+
+ align:start position:0%
+cryptical but it's just to instead of
+using somehow digital numbers you just
+
+ align:start position:0%
+using somehow digital numbers you just
+ 
+
+ align:start position:0%
+using somehow digital numbers you just
+multiply you're just thinking about you
+
+ align:start position:0%
+multiply you're just thinking about you
+ 
+
+ align:start position:0%
+multiply you're just thinking about you
+want this and that many uh by so uh like
+
+ align:start position:0%
+want this and that many uh by so uh like
+ 
+
+ align:start position:0%
+want this and that many uh by so uh like
+the n is referring to the number of
+
+ align:start position:0%
+the n is referring to the number of
+ 
+
+ align:start position:0%
+the n is referring to the number of
+digits but including the digit that is
+
+ align:start position:0%
+digits but including the digit that is
+ 
+
+ align:start position:0%
+digits but including the digit that is
+for the the point right so it's actually
+
+ align:start position:0%
+for the the point right so it's actually
+ 
+
+ align:start position:0%
+for the the point right so it's actually
+not very cryptical but it maybe sounds a
+
+ align:start position:0%
+not very cryptical but it maybe sounds a
+ 
+
+ align:start position:0%
+not very cryptical but it maybe sounds a
+little formal here okay so we have a n
+
+ align:start position:0%
+little formal here okay so we have a n
+ 
+
+ align:start position:0%
+little formal here okay so we have a n
+is a increasing sequence okay now why is
+
+ align:start position:0%
+is a increasing sequence okay now why is
+ 
+
+ align:start position:0%
+is a increasing sequence okay now why is
+a n bounded right
+
+ align:start position:0%
+a n bounded right
+ 
+
+ align:start position:0%
+a n bounded right
+so but the a is defined from the bn
+
+ align:start position:0%
+so but the a is defined from the bn
+ 
+
+ align:start position:0%
+so but the a is defined from the bn
+so in order to show that a n is bounded
+
+ align:start position:0%
+so in order to show that a n is bounded
+ 
+
+ align:start position:0%
+so in order to show that a n is bounded
+you have to figure out you have to
+
+ align:start position:0%
+you have to figure out you have to
+ 
+
+ align:start position:0%
+you have to figure out you have to
+figure out what is a bound for the BN
+
+ align:start position:0%
+figure out what is a bound for the BN
+ 
+
+ align:start position:0%
+figure out what is a bound for the BN
+right but you have this here bn is the
+
+ align:start position:0%
+right but you have this here bn is the
+ 
+
+ align:start position:0%
+right but you have this here bn is the
+largest such number if I take if I take
+
+ align:start position:0%
+largest such number if I take if I take
+ 
+
+ align:start position:0%
+largest such number if I take if I take
+two * 10 ^ n minus one suppose I take
+
+ align:start position:0%
+two * 10 ^ n minus one suppose I take
+ 
+
+ align:start position:0%
+two * 10 ^ n minus one suppose I take
+this number here right and I square it
+
+ align:start position:0%
+this number here right and I square it
+ 
+
+ align:start position:0%
+this number here right and I square it
+this is a definitely a integer I square
+
+ align:start position:0%
+this is a definitely a integer I square
+ 
+
+ align:start position:0%
+this is a definitely a integer I square
+it then I'm getting 4 * 10 ^ 2 n - 2
+
+ align:start position:0%
+it then I'm getting 4 * 10 ^ 2 n - 2
+ 
+
+ align:start position:0%
+it then I'm getting 4 * 10 ^ 2 n - 2
+right so this thing here This here is
+
+ align:start position:0%
+right so this thing here This here is
+ 
+
+ align:start position:0%
+right so this thing here This here is
+the same as over here but it's now four.
+
+ align:start position:0%
+the same as over here but it's now four.
+ 
+
+ align:start position:0%
+the same as over here but it's now four.
+So this number here would not be allowed
+
+ align:start position:0%
+So this number here would not be allowed
+ 
+
+ align:start position:0%
+So this number here would not be allowed
+as a bn. In fact it would be larger than
+
+ align:start position:0%
+as a bn. In fact it would be larger than
+ 
+
+ align:start position:0%
+as a bn. In fact it would be larger than
+bn. Right? So this here so bn is less
+
+ align:start position:0%
+bn. Right? So this here so bn is less
+ 
+
+ align:start position:0%
+bn. Right? So this here so bn is less
+than 2 to the^ 10 to the n minus one.
+
+ align:start position:0%
+than 2 to the^ 10 to the n minus one.
+ 
+
+ align:start position:0%
+than 2 to the^ 10 to the n minus one.
+Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that a n
+
+ align:start position:0%
+So this means that a n
+ 
+
+ align:start position:0%
+So this means that a n
+which is equal to bn over 10 ^ n minus
+
+ align:start position:0%
+which is equal to bn over 10 ^ n minus
+ 
+
+ align:start position:0%
+which is equal to bn over 10 ^ n minus
+one but this is now you see less or
+
+ align:start position:0%
+one but this is now you see less or
+ 
+
+ align:start position:0%
+one but this is now you see less or
+equal to two right
+
+ align:start position:0%
+equal to two right
+ 
+
+ align:start position:0%
+equal to two right
+so the sequence a n that we have defined
+
+ align:start position:0%
+so the sequence a n that we have defined
+ 
+
+ align:start position:0%
+so the sequence a n that we have defined
+is uh as you would have expected they
+
+ align:start position:0%
+is uh as you would have expected they
+ 
+
+ align:start position:0%
+is uh as you would have expected they
+are they're increasing because they
+
+ align:start position:0%
+are they're increasing because they
+ 
+
+ align:start position:0%
+are they're increasing because they
+really define the way they're really if
+
+ align:start position:0%
+really define the way they're really if
+ 
+
+ align:start position:0%
+really define the way they're really if
+you think about it is really defined to
+
+ align:start position:0%
+you think about it is really defined to
+ 
+
+ align:start position:0%
+you think about it is really defined to
+take you know the number of digits sort
+
+ align:start position:0%
+take you know the number of digits sort
+ 
+
+ align:start position:0%
+take you know the number of digits sort
+of it's going to be like the number of
+
+ align:start position:0%
+of it's going to be like the number of
+ 
+
+ align:start position:0%
+of it's going to be like the number of
+digits in square roo including the one
+
+ align:start position:0%
+digits in square roo including the one
+ 
+
+ align:start position:0%
+digits in square roo including the one
+the starting one right
+
+ align:start position:0%
+the starting one right
+ 
+
+ align:start position:0%
+the starting one right
+so and so
+
+ align:start position:0%
+so and so
+ 
+
+ align:start position:0%
+so and so
+um and so they all are going to be less
+
+ align:start position:0%
+um and so they all are going to be less
+ 
+
+ align:start position:0%
+um and so they all are going to be less
+than two right okay now
+
+ align:start position:0%
+than two right okay now
+ 
+
+ align:start position:0%
+than two right okay now
+let's try to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So now um we have so we have that
+
+ align:start position:0%
+Right. So now um we have so we have that
+ 
+
+ align:start position:0%
+Right. So now um we have so we have that
+a n is an increasing sequence and is
+
+ align:start position:0%
+a n is an increasing sequence and is
+ 
+
+ align:start position:0%
+a n is an increasing sequence and is
+bounded.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a end here uh is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the monitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh convergence here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So the a is convergent by the
+
+ align:start position:0%
+Right? So the a is convergent by the
+ 
+
+ align:start position:0%
+Right? So the a is convergent by the
+monotone convergence.
+
+ align:start position:0%
+monotone convergence.
+ 
+
+ align:start position:0%
+monotone convergence.
+But now if I'm looking at a n squ a n
+
+ align:start position:0%
+But now if I'm looking at a n squ a n
+ 
+
+ align:start position:0%
+But now if I'm looking at a n squ a n
+squ well a n squ it's the same as a end
+
+ align:start position:0%
+squ well a n squ it's the same as a end
+ 
+
+ align:start position:0%
+squ well a n squ it's the same as a end
+obviously times a n right but um but um
+
+ align:start position:0%
+obviously times a n right but um but um
+ 
+
+ align:start position:0%
+obviously times a n right but um but um
+but uh a n by definition was bn divided
+
+ align:start position:0%
+but uh a n by definition was bn divided
+ 
+
+ align:start position:0%
+but uh a n by definition was bn divided
+by 10
+
+ align:start position:0%
+by 10
+ 
+
+ align:start position:0%
+by 10
+uh uh 10 to the power uh n - one right
+
+ align:start position:0%
+uh uh 10 to the power uh n - one right
+ 
+
+ align:start position:0%
+uh uh 10 to the power uh n - one right
+and so I can write like this
+
+ align:start position:0%
+and so I can write like this
+ 
+
+ align:start position:0%
+and so I can write like this
+10 ^ n minus one and so you see that you
+
+ align:start position:0%
+10 ^ n minus one and so you see that you
+ 
+
+ align:start position:0%
+10 ^ n minus one and so you see that you
+can write this as bn^ squ and then these
+
+ align:start position:0%
+can write this as bn^ squ and then these
+ 
+
+ align:start position:0%
+can write this as bn^ squ and then these
+here combines to 2 n minus 2 right and
+
+ align:start position:0%
+here combines to 2 n minus 2 right and
+ 
+
+ align:start position:0%
+here combines to 2 n minus 2 right and
+by assumption
+
+ align:start position:0%
+by assumption
+ 
+
+ align:start position:0%
+by assumption
+if you divide by this here this thing
+
+ align:start position:0%
+if you divide by this here this thing
+ 
+
+ align:start position:0%
+if you divide by this here this thing
+here is lesser equal to two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have that. So you have that a n
+
+ align:start position:0%
+so you have that. So you have that a n
+ 
+
+ align:start position:0%
+so you have that. So you have that a n
+converts to a. And if you want to think
+
+ align:start position:0%
+converts to a. And if you want to think
+ 
+
+ align:start position:0%
+converts to a. And if you want to think
+about it, you think about this sequence
+
+ align:start position:0%
+about it, you think about this sequence
+ 
+
+ align:start position:0%
+about it, you think about this sequence
+again.
+
+ align:start position:0%
+again.
+ 
+
+ align:start position:0%
+again.
+And so now you know that a n by this uh
+
+ align:start position:0%
+And so now you know that a n by this uh
+ 
+
+ align:start position:0%
+And so now you know that a n by this uh
+by the product rule for sequences a n
+
+ align:start position:0%
+by the product rule for sequences a n
+ 
+
+ align:start position:0%
+by the product rule for sequences a n
+times a n the sequence times itself is
+
+ align:start position:0%
+times a n the sequence times itself is
+ 
+
+ align:start position:0%
+times a n the sequence times itself is
+converging to a n square a square.
+
+ align:start position:0%
+converging to a n square a square.
+ 
+
+ align:start position:0%
+converging to a n square a square.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And this thing here because they are
+
+ align:start position:0%
+And this thing here because they are
+ 
+
+ align:start position:0%
+And this thing here because they are
+because each of these squares here each
+
+ align:start position:0%
+because each of these squares here each
+ 
+
+ align:start position:0%
+because each of these squares here each
+of them is less or equal to two then the
+
+ align:start position:0%
+of them is less or equal to two then the
+ 
+
+ align:start position:0%
+of them is less or equal to two then the
+limit must be lesser equal to two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What I want to prove now is that this a
+
+ align:start position:0%
+What I want to prove now is that this a
+ 
+
+ align:start position:0%
+What I want to prove now is that this a
+that we get as a limit that the square
+
+ align:start position:0%
+that we get as a limit that the square
+ 
+
+ align:start position:0%
+that we get as a limit that the square
+is in fact equal to two. So I want to
+
+ align:start position:0%
+is in fact equal to two. So I want to
+ 
+
+ align:start position:0%
+is in fact equal to two. So I want to
+show that it's the square is so I have
+
+ align:start position:0%
+show that it's the square is so I have
+ 
+
+ align:start position:0%
+show that it's the square is so I have
+so I have so you know when we're doing
+
+ align:start position:0%
+so I have so you know when we're doing
+ 
+
+ align:start position:0%
+so I have so you know when we're doing
+it this this is one more proof of that
+
+ align:start position:0%
+it this this is one more proof of that
+ 
+
+ align:start position:0%
+it this this is one more proof of that
+square root of two is a real number but
+
+ align:start position:0%
+square root of two is a real number but
+ 
+
+ align:start position:0%
+square root of two is a real number but
+this is sort of in a way how you think
+
+ align:start position:0%
+this is sort of in a way how you think
+ 
+
+ align:start position:0%
+this is sort of in a way how you think
+about it in terms of the uh decimals
+
+ align:start position:0%
+about it in terms of the uh decimals
+ 
+
+ align:start position:0%
+about it in terms of the uh decimals
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so we have this sequence a n and we
+
+ align:start position:0%
+and so we have this sequence a n and we
+ 
+
+ align:start position:0%
+and so we have this sequence a n and we
+have proven that it's converging to some
+
+ align:start position:0%
+have proven that it's converging to some
+ 
+
+ align:start position:0%
+have proven that it's converging to some
+a and we've shown that this a here has a
+
+ align:start position:0%
+a and we've shown that this a here has a
+ 
+
+ align:start position:0%
+a and we've shown that this a here has a
+property that is lesser a squ is lesser
+
+ align:start position:0%
+property that is lesser a squ is lesser
+ 
+
+ align:start position:0%
+property that is lesser a squ is lesser
+equal to true. So I want to prove so I
+
+ align:start position:0%
+equal to true. So I want to prove so I
+ 
+
+ align:start position:0%
+equal to true. So I want to prove so I
+want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a and
+
+ align:start position:0%
+that a and
+ 
+
+ align:start position:0%
+that a and
+that sorry that a squ is actually equal
+
+ align:start position:0%
+that sorry that a squ is actually equal
+ 
+
+ align:start position:0%
+that sorry that a squ is actually equal
+to not one but two right that's what I
+
+ align:start position:0%
+to not one but two right that's what I
+ 
+
+ align:start position:0%
+to not one but two right that's what I
+want to prove right and but I already
+
+ align:start position:0%
+want to prove right and but I already
+ 
+
+ align:start position:0%
+want to prove right and but I already
+proven that a squ is less or equal to
+
+ align:start position:0%
+proven that a squ is less or equal to
+ 
+
+ align:start position:0%
+proven that a squ is less or equal to
+two so enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to show
+
+ align:start position:0%
+to show
+ 
+
+ align:start position:0%
+to show
+that a squ is bigger = to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's try to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to use this is going to be
+
+ align:start position:0%
+and I'm going to use this is going to be
+ 
+
+ align:start position:0%
+and I'm going to use this is going to be
+another illustration of the algebraic
+
+ align:start position:0%
+another illustration of the algebraic
+ 
+
+ align:start position:0%
+another illustration of the algebraic
+rules for sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I I haven't really I mean I I here now I
+
+ align:start position:0%
+I I haven't really I mean I I here now I
+ 
+
+ align:start position:0%
+I I haven't really I mean I I here now I
+really you know to prove
+
+ align:start position:0%
+really you know to prove
+ 
+
+ align:start position:0%
+really you know to prove
+that is less or equal to two. I didn't
+
+ align:start position:0%
+that is less or equal to two. I didn't
+ 
+
+ align:start position:0%
+that is less or equal to two. I didn't
+use fully the definition of the A
+
+ align:start position:0%
+use fully the definition of the A
+ 
+
+ align:start position:0%
+use fully the definition of the A
+because I didn't use I didn't really use
+
+ align:start position:0%
+because I didn't use I didn't really use
+ 
+
+ align:start position:0%
+because I didn't use I didn't really use
+that it was the largest such that A was
+
+ align:start position:0%
+that it was the largest such that A was
+ 
+
+ align:start position:0%
+that it was the largest such that A was
+defined in terms of BN where BN was the
+
+ align:start position:0%
+defined in terms of BN where BN was the
+ 
+
+ align:start position:0%
+defined in terms of BN where BN was the
+largest such uh such um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such number
+
+ align:start position:0%
+such number
+ 
+
+ align:start position:0%
+such number
+and so if I'm looking at
+
+ align:start position:0%
+and so if I'm looking at
+ 
+
+ align:start position:0%
+and so if I'm looking at
+suppose now I'm looking at BN
+
+ align:start position:0%
+suppose now I'm looking at BN
+ 
+
+ align:start position:0%
+suppose now I'm looking at BN
+and I'm adding one
+
+ align:start position:0%
+and I'm adding one
+ 
+
+ align:start position:0%
+and I'm adding one
+and I'm squaring it. Right?
+
+ align:start position:0%
+and I'm squaring it. Right?
+ 
+
+ align:start position:0%
+and I'm squaring it. Right?
+Well, this here cannot also be smaller
+
+ align:start position:0%
+Well, this here cannot also be smaller
+ 
+
+ align:start position:0%
+Well, this here cannot also be smaller
+than this here because then then then
+
+ align:start position:0%
+than this here because then then then
+ 
+
+ align:start position:0%
+than this here because then then then
+the BN should have been this thing here,
+
+ align:start position:0%
+the BN should have been this thing here,
+ 
+
+ align:start position:0%
+the BN should have been this thing here,
+right? So, this here must actually be
+
+ align:start position:0%
+right? So, this here must actually be
+ 
+
+ align:start position:0%
+right? So, this here must actually be
+strictly larger than 2 10 ^ 2nus 2.
+
+ align:start position:0%
+strictly larger than 2 10 ^ 2nus 2.
+ 
+
+ align:start position:0%
+strictly larger than 2 10 ^ 2nus 2.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so now you write,
+
+ align:start position:0%
+And so now you write,
+ 
+
+ align:start position:0%
+And so now you write,
+you know, you just divide by by this
+
+ align:start position:0%
+you know, you just divide by by this
+ 
+
+ align:start position:0%
+you know, you just divide by by this
+here on both sides. So you have b n + 1
+
+ align:start position:0%
+here on both sides. So you have b n + 1
+ 
+
+ align:start position:0%
+here on both sides. So you have b n + 1
+squared and you divide it by 10 to the
+
+ align:start position:0%
+squared and you divide it by 10 to the
+ 
+
+ align:start position:0%
+squared and you divide it by 10 to the
+power 2 n - 2. So you know that this
+
+ align:start position:0%
+power 2 n - 2. So you know that this
+ 
+
+ align:start position:0%
+power 2 n - 2. So you know that this
+thing is bigger than two.
+
+ align:start position:0%
+thing is bigger than two.
+ 
+
+ align:start position:0%
+thing is bigger than two.
+So now but you can write this in here.
+
+ align:start position:0%
+So now but you can write this in here.
+ 
+
+ align:start position:0%
+So now but you can write this in here.
+This denominator 10 ^ 2 nus 2 you can
+
+ align:start position:0%
+This denominator 10 ^ 2 nus 2 you can
+ 
+
+ align:start position:0%
+This denominator 10 ^ 2 nus 2 you can
+write as 10 ^ n -1 * 10 ^ n minus one.
+
+ align:start position:0%
+write as 10 ^ n -1 * 10 ^ n minus one.
+ 
+
+ align:start position:0%
+write as 10 ^ n -1 * 10 ^ n minus one.
+So in this way you can split this up and
+
+ align:start position:0%
+So in this way you can split this up and
+ 
+
+ align:start position:0%
+So in this way you can split this up and
+you can write it as bn + 1 over uh 10 ^
+
+ align:start position:0%
+you can write it as bn + 1 over uh 10 ^
+ 
+
+ align:start position:0%
+you can write it as bn + 1 over uh 10 ^
+n minus one
+
+ align:start position:0%
+n minus one
+ 
+
+ align:start position:0%
+n minus one
+and then times itself.
+
+ align:start position:0%
+and then times itself.
+ 
+
+ align:start position:0%
+and then times itself.
+This is is just to make sure that it's
+
+ align:start position:0%
+This is is just to make sure that it's
+ 
+
+ align:start position:0%
+This is is just to make sure that it's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+it's BN and then to the BN you're adding
+
+ align:start position:0%
+it's BN and then to the BN you're adding
+ 
+
+ align:start position:0%
+it's BN and then to the BN you're adding
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+So like that
+
+ align:start position:0%
+So like that
+ 
+
+ align:start position:0%
+So like that
+you write like that.
+
+ align:start position:0%
+you write like that.
+ 
+
+ align:start position:0%
+you write like that.
+But you see this thing here, this is
+
+ align:start position:0%
+But you see this thing here, this is
+ 
+
+ align:start position:0%
+But you see this thing here, this is
+this here, this thing here. You can
+
+ align:start position:0%
+this here, this thing here. You can
+ 
+
+ align:start position:0%
+this here, this thing here. You can
+split the fraction up. You can write it
+
+ align:start position:0%
+split the fraction up. You can write it
+ 
+
+ align:start position:0%
+split the fraction up. You can write it
+as bn
+
+ align:start position:0%
+as bn
+ 
+
+ align:start position:0%
+as bn
+uh over 10 ^ n minus one. And then you
+
+ align:start position:0%
+uh over 10 ^ n minus one. And then you
+ 
+
+ align:start position:0%
+uh over 10 ^ n minus one. And then you
+can add 1 / 10 ^ nus1
+
+ align:start position:0%
+can add 1 / 10 ^ nus1
+ 
+
+ align:start position:0%
+can add 1 / 10 ^ nus1
+and then you can multiply that by
+
+ align:start position:0%
+and then you can multiply that by
+ 
+
+ align:start position:0%
+and then you can multiply that by
+itself. Right? You can write it like
+
+ align:start position:0%
+itself. Right? You can write it like
+ 
+
+ align:start position:0%
+itself. Right? You can write it like
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? But now now
+
+ align:start position:0%
+Right? But now now
+ 
+
+ align:start position:0%
+Right? But now now
+you see now I can write this in here
+
+ align:start position:0%
+you see now I can write this in here
+ 
+
+ align:start position:0%
+you see now I can write this in here
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+so now I can think about it in a
+
+ align:start position:0%
+so now I can think about it in a
+ 
+
+ align:start position:0%
+so now I can think about it in a
+slightly different way. So I have that.
+
+ align:start position:0%
+slightly different way. So I have that.
+ 
+
+ align:start position:0%
+slightly different way. So I have that.
+So so I can write this thing here. This
+
+ align:start position:0%
+So so I can write this thing here. This
+ 
+
+ align:start position:0%
+So so I can write this thing here. This
+thing here is just that is the
+
+ align:start position:0%
+thing here is just that is the
+ 
+
+ align:start position:0%
+thing here is just that is the
+definition of a n.
+
+ align:start position:0%
+definition of a n.
+ 
+
+ align:start position:0%
+definition of a n.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+So I can say so what I have here is that
+
+ align:start position:0%
+So I can say so what I have here is that
+ 
+
+ align:start position:0%
+So I can say so what I have here is that
+a n + 1 / 10 ^ n minus one times itself
+
+ align:start position:0%
+a n + 1 / 10 ^ n minus one times itself
+ 
+
+ align:start position:0%
+a n + 1 / 10 ^ n minus one times itself
+but I'm I would just write it nicely out
+
+ align:start position:0%
+but I'm I would just write it nicely out
+ 
+
+ align:start position:0%
+but I'm I would just write it nicely out
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this thing here remember the way
+
+ align:start position:0%
+that this thing here remember the way
+ 
+
+ align:start position:0%
+that this thing here remember the way
+the it go that this is equal to that
+
+ align:start position:0%
+the it go that this is equal to that
+ 
+
+ align:start position:0%
+the it go that this is equal to that
+which is bigger than one two so this
+
+ align:start position:0%
+which is bigger than one two so this
+ 
+
+ align:start position:0%
+which is bigger than one two so this
+here is bigger than two
+
+ align:start position:0%
+here is bigger than two
+ 
+
+ align:start position:0%
+here is bigger than two
+right Now 10 1 / 10 to the n you can
+
+ align:start position:0%
+right Now 10 1 / 10 to the n you can
+ 
+
+ align:start position:0%
+right Now 10 1 / 10 to the n you can
+think about that as a sequence right you
+
+ align:start position:0%
+think about that as a sequence right you
+ 
+
+ align:start position:0%
+think about that as a sequence right you
+can think about this as a sequence that
+
+ align:start position:0%
+can think about this as a sequence that
+ 
+
+ align:start position:0%
+can think about this as a sequence that
+sequence go to zero this here goes to a
+
+ align:start position:0%
+sequence go to zero this here goes to a
+ 
+
+ align:start position:0%
+sequence go to zero this here goes to a
+the sum of these two sequences by the
+
+ align:start position:0%
+the sum of these two sequences by the
+ 
+
+ align:start position:0%
+the sum of these two sequences by the
+algebraic rules go to the sum of the
+
+ align:start position:0%
+algebraic rules go to the sum of the
+ 
+
+ align:start position:0%
+algebraic rules go to the sum of the
+limits so this is a plus zero so that's
+
+ align:start position:0%
+limits so this is a plus zero so that's
+ 
+
+ align:start position:0%
+limits so this is a plus zero so that's
+a so this thing here goes to a and and
+
+ align:start position:0%
+a so this thing here goes to a and and
+ 
+
+ align:start position:0%
+a so this thing here goes to a and and
+this is the same so this goes to a so
+
+ align:start position:0%
+this is the same so this goes to a so
+ 
+
+ align:start position:0%
+this is the same so this goes to a so
+you see that the limit here then goes to
+
+ align:start position:0%
+you see that the limit here then goes to
+ 
+
+ align:start position:0%
+you see that the limit here then goes to
+by the product rule for the limits. The
+
+ align:start position:0%
+by the product rule for the limits. The
+ 
+
+ align:start position:0%
+by the product rule for the limits. The
+limit here is so you get that a squared
+
+ align:start position:0%
+limit here is so you get that a squared
+ 
+
+ align:start position:0%
+limit here is so you get that a squared
+here and since it holds for each element
+
+ align:start position:0%
+here and since it holds for each element
+ 
+
+ align:start position:0%
+here and since it holds for each element
+then it also holds for the limit right
+
+ align:start position:0%
+then it also holds for the limit right
+ 
+
+ align:start position:0%
+then it also holds for the limit right
+except you had to be a little bit
+
+ align:start position:0%
+except you had to be a little bit
+ 
+
+ align:start position:0%
+except you had to be a little bit
+careful it's may not be strict
+
+ align:start position:0%
+careful it's may not be strict
+ 
+
+ align:start position:0%
+careful it's may not be strict
+inequality but just big or equal to and
+
+ align:start position:0%
+inequality but just big or equal to and
+ 
+
+ align:start position:0%
+inequality but just big or equal to and
+of course in fact it is by equal to
+
+ align:start position:0%
+of course in fact it is by equal to
+ 
+
+ align:start position:0%
+of course in fact it is by equal to
+because now you have established the
+
+ align:start position:0%
+because now you have established the
+ 
+
+ align:start position:0%
+because now you have established the
+other inequality that a^2 was bigger
+
+ align:start position:0%
+other inequality that a^2 was bigger
+ 
+
+ align:start position:0%
+other inequality that a^2 was bigger
+equal to 2. We had already proven that
+
+ align:start position:0%
+equal to 2. We had already proven that
+ 
+
+ align:start position:0%
+equal to 2. We had already proven that
+a^2 was less or equal to two. So you
+
+ align:start position:0%
+a^2 was less or equal to two. So you
+ 
+
+ align:start position:0%
+a^2 was less or equal to two. So you
+conclude that a^2 is equal to two.
+
+ align:start position:0%
+conclude that a^2 is equal to two.
+ 
+
+ align:start position:0%
+conclude that a^2 is equal to two.
+If you kind of just think about it, this
+
+ align:start position:0%
+If you kind of just think about it, this
+ 
+
+ align:start position:0%
+If you kind of just think about it, this
+is really how it sounds maybe a little
+
+ align:start position:0%
+is really how it sounds maybe a little
+ 
+
+ align:start position:0%
+is really how it sounds maybe a little
+bit convoluted, but it's really kind of
+
+ align:start position:0%
+bit convoluted, but it's really kind of
+ 
+
+ align:start position:0%
+bit convoluted, but it's really kind of
+writing down precisely what you think
+
+ align:start position:0%
+writing down precisely what you think
+ 
+
+ align:start position:0%
+writing down precisely what you think
+about when you're singing about a square
+
+ align:start position:0%
+about when you're singing about a square
+ 
+
+ align:start position:0%
+about when you're singing about a square
+root of two because you think about the
+
+ align:start position:0%
+root of two because you think about the
+ 
+
+ align:start position:0%
+root of two because you think about the
+number of digits. And so if you take,
+
+ align:start position:0%
+number of digits. And so if you take,
+ 
+
+ align:start position:0%
+number of digits. And so if you take,
+you know, including the first the one in
+
+ align:start position:0%
+you know, including the first the one in
+ 
+
+ align:start position:0%
+you know, including the first the one in
+1.4 four B including that one. If you
+
+ align:start position:0%
+1.4 four B including that one. If you
+ 
+
+ align:start position:0%
+1.4 four B including that one. If you
+think about the number of digits
+
+ align:start position:0%
+think about the number of digits
+ 
+
+ align:start position:0%
+think about the number of digits
+like the A N then the A end is really
+
+ align:start position:0%
+like the A N then the A end is really
+ 
+
+ align:start position:0%
+like the A N then the A end is really
+defined if you were to make it precise
+
+ align:start position:0%
+defined if you were to make it precise
+ 
+
+ align:start position:0%
+defined if you were to make it precise
+you would define it in terms of this
+
+ align:start position:0%
+you would define it in terms of this
+ 
+
+ align:start position:0%
+you would define it in terms of this
+other sequence BN. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now the next thing is so this
+
+ align:start position:0%
+Okay. So now the next thing is so this
+ 
+
+ align:start position:0%
+Okay. So now the next thing is so this
+was just like
+
+ align:start position:0%
+was just like
+ 
+
+ align:start position:0%
+was just like
+a little illustration of how the mono
+
+ align:start position:0%
+a little illustration of how the mono
+ 
+
+ align:start position:0%
+a little illustration of how the mono
+convergence theorem worked.
+
+ align:start position:0%
+convergence theorem worked.
+ 
+
+ align:start position:0%
+convergence theorem worked.
+and and and and then and we this will
+
+ align:start position:0%
+and and and and then and we this will
+ 
+
+ align:start position:0%
+and and and and then and we this will
+you know play an important role next
+
+ align:start position:0%
+you know play an important role next
+ 
+
+ align:start position:0%
+you know play an important role next
+time we Yeah.
+
+ align:start position:0%
+time we Yeah.
+ 
+
+ align:start position:0%
+time we Yeah.
+>> So uh the reason why at the top we have
+
+ align:start position:0%
+>> So uh the reason why at the top we have
+ 
+
+ align:start position:0%
+>> So uh the reason why at the top we have
+like strictly greater than two and then
+
+ align:start position:0%
+like strictly greater than two and then
+ 
+
+ align:start position:0%
+like strictly greater than two and then
+at the bottom we have greater or equal
+
+ align:start position:0%
+at the bottom we have greater or equal
+ 
+
+ align:start position:0%
+at the bottom we have greater or equal
+to because the a and the a limits
+
+ align:start position:0%
+to because the a and the a limits
+ 
+
+ align:start position:0%
+to because the a and the a limits
+whereas on the top we're considering
+
+ align:start position:0%
+whereas on the top we're considering
+ 
+
+ align:start position:0%
+whereas on the top we're considering
+each element.
+
+ align:start position:0%
+each element.
+ 
+
+ align:start position:0%
+each element.
+>> So so this um the a
+
+ align:start position:0%
+>> So so this um the a
+ 
+
+ align:start position:0%
+>> So so this um the a
+this you were talking about this here
+
+ align:start position:0%
+this you were talking about this here
+ 
+
+ align:start position:0%
+this you were talking about this here
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah. So the a n converts to a right
+
+ align:start position:0%
+>> Yeah. So the a n converts to a right
+ 
+
+ align:start position:0%
+>> Yeah. So the a n converts to a right
+this here you I think about this here.
+
+ align:start position:0%
+this here you I think about this here.
+ 
+
+ align:start position:0%
+this here you I think about this here.
+So think about a sequence plus another
+
+ align:start position:0%
+So think about a sequence plus another
+ 
+
+ align:start position:0%
+So think about a sequence plus another
+sequence, right? This sequence here
+
+ align:start position:0%
+sequence, right? This sequence here
+ 
+
+ align:start position:0%
+sequence, right? This sequence here
+converts to zero, right? So the sum of
+
+ align:start position:0%
+converts to zero, right? So the sum of
+ 
+
+ align:start position:0%
+converts to zero, right? So the sum of
+these two sequences converts to zero.
+
+ align:start position:0%
+these two sequences converts to zero.
+ 
+
+ align:start position:0%
+these two sequences converts to zero.
+And likewise for this and then I'm
+
+ align:start position:0%
+And likewise for this and then I'm
+ 
+
+ align:start position:0%
+And likewise for this and then I'm
+thinking about it as a product of this
+
+ align:start position:0%
+thinking about it as a product of this
+ 
+
+ align:start position:0%
+thinking about it as a product of this
+sequence with that sequence. And so but
+
+ align:start position:0%
+sequence with that sequence. And so but
+ 
+
+ align:start position:0%
+sequence with that sequence. And so but
+but it's like each element is in that in
+
+ align:start position:0%
+but it's like each element is in that in
+ 
+
+ align:start position:0%
+but it's like each element is in that in
+this in the product sequence is strictly
+
+ align:start position:0%
+this in the product sequence is strictly
+ 
+
+ align:start position:0%
+this in the product sequence is strictly
+bigger than two. But it doesn't
+
+ align:start position:0%
+bigger than two. But it doesn't
+ 
+
+ align:start position:0%
+bigger than two. But it doesn't
+necessarily mean that the limit is
+
+ align:start position:0%
+necessarily mean that the limit is
+ 
+
+ align:start position:0%
+necessarily mean that the limit is
+strictly but the limit has to be bigger
+
+ align:start position:0%
+strictly but the limit has to be bigger
+ 
+
+ align:start position:0%
+strictly but the limit has to be bigger
+than two, right? Because they could kind
+
+ align:start position:0%
+than two, right? Because they could kind
+ 
+
+ align:start position:0%
+than two, right? Because they could kind
+of approach two and that's exactly what
+
+ align:start position:0%
+of approach two and that's exactly what
+ 
+
+ align:start position:0%
+of approach two and that's exactly what
+happened of course. Yeah.
+
+ align:start position:0%
+happened of course. Yeah.
+ 
+
+ align:start position:0%
+happened of course. Yeah.
+Uh okay. So and and so I also just want
+
+ align:start position:0%
+Uh okay. So and and so I also just want
+ 
+
+ align:start position:0%
+Uh okay. So and and so I also just want
+to say that this with lee soup and le
+
+ align:start position:0%
+to say that this with lee soup and le
+ 
+
+ align:start position:0%
+to say that this with lee soup and le
+mint well we didn't actually define it
+
+ align:start position:0%
+mint well we didn't actually define it
+ 
+
+ align:start position:0%
+mint well we didn't actually define it
+but I defined you know and this is it is
+
+ align:start position:0%
+but I defined you know and this is it is
+ 
+
+ align:start position:0%
+but I defined you know and this is it is
+how you defining but but we haven't
+
+ align:start position:0%
+how you defining but but we haven't
+ 
+
+ align:start position:0%
+how you defining but but we haven't
+talked about that concept yet but this I
+
+ align:start position:0%
+talked about that concept yet but this I
+ 
+
+ align:start position:0%
+talked about that concept yet but this I
+talked about with that if you take a
+
+ align:start position:0%
+talked about with that if you take a
+ 
+
+ align:start position:0%
+talked about with that if you take a
+boundary sequence then you could form
+
+ align:start position:0%
+boundary sequence then you could form
+ 
+
+ align:start position:0%
+boundary sequence then you could form
+two mono sequences this this will play a
+
+ align:start position:0%
+two mono sequences this this will play a
+ 
+
+ align:start position:0%
+two mono sequences this this will play a
+really important role for several things
+
+ align:start position:0%
+really important role for several things
+ 
+
+ align:start position:0%
+really important role for several things
+this is how one define the soup and the
+
+ align:start position:0%
+this is how one define the soup and the
+ 
+
+ align:start position:0%
+this is how one define the soup and the
+min haven't talked about those yet. It's
+
+ align:start position:0%
+min haven't talked about those yet. It's
+ 
+
+ align:start position:0%
+min haven't talked about those yet. It's
+also going to be used
+
+ align:start position:0%
+also going to be used
+ 
+
+ align:start position:0%
+also going to be used
+to prove an important theorem really
+
+ align:start position:0%
+to prove an important theorem really
+ 
+
+ align:start position:0%
+to prove an important theorem really
+important theorem and that's what and
+
+ align:start position:0%
+important theorem and that's what and
+ 
+
+ align:start position:0%
+important theorem and that's what and
+that I will talk about that theorem next
+
+ align:start position:0%
+that I will talk about that theorem next
+ 
+
+ align:start position:0%
+that I will talk about that theorem next
+but we won't prove it before next time.
+
+ align:start position:0%
+but we won't prove it before next time.
+ 
+
+ align:start position:0%
+but we won't prove it before next time.
+So what is what is that stuff going to
+
+ align:start position:0%
+So what is what is that stuff going to
+ 
+
+ align:start position:0%
+So what is what is that stuff going to
+be used
+
+ align:start position:0%
+be used
+ 
+
+ align:start position:0%
+be used
+and and and how does the monotone in
+
+ align:start position:0%
+and and and how does the monotone in
+ 
+
+ align:start position:0%
+and and and how does the monotone in
+what is another application and in fact
+
+ align:start position:0%
+what is another application and in fact
+ 
+
+ align:start position:0%
+what is another application and in fact
+there'll be several other applications
+
+ align:start position:0%
+there'll be several other applications
+ 
+
+ align:start position:0%
+there'll be several other applications
+of the monotone convergence theorem
+
+ align:start position:0%
+of the monotone convergence theorem
+ 
+
+ align:start position:0%
+of the monotone convergence theorem
+but so here is um here's a really
+
+ align:start position:0%
+but so here is um here's a really
+ 
+
+ align:start position:0%
+but so here is um here's a really
+important concept
+
+ align:start position:0%
+important concept
+ 
+
+ align:start position:0%
+important concept
+and so sometimes it's hard to you know
+
+ align:start position:0%
+and so sometimes it's hard to you know
+ 
+
+ align:start position:0%
+and so sometimes it's hard to you know
+in in if it was a monotom sequence then
+
+ align:start position:0%
+in in if it was a monotom sequence then
+ 
+
+ align:start position:0%
+in in if it was a monotom sequence then
+you could kind of write down explicitly
+
+ align:start position:0%
+you could kind of write down explicitly
+ 
+
+ align:start position:0%
+you could kind of write down explicitly
+what the limits were, right? And in all
+
+ align:start position:0%
+what the limits were, right? And in all
+ 
+
+ align:start position:0%
+what the limits were, right? And in all
+of the examples we saw so far, it was
+
+ align:start position:0%
+of the examples we saw so far, it was
+ 
+
+ align:start position:0%
+of the examples we saw so far, it was
+easy to write down the limits, but in
+
+ align:start position:0%
+easy to write down the limits, but in
+ 
+
+ align:start position:0%
+easy to write down the limits, but in
+general,
+
+ align:start position:0%
+general,
+ 
+
+ align:start position:0%
+general,
+you might not be able to write down the
+
+ align:start position:0%
+you might not be able to write down the
+ 
+
+ align:start position:0%
+you might not be able to write down the
+limits, but you want to prove that the
+
+ align:start position:0%
+limits, but you want to prove that the
+ 
+
+ align:start position:0%
+limits, but you want to prove that the
+limit exists. And so, this is the
+
+ align:start position:0%
+limit exists. And so, this is the
+ 
+
+ align:start position:0%
+limit exists. And so, this is the
+following notion that is then becomes
+
+ align:start position:0%
+following notion that is then becomes
+ 
+
+ align:start position:0%
+following notion that is then becomes
+really handy, and that's a notion of a
+
+ align:start position:0%
+really handy, and that's a notion of a
+ 
+
+ align:start position:0%
+really handy, and that's a notion of a
+cushy sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what is a cushy sequence? So a cushi
+
+ align:start position:0%
+So what is a cushy sequence? So a cushi
+ 
+
+ align:start position:0%
+So what is a cushy sequence? So a cushi
+sequence. So it's a sequence a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon greater than zero there exist
+
+ align:start position:0%
+epsilon greater than zero there exist
+ 
+
+ align:start position:0%
+epsilon greater than zero there exist
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+there exist a natural number n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if n and m are bigger than this natural
+
+ align:start position:0%
+if n and m are bigger than this natural
+ 
+
+ align:start position:0%
+if n and m are bigger than this natural
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+two elements a n and and a m are less
+
+ align:start position:0%
+two elements a n and and a m are less
+ 
+
+ align:start position:0%
+two elements a n and and a m are less
+than epsilon apart.
+
+ align:start position:0%
+than epsilon apart.
+ 
+
+ align:start position:0%
+than epsilon apart.
+So like the so this is a different
+
+ align:start position:0%
+So like the so this is a different
+ 
+
+ align:start position:0%
+So like the so this is a different
+notion than convergence. Convergence
+
+ align:start position:0%
+notion than convergence. Convergence
+ 
+
+ align:start position:0%
+notion than convergence. Convergence
+say that if you that a sequence is
+
+ align:start position:0%
+say that if you that a sequence is
+ 
+
+ align:start position:0%
+say that if you that a sequence is
+convergent if everything kind of far out
+
+ align:start position:0%
+convergent if everything kind of far out
+ 
+
+ align:start position:0%
+convergent if everything kind of far out
+accumulates around the limit. Right?
+
+ align:start position:0%
+accumulates around the limit. Right?
+ 
+
+ align:start position:0%
+accumulates around the limit. Right?
+This here say that that and
+
+ align:start position:0%
+This here say that that and
+ 
+
+ align:start position:0%
+This here say that that and
+and of course it will. So this has say
+
+ align:start position:0%
+and of course it will. So this has say
+ 
+
+ align:start position:0%
+and of course it will. So this has say
+that if you that a cushie sequence
+
+ align:start position:0%
+that if you that a cushie sequence
+ 
+
+ align:start position:0%
+that if you that a cushie sequence
+that's a sequence so that if you are far
+
+ align:start position:0%
+that's a sequence so that if you are far
+ 
+
+ align:start position:0%
+that's a sequence so that if you are far
+out then syncs a bunch together
+
+ align:start position:0%
+out then syncs a bunch together
+ 
+
+ align:start position:0%
+out then syncs a bunch together
+basically right now of course we will
+
+ align:start position:0%
+basically right now of course we will
+ 
+
+ align:start position:0%
+basically right now of course we will
+prove and so we prove for the on r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will prove that the cy sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we prove
+
+ align:start position:0%
+so we prove
+ 
+
+ align:start position:0%
+so we prove
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so we prove the following
+
+ align:start position:0%
+so we prove the following
+ 
+
+ align:start position:0%
+so we prove the following
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+put for
+
+ align:start position:0%
+put for
+ 
+
+ align:start position:0%
+put for
+that that's on R but everything is on R
+
+ align:start position:0%
+that that's on R but everything is on R
+ 
+
+ align:start position:0%
+that that's on R but everything is on R
+at the moment uh that any that a
+
+ align:start position:0%
+at the moment uh that any that a
+ 
+
+ align:start position:0%
+at the moment uh that any that a
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a cushy sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only if it is
+
+ align:start position:0%
+only if it is
+ 
+
+ align:start position:0%
+only if it is
+convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I won't prove this now but but
+
+ align:start position:0%
+Okay, I won't prove this now but but
+ 
+
+ align:start position:0%
+Okay, I won't prove this now but but
+I'll prove this next time
+
+ align:start position:0%
+I'll prove this next time
+ 
+
+ align:start position:0%
+I'll prove this next time
+and and again the proof of this involve
+
+ align:start position:0%
+and and again the proof of this involve
+ 
+
+ align:start position:0%
+and and again the proof of this involve
+this stuff with we define these two
+
+ align:start position:0%
+this stuff with we define these two
+ 
+
+ align:start position:0%
+this stuff with we define these two
+sequences from a bounded sequence. So it
+
+ align:start position:0%
+sequences from a bounded sequence. So it
+ 
+
+ align:start position:0%
+sequences from a bounded sequence. So it
+it would be useful there. Um
+
+ align:start position:0%
+it would be useful there. Um
+ 
+
+ align:start position:0%
+it would be useful there. Um
+uh now let me give you some examples. Um
+
+ align:start position:0%
+uh now let me give you some examples. Um
+ 
+
+ align:start position:0%
+uh now let me give you some examples. Um
+so one uh one uh
+
+ align:start position:0%
+so one uh one uh
+ 
+
+ align:start position:0%
+so one uh one uh
+one um example and the thing is that
+
+ align:start position:0%
+one um example and the thing is that
+ 
+
+ align:start position:0%
+one um example and the thing is that
+that and we'll get to that later but as
+
+ align:start position:0%
+that and we'll get to that later but as
+ 
+
+ align:start position:0%
+that and we'll get to that later but as
+at the moment we talk everything is in R
+
+ align:start position:0%
+at the moment we talk everything is in R
+ 
+
+ align:start position:0%
+at the moment we talk everything is in R
+and then we will later generalize this
+
+ align:start position:0%
+and then we will later generalize this
+ 
+
+ align:start position:0%
+and then we will later generalize this
+right and so to generalize this a lot of
+
+ align:start position:0%
+right and so to generalize this a lot of
+ 
+
+ align:start position:0%
+right and so to generalize this a lot of
+these concepts work much more general
+
+ align:start position:0%
+these concepts work much more general
+ 
+
+ align:start position:0%
+these concepts work much more general
+and and that's extremely useful and Um
+
+ align:start position:0%
+and and that's extremely useful and Um
+ 
+
+ align:start position:0%
+and and that's extremely useful and Um
+and it can be used to
+
+ align:start position:0%
+and it can be used to
+ 
+
+ align:start position:0%
+and it can be used to
+find solutions to differential equations
+
+ align:start position:0%
+find solutions to differential equations
+ 
+
+ align:start position:0%
+find solutions to differential equations
+but uh and but then you have to abstract
+
+ align:start position:0%
+but uh and but then you have to abstract
+ 
+
+ align:start position:0%
+but uh and but then you have to abstract
+these concepts. So uh to where sequences
+
+ align:start position:0%
+these concepts. So uh to where sequences
+ 
+
+ align:start position:0%
+these concepts. So uh to where sequences
+are not anymore real numbers but they
+
+ align:start position:0%
+are not anymore real numbers but they
+ 
+
+ align:start position:0%
+are not anymore real numbers but they
+are of some other space and then you
+
+ align:start position:0%
+are of some other space and then you
+ 
+
+ align:start position:0%
+are of some other space and then you
+have to talk about convergence etc.
+
+ align:start position:0%
+have to talk about convergence etc.
+ 
+
+ align:start position:0%
+have to talk about convergence etc.
+And so you can use this to to define um
+
+ align:start position:0%
+And so you can use this to to define um
+ 
+
+ align:start position:0%
+And so you can use this to to define um
+solutions to def to show that various
+
+ align:start position:0%
+solutions to def to show that various
+ 
+
+ align:start position:0%
+solutions to def to show that various
+differential equations
+
+ align:start position:0%
+differential equations
+ 
+
+ align:start position:0%
+differential equations
+uh have solutions. Okay. And so that
+
+ align:start position:0%
+uh have solutions. Okay. And so that
+ 
+
+ align:start position:0%
+uh have solutions. Okay. And so that
+often goes over using what's called the
+
+ align:start position:0%
+often goes over using what's called the
+ 
+
+ align:start position:0%
+often goes over using what's called the
+contracting mapping the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mapping.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and the contracting mappings
+
+ align:start position:0%
+and and the contracting mappings
+ 
+
+ align:start position:0%
+and and the contracting mappings
+theorem, you know, have all kind of
+
+ align:start position:0%
+theorem, you know, have all kind of
+ 
+
+ align:start position:0%
+theorem, you know, have all kind of
+forms and uh the but they're all, you
+
+ align:start position:0%
+forms and uh the but they're all, you
+ 
+
+ align:start position:0%
+forms and uh the but they're all, you
+know, it's just a matter of what space
+
+ align:start position:0%
+know, it's just a matter of what space
+ 
+
+ align:start position:0%
+know, it's just a matter of what space
+you're looking at and and so on. Uh but
+
+ align:start position:0%
+you're looking at and and so on. Uh but
+ 
+
+ align:start position:0%
+you're looking at and and so on. Uh but
+so we're looking at R here in this case.
+
+ align:start position:0%
+so we're looking at R here in this case.
+ 
+
+ align:start position:0%
+so we're looking at R here in this case.
+And so the contracting mapping theorem,
+
+ align:start position:0%
+And so the contracting mapping theorem,
+ 
+
+ align:start position:0%
+And so the contracting mapping theorem,
+that's a map is just a it's just a map
+
+ align:start position:0%
+that's a map is just a it's just a map
+ 
+
+ align:start position:0%
+that's a map is just a it's just a map
+here now from R to R.
+
+ align:start position:0%
+here now from R to R.
+ 
+
+ align:start position:0%
+here now from R to R.
+And that the map is contracting means
+
+ align:start position:0%
+And that the map is contracting means
+ 
+
+ align:start position:0%
+And that the map is contracting means
+that if you take two elements
+
+ align:start position:0%
+that if you take two elements
+ 
+
+ align:start position:0%
+that if you take two elements
+uh in
+
+ align:start position:0%
+uh in
+ 
+
+ align:start position:0%
+uh in
+uh so it means that sorry T is a
+
+ align:start position:0%
+uh so it means that sorry T is a
+ 
+
+ align:start position:0%
+uh so it means that sorry T is a
+contracting map
+
+ align:start position:0%
+contracting map
+ 
+
+ align:start position:0%
+contracting map
+is a contracting map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+if they exist.
+
+ align:start position:0%
+if they exist.
+ 
+
+ align:start position:0%
+if they exist.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is really important. C is is
+
+ align:start position:0%
+And this is really important. C is is
+ 
+
+ align:start position:0%
+And this is really important. C is is
+positive. I mean that's not important.
+
+ align:start position:0%
+positive. I mean that's not important.
+ 
+
+ align:start position:0%
+positive. I mean that's not important.
+It sort of had to be positive. So that's
+
+ align:start position:0%
+It sort of had to be positive. So that's
+ 
+
+ align:start position:0%
+It sort of had to be positive. So that's
+but the the the important point is that
+
+ align:start position:0%
+but the the the important point is that
+ 
+
+ align:start position:0%
+but the the the important point is that
+C has to be strictly less than one. That
+
+ align:start position:0%
+C has to be strictly less than one. That
+ 
+
+ align:start position:0%
+C has to be strictly less than one. That
+that's a crucial point.
+
+ align:start position:0%
+that's a crucial point.
+ 
+
+ align:start position:0%
+that's a crucial point.
+Um and then it then it has a property
+
+ align:start position:0%
+Um and then it then it has a property
+ 
+
+ align:start position:0%
+Um and then it then it has a property
+that when you apply when you take X and
+
+ align:start position:0%
+that when you apply when you take X and
+ 
+
+ align:start position:0%
+that when you apply when you take X and
+Y in this in R and you're looking at the
+
+ align:start position:0%
+Y in this in R and you're looking at the
+ 
+
+ align:start position:0%
+Y in this in R and you're looking at the
+how close X and Y are together. So the
+
+ align:start position:0%
+how close X and Y are together. So the
+ 
+
+ align:start position:0%
+how close X and Y are together. So the
+how close that the image
+
+ align:start position:0%
+how close that the image
+ 
+
+ align:start position:0%
+how close that the image
+uh under t of x and y how close they are
+
+ align:start position:0%
+uh under t of x and y how close they are
+ 
+
+ align:start position:0%
+uh under t of x and y how close they are
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+then those have to be some factor and
+
+ align:start position:0%
+then those have to be some factor and
+ 
+
+ align:start position:0%
+then those have to be some factor and
+this is the factor the c is the factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that has so they have to come
+
+ align:start position:0%
+and that has so they have to come
+ 
+
+ align:start position:0%
+and that has so they have to come
+closer. This is why c have to be
+
+ align:start position:0%
+closer. This is why c have to be
+ 
+
+ align:start position:0%
+closer. This is why c have to be
+strictly less than one because they have
+
+ align:start position:0%
+strictly less than one because they have
+ 
+
+ align:start position:0%
+strictly less than one because they have
+to come closer. If they come closer by a
+
+ align:start position:0%
+to come closer. If they come closer by a
+ 
+
+ align:start position:0%
+to come closer. If they come closer by a
+factor than the original one was then
+
+ align:start position:0%
+factor than the original one was then
+ 
+
+ align:start position:0%
+factor than the original one was then
+then so the contracting mapping theorem
+
+ align:start position:0%
+then so the contracting mapping theorem
+ 
+
+ align:start position:0%
+then so the contracting mapping theorem
+say so this is a contracting map sorry
+
+ align:start position:0%
+say so this is a contracting map sorry
+ 
+
+ align:start position:0%
+say so this is a contracting map sorry
+so a contracting map is a map from R to
+
+ align:start position:0%
+so a contracting map is a map from R to
+ 
+
+ align:start position:0%
+so a contracting map is a map from R to
+R so that there exists some constant
+
+ align:start position:0%
+R so that there exists some constant
+ 
+
+ align:start position:0%
+R so that there exists some constant
+strictly less than one so that for all X
+
+ align:start position:0%
+strictly less than one so that for all X
+ 
+
+ align:start position:0%
+strictly less than one so that for all X
+and Y you have that the difference
+
+ align:start position:0%
+and Y you have that the difference
+ 
+
+ align:start position:0%
+and Y you have that the difference
+between the images is this factor that
+
+ align:start position:0%
+between the images is this factor that
+ 
+
+ align:start position:0%
+between the images is this factor that
+is strictly less than on with what they
+
+ align:start position:0%
+is strictly less than on with what they
+ 
+
+ align:start position:0%
+is strictly less than on with what they
+were originally
+
+ align:start position:0%
+were originally
+ 
+
+ align:start position:0%
+were originally
+and so now you get the contracting
+
+ align:start position:0%
+and so now you get the contracting
+ 
+
+ align:start position:0%
+and so now you get the contracting
+mapping theorem and we'll talk about the
+
+ align:start position:0%
+mapping theorem and we'll talk about the
+ 
+
+ align:start position:0%
+mapping theorem and we'll talk about the
+proof next time and and again this you
+
+ align:start position:0%
+proof next time and and again this you
+ 
+
+ align:start position:0%
+proof next time and and again this you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+you know once you have know the more
+
+ align:start position:0%
+you know once you have know the more
+ 
+
+ align:start position:0%
+you know once you have know the more
+abstract concepts then it's quite easy I
+
+ align:start position:0%
+abstract concepts then it's quite easy I
+ 
+
+ align:start position:0%
+abstract concepts then it's quite easy I
+mean the proof is going to be the same
+
+ align:start position:0%
+mean the proof is going to be the same
+ 
+
+ align:start position:0%
+mean the proof is going to be the same
+etc etc and will give you existence of
+
+ align:start position:0%
+etc etc and will give you existence of
+ 
+
+ align:start position:0%
+etc etc and will give you existence of
+solutions to a lot of differential
+
+ align:start position:0%
+solutions to a lot of differential
+ 
+
+ align:start position:0%
+solutions to a lot of differential
+equation so this is the contracting
+
+ align:start position:0%
+equation so this is the contracting
+ 
+
+ align:start position:0%
+equation so this is the contracting
+mapping term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it say the following that if
+
+ align:start position:0%
+So it say the following that if
+ 
+
+ align:start position:0%
+So it say the following that if
+uh t from r to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a contracting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+then C
+
+ align:start position:0%
+then C
+ 
+
+ align:start position:0%
+then C
+has a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It has a fixed point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this means that t of x is equal to
+
+ align:start position:0%
+And this means that t of x is equal to
+ 
+
+ align:start position:0%
+And this means that t of x is equal to
+x. And when you apply this theorem,
+
+ align:start position:0%
+x. And when you apply this theorem,
+ 
+
+ align:start position:0%
+x. And when you apply this theorem,
+the contract. So this is the contracting
+
+ align:start position:0%
+the contract. So this is the contracting
+ 
+
+ align:start position:0%
+the contract. So this is the contracting
+mapping. And again, it's crucial that
+
+ align:start position:0%
+mapping. And again, it's crucial that
+ 
+
+ align:start position:0%
+mapping. And again, it's crucial that
+this C is less than one. That's what
+
+ align:start position:0%
+this C is less than one. That's what
+ 
+
+ align:start position:0%
+this C is less than one. That's what
+makes everything go. If it's if it was
+
+ align:start position:0%
+makes everything go. If it's if it was
+ 
+
+ align:start position:0%
+makes everything go. If it's if it was
+equal to one, you wouldn't get anything.
+
+ align:start position:0%
+equal to one, you wouldn't get anything.
+ 
+
+ align:start position:0%
+equal to one, you wouldn't get anything.
+Okay? It has to be strictly less than
+
+ align:start position:0%
+Okay? It has to be strictly less than
+ 
+
+ align:start position:0%
+Okay? It has to be strictly less than
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+And this thing here, if you set it up
+
+ align:start position:0%
+And this thing here, if you set it up
+ 
+
+ align:start position:0%
+And this thing here, if you set it up
+more generally, you know, if the spaces
+
+ align:start position:0%
+more generally, you know, if the spaces
+ 
+
+ align:start position:0%
+more generally, you know, if the spaces
+are more general than just the real
+
+ align:start position:0%
+are more general than just the real
+ 
+
+ align:start position:0%
+are more general than just the real
+numbers, then then this here will be
+
+ align:start position:0%
+numbers, then then this here will be
+ 
+
+ align:start position:0%
+numbers, then then this here will be
+that you have a solution. It it could be
+
+ align:start position:0%
+that you have a solution. It it could be
+ 
+
+ align:start position:0%
+that you have a solution. It it could be
+it can be applied to many other things,
+
+ align:start position:0%
+it can be applied to many other things,
+ 
+
+ align:start position:0%
+it can be applied to many other things,
+but it could be that you have a solution
+
+ align:start position:0%
+but it could be that you have a solution
+ 
+
+ align:start position:0%
+but it could be that you have a solution
+to a differential equation. This
+
+ align:start position:0%
+to a differential equation. This
+ 
+
+ align:start position:0%
+to a differential equation. This
+statement here, you know, is like a
+
+ align:start position:0%
+statement here, you know, is like a
+ 
+
+ align:start position:0%
+statement here, you know, is like a
+standard application to get solutions to
+
+ align:start position:0%
+standard application to get solutions to
+ 
+
+ align:start position:0%
+standard application to get solutions to
+differential equations and you know, you
+
+ align:start position:0%
+differential equations and you know, you
+ 
+
+ align:start position:0%
+differential equations and you know, you
+can do use for all kind of stuff. Okay.
+
+ align:start position:0%
+can do use for all kind of stuff. Okay.
+ 
+
+ align:start position:0%
+can do use for all kind of stuff. Okay.
+And so uh so we'll talk about that next
+
+ align:start position:0%
+And so uh so we'll talk about that next
+ 
+
+ align:start position:0%
+And so uh so we'll talk about that next
+time. Uh and not maybe not the the the I
+
+ align:start position:0%
+time. Uh and not maybe not the the the I
+ 
+
+ align:start position:0%
+time. Uh and not maybe not the the the I
+talk about the contracting mapping the
+
+ align:start position:0%
+talk about the contracting mapping the
+ 
+
+ align:start position:0%
+talk about the contracting mapping the
+won't talk quite yet about the
+
+ align:start position:0%
+won't talk quite yet about the
+ 
+
+ align:start position:0%
+won't talk quite yet about the
+applications.
+
+ align:start position:0%
+applications.
+ 
+
+ align:start position:0%
+applications.
+Any questions?
+
+ align:start position:0%
+Any questions?
+ 
+
+ align:start position:0%
+Any questions?
+Okay. Great.
\ No newline at end of file
diff --git a/Fce9xf_kjyc.txt b/Fce9xf_kjyc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ac51bc17c93437c00d731e537e0bb7e00f9d90f9
--- /dev/null
+++ b/Fce9xf_kjyc.txt
@@ -0,0 +1,17979 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the first part of our new kind of
+
+ align:start position:0%
+on the first part of our new kind of
+ 
+
+ align:start position:0%
+on the first part of our new kind of
+material new set of material on quantum
+
+ align:start position:0%
+material new set of material on quantum
+ 
+
+ align:start position:0%
+material new set of material on quantum
+theory so we talked a bit about uh the
+
+ align:start position:0%
+theory so we talked a bit about uh the
+ 
+
+ align:start position:0%
+theory so we talked a bit about uh the
+road toward relativity uh in in this
+
+ align:start position:0%
+road toward relativity uh in in this
+ 
+
+ align:start position:0%
+road toward relativity uh in in this
+first few
+
+ align:start position:0%
+first few
+ 
+
+ align:start position:0%
+first few
+uh class sessions we're going to Pivot
+
+ align:start position:0%
+uh class sessions we're going to Pivot
+ 
+
+ align:start position:0%
+uh class sessions we're going to Pivot
+now and talk about this other sort of
+
+ align:start position:0%
+now and talk about this other sort of
+ 
+
+ align:start position:0%
+now and talk about this other sort of
+amazing uh edifice of what becomes known
+
+ align:start position:0%
+amazing uh edifice of what becomes known
+ 
+
+ align:start position:0%
+amazing uh edifice of what becomes known
+as modern physics quantum theory as as
+
+ align:start position:0%
+as modern physics quantum theory as as
+ 
+
+ align:start position:0%
+as modern physics quantum theory as as
+that was getting pieced together over
+
+ align:start position:0%
+that was getting pieced together over
+ 
+
+ align:start position:0%
+that was getting pieced together over
+the first kind of quarter Century or so
+
+ align:start position:0%
+the first kind of quarter Century or so
+ 
+
+ align:start position:0%
+the first kind of quarter Century or so
+of the 20th century uh so for this
+
+ align:start position:0%
+of the 20th century uh so for this
+ 
+
+ align:start position:0%
+of the 20th century uh so for this
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+which has been this class session and
+
+ align:start position:0%
+which has been this class session and
+ 
+
+ align:start position:0%
+which has been this class session and
+the next one talking about what came to
+
+ align:start position:0%
+the next one talking about what came to
+ 
+
+ align:start position:0%
+the next one talking about what came to
+be known as old quantum theory of course
+
+ align:start position:0%
+be known as old quantum theory of course
+ 
+
+ align:start position:0%
+be known as old quantum theory of course
+it only became known as old quantum
+
+ align:start position:0%
+it only became known as old quantum
+ 
+
+ align:start position:0%
+it only became known as old quantum
+theory once there was a new quantum
+
+ align:start position:0%
+theory once there was a new quantum
+ 
+
+ align:start position:0%
+theory once there was a new quantum
+theory that seemed to replace it and so
+
+ align:start position:0%
+theory that seemed to replace it and so
+ 
+
+ align:start position:0%
+theory that seemed to replace it and so
+physicists themselves introduced the
+
+ align:start position:0%
+physicists themselves introduced the
+ 
+
+ align:start position:0%
+physicists themselves introduced the
+term old quantum theory kind of within
+
+ align:start position:0%
+term old quantum theory kind of within
+ 
+
+ align:start position:0%
+term old quantum theory kind of within
+the time zone that we'll be talking
+
+ align:start position:0%
+the time zone that we'll be talking
+ 
+
+ align:start position:0%
+the time zone that we'll be talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+so in their own Reckoning
+
+ align:start position:0%
+so in their own Reckoning
+ 
+
+ align:start position:0%
+so in their own Reckoning
+by the mid to late 1920s physicists
+
+ align:start position:0%
+by the mid to late 1920s physicists
+ 
+
+ align:start position:0%
+by the mid to late 1920s physicists
+began to refer by the term of old
+
+ align:start position:0%
+began to refer by the term of old
+ 
+
+ align:start position:0%
+began to refer by the term of old
+quantum theory to this collection of
+
+ align:start position:0%
+quantum theory to this collection of
+ 
+
+ align:start position:0%
+quantum theory to this collection of
+work that it unfolded really between
+
+ align:start position:0%
+work that it unfolded really between
+ 
+
+ align:start position:0%
+work that it unfolded really between
+around 1900 and 1924 that looked like
+
+ align:start position:0%
+around 1900 and 1924 that looked like
+ 
+
+ align:start position:0%
+around 1900 and 1924 that looked like
+the old period once the new stuff had
+
+ align:start position:0%
+the old period once the new stuff had
+ 
+
+ align:start position:0%
+the old period once the new stuff had
+begun to coalesce in 1925 and 26 and so
+
+ align:start position:0%
+begun to coalesce in 1925 and 26 and so
+ 
+
+ align:start position:0%
+begun to coalesce in 1925 and 26 and so
+on now here I have an asterisk hope you
+
+ align:start position:0%
+on now here I have an asterisk hope you
+ 
+
+ align:start position:0%
+on now here I have an asterisk hope you
+can see that these dates are approximate
+
+ align:start position:0%
+can see that these dates are approximate
+ 
+
+ align:start position:0%
+can see that these dates are approximate
+one of the things we'll be really
+
+ align:start position:0%
+one of the things we'll be really
+ 
+
+ align:start position:0%
+one of the things we'll be really
+sitting with throughout these first few
+
+ align:start position:0%
+sitting with throughout these first few
+ 
+
+ align:start position:0%
+sitting with throughout these first few
+uh discussions about about quantum
+
+ align:start position:0%
+uh discussions about about quantum
+ 
+
+ align:start position:0%
+uh discussions about about quantum
+theory is just how much sort of in play
+
+ align:start position:0%
+theory is just how much sort of in play
+ 
+
+ align:start position:0%
+theory is just how much sort of in play
+these developments remained well after
+
+ align:start position:0%
+these developments remained well after
+ 
+
+ align:start position:0%
+these developments remained well after
+the kind of um nominal date in which
+
+ align:start position:0%
+the kind of um nominal date in which
+ 
+
+ align:start position:0%
+the kind of um nominal date in which
+they were put forward much like we saw
+
+ align:start position:0%
+they were put forward much like we saw
+ 
+
+ align:start position:0%
+they were put forward much like we saw
+with relativity
+
+ align:start position:0%
+with relativity
+ 
+
+ align:start position:0%
+with relativity
+it wasn't that Einstein published his
+
+ align:start position:0%
+it wasn't that Einstein published his
+ 
+
+ align:start position:0%
+it wasn't that Einstein published his
+paper on the electrodynamics of moving
+
+ align:start position:0%
+paper on the electrodynamics of moving
+ 
+
+ align:start position:0%
+paper on the electrodynamics of moving
+bodies in 1905 and then sort of the next
+
+ align:start position:0%
+bodies in 1905 and then sort of the next
+ 
+
+ align:start position:0%
+bodies in 1905 and then sort of the next
+day everyone woke up and was a devoted
+
+ align:start position:0%
+day everyone woke up and was a devoted
+ 
+
+ align:start position:0%
+day everyone woke up and was a devoted
+einsteinian or um or a convinced
+
+ align:start position:0%
+einsteinian or um or a convinced
+ 
+
+ align:start position:0%
+einsteinian or um or a convinced
+relativist likewise here with these
+
+ align:start position:0%
+relativist likewise here with these
+ 
+
+ align:start position:0%
+relativist likewise here with these
+developments on on uh the early steps
+
+ align:start position:0%
+developments on on uh the early steps
+ 
+
+ align:start position:0%
+developments on on uh the early steps
+toward quantum mechanics that these
+
+ align:start position:0%
+toward quantum mechanics that these
+ 
+
+ align:start position:0%
+toward quantum mechanics that these
+these ideas themselves were unfolding
+
+ align:start position:0%
+these ideas themselves were unfolding
+ 
+
+ align:start position:0%
+these ideas themselves were unfolding
+over time they were subject to sometimes
+
+ align:start position:0%
+over time they were subject to sometimes
+ 
+
+ align:start position:0%
+over time they were subject to sometimes
+quite wide-ranging debate and and
+
+ align:start position:0%
+quite wide-ranging debate and and
+ 
+
+ align:start position:0%
+quite wide-ranging debate and and
+varying interpretation so these dates
+
+ align:start position:0%
+varying interpretation so these dates
+ 
+
+ align:start position:0%
+varying interpretation so these dates
+are really meant to be approximate to
+
+ align:start position:0%
+are really meant to be approximate to
+ 
+
+ align:start position:0%
+are really meant to be approximate to
+help us understand the kind of General
+
+ align:start position:0%
+help us understand the kind of General
+ 
+
+ align:start position:0%
+help us understand the kind of General
+flow of this body of work between
+
+ align:start position:0%
+flow of this body of work between
+ 
+
+ align:start position:0%
+flow of this body of work between
+roughly 1900
+
+ align:start position:0%
+roughly 1900
+ 
+
+ align:start position:0%
+roughly 1900
+in 1924. so I I find it helpful to
+
+ align:start position:0%
+in 1924. so I I find it helpful to
+ 
+
+ align:start position:0%
+in 1924. so I I find it helpful to
+divide up that first period of roughly
+
+ align:start position:0%
+divide up that first period of roughly
+ 
+
+ align:start position:0%
+divide up that first period of roughly
+25 years or so into a set of
+
+ align:start position:0%
+25 years or so into a set of
+ 
+
+ align:start position:0%
+25 years or so into a set of
+developments in which physicists began
+
+ align:start position:0%
+developments in which physicists began
+ 
+
+ align:start position:0%
+developments in which physicists began
+rethinking the nature of light that's
+
+ align:start position:0%
+rethinking the nature of light that's
+ 
+
+ align:start position:0%
+rethinking the nature of light that's
+what we'll talk about today today's
+
+ align:start position:0%
+what we'll talk about today today's
+ 
+
+ align:start position:0%
+what we'll talk about today today's
+rethinking light and they're really kind
+
+ align:start position:0%
+rethinking light and they're really kind
+ 
+
+ align:start position:0%
+rethinking light and they're really kind
+of interwoven with those developments as
+
+ align:start position:0%
+of interwoven with those developments as
+ 
+
+ align:start position:0%
+of interwoven with those developments as
+we'll see in our next class session
+
+ align:start position:0%
+we'll see in our next class session
+ 
+
+ align:start position:0%
+we'll see in our next class session
+we're a series of uh kind of equally
+
+ align:start position:0%
+we're a series of uh kind of equally
+ 
+
+ align:start position:0%
+we're a series of uh kind of equally
+surprising developments uh in which
+
+ align:start position:0%
+surprising developments uh in which
+ 
+
+ align:start position:0%
+surprising developments uh in which
+physicists were rethinking the nature of
+
+ align:start position:0%
+physicists were rethinking the nature of
+ 
+
+ align:start position:0%
+physicists were rethinking the nature of
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+they didn't always make that division so
+
+ align:start position:0%
+they didn't always make that division so
+ 
+
+ align:start position:0%
+they didn't always make that division so
+clear at the time but again with a bit
+
+ align:start position:0%
+clear at the time but again with a bit
+ 
+
+ align:start position:0%
+clear at the time but again with a bit
+of hindsight once the newer work began
+
+ align:start position:0%
+of hindsight once the newer work began
+ 
+
+ align:start position:0%
+of hindsight once the newer work began
+to coalesce what we now call quantum
+
+ align:start position:0%
+to coalesce what we now call quantum
+ 
+
+ align:start position:0%
+to coalesce what we now call quantum
+mechanics this kind of division of the
+
+ align:start position:0%
+mechanics this kind of division of the
+ 
+
+ align:start position:0%
+mechanics this kind of division of the
+strands within old quantum theory made a
+
+ align:start position:0%
+strands within old quantum theory made a
+ 
+
+ align:start position:0%
+strands within old quantum theory made a
+bit more sense
+
+ align:start position:0%
+bit more sense
+ 
+
+ align:start position:0%
+bit more sense
+and again just a reminder for today it's
+
+ align:start position:0%
+and again just a reminder for today it's
+ 
+
+ align:start position:0%
+and again just a reminder for today it's
+thoroughly optional as always but for
+
+ align:start position:0%
+thoroughly optional as always but for
+ 
+
+ align:start position:0%
+thoroughly optional as always but for
+those who might be interested in having
+
+ align:start position:0%
+those who might be interested in having
+ 
+
+ align:start position:0%
+those who might be interested in having
+more time
+
+ align:start position:0%
+more time
+ 
+
+ align:start position:0%
+more time
+I did post some additional lecture notes
+
+ align:start position:0%
+I did post some additional lecture notes
+ 
+
+ align:start position:0%
+I did post some additional lecture notes
+on the canvas site they're going to go
+
+ align:start position:0%
+on the canvas site they're going to go
+ 
+
+ align:start position:0%
+on the canvas site they're going to go
+go into a little more detail about Parts
+
+ align:start position:0%
+go into a little more detail about Parts
+ 
+
+ align:start position:0%
+go into a little more detail about Parts
+one and three for today's material in
+
+ align:start position:0%
+one and three for today's material in
+ 
+
+ align:start position:0%
+one and three for today's material in
+particular both black body radiation and
+
+ align:start position:0%
+particular both black body radiation and
+ 
+
+ align:start position:0%
+particular both black body radiation and
+competence Gathering so if some ideas go
+
+ align:start position:0%
+competence Gathering so if some ideas go
+ 
+
+ align:start position:0%
+competence Gathering so if some ideas go
+by really quickly or you have no idea
+
+ align:start position:0%
+by really quickly or you have no idea
+ 
+
+ align:start position:0%
+by really quickly or you have no idea
+where that particular equation came from
+
+ align:start position:0%
+where that particular equation came from
+ 
+
+ align:start position:0%
+where that particular equation came from
+uh there is a bit more that you can
+
+ align:start position:0%
+uh there is a bit more that you can
+ 
+
+ align:start position:0%
+uh there is a bit more that you can
+delve into on the course site okay
+
+ align:start position:0%
+delve into on the course site okay
+ 
+
+ align:start position:0%
+delve into on the course site okay
+so before we even talk about who was
+
+ align:start position:0%
+so before we even talk about who was
+ 
+
+ align:start position:0%
+so before we even talk about who was
+rethinking light where and when it's
+
+ align:start position:0%
+rethinking light where and when it's
+ 
+
+ align:start position:0%
+rethinking light where and when it's
+really helpful it's very important to to
+
+ align:start position:0%
+really helpful it's very important to to
+ 
+
+ align:start position:0%
+really helpful it's very important to to
+step back and get remind yourself again
+
+ align:start position:0%
+step back and get remind yourself again
+ 
+
+ align:start position:0%
+step back and get remind yourself again
+of where this is happening uh and and
+
+ align:start position:0%
+of where this is happening uh and and
+ 
+
+ align:start position:0%
+of where this is happening uh and and
+why was happening at that time so a lot
+
+ align:start position:0%
+why was happening at that time so a lot
+ 
+
+ align:start position:0%
+why was happening at that time so a lot
+of the work that we're focusing on
+
+ align:start position:0%
+of the work that we're focusing on
+ 
+
+ align:start position:0%
+of the work that we're focusing on
+around on on today's uh class in
+
+ align:start position:0%
+around on on today's uh class in
+ 
+
+ align:start position:0%
+around on on today's uh class in
+particular not all of it but a lot of it
+
+ align:start position:0%
+particular not all of it but a lot of it
+ 
+
+ align:start position:0%
+particular not all of it but a lot of it
+what's happening within this newly
+
+ align:start position:0%
+what's happening within this newly
+ 
+
+ align:start position:0%
+what's happening within this newly
+unified country called Germany we saw
+
+ align:start position:0%
+unified country called Germany we saw
+ 
+
+ align:start position:0%
+unified country called Germany we saw
+this a few times there was no country of
+
+ align:start position:0%
+this a few times there was no country of
+ 
+
+ align:start position:0%
+this a few times there was no country of
+Germany until 1871 they were
+
+ align:start position:0%
+Germany until 1871 they were
+ 
+
+ align:start position:0%
+Germany until 1871 they were
+german-speaking territories but a single
+
+ align:start position:0%
+german-speaking territories but a single
+ 
+
+ align:start position:0%
+german-speaking territories but a single
+unified National country called Germany
+
+ align:start position:0%
+unified National country called Germany
+ 
+
+ align:start position:0%
+unified National country called Germany
+emerged really in out as one outcome of
+
+ align:start position:0%
+emerged really in out as one outcome of
+ 
+
+ align:start position:0%
+emerged really in out as one outcome of
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+
+ align:start position:0%
+the franco-prussian war the but the
+ 
+
+ align:start position:0%
+the franco-prussian war the but the
+Prussian State war against the country
+
+ align:start position:0%
+Prussian State war against the country
+ 
+
+ align:start position:0%
+Prussian State war against the country
+of France
+
+ align:start position:0%
+of France
+ 
+
+ align:start position:0%
+of France
+not too long before Einstein himself was
+
+ align:start position:0%
+not too long before Einstein himself was
+ 
+
+ align:start position:0%
+not too long before Einstein himself was
+born one of the things that the new
+
+ align:start position:0%
+born one of the things that the new
+ 
+
+ align:start position:0%
+born one of the things that the new
+country of Germany began to do was to
+
+ align:start position:0%
+country of Germany began to do was to
+ 
+
+ align:start position:0%
+country of Germany began to do was to
+invest very aggressively in a program of
+
+ align:start position:0%
+invest very aggressively in a program of
+ 
+
+ align:start position:0%
+invest very aggressively in a program of
+rapid industrialization once it became a
+
+ align:start position:0%
+rapid industrialization once it became a
+ 
+
+ align:start position:0%
+rapid industrialization once it became a
+single unified country the new leaders
+
+ align:start position:0%
+single unified country the new leaders
+ 
+
+ align:start position:0%
+single unified country the new leaders
+of the country looked around and and
+
+ align:start position:0%
+of the country looked around and and
+ 
+
+ align:start position:0%
+of the country looked around and and
+were concerned that they were falling
+
+ align:start position:0%
+were concerned that they were falling
+ 
+
+ align:start position:0%
+were concerned that they were falling
+far behind other European Neighbors in
+
+ align:start position:0%
+far behind other European Neighbors in
+ 
+
+ align:start position:0%
+far behind other European Neighbors in
+basic industrial capacity especially
+
+ align:start position:0%
+basic industrial capacity especially
+ 
+
+ align:start position:0%
+basic industrial capacity especially
+Britain to well to some degree they
+
+ align:start position:0%
+Britain to well to some degree they
+ 
+
+ align:start position:0%
+Britain to well to some degree they
+worried about France so they had
+
+ align:start position:0%
+worried about France so they had
+ 
+
+ align:start position:0%
+worried about France so they had
+prevailed in the in the recent War
+
+ align:start position:0%
+prevailed in the in the recent War
+ 
+
+ align:start position:0%
+prevailed in the in the recent War
+so the country begins investing quite a
+
+ align:start position:0%
+so the country begins investing quite a
+ 
+
+ align:start position:0%
+so the country begins investing quite a
+lot in in industrialization that often
+
+ align:start position:0%
+lot in in industrialization that often
+ 
+
+ align:start position:0%
+lot in in industrialization that often
+meant investing in science and
+
+ align:start position:0%
+meant investing in science and
+ 
+
+ align:start position:0%
+meant investing in science and
+technology what we would Now call
+
+ align:start position:0%
+technology what we would Now call
+ 
+
+ align:start position:0%
+technology what we would Now call
+science and engineering
+
+ align:start position:0%
+science and engineering
+ 
+
+ align:start position:0%
+science and engineering
+so a few years into this new country's
+
+ align:start position:0%
+so a few years into this new country's
+ 
+
+ align:start position:0%
+so a few years into this new country's
+life its existence the leaders put
+
+ align:start position:0%
+life its existence the leaders put
+ 
+
+ align:start position:0%
+life its existence the leaders put
+together a new kind of Institute not
+
+ align:start position:0%
+together a new kind of Institute not
+ 
+
+ align:start position:0%
+together a new kind of Institute not
+just new to Germany kind of knew even
+
+ align:start position:0%
+just new to Germany kind of knew even
+ 
+
+ align:start position:0%
+just new to Germany kind of knew even
+across Europe especially designed
+
+ align:start position:0%
+across Europe especially designed
+ 
+
+ align:start position:0%
+across Europe especially designed
+government-funded Institute called the
+
+ align:start position:0%
+government-funded Institute called the
+ 
+
+ align:start position:0%
+government-funded Institute called the
+physic College technician hi seanstalk
+
+ align:start position:0%
+physic College technician hi seanstalk
+ 
+
+ align:start position:0%
+physic College technician hi seanstalk
+which is fun to say we can just call it
+
+ align:start position:0%
+which is fun to say we can just call it
+ 
+
+ align:start position:0%
+which is fun to say we can just call it
+by its initials of PTR that really stood
+
+ align:start position:0%
+by its initials of PTR that really stood
+ 
+
+ align:start position:0%
+by its initials of PTR that really stood
+for the Imperial or the kind of German
+
+ align:start position:0%
+for the Imperial or the kind of German
+ 
+
+ align:start position:0%
+for the Imperial or the kind of German
+National physical Technical Institute
+
+ align:start position:0%
+National physical Technical Institute
+ 
+
+ align:start position:0%
+National physical Technical Institute
+the PTR
+
+ align:start position:0%
+the PTR
+ 
+
+ align:start position:0%
+the PTR
+the idea was that this new kind of space
+
+ align:start position:0%
+the idea was that this new kind of space
+ 
+
+ align:start position:0%
+the idea was that this new kind of space
+this new institution should foster
+
+ align:start position:0%
+this new institution should foster
+ 
+
+ align:start position:0%
+this new institution should foster
+several kinds of research and try to get
+
+ align:start position:0%
+several kinds of research and try to get
+ 
+
+ align:start position:0%
+several kinds of research and try to get
+them kind of talking together to really
+
+ align:start position:0%
+them kind of talking together to really
+ 
+
+ align:start position:0%
+them kind of talking together to really
+help jump start what the country's
+
+ align:start position:0%
+help jump start what the country's
+ 
+
+ align:start position:0%
+help jump start what the country's
+leaders hope to be this uh this uh very
+
+ align:start position:0%
+leaders hope to be this uh this uh very
+ 
+
+ align:start position:0%
+leaders hope to be this uh this uh very
+rapid uh pace of industrialization so
+
+ align:start position:0%
+rapid uh pace of industrialization so
+ 
+
+ align:start position:0%
+rapid uh pace of industrialization so
+the PTR was designed on purpose to
+
+ align:start position:0%
+the PTR was designed on purpose to
+ 
+
+ align:start position:0%
+the PTR was designed on purpose to
+foster a search into basic science into
+
+ align:start position:0%
+foster a search into basic science into
+ 
+
+ align:start position:0%
+foster a search into basic science into
+a kind of curiosity driven research in
+
+ align:start position:0%
+a kind of curiosity driven research in
+ 
+
+ align:start position:0%
+a kind of curiosity driven research in
+physics and chemistry in related areas
+
+ align:start position:0%
+physics and chemistry in related areas
+ 
+
+ align:start position:0%
+physics and chemistry in related areas
+but also uh also support work in applied
+
+ align:start position:0%
+but also uh also support work in applied
+ 
+
+ align:start position:0%
+but also uh also support work in applied
+research and Industrial Development so
+
+ align:start position:0%
+research and Industrial Development so
+ 
+
+ align:start position:0%
+research and Industrial Development so
+it's pretty similar to what would soon
+
+ align:start position:0%
+it's pretty similar to what would soon
+ 
+
+ align:start position:0%
+it's pretty similar to what would soon
+be developed in the United States it was
+
+ align:start position:0%
+be developed in the United States it was
+ 
+
+ align:start position:0%
+be developed in the United States it was
+originally called the U.S Bureau of
+
+ align:start position:0%
+originally called the U.S Bureau of
+ 
+
+ align:start position:0%
+originally called the U.S Bureau of
+Standards now you might know it by the
+
+ align:start position:0%
+Standards now you might know it by the
+ 
+
+ align:start position:0%
+Standards now you might know it by the
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+the National Institute of Standards and
+
+ align:start position:0%
+the National Institute of Standards and
+ 
+
+ align:start position:0%
+the National Institute of Standards and
+technology or nist which has several
+
+ align:start position:0%
+technology or nist which has several
+ 
+
+ align:start position:0%
+technology or nist which has several
+kind of National Laboratory sites
+
+ align:start position:0%
+kind of National Laboratory sites
+ 
+
+ align:start position:0%
+kind of National Laboratory sites
+throughout the US the PTR was in that
+
+ align:start position:0%
+throughout the US the PTR was in that
+ 
+
+ align:start position:0%
+throughout the US the PTR was in that
+mold it was really forming that mold
+
+ align:start position:0%
+mold it was really forming that mold
+ 
+
+ align:start position:0%
+mold it was really forming that mold
+government sponsored to try to to
+
+ align:start position:0%
+government sponsored to try to to
+ 
+
+ align:start position:0%
+government sponsored to try to to
+encourage certain kinds of research both
+
+ align:start position:0%
+encourage certain kinds of research both
+ 
+
+ align:start position:0%
+encourage certain kinds of research both
+in basic sciences and uh industrial
+
+ align:start position:0%
+in basic sciences and uh industrial
+ 
+
+ align:start position:0%
+in basic sciences and uh industrial
+applications
+
+ align:start position:0%
+applications
+ 
+
+ align:start position:0%
+applications
+one of the earliest pressing priorities
+
+ align:start position:0%
+one of the earliest pressing priorities
+ 
+
+ align:start position:0%
+one of the earliest pressing priorities
+for this new Institute
+
+ align:start position:0%
+for this new Institute
+ 
+
+ align:start position:0%
+for this new Institute
+was to evaluate competing proposals for
+
+ align:start position:0%
+was to evaluate competing proposals for
+ 
+
+ align:start position:0%
+was to evaluate competing proposals for
+things for Public Works projects like
+
+ align:start position:0%
+things for Public Works projects like
+ 
+
+ align:start position:0%
+things for Public Works projects like
+large-scale electric street lighting
+
+ align:start position:0%
+large-scale electric street lighting
+ 
+
+ align:start position:0%
+large-scale electric street lighting
+some of you may know the incandescent
+
+ align:start position:0%
+some of you may know the incandescent
+ 
+
+ align:start position:0%
+some of you may know the incandescent
+light bulb electric light bulbs were
+
+ align:start position:0%
+light bulb electric light bulbs were
+ 
+
+ align:start position:0%
+light bulb electric light bulbs were
+actually quite new people think about
+
+ align:start position:0%
+actually quite new people think about
+ 
+
+ align:start position:0%
+actually quite new people think about
+people like Thomas Edison
+
+ align:start position:0%
+people like Thomas Edison
+ 
+
+ align:start position:0%
+people like Thomas Edison
+and others in the United States similar
+
+ align:start position:0%
+and others in the United States similar
+ 
+
+ align:start position:0%
+and others in the United States similar
+work going on elsewhere and one of the
+
+ align:start position:0%
+work going on elsewhere and one of the
+ 
+
+ align:start position:0%
+work going on elsewhere and one of the
+earliest efforts was to put this new
+
+ align:start position:0%
+earliest efforts was to put this new
+ 
+
+ align:start position:0%
+earliest efforts was to put this new
+kind of Technology an incandescent light
+
+ align:start position:0%
+kind of Technology an incandescent light
+ 
+
+ align:start position:0%
+kind of Technology an incandescent light
+bulb and electric light bulb into use in
+
+ align:start position:0%
+bulb and electric light bulb into use in
+ 
+
+ align:start position:0%
+bulb and electric light bulb into use in
+kind of public spaces imagine the
+
+ align:start position:0%
+kind of public spaces imagine the
+ 
+
+ align:start position:0%
+kind of public spaces imagine the
+difference for City Life for Commerce
+
+ align:start position:0%
+difference for City Life for Commerce
+ 
+
+ align:start position:0%
+difference for City Life for Commerce
+for uh for for communities in general if
+
+ align:start position:0%
+for uh for for communities in general if
+ 
+
+ align:start position:0%
+for uh for for communities in general if
+cities were at pitch dark uh just as
+
+ align:start position:0%
+cities were at pitch dark uh just as
+ 
+
+ align:start position:0%
+cities were at pitch dark uh just as
+soon as the sun went down now of course
+
+ align:start position:0%
+soon as the sun went down now of course
+ 
+
+ align:start position:0%
+soon as the sun went down now of course
+there were many many competing ideas
+
+ align:start position:0%
+there were many many competing ideas
+ 
+
+ align:start position:0%
+there were many many competing ideas
+about how to do that how to do it
+
+ align:start position:0%
+about how to do that how to do it
+ 
+
+ align:start position:0%
+about how to do that how to do it
+efficiently how to make the right kinds
+
+ align:start position:0%
+efficiently how to make the right kinds
+ 
+
+ align:start position:0%
+efficiently how to make the right kinds
+of bulbs that could give out a lot of
+
+ align:start position:0%
+of bulbs that could give out a lot of
+ 
+
+ align:start position:0%
+of bulbs that could give out a lot of
+light with hopefully not too much power
+
+ align:start position:0%
+light with hopefully not too much power
+ 
+
+ align:start position:0%
+light with hopefully not too much power
+usage and so on and so one of the first
+
+ align:start position:0%
+usage and so on and so one of the first
+ 
+
+ align:start position:0%
+usage and so on and so one of the first
+questions of his new PTR had to wrestle
+
+ align:start position:0%
+questions of his new PTR had to wrestle
+ 
+
+ align:start position:0%
+questions of his new PTR had to wrestle
+with was how to compare these competing
+
+ align:start position:0%
+with was how to compare these competing
+ 
+
+ align:start position:0%
+with was how to compare these competing
+proposals for things like electric
+
+ align:start position:0%
+proposals for things like electric
+ 
+
+ align:start position:0%
+proposals for things like electric
+street lighting what they were asking
+
+ align:start position:0%
+street lighting what they were asking
+ 
+
+ align:start position:0%
+street lighting what they were asking
+about is how can you measure the amount
+
+ align:start position:0%
+about is how can you measure the amount
+ 
+
+ align:start position:0%
+about is how can you measure the amount
+of light that comes out from these very
+
+ align:start position:0%
+of light that comes out from these very
+ 
+
+ align:start position:0%
+of light that comes out from these very
+hot filaments in these electric bulbs
+
+ align:start position:0%
+hot filaments in these electric bulbs
+ 
+
+ align:start position:0%
+hot filaments in these electric bulbs
+now people had known for a long long
+
+ align:start position:0%
+now people had known for a long long
+ 
+
+ align:start position:0%
+now people had known for a long long
+time long before the PTR humans had
+
+ align:start position:0%
+time long before the PTR humans had
+ 
+
+ align:start position:0%
+time long before the PTR humans had
+known that when materials are heated up
+
+ align:start position:0%
+known that when materials are heated up
+ 
+
+ align:start position:0%
+known that when materials are heated up
+to a sufficiently high temperature
+
+ align:start position:0%
+to a sufficiently high temperature
+ 
+
+ align:start position:0%
+to a sufficiently high temperature
+they'll begin to Glow they'll give off
+
+ align:start position:0%
+they'll begin to Glow they'll give off
+ 
+
+ align:start position:0%
+they'll begin to Glow they'll give off
+some kind of radiation some light think
+
+ align:start position:0%
+some kind of radiation some light think
+ 
+
+ align:start position:0%
+some kind of radiation some light think
+about very casual observations like uh
+
+ align:start position:0%
+about very casual observations like uh
+ 
+
+ align:start position:0%
+about very casual observations like uh
+Embers glowing in a fireplace or
+
+ align:start position:0%
+Embers glowing in a fireplace or
+ 
+
+ align:start position:0%
+Embers glowing in a fireplace or
+charcoals on a grill or now tragically
+
+ align:start position:0%
+charcoals on a grill or now tragically
+ 
+
+ align:start position:0%
+charcoals on a grill or now tragically
+the photographs we see from these
+
+ align:start position:0%
+the photographs we see from these
+ 
+
+ align:start position:0%
+the photographs we see from these
+horrific uh you know forest fires out in
+
+ align:start position:0%
+horrific uh you know forest fires out in
+ 
+
+ align:start position:0%
+horrific uh you know forest fires out in
+California and up and down the West
+
+ align:start position:0%
+California and up and down the West
+ 
+
+ align:start position:0%
+California and up and down the West
+Coast when you heat stuff up to a high
+
+ align:start position:0%
+Coast when you heat stuff up to a high
+ 
+
+ align:start position:0%
+Coast when you heat stuff up to a high
+enough temperature it will give off
+
+ align:start position:0%
+enough temperature it will give off
+ 
+
+ align:start position:0%
+enough temperature it will give off
+light it will glow
+
+ align:start position:0%
+light it will glow
+ 
+
+ align:start position:0%
+light it will glow
+and in fact the color of the emitted
+
+ align:start position:0%
+and in fact the color of the emitted
+ 
+
+ align:start position:0%
+and in fact the color of the emitted
+light shifts with the temperature to
+
+ align:start position:0%
+light shifts with the temperature to
+ 
+
+ align:start position:0%
+light shifts with the temperature to
+which the object has been heated so the
+
+ align:start position:0%
+which the object has been heated so the
+ 
+
+ align:start position:0%
+which the object has been heated so the
+colors the main frequencies of light
+
+ align:start position:0%
+colors the main frequencies of light
+ 
+
+ align:start position:0%
+colors the main frequencies of light
+that dominate that glow will shift uh
+
+ align:start position:0%
+that dominate that glow will shift uh
+ 
+
+ align:start position:0%
+that dominate that glow will shift uh
+with temperature and that was again
+
+ align:start position:0%
+with temperature and that was again
+ 
+
+ align:start position:0%
+with temperature and that was again
+something was known kind of casually
+
+ align:start position:0%
+something was known kind of casually
+ 
+
+ align:start position:0%
+something was known kind of casually
+long before it was a PTR
+
+ align:start position:0%
+long before it was a PTR
+ 
+
+ align:start position:0%
+long before it was a PTR
+well that feeds into this very specific
+
+ align:start position:0%
+well that feeds into this very specific
+ 
+
+ align:start position:0%
+well that feeds into this very specific
+work at this new Institute the PTR
+
+ align:start position:0%
+work at this new Institute the PTR
+ 
+
+ align:start position:0%
+work at this new Institute the PTR
+because one of the group one of the
+
+ align:start position:0%
+because one of the group one of the
+ 
+
+ align:start position:0%
+because one of the group one of the
+tasks of the new group was to figure out
+
+ align:start position:0%
+tasks of the new group was to figure out
+ 
+
+ align:start position:0%
+tasks of the new group was to figure out
+calibrations for these different kinds
+
+ align:start position:0%
+calibrations for these different kinds
+ 
+
+ align:start position:0%
+calibrations for these different kinds
+of electric light
+
+ align:start position:0%
+of electric light
+ 
+
+ align:start position:0%
+of electric light
+Technologies these proposals and what
+
+ align:start position:0%
+Technologies these proposals and what
+ 
+
+ align:start position:0%
+Technologies these proposals and what
+the pgr researchers began to notice was
+
+ align:start position:0%
+the pgr researchers began to notice was
+ 
+
+ align:start position:0%
+the pgr researchers began to notice was
+it looked like there was a kind of
+
+ align:start position:0%
+it looked like there was a kind of
+ 
+
+ align:start position:0%
+it looked like there was a kind of
+universal or shared pattern in the kind
+
+ align:start position:0%
+universal or shared pattern in the kind
+ 
+
+ align:start position:0%
+universal or shared pattern in the kind
+of light in the pattern of light that
+
+ align:start position:0%
+of light in the pattern of light that
+ 
+
+ align:start position:0%
+of light in the pattern of light that
+came out from various objects when they
+
+ align:start position:0%
+came out from various objects when they
+ 
+
+ align:start position:0%
+came out from various objects when they
+were heated to high temperatures and
+
+ align:start position:0%
+were heated to high temperatures and
+ 
+
+ align:start position:0%
+were heated to high temperatures and
+they thought it was Universal because it
+
+ align:start position:0%
+they thought it was Universal because it
+ 
+
+ align:start position:0%
+they thought it was Universal because it
+looked like the pattern of Light how
+
+ align:start position:0%
+looked like the pattern of Light how
+ 
+
+ align:start position:0%
+looked like the pattern of Light how
+much light came out at which particular
+
+ align:start position:0%
+much light came out at which particular
+ 
+
+ align:start position:0%
+much light came out at which particular
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+seemed to depend only on the temperature
+
+ align:start position:0%
+seemed to depend only on the temperature
+ 
+
+ align:start position:0%
+seemed to depend only on the temperature
+to which those materials have been
+
+ align:start position:0%
+to which those materials have been
+ 
+
+ align:start position:0%
+to which those materials have been
+heated but not on the mechanic on the
+
+ align:start position:0%
+heated but not on the mechanic on the
+ 
+
+ align:start position:0%
+heated but not on the mechanic on the
+material kind of chemical makeup of the
+
+ align:start position:0%
+material kind of chemical makeup of the
+ 
+
+ align:start position:0%
+material kind of chemical makeup of the
+materials themselves different kinds of
+
+ align:start position:0%
+materials themselves different kinds of
+ 
+
+ align:start position:0%
+materials themselves different kinds of
+filaments for example even if they were
+
+ align:start position:0%
+filaments for example even if they were
+ 
+
+ align:start position:0%
+filaments for example even if they were
+made up from an entirely different
+
+ align:start position:0%
+made up from an entirely different
+ 
+
+ align:start position:0%
+made up from an entirely different
+atoms and molecules would glow with the
+
+ align:start position:0%
+atoms and molecules would glow with the
+ 
+
+ align:start position:0%
+atoms and molecules would glow with the
+same kind of pattern once they were
+
+ align:start position:0%
+same kind of pattern once they were
+ 
+
+ align:start position:0%
+same kind of pattern once they were
+heated to a sufficiently high
+
+ align:start position:0%
+heated to a sufficiently high
+ 
+
+ align:start position:0%
+heated to a sufficiently high
+temperature at least it looked like that
+
+ align:start position:0%
+temperature at least it looked like that
+ 
+
+ align:start position:0%
+temperature at least it looked like that
+might be the case in these early tests
+
+ align:start position:0%
+might be the case in these early tests
+ 
+
+ align:start position:0%
+might be the case in these early tests
+to calibrate these different kinds of
+
+ align:start position:0%
+to calibrate these different kinds of
+ 
+
+ align:start position:0%
+to calibrate these different kinds of
+electric light fixtures and so on
+
+ align:start position:0%
+electric light fixtures and so on
+ 
+
+ align:start position:0%
+electric light fixtures and so on
+so these researchers began to postulate
+
+ align:start position:0%
+so these researchers began to postulate
+ 
+
+ align:start position:0%
+so these researchers began to postulate
+that there was some ideal so-called
+
+ align:start position:0%
+that there was some ideal so-called
+ 
+
+ align:start position:0%
+that there was some ideal so-called
+black body the idea was imagine an
+
+ align:start position:0%
+black body the idea was imagine an
+ 
+
+ align:start position:0%
+black body the idea was imagine an
+object that absorbed all the light that
+
+ align:start position:0%
+object that absorbed all the light that
+ 
+
+ align:start position:0%
+object that absorbed all the light that
+fell upon it and reflected none back so
+
+ align:start position:0%
+fell upon it and reflected none back so
+ 
+
+ align:start position:0%
+fell upon it and reflected none back so
+it would appeal to our eyes to be black
+
+ align:start position:0%
+it would appeal to our eyes to be black
+ 
+
+ align:start position:0%
+it would appeal to our eyes to be black
+it would reflect no light at all we'd
+
+ align:start position:0%
+it would reflect no light at all we'd
+ 
+
+ align:start position:0%
+it would reflect no light at all we'd
+see it as emitting uh reflecting no
+
+ align:start position:0%
+see it as emitting uh reflecting no
+ 
+
+ align:start position:0%
+see it as emitting uh reflecting no
+light at all
+
+ align:start position:0%
+light at all
+ 
+
+ align:start position:0%
+light at all
+so so you want to sort of remove any
+
+ align:start position:0%
+so so you want to sort of remove any
+ 
+
+ align:start position:0%
+so so you want to sort of remove any
+accidents of the kind of light that
+
+ align:start position:0%
+accidents of the kind of light that
+ 
+
+ align:start position:0%
+accidents of the kind of light that
+might have shown on it and concentrate
+
+ align:start position:0%
+might have shown on it and concentrate
+ 
+
+ align:start position:0%
+might have shown on it and concentrate
+on the light being emitted by this
+
+ align:start position:0%
+on the light being emitted by this
+ 
+
+ align:start position:0%
+on the light being emitted by this
+so-called black body when you heat that
+
+ align:start position:0%
+so-called black body when you heat that
+ 
+
+ align:start position:0%
+so-called black body when you heat that
+object up to a high temperature
+
+ align:start position:0%
+object up to a high temperature
+ 
+
+ align:start position:0%
+object up to a high temperature
+and it shouldn't have mattered whether
+
+ align:start position:0%
+and it shouldn't have mattered whether
+ 
+
+ align:start position:0%
+and it shouldn't have mattered whether
+the black body was actually made of wood
+
+ align:start position:0%
+the black body was actually made of wood
+ 
+
+ align:start position:0%
+the black body was actually made of wood
+or charcoal or anything else if it
+
+ align:start position:0%
+or charcoal or anything else if it
+ 
+
+ align:start position:0%
+or charcoal or anything else if it
+really is a universal glow that you can
+
+ align:start position:0%
+really is a universal glow that you can
+ 
+
+ align:start position:0%
+really is a universal glow that you can
+imagine is idealized kind of otherwise
+
+ align:start position:0%
+imagine is idealized kind of otherwise
+ 
+
+ align:start position:0%
+imagine is idealized kind of otherwise
+unspecified kind of object of black body
+
+ align:start position:0%
+unspecified kind of object of black body
+ 
+
+ align:start position:0%
+unspecified kind of object of black body
+and therefore this when you heat this
+
+ align:start position:0%
+and therefore this when you heat this
+ 
+
+ align:start position:0%
+and therefore this when you heat this
+object this mysterious or hypothetical
+
+ align:start position:0%
+object this mysterious or hypothetical
+ 
+
+ align:start position:0%
+object this mysterious or hypothetical
+object up to a sufficiently high
+
+ align:start position:0%
+object up to a sufficiently high
+ 
+
+ align:start position:0%
+object up to a sufficiently high
+temperature the pattern of light that
+
+ align:start position:0%
+temperature the pattern of light that
+ 
+
+ align:start position:0%
+temperature the pattern of light that
+would be emitted uh should tell you
+
+ align:start position:0%
+would be emitted uh should tell you
+ 
+
+ align:start position:0%
+would be emitted uh should tell you
+something about about Universal
+
+ align:start position:0%
+something about about Universal
+ 
+
+ align:start position:0%
+something about about Universal
+properties not The Accidental features
+
+ align:start position:0%
+properties not The Accidental features
+ 
+
+ align:start position:0%
+properties not The Accidental features
+of this or that chemical material
+
+ align:start position:0%
+of this or that chemical material
+ 
+
+ align:start position:0%
+of this or that chemical material
+so this Universal black body Spectrum or
+
+ align:start position:0%
+so this Universal black body Spectrum or
+ 
+
+ align:start position:0%
+so this Universal black body Spectrum or
+at least the hypothesis there might be
+
+ align:start position:0%
+at least the hypothesis there might be
+ 
+
+ align:start position:0%
+at least the hypothesis there might be
+this Universal Behavior that's
+
+ align:start position:0%
+this Universal Behavior that's
+ 
+
+ align:start position:0%
+this Universal Behavior that's
+interesting for at least two reasons of
+
+ align:start position:0%
+interesting for at least two reasons of
+ 
+
+ align:start position:0%
+interesting for at least two reasons of
+exactly the kinds of things that this
+
+ align:start position:0%
+exactly the kinds of things that this
+ 
+
+ align:start position:0%
+exactly the kinds of things that this
+this new PTR had been set up um to to
+
+ align:start position:0%
+this new PTR had been set up um to to
+ 
+
+ align:start position:0%
+this new PTR had been set up um to to
+Foster this could be really useful for
+
+ align:start position:0%
+Foster this could be really useful for
+ 
+
+ align:start position:0%
+Foster this could be really useful for
+calibrations and standardization take
+
+ align:start position:0%
+calibrations and standardization take
+ 
+
+ align:start position:0%
+calibrations and standardization take
+any new um electric light fixture or
+
+ align:start position:0%
+any new um electric light fixture or
+ 
+
+ align:start position:0%
+any new um electric light fixture or
+similar device you should now have a
+
+ align:start position:0%
+similar device you should now have a
+ 
+
+ align:start position:0%
+similar device you should now have a
+universal standard against which one
+
+ align:start position:0%
+universal standard against which one
+ 
+
+ align:start position:0%
+universal standard against which one
+could measure its own light output what
+
+ align:start position:0%
+could measure its own light output what
+ 
+
+ align:start position:0%
+could measure its own light output what
+pattern of light would come out uh from
+
+ align:start position:0%
+pattern of light would come out uh from
+ 
+
+ align:start position:0%
+pattern of light would come out uh from
+say this or that filament because now
+
+ align:start position:0%
+say this or that filament because now
+ 
+
+ align:start position:0%
+say this or that filament because now
+you have a universal standard with which
+
+ align:start position:0%
+you have a universal standard with which
+ 
+
+ align:start position:0%
+you have a universal standard with which
+to compare it it also suggested this
+
+ align:start position:0%
+to compare it it also suggested this
+ 
+
+ align:start position:0%
+to compare it it also suggested this
+might tell us something deeply
+
+ align:start position:0%
+might tell us something deeply
+ 
+
+ align:start position:0%
+might tell us something deeply
+fundamental and very basic about the
+
+ align:start position:0%
+fundamental and very basic about the
+ 
+
+ align:start position:0%
+fundamental and very basic about the
+interactions between light and matter it
+
+ align:start position:0%
+interactions between light and matter it
+ 
+
+ align:start position:0%
+interactions between light and matter it
+shouldn't matter whether you're talking
+
+ align:start position:0%
+shouldn't matter whether you're talking
+ 
+
+ align:start position:0%
+shouldn't matter whether you're talking
+about this kind of material fulfillment
+
+ align:start position:0%
+about this kind of material fulfillment
+ 
+
+ align:start position:0%
+about this kind of material fulfillment
+or that kind this tells us perhaps
+
+ align:start position:0%
+or that kind this tells us perhaps
+ 
+
+ align:start position:0%
+or that kind this tells us perhaps
+something very Universal about light and
+
+ align:start position:0%
+something very Universal about light and
+ 
+
+ align:start position:0%
+something very Universal about light and
+matter at its at their core
+
+ align:start position:0%
+matter at its at their core
+ 
+
+ align:start position:0%
+matter at its at their core
+so these researchers at this newly uh
+
+ align:start position:0%
+so these researchers at this newly uh
+ 
+
+ align:start position:0%
+so these researchers at this newly uh
+generously funded physical College
+
+ align:start position:0%
+generously funded physical College
+ 
+
+ align:start position:0%
+generously funded physical College
+Technologies to help the PTR they began
+
+ align:start position:0%
+Technologies to help the PTR they began
+ 
+
+ align:start position:0%
+Technologies to help the PTR they began
+conducting more and more sensitive
+
+ align:start position:0%
+conducting more and more sensitive
+ 
+
+ align:start position:0%
+conducting more and more sensitive
+experiments on the pattern of light what
+
+ align:start position:0%
+experiments on the pattern of light what
+ 
+
+ align:start position:0%
+experiments on the pattern of light what
+became known as the spectrum of light
+
+ align:start position:0%
+became known as the spectrum of light
+ 
+
+ align:start position:0%
+became known as the spectrum of light
+that was emitted from these black bodies
+
+ align:start position:0%
+that was emitted from these black bodies
+ 
+
+ align:start position:0%
+that was emitted from these black bodies
+over the course of the 1880s and 1890s
+
+ align:start position:0%
+over the course of the 1880s and 1890s
+ 
+
+ align:start position:0%
+over the course of the 1880s and 1890s
+soon after the PTR itself had been
+
+ align:start position:0%
+soon after the PTR itself had been
+ 
+
+ align:start position:0%
+soon after the PTR itself had been
+founded and they began finding curves
+
+ align:start position:0%
+founded and they began finding curves
+ 
+
+ align:start position:0%
+founded and they began finding curves
+that looked like this now in the early
+
+ align:start position:0%
+that looked like this now in the early
+ 
+
+ align:start position:0%
+that looked like this now in the early
+data this was an example of real
+
+ align:start position:0%
+data this was an example of real
+ 
+
+ align:start position:0%
+data this was an example of real
+published data from the pgr researchers
+
+ align:start position:0%
+published data from the pgr researchers
+ 
+
+ align:start position:0%
+published data from the pgr researchers
+number in Princeton
+
+ align:start position:0%
+number in Princeton
+ 
+
+ align:start position:0%
+number in Princeton
+they often would plot the Spectrum the
+
+ align:start position:0%
+they often would plot the Spectrum the
+ 
+
+ align:start position:0%
+they often would plot the Spectrum the
+amount of energy came out as one vary
+
+ align:start position:0%
+amount of energy came out as one vary
+ 
+
+ align:start position:0%
+amount of energy came out as one vary
+the wavelength of light typically these
+
+ align:start position:0%
+the wavelength of light typically these
+ 
+
+ align:start position:0%
+the wavelength of light typically these
+days we tend to characterize in terms of
+
+ align:start position:0%
+days we tend to characterize in terms of
+ 
+
+ align:start position:0%
+days we tend to characterize in terms of
+the frequency but remember that's an
+
+ align:start position:0%
+the frequency but remember that's an
+ 
+
+ align:start position:0%
+the frequency but remember that's an
+easy Choice a trade-off we can always
+
+ align:start position:0%
+easy Choice a trade-off we can always
+ 
+
+ align:start position:0%
+easy Choice a trade-off we can always
+relate the frequency of the light that
+
+ align:start position:0%
+relate the frequency of the light that
+ 
+
+ align:start position:0%
+relate the frequency of the light that
+comes out new we'll use the Greek letter
+
+ align:start position:0%
+comes out new we'll use the Greek letter
+ 
+
+ align:start position:0%
+comes out new we'll use the Greek letter
+new that's inversely proportional to the
+
+ align:start position:0%
+new that's inversely proportional to the
+ 
+
+ align:start position:0%
+new that's inversely proportional to the
+wavelength like in these data here and
+
+ align:start position:0%
+wavelength like in these data here and
+ 
+
+ align:start position:0%
+wavelength like in these data here and
+the consonant proportionality is just
+
+ align:start position:0%
+the consonant proportionality is just
+ 
+
+ align:start position:0%
+the consonant proportionality is just
+given by the speed at which those light
+
+ align:start position:0%
+given by the speed at which those light
+ 
+
+ align:start position:0%
+given by the speed at which those light
+waves are traveling the speed of light
+
+ align:start position:0%
+waves are traveling the speed of light
+ 
+
+ align:start position:0%
+waves are traveling the speed of light
+so let's look at this curve Uh u u is a
+
+ align:start position:0%
+so let's look at this curve Uh u u is a
+ 
+
+ align:start position:0%
+so let's look at this curve Uh u u is a
+certain kind of quantity called a
+
+ align:start position:0%
+certain kind of quantity called a
+ 
+
+ align:start position:0%
+certain kind of quantity called a
+spectral energy density
+
+ align:start position:0%
+spectral energy density
+ 
+
+ align:start position:0%
+spectral energy density
+that's kind of a mouthful and again I go
+
+ align:start position:0%
+that's kind of a mouthful and again I go
+ 
+
+ align:start position:0%
+that's kind of a mouthful and again I go
+through some distance some more details
+
+ align:start position:0%
+through some distance some more details
+ 
+
+ align:start position:0%
+through some distance some more details
+in the optional lecture notes what this
+
+ align:start position:0%
+in the optional lecture notes what this
+ 
+
+ align:start position:0%
+in the optional lecture notes what this
+curve what these curves are showing is
+
+ align:start position:0%
+curve what these curves are showing is
+ 
+
+ align:start position:0%
+curve what these curves are showing is
+the amount of energy per unit volume and
+
+ align:start position:0%
+the amount of energy per unit volume and
+ 
+
+ align:start position:0%
+the amount of energy per unit volume and
+in some region of space
+
+ align:start position:0%
+in some region of space
+ 
+
+ align:start position:0%
+in some region of space
+per frequency so how much light gets
+
+ align:start position:0%
+per frequency so how much light gets
+ 
+
+ align:start position:0%
+per frequency so how much light gets
+shown out in the form of how much energy
+
+ align:start position:0%
+shown out in the form of how much energy
+ 
+
+ align:start position:0%
+shown out in the form of how much energy
+get shown out in the form of radiation
+
+ align:start position:0%
+get shown out in the form of radiation
+ 
+
+ align:start position:0%
+get shown out in the form of radiation
+in some box of fixed size within per
+
+ align:start position:0%
+in some box of fixed size within per
+ 
+
+ align:start position:0%
+in some box of fixed size within per
+unit volume as you vary the color of the
+
+ align:start position:0%
+unit volume as you vary the color of the
+ 
+
+ align:start position:0%
+unit volume as you vary the color of the
+light and so it suggests you get a
+
+ align:start position:0%
+light and so it suggests you get a
+ 
+
+ align:start position:0%
+light and so it suggests you get a
+certain amount of energy radiated for
+
+ align:start position:0%
+certain amount of energy radiated for
+ 
+
+ align:start position:0%
+certain amount of energy radiated for
+one color as you vary the frequency of
+
+ align:start position:0%
+one color as you vary the frequency of
+ 
+
+ align:start position:0%
+one color as you vary the frequency of
+the light a different amount of energy
+
+ align:start position:0%
+the light a different amount of energy
+ 
+
+ align:start position:0%
+the light a different amount of energy
+comes out in this case more energy as
+
+ align:start position:0%
+comes out in this case more energy as
+ 
+
+ align:start position:0%
+comes out in this case more energy as
+you go to a higher frequency different
+
+ align:start position:0%
+you go to a higher frequency different
+ 
+
+ align:start position:0%
+you go to a higher frequency different
+color and so on
+
+ align:start position:0%
+color and so on
+ 
+
+ align:start position:0%
+color and so on
+and what it was uh what what the
+
+ align:start position:0%
+and what it was uh what what the
+ 
+
+ align:start position:0%
+and what it was uh what what the
+researchers kept finding was that the
+
+ align:start position:0%
+researchers kept finding was that the
+ 
+
+ align:start position:0%
+researchers kept finding was that the
+nature of this curve depended only on
+
+ align:start position:0%
+nature of this curve depended only on
+ 
+
+ align:start position:0%
+nature of this curve depended only on
+the temperature to which the objects
+
+ align:start position:0%
+the temperature to which the objects
+ 
+
+ align:start position:0%
+the temperature to which the objects
+have been heated but not the material
+
+ align:start position:0%
+have been heated but not the material
+ 
+
+ align:start position:0%
+have been heated but not the material
+composition of those objects this
+
+ align:start position:0%
+composition of those objects this
+ 
+
+ align:start position:0%
+composition of those objects this
+Universal feature became more and more
+
+ align:start position:0%
+Universal feature became more and more
+ 
+
+ align:start position:0%
+Universal feature became more and more
+evidence as they conducted more and more
+
+ align:start position:0%
+evidence as they conducted more and more
+ 
+
+ align:start position:0%
+evidence as they conducted more and more
+tests
+
+ align:start position:0%
+tests
+ 
+
+ align:start position:0%
+tests
+and so this is a plot now showing the
+
+ align:start position:0%
+and so this is a plot now showing the
+ 
+
+ align:start position:0%
+and so this is a plot now showing the
+the form of this spectral energy density
+
+ align:start position:0%
+the form of this spectral energy density
+ 
+
+ align:start position:0%
+the form of this spectral energy density
+for three different temperatures it
+
+ align:start position:0%
+for three different temperatures it
+ 
+
+ align:start position:0%
+for three different temperatures it
+varies only with temperature it's
+
+ align:start position:0%
+varies only with temperature it's
+ 
+
+ align:start position:0%
+varies only with temperature it's
+considered a relatively low temperature
+
+ align:start position:0%
+considered a relatively low temperature
+ 
+
+ align:start position:0%
+considered a relatively low temperature
+here so medium temperature and some high
+
+ align:start position:0%
+here so medium temperature and some high
+ 
+
+ align:start position:0%
+here so medium temperature and some high
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+already we see the trend becomes pretty
+
+ align:start position:0%
+already we see the trend becomes pretty
+ 
+
+ align:start position:0%
+already we see the trend becomes pretty
+clear as you raise the temperature to
+
+ align:start position:0%
+clear as you raise the temperature to
+ 
+
+ align:start position:0%
+clear as you raise the temperature to
+which you've heated that black body that
+
+ align:start position:0%
+which you've heated that black body that
+ 
+
+ align:start position:0%
+which you've heated that black body that
+object the amount of energy that's
+
+ align:start position:0%
+object the amount of energy that's
+ 
+
+ align:start position:0%
+object the amount of energy that's
+radiated grows so you get more and more
+
+ align:start position:0%
+radiated grows so you get more and more
+ 
+
+ align:start position:0%
+radiated grows so you get more and more
+energy coming out the the area under
+
+ align:start position:0%
+energy coming out the the area under
+ 
+
+ align:start position:0%
+energy coming out the the area under
+this curve of the blue one is much
+
+ align:start position:0%
+this curve of the blue one is much
+ 
+
+ align:start position:0%
+this curve of the blue one is much
+larger than the area under the either
+
+ align:start position:0%
+larger than the area under the either
+ 
+
+ align:start position:0%
+larger than the area under the either
+the other curves
+
+ align:start position:0%
+the other curves
+ 
+
+ align:start position:0%
+the other curves
+total energy output where the intensity
+
+ align:start position:0%
+total energy output where the intensity
+ 
+
+ align:start position:0%
+total energy output where the intensity
+increases with temperature and the peak
+
+ align:start position:0%
+increases with temperature and the peak
+ 
+
+ align:start position:0%
+increases with temperature and the peak
+frequency the frequency at which which
+
+ align:start position:0%
+frequency the frequency at which which
+ 
+
+ align:start position:0%
+frequency the frequency at which which
+most energy gets emitted uh in the form
+
+ align:start position:0%
+most energy gets emitted uh in the form
+ 
+
+ align:start position:0%
+most energy gets emitted uh in the form
+of light that also shifts to higher and
+
+ align:start position:0%
+of light that also shifts to higher and
+ 
+
+ align:start position:0%
+of light that also shifts to higher and
+higher frequency so at a relatively low
+
+ align:start position:0%
+higher frequency so at a relatively low
+ 
+
+ align:start position:0%
+higher frequency so at a relatively low
+temperature the highest the peak
+
+ align:start position:0%
+temperature the highest the peak
+ 
+
+ align:start position:0%
+temperature the highest the peak
+frequency is a kind of reddish color as
+
+ align:start position:0%
+frequency is a kind of reddish color as
+ 
+
+ align:start position:0%
+frequency is a kind of reddish color as
+you increase the temperature it shifts
+
+ align:start position:0%
+you increase the temperature it shifts
+ 
+
+ align:start position:0%
+you increase the temperature it shifts
+through the Spectrum uh to our engine
+
+ align:start position:0%
+through the Spectrum uh to our engine
+ 
+
+ align:start position:0%
+through the Spectrum uh to our engine
+ultimately to the blue end so you have
+
+ align:start position:0%
+ultimately to the blue end so you have
+ 
+
+ align:start position:0%
+ultimately to the blue end so you have
+this pattern emerging
+
+ align:start position:0%
+this pattern emerging
+ 
+
+ align:start position:0%
+this pattern emerging
+so as the empirical pattern has these
+
+ align:start position:0%
+so as the empirical pattern has these
+ 
+
+ align:start position:0%
+so as the empirical pattern has these
+empirical measurements in the in the
+
+ align:start position:0%
+empirical measurements in the in the
+ 
+
+ align:start position:0%
+empirical measurements in the in the
+Laboratories became more and more clear
+
+ align:start position:0%
+Laboratories became more and more clear
+ 
+
+ align:start position:0%
+Laboratories became more and more clear
+how do you make sense of that pattern
+
+ align:start position:0%
+how do you make sense of that pattern
+ 
+
+ align:start position:0%
+how do you make sense of that pattern
+that actually was very very non-trivial
+
+ align:start position:0%
+that actually was very very non-trivial
+ 
+
+ align:start position:0%
+that actually was very very non-trivial
+that was not at all clear to these early
+
+ align:start position:0%
+that was not at all clear to these early
+ 
+
+ align:start position:0%
+that was not at all clear to these early
+researchers
+
+ align:start position:0%
+researchers
+ 
+
+ align:start position:0%
+researchers
+so one of the first to really delve into
+
+ align:start position:0%
+so one of the first to really delve into
+ 
+
+ align:start position:0%
+so one of the first to really delve into
+this try to get a theoretical
+
+ align:start position:0%
+this try to get a theoretical
+ 
+
+ align:start position:0%
+this try to get a theoretical
+explanation for that pattern was MOX
+
+ align:start position:0%
+explanation for that pattern was MOX
+ 
+
+ align:start position:0%
+explanation for that pattern was MOX
+plot so plug had only recently moved to
+
+ align:start position:0%
+plot so plug had only recently moved to
+ 
+
+ align:start position:0%
+plot so plug had only recently moved to
+Berlin he was one of the first people in
+
+ align:start position:0%
+Berlin he was one of the first people in
+ 
+
+ align:start position:0%
+Berlin he was one of the first people in
+all of Germany to have this full
+
+ align:start position:0%
+all of Germany to have this full
+ 
+
+ align:start position:0%
+all of Germany to have this full
+Professor this special ordinarius
+
+ align:start position:0%
+Professor this special ordinarius
+ 
+
+ align:start position:0%
+Professor this special ordinarius
+professor chair in theoretical physics
+
+ align:start position:0%
+professor chair in theoretical physics
+ 
+
+ align:start position:0%
+professor chair in theoretical physics
+remember we talked several weeks ago
+
+ align:start position:0%
+remember we talked several weeks ago
+ 
+
+ align:start position:0%
+remember we talked several weeks ago
+several classes ago that until the later
+
+ align:start position:0%
+several classes ago that until the later
+ 
+
+ align:start position:0%
+several classes ago that until the later
+years of the 19th century
+
+ align:start position:0%
+years of the 19th century
+ 
+
+ align:start position:0%
+years of the 19th century
+especially in the German language
+
+ align:start position:0%
+especially in the German language
+ 
+
+ align:start position:0%
+especially in the German language
+universities there will be one full
+
+ align:start position:0%
+universities there will be one full
+ 
+
+ align:start position:0%
+universities there will be one full
+Professor one ordinarius
+
+ align:start position:0%
+Professor one ordinarius
+ 
+
+ align:start position:0%
+Professor one ordinarius
+for all of physics and that person was
+
+ align:start position:0%
+for all of physics and that person was
+ 
+
+ align:start position:0%
+for all of physics and that person was
+sort of by default on experimental
+
+ align:start position:0%
+sort of by default on experimental
+ 
+
+ align:start position:0%
+sort of by default on experimental
+physicist only by the later Decades of
+
+ align:start position:0%
+physicist only by the later Decades of
+ 
+
+ align:start position:0%
+physicist only by the later Decades of
+the 19th century where there are
+
+ align:start position:0%
+the 19th century where there are
+ 
+
+ align:start position:0%
+the 19th century where there are
+sometimes two full professors of physics
+
+ align:start position:0%
+sometimes two full professors of physics
+ 
+
+ align:start position:0%
+sometimes two full professors of physics
+one to handle experiment and one for
+
+ align:start position:0%
+one to handle experiment and one for
+ 
+
+ align:start position:0%
+one to handle experiment and one for
+Theory clock was one of these early
+
+ align:start position:0%
+Theory clock was one of these early
+ 
+
+ align:start position:0%
+Theory clock was one of these early
+ordinary suppressors of theoretical
+
+ align:start position:0%
+ordinary suppressors of theoretical
+ 
+
+ align:start position:0%
+ordinary suppressors of theoretical
+physics in Berlin starting in the early
+
+ align:start position:0%
+physics in Berlin starting in the early
+ 
+
+ align:start position:0%
+physics in Berlin starting in the early
+1890s he was not at the PTR but he was
+
+ align:start position:0%
+1890s he was not at the PTR but he was
+ 
+
+ align:start position:0%
+1890s he was not at the PTR but he was
+nearby and he was in touch with his
+
+ align:start position:0%
+nearby and he was in touch with his
+ 
+
+ align:start position:0%
+nearby and he was in touch with his
+colleagues there clock was an expert in
+
+ align:start position:0%
+colleagues there clock was an expert in
+ 
+
+ align:start position:0%
+colleagues there clock was an expert in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+on the new work on statistical mechanics
+
+ align:start position:0%
+on the new work on statistical mechanics
+ 
+
+ align:start position:0%
+on the new work on statistical mechanics
+by people like James Clark Maxwell and
+
+ align:start position:0%
+by people like James Clark Maxwell and
+ 
+
+ align:start position:0%
+by people like James Clark Maxwell and
+Elizabeth Walton and others how do you
+
+ align:start position:0%
+Elizabeth Walton and others how do you
+ 
+
+ align:start position:0%
+Elizabeth Walton and others how do you
+make sense of large collections of
+
+ align:start position:0%
+make sense of large collections of
+ 
+
+ align:start position:0%
+make sense of large collections of
+objects like uh like molecules in a gas
+
+ align:start position:0%
+objects like uh like molecules in a gas
+ 
+
+ align:start position:0%
+objects like uh like molecules in a gas
+how do you assess their Collective
+
+ align:start position:0%
+how do you assess their Collective
+ 
+
+ align:start position:0%
+how do you assess their Collective
+property that's what you focus on
+
+ align:start position:0%
+property that's what you focus on
+ 
+
+ align:start position:0%
+property that's what you focus on
+because he was now closed in PTR he
+
+ align:start position:0%
+because he was now closed in PTR he
+ 
+
+ align:start position:0%
+because he was now closed in PTR he
+began paying more and more attention to
+
+ align:start position:0%
+began paying more and more attention to
+ 
+
+ align:start position:0%
+began paying more and more attention to
+this black body research as well and he
+
+ align:start position:0%
+this black body research as well and he
+ 
+
+ align:start position:0%
+this black body research as well and he
+realizes many others did it was really
+
+ align:start position:0%
+realizes many others did it was really
+ 
+
+ align:start position:0%
+realizes many others did it was really
+really hard to make sense of his
+
+ align:start position:0%
+really hard to make sense of his
+ 
+
+ align:start position:0%
+really hard to make sense of his
+characteristic pattern that seemingly
+
+ align:start position:0%
+characteristic pattern that seemingly
+ 
+
+ align:start position:0%
+characteristic pattern that seemingly
+Universal shape of this black body
+
+ align:start position:0%
+Universal shape of this black body
+ 
+
+ align:start position:0%
+Universal shape of this black body
+Spectrum uh the amount of energy per
+
+ align:start position:0%
+Spectrum uh the amount of energy per
+ 
+
+ align:start position:0%
+Spectrum uh the amount of energy per
+unit volume per frequency and in fact if
+
+ align:start position:0%
+unit volume per frequency and in fact if
+ 
+
+ align:start position:0%
+unit volume per frequency and in fact if
+you used quite standard by that point
+
+ align:start position:0%
+you used quite standard by that point
+ 
+
+ align:start position:0%
+you used quite standard by that point
+very familiar arguments from people like
+
+ align:start position:0%
+very familiar arguments from people like
+ 
+
+ align:start position:0%
+very familiar arguments from people like
+boltzmann and Maxwell the kind of people
+
+ align:start position:0%
+boltzmann and Maxwell the kind of people
+ 
+
+ align:start position:0%
+boltzmann and Maxwell the kind of people
+whose work plaque was an expert in
+
+ align:start position:0%
+whose work plaque was an expert in
+ 
+
+ align:start position:0%
+whose work plaque was an expert in
+studying
+
+ align:start position:0%
+studying
+ 
+
+ align:start position:0%
+studying
+you should predict a very different
+
+ align:start position:0%
+you should predict a very different
+ 
+
+ align:start position:0%
+you should predict a very different
+behavior from first principles in fact
+
+ align:start position:0%
+behavior from first principles in fact
+ 
+
+ align:start position:0%
+behavior from first principles in fact
+it should look like this this dashed
+
+ align:start position:0%
+it should look like this this dashed
+ 
+
+ align:start position:0%
+it should look like this this dashed
+purple curve which doesn't look anything
+
+ align:start position:0%
+purple curve which doesn't look anything
+ 
+
+ align:start position:0%
+purple curve which doesn't look anything
+like the ultimate curve that was
+
+ align:start position:0%
+like the ultimate curve that was
+ 
+
+ align:start position:0%
+like the ultimate curve that was
+measured they agree very well at very
+
+ align:start position:0%
+measured they agree very well at very
+ 
+
+ align:start position:0%
+measured they agree very well at very
+low frequencies they both overlap here
+
+ align:start position:0%
+low frequencies they both overlap here
+ 
+
+ align:start position:0%
+low frequencies they both overlap here
+but then you see a very significant
+
+ align:start position:0%
+but then you see a very significant
+ 
+
+ align:start position:0%
+but then you see a very significant
+difference between their patterns and in
+
+ align:start position:0%
+difference between their patterns and in
+ 
+
+ align:start position:0%
+difference between their patterns and in
+fact this purple one became known as the
+
+ align:start position:0%
+fact this purple one became known as the
+ 
+
+ align:start position:0%
+fact this purple one became known as the
+ultraviolet catastrophe I love that term
+
+ align:start position:0%
+ultraviolet catastrophe I love that term
+ 
+
+ align:start position:0%
+ultraviolet catastrophe I love that term
+it's a catastrophe
+
+ align:start position:0%
+it's a catastrophe
+ 
+
+ align:start position:0%
+it's a catastrophe
+if you follow the then standard
+
+ align:start position:0%
+if you follow the then standard
+ 
+
+ align:start position:0%
+if you follow the then standard
+arguments and I go through these again
+
+ align:start position:0%
+arguments and I go through these again
+ 
+
+ align:start position:0%
+arguments and I go through these again
+in some more detail on those optional
+
+ align:start position:0%
+in some more detail on those optional
+ 
+
+ align:start position:0%
+in some more detail on those optional
+lecture notes then the theoretical
+
+ align:start position:0%
+lecture notes then the theoretical
+ 
+
+ align:start position:0%
+lecture notes then the theoretical
+models seem to predict that you should
+
+ align:start position:0%
+models seem to predict that you should
+ 
+
+ align:start position:0%
+models seem to predict that you should
+get more and more energy per volume as
+
+ align:start position:0%
+get more and more energy per volume as
+ 
+
+ align:start position:0%
+get more and more energy per volume as
+you raise the frequency and it should
+
+ align:start position:0%
+you raise the frequency and it should
+ 
+
+ align:start position:0%
+you raise the frequency and it should
+grow without bound it should never stop
+
+ align:start position:0%
+grow without bound it should never stop
+ 
+
+ align:start position:0%
+grow without bound it should never stop
+so it seemed like everything should be
+
+ align:start position:0%
+so it seemed like everything should be
+ 
+
+ align:start position:0%
+so it seemed like everything should be
+glowing infinitely all the time we
+
+ align:start position:0%
+glowing infinitely all the time we
+ 
+
+ align:start position:0%
+glowing infinitely all the time we
+clearly don't see that
+
+ align:start position:0%
+clearly don't see that
+ 
+
+ align:start position:0%
+clearly don't see that
+that argument came from kind of two
+
+ align:start position:0%
+that argument came from kind of two
+ 
+
+ align:start position:0%
+that argument came from kind of two
+different pieces again I go through that
+
+ align:start position:0%
+different pieces again I go through that
+ 
+
+ align:start position:0%
+different pieces again I go through that
+in a bit more detail in the notes but
+
+ align:start position:0%
+in a bit more detail in the notes but
+ 
+
+ align:start position:0%
+in a bit more detail in the notes but
+the high level summary is that according
+
+ align:start position:0%
+the high level summary is that according
+ 
+
+ align:start position:0%
+the high level summary is that according
+to to work by people like Maxwell and
+
+ align:start position:0%
+to to work by people like Maxwell and
+ 
+
+ align:start position:0%
+to to work by people like Maxwell and
+boltzmann very well established by by
+
+ align:start position:0%
+boltzmann very well established by by
+ 
+
+ align:start position:0%
+boltzmann very well established by by
+the time a plonk began to worry about
+
+ align:start position:0%
+the time a plonk began to worry about
+ 
+
+ align:start position:0%
+the time a plonk began to worry about
+this stuff in thermal equilibrium very
+
+ align:start position:0%
+this stuff in thermal equilibrium very
+ 
+
+ align:start position:0%
+this stuff in thermal equilibrium very
+generally it had been argued each degree
+
+ align:start position:0%
+generally it had been argued each degree
+ 
+
+ align:start position:0%
+generally it had been argued each degree
+of Freedom each way that these um either
+
+ align:start position:0%
+of Freedom each way that these um either
+ 
+
+ align:start position:0%
+of Freedom each way that these um either
+either uh light waves or little bits of
+
+ align:start position:0%
+either uh light waves or little bits of
+ 
+
+ align:start position:0%
+either uh light waves or little bits of
+matter in that block body each of these
+
+ align:start position:0%
+matter in that block body each of these
+ 
+
+ align:start position:0%
+matter in that block body each of these
+things should should share a kind of
+
+ align:start position:0%
+things should should share a kind of
+ 
+
+ align:start position:0%
+things should should share a kind of
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+um energy
+
+ align:start position:0%
+um energy
+ 
+
+ align:start position:0%
+um energy
+proportional to the temperature to which
+
+ align:start position:0%
+proportional to the temperature to which
+ 
+
+ align:start position:0%
+proportional to the temperature to which
+the object have been heated and with the
+
+ align:start position:0%
+the object have been heated and with the
+ 
+
+ align:start position:0%
+the object have been heated and with the
+proportionality known as a constant
+
+ align:start position:0%
+proportionality known as a constant
+ 
+
+ align:start position:0%
+proportionality known as a constant
+known as K We Now call that Boltzmann's
+
+ align:start position:0%
+known as K We Now call that Boltzmann's
+ 
+
+ align:start position:0%
+known as K We Now call that Boltzmann's
+constant this was known as the
+
+ align:start position:0%
+constant this was known as the
+ 
+
+ align:start position:0%
+constant this was known as the
+equipartition theorem that each way in
+
+ align:start position:0%
+equipartition theorem that each way in
+ 
+
+ align:start position:0%
+equipartition theorem that each way in
+which a system could kind of Wiggle or
+
+ align:start position:0%
+which a system could kind of Wiggle or
+ 
+
+ align:start position:0%
+which a system could kind of Wiggle or
+move these so-called degree of Freedom
+
+ align:start position:0%
+move these so-called degree of Freedom
+ 
+
+ align:start position:0%
+move these so-called degree of Freedom
+should be uh should have an equal
+
+ align:start position:0%
+should be uh should have an equal
+ 
+
+ align:start position:0%
+should be uh should have an equal
+average energy that's step one step two
+
+ align:start position:0%
+average energy that's step one step two
+ 
+
+ align:start position:0%
+average energy that's step one step two
+using Maxwell's treatment of light of
+
+ align:start position:0%
+using Maxwell's treatment of light of
+ 
+
+ align:start position:0%
+using Maxwell's treatment of light of
+electromagnetic radiation
+
+ align:start position:0%
+electromagnetic radiation
+ 
+
+ align:start position:0%
+electromagnetic radiation
+you you the argument was that this um
+
+ align:start position:0%
+you you the argument was that this um
+ 
+
+ align:start position:0%
+you you the argument was that this um
+the number of radiation modes degrees of
+
+ align:start position:0%
+the number of radiation modes degrees of
+ 
+
+ align:start position:0%
+the number of radiation modes degrees of
+freedom per unit volume per frequency
+
+ align:start position:0%
+freedom per unit volume per frequency
+ 
+
+ align:start position:0%
+freedom per unit volume per frequency
+should go like new squared combine those
+
+ align:start position:0%
+should go like new squared combine those
+ 
+
+ align:start position:0%
+should go like new squared combine those
+together you get this expectation that
+
+ align:start position:0%
+together you get this expectation that
+ 
+
+ align:start position:0%
+together you get this expectation that
+that the spectral energy density U
+
+ align:start position:0%
+that the spectral energy density U
+ 
+
+ align:start position:0%
+that the spectral energy density U
+should grow quadratically grow as a
+
+ align:start position:0%
+should grow quadratically grow as a
+ 
+
+ align:start position:0%
+should grow quadratically grow as a
+square of the frequency without bath it
+
+ align:start position:0%
+square of the frequency without bath it
+ 
+
+ align:start position:0%
+square of the frequency without bath it
+should rise about linear so everything
+
+ align:start position:0%
+should rise about linear so everything
+ 
+
+ align:start position:0%
+should rise about linear so everything
+should be glowing all the time giving
+
+ align:start position:0%
+should be glowing all the time giving
+ 
+
+ align:start position:0%
+should be glowing all the time giving
+off infinite energy that clearly is not
+
+ align:start position:0%
+off infinite energy that clearly is not
+ 
+
+ align:start position:0%
+off infinite energy that clearly is not
+what we see
+
+ align:start position:0%
+what we see
+ 
+
+ align:start position:0%
+what we see
+so clock as I say had special access to
+
+ align:start position:0%
+so clock as I say had special access to
+ 
+
+ align:start position:0%
+so clock as I say had special access to
+these to his colleagues doing these
+
+ align:start position:0%
+these to his colleagues doing these
+ 
+
+ align:start position:0%
+these to his colleagues doing these
+experiments sort of in real time he knew
+
+ align:start position:0%
+experiments sort of in real time he knew
+ 
+
+ align:start position:0%
+experiments sort of in real time he knew
+better better than anyone that the real
+
+ align:start position:0%
+better better than anyone that the real
+ 
+
+ align:start position:0%
+better better than anyone that the real
+curves looked nothing like this this art
+
+ align:start position:0%
+curves looked nothing like this this art
+ 
+
+ align:start position:0%
+curves looked nothing like this this art
+this sort of uh constantly growing curve
+
+ align:start position:0%
+this sort of uh constantly growing curve
+ 
+
+ align:start position:0%
+this sort of uh constantly growing curve
+of the ultraviolet catastrophe
+
+ align:start position:0%
+of the ultraviolet catastrophe
+ 
+
+ align:start position:0%
+of the ultraviolet catastrophe
+everyone knew that these curves must
+
+ align:start position:0%
+everyone knew that these curves must
+ 
+
+ align:start position:0%
+everyone knew that these curves must
+begin to fall with increasing frequency
+
+ align:start position:0%
+begin to fall with increasing frequency
+ 
+
+ align:start position:0%
+begin to fall with increasing frequency
+Planck had an extra Insight or extra
+
+ align:start position:0%
+Planck had an extra Insight or extra
+ 
+
+ align:start position:0%
+Planck had an extra Insight or extra
+information not just that the curb
+
+ align:start position:0%
+information not just that the curb
+ 
+
+ align:start position:0%
+information not just that the curb
+should fall but how it should fall the
+
+ align:start position:0%
+should fall but how it should fall the
+ 
+
+ align:start position:0%
+should fall but how it should fall the
+the actual shape of that curve like this
+
+ align:start position:0%
+the actual shape of that curve like this
+ 
+
+ align:start position:0%
+the actual shape of that curve like this
+part here basically this part here in in
+
+ align:start position:0%
+part here basically this part here in in
+ 
+
+ align:start position:0%
+part here basically this part here in in
+wavelength how should that curve Begin
+
+ align:start position:0%
+wavelength how should that curve Begin
+ 
+
+ align:start position:0%
+wavelength how should that curve Begin
+to Fall as you go to shorter and shorter
+
+ align:start position:0%
+to Fall as you go to shorter and shorter
+ 
+
+ align:start position:0%
+to Fall as you go to shorter and shorter
+wavelengths or higher and higher
+
+ align:start position:0%
+wavelengths or higher and higher
+ 
+
+ align:start position:0%
+wavelengths or higher and higher
+frequencies so he began to Tinker and in
+
+ align:start position:0%
+frequencies so he began to Tinker and in
+ 
+
+ align:start position:0%
+frequencies so he began to Tinker and in
+fact very famously on a particular date
+
+ align:start position:0%
+fact very famously on a particular date
+ 
+
+ align:start position:0%
+fact very famously on a particular date
+December 14 1900 he presented a paper to
+
+ align:start position:0%
+December 14 1900 he presented a paper to
+ 
+
+ align:start position:0%
+December 14 1900 he presented a paper to
+his colleagues at a physics society
+
+ align:start position:0%
+his colleagues at a physics society
+ 
+
+ align:start position:0%
+his colleagues at a physics society
+meeting in which he presented this form
+
+ align:start position:0%
+meeting in which he presented this form
+ 
+
+ align:start position:0%
+meeting in which he presented this form
+for uh for the this spectral energy
+
+ align:start position:0%
+for uh for the this spectral energy
+ 
+
+ align:start position:0%
+for uh for the this spectral energy
+density but it should rise not as new
+
+ align:start position:0%
+density but it should rise not as new
+ 
+
+ align:start position:0%
+density but it should rise not as new
+squared like that ultraviolet
+
+ align:start position:0%
+squared like that ultraviolet
+ 
+
+ align:start position:0%
+squared like that ultraviolet
+catastrophe but it actually have this a
+
+ align:start position:0%
+catastrophe but it actually have this a
+ 
+
+ align:start position:0%
+catastrophe but it actually have this a
+bit more complicated structure
+
+ align:start position:0%
+bit more complicated structure
+ 
+
+ align:start position:0%
+bit more complicated structure
+and this was really interesting because
+
+ align:start position:0%
+and this was really interesting because
+ 
+
+ align:start position:0%
+and this was really interesting because
+it would match very well that both the
+
+ align:start position:0%
+it would match very well that both the
+ 
+
+ align:start position:0%
+it would match very well that both the
+arguments from people like boltzmann uh
+
+ align:start position:0%
+arguments from people like boltzmann uh
+ 
+
+ align:start position:0%
+arguments from people like boltzmann uh
+and Maxwell in in one region of the
+
+ align:start position:0%
+and Maxwell in in one region of the
+ 
+
+ align:start position:0%
+and Maxwell in in one region of the
+graph for sorry for very uh low
+
+ align:start position:0%
+graph for sorry for very uh low
+ 
+
+ align:start position:0%
+graph for sorry for very uh low
+frequency very long wavelengths so over
+
+ align:start position:0%
+frequency very long wavelengths so over
+ 
+
+ align:start position:0%
+frequency very long wavelengths so over
+here on this real data over here on this
+
+ align:start position:0%
+here on this real data over here on this
+ 
+
+ align:start position:0%
+here on this real data over here on this
+plot it converges to the to the original
+
+ align:start position:0%
+plot it converges to the to the original
+ 
+
+ align:start position:0%
+plot it converges to the to the original
+expectation but then it kind of has this
+
+ align:start position:0%
+expectation but then it kind of has this
+ 
+
+ align:start position:0%
+expectation but then it kind of has this
+natural turnaround and so that at higher
+
+ align:start position:0%
+natural turnaround and so that at higher
+ 
+
+ align:start position:0%
+natural turnaround and so that at higher
+frequencies at shorter wavelengths in
+
+ align:start position:0%
+frequencies at shorter wavelengths in
+ 
+
+ align:start position:0%
+frequencies at shorter wavelengths in
+fact you should have this gently
+
+ align:start position:0%
+fact you should have this gently
+ 
+
+ align:start position:0%
+fact you should have this gently
+decaying tail this exponential tail both
+
+ align:start position:0%
+decaying tail this exponential tail both
+ 
+
+ align:start position:0%
+decaying tail this exponential tail both
+of those features are contained in this
+
+ align:start position:0%
+of those features are contained in this
+ 
+
+ align:start position:0%
+of those features are contained in this
+one expression as you take the
+
+ align:start position:0%
+one expression as you take the
+ 
+
+ align:start position:0%
+one expression as you take the
+appropriate limits he also had to
+
+ align:start position:0%
+appropriate limits he also had to
+ 
+
+ align:start position:0%
+appropriate limits he also had to
+introduce this new constant H which had
+
+ align:start position:0%
+introduce this new constant H which had
+ 
+
+ align:start position:0%
+introduce this new constant H which had
+not been introduced before we now call
+
+ align:start position:0%
+not been introduced before we now call
+ 
+
+ align:start position:0%
+not been introduced before we now call
+it Planck's constant
+
+ align:start position:0%
+it Planck's constant
+ 
+
+ align:start position:0%
+it Planck's constant
+now as at least in part to make his
+
+ align:start position:0%
+now as at least in part to make his
+ 
+
+ align:start position:0%
+now as at least in part to make his
+units match the quantity KT has units of
+
+ align:start position:0%
+units match the quantity KT has units of
+ 
+
+ align:start position:0%
+units match the quantity KT has units of
+energy T is a temperature K boatswain
+
+ align:start position:0%
+energy T is a temperature K boatswain
+ 
+
+ align:start position:0%
+energy T is a temperature K boatswain
+constant together form units of energy
+
+ align:start position:0%
+constant together form units of energy
+ 
+
+ align:start position:0%
+constant together form units of energy
+new here is the frequency one over time
+
+ align:start position:0%
+new here is the frequency one over time
+ 
+
+ align:start position:0%
+new here is the frequency one over time
+like one over seconds hurts so that
+
+ align:start position:0%
+like one over seconds hurts so that
+ 
+
+ align:start position:0%
+like one over seconds hurts so that
+doesn't have the same units as energy so
+
+ align:start position:0%
+doesn't have the same units as energy so
+ 
+
+ align:start position:0%
+doesn't have the same units as energy so
+we added this this extra kind of fudge
+
+ align:start position:0%
+we added this this extra kind of fudge
+ 
+
+ align:start position:0%
+we added this this extra kind of fudge
+called H to make sure the units would
+
+ align:start position:0%
+called H to make sure the units would
+ 
+
+ align:start position:0%
+called H to make sure the units would
+match and also to try to begin to match
+
+ align:start position:0%
+match and also to try to begin to match
+ 
+
+ align:start position:0%
+match and also to try to begin to match
+the actual quantitative shape of the
+
+ align:start position:0%
+the actual quantitative shape of the
+ 
+
+ align:start position:0%
+the actual quantitative shape of the
+data from his comics
+
+ align:start position:0%
+data from his comics
+ 
+
+ align:start position:0%
+data from his comics
+so in this treatment at the very closing
+
+ align:start position:0%
+so in this treatment at the very closing
+ 
+
+ align:start position:0%
+so in this treatment at the very closing
+days of the year 1900 plonk introduced
+
+ align:start position:0%
+days of the year 1900 plonk introduced
+ 
+
+ align:start position:0%
+days of the year 1900 plonk introduced
+not only a new form for the spectral
+
+ align:start position:0%
+not only a new form for the spectral
+ 
+
+ align:start position:0%
+not only a new form for the spectral
+energy density again there's more on
+
+ align:start position:0%
+energy density again there's more on
+ 
+
+ align:start position:0%
+energy density again there's more on
+that on on that in those lecture notes
+
+ align:start position:0%
+that on on that in those lecture notes
+ 
+
+ align:start position:0%
+that on on that in those lecture notes
+he also introduces this new Universal
+
+ align:start position:0%
+he also introduces this new Universal
+ 
+
+ align:start position:0%
+he also introduces this new Universal
+constant We Now call Planck's cost it's
+
+ align:start position:0%
+constant We Now call Planck's cost it's
+ 
+
+ align:start position:0%
+constant We Now call Planck's cost it's
+this number H just a constant it really
+
+ align:start position:0%
+this number H just a constant it really
+ 
+
+ align:start position:0%
+this number H just a constant it really
+sets the scale for these departures
+
+ align:start position:0%
+sets the scale for these departures
+ 
+
+ align:start position:0%
+sets the scale for these departures
+based on the calculations we would make
+
+ align:start position:0%
+based on the calculations we would make
+ 
+
+ align:start position:0%
+based on the calculations we would make
+from Newton's physics or even maximums
+
+ align:start position:0%
+from Newton's physics or even maximums
+ 
+
+ align:start position:0%
+from Newton's physics or even maximums
+equations how much do these newer ideas
+
+ align:start position:0%
+equations how much do these newer ideas
+ 
+
+ align:start position:0%
+equations how much do these newer ideas
+of what becomes known as quantum theory
+
+ align:start position:0%
+of what becomes known as quantum theory
+ 
+
+ align:start position:0%
+of what becomes known as quantum theory
+how much should they depart or when
+
+ align:start position:0%
+how much should they depart or when
+ 
+
+ align:start position:0%
+how much should they depart or when
+should we expect a deviation
+
+ align:start position:0%
+should we expect a deviation
+ 
+
+ align:start position:0%
+should we expect a deviation
+and plonk's value that he inferred from
+
+ align:start position:0%
+and plonk's value that he inferred from
+ 
+
+ align:start position:0%
+and plonk's value that he inferred from
+his colleagues measurements at the PTR
+
+ align:start position:0%
+his colleagues measurements at the PTR
+ 
+
+ align:start position:0%
+his colleagues measurements at the PTR
+was actually remarkably close to the
+
+ align:start position:0%
+was actually remarkably close to the
+ 
+
+ align:start position:0%
+was actually remarkably close to the
+modern value we use to this day here's a
+
+ align:start position:0%
+modern value we use to this day here's a
+ 
+
+ align:start position:0%
+modern value we use to this day here's a
+modern value Planck's inferred value is
+
+ align:start position:0%
+modern value Planck's inferred value is
+ 
+
+ align:start position:0%
+modern value Planck's inferred value is
+pretty close
+
+ align:start position:0%
+pretty close
+ 
+
+ align:start position:0%
+pretty close
+in units that are familiar for kind of
+
+ align:start position:0%
+in units that are familiar for kind of
+ 
+
+ align:start position:0%
+in units that are familiar for kind of
+macroscopic everyday human activities
+
+ align:start position:0%
+macroscopic everyday human activities
+ 
+
+ align:start position:0%
+macroscopic everyday human activities
+the so-called CGS system when we measure
+
+ align:start position:0%
+the so-called CGS system when we measure
+ 
+
+ align:start position:0%
+the so-called CGS system when we measure
+distances in centimeters masses and
+
+ align:start position:0%
+distances in centimeters masses and
+ 
+
+ align:start position:0%
+distances in centimeters masses and
+grams and times and seconds that's where
+
+ align:start position:0%
+grams and times and seconds that's where
+ 
+
+ align:start position:0%
+grams and times and seconds that's where
+the CGS comes from energy as you may
+
+ align:start position:0%
+the CGS comes from energy as you may
+ 
+
+ align:start position:0%
+the CGS comes from energy as you may
+recall is given this unit of an ER which
+
+ align:start position:0%
+recall is given this unit of an ER which
+ 
+
+ align:start position:0%
+recall is given this unit of an ER which
+really is just one gram uh centimeter
+
+ align:start position:0%
+really is just one gram uh centimeter
+ 
+
+ align:start position:0%
+really is just one gram uh centimeter
+squared per second squared in those CGS
+
+ align:start position:0%
+squared per second squared in those CGS
+ 
+
+ align:start position:0%
+squared per second squared in those CGS
+units H is incredibly small it's
+
+ align:start position:0%
+units H is incredibly small it's
+ 
+
+ align:start position:0%
+units H is incredibly small it's
+exponentially tiny in those natural
+
+ align:start position:0%
+exponentially tiny in those natural
+ 
+
+ align:start position:0%
+exponentially tiny in those natural
+units for kind of human scaled affairs
+
+ align:start position:0%
+units for kind of human scaled affairs
+ 
+
+ align:start position:0%
+units for kind of human scaled affairs
+so H is small if we consider for example
+
+ align:start position:0%
+so H is small if we consider for example
+ 
+
+ align:start position:0%
+so H is small if we consider for example
+drop a single grape
+
+ align:start position:0%
+drop a single grape
+ 
+
+ align:start position:0%
+drop a single grape
+from a height of five centimeters
+
+ align:start position:0%
+from a height of five centimeters
+ 
+
+ align:start position:0%
+from a height of five centimeters
+roughly two inches and then ask what's
+
+ align:start position:0%
+roughly two inches and then ask what's
+ 
+
+ align:start position:0%
+roughly two inches and then ask what's
+the kinetic energy that grape will
+
+ align:start position:0%
+the kinetic energy that grape will
+ 
+
+ align:start position:0%
+the kinetic energy that grape will
+acquire over that very short Journey let
+
+ align:start position:0%
+acquire over that very short Journey let
+ 
+
+ align:start position:0%
+acquire over that very short Journey let
+the grape fall from rest a total of five
+
+ align:start position:0%
+the grape fall from rest a total of five
+ 
+
+ align:start position:0%
+the grape fall from rest a total of five
+centimeters multiply its acquired
+
+ align:start position:0%
+centimeters multiply its acquired
+ 
+
+ align:start position:0%
+centimeters multiply its acquired
+kinetic energy times the duration during
+
+ align:start position:0%
+kinetic energy times the duration during
+ 
+
+ align:start position:0%
+kinetic energy times the duration during
+which it was falling roughly a second or
+
+ align:start position:0%
+which it was falling roughly a second or
+ 
+
+ align:start position:0%
+which it was falling roughly a second or
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and yet an enormous amount of energy
+
+ align:start position:0%
+and yet an enormous amount of energy
+ 
+
+ align:start position:0%
+and yet an enormous amount of energy
+times time if we measure in this Planck
+
+ align:start position:0%
+times time if we measure in this Planck
+ 
+
+ align:start position:0%
+times time if we measure in this Planck
+uh in in these Planck units so just that
+
+ align:start position:0%
+uh in in these Planck units so just that
+ 
+
+ align:start position:0%
+uh in in these Planck units so just that
+tiny little grape falling for about one
+
+ align:start position:0%
+tiny little grape falling for about one
+ 
+
+ align:start position:0%
+tiny little grape falling for about one
+second from roughly two inches high has
+
+ align:start position:0%
+second from roughly two inches high has
+ 
+
+ align:start position:0%
+second from roughly two inches high has
+10 to the 28 of plant units of energy
+
+ align:start position:0%
+10 to the 28 of plant units of energy
+ 
+
+ align:start position:0%
+10 to the 28 of plant units of energy
+time some of you might know that this
+
+ align:start position:0%
+time some of you might know that this
+ 
+
+ align:start position:0%
+time some of you might know that this
+this particular combination of units and
+
+ align:start position:0%
+this particular combination of units and
+ 
+
+ align:start position:0%
+this particular combination of units and
+energy times a Time unit Eric's seconds
+
+ align:start position:0%
+energy times a Time unit Eric's seconds
+ 
+
+ align:start position:0%
+energy times a Time unit Eric's seconds
+is also the units in which we measure
+
+ align:start position:0%
+is also the units in which we measure
+ 
+
+ align:start position:0%
+is also the units in which we measure
+things like angular momentum what's the
+
+ align:start position:0%
+things like angular momentum what's the
+ 
+
+ align:start position:0%
+things like angular momentum what's the
+momentum of the sort of circular motion
+
+ align:start position:0%
+momentum of the sort of circular motion
+ 
+
+ align:start position:0%
+momentum of the sort of circular motion
+so again let's take a kind of household
+
+ align:start position:0%
+so again let's take a kind of household
+ 
+
+ align:start position:0%
+so again let's take a kind of household
+example instead of dropping a grape
+
+ align:start position:0%
+example instead of dropping a grape
+ 
+
+ align:start position:0%
+example instead of dropping a grape
+imagine some really annoying house fly
+
+ align:start position:0%
+imagine some really annoying house fly
+ 
+
+ align:start position:0%
+imagine some really annoying house fly
+they're kind of buzzing around your head
+
+ align:start position:0%
+they're kind of buzzing around your head
+ 
+
+ align:start position:0%
+they're kind of buzzing around your head
+at some radius of you know a couple
+
+ align:start position:0%
+at some radius of you know a couple
+ 
+
+ align:start position:0%
+at some radius of you know a couple
+centimeters from your head super
+
+ align:start position:0%
+centimeters from your head super
+ 
+
+ align:start position:0%
+centimeters from your head super
+annoying what's the angular momentum
+
+ align:start position:0%
+annoying what's the angular momentum
+ 
+
+ align:start position:0%
+annoying what's the angular momentum
+with that tiny little fly as it just
+
+ align:start position:0%
+with that tiny little fly as it just
+ 
+
+ align:start position:0%
+with that tiny little fly as it just
+buzzes kind of lazily around your head
+
+ align:start position:0%
+buzzes kind of lazily around your head
+ 
+
+ align:start position:0%
+buzzes kind of lazily around your head
+again it will have angular momentum
+
+ align:start position:0%
+again it will have angular momentum
+ 
+
+ align:start position:0%
+again it will have angular momentum
+exponentially large if we were to
+
+ align:start position:0%
+exponentially large if we were to
+ 
+
+ align:start position:0%
+exponentially large if we were to
+measure it in units of these of Planck's
+
+ align:start position:0%
+measure it in units of these of Planck's
+ 
+
+ align:start position:0%
+measure it in units of these of Planck's
+constant again around 10 to the 28th
+
+ align:start position:0%
+constant again around 10 to the 28th
+ 
+
+ align:start position:0%
+constant again around 10 to the 28th
+okay on which we expect to find strange
+
+ align:start position:0%
+okay on which we expect to find strange
+ 
+
+ align:start position:0%
+okay on which we expect to find strange
+Quantum features in our everyday life
+
+ align:start position:0%
+Quantum features in our everyday life
+ 
+
+ align:start position:0%
+Quantum features in our everyday life
+grapes house flies Automobiles and so on
+
+ align:start position:0%
+grapes house flies Automobiles and so on
+ 
+
+ align:start position:0%
+grapes house flies Automobiles and so on
+and yet plug could only make sense of
+
+ align:start position:0%
+and yet plug could only make sense of
+ 
+
+ align:start position:0%
+and yet plug could only make sense of
+that pgr data if you introduced this new
+
+ align:start position:0%
+that pgr data if you introduced this new
+ 
+
+ align:start position:0%
+that pgr data if you introduced this new
+scale this new constant very different
+
+ align:start position:0%
+scale this new constant very different
+ 
+
+ align:start position:0%
+scale this new constant very different
+from Human Experience and yet not zero
+
+ align:start position:0%
+from Human Experience and yet not zero
+ 
+
+ align:start position:0%
+from Human Experience and yet not zero
+some finite value even if it's small in
+
+ align:start position:0%
+some finite value even if it's small in
+ 
+
+ align:start position:0%
+some finite value even if it's small in
+our human terms
+
+ align:start position:0%
+our human terms
+ 
+
+ align:start position:0%
+our human terms
+now one of the readings you had for
+
+ align:start position:0%
+now one of the readings you had for
+ 
+
+ align:start position:0%
+now one of the readings you had for
+today was by the historian Thomas Kuhn
+
+ align:start position:0%
+today was by the historian Thomas Kuhn
+ 
+
+ align:start position:0%
+today was by the historian Thomas Kuhn
+Kuhn wrote a really fascinating book
+
+ align:start position:0%
+Kuhn wrote a really fascinating book
+ 
+
+ align:start position:0%
+Kuhn wrote a really fascinating book
+here's here's the book cover and the
+
+ align:start position:0%
+here's here's the book cover and the
+ 
+
+ align:start position:0%
+here's here's the book cover and the
+kind of uh article version that you had
+
+ align:start position:0%
+kind of uh article version that you had
+ 
+
+ align:start position:0%
+kind of uh article version that you had
+draws on the same body of work and I
+
+ align:start position:0%
+draws on the same body of work and I
+ 
+
+ align:start position:0%
+draws on the same body of work and I
+find this super fascinating so we know
+
+ align:start position:0%
+find this super fascinating so we know
+ 
+
+ align:start position:0%
+find this super fascinating so we know
+that Planck published that formula the
+
+ align:start position:0%
+that Planck published that formula the
+ 
+
+ align:start position:0%
+that Planck published that formula the
+one that I showed before uh where the
+
+ align:start position:0%
+one that I showed before uh where the
+ 
+
+ align:start position:0%
+one that I showed before uh where the
+frequencies you go like Nu cubed over e
+
+ align:start position:0%
+frequencies you go like Nu cubed over e
+ 
+
+ align:start position:0%
+frequencies you go like Nu cubed over e
+to the H Nu over KT minus one this we
+
+ align:start position:0%
+to the H Nu over KT minus one this we
+ 
+
+ align:start position:0%
+to the H Nu over KT minus one this we
+now call that the Planck Spectrum we use
+
+ align:start position:0%
+now call that the Planck Spectrum we use
+ 
+
+ align:start position:0%
+now call that the Planck Spectrum we use
+it all the time we know exactly when he
+
+ align:start position:0%
+it all the time we know exactly when he
+ 
+
+ align:start position:0%
+it all the time we know exactly when he
+wrote it down and published it but we
+
+ align:start position:0%
+wrote it down and published it but we
+ 
+
+ align:start position:0%
+wrote it down and published it but we
+still don't really know or still
+
+ align:start position:0%
+still don't really know or still
+ 
+
+ align:start position:0%
+still don't really know or still
+controversial is what did Planck think
+
+ align:start position:0%
+controversial is what did Planck think
+ 
+
+ align:start position:0%
+controversial is what did Planck think
+he was doing when he wrote down that
+
+ align:start position:0%
+he was doing when he wrote down that
+ 
+
+ align:start position:0%
+he was doing when he wrote down that
+expression how did Planck interpret his
+
+ align:start position:0%
+expression how did Planck interpret his
+ 
+
+ align:start position:0%
+expression how did Planck interpret his
+own equation here we are yet again
+
+ align:start position:0%
+own equation here we are yet again
+ 
+
+ align:start position:0%
+own equation here we are yet again
+thrown into this really I think
+
+ align:start position:0%
+thrown into this really I think
+ 
+
+ align:start position:0%
+thrown into this really I think
+delicious question of how a single
+
+ align:start position:0%
+delicious question of how a single
+ 
+
+ align:start position:0%
+delicious question of how a single
+equation could be subject to many often
+
+ align:start position:0%
+equation could be subject to many often
+ 
+
+ align:start position:0%
+equation could be subject to many often
+competing interpretations and was
+
+ align:start position:0%
+competing interpretations and was
+ 
+
+ align:start position:0%
+competing interpretations and was
+among the first to try to argue
+
+ align:start position:0%
+among the first to try to argue
+ 
+
+ align:start position:0%
+among the first to try to argue
+in particular that plugs own roots to
+
+ align:start position:0%
+in particular that plugs own roots to
+ 
+
+ align:start position:0%
+in particular that plugs own roots to
+that now very famous equation looked
+
+ align:start position:0%
+that now very famous equation looked
+ 
+
+ align:start position:0%
+that now very famous equation looked
+nothing like what we how we interpreted
+
+ align:start position:0%
+nothing like what we how we interpreted
+ 
+
+ align:start position:0%
+nothing like what we how we interpreted
+the result so when we derive plug's
+
+ align:start position:0%
+the result so when we derive plug's
+ 
+
+ align:start position:0%
+the result so when we derive plug's
+expression like for example in my own
+
+ align:start position:0%
+expression like for example in my own
+ 
+
+ align:start position:0%
+expression like for example in my own
+notes or any textbook you might you
+
+ align:start position:0%
+notes or any textbook you might you
+ 
+
+ align:start position:0%
+notes or any textbook you might you
+might look it up in a modern textbook we
+
+ align:start position:0%
+might look it up in a modern textbook we
+ 
+
+ align:start position:0%
+might look it up in a modern textbook we
+say we get Planck's result for that form
+
+ align:start position:0%
+say we get Planck's result for that form
+ 
+
+ align:start position:0%
+say we get Planck's result for that form
+for this spectral energy density by
+
+ align:start position:0%
+for this spectral energy density by
+ 
+
+ align:start position:0%
+for this spectral energy density by
+making a new conceptual leap by
+
+ align:start position:0%
+making a new conceptual leap by
+ 
+
+ align:start position:0%
+making a new conceptual leap by
+requiring that the energy exchange
+
+ align:start position:0%
+requiring that the energy exchange
+ 
+
+ align:start position:0%
+requiring that the energy exchange
+between matter and radiation can't take
+
+ align:start position:0%
+between matter and radiation can't take
+ 
+
+ align:start position:0%
+between matter and radiation can't take
+any old value it can't be 6 or 6.001 or
+
+ align:start position:0%
+any old value it can't be 6 or 6.001 or
+ 
+
+ align:start position:0%
+any old value it can't be 6 or 6.001 or
+6.002 in appropriate units but how to
+
+ align:start position:0%
+6.002 in appropriate units but how to
+ 
+
+ align:start position:0%
+6.002 in appropriate units but how to
+come chunked has to come quantized in
+
+ align:start position:0%
+come chunked has to come quantized in
+ 
+
+ align:start position:0%
+come chunked has to come quantized in
+these units of a particular size flux
+
+ align:start position:0%
+these units of a particular size flux
+ 
+
+ align:start position:0%
+these units of a particular size flux
+constant H times the frequency of the
+
+ align:start position:0%
+constant H times the frequency of the
+ 
+
+ align:start position:0%
+constant H times the frequency of the
+light involved rather than than treating
+
+ align:start position:0%
+light involved rather than than treating
+ 
+
+ align:start position:0%
+light involved rather than than treating
+the sort of energy exchange between
+
+ align:start position:0%
+the sort of energy exchange between
+ 
+
+ align:start position:0%
+the sort of energy exchange between
+matter and radiation as continuous the
+
+ align:start position:0%
+matter and radiation as continuous the
+ 
+
+ align:start position:0%
+matter and radiation as continuous the
+way we would if we were describing light
+
+ align:start position:0%
+way we would if we were describing light
+ 
+
+ align:start position:0%
+way we would if we were describing light
+for example as maxwellian waves it
+
+ align:start position:0%
+for example as maxwellian waves it
+ 
+
+ align:start position:0%
+for example as maxwellian waves it
+shouldn't matter what the frequency is
+
+ align:start position:0%
+shouldn't matter what the frequency is
+ 
+
+ align:start position:0%
+shouldn't matter what the frequency is
+of that wave we know how to calculate
+
+ align:start position:0%
+of that wave we know how to calculate
+ 
+
+ align:start position:0%
+of that wave we know how to calculate
+the energy associated with any process
+
+ align:start position:0%
+the energy associated with any process
+ 
+
+ align:start position:0%
+the energy associated with any process
+and there should be no limit no chunking
+
+ align:start position:0%
+and there should be no limit no chunking
+ 
+
+ align:start position:0%
+and there should be no limit no chunking
+or quantization
+
+ align:start position:0%
+or quantization
+ 
+
+ align:start position:0%
+or quantization
+so Chrome was asking very very directly
+
+ align:start position:0%
+so Chrome was asking very very directly
+ 
+
+ align:start position:0%
+so Chrome was asking very very directly
+did Mark's Planck think that's what he
+
+ align:start position:0%
+did Mark's Planck think that's what he
+ 
+
+ align:start position:0%
+did Mark's Planck think that's what he
+was doing in around 1900 when he
+
+ align:start position:0%
+was doing in around 1900 when he
+ 
+
+ align:start position:0%
+was doing in around 1900 when he
+introduced what we now call Planck's
+
+ align:start position:0%
+introduced what we now call Planck's
+ 
+
+ align:start position:0%
+introduced what we now call Planck's
+formula and so just to give the
+
+ align:start position:0%
+formula and so just to give the
+ 
+
+ align:start position:0%
+formula and so just to give the
+highlight of kuhn's article it's a
+
+ align:start position:0%
+highlight of kuhn's article it's a
+ 
+
+ align:start position:0%
+highlight of kuhn's article it's a
+complicated article if it was confusing
+
+ align:start position:0%
+complicated article if it was confusing
+ 
+
+ align:start position:0%
+complicated article if it was confusing
+that's okay I want to talk through what
+
+ align:start position:0%
+that's okay I want to talk through what
+ 
+
+ align:start position:0%
+that's okay I want to talk through what
+I consider the kind of headline news the
+
+ align:start position:0%
+I consider the kind of headline news the
+ 
+
+ align:start position:0%
+I consider the kind of headline news the
+main takeaways from Coons architecture
+
+ align:start position:0%
+main takeaways from Coons architecture
+ 
+
+ align:start position:0%
+main takeaways from Coons architecture
+it's a very complicated writing here's
+
+ align:start position:0%
+it's a very complicated writing here's
+ 
+
+ align:start position:0%
+it's a very complicated writing here's
+what I consider the biggest Revelations
+
+ align:start position:0%
+what I consider the biggest Revelations
+ 
+
+ align:start position:0%
+what I consider the biggest Revelations
+so argues that in Plants original
+
+ align:start position:0%
+so argues that in Plants original
+ 
+
+ align:start position:0%
+so argues that in Plants original
+derivation this now very famous
+
+ align:start position:0%
+derivation this now very famous
+ 
+
+ align:start position:0%
+derivation this now very famous
+canonical formula Planck fixed the total
+
+ align:start position:0%
+canonical formula Planck fixed the total
+ 
+
+ align:start position:0%
+canonical formula Planck fixed the total
+energy of the system all the Imagine
+
+ align:start position:0%
+energy of the system all the Imagine
+ 
+
+ align:start position:0%
+energy of the system all the Imagine
+little kind of resonators or kind of
+
+ align:start position:0%
+little kind of resonators or kind of
+ 
+
+ align:start position:0%
+little kind of resonators or kind of
+Make-Believe molecules in that black
+
+ align:start position:0%
+Make-Believe molecules in that black
+ 
+
+ align:start position:0%
+Make-Believe molecules in that black
+body he fixed the total energy of that
+
+ align:start position:0%
+body he fixed the total energy of that
+ 
+
+ align:start position:0%
+body he fixed the total energy of that
+system to be an integer number of these
+
+ align:start position:0%
+system to be an integer number of these
+ 
+
+ align:start position:0%
+system to be an integer number of these
+units H new but he according to
+
+ align:start position:0%
+units H new but he according to
+ 
+
+ align:start position:0%
+units H new but he according to
+plant did not fix each actual resonator
+
+ align:start position:0%
+plant did not fix each actual resonator
+ 
+
+ align:start position:0%
+plant did not fix each actual resonator
+each each degree of freedom of that
+
+ align:start position:0%
+each each degree of freedom of that
+ 
+
+ align:start position:0%
+each each degree of freedom of that
+system to separately be have uh this
+
+ align:start position:0%
+system to separately be have uh this
+ 
+
+ align:start position:0%
+system to separately be have uh this
+value H Nu so that plaque was fixing the
+
+ align:start position:0%
+value H Nu so that plaque was fixing the
+ 
+
+ align:start position:0%
+value H Nu so that plaque was fixing the
+total energy for convenience as a kind
+
+ align:start position:0%
+total energy for convenience as a kind
+ 
+
+ align:start position:0%
+total energy for convenience as a kind
+of accounting trick not fixing the unit
+
+ align:start position:0%
+of accounting trick not fixing the unit
+ 
+
+ align:start position:0%
+of accounting trick not fixing the unit
+of each moving part
+
+ align:start position:0%
+of each moving part
+ 
+
+ align:start position:0%
+of each moving part
+whereas today again as I go through in
+
+ align:start position:0%
+whereas today again as I go through in
+ 
+
+ align:start position:0%
+whereas today again as I go through in
+some details in those notes we derive
+
+ align:start position:0%
+some details in those notes we derive
+ 
+
+ align:start position:0%
+some details in those notes we derive
+plant's result by fixing the allowable
+
+ align:start position:0%
+plant's result by fixing the allowable
+ 
+
+ align:start position:0%
+plant's result by fixing the allowable
+energy of each individual part each sort
+
+ align:start position:0%
+energy of each individual part each sort
+ 
+
+ align:start position:0%
+energy of each individual part each sort
+of e sub I so to speak okay in plug's
+
+ align:start position:0%
+of e sub I so to speak okay in plug's
+ 
+
+ align:start position:0%
+of e sub I so to speak okay in plug's
+description as reconstruction uh
+
+ align:start position:0%
+description as reconstruction uh
+ 
+
+ align:start position:0%
+description as reconstruction uh
+the energies for each of these
+
+ align:start position:0%
+the energies for each of these
+ 
+
+ align:start position:0%
+the energies for each of these
+subsystems each kind of moving part
+
+ align:start position:0%
+subsystems each kind of moving part
+ 
+
+ align:start position:0%
+subsystems each kind of moving part
+according to plug's original derivation
+
+ align:start position:0%
+according to plug's original derivation
+ 
+
+ align:start position:0%
+according to plug's original derivation
+was actually assumed to fall within some
+
+ align:start position:0%
+was actually assumed to fall within some
+ 
+
+ align:start position:0%
+was actually assumed to fall within some
+continuous range between e and e plus
+
+ align:start position:0%
+continuous range between e and e plus
+ 
+
+ align:start position:0%
+continuous range between e and e plus
+Delta e not fixed kind of you know
+
+ align:start position:0%
+Delta e not fixed kind of you know
+ 
+
+ align:start position:0%
+Delta e not fixed kind of you know
+snapping in place in these quantized
+
+ align:start position:0%
+snapping in place in these quantized
+ 
+
+ align:start position:0%
+snapping in place in these quantized
+units
+
+ align:start position:0%
+units
+ 
+
+ align:start position:0%
+units
+so goes on it's a very complicated
+
+ align:start position:0%
+so goes on it's a very complicated
+ 
+
+ align:start position:0%
+so goes on it's a very complicated
+argument the book is even more
+
+ align:start position:0%
+argument the book is even more
+ 
+
+ align:start position:0%
+argument the book is even more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+but according to Coon's analysis plant
+
+ align:start position:0%
+but according to Coon's analysis plant
+ 
+
+ align:start position:0%
+but according to Coon's analysis plant
+uses bins of size we might call it uses
+
+ align:start position:0%
+uses bins of size we might call it uses
+ 
+
+ align:start position:0%
+uses bins of size we might call it uses
+the Greek letter Epsilon bins of size H
+
+ align:start position:0%
+the Greek letter Epsilon bins of size H
+ 
+
+ align:start position:0%
+the Greek letter Epsilon bins of size H
+Nu for his accounting but again only to
+
+ align:start position:0%
+Nu for his accounting but again only to
+ 
+
+ align:start position:0%
+Nu for his accounting but again only to
+say how many of these sort of resonators
+
+ align:start position:0%
+say how many of these sort of resonators
+ 
+
+ align:start position:0%
+say how many of these sort of resonators
+or oscillators again roughly speaking
+
+ align:start position:0%
+or oscillators again roughly speaking
+ 
+
+ align:start position:0%
+or oscillators again roughly speaking
+moving Parts how many of them had
+
+ align:start position:0%
+moving Parts how many of them had
+ 
+
+ align:start position:0%
+moving Parts how many of them had
+energies within you know within zero and
+
+ align:start position:0%
+energies within you know within zero and
+ 
+
+ align:start position:0%
+energies within you know within zero and
+Epsilon within one unit between one and
+
+ align:start position:0%
+Epsilon within one unit between one and
+ 
+
+ align:start position:0%
+Epsilon within one unit between one and
+two units not that they had to have
+
+ align:start position:0%
+two units not that they had to have
+ 
+
+ align:start position:0%
+two units not that they had to have
+exactly one or two units the way we'd
+
+ align:start position:0%
+exactly one or two units the way we'd
+ 
+
+ align:start position:0%
+exactly one or two units the way we'd
+say today
+
+ align:start position:0%
+say today
+ 
+
+ align:start position:0%
+say today
+moreover a goes on again he does
+
+ align:start position:0%
+moreover a goes on again he does
+ 
+
+ align:start position:0%
+moreover a goes on again he does
+this even in more detail in this longer
+
+ align:start position:0%
+this even in more detail in this longer
+ 
+
+ align:start position:0%
+this even in more detail in this longer
+book years later six years later flock
+
+ align:start position:0%
+book years later six years later flock
+ 
+
+ align:start position:0%
+book years later six years later flock
+was giving lectures at the University
+
+ align:start position:0%
+was giving lectures at the University
+ 
+
+ align:start position:0%
+was giving lectures at the University
+about this topic and he still spoke in
+
+ align:start position:0%
+about this topic and he still spoke in
+ 
+
+ align:start position:0%
+about this topic and he still spoke in
+his lecture notes of a kind of
+
+ align:start position:0%
+his lecture notes of a kind of
+ 
+
+ align:start position:0%
+his lecture notes of a kind of
+continuous rather than quantized energy
+
+ align:start position:0%
+continuous rather than quantized energy
+ 
+
+ align:start position:0%
+continuous rather than quantized energy
+exchange it wasn't just a kind of
+
+ align:start position:0%
+exchange it wasn't just a kind of
+ 
+
+ align:start position:0%
+exchange it wasn't just a kind of
+momentary lapse in December of 1900
+
+ align:start position:0%
+momentary lapse in December of 1900
+ 
+
+ align:start position:0%
+momentary lapse in December of 1900
+Argus Thomas it was years and years
+
+ align:start position:0%
+Argus Thomas it was years and years
+ 
+
+ align:start position:0%
+Argus Thomas it was years and years
+during which Planck thought about his
+
+ align:start position:0%
+during which Planck thought about his
+ 
+
+ align:start position:0%
+during which Planck thought about his
+own equation quite differently than the
+
+ align:start position:0%
+own equation quite differently than the
+ 
+
+ align:start position:0%
+own equation quite differently than the
+way we would today even though the
+
+ align:start position:0%
+way we would today even though the
+ 
+
+ align:start position:0%
+way we would today even though the
+equation itself hasn't changed now
+
+ align:start position:0%
+equation itself hasn't changed now
+ 
+
+ align:start position:0%
+equation itself hasn't changed now
+that's Coon's argument he has lots of
+
+ align:start position:0%
+that's Coon's argument he has lots of
+ 
+
+ align:start position:0%
+that's Coon's argument he has lots of
+evidence that I found very interesting
+
+ align:start position:0%
+evidence that I found very interesting
+ 
+
+ align:start position:0%
+evidence that I found very interesting
+it's also really complicated there's a
+
+ align:start position:0%
+it's also really complicated there's a
+ 
+
+ align:start position:0%
+it's also really complicated there's a
+fascinating much more recent article uh
+
+ align:start position:0%
+fascinating much more recent article uh
+ 
+
+ align:start position:0%
+fascinating much more recent article uh
+by the physicist and historian Michael
+
+ align:start position:0%
+by the physicist and historian Michael
+ 
+
+ align:start position:0%
+by the physicist and historian Michael
+nauenberg you can look up uh that
+
+ align:start position:0%
+nauenberg you can look up uh that
+ 
+
+ align:start position:0%
+nauenberg you can look up uh that
+actually draws sort of the opposite
+
+ align:start position:0%
+actually draws sort of the opposite
+ 
+
+ align:start position:0%
+actually draws sort of the opposite
+conclusion that plug had a much more
+
+ align:start position:0%
+conclusion that plug had a much more
+ 
+
+ align:start position:0%
+conclusion that plug had a much more
+similar notion of what we have today
+
+ align:start position:0%
+similar notion of what we have today
+ 
+
+ align:start position:0%
+similar notion of what we have today
+even as always 1900 it's really
+
+ align:start position:0%
+even as always 1900 it's really
+ 
+
+ align:start position:0%
+even as always 1900 it's really
+complicated so I don't know who of these
+
+ align:start position:0%
+complicated so I don't know who of these
+ 
+
+ align:start position:0%
+complicated so I don't know who of these
+analysts is right what I do know is it
+
+ align:start position:0%
+analysts is right what I do know is it
+ 
+
+ align:start position:0%
+analysts is right what I do know is it
+was really really not clear even to
+
+ align:start position:0%
+was really really not clear even to
+ 
+
+ align:start position:0%
+was really really not clear even to
+plant's own contemporaries what exactly
+
+ align:start position:0%
+plant's own contemporaries what exactly
+ 
+
+ align:start position:0%
+plant's own contemporaries what exactly
+to make of this new formula
+
+ align:start position:0%
+to make of this new formula
+ 
+
+ align:start position:0%
+to make of this new formula
+and plonk himself was not shy about that
+
+ align:start position:0%
+and plonk himself was not shy about that
+ 
+
+ align:start position:0%
+and plonk himself was not shy about that
+he wrote to a colleague decades later 31
+
+ align:start position:0%
+he wrote to a colleague decades later 31
+ 
+
+ align:start position:0%
+he wrote to a colleague decades later 31
+years after deriving his now famous
+
+ align:start position:0%
+years after deriving his now famous
+ 
+
+ align:start position:0%
+years after deriving his now famous
+equation he wrote what I did back in
+
+ align:start position:0%
+equation he wrote what I did back in
+ 
+
+ align:start position:0%
+equation he wrote what I did back in
+1900 can be described as simply an act
+
+ align:start position:0%
+1900 can be described as simply an act
+ 
+
+ align:start position:0%
+1900 can be described as simply an act
+of desperation he was trying to match
+
+ align:start position:0%
+of desperation he was trying to match
+ 
+
+ align:start position:0%
+of desperation he was trying to match
+the updated data from the PTR he knew
+
+ align:start position:0%
+the updated data from the PTR he knew
+ 
+
+ align:start position:0%
+the updated data from the PTR he knew
+that curve couldn't just keep Rising
+
+ align:start position:0%
+that curve couldn't just keep Rising
+ 
+
+ align:start position:0%
+that curve couldn't just keep Rising
+forever he was desperate and choosing
+
+ align:start position:0%
+forever he was desperate and choosing
+ 
+
+ align:start position:0%
+forever he was desperate and choosing
+these bins of fixed quantized size plan
+
+ align:start position:0%
+these bins of fixed quantized size plan
+ 
+
+ align:start position:0%
+these bins of fixed quantized size plan
+continued was purely a formal assumption
+
+ align:start position:0%
+continued was purely a formal assumption
+ 
+
+ align:start position:0%
+continued was purely a formal assumption
+and I really did not give it much
+
+ align:start position:0%
+and I really did not give it much
+ 
+
+ align:start position:0%
+and I really did not give it much
+thought which is interesting
+
+ align:start position:0%
+thought which is interesting
+ 
+
+ align:start position:0%
+thought which is interesting
+so let me pause there that's what I want
+
+ align:start position:0%
+so let me pause there that's what I want
+ 
+
+ align:start position:0%
+so let me pause there that's what I want
+to share about Planck and the black body
+
+ align:start position:0%
+to share about Planck and the black body
+ 
+
+ align:start position:0%
+to share about Planck and the black body
+Spectrum any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Jade asked a good question in the
+
+ align:start position:0%
+uh Jade asked a good question in the
+ 
+
+ align:start position:0%
+uh Jade asked a good question in the
+chat how do they measure the spectral
+
+ align:start position:0%
+chat how do they measure the spectral
+ 
+
+ align:start position:0%
+chat how do they measure the spectral
+energy density very good so the short
+
+ align:start position:0%
+energy density very good so the short
+ 
+
+ align:start position:0%
+energy density very good so the short
+answer is this is the kind of thing that
+
+ align:start position:0%
+answer is this is the kind of thing that
+ 
+
+ align:start position:0%
+answer is this is the kind of thing that
+the that the experimentalists at the pgr
+
+ align:start position:0%
+the that the experimentalists at the pgr
+ 
+
+ align:start position:0%
+the that the experimentalists at the pgr
+were very very good at so they could use
+
+ align:start position:0%
+were very very good at so they could use
+ 
+
+ align:start position:0%
+were very very good at so they could use
+basically things like
+
+ align:start position:0%
+basically things like
+ 
+
+ align:start position:0%
+basically things like
+um a diffraction gratings and they might
+
+ align:start position:0%
+um a diffraction gratings and they might
+ 
+
+ align:start position:0%
+um a diffraction gratings and they might
+have even had access to to fine prisons
+
+ align:start position:0%
+have even had access to to fine prisons
+ 
+
+ align:start position:0%
+have even had access to to fine prisons
+to to measure very specific energy
+
+ align:start position:0%
+to to measure very specific energy
+ 
+
+ align:start position:0%
+to to measure very specific energy
+outputs in very specific um wavelength
+
+ align:start position:0%
+outputs in very specific um wavelength
+ 
+
+ align:start position:0%
+outputs in very specific um wavelength
+bids so that that's the kind of thing
+
+ align:start position:0%
+bids so that that's the kind of thing
+ 
+
+ align:start position:0%
+bids so that that's the kind of thing
+they were getting very good at I think
+
+ align:start position:0%
+they were getting very good at I think
+ 
+
+ align:start position:0%
+they were getting very good at I think
+they did mostly use diffraction rate so
+
+ align:start position:0%
+they did mostly use diffraction rate so
+ 
+
+ align:start position:0%
+they did mostly use diffraction rate so
+I'm not positive so they could they had
+
+ align:start position:0%
+I'm not positive so they could they had
+ 
+
+ align:start position:0%
+I'm not positive so they could they had
+a cavity a kind of evacuated chamber
+
+ align:start position:0%
+a cavity a kind of evacuated chamber
+ 
+
+ align:start position:0%
+a cavity a kind of evacuated chamber
+they could heat up kind of in an oven
+
+ align:start position:0%
+they could heat up kind of in an oven
+ 
+
+ align:start position:0%
+they could heat up kind of in an oven
+with a little hole in the side so mostly
+
+ align:start position:0%
+with a little hole in the side so mostly
+ 
+
+ align:start position:0%
+with a little hole in the side so mostly
+had this empty space that would heat up
+
+ align:start position:0%
+had this empty space that would heat up
+ 
+
+ align:start position:0%
+had this empty space that would heat up
+and they would let a little a cavity let
+
+ align:start position:0%
+and they would let a little a cavity let
+ 
+
+ align:start position:0%
+and they would let a little a cavity let
+a little bit of this light sneak out a
+
+ align:start position:0%
+a little bit of this light sneak out a
+ 
+
+ align:start position:0%
+a little bit of this light sneak out a
+little window
+
+ align:start position:0%
+little window
+ 
+
+ align:start position:0%
+little window
+uh and that's what was taking the place
+
+ align:start position:0%
+uh and that's what was taking the place
+ 
+
+ align:start position:0%
+uh and that's what was taking the place
+of this black body so no light was
+
+ align:start position:0%
+of this black body so no light was
+ 
+
+ align:start position:0%
+of this black body so no light was
+coming in onto that box it was sealed up
+
+ align:start position:0%
+coming in onto that box it was sealed up
+ 
+
+ align:start position:0%
+coming in onto that box it was sealed up
+like a kind of metal trap cavity a
+
+ align:start position:0%
+like a kind of metal trap cavity a
+ 
+
+ align:start position:0%
+like a kind of metal trap cavity a
+little light escapes to a little
+
+ align:start position:0%
+little light escapes to a little
+ 
+
+ align:start position:0%
+little light escapes to a little
+porthole and so what you should be
+
+ align:start position:0%
+porthole and so what you should be
+ 
+
+ align:start position:0%
+porthole and so what you should be
+measuring is only the light due to this
+
+ align:start position:0%
+measuring is only the light due to this
+ 
+
+ align:start position:0%
+measuring is only the light due to this
+kind of thermal radiation because
+
+ align:start position:0%
+kind of thermal radiation because
+ 
+
+ align:start position:0%
+kind of thermal radiation because
+nothing is reflecting on that stuff
+
+ align:start position:0%
+nothing is reflecting on that stuff
+ 
+
+ align:start position:0%
+nothing is reflecting on that stuff
+that's how they made the black body in
+
+ align:start position:0%
+that's how they made the black body in
+ 
+
+ align:start position:0%
+that's how they made the black body in
+in real life in the actual experience
+
+ align:start position:0%
+in real life in the actual experience
+ 
+
+ align:start position:0%
+in real life in the actual experience
+then they could subject that light that
+
+ align:start position:0%
+then they could subject that light that
+ 
+
+ align:start position:0%
+then they could subject that light that
+came out to very fine measurements by
+
+ align:start position:0%
+came out to very fine measurements by
+ 
+
+ align:start position:0%
+came out to very fine measurements by
+splitting up into into its colors with
+
+ align:start position:0%
+splitting up into into its colors with
+ 
+
+ align:start position:0%
+splitting up into into its colors with
+with things like diffraction gratings or
+
+ align:start position:0%
+with things like diffraction gratings or
+ 
+
+ align:start position:0%
+with things like diffraction gratings or
+prisms
+
+ align:start position:0%
+prisms
+ 
+
+ align:start position:0%
+prisms
+and then and then measure let's see they
+
+ align:start position:0%
+and then and then measure let's see they
+ 
+
+ align:start position:0%
+and then and then measure let's see they
+must have measured the intensity of the
+
+ align:start position:0%
+must have measured the intensity of the
+ 
+
+ align:start position:0%
+must have measured the intensity of the
+brightness they must have had some kind
+
+ align:start position:0%
+brightness they must have had some kind
+ 
+
+ align:start position:0%
+brightness they must have had some kind
+of photo meters and I'm not sure how
+
+ align:start position:0%
+of photo meters and I'm not sure how
+ 
+
+ align:start position:0%
+of photo meters and I'm not sure how
+they did that we can look it up but they
+
+ align:start position:0%
+they did that we can look it up but they
+ 
+
+ align:start position:0%
+they did that we can look it up but they
+were good at measuring very finely
+
+ align:start position:0%
+were good at measuring very finely
+ 
+
+ align:start position:0%
+were good at measuring very finely
+detailed um uh wavelengths in fact
+
+ align:start position:0%
+detailed um uh wavelengths in fact
+ 
+
+ align:start position:0%
+detailed um uh wavelengths in fact
+they're getting better in the core over
+
+ align:start position:0%
+they're getting better in the core over
+ 
+
+ align:start position:0%
+they're getting better in the core over
+the 1890s in various parts of the
+
+ align:start position:0%
+the 1890s in various parts of the
+ 
+
+ align:start position:0%
+the 1890s in various parts of the
+spectrum they knew some of the early
+
+ align:start position:0%
+spectrum they knew some of the early
+ 
+
+ align:start position:0%
+spectrum they knew some of the early
+data points early on the ones that
+
+ align:start position:0%
+data points early on the ones that
+ 
+
+ align:start position:0%
+data points early on the ones that
+matched this Rising curve that looks
+
+ align:start position:0%
+matched this Rising curve that looks
+ 
+
+ align:start position:0%
+matched this Rising curve that looks
+like it would lead to this runaway
+
+ align:start position:0%
+like it would lead to this runaway
+ 
+
+ align:start position:0%
+like it would lead to this runaway
+energy this so-called ultraviolet
+
+ align:start position:0%
+energy this so-called ultraviolet
+ 
+
+ align:start position:0%
+energy this so-called ultraviolet
+catastrophe the earliest data were at
+
+ align:start position:0%
+catastrophe the earliest data were at
+ 
+
+ align:start position:0%
+catastrophe the earliest data were at
+low wavelengths uh small frequencies we
+
+ align:start position:0%
+low wavelengths uh small frequencies we
+ 
+
+ align:start position:0%
+low wavelengths uh small frequencies we
+really did go like Nu squared and what
+
+ align:start position:0%
+really did go like Nu squared and what
+ 
+
+ align:start position:0%
+really did go like Nu squared and what
+was most important as everyone knew was
+
+ align:start position:0%
+was most important as everyone knew was
+ 
+
+ align:start position:0%
+was most important as everyone knew was
+to measure the other end of the spectrum
+
+ align:start position:0%
+to measure the other end of the spectrum
+ 
+
+ align:start position:0%
+to measure the other end of the spectrum
+that couldn't keep Rising forever and
+
+ align:start position:0%
+that couldn't keep Rising forever and
+ 
+
+ align:start position:0%
+that couldn't keep Rising forever and
+the PTR researchers like Lumber and
+
+ align:start position:0%
+the PTR researchers like Lumber and
+ 
+
+ align:start position:0%
+the PTR researchers like Lumber and
+Princeton were getting more and more
+
+ align:start position:0%
+Princeton were getting more and more
+ 
+
+ align:start position:0%
+Princeton were getting more and more
+data at the other part of the spectrum
+
+ align:start position:0%
+data at the other part of the spectrum
+ 
+
+ align:start position:0%
+data at the other part of the spectrum
+at shorter wavelengths higher
+
+ align:start position:0%
+at shorter wavelengths higher
+ 
+
+ align:start position:0%
+at shorter wavelengths higher
+frequencies and watching just how that
+
+ align:start position:0%
+frequencies and watching just how that
+ 
+
+ align:start position:0%
+frequencies and watching just how that
+curve began to fall what we now would
+
+ align:start position:0%
+curve began to fall what we now would
+ 
+
+ align:start position:0%
+curve began to fall what we now would
+recognize as this kind of exponential
+
+ align:start position:0%
+recognize as this kind of exponential
+ 
+
+ align:start position:0%
+recognize as this kind of exponential
+tale so they were doing that again with
+
+ align:start position:0%
+tale so they were doing that again with
+ 
+
+ align:start position:0%
+tale so they were doing that again with
+with with more and more precision
+
+ align:start position:0%
+with with more and more precision
+ 
+
+ align:start position:0%
+with with more and more precision
+excellent question Johan asks a very
+
+ align:start position:0%
+excellent question Johan asks a very
+ 
+
+ align:start position:0%
+excellent question Johan asks a very
+good question how to do that with a
+
+ align:start position:0%
+good question how to do that with a
+ 
+
+ align:start position:0%
+good question how to do that with a
+graph and calculator he was no Cambridge
+
+ align:start position:0%
+graph and calculator he was no Cambridge
+ 
+
+ align:start position:0%
+graph and calculator he was no Cambridge
+Wrangler but Planck was a pretty well
+
+ align:start position:0%
+Wrangler but Planck was a pretty well
+ 
+
+ align:start position:0%
+Wrangler but Planck was a pretty well
+trained mathematical physicist it was
+
+ align:start position:0%
+trained mathematical physicist it was
+ 
+
+ align:start position:0%
+trained mathematical physicist it was
+painstack and the real factors is
+
+ align:start position:0%
+painstack and the real factors is
+ 
+
+ align:start position:0%
+painstack and the real factors is
+painstaking and also how did he come up
+
+ align:start position:0%
+painstaking and also how did he come up
+ 
+
+ align:start position:0%
+painstaking and also how did he come up
+with these particular forms or his
+
+ align:start position:0%
+with these particular forms or his
+ 
+
+ align:start position:0%
+with these particular forms or his
+equations you know you can read Thomas
+
+ align:start position:0%
+equations you know you can read Thomas
+ 
+
+ align:start position:0%
+equations you know you can read Thomas
+Coons like 400 page monograph which I
+
+ align:start position:0%
+Coons like 400 page monograph which I
+ 
+
+ align:start position:0%
+Coons like 400 page monograph which I
+have forced rather encouraged some of
+
+ align:start position:0%
+have forced rather encouraged some of
+ 
+
+ align:start position:0%
+have forced rather encouraged some of
+the Tas to do directly uh I would say
+
+ align:start position:0%
+the Tas to do directly uh I would say
+ 
+
+ align:start position:0%
+the Tas to do directly uh I would say
+encouraged uh I reread it every few
+
+ align:start position:0%
+encouraged uh I reread it every few
+ 
+
+ align:start position:0%
+encouraged uh I reread it every few
+years it's really complicated I mean
+
+ align:start position:0%
+years it's really complicated I mean
+ 
+
+ align:start position:0%
+years it's really complicated I mean
+what was plant doing what was doing when
+
+ align:start position:0%
+what was plant doing what was doing when
+ 
+
+ align:start position:0%
+what was plant doing what was doing when
+what did he think he was doing that is
+
+ align:start position:0%
+what did he think he was doing that is
+ 
+
+ align:start position:0%
+what did he think he was doing that is
+really complicated and other really
+
+ align:start position:0%
+really complicated and other really
+ 
+
+ align:start position:0%
+really complicated and other really
+smart dedicated researchers like Michael
+
+ align:start position:0%
+smart dedicated researchers like Michael
+ 
+
+ align:start position:0%
+smart dedicated researchers like Michael
+nalmer come back to some of the same
+
+ align:start position:0%
+nalmer come back to some of the same
+ 
+
+ align:start position:0%
+nalmer come back to some of the same
+materials the same obscure lecture notes
+
+ align:start position:0%
+materials the same obscure lecture notes
+ 
+
+ align:start position:0%
+materials the same obscure lecture notes
+the same Publications he says no look
+
+ align:start position:0%
+the same Publications he says no look
+ 
+
+ align:start position:0%
+the same Publications he says no look
+very carefully the equation 25 B he does
+
+ align:start position:0%
+very carefully the equation 25 B he does
+ 
+
+ align:start position:0%
+very carefully the equation 25 B he does
+something else there it gets really
+
+ align:start position:0%
+something else there it gets really
+ 
+
+ align:start position:0%
+something else there it gets really
+really hard
+
+ align:start position:0%
+really hard
+ 
+
+ align:start position:0%
+really hard
+what is clear as I'll say actually the
+
+ align:start position:0%
+what is clear as I'll say actually the
+ 
+
+ align:start position:0%
+what is clear as I'll say actually the
+next section is that some other of
+
+ align:start position:0%
+next section is that some other of
+ 
+
+ align:start position:0%
+next section is that some other of
+plant's own contemporaries like it's
+
+ align:start position:0%
+plant's own contemporaries like it's
+ 
+
+ align:start position:0%
+plant's own contemporaries like it's
+still a very young Albert Einstein
+
+ align:start position:0%
+still a very young Albert Einstein
+ 
+
+ align:start position:0%
+still a very young Albert Einstein
+Einstein was convinced that plug
+
+ align:start position:0%
+Einstein was convinced that plug
+ 
+
+ align:start position:0%
+Einstein was convinced that plug
+actually hadn't gone far enough so it's
+
+ align:start position:0%
+actually hadn't gone far enough so it's
+ 
+
+ align:start position:0%
+actually hadn't gone far enough so it's
+not just historians who debate this the
+
+ align:start position:0%
+not just historians who debate this the
+ 
+
+ align:start position:0%
+not just historians who debate this the
+better part of a century later after
+
+ align:start position:0%
+better part of a century later after
+ 
+
+ align:start position:0%
+better part of a century later after
+plonk even some contemporaries who are
+
+ align:start position:0%
+plonk even some contemporaries who are
+ 
+
+ align:start position:0%
+plonk even some contemporaries who are
+trying to make sense of Planck's on
+
+ align:start position:0%
+trying to make sense of Planck's on
+ 
+
+ align:start position:0%
+trying to make sense of Planck's on
+argument thought that plant's reasoning
+
+ align:start position:0%
+argument thought that plant's reasoning
+ 
+
+ align:start position:0%
+argument thought that plant's reasoning
+was at best muddled and may be different
+
+ align:start position:0%
+was at best muddled and may be different
+ 
+
+ align:start position:0%
+was at best muddled and may be different
+from what they themselves thought about
+
+ align:start position:0%
+from what they themselves thought about
+ 
+
+ align:start position:0%
+from what they themselves thought about
+and that's why I like that letter that
+
+ align:start position:0%
+and that's why I like that letter that
+ 
+
+ align:start position:0%
+and that's why I like that letter that
+plot wrote in the early 30s saying yeah
+
+ align:start position:0%
+plot wrote in the early 30s saying yeah
+ 
+
+ align:start position:0%
+plot wrote in the early 30s saying yeah
+like I didn't know what I was doing is
+
+ align:start position:0%
+like I didn't know what I was doing is
+ 
+
+ align:start position:0%
+like I didn't know what I was doing is
+essentially how I read that quote I was
+
+ align:start position:0%
+essentially how I read that quote I was
+ 
+
+ align:start position:0%
+essentially how I read that quote I was
+desperate
+
+ align:start position:0%
+desperate
+ 
+
+ align:start position:0%
+desperate
+so I think that's really interesting any
+
+ align:start position:0%
+so I think that's really interesting any
+ 
+
+ align:start position:0%
+so I think that's really interesting any
+other questions on the black body
+
+ align:start position:0%
+other questions on the black body
+ 
+
+ align:start position:0%
+other questions on the black body
+Specter or plugs formula
+
+ align:start position:0%
+Specter or plugs formula
+ 
+
+ align:start position:0%
+Specter or plugs formula
+if not let's go on and see what Einstein
+
+ align:start position:0%
+if not let's go on and see what Einstein
+ 
+
+ align:start position:0%
+if not let's go on and see what Einstein
+begins to do with that in that same uh
+
+ align:start position:0%
+begins to do with that in that same uh
+ 
+
+ align:start position:0%
+begins to do with that in that same uh
+famous year of 1905. so let's go to that
+
+ align:start position:0%
+famous year of 1905. so let's go to that
+ 
+
+ align:start position:0%
+famous year of 1905. so let's go to that
+next part so now we're going to talk
+
+ align:start position:0%
+next part so now we're going to talk
+ 
+
+ align:start position:0%
+next part so now we're going to talk
+about uh Einstein and what becomes known
+
+ align:start position:0%
+about uh Einstein and what becomes known
+ 
+
+ align:start position:0%
+about uh Einstein and what becomes known
+as the photoelectric effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it turns out
+
+ align:start position:0%
+it turns out
+ 
+
+ align:start position:0%
+it turns out
+plug was was concerned about the
+
+ align:start position:0%
+plug was was concerned about the
+ 
+
+ align:start position:0%
+plug was was concerned about the
+interaction between light and matter he
+
+ align:start position:0%
+interaction between light and matter he
+ 
+
+ align:start position:0%
+interaction between light and matter he
+wasn't even in his own writings talking
+
+ align:start position:0%
+wasn't even in his own writings talking
+ 
+
+ align:start position:0%
+wasn't even in his own writings talking
+about the the propagation of light on
+
+ align:start position:0%
+about the the propagation of light on
+ 
+
+ align:start position:0%
+about the the propagation of light on
+his own for which he just took right off
+
+ align:start position:0%
+his own for which he just took right off
+ 
+
+ align:start position:0%
+his own for which he just took right off
+the shelf Maxwell's by then quite
+
+ align:start position:0%
+the shelf Maxwell's by then quite
+ 
+
+ align:start position:0%
+the shelf Maxwell's by then quite
+standard treatment the light is clearly
+
+ align:start position:0%
+standard treatment the light is clearly
+ 
+
+ align:start position:0%
+standard treatment the light is clearly
+a continuous wave spread out through
+
+ align:start position:0%
+a continuous wave spread out through
+ 
+
+ align:start position:0%
+a continuous wave spread out through
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and so in 1905 just a few years later
+
+ align:start position:0%
+and so in 1905 just a few years later
+ 
+
+ align:start position:0%
+and so in 1905 just a few years later
+young Albert Einstein as we know still
+
+ align:start position:0%
+young Albert Einstein as we know still
+ 
+
+ align:start position:0%
+young Albert Einstein as we know still
+Pat mcclurk third class
+
+ align:start position:0%
+Pat mcclurk third class
+ 
+
+ align:start position:0%
+Pat mcclurk third class
+began to think about the nature of light
+
+ align:start position:0%
+began to think about the nature of light
+ 
+
+ align:start position:0%
+began to think about the nature of light
+on its own even when it's not
+
+ align:start position:0%
+on its own even when it's not
+ 
+
+ align:start position:0%
+on its own even when it's not
+necessarily interacting with matter this
+
+ align:start position:0%
+necessarily interacting with matter this
+ 
+
+ align:start position:0%
+necessarily interacting with matter this
+was actually the first of these four
+
+ align:start position:0%
+was actually the first of these four
+ 
+
+ align:start position:0%
+was actually the first of these four
+kind of amazing or surprising papers
+
+ align:start position:0%
+kind of amazing or surprising papers
+ 
+
+ align:start position:0%
+kind of amazing or surprising papers
+that Einstein wound up submitting to the
+
+ align:start position:0%
+that Einstein wound up submitting to the
+ 
+
+ align:start position:0%
+that Einstein wound up submitting to the
+island of Physique in that year in 1905.
+
+ align:start position:0%
+island of Physique in that year in 1905.
+ 
+
+ align:start position:0%
+island of Physique in that year in 1905.
+the first of them that he sent into the
+
+ align:start position:0%
+the first of them that he sent into the
+ 
+
+ align:start position:0%
+the first of them that he sent into the
+journal in back in March of that year
+
+ align:start position:0%
+journal in back in March of that year
+ 
+
+ align:start position:0%
+journal in back in March of that year
+was the one on what he calls light
+
+ align:start position:0%
+was the one on what he calls light
+ 
+
+ align:start position:0%
+was the one on what he calls light
+quanta
+
+ align:start position:0%
+quanta
+ 
+
+ align:start position:0%
+quanta
+now Einstein was thinking not only about
+
+ align:start position:0%
+now Einstein was thinking not only about
+ 
+
+ align:start position:0%
+now Einstein was thinking not only about
+Planck's work he was to think about that
+
+ align:start position:0%
+Planck's work he was to think about that
+ 
+
+ align:start position:0%
+Planck's work he was to think about that
+they had other recent experiments or
+
+ align:start position:0%
+they had other recent experiments or
+ 
+
+ align:start position:0%
+they had other recent experiments or
+descriptions of light in mind as well
+
+ align:start position:0%
+descriptions of light in mind as well
+ 
+
+ align:start position:0%
+descriptions of light in mind as well
+one of which the one that that he was
+
+ align:start position:0%
+one of which the one that that he was
+ 
+
+ align:start position:0%
+one of which the one that that he was
+even more kind of focused on
+
+ align:start position:0%
+even more kind of focused on
+ 
+
+ align:start position:0%
+even more kind of focused on
+was a series of again kind of puzzling
+
+ align:start position:0%
+was a series of again kind of puzzling
+ 
+
+ align:start position:0%
+was a series of again kind of puzzling
+experimental results that had just been
+
+ align:start position:0%
+experimental results that had just been
+ 
+
+ align:start position:0%
+experimental results that had just been
+coming out uh Through The Years up
+
+ align:start position:0%
+coming out uh Through The Years up
+ 
+
+ align:start position:0%
+coming out uh Through The Years up
+through 1902 by the German researcher
+
+ align:start position:0%
+through 1902 by the German researcher
+ 
+
+ align:start position:0%
+through 1902 by the German researcher
+Philip Leonard if that name sounds
+
+ align:start position:0%
+Philip Leonard if that name sounds
+ 
+
+ align:start position:0%
+Philip Leonard if that name sounds
+familiar it's because we just talked
+
+ align:start position:0%
+familiar it's because we just talked
+ 
+
+ align:start position:0%
+familiar it's because we just talked
+briefly about Leonard in the previous
+
+ align:start position:0%
+briefly about Leonard in the previous
+ 
+
+ align:start position:0%
+briefly about Leonard in the previous
+lecture Leonard went on years later to
+
+ align:start position:0%
+lecture Leonard went on years later to
+ 
+
+ align:start position:0%
+lecture Leonard went on years later to
+become one of the kind of front uh front
+
+ align:start position:0%
+become one of the kind of front uh front
+ 
+
+ align:start position:0%
+become one of the kind of front uh front
+men so to speak of that Deutsche
+
+ align:start position:0%
+men so to speak of that Deutsche
+ 
+
+ align:start position:0%
+men so to speak of that Deutsche
+physique movement what are the people
+
+ align:start position:0%
+physique movement what are the people
+ 
+
+ align:start position:0%
+physique movement what are the people
+who would begin denouncing Einstein and
+
+ align:start position:0%
+who would begin denouncing Einstein and
+ 
+
+ align:start position:0%
+who would begin denouncing Einstein and
+relativity starting as early as 1920.
+
+ align:start position:0%
+relativity starting as early as 1920.
+ 
+
+ align:start position:0%
+relativity starting as early as 1920.
+Leonard was conducting these experiments
+
+ align:start position:0%
+Leonard was conducting these experiments
+ 
+
+ align:start position:0%
+Leonard was conducting these experiments
+at what became known as the
+
+ align:start position:0%
+at what became known as the
+ 
+
+ align:start position:0%
+at what became known as the
+photoelectric effect in the early years
+
+ align:start position:0%
+photoelectric effect in the early years
+ 
+
+ align:start position:0%
+photoelectric effect in the early years
+of the 20th century he his the sort of
+
+ align:start position:0%
+of the 20th century he his the sort of
+ 
+
+ align:start position:0%
+of the 20th century he his the sort of
+sharpest the clearest experimental
+
+ align:start position:0%
+sharpest the clearest experimental
+ 
+
+ align:start position:0%
+sharpest the clearest experimental
+results were published in 1902 he was
+
+ align:start position:0%
+results were published in 1902 he was
+ 
+
+ align:start position:0%
+results were published in 1902 he was
+recognized very early on for that work
+
+ align:start position:0%
+recognized very early on for that work
+ 
+
+ align:start position:0%
+recognized very early on for that work
+he won the Nobel Prize in 1905. the very
+
+ align:start position:0%
+he won the Nobel Prize in 1905. the very
+ 
+
+ align:start position:0%
+he won the Nobel Prize in 1905. the very
+year that Einstein
+
+ align:start position:0%
+year that Einstein
+ 
+
+ align:start position:0%
+year that Einstein
+begins trying to come up with a
+
+ align:start position:0%
+begins trying to come up with a
+ 
+
+ align:start position:0%
+begins trying to come up with a
+theoretical explanation uh for these uh
+
+ align:start position:0%
+theoretical explanation uh for these uh
+ 
+
+ align:start position:0%
+theoretical explanation uh for these uh
+experimental results so what were what
+
+ align:start position:0%
+experimental results so what were what
+ 
+
+ align:start position:0%
+experimental results so what were what
+were Leonard's results here again in
+
+ align:start position:0%
+were Leonard's results here again in
+ 
+
+ align:start position:0%
+were Leonard's results here again in
+kind of cartoon form is the are the
+
+ align:start position:0%
+kind of cartoon form is the are the
+ 
+
+ align:start position:0%
+kind of cartoon form is the are the
+fundamentals of the experiments that
+
+ align:start position:0%
+fundamentals of the experiments that
+ 
+
+ align:start position:0%
+fundamentals of the experiments that
+Leonard uh was was pursuing in fact
+
+ align:start position:0%
+Leonard uh was was pursuing in fact
+ 
+
+ align:start position:0%
+Leonard uh was was pursuing in fact
+others around the world were doing
+
+ align:start position:0%
+others around the world were doing
+ 
+
+ align:start position:0%
+others around the world were doing
+similar things Leonard had in some sense
+
+ align:start position:0%
+similar things Leonard had in some sense
+ 
+
+ align:start position:0%
+similar things Leonard had in some sense
+the kind of cleanest data that forced
+
+ align:start position:0%
+the kind of cleanest data that forced
+ 
+
+ align:start position:0%
+the kind of cleanest data that forced
+the kind of most sharp Showdown with how
+
+ align:start position:0%
+the kind of most sharp Showdown with how
+ 
+
+ align:start position:0%
+the kind of most sharp Showdown with how
+to make sense of these results others
+
+ align:start position:0%
+to make sense of these results others
+ 
+
+ align:start position:0%
+to make sense of these results others
+are doing similar things he had a very
+
+ align:start position:0%
+are doing similar things he had a very
+ 
+
+ align:start position:0%
+are doing similar things he had a very
+simple kind of apparatus so these two
+
+ align:start position:0%
+simple kind of apparatus so these two
+ 
+
+ align:start position:0%
+simple kind of apparatus so these two
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+um pieces here represent metallic
+
+ align:start position:0%
+um pieces here represent metallic
+ 
+
+ align:start position:0%
+um pieces here represent metallic
+conducting plates
+
+ align:start position:0%
+conducting plates
+ 
+
+ align:start position:0%
+conducting plates
+and across the Lennard could apply a
+
+ align:start position:0%
+and across the Lennard could apply a
+ 
+
+ align:start position:0%
+and across the Lennard could apply a
+voltage of a of an amount he could vary
+
+ align:start position:0%
+voltage of a of an amount he could vary
+ 
+
+ align:start position:0%
+voltage of a of an amount he could vary
+he had a tunable voltage between his
+
+ align:start position:0%
+he had a tunable voltage between his
+ 
+
+ align:start position:0%
+he had a tunable voltage between his
+conducting plates he would then direct
+
+ align:start position:0%
+conducting plates he would then direct
+ 
+
+ align:start position:0%
+conducting plates he would then direct
+an ultraviolet light source sorry an
+
+ align:start position:0%
+an ultraviolet light source sorry an
+ 
+
+ align:start position:0%
+an ultraviolet light source sorry an
+ultraviolet light source onto one of
+
+ align:start position:0%
+ultraviolet light source onto one of
+ 
+
+ align:start position:0%
+ultraviolet light source onto one of
+those plates so he has some source of
+
+ align:start position:0%
+those plates so he has some source of
+ 
+
+ align:start position:0%
+those plates so he has some source of
+ultraviolet light shining it on one of
+
+ align:start position:0%
+ultraviolet light shining it on one of
+ 
+
+ align:start position:0%
+ultraviolet light shining it on one of
+those flights
+
+ align:start position:0%
+those flights
+ 
+
+ align:start position:0%
+those flights
+and under certain conditions the light
+
+ align:start position:0%
+and under certain conditions the light
+ 
+
+ align:start position:0%
+and under certain conditions the light
+source when it irradiates that plate
+
+ align:start position:0%
+source when it irradiates that plate
+ 
+
+ align:start position:0%
+source when it irradiates that plate
+would eject would kick out some
+
+ align:start position:0%
+would eject would kick out some
+ 
+
+ align:start position:0%
+would eject would kick out some
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+the electrons are then traveled toward
+
+ align:start position:0%
+the electrons are then traveled toward
+ 
+
+ align:start position:0%
+the electrons are then traveled toward
+the other conducting plate completing a
+
+ align:start position:0%
+the other conducting plate completing a
+ 
+
+ align:start position:0%
+the other conducting plate completing a
+circuit so when the light kicked out
+
+ align:start position:0%
+circuit so when the light kicked out
+ 
+
+ align:start position:0%
+circuit so when the light kicked out
+electrons ejected electrons from this
+
+ align:start position:0%
+electrons ejected electrons from this
+ 
+
+ align:start position:0%
+electrons ejected electrons from this
+um so-called cathode
+
+ align:start position:0%
+um so-called cathode
+ 
+
+ align:start position:0%
+um so-called cathode
+for that metal conducting plate you
+
+ align:start position:0%
+for that metal conducting plate you
+ 
+
+ align:start position:0%
+for that metal conducting plate you
+could complete a circuit because
+
+ align:start position:0%
+could complete a circuit because
+ 
+
+ align:start position:0%
+could complete a circuit because
+electrons would now travel through the
+
+ align:start position:0%
+electrons would now travel through the
+ 
+
+ align:start position:0%
+electrons would now travel through the
+intervening space and hit this plate and
+
+ align:start position:0%
+intervening space and hit this plate and
+ 
+
+ align:start position:0%
+intervening space and hit this plate and
+you'd know you had electric current
+
+ align:start position:0%
+you'd know you had electric current
+ 
+
+ align:start position:0%
+you'd know you had electric current
+flowing because he hooked up an ammeter
+
+ align:start position:0%
+flowing because he hooked up an ammeter
+ 
+
+ align:start position:0%
+flowing because he hooked up an ammeter
+a measure of electric current so he knew
+
+ align:start position:0%
+a measure of electric current so he knew
+ 
+
+ align:start position:0%
+a measure of electric current so he knew
+he had current flowing you know
+
+ align:start position:0%
+he had current flowing you know
+ 
+
+ align:start position:0%
+he had current flowing you know
+electrons have been kicked out of the
+
+ align:start position:0%
+electrons have been kicked out of the
+ 
+
+ align:start position:0%
+electrons have been kicked out of the
+metal when the ammeter measured an
+
+ align:start position:0%
+metal when the ammeter measured an
+ 
+
+ align:start position:0%
+metal when the ammeter measured an
+electric current and then he could use
+
+ align:start position:0%
+electric current and then he could use
+ 
+
+ align:start position:0%
+electric current and then he could use
+this tunable voltage it could change the
+
+ align:start position:0%
+this tunable voltage it could change the
+ 
+
+ align:start position:0%
+this tunable voltage it could change the
+amount of voltage applied to basically
+
+ align:start position:0%
+amount of voltage applied to basically
+ 
+
+ align:start position:0%
+amount of voltage applied to basically
+ask how much energy where those
+
+ align:start position:0%
+ask how much energy where those
+ 
+
+ align:start position:0%
+ask how much energy where those
+electrons kicked out with
+
+ align:start position:0%
+electrons kicked out with
+ 
+
+ align:start position:0%
+electrons kicked out with
+by asking how strong a voltage he had to
+
+ align:start position:0%
+by asking how strong a voltage he had to
+ 
+
+ align:start position:0%
+by asking how strong a voltage he had to
+tune up to block their passage so we
+
+ align:start position:0%
+tune up to block their passage so we
+ 
+
+ align:start position:0%
+tune up to block their passage so we
+when he when he um applied basically no
+
+ align:start position:0%
+when he when he um applied basically no
+ 
+
+ align:start position:0%
+when he when he um applied basically no
+voltage the electrons would would come
+
+ align:start position:0%
+voltage the electrons would would come
+ 
+
+ align:start position:0%
+voltage the electrons would would come
+across and play an incomplete circuit so
+
+ align:start position:0%
+across and play an incomplete circuit so
+ 
+
+ align:start position:0%
+across and play an incomplete circuit so
+how much kind of countervailing voltage
+
+ align:start position:0%
+how much kind of countervailing voltage
+ 
+
+ align:start position:0%
+how much kind of countervailing voltage
+with an art have to apply to block their
+
+ align:start position:0%
+with an art have to apply to block their
+ 
+
+ align:start position:0%
+with an art have to apply to block their
+passage a kind of repulsive Electro for
+
+ align:start position:0%
+passage a kind of repulsive Electro for
+ 
+
+ align:start position:0%
+passage a kind of repulsive Electro for
+electric force to basically repel the
+
+ align:start position:0%
+electric force to basically repel the
+ 
+
+ align:start position:0%
+electric force to basically repel the
+electrons away from reaching this far
+
+ align:start position:0%
+electrons away from reaching this far
+ 
+
+ align:start position:0%
+electrons away from reaching this far
+plate so when will the current stop that
+
+ align:start position:0%
+plate so when will the current stop that
+ 
+
+ align:start position:0%
+plate so when will the current stop that
+he knows what's called the stopping
+
+ align:start position:0%
+he knows what's called the stopping
+ 
+
+ align:start position:0%
+he knows what's called the stopping
+voltage and that tells them exactly how
+
+ align:start position:0%
+voltage and that tells them exactly how
+ 
+
+ align:start position:0%
+voltage and that tells them exactly how
+much energy the electrons had
+
+ align:start position:0%
+much energy the electrons had
+ 
+
+ align:start position:0%
+much energy the electrons had
+because he had to counteract that much
+
+ align:start position:0%
+because he had to counteract that much
+ 
+
+ align:start position:0%
+because he had to counteract that much
+energy that much sort of electrostatic
+
+ align:start position:0%
+energy that much sort of electrostatic
+ 
+
+ align:start position:0%
+energy that much sort of electrostatic
+force to to turn off that current so now
+
+ align:start position:0%
+force to to turn off that current so now
+ 
+
+ align:start position:0%
+force to to turn off that current so now
+he can start comparing the stopping
+
+ align:start position:0%
+he can start comparing the stopping
+ 
+
+ align:start position:0%
+he can start comparing the stopping
+voltage which for him is a measure of
+
+ align:start position:0%
+voltage which for him is a measure of
+ 
+
+ align:start position:0%
+voltage which for him is a measure of
+the energy with which these electrons
+
+ align:start position:0%
+the energy with which these electrons
+ 
+
+ align:start position:0%
+the energy with which these electrons
+are ejected so we can compare the energy
+
+ align:start position:0%
+are ejected so we can compare the energy
+ 
+
+ align:start position:0%
+are ejected so we can compare the energy
+of the electrons with the frequency of
+
+ align:start position:0%
+of the electrons with the frequency of
+ 
+
+ align:start position:0%
+of the electrons with the frequency of
+this light source he shines light of
+
+ align:start position:0%
+this light source he shines light of
+ 
+
+ align:start position:0%
+this light source he shines light of
+certain frequencies within the
+
+ align:start position:0%
+certain frequencies within the
+ 
+
+ align:start position:0%
+certain frequencies within the
+ultraviolet range onto this metallic
+
+ align:start position:0%
+ultraviolet range onto this metallic
+ 
+
+ align:start position:0%
+ultraviolet range onto this metallic
+plate and he measures the amount of
+
+ align:start position:0%
+plate and he measures the amount of
+ 
+
+ align:start position:0%
+plate and he measures the amount of
+energy of the ejected electrons and
+
+ align:start position:0%
+energy of the ejected electrons and
+ 
+
+ align:start position:0%
+energy of the ejected electrons and
+again a kind of cleaned up form the data
+
+ align:start position:0%
+again a kind of cleaned up form the data
+ 
+
+ align:start position:0%
+again a kind of cleaned up form the data
+started looking like this they had a
+
+ align:start position:0%
+started looking like this they had a
+ 
+
+ align:start position:0%
+started looking like this they had a
+very specific very striking shape
+
+ align:start position:0%
+very specific very striking shape
+ 
+
+ align:start position:0%
+very specific very striking shape
+so on a plot of the energy of the
+
+ align:start position:0%
+so on a plot of the energy of the
+ 
+
+ align:start position:0%
+so on a plot of the energy of the
+electrode ejected electrons versus the
+
+ align:start position:0%
+electrode ejected electrons versus the
+ 
+
+ align:start position:0%
+electrode ejected electrons versus the
+frequency of the incident light the
+
+ align:start position:0%
+frequency of the incident light the
+ 
+
+ align:start position:0%
+frequency of the incident light the
+energy electrons seem to rise linearly
+
+ align:start position:0%
+energy electrons seem to rise linearly
+ 
+
+ align:start position:0%
+energy electrons seem to rise linearly
+but only above some threshold frequency
+
+ align:start position:0%
+but only above some threshold frequency
+ 
+
+ align:start position:0%
+but only above some threshold frequency
+so as the light was tuned to lower and
+
+ align:start position:0%
+so as the light was tuned to lower and
+ 
+
+ align:start position:0%
+so as the light was tuned to lower and
+lower frequencies the light that's being
+
+ align:start position:0%
+lower frequencies the light that's being
+ 
+
+ align:start position:0%
+lower frequencies the light that's being
+shown from this Source there'd be no
+
+ align:start position:0%
+shown from this Source there'd be no
+ 
+
+ align:start position:0%
+shown from this Source there'd be no
+electrons ejected at all there would be
+
+ align:start position:0%
+electrons ejected at all there would be
+ 
+
+ align:start position:0%
+electrons ejected at all there would be
+zero electrons ejected no energy
+
+ align:start position:0%
+zero electrons ejected no energy
+ 
+
+ align:start position:0%
+zero electrons ejected no energy
+Crossing that Gap after you reach some
+
+ align:start position:0%
+Crossing that Gap after you reach some
+ 
+
+ align:start position:0%
+Crossing that Gap after you reach some
+very specific threshold frequency of the
+
+ align:start position:0%
+very specific threshold frequency of the
+ 
+
+ align:start position:0%
+very specific threshold frequency of the
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+you start kicking electrons out as you
+
+ align:start position:0%
+you start kicking electrons out as you
+ 
+
+ align:start position:0%
+you start kicking electrons out as you
+increase the frequency of that light the
+
+ align:start position:0%
+increase the frequency of that light the
+ 
+
+ align:start position:0%
+increase the frequency of that light the
+energy that those electrons carry Rises
+
+ align:start position:0%
+energy that those electrons carry Rises
+ 
+
+ align:start position:0%
+energy that those electrons carry Rises
+the energy of the electrons seem to rise
+
+ align:start position:0%
+the energy of the electrons seem to rise
+ 
+
+ align:start position:0%
+the energy of the electrons seem to rise
+only with passenger depend only with the
+
+ align:start position:0%
+only with passenger depend only with the
+ 
+
+ align:start position:0%
+only with passenger depend only with the
+frequency of that light not with the
+
+ align:start position:0%
+frequency of that light not with the
+ 
+
+ align:start position:0%
+frequency of that light not with the
+intensity you can make this a brighter
+
+ align:start position:0%
+intensity you can make this a brighter
+ 
+
+ align:start position:0%
+intensity you can make this a brighter
+or less bright light source holding the
+
+ align:start position:0%
+or less bright light source holding the
+ 
+
+ align:start position:0%
+or less bright light source holding the
+frequency fixed and that had no impact
+
+ align:start position:0%
+frequency fixed and that had no impact
+ 
+
+ align:start position:0%
+frequency fixed and that had no impact
+on the stopping voltage on the amount of
+
+ align:start position:0%
+on the stopping voltage on the amount of
+ 
+
+ align:start position:0%
+on the stopping voltage on the amount of
+energy required to stop those electrons
+
+ align:start position:0%
+energy required to stop those electrons
+ 
+
+ align:start position:0%
+energy required to stop those electrons
+from traversing that that Gap seemed
+
+ align:start position:0%
+from traversing that that Gap seemed
+ 
+
+ align:start position:0%
+from traversing that that Gap seemed
+pretty strange why was that so strange
+
+ align:start position:0%
+pretty strange why was that so strange
+ 
+
+ align:start position:0%
+pretty strange why was that so strange
+why is it strange to have a threshold
+
+ align:start position:0%
+why is it strange to have a threshold
+ 
+
+ align:start position:0%
+why is it strange to have a threshold
+frequency and why was it strange to have
+
+ align:start position:0%
+frequency and why was it strange to have
+ 
+
+ align:start position:0%
+frequency and why was it strange to have
+the energy of the electrons independent
+
+ align:start position:0%
+the energy of the electrons independent
+ 
+
+ align:start position:0%
+the energy of the electrons independent
+of the intensity of that light depending
+
+ align:start position:0%
+of the intensity of that light depending
+ 
+
+ align:start position:0%
+of the intensity of that light depending
+only on the frequency of the line well
+
+ align:start position:0%
+only on the frequency of the line well
+ 
+
+ align:start position:0%
+only on the frequency of the line well
+again if one took on Maxwell's by then
+
+ align:start position:0%
+again if one took on Maxwell's by then
+ 
+
+ align:start position:0%
+again if one took on Maxwell's by then
+quite standard description of
+
+ align:start position:0%
+quite standard description of
+ 
+
+ align:start position:0%
+quite standard description of
+electromagnetic waves including in the
+
+ align:start position:0%
+electromagnetic waves including in the
+ 
+
+ align:start position:0%
+electromagnetic waves including in the
+ultraviolet part of the spectrum the
+
+ align:start position:0%
+ultraviolet part of the spectrum the
+ 
+
+ align:start position:0%
+ultraviolet part of the spectrum the
+energy carried by those light waves from
+
+ align:start position:0%
+energy carried by those light waves from
+ 
+
+ align:start position:0%
+energy carried by those light waves from
+from Leonard's device should have been
+
+ align:start position:0%
+from Leonard's device should have been
+ 
+
+ align:start position:0%
+from Leonard's device should have been
+proportional to the waves intensity the
+
+ align:start position:0%
+proportional to the waves intensity the
+ 
+
+ align:start position:0%
+proportional to the waves intensity the
+energy sort of script e here with
+
+ align:start position:0%
+energy sort of script e here with
+ 
+
+ align:start position:0%
+energy sort of script e here with
+proportions to the intensity of the
+
+ align:start position:0%
+proportions to the intensity of the
+ 
+
+ align:start position:0%
+proportions to the intensity of the
+Waves the intensity in turn went by this
+
+ align:start position:0%
+Waves the intensity in turn went by this
+ 
+
+ align:start position:0%
+Waves the intensity in turn went by this
+square of those field strengths the
+
+ align:start position:0%
+square of those field strengths the
+ 
+
+ align:start position:0%
+square of those field strengths the
+electric and magnetic field strengths so
+
+ align:start position:0%
+electric and magnetic field strengths so
+ 
+
+ align:start position:0%
+electric and magnetic field strengths so
+why shouldn't Leonard have been able to
+
+ align:start position:0%
+why shouldn't Leonard have been able to
+ 
+
+ align:start position:0%
+why shouldn't Leonard have been able to
+to get very large amplitude Fields high
+
+ align:start position:0%
+to get very large amplitude Fields high
+ 
+
+ align:start position:0%
+to get very large amplitude Fields high
+intensity fields that happen to have a
+
+ align:start position:0%
+intensity fields that happen to have a
+ 
+
+ align:start position:0%
+intensity fields that happen to have a
+long wavelength that were that were a
+
+ align:start position:0%
+long wavelength that were that were a
+ 
+
+ align:start position:0%
+long wavelength that were that were a
+low frequency that should carry as much
+
+ align:start position:0%
+low frequency that should carry as much
+ 
+
+ align:start position:0%
+low frequency that should carry as much
+energy as a short frequency wave out of
+
+ align:start position:0%
+energy as a short frequency wave out of
+ 
+
+ align:start position:0%
+energy as a short frequency wave out of
+a smaller amplitude meaning why couldn't
+
+ align:start position:0%
+a smaller amplitude meaning why couldn't
+ 
+
+ align:start position:0%
+a smaller amplitude meaning why couldn't
+you tune the intensity up and uh and
+
+ align:start position:0%
+you tune the intensity up and uh and
+ 
+
+ align:start position:0%
+you tune the intensity up and uh and
+still get electrons ejected all the way
+
+ align:start position:0%
+still get electrons ejected all the way
+ 
+
+ align:start position:0%
+still get electrons ejected all the way
+down here
+
+ align:start position:0%
+down here
+ 
+
+ align:start position:0%
+down here
+if light really acted like maxwellian
+
+ align:start position:0%
+if light really acted like maxwellian
+ 
+
+ align:start position:0%
+if light really acted like maxwellian
+waves why should there be any threshold
+
+ align:start position:0%
+waves why should there be any threshold
+ 
+
+ align:start position:0%
+waves why should there be any threshold
+of frequency at all you could always
+
+ align:start position:0%
+of frequency at all you could always
+ 
+
+ align:start position:0%
+of frequency at all you could always
+tune up the intensity of low frequent
+
+ align:start position:0%
+tune up the intensity of low frequent
+ 
+
+ align:start position:0%
+tune up the intensity of low frequent
+lower frequency light was at least the
+
+ align:start position:0%
+lower frequency light was at least the
+ 
+
+ align:start position:0%
+lower frequency light was at least the
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+likewise according to Maxwell's work
+
+ align:start position:0%
+likewise according to Maxwell's work
+ 
+
+ align:start position:0%
+likewise according to Maxwell's work
+turning the argument around once you do
+
+ align:start position:0%
+turning the argument around once you do
+ 
+
+ align:start position:0%
+turning the argument around once you do
+kick electrons out above that threshold
+
+ align:start position:0%
+kick electrons out above that threshold
+ 
+
+ align:start position:0%
+kick electrons out above that threshold
+why should the energy that they carry be
+
+ align:start position:0%
+why should the energy that they carry be
+ 
+
+ align:start position:0%
+why should the energy that they carry be
+independent of what people thought would
+
+ align:start position:0%
+independent of what people thought would
+ 
+
+ align:start position:0%
+independent of what people thought would
+be the energy imparted by the Light the
+
+ align:start position:0%
+be the energy imparted by the Light the
+ 
+
+ align:start position:0%
+be the energy imparted by the Light the
+energy and parted by the light again
+
+ align:start position:0%
+energy and parted by the light again
+ 
+
+ align:start position:0%
+energy and parted by the light again
+should vary like the intensity and yet
+
+ align:start position:0%
+should vary like the intensity and yet
+ 
+
+ align:start position:0%
+should vary like the intensity and yet
+the energy that these electrons get kind
+
+ align:start position:0%
+the energy that these electrons get kind
+ 
+
+ align:start position:0%
+the energy that these electrons get kind
+of kicked out with seem not to depend on
+
+ align:start position:0%
+of kicked out with seem not to depend on
+ 
+
+ align:start position:0%
+of kicked out with seem not to depend on
+the brightness the intensity of the
+
+ align:start position:0%
+the brightness the intensity of the
+ 
+
+ align:start position:0%
+the brightness the intensity of the
+source only on the frequency okay so
+
+ align:start position:0%
+source only on the frequency okay so
+ 
+
+ align:start position:0%
+source only on the frequency okay so
+that was um becoming increasingly clear
+
+ align:start position:0%
+that was um becoming increasingly clear
+ 
+
+ align:start position:0%
+that was um becoming increasingly clear
+experimental data so clear that Leonard
+
+ align:start position:0%
+experimental data so clear that Leonard
+ 
+
+ align:start position:0%
+experimental data so clear that Leonard
+received the prize just a few years
+
+ align:start position:0%
+received the prize just a few years
+ 
+
+ align:start position:0%
+received the prize just a few years
+later the Nobel Prize but it was by no
+
+ align:start position:0%
+later the Nobel Prize but it was by no
+ 
+
+ align:start position:0%
+later the Nobel Prize but it was by no
+means clear how to make sense of that
+
+ align:start position:0%
+means clear how to make sense of that
+ 
+
+ align:start position:0%
+means clear how to make sense of that
+combination of results so Einstein's
+
+ align:start position:0%
+combination of results so Einstein's
+ 
+
+ align:start position:0%
+combination of results so Einstein's
+first paper of this uh remarkable year
+
+ align:start position:0%
+first paper of this uh remarkable year
+ 
+
+ align:start position:0%
+first paper of this uh remarkable year
+of 1905
+
+ align:start position:0%
+of 1905
+ 
+
+ align:start position:0%
+of 1905
+was was trying to tackle this directly
+
+ align:start position:0%
+was was trying to tackle this directly
+ 
+
+ align:start position:0%
+was was trying to tackle this directly
+in fact in a letter to one of his
+
+ align:start position:0%
+in fact in a letter to one of his
+ 
+
+ align:start position:0%
+in fact in a letter to one of his
+friends to from the Olympia Academy his
+
+ align:start position:0%
+friends to from the Olympia Academy his
+ 
+
+ align:start position:0%
+friends to from the Olympia Academy his
+friend uh Conrad had beat here Einstein
+
+ align:start position:0%
+friend uh Conrad had beat here Einstein
+ 
+
+ align:start position:0%
+friend uh Conrad had beat here Einstein
+actually called this his most radical of
+
+ align:start position:0%
+actually called this his most radical of
+ 
+
+ align:start position:0%
+actually called this his most radical of
+all the Patriots he was working on that
+
+ align:start position:0%
+all the Patriots he was working on that
+ 
+
+ align:start position:0%
+all the Patriots he was working on that
+year he thought this was the most
+
+ align:start position:0%
+year he thought this was the most
+ 
+
+ align:start position:0%
+year he thought this was the most
+strange or most unexpected
+
+ align:start position:0%
+strange or most unexpected
+ 
+
+ align:start position:0%
+strange or most unexpected
+more so than relativity more so than all
+
+ align:start position:0%
+more so than relativity more so than all
+ 
+
+ align:start position:0%
+more so than relativity more so than all
+the all there is so what he offers he
+
+ align:start position:0%
+the all there is so what he offers he
+ 
+
+ align:start position:0%
+the all there is so what he offers he
+calls a heuristic explanation you see in
+
+ align:start position:0%
+calls a heuristic explanation you see in
+ 
+
+ align:start position:0%
+calls a heuristic explanation you see in
+the title uh oilistician a heuristic
+
+ align:start position:0%
+the title uh oilistician a heuristic
+ 
+
+ align:start position:0%
+the title uh oilistician a heuristic
+kind of hypothetical or a suggestive
+
+ align:start position:0%
+kind of hypothetical or a suggestive
+ 
+
+ align:start position:0%
+kind of hypothetical or a suggestive
+explanation he's not saying Eureka I
+
+ align:start position:0%
+explanation he's not saying Eureka I
+ 
+
+ align:start position:0%
+explanation he's not saying Eureka I
+found it he's he's being maybe
+
+ align:start position:0%
+found it he's he's being maybe
+ 
+
+ align:start position:0%
+found it he's he's being maybe
+uncharacteristically a bit more kind of
+
+ align:start position:0%
+uncharacteristically a bit more kind of
+ 
+
+ align:start position:0%
+uncharacteristically a bit more kind of
+modest here he says here's one way to
+
+ align:start position:0%
+modest here he says here's one way to
+ 
+
+ align:start position:0%
+modest here he says here's one way to
+think about these results
+
+ align:start position:0%
+think about these results
+ 
+
+ align:start position:0%
+think about these results
+a heuristic idea would be to say uh what
+
+ align:start position:0%
+a heuristic idea would be to say uh what
+ 
+
+ align:start position:0%
+a heuristic idea would be to say uh what
+if light itself were quantized what if
+
+ align:start position:0%
+if light itself were quantized what if
+ 
+
+ align:start position:0%
+if light itself were quantized what if
+light traveled through space not like a
+
+ align:start position:0%
+light traveled through space not like a
+ 
+
+ align:start position:0%
+light traveled through space not like a
+continuous spread out wave like
+
+ align:start position:0%
+continuous spread out wave like
+ 
+
+ align:start position:0%
+continuous spread out wave like
+Maxwell's Theory would suggest but
+
+ align:start position:0%
+Maxwell's Theory would suggest but
+ 
+
+ align:start position:0%
+Maxwell's Theory would suggest but
+instead like a collection of localized
+
+ align:start position:0%
+instead like a collection of localized
+ 
+
+ align:start position:0%
+instead like a collection of localized
+quanta
+
+ align:start position:0%
+quanta
+ 
+
+ align:start position:0%
+quanta
+here's a quotation from this paper in
+
+ align:start position:0%
+here's a quotation from this paper in
+ 
+
+ align:start position:0%
+here's a quotation from this paper in
+1905 in English who translated English
+
+ align:start position:0%
+1905 in English who translated English
+ 
+
+ align:start position:0%
+1905 in English who translated English
+he writes that it seems to me these
+
+ align:start position:0%
+he writes that it seems to me these
+ 
+
+ align:start position:0%
+he writes that it seems to me these
+observations about the production of
+
+ align:start position:0%
+observations about the production of
+ 
+
+ align:start position:0%
+observations about the production of
+cathode rays those ejected electrons off
+
+ align:start position:0%
+cathode rays those ejected electrons off
+ 
+
+ align:start position:0%
+cathode rays those ejected electrons off
+that cathode by ultraviolet light he's
+
+ align:start position:0%
+that cathode by ultraviolet light he's
+ 
+
+ align:start position:0%
+that cathode by ultraviolet light he's
+now talking about Leonard's experiments
+
+ align:start position:0%
+now talking about Leonard's experiments
+ 
+
+ align:start position:0%
+now talking about Leonard's experiments
+it seems like these observations are
+
+ align:start position:0%
+it seems like these observations are
+ 
+
+ align:start position:0%
+it seems like these observations are
+more readily understood if one assumes
+
+ align:start position:0%
+more readily understood if one assumes
+ 
+
+ align:start position:0%
+more readily understood if one assumes
+the energy of light is discontinuously
+
+ align:start position:0%
+the energy of light is discontinuously
+ 
+
+ align:start position:0%
+the energy of light is discontinuously
+distributed in space
+
+ align:start position:0%
+distributed in space
+ 
+
+ align:start position:0%
+distributed in space
+the energy of a light Ray spreading out
+
+ align:start position:0%
+the energy of a light Ray spreading out
+ 
+
+ align:start position:0%
+the energy of a light Ray spreading out
+from a point source is not continuously
+
+ align:start position:0%
+from a point source is not continuously
+ 
+
+ align:start position:0%
+from a point source is not continuously
+distributed over an increasing space
+
+ align:start position:0%
+distributed over an increasing space
+ 
+
+ align:start position:0%
+distributed over an increasing space
+like a wave would be like a Maximilian
+
+ align:start position:0%
+like a wave would be like a Maximilian
+ 
+
+ align:start position:0%
+like a wave would be like a Maximilian
+wave or an ocean wave intent but rather
+
+ align:start position:0%
+wave or an ocean wave intent but rather
+ 
+
+ align:start position:0%
+wave or an ocean wave intent but rather
+consists of a finite number of energy
+
+ align:start position:0%
+consists of a finite number of energy
+ 
+
+ align:start position:0%
+consists of a finite number of energy
+quanta
+
+ align:start position:0%
+quanta
+ 
+
+ align:start position:0%
+quanta
+which are localized at points in space
+
+ align:start position:0%
+which are localized at points in space
+ 
+
+ align:start position:0%
+which are localized at points in space
+which move without dividing they are
+
+ align:start position:0%
+which move without dividing they are
+ 
+
+ align:start position:0%
+which move without dividing they are
+literally can't be further divided they
+
+ align:start position:0%
+literally can't be further divided they
+ 
+
+ align:start position:0%
+literally can't be further divided they
+are quantized and which can only be
+
+ align:start position:0%
+are quantized and which can only be
+ 
+
+ align:start position:0%
+are quantized and which can only be
+produced and absorbed as complete units
+
+ align:start position:0%
+produced and absorbed as complete units
+ 
+
+ align:start position:0%
+produced and absorbed as complete units
+these become known as light quanta as
+
+ align:start position:0%
+these become known as light quanta as
+ 
+
+ align:start position:0%
+these become known as light quanta as
+little particles or corpuscles of light
+
+ align:start position:0%
+little particles or corpuscles of light
+ 
+
+ align:start position:0%
+little particles or corpuscles of light
+rather than what was by then going back
+
+ align:start position:0%
+rather than what was by then going back
+ 
+
+ align:start position:0%
+rather than what was by then going back
+to 1800 let alone the 1860s the taken
+
+ align:start position:0%
+to 1800 let alone the 1860s the taken
+ 
+
+ align:start position:0%
+to 1800 let alone the 1860s the taken
+for granted assumption that light was a
+
+ align:start position:0%
+for granted assumption that light was a
+ 
+
+ align:start position:0%
+for granted assumption that light was a
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+going all the way back to say Thomas
+
+ align:start position:0%
+going all the way back to say Thomas
+ 
+
+ align:start position:0%
+going all the way back to say Thomas
+Young's work or the work of several
+
+ align:start position:0%
+Young's work or the work of several
+ 
+
+ align:start position:0%
+Young's work or the work of several
+French Scholars so Einstein is
+
+ align:start position:0%
+French Scholars so Einstein is
+ 
+
+ align:start position:0%
+French Scholars so Einstein is
+suggesting heuristically he's not saying
+
+ align:start position:0%
+suggesting heuristically he's not saying
+ 
+
+ align:start position:0%
+suggesting heuristically he's not saying
+this must be the case he's saying it's
+
+ align:start position:0%
+this must be the case he's saying it's
+ 
+
+ align:start position:0%
+this must be the case he's saying it's
+suggestive and worse worth considering
+
+ align:start position:0%
+suggestive and worse worth considering
+ 
+
+ align:start position:0%
+suggestive and worse worth considering
+that experiments like Leonard's might
+
+ align:start position:0%
+that experiments like Leonard's might
+ 
+
+ align:start position:0%
+that experiments like Leonard's might
+make sense if we change entirely
+
+ align:start position:0%
+make sense if we change entirely
+ 
+
+ align:start position:0%
+make sense if we change entirely
+everything we know about light
+
+ align:start position:0%
+everything we know about light
+ 
+
+ align:start position:0%
+everything we know about light
+so why would that help let's go back to
+
+ align:start position:0%
+so why would that help let's go back to
+ 
+
+ align:start position:0%
+so why would that help let's go back to
+this kind of cartoon version of
+
+ align:start position:0%
+this kind of cartoon version of
+ 
+
+ align:start position:0%
+this kind of cartoon version of
+Leonard's data Einstein was in fact
+
+ align:start position:0%
+Leonard's data Einstein was in fact
+ 
+
+ align:start position:0%
+Leonard's data Einstein was in fact
+following on the nard's experiments the
+
+ align:start position:0%
+following on the nard's experiments the
+ 
+
+ align:start position:0%
+following on the nard's experiments the
+Publications quite closely much much
+
+ align:start position:0%
+Publications quite closely much much
+ 
+
+ align:start position:0%
+Publications quite closely much much
+more closely than anything like the
+
+ align:start position:0%
+more closely than anything like the
+ 
+
+ align:start position:0%
+more closely than anything like the
+Michael's Immortal experiment he really
+
+ align:start position:0%
+Michael's Immortal experiment he really
+ 
+
+ align:start position:0%
+Michael's Immortal experiment he really
+was looking up Leonard's papers and
+
+ align:start position:0%
+was looking up Leonard's papers and
+ 
+
+ align:start position:0%
+was looking up Leonard's papers and
+looking at the graphs and tables very
+
+ align:start position:0%
+looking at the graphs and tables very
+ 
+
+ align:start position:0%
+looking at the graphs and tables very
+carefully Einstein recognized that it
+
+ align:start position:0%
+carefully Einstein recognized that it
+ 
+
+ align:start position:0%
+carefully Einstein recognized that it
+wasn't only a linear relationship
+
+ align:start position:0%
+wasn't only a linear relationship
+ 
+
+ align:start position:0%
+wasn't only a linear relationship
+between the energy of those ejected
+
+ align:start position:0%
+between the energy of those ejected
+ 
+
+ align:start position:0%
+between the energy of those ejected
+electrons and the frequency of the
+
+ align:start position:0%
+electrons and the frequency of the
+ 
+
+ align:start position:0%
+electrons and the frequency of the
+incident light but the slope in
+
+ align:start position:0%
+incident light but the slope in
+ 
+
+ align:start position:0%
+incident light but the slope in
+particular looked awfully close to this
+
+ align:start position:0%
+particular looked awfully close to this
+ 
+
+ align:start position:0%
+particular looked awfully close to this
+new value that had just been introduced
+
+ align:start position:0%
+new value that had just been introduced
+ 
+
+ align:start position:0%
+new value that had just been introduced
+in a totally different context by MOX
+
+ align:start position:0%
+in a totally different context by MOX
+ 
+
+ align:start position:0%
+in a totally different context by MOX
+plunk the slope of this plot looked very
+
+ align:start position:0%
+plunk the slope of this plot looked very
+ 
+
+ align:start position:0%
+plunk the slope of this plot looked very
+much like Planck's constant H that's
+
+ align:start position:0%
+much like Planck's constant H that's
+ 
+
+ align:start position:0%
+much like Planck's constant H that's
+something that Einstein begins to
+
+ align:start position:0%
+something that Einstein begins to
+ 
+
+ align:start position:0%
+something that Einstein begins to
+recognize by going carefully over these
+
+ align:start position:0%
+recognize by going carefully over these
+ 
+
+ align:start position:0%
+recognize by going carefully over these
+experimental results
+
+ align:start position:0%
+experimental results
+ 
+
+ align:start position:0%
+experimental results
+so that leads Einstein to think in the
+
+ align:start position:0%
+so that leads Einstein to think in the
+ 
+
+ align:start position:0%
+so that leads Einstein to think in the
+following way what if each of these
+
+ align:start position:0%
+following way what if each of these
+ 
+
+ align:start position:0%
+following way what if each of these
+discrete little bundles of light energy
+
+ align:start position:0%
+discrete little bundles of light energy
+ 
+
+ align:start position:0%
+discrete little bundles of light energy
+what if each individual like Quantum
+
+ align:start position:0%
+what if each individual like Quantum
+ 
+
+ align:start position:0%
+what if each individual like Quantum
+carried a fixed amount of energy
+
+ align:start position:0%
+carried a fixed amount of energy
+ 
+
+ align:start position:0%
+carried a fixed amount of energy
+proportional to the frequency of light
+
+ align:start position:0%
+proportional to the frequency of light
+ 
+
+ align:start position:0%
+proportional to the frequency of light
+with the constant of proportionality
+
+ align:start position:0%
+with the constant of proportionality
+ 
+
+ align:start position:0%
+with the constant of proportionality
+being this new constant introduced by
+
+ align:start position:0%
+being this new constant introduced by
+ 
+
+ align:start position:0%
+being this new constant introduced by
+MOX block what if light quanta these
+
+ align:start position:0%
+MOX block what if light quanta these
+ 
+
+ align:start position:0%
+MOX block what if light quanta these
+indivisible pellets of light had to
+
+ align:start position:0%
+indivisible pellets of light had to
+ 
+
+ align:start position:0%
+indivisible pellets of light had to
+carry a fixed quantized amount of energy
+
+ align:start position:0%
+carry a fixed quantized amount of energy
+ 
+
+ align:start position:0%
+carry a fixed quantized amount of energy
+not some continuous range that could
+
+ align:start position:0%
+not some continuous range that could
+ 
+
+ align:start position:0%
+not some continuous range that could
+have been any old value
+
+ align:start position:0%
+have been any old value
+ 
+
+ align:start position:0%
+have been any old value
+if that's the case then you have on this
+
+ align:start position:0%
+if that's the case then you have on this
+ 
+
+ align:start position:0%
+if that's the case then you have on this
+photocathode on this conducting plate in
+
+ align:start position:0%
+photocathode on this conducting plate in
+ 
+
+ align:start position:0%
+photocathode on this conducting plate in
+lennar's experiment you have raining
+
+ align:start position:0%
+lennar's experiment you have raining
+ 
+
+ align:start position:0%
+lennar's experiment you have raining
+down on it pellets and pellets each
+
+ align:start position:0%
+down on it pellets and pellets each
+ 
+
+ align:start position:0%
+down on it pellets and pellets each
+carrying a fixed amount of energy age
+
+ align:start position:0%
+carrying a fixed amount of energy age
+ 
+
+ align:start position:0%
+carrying a fixed amount of energy age
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+so then you can imagine an individual
+
+ align:start position:0%
+so then you can imagine an individual
+ 
+
+ align:start position:0%
+so then you can imagine an individual
+like Quantum not some spread out wave an
+
+ align:start position:0%
+like Quantum not some spread out wave an
+ 
+
+ align:start position:0%
+like Quantum not some spread out wave an
+individual particle basically smacking
+
+ align:start position:0%
+individual particle basically smacking
+ 
+
+ align:start position:0%
+individual particle basically smacking
+into an individual electron now it looks
+
+ align:start position:0%
+into an individual electron now it looks
+ 
+
+ align:start position:0%
+into an individual electron now it looks
+like colliding billiard balls so how
+
+ align:start position:0%
+like colliding billiard balls so how
+ 
+
+ align:start position:0%
+like colliding billiard balls so how
+will the energy of the electron change
+
+ align:start position:0%
+will the energy of the electron change
+ 
+
+ align:start position:0%
+will the energy of the electron change
+after it gets smacked by a discrete
+
+ align:start position:0%
+after it gets smacked by a discrete
+ 
+
+ align:start position:0%
+after it gets smacked by a discrete
+pellet of energy a light Quantum with
+
+ align:start position:0%
+pellet of energy a light Quantum with
+ 
+
+ align:start position:0%
+pellet of energy a light Quantum with
+energy H Nu the electron should acquire
+
+ align:start position:0%
+energy H Nu the electron should acquire
+ 
+
+ align:start position:0%
+energy H Nu the electron should acquire
+a predictable amount of energy it should
+
+ align:start position:0%
+a predictable amount of energy it should
+ 
+
+ align:start position:0%
+a predictable amount of energy it should
+absorb that energy carried by the Light
+
+ align:start position:0%
+absorb that energy carried by the Light
+ 
+
+ align:start position:0%
+absorb that energy carried by the Light
+quantum
+
+ align:start position:0%
+quantum
+ 
+
+ align:start position:0%
+quantum
+and it will and yet there will be some
+
+ align:start position:0%
+and it will and yet there will be some
+ 
+
+ align:start position:0%
+and it will and yet there will be some
+some extra energy kind of holding that
+
+ align:start position:0%
+some extra energy kind of holding that
+ 
+
+ align:start position:0%
+some extra energy kind of holding that
+electron bound to its uh atoms and
+
+ align:start position:0%
+electron bound to its uh atoms and
+ 
+
+ align:start position:0%
+electron bound to its uh atoms and
+molecules in the metal that became known
+
+ align:start position:0%
+molecules in the metal that became known
+ 
+
+ align:start position:0%
+molecules in the metal that became known
+as the work function that's kind of like
+
+ align:start position:0%
+as the work function that's kind of like
+ 
+
+ align:start position:0%
+as the work function that's kind of like
+The Binding energy these aren't free
+
+ align:start position:0%
+The Binding energy these aren't free
+ 
+
+ align:start position:0%
+The Binding energy these aren't free
+electrons in in space these electrons
+
+ align:start position:0%
+electrons in in space these electrons
+ 
+
+ align:start position:0%
+electrons in in space these electrons
+bound to a piece of metal there's some
+
+ align:start position:0%
+bound to a piece of metal there's some
+ 
+
+ align:start position:0%
+bound to a piece of metal there's some
+intermolecular or Atomic forces whatever
+
+ align:start position:0%
+intermolecular or Atomic forces whatever
+ 
+
+ align:start position:0%
+intermolecular or Atomic forces whatever
+they are they might vary by material
+
+ align:start position:0%
+they are they might vary by material
+ 
+
+ align:start position:0%
+they are they might vary by material
+there's some function that was often
+
+ align:start position:0%
+there's some function that was often
+ 
+
+ align:start position:0%
+there's some function that was often
+called uh by the Greek letter Capital
+
+ align:start position:0%
+called uh by the Greek letter Capital
+ 
+
+ align:start position:0%
+called uh by the Greek letter Capital
+Phi again a kind of binding energy
+
+ align:start position:0%
+Phi again a kind of binding energy
+ 
+
+ align:start position:0%
+Phi again a kind of binding energy
+and so the electron won't be kicked out
+
+ align:start position:0%
+and so the electron won't be kicked out
+ 
+
+ align:start position:0%
+and so the electron won't be kicked out
+of that piece of metal unless the energy
+
+ align:start position:0%
+of that piece of metal unless the energy
+ 
+
+ align:start position:0%
+of that piece of metal unless the energy
+it absorbs from that discrete like
+
+ align:start position:0%
+it absorbs from that discrete like
+ 
+
+ align:start position:0%
+it absorbs from that discrete like
+Quantum exceeds that binding energy the
+
+ align:start position:0%
+Quantum exceeds that binding energy the
+ 
+
+ align:start position:0%
+Quantum exceeds that binding energy the
+energy holding it in place has to be
+
+ align:start position:0%
+energy holding it in place has to be
+ 
+
+ align:start position:0%
+energy holding it in place has to be
+overcome or exceeded By the Light by the
+
+ align:start position:0%
+overcome or exceeded By the Light by the
+ 
+
+ align:start position:0%
+overcome or exceeded By the Light by the
+energy transferred by that light quantum
+
+ align:start position:0%
+energy transferred by that light quantum
+ 
+
+ align:start position:0%
+energy transferred by that light quantum
+if that's the case then of course there
+
+ align:start position:0%
+if that's the case then of course there
+ 
+
+ align:start position:0%
+if that's the case then of course there
+should be a threshold frequency only
+
+ align:start position:0%
+should be a threshold frequency only
+ 
+
+ align:start position:0%
+should be a threshold frequency only
+when each individual Quantum of light
+
+ align:start position:0%
+when each individual Quantum of light
+ 
+
+ align:start position:0%
+when each individual Quantum of light
+each little pellet a discrete carrier of
+
+ align:start position:0%
+each little pellet a discrete carrier of
+ 
+
+ align:start position:0%
+each little pellet a discrete carrier of
+energy in that incoming light
+
+ align:start position:0%
+energy in that incoming light
+ 
+
+ align:start position:0%
+energy in that incoming light
+carries enough energy individually to
+
+ align:start position:0%
+carries enough energy individually to
+ 
+
+ align:start position:0%
+carries enough energy individually to
+overcome that binding energy or the work
+
+ align:start position:0%
+overcome that binding energy or the work
+ 
+
+ align:start position:0%
+overcome that binding energy or the work
+function only then would any electrons
+
+ align:start position:0%
+function only then would any electrons
+ 
+
+ align:start position:0%
+function only then would any electrons
+be ejected from that piece of metal
+
+ align:start position:0%
+be ejected from that piece of metal
+ 
+
+ align:start position:0%
+be ejected from that piece of metal
+so the threshold frequency should depend
+
+ align:start position:0%
+so the threshold frequency should depend
+ 
+
+ align:start position:0%
+so the threshold frequency should depend
+on that binding energy that work
+
+ align:start position:0%
+on that binding energy that work
+ 
+
+ align:start position:0%
+on that binding energy that work
+function divided by plot's constant
+
+ align:start position:0%
+function divided by plot's constant
+ 
+
+ align:start position:0%
+function divided by plot's constant
+basically what's the threshold that
+
+ align:start position:0%
+basically what's the threshold that
+ 
+
+ align:start position:0%
+basically what's the threshold that
+would set this energy exactly to zero as
+
+ align:start position:0%
+would set this energy exactly to zero as
+ 
+
+ align:start position:0%
+would set this energy exactly to zero as
+opposed to it having a negative energy
+
+ align:start position:0%
+opposed to it having a negative energy
+ 
+
+ align:start position:0%
+opposed to it having a negative energy
+we should say it's bound in place so you
+
+ align:start position:0%
+we should say it's bound in place so you
+ 
+
+ align:start position:0%
+we should say it's bound in place so you
+just solve for when does the electron
+
+ align:start position:0%
+just solve for when does the electron
+ 
+
+ align:start position:0%
+just solve for when does the electron
+just cross that threshold as energy
+
+ align:start position:0%
+just cross that threshold as energy
+ 
+
+ align:start position:0%
+just cross that threshold as energy
+oh it's when Nu equals Phi over H that
+
+ align:start position:0%
+oh it's when Nu equals Phi over H that
+ 
+
+ align:start position:0%
+oh it's when Nu equals Phi over H that
+would that would give you the threshold
+
+ align:start position:0%
+would that would give you the threshold
+ 
+
+ align:start position:0%
+would that would give you the threshold
+any additional energy any higher energy
+
+ align:start position:0%
+any additional energy any higher energy
+ 
+
+ align:start position:0%
+any additional energy any higher energy
+carried by light quanta as you tune the
+
+ align:start position:0%
+carried by light quanta as you tune the
+ 
+
+ align:start position:0%
+carried by light quanta as you tune the
+frequency the incident light higher and
+
+ align:start position:0%
+frequency the incident light higher and
+ 
+
+ align:start position:0%
+frequency the incident light higher and
+higher each electron will absorb more
+
+ align:start position:0%
+higher each electron will absorb more
+ 
+
+ align:start position:0%
+higher each electron will absorb more
+energy than that threshold and it will
+
+ align:start position:0%
+energy than that threshold and it will
+ 
+
+ align:start position:0%
+energy than that threshold and it will
+continue to grow linearly with slope h
+
+ align:start position:0%
+continue to grow linearly with slope h
+ 
+
+ align:start position:0%
+continue to grow linearly with slope h
+so the idea that Einstein puts together
+
+ align:start position:0%
+so the idea that Einstein puts together
+ 
+
+ align:start position:0%
+so the idea that Einstein puts together
+is heuristic it is suggestive idea in
+
+ align:start position:0%
+is heuristic it is suggestive idea in
+ 
+
+ align:start position:0%
+is heuristic it is suggestive idea in
+this 1905 paper is that the light
+
+ align:start position:0%
+this 1905 paper is that the light
+ 
+
+ align:start position:0%
+this 1905 paper is that the light
+shining on this metal plate is not some
+
+ align:start position:0%
+shining on this metal plate is not some
+ 
+
+ align:start position:0%
+shining on this metal plate is not some
+extended continuous wave kind of lapping
+
+ align:start position:0%
+extended continuous wave kind of lapping
+ 
+
+ align:start position:0%
+extended continuous wave kind of lapping
+up on shore like a Maximilian wave but
+
+ align:start position:0%
+up on shore like a Maximilian wave but
+ 
+
+ align:start position:0%
+up on shore like a Maximilian wave but
+actually a shower of discrete marbles
+
+ align:start position:0%
+actually a shower of discrete marbles
+ 
+
+ align:start position:0%
+actually a shower of discrete marbles
+Each of which could Collide like two
+
+ align:start position:0%
+Each of which could Collide like two
+ 
+
+ align:start position:0%
+Each of which could Collide like two
+body collisions like billiard balls on a
+
+ align:start position:0%
+body collisions like billiard balls on a
+ 
+
+ align:start position:0%
+body collisions like billiard balls on a
+on a billion table or you know on pool
+
+ align:start position:0%
+on a billion table or you know on pool
+ 
+
+ align:start position:0%
+on a billion table or you know on pool
+table they would have two body
+
+ align:start position:0%
+table they would have two body
+ 
+
+ align:start position:0%
+table they would have two body
+collisions Each of which can then impart
+
+ align:start position:0%
+collisions Each of which can then impart
+ 
+
+ align:start position:0%
+collisions Each of which can then impart
+certain energy uh to to their to their
+
+ align:start position:0%
+certain energy uh to to their to their
+ 
+
+ align:start position:0%
+certain energy uh to to their to their
+colliding electrons so I like to think
+
+ align:start position:0%
+colliding electrons so I like to think
+ 
+
+ align:start position:0%
+colliding electrons so I like to think
+of it this way imagine electrons are
+
+ align:start position:0%
+of it this way imagine electrons are
+ 
+
+ align:start position:0%
+of it this way imagine electrons are
+like a bucket full of ping-pong balls so
+
+ align:start position:0%
+like a bucket full of ping-pong balls so
+ 
+
+ align:start position:0%
+like a bucket full of ping-pong balls so
+ordinarily they're Bound in place that's
+
+ align:start position:0%
+ordinarily they're Bound in place that's
+ 
+
+ align:start position:0%
+ordinarily they're Bound in place that's
+like that work function the ping pong
+
+ align:start position:0%
+like that work function the ping pong
+ 
+
+ align:start position:0%
+like that work function the ping pong
+balls aren't free to move any old place
+
+ align:start position:0%
+balls aren't free to move any old place
+ 
+
+ align:start position:0%
+balls aren't free to move any old place
+they're stuck they have a certain kind
+
+ align:start position:0%
+they're stuck they have a certain kind
+ 
+
+ align:start position:0%
+they're stuck they have a certain kind
+of binding energy think of that as like
+
+ align:start position:0%
+of binding energy think of that as like
+ 
+
+ align:start position:0%
+of binding energy think of that as like
+that work function Phi
+
+ align:start position:0%
+that work function Phi
+ 
+
+ align:start position:0%
+that work function Phi
+then you start chucking marbles at it
+
+ align:start position:0%
+then you start chucking marbles at it
+ 
+
+ align:start position:0%
+then you start chucking marbles at it
+you imagine like flinging marbles into
+
+ align:start position:0%
+you imagine like flinging marbles into
+ 
+
+ align:start position:0%
+you imagine like flinging marbles into
+that bucket
+
+ align:start position:0%
+that bucket
+ 
+
+ align:start position:0%
+that bucket
+if the marbles individually carry enough
+
+ align:start position:0%
+if the marbles individually carry enough
+ 
+
+ align:start position:0%
+if the marbles individually carry enough
+energy they're going to collide with
+
+ align:start position:0%
+energy they're going to collide with
+ 
+
+ align:start position:0%
+energy they're going to collide with
+individual ping-pong balls and if
+
+ align:start position:0%
+individual ping-pong balls and if
+ 
+
+ align:start position:0%
+individual ping-pong balls and if
+they're Inc if a marbles incoming energy
+
+ align:start position:0%
+they're Inc if a marbles incoming energy
+ 
+
+ align:start position:0%
+they're Inc if a marbles incoming energy
+is more than this binding energy holding
+
+ align:start position:0%
+is more than this binding energy holding
+ 
+
+ align:start position:0%
+is more than this binding energy holding
+the ping-pong balls in the bucket you'll
+
+ align:start position:0%
+the ping-pong balls in the bucket you'll
+ 
+
+ align:start position:0%
+the ping-pong balls in the bucket you'll
+kick a few out that's the picture that
+
+ align:start position:0%
+kick a few out that's the picture that
+ 
+
+ align:start position:0%
+kick a few out that's the picture that
+Einstein has in mind in that same
+
+ align:start position:0%
+Einstein has in mind in that same
+ 
+
+ align:start position:0%
+Einstein has in mind in that same
+actually quite long article this very
+
+ align:start position:0%
+actually quite long article this very
+ 
+
+ align:start position:0%
+actually quite long article this very
+same article in 1905 Einstein also
+
+ align:start position:0%
+same article in 1905 Einstein also
+ 
+
+ align:start position:0%
+same article in 1905 Einstein also
+revisits plug starvation of the black
+
+ align:start position:0%
+revisits plug starvation of the black
+ 
+
+ align:start position:0%
+revisits plug starvation of the black
+body formula that that function that we
+
+ align:start position:0%
+body formula that that function that we
+ 
+
+ align:start position:0%
+body formula that that function that we
+called the spectral energy density
+
+ align:start position:0%
+called the spectral energy density
+ 
+
+ align:start position:0%
+called the spectral energy density
+little U and he rederives plot's formula
+
+ align:start position:0%
+little U and he rederives plot's formula
+ 
+
+ align:start position:0%
+little U and he rederives plot's formula
+assuming that the radiation being
+
+ align:start position:0%
+assuming that the radiation being
+ 
+
+ align:start position:0%
+assuming that the radiation being
+emitted from that cavity radiation
+
+ align:start position:0%
+emitted from that cavity radiation
+ 
+
+ align:start position:0%
+emitted from that cavity radiation
+could be treated like a gas of these
+
+ align:start position:0%
+could be treated like a gas of these
+ 
+
+ align:start position:0%
+could be treated like a gas of these
+individual particles Each of which has a
+
+ align:start position:0%
+individual particles Each of which has a
+ 
+
+ align:start position:0%
+individual particles Each of which has a
+quantized energy equals H Nu this is the
+
+ align:start position:0%
+quantized energy equals H Nu this is the
+ 
+
+ align:start position:0%
+quantized energy equals H Nu this is the
+modern derivation that we inherit and
+
+ align:start position:0%
+modern derivation that we inherit and
+ 
+
+ align:start position:0%
+modern derivation that we inherit and
+use today that's much more like the
+
+ align:start position:0%
+use today that's much more like the
+ 
+
+ align:start position:0%
+use today that's much more like the
+derivation I give in those brief
+
+ align:start position:0%
+derivation I give in those brief
+ 
+
+ align:start position:0%
+derivation I give in those brief
+optional notes so in the same article
+
+ align:start position:0%
+optional notes so in the same article
+ 
+
+ align:start position:0%
+optional notes so in the same article
+Einstein both kind of offers a heuristic
+
+ align:start position:0%
+Einstein both kind of offers a heuristic
+ 
+
+ align:start position:0%
+Einstein both kind of offers a heuristic
+explanation for Leonard's otherwise
+
+ align:start position:0%
+explanation for Leonard's otherwise
+ 
+
+ align:start position:0%
+explanation for Leonard's otherwise
+quite puzzling experiment results he
+
+ align:start position:0%
+quite puzzling experiment results he
+ 
+
+ align:start position:0%
+quite puzzling experiment results he
+revisits and kind of reinterprets clocks
+
+ align:start position:0%
+revisits and kind of reinterprets clocks
+ 
+
+ align:start position:0%
+revisits and kind of reinterprets clocks
+own by now rather a well-known
+
+ align:start position:0%
+own by now rather a well-known
+ 
+
+ align:start position:0%
+own by now rather a well-known
+expression for Black by variation all
+
+ align:start position:0%
+expression for Black by variation all
+ 
+
+ align:start position:0%
+expression for Black by variation all
+from the starting point of view that
+
+ align:start position:0%
+from the starting point of view that
+ 
+
+ align:start position:0%
+from the starting point of view that
+light is quantized and each individual
+
+ align:start position:0%
+light is quantized and each individual
+ 
+
+ align:start position:0%
+light is quantized and each individual
+like Quantum carries a unit amount of
+
+ align:start position:0%
+like Quantum carries a unit amount of
+ 
+
+ align:start position:0%
+like Quantum carries a unit amount of
+energy set by H Nu so we might figure
+
+ align:start position:0%
+energy set by H Nu so we might figure
+ 
+
+ align:start position:0%
+energy set by H Nu so we might figure
+okay he solved everything everyone must
+
+ align:start position:0%
+okay he solved everything everyone must
+ 
+
+ align:start position:0%
+okay he solved everything everyone must
+have been convinced right
+
+ align:start position:0%
+have been convinced right
+ 
+
+ align:start position:0%
+have been convinced right
+no no no we've learned from this course
+
+ align:start position:0%
+no no no we've learned from this course
+ 
+
+ align:start position:0%
+no no no we've learned from this course
+already things you hardly are hardly
+
+ align:start position:0%
+already things you hardly are hardly
+ 
+
+ align:start position:0%
+already things you hardly are hardly
+ever work that way and in Einstein's
+
+ align:start position:0%
+ever work that way and in Einstein's
+ 
+
+ align:start position:0%
+ever work that way and in Einstein's
+case in particular remember he was still
+
+ align:start position:0%
+case in particular remember he was still
+ 
+
+ align:start position:0%
+case in particular remember he was still
+a little-known patent clerk kind of out
+
+ align:start position:0%
+a little-known patent clerk kind of out
+ 
+
+ align:start position:0%
+a little-known patent clerk kind of out
+of the of the main Elite centers of
+
+ align:start position:0%
+of the of the main Elite centers of
+ 
+
+ align:start position:0%
+of the of the main Elite centers of
+research
+
+ align:start position:0%
+research
+ 
+
+ align:start position:0%
+research
+this was facing enormous skepticism even
+
+ align:start position:0%
+this was facing enormous skepticism even
+ 
+
+ align:start position:0%
+this was facing enormous skepticism even
+years after Einstein himself became much
+
+ align:start position:0%
+years after Einstein himself became much
+ 
+
+ align:start position:0%
+years after Einstein himself became much
+more prominent it was really more than
+
+ align:start position:0%
+more prominent it was really more than
+ 
+
+ align:start position:0%
+more prominent it was really more than
+15 years until the majority of members
+
+ align:start position:0%
+15 years until the majority of members
+ 
+
+ align:start position:0%
+15 years until the majority of members
+of the physics Community really took
+
+ align:start position:0%
+of the physics Community really took
+ 
+
+ align:start position:0%
+of the physics Community really took
+this idea at all seriously and here's
+
+ align:start position:0%
+this idea at all seriously and here's
+ 
+
+ align:start position:0%
+this idea at all seriously and here's
+again one of my favorite examples of
+
+ align:start position:0%
+again one of my favorite examples of
+ 
+
+ align:start position:0%
+again one of my favorite examples of
+that here's our again our old friend box
+
+ align:start position:0%
+that here's our again our old friend box
+ 
+
+ align:start position:0%
+that here's our again our old friend box
+plug writing this is a letter of
+
+ align:start position:0%
+plug writing this is a letter of
+ 
+
+ align:start position:0%
+plug writing this is a letter of
+recommendation he's trying to say how
+
+ align:start position:0%
+recommendation he's trying to say how
+ 
+
+ align:start position:0%
+recommendation he's trying to say how
+great Einstein's work is by 1913. how
+
+ align:start position:0%
+great Einstein's work is by 1913. how
+ 
+
+ align:start position:0%
+great Einstein's work is by 1913. how
+does Einstein is no longer the unknown
+
+ align:start position:0%
+does Einstein is no longer the unknown
+ 
+
+ align:start position:0%
+does Einstein is no longer the unknown
+patent click
+
+ align:start position:0%
+patent click
+ 
+
+ align:start position:0%
+patent click
+Clark was trying to convince his
+
+ align:start position:0%
+Clark was trying to convince his
+ 
+
+ align:start position:0%
+Clark was trying to convince his
+colleagues to offer a very prestigious
+
+ align:start position:0%
+colleagues to offer a very prestigious
+ 
+
+ align:start position:0%
+colleagues to offer a very prestigious
+new job to Einstein at the Prussian
+
+ align:start position:0%
+new job to Einstein at the Prussian
+ 
+
+ align:start position:0%
+new job to Einstein at the Prussian
+Academy of Sciences which in fact
+
+ align:start position:0%
+Academy of Sciences which in fact
+ 
+
+ align:start position:0%
+Academy of Sciences which in fact
+Einstein would would soon be offered
+
+ align:start position:0%
+Einstein would would soon be offered
+ 
+
+ align:start position:0%
+Einstein would would soon be offered
+we'd move to Berlin and in his letter
+
+ align:start position:0%
+we'd move to Berlin and in his letter
+ 
+
+ align:start position:0%
+we'd move to Berlin and in his letter
+saying how great Einstein's work is
+
+ align:start position:0%
+saying how great Einstein's work is
+ 
+
+ align:start position:0%
+saying how great Einstein's work is
+plugs as the following in some one can
+
+ align:start position:0%
+plugs as the following in some one can
+ 
+
+ align:start position:0%
+plugs as the following in some one can
+say there is hardly one among the great
+
+ align:start position:0%
+say there is hardly one among the great
+ 
+
+ align:start position:0%
+say there is hardly one among the great
+problems in which modern physics is so
+
+ align:start position:0%
+problems in which modern physics is so
+ 
+
+ align:start position:0%
+problems in which modern physics is so
+rich to which eyesight has not made a
+
+ align:start position:0%
+rich to which eyesight has not made a
+ 
+
+ align:start position:0%
+rich to which eyesight has not made a
+remarkable contribution that sounds nice
+
+ align:start position:0%
+remarkable contribution that sounds nice
+ 
+
+ align:start position:0%
+remarkable contribution that sounds nice
+that he may sometimes have missed the
+
+ align:start position:0%
+that he may sometimes have missed the
+ 
+
+ align:start position:0%
+that he may sometimes have missed the
+Target in his speculations as for
+
+ align:start position:0%
+Target in his speculations as for
+ 
+
+ align:start position:0%
+Target in his speculations as for
+example in his hypothesis of like quanta
+
+ align:start position:0%
+example in his hypothesis of like quanta
+ 
+
+ align:start position:0%
+example in his hypothesis of like quanta
+cannot really be held too much against
+
+ align:start position:0%
+cannot really be held too much against
+ 
+
+ align:start position:0%
+cannot really be held too much against
+him which is to say a lot of the work
+
+ align:start position:0%
+him which is to say a lot of the work
+ 
+
+ align:start position:0%
+him which is to say a lot of the work
+this person has done is very interesting
+
+ align:start position:0%
+this person has done is very interesting
+ 
+
+ align:start position:0%
+this person has done is very interesting
+he's clearly mistaken about light quanta
+
+ align:start position:0%
+he's clearly mistaken about light quanta
+ 
+
+ align:start position:0%
+he's clearly mistaken about light quanta
+but let's let him into our new club
+
+ align:start position:0%
+but let's let him into our new club
+ 
+
+ align:start position:0%
+but let's let him into our new club
+anyway I find that terrific okay let me
+
+ align:start position:0%
+anyway I find that terrific okay let me
+ 
+
+ align:start position:0%
+anyway I find that terrific okay let me
+pause there again ask any questions on
+
+ align:start position:0%
+pause there again ask any questions on
+ 
+
+ align:start position:0%
+pause there again ask any questions on
+the like Quantum work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fisher asks in Einstein's paper
+
+ align:start position:0%
+Fisher asks in Einstein's paper
+ 
+
+ align:start position:0%
+Fisher asks in Einstein's paper
+it didn't make any nods in Newton's
+
+ align:start position:0%
+it didn't make any nods in Newton's
+ 
+
+ align:start position:0%
+it didn't make any nods in Newton's
+original thought that life was Corpus
+
+ align:start position:0%
+original thought that life was Corpus
+ 
+
+ align:start position:0%
+original thought that life was Corpus
+was very good honestly I don't remember
+
+ align:start position:0%
+was very good honestly I don't remember
+ 
+
+ align:start position:0%
+was very good honestly I don't remember
+that's an excellent question let me back
+
+ align:start position:0%
+that's an excellent question let me back
+ 
+
+ align:start position:0%
+that's an excellent question let me back
+up others might know as well it was
+
+ align:start position:0%
+up others might know as well it was
+ 
+
+ align:start position:0%
+up others might know as well it was
+worth emphasizing the the big picture
+
+ align:start position:0%
+worth emphasizing the the big picture
+ 
+
+ align:start position:0%
+worth emphasizing the the big picture
+question it does light consist of waves
+
+ align:start position:0%
+question it does light consist of waves
+ 
+
+ align:start position:0%
+question it does light consist of waves
+or particles that actually has a really
+
+ align:start position:0%
+or particles that actually has a really
+ 
+
+ align:start position:0%
+or particles that actually has a really
+long history I guess I gave a little
+
+ align:start position:0%
+long history I guess I gave a little
+ 
+
+ align:start position:0%
+long history I guess I gave a little
+preview of that although I didn't Linger
+
+ align:start position:0%
+preview of that although I didn't Linger
+ 
+
+ align:start position:0%
+preview of that although I didn't Linger
+on it even in one of our first class
+
+ align:start position:0%
+on it even in one of our first class
+ 
+
+ align:start position:0%
+on it even in one of our first class
+sessions for this class you might know
+
+ align:start position:0%
+sessions for this class you might know
+ 
+
+ align:start position:0%
+sessions for this class you might know
+from other readings or other classes
+
+ align:start position:0%
+from other readings or other classes
+ 
+
+ align:start position:0%
+from other readings or other classes
+the reason was actually a big deal
+
+ align:start position:0%
+the reason was actually a big deal
+ 
+
+ align:start position:0%
+the reason was actually a big deal
+around 1800 going back to sort of early
+
+ align:start position:0%
+around 1800 going back to sort of early
+ 
+
+ align:start position:0%
+around 1800 going back to sort of early
+in what Michael Faraday's own career it
+
+ align:start position:0%
+in what Michael Faraday's own career it
+ 
+
+ align:start position:0%
+in what Michael Faraday's own career it
+was a big deal to think of light as
+
+ align:start position:0%
+was a big deal to think of light as
+ 
+
+ align:start position:0%
+was a big deal to think of light as
+waves because since at least Newton's
+
+ align:start position:0%
+waves because since at least Newton's
+ 
+
+ align:start position:0%
+waves because since at least Newton's
+day another century and a quarter before
+
+ align:start position:0%
+day another century and a quarter before
+ 
+
+ align:start position:0%
+day another century and a quarter before
+that going back to the later years of
+
+ align:start position:0%
+that going back to the later years of
+ 
+
+ align:start position:0%
+that going back to the later years of
+the 17th century the 1660s and so on
+
+ align:start position:0%
+the 17th century the 1660s and so on
+ 
+
+ align:start position:0%
+the 17th century the 1660s and so on
+Newton and other leading Scholars had
+
+ align:start position:0%
+Newton and other leading Scholars had
+ 
+
+ align:start position:0%
+Newton and other leading Scholars had
+convinced themselves the light actually
+
+ align:start position:0%
+convinced themselves the light actually
+ 
+
+ align:start position:0%
+convinced themselves the light actually
+consisted of a stream of particles
+
+ align:start position:0%
+consisted of a stream of particles
+ 
+
+ align:start position:0%
+consisted of a stream of particles
+Newton called them corpuscles exactly as
+
+ align:start position:0%
+Newton called them corpuscles exactly as
+ 
+
+ align:start position:0%
+Newton called them corpuscles exactly as
+Fisher says so Newton was convinced that
+
+ align:start position:0%
+Fisher says so Newton was convinced that
+ 
+
+ align:start position:0%
+Fisher says so Newton was convinced that
+light was corpuscular we might now say
+
+ align:start position:0%
+light was corpuscular we might now say
+ 
+
+ align:start position:0%
+light was corpuscular we might now say
+the light was made up of a stream of
+
+ align:start position:0%
+the light was made up of a stream of
+ 
+
+ align:start position:0%
+the light was made up of a stream of
+particles that's in 1660s 70s 80s would
+
+ align:start position:0%
+particles that's in 1660s 70s 80s would
+ 
+
+ align:start position:0%
+particles that's in 1660s 70s 80s would
+become super influential he writes a
+
+ align:start position:0%
+become super influential he writes a
+ 
+
+ align:start position:0%
+become super influential he writes a
+whole book called Optics Newton does
+
+ align:start position:0%
+whole book called Optics Newton does
+ 
+
+ align:start position:0%
+whole book called Optics Newton does
+first published in round 1703 or
+
+ align:start position:0%
+first published in round 1703 or
+ 
+
+ align:start position:0%
+first published in round 1703 or
+something like that I was like okay
+
+ align:start position:0%
+something like that I was like okay
+ 
+
+ align:start position:0%
+something like that I was like okay
+Newton has spoken lights particles got
+
+ align:start position:0%
+Newton has spoken lights particles got
+ 
+
+ align:start position:0%
+Newton has spoken lights particles got
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and so it was a pretty big deal when
+
+ align:start position:0%
+and so it was a pretty big deal when
+ 
+
+ align:start position:0%
+and so it was a pretty big deal when
+about a hundred years after that the
+
+ align:start position:0%
+about a hundred years after that the
+ 
+
+ align:start position:0%
+about a hundred years after that the
+consensus shifts both in Britain and in
+
+ align:start position:0%
+consensus shifts both in Britain and in
+ 
+
+ align:start position:0%
+consensus shifts both in Britain and in
+France and ultimately many many other
+
+ align:start position:0%
+France and ultimately many many other
+ 
+
+ align:start position:0%
+France and ultimately many many other
+places but hang on light seems to have
+
+ align:start position:0%
+places but hang on light seems to have
+ 
+
+ align:start position:0%
+places but hang on light seems to have
+all these wave-like properties like
+
+ align:start position:0%
+all these wave-like properties like
+ 
+
+ align:start position:0%
+all these wave-like properties like
+interference and diffraction and
+
+ align:start position:0%
+interference and diffraction and
+ 
+
+ align:start position:0%
+interference and diffraction and
+refraction and all these things that
+
+ align:start position:0%
+refraction and all these things that
+ 
+
+ align:start position:0%
+refraction and all these things that
+helped set in motion the ideas of a
+
+ align:start position:0%
+helped set in motion the ideas of a
+ 
+
+ align:start position:0%
+helped set in motion the ideas of a
+light-bearing ether if light is a wave
+
+ align:start position:0%
+light-bearing ether if light is a wave
+ 
+
+ align:start position:0%
+light-bearing ether if light is a wave
+what does it wave in so you have these
+
+ align:start position:0%
+what does it wave in so you have these
+ 
+
+ align:start position:0%
+what does it wave in so you have these
+huge kind of century long shifts between
+
+ align:start position:0%
+huge kind of century long shifts between
+ 
+
+ align:start position:0%
+huge kind of century long shifts between
+assumptions about just what's light made
+
+ align:start position:0%
+assumptions about just what's light made
+ 
+
+ align:start position:0%
+assumptions about just what's light made
+of in general let alone these specific
+
+ align:start position:0%
+of in general let alone these specific
+ 
+
+ align:start position:0%
+of in general let alone these specific
+questions about how it interacts with
+
+ align:start position:0%
+questions about how it interacts with
+ 
+
+ align:start position:0%
+questions about how it interacts with
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+so it was certainly well known well
+
+ align:start position:0%
+so it was certainly well known well
+ 
+
+ align:start position:0%
+so it was certainly well known well
+before Einstein's day that Newton had
+
+ align:start position:0%
+before Einstein's day that Newton had
+ 
+
+ align:start position:0%
+before Einstein's day that Newton had
+been let's say a corpuscularist but it's
+
+ align:start position:0%
+been let's say a corpuscularist but it's
+ 
+
+ align:start position:0%
+been let's say a corpuscularist but it's
+a great question Fisher and I'd have to
+
+ align:start position:0%
+a great question Fisher and I'd have to
+ 
+
+ align:start position:0%
+a great question Fisher and I'd have to
+go back to my own copy uh in English
+
+ align:start position:0%
+go back to my own copy uh in English
+ 
+
+ align:start position:0%
+go back to my own copy uh in English
+translation my German to see whether
+
+ align:start position:0%
+translation my German to see whether
+ 
+
+ align:start position:0%
+translation my German to see whether
+Einstein paused to to reflect on that I
+
+ align:start position:0%
+Einstein paused to to reflect on that I
+ 
+
+ align:start position:0%
+Einstein paused to to reflect on that I
+don't remember interesting question
+
+ align:start position:0%
+don't remember interesting question
+ 
+
+ align:start position:0%
+don't remember interesting question
+uh Gary asked having written as a
+
+ align:start position:0%
+uh Gary asked having written as a
+ 
+
+ align:start position:0%
+uh Gary asked having written as a
+heuristic did Einstein believe it'd be
+
+ align:start position:0%
+heuristic did Einstein believe it'd be
+ 
+
+ align:start position:0%
+heuristic did Einstein believe it'd be
+quantitative fiber only later very good
+
+ align:start position:0%
+quantitative fiber only later very good
+ 
+
+ align:start position:0%
+quantitative fiber only later very good
+carry so my best understanding uh and
+
+ align:start position:0%
+carry so my best understanding uh and
+ 
+
+ align:start position:0%
+carry so my best understanding uh and
+again I haven't looked has directly in
+
+ align:start position:0%
+again I haven't looked has directly in
+ 
+
+ align:start position:0%
+again I haven't looked has directly in
+this but from my colleagues who have
+
+ align:start position:0%
+this but from my colleagues who have
+ 
+
+ align:start position:0%
+this but from my colleagues who have
+really poured over Einstein's
+
+ align:start position:0%
+really poured over Einstein's
+ 
+
+ align:start position:0%
+really poured over Einstein's
+um uh at the time unpublished
+
+ align:start position:0%
+um uh at the time unpublished
+ 
+
+ align:start position:0%
+um uh at the time unpublished
+correspondence his notes and so again we
+
+ align:start position:0%
+correspondence his notes and so again we
+ 
+
+ align:start position:0%
+correspondence his notes and so again we
+have a huge documentary base of how his
+
+ align:start position:0%
+have a huge documentary base of how his
+ 
+
+ align:start position:0%
+have a huge documentary base of how his
+thinking was evolving in those years
+
+ align:start position:0%
+thinking was evolving in those years
+ 
+
+ align:start position:0%
+thinking was evolving in those years
+it seems that Einstein thought this
+
+ align:start position:0%
+it seems that Einstein thought this
+ 
+
+ align:start position:0%
+it seems that Einstein thought this
+really really was true but for once he
+
+ align:start position:0%
+really really was true but for once he
+ 
+
+ align:start position:0%
+really really was true but for once he
+kind of hedged uh rhetorically so it
+
+ align:start position:0%
+kind of hedged uh rhetorically so it
+ 
+
+ align:start position:0%
+kind of hedged uh rhetorically so it
+seems that he was offering a heuristic
+
+ align:start position:0%
+seems that he was offering a heuristic
+ 
+
+ align:start position:0%
+seems that he was offering a heuristic
+explanation and going through actually a
+
+ align:start position:0%
+explanation and going through actually a
+ 
+
+ align:start position:0%
+explanation and going through actually a
+whole number of of episodes or scenarios
+
+ align:start position:0%
+whole number of of episodes or scenarios
+ 
+
+ align:start position:0%
+whole number of of episodes or scenarios
+where this suggestive hypothesis might
+
+ align:start position:0%
+where this suggestive hypothesis might
+ 
+
+ align:start position:0%
+where this suggestive hypothesis might
+be helpful
+
+ align:start position:0%
+be helpful
+ 
+
+ align:start position:0%
+be helpful
+but it seems that he was
+
+ align:start position:0%
+but it seems that he was
+ 
+
+ align:start position:0%
+but it seems that he was
+um he thought there was that this was
+
+ align:start position:0%
+um he thought there was that this was
+ 
+
+ align:start position:0%
+um he thought there was that this was
+not only a fiction
+
+ align:start position:0%
+not only a fiction
+ 
+
+ align:start position:0%
+not only a fiction
+uh he was however not sure how to square
+
+ align:start position:0%
+uh he was however not sure how to square
+ 
+
+ align:start position:0%
+uh he was however not sure how to square
+this in 1905 he wasn't sure how to
+
+ align:start position:0%
+this in 1905 he wasn't sure how to
+ 
+
+ align:start position:0%
+this in 1905 he wasn't sure how to
+square that with a centuries worth of
+
+ align:start position:0%
+square that with a centuries worth of
+ 
+
+ align:start position:0%
+square that with a centuries worth of
+evidence that light had wave-like
+
+ align:start position:0%
+evidence that light had wave-like
+ 
+
+ align:start position:0%
+evidence that light had wave-like
+Behavior like reflection refraction
+
+ align:start position:0%
+Behavior like reflection refraction
+ 
+
+ align:start position:0%
+Behavior like reflection refraction
+diffraction
+
+ align:start position:0%
+diffraction
+ 
+
+ align:start position:0%
+diffraction
+interference in general so it's not that
+
+ align:start position:0%
+interference in general so it's not that
+ 
+
+ align:start position:0%
+interference in general so it's not that
+I said uh there's nothing ever wavy
+
+ align:start position:0%
+I said uh there's nothing ever wavy
+ 
+
+ align:start position:0%
+I said uh there's nothing ever wavy
+about light you know it's always only
+
+ align:start position:0%
+about light you know it's always only
+ 
+
+ align:start position:0%
+about light you know it's always only
+particles but he was certainly and in
+
+ align:start position:0%
+particles but he was certainly and in
+ 
+
+ align:start position:0%
+particles but he was certainly and in
+his own kind of more private musings he
+
+ align:start position:0%
+his own kind of more private musings he
+ 
+
+ align:start position:0%
+his own kind of more private musings he
+seemed to think that one had to adopt
+
+ align:start position:0%
+seemed to think that one had to adopt
+ 
+
+ align:start position:0%
+seemed to think that one had to adopt
+these um it's really like particles a
+
+ align:start position:0%
+these um it's really like particles a
+ 
+
+ align:start position:0%
+these um it's really like particles a
+position in some scenarios more than
+
+ align:start position:0%
+position in some scenarios more than
+ 
+
+ align:start position:0%
+position in some scenarios more than
+others he was groping toward what we
+
+ align:start position:0%
+others he was groping toward what we
+ 
+
+ align:start position:0%
+others he was groping toward what we
+what what we see actually in the next
+
+ align:start position:0%
+what what we see actually in the next
+ 
+
+ align:start position:0%
+what what we see actually in the next
+part of today's class and it will chase
+
+ align:start position:0%
+part of today's class and it will chase
+ 
+
+ align:start position:0%
+part of today's class and it will chase
+us through upcoming class sessions he
+
+ align:start position:0%
+us through upcoming class sessions he
+ 
+
+ align:start position:0%
+us through upcoming class sessions he
+was beginning to Grapple with what would
+
+ align:start position:0%
+was beginning to Grapple with what would
+ 
+
+ align:start position:0%
+was beginning to Grapple with what would
+come to be called wave particle duality
+
+ align:start position:0%
+come to be called wave particle duality
+ 
+
+ align:start position:0%
+come to be called wave particle duality
+he certainly wasn't calling that yet in
+
+ align:start position:0%
+he certainly wasn't calling that yet in
+ 
+
+ align:start position:0%
+he certainly wasn't calling that yet in
+1905 but he was already as as his
+
+ align:start position:0%
+1905 but he was already as as his
+ 
+
+ align:start position:0%
+1905 but he was already as as his
+additional kind of documents from the
+
+ align:start position:0%
+additional kind of documents from the
+ 
+
+ align:start position:0%
+additional kind of documents from the
+time seemed to suggest
+
+ align:start position:0%
+time seemed to suggest
+ 
+
+ align:start position:0%
+time seemed to suggest
+he was already grappling with we really
+
+ align:start position:0%
+he was already grappling with we really
+ 
+
+ align:start position:0%
+he was already grappling with we really
+really need to treat light like waves
+
+ align:start position:0%
+really need to treat light like waves
+ 
+
+ align:start position:0%
+really need to treat light like waves
+for certain scenarios interference
+
+ align:start position:0%
+for certain scenarios interference
+ 
+
+ align:start position:0%
+for certain scenarios interference
+fringes being an obvious one and yet he
+
+ align:start position:0%
+fringes being an obvious one and yet he
+ 
+
+ align:start position:0%
+fringes being an obvious one and yet he
+in his own kind of you know heart of
+
+ align:start position:0%
+in his own kind of you know heart of
+ 
+
+ align:start position:0%
+in his own kind of you know heart of
+hearts he seemed pretty convinced that
+
+ align:start position:0%
+hearts he seemed pretty convinced that
+ 
+
+ align:start position:0%
+hearts he seemed pretty convinced that
+this corpuscular or Quantum nature
+
+ align:start position:0%
+this corpuscular or Quantum nature
+ 
+
+ align:start position:0%
+this corpuscular or Quantum nature
+seemed more than just a coincidence in
+
+ align:start position:0%
+seemed more than just a coincidence in
+ 
+
+ align:start position:0%
+seemed more than just a coincidence in
+other kinds of scenarios and that would
+
+ align:start position:0%
+other kinds of scenarios and that would
+ 
+
+ align:start position:0%
+other kinds of scenarios and that would
+kind of become um more and more of a
+
+ align:start position:0%
+kind of become um more and more of a
+ 
+
+ align:start position:0%
+kind of become um more and more of a
+a paradox to some or a challenge even
+
+ align:start position:0%
+a paradox to some or a challenge even
+ 
+
+ align:start position:0%
+a paradox to some or a challenge even
+Beyond Einstein himself
+
+ align:start position:0%
+Beyond Einstein himself
+ 
+
+ align:start position:0%
+Beyond Einstein himself
+and so the real question actually
+
+ align:start position:0%
+and so the real question actually
+ 
+
+ align:start position:0%
+and so the real question actually
+becomes why was Einstein hedging his
+
+ align:start position:0%
+becomes why was Einstein hedging his
+ 
+
+ align:start position:0%
+becomes why was Einstein hedging his
+bets rhetorically rather than what did
+
+ align:start position:0%
+bets rhetorically rather than what did
+ 
+
+ align:start position:0%
+bets rhetorically rather than what did
+he really believe because we saw in in
+
+ align:start position:0%
+he really believe because we saw in in
+ 
+
+ align:start position:0%
+he really believe because we saw in in
+his paper just a few weeks later that he
+
+ align:start position:0%
+his paper just a few weeks later that he
+ 
+
+ align:start position:0%
+his paper just a few weeks later that he
+submits on the electrodynamics of living
+
+ align:start position:0%
+submits on the electrodynamics of living
+ 
+
+ align:start position:0%
+submits on the electrodynamics of living
+bodies he's certainly not shy about
+
+ align:start position:0%
+bodies he's certainly not shy about
+ 
+
+ align:start position:0%
+bodies he's certainly not shy about
+dismissing The Ether he's making other
+
+ align:start position:0%
+dismissing The Ether he's making other
+ 
+
+ align:start position:0%
+dismissing The Ether he's making other
+rather bold and almost almost like
+
+ align:start position:0%
+rather bold and almost almost like
+ 
+
+ align:start position:0%
+rather bold and almost almost like
+irresponsible statements uh given the
+
+ align:start position:0%
+irresponsible statements uh given the
+ 
+
+ align:start position:0%
+irresponsible statements uh given the
+standard assumptions of his day he
+
+ align:start position:0%
+standard assumptions of his day he
+ 
+
+ align:start position:0%
+standard assumptions of his day he
+wasn't shy in 1905. with this particular
+
+ align:start position:0%
+wasn't shy in 1905. with this particular
+ 
+
+ align:start position:0%
+wasn't shy in 1905. with this particular
+one I imagine it was more like he didn't
+
+ align:start position:0%
+one I imagine it was more like he didn't
+ 
+
+ align:start position:0%
+one I imagine it was more like he didn't
+yet know how to square the circle here
+
+ align:start position:0%
+yet know how to square the circle here
+ 
+
+ align:start position:0%
+yet know how to square the circle here
+of what comes to be known as wave
+
+ align:start position:0%
+of what comes to be known as wave
+ 
+
+ align:start position:0%
+of what comes to be known as wave
+particle duality so that's a great
+
+ align:start position:0%
+particle duality so that's a great
+ 
+
+ align:start position:0%
+particle duality so that's a great
+question again we'll see an example of
+
+ align:start position:0%
+question again we'll see an example of
+ 
+
+ align:start position:0%
+question again we'll see an example of
+that even in the next part today and and
+
+ align:start position:0%
+that even in the next part today and and
+ 
+
+ align:start position:0%
+that even in the next part today and and
+we'll see Echoes of that throughout the
+
+ align:start position:0%
+we'll see Echoes of that throughout the
+ 
+
+ align:start position:0%
+we'll see Echoes of that throughout the
+next few classes
+
+ align:start position:0%
+next few classes
+ 
+
+ align:start position:0%
+next few classes
+any other questions on on the
+
+ align:start position:0%
+any other questions on on the
+ 
+
+ align:start position:0%
+any other questions on on the
+photoelectric effect on what was Leonard
+
+ align:start position:0%
+photoelectric effect on what was Leonard
+ 
+
+ align:start position:0%
+photoelectric effect on what was Leonard
+measuring
+
+ align:start position:0%
+measuring
+ 
+
+ align:start position:0%
+measuring
+on Einstein's explanation it's all
+
+ align:start position:0%
+on Einstein's explanation it's all
+ 
+
+ align:start position:0%
+on Einstein's explanation it's all
+pretty clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great good questions
+
+ align:start position:0%
+great good questions
+ 
+
+ align:start position:0%
+great good questions
+let's look at this last part for today
+
+ align:start position:0%
+let's look at this last part for today
+ 
+
+ align:start position:0%
+let's look at this last part for today
+why did anyone begin to take light quads
+
+ align:start position:0%
+why did anyone begin to take light quads
+ 
+
+ align:start position:0%
+why did anyone begin to take light quads
+up a bit more seriously one of the most
+
+ align:start position:0%
+up a bit more seriously one of the most
+ 
+
+ align:start position:0%
+up a bit more seriously one of the most
+compelling uh sort of sets of new
+
+ align:start position:0%
+compelling uh sort of sets of new
+ 
+
+ align:start position:0%
+compelling uh sort of sets of new
+information new inputs for this
+
+ align:start position:0%
+information new inputs for this
+ 
+
+ align:start position:0%
+information new inputs for this
+came yet again from a laboratory in the
+
+ align:start position:0%
+came yet again from a laboratory in the
+ 
+
+ align:start position:0%
+came yet again from a laboratory in the
+United States which again is itself
+
+ align:start position:0%
+United States which again is itself
+ 
+
+ align:start position:0%
+United States which again is itself
+still pretty unusual this was among the
+
+ align:start position:0%
+still pretty unusual this was among the
+ 
+
+ align:start position:0%
+still pretty unusual this was among the
+next set of really significant
+
+ align:start position:0%
+next set of really significant
+ 
+
+ align:start position:0%
+next set of really significant
+experimental work in physics that got uh
+
+ align:start position:0%
+experimental work in physics that got uh
+ 
+
+ align:start position:0%
+experimental work in physics that got uh
+even the experts sometimes very snobby
+
+ align:start position:0%
+even the experts sometimes very snobby
+ 
+
+ align:start position:0%
+even the experts sometimes very snobby
+experts uh in Western Europe to pay
+
+ align:start position:0%
+experts uh in Western Europe to pay
+ 
+
+ align:start position:0%
+experts uh in Western Europe to pay
+attention this is now decades after
+
+ align:start position:0%
+attention this is now decades after
+ 
+
+ align:start position:0%
+attention this is now decades after
+Albert Michelson and the Michael symbol
+
+ align:start position:0%
+Albert Michelson and the Michael symbol
+ 
+
+ align:start position:0%
+Albert Michelson and the Michael symbol
+experiment is now the early 1920s not
+
+ align:start position:0%
+experiment is now the early 1920s not
+ 
+
+ align:start position:0%
+experiment is now the early 1920s not
+the 1880s but this was again an example
+
+ align:start position:0%
+the 1880s but this was again an example
+ 
+
+ align:start position:0%
+the 1880s but this was again an example
+held up almost immediately for for real
+
+ align:start position:0%
+held up almost immediately for for real
+ 
+
+ align:start position:0%
+held up almost immediately for for real
+acclaim
+
+ align:start position:0%
+acclaim
+ 
+
+ align:start position:0%
+acclaim
+a series of experiments performed by the
+
+ align:start position:0%
+a series of experiments performed by the
+ 
+
+ align:start position:0%
+a series of experiments performed by the
+physicist Arthur Compton at the
+
+ align:start position:0%
+physicist Arthur Compton at the
+ 
+
+ align:start position:0%
+physicist Arthur Compton at the
+University of Chicago in 1922. here's
+
+ align:start position:0%
+University of Chicago in 1922. here's
+ 
+
+ align:start position:0%
+University of Chicago in 1922. here's
+Compton he looks like a kind of movie
+
+ align:start position:0%
+Compton he looks like a kind of movie
+ 
+
+ align:start position:0%
+Compton he looks like a kind of movie
+star you might recognize the name
+
+ align:start position:0%
+star you might recognize the name
+ 
+
+ align:start position:0%
+star you might recognize the name
+Compton Arthur's brother was Carl
+
+ align:start position:0%
+Compton Arthur's brother was Carl
+ 
+
+ align:start position:0%
+Compton Arthur's brother was Carl
+Compton also of trained physicist Carl
+
+ align:start position:0%
+Compton also of trained physicist Carl
+ 
+
+ align:start position:0%
+Compton also of trained physicist Carl
+Compton then went on to a different kind
+
+ align:start position:0%
+Compton then went on to a different kind
+ 
+
+ align:start position:0%
+Compton then went on to a different kind
+of career he became the president of MIT
+
+ align:start position:0%
+of career he became the president of MIT
+ 
+
+ align:start position:0%
+of career he became the president of MIT
+starting in 1930 and you served for
+
+ align:start position:0%
+starting in 1930 and you served for
+ 
+
+ align:start position:0%
+starting in 1930 and you served for
+nearly 20 years
+
+ align:start position:0%
+nearly 20 years
+ 
+
+ align:start position:0%
+nearly 20 years
+so a number of enormous enormously
+
+ align:start position:0%
+so a number of enormous enormously
+ 
+
+ align:start position:0%
+so a number of enormous enormously
+consequential reforms at MIT were put in
+
+ align:start position:0%
+consequential reforms at MIT were put in
+ 
+
+ align:start position:0%
+consequential reforms at MIT were put in
+place by Carl Compton just at the
+
+ align:start position:0%
+place by Carl Compton just at the
+ 
+
+ align:start position:0%
+place by Carl Compton just at the
+moments are around the same time that
+
+ align:start position:0%
+moments are around the same time that
+ 
+
+ align:start position:0%
+moments are around the same time that
+his brother Arthur Compton was
+
+ align:start position:0%
+his brother Arthur Compton was
+ 
+
+ align:start position:0%
+his brother Arthur Compton was
+experimenting on the nature of light and
+
+ align:start position:0%
+experimenting on the nature of light and
+ 
+
+ align:start position:0%
+experimenting on the nature of light and
+again as I say this was one of the sets
+
+ align:start position:0%
+again as I say this was one of the sets
+ 
+
+ align:start position:0%
+again as I say this was one of the sets
+of new kind of inputs coming out of U.S
+
+ align:start position:0%
+of new kind of inputs coming out of U.S
+ 
+
+ align:start position:0%
+of new kind of inputs coming out of U.S
+based Laboratories that really began to
+
+ align:start position:0%
+based Laboratories that really began to
+ 
+
+ align:start position:0%
+based Laboratories that really began to
+make even experts in Europe uh pay close
+
+ align:start position:0%
+make even experts in Europe uh pay close
+ 
+
+ align:start position:0%
+make even experts in Europe uh pay close
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+so Compton Arthur Compton had not set
+
+ align:start position:0%
+so Compton Arthur Compton had not set
+ 
+
+ align:start position:0%
+so Compton Arthur Compton had not set
+out to test Einstein's hypothesis he
+
+ align:start position:0%
+out to test Einstein's hypothesis he
+ 
+
+ align:start position:0%
+out to test Einstein's hypothesis he
+like everyone practically everyone in
+
+ align:start position:0%
+like everyone practically everyone in
+ 
+
+ align:start position:0%
+like everyone practically everyone in
+the field remained pretty skeptical much
+
+ align:start position:0%
+the field remained pretty skeptical much
+ 
+
+ align:start position:0%
+the field remained pretty skeptical much
+like in that letter uh from from Max
+
+ align:start position:0%
+like in that letter uh from from Max
+ 
+
+ align:start position:0%
+like in that letter uh from from Max
+Planck from 1913. they figured Einstein
+
+ align:start position:0%
+Planck from 1913. they figured Einstein
+ 
+
+ align:start position:0%
+Planck from 1913. they figured Einstein
+by this point had was pretty smart had
+
+ align:start position:0%
+by this point had was pretty smart had
+ 
+
+ align:start position:0%
+by this point had was pretty smart had
+some amazing um successes to his career
+
+ align:start position:0%
+some amazing um successes to his career
+ 
+
+ align:start position:0%
+some amazing um successes to his career
+but this light Quantum thing was
+
+ align:start position:0%
+but this light Quantum thing was
+ 
+
+ align:start position:0%
+but this light Quantum thing was
+probably not one of them
+
+ align:start position:0%
+probably not one of them
+ 
+
+ align:start position:0%
+probably not one of them
+competency I was really interested in
+
+ align:start position:0%
+competency I was really interested in
+ 
+
+ align:start position:0%
+competency I was really interested in
+the behavior of high energy X-rays and
+
+ align:start position:0%
+the behavior of high energy X-rays and
+ 
+
+ align:start position:0%
+the behavior of high energy X-rays and
+how these x-rays would interact with
+
+ align:start position:0%
+how these x-rays would interact with
+ 
+
+ align:start position:0%
+how these x-rays would interact with
+little bits of matter so he was
+
+ align:start position:0%
+little bits of matter so he was
+ 
+
+ align:start position:0%
+little bits of matter so he was
+conducting experience by basically
+
+ align:start position:0%
+conducting experience by basically
+ 
+
+ align:start position:0%
+conducting experience by basically
+beaming x-rays very high energy
+
+ align:start position:0%
+beaming x-rays very high energy
+ 
+
+ align:start position:0%
+beaming x-rays very high energy
+electromagnetic light as far as he was
+
+ align:start position:0%
+electromagnetic light as far as he was
+ 
+
+ align:start position:0%
+electromagnetic light as far as he was
+concerned maxwellian waves a very short
+
+ align:start position:0%
+concerned maxwellian waves a very short
+ 
+
+ align:start position:0%
+concerned maxwellian waves a very short
+wavelength very high frequency
+
+ align:start position:0%
+wavelength very high frequency
+ 
+
+ align:start position:0%
+wavelength very high frequency
+and bouncing them off of graphite
+
+ align:start position:0%
+and bouncing them off of graphite
+ 
+
+ align:start position:0%
+and bouncing them off of graphite
+basically carbon molecules uh so we
+
+ align:start position:0%
+basically carbon molecules uh so we
+ 
+
+ align:start position:0%
+basically carbon molecules uh so we
+wanted to bounce them off the electrons
+
+ align:start position:0%
+wanted to bounce them off the electrons
+ 
+
+ align:start position:0%
+wanted to bounce them off the electrons
+in carbon
+
+ align:start position:0%
+in carbon
+ 
+
+ align:start position:0%
+in carbon
+what Compton was measuring in particular
+
+ align:start position:0%
+what Compton was measuring in particular
+ 
+
+ align:start position:0%
+what Compton was measuring in particular
+was change in the wavelength in the
+
+ align:start position:0%
+was change in the wavelength in the
+ 
+
+ align:start position:0%
+was change in the wavelength in the
+wavelength of those uh electromagnetic
+
+ align:start position:0%
+wavelength of those uh electromagnetic
+ 
+
+ align:start position:0%
+wavelength of those uh electromagnetic
+waves the x-rays after scattering so
+
+ align:start position:0%
+waves the x-rays after scattering so
+ 
+
+ align:start position:0%
+waves the x-rays after scattering so
+remote you're familiar of course for any
+
+ align:start position:0%
+remote you're familiar of course for any
+ 
+
+ align:start position:0%
+remote you're familiar of course for any
+of these maxwellian waves we can measure
+
+ align:start position:0%
+of these maxwellian waves we can measure
+ 
+
+ align:start position:0%
+of these maxwellian waves we can measure
+the wavelength the distance uh the
+
+ align:start position:0%
+the wavelength the distance uh the
+ 
+
+ align:start position:0%
+the wavelength the distance uh the
+physical distance between neighboring
+
+ align:start position:0%
+physical distance between neighboring
+ 
+
+ align:start position:0%
+physical distance between neighboring
+crests neighboring peaks of say the
+
+ align:start position:0%
+crests neighboring peaks of say the
+ 
+
+ align:start position:0%
+crests neighboring peaks of say the
+associated electric field so what
+
+ align:start position:0%
+associated electric field so what
+ 
+
+ align:start position:0%
+associated electric field so what
+Compton was doing in his laboratory was
+
+ align:start position:0%
+Compton was doing in his laboratory was
+ 
+
+ align:start position:0%
+Compton was doing in his laboratory was
+measuring the wavelength prior to
+
+ align:start position:0%
+measuring the wavelength prior to
+ 
+
+ align:start position:0%
+measuring the wavelength prior to
+scattering and the way the shifted
+
+ align:start position:0%
+scattering and the way the shifted
+ 
+
+ align:start position:0%
+scattering and the way the shifted
+wavelength following scattering so the
+
+ align:start position:0%
+wavelength following scattering so the
+ 
+
+ align:start position:0%
+wavelength following scattering so the
+prime here means after the scattering he
+
+ align:start position:0%
+prime here means after the scattering he
+ 
+
+ align:start position:0%
+prime here means after the scattering he
+knew the wavelength ahead of time he
+
+ align:start position:0%
+knew the wavelength ahead of time he
+ 
+
+ align:start position:0%
+knew the wavelength ahead of time he
+could control that with his apparatus he
+
+ align:start position:0%
+could control that with his apparatus he
+ 
+
+ align:start position:0%
+could control that with his apparatus he
+could then use very much like the pgr it
+
+ align:start position:0%
+could then use very much like the pgr it
+ 
+
+ align:start position:0%
+could then use very much like the pgr it
+could use very finely spaced diffraction
+
+ align:start position:0%
+could use very finely spaced diffraction
+ 
+
+ align:start position:0%
+could use very finely spaced diffraction
+gratings and similar techniques to
+
+ align:start position:0%
+gratings and similar techniques to
+ 
+
+ align:start position:0%
+gratings and similar techniques to
+measure the shift in wavelength after
+
+ align:start position:0%
+measure the shift in wavelength after
+ 
+
+ align:start position:0%
+measure the shift in wavelength after
+the x-rays have basically scattered off
+
+ align:start position:0%
+the x-rays have basically scattered off
+ 
+
+ align:start position:0%
+the x-rays have basically scattered off
+these electrons
+
+ align:start position:0%
+these electrons
+ 
+
+ align:start position:0%
+these electrons
+he found that there was a shift the the
+
+ align:start position:0%
+he found that there was a shift the the
+ 
+
+ align:start position:0%
+he found that there was a shift the the
+wavelength following Collision was not
+
+ align:start position:0%
+wavelength following Collision was not
+ 
+
+ align:start position:0%
+wavelength following Collision was not
+equal to the wavelength prior to
+
+ align:start position:0%
+equal to the wavelength prior to
+ 
+
+ align:start position:0%
+equal to the wavelength prior to
+Collision and it was a very specific
+
+ align:start position:0%
+Collision and it was a very specific
+ 
+
+ align:start position:0%
+Collision and it was a very specific
+angular dependence that the angle at
+
+ align:start position:0%
+angular dependence that the angle at
+ 
+
+ align:start position:0%
+angular dependence that the angle at
+which these x-rays bounced off is angle
+
+ align:start position:0%
+which these x-rays bounced off is angle
+ 
+
+ align:start position:0%
+which these x-rays bounced off is angle
+Theta uh was somehow related to this
+
+ align:start position:0%
+Theta uh was somehow related to this
+ 
+
+ align:start position:0%
+Theta uh was somehow related to this
+degree in which their wavelength changed
+
+ align:start position:0%
+degree in which their wavelength changed
+ 
+
+ align:start position:0%
+degree in which their wavelength changed
+and that is to say the shift in
+
+ align:start position:0%
+and that is to say the shift in
+ 
+
+ align:start position:0%
+and that is to say the shift in
+wavelength went like one minus cosine of
+
+ align:start position:0%
+wavelength went like one minus cosine of
+ 
+
+ align:start position:0%
+wavelength went like one minus cosine of
+the light waves scattering angle and
+
+ align:start position:0%
+the light waves scattering angle and
+ 
+
+ align:start position:0%
+the light waves scattering angle and
+that's what you can measure you can see
+
+ align:start position:0%
+that's what you can measure you can see
+ 
+
+ align:start position:0%
+that's what you can measure you can see
+here it's mounted on a wheel it could
+
+ align:start position:0%
+here it's mounted on a wheel it could
+ 
+
+ align:start position:0%
+here it's mounted on a wheel it could
+actually pivot his kind of diffraction
+
+ align:start position:0%
+actually pivot his kind of diffraction
+ 
+
+ align:start position:0%
+actually pivot his kind of diffraction
+gratings essentially and measure the
+
+ align:start position:0%
+gratings essentially and measure the
+ 
+
+ align:start position:0%
+gratings essentially and measure the
+scattered light at different angles as
+
+ align:start position:0%
+scattered light at different angles as
+ 
+
+ align:start position:0%
+scattered light at different angles as
+it bounced off that graphite Target
+
+ align:start position:0%
+it bounced off that graphite Target
+ 
+
+ align:start position:0%
+it bounced off that graphite Target
+so Compton was convinced this could be
+
+ align:start position:0%
+so Compton was convinced this could be
+ 
+
+ align:start position:0%
+so Compton was convinced this could be
+made sense of using you know the totally
+
+ align:start position:0%
+made sense of using you know the totally
+ 
+
+ align:start position:0%
+made sense of using you know the totally
+standard by that point maxwellian
+
+ align:start position:0%
+standard by that point maxwellian
+ 
+
+ align:start position:0%
+standard by that point maxwellian
+electromagnetic waves these were high
+
+ align:start position:0%
+electromagnetic waves these were high
+ 
+
+ align:start position:0%
+electromagnetic waves these were high
+frequency maximal waves scattering off
+
+ align:start position:0%
+frequency maximal waves scattering off
+ 
+
+ align:start position:0%
+frequency maximal waves scattering off
+of a certain Target and yet try and try
+
+ align:start position:0%
+of a certain Target and yet try and try
+ 
+
+ align:start position:0%
+of a certain Target and yet try and try
+and try as he might he could not come up
+
+ align:start position:0%
+and try as he might he could not come up
+ 
+
+ align:start position:0%
+and try as he might he could not come up
+with any sensible explanation or
+
+ align:start position:0%
+with any sensible explanation or
+ 
+
+ align:start position:0%
+with any sensible explanation or
+accounting for this empirical
+
+ align:start position:0%
+accounting for this empirical
+ 
+
+ align:start position:0%
+accounting for this empirical
+relationship when he kept finding
+
+ align:start position:0%
+relationship when he kept finding
+ 
+
+ align:start position:0%
+relationship when he kept finding
+conducting the experiment measuring more
+
+ align:start position:0%
+conducting the experiment measuring more
+ 
+
+ align:start position:0%
+conducting the experiment measuring more
+and more carefully the shift in
+
+ align:start position:0%
+and more carefully the shift in
+ 
+
+ align:start position:0%
+and more carefully the shift in
+frequency with uh with the scattered
+
+ align:start position:0%
+frequency with uh with the scattered
+ 
+
+ align:start position:0%
+frequency with uh with the scattered
+angle he couldn't come up with any kind
+
+ align:start position:0%
+angle he couldn't come up with any kind
+ 
+
+ align:start position:0%
+angle he couldn't come up with any kind
+of theoretical explanation that would
+
+ align:start position:0%
+of theoretical explanation that would
+ 
+
+ align:start position:0%
+of theoretical explanation that would
+account for that shift until in yet
+
+ align:start position:0%
+account for that shift until in yet
+ 
+
+ align:start position:0%
+account for that shift until in yet
+another kind of active desperation much
+
+ align:start position:0%
+another kind of active desperation much
+ 
+
+ align:start position:0%
+another kind of active desperation much
+like Mark's Planck he then kind of
+
+ align:start position:0%
+like Mark's Planck he then kind of
+ 
+
+ align:start position:0%
+like Mark's Planck he then kind of
+grudgingly tries on takes on this
+
+ align:start position:0%
+grudgingly tries on takes on this
+ 
+
+ align:start position:0%
+grudgingly tries on takes on this
+einsteinian hypothesis or heuristic
+
+ align:start position:0%
+einsteinian hypothesis or heuristic
+ 
+
+ align:start position:0%
+einsteinian hypothesis or heuristic
+suggestion only when Arthur Compton
+
+ align:start position:0%
+suggestion only when Arthur Compton
+ 
+
+ align:start position:0%
+suggestion only when Arthur Compton
+again kind of grudgingly adopts this
+
+ align:start position:0%
+again kind of grudgingly adopts this
+ 
+
+ align:start position:0%
+again kind of grudgingly adopts this
+suggestion from Albert Einstein to treat
+
+ align:start position:0%
+suggestion from Albert Einstein to treat
+ 
+
+ align:start position:0%
+suggestion from Albert Einstein to treat
+light in this case the very high energy
+
+ align:start position:0%
+light in this case the very high energy
+ 
+
+ align:start position:0%
+light in this case the very high energy
+x-rays as little collections of discrete
+
+ align:start position:0%
+x-rays as little collections of discrete
+ 
+
+ align:start position:0%
+x-rays as little collections of discrete
+particles each with her own discrete
+
+ align:start position:0%
+particles each with her own discrete
+ 
+
+ align:start position:0%
+particles each with her own discrete
+packets of energy rather than as
+
+ align:start position:0%
+packets of energy rather than as
+ 
+
+ align:start position:0%
+packets of energy rather than as
+Maximilian waves only then can he make
+
+ align:start position:0%
+Maximilian waves only then can he make
+ 
+
+ align:start position:0%
+Maximilian waves only then can he make
+sense of this empirical pattern in his
+
+ align:start position:0%
+sense of this empirical pattern in his
+ 
+
+ align:start position:0%
+sense of this empirical pattern in his
+laboratory
+
+ align:start position:0%
+laboratory
+ 
+
+ align:start position:0%
+laboratory
+so here's the diagram from his actual
+
+ align:start position:0%
+so here's the diagram from his actual
+ 
+
+ align:start position:0%
+so here's the diagram from his actual
+published article in the physical view
+
+ align:start position:0%
+published article in the physical view
+ 
+
+ align:start position:0%
+published article in the physical view
+it was submitted in the very closing
+
+ align:start position:0%
+it was submitted in the very closing
+ 
+
+ align:start position:0%
+it was submitted in the very closing
+days of calendar year 1922 was published
+
+ align:start position:0%
+days of calendar year 1922 was published
+ 
+
+ align:start position:0%
+days of calendar year 1922 was published
+on Spring of 23. uh so here's the actual
+
+ align:start position:0%
+on Spring of 23. uh so here's the actual
+ 
+
+ align:start position:0%
+on Spring of 23. uh so here's the actual
+illustration from his article and again
+
+ align:start position:0%
+illustration from his article and again
+ 
+
+ align:start position:0%
+illustration from his article and again
+in the in the accompanying
+
+ align:start position:0%
+in the in the accompanying
+ 
+
+ align:start position:0%
+in the in the accompanying
+um optional lecture notes I go through
+
+ align:start position:0%
+um optional lecture notes I go through
+ 
+
+ align:start position:0%
+um optional lecture notes I go through
+the the the algebra that were slowly so
+
+ align:start position:0%
+the the the algebra that were slowly so
+ 
+
+ align:start position:0%
+the the the algebra that were slowly so
+I'm going to show you where he gets
+
+ align:start position:0%
+I'm going to show you where he gets
+ 
+
+ align:start position:0%
+I'm going to show you where he gets
+don't worry if if some of these steps
+
+ align:start position:0%
+don't worry if if some of these steps
+ 
+
+ align:start position:0%
+don't worry if if some of these steps
+are hard to do in your head they're hard
+
+ align:start position:0%
+are hard to do in your head they're hard
+ 
+
+ align:start position:0%
+are hard to do in your head they're hard
+for me to do in my head take your time
+
+ align:start position:0%
+for me to do in my head take your time
+ 
+
+ align:start position:0%
+for me to do in my head take your time
+if you'd like and go through the the
+
+ align:start position:0%
+if you'd like and go through the the
+ 
+
+ align:start position:0%
+if you'd like and go through the the
+algebra in the notes so what what
+
+ align:start position:0%
+algebra in the notes so what what
+ 
+
+ align:start position:0%
+algebra in the notes so what what
+Compton winds up doing is treating the
+
+ align:start position:0%
+Compton winds up doing is treating the
+ 
+
+ align:start position:0%
+Compton winds up doing is treating the
+interaction between the incoming x-ray
+
+ align:start position:0%
+interaction between the incoming x-ray
+ 
+
+ align:start position:0%
+interaction between the incoming x-ray
+that's what's here we now by the
+
+ align:start position:0%
+that's what's here we now by the
+ 
+
+ align:start position:0%
+that's what's here we now by the
+published version has uh decided to call
+
+ align:start position:0%
+published version has uh decided to call
+ 
+
+ align:start position:0%
+published version has uh decided to call
+this incident light Quantum is already
+
+ align:start position:0%
+this incident light Quantum is already
+ 
+
+ align:start position:0%
+this incident light Quantum is already
+now now you borrowing Einstein's ideas
+
+ align:start position:0%
+now now you borrowing Einstein's ideas
+ 
+
+ align:start position:0%
+now now you borrowing Einstein's ideas
+it's not where we started
+
+ align:start position:0%
+it's not where we started
+ 
+
+ align:start position:0%
+it's not where we started
+pardon me
+
+ align:start position:0%
+pardon me
+ 
+
+ align:start position:0%
+pardon me
+so here's the incoming x-ray
+
+ align:start position:0%
+so here's the incoming x-ray
+ 
+
+ align:start position:0%
+so here's the incoming x-ray
+and how would you characterize
+
+ align:start position:0%
+and how would you characterize
+ 
+
+ align:start position:0%
+and how would you characterize
+the energy or the momentum of that of
+
+ align:start position:0%
+the energy or the momentum of that of
+ 
+
+ align:start position:0%
+the energy or the momentum of that of
+that incoming source of light
+
+ align:start position:0%
+that incoming source of light
+ 
+
+ align:start position:0%
+that incoming source of light
+that's what Compton starts with before
+
+ align:start position:0%
+that's what Compton starts with before
+ 
+
+ align:start position:0%
+that's what Compton starts with before
+Collision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so even
+
+ align:start position:0%
+so even
+ 
+
+ align:start position:0%
+so even
+by Matt using Maxwell's Theory
+
+ align:start position:0%
+by Matt using Maxwell's Theory
+ 
+
+ align:start position:0%
+by Matt using Maxwell's Theory
+people knew they could
+
+ align:start position:0%
+people knew they could
+ 
+
+ align:start position:0%
+people knew they could
+calculate an Associated momentum carried
+
+ align:start position:0%
+calculate an Associated momentum carried
+ 
+
+ align:start position:0%
+calculate an Associated momentum carried
+by a light wave
+
+ align:start position:0%
+by a light wave
+ 
+
+ align:start position:0%
+by a light wave
+is related to things like the pointing
+
+ align:start position:0%
+is related to things like the pointing
+ 
+
+ align:start position:0%
+is related to things like the pointing
+Vector joining it super fancy but
+
+ align:start position:0%
+Vector joining it super fancy but
+ 
+
+ align:start position:0%
+Vector joining it super fancy but
+basically Maxwell's equations suggested
+
+ align:start position:0%
+basically Maxwell's equations suggested
+ 
+
+ align:start position:0%
+basically Maxwell's equations suggested
+the momentum carried by radiation by
+
+ align:start position:0%
+the momentum carried by radiation by
+ 
+
+ align:start position:0%
+the momentum carried by radiation by
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+is equal to the energy carried by that
+
+ align:start position:0%
+is equal to the energy carried by that
+ 
+
+ align:start position:0%
+is equal to the energy carried by that
+light wave divided by its speed that was
+
+ align:start position:0%
+light wave divided by its speed that was
+ 
+
+ align:start position:0%
+light wave divided by its speed that was
+again a kind of classical result even
+
+ align:start position:0%
+again a kind of classical result even
+ 
+
+ align:start position:0%
+again a kind of classical result even
+from wave theory of light and now
+
+ align:start position:0%
+from wave theory of light and now
+ 
+
+ align:start position:0%
+from wave theory of light and now
+confidence starts adding in this new
+
+ align:start position:0%
+confidence starts adding in this new
+ 
+
+ align:start position:0%
+confidence starts adding in this new
+heuristic stuff from Einstein what if
+
+ align:start position:0%
+heuristic stuff from Einstein what if
+ 
+
+ align:start position:0%
+heuristic stuff from Einstein what if
+each individual light quantum
+
+ align:start position:0%
+each individual light quantum
+ 
+
+ align:start position:0%
+each individual light quantum
+and now I'll be a little anachronistic
+
+ align:start position:0%
+and now I'll be a little anachronistic
+ 
+
+ align:start position:0%
+and now I'll be a little anachronistic
+and just use the term Photon that's not
+
+ align:start position:0%
+and just use the term Photon that's not
+ 
+
+ align:start position:0%
+and just use the term Photon that's not
+the term that Compton used it gets
+
+ align:start position:0%
+the term that Compton used it gets
+ 
+
+ align:start position:0%
+the term that Compton used it gets
+introduced soon after competence results
+
+ align:start position:0%
+introduced soon after competence results
+ 
+
+ align:start position:0%
+introduced soon after competence results
+so by the 19 within the 1920s it had
+
+ align:start position:0%
+so by the 19 within the 1920s it had
+ 
+
+ align:start position:0%
+so by the 19 within the 1920s it had
+already become common to use the term
+
+ align:start position:0%
+already become common to use the term
+ 
+
+ align:start position:0%
+already become common to use the term
+Photon as we still do today to describe
+
+ align:start position:0%
+Photon as we still do today to describe
+ 
+
+ align:start position:0%
+Photon as we still do today to describe
+these like
+
+ align:start position:0%
+these like
+ 
+
+ align:start position:0%
+these like
+so now let's take on Einstein's
+
+ align:start position:0%
+so now let's take on Einstein's
+ 
+
+ align:start position:0%
+so now let's take on Einstein's
+suggestion that each individual Photon
+
+ align:start position:0%
+suggestion that each individual Photon
+ 
+
+ align:start position:0%
+suggestion that each individual Photon
+of light carries a quantized amount of
+
+ align:start position:0%
+of light carries a quantized amount of
+ 
+
+ align:start position:0%
+of light carries a quantized amount of
+energy proportional to its frequency
+
+ align:start position:0%
+energy proportional to its frequency
+ 
+
+ align:start position:0%
+energy proportional to its frequency
+then let's use the usual relation for
+
+ align:start position:0%
+then let's use the usual relation for
+ 
+
+ align:start position:0%
+then let's use the usual relation for
+any wave between frequency and
+
+ align:start position:0%
+any wave between frequency and
+ 
+
+ align:start position:0%
+any wave between frequency and
+wavelength with the constant of
+
+ align:start position:0%
+wavelength with the constant of
+ 
+
+ align:start position:0%
+wavelength with the constant of
+proportionality the speed
+
+ align:start position:0%
+proportionality the speed
+ 
+
+ align:start position:0%
+proportionality the speed
+so now you can come back to this sort of
+
+ align:start position:0%
+so now you can come back to this sort of
+ 
+
+ align:start position:0%
+so now you can come back to this sort of
+maxwellian expression for the momentum
+
+ align:start position:0%
+maxwellian expression for the momentum
+ 
+
+ align:start position:0%
+maxwellian expression for the momentum
+carried by a classical light wave kind
+
+ align:start position:0%
+carried by a classical light wave kind
+ 
+
+ align:start position:0%
+carried by a classical light wave kind
+of add in this new einstein-like Quantum
+
+ align:start position:0%
+of add in this new einstein-like Quantum
+ 
+
+ align:start position:0%
+of add in this new einstein-like Quantum
+thing and come up with an expression for
+
+ align:start position:0%
+thing and come up with an expression for
+ 
+
+ align:start position:0%
+thing and come up with an expression for
+the momentum carried by each individual
+
+ align:start position:0%
+the momentum carried by each individual
+ 
+
+ align:start position:0%
+the momentum carried by each individual
+Photon or light Quantum and that would
+
+ align:start position:0%
+Photon or light Quantum and that would
+ 
+
+ align:start position:0%
+Photon or light Quantum and that would
+be the energy
+
+ align:start position:0%
+be the energy
+ 
+
+ align:start position:0%
+be the energy
+divided by its speed H over lamb
+
+ align:start position:0%
+divided by its speed H over lamb
+ 
+
+ align:start position:0%
+divided by its speed H over lamb
+remember that's not where Compton starts
+
+ align:start position:0%
+remember that's not where Compton starts
+ 
+
+ align:start position:0%
+remember that's not where Compton starts
+that's where it gets out of desperation
+
+ align:start position:0%
+that's where it gets out of desperation
+ 
+
+ align:start position:0%
+that's where it gets out of desperation
+so now Compton has an expression for
+
+ align:start position:0%
+so now Compton has an expression for
+ 
+
+ align:start position:0%
+so now Compton has an expression for
+both the momentum and the energy of this
+
+ align:start position:0%
+both the momentum and the energy of this
+ 
+
+ align:start position:0%
+both the momentum and the energy of this
+light Quantum prior to scattering
+
+ align:start position:0%
+light Quantum prior to scattering
+ 
+
+ align:start position:0%
+light Quantum prior to scattering
+he's going to treat this as I say like a
+
+ align:start position:0%
+he's going to treat this as I say like a
+ 
+
+ align:start position:0%
+he's going to treat this as I say like a
+two-body problem as if these were two
+
+ align:start position:0%
+two-body problem as if these were two
+ 
+
+ align:start position:0%
+two-body problem as if these were two
+billiard balls rather than like a wave
+
+ align:start position:0%
+billiard balls rather than like a wave
+ 
+
+ align:start position:0%
+billiard balls rather than like a wave
+scattering off of a little chunk of
+
+ align:start position:0%
+scattering off of a little chunk of
+ 
+
+ align:start position:0%
+scattering off of a little chunk of
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+so prior to the Collision he's going to
+
+ align:start position:0%
+so prior to the Collision he's going to
+ 
+
+ align:start position:0%
+so prior to the Collision he's going to
+say this electron over here this target
+
+ align:start position:0%
+say this electron over here this target
+ 
+
+ align:start position:0%
+say this electron over here this target
+has a little dot here is just sitting
+
+ align:start position:0%
+has a little dot here is just sitting
+ 
+
+ align:start position:0%
+has a little dot here is just sitting
+there at rest it's momentum is zero it
+
+ align:start position:0%
+there at rest it's momentum is zero it
+ 
+
+ align:start position:0%
+there at rest it's momentum is zero it
+has no velocity
+
+ align:start position:0%
+has no velocity
+ 
+
+ align:start position:0%
+has no velocity
+and it has some rest energy MC squared
+
+ align:start position:0%
+and it has some rest energy MC squared
+ 
+
+ align:start position:0%
+and it has some rest energy MC squared
+Remember by 1922 Einstein's work on
+
+ align:start position:0%
+Remember by 1922 Einstein's work on
+ 
+
+ align:start position:0%
+Remember by 1922 Einstein's work on
+relativity was indeed much more better
+
+ align:start position:0%
+relativity was indeed much more better
+ 
+
+ align:start position:0%
+relativity was indeed much more better
+known and uh seemed to have passed a
+
+ align:start position:0%
+known and uh seemed to have passed a
+ 
+
+ align:start position:0%
+known and uh seemed to have passed a
+number of tests so Compton had no qualms
+
+ align:start position:0%
+number of tests so Compton had no qualms
+ 
+
+ align:start position:0%
+number of tests so Compton had no qualms
+about borrowing Isis work on relativity
+
+ align:start position:0%
+about borrowing Isis work on relativity
+ 
+
+ align:start position:0%
+about borrowing Isis work on relativity
+including things like this rest energy
+
+ align:start position:0%
+including things like this rest energy
+ 
+
+ align:start position:0%
+including things like this rest energy
+mc squared even though he was not going
+
+ align:start position:0%
+mc squared even though he was not going
+ 
+
+ align:start position:0%
+mc squared even though he was not going
+into this convinced of the like Quantum
+
+ align:start position:0%
+into this convinced of the like Quantum
+ 
+
+ align:start position:0%
+into this convinced of the like Quantum
+set so now I have the ingredients we
+
+ align:start position:0%
+set so now I have the ingredients we
+ 
+
+ align:start position:0%
+set so now I have the ingredients we
+need to describe the two scattering
+
+ align:start position:0%
+need to describe the two scattering
+ 
+
+ align:start position:0%
+need to describe the two scattering
+billiard balls the two objects prior to
+
+ align:start position:0%
+billiard balls the two objects prior to
+ 
+
+ align:start position:0%
+billiard balls the two objects prior to
+Collision we can characterize the energy
+
+ align:start position:0%
+Collision we can characterize the energy
+ 
+
+ align:start position:0%
+Collision we can characterize the energy
+and momentum of the incoming x-ray as a
+
+ align:start position:0%
+and momentum of the incoming x-ray as a
+ 
+
+ align:start position:0%
+and momentum of the incoming x-ray as a
+collection of discrete palette-like
+
+ align:start position:0%
+collection of discrete palette-like
+ 
+
+ align:start position:0%
+collection of discrete palette-like
+light quanta we have the energy momentum
+
+ align:start position:0%
+light quanta we have the energy momentum
+ 
+
+ align:start position:0%
+light quanta we have the energy momentum
+before Collision of the target is
+
+ align:start position:0%
+before Collision of the target is
+ 
+
+ align:start position:0%
+before Collision of the target is
+electron just sitting still about to get
+
+ align:start position:0%
+electron just sitting still about to get
+ 
+
+ align:start position:0%
+electron just sitting still about to get
+smacked
+
+ align:start position:0%
+smacked
+ 
+
+ align:start position:0%
+smacked
+after the Collision the light Quantum
+
+ align:start position:0%
+after the Collision the light Quantum
+ 
+
+ align:start position:0%
+after the Collision the light Quantum
+gets scattered off at some angle Theta
+
+ align:start position:0%
+gets scattered off at some angle Theta
+ 
+
+ align:start position:0%
+gets scattered off at some angle Theta
+compared to its incoming Direction
+
+ align:start position:0%
+compared to its incoming Direction
+ 
+
+ align:start position:0%
+compared to its incoming Direction
+that's the angle Theta here it now has
+
+ align:start position:0%
+that's the angle Theta here it now has
+ 
+
+ align:start position:0%
+that's the angle Theta here it now has
+in general some different wavelength so
+
+ align:start position:0%
+in general some different wavelength so
+ 
+
+ align:start position:0%
+in general some different wavelength so
+the momentum of that Photon Compton out
+
+ align:start position:0%
+the momentum of that Photon Compton out
+ 
+
+ align:start position:0%
+the momentum of that Photon Compton out
+of taking on Einstein's work is going to
+
+ align:start position:0%
+of taking on Einstein's work is going to
+ 
+
+ align:start position:0%
+of taking on Einstein's work is going to
+be given by some Universal constant that
+
+ align:start position:0%
+be given by some Universal constant that
+ 
+
+ align:start position:0%
+be given by some Universal constant that
+hasn't changed that's just Planck's
+
+ align:start position:0%
+hasn't changed that's just Planck's
+ 
+
+ align:start position:0%
+hasn't changed that's just Planck's
+constant but the wavelength indeed might
+
+ align:start position:0%
+constant but the wavelength indeed might
+ 
+
+ align:start position:0%
+constant but the wavelength indeed might
+have changed in fact he was measuring
+
+ align:start position:0%
+have changed in fact he was measuring
+ 
+
+ align:start position:0%
+have changed in fact he was measuring
+exactly that change in wavelength
+
+ align:start position:0%
+exactly that change in wavelength
+ 
+
+ align:start position:0%
+exactly that change in wavelength
+likewise the energy of photon therefore
+
+ align:start position:0%
+likewise the energy of photon therefore
+ 
+
+ align:start position:0%
+likewise the energy of photon therefore
+will change because it's wavelength will
+
+ align:start position:0%
+will change because it's wavelength will
+ 
+
+ align:start position:0%
+will change because it's wavelength will
+change so he has now an expression for
+
+ align:start position:0%
+change so he has now an expression for
+ 
+
+ align:start position:0%
+change so he has now an expression for
+energy momentum of a light Quantum
+
+ align:start position:0%
+energy momentum of a light Quantum
+ 
+
+ align:start position:0%
+energy momentum of a light Quantum
+following collision and likewise the
+
+ align:start position:0%
+following collision and likewise the
+ 
+
+ align:start position:0%
+following collision and likewise the
+electrons now been smacked by some very
+
+ align:start position:0%
+electrons now been smacked by some very
+ 
+
+ align:start position:0%
+electrons now been smacked by some very
+high energy pellet this high energy
+
+ align:start position:0%
+high energy pellet this high energy
+ 
+
+ align:start position:0%
+high energy pellet this high energy
+light Quantum of the x-rays
+
+ align:start position:0%
+light Quantum of the x-rays
+ 
+
+ align:start position:0%
+light Quantum of the x-rays
+so now it will recoil at some other uh
+
+ align:start position:0%
+so now it will recoil at some other uh
+ 
+
+ align:start position:0%
+so now it will recoil at some other uh
+in some other direction some angle let's
+
+ align:start position:0%
+in some other direction some angle let's
+ 
+
+ align:start position:0%
+in some other direction some angle let's
+call it Phi after getting smacked by the
+
+ align:start position:0%
+call it Phi after getting smacked by the
+ 
+
+ align:start position:0%
+call it Phi after getting smacked by the
+incoming like one so now it has some
+
+ align:start position:0%
+incoming like one so now it has some
+ 
+
+ align:start position:0%
+incoming like one so now it has some
+non-zero momentum in fact if it's a high
+
+ align:start position:0%
+non-zero momentum in fact if it's a high
+ 
+
+ align:start position:0%
+non-zero momentum in fact if it's a high
+enough energy incoming x-ray x-rays are
+
+ align:start position:0%
+enough energy incoming x-ray x-rays are
+ 
+
+ align:start position:0%
+enough energy incoming x-ray x-rays are
+very energetic light waves in general an
+
+ align:start position:0%
+very energetic light waves in general an
+ 
+
+ align:start position:0%
+very energetic light waves in general an
+electron might actually acquire a
+
+ align:start position:0%
+electron might actually acquire a
+ 
+
+ align:start position:0%
+electron might actually acquire a
+relativistic momentum it's it's recoil
+
+ align:start position:0%
+relativistic momentum it's it's recoil
+ 
+
+ align:start position:0%
+relativistic momentum it's it's recoil
+speed could in general be comparable to
+
+ align:start position:0%
+speed could in general be comparable to
+ 
+
+ align:start position:0%
+speed could in general be comparable to
+the speed of light it could get quite a
+
+ align:start position:0%
+the speed of light it could get quite a
+ 
+
+ align:start position:0%
+the speed of light it could get quite a
+Junt from that Collision so again
+
+ align:start position:0%
+Junt from that Collision so again
+ 
+
+ align:start position:0%
+Junt from that Collision so again
+Compton uses by then the standard uh
+
+ align:start position:0%
+Compton uses by then the standard uh
+ 
+
+ align:start position:0%
+Compton uses by then the standard uh
+relativistic Expressions momentum and
+
+ align:start position:0%
+relativistic Expressions momentum and
+ 
+
+ align:start position:0%
+relativistic Expressions momentum and
+likewise for energy and again I have a
+
+ align:start position:0%
+likewise for energy and again I have a
+ 
+
+ align:start position:0%
+likewise for energy and again I have a
+set of lecture notes that were optional
+
+ align:start position:0%
+set of lecture notes that were optional
+ 
+
+ align:start position:0%
+set of lecture notes that were optional
+on the canvas site from when we talked
+
+ align:start position:0%
+on the canvas site from when we talked
+ 
+
+ align:start position:0%
+on the canvas site from when we talked
+about Einstein and relativity to go over
+
+ align:start position:0%
+about Einstein and relativity to go over
+ 
+
+ align:start position:0%
+about Einstein and relativity to go over
+things like E equals MC squared
+
+ align:start position:0%
+things like E equals MC squared
+ 
+
+ align:start position:0%
+things like E equals MC squared
+relativistic momentum and all that so
+
+ align:start position:0%
+relativistic momentum and all that so
+ 
+
+ align:start position:0%
+relativistic momentum and all that so
+you you have a chance to go back to
+
+ align:start position:0%
+you you have a chance to go back to
+ 
+
+ align:start position:0%
+you you have a chance to go back to
+those notes if that's not familiar this
+
+ align:start position:0%
+those notes if that's not familiar this
+ 
+
+ align:start position:0%
+those notes if that's not familiar this
+point just to let us know this for what
+
+ align:start position:0%
+point just to let us know this for what
+ 
+
+ align:start position:0%
+point just to let us know this for what
+we need to know today this stuff was by
+
+ align:start position:0%
+we need to know today this stuff was by
+ 
+
+ align:start position:0%
+we need to know today this stuff was by
+that point kind of standard issue
+
+ align:start position:0%
+that point kind of standard issue
+ 
+
+ align:start position:0%
+that point kind of standard issue
+Compton was doing nothing controversial
+
+ align:start position:0%
+Compton was doing nothing controversial
+ 
+
+ align:start position:0%
+Compton was doing nothing controversial
+here in adopting the relativistic energy
+
+ align:start position:0%
+here in adopting the relativistic energy
+ 
+
+ align:start position:0%
+here in adopting the relativistic energy
+and momentum for the scattered electron
+
+ align:start position:0%
+and momentum for the scattered electron
+ 
+
+ align:start position:0%
+and momentum for the scattered electron
+okay now he does what anyone would do
+
+ align:start position:0%
+okay now he does what anyone would do
+ 
+
+ align:start position:0%
+okay now he does what anyone would do
+when you have two particles colliding
+
+ align:start position:0%
+when you have two particles colliding
+ 
+
+ align:start position:0%
+when you have two particles colliding
+not a wave smacking into the shore but
+
+ align:start position:0%
+not a wave smacking into the shore but
+ 
+
+ align:start position:0%
+not a wave smacking into the shore but
+two discrete little bundles of energy
+
+ align:start position:0%
+two discrete little bundles of energy
+ 
+
+ align:start position:0%
+two discrete little bundles of energy
+that Collide like billiard balls on a
+
+ align:start position:0%
+that Collide like billiard balls on a
+ 
+
+ align:start position:0%
+that Collide like billiard balls on a
+pool table
+
+ align:start position:0%
+pool table
+ 
+
+ align:start position:0%
+pool table
+one thing we have to do in any two body
+
+ align:start position:0%
+one thing we have to do in any two body
+ 
+
+ align:start position:0%
+one thing we have to do in any two body
+collision is conserve energy just as we
+
+ align:start position:0%
+collision is conserve energy just as we
+ 
+
+ align:start position:0%
+collision is conserve energy just as we
+would do uh in ordinary Newtonian
+
+ align:start position:0%
+would do uh in ordinary Newtonian
+ 
+
+ align:start position:0%
+would do uh in ordinary Newtonian
+mechanics so what's the total energy
+
+ align:start position:0%
+mechanics so what's the total energy
+ 
+
+ align:start position:0%
+mechanics so what's the total energy
+coming in uh before Collision the
+
+ align:start position:0%
+coming in uh before Collision the
+ 
+
+ align:start position:0%
+coming in uh before Collision the
+incoming energy of the photon this one
+
+ align:start position:0%
+incoming energy of the photon this one
+ 
+
+ align:start position:0%
+incoming energy of the photon this one
+here the incoming energy electrons just
+
+ align:start position:0%
+here the incoming energy electrons just
+ 
+
+ align:start position:0%
+here the incoming energy electrons just
+its rest mass and that total energy has
+
+ align:start position:0%
+its rest mass and that total energy has
+ 
+
+ align:start position:0%
+its rest mass and that total energy has
+to balance the total energy ecosystem
+
+ align:start position:0%
+to balance the total energy ecosystem
+ 
+
+ align:start position:0%
+to balance the total energy ecosystem
+following Collision so he has his
+
+ align:start position:0%
+following Collision so he has his
+ 
+
+ align:start position:0%
+following Collision so he has his
+corresponding expressions for the energy
+
+ align:start position:0%
+corresponding expressions for the energy
+ 
+
+ align:start position:0%
+corresponding expressions for the energy
+of the photon and the electron following
+
+ align:start position:0%
+of the photon and the electron following
+ 
+
+ align:start position:0%
+of the photon and the electron following
+scattering and we can now fill in from
+
+ align:start position:0%
+scattering and we can now fill in from
+ 
+
+ align:start position:0%
+scattering and we can now fill in from
+this table what those values should be
+
+ align:start position:0%
+this table what those values should be
+ 
+
+ align:start position:0%
+this table what those values should be
+likewise we have to conserve momentum as
+
+ align:start position:0%
+likewise we have to conserve momentum as
+ 
+
+ align:start position:0%
+likewise we have to conserve momentum as
+we all know momentum is a vector
+
+ align:start position:0%
+we all know momentum is a vector
+ 
+
+ align:start position:0%
+we all know momentum is a vector
+quantity so we have to conserve momentum
+
+ align:start position:0%
+quantity so we have to conserve momentum
+ 
+
+ align:start position:0%
+quantity so we have to conserve momentum
+both in the sort of X Direction along
+
+ align:start position:0%
+both in the sort of X Direction along
+ 
+
+ align:start position:0%
+both in the sort of X Direction along
+the original direction of travel for the
+
+ align:start position:0%
+the original direction of travel for the
+ 
+
+ align:start position:0%
+the original direction of travel for the
+incoming uh light Quantum as well as in
+
+ align:start position:0%
+incoming uh light Quantum as well as in
+ 
+
+ align:start position:0%
+incoming uh light Quantum as well as in
+the perpendicular Direction this case
+
+ align:start position:0%
+the perpendicular Direction this case
+ 
+
+ align:start position:0%
+the perpendicular Direction this case
+the Y Direction and so again this is
+
+ align:start position:0%
+the Y Direction and so again this is
+ 
+
+ align:start position:0%
+the Y Direction and so again this is
+done in a bit more detail in the notes
+
+ align:start position:0%
+done in a bit more detail in the notes
+ 
+
+ align:start position:0%
+done in a bit more detail in the notes
+if this uh is hard to kind of parse in
+
+ align:start position:0%
+if this uh is hard to kind of parse in
+ 
+
+ align:start position:0%
+if this uh is hard to kind of parse in
+real time but the upshot is this Compton
+
+ align:start position:0%
+real time but the upshot is this Compton
+ 
+
+ align:start position:0%
+real time but the upshot is this Compton
+is doing completely standard stuff for
+
+ align:start position:0%
+is doing completely standard stuff for
+ 
+
+ align:start position:0%
+is doing completely standard stuff for
+two body scattering once he's done the
+
+ align:start position:0%
+two body scattering once he's done the
+ 
+
+ align:start position:0%
+two body scattering once he's done the
+non-standard thing of treating this
+
+ align:start position:0%
+non-standard thing of treating this
+ 
+
+ align:start position:0%
+non-standard thing of treating this
+light as an incoming pellet or particle
+
+ align:start position:0%
+light as an incoming pellet or particle
+ 
+
+ align:start position:0%
+light as an incoming pellet or particle
+so now what's so great is the Compton
+
+ align:start position:0%
+so now what's so great is the Compton
+ 
+
+ align:start position:0%
+so now what's so great is the Compton
+has three equations for three unknowns
+
+ align:start position:0%
+has three equations for three unknowns
+ 
+
+ align:start position:0%
+has three equations for three unknowns
+which is now Rewritten those expressions
+
+ align:start position:0%
+which is now Rewritten those expressions
+ 
+
+ align:start position:0%
+which is now Rewritten those expressions
+we just had
+
+ align:start position:0%
+we just had
+ 
+
+ align:start position:0%
+we just had
+by treating a problem like ordinary two
+
+ align:start position:0%
+by treating a problem like ordinary two
+ 
+
+ align:start position:0%
+by treating a problem like ordinary two
+bodies scattering between discrete
+
+ align:start position:0%
+bodies scattering between discrete
+ 
+
+ align:start position:0%
+bodies scattering between discrete
+localized particles copper has three
+
+ align:start position:0%
+localized particles copper has three
+ 
+
+ align:start position:0%
+localized particles copper has three
+Expressions conservation of energy
+
+ align:start position:0%
+Expressions conservation of energy
+ 
+
+ align:start position:0%
+Expressions conservation of energy
+conservation momentum in each of the two
+
+ align:start position:0%
+conservation momentum in each of the two
+ 
+
+ align:start position:0%
+conservation momentum in each of the two
+perpendicular directions and he has
+
+ align:start position:0%
+perpendicular directions and he has
+ 
+
+ align:start position:0%
+perpendicular directions and he has
+three unknowns he doesn't know what the
+
+ align:start position:0%
+three unknowns he doesn't know what the
+ 
+
+ align:start position:0%
+three unknowns he doesn't know what the
+scattered wavelength is and he doesn't
+
+ align:start position:0%
+scattered wavelength is and he doesn't
+ 
+
+ align:start position:0%
+scattered wavelength is and he doesn't
+know what the angles of scatter are
+
+ align:start position:0%
+know what the angles of scatter are
+ 
+
+ align:start position:0%
+know what the angles of scatter are
+either the angle Theta for the light
+
+ align:start position:0%
+either the angle Theta for the light
+ 
+
+ align:start position:0%
+either the angle Theta for the light
+Quantum or the angle Phi for the
+
+ align:start position:0%
+Quantum or the angle Phi for the
+ 
+
+ align:start position:0%
+Quantum or the angle Phi for the
+recoiling electron so as now it's just
+
+ align:start position:0%
+recoiling electron so as now it's just
+ 
+
+ align:start position:0%
+recoiling electron so as now it's just
+algebra he has three equations for three
+
+ align:start position:0%
+algebra he has three equations for three
+ 
+
+ align:start position:0%
+algebra he has three equations for three
+unknowns and as you'll see in the notes
+
+ align:start position:0%
+unknowns and as you'll see in the notes
+ 
+
+ align:start position:0%
+unknowns and as you'll see in the notes
+uh now it's really just a short number
+
+ align:start position:0%
+uh now it's really just a short number
+ 
+
+ align:start position:0%
+uh now it's really just a short number
+of steps to do to relate the the change
+
+ align:start position:0%
+of steps to do to relate the the change
+ 
+
+ align:start position:0%
+of steps to do to relate the the change
+in wavelength the the Lambda Prime
+
+ align:start position:0%
+in wavelength the the Lambda Prime
+ 
+
+ align:start position:0%
+in wavelength the the Lambda Prime
+following scattering compare that to the
+
+ align:start position:0%
+following scattering compare that to the
+ 
+
+ align:start position:0%
+following scattering compare that to the
+incoming wavelength which you can
+
+ align:start position:0%
+incoming wavelength which you can
+ 
+
+ align:start position:0%
+incoming wavelength which you can
+control he controls the X-ray source
+
+ align:start position:0%
+control he controls the X-ray source
+ 
+
+ align:start position:0%
+control he controls the X-ray source
+and it and it gets related in an
+
+ align:start position:0%
+and it and it gets related in an
+ 
+
+ align:start position:0%
+and it and it gets related in an
+automatic way to that scattering angle
+
+ align:start position:0%
+automatic way to that scattering angle
+ 
+
+ align:start position:0%
+automatic way to that scattering angle
+and exactly the form that content had
+
+ align:start position:0%
+and exactly the form that content had
+ 
+
+ align:start position:0%
+and exactly the form that content had
+been finding empirically not only does
+
+ align:start position:0%
+been finding empirically not only does
+ 
+
+ align:start position:0%
+been finding empirically not only does
+it get the angular dependence correct or
+
+ align:start position:0%
+it get the angular dependence correct or
+ 
+
+ align:start position:0%
+it get the angular dependence correct or
+at least matches his his uh empirical
+
+ align:start position:0%
+at least matches his his uh empirical
+ 
+
+ align:start position:0%
+at least matches his his uh empirical
+results he actually even finds a
+
+ align:start position:0%
+results he actually even finds a
+ 
+
+ align:start position:0%
+results he actually even finds a
+quantitative shift is coefficient the
+
+ align:start position:0%
+quantitative shift is coefficient the
+ 
+
+ align:start position:0%
+quantitative shift is coefficient the
+amount by which the wavelength should
+
+ align:start position:0%
+amount by which the wavelength should
+ 
+
+ align:start position:0%
+amount by which the wavelength should
+shift is now fixed by these Universal
+
+ align:start position:0%
+shift is now fixed by these Universal
+ 
+
+ align:start position:0%
+shift is now fixed by these Universal
+constants Planck's constant the mass of
+
+ align:start position:0%
+constants Planck's constant the mass of
+ 
+
+ align:start position:0%
+constants Planck's constant the mass of
+the electron that Target and the speed
+
+ align:start position:0%
+the electron that Target and the speed
+ 
+
+ align:start position:0%
+the electron that Target and the speed
+of light
+
+ align:start position:0%
+of light
+ 
+
+ align:start position:0%
+of light
+and so competent is treating light-like
+
+ align:start position:0%
+and so competent is treating light-like
+ 
+
+ align:start position:0%
+and so competent is treating light-like
+particles and he's measuring changes in
+
+ align:start position:0%
+particles and he's measuring changes in
+ 
+
+ align:start position:0%
+particles and he's measuring changes in
+a wave like just just going back to
+
+ align:start position:0%
+a wave like just just going back to
+ 
+
+ align:start position:0%
+a wave like just just going back to
+Gary's point from a few moments ago
+
+ align:start position:0%
+Gary's point from a few moments ago
+ 
+
+ align:start position:0%
+Gary's point from a few moments ago
+Compton is now finding further kind of
+
+ align:start position:0%
+Compton is now finding further kind of
+ 
+
+ align:start position:0%
+Compton is now finding further kind of
+examples where kind of half the time he
+
+ align:start position:0%
+examples where kind of half the time he
+ 
+
+ align:start position:0%
+examples where kind of half the time he
+has to pretend that light is just a wave
+
+ align:start position:0%
+has to pretend that light is just a wave
+ 
+
+ align:start position:0%
+has to pretend that light is just a wave
+because he's measuring wave-like
+
+ align:start position:0%
+because he's measuring wave-like
+ 
+
+ align:start position:0%
+because he's measuring wave-like
+properties like wavelength is sort of
+
+ align:start position:0%
+properties like wavelength is sort of
+ 
+
+ align:start position:0%
+properties like wavelength is sort of
+necessarily a wave-like property is the
+
+ align:start position:0%
+necessarily a wave-like property is the
+ 
+
+ align:start position:0%
+necessarily a wave-like property is the
+distance between crests of a wave after
+
+ align:start position:0%
+distance between crests of a wave after
+ 
+
+ align:start position:0%
+distance between crests of a wave after
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+that's what he's controlling and
+
+ align:start position:0%
+that's what he's controlling and
+ 
+
+ align:start position:0%
+that's what he's controlling and
+measuring that's that's his empirical
+
+ align:start position:0%
+measuring that's that's his empirical
+ 
+
+ align:start position:0%
+measuring that's that's his empirical
+input is a wave-like quantity shift in
+
+ align:start position:0%
+input is a wave-like quantity shift in
+ 
+
+ align:start position:0%
+input is a wave-like quantity shift in
+wavelength and yet he's accounting for
+
+ align:start position:0%
+wavelength and yet he's accounting for
+ 
+
+ align:start position:0%
+wavelength and yet he's accounting for
+that uh by talking about a kind of
+
+ align:start position:0%
+that uh by talking about a kind of
+ 
+
+ align:start position:0%
+that uh by talking about a kind of
+discrete particle scattering off another
+
+ align:start position:0%
+discrete particle scattering off another
+ 
+
+ align:start position:0%
+discrete particle scattering off another
+discrete particle uh and so this becomes
+
+ align:start position:0%
+discrete particle uh and so this becomes
+ 
+
+ align:start position:0%
+discrete particle uh and so this becomes
+known as the Compton wave of length this
+
+ align:start position:0%
+known as the Compton wave of length this
+ 
+
+ align:start position:0%
+known as the Compton wave of length this
+combination of fundamental constants
+
+ align:start position:0%
+combination of fundamental constants
+ 
+
+ align:start position:0%
+combination of fundamental constants
+that tells us how much the wavelength of
+
+ align:start position:0%
+that tells us how much the wavelength of
+ 
+
+ align:start position:0%
+that tells us how much the wavelength of
+the scattered light should shift as when
+
+ align:start position:0%
+the scattered light should shift as when
+ 
+
+ align:start position:0%
+the scattered light should shift as when
+changes the angle what's the overall
+
+ align:start position:0%
+changes the angle what's the overall
+ 
+
+ align:start position:0%
+changes the angle what's the overall
+scale by which this wave in this should
+
+ align:start position:0%
+scale by which this wave in this should
+ 
+
+ align:start position:0%
+scale by which this wave in this should
+shift
+
+ align:start position:0%
+shift
+ 
+
+ align:start position:0%
+shift
+and so this becomes a kind of yet
+
+ align:start position:0%
+and so this becomes a kind of yet
+ 
+
+ align:start position:0%
+and so this becomes a kind of yet
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+um hybrid or blend of particle-like and
+
+ align:start position:0%
+um hybrid or blend of particle-like and
+ 
+
+ align:start position:0%
+um hybrid or blend of particle-like and
+wave-like ways of reasoning about light
+
+ align:start position:0%
+wave-like ways of reasoning about light
+ 
+
+ align:start position:0%
+wave-like ways of reasoning about light
+as I mentioned I think in in the lecture
+
+ align:start position:0%
+as I mentioned I think in in the lecture
+ 
+
+ align:start position:0%
+as I mentioned I think in in the lecture
+notes for today this work much like
+
+ align:start position:0%
+notes for today this work much like
+ 
+
+ align:start position:0%
+notes for today this work much like
+Philip Leonards was immediately greeted
+
+ align:start position:0%
+Philip Leonards was immediately greeted
+ 
+
+ align:start position:0%
+Philip Leonards was immediately greeted
+uh as very important uh Compton received
+
+ align:start position:0%
+uh as very important uh Compton received
+ 
+
+ align:start position:0%
+uh as very important uh Compton received
+a Nobel Prize I think by 1927. the paper
+
+ align:start position:0%
+a Nobel Prize I think by 1927. the paper
+ 
+
+ align:start position:0%
+a Nobel Prize I think by 1927. the paper
+was published in the spring of 1923. so
+
+ align:start position:0%
+was published in the spring of 1923. so
+ 
+
+ align:start position:0%
+was published in the spring of 1923. so
+much like with Leonard's work
+
+ align:start position:0%
+much like with Leonard's work
+ 
+
+ align:start position:0%
+much like with Leonard's work
+just a handful of years past between the
+
+ align:start position:0%
+just a handful of years past between the
+ 
+
+ align:start position:0%
+just a handful of years past between the
+very first publication of these
+
+ align:start position:0%
+very first publication of these
+ 
+
+ align:start position:0%
+very first publication of these
+experimental results and the work being
+
+ align:start position:0%
+experimental results and the work being
+ 
+
+ align:start position:0%
+experimental results and the work being
+honored with the Nobel Prize so people
+
+ align:start position:0%
+honored with the Nobel Prize so people
+ 
+
+ align:start position:0%
+honored with the Nobel Prize so people
+were paying attention to Compton's work
+
+ align:start position:0%
+were paying attention to Compton's work
+ 
+
+ align:start position:0%
+were paying attention to Compton's work
+very closely very carefully in real time
+
+ align:start position:0%
+very closely very carefully in real time
+ 
+
+ align:start position:0%
+very closely very carefully in real time
+it was this kind of work that began to
+
+ align:start position:0%
+it was this kind of work that began to
+ 
+
+ align:start position:0%
+it was this kind of work that began to
+convince even the remaining Skeptics uh
+
+ align:start position:0%
+convince even the remaining Skeptics uh
+ 
+
+ align:start position:0%
+convince even the remaining Skeptics uh
+that Einstein's heuristic suggestion
+
+ align:start position:0%
+that Einstein's heuristic suggestion
+ 
+
+ align:start position:0%
+that Einstein's heuristic suggestion
+that like should be treated at least in
+
+ align:start position:0%
+that like should be treated at least in
+ 
+
+ align:start position:0%
+that like should be treated at least in
+some aspects like a collection of
+
+ align:start position:0%
+some aspects like a collection of
+ 
+
+ align:start position:0%
+some aspects like a collection of
+particles that finally begins to gel and
+
+ align:start position:0%
+particles that finally begins to gel and
+ 
+
+ align:start position:0%
+particles that finally begins to gel and
+Achieve something like Community
+
+ align:start position:0%
+Achieve something like Community
+ 
+
+ align:start position:0%
+Achieve something like Community
+agreement whereas in Einstein's earlier
+
+ align:start position:0%
+agreement whereas in Einstein's earlier
+ 
+
+ align:start position:0%
+agreement whereas in Einstein's earlier
+Expressions that had been lacked okay
+
+ align:start position:0%
+Expressions that had been lacked okay
+ 
+
+ align:start position:0%
+Expressions that had been lacked okay
+let me sum
+
+ align:start position:0%
+let me sum
+ 
+
+ align:start position:0%
+let me sum
+and we'll have some more questions
+
+ align:start position:0%
+and we'll have some more questions
+ 
+
+ align:start position:0%
+and we'll have some more questions
+so these three moments in what became is
+
+ align:start position:0%
+so these three moments in what became is
+ 
+
+ align:start position:0%
+so these three moments in what became is
+known as old quantum theory each moment
+
+ align:start position:0%
+known as old quantum theory each moment
+ 
+
+ align:start position:0%
+known as old quantum theory each moment
+of physicists grappling with the nature
+
+ align:start position:0%
+of physicists grappling with the nature
+ 
+
+ align:start position:0%
+of physicists grappling with the nature
+of light
+
+ align:start position:0%
+of light
+ 
+
+ align:start position:0%
+of light
+I remember it's not happening kind of in
+
+ align:start position:0%
+I remember it's not happening kind of in
+ 
+
+ align:start position:0%
+I remember it's not happening kind of in
+a vacuum to begin to understand why
+
+ align:start position:0%
+a vacuum to begin to understand why
+ 
+
+ align:start position:0%
+a vacuum to begin to understand why
+anyone cared at all let alone invested
+
+ align:start position:0%
+anyone cared at all let alone invested
+ 
+
+ align:start position:0%
+anyone cared at all let alone invested
+with such priority in these particular
+
+ align:start position:0%
+with such priority in these particular
+ 
+
+ align:start position:0%
+with such priority in these particular
+experiments uh that really does go back
+
+ align:start position:0%
+experiments uh that really does go back
+ 
+
+ align:start position:0%
+experiments uh that really does go back
+to kind of larger framing of a newly
+
+ align:start position:0%
+to kind of larger framing of a newly
+ 
+
+ align:start position:0%
+to kind of larger framing of a newly
+independent country of Germany uh
+
+ align:start position:0%
+independent country of Germany uh
+ 
+
+ align:start position:0%
+independent country of Germany uh
+Decisions by its leadership to invest in
+
+ align:start position:0%
+Decisions by its leadership to invest in
+ 
+
+ align:start position:0%
+Decisions by its leadership to invest in
+industrialization to make new kinds of
+
+ align:start position:0%
+industrialization to make new kinds of
+ 
+
+ align:start position:0%
+industrialization to make new kinds of
+places like the PTR and so on it's
+
+ align:start position:0%
+places like the PTR and so on it's
+ 
+
+ align:start position:0%
+places like the PTR and so on it's
+within those spaces for specific kind of
+
+ align:start position:0%
+within those spaces for specific kind of
+ 
+
+ align:start position:0%
+within those spaces for specific kind of
+industrial uh applications like electric
+
+ align:start position:0%
+industrial uh applications like electric
+ 
+
+ align:start position:0%
+industrial uh applications like electric
+street lighting that they were really
+
+ align:start position:0%
+street lighting that they were really
+ 
+
+ align:start position:0%
+street lighting that they were really
+committed to studying things like black
+
+ align:start position:0%
+committed to studying things like black
+ 
+
+ align:start position:0%
+committed to studying things like black
+body radiation uh and what it might
+
+ align:start position:0%
+body radiation uh and what it might
+ 
+
+ align:start position:0%
+body radiation uh and what it might
+reveal about Universal properties of
+
+ align:start position:0%
+reveal about Universal properties of
+ 
+
+ align:start position:0%
+reveal about Universal properties of
+light and matter
+
+ align:start position:0%
+light and matter
+ 
+
+ align:start position:0%
+light and matter
+box Planck had just moved to Berlin uh
+
+ align:start position:0%
+box Planck had just moved to Berlin uh
+ 
+
+ align:start position:0%
+box Planck had just moved to Berlin uh
+as this full professor of theoretical
+
+ align:start position:0%
+as this full professor of theoretical
+ 
+
+ align:start position:0%
+as this full professor of theoretical
+physics do a pretty rare job to hold
+
+ align:start position:0%
+physics do a pretty rare job to hold
+ 
+
+ align:start position:0%
+physics do a pretty rare job to hold
+within any German University he was
+
+ align:start position:0%
+within any German University he was
+ 
+
+ align:start position:0%
+within any German University he was
+close by to PTR and he was getting
+
+ align:start position:0%
+close by to PTR and he was getting
+ 
+
+ align:start position:0%
+close by to PTR and he was getting
+updates from his colleagues sometimes
+
+ align:start position:0%
+updates from his colleagues sometimes
+ 
+
+ align:start position:0%
+updates from his colleagues sometimes
+day by day with their increasingly
+
+ align:start position:0%
+day by day with their increasingly
+ 
+
+ align:start position:0%
+day by day with their increasingly
+precise measurements of that Spectrum
+
+ align:start position:0%
+precise measurements of that Spectrum
+ 
+
+ align:start position:0%
+precise measurements of that Spectrum
+the pattern of radiation emitted when
+
+ align:start position:0%
+the pattern of radiation emitted when
+ 
+
+ align:start position:0%
+the pattern of radiation emitted when
+you heat up any material to a
+
+ align:start position:0%
+you heat up any material to a
+ 
+
+ align:start position:0%
+you heat up any material to a
+sufficiently high temperature no matter
+
+ align:start position:0%
+sufficiently high temperature no matter
+ 
+
+ align:start position:0%
+sufficiently high temperature no matter
+how he got there by the end of December
+
+ align:start position:0%
+how he got there by the end of December
+ 
+
+ align:start position:0%
+how he got there by the end of December
+plant could introduced this now uh now
+
+ align:start position:0%
+plant could introduced this now uh now
+ 
+
+ align:start position:0%
+plant could introduced this now uh now
+famous expression for the uh spectral
+
+ align:start position:0%
+famous expression for the uh spectral
+ 
+
+ align:start position:0%
+famous expression for the uh spectral
+energy density to get there he had
+
+ align:start position:0%
+energy density to get there he had
+ 
+
+ align:start position:0%
+energy density to get there he had
+introduced this new constant of nature I
+
+ align:start position:0%
+introduced this new constant of nature I
+ 
+
+ align:start position:0%
+introduced this new constant of nature I
+mean I'll call it plugs constant very
+
+ align:start position:0%
+mean I'll call it plugs constant very
+ 
+
+ align:start position:0%
+mean I'll call it plugs constant very
+very tiny in human scales and yet not
+
+ align:start position:0%
+very tiny in human scales and yet not
+ 
+
+ align:start position:0%
+very tiny in human scales and yet not
+zero and then we saw that whatever
+
+ align:start position:0%
+zero and then we saw that whatever
+ 
+
+ align:start position:0%
+zero and then we saw that whatever
+Planck thought that meant within a few
+
+ align:start position:0%
+Planck thought that meant within a few
+ 
+
+ align:start position:0%
+Planck thought that meant within a few
+years Einstein takes that up
+
+ align:start position:0%
+years Einstein takes that up
+ 
+
+ align:start position:0%
+years Einstein takes that up
+in a sense treats it more seriously than
+
+ align:start position:0%
+in a sense treats it more seriously than
+ 
+
+ align:start position:0%
+in a sense treats it more seriously than
+Planck himself had even done so Einstein
+
+ align:start position:0%
+Planck himself had even done so Einstein
+ 
+
+ align:start position:0%
+Planck himself had even done so Einstein
+not only redrives plant's result from a
+
+ align:start position:0%
+not only redrives plant's result from a
+ 
+
+ align:start position:0%
+not only redrives plant's result from a
+very specific conceptual starting point
+
+ align:start position:0%
+very specific conceptual starting point
+ 
+
+ align:start position:0%
+very specific conceptual starting point
+what if light consists of collections of
+
+ align:start position:0%
+what if light consists of collections of
+ 
+
+ align:start position:0%
+what if light consists of collections of
+discrete quanta soon to be called
+
+ align:start position:0%
+discrete quanta soon to be called
+ 
+
+ align:start position:0%
+discrete quanta soon to be called
+photons and that same uh kind of New
+
+ align:start position:0%
+photons and that same uh kind of New
+ 
+
+ align:start position:0%
+photons and that same uh kind of New
+Concept new new set of ideas uh helps
+
+ align:start position:0%
+Concept new new set of ideas uh helps
+ 
+
+ align:start position:0%
+Concept new new set of ideas uh helps
+Einstein make sense of experiments like
+
+ align:start position:0%
+Einstein make sense of experiments like
+ 
+
+ align:start position:0%
+Einstein make sense of experiments like
+Leonards on the photoelectric effect
+
+ align:start position:0%
+Leonards on the photoelectric effect
+ 
+
+ align:start position:0%
+Leonards on the photoelectric effect
+however as I've emphasized many times
+
+ align:start position:0%
+however as I've emphasized many times
+ 
+
+ align:start position:0%
+however as I've emphasized many times
+that seemed to be compelling to Einstein
+
+ align:start position:0%
+that seemed to be compelling to Einstein
+ 
+
+ align:start position:0%
+that seemed to be compelling to Einstein
+in 1905 but to very few others for years
+
+ align:start position:0%
+in 1905 but to very few others for years
+ 
+
+ align:start position:0%
+in 1905 but to very few others for years
+and years later and they really took the
+
+ align:start position:0%
+and years later and they really took the
+ 
+
+ align:start position:0%
+and years later and they really took the
+better part of two decades until
+
+ align:start position:0%
+better part of two decades until
+ 
+
+ align:start position:0%
+better part of two decades until
+consensus began to converge around this
+
+ align:start position:0%
+consensus began to converge around this
+ 
+
+ align:start position:0%
+consensus began to converge around this
+idea of light quanta or photons a very
+
+ align:start position:0%
+idea of light quanta or photons a very
+ 
+
+ align:start position:0%
+idea of light quanta or photons a very
+important piece of that was these new
+
+ align:start position:0%
+important piece of that was these new
+ 
+
+ align:start position:0%
+important piece of that was these new
+set of experiments by Arthur Compton at
+
+ align:start position:0%
+set of experiments by Arthur Compton at
+ 
+
+ align:start position:0%
+set of experiments by Arthur Compton at
+Chicago
+
+ align:start position:0%
+Chicago
+ 
+
+ align:start position:0%
+Chicago
+where you can only make sense of his of
+
+ align:start position:0%
+where you can only make sense of his of
+ 
+
+ align:start position:0%
+where you can only make sense of his of
+his own new results like doing this kind
+
+ align:start position:0%
+his own new results like doing this kind
+ 
+
+ align:start position:0%
+his own new results like doing this kind
+of dance by talking about uh x-rays as
+
+ align:start position:0%
+of dance by talking about uh x-rays as
+ 
+
+ align:start position:0%
+of dance by talking about uh x-rays as
+waves with wavelengths and then
+
+ align:start position:0%
+waves with wavelengths and then
+ 
+
+ align:start position:0%
+waves with wavelengths and then
+accounting for the shift of those
+
+ align:start position:0%
+accounting for the shift of those
+ 
+
+ align:start position:0%
+accounting for the shift of those
+wave-like properties uh in terms of the
+
+ align:start position:0%
+wave-like properties uh in terms of the
+ 
+
+ align:start position:0%
+wave-like properties uh in terms of the
+particulate or quantum-like scattering
+
+ align:start position:0%
+particulate or quantum-like scattering
+ 
+
+ align:start position:0%
+particulate or quantum-like scattering
+of discrete bodies so I'll stop there we
+
+ align:start position:0%
+of discrete bodies so I'll stop there we
+ 
+
+ align:start position:0%
+of discrete bodies so I'll stop there we
+got time for some more questions and
+
+ align:start position:0%
+got time for some more questions and
+ 
+
+ align:start position:0%
+got time for some more questions and
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+so uh let's see Stanley writes is there
+
+ align:start position:0%
+so uh let's see Stanley writes is there
+ 
+
+ align:start position:0%
+so uh let's see Stanley writes is there
+a reason Compton was able to measure
+
+ align:start position:0%
+a reason Compton was able to measure
+ 
+
+ align:start position:0%
+a reason Compton was able to measure
+enter was this able to assume energy was
+
+ align:start position:0%
+enter was this able to assume energy was
+ 
+
+ align:start position:0%
+enter was this able to assume energy was
+conserved oh very good
+
+ align:start position:0%
+conserved oh very good
+ 
+
+ align:start position:0%
+conserved oh very good
+how do you know energy was not lost in a
+
+ align:start position:0%
+how do you know energy was not lost in a
+ 
+
+ align:start position:0%
+how do you know energy was not lost in a
+sense that was actually an assumption
+
+ align:start position:0%
+sense that was actually an assumption
+ 
+
+ align:start position:0%
+sense that was actually an assumption
+Stanley it's an excellent question
+
+ align:start position:0%
+Stanley it's an excellent question
+ 
+
+ align:start position:0%
+Stanley it's an excellent question
+and in fact it's a very powerful
+
+ align:start position:0%
+and in fact it's a very powerful
+ 
+
+ align:start position:0%
+and in fact it's a very powerful
+question because around the same time
+
+ align:start position:0%
+question because around the same time
+ 
+
+ align:start position:0%
+question because around the same time
+other leading figures like Niels Bohr
+
+ align:start position:0%
+other leading figures like Niels Bohr
+ 
+
+ align:start position:0%
+other leading figures like Niels Bohr
+himself almost exactly the same time
+
+ align:start position:0%
+himself almost exactly the same time
+ 
+
+ align:start position:0%
+himself almost exactly the same time
+right by 1923 and 24 in fact
+
+ align:start position:0%
+right by 1923 and 24 in fact
+ 
+
+ align:start position:0%
+right by 1923 and 24 in fact
+Neil's boring responding to other kind
+
+ align:start position:0%
+Neil's boring responding to other kind
+ 
+
+ align:start position:0%
+Neil's boring responding to other kind
+of curious features of recent results
+
+ align:start position:0%
+of curious features of recent results
+ 
+
+ align:start position:0%
+of curious features of recent results
+suggested that that maybe uh energy is
+
+ align:start position:0%
+suggested that that maybe uh energy is
+ 
+
+ align:start position:0%
+suggested that that maybe uh energy is
+not conserved at the scale of atoms and
+
+ align:start position:0%
+not conserved at the scale of atoms and
+ 
+
+ align:start position:0%
+not conserved at the scale of atoms and
+parts of atoms competent didn't go that
+
+ align:start position:0%
+parts of atoms competent didn't go that
+ 
+
+ align:start position:0%
+parts of atoms competent didn't go that
+far and most of his colleagues never
+
+ align:start position:0%
+far and most of his colleagues never
+ 
+
+ align:start position:0%
+far and most of his colleagues never
+went so far even board switched back and
+
+ align:start position:0%
+went so far even board switched back and
+ 
+
+ align:start position:0%
+went so far even board switched back and
+said nope energies have been considered
+
+ align:start position:0%
+said nope energies have been considered
+ 
+
+ align:start position:0%
+said nope energies have been considered
+so Compton was basically taking on board
+
+ align:start position:0%
+so Compton was basically taking on board
+ 
+
+ align:start position:0%
+so Compton was basically taking on board
+the Assumption just an assumption that
+
+ align:start position:0%
+the Assumption just an assumption that
+ 
+
+ align:start position:0%
+the Assumption just an assumption that
+energy is is conserved always even at
+
+ align:start position:0%
+energy is is conserved always even at
+ 
+
+ align:start position:0%
+energy is is conserved always even at
+the atomic scale that was not proven
+
+ align:start position:0%
+the atomic scale that was not proven
+ 
+
+ align:start position:0%
+the atomic scale that was not proven
+that was an assumption what company was
+
+ align:start position:0%
+that was an assumption what company was
+ 
+
+ align:start position:0%
+that was an assumption what company was
+trying to do was basically make as few
+
+ align:start position:0%
+trying to do was basically make as few
+ 
+
+ align:start position:0%
+trying to do was basically make as few
+changes as needed to a kind of
+
+ align:start position:0%
+changes as needed to a kind of
+ 
+
+ align:start position:0%
+changes as needed to a kind of
+straightforward way of analyzing the
+
+ align:start position:0%
+straightforward way of analyzing the
+ 
+
+ align:start position:0%
+straightforward way of analyzing the
+scattering data how would we how would
+
+ align:start position:0%
+scattering data how would we how would
+ 
+
+ align:start position:0%
+scattering data how would we how would
+any of us analyze say the Collision of
+
+ align:start position:0%
+any of us analyze say the Collision of
+ 
+
+ align:start position:0%
+any of us analyze say the Collision of
+two you know of two balls um on human
+
+ align:start position:0%
+two you know of two balls um on human
+ 
+
+ align:start position:0%
+two you know of two balls um on human
+scales to a billion balls of baseball
+
+ align:start position:0%
+scales to a billion balls of baseball
+ 
+
+ align:start position:0%
+scales to a billion balls of baseball
+and a baseball bat any of these things
+
+ align:start position:0%
+and a baseball bat any of these things
+ 
+
+ align:start position:0%
+and a baseball bat any of these things
+we would assume energy is conserved we
+
+ align:start position:0%
+we would assume energy is conserved we
+ 
+
+ align:start position:0%
+we would assume energy is conserved we
+would assume momentum is conserved in
+
+ align:start position:0%
+would assume momentum is conserved in
+ 
+
+ align:start position:0%
+would assume momentum is conserved in
+each of its relevance
+
+ align:start position:0%
+each of its relevance
+ 
+
+ align:start position:0%
+each of its relevance
+components and that's what Compton's
+
+ align:start position:0%
+components and that's what Compton's
+ 
+
+ align:start position:0%
+components and that's what Compton's
+doing and that was actually what most
+
+ align:start position:0%
+doing and that was actually what most
+ 
+
+ align:start position:0%
+doing and that was actually what most
+physicists continue to do although
+
+ align:start position:0%
+physicists continue to do although
+ 
+
+ align:start position:0%
+physicists continue to do although
+you're quite right to point out Stanley
+
+ align:start position:0%
+you're quite right to point out Stanley
+ 
+
+ align:start position:0%
+you're quite right to point out Stanley
+that really was an assumption it wasn't
+
+ align:start position:0%
+that really was an assumption it wasn't
+ 
+
+ align:start position:0%
+that really was an assumption it wasn't
+um written in stone it wasn't guaranteed
+
+ align:start position:0%
+um written in stone it wasn't guaranteed
+ 
+
+ align:start position:0%
+um written in stone it wasn't guaranteed
+nowadays we look back we have tons and
+
+ align:start position:0%
+nowadays we look back we have tons and
+ 
+
+ align:start position:0%
+nowadays we look back we have tons and
+tons of reasons to think that energy
+
+ align:start position:0%
+tons of reasons to think that energy
+ 
+
+ align:start position:0%
+tons of reasons to think that energy
+really is conserved even at the atomic
+
+ align:start position:0%
+really is conserved even at the atomic
+ 
+
+ align:start position:0%
+really is conserved even at the atomic
+scale even when we think about light
+
+ align:start position:0%
+scale even when we think about light
+ 
+
+ align:start position:0%
+scale even when we think about light
+quanta that was by no means uh um sort
+
+ align:start position:0%
+quanta that was by no means uh um sort
+ 
+
+ align:start position:0%
+quanta that was by no means uh um sort
+of hard and fast uh evidence at the time
+
+ align:start position:0%
+of hard and fast uh evidence at the time
+ 
+
+ align:start position:0%
+of hard and fast uh evidence at the time
+Compton assumed it and that helped him
+
+ align:start position:0%
+Compton assumed it and that helped him
+ 
+
+ align:start position:0%
+Compton assumed it and that helped him
+get the results that he otherwise was
+
+ align:start position:0%
+get the results that he otherwise was
+ 
+
+ align:start position:0%
+get the results that he otherwise was
+aiming to explain
+
+ align:start position:0%
+aiming to explain
+ 
+
+ align:start position:0%
+aiming to explain
+excellent question Obi asks it's
+
+ align:start position:0%
+excellent question Obi asks it's
+ 
+
+ align:start position:0%
+excellent question Obi asks it's
+interesting that Einstein acceptance
+
+ align:start position:0%
+interesting that Einstein acceptance
+ 
+
+ align:start position:0%
+interesting that Einstein acceptance
+Duality because then he rejected The
+
+ align:start position:0%
+Duality because then he rejected The
+ 
+
+ align:start position:0%
+Duality because then he rejected The
+Ether before because it required
+
+ align:start position:0%
+Ether before because it required
+ 
+
+ align:start position:0%
+Ether before because it required
+conflicting explanations oh we I agree
+
+ align:start position:0%
+conflicting explanations oh we I agree
+ 
+
+ align:start position:0%
+conflicting explanations oh we I agree
+that's an excellent point actually
+
+ align:start position:0%
+that's an excellent point actually
+ 
+
+ align:start position:0%
+that's an excellent point actually
+you're totally right so what one might
+
+ align:start position:0%
+you're totally right so what one might
+ 
+
+ align:start position:0%
+you're totally right so what one might
+have expected Einstein to say the
+
+ align:start position:0%
+have expected Einstein to say the
+ 
+
+ align:start position:0%
+have expected Einstein to say the
+Assumption of Maximilian waves is merely
+
+ align:start position:0%
+Assumption of Maximilian waves is merely
+ 
+
+ align:start position:0%
+Assumption of Maximilian waves is merely
+Superfluous right there's the same
+
+ align:start position:0%
+Superfluous right there's the same
+ 
+
+ align:start position:0%
+Superfluous right there's the same
+language you use about The Ether
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wondered got me back to Gary's point
+
+ align:start position:0%
+I wondered got me back to Gary's point
+ 
+
+ align:start position:0%
+I wondered got me back to Gary's point
+from earlier I wonder
+
+ align:start position:0%
+from earlier I wonder
+ 
+
+ align:start position:0%
+from earlier I wonder
+if Einstein didn't make that move here
+
+ align:start position:0%
+if Einstein didn't make that move here
+ 
+
+ align:start position:0%
+if Einstein didn't make that move here
+because he himself knew that there were
+
+ align:start position:0%
+because he himself knew that there were
+ 
+
+ align:start position:0%
+because he himself knew that there were
+things that he thought wave-like
+
+ align:start position:0%
+things that he thought wave-like
+ 
+
+ align:start position:0%
+things that he thought wave-like
+properties really could explain I think
+
+ align:start position:0%
+properties really could explain I think
+ 
+
+ align:start position:0%
+properties really could explain I think
+Einstein had convinced himself by 1905
+
+ align:start position:0%
+Einstein had convinced himself by 1905
+ 
+
+ align:start position:0%
+Einstein had convinced himself by 1905
+that invoking The luminiferous Ether
+
+ align:start position:0%
+that invoking The luminiferous Ether
+ 
+
+ align:start position:0%
+that invoking The luminiferous Ether
+didn't help people understand anything
+
+ align:start position:0%
+didn't help people understand anything
+ 
+
+ align:start position:0%
+didn't help people understand anything
+that it was meant to explain that the
+
+ align:start position:0%
+that it was meant to explain that the
+ 
+
+ align:start position:0%
+that it was meant to explain that the
+easiest meant to explain
+
+ align:start position:0%
+easiest meant to explain
+ 
+
+ align:start position:0%
+easiest meant to explain
+thinking about lightest waves still had
+
+ align:start position:0%
+thinking about lightest waves still had
+ 
+
+ align:start position:0%
+thinking about lightest waves still had
+explanatory power for things like
+
+ align:start position:0%
+explanatory power for things like
+ 
+
+ align:start position:0%
+explanatory power for things like
+interference diffraction refraction so I
+
+ align:start position:0%
+interference diffraction refraction so I
+ 
+
+ align:start position:0%
+interference diffraction refraction so I
+think he he was I'm assuming we can go
+
+ align:start position:0%
+think he he was I'm assuming we can go
+ 
+
+ align:start position:0%
+think he he was I'm assuming we can go
+back and look more and other Scholars
+
+ align:start position:0%
+back and look more and other Scholars
+ 
+
+ align:start position:0%
+back and look more and other Scholars
+look more carefully this
+
+ align:start position:0%
+look more carefully this
+ 
+
+ align:start position:0%
+look more carefully this
+my assumption is that Einstein didn't
+
+ align:start position:0%
+my assumption is that Einstein didn't
+ 
+
+ align:start position:0%
+my assumption is that Einstein didn't
+want to give up on waves as as never
+
+ align:start position:0%
+want to give up on waves as as never
+ 
+
+ align:start position:0%
+want to give up on waves as as never
+being helpful to think about light
+
+ align:start position:0%
+being helpful to think about light
+ 
+
+ align:start position:0%
+being helpful to think about light
+because of this body of evidence that he
+
+ align:start position:0%
+because of this body of evidence that he
+ 
+
+ align:start position:0%
+because of this body of evidence that he
+thought really could be for which a wave
+
+ align:start position:0%
+thought really could be for which a wave
+ 
+
+ align:start position:0%
+thought really could be for which a wave
+explanation was actually helpful
+
+ align:start position:0%
+explanation was actually helpful
+ 
+
+ align:start position:0%
+explanation was actually helpful
+whereas he had convinced himself partly
+
+ align:start position:0%
+whereas he had convinced himself partly
+ 
+
+ align:start position:0%
+whereas he had convinced himself partly
+from his reading Advanced Mock and so
+
+ align:start position:0%
+from his reading Advanced Mock and so
+ 
+
+ align:start position:0%
+from his reading Advanced Mock and so
+I'm that invoking an ether seems never
+
+ align:start position:0%
+I'm that invoking an ether seems never
+ 
+
+ align:start position:0%
+I'm that invoking an ether seems never
+to be helpful right wave-like behaviors
+
+ align:start position:0%
+to be helpful right wave-like behaviors
+ 
+
+ align:start position:0%
+to be helpful right wave-like behaviors
+there were all kinds of phenomena even
+
+ align:start position:0%
+there were all kinds of phenomena even
+ 
+
+ align:start position:0%
+there were all kinds of phenomena even
+in casual daily experience in Precision
+
+ align:start position:0%
+in casual daily experience in Precision
+ 
+
+ align:start position:0%
+in casual daily experience in Precision
+experiments where things like
+
+ align:start position:0%
+experiments where things like
+ 
+
+ align:start position:0%
+experiments where things like
+interference fringes and so on were
+
+ align:start position:0%
+interference fringes and so on were
+ 
+
+ align:start position:0%
+interference fringes and so on were
+essential
+
+ align:start position:0%
+essential
+ 
+
+ align:start position:0%
+essential
+that's my guess Roy Einstein um kind of
+
+ align:start position:0%
+that's my guess Roy Einstein um kind of
+ 
+
+ align:start position:0%
+that's my guess Roy Einstein um kind of
+called this heuristic didn't announce
+
+ align:start position:0%
+called this heuristic didn't announce
+ 
+
+ align:start position:0%
+called this heuristic didn't announce
+that you know notion everything about
+
+ align:start position:0%
+that you know notion everything about
+ 
+
+ align:start position:0%
+that you know notion everything about
+light waves again and again Einstein
+
+ align:start position:0%
+light waves again and again Einstein
+ 
+
+ align:start position:0%
+light waves again and again Einstein
+becomes one of the most kind of um
+
+ align:start position:0%
+becomes one of the most kind of um
+ 
+
+ align:start position:0%
+becomes one of the most kind of um
+frankly Fearless One of the most
+
+ align:start position:0%
+frankly Fearless One of the most
+ 
+
+ align:start position:0%
+frankly Fearless One of the most
+conceptually daring to say
+
+ align:start position:0%
+conceptually daring to say
+ 
+
+ align:start position:0%
+conceptually daring to say
+um and really trying to pursue this way
+
+ align:start position:0%
+um and really trying to pursue this way
+ 
+
+ align:start position:0%
+um and really trying to pursue this way
+of particle duality over the next kind
+
+ align:start position:0%
+of particle duality over the next kind
+ 
+
+ align:start position:0%
+of particle duality over the next kind
+of two decades he really kind of sits
+
+ align:start position:0%
+of two decades he really kind of sits
+ 
+
+ align:start position:0%
+of two decades he really kind of sits
+with it he doesn't say oh this hurts my
+
+ align:start position:0%
+with it he doesn't say oh this hurts my
+ 
+
+ align:start position:0%
+with it he doesn't say oh this hurts my
+head it must be one or the other he
+
+ align:start position:0%
+head it must be one or the other he
+ 
+
+ align:start position:0%
+head it must be one or the other he
+actually digs in actually
+
+ align:start position:0%
+actually digs in actually
+ 
+
+ align:start position:0%
+actually digs in actually
+uh in a series of developments
+
+ align:start position:0%
+uh in a series of developments
+ 
+
+ align:start position:0%
+uh in a series of developments
+throughout what becomes known as as
+
+ align:start position:0%
+throughout what becomes known as as
+ 
+
+ align:start position:0%
+throughout what becomes known as as
+quantum mechanics so he really found
+
+ align:start position:0%
+quantum mechanics so he really found
+ 
+
+ align:start position:0%
+quantum mechanics so he really found
+this kind of delicious and enticing
+
+ align:start position:0%
+this kind of delicious and enticing
+ 
+
+ align:start position:0%
+this kind of delicious and enticing
+maybe those are the wrong words to use
+
+ align:start position:0%
+maybe those are the wrong words to use
+ 
+
+ align:start position:0%
+maybe those are the wrong words to use
+but he certainly found it worth sitting
+
+ align:start position:0%
+but he certainly found it worth sitting
+ 
+
+ align:start position:0%
+but he certainly found it worth sitting
+with as opposed to it must be a or b
+
+ align:start position:0%
+with as opposed to it must be a or b
+ 
+
+ align:start position:0%
+with as opposed to it must be a or b
+um and we'll see some examples of that
+
+ align:start position:0%
+um and we'll see some examples of that
+ 
+
+ align:start position:0%
+um and we'll see some examples of that
+again in the coming class sessions
+
+ align:start position:0%
+again in the coming class sessions
+ 
+
+ align:start position:0%
+again in the coming class sessions
+excellent observation though any other
+
+ align:start position:0%
+excellent observation though any other
+ 
+
+ align:start position:0%
+excellent observation though any other
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since I have three minutes I'll share
+
+ align:start position:0%
+since I have three minutes I'll share
+ 
+
+ align:start position:0%
+since I have three minutes I'll share
+the following uh one of the things that
+
+ align:start position:0%
+the following uh one of the things that
+ 
+
+ align:start position:0%
+the following uh one of the things that
+was done by not Arthur Compton but by
+
+ align:start position:0%
+was done by not Arthur Compton but by
+ 
+
+ align:start position:0%
+was done by not Arthur Compton but by
+Carl Compton soon after he became
+
+ align:start position:0%
+Carl Compton soon after he became
+ 
+
+ align:start position:0%
+Carl Compton soon after he became
+president in 1930 president of MIT
+
+ align:start position:0%
+president in 1930 president of MIT
+ 
+
+ align:start position:0%
+president in 1930 president of MIT
+and this is for all you physics majors
+
+ align:start position:0%
+and this is for all you physics majors
+ 
+
+ align:start position:0%
+and this is for all you physics majors
+and my apologies to every other
+
+ align:start position:0%
+and my apologies to every other
+ 
+
+ align:start position:0%
+and my apologies to every other
+engineering major you know who you are
+
+ align:start position:0%
+engineering major you know who you are
+ 
+
+ align:start position:0%
+engineering major you know who you are
+Compton decided that MIT become too
+
+ align:start position:0%
+Compton decided that MIT become too
+ 
+
+ align:start position:0%
+Compton decided that MIT become too
+closely aligned to both engineering and
+
+ align:start position:0%
+closely aligned to both engineering and
+ 
+
+ align:start position:0%
+closely aligned to both engineering and
+Industry he thought his Compton's own
+
+ align:start position:0%
+Industry he thought his Compton's own
+ 
+
+ align:start position:0%
+Industry he thought his Compton's own
+words the MIT had sold its soul to
+
+ align:start position:0%
+words the MIT had sold its soul to
+ 
+
+ align:start position:0%
+words the MIT had sold its soul to
+industrialists and so it was time for
+
+ align:start position:0%
+industrialists and so it was time for
+ 
+
+ align:start position:0%
+industrialists and so it was time for
+MIT to redouble on the basic Sciences
+
+ align:start position:0%
+MIT to redouble on the basic Sciences
+ 
+
+ align:start position:0%
+MIT to redouble on the basic Sciences
+it was at this time starting in 1930
+
+ align:start position:0%
+it was at this time starting in 1930
+ 
+
+ align:start position:0%
+it was at this time starting in 1930
+when Compton Carl Compton put into a
+
+ align:start position:0%
+when Compton Carl Compton put into a
+ 
+
+ align:start position:0%
+when Compton Carl Compton put into a
+reform that every single undergraduate
+
+ align:start position:0%
+reform that every single undergraduate
+ 
+
+ align:start position:0%
+reform that every single undergraduate
+MIT had to take two whole years of
+
+ align:start position:0%
+MIT had to take two whole years of
+ 
+
+ align:start position:0%
+MIT had to take two whole years of
+physics you little whips kidding just
+
+ align:start position:0%
+physics you little whips kidding just
+ 
+
+ align:start position:0%
+physics you little whips kidding just
+kidding you wonderful students only have
+
+ align:start position:0%
+kidding you wonderful students only have
+ 
+
+ align:start position:0%
+kidding you wonderful students only have
+to take one year of physics because MIT
+
+ align:start position:0%
+to take one year of physics because MIT
+ 
+
+ align:start position:0%
+to take one year of physics because MIT
+relented in 1965. for 35 years Carl
+
+ align:start position:0%
+relented in 1965. for 35 years Carl
+ 
+
+ align:start position:0%
+relented in 1965. for 35 years Carl
+Compton's Vision held and literally
+
+ align:start position:0%
+Compton's Vision held and literally
+ 
+
+ align:start position:0%
+Compton's Vision held and literally
+every every ma2 student whether they
+
+ align:start position:0%
+every every ma2 student whether they
+ 
+
+ align:start position:0%
+every every ma2 student whether they
+were management majors at the Sloan
+
+ align:start position:0%
+were management majors at the Sloan
+ 
+
+ align:start position:0%
+were management majors at the Sloan
+school I'm looking at Gary or you know
+
+ align:start position:0%
+school I'm looking at Gary or you know
+ 
+
+ align:start position:0%
+school I'm looking at Gary or you know
+economics major or history or or
+
+ align:start position:0%
+economics major or history or or
+ 
+
+ align:start position:0%
+economics major or history or or
+mathematics had to take two years of
+
+ align:start position:0%
+mathematics had to take two years of
+ 
+
+ align:start position:0%
+mathematics had to take two years of
+physics it wasn't quite the Cambridge
+
+ align:start position:0%
+physics it wasn't quite the Cambridge
+ 
+
+ align:start position:0%
+physics it wasn't quite the Cambridge
+Wranglers but we had to two years
+
+ align:start position:0%
+Wranglers but we had to two years
+ 
+
+ align:start position:0%
+Wranglers but we had to two years
+because Carl Compton the physicist was
+
+ align:start position:0%
+because Carl Compton the physicist was
+ 
+
+ align:start position:0%
+because Carl Compton the physicist was
+convinced that we had to have a whole
+
+ align:start position:0%
+convinced that we had to have a whole
+ 
+
+ align:start position:0%
+convinced that we had to have a whole
+new emphasis on on the so-called basic
+
+ align:start position:0%
+new emphasis on on the so-called basic
+ 
+
+ align:start position:0%
+new emphasis on on the so-called basic
+Sciences it's at this time when the
+
+ align:start position:0%
+Sciences it's at this time when the
+ 
+
+ align:start position:0%
+Sciences it's at this time when the
+laboratory requirements start coming in
+
+ align:start position:0%
+laboratory requirements start coming in
+ 
+
+ align:start position:0%
+laboratory requirements start coming in
+for uh biology and chemistry and
+
+ align:start position:0%
+for uh biology and chemistry and
+ 
+
+ align:start position:0%
+for uh biology and chemistry and
+Mathematics
+
+ align:start position:0%
+Mathematics
+ 
+
+ align:start position:0%
+Mathematics
+it was only uh 35 years later in the
+
+ align:start position:0%
+it was only uh 35 years later in the
+ 
+
+ align:start position:0%
+it was only uh 35 years later in the
+mid-1960s when some um some colleagues
+
+ align:start position:0%
+mid-1960s when some um some colleagues
+ 
+
+ align:start position:0%
+mid-1960s when some um some colleagues
+long after uh Carl Compton sat down and
+
+ align:start position:0%
+long after uh Carl Compton sat down and
+ 
+
+ align:start position:0%
+long after uh Carl Compton sat down and
+said maybe that's too much physics for
+
+ align:start position:0%
+said maybe that's too much physics for
+ 
+
+ align:start position:0%
+said maybe that's too much physics for
+every single student and honestly when I
+
+ align:start position:0%
+every single student and honestly when I
+ 
+
+ align:start position:0%
+every single student and honestly when I
+started teaching at MIT in 2000 some of
+
+ align:start position:0%
+started teaching at MIT in 2000 some of
+ 
+
+ align:start position:0%
+started teaching at MIT in 2000 some of
+my then rather senior colleagues still
+
+ align:start position:0%
+my then rather senior colleagues still
+ 
+
+ align:start position:0%
+my then rather senior colleagues still
+remembered 1965 and thought everything
+
+ align:start position:0%
+remembered 1965 and thought everything
+ 
+
+ align:start position:0%
+remembered 1965 and thought everything
+had gone downhill since then those
+
+ align:start position:0%
+had gone downhill since then those
+ 
+
+ align:start position:0%
+had gone downhill since then those
+people have since retired but like MIT
+
+ align:start position:0%
+people have since retired but like MIT
+ 
+
+ align:start position:0%
+people have since retired but like MIT
+has never been the same in their point
+
+ align:start position:0%
+has never been the same in their point
+ 
+
+ align:start position:0%
+has never been the same in their point
+of view since we gave up forcing slash
+
+ align:start position:0%
+of view since we gave up forcing slash
+ 
+
+ align:start position:0%
+of view since we gave up forcing slash
+inviting every single undergraduate to
+
+ align:start position:0%
+inviting every single undergraduate to
+ 
+
+ align:start position:0%
+inviting every single undergraduate to
+take two whole years of physics so
+
+ align:start position:0%
+take two whole years of physics so
+ 
+
+ align:start position:0%
+take two whole years of physics so
+that's one of the legacies of Carla
+
+ align:start position:0%
+that's one of the legacies of Carla
+ 
+
+ align:start position:0%
+that's one of the legacies of Carla
+Compton not Arthur Compton
+
+ align:start position:0%
+Compton not Arthur Compton
+ 
+
+ align:start position:0%
+Compton not Arthur Compton
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's true Alex puts in the chat where
+
+ align:start position:0%
+it's true Alex puts in the chat where
+ 
+
+ align:start position:0%
+it's true Alex puts in the chat where
+the problem sets originally questions
+
+ align:start position:0%
+the problem sets originally questions
+ 
+
+ align:start position:0%
+the problem sets originally questions
+from industry many of them were in fact
+
+ align:start position:0%
+from industry many of them were in fact
+ 
+
+ align:start position:0%
+from industry many of them were in fact
+if not problem sets then certainly
+
+ align:start position:0%
+if not problem sets then certainly
+ 
+
+ align:start position:0%
+if not problem sets then certainly
+research projects there was a kind of um
+
+ align:start position:0%
+research projects there was a kind of um
+ 
+
+ align:start position:0%
+research projects there was a kind of um
+research for hire program which which
+
+ align:start position:0%
+research for hire program which which
+ 
+
+ align:start position:0%
+research for hire program which which
+never really ended but was was a very
+
+ align:start position:0%
+never really ended but was was a very
+ 
+
+ align:start position:0%
+never really ended but was was a very
+high focus at MIT starting soon after
+
+ align:start position:0%
+high focus at MIT starting soon after
+ 
+
+ align:start position:0%
+high focus at MIT starting soon after
+the first world war after in the years
+
+ align:start position:0%
+the first world war after in the years
+ 
+
+ align:start position:0%
+the first world war after in the years
+right after 1918. it was called the MIT
+
+ align:start position:0%
+right after 1918. it was called the MIT
+ 
+
+ align:start position:0%
+right after 1918. it was called the MIT
+plan or the tech plan
+
+ align:start position:0%
+plan or the tech plan
+ 
+
+ align:start position:0%
+plan or the tech plan
+and roughly 12 to 15 years into that
+
+ align:start position:0%
+and roughly 12 to 15 years into that
+ 
+
+ align:start position:0%
+and roughly 12 to 15 years into that
+there was a kind of correct course
+
+ align:start position:0%
+there was a kind of correct course
+ 
+
+ align:start position:0%
+there was a kind of correct course
+correction and people like Carl
+
+ align:start position:0%
+correction and people like Carl
+ 
+
+ align:start position:0%
+correction and people like Carl
+conference that we have to rejigger that
+
+ align:start position:0%
+conference that we have to rejigger that
+ 
+
+ align:start position:0%
+conference that we have to rejigger that
+Fisher says I assume this requirement
+
+ align:start position:0%
+Fisher says I assume this requirement
+ 
+
+ align:start position:0%
+Fisher says I assume this requirement
+naturally only applied to physics and
+
+ align:start position:0%
+naturally only applied to physics and
+ 
+
+ align:start position:0%
+naturally only applied to physics and
+how about no that's right Fisher's
+
+ align:start position:0%
+how about no that's right Fisher's
+ 
+
+ align:start position:0%
+how about no that's right Fisher's
+exactly right so the requirement of two
+
+ align:start position:0%
+exactly right so the requirement of two
+ 
+
+ align:start position:0%
+exactly right so the requirement of two
+years a physics coursework applied only
+
+ align:start position:0%
+years a physics coursework applied only
+ 
+
+ align:start position:0%
+years a physics coursework applied only
+to physics for every single
+
+ align:start position:0%
+to physics for every single
+ 
+
+ align:start position:0%
+to physics for every single
+undergraduate and grudgingly if you had
+
+ align:start position:0%
+undergraduate and grudgingly if you had
+ 
+
+ align:start position:0%
+undergraduate and grudgingly if you had
+to take chemistry or biology fine that
+
+ align:start position:0%
+to take chemistry or biology fine that
+ 
+
+ align:start position:0%
+to take chemistry or biology fine that
+was required you have to take
+
+ align:start position:0%
+was required you have to take
+ 
+
+ align:start position:0%
+was required you have to take
+Laboratories I had to take at least one
+
+ align:start position:0%
+Laboratories I had to take at least one
+ 
+
+ align:start position:0%
+Laboratories I had to take at least one
+year of mathematics so we can recognize
+
+ align:start position:0%
+year of mathematics so we can recognize
+ 
+
+ align:start position:0%
+year of mathematics so we can recognize
+parts of our so-called girs to this day
+
+ align:start position:0%
+parts of our so-called girs to this day
+ 
+
+ align:start position:0%
+parts of our so-called girs to this day
+survive from Carl Compton's era even
+
+ align:start position:0%
+survive from Carl Compton's era even
+ 
+
+ align:start position:0%
+survive from Carl Compton's era even
+though critically the one horrible moral
+
+ align:start position:0%
+though critically the one horrible moral
+ 
+
+ align:start position:0%
+though critically the one horrible moral
+lapse According to some of my colleagues
+
+ align:start position:0%
+lapse According to some of my colleagues
+ 
+
+ align:start position:0%
+lapse According to some of my colleagues
+was dropping the two years of physics in
+
+ align:start position:0%
+was dropping the two years of physics in
+ 
+
+ align:start position:0%
+was dropping the two years of physics in
+place of only one I leave you with that
+
+ align:start position:0%
+place of only one I leave you with that
+ 
+
+ align:start position:0%
+place of only one I leave you with that
+thought uh I invite you all to take more
+
+ align:start position:0%
+thought uh I invite you all to take more
+ 
+
+ align:start position:0%
+thought uh I invite you all to take more
+than one year of physics I think many of
+
+ align:start position:0%
+than one year of physics I think many of
+ 
+
+ align:start position:0%
+than one year of physics I think many of
+you have been anyway because of physics
+
+ align:start position:0%
+you have been anyway because of physics
+ 
+
+ align:start position:0%
+you have been anyway because of physics
+Majors that's Carl Compton I'd like to
+
+ align:start position:0%
+Majors that's Carl Compton I'd like to
+ 
+
+ align:start position:0%
+Majors that's Carl Compton I'd like to
+talk more about Carl Compton and MIT in
+
+ align:start position:0%
+talk more about Carl Compton and MIT in
+ 
+
+ align:start position:0%
+talk more about Carl Compton and MIT in
+the coming weeks when we talk about MIT
+
+ align:start position:0%
+the coming weeks when we talk about MIT
+ 
+
+ align:start position:0%
+the coming weeks when we talk about MIT
+in the second world war and radar we'll
+
+ align:start position:0%
+in the second world war and radar we'll
+ 
+
+ align:start position:0%
+in the second world war and radar we'll
+hear Carl Compton's name again soon in
+
+ align:start position:0%
+hear Carl Compton's name again soon in
+ 
+
+ align:start position:0%
+hear Carl Compton's name again soon in
+the meantime we'll pause and sit with
+
+ align:start position:0%
+the meantime we'll pause and sit with
+ 
+
+ align:start position:0%
+the meantime we'll pause and sit with
+Arthur Compton's results for which again
+
+ align:start position:0%
+Arthur Compton's results for which again
+ 
+
+ align:start position:0%
+Arthur Compton's results for which again
+there's more of the algebra in those
+
+ align:start position:0%
+there's more of the algebra in those
+ 
+
+ align:start position:0%
+there's more of the algebra in those
+notes if if that went by too quickly any
+
+ align:start position:0%
+notes if if that went by too quickly any
+ 
+
+ align:start position:0%
+notes if if that went by too quickly any
+other questions uh about this material
+
+ align:start position:0%
+other questions uh about this material
+ 
+
+ align:start position:0%
+other questions uh about this material
+anyone wish that everyone had to take
+
+ align:start position:0%
+anyone wish that everyone had to take
+ 
+
+ align:start position:0%
+anyone wish that everyone had to take
+two years of physics or any other
+
+ align:start position:0%
+two years of physics or any other
+ 
+
+ align:start position:0%
+two years of physics or any other
+comments on on today's class
+
+ align:start position:0%
+comments on on today's class
+ 
+
+ align:start position:0%
+comments on on today's class
+if not I'll leave it there I'll wish you
+
+ align:start position:0%
+if not I'll leave it there I'll wish you
+ 
+
+ align:start position:0%
+if not I'll leave it there I'll wish you
+good luck wrapping up your paper one
+
+ align:start position:0%
+good luck wrapping up your paper one
+ 
+
+ align:start position:0%
+good luck wrapping up your paper one
+draft please don't forget let's do this
+
+ align:start position:0%
+draft please don't forget let's do this
+ 
+
+ align:start position:0%
+draft please don't forget let's do this
+Friday and we'll pick up the story of
+
+ align:start position:0%
+Friday and we'll pick up the story of
+ 
+
+ align:start position:0%
+Friday and we'll pick up the story of
+old quantum theory again with our next
+
+ align:start position:0%
+old quantum theory again with our next
+ 
+
+ align:start position:0%
+old quantum theory again with our next
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+thanks so much gang stay well
\ No newline at end of file
diff --git a/HxfSOdFOqkk.txt b/HxfSOdFOqkk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c0753bbf02a53981e10c4fef2e3846ab7392d3a
--- /dev/null
+++ b/HxfSOdFOqkk.txt
@@ -0,0 +1,3080 @@
+align:start position:0%
+ 
+all right you're probably wondering why
+
+ align:start position:0%
+all right you're probably wondering why
+ 
+
+ align:start position:0%
+all right you're probably wondering why
+there's so many pipes out here
+
+ align:start position:0%
+there's so many pipes out here
+ 
+
+ align:start position:0%
+there's so many pipes out here
+um back in um
+
+ align:start position:0%
+um back in um
+ 
+
+ align:start position:0%
+um back in um
+back in 1985 80 actually earlier in 93
+
+ align:start position:0%
+back in 1985 80 actually earlier in 93
+ 
+
+ align:start position:0%
+back in 1985 80 actually earlier in 93
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+we uh we had we had just we had
+
+ align:start position:0%
+we uh we had we had just we had
+ 
+
+ align:start position:0%
+we uh we had we had just we had
+discovered the sewage plume we were
+
+ align:start position:0%
+discovered the sewage plume we were
+ 
+
+ align:start position:0%
+discovered the sewage plume we were
+beginning to get a feeling for what it
+
+ align:start position:0%
+beginning to get a feeling for what it
+ 
+
+ align:start position:0%
+beginning to get a feeling for what it
+looked like and everything else
+
+ align:start position:0%
+looked like and everything else
+ 
+
+ align:start position:0%
+looked like and everything else
+and um one of the big questions at the
+
+ align:start position:0%
+and um one of the big questions at the
+ 
+
+ align:start position:0%
+and um one of the big questions at the
+time in in the hydro groundwater
+
+ align:start position:0%
+time in in the hydro groundwater
+ 
+
+ align:start position:0%
+time in in the hydro groundwater
+hydrology was the rate at which
+
+ align:start position:0%
+hydrology was the rate at which
+ 
+
+ align:start position:0%
+hydrology was the rate at which
+contaminants disperse
+
+ align:start position:0%
+contaminants disperse
+ 
+
+ align:start position:0%
+contaminants disperse
+you know how how quickly will if you put
+
+ align:start position:0%
+you know how how quickly will if you put
+ 
+
+ align:start position:0%
+you know how how quickly will if you put
+in a if you had a spill
+
+ align:start position:0%
+in a if you had a spill
+ 
+
+ align:start position:0%
+in a if you had a spill
+from a septic tank or a you know fuel
+
+ align:start position:0%
+from a septic tank or a you know fuel
+ 
+
+ align:start position:0%
+from a septic tank or a you know fuel
+spill or whatever else
+
+ align:start position:0%
+spill or whatever else
+ 
+
+ align:start position:0%
+spill or whatever else
+and and it got in the aquifer and it
+
+ align:start position:0%
+and and it got in the aquifer and it
+ 
+
+ align:start position:0%
+and and it got in the aquifer and it
+begins to migrate with the natural
+
+ align:start position:0%
+begins to migrate with the natural
+ 
+
+ align:start position:0%
+begins to migrate with the natural
+groundwater flow how quickly would it
+
+ align:start position:0%
+groundwater flow how quickly would it
+ 
+
+ align:start position:0%
+groundwater flow how quickly would it
+get diluted and dispersed to the point
+
+ align:start position:0%
+get diluted and dispersed to the point
+ 
+
+ align:start position:0%
+get diluted and dispersed to the point
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+it wouldn't be a problem and there were
+
+ align:start position:0%
+it wouldn't be a problem and there were
+ 
+
+ align:start position:0%
+it wouldn't be a problem and there were
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+ideas about how quickly that happened
+
+ align:start position:0%
+ideas about how quickly that happened
+ 
+
+ align:start position:0%
+ideas about how quickly that happened
+and what caused it
+
+ align:start position:0%
+and what caused it
+ 
+
+ align:start position:0%
+and what caused it
+and what they what a number of folks
+
+ align:start position:0%
+and what they what a number of folks
+ 
+
+ align:start position:0%
+and what they what a number of folks
+were able to demonstrate is that
+
+ align:start position:0%
+were able to demonstrate is that
+ 
+
+ align:start position:0%
+were able to demonstrate is that
+the primary cause of the dispersion in
+
+ align:start position:0%
+the primary cause of the dispersion in
+ 
+
+ align:start position:0%
+the primary cause of the dispersion in
+groundwater
+
+ align:start position:0%
+groundwater
+ 
+
+ align:start position:0%
+groundwater
+unlike in surface waters or in the
+
+ align:start position:0%
+unlike in surface waters or in the
+ 
+
+ align:start position:0%
+unlike in surface waters or in the
+atmosphere which is turbulence there's
+
+ align:start position:0%
+atmosphere which is turbulence there's
+ 
+
+ align:start position:0%
+atmosphere which is turbulence there's
+no turbulence in groundwater it moves
+
+ align:start position:0%
+no turbulence in groundwater it moves
+ 
+
+ align:start position:0%
+no turbulence in groundwater it moves
+through slowly
+
+ align:start position:0%
+through slowly
+ 
+
+ align:start position:0%
+through slowly
+you probably have you know heard about
+
+ align:start position:0%
+you probably have you know heard about
+ 
+
+ align:start position:0%
+you probably have you know heard about
+laminar flow it's really kind of almost
+
+ align:start position:0%
+laminar flow it's really kind of almost
+ 
+
+ align:start position:0%
+laminar flow it's really kind of almost
+limiter
+
+ align:start position:0%
+limiter
+ 
+
+ align:start position:0%
+limiter
+is is the actual heterogeneity of the
+
+ align:start position:0%
+is is the actual heterogeneity of the
+ 
+
+ align:start position:0%
+is is the actual heterogeneity of the
+subsurface
+
+ align:start position:0%
+subsurface
+ 
+
+ align:start position:0%
+subsurface
+in other words even the most uniform
+
+ align:start position:0%
+in other words even the most uniform
+ 
+
+ align:start position:0%
+in other words even the most uniform
+quote unquote aquifer like a sand and
+
+ align:start position:0%
+quote unquote aquifer like a sand and
+ 
+
+ align:start position:0%
+quote unquote aquifer like a sand and
+gravel outwash like this is
+
+ align:start position:0%
+gravel outwash like this is
+ 
+
+ align:start position:0%
+gravel outwash like this is
+actually has a fair amount of lensing
+
+ align:start position:0%
+actually has a fair amount of lensing
+ 
+
+ align:start position:0%
+actually has a fair amount of lensing
+and layering because it's a natural
+
+ align:start position:0%
+and layering because it's a natural
+ 
+
+ align:start position:0%
+and layering because it's a natural
+geologic deposit
+
+ align:start position:0%
+geologic deposit
+ 
+
+ align:start position:0%
+geologic deposit
+you know it has beds you know
+
+ align:start position:0%
+you know it has beds you know
+ 
+
+ align:start position:0%
+you know it has beds you know
+sedimentation beds from
+
+ align:start position:0%
+sedimentation beds from
+ 
+
+ align:start position:0%
+sedimentation beds from
+running water so some some pioneers like
+
+ align:start position:0%
+running water so some some pioneers like
+ 
+
+ align:start position:0%
+running water so some some pioneers like
+lynn gelhar i don't know if lynn
+
+ align:start position:0%
+lynn gelhar i don't know if lynn
+ 
+
+ align:start position:0%
+lynn gelhar i don't know if lynn
+gelhardt comes into the lab at all or
+
+ align:start position:0%
+gelhardt comes into the lab at all or
+ 
+
+ align:start position:0%
+gelhardt comes into the lab at all or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+anybody know lynn gelhart professor at
+
+ align:start position:0%
+anybody know lynn gelhart professor at
+ 
+
+ align:start position:0%
+anybody know lynn gelhart professor at
+mit he's retired now
+
+ align:start position:0%
+mit he's retired now
+ 
+
+ align:start position:0%
+mit he's retired now
+was one of the people who actually was
+
+ align:start position:0%
+was one of the people who actually was
+ 
+
+ align:start position:0%
+was one of the people who actually was
+able to demonstrate how you could
+
+ align:start position:0%
+able to demonstrate how you could
+ 
+
+ align:start position:0%
+able to demonstrate how you could
+predict the rate of dispersion if you
+
+ align:start position:0%
+predict the rate of dispersion if you
+ 
+
+ align:start position:0%
+predict the rate of dispersion if you
+could characterize the heterogeneity of
+
+ align:start position:0%
+could characterize the heterogeneity of
+ 
+
+ align:start position:0%
+could characterize the heterogeneity of
+the aquifer
+
+ align:start position:0%
+the aquifer
+ 
+
+ align:start position:0%
+the aquifer
+so if you could find some way of
+
+ align:start position:0%
+so if you could find some way of
+ 
+
+ align:start position:0%
+so if you could find some way of
+statistically characterizing how the
+
+ align:start position:0%
+statistically characterizing how the
+ 
+
+ align:start position:0%
+statistically characterizing how the
+hydraulic conductivity varied from place
+
+ align:start position:0%
+hydraulic conductivity varied from place
+ 
+
+ align:start position:0%
+hydraulic conductivity varied from place
+to place and how long
+
+ align:start position:0%
+to place and how long
+ 
+
+ align:start position:0%
+to place and how long
+the lenses and layers were and how thick
+
+ align:start position:0%
+the lenses and layers were and how thick
+ 
+
+ align:start position:0%
+the lenses and layers were and how thick
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+that you could actually predict how
+
+ align:start position:0%
+that you could actually predict how
+ 
+
+ align:start position:0%
+that you could actually predict how
+rapidly contaminants would disperse
+
+ align:start position:0%
+rapidly contaminants would disperse
+ 
+
+ align:start position:0%
+rapidly contaminants would disperse
+so he and a few others had come up with
+
+ align:start position:0%
+so he and a few others had come up with
+ 
+
+ align:start position:0%
+so he and a few others had come up with
+various stochastic
+
+ align:start position:0%
+various stochastic
+ 
+
+ align:start position:0%
+various stochastic
+uh models of that process and the idea
+
+ align:start position:0%
+uh models of that process and the idea
+ 
+
+ align:start position:0%
+uh models of that process and the idea
+was that you know is there any reality
+
+ align:start position:0%
+was that you know is there any reality
+ 
+
+ align:start position:0%
+was that you know is there any reality
+to them at all
+
+ align:start position:0%
+to them at all
+ 
+
+ align:start position:0%
+to them at all
+so um we teamed up with uh professor
+
+ align:start position:0%
+so um we teamed up with uh professor
+ 
+
+ align:start position:0%
+so um we teamed up with uh professor
+gelhart at mit
+
+ align:start position:0%
+gelhart at mit
+ 
+
+ align:start position:0%
+gelhart at mit
+one of his phd students lynn uh steve
+
+ align:start position:0%
+one of his phd students lynn uh steve
+ 
+
+ align:start position:0%
+one of his phd students lynn uh steve
+garrobinian and i
+
+ align:start position:0%
+garrobinian and i
+ 
+
+ align:start position:0%
+garrobinian and i
+and a few others uh that we hired to
+
+ align:start position:0%
+and a few others uh that we hired to
+ 
+
+ align:start position:0%
+and a few others uh that we hired to
+help us out and we ran a tracer
+
+ align:start position:0%
+help us out and we ran a tracer
+ 
+
+ align:start position:0%
+help us out and we ran a tracer
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+to try to measure the rate of dispersion
+
+ align:start position:0%
+to try to measure the rate of dispersion
+ 
+
+ align:start position:0%
+to try to measure the rate of dispersion
+in the aquifer so our idea was we would
+
+ align:start position:0%
+in the aquifer so our idea was we would
+ 
+
+ align:start position:0%
+in the aquifer so our idea was we would
+create our own little
+
+ align:start position:0%
+create our own little
+ 
+
+ align:start position:0%
+create our own little
+plume and we would monitor it as it
+
+ align:start position:0%
+plume and we would monitor it as it
+ 
+
+ align:start position:0%
+plume and we would monitor it as it
+moved through the aquifer and actually
+
+ align:start position:0%
+moved through the aquifer and actually
+ 
+
+ align:start position:0%
+moved through the aquifer and actually
+by collecting water samples in three
+
+ align:start position:0%
+by collecting water samples in three
+ 
+
+ align:start position:0%
+by collecting water samples in three
+dimensions so we'd have a detailed 3d
+
+ align:start position:0%
+dimensions so we'd have a detailed 3d
+ 
+
+ align:start position:0%
+dimensions so we'd have a detailed 3d
+snapshot of this tracer plume
+
+ align:start position:0%
+snapshot of this tracer plume
+ 
+
+ align:start position:0%
+snapshot of this tracer plume
+we could actually measure how rapidly it
+
+ align:start position:0%
+we could actually measure how rapidly it
+ 
+
+ align:start position:0%
+we could actually measure how rapidly it
+dispersed and spread
+
+ align:start position:0%
+dispersed and spread
+ 
+
+ align:start position:0%
+dispersed and spread
+and then we could compare that to other
+
+ align:start position:0%
+and then we could compare that to other
+ 
+
+ align:start position:0%
+and then we could compare that to other
+measurements of the aquifer's
+
+ align:start position:0%
+measurements of the aquifer's
+ 
+
+ align:start position:0%
+measurements of the aquifer's
+heterogeneity and see if the theories
+
+ align:start position:0%
+heterogeneity and see if the theories
+ 
+
+ align:start position:0%
+heterogeneity and see if the theories
+were right
+
+ align:start position:0%
+were right
+ 
+
+ align:start position:0%
+were right
+so it was it was a a massive tracer
+
+ align:start position:0%
+so it was it was a a massive tracer
+ 
+
+ align:start position:0%
+so it was it was a a massive tracer
+experiment so what we did is uh
+
+ align:start position:0%
+experiment so what we did is uh
+ 
+
+ align:start position:0%
+experiment so what we did is uh
+we picked this spot somebody had asked
+
+ align:start position:0%
+we picked this spot somebody had asked
+ 
+
+ align:start position:0%
+we picked this spot somebody had asked
+me why did you pick this spot
+
+ align:start position:0%
+me why did you pick this spot
+ 
+
+ align:start position:0%
+me why did you pick this spot
+uh well we picked this spot to run the
+
+ align:start position:0%
+uh well we picked this spot to run the
+ 
+
+ align:start position:0%
+uh well we picked this spot to run the
+tracer experiment for a couple of
+
+ align:start position:0%
+tracer experiment for a couple of
+ 
+
+ align:start position:0%
+tracer experiment for a couple of
+reasons first of all it was an abandoned
+
+ align:start position:0%
+reasons first of all it was an abandoned
+ 
+
+ align:start position:0%
+reasons first of all it was an abandoned
+gravel pit
+
+ align:start position:0%
+gravel pit
+ 
+
+ align:start position:0%
+gravel pit
+and uh so it was flat and easy to work
+
+ align:start position:0%
+and uh so it was flat and easy to work
+ 
+
+ align:start position:0%
+and uh so it was flat and easy to work
+in secondly it was on state-owned land
+
+ align:start position:0%
+in secondly it was on state-owned land
+ 
+
+ align:start position:0%
+in secondly it was on state-owned land
+so we had permission to do it
+
+ align:start position:0%
+so we had permission to do it
+ 
+
+ align:start position:0%
+so we had permission to do it
+and thirdly uh the groundwater was
+
+ align:start position:0%
+and thirdly uh the groundwater was
+ 
+
+ align:start position:0%
+and thirdly uh the groundwater was
+already contaminated here
+
+ align:start position:0%
+already contaminated here
+ 
+
+ align:start position:0%
+already contaminated here
+because of the sewage disposal so we
+
+ align:start position:0%
+because of the sewage disposal so we
+ 
+
+ align:start position:0%
+because of the sewage disposal so we
+were able to get permission from the
+
+ align:start position:0%
+were able to get permission from the
+ 
+
+ align:start position:0%
+were able to get permission from the
+state to create our own plume within a
+
+ align:start position:0%
+state to create our own plume within a
+ 
+
+ align:start position:0%
+state to create our own plume within a
+plume
+
+ align:start position:0%
+plume
+ 
+
+ align:start position:0%
+plume
+you know if we had gone through a
+
+ align:start position:0%
+you know if we had gone through a
+ 
+
+ align:start position:0%
+you know if we had gone through a
+pristine aquifer they would have gone
+
+ align:start position:0%
+pristine aquifer they would have gone
+ 
+
+ align:start position:0%
+pristine aquifer they would have gone
+are you nuts you want to add a
+
+ align:start position:0%
+are you nuts you want to add a
+ 
+
+ align:start position:0%
+are you nuts you want to add a
+contaminant
+
+ align:start position:0%
+contaminant
+ 
+
+ align:start position:0%
+contaminant
+you know so uh so we were able to do it
+
+ align:start position:0%
+you know so uh so we were able to do it
+ 
+
+ align:start position:0%
+you know so uh so we were able to do it
+right here so what we did on uh
+
+ align:start position:0%
+right here so what we did on uh
+ 
+
+ align:start position:0%
+right here so what we did on uh
+in july 1985 we uh see the three wells
+
+ align:start position:0%
+in july 1985 we uh see the three wells
+ 
+
+ align:start position:0%
+in july 1985 we uh see the three wells
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+yellow labels up there the three wells
+
+ align:start position:0%
+yellow labels up there the three wells
+ 
+
+ align:start position:0%
+yellow labels up there the three wells
+those are all screened uh just below the
+
+ align:start position:0%
+those are all screened uh just below the
+ 
+
+ align:start position:0%
+those are all screened uh just below the
+water table they're shallow wells
+
+ align:start position:0%
+water table they're shallow wells
+ 
+
+ align:start position:0%
+water table they're shallow wells
+we uh we pumped two thousand gallons of
+
+ align:start position:0%
+we uh we pumped two thousand gallons of
+ 
+
+ align:start position:0%
+we uh we pumped two thousand gallons of
+water out of the aquifer into tanks
+
+ align:start position:0%
+water out of the aquifer into tanks
+ 
+
+ align:start position:0%
+water out of the aquifer into tanks
+this was clean groundwater pristine
+
+ align:start position:0%
+this was clean groundwater pristine
+ 
+
+ align:start position:0%
+this was clean groundwater pristine
+groundwater we added a number of traces
+
+ align:start position:0%
+groundwater we added a number of traces
+ 
+
+ align:start position:0%
+groundwater we added a number of traces
+to the water and in particular the one
+
+ align:start position:0%
+to the water and in particular the one
+ 
+
+ align:start position:0%
+to the water and in particular the one
+i'll talk about today is bromide
+
+ align:start position:0%
+i'll talk about today is bromide
+ 
+
+ align:start position:0%
+i'll talk about today is bromide
+uh like chloride it's very non-reactive
+
+ align:start position:0%
+uh like chloride it's very non-reactive
+ 
+
+ align:start position:0%
+uh like chloride it's very non-reactive
+so it's a good tracer of the water
+
+ align:start position:0%
+so it's a good tracer of the water
+ 
+
+ align:start position:0%
+so it's a good tracer of the water
+and bromide levels in the aquifer
+
+ align:start position:0%
+and bromide levels in the aquifer
+ 
+
+ align:start position:0%
+and bromide levels in the aquifer
+naturally are very low so we had a good
+
+ align:start position:0%
+naturally are very low so we had a good
+ 
+
+ align:start position:0%
+naturally are very low so we had a good
+signature of the water we put in as
+
+ align:start position:0%
+signature of the water we put in as
+ 
+
+ align:start position:0%
+signature of the water we put in as
+opposed to the background water
+
+ align:start position:0%
+opposed to the background water
+ 
+
+ align:start position:0%
+opposed to the background water
+right and then we uh we injected it over
+
+ align:start position:0%
+right and then we uh we injected it over
+ 
+
+ align:start position:0%
+right and then we uh we injected it over
+a very short period of time
+
+ align:start position:0%
+a very short period of time
+ 
+
+ align:start position:0%
+a very short period of time
+about a day took about about 19 hours
+
+ align:start position:0%
+about a day took about about 19 hours
+ 
+
+ align:start position:0%
+about a day took about about 19 hours
+into those three wells
+
+ align:start position:0%
+into those three wells
+ 
+
+ align:start position:0%
+into those three wells
+so what we did is we created a pulse
+
+ align:start position:0%
+so what we did is we created a pulse
+ 
+
+ align:start position:0%
+so what we did is we created a pulse
+you know on the time scale of years
+
+ align:start position:0%
+you know on the time scale of years
+ 
+
+ align:start position:0%
+you know on the time scale of years
+essentially instantaneous pulse in the
+
+ align:start position:0%
+essentially instantaneous pulse in the
+ 
+
+ align:start position:0%
+essentially instantaneous pulse in the
+aquifer
+
+ align:start position:0%
+aquifer
+ 
+
+ align:start position:0%
+aquifer
+a bromide cloud and if you just did some
+
+ align:start position:0%
+a bromide cloud and if you just did some
+ 
+
+ align:start position:0%
+a bromide cloud and if you just did some
+simple calculations it would have been
+
+ align:start position:0%
+simple calculations it would have been
+ 
+
+ align:start position:0%
+simple calculations it would have been
+about four meters by four meters by
+
+ align:start position:0%
+about four meters by four meters by
+ 
+
+ align:start position:0%
+about four meters by four meters by
+three meters
+
+ align:start position:0%
+three meters
+ 
+
+ align:start position:0%
+three meters
+now it didn't go in that thing more like
+
+ align:start position:0%
+now it didn't go in that thing more like
+ 
+
+ align:start position:0%
+now it didn't go in that thing more like
+a beautiful box but that was roughly the
+
+ align:start position:0%
+a beautiful box but that was roughly the
+ 
+
+ align:start position:0%
+a beautiful box but that was roughly the
+size we expected it to be
+
+ align:start position:0%
+size we expected it to be
+ 
+
+ align:start position:0%
+size we expected it to be
+all right and then what we did is we
+
+ align:start position:0%
+all right and then what we did is we
+ 
+
+ align:start position:0%
+all right and then what we did is we
+then let the natural flow carry it
+
+ align:start position:0%
+then let the natural flow carry it
+ 
+
+ align:start position:0%
+then let the natural flow carry it
+downstream how did we know which way it
+
+ align:start position:0%
+downstream how did we know which way it
+ 
+
+ align:start position:0%
+downstream how did we know which way it
+would go we'd done all those water table
+
+ align:start position:0%
+would go we'd done all those water table
+ 
+
+ align:start position:0%
+would go we'd done all those water table
+wells first we had mapped the water
+
+ align:start position:0%
+wells first we had mapped the water
+ 
+
+ align:start position:0%
+wells first we had mapped the water
+table out here in detail
+
+ align:start position:0%
+table out here in detail
+ 
+
+ align:start position:0%
+table out here in detail
+and we could predict which direction it
+
+ align:start position:0%
+and we could predict which direction it
+ 
+
+ align:start position:0%
+and we could predict which direction it
+would take more or less
+
+ align:start position:0%
+would take more or less
+ 
+
+ align:start position:0%
+would take more or less
+all right and uh so then we started to
+
+ align:start position:0%
+all right and uh so then we started to
+ 
+
+ align:start position:0%
+all right and uh so then we started to
+track it
+
+ align:start position:0%
+track it
+ 
+
+ align:start position:0%
+track it
+and the way we did that was by using
+
+ align:start position:0%
+and the way we did that was by using
+ 
+
+ align:start position:0%
+and the way we did that was by using
+these multi-level samplers that we had
+
+ align:start position:0%
+these multi-level samplers that we had
+ 
+
+ align:start position:0%
+these multi-level samplers that we had
+drilled out ahead of it
+
+ align:start position:0%
+drilled out ahead of it
+ 
+
+ align:start position:0%
+drilled out ahead of it
+right so you can just imagine this
+
+ align:start position:0%
+right so you can just imagine this
+ 
+
+ align:start position:0%
+right so you can just imagine this
+process we um
+
+ align:start position:0%
+process we um
+ 
+
+ align:start position:0%
+process we um
+we inject the tracer and we had put in
+
+ align:start position:0%
+we inject the tracer and we had put in
+ 
+
+ align:start position:0%
+we inject the tracer and we had put in
+about 10 rows of samplers and we would
+
+ align:start position:0%
+about 10 rows of samplers and we would
+ 
+
+ align:start position:0%
+about 10 rows of samplers and we would
+come out here and look at them wow look
+
+ align:start position:0%
+come out here and look at them wow look
+ 
+
+ align:start position:0%
+come out here and look at them wow look
+at all those wells isn't that cool
+
+ align:start position:0%
+at all those wells isn't that cool
+ 
+
+ align:start position:0%
+at all those wells isn't that cool
+there were about 80 of them at the time
+
+ align:start position:0%
+there were about 80 of them at the time
+ 
+
+ align:start position:0%
+there were about 80 of them at the time
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we injected the tracers and then right
+
+ align:start position:0%
+we injected the tracers and then right
+ 
+
+ align:start position:0%
+we injected the tracers and then right
+away i think the first time we did a
+
+ align:start position:0%
+away i think the first time we did a
+ 
+
+ align:start position:0%
+away i think the first time we did a
+sampling was 13 days later we went out
+
+ align:start position:0%
+sampling was 13 days later we went out
+ 
+
+ align:start position:0%
+sampling was 13 days later we went out
+and sampled as many of these multi-level
+
+ align:start position:0%
+and sampled as many of these multi-level
+ 
+
+ align:start position:0%
+and sampled as many of these multi-level
+samples as we could
+
+ align:start position:0%
+samples as we could
+ 
+
+ align:start position:0%
+samples as we could
+ran back to the lab and then analyzed
+
+ align:start position:0%
+ran back to the lab and then analyzed
+ 
+
+ align:start position:0%
+ran back to the lab and then analyzed
+the samples for bromide
+
+ align:start position:0%
+the samples for bromide
+ 
+
+ align:start position:0%
+the samples for bromide
+and tried to figure out where this
+
+ align:start position:0%
+and tried to figure out where this
+ 
+
+ align:start position:0%
+and tried to figure out where this
+tracer cloud was how big was it
+
+ align:start position:0%
+tracer cloud was how big was it
+ 
+
+ align:start position:0%
+tracer cloud was how big was it
+and on that basis we then would build
+
+ align:start position:0%
+and on that basis we then would build
+ 
+
+ align:start position:0%
+and on that basis we then would build
+more samplers
+
+ align:start position:0%
+more samplers
+ 
+
+ align:start position:0%
+more samplers
+get out ahead of where the cloud was
+
+ align:start position:0%
+get out ahead of where the cloud was
+ 
+
+ align:start position:0%
+get out ahead of where the cloud was
+going to go next based on our
+
+ align:start position:0%
+going to go next based on our
+ 
+
+ align:start position:0%
+going to go next based on our
+predictions
+
+ align:start position:0%
+predictions
+ 
+
+ align:start position:0%
+predictions
+drilled more samplers and then we
+
+ align:start position:0%
+drilled more samplers and then we
+ 
+
+ align:start position:0%
+drilled more samplers and then we
+leapfrogged for two years that way
+
+ align:start position:0%
+leapfrogged for two years that way
+ 
+
+ align:start position:0%
+leapfrogged for two years that way
+all the way down across the gravel pit
+
+ align:start position:0%
+all the way down across the gravel pit
+ 
+
+ align:start position:0%
+all the way down across the gravel pit
+so all these samplers were put in as
+
+ align:start position:0%
+so all these samplers were put in as
+ 
+
+ align:start position:0%
+so all these samplers were put in as
+part of that treasure test
+
+ align:start position:0%
+part of that treasure test
+ 
+
+ align:start position:0%
+part of that treasure test
+back in 1985. um
+
+ align:start position:0%
+back in 1985. um
+ 
+
+ align:start position:0%
+back in 1985. um
+these are all multi-level samplers so
+
+ align:start position:0%
+these are all multi-level samplers so
+ 
+
+ align:start position:0%
+these are all multi-level samplers so
+you're looking at a well field here this
+
+ align:start position:0%
+you're looking at a well field here this
+ 
+
+ align:start position:0%
+you're looking at a well field here this
+we've now since run about 70 tracer
+
+ align:start position:0%
+we've now since run about 70 tracer
+ 
+
+ align:start position:0%
+we've now since run about 70 tracer
+experiments out here so we've added some
+
+ align:start position:0%
+experiments out here so we've added some
+ 
+
+ align:start position:0%
+experiments out here so we've added some
+as we go along
+
+ align:start position:0%
+as we go along
+ 
+
+ align:start position:0%
+as we go along
+there's about a thousand out here which
+
+ align:start position:0%
+there's about a thousand out here which
+ 
+
+ align:start position:0%
+there's about a thousand out here which
+means there's 15 000 sampling points
+
+ align:start position:0%
+means there's 15 000 sampling points
+ 
+
+ align:start position:0%
+means there's 15 000 sampling points
+in the gravel pad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question i i would guess
+
+ align:start position:0%
+that's a good question i i would guess
+ 
+
+ align:start position:0%
+that's a good question i i would guess
+uh it's hard it's hard to really put a
+
+ align:start position:0%
+uh it's hard it's hard to really put a
+ 
+
+ align:start position:0%
+uh it's hard it's hard to really put a
+number on it
+
+ align:start position:0%
+number on it
+ 
+
+ align:start position:0%
+number on it
+but let's just say a million dollars i
+
+ align:start position:0%
+but let's just say a million dollars i
+ 
+
+ align:start position:0%
+but let's just say a million dollars i
+mean i just
+
+ align:start position:0%
+mean i just
+ 
+
+ align:start position:0%
+mean i just
+i have no way of really telling you
+
+ align:start position:0%
+i have no way of really telling you
+ 
+
+ align:start position:0%
+i have no way of really telling you
+because it's old dollars versus new
+
+ align:start position:0%
+because it's old dollars versus new
+ 
+
+ align:start position:0%
+because it's old dollars versus new
+dollars and you know
+
+ align:start position:0%
+dollars and you know
+ 
+
+ align:start position:0%
+dollars and you know
+it's really hard to say and then we had
+
+ align:start position:0%
+it's really hard to say and then we had
+ 
+
+ align:start position:0%
+it's really hard to say and then we had
+a lot of researchers work with us that i
+
+ align:start position:0%
+a lot of researchers work with us that i
+ 
+
+ align:start position:0%
+a lot of researchers work with us that i
+didn't control their money
+
+ align:start position:0%
+didn't control their money
+ 
+
+ align:start position:0%
+didn't control their money
+you know i didn't fund them so uh my
+
+ align:start position:0%
+you know i didn't fund them so uh my
+ 
+
+ align:start position:0%
+you know i didn't fund them so uh my
+budgets were always less than a half a
+
+ align:start position:0%
+budgets were always less than a half a
+ 
+
+ align:start position:0%
+budgets were always less than a half a
+million
+
+ align:start position:0%
+million
+ 
+
+ align:start position:0%
+million
+they were they were uh typically a
+
+ align:start position:0%
+they were they were uh typically a
+ 
+
+ align:start position:0%
+they were they were uh typically a
+couple hundred thousand but then that
+
+ align:start position:0%
+couple hundred thousand but then that
+ 
+
+ align:start position:0%
+couple hundred thousand but then that
+was 1984 dollars you know so i don't
+
+ align:start position:0%
+was 1984 dollars you know so i don't
+ 
+
+ align:start position:0%
+was 1984 dollars you know so i don't
+know what it would be today
+
+ align:start position:0%
+know what it would be today
+ 
+
+ align:start position:0%
+know what it would be today
+so did you prove the stochastic model i
+
+ align:start position:0%
+so did you prove the stochastic model i
+ 
+
+ align:start position:0%
+so did you prove the stochastic model i
+came out uh frequently closed
+
+ align:start position:0%
+came out uh frequently closed
+ 
+
+ align:start position:0%
+came out uh frequently closed
+the one thing that surprised us was that
+
+ align:start position:0%
+the one thing that surprised us was that
+ 
+
+ align:start position:0%
+the one thing that surprised us was that
+the heterogeneity was much even though
+
+ align:start position:0%
+the heterogeneity was much even though
+ 
+
+ align:start position:0%
+the heterogeneity was much even though
+it looks heterogeneous
+
+ align:start position:0%
+it looks heterogeneous
+ 
+
+ align:start position:0%
+it looks heterogeneous
+i was going to take a pit for you today
+
+ align:start position:0%
+i was going to take a pit for you today
+ 
+
+ align:start position:0%
+i was going to take a pit for you today
+and i said no i'm not taking a fit for
+
+ align:start position:0%
+and i said no i'm not taking a fit for
+ 
+
+ align:start position:0%
+and i said no i'm not taking a fit for
+them today
+
+ align:start position:0%
+them today
+ 
+
+ align:start position:0%
+them today
+but uh it looks very very heterogeneous
+
+ align:start position:0%
+but uh it looks very very heterogeneous
+ 
+
+ align:start position:0%
+but uh it looks very very heterogeneous
+when you look at the lenses and layers
+
+ align:start position:0%
+when you look at the lenses and layers
+ 
+
+ align:start position:0%
+when you look at the lenses and layers
+but it's not that i'm a hydrological
+
+ align:start position:0%
+but it's not that i'm a hydrological
+ 
+
+ align:start position:0%
+but it's not that i'm a hydrological
+point of view it's pretty uniform
+
+ align:start position:0%
+point of view it's pretty uniform
+ 
+
+ align:start position:0%
+point of view it's pretty uniform
+and then we ran another test in 95 93 to
+
+ align:start position:0%
+and then we ran another test in 95 93 to
+ 
+
+ align:start position:0%
+and then we ran another test in 95 93 to
+95 another large-scale test where we did
+
+ align:start position:0%
+95 another large-scale test where we did
+ 
+
+ align:start position:0%
+95 another large-scale test where we did
+different reactive species
+
+ align:start position:0%
+different reactive species
+ 
+
+ align:start position:0%
+different reactive species
+but we again did bromide and got a very
+
+ align:start position:0%
+but we again did bromide and got a very
+ 
+
+ align:start position:0%
+but we again did bromide and got a very
+similar number
+
+ align:start position:0%
+similar number
+ 
+
+ align:start position:0%
+similar number
+uh so and it matched up again the
+
+ align:start position:0%
+uh so and it matched up again the
+ 
+
+ align:start position:0%
+uh so and it matched up again the
+stochastics pretty well
+
+ align:start position:0%
+stochastics pretty well
+ 
+
+ align:start position:0%
+stochastics pretty well
+so in fact the number of mit i think i
+
+ align:start position:0%
+so in fact the number of mit i think i
+ 
+
+ align:start position:0%
+so in fact the number of mit i think i
+want to tell you three mit phd thesis
+
+ align:start position:0%
+want to tell you three mit phd thesis
+ 
+
+ align:start position:0%
+want to tell you three mit phd thesis
+arose out of this test
+
+ align:start position:0%
+arose out of this test
+ 
+
+ align:start position:0%
+arose out of this test
+um so uh it was a fair number of
+
+ align:start position:0%
+um so uh it was a fair number of
+ 
+
+ align:start position:0%
+um so uh it was a fair number of
+mit folks were involved uh mainly lynn
+
+ align:start position:0%
+mit folks were involved uh mainly lynn
+ 
+
+ align:start position:0%
+mit folks were involved uh mainly lynn
+gelhardt students
+
+ align:start position:0%
+gelhardt students
+ 
+
+ align:start position:0%
+gelhardt students
+um and um so the way we sample them you
+
+ align:start position:0%
+um and um so the way we sample them you
+ 
+
+ align:start position:0%
+um and um so the way we sample them you
+can imagine trying to sample this
+
+ align:start position:0%
+can imagine trying to sample this
+ 
+
+ align:start position:0%
+can imagine trying to sample this
+the way we sample them you can imagine
+
+ align:start position:0%
+the way we sample them you can imagine
+ 
+
+ align:start position:0%
+the way we sample them you can imagine
+we come out here and we gotta take a
+
+ align:start position:0%
+we come out here and we gotta take a
+ 
+
+ align:start position:0%
+we come out here and we gotta take a
+snapshot of where the cloud is
+
+ align:start position:0%
+snapshot of where the cloud is
+ 
+
+ align:start position:0%
+snapshot of where the cloud is
+and we had a team of five of us we had
+
+ align:start position:0%
+and we had a team of five of us we had
+ 
+
+ align:start position:0%
+and we had a team of five of us we had
+two carts like this
+
+ align:start position:0%
+two carts like this
+ 
+
+ align:start position:0%
+two carts like this
+and instead of something one tube at a
+
+ align:start position:0%
+and instead of something one tube at a
+ 
+
+ align:start position:0%
+and instead of something one tube at a
+time we would hook up the milking
+
+ align:start position:0%
+time we would hook up the milking
+ 
+
+ align:start position:0%
+time we would hook up the milking
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+like this and we had a chart that told
+
+ align:start position:0%
+like this and we had a chart that told
+ 
+
+ align:start position:0%
+like this and we had a chart that told
+us how much water we had to purge out to
+
+ align:start position:0%
+us how much water we had to purge out to
+ 
+
+ align:start position:0%
+us how much water we had to purge out to
+get rid of the old water
+
+ align:start position:0%
+get rid of the old water
+ 
+
+ align:start position:0%
+get rid of the old water
+and we would turn on the milking machine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they would all start to pump if
+
+ align:start position:0%
+and they would all start to pump if
+ 
+
+ align:start position:0%
+and they would all start to pump if
+we're lucky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and um so the person would sit here
+
+ align:start position:0%
+okay and um so the person would sit here
+ 
+
+ align:start position:0%
+okay and um so the person would sit here
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+they were the they would attach the
+
+ align:start position:0%
+they were the they would attach the
+ 
+
+ align:start position:0%
+they were the they would attach the
+milky machine and run the cart in order
+
+ align:start position:0%
+milky machine and run the cart in order
+ 
+
+ align:start position:0%
+milky machine and run the cart in order
+not to pump too much out of any one port
+
+ align:start position:0%
+not to pump too much out of any one port
+ 
+
+ align:start position:0%
+not to pump too much out of any one port
+because some yield really well you had a
+
+ align:start position:0%
+because some yield really well you had a
+ 
+
+ align:start position:0%
+because some yield really well you had a
+little cliff where you could stop the
+
+ align:start position:0%
+little cliff where you could stop the
+ 
+
+ align:start position:0%
+little cliff where you could stop the
+flow on one that was getting ahead of
+
+ align:start position:0%
+flow on one that was getting ahead of
+ 
+
+ align:start position:0%
+flow on one that was getting ahead of
+the others
+
+ align:start position:0%
+the others
+ 
+
+ align:start position:0%
+the others
+okay and we had these 60 milliliter
+
+ align:start position:0%
+okay and we had these 60 milliliter
+ 
+
+ align:start position:0%
+okay and we had these 60 milliliter
+bottles here what we would do is we
+
+ align:start position:0%
+bottles here what we would do is we
+ 
+
+ align:start position:0%
+bottles here what we would do is we
+would shove these in here
+
+ align:start position:0%
+would shove these in here
+ 
+
+ align:start position:0%
+would shove these in here
+and these were our rinse racks so let's
+
+ align:start position:0%
+and these were our rinse racks so let's
+ 
+
+ align:start position:0%
+and these were our rinse racks so let's
+say the chart said at this distance with
+
+ align:start position:0%
+say the chart said at this distance with
+ 
+
+ align:start position:0%
+say the chart said at this distance with
+this depth
+
+ align:start position:0%
+this depth
+ 
+
+ align:start position:0%
+this depth
+we need to pump out about 300
+
+ align:start position:0%
+we need to pump out about 300
+ 
+
+ align:start position:0%
+we need to pump out about 300
+milliliters before you can take a sample
+
+ align:start position:0%
+milliliters before you can take a sample
+ 
+
+ align:start position:0%
+milliliters before you can take a sample
+we knew that was say five wrenches so we
+
+ align:start position:0%
+we knew that was say five wrenches so we
+ 
+
+ align:start position:0%
+we knew that was say five wrenches so we
+would shove this in
+
+ align:start position:0%
+would shove this in
+ 
+
+ align:start position:0%
+would shove this in
+we would fill them up when one side of
+
+ align:start position:0%
+we would fill them up when one side of
+ 
+
+ align:start position:0%
+we would fill them up when one side of
+the fill up would close it off when we
+
+ align:start position:0%
+the fill up would close it off when we
+ 
+
+ align:start position:0%
+the fill up would close it off when we
+had it all filled we would do this
+
+ align:start position:0%
+had it all filled we would do this
+ 
+
+ align:start position:0%
+had it all filled we would do this
+dump it off it would go into a bucket
+
+ align:start position:0%
+dump it off it would go into a bucket
+ 
+
+ align:start position:0%
+dump it off it would go into a bucket
+you shove it back in until you did your
+
+ align:start position:0%
+you shove it back in until you did your
+ 
+
+ align:start position:0%
+you shove it back in until you did your
+rinses
+
+ align:start position:0%
+rinses
+ 
+
+ align:start position:0%
+rinses
+then the person behind who was the
+
+ align:start position:0%
+then the person behind who was the
+ 
+
+ align:start position:0%
+then the person behind who was the
+bottle capper and the
+
+ align:start position:0%
+bottle capper and the
+ 
+
+ align:start position:0%
+bottle capper and the
+that's their job the cap bottles for
+
+ align:start position:0%
+that's their job the cap bottles for
+ 
+
+ align:start position:0%
+that's their job the cap bottles for
+four days straight um
+
+ align:start position:0%
+four days straight um
+ 
+
+ align:start position:0%
+four days straight um
+would have loaded a rack with the sample
+
+ align:start position:0%
+would have loaded a rack with the sample
+ 
+
+ align:start position:0%
+would have loaded a rack with the sample
+bottles in you'd shove that in fill your
+
+ align:start position:0%
+bottles in you'd shove that in fill your
+ 
+
+ align:start position:0%
+bottles in you'd shove that in fill your
+bottles up
+
+ align:start position:0%
+bottles up
+ 
+
+ align:start position:0%
+bottles up
+give it to them they'd cap them all like
+
+ align:start position:0%
+give it to them they'd cap them all like
+ 
+
+ align:start position:0%
+give it to them they'd cap them all like
+a madman while you went on to the next
+
+ align:start position:0%
+a madman while you went on to the next
+ 
+
+ align:start position:0%
+a madman while you went on to the next
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and we would do that uh and we had uh so
+
+ align:start position:0%
+and we would do that uh and we had uh so
+ 
+
+ align:start position:0%
+and we would do that uh and we had uh so
+we had two carts and then we had the
+
+ align:start position:0%
+we had two carts and then we had the
+ 
+
+ align:start position:0%
+we had two carts and then we had the
+field general
+
+ align:start position:0%
+field general
+ 
+
+ align:start position:0%
+field general
+um anybody live at mccormick no that's
+
+ align:start position:0%
+um anybody live at mccormick no that's
+ 
+
+ align:start position:0%
+um anybody live at mccormick no that's
+an undergraduate dorm i guess right
+
+ align:start position:0%
+an undergraduate dorm i guess right
+ 
+
+ align:start position:0%
+an undergraduate dorm i guess right
+you know kathy hess yeah yeah
+
+ align:start position:0%
+you know kathy hess yeah yeah
+ 
+
+ align:start position:0%
+you know kathy hess yeah yeah
+kathy hess is the house mother at
+
+ align:start position:0%
+kathy hess is the house mother at
+ 
+
+ align:start position:0%
+kathy hess is the house mother at
+mccormick right or whenever you guys
+
+ align:start position:0%
+mccormick right or whenever you guys
+ 
+
+ align:start position:0%
+mccormick right or whenever you guys
+dorm
+
+ align:start position:0%
+dorm
+ 
+
+ align:start position:0%
+dorm
+house master she's my house she's my
+
+ align:start position:0%
+house master she's my house she's my
+ 
+
+ align:start position:0%
+house master she's my house she's my
+co-worker i call it val's mother
+
+ align:start position:0%
+co-worker i call it val's mother
+ 
+
+ align:start position:0%
+co-worker i call it val's mother
+uh there are some times when we sampled
+
+ align:start position:0%
+uh there are some times when we sampled
+ 
+
+ align:start position:0%
+uh there are some times when we sampled
+300 multi-level samplers
+
+ align:start position:0%
+300 multi-level samplers
+ 
+
+ align:start position:0%
+300 multi-level samplers
+three samples each port in three days
+
+ align:start position:0%
+three samples each port in three days
+ 
+
+ align:start position:0%
+three samples each port in three days
+so we could really fly take a snapshot
+
+ align:start position:0%
+so we could really fly take a snapshot
+ 
+
+ align:start position:0%
+so we could really fly take a snapshot
+we did that i think 18 times in the
+
+ align:start position:0%
+we did that i think 18 times in the
+ 
+
+ align:start position:0%
+we did that i think 18 times in the
+course of two years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very quickly because we didn't have much
+
+ align:start position:0%
+very quickly because we didn't have much
+ 
+
+ align:start position:0%
+very quickly because we didn't have much
+time we had to get it going right away
+
+ align:start position:0%
+time we had to get it going right away
+ 
+
+ align:start position:0%
+time we had to get it going right away
+we also went to the university of
+
+ align:start position:0%
+we also went to the university of
+ 
+
+ align:start position:0%
+we also went to the university of
+waterloo who had done some similar
+
+ align:start position:0%
+waterloo who had done some similar
+ 
+
+ align:start position:0%
+waterloo who had done some similar
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+and um and you know really borrowed a
+
+ align:start position:0%
+and um and you know really borrowed a
+ 
+
+ align:start position:0%
+and um and you know really borrowed a
+lot of their ideas to be
+
+ align:start position:0%
+lot of their ideas to be
+ 
+
+ align:start position:0%
+lot of their ideas to be
+to be honest so uh you know we won't go
+
+ align:start position:0%
+to be honest so uh you know we won't go
+ 
+
+ align:start position:0%
+to be honest so uh you know we won't go
+into it in any more detail in that
+
+ align:start position:0%
+into it in any more detail in that
+ 
+
+ align:start position:0%
+into it in any more detail in that
+just to give you a sense for how it
+
+ align:start position:0%
+just to give you a sense for how it
+ 
+
+ align:start position:0%
+just to give you a sense for how it
+worked on page 10
+
+ align:start position:0%
+worked on page 10
+ 
+
+ align:start position:0%
+worked on page 10
+it just shows you and 11 just shows you
+
+ align:start position:0%
+it just shows you and 11 just shows you
+ 
+
+ align:start position:0%
+it just shows you and 11 just shows you
+a couple of the results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uh and i won't go any further than
+
+ align:start position:0%
+the uh and i won't go any further than
+ 
+
+ align:start position:0%
+the uh and i won't go any further than
+that except to say that
+
+ align:start position:0%
+that except to say that
+ 
+
+ align:start position:0%
+that except to say that
+what we've discovered was when you
+
+ align:start position:0%
+what we've discovered was when you
+ 
+
+ align:start position:0%
+what we've discovered was when you
+injected the tracer as i mentioned
+
+ align:start position:0%
+injected the tracer as i mentioned
+ 
+
+ align:start position:0%
+injected the tracer as i mentioned
+before it was a pretty small volume
+
+ align:start position:0%
+before it was a pretty small volume
+ 
+
+ align:start position:0%
+before it was a pretty small volume
+within 30 days the tracer cloud was
+
+ align:start position:0%
+within 30 days the tracer cloud was
+ 
+
+ align:start position:0%
+within 30 days the tracer cloud was
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+pretty large in fact uh why don't we get
+
+ align:start position:0%
+pretty large in fact uh why don't we get
+ 
+
+ align:start position:0%
+pretty large in fact uh why don't we get
+uh we might as well do this it won't
+
+ align:start position:0%
+uh we might as well do this it won't
+ 
+
+ align:start position:0%
+uh we might as well do this it won't
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+a second see if i can figure this out
+
+ align:start position:0%
+a second see if i can figure this out
+ 
+
+ align:start position:0%
+a second see if i can figure this out
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hey pete can i send you up as a runner
+
+ align:start position:0%
+hey pete can i send you up as a runner
+ 
+
+ align:start position:0%
+hey pete can i send you up as a runner
+and eric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want you to find i want you to go up
+
+ align:start position:0%
+i want you to find i want you to go up
+ 
+
+ align:start position:0%
+i want you to find i want you to go up
+to uh row one up there at the beginning
+
+ align:start position:0%
+to uh row one up there at the beginning
+ 
+
+ align:start position:0%
+to uh row one up there at the beginning
+and i want eric to find row 17.
+
+ align:start position:0%
+and i want eric to find row 17.
+ 
+
+ align:start position:0%
+and i want eric to find row 17.
+he'll say 17 on the covers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faster and faster think of them as
+
+ align:start position:0%
+faster and faster think of them as
+ 
+
+ align:start position:0%
+faster and faster think of them as
+little bromides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there you go so by
+
+ align:start position:0%
+okay so there you go so by
+ 
+
+ align:start position:0%
+okay so there you go so by
+by 33 days the tracer cloud had moved
+
+ align:start position:0%
+by 33 days the tracer cloud had moved
+ 
+
+ align:start position:0%
+by 33 days the tracer cloud had moved
+from those injection points
+
+ align:start position:0%
+from those injection points
+ 
+
+ align:start position:0%
+from those injection points
+to where the one milligram per liter
+
+ align:start position:0%
+to where the one milligram per liter
+ 
+
+ align:start position:0%
+to where the one milligram per liter
+contour would have been this far south
+
+ align:start position:0%
+contour would have been this far south
+ 
+
+ align:start position:0%
+contour would have been this far south
+and that far north so it spread very
+
+ align:start position:0%
+and that far north so it spread very
+ 
+
+ align:start position:0%
+and that far north so it spread very
+very rapidly
+
+ align:start position:0%
+very rapidly
+ 
+
+ align:start position:0%
+very rapidly
+you know in a short period of time so by
+
+ align:start position:0%
+you know in a short period of time so by
+ 
+
+ align:start position:0%
+you know in a short period of time so by
+33 days this claw was already
+
+ align:start position:0%
+33 days this claw was already
+ 
+
+ align:start position:0%
+33 days this claw was already
+like 100 feet long but very very narrow
+
+ align:start position:0%
+like 100 feet long but very very narrow
+ 
+
+ align:start position:0%
+like 100 feet long but very very narrow
+it never got very narrow and then they
+
+ align:start position:0%
+it never got very narrow and then they
+ 
+
+ align:start position:0%
+it never got very narrow and then they
+migrated forward at a rate of one and a
+
+ align:start position:0%
+migrated forward at a rate of one and a
+ 
+
+ align:start position:0%
+migrated forward at a rate of one and a
+half feet per day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh pete go to row 20 and eric
+
+ align:start position:0%
+so uh pete go to row 20 and eric
+ 
+
+ align:start position:0%
+so uh pete go to row 20 and eric
+you got to go to row 37.
+
+ align:start position:0%
+you got to go to row 37.
+ 
+
+ align:start position:0%
+you got to go to row 37.
+i think i have to leapfrog
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by 139 days row 27
+
+ align:start position:0%
+so by 139 days row 27
+ 
+
+ align:start position:0%
+so by 139 days row 27
+actually it's going to be beyond all of
+
+ align:start position:0%
+actually it's going to be beyond all of
+ 
+
+ align:start position:0%
+actually it's going to be beyond all of
+us here i think to row
+
+ align:start position:0%
+us here i think to row
+ 
+
+ align:start position:0%
+us here i think to row
+what did i tell you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no you're 20. and he's 37.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can see how how quickly it it uh
+
+ align:start position:0%
+so you can see how how quickly it it uh
+ 
+
+ align:start position:0%
+so you can see how how quickly it it uh
+spread in the longitudinal direction
+
+ align:start position:0%
+spread in the longitudinal direction
+ 
+
+ align:start position:0%
+spread in the longitudinal direction
+that's exactly what the stochastic
+
+ align:start position:0%
+that's exactly what the stochastic
+ 
+
+ align:start position:0%
+that's exactly what the stochastic
+theory said
+
+ align:start position:0%
+theory said
+ 
+
+ align:start position:0%
+theory said
+that most of the spreading should take
+
+ align:start position:0%
+that most of the spreading should take
+ 
+
+ align:start position:0%
+that most of the spreading should take
+place in the direction of flow and the
+
+ align:start position:0%
+place in the direction of flow and the
+ 
+
+ align:start position:0%
+place in the direction of flow and the
+plume actually never got very wide
+
+ align:start position:0%
+plume actually never got very wide
+ 
+
+ align:start position:0%
+plume actually never got very wide
+horizontally and in the vertical it
+
+ align:start position:0%
+horizontally and in the vertical it
+ 
+
+ align:start position:0%
+horizontally and in the vertical it
+stayed very very narrow
+
+ align:start position:0%
+stayed very very narrow
+ 
+
+ align:start position:0%
+stayed very very narrow
+uh it was only about uh six or seven
+
+ align:start position:0%
+uh it was only about uh six or seven
+ 
+
+ align:start position:0%
+uh it was only about uh six or seven
+meters thick
+
+ align:start position:0%
+meters thick
+ 
+
+ align:start position:0%
+meters thick
+there he is so that's how that's how
+
+ align:start position:0%
+there he is so that's how that's how
+ 
+
+ align:start position:0%
+there he is so that's how that's how
+long on the 139th day our sampling had
+
+ align:start position:0%
+long on the 139th day our sampling had
+ 
+
+ align:start position:0%
+long on the 139th day our sampling had
+to encompass
+
+ align:start position:0%
+to encompass
+ 
+
+ align:start position:0%
+to encompass
+all the samples from beyond pete to
+
+ align:start position:0%
+all the samples from beyond pete to
+ 
+
+ align:start position:0%
+all the samples from beyond pete to
+beyond eric
+
+ align:start position:0%
+beyond eric
+ 
+
+ align:start position:0%
+beyond eric
+and that was only 139 days okay
+
+ align:start position:0%
+and that was only 139 days okay
+ 
+
+ align:start position:0%
+and that was only 139 days okay
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we always did it with five people we
+
+ align:start position:0%
+we always did it with five people we
+ 
+
+ align:start position:0%
+we always did it with five people we
+always did it with five people wow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no we just we just worked an extra day
+
+ align:start position:0%
+no we just we just worked an extra day
+ 
+
+ align:start position:0%
+no we just we just worked an extra day
+yeah we just worked faster we got pretty
+
+ align:start position:0%
+yeah we just worked faster we got pretty
+ 
+
+ align:start position:0%
+yeah we just worked faster we got pretty
+good at it we were damn good at it
+
+ align:start position:0%
+good at it we were damn good at it
+ 
+
+ align:start position:0%
+good at it we were damn good at it
+we collected 100 000 water samples for
+
+ align:start position:0%
+we collected 100 000 water samples for
+ 
+
+ align:start position:0%
+we collected 100 000 water samples for
+the experiment
\ No newline at end of file
diff --git a/JtJ3v__Rx7E.txt b/JtJ3v__Rx7E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30a0dd4cb5909e824e18051d362bbf0a7b8845cd
--- /dev/null
+++ b/JtJ3v__Rx7E.txt
@@ -0,0 +1,7536 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ 
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in the last several lectures we've
+
+ align:start position:0%
+in the last several lectures we've
+ 
+
+ align:start position:0%
+in the last several lectures we've
+considered a number of procedures for
+
+ align:start position:0%
+considered a number of procedures for
+ 
+
+ align:start position:0%
+considered a number of procedures for
+Designing digital filters for infinite
+
+ align:start position:0%
+Designing digital filters for infinite
+ 
+
+ align:start position:0%
+Designing digital filters for infinite
+impulse response for the class of
+
+ align:start position:0%
+impulse response for the class of
+ 
+
+ align:start position:0%
+impulse response for the class of
+infinite impulse response
+
+ align:start position:0%
+infinite impulse response
+ 
+
+ align:start position:0%
+infinite impulse response
+filters and the two primary design
+
+ align:start position:0%
+filters and the two primary design
+ 
+
+ align:start position:0%
+filters and the two primary design
+techniques that we considered in fact
+
+ align:start position:0%
+techniques that we considered in fact
+ 
+
+ align:start position:0%
+techniques that we considered in fact
+the two useful design techniques that we
+
+ align:start position:0%
+the two useful design techniques that we
+ 
+
+ align:start position:0%
+the two useful design techniques that we
+developed were the techniques which we
+
+ align:start position:0%
+developed were the techniques which we
+ 
+
+ align:start position:0%
+developed were the techniques which we
+referred to as impulse and variance and
+
+ align:start position:0%
+referred to as impulse and variance and
+ 
+
+ align:start position:0%
+referred to as impulse and variance and
+also the bilinear
+
+ align:start position:0%
+also the bilinear
+ 
+
+ align:start position:0%
+also the bilinear
+transformation you recall hopefully that
+
+ align:start position:0%
+transformation you recall hopefully that
+ 
+
+ align:start position:0%
+transformation you recall hopefully that
+both of these techniques are techniques
+
+ align:start position:0%
+both of these techniques are techniques
+ 
+
+ align:start position:0%
+both of these techniques are techniques
+that correspond to mapping a continuous
+
+ align:start position:0%
+that correspond to mapping a continuous
+ 
+
+ align:start position:0%
+that correspond to mapping a continuous
+time or analog filter to a digital
+
+ align:start position:0%
+time or analog filter to a digital
+ 
+
+ align:start position:0%
+time or analog filter to a digital
+filter what I'd like to do in this
+
+ align:start position:0%
+filter what I'd like to do in this
+ 
+
+ align:start position:0%
+filter what I'd like to do in this
+lecture is consider an example of the
+
+ align:start position:0%
+lecture is consider an example of the
+ 
+
+ align:start position:0%
+lecture is consider an example of the
+design of a digital low pass filter
+
+ align:start position:0%
+design of a digital low pass filter
+ 
+
+ align:start position:0%
+design of a digital low pass filter
+using each of these techniques using
+
+ align:start position:0%
+using each of these techniques using
+ 
+
+ align:start position:0%
+using each of these techniques using
+impulse and variance and the bilinear
+
+ align:start position:0%
+impulse and variance and the bilinear
+ 
+
+ align:start position:0%
+impulse and variance and the bilinear
+transformation and hopefully this will
+
+ align:start position:0%
+transformation and hopefully this will
+ 
+
+ align:start position:0%
+transformation and hopefully this will
+give you a better feeling for how both
+
+ align:start position:0%
+give you a better feeling for how both
+ 
+
+ align:start position:0%
+give you a better feeling for how both
+both of these techniques
+
+ align:start position:0%
+both of these techniques
+ 
+
+ align:start position:0%
+both of these techniques
+work the class of analog filters that I
+
+ align:start position:0%
+work the class of analog filters that I
+ 
+
+ align:start position:0%
+work the class of analog filters that I
+would like to use are the class of
+
+ align:start position:0%
+would like to use are the class of
+ 
+
+ align:start position:0%
+would like to use are the class of
+so-called analog Butterworth filters
+
+ align:start position:0%
+so-called analog Butterworth filters
+ 
+
+ align:start position:0%
+so-called analog Butterworth filters
+which are a useful class of low pass
+
+ align:start position:0%
+which are a useful class of low pass
+ 
+
+ align:start position:0%
+which are a useful class of low pass
+analog and digital filters and also a
+
+ align:start position:0%
+analog and digital filters and also a
+ 
+
+ align:start position:0%
+analog and digital filters and also a
+relatively simple
+
+ align:start position:0%
+relatively simple
+ 
+
+ align:start position:0%
+relatively simple
+class to first of all Define the class
+
+ align:start position:0%
+class to first of all Define the class
+ 
+
+ align:start position:0%
+class to first of all Define the class
+of analog filters that we're considering
+
+ align:start position:0%
+of analog filters that we're considering
+ 
+
+ align:start position:0%
+of analog filters that we're considering
+they are the class of analog Butterworth
+
+ align:start position:0%
+they are the class of analog Butterworth
+ 
+
+ align:start position:0%
+they are the class of analog Butterworth
+filters and this class of filters is
+
+ align:start position:0%
+filters and this class of filters is
+ 
+
+ align:start position:0%
+filters and this class of filters is
+defined by the analog system function H
+
+ align:start position:0%
+defined by the analog system function H
+ 
+
+ align:start position:0%
+defined by the analog system function H
+Suba of J Omega magnitude squared of the
+
+ align:start position:0%
+Suba of J Omega magnitude squared of the
+ 
+
+ align:start position:0%
+Suba of J Omega magnitude squared of the
+form 1 over 1 + J Omega / J Omega Sub C
+
+ align:start position:0%
+form 1 over 1 + J Omega / J Omega Sub C
+ 
+
+ align:start position:0%
+form 1 over 1 + J Omega / J Omega Sub C
+to the 2 N now there are two parameters
+
+ align:start position:0%
+to the 2 N now there are two parameters
+ 
+
+ align:start position:0%
+to the 2 N now there are two parameters
+in this expression one is the what's
+
+ align:start position:0%
+in this expression one is the what's
+ 
+
+ align:start position:0%
+in this expression one is the what's
+referred to often as the cutoff
+
+ align:start position:0%
+referred to often as the cutoff
+ 
+
+ align:start position:0%
+referred to often as the cutoff
+frequency Omega Sub C and the second is
+
+ align:start position:0%
+frequency Omega Sub C and the second is
+ 
+
+ align:start position:0%
+frequency Omega Sub C and the second is
+the order of the filter namely n let me
+
+ align:start position:0%
+the order of the filter namely n let me
+ 
+
+ align:start position:0%
+the order of the filter namely n let me
+remind you that we're looking at here an
+
+ align:start position:0%
+remind you that we're looking at here an
+ 
+
+ align:start position:0%
+remind you that we're looking at here an
+expression for the squared magnitude
+
+ align:start position:0%
+expression for the squared magnitude
+ 
+
+ align:start position:0%
+expression for the squared magnitude
+function and so we have a 2N here but in
+
+ align:start position:0%
+function and so we have a 2N here but in
+ 
+
+ align:start position:0%
+function and so we have a 2N here but in
+fact n is what corresponds to the order
+
+ align:start position:0%
+fact n is what corresponds to the order
+ 
+
+ align:start position:0%
+fact n is what corresponds to the order
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+filter well if we look at this frequency
+
+ align:start position:0%
+filter well if we look at this frequency
+ 
+
+ align:start position:0%
+filter well if we look at this frequency
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+characteristic we observe that at Omega
+
+ align:start position:0%
+characteristic we observe that at Omega
+ 
+
+ align:start position:0%
+characteristic we observe that at Omega
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+the gain or the magnitude squared is
+
+ align:start position:0%
+the gain or the magnitude squared is
+ 
+
+ align:start position:0%
+the gain or the magnitude squared is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+Unity at Omega equal to Omega
+
+ align:start position:0%
+Unity at Omega equal to Omega
+ 
+
+ align:start position:0%
+Unity at Omega equal to Omega
+subc the JS of course cancel out and
+
+ align:start position:0%
+subc the JS of course cancel out and
+ 
+
+ align:start position:0%
+subc the JS of course cancel out and
+Omega equal to Omega Sub C we this term
+
+ align:start position:0%
+Omega equal to Omega Sub C we this term
+ 
+
+ align:start position:0%
+Omega equal to Omega Sub C we this term
+then is equal to one and we have for the
+
+ align:start position:0%
+then is equal to one and we have for the
+ 
+
+ align:start position:0%
+then is equal to one and we have for the
+magnitude squared function a half or for
+
+ align:start position:0%
+magnitude squared function a half or for
+ 
+
+ align:start position:0%
+magnitude squared function a half or for
+the magnitude function which is what
+
+ align:start position:0%
+the magnitude function which is what
+ 
+
+ align:start position:0%
+the magnitude function which is what
+we're looking at
+
+ align:start position:0%
+we're looking at
+ 
+
+ align:start position:0%
+we're looking at
+here 1 / the < TK of two so at Omega
+
+ align:start position:0%
+here 1 / the < TK of two so at Omega
+ 
+
+ align:start position:0%
+here 1 / the < TK of two so at Omega
+equal to Omega Sub C an analog
+
+ align:start position:0%
+equal to Omega Sub C an analog
+ 
+
+ align:start position:0%
+equal to Omega Sub C an analog
+Butterworth filter has a magnitude which
+
+ align:start position:0%
+Butterworth filter has a magnitude which
+ 
+
+ align:start position:0%
+Butterworth filter has a magnitude which
+is down by 1 over the < TK of 2 and the
+
+ align:start position:0%
+is down by 1 over the < TK of 2 and the
+ 
+
+ align:start position:0%
+is down by 1 over the < TK of 2 and the
+other important characteristic is that
+
+ align:start position:0%
+other important characteristic is that
+ 
+
+ align:start position:0%
+other important characteristic is that
+the frequency response is a monotonic
+
+ align:start position:0%
+the frequency response is a monotonic
+ 
+
+ align:start position:0%
+the frequency response is a monotonic
+function of capital Omega so that as
+
+ align:start position:0%
+function of capital Omega so that as
+ 
+
+ align:start position:0%
+function of capital Omega so that as
+capital Omega increases from zero to
+
+ align:start position:0%
+capital Omega increases from zero to
+ 
+
+ align:start position:0%
+capital Omega increases from zero to
+Infinity the magnitude or the frequency
+
+ align:start position:0%
+Infinity the magnitude or the frequency
+ 
+
+ align:start position:0%
+Infinity the magnitude or the frequency
+response is a monotonic
+
+ align:start position:0%
+response is a monotonic
+ 
+
+ align:start position:0%
+response is a monotonic
+function well we observe ve that the cut
+
+ align:start position:0%
+function well we observe ve that the cut
+ 
+
+ align:start position:0%
+function well we observe ve that the cut
+off frequency the parameter Omega
+
+ align:start position:0%
+off frequency the parameter Omega
+ 
+
+ align:start position:0%
+off frequency the parameter Omega
+subc adjusts in a sense where we might
+
+ align:start position:0%
+subc adjusts in a sense where we might
+ 
+
+ align:start position:0%
+subc adjusts in a sense where we might
+divide the frequency characteristic into
+
+ align:start position:0%
+divide the frequency characteristic into
+ 
+
+ align:start position:0%
+divide the frequency characteristic into
+pass band transition band and stop band
+
+ align:start position:0%
+pass band transition band and stop band
+ 
+
+ align:start position:0%
+pass band transition band and stop band
+we have another parameter which is the
+
+ align:start position:0%
+we have another parameter which is the
+ 
+
+ align:start position:0%
+we have another parameter which is the
+parameter n the order of the filter and
+
+ align:start position:0%
+parameter n the order of the filter and
+ 
+
+ align:start position:0%
+parameter n the order of the filter and
+basically the effect that the parameter
+
+ align:start position:0%
+basically the effect that the parameter
+ 
+
+ align:start position:0%
+basically the effect that the parameter
+n has is to affect the shape of this
+
+ align:start position:0%
+n has is to affect the shape of this
+ 
+
+ align:start position:0%
+n has is to affect the shape of this
+frequency response in the sense that if
+
+ align:start position:0%
+frequency response in the sense that if
+ 
+
+ align:start position:0%
+frequency response in the sense that if
+capital N is
+
+ align:start position:0%
+capital N is
+ 
+
+ align:start position:0%
+capital N is
+larger the frequency response tends to
+
+ align:start position:0%
+larger the frequency response tends to
+ 
+
+ align:start position:0%
+larger the frequency response tends to
+be flatter longer so that for a larger
+
+ align:start position:0%
+be flatter longer so that for a larger
+ 
+
+ align:start position:0%
+be flatter longer so that for a larger
+nend than what I've drawn with the black
+
+ align:start position:0%
+nend than what I've drawn with the black
+ 
+
+ align:start position:0%
+nend than what I've drawn with the black
+curve the frequency response might look
+
+ align:start position:0%
+curve the frequency response might look
+ 
+
+ align:start position:0%
+curve the frequency response might look
+more like this and then drop off
+
+ align:start position:0%
+more like this and then drop off
+ 
+
+ align:start position:0%
+more like this and then drop off
+sharper whereas if capital N is smaller
+
+ align:start position:0%
+sharper whereas if capital N is smaller
+ 
+
+ align:start position:0%
+sharper whereas if capital N is smaller
+then it will be less flat in the pass
+
+ align:start position:0%
+then it will be less flat in the pass
+ 
+
+ align:start position:0%
+then it will be less flat in the pass
+band and drop off more slowly
+
+ align:start position:0%
+band and drop off more slowly
+ 
+
+ align:start position:0%
+band and drop off more slowly
+so in fact the way that I've drawn it
+
+ align:start position:0%
+so in fact the way that I've drawn it
+ 
+
+ align:start position:0%
+so in fact the way that I've drawn it
+here this is the behavior of the
+
+ align:start position:0%
+here this is the behavior of the
+ 
+
+ align:start position:0%
+here this is the behavior of the
+frequency response curve as the
+
+ align:start position:0%
+frequency response curve as the
+ 
+
+ align:start position:0%
+frequency response curve as the
+parameter capital
+
+ align:start position:0%
+parameter capital
+ 
+
+ align:start position:0%
+parameter capital
+N
+
+ align:start position:0%
+N
+ 
+
+ align:start position:0%
+N
+increases so the higher the order of the
+
+ align:start position:0%
+increases so the higher the order of the
+ 
+
+ align:start position:0%
+increases so the higher the order of the
+filter the sharper the drop from what we
+
+ align:start position:0%
+filter the sharper the drop from what we
+ 
+
+ align:start position:0%
+filter the sharper the drop from what we
+could consider as a pass band region
+
+ align:start position:0%
+could consider as a pass band region
+ 
+
+ align:start position:0%
+could consider as a pass band region
+into a stop band region and obviously
+
+ align:start position:0%
+into a stop band region and obviously
+ 
+
+ align:start position:0%
+into a stop band region and obviously
+then the sharper the filter we want the
+
+ align:start position:0%
+then the sharper the filter we want the
+ 
+
+ align:start position:0%
+then the sharper the filter we want the
+higher order filter we would
+
+ align:start position:0%
+higher order filter we would
+ 
+
+ align:start position:0%
+higher order filter we would
+design now to look at the pole zero
+
+ align:start position:0%
+design now to look at the pole zero
+ 
+
+ align:start position:0%
+design now to look at the pole zero
+pattern or the zero pattern really of
+
+ align:start position:0%
+pattern or the zero pattern really of
+ 
+
+ align:start position:0%
+pattern or the zero pattern really of
+the Butterworth
+
+ align:start position:0%
+the Butterworth
+ 
+
+ align:start position:0%
+the Butterworth
+filter we can convert this
+
+ align:start position:0%
+filter we can convert this
+ 
+
+ align:start position:0%
+filter we can convert this
+expression into an expression
+
+ align:start position:0%
+expression into an expression
+ 
+
+ align:start position:0%
+expression into an expression
+relating the magnitude squared function
+
+ align:start position:0%
+relating the magnitude squared function
+ 
+
+ align:start position:0%
+relating the magnitude squared function
+expressed in terms of the llast
+
+ align:start position:0%
+expressed in terms of the llast
+ 
+
+ align:start position:0%
+expressed in terms of the llast
+transform variable s and so this
+
+ align:start position:0%
+transform variable s and so this
+ 
+
+ align:start position:0%
+transform variable s and so this
+expression corresponds to the product H
+
+ align:start position:0%
+expression corresponds to the product H
+ 
+
+ align:start position:0%
+expression corresponds to the product H
+sub a of s * H sub a of minus s
+
+ align:start position:0%
+sub a of s * H sub a of minus s
+ 
+
+ align:start position:0%
+sub a of s * H sub a of minus s
+evaluated at s = j
+
+ align:start position:0%
+evaluated at s = j
+ 
+
+ align:start position:0%
+evaluated at s = j
+Omega in which case the J Omega is what
+
+ align:start position:0%
+Omega in which case the J Omega is what
+ 
+
+ align:start position:0%
+Omega in which case the J Omega is what
+corresponds to S and so H sub of s * H
+
+ align:start position:0%
+corresponds to S and so H sub of s * H
+ 
+
+ align:start position:0%
+corresponds to S and so H sub of s * H
+sub a of minus s is of the form 1/ 1 + S
+
+ align:start position:0%
+sub a of minus s is of the form 1/ 1 + S
+ 
+
+ align:start position:0%
+sub a of minus s is of the form 1/ 1 + S
+/ J Omega
+
+ align:start position:0%
+/ J Omega
+ 
+
+ align:start position:0%
+/ J Omega
+subc raised to the 2 N
+
+ align:start position:0%
+subc raised to the 2 N
+ 
+
+ align:start position:0%
+subc raised to the 2 N
+power well what we re recognize is that
+
+ align:start position:0%
+power well what we re recognize is that
+ 
+
+ align:start position:0%
+power well what we re recognize is that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+expression has poles if we solve this
+
+ align:start position:0%
+expression has poles if we solve this
+ 
+
+ align:start position:0%
+expression has poles if we solve this
+equation this expression has poles at of
+
+ align:start position:0%
+equation this expression has poles at of
+ 
+
+ align:start position:0%
+equation this expression has poles at of
+course the roots of the denominator
+
+ align:start position:0%
+course the roots of the denominator
+ 
+
+ align:start position:0%
+course the roots of the denominator
+polinomial or at s equal to minus1 to
+
+ align:start position:0%
+polinomial or at s equal to minus1 to
+ 
+
+ align:start position:0%
+polinomial or at s equal to minus1 to
+the 1/ 2N * J Omega Sub C that's simply
+
+ align:start position:0%
+the 1/ 2N * J Omega Sub C that's simply
+ 
+
+ align:start position:0%
+the 1/ 2N * J Omega Sub C that's simply
+solving the equation with this
+
+ align:start position:0%
+solving the equation with this
+ 
+
+ align:start position:0%
+solving the equation with this
+denominator polinomial equal to
+
+ align:start position:0%
+denominator polinomial equal to
+ 
+
+ align:start position:0%
+denominator polinomial equal to
+zero well we can see more spe
+
+ align:start position:0%
+zero well we can see more spe
+ 
+
+ align:start position:0%
+zero well we can see more spe
+specifically where these poles lie in
+
+ align:start position:0%
+specifically where these poles lie in
+ 
+
+ align:start position:0%
+specifically where these poles lie in
+the S
+
+ align:start position:0%
+the S
+ 
+
+ align:start position:0%
+the S
+plane by recognizing that these are the
+
+ align:start position:0%
+plane by recognizing that these are the
+ 
+
+ align:start position:0%
+plane by recognizing that these are the
+2 N roots of
+
+ align:start position:0%
+2 N roots of
+ 
+
+ align:start position:0%
+2 N roots of
+minus1 and then we have a j which
+
+ align:start position:0%
+minus1 and then we have a j which
+ 
+
+ align:start position:0%
+minus1 and then we have a j which
+corresponds to e to J Pi uh e to the J
+
+ align:start position:0%
+corresponds to e to J Pi uh e to the J
+ 
+
+ align:start position:0%
+corresponds to e to J Pi uh e to the J
+pi/ 2 so we can rewrite this expression
+
+ align:start position:0%
+pi/ 2 so we can rewrite this expression
+ 
+
+ align:start position:0%
+pi/ 2 so we can rewrite this expression
+for the poles as
+
+ align:start position:0%
+for the poles as
+ 
+
+ align:start position:0%
+for the poles as
+s equal to e to J pi/ 2X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's that's one of the roots of minus1
+
+ align:start position:0%
+that's that's one of the roots of minus1
+ 
+
+ align:start position:0%
+that's that's one of the roots of minus1
+plus K * 2 pi where K is an integer this
+
+ align:start position:0%
+plus K * 2 pi where K is an integer this
+ 
+
+ align:start position:0%
+plus K * 2 pi where K is an integer this
+generates the roots of
+
+ align:start position:0%
+generates the roots of
+ 
+
+ align:start position:0%
+generates the roots of
+minus1 we need to multiply by J and we
+
+ align:start position:0%
+minus1 we need to multiply by J and we
+ 
+
+ align:start position:0%
+minus1 we need to multiply by J and we
+can do that by multiplying by e to the J
+
+ align:start position:0%
+can do that by multiplying by e to the J
+ 
+
+ align:start position:0%
+can do that by multiplying by e to the J
+Pi / 2 which is equal to J times Omega
+
+ align:start position:0%
+Pi / 2 which is equal to J times Omega
+ 
+
+ align:start position:0%
+Pi / 2 which is equal to J times Omega
+Sub C which is the cutof frequency
+
+ align:start position:0%
+Sub C which is the cutof frequency
+ 
+
+ align:start position:0%
+Sub C which is the cutof frequency
+parameter for the Butterworth
+
+ align:start position:0%
+parameter for the Butterworth
+ 
+
+ align:start position:0%
+parameter for the Butterworth
+filter so this then specifies where the
+
+ align:start position:0%
+filter so this then specifies where the
+ 
+
+ align:start position:0%
+filter so this then specifies where the
+pole locations are for the Butterworth
+
+ align:start position:0%
+pole locations are for the Butterworth
+ 
+
+ align:start position:0%
+pole locations are for the Butterworth
+filter for example if we consider the
+
+ align:start position:0%
+filter for example if we consider the
+ 
+
+ align:start position:0%
+filter for example if we consider the
+case let's say with n equal to
+
+ align:start position:0%
+case let's say with n equal to
+ 
+
+ align:start position:0%
+case let's say with n equal to
+3 K let's say equal to
+
+ align:start position:0%
+3 K let's say equal to
+ 
+
+ align:start position:0%
+3 K let's say equal to
+zero that says then that we have a poll
+
+ align:start position:0%
+zero that says then that we have a poll
+ 
+
+ align:start position:0%
+zero that says then that we have a poll
+at e to the J Pi / 6 e to the J pi/
+
+ align:start position:0%
+at e to the J Pi / 6 e to the J pi/
+ 
+
+ align:start position:0%
+at e to the J Pi / 6 e to the J pi/
+6 time e to J Pi / 2 in other words we
+
+ align:start position:0%
+6 time e to J Pi / 2 in other words we
+ 
+
+ align:start position:0%
+6 time e to J Pi / 2 in other words we
+have a pole in the S plane at an angle
+
+ align:start position:0%
+have a pole in the S plane at an angle
+ 
+
+ align:start position:0%
+have a pole in the S plane at an angle
+of < / 6 + piun / 2 which corresponds to
+
+ align:start position:0%
+of < / 6 + piun / 2 which corresponds to
+ 
+
+ align:start position:0%
+of < / 6 + piun / 2 which corresponds to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+location then we'll have poles
+
+ align:start position:0%
+location then we'll have poles
+ 
+
+ align:start position:0%
+location then we'll have poles
+distributed in angle around a circle in
+
+ align:start position:0%
+distributed in angle around a circle in
+ 
+
+ align:start position:0%
+distributed in angle around a circle in
+the S plane distributed in an angle
+
+ align:start position:0%
+the S plane distributed in an angle
+ 
+
+ align:start position:0%
+the S plane distributed in an angle
+where the angular spacing is pi over3
+
+ align:start position:0%
+where the angular spacing is pi over3
+ 
+
+ align:start position:0%
+where the angular spacing is pi over3
+the pi over3 arising from a
+
+ align:start position:0%
+the pi over3 arising from a
+ 
+
+ align:start position:0%
+the pi over3 arising from a
+consideration of 2 pi k / 2N where in
+
+ align:start position:0%
+consideration of 2 pi k / 2N where in
+ 
+
+ align:start position:0%
+consideration of 2 pi k / 2N where in
+this case n is equal to
+
+ align:start position:0%
+this case n is equal to
+ 
+
+ align:start position:0%
+this case n is equal to
+6 so these poles are
+
+ align:start position:0%
+6 so these poles are
+ 
+
+ align:start position:0%
+6 so these poles are
+distributed equally spaced an angle on a
+
+ align:start position:0%
+distributed equally spaced an angle on a
+ 
+
+ align:start position:0%
+distributed equally spaced an angle on a
+circle in the S plane for n equal to 3
+
+ align:start position:0%
+circle in the S plane for n equal to 3
+ 
+
+ align:start position:0%
+circle in the S plane for n equal to 3
+the angular spacing is pi over 3 for k
+
+ align:start position:0%
+the angular spacing is pi over 3 for k
+ 
+
+ align:start position:0%
+the angular spacing is pi over 3 for k
+equal to zero that first pole
+
+ align:start position:0%
+equal to zero that first pole
+ 
+
+ align:start position:0%
+equal to zero that first pole
+corresponds to this one and then we
+
+ align:start position:0%
+corresponds to this one and then we
+ 
+
+ align:start position:0%
+corresponds to this one and then we
+continue
+
+ align:start position:0%
+continue
+ 
+
+ align:start position:0%
+continue
+around now these are poles distributed
+
+ align:start position:0%
+around now these are poles distributed
+ 
+
+ align:start position:0%
+around now these are poles distributed
+on a circle which tends to look like the
+
+ align:start position:0%
+on a circle which tends to look like the
+ 
+
+ align:start position:0%
+on a circle which tends to look like the
+Z plane
+
+ align:start position:0%
+Z plane
+ 
+
+ align:start position:0%
+Z plane
+but I stress that what we're talking
+
+ align:start position:0%
+but I stress that what we're talking
+ 
+
+ align:start position:0%
+but I stress that what we're talking
+about here is the S plane in particular
+
+ align:start position:0%
+about here is the S plane in particular
+ 
+
+ align:start position:0%
+about here is the S plane in particular
+we're talking about the analog frequency
+
+ align:start position:0%
+we're talking about the analog frequency
+ 
+
+ align:start position:0%
+we're talking about the analog frequency
+response design that is the class of
+
+ align:start position:0%
+response design that is the class of
+ 
+
+ align:start position:0%
+response design that is the class of
+analog Butterworth filters which we're
+
+ align:start position:0%
+analog Butterworth filters which we're
+ 
+
+ align:start position:0%
+analog Butterworth filters which we're
+then going to map to digital filters so
+
+ align:start position:0%
+then going to map to digital filters so
+ 
+
+ align:start position:0%
+then going to map to digital filters so
+this is a circle in the S plane it's
+
+ align:start position:0%
+this is a circle in the S plane it's
+ 
+
+ align:start position:0%
+this is a circle in the S plane it's
+often referred to as the Butterworth
+
+ align:start position:0%
+often referred to as the Butterworth
+ 
+
+ align:start position:0%
+often referred to as the Butterworth
+Circle and it has a radius which is
+
+ align:start position:0%
+Circle and it has a radius which is
+ 
+
+ align:start position:0%
+Circle and it has a radius which is
+equal to Omega
+
+ align:start position:0%
+equal to Omega
+ 
+
+ align:start position:0%
+equal to Omega
+subc in designing
+
+ align:start position:0%
+subc in designing
+ 
+
+ align:start position:0%
+subc in designing
+a an analog Butterworth filter then the
+
+ align:start position:0%
+a an analog Butterworth filter then the
+ 
+
+ align:start position:0%
+a an analog Butterworth filter then the
+procedure is to appropriately choose
+
+ align:start position:0%
+procedure is to appropriately choose
+ 
+
+ align:start position:0%
+procedure is to appropriately choose
+this the parameters Omega subc and
+
+ align:start position:0%
+this the parameters Omega subc and
+ 
+
+ align:start position:0%
+this the parameters Omega subc and
+capital N those are the parameters of
+
+ align:start position:0%
+capital N those are the parameters of
+ 
+
+ align:start position:0%
+capital N those are the parameters of
+the analog Butterworth
+
+ align:start position:0%
+the analog Butterworth
+ 
+
+ align:start position:0%
+the analog Butterworth
+filter and
+
+ align:start position:0%
+filter and
+ 
+
+ align:start position:0%
+filter and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+from the poles distributed on the
+
+ align:start position:0%
+from the poles distributed on the
+ 
+
+ align:start position:0%
+from the poles distributed on the
+Butterworth Circle this gives us the
+
+ align:start position:0%
+Butterworth Circle this gives us the
+ 
+
+ align:start position:0%
+Butterworth Circle this gives us the
+pole locations for the product H sub a
+
+ align:start position:0%
+pole locations for the product H sub a
+ 
+
+ align:start position:0%
+pole locations for the product H sub a
+of x s time H sub a of minus
+
+ align:start position:0%
+of x s time H sub a of minus
+ 
+
+ align:start position:0%
+of x s time H sub a of minus
+s we can then simply
+
+ align:start position:0%
+s we can then simply
+ 
+
+ align:start position:0%
+s we can then simply
+associate with the transfer function H
+
+ align:start position:0%
+associate with the transfer function H
+ 
+
+ align:start position:0%
+associate with the transfer function H
+sub a of s the poles in the left half
+
+ align:start position:0%
+sub a of s the poles in the left half
+ 
+
+ align:start position:0%
+sub a of s the poles in the left half
+plane to generate a stable filter and
+
+ align:start position:0%
+plane to generate a stable filter and
+ 
+
+ align:start position:0%
+plane to generate a stable filter and
+then the ones which are contributed by
+
+ align:start position:0%
+then the ones which are contributed by
+ 
+
+ align:start position:0%
+then the ones which are contributed by
+the factor H Suba of minus s are the
+
+ align:start position:0%
+the factor H Suba of minus s are the
+ 
+
+ align:start position:0%
+the factor H Suba of minus s are the
+corresponding image poles in the right
+
+ align:start position:0%
+corresponding image poles in the right
+ 
+
+ align:start position:0%
+corresponding image poles in the right
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+plane procedure then is to design a
+
+ align:start position:0%
+plane procedure then is to design a
+ 
+
+ align:start position:0%
+plane procedure then is to design a
+squared magnitude
+
+ align:start position:0%
+squared magnitude
+ 
+
+ align:start position:0%
+squared magnitude
+function talking about a Butterworth
+
+ align:start position:0%
+function talking about a Butterworth
+ 
+
+ align:start position:0%
+function talking about a Butterworth
+filter we choose these parameters Omega
+
+ align:start position:0%
+filter we choose these parameters Omega
+ 
+
+ align:start position:0%
+filter we choose these parameters Omega
+subc and N that tells us where the poles
+
+ align:start position:0%
+subc and N that tells us where the poles
+ 
+
+ align:start position:0%
+subc and N that tells us where the poles
+are located on the Butterworth
+
+ align:start position:0%
+are located on the Butterworth
+ 
+
+ align:start position:0%
+are located on the Butterworth
+circle from the pole locations for the
+
+ align:start position:0%
+circle from the pole locations for the
+ 
+
+ align:start position:0%
+circle from the pole locations for the
+squared magnitude function then we can
+
+ align:start position:0%
+squared magnitude function then we can
+ 
+
+ align:start position:0%
+squared magnitude function then we can
+factor that into H sub a of s * H sub a
+
+ align:start position:0%
+factor that into H sub a of s * H sub a
+ 
+
+ align:start position:0%
+factor that into H sub a of s * H sub a
+of minus s by choosing the poles that
+
+ align:start position:0%
+of minus s by choosing the poles that
+ 
+
+ align:start position:0%
+of minus s by choosing the poles that
+fall in the left half plane to give us a
+
+ align:start position:0%
+fall in the left half plane to give us a
+ 
+
+ align:start position:0%
+fall in the left half plane to give us a
+causal stable analog filter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right well that is an analog filter
+
+ align:start position:0%
+all right well that is an analog filter
+ 
+
+ align:start position:0%
+all right well that is an analog filter
+what we would like to talk about is the
+
+ align:start position:0%
+what we would like to talk about is the
+ 
+
+ align:start position:0%
+what we would like to talk about is the
+design of a digital filter and the
+
+ align:start position:0%
+design of a digital filter and the
+ 
+
+ align:start position:0%
+design of a digital filter and the
+procedure that we're going to go through
+
+ align:start position:0%
+procedure that we're going to go through
+ 
+
+ align:start position:0%
+procedure that we're going to go through
+is to choose a set of specs for the
+
+ align:start position:0%
+is to choose a set of specs for the
+ 
+
+ align:start position:0%
+is to choose a set of specs for the
+digital
+
+ align:start position:0%
+digital
+ 
+
+ align:start position:0%
+digital
+filter and then decide on what the
+
+ align:start position:0%
+filter and then decide on what the
+ 
+
+ align:start position:0%
+filter and then decide on what the
+corresponding specifications should be
+
+ align:start position:0%
+corresponding specifications should be
+ 
+
+ align:start position:0%
+corresponding specifications should be
+for the analog filter depending on
+
+ align:start position:0%
+for the analog filter depending on
+ 
+
+ align:start position:0%
+for the analog filter depending on
+whether we're using impulse and variance
+
+ align:start position:0%
+whether we're using impulse and variance
+ 
+
+ align:start position:0%
+whether we're using impulse and variance
+or the bilinear
+
+ align:start position:0%
+or the bilinear
+ 
+
+ align:start position:0%
+or the bilinear
+transformation the design the analog
+
+ align:start position:0%
+transformation the design the analog
+ 
+
+ align:start position:0%
+transformation the design the analog
+filter and then map the result to a
+
+ align:start position:0%
+filter and then map the result to a
+ 
+
+ align:start position:0%
+filter and then map the result to a
+digital filter using one of those two
+
+ align:start position:0%
+digital filter using one of those two
+ 
+
+ align:start position:0%
+digital filter using one of those two
+techniques so let's choose a set of
+
+ align:start position:0%
+techniques so let's choose a set of
+ 
+
+ align:start position:0%
+techniques so let's choose a set of
+digital filter
+
+ align:start position:0%
+digital filter
+ 
+
+ align:start position:0%
+digital filter
+specifications for a digital low pass
+
+ align:start position:0%
+specifications for a digital low pass
+ 
+
+ align:start position:0%
+specifications for a digital low pass
+filter with a pass band which occurs for
+
+ align:start position:0%
+filter with a pass band which occurs for
+ 
+
+ align:start position:0%
+filter with a pass band which occurs for
+frequencies now in the digital domain
+
+ align:start position:0%
+frequencies now in the digital domain
+ 
+
+ align:start position:0%
+frequencies now in the digital domain
+for frequencies below 02 pi
+
+ align:start position:0%
+for frequencies below 02 pi
+ 
+
+ align:start position:0%
+for frequencies below 02 pi
+and a stop band region that occurs for
+
+ align:start position:0%
+and a stop band region that occurs for
+ 
+
+ align:start position:0%
+and a stop band region that occurs for
+frequencies greater than 3 pi and the
+
+ align:start position:0%
+frequencies greater than 3 pi and the
+ 
+
+ align:start position:0%
+frequencies greater than 3 pi and the
+transition band then of course is the
+
+ align:start position:0%
+transition band then of course is the
+ 
+
+ align:start position:0%
+transition band then of course is the
+region in between
+
+ align:start position:0%
+region in between
+ 
+
+ align:start position:0%
+region in between
+those so we would like to design a
+
+ align:start position:0%
+those so we would like to design a
+ 
+
+ align:start position:0%
+those so we would like to design a
+digital filter which stays within some
+
+ align:start position:0%
+digital filter which stays within some
+ 
+
+ align:start position:0%
+digital filter which stays within some
+limits in this pass band region drops
+
+ align:start position:0%
+limits in this pass band region drops
+ 
+
+ align:start position:0%
+limits in this pass band region drops
+below Su limit Delta Subs in the stop
+
+ align:start position:0%
+below Su limit Delta Subs in the stop
+ 
+
+ align:start position:0%
+below Su limit Delta Subs in the stop
+band region and will choose as the
+
+ align:start position:0%
+band region and will choose as the
+ 
+
+ align:start position:0%
+band region and will choose as the
+limits in the pass band Unity for the
+
+ align:start position:0%
+limits in the pass band Unity for the
+ 
+
+ align:start position:0%
+limits in the pass band Unity for the
+upper limit and 1 minus Delta sub for
+
+ align:start position:0%
+upper limit and 1 minus Delta sub for
+ 
+
+ align:start position:0%
+upper limit and 1 minus Delta sub for
+the lower limit where Delta sub 1 minus
+
+ align:start position:0%
+the lower limit where Delta sub 1 minus
+ 
+
+ align:start position:0%
+the lower limit where Delta sub 1 minus
+Delta subp might not and in fact it
+
+ align:start position:0%
+Delta subp might not and in fact it
+ 
+
+ align:start position:0%
+Delta subp might not and in fact it
+won't turn out to be 1 over theare < TK
+
+ align:start position:0%
+won't turn out to be 1 over theare < TK
+ 
+
+ align:start position:0%
+won't turn out to be 1 over theare < TK
+of two in other words this cut off
+
+ align:start position:0%
+of two in other words this cut off
+ 
+
+ align:start position:0%
+of two in other words this cut off
+frequency will not necessarily
+
+ align:start position:0%
+frequency will not necessarily
+ 
+
+ align:start position:0%
+frequency will not necessarily
+correspond to the parameter Omega subc
+
+ align:start position:0%
+correspond to the parameter Omega subc
+ 
+
+ align:start position:0%
+correspond to the parameter Omega subc
+for the Butterworth
+
+ align:start position:0%
+for the Butterworth
+ 
+
+ align:start position:0%
+for the Butterworth
+filter all right well so let's choose a
+
+ align:start position:0%
+filter all right well so let's choose a
+ 
+
+ align:start position:0%
+filter all right well so let's choose a
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+specifications the ones that I've chosen
+
+ align:start position:0%
+specifications the ones that I've chosen
+ 
+
+ align:start position:0%
+specifications the ones that I've chosen
+are the requirement that the frequency
+
+ align:start position:0%
+are the requirement that the frequency
+ 
+
+ align:start position:0%
+are the requirement that the frequency
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+characteristic be within 1 DB of unity
+
+ align:start position:0%
+characteristic be within 1 DB of unity
+ 
+
+ align:start position:0%
+characteristic be within 1 DB of unity
+in the pass band in other words the
+
+ align:start position:0%
+in the pass band in other words the
+ 
+
+ align:start position:0%
+in the pass band in other words the
+requirement that 1 minus Delta subp be
+
+ align:start position:0%
+requirement that 1 minus Delta subp be
+ 
+
+ align:start position:0%
+requirement that 1 minus Delta subp be
+greater than or equal to minus1 DB so
+
+ align:start position:0%
+greater than or equal to minus1 DB so
+ 
+
+ align:start position:0%
+greater than or equal to minus1 DB so
+this deviation must be less than 1
+
+ align:start position:0%
+this deviation must be less than 1
+ 
+
+ align:start position:0%
+this deviation must be less than 1
+DB and then the requirement that in the
+
+ align:start position:0%
+DB and then the requirement that in the
+ 
+
+ align:start position:0%
+DB and then the requirement that in the
+stop band The fre quency response
+
+ align:start position:0%
+stop band The fre quency response
+ 
+
+ align:start position:0%
+stop band The fre quency response
+characteristic is
+
+ align:start position:0%
+characteristic is
+ 
+
+ align:start position:0%
+characteristic is
+below 15 DB minus 15 DB in other words
+
+ align:start position:0%
+below 15 DB minus 15 DB in other words
+ 
+
+ align:start position:0%
+below 15 DB minus 15 DB in other words
+the stop band attenuation for
+
+ align:start position:0%
+the stop band attenuation for
+ 
+
+ align:start position:0%
+the stop band attenuation for
+frequencies greater than. 3 Pi is
+
+ align:start position:0%
+frequencies greater than. 3 Pi is
+ 
+
+ align:start position:0%
+frequencies greater than. 3 Pi is
+greater than minus 15 DB it's further
+
+ align:start position:0%
+greater than minus 15 DB it's further
+ 
+
+ align:start position:0%
+greater than minus 15 DB it's further
+down than minus5 DB so Delta Subs is
+
+ align:start position:0%
+down than minus5 DB so Delta Subs is
+ 
+
+ align:start position:0%
+down than minus5 DB so Delta Subs is
+less than or equal to minus5
+
+ align:start position:0%
+less than or equal to minus5
+ 
+
+ align:start position:0%
+less than or equal to minus5
+DB the one other specification that
+
+ align:start position:0%
+DB the one other specification that
+ 
+
+ align:start position:0%
+DB the one other specification that
+we'll impose or in fact it's really a
+
+ align:start position:0%
+we'll impose or in fact it's really a
+ 
+
+ align:start position:0%
+we'll impose or in fact it's really a
+consequence that will result from using
+
+ align:start position:0%
+consequence that will result from using
+ 
+
+ align:start position:0%
+consequence that will result from using
+a Butterworth filter is the fact that
+
+ align:start position:0%
+a Butterworth filter is the fact that
+ 
+
+ align:start position:0%
+a Butterworth filter is the fact that
+the frequency characteristic is
+
+ align:start position:0%
+the frequency characteristic is
+ 
+
+ align:start position:0%
+the frequency characteristic is
+monotonic so we have the pass band Edge
+
+ align:start position:0%
+monotonic so we have the pass band Edge
+ 
+
+ align:start position:0%
+monotonic so we have the pass band Edge
+the stop band Edge the pass band Ripple
+
+ align:start position:0%
+the stop band Edge the pass band Ripple
+ 
+
+ align:start position:0%
+the stop band Edge the pass band Ripple
+or deviation and the stop band rippler
+
+ align:start position:0%
+or deviation and the stop band rippler
+ 
+
+ align:start position:0%
+or deviation and the stop band rippler
+deviation and we can of course rewrite
+
+ align:start position:0%
+deviation and we can of course rewrite
+ 
+
+ align:start position:0%
+deviation and we can of course rewrite
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+specifications in terms of requirements
+
+ align:start position:0%
+specifications in terms of requirements
+ 
+
+ align:start position:0%
+specifications in terms of requirements
+on the trans for function or frequency
+
+ align:start position:0%
+on the trans for function or frequency
+ 
+
+ align:start position:0%
+on the trans for function or frequency
+response the magnitude of the frequency
+
+ align:start position:0%
+response the magnitude of the frequency
+ 
+
+ align:start position:0%
+response the magnitude of the frequency
+response the requirement that the
+
+ align:start position:0%
+response the requirement that the
+ 
+
+ align:start position:0%
+response the requirement that the
+deviation be less than 1 DB in the pass
+
+ align:start position:0%
+deviation be less than 1 DB in the pass
+ 
+
+ align:start position:0%
+deviation be less than 1 DB in the pass
+band is the requirement then the 20 log
+
+ align:start position:0%
+band is the requirement then the 20 log
+ 
+
+ align:start position:0%
+band is the requirement then the 20 log
+to the base 10 of the magnitude of the
+
+ align:start position:0%
+to the base 10 of the magnitude of the
+ 
+
+ align:start position:0%
+to the base 10 of the magnitude of the
+frequency response that's the deviation
+
+ align:start position:0%
+frequency response that's the deviation
+ 
+
+ align:start position:0%
+frequency response that's the deviation
+DB be greater than or equal to
+
+ align:start position:0%
+DB be greater than or equal to
+ 
+
+ align:start position:0%
+DB be greater than or equal to
+minus1 or that the magnitude be greater
+
+ align:start position:0%
+minus1 or that the magnitude be greater
+ 
+
+ align:start position:0%
+minus1 or that the magnitude be greater
+than equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10-05 and of course we want it also to
+
+ align:start position:0%
+10-05 and of course we want it also to
+ 
+
+ align:start position:0%
+10-05 and of course we want it also to
+be less than unity and that's an implied
+
+ align:start position:0%
+be less than unity and that's an implied
+ 
+
+ align:start position:0%
+be less than unity and that's an implied
+condition so it must be less than unity
+
+ align:start position:0%
+condition so it must be less than unity
+ 
+
+ align:start position:0%
+condition so it must be less than unity
+and must be greater than or equal to
+
+ align:start position:0%
+and must be greater than or equal to
+ 
+
+ align:start position:0%
+and must be greater than or equal to
+10us 05 for frequencies from zero to 0 2
+
+ align:start position:0%
+10us 05 for frequencies from zero to 0 2
+ 
+
+ align:start position:0%
+10us 05 for frequencies from zero to 0 2
+pi so in particular since it's monotonic
+
+ align:start position:0%
+pi so in particular since it's monotonic
+ 
+
+ align:start position:0%
+pi so in particular since it's monotonic
+we'll impose that condition at the
+
+ align:start position:0%
+we'll impose that condition at the
+ 
+
+ align:start position:0%
+we'll impose that condition at the
+frequency 2 pi corresponding to the end
+
+ align:start position:0%
+frequency 2 pi corresponding to the end
+ 
+
+ align:start position:0%
+frequency 2 pi corresponding to the end
+of the stop band and the beginning of
+
+ align:start position:0%
+of the stop band and the beginning of
+ 
+
+ align:start position:0%
+of the stop band and the beginning of
+the transition
+
+ align:start position:0%
+the transition
+ 
+
+ align:start position:0%
+the transition
+band the second condition that we impose
+
+ align:start position:0%
+band the second condition that we impose
+ 
+
+ align:start position:0%
+band the second condition that we impose
+is the condition that by the time we get
+
+ align:start position:0%
+is the condition that by the time we get
+ 
+
+ align:start position:0%
+is the condition that by the time we get
+to Omega equal to 3
+
+ align:start position:0%
+to Omega equal to 3
+ 
+
+ align:start position:0%
+to Omega equal to 3
+Pi we would like the frequency response
+
+ align:start position:0%
+Pi we would like the frequency response
+ 
+
+ align:start position:0%
+Pi we would like the frequency response
+to be down at least 15 DB and more if
+
+ align:start position:0%
+to be down at least 15 DB and more if
+ 
+
+ align:start position:0%
+to be down at least 15 DB and more if
+possible but the condition is that the
+
+ align:start position:0%
+possible but the condition is that the
+ 
+
+ align:start position:0%
+possible but the condition is that the
+20 log to the base 10 of the magnitude
+
+ align:start position:0%
+20 log to the base 10 of the magnitude
+ 
+
+ align:start position:0%
+20 log to the base 10 of the magnitude
+at Omega equal to3 3 Pi must be less
+
+ align:start position:0%
+at Omega equal to3 3 Pi must be less
+ 
+
+ align:start position:0%
+at Omega equal to3 3 Pi must be less
+than or equal to
+
+ align:start position:0%
+than or equal to
+ 
+
+ align:start position:0%
+than or equal to
+minus5 so this says we must be further
+
+ align:start position:0%
+minus5 so this says we must be further
+ 
+
+ align:start position:0%
+minus5 so this says we must be further
+down than 15 DB or we can translate that
+
+ align:start position:0%
+down than 15 DB or we can translate that
+ 
+
+ align:start position:0%
+down than 15 DB or we can translate that
+into a condition on the magnitude so
+
+ align:start position:0%
+into a condition on the magnitude so
+ 
+
+ align:start position:0%
+into a condition on the magnitude so
+that the magnitude of that frequency is
+
+ align:start position:0%
+that the magnitude of that frequency is
+ 
+
+ align:start position:0%
+that the magnitude of that frequency is
+less than or equal to 10 minus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+75 well let's consider two we want to
+
+ align:start position:0%
+75 well let's consider two we want to
+ 
+
+ align:start position:0%
+75 well let's consider two we want to
+consider two design procedures let's
+
+ align:start position:0%
+consider two design procedures let's
+ 
+
+ align:start position:0%
+consider two design procedures let's
+first consider the impulse and variant
+
+ align:start position:0%
+first consider the impulse and variant
+ 
+
+ align:start position:0%
+first consider the impulse and variant
+design procedure in which case we would
+
+ align:start position:0%
+design procedure in which case we would
+ 
+
+ align:start position:0%
+design procedure in which case we would
+like to convert these
+
+ align:start position:0%
+like to convert these
+ 
+
+ align:start position:0%
+like to convert these
+specifications on the digital
+
+ align:start position:0%
+specifications on the digital
+ 
+
+ align:start position:0%
+specifications on the digital
+filter
+
+ align:start position:0%
+filter
+ 
+
+ align:start position:0%
+filter
+to corresponding specifications on the
+
+ align:start position:0%
+to corresponding specifications on the
+ 
+
+ align:start position:0%
+to corresponding specifications on the
+analog
+
+ align:start position:0%
+analog
+ 
+
+ align:start position:0%
+analog
+filter now we know that from discussions
+
+ align:start position:0%
+filter now we know that from discussions
+ 
+
+ align:start position:0%
+filter now we know that from discussions
+that we've had
+
+ align:start position:0%
+that we've had
+ 
+
+ align:start position:0%
+that we've had
+previously that if we have an analog
+
+ align:start position:0%
+previously that if we have an analog
+ 
+
+ align:start position:0%
+previously that if we have an analog
+frequency response and we apply impulse
+
+ align:start position:0%
+frequency response and we apply impulse
+ 
+
+ align:start position:0%
+frequency response and we apply impulse
+and variance to the impulse response the
+
+ align:start position:0%
+and variance to the impulse response the
+ 
+
+ align:start position:0%
+and variance to the impulse response the
+digital frequency response consists of
+
+ align:start position:0%
+digital frequency response consists of
+ 
+
+ align:start position:0%
+digital frequency response consists of
+the analog frequency response scaled in
+
+ align:start position:0%
+the analog frequency response scaled in
+ 
+
+ align:start position:0%
+the analog frequency response scaled in
+frequency so that Capital Omega is equal
+
+ align:start position:0%
+frequency so that Capital Omega is equal
+ 
+
+ align:start position:0%
+frequency so that Capital Omega is equal
+to little Omega / capital
+
+ align:start position:0%
+to little Omega / capital
+ 
+
+ align:start position:0%
+to little Omega / capital
+T and then that scaled replica of H Suba
+
+ align:start position:0%
+T and then that scaled replica of H Suba
+ 
+
+ align:start position:0%
+T and then that scaled replica of H Suba
+added to itself delayed by little Omega
+
+ align:start position:0%
+added to itself delayed by little Omega
+ 
+
+ align:start position:0%
+added to itself delayed by little Omega
+equal to 2 pi 4 Pi Etc that is multiples
+
+ align:start position:0%
+equal to 2 pi 4 Pi Etc that is multiples
+ 
+
+ align:start position:0%
+equal to 2 pi 4 Pi Etc that is multiples
+of 2
+
+ align:start position:0%
+of 2
+ 
+
+ align:start position:0%
+of 2
+pi so that means then that the analog
+
+ align:start position:0%
+pi so that means then that the analog
+ 
+
+ align:start position:0%
+pi so that means then that the analog
+filter will that the digital filter is
+
+ align:start position:0%
+filter will that the digital filter is
+ 
+
+ align:start position:0%
+filter will that the digital filter is
+scaled repeated replicas of the analog
+
+ align:start position:0%
+scaled repeated replicas of the analog
+ 
+
+ align:start position:0%
+scaled repeated replicas of the analog
+filter and so we would choose the analog
+
+ align:start position:0%
+filter and so we would choose the analog
+ 
+
+ align:start position:0%
+filter and so we would choose the analog
+filter to have similar specifications to
+
+ align:start position:0%
+filter to have similar specifications to
+ 
+
+ align:start position:0%
+filter to have similar specifications to
+the digital
+
+ align:start position:0%
+the digital
+ 
+
+ align:start position:0%
+the digital
+filter but with the corresponding
+
+ align:start position:0%
+filter but with the corresponding
+ 
+
+ align:start position:0%
+filter but with the corresponding
+frequency parameters dictated by this
+
+ align:start position:0%
+frequency parameters dictated by this
+ 
+
+ align:start position:0%
+frequency parameters dictated by this
+transformation Capital Omega equal to
+
+ align:start position:0%
+transformation Capital Omega equal to
+ 
+
+ align:start position:0%
+transformation Capital Omega equal to
+little Omega / capital t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that of course neglects aliasing
+
+ align:start position:0%
+well that of course neglects aliasing
+ 
+
+ align:start position:0%
+well that of course neglects aliasing
+and in fact as we go through the impulse
+
+ align:start position:0%
+and in fact as we go through the impulse
+ 
+
+ align:start position:0%
+and in fact as we go through the impulse
+invariant design will initially neglect
+
+ align:start position:0%
+invariant design will initially neglect
+ 
+
+ align:start position:0%
+invariant design will initially neglect
+aliasing and uh a rationale for doing
+
+ align:start position:0%
+aliasing and uh a rationale for doing
+ 
+
+ align:start position:0%
+aliasing and uh a rationale for doing
+this or a reason why in fact it's not
+
+ align:start position:0%
+this or a reason why in fact it's not
+ 
+
+ align:start position:0%
+this or a reason why in fact it's not
+unreasonable to do that will emerge as
+
+ align:start position:0%
+unreasonable to do that will emerge as
+ 
+
+ align:start position:0%
+unreasonable to do that will emerge as
+we go through the example so for the
+
+ align:start position:0%
+we go through the example so for the
+ 
+
+ align:start position:0%
+we go through the example so for the
+time being in fact we're going to
+
+ align:start position:0%
+time being in fact we're going to
+ 
+
+ align:start position:0%
+time being in fact we're going to
+neglect
+
+ align:start position:0%
+neglect
+ 
+
+ align:start position:0%
+neglect
+alosine so that we'll think of the
+
+ align:start position:0%
+alosine so that we'll think of the
+ 
+
+ align:start position:0%
+alosine so that we'll think of the
+analog and digital frequency responses
+
+ align:start position:0%
+analog and digital frequency responses
+ 
+
+ align:start position:0%
+analog and digital frequency responses
+as simply related by the substitution of
+
+ align:start position:0%
+as simply related by the substitution of
+ 
+
+ align:start position:0%
+as simply related by the substitution of
+frequency variable Capital Omega equal
+
+ align:start position:0%
+frequency variable Capital Omega equal
+ 
+
+ align:start position:0%
+frequency variable Capital Omega equal
+to little Omega divided capital
+
+ align:start position:0%
+to little Omega divided capital
+ 
+
+ align:start position:0%
+to little Omega divided capital
+T well that leads us
+
+ align:start position:0%
+T well that leads us
+ 
+
+ align:start position:0%
+T well that leads us
+then to the
+
+ align:start position:0%
+then to the
+ 
+
+ align:start position:0%
+then to the
+analog frequency response which I've
+
+ align:start position:0%
+analog frequency response which I've
+ 
+
+ align:start position:0%
+analog frequency response which I've
+depicted
+
+ align:start position:0%
+depicted
+ 
+
+ align:start position:0%
+depicted
+here we had a factor of 1 over capital T
+
+ align:start position:0%
+here we had a factor of 1 over capital T
+ 
+
+ align:start position:0%
+here we had a factor of 1 over capital T
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+amplitude of this
+
+ align:start position:0%
+amplitude of this
+ 
+
+ align:start position:0%
+amplitude of this
+expression so for the digital filter to
+
+ align:start position:0%
+expression so for the digital filter to
+ 
+
+ align:start position:0%
+expression so for the digital filter to
+result with an amplitude of unity at DC
+
+ align:start position:0%
+result with an amplitude of unity at DC
+ 
+
+ align:start position:0%
+result with an amplitude of unity at DC
+we would scale the analog frequency
+
+ align:start position:0%
+we would scale the analog frequency
+ 
+
+ align:start position:0%
+we would scale the analog frequency
+response by capital
+
+ align:start position:0%
+response by capital
+ 
+
+ align:start position:0%
+response by capital
+T so the
+
+ align:start position:0%
+T so the
+ 
+
+ align:start position:0%
+T so the
+important values then in capital Omega
+
+ align:start position:0%
+important values then in capital Omega
+ 
+
+ align:start position:0%
+important values then in capital Omega
+are the ones corresponding to little
+
+ align:start position:0%
+are the ones corresponding to little
+ 
+
+ align:start position:0%
+are the ones corresponding to little
+Omega equal to0 2
+
+ align:start position:0%
+Omega equal to0 2
+ 
+
+ align:start position:0%
+Omega equal to0 2
+pi or since Capital Omega is equal to
+
+ align:start position:0%
+pi or since Capital Omega is equal to
+ 
+
+ align:start position:0%
+pi or since Capital Omega is equal to
+little Omega / capital t we have a pass
+
+ align:start position:0%
+little Omega / capital t we have a pass
+ 
+
+ align:start position:0%
+little Omega / capital t we have a pass
+band Edge occurring at cap Omega equal
+
+ align:start position:0%
+band Edge occurring at cap Omega equal
+ 
+
+ align:start position:0%
+band Edge occurring at cap Omega equal
+to0 2 pi over capital T and A stop band
+
+ align:start position:0%
+to0 2 pi over capital T and A stop band
+ 
+
+ align:start position:0%
+to0 2 pi over capital T and A stop band
+Edge equal to 3 pi over capital
+
+ align:start position:0%
+Edge equal to 3 pi over capital
+ 
+
+ align:start position:0%
+Edge equal to 3 pi over capital
+T at this pass band Edge according to
+
+ align:start position:0%
+T at this pass band Edge according to
+ 
+
+ align:start position:0%
+T at this pass band Edge according to
+the specifications on the digital filter
+
+ align:start position:0%
+the specifications on the digital filter
+ 
+
+ align:start position:0%
+the specifications on the digital filter
+that we want we would like the frequency
+
+ align:start position:0%
+that we want we would like the frequency
+ 
+
+ align:start position:0%
+that we want we would like the frequency
+response for frequencies below this in
+
+ align:start position:0%
+response for frequencies below this in
+ 
+
+ align:start position:0%
+response for frequencies below this in
+other words in the pass band to be
+
+ align:start position:0%
+other words in the pass band to be
+ 
+
+ align:start position:0%
+other words in the pass band to be
+between capital t and capital T * 10us
+
+ align:start position:0%
+between capital t and capital T * 10us
+ 
+
+ align:start position:0%
+between capital t and capital T * 10us
+05 that's the guarantee that we have
+
+ align:start position:0%
+05 that's the guarantee that we have
+ 
+
+ align:start position:0%
+05 that's the guarantee that we have
+less than 1 DB Ripple in the pass band
+
+ align:start position:0%
+less than 1 DB Ripple in the pass band
+ 
+
+ align:start position:0%
+less than 1 DB Ripple in the pass band
+and for frequencies greater than 3 Pi we
+
+ align:start position:0%
+and for frequencies greater than 3 Pi we
+ 
+
+ align:start position:0%
+and for frequencies greater than 3 Pi we
+would like to be below capital T * 10us
+
+ align:start position:0%
+would like to be below capital T * 10us
+ 
+
+ align:start position:0%
+would like to be below capital T * 10us
+75 that's to guarantee that we're down
+
+ align:start position:0%
+75 that's to guarantee that we're down
+ 
+
+ align:start position:0%
+75 that's to guarantee that we're down
+15 DB or more in the stop
+
+ align:start position:0%
+15 DB or more in the stop
+ 
+
+ align:start position:0%
+15 DB or more in the stop
+band the way I've drawn it here I've
+
+ align:start position:0%
+band the way I've drawn it here I've
+ 
+
+ align:start position:0%
+band the way I've drawn it here I've
+implied that I will exactly meet the
+
+ align:start position:0%
+implied that I will exactly meet the
+ 
+
+ align:start position:0%
+implied that I will exactly meet the
+specifications at the pass band Edge and
+
+ align:start position:0%
+specifications at the pass band Edge and
+ 
+
+ align:start position:0%
+specifications at the pass band Edge and
+exactly meet the specifications at the
+
+ align:start position:0%
+exactly meet the specifications at the
+ 
+
+ align:start position:0%
+exactly meet the specifications at the
+stop band Edge you can imagine of course
+
+ align:start position:0%
+stop band Edge you can imagine of course
+ 
+
+ align:start position:0%
+stop band Edge you can imagine of course
+that if I did that and then converted to
+
+ align:start position:0%
+that if I did that and then converted to
+ 
+
+ align:start position:0%
+that if I did that and then converted to
+a digital filter using impulse and
+
+ align:start position:0%
+a digital filter using impulse and
+ 
+
+ align:start position:0%
+a digital filter using impulse and
+variance that there would be an effect
+
+ align:start position:0%
+variance that there would be an effect
+ 
+
+ align:start position:0%
+variance that there would be an effect
+due to aliasing which in fact would
+
+ align:start position:0%
+due to aliasing which in fact would
+ 
+
+ align:start position:0%
+due to aliasing which in fact would
+would result in my not meeting exactly
+
+ align:start position:0%
+would result in my not meeting exactly
+ 
+
+ align:start position:0%
+would result in my not meeting exactly
+the specifications at the stop band Edge
+
+ align:start position:0%
+the specifications at the stop band Edge
+ 
+
+ align:start position:0%
+the specifications at the stop band Edge
+and that's a point that we'll deal with
+
+ align:start position:0%
+and that's a point that we'll deal with
+ 
+
+ align:start position:0%
+and that's a point that we'll deal with
+in a few minutes
+
+ align:start position:0%
+in a few minutes
+ 
+
+ align:start position:0%
+in a few minutes
+all right well now we have our
+
+ align:start position:0%
+all right well now we have our
+ 
+
+ align:start position:0%
+all right well now we have our
+specifications let me incidentally point
+
+ align:start position:0%
+specifications let me incidentally point
+ 
+
+ align:start position:0%
+specifications let me incidentally point
+out that there's this parameter capital
+
+ align:start position:0%
+out that there's this parameter capital
+ 
+
+ align:start position:0%
+out that there's this parameter capital
+T that we're carrying
+
+ align:start position:0%
+T that we're carrying
+ 
+
+ align:start position:0%
+T that we're carrying
+around and as I'll justify partly on the
+
+ align:start position:0%
+around and as I'll justify partly on the
+ 
+
+ align:start position:0%
+around and as I'll justify partly on the
+basis of this example the parameter
+
+ align:start position:0%
+basis of this example the parameter
+ 
+
+ align:start position:0%
+basis of this example the parameter
+capital t is an irrelevant parameter
+
+ align:start position:0%
+capital t is an irrelevant parameter
+ 
+
+ align:start position:0%
+capital t is an irrelevant parameter
+it's a parameter that will disappear
+
+ align:start position:0%
+it's a parameter that will disappear
+ 
+
+ align:start position:0%
+it's a parameter that will disappear
+we'll carry it through with us for this
+
+ align:start position:0%
+we'll carry it through with us for this
+ 
+
+ align:start position:0%
+we'll carry it through with us for this
+one example but for other example
+
+ align:start position:0%
+one example but for other example
+ 
+
+ align:start position:0%
+one example but for other example
+examples and problems that you work
+
+ align:start position:0%
+examples and problems that you work
+ 
+
+ align:start position:0%
+examples and problems that you work
+through the study
+
+ align:start position:0%
+through the study
+ 
+
+ align:start position:0%
+through the study
+guide uh the you should have absorbed
+
+ align:start position:0%
+guide uh the you should have absorbed
+ 
+
+ align:start position:0%
+guide uh the you should have absorbed
+the fact that capital t is irrelevant
+
+ align:start position:0%
+the fact that capital t is irrelevant
+ 
+
+ align:start position:0%
+the fact that capital t is irrelevant
+and in fact capital T can be chosen
+
+ align:start position:0%
+and in fact capital T can be chosen
+ 
+
+ align:start position:0%
+and in fact capital T can be chosen
+equal to Unity but let's carry it
+
+ align:start position:0%
+equal to Unity but let's carry it
+ 
+
+ align:start position:0%
+equal to Unity but let's carry it
+through in this example and just see how
+
+ align:start position:0%
+through in this example and just see how
+ 
+
+ align:start position:0%
+through in this example and just see how
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+disappears all right well so we want the
+
+ align:start position:0%
+disappears all right well so we want the
+ 
+
+ align:start position:0%
+disappears all right well so we want the
+analog Butterworth
+
+ align:start position:0%
+analog Butterworth
+ 
+
+ align:start position:0%
+analog Butterworth
+filter meaning these
+
+ align:start position:0%
+filter meaning these
+ 
+
+ align:start position:0%
+filter meaning these
+specifications and we want it at Omega
+
+ align:start position:0%
+specifications and we want it at Omega
+ 
+
+ align:start position:0%
+specifications and we want it at Omega
+equal to zero to have a gain magnitude
+
+ align:start position:0%
+equal to zero to have a gain magnitude
+ 
+
+ align:start position:0%
+equal to zero to have a gain magnitude
+squared function to be t^2 so that the
+
+ align:start position:0%
+squared function to be t^2 so that the
+ 
+
+ align:start position:0%
+squared function to be t^2 so that the
+magnitude is T so here we have the form
+
+ align:start position:0%
+magnitude is T so here we have the form
+ 
+
+ align:start position:0%
+magnitude is T so here we have the form
+then of the analog Butterworth
+
+ align:start position:0%
+then of the analog Butterworth
+ 
+
+ align:start position:0%
+then of the analog Butterworth
+filter and in order to meet these
+
+ align:start position:0%
+filter and in order to meet these
+ 
+
+ align:start position:0%
+filter and in order to meet these
+specifications at this frequency and
+
+ align:start position:0%
+specifications at this frequency and
+ 
+
+ align:start position:0%
+specifications at this frequency and
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one we then have two
+
+ align:start position:0%
+one we then have two
+ 
+
+ align:start position:0%
+one we then have two
+equations one equation says that at
+
+ align:start position:0%
+equations one equation says that at
+ 
+
+ align:start position:0%
+equations one equation says that at
+Capital Omega equal to 2 pi over capital
+
+ align:start position:0%
+Capital Omega equal to 2 pi over capital
+ 
+
+ align:start position:0%
+Capital Omega equal to 2 pi over capital
+T we would like the
+
+ align:start position:0%
+T we would like the
+ 
+
+ align:start position:0%
+T we would like the
+value of the magnitude squared well the
+
+ align:start position:0%
+value of the magnitude squared well the
+ 
+
+ align:start position:0%
+value of the magnitude squared well the
+magnitude function to be T * 10us
+
+ align:start position:0%
+magnitude function to be T * 10us
+ 
+
+ align:start position:0%
+magnitude function to be T * 10us
+05 which implies that this denominator
+
+ align:start position:0%
+05 which implies that this denominator
+ 
+
+ align:start position:0%
+05 which implies that this denominator
+should be equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10.1 second of all at the stop Bend
+
+ align:start position:0%
+10.1 second of all at the stop Bend
+ 
+
+ align:start position:0%
+10.1 second of all at the stop Bend
+frequency 3 Pi / capital
+
+ align:start position:0%
+frequency 3 Pi / capital
+ 
+
+ align:start position:0%
+frequency 3 Pi / capital
+T the fact that we want that to be the
+
+ align:start position:0%
+T the fact that we want that to be the
+ 
+
+ align:start position:0%
+T the fact that we want that to be the
+magnitude to be T * 10
+
+ align:start position:0%
+magnitude to be T * 10
+ 
+
+ align:start position:0%
+magnitude to be T * 10
+-75 implies the magnitude squared is of
+
+ align:start position:0%
+-75 implies the magnitude squared is of
+ 
+
+ align:start position:0%
+-75 implies the magnitude squared is of
+course the square of that and we want
+
+ align:start position:0%
+course the square of that and we want
+ 
+
+ align:start position:0%
+course the square of that and we want
+then the denominator to be equal to 10^
+
+ align:start position:0%
+then the denominator to be equal to 10^
+ 
+
+ align:start position:0%
+then the denominator to be equal to 10^
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+1.5 so we have two points that we're
+
+ align:start position:0%
+1.5 so we have two points that we're
+ 
+
+ align:start position:0%
+1.5 so we have two points that we're
+trying to nail down we have two
+
+ align:start position:0%
+trying to nail down we have two
+ 
+
+ align:start position:0%
+trying to nail down we have two
+parameters Omega Sub C and
+
+ align:start position:0%
+parameters Omega Sub C and
+ 
+
+ align:start position:0%
+parameters Omega Sub C and
+N from these two points that we're
+
+ align:start position:0%
+N from these two points that we're
+ 
+
+ align:start position:0%
+N from these two points that we're
+trying to nail down we get two
+
+ align:start position:0%
+trying to nail down we get two
+ 
+
+ align:start position:0%
+trying to nail down we get two
+equations and we can now solve these
+
+ align:start position:0%
+equations and we can now solve these
+ 
+
+ align:start position:0%
+equations and we can now solve these
+equations for our parameters Omega Sub C
+
+ align:start position:0%
+equations for our parameters Omega Sub C
+ 
+
+ align:start position:0%
+equations for our parameters Omega Sub C
+and capital
+
+ align:start position:0%
+and capital
+ 
+
+ align:start position:0%
+and capital
+N well if we do that and it's a little
+
+ align:start position:0%
+N well if we do that and it's a little
+ 
+
+ align:start position:0%
+N well if we do that and it's a little
+tedious to do it let me point out
+
+ align:start position:0%
+tedious to do it let me point out
+ 
+
+ align:start position:0%
+tedious to do it let me point out
+incidentally since we're trying to keep
+
+ align:start position:0%
+incidentally since we're trying to keep
+ 
+
+ align:start position:0%
+incidentally since we're trying to keep
+track of this capital T that capital T
+
+ align:start position:0%
+track of this capital T that capital T
+ 
+
+ align:start position:0%
+track of this capital T that capital T
+drops down into the numerator and so in
+
+ align:start position:0%
+drops down into the numerator and so in
+ 
+
+ align:start position:0%
+drops down into the numerator and so in
+fact we can solve for capital n and
+
+ align:start position:0%
+fact we can solve for capital n and
+ 
+
+ align:start position:0%
+fact we can solve for capital n and
+Omega Sub C time capital T in other
+
+ align:start position:0%
+Omega Sub C time capital T in other
+ 
+
+ align:start position:0%
+Omega Sub C time capital T in other
+words we can just move this down here
+
+ align:start position:0%
+words we can just move this down here
+ 
+
+ align:start position:0%
+words we can just move this down here
+algebraically and so we have then
+
+ align:start position:0%
+algebraically and so we have then
+ 
+
+ align:start position:0%
+algebraically and so we have then
+instead of the parameter Omega Sub C we
+
+ align:start position:0%
+instead of the parameter Omega Sub C we
+ 
+
+ align:start position:0%
+instead of the parameter Omega Sub C we
+have the parameter Omega Sub C * capital
+
+ align:start position:0%
+have the parameter Omega Sub C * capital
+ 
+
+ align:start position:0%
+have the parameter Omega Sub C * capital
+T all right if you grind through these
+
+ align:start position:0%
+T all right if you grind through these
+ 
+
+ align:start position:0%
+T all right if you grind through these
+two equations what results is a value
+
+ align:start position:0%
+two equations what results is a value
+ 
+
+ align:start position:0%
+two equations what results is a value
+for n equal to 5. 8858 and probably some
+
+ align:start position:0%
+for n equal to 5. 8858 and probably some
+ 
+
+ align:start position:0%
+for n equal to 5. 8858 and probably some
+other digits and Omega Sub C capital t
+
+ align:start position:0%
+other digits and Omega Sub C capital t
+ 
+
+ align:start position:0%
+other digits and Omega Sub C capital t
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+7474 and we could imagine that at this
+
+ align:start position:0%
+7474 and we could imagine that at this
+ 
+
+ align:start position:0%
+7474 and we could imagine that at this
+point we're done except
+
+ align:start position:0%
+point we're done except
+ 
+
+ align:start position:0%
+point we're done except
+that the parameter
+
+ align:start position:0%
+that the parameter
+ 
+
+ align:start position:0%
+that the parameter
+n corresponding to the order of the
+
+ align:start position:0%
+n corresponding to the order of the
+ 
+
+ align:start position:0%
+n corresponding to the order of the
+filter of course has to be an
+
+ align:start position:0%
+filter of course has to be an
+ 
+
+ align:start position:0%
+filter of course has to be an
+integer so what that means is that we
+
+ align:start position:0%
+integer so what that means is that we
+ 
+
+ align:start position:0%
+integer so what that means is that we
+can't use a value of n as I've indicated
+
+ align:start position:0%
+can't use a value of n as I've indicated
+ 
+
+ align:start position:0%
+can't use a value of n as I've indicated
+here we need an integer
+
+ align:start position:0%
+here we need an integer
+ 
+
+ align:start position:0%
+here we need an integer
+value also if we were to round this down
+
+ align:start position:0%
+value also if we were to round this down
+ 
+
+ align:start position:0%
+value also if we were to round this down
+or truncate it down to a choice of n
+
+ align:start position:0%
+or truncate it down to a choice of n
+ 
+
+ align:start position:0%
+or truncate it down to a choice of n
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+5 then since the order is lower you can
+
+ align:start position:0%
+5 then since the order is lower you can
+ 
+
+ align:start position:0%
+5 then since the order is lower you can
+imagine that the filter characteristics
+
+ align:start position:0%
+imagine that the filter characteristics
+ 
+
+ align:start position:0%
+imagine that the filter characteristics
+won't be as good in other words we're
+
+ align:start position:0%
+won't be as good in other words we're
+ 
+
+ align:start position:0%
+won't be as good in other words we're
+not going to meet these
+
+ align:start position:0%
+not going to meet these
+ 
+
+ align:start position:0%
+not going to meet these
+specifications so the other choice then
+
+ align:start position:0%
+specifications so the other choice then
+ 
+
+ align:start position:0%
+specifications so the other choice then
+is to use instead of this value of n use
+
+ align:start position:0%
+is to use instead of this value of n use
+ 
+
+ align:start position:0%
+is to use instead of this value of n use
+a value of n equal to six in other words
+
+ align:start position:0%
+a value of n equal to six in other words
+ 
+
+ align:start position:0%
+a value of n equal to six in other words
+round up to the highest to the next
+
+ align:start position:0%
+round up to the highest to the next
+ 
+
+ align:start position:0%
+round up to the highest to the next
+integer value and if we do that then
+
+ align:start position:0%
+integer value and if we do that then
+ 
+
+ align:start position:0%
+integer value and if we do that then
+these two equations will no longer be
+
+ align:start position:0%
+these two equations will no longer be
+ 
+
+ align:start position:0%
+these two equations will no longer be
+satisfed
+
+ align:start position:0%
+satisfed
+ 
+
+ align:start position:0%
+satisfed
+F we're now using a higher order filter
+
+ align:start position:0%
+F we're now using a higher order filter
+ 
+
+ align:start position:0%
+F we're now using a higher order filter
+than these equations would
+
+ align:start position:0%
+than these equations would
+ 
+
+ align:start position:0%
+than these equations would
+dictate of course we're using an integer
+
+ align:start position:0%
+dictate of course we're using an integer
+ 
+
+ align:start position:0%
+dictate of course we're using an integer
+order because that's what we need we're
+
+ align:start position:0%
+order because that's what we need we're
+ 
+
+ align:start position:0%
+order because that's what we need we're
+using a third order filter uh I'm sorry
+
+ align:start position:0%
+using a third order filter uh I'm sorry
+ 
+
+ align:start position:0%
+using a third order filter uh I'm sorry
+a sixth order
+
+ align:start position:0%
+a sixth order
+ 
+
+ align:start position:0%
+a sixth order
+filter and what that means is that if we
+
+ align:start position:0%
+filter and what that means is that if we
+ 
+
+ align:start position:0%
+filter and what that means is that if we
+choose n equal to
+
+ align:start position:0%
+choose n equal to
+ 
+
+ align:start position:0%
+choose n equal to
+6 we can satisfy this
+
+ align:start position:0%
+6 we can satisfy this
+ 
+
+ align:start position:0%
+6 we can satisfy this
+equation or we can satisfy this equation
+
+ align:start position:0%
+equation or we can satisfy this equation
+ 
+
+ align:start position:0%
+equation or we can satisfy this equation
+but we can't satisfy both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well which one should we try to meet and
+
+ align:start position:0%
+well which one should we try to meet and
+ 
+
+ align:start position:0%
+well which one should we try to meet and
+which one should we
+
+ align:start position:0%
+which one should we
+ 
+
+ align:start position:0%
+which one should we
+exceed well we know that with impulse
+
+ align:start position:0%
+exceed well we know that with impulse
+ 
+
+ align:start position:0%
+exceed well we know that with impulse
+and variance there is the issue of
+
+ align:start position:0%
+and variance there is the issue of
+ 
+
+ align:start position:0%
+and variance there is the issue of
+aliasing and so in fact in impulse and
+
+ align:start position:0%
+aliasing and so in fact in impulse and
+ 
+
+ align:start position:0%
+aliasing and so in fact in impulse and
+variant design it will often happen that
+
+ align:start position:0%
+variant design it will often happen that
+ 
+
+ align:start position:0%
+variant design it will often happen that
+although we design exactly to meet the
+
+ align:start position:0%
+although we design exactly to meet the
+ 
+
+ align:start position:0%
+although we design exactly to meet the
+Stop and
+
+ align:start position:0%
+Stop and
+ 
+
+ align:start position:0%
+Stop and
+specifications the Stop and
+
+ align:start position:0%
+specifications the Stop and
+ 
+
+ align:start position:0%
+specifications the Stop and
+specifications won't be met because of
+
+ align:start position:0%
+specifications won't be met because of
+ 
+
+ align:start position:0%
+specifications won't be met because of
+iing consequently given the flexibility
+
+ align:start position:0%
+iing consequently given the flexibility
+ 
+
+ align:start position:0%
+iing consequently given the flexibility
+that we have due to the fact that we can
+
+ align:start position:0%
+that we have due to the fact that we can
+ 
+
+ align:start position:0%
+that we have due to the fact that we can
+actually Implement a higher order filter
+
+ align:start position:0%
+actually Implement a higher order filter
+ 
+
+ align:start position:0%
+actually Implement a higher order filter
+than these equations
+
+ align:start position:0%
+than these equations
+ 
+
+ align:start position:0%
+than these equations
+dictate to compensate for aliasing we
+
+ align:start position:0%
+dictate to compensate for aliasing we
+ 
+
+ align:start position:0%
+dictate to compensate for aliasing we
+can exceed the stop band specifications
+
+ align:start position:0%
+can exceed the stop band specifications
+ 
+
+ align:start position:0%
+can exceed the stop band specifications
+and meet exactly the pass band
+
+ align:start position:0%
+and meet exactly the pass band
+ 
+
+ align:start position:0%
+and meet exactly the pass band
+specifications so if we substitute for n
+
+ align:start position:0%
+specifications so if we substitute for n
+ 
+
+ align:start position:0%
+specifications so if we substitute for n
+Nal 6 into this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that then requires that Omega sub CT be
+
+ align:start position:0%
+that then requires that Omega sub CT be
+ 
+
+ align:start position:0%
+that then requires that Omega sub CT be
+such that we exactly meet the pass band
+
+ align:start position:0%
+such that we exactly meet the pass band
+ 
+
+ align:start position:0%
+such that we exactly meet the pass band
+specifications in which case this
+
+ align:start position:0%
+specifications in which case this
+ 
+
+ align:start position:0%
+specifications in which case this
+equation won't be met in fact what will
+
+ align:start position:0%
+equation won't be met in fact what will
+ 
+
+ align:start position:0%
+equation won't be met in fact what will
+happen at the stopend edge is that the
+
+ align:start position:0%
+happen at the stopend edge is that the
+ 
+
+ align:start position:0%
+happen at the stopend edge is that the
+stopend specifications will be
+
+ align:start position:0%
+stopend specifications will be
+ 
+
+ align:start position:0%
+stopend specifications will be
+exceeded if we do this then we have for
+
+ align:start position:0%
+exceeded if we do this then we have for
+ 
+
+ align:start position:0%
+exceeded if we do this then we have for
+the equation that we solve for Omega sub
+
+ align:start position:0%
+the equation that we solve for Omega sub
+ 
+
+ align:start position:0%
+the equation that we solve for Omega sub
+CT from the equation which specified The
+
+ align:start position:0%
+CT from the equation which specified The
+ 
+
+ align:start position:0%
+CT from the equation which specified The
+passband Edge which is where we're going
+
+ align:start position:0%
+passband Edge which is where we're going
+ 
+
+ align:start position:0%
+passband Edge which is where we're going
+to meet the specs and what results then
+
+ align:start position:0%
+to meet the specs and what results then
+ 
+
+ align:start position:0%
+to meet the specs and what results then
+is for Omega sub
+
+ align:start position:0%
+is for Omega sub
+ 
+
+ align:start position:0%
+is for Omega sub
+CT this value rather than the previous
+
+ align:start position:0%
+CT this value rather than the previous
+ 
+
+ align:start position:0%
+CT this value rather than the previous
+value that had been obtained from the
+
+ align:start position:0%
+value that had been obtained from the
+ 
+
+ align:start position:0%
+value that had been obtained from the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+equations well from these parameters
+
+ align:start position:0%
+equations well from these parameters
+ 
+
+ align:start position:0%
+equations well from these parameters
+then we can we have that Omega subc is
+
+ align:start position:0%
+then we can we have that Omega subc is
+ 
+
+ align:start position:0%
+then we can we have that Omega subc is
+7032 by capital T we can substitute
+
+ align:start position:0%
+7032 by capital T we can substitute
+ 
+
+ align:start position:0%
+7032 by capital T we can substitute
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+parameters into the form for the squared
+
+ align:start position:0%
+parameters into the form for the squared
+ 
+
+ align:start position:0%
+parameters into the form for the squared
+magnitude function H sub a of s * H sub
+
+ align:start position:0%
+magnitude function H sub a of s * H sub
+ 
+
+ align:start position:0%
+magnitude function H sub a of s * H sub
+a of minus s and actually it's this
+
+ align:start position:0%
+a of minus s and actually it's this
+ 
+
+ align:start position:0%
+a of minus s and actually it's this
+raised to the 2N which is the 2 * 6th
+
+ align:start position:0%
+raised to the 2N which is the 2 * 6th
+ 
+
+ align:start position:0%
+raised to the 2N which is the 2 * 6th
+power which is the 12th power so this
+
+ align:start position:0%
+power which is the 12th power so this
+ 
+
+ align:start position:0%
+power which is the 12th power so this
+then is the form for the analog squared
+
+ align:start position:0%
+then is the form for the analog squared
+ 
+
+ align:start position:0%
+then is the form for the analog squared
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+function now notice that the parameter
+
+ align:start position:0%
+function now notice that the parameter
+ 
+
+ align:start position:0%
+function now notice that the parameter
+capital T still hasn't disappeared we
+
+ align:start position:0%
+capital T still hasn't disappeared we
+ 
+
+ align:start position:0%
+capital T still hasn't disappeared we
+still have it we have it there and we
+
+ align:start position:0%
+still have it we have it there and we
+ 
+
+ align:start position:0%
+still have it we have it there and we
+have it here but notice that when we
+
+ align:start position:0%
+have it here but notice that when we
+ 
+
+ align:start position:0%
+have it here but notice that when we
+substitute in for Omega Sub C this
+
+ align:start position:0%
+substitute in for Omega Sub C this
+ 
+
+ align:start position:0%
+substitute in for Omega Sub C this
+number divided by capital T if you track
+
+ align:start position:0%
+number divided by capital T if you track
+ 
+
+ align:start position:0%
+number divided by capital T if you track
+through that
+
+ align:start position:0%
+through that
+ 
+
+ align:start position:0%
+through that
+algebra capital T reappears in this
+
+ align:start position:0%
+algebra capital T reappears in this
+ 
+
+ align:start position:0%
+algebra capital T reappears in this
+expression at as a multiplier on S that
+
+ align:start position:0%
+expression at as a multiplier on S that
+ 
+
+ align:start position:0%
+expression at as a multiplier on S that
+is we had 7032 divided by capital T that
+
+ align:start position:0%
+is we had 7032 divided by capital T that
+ 
+
+ align:start position:0%
+is we had 7032 divided by capital T that
+gets reflected back up into this
+
+ align:start position:0%
+gets reflected back up into this
+ 
+
+ align:start position:0%
+gets reflected back up into this
+numerator so that we have S * cap
+
+ align:start position:0%
+numerator so that we have S * cap
+ 
+
+ align:start position:0%
+numerator so that we have S * cap
+capital T well let's see what that
+
+ align:start position:0%
+capital T well let's see what that
+ 
+
+ align:start position:0%
+capital T well let's see what that
+means suppose that capital T were equal
+
+ align:start position:0%
+means suppose that capital T were equal
+ 
+
+ align:start position:0%
+means suppose that capital T were equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one and we got an analog impulse
+
+ align:start position:0%
+one and we got an analog impulse
+ 
+
+ align:start position:0%
+one and we got an analog impulse
+response H Suba of
+
+ align:start position:0%
+response H Suba of
+ 
+
+ align:start position:0%
+response H Suba of
+t or the system function H sub B of
+
+ align:start position:0%
+t or the system function H sub B of
+ 
+
+ align:start position:0%
+t or the system function H sub B of
+s If
+
+ align:start position:0%
+s If
+ 
+
+ align:start position:0%
+s If
+instead we reinserted capital T and
+
+ align:start position:0%
+instead we reinserted capital T and
+ 
+
+ align:start position:0%
+instead we reinserted capital T and
+considered H Suba of s * capital
+
+ align:start position:0%
+considered H Suba of s * capital
+ 
+
+ align:start position:0%
+considered H Suba of s * capital
+T multip IED by capital
+
+ align:start position:0%
+T multip IED by capital
+ 
+
+ align:start position:0%
+T multip IED by capital
+T that impulse response would be related
+
+ align:start position:0%
+T that impulse response would be related
+ 
+
+ align:start position:0%
+T that impulse response would be related
+to this one by simply a Time scaling
+
+ align:start position:0%
+to this one by simply a Time scaling
+ 
+
+ align:start position:0%
+to this one by simply a Time scaling
+that in other words this one would be
+
+ align:start position:0%
+that in other words this one would be
+ 
+
+ align:start position:0%
+that in other words this one would be
+replaced by H Suba of T divided capital
+
+ align:start position:0%
+replaced by H Suba of T divided capital
+ 
+
+ align:start position:0%
+replaced by H Suba of T divided capital
+T well let's look at this and ask what
+
+ align:start position:0%
+T well let's look at this and ask what
+ 
+
+ align:start position:0%
+T well let's look at this and ask what
+happens when we sample it at samples
+
+ align:start position:0%
+happens when we sample it at samples
+ 
+
+ align:start position:0%
+happens when we sample it at samples
+spaced by capital T so we we look at
+
+ align:start position:0%
+spaced by capital T so we we look at
+ 
+
+ align:start position:0%
+spaced by capital T so we we look at
+this impulse response with t replaced by
+
+ align:start position:0%
+this impulse response with t replaced by
+ 
+
+ align:start position:0%
+this impulse response with t replaced by
+n * capital
+
+ align:start position:0%
+n * capital
+ 
+
+ align:start position:0%
+n * capital
+T as we've specified here and we observe
+
+ align:start position:0%
+T as we've specified here and we observe
+ 
+
+ align:start position:0%
+T as we've specified here and we observe
+that no matter what we pick capital T to
+
+ align:start position:0%
+that no matter what we pick capital T to
+ 
+
+ align:start position:0%
+that no matter what we pick capital T to
+be that parameter disappears because
+
+ align:start position:0%
+be that parameter disappears because
+ 
+
+ align:start position:0%
+be that parameter disappears because
+little t equal to n * capital T gives us
+
+ align:start position:0%
+little t equal to n * capital T gives us
+ 
+
+ align:start position:0%
+little t equal to n * capital T gives us
+samples H sub a of n which are exactly
+
+ align:start position:0%
+samples H sub a of n which are exactly
+ 
+
+ align:start position:0%
+samples H sub a of n which are exactly
+the same samples that we would get no
+
+ align:start position:0%
+the same samples that we would get no
+ 
+
+ align:start position:0%
+the same samples that we would get no
+matter how we chose the parameter
+
+ align:start position:0%
+matter how we chose the parameter
+ 
+
+ align:start position:0%
+matter how we chose the parameter
+capital T or equivalently whether or not
+
+ align:start position:0%
+capital T or equivalently whether or not
+ 
+
+ align:start position:0%
+capital T or equivalently whether or not
+we chose the parameter capital t equal
+
+ align:start position:0%
+we chose the parameter capital t equal
+ 
+
+ align:start position:0%
+we chose the parameter capital t equal
+to Unity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that it requires a little
+
+ align:start position:0%
+I think that it requires a little
+ 
+
+ align:start position:0%
+I think that it requires a little
+reflection to absorb this point it's
+
+ align:start position:0%
+reflection to absorb this point it's
+ 
+
+ align:start position:0%
+reflection to absorb this point it's
+basically tied to the fact that the
+
+ align:start position:0%
+basically tied to the fact that the
+ 
+
+ align:start position:0%
+basically tied to the fact that the
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+response is specified for the digital
+
+ align:start position:0%
+response is specified for the digital
+ 
+
+ align:start position:0%
+response is specified for the digital
+filter not for the analog filter and
+
+ align:start position:0%
+filter not for the analog filter and
+ 
+
+ align:start position:0%
+filter not for the analog filter and
+specifying the frequency response for
+
+ align:start position:0%
+specifying the frequency response for
+ 
+
+ align:start position:0%
+specifying the frequency response for
+the digital filter in effect specifies
+
+ align:start position:0%
+the digital filter in effect specifies
+ 
+
+ align:start position:0%
+the digital filter in effect specifies
+Omega times Capital Omega time capital T
+
+ align:start position:0%
+Omega times Capital Omega time capital T
+ 
+
+ align:start position:0%
+Omega times Capital Omega time capital T
+well I leave it to you to uh think about
+
+ align:start position:0%
+well I leave it to you to uh think about
+ 
+
+ align:start position:0%
+well I leave it to you to uh think about
+this a little but the important point is
+
+ align:start position:0%
+this a little but the important point is
+ 
+
+ align:start position:0%
+this a little but the important point is
+that in fact this parameter T if we
+
+ align:start position:0%
+that in fact this parameter T if we
+ 
+
+ align:start position:0%
+that in fact this parameter T if we
+specify the
+
+ align:start position:0%
+specify the
+ 
+
+ align:start position:0%
+specify the
+filter in terms of digital
+
+ align:start position:0%
+filter in terms of digital
+ 
+
+ align:start position:0%
+filter in terms of digital
+specifications this parameter capital t
+
+ align:start position:0%
+specifications this parameter capital t
+ 
+
+ align:start position:0%
+specifications this parameter capital t
+is really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irrelevant all right well so here is our
+
+ align:start position:0%
+irrelevant all right well so here is our
+ 
+
+ align:start position:0%
+irrelevant all right well so here is our
+analog
+
+ align:start position:0%
+analog
+ 
+
+ align:start position:0%
+analog
+design and
+
+ align:start position:0%
+design and
+ 
+
+ align:start position:0%
+design and
+we can obtain H Suba of s from this
+
+ align:start position:0%
+we can obtain H Suba of s from this
+ 
+
+ align:start position:0%
+we can obtain H Suba of s from this
+according to the method that we talked
+
+ align:start position:0%
+according to the method that we talked
+ 
+
+ align:start position:0%
+according to the method that we talked
+about previously taking the left half
+
+ align:start position:0%
+about previously taking the left half
+ 
+
+ align:start position:0%
+about previously taking the left half
+plane poles of this expression
+
+ align:start position:0%
+plane poles of this expression
+ 
+
+ align:start position:0%
+plane poles of this expression
+converting those to a digital filter by
+
+ align:start position:0%
+converting those to a digital filter by
+ 
+
+ align:start position:0%
+converting those to a digital filter by
+using the transformation that we
+
+ align:start position:0%
+using the transformation that we
+ 
+
+ align:start position:0%
+using the transformation that we
+discussed in the previous two lectures
+
+ align:start position:0%
+discussed in the previous two lectures
+ 
+
+ align:start position:0%
+discussed in the previous two lectures
+expanding for example in terms of residu
+
+ align:start position:0%
+expanding for example in terms of residu
+ 
+
+ align:start position:0%
+expanding for example in terms of residu
+and poles and then applying the impulse
+
+ align:start position:0%
+and poles and then applying the impulse
+ 
+
+ align:start position:0%
+and poles and then applying the impulse
+and variant
+
+ align:start position:0%
+and variant
+ 
+
+ align:start position:0%
+and variant
+transformation and if we do that what
+
+ align:start position:0%
+transformation and if we do that what
+ 
+
+ align:start position:0%
+transformation and if we do that what
+what results is an analog uh I'm sorry a
+
+ align:start position:0%
+what results is an analog uh I'm sorry a
+ 
+
+ align:start position:0%
+what results is an analog uh I'm sorry a
+digital low pass filter which was the
+
+ align:start position:0%
+digital low pass filter which was the
+ 
+
+ align:start position:0%
+digital low pass filter which was the
+low pass filter that we set out to
+
+ align:start position:0%
+low pass filter that we set out to
+ 
+
+ align:start position:0%
+low pass filter that we set out to
+design and let me just show how those
+
+ align:start position:0%
+design and let me just show how those
+ 
+
+ align:start position:0%
+design and let me just show how those
+specifications or how that design comes
+
+ align:start position:0%
+specifications or how that design comes
+ 
+
+ align:start position:0%
+specifications or how that design comes
+out so this for the example that we've
+
+ align:start position:0%
+out so this for the example that we've
+ 
+
+ align:start position:0%
+out so this for the example that we've
+been talking about is a graph of the
+
+ align:start position:0%
+been talking about is a graph of the
+ 
+
+ align:start position:0%
+been talking about is a graph of the
+frequency response
+
+ align:start position:0%
+frequency response
+ 
+
+ align:start position:0%
+frequency response
+characteristics here is the magnitude as
+
+ align:start position:0%
+characteristics here is the magnitude as
+ 
+
+ align:start position:0%
+characteristics here is the magnitude as
+a function of digital frequency
+
+ align:start position:0%
+a function of digital frequency
+ 
+
+ align:start position:0%
+a function of digital frequency
+Omega and here is the same frequency
+
+ align:start position:0%
+Omega and here is the same frequency
+ 
+
+ align:start position:0%
+Omega and here is the same frequency
+response plotted in terms of
+
+ align:start position:0%
+response plotted in terms of
+ 
+
+ align:start position:0%
+response plotted in terms of
+DB and we see that we had a in the
+
+ align:start position:0%
+DB and we see that we had a in the
+ 
+
+ align:start position:0%
+DB and we see that we had a in the
+specifications a pass band Edge at 0 2
+
+ align:start position:0%
+specifications a pass band Edge at 0 2
+ 
+
+ align:start position:0%
+specifications a pass band Edge at 0 2
+pi a stop band Edge at 3
+
+ align:start position:0%
+pi a stop band Edge at 3
+ 
+
+ align:start position:0%
+pi a stop band Edge at 3
+Pi at0 2 pi we asked that the gain be
+
+ align:start position:0%
+Pi at0 2 pi we asked that the gain be
+ 
+
+ align:start position:0%
+Pi at0 2 pi we asked that the gain be
+down by
+
+ align:start position:0%
+down by
+ 
+
+ align:start position:0%
+down by
+1db and uh of course it's hard to tell
+
+ align:start position:0%
+1db and uh of course it's hard to tell
+ 
+
+ align:start position:0%
+1db and uh of course it's hard to tell
+exactly that we're down 1db but in fact
+
+ align:start position:0%
+exactly that we're down 1db but in fact
+ 
+
+ align:start position:0%
+exactly that we're down 1db but in fact
+we are and at Omega equal to 3 Pi our
+
+ align:start position:0%
+we are and at Omega equal to 3 Pi our
+ 
+
+ align:start position:0%
+we are and at Omega equal to 3 Pi our
+specification was that we wanted to be
+
+ align:start position:0%
+specification was that we wanted to be
+ 
+
+ align:start position:0%
+specification was that we wanted to be
+down by 15
+
+ align:start position:0%
+down by 15
+ 
+
+ align:start position:0%
+down by 15
+DB in fact we
+
+ align:start position:0%
+DB in fact we
+ 
+
+ align:start position:0%
+DB in fact we
+overcompensated because of the fact that
+
+ align:start position:0%
+overcompensated because of the fact that
+ 
+
+ align:start position:0%
+overcompensated because of the fact that
+we had to round the order of the filter
+
+ align:start position:0%
+we had to round the order of the filter
+ 
+
+ align:start position:0%
+we had to round the order of the filter
+up to an integer value and you can see
+
+ align:start position:0%
+up to an integer value and you can see
+ 
+
+ align:start position:0%
+up to an integer value and you can see
+in fact that if you look at this
+
+ align:start position:0%
+in fact that if you look at this
+ 
+
+ align:start position:0%
+in fact that if you look at this
+carefully we exceed the specifications
+
+ align:start position:0%
+carefully we exceed the specifications
+ 
+
+ align:start position:0%
+carefully we exceed the specifications
+at 3 Pi by a little bit in other words
+
+ align:start position:0%
+at 3 Pi by a little bit in other words
+ 
+
+ align:start position:0%
+at 3 Pi by a little bit in other words
+we're down by a little more than 15 DB
+
+ align:start position:0%
+we're down by a little more than 15 DB
+ 
+
+ align:start position:0%
+we're down by a little more than 15 DB
+in fact for this particular filter you
+
+ align:start position:0%
+in fact for this particular filter you
+ 
+
+ align:start position:0%
+in fact for this particular filter you
+can imagine that the effect of aliasing
+
+ align:start position:0%
+can imagine that the effect of aliasing
+ 
+
+ align:start position:0%
+can imagine that the effect of aliasing
+is in fact rather minimal because this
+
+ align:start position:0%
+is in fact rather minimal because this
+ 
+
+ align:start position:0%
+is in fact rather minimal because this
+frequency response by the time we get
+
+ align:start position:0%
+frequency response by the time we get
+ 
+
+ align:start position:0%
+frequency response by the time we get
+out to Pi is essentially zero here we're
+
+ align:start position:0%
+out to Pi is essentially zero here we're
+ 
+
+ align:start position:0%
+out to Pi is essentially zero here we're
+down to uh- 75 DB and that's of course
+
+ align:start position:0%
+down to uh- 75 DB and that's of course
+ 
+
+ align:start position:0%
+down to uh- 75 DB and that's of course
+the amount that would get alias back in
+
+ align:start position:0%
+the amount that would get alias back in
+ 
+
+ align:start position:0%
+the amount that would get alias back in
+so this is the resulting filter
+
+ align:start position:0%
+so this is the resulting filter
+ 
+
+ align:start position:0%
+so this is the resulting filter
+frequency characteristics for the
+
+ align:start position:0%
+frequency characteristics for the
+ 
+
+ align:start position:0%
+frequency characteristics for the
+impulse andari design where we exceed
+
+ align:start position:0%
+impulse andari design where we exceed
+ 
+
+ align:start position:0%
+impulse andari design where we exceed
+slightly the stop andand Edge
+
+ align:start position:0%
+slightly the stop andand Edge
+ 
+
+ align:start position:0%
+slightly the stop andand Edge
+specifications now the next thing that
+
+ align:start position:0%
+specifications now the next thing that
+ 
+
+ align:start position:0%
+specifications now the next thing that
+I'd like to go on to is the a the
+
+ align:start position:0%
+I'd like to go on to is the a the
+ 
+
+ align:start position:0%
+I'd like to go on to is the a the
+corresponding design the design of the
+
+ align:start position:0%
+corresponding design the design of the
+ 
+
+ align:start position:0%
+corresponding design the design of the
+corresponding Butterworth filter Now
+
+ align:start position:0%
+corresponding Butterworth filter Now
+ 
+
+ align:start position:0%
+corresponding Butterworth filter Now
+using the bilinear transformation rather
+
+ align:start position:0%
+using the bilinear transformation rather
+ 
+
+ align:start position:0%
+using the bilinear transformation rather
+than using impulse and
+
+ align:start position:0%
+than using impulse and
+ 
+
+ align:start position:0%
+than using impulse and
+variance I remind you that the basic
+
+ align:start position:0%
+variance I remind you that the basic
+ 
+
+ align:start position:0%
+variance I remind you that the basic
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+with the bilinear transformation as
+
+ align:start position:0%
+with the bilinear transformation as
+ 
+
+ align:start position:0%
+with the bilinear transformation as
+we've discussed in the last
+
+ align:start position:0%
+we've discussed in the last
+ 
+
+ align:start position:0%
+we've discussed in the last
+lectures is that we
+
+ align:start position:0%
+lectures is that we
+ 
+
+ align:start position:0%
+lectures is that we
+basically choose the digital the I'm
+
+ align:start position:0%
+basically choose the digital the I'm
+ 
+
+ align:start position:0%
+basically choose the digital the I'm
+sorry the
+
+ align:start position:0%
+sorry the
+ 
+
+ align:start position:0%
+sorry the
+analog
+
+ align:start position:0%
+analog
+ 
+
+ align:start position:0%
+analog
+specifications by pre-ww warping the
+
+ align:start position:0%
+specifications by pre-ww warping the
+ 
+
+ align:start position:0%
+specifications by pre-ww warping the
+critical frequencies for the digital
+
+ align:start position:0%
+critical frequencies for the digital
+ 
+
+ align:start position:0%
+critical frequencies for the digital
+filter through the nonlinear Distortion
+
+ align:start position:0%
+filter through the nonlinear Distortion
+ 
+
+ align:start position:0%
+filter through the nonlinear Distortion
+curve corresponding to the bilinear
+
+ align:start position:0%
+curve corresponding to the bilinear
+ 
+
+ align:start position:0%
+curve corresponding to the bilinear
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+so we would start here for the digital
+
+ align:start position:0%
+so we would start here for the digital
+ 
+
+ align:start position:0%
+so we would start here for the digital
+filter uh of course here we're talking
+
+ align:start position:0%
+filter uh of course here we're talking
+ 
+
+ align:start position:0%
+filter uh of course here we're talking
+about a monotonic filter rather than one
+
+ align:start position:0%
+about a monotonic filter rather than one
+ 
+
+ align:start position:0%
+about a monotonic filter rather than one
+that ripples but we have a pass band
+
+ align:start position:0%
+that ripples but we have a pass band
+ 
+
+ align:start position:0%
+that ripples but we have a pass band
+Edge at0 2 pi a stop band Edge at 3 Pi
+
+ align:start position:0%
+Edge at0 2 pi a stop band Edge at 3 Pi
+ 
+
+ align:start position:0%
+Edge at0 2 pi a stop band Edge at 3 Pi
+we reflect those critical frequencies
+
+ align:start position:0%
+we reflect those critical frequencies
+ 
+
+ align:start position:0%
+we reflect those critical frequencies
+through the arc tangent curve to obtain
+
+ align:start position:0%
+through the arc tangent curve to obtain
+ 
+
+ align:start position:0%
+through the arc tangent curve to obtain
+the corresponding critical frequencies
+
+ align:start position:0%
+the corresponding critical frequencies
+ 
+
+ align:start position:0%
+the corresponding critical frequencies
+for the analog Butterworth filter when
+
+ align:start position:0%
+for the analog Butterworth filter when
+ 
+
+ align:start position:0%
+for the analog Butterworth filter when
+the analog Butterworth filter is
+
+ align:start position:0%
+the analog Butterworth filter is
+ 
+
+ align:start position:0%
+the analog Butterworth filter is
+designed we then obtain the digital
+
+ align:start position:0%
+designed we then obtain the digital
+ 
+
+ align:start position:0%
+designed we then obtain the digital
+Butterworth filter by transforming this
+
+ align:start position:0%
+Butterworth filter by transforming this
+ 
+
+ align:start position:0%
+Butterworth filter by transforming this
+filter back through the bilinear
+
+ align:start position:0%
+filter back through the bilinear
+ 
+
+ align:start position:0%
+filter back through the bilinear
+transformation so let's look at how this
+
+ align:start position:0%
+transformation so let's look at how this
+ 
+
+ align:start position:0%
+transformation so let's look at how this
+design works then we have as we've just
+
+ align:start position:0%
+design works then we have as we've just
+ 
+
+ align:start position:0%
+design works then we have as we've just
+shown reflected on that curve we begin
+
+ align:start position:0%
+shown reflected on that curve we begin
+ 
+
+ align:start position:0%
+shown reflected on that curve we begin
+with the digital frequency specification
+
+ align:start position:0%
+with the digital frequency specification
+ 
+
+ align:start position:0%
+with the digital frequency specification
+reflect those through the bilinear
+
+ align:start position:0%
+reflect those through the bilinear
+ 
+
+ align:start position:0%
+reflect those through the bilinear
+warping curve to the analog
+
+ align:start position:0%
+warping curve to the analog
+ 
+
+ align:start position:0%
+warping curve to the analog
+specifications and consequently the
+
+ align:start position:0%
+specifications and consequently the
+ 
+
+ align:start position:0%
+specifications and consequently the
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+frequencies and let me emphasize first
+
+ align:start position:0%
+frequencies and let me emphasize first
+ 
+
+ align:start position:0%
+frequencies and let me emphasize first
+of all that just as with impulse and
+
+ align:start position:0%
+of all that just as with impulse and
+ 
+
+ align:start position:0%
+of all that just as with impulse and
+variance you can show that the parameter
+
+ align:start position:0%
+variance you can show that the parameter
+ 
+
+ align:start position:0%
+variance you can show that the parameter
+capital t is an irrelevant parameter we
+
+ align:start position:0%
+capital t is an irrelevant parameter we
+ 
+
+ align:start position:0%
+capital t is an irrelevant parameter we
+could in fact carry it all the way
+
+ align:start position:0%
+could in fact carry it all the way
+ 
+
+ align:start position:0%
+could in fact carry it all the way
+through and what would happen is that we
+
+ align:start position:0%
+through and what would happen is that we
+ 
+
+ align:start position:0%
+through and what would happen is that we
+can we would would find that no matter
+
+ align:start position:0%
+can we would would find that no matter
+ 
+
+ align:start position:0%
+can we would would find that no matter
+what we chose capital T to be the
+
+ align:start position:0%
+what we chose capital T to be the
+ 
+
+ align:start position:0%
+what we chose capital T to be the
+digital filter design that resulted
+
+ align:start position:0%
+digital filter design that resulted
+ 
+
+ align:start position:0%
+digital filter design that resulted
+would be exactly the same so in fact for
+
+ align:start position:0%
+would be exactly the same so in fact for
+ 
+
+ align:start position:0%
+would be exactly the same so in fact for
+this example I'll work through it simply
+
+ align:start position:0%
+this example I'll work through it simply
+ 
+
+ align:start position:0%
+this example I'll work through it simply
+with capital t equal to
+
+ align:start position:0%
+with capital t equal to
+ 
+
+ align:start position:0%
+with capital t equal to
+1 all right with capital t equal to one
+
+ align:start position:0%
+1 all right with capital t equal to one
+ 
+
+ align:start position:0%
+1 all right with capital t equal to one
+we reflect these critical frequencies
+
+ align:start position:0%
+we reflect these critical frequencies
+ 
+
+ align:start position:0%
+we reflect these critical frequencies
+into this pass band frequency Edge and
+
+ align:start position:0%
+into this pass band frequency Edge and
+ 
+
+ align:start position:0%
+into this pass band frequency Edge and
+this stopend Edge and consequently the
+
+ align:start position:0%
+this stopend Edge and consequently the
+ 
+
+ align:start position:0%
+this stopend Edge and consequently the
+the analog filter this is the analog
+
+ align:start position:0%
+the analog filter this is the analog
+ 
+
+ align:start position:0%
+the analog filter this is the analog
+filter the analog filter that we design
+
+ align:start position:0%
+filter the analog filter that we design
+ 
+
+ align:start position:0%
+filter the analog filter that we design
+is one that meets these
+
+ align:start position:0%
+is one that meets these
+ 
+
+ align:start position:0%
+is one that meets these
+specifications and consequently we we
+
+ align:start position:0%
+specifications and consequently we we
+ 
+
+ align:start position:0%
+specifications and consequently we we
+have again the two equations that say
+
+ align:start position:0%
+have again the two equations that say
+ 
+
+ align:start position:0%
+have again the two equations that say
+that at the pass band
+
+ align:start position:0%
+that at the pass band
+ 
+
+ align:start position:0%
+that at the pass band
+Edge we want the magnitude to
+
+ align:start position:0%
+Edge we want the magnitude to
+ 
+
+ align:start position:0%
+Edge we want the magnitude to
+be within One DB of unity and at the
+
+ align:start position:0%
+be within One DB of unity and at the
+ 
+
+ align:start position:0%
+be within One DB of unity and at the
+stop band Edge we want the magnitude to
+
+ align:start position:0%
+stop band Edge we want the magnitude to
+ 
+
+ align:start position:0%
+stop band Edge we want the magnitude to
+be less than down down by more than 15
+
+ align:start position:0%
+be less than down down by more than 15
+ 
+
+ align:start position:0%
+be less than down down by more than 15
+DB and the two equations that result are
+
+ align:start position:0%
+DB and the two equations that result are
+ 
+
+ align:start position:0%
+DB and the two equations that result are
+these exactly the same as we had in the
+
+ align:start position:0%
+these exactly the same as we had in the
+ 
+
+ align:start position:0%
+these exactly the same as we had in the
+impulse and variant case except that the
+
+ align:start position:0%
+impulse and variant case except that the
+ 
+
+ align:start position:0%
+impulse and variant case except that the
+frequencies are
+
+ align:start position:0%
+frequencies are
+ 
+
+ align:start position:0%
+frequencies are
+different so now substituting in for the
+
+ align:start position:0%
+different so now substituting in for the
+ 
+
+ align:start position:0%
+different so now substituting in for the
+form of the analog Butterworth filter
+
+ align:start position:0%
+form of the analog Butterworth filter
+ 
+
+ align:start position:0%
+form of the analog Butterworth filter
+into these
+
+ align:start position:0%
+into these
+ 
+
+ align:start position:0%
+into these
+expressions and setting this up for
+
+ align:start position:0%
+expressions and setting this up for
+ 
+
+ align:start position:0%
+expressions and setting this up for
+equality in these Expressions what
+
+ align:start position:0%
+equality in these Expressions what
+ 
+
+ align:start position:0%
+equality in these Expressions what
+results then are the two equations which
+
+ align:start position:0%
+results then are the two equations which
+ 
+
+ align:start position:0%
+results then are the two equations which
+are identical to the two equations that
+
+ align:start position:0%
+are identical to the two equations that
+ 
+
+ align:start position:0%
+are identical to the two equations that
+we had for the impulse and variant
+
+ align:start position:0%
+we had for the impulse and variant
+ 
+
+ align:start position:0%
+we had for the impulse and variant
+design except that the
+
+ align:start position:0%
+design except that the
+ 
+
+ align:start position:0%
+design except that the
+frequencies at which the pass band and
+
+ align:start position:0%
+frequencies at which the pass band and
+ 
+
+ align:start position:0%
+frequencies at which the pass band and
+stop band edges of the analog
+
+ align:start position:0%
+stop band edges of the analog
+ 
+
+ align:start position:0%
+stop band edges of the analog
+Butterworth filter fall are different
+
+ align:start position:0%
+Butterworth filter fall are different
+ 
+
+ align:start position:0%
+Butterworth filter fall are different
+they're different because of the warping
+
+ align:start position:0%
+they're different because of the warping
+ 
+
+ align:start position:0%
+they're different because of the warping
+of the bilinear curve or the pre warping
+
+ align:start position:0%
+of the bilinear curve or the pre warping
+ 
+
+ align:start position:0%
+of the bilinear curve or the pre warping
+that we have to apply so these are the
+
+ align:start position:0%
+that we have to apply so these are the
+ 
+
+ align:start position:0%
+that we have to apply so these are the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+equations and the resulting if we solve
+
+ align:start position:0%
+equations and the resulting if we solve
+ 
+
+ align:start position:0%
+equations and the resulting if we solve
+these two equations for capital N the
+
+ align:start position:0%
+these two equations for capital N the
+ 
+
+ align:start position:0%
+these two equations for capital N the
+result the resulting value for capital N
+
+ align:start position:0%
+result the resulting value for capital N
+ 
+
+ align:start position:0%
+result the resulting value for capital N
+is 5.3 and some digits notice
+
+ align:start position:0%
+is 5.3 and some digits notice
+ 
+
+ align:start position:0%
+is 5.3 and some digits notice
+incidentally that it's less than it was
+
+ align:start position:0%
+incidentally that it's less than it was
+ 
+
+ align:start position:0%
+incidentally that it's less than it was
+for the impulse invariant design and in
+
+ align:start position:0%
+for the impulse invariant design and in
+ 
+
+ align:start position:0%
+for the impulse invariant design and in
+general that's a characteristic of the
+
+ align:start position:0%
+general that's a characteristic of the
+ 
+
+ align:start position:0%
+general that's a characteristic of the
+bilinear transformation but so it's less
+
+ align:start position:0%
+bilinear transformation but so it's less
+ 
+
+ align:start position:0%
+bilinear transformation but so it's less
+but it is non
+
+ align:start position:0%
+but it is non
+ 
+
+ align:start position:0%
+but it is non
+integer so the first thing we can ask
+
+ align:start position:0%
+integer so the first thing we can ask
+ 
+
+ align:start position:0%
+integer so the first thing we can ask
+again is could we just simply truncate
+
+ align:start position:0%
+again is could we just simply truncate
+ 
+
+ align:start position:0%
+again is could we just simply truncate
+this down or round it down to the
+
+ align:start position:0%
+this down or round it down to the
+ 
+
+ align:start position:0%
+this down or round it down to the
+nearest integer value in other words N
+
+ align:start position:0%
+nearest integer value in other words N
+ 
+
+ align:start position:0%
+nearest integer value in other words N
+equals 5 but of course if we did that
+
+ align:start position:0%
+equals 5 but of course if we did that
+ 
+
+ align:start position:0%
+equals 5 but of course if we did that
+then we wouldn't be able to pick Omega
+
+ align:start position:0%
+then we wouldn't be able to pick Omega
+ 
+
+ align:start position:0%
+then we wouldn't be able to pick Omega
+Sub C so that these equations were
+
+ align:start position:0%
+Sub C so that these equations were
+ 
+
+ align:start position:0%
+Sub C so that these equations were
+satisfied or so that the specifications
+
+ align:start position:0%
+satisfied or so that the specifications
+ 
+
+ align:start position:0%
+satisfied or so that the specifications
+were met or exceeded so in fact we need
+
+ align:start position:0%
+were met or exceeded so in fact we need
+ 
+
+ align:start position:0%
+were met or exceeded so in fact we need
+to choose we have to choose n equal to 6
+
+ align:start position:0%
+to choose we have to choose n equal to 6
+ 
+
+ align:start position:0%
+to choose we have to choose n equal to 6
+we have to choose the next highest
+
+ align:start position:0%
+we have to choose the next highest
+ 
+
+ align:start position:0%
+we have to choose the next highest
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+value choosing n equal to 6 we then have
+
+ align:start position:0%
+value choosing n equal to 6 we then have
+ 
+
+ align:start position:0%
+value choosing n equal to 6 we then have
+the choice of exactly satisfying this
+
+ align:start position:0%
+the choice of exactly satisfying this
+ 
+
+ align:start position:0%
+the choice of exactly satisfying this
+equation or exactly satisfying this
+
+ align:start position:0%
+equation or exactly satisfying this
+ 
+
+ align:start position:0%
+equation or exactly satisfying this
+equation or in fact not satisfying
+
+ align:start position:0%
+equation or in fact not satisfying
+ 
+
+ align:start position:0%
+equation or in fact not satisfying
+either one of them but playing back and
+
+ align:start position:0%
+either one of them but playing back and
+ 
+
+ align:start position:0%
+either one of them but playing back and
+forth between the
+
+ align:start position:0%
+forth between the
+ 
+
+ align:start position:0%
+forth between the
+two well let's do it in a particular way
+
+ align:start position:0%
+two well let's do it in a particular way
+ 
+
+ align:start position:0%
+two well let's do it in a particular way
+we can for
+
+ align:start position:0%
+we can for
+ 
+
+ align:start position:0%
+we can for
+example exactly meet the stop Bend
+
+ align:start position:0%
+example exactly meet the stop Bend
+ 
+
+ align:start position:0%
+example exactly meet the stop Bend
+specific ations in other words we can
+
+ align:start position:0%
+specific ations in other words we can
+ 
+
+ align:start position:0%
+specific ations in other words we can
+use Nal 6 in this equation and solve for
+
+ align:start position:0%
+use Nal 6 in this equation and solve for
+ 
+
+ align:start position:0%
+use Nal 6 in this equation and solve for
+Omega Sub C in which case the pass band
+
+ align:start position:0%
+Omega Sub C in which case the pass band
+ 
+
+ align:start position:0%
+Omega Sub C in which case the pass band
+specifications will be
+
+ align:start position:0%
+specifications will be
+ 
+
+ align:start position:0%
+specifications will be
+exceeded recall that in the impulse and
+
+ align:start position:0%
+exceeded recall that in the impulse and
+ 
+
+ align:start position:0%
+exceeded recall that in the impulse and
+variant design we did it the other way
+
+ align:start position:0%
+variant design we did it the other way
+ 
+
+ align:start position:0%
+variant design we did it the other way
+around we met exactly the pass band
+
+ align:start position:0%
+around we met exactly the pass band
+ 
+
+ align:start position:0%
+around we met exactly the pass band
+specifications in which case the stop
+
+ align:start position:0%
+specifications in which case the stop
+ 
+
+ align:start position:0%
+specifications in which case the stop
+Bend specs were exceeded but there we
+
+ align:start position:0%
+Bend specs were exceeded but there we
+ 
+
+ align:start position:0%
+Bend specs were exceeded but there we
+had a good reason for doing that the
+
+ align:start position:0%
+had a good reason for doing that the
+ 
+
+ align:start position:0%
+had a good reason for doing that the
+reason that we did that is because we
+
+ align:start position:0%
+reason that we did that is because we
+ 
+
+ align:start position:0%
+reason that we did that is because we
+knew in advance that in any case the p b
+
+ align:start position:0%
+knew in advance that in any case the p b
+ 
+
+ align:start position:0%
+knew in advance that in any case the p b
+specs wouldn't be met exactly because of
+
+ align:start position:0%
+specs wouldn't be met exactly because of
+ 
+
+ align:start position:0%
+specs wouldn't be met exactly because of
+the effect of aliasing for the bilinear
+
+ align:start position:0%
+the effect of aliasing for the bilinear
+ 
+
+ align:start position:0%
+the effect of aliasing for the bilinear
+transformation we don't have a problem
+
+ align:start position:0%
+transformation we don't have a problem
+ 
+
+ align:start position:0%
+transformation we don't have a problem
+with aliasing so in fact we're free to
+
+ align:start position:0%
+with aliasing so in fact we're free to
+ 
+
+ align:start position:0%
+with aliasing so in fact we're free to
+play with this flexibility in a more
+
+ align:start position:0%
+play with this flexibility in a more
+ 
+
+ align:start position:0%
+play with this flexibility in a more
+General way all right well in any case
+
+ align:start position:0%
+General way all right well in any case
+ 
+
+ align:start position:0%
+General way all right well in any case
+then if we meet the stop end specs
+
+ align:start position:0%
+then if we meet the stop end specs
+ 
+
+ align:start position:0%
+then if we meet the stop end specs
+substituting n equal 6 in this equation
+
+ align:start position:0%
+substituting n equal 6 in this equation
+ 
+
+ align:start position:0%
+substituting n equal 6 in this equation
+and solving for Omega Sub C we end up
+
+ align:start position:0%
+and solving for Omega Sub C we end up
+ 
+
+ align:start position:0%
+and solving for Omega Sub C we end up
+with a value for Omega subc which is 766
+
+ align:start position:0%
+with a value for Omega subc which is 766
+ 
+
+ align:start position:0%
+with a value for Omega subc which is 766
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+two and so this then gives us the
+
+ align:start position:0%
+two and so this then gives us the
+ 
+
+ align:start position:0%
+two and so this then gives us the
+parameters Omega Sub C and N for the
+
+ align:start position:0%
+parameters Omega Sub C and N for the
+ 
+
+ align:start position:0%
+parameters Omega Sub C and N for the
+analog Butterworth
+
+ align:start position:0%
+analog Butterworth
+ 
+
+ align:start position:0%
+analog Butterworth
+filter we can then use those
+
+ align:start position:0%
+filter we can then use those
+ 
+
+ align:start position:0%
+filter we can then use those
+specifications again to generate the
+
+ align:start position:0%
+specifications again to generate the
+ 
+
+ align:start position:0%
+specifications again to generate the
+pole pattern for the squared magnitude
+
+ align:start position:0%
+pole pattern for the squared magnitude
+ 
+
+ align:start position:0%
+pole pattern for the squared magnitude
+function H sub a of stimes H sub a of
+
+ align:start position:0%
+function H sub a of stimes H sub a of
+ 
+
+ align:start position:0%
+function H sub a of stimes H sub a of
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s factor this by choosing the left half
+
+ align:start position:0%
+s factor this by choosing the left half
+ 
+
+ align:start position:0%
+s factor this by choosing the left half
+plane poles in the S plane and then
+
+ align:start position:0%
+plane poles in the S plane and then
+ 
+
+ align:start position:0%
+plane poles in the S plane and then
+mapping this function to a digital
+
+ align:start position:0%
+mapping this function to a digital
+ 
+
+ align:start position:0%
+mapping this function to a digital
+filter using the bilinear transformation
+
+ align:start position:0%
+filter using the bilinear transformation
+ 
+
+ align:start position:0%
+filter using the bilinear transformation
+and let's now look at how this filter
+
+ align:start position:0%
+and let's now look at how this filter
+ 
+
+ align:start position:0%
+and let's now look at how this filter
+comes out as compared with
+
+ align:start position:0%
+comes out as compared with
+ 
+
+ align:start position:0%
+comes out as compared with
+the digital filter that we obtained by
+
+ align:start position:0%
+the digital filter that we obtained by
+ 
+
+ align:start position:0%
+the digital filter that we obtained by
+digital Butterworth filter that we
+
+ align:start position:0%
+digital Butterworth filter that we
+ 
+
+ align:start position:0%
+digital Butterworth filter that we
+obtained by using impulse and
+
+ align:start position:0%
+obtained by using impulse and
+ 
+
+ align:start position:0%
+obtained by using impulse and
+variance well again I have a display of
+
+ align:start position:0%
+variance well again I have a display of
+ 
+
+ align:start position:0%
+variance well again I have a display of
+the mag magnitude of the frequency
+
+ align:start position:0%
+the mag magnitude of the frequency
+ 
+
+ align:start position:0%
+the mag magnitude of the frequency
+response and also the gain in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DB from what you may recall from the
+
+ align:start position:0%
+DB from what you may recall from the
+ 
+
+ align:start position:0%
+DB from what you may recall from the
+curve that I showed
+
+ align:start position:0%
+curve that I showed
+ 
+
+ align:start position:0%
+curve that I showed
+previously this looks roughly the same
+
+ align:start position:0%
+previously this looks roughly the same
+ 
+
+ align:start position:0%
+previously this looks roughly the same
+it's it's a monotonic filter and drops
+
+ align:start position:0%
+it's it's a monotonic filter and drops
+ 
+
+ align:start position:0%
+it's it's a monotonic filter and drops
+off U it's down by some amount at 0 2 pi
+
+ align:start position:0%
+off U it's down by some amount at 0 2 pi
+ 
+
+ align:start position:0%
+off U it's down by some amount at 0 2 pi
+and the stop Bend is at 3
+
+ align:start position:0%
+and the stop Bend is at 3
+ 
+
+ align:start position:0%
+and the stop Bend is at 3
+Pi in particular according to the
+
+ align:start position:0%
+Pi in particular according to the
+ 
+
+ align:start position:0%
+Pi in particular according to the
+specifications we wanted this to be down
+
+ align:start position:0%
+specifications we wanted this to be down
+ 
+
+ align:start position:0%
+specifications we wanted this to be down
+by no more than 1 DB at 0 2 pi well uh
+
+ align:start position:0%
+by no more than 1 DB at 0 2 pi well uh
+ 
+
+ align:start position:0%
+by no more than 1 DB at 0 2 pi well uh
+it's hard to again to see that this is 1
+
+ align:start position:0%
+it's hard to again to see that this is 1
+ 
+
+ align:start position:0%
+it's hard to again to see that this is 1
+DB or less but if we look at 3 Pi we can
+
+ align:start position:0%
+DB or less but if we look at 3 Pi we can
+ 
+
+ align:start position:0%
+DB or less but if we look at 3 Pi we can
+see that this is in fact exactly down by
+
+ align:start position:0%
+see that this is in fact exactly down by
+ 
+
+ align:start position:0%
+see that this is in fact exactly down by
+15 DB and that's the way that's the way
+
+ align:start position:0%
+15 DB and that's the way that's the way
+ 
+
+ align:start position:0%
+15 DB and that's the way that's the way
+that we designed it we designed it to
+
+ align:start position:0%
+that we designed it we designed it to
+ 
+
+ align:start position:0%
+that we designed it we designed it to
+exactly meet the stop end cut off and
+
+ align:start position:0%
+exactly meet the stop end cut off and
+ 
+
+ align:start position:0%
+exactly meet the stop end cut off and
+exceed the pass fand cut
+
+ align:start position:0%
+exceed the pass fand cut
+ 
+
+ align:start position:0%
+exceed the pass fand cut
+off and then the frequency response
+
+ align:start position:0%
+off and then the frequency response
+ 
+
+ align:start position:0%
+off and then the frequency response
+continues on from there uh it's
+
+ align:start position:0%
+continues on from there uh it's
+ 
+
+ align:start position:0%
+continues on from there uh it's
+interesting in fact to compare the
+
+ align:start position:0%
+interesting in fact to compare the
+ 
+
+ align:start position:0%
+interesting in fact to compare the
+design that we got from the bilinear
+
+ align:start position:0%
+design that we got from the bilinear
+ 
+
+ align:start position:0%
+design that we got from the bilinear
+transformation with the design that we
+
+ align:start position:0%
+transformation with the design that we
+ 
+
+ align:start position:0%
+transformation with the design that we
+got previously with impulse and variance
+
+ align:start position:0%
+got previously with impulse and variance
+ 
+
+ align:start position:0%
+got previously with impulse and variance
+and let me do that by superimposing the
+
+ align:start position:0%
+and let me do that by superimposing the
+ 
+
+ align:start position:0%
+and let me do that by superimposing the
+two of them so that the one that I'm
+
+ align:start position:0%
+two of them so that the one that I'm
+ 
+
+ align:start position:0%
+two of them so that the one that I'm
+putting on now is the impulse and
+
+ align:start position:0%
+putting on now is the impulse and
+ 
+
+ align:start position:0%
+putting on now is the impulse and
+variant design and let me just lay
+
+ align:start position:0%
+variant design and let me just lay
+ 
+
+ align:start position:0%
+variant design and let me just lay
+on top of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other okay I think I can
+
+ align:start position:0%
+other okay I think I can
+ 
+
+ align:start position:0%
+other okay I think I can
+uh you can see incidentally that looking
+
+ align:start position:0%
+uh you can see incidentally that looking
+ 
+
+ align:start position:0%
+uh you can see incidentally that looking
+at the frequency response on a magnitude
+
+ align:start position:0%
+at the frequency response on a magnitude
+ 
+
+ align:start position:0%
+at the frequency response on a magnitude
+plot there in fact there are some
+
+ align:start position:0%
+plot there in fact there are some
+ 
+
+ align:start position:0%
+plot there in fact there are some
+differences this line has gotten a
+
+ align:start position:0%
+differences this line has gotten a
+ 
+
+ align:start position:0%
+differences this line has gotten a
+little thicker uh that is the two don't
+
+ align:start position:0%
+little thicker uh that is the two don't
+ 
+
+ align:start position:0%
+little thicker uh that is the two don't
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+superimpose but you can't really see the
+
+ align:start position:0%
+superimpose but you can't really see the
+ 
+
+ align:start position:0%
+superimpose but you can't really see the
+differences whereas you can when we look
+
+ align:start position:0%
+differences whereas you can when we look
+ 
+
+ align:start position:0%
+differences whereas you can when we look
+at this on a logarithmic plot in
+
+ align:start position:0%
+at this on a logarithmic plot in
+ 
+
+ align:start position:0%
+at this on a logarithmic plot in
+particular this is the frequency
+
+ align:start position:0%
+particular this is the frequency
+ 
+
+ align:start position:0%
+particular this is the frequency
+response that corresponded to the
+
+ align:start position:0%
+response that corresponded to the
+ 
+
+ align:start position:0%
+response that corresponded to the
+bilinear
+
+ align:start position:0%
+bilinear
+ 
+
+ align:start position:0%
+bilinear
+transformation this is the frequency
+
+ align:start position:0%
+transformation this is the frequency
+ 
+
+ align:start position:0%
+transformation this is the frequency
+response that corresponded to impulse
+
+ align:start position:0%
+response that corresponded to impulse
+ 
+
+ align:start position:0%
+response that corresponded to impulse
+and variance and this is in general a
+
+ align:start position:0%
+and variance and this is in general a
+ 
+
+ align:start position:0%
+and variance and this is in general a
+characteristic of the use of the
+
+ align:start position:0%
+characteristic of the use of the
+ 
+
+ align:start position:0%
+characteristic of the use of the
+bilinear
+
+ align:start position:0%
+bilinear
+ 
+
+ align:start position:0%
+bilinear
+transformation it's a result essentially
+
+ align:start position:0%
+transformation it's a result essentially
+ 
+
+ align:start position:0%
+transformation it's a result essentially
+of the frequency Distortion because
+
+ align:start position:0%
+of the frequency Distortion because
+ 
+
+ align:start position:0%
+of the frequency Distortion because
+we've taken the frequency axis in the
+
+ align:start position:0%
+we've taken the frequency axis in the
+ 
+
+ align:start position:0%
+we've taken the frequency axis in the
+the continuous time frequency axis as as
+
+ align:start position:0%
+the continuous time frequency axis as as
+ 
+
+ align:start position:0%
+the continuous time frequency axis as as
+you run along it at a constant rate it
+
+ align:start position:0%
+you run along it at a constant rate it
+ 
+
+ align:start position:0%
+you run along it at a constant rate it
+gets compressed more and more into the
+
+ align:start position:0%
+gets compressed more and more into the
+ 
+
+ align:start position:0%
+gets compressed more and more into the
+frequencies into the along the digital
+
+ align:start position:0%
+frequencies into the along the digital
+ 
+
+ align:start position:0%
+frequencies into the along the digital
+frequency axis that wasn't well said but
+
+ align:start position:0%
+frequency axis that wasn't well said but
+ 
+
+ align:start position:0%
+frequency axis that wasn't well said but
+uh what I what I really mean to say is
+
+ align:start position:0%
+uh what I what I really mean to say is
+ 
+
+ align:start position:0%
+uh what I what I really mean to say is
+as we walk along here at a constant rate
+
+ align:start position:0%
+as we walk along here at a constant rate
+ 
+
+ align:start position:0%
+as we walk along here at a constant rate
+the farther we walk the faster we're
+
+ align:start position:0%
+the farther we walk the faster we're
+ 
+
+ align:start position:0%
+the farther we walk the faster we're
+running along the J Omega axis and
+
+ align:start position:0%
+running along the J Omega axis and
+ 
+
+ align:start position:0%
+running along the J Omega axis and
+that's why in fact this will the the use
+
+ align:start position:0%
+that's why in fact this will the the use
+ 
+
+ align:start position:0%
+that's why in fact this will the the use
+of the bilinear transformation
+
+ align:start position:0%
+of the bilinear transformation
+ 
+
+ align:start position:0%
+of the bilinear transformation
+on a low pass filter will give higher
+
+ align:start position:0%
+on a low pass filter will give higher
+ 
+
+ align:start position:0%
+on a low pass filter will give higher
+frequency atten better attenuation at
+
+ align:start position:0%
+frequency atten better attenuation at
+ 
+
+ align:start position:0%
+frequency atten better attenuation at
+the higher frequencies then impulse and
+
+ align:start position:0%
+the higher frequencies then impulse and
+ 
+
+ align:start position:0%
+the higher frequencies then impulse and
+variance will and I don't know if you
+
+ align:start position:0%
+variance will and I don't know if you
+ 
+
+ align:start position:0%
+variance will and I don't know if you
+can really see the fact that the uh pass
+
+ align:start position:0%
+can really see the fact that the uh pass
+ 
+
+ align:start position:0%
+can really see the fact that the uh pass
+band specs were exceeded for
+
+ align:start position:0%
+band specs were exceeded for
+ 
+
+ align:start position:0%
+band specs were exceeded for
+the um for the impulse for the bilinear
+
+ align:start position:0%
+the um for the impulse for the bilinear
+ 
+
+ align:start position:0%
+the um for the impulse for the bilinear
+design uh in fact when you look at these
+
+ align:start position:0%
+design uh in fact when you look at these
+ 
+
+ align:start position:0%
+design uh in fact when you look at these
+view graphs in the study guide I think
+
+ align:start position:0%
+view graphs in the study guide I think
+ 
+
+ align:start position:0%
+view graphs in the study guide I think
+you'll see that for impulse and variance
+
+ align:start position:0%
+you'll see that for impulse and variance
+ 
+
+ align:start position:0%
+you'll see that for impulse and variance
+the uh curve is slightly lower than it
+
+ align:start position:0%
+the uh curve is slightly lower than it
+ 
+
+ align:start position:0%
+the uh curve is slightly lower than it
+is for the bilinear
+
+ align:start position:0%
+is for the bilinear
+ 
+
+ align:start position:0%
+is for the bilinear
+transformation okay well look this is a
+
+ align:start position:0%
+transformation okay well look this is a
+ 
+
+ align:start position:0%
+transformation okay well look this is a
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+example that hopefully at least
+
+ align:start position:0%
+example that hopefully at least
+ 
+
+ align:start position:0%
+example that hopefully at least
+illustrates for you the basic procedure
+
+ align:start position:0%
+illustrates for you the basic procedure
+ 
+
+ align:start position:0%
+illustrates for you the basic procedure
+involved in carrying through a design of
+
+ align:start position:0%
+involved in carrying through a design of
+ 
+
+ align:start position:0%
+involved in carrying through a design of
+an infinite impulse response filter
+
+ align:start position:0%
+an infinite impulse response filter
+ 
+
+ align:start position:0%
+an infinite impulse response filter
+using impulse and variance and the
+
+ align:start position:0%
+using impulse and variance and the
+ 
+
+ align:start position:0%
+using impulse and variance and the
+bilinear transformation
+
+ align:start position:0%
+bilinear transformation
+ 
+
+ align:start position:0%
+bilinear transformation
+there are other examples that are
+
+ align:start position:0%
+there are other examples that are
+ 
+
+ align:start position:0%
+there are other examples that are
+considered in the text there is a
+
+ align:start position:0%
+considered in the text there is a
+ 
+
+ align:start position:0%
+considered in the text there is a
+discussion of um digital butter uh
+
+ align:start position:0%
+discussion of um digital butter uh
+ 
+
+ align:start position:0%
+discussion of um digital butter uh
+digital chbby Chef filters in other
+
+ align:start position:0%
+digital chbby Chef filters in other
+ 
+
+ align:start position:0%
+digital chbby Chef filters in other
+words digital designs beginning from an
+
+ align:start position:0%
+words digital designs beginning from an
+ 
+
+ align:start position:0%
+words digital designs beginning from an
+analog chbby Chef filter and you'll also
+
+ align:start position:0%
+analog chbby Chef filter and you'll also
+ 
+
+ align:start position:0%
+analog chbby Chef filter and you'll also
+have an opportunity to carry through
+
+ align:start position:0%
+have an opportunity to carry through
+ 
+
+ align:start position:0%
+have an opportunity to carry through
+some designs in the study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guide a point that I would like to
+
+ align:start position:0%
+guide a point that I would like to
+ 
+
+ align:start position:0%
+guide a point that I would like to
+mention briefly is that most of the
+
+ align:start position:0%
+mention briefly is that most of the
+ 
+
+ align:start position:0%
+mention briefly is that most of the
+discussion in fact all of the discussion
+
+ align:start position:0%
+discussion in fact all of the discussion
+ 
+
+ align:start position:0%
+discussion in fact all of the discussion
+that we've gone through has focused
+
+ align:start position:0%
+that we've gone through has focused
+ 
+
+ align:start position:0%
+that we've gone through has focused
+entirely on low pass filters in fact the
+
+ align:start position:0%
+entirely on low pass filters in fact the
+ 
+
+ align:start position:0%
+entirely on low pass filters in fact the
+discussion generalizes in a fairly
+
+ align:start position:0%
+discussion generalizes in a fairly
+ 
+
+ align:start position:0%
+discussion generalizes in a fairly
+straightforward way to band pass band
+
+ align:start position:0%
+straightforward way to band pass band
+ 
+
+ align:start position:0%
+straightforward way to band pass band
+stop High Pass Etc filters in particular
+
+ align:start position:0%
+stop High Pass Etc filters in particular
+ 
+
+ align:start position:0%
+stop High Pass Etc filters in particular
+as is discussed in some detail in the
+
+ align:start position:0%
+as is discussed in some detail in the
+ 
+
+ align:start position:0%
+as is discussed in some detail in the
+text there are a class of frequency
+
+ align:start position:0%
+text there are a class of frequency
+ 
+
+ align:start position:0%
+text there are a class of frequency
+Transformations that allow low pass
+
+ align:start position:0%
+Transformations that allow low pass
+ 
+
+ align:start position:0%
+Transformations that allow low pass
+designs to get converted to band stop
+
+ align:start position:0%
+designs to get converted to band stop
+ 
+
+ align:start position:0%
+designs to get converted to band stop
+and Pass High Pass Etc
+
+ align:start position:0%
+and Pass High Pass Etc
+ 
+
+ align:start position:0%
+and Pass High Pass Etc
+designs so this concludes our discussion
+
+ align:start position:0%
+designs so this concludes our discussion
+ 
+
+ align:start position:0%
+designs so this concludes our discussion
+of design procedures
+
+ align:start position:0%
+of design procedures
+ 
+
+ align:start position:0%
+of design procedures
+for recursive or infinite impulse
+
+ align:start position:0%
+for recursive or infinite impulse
+ 
+
+ align:start position:0%
+for recursive or infinite impulse
+response digital filters in the next
+
+ align:start position:0%
+response digital filters in the next
+ 
+
+ align:start position:0%
+response digital filters in the next
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+I'll discuss the design of finite
+
+ align:start position:0%
+I'll discuss the design of finite
+ 
+
+ align:start position:0%
+I'll discuss the design of finite
+impulse response filters and in
+
+ align:start position:0%
+impulse response filters and in
+ 
+
+ align:start position:0%
+impulse response filters and in
+particular introduce a number of designs
+
+ align:start position:0%
+particular introduce a number of designs
+ 
+
+ align:start position:0%
+particular introduce a number of designs
+uh one of which corresponds to a class
+
+ align:start position:0%
+uh one of which corresponds to a class
+ 
+
+ align:start position:0%
+uh one of which corresponds to a class
+of algor rmic designs thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/JvtqThS69bw.txt b/JvtqThS69bw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc49e800d157206b07b1cfa0bf532d3fdf153861
--- /dev/null
+++ b/JvtqThS69bw.txt
@@ -0,0 +1,1827 @@
+align:start position:0%
+ 
+in this video we'll see how to build a
+
+ align:start position:0%
+in this video we'll see how to build a
+ 
+
+ align:start position:0%
+in this video we'll see how to build a
+cart model in our let's start by reading
+
+ align:start position:0%
+cart model in our let's start by reading
+ 
+
+ align:start position:0%
+cart model in our let's start by reading
+in the data file Stephens CSV will call
+
+ align:start position:0%
+in the data file Stephens CSV will call
+ 
+
+ align:start position:0%
+in the data file Stephens CSV will call
+our data frame Stephens and use the read
+
+ align:start position:0%
+our data frame Stephens and use the read
+ 
+
+ align:start position:0%
+our data frame Stephens and use the read
+dot CSV function to read in the data
+
+ align:start position:0%
+dot CSV function to read in the data
+ 
+
+ align:start position:0%
+dot CSV function to read in the data
+file Stephens
+
+ align:start position:0%
+file Stephens
+ 
+
+ align:start position:0%
+file Stephens
+dot CSV remember to navigate to the
+
+ align:start position:0%
+dot CSV remember to navigate to the
+ 
+
+ align:start position:0%
+dot CSV remember to navigate to the
+directory on your computer containing
+
+ align:start position:0%
+directory on your computer containing
+ 
+
+ align:start position:0%
+directory on your computer containing
+the file Stephens CSV first now let's
+
+ align:start position:0%
+the file Stephens CSV first now let's
+ 
+
+ align:start position:0%
+the file Stephens CSV first now let's
+take a look at our data using the STR
+
+ align:start position:0%
+take a look at our data using the STR
+ 
+
+ align:start position:0%
+take a look at our data using the STR
+function we have five hundred and
+
+ align:start position:0%
+function we have five hundred and
+ 
+
+ align:start position:0%
+function we have five hundred and
+sixty-six observations or Supreme Court
+
+ align:start position:0%
+sixty-six observations or Supreme Court
+ 
+
+ align:start position:0%
+sixty-six observations or Supreme Court
+cases and nine different variables
+
+ align:start position:0%
+cases and nine different variables
+ 
+
+ align:start position:0%
+cases and nine different variables
+docket is just a unique identifier for
+
+ align:start position:0%
+docket is just a unique identifier for
+ 
+
+ align:start position:0%
+docket is just a unique identifier for
+each case and turn'd is the year of the
+
+ align:start position:0%
+each case and turn'd is the year of the
+ 
+
+ align:start position:0%
+each case and turn'd is the year of the
+case then we have our six independent
+
+ align:start position:0%
+case then we have our six independent
+ 
+
+ align:start position:0%
+case then we have our six independent
+variables the circuit court of origin
+
+ align:start position:0%
+variables the circuit court of origin
+ 
+
+ align:start position:0%
+variables the circuit court of origin
+the issue area of the case the type of
+
+ align:start position:0%
+the issue area of the case the type of
+ 
+
+ align:start position:0%
+the issue area of the case the type of
+petitioner the type of respondent the
+
+ align:start position:0%
+petitioner the type of respondent the
+ 
+
+ align:start position:0%
+petitioner the type of respondent the
+lower court direction and whether or not
+
+ align:start position:0%
+lower court direction and whether or not
+ 
+
+ align:start position:0%
+lower court direction and whether or not
+the petitioner argued that a law or
+
+ align:start position:0%
+the petitioner argued that a law or
+ 
+
+ align:start position:0%
+the petitioner argued that a law or
+practice was unconstitutional the last
+
+ align:start position:0%
+practice was unconstitutional the last
+ 
+
+ align:start position:0%
+practice was unconstitutional the last
+variable is our dependent variable
+
+ align:start position:0%
+variable is our dependent variable
+ 
+
+ align:start position:0%
+variable is our dependent variable
+whether or not justice Stevens voted to
+
+ align:start position:0%
+whether or not justice Stevens voted to
+ 
+
+ align:start position:0%
+whether or not justice Stevens voted to
+reverse the case one for reverse and
+
+ align:start position:0%
+reverse the case one for reverse and
+ 
+
+ align:start position:0%
+reverse the case one for reverse and
+zero for affirm now before building
+
+ align:start position:0%
+zero for affirm now before building
+ 
+
+ align:start position:0%
+zero for affirm now before building
+models we need to split our data into a
+
+ align:start position:0%
+models we need to split our data into a
+ 
+
+ align:start position:0%
+models we need to split our data into a
+training set and a testing set we'll do
+
+ align:start position:0%
+training set and a testing set we'll do
+ 
+
+ align:start position:0%
+training set and a testing set we'll do
+this using the sample dot split function
+
+ align:start position:0%
+this using the sample dot split function
+ 
+
+ align:start position:0%
+this using the sample dot split function
+like we did last week for logistic
+
+ align:start position:0%
+like we did last week for logistic
+ 
+
+ align:start position:0%
+like we did last week for logistic
+regression first we need to load the
+
+ align:start position:0%
+regression first we need to load the
+ 
+
+ align:start position:0%
+regression first we need to load the
+package CA tools with library CA tools
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so that we all get the same split we
+
+ align:start position:0%
+now so that we all get the same split we
+ 
+
+ align:start position:0%
+now so that we all get the same split we
+need to set the seed remember that this
+
+ align:start position:0%
+need to set the seed remember that this
+ 
+
+ align:start position:0%
+need to set the seed remember that this
+can be any number as long as we all use
+
+ align:start position:0%
+can be any number as long as we all use
+ 
+
+ align:start position:0%
+can be any number as long as we all use
+the same number let's set the seed to
+
+ align:start position:0%
+the same number let's set the seed to
+ 
+
+ align:start position:0%
+the same number let's set the seed to
+3,000 now let's create our split we'll
+
+ align:start position:0%
+3,000 now let's create our split we'll
+ 
+
+ align:start position:0%
+3,000 now let's create our split we'll
+call it SPL and we'll use the sample dot
+
+ align:start position:0%
+call it SPL and we'll use the sample dot
+ 
+
+ align:start position:0%
+call it SPL and we'll use the sample dot
+split function where the first argument
+
+ align:start position:0%
+split function where the first argument
+ 
+
+ align:start position:0%
+split function where the first argument
+needs to be
+
+ align:start position:0%
+needs to be
+ 
+
+ align:start position:0%
+needs to be
+outcome variable Stephens reverse and
+
+ align:start position:0%
+outcome variable Stephens reverse and
+ 
+
+ align:start position:0%
+outcome variable Stephens reverse and
+then the second argument is the split
+
+ align:start position:0%
+then the second argument is the split
+ 
+
+ align:start position:0%
+then the second argument is the split
+ratio or the percentage of data that we
+
+ align:start position:0%
+ratio or the percentage of data that we
+ 
+
+ align:start position:0%
+ratio or the percentage of data that we
+want to put in the training set in this
+
+ align:start position:0%
+want to put in the training set in this
+ 
+
+ align:start position:0%
+want to put in the training set in this
+case we'll put 70% of the data in the
+
+ align:start position:0%
+case we'll put 70% of the data in the
+ 
+
+ align:start position:0%
+case we'll put 70% of the data in the
+training set now let's create our
+
+ align:start position:0%
+training set now let's create our
+ 
+
+ align:start position:0%
+training set now let's create our
+training and testing sets using the
+
+ align:start position:0%
+training and testing sets using the
+ 
+
+ align:start position:0%
+training and testing sets using the
+subset function we'll call our training
+
+ align:start position:0%
+subset function we'll call our training
+ 
+
+ align:start position:0%
+subset function we'll call our training
+set train and we'll take a subset of
+
+ align:start position:0%
+set train and we'll take a subset of
+ 
+
+ align:start position:0%
+set train and we'll take a subset of
+Stephens only taking the observations
+
+ align:start position:0%
+Stephens only taking the observations
+ 
+
+ align:start position:0%
+Stephens only taking the observations
+for which SPL is equal to true we'll
+
+ align:start position:0%
+for which SPL is equal to true we'll
+ 
+
+ align:start position:0%
+for which SPL is equal to true we'll
+call our testing set test and here take
+
+ align:start position:0%
+call our testing set test and here take
+ 
+
+ align:start position:0%
+call our testing set test and here take
+a subset of Stephens but this time
+
+ align:start position:0%
+a subset of Stephens but this time
+ 
+
+ align:start position:0%
+a subset of Stephens but this time
+taking the observations for which SPL is
+
+ align:start position:0%
+taking the observations for which SPL is
+ 
+
+ align:start position:0%
+taking the observations for which SPL is
+equal to false now we're ready to build
+
+ align:start position:0%
+equal to false now we're ready to build
+ 
+
+ align:start position:0%
+equal to false now we're ready to build
+our cart model first we need to install
+
+ align:start position:0%
+our cart model first we need to install
+ 
+
+ align:start position:0%
+our cart model first we need to install
+and load the are part package and the
+
+ align:start position:0%
+and load the are part package and the
+ 
+
+ align:start position:0%
+and load the are part package and the
+are part plotting package remember that
+
+ align:start position:0%
+are part plotting package remember that
+ 
+
+ align:start position:0%
+are part plotting package remember that
+to install a new package we use the
+
+ align:start position:0%
+to install a new package we use the
+ 
+
+ align:start position:0%
+to install a new package we use the
+install dot packages function and then
+
+ align:start position:0%
+install dot packages function and then
+ 
+
+ align:start position:0%
+install dot packages function and then
+in parentheses in quotes
+
+ align:start position:0%
+in parentheses in quotes
+ 
+
+ align:start position:0%
+in parentheses in quotes
+give the name of the package we want to
+
+ align:start position:0%
+give the name of the package we want to
+ 
+
+ align:start position:0%
+give the name of the package we want to
+install in this case our part after you
+
+ align:start position:0%
+install in this case our part after you
+ 
+
+ align:start position:0%
+install in this case our part after you
+hit enter a Korean mere should pop up
+
+ align:start position:0%
+hit enter a Korean mere should pop up
+ 
+
+ align:start position:0%
+hit enter a Korean mere should pop up
+asking you to pick a location near you
+
+ align:start position:0%
+asking you to pick a location near you
+ 
+
+ align:start position:0%
+asking you to pick a location near you
+go ahead and pick the appropriate
+
+ align:start position:0%
+go ahead and pick the appropriate
+ 
+
+ align:start position:0%
+go ahead and pick the appropriate
+location in my case I'll pick
+
+ align:start position:0%
+location in my case I'll pick
+ 
+
+ align:start position:0%
+location in my case I'll pick
+Pennsylvania in the United States and
+
+ align:start position:0%
+Pennsylvania in the United States and
+ 
+
+ align:start position:0%
+Pennsylvania in the United States and
+hit OK you should see some lines running
+
+ align:start position:0%
+hit OK you should see some lines running
+ 
+
+ align:start position:0%
+hit OK you should see some lines running
+your our console and then when you're
+
+ align:start position:0%
+your our console and then when you're
+ 
+
+ align:start position:0%
+your our console and then when you're
+back to the blinking cursor load the
+
+ align:start position:0%
+back to the blinking cursor load the
+ 
+
+ align:start position:0%
+back to the blinking cursor load the
+package with library our part now let's
+
+ align:start position:0%
+package with library our part now let's
+ 
+
+ align:start position:0%
+package with library our part now let's
+install the package
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our part dot plot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again some line should run in your our
+
+ align:start position:0%
+again some line should run in your our
+ 
+
+ align:start position:0%
+again some line should run in your our
+console and when you're back to the
+
+ align:start position:0%
+console and when you're back to the
+ 
+
+ align:start position:0%
+console and when you're back to the
+blinking cursor load the package with
+
+ align:start position:0%
+blinking cursor load the package with
+ 
+
+ align:start position:0%
+blinking cursor load the package with
+library our part dot plot now we can
+
+ align:start position:0%
+library our part dot plot now we can
+ 
+
+ align:start position:0%
+library our part dot plot now we can
+create our cart model using the our part
+
+ align:start position:0%
+create our cart model using the our part
+ 
+
+ align:start position:0%
+create our cart model using the our part
+function we'll call our model Stephens
+
+ align:start position:0%
+function we'll call our model Stephens
+ 
+
+ align:start position:0%
+function we'll call our model Stephens
+tree and we'll use the art part function
+
+ align:start position:0%
+tree and we'll use the art part function
+ 
+
+ align:start position:0%
+tree and we'll use the art part function
+where the first argument is the same as
+
+ align:start position:0%
+where the first argument is the same as
+ 
+
+ align:start position:0%
+where the first argument is the same as
+if we were building a linear or logistic
+
+ align:start position:0%
+if we were building a linear or logistic
+ 
+
+ align:start position:0%
+if we were building a linear or logistic
+regression model we give our dependent
+
+ align:start position:0%
+regression model we give our dependent
+ 
+
+ align:start position:0%
+regression model we give our dependent
+variable in our case reverse followed by
+
+ align:start position:0%
+variable in our case reverse followed by
+ 
+
+ align:start position:0%
+variable in our case reverse followed by
+a tilde sign and then the independent
+
+ align:start position:0%
+a tilde sign and then the independent
+ 
+
+ align:start position:0%
+a tilde sign and then the independent
+variable is separated by plus signs so
+
+ align:start position:0%
+variable is separated by plus signs so
+ 
+
+ align:start position:0%
+variable is separated by plus signs so
+circuit plus issue plus petitioner plus
+
+ align:start position:0%
+circuit plus issue plus petitioner plus
+ 
+
+ align:start position:0%
+circuit plus issue plus petitioner plus
+respondent plus lower-court
+
+ align:start position:0%
+respondent plus lower-court
+ 
+
+ align:start position:0%
+respondent plus lower-court
+plus unconstitutional we also need to
+
+ align:start position:0%
+plus unconstitutional we also need to
+ 
+
+ align:start position:0%
+plus unconstitutional we also need to
+give our data set that should be used to
+
+ align:start position:0%
+give our data set that should be used to
+ 
+
+ align:start position:0%
+give our data set that should be used to
+build our model which in our case is
+
+ align:start position:0%
+build our model which in our case is
+ 
+
+ align:start position:0%
+build our model which in our case is
+trained now we'll give two additional
+
+ align:start position:0%
+trained now we'll give two additional
+ 
+
+ align:start position:0%
+trained now we'll give two additional
+arguments here
+
+ align:start position:0%
+arguments here
+ 
+
+ align:start position:0%
+arguments here
+the first one is method equals class
+
+ align:start position:0%
+the first one is method equals class
+ 
+
+ align:start position:0%
+the first one is method equals class
+this tells our part to build a
+
+ align:start position:0%
+this tells our part to build a
+ 
+
+ align:start position:0%
+this tells our part to build a
+classification tree instead of a
+
+ align:start position:0%
+classification tree instead of a
+ 
+
+ align:start position:0%
+classification tree instead of a
+regression tree you'll see how we can
+
+ align:start position:0%
+regression tree you'll see how we can
+ 
+
+ align:start position:0%
+regression tree you'll see how we can
+create regression trees in recitation
+
+ align:start position:0%
+create regression trees in recitation
+ 
+
+ align:start position:0%
+create regression trees in recitation
+the last argument we'll give is min
+
+ align:start position:0%
+the last argument we'll give is min
+ 
+
+ align:start position:0%
+the last argument we'll give is min
+bucket equals 25 this limits the tree so
+
+ align:start position:0%
+bucket equals 25 this limits the tree so
+ 
+
+ align:start position:0%
+bucket equals 25 this limits the tree so
+that it doesn't over fit to our training
+
+ align:start position:0%
+that it doesn't over fit to our training
+ 
+
+ align:start position:0%
+that it doesn't over fit to our training
+set we selected a value of 25 but we
+
+ align:start position:0%
+set we selected a value of 25 but we
+ 
+
+ align:start position:0%
+set we selected a value of 25 but we
+could pick a smaller or larger value
+
+ align:start position:0%
+could pick a smaller or larger value
+ 
+
+ align:start position:0%
+could pick a smaller or larger value
+we'll see another way to limit the tree
+
+ align:start position:0%
+we'll see another way to limit the tree
+ 
+
+ align:start position:0%
+we'll see another way to limit the tree
+later in this lecture now let's plot our
+
+ align:start position:0%
+later in this lecture now let's plot our
+ 
+
+ align:start position:0%
+later in this lecture now let's plot our
+tree using the PRP function where the
+
+ align:start position:0%
+tree using the PRP function where the
+ 
+
+ align:start position:0%
+tree using the PRP function where the
+only argument is the name of our model
+
+ align:start position:0%
+only argument is the name of our model
+ 
+
+ align:start position:0%
+only argument is the name of our model
+Stephens tree you should see the tree
+
+ align:start position:0%
+Stephens tree you should see the tree
+ 
+
+ align:start position:0%
+Stephens tree you should see the tree
+pop up in the graphics window the first
+
+ align:start position:0%
+pop up in the graphics window the first
+ 
+
+ align:start position:0%
+pop up in the graphics window the first
+split of our tree is whether or not the
+
+ align:start position:0%
+split of our tree is whether or not the
+ 
+
+ align:start position:0%
+split of our tree is whether or not the
+lower court decision is liberal if it is
+
+ align:start position:0%
+lower court decision is liberal if it is
+ 
+
+ align:start position:0%
+lower court decision is liberal if it is
+then we move to the left in the tree and
+
+ align:start position:0%
+then we move to the left in the tree and
+ 
+
+ align:start position:0%
+then we move to the left in the tree and
+we check the respondent if the
+
+ align:start position:0%
+we check the respondent if the
+ 
+
+ align:start position:0%
+we check the respondent if the
+respondent is a
+
+ align:start position:0%
+respondent is a
+ 
+
+ align:start position:0%
+respondent is a
+defendant injured person politician
+
+ align:start position:0%
+defendant injured person politician
+ 
+
+ align:start position:0%
+defendant injured person politician
+state or the United States we predict a
+
+ align:start position:0%
+state or the United States we predict a
+ 
+
+ align:start position:0%
+state or the United States we predict a
+zero or affirm you can see here that the
+
+ align:start position:0%
+zero or affirm you can see here that the
+ 
+
+ align:start position:0%
+zero or affirm you can see here that the
+PRP function abbreviates the values of
+
+ align:start position:0%
+PRP function abbreviates the values of
+ 
+
+ align:start position:0%
+PRP function abbreviates the values of
+the independent variables if you're not
+
+ align:start position:0%
+the independent variables if you're not
+ 
+
+ align:start position:0%
+the independent variables if you're not
+sure what the abbreviations are you
+
+ align:start position:0%
+sure what the abbreviations are you
+ 
+
+ align:start position:0%
+sure what the abbreviations are you
+could create a table of the variable to
+
+ align:start position:0%
+could create a table of the variable to
+ 
+
+ align:start position:0%
+could create a table of the variable to
+see all of the possible values PRP will
+
+ align:start position:0%
+see all of the possible values PRP will
+ 
+
+ align:start position:0%
+see all of the possible values PRP will
+select the abbreviation so that they're
+
+ align:start position:0%
+select the abbreviation so that they're
+ 
+
+ align:start position:0%
+select the abbreviation so that they're
+uniquely identifiable so if you made a
+
+ align:start position:0%
+uniquely identifiable so if you made a
+ 
+
+ align:start position:0%
+uniquely identifiable so if you made a
+table you can see that CRI stands for
+
+ align:start position:0%
+table you can see that CRI stands for
+ 
+
+ align:start position:0%
+table you can see that CRI stands for
+criminal defendant inj stands for
+
+ align:start position:0%
+criminal defendant inj stands for
+ 
+
+ align:start position:0%
+criminal defendant inj stands for
+injured person etc so now moving on in
+
+ align:start position:0%
+injured person etc so now moving on in
+ 
+
+ align:start position:0%
+injured person etc so now moving on in
+our tree if the respondent is not one of
+
+ align:start position:0%
+our tree if the respondent is not one of
+ 
+
+ align:start position:0%
+our tree if the respondent is not one of
+these types we move on to the next split
+
+ align:start position:0%
+these types we move on to the next split
+ 
+
+ align:start position:0%
+these types we move on to the next split
+and we check the petitioner if the
+
+ align:start position:0%
+and we check the petitioner if the
+ 
+
+ align:start position:0%
+and we check the petitioner if the
+petitioner is a city employee employer
+
+ align:start position:0%
+petitioner is a city employee employer
+ 
+
+ align:start position:0%
+petitioner is a city employee employer
+government official or politician then
+
+ align:start position:0%
+government official or politician then
+ 
+
+ align:start position:0%
+government official or politician then
+we predict a zero or affirm if not then
+
+ align:start position:0%
+we predict a zero or affirm if not then
+ 
+
+ align:start position:0%
+we predict a zero or affirm if not then
+we check the Circuit Court of origin if
+
+ align:start position:0%
+we check the Circuit Court of origin if
+ 
+
+ align:start position:0%
+we check the Circuit Court of origin if
+it's the tenth first third fourth DC or
+
+ align:start position:0%
+it's the tenth first third fourth DC or
+ 
+
+ align:start position:0%
+it's the tenth first third fourth DC or
+federal court then we predict zero
+
+ align:start position:0%
+federal court then we predict zero
+ 
+
+ align:start position:0%
+federal court then we predict zero
+otherwise we predict one or reverse we
+
+ align:start position:0%
+otherwise we predict one or reverse we
+ 
+
+ align:start position:0%
+otherwise we predict one or reverse we
+can repeat the same process on the other
+
+ align:start position:0%
+can repeat the same process on the other
+ 
+
+ align:start position:0%
+can repeat the same process on the other
+side of the tree if the lower court
+
+ align:start position:0%
+side of the tree if the lower court
+ 
+
+ align:start position:0%
+side of the tree if the lower court
+decision is not liberal comparing this
+
+ align:start position:0%
+decision is not liberal comparing this
+ 
+
+ align:start position:0%
+decision is not liberal comparing this
+to a logistic regression model we can
+
+ align:start position:0%
+to a logistic regression model we can
+ 
+
+ align:start position:0%
+to a logistic regression model we can
+see that it's very interpretable a car
+
+ align:start position:0%
+see that it's very interpretable a car
+ 
+
+ align:start position:0%
+see that it's very interpretable a car
+tree is a series of decision rules which
+
+ align:start position:0%
+tree is a series of decision rules which
+ 
+
+ align:start position:0%
+tree is a series of decision rules which
+can easily be explained now let's see
+
+ align:start position:0%
+can easily be explained now let's see
+ 
+
+ align:start position:0%
+can easily be explained now let's see
+how well our cart model does I'm making
+
+ align:start position:0%
+how well our cart model does I'm making
+ 
+
+ align:start position:0%
+how well our cart model does I'm making
+predictions for the test set so back in
+
+ align:start position:0%
+predictions for the test set so back in
+ 
+
+ align:start position:0%
+predictions for the test set so back in
+our our console we'll call our
+
+ align:start position:0%
+our our console we'll call our
+ 
+
+ align:start position:0%
+our our console we'll call our
+predictions predict cart and we'll use
+
+ align:start position:0%
+predictions predict cart and we'll use
+ 
+
+ align:start position:0%
+predictions predict cart and we'll use
+the predict function where the first
+
+ align:start position:0%
+the predict function where the first
+ 
+
+ align:start position:0%
+the predict function where the first
+argument is the name of our model
+
+ align:start position:0%
+argument is the name of our model
+ 
+
+ align:start position:0%
+argument is the name of our model
+Stephens tree the second argument is the
+
+ align:start position:0%
+Stephens tree the second argument is the
+ 
+
+ align:start position:0%
+Stephens tree the second argument is the
+new data we want to make predictions for
+
+ align:start position:0%
+new data we want to make predictions for
+ 
+
+ align:start position:0%
+new data we want to make predictions for
+tests and we'll add a third argument
+
+ align:start position:0%
+tests and we'll add a third argument
+ 
+
+ align:start position:0%
+tests and we'll add a third argument
+here which is type equals class
+
+ align:start position:0%
+here which is type equals class
+ 
+
+ align:start position:0%
+here which is type equals class
+we need to give this argument we're
+
+ align:start position:0%
+we need to give this argument we're
+ 
+
+ align:start position:0%
+we need to give this argument we're
+making predictions for our cart model if
+
+ align:start position:0%
+making predictions for our cart model if
+ 
+
+ align:start position:0%
+making predictions for our cart model if
+we want the majority class predictions
+
+ align:start position:0%
+we want the majority class predictions
+ 
+
+ align:start position:0%
+we want the majority class predictions
+this is like using a threshold of 0.5
+
+ align:start position:0%
+this is like using a threshold of 0.5
+ 
+
+ align:start position:0%
+this is like using a threshold of 0.5
+we'll see in a few minutes how we can
+
+ align:start position:0%
+we'll see in a few minutes how we can
+ 
+
+ align:start position:0%
+we'll see in a few minutes how we can
+leave this argument out and still get
+
+ align:start position:0%
+leave this argument out and still get
+ 
+
+ align:start position:0%
+leave this argument out and still get
+probabilities from our cart model now
+
+ align:start position:0%
+probabilities from our cart model now
+ 
+
+ align:start position:0%
+probabilities from our cart model now
+let's compute the accuracy of our model
+
+ align:start position:0%
+let's compute the accuracy of our model
+ 
+
+ align:start position:0%
+let's compute the accuracy of our model
+by building a confusion matrix so we'll
+
+ align:start position:0%
+by building a confusion matrix so we'll
+ 
+
+ align:start position:0%
+by building a confusion matrix so we'll
+use the table function and first give
+
+ align:start position:0%
+use the table function and first give
+ 
+
+ align:start position:0%
+use the table function and first give
+the true outcome values test reverse and
+
+ align:start position:0%
+the true outcome values test reverse and
+ 
+
+ align:start position:0%
+the true outcome values test reverse and
+then our predictions predict cart to
+
+ align:start position:0%
+then our predictions predict cart to
+ 
+
+ align:start position:0%
+then our predictions predict cart to
+compute the accuracy we need to add up
+
+ align:start position:0%
+compute the accuracy we need to add up
+ 
+
+ align:start position:0%
+compute the accuracy we need to add up
+the observations we got correct 41 plus
+
+ align:start position:0%
+the observations we got correct 41 plus
+ 
+
+ align:start position:0%
+the observations we got correct 41 plus
+71 divided by the total number of
+
+ align:start position:0%
+71 divided by the total number of
+ 
+
+ align:start position:0%
+71 divided by the total number of
+observations in the table or the total
+
+ align:start position:0%
+observations in the table or the total
+ 
+
+ align:start position:0%
+observations in the table or the total
+number of observations in our test set
+
+ align:start position:0%
+number of observations in our test set
+ 
+
+ align:start position:0%
+number of observations in our test set
+so the accuracy of our cart model is
+
+ align:start position:0%
+so the accuracy of our cart model is
+ 
+
+ align:start position:0%
+so the accuracy of our cart model is
+0.65 9 if you were to build a logistic
+
+ align:start position:0%
+0.65 9 if you were to build a logistic
+ 
+
+ align:start position:0%
+0.65 9 if you were to build a logistic
+regression model you would get an
+
+ align:start position:0%
+regression model you would get an
+ 
+
+ align:start position:0%
+regression model you would get an
+accuracy of 0.6 65 and a baseline model
+
+ align:start position:0%
+accuracy of 0.6 65 and a baseline model
+ 
+
+ align:start position:0%
+accuracy of 0.6 65 and a baseline model
+that always predicts reverse the most
+
+ align:start position:0%
+that always predicts reverse the most
+ 
+
+ align:start position:0%
+that always predicts reverse the most
+common outcome has an accuracy of 0.5
+
+ align:start position:0%
+common outcome has an accuracy of 0.5
+ 
+
+ align:start position:0%
+common outcome has an accuracy of 0.5
+4/7 so our cart model significantly
+
+ align:start position:0%
+4/7 so our cart model significantly
+ 
+
+ align:start position:0%
+4/7 so our cart model significantly
+beats the baseline and is competitive
+
+ align:start position:0%
+beats the baseline and is competitive
+ 
+
+ align:start position:0%
+beats the baseline and is competitive
+with logistic regression it's also much
+
+ align:start position:0%
+with logistic regression it's also much
+ 
+
+ align:start position:0%
+with logistic regression it's also much
+more interpretable than a logistic
+
+ align:start position:0%
+more interpretable than a logistic
+ 
+
+ align:start position:0%
+more interpretable than a logistic
+regression model would be lastly to
+
+ align:start position:0%
+regression model would be lastly to
+ 
+
+ align:start position:0%
+regression model would be lastly to
+evaluate our model let's generate an ROC
+
+ align:start position:0%
+evaluate our model let's generate an ROC
+ 
+
+ align:start position:0%
+evaluate our model let's generate an ROC
+curve for our cart model using the ROC r
+
+ align:start position:0%
+curve for our cart model using the ROC r
+ 
+
+ align:start position:0%
+curve for our cart model using the ROC r
+package first we need to load the
+
+ align:start position:0%
+package first we need to load the
+ 
+
+ align:start position:0%
+package first we need to load the
+package with the library function and
+
+ align:start position:0%
+package with the library function and
+ 
+
+ align:start position:0%
+package with the library function and
+then we need to generate our predictions
+
+ align:start position:0%
+then we need to generate our predictions
+ 
+
+ align:start position:0%
+then we need to generate our predictions
+again this time without the type equals
+
+ align:start position:0%
+again this time without the type equals
+ 
+
+ align:start position:0%
+again this time without the type equals
+class argument we'll call them predict
+
+ align:start position:0%
+class argument we'll call them predict
+ 
+
+ align:start position:0%
+class argument we'll call them predict
+ROC and we'll use the predict function
+
+ align:start position:0%
+ROC and we'll use the predict function
+ 
+
+ align:start position:0%
+ROC and we'll use the predict function
+giving just as the two arguments
+
+ align:start position:0%
+giving just as the two arguments
+ 
+
+ align:start position:0%
+giving just as the two arguments
+Stephens tree and new data equals test
+
+ align:start position:0%
+Stephens tree and new data equals test
+ 
+
+ align:start position:0%
+Stephens tree and new data equals test
+let's take a look at what this looks
+
+ align:start position:0%
+let's take a look at what this looks
+ 
+
+ align:start position:0%
+let's take a look at what this looks
+like by just typing predict ROC and
+
+ align:start position:0%
+like by just typing predict ROC and
+ 
+
+ align:start position:0%
+like by just typing predict ROC and
+hitting enter for each observation in
+
+ align:start position:0%
+hitting enter for each observation in
+ 
+
+ align:start position:0%
+hitting enter for each observation in
+the test set it gives two numbers which
+
+ align:start position:0%
+the test set it gives two numbers which
+ 
+
+ align:start position:0%
+the test set it gives two numbers which
+can be thought of as the probability of
+
+ align:start position:0%
+can be thought of as the probability of
+ 
+
+ align:start position:0%
+can be thought of as the probability of
+outcome 0 and the probability of outcome
+
+ align:start position:0%
+outcome 0 and the probability of outcome
+ 
+
+ align:start position:0%
+outcome 0 and the probability of outcome
+1 more concretely each
+
+ align:start position:0%
+1 more concretely each
+ 
+
+ align:start position:0%
+1 more concretely each
+that observation is classified into a
+
+ align:start position:0%
+that observation is classified into a
+ 
+
+ align:start position:0%
+that observation is classified into a
+subset or bucket of our cart tree these
+
+ align:start position:0%
+subset or bucket of our cart tree these
+ 
+
+ align:start position:0%
+subset or bucket of our cart tree these
+numbers give the percentage of training
+
+ align:start position:0%
+numbers give the percentage of training
+ 
+
+ align:start position:0%
+numbers give the percentage of training
+set data in that subset without comes
+
+ align:start position:0%
+set data in that subset without comes
+ 
+
+ align:start position:0%
+set data in that subset without comes
+zero and the percentage of data in the
+
+ align:start position:0%
+zero and the percentage of data in the
+ 
+
+ align:start position:0%
+zero and the percentage of data in the
+training set in that subset with outcome
+
+ align:start position:0%
+training set in that subset with outcome
+ 
+
+ align:start position:0%
+training set in that subset with outcome
+1 we'll use the second column as our
+
+ align:start position:0%
+1 we'll use the second column as our
+ 
+
+ align:start position:0%
+1 we'll use the second column as our
+probabilities to generate an ROC curve
+
+ align:start position:0%
+probabilities to generate an ROC curve
+ 
+
+ align:start position:0%
+probabilities to generate an ROC curve
+so just like we did last week for
+
+ align:start position:0%
+so just like we did last week for
+ 
+
+ align:start position:0%
+so just like we did last week for
+logistic regression
+
+ align:start position:0%
+logistic regression
+ 
+
+ align:start position:0%
+logistic regression
+we'll start by using the prediction
+
+ align:start position:0%
+we'll start by using the prediction
+ 
+
+ align:start position:0%
+we'll start by using the prediction
+function we'll call the output pred and
+
+ align:start position:0%
+function we'll call the output pred and
+ 
+
+ align:start position:0%
+function we'll call the output pred and
+then use prediction where the first
+
+ align:start position:0%
+then use prediction where the first
+ 
+
+ align:start position:0%
+then use prediction where the first
+argument is the second column of predict
+
+ align:start position:0%
+argument is the second column of predict
+ 
+
+ align:start position:0%
+argument is the second column of predict
+ROC which we can access with square
+
+ align:start position:0%
+ROC which we can access with square
+ 
+
+ align:start position:0%
+ROC which we can access with square
+brackets and the second argument is the
+
+ align:start position:0%
+brackets and the second argument is the
+ 
+
+ align:start position:0%
+brackets and the second argument is the
+true outcome values test reverse now we
+
+ align:start position:0%
+true outcome values test reverse now we
+ 
+
+ align:start position:0%
+true outcome values test reverse now we
+need to use the performance function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the first argument is the outcome
+
+ align:start position:0%
+where the first argument is the outcome
+ 
+
+ align:start position:0%
+where the first argument is the outcome
+of the prediction function and then the
+
+ align:start position:0%
+of the prediction function and then the
+ 
+
+ align:start position:0%
+of the prediction function and then the
+next two arguments are true positive
+
+ align:start position:0%
+next two arguments are true positive
+ 
+
+ align:start position:0%
+next two arguments are true positive
+rate and false positive rate what we
+
+ align:start position:0%
+rate and false positive rate what we
+ 
+
+ align:start position:0%
+rate and false positive rate what we
+want on the x and y-axes of our ROC
+
+ align:start position:0%
+want on the x and y-axes of our ROC
+ 
+
+ align:start position:0%
+want on the x and y-axes of our ROC
+curve now we can just plot our ROC curve
+
+ align:start position:0%
+curve now we can just plot our ROC curve
+ 
+
+ align:start position:0%
+curve now we can just plot our ROC curve
+by typing plot PD our f if you switch
+
+ align:start position:0%
+by typing plot PD our f if you switch
+ 
+
+ align:start position:0%
+by typing plot PD our f if you switch
+back to your graphics window you should
+
+ align:start position:0%
+back to your graphics window you should
+ 
+
+ align:start position:0%
+back to your graphics window you should
+see the ROC curve for our model in the
+
+ align:start position:0%
+see the ROC curve for our model in the
+ 
+
+ align:start position:0%
+see the ROC curve for our model in the
+next quick question we'll ask you to
+
+ align:start position:0%
+next quick question we'll ask you to
+ 
+
+ align:start position:0%
+next quick question we'll ask you to
+compute the test set AUC of this model
\ No newline at end of file
diff --git a/JxDTBbXKvyo.txt b/JxDTBbXKvyo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6aa8ff84be378cd1a6db5111df9bf55d5c3ed10
--- /dev/null
+++ b/JxDTBbXKvyo.txt
@@ -0,0 +1,14523 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I always get a little afraid
+
+ align:start position:0%
+ocw.mit.edu I always get a little afraid
+ 
+
+ align:start position:0%
+ocw.mit.edu I always get a little afraid
+when I hear somebody call me an expert
+
+ align:start position:0%
+when I hear somebody call me an expert
+ 
+
+ align:start position:0%
+when I hear somebody call me an expert
+Cu uh I think that's a term you should
+
+ align:start position:0%
+Cu uh I think that's a term you should
+ 
+
+ align:start position:0%
+Cu uh I think that's a term you should
+fear um I I want to consider myself a
+
+ align:start position:0%
+fear um I I want to consider myself a
+ 
+
+ align:start position:0%
+fear um I I want to consider myself a
+learner um and and be in that Journey
+
+ align:start position:0%
+learner um and and be in that Journey
+ 
+
+ align:start position:0%
+learner um and and be in that Journey
+with you all today uh before we get
+
+ align:start position:0%
+with you all today uh before we get
+ 
+
+ align:start position:0%
+with you all today uh before we get
+started I wanted to also uh tell us
+
+ align:start position:0%
+started I wanted to also uh tell us
+ 
+
+ align:start position:0%
+started I wanted to also uh tell us
+about a or have a guest introduce
+
+ align:start position:0%
+about a or have a guest introduce
+ 
+
+ align:start position:0%
+about a or have a guest introduce
+themselves if if she doesn't mind
+
+ align:start position:0%
+themselves if if she doesn't mind
+ 
+
+ align:start position:0%
+themselves if if she doesn't mind
+Florence hazeline is uh is the director
+
+ align:start position:0%
+Florence hazeline is uh is the director
+ 
+
+ align:start position:0%
+Florence hazeline is uh is the director
+of population studies Center for
+
+ align:start position:0%
+of population studies Center for
+ 
+
+ align:start position:0%
+of population studies Center for
+director for the center for population
+
+ align:start position:0%
+director for the center for population
+ 
+
+ align:start position:0%
+director for the center for population
+studies at the NIH and she's an adviser
+
+ align:start position:0%
+studies at the NIH and she's an adviser
+ 
+
+ align:start position:0%
+studies at the NIH and she's an adviser
+uh to to SAA
+
+ align:start position:0%
+uh to to SAA
+ 
+
+ align:start position:0%
+uh to to SAA
+and would you like to say just a few
+
+ align:start position:0%
+and would you like to say just a few
+ 
+
+ align:start position:0%
+and would you like to say just a few
+words about what you're doing and course
+
+ align:start position:0%
+words about what you're doing and course
+ 
+
+ align:start position:0%
+words about what you're doing and course
+seven and I continuously lose my brass
+
+ align:start position:0%
+seven and I continuously lose my brass
+ 
+
+ align:start position:0%
+seven and I continuously lose my brass
+wrap great so Florence is here take
+
+ align:start position:0%
+wrap great so Florence is here take
+ 
+
+ align:start position:0%
+wrap great so Florence is here take
+advantage of her she's uh just developed
+
+ align:start position:0%
+advantage of her she's uh just developed
+ 
+
+ align:start position:0%
+advantage of her she's uh just developed
+she was telling me just before class
+
+ align:start position:0%
+she was telling me just before class
+ 
+
+ align:start position:0%
+she was telling me just before class
+some some wonderful uh uh apps some some
+
+ align:start position:0%
+some some wonderful uh uh apps some some
+ 
+
+ align:start position:0%
+some some wonderful uh uh apps some some
+for iPhone and I'm guessing the iPad as
+
+ align:start position:0%
+for iPhone and I'm guessing the iPad as
+ 
+
+ align:start position:0%
+for iPhone and I'm guessing the iPad as
+well uh have to do with contraception
+
+ align:start position:0%
+well uh have to do with contraception
+ 
+
+ align:start position:0%
+well uh have to do with contraception
+really really good stuff so good
+
+ align:start position:0%
+really really good stuff so good
+ 
+
+ align:start position:0%
+really really good stuff so good
+resource for
+
+ align:start position:0%
+resource for
+ 
+
+ align:start position:0%
+resource for
+you uh we're going to be talking about
+
+ align:start position:0%
+you uh we're going to be talking about
+ 
+
+ align:start position:0%
+you uh we're going to be talking about
+quality improvement a bit today we're
+
+ align:start position:0%
+quality improvement a bit today we're
+ 
+
+ align:start position:0%
+quality improvement a bit today we're
+going to be talking about how to to
+
+ align:start position:0%
+going to be talking about how to to
+ 
+
+ align:start position:0%
+going to be talking about how to to
+engage in quality improvement um as we
+
+ align:start position:0%
+engage in quality improvement um as we
+ 
+
+ align:start position:0%
+engage in quality improvement um as we
+go if you have questions please feel
+
+ align:start position:0%
+go if you have questions please feel
+ 
+
+ align:start position:0%
+go if you have questions please feel
+free to stop me I'm very informal
+
+ align:start position:0%
+free to stop me I'm very informal
+ 
+
+ align:start position:0%
+free to stop me I'm very informal
+generally as a presenter and I'm used to
+
+ align:start position:0%
+generally as a presenter and I'm used to
+ 
+
+ align:start position:0%
+generally as a presenter and I'm used to
+presenting to groups who are working in
+
+ align:start position:0%
+presenting to groups who are working in
+ 
+
+ align:start position:0%
+presenting to groups who are working in
+small tables and less in a Stadium
+
+ align:start position:0%
+small tables and less in a Stadium
+ 
+
+ align:start position:0%
+small tables and less in a Stadium
+Theater style uh uh presentation
+
+ align:start position:0%
+Theater style uh uh presentation
+ 
+
+ align:start position:0%
+Theater style uh uh presentation
+so what we're going to cover in brief
+
+ align:start position:0%
+so what we're going to cover in brief
+ 
+
+ align:start position:0%
+so what we're going to cover in brief
+I'm going to tell you a little bit about
+
+ align:start position:0%
+I'm going to tell you a little bit about
+ 
+
+ align:start position:0%
+I'm going to tell you a little bit about
+quality improvement where it has its
+
+ align:start position:0%
+quality improvement where it has its
+ 
+
+ align:start position:0%
+quality improvement where it has its
+Origins um we'll talk about how it came
+
+ align:start position:0%
+Origins um we'll talk about how it came
+ 
+
+ align:start position:0%
+Origins um we'll talk about how it came
+to be and Healthcare I'll tell you a
+
+ align:start position:0%
+to be and Healthcare I'll tell you a
+ 
+
+ align:start position:0%
+to be and Healthcare I'll tell you a
+little bit about the institute for
+
+ align:start position:0%
+little bit about the institute for
+ 
+
+ align:start position:0%
+little bit about the institute for
+healthcare Improvement we'll talk about
+
+ align:start position:0%
+healthcare Improvement we'll talk about
+ 
+
+ align:start position:0%
+healthcare Improvement we'll talk about
+the system of profound knowledge anybody
+
+ align:start position:0%
+the system of profound knowledge anybody
+ 
+
+ align:start position:0%
+the system of profound knowledge anybody
+ever heard of the system of profound
+
+ align:start position:0%
+ever heard of the system of profound
+ 
+
+ align:start position:0%
+ever heard of the system of profound
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+before nobody okay good so that'll be
+
+ align:start position:0%
+before nobody okay good so that'll be
+ 
+
+ align:start position:0%
+before nobody okay good so that'll be
+new we'll do a little bit on systems
+
+ align:start position:0%
+new we'll do a little bit on systems
+ 
+
+ align:start position:0%
+new we'll do a little bit on systems
+thinking and then we'll talk about
+
+ align:start position:0%
+thinking and then we'll talk about
+ 
+
+ align:start position:0%
+thinking and then we'll talk about
+something called the model for
+
+ align:start position:0%
+something called the model for
+ 
+
+ align:start position:0%
+something called the model for
+improvement we'll wrap up with that so
+
+ align:start position:0%
+improvement we'll wrap up with that so
+ 
+
+ align:start position:0%
+improvement we'll wrap up with that so
+as we go please feel free to to engage
+
+ align:start position:0%
+as we go please feel free to to engage
+ 
+
+ align:start position:0%
+as we go please feel free to to engage
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+questions all right so brief history
+
+ align:start position:0%
+questions all right so brief history
+ 
+
+ align:start position:0%
+questions all right so brief history
+there's uh two or three people that are
+
+ align:start position:0%
+there's uh two or three people that are
+ 
+
+ align:start position:0%
+there's uh two or three people that are
+incredibly important and you may
+
+ align:start position:0%
+incredibly important and you may
+ 
+
+ align:start position:0%
+incredibly important and you may
+recognize some of these faces so the the
+
+ align:start position:0%
+recognize some of these faces so the the
+ 
+
+ align:start position:0%
+recognize some of these faces so the the
+three kind of people that are often
+
+ align:start position:0%
+three kind of people that are often
+ 
+
+ align:start position:0%
+three kind of people that are often
+credited with the creation of of quality
+
+ align:start position:0%
+credited with the creation of of quality
+ 
+
+ align:start position:0%
+credited with the creation of of quality
+improvement as a as a discipline are
+
+ align:start position:0%
+improvement as a as a discipline are
+ 
+
+ align:start position:0%
+improvement as a as a discipline are
+Walter
+
+ align:start position:0%
+Walter
+ 
+
+ align:start position:0%
+Walter
+schart uh Edwards Deming and Joseph Jan
+
+ align:start position:0%
+schart uh Edwards Deming and Joseph Jan
+ 
+
+ align:start position:0%
+schart uh Edwards Deming and Joseph Jan
+both Deming and Jiran were students of
+
+ align:start position:0%
+both Deming and Jiran were students of
+ 
+
+ align:start position:0%
+both Deming and Jiran were students of
+Walter schuhart and I think Leo
+
+ align:start position:0%
+Walter schuhart and I think Leo
+ 
+
+ align:start position:0%
+Walter schuhart and I think Leo
+mentioned a bit about this before but
+
+ align:start position:0%
+mentioned a bit about this before but
+ 
+
+ align:start position:0%
+mentioned a bit about this before but
+Walter schuhart uh was a statistician
+
+ align:start position:0%
+Walter schuhart uh was a statistician
+ 
+
+ align:start position:0%
+Walter schuhart uh was a statistician
+who was working in the early part of the
+
+ align:start position:0%
+who was working in the early part of the
+ 
+
+ align:start position:0%
+who was working in the early part of the
+last century and he is responsible for
+
+ align:start position:0%
+last century and he is responsible for
+ 
+
+ align:start position:0%
+last century and he is responsible for
+for something we call statistical
+
+ align:start position:0%
+for something we call statistical
+ 
+
+ align:start position:0%
+for something we call statistical
+process control methods so he uh took uh
+
+ align:start position:0%
+process control methods so he uh took uh
+ 
+
+ align:start position:0%
+process control methods so he uh took uh
+statistics in a New Direction took it
+
+ align:start position:0%
+statistics in a New Direction took it
+ 
+
+ align:start position:0%
+statistics in a New Direction took it
+away from classical uh sort of
+
+ align:start position:0%
+away from classical uh sort of
+ 
+
+ align:start position:0%
+away from classical uh sort of
+descriptive statistics and looked at how
+
+ align:start position:0%
+descriptive statistics and looked at how
+ 
+
+ align:start position:0%
+descriptive statistics and looked at how
+we could understand systems over time
+
+ align:start position:0%
+we could understand systems over time
+ 
+
+ align:start position:0%
+we could understand systems over time
+could we get to a place where we could
+
+ align:start position:0%
+could we get to a place where we could
+ 
+
+ align:start position:0%
+could we get to a place where we could
+understand performance and actually
+
+ align:start position:0%
+understand performance and actually
+ 
+
+ align:start position:0%
+understand performance and actually
+predict Performance Based on stable
+
+ align:start position:0%
+predict Performance Based on stable
+ 
+
+ align:start position:0%
+predict Performance Based on stable
+systems so this is Walter
+
+ align:start position:0%
+systems so this is Walter
+ 
+
+ align:start position:0%
+systems so this is Walter
+schart and he was a a very very deep
+
+ align:start position:0%
+schart and he was a a very very deep
+ 
+
+ align:start position:0%
+schart and he was a a very very deep
+thinker in that regard although he
+
+ align:start position:0%
+thinker in that regard although he
+ 
+
+ align:start position:0%
+thinker in that regard although he
+wasn't really interested in healthcare
+
+ align:start position:0%
+wasn't really interested in healthcare
+ 
+
+ align:start position:0%
+wasn't really interested in healthcare
+he was mostly focused on
+
+ align:start position:0%
+he was mostly focused on
+ 
+
+ align:start position:0%
+he was mostly focused on
+manufacturing his uh pupil and the
+
+ align:start position:0%
+manufacturing his uh pupil and the
+ 
+
+ align:start position:0%
+manufacturing his uh pupil and the
+person we're going to talk most about
+
+ align:start position:0%
+person we're going to talk most about
+ 
+
+ align:start position:0%
+person we're going to talk most about
+today was uh Edwards Deming and Deming
+
+ align:start position:0%
+today was uh Edwards Deming and Deming
+ 
+
+ align:start position:0%
+today was uh Edwards Deming and Deming
+took it a step further he was also a
+
+ align:start position:0%
+took it a step further he was also a
+ 
+
+ align:start position:0%
+took it a step further he was also a
+statistician he learned quite a lot from
+
+ align:start position:0%
+statistician he learned quite a lot from
+ 
+
+ align:start position:0%
+statistician he learned quite a lot from
+Walter schuhart and they wrote a couple
+
+ align:start position:0%
+Walter schuhart and they wrote a couple
+ 
+
+ align:start position:0%
+Walter schuhart and they wrote a couple
+of books together on the subject of
+
+ align:start position:0%
+of books together on the subject of
+ 
+
+ align:start position:0%
+of books together on the subject of
+statistical process control but Deming
+
+ align:start position:0%
+statistical process control but Deming
+ 
+
+ align:start position:0%
+statistical process control but Deming
+actually thought that there were some
+
+ align:start position:0%
+actually thought that there were some
+ 
+
+ align:start position:0%
+actually thought that there were some
+other things that were going to be
+
+ align:start position:0%
+other things that were going to be
+ 
+
+ align:start position:0%
+other things that were going to be
+critically important not only to
+
+ align:start position:0%
+critically important not only to
+ 
+
+ align:start position:0%
+critically important not only to
+understanding systems but if you wanted
+
+ align:start position:0%
+understanding systems but if you wanted
+ 
+
+ align:start position:0%
+understanding systems but if you wanted
+to change systems if you wanted to make
+
+ align:start position:0%
+to change systems if you wanted to make
+ 
+
+ align:start position:0%
+to change systems if you wanted to make
+them better what was the knowledge that
+
+ align:start position:0%
+them better what was the knowledge that
+ 
+
+ align:start position:0%
+them better what was the knowledge that
+you needed to leverage in order to do
+
+ align:start position:0%
+you needed to leverage in order to do
+ 
+
+ align:start position:0%
+you needed to leverage in order to do
+that right and and we're going to talk
+
+ align:start position:0%
+that right and and we're going to talk
+ 
+
+ align:start position:0%
+that right and and we're going to talk
+more about that and and he gave us what
+
+ align:start position:0%
+more about that and and he gave us what
+ 
+
+ align:start position:0%
+more about that and and he gave us what
+we call the system of profound knowledge
+
+ align:start position:0%
+we call the system of profound knowledge
+ 
+
+ align:start position:0%
+we call the system of profound knowledge
+Joseph Jan was also a very important
+
+ align:start position:0%
+Joseph Jan was also a very important
+ 
+
+ align:start position:0%
+Joseph Jan was also a very important
+thinker at the same time period um and
+
+ align:start position:0%
+thinker at the same time period um and
+ 
+
+ align:start position:0%
+thinker at the same time period um and
+he focused his efforts on three
+
+ align:start position:0%
+he focused his efforts on three
+ 
+
+ align:start position:0%
+he focused his efforts on three
+different things whereas Deming was
+
+ align:start position:0%
+different things whereas Deming was
+ 
+
+ align:start position:0%
+different things whereas Deming was
+focused almost exclusively on quality
+
+ align:start position:0%
+focused almost exclusively on quality
+ 
+
+ align:start position:0%
+focused almost exclusively on quality
+improvement Jiran had what we call the
+
+ align:start position:0%
+improvement Jiran had what we call the
+ 
+
+ align:start position:0%
+improvement Jiran had what we call the
+Duran Trilogy he was focused on three
+
+ align:start position:0%
+Duran Trilogy he was focused on three
+ 
+
+ align:start position:0%
+Duran Trilogy he was focused on three
+things quality assurance quality
+
+ align:start position:0%
+things quality assurance quality
+ 
+
+ align:start position:0%
+things quality assurance quality
+improvement and quality design and so he
+
+ align:start position:0%
+improvement and quality design and so he
+ 
+
+ align:start position:0%
+improvement and quality design and so he
+was interested in designing systems
+
+ align:start position:0%
+was interested in designing systems
+ 
+
+ align:start position:0%
+was interested in designing systems
+assuring that they were achieving the
+
+ align:start position:0%
+assuring that they were achieving the
+ 
+
+ align:start position:0%
+assuring that they were achieving the
+the the stability that was called called
+
+ align:start position:0%
+the the stability that was called called
+ 
+
+ align:start position:0%
+the the stability that was called called
+for by the customer and then figuring
+
+ align:start position:0%
+for by the customer and then figuring
+ 
+
+ align:start position:0%
+for by the customer and then figuring
+out how to improve upon the quality of
+
+ align:start position:0%
+out how to improve upon the quality of
+ 
+
+ align:start position:0%
+out how to improve upon the quality of
+the product or service that that that
+
+ align:start position:0%
+the product or service that that that
+ 
+
+ align:start position:0%
+the product or service that that that
+system was was seeking to serve okay so
+
+ align:start position:0%
+system was was seeking to serve okay so
+ 
+
+ align:start position:0%
+system was was seeking to serve okay so
+those are sort of three three important
+
+ align:start position:0%
+those are sort of three three important
+ 
+
+ align:start position:0%
+those are sort of three three important
+people uh Deming did a lot of his work
+
+ align:start position:0%
+people uh Deming did a lot of his work
+ 
+
+ align:start position:0%
+people uh Deming did a lot of his work
+in Japan after World War II he worked
+
+ align:start position:0%
+in Japan after World War II he worked
+ 
+
+ align:start position:0%
+in Japan after World War II he worked
+with our US military during the World
+
+ align:start position:0%
+with our US military during the World
+ 
+
+ align:start position:0%
+with our US military during the World
+War II and then afterwards with the
+
+ align:start position:0%
+War II and then afterwards with the
+ 
+
+ align:start position:0%
+War II and then afterwards with the
+rebuilding of the Japanese economy have
+
+ align:start position:0%
+rebuilding of the Japanese economy have
+ 
+
+ align:start position:0%
+rebuilding of the Japanese economy have
+people heard of of Deming before couple
+
+ align:start position:0%
+people heard of of Deming before couple
+ 
+
+ align:start position:0%
+people heard of of Deming before couple
+people right yeah good uh so uh how many
+
+ align:start position:0%
+people right yeah good uh so uh how many
+ 
+
+ align:start position:0%
+people right yeah good uh so uh how many
+have heard of Toyota production system
+
+ align:start position:0%
+have heard of Toyota production system
+ 
+
+ align:start position:0%
+have heard of Toyota production system
+or lean manufacturing more people have
+
+ align:start position:0%
+or lean manufacturing more people have
+ 
+
+ align:start position:0%
+or lean manufacturing more people have
+heard of that all of that is an
+
+ align:start position:0%
+heard of that all of that is an
+ 
+
+ align:start position:0%
+heard of that all of that is an
+outgrowth of what he started in Japan in
+
+ align:start position:0%
+outgrowth of what he started in Japan in
+ 
+
+ align:start position:0%
+outgrowth of what he started in Japan in
+in the early 1950s and we're going to
+
+ align:start position:0%
+in the early 1950s and we're going to
+ 
+
+ align:start position:0%
+in the early 1950s and we're going to
+talk a bit about that today as well
+
+ align:start position:0%
+talk a bit about that today as well
+ 
+
+ align:start position:0%
+talk a bit about that today as well
+so Deming system of profound
+
+ align:start position:0%
+so Deming system of profound
+ 
+
+ align:start position:0%
+so Deming system of profound
+knowledge most aply described in his
+
+ align:start position:0%
+knowledge most aply described in his
+ 
+
+ align:start position:0%
+knowledge most aply described in his
+book the new economics which was
+
+ align:start position:0%
+book the new economics which was
+ 
+
+ align:start position:0%
+book the new economics which was
+published in the early 90s just shortly
+
+ align:start position:0%
+published in the early 90s just shortly
+ 
+
+ align:start position:0%
+published in the early 90s just shortly
+before his death Deming was a he was a
+
+ align:start position:0%
+before his death Deming was a he was a
+ 
+
+ align:start position:0%
+before his death Deming was a he was a
+person who was absolutely passionate
+
+ align:start position:0%
+person who was absolutely passionate
+ 
+
+ align:start position:0%
+person who was absolutely passionate
+about quality improvement uh he lived to
+
+ align:start position:0%
+about quality improvement uh he lived to
+ 
+
+ align:start position:0%
+about quality improvement uh he lived to
+be 93 years old he gave his last 4-day
+
+ align:start position:0%
+be 93 years old he gave his last 4-day
+ 
+
+ align:start position:0%
+be 93 years old he gave his last 4-day
+seminar on quality improvement at the
+
+ align:start position:0%
+seminar on quality improvement at the
+ 
+
+ align:start position:0%
+seminar on quality improvement at the
+age of 93 2 weeks before he passed away
+
+ align:start position:0%
+age of 93 2 weeks before he passed away
+ 
+
+ align:start position:0%
+age of 93 2 weeks before he passed away
+from a wheelchair on oxygen he made it
+
+ align:start position:0%
+from a wheelchair on oxygen he made it
+ 
+
+ align:start position:0%
+from a wheelchair on oxygen he made it
+his life's mission to focus on improving
+
+ align:start position:0%
+his life's mission to focus on improving
+ 
+
+ align:start position:0%
+his life's mission to focus on improving
+systems he felt that there was a
+
+ align:start position:0%
+systems he felt that there was a
+ 
+
+ align:start position:0%
+systems he felt that there was a
+tremendous amount of waste uh and
+
+ align:start position:0%
+tremendous amount of waste uh and
+ 
+
+ align:start position:0%
+tremendous amount of waste uh and
+inefficiency that existed in systems
+
+ align:start position:0%
+inefficiency that existed in systems
+ 
+
+ align:start position:0%
+inefficiency that existed in systems
+whether they be manufacturing service
+
+ align:start position:0%
+whether they be manufacturing service
+ 
+
+ align:start position:0%
+whether they be manufacturing service
+industry or later in his life during
+
+ align:start position:0%
+industry or later in his life during
+ 
+
+ align:start position:0%
+industry or later in his life during
+sort of the last decade of his life in
+
+ align:start position:0%
+sort of the last decade of his life in
+ 
+
+ align:start position:0%
+sort of the last decade of his life in
+healthcare um and he gave us uh the
+
+ align:start position:0%
+healthcare um and he gave us uh the
+ 
+
+ align:start position:0%
+healthcare um and he gave us uh the
+system of profound knowledge which I'm
+
+ align:start position:0%
+system of profound knowledge which I'm
+ 
+
+ align:start position:0%
+system of profound knowledge which I'm
+going to describe in a second
+
+ align:start position:0%
+going to describe in a second
+ 
+
+ align:start position:0%
+going to describe in a second
+before I do that though I want to talk a
+
+ align:start position:0%
+before I do that though I want to talk a
+ 
+
+ align:start position:0%
+before I do that though I want to talk a
+little bit about the institute for
+
+ align:start position:0%
+little bit about the institute for
+ 
+
+ align:start position:0%
+little bit about the institute for
+healthcare Improvement so uh Deming was
+
+ align:start position:0%
+healthcare Improvement so uh Deming was
+ 
+
+ align:start position:0%
+healthcare Improvement so uh Deming was
+holding one of his 4day seminars in 1987
+
+ align:start position:0%
+holding one of his 4day seminars in 1987
+ 
+
+ align:start position:0%
+holding one of his 4day seminars in 1987
+and there was a doctor in the audience
+
+ align:start position:0%
+and there was a doctor in the audience
+ 
+
+ align:start position:0%
+and there was a doctor in the audience
+by the name of Don Berwick who uh Leo
+
+ align:start position:0%
+by the name of Don Berwick who uh Leo
+ 
+
+ align:start position:0%
+by the name of Don Berwick who uh Leo
+introduced us to a couple weeks
+
+ align:start position:0%
+introduced us to a couple weeks
+ 
+
+ align:start position:0%
+introduced us to a couple weeks
+ago Don was uh working here in in Boston
+
+ align:start position:0%
+ago Don was uh working here in in Boston
+ 
+
+ align:start position:0%
+ago Don was uh working here in in Boston
+as a pediatrician and he was seeing that
+
+ align:start position:0%
+as a pediatrician and he was seeing that
+ 
+
+ align:start position:0%
+as a pediatrician and he was seeing that
+a lot of patients were being harmed uh
+
+ align:start position:0%
+a lot of patients were being harmed uh
+ 
+
+ align:start position:0%
+a lot of patients were being harmed uh
+in the hospitals where he was working
+
+ align:start position:0%
+in the hospitals where he was working
+ 
+
+ align:start position:0%
+in the hospitals where he was working
+and he also knew internally no matter
+
+ align:start position:0%
+and he also knew internally no matter
+ 
+
+ align:start position:0%
+and he also knew internally no matter
+how hard he worked he couldn't always
+
+ align:start position:0%
+how hard he worked he couldn't always
+ 
+
+ align:start position:0%
+how hard he worked he couldn't always
+provide the same level of quality of
+
+ align:start position:0%
+provide the same level of quality of
+ 
+
+ align:start position:0%
+provide the same level of quality of
+care to every one of his patients and
+
+ align:start position:0%
+care to every one of his patients and
+ 
+
+ align:start position:0%
+care to every one of his patients and
+that bothered him as an individual right
+
+ align:start position:0%
+that bothered him as an individual right
+ 
+
+ align:start position:0%
+that bothered him as an individual right
+and so he was looking for answers for
+
+ align:start position:0%
+and so he was looking for answers for
+ 
+
+ align:start position:0%
+and so he was looking for answers for
+that and he actually went and and and
+
+ align:start position:0%
+that and he actually went and and and
+ 
+
+ align:start position:0%
+that and he actually went and and and
+attended Dr deming's seminar for four
+
+ align:start position:0%
+attended Dr deming's seminar for four
+ 
+
+ align:start position:0%
+attended Dr deming's seminar for four
+days after the first day he thought this
+
+ align:start position:0%
+days after the first day he thought this
+ 
+
+ align:start position:0%
+days after the first day he thought this
+guy is crazy got on a plane flew back to
+
+ align:start position:0%
+guy is crazy got on a plane flew back to
+ 
+
+ align:start position:0%
+guy is crazy got on a plane flew back to
+Boston in the middle of the night he had
+
+ align:start position:0%
+Boston in the middle of the night he had
+ 
+
+ align:start position:0%
+Boston in the middle of the night he had
+this Epiphany that actually there's
+
+ align:start position:0%
+this Epiphany that actually there's
+ 
+
+ align:start position:0%
+this Epiphany that actually there's
+something to this system's thinking
+
+ align:start position:0%
+something to this system's thinking
+ 
+
+ align:start position:0%
+something to this system's thinking
+there's something to quality improvement
+
+ align:start position:0%
+there's something to quality improvement
+ 
+
+ align:start position:0%
+there's something to quality improvement
+that I need to learn about he flew back
+
+ align:start position:0%
+that I need to learn about he flew back
+ 
+
+ align:start position:0%
+that I need to learn about he flew back
+the following morning on the early
+
+ align:start position:0%
+the following morning on the early
+ 
+
+ align:start position:0%
+the following morning on the early
+morning flight finished the seminar and
+
+ align:start position:0%
+morning flight finished the seminar and
+ 
+
+ align:start position:0%
+morning flight finished the seminar and
+at the end of that he developed an idea
+
+ align:start position:0%
+at the end of that he developed an idea
+ 
+
+ align:start position:0%
+at the end of that he developed an idea
+for a demonstration project and he
+
+ align:start position:0%
+for a demonstration project and he
+ 
+
+ align:start position:0%
+for a demonstration project and he
+sought some funding and he partnered 16
+
+ align:start position:0%
+sought some funding and he partnered 16
+ 
+
+ align:start position:0%
+sought some funding and he partnered 16
+hospitals in the in the Boston area with
+
+ align:start position:0%
+hospitals in the in the Boston area with
+ 
+
+ align:start position:0%
+hospitals in the in the Boston area with
+industry leaders in quality improvement
+
+ align:start position:0%
+industry leaders in quality improvement
+ 
+
+ align:start position:0%
+industry leaders in quality improvement
+people who had been using uh Dr deming's
+
+ align:start position:0%
+people who had been using uh Dr deming's
+ 
+
+ align:start position:0%
+people who had been using uh Dr deming's
+methods for years and years so he would
+
+ align:start position:0%
+methods for years and years so he would
+ 
+
+ align:start position:0%
+methods for years and years so he would
+partner people with uh electric
+
+ align:start position:0%
+partner people with uh electric
+ 
+
+ align:start position:0%
+partner people with uh electric
+companies and manufacturing companies to
+
+ align:start position:0%
+companies and manufacturing companies to
+ 
+
+ align:start position:0%
+companies and manufacturing companies to
+see how they could learn about quality
+
+ align:start position:0%
+see how they could learn about quality
+ 
+
+ align:start position:0%
+see how they could learn about quality
+improvement and bring that into
+
+ align:start position:0%
+improvement and bring that into
+ 
+
+ align:start position:0%
+improvement and bring that into
+Healthcare that demonstration proc
+
+ align:start position:0%
+Healthcare that demonstration proc
+ 
+
+ align:start position:0%
+Healthcare that demonstration proc
+project lasted a couple of years and at
+
+ align:start position:0%
+project lasted a couple of years and at
+ 
+
+ align:start position:0%
+project lasted a couple of years and at
+the end of it there was a lot of really
+
+ align:start position:0%
+the end of it there was a lot of really
+ 
+
+ align:start position:0%
+the end of it there was a lot of really
+good learning about how we could improve
+
+ align:start position:0%
+good learning about how we could improve
+ 
+
+ align:start position:0%
+good learning about how we could improve
+uh systems of healthare so uh we decided
+
+ align:start position:0%
+uh systems of healthare so uh we decided
+ 
+
+ align:start position:0%
+uh systems of healthare so uh we decided
+to create ihi at that time so that was
+
+ align:start position:0%
+to create ihi at that time so that was
+ 
+
+ align:start position:0%
+to create ihi at that time so that was
+in 1991 and ihi is is based here in
+
+ align:start position:0%
+in 1991 and ihi is is based here in
+ 
+
+ align:start position:0%
+in 1991 and ihi is is based here in
+Harvard Square has been working on
+
+ align:start position:0%
+Harvard Square has been working on
+ 
+
+ align:start position:0%
+Harvard Square has been working on
+improving Health Care Systems using uh
+
+ align:start position:0%
+improving Health Care Systems using uh
+ 
+
+ align:start position:0%
+improving Health Care Systems using uh
+uh quality improvement methods for the
+
+ align:start position:0%
+uh quality improvement methods for the
+ 
+
+ align:start position:0%
+uh quality improvement methods for the
+last 20 years or so so I've had the
+
+ align:start position:0%
+last 20 years or so so I've had the
+ 
+
+ align:start position:0%
+last 20 years or so so I've had the
+opportunity to work for them for the
+
+ align:start position:0%
+opportunity to work for them for the
+ 
+
+ align:start position:0%
+opportunity to work for them for the
+last five years or so and as Elliot
+
+ align:start position:0%
+last five years or so and as Elliot
+ 
+
+ align:start position:0%
+last five years or so and as Elliot
+pointed out I've been doing that mostly
+
+ align:start position:0%
+pointed out I've been doing that mostly
+ 
+
+ align:start position:0%
+pointed out I've been doing that mostly
+in resource constraints environments um
+
+ align:start position:0%
+in resource constraints environments um
+ 
+
+ align:start position:0%
+in resource constraints environments um
+and I think that's really where quality
+
+ align:start position:0%
+and I think that's really where quality
+ 
+
+ align:start position:0%
+and I think that's really where quality
+improvement uh is at its best in places
+
+ align:start position:0%
+improvement uh is at its best in places
+ 
+
+ align:start position:0%
+improvement uh is at its best in places
+where you've got to optimize what you
+
+ align:start position:0%
+where you've got to optimize what you
+ 
+
+ align:start position:0%
+where you've got to optimize what you
+have because you don't have anything
+
+ align:start position:0%
+have because you don't have anything
+ 
+
+ align:start position:0%
+have because you don't have anything
+extra to to give so what is quality
+
+ align:start position:0%
+extra to to give so what is quality
+ 
+
+ align:start position:0%
+extra to to give so what is quality
+improvement what is the system of
+
+ align:start position:0%
+improvement what is the system of
+ 
+
+ align:start position:0%
+improvement what is the system of
+profound knowledge okay system of
+
+ align:start position:0%
+profound knowledge okay system of
+ 
+
+ align:start position:0%
+profound knowledge okay system of
+profound knowledge is a way of looking
+
+ align:start position:0%
+profound knowledge is a way of looking
+ 
+
+ align:start position:0%
+profound knowledge is a way of looking
+at an organization or a system that's
+
+ align:start position:0%
+at an organization or a system that's
+ 
+
+ align:start position:0%
+at an organization or a system that's
+trying to provide a service so if I'm
+
+ align:start position:0%
+trying to provide a service so if I'm
+ 
+
+ align:start position:0%
+trying to provide a service so if I'm
+looking at a Health Care System a single
+
+ align:start position:0%
+looking at a Health Care System a single
+ 
+
+ align:start position:0%
+looking at a Health Care System a single
+Hospital a clinic or even a whole
+
+ align:start position:0%
+Hospital a clinic or even a whole
+ 
+
+ align:start position:0%
+Hospital a clinic or even a whole
+healthare system right I can use this
+
+ align:start position:0%
+healthare system right I can use this
+ 
+
+ align:start position:0%
+healthare system right I can use this
+sort of a lens if you
+
+ align:start position:0%
+sort of a lens if you
+ 
+
+ align:start position:0%
+sort of a lens if you
+will as a way to understand performance
+
+ align:start position:0%
+will as a way to understand performance
+ 
+
+ align:start position:0%
+will as a way to understand performance
+okay and Demi argued that there were
+
+ align:start position:0%
+okay and Demi argued that there were
+ 
+
+ align:start position:0%
+okay and Demi argued that there were
+four really key components here okay the
+
+ align:start position:0%
+four really key components here okay the
+ 
+
+ align:start position:0%
+four really key components here okay the
+first was appreciation of the system do
+
+ align:start position:0%
+first was appreciation of the system do
+ 
+
+ align:start position:0%
+first was appreciation of the system do
+you have a way of viewing all of the
+
+ align:start position:0%
+you have a way of viewing all of the
+ 
+
+ align:start position:0%
+you have a way of viewing all of the
+processes that exist within a system all
+
+ align:start position:0%
+processes that exist within a system all
+ 
+
+ align:start position:0%
+processes that exist within a system all
+of the work that is happening on a
+
+ align:start position:0%
+of the work that is happening on a
+ 
+
+ align:start position:0%
+of the work that is happening on a
+day-to-day basis work that's happening
+
+ align:start position:0%
+day-to-day basis work that's happening
+ 
+
+ align:start position:0%
+day-to-day basis work that's happening
+between caregivers and patients between
+
+ align:start position:0%
+between caregivers and patients between
+ 
+
+ align:start position:0%
+between caregivers and patients between
+managers and caregivers between support
+
+ align:start position:0%
+managers and caregivers between support
+ 
+
+ align:start position:0%
+managers and caregivers between support
+staff and each other right all the
+
+ align:start position:0%
+staff and each other right all the
+ 
+
+ align:start position:0%
+staff and each other right all the
+different things that are happening do
+
+ align:start position:0%
+different things that are happening do
+ 
+
+ align:start position:0%
+different things that are happening do
+you have a way of articulating that I'm
+
+ align:start position:0%
+you have a way of articulating that I'm
+ 
+
+ align:start position:0%
+you have a way of articulating that I'm
+actually going to introduce you to to a
+
+ align:start position:0%
+actually going to introduce you to to a
+ 
+
+ align:start position:0%
+actually going to introduce you to to a
+mechanism for that this morning so
+
+ align:start position:0%
+mechanism for that this morning so
+ 
+
+ align:start position:0%
+mechanism for that this morning so
+appreciation of the system do you have
+
+ align:start position:0%
+appreciation of the system do you have
+ 
+
+ align:start position:0%
+appreciation of the system do you have
+that view can you see everything at once
+
+ align:start position:0%
+that view can you see everything at once
+ 
+
+ align:start position:0%
+that view can you see everything at once
+because if you get busy trying to
+
+ align:start position:0%
+because if you get busy trying to
+ 
+
+ align:start position:0%
+because if you get busy trying to
+improve one thing you can actually sub
+
+ align:start position:0%
+improve one thing you can actually sub
+ 
+
+ align:start position:0%
+improve one thing you can actually sub
+optimize the whole system he also knew
+
+ align:start position:0%
+optimize the whole system he also knew
+ 
+
+ align:start position:0%
+optimize the whole system he also knew
+that there was the importance of data
+
+ align:start position:0%
+that there was the importance of data
+ 
+
+ align:start position:0%
+that there was the importance of data
+right the importance of of understanding
+
+ align:start position:0%
+right the importance of of understanding
+ 
+
+ align:start position:0%
+right the importance of of understanding
+variation and understanding stability
+
+ align:start position:0%
+variation and understanding stability
+ 
+
+ align:start position:0%
+variation and understanding stability
+that's where he got his start with
+
+ align:start position:0%
+that's where he got his start with
+ 
+
+ align:start position:0%
+that's where he got his start with
+Walter shuart so he he knew that you
+
+ align:start position:0%
+Walter shuart so he he knew that you
+ 
+
+ align:start position:0%
+Walter shuart so he he knew that you
+needed to be able to understand each
+
+ align:start position:0%
+needed to be able to understand each
+ 
+
+ align:start position:0%
+needed to be able to understand each
+process and measure it and understand if
+
+ align:start position:0%
+process and measure it and understand if
+ 
+
+ align:start position:0%
+process and measure it and understand if
+it was predictably performing into the
+
+ align:start position:0%
+it was predictably performing into the
+ 
+
+ align:start position:0%
+it was predictably performing into the
+future we're not going to touch so much
+
+ align:start position:0%
+future we're not going to touch so much
+ 
+
+ align:start position:0%
+future we're not going to touch so much
+on that today although I would like to I
+
+ align:start position:0%
+on that today although I would like to I
+ 
+
+ align:start position:0%
+on that today although I would like to I
+think it's a really fun topic Deming
+
+ align:start position:0%
+think it's a really fun topic Deming
+ 
+
+ align:start position:0%
+think it's a really fun topic Deming
+also knew that psychology was incredibly
+
+ align:start position:0%
+also knew that psychology was incredibly
+ 
+
+ align:start position:0%
+also knew that psychology was incredibly
+important motivation what gets people to
+
+ align:start position:0%
+important motivation what gets people to
+ 
+
+ align:start position:0%
+important motivation what gets people to
+work in the morning what gets them doing
+
+ align:start position:0%
+work in the morning what gets them doing
+ 
+
+ align:start position:0%
+work in the morning what gets them doing
+things what gets them excited about
+
+ align:start position:0%
+things what gets them excited about
+ 
+
+ align:start position:0%
+things what gets them excited about
+their work right so he knew that
+
+ align:start position:0%
+their work right so he knew that
+ 
+
+ align:start position:0%
+their work right so he knew that
+psychology was critically important and
+
+ align:start position:0%
+psychology was critically important and
+ 
+
+ align:start position:0%
+psychology was critically important and
+and there's a piece of this which is
+
+ align:start position:0%
+and there's a piece of this which is
+ 
+
+ align:start position:0%
+and there's a piece of this which is
+sort of the culture of an organization
+
+ align:start position:0%
+sort of the culture of an organization
+ 
+
+ align:start position:0%
+sort of the culture of an organization
+is it a is it a punitive organization
+
+ align:start position:0%
+is it a is it a punitive organization
+ 
+
+ align:start position:0%
+is it a is it a punitive organization
+internally is it one that rewards
+
+ align:start position:0%
+internally is it one that rewards
+ 
+
+ align:start position:0%
+internally is it one that rewards
+Innovation is it a learning organization
+
+ align:start position:0%
+Innovation is it a learning organization
+ 
+
+ align:start position:0%
+Innovation is it a learning organization
+that encourages people to constantly be
+
+ align:start position:0%
+that encourages people to constantly be
+ 
+
+ align:start position:0%
+that encourages people to constantly be
+testing and learning failing often right
+
+ align:start position:0%
+testing and learning failing often right
+ 
+
+ align:start position:0%
+testing and learning failing often right
+so he knew that that was going to be
+
+ align:start position:0%
+so he knew that that was going to be
+ 
+
+ align:start position:0%
+so he knew that that was going to be
+critically important and the last piece
+
+ align:start position:0%
+critically important and the last piece
+ 
+
+ align:start position:0%
+critically important and the last piece
+he had was the theory of knowledge we're
+
+ align:start position:0%
+he had was the theory of knowledge we're
+ 
+
+ align:start position:0%
+he had was the theory of knowledge we're
+going to talk a bit about that as well
+
+ align:start position:0%
+going to talk a bit about that as well
+ 
+
+ align:start position:0%
+going to talk a bit about that as well
+today theory of knowledge sometimes
+
+ align:start position:0%
+today theory of knowledge sometimes
+ 
+
+ align:start position:0%
+today theory of knowledge sometimes
+people call it epistemology uh sometimes
+
+ align:start position:0%
+people call it epistemology uh sometimes
+ 
+
+ align:start position:0%
+people call it epistemology uh sometimes
+talk about the scientific method I like
+
+ align:start position:0%
+talk about the scientific method I like
+ 
+
+ align:start position:0%
+talk about the scientific method I like
+to think of it this as this way is uh
+
+ align:start position:0%
+to think of it this as this way is uh
+ 
+
+ align:start position:0%
+to think of it this as this way is uh
+can you articulate what you believe
+
+ align:start position:0%
+can you articulate what you believe
+ 
+
+ align:start position:0%
+can you articulate what you believe
+about why things are the way that they
+
+ align:start position:0%
+about why things are the way that they
+ 
+
+ align:start position:0%
+about why things are the way that they
+are can you do
+
+ align:start position:0%
+are can you do
+ 
+
+ align:start position:0%
+are can you do
+that if you can that's great because it
+
+ align:start position:0%
+that if you can that's great because it
+ 
+
+ align:start position:0%
+that if you can that's great because it
+gives you a testable starting place
+
+ align:start position:0%
+gives you a testable starting place
+ 
+
+ align:start position:0%
+gives you a testable starting place
+right because whatever you believe is
+
+ align:start position:0%
+right because whatever you believe is
+ 
+
+ align:start position:0%
+right because whatever you believe is
+going to influence what you decide to
+
+ align:start position:0%
+going to influence what you decide to
+ 
+
+ align:start position:0%
+going to influence what you decide to
+change when you go to improve a system
+
+ align:start position:0%
+change when you go to improve a system
+ 
+
+ align:start position:0%
+change when you go to improve a system
+if I am doing some work in South Africa
+
+ align:start position:0%
+if I am doing some work in South Africa
+ 
+
+ align:start position:0%
+if I am doing some work in South Africa
+and I believe at one particular hospital
+
+ align:start position:0%
+and I believe at one particular hospital
+ 
+
+ align:start position:0%
+and I believe at one particular hospital
+that the reason we have poor outcomes
+
+ align:start position:0%
+that the reason we have poor outcomes
+ 
+
+ align:start position:0%
+that the reason we have poor outcomes
+for our patients is because nurses are
+
+ align:start position:0%
+for our patients is because nurses are
+ 
+
+ align:start position:0%
+for our patients is because nurses are
+lazy
+
+ align:start position:0%
+lazy
+ 
+
+ align:start position:0%
+lazy
+then that's going to control what I
+
+ align:start position:0%
+then that's going to control what I
+ 
+
+ align:start position:0%
+then that's going to control what I
+decide to change I'm going to do
+
+ align:start position:0%
+decide to change I'm going to do
+ 
+
+ align:start position:0%
+decide to change I'm going to do
+something to remove the laziness of
+
+ align:start position:0%
+something to remove the laziness of
+ 
+
+ align:start position:0%
+something to remove the laziness of
+nurses now I do not actually believe
+
+ align:start position:0%
+nurses now I do not actually believe
+ 
+
+ align:start position:0%
+nurses now I do not actually believe
+nurses are lazy I think they're the
+
+ align:start position:0%
+nurses are lazy I think they're the
+ 
+
+ align:start position:0%
+nurses are lazy I think they're the
+hardest working people in healthcare but
+
+ align:start position:0%
+hardest working people in healthcare but
+ 
+
+ align:start position:0%
+hardest working people in healthcare but
+if I believe that if that's my theory if
+
+ align:start position:0%
+if I believe that if that's my theory if
+ 
+
+ align:start position:0%
+if I believe that if that's my theory if
+that's my starting place then that
+
+ align:start position:0%
+that's my starting place then that
+ 
+
+ align:start position:0%
+that's my starting place then that
+changes what I decide to change in a
+
+ align:start position:0%
+changes what I decide to change in a
+ 
+
+ align:start position:0%
+changes what I decide to change in a
+system if I instead think that it's a
+
+ align:start position:0%
+system if I instead think that it's a
+ 
+
+ align:start position:0%
+system if I instead think that it's a
+process orientation problem or it's a
+
+ align:start position:0%
+process orientation problem or it's a
+ 
+
+ align:start position:0%
+process orientation problem or it's a
+problem with Physicians or it's a
+
+ align:start position:0%
+problem with Physicians or it's a
+ 
+
+ align:start position:0%
+problem with Physicians or it's a
+problem with technology or resources
+
+ align:start position:0%
+problem with technology or resources
+ 
+
+ align:start position:0%
+problem with technology or resources
+then that's what I'm going to go after a
+
+ align:start position:0%
+then that's what I'm going to go after a
+ 
+
+ align:start position:0%
+then that's what I'm going to go after a
+lot of people never get to the place
+
+ align:start position:0%
+lot of people never get to the place
+ 
+
+ align:start position:0%
+lot of people never get to the place
+where they are articulate what they
+
+ align:start position:0%
+where they are articulate what they
+ 
+
+ align:start position:0%
+where they are articulate what they
+believe about why things are the way
+
+ align:start position:0%
+believe about why things are the way
+ 
+
+ align:start position:0%
+believe about why things are the way
+that they are they internalize
+
+ align:start position:0%
+that they are they internalize
+ 
+
+ align:start position:0%
+that they are they internalize
+assumptions and then they start towards
+
+ align:start position:0%
+assumptions and then they start towards
+ 
+
+ align:start position:0%
+assumptions and then they start towards
+Solutions based on those
+
+ align:start position:0%
+Solutions based on those
+ 
+
+ align:start position:0%
+Solutions based on those
+assumptions often we hear about
+
+ align:start position:0%
+assumptions often we hear about
+ 
+
+ align:start position:0%
+assumptions often we hear about
+especially in resource constrained
+
+ align:start position:0%
+especially in resource constrained
+ 
+
+ align:start position:0%
+especially in resource constrained
+environments what tell you what we need
+
+ align:start position:0%
+environments what tell you what we need
+ 
+
+ align:start position:0%
+environments what tell you what we need
+we need more hospitals we need to build
+
+ align:start position:0%
+we need more hospitals we need to build
+ 
+
+ align:start position:0%
+we need more hospitals we need to build
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+hospitals right what's the underlying
+
+ align:start position:0%
+hospitals right what's the underlying
+ 
+
+ align:start position:0%
+hospitals right what's the underlying
+assumption that the infrastructure is
+
+ align:start position:0%
+assumption that the infrastructure is
+ 
+
+ align:start position:0%
+assumption that the infrastructure is
+inadequate right and then there is even
+
+ align:start position:0%
+inadequate right and then there is even
+ 
+
+ align:start position:0%
+inadequate right and then there is even
+further assumptions behind that about
+
+ align:start position:0%
+further assumptions behind that about
+ 
+
+ align:start position:0%
+further assumptions behind that about
+why the infrastructure is inadequate
+
+ align:start position:0%
+why the infrastructure is inadequate
+ 
+
+ align:start position:0%
+why the infrastructure is inadequate
+right we hear we need more healthcare
+
+ align:start position:0%
+right we hear we need more healthcare
+ 
+
+ align:start position:0%
+right we hear we need more healthcare
+workers right we need need more money
+
+ align:start position:0%
+workers right we need need more money
+ 
+
+ align:start position:0%
+workers right we need need more money
+what we know from us healthc care is
+
+ align:start position:0%
+what we know from us healthc care is
+ 
+
+ align:start position:0%
+what we know from us healthc care is
+that's not likely the case right Leo
+
+ align:start position:0%
+that's not likely the case right Leo
+ 
+
+ align:start position:0%
+that's not likely the case right Leo
+told us about us healthare right we
+
+ align:start position:0%
+told us about us healthare right we
+ 
+
+ align:start position:0%
+told us about us healthare right we
+spend twice as much money as the next
+
+ align:start position:0%
+spend twice as much money as the next
+ 
+
+ align:start position:0%
+spend twice as much money as the next
+country to get not as good care so it
+
+ align:start position:0%
+country to get not as good care so it
+ 
+
+ align:start position:0%
+country to get not as good care so it
+may not be a resource issue but we need
+
+ align:start position:0%
+may not be a resource issue but we need
+ 
+
+ align:start position:0%
+may not be a resource issue but we need
+to question that if that's our starting
+
+ align:start position:0%
+to question that if that's our starting
+ 
+
+ align:start position:0%
+to question that if that's our starting
+place we need a place to to start
+
+ align:start position:0%
+place we need a place to to start
+ 
+
+ align:start position:0%
+place we need a place to to start
+testing so the theory of knowledge so
+
+ align:start position:0%
+testing so the theory of knowledge so
+ 
+
+ align:start position:0%
+testing so the theory of knowledge so
+these four components which are driven
+
+ align:start position:0%
+these four components which are driven
+ 
+
+ align:start position:0%
+these four components which are driven
+by the values of the organization that
+
+ align:start position:0%
+by the values of the organization that
+ 
+
+ align:start position:0%
+by the values of the organization that
+we're looking at right we're going to
+
+ align:start position:0%
+we're looking at right we're going to
+ 
+
+ align:start position:0%
+we're looking at right we're going to
+leverage those along with something we
+
+ align:start position:0%
+leverage those along with something we
+ 
+
+ align:start position:0%
+leverage those along with something we
+call subject matter expertise so
+
+ align:start position:0%
+call subject matter expertise so
+ 
+
+ align:start position:0%
+call subject matter expertise so
+Florence and I were just talking about
+
+ align:start position:0%
+Florence and I were just talking about
+ 
+
+ align:start position:0%
+Florence and I were just talking about
+this so so important it's really
+
+ align:start position:0%
+this so so important it's really
+ 
+
+ align:start position:0%
+this so so important it's really
+important to have somebody who can think
+
+ align:start position:0%
+important to have somebody who can think
+ 
+
+ align:start position:0%
+important to have somebody who can think
+from an improvement perspective who can
+
+ align:start position:0%
+from an improvement perspective who can
+ 
+
+ align:start position:0%
+from an improvement perspective who can
+leverage the system of profound
+
+ align:start position:0%
+leverage the system of profound
+ 
+
+ align:start position:0%
+leverage the system of profound
+knowledge but we also need somebody
+
+ align:start position:0%
+knowledge but we also need somebody
+ 
+
+ align:start position:0%
+knowledge but we also need somebody
+who's a subject matter expert right if
+
+ align:start position:0%
+who's a subject matter expert right if
+ 
+
+ align:start position:0%
+who's a subject matter expert right if
+I'm going into Ghana and I want to help
+
+ align:start position:0%
+I'm going into Ghana and I want to help
+ 
+
+ align:start position:0%
+I'm going into Ghana and I want to help
+uh the country of Ghana to reduce under
+
+ align:start position:0%
+uh the country of Ghana to reduce under
+ 
+
+ align:start position:0%
+uh the country of Ghana to reduce under
+five mortality then I need to be working
+
+ align:start position:0%
+five mortality then I need to be working
+ 
+
+ align:start position:0%
+five mortality then I need to be working
+with some people who know about under
+
+ align:start position:0%
+with some people who know about under
+ 
+
+ align:start position:0%
+with some people who know about under
+five mortality I need to be working with
+
+ align:start position:0%
+five mortality I need to be working with
+ 
+
+ align:start position:0%
+five mortality I need to be working with
+some real experts in that environment
+
+ align:start position:0%
+some real experts in that environment
+ 
+
+ align:start position:0%
+some real experts in that environment
+clinicians nurses doctors counselors
+
+ align:start position:0%
+clinicians nurses doctors counselors
+ 
+
+ align:start position:0%
+clinicians nurses doctors counselors
+people who are working with communities
+
+ align:start position:0%
+people who are working with communities
+ 
+
+ align:start position:0%
+people who are working with communities
+who understand the context and
+
+ align:start position:0%
+who understand the context and
+ 
+
+ align:start position:0%
+who understand the context and
+understand the culture where I'm working
+
+ align:start position:0%
+understand the culture where I'm working
+ 
+
+ align:start position:0%
+understand the culture where I'm working
+right and I need to combine that with
+
+ align:start position:0%
+right and I need to combine that with
+ 
+
+ align:start position:0%
+right and I need to combine that with
+profound knowledge with this ability to
+
+ align:start position:0%
+profound knowledge with this ability to
+ 
+
+ align:start position:0%
+profound knowledge with this ability to
+look at Psychology to appreciate the
+
+ align:start position:0%
+look at Psychology to appreciate the
+ 
+
+ align:start position:0%
+look at Psychology to appreciate the
+system to articulate what I believe and
+
+ align:start position:0%
+system to articulate what I believe and
+ 
+
+ align:start position:0%
+system to articulate what I believe and
+to understand performance right if I
+
+ align:start position:0%
+to understand performance right if I
+ 
+
+ align:start position:0%
+to understand performance right if I
+want to achieve Improvement so it's
+
+ align:start position:0%
+want to achieve Improvement so it's
+ 
+
+ align:start position:0%
+want to achieve Improvement so it's
+where you those two things come together
+
+ align:start position:0%
+where you those two things come together
+ 
+
+ align:start position:0%
+where you those two things come together
+that we can actually take quality
+
+ align:start position:0%
+that we can actually take quality
+ 
+
+ align:start position:0%
+that we can actually take quality
+improvement forward right
+
+ align:start position:0%
+improvement forward right
+ 
+
+ align:start position:0%
+improvement forward right
+unfortunately most of us in our formal
+
+ align:start position:0%
+unfortunately most of us in our formal
+ 
+
+ align:start position:0%
+unfortunately most of us in our formal
+education we just learn this we learn
+
+ align:start position:0%
+education we just learn this we learn
+ 
+
+ align:start position:0%
+education we just learn this we learn
+subject matter knowledge right we go
+
+ align:start position:0%
+subject matter knowledge right we go
+ 
+
+ align:start position:0%
+subject matter knowledge right we go
+through our formal education becoming
+
+ align:start position:0%
+through our formal education becoming
+ 
+
+ align:start position:0%
+through our formal education becoming
+ever more expert at a particular thing
+
+ align:start position:0%
+ever more expert at a particular thing
+ 
+
+ align:start position:0%
+ever more expert at a particular thing
+right so Florence you told me you're a
+
+ align:start position:0%
+right so Florence you told me you're a
+ 
+
+ align:start position:0%
+right so Florence you told me you're a
+physician right what type of
+
+ align:start position:0%
+physician right what type of
+ 
+
+ align:start position:0%
+physician right what type of
+gynecologist right
+
+ align:start position:0%
+gynecologist right
+ 
+
+ align:start position:0%
+gynecologist right
+Leo also a physician ICU right would you
+
+ align:start position:0%
+Leo also a physician ICU right would you
+ 
+
+ align:start position:0%
+Leo also a physician ICU right would you
+feel real competent delivering
+
+ align:start position:0%
+feel real competent delivering
+ 
+
+ align:start position:0%
+feel real competent delivering
+gynecological
+
+ align:start position:0%
+gynecological
+ 
+
+ align:start position:0%
+gynecological
+Services how about vice versa we think
+
+ align:start position:0%
+Services how about vice versa we think
+ 
+
+ align:start position:0%
+Services how about vice versa we think
+we can do anything yeah right
+
+ align:start position:0%
+we can do anything yeah right
+ 
+
+ align:start position:0%
+we can do anything yeah right
+the idea there is medicine is especially
+
+ align:start position:0%
+the idea there is medicine is especially
+ 
+
+ align:start position:0%
+the idea there is medicine is especially
+prone to this specialization right we're
+
+ align:start position:0%
+prone to this specialization right we're
+ 
+
+ align:start position:0%
+prone to this specialization right we're
+constantly learning more and more
+
+ align:start position:0%
+constantly learning more and more
+ 
+
+ align:start position:0%
+constantly learning more and more
+information getting more and more
+
+ align:start position:0%
+information getting more and more
+ 
+
+ align:start position:0%
+information getting more and more
+specific about what we can do and
+
+ align:start position:0%
+specific about what we can do and
+ 
+
+ align:start position:0%
+specific about what we can do and
+becoming the best at that but that comes
+
+ align:start position:0%
+becoming the best at that but that comes
+ 
+
+ align:start position:0%
+becoming the best at that but that comes
+at a cost it comes at a cost of not
+
+ align:start position:0%
+at a cost it comes at a cost of not
+ 
+
+ align:start position:0%
+at a cost it comes at a cost of not
+understanding the culture the motivation
+
+ align:start position:0%
+understanding the culture the motivation
+ 
+
+ align:start position:0%
+understanding the culture the motivation
+the performance without be without the
+
+ align:start position:0%
+the performance without be without the
+ 
+
+ align:start position:0%
+the performance without be without the
+ability to see the big picture of what's
+
+ align:start position:0%
+ability to see the big picture of what's
+ 
+
+ align:start position:0%
+ability to see the big picture of what's
+going on for the Whole Health System
+
+ align:start position:0%
+going on for the Whole Health System
+ 
+
+ align:start position:0%
+going on for the Whole Health System
+right so bringing those two things
+
+ align:start position:0%
+right so bringing those two things
+ 
+
+ align:start position:0%
+right so bringing those two things
+together is critically important
+
+ align:start position:0%
+together is critically important
+ 
+
+ align:start position:0%
+together is critically important
+does that make sense to
+
+ align:start position:0%
+does that make sense to
+ 
+
+ align:start position:0%
+does that make sense to
+folks I get so scared when it's such a
+
+ align:start position:0%
+folks I get so scared when it's such a
+ 
+
+ align:start position:0%
+folks I get so scared when it's such a
+silent
+
+ align:start position:0%
+silent
+ 
+
+ align:start position:0%
+silent
+audience any questions on this so
+
+ align:start position:0%
+audience any questions on this so
+ 
+
+ align:start position:0%
+audience any questions on this so
+far all
+
+ align:start position:0%
+far all
+ 
+
+ align:start position:0%
+far all
+right okay so here's what I want you to
+
+ align:start position:0%
+right okay so here's what I want you to
+ 
+
+ align:start position:0%
+right okay so here's what I want you to
+do I know a lot of you have computers so
+
+ align:start position:0%
+do I know a lot of you have computers so
+ 
+
+ align:start position:0%
+do I know a lot of you have computers so
+maybe bring up a spreadsheet or one note
+
+ align:start position:0%
+maybe bring up a spreadsheet or one note
+ 
+
+ align:start position:0%
+maybe bring up a spreadsheet or one note
+Word document something like that do it
+
+ align:start position:0%
+Word document something like that do it
+ 
+
+ align:start position:0%
+Word document something like that do it
+in your head for those who have paper
+
+ align:start position:0%
+in your head for those who have paper
+ 
+
+ align:start position:0%
+in your head for those who have paper
+get out a sheet of paper and a pen okay
+
+ align:start position:0%
+get out a sheet of paper and a pen okay
+ 
+
+ align:start position:0%
+get out a sheet of paper and a pen okay
+here's what I want you to do okay I want
+
+ align:start position:0%
+here's what I want you to do okay I want
+ 
+
+ align:start position:0%
+here's what I want you to do okay I want
+you to choose a number between three and
+
+ align:start position:0%
+you to choose a number between three and
+ 
+
+ align:start position:0%
+you to choose a number between three and
+nine write that down 3 4 5 six 7 8 n
+
+ align:start position:0%
+nine write that down 3 4 5 six 7 8 n
+ 
+
+ align:start position:0%
+nine write that down 3 4 5 six 7 8 n
+okay you have a
+
+ align:start position:0%
+okay you have a
+ 
+
+ align:start position:0%
+okay you have a
+number yes okay good yeah there we go
+
+ align:start position:0%
+number yes okay good yeah there we go
+ 
+
+ align:start position:0%
+number yes okay good yeah there we go
+all right I like Peter all right Next
+
+ align:start position:0%
+all right I like Peter all right Next
+ 
+
+ align:start position:0%
+all right I like Peter all right Next
+Step I want you to multiply your number
+
+ align:start position:0%
+Step I want you to multiply your number
+ 
+
+ align:start position:0%
+Step I want you to multiply your number
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+nine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you got that so if you had three
+
+ align:start position:0%
+okay you got that so if you had three
+ 
+
+ align:start position:0%
+okay you got that so if you had three
+your new number is
+
+ align:start position:0%
+your new number is
+ 
+
+ align:start position:0%
+your new number is
+what on the spot 3 *
+
+ align:start position:0%
+what on the spot 3 *
+ 
+
+ align:start position:0%
+what on the spot 3 *
+9 27 good job I'm with Lao I need the
+
+ align:start position:0%
+9 27 good job I'm with Lao I need the
+ 
+
+ align:start position:0%
+9 27 good job I'm with Lao I need the
+calculator all
+
+ align:start position:0%
+calculator all
+ 
+
+ align:start position:0%
+calculator all
+right I want you to add 12 to this new
+
+ align:start position:0%
+right I want you to add 12 to this new
+ 
+
+ align:start position:0%
+right I want you to add 12 to this new
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay got it fast right all right okay
+
+ align:start position:0%
+okay got it fast right all right okay
+ 
+
+ align:start position:0%
+okay got it fast right all right okay
+everybody have a two-digit number just
+
+ align:start position:0%
+everybody have a two-digit number just
+ 
+
+ align:start position:0%
+everybody have a two-digit number just
+real quick if you ended up with
+
+ align:start position:0%
+real quick if you ended up with
+ 
+
+ align:start position:0%
+real quick if you ended up with
+something over a 100 under 10 we're in
+
+ align:start position:0%
+something over a 100 under 10 we're in
+ 
+
+ align:start position:0%
+something over a 100 under 10 we're in
+trouble here just want to make sure okay
+
+ align:start position:0%
+trouble here just want to make sure okay
+ 
+
+ align:start position:0%
+trouble here just want to make sure okay
+I want you to take those two digits and
+
+ align:start position:0%
+I want you to take those two digits and
+ 
+
+ align:start position:0%
+I want you to take those two digits and
+add them together so if my number was 18
+
+ align:start position:0%
+add them together so if my number was 18
+ 
+
+ align:start position:0%
+add them together so if my number was 18
+I would take 1 + 8 that would equal
+
+ align:start position:0%
+I would take 1 + 8 that would equal
+ 
+
+ align:start position:0%
+I would take 1 + 8 that would equal
+9 you got that all right math is almost
+
+ align:start position:0%
+9 you got that all right math is almost
+ 
+
+ align:start position:0%
+9 you got that all right math is almost
+done for the day I know you guys weren't
+
+ align:start position:0%
+done for the day I know you guys weren't
+ 
+
+ align:start position:0%
+done for the day I know you guys weren't
+expecting that this morning early in the
+
+ align:start position:0%
+expecting that this morning early in the
+ 
+
+ align:start position:0%
+expecting that this morning early in the
+morning all right divide that number by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three should have a one-digit number
+
+ align:start position:0%
+three should have a one-digit number
+ 
+
+ align:start position:0%
+three should have a one-digit number
+everybody got a one-digit
+
+ align:start position:0%
+everybody got a one-digit
+ 
+
+ align:start position:0%
+everybody got a one-digit
+number all right now whatever your
+
+ align:start position:0%
+number all right now whatever your
+ 
+
+ align:start position:0%
+number all right now whatever your
+number is I want you to convert it to a
+
+ align:start position:0%
+number is I want you to convert it to a
+ 
+
+ align:start position:0%
+number is I want you to convert it to a
+letter so if your number is one you now
+
+ align:start position:0%
+letter so if your number is one you now
+ 
+
+ align:start position:0%
+letter so if your number is one you now
+have the letter A if your number is two
+
+ align:start position:0%
+have the letter A if your number is two
+ 
+
+ align:start position:0%
+have the letter A if your number is two
+you have the letter b and and so on have
+
+ align:start position:0%
+you have the letter b and and so on have
+ 
+
+ align:start position:0%
+you have the letter b and and so on have
+you got your
+
+ align:start position:0%
+you got your
+ 
+
+ align:start position:0%
+you got your
+letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I want you to write down the name
+
+ align:start position:0%
+okay I want you to write down the name
+ 
+
+ align:start position:0%
+okay I want you to write down the name
+of a country that begins with your
+
+ align:start position:0%
+of a country that begins with your
+ 
+
+ align:start position:0%
+of a country that begins with your
+letter okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right Next Step whatever your letter was
+
+ align:start position:0%
+right Next Step whatever your letter was
+ 
+
+ align:start position:0%
+right Next Step whatever your letter was
+I want you to take the next letter in
+
+ align:start position:0%
+I want you to take the next letter in
+ 
+
+ align:start position:0%
+I want you to take the next letter in
+the alphabet so if my letter was a my
+
+ align:start position:0%
+the alphabet so if my letter was a my
+ 
+
+ align:start position:0%
+the alphabet so if my letter was a my
+new letter is B okay let's take that
+
+ align:start position:0%
+new letter is B okay let's take that
+ 
+
+ align:start position:0%
+new letter is B okay let's take that
+letter I want you to write down the name
+
+ align:start position:0%
+letter I want you to write down the name
+ 
+
+ align:start position:0%
+letter I want you to write down the name
+of an animal that begins with that
+
+ align:start position:0%
+of an animal that begins with that
+ 
+
+ align:start position:0%
+of an animal that begins with that
+letter okay so it can't be a bird or an
+
+ align:start position:0%
+letter okay so it can't be a bird or an
+ 
+
+ align:start position:0%
+letter okay so it can't be a bird or an
+insect or a fish I want like a land
+
+ align:start position:0%
+insect or a fish I want like a land
+ 
+
+ align:start position:0%
+insect or a fish I want like a land
+dwelling mammal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+it all right last step here I want you
+
+ align:start position:0%
+it all right last step here I want you
+ 
+
+ align:start position:0%
+it all right last step here I want you
+to write down the color of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animal the color of the
+
+ align:start position:0%
+animal the color of the
+ 
+
+ align:start position:0%
+animal the color of the
+animal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right yall with
+
+ align:start position:0%
+okay all right yall with
+ 
+
+ align:start position:0%
+okay all right yall with
+me there you go
+
+ align:start position:0%
+me there you go
+ 
+
+ align:start position:0%
+me there you go
+okay any
+
+ align:start position:0%
+okay any
+ 
+
+ align:start position:0%
+okay any
+what country did you have Denmark
+
+ align:start position:0%
+what country did you have Denmark
+ 
+
+ align:start position:0%
+what country did you have Denmark
+Denmark what animal did you
+
+ align:start position:0%
+Denmark what animal did you
+ 
+
+ align:start position:0%
+Denmark what animal did you
+have what color is an
+
+ align:start position:0%
+have what color is an
+ 
+
+ align:start position:0%
+have what color is an
+elephant how many people had a gray
+
+ align:start position:0%
+elephant how many people had a gray
+ 
+
+ align:start position:0%
+elephant how many people had a gray
+elephant in
+
+ align:start position:0%
+elephant in
+ 
+
+ align:start position:0%
+elephant in
+Denmark wow wow that's
+
+ align:start position:0%
+Denmark wow wow that's
+ 
+
+ align:start position:0%
+Denmark wow wow that's
+incredible now Annie one quick question
+
+ align:start position:0%
+incredible now Annie one quick question
+ 
+
+ align:start position:0%
+incredible now Annie one quick question
+here what number did you start
+
+ align:start position:0%
+here what number did you start
+ 
+
+ align:start position:0%
+here what number did you start
+with six did you all start with six you
+
+ align:start position:0%
+with six did you all start with six you
+ 
+
+ align:start position:0%
+with six did you all start with six you
+started with six but no what what what
+
+ align:start position:0%
+started with six but no what what what
+ 
+
+ align:start position:0%
+started with six but no what what what
+was seven five eight
+
+ align:start position:0%
+was seven five eight
+ 
+
+ align:start position:0%
+was seven five eight
+right wow amazing so there's some
+
+ align:start position:0%
+right wow amazing so there's some
+ 
+
+ align:start position:0%
+right wow amazing so there's some
+there's some variation here there's a
+
+ align:start position:0%
+there's some variation here there's a
+ 
+
+ align:start position:0%
+there's some variation here there's a
+few people who might have gotten
+
+ align:start position:0%
+few people who might have gotten
+ 
+
+ align:start position:0%
+few people who might have gotten
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+different but what
+
+ align:start position:0%
+different but what
+ 
+
+ align:start position:0%
+different but what
+happened you had some free choice here
+
+ align:start position:0%
+happened you had some free choice here
+ 
+
+ align:start position:0%
+happened you had some free choice here
+you could have chose any number right
+
+ align:start position:0%
+you could have chose any number right
+ 
+
+ align:start position:0%
+you could have chose any number right
+you made the
+
+ align:start position:0%
+you made the
+ 
+
+ align:start position:0%
+you made the
+decision what happened was the process
+
+ align:start position:0%
+decision what happened was the process
+ 
+
+ align:start position:0%
+decision what happened was the process
+took over right we put you into a
+
+ align:start position:0%
+took over right we put you into a
+ 
+
+ align:start position:0%
+took over right we put you into a
+process and we started the dec the the
+
+ align:start position:0%
+process and we started the dec the the
+ 
+
+ align:start position:0%
+process and we started the dec the the
+process started to make decisions about
+
+ align:start position:0%
+process started to make decisions about
+ 
+
+ align:start position:0%
+process started to make decisions about
+what your outcome was going to be right
+
+ align:start position:0%
+what your outcome was going to be right
+ 
+
+ align:start position:0%
+what your outcome was going to be right
+now in any given room about nine out of
+
+ align:start position:0%
+now in any given room about nine out of
+ 
+
+ align:start position:0%
+now in any given room about nine out of
+10 people are going to get a gray
+
+ align:start position:0%
+10 people are going to get a gray
+ 
+
+ align:start position:0%
+10 people are going to get a gray
+elephant in
+
+ align:start position:0%
+elephant in
+ 
+
+ align:start position:0%
+elephant in
+Denmark you get a few people who are
+
+ align:start position:0%
+Denmark you get a few people who are
+ 
+
+ align:start position:0%
+Denmark you get a few people who are
+going to get a Eland in the Dominican
+
+ align:start position:0%
+going to get a Eland in the Dominican
+ 
+
+ align:start position:0%
+going to get a Eland in the Dominican
+Republic or something like that right
+
+ align:start position:0%
+Republic or something like that right
+ 
+
+ align:start position:0%
+Republic or something like that right
+but that's pretty rare right and this is
+
+ align:start position:0%
+but that's pretty rare right and this is
+ 
+
+ align:start position:0%
+but that's pretty rare right and this is
+an important lesson that Deming gave us
+
+ align:start position:0%
+an important lesson that Deming gave us
+ 
+
+ align:start position:0%
+an important lesson that Deming gave us
+about appreciation of systems okay so
+
+ align:start position:0%
+about appreciation of systems okay so
+ 
+
+ align:start position:0%
+about appreciation of systems okay so
+Deming argued from a statistical
+
+ align:start position:0%
+Deming argued from a statistical
+ 
+
+ align:start position:0%
+Deming argued from a statistical
+perspective that about 95% of all the
+
+ align:start position:0%
+perspective that about 95% of all the
+ 
+
+ align:start position:0%
+perspective that about 95% of all the
+variation we see in stable performance
+
+ align:start position:0%
+variation we see in stable performance
+ 
+
+ align:start position:0%
+variation we see in stable performance
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+systems is the responsibility of the
+
+ align:start position:0%
+systems is the responsibility of the
+ 
+
+ align:start position:0%
+systems is the responsibility of the
+system itself not of the individual
+
+ align:start position:0%
+system itself not of the individual
+ 
+
+ align:start position:0%
+system itself not of the individual
+workers right I know it's only about
+
+ align:start position:0%
+workers right I know it's only about
+ 
+
+ align:start position:0%
+workers right I know it's only about
+5% so a lot of times we hear
+
+ align:start position:0%
+5% so a lot of times we hear
+ 
+
+ align:start position:0%
+5% so a lot of times we hear
+admonishments you know if people just
+
+ align:start position:0%
+admonishments you know if people just
+ 
+
+ align:start position:0%
+admonishments you know if people just
+worked harder you know maybe if we paid
+
+ align:start position:0%
+worked harder you know maybe if we paid
+ 
+
+ align:start position:0%
+worked harder you know maybe if we paid
+them a little
+
+ align:start position:0%
+them a little
+ 
+
+ align:start position:0%
+them a little
+more right maybe if we punished them
+
+ align:start position:0%
+more right maybe if we punished them
+ 
+
+ align:start position:0%
+more right maybe if we punished them
+then we'd really get something done
+
+ align:start position:0%
+then we'd really get something done
+ 
+
+ align:start position:0%
+then we'd really get something done
+right the reality is that's not the case
+
+ align:start position:0%
+right the reality is that's not the case
+ 
+
+ align:start position:0%
+right the reality is that's not the case
+it's a system that controls the outcome
+
+ align:start position:0%
+it's a system that controls the outcome
+ 
+
+ align:start position:0%
+it's a system that controls the outcome
+so if I'm in a resource constrained
+
+ align:start position:0%
+so if I'm in a resource constrained
+ 
+
+ align:start position:0%
+so if I'm in a resource constrained
+environment and I see really high
+
+ align:start position:0%
+environment and I see really high
+ 
+
+ align:start position:0%
+environment and I see really high
+mortality rates let's say I'm in Ghana
+
+ align:start position:0%
+mortality rates let's say I'm in Ghana
+ 
+
+ align:start position:0%
+mortality rates let's say I'm in Ghana
+and I have you know 80 uh uh deaths in
+
+ align:start position:0%
+and I have you know 80 uh uh deaths in
+ 
+
+ align:start position:0%
+and I have you know 80 uh uh deaths in
+children under the age of five for every
+
+ align:start position:0%
+children under the age of five for every
+ 
+
+ align:start position:0%
+children under the age of five for every
+thousand live births right that is a
+
+ align:start position:0%
+thousand live births right that is a
+ 
+
+ align:start position:0%
+thousand live births right that is a
+product of the system that I'm in it's
+
+ align:start position:0%
+product of the system that I'm in it's
+ 
+
+ align:start position:0%
+product of the system that I'm in it's
+no one person's fault it's not laziness
+
+ align:start position:0%
+no one person's fault it's not laziness
+ 
+
+ align:start position:0%
+no one person's fault it's not laziness
+on the part of the workers it is the
+
+ align:start position:0%
+on the part of the workers it is the
+ 
+
+ align:start position:0%
+on the part of the workers it is the
+system itself right Leo introduced us to
+
+ align:start position:0%
+system itself right Leo introduced us to
+ 
+
+ align:start position:0%
+system itself right Leo introduced us to
+the concept of every system being
+
+ align:start position:0%
+the concept of every system being
+ 
+
+ align:start position:0%
+the concept of every system being
+perfectly designed to achieve the
+
+ align:start position:0%
+perfectly designed to achieve the
+ 
+
+ align:start position:0%
+perfectly designed to achieve the
+results it gets that's what he's talking
+
+ align:start position:0%
+results it gets that's what he's talking
+ 
+
+ align:start position:0%
+results it gets that's what he's talking
+about right there okay that's what he's
+
+ align:start position:0%
+about right there okay that's what he's
+ 
+
+ align:start position:0%
+about right there okay that's what he's
+talking about right there does that make
+
+ align:start position:0%
+talking about right there does that make
+ 
+
+ align:start position:0%
+talking about right there does that make
+sense to folks this is an incredibly
+
+ align:start position:0%
+sense to folks this is an incredibly
+ 
+
+ align:start position:0%
+sense to folks this is an incredibly
+important concept when you start to
+
+ align:start position:0%
+important concept when you start to
+ 
+
+ align:start position:0%
+important concept when you start to
+think about quality improvement right
+
+ align:start position:0%
+think about quality improvement right
+ 
+
+ align:start position:0%
+think about quality improvement right
+this quality improvement needs to be
+
+ align:start position:0%
+this quality improvement needs to be
+ 
+
+ align:start position:0%
+this quality improvement needs to be
+leveraged on the system not on the
+
+ align:start position:0%
+leveraged on the system not on the
+ 
+
+ align:start position:0%
+leveraged on the system not on the
+individuals so let's let's do another
+
+ align:start position:0%
+individuals so let's let's do another
+ 
+
+ align:start position:0%
+individuals so let's let's do another
+example Leo come come come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you're a pretty healthy guy
+
+ align:start position:0%
+here you're a pretty healthy guy
+ 
+
+ align:start position:0%
+here you're a pretty healthy guy
+right exercise frequently all right Le I
+
+ align:start position:0%
+right exercise frequently all right Le I
+ 
+
+ align:start position:0%
+right exercise frequently all right Le I
+want you to jump up and touch the
+
+ align:start position:0%
+want you to jump up and touch the
+ 
+
+ align:start position:0%
+want you to jump up and touch the
+ceiling
+
+ align:start position:0%
+ceiling
+ 
+
+ align:start position:0%
+ceiling
+can you do that for me they can't see it
+
+ align:start position:0%
+can you do that for me they can't see it
+ 
+
+ align:start position:0%
+can you do that for me they can't see it
+though no go ahead just just give it a
+
+ align:start position:0%
+though no go ahead just just give it a
+ 
+
+ align:start position:0%
+though no go ahead just just give it a
+jump give it a shot
+
+ align:start position:0%
+jump give it a shot
+ 
+
+ align:start position:0%
+jump give it a shot
+seriously all right that wasn't too good
+
+ align:start position:0%
+seriously all right that wasn't too good
+ 
+
+ align:start position:0%
+seriously all right that wasn't too good
+I don't think he's properly I I I don't
+
+ align:start position:0%
+I don't think he's properly I I I don't
+ 
+
+ align:start position:0%
+I don't think he's properly I I I don't
+think he's properly motivated Leo here's
+
+ align:start position:0%
+think he's properly motivated Leo here's
+ 
+
+ align:start position:0%
+think he's properly motivated Leo here's
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+money if you could touch a ceiling you
+
+ align:start position:0%
+money if you could touch a ceiling you
+ 
+
+ align:start position:0%
+money if you could touch a ceiling you
+can have all that money you think you
+
+ align:start position:0%
+can have all that money you think you
+ 
+
+ align:start position:0%
+can have all that money you think you
+could do it oh it's some the
+
+ align:start position:0%
+could do it oh it's some the
+ 
+
+ align:start position:0%
+could do it oh it's some the
+Trap right it's a system right we talk
+
+ align:start position:0%
+Trap right it's a system right we talk
+ 
+
+ align:start position:0%
+Trap right it's a system right we talk
+about pay for performance you can't
+
+ align:start position:0%
+about pay for performance you can't
+ 
+
+ align:start position:0%
+about pay for performance you can't
+really pay for performance when a system
+
+ align:start position:0%
+really pay for performance when a system
+ 
+
+ align:start position:0%
+really pay for performance when a system
+is controlling the outcome right there's
+
+ align:start position:0%
+is controlling the outcome right there's
+ 
+
+ align:start position:0%
+is controlling the outcome right there's
+no way he's ever going to touch the
+
+ align:start position:0%
+no way he's ever going to touch the
+ 
+
+ align:start position:0%
+no way he's ever going to touch the
+ceiling not not just from a standing
+
+ align:start position:0%
+ceiling not not just from a standing
+ 
+
+ align:start position:0%
+ceiling not not just from a standing
+jump so it's incredibly important to
+
+ align:start position:0%
+jump so it's incredibly important to
+ 
+
+ align:start position:0%
+jump so it's incredibly important to
+have that systems view what I want to
+
+ align:start position:0%
+have that systems view what I want to
+ 
+
+ align:start position:0%
+have that systems view what I want to
+introduce you to is a tool that Demi
+
+ align:start position:0%
+introduce you to is a tool that Demi
+ 
+
+ align:start position:0%
+introduce you to is a tool that Demi
+gave us for starting to develop that now
+
+ align:start position:0%
+gave us for starting to develop that now
+ 
+
+ align:start position:0%
+gave us for starting to develop that now
+we're going to look at it conceptually
+
+ align:start position:0%
+we're going to look at it conceptually
+ 
+
+ align:start position:0%
+we're going to look at it conceptually
+but you can do it very very specifically
+
+ align:start position:0%
+but you can do it very very specifically
+ 
+
+ align:start position:0%
+but you can do it very very specifically
+for any system that you work in okay so
+
+ align:start position:0%
+for any system that you work in okay so
+ 
+
+ align:start position:0%
+for any system that you work in okay so
+what is a system it's a collection of
+
+ align:start position:0%
+what is a system it's a collection of
+ 
+
+ align:start position:0%
+what is a system it's a collection of
+processes working together towards a
+
+ align:start position:0%
+processes working together towards a
+ 
+
+ align:start position:0%
+processes working together towards a
+defined output that's that's how we
+
+ align:start position:0%
+defined output that's that's how we
+ 
+
+ align:start position:0%
+defined output that's that's how we
+would Define that right
+
+ align:start position:0%
+would Define that right
+ 
+
+ align:start position:0%
+would Define that right
+so and Demi would argue it's where you
+
+ align:start position:0%
+so and Demi would argue it's where you
+ 
+
+ align:start position:0%
+so and Demi would argue it's where you
+draw the circle right it could be a
+
+ align:start position:0%
+draw the circle right it could be a
+ 
+
+ align:start position:0%
+draw the circle right it could be a
+single process it could be uh say
+
+ align:start position:0%
+single process it could be uh say
+ 
+
+ align:start position:0%
+single process it could be uh say
+something like antinal care which is a
+
+ align:start position:0%
+something like antinal care which is a
+ 
+
+ align:start position:0%
+something like antinal care which is a
+single process or we could take into
+
+ align:start position:0%
+single process or we could take into
+ 
+
+ align:start position:0%
+single process or we could take into
+account labor and delivery as well even
+
+ align:start position:0%
+account labor and delivery as well even
+ 
+
+ align:start position:0%
+account labor and delivery as well even
+postnatal care now we're grouping a set
+
+ align:start position:0%
+postnatal care now we're grouping a set
+ 
+
+ align:start position:0%
+postnatal care now we're grouping a set
+of processes together that are working
+
+ align:start position:0%
+of processes together that are working
+ 
+
+ align:start position:0%
+of processes together that are working
+towards a defined output which might be
+
+ align:start position:0%
+towards a defined output which might be
+ 
+
+ align:start position:0%
+towards a defined output which might be
+a healthy child right we might even say
+
+ align:start position:0%
+a healthy child right we might even say
+ 
+
+ align:start position:0%
+a healthy child right we might even say
+it's the Continuum of Care from birth
+
+ align:start position:0%
+it's the Continuum of Care from birth
+ 
+
+ align:start position:0%
+it's the Continuum of Care from birth
+through death so now we're talking about
+
+ align:start position:0%
+through death so now we're talking about
+ 
+
+ align:start position:0%
+through death so now we're talking about
+everything we're talking about uh
+
+ align:start position:0%
+everything we're talking about uh
+ 
+
+ align:start position:0%
+everything we're talking about uh
+chronic disease management we're talking
+
+ align:start position:0%
+chronic disease management we're talking
+ 
+
+ align:start position:0%
+chronic disease management we're talking
+about acute care settings Emergency
+
+ align:start position:0%
+about acute care settings Emergency
+ 
+
+ align:start position:0%
+about acute care settings Emergency
+Settings all that can be put into a
+
+ align:start position:0%
+Settings all that can be put into a
+ 
+
+ align:start position:0%
+Settings all that can be put into a
+system right you get to
+
+ align:start position:0%
+system right you get to
+ 
+
+ align:start position:0%
+system right you get to
+decide the larger you draw the circle
+
+ align:start position:0%
+decide the larger you draw the circle
+ 
+
+ align:start position:0%
+decide the larger you draw the circle
+the more complex the interactions are
+
+ align:start position:0%
+the more complex the interactions are
+ 
+
+ align:start position:0%
+the more complex the interactions are
+going to become and so it's more and
+
+ align:start position:0%
+going to become and so it's more and
+ 
+
+ align:start position:0%
+going to become and so it's more and
+more important to have the ability to
+
+ align:start position:0%
+more important to have the ability to
+ 
+
+ align:start position:0%
+more important to have the ability to
+see what's going on now I think Leo you
+
+ align:start position:0%
+see what's going on now I think Leo you
+ 
+
+ align:start position:0%
+see what's going on now I think Leo you
+you you attributed this quote to Don
+
+ align:start position:0%
+you you attributed this quote to Don
+ 
+
+ align:start position:0%
+you you attributed this quote to Don
+Berwick and I'm I'm attributing it to
+
+ align:start position:0%
+Berwick and I'm I'm attributing it to
+ 
+
+ align:start position:0%
+Berwick and I'm I'm attributing it to
+Paul Balden and they're very good
+
+ align:start position:0%
+Paul Balden and they're very good
+ 
+
+ align:start position:0%
+Paul Balden and they're very good
+friends um and and both of them say that
+
+ align:start position:0%
+friends um and and both of them say that
+ 
+
+ align:start position:0%
+friends um and and both of them say that
+the other person said this so it's
+
+ align:start position:0%
+the other person said this so it's
+ 
+
+ align:start position:0%
+the other person said this so it's
+actually it's quite funny they argue
+
+ align:start position:0%
+actually it's quite funny they argue
+ 
+
+ align:start position:0%
+actually it's quite funny they argue
+about it all the time um so I figured I
+
+ align:start position:0%
+about it all the time um so I figured I
+ 
+
+ align:start position:0%
+about it all the time um so I figured I
+would do the different one since you
+
+ align:start position:0%
+would do the different one since you
+ 
+
+ align:start position:0%
+would do the different one since you
+said it was Don's all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the best tool for
+
+ align:start position:0%
+so what's the best tool for
+ 
+
+ align:start position:0%
+so what's the best tool for
+understanding systems right there's lots
+
+ align:start position:0%
+understanding systems right there's lots
+ 
+
+ align:start position:0%
+understanding systems right there's lots
+of tools we can use we're going to talk
+
+ align:start position:0%
+of tools we can use we're going to talk
+ 
+
+ align:start position:0%
+of tools we can use we're going to talk
+about two this morning all right but
+
+ align:start position:0%
+about two this morning all right but
+ 
+
+ align:start position:0%
+about two this morning all right but
+it's really important that when you
+
+ align:start position:0%
+it's really important that when you
+ 
+
+ align:start position:0%
+it's really important that when you
+approach a a problem A System's problem
+
+ align:start position:0%
+approach a a problem A System's problem
+ 
+
+ align:start position:0%
+approach a a problem A System's problem
+that you have a perspective of which
+
+ align:start position:0%
+that you have a perspective of which
+ 
+
+ align:start position:0%
+that you have a perspective of which
+tool right has everyone ever heard the
+
+ align:start position:0%
+tool right has everyone ever heard the
+ 
+
+ align:start position:0%
+tool right has everyone ever heard the
+saying you when all you have is a hammer
+
+ align:start position:0%
+saying you when all you have is a hammer
+ 
+
+ align:start position:0%
+saying you when all you have is a hammer
+the whole world looks like a nail
+
+ align:start position:0%
+the whole world looks like a nail
+ 
+
+ align:start position:0%
+the whole world looks like a nail
+right so important when you're
+
+ align:start position:0%
+right so important when you're
+ 
+
+ align:start position:0%
+right so important when you're
+approaching A System's problem to
+
+ align:start position:0%
+approaching A System's problem to
+ 
+
+ align:start position:0%
+approaching A System's problem to
+approach it with a series of tools and
+
+ align:start position:0%
+approach it with a series of tools and
+ 
+
+ align:start position:0%
+approach it with a series of tools and
+and and try to choose something that's
+
+ align:start position:0%
+and and try to choose something that's
+ 
+
+ align:start position:0%
+and and try to choose something that's
+going to work
+
+ align:start position:0%
+going to work
+ 
+
+ align:start position:0%
+going to work
+appropriately okay so what I'm going to
+
+ align:start position:0%
+appropriately okay so what I'm going to
+ 
+
+ align:start position:0%
+appropriately okay so what I'm going to
+introduce today is is deming's linkage
+
+ align:start position:0%
+introduce today is is deming's linkage
+ 
+
+ align:start position:0%
+introduce today is is deming's linkage
+of process this is adapted from
+
+ align:start position:0%
+of process this is adapted from
+ 
+
+ align:start position:0%
+of process this is adapted from
+Associates and process Improvement a
+
+ align:start position:0%
+Associates and process Improvement a
+ 
+
+ align:start position:0%
+Associates and process Improvement a
+group of his students who have taken his
+
+ align:start position:0%
+group of his students who have taken his
+ 
+
+ align:start position:0%
+group of his students who have taken his
+work further um and linkage a process is
+
+ align:start position:0%
+work further um and linkage a process is
+ 
+
+ align:start position:0%
+work further um and linkage a process is
+a is a way of viewing all of the work
+
+ align:start position:0%
+a is a way of viewing all of the work
+ 
+
+ align:start position:0%
+a is a way of viewing all of the work
+that is happening within a system Demi
+
+ align:start position:0%
+that is happening within a system Demi
+ 
+
+ align:start position:0%
+that is happening within a system Demi
+argued he he said one of his famous
+
+ align:start position:0%
+argued he he said one of his famous
+ 
+
+ align:start position:0%
+argued he he said one of his famous
+quotes was all work is a process or all
+
+ align:start position:0%
+quotes was all work is a process or all
+ 
+
+ align:start position:0%
+quotes was all work is a process or all
+processes as work one of the
+
+ align:start position:0%
+processes as work one of the
+ 
+
+ align:start position:0%
+processes as work one of the
+two he said a an organization starts
+
+ align:start position:0%
+two he said a an organization starts
+ 
+
+ align:start position:0%
+two he said a an organization starts
+with a purpose okay a system starts with
+
+ align:start position:0%
+with a purpose okay a system starts with
+ 
+
+ align:start position:0%
+with a purpose okay a system starts with
+a purpose and we need to Define what
+
+ align:start position:0%
+a purpose and we need to Define what
+ 
+
+ align:start position:0%
+a purpose and we need to Define what
+that is what is that particular thing
+
+ align:start position:0%
+that is what is that particular thing
+ 
+
+ align:start position:0%
+that is what is that particular thing
+why do we exist as an organization okay
+
+ align:start position:0%
+why do we exist as an organization okay
+ 
+
+ align:start position:0%
+why do we exist as an organization okay
+do we have a sense of
+
+ align:start position:0%
+do we have a sense of
+ 
+
+ align:start position:0%
+do we have a sense of
+that that's going to control what our
+
+ align:start position:0%
+that that's going to control what our
+ 
+
+ align:start position:0%
+that that's going to control what our
+outcome will be what our sort of uh what
+
+ align:start position:0%
+outcome will be what our sort of uh what
+ 
+
+ align:start position:0%
+outcome will be what our sort of uh what
+it is we're going to produce for our
+
+ align:start position:0%
+it is we're going to produce for our
+ 
+
+ align:start position:0%
+it is we're going to produce for our
+clients so uh that's that's important
+
+ align:start position:0%
+clients so uh that's that's important
+ 
+
+ align:start position:0%
+clients so uh that's that's important
+from a health perspective that might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what say that again improved health
+
+ align:start position:0%
+what say that again improved health
+ 
+
+ align:start position:0%
+what say that again improved health
+status yeah improved health status right
+
+ align:start position:0%
+status yeah improved health status right
+ 
+
+ align:start position:0%
+status yeah improved health status right
+right we ever heard that health for all
+
+ align:start position:0%
+right we ever heard that health for all
+ 
+
+ align:start position:0%
+right we ever heard that health for all
+things like that sort of sort of vague
+
+ align:start position:0%
+things like that sort of sort of vague
+ 
+
+ align:start position:0%
+things like that sort of sort of vague
+things right or it could be something
+
+ align:start position:0%
+things right or it could be something
+ 
+
+ align:start position:0%
+things right or it could be something
+very specific it could be a particular
+
+ align:start position:0%
+very specific it could be a particular
+ 
+
+ align:start position:0%
+very specific it could be a particular
+outcome from say a surgery okay so
+
+ align:start position:0%
+outcome from say a surgery okay so
+ 
+
+ align:start position:0%
+outcome from say a surgery okay so
+whatever it is we want to be very clear
+
+ align:start position:0%
+whatever it is we want to be very clear
+ 
+
+ align:start position:0%
+whatever it is we want to be very clear
+about what it is that our
+
+ align:start position:0%
+about what it is that our
+ 
+
+ align:start position:0%
+about what it is that our
+outcome the outcome that we want to
+
+ align:start position:0%
+outcome the outcome that we want to
+ 
+
+ align:start position:0%
+outcome the outcome that we want to
+deliver now Deming said that there is
+
+ align:start position:0%
+deliver now Deming said that there is
+ 
+
+ align:start position:0%
+deliver now Deming said that there is
+work that we do that is focused on
+
+ align:start position:0%
+work that we do that is focused on
+ 
+
+ align:start position:0%
+work that we do that is focused on
+producing that outcome so let's take uh
+
+ align:start position:0%
+producing that outcome so let's take uh
+ 
+
+ align:start position:0%
+producing that outcome so let's take uh
+uh maternal mortality I know that's a an
+
+ align:start position:0%
+uh maternal mortality I know that's a an
+ 
+
+ align:start position:0%
+uh maternal mortality I know that's a an
+issue for a lot of folks in here and
+
+ align:start position:0%
+issue for a lot of folks in here and
+ 
+
+ align:start position:0%
+issue for a lot of folks in here and
+that are people are interested in in ch
+
+ align:start position:0%
+that are people are interested in in ch
+ 
+
+ align:start position:0%
+that are people are interested in in ch
+Early Childhood mortality it's something
+
+ align:start position:0%
+Early Childhood mortality it's something
+ 
+
+ align:start position:0%
+Early Childhood mortality it's something
+that's I'm interested in okay uh there
+
+ align:start position:0%
+that's I'm interested in okay uh there
+ 
+
+ align:start position:0%
+that's I'm interested in okay uh there
+are things that we do we provide antinal
+
+ align:start position:0%
+are things that we do we provide antinal
+ 
+
+ align:start position:0%
+are things that we do we provide antinal
+care we want to get people in early we
+
+ align:start position:0%
+care we want to get people in early we
+ 
+
+ align:start position:0%
+care we want to get people in early we
+want to get pregnant women in early and
+
+ align:start position:0%
+want to get pregnant women in early and
+ 
+
+ align:start position:0%
+want to get pregnant women in early and
+identify them as as being pregnant and
+
+ align:start position:0%
+identify them as as being pregnant and
+ 
+
+ align:start position:0%
+identify them as as being pregnant and
+then start delivering a set of Services
+
+ align:start position:0%
+then start delivering a set of Services
+ 
+
+ align:start position:0%
+then start delivering a set of Services
+immunizations care monitoring their
+
+ align:start position:0%
+immunizations care monitoring their
+ 
+
+ align:start position:0%
+immunizations care monitoring their
+pregnancy uh right there's a certain
+
+ align:start position:0%
+pregnancy uh right there's a certain
+ 
+
+ align:start position:0%
+pregnancy uh right there's a certain
+level of patient care that's taking
+
+ align:start position:0%
+level of patient care that's taking
+ 
+
+ align:start position:0%
+level of patient care that's taking
+place Deming called this the Mainstay
+
+ align:start position:0%
+place Deming called this the Mainstay
+ 
+
+ align:start position:0%
+place Deming called this the Mainstay
+processes okay these are things that you
+
+ align:start position:0%
+processes okay these are things that you
+ 
+
+ align:start position:0%
+processes okay these are things that you
+are doing to get the outcome that you
+
+ align:start position:0%
+are doing to get the outcome that you
+ 
+
+ align:start position:0%
+are doing to get the outcome that you
+want right if it were surgical care it
+
+ align:start position:0%
+want right if it were surgical care it
+ 
+
+ align:start position:0%
+want right if it were surgical care it
+would be doing the surgery going into
+
+ align:start position:0%
+would be doing the surgery going into
+ 
+
+ align:start position:0%
+would be doing the surgery going into
+the theater with the patient surgical
+
+ align:start position:0%
+the theater with the patient surgical
+ 
+
+ align:start position:0%
+the theater with the patient surgical
+team delivering the surgery right does
+
+ align:start position:0%
+team delivering the surgery right does
+ 
+
+ align:start position:0%
+team delivering the surgery right does
+that make
+
+ align:start position:0%
+that make
+ 
+
+ align:start position:0%
+that make
+sense no yes okay so we could map each
+
+ align:start position:0%
+sense no yes okay so we could map each
+ 
+
+ align:start position:0%
+sense no yes okay so we could map each
+one of those
+
+ align:start position:0%
+one of those
+ 
+
+ align:start position:0%
+one of those
+processes right there's a process for
+
+ align:start position:0%
+processes right there's a process for
+ 
+
+ align:start position:0%
+processes right there's a process for
+registering the patient there's a
+
+ align:start position:0%
+registering the patient there's a
+ 
+
+ align:start position:0%
+registering the patient there's a
+process for their first visit there's a
+
+ align:start position:0%
+process for their first visit there's a
+ 
+
+ align:start position:0%
+process for their first visit there's a
+separate process with a whole bunch of
+
+ align:start position:0%
+separate process with a whole bunch of
+ 
+
+ align:start position:0%
+separate process with a whole bunch of
+steps for their second visit third visit
+
+ align:start position:0%
+steps for their second visit third visit
+ 
+
+ align:start position:0%
+steps for their second visit third visit
+Etc okay and all of that is the main
+
+ align:start position:0%
+Etc okay and all of that is the main
+ 
+
+ align:start position:0%
+Etc okay and all of that is the main
+stay leading to a particular
+
+ align:start position:0%
+stay leading to a particular
+ 
+
+ align:start position:0%
+stay leading to a particular
+outcome in order to do that work we need
+
+ align:start position:0%
+outcome in order to do that work we need
+ 
+
+ align:start position:0%
+outcome in order to do that work we need
+supplies right we need an environment to
+
+ align:start position:0%
+supplies right we need an environment to
+ 
+
+ align:start position:0%
+supplies right we need an environment to
+work in we need the people the workers
+
+ align:start position:0%
+work in we need the people the workers
+ 
+
+ align:start position:0%
+work in we need the people the workers
+who can actually do the work right
+
+ align:start position:0%
+who can actually do the work right
+ 
+
+ align:start position:0%
+who can actually do the work right
+there's their education there's the the
+
+ align:start position:0%
+there's their education there's the the
+ 
+
+ align:start position:0%
+there's their education there's the the
+drugs that we need the pharmaceutical
+
+ align:start position:0%
+drugs that we need the pharmaceutical
+ 
+
+ align:start position:0%
+drugs that we need the pharmaceutical
+stuff that we we take advantage of all
+
+ align:start position:0%
+stuff that we we take advantage of all
+ 
+
+ align:start position:0%
+stuff that we we take advantage of all
+of that is going into to our main stay
+
+ align:start position:0%
+of that is going into to our main stay
+ 
+
+ align:start position:0%
+of that is going into to our main stay
+in order to provide care to our patients
+
+ align:start position:0%
+in order to provide care to our patients
+ 
+
+ align:start position:0%
+in order to provide care to our patients
+to get the outcome that we want right
+
+ align:start position:0%
+to get the outcome that we want right
+ 
+
+ align:start position:0%
+to get the outcome that we want right
+and all of that can be articulated as
+
+ align:start position:0%
+and all of that can be articulated as
+ 
+
+ align:start position:0%
+and all of that can be articulated as
+well each one of those processes has a
+
+ align:start position:0%
+well each one of those processes has a
+ 
+
+ align:start position:0%
+well each one of those processes has a
+whole set of steps that we can look at
+
+ align:start position:0%
+whole set of steps that we can look at
+ 
+
+ align:start position:0%
+whole set of steps that we can look at
+does that make sense and one process
+
+ align:start position:0%
+does that make sense and one process
+ 
+
+ align:start position:0%
+does that make sense and one process
+leads to another yeah straightforward
+
+ align:start position:0%
+leads to another yeah straightforward
+ 
+
+ align:start position:0%
+leads to another yeah straightforward
+okay well here's where it gets a little
+
+ align:start position:0%
+okay well here's where it gets a little
+ 
+
+ align:start position:0%
+okay well here's where it gets a little
+more complicated okay now there's some
+
+ align:start position:0%
+more complicated okay now there's some
+ 
+
+ align:start position:0%
+more complicated okay now there's some
+other things that are going on right
+
+ align:start position:0%
+other things that are going on right
+ 
+
+ align:start position:0%
+other things that are going on right
+that have nothing to do with actual
+
+ align:start position:0%
+that have nothing to do with actual
+ 
+
+ align:start position:0%
+that have nothing to do with actual
+patient care right now they're related
+
+ align:start position:0%
+patient care right now they're related
+ 
+
+ align:start position:0%
+patient care right now they're related
+but they're different right they're not
+
+ align:start position:0%
+but they're different right they're not
+ 
+
+ align:start position:0%
+but they're different right they're not
+they are not the business of delivering
+
+ align:start position:0%
+they are not the business of delivering
+ 
+
+ align:start position:0%
+they are not the business of delivering
+the care one of those things is the
+
+ align:start position:0%
+the care one of those things is the
+ 
+
+ align:start position:0%
+the care one of those things is the
+business of monitoring the delivery of
+
+ align:start position:0%
+business of monitoring the delivery of
+ 
+
+ align:start position:0%
+business of monitoring the delivery of
+that care right so we have measurement
+
+ align:start position:0%
+that care right so we have measurement
+ 
+
+ align:start position:0%
+that care right so we have measurement
+and feedback should be a part of a
+
+ align:start position:0%
+and feedback should be a part of a
+ 
+
+ align:start position:0%
+and feedback should be a part of a
+system okay and that's the part that I
+
+ align:start position:0%
+system okay and that's the part that I
+ 
+
+ align:start position:0%
+system okay and that's the part that I
+think we're focusing on very closely uh
+
+ align:start position:0%
+think we're focusing on very closely uh
+ 
+
+ align:start position:0%
+think we're focusing on very closely uh
+uh this semester but how do we get that
+
+ align:start position:0%
+uh this semester but how do we get that
+ 
+
+ align:start position:0%
+uh this semester but how do we get that
+right right and there's sort of two
+
+ align:start position:0%
+right right and there's sort of two
+ 
+
+ align:start position:0%
+right right and there's sort of two
+voices here there's the voice of the
+
+ align:start position:0%
+voices here there's the voice of the
+ 
+
+ align:start position:0%
+voices here there's the voice of the
+customer right which is a work that this
+
+ align:start position:0%
+customer right which is a work that this
+ 
+
+ align:start position:0%
+customer right which is a work that this
+that the customer is telling us about
+
+ align:start position:0%
+that the customer is telling us about
+ 
+
+ align:start position:0%
+that the customer is telling us about
+how well things are going right if we're
+
+ align:start position:0%
+how well things are going right if we're
+ 
+
+ align:start position:0%
+how well things are going right if we're
+providing surgical care and our patients
+
+ align:start position:0%
+providing surgical care and our patients
+ 
+
+ align:start position:0%
+providing surgical care and our patients
+are dying on the table what's the voice
+
+ align:start position:0%
+are dying on the table what's the voice
+ 
+
+ align:start position:0%
+are dying on the table what's the voice
+of the customer telling
+
+ align:start position:0%
+of the customer telling
+ 
+
+ align:start position:0%
+of the customer telling
+us we're not doing too good right
+
+ align:start position:0%
+us we're not doing too good right
+ 
+
+ align:start position:0%
+us we're not doing too good right
+mortality is high that's not good that's
+
+ align:start position:0%
+mortality is high that's not good that's
+ 
+
+ align:start position:0%
+mortality is high that's not good that's
+not what we want right in Ghana where we
+
+ align:start position:0%
+not what we want right in Ghana where we
+ 
+
+ align:start position:0%
+not what we want right in Ghana where we
+have high under five mortality right we
+
+ align:start position:0%
+have high under five mortality right we
+ 
+
+ align:start position:0%
+have high under five mortality right we
+know we're not doing too good the
+
+ align:start position:0%
+know we're not doing too good the
+ 
+
+ align:start position:0%
+know we're not doing too good the
+mortality data is telling us that we
+
+ align:start position:0%
+mortality data is telling us that we
+ 
+
+ align:start position:0%
+mortality data is telling us that we
+need to be doing better okay we also
+
+ align:start position:0%
+need to be doing better okay we also
+ 
+
+ align:start position:0%
+need to be doing better okay we also
+have the voice of the process okay the
+
+ align:start position:0%
+have the voice of the process okay the
+ 
+
+ align:start position:0%
+have the voice of the process okay the
+voice of the system so we can measure
+
+ align:start position:0%
+voice of the system so we can measure
+ 
+
+ align:start position:0%
+voice of the system so we can measure
+our ability to provide care and we do
+
+ align:start position:0%
+our ability to provide care and we do
+ 
+
+ align:start position:0%
+our ability to provide care and we do
+that all the time don't we we look at
+
+ align:start position:0%
+that all the time don't we we look at
+ 
+
+ align:start position:0%
+that all the time don't we we look at
+things like weight times patient volumes
+
+ align:start position:0%
+things like weight times patient volumes
+ 
+
+ align:start position:0%
+things like weight times patient volumes
+throughput we look at patient
+
+ align:start position:0%
+throughput we look at patient
+ 
+
+ align:start position:0%
+throughput we look at patient
+satisfaction which would be on this
+
+ align:start position:0%
+satisfaction which would be on this
+ 
+
+ align:start position:0%
+satisfaction which would be on this
+other side looking backwards okay so we
+
+ align:start position:0%
+other side looking backwards okay so we
+ 
+
+ align:start position:0%
+other side looking backwards okay so we
+have these two things that we're
+
+ align:start position:0%
+have these two things that we're
+ 
+
+ align:start position:0%
+have these two things that we're
+measuring the measure the voice of the
+
+ align:start position:0%
+measuring the measure the voice of the
+ 
+
+ align:start position:0%
+measuring the measure the voice of the
+system and the voice of the
+
+ align:start position:0%
+system and the voice of the
+ 
+
+ align:start position:0%
+system and the voice of the
+customer another part of a good system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah or how toch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ours definitely definitely so I think
+
+ align:start position:0%
+ours definitely definitely so I think
+ 
+
+ align:start position:0%
+ours definitely definitely so I think
+what you're describing is the
+
+ align:start position:0%
+what you're describing is the
+ 
+
+ align:start position:0%
+what you're describing is the
+interaction between understanding
+
+ align:start position:0%
+interaction between understanding
+ 
+
+ align:start position:0%
+interaction between understanding
+variation in our system and what we
+
+ align:start position:0%
+variation in our system and what we
+ 
+
+ align:start position:0%
+variation in our system and what we
+believe about why things are the way
+
+ align:start position:0%
+believe about why things are the way
+ 
+
+ align:start position:0%
+believe about why things are the way
+that they are so we're going to we're
+
+ align:start position:0%
+that they are so we're going to we're
+ 
+
+ align:start position:0%
+that they are so we're going to we're
+going to try and articulate that we're
+
+ align:start position:0%
+going to try and articulate that we're
+ 
+
+ align:start position:0%
+going to try and articulate that we're
+going to write it down somewhere maybe
+
+ align:start position:0%
+going to write it down somewhere maybe
+ 
+
+ align:start position:0%
+going to write it down somewhere maybe
+in a project Charter okay and we're
+
+ align:start position:0%
+in a project Charter okay and we're
+ 
+
+ align:start position:0%
+in a project Charter okay and we're
+going to lay out a set of measures that
+
+ align:start position:0%
+going to lay out a set of measures that
+ 
+
+ align:start position:0%
+going to lay out a set of measures that
+we think will be important so if I want
+
+ align:start position:0%
+we think will be important so if I want
+ 
+
+ align:start position:0%
+we think will be important so if I want
+to reduce under five mortality one of
+
+ align:start position:0%
+to reduce under five mortality one of
+ 
+
+ align:start position:0%
+to reduce under five mortality one of
+the things I need to do is measure under
+
+ align:start position:0%
+the things I need to do is measure under
+ 
+
+ align:start position:0%
+the things I need to do is measure under
+five mortality to see if I'm reducing it
+
+ align:start position:0%
+five mortality to see if I'm reducing it
+ 
+
+ align:start position:0%
+five mortality to see if I'm reducing it
+right if I'm consistently trying to
+
+ align:start position:0%
+right if I'm consistently trying to
+ 
+
+ align:start position:0%
+right if I'm consistently trying to
+change things motivate
+
+ align:start position:0%
+change things motivate
+ 
+
+ align:start position:0%
+change things motivate
+employees uh uh you know build a new
+
+ align:start position:0%
+employees uh uh you know build a new
+ 
+
+ align:start position:0%
+employees uh uh you know build a new
+hospital buy some ambulances then I'm
+
+ align:start position:0%
+hospital buy some ambulances then I'm
+ 
+
+ align:start position:0%
+hospital buy some ambulances then I'm
+going to be looking to My outcome
+
+ align:start position:0%
+going to be looking to My outcome
+ 
+
+ align:start position:0%
+going to be looking to My outcome
+measure to say is it working right is it
+
+ align:start position:0%
+measure to say is it working right is it
+ 
+
+ align:start position:0%
+measure to say is it working right is it
+working now if under five mortality just
+
+ align:start position:0%
+working now if under five mortality just
+ 
+
+ align:start position:0%
+working now if under five mortality just
+stays constant predictable stable over
+
+ align:start position:0%
+stays constant predictable stable over
+ 
+
+ align:start position:0%
+stays constant predictable stable over
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+what do I how does that change my
+
+ align:start position:0%
+what do I how does that change my
+ 
+
+ align:start position:0%
+what do I how does that change my
+theory so that that would tell me my
+
+ align:start position:0%
+theory so that that would tell me my
+ 
+
+ align:start position:0%
+theory so that that would tell me my
+theory is wrong there's some learning
+
+ align:start position:0%
+theory is wrong there's some learning
+ 
+
+ align:start position:0%
+theory is wrong there's some learning
+that needs to go on I built all these
+
+ align:start position:0%
+that needs to go on I built all these
+ 
+
+ align:start position:0%
+that needs to go on I built all these
+hospitals I bought all these ambulances
+
+ align:start position:0%
+hospitals I bought all these ambulances
+ 
+
+ align:start position:0%
+hospitals I bought all these ambulances
+I motivated all these people mortality
+
+ align:start position:0%
+I motivated all these people mortality
+ 
+
+ align:start position:0%
+I motivated all these people mortality
+stayed exactly the same well guess what
+
+ align:start position:0%
+stayed exactly the same well guess what
+ 
+
+ align:start position:0%
+stayed exactly the same well guess what
+those weren't the answer to changing
+
+ align:start position:0%
+those weren't the answer to changing
+ 
+
+ align:start position:0%
+those weren't the answer to changing
+mortality something else is involved so
+
+ align:start position:0%
+mortality something else is involved so
+ 
+
+ align:start position:0%
+mortality something else is involved so
+now we have to evolve our Theory right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that's exactly right that and
+
+ align:start position:0%
+so so that's exactly right that and
+ 
+
+ align:start position:0%
+so so that's exactly right that and
+that's where the learning begins so if
+
+ align:start position:0%
+that's where the learning begins so if
+ 
+
+ align:start position:0%
+that's where the learning begins so if
+we're doing quality improvement we want
+
+ align:start position:0%
+we're doing quality improvement we want
+ 
+
+ align:start position:0%
+we're doing quality improvement we want
+to we want to then change our
+
+ align:start position:0%
+to we want to then change our
+ 
+
+ align:start position:0%
+to we want to then change our
+assumptions so when the when the data
+
+ align:start position:0%
+assumptions so when the when the data
+ 
+
+ align:start position:0%
+assumptions so when the when the data
+starts to tell us that our assumptions
+
+ align:start position:0%
+starts to tell us that our assumptions
+ 
+
+ align:start position:0%
+starts to tell us that our assumptions
+are incorrect or incomplete then we need
+
+ align:start position:0%
+are incorrect or incomplete then we need
+ 
+
+ align:start position:0%
+are incorrect or incomplete then we need
+to add to them or we need to evolve them
+
+ align:start position:0%
+to add to them or we need to evolve them
+ 
+
+ align:start position:0%
+to add to them or we need to evolve them
+and then test again and test again and
+
+ align:start position:0%
+and then test again and test again and
+ 
+
+ align:start position:0%
+and then test again and test again and
+we're going to see that in just a second
+
+ align:start position:0%
+we're going to see that in just a second
+ 
+
+ align:start position:0%
+we're going to see that in just a second
+yeah that's a great question that's
+
+ align:start position:0%
+yeah that's a great question that's
+ 
+
+ align:start position:0%
+yeah that's a great question that's
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+on so another part of a good system is
+
+ align:start position:0%
+on so another part of a good system is
+ 
+
+ align:start position:0%
+on so another part of a good system is
+is looking to the fure future right so
+
+ align:start position:0%
+is looking to the fure future right so
+ 
+
+ align:start position:0%
+is looking to the fure future right so
+Deming called this market research right
+
+ align:start position:0%
+Deming called this market research right
+ 
+
+ align:start position:0%
+Deming called this market research right
+we might call it
+
+ align:start position:0%
+we might call it
+ 
+
+ align:start position:0%
+we might call it
+foresight if we look at Health Systems
+
+ align:start position:0%
+foresight if we look at Health Systems
+ 
+
+ align:start position:0%
+foresight if we look at Health Systems
+globally for the last 100 years or so
+
+ align:start position:0%
+globally for the last 100 years or so
+ 
+
+ align:start position:0%
+globally for the last 100 years or so
+most of them have been built to focus on
+
+ align:start position:0%
+most of them have been built to focus on
+ 
+
+ align:start position:0%
+most of them have been built to focus on
+acute care people get sick they go to
+
+ align:start position:0%
+acute care people get sick they go to
+ 
+
+ align:start position:0%
+acute care people get sick they go to
+the hospital we admit them we get them
+
+ align:start position:0%
+the hospital we admit them we get them
+ 
+
+ align:start position:0%
+the hospital we admit them we get them
+better we send them home but what's
+
+ align:start position:0%
+better we send them home but what's
+ 
+
+ align:start position:0%
+better we send them home but what's
+coming next what's the big issue that's
+
+ align:start position:0%
+coming next what's the big issue that's
+ 
+
+ align:start position:0%
+coming next what's the big issue that's
+coming yeah chronic care right think
+
+ align:start position:0%
+coming yeah chronic care right think
+ 
+
+ align:start position:0%
+coming yeah chronic care right think
+think about think about Africa right for
+
+ align:start position:0%
+think about think about Africa right for
+ 
+
+ align:start position:0%
+think about think about Africa right for
+a second HIV big problem there right
+
+ align:start position:0%
+a second HIV big problem there right
+ 
+
+ align:start position:0%
+a second HIV big problem there right
+right it used to be for the last 10 15
+
+ align:start position:0%
+right it used to be for the last 10 15
+ 
+
+ align:start position:0%
+right it used to be for the last 10 15
+years we were really focused on delivery
+
+ align:start position:0%
+years we were really focused on delivery
+ 
+
+ align:start position:0%
+years we were really focused on delivery
+of anr anti retroviral medication to
+
+ align:start position:0%
+of anr anti retroviral medication to
+ 
+
+ align:start position:0%
+of anr anti retroviral medication to
+people in Africa right in an acute care
+
+ align:start position:0%
+people in Africa right in an acute care
+ 
+
+ align:start position:0%
+people in Africa right in an acute care
+environment and suddenly we're waking up
+
+ align:start position:0%
+environment and suddenly we're waking up
+ 
+
+ align:start position:0%
+environment and suddenly we're waking up
+to the realization we've got to actually
+
+ align:start position:0%
+to the realization we've got to actually
+ 
+
+ align:start position:0%
+to the realization we've got to actually
+provide chronic care to these same
+
+ align:start position:0%
+provide chronic care to these same
+ 
+
+ align:start position:0%
+provide chronic care to these same
+people indefinitely right and that's
+
+ align:start position:0%
+people indefinitely right and that's
+ 
+
+ align:start position:0%
+people indefinitely right and that's
+really really important it's really
+
+ align:start position:0%
+really really important it's really
+ 
+
+ align:start position:0%
+really really important it's really
+important to have the foresight and to
+
+ align:start position:0%
+important to have the foresight and to
+ 
+
+ align:start position:0%
+important to have the foresight and to
+have a mechanism for looking for what's
+
+ align:start position:0%
+have a mechanism for looking for what's
+ 
+
+ align:start position:0%
+have a mechanism for looking for what's
+next so if we want to continue to be
+
+ align:start position:0%
+next so if we want to continue to be
+ 
+
+ align:start position:0%
+next so if we want to continue to be
+relevant to our customers to our clients
+
+ align:start position:0%
+relevant to our customers to our clients
+ 
+
+ align:start position:0%
+relevant to our customers to our clients
+we need to be paying attention to what
+
+ align:start position:0%
+we need to be paying attention to what
+ 
+
+ align:start position:0%
+we need to be paying attention to what
+their needs are going to be not just
+
+ align:start position:0%
+their needs are going to be not just
+ 
+
+ align:start position:0%
+their needs are going to be not just
+right now but what they're going to be
+
+ align:start position:0%
+right now but what they're going to be
+ 
+
+ align:start position:0%
+right now but what they're going to be
+in the future yeah so having that
+
+ align:start position:0%
+in the future yeah so having that
+ 
+
+ align:start position:0%
+in the future yeah so having that
+process of work articulated for any
+
+ align:start position:0%
+process of work articulated for any
+ 
+
+ align:start position:0%
+process of work articulated for any
+system is important and if you look at
+
+ align:start position:0%
+system is important and if you look at
+ 
+
+ align:start position:0%
+system is important and if you look at
+really successful organizations whether
+
+ align:start position:0%
+really successful organizations whether
+ 
+
+ align:start position:0%
+really successful organizations whether
+their health systems or corporations or
+
+ align:start position:0%
+their health systems or corporations or
+ 
+
+ align:start position:0%
+their health systems or corporations or
+whatever they have that they're looking
+
+ align:start position:0%
+whatever they have that they're looking
+ 
+
+ align:start position:0%
+whatever they have that they're looking
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+Future some of them in the case of like
+
+ align:start position:0%
+Future some of them in the case of like
+ 
+
+ align:start position:0%
+Future some of them in the case of like
+apple and apps they're inventing the
+
+ align:start position:0%
+apple and apps they're inventing the
+ 
+
+ align:start position:0%
+apple and apps they're inventing the
+future they're telling us what we need
+
+ align:start position:0%
+future they're telling us what we need
+ 
+
+ align:start position:0%
+future they're telling us what we need
+before we know we need it right okay
+
+ align:start position:0%
+before we know we need it right okay
+ 
+
+ align:start position:0%
+before we know we need it right okay
+all of that needs to feed into a
+
+ align:start position:0%
+all of that needs to feed into a
+ 
+
+ align:start position:0%
+all of that needs to feed into a
+mechanism which is a plan to improve
+
+ align:start position:0%
+mechanism which is a plan to improve
+ 
+
+ align:start position:0%
+mechanism which is a plan to improve
+right we want the ability to improve
+
+ align:start position:0%
+right we want the ability to improve
+ 
+
+ align:start position:0%
+right we want the ability to improve
+something we need to actually have a
+
+ align:start position:0%
+something we need to actually have a
+ 
+
+ align:start position:0%
+something we need to actually have a
+mechanism for doing that we need to have
+
+ align:start position:0%
+mechanism for doing that we need to have
+ 
+
+ align:start position:0%
+mechanism for doing that we need to have
+that in place okay and then we actually
+
+ align:start position:0%
+that in place okay and then we actually
+ 
+
+ align:start position:0%
+that in place okay and then we actually
+need the work of doing that now all of
+
+ align:start position:0%
+need the work of doing that now all of
+ 
+
+ align:start position:0%
+need the work of doing that now all of
+that is different from delivery of care
+
+ align:start position:0%
+that is different from delivery of care
+ 
+
+ align:start position:0%
+that is different from delivery of care
+to patients or manufactured of product
+
+ align:start position:0%
+to patients or manufactured of product
+ 
+
+ align:start position:0%
+to patients or manufactured of product
+right that's all different that's not
+
+ align:start position:0%
+right that's all different that's not
+ 
+
+ align:start position:0%
+right that's all different that's not
+the work of the caregivers who's that
+
+ align:start position:0%
+the work of the caregivers who's that
+ 
+
+ align:start position:0%
+the work of the caregivers who's that
+the work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of who does that stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who who who has the power to change a
+
+ align:start position:0%
+who who who has the power to change a
+ 
+
+ align:start position:0%
+who who who has the power to change a
+system is it the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nurse yeah it's that minister of Health
+
+ align:start position:0%
+nurse yeah it's that minister of Health
+ 
+
+ align:start position:0%
+nurse yeah it's that minister of Health
+right it's that CEO of the hospital it's
+
+ align:start position:0%
+right it's that CEO of the hospital it's
+ 
+
+ align:start position:0%
+right it's that CEO of the hospital it's
+those senior leaders who had the ability
+
+ align:start position:0%
+those senior leaders who had the ability
+ 
+
+ align:start position:0%
+those senior leaders who had the ability
+to say actually we're going to change
+
+ align:start position:0%
+to say actually we're going to change
+ 
+
+ align:start position:0%
+to say actually we're going to change
+our policy here we know that we need to
+
+ align:start position:0%
+our policy here we know that we need to
+ 
+
+ align:start position:0%
+our policy here we know that we need to
+do something different in the future so
+
+ align:start position:0%
+do something different in the future so
+ 
+
+ align:start position:0%
+do something different in the future so
+this is the role of management and that
+
+ align:start position:0%
+this is the role of management and that
+ 
+
+ align:start position:0%
+this is the role of management and that
+role of improvement and redesign
+
+ align:start position:0%
+role of improvement and redesign
+ 
+
+ align:start position:0%
+role of improvement and redesign
+constantly is is the role of Management
+
+ align:start position:0%
+constantly is is the role of Management
+ 
+
+ align:start position:0%
+constantly is is the role of Management
+workers can help you understand where
+
+ align:start position:0%
+workers can help you understand where
+ 
+
+ align:start position:0%
+workers can help you understand where
+the process is broken they can tell you
+
+ align:start position:0%
+the process is broken they can tell you
+ 
+
+ align:start position:0%
+the process is broken they can tell you
+when you're getting that gray elephant
+
+ align:start position:0%
+when you're getting that gray elephant
+ 
+
+ align:start position:0%
+when you're getting that gray elephant
+when when what you really want is a pink
+
+ align:start position:0%
+when when what you really want is a pink
+ 
+
+ align:start position:0%
+when when what you really want is a pink
+elephant right but it's up to the
+
+ align:start position:0%
+elephant right but it's up to the
+ 
+
+ align:start position:0%
+elephant right but it's up to the
+managers to empower the workers to begin
+
+ align:start position:0%
+managers to empower the workers to begin
+ 
+
+ align:start position:0%
+managers to empower the workers to begin
+to make changes so that's going to be a
+
+ align:start position:0%
+to make changes so that's going to be a
+ 
+
+ align:start position:0%
+to make changes so that's going to be a
+critically important concept there's one
+
+ align:start position:0%
+critically important concept there's one
+ 
+
+ align:start position:0%
+critically important concept there's one
+other thing that's missing if I'm
+
+ align:start position:0%
+other thing that's missing if I'm
+ 
+
+ align:start position:0%
+other thing that's missing if I'm
+providing surgical care uh and I bring
+
+ align:start position:0%
+providing surgical care uh and I bring
+ 
+
+ align:start position:0%
+providing surgical care uh and I bring
+in my first patient of the day and get
+
+ align:start position:0%
+in my first patient of the day and get
+ 
+
+ align:start position:0%
+in my first patient of the day and get
+my surgical team in there and do surgery
+
+ align:start position:0%
+my surgical team in there and do surgery
+ 
+
+ align:start position:0%
+my surgical team in there and do surgery
+and then I wheel out to the ICU to get
+
+ align:start position:0%
+and then I wheel out to the ICU to get
+ 
+
+ align:start position:0%
+and then I wheel out to the ICU to get
+better and I go back in can I just go
+
+ align:start position:0%
+better and I go back in can I just go
+ 
+
+ align:start position:0%
+better and I go back in can I just go
+ahead and start another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surgery no we got to have somebody who
+
+ align:start position:0%
+surgery no we got to have somebody who
+ 
+
+ align:start position:0%
+surgery no we got to have somebody who
+comes in and cleans up right all that
+
+ align:start position:0%
+comes in and cleans up right all that
+ 
+
+ align:start position:0%
+comes in and cleans up right all that
+Blood and Guts and stuff everywhere and
+
+ align:start position:0%
+Blood and Guts and stuff everywhere and
+ 
+
+ align:start position:0%
+Blood and Guts and stuff everywhere and
+infection could be rampant that's not
+
+ align:start position:0%
+infection could be rampant that's not
+ 
+
+ align:start position:0%
+infection could be rampant that's not
+good so we have a whole set of support
+
+ align:start position:0%
+good so we have a whole set of support
+ 
+
+ align:start position:0%
+good so we have a whole set of support
+processes we have a whole set of work
+
+ align:start position:0%
+processes we have a whole set of work
+ 
+
+ align:start position:0%
+processes we have a whole set of work
+that's focused on empowering our ability
+
+ align:start position:0%
+that's focused on empowering our ability
+ 
+
+ align:start position:0%
+that's focused on empowering our ability
+to provide the main stay right all the
+
+ align:start position:0%
+to provide the main stay right all the
+ 
+
+ align:start position:0%
+to provide the main stay right all the
+things that we need in order order to
+
+ align:start position:0%
+things that we need in order order to
+ 
+
+ align:start position:0%
+things that we need in order order to
+keep the day-to-day running well right
+
+ align:start position:0%
+keep the day-to-day running well right
+ 
+
+ align:start position:0%
+keep the day-to-day running well right
+so those can be things like maintenance
+
+ align:start position:0%
+so those can be things like maintenance
+ 
+
+ align:start position:0%
+so those can be things like maintenance
+it Finance all these types of
+
+ align:start position:0%
+it Finance all these types of
+ 
+
+ align:start position:0%
+it Finance all these types of
+departments that are critically
+
+ align:start position:0%
+departments that are critically
+ 
+
+ align:start position:0%
+departments that are critically
+important they don't actually provide
+
+ align:start position:0%
+important they don't actually provide
+ 
+
+ align:start position:0%
+important they don't actually provide
+care directly to patients but they
+
+ align:start position:0%
+care directly to patients but they
+ 
+
+ align:start position:0%
+care directly to patients but they
+create the environment by which we can
+
+ align:start position:0%
+create the environment by which we can
+ 
+
+ align:start position:0%
+create the environment by which we can
+provide care to patients right now
+
+ align:start position:0%
+provide care to patients right now
+ 
+
+ align:start position:0%
+provide care to patients right now
+you'll notice there's no chronology here
+
+ align:start position:0%
+you'll notice there's no chronology here
+ 
+
+ align:start position:0%
+you'll notice there's no chronology here
+there's no beginning there's no end it's
+
+ align:start position:0%
+there's no beginning there's no end it's
+ 
+
+ align:start position:0%
+there's no beginning there's no end it's
+quite circular that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this balance between the feedback and
+
+ align:start position:0%
+this balance between the feedback and
+ 
+
+ align:start position:0%
+this balance between the feedback and
+the assumptions a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+timei organizations or even governmental
+
+ align:start position:0%
+timei organizations or even governmental
+ 
+
+ align:start position:0%
+timei organizations or even governmental
+agencies they even though their
+
+ align:start position:0%
+agencies they even though their
+ 
+
+ align:start position:0%
+agencies they even though their
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+are contradicted by the feedback they
+
+ align:start position:0%
+are contradicted by the feedback they
+ 
+
+ align:start position:0%
+are contradicted by the feedback they
+still assumption they
+
+ align:start position:0%
+still assumption they
+ 
+
+ align:start position:0%
+still assumption they
+continue
+
+ align:start position:0%
+continue
+ 
+
+ align:start position:0%
+continue
+ofil everyone know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I couldn't agree
+
+ align:start position:0%
+I couldn't agree
+ 
+
+ align:start position:0%
+I couldn't agree
+more it's it's a tremendous problem and
+
+ align:start position:0%
+more it's it's a tremendous problem and
+ 
+
+ align:start position:0%
+more it's it's a tremendous problem and
+why do you think that
+
+ align:start position:0%
+why do you think that
+ 
+
+ align:start position:0%
+why do you think that
+is because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and could go
+
+ align:start position:0%
+and could go
+ 
+
+ align:start position:0%
+and could go
+beyond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down develop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+countries developing countries so like
+
+ align:start position:0%
+countries developing countries so like
+ 
+
+ align:start position:0%
+countries developing countries so like
+all the knowledge is on the developed
+
+ align:start position:0%
+all the knowledge is on the developed
+ 
+
+ align:start position:0%
+all the knowledge is on the developed
+country side
+
+ align:start position:0%
+country side
+ 
+
+ align:start position:0%
+country side
+sometimes they say those feedback are
+
+ align:start position:0%
+sometimes they say those feedback are
+ 
+
+ align:start position:0%
+sometimes they say those feedback are
+not they don't have we can't trust those
+
+ align:start position:0%
+not they don't have we can't trust those
+ 
+
+ align:start position:0%
+not they don't have we can't trust those
+feedbacks because they don't have the
+
+ align:start position:0%
+feedbacks because they don't have the
+ 
+
+ align:start position:0%
+feedbacks because they don't have the
+knowledge have
+
+ align:start position:0%
+knowledge have
+ 
+
+ align:start position:0%
+knowledge have
+knowledge it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people we trust their capacity we trust
+
+ align:start position:0%
+people we trust their capacity we trust
+ 
+
+ align:start position:0%
+people we trust their capacity we trust
+their feedback the way they process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enties so it's
+
+ align:start position:0%
+enties so it's
+ 
+
+ align:start position:0%
+enties so it's
+big it's a huge issue can we see them as
+
+ align:start position:0%
+big it's a huge issue can we see them as
+ 
+
+ align:start position:0%
+big it's a huge issue can we see them as
+we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I I I think it is a deep problem
+
+ align:start position:0%
+yeah I I I think it is a deep problem
+ 
+
+ align:start position:0%
+yeah I I I think it is a deep problem
+and I think what you're describing in my
+
+ align:start position:0%
+and I think what you're describing in my
+ 
+
+ align:start position:0%
+and I think what you're describing in my
+mind is a disconnect between the feedack
+
+ align:start position:0%
+mind is a disconnect between the feedack
+ 
+
+ align:start position:0%
+mind is a disconnect between the feedack
+that's coming through and the and people
+
+ align:start position:0%
+that's coming through and the and people
+ 
+
+ align:start position:0%
+that's coming through and the and people
+not being receptive to it we've got 50
+
+ align:start position:0%
+not being receptive to it we've got 50
+ 
+
+ align:start position:0%
+not being receptive to it we've got 50
+60 years of case studies of development
+
+ align:start position:0%
+60 years of case studies of development
+ 
+
+ align:start position:0%
+60 years of case studies of development
+projects that
+
+ align:start position:0%
+projects that
+ 
+
+ align:start position:0%
+projects that
+have failed right they haven't done well
+
+ align:start position:0%
+have failed right they haven't done well
+ 
+
+ align:start position:0%
+have failed right they haven't done well
+and we haven't done a good job of
+
+ align:start position:0%
+and we haven't done a good job of
+ 
+
+ align:start position:0%
+and we haven't done a good job of
+learning from that failure quality
+
+ align:start position:0%
+learning from that failure quality
+ 
+
+ align:start position:0%
+learning from that failure quality
+improvement at its core is about failing
+
+ align:start position:0%
+improvement at its core is about failing
+ 
+
+ align:start position:0%
+improvement at its core is about failing
+often to succeed sooner it's about
+
+ align:start position:0%
+often to succeed sooner it's about
+ 
+
+ align:start position:0%
+often to succeed sooner it's about
+learning from failure establishing
+
+ align:start position:0%
+learning from failure establishing
+ 
+
+ align:start position:0%
+learning from failure establishing
+feedback mechanisms that we can learn
+
+ align:start position:0%
+feedback mechanisms that we can learn
+ 
+
+ align:start position:0%
+feedback mechanisms that we can learn
+from rather than putting the blinders on
+
+ align:start position:0%
+from rather than putting the blinders on
+ 
+
+ align:start position:0%
+from rather than putting the blinders on
+and just going with our assumptions so
+
+ align:start position:0%
+and just going with our assumptions so
+ 
+
+ align:start position:0%
+and just going with our assumptions so
+we have to be open if we're going to be
+
+ align:start position:0%
+we have to be open if we're going to be
+ 
+
+ align:start position:0%
+we have to be open if we're going to be
+doing quality improvement we have to be
+
+ align:start position:0%
+doing quality improvement we have to be
+ 
+
+ align:start position:0%
+doing quality improvement we have to be
+open to constantly learning and if a
+
+ align:start position:0%
+open to constantly learning and if a
+ 
+
+ align:start position:0%
+open to constantly learning and if a
+project fails we need to actually say
+
+ align:start position:0%
+project fails we need to actually say
+ 
+
+ align:start position:0%
+project fails we need to actually say
+why did it fail was it you know was it
+
+ align:start position:0%
+why did it fail was it you know was it
+ 
+
+ align:start position:0%
+why did it fail was it you know was it
+because we had bad assumptions maybe was
+
+ align:start position:0%
+because we had bad assumptions maybe was
+ 
+
+ align:start position:0%
+because we had bad assumptions maybe was
+it because we had bad people probably
+
+ align:start position:0%
+it because we had bad people probably
+ 
+
+ align:start position:0%
+it because we had bad people probably
+not right it's those things what's hard
+
+ align:start position:0%
+not right it's those things what's hard
+ 
+
+ align:start position:0%
+not right it's those things what's hard
+is getting leaders in place who have
+
+ align:start position:0%
+is getting leaders in place who have
+ 
+
+ align:start position:0%
+is getting leaders in place who have
+that perspective who have the ability to
+
+ align:start position:0%
+that perspective who have the ability to
+ 
+
+ align:start position:0%
+that perspective who have the ability to
+have a systems View and to actually
+
+ align:start position:0%
+have a systems View and to actually
+ 
+
+ align:start position:0%
+have a systems View and to actually
+understand how they can use data to
+
+ align:start position:0%
+understand how they can use data to
+ 
+
+ align:start position:0%
+understand how they can use data to
+their advantage to manage and redesign
+
+ align:start position:0%
+their advantage to manage and redesign
+ 
+
+ align:start position:0%
+their advantage to manage and redesign
+their systems that would be my thinking
+
+ align:start position:0%
+their systems that would be my thinking
+ 
+
+ align:start position:0%
+their systems that would be my thinking
+but I I see it all the time I think
+
+ align:start position:0%
+but I I see it all the time I think
+ 
+
+ align:start position:0%
+but I I see it all the time I think
+you're absolutely right that there's
+
+ align:start position:0%
+you're absolutely right that there's
+ 
+
+ align:start position:0%
+you're absolutely right that there's
+some there's some real deep issues that
+
+ align:start position:0%
+some there's some real deep issues that
+ 
+
+ align:start position:0%
+some there's some real deep issues that
+need to be tackled but in my mind it's
+
+ align:start position:0%
+need to be tackled but in my mind it's
+ 
+
+ align:start position:0%
+need to be tackled but in my mind it's
+got to start up here it's got to start
+
+ align:start position:0%
+got to start up here it's got to start
+ 
+
+ align:start position:0%
+got to start up here it's got to start
+with the with the leadership to be able
+
+ align:start position:0%
+with the with the leadership to be able
+ 
+
+ align:start position:0%
+with the with the leadership to be able
+to engage and and learn about that
+
+ align:start position:0%
+to engage and and learn about that
+ 
+
+ align:start position:0%
+to engage and and learn about that
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+yes I want to
+
+ align:start position:0%
+yes I want to
+ 
+
+ align:start position:0%
+yes I want to
+propose simpler reason for
+
+ align:start position:0%
+propose simpler reason for
+ 
+
+ align:start position:0%
+propose simpler reason for
+between assumtions and
+
+ align:start position:0%
+between assumtions and
+ 
+
+ align:start position:0%
+between assumtions and
+feedb in some it Tak a lot of money to
+
+ align:start position:0%
+feedb in some it Tak a lot of money to
+ 
+
+ align:start position:0%
+feedb in some it Tak a lot of money to
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+are problems people don't change people
+
+ align:start position:0%
+are problems people don't change people
+ 
+
+ align:start position:0%
+are problems people don't change people
+get used
+
+ align:start position:0%
+get used
+ 
+
+ align:start position:0%
+get used
+to underline everything is the fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sy yeah yeah you you may absolutely be
+
+ align:start position:0%
+Sy yeah yeah you you may absolutely be
+ 
+
+ align:start position:0%
+Sy yeah yeah you you may absolutely be
+right I I think one thing that's
+
+ align:start position:0%
+right I I think one thing that's
+ 
+
+ align:start position:0%
+right I I think one thing that's
+critically important when we think about
+
+ align:start position:0%
+critically important when we think about
+ 
+
+ align:start position:0%
+critically important when we think about
+quality improvement is we're talking
+
+ align:start position:0%
+quality improvement is we're talking
+ 
+
+ align:start position:0%
+quality improvement is we're talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+continuous redesign of an existing
+
+ align:start position:0%
+continuous redesign of an existing
+ 
+
+ align:start position:0%
+continuous redesign of an existing
+system right so it's important from our
+
+ align:start position:0%
+system right so it's important from our
+ 
+
+ align:start position:0%
+system right so it's important from our
+perspective if we're going to be
+
+ align:start position:0%
+perspective if we're going to be
+ 
+
+ align:start position:0%
+perspective if we're going to be
+advising people or we're going to be
+
+ align:start position:0%
+advising people or we're going to be
+ 
+
+ align:start position:0%
+advising people or we're going to be
+helping them to improve that we're not
+
+ align:start position:0%
+helping them to improve that we're not
+ 
+
+ align:start position:0%
+helping them to improve that we're not
+necessarily proposing to eliminate
+
+ align:start position:0%
+necessarily proposing to eliminate
+ 
+
+ align:start position:0%
+necessarily proposing to eliminate
+everything that's existed before right
+
+ align:start position:0%
+everything that's existed before right
+ 
+
+ align:start position:0%
+everything that's existed before right
+the world is is broken in many ways we
+
+ align:start position:0%
+the world is is broken in many ways we
+ 
+
+ align:start position:0%
+the world is is broken in many ways we
+have to work to improve what we have
+
+ align:start position:0%
+have to work to improve what we have
+ 
+
+ align:start position:0%
+have to work to improve what we have
+that's our starting place I could never
+
+ align:start position:0%
+that's our starting place I could never
+ 
+
+ align:start position:0%
+that's our starting place I could never
+imagine entering a you know a country or
+
+ align:start position:0%
+imagine entering a you know a country or
+ 
+
+ align:start position:0%
+imagine entering a you know a country or
+a city or a hospital or something ins
+
+ align:start position:0%
+a city or a hospital or something ins
+ 
+
+ align:start position:0%
+a city or a hospital or something ins
+saying actually we just need to tear
+
+ align:start position:0%
+saying actually we just need to tear
+ 
+
+ align:start position:0%
+saying actually we just need to tear
+down and build up from scratch again
+
+ align:start position:0%
+down and build up from scratch again
+ 
+
+ align:start position:0%
+down and build up from scratch again
+what it might be nice if we had the
+
+ align:start position:0%
+what it might be nice if we had the
+ 
+
+ align:start position:0%
+what it might be nice if we had the
+resources but I think you're right it's
+
+ align:start position:0%
+resources but I think you're right it's
+ 
+
+ align:start position:0%
+resources but I think you're right it's
+it is there now what can we do to make
+
+ align:start position:0%
+it is there now what can we do to make
+ 
+
+ align:start position:0%
+it is there now what can we do to make
+it better what can we do to constantly
+
+ align:start position:0%
+it better what can we do to constantly
+ 
+
+ align:start position:0%
+it better what can we do to constantly
+redesign that and make it better so I'm
+
+ align:start position:0%
+redesign that and make it better so I'm
+ 
+
+ align:start position:0%
+redesign that and make it better so I'm
+conscious of our time I want us to to
+
+ align:start position:0%
+conscious of our time I want us to to
+ 
+
+ align:start position:0%
+conscious of our time I want us to to
+move to another tool which is time bound
+
+ align:start position:0%
+move to another tool which is time bound
+ 
+
+ align:start position:0%
+move to another tool which is time bound
+unlike the linkage of process um but
+
+ align:start position:0%
+unlike the linkage of process um but
+ 
+
+ align:start position:0%
+unlike the linkage of process um but
+also gives us an ability to see inside
+
+ align:start position:0%
+also gives us an ability to see inside
+ 
+
+ align:start position:0%
+also gives us an ability to see inside
+the system so if we have the ability to
+
+ align:start position:0%
+the system so if we have the ability to
+ 
+
+ align:start position:0%
+the system so if we have the ability to
+articulate each of these processes okay
+
+ align:start position:0%
+articulate each of these processes okay
+ 
+
+ align:start position:0%
+articulate each of these processes okay
+we can start to see the complexity that
+
+ align:start position:0%
+we can start to see the complexity that
+ 
+
+ align:start position:0%
+we can start to see the complexity that
+exists within the organization or system
+
+ align:start position:0%
+exists within the organization or system
+ 
+
+ align:start position:0%
+exists within the organization or system
+that we're trying to improve okay The
+
+ align:start position:0%
+that we're trying to improve okay The
+ 
+
+ align:start position:0%
+that we're trying to improve okay The
+Next Step then is to actually see
+
+ align:start position:0%
+Next Step then is to actually see
+ 
+
+ align:start position:0%
+Next Step then is to actually see
+individual processes the things that
+
+ align:start position:0%
+individual processes the things that
+ 
+
+ align:start position:0%
+individual processes the things that
+we're going to focus on improving right
+
+ align:start position:0%
+we're going to focus on improving right
+ 
+
+ align:start position:0%
+we're going to focus on improving right
+and for that we would use a process
+
+ align:start position:0%
+and for that we would use a process
+ 
+
+ align:start position:0%
+and for that we would use a process
+map okay you guys have probably heard it
+
+ align:start position:0%
+map okay you guys have probably heard it
+ 
+
+ align:start position:0%
+map okay you guys have probably heard it
+referred to as other things
+
+ align:start position:0%
+referred to as other things
+ 
+
+ align:start position:0%
+referred to as other things
+flowchart causal Loop diagram value
+
+ align:start position:0%
+flowchart causal Loop diagram value
+ 
+
+ align:start position:0%
+flowchart causal Loop diagram value
+stream analysis you guys heard those
+
+ align:start position:0%
+stream analysis you guys heard those
+ 
+
+ align:start position:0%
+stream analysis you guys heard those
+terms before right pretty
+
+ align:start position:0%
+terms before right pretty
+ 
+
+ align:start position:0%
+terms before right pretty
+straightforward right this is a way now
+
+ align:start position:0%
+straightforward right this is a way now
+ 
+
+ align:start position:0%
+straightforward right this is a way now
+of saying we're actually going to get
+
+ align:start position:0%
+of saying we're actually going to get
+ 
+
+ align:start position:0%
+of saying we're actually going to get
+away from the big picture view we're
+
+ align:start position:0%
+away from the big picture view we're
+ 
+
+ align:start position:0%
+away from the big picture view we're
+going to drill down into a very specific
+
+ align:start position:0%
+going to drill down into a very specific
+ 
+
+ align:start position:0%
+going to drill down into a very specific
+focused area okay and we can do that uh
+
+ align:start position:0%
+focused area okay and we can do that uh
+ 
+
+ align:start position:0%
+focused area okay and we can do that uh
+uh using some of these tools I'm not
+
+ align:start position:0%
+uh using some of these tools I'm not
+ 
+
+ align:start position:0%
+uh using some of these tools I'm not
+going to go through this but process
+
+ align:start position:0%
+going to go through this but process
+ 
+
+ align:start position:0%
+going to go through this but process
+maps have a very specific uh language
+
+ align:start position:0%
+maps have a very specific uh language
+ 
+
+ align:start position:0%
+maps have a very specific uh language
+that they use certain shapes mean
+
+ align:start position:0%
+that they use certain shapes mean
+ 
+
+ align:start position:0%
+that they use certain shapes mean
+certain things and you'll have this so
+
+ align:start position:0%
+certain things and you'll have this so
+ 
+
+ align:start position:0%
+certain things and you'll have this so
+you can check it out later okay here's a
+
+ align:start position:0%
+you can check it out later okay here's a
+ 
+
+ align:start position:0%
+you can check it out later okay here's a
+very simple one that doesn't use all
+
+ align:start position:0%
+very simple one that doesn't use all
+ 
+
+ align:start position:0%
+very simple one that doesn't use all
+that complex language but here would be
+
+ align:start position:0%
+that complex language but here would be
+ 
+
+ align:start position:0%
+that complex language but here would be
+an example for uh uh pmtct care okay
+
+ align:start position:0%
+an example for uh uh pmtct care okay
+ 
+
+ align:start position:0%
+an example for uh uh pmtct care okay
+prevention of motherto child
+
+ align:start position:0%
+prevention of motherto child
+ 
+
+ align:start position:0%
+prevention of motherto child
+transmission of HIV right very simple
+
+ align:start position:0%
+transmission of HIV right very simple
+ 
+
+ align:start position:0%
+transmission of HIV right very simple
+process map here here we've got five six
+
+ align:start position:0%
+process map here here we've got five six
+ 
+
+ align:start position:0%
+process map here here we've got five six
+steps to uh to uh providing care to
+
+ align:start position:0%
+steps to uh to uh providing care to
+ 
+
+ align:start position:0%
+steps to uh to uh providing care to
+reduce transmission of HIV to children
+
+ align:start position:0%
+reduce transmission of HIV to children
+ 
+
+ align:start position:0%
+reduce transmission of HIV to children
+okay very very simple it shows us now
+
+ align:start position:0%
+okay very very simple it shows us now
+ 
+
+ align:start position:0%
+okay very very simple it shows us now
+the outcome that we might be measuring
+
+ align:start position:0%
+the outcome that we might be measuring
+ 
+
+ align:start position:0%
+the outcome that we might be measuring
+the process measure in this case might
+
+ align:start position:0%
+the process measure in this case might
+ 
+
+ align:start position:0%
+the process measure in this case might
+be our transmission rate okay but at
+
+ align:start position:0%
+be our transmission rate okay but at
+ 
+
+ align:start position:0%
+be our transmission rate okay but at
+each step we could measure how we're
+
+ align:start position:0%
+each step we could measure how we're
+ 
+
+ align:start position:0%
+each step we could measure how we're
+doing we could see how we're doing in
+
+ align:start position:0%
+doing we could see how we're doing in
+ 
+
+ align:start position:0%
+doing we could see how we're doing in
+terms of providing H testing we could
+
+ align:start position:0%
+terms of providing H testing we could
+ 
+
+ align:start position:0%
+terms of providing H testing we could
+see how we're doing in providing dual
+
+ align:start position:0%
+see how we're doing in providing dual
+ 
+
+ align:start position:0%
+see how we're doing in providing dual
+therapy or art uh uh to uh pregnant
+
+ align:start position:0%
+therapy or art uh uh to uh pregnant
+ 
+
+ align:start position:0%
+therapy or art uh uh to uh pregnant
+women okay we could do all of that as as
+
+ align:start position:0%
+women okay we could do all of that as as
+ 
+
+ align:start position:0%
+women okay we could do all of that as as
+uh individual uh measures or step
+
+ align:start position:0%
+uh individual uh measures or step
+ 
+
+ align:start position:0%
+uh individual uh measures or step
+measures within a particular process so
+
+ align:start position:0%
+measures within a particular process so
+ 
+
+ align:start position:0%
+measures within a particular process so
+that's an example a process map that
+
+ align:start position:0%
+that's an example a process map that
+ 
+
+ align:start position:0%
+that's an example a process map that
+helps us to get in and if we found that
+
+ align:start position:0%
+helps us to get in and if we found that
+ 
+
+ align:start position:0%
+helps us to get in and if we found that
+we were sort of falling down here our
+
+ align:start position:0%
+we were sort of falling down here our
+ 
+
+ align:start position:0%
+we were sort of falling down here our
+inability to conduct lab tests okay then
+
+ align:start position:0%
+inability to conduct lab tests okay then
+ 
+
+ align:start position:0%
+inability to conduct lab tests okay then
+that's where we might focus our
+
+ align:start position:0%
+that's where we might focus our
+ 
+
+ align:start position:0%
+that's where we might focus our
+Improvement but again data becomes
+
+ align:start position:0%
+Improvement but again data becomes
+ 
+
+ align:start position:0%
+Improvement but again data becomes
+critically important for showing us our
+
+ align:start position:0%
+critically important for showing us our
+ 
+
+ align:start position:0%
+critically important for showing us our
+current performance and where we want to
+
+ align:start position:0%
+current performance and where we want to
+ 
+
+ align:start position:0%
+current performance and where we want to
+focus our Improvement and helping us to
+
+ align:start position:0%
+focus our Improvement and helping us to
+ 
+
+ align:start position:0%
+focus our Improvement and helping us to
+re-evaluate our assumptions okay so we
+
+ align:start position:0%
+re-evaluate our assumptions okay so we
+ 
+
+ align:start position:0%
+re-evaluate our assumptions okay so we
+see a high transmission rate and we make
+
+ align:start position:0%
+see a high transmission rate and we make
+ 
+
+ align:start position:0%
+see a high transmission rate and we make
+an assumption about that transmission
+
+ align:start position:0%
+an assumption about that transmission
+ 
+
+ align:start position:0%
+an assumption about that transmission
+rate right but what this does is it
+
+ align:start position:0%
+rate right but what this does is it
+ 
+
+ align:start position:0%
+rate right but what this does is it
+allows us to go in and figure out
+
+ align:start position:0%
+allows us to go in and figure out
+ 
+
+ align:start position:0%
+allows us to go in and figure out
+exactly where the problem is it gives us
+
+ align:start position:0%
+exactly where the problem is it gives us
+ 
+
+ align:start position:0%
+exactly where the problem is it gives us
+a starting place for for that and we can
+
+ align:start position:0%
+a starting place for for that and we can
+ 
+
+ align:start position:0%
+a starting place for for that and we can
+measure each one of those
+
+ align:start position:0%
+measure each one of those
+ 
+
+ align:start position:0%
+measure each one of those
+steps here's an example from data flow
+
+ align:start position:0%
+steps here's an example from data flow
+ 
+
+ align:start position:0%
+steps here's an example from data flow
+okay some some some work can be around
+
+ align:start position:0%
+okay some some some work can be around
+ 
+
+ align:start position:0%
+okay some some some work can be around
+the information uh uh that's flowing
+
+ align:start position:0%
+the information uh uh that's flowing
+ 
+
+ align:start position:0%
+the information uh uh that's flowing
+through a system right patients flow
+
+ align:start position:0%
+through a system right patients flow
+ 
+
+ align:start position:0%
+through a system right patients flow
+through a system but so does information
+
+ align:start position:0%
+through a system but so does information
+ 
+
+ align:start position:0%
+through a system but so does information
+about them right and that can be
+
+ align:start position:0%
+about them right and that can be
+ 
+
+ align:start position:0%
+about them right and that can be
+critically important as well I mean it's
+
+ align:start position:0%
+critically important as well I mean it's
+ 
+
+ align:start position:0%
+critically important as well I mean it's
+a it's a terribly important thing it's
+
+ align:start position:0%
+a it's a terribly important thing it's
+ 
+
+ align:start position:0%
+a it's a terribly important thing it's
+the focus of why we're here we need
+
+ align:start position:0%
+the focus of why we're here we need
+ 
+
+ align:start position:0%
+the focus of why we're here we need
+information we need good information
+
+ align:start position:0%
+information we need good information
+ 
+
+ align:start position:0%
+information we need good information
+systems in in order to understand
+
+ align:start position:0%
+systems in in order to understand
+ 
+
+ align:start position:0%
+systems in in order to understand
+performance so that we can improve care
+
+ align:start position:0%
+performance so that we can improve care
+ 
+
+ align:start position:0%
+performance so that we can improve care
+delivery for patients right if we are uh
+
+ align:start position:0%
+delivery for patients right if we are uh
+ 
+
+ align:start position:0%
+delivery for patients right if we are uh
+having mistakes take place in the
+
+ align:start position:0%
+having mistakes take place in the
+ 
+
+ align:start position:0%
+having mistakes take place in the
+transfer of information or even in the
+
+ align:start position:0%
+transfer of information or even in the
+ 
+
+ align:start position:0%
+transfer of information or even in the
+recording of information at individual
+
+ align:start position:0%
+recording of information at individual
+ 
+
+ align:start position:0%
+recording of information at individual
+locations then we're in trouble right so
+
+ align:start position:0%
+locations then we're in trouble right so
+ 
+
+ align:start position:0%
+locations then we're in trouble right so
+as much as we might map a care Journey
+
+ align:start position:0%
+as much as we might map a care Journey
+ 
+
+ align:start position:0%
+as much as we might map a care Journey
+for an individual patient as in the
+
+ align:start position:0%
+for an individual patient as in the
+ 
+
+ align:start position:0%
+for an individual patient as in the
+process map before we might want to map
+
+ align:start position:0%
+process map before we might want to map
+ 
+
+ align:start position:0%
+process map before we might want to map
+also the data Journey okay and so as you
+
+ align:start position:0%
+also the data Journey okay and so as you
+ 
+
+ align:start position:0%
+also the data Journey okay and so as you
+think about your projects you might
+
+ align:start position:0%
+think about your projects you might
+ 
+
+ align:start position:0%
+think about your projects you might
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+how is data moving for what we're for
+
+ align:start position:0%
+how is data moving for what we're for
+ 
+
+ align:start position:0%
+how is data moving for what we're for
+for for for us you know what is the
+
+ align:start position:0%
+for for for us you know what is the
+ 
+
+ align:start position:0%
+for for for us you know what is the
+information where is it first being
+
+ align:start position:0%
+information where is it first being
+ 
+
+ align:start position:0%
+information where is it first being
+captured is it being aggregated anywhere
+
+ align:start position:0%
+captured is it being aggregated anywhere
+ 
+
+ align:start position:0%
+captured is it being aggregated anywhere
+is it moving from one location to
+
+ align:start position:0%
+is it moving from one location to
+ 
+
+ align:start position:0%
+is it moving from one location to
+another because just like a patient data
+
+ align:start position:0%
+another because just like a patient data
+ 
+
+ align:start position:0%
+another because just like a patient data
+errors can be introduced whenever
+
+ align:start position:0%
+errors can be introduced whenever
+ 
+
+ align:start position:0%
+errors can be introduced whenever
+there's a handoff right whenever there's
+
+ align:start position:0%
+there's a handoff right whenever there's
+ 
+
+ align:start position:0%
+there's a handoff right whenever there's
+something that's different or changes we
+
+ align:start position:0%
+something that's different or changes we
+ 
+
+ align:start position:0%
+something that's different or changes we
+see that all the time okay we see big
+
+ align:start position:0%
+see that all the time okay we see big
+ 
+
+ align:start position:0%
+see that all the time okay we see big
+errors get you know data entry errors
+
+ align:start position:0%
+errors get you know data entry errors
+ 
+
+ align:start position:0%
+errors get you know data entry errors
+right all that kind of stuff so data has
+
+ align:start position:0%
+right all that kind of stuff so data has
+ 
+
+ align:start position:0%
+right all that kind of stuff so data has
+its own own flow as well having an
+
+ align:start position:0%
+its own own flow as well having an
+ 
+
+ align:start position:0%
+its own own flow as well having an
+ability to map that can help us to
+
+ align:start position:0%
+ability to map that can help us to
+ 
+
+ align:start position:0%
+ability to map that can help us to
+Target where we would like to leverage
+
+ align:start position:0%
+Target where we would like to leverage
+ 
+
+ align:start position:0%
+Target where we would like to leverage
+Improvement where we would like to make
+
+ align:start position:0%
+Improvement where we would like to make
+ 
+
+ align:start position:0%
+Improvement where we would like to make
+a change to our
+
+ align:start position:0%
+a change to our
+ 
+
+ align:start position:0%
+a change to our
+system all
+
+ align:start position:0%
+system all
+ 
+
+ align:start position:0%
+system all
+right how are we doing on time
+
+ align:start position:0%
+right how are we doing on time
+ 
+
+ align:start position:0%
+right how are we doing on time
+Le good hour oh really all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right setting names so this is
+
+ align:start position:0%
+right all right setting names so this is
+ 
+
+ align:start position:0%
+right all right setting names so this is
+the beginning this is where we've
+
+ align:start position:0%
+the beginning this is where we've
+ 
+
+ align:start position:0%
+the beginning this is where we've
+articulated what we believe and now
+
+ align:start position:0%
+articulated what we believe and now
+ 
+
+ align:start position:0%
+articulated what we believe and now
+we're gonna we're gonna we're going to
+
+ align:start position:0%
+we're gonna we're gonna we're going to
+ 
+
+ align:start position:0%
+we're gonna we're gonna we're going to
+start off and say what it is we want to
+
+ align:start position:0%
+start off and say what it is we want to
+ 
+
+ align:start position:0%
+start off and say what it is we want to
+accomplish okay so here's something
+
+ align:start position:0%
+accomplish okay so here's something
+ 
+
+ align:start position:0%
+accomplish okay so here's something
+about setting a name if you want to
+
+ align:start position:0%
+about setting a name if you want to
+ 
+
+ align:start position:0%
+about setting a name if you want to
+improve a data system or you want to
+
+ align:start position:0%
+improve a data system or you want to
+ 
+
+ align:start position:0%
+improve a data system or you want to
+improve a care system I'm going to
+
+ align:start position:0%
+improve a care system I'm going to
+ 
+
+ align:start position:0%
+improve a care system I'm going to
+challenge you with this statement
+
+ align:start position:0%
+challenge you with this statement
+ 
+
+ align:start position:0%
+challenge you with this statement
+whatever you want to accomplish should
+
+ align:start position:0%
+whatever you want to accomplish should
+ 
+
+ align:start position:0%
+whatever you want to accomplish should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+impossible within the current system
+
+ align:start position:0%
+impossible within the current system
+ 
+
+ align:start position:0%
+impossible within the current system
+should be impossible a lot of people
+
+ align:start position:0%
+should be impossible a lot of people
+ 
+
+ align:start position:0%
+should be impossible a lot of people
+will laugh at that why would you say
+
+ align:start position:0%
+will laugh at that why would you say
+ 
+
+ align:start position:0%
+will laugh at that why would you say
+that Brandon why do you guys think I
+
+ align:start position:0%
+that Brandon why do you guys think I
+ 
+
+ align:start position:0%
+that Brandon why do you guys think I
+said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+possible exactly every system perfectly
+
+ align:start position:0%
+possible exactly every system perfectly
+ 
+
+ align:start position:0%
+possible exactly every system perfectly
+designed to achieve the results it
+
+ align:start position:0%
+designed to achieve the results it
+ 
+
+ align:start position:0%
+designed to achieve the results it
+gets that's right wouldn't need changes
+
+ align:start position:0%
+gets that's right wouldn't need changes
+ 
+
+ align:start position:0%
+gets that's right wouldn't need changes
+if you were already achieving right so
+
+ align:start position:0%
+if you were already achieving right so
+ 
+
+ align:start position:0%
+if you were already achieving right so
+that's what I mean by impossible okay it
+
+ align:start position:0%
+that's what I mean by impossible okay it
+ 
+
+ align:start position:0%
+that's what I mean by impossible okay it
+requires transformational change it
+
+ align:start position:0%
+requires transformational change it
+ 
+
+ align:start position:0%
+requires transformational change it
+requires you to do something that is
+
+ align:start position:0%
+requires you to do something that is
+ 
+
+ align:start position:0%
+requires you to do something that is
+fundamentally different than what's
+
+ align:start position:0%
+fundamentally different than what's
+ 
+
+ align:start position:0%
+fundamentally different than what's
+happening right now in the status quo
+
+ align:start position:0%
+happening right now in the status quo
+ 
+
+ align:start position:0%
+happening right now in the status quo
+right so that transformational
+
+ align:start position:0%
+right so that transformational
+ 
+
+ align:start position:0%
+right so that transformational
+change is is a redesign of the system or
+
+ align:start position:0%
+change is is a redesign of the system or
+ 
+
+ align:start position:0%
+change is is a redesign of the system or
+redesign of an individual process within
+
+ align:start position:0%
+redesign of an individual process within
+ 
+
+ align:start position:0%
+redesign of an individual process within
+the system okay and that fundamental
+
+ align:start position:0%
+the system okay and that fundamental
+ 
+
+ align:start position:0%
+the system okay and that fundamental
+change will yield a change in
+
+ align:start position:0%
+change will yield a change in
+ 
+
+ align:start position:0%
+change will yield a change in
+performance right Better or Worse okay
+
+ align:start position:0%
+performance right Better or Worse okay
+ 
+
+ align:start position:0%
+performance right Better or Worse okay
+so in terms of when you're setting a
+
+ align:start position:0%
+so in terms of when you're setting a
+ 
+
+ align:start position:0%
+so in terms of when you're setting a
+name it should be ambitious it it has to
+
+ align:start position:0%
+name it should be ambitious it it has to
+ 
+
+ align:start position:0%
+name it should be ambitious it it has to
+be measurable okay it needs to be time
+
+ align:start position:0%
+be measurable okay it needs to be time
+ 
+
+ align:start position:0%
+be measurable okay it needs to be time
+limited and it needs to be as specific
+
+ align:start position:0%
+limited and it needs to be as specific
+ 
+
+ align:start position:0%
+limited and it needs to be as specific
+as possible right so often we come
+
+ align:start position:0%
+as possible right so often we come
+ 
+
+ align:start position:0%
+as possible right so often we come
+across Improvement initiatives that are
+
+ align:start position:0%
+across Improvement initiatives that are
+ 
+
+ align:start position:0%
+across Improvement initiatives that are
+vague right what's an example of a vague
+
+ align:start position:0%
+vague right what's an example of a vague
+ 
+
+ align:start position:0%
+vague right what's an example of a vague
+Improvement initiative I would love to
+
+ align:start position:0%
+Improvement initiative I would love to
+ 
+
+ align:start position:0%
+Improvement initiative I would love to
+reduce child mortality in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world that's vague right that's not an a
+
+ align:start position:0%
+world that's vague right that's not an a
+ 
+
+ align:start position:0%
+world that's vague right that's not an a
+that's a that's something else I'm not
+
+ align:start position:0%
+that's a that's something else I'm not
+ 
+
+ align:start position:0%
+that's a that's something else I'm not
+sure what that is I want to reduce under
+
+ align:start position:0%
+sure what that is I want to reduce under
+ 
+
+ align:start position:0%
+sure what that is I want to reduce under
+five mortality in one District by
+
+ align:start position:0%
+five mortality in one District by
+ 
+
+ align:start position:0%
+five mortality in one District by
+40% by January 2012 now that's specific
+
+ align:start position:0%
+40% by January 2012 now that's specific
+ 
+
+ align:start position:0%
+40% by January 2012 now that's specific
+it's time limited it's measurable right
+
+ align:start position:0%
+it's time limited it's measurable right
+ 
+
+ align:start position:0%
+it's time limited it's measurable right
+it gives me a geographic location to to
+
+ align:start position:0%
+it gives me a geographic location to to
+ 
+
+ align:start position:0%
+it gives me a geographic location to to
+fixate on now we're talking about
+
+ align:start position:0%
+fixate on now we're talking about
+ 
+
+ align:start position:0%
+fixate on now we're talking about
+something that we could actually start
+
+ align:start position:0%
+something that we could actually start
+ 
+
+ align:start position:0%
+something that we could actually start
+to wrap our minds around we're starting
+
+ align:start position:0%
+to wrap our minds around we're starting
+ 
+
+ align:start position:0%
+to wrap our minds around we're starting
+to draw that circle around our system
+
+ align:start position:0%
+to draw that circle around our system
+ 
+
+ align:start position:0%
+to draw that circle around our system
+where we're going to put the boundaries
+
+ align:start position:0%
+where we're going to put the boundaries
+ 
+
+ align:start position:0%
+where we're going to put the boundaries
+of what we try to improve okay does that
+
+ align:start position:0%
+of what we try to improve okay does that
+ 
+
+ align:start position:0%
+of what we try to improve okay does that
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+sense yes shouldn't you already
+
+ align:start position:0%
+sense yes shouldn't you already
+ 
+
+ align:start position:0%
+sense yes shouldn't you already
+understand the system before you try to
+
+ align:start position:0%
+understand the system before you try to
+ 
+
+ align:start position:0%
+understand the system before you try to
+change it like if you set your aims
+
+ align:start position:0%
+change it like if you set your aims
+ 
+
+ align:start position:0%
+change it like if you set your aims
+before you actually understand the
+
+ align:start position:0%
+before you actually understand the
+ 
+
+ align:start position:0%
+before you actually understand the
+system isn't it
+
+ align:start position:0%
+system isn't it
+ 
+
+ align:start position:0%
+system isn't it
+backwards I would argue yes I mean I
+
+ align:start position:0%
+backwards I would argue yes I mean I
+ 
+
+ align:start position:0%
+backwards I would argue yes I mean I
+think if if you don't know anything
+
+ align:start position:0%
+think if if you don't know anything
+ 
+
+ align:start position:0%
+think if if you don't know anything
+about your system you probably don't
+
+ align:start position:0%
+about your system you probably don't
+ 
+
+ align:start position:0%
+about your system you probably don't
+want to change it because you're likely
+
+ align:start position:0%
+want to change it because you're likely
+ 
+
+ align:start position:0%
+want to change it because you're likely
+to make it worse right but lots of
+
+ align:start position:0%
+to make it worse right but lots of
+ 
+
+ align:start position:0%
+to make it worse right but lots of
+people don't think that way lots of
+
+ align:start position:0%
+people don't think that way lots of
+ 
+
+ align:start position:0%
+people don't think that way lots of
+people just see an outcome that they
+
+ align:start position:0%
+people just see an outcome that they
+ 
+
+ align:start position:0%
+people just see an outcome that they
+don't like and say well I've got some
+
+ align:start position:0%
+don't like and say well I've got some
+ 
+
+ align:start position:0%
+don't like and say well I've got some
+assumptions about why that is let me put
+
+ align:start position:0%
+assumptions about why that is let me put
+ 
+
+ align:start position:0%
+assumptions about why that is let me put
+some resources towards it and see what
+
+ align:start position:0%
+some resources towards it and see what
+ 
+
+ align:start position:0%
+some resources towards it and see what
+we can do to change it without that that
+
+ align:start position:0%
+we can do to change it without that that
+ 
+
+ align:start position:0%
+we can do to change it without that that
+deeper understanding yeah definitely
+
+ align:start position:0%
+deeper understanding yeah definitely
+ 
+
+ align:start position:0%
+deeper understanding yeah definitely
+yeah good all right so what are you
+
+ align:start position:0%
+yeah good all right so what are you
+ 
+
+ align:start position:0%
+yeah good all right so what are you
+trying to accomplish time limited so how
+
+ align:start position:0%
+trying to accomplish time limited so how
+ 
+
+ align:start position:0%
+trying to accomplish time limited so how
+much and by when are the kind of things
+
+ align:start position:0%
+much and by when are the kind of things
+ 
+
+ align:start position:0%
+much and by when are the kind of things
+that you want to focus on so I would
+
+ align:start position:0%
+that you want to focus on so I would
+ 
+
+ align:start position:0%
+that you want to focus on so I would
+challenge you to do with your project
+
+ align:start position:0%
+challenge you to do with your project
+ 
+
+ align:start position:0%
+challenge you to do with your project
+teams right is as you get together for
+
+ align:start position:0%
+teams right is as you get together for
+ 
+
+ align:start position:0%
+teams right is as you get together for
+the first time think about the system
+
+ align:start position:0%
+the first time think about the system
+ 
+
+ align:start position:0%
+the first time think about the system
+where are you going to draw your circle
+
+ align:start position:0%
+where are you going to draw your circle
+ 
+
+ align:start position:0%
+where are you going to draw your circle
+right what are the processes that that
+
+ align:start position:0%
+right what are the processes that that
+ 
+
+ align:start position:0%
+right what are the processes that that
+you're working with or even just a
+
+ align:start position:0%
+you're working with or even just a
+ 
+
+ align:start position:0%
+you're working with or even just a
+single process that you're working with
+
+ align:start position:0%
+single process that you're working with
+ 
+
+ align:start position:0%
+single process that you're working with
+and then what do you know about it what
+
+ align:start position:0%
+and then what do you know about it what
+ 
+
+ align:start position:0%
+and then what do you know about it what
+information do you have that can inform
+
+ align:start position:0%
+information do you have that can inform
+ 
+
+ align:start position:0%
+information do you have that can inform
+the development of an name so for your
+
+ align:start position:0%
+the development of an name so for your
+ 
+
+ align:start position:0%
+the development of an name so for your
+team and you think about your project
+
+ align:start position:0%
+team and you think about your project
+ 
+
+ align:start position:0%
+team and you think about your project
+what are you trying to
+
+ align:start position:0%
+what are you trying to
+ 
+
+ align:start position:0%
+what are you trying to
+accomplish be as specific as you
+
+ align:start position:0%
+accomplish be as specific as you
+ 
+
+ align:start position:0%
+accomplish be as specific as you
+possibly can you got a few weeks be
+
+ align:start position:0%
+possibly can you got a few weeks be
+ 
+
+ align:start position:0%
+possibly can you got a few weeks be
+specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's it's it's enough to
+
+ align:start position:0%
+yeah it's it's it's enough to
+ 
+
+ align:start position:0%
+yeah it's it's it's enough to
+change yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitely so I agree uh for the
+
+ align:start position:0%
+definitely so I agree uh for the
+ 
+
+ align:start position:0%
+definitely so I agree uh for the
+purposes of here learning about process
+
+ align:start position:0%
+purposes of here learning about process
+ 
+
+ align:start position:0%
+purposes of here learning about process
+Improvement this is your learning
+
+ align:start position:0%
+Improvement this is your learning
+ 
+
+ align:start position:0%
+Improvement this is your learning
+laboratory this is your opportunity to
+
+ align:start position:0%
+laboratory this is your opportunity to
+ 
+
+ align:start position:0%
+laboratory this is your opportunity to
+learn about quality improvement you're
+
+ align:start position:0%
+learn about quality improvement you're
+ 
+
+ align:start position:0%
+learn about quality improvement you're
+asking a very fundamental question which
+
+ align:start position:0%
+asking a very fundamental question which
+ 
+
+ align:start position:0%
+asking a very fundamental question which
+is how big of a circle do I draw do I
+
+ align:start position:0%
+is how big of a circle do I draw do I
+ 
+
+ align:start position:0%
+is how big of a circle do I draw do I
+draw it around a single process well if
+
+ align:start position:0%
+draw it around a single process well if
+ 
+
+ align:start position:0%
+draw it around a single process well if
+my focus is on learning yeah because
+
+ align:start position:0%
+my focus is on learning yeah because
+ 
+
+ align:start position:0%
+my focus is on learning yeah because
+that gives me something manageable if my
+
+ align:start position:0%
+that gives me something manageable if my
+ 
+
+ align:start position:0%
+that gives me something manageable if my
+focus were to actually change the
+
+ align:start position:0%
+focus were to actually change the
+ 
+
+ align:start position:0%
+focus were to actually change the
+outcome of a system then I'm going to
+
+ align:start position:0%
+outcome of a system then I'm going to
+ 
+
+ align:start position:0%
+outcome of a system then I'm going to
+need to expand that Circle to include
+
+ align:start position:0%
+need to expand that Circle to include
+ 
+
+ align:start position:0%
+need to expand that Circle to include
+some other things that are going to be
+
+ align:start position:0%
+some other things that are going to be
+ 
+
+ align:start position:0%
+some other things that are going to be
+uh participating in in driving the
+
+ align:start position:0%
+uh participating in in driving the
+ 
+
+ align:start position:0%
+uh participating in in driving the
+outcome that I'm looking for absolutely
+
+ align:start position:0%
+outcome that I'm looking for absolutely
+ 
+
+ align:start position:0%
+outcome that I'm looking for absolutely
+and that is a fundamental question that
+
+ align:start position:0%
+and that is a fundamental question that
+ 
+
+ align:start position:0%
+and that is a fundamental question that
+every quality improvement team has to
+
+ align:start position:0%
+every quality improvement team has to
+ 
+
+ align:start position:0%
+every quality improvement team has to
+answer right
+
+ align:start position:0%
+answer right
+ 
+
+ align:start position:0%
+answer right
+definitely if you're a CEO or you're a
+
+ align:start position:0%
+definitely if you're a CEO or you're a
+ 
+
+ align:start position:0%
+definitely if you're a CEO or you're a
+minister of Health it's a really hard
+
+ align:start position:0%
+minister of Health it's a really hard
+ 
+
+ align:start position:0%
+minister of Health it's a really hard
+question because now you're saying how
+
+ align:start position:0%
+question because now you're saying how
+ 
+
+ align:start position:0%
+question because now you're saying how
+do I do that strategically how do I
+
+ align:start position:0%
+do I do that strategically how do I
+ 
+
+ align:start position:0%
+do I do that strategically how do I
+choose which parts do I you know do I
+
+ align:start position:0%
+choose which parts do I you know do I
+ 
+
+ align:start position:0%
+choose which parts do I you know do I
+improve maintenance do I build a
+
+ align:start position:0%
+improve maintenance do I build a
+ 
+
+ align:start position:0%
+improve maintenance do I build a
+building here do I improve the clinical
+
+ align:start position:0%
+building here do I improve the clinical
+ 
+
+ align:start position:0%
+building here do I improve the clinical
+process of care over there can I get
+
+ align:start position:0%
+process of care over there can I get
+ 
+
+ align:start position:0%
+process of care over there can I get
+those things to line up and work
+
+ align:start position:0%
+those things to line up and work
+ 
+
+ align:start position:0%
+those things to line up and work
+together right that's that's going to be
+
+ align:start position:0%
+together right that's that's going to be
+ 
+
+ align:start position:0%
+together right that's that's going to be
+a different question be a hard question
+
+ align:start position:0%
+a different question be a hard question
+ 
+
+ align:start position:0%
+a different question be a hard question
+to answer so think about this this is my
+
+ align:start position:0%
+to answer so think about this this is my
+ 
+
+ align:start position:0%
+to answer so think about this this is my
+challenge to you okay all right when
+
+ align:start position:0%
+challenge to you okay all right when
+ 
+
+ align:start position:0%
+challenge to you okay all right when
+you're reviewing it there's some key
+
+ align:start position:0%
+you're reviewing it there's some key
+ 
+
+ align:start position:0%
+you're reviewing it there's some key
+questions that you can be asking to
+
+ align:start position:0%
+questions that you can be asking to
+ 
+
+ align:start position:0%
+questions that you can be asking to
+yourselves okay is it specific is it
+
+ align:start position:0%
+yourselves okay is it specific is it
+ 
+
+ align:start position:0%
+yourselves okay is it specific is it
+ambitious is it clear to anyone who will
+
+ align:start position:0%
+ambitious is it clear to anyone who will
+ 
+
+ align:start position:0%
+ambitious is it clear to anyone who will
+read it right so if you just went out on
+
+ align:start position:0%
+read it right so if you just went out on
+ 
+
+ align:start position:0%
+read it right so if you just went out on
+the street and said hey read this do you
+
+ align:start position:0%
+the street and said hey read this do you
+ 
+
+ align:start position:0%
+the street and said hey read this do you
+have an idea what I'm trying to do they
+
+ align:start position:0%
+have an idea what I'm trying to do they
+ 
+
+ align:start position:0%
+have an idea what I'm trying to do they
+should be able to say yes they should be
+
+ align:start position:0%
+should be able to say yes they should be
+ 
+
+ align:start position:0%
+should be able to say yes they should be
+able to read it and say yeah I got a
+
+ align:start position:0%
+able to read it and say yeah I got a
+ 
+
+ align:start position:0%
+able to read it and say yeah I got a
+good idea of what you're trying to
+
+ align:start position:0%
+good idea of what you're trying to
+ 
+
+ align:start position:0%
+good idea of what you're trying to
+accomplish if it's like that it's a good
+
+ align:start position:0%
+accomplish if it's like that it's a good
+ 
+
+ align:start position:0%
+accomplish if it's like that it's a good
+indication that you have a good handle
+
+ align:start position:0%
+indication that you have a good handle
+ 
+
+ align:start position:0%
+indication that you have a good handle
+on what it is you're trying to
+
+ align:start position:0%
+on what it is you're trying to
+ 
+
+ align:start position:0%
+on what it is you're trying to
+accomplish you have a good handle on the
+
+ align:start position:0%
+accomplish you have a good handle on the
+ 
+
+ align:start position:0%
+accomplish you have a good handle on the
+system that you're working within and
+
+ align:start position:0%
+system that you're working within and
+ 
+
+ align:start position:0%
+system that you're working within and
+that Circle that you've
+
+ align:start position:0%
+that Circle that you've
+ 
+
+ align:start position:0%
+that Circle that you've
+drawn okay and then ask people to
+
+ align:start position:0%
+drawn okay and then ask people to
+ 
+
+ align:start position:0%
+drawn okay and then ask people to
+improve it ask them where could it be
+
+ align:start position:0%
+improve it ask them where could it be
+ 
+
+ align:start position:0%
+improve it ask them where could it be
+clearer where could I improve this where
+
+ align:start position:0%
+clearer where could I improve this where
+ 
+
+ align:start position:0%
+clearer where could I improve this where
+could I make it
+
+ align:start position:0%
+could I make it
+ 
+
+ align:start position:0%
+could I make it
+better okay so the last thing I want to
+
+ align:start position:0%
+better okay so the last thing I want to
+ 
+
+ align:start position:0%
+better okay so the last thing I want to
+talk about today is the model for
+
+ align:start position:0%
+talk about today is the model for
+ 
+
+ align:start position:0%
+talk about today is the model for
+improvement and this is a very specific
+
+ align:start position:0%
+improvement and this is a very specific
+ 
+
+ align:start position:0%
+improvement and this is a very specific
+model that is uh developed from the work
+
+ align:start position:0%
+model that is uh developed from the work
+ 
+
+ align:start position:0%
+model that is uh developed from the work
+of Walter schuhart and and Edwards
+
+ align:start position:0%
+of Walter schuhart and and Edwards
+ 
+
+ align:start position:0%
+of Walter schuhart and and Edwards
+Deming okay and it's a mechanism for
+
+ align:start position:0%
+Deming okay and it's a mechanism for
+ 
+
+ align:start position:0%
+Deming okay and it's a mechanism for
+actually making changes in a system or
+
+ align:start position:0%
+actually making changes in a system or
+ 
+
+ align:start position:0%
+actually making changes in a system or
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+process so it is in my mind a a really
+
+ align:start position:0%
+process so it is in my mind a a really
+ 
+
+ align:start position:0%
+process so it is in my mind a a really
+powerful mechanism um for for driving
+
+ align:start position:0%
+powerful mechanism um for for driving
+ 
+
+ align:start position:0%
+powerful mechanism um for for driving
+quality improvement it's not the only
+
+ align:start position:0%
+quality improvement it's not the only
+ 
+
+ align:start position:0%
+quality improvement it's not the only
+mechanism but it is one okay so again
+
+ align:start position:0%
+mechanism but it is one okay so again
+ 
+
+ align:start position:0%
+mechanism but it is one okay so again
+now we're we're focusing here on theory
+
+ align:start position:0%
+now we're we're focusing here on theory
+ 
+
+ align:start position:0%
+now we're we're focusing here on theory
+of knowledge constantly learning the
+
+ align:start position:0%
+of knowledge constantly learning the
+ 
+
+ align:start position:0%
+of knowledge constantly learning the
+model for improvement in many ways is
+
+ align:start position:0%
+model for improvement in many ways is
+ 
+
+ align:start position:0%
+model for improvement in many ways is
+the application of the scientific method
+
+ align:start position:0%
+the application of the scientific method
+ 
+
+ align:start position:0%
+the application of the scientific method
+through quality
+
+ align:start position:0%
+through quality
+ 
+
+ align:start position:0%
+through quality
+improvement and it's a way of engaging
+
+ align:start position:0%
+improvement and it's a way of engaging
+ 
+
+ align:start position:0%
+improvement and it's a way of engaging
+teams of people and helping to
+
+ align:start position:0%
+teams of people and helping to
+ 
+
+ align:start position:0%
+teams of people and helping to
+understand their pers perspective and
+
+ align:start position:0%
+understand their pers perspective and
+ 
+
+ align:start position:0%
+understand their pers perspective and
+getting them motivated to
+
+ align:start position:0%
+getting them motivated to
+ 
+
+ align:start position:0%
+getting them motivated to
+change okay here it is it's described uh
+
+ align:start position:0%
+change okay here it is it's described uh
+ 
+
+ align:start position:0%
+change okay here it is it's described uh
+by uh in the Improvement guide that's
+
+ align:start position:0%
+by uh in the Improvement guide that's
+ 
+
+ align:start position:0%
+by uh in the Improvement guide that's
+LLY at all there's a reference at the
+
+ align:start position:0%
+LLY at all there's a reference at the
+ 
+
+ align:start position:0%
+LLY at all there's a reference at the
+end okay it involves three questions and
+
+ align:start position:0%
+end okay it involves three questions and
+ 
+
+ align:start position:0%
+end okay it involves three questions and
+something called a plan do study act
+
+ align:start position:0%
+something called a plan do study act
+ 
+
+ align:start position:0%
+something called a plan do study act
+cycle so we'll talk about the plan to
+
+ align:start position:0%
+cycle so we'll talk about the plan to
+ 
+
+ align:start position:0%
+cycle so we'll talk about the plan to
+study act cycle in more detail in a
+
+ align:start position:0%
+study act cycle in more detail in a
+ 
+
+ align:start position:0%
+study act cycle in more detail in a
+minute but what I want to focus on for
+
+ align:start position:0%
+minute but what I want to focus on for
+ 
+
+ align:start position:0%
+minute but what I want to focus on for
+the first part are the three questions
+
+ align:start position:0%
+the first part are the three questions
+ 
+
+ align:start position:0%
+the first part are the three questions
+so when you're approaching a quality
+
+ align:start position:0%
+so when you're approaching a quality
+ 
+
+ align:start position:0%
+so when you're approaching a quality
+improvement project the three questions
+
+ align:start position:0%
+improvement project the three questions
+ 
+
+ align:start position:0%
+improvement project the three questions
+are critically important what are you
+
+ align:start position:0%
+are critically important what are you
+ 
+
+ align:start position:0%
+are critically important what are you
+trying to accomplish you can do this at
+
+ align:start position:0%
+trying to accomplish you can do this at
+ 
+
+ align:start position:0%
+trying to accomplish you can do this at
+the macro level for the project itself
+
+ align:start position:0%
+the macro level for the project itself
+ 
+
+ align:start position:0%
+the macro level for the project itself
+or you can do it for an individual
+
+ align:start position:0%
+or you can do it for an individual
+ 
+
+ align:start position:0%
+or you can do it for an individual
+learning cycle okay you can do it for an
+
+ align:start position:0%
+learning cycle okay you can do it for an
+ 
+
+ align:start position:0%
+learning cycle okay you can do it for an
+individual learning
+
+ align:start position:0%
+individual learning
+ 
+
+ align:start position:0%
+individual learning
+cycle what change can we make that will
+
+ align:start position:0%
+cycle what change can we make that will
+ 
+
+ align:start position:0%
+cycle what change can we make that will
+result in Improvement so coming out of
+
+ align:start position:0%
+result in Improvement so coming out of
+ 
+
+ align:start position:0%
+result in Improvement so coming out of
+our assumptions and our thoughts and the
+
+ align:start position:0%
+our assumptions and our thoughts and the
+ 
+
+ align:start position:0%
+our assumptions and our thoughts and the
+information that we have about our
+
+ align:start position:0%
+information that we have about our
+ 
+
+ align:start position:0%
+information that we have about our
+system what are all the things that we
+
+ align:start position:0%
+system what are all the things that we
+ 
+
+ align:start position:0%
+system what are all the things that we
+think we could do differently that we
+
+ align:start position:0%
+think we could do differently that we
+ 
+
+ align:start position:0%
+think we could do differently that we
+could change about the status quo okay
+
+ align:start position:0%
+could change about the status quo okay
+ 
+
+ align:start position:0%
+could change about the status quo okay
+and then how we know that A change is an
+
+ align:start position:0%
+and then how we know that A change is an
+ 
+
+ align:start position:0%
+and then how we know that A change is an
+improvement how are we going to measure
+
+ align:start position:0%
+improvement how are we going to measure
+ 
+
+ align:start position:0%
+improvement how are we going to measure
+whether or not what we're doing
+
+ align:start position:0%
+whether or not what we're doing
+ 
+
+ align:start position:0%
+whether or not what we're doing
+different differently is better than
+
+ align:start position:0%
+different differently is better than
+ 
+
+ align:start position:0%
+different differently is better than
+what is right now does that make sense
+
+ align:start position:0%
+what is right now does that make sense
+ 
+
+ align:start position:0%
+what is right now does that make sense
+so those three questions are important
+
+ align:start position:0%
+so those three questions are important
+ 
+
+ align:start position:0%
+so those three questions are important
+all three of them are important so that
+
+ align:start position:0%
+all three of them are important so that
+ 
+
+ align:start position:0%
+all three of them are important so that
+measurement piece is going to inform
+
+ align:start position:0%
+measurement piece is going to inform
+ 
+
+ align:start position:0%
+measurement piece is going to inform
+whether or not the changes we made are
+
+ align:start position:0%
+whether or not the changes we made are
+ 
+
+ align:start position:0%
+whether or not the changes we made are
+good and whether or not we should try
+
+ align:start position:0%
+good and whether or not we should try
+ 
+
+ align:start position:0%
+good and whether or not we should try
+something else or evolve our Theory
+
+ align:start position:0%
+something else or evolve our Theory
+ 
+
+ align:start position:0%
+something else or evolve our Theory
+right or even change our Focus all of
+
+ align:start position:0%
+right or even change our Focus all of
+ 
+
+ align:start position:0%
+right or even change our Focus all of
+that when you have them in place then
+
+ align:start position:0%
+that when you have them in place then
+ 
+
+ align:start position:0%
+that when you have them in place then
+get driven by the pdsa cycle which is a
+
+ align:start position:0%
+get driven by the pdsa cycle which is a
+ 
+
+ align:start position:0%
+get driven by the pdsa cycle which is a
+mechanism for testing change in a
+
+ align:start position:0%
+mechanism for testing change in a
+ 
+
+ align:start position:0%
+mechanism for testing change in a
+non-threatening way to a system
+
+ align:start position:0%
+non-threatening way to a system
+ 
+
+ align:start position:0%
+non-threatening way to a system
+okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is really the aim setting yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Patrick yes we're GNA talk about that in
+
+ align:start position:0%
+Patrick yes we're GNA talk about that in
+ 
+
+ align:start position:0%
+Patrick yes we're GNA talk about that in
+in a lot of detail in just two minutes
+
+ align:start position:0%
+in a lot of detail in just two minutes
+ 
+
+ align:start position:0%
+in a lot of detail in just two minutes
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+okay definitely hold on to that though
+
+ align:start position:0%
+okay definitely hold on to that though
+ 
+
+ align:start position:0%
+okay definitely hold on to that though
+don't let me get away from that right
+
+ align:start position:0%
+don't let me get away from that right
+ 
+
+ align:start position:0%
+don't let me get away from that right
+okay so what are we trying to accomplish
+
+ align:start position:0%
+okay so what are we trying to accomplish
+ 
+
+ align:start position:0%
+okay so what are we trying to accomplish
+project aim but then when we have come
+
+ align:start position:0%
+project aim but then when we have come
+ 
+
+ align:start position:0%
+project aim but then when we have come
+up with a specific change that we want
+
+ align:start position:0%
+up with a specific change that we want
+ 
+
+ align:start position:0%
+up with a specific change that we want
+to make a specific aim for testing that
+
+ align:start position:0%
+to make a specific aim for testing that
+ 
+
+ align:start position:0%
+to make a specific aim for testing that
+change right if my aim overall is to
+
+ align:start position:0%
+change right if my aim overall is to
+ 
+
+ align:start position:0%
+change right if my aim overall is to
+reduce HIV transmission but the change
+
+ align:start position:0%
+reduce HIV transmission but the change
+ 
+
+ align:start position:0%
+reduce HIV transmission but the change
+that I'm making is one to increase HIV
+
+ align:start position:0%
+that I'm making is one to increase HIV
+ 
+
+ align:start position:0%
+that I'm making is one to increase HIV
+testing then I need to have an aim just
+
+ align:start position:0%
+testing then I need to have an aim just
+ 
+
+ align:start position:0%
+testing then I need to have an aim just
+for that right I need to have an aim
+
+ align:start position:0%
+for that right I need to have an aim
+ 
+
+ align:start position:0%
+for that right I need to have an aim
+just for that so it's maybe increasing
+
+ align:start position:0%
+just for that so it's maybe increasing
+ 
+
+ align:start position:0%
+just for that so it's maybe increasing
+testing by how much where for what
+
+ align:start position:0%
+testing by how much where for what
+ 
+
+ align:start position:0%
+testing by how much where for what
+population all that kind of thing okay
+
+ align:start position:0%
+population all that kind of thing okay
+ 
+
+ align:start position:0%
+population all that kind of thing okay
+what change can we make that will result
+
+ align:start position:0%
+what change can we make that will result
+ 
+
+ align:start position:0%
+what change can we make that will result
+in an improvement so where do we go out
+
+ align:start position:0%
+in an improvement so where do we go out
+ 
+
+ align:start position:0%
+in an improvement so where do we go out
+and find change
+
+ align:start position:0%
+and find change
+ 
+
+ align:start position:0%
+and find change
+ideas how do we know what to do
+
+ align:start position:0%
+ideas how do we know what to do
+ 
+
+ align:start position:0%
+ideas how do we know what to do
+differently here are some ideas okay the
+
+ align:start position:0%
+differently here are some ideas okay the
+ 
+
+ align:start position:0%
+differently here are some ideas okay the
+first place that I'm always going to
+
+ align:start position:0%
+first place that I'm always going to
+ 
+
+ align:start position:0%
+first place that I'm always going to
+look if I'm working within a system is
+
+ align:start position:0%
+look if I'm working within a system is
+ 
+
+ align:start position:0%
+look if I'm working within a system is
+to the people who are providing the
+
+ align:start position:0%
+to the people who are providing the
+ 
+
+ align:start position:0%
+to the people who are providing the
+service remember what I said way back at
+
+ align:start position:0%
+service remember what I said way back at
+ 
+
+ align:start position:0%
+service remember what I said way back at
+the beginning about subject matter
+
+ align:start position:0%
+the beginning about subject matter
+ 
+
+ align:start position:0%
+the beginning about subject matter
+experts these are their subject matter
+
+ align:start position:0%
+experts these are their subject matter
+ 
+
+ align:start position:0%
+experts these are their subject matter
+experts these are the folks who may be
+
+ align:start position:0%
+experts these are the folks who may be
+ 
+
+ align:start position:0%
+experts these are the folks who may be
+researchers in the field and have real
+
+ align:start position:0%
+researchers in the field and have real
+ 
+
+ align:start position:0%
+researchers in the field and have real
+deep knowledge about what works and what
+
+ align:start position:0%
+deep knowledge about what works and what
+ 
+
+ align:start position:0%
+deep knowledge about what works and what
+doesn't work or they could be Frontline
+
+ align:start position:0%
+doesn't work or they could be Frontline
+ 
+
+ align:start position:0%
+doesn't work or they could be Frontline
+caregivers who are running into systems
+
+ align:start position:0%
+caregivers who are running into systems
+ 
+
+ align:start position:0%
+caregivers who are running into systems
+barriers every day who are running into
+
+ align:start position:0%
+barriers every day who are running into
+ 
+
+ align:start position:0%
+barriers every day who are running into
+things that they don't like and they're
+
+ align:start position:0%
+things that they don't like and they're
+ 
+
+ align:start position:0%
+things that they don't like and they're
+having to work around those barriers
+
+ align:start position:0%
+having to work around those barriers
+ 
+
+ align:start position:0%
+having to work around those barriers
+right they're going to be a good source
+
+ align:start position:0%
+right they're going to be a good source
+ 
+
+ align:start position:0%
+right they're going to be a good source
+for understanding what you could be
+
+ align:start position:0%
+for understanding what you could be
+ 
+
+ align:start position:0%
+for understanding what you could be
+doing differently walk into any Hospital
+
+ align:start position:0%
+doing differently walk into any Hospital
+ 
+
+ align:start position:0%
+doing differently walk into any Hospital
+in Boston after class
+
+ align:start position:0%
+in Boston after class
+ 
+
+ align:start position:0%
+in Boston after class
+today pull aside one clinician and say
+
+ align:start position:0%
+today pull aside one clinician and say
+ 
+
+ align:start position:0%
+today pull aside one clinician and say
+tomorrow when you come to work if you
+
+ align:start position:0%
+tomorrow when you come to work if you
+ 
+
+ align:start position:0%
+tomorrow when you come to work if you
+could do one thing differently what
+
+ align:start position:0%
+could do one thing differently what
+ 
+
+ align:start position:0%
+could do one thing differently what
+would it be as you would have change
+
+ align:start position:0%
+would it be as you would have change
+ 
+
+ align:start position:0%
+would it be as you would have change
+ideas coming coming out of of every
+
+ align:start position:0%
+ideas coming coming out of of every
+ 
+
+ align:start position:0%
+ideas coming coming out of of every
+pocket I mean people have things that
+
+ align:start position:0%
+pocket I mean people have things that
+ 
+
+ align:start position:0%
+pocket I mean people have things that
+that frustrate them about their job and
+
+ align:start position:0%
+that frustrate them about their job and
+ 
+
+ align:start position:0%
+that frustrate them about their job and
+they have Solutions but often they don't
+
+ align:start position:0%
+they have Solutions but often they don't
+ 
+
+ align:start position:0%
+they have Solutions but often they don't
+feel empowered to enact those Solutions
+
+ align:start position:0%
+feel empowered to enact those Solutions
+ 
+
+ align:start position:0%
+feel empowered to enact those Solutions
+right so one place to look for those
+
+ align:start position:0%
+right so one place to look for those
+ 
+
+ align:start position:0%
+right so one place to look for those
+ideas is is from the people who are who
+
+ align:start position:0%
+ideas is is from the people who are who
+ 
+
+ align:start position:0%
+ideas is is from the people who are who
+who are living it every day the clients
+
+ align:start position:0%
+who are living it every day the clients
+ 
+
+ align:start position:0%
+who are living it every day the clients
+themselves particularly in health care
+
+ align:start position:0%
+themselves particularly in health care
+ 
+
+ align:start position:0%
+themselves particularly in health care
+right we often forget about patients
+
+ align:start position:0%
+right we often forget about patients
+ 
+
+ align:start position:0%
+right we often forget about patients
+we're so focused on the system and the
+
+ align:start position:0%
+we're so focused on the system and the
+ 
+
+ align:start position:0%
+we're so focused on the system and the
+caregivers that we forget about the
+
+ align:start position:0%
+caregivers that we forget about the
+ 
+
+ align:start position:0%
+caregivers that we forget about the
+patients themselves and their needs and
+
+ align:start position:0%
+patients themselves and their needs and
+ 
+
+ align:start position:0%
+patients themselves and their needs and
+the challenges that they have to
+
+ align:start position:0%
+the challenges that they have to
+ 
+
+ align:start position:0%
+the challenges that they have to
+accessing care particularly in resource
+
+ align:start position:0%
+accessing care particularly in resource
+ 
+
+ align:start position:0%
+accessing care particularly in resource
+constrainted environments right I've
+
+ align:start position:0%
+constrainted environments right I've
+ 
+
+ align:start position:0%
+constrainted environments right I've
+worked with clinics where you know
+
+ align:start position:0%
+worked with clinics where you know
+ 
+
+ align:start position:0%
+worked with clinics where you know
+people have to travel 50 70 kilm right
+
+ align:start position:0%
+people have to travel 50 70 kilm right
+ 
+
+ align:start position:0%
+people have to travel 50 70 kilm right
+all before 8: a.m. and then wait to get
+
+ align:start position:0%
+all before 8: a.m. and then wait to get
+ 
+
+ align:start position:0%
+all before 8: a.m. and then wait to get
+care and then travel back at tremendous
+
+ align:start position:0%
+care and then travel back at tremendous
+ 
+
+ align:start position:0%
+care and then travel back at tremendous
+cost right to themselves to their family
+
+ align:start position:0%
+cost right to themselves to their family
+ 
+
+ align:start position:0%
+cost right to themselves to their family
+to their work whatever it is right are
+
+ align:start position:0%
+to their work whatever it is right are
+ 
+
+ align:start position:0%
+to their work whatever it is right are
+we taking that into account clients can
+
+ align:start position:0%
+we taking that into account clients can
+ 
+
+ align:start position:0%
+we taking that into account clients can
+have ideas about where we can do things
+
+ align:start position:0%
+have ideas about where we can do things
+ 
+
+ align:start position:0%
+have ideas about where we can do things
+differently and how we can improve our
+
+ align:start position:0%
+differently and how we can improve our
+ 
+
+ align:start position:0%
+differently and how we can improve our
+systems of course best practices and
+
+ align:start position:0%
+systems of course best practices and
+ 
+
+ align:start position:0%
+systems of course best practices and
+guidelines are important we can't forget
+
+ align:start position:0%
+guidelines are important we can't forget
+ 
+
+ align:start position:0%
+guidelines are important we can't forget
+you know that guidelines are in place
+
+ align:start position:0%
+you know that guidelines are in place
+ 
+
+ align:start position:0%
+you know that guidelines are in place
+for a reason because people have done
+
+ align:start position:0%
+for a reason because people have done
+ 
+
+ align:start position:0%
+for a reason because people have done
+some serious thinking around the topics
+
+ align:start position:0%
+some serious thinking around the topics
+ 
+
+ align:start position:0%
+some serious thinking around the topics
+and the and the processes that we're
+
+ align:start position:0%
+and the and the processes that we're
+ 
+
+ align:start position:0%
+and the and the processes that we're
+trying to improve and a lot of places
+
+ align:start position:0%
+trying to improve and a lot of places
+ 
+
+ align:start position:0%
+trying to improve and a lot of places
+have good policies and guidelines in
+
+ align:start position:0%
+have good policies and guidelines in
+ 
+
+ align:start position:0%
+have good policies and guidelines in
+place we we you know we develop great
+
+ align:start position:0%
+place we we you know we develop great
+ 
+
+ align:start position:0%
+place we we you know we develop great
+recommendations frequently at places
+
+ align:start position:0%
+recommendations frequently at places
+ 
+
+ align:start position:0%
+recommendations frequently at places
+like UNICEF World Health individual
+
+ align:start position:0%
+like UNICEF World Health individual
+ 
+
+ align:start position:0%
+like UNICEF World Health individual
+ministries of Health come up with great
+
+ align:start position:0%
+ministries of Health come up with great
+ 
+
+ align:start position:0%
+ministries of Health come up with great
+guidelines right now their their
+
+ align:start position:0%
+guidelines right now their their
+ 
+
+ align:start position:0%
+guidelines right now their their
+reliable implementation is a completely
+
+ align:start position:0%
+reliable implementation is a completely
+ 
+
+ align:start position:0%
+reliable implementation is a completely
+different matter but there could be some
+
+ align:start position:0%
+different matter but there could be some
+ 
+
+ align:start position:0%
+different matter but there could be some
+great ideas contained therein about how
+
+ align:start position:0%
+great ideas contained therein about how
+ 
+
+ align:start position:0%
+great ideas contained therein about how
+we can improve systems
+
+ align:start position:0%
+we can improve systems
+ 
+
+ align:start position:0%
+we can improve systems
+okay change
+
+ align:start position:0%
+okay change
+ 
+
+ align:start position:0%
+okay change
+Concepts these are these are something
+
+ align:start position:0%
+Concepts these are these are something
+ 
+
+ align:start position:0%
+Concepts these are these are something
+that you can uh learn more about uh but
+
+ align:start position:0%
+that you can uh learn more about uh but
+ 
+
+ align:start position:0%
+that you can uh learn more about uh but
+you know things that could be could lead
+
+ align:start position:0%
+you know things that could be could lead
+ 
+
+ align:start position:0%
+you know things that could be could lead
+to lots of different specific ideas okay
+
+ align:start position:0%
+to lots of different specific ideas okay
+ 
+
+ align:start position:0%
+to lots of different specific ideas okay
+um improve throughput eliminate waste
+
+ align:start position:0%
+um improve throughput eliminate waste
+ 
+
+ align:start position:0%
+um improve throughput eliminate waste
+these are Concepts but they could be
+
+ align:start position:0%
+these are Concepts but they could be
+ 
+
+ align:start position:0%
+these are Concepts but they could be
+leveraged into very specific actionable
+
+ align:start position:0%
+leveraged into very specific actionable
+ 
+
+ align:start position:0%
+leveraged into very specific actionable
+items now you can use structured
+
+ align:start position:0%
+items now you can use structured
+ 
+
+ align:start position:0%
+items now you can use structured
+creativity there's great thinkers people
+
+ align:start position:0%
+creativity there's great thinkers people
+ 
+
+ align:start position:0%
+creativity there's great thinkers people
+like Edward debono who have done a lot
+
+ align:start position:0%
+like Edward debono who have done a lot
+ 
+
+ align:start position:0%
+like Edward debono who have done a lot
+to help us understand how we could use
+
+ align:start position:0%
+to help us understand how we could use
+ 
+
+ align:start position:0%
+to help us understand how we could use
+structured creativity right A lot of
+
+ align:start position:0%
+structured creativity right A lot of
+ 
+
+ align:start position:0%
+structured creativity right A lot of
+people think well that person's creative
+
+ align:start position:0%
+people think well that person's creative
+ 
+
+ align:start position:0%
+people think well that person's creative
+and that person's not right but actually
+
+ align:start position:0%
+and that person's not right but actually
+ 
+
+ align:start position:0%
+and that person's not right but actually
+we can all be creative if we learn some
+
+ align:start position:0%
+we can all be creative if we learn some
+ 
+
+ align:start position:0%
+we can all be creative if we learn some
+tools to help us overcome our our normal
+
+ align:start position:0%
+tools to help us overcome our our normal
+ 
+
+ align:start position:0%
+tools to help us overcome our our normal
+perceptual sort of ruts that we get
+
+ align:start position:0%
+perceptual sort of ruts that we get
+ 
+
+ align:start position:0%
+perceptual sort of ruts that we get
+into and doing some root cause analysis
+
+ align:start position:0%
+into and doing some root cause analysis
+ 
+
+ align:start position:0%
+into and doing some root cause analysis
+right understanding the process talking
+
+ align:start position:0%
+right understanding the process talking
+ 
+
+ align:start position:0%
+right understanding the process talking
+with folks about what's wrong can often
+
+ align:start position:0%
+with folks about what's wrong can often
+ 
+
+ align:start position:0%
+with folks about what's wrong can often
+lead to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas last bit how will we know that A
+
+ align:start position:0%
+ideas last bit how will we know that A
+ 
+
+ align:start position:0%
+ideas last bit how will we know that A
+change is an improvement here we've got
+
+ align:start position:0%
+change is an improvement here we've got
+ 
+
+ align:start position:0%
+change is an improvement here we've got
+to measure we have to know for an
+
+ align:start position:0%
+to measure we have to know for an
+ 
+
+ align:start position:0%
+to measure we have to know for an
+individual step in the process or for
+
+ align:start position:0%
+individual step in the process or for
+ 
+
+ align:start position:0%
+individual step in the process or for
+the whole process itself or for the the
+
+ align:start position:0%
+the whole process itself or for the the
+ 
+
+ align:start position:0%
+the whole process itself or for the the
+outcome for the whole system how we're
+
+ align:start position:0%
+outcome for the whole system how we're
+ 
+
+ align:start position:0%
+outcome for the whole system how we're
+doing this often is neglected by folks
+
+ align:start position:0%
+doing this often is neglected by folks
+ 
+
+ align:start position:0%
+doing this often is neglected by folks
+right we're interested in the patient
+
+ align:start position:0%
+right we're interested in the patient
+ 
+
+ align:start position:0%
+right we're interested in the patient
+that's right in front of us but we need
+
+ align:start position:0%
+that's right in front of us but we need
+ 
+
+ align:start position:0%
+that's right in front of us but we need
+to have the perception we need to have
+
+ align:start position:0%
+to have the perception we need to have
+ 
+
+ align:start position:0%
+to have the perception we need to have
+the awareness of what's going on around
+
+ align:start position:0%
+the awareness of what's going on around
+ 
+
+ align:start position:0%
+the awareness of what's going on around
+us okay so each change idea has to have
+
+ align:start position:0%
+us okay so each change idea has to have
+ 
+
+ align:start position:0%
+us okay so each change idea has to have
+measurement associated with it if I'm
+
+ align:start position:0%
+measurement associated with it if I'm
+ 
+
+ align:start position:0%
+measurement associated with it if I'm
+going to implement a new data system how
+
+ align:start position:0%
+going to implement a new data system how
+ 
+
+ align:start position:0%
+going to implement a new data system how
+am I going to know that that's better
+
+ align:start position:0%
+am I going to know that that's better
+ 
+
+ align:start position:0%
+am I going to know that that's better
+than the paper based system I've been
+
+ align:start position:0%
+than the paper based system I've been
+ 
+
+ align:start position:0%
+than the paper based system I've been
+using for the last 20 years what do I
+
+ align:start position:0%
+using for the last 20 years what do I
+ 
+
+ align:start position:0%
+using for the last 20 years what do I
+know about the performance of the paper
+
+ align:start position:0%
+know about the performance of the paper
+ 
+
+ align:start position:0%
+know about the performance of the paper
+based system that tells me that I need
+
+ align:start position:0%
+based system that tells me that I need
+ 
+
+ align:start position:0%
+based system that tells me that I need
+to change away from that
+
+ align:start position:0%
+to change away from that
+ 
+
+ align:start position:0%
+to change away from that
+right you've got to have a way to
+
+ align:start position:0%
+right you've got to have a way to
+ 
+
+ align:start position:0%
+right you've got to have a way to
+measure so that when you do something
+
+ align:start position:0%
+measure so that when you do something
+ 
+
+ align:start position:0%
+measure so that when you do something
+different when you try it out for the
+
+ align:start position:0%
+different when you try it out for the
+ 
+
+ align:start position:0%
+different when you try it out for the
+first time you know that it's an
+
+ align:start position:0%
+first time you know that it's an
+ 
+
+ align:start position:0%
+first time you know that it's an
+improvement so Patrick coming to your
+
+ align:start position:0%
+improvement so Patrick coming to your
+ 
+
+ align:start position:0%
+improvement so Patrick coming to your
+question what about this thing what
+
+ align:start position:0%
+question what about this thing what
+ 
+
+ align:start position:0%
+question what about this thing what
+about the plan do study act cycle so uh
+
+ align:start position:0%
+about the plan do study act cycle so uh
+ 
+
+ align:start position:0%
+about the plan do study act cycle so uh
+a lot of times it's called the Deming
+
+ align:start position:0%
+a lot of times it's called the Deming
+ 
+
+ align:start position:0%
+a lot of times it's called the Deming
+cycle Deming called it the shoe har
+
+ align:start position:0%
+cycle Deming called it the shoe har
+ 
+
+ align:start position:0%
+cycle Deming called it the shoe har
+cycle he said it got it from shoe har
+
+ align:start position:0%
+cycle he said it got it from shoe har
+ 
+
+ align:start position:0%
+cycle he said it got it from shoe har
+but really this is a way of what we call
+
+ align:start position:0%
+but really this is a way of what we call
+ 
+
+ align:start position:0%
+but really this is a way of what we call
+Rapid cycle learning it's a way of
+
+ align:start position:0%
+Rapid cycle learning it's a way of
+ 
+
+ align:start position:0%
+Rapid cycle learning it's a way of
+learning very quickly whether or not the
+
+ align:start position:0%
+learning very quickly whether or not the
+ 
+
+ align:start position:0%
+learning very quickly whether or not the
+idea we have uh will work and I'm going
+
+ align:start position:0%
+idea we have uh will work and I'm going
+ 
+
+ align:start position:0%
+idea we have uh will work and I'm going
+to tell a story and just a second about
+
+ align:start position:0%
+to tell a story and just a second about
+ 
+
+ align:start position:0%
+to tell a story and just a second about
+that it starts with a plan okay it
+
+ align:start position:0%
+that it starts with a plan okay it
+ 
+
+ align:start position:0%
+that it starts with a plan okay it
+starts with a specific aim for that
+
+ align:start position:0%
+starts with a specific aim for that
+ 
+
+ align:start position:0%
+starts with a specific aim for that
+particular change idea okay we State the
+
+ align:start position:0%
+particular change idea okay we State the
+ 
+
+ align:start position:0%
+particular change idea okay we State the
+objective what it is we're trying to
+
+ align:start position:0%
+objective what it is we're trying to
+ 
+
+ align:start position:0%
+objective what it is we're trying to
+accomplish through that I change idea
+
+ align:start position:0%
+accomplish through that I change idea
+ 
+
+ align:start position:0%
+accomplish through that I change idea
+we're trying to increase HIV testing
+
+ align:start position:0%
+we're trying to increase HIV testing
+ 
+
+ align:start position:0%
+we're trying to increase HIV testing
+we're trying to increase immunization
+
+ align:start position:0%
+we're trying to increase immunization
+ 
+
+ align:start position:0%
+we're trying to increase immunization
+rates whatever it is then we start
+
+ align:start position:0%
+rates whatever it is then we start
+ 
+
+ align:start position:0%
+rates whatever it is then we start
+answering some very specific questions
+
+ align:start position:0%
+answering some very specific questions
+ 
+
+ align:start position:0%
+answering some very specific questions
+we start answering questions like who's
+
+ align:start position:0%
+we start answering questions like who's
+ 
+
+ align:start position:0%
+we start answering questions like who's
+going to try this out right it's going
+
+ align:start position:0%
+going to try this out right it's going
+ 
+
+ align:start position:0%
+going to try this out right it's going
+to be nurse Judy
+
+ align:start position:0%
+to be nurse Judy
+ 
+
+ align:start position:0%
+to be nurse Judy
+okay she's going to try it out and when
+
+ align:start position:0%
+okay she's going to try it out and when
+ 
+
+ align:start position:0%
+okay she's going to try it out and when
+is she going to do this she's going to
+
+ align:start position:0%
+is she going to do this she's going to
+ 
+
+ align:start position:0%
+is she going to do this she's going to
+do it on Monday morning at 9:00 a.m.
+
+ align:start position:0%
+do it on Monday morning at 9:00 a.m.
+ 
+
+ align:start position:0%
+do it on Monday morning at 9:00 a.m.
+okay and where is she going to do it
+
+ align:start position:0%
+okay and where is she going to do it
+ 
+
+ align:start position:0%
+okay and where is she going to do it
+she's going to do it at Clinic X okay
+
+ align:start position:0%
+she's going to do it at Clinic X okay
+ 
+
+ align:start position:0%
+she's going to do it at Clinic X okay
+and who is she going to do it with she's
+
+ align:start position:0%
+and who is she going to do it with she's
+ 
+
+ align:start position:0%
+and who is she going to do it with she's
+going to do it on the first 10 patients
+
+ align:start position:0%
+going to do it on the first 10 patients
+ 
+
+ align:start position:0%
+going to do it on the first 10 patients
+that walk in that day it becomes very
+
+ align:start position:0%
+that walk in that day it becomes very
+ 
+
+ align:start position:0%
+that walk in that day it becomes very
+specific it's like planning a small
+
+ align:start position:0%
+specific it's like planning a small
+ 
+
+ align:start position:0%
+specific it's like planning a small
+experiment just for a single small
+
+ align:start position:0%
+experiment just for a single small
+ 
+
+ align:start position:0%
+experiment just for a single small
+moment in time right we're not talking
+
+ align:start position:0%
+moment in time right we're not talking
+ 
+
+ align:start position:0%
+moment in time right we're not talking
+about a grand plan to redesign the
+
+ align:start position:0%
+about a grand plan to redesign the
+ 
+
+ align:start position:0%
+about a grand plan to redesign the
+entire system in one cycle and it's
+
+ align:start position:0%
+entire system in one cycle and it's
+ 
+
+ align:start position:0%
+entire system in one cycle and it's
+going to take us six months or a year
+
+ align:start position:0%
+going to take us six months or a year
+ 
+
+ align:start position:0%
+going to take us six months or a year
+we're talking about something very very
+
+ align:start position:0%
+we're talking about something very very
+ 
+
+ align:start position:0%
+we're talking about something very very
+small something we can accomplish in one
+
+ align:start position:0%
+small something we can accomplish in one
+ 
+
+ align:start position:0%
+small something we can accomplish in one
+day or within one week okay something
+
+ align:start position:0%
+day or within one week okay something
+ 
+
+ align:start position:0%
+day or within one week okay something
+very very rapid cycle learning it's all
+
+ align:start position:0%
+very very rapid cycle learning it's all
+ 
+
+ align:start position:0%
+very very rapid cycle learning it's all
+about right now okay so we're going to
+
+ align:start position:0%
+about right now okay so we're going to
+ 
+
+ align:start position:0%
+about right now okay so we're going to
+plan that out we're going to articulate
+
+ align:start position:0%
+plan that out we're going to articulate
+ 
+
+ align:start position:0%
+plan that out we're going to articulate
+all of that we're going to write it all
+
+ align:start position:0%
+all of that we're going to write it all
+ 
+
+ align:start position:0%
+all of that we're going to write it all
+down and then we're going to go out and
+
+ align:start position:0%
+down and then we're going to go out and
+ 
+
+ align:start position:0%
+down and then we're going to go out and
+we're going to do it so nurse Judy
+
+ align:start position:0%
+we're going to do it so nurse Judy
+ 
+
+ align:start position:0%
+we're going to do it so nurse Judy
+Monday morning 9:00 a.m. she's waiting
+
+ align:start position:0%
+Monday morning 9:00 a.m. she's waiting
+ 
+
+ align:start position:0%
+Monday morning 9:00 a.m. she's waiting
+there for the first 10 patients at
+
+ align:start position:0%
+there for the first 10 patients at
+ 
+
+ align:start position:0%
+there for the first 10 patients at
+Clinic X to come in as those patients
+
+ align:start position:0%
+Clinic X to come in as those patients
+ 
+
+ align:start position:0%
+Clinic X to come in as those patients
+come through the door she's going to
+
+ align:start position:0%
+come through the door she's going to
+ 
+
+ align:start position:0%
+come through the door she's going to
+test the this particular change idea
+
+ align:start position:0%
+test the this particular change idea
+ 
+
+ align:start position:0%
+test the this particular change idea
+whatever it is
+
+ align:start position:0%
+whatever it is
+ 
+
+ align:start position:0%
+whatever it is
+okay might be a new data collection
+
+ align:start position:0%
+okay might be a new data collection
+ 
+
+ align:start position:0%
+okay might be a new data collection
+mechanism it might be a new way of
+
+ align:start position:0%
+mechanism it might be a new way of
+ 
+
+ align:start position:0%
+mechanism it might be a new way of
+immunizing patients whatever it is okay
+
+ align:start position:0%
+immunizing patients whatever it is okay
+ 
+
+ align:start position:0%
+immunizing patients whatever it is okay
+and then she's going to document
+
+ align:start position:0%
+and then she's going to document
+ 
+
+ align:start position:0%
+and then she's going to document
+everything that's going on so she's
+
+ align:start position:0%
+everything that's going on so she's
+ 
+
+ align:start position:0%
+everything that's going on so she's
+going to document not only the
+
+ align:start position:0%
+going to document not only the
+ 
+
+ align:start position:0%
+going to document not only the
+measurement that we have articulated in
+
+ align:start position:0%
+measurement that we have articulated in
+ 
+
+ align:start position:0%
+measurement that we have articulated in
+the plan right but she's also going to
+
+ align:start position:0%
+the plan right but she's also going to
+ 
+
+ align:start position:0%
+the plan right but she's also going to
+document anything out of the ordinary
+
+ align:start position:0%
+document anything out of the ordinary
+ 
+
+ align:start position:0%
+document anything out of the ordinary
+anything that she's learning that she
+
+ align:start position:0%
+anything that she's learning that she
+ 
+
+ align:start position:0%
+anything that she's learning that she
+hadn't predicted anything that is
+
+ align:start position:0%
+hadn't predicted anything that is
+ 
+
+ align:start position:0%
+hadn't predicted anything that is
+against the assumptions that she made or
+
+ align:start position:0%
+against the assumptions that she made or
+ 
+
+ align:start position:0%
+against the assumptions that she made or
+that the team made together so she's
+
+ align:start position:0%
+that the team made together so she's
+ 
+
+ align:start position:0%
+that the team made together so she's
+going to capture that information during
+
+ align:start position:0%
+going to capture that information during
+ 
+
+ align:start position:0%
+going to capture that information during
+the due phase right now the study phase
+
+ align:start position:0%
+the due phase right now the study phase
+ 
+
+ align:start position:0%
+the due phase right now the study phase
+is where we start to look at what we
+
+ align:start position:0%
+is where we start to look at what we
+ 
+
+ align:start position:0%
+is where we start to look at what we
+learned and the study phase builds upon
+
+ align:start position:0%
+learned and the study phase builds upon
+ 
+
+ align:start position:0%
+learned and the study phase builds upon
+a very important part of the plan now
+
+ align:start position:0%
+a very important part of the plan now
+ 
+
+ align:start position:0%
+a very important part of the plan now
+the second bullet in the plan there it
+
+ align:start position:0%
+the second bullet in the plan there it
+ 
+
+ align:start position:0%
+the second bullet in the plan there it
+says make
+
+ align:start position:0%
+says make
+ 
+
+ align:start position:0%
+says make
+predictions nurse Judy and her quality
+
+ align:start position:0%
+predictions nurse Judy and her quality
+ 
+
+ align:start position:0%
+predictions nurse Judy and her quality
+improvement team when they're planning
+
+ align:start position:0%
+improvement team when they're planning
+ 
+
+ align:start position:0%
+improvement team when they're planning
+what they're going to do on Monday
+
+ align:start position:0%
+what they're going to do on Monday
+ 
+
+ align:start position:0%
+what they're going to do on Monday
+morning they're going to make a
+
+ align:start position:0%
+morning they're going to make a
+ 
+
+ align:start position:0%
+morning they're going to make a
+prediction about how performance will
+
+ align:start position:0%
+prediction about how performance will
+ 
+
+ align:start position:0%
+prediction about how performance will
+change for those 10 patients okay
+
+ align:start position:0%
+change for those 10 patients okay
+ 
+
+ align:start position:0%
+change for those 10 patients okay
+and they're going to write that out all
+
+ align:start position:0%
+and they're going to write that out all
+ 
+
+ align:start position:0%
+and they're going to write that out all
+10 patients are going to get their
+
+ align:start position:0%
+10 patients are going to get their
+ 
+
+ align:start position:0%
+10 patients are going to get their
+immunization today as opposed to the
+
+ align:start position:0%
+immunization today as opposed to the
+ 
+
+ align:start position:0%
+immunization today as opposed to the
+five who got them last week okay they're
+
+ align:start position:0%
+five who got them last week okay they're
+ 
+
+ align:start position:0%
+five who got them last week okay they're
+going to write out that prediction when
+
+ align:start position:0%
+going to write out that prediction when
+ 
+
+ align:start position:0%
+going to write out that prediction when
+it comes to the study phase they're
+
+ align:start position:0%
+it comes to the study phase they're
+ 
+
+ align:start position:0%
+it comes to the study phase they're
+going to compare what did we learn that
+
+ align:start position:0%
+going to compare what did we learn that
+ 
+
+ align:start position:0%
+going to compare what did we learn that
+we didn't anticipate and did we achieve
+
+ align:start position:0%
+we didn't anticipate and did we achieve
+ 
+
+ align:start position:0%
+we didn't anticipate and did we achieve
+what we predicted we would okay and if
+
+ align:start position:0%
+what we predicted we would okay and if
+ 
+
+ align:start position:0%
+what we predicted we would okay and if
+not why
+
+ align:start position:0%
+not why
+ 
+
+ align:start position:0%
+not why
+not right we're going to lay all that
+
+ align:start position:0%
+not right we're going to lay all that
+ 
+
+ align:start position:0%
+not right we're going to lay all that
+out and ask those questions and have
+
+ align:start position:0%
+out and ask those questions and have
+ 
+
+ align:start position:0%
+out and ask those questions and have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+conversation Monday afternoon during our
+
+ align:start position:0%
+conversation Monday afternoon during our
+ 
+
+ align:start position:0%
+conversation Monday afternoon during our
+lunch break
+
+ align:start position:0%
+lunch break
+ 
+
+ align:start position:0%
+lunch break
+okay and then we're going to make a
+
+ align:start position:0%
+okay and then we're going to make a
+ 
+
+ align:start position:0%
+okay and then we're going to make a
+decision about what to do next if that
+
+ align:start position:0%
+decision about what to do next if that
+ 
+
+ align:start position:0%
+decision about what to do next if that
+change idea was successful we might
+
+ align:start position:0%
+change idea was successful we might
+ 
+
+ align:start position:0%
+change idea was successful we might
+decide you know that's great it worked
+
+ align:start position:0%
+decide you know that's great it worked
+ 
+
+ align:start position:0%
+decide you know that's great it worked
+really well we want to try it again but
+
+ align:start position:0%
+really well we want to try it again but
+ 
+
+ align:start position:0%
+really well we want to try it again but
+on a larger scale instead of 10 patients
+
+ align:start position:0%
+on a larger scale instead of 10 patients
+ 
+
+ align:start position:0%
+on a larger scale instead of 10 patients
+we're going to scale it up to 50
+
+ align:start position:0%
+we're going to scale it up to 50
+ 
+
+ align:start position:0%
+we're going to scale it up to 50
+patients okay so that's what we're going
+
+ align:start position:0%
+patients okay so that's what we're going
+ 
+
+ align:start position:0%
+patients okay so that's what we're going
+to do during the action phase if it
+
+ align:start position:0%
+to do during the action phase if it
+ 
+
+ align:start position:0%
+to do during the action phase if it
+works marginally well but we think we
+
+ align:start position:0%
+works marginally well but we think we
+ 
+
+ align:start position:0%
+works marginally well but we think we
+learned how to do it better then we
+
+ align:start position:0%
+learned how to do it better then we
+ 
+
+ align:start position:0%
+learned how to do it better then we
+might say you you know instead of
+
+ align:start position:0%
+might say you you know instead of
+ 
+
+ align:start position:0%
+might say you you know instead of
+adopting this we're going to adapt it
+
+ align:start position:0%
+adopting this we're going to adapt it
+ 
+
+ align:start position:0%
+adopting this we're going to adapt it
+we're going to run it again on 10
+
+ align:start position:0%
+we're going to run it again on 10
+ 
+
+ align:start position:0%
+we're going to run it again on 10
+patients on Tuesday morning but with
+
+ align:start position:0%
+patients on Tuesday morning but with
+ 
+
+ align:start position:0%
+patients on Tuesday morning but with
+this slight
+
+ align:start position:0%
+this slight
+ 
+
+ align:start position:0%
+this slight
+alteration right because we learned
+
+ align:start position:0%
+alteration right because we learned
+ 
+
+ align:start position:0%
+alteration right because we learned
+something during that study phase about
+
+ align:start position:0%
+something during that study phase about
+ 
+
+ align:start position:0%
+something during that study phase about
+what worked and what didn't work with
+
+ align:start position:0%
+what worked and what didn't work with
+ 
+
+ align:start position:0%
+what worked and what didn't work with
+the first 10
+
+ align:start position:0%
+the first 10
+ 
+
+ align:start position:0%
+the first 10
+patients
+
+ align:start position:0%
+patients
+ 
+
+ align:start position:0%
+patients
+okay or it might be a colossal failure
+
+ align:start position:0%
+okay or it might be a colossal failure
+ 
+
+ align:start position:0%
+okay or it might be a colossal failure
+and that's totally fine too that's
+
+ align:start position:0%
+and that's totally fine too that's
+ 
+
+ align:start position:0%
+and that's totally fine too that's
+absolutely a fine thing so if it failed
+
+ align:start position:0%
+absolutely a fine thing so if it failed
+ 
+
+ align:start position:0%
+absolutely a fine thing so if it failed
+then we want to talk about that we want
+
+ align:start position:0%
+then we want to talk about that we want
+ 
+
+ align:start position:0%
+then we want to talk about that we want
+to embrace that and then we'll say okay
+
+ align:start position:0%
+to embrace that and then we'll say okay
+ 
+
+ align:start position:0%
+to embrace that and then we'll say okay
+well why did it fail what does that tell
+
+ align:start position:0%
+well why did it fail what does that tell
+ 
+
+ align:start position:0%
+well why did it fail what does that tell
+us about how we should change our
+
+ align:start position:0%
+us about how we should change our
+ 
+
+ align:start position:0%
+us about how we should change our
+assumptions how should we change our
+
+ align:start position:0%
+assumptions how should we change our
+ 
+
+ align:start position:0%
+assumptions how should we change our
+Theory and what different idea would we
+
+ align:start position:0%
+Theory and what different idea would we
+ 
+
+ align:start position:0%
+Theory and what different idea would we
+like to change or like to test as a
+
+ align:start position:0%
+like to change or like to test as a
+ 
+
+ align:start position:0%
+like to change or like to test as a
+result okay so what different idea do we
+
+ align:start position:0%
+result okay so what different idea do we
+ 
+
+ align:start position:0%
+result okay so what different idea do we
+want to test as a result right and then
+
+ align:start position:0%
+want to test as a result right and then
+ 
+
+ align:start position:0%
+want to test as a result right and then
+we're going to do that on Tuesday make
+
+ align:start position:0%
+we're going to do that on Tuesday make
+ 
+
+ align:start position:0%
+we're going to do that on Tuesday make
+some new predictions and make a new plan
+
+ align:start position:0%
+some new predictions and make a new plan
+ 
+
+ align:start position:0%
+some new predictions and make a new plan
+so we can do all of that through the
+
+ align:start position:0%
+so we can do all of that through the
+ 
+
+ align:start position:0%
+so we can do all of that through the
+pdsa cycle okay all that's very very
+
+ align:start position:0%
+pdsa cycle okay all that's very very
+ 
+
+ align:start position:0%
+pdsa cycle okay all that's very very
+specific this has been done for 70 years
+
+ align:start position:0%
+specific this has been done for 70 years
+ 
+
+ align:start position:0%
+specific this has been done for 70 years
+in manufacturing right Toyota runs on on
+
+ align:start position:0%
+in manufacturing right Toyota runs on on
+ 
+
+ align:start position:0%
+in manufacturing right Toyota runs on on
+average A th000 pdsa Cycles a day in
+
+ align:start position:0%
+average A th000 pdsa Cycles a day in
+ 
+
+ align:start position:0%
+average A th000 pdsa Cycles a day in
+their manufacturing plants around the
+
+ align:start position:0%
+their manufacturing plants around the
+ 
+
+ align:start position:0%
+their manufacturing plants around the
+world okay in healthcare we're still
+
+ align:start position:0%
+world okay in healthcare we're still
+ 
+
+ align:start position:0%
+world okay in healthcare we're still
+learning how to do this and we have some
+
+ align:start position:0%
+learning how to do this and we have some
+ 
+
+ align:start position:0%
+learning how to do this and we have some
+special considerations right we're not
+
+ align:start position:0%
+special considerations right we're not
+ 
+
+ align:start position:0%
+special considerations right we're not
+building cars we're working with
+
+ align:start position:0%
+building cars we're working with
+ 
+
+ align:start position:0%
+building cars we're working with
+patients so we always need to make sure
+
+ align:start position:0%
+patients so we always need to make sure
+ 
+
+ align:start position:0%
+patients so we always need to make sure
+that we're not doing things that could
+
+ align:start position:0%
+that we're not doing things that could
+ 
+
+ align:start position:0%
+that we're not doing things that could
+harm patients but there's lots that we
+
+ align:start position:0%
+harm patients but there's lots that we
+ 
+
+ align:start position:0%
+harm patients but there's lots that we
+can do in terms of changing Data Systems
+
+ align:start position:0%
+can do in terms of changing Data Systems
+ 
+
+ align:start position:0%
+can do in terms of changing Data Systems
+changing the flow of a clinic changing
+
+ align:start position:0%
+changing the flow of a clinic changing
+ 
+
+ align:start position:0%
+changing the flow of a clinic changing
+the order in which we do certain things
+
+ align:start position:0%
+the order in which we do certain things
+ 
+
+ align:start position:0%
+the order in which we do certain things
+that's safe but still needs to be tested
+
+ align:start position:0%
+that's safe but still needs to be tested
+ 
+
+ align:start position:0%
+that's safe but still needs to be tested
+to understand if it will impact the
+
+ align:start position:0%
+to understand if it will impact the
+ 
+
+ align:start position:0%
+to understand if it will impact the
+reliability of care that we're
+
+ align:start position:0%
+reliability of care that we're
+ 
+
+ align:start position:0%
+reliability of care that we're
+providing so that's that's the pdsa
+
+ align:start position:0%
+providing so that's that's the pdsa
+ 
+
+ align:start position:0%
+providing so that's that's the pdsa
+cycle and that's the second half of the
+
+ align:start position:0%
+cycle and that's the second half of the
+ 
+
+ align:start position:0%
+cycle and that's the second half of the
+model for improvement
+
+ align:start position:0%
+model for improvement
+ 
+
+ align:start position:0%
+model for improvement
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay all right so my second challenge to
+
+ align:start position:0%
+okay all right so my second challenge to
+ 
+
+ align:start position:0%
+okay all right so my second challenge to
+you is to develop a pdsa with your team
+
+ align:start position:0%
+you is to develop a pdsa with your team
+ 
+
+ align:start position:0%
+you is to develop a pdsa with your team
+right it could be a pdsa to see if
+
+ align:start position:0%
+right it could be a pdsa to see if
+ 
+
+ align:start position:0%
+right it could be a pdsa to see if
+you've got an idea that can improve
+
+ align:start position:0%
+you've got an idea that can improve
+ 
+
+ align:start position:0%
+you've got an idea that can improve
+something or it could be a pdsa simply
+
+ align:start position:0%
+something or it could be a pdsa simply
+ 
+
+ align:start position:0%
+something or it could be a pdsa simply
+to learn about the system that you're
+
+ align:start position:0%
+to learn about the system that you're
+ 
+
+ align:start position:0%
+to learn about the system that you're
+trying to to improve okay but I would
+
+ align:start position:0%
+trying to to improve okay but I would
+ 
+
+ align:start position:0%
+trying to to improve okay but I would
+challenge you with your project teams as
+
+ align:start position:0%
+challenge you with your project teams as
+ 
+
+ align:start position:0%
+challenge you with your project teams as
+you as you start to think about things
+
+ align:start position:0%
+you as you start to think about things
+ 
+
+ align:start position:0%
+you as you start to think about things
+how could we use this this methodology
+
+ align:start position:0%
+how could we use this this methodology
+ 
+
+ align:start position:0%
+how could we use this this methodology
+how could we use a pdsa cycle to learn
+
+ align:start position:0%
+how could we use a pdsa cycle to learn
+ 
+
+ align:start position:0%
+how could we use a pdsa cycle to learn
+about how to improve the data systems
+
+ align:start position:0%
+about how to improve the data systems
+ 
+
+ align:start position:0%
+about how to improve the data systems
+that we're working
+
+ align:start position:0%
+that we're working
+ 
+
+ align:start position:0%
+that we're working
+on all right here's a potential form you
+
+ align:start position:0%
+on all right here's a potential form you
+ 
+
+ align:start position:0%
+on all right here's a potential form you
+can use I can give this to you if you
+
+ align:start position:0%
+can use I can give this to you if you
+ 
+
+ align:start position:0%
+can use I can give this to you if you
+want of how you can write things down
+
+ align:start position:0%
+want of how you can write things down
+ 
+
+ align:start position:0%
+want of how you can write things down
+and have a data capture tool for each of
+
+ align:start position:0%
+and have a data capture tool for each of
+ 
+
+ align:start position:0%
+and have a data capture tool for each of
+individual pdsa
+
+ align:start position:0%
+individual pdsa
+ 
+
+ align:start position:0%
+individual pdsa
+cycle Okay and like I said you want to
+
+ align:start position:0%
+cycle Okay and like I said you want to
+ 
+
+ align:start position:0%
+cycle Okay and like I said you want to
+slowly build up as you go right actually
+
+ align:start position:0%
+slowly build up as you go right actually
+ 
+
+ align:start position:0%
+slowly build up as you go right actually
+rapidly but as fast as you can right
+
+ align:start position:0%
+rapidly but as fast as you can right
+ 
+
+ align:start position:0%
+rapidly but as fast as you can right
+some hospitals will do three four five
+
+ align:start position:0%
+some hospitals will do three four five
+ 
+
+ align:start position:0%
+some hospitals will do three four five
+pdsa a week on an individual process
+
+ align:start position:0%
+pdsa a week on an individual process
+ 
+
+ align:start position:0%
+pdsa a week on an individual process
+right maybe 50 across a whole hospital
+
+ align:start position:0%
+right maybe 50 across a whole hospital
+ 
+
+ align:start position:0%
+right maybe 50 across a whole hospital
+it's great so here's uh here's Julie
+
+ align:start position:0%
+it's great so here's uh here's Julie
+ 
+
+ align:start position:0%
+it's great so here's uh here's Julie
+Julie is a nurse that I had the
+
+ align:start position:0%
+Julie is a nurse that I had the
+ 
+
+ align:start position:0%
+Julie is a nurse that I had the
+opportunity to work with in South Africa
+
+ align:start position:0%
+opportunity to work with in South Africa
+ 
+
+ align:start position:0%
+opportunity to work with in South Africa
+and I wanted to give you a real life
+
+ align:start position:0%
+and I wanted to give you a real life
+ 
+
+ align:start position:0%
+and I wanted to give you a real life
+story of how we could use
+
+ align:start position:0%
+story of how we could use
+ 
+
+ align:start position:0%
+story of how we could use
+pdsa okay so Julie uh is a fantastic
+
+ align:start position:0%
+pdsa okay so Julie uh is a fantastic
+ 
+
+ align:start position:0%
+pdsa okay so Julie uh is a fantastic
+nurse she's a HIV nurse and she was uh
+
+ align:start position:0%
+nurse she's a HIV nurse and she was uh
+ 
+
+ align:start position:0%
+nurse she's a HIV nurse and she was uh
+focused on uh uh on voluntary counseling
+
+ align:start position:0%
+focused on uh uh on voluntary counseling
+ 
+
+ align:start position:0%
+focused on uh uh on voluntary counseling
+and testing of HIV Services right Julie
+
+ align:start position:0%
+and testing of HIV Services right Julie
+ 
+
+ align:start position:0%
+and testing of HIV Services right Julie
+is a a tremendous tremendously hard
+
+ align:start position:0%
+is a a tremendous tremendously hard
+ 
+
+ align:start position:0%
+is a a tremendous tremendously hard
+worker really devoted to her community
+
+ align:start position:0%
+worker really devoted to her community
+ 
+
+ align:start position:0%
+worker really devoted to her community
+and as uh uh as we started to increase
+
+ align:start position:0%
+and as uh uh as we started to increase
+ 
+
+ align:start position:0%
+and as uh uh as we started to increase
+uh VCT we started to increase the total
+
+ align:start position:0%
+uh VCT we started to increase the total
+ 
+
+ align:start position:0%
+uh VCT we started to increase the total
+number of people who are testing H
+
+ align:start position:0%
+number of people who are testing H
+ 
+
+ align:start position:0%
+number of people who are testing H
+positive uh we we had perfect
+
+ align:start position:0%
+positive uh we we had perfect
+ 
+
+ align:start position:0%
+positive uh we we had perfect
+performance on testing but that led to a
+
+ align:start position:0%
+performance on testing but that led to a
+ 
+
+ align:start position:0%
+performance on testing but that led to a
+huge influx of new patients who needed
+
+ align:start position:0%
+huge influx of new patients who needed
+ 
+
+ align:start position:0%
+huge influx of new patients who needed
+treatment unanticipated consequence of
+
+ align:start position:0%
+treatment unanticipated consequence of
+ 
+
+ align:start position:0%
+treatment unanticipated consequence of
+improved care right nothing wrong with
+
+ align:start position:0%
+improved care right nothing wrong with
+ 
+
+ align:start position:0%
+improved care right nothing wrong with
+that that's a good problem to have but
+
+ align:start position:0%
+that that's a good problem to have but
+ 
+
+ align:start position:0%
+that that's a good problem to have but
+now we're overwhelming our chronic care
+
+ align:start position:0%
+now we're overwhelming our chronic care
+ 
+
+ align:start position:0%
+now we're overwhelming our chronic care
+abilities and Julie was working at at a
+
+ align:start position:0%
+abilities and Julie was working at at a
+ 
+
+ align:start position:0%
+abilities and Julie was working at at a
+hospital where they were starting to see
+
+ align:start position:0%
+hospital where they were starting to see
+ 
+
+ align:start position:0%
+hospital where they were starting to see
+upwards of 300 patients a day just to
+
+ align:start position:0%
+upwards of 300 patients a day just to
+ 
+
+ align:start position:0%
+upwards of 300 patients a day just to
+provide chronic care let alone new
+
+ align:start position:0%
+provide chronic care let alone new
+ 
+
+ align:start position:0%
+provide chronic care let alone new
+patients who are coming in the door okay
+
+ align:start position:0%
+patients who are coming in the door okay
+ 
+
+ align:start position:0%
+patients who are coming in the door okay
+so we had this problem where we had so
+
+ align:start position:0%
+so we had this problem where we had so
+ 
+
+ align:start position:0%
+so we had this problem where we had so
+much chronic care going on that we were
+
+ align:start position:0%
+much chronic care going on that we were
+ 
+
+ align:start position:0%
+much chronic care going on that we were
+running out of resources to provide care
+
+ align:start position:0%
+running out of resources to provide care
+ 
+
+ align:start position:0%
+running out of resources to provide care
+to new patients and there we were
+
+ align:start position:0%
+to new patients and there we were
+ 
+
+ align:start position:0%
+to new patients and there we were
+starting to build build up a queue we
+
+ align:start position:0%
+starting to build build up a queue we
+ 
+
+ align:start position:0%
+starting to build build up a queue we
+were getting a line of people who were
+
+ align:start position:0%
+were getting a line of people who were
+ 
+
+ align:start position:0%
+were getting a line of people who were
+waiting to get on to treatment so this
+
+ align:start position:0%
+waiting to get on to treatment so this
+ 
+
+ align:start position:0%
+waiting to get on to treatment so this
+was uh this was quite a while ago and we
+
+ align:start position:0%
+was uh this was quite a while ago and we
+ 
+
+ align:start position:0%
+was uh this was quite a while ago and we
+thought well what could we do about this
+
+ align:start position:0%
+thought well what could we do about this
+ 
+
+ align:start position:0%
+thought well what could we do about this
+and Julie said well you know we've got
+
+ align:start position:0%
+and Julie said well you know we've got
+ 
+
+ align:start position:0%
+and Julie said well you know we've got
+all these clinics that refer patients to
+
+ align:start position:0%
+all these clinics that refer patients to
+ 
+
+ align:start position:0%
+all these clinics that refer patients to
+us for care what if we started doing
+
+ align:start position:0%
+us for care what if we started doing
+ 
+
+ align:start position:0%
+us for care what if we started doing
+chronic Care at the
+
+ align:start position:0%
+chronic Care at the
+ 
+
+ align:start position:0%
+chronic Care at the
+clinics okay what if we did chronic Care
+
+ align:start position:0%
+clinics okay what if we did chronic Care
+ 
+
+ align:start position:0%
+clinics okay what if we did chronic Care
+at the clinics instead of here at the
+
+ align:start position:0%
+at the clinics instead of here at the
+ 
+
+ align:start position:0%
+at the clinics instead of here at the
+hospital that could free up space for us
+
+ align:start position:0%
+hospital that could free up space for us
+ 
+
+ align:start position:0%
+hospital that could free up space for us
+to initiate new patients on to treatment
+
+ align:start position:0%
+to initiate new patients on to treatment
+ 
+
+ align:start position:0%
+to initiate new patients on to treatment
+so that's a that's a great idea that's a
+
+ align:start position:0%
+so that's a that's a great idea that's a
+ 
+
+ align:start position:0%
+so that's a that's a great idea that's a
+fantastic idea how are we going to do
+
+ align:start position:0%
+fantastic idea how are we going to do
+ 
+
+ align:start position:0%
+fantastic idea how are we going to do
+that no one had ever done that in this
+
+ align:start position:0%
+that no one had ever done that in this
+ 
+
+ align:start position:0%
+that no one had ever done that in this
+particular particular District before so
+
+ align:start position:0%
+particular particular District before so
+ 
+
+ align:start position:0%
+particular particular District before so
+how are we going to do that nobody knows
+
+ align:start position:0%
+how are we going to do that nobody knows
+ 
+
+ align:start position:0%
+how are we going to do that nobody knows
+how so we said well let's let's plan a
+
+ align:start position:0%
+how so we said well let's let's plan a
+ 
+
+ align:start position:0%
+how so we said well let's let's plan a
+pdsa we came up with a seven-step plan
+
+ align:start position:0%
+pdsa we came up with a seven-step plan
+ 
+
+ align:start position:0%
+pdsa we came up with a seven-step plan
+it involved things like making sure we
+
+ align:start position:0%
+it involved things like making sure we
+ 
+
+ align:start position:0%
+it involved things like making sure we
+had the drugs prepackaged and sent ahead
+
+ align:start position:0%
+had the drugs prepackaged and sent ahead
+ 
+
+ align:start position:0%
+had the drugs prepackaged and sent ahead
+of time to the clinic notification of
+
+ align:start position:0%
+of time to the clinic notification of
+ 
+
+ align:start position:0%
+of time to the clinic notification of
+the patients make sure that they were
+
+ align:start position:0%
+the patients make sure that they were
+ 
+
+ align:start position:0%
+the patients make sure that they were
+ready and willing to accept treatment at
+
+ align:start position:0%
+ready and willing to accept treatment at
+ 
+
+ align:start position:0%
+ready and willing to accept treatment at
+a clinic instead of at the hospital
+
+ align:start position:0%
+a clinic instead of at the hospital
+ 
+
+ align:start position:0%
+a clinic instead of at the hospital
+there's all there's seven steps that we
+
+ align:start position:0%
+there's all there's seven steps that we
+ 
+
+ align:start position:0%
+there's all there's seven steps that we
+had in place and we said okay all right
+
+ align:start position:0%
+had in place and we said okay all right
+ 
+
+ align:start position:0%
+had in place and we said okay all right
+Julia we're ready on Monday we're going
+
+ align:start position:0%
+Julia we're ready on Monday we're going
+ 
+
+ align:start position:0%
+Julia we're ready on Monday we're going
+to try it with two patients and so we
+
+ align:start position:0%
+to try it with two patients and so we
+ 
+
+ align:start position:0%
+to try it with two patients and so we
+did we had two patients who were willing
+
+ align:start position:0%
+did we had two patients who were willing
+ 
+
+ align:start position:0%
+did we had two patients who were willing
+participants and they said yes we would
+
+ align:start position:0%
+participants and they said yes we would
+ 
+
+ align:start position:0%
+participants and they said yes we would
+like to try to get our treatment at our
+
+ align:start position:0%
+like to try to get our treatment at our
+ 
+
+ align:start position:0%
+like to try to get our treatment at our
+local Clinic instead of at the hospital
+
+ align:start position:0%
+local Clinic instead of at the hospital
+ 
+
+ align:start position:0%
+local Clinic instead of at the hospital
+this month so those two patients
+
+ align:start position:0%
+this month so those two patients
+ 
+
+ align:start position:0%
+this month so those two patients
+went and wouldn't you know it only one
+
+ align:start position:0%
+went and wouldn't you know it only one
+ 
+
+ align:start position:0%
+went and wouldn't you know it only one
+of them got their
+
+ align:start position:0%
+of them got their
+ 
+
+ align:start position:0%
+of them got their
+medication so we predicted both of them
+
+ align:start position:0%
+medication so we predicted both of them
+ 
+
+ align:start position:0%
+medication so we predicted both of them
+would get it and only one did so we said
+
+ align:start position:0%
+would get it and only one did so we said
+ 
+
+ align:start position:0%
+would get it and only one did so we said
+what happened and we did during the
+
+ align:start position:0%
+what happened and we did during the
+ 
+
+ align:start position:0%
+what happened and we did during the
+study phase We examined the situation we
+
+ align:start position:0%
+study phase We examined the situation we
+ 
+
+ align:start position:0%
+study phase We examined the situation we
+realized that we had missed a step we
+
+ align:start position:0%
+realized that we had missed a step we
+ 
+
+ align:start position:0%
+realized that we had missed a step we
+had missed a step in connecting the
+
+ align:start position:0%
+had missed a step in connecting the
+ 
+
+ align:start position:0%
+had missed a step in connecting the
+pharmacy with the clinic okay and so it
+
+ align:start position:0%
+pharmacy with the clinic okay and so it
+ 
+
+ align:start position:0%
+pharmacy with the clinic okay and so it
+was a failure now it was a really good
+
+ align:start position:0%
+was a failure now it was a really good
+ 
+
+ align:start position:0%
+was a failure now it was a really good
+idea but if we had gone to full scale
+
+ align:start position:0%
+idea but if we had gone to full scale
+ 
+
+ align:start position:0%
+idea but if we had gone to full scale
+right away and we had had a 50% failure
+
+ align:start position:0%
+right away and we had had a 50% failure
+ 
+
+ align:start position:0%
+right away and we had had a 50% failure
+rate that would have been catastrophic
+
+ align:start position:0%
+rate that would have been catastrophic
+ 
+
+ align:start position:0%
+rate that would have been catastrophic
+for our HIV patients because it was two
+
+ align:start position:0%
+for our HIV patients because it was two
+ 
+
+ align:start position:0%
+for our HIV patients because it was two
+patients it was real easy to just call
+
+ align:start position:0%
+patients it was real easy to just call
+ 
+
+ align:start position:0%
+patients it was real easy to just call
+that patient up and say hey come to the
+
+ align:start position:0%
+that patient up and say hey come to the
+ 
+
+ align:start position:0%
+that patient up and say hey come to the
+hospital tomorrow we'll pay for the taxi
+
+ align:start position:0%
+hospital tomorrow we'll pay for the taxi
+ 
+
+ align:start position:0%
+hospital tomorrow we'll pay for the taxi
+fee and uh and we'll get you your
+
+ align:start position:0%
+fee and uh and we'll get you your
+ 
+
+ align:start position:0%
+fee and uh and we'll get you your
+medication now we learned what happened
+
+ align:start position:0%
+medication now we learned what happened
+ 
+
+ align:start position:0%
+medication now we learned what happened
+we fixed that we went from a seven step
+
+ align:start position:0%
+we fixed that we went from a seven step
+ 
+
+ align:start position:0%
+we fixed that we went from a seven step
+to an E step and the following week we
+
+ align:start position:0%
+to an E step and the following week we
+ 
+
+ align:start position:0%
+to an E step and the following week we
+down referred five patients okay
+
+ align:start position:0%
+down referred five patients okay
+ 
+
+ align:start position:0%
+down referred five patients okay
+five patients worked great all five
+
+ align:start position:0%
+five patients worked great all five
+ 
+
+ align:start position:0%
+five patients worked great all five
+patients got their medication we felt
+
+ align:start position:0%
+patients got their medication we felt
+ 
+
+ align:start position:0%
+patients got their medication we felt
+good about that we uh learned a few more
+
+ align:start position:0%
+good about that we uh learned a few more
+ 
+
+ align:start position:0%
+good about that we uh learned a few more
+things so the next week we down referred
+
+ align:start position:0%
+things so the next week we down referred
+ 
+
+ align:start position:0%
+things so the next week we down referred
+15 right worked perfect no problems the
+
+ align:start position:0%
+15 right worked perfect no problems the
+ 
+
+ align:start position:0%
+15 right worked perfect no problems the
+next week we down referred 50 right it
+
+ align:start position:0%
+next week we down referred 50 right it
+ 
+
+ align:start position:0%
+next week we down referred 50 right it
+took us five weeks to go from zero to
+
+ align:start position:0%
+took us five weeks to go from zero to
+ 
+
+ align:start position:0%
+took us five weeks to go from zero to
+down referring everybody in that
+
+ align:start position:0%
+down referring everybody in that
+ 
+
+ align:start position:0%
+down referring everybody in that
+particular catchman area to their local
+
+ align:start position:0%
+particular catchman area to their local
+ 
+
+ align:start position:0%
+particular catchman area to their local
+Clinic okay so but we were able to do
+
+ align:start position:0%
+Clinic okay so but we were able to do
+ 
+
+ align:start position:0%
+Clinic okay so but we were able to do
+that using the pdsa cycle and learning
+
+ align:start position:0%
+that using the pdsa cycle and learning
+ 
+
+ align:start position:0%
+that using the pdsa cycle and learning
+about what the limits were of of our
+
+ align:start position:0%
+about what the limits were of of our
+ 
+
+ align:start position:0%
+about what the limits were of of our
+implementation so it's a good example of
+
+ align:start position:0%
+implementation so it's a good example of
+ 
+
+ align:start position:0%
+implementation so it's a good example of
+of how you can scale up and learn
+
+ align:start position:0%
+of how you can scale up and learn
+ 
+
+ align:start position:0%
+of how you can scale up and learn
+quickly about uh uh Improvement in your
+
+ align:start position:0%
+quickly about uh uh Improvement in your
+ 
+
+ align:start position:0%
+quickly about uh uh Improvement in your
+system all right
+
+ align:start position:0%
+system all right
+ 
+
+ align:start position:0%
+system all right
+so what's the lesson there you also have
+
+ align:start position:0%
+so what's the lesson there you also have
+ 
+
+ align:start position:0%
+so what's the lesson there you also have
+to think ahead okay because with scale
+
+ align:start position:0%
+to think ahead okay because with scale
+ 
+
+ align:start position:0%
+to think ahead okay because with scale
+comes new problems unanticipated
+
+ align:start position:0%
+comes new problems unanticipated
+ 
+
+ align:start position:0%
+comes new problems unanticipated
+problems when you're working with one
+
+ align:start position:0%
+problems when you're working with one
+ 
+
+ align:start position:0%
+problems when you're working with one
+two five patients yeah pretty easy you
+
+ align:start position:0%
+two five patients yeah pretty easy you
+ 
+
+ align:start position:0%
+two five patients yeah pretty easy you
+can call them up on the phone you can
+
+ align:start position:0%
+can call them up on the phone you can
+ 
+
+ align:start position:0%
+can call them up on the phone you can
+get them on a taxi when you start
+
+ align:start position:0%
+get them on a taxi when you start
+ 
+
+ align:start position:0%
+get them on a taxi when you start
+working with 50 100 a th000 10,000 you
+
+ align:start position:0%
+working with 50 100 a th000 10,000 you
+ 
+
+ align:start position:0%
+working with 50 100 a th000 10,000 you
+have new problems so if you're using the
+
+ align:start position:0%
+have new problems so if you're using the
+ 
+
+ align:start position:0%
+have new problems so if you're using the
+pdsa cycle you always want to be
+
+ align:start position:0%
+pdsa cycle you always want to be
+ 
+
+ align:start position:0%
+pdsa cycle you always want to be
+thinking two three steps ahead when I
+
+ align:start position:0%
+thinking two three steps ahead when I
+ 
+
+ align:start position:0%
+thinking two three steps ahead when I
+scale this up what what's going to
+
+ align:start position:0%
+scale this up what what's going to
+ 
+
+ align:start position:0%
+scale this up what what's going to
+happen right is there going to be a
+
+ align:start position:0%
+happen right is there going to be a
+ 
+
+ align:start position:0%
+happen right is there going to be a
+failure here associated with scale
+
+ align:start position:0%
+failure here associated with scale
+ 
+
+ align:start position:0%
+failure here associated with scale
+that's going to introduce something that
+
+ align:start position:0%
+that's going to introduce something that
+ 
+
+ align:start position:0%
+that's going to introduce something that
+we're not anticipating right if you can
+
+ align:start position:0%
+we're not anticipating right if you can
+ 
+
+ align:start position:0%
+we're not anticipating right if you can
+do that early in the process you can
+
+ align:start position:0%
+do that early in the process you can
+ 
+
+ align:start position:0%
+do that early in the process you can
+start to plan for that make adjustments
+
+ align:start position:0%
+start to plan for that make adjustments
+ 
+
+ align:start position:0%
+start to plan for that make adjustments
+to the change
+
+ align:start position:0%
+to the change
+ 
+
+ align:start position:0%
+to the change
+idea all right so knowing when to
+
+ align:start position:0%
+idea all right so knowing when to
+ 
+
+ align:start position:0%
+idea all right so knowing when to
+implement A Change Is is CRI critically
+
+ align:start position:0%
+implement A Change Is is CRI critically
+ 
+
+ align:start position:0%
+implement A Change Is is CRI critically
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+okay there's times where you're
+
+ align:start position:0%
+okay there's times where you're
+ 
+
+ align:start position:0%
+okay there's times where you're
+developing change times where you're
+
+ align:start position:0%
+developing change times where you're
+ 
+
+ align:start position:0%
+developing change times where you're
+testing change and times where you're
+
+ align:start position:0%
+testing change and times where you're
+ 
+
+ align:start position:0%
+testing change and times where you're
+implementing change implementing change
+
+ align:start position:0%
+implementing change implementing change
+ 
+
+ align:start position:0%
+implementing change implementing change
+is different than testing you have a
+
+ align:start position:0%
+is different than testing you have a
+ 
+
+ align:start position:0%
+is different than testing you have a
+great idea you're innovating something
+
+ align:start position:0%
+great idea you're innovating something
+ 
+
+ align:start position:0%
+great idea you're innovating something
+you're testing it out you think this is
+
+ align:start position:0%
+you're testing it out you think this is
+ 
+
+ align:start position:0%
+you're testing it out you think this is
+fantastic this down referral process at
+
+ align:start position:0%
+fantastic this down referral process at
+ 
+
+ align:start position:0%
+fantastic this down referral process at
+a shi Hospital fantastic right great
+
+ align:start position:0%
+a shi Hospital fantastic right great
+ 
+
+ align:start position:0%
+a shi Hospital fantastic right great
+testing now we're ready to implement now
+
+ align:start position:0%
+testing now we're ready to implement now
+ 
+
+ align:start position:0%
+testing now we're ready to implement now
+what are we talking about we're talking
+
+ align:start position:0%
+what are we talking about we're talking
+ 
+
+ align:start position:0%
+what are we talking about we're talking
+about changing policy we're talking
+
+ align:start position:0%
+about changing policy we're talking
+ 
+
+ align:start position:0%
+about changing policy we're talking
+about rewriting job descriptions right
+
+ align:start position:0%
+about rewriting job descriptions right
+ 
+
+ align:start position:0%
+about rewriting job descriptions right
+we're talking about developing new
+
+ align:start position:0%
+we're talking about developing new
+ 
+
+ align:start position:0%
+we're talking about developing new
+training curriculum we're talking about
+
+ align:start position:0%
+training curriculum we're talking about
+ 
+
+ align:start position:0%
+training curriculum we're talking about
+re-education of the workforce that
+
+ align:start position:0%
+re-education of the workforce that
+ 
+
+ align:start position:0%
+re-education of the workforce that
+exists right all of that which is not in
+
+ align:start position:0%
+exists right all of that which is not in
+ 
+
+ align:start position:0%
+exists right all of that which is not in
+the Mainstay delivery of care but is in
+
+ align:start position:0%
+the Mainstay delivery of care but is in
+ 
+
+ align:start position:0%
+the Mainstay delivery of care but is in
+the support processes is in the redesign
+
+ align:start position:0%
+the support processes is in the redesign
+ 
+
+ align:start position:0%
+the support processes is in the redesign
+processes implementation is a whole
+
+ align:start position:0%
+processes implementation is a whole
+ 
+
+ align:start position:0%
+processes implementation is a whole
+different animal so when you get ready
+
+ align:start position:0%
+different animal so when you get ready
+ 
+
+ align:start position:0%
+different animal so when you get ready
+to take that new idea to implementation
+
+ align:start position:0%
+to take that new idea to implementation
+ 
+
+ align:start position:0%
+to take that new idea to implementation
+you have to think about all of those
+
+ align:start position:0%
+you have to think about all of those
+ 
+
+ align:start position:0%
+you have to think about all of those
+different things that are going to come
+
+ align:start position:0%
+different things that are going to come
+ 
+
+ align:start position:0%
+different things that are going to come
+together to make sure that that change
+
+ align:start position:0%
+together to make sure that that change
+ 
+
+ align:start position:0%
+together to make sure that that change
+idea continues to be a success one of
+
+ align:start position:0%
+idea continues to be a success one of
+ 
+
+ align:start position:0%
+idea continues to be a success one of
+the failures of lots of projects is they
+
+ align:start position:0%
+the failures of lots of projects is they
+ 
+
+ align:start position:0%
+the failures of lots of projects is they
+have a great idea they go in they try it
+
+ align:start position:0%
+have a great idea they go in they try it
+ 
+
+ align:start position:0%
+have a great idea they go in they try it
+out they start using it everywhere and
+
+ align:start position:0%
+out they start using it everywhere and
+ 
+
+ align:start position:0%
+out they start using it everywhere and
+then what happens the money runs out
+
+ align:start position:0%
+then what happens the money runs out
+ 
+
+ align:start position:0%
+then what happens the money runs out
+because the funders is moving on to a
+
+ align:start position:0%
+because the funders is moving on to a
+ 
+
+ align:start position:0%
+because the funders is moving on to a
+new cycle and nobody bothered to change
+
+ align:start position:0%
+new cycle and nobody bothered to change
+ 
+
+ align:start position:0%
+new cycle and nobody bothered to change
+the job description nobody bother to
+
+ align:start position:0%
+the job description nobody bother to
+ 
+
+ align:start position:0%
+the job description nobody bother to
+rewrite the policy that new group of
+
+ align:start position:0%
+rewrite the policy that new group of
+ 
+
+ align:start position:0%
+rewrite the policy that new group of
+doctors rotated in from a different
+
+ align:start position:0%
+doctors rotated in from a different
+ 
+
+ align:start position:0%
+doctors rotated in from a different
+place and didn't know anything about it
+
+ align:start position:0%
+place and didn't know anything about it
+ 
+
+ align:start position:0%
+place and didn't know anything about it
+and suddenly that wonderful change is
+
+ align:start position:0%
+and suddenly that wonderful change is
+ 
+
+ align:start position:0%
+and suddenly that wonderful change is
+lost so implementation requires us to
+
+ align:start position:0%
+lost so implementation requires us to
+ 
+
+ align:start position:0%
+lost so implementation requires us to
+pay attention to those details those
+
+ align:start position:0%
+pay attention to those details those
+ 
+
+ align:start position:0%
+pay attention to those details those
+things that we're going to encounter
+
+ align:start position:0%
+things that we're going to encounter
+ 
+
+ align:start position:0%
+things that we're going to encounter
+particularly in resource constrainted
+
+ align:start position:0%
+particularly in resource constrainted
+ 
+
+ align:start position:0%
+particularly in resource constrainted
+environments where where we we uh have
+
+ align:start position:0%
+environments where where we we uh have
+ 
+
+ align:start position:0%
+environments where where we we uh have
+turnover okay so here's a this is from
+
+ align:start position:0%
+turnover okay so here's a this is from
+ 
+
+ align:start position:0%
+turnover okay so here's a this is from
+the Improvement guide as well uh it's a
+
+ align:start position:0%
+the Improvement guide as well uh it's a
+ 
+
+ align:start position:0%
+the Improvement guide as well uh it's a
+great little table that I would refer
+
+ align:start position:0%
+great little table that I would refer
+ 
+
+ align:start position:0%
+great little table that I would refer
+you to when you start thinking about if
+
+ align:start position:0%
+you to when you start thinking about if
+ 
+
+ align:start position:0%
+you to when you start thinking about if
+you wanted to implement an idea when you
+
+ align:start position:0%
+you wanted to implement an idea when you
+ 
+
+ align:start position:0%
+you wanted to implement an idea when you
+should do so there are three key factors
+
+ align:start position:0%
+should do so there are three key factors
+ 
+
+ align:start position:0%
+should do so there are three key factors
+one are people ready for
+
+ align:start position:0%
+one are people ready for
+ 
+
+ align:start position:0%
+one are people ready for
+change hugely important right that's the
+
+ align:start position:0%
+change hugely important right that's the
+ 
+
+ align:start position:0%
+change hugely important right that's the
+psychology component when we talk about
+
+ align:start position:0%
+psychology component when we talk about
+ 
+
+ align:start position:0%
+psychology component when we talk about
+profound knowledge are they resistant
+
+ align:start position:0%
+profound knowledge are they resistant
+ 
+
+ align:start position:0%
+profound knowledge are they resistant
+are they indifferent or are they ready
+
+ align:start position:0%
+are they indifferent or are they ready
+ 
+
+ align:start position:0%
+are they indifferent or are they ready
+right if people are not ready you're not
+
+ align:start position:0%
+right if people are not ready you're not
+ 
+
+ align:start position:0%
+right if people are not ready you're not
+ready to
+
+ align:start position:0%
+ready to
+ 
+
+ align:start position:0%
+ready to
+implement if there's any kind of
+
+ align:start position:0%
+implement if there's any kind of
+ 
+
+ align:start position:0%
+implement if there's any kind of
+resistance at all you're still looking
+
+ align:start position:0%
+resistance at all you're still looking
+ 
+
+ align:start position:0%
+resistance at all you're still looking
+at small tests of change one patient two
+
+ align:start position:0%
+at small tests of change one patient two
+ 
+
+ align:start position:0%
+at small tests of change one patient two
+patients one week one day okay do you
+
+ align:start position:0%
+patients one week one day okay do you
+ 
+
+ align:start position:0%
+patients one week one day okay do you
+have confidence do you have a high
+
+ align:start position:0%
+have confidence do you have a high
+ 
+
+ align:start position:0%
+have confidence do you have a high
+degree of belief that this change is
+
+ align:start position:0%
+degree of belief that this change is
+ 
+
+ align:start position:0%
+degree of belief that this change is
+going to be beneficial that it's going
+
+ align:start position:0%
+going to be beneficial that it's going
+ 
+
+ align:start position:0%
+going to be beneficial that it's going
+to be better than the status quo okay if
+
+ align:start position:0%
+to be better than the status quo okay if
+ 
+
+ align:start position:0%
+to be better than the status quo okay if
+you don't more testing is
+
+ align:start position:0%
+you don't more testing is
+ 
+
+ align:start position:0%
+you don't more testing is
+needed and then the Third is what is the
+
+ align:start position:0%
+needed and then the Third is what is the
+ 
+
+ align:start position:0%
+needed and then the Third is what is the
+cost of failure right now this could be
+
+ align:start position:0%
+cost of failure right now this could be
+ 
+
+ align:start position:0%
+cost of failure right now this could be
+Financial cost there could be time cost
+
+ align:start position:0%
+Financial cost there could be time cost
+ 
+
+ align:start position:0%
+Financial cost there could be time cost
+could be human resource cost it could be
+
+ align:start position:0%
+could be human resource cost it could be
+ 
+
+ align:start position:0%
+could be human resource cost it could be
+cost in terms of lives okay so what is
+
+ align:start position:0%
+cost in terms of lives okay so what is
+ 
+
+ align:start position:0%
+cost in terms of lives okay so what is
+the cost of failure right is it high or
+
+ align:start position:0%
+the cost of failure right is it high or
+ 
+
+ align:start position:0%
+the cost of failure right is it high or
+low implementation is only ready when
+
+ align:start position:0%
+low implementation is only ready when
+ 
+
+ align:start position:0%
+low implementation is only ready when
+you have a high degree of belief that
+
+ align:start position:0%
+you have a high degree of belief that
+ 
+
+ align:start position:0%
+you have a high degree of belief that
+what you're doing is better than the
+
+ align:start position:0%
+what you're doing is better than the
+ 
+
+ align:start position:0%
+what you're doing is better than the
+status quo the cost of failure is low
+
+ align:start position:0%
+status quo the cost of failure is low
+ 
+
+ align:start position:0%
+status quo the cost of failure is low
+and people are excited and ready for
+
+ align:start position:0%
+and people are excited and ready for
+ 
+
+ align:start position:0%
+and people are excited and ready for
+change right so it's an assessment of
+
+ align:start position:0%
+change right so it's an assessment of
+ 
+
+ align:start position:0%
+change right so it's an assessment of
+all three of those things is that does
+
+ align:start position:0%
+all three of those things is that does
+ 
+
+ align:start position:0%
+all three of those things is that does
+that make
+
+ align:start position:0%
+that make
+ 
+
+ align:start position:0%
+that make
+sense so as you think about your
+
+ align:start position:0%
+sense so as you think about your
+ 
+
+ align:start position:0%
+sense so as you think about your
+projects you think about what you're
+
+ align:start position:0%
+projects you think about what you're
+ 
+
+ align:start position:0%
+projects you think about what you're
+going to change and what you're going to
+
+ align:start position:0%
+going to change and what you're going to
+ 
+
+ align:start position:0%
+going to change and what you're going to
+take potentially to scale having
+
+ align:start position:0%
+take potentially to scale having
+ 
+
+ align:start position:0%
+take potentially to scale having
+thoughtfulness around these things as
+
+ align:start position:0%
+thoughtfulness around these things as
+ 
+
+ align:start position:0%
+thoughtfulness around these things as
+well as what are the implementation
+
+ align:start position:0%
+well as what are the implementation
+ 
+
+ align:start position:0%
+well as what are the implementation
+issues associated with introducing a new
+
+ align:start position:0%
+issues associated with introducing a new
+ 
+
+ align:start position:0%
+issues associated with introducing a new
+technology a new process a new system
+
+ align:start position:0%
+technology a new process a new system
+ 
+
+ align:start position:0%
+technology a new process a new system
+whatever it is is going to be critically
+
+ align:start position:0%
+whatever it is is going to be critically
+ 
+
+ align:start position:0%
+whatever it is is going to be critically
+important all right I think we'll stop
+
+ align:start position:0%
+important all right I think we'll stop
+ 
+
+ align:start position:0%
+important all right I think we'll stop
+there I threw up the discussion
+
+ align:start position:0%
+there I threw up the discussion
+ 
+
+ align:start position:0%
+there I threw up the discussion
+questions from the syllabus uh but uh
+
+ align:start position:0%
+questions from the syllabus uh but uh
+ 
+
+ align:start position:0%
+questions from the syllabus uh but uh
+stop there question yeah ellot as a
\ No newline at end of file
diff --git a/JzW4RYICOdA.txt b/JzW4RYICOdA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fb594762043768d835436ee3070c8a57be0b5d7d
--- /dev/null
+++ b/JzW4RYICOdA.txt
@@ -0,0 +1,6227 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+William Klemperer
+
+ align:start position:0%
+William Klemperer
+ 
+
+ align:start position:0%
+William Klemperer
+was was my thesis advisor and he died
+
+ align:start position:0%
+was was my thesis advisor and he died
+ 
+
+ align:start position:0%
+was was my thesis advisor and he died
+yesterday it also happens that the
+
+ align:start position:0%
+yesterday it also happens that the
+ 
+
+ align:start position:0%
+yesterday it also happens that the
+subject of this lecture is the it's
+
+ align:start position:0%
+subject of this lecture is the it's
+ 
+
+ align:start position:0%
+subject of this lecture is the it's
+really the core of what I got from him
+
+ align:start position:0%
+really the core of what I got from him
+ 
+
+ align:start position:0%
+really the core of what I got from him
+he showed me how to evaluate matrix
+
+ align:start position:0%
+he showed me how to evaluate matrix
+ 
+
+ align:start position:0%
+he showed me how to evaluate matrix
+elements of many electron operators
+
+ align:start position:0%
+elements of many electron operators
+ 
+
+ align:start position:0%
+elements of many electron operators
+which is the key to being able to
+
+ align:start position:0%
+which is the key to being able to
+ 
+
+ align:start position:0%
+which is the key to being able to
+interpret not just tabulate electronic
+
+ align:start position:0%
+interpret not just tabulate electronic
+ 
+
+ align:start position:0%
+interpret not just tabulate electronic
+properties of atoms and molecules our
+
+ align:start position:0%
+properties of atoms and molecules our
+ 
+
+ align:start position:0%
+properties of atoms and molecules our
+goal is to be able to reduce the
+
+ align:start position:0%
+goal is to be able to reduce the
+ 
+
+ align:start position:0%
+goal is to be able to reduce the
+complexity of electronic structure which
+
+ align:start position:0%
+complexity of electronic structure which
+ 
+
+ align:start position:0%
+complexity of electronic structure which
+is really complicated the electrons
+
+ align:start position:0%
+is really complicated the electrons
+ 
+
+ align:start position:0%
+is really complicated the electrons
+interact with each other really strongly
+
+ align:start position:0%
+interact with each other really strongly
+ 
+
+ align:start position:0%
+interact with each other really strongly
+and there are a lot of them and it's
+
+ align:start position:0%
+and there are a lot of them and it's
+ 
+
+ align:start position:0%
+and there are a lot of them and it's
+very hard to separate the complexity of
+
+ align:start position:0%
+very hard to separate the complexity of
+ 
+
+ align:start position:0%
+very hard to separate the complexity of
+the many body interactions into things
+
+ align:start position:0%
+the many body interactions into things
+ 
+
+ align:start position:0%
+the many body interactions into things
+that we can put in our head and
+
+ align:start position:0%
+that we can put in our head and
+ 
+
+ align:start position:0%
+that we can put in our head and
+interpret and the whole goal of this
+
+ align:start position:0%
+interpret and the whole goal of this
+ 
+
+ align:start position:0%
+interpret and the whole goal of this
+course is to give you the tools to
+
+ align:start position:0%
+course is to give you the tools to
+ 
+
+ align:start position:0%
+course is to give you the tools to
+interpret complicated phenomena we have
+
+ align:start position:0%
+interpret complicated phenomena we have
+ 
+
+ align:start position:0%
+interpret complicated phenomena we have
+the vibrational problem as a way of
+
+ align:start position:0%
+the vibrational problem as a way of
+ 
+
+ align:start position:0%
+the vibrational problem as a way of
+understanding inter nuclear interactions
+
+ align:start position:0%
+understanding inter nuclear interactions
+ 
+
+ align:start position:0%
+understanding inter nuclear interactions
+nuclear motions we have electronic
+
+ align:start position:0%
+nuclear motions we have electronic
+ 
+
+ align:start position:0%
+nuclear motions we have electronic
+structure and the hydrogen atom as a way
+
+ align:start position:0%
+structure and the hydrogen atom as a way
+ 
+
+ align:start position:0%
+structure and the hydrogen atom as a way
+of understanding what electronic
+
+ align:start position:0%
+of understanding what electronic
+ 
+
+ align:start position:0%
+of understanding what electronic
+structure is and to reduce it to
+
+ align:start position:0%
+structure is and to reduce it to
+ 
+
+ align:start position:0%
+structure is and to reduce it to
+basically the things we learn about
+
+ align:start position:0%
+basically the things we learn about
+ 
+
+ align:start position:0%
+basically the things we learn about
+hydrogen when we go to molecular orbital
+
+ align:start position:0%
+hydrogen when we go to molecular orbital
+ 
+
+ align:start position:0%
+hydrogen when we go to molecular orbital
+Theory we take what we know about atoms
+
+ align:start position:0%
+Theory we take what we know about atoms
+ 
+
+ align:start position:0%
+Theory we take what we know about atoms
+and build a minimally complex complex
+
+ align:start position:0%
+and build a minimally complex complex
+ 
+
+ align:start position:0%
+and build a minimally complex complex
+interpretive picture which is sort of a
+
+ align:start position:0%
+interpretive picture which is sort of a
+ 
+
+ align:start position:0%
+interpretive picture which is sort of a
+framework for understanding
+
+ align:start position:0%
+framework for understanding
+ 
+
+ align:start position:0%
+framework for understanding
+complicated molecular interactions so
+
+ align:start position:0%
+complicated molecular interactions so
+ 
+
+ align:start position:0%
+complicated molecular interactions so
+one of the most important things about
+
+ align:start position:0%
+one of the most important things about
+ 
+
+ align:start position:0%
+one of the most important things about
+understanding electronic structure is
+
+ align:start position:0%
+understanding electronic structure is
+ 
+
+ align:start position:0%
+understanding electronic structure is
+how do we deal with many electron wave
+
+ align:start position:0%
+how do we deal with many electron wave
+ 
+
+ align:start position:0%
+how do we deal with many electron wave
+functions one of the terrible problems
+
+ align:start position:0%
+functions one of the terrible problems
+ 
+
+ align:start position:0%
+functions one of the terrible problems
+is that the electrons are
+
+ align:start position:0%
+is that the electrons are
+ 
+
+ align:start position:0%
+is that the electrons are
+indistinguishable and so we have to
+
+ align:start position:0%
+indistinguishable and so we have to
+ 
+
+ align:start position:0%
+indistinguishable and so we have to
+ensure that the wave functions are anti
+
+ align:start position:0%
+ensure that the wave functions are anti
+ 
+
+ align:start position:0%
+ensure that the wave functions are anti
+symmetric with respect to permutation of
+
+ align:start position:0%
+symmetric with respect to permutation of
+ 
+
+ align:start position:0%
+symmetric with respect to permutation of
+every pair every pair of electrons not
+
+ align:start position:0%
+every pair every pair of electrons not
+ 
+
+ align:start position:0%
+every pair every pair of electrons not
+just two and helium we just dealt with
+
+ align:start position:0%
+just two and helium we just dealt with
+ 
+
+ align:start position:0%
+just two and helium we just dealt with
+two and that wasn't so bad but when we
+
+ align:start position:0%
+two and that wasn't so bad but when we
+ 
+
+ align:start position:0%
+two and that wasn't so bad but when we
+deal with n electrons what we are going
+
+ align:start position:0%
+deal with n electrons what we are going
+ 
+
+ align:start position:0%
+deal with n electrons what we are going
+to discover is that in order to anti
+
+ align:start position:0%
+to discover is that in order to anti
+ 
+
+ align:start position:0%
+to discover is that in order to anti
+symmetrize the wave function we have to
+
+ align:start position:0%
+symmetrize the wave function we have to
+ 
+
+ align:start position:0%
+symmetrize the wave function we have to
+write a determinantal wave function a
+
+ align:start position:0%
+write a determinantal wave function a
+ 
+
+ align:start position:0%
+write a determinantal wave function a
+determinant of orbitals and when you
+
+ align:start position:0%
+determinant of orbitals and when you
+ 
+
+ align:start position:0%
+determinant of orbitals and when you
+expand it and by n determinant you get n
+
+ align:start position:0%
+expand it and by n determinant you get n
+ 
+
+ align:start position:0%
+expand it and by n determinant you get n
+factorial terms and when you calculate
+
+ align:start position:0%
+factorial terms and when you calculate
+ 
+
+ align:start position:0%
+factorial terms and when you calculate
+matrix elements you have n factorial
+
+ align:start position:0%
+matrix elements you have n factorial
+ 
+
+ align:start position:0%
+matrix elements you have n factorial
+squared integrals so you're not going to
+
+ align:start position:0%
+squared integrals so you're not going to
+ 
+
+ align:start position:0%
+squared integrals so you're not going to
+be handling these one at a time and
+
+ align:start position:0%
+be handling these one at a time and
+ 
+
+ align:start position:0%
+be handling these one at a time and
+looking and looking at them lovingly
+
+ align:start position:0%
+looking and looking at them lovingly
+ 
+
+ align:start position:0%
+looking and looking at them lovingly
+you're going to want to be able to take
+
+ align:start position:0%
+you're going to want to be able to take
+ 
+
+ align:start position:0%
+you're going to want to be able to take
+these things and extract what is the
+
+ align:start position:0%
+these things and extract what is the
+ 
+
+ align:start position:0%
+these things and extract what is the
+important thing about the electronic
+
+ align:start position:0%
+important thing about the electronic
+ 
+
+ align:start position:0%
+important thing about the electronic
+structure that you're going to need to
+
+ align:start position:0%
+structure that you're going to need to
+ 
+
+ align:start position:0%
+structure that you're going to need to
+know and as a graduate student I was
+
+ align:start position:0%
+know and as a graduate student I was
+ 
+
+ align:start position:0%
+know and as a graduate student I was
+collecting numbers I was collecting
+
+ align:start position:0%
+collecting numbers I was collecting
+ 
+
+ align:start position:0%
+collecting numbers I was collecting
+numbers about spectroscopic
+
+ align:start position:0%
+numbers about spectroscopic
+ 
+
+ align:start position:0%
+numbers about spectroscopic
+perturbations where non-degenerate
+
+ align:start position:0%
+perturbations where non-degenerate
+ 
+
+ align:start position:0%
+perturbations where non-degenerate
+perturbation theory breaks down and
+
+ align:start position:0%
+perturbation theory breaks down and
+ 
+
+ align:start position:0%
+perturbation theory breaks down and
+interesting things happened but this was
+
+ align:start position:0%
+interesting things happened but this was
+ 
+
+ align:start position:0%
+interesting things happened but this was
+something that nobody in the world was
+
+ align:start position:0%
+something that nobody in the world was
+ 
+
+ align:start position:0%
+something that nobody in the world was
+interested in because it was the
+
+ align:start position:0%
+interested in because it was the
+ 
+
+ align:start position:0%
+interested in because it was the
+breaking of the usual patterns and I was
+
+ align:start position:0%
+breaking of the usual patterns and I was
+ 
+
+ align:start position:0%
+breaking of the usual patterns and I was
+convinced that I had collected some
+
+ align:start position:0%
+convinced that I had collected some
+ 
+
+ align:start position:0%
+convinced that I had collected some
+stuff that told an interesting story and
+
+ align:start position:0%
+stuff that told an interesting story and
+ 
+
+ align:start position:0%
+stuff that told an interesting story and
+I told Klemperer about this and he said
+
+ align:start position:0%
+I told Klemperer about this and he said
+ 
+
+ align:start position:0%
+I told Klemperer about this and he said
+well have you thought about how to
+
+ align:start position:0%
+well have you thought about how to
+ 
+
+ align:start position:0%
+well have you thought about how to
+evaluate the these integrals that you're
+
+ align:start position:0%
+evaluate the these integrals that you're
+ 
+
+ align:start position:0%
+evaluate the these integrals that you're
+these numbers that you are extracting
+
+ align:start position:0%
+these numbers that you are extracting
+ 
+
+ align:start position:0%
+these numbers that you are extracting
+from the spectrum by doing some tricks
+
+ align:start position:0%
+from the spectrum by doing some tricks
+ 
+
+ align:start position:0%
+from the spectrum by doing some tricks
+with the many electron wave functions
+
+ align:start position:0%
+with the many electron wave functions
+ 
+
+ align:start position:0%
+with the many electron wave functions
+and then he showed me and a scrap of
+
+ align:start position:0%
+and then he showed me and a scrap of
+ 
+
+ align:start position:0%
+and then he showed me and a scrap of
+paper how to do it and I was launched
+
+ align:start position:0%
+paper how to do it and I was launched
+ 
+
+ align:start position:0%
+paper how to do it and I was launched
+that was it that has been the foundation
+
+ align:start position:0%
+that was it that has been the foundation
+ 
+
+ align:start position:0%
+that was it that has been the foundation
+of my career for the last 50 years and I
+
+ align:start position:0%
+of my career for the last 50 years and I
+ 
+
+ align:start position:0%
+of my career for the last 50 years and I
+didn't think that klemper knew that I
+
+ align:start position:0%
+didn't think that klemper knew that I
+ 
+
+ align:start position:0%
+didn't think that klemper knew that I
+didn't think anybody do it because I
+
+ align:start position:0%
+didn't think anybody do it because I
+ 
+
+ align:start position:0%
+didn't think anybody do it because I
+didn't think it was to be knowable but
+
+ align:start position:0%
+didn't think it was to be knowable but
+ 
+
+ align:start position:0%
+didn't think it was to be knowable but
+he just gave it to me in a silver
+
+ align:start position:0%
+he just gave it to me in a silver
+ 
+
+ align:start position:0%
+he just gave it to me in a silver
+platter and so I'm going to try to give
+
+ align:start position:0%
+platter and so I'm going to try to give
+ 
+
+ align:start position:0%
+platter and so I'm going to try to give
+you at least the rudiments of what it is
+
+ align:start position:0%
+you at least the rudiments of what it is
+ 
+
+ align:start position:0%
+you at least the rudiments of what it is
+you're up against and how you reduce
+
+ align:start position:0%
+you're up against and how you reduce
+ 
+
+ align:start position:0%
+you're up against and how you reduce
+them to things that you care about that
+
+ align:start position:0%
+them to things that you care about that
+ 
+
+ align:start position:0%
+them to things that you care about that
+you can think about and you can
+
+ align:start position:0%
+you can think about and you can
+ 
+
+ align:start position:0%
+you can think about and you can
+understand the hydrogen atom in rather
+
+ align:start position:0%
+understand the hydrogen atom in rather
+ 
+
+ align:start position:0%
+understand the hydrogen atom in rather
+complete detail or at least you can
+
+ align:start position:0%
+complete detail or at least you can
+ 
+
+ align:start position:0%
+complete detail or at least you can
+understand how one observable relates to
+
+ align:start position:0%
+understand how one observable relates to
+ 
+
+ align:start position:0%
+understand how one observable relates to
+another and so the relationship between
+
+ align:start position:0%
+another and so the relationship between
+ 
+
+ align:start position:0%
+another and so the relationship between
+the effective quantum number and the
+
+ align:start position:0%
+the effective quantum number and the
+ 
+
+ align:start position:0%
+the effective quantum number and the
+ionization energy of a state then
+
+ align:start position:0%
+ionization energy of a state then
+ 
+
+ align:start position:0%
+ionization energy of a state then
+provides a hydrogen atom based
+
+ align:start position:0%
+provides a hydrogen atom based
+ 
+
+ align:start position:0%
+provides a hydrogen atom based
+structural model for everything you can
+
+ align:start position:0%
+structural model for everything you can
+ 
+
+ align:start position:0%
+structural model for everything you can
+observe now spectroscopy have the
+
+ align:start position:0%
+observe now spectroscopy have the
+ 
+
+ align:start position:0%
+observe now spectroscopy have the
+unfortunate habit of saying we're
+
+ align:start position:0%
+unfortunate habit of saying we're
+ 
+
+ align:start position:0%
+unfortunate habit of saying we're
+interested in is structure structure is
+
+ align:start position:0%
+interested in is structure structure is
+ 
+
+ align:start position:0%
+interested in is structure structure is
+static dynamics is magical and special
+
+ align:start position:0%
+static dynamics is magical and special
+ 
+
+ align:start position:0%
+static dynamics is magical and special
+and hard but if you understand structure
+
+ align:start position:0%
+and hard but if you understand structure
+ 
+
+ align:start position:0%
+and hard but if you understand structure
+in a way which is not the exact eigen
+
+ align:start position:0%
+in a way which is not the exact eigen
+ 
+
+ align:start position:0%
+in a way which is not the exact eigen
+States not the exact wave functions but
+
+ align:start position:0%
+States not the exact wave functions but
+ 
+
+ align:start position:0%
+States not the exact wave functions but
+something that the molecule was trying
+
+ align:start position:0%
+something that the molecule was trying
+ 
+
+ align:start position:0%
+something that the molecule was trying
+to do and sort of missed and the the
+
+ align:start position:0%
+to do and sort of missed and the the
+ 
+
+ align:start position:0%
+to do and sort of missed and the the
+dynamics is just what happens when this
+
+ align:start position:0%
+dynamics is just what happens when this
+ 
+
+ align:start position:0%
+dynamics is just what happens when this
+preparation isn't an eigenstate which
+
+ align:start position:0%
+preparation isn't an eigenstate which
+ 
+
+ align:start position:0%
+preparation isn't an eigenstate which
+would be boring and you get dynamics
+
+ align:start position:0%
+would be boring and you get dynamics
+ 
+
+ align:start position:0%
+would be boring and you get dynamics
+which you can understand as opposed to
+
+ align:start position:0%
+which you can understand as opposed to
+ 
+
+ align:start position:0%
+which you can understand as opposed to
+just say I'm going to I'm going to
+
+ align:start position:0%
+just say I'm going to I'm going to
+ 
+
+ align:start position:0%
+just say I'm going to I'm going to
+tabulate the dynamics to still do you
+
+ align:start position:0%
+tabulate the dynamics to still do you
+ 
+
+ align:start position:0%
+tabulate the dynamics to still do you
+don't know anything unless you have a
+
+ align:start position:0%
+don't know anything unless you have a
+ 
+
+ align:start position:0%
+don't know anything unless you have a
+reductionist picture of what's going on
+
+ align:start position:0%
+reductionist picture of what's going on
+ 
+
+ align:start position:0%
+reductionist picture of what's going on
+and since the hardest part of dealing
+
+ align:start position:0%
+and since the hardest part of dealing
+ 
+
+ align:start position:0%
+and since the hardest part of dealing
+with molecules is the fact that they
+
+ align:start position:0%
+with molecules is the fact that they
+ 
+
+ align:start position:0%
+with molecules is the fact that they
+have a lot of electrons this is really
+
+ align:start position:0%
+have a lot of electrons this is really
+ 
+
+ align:start position:0%
+have a lot of electrons this is really
+the core of being able to do important
+
+ align:start position:0%
+the core of being able to do important
+ 
+
+ align:start position:0%
+the core of being able to do important
+stuff now
+
+ align:start position:0%
+stuff now
+ 
+
+ align:start position:0%
+stuff now
+it's it's a horrendously complicated
+
+ align:start position:0%
+it's it's a horrendously complicated
+ 
+
+ align:start position:0%
+it's it's a horrendously complicated
+problem and notationally awkward too and
+
+ align:start position:0%
+problem and notationally awkward too and
+ 
+
+ align:start position:0%
+problem and notationally awkward too and
+let me just try to let me try to explain
+
+ align:start position:0%
+let me just try to let me try to explain
+ 
+
+ align:start position:0%
+let me just try to let me try to explain
+it and I'm going to try to do this
+
+ align:start position:0%
+it and I'm going to try to do this
+ 
+
+ align:start position:0%
+it and I'm going to try to do this
+without too much reliance on my notes
+
+ align:start position:0%
+without too much reliance on my notes
+ 
+
+ align:start position:0%
+without too much reliance on my notes
+because they're terrible okay but we
+
+ align:start position:0%
+because they're terrible okay but we
+ 
+
+ align:start position:0%
+because they're terrible okay but we
+have we talked about helium and helium
+
+ align:start position:0%
+have we talked about helium and helium
+ 
+
+ align:start position:0%
+have we talked about helium and helium
+has two electrons and there is this 1
+
+ align:start position:0%
+has two electrons and there is this 1
+ 
+
+ align:start position:0%
+has two electrons and there is this 1
+over r12 interaction between electrons
+
+ align:start position:0%
+over r12 interaction between electrons
+ 
+
+ align:start position:0%
+over r12 interaction between electrons
+which looks innocent enough you can
+
+ align:start position:0%
+which looks innocent enough you can
+ 
+
+ align:start position:0%
+which looks innocent enough you can
+write it down and you know just a few
+
+ align:start position:0%
+write it down and you know just a few
+ 
+
+ align:start position:0%
+write it down and you know just a few
+symbols but and we can call it the first
+
+ align:start position:0%
+symbols but and we can call it the first
+ 
+
+ align:start position:0%
+symbols but and we can call it the first
+order perturbation but that's really a
+
+ align:start position:0%
+order perturbation but that's really a
+ 
+
+ align:start position:0%
+order perturbation but that's really a
+lie because it's as big as almost
+
+ align:start position:0%
+lie because it's as big as almost
+ 
+
+ align:start position:0%
+lie because it's as big as almost
+everything else and so yeah we can in
+
+ align:start position:0%
+everything else and so yeah we can in
+ 
+
+ align:start position:0%
+everything else and so yeah we can in
+fact do a series of approximations one
+
+ align:start position:0%
+fact do a series of approximations one
+ 
+
+ align:start position:0%
+fact do a series of approximations one
+is ignore it they're not interacting
+
+ align:start position:0%
+is ignore it they're not interacting
+ 
+
+ align:start position:0%
+is ignore it they're not interacting
+electron approximation and that's
+
+ align:start position:0%
+electron approximation and that's
+ 
+
+ align:start position:0%
+electron approximation and that's
+basically repackaging hydrogen and it's
+
+ align:start position:0%
+basically repackaging hydrogen and it's
+ 
+
+ align:start position:0%
+basically repackaging hydrogen and it's
+not quite enough and then we can say ok
+
+ align:start position:0%
+not quite enough and then we can say ok
+ 
+
+ align:start position:0%
+not quite enough and then we can say ok
+let's let's calculate the first order
+
+ align:start position:0%
+let's let's calculate the first order
+ 
+
+ align:start position:0%
+let's let's calculate the first order
+energy by calculating expectation values
+
+ align:start position:0%
+energy by calculating expectation values
+ 
+
+ align:start position:0%
+energy by calculating expectation values
+of H 1 2 so that's a 1 that's and that's
+
+ align:start position:0%
+of H 1 2 so that's a 1 that's and that's
+ 
+
+ align:start position:0%
+of H 1 2 so that's a 1 that's and that's
+almost enough to give us a sense of what
+
+ align:start position:0%
+almost enough to give us a sense of what
+ 
+
+ align:start position:0%
+almost enough to give us a sense of what
+is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok 1 over r12 commutator with with any
+
+ align:start position:0%
+ok 1 over r12 commutator with with any
+ 
+
+ align:start position:0%
+ok 1 over r12 commutator with with any
+electron that's not 0 1 over r12
+
+ align:start position:0%
+electron that's not 0 1 over r12
+ 
+
+ align:start position:0%
+electron that's not 0 1 over r12
+commutator with any any orbital angular
+
+ align:start position:0%
+commutator with any any orbital angular
+ 
+
+ align:start position:0%
+commutator with any any orbital angular
+momentum any momentum not 0 so that
+
+ align:start position:0%
+momentum any momentum not 0 so that
+ 
+
+ align:start position:0%
+momentum any momentum not 0 so that
+means that L and n are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good a lot of members let's have good
+
+ align:start position:0%
+good a lot of members let's have good
+ 
+
+ align:start position:0%
+good a lot of members let's have good
+quantum number what's the definition of
+
+ align:start position:0%
+quantum number what's the definition of
+ 
+
+ align:start position:0%
+quantum number what's the definition of
+a good quantum number come on this is an
+
+ align:start position:0%
+a good quantum number come on this is an
+ 
+
+ align:start position:0%
+a good quantum number come on this is an
+important question yes that's that's
+
+ align:start position:0%
+important question yes that's that's
+ 
+
+ align:start position:0%
+important question yes that's that's
+maybe 70% of what I want you can put
+
+ align:start position:0%
+maybe 70% of what I want you can put
+ 
+
+ align:start position:0%
+maybe 70% of what I want you can put
+into a formula that means it's a
+
+ align:start position:0%
+into a formula that means it's a
+ 
+
+ align:start position:0%
+into a formula that means it's a
+rigorously good thing it means it
+
+ align:start position:0%
+rigorously good thing it means it
+ 
+
+ align:start position:0%
+rigorously good thing it means it
+commutes with the Hamiltonian a
+
+ align:start position:0%
+commutes with the Hamiltonian a
+ 
+
+ align:start position:0%
+commutes with the Hamiltonian a
+rigorously good quantum number is an
+
+ align:start position:0%
+rigorously good quantum number is an
+ 
+
+ align:start position:0%
+rigorously good quantum number is an
+corresponds to an eigenvalue of an
+
+ align:start position:0%
+corresponds to an eigenvalue of an
+ 
+
+ align:start position:0%
+corresponds to an eigenvalue of an
+operator that commutes with the
+
+ align:start position:0%
+operator that commutes with the
+ 
+
+ align:start position:0%
+operator that commutes with the
+Hamiltonian so hydrogen we rely on NL to
+
+ align:start position:0%
+Hamiltonian so hydrogen we rely on NL to
+ 
+
+ align:start position:0%
+Hamiltonian so hydrogen we rely on NL to
+get almost everything but here we find
+
+ align:start position:0%
+get almost everything but here we find
+ 
+
+ align:start position:0%
+get almost everything but here we find
+that in addition to this being not small
+
+ align:start position:0%
+that in addition to this being not small
+ 
+
+ align:start position:0%
+that in addition to this being not small
+it destroys the foundation of our
+
+ align:start position:0%
+it destroys the foundation of our
+ 
+
+ align:start position:0%
+it destroys the foundation of our
+picture and so how do we how do we think
+
+ align:start position:0%
+picture and so how do we how do we think
+ 
+
+ align:start position:0%
+picture and so how do we how do we think
+that we can make any sense of many
+
+ align:start position:0%
+that we can make any sense of many
+ 
+
+ align:start position:0%
+that we can make any sense of many
+electron atoms and molecules well it
+
+ align:start position:0%
+electron atoms and molecules well it
+ 
+
+ align:start position:0%
+electron atoms and molecules well it
+turns out we can hide most of the
+
+ align:start position:0%
+turns out we can hide most of the
+ 
+
+ align:start position:0%
+turns out we can hide most of the
+complexity and most of the complexity is
+
+ align:start position:0%
+complexity and most of the complexity is
+ 
+
+ align:start position:0%
+complexity and most of the complexity is
+just working out the rules for
+
+ align:start position:0%
+just working out the rules for
+ 
+
+ align:start position:0%
+just working out the rules for
+calculating these matrix elements the
+
+ align:start position:0%
+calculating these matrix elements the
+ 
+
+ align:start position:0%
+calculating these matrix elements the
+matrix elements of operators that we
+
+ align:start position:0%
+matrix elements of operators that we
+ 
+
+ align:start position:0%
+matrix elements of operators that we
+care about like transition moments
+
+ align:start position:0%
+care about like transition moments
+ 
+
+ align:start position:0%
+care about like transition moments
+spin-orbit same and effect things that
+
+ align:start position:0%
+spin-orbit same and effect things that
+ 
+
+ align:start position:0%
+spin-orbit same and effect things that
+that they correspond to how we observe
+
+ align:start position:0%
+that they correspond to how we observe
+ 
+
+ align:start position:0%
+that they correspond to how we observe
+atomic and molecular structure and and
+
+ align:start position:0%
+atomic and molecular structure and and
+ 
+
+ align:start position:0%
+atomic and molecular structure and and
+so the main obstacle to being able to
+
+ align:start position:0%
+so the main obstacle to being able to
+ 
+
+ align:start position:0%
+so the main obstacle to being able to
+evaluate these matrix elements is the
+
+ align:start position:0%
+evaluate these matrix elements is the
+ 
+
+ align:start position:0%
+evaluate these matrix elements is the
+permutation requirement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it turns out that there is a really
+
+ align:start position:0%
+and it turns out that there is a really
+ 
+
+ align:start position:0%
+and it turns out that there is a really
+simple way of dealing with the
+
+ align:start position:0%
+simple way of dealing with the
+ 
+
+ align:start position:0%
+simple way of dealing with the
+requirements for electron permutation
+
+ align:start position:0%
+requirements for electron permutation
+ 
+
+ align:start position:0%
+requirements for electron permutation
+and that that is to write the wave
+
+ align:start position:0%
+and that that is to write the wave
+ 
+
+ align:start position:0%
+and that that is to write the wave
+function as a determinant of one
+
+ align:start position:0%
+function as a determinant of one
+ 
+
+ align:start position:0%
+function as a determinant of one
+electron orbitals because a determinant
+
+ align:start position:0%
+electron orbitals because a determinant
+ 
+
+ align:start position:0%
+electron orbitals because a determinant
+has to three really important problems
+
+ align:start position:0%
+has to three really important problems
+ 
+
+ align:start position:0%
+has to three really important problems
+with properties one it changes its sign
+
+ align:start position:0%
+with properties one it changes its sign
+ 
+
+ align:start position:0%
+with properties one it changes its sign
+when you permute any two columns - it
+
+ align:start position:0%
+when you permute any two columns - it
+ 
+
+ align:start position:0%
+when you permute any two columns - it
+changes its sign when you permute any
+
+ align:start position:0%
+changes its sign when you permute any
+ 
+
+ align:start position:0%
+changes its sign when you permute any
+two rows and three if you have two
+
+ align:start position:0%
+two rows and three if you have two
+ 
+
+ align:start position:0%
+two rows and three if you have two
+identical columns or rows at 0 that's
+
+ align:start position:0%
+identical columns or rows at 0 that's
+ 
+
+ align:start position:0%
+identical columns or rows at 0 that's
+that's really fantastic and that is the
+
+ align:start position:0%
+that's really fantastic and that is the
+ 
+
+ align:start position:0%
+that's really fantastic and that is the
+Pauli exclusion principle not what you
+
+ align:start position:0%
+Pauli exclusion principle not what you
+ 
+
+ align:start position:0%
+Pauli exclusion principle not what you
+learned in high school what you learned
+
+ align:start position:0%
+learned in high school what you learned
+ 
+
+ align:start position:0%
+learned in high school what you learned
+is a small consequence of that so if we
+
+ align:start position:0%
+is a small consequence of that so if we
+ 
+
+ align:start position:0%
+is a small consequence of that so if we
+can build at a symmetric wave functions
+
+ align:start position:0%
+can build at a symmetric wave functions
+ 
+
+ align:start position:0%
+can build at a symmetric wave functions
+we have alpha we have we can only put
+
+ align:start position:0%
+we have alpha we have we can only put
+ 
+
+ align:start position:0%
+we have alpha we have we can only put
+one electron in an orbital we have all
+
+ align:start position:0%
+one electron in an orbital we have all
+ 
+
+ align:start position:0%
+one electron in an orbital we have all
+sorts of stuff but it's too complicated
+
+ align:start position:0%
+sorts of stuff but it's too complicated
+ 
+
+ align:start position:0%
+sorts of stuff but it's too complicated
+to tell a student in high school that
+
+ align:start position:0%
+to tell a student in high school that
+ 
+
+ align:start position:0%
+to tell a student in high school that
+you can't just the question of
+
+ align:start position:0%
+you can't just the question of
+ 
+
+ align:start position:0%
+you can't just the question of
+indistinguishable electrons is such a
+
+ align:start position:0%
+indistinguishable electrons is such a
+ 
+
+ align:start position:0%
+indistinguishable electrons is such a
+subtle thing that you can't say well
+
+ align:start position:0%
+subtle thing that you can't say well
+ 
+
+ align:start position:0%
+subtle thing that you can't say well
+they have to be anti symmetric that but
+
+ align:start position:0%
+they have to be anti symmetric that but
+ 
+
+ align:start position:0%
+they have to be anti symmetric that but
+it's easy to say you can't put more than
+
+ align:start position:0%
+it's easy to say you can't put more than
+ 
+
+ align:start position:0%
+it's easy to say you can't put more than
+one electron in a in a spin orbital but
+
+ align:start position:0%
+one electron in a in a spin orbital but
+ 
+
+ align:start position:0%
+one electron in a in a spin orbital but
+we don't talk about spin orbitals we say
+
+ align:start position:0%
+we don't talk about spin orbitals we say
+ 
+
+ align:start position:0%
+we don't talk about spin orbitals we say
+we can't put more than two electrons in
+
+ align:start position:0%
+we can't put more than two electrons in
+ 
+
+ align:start position:0%
+we can't put more than two electrons in
+an orbital because we're protecting you
+
+ align:start position:0%
+an orbital because we're protecting you
+ 
+
+ align:start position:0%
+an orbital because we're protecting you
+from from unnecessary knowledge ok well
+
+ align:start position:0%
+from from unnecessary knowledge ok well
+ 
+
+ align:start position:0%
+from from unnecessary knowledge ok well
+I'm not gonna protect you ok so we know
+
+ align:start position:0%
+I'm not gonna protect you ok so we know
+ 
+
+ align:start position:0%
+I'm not gonna protect you ok so we know
+that the Hamiltonian passed it
+
+ align:start position:0%
+that the Hamiltonian passed it
+ 
+
+ align:start position:0%
+that the Hamiltonian passed it
+commute with these capital letters mean
+
+ align:start position:0%
+commute with these capital letters mean
+ 
+
+ align:start position:0%
+commute with these capital letters mean
+many electron angular momenta and this
+
+ align:start position:0%
+many electron angular momenta and this
+ 
+
+ align:start position:0%
+many electron angular momenta and this
+is the spin this is the projection of
+
+ align:start position:0%
+is the spin this is the projection of
+ 
+
+ align:start position:0%
+is the spin this is the projection of
+the spin we know this is true because
+
+ align:start position:0%
+the spin we know this is true because
+ 
+
+ align:start position:0%
+the spin we know this is true because
+the Hamiltonian doesn't operate on spin
+
+ align:start position:0%
+the Hamiltonian doesn't operate on spin
+ 
+
+ align:start position:0%
+the Hamiltonian doesn't operate on spin
+it's a trivial result but it's a very
+
+ align:start position:0%
+it's a trivial result but it's a very
+ 
+
+ align:start position:0%
+it's a trivial result but it's a very
+important result ok so we have to worry
+
+ align:start position:0%
+important result ok so we have to worry
+ 
+
+ align:start position:0%
+important result ok so we have to worry
+about spin and spin eigenstates and
+
+ align:start position:0%
+about spin and spin eigenstates and
+ 
+
+ align:start position:0%
+about spin and spin eigenstates and
+other things like that
+
+ align:start position:0%
+other things like that
+ 
+
+ align:start position:0%
+other things like that
+okay so Slater determines Jacey Slater
+
+ align:start position:0%
+okay so Slater determines Jacey Slater
+ 
+
+ align:start position:0%
+okay so Slater determines Jacey Slater
+was an MIT professor in physics he
+
+ align:start position:0%
+was an MIT professor in physics he
+ 
+
+ align:start position:0%
+was an MIT professor in physics he
+invented these things in 1929 I have a
+
+ align:start position:0%
+invented these things in 1929 I have a
+ 
+
+ align:start position:0%
+invented these things in 1929 I have a
+reference I I don't know if I've ever
+
+ align:start position:0%
+reference I I don't know if I've ever
+ 
+
+ align:start position:0%
+reference I I don't know if I've ever
+read this paper but it it's probably
+
+ align:start position:0%
+read this paper but it it's probably
+ 
+
+ align:start position:0%
+read this paper but it it's probably
+beautiful so basically what Slater did
+
+ align:start position:0%
+beautiful so basically what Slater did
+ 
+
+ align:start position:0%
+beautiful so basically what Slater did
+is showed yeah you can you can do the
+
+ align:start position:0%
+is showed yeah you can you can do the
+ 
+
+ align:start position:0%
+is showed yeah you can you can do the
+necessary algebra to deal with any atom
+
+ align:start position:0%
+necessary algebra to deal with any atom
+ 
+
+ align:start position:0%
+necessary algebra to deal with any atom
+and to be able to reduce an atom to a
+
+ align:start position:0%
+and to be able to reduce an atom to a
+ 
+
+ align:start position:0%
+and to be able to reduce an atom to a
+small number of integrals do you really
+
+ align:start position:0%
+small number of integrals do you really
+ 
+
+ align:start position:0%
+small number of integrals do you really
+care about and there are two ways of
+
+ align:start position:0%
+care about and there are two ways of
+ 
+
+ align:start position:0%
+care about and there are two ways of
+doing this one is the truth and when
+
+ align:start position:0%
+doing this one is the truth and when
+ 
+
+ align:start position:0%
+doing this one is the truth and when
+it's a fit model now the truth
+
+ align:start position:0%
+it's a fit model now the truth
+ 
+
+ align:start position:0%
+it's a fit model now the truth
+is really boring because you lose all
+
+ align:start position:0%
+is really boring because you lose all
+ 
+
+ align:start position:0%
+is really boring because you lose all
+the insights and the fit model this
+
+ align:start position:0%
+the insights and the fit model this
+ 
+
+ align:start position:0%
+the insights and the fit model this
+gives you the things you have to think
+
+ align:start position:0%
+gives you the things you have to think
+ 
+
+ align:start position:0%
+gives you the things you have to think
+about and understand and a fit model
+
+ align:start position:0%
+about and understand and a fit model
+ 
+
+ align:start position:0%
+about and understand and a fit model
+also tells you what are the important
+
+ align:start position:0%
+also tells you what are the important
+ 
+
+ align:start position:0%
+also tells you what are the important
+actors and maybe they're in costume
+
+ align:start position:0%
+actors and maybe they're in costume
+ 
+
+ align:start position:0%
+actors and maybe they're in costume
+maybe they're not but you know we can we
+
+ align:start position:0%
+maybe they're not but you know we can we
+ 
+
+ align:start position:0%
+maybe they're not but you know we can we
+can deal with them but the truth is
+
+ align:start position:0%
+can deal with them but the truth is
+ 
+
+ align:start position:0%
+can deal with them but the truth is
+really very complicated and as I said
+
+ align:start position:0%
+really very complicated and as I said
+ 
+
+ align:start position:0%
+really very complicated and as I said
+many times when you go from hydrogen to
+
+ align:start position:0%
+many times when you go from hydrogen to
+ 
+
+ align:start position:0%
+many times when you go from hydrogen to
+helium you can't solve the shorter
+
+ align:start position:0%
+helium you can't solve the shorter
+ 
+
+ align:start position:0%
+helium you can't solve the shorter
+equation exactly this was a this was
+
+ align:start position:0%
+equation exactly this was a this was
+ 
+
+ align:start position:0%
+equation exactly this was a this was
+perhaps a little bit of a surprise but I
+
+ align:start position:0%
+perhaps a little bit of a surprise but I
+ 
+
+ align:start position:0%
+perhaps a little bit of a surprise but I
+think it was only surprising newspapers
+
+ align:start position:0%
+think it was only surprising newspapers
+ 
+
+ align:start position:0%
+think it was only surprising newspapers
+I think physicists knew immediately when
+
+ align:start position:0%
+I think physicists knew immediately when
+ 
+
+ align:start position:0%
+I think physicists knew immediately when
+you go from a two-body problem to a
+
+ align:start position:0%
+you go from a two-body problem to a
+ 
+
+ align:start position:0%
+you go from a two-body problem to a
+three-body problem there is no way you
+
+ align:start position:0%
+three-body problem there is no way you
+ 
+
+ align:start position:0%
+three-body problem there is no way you
+can have an exact solution and that's
+
+ align:start position:0%
+can have an exact solution and that's
+ 
+
+ align:start position:0%
+can have an exact solution and that's
+the truth you can't solve helium or any
+
+ align:start position:0%
+the truth you can't solve helium or any
+ 
+
+ align:start position:0%
+the truth you can't solve helium or any
+more than one electron problem exactly
+
+ align:start position:0%
+more than one electron problem exactly
+ 
+
+ align:start position:0%
+more than one electron problem exactly
+but you can do really well and it just
+
+ align:start position:0%
+but you can do really well and it just
+ 
+
+ align:start position:0%
+but you can do really well and it just
+cost computer time and if the computer
+
+ align:start position:0%
+cost computer time and if the computer
+ 
+
+ align:start position:0%
+cost computer time and if the computer
+is doing the work you don't really care
+
+ align:start position:0%
+is doing the work you don't really care
+ 
+
+ align:start position:0%
+is doing the work you don't really care
+because once you've told the computer
+
+ align:start position:0%
+because once you've told the computer
+ 
+
+ align:start position:0%
+because once you've told the computer
+the rules then it's off to the races you
+
+ align:start position:0%
+the rules then it's off to the races you
+ 
+
+ align:start position:0%
+the rules then it's off to the races you
+can go have lunch or you can go have a
+
+ align:start position:0%
+can go have lunch or you can go have a
+ 
+
+ align:start position:0%
+can go have lunch or you can go have a
+life and come back and and the computer
+
+ align:start position:0%
+life and come back and and the computer
+ 
+
+ align:start position:0%
+life and come back and and the computer
+will tell you whether you made a mistake
+
+ align:start position:0%
+will tell you whether you made a mistake
+ 
+
+ align:start position:0%
+will tell you whether you made a mistake
+and you're getting a nonsense result or
+
+ align:start position:0%
+and you're getting a nonsense result or
+ 
+
+ align:start position:0%
+and you're getting a nonsense result or
+that you have the correct result okay so
+
+ align:start position:0%
+that you have the correct result okay so
+ 
+
+ align:start position:0%
+that you have the correct result okay so
+what we know is this permutation
+
+ align:start position:0%
+what we know is this permutation
+ 
+
+ align:start position:0%
+what we know is this permutation
+operator operating on any two electron
+
+ align:start position:0%
+operator operating on any two electron
+ 
+
+ align:start position:0%
+operator operating on any two electron
+function has to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm skipping steps and I've I I
+
+ align:start position:0%
+okay I'm skipping steps and I've I I
+ 
+
+ align:start position:0%
+okay I'm skipping steps and I've I I
+know it's a really kind of stupid
+
+ align:start position:0%
+know it's a really kind of stupid
+ 
+
+ align:start position:0%
+know it's a really kind of stupid
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+p21 which has to be equal to - okay
+
+ align:start position:0%
+p21 which has to be equal to - okay
+ 
+
+ align:start position:0%
+p21 which has to be equal to - okay
+that's that's and now if you fly the
+
+ align:start position:0%
+that's that's and now if you fly the
+ 
+
+ align:start position:0%
+that's that's and now if you fly the
+permutation operator twice you get back
+
+ align:start position:0%
+permutation operator twice you get back
+ 
+
+ align:start position:0%
+permutation operator twice you get back
+to the same thing so there's only two
+
+ align:start position:0%
+to the same thing so there's only two
+ 
+
+ align:start position:0%
+to the same thing so there's only two
+possible eigenvalues you can have minus
+
+ align:start position:0%
+possible eigenvalues you can have minus
+ 
+
+ align:start position:0%
+possible eigenvalues you can have minus
+1 or plus 1 and the minus 1 corresponds
+
+ align:start position:0%
+1 or plus 1 and the minus 1 corresponds
+ 
+
+ align:start position:0%
+1 or plus 1 and the minus 1 corresponds
+to fermions things that have
+
+ align:start position:0%
+to fermions things that have
+ 
+
+ align:start position:0%
+to fermions things that have
+half-integer spin like electrons and the
+
+ align:start position:0%
+half-integer spin like electrons and the
+ 
+
+ align:start position:0%
+half-integer spin like electrons and the
+plus 1 head of course - such things that
+
+ align:start position:0%
+plus 1 head of course - such things that
+ 
+
+ align:start position:0%
+plus 1 head of course - such things that
+have integer spin like photons and
+
+ align:start position:0%
+have integer spin like photons and
+ 
+
+ align:start position:0%
+have integer spin like photons and
+vibrance and other things and actually
+
+ align:start position:0%
+vibrance and other things and actually
+ 
+
+ align:start position:0%
+vibrance and other things and actually
+it's harder to construct a symmetric
+
+ align:start position:0%
+it's harder to construct a symmetric
+ 
+
+ align:start position:0%
+it's harder to construct a symmetric
+function than an anti-symmetric function
+
+ align:start position:0%
+function than an anti-symmetric function
+ 
+
+ align:start position:0%
+function than an anti-symmetric function
+but the thing is you've got lots of
+
+ align:start position:0%
+but the thing is you've got lots of
+ 
+
+ align:start position:0%
+but the thing is you've got lots of
+electrons and you have very few quanta
+
+ align:start position:0%
+electrons and you have very few quanta
+ 
+
+ align:start position:0%
+electrons and you have very few quanta
+of vibrations in a single mode and you
+
+ align:start position:0%
+of vibrations in a single mode and you
+ 
+
+ align:start position:0%
+of vibrations in a single mode and you
+have very few photons interacting with a
+
+ align:start position:0%
+have very few photons interacting with a
+ 
+
+ align:start position:0%
+have very few photons interacting with a
+molecule at once and so the symmetry of
+
+ align:start position:0%
+molecule at once and so the symmetry of
+ 
+
+ align:start position:0%
+molecule at once and so the symmetry of
+the cement of the the boson symmetry is
+
+ align:start position:0%
+the cement of the the boson symmetry is
+ 
+
+ align:start position:0%
+the cement of the the boson symmetry is
+less important in most applications and
+
+ align:start position:0%
+less important in most applications and
+ 
+
+ align:start position:0%
+less important in most applications and
+so we just have to kill this one ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose we want to talk about
+
+ align:start position:0%
+so suppose we want to talk about
+ 
+
+ align:start position:0%
+so suppose we want to talk about
+something like this the 1 s 2 s
+
+ align:start position:0%
+something like this the 1 s 2 s
+ 
+
+ align:start position:0%
+something like this the 1 s 2 s
+configuration a configuration is the
+
+ align:start position:0%
+configuration a configuration is the
+ 
+
+ align:start position:0%
+configuration a configuration is the
+list of the occupied orbitals not the
+
+ align:start position:0%
+list of the occupied orbitals not the
+ 
+
+ align:start position:0%
+list of the occupied orbitals not the
+occupied spin orbitals which is a spin
+
+ align:start position:0%
+occupied spin orbitals which is a spin
+ 
+
+ align:start position:0%
+occupied spin orbitals which is a spin
+associated with an orbital which is what
+
+ align:start position:0%
+associated with an orbital which is what
+ 
+
+ align:start position:0%
+associated with an orbital which is what
+I the world of spin orbitals is where I
+
+ align:start position:0%
+I the world of spin orbitals is where I
+ 
+
+ align:start position:0%
+I the world of spin orbitals is where I
+live
+
+ align:start position:0%
+live
+ 
+
+ align:start position:0%
+live
+but we we do that for a reason okay and
+
+ align:start position:0%
+but we we do that for a reason okay and
+ 
+
+ align:start position:0%
+but we we do that for a reason okay and
+so this 2 electron thing can be
+
+ align:start position:0%
+so this 2 electron thing can be
+ 
+
+ align:start position:0%
+so this 2 electron thing can be
+expressed as a space part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are various conventions that I'm
+
+ align:start position:0%
+there are various conventions that I'm
+ 
+
+ align:start position:0%
+there are various conventions that I'm
+just been part and alpha 1 beta 2 and
+
+ align:start position:0%
+just been part and alpha 1 beta 2 and
+ 
+
+ align:start position:0%
+just been part and alpha 1 beta 2 and
+then we have minus or plus there you
+
+ align:start position:0%
+then we have minus or plus there you
+ 
+
+ align:start position:0%
+then we have minus or plus there you
+know 1 alpha 2 I'm looking at my notes
+
+ align:start position:0%
+know 1 alpha 2 I'm looking at my notes
+ 
+
+ align:start position:0%
+know 1 alpha 2 I'm looking at my notes
+because some people always can keep the
+
+ align:start position:0%
+because some people always can keep the
+ 
+
+ align:start position:0%
+because some people always can keep the
+electron in the first position and some
+
+ align:start position:0%
+electron in the first position and some
+ 
+
+ align:start position:0%
+electron in the first position and some
+people keep always this the the orbital
+
+ align:start position:0%
+people keep always this the the orbital
+ 
+
+ align:start position:0%
+people keep always this the the orbital
+in the first position and it doesn't
+
+ align:start position:0%
+in the first position and it doesn't
+ 
+
+ align:start position:0%
+in the first position and it doesn't
+matter because you can you can permute
+
+ align:start position:0%
+matter because you can you can permute
+ 
+
+ align:start position:0%
+matter because you can you can permute
+REOs or columns but i just want to write
+
+ align:start position:0%
+REOs or columns but i just want to write
+ 
+
+ align:start position:0%
+REOs or columns but i just want to write
+what is in my notes okay so this thing
+
+ align:start position:0%
+what is in my notes okay so this thing
+ 
+
+ align:start position:0%
+what is in my notes okay so this thing
+this two electron function has two has
+
+ align:start position:0%
+this two electron function has two has
+ 
+
+ align:start position:0%
+this two electron function has two has
+two anti symmetrized possibilities and
+
+ align:start position:0%
+two anti symmetrized possibilities and
+ 
+
+ align:start position:0%
+two anti symmetrized possibilities and
+one is a singlet and one is a triplet so
+
+ align:start position:0%
+one is a singlet and one is a triplet so
+ 
+
+ align:start position:0%
+one is a singlet and one is a triplet so
+s equals 0 s equals 1 we recognize this
+
+ align:start position:0%
+s equals 0 s equals 1 we recognize this
+ 
+
+ align:start position:0%
+s equals 0 s equals 1 we recognize this
+alpha beta minus beta alpha as the
+
+ align:start position:0%
+alpha beta minus beta alpha as the
+ 
+
+ align:start position:0%
+alpha beta minus beta alpha as the
+singlet spin state and alpha beta plus
+
+ align:start position:0%
+singlet spin state and alpha beta plus
+ 
+
+ align:start position:0%
+singlet spin state and alpha beta plus
+beta alpha as the triplets in state so
+
+ align:start position:0%
+beta alpha as the triplets in state so
+ 
+
+ align:start position:0%
+beta alpha as the triplets in state so
+we have alpha beta plus beta alpha and
+
+ align:start position:0%
+we have alpha beta plus beta alpha and
+ 
+
+ align:start position:0%
+we have alpha beta plus beta alpha and
+alpha alpha and beta beta and we have
+
+ align:start position:0%
+alpha alpha and beta beta and we have
+ 
+
+ align:start position:0%
+alpha alpha and beta beta and we have
+alpha beta minus beta alpha so we call s
+
+ align:start position:0%
+alpha beta minus beta alpha so we call s
+ 
+
+ align:start position:0%
+alpha beta minus beta alpha so we call s
+equals 0 a singlet and this a triplet
+
+ align:start position:0%
+equals 0 a singlet and this a triplet
+ 
+
+ align:start position:0%
+equals 0 a singlet and this a triplet
+because of the number of states and this
+
+ align:start position:0%
+because of the number of states and this
+ 
+
+ align:start position:0%
+because of the number of states and this
+wave function has as the necessary spin
+
+ align:start position:0%
+wave function has as the necessary spin
+ 
+
+ align:start position:0%
+wave function has as the necessary spin
+symmetry and the necessary permutation
+
+ align:start position:0%
+symmetry and the necessary permutation
+ 
+
+ align:start position:0%
+symmetry and the necessary permutation
+symmetry ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if instead of two electrons we have
+
+ align:start position:0%
+so if instead of two electrons we have
+ 
+
+ align:start position:0%
+so if instead of two electrons we have
+1/2 n then mr. Slater says so that's a
+
+ align:start position:0%
+1/2 n then mr. Slater says so that's a
+ 
+
+ align:start position:0%
+1/2 n then mr. Slater says so that's a
+determinant and then by n determinant
+
+ align:start position:0%
+determinant and then by n determinant
+ 
+
+ align:start position:0%
+determinant and then by n determinant
+and the rows correspond to the electrons
+
+ align:start position:0%
+and the rows correspond to the electrons
+ 
+
+ align:start position:0%
+and the rows correspond to the electrons
+and the columns correspond to the
+
+ align:start position:0%
+and the columns correspond to the
+ 
+
+ align:start position:0%
+and the columns correspond to the
+orbitals now this because of the
+
+ align:start position:0%
+orbitals now this because of the
+ 
+
+ align:start position:0%
+orbitals now this because of the
+properties of a determinant at a is anti
+
+ align:start position:0%
+properties of a determinant at a is anti
+ 
+
+ align:start position:0%
+properties of a determinant at a is anti
+symmetric with respect to permutation of
+
+ align:start position:0%
+symmetric with respect to permutation of
+ 
+
+ align:start position:0%
+symmetric with respect to permutation of
+any two electrons or any two orbitals
+
+ align:start position:0%
+any two electrons or any two orbitals
+ 
+
+ align:start position:0%
+any two electrons or any two orbitals
+but we don't really care about the
+
+ align:start position:0%
+but we don't really care about the
+ 
+
+ align:start position:0%
+but we don't really care about the
+permutation of the orbitals because
+
+ align:start position:0%
+permutation of the orbitals because
+ 
+
+ align:start position:0%
+permutation of the orbitals because
+really the same thing as permutation and
+
+ align:start position:0%
+really the same thing as permutation and
+ 
+
+ align:start position:0%
+really the same thing as permutation and
+so this n factorial is a consequence of
+
+ align:start position:0%
+so this n factorial is a consequence of
+ 
+
+ align:start position:0%
+so this n factorial is a consequence of
+normalization because when you expand an
+
+ align:start position:0%
+normalization because when you expand an
+ 
+
+ align:start position:0%
+normalization because when you expand an
+N by n determinant you get n factorial
+
+ align:start position:0%
+N by n determinant you get n factorial
+ 
+
+ align:start position:0%
+N by n determinant you get n factorial
+additive products of n functions looks
+
+ align:start position:0%
+additive products of n functions looks
+ 
+
+ align:start position:0%
+additive products of n functions looks
+horrible and because we're normalizing
+
+ align:start position:0%
+horrible and because we're normalizing
+ 
+
+ align:start position:0%
+horrible and because we're normalizing
+we need this 1 over the square root of n
+
+ align:start position:0%
+we need this 1 over the square root of n
+ 
+
+ align:start position:0%
+we need this 1 over the square root of n
+factorial in order to have this thing
+
+ align:start position:0%
+factorial in order to have this thing
+ 
+
+ align:start position:0%
+factorial in order to have this thing
+come out to be 1 when you calculating
+
+ align:start position:0%
+come out to be 1 when you calculating
+ 
+
+ align:start position:0%
+come out to be 1 when you calculating
+the normalization integral okay now this
+
+ align:start position:0%
+the normalization integral okay now this
+ 
+
+ align:start position:0%
+the normalization integral okay now this
+notation is horrible because you've got
+
+ align:start position:0%
+notation is horrible because you've got
+ 
+
+ align:start position:0%
+notation is horrible because you've got
+too many symbols and so depending on
+
+ align:start position:0%
+too many symbols and so depending on
+ 
+
+ align:start position:0%
+too many symbols and so depending on
+what you're trying to convey you reduce
+
+ align:start position:0%
+what you're trying to convey you reduce
+ 
+
+ align:start position:0%
+what you're trying to convey you reduce
+the symbols and you can reduce it simply
+
+ align:start position:0%
+the symbols and you can reduce it simply
+ 
+
+ align:start position:0%
+the symbols and you can reduce it simply
+by instead of writing sy every time just
+
+ align:start position:0%
+by instead of writing sy every time just
+ 
+
+ align:start position:0%
+by instead of writing sy every time just
+writing the state or you can it since
+
+ align:start position:0%
+writing the state or you can it since
+ 
+
+ align:start position:0%
+writing the state or you can it since
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you don't need to sigh you don't need
+
+ align:start position:0%
+you don't need to sigh you don't need
+ 
+
+ align:start position:0%
+you don't need to sigh you don't need
+the state letter you can just have the
+
+ align:start position:0%
+the state letter you can just have the
+ 
+
+ align:start position:0%
+the state letter you can just have the
+state number and but the best way to do
+
+ align:start position:0%
+state number and but the best way to do
+ 
+
+ align:start position:0%
+state number and but the best way to do
+this is simply to say this is just the
+
+ align:start position:0%
+this is simply to say this is just the
+ 
+
+ align:start position:0%
+this is simply to say this is just the
+main diagonal of the determinant it
+
+ align:start position:0%
+main diagonal of the determinant it
+ 
+
+ align:start position:0%
+main diagonal of the determinant it
+conveys everything you need
+
+ align:start position:0%
+conveys everything you need
+ 
+
+ align:start position:0%
+conveys everything you need
+again if you permute any two of these
+
+ align:start position:0%
+again if you permute any two of these
+ 
+
+ align:start position:0%
+again if you permute any two of these
+guys any adjacent pair the sign changes
+
+ align:start position:0%
+guys any adjacent pair the sign changes
+ 
+
+ align:start position:0%
+guys any adjacent pair the sign changes
+and it contains everything you need and
+
+ align:start position:0%
+and it contains everything you need and
+ 
+
+ align:start position:0%
+and it contains everything you need and
+it's and it doesn't require you to look
+
+ align:start position:0%
+it's and it doesn't require you to look
+ 
+
+ align:start position:0%
+it's and it doesn't require you to look
+at stuff you're not going to use and
+
+ align:start position:0%
+at stuff you're not going to use and
+ 
+
+ align:start position:0%
+at stuff you're not going to use and
+your goal is going to be to take these
+
+ align:start position:0%
+your goal is going to be to take these
+ 
+
+ align:start position:0%
+your goal is going to be to take these
+things and calculate matrix of of them
+
+ align:start position:0%
+things and calculate matrix of of them
+ 
+
+ align:start position:0%
+things and calculate matrix of of them
+and so you'll be dealing with the
+
+ align:start position:0%
+and so you'll be dealing with the
+ 
+
+ align:start position:0%
+and so you'll be dealing with the
+orbitals one or two at a time
+
+ align:start position:0%
+orbitals one or two at a time
+ 
+
+ align:start position:0%
+orbitals one or two at a time
+and this is very convenient and soon you
+
+ align:start position:0%
+and this is very convenient and soon you
+ 
+
+ align:start position:0%
+and this is very convenient and soon you
+start to take this forever granted that
+
+ align:start position:0%
+start to take this forever granted that
+ 
+
+ align:start position:0%
+start to take this forever granted that
+it's a very simple thing but it isn't
+
+ align:start position:0%
+it's a very simple thing but it isn't
+ 
+
+ align:start position:0%
+it's a very simple thing but it isn't
+because you're doing a huge number of
+
+ align:start position:0%
+because you're doing a huge number of
+ 
+
+ align:start position:0%
+because you're doing a huge number of
+tricks okay I'm going to skip over
+
+ align:start position:0%
+tricks okay I'm going to skip over
+ 
+
+ align:start position:0%
+tricks okay I'm going to skip over
+what's in my notes demonstrating that
+
+ align:start position:0%
+what's in my notes demonstrating that
+ 
+
+ align:start position:0%
+what's in my notes demonstrating that
+for a two-by-two that what I asserted is
+
+ align:start position:0%
+for a two-by-two that what I asserted is
+ 
+
+ align:start position:0%
+for a two-by-two that what I asserted is
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+you can do that very easily and so okay
+
+ align:start position:0%
+you can do that very easily and so okay
+ 
+
+ align:start position:0%
+you can do that very easily and so okay
+so we can count and we have an atom and
+
+ align:start position:0%
+so we can count and we have an atom and
+ 
+
+ align:start position:0%
+so we can count and we have an atom and
+we know how many electrons it has and so
+
+ align:start position:0%
+we know how many electrons it has and so
+ 
+
+ align:start position:0%
+we know how many electrons it has and so
+we immediately know what our job is
+
+ align:start position:0%
+we immediately know what our job is
+ 
+
+ align:start position:0%
+we immediately know what our job is
+going to be we're going to be having to
+
+ align:start position:0%
+going to be we're going to be having to
+ 
+
+ align:start position:0%
+going to be we're going to be having to
+write some Slater determinant of those
+
+ align:start position:0%
+write some Slater determinant of those
+ 
+
+ align:start position:0%
+write some Slater determinant of those
+number of electrons and the goal is to
+
+ align:start position:0%
+number of electrons and the goal is to
+ 
+
+ align:start position:0%
+number of electrons and the goal is to
+be able to do the algebra in a way that
+
+ align:start position:0%
+be able to do the algebra in a way that
+ 
+
+ align:start position:0%
+be able to do the algebra in a way that
+maybe you can't describe to your friends
+
+ align:start position:0%
+maybe you can't describe to your friends
+ 
+
+ align:start position:0%
+maybe you can't describe to your friends
+because it's too complicated I'm faced
+
+ align:start position:0%
+because it's too complicated I'm faced
+ 
+
+ align:start position:0%
+because it's too complicated I'm faced
+with the the the problem of trying to
+
+ align:start position:0%
+with the the the problem of trying to
+ 
+
+ align:start position:0%
+with the the the problem of trying to
+explain how to do this algebra but it is
+
+ align:start position:0%
+explain how to do this algebra but it is
+ 
+
+ align:start position:0%
+explain how to do this algebra but it is
+something that you can learn and you
+
+ align:start position:0%
+something that you can learn and you
+ 
+
+ align:start position:0%
+something that you can learn and you
+can't add ask a computer to do it and
+
+ align:start position:0%
+can't add ask a computer to do it and
+ 
+
+ align:start position:0%
+can't add ask a computer to do it and
+there are all sorts of intuitive
+
+ align:start position:0%
+there are all sorts of intuitive
+ 
+
+ align:start position:0%
+there are all sorts of intuitive
+shortcuts
+
+ align:start position:0%
+shortcuts
+ 
+
+ align:start position:0%
+shortcuts
+you can look at a problem and you could
+
+ align:start position:0%
+you can look at a problem and you could
+ 
+
+ align:start position:0%
+you can look at a problem and you could
+say yeah I understand okay so you're
+
+ align:start position:0%
+say yeah I understand okay so you're
+ 
+
+ align:start position:0%
+say yeah I understand okay so you're
+used to orbitals and it's perfectly
+
+ align:start position:0%
+used to orbitals and it's perfectly
+ 
+
+ align:start position:0%
+used to orbitals and it's perfectly
+reasonable because for hydrogen we have
+
+ align:start position:0%
+reasonable because for hydrogen we have
+ 
+
+ align:start position:0%
+reasonable because for hydrogen we have
+orbitals and there's only one orbital
+
+ align:start position:0%
+orbitals and there's only one orbital
+ 
+
+ align:start position:0%
+orbitals and there's only one orbital
+and it could have either spin we don't
+
+ align:start position:0%
+and it could have either spin we don't
+ 
+
+ align:start position:0%
+and it could have either spin we don't
+mess with that now we're going to talk
+
+ align:start position:0%
+mess with that now we're going to talk
+ 
+
+ align:start position:0%
+mess with that now we're going to talk
+about spindles and that's just the
+
+ align:start position:0%
+about spindles and that's just the
+ 
+
+ align:start position:0%
+about spindles and that's just the
+combination of the name of the orbital
+
+ align:start position:0%
+combination of the name of the orbital
+ 
+
+ align:start position:0%
+combination of the name of the orbital
+with whether the spin is up or down and
+
+ align:start position:0%
+with whether the spin is up or down and
+ 
+
+ align:start position:0%
+with whether the spin is up or down and
+the reason for this is it's easier to do
+
+ align:start position:0%
+the reason for this is it's easier to do
+ 
+
+ align:start position:0%
+the reason for this is it's easier to do
+the algebra and the reason the algebra
+
+ align:start position:0%
+the algebra and the reason the algebra
+ 
+
+ align:start position:0%
+the algebra and the reason the algebra
+is it's initially harder to do the
+
+ align:start position:0%
+is it's initially harder to do the
+ 
+
+ align:start position:0%
+is it's initially harder to do the
+algebra because there certainly certain
+
+ align:start position:0%
+algebra because there certainly certain
+ 
+
+ align:start position:0%
+algebra because there certainly certain
+selection rules and stuff like that but
+
+ align:start position:0%
+selection rules and stuff like that but
+ 
+
+ align:start position:0%
+selection rules and stuff like that but
+once you know how to do it you do the
+
+ align:start position:0%
+once you know how to do it you do the
+ 
+
+ align:start position:0%
+once you know how to do it you do the
+algebra and then all of a sudden
+
+ align:start position:0%
+algebra and then all of a sudden
+ 
+
+ align:start position:0%
+algebra and then all of a sudden
+everything pops out in a very useful
+
+ align:start position:0%
+everything pops out in a very useful
+ 
+
+ align:start position:0%
+everything pops out in a very useful
+form okay so the stick diagrams are very
+
+ align:start position:0%
+form okay so the stick diagrams are very
+ 
+
+ align:start position:0%
+form okay so the stick diagrams are very
+important but now I'm specifying the
+
+ align:start position:0%
+important but now I'm specifying the
+ 
+
+ align:start position:0%
+important but now I'm specifying the
+stick diagrams as spin orbitals rather
+
+ align:start position:0%
+stick diagrams as spin orbitals rather
+ 
+
+ align:start position:0%
+stick diagrams as spin orbitals rather
+than orbitals now another point there
+
+ align:start position:0%
+than orbitals now another point there
+ 
+
+ align:start position:0%
+than orbitals now another point there
+are rules for how so we the number of
+
+ align:start position:0%
+are rules for how so we the number of
+ 
+
+ align:start position:0%
+are rules for how so we the number of
+spin orbitals different between the left
+
+ align:start position:0%
+spin orbitals different between the left
+ 
+
+ align:start position:0%
+spin orbitals different between the left
+hand side and the right hand side of a
+
+ align:start position:0%
+hand side and the right hand side of a
+ 
+
+ align:start position:0%
+hand side and the right hand side of a
+matrix element there are rules that are
+
+ align:start position:0%
+matrix element there are rules that are
+ 
+
+ align:start position:0%
+matrix element there are rules that are
+easily described and so for every kind
+
+ align:start position:0%
+easily described and so for every kind
+ 
+
+ align:start position:0%
+easily described and so for every kind
+of orbital an orbital that has that is a
+
+ align:start position:0%
+of orbital an orbital that has that is a
+ 
+
+ align:start position:0%
+of orbital an orbital that has that is a
+scalar that doesn't doesn't depend on
+
+ align:start position:0%
+scalar that doesn't doesn't depend on
+ 
+
+ align:start position:0%
+scalar that doesn't doesn't depend on
+quantum numbers that has a selectable
+
+ align:start position:0%
+quantum numbers that has a selectable
+ 
+
+ align:start position:0%
+quantum numbers that has a selectable
+Delta a so of 0 and for something like a
+
+ align:start position:0%
+Delta a so of 0 and for something like a
+ 
+
+ align:start position:0%
+Delta a so of 0 and for something like a
+one electron operator that has a
+
+ align:start position:0%
+one electron operator that has a
+ 
+
+ align:start position:0%
+one electron operator that has a
+selection rule Delta at spin orbit of
+
+ align:start position:0%
+selection rule Delta at spin orbit of
+ 
+
+ align:start position:0%
+selection rule Delta at spin orbit of
+spin orbital of 1 and 0 and then we have
+
+ align:start position:0%
+spin orbital of 1 and 0 and then we have
+ 
+
+ align:start position:0%
+spin orbital of 1 and 0 and then we have
+our friend 1 over R IJ that has a
+
+ align:start position:0%
+our friend 1 over R IJ that has a
+ 
+
+ align:start position:0%
+our friend 1 over R IJ that has a
+selection rule Delta spin orbital of 2 1
+
+ align:start position:0%
+selection rule Delta spin orbital of 2 1
+ 
+
+ align:start position:0%
+selection rule Delta spin orbital of 2 1
+and 0 and the
+
+ align:start position:0%
+and 0 and the
+ 
+
+ align:start position:0%
+and 0 and the
+for each something you work out and then
+
+ align:start position:0%
+for each something you work out and then
+ 
+
+ align:start position:0%
+for each something you work out and then
+you know how to do it and I'm going to
+
+ align:start position:0%
+you know how to do it and I'm going to
+ 
+
+ align:start position:0%
+you know how to do it and I'm going to
+try to give you just a little bit of a
+
+ align:start position:0%
+try to give you just a little bit of a
+ 
+
+ align:start position:0%
+try to give you just a little bit of a
+taste of this okay so we've already
+
+ align:start position:0%
+taste of this okay so we've already
+ 
+
+ align:start position:0%
+taste of this okay so we've already
+looked at something like this but we did
+
+ align:start position:0%
+looked at something like this but we did
+ 
+
+ align:start position:0%
+looked at something like this but we did
+we use a slightly different notation so
+
+ align:start position:0%
+we use a slightly different notation so
+ 
+
+ align:start position:0%
+we use a slightly different notation so
+I'm going to go back and we have 1s
+
+ align:start position:0%
+I'm going to go back and we have 1s
+ 
+
+ align:start position:0%
+I'm going to go back and we have 1s
+alpha 1 s beta 2 s alpha 2 s beta and so
+
+ align:start position:0%
+alpha 1 s beta 2 s alpha 2 s beta and so
+ 
+
+ align:start position:0%
+alpha 1 s beta 2 s alpha 2 s beta and so
+for the ground state of helium 1 s
+
+ align:start position:0%
+for the ground state of helium 1 s
+ 
+
+ align:start position:0%
+for the ground state of helium 1 s
+squared and we would do this and I mean
+
+ align:start position:0%
+squared and we would do this and I mean
+ 
+
+ align:start position:0%
+squared and we would do this and I mean
+the stick diagrams are great because
+
+ align:start position:0%
+the stick diagrams are great because
+ 
+
+ align:start position:0%
+the stick diagrams are great because
+it's it's easier to see on a picture
+
+ align:start position:0%
+it's it's easier to see on a picture
+ 
+
+ align:start position:0%
+it's it's easier to see on a picture
+what are the weather who are the actors
+
+ align:start position:0%
+what are the weather who are the actors
+ 
+
+ align:start position:0%
+what are the weather who are the actors
+in have I am I included all of them or
+
+ align:start position:0%
+in have I am I included all of them or
+ 
+
+ align:start position:0%
+in have I am I included all of them or
+if I'm left something out and so now we
+
+ align:start position:0%
+if I'm left something out and so now we
+ 
+
+ align:start position:0%
+if I'm left something out and so now we
+were interested in the stick diagram for
+
+ align:start position:0%
+were interested in the stick diagram for
+ 
+
+ align:start position:0%
+were interested in the stick diagram for
+the 1 s 2 s configuration and there are
+
+ align:start position:0%
+the 1 s 2 s configuration and there are
+ 
+
+ align:start position:0%
+the 1 s 2 s configuration and there are
+several kinds of 1 s 2 s configurations
+
+ align:start position:0%
+several kinds of 1 s 2 s configurations
+ 
+
+ align:start position:0%
+several kinds of 1 s 2 s configurations
+depending on what the alpha beta are so
+
+ align:start position:0%
+depending on what the alpha beta are so
+ 
+
+ align:start position:0%
+depending on what the alpha beta are so
+we have 1 s alpha 2 s alpha and we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 s alpha 2 s beta 1 s beta 2 s alpha 2
+
+ align:start position:0%
+1 s alpha 2 s beta 1 s beta 2 s alpha 2
+ 
+
+ align:start position:0%
+1 s alpha 2 s beta 1 s beta 2 s alpha 2
+s alpha minus beta 2 s data so there's
+
+ align:start position:0%
+s alpha minus beta 2 s data so there's
+ 
+
+ align:start position:0%
+s alpha minus beta 2 s data so there's
+four guys and we can put our arrows on
+
+ align:start position:0%
+four guys and we can put our arrows on
+ 
+
+ align:start position:0%
+four guys and we can put our arrows on
+these things and we we know everything
+
+ align:start position:0%
+these things and we we know everything
+ 
+
+ align:start position:0%
+these things and we we know everything
+we need to know about these guys we
+
+ align:start position:0%
+we need to know about these guys we
+ 
+
+ align:start position:0%
+we need to know about these guys we
+tells us what to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well when we do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the diagonal matrix elements of the
+
+ align:start position:0%
+the diagonal matrix elements of the
+ 
+
+ align:start position:0%
+the diagonal matrix elements of the
+Hamiltonian the one over R IJ
+
+ align:start position:0%
+Hamiltonian the one over R IJ
+ 
+
+ align:start position:0%
+Hamiltonian the one over R IJ
+Hamiltonian can be expressed and we use
+
+ align:start position:0%
+Hamiltonian can be expressed and we use
+ 
+
+ align:start position:0%
+Hamiltonian can be expressed and we use
+this notation J tilde minus K tilde so
+
+ align:start position:0%
+this notation J tilde minus K tilde so
+ 
+
+ align:start position:0%
+this notation J tilde minus K tilde so
+for every two-electron thing we're going
+
+ align:start position:0%
+for every two-electron thing we're going
+ 
+
+ align:start position:0%
+for every two-electron thing we're going
+to get this kind of now these are simple
+
+ align:start position:0%
+to get this kind of now these are simple
+ 
+
+ align:start position:0%
+to get this kind of now these are simple
+integrals and some of them are zero
+
+ align:start position:0%
+integrals and some of them are zero
+ 
+
+ align:start position:0%
+integrals and some of them are zero
+because this doesn't operate on spins
+
+ align:start position:0%
+because this doesn't operate on spins
+ 
+
+ align:start position:0%
+because this doesn't operate on spins
+and so the if you if you had a 1s alpha
+
+ align:start position:0%
+and so the if you if you had a 1s alpha
+ 
+
+ align:start position:0%
+and so the if you if you had a 1s alpha
+2 s beta 1 R IJ 1 s beta 2 s alpha then
+
+ align:start position:0%
+2 s beta 1 R IJ 1 s beta 2 s alpha then
+ 
+
+ align:start position:0%
+2 s beta 1 R IJ 1 s beta 2 s alpha then
+the 1s alpha with the one s beta is 0
+
+ align:start position:0%
+the 1s alpha with the one s beta is 0
+ 
+
+ align:start position:0%
+the 1s alpha with the one s beta is 0
+the 1s alpha with the 2's alpha is not 0
+
+ align:start position:0%
+the 1s alpha with the 2's alpha is not 0
+ 
+
+ align:start position:0%
+the 1s alpha with the 2's alpha is not 0
+etc there are all sorts of stuff but
+
+ align:start position:0%
+etc there are all sorts of stuff but
+ 
+
+ align:start position:0%
+etc there are all sorts of stuff but
+this tilde notation says well this is
+
+ align:start position:0%
+this tilde notation says well this is
+ 
+
+ align:start position:0%
+this tilde notation says well this is
+what we start with and we have to
+
+ align:start position:0%
+what we start with and we have to
+ 
+
+ align:start position:0%
+what we start with and we have to
+convert it into things that really
+
+ align:start position:0%
+convert it into things that really
+ 
+
+ align:start position:0%
+convert it into things that really
+matter so the operation of removing the
+
+ align:start position:0%
+matter so the operation of removing the
+ 
+
+ align:start position:0%
+matter so the operation of removing the
+tilde requires a little bit of work a
+
+ align:start position:0%
+tilde requires a little bit of work a
+ 
+
+ align:start position:0%
+tilde requires a little bit of work a
+little bit of thought and that's why my
+
+ align:start position:0%
+little bit of thought and that's why my
+ 
+
+ align:start position:0%
+little bit of thought and that's why my
+notes are crafted because I can't
+
+ align:start position:0%
+notes are crafted because I can't
+ 
+
+ align:start position:0%
+notes are crafted because I can't
+explain it well enough to really teach
+
+ align:start position:0%
+explain it well enough to really teach
+ 
+
+ align:start position:0%
+explain it well enough to really teach
+this but let's just so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when when we do the 1 s squared the j1 s
+
+ align:start position:0%
+when when we do the 1 s squared the j1 s
+ 
+
+ align:start position:0%
+when when we do the 1 s squared the j1 s
+squared tilde is equal to the j1 s
+
+ align:start position:0%
+squared tilde is equal to the j1 s
+ 
+
+ align:start position:0%
+squared tilde is equal to the j1 s
+squared because the spins take care of
+
+ align:start position:0%
+squared because the spins take care of
+ 
+
+ align:start position:0%
+squared because the spins take care of
+themselves but K tilde 1 s squared is
+
+ align:start position:0%
+themselves but K tilde 1 s squared is
+ 
+
+ align:start position:0%
+themselves but K tilde 1 s squared is
+equal to 0 because we when we we do 1 s
+
+ align:start position:0%
+equal to 0 because we when we we do 1 s
+ 
+
+ align:start position:0%
+equal to 0 because we when we we do 1 s
+squared we have an alpha with an alpha
+
+ align:start position:0%
+squared we have an alpha with an alpha
+ 
+
+ align:start position:0%
+squared we have an alpha with an alpha
+for the J term and an alpha with the
+
+ align:start position:0%
+for the J term and an alpha with the
+ 
+
+ align:start position:0%
+for the J term and an alpha with the
+beta for the K term and alpha with beta
+
+ align:start position:0%
+beta for the K term and alpha with beta
+ 
+
+ align:start position:0%
+beta for the K term and alpha with beta
+is 0 because the operator cannot change
+
+ align:start position:0%
+is 0 because the operator cannot change
+ 
+
+ align:start position:0%
+is 0 because the operator cannot change
+alpha and two beta ok so but so this
+
+ align:start position:0%
+alpha and two beta ok so but so this
+ 
+
+ align:start position:0%
+alpha and two beta ok so but so this
+tilde notation is a convenient thing
+
+ align:start position:0%
+tilde notation is a convenient thing
+ 
+
+ align:start position:0%
+tilde notation is a convenient thing
+because you can use any Slater
+
+ align:start position:0%
+because you can use any Slater
+ 
+
+ align:start position:0%
+because you can use any Slater
+determinant and you can express it in
+
+ align:start position:0%
+determinant and you can express it in
+ 
+
+ align:start position:0%
+determinant and you can express it in
+terms of J's and KS and the sign comes
+
+ align:start position:0%
+terms of J's and KS and the sign comes
+ 
+
+ align:start position:0%
+terms of J's and KS and the sign comes
+from switching the order of the orbitals
+
+ align:start position:0%
+from switching the order of the orbitals
+ 
+
+ align:start position:0%
+from switching the order of the orbitals
+that's how the determinants work and and
+
+ align:start position:0%
+that's how the determinants work and and
+ 
+
+ align:start position:0%
+that's how the determinants work and and
+so you could your you're going to see a
+
+ align:start position:0%
+so you could your you're going to see a
+ 
+
+ align:start position:0%
+so you could your you're going to see a
+whole bunch of stuff but removing the
+
+ align:start position:0%
+whole bunch of stuff but removing the
+ 
+
+ align:start position:0%
+whole bunch of stuff but removing the
+tilde is the tricky business ok now when
+
+ align:start position:0%
+tilde is the tricky business ok now when
+ 
+
+ align:start position:0%
+tilde is the tricky business ok now when
+you get a problem where you have a
+
+ align:start position:0%
+you get a problem where you have a
+ 
+
+ align:start position:0%
+you get a problem where you have a
+configuration where a single Slater is
+
+ align:start position:0%
+configuration where a single Slater is
+ 
+
+ align:start position:0%
+configuration where a single Slater is
+not sufficient in other words in order
+
+ align:start position:0%
+not sufficient in other words in order
+ 
+
+ align:start position:0%
+not sufficient in other words in order
+to make an eigenstate of s squared or SZ
+
+ align:start position:0%
+to make an eigenstate of s squared or SZ
+ 
+
+ align:start position:0%
+to make an eigenstate of s squared or SZ
+you sometimes need two or more Slater's
+
+ align:start position:0%
+you sometimes need two or more Slater's
+ 
+
+ align:start position:0%
+you sometimes need two or more Slater's
+and you have to use a particular linear
+
+ align:start position:0%
+and you have to use a particular linear
+ 
+
+ align:start position:0%
+and you have to use a particular linear
+combination of them to get the right
+
+ align:start position:0%
+combination of them to get the right
+ 
+
+ align:start position:0%
+combination of them to get the right
+value of s and SC and then what happens
+
+ align:start position:0%
+value of s and SC and then what happens
+ 
+
+ align:start position:0%
+value of s and SC and then what happens
+is you're looking at matrix
+
+ align:start position:0%
+is you're looking at matrix
+ 
+
+ align:start position:0%
+is you're looking at matrix
+elements between of the 1 over RI J
+
+ align:start position:0%
+elements between of the 1 over RI J
+ 
+
+ align:start position:0%
+elements between of the 1 over RI J
+operator between Slater's now this is a
+
+ align:start position:0%
+operator between Slater's now this is a
+ 
+
+ align:start position:0%
+operator between Slater's now this is a
+headache and you know I could talk until
+
+ align:start position:0%
+headache and you know I could talk until
+ 
+
+ align:start position:0%
+headache and you know I could talk until
+I'm blue in the face and I cannot make
+
+ align:start position:0%
+I'm blue in the face and I cannot make
+ 
+
+ align:start position:0%
+I'm blue in the face and I cannot make
+it clear that how to do this because
+
+ align:start position:0%
+it clear that how to do this because
+ 
+
+ align:start position:0%
+it clear that how to do this because
+it's just awful but you know some things
+
+ align:start position:0%
+it's just awful but you know some things
+ 
+
+ align:start position:0%
+it's just awful but you know some things
+in life are worth suffering for and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway in the 1 s 2 s situation when you
+
+ align:start position:0%
+anyway in the 1 s 2 s situation when you
+ 
+
+ align:start position:0%
+anyway in the 1 s 2 s situation when you
+do everything right you get this is just
+
+ align:start position:0%
+do everything right you get this is just
+ 
+
+ align:start position:0%
+do everything right you get this is just
+a general notation for a 2 electron wave
+
+ align:start position:0%
+a general notation for a 2 electron wave
+ 
+
+ align:start position:0%
+a general notation for a 2 electron wave
+function 1 over R 1 to 2 so these guys
+
+ align:start position:0%
+function 1 over R 1 to 2 so these guys
+ 
+
+ align:start position:0%
+function 1 over R 1 to 2 so these guys
+are eigenfunctions of s squared of SC
+
+ align:start position:0%
+are eigenfunctions of s squared of SC
+ 
+
+ align:start position:0%
+are eigenfunctions of s squared of SC
+and when you do that you get 1/2 times 2
+
+ align:start position:0%
+and when you do that you get 1/2 times 2
+ 
+
+ align:start position:0%
+and when you do that you get 1/2 times 2
+J 1 s 2 s minus or plus 2 K 1 s 2 s
+
+ align:start position:0%
+J 1 s 2 s minus or plus 2 K 1 s 2 s
+ 
+
+ align:start position:0%
+J 1 s 2 s minus or plus 2 K 1 s 2 s
+remember when you have mismatched alpha
+
+ align:start position:0%
+remember when you have mismatched alpha
+ 
+
+ align:start position:0%
+remember when you have mismatched alpha
+and beta the k's are 0 but when you have
+
+ align:start position:0%
+and beta the k's are 0 but when you have
+ 
+
+ align:start position:0%
+and beta the k's are 0 but when you have
+k the 1 over r IJ matrix elements
+
+ align:start position:0%
+k the 1 over r IJ matrix elements
+ 
+
+ align:start position:0%
+k the 1 over r IJ matrix elements
+between two slater's you could fix that
+
+ align:start position:0%
+between two slater's you could fix that
+ 
+
+ align:start position:0%
+between two slater's you could fix that
+and so this is this is why it's so hard
+
+ align:start position:0%
+and so this is this is why it's so hard
+ 
+
+ align:start position:0%
+and so this is this is why it's so hard
+to explain because you know yes I'm not
+
+ align:start position:0%
+to explain because you know yes I'm not
+ 
+
+ align:start position:0%
+to explain because you know yes I'm not
+even going to apologize anymore
+
+ align:start position:0%
+even going to apologize anymore
+ 
+
+ align:start position:0%
+even going to apologize anymore
+ok so this is what you do and the notes
+
+ align:start position:0%
+ok so this is what you do and the notes
+ 
+
+ align:start position:0%
+ok so this is what you do and the notes
+are pretty clear about how to do them
+
+ align:start position:0%
+are pretty clear about how to do them
+ 
+
+ align:start position:0%
+are pretty clear about how to do them
+and what the problems are
+
+ align:start position:0%
+and what the problems are
+ 
+
+ align:start position:0%
+and what the problems are
+but lecturing on it would be a little
+
+ align:start position:0%
+but lecturing on it would be a little
+ 
+
+ align:start position:0%
+but lecturing on it would be a little
+bit hard ok so now what are we going to
+
+ align:start position:0%
+bit hard ok so now what are we going to
+ 
+
+ align:start position:0%
+bit hard ok so now what are we going to
+do with it well we'd like qualitative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuff and interpretive stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay qualitative is one's rules now if
+
+ align:start position:0%
+okay qualitative is one's rules now if
+ 
+
+ align:start position:0%
+okay qualitative is one's rules now if
+you looked at a hundred textbooks
+
+ align:start position:0%
+you looked at a hundred textbooks
+ 
+
+ align:start position:0%
+you looked at a hundred textbooks
+I think 95 of them will have Quinn's
+
+ align:start position:0%
+I think 95 of them will have Quinn's
+ 
+
+ align:start position:0%
+I think 95 of them will have Quinn's
+rules wrong you're never going to make
+
+ align:start position:0%
+rules wrong you're never going to make
+ 
+
+ align:start position:0%
+rules wrong you're never going to make
+that mistake and interpretive well we
+
+ align:start position:0%
+that mistake and interpretive well we
+ 
+
+ align:start position:0%
+that mistake and interpretive well we
+want to know the trends of things and we
+
+ align:start position:0%
+want to know the trends of things and we
+ 
+
+ align:start position:0%
+want to know the trends of things and we
+want to be able to do something like
+
+ align:start position:0%
+want to be able to do something like
+ 
+
+ align:start position:0%
+want to be able to do something like
+what you did in freshman chemistry
+
+ align:start position:0%
+what you did in freshman chemistry
+ 
+
+ align:start position:0%
+what you did in freshman chemistry
+shielding now you probably memorize some
+
+ align:start position:0%
+shielding now you probably memorize some
+ 
+
+ align:start position:0%
+shielding now you probably memorize some
+rules about what shields what and but
+
+ align:start position:0%
+rules about what shields what and but
+ 
+
+ align:start position:0%
+rules about what shields what and but
+I'm gonna give you a little bit more
+
+ align:start position:0%
+I'm gonna give you a little bit more
+ 
+
+ align:start position:0%
+I'm gonna give you a little bit more
+insight into that so we're going to talk
+
+ align:start position:0%
+insight into that so we're going to talk
+ 
+
+ align:start position:0%
+insight into that so we're going to talk
+about this for the rest of the lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you specify configuration and this
+
+ align:start position:0%
+you specify configuration and this
+ 
+
+ align:start position:0%
+you specify configuration and this
+configuration might be two electrons to
+
+ align:start position:0%
+configuration might be two electrons to
+ 
+
+ align:start position:0%
+configuration might be two electrons to
+spin orbitals to orbital sub Z or 3 or
+
+ align:start position:0%
+spin orbitals to orbital sub Z or 3 or
+ 
+
+ align:start position:0%
+spin orbitals to orbital sub Z or 3 or
+10 and you know often when you specify
+
+ align:start position:0%
+10 and you know often when you specify
+ 
+
+ align:start position:0%
+10 and you know often when you specify
+the occupied orbitals you neglect the
+
+ align:start position:0%
+the occupied orbitals you neglect the
+ 
+
+ align:start position:0%
+the occupied orbitals you neglect the
+filled ones which is nice because you
+
+ align:start position:0%
+filled ones which is nice because you
+ 
+
+ align:start position:0%
+filled ones which is nice because you
+have fewer things to worry about
+
+ align:start position:0%
+have fewer things to worry about
+ 
+
+ align:start position:0%
+have fewer things to worry about
+because filled orbitals have spin zero
+
+ align:start position:0%
+because filled orbitals have spin zero
+ 
+
+ align:start position:0%
+because filled orbitals have spin zero
+and you don't have to do anything there
+
+ align:start position:0%
+and you don't have to do anything there
+ 
+
+ align:start position:0%
+and you don't have to do anything there
+automatically and I Sigma tries and they
+
+ align:start position:0%
+automatically and I Sigma tries and they
+ 
+
+ align:start position:0%
+automatically and I Sigma tries and they
+basically act as a charge distribution
+
+ align:start position:0%
+basically act as a charge distribution
+ 
+
+ align:start position:0%
+basically act as a charge distribution
+in the core that is sampled by the
+
+ align:start position:0%
+in the core that is sampled by the
+ 
+
+ align:start position:0%
+in the core that is sampled by the
+electrons outside and so you need some
+
+ align:start position:0%
+electrons outside and so you need some
+ 
+
+ align:start position:0%
+electrons outside and so you need some
+sort of a set of rules for how do that
+
+ align:start position:0%
+sort of a set of rules for how do that
+ 
+
+ align:start position:0%
+sort of a set of rules for how do that
+how does that work and that's shielding
+
+ align:start position:0%
+how does that work and that's shielding
+ 
+
+ align:start position:0%
+how does that work and that's shielding
+but okay so we first we specify a
+
+ align:start position:0%
+but okay so we first we specify a
+ 
+
+ align:start position:0%
+but okay so we first we specify a
+configuration and you also learned in
+
+ align:start position:0%
+configuration and you also learned in
+ 
+
+ align:start position:0%
+configuration and you also learned in
+high school probably how to determine
+
+ align:start position:0%
+high school probably how to determine
+ 
+
+ align:start position:0%
+high school probably how to determine
+the elf s J terms the result from this
+
+ align:start position:0%
+the elf s J terms the result from this
+ 
+
+ align:start position:0%
+the elf s J terms the result from this
+configuration by some magical crossing
+
+ align:start position:0%
+configuration by some magical crossing
+ 
+
+ align:start position:0%
+configuration by some magical crossing
+out of boxes and if you didn't I'm glad
+
+ align:start position:0%
+out of boxes and if you didn't I'm glad
+ 
+
+ align:start position:0%
+out of boxes and if you didn't I'm glad
+because it would have just clouded your
+
+ align:start position:0%
+because it would have just clouded your
+ 
+
+ align:start position:0%
+because it would have just clouded your
+mind and caused earlier insanity then
+
+ align:start position:0%
+mind and caused earlier insanity then
+ 
+
+ align:start position:0%
+mind and caused earlier insanity then
+you know that MIT causes so anyway so we
+
+ align:start position:0%
+you know that MIT causes so anyway so we
+ 
+
+ align:start position:0%
+you know that MIT causes so anyway so we
+have orbital angular momentum and we can
+
+ align:start position:0%
+have orbital angular momentum and we can
+ 
+
+ align:start position:0%
+have orbital angular momentum and we can
+add the orbital angular momenta of the
+
+ align:start position:0%
+add the orbital angular momenta of the
+ 
+
+ align:start position:0%
+add the orbital angular momenta of the
+electrons and following certain rules
+
+ align:start position:0%
+electrons and following certain rules
+ 
+
+ align:start position:0%
+electrons and following certain rules
+and we have spin angular momenta and J
+
+ align:start position:0%
+and we have spin angular momenta and J
+ 
+
+ align:start position:0%
+and we have spin angular momenta and J
+is equal to a vector sum of LNS and we
+
+ align:start position:0%
+is equal to a vector sum of LNS and we
+ 
+
+ align:start position:0%
+is equal to a vector sum of LNS and we
+say we have an LS term like triplet P
+
+ align:start position:0%
+say we have an LS term like triplet P
+ 
+
+ align:start position:0%
+say we have an LS term like triplet P
+and it could have J is equal to L plus L
+
+ align:start position:0%
+and it could have J is equal to L plus L
+ 
+
+ align:start position:0%
+and it could have J is equal to L plus L
+plus s L plus s minus 1 down to l minus
+
+ align:start position:0%
+plus s L plus s minus 1 down to l minus
+ 
+
+ align:start position:0%
+plus s L plus s minus 1 down to l minus
+s absolute value these are the possible
+
+ align:start position:0%
+s absolute value these are the possible
+ 
+
+ align:start position:0%
+s absolute value these are the possible
+J's
+
+ align:start position:0%
+J's
+ 
+
+ align:start position:0%
+J's
+and so hones rules is all about of all
+
+ align:start position:0%
+and so hones rules is all about of all
+ 
+
+ align:start position:0%
+and so hones rules is all about of all
+of the states that belong to a
+
+ align:start position:0%
+of the states that belong to a
+ 
+
+ align:start position:0%
+of the states that belong to a
+particular configuration which one is
+
+ align:start position:0%
+particular configuration which one is
+ 
+
+ align:start position:0%
+particular configuration which one is
+the lowest one which one not the second
+
+ align:start position:0%
+the lowest one which one not the second
+ 
+
+ align:start position:0%
+the lowest one which one not the second
+lowest which one is the lowest and why
+
+ align:start position:0%
+lowest which one is the lowest and why
+ 
+
+ align:start position:0%
+lowest which one is the lowest and why
+do we care because in statistical
+
+ align:start position:0%
+do we care because in statistical
+ 
+
+ align:start position:0%
+do we care because in statistical
+mechanics everything is dominated by the
+
+ align:start position:0%
+mechanics everything is dominated by the
+ 
+
+ align:start position:0%
+mechanics everything is dominated by the
+lowest energy state and so if you can
+
+ align:start position:0%
+lowest energy state and so if you can
+ 
+
+ align:start position:0%
+lowest energy state and so if you can
+figure out what is the lowest energy
+
+ align:start position:0%
+figure out what is the lowest energy
+ 
+
+ align:start position:0%
+figure out what is the lowest energy
+state you basically got as much as most
+
+ align:start position:0%
+state you basically got as much as most
+ 
+
+ align:start position:0%
+state you basically got as much as most
+people are going to want so you want to
+
+ align:start position:0%
+people are going to want so you want to
+ 
+
+ align:start position:0%
+people are going to want so you want to
+know what is what are L s and J for the
+
+ align:start position:0%
+know what is what are L s and J for the
+ 
+
+ align:start position:0%
+know what is what are L s and J for the
+lowest energy state of a configuration
+
+ align:start position:0%
+lowest energy state of a configuration
+ 
+
+ align:start position:0%
+lowest energy state of a configuration
+configurations are typically far apart
+
+ align:start position:0%
+configurations are typically far apart
+ 
+
+ align:start position:0%
+configurations are typically far apart
+in energy so if you know what the lowest
+
+ align:start position:0%
+in energy so if you know what the lowest
+ 
+
+ align:start position:0%
+in energy so if you know what the lowest
+energy configuration is and the lowest
+
+ align:start position:0%
+energy configuration is and the lowest
+ 
+
+ align:start position:0%
+energy configuration is and the lowest
+energy state of it as far as your
+
+ align:start position:0%
+energy state of it as far as your
+ 
+
+ align:start position:0%
+energy state of it as far as your
+friends the specific mechanician 's you
+
+ align:start position:0%
+friends the specific mechanician 's you
+ 
+
+ align:start position:0%
+friends the specific mechanician 's you
+can tell them how to write their
+
+ align:start position:0%
+can tell them how to write their
+ 
+
+ align:start position:0%
+can tell them how to write their
+partition functions and the rest is
+
+ align:start position:0%
+partition functions and the rest is
+ 
+
+ align:start position:0%
+partition functions and the rest is
+details and mostly you don't want
+
+ align:start position:0%
+details and mostly you don't want
+ 
+
+ align:start position:0%
+details and mostly you don't want
+details and if your friends tell you
+
+ align:start position:0%
+details and if your friends tell you
+ 
+
+ align:start position:0%
+details and if your friends tell you
+they want details well you tell them
+
+ align:start position:0%
+they want details well you tell them
+ 
+
+ align:start position:0%
+they want details well you tell them
+this is what you have to do but it's no
+
+ align:start position:0%
+this is what you have to do but it's no
+ 
+
+ align:start position:0%
+this is what you have to do but it's no
+simple three quince rules okay so whose
+
+ align:start position:0%
+simple three quince rules okay so whose
+ 
+
+ align:start position:0%
+simple three quince rules okay so whose
+rules you look at all of the lsj states
+
+ align:start position:0%
+rules you look at all of the lsj states
+ 
+
+ align:start position:0%
+rules you look at all of the lsj states
+that are possible from a particular
+
+ align:start position:0%
+that are possible from a particular
+ 
+
+ align:start position:0%
+that are possible from a particular
+configuration and you can use the
+
+ align:start position:0%
+configuration and you can use the
+ 
+
+ align:start position:0%
+configuration and you can use the
+crossing out of MLMs boxes if you want
+
+ align:start position:0%
+crossing out of MLMs boxes if you want
+ 
+
+ align:start position:0%
+crossing out of MLMs boxes if you want
+and I could tell you why you would do
+
+ align:start position:0%
+and I could tell you why you would do
+ 
+
+ align:start position:0%
+and I could tell you why you would do
+that but I don't want to cause insanity
+
+ align:start position:0%
+that but I don't want to cause insanity
+ 
+
+ align:start position:0%
+that but I don't want to cause insanity
+at this stage either but you know I'm an
+
+ align:start position:0%
+at this stage either but you know I'm an
+ 
+
+ align:start position:0%
+at this stage either but you know I'm an
+expert at that and you can also use
+
+ align:start position:0%
+expert at that and you can also use
+ 
+
+ align:start position:0%
+expert at that and you can also use
+lowering operators to generate all the
+
+ align:start position:0%
+lowering operators to generate all the
+ 
+
+ align:start position:0%
+lowering operators to generate all the
+states once you know stuff okay so once
+
+ align:start position:0%
+states once you know stuff okay so once
+ 
+
+ align:start position:0%
+states once you know stuff okay so once
+you know all the states horn says which
+
+ align:start position:0%
+you know all the states horn says which
+ 
+
+ align:start position:0%
+you know all the states horn says which
+one of these has the largest S which one
+
+ align:start position:0%
+one of these has the largest S which one
+ 
+
+ align:start position:0%
+one of these has the largest S which one
+that's easy to know and for example if
+
+ align:start position:0%
+that's easy to know and for example if
+ 
+
+ align:start position:0%
+that's easy to know and for example if
+you had 2p squared you're going to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sing
+
+ align:start position:0%
+sing
+ 
+
+ align:start position:0%
+sing
+d triplet P and Sigma s and well here's
+
+ align:start position:0%
+d triplet P and Sigma s and well here's
+ 
+
+ align:start position:0%
+d triplet P and Sigma s and well here's
+the triplet that has a large tes
+
+ align:start position:0%
+the triplet that has a large tes
+ 
+
+ align:start position:0%
+the triplet that has a large tes
+so the triplet P is the lowest energy
+
+ align:start position:0%
+so the triplet P is the lowest energy
+ 
+
+ align:start position:0%
+so the triplet P is the lowest energy
+state now if there if there were
+
+ align:start position:0%
+state now if there if there were
+ 
+
+ align:start position:0%
+state now if there if there were
+multiple Triplets as there would be say
+
+ align:start position:0%
+multiple Triplets as there would be say
+ 
+
+ align:start position:0%
+multiple Triplets as there would be say
+4 2 P 3 D then you'd have to decide
+
+ align:start position:0%
+4 2 P 3 D then you'd have to decide
+ 
+
+ align:start position:0%
+4 2 P 3 D then you'd have to decide
+which of those triplets is the lowest
+
+ align:start position:0%
+which of those triplets is the lowest
+ 
+
+ align:start position:0%
+which of those triplets is the lowest
+and all you care about all you're
+
+ align:start position:0%
+and all you care about all you're
+ 
+
+ align:start position:0%
+and all you care about all you're
+allowed to say is which one is the
+
+ align:start position:0%
+allowed to say is which one is the
+ 
+
+ align:start position:0%
+allowed to say is which one is the
+lowest and it's the one with the maximum
+
+ align:start position:0%
+lowest and it's the one with the maximum
+ 
+
+ align:start position:0%
+lowest and it's the one with the maximum
+L and then the last step is which what
+
+ align:start position:0%
+L and then the last step is which what
+ 
+
+ align:start position:0%
+L and then the last step is which what
+is the lowest J for that LS state and
+
+ align:start position:0%
+is the lowest J for that LS state and
+ 
+
+ align:start position:0%
+is the lowest J for that LS state and
+that's kind of cute because ya so you
+
+ align:start position:0%
+that's kind of cute because ya so you
+ 
+
+ align:start position:0%
+that's kind of cute because ya so you
+have the P shellers there's for a a PL
+
+ align:start position:0%
+have the P shellers there's for a a PL
+ 
+
+ align:start position:0%
+have the P shellers there's for a a PL
+you can have 6 P orbitals to fill the
+
+ align:start position:0%
+you can have 6 P orbitals to fill the
+ 
+
+ align:start position:0%
+you can have 6 P orbitals to fill the
+shelves 1 alpha 1 beta 2 elf I was 0
+
+ align:start position:0%
+shelves 1 alpha 1 beta 2 elf I was 0
+ 
+
+ align:start position:0%
+shelves 1 alpha 1 beta 2 elf I was 0
+alpha 0 beta etc so the degeneracy of a
+
+ align:start position:0%
+alpha 0 beta etc so the degeneracy of a
+ 
+
+ align:start position:0%
+alpha 0 beta etc so the degeneracy of a
+p electra p orbital is 6 if you have P
+
+ align:start position:0%
+p electra p orbital is 6 if you have P
+ 
+
+ align:start position:0%
+p electra p orbital is 6 if you have P
+to n where n is less than or equal less
+
+ align:start position:0%
+to n where n is less than or equal less
+ 
+
+ align:start position:0%
+to n where n is less than or equal less
+than 3 you have a less than half filled
+
+ align:start position:0%
+than 3 you have a less than half filled
+ 
+
+ align:start position:0%
+than 3 you have a less than half filled
+shell and then lowest is J equal L minus
+
+ align:start position:0%
+shell and then lowest is J equal L minus
+ 
+
+ align:start position:0%
+shell and then lowest is J equal L minus
+s absolute value and if n is greater
+
+ align:start position:0%
+s absolute value and if n is greater
+ 
+
+ align:start position:0%
+s absolute value and if n is greater
+than 3 you have the lowest being the
+
+ align:start position:0%
+than 3 you have the lowest being the
+ 
+
+ align:start position:0%
+than 3 you have the lowest being the
+highest possible value J
+
+ align:start position:0%
+highest possible value J
+ 
+
+ align:start position:0%
+highest possible value J
+is equal to L plus s so for L and
+
+ align:start position:0%
+is equal to L plus s so for L and
+ 
+
+ align:start position:0%
+is equal to L plus s so for L and
+greater than three and now when you have
+
+ align:start position:0%
+greater than three and now when you have
+ 
+
+ align:start position:0%
+greater than three and now when you have
+a half-filled shell the lowest state is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's usually an S state with the maximum
+
+ align:start position:0%
+it's usually an S state with the maximum
+ 
+
+ align:start position:0%
+it's usually an S state with the maximum
+spin but it doesn't matter that there's
+
+ align:start position:0%
+spin but it doesn't matter that there's
+ 
+
+ align:start position:0%
+spin but it doesn't matter that there's
+when you have a less than or more than
+
+ align:start position:0%
+when you have a less than or more than
+ 
+
+ align:start position:0%
+when you have a less than or more than
+half filled shell you have generally a
+
+ align:start position:0%
+half filled shell you have generally a
+ 
+
+ align:start position:0%
+half filled shell you have generally a
+state with orbital angular momentum not
+
+ align:start position:0%
+state with orbital angular momentum not
+ 
+
+ align:start position:0%
+state with orbital angular momentum not
+equal to 0 and you have spin orbit
+
+ align:start position:0%
+equal to 0 and you have spin orbit
+ 
+
+ align:start position:0%
+equal to 0 and you have spin orbit
+splitting of that and so you do want to
+
+ align:start position:0%
+splitting of that and so you do want to
+ 
+
+ align:start position:0%
+splitting of that and so you do want to
+care which what is the lowest J but when
+
+ align:start position:0%
+care which what is the lowest J but when
+ 
+
+ align:start position:0%
+care which what is the lowest J but when
+n is equal to 3 the lowest state it's
+
+ align:start position:0%
+n is equal to 3 the lowest state it's
+ 
+
+ align:start position:0%
+n is equal to 3 the lowest state it's
+usually at a state it doesn't have a
+
+ align:start position:0%
+usually at a state it doesn't have a
+ 
+
+ align:start position:0%
+usually at a state it doesn't have a
+spin orbit splitting and it just has one
+
+ align:start position:0%
+spin orbit splitting and it just has one
+ 
+
+ align:start position:0%
+spin orbit splitting and it just has one
+value of J which is whatever the spin is
+
+ align:start position:0%
+value of J which is whatever the spin is
+ 
+
+ align:start position:0%
+value of J which is whatever the spin is
+okay so one's rule tell you how to
+
+ align:start position:0%
+okay so one's rule tell you how to
+ 
+
+ align:start position:0%
+okay so one's rule tell you how to
+identify without knowing beans what is
+
+ align:start position:0%
+identify without knowing beans what is
+ 
+
+ align:start position:0%
+identify without knowing beans what is
+the lowest energy state and it's never
+
+ align:start position:0%
+the lowest energy state and it's never
+ 
+
+ align:start position:0%
+the lowest energy state and it's never
+wrong and well maybe sometimes wrong but
+
+ align:start position:0%
+wrong and well maybe sometimes wrong but
+ 
+
+ align:start position:0%
+wrong and well maybe sometimes wrong but
+that's because of one of my things where
+
+ align:start position:0%
+that's because of one of my things where
+ 
+
+ align:start position:0%
+that's because of one of my things where
+you have a perturbation between states
+
+ align:start position:0%
+you have a perturbation between states
+ 
+
+ align:start position:0%
+you have a perturbation between states
+belonging to do configurations but
+
+ align:start position:0%
+belonging to do configurations but
+ 
+
+ align:start position:0%
+belonging to do configurations but
+people get really excited when they
+
+ align:start position:0%
+people get really excited when they
+ 
+
+ align:start position:0%
+people get really excited when they
+discover a violation of winds rules and
+
+ align:start position:0%
+discover a violation of winds rules and
+ 
+
+ align:start position:0%
+discover a violation of winds rules and
+it's just trivial so there's this ok and
+
+ align:start position:0%
+it's just trivial so there's this ok and
+ 
+
+ align:start position:0%
+it's just trivial so there's this ok and
+then what time is it I have a few
+
+ align:start position:0%
+then what time is it I have a few
+ 
+
+ align:start position:0%
+then what time is it I have a few
+minutes to talk about shielding and I
+
+ align:start position:0%
+minutes to talk about shielding and I
+ 
+
+ align:start position:0%
+minutes to talk about shielding and I
+will okay so we have a nucleus and it
+
+ align:start position:0%
+will okay so we have a nucleus and it
+ 
+
+ align:start position:0%
+will okay so we have a nucleus and it
+has a charge of Z their nucleus there's
+
+ align:start position:0%
+has a charge of Z their nucleus there's
+ 
+
+ align:start position:0%
+has a charge of Z their nucleus there's
+no electrons so the atomic number is the
+
+ align:start position:0%
+no electrons so the atomic number is the
+ 
+
+ align:start position:0%
+no electrons so the atomic number is the
+charge and then we have a filled shell
+
+ align:start position:0%
+charge and then we have a filled shell
+ 
+
+ align:start position:0%
+charge and then we have a filled shell
+around it
+
+ align:start position:0%
+around it
+ 
+
+ align:start position:0%
+around it
+it's spherically symmetric and so if we
+
+ align:start position:0%
+it's spherically symmetric and so if we
+ 
+
+ align:start position:0%
+it's spherically symmetric and so if we
+penetrate inside of it what we see
+
+ align:start position:0%
+penetrate inside of it what we see
+ 
+
+ align:start position:0%
+penetrate inside of it what we see
+suppose we penetrate inside to this
+
+ align:start position:0%
+suppose we penetrate inside to this
+ 
+
+ align:start position:0%
+suppose we penetrate inside to this
+point what we see is only the plus Z
+
+ align:start position:0%
+point what we see is only the plus Z
+ 
+
+ align:start position:0%
+point what we see is only the plus Z
+minus the number of electron
+
+ align:start position:0%
+minus the number of electron
+ 
+
+ align:start position:0%
+minus the number of electron
+inside this fear now if you took
+
+ align:start position:0%
+inside this fear now if you took
+ 
+
+ align:start position:0%
+inside this fear now if you took
+electricity and magnetism you can prove
+
+ align:start position:0%
+electricity and magnetism you can prove
+ 
+
+ align:start position:0%
+electricity and magnetism you can prove
+this if you didn't you can accept it and
+
+ align:start position:0%
+this if you didn't you can accept it and
+ 
+
+ align:start position:0%
+this if you didn't you can accept it and
+so outside the nucleus the charge is
+
+ align:start position:0%
+so outside the nucleus the charge is
+ 
+
+ align:start position:0%
+so outside the nucleus the charge is
+plus one because you have a neutral atom
+
+ align:start position:0%
+plus one because you have a neutral atom
+ 
+
+ align:start position:0%
+plus one because you have a neutral atom
+and and then when you penetrate inside
+
+ align:start position:0%
+and and then when you penetrate inside
+ 
+
+ align:start position:0%
+and and then when you penetrate inside
+this region of dense charge and all spin
+
+ align:start position:0%
+this region of dense charge and all spin
+ 
+
+ align:start position:0%
+this region of dense charge and all spin
+all of the spins are generally paired
+
+ align:start position:0%
+all of the spins are generally paired
+ 
+
+ align:start position:0%
+all of the spins are generally paired
+this is spherical and you you so what
+
+ align:start position:0%
+this is spherical and you you so what
+ 
+
+ align:start position:0%
+this is spherical and you you so what
+you end up seeing is Z effective as
+
+ align:start position:0%
+you end up seeing is Z effective as
+ 
+
+ align:start position:0%
+you end up seeing is Z effective as
+opposed to Z true and let's say here's
+
+ align:start position:0%
+opposed to Z true and let's say here's
+ 
+
+ align:start position:0%
+opposed to Z true and let's say here's
+our zero where this is zero and so
+
+ align:start position:0%
+our zero where this is zero and so
+ 
+
+ align:start position:0%
+our zero where this is zero and so
+beyond our zero the charge that you see
+
+ align:start position:0%
+beyond our zero the charge that you see
+ 
+
+ align:start position:0%
+beyond our zero the charge that you see
+is plus one at zero you see a charge of
+
+ align:start position:0%
+is plus one at zero you see a charge of
+ 
+
+ align:start position:0%
+is plus one at zero you see a charge of
+Z and so what ends up happening is you
+
+ align:start position:0%
+Z and so what ends up happening is you
+ 
+
+ align:start position:0%
+Z and so what ends up happening is you
+get at Z effective which is dependent on
+
+ align:start position:0%
+get at Z effective which is dependent on
+ 
+
+ align:start position:0%
+get at Z effective which is dependent on
+distance from the nucleus and it goes
+
+ align:start position:0%
+distance from the nucleus and it goes
+ 
+
+ align:start position:0%
+distance from the nucleus and it goes
+from the integer value that you know
+
+ align:start position:0%
+from the integer value that you know
+ 
+
+ align:start position:0%
+from the integer value that you know
+from the the atomic number down to one
+
+ align:start position:0%
+from the the atomic number down to one
+ 
+
+ align:start position:0%
+from the the atomic number down to one
+because you've taken one electron away
+
+ align:start position:0%
+because you've taken one electron away
+ 
+
+ align:start position:0%
+because you've taken one electron away
+from a neutral atom and taking it
+
+ align:start position:0%
+from a neutral atom and taking it
+ 
+
+ align:start position:0%
+from a neutral atom and taking it
+outside and now we have this wonderful
+
+ align:start position:0%
+outside and now we have this wonderful
+ 
+
+ align:start position:0%
+outside and now we have this wonderful
+thing called the centrifugal barrier so
+
+ align:start position:0%
+thing called the centrifugal barrier so
+ 
+
+ align:start position:0%
+thing called the centrifugal barrier so
+if we have a state that has a non zero
+
+ align:start position:0%
+if we have a state that has a non zero
+ 
+
+ align:start position:0%
+if we have a state that has a non zero
+value of L well if we have a state with
+
+ align:start position:0%
+value of L well if we have a state with
+ 
+
+ align:start position:0%
+value of L well if we have a state with
+a zero value of all it can penetrate all
+
+ align:start position:0%
+a zero value of all it can penetrate all
+ 
+
+ align:start position:0%
+a zero value of all it can penetrate all
+the way into the car to the nucleus and
+
+ align:start position:0%
+the way into the car to the nucleus and
+ 
+
+ align:start position:0%
+the way into the car to the nucleus and
+so that means that the shielding is less
+
+ align:start position:0%
+so that means that the shielding is less
+ 
+
+ align:start position:0%
+so that means that the shielding is less
+for s orbitals and now if we have a non
+
+ align:start position:0%
+for s orbitals and now if we have a non
+ 
+
+ align:start position:0%
+for s orbitals and now if we have a non
+zero L it can't get in so far and the
+
+ align:start position:0%
+zero L it can't get in so far and the
+ 
+
+ align:start position:0%
+zero L it can't get in so far and the
+larger the L is the less the less it can
+
+ align:start position:0%
+larger the L is the less the less it can
+ 
+
+ align:start position:0%
+larger the L is the less the less it can
+see this extra charge so High Elves are
+
+ align:start position:0%
+see this extra charge so High Elves are
+ 
+
+ align:start position:0%
+see this extra charge so High Elves are
+very well shielded low ELLs are not so
+
+ align:start position:0%
+very well shielded low ELLs are not so
+ 
+
+ align:start position:0%
+very well shielded low ELLs are not so
+well shielded and the shielding goes as
+
+ align:start position:0%
+well shielded and the shielding goes as
+ 
+
+ align:start position:0%
+well shielded and the shielding goes as
+most I mean s least shielded P less so
+
+ align:start position:0%
+most I mean s least shielded P less so
+ 
+
+ align:start position:0%
+most I mean s least shielded P less so
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+now there's some other interesting
+
+ align:start position:0%
+now there's some other interesting
+ 
+
+ align:start position:0%
+now there's some other interesting
+things which you know I hate to say this
+
+ align:start position:0%
+things which you know I hate to say this
+ 
+
+ align:start position:0%
+things which you know I hate to say this
+but comparing 511 1 or 511 to to the 309
+
+ align:start position:0%
+but comparing 511 1 or 511 to to the 309
+ 
+
+ align:start position:0%
+but comparing 511 1 or 511 to to the 309
+1 there is this business of what happens
+
+ align:start position:0%
+1 there is this business of what happens
+ 
+
+ align:start position:0%
+1 there is this business of what happens
+when you start to so when you have you
+
+ align:start position:0%
+when you start to so when you have you
+ 
+
+ align:start position:0%
+when you start to so when you have you
+start with potassium and so you put an
+
+ align:start position:0%
+start with potassium and so you put an
+ 
+
+ align:start position:0%
+start with potassium and so you put an
+electron in the 4s not in the 3d orbital
+
+ align:start position:0%
+electron in the 4s not in the 3d orbital
+ 
+
+ align:start position:0%
+electron in the 4s not in the 3d orbital
+right why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the 4s sees the the the larger
+
+ align:start position:0%
+well the 4s sees the the the larger
+ 
+
+ align:start position:0%
+well the 4s sees the the the larger
+charge is less shielded so it goes in
+
+ align:start position:0%
+charge is less shielded so it goes in
+ 
+
+ align:start position:0%
+charge is less shielded so it goes in
+then when you go from potassium to
+
+ align:start position:0%
+then when you go from potassium to
+ 
+
+ align:start position:0%
+then when you go from potassium to
+calcium you put another electron in this
+
+ align:start position:0%
+calcium you put another electron in this
+ 
+
+ align:start position:0%
+calcium you put another electron in this
+and that's true so you for calcium you
+
+ align:start position:0%
+and that's true so you for calcium you
+ 
+
+ align:start position:0%
+and that's true so you for calcium you
+have a 4 s squared and 4s 3d is a higher
+
+ align:start position:0%
+have a 4 s squared and 4s 3d is a higher
+ 
+
+ align:start position:0%
+have a 4 s squared and 4s 3d is a higher
+lying state now you take an electron I'm
+
+ align:start position:0%
+lying state now you take an electron I'm
+ 
+
+ align:start position:0%
+lying state now you take an electron I'm
+cooking my my own goose if you take one
+
+ align:start position:0%
+cooking my my own goose if you take one
+ 
+
+ align:start position:0%
+cooking my my own goose if you take one
+of these electrons away this is not the
+
+ align:start position:0%
+of these electrons away this is not the
+ 
+
+ align:start position:0%
+of these electrons away this is not the
+way I wanted it to come out you end up
+
+ align:start position:0%
+way I wanted it to come out you end up
+ 
+
+ align:start position:0%
+way I wanted it to come out you end up
+having you find yourself in a 3d state
+
+ align:start position:0%
+having you find yourself in a 3d state
+ 
+
+ align:start position:0%
+having you find yourself in a 3d state
+because 3d penetrates a little bit under
+
+ align:start position:0%
+because 3d penetrates a little bit under
+ 
+
+ align:start position:0%
+because 3d penetrates a little bit under
+4s and you I can't do I can't explain it
+
+ align:start position:0%
+4s and you I can't do I can't explain it
+ 
+
+ align:start position:0%
+4s and you I can't do I can't explain it
+in a way that's gonna make sense I
+
+ align:start position:0%
+in a way that's gonna make sense I
+ 
+
+ align:start position:0%
+in a way that's gonna make sense I
+really wanted to because I I I care so
+
+ align:start position:0%
+really wanted to because I I I care so
+ 
+
+ align:start position:0%
+really wanted to because I I I care so
+much about these simple arguments but I
+
+ align:start position:0%
+much about these simple arguments but I
+ 
+
+ align:start position:0%
+much about these simple arguments but I
+I I will just be wasting your time so
+
+ align:start position:0%
+I I will just be wasting your time so
+ 
+
+ align:start position:0%
+I I will just be wasting your time so
+the order in which you fill orbitals
+
+ align:start position:0%
+the order in which you fill orbitals
+ 
+
+ align:start position:0%
+the order in which you fill orbitals
+comes out naturally different from the
+
+ align:start position:0%
+comes out naturally different from the
+ 
+
+ align:start position:0%
+comes out naturally different from the
+Orval order in which you removal
+
+ align:start position:0%
+Orval order in which you removal
+ 
+
+ align:start position:0%
+Orval order in which you removal
+electrons form orbitals and the
+
+ align:start position:0%
+electrons form orbitals and the
+ 
+
+ align:start position:0%
+electrons form orbitals and the
+shielding arguments are capable of
+
+ align:start position:0%
+shielding arguments are capable of
+ 
+
+ align:start position:0%
+shielding arguments are capable of
+explaining that okay so this is the end
+
+ align:start position:0%
+explaining that okay so this is the end
+ 
+
+ align:start position:0%
+explaining that okay so this is the end
+of atoms and I've asked you to two to
+
+ align:start position:0%
+of atoms and I've asked you to two to
+ 
+
+ align:start position:0%
+of atoms and I've asked you to two to
+observe some complicated algebra which
+
+ align:start position:0%
+observe some complicated algebra which
+ 
+
+ align:start position:0%
+observe some complicated algebra which
+you're never going to do or at least
+
+ align:start position:0%
+you're never going to do or at least
+ 
+
+ align:start position:0%
+you're never going to do or at least
+never going to do much of everything you
+
+ align:start position:0%
+never going to do much of everything you
+ 
+
+ align:start position:0%
+never going to do much of everything you
+need to know about atoms you can tell a
+
+ align:start position:0%
+need to know about atoms you can tell a
+ 
+
+ align:start position:0%
+need to know about atoms you can tell a
+computer and it can do it now molecules
+
+ align:start position:0%
+computer and it can do it now molecules
+ 
+
+ align:start position:0%
+computer and it can do it now molecules
+are much more complicated and that's
+
+ align:start position:0%
+are much more complicated and that's
+ 
+
+ align:start position:0%
+are much more complicated and that's
+we're going to start on next time we're
+
+ align:start position:0%
+we're going to start on next time we're
+ 
+
+ align:start position:0%
+we're going to start on next time we're
+going to start with molecular orbital
+
+ align:start position:0%
+going to start with molecular orbital
+ 
+
+ align:start position:0%
+going to start with molecular orbital
+theory and I'm not going to be cos n
+
+ align:start position:0%
+theory and I'm not going to be cos n
+ 
+
+ align:start position:0%
+theory and I'm not going to be cos n
+ting the normal textbook approach I'm
+
+ align:start position:0%
+ting the normal textbook approach I'm
+ 
+
+ align:start position:0%
+ting the normal textbook approach I'm
+going to present an interpretive
+
+ align:start position:0%
+going to present an interpretive
+ 
+
+ align:start position:0%
+going to present an interpretive
+approach where you understand why things
+
+ align:start position:0%
+approach where you understand why things
+ 
+
+ align:start position:0%
+approach where you understand why things
+happen as opposed to memorize just
+
+ align:start position:0%
+happen as opposed to memorize just
+ 
+
+ align:start position:0%
+happen as opposed to memorize just
+symmetries and filling orders and so on
+
+ align:start position:0%
+symmetries and filling orders and so on
+ 
+
+ align:start position:0%
+symmetries and filling orders and so on
+okay I'll see you on Wednesday
\ No newline at end of file
diff --git a/K2cYzRGjWrE.txt b/K2cYzRGjWrE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cff9497ccb155a0f8384f3377a0d29182eb4c1e3
--- /dev/null
+++ b/K2cYzRGjWrE.txt
@@ -0,0 +1,355 @@
+align:start position:0%
+ 
+Open education here means open resources
+
+ align:start position:0%
+Open education here means open resources
+ 
+
+ align:start position:0%
+Open education here means open resources
+in and outside of the classroom for our
+
+ align:start position:0%
+in and outside of the classroom for our
+ 
+
+ align:start position:0%
+in and outside of the classroom for our
+students.
+
+ align:start position:0%
+students.
+ 
+
+ align:start position:0%
+students.
+We're inventing a more open future for
+
+ align:start position:0%
+We're inventing a more open future for
+ 
+
+ align:start position:0%
+We're inventing a more open future for
+all curious minds by sharing a treasure
+
+ align:start position:0%
+all curious minds by sharing a treasure
+ 
+
+ align:start position:0%
+all curious minds by sharing a treasure
+of knowledge for you to discover
+
+ align:start position:0%
+of knowledge for you to discover
+ 
+
+ align:start position:0%
+of knowledge for you to discover
+anywhere, anytime.
+
+ align:start position:0%
+anywhere, anytime.
+ 
+
+ align:start position:0%
+anywhere, anytime.
+We're rethinking open by recognizing
+
+ align:start position:0%
+We're rethinking open by recognizing
+ 
+
+ align:start position:0%
+We're rethinking open by recognizing
+voices and expertise from people of
+
+ align:start position:0%
+voices and expertise from people of
+ 
+
+ align:start position:0%
+voices and expertise from people of
+diverse backgrounds are absolutely
+
+ align:start position:0%
+diverse backgrounds are absolutely
+ 
+
+ align:start position:0%
+diverse backgrounds are absolutely
+necessary for expanding and growing open
+
+ align:start position:0%
+necessary for expanding and growing open
+ 
+
+ align:start position:0%
+necessary for expanding and growing open
+educational resources.
+
+ align:start position:0%
+educational resources.
+ 
+
+ align:start position:0%
+educational resources.
+>> 20% of our faculty have adapted, adopted
+
+ align:start position:0%
+>> 20% of our faculty have adapted, adopted
+ 
+
+ align:start position:0%
+>> 20% of our faculty have adapted, adopted
+and/or created OEER. We are inventing a
+
+ align:start position:0%
+and/or created OEER. We are inventing a
+ 
+
+ align:start position:0%
+and/or created OEER. We are inventing a
+more open future for all consumers and
+
+ align:start position:0%
+more open future for all consumers and
+ 
+
+ align:start position:0%
+more open future for all consumers and
+producers of knowledge by leading in the
+
+ align:start position:0%
+producers of knowledge by leading in the
+ 
+
+ align:start position:0%
+producers of knowledge by leading in the
+development of sustainable open
+
+ align:start position:0%
+development of sustainable open
+ 
+
+ align:start position:0%
+development of sustainable open
+publishing models and open-source
+
+ align:start position:0%
+publishing models and open-source
+ 
+
+ align:start position:0%
+publishing models and open-source
+publishing technologies. We are
+
+ align:start position:0%
+publishing technologies. We are
+ 
+
+ align:start position:0%
+publishing technologies. We are
+relentless in our pursuit of a more open
+
+ align:start position:0%
+relentless in our pursuit of a more open
+ 
+
+ align:start position:0%
+relentless in our pursuit of a more open
+and equitable scholarly landscape.
+
+ align:start position:0%
+and equitable scholarly landscape.
+ 
+
+ align:start position:0%
+and equitable scholarly landscape.
+>> Open is democratizing learning and
+
+ align:start position:0%
+>> Open is democratizing learning and
+ 
+
+ align:start position:0%
+>> Open is democratizing learning and
+knowledge to the world.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here. Open is in our DNA.
+
+ align:start position:0%
+here. Open is in our DNA.
+ 
+
+ align:start position:0%
+here. Open is in our DNA.
+>> It captures Arab commitment to sharing
+
+ align:start position:0%
+>> It captures Arab commitment to sharing
+ 
+
+ align:start position:0%
+>> It captures Arab commitment to sharing
+our best educational contributions in a
+
+ align:start position:0%
+our best educational contributions in a
+ 
+
+ align:start position:0%
+our best educational contributions in a
+way that everyone can build on them and
+
+ align:start position:0%
+way that everyone can build on them and
+ 
+
+ align:start position:0%
+way that everyone can build on them and
+make them even better.
+
+ align:start position:0%
+make them even better.
+ 
+
+ align:start position:0%
+make them even better.
+>> Here, openness is a core value. We share
+
+ align:start position:0%
+>> Here, openness is a core value. We share
+ 
+
+ align:start position:0%
+>> Here, openness is a core value. We share
+information, innovations and ideas with
+
+ align:start position:0%
+information, innovations and ideas with
+ 
+
+ align:start position:0%
+information, innovations and ideas with
+enthusiasm. We champion open courseware,
+
+ align:start position:0%
+enthusiasm. We champion open courseware,
+ 
+
+ align:start position:0%
+enthusiasm. We champion open courseware,
+open access, and open science. All
+
+ align:start position:0%
+open access, and open science. All
+ 
+
+ align:start position:0%
+open access, and open science. All
+crucial to our mission. Our doors are
+
+ align:start position:0%
+crucial to our mission. Our doors are
+ 
+
+ align:start position:0%
+crucial to our mission. Our doors are
+open, too. So, come join us.
+
+ align:start position:0%
+open, too. So, come join us.
+ 
+
+ align:start position:0%
+open, too. So, come join us.
+>> Come join us.
+
+ align:start position:0%
+>> Come join us.
+ 
+
+ align:start position:0%
+>> Come join us.
+>> Come join us.
+
+ align:start position:0%
+>> Come join us.
+ 
+
+ align:start position:0%
+>> Come join us.
+>> Come invent with us.
+
+ align:start position:0%
+>> Come invent with us.
+ 
+
+ align:start position:0%
+>> Come invent with us.
+>> Come invent with us.
+
+ align:start position:0%
+>> Come invent with us.
+ 
+
+ align:start position:0%
+>> Come invent with us.
+>> We can't wait to welcome you.
+
+ align:start position:0%
+>> We can't wait to welcome you.
+ 
+
+ align:start position:0%
+>> We can't wait to welcome you.
+>> I think you would enjoy seeing Cambridge
+
+ align:start position:0%
+>> I think you would enjoy seeing Cambridge
+ 
+
+ align:start position:0%
+>> I think you would enjoy seeing Cambridge
+and I certainly look forward to meeting
+
+ align:start position:0%
+and I certainly look forward to meeting
+ 
+
+ align:start position:0%
+and I certainly look forward to meeting
+you. So, let's do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/K7QVIqV2QMk.txt b/K7QVIqV2QMk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2e0afdea258b2c3eb9c01f8baac5116c7a635524
--- /dev/null
+++ b/K7QVIqV2QMk.txt
@@ -0,0 +1,23931 @@
+align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+welcome everyone to lecture 13 of 1413.
+
+ align:start position:0%
+welcome everyone to lecture 13 of 1413.
+ 
+
+ align:start position:0%
+welcome everyone to lecture 13 of 1413.
+this is my last lecture on social
+
+ align:start position:0%
+this is my last lecture on social
+ 
+
+ align:start position:0%
+this is my last lecture on social
+preferences i hope all of you are
+
+ align:start position:0%
+preferences i hope all of you are
+ 
+
+ align:start position:0%
+preferences i hope all of you are
+doing fine remotely hang in there i know
+
+ align:start position:0%
+doing fine remotely hang in there i know
+ 
+
+ align:start position:0%
+doing fine remotely hang in there i know
+this is a very difficult time
+
+ align:start position:0%
+this is a very difficult time
+ 
+
+ align:start position:0%
+this is a very difficult time
+this lecture is a bit of a more
+
+ align:start position:0%
+this lecture is a bit of a more
+ 
+
+ align:start position:0%
+this lecture is a bit of a more
+uplifting lecture than the previous ones
+
+ align:start position:0%
+uplifting lecture than the previous ones
+ 
+
+ align:start position:0%
+uplifting lecture than the previous ones
+well the previous ones have looked at
+
+ align:start position:0%
+well the previous ones have looked at
+ 
+
+ align:start position:0%
+well the previous ones have looked at
+social preferences how we can measure
+
+ align:start position:0%
+social preferences how we can measure
+ 
+
+ align:start position:0%
+social preferences how we can measure
+social preferences
+
+ align:start position:0%
+social preferences
+ 
+
+ align:start position:0%
+social preferences
+and how can we perhaps isolate pure
+
+ align:start position:0%
+and how can we perhaps isolate pure
+ 
+
+ align:start position:0%
+and how can we perhaps isolate pure
+altruism
+
+ align:start position:0%
+altruism
+ 
+
+ align:start position:0%
+altruism
+do people really want others to be
+
+ align:start position:0%
+do people really want others to be
+ 
+
+ align:start position:0%
+do people really want others to be
+better for their own sake
+
+ align:start position:0%
+better for their own sake
+ 
+
+ align:start position:0%
+better for their own sake
+even if nobody knows about it either
+
+ align:start position:0%
+even if nobody knows about it either
+ 
+
+ align:start position:0%
+even if nobody knows about it either
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+or or whether there's no feedback um
+
+ align:start position:0%
+or or whether there's no feedback um
+ 
+
+ align:start position:0%
+or or whether there's no feedback um
+we sort of found out that like it seems
+
+ align:start position:0%
+we sort of found out that like it seems
+ 
+
+ align:start position:0%
+we sort of found out that like it seems
+like what looks a lot like
+
+ align:start position:0%
+like what looks a lot like
+ 
+
+ align:start position:0%
+like what looks a lot like
+altruism people are nice to each other
+
+ align:start position:0%
+altruism people are nice to each other
+ 
+
+ align:start position:0%
+altruism people are nice to each other
+it's not pure altruism in the sense that
+
+ align:start position:0%
+it's not pure altruism in the sense that
+ 
+
+ align:start position:0%
+it's not pure altruism in the sense that
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+they really want others to do well
+
+ align:start position:0%
+they really want others to do well
+ 
+
+ align:start position:0%
+they really want others to do well
+instead
+
+ align:start position:0%
+instead
+ 
+
+ align:start position:0%
+instead
+they want to either look good in front
+
+ align:start position:0%
+they want to either look good in front
+ 
+
+ align:start position:0%
+they want to either look good in front
+of others or like you know they're
+
+ align:start position:0%
+of others or like you know they're
+ 
+
+ align:start position:0%
+of others or like you know they're
+worried about reciprocity or sort of any
+
+ align:start position:0%
+worried about reciprocity or sort of any
+ 
+
+ align:start position:0%
+worried about reciprocity or sort of any
+other negative feedback from others
+
+ align:start position:0%
+other negative feedback from others
+ 
+
+ align:start position:0%
+other negative feedback from others
+or it might be they might want uh to
+
+ align:start position:0%
+or it might be they might want uh to
+ 
+
+ align:start position:0%
+or it might be they might want uh to
+protect their self-image they want to
+
+ align:start position:0%
+protect their self-image they want to
+ 
+
+ align:start position:0%
+protect their self-image they want to
+look good
+
+ align:start position:0%
+look good
+ 
+
+ align:start position:0%
+look good
+in front of themselves and they try to
+
+ align:start position:0%
+in front of themselves and they try to
+ 
+
+ align:start position:0%
+in front of themselves and they try to
+figure out ways to
+
+ align:start position:0%
+figure out ways to
+ 
+
+ align:start position:0%
+figure out ways to
+um deceive themselves that they're nice
+
+ align:start position:0%
+um deceive themselves that they're nice
+ 
+
+ align:start position:0%
+um deceive themselves that they're nice
+and if given the opportunity to not be
+
+ align:start position:0%
+and if given the opportunity to not be
+ 
+
+ align:start position:0%
+and if given the opportunity to not be
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+people actually seem to be not as nice
+
+ align:start position:0%
+people actually seem to be not as nice
+ 
+
+ align:start position:0%
+people actually seem to be not as nice
+as one might think from pure dictator
+
+ align:start position:0%
+as one might think from pure dictator
+ 
+
+ align:start position:0%
+as one might think from pure dictator
+games or
+
+ align:start position:0%
+games or
+ 
+
+ align:start position:0%
+games or
+ultimatum games that we observe this
+
+ align:start position:0%
+ultimatum games that we observe this
+ 
+
+ align:start position:0%
+ultimatum games that we observe this
+lecture is a bit more
+
+ align:start position:0%
+lecture is a bit more
+ 
+
+ align:start position:0%
+lecture is a bit more
+uplifting in the sense that it talks
+
+ align:start position:0%
+uplifting in the sense that it talks
+ 
+
+ align:start position:0%
+uplifting in the sense that it talks
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+field evidence on social preferences and
+
+ align:start position:0%
+field evidence on social preferences and
+ 
+
+ align:start position:0%
+field evidence on social preferences and
+in particular
+
+ align:start position:0%
+in particular
+ 
+
+ align:start position:0%
+in particular
+we're going to ask the question about
+
+ align:start position:0%
+we're going to ask the question about
+ 
+
+ align:start position:0%
+we're going to ask the question about
+how can or can policies increase
+
+ align:start position:0%
+how can or can policies increase
+ 
+
+ align:start position:0%
+how can or can policies increase
+pro-sociality in certain ways we're
+
+ align:start position:0%
+pro-sociality in certain ways we're
+ 
+
+ align:start position:0%
+pro-sociality in certain ways we're
+going to talk about three broad
+
+ align:start position:0%
+going to talk about three broad
+ 
+
+ align:start position:0%
+going to talk about three broad
+sets of studies first we're going to
+
+ align:start position:0%
+sets of studies first we're going to
+ 
+
+ align:start position:0%
+sets of studies first we're going to
+talk about social preferences at the
+
+ align:start position:0%
+talk about social preferences at the
+ 
+
+ align:start position:0%
+talk about social preferences at the
+workplace
+
+ align:start position:0%
+workplace
+ 
+
+ align:start position:0%
+workplace
+i'm going to talk about the impact of
+
+ align:start position:0%
+i'm going to talk about the impact of
+ 
+
+ align:start position:0%
+i'm going to talk about the impact of
+relative pay
+
+ align:start position:0%
+relative pay
+ 
+
+ align:start position:0%
+relative pay
+on productivity we talked about this
+
+ align:start position:0%
+on productivity we talked about this
+ 
+
+ align:start position:0%
+on productivity we talked about this
+last time at the end of the lecture a
+
+ align:start position:0%
+last time at the end of the lecture a
+ 
+
+ align:start position:0%
+last time at the end of the lecture a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+but i'm going to just restart from
+
+ align:start position:0%
+but i'm going to just restart from
+ 
+
+ align:start position:0%
+but i'm going to just restart from
+scratch to sort of explain that a little
+
+ align:start position:0%
+scratch to sort of explain that a little
+ 
+
+ align:start position:0%
+scratch to sort of explain that a little
+bit better
+
+ align:start position:0%
+bit better
+ 
+
+ align:start position:0%
+bit better
+then we're going to talk about the
+
+ align:start position:0%
+then we're going to talk about the
+ 
+
+ align:start position:0%
+then we're going to talk about the
+morale effects of pay inequality
+
+ align:start position:0%
+morale effects of pay inequality
+ 
+
+ align:start position:0%
+morale effects of pay inequality
+what happens to worker inequality when
+
+ align:start position:0%
+what happens to worker inequality when
+ 
+
+ align:start position:0%
+what happens to worker inequality when
+people are paid
+
+ align:start position:0%
+people are paid
+ 
+
+ align:start position:0%
+people are paid
+unequally and is that a good idea
+
+ align:start position:0%
+unequally and is that a good idea
+ 
+
+ align:start position:0%
+unequally and is that a good idea
+there's also a very nice paper in ethnic
+
+ align:start position:0%
+there's also a very nice paper in ethnic
+ 
+
+ align:start position:0%
+there's also a very nice paper in ethnic
+divisions and production in firms
+
+ align:start position:0%
+divisions and production in firms
+ 
+
+ align:start position:0%
+divisions and production in firms
+we're going to talk about this a little
+
+ align:start position:0%
+we're going to talk about this a little
+ 
+
+ align:start position:0%
+we're going to talk about this a little
+bit in recitation
+
+ align:start position:0%
+bit in recitation
+ 
+
+ align:start position:0%
+bit in recitation
+number two we're going to talk about um
+
+ align:start position:0%
+number two we're going to talk about um
+ 
+
+ align:start position:0%
+number two we're going to talk about um
+uh whether policies can
+
+ align:start position:0%
+uh whether policies can
+ 
+
+ align:start position:0%
+uh whether policies can
+induce uh prosecutionality in particular
+
+ align:start position:0%
+induce uh prosecutionality in particular
+ 
+
+ align:start position:0%
+induce uh prosecutionality in particular
+in a focus on mixing this is sort of the
+
+ align:start position:0%
+in a focus on mixing this is sort of the
+ 
+
+ align:start position:0%
+in a focus on mixing this is sort of the
+called the contact hypothesis when you
+
+ align:start position:0%
+called the contact hypothesis when you
+ 
+
+ align:start position:0%
+called the contact hypothesis when you
+mix people from different backgrounds
+
+ align:start position:0%
+mix people from different backgrounds
+ 
+
+ align:start position:0%
+mix people from different backgrounds
+do they become nicer to each other in
+
+ align:start position:0%
+do they become nicer to each other in
+ 
+
+ align:start position:0%
+do they become nicer to each other in
+various ways
+
+ align:start position:0%
+various ways
+ 
+
+ align:start position:0%
+various ways
+um you know discuss a very nice paper by
+
+ align:start position:0%
+um you know discuss a very nice paper by
+ 
+
+ align:start position:0%
+um you know discuss a very nice paper by
+gautam rao on mixing rich and poor
+
+ align:start position:0%
+gautam rao on mixing rich and poor
+ 
+
+ align:start position:0%
+gautam rao on mixing rich and poor
+children in school they're going to talk
+
+ align:start position:0%
+children in school they're going to talk
+ 
+
+ align:start position:0%
+children in school they're going to talk
+very briefly about mixing cricket
+
+ align:start position:0%
+very briefly about mixing cricket
+ 
+
+ align:start position:0%
+very briefly about mixing cricket
+players
+
+ align:start position:0%
+players
+ 
+
+ align:start position:0%
+players
+in india to reduce tensions across
+
+ align:start position:0%
+in india to reduce tensions across
+ 
+
+ align:start position:0%
+in india to reduce tensions across
+castes or make people from different
+
+ align:start position:0%
+castes or make people from different
+ 
+
+ align:start position:0%
+castes or make people from different
+casts
+
+ align:start position:0%
+casts
+ 
+
+ align:start position:0%
+casts
+perhaps more pro-social to each other
+
+ align:start position:0%
+perhaps more pro-social to each other
+ 
+
+ align:start position:0%
+perhaps more pro-social to each other
+i'm going to also briefly mention a
+
+ align:start position:0%
+i'm going to also briefly mention a
+ 
+
+ align:start position:0%
+i'm going to also briefly mention a
+study on mixing roommates in college
+
+ align:start position:0%
+study on mixing roommates in college
+ 
+
+ align:start position:0%
+study on mixing roommates in college
+by coronado finally we're going to talk
+
+ align:start position:0%
+by coronado finally we're going to talk
+ 
+
+ align:start position:0%
+by coronado finally we're going to talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+whether people perhaps underestimate the
+
+ align:start position:0%
+whether people perhaps underestimate the
+ 
+
+ align:start position:0%
+whether people perhaps underestimate the
+benefits of prosociality
+
+ align:start position:0%
+benefits of prosociality
+ 
+
+ align:start position:0%
+benefits of prosociality
+in particular i'm going to show you a
+
+ align:start position:0%
+in particular i'm going to show you a
+ 
+
+ align:start position:0%
+in particular i'm going to show you a
+study on people undervaluing gratitude
+
+ align:start position:0%
+study on people undervaluing gratitude
+ 
+
+ align:start position:0%
+study on people undervaluing gratitude
+so when people write letters of
+
+ align:start position:0%
+so when people write letters of
+ 
+
+ align:start position:0%
+so when people write letters of
+gratitude do others
+
+ align:start position:0%
+gratitude do others
+ 
+
+ align:start position:0%
+gratitude do others
+or do they understand how others might
+
+ align:start position:0%
+or do they understand how others might
+ 
+
+ align:start position:0%
+or do they understand how others might
+react and
+
+ align:start position:0%
+react and
+ 
+
+ align:start position:0%
+react and
+perhaps can be is there perhaps some
+
+ align:start position:0%
+perhaps can be is there perhaps some
+ 
+
+ align:start position:0%
+perhaps can be is there perhaps some
+evidence that people
+
+ align:start position:0%
+evidence that people
+ 
+
+ align:start position:0%
+evidence that people
+are not pro-social enough because they
+
+ align:start position:0%
+are not pro-social enough because they
+ 
+
+ align:start position:0%
+are not pro-social enough because they
+misunderstand
+
+ align:start position:0%
+misunderstand
+ 
+
+ align:start position:0%
+misunderstand
+the effects that that might have on
+
+ align:start position:0%
+the effects that that might have on
+ 
+
+ align:start position:0%
+the effects that that might have on
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+okay so let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me start with social preferences at
+
+ align:start position:0%
+let me start with social preferences at
+ 
+
+ align:start position:0%
+let me start with social preferences at
+the workplace so
+
+ align:start position:0%
+the workplace so
+ 
+
+ align:start position:0%
+the workplace so
+um bandaranadel is a very nice study
+
+ align:start position:0%
+um bandaranadel is a very nice study
+ 
+
+ align:start position:0%
+um bandaranadel is a very nice study
+that looks at the impact of relative pay
+
+ align:start position:0%
+that looks at the impact of relative pay
+ 
+
+ align:start position:0%
+that looks at the impact of relative pay
+on productivity
+
+ align:start position:0%
+on productivity
+ 
+
+ align:start position:0%
+on productivity
+this is field evidence from a fruit farm
+
+ align:start position:0%
+this is field evidence from a fruit farm
+ 
+
+ align:start position:0%
+this is field evidence from a fruit farm
+in the uk it's literally field evidence
+
+ align:start position:0%
+in the uk it's literally field evidence
+ 
+
+ align:start position:0%
+in the uk it's literally field evidence
+because it's from fruit picking farms
+
+ align:start position:0%
+because it's from fruit picking farms
+ 
+
+ align:start position:0%
+because it's from fruit picking farms
+from food fields
+
+ align:start position:0%
+from food fields
+ 
+
+ align:start position:0%
+from food fields
+the study looks at two types of payment
+
+ align:start position:0%
+the study looks at two types of payment
+ 
+
+ align:start position:0%
+the study looks at two types of payment
+schemes these are
+
+ align:start position:0%
+schemes these are
+ 
+
+ align:start position:0%
+schemes these are
+piece rates workers are paid per unit of
+
+ align:start position:0%
+piece rates workers are paid per unit of
+ 
+
+ align:start position:0%
+piece rates workers are paid per unit of
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+and the second scheme is relative pay
+
+ align:start position:0%
+and the second scheme is relative pay
+ 
+
+ align:start position:0%
+and the second scheme is relative pay
+workers are paid relative to others
+
+ align:start position:0%
+workers are paid relative to others
+ 
+
+ align:start position:0%
+workers are paid relative to others
+we might sort of think that relative pay
+
+ align:start position:0%
+we might sort of think that relative pay
+ 
+
+ align:start position:0%
+we might sort of think that relative pay
+is a good way to incentivize workers
+
+ align:start position:0%
+is a good way to incentivize workers
+ 
+
+ align:start position:0%
+is a good way to incentivize workers
+because you know you want to do better
+
+ align:start position:0%
+because you know you want to do better
+ 
+
+ align:start position:0%
+because you know you want to do better
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+uh your neighbor and there's sort of a
+
+ align:start position:0%
+uh your neighbor and there's sort of a
+ 
+
+ align:start position:0%
+uh your neighbor and there's sort of a
+competition
+
+ align:start position:0%
+competition
+ 
+
+ align:start position:0%
+competition
+of who does best and in principle it
+
+ align:start position:0%
+of who does best and in principle it
+ 
+
+ align:start position:0%
+of who does best and in principle it
+could be that like that really if you
+
+ align:start position:0%
+could be that like that really if you
+ 
+
+ align:start position:0%
+could be that like that really if you
+only care about yourself that really
+
+ align:start position:0%
+only care about yourself that really
+ 
+
+ align:start position:0%
+only care about yourself that really
+gets people to work very hard
+
+ align:start position:0%
+gets people to work very hard
+ 
+
+ align:start position:0%
+gets people to work very hard
+now what bandiera now look at is like
+
+ align:start position:0%
+now what bandiera now look at is like
+ 
+
+ align:start position:0%
+now what bandiera now look at is like
+does or how does the
+
+ align:start position:0%
+does or how does the
+ 
+
+ align:start position:0%
+does or how does the
+introduction of relative pay affect
+
+ align:start position:0%
+introduction of relative pay affect
+ 
+
+ align:start position:0%
+introduction of relative pay affect
+workers
+
+ align:start position:0%
+workers
+ 
+
+ align:start position:0%
+workers
+effort and output now one thing they
+
+ align:start position:0%
+effort and output now one thing they
+ 
+
+ align:start position:0%
+effort and output now one thing they
+notice is that
+
+ align:start position:0%
+notice is that
+ 
+
+ align:start position:0%
+notice is that
+while um relative incentives might be
+
+ align:start position:0%
+while um relative incentives might be
+ 
+
+ align:start position:0%
+while um relative incentives might be
+good because you might sort of
+
+ align:start position:0%
+good because you might sort of
+ 
+
+ align:start position:0%
+good because you might sort of
+induce people to want to be better than
+
+ align:start position:0%
+induce people to want to be better than
+ 
+
+ align:start position:0%
+induce people to want to be better than
+their um
+
+ align:start position:0%
+their um
+ 
+
+ align:start position:0%
+their um
+their neighbors or their co-workers
+
+ align:start position:0%
+their neighbors or their co-workers
+ 
+
+ align:start position:0%
+their neighbors or their co-workers
+there's also a negative
+
+ align:start position:0%
+there's also a negative
+ 
+
+ align:start position:0%
+there's also a negative
+externality of relative pay that is the
+
+ align:start position:0%
+externality of relative pay that is the
+ 
+
+ align:start position:0%
+externality of relative pay that is the
+idea that increasing
+
+ align:start position:0%
+idea that increasing
+ 
+
+ align:start position:0%
+idea that increasing
+your own pay comes at the cost of others
+
+ align:start position:0%
+your own pay comes at the cost of others
+ 
+
+ align:start position:0%
+your own pay comes at the cost of others
+pay
+
+ align:start position:0%
+pay
+ 
+
+ align:start position:0%
+pay
+that is to say if there's relative pay
+
+ align:start position:0%
+that is to say if there's relative pay
+ 
+
+ align:start position:0%
+that is to say if there's relative pay
+and i work really hard
+
+ align:start position:0%
+and i work really hard
+ 
+
+ align:start position:0%
+and i work really hard
+i'm paid how i do relative to my friends
+
+ align:start position:0%
+i'm paid how i do relative to my friends
+ 
+
+ align:start position:0%
+i'm paid how i do relative to my friends
+or others that i'm working with
+
+ align:start position:0%
+or others that i'm working with
+ 
+
+ align:start position:0%
+or others that i'm working with
+well if i'm working really hard and do
+
+ align:start position:0%
+well if i'm working really hard and do
+ 
+
+ align:start position:0%
+well if i'm working really hard and do
+better than my friends i'm going to be
+
+ align:start position:0%
+better than my friends i'm going to be
+ 
+
+ align:start position:0%
+better than my friends i'm going to be
+paid more
+
+ align:start position:0%
+paid more
+ 
+
+ align:start position:0%
+paid more
+but at the same time my friends for any
+
+ align:start position:0%
+but at the same time my friends for any
+ 
+
+ align:start position:0%
+but at the same time my friends for any
+effort that i put in
+
+ align:start position:0%
+effort that i put in
+ 
+
+ align:start position:0%
+effort that i put in
+my friends are going to be paid less and
+
+ align:start position:0%
+my friends are going to be paid less and
+ 
+
+ align:start position:0%
+my friends are going to be paid less and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+workers sort of anticipating these
+
+ align:start position:0%
+workers sort of anticipating these
+ 
+
+ align:start position:0%
+workers sort of anticipating these
+impacts on on others
+
+ align:start position:0%
+impacts on on others
+ 
+
+ align:start position:0%
+impacts on on others
+might reduce their effort if they care
+
+ align:start position:0%
+might reduce their effort if they care
+ 
+
+ align:start position:0%
+might reduce their effort if they care
+about others right if i'm really worried
+
+ align:start position:0%
+about others right if i'm really worried
+ 
+
+ align:start position:0%
+about others right if i'm really worried
+about like if there's relative pay and i
+
+ align:start position:0%
+about like if there's relative pay and i
+ 
+
+ align:start position:0%
+about like if there's relative pay and i
+work really hard my friends are going to
+
+ align:start position:0%
+work really hard my friends are going to
+ 
+
+ align:start position:0%
+work really hard my friends are going to
+look bad
+
+ align:start position:0%
+look bad
+ 
+
+ align:start position:0%
+look bad
+they're going to be relatively uh
+
+ align:start position:0%
+they're going to be relatively uh
+ 
+
+ align:start position:0%
+they're going to be relatively uh
+unproductive
+
+ align:start position:0%
+unproductive
+ 
+
+ align:start position:0%
+unproductive
+and i worry that they might not be paid
+
+ align:start position:0%
+and i worry that they might not be paid
+ 
+
+ align:start position:0%
+and i worry that they might not be paid
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+then um i might reduce my effort and
+
+ align:start position:0%
+then um i might reduce my effort and
+ 
+
+ align:start position:0%
+then um i might reduce my effort and
+sort of everybody might do that and then
+
+ align:start position:0%
+sort of everybody might do that and then
+ 
+
+ align:start position:0%
+sort of everybody might do that and then
+the introduction of relative pay or the
+
+ align:start position:0%
+the introduction of relative pay or the
+ 
+
+ align:start position:0%
+the introduction of relative pay or the
+relative pay schemes might actually not
+
+ align:start position:0%
+relative pay schemes might actually not
+ 
+
+ align:start position:0%
+relative pay schemes might actually not
+be particularly
+
+ align:start position:0%
+be particularly
+ 
+
+ align:start position:0%
+be particularly
+uh effective or effective way of
+
+ align:start position:0%
+uh effective or effective way of
+ 
+
+ align:start position:0%
+uh effective or effective way of
+incentivizing
+
+ align:start position:0%
+incentivizing
+ 
+
+ align:start position:0%
+incentivizing
+and motivating workers so there's sort
+
+ align:start position:0%
+and motivating workers so there's sort
+ 
+
+ align:start position:0%
+and motivating workers so there's sort
+of this tension that relative pain
+
+ align:start position:0%
+of this tension that relative pain
+ 
+
+ align:start position:0%
+of this tension that relative pain
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+could work quite well but if people
+
+ align:start position:0%
+could work quite well but if people
+ 
+
+ align:start position:0%
+could work quite well but if people
+really care a lot about others
+
+ align:start position:0%
+really care a lot about others
+ 
+
+ align:start position:0%
+really care a lot about others
+then it might not work at all it might
+
+ align:start position:0%
+then it might not work at all it might
+ 
+
+ align:start position:0%
+then it might not work at all it might
+actually backfire in some ways
+
+ align:start position:0%
+actually backfire in some ways
+ 
+
+ align:start position:0%
+actually backfire in some ways
+notice that it could be either that
+
+ align:start position:0%
+notice that it could be either that
+ 
+
+ align:start position:0%
+notice that it could be either that
+people care about others
+
+ align:start position:0%
+people care about others
+ 
+
+ align:start position:0%
+people care about others
+for their own sake in the sense that
+
+ align:start position:0%
+for their own sake in the sense that
+ 
+
+ align:start position:0%
+for their own sake in the sense that
+like you might care about them
+
+ align:start position:0%
+like you might care about them
+ 
+
+ align:start position:0%
+like you might care about them
+because you want them to have high
+
+ align:start position:0%
+because you want them to have high
+ 
+
+ align:start position:0%
+because you want them to have high
+earnings or you might care about
+
+ align:start position:0%
+earnings or you might care about
+ 
+
+ align:start position:0%
+earnings or you might care about
+others earnings not because you actually
+
+ align:start position:0%
+others earnings not because you actually
+ 
+
+ align:start position:0%
+others earnings not because you actually
+care about the outcomes per se
+
+ align:start position:0%
+care about the outcomes per se
+ 
+
+ align:start position:0%
+care about the outcomes per se
+but rather because you're worried about
+
+ align:start position:0%
+but rather because you're worried about
+ 
+
+ align:start position:0%
+but rather because you're worried about
+negative repercussions right if these
+
+ align:start position:0%
+negative repercussions right if these
+ 
+
+ align:start position:0%
+negative repercussions right if these
+are your friends and you worked really
+
+ align:start position:0%
+are your friends and you worked really
+ 
+
+ align:start position:0%
+are your friends and you worked really
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+well at night your friends might really
+
+ align:start position:0%
+well at night your friends might really
+ 
+
+ align:start position:0%
+well at night your friends might really
+not be happy and there might be sort of
+
+ align:start position:0%
+not be happy and there might be sort of
+ 
+
+ align:start position:0%
+not be happy and there might be sort of
+retribution against you
+
+ align:start position:0%
+retribution against you
+ 
+
+ align:start position:0%
+retribution against you
+socially or in some other ways if you
+
+ align:start position:0%
+socially or in some other ways if you
+ 
+
+ align:start position:0%
+socially or in some other ways if you
+work too hard if you cause them
+
+ align:start position:0%
+work too hard if you cause them
+ 
+
+ align:start position:0%
+work too hard if you cause them
+their earnings to go down okay
+
+ align:start position:0%
+their earnings to go down okay
+ 
+
+ align:start position:0%
+their earnings to go down okay
+so now what does this paper do it looks
+
+ align:start position:0%
+so now what does this paper do it looks
+ 
+
+ align:start position:0%
+so now what does this paper do it looks
+at how does switching to
+
+ align:start position:0%
+at how does switching to
+ 
+
+ align:start position:0%
+at how does switching to
+to piece rates affect the people's
+
+ align:start position:0%
+to piece rates affect the people's
+ 
+
+ align:start position:0%
+to piece rates affect the people's
+productivity um
+
+ align:start position:0%
+productivity um
+ 
+
+ align:start position:0%
+productivity um
+so the study has personnel data from a
+
+ align:start position:0%
+so the study has personnel data from a
+ 
+
+ align:start position:0%
+so the study has personnel data from a
+food farm in the uk
+
+ align:start position:0%
+food farm in the uk
+ 
+
+ align:start position:0%
+food farm in the uk
+they measure productivity as a function
+
+ align:start position:0%
+they measure productivity as a function
+ 
+
+ align:start position:0%
+they measure productivity as a function
+of their compensation scheme
+
+ align:start position:0%
+of their compensation scheme
+ 
+
+ align:start position:0%
+of their compensation scheme
+this is a quasi-field experiment the
+
+ align:start position:0%
+this is a quasi-field experiment the
+ 
+
+ align:start position:0%
+this is a quasi-field experiment the
+timeline is as follows
+
+ align:start position:0%
+timeline is as follows
+ 
+
+ align:start position:0%
+timeline is as follows
+for the first eight weeks of the 2002
+
+ align:start position:0%
+for the first eight weeks of the 2002
+ 
+
+ align:start position:0%
+for the first eight weeks of the 2002
+picking season
+
+ align:start position:0%
+picking season
+ 
+
+ align:start position:0%
+picking season
+fruit pickers were compensated relative
+
+ align:start position:0%
+fruit pickers were compensated relative
+ 
+
+ align:start position:0%
+fruit pickers were compensated relative
+on a relative performance scheme so um
+
+ align:start position:0%
+on a relative performance scheme so um
+ 
+
+ align:start position:0%
+on a relative performance scheme so um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the per fruit piece the per piece rate
+
+ align:start position:0%
+the per fruit piece the per piece rate
+ 
+
+ align:start position:0%
+the per fruit piece the per piece rate
+is decreasing in average productivity
+
+ align:start position:0%
+is decreasing in average productivity
+ 
+
+ align:start position:0%
+is decreasing in average productivity
+right so like if everybody works really
+
+ align:start position:0%
+right so like if everybody works really
+ 
+
+ align:start position:0%
+right so like if everybody works really
+hard and i don't if i'm relatively bad
+
+ align:start position:0%
+hard and i don't if i'm relatively bad
+ 
+
+ align:start position:0%
+hard and i don't if i'm relatively bad
+compared to other i get less
+
+ align:start position:0%
+compared to other i get less
+ 
+
+ align:start position:0%
+compared to other i get less
+than others the incentive to keep this
+
+ align:start position:0%
+than others the incentive to keep this
+ 
+
+ align:start position:0%
+than others the incentive to keep this
+is sort of an incentive to keep as i
+
+ align:start position:0%
+is sort of an incentive to keep as i
+ 
+
+ align:start position:0%
+is sort of an incentive to keep as i
+discussed
+
+ align:start position:0%
+discussed
+ 
+
+ align:start position:0%
+discussed
+to keep the productivity low if you care
+
+ align:start position:0%
+to keep the productivity low if you care
+ 
+
+ align:start position:0%
+to keep the productivity low if you care
+about others
+
+ align:start position:0%
+about others
+ 
+
+ align:start position:0%
+about others
+and then in the next eight weeks
+
+ align:start position:0%
+and then in the next eight weeks
+ 
+
+ align:start position:0%
+and then in the next eight weeks
+compensation was switched to a flat
+
+ align:start position:0%
+compensation was switched to a flat
+ 
+
+ align:start position:0%
+compensation was switched to a flat
+piece rate per fruit
+
+ align:start position:0%
+piece rate per fruit
+ 
+
+ align:start position:0%
+piece rate per fruit
+so that's essentially just like you're
+
+ align:start position:0%
+so that's essentially just like you're
+ 
+
+ align:start position:0%
+so that's essentially just like you're
+paid by however you
+
+ align:start position:0%
+paid by however you
+ 
+
+ align:start position:0%
+paid by however you
+how much you produce how many kilograms
+
+ align:start position:0%
+how much you produce how many kilograms
+ 
+
+ align:start position:0%
+how much you produce how many kilograms
+of fruit you
+
+ align:start position:0%
+of fruit you
+ 
+
+ align:start position:0%
+of fruit you
+collect and the payment is
+
+ align:start position:0%
+collect and the payment is
+ 
+
+ align:start position:0%
+collect and the payment is
+entirely disjoint or independent of what
+
+ align:start position:0%
+entirely disjoint or independent of what
+ 
+
+ align:start position:0%
+entirely disjoint or independent of what
+other peoples do that's like a classic
+
+ align:start position:0%
+other peoples do that's like a classic
+ 
+
+ align:start position:0%
+other peoples do that's like a classic
+piece rate
+
+ align:start position:0%
+piece rate
+ 
+
+ align:start position:0%
+piece rate
+payment so the externalities are
+
+ align:start position:0%
+payment so the externalities are
+ 
+
+ align:start position:0%
+payment so the externalities are
+entirely shut down
+
+ align:start position:0%
+entirely shut down
+ 
+
+ align:start position:0%
+entirely shut down
+if i work really hard i'm going to be
+
+ align:start position:0%
+if i work really hard i'm going to be
+ 
+
+ align:start position:0%
+if i work really hard i'm going to be
+paid
+
+ align:start position:0%
+paid
+ 
+
+ align:start position:0%
+paid
+there's no effect whatsoever on my
+
+ align:start position:0%
+there's no effect whatsoever on my
+ 
+
+ align:start position:0%
+there's no effect whatsoever on my
+fellow workers
+
+ align:start position:0%
+fellow workers
+ 
+
+ align:start position:0%
+fellow workers
+the switch was announced on the day the
+
+ align:start position:0%
+the switch was announced on the day the
+ 
+
+ align:start position:0%
+the switch was announced on the day the
+change took place so it came as a
+
+ align:start position:0%
+change took place so it came as a
+ 
+
+ align:start position:0%
+change took place so it came as a
+surprise to workers we so we should not
+
+ align:start position:0%
+surprise to workers we so we should not
+ 
+
+ align:start position:0%
+surprise to workers we so we should not
+be worried about sort of
+
+ align:start position:0%
+be worried about sort of
+ 
+
+ align:start position:0%
+be worried about sort of
+pre-trends or productivity going up over
+
+ align:start position:0%
+pre-trends or productivity going up over
+ 
+
+ align:start position:0%
+pre-trends or productivity going up over
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+anyway now what the people find is a
+
+ align:start position:0%
+anyway now what the people find is a
+ 
+
+ align:start position:0%
+anyway now what the people find is a
+dramatic increase in productivity with
+
+ align:start position:0%
+dramatic increase in productivity with
+ 
+
+ align:start position:0%
+dramatic increase in productivity with
+the introduction of piece rates
+
+ align:start position:0%
+the introduction of piece rates
+ 
+
+ align:start position:0%
+the introduction of piece rates
+that is to say um what you see here in
+
+ align:start position:0%
+that is to say um what you see here in
+ 
+
+ align:start position:0%
+that is to say um what you see here in
+the figure is
+
+ align:start position:0%
+the figure is
+ 
+
+ align:start position:0%
+the figure is
+the average worker productivity for two
+
+ align:start position:0%
+the average worker productivity for two
+ 
+
+ align:start position:0%
+the average worker productivity for two
+of the fields so this essentially like
+
+ align:start position:0%
+of the fields so this essentially like
+ 
+
+ align:start position:0%
+of the fields so this essentially like
+broad big fields where people work on
+
+ align:start position:0%
+broad big fields where people work on
+ 
+
+ align:start position:0%
+broad big fields where people work on
+i'm showing you sort of the data for two
+
+ align:start position:0%
+i'm showing you sort of the data for two
+ 
+
+ align:start position:0%
+i'm showing you sort of the data for two
+of those fields for which essentially on
+
+ align:start position:0%
+of those fields for which essentially on
+ 
+
+ align:start position:0%
+of those fields for which essentially on
+most days
+
+ align:start position:0%
+most days
+ 
+
+ align:start position:0%
+most days
+there was actually production workers
+
+ align:start position:0%
+there was actually production workers
+ 
+
+ align:start position:0%
+there was actually production workers
+were picking fruit
+
+ align:start position:0%
+were picking fruit
+ 
+
+ align:start position:0%
+were picking fruit
+what you see on the left side of the
+
+ align:start position:0%
+what you see on the left side of the
+ 
+
+ align:start position:0%
+what you see on the left side of the
+graph is um
+
+ align:start position:0%
+graph is um
+ 
+
+ align:start position:0%
+graph is um
+when uh people were working under under
+
+ align:start position:0%
+when uh people were working under under
+ 
+
+ align:start position:0%
+when uh people were working under under
+relative pay
+
+ align:start position:0%
+relative pay
+ 
+
+ align:start position:0%
+relative pay
+there you see essentially relative flat
+
+ align:start position:0%
+there you see essentially relative flat
+ 
+
+ align:start position:0%
+there you see essentially relative flat
+productivity
+
+ align:start position:0%
+productivity
+ 
+
+ align:start position:0%
+productivity
+people had about like five kilograms
+
+ align:start position:0%
+people had about like five kilograms
+ 
+
+ align:start position:0%
+people had about like five kilograms
+picked about five kilograms per hour
+
+ align:start position:0%
+picked about five kilograms per hour
+ 
+
+ align:start position:0%
+picked about five kilograms per hour
+that doesn't seem to be any trend
+
+ align:start position:0%
+that doesn't seem to be any trend
+ 
+
+ align:start position:0%
+that doesn't seem to be any trend
+upwards over time so before the new
+
+ align:start position:0%
+upwards over time so before the new
+ 
+
+ align:start position:0%
+upwards over time so before the new
+policy was introduced essentially
+
+ align:start position:0%
+policy was introduced essentially
+ 
+
+ align:start position:0%
+policy was introduced essentially
+workers were
+
+ align:start position:0%
+workers were
+ 
+
+ align:start position:0%
+workers were
+producing um or picking their food at a
+
+ align:start position:0%
+producing um or picking their food at a
+ 
+
+ align:start position:0%
+producing um or picking their food at a
+relatively constant rate over time about
+
+ align:start position:0%
+relatively constant rate over time about
+ 
+
+ align:start position:0%
+relatively constant rate over time about
+five kilograms
+
+ align:start position:0%
+five kilograms
+ 
+
+ align:start position:0%
+five kilograms
+per hour there was no trends as i said
+
+ align:start position:0%
+per hour there was no trends as i said
+ 
+
+ align:start position:0%
+per hour there was no trends as i said
+now then you see so the vertical line um
+
+ align:start position:0%
+now then you see so the vertical line um
+ 
+
+ align:start position:0%
+now then you see so the vertical line um
+in the middle
+
+ align:start position:0%
+in the middle
+ 
+
+ align:start position:0%
+in the middle
+this is when um piece rates were in fact
+
+ align:start position:0%
+this is when um piece rates were in fact
+ 
+
+ align:start position:0%
+this is when um piece rates were in fact
+um uh introduced so there was no
+
+ align:start position:0%
+um uh introduced so there was no
+ 
+
+ align:start position:0%
+um uh introduced so there was no
+relative pay anymore and now they were
+
+ align:start position:0%
+relative pay anymore and now they were
+ 
+
+ align:start position:0%
+relative pay anymore and now they were
+people were paid by piece rate
+
+ align:start position:0%
+people were paid by piece rate
+ 
+
+ align:start position:0%
+people were paid by piece rate
+and that increased productivity by over
+
+ align:start position:0%
+and that increased productivity by over
+ 
+
+ align:start position:0%
+and that increased productivity by over
+50 so workers became a lot more
+
+ align:start position:0%
+50 so workers became a lot more
+ 
+
+ align:start position:0%
+50 so workers became a lot more
+productive
+
+ align:start position:0%
+productive
+ 
+
+ align:start position:0%
+productive
+after that um that's true for both of
+
+ align:start position:0%
+after that um that's true for both of
+ 
+
+ align:start position:0%
+after that um that's true for both of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+fields it is not the case that the
+
+ align:start position:0%
+fields it is not the case that the
+ 
+
+ align:start position:0%
+fields it is not the case that the
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+payment per unit of output per kilogram
+
+ align:start position:0%
+payment per unit of output per kilogram
+ 
+
+ align:start position:0%
+payment per unit of output per kilogram
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+for people were paid were actually was
+
+ align:start position:0%
+for people were paid were actually was
+ 
+
+ align:start position:0%
+for people were paid were actually was
+going up so you might sort of say well
+
+ align:start position:0%
+going up so you might sort of say well
+ 
+
+ align:start position:0%
+going up so you might sort of say well
+you know if the piece rate was actually
+
+ align:start position:0%
+you know if the piece rate was actually
+ 
+
+ align:start position:0%
+you know if the piece rate was actually
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+um under the piece rate payments
+
+ align:start position:0%
+um under the piece rate payments
+ 
+
+ align:start position:0%
+um under the piece rate payments
+on the right side of the screen well
+
+ align:start position:0%
+on the right side of the screen well
+ 
+
+ align:start position:0%
+on the right side of the screen well
+maybe then you know of the graph then
+
+ align:start position:0%
+maybe then you know of the graph then
+ 
+
+ align:start position:0%
+maybe then you know of the graph then
+maybe workers would just be more
+
+ align:start position:0%
+maybe workers would just be more
+ 
+
+ align:start position:0%
+maybe workers would just be more
+productive
+
+ align:start position:0%
+productive
+ 
+
+ align:start position:0%
+productive
+but in fact if you look at sort of the
+
+ align:start position:0%
+but in fact if you look at sort of the
+ 
+
+ align:start position:0%
+but in fact if you look at sort of the
+piece rate over time if anything the
+
+ align:start position:0%
+piece rate over time if anything the
+ 
+
+ align:start position:0%
+piece rate over time if anything the
+piece rates actually went down over time
+
+ align:start position:0%
+piece rates actually went down over time
+ 
+
+ align:start position:0%
+piece rates actually went down over time
+what the
+
+ align:start position:0%
+what the
+ 
+
+ align:start position:0%
+what the
+company was paying so that is to say
+
+ align:start position:0%
+company was paying so that is to say
+ 
+
+ align:start position:0%
+company was paying so that is to say
+the introduction of those piece rates
+
+ align:start position:0%
+the introduction of those piece rates
+ 
+
+ align:start position:0%
+the introduction of those piece rates
+the productivity effect is not explained
+
+ align:start position:0%
+the productivity effect is not explained
+ 
+
+ align:start position:0%
+the productivity effect is not explained
+by workers being paid more
+
+ align:start position:0%
+by workers being paid more
+ 
+
+ align:start position:0%
+by workers being paid more
+per unit of output instead it seems to
+
+ align:start position:0%
+per unit of output instead it seems to
+ 
+
+ align:start position:0%
+per unit of output instead it seems to
+be really coming from the different
+
+ align:start position:0%
+be really coming from the different
+ 
+
+ align:start position:0%
+be really coming from the different
+incentives
+
+ align:start position:0%
+incentives
+ 
+
+ align:start position:0%
+incentives
+people workers have when it comes to how
+
+ align:start position:0%
+people workers have when it comes to how
+ 
+
+ align:start position:0%
+people workers have when it comes to how
+their productivity
+
+ align:start position:0%
+their productivity
+ 
+
+ align:start position:0%
+their productivity
+affects their fellow workers on the
+
+ align:start position:0%
+affects their fellow workers on the
+ 
+
+ align:start position:0%
+affects their fellow workers on the
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+now you might have sort of like two
+
+ align:start position:0%
+now you might have sort of like two
+ 
+
+ align:start position:0%
+now you might have sort of like two
+potential explanation here for this um
+
+ align:start position:0%
+potential explanation here for this um
+ 
+
+ align:start position:0%
+potential explanation here for this um
+uh evidence one is social preferences so
+
+ align:start position:0%
+uh evidence one is social preferences so
+ 
+
+ align:start position:0%
+uh evidence one is social preferences so
+you might work
+
+ align:start position:0%
+you might work
+ 
+
+ align:start position:0%
+you might work
+less um to help others under relative um
+
+ align:start position:0%
+less um to help others under relative um
+ 
+
+ align:start position:0%
+less um to help others under relative um
+uh incentives right and you might um
+
+ align:start position:0%
+uh incentives right and you might um
+ 
+
+ align:start position:0%
+uh incentives right and you might um
+um even less when your friends benefits
+
+ align:start position:0%
+um even less when your friends benefits
+ 
+
+ align:start position:0%
+um even less when your friends benefits
+you if you have many
+
+ align:start position:0%
+you if you have many
+ 
+
+ align:start position:0%
+you if you have many
+uh friends on a certain field that work
+
+ align:start position:0%
+uh friends on a certain field that work
+ 
+
+ align:start position:0%
+uh friends on a certain field that work
+with you
+
+ align:start position:0%
+with you
+ 
+
+ align:start position:0%
+with you
+well then you might be particularly
+
+ align:start position:0%
+well then you might be particularly
+ 
+
+ align:start position:0%
+well then you might be particularly
+inclined to not work very hard
+
+ align:start position:0%
+inclined to not work very hard
+ 
+
+ align:start position:0%
+inclined to not work very hard
+because you will care a lot more um uh
+
+ align:start position:0%
+because you will care a lot more um uh
+ 
+
+ align:start position:0%
+because you will care a lot more um uh
+for them
+
+ align:start position:0%
+for them
+ 
+
+ align:start position:0%
+for them
+and this is sort of exactly what they
+
+ align:start position:0%
+and this is sort of exactly what they
+ 
+
+ align:start position:0%
+and this is sort of exactly what they
+find in this paper uh these effects are
+
+ align:start position:0%
+find in this paper uh these effects are
+ 
+
+ align:start position:0%
+find in this paper uh these effects are
+stronger when they're more
+
+ align:start position:0%
+stronger when they're more
+ 
+
+ align:start position:0%
+stronger when they're more
+um friends on the field uh for a
+
+ align:start position:0%
+um friends on the field uh for a
+ 
+
+ align:start position:0%
+um friends on the field uh for a
+particular worker
+
+ align:start position:0%
+particular worker
+ 
+
+ align:start position:0%
+particular worker
+second however it's also like a repeated
+
+ align:start position:0%
+second however it's also like a repeated
+ 
+
+ align:start position:0%
+second however it's also like a repeated
+game that is to say
+
+ align:start position:0%
+game that is to say
+ 
+
+ align:start position:0%
+game that is to say
+the the sort of a low effort equilibrium
+
+ align:start position:0%
+the the sort of a low effort equilibrium
+ 
+
+ align:start position:0%
+the the sort of a low effort equilibrium
+where essentially if there's relative
+
+ align:start position:0%
+where essentially if there's relative
+ 
+
+ align:start position:0%
+where essentially if there's relative
+pay
+
+ align:start position:0%
+pay
+ 
+
+ align:start position:0%
+pay
+we can just all agree everybody on the
+
+ align:start position:0%
+we can just all agree everybody on the
+ 
+
+ align:start position:0%
+we can just all agree everybody on the
+field might sort of agree that not
+
+ align:start position:0%
+field might sort of agree that not
+ 
+
+ align:start position:0%
+field might sort of agree that not
+working particularly hard
+
+ align:start position:0%
+working particularly hard
+ 
+
+ align:start position:0%
+working particularly hard
+is uh is a good idea because we are
+
+ align:start position:0%
+is uh is a good idea because we are
+ 
+
+ align:start position:0%
+is uh is a good idea because we are
+essentially paid relatively anyway
+
+ align:start position:0%
+essentially paid relatively anyway
+ 
+
+ align:start position:0%
+essentially paid relatively anyway
+so if everybody doubles their effort
+
+ align:start position:0%
+so if everybody doubles their effort
+ 
+
+ align:start position:0%
+so if everybody doubles their effort
+nothing is going to pay
+
+ align:start position:0%
+nothing is going to pay
+ 
+
+ align:start position:0%
+nothing is going to pay
+there's nothing that's going to happen
+
+ align:start position:0%
+there's nothing that's going to happen
+ 
+
+ align:start position:0%
+there's nothing that's going to happen
+to workers compensation
+
+ align:start position:0%
+to workers compensation
+ 
+
+ align:start position:0%
+to workers compensation
+so you might as well just decide
+
+ align:start position:0%
+so you might as well just decide
+ 
+
+ align:start position:0%
+so you might as well just decide
+everybody could just decide work half as
+
+ align:start position:0%
+everybody could just decide work half as
+ 
+
+ align:start position:0%
+everybody could just decide work half as
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+and we're going to be paid the same and
+
+ align:start position:0%
+and we're going to be paid the same and
+ 
+
+ align:start position:0%
+and we're going to be paid the same and
+as long as we sort of can
+
+ align:start position:0%
+as long as we sort of can
+ 
+
+ align:start position:0%
+as long as we sort of can
+sustain at equilibrium that's a good
+
+ align:start position:0%
+sustain at equilibrium that's a good
+ 
+
+ align:start position:0%
+sustain at equilibrium that's a good
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+of course in any given period
+
+ align:start position:0%
+of course in any given period
+ 
+
+ align:start position:0%
+of course in any given period
+any given worker might have the
+
+ align:start position:0%
+any given worker might have the
+ 
+
+ align:start position:0%
+any given worker might have the
+incentives to deviate from this
+
+ align:start position:0%
+incentives to deviate from this
+ 
+
+ align:start position:0%
+incentives to deviate from this
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+because on any given day if you work
+
+ align:start position:0%
+because on any given day if you work
+ 
+
+ align:start position:0%
+because on any given day if you work
+really hard you're going to be paid a
+
+ align:start position:0%
+really hard you're going to be paid a
+ 
+
+ align:start position:0%
+really hard you're going to be paid a
+lot more
+
+ align:start position:0%
+lot more
+ 
+
+ align:start position:0%
+lot more
+for that today and so um
+
+ align:start position:0%
+for that today and so um
+ 
+
+ align:start position:0%
+for that today and so um
+how might we be able to disentangle that
+
+ align:start position:0%
+how might we be able to disentangle that
+ 
+
+ align:start position:0%
+how might we be able to disentangle that
+well um what bandiera
+
+ align:start position:0%
+well um what bandiera
+ 
+
+ align:start position:0%
+well um what bandiera
+have is they have also some variation in
+
+ align:start position:0%
+have is they have also some variation in
+ 
+
+ align:start position:0%
+have is they have also some variation in
+the types of fruits that
+
+ align:start position:0%
+the types of fruits that
+ 
+
+ align:start position:0%
+the types of fruits that
+were collected what do i mean by that
+
+ align:start position:0%
+were collected what do i mean by that
+ 
+
+ align:start position:0%
+were collected what do i mean by that
+well if you think about what you need to
+
+ align:start position:0%
+well if you think about what you need to
+ 
+
+ align:start position:0%
+well if you think about what you need to
+be able to
+
+ align:start position:0%
+be able to
+ 
+
+ align:start position:0%
+be able to
+disentangle these what you might want to
+
+ align:start position:0%
+disentangle these what you might want to
+ 
+
+ align:start position:0%
+disentangle these what you might want to
+have is like differences in the
+
+ align:start position:0%
+have is like differences in the
+ 
+
+ align:start position:0%
+have is like differences in the
+observability of effort right so if i
+
+ align:start position:0%
+observability of effort right so if i
+ 
+
+ align:start position:0%
+observability of effort right so if i
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+see what my co-worker does i can like
+
+ align:start position:0%
+see what my co-worker does i can like
+ 
+
+ align:start position:0%
+see what my co-worker does i can like
+punish them very effectively i can just
+
+ align:start position:0%
+punish them very effectively i can just
+ 
+
+ align:start position:0%
+punish them very effectively i can just
+know like whenever um
+
+ align:start position:0%
+know like whenever um
+ 
+
+ align:start position:0%
+know like whenever um
+frank is working really hard my
+
+ align:start position:0%
+frank is working really hard my
+ 
+
+ align:start position:0%
+frank is working really hard my
+co-workers might
+
+ align:start position:0%
+co-workers might
+ 
+
+ align:start position:0%
+co-workers might
+want to punish me um and then it's very
+
+ align:start position:0%
+want to punish me um and then it's very
+ 
+
+ align:start position:0%
+want to punish me um and then it's very
+hard for me to work really hard because
+
+ align:start position:0%
+hard for me to work really hard because
+ 
+
+ align:start position:0%
+hard for me to work really hard because
+you know i'm getting trouble at night
+
+ align:start position:0%
+you know i'm getting trouble at night
+ 
+
+ align:start position:0%
+you know i'm getting trouble at night
+after work with my co-workers or the
+
+ align:start position:0%
+after work with my co-workers or the
+ 
+
+ align:start position:0%
+after work with my co-workers or the
+next day everybody might also work
+
+ align:start position:0%
+next day everybody might also work
+ 
+
+ align:start position:0%
+next day everybody might also work
+really hard and i kind of don't want
+
+ align:start position:0%
+really hard and i kind of don't want
+ 
+
+ align:start position:0%
+really hard and i kind of don't want
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+on the other hand if i can hide how hard
+
+ align:start position:0%
+on the other hand if i can hide how hard
+ 
+
+ align:start position:0%
+on the other hand if i can hide how hard
+i'm working well then you know
+
+ align:start position:0%
+i'm working well then you know
+ 
+
+ align:start position:0%
+i'm working well then you know
+i might secretly work really hard and my
+
+ align:start position:0%
+i might secretly work really hard and my
+ 
+
+ align:start position:0%
+i might secretly work really hard and my
+co-workers might not even
+
+ align:start position:0%
+co-workers might not even
+ 
+
+ align:start position:0%
+co-workers might not even
+find out so then um if that's the case
+
+ align:start position:0%
+find out so then um if that's the case
+ 
+
+ align:start position:0%
+find out so then um if that's the case
+in the repeated game um the repeated
+
+ align:start position:0%
+in the repeated game um the repeated
+ 
+
+ align:start position:0%
+in the repeated game um the repeated
+game equilibrium might not just be
+
+ align:start position:0%
+game equilibrium might not just be
+ 
+
+ align:start position:0%
+game equilibrium might not just be
+might just not be enforceable as in like
+
+ align:start position:0%
+might just not be enforceable as in like
+ 
+
+ align:start position:0%
+might just not be enforceable as in like
+i might just tell my friends oh i wasn't
+
+ align:start position:0%
+i might just tell my friends oh i wasn't
+ 
+
+ align:start position:0%
+i might just tell my friends oh i wasn't
+really working hard but in fact i was
+
+ align:start position:0%
+really working hard but in fact i was
+ 
+
+ align:start position:0%
+really working hard but in fact i was
+and like
+
+ align:start position:0%
+and like
+ 
+
+ align:start position:0%
+and like
+they have no way of finding out because
+
+ align:start position:0%
+they have no way of finding out because
+ 
+
+ align:start position:0%
+they have no way of finding out because
+i was sort of
+
+ align:start position:0%
+i was sort of
+ 
+
+ align:start position:0%
+i was sort of
+unobservable if instead i really care
+
+ align:start position:0%
+unobservable if instead i really care
+ 
+
+ align:start position:0%
+unobservable if instead i really care
+about them if i'm really interested in
+
+ align:start position:0%
+about them if i'm really interested in
+ 
+
+ align:start position:0%
+about them if i'm really interested in
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+um in their well-being overall in their
+
+ align:start position:0%
+um in their well-being overall in their
+ 
+
+ align:start position:0%
+um in their well-being overall in their
+payment
+
+ align:start position:0%
+payment
+ 
+
+ align:start position:0%
+payment
+it doesn't matter whether my effort is
+
+ align:start position:0%
+it doesn't matter whether my effort is
+ 
+
+ align:start position:0%
+it doesn't matter whether my effort is
+observable regardless of how observable
+
+ align:start position:0%
+observable regardless of how observable
+ 
+
+ align:start position:0%
+observable regardless of how observable
+my effort is i will not work really very
+
+ align:start position:0%
+my effort is i will not work really very
+ 
+
+ align:start position:0%
+my effort is i will not work really very
+hard because not working hard makes them
+
+ align:start position:0%
+hard because not working hard makes them
+ 
+
+ align:start position:0%
+hard because not working hard makes them
+better off
+
+ align:start position:0%
+better off
+ 
+
+ align:start position:0%
+better off
+so if you just had some differences in
+
+ align:start position:0%
+so if you just had some differences in
+ 
+
+ align:start position:0%
+so if you just had some differences in
+observability
+
+ align:start position:0%
+observability
+ 
+
+ align:start position:0%
+observability
+in effort how hard people work we could
+
+ align:start position:0%
+in effort how hard people work we could
+ 
+
+ align:start position:0%
+in effort how hard people work we could
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+disentangle these two um explanations
+
+ align:start position:0%
+disentangle these two um explanations
+ 
+
+ align:start position:0%
+disentangle these two um explanations
+so um bandiera and i'll have this very
+
+ align:start position:0%
+so um bandiera and i'll have this very
+ 
+
+ align:start position:0%
+so um bandiera and i'll have this very
+nice variation they have
+
+ align:start position:0%
+nice variation they have
+ 
+
+ align:start position:0%
+nice variation they have
+two fruits they're fruit type one which
+
+ align:start position:0%
+two fruits they're fruit type one which
+ 
+
+ align:start position:0%
+two fruits they're fruit type one which
+are strawberries
+
+ align:start position:0%
+are strawberries
+ 
+
+ align:start position:0%
+are strawberries
+and they have fruit of type two which
+
+ align:start position:0%
+and they have fruit of type two which
+ 
+
+ align:start position:0%
+and they have fruit of type two which
+are raspberries
+
+ align:start position:0%
+are raspberries
+ 
+
+ align:start position:0%
+are raspberries
+if you ever have picked strawberries you
+
+ align:start position:0%
+if you ever have picked strawberries you
+ 
+
+ align:start position:0%
+if you ever have picked strawberries you
+would know that
+
+ align:start position:0%
+would know that
+ 
+
+ align:start position:0%
+would know that
+strawberries it's very easy these are
+
+ align:start position:0%
+strawberries it's very easy these are
+ 
+
+ align:start position:0%
+strawberries it's very easy these are
+like essentially very flat
+
+ align:start position:0%
+like essentially very flat
+ 
+
+ align:start position:0%
+like essentially very flat
+and low fruit that when somebody picks
+
+ align:start position:0%
+and low fruit that when somebody picks
+ 
+
+ align:start position:0%
+and low fruit that when somebody picks
+strawberries it's very easy to see how
+
+ align:start position:0%
+strawberries it's very easy to see how
+ 
+
+ align:start position:0%
+strawberries it's very easy to see how
+fast somebody works how much
+
+ align:start position:0%
+fast somebody works how much
+ 
+
+ align:start position:0%
+fast somebody works how much
+anybody picks and so on because you can
+
+ align:start position:0%
+anybody picks and so on because you can
+ 
+
+ align:start position:0%
+anybody picks and so on because you can
+just see across the entire field you can
+
+ align:start position:0%
+just see across the entire field you can
+ 
+
+ align:start position:0%
+just see across the entire field you can
+see essentially what all of your
+
+ align:start position:0%
+see essentially what all of your
+ 
+
+ align:start position:0%
+see essentially what all of your
+co-workers are doing
+
+ align:start position:0%
+co-workers are doing
+ 
+
+ align:start position:0%
+co-workers are doing
+in contrast if you look at strawberries
+
+ align:start position:0%
+in contrast if you look at strawberries
+ 
+
+ align:start position:0%
+in contrast if you look at strawberries
+sorry if you look at raspberries these
+
+ align:start position:0%
+sorry if you look at raspberries these
+ 
+
+ align:start position:0%
+sorry if you look at raspberries these
+are bushes so you can essentially
+
+ align:start position:0%
+are bushes so you can essentially
+ 
+
+ align:start position:0%
+are bushes so you can essentially
+literally hide behind the boat hide
+
+ align:start position:0%
+literally hide behind the boat hide
+ 
+
+ align:start position:0%
+literally hide behind the boat hide
+behind the bushes and work really hard
+
+ align:start position:0%
+behind the bushes and work really hard
+ 
+
+ align:start position:0%
+behind the bushes and work really hard
+to pick really hard
+
+ align:start position:0%
+to pick really hard
+ 
+
+ align:start position:0%
+to pick really hard
+and fast without others noticing so
+
+ align:start position:0%
+and fast without others noticing so
+ 
+
+ align:start position:0%
+and fast without others noticing so
+essentially productivity
+
+ align:start position:0%
+essentially productivity
+ 
+
+ align:start position:0%
+essentially productivity
+is at least more unobserved than for
+
+ align:start position:0%
+is at least more unobserved than for
+ 
+
+ align:start position:0%
+is at least more unobserved than for
+strawberries now what bundier at all
+
+ align:start position:0%
+strawberries now what bundier at all
+ 
+
+ align:start position:0%
+strawberries now what bundier at all
+then find in fact is no impact of the
+
+ align:start position:0%
+then find in fact is no impact of the
+ 
+
+ align:start position:0%
+then find in fact is no impact of the
+piece rate on fruits
+
+ align:start position:0%
+piece rate on fruits
+ 
+
+ align:start position:0%
+piece rate on fruits
+of type type 2 which is raspberries
+
+ align:start position:0%
+of type type 2 which is raspberries
+ 
+
+ align:start position:0%
+of type type 2 which is raspberries
+so that sort of suggests there is no
+
+ align:start position:0%
+so that sort of suggests there is no
+ 
+
+ align:start position:0%
+so that sort of suggests there is no
+evidence of pure altruism
+
+ align:start position:0%
+evidence of pure altruism
+ 
+
+ align:start position:0%
+evidence of pure altruism
+and the effects perhaps could be driven
+
+ align:start position:0%
+and the effects perhaps could be driven
+ 
+
+ align:start position:0%
+and the effects perhaps could be driven
+by um
+
+ align:start position:0%
+by um
+ 
+
+ align:start position:0%
+by um
+reciprocity this is kind of consistent
+
+ align:start position:0%
+reciprocity this is kind of consistent
+ 
+
+ align:start position:0%
+reciprocity this is kind of consistent
+with what we had found before
+
+ align:start position:0%
+with what we had found before
+ 
+
+ align:start position:0%
+with what we had found before
+when you remember the dictator ultimatum
+
+ align:start position:0%
+when you remember the dictator ultimatum
+ 
+
+ align:start position:0%
+when you remember the dictator ultimatum
+games that we showed you
+
+ align:start position:0%
+games that we showed you
+ 
+
+ align:start position:0%
+games that we showed you
+it looked a lot like people are
+
+ align:start position:0%
+it looked a lot like people are
+ 
+
+ align:start position:0%
+it looked a lot like people are
+altruistic they care about others
+
+ align:start position:0%
+altruistic they care about others
+ 
+
+ align:start position:0%
+altruistic they care about others
+but when you look at their actual
+
+ align:start position:0%
+but when you look at their actual
+ 
+
+ align:start position:0%
+but when you look at their actual
+motives when you look at little when you
+
+ align:start position:0%
+motives when you look at little when you
+ 
+
+ align:start position:0%
+motives when you look at little when you
+dig a little deeper we find out that in
+
+ align:start position:0%
+dig a little deeper we find out that in
+ 
+
+ align:start position:0%
+dig a little deeper we find out that in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+this is driven uh by reciprocity or by
+
+ align:start position:0%
+this is driven uh by reciprocity or by
+ 
+
+ align:start position:0%
+this is driven uh by reciprocity or by
+worries about repeated game effects
+
+ align:start position:0%
+worries about repeated game effects
+ 
+
+ align:start position:0%
+worries about repeated game effects
+or worries about essentially just
+
+ align:start position:0%
+or worries about essentially just
+ 
+
+ align:start position:0%
+or worries about essentially just
+retribution either on the field that
+
+ align:start position:0%
+retribution either on the field that
+ 
+
+ align:start position:0%
+retribution either on the field that
+you know other people will work also
+
+ align:start position:0%
+you know other people will work also
+ 
+
+ align:start position:0%
+you know other people will work also
+really hard if i will work really hard
+
+ align:start position:0%
+really hard if i will work really hard
+ 
+
+ align:start position:0%
+really hard if i will work really hard
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+or you know socially after work my
+
+ align:start position:0%
+or you know socially after work my
+ 
+
+ align:start position:0%
+or you know socially after work my
+co-workers might be really mean to me
+
+ align:start position:0%
+co-workers might be really mean to me
+ 
+
+ align:start position:0%
+co-workers might be really mean to me
+they might even beat me up or they might
+
+ align:start position:0%
+they might even beat me up or they might
+ 
+
+ align:start position:0%
+they might even beat me up or they might
+not be my friends um anymore
+
+ align:start position:0%
+not be my friends um anymore
+ 
+
+ align:start position:0%
+not be my friends um anymore
+and this is um um here so the regression
+
+ align:start position:0%
+and this is um um here so the regression
+ 
+
+ align:start position:0%
+and this is um um here so the regression
+tables that show you this
+
+ align:start position:0%
+tables that show you this
+ 
+
+ align:start position:0%
+tables that show you this
+the first column you see fruit type 2.
+
+ align:start position:0%
+the first column you see fruit type 2.
+ 
+
+ align:start position:0%
+the first column you see fruit type 2.
+again these are the raspberries this is
+
+ align:start position:0%
+again these are the raspberries this is
+ 
+
+ align:start position:0%
+again these are the raspberries this is
+when things are
+
+ align:start position:0%
+when things are
+ 
+
+ align:start position:0%
+when things are
+unobserved there's no effect of
+
+ align:start position:0%
+unobserved there's no effect of
+ 
+
+ align:start position:0%
+unobserved there's no effect of
+introducing the piece rate
+
+ align:start position:0%
+introducing the piece rate
+ 
+
+ align:start position:0%
+introducing the piece rate
+in contrast if you look at column two
+
+ align:start position:0%
+in contrast if you look at column two
+ 
+
+ align:start position:0%
+in contrast if you look at column two
+this is fruit type
+
+ align:start position:0%
+this is fruit type
+ 
+
+ align:start position:0%
+this is fruit type
+one these are strawberries and there's
+
+ align:start position:0%
+one these are strawberries and there's
+ 
+
+ align:start position:0%
+one these are strawberries and there's
+large productivity effects of
+
+ align:start position:0%
+large productivity effects of
+ 
+
+ align:start position:0%
+large productivity effects of
+strawberries
+
+ align:start position:0%
+strawberries
+ 
+
+ align:start position:0%
+strawberries
+there so these results again highlight
+
+ align:start position:0%
+there so these results again highlight
+ 
+
+ align:start position:0%
+there so these results again highlight
+the importance of
+
+ align:start position:0%
+the importance of
+ 
+
+ align:start position:0%
+the importance of
+setting the incentives carefully small
+
+ align:start position:0%
+setting the incentives carefully small
+ 
+
+ align:start position:0%
+setting the incentives carefully small
+details matter and you really want to be
+
+ align:start position:0%
+details matter and you really want to be
+ 
+
+ align:start position:0%
+details matter and you really want to be
+very careful and like how you said
+
+ align:start position:0%
+very careful and like how you said
+ 
+
+ align:start position:0%
+very careful and like how you said
+relative incentives
+
+ align:start position:0%
+relative incentives
+ 
+
+ align:start position:0%
+relative incentives
+that in principle seem like a good idea
+
+ align:start position:0%
+that in principle seem like a good idea
+ 
+
+ align:start position:0%
+that in principle seem like a good idea
+because they sort of provide steep
+
+ align:start position:0%
+because they sort of provide steep
+ 
+
+ align:start position:0%
+because they sort of provide steep
+incentives to workers
+
+ align:start position:0%
+incentives to workers
+ 
+
+ align:start position:0%
+incentives to workers
+but in practice might actually not work
+
+ align:start position:0%
+but in practice might actually not work
+ 
+
+ align:start position:0%
+but in practice might actually not work
+particularly well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the second paper we're going to
+
+ align:start position:0%
+okay so the second paper we're going to
+ 
+
+ align:start position:0%
+okay so the second paper we're going to
+look at is brazil these are the morale
+
+ align:start position:0%
+look at is brazil these are the morale
+ 
+
+ align:start position:0%
+look at is brazil these are the morale
+effects of pay inequality
+
+ align:start position:0%
+effects of pay inequality
+ 
+
+ align:start position:0%
+effects of pay inequality
+this is a very nice randomized field
+
+ align:start position:0%
+this is a very nice randomized field
+ 
+
+ align:start position:0%
+this is a very nice randomized field
+experiment in rural india with lower
+
+ align:start position:0%
+experiment in rural india with lower
+ 
+
+ align:start position:0%
+experiment in rural india with lower
+skill
+
+ align:start position:0%
+skill
+ 
+
+ align:start position:0%
+skill
+manufacturing workers the question the
+
+ align:start position:0%
+manufacturing workers the question the
+ 
+
+ align:start position:0%
+manufacturing workers the question the
+authors ask
+
+ align:start position:0%
+authors ask
+ 
+
+ align:start position:0%
+authors ask
+is do workers care about relative pay
+
+ align:start position:0%
+is do workers care about relative pay
+ 
+
+ align:start position:0%
+is do workers care about relative pay
+and perhaps why do we see so little
+
+ align:start position:0%
+and perhaps why do we see so little
+ 
+
+ align:start position:0%
+and perhaps why do we see so little
+variation in pay across settings so what
+
+ align:start position:0%
+variation in pay across settings so what
+ 
+
+ align:start position:0%
+variation in pay across settings so what
+we often see in many companies
+
+ align:start position:0%
+we often see in many companies
+ 
+
+ align:start position:0%
+we often see in many companies
+in india but also in other places also
+
+ align:start position:0%
+in india but also in other places also
+ 
+
+ align:start position:0%
+in india but also in other places also
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+certain villages in india what we see is
+
+ align:start position:0%
+certain villages in india what we see is
+ 
+
+ align:start position:0%
+certain villages in india what we see is
+wages tend to be very compressed
+
+ align:start position:0%
+wages tend to be very compressed
+ 
+
+ align:start position:0%
+wages tend to be very compressed
+so workers essentially earn the exact
+
+ align:start position:0%
+so workers essentially earn the exact
+ 
+
+ align:start position:0%
+so workers essentially earn the exact
+same wage
+
+ align:start position:0%
+same wage
+ 
+
+ align:start position:0%
+same wage
+regardless of their um underlying
+
+ align:start position:0%
+regardless of their um underlying
+ 
+
+ align:start position:0%
+regardless of their um underlying
+productivity
+
+ align:start position:0%
+productivity
+ 
+
+ align:start position:0%
+productivity
+experience and so on good and bad
+
+ align:start position:0%
+experience and so on good and bad
+ 
+
+ align:start position:0%
+experience and so on good and bad
+workers tend to work exactly
+
+ align:start position:0%
+workers tend to work exactly
+ 
+
+ align:start position:0%
+workers tend to work exactly
+tend to earn exactly the same amount of
+
+ align:start position:0%
+tend to earn exactly the same amount of
+ 
+
+ align:start position:0%
+tend to earn exactly the same amount of
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+for per day or per hour and the like
+
+ align:start position:0%
+for per day or per hour and the like
+ 
+
+ align:start position:0%
+for per day or per hour and the like
+economists think that's inefficient
+
+ align:start position:0%
+economists think that's inefficient
+ 
+
+ align:start position:0%
+economists think that's inefficient
+because you know if you want to hire
+
+ align:start position:0%
+because you know if you want to hire
+ 
+
+ align:start position:0%
+because you know if you want to hire
+somebody who's really really productive
+
+ align:start position:0%
+somebody who's really really productive
+ 
+
+ align:start position:0%
+somebody who's really really productive
+you might want to hire pay them more
+
+ align:start position:0%
+you might want to hire pay them more
+ 
+
+ align:start position:0%
+you might want to hire pay them more
+if you want to hire somebody who's not
+
+ align:start position:0%
+if you want to hire somebody who's not
+ 
+
+ align:start position:0%
+if you want to hire somebody who's not
+that productive you might want to pay
+
+ align:start position:0%
+that productive you might want to pay
+ 
+
+ align:start position:0%
+that productive you might want to pay
+them less
+
+ align:start position:0%
+them less
+ 
+
+ align:start position:0%
+them less
+you might actually want to pay them less
+
+ align:start position:0%
+you might actually want to pay them less
+ 
+
+ align:start position:0%
+you might actually want to pay them less
+than the prevailing wage
+
+ align:start position:0%
+than the prevailing wage
+ 
+
+ align:start position:0%
+than the prevailing wage
+but you might not be able to do so
+
+ align:start position:0%
+but you might not be able to do so
+ 
+
+ align:start position:0%
+but you might not be able to do so
+because the norm is that
+
+ align:start position:0%
+because the norm is that
+ 
+
+ align:start position:0%
+because the norm is that
+you have to pay them the prevailing wage
+
+ align:start position:0%
+you have to pay them the prevailing wage
+ 
+
+ align:start position:0%
+you have to pay them the prevailing wage
+and then you might end up
+
+ align:start position:0%
+and then you might end up
+ 
+
+ align:start position:0%
+and then you might end up
+not hiring that person and that person
+
+ align:start position:0%
+not hiring that person and that person
+ 
+
+ align:start position:0%
+not hiring that person and that person
+might end up being unemployed
+
+ align:start position:0%
+might end up being unemployed
+ 
+
+ align:start position:0%
+might end up being unemployed
+even though it would you would be very
+
+ align:start position:0%
+even though it would you would be very
+ 
+
+ align:start position:0%
+even though it would you would be very
+happy to to pay them at a lower wage
+
+ align:start position:0%
+happy to to pay them at a lower wage
+ 
+
+ align:start position:0%
+happy to to pay them at a lower wage
+this is really a really relevant
+
+ align:start position:0%
+this is really a really relevant
+ 
+
+ align:start position:0%
+this is really a really relevant
+question or sorry there's a second
+
+ align:start position:0%
+question or sorry there's a second
+ 
+
+ align:start position:0%
+question or sorry there's a second
+question the authors ask is
+
+ align:start position:0%
+question the authors ask is
+ 
+
+ align:start position:0%
+question the authors ask is
+what is the notion of the underlying
+
+ align:start position:0%
+what is the notion of the underlying
+ 
+
+ align:start position:0%
+what is the notion of the underlying
+notion of fairness
+
+ align:start position:0%
+notion of fairness
+ 
+
+ align:start position:0%
+notion of fairness
+what is kind of a fair and what's not
+
+ align:start position:0%
+what is kind of a fair and what's not
+ 
+
+ align:start position:0%
+what is kind of a fair and what's not
+fair as in like
+
+ align:start position:0%
+fair as in like
+ 
+
+ align:start position:0%
+fair as in like
+if there is wage dispersion across
+
+ align:start position:0%
+if there is wage dispersion across
+ 
+
+ align:start position:0%
+if there is wage dispersion across
+workers
+
+ align:start position:0%
+workers
+ 
+
+ align:start position:0%
+workers
+within teams or within a certain for our
+
+ align:start position:0%
+within teams or within a certain for our
+ 
+
+ align:start position:0%
+within teams or within a certain for our
+firm are there some circumstances under
+
+ align:start position:0%
+firm are there some circumstances under
+ 
+
+ align:start position:0%
+firm are there some circumstances under
+which that's okay to do are there some
+
+ align:start position:0%
+which that's okay to do are there some
+ 
+
+ align:start position:0%
+which that's okay to do are there some
+good justification that workers are
+
+ align:start position:0%
+good justification that workers are
+ 
+
+ align:start position:0%
+good justification that workers are
+uh okay with or in contrast
+
+ align:start position:0%
+uh okay with or in contrast
+ 
+
+ align:start position:0%
+uh okay with or in contrast
+or uh is it just always bad to do so so
+
+ align:start position:0%
+or uh is it just always bad to do so so
+ 
+
+ align:start position:0%
+or uh is it just always bad to do so so
+can we sort of find some situation on
+
+ align:start position:0%
+can we sort of find some situation on
+ 
+
+ align:start position:0%
+can we sort of find some situation on
+which under which
+
+ align:start position:0%
+which under which
+ 
+
+ align:start position:0%
+which under which
+uh it's justified for workers or not or
+
+ align:start position:0%
+uh it's justified for workers or not or
+ 
+
+ align:start position:0%
+uh it's justified for workers or not or
+is it just like we cannot pay half pay
+
+ align:start position:0%
+is it just like we cannot pay half pay
+ 
+
+ align:start position:0%
+is it just like we cannot pay half pay
+inequality under any circumstances
+
+ align:start position:0%
+inequality under any circumstances
+ 
+
+ align:start position:0%
+inequality under any circumstances
+in those kinds of firms this is
+
+ align:start position:0%
+in those kinds of firms this is
+ 
+
+ align:start position:0%
+in those kinds of firms this is
+potentially quite relevant for
+
+ align:start position:0%
+potentially quite relevant for
+ 
+
+ align:start position:0%
+potentially quite relevant for
+many features of the labor market it
+
+ align:start position:0%
+many features of the labor market it
+ 
+
+ align:start position:0%
+many features of the labor market it
+might explain
+
+ align:start position:0%
+might explain
+ 
+
+ align:start position:0%
+might explain
+wage compression that's what i'm saying
+
+ align:start position:0%
+wage compression that's what i'm saying
+ 
+
+ align:start position:0%
+wage compression that's what i'm saying
+like words tend to be fairly compressed
+
+ align:start position:0%
+like words tend to be fairly compressed
+ 
+
+ align:start position:0%
+like words tend to be fairly compressed
+even if productivity is fairly dispersed
+
+ align:start position:0%
+even if productivity is fairly dispersed
+ 
+
+ align:start position:0%
+even if productivity is fairly dispersed
+across workers
+
+ align:start position:0%
+across workers
+ 
+
+ align:start position:0%
+across workers
+there tends to be lots of wage rigidity
+
+ align:start position:0%
+there tends to be lots of wage rigidity
+ 
+
+ align:start position:0%
+there tends to be lots of wage rigidity
+wages tend to not move very much
+
+ align:start position:0%
+wages tend to not move very much
+ 
+
+ align:start position:0%
+wages tend to not move very much
+it seems to be employers have trouble um
+
+ align:start position:0%
+it seems to be employers have trouble um
+ 
+
+ align:start position:0%
+it seems to be employers have trouble um
+adjusting wages or they are reluctant to
+
+ align:start position:0%
+adjusting wages or they are reluctant to
+ 
+
+ align:start position:0%
+adjusting wages or they are reluctant to
+adjust people's wages much in particular
+
+ align:start position:0%
+adjust people's wages much in particular
+ 
+
+ align:start position:0%
+adjust people's wages much in particular
+when it comes to like downward rigidity
+
+ align:start position:0%
+when it comes to like downward rigidity
+ 
+
+ align:start position:0%
+when it comes to like downward rigidity
+we talked about this a little bit
+
+ align:start position:0%
+we talked about this a little bit
+ 
+
+ align:start position:0%
+we talked about this a little bit
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+when we talked about reference
+
+ align:start position:0%
+when we talked about reference
+ 
+
+ align:start position:0%
+when we talked about reference
+dependence um we can also think that
+
+ align:start position:0%
+dependence um we can also think that
+ 
+
+ align:start position:0%
+dependence um we can also think that
+help this can help us think about like
+
+ align:start position:0%
+help this can help us think about like
+ 
+
+ align:start position:0%
+help this can help us think about like
+sorting of workers into firms and
+
+ align:start position:0%
+sorting of workers into firms and
+ 
+
+ align:start position:0%
+sorting of workers into firms and
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+uh we can think about firm boundaries in
+
+ align:start position:0%
+uh we can think about firm boundaries in
+ 
+
+ align:start position:0%
+uh we can think about firm boundaries in
+a sense to say like
+
+ align:start position:0%
+a sense to say like
+ 
+
+ align:start position:0%
+a sense to say like
+should they be really large firms or a
+
+ align:start position:0%
+should they be really large firms or a
+ 
+
+ align:start position:0%
+should they be really large firms or a
+number of small firms
+
+ align:start position:0%
+number of small firms
+ 
+
+ align:start position:0%
+number of small firms
+if you think the relative comparison is
+
+ align:start position:0%
+if you think the relative comparison is
+ 
+
+ align:start position:0%
+if you think the relative comparison is
+uh across workers within firms that
+
+ align:start position:0%
+uh across workers within firms that
+ 
+
+ align:start position:0%
+uh across workers within firms that
+would sort of say well we should
+
+ align:start position:0%
+would sort of say well we should
+ 
+
+ align:start position:0%
+would sort of say well we should
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+have a lot of small firms and then each
+
+ align:start position:0%
+have a lot of small firms and then each
+ 
+
+ align:start position:0%
+have a lot of small firms and then each
+of these small firms could have
+
+ align:start position:0%
+of these small firms could have
+ 
+
+ align:start position:0%
+of these small firms could have
+different wages
+
+ align:start position:0%
+different wages
+ 
+
+ align:start position:0%
+different wages
+as opposed to like one large firm where
+
+ align:start position:0%
+as opposed to like one large firm where
+ 
+
+ align:start position:0%
+as opposed to like one large firm where
+like essentially everybody has to be
+
+ align:start position:0%
+like essentially everybody has to be
+ 
+
+ align:start position:0%
+like essentially everybody has to be
+paid more or less
+
+ align:start position:0%
+paid more or less
+ 
+
+ align:start position:0%
+paid more or less
+the same and we might think that's
+
+ align:start position:0%
+the same and we might think that's
+ 
+
+ align:start position:0%
+the same and we might think that's
+inefficient because there's returns to
+
+ align:start position:0%
+inefficient because there's returns to
+ 
+
+ align:start position:0%
+inefficient because there's returns to
+scale of having like a large
+
+ align:start position:0%
+scale of having like a large
+ 
+
+ align:start position:0%
+scale of having like a large
+um firm think about us that is also
+
+ align:start position:0%
+um firm think about us that is also
+ 
+
+ align:start position:0%
+um firm think about us that is also
+relevant for some hr
+
+ align:start position:0%
+relevant for some hr
+ 
+
+ align:start position:0%
+relevant for some hr
+policies in terms of like how do you pay
+
+ align:start position:0%
+policies in terms of like how do you pay
+ 
+
+ align:start position:0%
+policies in terms of like how do you pay
+workers how do you set wages and so on
+
+ align:start position:0%
+workers how do you set wages and so on
+ 
+
+ align:start position:0%
+workers how do you set wages and so on
+so as motivation in a study the authors
+
+ align:start position:0%
+so as motivation in a study the authors
+ 
+
+ align:start position:0%
+so as motivation in a study the authors
+ask people the certain
+
+ align:start position:0%
+ask people the certain
+ 
+
+ align:start position:0%
+ask people the certain
+the following questions the question is
+
+ align:start position:0%
+the following questions the question is
+ 
+
+ align:start position:0%
+the following questions the question is
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+three this is rural india and rissa
+
+ align:start position:0%
+three this is rural india and rissa
+ 
+
+ align:start position:0%
+three this is rural india and rissa
+a relatively poor area
+
+ align:start position:0%
+a relatively poor area
+ 
+
+ align:start position:0%
+a relatively poor area
+with lots of small scale manufacturing
+
+ align:start position:0%
+with lots of small scale manufacturing
+ 
+
+ align:start position:0%
+with lots of small scale manufacturing
+the question is three people from a
+
+ align:start position:0%
+the question is three people from a
+ 
+
+ align:start position:0%
+the question is three people from a
+village get hired to work on a
+
+ align:start position:0%
+village get hired to work on a
+ 
+
+ align:start position:0%
+village get hired to work on a
+construction site together
+
+ align:start position:0%
+construction site together
+ 
+
+ align:start position:0%
+construction site together
+the prevailing wage is 250 rupees in the
+
+ align:start position:0%
+the prevailing wage is 250 rupees in the
+ 
+
+ align:start position:0%
+the prevailing wage is 250 rupees in the
+village that's kind of the standard wage
+
+ align:start position:0%
+village that's kind of the standard wage
+ 
+
+ align:start position:0%
+village that's kind of the standard wage
+in the village each village tends to
+
+ align:start position:0%
+in the village each village tends to
+ 
+
+ align:start position:0%
+in the village each village tends to
+have like a prevailing weight which is
+
+ align:start position:0%
+have like a prevailing weight which is
+ 
+
+ align:start position:0%
+have like a prevailing weight which is
+like how much people are paid usually
+
+ align:start position:0%
+like how much people are paid usually
+ 
+
+ align:start position:0%
+like how much people are paid usually
+the contractor pays them uh 200 250
+
+ align:start position:0%
+the contractor pays them uh 200 250
+ 
+
+ align:start position:0%
+the contractor pays them uh 200 250
+rupees per day
+
+ align:start position:0%
+rupees per day
+ 
+
+ align:start position:0%
+rupees per day
+how well will they work together and
+
+ align:start position:0%
+how well will they work together and
+ 
+
+ align:start position:0%
+how well will they work together and
+what you see is what respondents tend to
+
+ align:start position:0%
+what you see is what respondents tend to
+ 
+
+ align:start position:0%
+what you see is what respondents tend to
+say is like 80 percent of respondents
+
+ align:start position:0%
+say is like 80 percent of respondents
+ 
+
+ align:start position:0%
+say is like 80 percent of respondents
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+uh uh people work very well together
+
+ align:start position:0%
+uh uh people work very well together
+ 
+
+ align:start position:0%
+uh uh people work very well together
+uh 20 say as well as usual and zero
+
+ align:start position:0%
+uh 20 say as well as usual and zero
+ 
+
+ align:start position:0%
+uh 20 say as well as usual and zero
+percent say there will be conflict so
+
+ align:start position:0%
+percent say there will be conflict so
+ 
+
+ align:start position:0%
+percent say there will be conflict so
+that's kind of like seems like paying
+
+ align:start position:0%
+that's kind of like seems like paying
+ 
+
+ align:start position:0%
+that's kind of like seems like paying
+everybody the same
+
+ align:start position:0%
+everybody the same
+ 
+
+ align:start position:0%
+everybody the same
+is a socially acceptable thing to do
+
+ align:start position:0%
+is a socially acceptable thing to do
+ 
+
+ align:start position:0%
+is a socially acceptable thing to do
+everybody seems happy
+
+ align:start position:0%
+everybody seems happy
+ 
+
+ align:start position:0%
+everybody seems happy
+with that in contrast if you ask the
+
+ align:start position:0%
+with that in contrast if you ask the
+ 
+
+ align:start position:0%
+with that in contrast if you ask the
+following which is the contractor pays
+
+ align:start position:0%
+following which is the contractor pays
+ 
+
+ align:start position:0%
+following which is the contractor pays
+them different
+
+ align:start position:0%
+them different
+ 
+
+ align:start position:0%
+them different
+wages if the contractor tractor pays 250
+
+ align:start position:0%
+wages if the contractor tractor pays 250
+ 
+
+ align:start position:0%
+wages if the contractor tractor pays 250
+per day to 70 percent and put 290 per
+
+ align:start position:0%
+per day to 70 percent and put 290 per
+ 
+
+ align:start position:0%
+per day to 70 percent and put 290 per
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+how well will they work together
+
+ align:start position:0%
+how well will they work together
+ 
+
+ align:start position:0%
+how well will they work together
+and so now um what you see here is when
+
+ align:start position:0%
+and so now um what you see here is when
+ 
+
+ align:start position:0%
+and so now um what you see here is when
+there's differences
+
+ align:start position:0%
+there's differences
+ 
+
+ align:start position:0%
+there's differences
+are cross pay 94 percent of workers
+
+ align:start position:0%
+are cross pay 94 percent of workers
+ 
+
+ align:start position:0%
+are cross pay 94 percent of workers
+say there will be conflict now it
+
+ align:start position:0%
+say there will be conflict now it
+ 
+
+ align:start position:0%
+say there will be conflict now it
+doesn't specify here at least in this
+
+ align:start position:0%
+doesn't specify here at least in this
+ 
+
+ align:start position:0%
+doesn't specify here at least in this
+version of the question it doesn't
+
+ align:start position:0%
+version of the question it doesn't
+ 
+
+ align:start position:0%
+version of the question it doesn't
+specify
+
+ align:start position:0%
+specify
+ 
+
+ align:start position:0%
+specify
+whether that's to do with like
+
+ align:start position:0%
+whether that's to do with like
+ 
+
+ align:start position:0%
+whether that's to do with like
+underlying productivity differences so
+
+ align:start position:0%
+underlying productivity differences so
+ 
+
+ align:start position:0%
+underlying productivity differences so
+why is it that some workers are paid
+
+ align:start position:0%
+why is it that some workers are paid
+ 
+
+ align:start position:0%
+why is it that some workers are paid
+different than others
+
+ align:start position:0%
+different than others
+ 
+
+ align:start position:0%
+different than others
+however it's very strong suggestive
+
+ align:start position:0%
+however it's very strong suggestive
+ 
+
+ align:start position:0%
+however it's very strong suggestive
+evidence that
+
+ align:start position:0%
+evidence that
+ 
+
+ align:start position:0%
+evidence that
+workers might be really unhappy and
+
+ align:start position:0%
+workers might be really unhappy and
+ 
+
+ align:start position:0%
+workers might be really unhappy and
+there will be conflict across workers
+
+ align:start position:0%
+there will be conflict across workers
+ 
+
+ align:start position:0%
+there will be conflict across workers
+if they pay different wages in the same
+
+ align:start position:0%
+if they pay different wages in the same
+ 
+
+ align:start position:0%
+if they pay different wages in the same
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+team or at least on the same
+
+ align:start position:0%
+team or at least on the same
+ 
+
+ align:start position:0%
+team or at least on the same
+construction site
+
+ align:start position:0%
+construction site
+ 
+
+ align:start position:0%
+construction site
+and then okay of course if you're like
+
+ align:start position:0%
+and then okay of course if you're like
+ 
+
+ align:start position:0%
+and then okay of course if you're like
+an employer you might be quite worried
+
+ align:start position:0%
+an employer you might be quite worried
+ 
+
+ align:start position:0%
+an employer you might be quite worried
+about paying people different wages
+
+ align:start position:0%
+about paying people different wages
+ 
+
+ align:start position:0%
+about paying people different wages
+because if there's conflict presumably
+
+ align:start position:0%
+because if there's conflict presumably
+ 
+
+ align:start position:0%
+because if there's conflict presumably
+workers will not work
+
+ align:start position:0%
+workers will not work
+ 
+
+ align:start position:0%
+workers will not work
+or collaborate as well as they could
+
+ align:start position:0%
+or collaborate as well as they could
+ 
+
+ align:start position:0%
+or collaborate as well as they could
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+okay so now the author set up a very
+
+ align:start position:0%
+okay so now the author set up a very
+ 
+
+ align:start position:0%
+okay so now the author set up a very
+nice field experiment that looks like
+
+ align:start position:0%
+nice field experiment that looks like
+ 
+
+ align:start position:0%
+nice field experiment that looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so there's 10 production units of three
+
+ align:start position:0%
+so there's 10 production units of three
+ 
+
+ align:start position:0%
+so there's 10 production units of three
+workers each
+
+ align:start position:0%
+workers each
+ 
+
+ align:start position:0%
+workers each
+in each factory so think of factories
+
+ align:start position:0%
+in each factory so think of factories
+ 
+
+ align:start position:0%
+in each factory so think of factories
+like work sites
+
+ align:start position:0%
+like work sites
+ 
+
+ align:start position:0%
+like work sites
+factories and parenthood and quotation
+
+ align:start position:0%
+factories and parenthood and quotation
+ 
+
+ align:start position:0%
+factories and parenthood and quotation
+marks because it's really not just a
+
+ align:start position:0%
+marks because it's really not just a
+ 
+
+ align:start position:0%
+marks because it's really not just a
+factory as you might sort of imagine it
+
+ align:start position:0%
+factory as you might sort of imagine it
+ 
+
+ align:start position:0%
+factory as you might sort of imagine it
+it's really like a small work site an
+
+ align:start position:0%
+it's really like a small work site an
+ 
+
+ align:start position:0%
+it's really like a small work site an
+office where people are working in
+
+ align:start position:0%
+office where people are working in
+ 
+
+ align:start position:0%
+office where people are working in
+different areas
+
+ align:start position:0%
+different areas
+ 
+
+ align:start position:0%
+different areas
+there's 10 units of three workers each
+
+ align:start position:0%
+there's 10 units of three workers each
+ 
+
+ align:start position:0%
+there's 10 units of three workers each
+so it's not a huge office
+
+ align:start position:0%
+so it's not a huge office
+ 
+
+ align:start position:0%
+so it's not a huge office
+each unit of three workers produces
+
+ align:start position:0%
+each unit of three workers produces
+ 
+
+ align:start position:0%
+each unit of three workers produces
+different products so like each unit has
+
+ align:start position:0%
+different products so like each unit has
+ 
+
+ align:start position:0%
+different products so like each unit has
+like one
+
+ align:start position:0%
+like one
+ 
+
+ align:start position:0%
+like one
+product for example unit one makes
+
+ align:start position:0%
+product for example unit one makes
+ 
+
+ align:start position:0%
+product for example unit one makes
+brooms unit two makes
+
+ align:start position:0%
+brooms unit two makes
+ 
+
+ align:start position:0%
+brooms unit two makes
+incense sticks union 3 makes
+
+ align:start position:0%
+incense sticks union 3 makes
+ 
+
+ align:start position:0%
+incense sticks union 3 makes
+leaf plates and so on so each unit has
+
+ align:start position:0%
+leaf plates and so on so each unit has
+ 
+
+ align:start position:0%
+leaf plates and so on so each unit has
+like one
+
+ align:start position:0%
+like one
+ 
+
+ align:start position:0%
+like one
+item of production now why are the
+
+ align:start position:0%
+item of production now why are the
+ 
+
+ align:start position:0%
+item of production now why are the
+different units is essentially to
+
+ align:start position:0%
+different units is essentially to
+ 
+
+ align:start position:0%
+different units is essentially to
+separate workers into different lines of
+
+ align:start position:0%
+separate workers into different lines of
+ 
+
+ align:start position:0%
+separate workers into different lines of
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+so what we're going to expect is that
+
+ align:start position:0%
+so what we're going to expect is that
+ 
+
+ align:start position:0%
+so what we're going to expect is that
+workers are going to compare each
+
+ align:start position:0%
+workers are going to compare each
+ 
+
+ align:start position:0%
+workers are going to compare each
+other's
+
+ align:start position:0%
+other's
+ 
+
+ align:start position:0%
+other's
+within unit but not so much across units
+
+ align:start position:0%
+within unit but not so much across units
+ 
+
+ align:start position:0%
+within unit but not so much across units
+because if i make brooms and you make
+
+ align:start position:0%
+because if i make brooms and you make
+ 
+
+ align:start position:0%
+because if i make brooms and you make
+instant sticks that's very different
+
+ align:start position:0%
+instant sticks that's very different
+ 
+
+ align:start position:0%
+instant sticks that's very different
+work in some ways but if you make the
+
+ align:start position:0%
+work in some ways but if you make the
+ 
+
+ align:start position:0%
+work in some ways but if you make the
+exact same thing the natural
+
+ align:start position:0%
+exact same thing the natural
+ 
+
+ align:start position:0%
+exact same thing the natural
+comparison now for workers to compare
+
+ align:start position:0%
+comparison now for workers to compare
+ 
+
+ align:start position:0%
+comparison now for workers to compare
+yourself with another worker
+
+ align:start position:0%
+yourself with another worker
+ 
+
+ align:start position:0%
+yourself with another worker
+all unit members so everybody in a given
+
+ align:start position:0%
+all unit members so everybody in a given
+ 
+
+ align:start position:0%
+all unit members so everybody in a given
+unit makes the exact same product so
+
+ align:start position:0%
+unit makes the exact same product so
+ 
+
+ align:start position:0%
+unit makes the exact same product so
+everybody in unit
+
+ align:start position:0%
+everybody in unit
+ 
+
+ align:start position:0%
+everybody in unit
+one who has like three workers makes
+
+ align:start position:0%
+one who has like three workers makes
+ 
+
+ align:start position:0%
+one who has like three workers makes
+brooms
+
+ align:start position:0%
+brooms
+ 
+
+ align:start position:0%
+brooms
+everybody in unit 2 makes incense sticks
+
+ align:start position:0%
+everybody in unit 2 makes incense sticks
+ 
+
+ align:start position:0%
+everybody in unit 2 makes incense sticks
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+now the key experimental variation in
+
+ align:start position:0%
+now the key experimental variation in
+ 
+
+ align:start position:0%
+now the key experimental variation in
+the in the experiment
+
+ align:start position:0%
+the in the experiment
+ 
+
+ align:start position:0%
+the in the experiment
+is wage dispersion across workers within
+
+ align:start position:0%
+is wage dispersion across workers within
+ 
+
+ align:start position:0%
+is wage dispersion across workers within
+teams
+
+ align:start position:0%
+teams
+ 
+
+ align:start position:0%
+teams
+finally there's uh also um and i'll get
+
+ align:start position:0%
+finally there's uh also um and i'll get
+ 
+
+ align:start position:0%
+finally there's uh also um and i'll get
+back to that at the end production tasks
+
+ align:start position:0%
+back to that at the end production tasks
+ 
+
+ align:start position:0%
+back to that at the end production tasks
+vary in their observability of uh
+
+ align:start position:0%
+vary in their observability of uh
+ 
+
+ align:start position:0%
+vary in their observability of uh
+performance
+
+ align:start position:0%
+performance
+ 
+
+ align:start position:0%
+performance
+so that is to say for some tasks it just
+
+ align:start position:0%
+so that is to say for some tasks it just
+ 
+
+ align:start position:0%
+so that is to say for some tasks it just
+happens to be that it's
+
+ align:start position:0%
+happens to be that it's
+ 
+
+ align:start position:0%
+happens to be that it's
+much easier to understand how productive
+
+ align:start position:0%
+much easier to understand how productive
+ 
+
+ align:start position:0%
+much easier to understand how productive
+your co-worker is than in other
+
+ align:start position:0%
+your co-worker is than in other
+ 
+
+ align:start position:0%
+your co-worker is than in other
+tasks okay so now what is the
+
+ align:start position:0%
+tasks okay so now what is the
+ 
+
+ align:start position:0%
+tasks okay so now what is the
+variation in relative pay so here you
+
+ align:start position:0%
+variation in relative pay so here you
+ 
+
+ align:start position:0%
+variation in relative pay so here you
+see um
+
+ align:start position:0%
+see um
+ 
+
+ align:start position:0%
+see um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+people are paid depending on their
+
+ align:start position:0%
+people are paid depending on their
+ 
+
+ align:start position:0%
+people are paid depending on their
+worker rank
+
+ align:start position:0%
+worker rank
+ 
+
+ align:start position:0%
+worker rank
+there's four different regimes of pay in
+
+ align:start position:0%
+there's four different regimes of pay in
+ 
+
+ align:start position:0%
+there's four different regimes of pay in
+the different columns
+
+ align:start position:0%
+the different columns
+ 
+
+ align:start position:0%
+the different columns
+heterogeneous compressed l compressed m
+
+ align:start position:0%
+heterogeneous compressed l compressed m
+ 
+
+ align:start position:0%
+heterogeneous compressed l compressed m
+and compress
+
+ align:start position:0%
+and compress
+ 
+
+ align:start position:0%
+and compress
+h workers are sorted so there's a
+
+ align:start position:0%
+h workers are sorted so there's a
+ 
+
+ align:start position:0%
+h workers are sorted so there's a
+baseline period where workers are worked
+
+ align:start position:0%
+baseline period where workers are worked
+ 
+
+ align:start position:0%
+baseline period where workers are worked
+for a few days
+
+ align:start position:0%
+for a few days
+ 
+
+ align:start position:0%
+for a few days
+and a few days are used to assess their
+
+ align:start position:0%
+and a few days are used to assess their
+ 
+
+ align:start position:0%
+and a few days are used to assess their
+baseline productivity
+
+ align:start position:0%
+baseline productivity
+ 
+
+ align:start position:0%
+baseline productivity
+they're ranked into three tertiles
+
+ align:start position:0%
+they're ranked into three tertiles
+ 
+
+ align:start position:0%
+they're ranked into three tertiles
+so there's like the low productive
+
+ align:start position:0%
+so there's like the low productive
+ 
+
+ align:start position:0%
+so there's like the low productive
+workers medium productivity and high
+
+ align:start position:0%
+workers medium productivity and high
+ 
+
+ align:start position:0%
+workers medium productivity and high
+productivity workers
+
+ align:start position:0%
+productivity workers
+ 
+
+ align:start position:0%
+productivity workers
+they're ranked essentially based on how
+
+ align:start position:0%
+they're ranked essentially based on how
+ 
+
+ align:start position:0%
+they're ranked essentially based on how
+well they did at baseline
+
+ align:start position:0%
+well they did at baseline
+ 
+
+ align:start position:0%
+well they did at baseline
+okay so if you're like really bad to
+
+ align:start position:0%
+okay so if you're like really bad to
+ 
+
+ align:start position:0%
+okay so if you're like really bad to
+start with you would be a low
+
+ align:start position:0%
+start with you would be a low
+ 
+
+ align:start position:0%
+start with you would be a low
+productivity worker if you're like an
+
+ align:start position:0%
+productivity worker if you're like an
+ 
+
+ align:start position:0%
+productivity worker if you're like an
+average worker it would be medium
+
+ align:start position:0%
+average worker it would be medium
+ 
+
+ align:start position:0%
+average worker it would be medium
+productivity
+
+ align:start position:0%
+productivity
+ 
+
+ align:start position:0%
+productivity
+and if you're really like highly
+
+ align:start position:0%
+and if you're really like highly
+ 
+
+ align:start position:0%
+and if you're really like highly
+productive worker you would be
+
+ align:start position:0%
+productive worker you would be
+ 
+
+ align:start position:0%
+productive worker you would be
+classified as
+
+ align:start position:0%
+classified as
+ 
+
+ align:start position:0%
+classified as
+high productivity workers notice that's
+
+ align:start position:0%
+high productivity workers notice that's
+ 
+
+ align:start position:0%
+high productivity workers notice that's
+always done for all of the different
+
+ align:start position:0%
+always done for all of the different
+ 
+
+ align:start position:0%
+always done for all of the different
+treatment groups
+
+ align:start position:0%
+treatment groups
+ 
+
+ align:start position:0%
+treatment groups
+the difference now is across these
+
+ align:start position:0%
+the difference now is across these
+ 
+
+ align:start position:0%
+the difference now is across these
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+regimes how workers are paid in the
+
+ align:start position:0%
+regimes how workers are paid in the
+ 
+
+ align:start position:0%
+regimes how workers are paid in the
+heterogeneous pay essentially there's
+
+ align:start position:0%
+heterogeneous pay essentially there's
+ 
+
+ align:start position:0%
+heterogeneous pay essentially there's
+differences in
+
+ align:start position:0%
+differences in
+ 
+
+ align:start position:0%
+differences in
+um across workers in the sense that like
+
+ align:start position:0%
+um across workers in the sense that like
+ 
+
+ align:start position:0%
+um across workers in the sense that like
+uh the low productivity workers are paid
+
+ align:start position:0%
+uh the low productivity workers are paid
+ 
+
+ align:start position:0%
+uh the low productivity workers are paid
+the low wage the median productivity pay
+
+ align:start position:0%
+the low wage the median productivity pay
+ 
+
+ align:start position:0%
+the low wage the median productivity pay
+workers are paid a medium wage and the
+
+ align:start position:0%
+workers are paid a medium wage and the
+ 
+
+ align:start position:0%
+workers are paid a medium wage and the
+high productivity workers are paid a
+
+ align:start position:0%
+high productivity workers are paid a
+ 
+
+ align:start position:0%
+high productivity workers are paid a
+high wage
+
+ align:start position:0%
+high wage
+ 
+
+ align:start position:0%
+high wage
+as you might expect that's sort of the
+
+ align:start position:0%
+as you might expect that's sort of the
+ 
+
+ align:start position:0%
+as you might expect that's sort of the
+natural thing to do in terms of you want
+
+ align:start position:0%
+natural thing to do in terms of you want
+ 
+
+ align:start position:0%
+natural thing to do in terms of you want
+to reward productivity
+
+ align:start position:0%
+to reward productivity
+ 
+
+ align:start position:0%
+to reward productivity
+the most productive workers you're going
+
+ align:start position:0%
+the most productive workers you're going
+ 
+
+ align:start position:0%
+the most productive workers you're going
+to pay
+
+ align:start position:0%
+to pay
+ 
+
+ align:start position:0%
+to pay
+the most notice that these wage
+
+ align:start position:0%
+the most notice that these wage
+ 
+
+ align:start position:0%
+the most notice that these wage
+differences are modest so even like the
+
+ align:start position:0%
+differences are modest so even like the
+ 
+
+ align:start position:0%
+differences are modest so even like the
+difference between
+
+ align:start position:0%
+difference between
+ 
+
+ align:start position:0%
+difference between
+a w high and w uh low are like uh
+
+ align:start position:0%
+a w high and w uh low are like uh
+ 
+
+ align:start position:0%
+a w high and w uh low are like uh
+uh uh only about like up to 10
+
+ align:start position:0%
+uh uh only about like up to 10
+ 
+
+ align:start position:0%
+uh uh only about like up to 10
+so really these are not huge differences
+
+ align:start position:0%
+so really these are not huge differences
+ 
+
+ align:start position:0%
+so really these are not huge differences
+it's not that the other guy if you are
+
+ align:start position:0%
+it's not that the other guy if you are
+ 
+
+ align:start position:0%
+it's not that the other guy if you are
+like a little productivity worker
+
+ align:start position:0%
+like a little productivity worker
+ 
+
+ align:start position:0%
+like a little productivity worker
+or if you get wlo it's not the other guy
+
+ align:start position:0%
+or if you get wlo it's not the other guy
+ 
+
+ align:start position:0%
+or if you get wlo it's not the other guy
+gets like twice as much it really is
+
+ align:start position:0%
+gets like twice as much it really is
+ 
+
+ align:start position:0%
+gets like twice as much it really is
+like modestly more
+
+ align:start position:0%
+like modestly more
+ 
+
+ align:start position:0%
+like modestly more
+but it is more money that they get now
+
+ align:start position:0%
+but it is more money that they get now
+ 
+
+ align:start position:0%
+but it is more money that they get now
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if you look at the other three regimes
+
+ align:start position:0%
+if you look at the other three regimes
+ 
+
+ align:start position:0%
+if you look at the other three regimes
+compressed l compressed m compressed age
+
+ align:start position:0%
+compressed l compressed m compressed age
+ 
+
+ align:start position:0%
+compressed l compressed m compressed age
+low productivity so in compressed l
+
+ align:start position:0%
+low productivity so in compressed l
+ 
+
+ align:start position:0%
+low productivity so in compressed l
+everybody gets the low wage and
+
+ align:start position:0%
+everybody gets the low wage and
+ 
+
+ align:start position:0%
+everybody gets the low wage and
+compressed m
+
+ align:start position:0%
+compressed m
+ 
+
+ align:start position:0%
+compressed m
+everybody gets the medium wage and
+
+ align:start position:0%
+everybody gets the medium wage and
+ 
+
+ align:start position:0%
+everybody gets the medium wage and
+compressed age
+
+ align:start position:0%
+compressed age
+ 
+
+ align:start position:0%
+compressed age
+everybody gets the high wage now the
+
+ align:start position:0%
+everybody gets the high wage now the
+ 
+
+ align:start position:0%
+everybody gets the high wage now the
+study now lets the authors compare
+
+ align:start position:0%
+study now lets the authors compare
+ 
+
+ align:start position:0%
+study now lets the authors compare
+the different columns for holding
+
+ align:start position:0%
+the different columns for holding
+ 
+
+ align:start position:0%
+the different columns for holding
+exactly constant baseline productivity
+
+ align:start position:0%
+exactly constant baseline productivity
+ 
+
+ align:start position:0%
+exactly constant baseline productivity
+and wage levels
+
+ align:start position:0%
+and wage levels
+ 
+
+ align:start position:0%
+and wage levels
+that is to say for instance we can
+
+ align:start position:0%
+that is to say for instance we can
+ 
+
+ align:start position:0%
+that is to say for instance we can
+compare the
+
+ align:start position:0%
+compare the
+ 
+
+ align:start position:0%
+compare the
+heterogeneous low the low productivity
+
+ align:start position:0%
+heterogeneous low the low productivity
+ 
+
+ align:start position:0%
+heterogeneous low the low productivity
+workers that happen to be randomized
+
+ align:start position:0%
+workers that happen to be randomized
+ 
+
+ align:start position:0%
+workers that happen to be randomized
+into like the heterogeneous treatments
+
+ align:start position:0%
+into like the heterogeneous treatments
+ 
+
+ align:start position:0%
+into like the heterogeneous treatments
+they receive wlo or uh compare them with
+
+ align:start position:0%
+they receive wlo or uh compare them with
+ 
+
+ align:start position:0%
+they receive wlo or uh compare them with
+like low productivity workers at
+
+ align:start position:0%
+like low productivity workers at
+ 
+
+ align:start position:0%
+like low productivity workers at
+baseline who happen to be randomized
+
+ align:start position:0%
+baseline who happen to be randomized
+ 
+
+ align:start position:0%
+baseline who happen to be randomized
+into a compressed l
+
+ align:start position:0%
+into a compressed l
+ 
+
+ align:start position:0%
+into a compressed l
+so i should have said more clearly
+
+ align:start position:0%
+so i should have said more clearly
+ 
+
+ align:start position:0%
+so i should have said more clearly
+people are randomized into any of these
+
+ align:start position:0%
+people are randomized into any of these
+ 
+
+ align:start position:0%
+people are randomized into any of these
+four groups
+
+ align:start position:0%
+four groups
+ 
+
+ align:start position:0%
+four groups
+and then depending on what your baseline
+
+ align:start position:0%
+and then depending on what your baseline
+ 
+
+ align:start position:0%
+and then depending on what your baseline
+productivity is you get the wages as i
+
+ align:start position:0%
+productivity is you get the wages as i
+ 
+
+ align:start position:0%
+productivity is you get the wages as i
+show here
+
+ align:start position:0%
+show here
+ 
+
+ align:start position:0%
+show here
+in the table so for example if you're
+
+ align:start position:0%
+in the table so for example if you're
+ 
+
+ align:start position:0%
+in the table so for example if you're
+like a low productivity worker you might
+
+ align:start position:0%
+like a low productivity worker you might
+ 
+
+ align:start position:0%
+like a low productivity worker you might
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+randomized into the heterogeneous
+
+ align:start position:0%
+randomized into the heterogeneous
+ 
+
+ align:start position:0%
+randomized into the heterogeneous
+treatment
+
+ align:start position:0%
+treatment
+ 
+
+ align:start position:0%
+treatment
+group you might receive w low or you
+
+ align:start position:0%
+group you might receive w low or you
+ 
+
+ align:start position:0%
+group you might receive w low or you
+might be randomized into the
+
+ align:start position:0%
+might be randomized into the
+ 
+
+ align:start position:0%
+might be randomized into the
+low compressed load treatment
+
+ align:start position:0%
+low compressed load treatment
+ 
+
+ align:start position:0%
+low compressed load treatment
+where you also receive wlo notice that
+
+ align:start position:0%
+where you also receive wlo notice that
+ 
+
+ align:start position:0%
+where you also receive wlo notice that
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+in both cases that worker is a low
+
+ align:start position:0%
+in both cases that worker is a low
+ 
+
+ align:start position:0%
+in both cases that worker is a low
+productivity worker
+
+ align:start position:0%
+productivity worker
+ 
+
+ align:start position:0%
+productivity worker
+uh in both cases the worker receives w
+
+ align:start position:0%
+uh in both cases the worker receives w
+ 
+
+ align:start position:0%
+uh in both cases the worker receives w
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+however what's different here now is
+
+ align:start position:0%
+however what's different here now is
+ 
+
+ align:start position:0%
+however what's different here now is
+that his co-worker his or her i think
+
+ align:start position:0%
+that his co-worker his or her i think
+ 
+
+ align:start position:0%
+that his co-worker his or her i think
+his in this case these are men
+
+ align:start position:0%
+his in this case these are men
+ 
+
+ align:start position:0%
+his in this case these are men
+co-workers are receiving either the same
+
+ align:start position:0%
+co-workers are receiving either the same
+ 
+
+ align:start position:0%
+co-workers are receiving either the same
+which is in compressed l
+
+ align:start position:0%
+which is in compressed l
+ 
+
+ align:start position:0%
+which is in compressed l
+or they receive higher wages uh in the
+
+ align:start position:0%
+or they receive higher wages uh in the
+ 
+
+ align:start position:0%
+or they receive higher wages uh in the
+heterogeneous wage treatment
+
+ align:start position:0%
+heterogeneous wage treatment
+ 
+
+ align:start position:0%
+heterogeneous wage treatment
+right so now we can look at like workers
+
+ align:start position:0%
+right so now we can look at like workers
+ 
+
+ align:start position:0%
+right so now we can look at like workers
+who have the exact same baseline
+
+ align:start position:0%
+who have the exact same baseline
+ 
+
+ align:start position:0%
+who have the exact same baseline
+productivity on average at least
+
+ align:start position:0%
+productivity on average at least
+ 
+
+ align:start position:0%
+productivity on average at least
+and have the exact same wage but what's
+
+ align:start position:0%
+and have the exact same wage but what's
+ 
+
+ align:start position:0%
+and have the exact same wage but what's
+being varied is like how much other
+
+ align:start position:0%
+being varied is like how much other
+ 
+
+ align:start position:0%
+being varied is like how much other
+workers are earning
+
+ align:start position:0%
+workers are earning
+ 
+
+ align:start position:0%
+workers are earning
+we can do this for low productivity
+
+ align:start position:0%
+we can do this for low productivity
+ 
+
+ align:start position:0%
+we can do this for low productivity
+workers we can also do it for medium
+
+ align:start position:0%
+workers we can also do it for medium
+ 
+
+ align:start position:0%
+workers we can also do it for medium
+productivity workers or
+
+ align:start position:0%
+productivity workers or
+ 
+
+ align:start position:0%
+productivity workers or
+also for high productivity workers i
+
+ align:start position:0%
+also for high productivity workers i
+ 
+
+ align:start position:0%
+also for high productivity workers i
+skipped the medium productivity worker
+
+ align:start position:0%
+skipped the medium productivity worker
+ 
+
+ align:start position:0%
+skipped the medium productivity worker
+but that's exactly the same
+
+ align:start position:0%
+but that's exactly the same
+ 
+
+ align:start position:0%
+but that's exactly the same
+for high productivity workers we can
+
+ align:start position:0%
+for high productivity workers we can
+ 
+
+ align:start position:0%
+for high productivity workers we can
+look at the workers who
+
+ align:start position:0%
+look at the workers who
+ 
+
+ align:start position:0%
+look at the workers who
+have been randomized into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heterogeneous treatment uh group or
+
+ align:start position:0%
+heterogeneous treatment uh group or
+ 
+
+ align:start position:0%
+heterogeneous treatment uh group or
+hedonist worker group
+
+ align:start position:0%
+hedonist worker group
+ 
+
+ align:start position:0%
+hedonist worker group
+uh sorry heterogeneous wage group where
+
+ align:start position:0%
+uh sorry heterogeneous wage group where
+ 
+
+ align:start position:0%
+uh sorry heterogeneous wage group where
+um the worker gets a wh but everybody
+
+ align:start position:0%
+um the worker gets a wh but everybody
+ 
+
+ align:start position:0%
+um the worker gets a wh but everybody
+else gets like a lower wage or we can
+
+ align:start position:0%
+else gets like a lower wage or we can
+ 
+
+ align:start position:0%
+else gets like a lower wage or we can
+compare that to
+
+ align:start position:0%
+compare that to
+ 
+
+ align:start position:0%
+compare that to
+a compressed age where everybody gets
+
+ align:start position:0%
+a compressed age where everybody gets
+ 
+
+ align:start position:0%
+a compressed age where everybody gets
+wh in that group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now what do you what do the
+
+ align:start position:0%
+okay so now what do you what do the
+ 
+
+ align:start position:0%
+okay so now what do you what do the
+authors find let's start with the
+
+ align:start position:0%
+authors find let's start with the
+ 
+
+ align:start position:0%
+authors find let's start with the
+low productivity workers at baseline
+
+ align:start position:0%
+low productivity workers at baseline
+ 
+
+ align:start position:0%
+low productivity workers at baseline
+remember the clean comparison here is
+
+ align:start position:0%
+remember the clean comparison here is
+ 
+
+ align:start position:0%
+remember the clean comparison here is
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+pay disparity this is the heterogeneous
+
+ align:start position:0%
+pay disparity this is the heterogeneous
+ 
+
+ align:start position:0%
+pay disparity this is the heterogeneous
+group pay disparity and compressed l
+
+ align:start position:0%
+group pay disparity and compressed l
+ 
+
+ align:start position:0%
+group pay disparity and compressed l
+which is like the group where everybody
+
+ align:start position:0%
+which is like the group where everybody
+ 
+
+ align:start position:0%
+which is like the group where everybody
+has paid
+
+ align:start position:0%
+has paid
+ 
+
+ align:start position:0%
+has paid
+the same now what the authors find and
+
+ align:start position:0%
+the same now what the authors find and
+ 
+
+ align:start position:0%
+the same now what the authors find and
+you see this in the graph
+
+ align:start position:0%
+you see this in the graph
+ 
+
+ align:start position:0%
+you see this in the graph
+fairly nicely which is like the
+
+ align:start position:0%
+fairly nicely which is like the
+ 
+
+ align:start position:0%
+fairly nicely which is like the
+productivities are like the red line and
+
+ align:start position:0%
+productivities are like the red line and
+ 
+
+ align:start position:0%
+productivities are like the red line and
+the blue line the productivity on the
+
+ align:start position:0%
+the blue line the productivity on the
+ 
+
+ align:start position:0%
+the blue line the productivity on the
+left side this is before the treatment
+
+ align:start position:0%
+left side this is before the treatment
+ 
+
+ align:start position:0%
+left side this is before the treatment
+starts
+
+ align:start position:0%
+starts
+ 
+
+ align:start position:0%
+starts
+for about over 10 days the productivity
+
+ align:start position:0%
+for about over 10 days the productivity
+ 
+
+ align:start position:0%
+for about over 10 days the productivity
+looks pretty much
+
+ align:start position:0%
+looks pretty much
+ 
+
+ align:start position:0%
+looks pretty much
+the same but then when you go to the
+
+ align:start position:0%
+the same but then when you go to the
+ 
+
+ align:start position:0%
+the same but then when you go to the
+right side of the graph
+
+ align:start position:0%
+right side of the graph
+ 
+
+ align:start position:0%
+right side of the graph
+not immediately but after a few days
+
+ align:start position:0%
+not immediately but after a few days
+ 
+
+ align:start position:0%
+not immediately but after a few days
+there seem to be
+
+ align:start position:0%
+there seem to be
+ 
+
+ align:start position:0%
+there seem to be
+a gap or a gap emerges between the red
+
+ align:start position:0%
+a gap or a gap emerges between the red
+ 
+
+ align:start position:0%
+a gap or a gap emerges between the red
+line and the blue line which is exactly
+
+ align:start position:0%
+line and the blue line which is exactly
+ 
+
+ align:start position:0%
+line and the blue line which is exactly
+the gap as you would expect
+
+ align:start position:0%
+the gap as you would expect
+ 
+
+ align:start position:0%
+the gap as you would expect
+if pay disperse the disparity
+
+ align:start position:0%
+if pay disperse the disparity
+ 
+
+ align:start position:0%
+if pay disperse the disparity
+makes workers less productive which is
+
+ align:start position:0%
+makes workers less productive which is
+ 
+
+ align:start position:0%
+makes workers less productive which is
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+they're workers who receive a low wage
+
+ align:start position:0%
+they're workers who receive a low wage
+ 
+
+ align:start position:0%
+they're workers who receive a low wage
+but others in their group are receiving
+
+ align:start position:0%
+but others in their group are receiving
+ 
+
+ align:start position:0%
+but others in their group are receiving
+higher wages are becoming
+
+ align:start position:0%
+higher wages are becoming
+ 
+
+ align:start position:0%
+higher wages are becoming
+less productive compared to workers
+
+ align:start position:0%
+less productive compared to workers
+ 
+
+ align:start position:0%
+less productive compared to workers
+that receive a low wage where others
+
+ align:start position:0%
+that receive a low wage where others
+ 
+
+ align:start position:0%
+that receive a low wage where others
+have the exact same
+
+ align:start position:0%
+have the exact same
+ 
+
+ align:start position:0%
+have the exact same
+productivity and you see this also in
+
+ align:start position:0%
+productivity and you see this also in
+ 
+
+ align:start position:0%
+productivity and you see this also in
+the regression tables you see about a 22
+
+ align:start position:0%
+the regression tables you see about a 22
+ 
+
+ align:start position:0%
+the regression tables you see about a 22
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+reduction in mean outputs and a 9
+
+ align:start position:0%
+reduction in mean outputs and a 9
+ 
+
+ align:start position:0%
+reduction in mean outputs and a 9
+reduction in in earnings which are
+
+ align:start position:0%
+reduction in in earnings which are
+ 
+
+ align:start position:0%
+reduction in in earnings which are
+pretty large effects so these are like
+
+ align:start position:0%
+pretty large effects so these are like
+ 
+
+ align:start position:0%
+pretty large effects so these are like
+large effects compared to like other
+
+ align:start position:0%
+large effects compared to like other
+ 
+
+ align:start position:0%
+large effects compared to like other
+interventions that people have
+
+ align:start position:0%
+interventions that people have
+ 
+
+ align:start position:0%
+interventions that people have
+tried interesting and you see a little
+
+ align:start position:0%
+tried interesting and you see a little
+ 
+
+ align:start position:0%
+tried interesting and you see a little
+bit like um
+
+ align:start position:0%
+bit like um
+ 
+
+ align:start position:0%
+bit like um
+well the treatment effect when you look
+
+ align:start position:0%
+well the treatment effect when you look
+ 
+
+ align:start position:0%
+well the treatment effect when you look
+at the graph initially looks not
+
+ align:start position:0%
+at the graph initially looks not
+ 
+
+ align:start position:0%
+at the graph initially looks not
+particularly large
+
+ align:start position:0%
+particularly large
+ 
+
+ align:start position:0%
+particularly large
+if anything it's this might not even be
+
+ align:start position:0%
+if anything it's this might not even be
+ 
+
+ align:start position:0%
+if anything it's this might not even be
+there after like a few days
+
+ align:start position:0%
+there after like a few days
+ 
+
+ align:start position:0%
+there after like a few days
+that treatment effect increases over
+
+ align:start position:0%
+that treatment effect increases over
+ 
+
+ align:start position:0%
+that treatment effect increases over
+time it becomes larger so
+
+ align:start position:0%
+time it becomes larger so
+ 
+
+ align:start position:0%
+time it becomes larger so
+over time people become less and less
+
+ align:start position:0%
+over time people become less and less
+ 
+
+ align:start position:0%
+over time people become less and less
+productive compared to the
+
+ align:start position:0%
+productive compared to the
+ 
+
+ align:start position:0%
+productive compared to the
+compressed wage treatment interestingly
+
+ align:start position:0%
+compressed wage treatment interestingly
+ 
+
+ align:start position:0%
+compressed wage treatment interestingly
+we find or the authors find
+
+ align:start position:0%
+we find or the authors find
+ 
+
+ align:start position:0%
+we find or the authors find
+similar effects for high rank high
+
+ align:start position:0%
+similar effects for high rank high
+ 
+
+ align:start position:0%
+similar effects for high rank high
+productivity workers
+
+ align:start position:0%
+productivity workers
+ 
+
+ align:start position:0%
+productivity workers
+so notice that these are now workers who
+
+ align:start position:0%
+so notice that these are now workers who
+ 
+
+ align:start position:0%
+so notice that these are now workers who
+either who are
+
+ align:start position:0%
+either who are
+ 
+
+ align:start position:0%
+either who are
+high productivity workers they receive
+
+ align:start position:0%
+high productivity workers they receive
+ 
+
+ align:start position:0%
+high productivity workers they receive
+the same wage in the pay disparity
+
+ align:start position:0%
+the same wage in the pay disparity
+ 
+
+ align:start position:0%
+the same wage in the pay disparity
+treatment and the compressed age
+
+ align:start position:0%
+treatment and the compressed age
+ 
+
+ align:start position:0%
+treatment and the compressed age
+treatment
+
+ align:start position:0%
+treatment
+ 
+
+ align:start position:0%
+treatment
+that have the same wage in one case they
+
+ align:start position:0%
+that have the same wage in one case they
+ 
+
+ align:start position:0%
+that have the same wage in one case they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+paid exactly the same in the other case
+
+ align:start position:0%
+paid exactly the same in the other case
+ 
+
+ align:start position:0%
+paid exactly the same in the other case
+they are paid
+
+ align:start position:0%
+they are paid
+ 
+
+ align:start position:0%
+they are paid
+more compared to their co-workers and
+
+ align:start position:0%
+more compared to their co-workers and
+ 
+
+ align:start position:0%
+more compared to their co-workers and
+what happens to me or what seems to be
+
+ align:start position:0%
+what happens to me or what seems to be
+ 
+
+ align:start position:0%
+what happens to me or what seems to be
+the case is that
+
+ align:start position:0%
+the case is that
+ 
+
+ align:start position:0%
+the case is that
+the compressed um high-pay workers
+
+ align:start position:0%
+the compressed um high-pay workers
+ 
+
+ align:start position:0%
+the compressed um high-pay workers
+they're in fact
+
+ align:start position:0%
+they're in fact
+ 
+
+ align:start position:0%
+they're in fact
+more productive compared to others you
+
+ align:start position:0%
+more productive compared to others you
+ 
+
+ align:start position:0%
+more productive compared to others you
+might have expected in some ways like if
+
+ align:start position:0%
+might have expected in some ways like if
+ 
+
+ align:start position:0%
+might have expected in some ways like if
+one guy
+
+ align:start position:0%
+one guy
+ 
+
+ align:start position:0%
+one guy
+gets paid high payment and others get
+
+ align:start position:0%
+gets paid high payment and others get
+ 
+
+ align:start position:0%
+gets paid high payment and others get
+paid less that makes the high pay worker
+
+ align:start position:0%
+paid less that makes the high pay worker
+ 
+
+ align:start position:0%
+paid less that makes the high pay worker
+more productive because maybe he feels
+
+ align:start position:0%
+more productive because maybe he feels
+ 
+
+ align:start position:0%
+more productive because maybe he feels
+good about himself that he's the high
+
+ align:start position:0%
+good about himself that he's the high
+ 
+
+ align:start position:0%
+good about himself that he's the high
+pay workers or maybe he feels like you
+
+ align:start position:0%
+pay workers or maybe he feels like you
+ 
+
+ align:start position:0%
+pay workers or maybe he feels like you
+prove himself or the like
+
+ align:start position:0%
+prove himself or the like
+ 
+
+ align:start position:0%
+prove himself or the like
+but instead what seems to be the case
+
+ align:start position:0%
+but instead what seems to be the case
+ 
+
+ align:start position:0%
+but instead what seems to be the case
+the group that works um
+
+ align:start position:0%
+the group that works um
+ 
+
+ align:start position:0%
+the group that works um
+in his team does not work well together
+
+ align:start position:0%
+in his team does not work well together
+ 
+
+ align:start position:0%
+in his team does not work well together
+or they just
+
+ align:start position:0%
+or they just
+ 
+
+ align:start position:0%
+or they just
+becomes uncomfortable to work with like
+
+ align:start position:0%
+becomes uncomfortable to work with like
+ 
+
+ align:start position:0%
+becomes uncomfortable to work with like
+somebody else who is like really mad at
+
+ align:start position:0%
+somebody else who is like really mad at
+ 
+
+ align:start position:0%
+somebody else who is like really mad at
+you for earning more
+
+ align:start position:0%
+you for earning more
+ 
+
+ align:start position:0%
+you for earning more
+than they do and so now the high
+
+ align:start position:0%
+than they do and so now the high
+ 
+
+ align:start position:0%
+than they do and so now the high
+pay workers in the compressed treatment
+
+ align:start position:0%
+pay workers in the compressed treatment
+ 
+
+ align:start position:0%
+pay workers in the compressed treatment
+in fact earn more
+
+ align:start position:0%
+in fact earn more
+ 
+
+ align:start position:0%
+in fact earn more
+or produce more than the uh high pay
+
+ align:start position:0%
+or produce more than the uh high pay
+ 
+
+ align:start position:0%
+or produce more than the uh high pay
+workers
+
+ align:start position:0%
+workers
+ 
+
+ align:start position:0%
+workers
+in the pay disparity treatment so that
+
+ align:start position:0%
+in the pay disparity treatment so that
+ 
+
+ align:start position:0%
+in the pay disparity treatment so that
+is to say the
+
+ align:start position:0%
+is to say the
+ 
+
+ align:start position:0%
+is to say the
+pay disparity or pain equality
+
+ align:start position:0%
+pay disparity or pain equality
+ 
+
+ align:start position:0%
+pay disparity or pain equality
+does not only reduce uh workers
+
+ align:start position:0%
+does not only reduce uh workers
+ 
+
+ align:start position:0%
+does not only reduce uh workers
+productivity for the low pay workers so
+
+ align:start position:0%
+productivity for the low pay workers so
+ 
+
+ align:start position:0%
+productivity for the low pay workers so
+not only the people who
+
+ align:start position:0%
+not only the people who
+ 
+
+ align:start position:0%
+not only the people who
+work the workers who are earning less
+
+ align:start position:0%
+work the workers who are earning less
+ 
+
+ align:start position:0%
+work the workers who are earning less
+compared to their coworkers
+
+ align:start position:0%
+compared to their coworkers
+ 
+
+ align:start position:0%
+compared to their coworkers
+and that's in some sense to be expected
+
+ align:start position:0%
+and that's in some sense to be expected
+ 
+
+ align:start position:0%
+and that's in some sense to be expected
+you might just be mad that everybody
+
+ align:start position:0%
+you might just be mad that everybody
+ 
+
+ align:start position:0%
+you might just be mad that everybody
+else or other people in your group
+
+ align:start position:0%
+else or other people in your group
+ 
+
+ align:start position:0%
+else or other people in your group
+are earning more then you might be
+
+ align:start position:0%
+are earning more then you might be
+ 
+
+ align:start position:0%
+are earning more then you might be
+unhappy and mad about that and just then
+
+ align:start position:0%
+unhappy and mad about that and just then
+ 
+
+ align:start position:0%
+unhappy and mad about that and just then
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+less instead it seems to be the case
+
+ align:start position:0%
+less instead it seems to be the case
+ 
+
+ align:start position:0%
+less instead it seems to be the case
+even the high productivity workers the
+
+ align:start position:0%
+even the high productivity workers the
+ 
+
+ align:start position:0%
+even the high productivity workers the
+workers who are
+
+ align:start position:0%
+workers who are
+ 
+
+ align:start position:0%
+workers who are
+earn more than others in their group are
+
+ align:start position:0%
+earn more than others in their group are
+ 
+
+ align:start position:0%
+earn more than others in their group are
+producing
+
+ align:start position:0%
+producing
+ 
+
+ align:start position:0%
+producing
+less compared to the control group where
+
+ align:start position:0%
+less compared to the control group where
+ 
+
+ align:start position:0%
+less compared to the control group where
+everybody earns the
+
+ align:start position:0%
+everybody earns the
+ 
+
+ align:start position:0%
+everybody earns the
+same so what do we learn from that well
+
+ align:start position:0%
+same so what do we learn from that well
+ 
+
+ align:start position:0%
+same so what do we learn from that well
+pay disparity lowers work
+
+ align:start position:0%
+pay disparity lowers work
+ 
+
+ align:start position:0%
+pay disparity lowers work
+performance for all team members um
+
+ align:start position:0%
+performance for all team members um
+ 
+
+ align:start position:0%
+performance for all team members um
+and so the interpretation of that is
+
+ align:start position:0%
+and so the interpretation of that is
+ 
+
+ align:start position:0%
+and so the interpretation of that is
+that that pay uh disparity
+
+ align:start position:0%
+that that pay uh disparity
+ 
+
+ align:start position:0%
+that that pay uh disparity
+undermines workers ability to cooperate
+
+ align:start position:0%
+undermines workers ability to cooperate
+ 
+
+ align:start position:0%
+undermines workers ability to cooperate
+cooperate in their own
+
+ align:start position:0%
+cooperate in their own
+ 
+
+ align:start position:0%
+cooperate in their own
+self-interests um the the paper has some
+
+ align:start position:0%
+self-interests um the the paper has some
+ 
+
+ align:start position:0%
+self-interests um the the paper has some
+additional evidence with some
+
+ align:start position:0%
+additional evidence with some
+ 
+
+ align:start position:0%
+additional evidence with some
+cooperative tasks
+
+ align:start position:0%
+cooperative tasks
+ 
+
+ align:start position:0%
+cooperative tasks
+where essentially workers are worse at
+
+ align:start position:0%
+where essentially workers are worse at
+ 
+
+ align:start position:0%
+where essentially workers are worse at
+cooperating with each other
+
+ align:start position:0%
+cooperating with each other
+ 
+
+ align:start position:0%
+cooperating with each other
+it seems to really be that workers are
+
+ align:start position:0%
+it seems to really be that workers are
+ 
+
+ align:start position:0%
+it seems to really be that workers are
+not happy
+
+ align:start position:0%
+not happy
+ 
+
+ align:start position:0%
+not happy
+to work in the same place with somebody
+
+ align:start position:0%
+to work in the same place with somebody
+ 
+
+ align:start position:0%
+to work in the same place with somebody
+else who
+
+ align:start position:0%
+else who
+ 
+
+ align:start position:0%
+else who
+earns less importantly the perceived
+
+ align:start position:0%
+earns less importantly the perceived
+ 
+
+ align:start position:0%
+earns less importantly the perceived
+justification
+
+ align:start position:0%
+justification
+ 
+
+ align:start position:0%
+justification
+is essential in mediating these effects
+
+ align:start position:0%
+is essential in mediating these effects
+ 
+
+ align:start position:0%
+is essential in mediating these effects
+that is to say i told you previously
+
+ align:start position:0%
+that is to say i told you previously
+ 
+
+ align:start position:0%
+that is to say i told you previously
+that for some tasks it was easier to
+
+ align:start position:0%
+that for some tasks it was easier to
+ 
+
+ align:start position:0%
+that for some tasks it was easier to
+see who's more productive than others
+
+ align:start position:0%
+see who's more productive than others
+ 
+
+ align:start position:0%
+see who's more productive than others
+especially at baseline just because in
+
+ align:start position:0%
+especially at baseline just because in
+ 
+
+ align:start position:0%
+especially at baseline just because in
+the task you know the differences across
+
+ align:start position:0%
+the task you know the differences across
+ 
+
+ align:start position:0%
+the task you know the differences across
+highly and less highly productive or
+
+ align:start position:0%
+highly and less highly productive or
+ 
+
+ align:start position:0%
+highly and less highly productive or
+lower high and low productivity workers
+
+ align:start position:0%
+lower high and low productivity workers
+ 
+
+ align:start position:0%
+lower high and low productivity workers
+was just wider and it's just easy to see
+
+ align:start position:0%
+was just wider and it's just easy to see
+ 
+
+ align:start position:0%
+was just wider and it's just easy to see
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+frank is really bad at this and somebody
+
+ align:start position:0%
+frank is really bad at this and somebody
+ 
+
+ align:start position:0%
+frank is really bad at this and somebody
+else is really good and for some tasks
+
+ align:start position:0%
+else is really good and for some tasks
+ 
+
+ align:start position:0%
+else is really good and for some tasks
+it's really easy to see that
+
+ align:start position:0%
+it's really easy to see that
+ 
+
+ align:start position:0%
+it's really easy to see that
+for others not so if it's really easy if
+
+ align:start position:0%
+for others not so if it's really easy if
+ 
+
+ align:start position:0%
+for others not so if it's really easy if
+there's a perceived justification
+
+ align:start position:0%
+there's a perceived justification
+ 
+
+ align:start position:0%
+there's a perceived justification
+for workers if workers sort of thought
+
+ align:start position:0%
+for workers if workers sort of thought
+ 
+
+ align:start position:0%
+for workers if workers sort of thought
+okay it's really easy to see who is more
+
+ align:start position:0%
+okay it's really easy to see who is more
+ 
+
+ align:start position:0%
+okay it's really easy to see who is more
+productive than others
+
+ align:start position:0%
+productive than others
+ 
+
+ align:start position:0%
+productive than others
+the effects are much weaker than when
+
+ align:start position:0%
+the effects are much weaker than when
+ 
+
+ align:start position:0%
+the effects are much weaker than when
+there is no perceived justification
+
+ align:start position:0%
+there is no perceived justification
+ 
+
+ align:start position:0%
+there is no perceived justification
+that is to say workers themselves are
+
+ align:start position:0%
+that is to say workers themselves are
+ 
+
+ align:start position:0%
+that is to say workers themselves are
+saying like if i'm saying like look
+
+ align:start position:0%
+saying like if i'm saying like look
+ 
+
+ align:start position:0%
+saying like if i'm saying like look
+there's this other worker who's really
+
+ align:start position:0%
+there's this other worker who's really
+ 
+
+ align:start position:0%
+there's this other worker who's really
+productive
+
+ align:start position:0%
+productive
+ 
+
+ align:start position:0%
+productive
+and if i'm sort of saying like hey look
+
+ align:start position:0%
+and if i'm sort of saying like hey look
+ 
+
+ align:start position:0%
+and if i'm sort of saying like hey look
+this is really obvious that they're more
+
+ align:start position:0%
+this is really obvious that they're more
+ 
+
+ align:start position:0%
+this is really obvious that they're more
+productive than i am
+
+ align:start position:0%
+productive than i am
+ 
+
+ align:start position:0%
+productive than i am
+it's only fair that they're earning more
+
+ align:start position:0%
+it's only fair that they're earning more
+ 
+
+ align:start position:0%
+it's only fair that they're earning more
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+these effects are much damp and there's
+
+ align:start position:0%
+these effects are much damp and there's
+ 
+
+ align:start position:0%
+these effects are much damp and there's
+much less in fact it's it's accepted
+
+ align:start position:0%
+much less in fact it's it's accepted
+ 
+
+ align:start position:0%
+much less in fact it's it's accepted
+and there's much less of a productivity
+
+ align:start position:0%
+and there's much less of a productivity
+ 
+
+ align:start position:0%
+and there's much less of a productivity
+effect if any
+
+ align:start position:0%
+effect if any
+ 
+
+ align:start position:0%
+effect if any
+uh if there's pay inequality however if
+
+ align:start position:0%
+uh if there's pay inequality however if
+ 
+
+ align:start position:0%
+uh if there's pay inequality however if
+it seems to be the case that we're kind
+
+ align:start position:0%
+it seems to be the case that we're kind
+ 
+
+ align:start position:0%
+it seems to be the case that we're kind
+of like producing the same thing
+
+ align:start position:0%
+of like producing the same thing
+ 
+
+ align:start position:0%
+of like producing the same thing
+if um and we're like similar sorry we're
+
+ align:start position:0%
+if um and we're like similar sorry we're
+ 
+
+ align:start position:0%
+if um and we're like similar sorry we're
+producing the same thing and we're
+
+ align:start position:0%
+producing the same thing and we're
+ 
+
+ align:start position:0%
+producing the same thing and we're
+equally good at it or approximately
+
+ align:start position:0%
+equally good at it or approximately
+ 
+
+ align:start position:0%
+equally good at it or approximately
+equally good
+
+ align:start position:0%
+equally good
+ 
+
+ align:start position:0%
+equally good
+and one person is paid more than i am
+
+ align:start position:0%
+and one person is paid more than i am
+ 
+
+ align:start position:0%
+and one person is paid more than i am
+for no good reason
+
+ align:start position:0%
+for no good reason
+ 
+
+ align:start position:0%
+for no good reason
+so it appears then workers are really
+
+ align:start position:0%
+so it appears then workers are really
+ 
+
+ align:start position:0%
+so it appears then workers are really
+not happy about that
+
+ align:start position:0%
+not happy about that
+ 
+
+ align:start position:0%
+not happy about that
+and work performance in particular
+
+ align:start position:0%
+and work performance in particular
+ 
+
+ align:start position:0%
+and work performance in particular
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+falls so what are the implications well
+
+ align:start position:0%
+falls so what are the implications well
+ 
+
+ align:start position:0%
+falls so what are the implications well
+this evidence sort of suggests that wage
+
+ align:start position:0%
+this evidence sort of suggests that wage
+ 
+
+ align:start position:0%
+this evidence sort of suggests that wage
+compression um
+
+ align:start position:0%
+compression um
+ 
+
+ align:start position:0%
+compression um
+may be more likely in some settings than
+
+ align:start position:0%
+may be more likely in some settings than
+ 
+
+ align:start position:0%
+may be more likely in some settings than
+in others right that's to say like
+
+ align:start position:0%
+in others right that's to say like
+ 
+
+ align:start position:0%
+in others right that's to say like
+if it's easy to justify if the
+
+ align:start position:0%
+if it's easy to justify if the
+ 
+
+ align:start position:0%
+if it's easy to justify if the
+production function or like the
+
+ align:start position:0%
+production function or like the
+ 
+
+ align:start position:0%
+production function or like the
+production process is such that all
+
+ align:start position:0%
+production process is such that all
+ 
+
+ align:start position:0%
+production process is such that all
+aspects of the production and the output
+
+ align:start position:0%
+aspects of the production and the output
+ 
+
+ align:start position:0%
+aspects of the production and the output
+or the performance are easy measurable
+
+ align:start position:0%
+or the performance are easy measurable
+ 
+
+ align:start position:0%
+or the performance are easy measurable
+measurable and observable for workers
+
+ align:start position:0%
+measurable and observable for workers
+ 
+
+ align:start position:0%
+measurable and observable for workers
+then you know workers might say
+
+ align:start position:0%
+then you know workers might say
+ 
+
+ align:start position:0%
+then you know workers might say
+it's okay if some workers are earning
+
+ align:start position:0%
+it's okay if some workers are earning
+ 
+
+ align:start position:0%
+it's okay if some workers are earning
+more than others
+
+ align:start position:0%
+more than others
+ 
+
+ align:start position:0%
+more than others
+however if that's not the case if
+
+ align:start position:0%
+however if that's not the case if
+ 
+
+ align:start position:0%
+however if that's not the case if
+there's a bunch of stuff in the work
+
+ align:start position:0%
+there's a bunch of stuff in the work
+ 
+
+ align:start position:0%
+there's a bunch of stuff in the work
+process that's really not observed maybe
+
+ align:start position:0%
+process that's really not observed maybe
+ 
+
+ align:start position:0%
+process that's really not observed maybe
+it's verbal or maybe it's just really
+
+ align:start position:0%
+it's verbal or maybe it's just really
+ 
+
+ align:start position:0%
+it's verbal or maybe it's just really
+hard to justify or hard to sort of
+
+ align:start position:0%
+hard to justify or hard to sort of
+ 
+
+ align:start position:0%
+hard to justify or hard to sort of
+assess in some
+
+ align:start position:0%
+assess in some
+ 
+
+ align:start position:0%
+assess in some
+tangible way then you know workers might
+
+ align:start position:0%
+tangible way then you know workers might
+ 
+
+ align:start position:0%
+tangible way then you know workers might
+be really unhappy
+
+ align:start position:0%
+be really unhappy
+ 
+
+ align:start position:0%
+be really unhappy
+and that might lead to wage compression
+
+ align:start position:0%
+and that might lead to wage compression
+ 
+
+ align:start position:0%
+and that might lead to wage compression
+because the employer might anticipate
+
+ align:start position:0%
+because the employer might anticipate
+ 
+
+ align:start position:0%
+because the employer might anticipate
+um that so overall that sort of says
+
+ align:start position:0%
+um that so overall that sort of says
+ 
+
+ align:start position:0%
+um that so overall that sort of says
+that like
+
+ align:start position:0%
+that like
+ 
+
+ align:start position:0%
+that like
+um relative comparisons matter quite a
+
+ align:start position:0%
+um relative comparisons matter quite a
+ 
+
+ align:start position:0%
+um relative comparisons matter quite a
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+fairness matters quite a bit and what's
+
+ align:start position:0%
+fairness matters quite a bit and what's
+ 
+
+ align:start position:0%
+fairness matters quite a bit and what's
+really key for an employer or anybody
+
+ align:start position:0%
+really key for an employer or anybody
+ 
+
+ align:start position:0%
+really key for an employer or anybody
+who sets incentives
+
+ align:start position:0%
+who sets incentives
+ 
+
+ align:start position:0%
+who sets incentives
+is to take into account these fairness
+
+ align:start position:0%
+is to take into account these fairness
+ 
+
+ align:start position:0%
+is to take into account these fairness
+consideration
+
+ align:start position:0%
+consideration
+ 
+
+ align:start position:0%
+consideration
+rations and one wants to really
+
+ align:start position:0%
+rations and one wants to really
+ 
+
+ align:start position:0%
+rations and one wants to really
+understand what is fair and what is not
+
+ align:start position:0%
+understand what is fair and what is not
+ 
+
+ align:start position:0%
+understand what is fair and what is not
+and upsetting workers by violating these
+
+ align:start position:0%
+and upsetting workers by violating these
+ 
+
+ align:start position:0%
+and upsetting workers by violating these
+fairness considerations or norms
+
+ align:start position:0%
+fairness considerations or norms
+ 
+
+ align:start position:0%
+fairness considerations or norms
+might be really really costly for an
+
+ align:start position:0%
+might be really really costly for an
+ 
+
+ align:start position:0%
+might be really really costly for an
+employer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the good news here is that like if
+
+ align:start position:0%
+so the good news here is that like if
+ 
+
+ align:start position:0%
+so the good news here is that like if
+one understands that well you know one
+
+ align:start position:0%
+one understands that well you know one
+ 
+
+ align:start position:0%
+one understands that well you know one
+can really sort of produce
+
+ align:start position:0%
+can really sort of produce
+ 
+
+ align:start position:0%
+can really sort of produce
+increase productivity quite a bit and in
+
+ align:start position:0%
+increase productivity quite a bit and in
+ 
+
+ align:start position:0%
+increase productivity quite a bit and in
+some cases
+
+ align:start position:0%
+some cases
+ 
+
+ align:start position:0%
+some cases
+wage inequality is actually fine one
+
+ align:start position:0%
+wage inequality is actually fine one
+ 
+
+ align:start position:0%
+wage inequality is actually fine one
+just has to be careful in figuring out
+
+ align:start position:0%
+just has to be careful in figuring out
+ 
+
+ align:start position:0%
+just has to be careful in figuring out
+when exactly is that the case
+
+ align:start position:0%
+when exactly is that the case
+ 
+
+ align:start position:0%
+when exactly is that the case
+okay as i said there's a very nice paper
+
+ align:start position:0%
+okay as i said there's a very nice paper
+ 
+
+ align:start position:0%
+okay as i said there's a very nice paper
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+jonah stewart on ethnic divisions and
+
+ align:start position:0%
+jonah stewart on ethnic divisions and
+ 
+
+ align:start position:0%
+jonah stewart on ethnic divisions and
+production and firms
+
+ align:start position:0%
+production and firms
+ 
+
+ align:start position:0%
+production and firms
+we're going to talk about that in
+
+ align:start position:0%
+we're going to talk about that in
+ 
+
+ align:start position:0%
+we're going to talk about that in
+recitation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the second part of this lecture
+
+ align:start position:0%
+okay the second part of this lecture
+ 
+
+ align:start position:0%
+okay the second part of this lecture
+we'll talk about
+
+ align:start position:0%
+we'll talk about
+ 
+
+ align:start position:0%
+we'll talk about
+policies to increase pro-sociality
+
+ align:start position:0%
+policies to increase pro-sociality
+ 
+
+ align:start position:0%
+policies to increase pro-sociality
+and so uh the first of these papers is a
+
+ align:start position:0%
+and so uh the first of these papers is a
+ 
+
+ align:start position:0%
+and so uh the first of these papers is a
+very nice recent paper by gautam rao
+
+ align:start position:0%
+very nice recent paper by gautam rao
+ 
+
+ align:start position:0%
+very nice recent paper by gautam rao
+that looks at the question are social
+
+ align:start position:0%
+that looks at the question are social
+ 
+
+ align:start position:0%
+that looks at the question are social
+preferences malleable
+
+ align:start position:0%
+preferences malleable
+ 
+
+ align:start position:0%
+preferences malleable
+like what are the origins of social
+
+ align:start position:0%
+like what are the origins of social
+ 
+
+ align:start position:0%
+like what are the origins of social
+preferences why is it that some people
+
+ align:start position:0%
+preferences why is it that some people
+ 
+
+ align:start position:0%
+preferences why is it that some people
+appear nicer
+
+ align:start position:0%
+appear nicer
+ 
+
+ align:start position:0%
+appear nicer
+than others and then you know once we
+
+ align:start position:0%
+than others and then you know once we
+ 
+
+ align:start position:0%
+than others and then you know once we
+understand that perhaps we can also
+
+ align:start position:0%
+understand that perhaps we can also
+ 
+
+ align:start position:0%
+understand that perhaps we can also
+understand what policies of anything
+
+ align:start position:0%
+understand what policies of anything
+ 
+
+ align:start position:0%
+understand what policies of anything
+anything can affect social preferences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the main question that this paper asks
+
+ align:start position:0%
+the main question that this paper asks
+ 
+
+ align:start position:0%
+the main question that this paper asks
+is how does being mixed with poor
+
+ align:start position:0%
+is how does being mixed with poor
+ 
+
+ align:start position:0%
+is how does being mixed with poor
+student in school affect the social
+
+ align:start position:0%
+student in school affect the social
+ 
+
+ align:start position:0%
+student in school affect the social
+preferences of
+
+ align:start position:0%
+preferences of
+ 
+
+ align:start position:0%
+preferences of
+rich students now in a lot of
+
+ align:start position:0%
+rich students now in a lot of
+ 
+
+ align:start position:0%
+rich students now in a lot of
+kind of policies where poor students are
+
+ align:start position:0%
+kind of policies where poor students are
+ 
+
+ align:start position:0%
+kind of policies where poor students are
+mixed with rich students
+
+ align:start position:0%
+mixed with rich students
+ 
+
+ align:start position:0%
+mixed with rich students
+you might ask the question how does it
+
+ align:start position:0%
+you might ask the question how does it
+ 
+
+ align:start position:0%
+you might ask the question how does it
+affect the poor student if a poor
+
+ align:start position:0%
+affect the poor student if a poor
+ 
+
+ align:start position:0%
+affect the poor student if a poor
+student for whatever reason
+
+ align:start position:0%
+student for whatever reason
+ 
+
+ align:start position:0%
+student for whatever reason
+would not be able to afford like a rich
+
+ align:start position:0%
+would not be able to afford like a rich
+ 
+
+ align:start position:0%
+would not be able to afford like a rich
+school or a rich student school
+
+ align:start position:0%
+school or a rich student school
+ 
+
+ align:start position:0%
+school or a rich student school
+and you sort of allow them by giving
+
+ align:start position:0%
+and you sort of allow them by giving
+ 
+
+ align:start position:0%
+and you sort of allow them by giving
+them scholarships or other policies
+
+ align:start position:0%
+them scholarships or other policies
+ 
+
+ align:start position:0%
+them scholarships or other policies
+uh uh often the question that people ask
+
+ align:start position:0%
+uh uh often the question that people ask
+ 
+
+ align:start position:0%
+uh uh often the question that people ask
+is like what are the benefits
+
+ align:start position:0%
+is like what are the benefits
+ 
+
+ align:start position:0%
+is like what are the benefits
+of doing that is this a poor student uh
+
+ align:start position:0%
+of doing that is this a poor student uh
+ 
+
+ align:start position:0%
+of doing that is this a poor student uh
+you know doing better in school or do
+
+ align:start position:0%
+you know doing better in school or do
+ 
+
+ align:start position:0%
+you know doing better in school or do
+they have different types of friends
+
+ align:start position:0%
+they have different types of friends
+ 
+
+ align:start position:0%
+they have different types of friends
+different networks and does that lead to
+
+ align:start position:0%
+different networks and does that lead to
+ 
+
+ align:start position:0%
+different networks and does that lead to
+better jobs and so on and so forth
+
+ align:start position:0%
+better jobs and so on and so forth
+ 
+
+ align:start position:0%
+better jobs and so on and so forth
+this question this paper asked a
+
+ align:start position:0%
+this question this paper asked a
+ 
+
+ align:start position:0%
+this question this paper asked a
+different question and asked the
+
+ align:start position:0%
+different question and asked the
+ 
+
+ align:start position:0%
+different question and asked the
+question about
+
+ align:start position:0%
+question about
+ 
+
+ align:start position:0%
+question about
+what is the effect of rich students if
+
+ align:start position:0%
+what is the effect of rich students if
+ 
+
+ align:start position:0%
+what is the effect of rich students if
+they randomly or quasi-randomly are
+
+ align:start position:0%
+they randomly or quasi-randomly are
+ 
+
+ align:start position:0%
+they randomly or quasi-randomly are
+exposed to
+
+ align:start position:0%
+exposed to
+ 
+
+ align:start position:0%
+exposed to
+uh being in class with additional or
+
+ align:start position:0%
+uh being in class with additional or
+ 
+
+ align:start position:0%
+uh being in class with additional or
+some more poor students um the paper
+
+ align:start position:0%
+some more poor students um the paper
+ 
+
+ align:start position:0%
+some more poor students um the paper
+exploits a policy change that um
+
+ align:start position:0%
+exploits a policy change that um
+ 
+
+ align:start position:0%
+exploits a policy change that um
+introduced an admissions quota of 20 for
+
+ align:start position:0%
+introduced an admissions quota of 20 for
+ 
+
+ align:start position:0%
+introduced an admissions quota of 20 for
+poor students in primary schools
+
+ align:start position:0%
+poor students in primary schools
+ 
+
+ align:start position:0%
+poor students in primary schools
+in in delhi delhi these are like rich
+
+ align:start position:0%
+in in delhi delhi these are like rich
+ 
+
+ align:start position:0%
+in in delhi delhi these are like rich
+private um primary schools the paper
+
+ align:start position:0%
+private um primary schools the paper
+ 
+
+ align:start position:0%
+private um primary schools the paper
+looks at two sources of variation
+
+ align:start position:0%
+looks at two sources of variation
+ 
+
+ align:start position:0%
+looks at two sources of variation
+there's variation across classrooms that
+
+ align:start position:0%
+there's variation across classrooms that
+ 
+
+ align:start position:0%
+there's variation across classrooms that
+allows the author to look at the overall
+
+ align:start position:0%
+allows the author to look at the overall
+ 
+
+ align:start position:0%
+allows the author to look at the overall
+effects so you can look at like
+
+ align:start position:0%
+effects so you can look at like
+ 
+
+ align:start position:0%
+effects so you can look at like
+within schools there's going to be like
+
+ align:start position:0%
+within schools there's going to be like
+ 
+
+ align:start position:0%
+within schools there's going to be like
+treated um uh
+
+ align:start position:0%
+treated um uh
+ 
+
+ align:start position:0%
+treated um uh
+uh uh uncontrolled courts because the
+
+ align:start position:0%
+uh uh uncontrolled courts because the
+ 
+
+ align:start position:0%
+uh uh uncontrolled courts because the
+policy was introduced
+
+ align:start position:0%
+policy was introduced
+ 
+
+ align:start position:0%
+policy was introduced
+uh at some point so for um some students
+
+ align:start position:0%
+uh at some point so for um some students
+ 
+
+ align:start position:0%
+uh at some point so for um some students
+uh uh they enjoyed the benefit of being
+
+ align:start position:0%
+uh uh they enjoyed the benefit of being
+ 
+
+ align:start position:0%
+uh uh they enjoyed the benefit of being
+in class with
+
+ align:start position:0%
+in class with
+ 
+
+ align:start position:0%
+in class with
+with poor students or the costs we'll
+
+ align:start position:0%
+with poor students or the costs we'll
+ 
+
+ align:start position:0%
+with poor students or the costs we'll
+see about that
+
+ align:start position:0%
+see about that
+ 
+
+ align:start position:0%
+see about that
+and for other schools they're already
+
+ align:start position:0%
+and for other schools they're already
+ 
+
+ align:start position:0%
+and for other schools they're already
+too far advanced they were like
+
+ align:start position:0%
+too far advanced they were like
+ 
+
+ align:start position:0%
+too far advanced they were like
+essentially before the pod they went to
+
+ align:start position:0%
+essentially before the pod they went to
+ 
+
+ align:start position:0%
+essentially before the pod they went to
+school before the policy was enacted
+
+ align:start position:0%
+school before the policy was enacted
+ 
+
+ align:start position:0%
+school before the policy was enacted
+and therefore um they were not exposed
+
+ align:start position:0%
+and therefore um they were not exposed
+ 
+
+ align:start position:0%
+and therefore um they were not exposed
+to having poor
+
+ align:start position:0%
+to having poor
+ 
+
+ align:start position:0%
+to having poor
+uh students in in school for for these
+
+ align:start position:0%
+uh students in in school for for these
+ 
+
+ align:start position:0%
+uh students in in school for for these
+treated schools there's essentially
+
+ align:start position:0%
+treated schools there's essentially
+ 
+
+ align:start position:0%
+treated schools there's essentially
+variation within school across cohorts
+
+ align:start position:0%
+variation within school across cohorts
+ 
+
+ align:start position:0%
+variation within school across cohorts
+um that we can look at look at um
+
+ align:start position:0%
+um that we can look at look at um
+ 
+
+ align:start position:0%
+um that we can look at look at um
+second within cohorts we can look at
+
+ align:start position:0%
+second within cohorts we can look at
+ 
+
+ align:start position:0%
+second within cohorts we can look at
+treated and uh
+
+ align:start position:0%
+treated and uh
+ 
+
+ align:start position:0%
+treated and uh
+control schools so some schools were
+
+ align:start position:0%
+control schools so some schools were
+ 
+
+ align:start position:0%
+control schools so some schools were
+getting
+
+ align:start position:0%
+getting
+ 
+
+ align:start position:0%
+getting
+additional poor kids and others did not
+
+ align:start position:0%
+additional poor kids and others did not
+ 
+
+ align:start position:0%
+additional poor kids and others did not
+i'll tell you about this in a second
+
+ align:start position:0%
+i'll tell you about this in a second
+ 
+
+ align:start position:0%
+i'll tell you about this in a second
+and then there's variation within
+
+ align:start position:0%
+and then there's variation within
+ 
+
+ align:start position:0%
+and then there's variation within
+classrooms to allow us to look at
+
+ align:start position:0%
+classrooms to allow us to look at
+ 
+
+ align:start position:0%
+classrooms to allow us to look at
+the role of personal interactions that
+
+ align:start position:0%
+the role of personal interactions that
+ 
+
+ align:start position:0%
+the role of personal interactions that
+sort of idiosyncratic assignments to
+
+ align:start position:0%
+sort of idiosyncratic assignments to
+ 
+
+ align:start position:0%
+sort of idiosyncratic assignments to
+study groups
+
+ align:start position:0%
+study groups
+ 
+
+ align:start position:0%
+study groups
+so some students happen to be in study
+
+ align:start position:0%
+so some students happen to be in study
+ 
+
+ align:start position:0%
+so some students happen to be in study
+groups with a poor kid and others
+
+ align:start position:0%
+groups with a poor kid and others
+ 
+
+ align:start position:0%
+groups with a poor kid and others
+were not
+
+ align:start position:0%
+were not
+ 
+
+ align:start position:0%
+were not
+now what does the study measure the
+
+ align:start position:0%
+now what does the study measure the
+ 
+
+ align:start position:0%
+now what does the study measure the
+study measures three broad set of
+
+ align:start position:0%
+study measures three broad set of
+ 
+
+ align:start position:0%
+study measures three broad set of
+outcomes
+
+ align:start position:0%
+outcomes
+ 
+
+ align:start position:0%
+outcomes
+it matters pro-social behavior and
+
+ align:start position:0%
+it matters pro-social behavior and
+ 
+
+ align:start position:0%
+it matters pro-social behavior and
+generosity this is very much what we
+
+ align:start position:0%
+generosity this is very much what we
+ 
+
+ align:start position:0%
+generosity this is very much what we
+have already looked at
+
+ align:start position:0%
+have already looked at
+ 
+
+ align:start position:0%
+have already looked at
+in particular it looks at dictator games
+
+ align:start position:0%
+in particular it looks at dictator games
+ 
+
+ align:start position:0%
+in particular it looks at dictator games
+and voluntary volunteering
+
+ align:start position:0%
+and voluntary volunteering
+ 
+
+ align:start position:0%
+and voluntary volunteering
+for charities at school the paper has a
+
+ align:start position:0%
+for charities at school the paper has a
+ 
+
+ align:start position:0%
+for charities at school the paper has a
+very nice
+
+ align:start position:0%
+very nice
+ 
+
+ align:start position:0%
+very nice
+mix of laboratory outcomes sort of
+
+ align:start position:0%
+mix of laboratory outcomes sort of
+ 
+
+ align:start position:0%
+mix of laboratory outcomes sort of
+measured in the field which is sort of
+
+ align:start position:0%
+measured in the field which is sort of
+ 
+
+ align:start position:0%
+measured in the field which is sort of
+the dictator games that you're all
+
+ align:start position:0%
+the dictator games that you're all
+ 
+
+ align:start position:0%
+the dictator games that you're all
+familiar with
+
+ align:start position:0%
+familiar with
+ 
+
+ align:start position:0%
+familiar with
+and field outcomes which is sort of
+
+ align:start position:0%
+and field outcomes which is sort of
+ 
+
+ align:start position:0%
+and field outcomes which is sort of
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+collect real-world outcomes in the sense
+
+ align:start position:0%
+collect real-world outcomes in the sense
+ 
+
+ align:start position:0%
+collect real-world outcomes in the sense
+of like things that are perhaps somewhat
+
+ align:start position:0%
+of like things that are perhaps somewhat
+ 
+
+ align:start position:0%
+of like things that are perhaps somewhat
+less contrived
+
+ align:start position:0%
+less contrived
+ 
+
+ align:start position:0%
+less contrived
+from the perspective of like kids in
+
+ align:start position:0%
+from the perspective of like kids in
+ 
+
+ align:start position:0%
+from the perspective of like kids in
+school and
+
+ align:start position:0%
+school and
+ 
+
+ align:start position:0%
+school and
+what's very nice about the study is that
+
+ align:start position:0%
+what's very nice about the study is that
+ 
+
+ align:start position:0%
+what's very nice about the study is that
+it seems to be that the results are very
+
+ align:start position:0%
+it seems to be that the results are very
+ 
+
+ align:start position:0%
+it seems to be that the results are very
+much aligned
+
+ align:start position:0%
+much aligned
+ 
+
+ align:start position:0%
+much aligned
+between sort of these lab outcomes the
+
+ align:start position:0%
+between sort of these lab outcomes the
+ 
+
+ align:start position:0%
+between sort of these lab outcomes the
+dictator game type outcomes
+
+ align:start position:0%
+dictator game type outcomes
+ 
+
+ align:start position:0%
+dictator game type outcomes
+and the field outcomes for just
+
+ align:start position:0%
+and the field outcomes for just
+ 
+
+ align:start position:0%
+and the field outcomes for just
+volunteering for charity at school in
+
+ align:start position:0%
+volunteering for charity at school in
+ 
+
+ align:start position:0%
+volunteering for charity at school in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+second the author looks at
+
+ align:start position:0%
+second the author looks at
+ 
+
+ align:start position:0%
+second the author looks at
+discrimination and social interactions
+
+ align:start position:0%
+discrimination and social interactions
+ 
+
+ align:start position:0%
+discrimination and social interactions
+in particular he does a little sports
+
+ align:start position:0%
+in particular he does a little sports
+ 
+
+ align:start position:0%
+in particular he does a little sports
+contest and looks at teammate selection
+
+ align:start position:0%
+contest and looks at teammate selection
+ 
+
+ align:start position:0%
+contest and looks at teammate selection
+among these students and then
+
+ align:start position:0%
+among these students and then
+ 
+
+ align:start position:0%
+among these students and then
+willingness to attend play dates with
+
+ align:start position:0%
+willingness to attend play dates with
+ 
+
+ align:start position:0%
+willingness to attend play dates with
+poor students finally the author also
+
+ align:start position:0%
+poor students finally the author also
+ 
+
+ align:start position:0%
+poor students finally the author also
+looks at academic outcomes in particular
+
+ align:start position:0%
+looks at academic outcomes in particular
+ 
+
+ align:start position:0%
+looks at academic outcomes in particular
+test scores and disciplinary infractions
+
+ align:start position:0%
+test scores and disciplinary infractions
+ 
+
+ align:start position:0%
+test scores and disciplinary infractions
+now why might one want to look at
+
+ align:start position:0%
+now why might one want to look at
+ 
+
+ align:start position:0%
+now why might one want to look at
+academic outcomes and why are we
+
+ align:start position:0%
+academic outcomes and why are we
+ 
+
+ align:start position:0%
+academic outcomes and why are we
+interested in social preferences
+
+ align:start position:0%
+interested in social preferences
+ 
+
+ align:start position:0%
+interested in social preferences
+there's several reasons for that in
+
+ align:start position:0%
+there's several reasons for that in
+ 
+
+ align:start position:0%
+there's several reasons for that in
+particular an important reason here is
+
+ align:start position:0%
+particular an important reason here is
+ 
+
+ align:start position:0%
+particular an important reason here is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um uh if you're against this type of
+
+ align:start position:0%
+um uh if you're against this type of
+ 
+
+ align:start position:0%
+um uh if you're against this type of
+policy i might sort of show you that
+
+ align:start position:0%
+policy i might sort of show you that
+ 
+
+ align:start position:0%
+policy i might sort of show you that
+oh you know adding poor children um uh
+
+ align:start position:0%
+oh you know adding poor children um uh
+ 
+
+ align:start position:0%
+oh you know adding poor children um uh
+might affect the the social preference
+
+ align:start position:0%
+might affect the the social preference
+ 
+
+ align:start position:0%
+might affect the the social preference
+of rich children and so on in various
+
+ align:start position:0%
+of rich children and so on in various
+ 
+
+ align:start position:0%
+of rich children and so on in various
+ways maybe discrimination goes down but
+
+ align:start position:0%
+ways maybe discrimination goes down but
+ 
+
+ align:start position:0%
+ways maybe discrimination goes down but
+perhaps it's the case that that all
+
+ align:start position:0%
+perhaps it's the case that that all
+ 
+
+ align:start position:0%
+perhaps it's the case that that all
+comes at the cost of academic
+
+ align:start position:0%
+comes at the cost of academic
+ 
+
+ align:start position:0%
+comes at the cost of academic
+performance
+
+ align:start position:0%
+performance
+ 
+
+ align:start position:0%
+performance
+but if you're trying to sort of
+
+ align:start position:0%
+but if you're trying to sort of
+ 
+
+ align:start position:0%
+but if you're trying to sort of
+implement this policy and uh
+
+ align:start position:0%
+implement this policy and uh
+ 
+
+ align:start position:0%
+implement this policy and uh
+you know persuade policy makers maybe
+
+ align:start position:0%
+you know persuade policy makers maybe
+ 
+
+ align:start position:0%
+you know persuade policy makers maybe
+teachers
+
+ align:start position:0%
+teachers
+ 
+
+ align:start position:0%
+teachers
+um or parents of like okay let's have
+
+ align:start position:0%
+um or parents of like okay let's have
+ 
+
+ align:start position:0%
+um or parents of like okay let's have
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+poor students in in in in your school
+
+ align:start position:0%
+poor students in in in in your school
+ 
+
+ align:start position:0%
+poor students in in in in your school
+well parents might sort of be okay fine
+
+ align:start position:0%
+well parents might sort of be okay fine
+ 
+
+ align:start position:0%
+well parents might sort of be okay fine
+there's going to be like some change in
+
+ align:start position:0%
+there's going to be like some change in
+ 
+
+ align:start position:0%
+there's going to be like some change in
+social preferences
+
+ align:start position:0%
+social preferences
+ 
+
+ align:start position:0%
+social preferences
+some change in discrimination but really
+
+ align:start position:0%
+some change in discrimination but really
+ 
+
+ align:start position:0%
+some change in discrimination but really
+what we care about is um
+
+ align:start position:0%
+what we care about is um
+ 
+
+ align:start position:0%
+what we care about is um
+uh test scores or um discipline at
+
+ align:start position:0%
+uh test scores or um discipline at
+ 
+
+ align:start position:0%
+uh test scores or um discipline at
+school and these poor kids might not be
+
+ align:start position:0%
+school and these poor kids might not be
+ 
+
+ align:start position:0%
+school and these poor kids might not be
+um might be worse in terms of like test
+
+ align:start position:0%
+um might be worse in terms of like test
+ 
+
+ align:start position:0%
+um might be worse in terms of like test
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+and they might have like negative peer
+
+ align:start position:0%
+and they might have like negative peer
+ 
+
+ align:start position:0%
+and they might have like negative peer
+effects in terms of like
+
+ align:start position:0%
+effects in terms of like
+ 
+
+ align:start position:0%
+effects in terms of like
+um a test scores but also in terms of
+
+ align:start position:0%
+um a test scores but also in terms of
+ 
+
+ align:start position:0%
+um a test scores but also in terms of
+disciplinary
+
+ align:start position:0%
+disciplinary
+ 
+
+ align:start position:0%
+disciplinary
+infractions and sort of as a policy
+
+ align:start position:0%
+infractions and sort of as a policy
+ 
+
+ align:start position:0%
+infractions and sort of as a policy
+question then it's really important to
+
+ align:start position:0%
+question then it's really important to
+ 
+
+ align:start position:0%
+question then it's really important to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+if there are some benefits in terms of
+
+ align:start position:0%
+if there are some benefits in terms of
+ 
+
+ align:start position:0%
+if there are some benefits in terms of
+pro-sociality or
+
+ align:start position:0%
+pro-sociality or
+ 
+
+ align:start position:0%
+pro-sociality or
+reduced discrimination do these benefits
+
+ align:start position:0%
+reduced discrimination do these benefits
+ 
+
+ align:start position:0%
+reduced discrimination do these benefits
+come at the cost of
+
+ align:start position:0%
+come at the cost of
+ 
+
+ align:start position:0%
+come at the cost of
+reduced academic performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now what is in fact the policy
+
+ align:start position:0%
+okay so now what is in fact the policy
+ 
+
+ align:start position:0%
+okay so now what is in fact the policy
+innovation in delhi in 2007
+
+ align:start position:0%
+innovation in delhi in 2007
+ 
+
+ align:start position:0%
+innovation in delhi in 2007
+there was a 20 admissions quota in
+
+ align:start position:0%
+there was a 20 admissions quota in
+ 
+
+ align:start position:0%
+there was a 20 admissions quota in
+private schools introduced
+
+ align:start position:0%
+private schools introduced
+ 
+
+ align:start position:0%
+private schools introduced
+for poor students in some of these
+
+ align:start position:0%
+for poor students in some of these
+ 
+
+ align:start position:0%
+for poor students in some of these
+private schools there's a household
+
+ align:start position:0%
+private schools there's a household
+ 
+
+ align:start position:0%
+private schools there's a household
+income
+
+ align:start position:0%
+income
+ 
+
+ align:start position:0%
+income
+cut off of two thousand dollars per year
+
+ align:start position:0%
+cut off of two thousand dollars per year
+ 
+
+ align:start position:0%
+cut off of two thousand dollars per year
+so these are not sort of the poorest of
+
+ align:start position:0%
+so these are not sort of the poorest of
+ 
+
+ align:start position:0%
+so these are not sort of the poorest of
+the poor of the students
+
+ align:start position:0%
+the poor of the students
+ 
+
+ align:start position:0%
+the poor of the students
+who who are qualified
+
+ align:start position:0%
+who who are qualified
+ 
+
+ align:start position:0%
+who who are qualified
+schools which received subsidy
+
+ align:start position:0%
+schools which received subsidy
+ 
+
+ align:start position:0%
+schools which received subsidy
+subsidized land from the government um
+
+ align:start position:0%
+subsidized land from the government um
+ 
+
+ align:start position:0%
+subsidized land from the government um
+were essentially um uh uh uh included in
+
+ align:start position:0%
+were essentially um uh uh uh included in
+ 
+
+ align:start position:0%
+were essentially um uh uh uh included in
+this policy change
+
+ align:start position:0%
+this policy change
+ 
+
+ align:start position:0%
+this policy change
+that's over 90 of elite private schools
+
+ align:start position:0%
+that's over 90 of elite private schools
+ 
+
+ align:start position:0%
+that's over 90 of elite private schools
+so think of these elite private schools
+
+ align:start position:0%
+so think of these elite private schools
+ 
+
+ align:start position:0%
+so think of these elite private schools
+these are really sort of like
+
+ align:start position:0%
+these are really sort of like
+ 
+
+ align:start position:0%
+these are really sort of like
+very rich kids or parents
+
+ align:start position:0%
+very rich kids or parents
+ 
+
+ align:start position:0%
+very rich kids or parents
+of these kids there was no fees for the
+
+ align:start position:0%
+of these kids there was no fees for the
+ 
+
+ align:start position:0%
+of these kids there was no fees for the
+poor kids because you know they would
+
+ align:start position:0%
+poor kids because you know they would
+ 
+
+ align:start position:0%
+poor kids because you know they would
+not be able to afford these fees anyway
+
+ align:start position:0%
+not be able to afford these fees anyway
+ 
+
+ align:start position:0%
+not be able to afford these fees anyway
+there was importantly also no tracking
+
+ align:start position:0%
+there was importantly also no tracking
+ 
+
+ align:start position:0%
+there was importantly also no tracking
+so it wasn't that like
+
+ align:start position:0%
+so it wasn't that like
+ 
+
+ align:start position:0%
+so it wasn't that like
+a high ability or high performance kids
+
+ align:start position:0%
+a high ability or high performance kids
+ 
+
+ align:start position:0%
+a high ability or high performance kids
+who do very well
+
+ align:start position:0%
+who do very well
+ 
+
+ align:start position:0%
+who do very well
+were like tracked in the lake high
+
+ align:start position:0%
+were like tracked in the lake high
+ 
+
+ align:start position:0%
+were like tracked in the lake high
+tracks and the good good tracks versus
+
+ align:start position:0%
+tracks and the good good tracks versus
+ 
+
+ align:start position:0%
+tracks and the good good tracks versus
+lower tracks
+
+ align:start position:0%
+lower tracks
+ 
+
+ align:start position:0%
+lower tracks
+instead everybody was mixed together
+
+ align:start position:0%
+instead everybody was mixed together
+ 
+
+ align:start position:0%
+instead everybody was mixed together
+poor and rich high performing low
+
+ align:start position:0%
+poor and rich high performing low
+ 
+
+ align:start position:0%
+poor and rich high performing low
+performing
+
+ align:start position:0%
+performing
+ 
+
+ align:start position:0%
+performing
+students and the poor kids were selected
+
+ align:start position:0%
+students and the poor kids were selected
+ 
+
+ align:start position:0%
+students and the poor kids were selected
+using lotteries
+
+ align:start position:0%
+using lotteries
+ 
+
+ align:start position:0%
+using lotteries
+which in principle also allows the
+
+ align:start position:0%
+which in principle also allows the
+ 
+
+ align:start position:0%
+which in principle also allows the
+author or others to look at
+
+ align:start position:0%
+author or others to look at
+ 
+
+ align:start position:0%
+author or others to look at
+the effect on those poor kids the
+
+ align:start position:0%
+the effect on those poor kids the
+ 
+
+ align:start position:0%
+the effect on those poor kids the
+students who are selected versus not
+
+ align:start position:0%
+students who are selected versus not
+ 
+
+ align:start position:0%
+students who are selected versus not
+to be clear this is not the subject of
+
+ align:start position:0%
+to be clear this is not the subject of
+ 
+
+ align:start position:0%
+to be clear this is not the subject of
+this paper
+
+ align:start position:0%
+this paper
+ 
+
+ align:start position:0%
+this paper
+just to give you a sense of the
+
+ align:start position:0%
+just to give you a sense of the
+ 
+
+ align:start position:0%
+just to give you a sense of the
+magnitude of like the
+
+ align:start position:0%
+magnitude of like the
+ 
+
+ align:start position:0%
+magnitude of like the
+uh uh the mixing you see i said um
+
+ align:start position:0%
+uh uh the mixing you see i said um
+ 
+
+ align:start position:0%
+uh uh the mixing you see i said um
+uh the average beneficiary um uh was
+
+ align:start position:0%
+uh the average beneficiary um uh was
+ 
+
+ align:start position:0%
+uh the average beneficiary um uh was
+sort of at the 25th um
+
+ align:start position:0%
+sort of at the 25th um
+ 
+
+ align:start position:0%
+sort of at the 25th um
+uh percentile of the uh income
+
+ align:start position:0%
+uh percentile of the uh income
+ 
+
+ align:start position:0%
+uh percentile of the uh income
+distribution in in
+
+ align:start position:0%
+distribution in in
+ 
+
+ align:start position:0%
+distribution in in
+in in delhi uh and wealthy students are
+
+ align:start position:0%
+in in delhi uh and wealthy students are
+ 
+
+ align:start position:0%
+in in delhi uh and wealthy students are
+very much on the
+
+ align:start position:0%
+very much on the
+ 
+
+ align:start position:0%
+very much on the
+um on the right tail
+
+ align:start position:0%
+um on the right tail
+ 
+
+ align:start position:0%
+um on the right tail
+sorry on the right tail of the
+
+ align:start position:0%
+sorry on the right tail of the
+ 
+
+ align:start position:0%
+sorry on the right tail of the
+distribution uh
+
+ align:start position:0%
+distribution uh
+ 
+
+ align:start position:0%
+distribution uh
+something like the 90th percentile 95th
+
+ align:start position:0%
+something like the 90th percentile 95th
+ 
+
+ align:start position:0%
+something like the 90th percentile 95th
+percentile which is about
+
+ align:start position:0%
+percentile which is about
+ 
+
+ align:start position:0%
+percentile which is about
+the west equivalent of that would be
+
+ align:start position:0%
+the west equivalent of that would be
+ 
+
+ align:start position:0%
+the west equivalent of that would be
+about two hundred thousand dollars um
+
+ align:start position:0%
+about two hundred thousand dollars um
+ 
+
+ align:start position:0%
+about two hundred thousand dollars um
+per year
+
+ align:start position:0%
+per year
+ 
+
+ align:start position:0%
+per year
+the average um uh beneficiary had like a
+
+ align:start position:0%
+the average um uh beneficiary had like a
+ 
+
+ align:start position:0%
+the average um uh beneficiary had like a
+u.s equivalent income of
+
+ align:start position:0%
+u.s equivalent income of
+ 
+
+ align:start position:0%
+u.s equivalent income of
+like 23 000 again these are not the
+
+ align:start position:0%
+like 23 000 again these are not the
+ 
+
+ align:start position:0%
+like 23 000 again these are not the
+poorest of the poor but relatively poor
+
+ align:start position:0%
+poorest of the poor but relatively poor
+ 
+
+ align:start position:0%
+poorest of the poor but relatively poor
+as about like an order of magnitude
+
+ align:start position:0%
+as about like an order of magnitude
+ 
+
+ align:start position:0%
+as about like an order of magnitude
+poorer than the average person in the
+
+ align:start position:0%
+poorer than the average person in the
+ 
+
+ align:start position:0%
+poorer than the average person in the
+actual school
+
+ align:start position:0%
+actual school
+ 
+
+ align:start position:0%
+actual school
+now this policy then induced large
+
+ align:start position:0%
+now this policy then induced large
+ 
+
+ align:start position:0%
+now this policy then induced large
+variation
+
+ align:start position:0%
+variation
+ 
+
+ align:start position:0%
+variation
+across classrooms you look at
+
+ align:start position:0%
+across classrooms you look at
+ 
+
+ align:start position:0%
+across classrooms you look at
+poor students in the fraction of for the
+
+ align:start position:0%
+poor students in the fraction of for the
+ 
+
+ align:start position:0%
+poor students in the fraction of for the
+number so you have poor students
+
+ align:start position:0%
+number so you have poor students
+ 
+
+ align:start position:0%
+number so you have poor students
+in by grade in 2011. i told you this
+
+ align:start position:0%
+in by grade in 2011. i told you this
+ 
+
+ align:start position:0%
+in by grade in 2011. i told you this
+the policy innovation was in 2007. so if
+
+ align:start position:0%
+the policy innovation was in 2007. so if
+ 
+
+ align:start position:0%
+the policy innovation was in 2007. so if
+you look in 2011 that's four years
+
+ align:start position:0%
+you look in 2011 that's four years
+ 
+
+ align:start position:0%
+you look in 2011 that's four years
+later anybody who is in
+
+ align:start position:0%
+later anybody who is in
+ 
+
+ align:start position:0%
+later anybody who is in
+grade four in 2011 has essentially
+
+ align:start position:0%
+grade four in 2011 has essentially
+ 
+
+ align:start position:0%
+grade four in 2011 has essentially
+no poor student in their class in those
+
+ align:start position:0%
+no poor student in their class in those
+ 
+
+ align:start position:0%
+no poor student in their class in those
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+schools so for students who are in 2011
+
+ align:start position:0%
+schools so for students who are in 2011
+ 
+
+ align:start position:0%
+schools so for students who are in 2011
+and grade four
+
+ align:start position:0%
+and grade four
+ 
+
+ align:start position:0%
+and grade four
+five or six that policy came too late
+
+ align:start position:0%
+five or six that policy came too late
+ 
+
+ align:start position:0%
+five or six that policy came too late
+they do not have any
+
+ align:start position:0%
+they do not have any
+ 
+
+ align:start position:0%
+they do not have any
+poor classmates in contrast if you look
+
+ align:start position:0%
+poor classmates in contrast if you look
+ 
+
+ align:start position:0%
+poor classmates in contrast if you look
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lower grades grades three two one
+
+ align:start position:0%
+the lower grades grades three two one
+ 
+
+ align:start position:0%
+the lower grades grades three two one
+and zero which are essentially uh
+
+ align:start position:0%
+and zero which are essentially uh
+ 
+
+ align:start position:0%
+and zero which are essentially uh
+preschool or zero minus one which is
+
+ align:start position:0%
+preschool or zero minus one which is
+ 
+
+ align:start position:0%
+preschool or zero minus one which is
+preschool grades
+
+ align:start position:0%
+preschool grades
+ 
+
+ align:start position:0%
+preschool grades
+uh there's lots of additional poor
+
+ align:start position:0%
+uh there's lots of additional poor
+ 
+
+ align:start position:0%
+uh there's lots of additional poor
+students now
+
+ align:start position:0%
+students now
+ 
+
+ align:start position:0%
+students now
+uh in those uh uh rich schools
+
+ align:start position:0%
+uh in those uh uh rich schools
+ 
+
+ align:start position:0%
+uh in those uh uh rich schools
+now again uh there's variation within
+
+ align:start position:0%
+now again uh there's variation within
+ 
+
+ align:start position:0%
+now again uh there's variation within
+schools and across schools the variation
+
+ align:start position:0%
+schools and across schools the variation
+ 
+
+ align:start position:0%
+schools and across schools the variation
+within schools is across classrooms
+
+ align:start position:0%
+within schools is across classrooms
+ 
+
+ align:start position:0%
+within schools is across classrooms
+that's kind of what i'm showing you
+
+ align:start position:0%
+that's kind of what i'm showing you
+ 
+
+ align:start position:0%
+that's kind of what i'm showing you
+um here um but there's also variation
+
+ align:start position:0%
+um here um but there's also variation
+ 
+
+ align:start position:0%
+um here um but there's also variation
+uh across schools so just to be clear
+
+ align:start position:0%
+uh across schools so just to be clear
+ 
+
+ align:start position:0%
+uh across schools so just to be clear
+the variation within schools
+
+ align:start position:0%
+the variation within schools
+ 
+
+ align:start position:0%
+the variation within schools
+across classrooms is like in the treated
+
+ align:start position:0%
+across classrooms is like in the treated
+ 
+
+ align:start position:0%
+across classrooms is like in the treated
+schools
+
+ align:start position:0%
+schools
+ 
+
+ align:start position:0%
+schools
+um there's some classes like the fourth
+
+ align:start position:0%
+um there's some classes like the fourth
+ 
+
+ align:start position:0%
+um there's some classes like the fourth
+grade
+
+ align:start position:0%
+grade
+ 
+
+ align:start position:0%
+grade
+have like essentially zero poor kids in
+
+ align:start position:0%
+have like essentially zero poor kids in
+ 
+
+ align:start position:0%
+have like essentially zero poor kids in
+their classes
+
+ align:start position:0%
+their classes
+ 
+
+ align:start position:0%
+their classes
+and uh the third grade in contrast
+
+ align:start position:0%
+and uh the third grade in contrast
+ 
+
+ align:start position:0%
+and uh the third grade in contrast
+have um lots of poor poor kids
+
+ align:start position:0%
+have um lots of poor poor kids
+ 
+
+ align:start position:0%
+have um lots of poor poor kids
+in the classroom we can do that
+
+ align:start position:0%
+in the classroom we can do that
+ 
+
+ align:start position:0%
+in the classroom we can do that
+comparison uh across classrooms within
+
+ align:start position:0%
+comparison uh across classrooms within
+ 
+
+ align:start position:0%
+comparison uh across classrooms within
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+in addition there's also variation
+
+ align:start position:0%
+in addition there's also variation
+ 
+
+ align:start position:0%
+in addition there's also variation
+across schools there's in particular
+
+ align:start position:0%
+across schools there's in particular
+ 
+
+ align:start position:0%
+across schools there's in particular
+there's treatment schools
+
+ align:start position:0%
+there's treatment schools
+ 
+
+ align:start position:0%
+there's treatment schools
+um which comply in 2007 as they were
+
+ align:start position:0%
+um which comply in 2007 as they were
+ 
+
+ align:start position:0%
+um which comply in 2007 as they were
+supposed to
+
+ align:start position:0%
+supposed to
+ 
+
+ align:start position:0%
+supposed to
+but then there's also delayed treatment
+
+ align:start position:0%
+but then there's also delayed treatment
+ 
+
+ align:start position:0%
+but then there's also delayed treatment
+schools which complied in 2008
+
+ align:start position:0%
+schools which complied in 2008
+ 
+
+ align:start position:0%
+schools which complied in 2008
+so the jump shifted by one quart so the
+
+ align:start position:0%
+so the jump shifted by one quart so the
+ 
+
+ align:start position:0%
+so the jump shifted by one quart so the
+court the jump that i showed you here
+
+ align:start position:0%
+court the jump that i showed you here
+ 
+
+ align:start position:0%
+court the jump that i showed you here
+um this is for the treatment schools
+
+ align:start position:0%
+um this is for the treatment schools
+ 
+
+ align:start position:0%
+um this is for the treatment schools
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+complied uh or this is for everybody
+
+ align:start position:0%
+complied uh or this is for everybody
+ 
+
+ align:start position:0%
+complied uh or this is for everybody
+that complied in 2007
+
+ align:start position:0%
+that complied in 2007
+ 
+
+ align:start position:0%
+that complied in 2007
+the delayed one complete a year later so
+
+ align:start position:0%
+the delayed one complete a year later so
+ 
+
+ align:start position:0%
+the delayed one complete a year later so
+you see them essentially
+
+ align:start position:0%
+you see them essentially
+ 
+
+ align:start position:0%
+you see them essentially
+somewhat later um uh increasing or one
+
+ align:start position:0%
+somewhat later um uh increasing or one
+ 
+
+ align:start position:0%
+somewhat later um uh increasing or one
+year later exactly
+
+ align:start position:0%
+year later exactly
+ 
+
+ align:start position:0%
+year later exactly
+increasing the fraction of poor kids in
+
+ align:start position:0%
+increasing the fraction of poor kids in
+ 
+
+ align:start position:0%
+increasing the fraction of poor kids in
+their classroom and then there's the
+
+ align:start position:0%
+their classroom and then there's the
+ 
+
+ align:start position:0%
+their classroom and then there's the
+control schools they were not subject to
+
+ align:start position:0%
+control schools they were not subject to
+ 
+
+ align:start position:0%
+control schools they were not subject to
+the policy at least until 2013
+
+ align:start position:0%
+the policy at least until 2013
+ 
+
+ align:start position:0%
+the policy at least until 2013
+so they had received
+
+ align:start position:0%
+so they had received
+ 
+
+ align:start position:0%
+so they had received
+they had received land from federal
+
+ align:start position:0%
+they had received land from federal
+ 
+
+ align:start position:0%
+they had received land from federal
+government or private foundations
+
+ align:start position:0%
+government or private foundations
+ 
+
+ align:start position:0%
+government or private foundations
+so essentially there was no treatment uh
+
+ align:start position:0%
+so essentially there was no treatment uh
+ 
+
+ align:start position:0%
+so essentially there was no treatment uh
+that is all students are rich in these
+
+ align:start position:0%
+that is all students are rich in these
+ 
+
+ align:start position:0%
+that is all students are rich in these
+types of classes
+
+ align:start position:0%
+types of classes
+ 
+
+ align:start position:0%
+types of classes
+so that was the the land receiving is
+
+ align:start position:0%
+so that was the the land receiving is
+ 
+
+ align:start position:0%
+so that was the the land receiving is
+essentially just uh that was like a
+
+ align:start position:0%
+essentially just uh that was like a
+ 
+
+ align:start position:0%
+essentially just uh that was like a
+fairly arbitrary rule in some ways uh so
+
+ align:start position:0%
+fairly arbitrary rule in some ways uh so
+ 
+
+ align:start position:0%
+fairly arbitrary rule in some ways uh so
+that sort of leads to
+
+ align:start position:0%
+that sort of leads to
+ 
+
+ align:start position:0%
+that sort of leads to
+at least quasi-random variation and some
+
+ align:start position:0%
+at least quasi-random variation and some
+ 
+
+ align:start position:0%
+at least quasi-random variation and some
+schools uh received
+
+ align:start position:0%
+schools uh received
+ 
+
+ align:start position:0%
+schools uh received
+the treatment and others um did not
+
+ align:start position:0%
+the treatment and others um did not
+ 
+
+ align:start position:0%
+the treatment and others um did not
+um now let me show you some outcomes so
+
+ align:start position:0%
+um now let me show you some outcomes so
+ 
+
+ align:start position:0%
+um now let me show you some outcomes so
+one outcome is our friend the dictator
+
+ align:start position:0%
+one outcome is our friend the dictator
+ 
+
+ align:start position:0%
+one outcome is our friend the dictator
+game which you've seen quite a bit and
+
+ align:start position:0%
+game which you've seen quite a bit and
+ 
+
+ align:start position:0%
+game which you've seen quite a bit and
+played already
+
+ align:start position:0%
+played already
+ 
+
+ align:start position:0%
+played already
+as well is students are allowed with 10
+
+ align:start position:0%
+as well is students are allowed with 10
+ 
+
+ align:start position:0%
+as well is students are allowed with 10
+rupees
+
+ align:start position:0%
+rupees
+ 
+
+ align:start position:0%
+rupees
+which is you know not very much that's
+
+ align:start position:0%
+which is you know not very much that's
+ 
+
+ align:start position:0%
+which is you know not very much that's
+about like 15 um
+
+ align:start position:0%
+about like 15 um
+ 
+
+ align:start position:0%
+about like 15 um
+cents and they choose to share um notice
+
+ align:start position:0%
+cents and they choose to share um notice
+ 
+
+ align:start position:0%
+cents and they choose to share um notice
+that these are
+
+ align:start position:0%
+that these are
+ 
+
+ align:start position:0%
+that these are
+pretty pretty young kids so 10 rupees is
+
+ align:start position:0%
+pretty pretty young kids so 10 rupees is
+ 
+
+ align:start position:0%
+pretty pretty young kids so 10 rupees is
+quite a bit of money for them they
+
+ align:start position:0%
+quite a bit of money for them they
+ 
+
+ align:start position:0%
+quite a bit of money for them they
+choose to share
+
+ align:start position:0%
+choose to share
+ 
+
+ align:start position:0%
+choose to share
+an amount as before between 0 and 10.
+
+ align:start position:0%
+an amount as before between 0 and 10.
+ 
+
+ align:start position:0%
+an amount as before between 0 and 10.
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i got them sets this up such that
+
+ align:start position:0%
+i got them sets this up such that
+ 
+
+ align:start position:0%
+i got them sets this up such that
+students could it was not just about the
+
+ align:start position:0%
+students could it was not just about the
+ 
+
+ align:start position:0%
+students could it was not just about the
+money but they also can exchange the
+
+ align:start position:0%
+money but they also can exchange the
+ 
+
+ align:start position:0%
+money but they also can exchange the
+money for candy later
+
+ align:start position:0%
+money for candy later
+ 
+
+ align:start position:0%
+money for candy later
+add one rupee per piece so that was a
+
+ align:start position:0%
+add one rupee per piece so that was a
+ 
+
+ align:start position:0%
+add one rupee per piece so that was a
+pretty um good deal
+
+ align:start position:0%
+pretty um good deal
+ 
+
+ align:start position:0%
+pretty um good deal
+then um the dictator games for the order
+
+ align:start position:0%
+then um the dictator games for the order
+ 
+
+ align:start position:0%
+then um the dictator games for the order
+was randomized the
+
+ align:start position:0%
+was randomized the
+ 
+
+ align:start position:0%
+was randomized the
+kids would play two games again these
+
+ align:start position:0%
+kids would play two games again these
+ 
+
+ align:start position:0%
+kids would play two games again these
+are all rich kids who do that
+
+ align:start position:0%
+are all rich kids who do that
+ 
+
+ align:start position:0%
+are all rich kids who do that
+they play first game one where the
+
+ align:start position:0%
+they play first game one where the
+ 
+
+ align:start position:0%
+they play first game one where the
+recipient is a poor student in a school
+
+ align:start position:0%
+recipient is a poor student in a school
+ 
+
+ align:start position:0%
+recipient is a poor student in a school
+for poor children
+
+ align:start position:0%
+for poor children
+ 
+
+ align:start position:0%
+for poor children
+and in game two it's a rich student in a
+
+ align:start position:0%
+and in game two it's a rich student in a
+ 
+
+ align:start position:0%
+and in game two it's a rich student in a
+private control school
+
+ align:start position:0%
+private control school
+ 
+
+ align:start position:0%
+private control school
+notice it's a control school to be clear
+
+ align:start position:0%
+notice it's a control school to be clear
+ 
+
+ align:start position:0%
+notice it's a control school to be clear
+so it's not a kid that they might know
+
+ align:start position:0%
+so it's not a kid that they might know
+ 
+
+ align:start position:0%
+so it's not a kid that they might know
+so the kids are
+
+ align:start position:0%
+so the kids are
+ 
+
+ align:start position:0%
+so the kids are
+chosen such that the kids were
+
+ align:start position:0%
+chosen such that the kids were
+ 
+
+ align:start position:0%
+chosen such that the kids were
+given the names and the photographs of
+
+ align:start position:0%
+given the names and the photographs of
+ 
+
+ align:start position:0%
+given the names and the photographs of
+the school shown to the subject to the
+
+ align:start position:0%
+the school shown to the subject to the
+ 
+
+ align:start position:0%
+the school shown to the subject to the
+kids
+
+ align:start position:0%
+kids
+ 
+
+ align:start position:0%
+kids
+so you could sort of see and this is
+
+ align:start position:0%
+so you could sort of see and this is
+ 
+
+ align:start position:0%
+so you could sort of see and this is
+verified in the briefing by the author
+
+ align:start position:0%
+verified in the briefing by the author
+ 
+
+ align:start position:0%
+verified in the briefing by the author
+is that the the the children understand
+
+ align:start position:0%
+is that the the the children understand
+ 
+
+ align:start position:0%
+is that the the the children understand
+very well
+
+ align:start position:0%
+very well
+ 
+
+ align:start position:0%
+very well
+who's a rich kid and who's a poor kid um
+
+ align:start position:0%
+who's a rich kid and who's a poor kid um
+ 
+
+ align:start position:0%
+who's a rich kid and who's a poor kid um
+but these are not kids that they would
+
+ align:start position:0%
+but these are not kids that they would
+ 
+
+ align:start position:0%
+but these are not kids that they would
+actually know
+
+ align:start position:0%
+actually know
+ 
+
+ align:start position:0%
+actually know
+and something that's a less interesting
+
+ align:start position:0%
+and something that's a less interesting
+ 
+
+ align:start position:0%
+and something that's a less interesting
+question if you have gone
+
+ align:start position:0%
+question if you have gone
+ 
+
+ align:start position:0%
+question if you have gone
+to school with somebody for a long time
+
+ align:start position:0%
+to school with somebody for a long time
+ 
+
+ align:start position:0%
+to school with somebody for a long time
+you might have seen them around
+
+ align:start position:0%
+you might have seen them around
+ 
+
+ align:start position:0%
+you might have seen them around
+in your schoolyard you might be nicer to
+
+ align:start position:0%
+in your schoolyard you might be nicer to
+ 
+
+ align:start position:0%
+in your schoolyard you might be nicer to
+them or less nice to them
+
+ align:start position:0%
+them or less nice to them
+ 
+
+ align:start position:0%
+them or less nice to them
+that's not what the study is looking at
+
+ align:start position:0%
+that's not what the study is looking at
+ 
+
+ align:start position:0%
+that's not what the study is looking at
+the study is looking at
+
+ align:start position:0%
+the study is looking at
+ 
+
+ align:start position:0%
+the study is looking at
+other kids in other schools that look
+
+ align:start position:0%
+other kids in other schools that look
+ 
+
+ align:start position:0%
+other kids in other schools that look
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+or look poor um both in terms of like
+
+ align:start position:0%
+or look poor um both in terms of like
+ 
+
+ align:start position:0%
+or look poor um both in terms of like
+the way um
+
+ align:start position:0%
+the way um
+ 
+
+ align:start position:0%
+the way um
+uh uh they're dressed and so on but in
+
+ align:start position:0%
+uh uh they're dressed and so on but in
+ 
+
+ align:start position:0%
+uh uh they're dressed and so on but in
+particular the way their school
+
+ align:start position:0%
+particular the way their school
+ 
+
+ align:start position:0%
+particular the way their school
+looks like so essentially these are now
+
+ align:start position:0%
+looks like so essentially these are now
+ 
+
+ align:start position:0%
+looks like so essentially these are now
+we're looking at social preferences
+
+ align:start position:0%
+we're looking at social preferences
+ 
+
+ align:start position:0%
+we're looking at social preferences
+towards
+
+ align:start position:0%
+towards
+ 
+
+ align:start position:0%
+towards
+other people people that these kids
+
+ align:start position:0%
+other people people that these kids
+ 
+
+ align:start position:0%
+other people people that these kids
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+okay so now what do we see so this is
+
+ align:start position:0%
+okay so now what do we see so this is
+ 
+
+ align:start position:0%
+okay so now what do we see so this is
+the generosity
+
+ align:start position:0%
+the generosity
+ 
+
+ align:start position:0%
+the generosity
+to the poor so like this is essentially
+
+ align:start position:0%
+to the poor so like this is essentially
+ 
+
+ align:start position:0%
+to the poor so like this is essentially
+the results from game number one
+
+ align:start position:0%
+the results from game number one
+ 
+
+ align:start position:0%
+the results from game number one
+again remember these are all um rich
+
+ align:start position:0%
+again remember these are all um rich
+ 
+
+ align:start position:0%
+again remember these are all um rich
+kids who are giving now to poor kids and
+
+ align:start position:0%
+kids who are giving now to poor kids and
+ 
+
+ align:start position:0%
+kids who are giving now to poor kids and
+the question now is
+
+ align:start position:0%
+the question now is
+ 
+
+ align:start position:0%
+the question now is
+is being exposed to or does being
+
+ align:start position:0%
+is being exposed to or does being
+ 
+
+ align:start position:0%
+is being exposed to or does being
+exposed to poor children
+
+ align:start position:0%
+exposed to poor children
+ 
+
+ align:start position:0%
+exposed to poor children
+um uh uh uh for several years
+
+ align:start position:0%
+um uh uh uh for several years
+ 
+
+ align:start position:0%
+um uh uh uh for several years
+does that affect um uh giving
+
+ align:start position:0%
+does that affect um uh giving
+ 
+
+ align:start position:0%
+does that affect um uh giving
+uh in the form of dictator games
+
+ align:start position:0%
+uh in the form of dictator games
+ 
+
+ align:start position:0%
+uh in the form of dictator games
+towards poor children to start with
+
+ align:start position:0%
+towards poor children to start with
+ 
+
+ align:start position:0%
+towards poor children to start with
+we're going to talk about rich students
+
+ align:start position:0%
+we're going to talk about rich students
+ 
+
+ align:start position:0%
+we're going to talk about rich students
+after that so here you see the
+
+ align:start position:0%
+after that so here you see the
+ 
+
+ align:start position:0%
+after that so here you see the
+generosity to the poor and controlled
+
+ align:start position:0%
+generosity to the poor and controlled
+ 
+
+ align:start position:0%
+generosity to the poor and controlled
+schools
+
+ align:start position:0%
+schools
+ 
+
+ align:start position:0%
+schools
+you see this is the percent given to the
+
+ align:start position:0%
+you see this is the percent given to the
+ 
+
+ align:start position:0%
+you see this is the percent given to the
+poor recipient
+
+ align:start position:0%
+poor recipient
+ 
+
+ align:start position:0%
+poor recipient
+it's remarkably similar to what we've
+
+ align:start position:0%
+it's remarkably similar to what we've
+ 
+
+ align:start position:0%
+it's remarkably similar to what we've
+seen previously which is about 28 or 30
+
+ align:start position:0%
+seen previously which is about 28 or 30
+ 
+
+ align:start position:0%
+seen previously which is about 28 or 30
+percent about 25
+
+ align:start position:0%
+percent about 25
+ 
+
+ align:start position:0%
+percent about 25
+is given to the poor uh kid in the
+
+ align:start position:0%
+is given to the poor uh kid in the
+ 
+
+ align:start position:0%
+is given to the poor uh kid in the
+control groups
+
+ align:start position:0%
+control groups
+ 
+
+ align:start position:0%
+control groups
+uh in the control schools um this
+
+ align:start position:0%
+uh in the control schools um this
+ 
+
+ align:start position:0%
+uh in the control schools um this
+fraction
+
+ align:start position:0%
+fraction
+ 
+
+ align:start position:0%
+fraction
+trend seems to trend up a little bit
+
+ align:start position:0%
+trend seems to trend up a little bit
+ 
+
+ align:start position:0%
+trend seems to trend up a little bit
+over time but it's also quite constant
+
+ align:start position:0%
+over time but it's also quite constant
+ 
+
+ align:start position:0%
+over time but it's also quite constant
+over time across grades you see here
+
+ align:start position:0%
+over time across grades you see here
+ 
+
+ align:start position:0%
+over time across grades you see here
+grades two
+
+ align:start position:0%
+grades two
+ 
+
+ align:start position:0%
+grades two
+three four and five on the x-axis and
+
+ align:start position:0%
+three four and five on the x-axis and
+ 
+
+ align:start position:0%
+three four and five on the x-axis and
+the y-axis is the percent given to the
+
+ align:start position:0%
+the y-axis is the percent given to the
+ 
+
+ align:start position:0%
+the y-axis is the percent given to the
+poor recipients
+
+ align:start position:0%
+poor recipients
+ 
+
+ align:start position:0%
+poor recipients
+now adding the treatment schools now we
+
+ align:start position:0%
+now adding the treatment schools now we
+ 
+
+ align:start position:0%
+now adding the treatment schools now we
+find uh
+
+ align:start position:0%
+find uh
+ 
+
+ align:start position:0%
+find uh
+that for two grades for grade two and
+
+ align:start position:0%
+that for two grades for grade two and
+ 
+
+ align:start position:0%
+that for two grades for grade two and
+grade three
+
+ align:start position:0%
+grade three
+ 
+
+ align:start position:0%
+grade three
+remember the graph that i showed you
+
+ align:start position:0%
+remember the graph that i showed you
+ 
+
+ align:start position:0%
+remember the graph that i showed you
+here you see that
+
+ align:start position:0%
+here you see that
+ 
+
+ align:start position:0%
+here you see that
+in grades three two one and so on these
+
+ align:start position:0%
+in grades three two one and so on these
+ 
+
+ align:start position:0%
+in grades three two one and so on these
+are the kids who are exposed
+
+ align:start position:0%
+are the kids who are exposed
+ 
+
+ align:start position:0%
+are the kids who are exposed
+to the poor children in class in
+
+ align:start position:0%
+to the poor children in class in
+ 
+
+ align:start position:0%
+to the poor children in class in
+contrast to grades four and five that
+
+ align:start position:0%
+contrast to grades four and five that
+ 
+
+ align:start position:0%
+contrast to grades four and five that
+have not been exposed to poor kids in
+
+ align:start position:0%
+have not been exposed to poor kids in
+ 
+
+ align:start position:0%
+have not been exposed to poor kids in
+their class
+
+ align:start position:0%
+their class
+ 
+
+ align:start position:0%
+their class
+so what this graph note shows is that
+
+ align:start position:0%
+so what this graph note shows is that
+ 
+
+ align:start position:0%
+so what this graph note shows is that
+exactly the grades
+
+ align:start position:0%
+exactly the grades
+ 
+
+ align:start position:0%
+exactly the grades
+three and two that have been exposed in
+
+ align:start position:0%
+three and two that have been exposed in
+ 
+
+ align:start position:0%
+three and two that have been exposed in
+the treatment groups that have been
+
+ align:start position:0%
+the treatment groups that have been
+ 
+
+ align:start position:0%
+the treatment groups that have been
+exposed to poor classmates
+
+ align:start position:0%
+exposed to poor classmates
+ 
+
+ align:start position:0%
+exposed to poor classmates
+these are exactly the students the
+
+ align:start position:0%
+these are exactly the students the
+ 
+
+ align:start position:0%
+these are exactly the students the
+grades where
+
+ align:start position:0%
+grades where
+ 
+
+ align:start position:0%
+grades where
+giving is higher um
+
+ align:start position:0%
+giving is higher um
+ 
+
+ align:start position:0%
+giving is higher um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+towards the poor compared to the control
+
+ align:start position:0%
+towards the poor compared to the control
+ 
+
+ align:start position:0%
+towards the poor compared to the control
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+but also compared to the older cohorts
+
+ align:start position:0%
+but also compared to the older cohorts
+ 
+
+ align:start position:0%
+but also compared to the older cohorts
+four and five the grade four and five
+
+ align:start position:0%
+four and five the grade four and five
+ 
+
+ align:start position:0%
+four and five the grade four and five
+when you look at grades four and five
+
+ align:start position:0%
+when you look at grades four and five
+ 
+
+ align:start position:0%
+when you look at grades four and five
+there you see essentially no difference
+
+ align:start position:0%
+there you see essentially no difference
+ 
+
+ align:start position:0%
+there you see essentially no difference
+between treatment and control schools
+
+ align:start position:0%
+between treatment and control schools
+ 
+
+ align:start position:0%
+between treatment and control schools
+so they seem to be very similar in
+
+ align:start position:0%
+so they seem to be very similar in
+ 
+
+ align:start position:0%
+so they seem to be very similar in
+contrast if you look at
+
+ align:start position:0%
+contrast if you look at
+ 
+
+ align:start position:0%
+contrast if you look at
+grades three and through where the
+
+ align:start position:0%
+grades three and through where the
+ 
+
+ align:start position:0%
+grades three and through where the
+treatment uh kids are
+
+ align:start position:0%
+treatment uh kids are
+ 
+
+ align:start position:0%
+treatment uh kids are
+exposed to the treatment by having the
+
+ align:start position:0%
+exposed to the treatment by having the
+ 
+
+ align:start position:0%
+exposed to the treatment by having the
+poor kids in their classrooms
+
+ align:start position:0%
+poor kids in their classrooms
+ 
+
+ align:start position:0%
+poor kids in their classrooms
+these are exactly the years where um
+
+ align:start position:0%
+these are exactly the years where um
+ 
+
+ align:start position:0%
+these are exactly the years where um
+giving goes up and goes up by quite a
+
+ align:start position:0%
+giving goes up and goes up by quite a
+ 
+
+ align:start position:0%
+giving goes up and goes up by quite a
+bit well the average
+
+ align:start position:0%
+bit well the average
+ 
+
+ align:start position:0%
+bit well the average
+was as i said before about 25 that goes
+
+ align:start position:0%
+was as i said before about 25 that goes
+ 
+
+ align:start position:0%
+was as i said before about 25 that goes
+up to about 35
+
+ align:start position:0%
+up to about 35
+ 
+
+ align:start position:0%
+up to about 35
+so that's a pretty large relative
+
+ align:start position:0%
+so that's a pretty large relative
+ 
+
+ align:start position:0%
+so that's a pretty large relative
+increase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in addition um as i told you there
+
+ align:start position:0%
+now in addition um as i told you there
+ 
+
+ align:start position:0%
+now in addition um as i told you there
+are also delayed treatment groups
+
+ align:start position:0%
+are also delayed treatment groups
+ 
+
+ align:start position:0%
+are also delayed treatment groups
+uh treatment schools so for those
+
+ align:start position:0%
+uh treatment schools so for those
+ 
+
+ align:start position:0%
+uh treatment schools so for those
+schools if you were in grade three
+
+ align:start position:0%
+schools if you were in grade three
+ 
+
+ align:start position:0%
+schools if you were in grade three
+it was also too late for you because the
+
+ align:start position:0%
+it was also too late for you because the
+ 
+
+ align:start position:0%
+it was also too late for you because the
+treatment was introduced only a year
+
+ align:start position:0%
+treatment was introduced only a year
+ 
+
+ align:start position:0%
+treatment was introduced only a year
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+so if you were in grade 3 you did not
+
+ align:start position:0%
+so if you were in grade 3 you did not
+ 
+
+ align:start position:0%
+so if you were in grade 3 you did not
+have any
+
+ align:start position:0%
+have any
+ 
+
+ align:start position:0%
+have any
+poor kids in your school now if you look
+
+ align:start position:0%
+poor kids in your school now if you look
+ 
+
+ align:start position:0%
+poor kids in your school now if you look
+at the yellow line here the yellow line
+
+ align:start position:0%
+at the yellow line here the yellow line
+ 
+
+ align:start position:0%
+at the yellow line here the yellow line
+looks very much like the green line
+
+ align:start position:0%
+looks very much like the green line
+ 
+
+ align:start position:0%
+looks very much like the green line
+that is for the delayed treatment
+
+ align:start position:0%
+that is for the delayed treatment
+ 
+
+ align:start position:0%
+that is for the delayed treatment
+schools there's no impact
+
+ align:start position:0%
+schools there's no impact
+ 
+
+ align:start position:0%
+schools there's no impact
+either they look very much like the
+
+ align:start position:0%
+either they look very much like the
+ 
+
+ align:start position:0%
+either they look very much like the
+control group schools
+
+ align:start position:0%
+control group schools
+ 
+
+ align:start position:0%
+control group schools
+as you would expect however
+
+ align:start position:0%
+as you would expect however
+ 
+
+ align:start position:0%
+as you would expect however
+in the late treatment schools in grade
+
+ align:start position:0%
+in the late treatment schools in grade
+ 
+
+ align:start position:0%
+in the late treatment schools in grade
+number two
+
+ align:start position:0%
+number two
+ 
+
+ align:start position:0%
+number two
+that's the grade where um the students
+
+ align:start position:0%
+that's the grade where um the students
+ 
+
+ align:start position:0%
+that's the grade where um the students
+are exposed
+
+ align:start position:0%
+are exposed
+ 
+
+ align:start position:0%
+are exposed
+the rich students are exposed to the
+
+ align:start position:0%
+the rich students are exposed to the
+ 
+
+ align:start position:0%
+the rich students are exposed to the
+poor kids you will see essentially
+
+ align:start position:0%
+poor kids you will see essentially
+ 
+
+ align:start position:0%
+poor kids you will see essentially
+similar effects
+
+ align:start position:0%
+similar effects
+ 
+
+ align:start position:0%
+similar effects
+to the treatment schools as you expect
+
+ align:start position:0%
+to the treatment schools as you expect
+ 
+
+ align:start position:0%
+to the treatment schools as you expect
+so that's fairly compelling evidence
+
+ align:start position:0%
+so that's fairly compelling evidence
+ 
+
+ align:start position:0%
+so that's fairly compelling evidence
+that really
+
+ align:start position:0%
+that really
+ 
+
+ align:start position:0%
+that really
+the differences that you see across
+
+ align:start position:0%
+the differences that you see across
+ 
+
+ align:start position:0%
+the differences that you see across
+these schools
+
+ align:start position:0%
+these schools
+ 
+
+ align:start position:0%
+these schools
+are driven by the treatment
+
+ align:start position:0%
+are driven by the treatment
+ 
+
+ align:start position:0%
+are driven by the treatment
+that was on the timing of the treatment
+
+ align:start position:0%
+that was on the timing of the treatment
+ 
+
+ align:start position:0%
+that was on the timing of the treatment
+as opposed to
+
+ align:start position:0%
+as opposed to
+ 
+
+ align:start position:0%
+as opposed to
+other potential effects due to like you
+
+ align:start position:0%
+other potential effects due to like you
+ 
+
+ align:start position:0%
+other potential effects due to like you
+know selection or maybe these schools
+
+ align:start position:0%
+know selection or maybe these schools
+ 
+
+ align:start position:0%
+know selection or maybe these schools
+are different and so on
+
+ align:start position:0%
+are different and so on
+ 
+
+ align:start position:0%
+are different and so on
+we see essentially no differences in
+
+ align:start position:0%
+we see essentially no differences in
+ 
+
+ align:start position:0%
+we see essentially no differences in
+grades four and five for
+
+ align:start position:0%
+grades four and five for
+ 
+
+ align:start position:0%
+grades four and five for
+any of the treatment and control schools
+
+ align:start position:0%
+any of the treatment and control schools
+ 
+
+ align:start position:0%
+any of the treatment and control schools
+you also
+
+ align:start position:0%
+you also
+ 
+
+ align:start position:0%
+you also
+see no difference in grade three for the
+
+ align:start position:0%
+see no difference in grade three for the
+ 
+
+ align:start position:0%
+see no difference in grade three for the
+delayed
+
+ align:start position:0%
+delayed
+ 
+
+ align:start position:0%
+delayed
+treatment schools compared to the
+
+ align:start position:0%
+treatment schools compared to the
+ 
+
+ align:start position:0%
+treatment schools compared to the
+control group in contrast
+
+ align:start position:0%
+control group in contrast
+ 
+
+ align:start position:0%
+control group in contrast
+we see clear differences in grade two
+
+ align:start position:0%
+we see clear differences in grade two
+ 
+
+ align:start position:0%
+we see clear differences in grade two
+for the delayed treatment schools
+
+ align:start position:0%
+for the delayed treatment schools
+ 
+
+ align:start position:0%
+for the delayed treatment schools
+compared to the control schools
+
+ align:start position:0%
+compared to the control schools
+ 
+
+ align:start position:0%
+compared to the control schools
+we also see a clear difference for the
+
+ align:start position:0%
+we also see a clear difference for the
+ 
+
+ align:start position:0%
+we also see a clear difference for the
+treatment schools compared to both
+
+ align:start position:0%
+treatment schools compared to both
+ 
+
+ align:start position:0%
+treatment schools compared to both
+the control schools and the delayed
+
+ align:start position:0%
+the control schools and the delayed
+ 
+
+ align:start position:0%
+the control schools and the delayed
+treatment schools
+
+ align:start position:0%
+treatment schools
+ 
+
+ align:start position:0%
+treatment schools
+as well so that's fairly compelling
+
+ align:start position:0%
+as well so that's fairly compelling
+ 
+
+ align:start position:0%
+as well so that's fairly compelling
+compelling evidence that
+
+ align:start position:0%
+compelling evidence that
+ 
+
+ align:start position:0%
+compelling evidence that
+game or play in dictator games changes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when students are exposed for quite a
+
+ align:start position:0%
+when students are exposed for quite a
+ 
+
+ align:start position:0%
+when students are exposed for quite a
+long time to poor kids in their
+
+ align:start position:0%
+long time to poor kids in their
+ 
+
+ align:start position:0%
+long time to poor kids in their
+classroom
+
+ align:start position:0%
+classroom
+ 
+
+ align:start position:0%
+classroom
+okay so now in addition um
+
+ align:start position:0%
+okay so now in addition um
+ 
+
+ align:start position:0%
+okay so now in addition um
+we will have a variation within a
+
+ align:start position:0%
+we will have a variation within a
+ 
+
+ align:start position:0%
+we will have a variation within a
+classroom so what i show you here this
+
+ align:start position:0%
+classroom so what i show you here this
+ 
+
+ align:start position:0%
+classroom so what i show you here this
+is all variation
+
+ align:start position:0%
+is all variation
+ 
+
+ align:start position:0%
+is all variation
+across classrooms that is to say if you
+
+ align:start position:0%
+across classrooms that is to say if you
+ 
+
+ align:start position:0%
+across classrooms that is to say if you
+have a poor kid in your classroom
+
+ align:start position:0%
+have a poor kid in your classroom
+ 
+
+ align:start position:0%
+have a poor kid in your classroom
+you will behave differently um or that
+
+ align:start position:0%
+you will behave differently um or that
+ 
+
+ align:start position:0%
+you will behave differently um or that
+will change your attitudes or you're
+
+ align:start position:0%
+will change your attitudes or you're
+ 
+
+ align:start position:0%
+will change your attitudes or you're
+giving in
+
+ align:start position:0%
+giving in
+ 
+
+ align:start position:0%
+giving in
+in dictator games uh towards
+
+ align:start position:0%
+in dictator games uh towards
+ 
+
+ align:start position:0%
+in dictator games uh towards
+the poor or other poor or children now
+
+ align:start position:0%
+the poor or other poor or children now
+ 
+
+ align:start position:0%
+the poor or other poor or children now
+in addition
+
+ align:start position:0%
+in addition
+ 
+
+ align:start position:0%
+in addition
+um the author also has um
+
+ align:start position:0%
+um the author also has um
+ 
+
+ align:start position:0%
+um the author also has um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+evidence of variation within classroom
+
+ align:start position:0%
+evidence of variation within classroom
+ 
+
+ align:start position:0%
+evidence of variation within classroom
+they let you think about for a second
+
+ align:start position:0%
+they let you think about for a second
+ 
+
+ align:start position:0%
+they let you think about for a second
+why is it important to also have
+
+ align:start position:0%
+why is it important to also have
+ 
+
+ align:start position:0%
+why is it important to also have
+variation within classroom
+
+ align:start position:0%
+variation within classroom
+ 
+
+ align:start position:0%
+variation within classroom
+isn't the evidence that we have here
+
+ align:start position:0%
+isn't the evidence that we have here
+ 
+
+ align:start position:0%
+isn't the evidence that we have here
+already compelling enough why do we need
+
+ align:start position:0%
+already compelling enough why do we need
+ 
+
+ align:start position:0%
+already compelling enough why do we need
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+and you think about this for a second
+
+ align:start position:0%
+and you think about this for a second
+ 
+
+ align:start position:0%
+and you think about this for a second
+the reason for that is that the diff and
+
+ align:start position:0%
+the reason for that is that the diff and
+ 
+
+ align:start position:0%
+the reason for that is that the diff and
+if the difference in differences
+
+ align:start position:0%
+if the difference in differences
+ 
+
+ align:start position:0%
+if the difference in differences
+comparing essentially across
+
+ align:start position:0%
+comparing essentially across
+ 
+
+ align:start position:0%
+comparing essentially across
+classrooms identifies the overall effect
+
+ align:start position:0%
+classrooms identifies the overall effect
+ 
+
+ align:start position:0%
+classrooms identifies the overall effect
+of having poor classmates in class
+
+ align:start position:0%
+of having poor classmates in class
+ 
+
+ align:start position:0%
+of having poor classmates in class
+that might be the result of like
+
+ align:start position:0%
+that might be the result of like
+ 
+
+ align:start position:0%
+that might be the result of like
+personal interactions
+
+ align:start position:0%
+personal interactions
+ 
+
+ align:start position:0%
+personal interactions
+but it might also be the result of like
+
+ align:start position:0%
+but it might also be the result of like
+ 
+
+ align:start position:0%
+but it might also be the result of like
+the teacher uh the curriculum might
+
+ align:start position:0%
+the teacher uh the curriculum might
+ 
+
+ align:start position:0%
+the teacher uh the curriculum might
+change your parents might change
+
+ align:start position:0%
+change your parents might change
+ 
+
+ align:start position:0%
+change your parents might change
+in some ways and just telling you like
+
+ align:start position:0%
+in some ways and just telling you like
+ 
+
+ align:start position:0%
+in some ways and just telling you like
+look there's these poor kids in your
+
+ align:start position:0%
+look there's these poor kids in your
+ 
+
+ align:start position:0%
+look there's these poor kids in your
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+the teachers might tell everybody oh you
+
+ align:start position:0%
+the teachers might tell everybody oh you
+ 
+
+ align:start position:0%
+the teachers might tell everybody oh you
+need to be nice to poor kids
+
+ align:start position:0%
+need to be nice to poor kids
+ 
+
+ align:start position:0%
+need to be nice to poor kids
+the curriculum might change it might
+
+ align:start position:0%
+the curriculum might change it might
+ 
+
+ align:start position:0%
+the curriculum might change it might
+sort of include things that tell you to
+
+ align:start position:0%
+sort of include things that tell you to
+ 
+
+ align:start position:0%
+sort of include things that tell you to
+be nice to poor kids and so on you might
+
+ align:start position:0%
+be nice to poor kids and so on you might
+ 
+
+ align:start position:0%
+be nice to poor kids and so on you might
+be sort of exposed to just different
+
+ align:start position:0%
+be sort of exposed to just different
+ 
+
+ align:start position:0%
+be sort of exposed to just different
+types of material
+
+ align:start position:0%
+types of material
+ 
+
+ align:start position:0%
+types of material
+so really given the evidence that we
+
+ align:start position:0%
+so really given the evidence that we
+ 
+
+ align:start position:0%
+so really given the evidence that we
+have here when you just compare across
+
+ align:start position:0%
+have here when you just compare across
+ 
+
+ align:start position:0%
+have here when you just compare across
+classrooms
+
+ align:start position:0%
+classrooms
+ 
+
+ align:start position:0%
+classrooms
+you cannot disentangle whether this is
+
+ align:start position:0%
+you cannot disentangle whether this is
+ 
+
+ align:start position:0%
+you cannot disentangle whether this is
+driven from like
+
+ align:start position:0%
+driven from like
+ 
+
+ align:start position:0%
+driven from like
+being personally um exposed in terms of
+
+ align:start position:0%
+being personally um exposed in terms of
+ 
+
+ align:start position:0%
+being personally um exposed in terms of
+interacting with poor children
+
+ align:start position:0%
+interacting with poor children
+ 
+
+ align:start position:0%
+interacting with poor children
+personally by just talking to them in
+
+ align:start position:0%
+personally by just talking to them in
+ 
+
+ align:start position:0%
+personally by just talking to them in
+certain ways and being exposed to them
+
+ align:start position:0%
+certain ways and being exposed to them
+ 
+
+ align:start position:0%
+certain ways and being exposed to them
+and like
+
+ align:start position:0%
+and like
+ 
+
+ align:start position:0%
+and like
+learning about them and so on so it
+
+ align:start position:0%
+learning about them and so on so it
+ 
+
+ align:start position:0%
+learning about them and so on so it
+cannot disentangle personal interactions
+
+ align:start position:0%
+cannot disentangle personal interactions
+ 
+
+ align:start position:0%
+cannot disentangle personal interactions
+from teacher curriculum changes that are
+
+ align:start position:0%
+from teacher curriculum changes that are
+ 
+
+ align:start position:0%
+from teacher curriculum changes that are
+essentially at the classroom level
+
+ align:start position:0%
+essentially at the classroom level
+ 
+
+ align:start position:0%
+essentially at the classroom level
+so in addition then gautam also has
+
+ align:start position:0%
+so in addition then gautam also has
+ 
+
+ align:start position:0%
+so in addition then gautam also has
+within classroom within classroom
+
+ align:start position:0%
+within classroom within classroom
+ 
+
+ align:start position:0%
+within classroom within classroom
+strategy
+
+ align:start position:0%
+strategy
+ 
+
+ align:start position:0%
+strategy
+that uh exploits the assignment to study
+
+ align:start position:0%
+that uh exploits the assignment to study
+ 
+
+ align:start position:0%
+that uh exploits the assignment to study
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+what is that doing is essentially it
+
+ align:start position:0%
+what is that doing is essentially it
+ 
+
+ align:start position:0%
+what is that doing is essentially it
+isolates the role of direct
+
+ align:start position:0%
+isolates the role of direct
+ 
+
+ align:start position:0%
+isolates the role of direct
+personal interactions and is not subject
+
+ align:start position:0%
+personal interactions and is not subject
+ 
+
+ align:start position:0%
+personal interactions and is not subject
+to sorting concerns another concern
+
+ align:start position:0%
+to sorting concerns another concern
+ 
+
+ align:start position:0%
+to sorting concerns another concern
+might be that
+
+ align:start position:0%
+might be that
+ 
+
+ align:start position:0%
+might be that
+you know you might sort of say oh oh in
+
+ align:start position:0%
+you know you might sort of say oh oh in
+ 
+
+ align:start position:0%
+you know you might sort of say oh oh in
+this school
+
+ align:start position:0%
+this school
+ 
+
+ align:start position:0%
+this school
+uh uh uh they're having like poor kids
+
+ align:start position:0%
+uh uh uh they're having like poor kids
+ 
+
+ align:start position:0%
+uh uh uh they're having like poor kids
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um uh that are led into this private
+
+ align:start position:0%
+um uh that are led into this private
+ 
+
+ align:start position:0%
+um uh that are led into this private
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+i'm gonna send my kids to somebody else
+
+ align:start position:0%
+i'm gonna send my kids to somebody else
+ 
+
+ align:start position:0%
+i'm gonna send my kids to somebody else
+so that's also an issue
+
+ align:start position:0%
+so that's also an issue
+ 
+
+ align:start position:0%
+so that's also an issue
+perhaps potentially in the uh uh
+
+ align:start position:0%
+perhaps potentially in the uh uh
+ 
+
+ align:start position:0%
+perhaps potentially in the uh uh
+in the evidence that i showed you before
+
+ align:start position:0%
+in the evidence that i showed you before
+ 
+
+ align:start position:0%
+in the evidence that i showed you before
+across classrooms that within classroom
+
+ align:start position:0%
+across classrooms that within classroom
+ 
+
+ align:start position:0%
+across classrooms that within classroom
+strategy is now looking at
+
+ align:start position:0%
+strategy is now looking at
+ 
+
+ align:start position:0%
+strategy is now looking at
+everybody who's in that classroom and
+
+ align:start position:0%
+everybody who's in that classroom and
+ 
+
+ align:start position:0%
+everybody who's in that classroom and
+looking at some kids where they're just
+
+ align:start position:0%
+looking at some kids where they're just
+ 
+
+ align:start position:0%
+looking at some kids where they're just
+randomly assigned to be in study groups
+
+ align:start position:0%
+randomly assigned to be in study groups
+ 
+
+ align:start position:0%
+randomly assigned to be in study groups
+with poor kids and others were not
+
+ align:start position:0%
+with poor kids and others were not
+ 
+
+ align:start position:0%
+with poor kids and others were not
+and that sort of allows to disentangle
+
+ align:start position:0%
+and that sort of allows to disentangle
+ 
+
+ align:start position:0%
+and that sort of allows to disentangle
+or allow us to isolate the
+
+ align:start position:0%
+or allow us to isolate the
+ 
+
+ align:start position:0%
+or allow us to isolate the
+effect of personal interactions so one
+
+ align:start position:0%
+effect of personal interactions so one
+ 
+
+ align:start position:0%
+effect of personal interactions so one
+hour a day
+
+ align:start position:0%
+hour a day
+ 
+
+ align:start position:0%
+hour a day
+um kids were working in small groups of
+
+ align:start position:0%
+um kids were working in small groups of
+ 
+
+ align:start position:0%
+um kids were working in small groups of
+two to four students
+
+ align:start position:0%
+two to four students
+ 
+
+ align:start position:0%
+two to four students
+remember this is for a very long period
+
+ align:start position:0%
+remember this is for a very long period
+ 
+
+ align:start position:0%
+remember this is for a very long period
+of time so like you know
+
+ align:start position:0%
+of time so like you know
+ 
+
+ align:start position:0%
+of time so like you know
+um it's one hour per day but it was also
+
+ align:start position:0%
+um it's one hour per day but it was also
+ 
+
+ align:start position:0%
+um it's one hour per day but it was also
+like for quite a bit of time it's not
+
+ align:start position:0%
+like for quite a bit of time it's not
+ 
+
+ align:start position:0%
+like for quite a bit of time it's not
+just like doing that once or twice it's
+
+ align:start position:0%
+just like doing that once or twice it's
+ 
+
+ align:start position:0%
+just like doing that once or twice it's
+for like an extended period of time
+
+ align:start position:0%
+for like an extended period of time
+ 
+
+ align:start position:0%
+for like an extended period of time
+and crucially some schools use the
+
+ align:start position:0%
+and crucially some schools use the
+ 
+
+ align:start position:0%
+and crucially some schools use the
+alphabetic order of first names to
+
+ align:start position:0%
+alphabetic order of first names to
+ 
+
+ align:start position:0%
+alphabetic order of first names to
+assign
+
+ align:start position:0%
+assign
+ 
+
+ align:start position:0%
+assign
+study groups so that's essentially
+
+ align:start position:0%
+study groups so that's essentially
+ 
+
+ align:start position:0%
+study groups so that's essentially
+exogenous variation in personal
+
+ align:start position:0%
+exogenous variation in personal
+ 
+
+ align:start position:0%
+exogenous variation in personal
+interactions
+
+ align:start position:0%
+interactions
+ 
+
+ align:start position:0%
+interactions
+other schools frequently um
+
+ align:start position:0%
+other schools frequently um
+ 
+
+ align:start position:0%
+other schools frequently um
+shuffled the groups and only um which
+
+ align:start position:0%
+shuffled the groups and only um which
+ 
+
+ align:start position:0%
+shuffled the groups and only um which
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+sort of uh everybody was equally exposed
+
+ align:start position:0%
+sort of uh everybody was equally exposed
+ 
+
+ align:start position:0%
+sort of uh everybody was equally exposed
+to those kinds of
+
+ align:start position:0%
+to those kinds of
+ 
+
+ align:start position:0%
+to those kinds of
+uh uh to two different students to your
+
+ align:start position:0%
+uh uh to two different students to your
+ 
+
+ align:start position:0%
+uh uh to two different students to your
+sometimes in study groups with
+
+ align:start position:0%
+sometimes in study groups with
+ 
+
+ align:start position:0%
+sometimes in study groups with
+rich students only and sometimes for
+
+ align:start position:0%
+rich students only and sometimes for
+ 
+
+ align:start position:0%
+rich students only and sometimes for
+poor students only
+
+ align:start position:0%
+poor students only
+ 
+
+ align:start position:0%
+poor students only
+in the first group where the alphabetic
+
+ align:start position:0%
+in the first group where the alphabetic
+ 
+
+ align:start position:0%
+in the first group where the alphabetic
+order was used
+
+ align:start position:0%
+order was used
+ 
+
+ align:start position:0%
+order was used
+you were either sort of in the study
+
+ align:start position:0%
+you were either sort of in the study
+ 
+
+ align:start position:0%
+you were either sort of in the study
+group where you happened to be
+
+ align:start position:0%
+group where you happened to be
+ 
+
+ align:start position:0%
+group where you happened to be
+next to somebody um
+
+ align:start position:0%
+next to somebody um
+ 
+
+ align:start position:0%
+next to somebody um
+uh uh who's a poor kid because they
+
+ align:start position:0%
+uh uh who's a poor kid because they
+ 
+
+ align:start position:0%
+uh uh who's a poor kid because they
+happen to be next to you in the alphabet
+
+ align:start position:0%
+happen to be next to you in the alphabet
+ 
+
+ align:start position:0%
+happen to be next to you in the alphabet
+or you're not and that stayed the same
+
+ align:start position:0%
+or you're not and that stayed the same
+ 
+
+ align:start position:0%
+or you're not and that stayed the same
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+what does this let us look at
+
+ align:start position:0%
+what does this let us look at
+ 
+
+ align:start position:0%
+what does this let us look at
+essentially the alphabetic order
+
+ align:start position:0%
+essentially the alphabetic order
+ 
+
+ align:start position:0%
+essentially the alphabetic order
+predicts
+
+ align:start position:0%
+predicts
+ 
+
+ align:start position:0%
+predicts
+um study partners so now you might say
+
+ align:start position:0%
+um study partners so now you might say
+ 
+
+ align:start position:0%
+um study partners so now you might say
+people with different names might also
+
+ align:start position:0%
+people with different names might also
+ 
+
+ align:start position:0%
+people with different names might also
+be different so it could just be that
+
+ align:start position:0%
+be different so it could just be that
+ 
+
+ align:start position:0%
+be different so it could just be that
+like my name
+
+ align:start position:0%
+like my name
+ 
+
+ align:start position:0%
+like my name
+because my name is different i'm more
+
+ align:start position:0%
+because my name is different i'm more
+ 
+
+ align:start position:0%
+because my name is different i'm more
+likely to be
+
+ align:start position:0%
+likely to be
+ 
+
+ align:start position:0%
+likely to be
+next in the alphabet to a poor student
+
+ align:start position:0%
+next in the alphabet to a poor student
+ 
+
+ align:start position:0%
+next in the alphabet to a poor student
+for example if i'm a rich kid and
+
+ align:start position:0%
+for example if i'm a rich kid and
+ 
+
+ align:start position:0%
+for example if i'm a rich kid and
+there's some
+
+ align:start position:0%
+there's some
+ 
+
+ align:start position:0%
+there's some
+names that are like more similar to poor
+
+ align:start position:0%
+names that are like more similar to poor
+ 
+
+ align:start position:0%
+names that are like more similar to poor
+kids names
+
+ align:start position:0%
+kids names
+ 
+
+ align:start position:0%
+kids names
+it could be that my parents are
+
+ align:start position:0%
+it could be that my parents are
+ 
+
+ align:start position:0%
+it could be that my parents are
+particularly tolerant they also gave me
+
+ align:start position:0%
+particularly tolerant they also gave me
+ 
+
+ align:start position:0%
+particularly tolerant they also gave me
+a name that
+
+ align:start position:0%
+a name that
+ 
+
+ align:start position:0%
+a name that
+sounds like a poor person and therefore
+
+ align:start position:0%
+sounds like a poor person and therefore
+ 
+
+ align:start position:0%
+sounds like a poor person and therefore
+i'm more likely to be in a study group
+
+ align:start position:0%
+i'm more likely to be in a study group
+ 
+
+ align:start position:0%
+i'm more likely to be in a study group
+with a poor
+
+ align:start position:0%
+with a poor
+ 
+
+ align:start position:0%
+with a poor
+other poor kid it's not and that's not
+
+ align:start position:0%
+other poor kid it's not and that's not
+ 
+
+ align:start position:0%
+other poor kid it's not and that's not
+then the impact of being in the study
+
+ align:start position:0%
+then the impact of being in the study
+ 
+
+ align:start position:0%
+then the impact of being in the study
+group but rather sort of selection just
+
+ align:start position:0%
+group but rather sort of selection just
+ 
+
+ align:start position:0%
+group but rather sort of selection just
+could be that
+
+ align:start position:0%
+could be that
+ 
+
+ align:start position:0%
+could be that
+names are different or people with
+
+ align:start position:0%
+names are different or people with
+ 
+
+ align:start position:0%
+names are different or people with
+different names are different so that's
+
+ align:start position:0%
+different names are different so that's
+ 
+
+ align:start position:0%
+different names are different so that's
+why having this control group is really
+
+ align:start position:0%
+why having this control group is really
+ 
+
+ align:start position:0%
+why having this control group is really
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+so what we can look at now is to say we
+
+ align:start position:0%
+so what we can look at now is to say we
+ 
+
+ align:start position:0%
+so what we can look at now is to say we
+can look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kids that have names adjacent to rich
+
+ align:start position:0%
+kids that have names adjacent to rich
+ 
+
+ align:start position:0%
+kids that have names adjacent to rich
+students and kids that have names
+
+ align:start position:0%
+students and kids that have names
+ 
+
+ align:start position:0%
+students and kids that have names
+adjacent to
+
+ align:start position:0%
+adjacent to
+ 
+
+ align:start position:0%
+adjacent to
+poor students so if you look at the left
+
+ align:start position:0%
+poor students so if you look at the left
+ 
+
+ align:start position:0%
+poor students so if you look at the left
+side is essentially looking at
+
+ align:start position:0%
+side is essentially looking at
+ 
+
+ align:start position:0%
+side is essentially looking at
+students that have their names adjacent
+
+ align:start position:0%
+students that have their names adjacent
+ 
+
+ align:start position:0%
+students that have their names adjacent
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+rich students only or students that have
+
+ align:start position:0%
+rich students only or students that have
+ 
+
+ align:start position:0%
+rich students only or students that have
+names adjacent to also some poor
+
+ align:start position:0%
+names adjacent to also some poor
+ 
+
+ align:start position:0%
+names adjacent to also some poor
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+when you look at that where the
+
+ align:start position:0%
+when you look at that where the
+ 
+
+ align:start position:0%
+when you look at that where the
+alphabetic order was not used
+
+ align:start position:0%
+alphabetic order was not used
+ 
+
+ align:start position:0%
+alphabetic order was not used
+the outcome here is now what's your
+
+ align:start position:0%
+the outcome here is now what's your
+ 
+
+ align:start position:0%
+the outcome here is now what's your
+share of having poor study partners and
+
+ align:start position:0%
+share of having poor study partners and
+ 
+
+ align:start position:0%
+share of having poor study partners and
+so there essentially there's no
+
+ align:start position:0%
+so there essentially there's no
+ 
+
+ align:start position:0%
+so there essentially there's no
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+as it should be because the alphabetic
+
+ align:start position:0%
+as it should be because the alphabetic
+ 
+
+ align:start position:0%
+as it should be because the alphabetic
+order was not used they were just
+
+ align:start position:0%
+order was not used they were just
+ 
+
+ align:start position:0%
+order was not used they were just
+shuffling around
+
+ align:start position:0%
+shuffling around
+ 
+
+ align:start position:0%
+shuffling around
+the kids all the time so it didn't
+
+ align:start position:0%
+the kids all the time so it didn't
+ 
+
+ align:start position:0%
+the kids all the time so it didn't
+really matter what your alphabet was it
+
+ align:start position:0%
+really matter what your alphabet was it
+ 
+
+ align:start position:0%
+really matter what your alphabet was it
+didn't really matter but
+
+ align:start position:0%
+didn't really matter but
+ 
+
+ align:start position:0%
+didn't really matter but
+but crucially we can still look at the
+
+ align:start position:0%
+but crucially we can still look at the
+ 
+
+ align:start position:0%
+but crucially we can still look at the
+alphabet we can look at
+
+ align:start position:0%
+alphabet we can look at
+ 
+
+ align:start position:0%
+alphabet we can look at
+kids that have names where adjacent in
+
+ align:start position:0%
+kids that have names where adjacent in
+ 
+
+ align:start position:0%
+kids that have names where adjacent in
+the alphabet there's only
+
+ align:start position:0%
+the alphabet there's only
+ 
+
+ align:start position:0%
+the alphabet there's only
+rich kids rich students or we can look
+
+ align:start position:0%
+rich kids rich students or we can look
+ 
+
+ align:start position:0%
+rich kids rich students or we can look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+kids that have names where adjacent to
+
+ align:start position:0%
+kids that have names where adjacent to
+ 
+
+ align:start position:0%
+kids that have names where adjacent to
+the alphabets they're poor students
+
+ align:start position:0%
+the alphabets they're poor students
+ 
+
+ align:start position:0%
+the alphabets they're poor students
+and here you see on the left side of the
+
+ align:start position:0%
+and here you see on the left side of the
+ 
+
+ align:start position:0%
+and here you see on the left side of the
+graph you see essentially no difference
+
+ align:start position:0%
+graph you see essentially no difference
+ 
+
+ align:start position:0%
+graph you see essentially no difference
+across these
+
+ align:start position:0%
+across these
+ 
+
+ align:start position:0%
+across these
+groups so they were equally likely to
+
+ align:start position:0%
+groups so they were equally likely to
+ 
+
+ align:start position:0%
+groups so they were equally likely to
+have a poor kid in their study group
+
+ align:start position:0%
+have a poor kid in their study group
+ 
+
+ align:start position:0%
+have a poor kid in their study group
+in contrast on the right side of the
+
+ align:start position:0%
+in contrast on the right side of the
+ 
+
+ align:start position:0%
+in contrast on the right side of the
+graph you see
+
+ align:start position:0%
+graph you see
+ 
+
+ align:start position:0%
+graph you see
+the alphabetic order was used to assign
+
+ align:start position:0%
+the alphabetic order was used to assign
+ 
+
+ align:start position:0%
+the alphabetic order was used to assign
+study groups so if you had a name
+
+ align:start position:0%
+study groups so if you had a name
+ 
+
+ align:start position:0%
+study groups so if you had a name
+adjacent
+
+ align:start position:0%
+adjacent
+ 
+
+ align:start position:0%
+adjacent
+to a poor student in the alphabet you're
+
+ align:start position:0%
+to a poor student in the alphabet you're
+ 
+
+ align:start position:0%
+to a poor student in the alphabet you're
+very very likely to have a poor kid
+
+ align:start position:0%
+very very likely to have a poor kid
+ 
+
+ align:start position:0%
+very very likely to have a poor kid
+assigned to you or be in your study
+
+ align:start position:0%
+assigned to you or be in your study
+ 
+
+ align:start position:0%
+assigned to you or be in your study
+group not always because you know
+
+ align:start position:0%
+group not always because you know
+ 
+
+ align:start position:0%
+group not always because you know
+sometimes these are groups of three so
+
+ align:start position:0%
+sometimes these are groups of three so
+ 
+
+ align:start position:0%
+sometimes these are groups of three so
+that sometimes you were
+
+ align:start position:0%
+that sometimes you were
+ 
+
+ align:start position:0%
+that sometimes you were
+lucky or unlucky depending on how you
+
+ align:start position:0%
+lucky or unlucky depending on how you
+ 
+
+ align:start position:0%
+lucky or unlucky depending on how you
+view it there were just sort of the
+
+ align:start position:0%
+view it there were just sort of the
+ 
+
+ align:start position:0%
+view it there were just sort of the
+group was like just above you or below
+
+ align:start position:0%
+group was like just above you or below
+ 
+
+ align:start position:0%
+group was like just above you or below
+you in the alphabet
+
+ align:start position:0%
+you in the alphabet
+ 
+
+ align:start position:0%
+you in the alphabet
+but most of the time if you have a name
+
+ align:start position:0%
+but most of the time if you have a name
+ 
+
+ align:start position:0%
+but most of the time if you have a name
+adjacent to approach student that
+
+ align:start position:0%
+adjacent to approach student that
+ 
+
+ align:start position:0%
+adjacent to approach student that
+student or any
+
+ align:start position:0%
+student or any
+ 
+
+ align:start position:0%
+student or any
+uh any poor student would be in your
+
+ align:start position:0%
+uh any poor student would be in your
+ 
+
+ align:start position:0%
+uh any poor student would be in your
+study group
+
+ align:start position:0%
+study group
+ 
+
+ align:start position:0%
+study group
+uh if you didn't have a name adjacent to
+
+ align:start position:0%
+uh if you didn't have a name adjacent to
+ 
+
+ align:start position:0%
+uh if you didn't have a name adjacent to
+you um
+
+ align:start position:0%
+you um
+ 
+
+ align:start position:0%
+you um
+or if you only had like rich student
+
+ align:start position:0%
+or if you only had like rich student
+ 
+
+ align:start position:0%
+or if you only had like rich student
+adjacent to you there's still a chance
+
+ align:start position:0%
+adjacent to you there's still a chance
+ 
+
+ align:start position:0%
+adjacent to you there's still a chance
+that you have a poor student in your
+
+ align:start position:0%
+that you have a poor student in your
+ 
+
+ align:start position:0%
+that you have a poor student in your
+study group because this could be just
+
+ align:start position:0%
+study group because this could be just
+ 
+
+ align:start position:0%
+study group because this could be just
+like you know not the person next to you
+
+ align:start position:0%
+like you know not the person next to you
+ 
+
+ align:start position:0%
+like you know not the person next to you
+but the person
+
+ align:start position:0%
+but the person
+ 
+
+ align:start position:0%
+but the person
+another person further down is in fact a
+
+ align:start position:0%
+another person further down is in fact a
+ 
+
+ align:start position:0%
+another person further down is in fact a
+poor student you end up in that group
+
+ align:start position:0%
+poor student you end up in that group
+ 
+
+ align:start position:0%
+poor student you end up in that group
+without
+
+ align:start position:0%
+without
+ 
+
+ align:start position:0%
+without
+that student remember these are groups
+
+ align:start position:0%
+that student remember these are groups
+ 
+
+ align:start position:0%
+that student remember these are groups
+of two to four students
+
+ align:start position:0%
+of two to four students
+ 
+
+ align:start position:0%
+of two to four students
+so it could just be that you're in a
+
+ align:start position:0%
+so it could just be that you're in a
+ 
+
+ align:start position:0%
+so it could just be that you're in a
+group of three to four student and not
+
+ align:start position:0%
+group of three to four student and not
+ 
+
+ align:start position:0%
+group of three to four student and not
+the person adjacent to you but the
+
+ align:start position:0%
+the person adjacent to you but the
+ 
+
+ align:start position:0%
+the person adjacent to you but the
+person after that
+
+ align:start position:0%
+person after that
+ 
+
+ align:start position:0%
+person after that
+ends up in your study group so you're
+
+ align:start position:0%
+ends up in your study group so you're
+ 
+
+ align:start position:0%
+ends up in your study group so you're
+still likely to have
+
+ align:start position:0%
+still likely to have
+ 
+
+ align:start position:0%
+still likely to have
+um or you know you have still like about
+
+ align:start position:0%
+um or you know you have still like about
+ 
+
+ align:start position:0%
+um or you know you have still like about
+like a 40
+
+ align:start position:0%
+like a 40
+ 
+
+ align:start position:0%
+like a 40
+chance of having a poor kid in your um
+
+ align:start position:0%
+chance of having a poor kid in your um
+ 
+
+ align:start position:0%
+chance of having a poor kid in your um
+in your study group but there's a huge
+
+ align:start position:0%
+in your study group but there's a huge
+ 
+
+ align:start position:0%
+in your study group but there's a huge
+difference between the two types of
+
+ align:start position:0%
+difference between the two types of
+ 
+
+ align:start position:0%
+difference between the two types of
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+um the name adjacent to the study group
+
+ align:start position:0%
+um the name adjacent to the study group
+ 
+
+ align:start position:0%
+um the name adjacent to the study group
+has like huge fraction about 90
+
+ align:start position:0%
+has like huge fraction about 90
+ 
+
+ align:start position:0%
+has like huge fraction about 90
+or uh versus 40 so crucially now we can
+
+ align:start position:0%
+or uh versus 40 so crucially now we can
+ 
+
+ align:start position:0%
+or uh versus 40 so crucially now we can
+compare
+
+ align:start position:0%
+compare
+ 
+
+ align:start position:0%
+compare
+for both types of schools for the
+
+ align:start position:0%
+for both types of schools for the
+ 
+
+ align:start position:0%
+for both types of schools for the
+schools on the right-hand side
+
+ align:start position:0%
+schools on the right-hand side
+ 
+
+ align:start position:0%
+schools on the right-hand side
+where essentially the names are very
+
+ align:start position:0%
+where essentially the names are very
+ 
+
+ align:start position:0%
+where essentially the names are very
+predictive of
+
+ align:start position:0%
+predictive of
+ 
+
+ align:start position:0%
+predictive of
+of having a poorest kid in uh in your
+
+ align:start position:0%
+of having a poorest kid in uh in your
+ 
+
+ align:start position:0%
+of having a poorest kid in uh in your
+study group
+
+ align:start position:0%
+study group
+ 
+
+ align:start position:0%
+study group
+versus on the left-hand side where the
+
+ align:start position:0%
+versus on the left-hand side where the
+ 
+
+ align:start position:0%
+versus on the left-hand side where the
+names are not predictive at all whether
+
+ align:start position:0%
+names are not predictive at all whether
+ 
+
+ align:start position:0%
+names are not predictive at all whether
+um you have a a poor kid in your study
+
+ align:start position:0%
+um you have a a poor kid in your study
+ 
+
+ align:start position:0%
+um you have a a poor kid in your study
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+and so we can like that way we can keep
+
+ align:start position:0%
+and so we can like that way we can keep
+ 
+
+ align:start position:0%
+and so we can like that way we can keep
+selection the same the types of name are
+
+ align:start position:0%
+selection the same the types of name are
+ 
+
+ align:start position:0%
+selection the same the types of name are
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+we are isolating the impact of having a
+
+ align:start position:0%
+we are isolating the impact of having a
+ 
+
+ align:start position:0%
+we are isolating the impact of having a
+poor kid
+
+ align:start position:0%
+poor kid
+ 
+
+ align:start position:0%
+poor kid
+in your study group now what does the
+
+ align:start position:0%
+in your study group now what does the
+ 
+
+ align:start position:0%
+in your study group now what does the
+author find he finds that
+
+ align:start position:0%
+author find he finds that
+ 
+
+ align:start position:0%
+author find he finds that
+this is what we showed you before which
+
+ align:start position:0%
+this is what we showed you before which
+ 
+
+ align:start position:0%
+this is what we showed you before which
+is about you know
+
+ align:start position:0%
+is about you know
+ 
+
+ align:start position:0%
+is about you know
+in the control group we had about uh in
+
+ align:start position:0%
+in the control group we had about uh in
+ 
+
+ align:start position:0%
+in the control group we had about uh in
+the dictator game
+
+ align:start position:0%
+the dictator game
+ 
+
+ align:start position:0%
+the dictator game
+these kids gave about 27 um
+
+ align:start position:0%
+these kids gave about 27 um
+ 
+
+ align:start position:0%
+these kids gave about 27 um
+uh 27 percent uh being having a poor kid
+
+ align:start position:0%
+uh 27 percent uh being having a poor kid
+ 
+
+ align:start position:0%
+uh 27 percent uh being having a poor kid
+in your classroom that's the evidence
+
+ align:start position:0%
+in your classroom that's the evidence
+ 
+
+ align:start position:0%
+in your classroom that's the evidence
+that i already showed you the treatment
+
+ align:start position:0%
+that i already showed you the treatment
+ 
+
+ align:start position:0%
+that i already showed you the treatment
+effect is about
+
+ align:start position:0%
+effect is about
+ 
+
+ align:start position:0%
+effect is about
+uh uh 12 percentage points that's fairly
+
+ align:start position:0%
+uh uh 12 percentage points that's fairly
+ 
+
+ align:start position:0%
+uh uh 12 percentage points that's fairly
+large that's almost like a 50
+
+ align:start position:0%
+large that's almost like a 50
+ 
+
+ align:start position:0%
+large that's almost like a 50
+a 50 increase a little bit less than
+
+ align:start position:0%
+a 50 increase a little bit less than
+ 
+
+ align:start position:0%
+a 50 increase a little bit less than
+that so that's a huge
+
+ align:start position:0%
+that so that's a huge
+ 
+
+ align:start position:0%
+that so that's a huge
+increase and then in addition um when
+
+ align:start position:0%
+increase and then in addition um when
+ 
+
+ align:start position:0%
+increase and then in addition um when
+you look at
+
+ align:start position:0%
+you look at
+ 
+
+ align:start position:0%
+you look at
+kids that have a poor study partner
+
+ align:start position:0%
+kids that have a poor study partner
+ 
+
+ align:start position:0%
+kids that have a poor study partner
+notice that these are things not
+
+ align:start position:0%
+notice that these are things not
+ 
+
+ align:start position:0%
+notice that these are things not
+necessarily additive but you have a poor
+
+ align:start position:0%
+necessarily additive but you have a poor
+ 
+
+ align:start position:0%
+necessarily additive but you have a poor
+study partner versus not
+
+ align:start position:0%
+study partner versus not
+ 
+
+ align:start position:0%
+study partner versus not
+there's an effect of about 7.5
+
+ align:start position:0%
+there's an effect of about 7.5
+ 
+
+ align:start position:0%
+there's an effect of about 7.5
+percentage points
+
+ align:start position:0%
+percentage points
+ 
+
+ align:start position:0%
+percentage points
+that's a pretty large effect so
+
+ align:start position:0%
+that's a pretty large effect so
+ 
+
+ align:start position:0%
+that's a pretty large effect so
+both of these things seem to matter
+
+ align:start position:0%
+both of these things seem to matter
+ 
+
+ align:start position:0%
+both of these things seem to matter
+personal interactions seem to be quite
+
+ align:start position:0%
+personal interactions seem to be quite
+ 
+
+ align:start position:0%
+personal interactions seem to be quite
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+but in addition there seem to be also
+
+ align:start position:0%
+but in addition there seem to be also
+ 
+
+ align:start position:0%
+but in addition there seem to be also
+some additional effects perhaps coming
+
+ align:start position:0%
+some additional effects perhaps coming
+ 
+
+ align:start position:0%
+some additional effects perhaps coming
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+classroom level you might so there's two
+
+ align:start position:0%
+classroom level you might so there's two
+ 
+
+ align:start position:0%
+classroom level you might so there's two
+types of effects that are possible here
+
+ align:start position:0%
+types of effects that are possible here
+ 
+
+ align:start position:0%
+types of effects that are possible here
+some types of effects could be from the
+
+ align:start position:0%
+some types of effects could be from the
+ 
+
+ align:start position:0%
+some types of effects could be from the
+teacher parents curriculum etc might be
+
+ align:start position:0%
+teacher parents curriculum etc might be
+ 
+
+ align:start position:0%
+teacher parents curriculum etc might be
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+or other things could be just like even
+
+ align:start position:0%
+or other things could be just like even
+ 
+
+ align:start position:0%
+or other things could be just like even
+if you don't have a poor kid in your
+
+ align:start position:0%
+if you don't have a poor kid in your
+ 
+
+ align:start position:0%
+if you don't have a poor kid in your
+study group you might still play with
+
+ align:start position:0%
+study group you might still play with
+ 
+
+ align:start position:0%
+study group you might still play with
+them or be friends with them or just
+
+ align:start position:0%
+them or be friends with them or just
+ 
+
+ align:start position:0%
+them or be friends with them or just
+seeing them around a new classroom
+
+ align:start position:0%
+seeing them around a new classroom
+ 
+
+ align:start position:0%
+seeing them around a new classroom
+might affect you but crucially crucially
+
+ align:start position:0%
+might affect you but crucially crucially
+ 
+
+ align:start position:0%
+might affect you but crucially crucially
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+personal interactions seem to be very
+
+ align:start position:0%
+personal interactions seem to be very
+ 
+
+ align:start position:0%
+personal interactions seem to be very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+as well now one question you might ask
+
+ align:start position:0%
+as well now one question you might ask
+ 
+
+ align:start position:0%
+as well now one question you might ask
+as well so far i showed you generosity
+
+ align:start position:0%
+as well so far i showed you generosity
+ 
+
+ align:start position:0%
+as well so far i showed you generosity
+towards
+
+ align:start position:0%
+towards
+ 
+
+ align:start position:0%
+towards
+poor children right so that was game
+
+ align:start position:0%
+poor children right so that was game
+ 
+
+ align:start position:0%
+poor children right so that was game
+number one we looked at
+
+ align:start position:0%
+number one we looked at
+ 
+
+ align:start position:0%
+number one we looked at
+what happens in the dictator games when
+
+ align:start position:0%
+what happens in the dictator games when
+ 
+
+ align:start position:0%
+what happens in the dictator games when
+a rich kid
+
+ align:start position:0%
+a rich kid
+ 
+
+ align:start position:0%
+a rich kid
+plays with a poor kid and the rich kids
+
+ align:start position:0%
+plays with a poor kid and the rich kids
+ 
+
+ align:start position:0%
+plays with a poor kid and the rich kids
+become nicer towards the
+
+ align:start position:0%
+become nicer towards the
+ 
+
+ align:start position:0%
+become nicer towards the
+poor kids now how about generosity
+
+ align:start position:0%
+poor kids now how about generosity
+ 
+
+ align:start position:0%
+poor kids now how about generosity
+towards
+
+ align:start position:0%
+towards
+ 
+
+ align:start position:0%
+towards
+other wealthy children well it turns out
+
+ align:start position:0%
+other wealthy children well it turns out
+ 
+
+ align:start position:0%
+other wealthy children well it turns out
+that that that increases as well
+
+ align:start position:0%
+that that that increases as well
+ 
+
+ align:start position:0%
+that that that increases as well
+there's a smaller effect size but it's
+
+ align:start position:0%
+there's a smaller effect size but it's
+ 
+
+ align:start position:0%
+there's a smaller effect size but it's
+still substantial and in fact um
+
+ align:start position:0%
+still substantial and in fact um
+ 
+
+ align:start position:0%
+still substantial and in fact um
+statistically uh significant
+
+ align:start position:0%
+statistically uh significant
+ 
+
+ align:start position:0%
+statistically uh significant
+so why might that be you might sort of
+
+ align:start position:0%
+so why might that be you might sort of
+ 
+
+ align:start position:0%
+so why might that be you might sort of
+ask well what's going on here
+
+ align:start position:0%
+ask well what's going on here
+ 
+
+ align:start position:0%
+ask well what's going on here
+so here's the the evidence you sort of
+
+ align:start position:0%
+so here's the the evidence you sort of
+ 
+
+ align:start position:0%
+so here's the the evidence you sort of
+see the
+
+ align:start position:0%
+see the
+ 
+
+ align:start position:0%
+see the
+changing giving to rich participants
+
+ align:start position:0%
+changing giving to rich participants
+ 
+
+ align:start position:0%
+changing giving to rich participants
+this is sort of like a distribution you
+
+ align:start position:0%
+this is sort of like a distribution you
+ 
+
+ align:start position:0%
+this is sort of like a distribution you
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+this is the share giving to the rich
+
+ align:start position:0%
+this is the share giving to the rich
+ 
+
+ align:start position:0%
+this is the share giving to the rich
+participant it seems to be what happens
+
+ align:start position:0%
+participant it seems to be what happens
+ 
+
+ align:start position:0%
+participant it seems to be what happens
+these are essentially the fraction of
+
+ align:start position:0%
+these are essentially the fraction of
+ 
+
+ align:start position:0%
+these are essentially the fraction of
+students in the different treatment
+
+ align:start position:0%
+students in the different treatment
+ 
+
+ align:start position:0%
+students in the different treatment
+versus control
+
+ align:start position:0%
+versus control
+ 
+
+ align:start position:0%
+versus control
+who gives 0 10 20 30 40 50 percent
+
+ align:start position:0%
+who gives 0 10 20 30 40 50 percent
+ 
+
+ align:start position:0%
+who gives 0 10 20 30 40 50 percent
+and what you see there's about a 10 um
+
+ align:start position:0%
+and what you see there's about a 10 um
+ 
+
+ align:start position:0%
+and what you see there's about a 10 um
+percentage points
+
+ align:start position:0%
+percentage points
+ 
+
+ align:start position:0%
+percentage points
+decrease in the fraction who gives zero
+
+ align:start position:0%
+decrease in the fraction who gives zero
+ 
+
+ align:start position:0%
+decrease in the fraction who gives zero
+and about uh eight something uh
+
+ align:start position:0%
+and about uh eight something uh
+ 
+
+ align:start position:0%
+and about uh eight something uh
+percentage points increase in the
+
+ align:start position:0%
+percentage points increase in the
+ 
+
+ align:start position:0%
+percentage points increase in the
+fraction who give
+
+ align:start position:0%
+fraction who give
+ 
+
+ align:start position:0%
+fraction who give
+fifty percent so it seems to be that
+
+ align:start position:0%
+fifty percent so it seems to be that
+ 
+
+ align:start position:0%
+fifty percent so it seems to be that
+there's quite a few students
+
+ align:start position:0%
+there's quite a few students
+ 
+
+ align:start position:0%
+there's quite a few students
+who move from zero um percent about like
+
+ align:start position:0%
+who move from zero um percent about like
+ 
+
+ align:start position:0%
+who move from zero um percent about like
+you know ten percent of them move from
+
+ align:start position:0%
+you know ten percent of them move from
+ 
+
+ align:start position:0%
+you know ten percent of them move from
+zero percent
+
+ align:start position:0%
+zero percent
+ 
+
+ align:start position:0%
+zero percent
+to um uh 50 and 50 50 is kind of like
+
+ align:start position:0%
+to um uh 50 and 50 50 is kind of like
+ 
+
+ align:start position:0%
+to um uh 50 and 50 50 is kind of like
+the equal
+
+ align:start position:0%
+the equal
+ 
+
+ align:start position:0%
+the equal
+allocation so rich kids are also
+
+ align:start position:0%
+allocation so rich kids are also
+ 
+
+ align:start position:0%
+allocation so rich kids are also
+becoming nicer towards
+
+ align:start position:0%
+becoming nicer towards
+ 
+
+ align:start position:0%
+becoming nicer towards
+rich kids in these dictator games so
+
+ align:start position:0%
+rich kids in these dictator games so
+ 
+
+ align:start position:0%
+rich kids in these dictator games so
+what's going on here
+
+ align:start position:0%
+what's going on here
+ 
+
+ align:start position:0%
+what's going on here
+um there's different potential
+
+ align:start position:0%
+um there's different potential
+ 
+
+ align:start position:0%
+um there's different potential
+explanations perhaps the most
+
+ align:start position:0%
+explanations perhaps the most
+ 
+
+ align:start position:0%
+explanations perhaps the most
+plausible explanation the study you know
+
+ align:start position:0%
+plausible explanation the study you know
+ 
+
+ align:start position:0%
+plausible explanation the study you know
+has some evidence on that
+
+ align:start position:0%
+has some evidence on that
+ 
+
+ align:start position:0%
+has some evidence on that
+um at the end of the day it's hard to
+
+ align:start position:0%
+um at the end of the day it's hard to
+ 
+
+ align:start position:0%
+um at the end of the day it's hard to
+sort of entirely nail this or like you
+
+ align:start position:0%
+sort of entirely nail this or like you
+ 
+
+ align:start position:0%
+sort of entirely nail this or like you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+rule out all other potential explanation
+
+ align:start position:0%
+rule out all other potential explanation
+ 
+
+ align:start position:0%
+rule out all other potential explanation
+but it's quite
+
+ align:start position:0%
+but it's quite
+ 
+
+ align:start position:0%
+but it's quite
+plausible that what's happening here is
+
+ align:start position:0%
+plausible that what's happening here is
+ 
+
+ align:start position:0%
+plausible that what's happening here is
+that like inequity
+
+ align:start position:0%
+that like inequity
+ 
+
+ align:start position:0%
+that like inequity
+students when you're exposed to poor
+
+ align:start position:0%
+students when you're exposed to poor
+ 
+
+ align:start position:0%
+students when you're exposed to poor
+children you're essentially
+
+ align:start position:0%
+children you're essentially
+ 
+
+ align:start position:0%
+children you're essentially
+um more averse to like inequality
+
+ align:start position:0%
+um more averse to like inequality
+ 
+
+ align:start position:0%
+um more averse to like inequality
+or inequity across people
+
+ align:start position:0%
+or inequity across people
+ 
+
+ align:start position:0%
+or inequity across people
+even in things in fairly trivial things
+
+ align:start position:0%
+even in things in fairly trivial things
+ 
+
+ align:start position:0%
+even in things in fairly trivial things
+that are such as
+
+ align:start position:0%
+that are such as
+ 
+
+ align:start position:0%
+that are such as
+dictator games now i told you before
+
+ align:start position:0%
+dictator games now i told you before
+ 
+
+ align:start position:0%
+dictator games now i told you before
+that's a little bit
+
+ align:start position:0%
+that's a little bit
+ 
+
+ align:start position:0%
+that's a little bit
+funny because dictator games obviously
+
+ align:start position:0%
+funny because dictator games obviously
+ 
+
+ align:start position:0%
+funny because dictator games obviously
+are very narrowly framing people and
+
+ align:start position:0%
+are very narrowly framing people and
+ 
+
+ align:start position:0%
+are very narrowly framing people and
+looking at essentially
+
+ align:start position:0%
+looking at essentially
+ 
+
+ align:start position:0%
+looking at essentially
+when very narrow outcomes um
+
+ align:start position:0%
+when very narrow outcomes um
+ 
+
+ align:start position:0%
+when very narrow outcomes um
+if we have like a 50 50 outcome in the
+
+ align:start position:0%
+if we have like a 50 50 outcome in the
+ 
+
+ align:start position:0%
+if we have like a 50 50 outcome in the
+dictator game that doesn't mean that our
+
+ align:start position:0%
+dictator game that doesn't mean that our
+ 
+
+ align:start position:0%
+dictator game that doesn't mean that our
+life is
+
+ align:start position:0%
+life is
+ 
+
+ align:start position:0%
+life is
+uh the same it might be you might be
+
+ align:start position:0%
+uh the same it might be you might be
+ 
+
+ align:start position:0%
+uh the same it might be you might be
+still much richer than i am
+
+ align:start position:0%
+still much richer than i am
+ 
+
+ align:start position:0%
+still much richer than i am
+so um having sort of equal outcomes in
+
+ align:start position:0%
+so um having sort of equal outcomes in
+ 
+
+ align:start position:0%
+so um having sort of equal outcomes in
+the dictator game 50 50 allocation in
+
+ align:start position:0%
+the dictator game 50 50 allocation in
+ 
+
+ align:start position:0%
+the dictator game 50 50 allocation in
+the dictator game
+
+ align:start position:0%
+the dictator game
+ 
+
+ align:start position:0%
+the dictator game
+might be narrowly framed in that
+
+ align:start position:0%
+might be narrowly framed in that
+ 
+
+ align:start position:0%
+might be narrowly framed in that
+particular game fair but of course it's
+
+ align:start position:0%
+particular game fair but of course it's
+ 
+
+ align:start position:0%
+particular game fair but of course it's
+not fair in the grand scheme of things
+
+ align:start position:0%
+not fair in the grand scheme of things
+ 
+
+ align:start position:0%
+not fair in the grand scheme of things
+but what seems to be the case is that um
+
+ align:start position:0%
+but what seems to be the case is that um
+ 
+
+ align:start position:0%
+but what seems to be the case is that um
+and there's some evidence other evidence
+
+ align:start position:0%
+and there's some evidence other evidence
+ 
+
+ align:start position:0%
+and there's some evidence other evidence
+in the paper that you can read if you
+
+ align:start position:0%
+in the paper that you can read if you
+ 
+
+ align:start position:0%
+in the paper that you can read if you
+would like
+
+ align:start position:0%
+would like
+ 
+
+ align:start position:0%
+would like
+it seems to be the case that um rich
+
+ align:start position:0%
+it seems to be the case that um rich
+ 
+
+ align:start position:0%
+it seems to be the case that um rich
+children become more averse to unequal
+
+ align:start position:0%
+children become more averse to unequal
+ 
+
+ align:start position:0%
+children become more averse to unequal
+outcomes in the world in general because
+
+ align:start position:0%
+outcomes in the world in general because
+ 
+
+ align:start position:0%
+outcomes in the world in general because
+they essentially see
+
+ align:start position:0%
+they essentially see
+ 
+
+ align:start position:0%
+they essentially see
+these poor kids who who are very smart
+
+ align:start position:0%
+these poor kids who who are very smart
+ 
+
+ align:start position:0%
+these poor kids who who are very smart
+and you know um
+
+ align:start position:0%
+and you know um
+ 
+
+ align:start position:0%
+and you know um
+are disadvantaged in terms of various
+
+ align:start position:0%
+are disadvantaged in terms of various
+ 
+
+ align:start position:0%
+are disadvantaged in terms of various
+ways from like having
+
+ align:start position:0%
+ways from like having
+ 
+
+ align:start position:0%
+ways from like having
+a lower wealth of their parents the rich
+
+ align:start position:0%
+a lower wealth of their parents the rich
+ 
+
+ align:start position:0%
+a lower wealth of their parents the rich
+kids become sort of more averse against
+
+ align:start position:0%
+kids become sort of more averse against
+ 
+
+ align:start position:0%
+kids become sort of more averse against
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and that translates even into like
+
+ align:start position:0%
+and that translates even into like
+ 
+
+ align:start position:0%
+and that translates even into like
+dictator games with
+
+ align:start position:0%
+dictator games with
+ 
+
+ align:start position:0%
+dictator games with
+other rich kids um in a very sort of
+
+ align:start position:0%
+other rich kids um in a very sort of
+ 
+
+ align:start position:0%
+other rich kids um in a very sort of
+minor thing in the world in in these
+
+ align:start position:0%
+minor thing in the world in in these
+ 
+
+ align:start position:0%
+minor thing in the world in in these
+dictator games
+
+ align:start position:0%
+dictator games
+ 
+
+ align:start position:0%
+dictator games
+again even though the dictator games
+
+ align:start position:0%
+again even though the dictator games
+ 
+
+ align:start position:0%
+again even though the dictator games
+actually don't change very much but they
+
+ align:start position:0%
+actually don't change very much but they
+ 
+
+ align:start position:0%
+actually don't change very much but they
+really seem to be
+
+ align:start position:0%
+really seem to be
+ 
+
+ align:start position:0%
+really seem to be
+averse to an equality of these outcomes
+
+ align:start position:0%
+averse to an equality of these outcomes
+ 
+
+ align:start position:0%
+averse to an equality of these outcomes
+and move them from the 10-0 allocation
+
+ align:start position:0%
+and move them from the 10-0 allocation
+ 
+
+ align:start position:0%
+and move them from the 10-0 allocation
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+50-50 even with these rich kids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that was like evidence on social
+
+ align:start position:0%
+okay so that was like evidence on social
+ 
+
+ align:start position:0%
+okay so that was like evidence on social
+preferences as measured by dictator
+
+ align:start position:0%
+preferences as measured by dictator
+ 
+
+ align:start position:0%
+preferences as measured by dictator
+games
+
+ align:start position:0%
+games
+ 
+
+ align:start position:0%
+games
+the paper also has some evidence on
+
+ align:start position:0%
+the paper also has some evidence on
+ 
+
+ align:start position:0%
+the paper also has some evidence on
+discrimination in particular a small
+
+ align:start position:0%
+discrimination in particular a small
+ 
+
+ align:start position:0%
+discrimination in particular a small
+field experiment on team selection
+
+ align:start position:0%
+field experiment on team selection
+ 
+
+ align:start position:0%
+field experiment on team selection
+so um what does the study do so the
+
+ align:start position:0%
+so um what does the study do so the
+ 
+
+ align:start position:0%
+so um what does the study do so the
+subjects
+
+ align:start position:0%
+subjects
+ 
+
+ align:start position:0%
+subjects
+are again students from two elite
+
+ align:start position:0%
+are again students from two elite
+ 
+
+ align:start position:0%
+are again students from two elite
+private schools so now it's like two of
+
+ align:start position:0%
+private schools so now it's like two of
+ 
+
+ align:start position:0%
+private schools so now it's like two of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+selected student schools are selected
+
+ align:start position:0%
+selected student schools are selected
+ 
+
+ align:start position:0%
+selected student schools are selected
+one is a treatment school
+
+ align:start position:0%
+one is a treatment school
+ 
+
+ align:start position:0%
+one is a treatment school
+one is a control group and in addition
+
+ align:start position:0%
+one is a control group and in addition
+ 
+
+ align:start position:0%
+one is a control group and in addition
+gautam invited athletic poor students
+
+ align:start position:0%
+gautam invited athletic poor students
+ 
+
+ align:start position:0%
+gautam invited athletic poor students
+from a public school
+
+ align:start position:0%
+from a public school
+ 
+
+ align:start position:0%
+from a public school
+importantly these are athletic students
+
+ align:start position:0%
+importantly these are athletic students
+ 
+
+ align:start position:0%
+importantly these are athletic students
+these are students who are better at
+
+ align:start position:0%
+these are students who are better at
+ 
+
+ align:start position:0%
+these are students who are better at
+sports than
+
+ align:start position:0%
+sports than
+ 
+
+ align:start position:0%
+sports than
+the rich kids you might think you know
+
+ align:start position:0%
+the rich kids you might think you know
+ 
+
+ align:start position:0%
+the rich kids you might think you know
+the poorer kids are better at sports
+
+ align:start position:0%
+the poorer kids are better at sports
+ 
+
+ align:start position:0%
+the poorer kids are better at sports
+than the rich kids anyway which is
+
+ align:start position:0%
+than the rich kids anyway which is
+ 
+
+ align:start position:0%
+than the rich kids anyway which is
+probably true
+
+ align:start position:0%
+probably true
+ 
+
+ align:start position:0%
+probably true
+but now these are particularly athletic
+
+ align:start position:0%
+but now these are particularly athletic
+ 
+
+ align:start position:0%
+but now these are particularly athletic
+students on purpose
+
+ align:start position:0%
+students on purpose
+ 
+
+ align:start position:0%
+students on purpose
+who are invited to attend a sports event
+
+ align:start position:0%
+who are invited to attend a sports event
+ 
+
+ align:start position:0%
+who are invited to attend a sports event
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+now students in this in this experiment
+
+ align:start position:0%
+now students in this in this experiment
+ 
+
+ align:start position:0%
+now students in this in this experiment
+in this game must
+
+ align:start position:0%
+in this game must
+ 
+
+ align:start position:0%
+in this game must
+choose teammates to run a relay race now
+
+ align:start position:0%
+choose teammates to run a relay race now
+ 
+
+ align:start position:0%
+choose teammates to run a relay race now
+when you know a rich kid who who is
+
+ align:start position:0%
+when you know a rich kid who who is
+ 
+
+ align:start position:0%
+when you know a rich kid who who is
+thinking about who
+
+ align:start position:0%
+thinking about who
+ 
+
+ align:start position:0%
+thinking about who
+who who should be in my team you can
+
+ align:start position:0%
+who who should be in my team you can
+ 
+
+ align:start position:0%
+who who should be in my team you can
+either choose like a rich kid
+
+ align:start position:0%
+either choose like a rich kid
+ 
+
+ align:start position:0%
+either choose like a rich kid
+who is kind of like similar to you and
+
+ align:start position:0%
+who is kind of like similar to you and
+ 
+
+ align:start position:0%
+who is kind of like similar to you and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in social ways or or you can choose a
+
+ align:start position:0%
+in social ways or or you can choose a
+ 
+
+ align:start position:0%
+in social ways or or you can choose a
+poor kid
+
+ align:start position:0%
+poor kid
+ 
+
+ align:start position:0%
+poor kid
+who whom you don't know very much you
+
+ align:start position:0%
+who whom you don't know very much you
+ 
+
+ align:start position:0%
+who whom you don't know very much you
+might actually not like the poor kids
+
+ align:start position:0%
+might actually not like the poor kids
+ 
+
+ align:start position:0%
+might actually not like the poor kids
+but you know the poor kid is a lot
+
+ align:start position:0%
+but you know the poor kid is a lot
+ 
+
+ align:start position:0%
+but you know the poor kid is a lot
+better in the in the running
+
+ align:start position:0%
+better in the in the running
+ 
+
+ align:start position:0%
+better in the in the running
+um so it might be like much better for
+
+ align:start position:0%
+um so it might be like much better for
+ 
+
+ align:start position:0%
+um so it might be like much better for
+you might be much more likely to win in
+
+ align:start position:0%
+you might be much more likely to win in
+ 
+
+ align:start position:0%
+you might be much more likely to win in
+the game
+
+ align:start position:0%
+the game
+ 
+
+ align:start position:0%
+the game
+because now your partner in the relay
+
+ align:start position:0%
+because now your partner in the relay
+ 
+
+ align:start position:0%
+because now your partner in the relay
+race is much faster so it's a very nice
+
+ align:start position:0%
+race is much faster so it's a very nice
+ 
+
+ align:start position:0%
+race is much faster so it's a very nice
+trade-off between ability
+
+ align:start position:0%
+trade-off between ability
+ 
+
+ align:start position:0%
+trade-off between ability
+choosing uh the fast runner versus
+
+ align:start position:0%
+choosing uh the fast runner versus
+ 
+
+ align:start position:0%
+choosing uh the fast runner versus
+social similarity
+
+ align:start position:0%
+social similarity
+ 
+
+ align:start position:0%
+social similarity
+and now what what um uh gotten then is
+
+ align:start position:0%
+and now what what um uh gotten then is
+ 
+
+ align:start position:0%
+and now what what um uh gotten then is
+doing is like he uh if you sort of
+
+ align:start position:0%
+doing is like he uh if you sort of
+ 
+
+ align:start position:0%
+doing is like he uh if you sort of
+choose the rich kid
+
+ align:start position:0%
+choose the rich kid
+ 
+
+ align:start position:0%
+choose the rich kid
+that's then a measure of discrimination
+
+ align:start position:0%
+that's then a measure of discrimination
+ 
+
+ align:start position:0%
+that's then a measure of discrimination
+because essentially
+
+ align:start position:0%
+because essentially
+ 
+
+ align:start position:0%
+because essentially
+you're choosing a worse runner um
+
+ align:start position:0%
+you're choosing a worse runner um
+ 
+
+ align:start position:0%
+you're choosing a worse runner um
+in favor of like um or because you want
+
+ align:start position:0%
+in favor of like um or because you want
+ 
+
+ align:start position:0%
+in favor of like um or because you want
+more social similarity
+
+ align:start position:0%
+more social similarity
+ 
+
+ align:start position:0%
+more social similarity
+you don't want to hang out with a poor
+
+ align:start position:0%
+you don't want to hang out with a poor
+ 
+
+ align:start position:0%
+you don't want to hang out with a poor
+kid instead you choose the rich kid
+
+ align:start position:0%
+kid instead you choose the rich kid
+ 
+
+ align:start position:0%
+kid instead you choose the rich kid
+which reduces your chances in the race
+
+ align:start position:0%
+which reduces your chances in the race
+ 
+
+ align:start position:0%
+which reduces your chances in the race
+but increases your time
+
+ align:start position:0%
+but increases your time
+ 
+
+ align:start position:0%
+but increases your time
+spent with the rich kids compared to
+
+ align:start position:0%
+spent with the rich kids compared to
+ 
+
+ align:start position:0%
+spent with the rich kids compared to
+like poor kids
+
+ align:start position:0%
+like poor kids
+ 
+
+ align:start position:0%
+like poor kids
+let me tell you a little bit more detail
+
+ align:start position:0%
+let me tell you a little bit more detail
+ 
+
+ align:start position:0%
+let me tell you a little bit more detail
+of the experiment
+
+ align:start position:0%
+of the experiment
+ 
+
+ align:start position:0%
+of the experiment
+uh stage one is randomization so it was
+
+ align:start position:0%
+uh stage one is randomization so it was
+ 
+
+ align:start position:0%
+uh stage one is randomization so it was
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the people were randomized to sessions
+
+ align:start position:0%
+the people were randomized to sessions
+ 
+
+ align:start position:0%
+the people were randomized to sessions
+with varying stakes
+
+ align:start position:0%
+with varying stakes
+ 
+
+ align:start position:0%
+with varying stakes
+there's uh 50 50 rupees 20 200 rupees
+
+ align:start position:0%
+there's uh 50 50 rupees 20 200 rupees
+ 
+
+ align:start position:0%
+there's uh 50 50 rupees 20 200 rupees
+500 rupees per
+
+ align:start position:0%
+500 rupees per
+ 
+
+ align:start position:0%
+500 rupees per
+uh student for the winning team this is
+
+ align:start position:0%
+uh student for the winning team this is
+ 
+
+ align:start position:0%
+uh student for the winning team this is
+a lot of money compared to like students
+
+ align:start position:0%
+a lot of money compared to like students
+ 
+
+ align:start position:0%
+a lot of money compared to like students
+usual pocket money right so they would
+
+ align:start position:0%
+usual pocket money right so they would
+ 
+
+ align:start position:0%
+usual pocket money right so they would
+get something like 10
+
+ align:start position:0%
+get something like 10
+ 
+
+ align:start position:0%
+get something like 10
+or 500 rupees um is like one months of
+
+ align:start position:0%
+or 500 rupees um is like one months of
+ 
+
+ align:start position:0%
+or 500 rupees um is like one months of
+uh pocket money that's like really high
+
+ align:start position:0%
+uh pocket money that's like really high
+ 
+
+ align:start position:0%
+uh pocket money that's like really high
+stakes for these kids
+
+ align:start position:0%
+stakes for these kids
+ 
+
+ align:start position:0%
+stakes for these kids
+um the price is varied essentially
+
+ align:start position:0%
+um the price is varied essentially
+ 
+
+ align:start position:0%
+um the price is varied essentially
+because it lets us like price out it
+
+ align:start position:0%
+because it lets us like price out it
+ 
+
+ align:start position:0%
+because it lets us like price out it
+gives us a price of discrimination
+
+ align:start position:0%
+gives us a price of discrimination
+ 
+
+ align:start position:0%
+gives us a price of discrimination
+lets us understand how much are students
+
+ align:start position:0%
+lets us understand how much are students
+ 
+
+ align:start position:0%
+lets us understand how much are students
+willing to give up in order
+
+ align:start position:0%
+willing to give up in order
+ 
+
+ align:start position:0%
+willing to give up in order
+um uh to not have to um or
+
+ align:start position:0%
+um uh to not have to um or
+ 
+
+ align:start position:0%
+um uh to not have to um or
+in order to uh be able to socialize with
+
+ align:start position:0%
+in order to uh be able to socialize with
+ 
+
+ align:start position:0%
+in order to uh be able to socialize with
+the rich kids compared to a poor kid
+
+ align:start position:0%
+the rich kids compared to a poor kid
+ 
+
+ align:start position:0%
+the rich kids compared to a poor kid
+there was brief mixing to start with to
+
+ align:start position:0%
+there was brief mixing to start with to
+ 
+
+ align:start position:0%
+there was brief mixing to start with to
+judge socio-economic status
+
+ align:start position:0%
+judge socio-economic status
+ 
+
+ align:start position:0%
+judge socio-economic status
+right so the kids were like allowed to
+
+ align:start position:0%
+right so the kids were like allowed to
+ 
+
+ align:start position:0%
+right so the kids were like allowed to
+mingle a little bit that would allow
+
+ align:start position:0%
+mingle a little bit that would allow
+ 
+
+ align:start position:0%
+mingle a little bit that would allow
+them to
+
+ align:start position:0%
+them to
+ 
+
+ align:start position:0%
+them to
+fairly easily understand who's a poor
+
+ align:start position:0%
+fairly easily understand who's a poor
+ 
+
+ align:start position:0%
+fairly easily understand who's a poor
+kid and who's a
+
+ align:start position:0%
+kid and who's a
+ 
+
+ align:start position:0%
+kid and who's a
+rich kid okay stage number two was
+
+ align:start position:0%
+rich kid okay stage number two was
+ 
+
+ align:start position:0%
+rich kid okay stage number two was
+ability revelation and team selection so
+
+ align:start position:0%
+ability revelation and team selection so
+ 
+
+ align:start position:0%
+ability revelation and team selection so
+you could essentially observe a
+
+ align:start position:0%
+you could essentially observe a
+ 
+
+ align:start position:0%
+you could essentially observe a
+two-person race
+
+ align:start position:0%
+two-person race
+ 
+
+ align:start position:0%
+two-person race
+usually it's one poor and one rich
+
+ align:start position:0%
+usually it's one poor and one rich
+ 
+
+ align:start position:0%
+usually it's one poor and one rich
+students neither is from their own
+
+ align:start position:0%
+students neither is from their own
+ 
+
+ align:start position:0%
+students neither is from their own
+schools so these are not
+
+ align:start position:0%
+schools so these are not
+ 
+
+ align:start position:0%
+schools so these are not
+students that you would know from school
+
+ align:start position:0%
+students that you would know from school
+ 
+
+ align:start position:0%
+students that you would know from school
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+but the uniforms make the school
+
+ align:start position:0%
+but the uniforms make the school
+ 
+
+ align:start position:0%
+but the uniforms make the school
+identifiable do you kind of know who's
+
+ align:start position:0%
+identifiable do you kind of know who's
+ 
+
+ align:start position:0%
+identifiable do you kind of know who's
+the rich kid and who's the poor kid
+
+ align:start position:0%
+the rich kid and who's the poor kid
+ 
+
+ align:start position:0%
+the rich kid and who's the poor kid
+now then you can pick which of these two
+
+ align:start position:0%
+now then you can pick which of these two
+ 
+
+ align:start position:0%
+now then you can pick which of these two
+runners you want to have as your
+
+ align:start position:0%
+runners you want to have as your
+ 
+
+ align:start position:0%
+runners you want to have as your
+partners
+
+ align:start position:0%
+partners
+ 
+
+ align:start position:0%
+partners
+so that is to say you see them run
+
+ align:start position:0%
+so that is to say you see them run
+ 
+
+ align:start position:0%
+so that is to say you see them run
+one by one it's very easy to see like
+
+ align:start position:0%
+one by one it's very easy to see like
+ 
+
+ align:start position:0%
+one by one it's very easy to see like
+who's faster and who's not
+
+ align:start position:0%
+who's faster and who's not
+ 
+
+ align:start position:0%
+who's faster and who's not
+and so again discrimination here is um
+
+ align:start position:0%
+and so again discrimination here is um
+ 
+
+ align:start position:0%
+and so again discrimination here is um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+interpreted as like picking the slow
+
+ align:start position:0%
+interpreted as like picking the slow
+ 
+
+ align:start position:0%
+interpreted as like picking the slow
+runner so if you pick the slower runner
+
+ align:start position:0%
+runner so if you pick the slower runner
+ 
+
+ align:start position:0%
+runner so if you pick the slower runner
+and then it must be because you like
+
+ align:start position:0%
+and then it must be because you like
+ 
+
+ align:start position:0%
+and then it must be because you like
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+some other characteristics about that
+
+ align:start position:0%
+some other characteristics about that
+ 
+
+ align:start position:0%
+some other characteristics about that
+person more the obvious characteristic
+
+ align:start position:0%
+person more the obvious characteristic
+ 
+
+ align:start position:0%
+person more the obvious characteristic
+here is that
+
+ align:start position:0%
+here is that
+ 
+
+ align:start position:0%
+here is that
+it's most likely going to be that kid is
+
+ align:start position:0%
+it's most likely going to be that kid is
+ 
+
+ align:start position:0%
+it's most likely going to be that kid is
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+okay then um uh
+
+ align:start position:0%
+okay then um uh
+ 
+
+ align:start position:0%
+okay then um uh
+stages three and four are on the choice
+
+ align:start position:0%
+stages three and four are on the choice
+ 
+
+ align:start position:0%
+stages three and four are on the choice
+implementation
+
+ align:start position:0%
+implementation
+ 
+
+ align:start position:0%
+implementation
+relay race so students are randomly
+
+ align:start position:0%
+relay race so students are randomly
+ 
+
+ align:start position:0%
+relay race so students are randomly
+picked to have their choices implemented
+
+ align:start position:0%
+picked to have their choices implemented
+ 
+
+ align:start position:0%
+picked to have their choices implemented
+so some of those choices
+
+ align:start position:0%
+so some of those choices
+ 
+
+ align:start position:0%
+so some of those choices
+this is again the strategy method some
+
+ align:start position:0%
+this is again the strategy method some
+ 
+
+ align:start position:0%
+this is again the strategy method some
+of these choices were actually randomly
+
+ align:start position:0%
+of these choices were actually randomly
+ 
+
+ align:start position:0%
+of these choices were actually randomly
+implemented
+
+ align:start position:0%
+implemented
+ 
+
+ align:start position:0%
+implemented
+so there's plausible deniability for um
+
+ align:start position:0%
+so there's plausible deniability for um
+ 
+
+ align:start position:0%
+so there's plausible deniability for um
+the students in the sense of like you
+
+ align:start position:0%
+the students in the sense of like you
+ 
+
+ align:start position:0%
+the students in the sense of like you
+could just uh
+
+ align:start position:0%
+could just uh
+ 
+
+ align:start position:0%
+could just uh
+you know you could just happen to be um
+
+ align:start position:0%
+you know you could just happen to be um
+ 
+
+ align:start position:0%
+you know you could just happen to be um
+randomized or
+
+ align:start position:0%
+randomized or
+ 
+
+ align:start position:0%
+randomized or
+you you happen to pick some students
+
+ align:start position:0%
+you you happen to pick some students
+ 
+
+ align:start position:0%
+you you happen to pick some students
+versus another uh
+
+ align:start position:0%
+versus another uh
+ 
+
+ align:start position:0%
+versus another uh
+could just be by chance that you are
+
+ align:start position:0%
+could just be by chance that you are
+ 
+
+ align:start position:0%
+could just be by chance that you are
+with one student versus another
+
+ align:start position:0%
+with one student versus another
+ 
+
+ align:start position:0%
+with one student versus another
+so you couldn't you're free to choose
+
+ align:start position:0%
+so you couldn't you're free to choose
+ 
+
+ align:start position:0%
+so you couldn't you're free to choose
+essentially provides you cover sometimes
+
+ align:start position:0%
+essentially provides you cover sometimes
+ 
+
+ align:start position:0%
+essentially provides you cover sometimes
+as we discussed before
+
+ align:start position:0%
+as we discussed before
+ 
+
+ align:start position:0%
+as we discussed before
+the computer is choosing so you always
+
+ align:start position:0%
+the computer is choosing so you always
+ 
+
+ align:start position:0%
+the computer is choosing so you always
+have an excuse so it's intended
+
+ align:start position:0%
+have an excuse so it's intended
+ 
+
+ align:start position:0%
+have an excuse so it's intended
+to reveal students true preferences as
+
+ align:start position:0%
+to reveal students true preferences as
+ 
+
+ align:start position:0%
+to reveal students true preferences as
+opposed to
+
+ align:start position:0%
+opposed to
+ 
+
+ align:start position:0%
+opposed to
+perhaps what they think that their
+
+ align:start position:0%
+perhaps what they think that their
+ 
+
+ align:start position:0%
+perhaps what they think that their
+friends want them to choose or uh
+
+ align:start position:0%
+friends want them to choose or uh
+ 
+
+ align:start position:0%
+friends want them to choose or uh
+the other runners then the relay races
+
+ align:start position:0%
+the other runners then the relay races
+ 
+
+ align:start position:0%
+the other runners then the relay races
+were actually held and prices were
+
+ align:start position:0%
+were actually held and prices were
+ 
+
+ align:start position:0%
+were actually held and prices were
+distributed as promised
+
+ align:start position:0%
+distributed as promised
+ 
+
+ align:start position:0%
+distributed as promised
+number four crucially there was a social
+
+ align:start position:0%
+number four crucially there was a social
+ 
+
+ align:start position:0%
+number four crucially there was a social
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+so if you picked like your teammate you
+
+ align:start position:0%
+so if you picked like your teammate you
+ 
+
+ align:start position:0%
+so if you picked like your teammate you
+actually have to spend two hours of
+
+ align:start position:0%
+actually have to spend two hours of
+ 
+
+ align:start position:0%
+actually have to spend two hours of
+playing with a teammate
+
+ align:start position:0%
+playing with a teammate
+ 
+
+ align:start position:0%
+playing with a teammate
+board games sports playgrounds and so on
+
+ align:start position:0%
+board games sports playgrounds and so on
+ 
+
+ align:start position:0%
+board games sports playgrounds and so on
+importantly this was pre-announced
+
+ align:start position:0%
+importantly this was pre-announced
+ 
+
+ align:start position:0%
+importantly this was pre-announced
+so now again as i said before when
+
+ align:start position:0%
+so now again as i said before when
+ 
+
+ align:start position:0%
+so now again as i said before when
+picking your partner
+
+ align:start position:0%
+picking your partner
+ 
+
+ align:start position:0%
+picking your partner
+you have the choice between either
+
+ align:start position:0%
+you have the choice between either
+ 
+
+ align:start position:0%
+you have the choice between either
+picking the fast
+
+ align:start position:0%
+picking the fast
+ 
+
+ align:start position:0%
+picking the fast
+poor kid which will really increase your
+
+ align:start position:0%
+poor kid which will really increase your
+ 
+
+ align:start position:0%
+poor kid which will really increase your
+probability of winning
+
+ align:start position:0%
+probability of winning
+ 
+
+ align:start position:0%
+probability of winning
+um or the rich kid who's kind of slow
+
+ align:start position:0%
+um or the rich kid who's kind of slow
+ 
+
+ align:start position:0%
+um or the rich kid who's kind of slow
+and will reduce your uh reduce your
+
+ align:start position:0%
+and will reduce your uh reduce your
+ 
+
+ align:start position:0%
+and will reduce your uh reduce your
+probability of winning
+
+ align:start position:0%
+probability of winning
+ 
+
+ align:start position:0%
+probability of winning
+but if you pick that poor kid or the
+
+ align:start position:0%
+but if you pick that poor kid or the
+ 
+
+ align:start position:0%
+but if you pick that poor kid or the
+rich kid you have to actually spend
+
+ align:start position:0%
+rich kid you have to actually spend
+ 
+
+ align:start position:0%
+rich kid you have to actually spend
+two hours with that teammate playing
+
+ align:start position:0%
+two hours with that teammate playing
+ 
+
+ align:start position:0%
+two hours with that teammate playing
+board game sports playground and so on
+
+ align:start position:0%
+board game sports playground and so on
+ 
+
+ align:start position:0%
+board game sports playground and so on
+and you might not want to do that with a
+
+ align:start position:0%
+and you might not want to do that with a
+ 
+
+ align:start position:0%
+and you might not want to do that with a
+poor kit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now first you know what is
+
+ align:start position:0%
+okay so now first you know what is
+ 
+
+ align:start position:0%
+okay so now first you know what is
+demand for um
+
+ align:start position:0%
+demand for um
+ 
+
+ align:start position:0%
+demand for um
+discrimination you can look at this
+
+ align:start position:0%
+discrimination you can look at this
+ 
+
+ align:start position:0%
+discrimination you can look at this
+graph it shows very nicely
+
+ align:start position:0%
+graph it shows very nicely
+ 
+
+ align:start position:0%
+graph it shows very nicely
+for the different prices as i said 500
+
+ align:start position:0%
+for the different prices as i said 500
+ 
+
+ align:start position:0%
+for the different prices as i said 500
+rupees for winning the rice
+
+ align:start position:0%
+rupees for winning the rice
+ 
+
+ align:start position:0%
+rupees for winning the rice
+200 rupees or 500 rupees if you look at
+
+ align:start position:0%
+200 rupees or 500 rupees if you look at
+ 
+
+ align:start position:0%
+200 rupees or 500 rupees if you look at
+500 rupees this is again one month of
+
+ align:start position:0%
+500 rupees this is again one month of
+ 
+
+ align:start position:0%
+500 rupees this is again one month of
+pocket money
+
+ align:start position:0%
+pocket money
+ 
+
+ align:start position:0%
+pocket money
+there's no difference between treated
+
+ align:start position:0%
+there's no difference between treated
+ 
+
+ align:start position:0%
+there's no difference between treated
+and untreated classrooms
+
+ align:start position:0%
+and untreated classrooms
+ 
+
+ align:start position:0%
+and untreated classrooms
+that is to say so there's ten percent of
+
+ align:start position:0%
+that is to say so there's ten percent of
+ 
+
+ align:start position:0%
+that is to say so there's ten percent of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+are um as you want discriminating the
+
+ align:start position:0%
+are um as you want discriminating the
+ 
+
+ align:start position:0%
+are um as you want discriminating the
+poor so ten percent or sorry
+
+ align:start position:0%
+poor so ten percent or sorry
+ 
+
+ align:start position:0%
+poor so ten percent or sorry
+this is less than ten percent is about
+
+ align:start position:0%
+this is less than ten percent is about
+ 
+
+ align:start position:0%
+this is less than ten percent is about
+um seven eight percent of students
+
+ align:start position:0%
+um seven eight percent of students
+ 
+
+ align:start position:0%
+um seven eight percent of students
+um pick the rich kids um even in the
+
+ align:start position:0%
+um pick the rich kids um even in the
+ 
+
+ align:start position:0%
+um pick the rich kids um even in the
+really really high stakes
+
+ align:start position:0%
+really really high stakes
+ 
+
+ align:start position:0%
+really really high stakes
+race that is to say when the stakes are
+
+ align:start position:0%
+race that is to say when the stakes are
+ 
+
+ align:start position:0%
+race that is to say when the stakes are
+500 rupees
+
+ align:start position:0%
+500 rupees
+ 
+
+ align:start position:0%
+500 rupees
+they're like about six seven eight
+
+ align:start position:0%
+they're like about six seven eight
+ 
+
+ align:start position:0%
+they're like about six seven eight
+percent of students
+
+ align:start position:0%
+percent of students
+ 
+
+ align:start position:0%
+percent of students
+who still pick the rich kid um and they
+
+ align:start position:0%
+who still pick the rich kid um and they
+ 
+
+ align:start position:0%
+who still pick the rich kid um and they
+sort of take into account
+
+ align:start position:0%
+sort of take into account
+ 
+
+ align:start position:0%
+sort of take into account
+the the um uh the chance that they that
+
+ align:start position:0%
+the the um uh the chance that they that
+ 
+
+ align:start position:0%
+the the um uh the chance that they that
+that might lose them the raise
+
+ align:start position:0%
+that might lose them the raise
+ 
+
+ align:start position:0%
+that might lose them the raise
+but um you know they don't have to spend
+
+ align:start position:0%
+but um you know they don't have to spend
+ 
+
+ align:start position:0%
+but um you know they don't have to spend
+two hours um
+
+ align:start position:0%
+two hours um
+ 
+
+ align:start position:0%
+two hours um
+uh with a poor kid than socializing now
+
+ align:start position:0%
+uh with a poor kid than socializing now
+ 
+
+ align:start position:0%
+uh with a poor kid than socializing now
+when you look at the lower prices
+
+ align:start position:0%
+when you look at the lower prices
+ 
+
+ align:start position:0%
+when you look at the lower prices
+the fraction as you expect this is the
+
+ align:start position:0%
+the fraction as you expect this is the
+ 
+
+ align:start position:0%
+the fraction as you expect this is the
+red line um
+
+ align:start position:0%
+red line um
+ 
+
+ align:start position:0%
+red line um
+sorry this is the green line the upper
+
+ align:start position:0%
+sorry this is the green line the upper
+ 
+
+ align:start position:0%
+sorry this is the green line the upper
+line the fraction would choose
+
+ align:start position:0%
+line the fraction would choose
+ 
+
+ align:start position:0%
+line the fraction would choose
+the rich kids the fraction who are
+
+ align:start position:0%
+the rich kids the fraction who are
+ 
+
+ align:start position:0%
+the rich kids the fraction who are
+discriminating against the poor
+
+ align:start position:0%
+discriminating against the poor
+ 
+
+ align:start position:0%
+discriminating against the poor
+increases
+
+ align:start position:0%
+increases
+ 
+
+ align:start position:0%
+increases
+as you expect so now it becomes cheaper
+
+ align:start position:0%
+as you expect so now it becomes cheaper
+ 
+
+ align:start position:0%
+as you expect so now it becomes cheaper
+it's only like the race is only 200
+
+ align:start position:0%
+it's only like the race is only 200
+ 
+
+ align:start position:0%
+it's only like the race is only 200
+rupees or 50 rupees
+
+ align:start position:0%
+rupees or 50 rupees
+ 
+
+ align:start position:0%
+rupees or 50 rupees
+you might be more inclined to pick the
+
+ align:start position:0%
+you might be more inclined to pick the
+ 
+
+ align:start position:0%
+you might be more inclined to pick the
+rich kid because you know the value of
+
+ align:start position:0%
+rich kid because you know the value of
+ 
+
+ align:start position:0%
+rich kid because you know the value of
+socializing stays the same
+
+ align:start position:0%
+socializing stays the same
+ 
+
+ align:start position:0%
+socializing stays the same
+but the cost of picking the regicate the
+
+ align:start position:0%
+but the cost of picking the regicate the
+ 
+
+ align:start position:0%
+but the cost of picking the regicate the
+cost of losing the race
+
+ align:start position:0%
+cost of losing the race
+ 
+
+ align:start position:0%
+cost of losing the race
+potentially at least is reduced right
+
+ align:start position:0%
+potentially at least is reduced right
+ 
+
+ align:start position:0%
+potentially at least is reduced right
+the and sort of if you look at 50 rupees
+
+ align:start position:0%
+the and sort of if you look at 50 rupees
+ 
+
+ align:start position:0%
+the and sort of if you look at 50 rupees
+the price 50 rupees um for the game
+
+ align:start position:0%
+the price 50 rupees um for the game
+ 
+
+ align:start position:0%
+the price 50 rupees um for the game
+for the relay race uh uh that's um
+
+ align:start position:0%
+for the relay race uh uh that's um
+ 
+
+ align:start position:0%
+for the relay race uh uh that's um
+about almost like 40 percent of students
+
+ align:start position:0%
+about almost like 40 percent of students
+ 
+
+ align:start position:0%
+about almost like 40 percent of students
+now pick the rich kid
+
+ align:start position:0%
+now pick the rich kid
+ 
+
+ align:start position:0%
+now pick the rich kid
+even though that might lose them the
+
+ align:start position:0%
+even though that might lose them the
+ 
+
+ align:start position:0%
+even though that might lose them the
+race and now crucially
+
+ align:start position:0%
+race and now crucially
+ 
+
+ align:start position:0%
+race and now crucially
+in red this is the dashed line below you
+
+ align:start position:0%
+in red this is the dashed line below you
+ 
+
+ align:start position:0%
+in red this is the dashed line below you
+can see the treated classrooms
+
+ align:start position:0%
+can see the treated classrooms
+ 
+
+ align:start position:0%
+can see the treated classrooms
+and what he finds is that for 500 rupees
+
+ align:start position:0%
+and what he finds is that for 500 rupees
+ 
+
+ align:start position:0%
+and what he finds is that for 500 rupees
+when the stakes are really really high
+
+ align:start position:0%
+when the stakes are really really high
+ 
+
+ align:start position:0%
+when the stakes are really really high
+there's no effect essentially it doesn't
+
+ align:start position:0%
+there's no effect essentially it doesn't
+ 
+
+ align:start position:0%
+there's no effect essentially it doesn't
+really matter whether you're in a
+
+ align:start position:0%
+really matter whether you're in a
+ 
+
+ align:start position:0%
+really matter whether you're in a
+treated or
+
+ align:start position:0%
+treated or
+ 
+
+ align:start position:0%
+treated or
+non-treated classroom in part perhaps
+
+ align:start position:0%
+non-treated classroom in part perhaps
+ 
+
+ align:start position:0%
+non-treated classroom in part perhaps
+because there's not much room for
+
+ align:start position:0%
+because there's not much room for
+ 
+
+ align:start position:0%
+because there's not much room for
+going lower than that so essentially
+
+ align:start position:0%
+going lower than that so essentially
+ 
+
+ align:start position:0%
+going lower than that so essentially
+there's no effect on
+
+ align:start position:0%
+there's no effect on
+ 
+
+ align:start position:0%
+there's no effect on
+on there because you know the stakes are
+
+ align:start position:0%
+on there because you know the stakes are
+ 
+
+ align:start position:0%
+on there because you know the stakes are
+really really high anyway there's not
+
+ align:start position:0%
+really really high anyway there's not
+ 
+
+ align:start position:0%
+really really high anyway there's not
+much discrimination
+
+ align:start position:0%
+much discrimination
+ 
+
+ align:start position:0%
+much discrimination
+and having had a treated class having
+
+ align:start position:0%
+and having had a treated class having
+ 
+
+ align:start position:0%
+and having had a treated class having
+had a poor kid in your classroom doesn't
+
+ align:start position:0%
+had a poor kid in your classroom doesn't
+ 
+
+ align:start position:0%
+had a poor kid in your classroom doesn't
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+change that but then very clearly for
+
+ align:start position:0%
+change that but then very clearly for
+ 
+
+ align:start position:0%
+change that but then very clearly for
+200 rupees and 50 rupees the lower
+
+ align:start position:0%
+200 rupees and 50 rupees the lower
+ 
+
+ align:start position:0%
+200 rupees and 50 rupees the lower
+stakes there's a clear difference
+
+ align:start position:0%
+stakes there's a clear difference
+ 
+
+ align:start position:0%
+stakes there's a clear difference
+between the green and the red lines that
+
+ align:start position:0%
+between the green and the red lines that
+ 
+
+ align:start position:0%
+between the green and the red lines that
+is to say there's a lot less
+
+ align:start position:0%
+is to say there's a lot less
+ 
+
+ align:start position:0%
+is to say there's a lot less
+discrimination
+
+ align:start position:0%
+discrimination
+ 
+
+ align:start position:0%
+discrimination
+towards the poor kids poor kids a lot
+
+ align:start position:0%
+towards the poor kids poor kids a lot
+ 
+
+ align:start position:0%
+towards the poor kids poor kids a lot
+more likely to be chosen
+
+ align:start position:0%
+more likely to be chosen
+ 
+
+ align:start position:0%
+more likely to be chosen
+when a student had in treated classrooms
+
+ align:start position:0%
+when a student had in treated classrooms
+ 
+
+ align:start position:0%
+when a student had in treated classrooms
+when somebody had a poor kid another
+
+ align:start position:0%
+when somebody had a poor kid another
+ 
+
+ align:start position:0%
+when somebody had a poor kid another
+poor kid
+
+ align:start position:0%
+poor kid
+ 
+
+ align:start position:0%
+poor kid
+in their classroom for several years so
+
+ align:start position:0%
+in their classroom for several years so
+ 
+
+ align:start position:0%
+in their classroom for several years so
+that's to say
+
+ align:start position:0%
+that's to say
+ 
+
+ align:start position:0%
+that's to say
+there's being exposed to these poor
+
+ align:start position:0%
+there's being exposed to these poor
+ 
+
+ align:start position:0%
+there's being exposed to these poor
+children reduces discrimination
+
+ align:start position:0%
+children reduces discrimination
+ 
+
+ align:start position:0%
+children reduces discrimination
+among the poor among the rich students
+
+ align:start position:0%
+among the poor among the rich students
+ 
+
+ align:start position:0%
+among the poor among the rich students
+uh subsequently
+
+ align:start position:0%
+uh subsequently
+ 
+
+ align:start position:0%
+uh subsequently
+um this is the sort of the same graph
+
+ align:start position:0%
+um this is the sort of the same graph
+ 
+
+ align:start position:0%
+um this is the sort of the same graph
+that i showed you before
+
+ align:start position:0%
+that i showed you before
+ 
+
+ align:start position:0%
+that i showed you before
+again that's sort of consistent with
+
+ align:start position:0%
+again that's sort of consistent with
+ 
+
+ align:start position:0%
+again that's sort of consistent with
+what we have before it gets a little
+
+ align:start position:0%
+what we have before it gets a little
+ 
+
+ align:start position:0%
+what we have before it gets a little
+messier than we had seen previously
+
+ align:start position:0%
+messier than we had seen previously
+ 
+
+ align:start position:0%
+messier than we had seen previously
+but similarly even within classrooms uh
+
+ align:start position:0%
+but similarly even within classrooms uh
+ 
+
+ align:start position:0%
+but similarly even within classrooms uh
+if you look at like grades two and three
+
+ align:start position:0%
+if you look at like grades two and three
+ 
+
+ align:start position:0%
+if you look at like grades two and three
+versus four and five
+
+ align:start position:0%
+versus four and five
+ 
+
+ align:start position:0%
+versus four and five
+uh uh the effects seem to be uh
+
+ align:start position:0%
+uh uh the effects seem to be uh
+ 
+
+ align:start position:0%
+uh uh the effects seem to be uh
+concentrated more pronouns
+
+ align:start position:0%
+concentrated more pronouns
+ 
+
+ align:start position:0%
+concentrated more pronouns
+in grades uh two and three
+
+ align:start position:0%
+in grades uh two and three
+ 
+
+ align:start position:0%
+in grades uh two and three
+now finally as i said we
+
+ align:start position:0%
+now finally as i said we
+ 
+
+ align:start position:0%
+now finally as i said we
+we look at test scores and discipline so
+
+ align:start position:0%
+we look at test scores and discipline so
+ 
+
+ align:start position:0%
+we look at test scores and discipline so
+arguably there are some positive effects
+
+ align:start position:0%
+arguably there are some positive effects
+ 
+
+ align:start position:0%
+arguably there are some positive effects
+on social preferences and
+
+ align:start position:0%
+on social preferences and
+ 
+
+ align:start position:0%
+on social preferences and
+as i said before the policy question now
+
+ align:start position:0%
+as i said before the policy question now
+ 
+
+ align:start position:0%
+as i said before the policy question now
+is does that come
+
+ align:start position:0%
+is does that come
+ 
+
+ align:start position:0%
+is does that come
+at the cost of academic achievement in
+
+ align:start position:0%
+at the cost of academic achievement in
+ 
+
+ align:start position:0%
+at the cost of academic achievement in
+some ways so is it that your rich kid
+
+ align:start position:0%
+some ways so is it that your rich kid
+ 
+
+ align:start position:0%
+some ways so is it that your rich kid
+now by being exposed to the poor kids
+
+ align:start position:0%
+now by being exposed to the poor kids
+ 
+
+ align:start position:0%
+now by being exposed to the poor kids
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+somewhat nicer and more friendly and
+
+ align:start position:0%
+somewhat nicer and more friendly and
+ 
+
+ align:start position:0%
+somewhat nicer and more friendly and
+less discriminating against the poor
+
+ align:start position:0%
+less discriminating against the poor
+ 
+
+ align:start position:0%
+less discriminating against the poor
+um that's all and good but is it the
+
+ align:start position:0%
+um that's all and good but is it the
+ 
+
+ align:start position:0%
+um that's all and good but is it the
+case now that cloud that um
+
+ align:start position:0%
+case now that cloud that um
+ 
+
+ align:start position:0%
+case now that cloud that um
+test scores go down so gautam finds no
+
+ align:start position:0%
+test scores go down so gautam finds no
+ 
+
+ align:start position:0%
+test scores go down so gautam finds no
+effect on aggregate
+
+ align:start position:0%
+effect on aggregate
+ 
+
+ align:start position:0%
+effect on aggregate
+uh an aggregate test score index there's
+
+ align:start position:0%
+uh an aggregate test score index there's
+ 
+
+ align:start position:0%
+uh an aggregate test score index there's
+zero effects on hindi and math
+
+ align:start position:0%
+zero effects on hindi and math
+ 
+
+ align:start position:0%
+zero effects on hindi and math
+there's a little bit of like um
+
+ align:start position:0%
+there's a little bit of like um
+ 
+
+ align:start position:0%
+there's a little bit of like um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a reduction in english scores of 0.09
+
+ align:start position:0%
+a reduction in english scores of 0.09
+ 
+
+ align:start position:0%
+a reduction in english scores of 0.09
+standard deviations that's marginally
+
+ align:start position:0%
+standard deviations that's marginally
+ 
+
+ align:start position:0%
+standard deviations that's marginally
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+you know that's suggestive but not
+
+ align:start position:0%
+you know that's suggestive but not
+ 
+
+ align:start position:0%
+you know that's suggestive but not
+perhaps
+
+ align:start position:0%
+perhaps
+ 
+
+ align:start position:0%
+perhaps
+particularly large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these effects are not not not
+
+ align:start position:0%
+so these effects are not not not
+ 
+
+ align:start position:0%
+so these effects are not not not
+particularly large in particular in
+
+ align:start position:0%
+particularly large in particular in
+ 
+
+ align:start position:0%
+particularly large in particular in
+aggregate so if you aggregate everything
+
+ align:start position:0%
+aggregate so if you aggregate everything
+ 
+
+ align:start position:0%
+aggregate so if you aggregate everything
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+there don't seem to be any uh
+
+ align:start position:0%
+there don't seem to be any uh
+ 
+
+ align:start position:0%
+there don't seem to be any uh
+significant effects
+
+ align:start position:0%
+significant effects
+ 
+
+ align:start position:0%
+significant effects
+so perhaps the english scores are
+
+ align:start position:0%
+so perhaps the english scores are
+ 
+
+ align:start position:0%
+so perhaps the english scores are
+suggestive
+
+ align:start position:0%
+suggestive
+ 
+
+ align:start position:0%
+suggestive
+but sort of not particularly large there
+
+ align:start position:0%
+but sort of not particularly large there
+ 
+
+ align:start position:0%
+but sort of not particularly large there
+are some mild effects on discipline
+
+ align:start position:0%
+are some mild effects on discipline
+ 
+
+ align:start position:0%
+are some mild effects on discipline
+interestingly there's an increase in
+
+ align:start position:0%
+interestingly there's an increase in
+ 
+
+ align:start position:0%
+interestingly there's an increase in
+swearing you think that's good or bad
+
+ align:start position:0%
+swearing you think that's good or bad
+ 
+
+ align:start position:0%
+swearing you think that's good or bad
+you can think about that um but sort of
+
+ align:start position:0%
+you can think about that um but sort of
+ 
+
+ align:start position:0%
+you can think about that um but sort of
+there seems to be a little bit of effect
+
+ align:start position:0%
+there seems to be a little bit of effect
+ 
+
+ align:start position:0%
+there seems to be a little bit of effect
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+like in terms of like language uses use
+
+ align:start position:0%
+like in terms of like language uses use
+ 
+
+ align:start position:0%
+like in terms of like language uses use
+usage
+
+ align:start position:0%
+usage
+ 
+
+ align:start position:0%
+usage
+uh there's no effects on violent and
+
+ align:start position:0%
+uh there's no effects on violent and
+ 
+
+ align:start position:0%
+uh there's no effects on violent and
+disruptive behavior which you might
+
+ align:start position:0%
+disruptive behavior which you might
+ 
+
+ align:start position:0%
+disruptive behavior which you might
+think is like
+
+ align:start position:0%
+think is like
+ 
+
+ align:start position:0%
+think is like
+a lot more damaging potentially
+
+ align:start position:0%
+a lot more damaging potentially
+ 
+
+ align:start position:0%
+a lot more damaging potentially
+okay so just summarizing what does the
+
+ align:start position:0%
+okay so just summarizing what does the
+ 
+
+ align:start position:0%
+okay so just summarizing what does the
+paper find well having
+
+ align:start position:0%
+paper find well having
+ 
+
+ align:start position:0%
+paper find well having
+poor classmates makes wealthy students
+
+ align:start position:0%
+poor classmates makes wealthy students
+ 
+
+ align:start position:0%
+poor classmates makes wealthy students
+more pro-social and generous
+
+ align:start position:0%
+more pro-social and generous
+ 
+
+ align:start position:0%
+more pro-social and generous
+they're more likely to volunteer for
+
+ align:start position:0%
+they're more likely to volunteer for
+ 
+
+ align:start position:0%
+they're more likely to volunteer for
+charities
+
+ align:start position:0%
+charities
+ 
+
+ align:start position:0%
+charities
+i didn't show you that evidence but
+
+ align:start position:0%
+i didn't show you that evidence but
+ 
+
+ align:start position:0%
+i didn't show you that evidence but
+that's another piece of evidence that he
+
+ align:start position:0%
+that's another piece of evidence that he
+ 
+
+ align:start position:0%
+that's another piece of evidence that he
+finds
+
+ align:start position:0%
+finds
+ 
+
+ align:start position:0%
+finds
+they're more likely to give in money and
+
+ align:start position:0%
+they're more likely to give in money and
+ 
+
+ align:start position:0%
+they're more likely to give in money and
+dictator games to give more
+
+ align:start position:0%
+dictator games to give more
+ 
+
+ align:start position:0%
+dictator games to give more
+higher fractions of their shared in
+
+ align:start position:0%
+higher fractions of their shared in
+ 
+
+ align:start position:0%
+higher fractions of their shared in
+dictator games
+
+ align:start position:0%
+dictator games
+ 
+
+ align:start position:0%
+dictator games
+they also choose more equitable
+
+ align:start position:0%
+they also choose more equitable
+ 
+
+ align:start position:0%
+they also choose more equitable
+outcomes and sort of disinterested
+
+ align:start position:0%
+outcomes and sort of disinterested
+ 
+
+ align:start position:0%
+outcomes and sort of disinterested
+third-party games where essentially you
+
+ align:start position:0%
+third-party games where essentially you
+ 
+
+ align:start position:0%
+third-party games where essentially you
+choose between two other
+
+ align:start position:0%
+choose between two other
+ 
+
+ align:start position:0%
+choose between two other
+students and their allocation so it's
+
+ align:start position:0%
+students and their allocation so it's
+ 
+
+ align:start position:0%
+students and their allocation so it's
+not just that they're more
+
+ align:start position:0%
+not just that they're more
+ 
+
+ align:start position:0%
+not just that they're more
+likely to willing to give up money that
+
+ align:start position:0%
+likely to willing to give up money that
+ 
+
+ align:start position:0%
+likely to willing to give up money that
+others get but also they're more likely
+
+ align:start position:0%
+others get but also they're more likely
+ 
+
+ align:start position:0%
+others get but also they're more likely
+to choose equal allocations
+
+ align:start position:0%
+to choose equal allocations
+ 
+
+ align:start position:0%
+to choose equal allocations
+in third-party games and disinterested
+
+ align:start position:0%
+in third-party games and disinterested
+ 
+
+ align:start position:0%
+in third-party games and disinterested
+games again i didn't show you that
+
+ align:start position:0%
+games again i didn't show you that
+ 
+
+ align:start position:0%
+games again i didn't show you that
+evidence but it seems to be
+
+ align:start position:0%
+evidence but it seems to be
+ 
+
+ align:start position:0%
+evidence but it seems to be
+that what's increasing here is sort of
+
+ align:start position:0%
+that what's increasing here is sort of
+ 
+
+ align:start position:0%
+that what's increasing here is sort of
+like inequality aversion
+
+ align:start position:0%
+like inequality aversion
+ 
+
+ align:start position:0%
+like inequality aversion
+um and these sort of disinterested um uh
+
+ align:start position:0%
+um and these sort of disinterested um uh
+ 
+
+ align:start position:0%
+um and these sort of disinterested um uh
+uh uh dictator or other types of games
+
+ align:start position:0%
+uh uh dictator or other types of games
+ 
+
+ align:start position:0%
+uh uh dictator or other types of games
+where essentially um these students by
+
+ align:start position:0%
+where essentially um these students by
+ 
+
+ align:start position:0%
+where essentially um these students by
+being exposed to poor kids
+
+ align:start position:0%
+being exposed to poor kids
+ 
+
+ align:start position:0%
+being exposed to poor kids
+are now more averse against
+
+ align:start position:0%
+are now more averse against
+ 
+
+ align:start position:0%
+are now more averse against
+unequal outcomes in these types of games
+
+ align:start position:0%
+unequal outcomes in these types of games
+ 
+
+ align:start position:0%
+unequal outcomes in these types of games
+second there is like less discrimination
+
+ align:start position:0%
+second there is like less discrimination
+ 
+
+ align:start position:0%
+second there is like less discrimination
+and more higher willingness to socialize
+
+ align:start position:0%
+and more higher willingness to socialize
+ 
+
+ align:start position:0%
+and more higher willingness to socialize
+with the poor
+
+ align:start position:0%
+with the poor
+ 
+
+ align:start position:0%
+with the poor
+they're more likely to choose poor
+
+ align:start position:0%
+they're more likely to choose poor
+ 
+
+ align:start position:0%
+they're more likely to choose poor
+teammates
+
+ align:start position:0%
+teammates
+ 
+
+ align:start position:0%
+teammates
+in sports contests they're also more
+
+ align:start position:0%
+in sports contests they're also more
+ 
+
+ align:start position:0%
+in sports contests they're also more
+willing to attend play dates with poor
+
+ align:start position:0%
+willing to attend play dates with poor
+ 
+
+ align:start position:0%
+willing to attend play dates with poor
+children again i didn't
+
+ align:start position:0%
+children again i didn't
+ 
+
+ align:start position:0%
+children again i didn't
+show you that evidence and then there's
+
+ align:start position:0%
+show you that evidence and then there's
+ 
+
+ align:start position:0%
+show you that evidence and then there's
+like some small negative effects on
+
+ align:start position:0%
+like some small negative effects on
+ 
+
+ align:start position:0%
+like some small negative effects on
+academic
+
+ align:start position:0%
+academic
+ 
+
+ align:start position:0%
+academic
+outcomes that i think are mostly
+
+ align:start position:0%
+outcomes that i think are mostly
+ 
+
+ align:start position:0%
+outcomes that i think are mostly
+negligible
+
+ align:start position:0%
+negligible
+ 
+
+ align:start position:0%
+negligible
+now there's an other work on the contact
+
+ align:start position:0%
+now there's an other work on the contact
+ 
+
+ align:start position:0%
+now there's an other work on the contact
+hypothesis which i showed you so the
+
+ align:start position:0%
+hypothesis which i showed you so the
+ 
+
+ align:start position:0%
+hypothesis which i showed you so the
+contact what is the contact hypothesis
+
+ align:start position:0%
+contact what is the contact hypothesis
+ 
+
+ align:start position:0%
+contact what is the contact hypothesis
+the contact hypothesis is from uh goes
+
+ align:start position:0%
+the contact hypothesis is from uh goes
+ 
+
+ align:start position:0%
+the contact hypothesis is from uh goes
+back to at least
+
+ align:start position:0%
+back to at least
+ 
+
+ align:start position:0%
+back to at least
+alport in 1954 which is the idea that
+
+ align:start position:0%
+alport in 1954 which is the idea that
+ 
+
+ align:start position:0%
+alport in 1954 which is the idea that
+interpersonal contacts reduces prejudice
+
+ align:start position:0%
+interpersonal contacts reduces prejudice
+ 
+
+ align:start position:0%
+interpersonal contacts reduces prejudice
+until certain conditions and not just
+
+ align:start position:0%
+until certain conditions and not just
+ 
+
+ align:start position:0%
+until certain conditions and not just
+prejudice but also
+
+ align:start position:0%
+prejudice but also
+ 
+
+ align:start position:0%
+prejudice but also
+changes attitudes and social preferences
+
+ align:start position:0%
+changes attitudes and social preferences
+ 
+
+ align:start position:0%
+changes attitudes and social preferences
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+so matt lowe who is a phd student here
+
+ align:start position:0%
+so matt lowe who is a phd student here
+ 
+
+ align:start position:0%
+so matt lowe who is a phd student here
+at mit has a very nice paper that looks
+
+ align:start position:0%
+at mit has a very nice paper that looks
+ 
+
+ align:start position:0%
+at mit has a very nice paper that looks
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+cricket tournaments and asks the
+
+ align:start position:0%
+cricket tournaments and asks the
+ 
+
+ align:start position:0%
+cricket tournaments and asks the
+question whether cricket leagues in
+
+ align:start position:0%
+question whether cricket leagues in
+ 
+
+ align:start position:0%
+question whether cricket leagues in
+india
+
+ align:start position:0%
+india
+ 
+
+ align:start position:0%
+india
+can increase cross-cast interaction and
+
+ align:start position:0%
+can increase cross-cast interaction and
+ 
+
+ align:start position:0%
+can increase cross-cast interaction and
+pro-sociality so what he does is he
+
+ align:start position:0%
+pro-sociality so what he does is he
+ 
+
+ align:start position:0%
+pro-sociality so what he does is he
+randomizes
+
+ align:start position:0%
+randomizes
+ 
+
+ align:start position:0%
+randomizes
+uh essentially cricket leaks and teams
+
+ align:start position:0%
+uh essentially cricket leaks and teams
+ 
+
+ align:start position:0%
+uh essentially cricket leaks and teams
+and cricket leaks
+
+ align:start position:0%
+and cricket leaks
+ 
+
+ align:start position:0%
+and cricket leaks
+where people across different casts are
+
+ align:start position:0%
+where people across different casts are
+ 
+
+ align:start position:0%
+where people across different casts are
+now more or less likely to play with
+
+ align:start position:0%
+now more or less likely to play with
+ 
+
+ align:start position:0%
+now more or less likely to play with
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+both in terms of like um he varies or
+
+ align:start position:0%
+both in terms of like um he varies or
+ 
+
+ align:start position:0%
+both in terms of like um he varies or
+there's variation in the study
+
+ align:start position:0%
+there's variation in the study
+ 
+
+ align:start position:0%
+there's variation in the study
+within teams so are you more or less
+
+ align:start position:0%
+within teams so are you more or less
+ 
+
+ align:start position:0%
+within teams so are you more or less
+likely to have
+
+ align:start position:0%
+likely to have
+ 
+
+ align:start position:0%
+likely to have
+a or people some people are more or less
+
+ align:start position:0%
+a or people some people are more or less
+ 
+
+ align:start position:0%
+a or people some people are more or less
+likely to have a
+
+ align:start position:0%
+likely to have a
+ 
+
+ align:start position:0%
+likely to have a
+lower higher caste a person from a
+
+ align:start position:0%
+lower higher caste a person from a
+ 
+
+ align:start position:0%
+lower higher caste a person from a
+different cast
+
+ align:start position:0%
+different cast
+ 
+
+ align:start position:0%
+different cast
+in their team and he has um variation in
+
+ align:start position:0%
+in their team and he has um variation in
+ 
+
+ align:start position:0%
+in their team and he has um variation in
+what he calls
+
+ align:start position:0%
+what he calls
+ 
+
+ align:start position:0%
+what he calls
+adversarial contact which is like
+
+ align:start position:0%
+adversarial contact which is like
+ 
+
+ align:start position:0%
+adversarial contact which is like
+they're more or less likely to be
+
+ align:start position:0%
+they're more or less likely to be
+ 
+
+ align:start position:0%
+they're more or less likely to be
+exposed to
+
+ align:start position:0%
+exposed to
+ 
+
+ align:start position:0%
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+
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+
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+you really
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+don't like your opponents you might see
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+they win against you or the like
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+ align:start position:0%
+they win against you or the like
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+ align:start position:0%
+so um this ad these adversarial
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+
+ align:start position:0%
+so um this ad these adversarial
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+of
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+of
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+
+ align:start position:0%
+uh make things um uh uh worse
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+
+ align:start position:0%
+uh make things um uh uh worse
+so um matt runs this experiment and
+
+ align:start position:0%
+so um matt runs this experiment and
+ 
+
+ align:start position:0%
+so um matt runs this experiment and
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+
+ align:start position:0%
+finds
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+
+ align:start position:0%
+finds
+evidence of increased cross-cast
+
+ align:start position:0%
+evidence of increased cross-cast
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+
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+
+ align:start position:0%
+they're also more likely to engage and
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+
+ align:start position:0%
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+trade um
+
+ align:start position:0%
+trade um
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+
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+
+ align:start position:0%
+or in economic exchange so much what
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+
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+
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+
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+gloves there's like left
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+
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+gloves there's like left
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+left gloves and right gloves and he has
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+
+ align:start position:0%
+left gloves and right gloves and he has
+the same for flip-flops left flip-flops
+
+ align:start position:0%
+the same for flip-flops left flip-flops
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+
+ align:start position:0%
+the same for flip-flops left flip-flops
+and right flip-flops
+
+ align:start position:0%
+and right flip-flops
+ 
+
+ align:start position:0%
+and right flip-flops
+and people are more likely to trade with
+
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+and people are more likely to trade with
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+
+ align:start position:0%
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+
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+somebody from another cast
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+
+ align:start position:0%
+somebody from another cast
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+
+ align:start position:0%
+if they have been uh on the same team
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+
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+
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+
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+
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+
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+
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+their
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+
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+
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+uh uh on their team of people from other
+ 
+
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+
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+they're more likely to engage in all
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+
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+
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+
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+
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+
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+more likely to engage in economic
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+
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+more likely to engage in economic
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+
+ align:start position:0%
+exchange with people from other
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+
+ align:start position:0%
+exchange with people from other
+casts so that's all true for
+
+ align:start position:0%
+casts so that's all true for
+ 
+
+ align:start position:0%
+casts so that's all true for
+um a collaborative contact that is to
+
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+um a collaborative contact that is to
+ 
+
+ align:start position:0%
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+
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+
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+
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+uh on the same team in contrast for
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+
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+uh on the same team in contrast for
+adversarial interactions when people are
+
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+adversarial interactions when people are
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+
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+in the opposite team
+
+ align:start position:0%
+in the opposite team
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+
+ align:start position:0%
+in the opposite team
+having more people from other casts are
+
+ align:start position:0%
+having more people from other casts are
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
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+casts
+ 
+
+ align:start position:0%
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+uh does not have these positive effects
+
+ align:start position:0%
+uh does not have these positive effects
+ 
+
+ align:start position:0%
+uh does not have these positive effects
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+
+ align:start position:0%
+and for some of these outcomes have even
+ 
+
+ align:start position:0%
+and for some of these outcomes have even
+negative effects
+
+ align:start position:0%
+negative effects
+ 
+
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+negative effects
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+
+ align:start position:0%
+so if anything it sort of backfires it
+ 
+
+ align:start position:0%
+so if anything it sort of backfires it
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+
+ align:start position:0%
+doesn't just
+ 
+
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+doesn't just
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+
+ align:start position:0%
+just a mere exposure to others if you
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+
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+just a mere exposure to others if you
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+ 
+
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+were sort of in an adversarial contact
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+does not really foster uh pro-sociality
+
+ align:start position:0%
+does not really foster uh pro-sociality
+ 
+
+ align:start position:0%
+does not really foster uh pro-sociality
+or any of these
+
+ align:start position:0%
+or any of these
+ 
+
+ align:start position:0%
+or any of these
+types of integration if anything it
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+ align:start position:0%
+types of integration if anything it
+ 
+
+ align:start position:0%
+types of integration if anything it
+backfires
+
+ align:start position:0%
+backfires
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+
+ align:start position:0%
+backfires
+now why is that important when you think
+
+ align:start position:0%
+now why is that important when you think
+ 
+
+ align:start position:0%
+now why is that important when you think
+about like for example attitudes towards
+
+ align:start position:0%
+about like for example attitudes towards
+ 
+
+ align:start position:0%
+about like for example attitudes towards
+immigrants
+
+ align:start position:0%
+immigrants
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+
+ align:start position:0%
+immigrants
+um it really matters hugely what types
+
+ align:start position:0%
+um it really matters hugely what types
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+
+ align:start position:0%
+um it really matters hugely what types
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+if they have perhaps like team pay
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+
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+
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+
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+
+ align:start position:0%
+same goal
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+
+ align:start position:0%
+same goal
+really that can it seems this evidence
+
+ align:start position:0%
+really that can it seems this evidence
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+suggests can foster pro-sociology
+ 
+
+ align:start position:0%
+suggests can foster pro-sociology
+uh and so on and so forth that leads to
+
+ align:start position:0%
+uh and so on and so forth that leads to
+ 
+
+ align:start position:0%
+uh and so on and so forth that leads to
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+reduced discrimination and so on and so
+
+ align:start position:0%
+reduced discrimination and so on and so
+ 
+
+ align:start position:0%
+reduced discrimination and so on and so
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+
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+forth so if sort of the incentives are
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+aligned or if we could sort of set up
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+incentives that are aligned
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+
+ align:start position:0%
+incentives that are aligned
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+people might become nicer to each other
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions might be fostered in
+
+ align:start position:0%
+interactions might be fostered in
+ 
+
+ align:start position:0%
+interactions might be fostered in
+contrast if contact is adversarial
+
+ align:start position:0%
+contrast if contact is adversarial
+ 
+
+ align:start position:0%
+contrast if contact is adversarial
+if you're worried that immigrants are
+
+ align:start position:0%
+if you're worried that immigrants are
+ 
+
+ align:start position:0%
+if you're worried that immigrants are
+taking away your jobs or like
+
+ align:start position:0%
+taking away your jobs or like
+ 
+
+ align:start position:0%
+taking away your jobs or like
+being exposed to immigrants might just
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+ align:start position:0%
+being exposed to immigrants might just
+ 
+
+ align:start position:0%
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+do the opposite right so you might see a
+
+ align:start position:0%
+do the opposite right so you might see a
+ 
+
+ align:start position:0%
+do the opposite right so you might see a
+lot of immigrants
+
+ align:start position:0%
+lot of immigrants
+ 
+
+ align:start position:0%
+lot of immigrants
+but in a way if you feel like you're in
+
+ align:start position:0%
+but in a way if you feel like you're in
+ 
+
+ align:start position:0%
+but in a way if you feel like you're in
+competition with them if they're
+
+ align:start position:0%
+competition with them if they're
+ 
+
+ align:start position:0%
+competition with them if they're
+adversarial if they're sort of you're
+
+ align:start position:0%
+adversarial if they're sort of you're
+ 
+
+ align:start position:0%
+adversarial if they're sort of you're
+your enemies in some ways or your
+
+ align:start position:0%
+your enemies in some ways or your
+ 
+
+ align:start position:0%
+your enemies in some ways or your
+opponents and like some competition for
+
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+ 
+
+ align:start position:0%
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+a job
+
+ align:start position:0%
+a job
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+
+ align:start position:0%
+a job
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+
+ align:start position:0%
+being exposed to them might things in
+ 
+
+ align:start position:0%
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+fact if anything
+
+ align:start position:0%
+fact if anything
+ 
+
+ align:start position:0%
+fact if anything
+uh uh uh uh worse
+
+ align:start position:0%
+uh uh uh uh worse
+ 
+
+ align:start position:0%
+uh uh uh uh worse
+um finally there's a another piece of
+
+ align:start position:0%
+um finally there's a another piece of
+ 
+
+ align:start position:0%
+um finally there's a another piece of
+very nice uh
+
+ align:start position:0%
+very nice uh
+ 
+
+ align:start position:0%
+very nice uh
+evidence by corn oidal this is um papers
+
+ align:start position:0%
+evidence by corn oidal this is um papers
+ 
+
+ align:start position:0%
+evidence by corn oidal this is um papers
+considering the
+
+ align:start position:0%
+considering the
+ 
+
+ align:start position:0%
+considering the
+impact of random interracial
+
+ align:start position:0%
+impact of random interracial
+ 
+
+ align:start position:0%
+impact of random interracial
+interactions among college roommates
+
+ align:start position:0%
+interactions among college roommates
+ 
+
+ align:start position:0%
+interactions among college roommates
+um in south africa on stereotypes
+
+ align:start position:0%
+um in south africa on stereotypes
+ 
+
+ align:start position:0%
+um in south africa on stereotypes
+attitudes and performance so what they
+
+ align:start position:0%
+attitudes and performance so what they
+ 
+
+ align:start position:0%
+attitudes and performance so what they
+look at essentially
+
+ align:start position:0%
+look at essentially
+ 
+
+ align:start position:0%
+look at essentially
+is roommates of different race um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduces so these are black and white
+
+ align:start position:0%
+reduces so these are black and white
+ 
+
+ align:start position:0%
+reduces so these are black and white
+students reduces
+
+ align:start position:0%
+students reduces
+ 
+
+ align:start position:0%
+students reduces
+white students stereotypes towards
+
+ align:start position:0%
+white students stereotypes towards
+ 
+
+ align:start position:0%
+white students stereotypes towards
+blacks and increases interracial
+
+ align:start position:0%
+blacks and increases interracial
+ 
+
+ align:start position:0%
+blacks and increases interracial
+friendships it also improves grades and
+
+ align:start position:0%
+friendships it also improves grades and
+ 
+
+ align:start position:0%
+friendships it also improves grades and
+lowers dropouts among blacks so there's
+
+ align:start position:0%
+lowers dropouts among blacks so there's
+ 
+
+ align:start position:0%
+lowers dropouts among blacks so there's
+sort of a number of positive effects
+
+ align:start position:0%
+sort of a number of positive effects
+ 
+
+ align:start position:0%
+sort of a number of positive effects
+of a very simple policy of like
+
+ align:start position:0%
+of a very simple policy of like
+ 
+
+ align:start position:0%
+of a very simple policy of like
+increasing contacts among roommates and
+
+ align:start position:0%
+increasing contacts among roommates and
+ 
+
+ align:start position:0%
+increasing contacts among roommates and
+again if you think about this evidence
+
+ align:start position:0%
+again if you think about this evidence
+ 
+
+ align:start position:0%
+again if you think about this evidence
+it seems to suggest that perhaps that's
+
+ align:start position:0%
+it seems to suggest that perhaps that's
+ 
+
+ align:start position:0%
+it seems to suggest that perhaps that's
+kind of like if you have a roommate
+
+ align:start position:0%
+kind of like if you have a roommate
+ 
+
+ align:start position:0%
+kind of like if you have a roommate
+that you're going to live with for quite
+
+ align:start position:0%
+that you're going to live with for quite
+ 
+
+ align:start position:0%
+that you're going to live with for quite
+a while that feels a lot like
+
+ align:start position:0%
+a while that feels a lot like
+ 
+
+ align:start position:0%
+a while that feels a lot like
+collaborative contact in the sense of
+
+ align:start position:0%
+collaborative contact in the sense of
+ 
+
+ align:start position:0%
+collaborative contact in the sense of
+like you're sort of stuck with that
+
+ align:start position:0%
+like you're sort of stuck with that
+ 
+
+ align:start position:0%
+like you're sort of stuck with that
+roommate for quite a while
+
+ align:start position:0%
+roommate for quite a while
+ 
+
+ align:start position:0%
+roommate for quite a while
+so you might as well sort of make the
+
+ align:start position:0%
+so you might as well sort of make the
+ 
+
+ align:start position:0%
+so you might as well sort of make the
+best out of it even if you initially
+
+ align:start position:0%
+best out of it even if you initially
+ 
+
+ align:start position:0%
+best out of it even if you initially
+don't like that person
+
+ align:start position:0%
+don't like that person
+ 
+
+ align:start position:0%
+don't like that person
+and you have the same objectives of
+
+ align:start position:0%
+and you have the same objectives of
+ 
+
+ align:start position:0%
+and you have the same objectives of
+being happy together living together
+
+ align:start position:0%
+being happy together living together
+ 
+
+ align:start position:0%
+being happy together living together
+and that really seems to foster and have
+
+ align:start position:0%
+and that really seems to foster and have
+ 
+
+ align:start position:0%
+and that really seems to foster and have
+some positive
+
+ align:start position:0%
+some positive
+ 
+
+ align:start position:0%
+some positive
+benefits
+
+ align:start position:0%
+benefits
+ 
+
+ align:start position:0%
+benefits
+so taking together that sort of says um
+
+ align:start position:0%
+so taking together that sort of says um
+ 
+
+ align:start position:0%
+so taking together that sort of says um
+so a you know the contact hypothesis
+
+ align:start position:0%
+so a you know the contact hypothesis
+ 
+
+ align:start position:0%
+so a you know the contact hypothesis
+seems to be broadly right
+
+ align:start position:0%
+seems to be broadly right
+ 
+
+ align:start position:0%
+seems to be broadly right
+uh contact to people who are different
+
+ align:start position:0%
+uh contact to people who are different
+ 
+
+ align:start position:0%
+uh contact to people who are different
+from you um
+
+ align:start position:0%
+from you um
+ 
+
+ align:start position:0%
+from you um
+uh might make you more tolerant or more
+
+ align:start position:0%
+uh might make you more tolerant or more
+ 
+
+ align:start position:0%
+uh might make you more tolerant or more
+pro-social
+
+ align:start position:0%
+pro-social
+ 
+
+ align:start position:0%
+pro-social
+towards them there might be more sort of
+
+ align:start position:0%
+towards them there might be more sort of
+ 
+
+ align:start position:0%
+towards them there might be more sort of
+integration of different groups
+
+ align:start position:0%
+integration of different groups
+ 
+
+ align:start position:0%
+integration of different groups
+but what really seems to matter quite a
+
+ align:start position:0%
+but what really seems to matter quite a
+ 
+
+ align:start position:0%
+but what really seems to matter quite a
+bit is the type of contact that people
+
+ align:start position:0%
+bit is the type of contact that people
+ 
+
+ align:start position:0%
+bit is the type of contact that people
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+exposed to okay so finally
+
+ align:start position:0%
+exposed to okay so finally
+ 
+
+ align:start position:0%
+exposed to okay so finally
+and relatively quickly i'll tell you a
+
+ align:start position:0%
+and relatively quickly i'll tell you a
+ 
+
+ align:start position:0%
+and relatively quickly i'll tell you a
+little bit about whether people
+
+ align:start position:0%
+little bit about whether people
+ 
+
+ align:start position:0%
+little bit about whether people
+underestimate the benefits of
+
+ align:start position:0%
+underestimate the benefits of
+ 
+
+ align:start position:0%
+underestimate the benefits of
+post-sociality i should mention that
+
+ align:start position:0%
+post-sociality i should mention that
+ 
+
+ align:start position:0%
+post-sociality i should mention that
+problem set three question two is in
+
+ align:start position:0%
+problem set three question two is in
+ 
+
+ align:start position:0%
+problem set three question two is in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+trying to ask you to do something
+
+ align:start position:0%
+trying to ask you to do something
+ 
+
+ align:start position:0%
+trying to ask you to do something
+related to that so you might want to
+
+ align:start position:0%
+related to that so you might want to
+ 
+
+ align:start position:0%
+related to that so you might want to
+actually do the problems at first before
+
+ align:start position:0%
+actually do the problems at first before
+ 
+
+ align:start position:0%
+actually do the problems at first before
+you finish this lecture
+
+ align:start position:0%
+you finish this lecture
+ 
+
+ align:start position:0%
+you finish this lecture
+uh at least sort of sorry not the entire
+
+ align:start position:0%
+uh at least sort of sorry not the entire
+ 
+
+ align:start position:0%
+uh at least sort of sorry not the entire
+problem set but like question two
+
+ align:start position:0%
+problem set but like question two
+ 
+
+ align:start position:0%
+problem set but like question two
+of problem set three um that will not
+
+ align:start position:0%
+of problem set three um that will not
+ 
+
+ align:start position:0%
+of problem set three um that will not
+take you
+
+ align:start position:0%
+take you
+ 
+
+ align:start position:0%
+take you
+very long um um uh to do so and it's
+
+ align:start position:0%
+very long um um uh to do so and it's
+ 
+
+ align:start position:0%
+very long um um uh to do so and it's
+more like a fun
+
+ align:start position:0%
+more like a fun
+ 
+
+ align:start position:0%
+more like a fun
+exercise that i thought would be nice
+
+ align:start position:0%
+exercise that i thought would be nice
+ 
+
+ align:start position:0%
+exercise that i thought would be nice
+for you to uh to engage in
+
+ align:start position:0%
+for you to uh to engage in
+ 
+
+ align:start position:0%
+for you to uh to engage in
+but anyway um this is a very nice paper
+
+ align:start position:0%
+but anyway um this is a very nice paper
+ 
+
+ align:start position:0%
+but anyway um this is a very nice paper
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+kumar and epley so that's a typo here i
+
+ align:start position:0%
+kumar and epley so that's a typo here i
+ 
+
+ align:start position:0%
+kumar and epley so that's a typo here i
+should say
+
+ align:start position:0%
+should say
+ 
+
+ align:start position:0%
+should say
+kumar neplay and the authors asked the
+
+ align:start position:0%
+kumar neplay and the authors asked the
+ 
+
+ align:start position:0%
+kumar neplay and the authors asked the
+question about
+
+ align:start position:0%
+question about
+ 
+
+ align:start position:0%
+question about
+do we have correct beliefs about the
+
+ align:start position:0%
+do we have correct beliefs about the
+ 
+
+ align:start position:0%
+do we have correct beliefs about the
+impacts of generosity
+
+ align:start position:0%
+impacts of generosity
+ 
+
+ align:start position:0%
+impacts of generosity
+and so what's the underlying reason here
+
+ align:start position:0%
+and so what's the underlying reason here
+ 
+
+ align:start position:0%
+and so what's the underlying reason here
+is well many pro-social acts require
+
+ align:start position:0%
+is well many pro-social acts require
+ 
+
+ align:start position:0%
+is well many pro-social acts require
+estimating the impacts on the recipient
+
+ align:start position:0%
+estimating the impacts on the recipient
+ 
+
+ align:start position:0%
+estimating the impacts on the recipient
+but if you give money to somebody in
+
+ align:start position:0%
+but if you give money to somebody in
+ 
+
+ align:start position:0%
+but if you give money to somebody in
+africa if you
+
+ align:start position:0%
+africa if you
+ 
+
+ align:start position:0%
+africa if you
+help anybody any people in need if you
+
+ align:start position:0%
+help anybody any people in need if you
+ 
+
+ align:start position:0%
+help anybody any people in need if you
+donate money in general if you
+
+ align:start position:0%
+donate money in general if you
+ 
+
+ align:start position:0%
+donate money in general if you
+like write letters of gratitude or if
+
+ align:start position:0%
+like write letters of gratitude or if
+ 
+
+ align:start position:0%
+like write letters of gratitude or if
+you do random acts of kindness
+
+ align:start position:0%
+you do random acts of kindness
+ 
+
+ align:start position:0%
+you do random acts of kindness
+it requires some sort of estimation of
+
+ align:start position:0%
+it requires some sort of estimation of
+ 
+
+ align:start position:0%
+it requires some sort of estimation of
+how is the other person going to feel
+
+ align:start position:0%
+how is the other person going to feel
+ 
+
+ align:start position:0%
+how is the other person going to feel
+if they receive uh if they're on the
+
+ align:start position:0%
+if they receive uh if they're on the
+ 
+
+ align:start position:0%
+if they receive uh if they're on the
+receiving end of this pro-social act
+
+ align:start position:0%
+receiving end of this pro-social act
+ 
+
+ align:start position:0%
+receiving end of this pro-social act
+now what eppley and kumar argue is
+
+ align:start position:0%
+now what eppley and kumar argue is
+ 
+
+ align:start position:0%
+now what eppley and kumar argue is
+people are
+
+ align:start position:0%
+people are
+ 
+
+ align:start position:0%
+people are
+subject to egocentric bias which may
+
+ align:start position:0%
+subject to egocentric bias which may
+ 
+
+ align:start position:0%
+subject to egocentric bias which may
+lead them
+
+ align:start position:0%
+lead them
+ 
+
+ align:start position:0%
+lead them
+to systematically underestimate the
+
+ align:start position:0%
+to systematically underestimate the
+ 
+
+ align:start position:0%
+to systematically underestimate the
+positive impacts of pro-sociology in
+
+ align:start position:0%
+positive impacts of pro-sociology in
+ 
+
+ align:start position:0%
+positive impacts of pro-sociology in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+gratitude letters and so why is that
+
+ align:start position:0%
+gratitude letters and so why is that
+ 
+
+ align:start position:0%
+gratitude letters and so why is that
+well it's because predicting others
+
+ align:start position:0%
+well it's because predicting others
+ 
+
+ align:start position:0%
+well it's because predicting others
+mental states is different
+
+ align:start position:0%
+mental states is different
+ 
+
+ align:start position:0%
+mental states is different
+difficult it's really hard to um
+
+ align:start position:0%
+difficult it's really hard to um
+ 
+
+ align:start position:0%
+difficult it's really hard to um
+for people to understand how another
+
+ align:start position:0%
+for people to understand how another
+ 
+
+ align:start position:0%
+for people to understand how another
+person might feel
+
+ align:start position:0%
+person might feel
+ 
+
+ align:start position:0%
+person might feel
+usually people would sort of think about
+
+ align:start position:0%
+usually people would sort of think about
+ 
+
+ align:start position:0%
+usually people would sort of think about
+themselves and sort of think about how
+
+ align:start position:0%
+themselves and sort of think about how
+ 
+
+ align:start position:0%
+themselves and sort of think about how
+would i feel and then what
+
+ align:start position:0%
+would i feel and then what
+ 
+
+ align:start position:0%
+would i feel and then what
+what would things be and how are things
+
+ align:start position:0%
+what would things be and how are things
+ 
+
+ align:start position:0%
+what would things be and how are things
+like and and it's very hard to
+
+ align:start position:0%
+like and and it's very hard to
+ 
+
+ align:start position:0%
+like and and it's very hard to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+uh how others might react to you
+
+ align:start position:0%
+uh how others might react to you
+ 
+
+ align:start position:0%
+uh how others might react to you
+it sort of requires perspective taking
+
+ align:start position:0%
+it sort of requires perspective taking
+ 
+
+ align:start position:0%
+it sort of requires perspective taking
+and that's sometimes
+
+ align:start position:0%
+and that's sometimes
+ 
+
+ align:start position:0%
+and that's sometimes
+tricky for people um to do so this is
+
+ align:start position:0%
+tricky for people um to do so this is
+ 
+
+ align:start position:0%
+tricky for people um to do so this is
+again um a very nice experiment by um
+
+ align:start position:0%
+again um a very nice experiment by um
+ 
+
+ align:start position:0%
+again um a very nice experiment by um
+kumar and nicolas apley not
+
+ align:start position:0%
+kumar and nicolas apley not
+ 
+
+ align:start position:0%
+kumar and nicolas apley not
+not nicolas last name but nick appley
+
+ align:start position:0%
+not nicolas last name but nick appley
+ 
+
+ align:start position:0%
+not nicolas last name but nick appley
+and they test whether people
+
+ align:start position:0%
+and they test whether people
+ 
+
+ align:start position:0%
+and they test whether people
+misunderstand the cause
+
+ align:start position:0%
+misunderstand the cause
+ 
+
+ align:start position:0%
+misunderstand the cause
+the consequences of showing appreciation
+
+ align:start position:0%
+the consequences of showing appreciation
+ 
+
+ align:start position:0%
+the consequences of showing appreciation
+and so what are these
+
+ align:start position:0%
+and so what are these
+ 
+
+ align:start position:0%
+and so what are these
+experiments there's a series of
+
+ align:start position:0%
+experiments there's a series of
+ 
+
+ align:start position:0%
+experiments there's a series of
+experiments that look at this what do
+
+ align:start position:0%
+experiments that look at this what do
+ 
+
+ align:start position:0%
+experiments that look at this what do
+they look like
+
+ align:start position:0%
+they look like
+ 
+
+ align:start position:0%
+they look like
+but what what they do is like they ask
+
+ align:start position:0%
+but what what they do is like they ask
+ 
+
+ align:start position:0%
+but what what they do is like they ask
+people uh
+
+ align:start position:0%
+people uh
+ 
+
+ align:start position:0%
+people uh
+mba students or subjects and expert
+
+ align:start position:0%
+mba students or subjects and expert
+ 
+
+ align:start position:0%
+mba students or subjects and expert
+subjects and experiments
+
+ align:start position:0%
+subjects and experiments
+ 
+
+ align:start position:0%
+subjects and experiments
+to pick a pro-social act that's writing
+
+ align:start position:0%
+to pick a pro-social act that's writing
+ 
+
+ align:start position:0%
+to pick a pro-social act that's writing
+a gratitude letter for example
+
+ align:start position:0%
+a gratitude letter for example
+ 
+
+ align:start position:0%
+a gratitude letter for example
+and then ask how the giver and the
+
+ align:start position:0%
+and then ask how the giver and the
+ 
+
+ align:start position:0%
+and then ask how the giver and the
+recipient will be affected
+
+ align:start position:0%
+recipient will be affected
+ 
+
+ align:start position:0%
+recipient will be affected
+in some cases only the recipient in some
+
+ align:start position:0%
+in some cases only the recipient in some
+ 
+
+ align:start position:0%
+in some cases only the recipient in some
+cases also
+
+ align:start position:0%
+cases also
+ 
+
+ align:start position:0%
+cases also
+the giver then they perform the
+
+ align:start position:0%
+the giver then they perform the
+ 
+
+ align:start position:0%
+the giver then they perform the
+pro-social act
+
+ align:start position:0%
+pro-social act
+ 
+
+ align:start position:0%
+pro-social act
+by for example writing a letter of
+
+ align:start position:0%
+by for example writing a letter of
+ 
+
+ align:start position:0%
+by for example writing a letter of
+gratitude and then assess how the giver
+
+ align:start position:0%
+gratitude and then assess how the giver
+ 
+
+ align:start position:0%
+gratitude and then assess how the giver
+and the recipients were actually
+
+ align:start position:0%
+and the recipients were actually
+ 
+
+ align:start position:0%
+and the recipients were actually
+affected by
+
+ align:start position:0%
+affected by
+ 
+
+ align:start position:0%
+affected by
+doing that and then you can compare that
+
+ align:start position:0%
+doing that and then you can compare that
+ 
+
+ align:start position:0%
+doing that and then you can compare that
+to item number two to the estimation
+
+ align:start position:0%
+to item number two to the estimation
+ 
+
+ align:start position:0%
+to item number two to the estimation
+ex-ante now what do they find
+
+ align:start position:0%
+ex-ante now what do they find
+ 
+
+ align:start position:0%
+ex-ante now what do they find
+they find uh clear evidence that when
+
+ align:start position:0%
+they find uh clear evidence that when
+ 
+
+ align:start position:0%
+they find uh clear evidence that when
+you look at like in particular when you
+
+ align:start position:0%
+you look at like in particular when you
+ 
+
+ align:start position:0%
+you look at like in particular when you
+look at the giver
+
+ align:start position:0%
+look at the giver
+ 
+
+ align:start position:0%
+look at the giver
+so these um graphs all show kind of like
+
+ align:start position:0%
+so these um graphs all show kind of like
+ 
+
+ align:start position:0%
+so these um graphs all show kind of like
+the predicted
+
+ align:start position:0%
+the predicted
+ 
+
+ align:start position:0%
+the predicted
+uh ratings the ratings is between zero
+
+ align:start position:0%
+uh ratings the ratings is between zero
+ 
+
+ align:start position:0%
+uh ratings the ratings is between zero
+and ten um
+
+ align:start position:0%
+and ten um
+ 
+
+ align:start position:0%
+and ten um
+about like um how um uh what's the
+
+ align:start position:0%
+about like um how um uh what's the
+ 
+
+ align:start position:0%
+about like um how um uh what's the
+experience how happy is the other person
+
+ align:start position:0%
+experience how happy is the other person
+ 
+
+ align:start position:0%
+experience how happy is the other person
+uh what is the surprise about receiving
+
+ align:start position:0%
+uh what is the surprise about receiving
+ 
+
+ align:start position:0%
+uh what is the surprise about receiving
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh this letter of gratitude in this
+
+ align:start position:0%
+uh this letter of gratitude in this
+ 
+
+ align:start position:0%
+uh this letter of gratitude in this
+example so people are more surprised
+
+ align:start position:0%
+example so people are more surprised
+ 
+
+ align:start position:0%
+example so people are more surprised
+than predicted
+
+ align:start position:0%
+than predicted
+ 
+
+ align:start position:0%
+than predicted
+they're also more surprised about the
+
+ align:start position:0%
+they're also more surprised about the
+ 
+
+ align:start position:0%
+they're also more surprised about the
+content than pre
+
+ align:start position:0%
+content than pre
+ 
+
+ align:start position:0%
+content than pre
+predicted um they also uh the
+
+ align:start position:0%
+predicted um they also uh the
+ 
+
+ align:start position:0%
+predicted um they also uh the
+recipient's mood is actually
+
+ align:start position:0%
+recipient's mood is actually
+ 
+
+ align:start position:0%
+recipient's mood is actually
+better than predicted and uh the
+
+ align:start position:0%
+better than predicted and uh the
+ 
+
+ align:start position:0%
+better than predicted and uh the
+awkwardness is also
+
+ align:start position:0%
+awkwardness is also
+ 
+
+ align:start position:0%
+awkwardness is also
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+that now if you also think for a little
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+uh how would one actually feel to
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
+like a long time ago and you know this
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+like a long time ago and you know this
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+
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+helped me a lot in my career and
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
+now what sort of like um some evidence
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+
+ align:start position:0%
+now what sort of like um some evidence
+uh
+
+ align:start position:0%
+uh
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+
+ align:start position:0%
+uh
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+ align:start position:0%
+some summary of that well so we tend to
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+systematically underestimate
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+it's also true so apple and schroeder
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+
+ align:start position:0%
+it's also true so apple and schroeder
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+ align:start position:0%
+argue um
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+
+ align:start position:0%
+argue um
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+ align:start position:0%
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+underestimate on average
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+ align:start position:0%
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+
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+ align:start position:0%
+and so on um but once you actually do
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+
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+and so on um but once you actually do
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+happy some people might be also grumpy
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+
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+ align:start position:0%
+so there are some questions about do
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+
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+
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+is not just by being selfish and
+ 
+
+ align:start position:0%
+is not just by being selfish and
+maximizing whatever
+
+ align:start position:0%
+maximizing whatever
+ 
+
+ align:start position:0%
+maximizing whatever
+outcomes we get but be really being nice
+
+ align:start position:0%
+outcomes we get but be really being nice
+ 
+
+ align:start position:0%
+outcomes we get but be really being nice
+towards others
+
+ align:start position:0%
+towards others
+ 
+
+ align:start position:0%
+towards others
+in part perhaps because it just makes us
+
+ align:start position:0%
+in part perhaps because it just makes us
+ 
+
+ align:start position:0%
+in part perhaps because it just makes us
+happy to see when others are happy
+
+ align:start position:0%
+happy to see when others are happy
+ 
+
+ align:start position:0%
+happy to see when others are happy
+perhaps it makes us happy because you
+
+ align:start position:0%
+perhaps it makes us happy because you
+ 
+
+ align:start position:0%
+perhaps it makes us happy because you
+know others will be the nicer toss
+
+ align:start position:0%
+know others will be the nicer toss
+ 
+
+ align:start position:0%
+know others will be the nicer toss
+and there's a question about can we make
+
+ align:start position:0%
+and there's a question about can we make
+ 
+
+ align:start position:0%
+and there's a question about can we make
+others and
+
+ align:start position:0%
+others and
+ 
+
+ align:start position:0%
+others and
+ourselves happier by being more
+
+ align:start position:0%
+ourselves happier by being more
+ 
+
+ align:start position:0%
+ourselves happier by being more
+pro-social
+
+ align:start position:0%
+pro-social
+ 
+
+ align:start position:0%
+pro-social
+perhaps um because we underestimate uh
+
+ align:start position:0%
+perhaps um because we underestimate uh
+ 
+
+ align:start position:0%
+perhaps um because we underestimate uh
+uh to start with
+
+ align:start position:0%
+uh to start with
+ 
+
+ align:start position:0%
+uh to start with
+uh what these effects um might be uh i
+
+ align:start position:0%
+uh what these effects um might be uh i
+ 
+
+ align:start position:0%
+uh what these effects um might be uh i
+don't think there's that much evidence
+
+ align:start position:0%
+don't think there's that much evidence
+ 
+
+ align:start position:0%
+don't think there's that much evidence
+on on this specific question but i'd
+
+ align:start position:0%
+on on this specific question but i'd
+ 
+
+ align:start position:0%
+on on this specific question but i'd
+love to uh learn more and when you think
+
+ align:start position:0%
+love to uh learn more and when you think
+ 
+
+ align:start position:0%
+love to uh learn more and when you think
+about like your own life
+
+ align:start position:0%
+about like your own life
+ 
+
+ align:start position:0%
+about like your own life
+you might wanna experiment uh uh for a
+
+ align:start position:0%
+you might wanna experiment uh uh for a
+ 
+
+ align:start position:0%
+you might wanna experiment uh uh for a
+while and seeing like
+
+ align:start position:0%
+while and seeing like
+ 
+
+ align:start position:0%
+while and seeing like
+um trying to be nicer trying to uh uh
+
+ align:start position:0%
+um trying to be nicer trying to uh uh
+ 
+
+ align:start position:0%
+um trying to be nicer trying to uh uh
+engage in random acts of kindness
+
+ align:start position:0%
+engage in random acts of kindness
+ 
+
+ align:start position:0%
+engage in random acts of kindness
+letters of gratitude
+
+ align:start position:0%
+letters of gratitude
+ 
+
+ align:start position:0%
+letters of gratitude
+and gratitude and so on that might be a
+
+ align:start position:0%
+and gratitude and so on that might be a
+ 
+
+ align:start position:0%
+and gratitude and so on that might be a
+nice habit to acquire
+
+ align:start position:0%
+nice habit to acquire
+ 
+
+ align:start position:0%
+nice habit to acquire
+and you might see it might may and might
+
+ align:start position:0%
+and you might see it might may and might
+ 
+
+ align:start position:0%
+and you might see it might may and might
+make you uh happier
+
+ align:start position:0%
+make you uh happier
+ 
+
+ align:start position:0%
+make you uh happier
+surely it will make the other person on
+
+ align:start position:0%
+surely it will make the other person on
+ 
+
+ align:start position:0%
+surely it will make the other person on
+the receiving end happier
+
+ align:start position:0%
+the receiving end happier
+ 
+
+ align:start position:0%
+the receiving end happier
+okay so let me sort of summarize what we
+
+ align:start position:0%
+okay so let me sort of summarize what we
+ 
+
+ align:start position:0%
+okay so let me sort of summarize what we
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+what we studied on social preferences so
+
+ align:start position:0%
+what we studied on social preferences so
+ 
+
+ align:start position:0%
+what we studied on social preferences so
+first others outcomes and utility matter
+
+ align:start position:0%
+first others outcomes and utility matter
+ 
+
+ align:start position:0%
+first others outcomes and utility matter
+for people's choices quite a bit
+
+ align:start position:0%
+for people's choices quite a bit
+ 
+
+ align:start position:0%
+for people's choices quite a bit
+so in their situation essentially people
+
+ align:start position:0%
+so in their situation essentially people
+ 
+
+ align:start position:0%
+so in their situation essentially people
+are willing to give to others and
+
+ align:start position:0%
+are willing to give to others and
+ 
+
+ align:start position:0%
+are willing to give to others and
+they're influenced by others
+
+ align:start position:0%
+they're influenced by others
+ 
+
+ align:start position:0%
+they're influenced by others
+in their choices now upon closer look
+
+ align:start position:0%
+in their choices now upon closer look
+ 
+
+ align:start position:0%
+in their choices now upon closer look
+there's not much evidence of pure
+
+ align:start position:0%
+there's not much evidence of pure
+ 
+
+ align:start position:0%
+there's not much evidence of pure
+altruism rarely does it seem that people
+
+ align:start position:0%
+altruism rarely does it seem that people
+ 
+
+ align:start position:0%
+altruism rarely does it seem that people
+just do stuff for others
+
+ align:start position:0%
+just do stuff for others
+ 
+
+ align:start position:0%
+just do stuff for others
+just for the sake of others doing well
+
+ align:start position:0%
+just for the sake of others doing well
+ 
+
+ align:start position:0%
+just for the sake of others doing well
+and that is to say like if people get
+
+ align:start position:0%
+and that is to say like if people get
+ 
+
+ align:start position:0%
+and that is to say like if people get
+the chance of like
+
+ align:start position:0%
+the chance of like
+ 
+
+ align:start position:0%
+the chance of like
+hiding their not so nice actions they
+
+ align:start position:0%
+hiding their not so nice actions they
+ 
+
+ align:start position:0%
+hiding their not so nice actions they
+will often take advantage of that
+
+ align:start position:0%
+will often take advantage of that
+ 
+
+ align:start position:0%
+will often take advantage of that
+the motivation there often is uh instead
+
+ align:start position:0%
+the motivation there often is uh instead
+ 
+
+ align:start position:0%
+the motivation there often is uh instead
+motivation to give to others or be nice
+
+ align:start position:0%
+motivation to give to others or be nice
+ 
+
+ align:start position:0%
+motivation to give to others or be nice
+to others to be pro-social
+
+ align:start position:0%
+to others to be pro-social
+ 
+
+ align:start position:0%
+to others to be pro-social
+is often saving face in front of others
+
+ align:start position:0%
+is often saving face in front of others
+ 
+
+ align:start position:0%
+is often saving face in front of others
+this is social image
+
+ align:start position:0%
+this is social image
+ 
+
+ align:start position:0%
+this is social image
+or themselves which is um self-image
+
+ align:start position:0%
+or themselves which is um self-image
+ 
+
+ align:start position:0%
+or themselves which is um self-image
+so here are so and because of that
+
+ align:start position:0%
+so here are so and because of that
+ 
+
+ align:start position:0%
+so here are so and because of that
+situational circumstances matter greatly
+
+ align:start position:0%
+situational circumstances matter greatly
+ 
+
+ align:start position:0%
+situational circumstances matter greatly
+societal norms are
+
+ align:start position:0%
+societal norms are
+ 
+
+ align:start position:0%
+societal norms are
+are really important to consider so when
+
+ align:start position:0%
+are really important to consider so when
+ 
+
+ align:start position:0%
+are really important to consider so when
+you think about like incentives or any
+
+ align:start position:0%
+you think about like incentives or any
+ 
+
+ align:start position:0%
+you think about like incentives or any
+sort of types of structures and
+
+ align:start position:0%
+sort of types of structures and
+ 
+
+ align:start position:0%
+sort of types of structures and
+organizations
+
+ align:start position:0%
+organizations
+ 
+
+ align:start position:0%
+organizations
+how might you um set incentives or how
+
+ align:start position:0%
+how might you um set incentives or how
+ 
+
+ align:start position:0%
+how might you um set incentives or how
+might we sort of
+
+ align:start position:0%
+might we sort of
+ 
+
+ align:start position:0%
+might we sort of
+structure certain groups or people
+
+ align:start position:0%
+structure certain groups or people
+ 
+
+ align:start position:0%
+structure certain groups or people
+working together
+
+ align:start position:0%
+working together
+ 
+
+ align:start position:0%
+working together
+understanding these norms and
+
+ align:start position:0%
+understanding these norms and
+ 
+
+ align:start position:0%
+understanding these norms and
+circumstances is key for fostering
+
+ align:start position:0%
+circumstances is key for fostering
+ 
+
+ align:start position:0%
+circumstances is key for fostering
+pro-sociology
+
+ align:start position:0%
+pro-sociology
+ 
+
+ align:start position:0%
+pro-sociology
+if you want people to be nice to each
+
+ align:start position:0%
+if you want people to be nice to each
+ 
+
+ align:start position:0%
+if you want people to be nice to each
+other you have to set it up in a way
+
+ align:start position:0%
+other you have to set it up in a way
+ 
+
+ align:start position:0%
+other you have to set it up in a way
+that it's maybe um
+
+ align:start position:0%
+that it's maybe um
+ 
+
+ align:start position:0%
+that it's maybe um
+observable what people do it's
+
+ align:start position:0%
+observable what people do it's
+ 
+
+ align:start position:0%
+observable what people do it's
+encouraged there's
+
+ align:start position:0%
+encouraged there's
+ 
+
+ align:start position:0%
+encouraged there's
+opportunities for reciprocity and so on
+
+ align:start position:0%
+opportunities for reciprocity and so on
+ 
+
+ align:start position:0%
+opportunities for reciprocity and so on
+so a lot of the design of society of
+
+ align:start position:0%
+so a lot of the design of society of
+ 
+
+ align:start position:0%
+so a lot of the design of society of
+like a firm of a group that you work in
+
+ align:start position:0%
+like a firm of a group that you work in
+ 
+
+ align:start position:0%
+like a firm of a group that you work in
+or a team that you work in really seems
+
+ align:start position:0%
+or a team that you work in really seems
+ 
+
+ align:start position:0%
+or a team that you work in really seems
+to matter
+
+ align:start position:0%
+to matter
+ 
+
+ align:start position:0%
+to matter
+so on the one hand as i said before it's
+
+ align:start position:0%
+so on the one hand as i said before it's
+ 
+
+ align:start position:0%
+so on the one hand as i said before it's
+a little bit disappointing that there's
+
+ align:start position:0%
+a little bit disappointing that there's
+ 
+
+ align:start position:0%
+a little bit disappointing that there's
+not much
+
+ align:start position:0%
+not much
+ 
+
+ align:start position:0%
+not much
+pure altruism but on the other hand if
+
+ align:start position:0%
+pure altruism but on the other hand if
+ 
+
+ align:start position:0%
+pure altruism but on the other hand if
+you sort of understand
+
+ align:start position:0%
+you sort of understand
+ 
+
+ align:start position:0%
+you sort of understand
+the motivations poor for people being to
+
+ align:start position:0%
+the motivations poor for people being to
+ 
+
+ align:start position:0%
+the motivations poor for people being to
+engage in
+
+ align:start position:0%
+engage in
+ 
+
+ align:start position:0%
+engage in
+acts that are good for others we can
+
+ align:start position:0%
+acts that are good for others we can
+ 
+
+ align:start position:0%
+acts that are good for others we can
+sort of design
+
+ align:start position:0%
+sort of design
+ 
+
+ align:start position:0%
+sort of design
+uh incentives and structures that people
+
+ align:start position:0%
+uh incentives and structures that people
+ 
+
+ align:start position:0%
+uh incentives and structures that people
+work in accordingly
+
+ align:start position:0%
+work in accordingly
+ 
+
+ align:start position:0%
+work in accordingly
+which will then create people being
+
+ align:start position:0%
+which will then create people being
+ 
+
+ align:start position:0%
+which will then create people being
+friendly and cooperative
+
+ align:start position:0%
+friendly and cooperative
+ 
+
+ align:start position:0%
+friendly and cooperative
+to each other second i showed you that
+
+ align:start position:0%
+to each other second i showed you that
+ 
+
+ align:start position:0%
+to each other second i showed you that
+social preferences matter at workplaces
+
+ align:start position:0%
+social preferences matter at workplaces
+ 
+
+ align:start position:0%
+social preferences matter at workplaces
+um relative pay can depress incentives
+
+ align:start position:0%
+um relative pay can depress incentives
+ 
+
+ align:start position:0%
+um relative pay can depress incentives
+to work
+
+ align:start position:0%
+to work
+ 
+
+ align:start position:0%
+to work
+this is the evidence by banjera the
+
+ align:start position:0%
+this is the evidence by banjera the
+ 
+
+ align:start position:0%
+this is the evidence by banjera the
+fruit pickers that i showed you
+
+ align:start position:0%
+fruit pickers that i showed you
+ 
+
+ align:start position:0%
+fruit pickers that i showed you
+pay inequality can lower performance by
+
+ align:start position:0%
+pay inequality can lower performance by
+ 
+
+ align:start position:0%
+pay inequality can lower performance by
+reduced morale so like in particular
+
+ align:start position:0%
+reduced morale so like in particular
+ 
+
+ align:start position:0%
+reduced morale so like in particular
+pay inequality is uh seemingly
+
+ align:start position:0%
+pay inequality is uh seemingly
+ 
+
+ align:start position:0%
+pay inequality is uh seemingly
+unjustified
+
+ align:start position:0%
+unjustified
+ 
+
+ align:start position:0%
+unjustified
+that's really bad for worker morale and
+
+ align:start position:0%
+that's really bad for worker morale and
+ 
+
+ align:start position:0%
+that's really bad for worker morale and
+might might lower
+
+ align:start position:0%
+might might lower
+ 
+
+ align:start position:0%
+might might lower
+our worker outputs and sort of
+
+ align:start position:0%
+our worker outputs and sort of
+ 
+
+ align:start position:0%
+our worker outputs and sort of
+attendance and so on
+
+ align:start position:0%
+attendance and so on
+ 
+
+ align:start position:0%
+attendance and so on
+third social preferences appear to be
+
+ align:start position:0%
+third social preferences appear to be
+ 
+
+ align:start position:0%
+third social preferences appear to be
+malleable
+
+ align:start position:0%
+malleable
+ 
+
+ align:start position:0%
+malleable
+and shaped by uh external factors
+
+ align:start position:0%
+and shaped by uh external factors
+ 
+
+ align:start position:0%
+and shaped by uh external factors
+in particular um there's evidence in
+
+ align:start position:0%
+in particular um there's evidence in
+ 
+
+ align:start position:0%
+in particular um there's evidence in
+favor of the
+
+ align:start position:0%
+favor of the
+ 
+
+ align:start position:0%
+favor of the
+contact hypothesis being exposed to
+
+ align:start position:0%
+contact hypothesis being exposed to
+ 
+
+ align:start position:0%
+contact hypothesis being exposed to
+others from different backgrounds really
+
+ align:start position:0%
+others from different backgrounds really
+ 
+
+ align:start position:0%
+others from different backgrounds really
+seems to uh
+
+ align:start position:0%
+seems to uh
+ 
+
+ align:start position:0%
+seems to uh
+make us more tolerant and more
+
+ align:start position:0%
+make us more tolerant and more
+ 
+
+ align:start position:0%
+make us more tolerant and more
+understanding more pro-social
+
+ align:start position:0%
+understanding more pro-social
+ 
+
+ align:start position:0%
+understanding more pro-social
+towards these other groups but also more
+
+ align:start position:0%
+towards these other groups but also more
+ 
+
+ align:start position:0%
+towards these other groups but also more
+pro-social perhaps
+
+ align:start position:0%
+pro-social perhaps
+ 
+
+ align:start position:0%
+pro-social perhaps
+in general which is the the evidence by
+
+ align:start position:0%
+in general which is the the evidence by
+ 
+
+ align:start position:0%
+in general which is the the evidence by
+gautam rao
+
+ align:start position:0%
+gautam rao
+ 
+
+ align:start position:0%
+gautam rao
+and then finally there's some evidence
+
+ align:start position:0%
+and then finally there's some evidence
+ 
+
+ align:start position:0%
+and then finally there's some evidence
+that bias beliefs may
+
+ align:start position:0%
+that bias beliefs may
+ 
+
+ align:start position:0%
+that bias beliefs may
+lower pro-sociality in a sense that like
+
+ align:start position:0%
+lower pro-sociality in a sense that like
+ 
+
+ align:start position:0%
+lower pro-sociality in a sense that like
+people might under
+
+ align:start position:0%
+people might under
+ 
+
+ align:start position:0%
+people might under
+invest potentially in how nice they are
+
+ align:start position:0%
+invest potentially in how nice they are
+ 
+
+ align:start position:0%
+invest potentially in how nice they are
+to others
+
+ align:start position:0%
+to others
+ 
+
+ align:start position:0%
+to others
+perhaps because they misunderstand what
+
+ align:start position:0%
+perhaps because they misunderstand what
+ 
+
+ align:start position:0%
+perhaps because they misunderstand what
+the effect of
+
+ align:start position:0%
+the effect of
+ 
+
+ align:start position:0%
+the effect of
+engaging in such pro-social act might
+
+ align:start position:0%
+engaging in such pro-social act might
+ 
+
+ align:start position:0%
+engaging in such pro-social act might
+have on others
+
+ align:start position:0%
+have on others
+ 
+
+ align:start position:0%
+have on others
+and so potentially correcting these
+
+ align:start position:0%
+and so potentially correcting these
+ 
+
+ align:start position:0%
+and so potentially correcting these
+beliefs or experimenting
+
+ align:start position:0%
+beliefs or experimenting
+ 
+
+ align:start position:0%
+beliefs or experimenting
+might sort of increase pro-sociality at
+
+ align:start position:0%
+might sort of increase pro-sociality at
+ 
+
+ align:start position:0%
+might sort of increase pro-sociality at
+least in some
+
+ align:start position:0%
+least in some
+ 
+
+ align:start position:0%
+least in some
+settings now um what's coming next what
+
+ align:start position:0%
+settings now um what's coming next what
+ 
+
+ align:start position:0%
+settings now um what's coming next what
+are the next lectures lecture number 14
+
+ align:start position:0%
+are the next lectures lecture number 14
+ 
+
+ align:start position:0%
+are the next lectures lecture number 14
+is about
+
+ align:start position:0%
+is about
+ 
+
+ align:start position:0%
+is about
+limited attention 15 is about projection
+
+ align:start position:0%
+limited attention 15 is about projection
+ 
+
+ align:start position:0%
+limited attention 15 is about projection
+and attribution bias
+
+ align:start position:0%
+and attribution bias
+ 
+
+ align:start position:0%
+and attribution bias
+this is the idea that people have
+
+ align:start position:0%
+this is the idea that people have
+ 
+
+ align:start position:0%
+this is the idea that people have
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+projecting how they might feel in
+
+ align:start position:0%
+projecting how they might feel in
+ 
+
+ align:start position:0%
+projecting how they might feel in
+different states of the world
+
+ align:start position:0%
+different states of the world
+ 
+
+ align:start position:0%
+different states of the world
+that is the idea if you're really hungry
+
+ align:start position:0%
+that is the idea if you're really hungry
+ 
+
+ align:start position:0%
+that is the idea if you're really hungry
+it's really hard to project how you
+
+ align:start position:0%
+it's really hard to project how you
+ 
+
+ align:start position:0%
+it's really hard to project how you
+might feel when you're not hungry and
+
+ align:start position:0%
+might feel when you're not hungry and
+ 
+
+ align:start position:0%
+might feel when you're not hungry and
+vice versa
+
+ align:start position:0%
+vice versa
+ 
+
+ align:start position:0%
+vice versa
+we're going to look at that and lecture
+
+ align:start position:0%
+we're going to look at that and lecture
+ 
+
+ align:start position:0%
+we're going to look at that and lecture
+16 and 17 we'll look
+
+ align:start position:0%
+16 and 17 we'll look
+ 
+
+ align:start position:0%
+16 and 17 we'll look
+more specifically about beliefs and
+
+ align:start position:0%
+more specifically about beliefs and
+ 
+
+ align:start position:0%
+more specifically about beliefs and
+learning we talked a little bit about
+
+ align:start position:0%
+learning we talked a little bit about
+ 
+
+ align:start position:0%
+learning we talked a little bit about
+beliefs already in various ways
+
+ align:start position:0%
+beliefs already in various ways
+ 
+
+ align:start position:0%
+beliefs already in various ways
+but they're now we're going to talk
+
+ align:start position:0%
+but they're now we're going to talk
+ 
+
+ align:start position:0%
+but they're now we're going to talk
+specifically about like biases and
+
+ align:start position:0%
+specifically about like biases and
+ 
+
+ align:start position:0%
+specifically about like biases and
+beliefs and
+
+ align:start position:0%
+beliefs and
+ 
+
+ align:start position:0%
+beliefs and
+learning as in like people um uh uh
+
+ align:start position:0%
+learning as in like people um uh uh
+ 
+
+ align:start position:0%
+learning as in like people um uh uh
+suboptimally learning perhaps because of
+
+ align:start position:0%
+suboptimally learning perhaps because of
+ 
+
+ align:start position:0%
+suboptimally learning perhaps because of
+um computational issues in a sense
+
+ align:start position:0%
+um computational issues in a sense
+ 
+
+ align:start position:0%
+um computational issues in a sense
+that's really hard to learn in some
+
+ align:start position:0%
+that's really hard to learn in some
+ 
+
+ align:start position:0%
+that's really hard to learn in some
+settings in part because of motivated
+
+ align:start position:0%
+settings in part because of motivated
+ 
+
+ align:start position:0%
+settings in part because of motivated
+beliefs
+
+ align:start position:0%
+beliefs
+ 
+
+ align:start position:0%
+beliefs
+people might be uh drive utility from
+
+ align:start position:0%
+people might be uh drive utility from
+ 
+
+ align:start position:0%
+people might be uh drive utility from
+their beliefs
+
+ align:start position:0%
+their beliefs
+ 
+
+ align:start position:0%
+their beliefs
+as in for example i might want to think
+
+ align:start position:0%
+as in for example i might want to think
+ 
+
+ align:start position:0%
+as in for example i might want to think
+that i'm a good-looking smart
+
+ align:start position:0%
+that i'm a good-looking smart
+ 
+
+ align:start position:0%
+that i'm a good-looking smart
+and a good teacher and if
+
+ align:start position:0%
+and a good teacher and if
+ 
+
+ align:start position:0%
+and a good teacher and if
+i get feedback on one way or the other i
+
+ align:start position:0%
+i get feedback on one way or the other i
+ 
+
+ align:start position:0%
+i get feedback on one way or the other i
+might react to
+
+ align:start position:0%
+might react to
+ 
+
+ align:start position:0%
+might react to
+positive feedback a lot more i might
+
+ align:start position:0%
+positive feedback a lot more i might
+ 
+
+ align:start position:0%
+positive feedback a lot more i might
+sort of update positively if somebody
+
+ align:start position:0%
+sort of update positively if somebody
+ 
+
+ align:start position:0%
+sort of update positively if somebody
+says frank you're really smart i might
+
+ align:start position:0%
+says frank you're really smart i might
+ 
+
+ align:start position:0%
+says frank you're really smart i might
+sort of update positively
+
+ align:start position:0%
+sort of update positively
+ 
+
+ align:start position:0%
+sort of update positively
+because i feel really good about it if
+
+ align:start position:0%
+because i feel really good about it if
+ 
+
+ align:start position:0%
+because i feel really good about it if
+somebody says and said frank you're not
+
+ align:start position:0%
+somebody says and said frank you're not
+ 
+
+ align:start position:0%
+somebody says and said frank you're not
+so smart i might mostly ignore that
+
+ align:start position:0%
+so smart i might mostly ignore that
+ 
+
+ align:start position:0%
+so smart i might mostly ignore that
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+because um it might make me feel bad
+
+ align:start position:0%
+because um it might make me feel bad
+ 
+
+ align:start position:0%
+because um it might make me feel bad
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+myself so that's all for now thank you
+
+ align:start position:0%
+myself so that's all for now thank you
+ 
+
+ align:start position:0%
+myself so that's all for now thank you
+so much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/KNRMz9YPCOY.txt b/KNRMz9YPCOY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ff4e863d43e8fb4a6aaa7f3fa7316777cb5840dd
--- /dev/null
+++ b/KNRMz9YPCOY.txt
@@ -0,0 +1,16184 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit open courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me say the big idea is
+
+ align:start position:0%
+okay let me say the big idea is
+ 
+
+ align:start position:0%
+okay let me say the big idea is
+for lqr trees again and you can tell me
+
+ align:start position:0%
+for lqr trees again and you can tell me
+ 
+
+ align:start position:0%
+for lqr trees again and you can tell me
+where you want more details
+
+ align:start position:0%
+where you want more details
+ 
+
+ align:start position:0%
+where you want more details
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the basic story
+
+ align:start position:0%
+here's the basic story
+ 
+
+ align:start position:0%
+here's the basic story
+i've got some goal i want to get to
+
+ align:start position:0%
+i've got some goal i want to get to
+ 
+
+ align:start position:0%
+i've got some goal i want to get to
+and i've got a lot of potential i'd like
+
+ align:start position:0%
+and i've got a lot of potential i'd like
+ 
+
+ align:start position:0%
+and i've got a lot of potential i'd like
+to be able to get there from every
+
+ align:start position:0%
+to be able to get there from every
+ 
+
+ align:start position:0%
+to be able to get there from every
+initial condition let's say
+
+ align:start position:0%
+initial condition let's say
+ 
+
+ align:start position:0%
+initial condition let's say
+so the idea was we know how to design we
+
+ align:start position:0%
+so the idea was we know how to design we
+ 
+
+ align:start position:0%
+so the idea was we know how to design we
+know how to stabilize trajectories so
+
+ align:start position:0%
+know how to stabilize trajectories so
+ 
+
+ align:start position:0%
+know how to stabilize trajectories so
+let's just pick a point at random
+
+ align:start position:0%
+let's just pick a point at random
+ 
+
+ align:start position:0%
+let's just pick a point at random
+design a path to the goal like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+design the
+
+ align:start position:0%
+design the
+ 
+
+ align:start position:0%
+design the
+ltv lqr stabilizer on this
+
+ align:start position:0%
+ltv lqr stabilizer on this
+ 
+
+ align:start position:0%
+ltv lqr stabilizer on this
+the great thing about that is first of
+
+ align:start position:0%
+the great thing about that is first of
+ 
+
+ align:start position:0%
+the great thing about that is first of
+all that it will locally stabilize the
+
+ align:start position:0%
+all that it will locally stabilize the
+ 
+
+ align:start position:0%
+all that it will locally stabilize the
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+but second of all because we can compute
+
+ align:start position:0%
+but second of all because we can compute
+ 
+
+ align:start position:0%
+but second of all because we can compute
+not only because we are given
+
+ align:start position:0%
+not only because we are given
+ 
+
+ align:start position:0%
+not only because we are given
+both u equals
+
+ align:start position:0%
+both u equals
+ 
+
+ align:start position:0%
+both u equals
+some time varying
+
+ align:start position:0%
+some time varying
+ 
+
+ align:start position:0%
+some time varying
+we have a feedback policy from from that
+
+ align:start position:0%
+we have a feedback policy from from that
+ 
+
+ align:start position:0%
+we have a feedback policy from from that
+but we're also given an estimate of
+
+ align:start position:0%
+but we're also given an estimate of
+ 
+
+ align:start position:0%
+but we're also given an estimate of
+the cost to go
+
+ align:start position:0%
+the cost to go
+ 
+
+ align:start position:0%
+the cost to go
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+time varying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+the roccati equation backwards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of that we when we're doing our
+
+ align:start position:0%
+because of that we when we're doing our
+ 
+
+ align:start position:0%
+because of that we when we're doing our
+lqr design we actually have a good
+
+ align:start position:0%
+lqr design we actually have a good
+ 
+
+ align:start position:0%
+lqr design we actually have a good
+candidate for a lyapunov function for
+
+ align:start position:0%
+candidate for a lyapunov function for
+ 
+
+ align:start position:0%
+candidate for a lyapunov function for
+the system
+
+ align:start position:0%
+the system
+ 
+
+ align:start position:0%
+the system
+around that trajectory
+
+ align:start position:0%
+around that trajectory
+ 
+
+ align:start position:0%
+around that trajectory
+so that's a that's an important
+
+ align:start position:0%
+so that's a that's an important
+ 
+
+ align:start position:0%
+so that's a that's an important
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+that when we do ltv lqr
+
+ align:start position:0%
+that when we do ltv lqr
+ 
+
+ align:start position:0%
+that when we do ltv lqr
+on a trajectory
+
+ align:start position:0%
+on a trajectory
+ 
+
+ align:start position:0%
+on a trajectory
+we get both okay
+
+ align:start position:0%
+we get both okay
+ 
+
+ align:start position:0%
+we get both okay
+now this thing
+
+ align:start position:0%
+now this thing
+ 
+
+ align:start position:0%
+now this thing
+for the linear system even the linear
+
+ align:start position:0%
+for the linear system even the linear
+ 
+
+ align:start position:0%
+for the linear system even the linear
+time varying system this is a truly
+
+ align:start position:0%
+time varying system this is a truly
+ 
+
+ align:start position:0%
+time varying system this is a truly
+openoff function from all initial states
+
+ align:start position:0%
+openoff function from all initial states
+ 
+
+ align:start position:0%
+openoff function from all initial states
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+this function will just only get smaller
+
+ align:start position:0%
+this function will just only get smaller
+ 
+
+ align:start position:0%
+this function will just only get smaller
+with time
+
+ align:start position:0%
+with time
+ 
+
+ align:start position:0%
+with time
+okay but on the action since the actual
+
+ align:start position:0%
+okay but on the action since the actual
+ 
+
+ align:start position:0%
+okay but on the action since the actual
+system is non-linear as i get farther
+
+ align:start position:0%
+system is non-linear as i get farther
+ 
+
+ align:start position:0%
+system is non-linear as i get farther
+from my trajectory
+
+ align:start position:0%
+from my trajectory
+ 
+
+ align:start position:0%
+from my trajectory
+some of the non-linearity is going to
+
+ align:start position:0%
+some of the non-linearity is going to
+ 
+
+ align:start position:0%
+some of the non-linearity is going to
+come in and corrupt
+
+ align:start position:0%
+come in and corrupt
+ 
+
+ align:start position:0%
+come in and corrupt
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+my lyapunov function
+
+ align:start position:0%
+my lyapunov function
+ 
+
+ align:start position:0%
+my lyapunov function
+at some point when i get far enough from
+
+ align:start position:0%
+at some point when i get far enough from
+ 
+
+ align:start position:0%
+at some point when i get far enough from
+the trajectory those higher order terms
+
+ align:start position:0%
+the trajectory those higher order terms
+ 
+
+ align:start position:0%
+the trajectory those higher order terms
+are going to mean that this thing
+
+ align:start position:0%
+are going to mean that this thing
+ 
+
+ align:start position:0%
+are going to mean that this thing
+doesn't have a negative
+
+ align:start position:0%
+doesn't have a negative
+ 
+
+ align:start position:0%
+doesn't have a negative
+time derivative right what i care about
+
+ align:start position:0%
+time derivative right what i care about
+ 
+
+ align:start position:0%
+time derivative right what i care about
+for the opera function
+
+ align:start position:0%
+for the opera function
+ 
+
+ align:start position:0%
+for the opera function
+is that this thing
+
+ align:start position:0%
+is that this thing
+ 
+
+ align:start position:0%
+is that this thing
+is less than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea with the certificates
+
+ align:start position:0%
+so the idea with the certificates
+ 
+
+ align:start position:0%
+so the idea with the certificates
+is to do a higher order polynomial
+
+ align:start position:0%
+is to do a higher order polynomial
+ 
+
+ align:start position:0%
+is to do a higher order polynomial
+expansion of the dynamics along this
+
+ align:start position:0%
+expansion of the dynamics along this
+ 
+
+ align:start position:0%
+expansion of the dynamics along this
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+and try to estimate the threshold
+
+ align:start position:0%
+and try to estimate the threshold
+ 
+
+ align:start position:0%
+and try to estimate the threshold
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+this stops being true
+
+ align:start position:0%
+this stops being true
+ 
+
+ align:start position:0%
+this stops being true
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that gives me
+
+ align:start position:0%
+and that gives me
+ 
+
+ align:start position:0%
+and that gives me
+essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a funnel if i do it everywhere in time
+
+ align:start position:0%
+a funnel if i do it everywhere in time
+ 
+
+ align:start position:0%
+a funnel if i do it everywhere in time
+that gives me a funnel along the
+
+ align:start position:0%
+that gives me a funnel along the
+ 
+
+ align:start position:0%
+that gives me a funnel along the
+trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over which i know the
+
+ align:start position:0%
+over which i know the
+ 
+
+ align:start position:0%
+over which i know the
+lqr
+
+ align:start position:0%
+lqr
+ 
+
+ align:start position:0%
+lqr
+cost to go
+
+ align:start position:0%
+cost to go
+ 
+
+ align:start position:0%
+cost to go
+is a liapanov function
+
+ align:start position:0%
+is a liapanov function
+ 
+
+ align:start position:0%
+is a liapanov function
+for the nonlinear system
+
+ align:start position:0%
+for the nonlinear system
+ 
+
+ align:start position:0%
+for the nonlinear system
+and it's mostly conservative the way
+
+ align:start position:0%
+and it's mostly conservative the way
+ 
+
+ align:start position:0%
+and it's mostly conservative the way
+that we can the way that we construct
+
+ align:start position:0%
+that we can the way that we construct
+ 
+
+ align:start position:0%
+that we can the way that we construct
+that threshold
+
+ align:start position:0%
+that threshold
+ 
+
+ align:start position:0%
+that threshold
+is mostly conservative
+
+ align:start position:0%
+is mostly conservative
+ 
+
+ align:start position:0%
+is mostly conservative
+the only weakness of it meaning the base
+
+ align:start position:0%
+the only weakness of it meaning the base
+ 
+
+ align:start position:0%
+the only weakness of it meaning the base
+the real base and attraction should be
+
+ align:start position:0%
+the real base and attraction should be
+ 
+
+ align:start position:0%
+the real base and attraction should be
+bigger than this estimate
+
+ align:start position:0%
+bigger than this estimate
+ 
+
+ align:start position:0%
+bigger than this estimate
+the only weakness is that i'm only doing
+
+ align:start position:0%
+the only weakness is that i'm only doing
+ 
+
+ align:start position:0%
+the only weakness is that i'm only doing
+it by doing a polynomial expansion of
+
+ align:start position:0%
+it by doing a polynomial expansion of
+ 
+
+ align:start position:0%
+it by doing a polynomial expansion of
+the system here so if there was a hard
+
+ align:start position:0%
+the system here so if there was a hard
+ 
+
+ align:start position:0%
+the system here so if there was a hard
+discontinuity right next to the
+
+ align:start position:0%
+discontinuity right next to the
+ 
+
+ align:start position:0%
+discontinuity right next to the
+trajectory that didn't show up in the
+
+ align:start position:0%
+trajectory that didn't show up in the
+ 
+
+ align:start position:0%
+trajectory that didn't show up in the
+taylor expansion then i wouldn't ever
+
+ align:start position:0%
+taylor expansion then i wouldn't ever
+ 
+
+ align:start position:0%
+taylor expansion then i wouldn't ever
+see it i'm not exhaustively searching
+
+ align:start position:0%
+see it i'm not exhaustively searching
+ 
+
+ align:start position:0%
+see it i'm not exhaustively searching
+this the non-linearity around that
+
+ align:start position:0%
+this the non-linearity around that
+ 
+
+ align:start position:0%
+this the non-linearity around that
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+i'm just saying along this trajectory
+
+ align:start position:0%
+i'm just saying along this trajectory
+ 
+
+ align:start position:0%
+i'm just saying along this trajectory
+what are the higher order expansion i do
+
+ align:start position:0%
+what are the higher order expansion i do
+ 
+
+ align:start position:0%
+what are the higher order expansion i do
+a taylor expansion of a third order
+
+ align:start position:0%
+a taylor expansion of a third order
+ 
+
+ align:start position:0%
+a taylor expansion of a third order
+fourth order whatever it takes
+
+ align:start position:0%
+fourth order whatever it takes
+ 
+
+ align:start position:0%
+fourth order whatever it takes
+and i use that to check when it breaks
+
+ align:start position:0%
+and i use that to check when it breaks
+ 
+
+ align:start position:0%
+and i use that to check when it breaks
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cost to go okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the certificate that's just if
+
+ align:start position:0%
+so that's the certificate that's just if
+ 
+
+ align:start position:0%
+so that's the certificate that's just if
+i have a single trajectory then i can
+
+ align:start position:0%
+i have a single trajectory then i can
+ 
+
+ align:start position:0%
+i have a single trajectory then i can
+use this the real cool thing is that
+
+ align:start position:0%
+use this the real cool thing is that
+ 
+
+ align:start position:0%
+use this the real cool thing is that
+thanks to pablo and and sasha mcgretzky
+
+ align:start position:0%
+thanks to pablo and and sasha mcgretzky
+ 
+
+ align:start position:0%
+thanks to pablo and and sasha mcgretzky
+we can do that efficiently with a convex
+
+ align:start position:0%
+we can do that efficiently with a convex
+ 
+
+ align:start position:0%
+we can do that efficiently with a convex
+optimization
+
+ align:start position:0%
+optimization
+ 
+
+ align:start position:0%
+optimization
+and then the idea is if i can do it for
+
+ align:start position:0%
+and then the idea is if i can do it for
+ 
+
+ align:start position:0%
+and then the idea is if i can do it for
+a single trajectory
+
+ align:start position:0%
+a single trajectory
+ 
+
+ align:start position:0%
+a single trajectory
+then why not put that back into a sort
+
+ align:start position:0%
+then why not put that back into a sort
+ 
+
+ align:start position:0%
+then why not put that back into a sort
+of an rrt kind of framework
+
+ align:start position:0%
+of an rrt kind of framework
+ 
+
+ align:start position:0%
+of an rrt kind of framework
+and try to build lots of trajectories
+
+ align:start position:0%
+and try to build lots of trajectories
+ 
+
+ align:start position:0%
+and try to build lots of trajectories
+that are stabilized
+
+ align:start position:0%
+that are stabilized
+ 
+
+ align:start position:0%
+that are stabilized
+okay so the first step was just to pick
+
+ align:start position:0%
+okay so the first step was just to pick
+ 
+
+ align:start position:0%
+okay so the first step was just to pick
+a point in random design a single
+
+ align:start position:0%
+a point in random design a single
+ 
+
+ align:start position:0%
+a point in random design a single
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+the second step is let's pick a new
+
+ align:start position:0%
+the second step is let's pick a new
+ 
+
+ align:start position:0%
+the second step is let's pick a new
+random point
+
+ align:start position:0%
+random point
+ 
+
+ align:start position:0%
+random point
+i don't actually have to go all the way
+
+ align:start position:0%
+i don't actually have to go all the way
+ 
+
+ align:start position:0%
+i don't actually have to go all the way
+back to my goal i just have to go to the
+
+ align:start position:0%
+back to my goal i just have to go to the
+ 
+
+ align:start position:0%
+back to my goal i just have to go to the
+nearest point on the current tree
+
+ align:start position:0%
+nearest point on the current tree
+ 
+
+ align:start position:0%
+nearest point on the current tree
+and stabilize that
+
+ align:start position:0%
+and stabilize that
+ 
+
+ align:start position:0%
+and stabilize that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and then i pick another point
+
+ align:start position:0%
+and then i pick another point
+ 
+
+ align:start position:0%
+and then i pick another point
+find the nearest point on the closer
+
+ align:start position:0%
+find the nearest point on the closer
+ 
+
+ align:start position:0%
+find the nearest point on the closer
+close on the tree
+
+ align:start position:0%
+close on the tree
+ 
+
+ align:start position:0%
+close on the tree
+build the trajectory and like that
+
+ align:start position:0%
+build the trajectory and like that
+ 
+
+ align:start position:0%
+build the trajectory and like that
+stabilize that
+
+ align:start position:0%
+stabilize that
+ 
+
+ align:start position:0%
+stabilize that
+right if i pick a new point and it's
+
+ align:start position:0%
+right if i pick a new point and it's
+ 
+
+ align:start position:0%
+right if i pick a new point and it's
+already in the basin of attraction i
+
+ align:start position:0%
+already in the basin of attraction i
+ 
+
+ align:start position:0%
+already in the basin of attraction i
+don't i don't need to add
+
+ align:start position:0%
+don't i don't need to add
+ 
+
+ align:start position:0%
+don't i don't need to add
+an edge that was that would be sort of a
+
+ align:start position:0%
+an edge that was that would be sort of a
+ 
+
+ align:start position:0%
+an edge that was that would be sort of a
+waste of my time
+
+ align:start position:0%
+waste of my time
+ 
+
+ align:start position:0%
+waste of my time
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the effect is i get these
+
+ align:start position:0%
+the effect is i get these
+ 
+
+ align:start position:0%
+the effect is i get these
+um i didn't say carefully what the
+
+ align:start position:0%
+um i didn't say carefully what the
+ 
+
+ align:start position:0%
+um i didn't say carefully what the
+results are because i can't prove them
+
+ align:start position:0%
+results are because i can't prove them
+ 
+
+ align:start position:0%
+results are because i can't prove them
+yet this is still hot off the press but
+
+ align:start position:0%
+yet this is still hot off the press but
+ 
+
+ align:start position:0%
+yet this is still hot off the press but
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+i can say that it probabilistically
+
+ align:start position:0%
+i can say that it probabilistically
+ 
+
+ align:start position:0%
+i can say that it probabilistically
+covers the reachable state space
+
+ align:start position:0%
+covers the reachable state space
+ 
+
+ align:start position:0%
+covers the reachable state space
+every place that i can get to the goal
+
+ align:start position:0%
+every place that i can get to the goal
+ 
+
+ align:start position:0%
+every place that i can get to the goal
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+there exists controller
+
+ align:start position:0%
+there exists controller
+ 
+
+ align:start position:0%
+there exists controller
+if i design enough samples i should be
+
+ align:start position:0%
+if i design enough samples i should be
+ 
+
+ align:start position:0%
+if i design enough samples i should be
+able to get to the goal
+
+ align:start position:0%
+able to get to the goal
+ 
+
+ align:start position:0%
+able to get to the goal
+given i do enough steps of my lqr tree
+
+ align:start position:0%
+given i do enough steps of my lqr tree
+ 
+
+ align:start position:0%
+given i do enough steps of my lqr tree
+so as time goes to infinity the entire
+
+ align:start position:0%
+so as time goes to infinity the entire
+ 
+
+ align:start position:0%
+so as time goes to infinity the entire
+space will be covered
+
+ align:start position:0%
+space will be covered
+ 
+
+ align:start position:0%
+space will be covered
+with basin of attraction of a controller
+
+ align:start position:0%
+with basin of attraction of a controller
+ 
+
+ align:start position:0%
+with basin of attraction of a controller
+that gets me to the goal which is a
+
+ align:start position:0%
+that gets me to the goal which is a
+ 
+
+ align:start position:0%
+that gets me to the goal which is a
+pretty powerful thing to say if you're
+
+ align:start position:0%
+pretty powerful thing to say if you're
+ 
+
+ align:start position:0%
+pretty powerful thing to say if you're
+willing to wait till time goes to
+
+ align:start position:0%
+willing to wait till time goes to
+ 
+
+ align:start position:0%
+willing to wait till time goes to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+practical thing that's nice about it is
+
+ align:start position:0%
+practical thing that's nice about it is
+ 
+
+ align:start position:0%
+practical thing that's nice about it is
+it seems to happen pretty quick with a
+
+ align:start position:0%
+it seems to happen pretty quick with a
+ 
+
+ align:start position:0%
+it seems to happen pretty quick with a
+handful with a fairly small number of
+
+ align:start position:0%
+handful with a fairly small number of
+ 
+
+ align:start position:0%
+handful with a fairly small number of
+trajectories
+
+ align:start position:0%
+trajectories
+ 
+
+ align:start position:0%
+trajectories
+yeah chuck you want to keep the knob in
+
+ align:start position:0%
+yeah chuck you want to keep the knob in
+ 
+
+ align:start position:0%
+yeah chuck you want to keep the knob in
+your system as that includes property
+
+ align:start position:0%
+your system as that includes property
+ 
+
+ align:start position:0%
+your system as that includes property
+would you have to let it sample inside
+
+ align:start position:0%
+would you have to let it sample inside
+ 
+
+ align:start position:0%
+would you have to let it sample inside
+the basics of attraction
+
+ align:start position:0%
+the basics of attraction
+ 
+
+ align:start position:0%
+the basics of attraction
+yeah so that's that's why i have to
+
+ align:start position:0%
+yeah so that's that's why i have to
+ 
+
+ align:start position:0%
+yeah so that's that's why i have to
+qualify the guarantees i'm only saying
+
+ align:start position:0%
+qualify the guarantees i'm only saying
+ 
+
+ align:start position:0%
+qualify the guarantees i'm only saying
+the non-linear system as represented as
+
+ align:start position:0%
+the non-linear system as represented as
+ 
+
+ align:start position:0%
+the non-linear system as represented as
+the taylor expansion around the
+
+ align:start position:0%
+the taylor expansion around the
+ 
+
+ align:start position:0%
+the taylor expansion around the
+trajectories that's the that's the
+
+ align:start position:0%
+trajectories that's the that's the
+ 
+
+ align:start position:0%
+trajectories that's the that's the
+weakness so it really only works for
+
+ align:start position:0%
+weakness so it really only works for
+ 
+
+ align:start position:0%
+weakness so it really only works for
+smooth systems if there's a cliff
+
+ align:start position:0%
+smooth systems if there's a cliff
+ 
+
+ align:start position:0%
+smooth systems if there's a cliff
+here and i'm designing a trajectory
+
+ align:start position:0%
+here and i'm designing a trajectory
+ 
+
+ align:start position:0%
+here and i'm designing a trajectory
+right here it might come up with a
+
+ align:start position:0%
+right here it might come up with a
+ 
+
+ align:start position:0%
+right here it might come up with a
+saying a basin of attractions here even
+
+ align:start position:0%
+saying a basin of attractions here even
+ 
+
+ align:start position:0%
+saying a basin of attractions here even
+though that's just not true
+
+ align:start position:0%
+though that's just not true
+ 
+
+ align:start position:0%
+though that's just not true
+okay if i smooth the cliff sorry john if
+
+ align:start position:0%
+okay if i smooth the cliff sorry john if
+ 
+
+ align:start position:0%
+okay if i smooth the cliff sorry john if
+i smooth the cliff
+
+ align:start position:0%
+i smooth the cliff
+ 
+
+ align:start position:0%
+i smooth the cliff
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+when i tailor expand here i can see that
+
+ align:start position:0%
+when i tailor expand here i can see that
+ 
+
+ align:start position:0%
+when i tailor expand here i can see that
+there's a cliff there then i'd like to
+
+ align:start position:0%
+there's a cliff there then i'd like to
+ 
+
+ align:start position:0%
+there's a cliff there then i'd like to
+think that the
+
+ align:start position:0%
+think that the
+ 
+
+ align:start position:0%
+think that the
+um that the uh certificates would would
+
+ align:start position:0%
+um that the uh certificates would would
+ 
+
+ align:start position:0%
+um that the uh certificates would would
+do the right thing but if it's a
+
+ align:start position:0%
+do the right thing but if it's a
+ 
+
+ align:start position:0%
+do the right thing but if it's a
+hardcliff that where the where the
+
+ align:start position:0%
+hardcliff that where the where the
+ 
+
+ align:start position:0%
+hardcliff that where the where the
+higher order expansion here doesn't see
+
+ align:start position:0%
+higher order expansion here doesn't see
+ 
+
+ align:start position:0%
+higher order expansion here doesn't see
+that cliff then there's no hope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question so just building
+
+ align:start position:0%
+that's a good question so just building
+ 
+
+ align:start position:0%
+that's a good question so just building
+more and more accurate certificates as
+
+ align:start position:0%
+more and more accurate certificates as
+ 
+
+ align:start position:0%
+more and more accurate certificates as
+time goes to infinity it could be
+
+ align:start position:0%
+time goes to infinity it could be
+ 
+
+ align:start position:0%
+time goes to infinity it could be
+it could be that it could be a good idea
+
+ align:start position:0%
+it could be that it could be a good idea
+ 
+
+ align:start position:0%
+it could be that it could be a good idea
+um my suspicion is that
+
+ align:start position:0%
+um my suspicion is that
+ 
+
+ align:start position:0%
+um my suspicion is that
+in practice this is going to be good
+
+ align:start position:0%
+in practice this is going to be good
+ 
+
+ align:start position:0%
+in practice this is going to be good
+enough for and and we're not going to
+
+ align:start position:0%
+enough for and and we're not going to
+ 
+
+ align:start position:0%
+enough for and and we're not going to
+want to do the
+
+ align:start position:0%
+want to do the
+ 
+
+ align:start position:0%
+want to do the
+maybe i'm just
+
+ align:start position:0%
+maybe i'm just
+ 
+
+ align:start position:0%
+maybe i'm just
+the kind of guy that cuts a corner cuts
+
+ align:start position:0%
+the kind of guy that cuts a corner cuts
+ 
+
+ align:start position:0%
+the kind of guy that cuts a corner cuts
+the corners but i think this is a pretty
+
+ align:start position:0%
+the corners but i think this is a pretty
+ 
+
+ align:start position:0%
+the corners but i think this is a pretty
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i use i whenever i design each
+
+ align:start position:0%
+so i use i whenever i design each
+ 
+
+ align:start position:0%
+so i use i whenever i design each
+trajectory i use der call why not
+
+ align:start position:0%
+trajectory i use der call why not
+ 
+
+ align:start position:0%
+trajectory i use der call why not
+but it's so so i can sort of say they're
+
+ align:start position:0%
+but it's so so i can sort of say they're
+ 
+
+ align:start position:0%
+but it's so so i can sort of say they're
+locally optimal in the branches that
+
+ align:start position:0%
+locally optimal in the branches that
+ 
+
+ align:start position:0%
+locally optimal in the branches that
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+just because that's easy to easy to
+
+ align:start position:0%
+just because that's easy to easy to
+ 
+
+ align:start position:0%
+just because that's easy to easy to
+accomplish but there's no sense in which
+
+ align:start position:0%
+accomplish but there's no sense in which
+ 
+
+ align:start position:0%
+accomplish but there's no sense in which
+it's globally optimal
+
+ align:start position:0%
+it's globally optimal
+ 
+
+ align:start position:0%
+it's globally optimal
+right so i just i just try to say that
+
+ align:start position:0%
+right so i just i just try to say that
+ 
+
+ align:start position:0%
+right so i just i just try to say that
+every state will eventually get there
+
+ align:start position:0%
+every state will eventually get there
+ 
+
+ align:start position:0%
+every state will eventually get there
+not that it'll get there optimally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but again if you're allowed to sample
+
+ align:start position:0%
+but again if you're allowed to sample
+ 
+
+ align:start position:0%
+but again if you're allowed to sample
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+the basis of attraction you would
+
+ align:start position:0%
+the basis of attraction you would
+ 
+
+ align:start position:0%
+the basis of attraction you would
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+get some kind of convergence to global
+
+ align:start position:0%
+get some kind of convergence to global
+ 
+
+ align:start position:0%
+get some kind of convergence to global
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are there are ways to try to get
+
+ align:start position:0%
+there are there are ways to try to get
+ 
+
+ align:start position:0%
+there are there are ways to try to get
+at that problem i don't think it's a one
+
+ align:start position:0%
+at that problem i don't think it's a one
+ 
+
+ align:start position:0%
+at that problem i don't think it's a one
+step change from what i said i think you
+
+ align:start position:0%
+step change from what i said i think you
+ 
+
+ align:start position:0%
+step change from what i said i think you
+have to do something more
+
+ align:start position:0%
+have to do something more
+ 
+
+ align:start position:0%
+have to do something more
+i mean any one of these trajectories
+
+ align:start position:0%
+i mean any one of these trajectories
+ 
+
+ align:start position:0%
+i mean any one of these trajectories
+right um
+
+ align:start position:0%
+right um
+ 
+
+ align:start position:0%
+right um
+maybe that's getting busy any one of
+
+ align:start position:0%
+maybe that's getting busy any one of
+ 
+
+ align:start position:0%
+maybe that's getting busy any one of
+those trajectories is just locally
+
+ align:start position:0%
+those trajectories is just locally
+ 
+
+ align:start position:0%
+those trajectories is just locally
+optimal right so let's consider the case
+
+ align:start position:0%
+optimal right so let's consider the case
+ 
+
+ align:start position:0%
+optimal right so let's consider the case
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+the goal is here there's a
+
+ align:start position:0%
+the goal is here there's a
+ 
+
+ align:start position:0%
+the goal is here there's a
+something here and i i did this and for
+
+ align:start position:0%
+something here and i i did this and for
+ 
+
+ align:start position:0%
+something here and i i did this and for
+some reason i got a
+
+ align:start position:0%
+some reason i got a
+ 
+
+ align:start position:0%
+some reason i got a
+trajectory like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is locally optimal but not
+
+ align:start position:0%
+which is locally optimal but not
+ 
+
+ align:start position:0%
+which is locally optimal but not
+globally optimal because there's a
+
+ align:start position:0%
+globally optimal because there's a
+ 
+
+ align:start position:0%
+globally optimal because there's a
+shorter path here so i need to somehow i
+
+ align:start position:0%
+shorter path here so i need to somehow i
+ 
+
+ align:start position:0%
+shorter path here so i need to somehow i
+would need to somehow include the
+
+ align:start position:0%
+would need to somehow include the
+ 
+
+ align:start position:0%
+would need to somehow include the
+mechanism which is i think what you're
+
+ align:start position:0%
+mechanism which is i think what you're
+ 
+
+ align:start position:0%
+mechanism which is i think what you're
+getting at to
+
+ align:start position:0%
+getting at to
+ 
+
+ align:start position:0%
+getting at to
+eventually take a dip
+
+ align:start position:0%
+eventually take a dip
+ 
+
+ align:start position:0%
+eventually take a dip
+find a different path to the same place
+
+ align:start position:0%
+find a different path to the same place
+ 
+
+ align:start position:0%
+find a different path to the same place
+and overwrite the old path and i don't
+
+ align:start position:0%
+and overwrite the old path and i don't
+ 
+
+ align:start position:0%
+and overwrite the old path and i don't
+have any
+
+ align:start position:0%
+have any
+ 
+
+ align:start position:0%
+have any
+mechanism for that inside and it turns
+
+ align:start position:0%
+mechanism for that inside and it turns
+ 
+
+ align:start position:0%
+mechanism for that inside and it turns
+out that's actually what i was going for
+
+ align:start position:0%
+out that's actually what i was going for
+ 
+
+ align:start position:0%
+out that's actually what i was going for
+initially turns out to be a little bit
+
+ align:start position:0%
+initially turns out to be a little bit
+ 
+
+ align:start position:0%
+initially turns out to be a little bit
+non-trivial to to do
+
+ align:start position:0%
+non-trivial to to do
+ 
+
+ align:start position:0%
+non-trivial to to do
+chris atkinson has a nice idea
+
+ align:start position:0%
+chris atkinson has a nice idea
+ 
+
+ align:start position:0%
+chris atkinson has a nice idea
+that that goes goes towards doing that a
+
+ align:start position:0%
+that that goes goes towards doing that a
+ 
+
+ align:start position:0%
+that that goes goes towards doing that a
+little bit more on composing trajectory
+
+ align:start position:0%
+little bit more on composing trajectory
+ 
+
+ align:start position:0%
+little bit more on composing trajectory
+libraries
+
+ align:start position:0%
+libraries
+ 
+
+ align:start position:0%
+libraries
+um but i i gave up optimality and tried
+
+ align:start position:0%
+um but i i gave up optimality and tried
+ 
+
+ align:start position:0%
+um but i i gave up optimality and tried
+to get coverage of with the basin of
+
+ align:start position:0%
+to get coverage of with the basin of
+ 
+
+ align:start position:0%
+to get coverage of with the basin of
+attraction
+
+ align:start position:0%
+attraction
+ 
+
+ align:start position:0%
+attraction
+in that design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so some of you been talking about to
+
+ align:start position:0%
+so so some of you been talking about to
+ 
+
+ align:start position:0%
+so so some of you been talking about to
+me about the projects and i've and
+
+ align:start position:0%
+me about the projects and i've and
+ 
+
+ align:start position:0%
+me about the projects and i've and
+have been asking about these things so
+
+ align:start position:0%
+have been asking about these things so
+ 
+
+ align:start position:0%
+have been asking about these things so
+so i think mark and matt are thinking
+
+ align:start position:0%
+so i think mark and matt are thinking
+ 
+
+ align:start position:0%
+so i think mark and matt are thinking
+about trying to to help with this i mean
+
+ align:start position:0%
+about trying to to help with this i mean
+ 
+
+ align:start position:0%
+about trying to to help with this i mean
+this is this is new i mean you guys can
+
+ align:start position:0%
+this is this is new i mean you guys can
+ 
+
+ align:start position:0%
+this is this is new i mean you guys can
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+definitely help with the the the idea so
+
+ align:start position:0%
+definitely help with the the the idea so
+ 
+
+ align:start position:0%
+definitely help with the the the idea so
+so i we're trying to figure out for
+
+ align:start position:0%
+so i we're trying to figure out for
+ 
+
+ align:start position:0%
+so i we're trying to figure out for
+instance if there's um actuator limits
+
+ align:start position:0%
+instance if there's um actuator limits
+ 
+
+ align:start position:0%
+instance if there's um actuator limits
+um these guys are talking about trying
+
+ align:start position:0%
+um these guys are talking about trying
+ 
+
+ align:start position:0%
+um these guys are talking about trying
+to figure out how to compute the
+
+ align:start position:0%
+to figure out how to compute the
+ 
+
+ align:start position:0%
+to figure out how to compute the
+certificates and even the lqr stabilizer
+
+ align:start position:0%
+certificates and even the lqr stabilizer
+ 
+
+ align:start position:0%
+certificates and even the lqr stabilizer
+if you if you not only have a quadratic
+
+ align:start position:0%
+if you if you not only have a quadratic
+ 
+
+ align:start position:0%
+if you if you not only have a quadratic
+cost on you but have some hard limits on
+
+ align:start position:0%
+cost on you but have some hard limits on
+ 
+
+ align:start position:0%
+cost on you but have some hard limits on
+you because that's a problem we actually
+
+ align:start position:0%
+you because that's a problem we actually
+ 
+
+ align:start position:0%
+you because that's a problem we actually
+hit in in practice so so one of the
+
+ align:start position:0%
+hit in in practice so so one of the
+ 
+
+ align:start position:0%
+hit in in practice so so one of the
+final projects in the class i think is
+
+ align:start position:0%
+final projects in the class i think is
+ 
+
+ align:start position:0%
+final projects in the class i think is
+going to be helping with that there's
+
+ align:start position:0%
+going to be helping with that there's
+ 
+
+ align:start position:0%
+going to be helping with that there's
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+problems of how do you design the
+
+ align:start position:0%
+problems of how do you design the
+ 
+
+ align:start position:0%
+problems of how do you design the
+stabilizer through impacts and in
+
+ align:start position:0%
+stabilizer through impacts and in
+ 
+
+ align:start position:0%
+stabilizer through impacts and in
+periodic systems there's lots of good
+
+ align:start position:0%
+periodic systems there's lots of good
+ 
+
+ align:start position:0%
+periodic systems there's lots of good
+questions so if you're if you're excited
+
+ align:start position:0%
+questions so if you're if you're excited
+ 
+
+ align:start position:0%
+questions so if you're if you're excited
+about that idea i'm definitely excited
+
+ align:start position:0%
+about that idea i'm definitely excited
+ 
+
+ align:start position:0%
+about that idea i'm definitely excited
+about the idea right now
+
+ align:start position:0%
+about the idea right now
+ 
+
+ align:start position:0%
+about the idea right now
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+i'll see what you wrote up today but we
+
+ align:start position:0%
+i'll see what you wrote up today but we
+ 
+
+ align:start position:0%
+i'll see what you wrote up today but we
+could maybe try to find a way to connect
+
+ align:start position:0%
+could maybe try to find a way to connect
+ 
+
+ align:start position:0%
+could maybe try to find a way to connect
+that i'd be i'd be thrilled to
+
+ align:start position:0%
+that i'd be i'd be thrilled to
+ 
+
+ align:start position:0%
+that i'd be i'd be thrilled to
+to have your help in making that idea
+
+ align:start position:0%
+to have your help in making that idea
+ 
+
+ align:start position:0%
+to have your help in making that idea
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+relevant
+
+ align:start position:0%
+relevant
+ 
+
+ align:start position:0%
+relevant
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is that sort of cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for something completely different
+
+ align:start position:0%
+now for something completely different
+ 
+
+ align:start position:0%
+now for something completely different
+although related of course
+
+ align:start position:0%
+although related of course
+ 
+
+ align:start position:0%
+although related of course
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in the lqr trees that basically in
+
+ align:start position:0%
+so in the lqr trees that basically in
+ 
+
+ align:start position:0%
+so in the lqr trees that basically in
+everything that we've done so far in
+
+ align:start position:0%
+everything that we've done so far in
+ 
+
+ align:start position:0%
+everything that we've done so far in
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+we've made a handful of
+
+ align:start position:0%
+we've made a handful of
+ 
+
+ align:start position:0%
+we've made a handful of
+of important
+
+ align:start position:0%
+of important
+ 
+
+ align:start position:0%
+of important
+assumptions right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the most important one probably is
+
+ align:start position:0%
+the most important one probably is
+ 
+
+ align:start position:0%
+the most important one probably is
+they've always assumed that we have the
+
+ align:start position:0%
+they've always assumed that we have the
+ 
+
+ align:start position:0%
+they've always assumed that we have the
+model of the system right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so next week we're going to get it how
+
+ align:start position:0%
+so next week we're going to get it how
+ 
+
+ align:start position:0%
+so next week we're going to get it how
+do you how do you do some of these
+
+ align:start position:0%
+do you how do you do some of these
+ 
+
+ align:start position:0%
+do you how do you do some of these
+optimizations when you don't even have a
+
+ align:start position:0%
+optimizations when you don't even have a
+ 
+
+ align:start position:0%
+optimizations when you don't even have a
+model okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've also assumed so far that the
+
+ align:start position:0%
+we've also assumed so far that the
+ 
+
+ align:start position:0%
+we've also assumed so far that the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the current state of the system is known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words the state of the robot is
+
+ align:start position:0%
+in other words the state of the robot is
+ 
+
+ align:start position:0%
+in other words the state of the robot is
+fully observable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i stop assuming that we gotta start
+
+ align:start position:0%
+if i stop assuming that we gotta start
+ 
+
+ align:start position:0%
+if i stop assuming that we gotta start
+getting into discussions about state
+
+ align:start position:0%
+getting into discussions about state
+ 
+
+ align:start position:0%
+getting into discussions about state
+estimation and we will towards the end
+
+ align:start position:0%
+estimation and we will towards the end
+ 
+
+ align:start position:0%
+estimation and we will towards the end
+of the class
+
+ align:start position:0%
+of the class
+ 
+
+ align:start position:0%
+of the class
+and there's another
+
+ align:start position:0%
+and there's another
+ 
+
+ align:start position:0%
+and there's another
+assumption we've been making which is
+
+ align:start position:0%
+assumption we've been making which is
+ 
+
+ align:start position:0%
+assumption we've been making which is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the dynamics
+
+ align:start position:0%
+the dynamics
+ 
+
+ align:start position:0%
+the dynamics
+are deterministic
+
+ align:start position:0%
+are deterministic
+ 
+
+ align:start position:0%
+are deterministic
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that that
+
+ align:start position:0%
+right that that
+ 
+
+ align:start position:0%
+right that that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+pretty much the system goes right
+
+ align:start position:0%
+pretty much the system goes right
+ 
+
+ align:start position:0%
+pretty much the system goes right
+where i think it's gonna go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no i chose to write that
+
+ align:start position:0%
+no i chose to write that
+ 
+
+ align:start position:0%
+no i chose to write that
+and then cross it out because that's not
+
+ align:start position:0%
+and then cross it out because that's not
+ 
+
+ align:start position:0%
+and then cross it out because that's not
+quite what we're assuming okay
+
+ align:start position:0%
+quite what we're assuming okay
+ 
+
+ align:start position:0%
+quite what we're assuming okay
+i wanted to i want to write that but but
+
+ align:start position:0%
+i wanted to i want to write that but but
+ 
+
+ align:start position:0%
+i wanted to i want to write that but but
+what are maybe what's a if we really
+
+ align:start position:0%
+what are maybe what's a if we really
+ 
+
+ align:start position:0%
+what are maybe what's a if we really
+were assuming that the dynamics were
+
+ align:start position:0%
+were assuming that the dynamics were
+ 
+
+ align:start position:0%
+were assuming that the dynamics were
+deterministic then we wouldn't have been
+
+ align:start position:0%
+deterministic then we wouldn't have been
+ 
+
+ align:start position:0%
+deterministic then we wouldn't have been
+spending much time talking about
+
+ align:start position:0%
+spending much time talking about
+ 
+
+ align:start position:0%
+spending much time talking about
+feedback at all
+
+ align:start position:0%
+feedback at all
+ 
+
+ align:start position:0%
+feedback at all
+we would have been just focused on
+
+ align:start position:0%
+we would have been just focused on
+ 
+
+ align:start position:0%
+we would have been just focused on
+open loop things right
+
+ align:start position:0%
+open loop things right
+ 
+
+ align:start position:0%
+open loop things right
+so let's think let's have a short
+
+ align:start position:0%
+so let's think let's have a short
+ 
+
+ align:start position:0%
+so let's think let's have a short
+philosophical argument about what we're
+
+ align:start position:0%
+philosophical argument about what we're
+ 
+
+ align:start position:0%
+philosophical argument about what we're
+actually doing here so we're not quite
+
+ align:start position:0%
+actually doing here so we're not quite
+ 
+
+ align:start position:0%
+actually doing here so we're not quite
+assuming that it's deterministic
+
+ align:start position:0%
+assuming that it's deterministic
+ 
+
+ align:start position:0%
+assuming that it's deterministic
+right maybe
+
+ align:start position:0%
+right maybe
+ 
+
+ align:start position:0%
+right maybe
+a better way to describe what we're
+
+ align:start position:0%
+a better way to describe what we're
+ 
+
+ align:start position:0%
+a better way to describe what we're
+doing is we're assuming
+
+ align:start position:0%
+doing is we're assuming
+ 
+
+ align:start position:0%
+doing is we're assuming
+something specific about the
+
+ align:start position:0%
+something specific about the
+ 
+
+ align:start position:0%
+something specific about the
+disturbances in the system
+
+ align:start position:0%
+disturbances in the system
+ 
+
+ align:start position:0%
+disturbances in the system
+we're really we're assuming that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disturbances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look like a change in initial conditions
+
+ align:start position:0%
+look like a change in initial conditions
+ 
+
+ align:start position:0%
+look like a change in initial conditions
+that's one way to say it right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an unmodeled change in initial
+
+ align:start position:0%
+an unmodeled change in initial
+ 
+
+ align:start position:0%
+an unmodeled change in initial
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right i
+
+ align:start position:0%
+right i
+ 
+
+ align:start position:0%
+right i
+by virtue of talking about these
+
+ align:start position:0%
+by virtue of talking about these
+ 
+
+ align:start position:0%
+by virtue of talking about these
+feedback stabilizers right
+
+ align:start position:0%
+feedback stabilizers right
+ 
+
+ align:start position:0%
+feedback stabilizers right
+the motivation is that okay i'm
+
+ align:start position:0%
+the motivation is that okay i'm
+ 
+
+ align:start position:0%
+the motivation is that okay i'm
+following this trajectory when the
+
+ align:start position:0%
+following this trajectory when the
+ 
+
+ align:start position:0%
+following this trajectory when the
+model's right are all is good if
+
+ align:start position:0%
+model's right are all is good if
+ 
+
+ align:start position:0%
+model's right are all is good if
+something does happen then okay it's
+
+ align:start position:0%
+something does happen then okay it's
+ 
+
+ align:start position:0%
+something does happen then okay it's
+going to move me somewhere in state
+
+ align:start position:0%
+going to move me somewhere in state
+ 
+
+ align:start position:0%
+going to move me somewhere in state
+space but as long as that's in the basin
+
+ align:start position:0%
+space but as long as that's in the basin
+ 
+
+ align:start position:0%
+space but as long as that's in the basin
+of attraction the whole idea of really a
+
+ align:start position:0%
+of attraction the whole idea of really a
+ 
+
+ align:start position:0%
+of attraction the whole idea of really a
+basis of attraction is going at the idea
+
+ align:start position:0%
+basis of attraction is going at the idea
+ 
+
+ align:start position:0%
+basis of attraction is going at the idea
+that i can handle disturbances by just
+
+ align:start position:0%
+that i can handle disturbances by just
+ 
+
+ align:start position:0%
+that i can handle disturbances by just
+being robust in state
+
+ align:start position:0%
+being robust in state
+ 
+
+ align:start position:0%
+being robust in state
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but that's actually sort of a subtle
+
+ align:start position:0%
+but that's actually sort of a subtle
+ 
+
+ align:start position:0%
+but that's actually sort of a subtle
+thing to assume right i want to be a
+
+ align:start position:0%
+thing to assume right i want to be a
+ 
+
+ align:start position:0%
+thing to assume right i want to be a
+little bit more explicit about what that
+
+ align:start position:0%
+little bit more explicit about what that
+ 
+
+ align:start position:0%
+little bit more explicit about what that
+means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really it sort of implies that we're
+
+ align:start position:0%
+really it sort of implies that we're
+ 
+
+ align:start position:0%
+really it sort of implies that we're
+assuming that
+
+ align:start position:0%
+assuming that
+ 
+
+ align:start position:0%
+assuming that
+disturbances are
+
+ align:start position:0%
+disturbances are
+ 
+
+ align:start position:0%
+disturbances are
+impulsive
+
+ align:start position:0%
+impulsive
+ 
+
+ align:start position:0%
+impulsive
+not constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instantaneous right impulsive
+
+ align:start position:0%
+instantaneous right impulsive
+ 
+
+ align:start position:0%
+instantaneous right impulsive
+if a disturbance was for my walking
+
+ align:start position:0%
+if a disturbance was for my walking
+ 
+
+ align:start position:0%
+if a disturbance was for my walking
+robot was
+
+ align:start position:0%
+robot was
+ 
+
+ align:start position:0%
+robot was
+um someone put a new weight on my leg
+
+ align:start position:0%
+um someone put a new weight on my leg
+ 
+
+ align:start position:0%
+um someone put a new weight on my leg
+then that's not
+
+ align:start position:0%
+then that's not
+ 
+
+ align:start position:0%
+then that's not
+something that our designs so far have
+
+ align:start position:0%
+something that our designs so far have
+ 
+
+ align:start position:0%
+something that our designs so far have
+handled because that's more like the
+
+ align:start position:0%
+handled because that's more like the
+ 
+
+ align:start position:0%
+handled because that's more like the
+model changed right we're talking about
+
+ align:start position:0%
+model changed right we're talking about
+ 
+
+ align:start position:0%
+model changed right we're talking about
+something that it moved me
+
+ align:start position:0%
+something that it moved me
+ 
+
+ align:start position:0%
+something that it moved me
+and now i have to deal with it right so
+
+ align:start position:0%
+and now i have to deal with it right so
+ 
+
+ align:start position:0%
+and now i have to deal with it right so
+if the disturbance lasts for a long time
+
+ align:start position:0%
+if the disturbance lasts for a long time
+ 
+
+ align:start position:0%
+if the disturbance lasts for a long time
+then that actually feels a lot more like
+
+ align:start position:0%
+then that actually feels a lot more like
+ 
+
+ align:start position:0%
+then that actually feels a lot more like
+a model change right but if it's
+
+ align:start position:0%
+a model change right but if it's
+ 
+
+ align:start position:0%
+a model change right but if it's
+impulsive i can sort of think of it as a
+
+ align:start position:0%
+impulsive i can sort of think of it as a
+ 
+
+ align:start position:0%
+impulsive i can sort of think of it as a
+change in initial condition
+
+ align:start position:0%
+change in initial condition
+ 
+
+ align:start position:0%
+change in initial condition
+and the other thing that that sort of
+
+ align:start position:0%
+and the other thing that that sort of
+ 
+
+ align:start position:0%
+and the other thing that that sort of
+implicitly assumes is that the
+
+ align:start position:0%
+implicitly assumes is that the
+ 
+
+ align:start position:0%
+implicitly assumes is that the
+disturbances are rare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right if i got impulsive disturbances
+
+ align:start position:0%
+right if i got impulsive disturbances
+ 
+
+ align:start position:0%
+right if i got impulsive disturbances
+a thousand times a second
+
+ align:start position:0%
+a thousand times a second
+ 
+
+ align:start position:0%
+a thousand times a second
+then again
+
+ align:start position:0%
+then again
+ 
+
+ align:start position:0%
+then again
+my completely deterministic
+
+ align:start position:0%
+my completely deterministic
+ 
+
+ align:start position:0%
+my completely deterministic
+analysis isn't probably the relevant
+
+ align:start position:0%
+analysis isn't probably the relevant
+ 
+
+ align:start position:0%
+analysis isn't probably the relevant
+one okay so that's those are sort of
+
+ align:start position:0%
+one okay so that's those are sort of
+ 
+
+ align:start position:0%
+one okay so that's those are sort of
+implicitly making these assumptions the
+
+ align:start position:0%
+implicitly making these assumptions the
+ 
+
+ align:start position:0%
+implicitly making these assumptions the
+whole thing the whole idea of talking
+
+ align:start position:0%
+whole thing the whole idea of talking
+ 
+
+ align:start position:0%
+whole thing the whole idea of talking
+about basis of attraction to
+
+ align:start position:0%
+about basis of attraction to
+ 
+
+ align:start position:0%
+about basis of attraction to
+deterministic systems and doing feedback
+
+ align:start position:0%
+deterministic systems and doing feedback
+ 
+
+ align:start position:0%
+deterministic systems and doing feedback
+design sort of implicitly makes that
+
+ align:start position:0%
+design sort of implicitly makes that
+ 
+
+ align:start position:0%
+design sort of implicitly makes that
+assumption right so so there's sort of
+
+ align:start position:0%
+assumption right so so there's sort of
+ 
+
+ align:start position:0%
+assumption right so so there's sort of
+three things there
+
+ align:start position:0%
+three things there
+ 
+
+ align:start position:0%
+three things there
+right the fact that it's unmodeled
+
+ align:start position:0%
+right the fact that it's unmodeled
+ 
+
+ align:start position:0%
+right the fact that it's unmodeled
+and impulsive and rare i guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if your disturbances
+
+ align:start position:0%
+if your disturbances
+ 
+
+ align:start position:0%
+if your disturbances
+are not
+
+ align:start position:0%
+are not
+ 
+
+ align:start position:0%
+are not
+instantaneous rare disturbances
+
+ align:start position:0%
+instantaneous rare disturbances
+ 
+
+ align:start position:0%
+instantaneous rare disturbances
+then i think i would advocate quickly
+
+ align:start position:0%
+then i think i would advocate quickly
+ 
+
+ align:start position:0%
+then i think i would advocate quickly
+for starting to think about
+
+ align:start position:0%
+for starting to think about
+ 
+
+ align:start position:0%
+for starting to think about
+your dynamics as not deterministic
+
+ align:start position:0%
+your dynamics as not deterministic
+ 
+
+ align:start position:0%
+your dynamics as not deterministic
+dynamics but as a stochastic dynamics
+
+ align:start position:0%
+dynamics but as a stochastic dynamics
+ 
+
+ align:start position:0%
+dynamics but as a stochastic dynamics
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and even if they are impulsive and rare
+
+ align:start position:0%
+and even if they are impulsive and rare
+ 
+
+ align:start position:0%
+and even if they are impulsive and rare
+but if you have a model of them
+
+ align:start position:0%
+but if you have a model of them
+ 
+
+ align:start position:0%
+but if you have a model of them
+then you should be still be able to do
+
+ align:start position:0%
+then you should be still be able to do
+ 
+
+ align:start position:0%
+then you should be still be able to do
+better by explicitly letting your
+
+ align:start position:0%
+better by explicitly letting your
+ 
+
+ align:start position:0%
+better by explicitly letting your
+feedback design
+
+ align:start position:0%
+feedback design
+ 
+
+ align:start position:0%
+feedback design
+reason about
+
+ align:start position:0%
+reason about
+ 
+
+ align:start position:0%
+reason about
+the stochastic dynamics
+
+ align:start position:0%
+the stochastic dynamics
+ 
+
+ align:start position:0%
+the stochastic dynamics
+okay so so today i want to start talking
+
+ align:start position:0%
+okay so so today i want to start talking
+ 
+
+ align:start position:0%
+okay so so today i want to start talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+i want to start breaking down our
+
+ align:start position:0%
+i want to start breaking down our
+ 
+
+ align:start position:0%
+i want to start breaking down our
+assumptions and throughout the rest of
+
+ align:start position:0%
+assumptions and throughout the rest of
+ 
+
+ align:start position:0%
+assumptions and throughout the rest of
+the class we're sort of going to try to
+
+ align:start position:0%
+the class we're sort of going to try to
+ 
+
+ align:start position:0%
+the class we're sort of going to try to
+break these down
+
+ align:start position:0%
+break these down
+ 
+
+ align:start position:0%
+break these down
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's start breaking down the assumption
+
+ align:start position:0%
+let's start breaking down the assumption
+ 
+
+ align:start position:0%
+let's start breaking down the assumption
+of deterministic
+
+ align:start position:0%
+of deterministic
+ 
+
+ align:start position:0%
+of deterministic
+dynamics okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couldn't we actually saw something like
+
+ align:start position:0%
+couldn't we actually saw something like
+ 
+
+ align:start position:0%
+couldn't we actually saw something like
+if we actually have a stochastic
+
+ align:start position:0%
+if we actually have a stochastic
+ 
+
+ align:start position:0%
+if we actually have a stochastic
+transition model and we move somewhere
+
+ align:start position:0%
+transition model and we move somewhere
+ 
+
+ align:start position:0%
+transition model and we move somewhere
+and then we're like a little bit off
+
+ align:start position:0%
+and then we're like a little bit off
+ 
+
+ align:start position:0%
+and then we're like a little bit off
+from the trajectory then we look at the
+
+ align:start position:0%
+from the trajectory then we look at the
+ 
+
+ align:start position:0%
+from the trajectory then we look at the
+policy which would bring this practice
+
+ align:start position:0%
+policy which would bring this practice
+ 
+
+ align:start position:0%
+policy which would bring this practice
+nomination and go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think the answer to your question is
+
+ align:start position:0%
+i think the answer to your question is
+ 
+
+ align:start position:0%
+i think the answer to your question is
+yes so one of the things we're going to
+
+ align:start position:0%
+yes so one of the things we're going to
+ 
+
+ align:start position:0%
+yes so one of the things we're going to
+do today is show that the
+
+ align:start position:0%
+do today is show that the
+ 
+
+ align:start position:0%
+do today is show that the
+it's sort of subtle that that's yes but
+
+ align:start position:0%
+it's sort of subtle that that's yes but
+ 
+
+ align:start position:0%
+it's sort of subtle that that's yes but
+anybody who knows linear quadratic
+
+ align:start position:0%
+anybody who knows linear quadratic
+ 
+
+ align:start position:0%
+anybody who knows linear quadratic
+gaussian control
+
+ align:start position:0%
+gaussian control
+ 
+
+ align:start position:0%
+gaussian control
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+well it turns out that we're actually
+
+ align:start position:0%
+well it turns out that we're actually
+ 
+
+ align:start position:0%
+well it turns out that we're actually
+doing linear quadratic gaussian control
+
+ align:start position:0%
+doing linear quadratic gaussian control
+ 
+
+ align:start position:0%
+doing linear quadratic gaussian control
+but that's that's sort of a surprising
+
+ align:start position:0%
+but that's that's sort of a surprising
+ 
+
+ align:start position:0%
+but that's that's sort of a surprising
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+in the specific case of linear dynamics
+
+ align:start position:0%
+in the specific case of linear dynamics
+ 
+
+ align:start position:0%
+in the specific case of linear dynamics
+quadratic cost gaussian noise then what
+
+ align:start position:0%
+quadratic cost gaussian noise then what
+ 
+
+ align:start position:0%
+quadratic cost gaussian noise then what
+you said is true
+
+ align:start position:0%
+you said is true
+ 
+
+ align:start position:0%
+you said is true
+so that's a special case that that we'll
+
+ align:start position:0%
+so that's a special case that that we'll
+ 
+
+ align:start position:0%
+so that's a special case that that we'll
+we'll see
+
+ align:start position:0%
+we'll see
+ 
+
+ align:start position:0%
+we'll see
+quickly um but
+
+ align:start position:0%
+quickly um but
+ 
+
+ align:start position:0%
+quickly um but
+in general it's not true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so
+
+ align:start position:0%
+right so so
+ 
+
+ align:start position:0%
+right so so
+and again this is leading into
+
+ align:start position:0%
+and again this is leading into
+ 
+
+ align:start position:0%
+and again this is leading into
+next week we're going to start talking
+
+ align:start position:0%
+next week we're going to start talking
+ 
+
+ align:start position:0%
+next week we're going to start talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+doing these
+
+ align:start position:0%
+doing these
+ 
+
+ align:start position:0%
+doing these
+optimal control derivations without any
+
+ align:start position:0%
+optimal control derivations without any
+ 
+
+ align:start position:0%
+optimal control derivations without any
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+but today let's think about what happens
+
+ align:start position:0%
+but today let's think about what happens
+ 
+
+ align:start position:0%
+but today let's think about what happens
+if we have a stochastic model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay lots of ways people there's lots of
+
+ align:start position:0%
+okay lots of ways people there's lots of
+ 
+
+ align:start position:0%
+okay lots of ways people there's lots of
+different notations people use to talk
+
+ align:start position:0%
+different notations people use to talk
+ 
+
+ align:start position:0%
+different notations people use to talk
+about stochastic dynamics the one i'll
+
+ align:start position:0%
+about stochastic dynamics the one i'll
+ 
+
+ align:start position:0%
+about stochastic dynamics the one i'll
+use is i think the most popular one we
+
+ align:start position:0%
+use is i think the most popular one we
+ 
+
+ align:start position:0%
+use is i think the most popular one we
+want we still got our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our standard
+
+ align:start position:0%
+our standard
+ 
+
+ align:start position:0%
+our standard
+equations of motion
+
+ align:start position:0%
+equations of motion
+ 
+
+ align:start position:0%
+equations of motion
+but we're going to add an additional
+
+ align:start position:0%
+but we're going to add an additional
+ 
+
+ align:start position:0%
+but we're going to add an additional
+input which is
+
+ align:start position:0%
+input which is
+ 
+
+ align:start position:0%
+input which is
+some disturbance w
+
+ align:start position:0%
+some disturbance w
+ 
+
+ align:start position:0%
+some disturbance w
+as an additional input into our dynamics
+
+ align:start position:0%
+as an additional input into our dynamics
+ 
+
+ align:start position:0%
+as an additional input into our dynamics
+where w of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is some noise process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but if we let the noise come in
+
+ align:start position:0%
+okay but if we let the noise come in
+ 
+
+ align:start position:0%
+okay but if we let the noise come in
+through an input here then we can still
+
+ align:start position:0%
+through an input here then we can still
+ 
+
+ align:start position:0%
+through an input here then we can still
+think about it as a deterministic
+
+ align:start position:0%
+think about it as a deterministic
+ 
+
+ align:start position:0%
+think about it as a deterministic
+function our dynamics is a deterministic
+
+ align:start position:0%
+function our dynamics is a deterministic
+ 
+
+ align:start position:0%
+function our dynamics is a deterministic
+function and keep it mostly the same as
+
+ align:start position:0%
+function and keep it mostly the same as
+ 
+
+ align:start position:0%
+function and keep it mostly the same as
+what we've been thinking about
+
+ align:start position:0%
+what we've been thinking about
+ 
+
+ align:start position:0%
+what we've been thinking about
+now some people don't
+
+ align:start position:0%
+now some people don't
+ 
+
+ align:start position:0%
+now some people don't
+like defining noise processes in
+
+ align:start position:0%
+like defining noise processes in
+ 
+
+ align:start position:0%
+like defining noise processes in
+continuous time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a little bit more natural to
+
+ align:start position:0%
+it's a little bit more natural to
+ 
+
+ align:start position:0%
+it's a little bit more natural to
+describe them in
+
+ align:start position:0%
+describe them in
+ 
+
+ align:start position:0%
+describe them in
+in discrete time and and as we've done
+
+ align:start position:0%
+in discrete time and and as we've done
+ 
+
+ align:start position:0%
+in discrete time and and as we've done
+in the other class let's do the sort of
+
+ align:start position:0%
+in the other class let's do the sort of
+ 
+
+ align:start position:0%
+in the other class let's do the sort of
+discrete time case first so in discrete
+
+ align:start position:0%
+discrete time case first so in discrete
+ 
+
+ align:start position:0%
+discrete time case first so in discrete
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same thing right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now it's maybe we can um
+
+ align:start position:0%
+but now it's maybe we can um
+ 
+
+ align:start position:0%
+but now it's maybe we can um
+we can it's easier to think about what
+
+ align:start position:0%
+we can it's easier to think about what
+ 
+
+ align:start position:0%
+we can it's easier to think about what
+wn might be so for instance w
+
+ align:start position:0%
+wn might be so for instance w
+ 
+
+ align:start position:0%
+wn might be so for instance w
+then might be some
+
+ align:start position:0%
+then might be some
+ 
+
+ align:start position:0%
+then might be some
+iid
+
+ align:start position:0%
+iid
+ 
+
+ align:start position:0%
+iid
+gaussian process or something like that
+
+ align:start position:0%
+gaussian process or something like that
+ 
+
+ align:start position:0%
+gaussian process or something like that
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is just a
+
+ align:start position:0%
+is just a
+ 
+
+ align:start position:0%
+is just a
+complicated way to say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at each
+
+ align:start position:0%
+at each
+ 
+
+ align:start position:0%
+at each
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+w and
+
+ align:start position:0%
+w and
+ 
+
+ align:start position:0%
+w and
+is is sampled
+
+ align:start position:0%
+is is sampled
+ 
+
+ align:start position:0%
+is is sampled
+independently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from a gaussian
+
+ align:start position:0%
+from a gaussian
+ 
+
+ align:start position:0%
+from a gaussian
+i'll say a normal distribution
+
+ align:start position:0%
+i'll say a normal distribution
+ 
+
+ align:start position:0%
+i'll say a normal distribution
+like something like that
+
+ align:start position:0%
+like something like that
+ 
+
+ align:start position:0%
+like something like that
+so when i'm simulating this in matlab if
+
+ align:start position:0%
+so when i'm simulating this in matlab if
+ 
+
+ align:start position:0%
+so when i'm simulating this in matlab if
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+you know i can i can simulate an iid
+
+ align:start position:0%
+you know i can i can simulate an iid
+ 
+
+ align:start position:0%
+you know i can i can simulate an iid
+gaussian process by just every every
+
+ align:start position:0%
+gaussian process by just every every
+ 
+
+ align:start position:0%
+gaussian process by just every every
+time step calling rand and yeah as if
+
+ align:start position:0%
+time step calling rand and yeah as if
+ 
+
+ align:start position:0%
+time step calling rand and yeah as if
+and it's independent from the w's i
+
+ align:start position:0%
+and it's independent from the w's i
+ 
+
+ align:start position:0%
+and it's independent from the w's i
+picked before
+
+ align:start position:0%
+picked before
+ 
+
+ align:start position:0%
+picked before
+that's a pretty good model
+
+ align:start position:0%
+that's a pretty good model
+ 
+
+ align:start position:0%
+that's a pretty good model
+now one thing i want to i want to
+
+ align:start position:0%
+now one thing i want to i want to
+ 
+
+ align:start position:0%
+now one thing i want to i want to
+avoid talking about today so far
+
+ align:start position:0%
+avoid talking about today so far
+ 
+
+ align:start position:0%
+avoid talking about today so far
+is let's still assume that we have um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perfect state information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i don't want to worry about sensor
+
+ align:start position:0%
+so i don't want to worry about sensor
+ 
+
+ align:start position:0%
+so i don't want to worry about sensor
+noise yet it turns out it'll be
+
+ align:start position:0%
+noise yet it turns out it'll be
+ 
+
+ align:start position:0%
+noise yet it turns out it'll be
+pretty natural to think about it with
+
+ align:start position:0%
+pretty natural to think about it with
+ 
+
+ align:start position:0%
+pretty natural to think about it with
+some of the same tools but let's just
+
+ align:start position:0%
+some of the same tools but let's just
+ 
+
+ align:start position:0%
+some of the same tools but let's just
+assume for now that when i'm in state x
+
+ align:start position:0%
+assume for now that when i'm in state x
+ 
+
+ align:start position:0%
+assume for now that when i'm in state x
+i know i'm in state x exactly
+
+ align:start position:0%
+i know i'm in state x exactly
+ 
+
+ align:start position:0%
+i know i'm in state x exactly
+but if i'm trying to think about into
+
+ align:start position:0%
+but if i'm trying to think about into
+ 
+
+ align:start position:0%
+but if i'm trying to think about into
+the future what's going to happen what's
+
+ align:start position:0%
+the future what's going to happen what's
+ 
+
+ align:start position:0%
+the future what's going to happen what's
+the optimal thing to do i have to worry
+
+ align:start position:0%
+the optimal thing to do i have to worry
+ 
+
+ align:start position:0%
+the optimal thing to do i have to worry
+about the fact that
+
+ align:start position:0%
+about the fact that
+ 
+
+ align:start position:0%
+about the fact that
+the noise
+
+ align:start position:0%
+the noise
+ 
+
+ align:start position:0%
+the noise
+in the system is going to push me around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we updated our our
+
+ align:start position:0%
+okay so we updated our our
+ 
+
+ align:start position:0%
+okay so we updated our our
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+our dynamic equation we better start if
+
+ align:start position:0%
+our dynamic equation we better start if
+ 
+
+ align:start position:0%
+our dynamic equation we better start if
+we're thinking about this in an optimal
+
+ align:start position:0%
+we're thinking about this in an optimal
+ 
+
+ align:start position:0%
+we're thinking about this in an optimal
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+um since we better also update our
+
+ align:start position:0%
+um since we better also update our
+ 
+
+ align:start position:0%
+um since we better also update our
+definition for optimality right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we it used to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we said j in the in the discrete
+
+ align:start position:0%
+that we said j in the in the discrete
+ 
+
+ align:start position:0%
+that we said j in the in the discrete
+time case was just some sum from
+
+ align:start position:0%
+time case was just some sum from
+ 
+
+ align:start position:0%
+time case was just some sum from
+n equals 0 to n
+
+ align:start position:0%
+n equals 0 to n
+ 
+
+ align:start position:0%
+n equals 0 to n
+of g
+
+ align:start position:0%
+of g
+ 
+
+ align:start position:0%
+of g
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the problem with that now is that
+
+ align:start position:0%
+the problem with that now is that
+ 
+
+ align:start position:0%
+the problem with that now is that
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+right this is going to be this is now a
+
+ align:start position:0%
+right this is going to be this is now a
+ 
+
+ align:start position:0%
+right this is going to be this is now a
+random process yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the same initial conditions
+
+ align:start position:0%
+from the same initial conditions
+ 
+
+ align:start position:0%
+from the same initial conditions
+with even the same open loop tape let's
+
+ align:start position:0%
+with even the same open loop tape let's
+ 
+
+ align:start position:0%
+with even the same open loop tape let's
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+the system
+
+ align:start position:0%
+the system
+ 
+
+ align:start position:0%
+the system
+five times
+
+ align:start position:0%
+five times
+ 
+
+ align:start position:0%
+five times
+this is going to be a different
+
+ align:start position:0%
+this is going to be a different
+ 
+
+ align:start position:0%
+this is going to be a different
+value every time i run it exit time
+
+ align:start position:0%
+value every time i run it exit time
+ 
+
+ align:start position:0%
+value every time i run it exit time
+three will be different on every time i
+
+ align:start position:0%
+three will be different on every time i
+ 
+
+ align:start position:0%
+three will be different on every time i
+run it
+
+ align:start position:0%
+run it
+ 
+
+ align:start position:0%
+run it
+okay which means j is also going to be a
+
+ align:start position:0%
+okay which means j is also going to be a
+ 
+
+ align:start position:0%
+okay which means j is also going to be a
+random variable
+
+ align:start position:0%
+random variable
+ 
+
+ align:start position:0%
+random variable
+or random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it doesn't quite make sense
+
+ align:start position:0%
+so it doesn't quite make sense
+ 
+
+ align:start position:0%
+so it doesn't quite make sense
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+my notion of optimality is is some
+
+ align:start position:0%
+my notion of optimality is is some
+ 
+
+ align:start position:0%
+my notion of optimality is is some
+random variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to choose a property of that
+
+ align:start position:0%
+we want to choose a property of that
+ 
+
+ align:start position:0%
+we want to choose a property of that
+random variable that we care about
+
+ align:start position:0%
+random variable that we care about
+ 
+
+ align:start position:0%
+random variable that we care about
+there's different schools again being
+
+ align:start position:0%
+there's different schools again being
+ 
+
+ align:start position:0%
+there's different schools again being
+philosophical a little bit there's
+
+ align:start position:0%
+philosophical a little bit there's
+ 
+
+ align:start position:0%
+philosophical a little bit there's
+different schools of thought and control
+
+ align:start position:0%
+different schools of thought and control
+ 
+
+ align:start position:0%
+different schools of thought and control
+theory right
+
+ align:start position:0%
+theory right
+ 
+
+ align:start position:0%
+theory right
+some people say the thing you should
+
+ align:start position:0%
+some people say the thing you should
+ 
+
+ align:start position:0%
+some people say the thing you should
+care about the only thing you should
+
+ align:start position:0%
+care about the only thing you should
+ 
+
+ align:start position:0%
+care about the only thing you should
+worry about is the worst case behavior
+
+ align:start position:0%
+worry about is the worst case behavior
+ 
+
+ align:start position:0%
+worry about is the worst case behavior
+you want to worry about the tales of
+
+ align:start position:0%
+you want to worry about the tales of
+ 
+
+ align:start position:0%
+you want to worry about the tales of
+your distributions right and make
+
+ align:start position:0%
+your distributions right and make
+ 
+
+ align:start position:0%
+your distributions right and make
+absolutely sure that my plane if i'm
+
+ align:start position:0%
+absolutely sure that my plane if i'm
+ 
+
+ align:start position:0%
+absolutely sure that my plane if i'm
+riding on a plane from here to
+
+ align:start position:0%
+riding on a plane from here to
+ 
+
+ align:start position:0%
+riding on a plane from here to
+california
+
+ align:start position:0%
+california
+ 
+
+ align:start position:0%
+california
+it's not going to fall out of the sky
+
+ align:start position:0%
+it's not going to fall out of the sky
+ 
+
+ align:start position:0%
+it's not going to fall out of the sky
+with sort of
+
+ align:start position:0%
+with sort of
+ 
+
+ align:start position:0%
+with sort of
+five nines of probabilities
+
+ align:start position:0%
+five nines of probabilities
+ 
+
+ align:start position:0%
+five nines of probabilities
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i actually don't subscribe okay when i'm
+
+ align:start position:0%
+i actually don't subscribe okay when i'm
+ 
+
+ align:start position:0%
+i actually don't subscribe okay when i'm
+riding on a plane i do subscribe to that
+
+ align:start position:0%
+riding on a plane i do subscribe to that
+ 
+
+ align:start position:0%
+riding on a plane i do subscribe to that
+okay but when i'm building robots that i
+
+ align:start position:0%
+okay but when i'm building robots that i
+ 
+
+ align:start position:0%
+okay but when i'm building robots that i
+don't have to
+
+ align:start position:0%
+don't have to
+ 
+
+ align:start position:0%
+don't have to
+you know put my life in jeopardy for uh
+
+ align:start position:0%
+you know put my life in jeopardy for uh
+ 
+
+ align:start position:0%
+you know put my life in jeopardy for uh
+i don't believe in that and i actually
+
+ align:start position:0%
+i don't believe in that and i actually
+ 
+
+ align:start position:0%
+i don't believe in that and i actually
+don't think animals do that i think if
+
+ align:start position:0%
+don't think animals do that i think if
+ 
+
+ align:start position:0%
+don't think animals do that i think if
+animals were so conservative so that's
+
+ align:start position:0%
+animals were so conservative so that's
+ 
+
+ align:start position:0%
+animals were so conservative so that's
+the robust control approach what i just
+
+ align:start position:0%
+the robust control approach what i just
+ 
+
+ align:start position:0%
+the robust control approach what i just
+described the worrying about the worst
+
+ align:start position:0%
+described the worrying about the worst
+ 
+
+ align:start position:0%
+described the worrying about the worst
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+and the problem with robust control the
+
+ align:start position:0%
+and the problem with robust control the
+ 
+
+ align:start position:0%
+and the problem with robust control the
+well documented well discussed problem
+
+ align:start position:0%
+well documented well discussed problem
+ 
+
+ align:start position:0%
+well documented well discussed problem
+with robust control is it tends to come
+
+ align:start position:0%
+with robust control is it tends to come
+ 
+
+ align:start position:0%
+with robust control is it tends to come
+up with conservative control strategies
+
+ align:start position:0%
+up with conservative control strategies
+ 
+
+ align:start position:0%
+up with conservative control strategies
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so if i'm worried about you know never
+
+ align:start position:0%
+so if i'm worried about you know never
+ 
+
+ align:start position:0%
+so if i'm worried about you know never
+running to a table then i'm never going
+
+ align:start position:0%
+running to a table then i'm never going
+ 
+
+ align:start position:0%
+running to a table then i'm never going
+to go anywhere near that table right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's another approach
+
+ align:start position:0%
+there's another approach
+ 
+
+ align:start position:0%
+there's another approach
+which i prefer that tends to go to be
+
+ align:start position:0%
+which i prefer that tends to go to be
+ 
+
+ align:start position:0%
+which i prefer that tends to go to be
+more common in the optimal control
+
+ align:start position:0%
+more common in the optimal control
+ 
+
+ align:start position:0%
+more common in the optimal control
+community is to worry about maximizing
+
+ align:start position:0%
+community is to worry about maximizing
+ 
+
+ align:start position:0%
+community is to worry about maximizing
+the expected returns okay
+
+ align:start position:0%
+the expected returns okay
+ 
+
+ align:start position:0%
+the expected returns okay
+so now let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's define
+
+ align:start position:0%
+let's define
+ 
+
+ align:start position:0%
+let's define
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+as the expected value
+
+ align:start position:0%
+as the expected value
+ 
+
+ align:start position:0%
+as the expected value
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+cost function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a really obvious reason why the
+
+ align:start position:0%
+there's a really obvious reason why the
+ 
+
+ align:start position:0%
+there's a really obvious reason why the
+optimal control people choose to do that
+
+ align:start position:0%
+optimal control people choose to do that
+ 
+
+ align:start position:0%
+optimal control people choose to do that
+it's because we already made a decision
+
+ align:start position:0%
+it's because we already made a decision
+ 
+
+ align:start position:0%
+it's because we already made a decision
+to do additive costs
+
+ align:start position:0%
+to do additive costs
+ 
+
+ align:start position:0%
+to do additive costs
+expectations play beautifully with
+
+ align:start position:0%
+expectations play beautifully with
+ 
+
+ align:start position:0%
+expectations play beautifully with
+with summations and so our life is going
+
+ align:start position:0%
+with summations and so our life is going
+ 
+
+ align:start position:0%
+with summations and so our life is going
+to stay clean and good if we're willing
+
+ align:start position:0%
+to stay clean and good if we're willing
+ 
+
+ align:start position:0%
+to stay clean and good if we're willing
+to do the expected value
+
+ align:start position:0%
+to do the expected value
+ 
+
+ align:start position:0%
+to do the expected value
+derivations okay
+
+ align:start position:0%
+derivations okay
+ 
+
+ align:start position:0%
+derivations okay
+but also philosophically i think that
+
+ align:start position:0%
+but also philosophically i think that
+ 
+
+ align:start position:0%
+but also philosophically i think that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+me as an animal i maximize my expected
+
+ align:start position:0%
+me as an animal i maximize my expected
+ 
+
+ align:start position:0%
+me as an animal i maximize my expected
+reward gazelle running through the field
+
+ align:start position:0%
+reward gazelle running through the field
+ 
+
+ align:start position:0%
+reward gazelle running through the field
+you know i think
+
+ align:start position:0%
+you know i think
+ 
+
+ align:start position:0%
+you know i think
+is maximizing expected reward i mean on
+
+ align:start position:0%
+is maximizing expected reward i mean on
+ 
+
+ align:start position:0%
+is maximizing expected reward i mean on
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+it's doing spectacularly well right
+
+ align:start position:0%
+it's doing spectacularly well right
+ 
+
+ align:start position:0%
+it's doing spectacularly well right
+and every once in a while it wipes out
+
+ align:start position:0%
+and every once in a while it wipes out
+ 
+
+ align:start position:0%
+and every once in a while it wipes out
+and falls down and breaks its leg gets
+
+ align:start position:0%
+and falls down and breaks its leg gets
+ 
+
+ align:start position:0%
+and falls down and breaks its leg gets
+eaten you know uh but but if it was
+
+ align:start position:0%
+eaten you know uh but but if it was
+ 
+
+ align:start position:0%
+eaten you know uh but but if it was
+worrying about that all the time then it
+
+ align:start position:0%
+worrying about that all the time then it
+ 
+
+ align:start position:0%
+worrying about that all the time then it
+would never run you know it as fast as
+
+ align:start position:0%
+would never run you know it as fast as
+ 
+
+ align:start position:0%
+would never run you know it as fast as
+it does
+
+ align:start position:0%
+it does
+ 
+
+ align:start position:0%
+it does
+so or as aggressively as it does
+
+ align:start position:0%
+so or as aggressively as it does
+ 
+
+ align:start position:0%
+so or as aggressively as it does
+so i think personally if you want to
+
+ align:start position:0%
+so i think personally if you want to
+ 
+
+ align:start position:0%
+so i think personally if you want to
+build aggressive robots right you've got
+
+ align:start position:0%
+build aggressive robots right you've got
+ 
+
+ align:start position:0%
+build aggressive robots right you've got
+to stop worrying about guarantees of
+
+ align:start position:0%
+to stop worrying about guarantees of
+ 
+
+ align:start position:0%
+to stop worrying about guarantees of
+stability of performance just try to
+
+ align:start position:0%
+stability of performance just try to
+ 
+
+ align:start position:0%
+stability of performance just try to
+maximize the average performance i think
+
+ align:start position:0%
+maximize the average performance i think
+ 
+
+ align:start position:0%
+maximize the average performance i think
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+that's where i've put my chips
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+so now just to be clear here so so x
+
+ align:start position:0%
+so now just to be clear here so so x
+ 
+
+ align:start position:0%
+so now just to be clear here so so x
+again every time i run it even with a
+
+ align:start position:0%
+again every time i run it even with a
+ 
+
+ align:start position:0%
+again every time i run it even with a
+an open loop u if i completely control u
+
+ align:start position:0%
+an open loop u if i completely control u
+ 
+
+ align:start position:0%
+an open loop u if i completely control u
+so u is not a random variable but a
+
+ align:start position:0%
+so u is not a random variable but a
+ 
+
+ align:start position:0%
+so u is not a random variable but a
+some open loop tape let's say
+
+ align:start position:0%
+some open loop tape let's say
+ 
+
+ align:start position:0%
+some open loop tape let's say
+x will still be a random variable
+
+ align:start position:0%
+x will still be a random variable
+ 
+
+ align:start position:0%
+x will still be a random variable
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+j is not right j is saying that given
+
+ align:start position:0%
+j is not right j is saying that given
+ 
+
+ align:start position:0%
+j is not right j is saying that given
+some control policy some initial
+
+ align:start position:0%
+some control policy some initial
+ 
+
+ align:start position:0%
+some control policy some initial
+conditions there is a
+
+ align:start position:0%
+conditions there is a
+ 
+
+ align:start position:0%
+conditions there is a
+well-defined cost that i expected cost
+
+ align:start position:0%
+well-defined cost that i expected cost
+ 
+
+ align:start position:0%
+well-defined cost that i expected cost
+that i receive and that's something i
+
+ align:start position:0%
+that i receive and that's something i
+ 
+
+ align:start position:0%
+that i receive and that's something i
+can optimize okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+i want to think about the implications
+
+ align:start position:0%
+i want to think about the implications
+ 
+
+ align:start position:0%
+i want to think about the implications
+of having
+
+ align:start position:0%
+of having
+ 
+
+ align:start position:0%
+of having
+these things turn into random variables
+
+ align:start position:0%
+these things turn into random variables
+ 
+
+ align:start position:0%
+these things turn into random variables
+with sort of a simple example okay
+
+ align:start position:0%
+with sort of a simple example okay
+ 
+
+ align:start position:0%
+with sort of a simple example okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in that example i like the one i like is
+
+ align:start position:0%
+in that example i like the one i like is
+ 
+
+ align:start position:0%
+in that example i like the one i like is
+a particle
+
+ align:start position:0%
+a particle
+ 
+
+ align:start position:0%
+a particle
+sitting in a bowl let's say a some
+
+ align:start position:0%
+sitting in a bowl let's say a some
+ 
+
+ align:start position:0%
+sitting in a bowl let's say a some
+particle in a potential well
+
+ align:start position:0%
+particle in a potential well
+ 
+
+ align:start position:0%
+particle in a potential well
+right so there's let's say gravity is
+
+ align:start position:0%
+right so there's let's say gravity is
+ 
+
+ align:start position:0%
+right so there's let's say gravity is
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i've got some bowl i'm sitting in
+
+ align:start position:0%
+and i've got some bowl i'm sitting in
+ 
+
+ align:start position:0%
+and i've got some bowl i'm sitting in
+and this particle is going to
+
+ align:start position:0%
+and this particle is going to
+ 
+
+ align:start position:0%
+and this particle is going to
+want to roll down that bowl
+
+ align:start position:0%
+want to roll down that bowl
+ 
+
+ align:start position:0%
+want to roll down that bowl
+okay but to make it interesting we're
+
+ align:start position:0%
+okay but to make it interesting we're
+ 
+
+ align:start position:0%
+okay but to make it interesting we're
+going to say that this particle is
+
+ align:start position:0%
+going to say that this particle is
+ 
+
+ align:start position:0%
+going to say that this particle is
+subject to brownian motion right do you
+
+ align:start position:0%
+subject to brownian motion right do you
+ 
+
+ align:start position:0%
+subject to brownian motion right do you
+guys know what brownie in motion is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess if you look down at a at a petri
+
+ align:start position:0%
+i guess if you look down at a at a petri
+ 
+
+ align:start position:0%
+i guess if you look down at a at a petri
+dish of some of very small things
+
+ align:start position:0%
+dish of some of very small things
+ 
+
+ align:start position:0%
+dish of some of very small things
+they don't sit still there's
+
+ align:start position:0%
+they don't sit still there's
+ 
+
+ align:start position:0%
+they don't sit still there's
+a debate about exactly the physical
+
+ align:start position:0%
+a debate about exactly the physical
+ 
+
+ align:start position:0%
+a debate about exactly the physical
+mechanisms of it but phenomenologically
+
+ align:start position:0%
+mechanisms of it but phenomenologically
+ 
+
+ align:start position:0%
+mechanisms of it but phenomenologically
+you can see you know a very small cells
+
+ align:start position:0%
+you can see you know a very small cells
+ 
+
+ align:start position:0%
+you can see you know a very small cells
+that are not actively um motile by
+
+ align:start position:0%
+that are not actively um motile by
+ 
+
+ align:start position:0%
+that are not actively um motile by
+themselves sort of move around in a
+
+ align:start position:0%
+themselves sort of move around in a
+ 
+
+ align:start position:0%
+themselves sort of move around in a
+random in a random fashion doing random
+
+ align:start position:0%
+random in a random fashion doing random
+ 
+
+ align:start position:0%
+random in a random fashion doing random
+walks and things like this so people um
+
+ align:start position:0%
+walks and things like this so people um
+ 
+
+ align:start position:0%
+walks and things like this so people um
+i won't get into the
+
+ align:start position:0%
+i won't get into the
+ 
+
+ align:start position:0%
+i won't get into the
+sort of philosophy of uh the
+
+ align:start position:0%
+sort of philosophy of uh the
+ 
+
+ align:start position:0%
+sort of philosophy of uh the
+philosophical debate of whether
+
+ align:start position:0%
+philosophical debate of whether
+ 
+
+ align:start position:0%
+philosophical debate of whether
+you know there exists stochasticity in
+
+ align:start position:0%
+you know there exists stochasticity in
+ 
+
+ align:start position:0%
+you know there exists stochasticity in
+the world but i think stochasticity is
+
+ align:start position:0%
+the world but i think stochasticity is
+ 
+
+ align:start position:0%
+the world but i think stochasticity is
+certainly a relevant model for a lot of
+
+ align:start position:0%
+certainly a relevant model for a lot of
+ 
+
+ align:start position:0%
+certainly a relevant model for a lot of
+things we're doing here
+
+ align:start position:0%
+things we're doing here
+ 
+
+ align:start position:0%
+things we're doing here
+yeah we don't want to get quantum
+
+ align:start position:0%
+yeah we don't want to get quantum
+ 
+
+ align:start position:0%
+yeah we don't want to get quantum
+in class
+
+ align:start position:0%
+in class
+ 
+
+ align:start position:0%
+in class
+okay but let's just say that this guy is
+
+ align:start position:0%
+okay but let's just say that this guy is
+ 
+
+ align:start position:0%
+okay but let's just say that this guy is
+is subject to the dynamics of this bowl
+
+ align:start position:0%
+is subject to the dynamics of this bowl
+ 
+
+ align:start position:0%
+is subject to the dynamics of this bowl
+but on top of that dynamics of this bowl
+
+ align:start position:0%
+but on top of that dynamics of this bowl
+ 
+
+ align:start position:0%
+but on top of that dynamics of this bowl
+it has a tendency to jitter around a
+
+ align:start position:0%
+it has a tendency to jitter around a
+ 
+
+ align:start position:0%
+it has a tendency to jitter around a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+okay so i'll write down the dynamics
+
+ align:start position:0%
+okay so i'll write down the dynamics
+ 
+
+ align:start position:0%
+okay so i'll write down the dynamics
+i'll keep it discrete for now so let's
+
+ align:start position:0%
+i'll keep it discrete for now so let's
+ 
+
+ align:start position:0%
+i'll keep it discrete for now so let's
+say um
+
+ align:start position:0%
+say um
+ 
+
+ align:start position:0%
+say um
+on every time step the difference you
+
+ align:start position:0%
+on every time step the difference you
+ 
+
+ align:start position:0%
+on every time step the difference you
+know the update
+
+ align:start position:0%
+know the update
+ 
+
+ align:start position:0%
+know the update
+it looks like
+
+ align:start position:0%
+it looks like
+ 
+
+ align:start position:0%
+it looks like
+the gradient of that bowl
+
+ align:start position:0%
+the gradient of that bowl
+ 
+
+ align:start position:0%
+the gradient of that bowl
+it's trying to get go down that bowl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus some random noise
+
+ align:start position:0%
+plus some random noise
+ 
+
+ align:start position:0%
+plus some random noise
+i'll call it z
+
+ align:start position:0%
+i'll call it z
+ 
+
+ align:start position:0%
+i'll call it z
+of n and this again i'll assume is
+
+ align:start position:0%
+of n and this again i'll assume is
+ 
+
+ align:start position:0%
+of n and this again i'll assume is
+iid
+
+ align:start position:0%
+iid
+ 
+
+ align:start position:0%
+iid
+independent identically distributed
+
+ align:start position:0%
+independent identically distributed
+ 
+
+ align:start position:0%
+independent identically distributed
+gaussian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you've never taken a class with
+
+ align:start position:0%
+so if you've never taken a class with
+ 
+
+ align:start position:0%
+so if you've never taken a class with
+all this
+
+ align:start position:0%
+all this
+ 
+
+ align:start position:0%
+all this
+random variables and everything i hope
+
+ align:start position:0%
+random variables and everything i hope
+ 
+
+ align:start position:0%
+random variables and everything i hope
+most of this will still come through
+
+ align:start position:0%
+most of this will still come through
+ 
+
+ align:start position:0%
+most of this will still come through
+i'll throw a few of these words and try
+
+ align:start position:0%
+i'll throw a few of these words and try
+ 
+
+ align:start position:0%
+i'll throw a few of these words and try
+to be soft about it if you have
+
+ align:start position:0%
+to be soft about it if you have
+ 
+
+ align:start position:0%
+to be soft about it if you have
+questions about any of these just ask me
+
+ align:start position:0%
+questions about any of these just ask me
+ 
+
+ align:start position:0%
+questions about any of these just ask me
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+that we're going to be able to say
+
+ align:start position:0%
+that we're going to be able to say
+ 
+
+ align:start position:0%
+that we're going to be able to say
+things that are fairly mechanically
+
+ align:start position:0%
+things that are fairly mechanically
+ 
+
+ align:start position:0%
+things that are fairly mechanically
+intuitive and and helpful so so i hope
+
+ align:start position:0%
+intuitive and and helpful so so i hope
+ 
+
+ align:start position:0%
+intuitive and and helpful so so i hope
+it's accessible to everybody and if it's
+
+ align:start position:0%
+it's accessible to everybody and if it's
+ 
+
+ align:start position:0%
+it's accessible to everybody and if it's
+not ask me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a reasonable
+
+ align:start position:0%
+okay so this is a reasonable
+ 
+
+ align:start position:0%
+okay so this is a reasonable
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+dynamical system now it's going it's
+
+ align:start position:0%
+dynamical system now it's going it's
+ 
+
+ align:start position:0%
+dynamical system now it's going it's
+tempting to on each update having gone
+
+ align:start position:0%
+tempting to on each update having gone
+ 
+
+ align:start position:0%
+tempting to on each update having gone
+down the gradient plus
+
+ align:start position:0%
+down the gradient plus
+ 
+
+ align:start position:0%
+down the gradient plus
+plus some random noise okay
+
+ align:start position:0%
+plus some random noise okay
+ 
+
+ align:start position:0%
+plus some random noise okay
+let's make the our lives easier by
+
+ align:start position:0%
+let's make the our lives easier by
+ 
+
+ align:start position:0%
+let's make the our lives easier by
+choosing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u of x to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about that that's pretty nice right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that makes it makes our life good if
+
+ align:start position:0%
+that makes it makes our life good if
+ 
+
+ align:start position:0%
+that makes it makes our life good if
+everything's quadratic then this thing
+
+ align:start position:0%
+everything's quadratic then this thing
+ 
+
+ align:start position:0%
+everything's quadratic then this thing
+turns out to be
+
+ align:start position:0%
+turns out to be
+ 
+
+ align:start position:0%
+turns out to be
+negative alpha x right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so just to make sure we're we're
+
+ align:start position:0%
+okay so just to make sure we're we're
+ 
+
+ align:start position:0%
+okay so just to make sure we're we're
+thinking about it if the noise is zero
+
+ align:start position:0%
+thinking about it if the noise is zero
+ 
+
+ align:start position:0%
+thinking about it if the noise is zero
+then what's going to happen
+
+ align:start position:0%
+then what's going to happen
+ 
+
+ align:start position:0%
+then what's going to happen
+in this system i've got a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i've got a
+
+ align:start position:0%
+i've got a
+ 
+
+ align:start position:0%
+i've got a
+discrete time system
+
+ align:start position:0%
+discrete time system
+ 
+
+ align:start position:0%
+discrete time system
+which if i move that back over the other
+
+ align:start position:0%
+which if i move that back over the other
+ 
+
+ align:start position:0%
+which if i move that back over the other
+side like we're accustomed to
+
+ align:start position:0%
+side like we're accustomed to
+ 
+
+ align:start position:0%
+side like we're accustomed to
+goes like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so what's how does that thing behave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where's the fixed point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at zero
+
+ align:start position:0%
+at zero
+ 
+
+ align:start position:0%
+at zero
+and when is it stable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when's it stable
+
+ align:start position:0%
+when's it stable
+ 
+
+ align:start position:0%
+when's it stable
+discrete time linear system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no you're thinking too continuous
+
+ align:start position:0%
+no you're thinking too continuous
+ 
+
+ align:start position:0%
+no you're thinking too continuous
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+in discrete time your bounds on your
+
+ align:start position:0%
+in discrete time your bounds on your
+ 
+
+ align:start position:0%
+in discrete time your bounds on your
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+between they have to be the absolute
+
+ align:start position:0%
+between they have to be the absolute
+ 
+
+ align:start position:0%
+between they have to be the absolute
+value has to be less than one right
+
+ align:start position:0%
+value has to be less than one right
+ 
+
+ align:start position:0%
+value has to be less than one right
+which i think in this case means alpha's
+
+ align:start position:0%
+which i think in this case means alpha's
+ 
+
+ align:start position:0%
+which i think in this case means alpha's
+got to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between zero and two yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody okay with it yeah
+
+ align:start position:0%
+everybody okay with it yeah
+ 
+
+ align:start position:0%
+everybody okay with it yeah
+that wasn't supposed to be the
+
+ align:start position:0%
+that wasn't supposed to be the
+ 
+
+ align:start position:0%
+that wasn't supposed to be the
+big insight for the lecture but
+
+ align:start position:0%
+big insight for the lecture but
+ 
+
+ align:start position:0%
+big insight for the lecture but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the reason i wanted to say that okay
+
+ align:start position:0%
+so the reason i wanted to say that okay
+ 
+
+ align:start position:0%
+so the reason i wanted to say that okay
+so we definitely have some stable
+
+ align:start position:0%
+so we definitely have some stable
+ 
+
+ align:start position:0%
+so we definitely have some stable
+dynamics um pushing us this way in this
+
+ align:start position:0%
+dynamics um pushing us this way in this
+ 
+
+ align:start position:0%
+dynamics um pushing us this way in this
+bowl right that's the the picture tells
+
+ align:start position:0%
+bowl right that's the the picture tells
+ 
+
+ align:start position:0%
+bowl right that's the the picture tells
+you that the the math tells you that
+
+ align:start position:0%
+you that the the math tells you that
+ 
+
+ align:start position:0%
+you that the the math tells you that
+we have some stable dynamics that's
+
+ align:start position:0%
+we have some stable dynamics that's
+ 
+
+ align:start position:0%
+we have some stable dynamics that's
+pushing us towards here
+
+ align:start position:0%
+pushing us towards here
+ 
+
+ align:start position:0%
+pushing us towards here
+and then we have something that's
+
+ align:start position:0%
+and then we have something that's
+ 
+
+ align:start position:0%
+and then we have something that's
+pushing us out which is that noise right
+
+ align:start position:0%
+pushing us out which is that noise right
+ 
+
+ align:start position:0%
+pushing us out which is that noise right
+if i was maybe just as a thought
+
+ align:start position:0%
+if i was maybe just as a thought
+ 
+
+ align:start position:0%
+if i was maybe just as a thought
+exercise if my bowl had been flat if
+
+ align:start position:0%
+exercise if my bowl had been flat if
+ 
+
+ align:start position:0%
+exercise if my bowl had been flat if
+alpha was zero
+
+ align:start position:0%
+alpha was zero
+ 
+
+ align:start position:0%
+alpha was zero
+and i've got this thing subject to
+
+ align:start position:0%
+and i've got this thing subject to
+ 
+
+ align:start position:0%
+and i've got this thing subject to
+brownian motion
+
+ align:start position:0%
+brownian motion
+ 
+
+ align:start position:0%
+brownian motion
+then if i look at it at time you know
+
+ align:start position:0%
+then if i look at it at time you know
+ 
+
+ align:start position:0%
+then if i look at it at time you know
+100 where is it going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean it could go sort of sort of
+
+ align:start position:0%
+i mean it could go sort of sort of
+ 
+
+ align:start position:0%
+i mean it could go sort of sort of
+anywhere yeah
+
+ align:start position:0%
+anywhere yeah
+ 
+
+ align:start position:0%
+anywhere yeah
+if it's in this bowl
+
+ align:start position:0%
+if it's in this bowl
+ 
+
+ align:start position:0%
+if it's in this bowl
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+um in subject to brownian motion then
+
+ align:start position:0%
+um in subject to brownian motion then
+ 
+
+ align:start position:0%
+um in subject to brownian motion then
+what's it where's it gonna be at time
+
+ align:start position:0%
+what's it where's it gonna be at time
+ 
+
+ align:start position:0%
+what's it where's it gonna be at time
+100.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'd expect that with high probability
+
+ align:start position:0%
+you'd expect that with high probability
+ 
+
+ align:start position:0%
+you'd expect that with high probability
+to be around here there's a chance i
+
+ align:start position:0%
+to be around here there's a chance i
+ 
+
+ align:start position:0%
+to be around here there's a chance i
+mean even it turns even with small noise
+
+ align:start position:0%
+mean even it turns even with small noise
+ 
+
+ align:start position:0%
+mean even it turns even with small noise
+right if i were to get um some sort of
+
+ align:start position:0%
+right if i were to get um some sort of
+ 
+
+ align:start position:0%
+right if i were to get um some sort of
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+abnormally rare large force in this
+
+ align:start position:0%
+abnormally rare large force in this
+ 
+
+ align:start position:0%
+abnormally rare large force in this
+direction 10 times in a row if i watch
+
+ align:start position:0%
+direction 10 times in a row if i watch
+ 
+
+ align:start position:0%
+direction 10 times in a row if i watch
+this gaussian process long enough you
+
+ align:start position:0%
+this gaussian process long enough you
+ 
+
+ align:start position:0%
+this gaussian process long enough you
+know i might i might look and find it
+
+ align:start position:0%
+know i might i might look and find it
+ 
+
+ align:start position:0%
+know i might i might look and find it
+here but that's going to be very low
+
+ align:start position:0%
+here but that's going to be very low
+ 
+
+ align:start position:0%
+here but that's going to be very low
+probability right
+
+ align:start position:0%
+probability right
+ 
+
+ align:start position:0%
+probability right
+so what i'd expect to find is if i watch
+
+ align:start position:0%
+so what i'd expect to find is if i watch
+ 
+
+ align:start position:0%
+so what i'd expect to find is if i watch
+it for some amount of time and i look at
+
+ align:start position:0%
+it for some amount of time and i look at
+ 
+
+ align:start position:0%
+it for some amount of time and i look at
+it as time as a 100 that it's probably
+
+ align:start position:0%
+it as time as a 100 that it's probably
+ 
+
+ align:start position:0%
+it as time as a 100 that it's probably
+going to be here
+
+ align:start position:0%
+going to be here
+ 
+
+ align:start position:0%
+going to be here
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+draw some probability distribution here
+
+ align:start position:0%
+draw some probability distribution here
+ 
+
+ align:start position:0%
+draw some probability distribution here
+and sure there's some tails here that'll
+
+ align:start position:0%
+and sure there's some tails here that'll
+ 
+
+ align:start position:0%
+and sure there's some tails here that'll
+that'll say if i looked maybe i'll find
+
+ align:start position:0%
+that'll say if i looked maybe i'll find
+ 
+
+ align:start position:0%
+that'll say if i looked maybe i'll find
+it there but that's pretty unlikely
+
+ align:start position:0%
+it there but that's pretty unlikely
+ 
+
+ align:start position:0%
+it there but that's pretty unlikely
+okay so hopefully when we're all done
+
+ align:start position:0%
+okay so hopefully when we're all done
+ 
+
+ align:start position:0%
+okay so hopefully when we're all done
+with this we're going to get that out
+
+ align:start position:0%
+with this we're going to get that out
+ 
+
+ align:start position:0%
+with this we're going to get that out
+it's not too hard to see it actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the that's the best way to see
+
+ align:start position:0%
+so what's the that's the best way to see
+ 
+
+ align:start position:0%
+so what's the that's the best way to see
+it so let's
+
+ align:start position:0%
+it so let's
+ 
+
+ align:start position:0%
+it so let's
+let's pretend that
+
+ align:start position:0%
+let's pretend that
+ 
+
+ align:start position:0%
+let's pretend that
+we're going back to our so this was the
+
+ align:start position:0%
+we're going back to our so this was the
+ 
+
+ align:start position:0%
+we're going back to our so this was the
+we're back to the noise case again right
+
+ align:start position:0%
+we're back to the noise case again right
+ 
+
+ align:start position:0%
+we're back to the noise case again right
+putting epsilon back in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can we compute then so if i know where i
+
+ align:start position:0%
+can we compute then so if i know where i
+ 
+
+ align:start position:0%
+can we compute then so if i know where i
+am at time n if i've my sensors are
+
+ align:start position:0%
+am at time n if i've my sensors are
+ 
+
+ align:start position:0%
+am at time n if i've my sensors are
+perfect like i said
+
+ align:start position:0%
+perfect like i said
+ 
+
+ align:start position:0%
+perfect like i said
+i know where i am at time n
+
+ align:start position:0%
+i know where i am at time n
+ 
+
+ align:start position:0%
+i know where i am at time n
+where am i going to be at time n plus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me let me write that as some
+
+ align:start position:0%
+so let me let me write that as some
+ 
+
+ align:start position:0%
+so let me let me write that as some
+probability distribution that
+
+ align:start position:0%
+probability distribution that
+ 
+
+ align:start position:0%
+probability distribution that
+i want to write where am i at probably
+
+ align:start position:0%
+i want to write where am i at probably
+ 
+
+ align:start position:0%
+i want to write where am i at probably
+at time
+
+ align:start position:0%
+at time
+ 
+
+ align:start position:0%
+at time
+n plus 1 given i'm i know where i am
+
+ align:start position:0%
+n plus 1 given i'm i know where i am
+ 
+
+ align:start position:0%
+n plus 1 given i'm i know where i am
+at time n
+
+ align:start position:0%
+at time n
+ 
+
+ align:start position:0%
+at time n
+what's that going to look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+awesome
+
+ align:start position:0%
+awesome
+ 
+
+ align:start position:0%
+awesome
+right so i'm going to be
+
+ align:start position:0%
+right so i'm going to be
+ 
+
+ align:start position:0%
+right so i'm going to be
+um probably i'm going to be 1 minus
+
+ align:start position:0%
+um probably i'm going to be 1 minus
+ 
+
+ align:start position:0%
+um probably i'm going to be 1 minus
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+xn away from where i was but then some
+
+ align:start position:0%
+xn away from where i was but then some
+ 
+
+ align:start position:0%
+xn away from where i was but then some
+gaussian distribution centered around
+
+ align:start position:0%
+gaussian distribution centered around
+ 
+
+ align:start position:0%
+gaussian distribution centered around
+that point right the deterministic part
+
+ align:start position:0%
+that point right the deterministic part
+ 
+
+ align:start position:0%
+that point right the deterministic part
+puts me here and then this this part
+
+ align:start position:0%
+puts me here and then this this part
+ 
+
+ align:start position:0%
+puts me here and then this this part
+then adds noise to that
+
+ align:start position:0%
+then adds noise to that
+ 
+
+ align:start position:0%
+then adds noise to that
+okay so that's going to be
+
+ align:start position:0%
+okay so that's going to be
+ 
+
+ align:start position:0%
+okay so that's going to be
+you know my full gaussian here
+
+ align:start position:0%
+you know my full gaussian here
+ 
+
+ align:start position:0%
+you know my full gaussian here
+2 pi sigma squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e to the negative
+
+ align:start position:0%
+e to the negative
+ 
+
+ align:start position:0%
+e to the negative
+x n plus 1
+
+ align:start position:0%
+x n plus 1
+ 
+
+ align:start position:0%
+x n plus 1
+minus 1 minus alpha
+
+ align:start position:0%
+minus 1 minus alpha
+ 
+
+ align:start position:0%
+minus 1 minus alpha
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+that whole thing squared
+
+ align:start position:0%
+that whole thing squared
+ 
+
+ align:start position:0%
+that whole thing squared
+all over 2 sigma squared yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you agree with that if i if i know where
+
+ align:start position:0%
+you agree with that if i if i know where
+ 
+
+ align:start position:0%
+you agree with that if i if i know where
+i am
+
+ align:start position:0%
+i am
+ 
+
+ align:start position:0%
+i am
+at time x n
+
+ align:start position:0%
+at time x n
+ 
+
+ align:start position:0%
+at time x n
+which by the way is equivalent
+
+ align:start position:0%
+which by the way is equivalent
+ 
+
+ align:start position:0%
+which by the way is equivalent
+in probability space
+
+ align:start position:0%
+in probability space
+ 
+
+ align:start position:0%
+in probability space
+to saying i have a a delta function here
+
+ align:start position:0%
+to saying i have a a delta function here
+ 
+
+ align:start position:0%
+to saying i have a a delta function here
+right i know where i am
+
+ align:start position:0%
+right i know where i am
+ 
+
+ align:start position:0%
+right i know where i am
+my probability distribution is a delta
+
+ align:start position:0%
+my probability distribution is a delta
+ 
+
+ align:start position:0%
+my probability distribution is a delta
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then on the next step i'm going to be
+
+ align:start position:0%
+then on the next step i'm going to be
+ 
+
+ align:start position:0%
+then on the next step i'm going to be
+1 minus alpha times that and i'm going
+
+ align:start position:0%
+1 minus alpha times that and i'm going
+ 
+
+ align:start position:0%
+1 minus alpha times that and i'm going
+to have a distribution which is mean of
+
+ align:start position:0%
+to have a distribution which is mean of
+ 
+
+ align:start position:0%
+to have a distribution which is mean of
+this right this is a gaussian
+
+ align:start position:0%
+this right this is a gaussian
+ 
+
+ align:start position:0%
+this right this is a gaussian
+distribution x minus mu
+
+ align:start position:0%
+distribution x minus mu
+ 
+
+ align:start position:0%
+distribution x minus mu
+over 2 sigma squared
+
+ align:start position:0%
+over 2 sigma squared
+ 
+
+ align:start position:0%
+over 2 sigma squared
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+this is the new x this is mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so now we have
+
+ align:start position:0%
+good so now we have
+ 
+
+ align:start position:0%
+good so now we have
+everything we need really to
+
+ align:start position:0%
+everything we need really to
+ 
+
+ align:start position:0%
+everything we need really to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to proceed so let's say
+
+ align:start position:0%
+to proceed so let's say
+ 
+
+ align:start position:0%
+to proceed so let's say
+i knew where i was at x
+
+ align:start position:0%
+i knew where i was at x
+ 
+
+ align:start position:0%
+i knew where i was at x
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+on x1 i'm going to be
+
+ align:start position:0%
+on x1 i'm going to be
+ 
+
+ align:start position:0%
+on x1 i'm going to be
+at the function described by this where
+
+ align:start position:0%
+at the function described by this where
+ 
+
+ align:start position:0%
+at the function described by this where
+am i going to be at x2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general i have to do
+
+ align:start position:0%
+in general i have to do
+ 
+
+ align:start position:0%
+in general i have to do
+the update and let me
+
+ align:start position:0%
+the update and let me
+ 
+
+ align:start position:0%
+the update and let me
+use the notation
+
+ align:start position:0%
+use the notation
+ 
+
+ align:start position:0%
+use the notation
+p of n plus one meaning the probability
+
+ align:start position:0%
+p of n plus one meaning the probability
+ 
+
+ align:start position:0%
+p of n plus one meaning the probability
+distribution over x at time n plus one
+
+ align:start position:0%
+distribution over x at time n plus one
+ 
+
+ align:start position:0%
+distribution over x at time n plus one
+so think of it as a different function
+
+ align:start position:0%
+so think of it as a different function
+ 
+
+ align:start position:0%
+so think of it as a different function
+at each discrete time
+
+ align:start position:0%
+at each discrete time
+ 
+
+ align:start position:0%
+at each discrete time
+notationally it's the cleanest i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to be i have to think about
+
+ align:start position:0%
+it's going to be i have to think about
+ 
+
+ align:start position:0%
+it's going to be i have to think about
+oops i did
+
+ align:start position:0%
+oops i did
+ 
+
+ align:start position:0%
+oops i did
+sorry this is a y yeah
+
+ align:start position:0%
+sorry this is a y yeah
+ 
+
+ align:start position:0%
+sorry this is a y yeah
+my fault
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i if i was
+
+ align:start position:0%
+so if i if i was
+ 
+
+ align:start position:0%
+so if i if i was
+i have to think about all the
+
+ align:start position:0%
+i have to think about all the
+ 
+
+ align:start position:0%
+i have to think about all the
+possibilities i want the probability
+
+ align:start position:0%
+possibilities i want the probability
+ 
+
+ align:start position:0%
+possibilities i want the probability
+that i was in y equals zero and then the
+
+ align:start position:0%
+that i was in y equals zero and then the
+ 
+
+ align:start position:0%
+that i was in y equals zero and then the
+probability being an x
+
+ align:start position:0%
+probability being an x
+ 
+
+ align:start position:0%
+probability being an x
+considering i was in y zero but also i
+
+ align:start position:0%
+considering i was in y zero but also i
+ 
+
+ align:start position:0%
+considering i was in y zero but also i
+had to think about what if y was one
+
+ align:start position:0%
+had to think about what if y was one
+ 
+
+ align:start position:0%
+had to think about what if y was one
+well what's the probability of that and
+
+ align:start position:0%
+well what's the probability of that and
+ 
+
+ align:start position:0%
+well what's the probability of that and
+i'm going to sum the whole thing up
+
+ align:start position:0%
+i'm going to sum the whole thing up
+ 
+
+ align:start position:0%
+i'm going to sum the whole thing up
+in a continuous way and i'm going to get
+
+ align:start position:0%
+in a continuous way and i'm going to get
+ 
+
+ align:start position:0%
+in a continuous way and i'm going to get
+my new probability of being at the new
+
+ align:start position:0%
+my new probability of being at the new
+ 
+
+ align:start position:0%
+my new probability of being at the new
+place you guys okay with this equation
+
+ align:start position:0%
+place you guys okay with this equation
+ 
+
+ align:start position:0%
+place you guys okay with this equation
+all right i have to consider all
+
+ align:start position:0%
+all right i have to consider all
+ 
+
+ align:start position:0%
+all right i have to consider all
+possible cases of where i was
+
+ align:start position:0%
+possible cases of where i was
+ 
+
+ align:start position:0%
+possible cases of where i was
+at time
+
+ align:start position:0%
+at time
+ 
+
+ align:start position:0%
+at time
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+that's given by this and then apply my
+
+ align:start position:0%
+that's given by this and then apply my
+ 
+
+ align:start position:0%
+that's given by this and then apply my
+dynamics which is given by this to get
+
+ align:start position:0%
+dynamics which is given by this to get
+ 
+
+ align:start position:0%
+dynamics which is given by this to get
+my new distribution
+
+ align:start position:0%
+my new distribution
+ 
+
+ align:start position:0%
+my new distribution
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hope that's okay but even if it's not it
+
+ align:start position:0%
+hope that's okay but even if it's not it
+ 
+
+ align:start position:0%
+hope that's okay but even if it's not it
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+you'll you'll still be okay here in a
+
+ align:start position:0%
+you'll you'll still be okay here in a
+ 
+
+ align:start position:0%
+you'll you'll still be okay here in a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can
+
+ align:start position:0%
+so we can
+ 
+
+ align:start position:0%
+so we can
+we can do that right so let's say that
+
+ align:start position:0%
+we can do that right so let's say that
+ 
+
+ align:start position:0%
+we can do that right so let's say that
+p of n
+
+ align:start position:0%
+p of n
+ 
+
+ align:start position:0%
+p of n
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is a delta function right that's what i
+
+ align:start position:0%
+is a delta function right that's what i
+ 
+
+ align:start position:0%
+is a delta function right that's what i
+said so i know my initial conditions
+
+ align:start position:0%
+said so i know my initial conditions
+ 
+
+ align:start position:0%
+said so i know my initial conditions
+i should have drawn it right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to match that that plot
+
+ align:start position:0%
+to match that that plot
+ 
+
+ align:start position:0%
+to match that that plot
+well then after one step
+
+ align:start position:0%
+well then after one step
+ 
+
+ align:start position:0%
+well then after one step
+it's going to just pick out the p of
+
+ align:start position:0%
+it's going to just pick out the p of
+ 
+
+ align:start position:0%
+it's going to just pick out the p of
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+this thing this
+
+ align:start position:0%
+this thing this
+ 
+
+ align:start position:0%
+this thing this
+gaussian
+
+ align:start position:0%
+gaussian
+ 
+
+ align:start position:0%
+gaussian
+centered at that y
+
+ align:start position:0%
+centered at that y
+ 
+
+ align:start position:0%
+centered at that y
+and at one step then
+
+ align:start position:0%
+and at one step then
+ 
+
+ align:start position:0%
+and at one step then
+i'm going to be at a gaussian
+
+ align:start position:0%
+i'm going to be at a gaussian
+ 
+
+ align:start position:0%
+i'm going to be at a gaussian
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of one minus alpha from where i was
+
+ align:start position:0%
+sort of one minus alpha from where i was
+ 
+
+ align:start position:0%
+sort of one minus alpha from where i was
+centered around 1 minus alpha from where
+
+ align:start position:0%
+centered around 1 minus alpha from where
+ 
+
+ align:start position:0%
+centered around 1 minus alpha from where
+i was right
+
+ align:start position:0%
+i was right
+ 
+
+ align:start position:0%
+i was right
+now in the next step i have to consider
+
+ align:start position:0%
+now in the next step i have to consider
+ 
+
+ align:start position:0%
+now in the next step i have to consider
+the fact that i could be anywhere in
+
+ align:start position:0%
+the fact that i could be anywhere in
+ 
+
+ align:start position:0%
+the fact that i could be anywhere in
+that gaussian weighted appropriate
+
+ align:start position:0%
+that gaussian weighted appropriate
+ 
+
+ align:start position:0%
+that gaussian weighted appropriate
+appropriately and i have to consider all
+
+ align:start position:0%
+appropriately and i have to consider all
+ 
+
+ align:start position:0%
+appropriately and i have to consider all
+the updates from those that's what this
+
+ align:start position:0%
+the updates from those that's what this
+ 
+
+ align:start position:0%
+the updates from those that's what this
+integral is doing
+
+ align:start position:0%
+integral is doing
+ 
+
+ align:start position:0%
+integral is doing
+and it turns out the magic of gaussians
+
+ align:start position:0%
+and it turns out the magic of gaussians
+ 
+
+ align:start position:0%
+and it turns out the magic of gaussians
+and linearity is that
+
+ align:start position:0%
+and linearity is that
+ 
+
+ align:start position:0%
+and linearity is that
+if p of y is a gaussian
+
+ align:start position:0%
+if p of y is a gaussian
+ 
+
+ align:start position:0%
+if p of y is a gaussian
+and i multiply it by another gaussian
+
+ align:start position:0%
+and i multiply it by another gaussian
+ 
+
+ align:start position:0%
+and i multiply it by another gaussian
+and integrate
+
+ align:start position:0%
+and integrate
+ 
+
+ align:start position:0%
+and integrate
+i get out of gaussian now life is good
+
+ align:start position:0%
+i get out of gaussian now life is good
+ 
+
+ align:start position:0%
+i get out of gaussian now life is good
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i'll i'll leave the actual
+
+ align:start position:0%
+so i'll i'll leave the actual
+ 
+
+ align:start position:0%
+so i'll i'll leave the actual
+math to your yeah what the heck i'll
+
+ align:start position:0%
+math to your yeah what the heck i'll
+ 
+
+ align:start position:0%
+math to your yeah what the heck i'll
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you get
+
+ align:start position:0%
+what you get
+ 
+
+ align:start position:0%
+what you get
+i can write the the answer if you push a
+
+ align:start position:0%
+i can write the the answer if you push a
+ 
+
+ align:start position:0%
+i can write the the answer if you push a
+gaussian through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turns out to be
+
+ align:start position:0%
+turns out to be
+ 
+
+ align:start position:0%
+turns out to be
+1 over
+
+ align:start position:0%
+1 over
+ 
+
+ align:start position:0%
+1 over
+square root of 2 pi
+
+ align:start position:0%
+square root of 2 pi
+ 
+
+ align:start position:0%
+square root of 2 pi
+sigma squared
+
+ align:start position:0%
+sigma squared
+ 
+
+ align:start position:0%
+sigma squared
+integral from negative infinity to
+
+ align:start position:0%
+integral from negative infinity to
+ 
+
+ align:start position:0%
+integral from negative infinity to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+of e to the negative
+
+ align:start position:0%
+of e to the negative
+ 
+
+ align:start position:0%
+of e to the negative
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let me actually write the
+
+ align:start position:0%
+let me actually write the
+ 
+
+ align:start position:0%
+let me actually write the
+skip that one line just to keep things
+
+ align:start position:0%
+skip that one line just to keep things
+ 
+
+ align:start position:0%
+skip that one line just to keep things
+moving
+
+ align:start position:0%
+moving
+ 
+
+ align:start position:0%
+moving
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's do one over one minus
+
+ align:start position:0%
+let's do one over one minus
+ 
+
+ align:start position:0%
+let's do one over one minus
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+square root of two pi c squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the probability of n
+
+ align:start position:0%
+that's the probability of n
+ 
+
+ align:start position:0%
+that's the probability of n
+at y prime one minus alpha
+
+ align:start position:0%
+at y prime one minus alpha
+ 
+
+ align:start position:0%
+at y prime one minus alpha
+d y alpha where y
+
+ align:start position:0%
+d y alpha where y
+ 
+
+ align:start position:0%
+d y alpha where y
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one minus alpha y
+
+ align:start position:0%
+one minus alpha y
+ 
+
+ align:start position:0%
+one minus alpha y
+let's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+haven't done a lot of work yet i just
+
+ align:start position:0%
+haven't done a lot of work yet i just
+ 
+
+ align:start position:0%
+haven't done a lot of work yet i just
+sort of changed coordinates into y prime
+
+ align:start position:0%
+sort of changed coordinates into y prime
+ 
+
+ align:start position:0%
+sort of changed coordinates into y prime
+and it turns out
+
+ align:start position:0%
+and it turns out
+ 
+
+ align:start position:0%
+and it turns out
+for instance if i look at for if i guess
+
+ align:start position:0%
+for instance if i look at for if i guess
+ 
+
+ align:start position:0%
+for instance if i look at for if i guess
+that the steady state is a gaussian form
+
+ align:start position:0%
+that the steady state is a gaussian form
+ 
+
+ align:start position:0%
+that the steady state is a gaussian form
+and i look for
+
+ align:start position:0%
+and i look for
+ 
+
+ align:start position:0%
+and i look for
+a place where this
+
+ align:start position:0%
+a place where this
+ 
+
+ align:start position:0%
+a place where this
+and this can possibly be the same
+
+ align:start position:0%
+and this can possibly be the same
+ 
+
+ align:start position:0%
+and this can possibly be the same
+function if i want to look at the steady
+
+ align:start position:0%
+function if i want to look at the steady
+ 
+
+ align:start position:0%
+function if i want to look at the steady
+state of this dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then i find that
+
+ align:start position:0%
+then i find that
+ 
+
+ align:start position:0%
+then i find that
+p star of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is one over
+
+ align:start position:0%
+is one over
+ 
+
+ align:start position:0%
+is one over
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+square root of two pi
+
+ align:start position:0%
+square root of two pi
+ 
+
+ align:start position:0%
+square root of two pi
+sigma zero
+
+ align:start position:0%
+sigma zero
+ 
+
+ align:start position:0%
+sigma zero
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+e to the negative
+
+ align:start position:0%
+e to the negative
+ 
+
+ align:start position:0%
+e to the negative
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+over two sigma zero squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a gaussian it's actually a mean
+
+ align:start position:0%
+it's a gaussian it's actually a mean
+ 
+
+ align:start position:0%
+it's a gaussian it's actually a mean
+zero gaussian
+
+ align:start position:0%
+zero gaussian
+ 
+
+ align:start position:0%
+zero gaussian
+is the steady state of that update
+
+ align:start position:0%
+is the steady state of that update
+ 
+
+ align:start position:0%
+is the steady state of that update
+okay which is just a few lines in the
+
+ align:start position:0%
+okay which is just a few lines in the
+ 
+
+ align:start position:0%
+okay which is just a few lines in the
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+sigma zero
+
+ align:start position:0%
+sigma zero
+ 
+
+ align:start position:0%
+sigma zero
+squared is
+
+ align:start position:0%
+squared is
+ 
+
+ align:start position:0%
+squared is
+sigma squared which is the noise from
+
+ align:start position:0%
+sigma squared which is the noise from
+ 
+
+ align:start position:0%
+sigma squared which is the noise from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+brownian motion
+
+ align:start position:0%
+brownian motion
+ 
+
+ align:start position:0%
+brownian motion
+minus alpha squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i think actually this these equations
+
+ align:start position:0%
+so i think actually this these equations
+ 
+
+ align:start position:0%
+so i think actually this these equations
+tell the entire
+
+ align:start position:0%
+tell the entire
+ 
+
+ align:start position:0%
+tell the entire
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+um if i
+
+ align:start position:0%
+um if i
+ 
+
+ align:start position:0%
+um if i
+start my system even from a
+
+ align:start position:0%
+start my system even from a
+ 
+
+ align:start position:0%
+start my system even from a
+from some
+
+ align:start position:0%
+from some
+ 
+
+ align:start position:0%
+from some
+well specifically if i start my system
+
+ align:start position:0%
+well specifically if i start my system
+ 
+
+ align:start position:0%
+well specifically if i start my system
+in a delta function or in a gaussian
+
+ align:start position:0%
+in a delta function or in a gaussian
+ 
+
+ align:start position:0%
+in a delta function or in a gaussian
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+of initial conditions then i'm going to
+
+ align:start position:0%
+of initial conditions then i'm going to
+ 
+
+ align:start position:0%
+of initial conditions then i'm going to
+be gaussian for the rest of time turns
+
+ align:start position:0%
+be gaussian for the rest of time turns
+ 
+
+ align:start position:0%
+be gaussian for the rest of time turns
+out even if it's not it'll it'll go to a
+
+ align:start position:0%
+out even if it's not it'll it'll go to a
+ 
+
+ align:start position:0%
+out even if it's not it'll it'll go to a
+stable gaussian right
+
+ align:start position:0%
+stable gaussian right
+ 
+
+ align:start position:0%
+stable gaussian right
+and if i watch if i look far enough into
+
+ align:start position:0%
+and if i watch if i look far enough into
+ 
+
+ align:start position:0%
+and if i watch if i look far enough into
+the future at the steady state
+
+ align:start position:0%
+the future at the steady state
+ 
+
+ align:start position:0%
+the future at the steady state
+of that probability distribution
+
+ align:start position:0%
+of that probability distribution
+ 
+
+ align:start position:0%
+of that probability distribution
+then it's actually going to be what we
+
+ align:start position:0%
+then it's actually going to be what we
+ 
+
+ align:start position:0%
+then it's actually going to be what we
+hoped we'd find it's a mean zero
+
+ align:start position:0%
+hoped we'd find it's a mean zero
+ 
+
+ align:start position:0%
+hoped we'd find it's a mean zero
+gaussian this was zero in my plot
+
+ align:start position:0%
+gaussian this was zero in my plot
+ 
+
+ align:start position:0%
+gaussian this was zero in my plot
+and its width its variance is given by
+
+ align:start position:0%
+and its width its variance is given by
+ 
+
+ align:start position:0%
+and its width its variance is given by
+two competing terms right
+
+ align:start position:0%
+two competing terms right
+ 
+
+ align:start position:0%
+two competing terms right
+you've got the noise
+
+ align:start position:0%
+you've got the noise
+ 
+
+ align:start position:0%
+you've got the noise
+from the brownian motion trying to push
+
+ align:start position:0%
+from the brownian motion trying to push
+ 
+
+ align:start position:0%
+from the brownian motion trying to push
+you out into larger variants
+
+ align:start position:0%
+you out into larger variants
+ 
+
+ align:start position:0%
+you out into larger variants
+and you've got the competing force of
+
+ align:start position:0%
+and you've got the competing force of
+ 
+
+ align:start position:0%
+and you've got the competing force of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+stability of the dynamics pushing you
+
+ align:start position:0%
+stability of the dynamics pushing you
+ 
+
+ align:start position:0%
+stability of the dynamics pushing you
+back in
+
+ align:start position:0%
+back in
+ 
+
+ align:start position:0%
+back in
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if alpha gets and you actually this
+
+ align:start position:0%
+so if alpha gets and you actually this
+ 
+
+ align:start position:0%
+so if alpha gets and you actually this
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+is valid exactly when alpha is
+
+ align:start position:0%
+is valid exactly when alpha is
+ 
+
+ align:start position:0%
+is valid exactly when alpha is
+between zero and two it doesn't go to
+
+ align:start position:0%
+between zero and two it doesn't go to
+ 
+
+ align:start position:0%
+between zero and two it doesn't go to
+zero in that regime yeah
+
+ align:start position:0%
+zero in that regime yeah
+ 
+
+ align:start position:0%
+zero in that regime yeah
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i want to look at that particle
+
+ align:start position:0%
+so if i want to look at that particle
+ 
+
+ align:start position:0%
+so if i want to look at that particle
+at time 100 or time 10 000
+
+ align:start position:0%
+at time 100 or time 10 000
+ 
+
+ align:start position:0%
+at time 100 or time 10 000
+then i should expect to see it
+
+ align:start position:0%
+then i should expect to see it
+ 
+
+ align:start position:0%
+then i should expect to see it
+somewhere with with probability given by
+
+ align:start position:0%
+somewhere with with probability given by
+ 
+
+ align:start position:0%
+somewhere with with probability given by
+this distribution
+
+ align:start position:0%
+this distribution
+ 
+
+ align:start position:0%
+this distribution
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know in the vicinity of that zero
+
+ align:start position:0%
+you know in the vicinity of that zero
+ 
+
+ align:start position:0%
+you know in the vicinity of that zero
+okay and that comes out of simple math
+
+ align:start position:0%
+okay and that comes out of simple math
+ 
+
+ align:start position:0%
+okay and that comes out of simple math
+of pushing
+
+ align:start position:0%
+of pushing
+ 
+
+ align:start position:0%
+of pushing
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+gaussian
+
+ align:start position:0%
+gaussian
+ 
+
+ align:start position:0%
+gaussian
+through this equation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you all probably unless you probably
+
+ align:start position:0%
+now you all probably unless you probably
+ 
+
+ align:start position:0%
+now you all probably unless you probably
+knew that before
+
+ align:start position:0%
+knew that before
+ 
+
+ align:start position:0%
+knew that before
+why do you know this before
+
+ align:start position:0%
+why do you know this before
+ 
+
+ align:start position:0%
+why do you know this before
+maybe not in this in this level of
+
+ align:start position:0%
+maybe not in this in this level of
+ 
+
+ align:start position:0%
+maybe not in this in this level of
+detail but
+
+ align:start position:0%
+detail but
+ 
+
+ align:start position:0%
+detail but
+why do many of you know this already
+
+ align:start position:0%
+why do many of you know this already
+ 
+
+ align:start position:0%
+why do many of you know this already
+it's a common filter right
+
+ align:start position:0%
+it's a common filter right
+ 
+
+ align:start position:0%
+it's a common filter right
+the common filtered forward
+
+ align:start position:0%
+the common filtered forward
+ 
+
+ align:start position:0%
+the common filtered forward
+process takes a gaussian shoves it
+
+ align:start position:0%
+process takes a gaussian shoves it
+ 
+
+ align:start position:0%
+process takes a gaussian shoves it
+through a linear system stays gaussian
+
+ align:start position:0%
+through a linear system stays gaussian
+ 
+
+ align:start position:0%
+through a linear system stays gaussian
+this is the single
+
+ align:start position:0%
+this is the single
+ 
+
+ align:start position:0%
+this is the single
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+a little more careful version maybe than
+
+ align:start position:0%
+a little more careful version maybe than
+ 
+
+ align:start position:0%
+a little more careful version maybe than
+you than you you do if you call matlab's
+
+ align:start position:0%
+you than you you do if you call matlab's
+ 
+
+ align:start position:0%
+you than you you do if you call matlab's
+common stuff
+
+ align:start position:0%
+common stuff
+ 
+
+ align:start position:0%
+common stuff
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+yeah so that's that's not a surprising
+
+ align:start position:0%
+yeah so that's that's not a surprising
+ 
+
+ align:start position:0%
+yeah so that's that's not a surprising
+result but i think it forces you to
+
+ align:start position:0%
+result but i think it forces you to
+ 
+
+ align:start position:0%
+result but i think it forces you to
+think about a couple things right so
+
+ align:start position:0%
+think about a couple things right so
+ 
+
+ align:start position:0%
+think about a couple things right so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like i said the stability of the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is critical in determining that final
+
+ align:start position:0%
+is critical in determining that final
+ 
+
+ align:start position:0%
+is critical in determining that final
+uh that final distribution
+
+ align:start position:0%
+uh that final distribution
+ 
+
+ align:start position:0%
+uh that final distribution
+but even more significantly than that
+
+ align:start position:0%
+but even more significantly than that
+ 
+
+ align:start position:0%
+but even more significantly than that
+there's some implications right of
+
+ align:start position:0%
+there's some implications right of
+ 
+
+ align:start position:0%
+there's some implications right of
+having these noise noise in the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implications of having stochastic
+
+ align:start position:0%
+implications of having stochastic
+ 
+
+ align:start position:0%
+implications of having stochastic
+dynamics okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you want to reason about
+
+ align:start position:0%
+if you want to reason about
+ 
+
+ align:start position:0%
+if you want to reason about
+the cost that you're going to incur
+
+ align:start position:0%
+the cost that you're going to incur
+ 
+
+ align:start position:0%
+the cost that you're going to incur
+given some policy
+
+ align:start position:0%
+given some policy
+ 
+
+ align:start position:0%
+given some policy
+for instance
+
+ align:start position:0%
+for instance
+ 
+
+ align:start position:0%
+for instance
+in order to reason about the future
+
+ align:start position:0%
+in order to reason about the future
+ 
+
+ align:start position:0%
+in order to reason about the future
+dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even though you know the current state
+
+ align:start position:0%
+even though you know the current state
+ 
+
+ align:start position:0%
+even though you know the current state
+you know so even given initial
+
+ align:start position:0%
+you know so even given initial
+ 
+
+ align:start position:0%
+you know so even given initial
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have to reason about
+
+ align:start position:0%
+you have to reason about
+ 
+
+ align:start position:0%
+you have to reason about
+it's not enough to just reason about x
+
+ align:start position:0%
+it's not enough to just reason about x
+ 
+
+ align:start position:0%
+it's not enough to just reason about x
+you have to reason about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that entire distribution p
+
+ align:start position:0%
+that entire distribution p
+ 
+
+ align:start position:0%
+that entire distribution p
+what i call p n of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+not just x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so as soon as we start doing
+
+ align:start position:0%
+okay so as soon as we start doing
+ 
+
+ align:start position:0%
+okay so as soon as we start doing
+stochastic stuff we have to change
+
+ align:start position:0%
+stochastic stuff we have to change
+ 
+
+ align:start position:0%
+stochastic stuff we have to change
+our view of the world the state x is not
+
+ align:start position:0%
+our view of the world the state x is not
+ 
+
+ align:start position:0%
+our view of the world the state x is not
+the only thing you care about moving
+
+ align:start position:0%
+the only thing you care about moving
+ 
+
+ align:start position:0%
+the only thing you care about moving
+forward you care about the probability
+
+ align:start position:0%
+forward you care about the probability
+ 
+
+ align:start position:0%
+forward you care about the probability
+distribution of states that you live in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would you say about the stability
+
+ align:start position:0%
+what would you say about the stability
+ 
+
+ align:start position:0%
+what would you say about the stability
+of this system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i asked you is that a stable system
+
+ align:start position:0%
+if i asked you is that a stable system
+ 
+
+ align:start position:0%
+if i asked you is that a stable system
+what would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say i'm asking and we're we're going to
+
+ align:start position:0%
+say i'm asking and we're we're going to
+ 
+
+ align:start position:0%
+say i'm asking and we're we're going to
+do that but i'm asking you for your
+
+ align:start position:0%
+do that but i'm asking you for your
+ 
+
+ align:start position:0%
+do that but i'm asking you for your
+intuition what would you guess would
+
+ align:start position:0%
+intuition what would you guess would
+ 
+
+ align:start position:0%
+intuition what would you guess would
+would you feel comfortable if i said
+
+ align:start position:0%
+would you feel comfortable if i said
+ 
+
+ align:start position:0%
+would you feel comfortable if i said
+it's a stable system let's move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some ways it's okay because
+
+ align:start position:0%
+in some ways it's okay because
+ 
+
+ align:start position:0%
+in some ways it's okay because
+the distribution is stable
+
+ align:start position:0%
+the distribution is stable
+ 
+
+ align:start position:0%
+the distribution is stable
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+is not stable
+
+ align:start position:0%
+is not stable
+ 
+
+ align:start position:0%
+is not stable
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i look at if i'm at there's no fixed
+
+ align:start position:0%
+if i look at if i'm at there's no fixed
+ 
+
+ align:start position:0%
+if i look at if i'm at there's no fixed
+point in x right the noise is going to
+
+ align:start position:0%
+point in x right the noise is going to
+ 
+
+ align:start position:0%
+point in x right the noise is going to
+keep moving me around okay
+
+ align:start position:0%
+keep moving me around okay
+ 
+
+ align:start position:0%
+keep moving me around okay
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i told you that p of x actually well i
+
+ align:start position:0%
+i told you that p of x actually well i
+ 
+
+ align:start position:0%
+i told you that p of x actually well i
+only told you it's a fixed point but i
+
+ align:start position:0%
+only told you it's a fixed point but i
+ 
+
+ align:start position:0%
+only told you it's a fixed point but i
+can tell you it's a stable fixed point
+
+ align:start position:0%
+can tell you it's a stable fixed point
+ 
+
+ align:start position:0%
+can tell you it's a stable fixed point
+p of x is actually stable okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+basically this equation right here this
+
+ align:start position:0%
+basically this equation right here this
+ 
+
+ align:start position:0%
+basically this equation right here this
+this update right here
+
+ align:start position:0%
+this update right here
+ 
+
+ align:start position:0%
+this update right here
+it's a very famous important thing
+
+ align:start position:0%
+it's a very famous important thing
+ 
+
+ align:start position:0%
+it's a very famous important thing
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+so important that it's called the master
+
+ align:start position:0%
+so important that it's called the master
+ 
+
+ align:start position:0%
+so important that it's called the master
+equation yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean don't just name it after some guy
+
+ align:start position:0%
+i mean don't just name it after some guy
+ 
+
+ align:start position:0%
+i mean don't just name it after some guy
+call it the master equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there are various versions of the
+
+ align:start position:0%
+and there are various versions of the
+ 
+
+ align:start position:0%
+and there are various versions of the
+master equation on specific problems
+
+ align:start position:0%
+master equation on specific problems
+ 
+
+ align:start position:0%
+master equation on specific problems
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+named after people's last names but
+
+ align:start position:0%
+named after people's last names but
+ 
+
+ align:start position:0%
+named after people's last names but
+but in general it's the master equation
+
+ align:start position:0%
+but in general it's the master equation
+ 
+
+ align:start position:0%
+but in general it's the master equation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can't forget how significant it
+
+ align:start position:0%
+so you can't forget how significant it
+ 
+
+ align:start position:0%
+so you can't forget how significant it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+and the idea is that the the in the
+
+ align:start position:0%
+and the idea is that the the in the
+ 
+
+ align:start position:0%
+and the idea is that the the in the
+master equation
+
+ align:start position:0%
+master equation
+ 
+
+ align:start position:0%
+master equation
+you're looking at the dynamics of the
+
+ align:start position:0%
+you're looking at the dynamics of the
+ 
+
+ align:start position:0%
+you're looking at the dynamics of the
+probability distribution not the
+
+ align:start position:0%
+probability distribution not the
+ 
+
+ align:start position:0%
+probability distribution not the
+dynamics of a single state the dynamics
+
+ align:start position:0%
+dynamics of a single state the dynamics
+ 
+
+ align:start position:0%
+dynamics of a single state the dynamics
+of a probability distribution okay so
+
+ align:start position:0%
+of a probability distribution okay so
+ 
+
+ align:start position:0%
+of a probability distribution okay so
+that probability distribution actually
+
+ align:start position:0%
+that probability distribution actually
+ 
+
+ align:start position:0%
+that probability distribution actually
+in the master equation is stable
+
+ align:start position:0%
+in the master equation is stable
+ 
+
+ align:start position:0%
+in the master equation is stable
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now there are more complicated cases
+
+ align:start position:0%
+now there are more complicated cases
+ 
+
+ align:start position:0%
+now there are more complicated cases
+actually right
+
+ align:start position:0%
+actually right
+ 
+
+ align:start position:0%
+actually right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's this thing going to do in the
+
+ align:start position:0%
+what's this thing going to do in the
+ 
+
+ align:start position:0%
+what's this thing going to do in the
+long run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to have a bimodal
+
+ align:start position:0%
+it's going to have a bimodal
+ 
+
+ align:start position:0%
+it's going to have a bimodal
+distribution in the long run
+
+ align:start position:0%
+distribution in the long run
+ 
+
+ align:start position:0%
+distribution in the long run
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+it would be
+
+ align:start position:0%
+it would be
+ 
+
+ align:start position:0%
+it would be
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+inappropriate to say either those points
+
+ align:start position:0%
+inappropriate to say either those points
+ 
+
+ align:start position:0%
+inappropriate to say either those points
+i mean they they that are that either of
+
+ align:start position:0%
+i mean they they that are that either of
+ 
+
+ align:start position:0%
+i mean they they that are that either of
+those points are fixed points for the
+
+ align:start position:0%
+those points are fixed points for the
+ 
+
+ align:start position:0%
+those points are fixed points for the
+deterministic case they are for the
+
+ align:start position:0%
+deterministic case they are for the
+ 
+
+ align:start position:0%
+deterministic case they are for the
+stochastic case they're not and you're
+
+ align:start position:0%
+stochastic case they're not and you're
+ 
+
+ align:start position:0%
+stochastic case they're not and you're
+right it's going to go to some
+
+ align:start position:0%
+right it's going to go to some
+ 
+
+ align:start position:0%
+right it's going to go to some
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+like this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have a decision point which of my 10
+
+ align:start position:0%
+i have a decision point which of my 10
+ 
+
+ align:start position:0%
+i have a decision point which of my 10
+pages i should do
+
+ align:start position:0%
+pages i should do
+ 
+
+ align:start position:0%
+pages i should do
+i could talk about um
+
+ align:start position:0%
+i could talk about um
+ 
+
+ align:start position:0%
+i could talk about um
+you know some examples of just
+
+ align:start position:0%
+you know some examples of just
+ 
+
+ align:start position:0%
+you know some examples of just
+stochastic dynamics for instance and
+
+ align:start position:0%
+stochastic dynamics for instance and
+ 
+
+ align:start position:0%
+stochastic dynamics for instance and
+walking robots
+
+ align:start position:0%
+walking robots
+ 
+
+ align:start position:0%
+walking robots
+or i could get to the
+
+ align:start position:0%
+or i could get to the
+ 
+
+ align:start position:0%
+or i could get to the
+optimal control of these of the more
+
+ align:start position:0%
+optimal control of these of the more
+ 
+
+ align:start position:0%
+optimal control of these of the more
+simple system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have to set john up for next week so
+
+ align:start position:0%
+i have to set john up for next week so
+ 
+
+ align:start position:0%
+i have to set john up for next week so
+so i guess i gotta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just tell you that that actually we've
+
+ align:start position:0%
+just tell you that that actually we've
+ 
+
+ align:start position:0%
+just tell you that that actually we've
+done some work
+
+ align:start position:0%
+done some work
+ 
+
+ align:start position:0%
+done some work
+thinking about uh for instance like the
+
+ align:start position:0%
+thinking about uh for instance like the
+ 
+
+ align:start position:0%
+thinking about uh for instance like the
+rimless wheel i'll just tell you the the
+
+ align:start position:0%
+rimless wheel i'll just tell you the the
+ 
+
+ align:start position:0%
+rimless wheel i'll just tell you the the
+setup and i won't tell you all the
+
+ align:start position:0%
+setup and i won't tell you all the
+ 
+
+ align:start position:0%
+setup and i won't tell you all the
+details
+
+ align:start position:0%
+details
+ 
+
+ align:start position:0%
+details
+so so here's a realistic example of that
+
+ align:start position:0%
+so so here's a realistic example of that
+ 
+
+ align:start position:0%
+so so here's a realistic example of that
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of dynamics take your rimless wheel
+
+ align:start position:0%
+sort of dynamics take your rimless wheel
+ 
+
+ align:start position:0%
+sort of dynamics take your rimless wheel
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+dynamics and let's say
+
+ align:start position:0%
+dynamics and let's say
+ 
+
+ align:start position:0%
+dynamics and let's say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+instead of walking down some
+
+ align:start position:0%
+instead of walking down some
+ 
+
+ align:start position:0%
+instead of walking down some
+some constant ramp let's say on every
+
+ align:start position:0%
+some constant ramp let's say on every
+ 
+
+ align:start position:0%
+some constant ramp let's say on every
+step the ramp angle is drawn from some
+
+ align:start position:0%
+step the ramp angle is drawn from some
+ 
+
+ align:start position:0%
+step the ramp angle is drawn from some
+distribution okay so this is passive
+
+ align:start position:0%
+distribution okay so this is passive
+ 
+
+ align:start position:0%
+distribution okay so this is passive
+walking on rough terrain
+
+ align:start position:0%
+walking on rough terrain
+ 
+
+ align:start position:0%
+walking on rough terrain
+and it turns out it's not it's not
+
+ align:start position:0%
+and it turns out it's not it's not
+ 
+
+ align:start position:0%
+and it turns out it's not it's not
+following a limit cycle anymore right
+
+ align:start position:0%
+following a limit cycle anymore right
+ 
+
+ align:start position:0%
+following a limit cycle anymore right
+but it's always it's it's long-term
+
+ align:start position:0%
+but it's always it's it's long-term
+ 
+
+ align:start position:0%
+but it's always it's it's long-term
+probability distribution
+
+ align:start position:0%
+probability distribution
+ 
+
+ align:start position:0%
+probability distribution
+is well there's there's a there's a
+
+ align:start position:0%
+is well there's there's a there's a
+ 
+
+ align:start position:0%
+is well there's there's a there's a
+slightly more complicated story
+
+ align:start position:0%
+slightly more complicated story
+ 
+
+ align:start position:0%
+slightly more complicated story
+if i look long enough
+
+ align:start position:0%
+if i look long enough
+ 
+
+ align:start position:0%
+if i look long enough
+this thing has an absorbing state right
+
+ align:start position:0%
+this thing has an absorbing state right
+ 
+
+ align:start position:0%
+this thing has an absorbing state right
+so if i if i take a big enough step
+
+ align:start position:0%
+so if i if i take a big enough step
+ 
+
+ align:start position:0%
+so if i if i take a big enough step
+then eventually i'm going to lose enough
+
+ align:start position:0%
+then eventually i'm going to lose enough
+ 
+
+ align:start position:0%
+then eventually i'm going to lose enough
+energy remember the deterministic system
+
+ align:start position:0%
+energy remember the deterministic system
+ 
+
+ align:start position:0%
+energy remember the deterministic system
+had two
+
+ align:start position:0%
+had two
+ 
+
+ align:start position:0%
+had two
+fixed points one was standing still the
+
+ align:start position:0%
+fixed points one was standing still the
+ 
+
+ align:start position:0%
+fixed points one was standing still the
+other one was rolling at a constant
+
+ align:start position:0%
+other one was rolling at a constant
+ 
+
+ align:start position:0%
+other one was rolling at a constant
+speed okay
+
+ align:start position:0%
+speed okay
+ 
+
+ align:start position:0%
+speed okay
+the standing still fixed point on rough
+
+ align:start position:0%
+the standing still fixed point on rough
+ 
+
+ align:start position:0%
+the standing still fixed point on rough
+terrain is an absorbing fixed point if i
+
+ align:start position:0%
+terrain is an absorbing fixed point if i
+ 
+
+ align:start position:0%
+terrain is an absorbing fixed point if i
+get there and i never take another
+
+ align:start position:0%
+get there and i never take another
+ 
+
+ align:start position:0%
+get there and i never take another
+another step that i'm never going to
+
+ align:start position:0%
+another step that i'm never going to
+ 
+
+ align:start position:0%
+another step that i'm never going to
+leave that fixed point so that is
+
+ align:start position:0%
+leave that fixed point so that is
+ 
+
+ align:start position:0%
+leave that fixed point so that is
+actually a true fixed point yeah
+
+ align:start position:0%
+actually a true fixed point yeah
+ 
+
+ align:start position:0%
+actually a true fixed point yeah
+the rolling fixed point you're going to
+
+ align:start position:0%
+the rolling fixed point you're going to
+ 
+
+ align:start position:0%
+the rolling fixed point you're going to
+tend to bounce around that fixed point
+
+ align:start position:0%
+tend to bounce around that fixed point
+ 
+
+ align:start position:0%
+tend to bounce around that fixed point
+so maybe this picture is something more
+
+ align:start position:0%
+so maybe this picture is something more
+ 
+
+ align:start position:0%
+so maybe this picture is something more
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the standing still fixed point if i get
+
+ align:start position:0%
+the standing still fixed point if i get
+ 
+
+ align:start position:0%
+the standing still fixed point if i get
+in there it's absorbing
+
+ align:start position:0%
+in there it's absorbing
+ 
+
+ align:start position:0%
+in there it's absorbing
+you know i'm never coming out
+
+ align:start position:0%
+you know i'm never coming out
+ 
+
+ align:start position:0%
+you know i'm never coming out
+but the rolling fix point you tend to be
+
+ align:start position:0%
+but the rolling fix point you tend to be
+ 
+
+ align:start position:0%
+but the rolling fix point you tend to be
+bounce around this limit cycle okay and
+
+ align:start position:0%
+bounce around this limit cycle okay and
+ 
+
+ align:start position:0%
+bounce around this limit cycle okay and
+then every once in a while in the
+
+ align:start position:0%
+then every once in a while in the
+ 
+
+ align:start position:0%
+then every once in a while in the
+stochastic
+
+ align:start position:0%
+stochastic
+ 
+
+ align:start position:0%
+stochastic
+dynamics case they say that these
+
+ align:start position:0%
+dynamics case they say that these
+ 
+
+ align:start position:0%
+dynamics case they say that these
+particles make an escape attempt so they
+
+ align:start position:0%
+particles make an escape attempt so they
+ 
+
+ align:start position:0%
+particles make an escape attempt so they
+call it right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and maybe
+
+ align:start position:0%
+okay and maybe
+ 
+
+ align:start position:0%
+okay and maybe
+shoot over and fall down
+
+ align:start position:0%
+shoot over and fall down
+ 
+
+ align:start position:0%
+shoot over and fall down
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it's really very beautiful if you
+
+ align:start position:0%
+and it's really very beautiful if you
+ 
+
+ align:start position:0%
+and it's really very beautiful if you
+watch the probability distributions as
+
+ align:start position:0%
+watch the probability distributions as
+ 
+
+ align:start position:0%
+watch the probability distributions as
+they propagate through the roomless
+
+ align:start position:0%
+they propagate through the roomless
+ 
+
+ align:start position:0%
+they propagate through the roomless
+wheel equations or the composite
+
+ align:start position:0%
+wheel equations or the composite
+ 
+
+ align:start position:0%
+wheel equations or the composite
+equations or you name it then
+
+ align:start position:0%
+equations or you name it then
+ 
+
+ align:start position:0%
+equations or you name it then
+what you get is you get this
+
+ align:start position:0%
+what you get is you get this
+ 
+
+ align:start position:0%
+what you get is you get this
+probability mass around here right for a
+
+ align:start position:0%
+probability mass around here right for a
+ 
+
+ align:start position:0%
+probability mass around here right for a
+long time it's pretty likely that i'm in
+
+ align:start position:0%
+long time it's pretty likely that i'm in
+ 
+
+ align:start position:0%
+long time it's pretty likely that i'm in
+this in the vicinity of that limit cycle
+
+ align:start position:0%
+this in the vicinity of that limit cycle
+ 
+
+ align:start position:0%
+this in the vicinity of that limit cycle
+right and then slowly as the time goes
+
+ align:start position:0%
+right and then slowly as the time goes
+ 
+
+ align:start position:0%
+right and then slowly as the time goes
+on the escape attempts continue to the
+
+ align:start position:0%
+on the escape attempts continue to the
+ 
+
+ align:start position:0%
+on the escape attempts continue to the
+point where this thing gets smaller and
+
+ align:start position:0%
+point where this thing gets smaller and
+ 
+
+ align:start position:0%
+point where this thing gets smaller and
+smaller until as time goes to infinity
+
+ align:start position:0%
+smaller until as time goes to infinity
+ 
+
+ align:start position:0%
+smaller until as time goes to infinity
+i'm only going to be standing still
+
+ align:start position:0%
+i'm only going to be standing still
+ 
+
+ align:start position:0%
+i'm only going to be standing still
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of negative pessimistic view of
+
+ align:start position:0%
+sort of negative pessimistic view of
+ 
+
+ align:start position:0%
+sort of negative pessimistic view of
+that work is to say that um
+
+ align:start position:0%
+that work is to say that um
+ 
+
+ align:start position:0%
+that work is to say that um
+you're always going to fall down you
+
+ align:start position:0%
+you're always going to fall down you
+ 
+
+ align:start position:0%
+you're always going to fall down you
+build the best robot you want but if you
+
+ align:start position:0%
+build the best robot you want but if you
+ 
+
+ align:start position:0%
+build the best robot you want but if you
+have a reasonable model of the dynamics
+
+ align:start position:0%
+have a reasonable model of the dynamics
+ 
+
+ align:start position:0%
+have a reasonable model of the dynamics
+it's always going to fall down right if
+
+ align:start position:0%
+it's always going to fall down right if
+ 
+
+ align:start position:0%
+it's always going to fall down right if
+you wait long enough
+
+ align:start position:0%
+you wait long enough
+ 
+
+ align:start position:0%
+you wait long enough
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+a mac truck is going to come along and
+
+ align:start position:0%
+a mac truck is going to come along and
+ 
+
+ align:start position:0%
+a mac truck is going to come along and
+hit it or or
+
+ align:start position:0%
+hit it or or
+ 
+
+ align:start position:0%
+hit it or or
+you know it's going to walk into a door
+
+ align:start position:0%
+you know it's going to walk into a door
+ 
+
+ align:start position:0%
+you know it's going to walk into a door
+or something like that you know you can
+
+ align:start position:0%
+or something like that you know you can
+ 
+
+ align:start position:0%
+or something like that you know you can
+do the best you want but it's going to
+
+ align:start position:0%
+do the best you want but it's going to
+ 
+
+ align:start position:0%
+do the best you want but it's going to
+fall down and that's it'll end up on
+
+ align:start position:0%
+fall down and that's it'll end up on
+ 
+
+ align:start position:0%
+fall down and that's it'll end up on
+youtube probably right
+
+ align:start position:0%
+youtube probably right
+ 
+
+ align:start position:0%
+youtube probably right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you're assuming your
+
+ align:start position:0%
+you're assuming your
+ 
+
+ align:start position:0%
+you're assuming your
+ramp distribution is actually gaussian
+
+ align:start position:0%
+ramp distribution is actually gaussian
+ 
+
+ align:start position:0%
+ramp distribution is actually gaussian
+that's what we decided yep
+
+ align:start position:0%
+that's what we decided yep
+ 
+
+ align:start position:0%
+that's what we decided yep
+but that doesn't actually imply that the
+
+ align:start position:0%
+but that doesn't actually imply that the
+ 
+
+ align:start position:0%
+but that doesn't actually imply that the
+um the posterior is gaussian because
+
+ align:start position:0%
+um the posterior is gaussian because
+ 
+
+ align:start position:0%
+um the posterior is gaussian because
+it's going through non-linear dynamics
+
+ align:start position:0%
+it's going through non-linear dynamics
+ 
+
+ align:start position:0%
+it's going through non-linear dynamics
+right but i mean in reality the random
+
+ align:start position:0%
+right but i mean in reality the random
+ 
+
+ align:start position:0%
+right but i mean in reality the random
+distribution is never going to be truly
+
+ align:start position:0%
+distribution is never going to be truly
+ 
+
+ align:start position:0%
+distribution is never going to be truly
+gaussian right because
+
+ align:start position:0%
+gaussian right because
+ 
+
+ align:start position:0%
+gaussian right because
+everything's gaussian if you uh if you
+
+ align:start position:0%
+everything's gaussian if you uh if you
+ 
+
+ align:start position:0%
+everything's gaussian if you uh if you
+get enough of i don't know i mean i
+
+ align:start position:0%
+get enough of i don't know i mean i
+ 
+
+ align:start position:0%
+get enough of i don't know i mean i
+think that's
+
+ align:start position:0%
+think that's
+ 
+
+ align:start position:0%
+think that's
+do you want to do stairs or something
+
+ align:start position:0%
+do you want to do stairs or something
+ 
+
+ align:start position:0%
+do you want to do stairs or something
+more specific
+
+ align:start position:0%
+more specific
+ 
+
+ align:start position:0%
+more specific
+oh well i'm just saying if if there is a
+
+ align:start position:0%
+oh well i'm just saying if if there is a
+ 
+
+ align:start position:0%
+oh well i'm just saying if if there is a
+hard limit on
+
+ align:start position:0%
+hard limit on
+ 
+
+ align:start position:0%
+hard limit on
+how steep your brand is oh you could
+
+ align:start position:0%
+how steep your brand is oh you could
+ 
+
+ align:start position:0%
+how steep your brand is oh you could
+guarantee that good very good point
+
+ align:start position:0%
+guarantee that good very good point
+ 
+
+ align:start position:0%
+guarantee that good very good point
+right so so if
+
+ align:start position:0%
+right so so if
+ 
+
+ align:start position:0%
+right so so if
+if the distributions don't didn't have
+
+ align:start position:0%
+if the distributions don't didn't have
+ 
+
+ align:start position:0%
+if the distributions don't didn't have
+tails then there are cases where i can
+
+ align:start position:0%
+tails then there are cases where i can
+ 
+
+ align:start position:0%
+tails then there are cases where i can
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+um it never going over but those tails
+
+ align:start position:0%
+um it never going over but those tails
+ 
+
+ align:start position:0%
+um it never going over but those tails
+actually have to be pretty steep the the
+
+ align:start position:0%
+actually have to be pretty steep the the
+ 
+
+ align:start position:0%
+actually have to be pretty steep the the
+limitations have to be pretty steep
+
+ align:start position:0%
+limitations have to be pretty steep
+ 
+
+ align:start position:0%
+limitations have to be pretty steep
+because you not you have to make sure
+
+ align:start position:0%
+because you not you have to make sure
+ 
+
+ align:start position:0%
+because you not you have to make sure
+that on a single step the damping
+
+ align:start position:0%
+that on a single step the damping
+ 
+
+ align:start position:0%
+that on a single step the damping
+overcomes the the biggest possible
+
+ align:start position:0%
+overcomes the the biggest possible
+ 
+
+ align:start position:0%
+overcomes the the biggest possible
+perturbation
+
+ align:start position:0%
+perturbation
+ 
+
+ align:start position:0%
+perturbation
+if on a single if your noise can ever be
+
+ align:start position:0%
+if on a single if your noise can ever be
+ 
+
+ align:start position:0%
+if on a single if your noise can ever be
+bigger than what you can take out in a
+
+ align:start position:0%
+bigger than what you can take out in a
+ 
+
+ align:start position:0%
+bigger than what you can take out in a
+single step then you will eventually as
+
+ align:start position:0%
+single step then you will eventually as
+ 
+
+ align:start position:0%
+single step then you will eventually as
+time goes to infinity find a way to get
+
+ align:start position:0%
+time goes to infinity find a way to get
+ 
+
+ align:start position:0%
+time goes to infinity find a way to get
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so katie
+
+ align:start position:0%
+so katie
+ 
+
+ align:start position:0%
+so katie
+bill did some nice work uh and and sort
+
+ align:start position:0%
+bill did some nice work uh and and sort
+ 
+
+ align:start position:0%
+bill did some nice work uh and and sort
+of quantifying the metastable dynamics
+
+ align:start position:0%
+of quantifying the metastable dynamics
+ 
+
+ align:start position:0%
+of quantifying the metastable dynamics
+of walking and actually i think that so
+
+ align:start position:0%
+of walking and actually i think that so
+ 
+
+ align:start position:0%
+of walking and actually i think that so
+it's called what we call the metastable
+
+ align:start position:0%
+it's called what we call the metastable
+ 
+
+ align:start position:0%
+it's called what we call the metastable
+because that distribution is is um
+
+ align:start position:0%
+because that distribution is is um
+ 
+
+ align:start position:0%
+because that distribution is is um
+long living it still makes sense to talk
+
+ align:start position:0%
+long living it still makes sense to talk
+ 
+
+ align:start position:0%
+long living it still makes sense to talk
+about where you'd expect this thing to
+
+ align:start position:0%
+about where you'd expect this thing to
+ 
+
+ align:start position:0%
+about where you'd expect this thing to
+be while it's walking but eventually we
+
+ align:start position:0%
+be while it's walking but eventually we
+ 
+
+ align:start position:0%
+be while it's walking but eventually we
+have to admit it's going to be it's
+
+ align:start position:0%
+have to admit it's going to be it's
+ 
+
+ align:start position:0%
+have to admit it's going to be it's
+going to go to
+
+ align:start position:0%
+going to go to
+ 
+
+ align:start position:0%
+going to go to
+falling down like a diamond
+
+ align:start position:0%
+falling down like a diamond
+ 
+
+ align:start position:0%
+falling down like a diamond
+is a diamond for a very long time but
+
+ align:start position:0%
+is a diamond for a very long time but
+ 
+
+ align:start position:0%
+is a diamond for a very long time but
+eventually it'll turn back into graphite
+
+ align:start position:0%
+eventually it'll turn back into graphite
+ 
+
+ align:start position:0%
+eventually it'll turn back into graphite
+okay so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so there's actually beautiful even
+
+ align:start position:0%
+good so there's actually beautiful even
+ 
+
+ align:start position:0%
+good so there's actually beautiful even
+if you don't care about control i think
+
+ align:start position:0%
+if you don't care about control i think
+ 
+
+ align:start position:0%
+if you don't care about control i think
+there's actually beautiful things that
+
+ align:start position:0%
+there's actually beautiful things that
+ 
+
+ align:start position:0%
+there's actually beautiful things that
+happen in stochastic dynamics but the
+
+ align:start position:0%
+happen in stochastic dynamics but the
+ 
+
+ align:start position:0%
+happen in stochastic dynamics but the
+thing that that matters here is we've
+
+ align:start position:0%
+thing that that matters here is we've
+ 
+
+ align:start position:0%
+thing that that matters here is we've
+switched hats we've now started thinking
+
+ align:start position:0%
+switched hats we've now started thinking
+ 
+
+ align:start position:0%
+switched hats we've now started thinking
+about probability distributions and how
+
+ align:start position:0%
+about probability distributions and how
+ 
+
+ align:start position:0%
+about probability distributions and how
+they evolve with dynamics and how we can
+
+ align:start position:0%
+they evolve with dynamics and how we can
+ 
+
+ align:start position:0%
+they evolve with dynamics and how we can
+change those probability distributions
+
+ align:start position:0%
+change those probability distributions
+ 
+
+ align:start position:0%
+change those probability distributions
+with control
+
+ align:start position:0%
+with control
+ 
+
+ align:start position:0%
+with control
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+if i could if i could control the shape
+
+ align:start position:0%
+if i could if i could control the shape
+ 
+
+ align:start position:0%
+if i could if i could control the shape
+of that right then i can control those
+
+ align:start position:0%
+of that right then i can control those
+ 
+
+ align:start position:0%
+of that right then i can control those
+probability distributions for instance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it turns out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's sort of
+
+ align:start position:0%
+it's sort of
+ 
+
+ align:start position:0%
+it's sort of
+trivial to work
+
+ align:start position:0%
+trivial to work
+ 
+
+ align:start position:0%
+trivial to work
+stochastic to solve stochastic optimal
+
+ align:start position:0%
+stochastic to solve stochastic optimal
+ 
+
+ align:start position:0%
+stochastic to solve stochastic optimal
+control problems
+
+ align:start position:0%
+control problems
+ 
+
+ align:start position:0%
+control problems
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+at least with with dynamic programming
+
+ align:start position:0%
+at least with with dynamic programming
+ 
+
+ align:start position:0%
+at least with with dynamic programming
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it works out because of this additive
+
+ align:start position:0%
+it works out because of this additive
+ 
+
+ align:start position:0%
+it works out because of this additive
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+that it's sort of no more expensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly no more expensive to solve the
+
+ align:start position:0%
+roughly no more expensive to solve the
+ 
+
+ align:start position:0%
+roughly no more expensive to solve the
+stochastic optimal control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the deterministic one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it matters i i maybe i should even
+
+ align:start position:0%
+and it matters i i maybe i should even
+ 
+
+ align:start position:0%
+and it matters i i maybe i should even
+make the point that it matters okay so
+
+ align:start position:0%
+make the point that it matters okay so
+ 
+
+ align:start position:0%
+make the point that it matters okay so
+so if i have a stochastic process
+
+ align:start position:0%
+so if i have a stochastic process
+ 
+
+ align:start position:0%
+so if i have a stochastic process
+and in general
+
+ align:start position:0%
+and in general
+ 
+
+ align:start position:0%
+and in general
+the optimal policy that you get from
+
+ align:start position:0%
+the optimal policy that you get from
+ 
+
+ align:start position:0%
+the optimal policy that you get from
+stochastic
+
+ align:start position:0%
+stochastic
+ 
+
+ align:start position:0%
+stochastic
+optimal control is going to be different
+
+ align:start position:0%
+optimal control is going to be different
+ 
+
+ align:start position:0%
+optimal control is going to be different
+than the one you get
+
+ align:start position:0%
+than the one you get
+ 
+
+ align:start position:0%
+than the one you get
+from deterministic optimal control
+
+ align:start position:0%
+from deterministic optimal control
+ 
+
+ align:start position:0%
+from deterministic optimal control
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so potentially in dramatic ways
+
+ align:start position:0%
+so potentially in dramatic ways
+ 
+
+ align:start position:0%
+so potentially in dramatic ways
+right let me let me try to make that
+
+ align:start position:0%
+right let me let me try to make that
+ 
+
+ align:start position:0%
+right let me let me try to make that
+that point here so imagine i've got my
+
+ align:start position:0%
+that point here so imagine i've got my
+ 
+
+ align:start position:0%
+that point here so imagine i've got my
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i've got a trash can robot i shouldn't
+
+ align:start position:0%
+i've got a trash can robot i shouldn't
+ 
+
+ align:start position:0%
+i've got a trash can robot i shouldn't
+call them check i got i've got a um
+
+ align:start position:0%
+call them check i got i've got a um
+ 
+
+ align:start position:0%
+call them check i got i've got a um
+you know what are they the
+
+ align:start position:0%
+you know what are they the
+ 
+
+ align:start position:0%
+you know what are they the
+uh what are the names of those little
+
+ align:start position:0%
+uh what are the names of those little
+ 
+
+ align:start position:0%
+uh what are the names of those little
+red robots pioneer robot or something
+
+ align:start position:0%
+red robots pioneer robot or something
+ 
+
+ align:start position:0%
+red robots pioneer robot or something
+like this yeah and uh um
+
+ align:start position:0%
+like this yeah and uh um
+ 
+
+ align:start position:0%
+like this yeah and uh um
+i want to get it from
+
+ align:start position:0%
+i want to get it from
+ 
+
+ align:start position:0%
+i want to get it from
+you know to this goal
+
+ align:start position:0%
+you know to this goal
+ 
+
+ align:start position:0%
+you know to this goal
+let's say i've got a cost function like
+
+ align:start position:0%
+let's say i've got a cost function like
+ 
+
+ align:start position:0%
+let's say i've got a cost function like
+this and i start over here and as i go i
+
+ align:start position:0%
+this and i start over here and as i go i
+ 
+
+ align:start position:0%
+this and i start over here and as i go i
+know that that my wheels slip or
+
+ align:start position:0%
+know that that my wheels slip or
+ 
+
+ align:start position:0%
+know that that my wheels slip or
+something like that my distributions are
+
+ align:start position:0%
+something like that my distributions are
+ 
+
+ align:start position:0%
+something like that my distributions are
+going to grow
+
+ align:start position:0%
+going to grow
+ 
+
+ align:start position:0%
+going to grow
+as i go yeah and i've got some ability
+
+ align:start position:0%
+as i go yeah and i've got some ability
+ 
+
+ align:start position:0%
+as i go yeah and i've got some ability
+to control them so they're not going to
+
+ align:start position:0%
+to control them so they're not going to
+ 
+
+ align:start position:0%
+to control them so they're not going to
+grow unbounded but let's say they're
+
+ align:start position:0%
+grow unbounded but let's say they're
+ 
+
+ align:start position:0%
+grow unbounded but let's say they're
+going to grow
+
+ align:start position:0%
+going to grow
+ 
+
+ align:start position:0%
+going to grow
+my path to the goal okay
+
+ align:start position:0%
+my path to the goal okay
+ 
+
+ align:start position:0%
+my path to the goal okay
+there'll be two competing forces
+
+ align:start position:0%
+there'll be two competing forces
+ 
+
+ align:start position:0%
+there'll be two competing forces
+there'll be the ability to to measure
+
+ align:start position:0%
+there'll be the ability to to measure
+ 
+
+ align:start position:0%
+there'll be the ability to to measure
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+fight against disturbances and there'll
+
+ align:start position:0%
+fight against disturbances and there'll
+ 
+
+ align:start position:0%
+fight against disturbances and there'll
+be the inevitable disturbances and those
+
+ align:start position:0%
+be the inevitable disturbances and those
+ 
+
+ align:start position:0%
+be the inevitable disturbances and those
+two will again combine into some sort of
+
+ align:start position:0%
+two will again combine into some sort of
+ 
+
+ align:start position:0%
+two will again combine into some sort of
+distribution over time okay
+
+ align:start position:0%
+distribution over time okay
+ 
+
+ align:start position:0%
+distribution over time okay
+now imagine
+
+ align:start position:0%
+now imagine
+ 
+
+ align:start position:0%
+now imagine
+like the scenario we talked about in the
+
+ align:start position:0%
+like the scenario we talked about in the
+ 
+
+ align:start position:0%
+like the scenario we talked about in the
+feedback case imagine
+
+ align:start position:0%
+feedback case imagine
+ 
+
+ align:start position:0%
+feedback case imagine
+my cost function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is like is zero everywhere
+
+ align:start position:0%
+is like is zero everywhere
+ 
+
+ align:start position:0%
+is like is zero everywhere
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative one at the goal
+
+ align:start position:0%
+negative one at the goal
+ 
+
+ align:start position:0%
+negative one at the goal
+i want to get to the goal
+
+ align:start position:0%
+i want to get to the goal
+ 
+
+ align:start position:0%
+i want to get to the goal
+and say you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something really big here yeah
+
+ align:start position:0%
+something really big here yeah
+ 
+
+ align:start position:0%
+something really big here yeah
+right there's sort of pits of fire in
+
+ align:start position:0%
+right there's sort of pits of fire in
+ 
+
+ align:start position:0%
+right there's sort of pits of fire in
+the middle of the lab
+
+ align:start position:0%
+the middle of the lab
+ 
+
+ align:start position:0%
+the middle of the lab
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+no i mean right so so i've got to make
+
+ align:start position:0%
+no i mean right so so i've got to make
+ 
+
+ align:start position:0%
+no i mean right so so i've got to make
+the point if it was one if it was just
+
+ align:start position:0%
+the point if it was one if it was just
+ 
+
+ align:start position:0%
+the point if it was one if it was just
+one i wouldn't make be as dramatic but
+
+ align:start position:0%
+one i wouldn't make be as dramatic but
+ 
+
+ align:start position:0%
+one i wouldn't make be as dramatic but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+long story short
+
+ align:start position:0%
+long story short
+ 
+
+ align:start position:0%
+long story short
+a stochastic optimal control solution
+
+ align:start position:0%
+a stochastic optimal control solution
+ 
+
+ align:start position:0%
+a stochastic optimal control solution
+is unlikely to choose this path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+even if even if the distributions are
+
+ align:start position:0%
+even if even if the distributions are
+ 
+
+ align:start position:0%
+even if even if the distributions are
+fairly tight
+
+ align:start position:0%
+fairly tight
+ 
+
+ align:start position:0%
+fairly tight
+zero times a big part of the probability
+
+ align:start position:0%
+zero times a big part of the probability
+ 
+
+ align:start position:0%
+zero times a big part of the probability
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+one e to the sixth times even a little
+
+ align:start position:0%
+one e to the sixth times even a little
+ 
+
+ align:start position:0%
+one e to the sixth times even a little
+part of the probability distribution is
+
+ align:start position:0%
+part of the probability distribution is
+ 
+
+ align:start position:0%
+part of the probability distribution is
+still a big number
+
+ align:start position:0%
+still a big number
+ 
+
+ align:start position:0%
+still a big number
+okay and so therefore there's a there's
+
+ align:start position:0%
+okay and so therefore there's a there's
+ 
+
+ align:start position:0%
+okay and so therefore there's a there's
+the expected value of going through here
+
+ align:start position:0%
+the expected value of going through here
+ 
+
+ align:start position:0%
+the expected value of going through here
+is that i'm going to incur quite a bit
+
+ align:start position:0%
+is that i'm going to incur quite a bit
+ 
+
+ align:start position:0%
+is that i'm going to incur quite a bit
+of cost does that make sense
+
+ align:start position:0%
+of cost does that make sense
+ 
+
+ align:start position:0%
+of cost does that make sense
+so so if i just did deterministic
+
+ align:start position:0%
+so so if i just did deterministic
+ 
+
+ align:start position:0%
+so so if i just did deterministic
+optimal control right we talked about
+
+ align:start position:0%
+optimal control right we talked about
+ 
+
+ align:start position:0%
+optimal control right we talked about
+using feedback to try to motivate not
+
+ align:start position:0%
+using feedback to try to motivate not
+ 
+
+ align:start position:0%
+using feedback to try to motivate not
+going through there but the really the
+
+ align:start position:0%
+going through there but the really the
+ 
+
+ align:start position:0%
+going through there but the really the
+more direct way is to think about
+
+ align:start position:0%
+more direct way is to think about
+ 
+
+ align:start position:0%
+more direct way is to think about
+the probability distributions right
+
+ align:start position:0%
+the probability distributions right
+ 
+
+ align:start position:0%
+the probability distributions right
+so if i can control my probabilities to
+
+ align:start position:0%
+so if i can control my probabilities to
+ 
+
+ align:start position:0%
+so if i can control my probabilities to
+the point where i know zero probability
+
+ align:start position:0%
+the point where i know zero probability
+ 
+
+ align:start position:0%
+the point where i know zero probability
+is going to be in here then sure go
+
+ align:start position:0%
+is going to be in here then sure go
+ 
+
+ align:start position:0%
+is going to be in here then sure go
+ahead through there and the
+
+ align:start position:0%
+ahead through there and the
+ 
+
+ align:start position:0%
+ahead through there and the
+deterministic one will probably find
+
+ align:start position:0%
+deterministic one will probably find
+ 
+
+ align:start position:0%
+deterministic one will probably find
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but the stochastic one if it realizes
+
+ align:start position:0%
+but the stochastic one if it realizes
+ 
+
+ align:start position:0%
+but the stochastic one if it realizes
+there's something we'll probably try to
+
+ align:start position:0%
+there's something we'll probably try to
+ 
+
+ align:start position:0%
+there's something we'll probably try to
+find a different path
+
+ align:start position:0%
+find a different path
+ 
+
+ align:start position:0%
+find a different path
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's a that's a
+
+ align:start position:0%
+so that's a that's a
+ 
+
+ align:start position:0%
+so that's a that's a
+uh one example but in general the
+
+ align:start position:0%
+uh one example but in general the
+ 
+
+ align:start position:0%
+uh one example but in general the
+stochastic optimal control policies are
+
+ align:start position:0%
+stochastic optimal control policies are
+ 
+
+ align:start position:0%
+stochastic optimal control policies are
+going to be different
+
+ align:start position:0%
+going to be different
+ 
+
+ align:start position:0%
+going to be different
+than the deterministic ones and and
+
+ align:start position:0%
+than the deterministic ones and and
+ 
+
+ align:start position:0%
+than the deterministic ones and and
+better and if you can if you have a
+
+ align:start position:0%
+better and if you can if you have a
+ 
+
+ align:start position:0%
+better and if you can if you have a
+reasonable model of the
+
+ align:start position:0%
+reasonable model of the
+ 
+
+ align:start position:0%
+reasonable model of the
+disturbances you'd expect to encounter
+
+ align:start position:0%
+disturbances you'd expect to encounter
+ 
+
+ align:start position:0%
+disturbances you'd expect to encounter
+then you should allow your optimal
+
+ align:start position:0%
+then you should allow your optimal
+ 
+
+ align:start position:0%
+then you should allow your optimal
+control tools to think about them
+
+ align:start position:0%
+control tools to think about them
+ 
+
+ align:start position:0%
+control tools to think about them
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+potentially each action can
+
+ align:start position:0%
+potentially each action can
+ 
+
+ align:start position:0%
+potentially each action can
+move you to any of the possible states
+
+ align:start position:0%
+move you to any of the possible states
+ 
+
+ align:start position:0%
+move you to any of the possible states
+well and deterministic case you can go
+
+ align:start position:0%
+well and deterministic case you can go
+ 
+
+ align:start position:0%
+well and deterministic case you can go
+to one state so when you do it back up
+
+ align:start position:0%
+to one state so when you do it back up
+ 
+
+ align:start position:0%
+to one state so when you do it back up
+this time it's slower
+
+ align:start position:0%
+this time it's slower
+ 
+
+ align:start position:0%
+this time it's slower
+right i knew someone was gonna so so i
+
+ align:start position:0%
+right i knew someone was gonna so so i
+ 
+
+ align:start position:0%
+right i knew someone was gonna so so i
+would say like you know essentially no i
+
+ align:start position:0%
+would say like you know essentially no i
+ 
+
+ align:start position:0%
+would say like you know essentially no i
+almost wrote essentially no time and the
+
+ align:start position:0%
+almost wrote essentially no time and the
+ 
+
+ align:start position:0%
+almost wrote essentially no time and the
+reason i want to make that comparison
+
+ align:start position:0%
+reason i want to make that comparison
+ 
+
+ align:start position:0%
+reason i want to make that comparison
+actually is because i want to compare it
+
+ align:start position:0%
+actually is because i want to compare it
+ 
+
+ align:start position:0%
+actually is because i want to compare it
+directly to the barycentric
+
+ align:start position:0%
+directly to the barycentric
+ 
+
+ align:start position:0%
+directly to the barycentric
+interpolation that we were doing before
+
+ align:start position:0%
+interpolation that we were doing before
+ 
+
+ align:start position:0%
+interpolation that we were doing before
+which is what i'm going to do in a
+
+ align:start position:0%
+which is what i'm going to do in a
+ 
+
+ align:start position:0%
+which is what i'm going to do in a
+second and that is already doing an
+
+ align:start position:0%
+second and that is already doing an
+ 
+
+ align:start position:0%
+second and that is already doing an
+interpolation already going through some
+
+ align:start position:0%
+interpolation already going through some
+ 
+
+ align:start position:0%
+interpolation already going through some
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+some some transition matrix yeah
+
+ align:start position:0%
+some some transition matrix yeah
+ 
+
+ align:start position:0%
+some some transition matrix yeah
+and it's probably true that the it may
+
+ align:start position:0%
+and it's probably true that the it may
+ 
+
+ align:start position:0%
+and it's probably true that the it may
+be true depending on your noise
+
+ align:start position:0%
+be true depending on your noise
+ 
+
+ align:start position:0%
+be true depending on your noise
+distributions that if you add a lot of
+
+ align:start position:0%
+distributions that if you add a lot of
+ 
+
+ align:start position:0%
+distributions that if you add a lot of
+noise that transition matrix will be
+
+ align:start position:0%
+noise that transition matrix will be
+ 
+
+ align:start position:0%
+noise that transition matrix will be
+more dense and therefore it might take
+
+ align:start position:0%
+more dense and therefore it might take
+ 
+
+ align:start position:0%
+more dense and therefore it might take
+more time depending on how you compute
+
+ align:start position:0%
+more time depending on how you compute
+ 
+
+ align:start position:0%
+more time depending on how you compute
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+my matlab implementation is the same
+
+ align:start position:0%
+my matlab implementation is the same
+ 
+
+ align:start position:0%
+my matlab implementation is the same
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+is that fair
+
+ align:start position:0%
+is that fair
+ 
+
+ align:start position:0%
+is that fair
+and it's no more complicated to write
+
+ align:start position:0%
+and it's no more complicated to write
+ 
+
+ align:start position:0%
+and it's no more complicated to write
+down how about that
+
+ align:start position:0%
+down how about that
+ 
+
+ align:start position:0%
+down how about that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll completely understand what what
+
+ align:start position:0%
+we'll completely understand what what
+ 
+
+ align:start position:0%
+we'll completely understand what what
+upwards was asking in just a second
+
+ align:start position:0%
+upwards was asking in just a second
+ 
+
+ align:start position:0%
+upwards was asking in just a second
+okay so why is it no more complicated
+
+ align:start position:0%
+okay so why is it no more complicated
+ 
+
+ align:start position:0%
+okay so why is it no more complicated
+to write for me to write down on the
+
+ align:start position:0%
+to write for me to write down on the
+ 
+
+ align:start position:0%
+to write for me to write down on the
+board the stochastic uh optimal control
+
+ align:start position:0%
+board the stochastic uh optimal control
+ 
+
+ align:start position:0%
+board the stochastic uh optimal control
+case in dynamic programming right um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember i said now this is i'm going to
+
+ align:start position:0%
+remember i said now this is i'm going to
+ 
+
+ align:start position:0%
+remember i said now this is i'm going to
+take the expected value of my additive
+
+ align:start position:0%
+take the expected value of my additive
+ 
+
+ align:start position:0%
+take the expected value of my additive
+cost right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first let's just think about what the
+
+ align:start position:0%
+so first let's just think about what the
+ 
+
+ align:start position:0%
+so first let's just think about what the
+implications are for for doing optimal
+
+ align:start position:0%
+implications are for for doing optimal
+ 
+
+ align:start position:0%
+implications are for for doing optimal
+control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so first of all i can take that
+
+ align:start position:0%
+right so first of all i can take that
+ 
+
+ align:start position:0%
+right so first of all i can take that
+expectation inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and now what's the probability of
+
+ align:start position:0%
+and now what's the probability of
+ 
+
+ align:start position:0%
+and now what's the probability of
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+or that what's the expected value of g
+
+ align:start position:0%
+or that what's the expected value of g
+ 
+
+ align:start position:0%
+or that what's the expected value of g
+at x and u n
+
+ align:start position:0%
+at x and u n
+ 
+
+ align:start position:0%
+at x and u n
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x has got some distribution given by p
+
+ align:start position:0%
+x has got some distribution given by p
+ 
+
+ align:start position:0%
+x has got some distribution given by p
+of x and yeah
+
+ align:start position:0%
+of x and yeah
+ 
+
+ align:start position:0%
+of x and yeah
+so it's this thing is going to work out
+
+ align:start position:0%
+so it's this thing is going to work out
+ 
+
+ align:start position:0%
+so it's this thing is going to work out
+to be you can always take the expected
+
+ align:start position:0%
+to be you can always take the expected
+ 
+
+ align:start position:0%
+to be you can always take the expected
+value of a function of x by just the
+
+ align:start position:0%
+value of a function of x by just the
+ 
+
+ align:start position:0%
+value of a function of x by just the
+that function times this distribution
+
+ align:start position:0%
+that function times this distribution
+ 
+
+ align:start position:0%
+that function times this distribution
+integrated this thing is going to work
+
+ align:start position:0%
+integrated this thing is going to work
+ 
+
+ align:start position:0%
+integrated this thing is going to work
+out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some integral over all possible states
+
+ align:start position:0%
+some integral over all possible states
+ 
+
+ align:start position:0%
+some integral over all possible states
+of g
+
+ align:start position:0%
+of g
+ 
+
+ align:start position:0%
+of g
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+u of n
+
+ align:start position:0%
+u of n
+ 
+
+ align:start position:0%
+u of n
+times p then
+
+ align:start position:0%
+times p then
+ 
+
+ align:start position:0%
+times p then
+x dx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you could imagine computing
+
+ align:start position:0%
+okay so you could imagine computing
+ 
+
+ align:start position:0%
+okay so you could imagine computing
+optimal policies by
+
+ align:start position:0%
+optimal policies by
+ 
+
+ align:start position:0%
+optimal policies by
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+figuring out the state distribution by
+
+ align:start position:0%
+figuring out the state distribution by
+ 
+
+ align:start position:0%
+figuring out the state distribution by
+that evolution i was talking about
+
+ align:start position:0%
+that evolution i was talking about
+ 
+
+ align:start position:0%
+that evolution i was talking about
+before right and then
+
+ align:start position:0%
+before right and then
+ 
+
+ align:start position:0%
+before right and then
+integrating over the possible states
+
+ align:start position:0%
+integrating over the possible states
+ 
+
+ align:start position:0%
+integrating over the possible states
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and the the costs for each state and
+
+ align:start position:0%
+and the the costs for each state and
+ 
+
+ align:start position:0%
+and the the costs for each state and
+figuring out our j figuring out a way to
+
+ align:start position:0%
+figuring out our j figuring out a way to
+ 
+
+ align:start position:0%
+figuring out our j figuring out a way to
+minimize that right i sort of only wrote
+
+ align:start position:0%
+minimize that right i sort of only wrote
+ 
+
+ align:start position:0%
+minimize that right i sort of only wrote
+that down to make it look hard okay
+
+ align:start position:0%
+that down to make it look hard okay
+ 
+
+ align:start position:0%
+that down to make it look hard okay
+turns out again just like before the
+
+ align:start position:0%
+turns out again just like before the
+ 
+
+ align:start position:0%
+turns out again just like before the
+recursive form is beautiful and simple
+
+ align:start position:0%
+recursive form is beautiful and simple
+ 
+
+ align:start position:0%
+recursive form is beautiful and simple
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can imagine doing it that way and
+
+ align:start position:0%
+so you can imagine doing it that way and
+ 
+
+ align:start position:0%
+so you can imagine doing it that way and
+that's really that's that's correct
+
+ align:start position:0%
+that's really that's that's correct
+ 
+
+ align:start position:0%
+that's really that's that's correct
+but just like before the dynamic
+
+ align:start position:0%
+but just like before the dynamic
+ 
+
+ align:start position:0%
+but just like before the dynamic
+programming solution exploits the
+
+ align:start position:0%
+programming solution exploits the
+ 
+
+ align:start position:0%
+programming solution exploits the
+recursive the additive form and does it
+
+ align:start position:0%
+recursive the additive form and does it
+ 
+
+ align:start position:0%
+recursive the additive form and does it
+a recursive solution which just works
+
+ align:start position:0%
+a recursive solution which just works
+ 
+
+ align:start position:0%
+a recursive solution which just works
+out beautifully okay
+
+ align:start position:0%
+out beautifully okay
+ 
+
+ align:start position:0%
+out beautifully okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i do
+
+ align:start position:0%
+so if i do
+ 
+
+ align:start position:0%
+so if i do
+j of x from time 0 being the expected
+
+ align:start position:0%
+j of x from time 0 being the expected
+ 
+
+ align:start position:0%
+j of x from time 0 being the expected
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+let's do the final cost
+
+ align:start position:0%
+let's do the final cost
+ 
+
+ align:start position:0%
+let's do the final cost
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's j of x
+
+ align:start position:0%
+what's j of x
+ 
+
+ align:start position:0%
+what's j of x
+capital n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my cost to go given i'm at the goal
+
+ align:start position:0%
+my cost to go given i'm at the goal
+ 
+
+ align:start position:0%
+my cost to go given i'm at the goal
+all right the time is the time is
+
+ align:start position:0%
+all right the time is the time is
+ 
+
+ align:start position:0%
+all right the time is the time is
+expired and i'm at state x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it expected value of h of x
+
+ align:start position:0%
+is it expected value of h of x
+ 
+
+ align:start position:0%
+is it expected value of h of x
+or is it just h what is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+awesome yeah if i know i'm already in
+
+ align:start position:0%
+awesome yeah if i know i'm already in
+ 
+
+ align:start position:0%
+awesome yeah if i know i'm already in
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there's no probabilities left yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then if i go backwards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j of x of time
+
+ align:start position:0%
+j of x of time
+ 
+
+ align:start position:0%
+j of x of time
+k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to work out to be
+
+ align:start position:0%
+is going to work out to be
+ 
+
+ align:start position:0%
+is going to work out to be
+min over u i should say j star of x
+
+ align:start position:0%
+min over u i should say j star of x
+ 
+
+ align:start position:0%
+min over u i should say j star of x
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+j star of x is going to be min over u
+
+ align:start position:0%
+j star of x is going to be min over u
+ 
+
+ align:start position:0%
+j star of x is going to be min over u
+the expected value of g x
+
+ align:start position:0%
+the expected value of g x
+ 
+
+ align:start position:0%
+the expected value of g x
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+plus j
+
+ align:start position:0%
+plus j
+ 
+
+ align:start position:0%
+plus j
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+w of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you buy that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the reinforcement learning
+
+ align:start position:0%
+okay so the reinforcement learning
+ 
+
+ align:start position:0%
+okay so the reinforcement learning
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+always like to say that
+
+ align:start position:0%
+always like to say that
+ 
+
+ align:start position:0%
+always like to say that
+the reward or the cost
+
+ align:start position:0%
+the reward or the cost
+ 
+
+ align:start position:0%
+the reward or the cost
+can also be
+
+ align:start position:0%
+can also be
+ 
+
+ align:start position:0%
+can also be
+a random
+
+ align:start position:0%
+a random
+ 
+
+ align:start position:0%
+a random
+process or random variable
+
+ align:start position:0%
+process or random variable
+ 
+
+ align:start position:0%
+process or random variable
+i'm always in this case where i design
+
+ align:start position:0%
+i'm always in this case where i design
+ 
+
+ align:start position:0%
+i'm always in this case where i design
+the cost
+
+ align:start position:0%
+the cost
+ 
+
+ align:start position:0%
+the cost
+it's a function of some random x but g
+
+ align:start position:0%
+it's a function of some random x but g
+ 
+
+ align:start position:0%
+it's a function of some random x but g
+is deterministic so actually i could
+
+ align:start position:0%
+is deterministic so actually i could
+ 
+
+ align:start position:0%
+is deterministic so actually i could
+take that expectation right inside here
+
+ align:start position:0%
+take that expectation right inside here
+ 
+
+ align:start position:0%
+take that expectation right inside here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and i just have to do a min over u of g
+
+ align:start position:0%
+and i just have to do a min over u of g
+ 
+
+ align:start position:0%
+and i just have to do a min over u of g
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+that's the expected value of my cost to
+
+ align:start position:0%
+that's the expected value of my cost to
+ 
+
+ align:start position:0%
+that's the expected value of my cost to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the nicest way to see how to implement
+
+ align:start position:0%
+the nicest way to see how to implement
+ 
+
+ align:start position:0%
+the nicest way to see how to implement
+that is let's go ahead and
+
+ align:start position:0%
+that is let's go ahead and
+ 
+
+ align:start position:0%
+that is let's go ahead and
+we've already discretized time let's
+
+ align:start position:0%
+we've already discretized time let's
+ 
+
+ align:start position:0%
+we've already discretized time let's
+discretize state and actions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now i have
+
+ align:start position:0%
+so now i have
+ 
+
+ align:start position:0%
+so now i have
+s of n plus one remember i switched to
+
+ align:start position:0%
+s of n plus one remember i switched to
+ 
+
+ align:start position:0%
+s of n plus one remember i switched to
+the s's and a's when i discretize things
+
+ align:start position:0%
+the s's and a's when i discretize things
+ 
+
+ align:start position:0%
+the s's and a's when i discretize things
+is now f of s n
+
+ align:start position:0%
+is now f of s n
+ 
+
+ align:start position:0%
+is now f of s n
+times some action
+
+ align:start position:0%
+times some action
+ 
+
+ align:start position:0%
+times some action
+times my
+
+ align:start position:0%
+times my
+ 
+
+ align:start position:0%
+times my
+noise
+
+ align:start position:0%
+noise
+ 
+
+ align:start position:0%
+noise
+and the advantage of discretizing state
+
+ align:start position:0%
+and the advantage of discretizing state
+ 
+
+ align:start position:0%
+and the advantage of discretizing state
+in actions is now i can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p of n plus 1
+
+ align:start position:0%
+p of n plus 1
+ 
+
+ align:start position:0%
+p of n plus 1
+which is a function of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can think of that as just a vector
+
+ align:start position:0%
+i can think of that as just a vector
+ 
+
+ align:start position:0%
+i can think of that as just a vector
+where the i th element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the probability
+
+ align:start position:0%
+is the probability
+ 
+
+ align:start position:0%
+is the probability
+that s
+
+ align:start position:0%
+that s
+ 
+
+ align:start position:0%
+that s
+of n plus one
+
+ align:start position:0%
+of n plus one
+ 
+
+ align:start position:0%
+of n plus one
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+s i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my probability distribution remember in
+
+ align:start position:0%
+my probability distribution remember in
+ 
+
+ align:start position:0%
+my probability distribution remember in
+general was a function in the in the
+
+ align:start position:0%
+general was a function in the in the
+ 
+
+ align:start position:0%
+general was a function in the in the
+in the particle in a bowl case it was a
+
+ align:start position:0%
+in the particle in a bowl case it was a
+ 
+
+ align:start position:0%
+in the particle in a bowl case it was a
+continuous gaussian function right
+
+ align:start position:0%
+continuous gaussian function right
+ 
+
+ align:start position:0%
+continuous gaussian function right
+if i discretize the state there
+
+ align:start position:0%
+if i discretize the state there
+ 
+
+ align:start position:0%
+if i discretize the state there
+then i can represent that as a vector
+
+ align:start position:0%
+then i can represent that as a vector
+ 
+
+ align:start position:0%
+then i can represent that as a vector
+saying what's the probability of being
+
+ align:start position:0%
+saying what's the probability of being
+ 
+
+ align:start position:0%
+saying what's the probability of being
+in state 1 what's the probability of
+
+ align:start position:0%
+in state 1 what's the probability of
+ 
+
+ align:start position:0%
+in state 1 what's the probability of
+being in state 2 probability state 3 and
+
+ align:start position:0%
+being in state 2 probability state 3 and
+ 
+
+ align:start position:0%
+being in state 2 probability state 3 and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the reason to discretize states is i
+
+ align:start position:0%
+so the reason to discretize states is i
+ 
+
+ align:start position:0%
+so the reason to discretize states is i
+can turn my continuous function into a
+
+ align:start position:0%
+can turn my continuous function into a
+ 
+
+ align:start position:0%
+can turn my continuous function into a
+into a vector
+
+ align:start position:0%
+into a vector
+ 
+
+ align:start position:0%
+into a vector
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i can turn this function into a into
+
+ align:start position:0%
+and i can turn this function into a into
+ 
+
+ align:start position:0%
+and i can turn this function into a into
+a transition probability matrix right
+
+ align:start position:0%
+a transition probability matrix right
+ 
+
+ align:start position:0%
+a transition probability matrix right
+i can
+
+ align:start position:0%
+i can
+ 
+
+ align:start position:0%
+i can
+so f
+
+ align:start position:0%
+so f
+ 
+
+ align:start position:0%
+so f
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+t i j
+
+ align:start position:0%
+t i j
+ 
+
+ align:start position:0%
+t i j
+which is the probability
+
+ align:start position:0%
+which is the probability
+ 
+
+ align:start position:0%
+which is the probability
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+landing in s j i should depends on the
+
+ align:start position:0%
+landing in s j i should depends on the
+ 
+
+ align:start position:0%
+landing in s j i should depends on the
+actions
+
+ align:start position:0%
+actions
+ 
+
+ align:start position:0%
+actions
+given i was in s i and i took action a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a matrix
+
+ align:start position:0%
+this is a matrix
+ 
+
+ align:start position:0%
+this is a matrix
+it's the transition matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+state distribution dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are going to just turn out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a pretty simple matrix equation that's
+
+ align:start position:0%
+a pretty simple matrix equation that's
+ 
+
+ align:start position:0%
+a pretty simple matrix equation that's
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh oops
+
+ align:start position:0%
+uh oops
+ 
+
+ align:start position:0%
+uh oops
+t i j p j at time
+
+ align:start position:0%
+t i j p j at time
+ 
+
+ align:start position:0%
+t i j p j at time
+um n plus one yeah so let me actually
+
+ align:start position:0%
+um n plus one yeah so let me actually
+ 
+
+ align:start position:0%
+um n plus one yeah so let me actually
+write the whole the real vector form
+
+ align:start position:0%
+write the whole the real vector form
+ 
+
+ align:start position:0%
+write the whole the real vector form
+that's really that's for a single
+
+ align:start position:0%
+that's really that's for a single
+ 
+
+ align:start position:0%
+that's really that's for a single
+element of it
+
+ align:start position:0%
+element of it
+ 
+
+ align:start position:0%
+element of it
+i could just write if i if i'm doing it
+
+ align:start position:0%
+i could just write if i if i'm doing it
+ 
+
+ align:start position:0%
+i could just write if i if i'm doing it
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+column vectors then it's actually going
+
+ align:start position:0%
+column vectors then it's actually going
+ 
+
+ align:start position:0%
+column vectors then it's actually going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+p of n
+
+ align:start position:0%
+p of n
+ 
+
+ align:start position:0%
+p of n
+times t of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+this is these two are vectors that's a
+
+ align:start position:0%
+this is these two are vectors that's a
+ 
+
+ align:start position:0%
+this is these two are vectors that's a
+matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and this is the
+
+ align:start position:0%
+so and this is the
+ 
+
+ align:start position:0%
+so and this is the
+discrete
+
+ align:start position:0%
+discrete
+ 
+
+ align:start position:0%
+discrete
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+discrete
+
+ align:start position:0%
+discrete
+ 
+
+ align:start position:0%
+discrete
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+discrete state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+master equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i use it as a column vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's make sure so so
+
+ align:start position:0%
+let's make sure so so
+ 
+
+ align:start position:0%
+let's make sure so so
+the probability of being
+
+ align:start position:0%
+the probability of being
+ 
+
+ align:start position:0%
+the probability of being
+in um
+
+ align:start position:0%
+in um
+ 
+
+ align:start position:0%
+in um
+state j
+
+ align:start position:0%
+state j
+ 
+
+ align:start position:0%
+state j
+given i was in state i
+
+ align:start position:0%
+given i was in state i
+ 
+
+ align:start position:0%
+given i was in state i
+should be the sum over
+
+ align:start position:0%
+should be the sum over
+ 
+
+ align:start position:0%
+should be the sum over
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right this thing
+
+ align:start position:0%
+all right this thing
+ 
+
+ align:start position:0%
+all right this thing
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+um being of s
+
+ align:start position:0%
+um being of s
+ 
+
+ align:start position:0%
+um being of s
+n plus one
+
+ align:start position:0%
+n plus one
+ 
+
+ align:start position:0%
+n plus one
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the probability what's that
+
+ align:start position:0%
+is the probability what's that
+ 
+
+ align:start position:0%
+is the probability what's that
+i think i had it right right
+
+ align:start position:0%
+i think i had it right right
+ 
+
+ align:start position:0%
+i think i had it right right
+it's it's not true but but i think
+
+ align:start position:0%
+it's it's not true but but i think
+ 
+
+ align:start position:0%
+it's it's not true but but i think
+that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i need a t transpose
+
+ align:start position:0%
+i need a t transpose
+ 
+
+ align:start position:0%
+i need a t transpose
+you just can't hit uh
+
+ align:start position:0%
+you just can't hit uh
+ 
+
+ align:start position:0%
+you just can't hit uh
+oh of course because i did this okay
+
+ align:start position:0%
+oh of course because i did this okay
+ 
+
+ align:start position:0%
+oh of course because i did this okay
+yeah sorry
+
+ align:start position:0%
+yeah sorry
+ 
+
+ align:start position:0%
+yeah sorry
+yeah i think the way i've got t defined
+
+ align:start position:0%
+yeah i think the way i've got t defined
+ 
+
+ align:start position:0%
+yeah i think the way i've got t defined
+but thank you that should be a transpose
+
+ align:start position:0%
+but thank you that should be a transpose
+ 
+
+ align:start position:0%
+but thank you that should be a transpose
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in which case i could
+
+ align:start position:0%
+in which case i could
+ 
+
+ align:start position:0%
+in which case i could
+have written it with the t the transpose
+
+ align:start position:0%
+have written it with the t the transpose
+ 
+
+ align:start position:0%
+have written it with the t the transpose
+too but
+
+ align:start position:0%
+too but
+ 
+
+ align:start position:0%
+too but
+if i transpose the whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't really matter if you like row
+
+ align:start position:0%
+it doesn't really matter if you like row
+ 
+
+ align:start position:0%
+it doesn't really matter if you like row
+vectors or column vectors the point is
+
+ align:start position:0%
+vectors or column vectors the point is
+ 
+
+ align:start position:0%
+vectors or column vectors the point is
+the master equation which looked a
+
+ align:start position:0%
+the master equation which looked a
+ 
+
+ align:start position:0%
+the master equation which looked a
+little scary before
+
+ align:start position:0%
+little scary before
+ 
+
+ align:start position:0%
+little scary before
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+turns into a simple matrix update in the
+
+ align:start position:0%
+turns into a simple matrix update in the
+ 
+
+ align:start position:0%
+turns into a simple matrix update in the
+discrete time discrete state case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you yeah use non-capturing things
+
+ align:start position:0%
+do you yeah use non-capturing things
+ 
+
+ align:start position:0%
+do you yeah use non-capturing things
+because you you have hardcover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so there's a question again just
+
+ align:start position:0%
+good so there's a question again just
+ 
+
+ align:start position:0%
+good so there's a question again just
+like we had the question in the
+
+ align:start position:0%
+like we had the question in the
+ 
+
+ align:start position:0%
+like we had the question in the
+in the you know when we did the
+
+ align:start position:0%
+in the you know when we did the
+ 
+
+ align:start position:0%
+in the you know when we did the
+dynamic programming for the value
+
+ align:start position:0%
+dynamic programming for the value
+ 
+
+ align:start position:0%
+dynamic programming for the value
+iteration of how you go from the
+
+ align:start position:0%
+iteration of how you go from the
+ 
+
+ align:start position:0%
+iteration of how you go from the
+continuous probabilities and continuous
+
+ align:start position:0%
+continuous probabilities and continuous
+ 
+
+ align:start position:0%
+continuous probabilities and continuous
+states back to the other one so again
+
+ align:start position:0%
+states back to the other one so again
+ 
+
+ align:start position:0%
+states back to the other one so again
+yeah so i would i would sample for my
+
+ align:start position:0%
+yeah so i would i would sample for my
+ 
+
+ align:start position:0%
+yeah so i would i would sample for my
+gaussian and fill out a transition
+
+ align:start position:0%
+gaussian and fill out a transition
+ 
+
+ align:start position:0%
+gaussian and fill out a transition
+probabilities as a close truncated
+
+ align:start position:0%
+probabilities as a close truncated
+ 
+
+ align:start position:0%
+probabilities as a close truncated
+representation of the gaussian
+
+ align:start position:0%
+representation of the gaussian
+ 
+
+ align:start position:0%
+representation of the gaussian
+and still interpolate
+
+ align:start position:0%
+and still interpolate
+ 
+
+ align:start position:0%
+and still interpolate
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+barycentric interpolators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the dp update works out to be just a
+
+ align:start position:0%
+the dp update works out to be just a
+ 
+
+ align:start position:0%
+the dp update works out to be just a
+simple if i'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the probability of being in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+let's see s
+
+ align:start position:0%
+let's see s
+ 
+
+ align:start position:0%
+let's see s
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+is the min over a
+
+ align:start position:0%
+is the min over a
+ 
+
+ align:start position:0%
+is the min over a
+the expected value from this equation
+
+ align:start position:0%
+the expected value from this equation
+ 
+
+ align:start position:0%
+the expected value from this equation
+can be taken care of with just the
+
+ align:start position:0%
+can be taken care of with just the
+ 
+
+ align:start position:0%
+can be taken care of with just the
+the transition matrix over here and i
+
+ align:start position:0%
+the transition matrix over here and i
+ 
+
+ align:start position:0%
+the transition matrix over here and i
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+maybe my vector g of a which is the cost
+
+ align:start position:0%
+maybe my vector g of a which is the cost
+ 
+
+ align:start position:0%
+maybe my vector g of a which is the cost
+of being in each
+
+ align:start position:0%
+of being in each
+ 
+
+ align:start position:0%
+of being in each
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+given i took that action
+
+ align:start position:0%
+given i took that action
+ 
+
+ align:start position:0%
+given i took that action
+sum over j
+
+ align:start position:0%
+sum over j
+ 
+
+ align:start position:0%
+sum over j
+t i j
+
+ align:start position:0%
+t i j
+ 
+
+ align:start position:0%
+t i j
+s j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j of sj
+
+ align:start position:0%
+j of sj
+ 
+
+ align:start position:0%
+j of sj
+k plus 1. yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i got i get rid of my uh expected
+
+ align:start position:0%
+and i got i get rid of my uh expected
+ 
+
+ align:start position:0%
+and i got i get rid of my uh expected
+values by just using that
+
+ align:start position:0%
+values by just using that
+ 
+
+ align:start position:0%
+values by just using that
+working directly with the transition
+
+ align:start position:0%
+working directly with the transition
+ 
+
+ align:start position:0%
+working directly with the transition
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i on this side
+
+ align:start position:0%
+i on this side
+ 
+
+ align:start position:0%
+i on this side
+j on this side many apologies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this turns out to be exactly the reason
+
+ align:start position:0%
+this turns out to be exactly the reason
+ 
+
+ align:start position:0%
+this turns out to be exactly the reason
+i said
+
+ align:start position:0%
+i said
+ 
+
+ align:start position:0%
+i said
+basically no more expensive to solve
+
+ align:start position:0%
+basically no more expensive to solve
+ 
+
+ align:start position:0%
+basically no more expensive to solve
+than the deterministic case is we
+
+ align:start position:0%
+than the deterministic case is we
+ 
+
+ align:start position:0%
+than the deterministic case is we
+already used this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we were doing the barycentric
+
+ align:start position:0%
+when we were doing the barycentric
+ 
+
+ align:start position:0%
+when we were doing the barycentric
+interpolation
+
+ align:start position:0%
+interpolation
+ 
+
+ align:start position:0%
+interpolation
+because our our problem in the the
+
+ align:start position:0%
+because our our problem in the the
+ 
+
+ align:start position:0%
+because our our problem in the the
+dynamic programming originally
+
+ align:start position:0%
+dynamic programming originally
+ 
+
+ align:start position:0%
+dynamic programming originally
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that when we started simulating this
+
+ align:start position:0%
+that when we started simulating this
+ 
+
+ align:start position:0%
+that when we started simulating this
+thing from from one node
+
+ align:start position:0%
+thing from from one node
+ 
+
+ align:start position:0%
+thing from from one node
+forward it didn't end up you know
+
+ align:start position:0%
+forward it didn't end up you know
+ 
+
+ align:start position:0%
+forward it didn't end up you know
+unless you were very very lucky it
+
+ align:start position:0%
+unless you were very very lucky it
+ 
+
+ align:start position:0%
+unless you were very very lucky it
+didn't end up right on top of another
+
+ align:start position:0%
+didn't end up right on top of another
+ 
+
+ align:start position:0%
+didn't end up right on top of another
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+so we already had said that we're going
+
+ align:start position:0%
+so we already had said that we're going
+ 
+
+ align:start position:0%
+so we already had said that we're going
+to estimate the new
+
+ align:start position:0%
+to estimate the new
+ 
+
+ align:start position:0%
+to estimate the new
+cost to go as an interpolation of the
+
+ align:start position:0%
+cost to go as an interpolation of the
+ 
+
+ align:start position:0%
+cost to go as an interpolation of the
+neighboring points of the value of the
+
+ align:start position:0%
+neighboring points of the value of the
+ 
+
+ align:start position:0%
+neighboring points of the value of the
+neighboring points where that weighting
+
+ align:start position:0%
+neighboring points where that weighting
+ 
+
+ align:start position:0%
+neighboring points where that weighting
+came from the bary-centric interpolators
+
+ align:start position:0%
+came from the bary-centric interpolators
+ 
+
+ align:start position:0%
+came from the bary-centric interpolators
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we're doing the exact same thing now
+
+ align:start position:0%
+we're doing the exact same thing now
+ 
+
+ align:start position:0%
+we're doing the exact same thing now
+in fact you could actually think of the
+
+ align:start position:0%
+in fact you could actually think of the
+ 
+
+ align:start position:0%
+in fact you could actually think of the
+barycentric interpolators as turning
+
+ align:start position:0%
+barycentric interpolators as turning
+ 
+
+ align:start position:0%
+barycentric interpolators as turning
+your deterministic problem into a
+
+ align:start position:0%
+your deterministic problem into a
+ 
+
+ align:start position:0%
+your deterministic problem into a
+stochastic problem
+
+ align:start position:0%
+stochastic problem
+ 
+
+ align:start position:0%
+stochastic problem
+where the probability of going into each
+
+ align:start position:0%
+where the probability of going into each
+ 
+
+ align:start position:0%
+where the probability of going into each
+of these neighbors is the interpolant
+
+ align:start position:0%
+of these neighbors is the interpolant
+ 
+
+ align:start position:0%
+of these neighbors is the interpolant
+okay so the reason the barycentric works
+
+ align:start position:0%
+okay so the reason the barycentric works
+ 
+
+ align:start position:0%
+okay so the reason the barycentric works
+beautifully is is that it fall it turns
+
+ align:start position:0%
+beautifully is is that it fall it turns
+ 
+
+ align:start position:0%
+beautifully is is that it fall it turns
+the deterministic case into a
+
+ align:start position:0%
+the deterministic case into a
+ 
+
+ align:start position:0%
+the deterministic case into a
+stochastic case
+
+ align:start position:0%
+stochastic case
+ 
+
+ align:start position:0%
+stochastic case
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and that's why i wanted to say that it's
+
+ align:start position:0%
+and that's why i wanted to say that it's
+ 
+
+ align:start position:0%
+and that's why i wanted to say that it's
+no more complex okay t might be more
+
+ align:start position:0%
+no more complex okay t might be more
+ 
+
+ align:start position:0%
+no more complex okay t might be more
+have less zeros in it in the case the
+
+ align:start position:0%
+have less zeros in it in the case the
+ 
+
+ align:start position:0%
+have less zeros in it in the case the
+general case if maybe with with some
+
+ align:start position:0%
+general case if maybe with with some
+ 
+
+ align:start position:0%
+general case if maybe with with some
+probability distribution it might be
+
+ align:start position:0%
+probability distribution it might be
+ 
+
+ align:start position:0%
+probability distribution it might be
+that i have to worry about hitting a lot
+
+ align:start position:0%
+that i have to worry about hitting a lot
+ 
+
+ align:start position:0%
+that i have to worry about hitting a lot
+more nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it might take more a few more cycles
+
+ align:start position:0%
+so it might take more a few more cycles
+ 
+
+ align:start position:0%
+so it might take more a few more cycles
+but but the equations are the same and
+
+ align:start position:0%
+but but the equations are the same and
+ 
+
+ align:start position:0%
+but but the equations are the same and
+my matlab code is the same
+
+ align:start position:0%
+my matlab code is the same
+ 
+
+ align:start position:0%
+my matlab code is the same
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+simultaneously or maybe conversely this
+
+ align:start position:0%
+simultaneously or maybe conversely this
+ 
+
+ align:start position:0%
+simultaneously or maybe conversely this
+helps actually tells you why we have
+
+ align:start position:0%
+helps actually tells you why we have
+ 
+
+ align:start position:0%
+helps actually tells you why we have
+problems with the barycentric
+
+ align:start position:0%
+problems with the barycentric
+ 
+
+ align:start position:0%
+problems with the barycentric
+interpolators right
+
+ align:start position:0%
+interpolators right
+ 
+
+ align:start position:0%
+interpolators right
+this is the remember the fundamental
+
+ align:start position:0%
+this is the remember the fundamental
+ 
+
+ align:start position:0%
+this is the remember the fundamental
+problems with the barycentric
+
+ align:start position:0%
+problems with the barycentric
+ 
+
+ align:start position:0%
+problems with the barycentric
+interpolators is that things sort of
+
+ align:start position:0%
+interpolators is that things sort of
+ 
+
+ align:start position:0%
+interpolators is that things sort of
+leaked away from the nominal
+
+ align:start position:0%
+leaked away from the nominal
+ 
+
+ align:start position:0%
+leaked away from the nominal
+trajectories and and our we had our
+
+ align:start position:0%
+trajectories and and our we had our
+ 
+
+ align:start position:0%
+trajectories and and our we had our
+chattering happening and the
+
+ align:start position:0%
+chattering happening and the
+ 
+
+ align:start position:0%
+chattering happening and the
+our our bang bang solution wasn't quite
+
+ align:start position:0%
+our our bang bang solution wasn't quite
+ 
+
+ align:start position:0%
+our our bang bang solution wasn't quite
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because now you can think of it as
+
+ align:start position:0%
+because now you can think of it as
+ 
+
+ align:start position:0%
+because now you can think of it as
+us is my deterministic problem assigning
+
+ align:start position:0%
+us is my deterministic problem assigning
+ 
+
+ align:start position:0%
+us is my deterministic problem assigning
+some probability of going to each of
+
+ align:start position:0%
+some probability of going to each of
+ 
+
+ align:start position:0%
+some probability of going to each of
+these neighbors and you can sort of see
+
+ align:start position:0%
+these neighbors and you can sort of see
+ 
+
+ align:start position:0%
+these neighbors and you can sort of see
+that that distribution is going to start
+
+ align:start position:0%
+that that distribution is going to start
+ 
+
+ align:start position:0%
+that that distribution is going to start
+slipping away from the from the nominal
+
+ align:start position:0%
+slipping away from the from the nominal
+ 
+
+ align:start position:0%
+slipping away from the from the nominal
+trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+excellent so this is actually
+
+ align:start position:0%
+excellent so this is actually
+ 
+
+ align:start position:0%
+excellent so this is actually
+very important
+
+ align:start position:0%
+very important
+ 
+
+ align:start position:0%
+very important
+stochastic optimal control
+
+ align:start position:0%
+stochastic optimal control
+ 
+
+ align:start position:0%
+stochastic optimal control
+is a beautiful thing if i can if i can
+
+ align:start position:0%
+is a beautiful thing if i can if i can
+ 
+
+ align:start position:0%
+is a beautiful thing if i can if i can
+model the
+
+ align:start position:0%
+model the
+ 
+
+ align:start position:0%
+model the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+disturbances in any reasonable way
+
+ align:start position:0%
+disturbances in any reasonable way
+ 
+
+ align:start position:0%
+disturbances in any reasonable way
+then i can get better policies by
+
+ align:start position:0%
+then i can get better policies by
+ 
+
+ align:start position:0%
+then i can get better policies by
+explicitly reasoning about them
+
+ align:start position:0%
+explicitly reasoning about them
+ 
+
+ align:start position:0%
+explicitly reasoning about them
+and just like we sort of said dynamic
+
+ align:start position:0%
+and just like we sort of said dynamic
+ 
+
+ align:start position:0%
+and just like we sort of said dynamic
+programming for low dimensional problems
+
+ align:start position:0%
+programming for low dimensional problems
+ 
+
+ align:start position:0%
+programming for low dimensional problems
+solves all these really hard problems
+
+ align:start position:0%
+solves all these really hard problems
+ 
+
+ align:start position:0%
+solves all these really hard problems
+that are analytically untractable and
+
+ align:start position:0%
+that are analytically untractable and
+ 
+
+ align:start position:0%
+that are analytically untractable and
+things like that it can even solve the
+
+ align:start position:0%
+things like that it can even solve the
+ 
+
+ align:start position:0%
+things like that it can even solve the
+stochastic problem with almost no more
+
+ align:start position:0%
+stochastic problem with almost no more
+ 
+
+ align:start position:0%
+stochastic problem with almost no more
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+low dimensional problems even
+
+ align:start position:0%
+low dimensional problems even
+ 
+
+ align:start position:0%
+low dimensional problems even
+complicated ones with complicated
+
+ align:start position:0%
+complicated ones with complicated
+ 
+
+ align:start position:0%
+complicated ones with complicated
+distributions
+
+ align:start position:0%
+distributions
+ 
+
+ align:start position:0%
+distributions
+dp can do the work for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a few more things to say
+
+ align:start position:0%
+a few more things to say
+ 
+
+ align:start position:0%
+a few more things to say
+there's one particular result which we
+
+ align:start position:0%
+there's one particular result which we
+ 
+
+ align:start position:0%
+there's one particular result which we
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+mentioned early
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i have to mention
+
+ align:start position:0%
+that i have to mention
+ 
+
+ align:start position:0%
+that i have to mention
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this dynamic programming update
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we use this in the in our analytical
+
+ align:start position:0%
+we use this in the in our analytical
+ 
+
+ align:start position:0%
+we use this in the in our analytical
+optimal control too right we use this as
+
+ align:start position:0%
+optimal control too right we use this as
+ 
+
+ align:start position:0%
+optimal control too right we use this as
+the basis to start designing things like
+
+ align:start position:0%
+the basis to start designing things like
+ 
+
+ align:start position:0%
+the basis to start designing things like
+our lqr controllers
+
+ align:start position:0%
+our lqr controllers
+ 
+
+ align:start position:0%
+our lqr controllers
+right and we turned it into the hbj
+
+ align:start position:0%
+right and we turned it into the hbj
+ 
+
+ align:start position:0%
+right and we turned it into the hbj
+and in the
+
+ align:start position:0%
+and in the
+ 
+
+ align:start position:0%
+and in the
+finite time case we didn't even turn it
+
+ align:start position:0%
+finite time case we didn't even turn it
+ 
+
+ align:start position:0%
+finite time case we didn't even turn it
+into the hbj we just started we started
+
+ align:start position:0%
+into the hbj we just started we started
+ 
+
+ align:start position:0%
+into the hbj we just started we started
+we can back this out with dynamic
+
+ align:start position:0%
+we can back this out with dynamic
+ 
+
+ align:start position:0%
+we can back this out with dynamic
+programming okay
+
+ align:start position:0%
+programming okay
+ 
+
+ align:start position:0%
+programming okay
+so we can actually use the same thing to
+
+ align:start position:0%
+so we can actually use the same thing to
+ 
+
+ align:start position:0%
+so we can actually use the same thing to
+analytically try to to design some
+
+ align:start position:0%
+analytically try to to design some
+ 
+
+ align:start position:0%
+analytically try to to design some
+controllers
+
+ align:start position:0%
+controllers
+ 
+
+ align:start position:0%
+controllers
+for stochastic optimal control cases
+
+ align:start position:0%
+for stochastic optimal control cases
+ 
+
+ align:start position:0%
+for stochastic optimal control cases
+and just like in the in the
+
+ align:start position:0%
+and just like in the in the
+ 
+
+ align:start position:0%
+and just like in the in the
+deterministic case there's one sort of
+
+ align:start position:0%
+deterministic case there's one sort of
+ 
+
+ align:start position:0%
+deterministic case there's one sort of
+outstanding result that everybody knows
+
+ align:start position:0%
+outstanding result that everybody knows
+ 
+
+ align:start position:0%
+outstanding result that everybody knows
+and uses
+
+ align:start position:0%
+and uses
+ 
+
+ align:start position:0%
+and uses
+and that's the linear
+
+ align:start position:0%
+and that's the linear
+ 
+
+ align:start position:0%
+and that's the linear
+quadratic regulator
+
+ align:start position:0%
+quadratic regulator
+ 
+
+ align:start position:0%
+quadratic regulator
+with gaussian noise
+
+ align:start position:0%
+with gaussian noise
+ 
+
+ align:start position:0%
+with gaussian noise
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lqg
+
+ align:start position:0%
+lqg
+ 
+
+ align:start position:0%
+lqg
+that's the shorthand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's two forms of it one of them is
+
+ align:start position:0%
+there's two forms of it one of them is
+ 
+
+ align:start position:0%
+there's two forms of it one of them is
+noise gaussian noise also on the sensors
+
+ align:start position:0%
+noise gaussian noise also on the sensors
+ 
+
+ align:start position:0%
+noise gaussian noise also on the sensors
+but let's just worry about the case
+
+ align:start position:0%
+but let's just worry about the case
+ 
+
+ align:start position:0%
+but let's just worry about the case
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+we know there's there's no uncertainty
+
+ align:start position:0%
+we know there's there's no uncertainty
+ 
+
+ align:start position:0%
+we know there's there's no uncertainty
+in the sensor is only the dynamic noise
+
+ align:start position:0%
+in the sensor is only the dynamic noise
+ 
+
+ align:start position:0%
+in the sensor is only the dynamic noise
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x n plus one
+
+ align:start position:0%
+x n plus one
+ 
+
+ align:start position:0%
+x n plus one
+is a it could be a of n it could be time
+
+ align:start position:0%
+is a it could be a of n it could be time
+ 
+
+ align:start position:0%
+is a it could be a of n it could be time
+varying or not
+
+ align:start position:0%
+varying or not
+ 
+
+ align:start position:0%
+varying or not
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+plus b
+
+ align:start position:0%
+plus b
+ 
+
+ align:start position:0%
+plus b
+n u of n
+
+ align:start position:0%
+n u of n
+ 
+
+ align:start position:0%
+n u of n
+plus w n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost function again is the quadratic
+
+ align:start position:0%
+cost function again is the quadratic
+ 
+
+ align:start position:0%
+cost function again is the quadratic
+regulator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you think is going to happen
+
+ align:start position:0%
+what do you think is going to happen
+ 
+
+ align:start position:0%
+what do you think is going to happen
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+someone who hasn't used it extensively
+
+ align:start position:0%
+someone who hasn't used it extensively
+ 
+
+ align:start position:0%
+someone who hasn't used it extensively
+in your work what is the what's going to
+
+ align:start position:0%
+in your work what is the what's going to
+ 
+
+ align:start position:0%
+in your work what is the what's going to
+change about our lqr solution
+
+ align:start position:0%
+change about our lqr solution
+ 
+
+ align:start position:0%
+change about our lqr solution
+think about stabilizing the pendulum or
+
+ align:start position:0%
+think about stabilizing the pendulum or
+ 
+
+ align:start position:0%
+think about stabilizing the pendulum or
+something okay let's say we're doing
+
+ align:start position:0%
+something okay let's say we're doing
+ 
+
+ align:start position:0%
+something okay let's say we're doing
+optimal control on the simple pendulum
+
+ align:start position:0%
+optimal control on the simple pendulum
+ 
+
+ align:start position:0%
+optimal control on the simple pendulum
+linearized around the top and now
+
+ align:start position:0%
+linearized around the top and now
+ 
+
+ align:start position:0%
+linearized around the top and now
+there's disturbances bouncing me around
+
+ align:start position:0%
+there's disturbances bouncing me around
+ 
+
+ align:start position:0%
+there's disturbances bouncing me around
+how would you act differently
+
+ align:start position:0%
+how would you act differently
+ 
+
+ align:start position:0%
+how would you act differently
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+some model of the disturbances
+
+ align:start position:0%
+some model of the disturbances
+ 
+
+ align:start position:0%
+some model of the disturbances
+in the linear case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you act differently if you
+
+ align:start position:0%
+how would you act differently if you
+ 
+
+ align:start position:0%
+how would you act differently if you
+know that somebody's going to be bumping
+
+ align:start position:0%
+know that somebody's going to be bumping
+ 
+
+ align:start position:0%
+know that somebody's going to be bumping
+me around with a mean zero let's keep w
+
+ align:start position:0%
+me around with a mean zero let's keep w
+ 
+
+ align:start position:0%
+me around with a mean zero let's keep w
+mean zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you act differently
+
+ align:start position:0%
+how would you act differently
+ 
+
+ align:start position:0%
+how would you act differently
+if you're a simple pendulum
+
+ align:start position:0%
+if you're a simple pendulum
+ 
+
+ align:start position:0%
+if you're a simple pendulum
+around the top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody else want to weigh in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's that
+
+ align:start position:0%
+what's that
+ 
+
+ align:start position:0%
+what's that
+you might increase your gain or
+
+ align:start position:0%
+you might increase your gain or
+ 
+
+ align:start position:0%
+you might increase your gain or
+something like that you think
+
+ align:start position:0%
+something like that you think
+ 
+
+ align:start position:0%
+something like that you think
+yeah it turns out you wouldn't act
+
+ align:start position:0%
+yeah it turns out you wouldn't act
+ 
+
+ align:start position:0%
+yeah it turns out you wouldn't act
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's one of the most surprising results
+
+ align:start position:0%
+it's one of the most surprising results
+ 
+
+ align:start position:0%
+it's one of the most surprising results
+i think of
+
+ align:start position:0%
+i think of
+ 
+
+ align:start position:0%
+i think of
+of stochastic optimal control
+
+ align:start position:0%
+of stochastic optimal control
+ 
+
+ align:start position:0%
+of stochastic optimal control
+it turns out
+
+ align:start position:0%
+it turns out
+ 
+
+ align:start position:0%
+it turns out
+that you're that you work it all out you
+
+ align:start position:0%
+that you're that you work it all out you
+ 
+
+ align:start position:0%
+that you're that you work it all out you
+put your costs like this it wouldn't you
+
+ align:start position:0%
+put your costs like this it wouldn't you
+ 
+
+ align:start position:0%
+put your costs like this it wouldn't you
+don't turn your gains up because of the
+
+ align:start position:0%
+don't turn your gains up because of the
+ 
+
+ align:start position:0%
+don't turn your gains up because of the
+disturbances or anything like that the
+
+ align:start position:0%
+disturbances or anything like that the
+ 
+
+ align:start position:0%
+disturbances or anything like that the
+optimal solution for the for the
+
+ align:start position:0%
+optimal solution for the for the
+ 
+
+ align:start position:0%
+optimal solution for the for the
+stochastic case is the same
+
+ align:start position:0%
+stochastic case is the same
+ 
+
+ align:start position:0%
+stochastic case is the same
+policy
+
+ align:start position:0%
+policy
+ 
+
+ align:start position:0%
+policy
+as the optimal solution for the
+
+ align:start position:0%
+as the optimal solution for the
+ 
+
+ align:start position:0%
+as the optimal solution for the
+deterministic case okay it's also true
+
+ align:start position:0%
+deterministic case okay it's also true
+ 
+
+ align:start position:0%
+deterministic case okay it's also true
+in continuous time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our inverse b transpose
+
+ align:start position:0%
+our inverse b transpose
+ 
+
+ align:start position:0%
+our inverse b transpose
+s of n
+
+ align:start position:0%
+s of n
+ 
+
+ align:start position:0%
+s of n
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+yeah it's the same
+
+ align:start position:0%
+yeah it's the same
+ 
+
+ align:start position:0%
+yeah it's the same
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+b of n here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did i write something funny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you know that that clock isn't
+
+ align:start position:0%
+did you know that that clock isn't
+ 
+
+ align:start position:0%
+did you know that that clock isn't
+moving
+
+ align:start position:0%
+moving
+ 
+
+ align:start position:0%
+moving
+no i didn't am i way off time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay thank you for telling me that i
+
+ align:start position:0%
+okay thank you for telling me that i
+ 
+
+ align:start position:0%
+okay thank you for telling me that i
+thought i had time
+
+ align:start position:0%
+thought i had time
+ 
+
+ align:start position:0%
+thought i had time
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+is the s the same
+
+ align:start position:0%
+is the s the same
+ 
+
+ align:start position:0%
+is the s the same
+the s is the same too oh sorry sorry
+
+ align:start position:0%
+the s is the same too oh sorry sorry
+ 
+
+ align:start position:0%
+the s is the same too oh sorry sorry
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+the s i wrote here is the same
+
+ align:start position:0%
+the s i wrote here is the same
+ 
+
+ align:start position:0%
+the s i wrote here is the same
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that is the same s that you get from the
+
+ align:start position:0%
+that is the same s that you get from the
+ 
+
+ align:start position:0%
+that is the same s that you get from the
+roccati equation but the total cost is
+
+ align:start position:0%
+roccati equation but the total cost is
+ 
+
+ align:start position:0%
+roccati equation but the total cost is
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+in the um
+
+ align:start position:0%
+in the um
+ 
+
+ align:start position:0%
+in the um
+so the policy is the same but
+
+ align:start position:0%
+so the policy is the same but
+ 
+
+ align:start position:0%
+so the policy is the same but
+so how much time do i really have do i
+
+ align:start position:0%
+so how much time do i really have do i
+ 
+
+ align:start position:0%
+so how much time do i really have do i
+have negative time already or am i
+
+ align:start position:0%
+have negative time already or am i
+ 
+
+ align:start position:0%
+have negative time already or am i
+sorry okay
+
+ align:start position:0%
+sorry okay
+ 
+
+ align:start position:0%
+sorry okay
+but j of n
+
+ align:start position:0%
+but j of n
+ 
+
+ align:start position:0%
+but j of n
+i thought it was just very exciting
+
+ align:start position:0%
+i thought it was just very exciting
+ 
+
+ align:start position:0%
+i thought it was just very exciting
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is is this this plus some expected value
+
+ align:start position:0%
+is is this this plus some expected value
+ 
+
+ align:start position:0%
+is is this this plus some expected value
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+the noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i was going to keep going for a long
+
+ align:start position:0%
+i was going to keep going for a long
+ 
+
+ align:start position:0%
+i was going to keep going for a long
+time probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it's the same s that you had before
+
+ align:start position:0%
+so it's the same s that you had before
+ 
+
+ align:start position:0%
+so it's the same s that you had before
+but the cost to go that you get is
+
+ align:start position:0%
+but the cost to go that you get is
+ 
+
+ align:start position:0%
+but the cost to go that you get is
+actually higher
+
+ align:start position:0%
+actually higher
+ 
+
+ align:start position:0%
+actually higher
+like as in a way that you might expect
+
+ align:start position:0%
+like as in a way that you might expect
+ 
+
+ align:start position:0%
+like as in a way that you might expect
+with it actually depends on the cost on
+
+ align:start position:0%
+with it actually depends on the cost on
+ 
+
+ align:start position:0%
+with it actually depends on the cost on
+the other s and so the s n comes from
+
+ align:start position:0%
+the other s and so the s n comes from
+ 
+
+ align:start position:0%
+the other s and so the s n comes from
+the deterministic ricotta equation but
+
+ align:start position:0%
+the deterministic ricotta equation but
+ 
+
+ align:start position:0%
+the deterministic ricotta equation but
+the cost to go gets bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's one of the most
+
+ align:start position:0%
+yeah so that's one of the most
+ 
+
+ align:start position:0%
+yeah so that's one of the most
+surprising i think results from
+
+ align:start position:0%
+surprising i think results from
+ 
+
+ align:start position:0%
+surprising i think results from
+stochastic optimal control is that
+
+ align:start position:0%
+stochastic optimal control is that
+ 
+
+ align:start position:0%
+stochastic optimal control is that
+in one case it tells you it's okay to do
+
+ align:start position:0%
+in one case it tells you it's okay to do
+ 
+
+ align:start position:0%
+in one case it tells you it's okay to do
+deterministic optimal control yeah
+
+ align:start position:0%
+deterministic optimal control yeah
+ 
+
+ align:start position:0%
+deterministic optimal control yeah
+in most cases it's not okay it won't
+
+ align:start position:0%
+in most cases it's not okay it won't
+ 
+
+ align:start position:0%
+in most cases it's not okay it won't
+give you the same thing
\ No newline at end of file
diff --git a/KoXTTlI7mIg.txt b/KoXTTlI7mIg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8140a69e4ff5b06c92c18a4960fd6bbea4915272
--- /dev/null
+++ b/KoXTTlI7mIg.txt
@@ -0,0 +1,243 @@
+align:start position:0%
+ 
+so in Italy we study a lot we do a lot
+
+ align:start position:0%
+so in Italy we study a lot we do a lot
+ 
+
+ align:start position:0%
+so in Italy we study a lot we do a lot
+of grammar and um logic uh structure of
+
+ align:start position:0%
+of grammar and um logic uh structure of
+ 
+
+ align:start position:0%
+of grammar and um logic uh structure of
+the sentence we study that a lot and we
+
+ align:start position:0%
+the sentence we study that a lot and we
+ 
+
+ align:start position:0%
+the sentence we study that a lot and we
+also study Latin so I'm used to think of
+
+ align:start position:0%
+also study Latin so I'm used to think of
+ 
+
+ align:start position:0%
+also study Latin so I'm used to think of
+um the language in terms of the
+
+ align:start position:0%
+um the language in terms of the
+ 
+
+ align:start position:0%
+um the language in terms of the
+different uh components and I noticed
+
+ align:start position:0%
+different uh components and I noticed
+ 
+
+ align:start position:0%
+different uh components and I noticed
+that maybe that's not so common among uh
+
+ align:start position:0%
+that maybe that's not so common among uh
+ 
+
+ align:start position:0%
+that maybe that's not so common among uh
+students here uh among American or
+
+ align:start position:0%
+students here uh among American or
+ 
+
+ align:start position:0%
+students here uh among American or
+International students
+
+ align:start position:0%
+International students
+ 
+
+ align:start position:0%
+International students
+um so that was a little bit of a
+
+ align:start position:0%
+um so that was a little bit of a
+ 
+
+ align:start position:0%
+um so that was a little bit of a
+challenge to help them to um to identify
+
+ align:start position:0%
+challenge to help them to um to identify
+ 
+
+ align:start position:0%
+challenge to help them to um to identify
+for example the different roles of a
+
+ align:start position:0%
+for example the different roles of a
+ 
+
+ align:start position:0%
+for example the different roles of a
+word in a sentence because in the
+
+ align:start position:0%
+word in a sentence because in the
+ 
+
+ align:start position:0%
+word in a sentence because in the
+English language is not so important you
+
+ align:start position:0%
+English language is not so important you
+ 
+
+ align:start position:0%
+English language is not so important you
+don't have you don't conjugate you don't
+
+ align:start position:0%
+don't have you don't conjugate you don't
+ 
+
+ align:start position:0%
+don't have you don't conjugate you don't
+change the endings of the adjectives
+
+ align:start position:0%
+change the endings of the adjectives
+ 
+
+ align:start position:0%
+change the endings of the adjectives
+while in Italian that makes a big
+
+ align:start position:0%
+while in Italian that makes a big
+ 
+
+ align:start position:0%
+while in Italian that makes a big
+difference so I needed to really help
+
+ align:start position:0%
+difference so I needed to really help
+ 
+
+ align:start position:0%
+difference so I needed to really help
+the students to
+
+ align:start position:0%
+the students to
+ 
+
+ align:start position:0%
+the students to
+identify the this part the structure of
+
+ align:start position:0%
+identify the this part the structure of
+ 
+
+ align:start position:0%
+identify the this part the structure of
+of the phrases that was maybe a little
+
+ align:start position:0%
+of the phrases that was maybe a little
+ 
+
+ align:start position:0%
+of the phrases that was maybe a little
+bit of a challenge but it was I expected
+
+ align:start position:0%
+bit of a challenge but it was I expected
+ 
+
+ align:start position:0%
+bit of a challenge but it was I expected
+it and also I had a few students who had
+
+ align:start position:0%
+it and also I had a few students who had
+ 
+
+ align:start position:0%
+it and also I had a few students who had
+learned Spanish before and it's very
+
+ align:start position:0%
+learned Spanish before and it's very
+ 
+
+ align:start position:0%
+learned Spanish before and it's very
+since well Italian and Spanish have the
+
+ align:start position:0%
+since well Italian and Spanish have the
+ 
+
+ align:start position:0%
+since well Italian and Spanish have the
+same origin then um I think for them the
+
+ align:start position:0%
+same origin then um I think for them the
+ 
+
+ align:start position:0%
+same origin then um I think for them the
+Big Challenge was to make the
+
+ align:start position:0%
+Big Challenge was to make the
+ 
+
+ align:start position:0%
+Big Challenge was to make the
+distinction between the two so it was
+
+ align:start position:0%
+distinction between the two so it was
+ 
+
+ align:start position:0%
+distinction between the two so it was
+easier in a sense to pick up but then um
+
+ align:start position:0%
+easier in a sense to pick up but then um
+ 
+
+ align:start position:0%
+easier in a sense to pick up but then um
+they had struggled a little to make the
+
+ align:start position:0%
+they had struggled a little to make the
+ 
+
+ align:start position:0%
+they had struggled a little to make the
+distinction to make a difference
\ No newline at end of file
diff --git a/LIDBqUPxNys.txt b/LIDBqUPxNys.txt
new file mode 100644
index 0000000000000000000000000000000000000000..75283a058a8d271a1f77e38070550ee9c0df16f9
--- /dev/null
+++ b/LIDBqUPxNys.txt
@@ -0,0 +1,14928 @@
+align:start position:0%
+ 
+doing right now is uh hopefully you're
+
+ align:start position:0%
+doing right now is uh hopefully you're
+ 
+
+ align:start position:0%
+doing right now is uh hopefully you're
+all reading uh chapter six on which
+
+ align:start position:0%
+all reading uh chapter six on which
+ 
+
+ align:start position:0%
+all reading uh chapter six on which
+covers the process of thermal
+
+ align:start position:0%
+covers the process of thermal
+ 
+
+ align:start position:0%
+covers the process of thermal
+oxidation last time we talked about uh
+
+ align:start position:0%
+oxidation last time we talked about uh
+ 
+
+ align:start position:0%
+oxidation last time we talked about uh
+General introduction to Thermal oxides
+
+ align:start position:0%
+General introduction to Thermal oxides
+ 
+
+ align:start position:0%
+General introduction to Thermal oxides
+in Silicon
+
+ align:start position:0%
+in Silicon
+ 
+
+ align:start position:0%
+in Silicon
+seamoss and uh we also talked about the
+
+ align:start position:0%
+seamoss and uh we also talked about the
+ 
+
+ align:start position:0%
+seamoss and uh we also talked about the
+metal oxide silicon or semiconductor
+
+ align:start position:0%
+metal oxide silicon or semiconductor
+ 
+
+ align:start position:0%
+metal oxide silicon or semiconductor
+capacitor and how uh electrical simple
+
+ align:start position:0%
+capacitor and how uh electrical simple
+ 
+
+ align:start position:0%
+capacitor and how uh electrical simple
+CV measurements can be used to
+
+ align:start position:0%
+CV measurements can be used to
+ 
+
+ align:start position:0%
+CV measurements can be used to
+understand the quality of the oxide and
+
+ align:start position:0%
+understand the quality of the oxide and
+ 
+
+ align:start position:0%
+understand the quality of the oxide and
+the charges that exist in that
+
+ align:start position:0%
+the charges that exist in that
+ 
+
+ align:start position:0%
+the charges that exist in that
+structure this time we're going to cover
+
+ align:start position:0%
+structure this time we're going to cover
+ 
+
+ align:start position:0%
+structure this time we're going to cover
+um a basic model called the deal Grove
+
+ align:start position:0%
+um a basic model called the deal Grove
+ 
+
+ align:start position:0%
+um a basic model called the deal Grove
+this is after the two people that's
+
+ align:start position:0%
+this is after the two people that's
+ 
+
+ align:start position:0%
+this is after the two people that's
+Bruce deal and Andy Grove um who came up
+
+ align:start position:0%
+Bruce deal and Andy Grove um who came up
+ 
+
+ align:start position:0%
+Bruce deal and Andy Grove um who came up
+with this linear par parabolic oxidation
+
+ align:start position:0%
+with this linear par parabolic oxidation
+ 
+
+ align:start position:0%
+with this linear par parabolic oxidation
+model it it really Remains the basic
+
+ align:start position:0%
+model it it really Remains the basic
+ 
+
+ align:start position:0%
+model it it really Remains the basic
+model used today um and then we'll talk
+
+ align:start position:0%
+model used today um and then we'll talk
+ 
+
+ align:start position:0%
+model used today um and then we'll talk
+about examples on how to use it uh and
+
+ align:start position:0%
+about examples on how to use it uh and
+ 
+
+ align:start position:0%
+about examples on how to use it uh and
+we'll finish up with other models of
+
+ align:start position:0%
+we'll finish up with other models of
+ 
+
+ align:start position:0%
+we'll finish up with other models of
+planer oxidation that are very useful in
+
+ align:start position:0%
+planer oxidation that are very useful in
+ 
+
+ align:start position:0%
+planer oxidation that are very useful in
+the very thin oxide regime um so I'm
+
+ align:start position:0%
+the very thin oxide regime um so I'm
+ 
+
+ align:start position:0%
+the very thin oxide regime um so I'm
+just curious how many people here have
+
+ align:start position:0%
+just curious how many people here have
+ 
+
+ align:start position:0%
+just curious how many people here have
+known or not known but have heard about
+
+ align:start position:0%
+known or not known but have heard about
+ 
+
+ align:start position:0%
+known or not known but have heard about
+the uh the de cve uh oxidation
+
+ align:start position:0%
+the uh the de cve uh oxidation
+ 
+
+ align:start position:0%
+the uh the de cve uh oxidation
+model so about uh maybe a little less
+
+ align:start position:0%
+model so about uh maybe a little less
+ 
+
+ align:start position:0%
+model so about uh maybe a little less
+than half or so okay so that works
+
+ align:start position:0%
+than half or so okay so that works
+ 
+
+ align:start position:0%
+than half or so okay so that works
+reasonably well it is it's we go through
+
+ align:start position:0%
+reasonably well it is it's we go through
+ 
+
+ align:start position:0%
+reasonably well it is it's we go through
+it because it's the basic model and then
+
+ align:start position:0%
+it because it's the basic model and then
+ 
+
+ align:start position:0%
+it because it's the basic model and then
+everything after that a lot of things
+
+ align:start position:0%
+everything after that a lot of things
+ 
+
+ align:start position:0%
+everything after that a lot of things
+after that tend to be corrections to the
+
+ align:start position:0%
+after that tend to be corrections to the
+ 
+
+ align:start position:0%
+after that tend to be corrections to the
+deal grow uh model so let's go on to
+
+ align:start position:0%
+deal grow uh model so let's go on to
+ 
+
+ align:start position:0%
+deal grow uh model so let's go on to
+slide number two and that shows the
+
+ align:start position:0%
+slide number two and that shows the
+ 
+
+ align:start position:0%
+slide number two and that shows the
+basic um sort of schematic setup for how
+
+ align:start position:0%
+basic um sort of schematic setup for how
+ 
+
+ align:start position:0%
+basic um sort of schematic setup for how
+uh de and Grove derive their model what
+
+ align:start position:0%
+uh de and Grove derive their model what
+ 
+
+ align:start position:0%
+uh de and Grove derive their model what
+it shows you is sort of turned sideways
+
+ align:start position:0%
+it shows you is sort of turned sideways
+ 
+
+ align:start position:0%
+it shows you is sort of turned sideways
+is you have a gas stream here on the
+
+ align:start position:0%
+is you have a gas stream here on the
+ 
+
+ align:start position:0%
+is you have a gas stream here on the
+left that's on top of the wafer um there
+
+ align:start position:0%
+left that's on top of the wafer um there
+ 
+
+ align:start position:0%
+left that's on top of the wafer um there
+is um a thermal uh an oxide being grown
+
+ align:start position:0%
+is um a thermal uh an oxide being grown
+ 
+
+ align:start position:0%
+is um a thermal uh an oxide being grown
+here in this white region the silicon
+
+ align:start position:0%
+here in this white region the silicon
+ 
+
+ align:start position:0%
+here in this white region the silicon
+dioxide and the pink on the right shows
+
+ align:start position:0%
+dioxide and the pink on the right shows
+ 
+
+ align:start position:0%
+dioxide and the pink on the right shows
+it's meant to represent the Silicon
+
+ align:start position:0%
+it's meant to represent the Silicon
+ 
+
+ align:start position:0%
+it's meant to represent the Silicon
+wafer and just to give you an order of
+
+ align:start position:0%
+wafer and just to give you an order of
+ 
+
+ align:start position:0%
+wafer and just to give you an order of
+magnitude scale the Silicon wafer is
+
+ align:start position:0%
+magnitude scale the Silicon wafer is
+ 
+
+ align:start position:0%
+magnitude scale the Silicon wafer is
+thick of course it's hundreds of microns
+
+ align:start position:0%
+thick of course it's hundreds of microns
+ 
+
+ align:start position:0%
+thick of course it's hundreds of microns
+this oxide that we're talking about
+
+ align:start position:0%
+this oxide that we're talking about
+ 
+
+ align:start position:0%
+this oxide that we're talking about
+growing is on the order of 0.1 0.01
+
+ align:start position:0%
+growing is on the order of 0.1 0.01
+ 
+
+ align:start position:0%
+growing is on the order of 0.1 0.01
+Micron being about 100 angstroms or 10
+
+ align:start position:0%
+Micron being about 100 angstroms or 10
+ 
+
+ align:start position:0%
+Micron being about 100 angstroms or 10
+nanometers up to maybe a micron that
+
+ align:start position:0%
+nanometers up to maybe a micron that
+ 
+
+ align:start position:0%
+nanometers up to maybe a micron that
+would be the range of reasonable
+
+ align:start position:0%
+would be the range of reasonable
+ 
+
+ align:start position:0%
+would be the range of reasonable
+thicknesses of which you would grow once
+
+ align:start position:0%
+thicknesses of which you would grow once
+ 
+
+ align:start position:0%
+thicknesses of which you would grow once
+you start growing more than a micron we
+
+ align:start position:0%
+you start growing more than a micron we
+ 
+
+ align:start position:0%
+you start growing more than a micron we
+as you'll see today um if you want to
+
+ align:start position:0%
+as you'll see today um if you want to
+ 
+
+ align:start position:0%
+as you'll see today um if you want to
+grow one or two three microns by a
+
+ align:start position:0%
+grow one or two three microns by a
+ 
+
+ align:start position:0%
+grow one or two three microns by a
+thermal process it gets pretty darn slow
+
+ align:start position:0%
+thermal process it gets pretty darn slow
+ 
+
+ align:start position:0%
+thermal process it gets pretty darn slow
+uh the kinetics are such that it becomes
+
+ align:start position:0%
+uh the kinetics are such that it becomes
+ 
+
+ align:start position:0%
+uh the kinetics are such that it becomes
+really not very practical uh so you
+
+ align:start position:0%
+really not very practical uh so you
+ 
+
+ align:start position:0%
+really not very practical uh so you
+don't see too many people growing oxides
+
+ align:start position:0%
+don't see too many people growing oxides
+ 
+
+ align:start position:0%
+don't see too many people growing oxides
+that are that much thicker than than a
+
+ align:start position:0%
+that are that much thicker than than a
+ 
+
+ align:start position:0%
+that are that much thicker than than a
+couple of microns if they need oxides
+
+ align:start position:0%
+couple of microns if they need oxides
+ 
+
+ align:start position:0%
+couple of microns if they need oxides
+that thick they do a different process
+
+ align:start position:0%
+that thick they do a different process
+ 
+
+ align:start position:0%
+that thick they do a different process
+uh called chemical vapor
+
+ align:start position:0%
+uh called chemical vapor
+ 
+
+ align:start position:0%
+uh called chemical vapor
+deposition so the basic idea of this
+
+ align:start position:0%
+deposition so the basic idea of this
+ 
+
+ align:start position:0%
+deposition so the basic idea of this
+model though is we have a gas stream
+
+ align:start position:0%
+model though is we have a gas stream
+ 
+
+ align:start position:0%
+model though is we have a gas stream
+here and there's a concentration C subg
+
+ align:start position:0%
+here and there's a concentration C subg
+ 
+
+ align:start position:0%
+here and there's a concentration C subg
+of the oxidant let's say it's oxygen
+
+ align:start position:0%
+of the oxidant let's say it's oxygen
+ 
+
+ align:start position:0%
+of the oxidant let's say it's oxygen
+could be oxygen could be water vapor but
+
+ align:start position:0%
+could be oxygen could be water vapor but
+ 
+
+ align:start position:0%
+could be oxygen could be water vapor but
+there has some concentration in the main
+
+ align:start position:0%
+there has some concentration in the main
+ 
+
+ align:start position:0%
+there has some concentration in the main
+gas uh flow in the main gas stream as
+
+ align:start position:0%
+gas uh flow in the main gas stream as
+ 
+
+ align:start position:0%
+gas uh flow in the main gas stream as
+you get closer to the oxide surf to the
+
+ align:start position:0%
+you get closer to the oxide surf to the
+ 
+
+ align:start position:0%
+you get closer to the oxide surf to the
+surface of the wafer which has oxide on
+
+ align:start position:0%
+surface of the wafer which has oxide on
+ 
+
+ align:start position:0%
+surface of the wafer which has oxide on
+it it has some um concentration C Subs
+
+ align:start position:0%
+it it has some um concentration C Subs
+ 
+
+ align:start position:0%
+it it has some um concentration C Subs
+right at the surface of the wafer there
+
+ align:start position:0%
+right at the surface of the wafer there
+ 
+
+ align:start position:0%
+right at the surface of the wafer there
+may be some boundary layer or whatever
+
+ align:start position:0%
+may be some boundary layer or whatever
+ 
+
+ align:start position:0%
+may be some boundary layer or whatever
+that causes a gradient to cross here but
+
+ align:start position:0%
+that causes a gradient to cross here but
+ 
+
+ align:start position:0%
+that causes a gradient to cross here but
+right at the surface of the wafer it's
+
+ align:start position:0%
+right at the surface of the wafer it's
+ 
+
+ align:start position:0%
+right at the surface of the wafer it's
+at CS in the G but in the gas phas in
+
+ align:start position:0%
+at CS in the G but in the gas phas in
+ 
+
+ align:start position:0%
+at CS in the G but in the gas phas in
+the solid right inside at the very uh
+
+ align:start position:0%
+the solid right inside at the very uh
+ 
+
+ align:start position:0%
+the solid right inside at the very uh
+Sur surface in the solid oxide this
+
+ align:start position:0%
+Sur surface in the solid oxide this
+ 
+
+ align:start position:0%
+Sur surface in the solid oxide this
+oxidant has some concentration C subo
+
+ align:start position:0%
+oxidant has some concentration C subo
+ 
+
+ align:start position:0%
+oxidant has some concentration C subo
+right at the surface or or c0 if you
+
+ align:start position:0%
+right at the surface or or c0 if you
+ 
+
+ align:start position:0%
+right at the surface or or c0 if you
+would like um and then there is some
+
+ align:start position:0%
+would like um and then there is some
+ 
+
+ align:start position:0%
+would like um and then there is some
+gradient uh of the oxidant I say of the
+
+ align:start position:0%
+gradient uh of the oxidant I say of the
+ 
+
+ align:start position:0%
+gradient uh of the oxidant I say of the
+oxygen molecule there's a gradient
+
+ align:start position:0%
+oxygen molecule there's a gradient
+ 
+
+ align:start position:0%
+oxygen molecule there's a gradient
+throughout the oxide and at the
+
+ align:start position:0%
+throughout the oxide and at the
+ 
+
+ align:start position:0%
+throughout the oxide and at the
+interface it has C subi the ey standing
+
+ align:start position:0%
+interface it has C subi the ey standing
+ 
+
+ align:start position:0%
+interface it has C subi the ey standing
+for the interface it has that
+
+ align:start position:0%
+for the interface it has that
+ 
+
+ align:start position:0%
+for the interface it has that
+concentration um and the um the basic
+
+ align:start position:0%
+concentration um and the um the basic
+ 
+
+ align:start position:0%
+concentration um and the um the basic
+chemical reactions that are happening
+
+ align:start position:0%
+chemical reactions that are happening
+ 
+
+ align:start position:0%
+chemical reactions that are happening
+now at the interface not at the oxide
+
+ align:start position:0%
+now at the interface not at the oxide
+ 
+
+ align:start position:0%
+now at the interface not at the oxide
+surface are shown here silicon plus
+
+ align:start position:0%
+surface are shown here silicon plus
+ 
+
+ align:start position:0%
+surface are shown here silicon plus
+oxygen going to S2 or silicon plus
+
+ align:start position:0%
+oxygen going to S2 or silicon plus
+ 
+
+ align:start position:0%
+oxygen going to S2 or silicon plus
+moisture uh H2O going to
+
+ align:start position:0%
+moisture uh H2O going to
+ 
+
+ align:start position:0%
+moisture uh H2O going to
+sio2 there and they're in the uh
+
+ align:start position:0%
+sio2 there and they're in the uh
+ 
+
+ align:start position:0%
+sio2 there and they're in the uh
+equations that we're going to derive the
+
+ align:start position:0%
+equations that we're going to derive the
+ 
+
+ align:start position:0%
+equations that we're going to derive the
+simple model there are three fluxes
+
+ align:start position:0%
+simple model there are three fluxes
+ 
+
+ align:start position:0%
+simple model there are three fluxes
+involved there's a flux F1 of oxidant um
+
+ align:start position:0%
+involved there's a flux F1 of oxidant um
+ 
+
+ align:start position:0%
+involved there's a flux F1 of oxidant um
+that has to uh be transported in the gas
+
+ align:start position:0%
+that has to uh be transported in the gas
+ 
+
+ align:start position:0%
+that has to uh be transported in the gas
+phas from the uh major portion of the
+
+ align:start position:0%
+phas from the uh major portion of the
+ 
+
+ align:start position:0%
+phas from the uh major portion of the
+gas phase in the center of the tube to
+
+ align:start position:0%
+gas phase in the center of the tube to
+ 
+
+ align:start position:0%
+gas phase in the center of the tube to
+the surface of the wafer that's one flux
+
+ align:start position:0%
+the surface of the wafer that's one flux
+ 
+
+ align:start position:0%
+the surface of the wafer that's one flux
+there's a flux F2 in the oxide this is
+
+ align:start position:0%
+there's a flux F2 in the oxide this is
+ 
+
+ align:start position:0%
+there's a flux F2 in the oxide this is
+the uh diffusion of the oxidant through
+
+ align:start position:0%
+the uh diffusion of the oxidant through
+ 
+
+ align:start position:0%
+the uh diffusion of the oxidant through
+the oxide and there's a finally a flux
+
+ align:start position:0%
+the oxide and there's a finally a flux
+ 
+
+ align:start position:0%
+the oxide and there's a finally a flux
+uh F3 which is the what's happening
+
+ align:start position:0%
+uh F3 which is the what's happening
+ 
+
+ align:start position:0%
+uh F3 which is the what's happening
+right at the interface as the O oxygen
+
+ align:start position:0%
+right at the interface as the O oxygen
+ 
+
+ align:start position:0%
+right at the interface as the O oxygen
+is incorporated into the growing
+
+ align:start position:0%
+is incorporated into the growing
+ 
+
+ align:start position:0%
+is incorporated into the growing
+oxide so let's go on to slide three um
+
+ align:start position:0%
+oxide so let's go on to slide three um
+ 
+
+ align:start position:0%
+oxide so let's go on to slide three um
+again on the upper uh upper diagram is
+
+ align:start position:0%
+again on the upper uh upper diagram is
+ 
+
+ align:start position:0%
+again on the upper uh upper diagram is
+exactly what I just shown you I've just
+
+ align:start position:0%
+exactly what I just shown you I've just
+ 
+
+ align:start position:0%
+exactly what I just shown you I've just
+shown you um for those of you who have
+
+ align:start position:0%
+shown you um for those of you who have
+ 
+
+ align:start position:0%
+shown you um for those of you who have
+forgotten on the upper right I'm
+
+ align:start position:0%
+forgotten on the upper right I'm
+ 
+
+ align:start position:0%
+forgotten on the upper right I'm
+reminding you what the definition of
+
+ align:start position:0%
+reminding you what the definition of
+ 
+
+ align:start position:0%
+reminding you what the definition of
+flux is what is a flux it's the number
+
+ align:start position:0%
+flux is what is a flux it's the number
+ 
+
+ align:start position:0%
+flux is what is a flux it's the number
+of particles it doesn't have to be in
+
+ align:start position:0%
+of particles it doesn't have to be in
+ 
+
+ align:start position:0%
+of particles it doesn't have to be in
+this case I'm talking about oxygen
+
+ align:start position:0%
+this case I'm talking about oxygen
+ 
+
+ align:start position:0%
+this case I'm talking about oxygen
+molecules or water vapor molec
+
+ align:start position:0%
+molecules or water vapor molec
+ 
+
+ align:start position:0%
+molecules or water vapor molec
+but it's the number of particles
+
+ align:start position:0%
+but it's the number of particles
+ 
+
+ align:start position:0%
+but it's the number of particles
+crossing a unit area so a unit area of
+
+ align:start position:0%
+crossing a unit area so a unit area of
+ 
+
+ align:start position:0%
+crossing a unit area so a unit area of
+in this in this direction here um per
+
+ align:start position:0%
+in this in this direction here um per
+ 
+
+ align:start position:0%
+in this in this direction here um per
+unit time so there's a flux uh in this
+
+ align:start position:0%
+unit time so there's a flux uh in this
+ 
+
+ align:start position:0%
+unit time so there's a flux uh in this
+case going from the left to the right in
+
+ align:start position:0%
+case going from the left to the right in
+ 
+
+ align:start position:0%
+case going from the left to the right in
+fact there's three different of them so
+
+ align:start position:0%
+fact there's three different of them so
+ 
+
+ align:start position:0%
+fact there's three different of them so
+uh what deal and Grove did was write
+
+ align:start position:0%
+uh what deal and Grove did was write
+ 
+
+ align:start position:0%
+uh what deal and Grove did was write
+down three very simple equations uh
+
+ align:start position:0%
+down three very simple equations uh
+ 
+
+ align:start position:0%
+down three very simple equations uh
+first order of flux equations which show
+
+ align:start position:0%
+first order of flux equations which show
+ 
+
+ align:start position:0%
+first order of flux equations which show
+these three these three um series parts
+
+ align:start position:0%
+these three these three um series parts
+ 
+
+ align:start position:0%
+these three these three um series parts
+of the process again they're all
+
+ align:start position:0%
+of the process again they're all
+ 
+
+ align:start position:0%
+of the process again they're all
+happening in series so there's a flux F1
+
+ align:start position:0%
+happening in series so there's a flux F1
+ 
+
+ align:start position:0%
+happening in series so there's a flux F1
+they wrote down using Henry's law so
+
+ align:start position:0%
+they wrote down using Henry's law so
+ 
+
+ align:start position:0%
+they wrote down using Henry's law so
+Henry's law just says in the gas-based
+
+ align:start position:0%
+Henry's law just says in the gas-based
+ 
+
+ align:start position:0%
+Henry's law just says in the gas-based
+transport if you have um a concentration
+
+ align:start position:0%
+transport if you have um a concentration
+ 
+
+ align:start position:0%
+transport if you have um a concentration
+a difference or a gradient here from
+
+ align:start position:0%
+a difference or a gradient here from
+ 
+
+ align:start position:0%
+a difference or a gradient here from
+from this point here in the center of
+
+ align:start position:0%
+from this point here in the center of
+ 
+
+ align:start position:0%
+from this point here in the center of
+where the gas flow is to the surface C
+
+ align:start position:0%
+where the gas flow is to the surface C
+ 
+
+ align:start position:0%
+where the gas flow is to the surface C
+Subs that in in uh that the you can
+
+ align:start position:0%
+Subs that in in uh that the you can
+ 
+
+ align:start position:0%
+Subs that in in uh that the you can
+write the flux as just some constant
+
+ align:start position:0%
+write the flux as just some constant
+ 
+
+ align:start position:0%
+write the flux as just some constant
+some a Henry's constant uh a constant
+
+ align:start position:0%
+some a Henry's constant uh a constant
+ 
+
+ align:start position:0%
+some a Henry's constant uh a constant
+number uh times the difference in the
+
+ align:start position:0%
+number uh times the difference in the
+ 
+
+ align:start position:0%
+number uh times the difference in the
+concentration between the Surface and
+
+ align:start position:0%
+concentration between the Surface and
+ 
+
+ align:start position:0%
+concentration between the Surface and
+the center of the G and and where the
+
+ align:start position:0%
+the center of the G and and where the
+ 
+
+ align:start position:0%
+the center of the G and and where the
+the the concentration is CG so that's a
+
+ align:start position:0%
+the the concentration is CG so that's a
+ 
+
+ align:start position:0%
+the the concentration is CG so that's a
+simple equation from Henry's law uh a
+
+ align:start position:0%
+simple equation from Henry's law uh a
+ 
+
+ align:start position:0%
+simple equation from Henry's law uh a
+second equation they wrote down was
+
+ align:start position:0%
+second equation they wrote down was
+ 
+
+ align:start position:0%
+second equation they wrote down was
+diffusion through the oxide and this
+
+ align:start position:0%
+diffusion through the oxide and this
+ 
+
+ align:start position:0%
+diffusion through the oxide and this
+comes from fix law fix first law
+
+ align:start position:0%
+comes from fix law fix first law
+ 
+
+ align:start position:0%
+comes from fix law fix first law
+hopefully some of you have seen this
+
+ align:start position:0%
+hopefully some of you have seen this
+ 
+
+ align:start position:0%
+hopefully some of you have seen this
+maybe not in this particular form when
+
+ align:start position:0%
+maybe not in this particular form when
+ 
+
+ align:start position:0%
+maybe not in this particular form when
+we talk about diffusion it'll become
+
+ align:start position:0%
+we talk about diffusion it'll become
+ 
+
+ align:start position:0%
+we talk about diffusion it'll become
+very obvious uh um but this is the fixed
+
+ align:start position:0%
+very obvious uh um but this is the fixed
+ 
+
+ align:start position:0%
+very obvious uh um but this is the fixed
+first law for diffusion through the
+
+ align:start position:0%
+first law for diffusion through the
+ 
+
+ align:start position:0%
+first law for diffusion through the
+oxide the flux F2 is just a constant
+
+ align:start position:0%
+oxide the flux F2 is just a constant
+ 
+
+ align:start position:0%
+oxide the flux F2 is just a constant
+number which we call the diffusivity D
+
+ align:start position:0%
+number which we call the diffusivity D
+ 
+
+ align:start position:0%
+number which we call the diffusivity D
+times the gradient of the diffusant DN
+
+ align:start position:0%
+times the gradient of the diffusant DN
+ 
+
+ align:start position:0%
+times the gradient of the diffusant DN
+by DX so where n is generally just the
+
+ align:start position:0%
+by DX so where n is generally just the
+ 
+
+ align:start position:0%
+by DX so where n is generally just the
+concentration of whatever is diffusing
+
+ align:start position:0%
+concentration of whatever is diffusing
+ 
+
+ align:start position:0%
+concentration of whatever is diffusing
+uh um and you can write that if this is
+
+ align:start position:0%
+uh um and you can write that if this is
+ 
+
+ align:start position:0%
+uh um and you can write that if this is
+a straight line writing the the gradient
+
+ align:start position:0%
+a straight line writing the the gradient
+ 
+
+ align:start position:0%
+a straight line writing the the gradient
+of a straight line is very simple it's
+
+ align:start position:0%
+of a straight line is very simple it's
+ 
+
+ align:start position:0%
+of a straight line is very simple it's
+just C at the surface Co minus C
+
+ align:start position:0%
+just C at the surface Co minus C
+ 
+
+ align:start position:0%
+just C at the surface Co minus C
+interface divided by the thickness of
+
+ align:start position:0%
+interface divided by the thickness of
+ 
+
+ align:start position:0%
+interface divided by the thickness of
+the oxide so it's a simple uh simple
+
+ align:start position:0%
+the oxide so it's a simple uh simple
+ 
+
+ align:start position:0%
+the oxide so it's a simple uh simple
+equation to write diffusion through the
+
+ align:start position:0%
+equation to write diffusion through the
+ 
+
+ align:start position:0%
+equation to write diffusion through the
+oxide um and finally F3 is the flux at
+
+ align:start position:0%
+oxide um and finally F3 is the flux at
+ 
+
+ align:start position:0%
+oxide um and finally F3 is the flux at
+the interface and this is just a surface
+
+ align:start position:0%
+the interface and this is just a surface
+ 
+
+ align:start position:0%
+the interface and this is just a surface
+reaction rate so we write this final
+
+ align:start position:0%
+reaction rate so we write this final
+ 
+
+ align:start position:0%
+reaction rate so we write this final
+flux as case Subs a constant which has
+
+ align:start position:0%
+flux as case Subs a constant which has
+ 
+
+ align:start position:0%
+flux as case Subs a constant which has
+to do with how rapidly the the reaction
+
+ align:start position:0%
+to do with how rapidly the the reaction
+ 
+
+ align:start position:0%
+to do with how rapidly the the reaction
+is taking place at the interface times
+
+ align:start position:0%
+is taking place at the interface times
+ 
+
+ align:start position:0%
+is taking place at the interface times
+the concentration of oxygen or water
+
+ align:start position:0%
+the concentration of oxygen or water
+ 
+
+ align:start position:0%
+the concentration of oxygen or water
+vapor right at the interface so three
+
+ align:start position:0%
+vapor right at the interface so three
+ 
+
+ align:start position:0%
+vapor right at the interface so three
+equations uh for each of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluxes so we go on to slide three now
+
+ align:start position:0%
+fluxes so we go on to slide three now
+ 
+
+ align:start position:0%
+fluxes so we go on to slide three now
+what what they're assuming is steady
+
+ align:start position:0%
+what what they're assuming is steady
+ 
+
+ align:start position:0%
+what what they're assuming is steady
+state condition and what we mean by
+
+ align:start position:0%
+state condition and what we mean by
+ 
+
+ align:start position:0%
+state condition and what we mean by
+steady state is um things are not
+
+ align:start position:0%
+steady state is um things are not
+ 
+
+ align:start position:0%
+steady state is um things are not
+changing with time uh these profiles so
+
+ align:start position:0%
+changing with time uh these profiles so
+ 
+
+ align:start position:0%
+changing with time uh these profiles so
+if I just go back one second to uh slide
+
+ align:start position:0%
+if I just go back one second to uh slide
+ 
+
+ align:start position:0%
+if I just go back one second to uh slide
+three is that this profile is there's no
+
+ align:start position:0%
+three is that this profile is there's no
+ 
+
+ align:start position:0%
+three is that this profile is there's no
+we're not in the transient phase this
+
+ align:start position:0%
+we're not in the transient phase this
+ 
+
+ align:start position:0%
+we're not in the transient phase this
+profile has now been established as a
+
+ align:start position:0%
+profile has now been established as a
+ 
+
+ align:start position:0%
+profile has now been established as a
+linear profile and a steady state it's
+
+ align:start position:0%
+linear profile and a steady state it's
+ 
+
+ align:start position:0%
+linear profile and a steady state it's
+it's not changing uh with with time
+
+ align:start position:0%
+it's not changing uh with with time
+ 
+
+ align:start position:0%
+it's not changing uh with with time
+there's you've established a constant
+
+ align:start position:0%
+there's you've established a constant
+ 
+
+ align:start position:0%
+there's you've established a constant
+profile so in those conditions then we
+
+ align:start position:0%
+profile so in those conditions then we
+ 
+
+ align:start position:0%
+profile so in those conditions then we
+can write down that the three fluxes in
+
+ align:start position:0%
+can write down that the three fluxes in
+ 
+
+ align:start position:0%
+can write down that the three fluxes in
+series are all equal to each other we
+
+ align:start position:0%
+series are all equal to each other we
+ 
+
+ align:start position:0%
+series are all equal to each other we
+don't have any buildup or any uh um or
+
+ align:start position:0%
+don't have any buildup or any uh um or
+ 
+
+ align:start position:0%
+don't have any buildup or any uh um or
+any sinks so F1 the flux throwing
+
+ align:start position:0%
+any sinks so F1 the flux throwing
+ 
+
+ align:start position:0%
+any sinks so F1 the flux throwing
+through the gas has to be equal to F2
+
+ align:start position:0%
+through the gas has to be equal to F2
+ 
+
+ align:start position:0%
+through the gas has to be equal to F2
+the flux diffusing through has to be
+
+ align:start position:0%
+the flux diffusing through has to be
+ 
+
+ align:start position:0%
+the flux diffusing through has to be
+equal to the reactive flux um so uh in
+
+ align:start position:0%
+equal to the reactive flux um so uh in
+ 
+
+ align:start position:0%
+equal to the reactive flux um so uh in
+that case then it's relatively simple if
+
+ align:start position:0%
+that case then it's relatively simple if
+ 
+
+ align:start position:0%
+that case then it's relatively simple if
+you sit down and you equate those three
+
+ align:start position:0%
+you sit down and you equate those three
+ 
+
+ align:start position:0%
+you sit down and you equate those three
+equations you can derive this formula
+
+ align:start position:0%
+equations you can derive this formula
+ 
+
+ align:start position:0%
+equations you can derive this formula
+here uh equation number four for con the
+
+ align:start position:0%
+here uh equation number four for con the
+ 
+
+ align:start position:0%
+here uh equation number four for con the
+concentration of the oxygen molecules of
+
+ align:start position:0%
+concentration of the oxygen molecules of
+ 
+
+ align:start position:0%
+concentration of the oxygen molecules of
+the water vapor C subi at the interface
+
+ align:start position:0%
+the water vapor C subi at the interface
+ 
+
+ align:start position:0%
+the water vapor C subi at the interface
+you can write it as some constant C star
+
+ align:start position:0%
+you can write it as some constant C star
+ 
+
+ align:start position:0%
+you can write it as some constant C star
+which we'll talk about where C star is
+
+ align:start position:0%
+which we'll talk about where C star is
+ 
+
+ align:start position:0%
+which we'll talk about where C star is
+the solubility of the oxidant um uh in
+
+ align:start position:0%
+the solubility of the oxidant um uh in
+ 
+
+ align:start position:0%
+the solubility of the oxidant um uh in
+the oxide divided by um a three term
+
+ align:start position:0%
+the oxide divided by um a three term
+ 
+
+ align:start position:0%
+the oxide divided by um a three term
+expression 1 plus the ratio of K sub s
+
+ align:start position:0%
+expression 1 plus the ratio of K sub s
+ 
+
+ align:start position:0%
+expression 1 plus the ratio of K sub s
+to H um so that tells us something about
+
+ align:start position:0%
+to H um so that tells us something about
+ 
+
+ align:start position:0%
+to H um so that tells us something about
+the ratio of the uh surface reaction
+
+ align:start position:0%
+the ratio of the uh surface reaction
+ 
+
+ align:start position:0%
+the ratio of the uh surface reaction
+coefficient to Henry's coefficient h
+
+ align:start position:0%
+coefficient to Henry's coefficient h
+ 
+
+ align:start position:0%
+coefficient to Henry's coefficient h
+plus Cas sub s XD X overd this is
+
+ align:start position:0%
+plus Cas sub s XD X overd this is
+ 
+
+ align:start position:0%
+plus Cas sub s XD X overd this is
+involving a diffusivity
+
+ align:start position:0%
+involving a diffusivity
+ 
+
+ align:start position:0%
+involving a diffusivity
+term uh and so what we are generally
+
+ align:start position:0%
+term uh and so what we are generally
+ 
+
+ align:start position:0%
+term uh and so what we are generally
+going to do in this if we we can
+
+ align:start position:0%
+going to do in this if we we can
+ 
+
+ align:start position:0%
+going to do in this if we we can
+actually simplify this equation by
+
+ align:start position:0%
+actually simplify this equation by
+ 
+
+ align:start position:0%
+actually simplify this equation by
+recognizing um that we're actually can
+
+ align:start position:0%
+recognizing um that we're actually can
+ 
+
+ align:start position:0%
+recognizing um that we're actually can
+neglect F1 the gas phase transport which
+
+ align:start position:0%
+neglect F1 the gas phase transport which
+ 
+
+ align:start position:0%
+neglect F1 the gas phase transport which
+is usually a very good approximation
+
+ align:start position:0%
+is usually a very good approximation
+ 
+
+ align:start position:0%
+is usually a very good approximation
+it's very fast so if I if I go back to
+
+ align:start position:0%
+it's very fast so if I if I go back to
+ 
+
+ align:start position:0%
+it's very fast so if I if I go back to
+this slide number three briefly this
+
+ align:start position:0%
+this slide number three briefly this
+ 
+
+ align:start position:0%
+this slide number three briefly this
+flux is this is happening much much
+
+ align:start position:0%
+flux is this is happening much much
+ 
+
+ align:start position:0%
+flux is this is happening much much
+faster than these two processes than the
+
+ align:start position:0%
+faster than these two processes than the
+ 
+
+ align:start position:0%
+faster than these two processes than the
+diffusion um through the solid or then
+
+ align:start position:0%
+diffusion um through the solid or then
+ 
+
+ align:start position:0%
+diffusion um through the solid or then
+or than the reaction as it happens to
+
+ align:start position:0%
+or than the reaction as it happens to
+ 
+
+ align:start position:0%
+or than the reaction as it happens to
+turn out in this case that won't always
+
+ align:start position:0%
+turn out in this case that won't always
+ 
+
+ align:start position:0%
+turn out in this case that won't always
+be the case for other processes when we
+
+ align:start position:0%
+be the case for other processes when we
+ 
+
+ align:start position:0%
+be the case for other processes when we
+talk about epitaxial growth or chemical
+
+ align:start position:0%
+talk about epitaxial growth or chemical
+ 
+
+ align:start position:0%
+talk about epitaxial growth or chemical
+vapor deposition uh It won't always be
+
+ align:start position:0%
+vapor deposition uh It won't always be
+ 
+
+ align:start position:0%
+vapor deposition uh It won't always be
+the case that you can ignore the
+
+ align:start position:0%
+the case that you can ignore the
+ 
+
+ align:start position:0%
+the case that you can ignore the
+gasphase transport but as it turns out
+
+ align:start position:0%
+gasphase transport but as it turns out
+ 
+
+ align:start position:0%
+gasphase transport but as it turns out
+the surface reaction is slow enough and
+
+ align:start position:0%
+the surface reaction is slow enough and
+ 
+
+ align:start position:0%
+the surface reaction is slow enough and
+the diffusion through the oxide is slow
+
+ align:start position:0%
+the diffusion through the oxide is slow
+ 
+
+ align:start position:0%
+the diffusion through the oxide is slow
+enough that it all that this that this
+
+ align:start position:0%
+enough that it all that this that this
+ 
+
+ align:start position:0%
+enough that it all that this that this
+is always very fast um and so we can the
+
+ align:start position:0%
+is always very fast um and so we can the
+ 
+
+ align:start position:0%
+is always very fast um and so we can the
+beautiful thing about oxidation is you
+
+ align:start position:0%
+beautiful thing about oxidation is you
+ 
+
+ align:start position:0%
+beautiful thing about oxidation is you
+can ignore gas phase transport and
+
+ align:start position:0%
+can ignore gas phase transport and
+ 
+
+ align:start position:0%
+can ignore gas phase transport and
+that's why you can design oxidation
+
+ align:start position:0%
+that's why you can design oxidation
+ 
+
+ align:start position:0%
+that's why you can design oxidation
+tubes to be very simple you just stand
+
+ align:start position:0%
+tubes to be very simple you just stand
+ 
+
+ align:start position:0%
+tubes to be very simple you just stand
+all the Wafers up and flow the oxygen
+
+ align:start position:0%
+all the Wafers up and flow the oxygen
+ 
+
+ align:start position:0%
+all the Wafers up and flow the oxygen
+through and you don't have to care about
+
+ align:start position:0%
+through and you don't have to care about
+ 
+
+ align:start position:0%
+through and you don't have to care about
+exactly how the gas flows when we talk
+
+ align:start position:0%
+exactly how the gas flows when we talk
+ 
+
+ align:start position:0%
+exactly how the gas flows when we talk
+about other processes uh like epaxial
+
+ align:start position:0%
+about other processes uh like epaxial
+ 
+
+ align:start position:0%
+about other processes uh like epaxial
+growth no such luxury by any means in
+
+ align:start position:0%
+growth no such luxury by any means in
+ 
+
+ align:start position:0%
+growth no such luxury by any means in
+that case this flux is extremely
+
+ align:start position:0%
+that case this flux is extremely
+ 
+
+ align:start position:0%
+that case this flux is extremely
+important and in fact it controls the
+
+ align:start position:0%
+important and in fact it controls the
+ 
+
+ align:start position:0%
+important and in fact it controls the
+process many times so but we're very
+
+ align:start position:0%
+process many times so but we're very
+ 
+
+ align:start position:0%
+process many times so but we're very
+lucky in oxide growth that these two
+
+ align:start position:0%
+lucky in oxide growth that these two
+ 
+
+ align:start position:0%
+lucky in oxide growth that these two
+processes F2 and F3 are slow so we could
+
+ align:start position:0%
+processes F2 and F3 are slow so we could
+ 
+
+ align:start position:0%
+processes F2 and F3 are slow so we could
+ignore
+
+ align:start position:0%
+ignore
+ 
+
+ align:start position:0%
+ignore
+F1 and that just ends up simplifying the
+
+ align:start position:0%
+F1 and that just ends up simplifying the
+ 
+
+ align:start position:0%
+F1 and that just ends up simplifying the
+equations to um a certain extent um and
+
+ align:start position:0%
+equations to um a certain extent um and
+ 
+
+ align:start position:0%
+equations to um a certain extent um and
+so by if I rearrange this um a little
+
+ align:start position:0%
+so by if I rearrange this um a little
+ 
+
+ align:start position:0%
+so by if I rearrange this um a little
+bit we we get equation uh number five
+
+ align:start position:0%
+bit we we get equation uh number five
+ 
+
+ align:start position:0%
+bit we we get equation uh number five
+here for the uh we're really interested
+
+ align:start position:0%
+here for the uh we're really interested
+ 
+
+ align:start position:0%
+here for the uh we're really interested
+in C subo here uh the concentration uh
+
+ align:start position:0%
+in C subo here uh the concentration uh
+ 
+
+ align:start position:0%
+in C subo here uh the concentration uh
+at the surface uh of the O
+
+ align:start position:0%
+at the surface uh of the O
+ 
+
+ align:start position:0%
+at the surface uh of the O
+oxidant so let me combine now this
+
+ align:start position:0%
+oxidant so let me combine now this
+ 
+
+ align:start position:0%
+oxidant so let me combine now this
+equation number four which tells me what
+
+ align:start position:0%
+equation number four which tells me what
+ 
+
+ align:start position:0%
+equation number four which tells me what
+the concentration of water or or oxygen
+
+ align:start position:0%
+the concentration of water or or oxygen
+ 
+
+ align:start position:0%
+the concentration of water or or oxygen
+is at the interface with um I'm going to
+
+ align:start position:0%
+is at the interface with um I'm going to
+ 
+
+ align:start position:0%
+is at the interface with um I'm going to
+combine this equation with equation
+
+ align:start position:0%
+combine this equation with equation
+ 
+
+ align:start position:0%
+combine this equation with equation
+three just going back again which just
+
+ align:start position:0%
+three just going back again which just
+ 
+
+ align:start position:0%
+three just going back again which just
+tells me the the uh surface reaction
+
+ align:start position:0%
+tells me the the uh surface reaction
+ 
+
+ align:start position:0%
+tells me the the uh surface reaction
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+flux uh and we get something like this
+
+ align:start position:0%
+flux uh and we get something like this
+ 
+
+ align:start position:0%
+flux uh and we get something like this
+that says it says that DX by DT so
+
+ align:start position:0%
+that says it says that DX by DT so
+ 
+
+ align:start position:0%
+that says it says that DX by DT so
+that's the rate of change of the
+
+ align:start position:0%
+that's the rate of change of the
+ 
+
+ align:start position:0%
+that's the rate of change of the
+thickness of the oxide DX by DT um we
+
+ align:start position:0%
+thickness of the oxide DX by DT um we
+ 
+
+ align:start position:0%
+thickness of the oxide DX by DT um we
+know we can write it as a flux divided
+
+ align:start position:0%
+know we can write it as a flux divided
+ 
+
+ align:start position:0%
+know we can write it as a flux divided
+by a concentration so N1 here is what
+
+ align:start position:0%
+by a concentration so N1 here is what
+ 
+
+ align:start position:0%
+by a concentration so N1 here is what
+anybody have an idea what N1 is just
+
+ align:start position:0%
+anybody have an idea what N1 is just
+ 
+
+ align:start position:0%
+anybody have an idea what N1 is just
+from dimensional
+
+ align:start position:0%
+from dimensional
+ 
+
+ align:start position:0%
+from dimensional
+arguments what kind of uh this is I I
+
+ align:start position:0%
+arguments what kind of uh this is I I
+ 
+
+ align:start position:0%
+arguments what kind of uh this is I I
+want to get DX by DT flux tells you the
+
+ align:start position:0%
+want to get DX by DT flux tells you the
+ 
+
+ align:start position:0%
+want to get DX by DT flux tells you the
+number of atoms per square
+
+ align:start position:0%
+number of atoms per square
+ 
+
+ align:start position:0%
+number of atoms per square
+centimeter per unit time so N1 has to
+
+ align:start position:0%
+centimeter per unit time so N1 has to
+ 
+
+ align:start position:0%
+centimeter per unit time so N1 has to
+have the units of the concentration per
+
+ align:start position:0%
+have the units of the concentration per
+ 
+
+ align:start position:0%
+have the units of the concentration per
+cubic centimeter basically um so so that
+
+ align:start position:0%
+cubic centimeter basically um so so that
+ 
+
+ align:start position:0%
+cubic centimeter basically um so so that
+it works out even just to work out
+
+ align:start position:0%
+it works out even just to work out
+ 
+
+ align:start position:0%
+it works out even just to work out
+dimensionally of course I don't have any
+
+ align:start position:0%
+dimensionally of course I don't have any
+ 
+
+ align:start position:0%
+dimensionally of course I don't have any
+chalk but that says what happens but if
+
+ align:start position:0%
+chalk but that says what happens but if
+ 
+
+ align:start position:0%
+chalk but that says what happens but if
+you work it out dimensionally flux has
+
+ align:start position:0%
+you work it out dimensionally flux has
+ 
+
+ align:start position:0%
+you work it out dimensionally flux has
+number of atoms per unit time per square
+
+ align:start position:0%
+number of atoms per unit time per square
+ 
+
+ align:start position:0%
+number of atoms per unit time per square
+centimeter this is the number of atoms
+
+ align:start position:0%
+centimeter this is the number of atoms
+ 
+
+ align:start position:0%
+centimeter this is the number of atoms
+in the oxide per cubic centimeter you
+
+ align:start position:0%
+in the oxide per cubic centimeter you
+ 
+
+ align:start position:0%
+in the oxide per cubic centimeter you
+end up with something like looks like
+
+ align:start position:0%
+end up with something like looks like
+ 
+
+ align:start position:0%
+end up with something like looks like
+cim per unit time or length per unit
+
+ align:start position:0%
+cim per unit time or length per unit
+ 
+
+ align:start position:0%
+cim per unit time or length per unit
+time so this is this is how uh quickly
+
+ align:start position:0%
+time so this is this is how uh quickly
+ 
+
+ align:start position:0%
+time so this is this is how uh quickly
+the oxide is growing the growth rate or
+
+ align:start position:0%
+the oxide is growing the growth rate or
+ 
+
+ align:start position:0%
+the oxide is growing the growth rate or
+the velocity which is what we're
+
+ align:start position:0%
+the velocity which is what we're
+ 
+
+ align:start position:0%
+the velocity which is what we're
+interested in the growth rate can be
+
+ align:start position:0%
+interested in the growth rate can be
+ 
+
+ align:start position:0%
+interested in the growth rate can be
+written uh like this it's the product of
+
+ align:start position:0%
+written uh like this it's the product of
+ 
+
+ align:start position:0%
+written uh like this it's the product of
+K Subs the surface reaction rate times
+
+ align:start position:0%
+K Subs the surface reaction rate times
+ 
+
+ align:start position:0%
+K Subs the surface reaction rate times
+the the C star C star is a solubility of
+
+ align:start position:0%
+the the C star C star is a solubility of
+ 
+
+ align:start position:0%
+the the C star C star is a solubility of
+the oxidant in the oxide so that's as
+
+ align:start position:0%
+the oxidant in the oxide so that's as
+ 
+
+ align:start position:0%
+the oxidant in the oxide so that's as
+much as as you can as you can put in at
+
+ align:start position:0%
+much as as you can as you can put in at
+ 
+
+ align:start position:0%
+much as as you can as you can put in at
+that temperature okay you might have
+
+ align:start position:0%
+that temperature okay you might have
+ 
+
+ align:start position:0%
+that temperature okay you might have
+more in the gas phase than that but
+
+ align:start position:0%
+more in the gas phase than that but
+ 
+
+ align:start position:0%
+more in the gas phase than that but
+that's how much will go in at that
+
+ align:start position:0%
+that's how much will go in at that
+ 
+
+ align:start position:0%
+that's how much will go in at that
+temperature C star divided by this
+
+ align:start position:0%
+temperature C star divided by this
+ 
+
+ align:start position:0%
+temperature C star divided by this
+denominator 1 plus K Subs over h plus K
+
+ align:start position:0%
+denominator 1 plus K Subs over h plus K
+ 
+
+ align:start position:0%
+denominator 1 plus K Subs over h plus K
+Subs x x over D so that's what that's
+
+ align:start position:0%
+Subs x x over D so that's what that's
+ 
+
+ align:start position:0%
+Subs x x over D so that's what that's
+telling us um the rate of growth of the
+
+ align:start position:0%
+telling us um the rate of growth of the
+ 
+
+ align:start position:0%
+telling us um the rate of growth of the
+oxide now we have it in terms of certain
+
+ align:start position:0%
+oxide now we have it in terms of certain
+ 
+
+ align:start position:0%
+oxide now we have it in terms of certain
+fundamental uh physical
+
+ align:start position:0%
+fundamental uh physical
+ 
+
+ align:start position:0%
+fundamental uh physical
+parameters so let's go on to um Slide
+
+ align:start position:0%
+parameters so let's go on to um Slide
+ 
+
+ align:start position:0%
+parameters so let's go on to um Slide
+Five we take that that was a simple
+
+ align:start position:0%
+Five we take that that was a simple
+ 
+
+ align:start position:0%
+Five we take that that was a simple
+if you want differential equation DX by
+
+ align:start position:0%
+if you want differential equation DX by
+ 
+
+ align:start position:0%
+if you want differential equation DX by
+DT just says you how rapidly it's uh the
+
+ align:start position:0%
+DT just says you how rapidly it's uh the
+ 
+
+ align:start position:0%
+DT just says you how rapidly it's uh the
+what is the velocity of of the growth
+
+ align:start position:0%
+what is the velocity of of the growth
+ 
+
+ align:start position:0%
+what is the velocity of of the growth
+and we integrate that if you look in the
+
+ align:start position:0%
+and we integrate that if you look in the
+ 
+
+ align:start position:0%
+and we integrate that if you look in the
+text it has some uh uh little bit of
+
+ align:start position:0%
+text it has some uh uh little bit of
+ 
+
+ align:start position:0%
+text it has some uh uh little bit of
+more detail on how you do the
+
+ align:start position:0%
+more detail on how you do the
+ 
+
+ align:start position:0%
+more detail on how you do the
+integration but you integrate it between
+
+ align:start position:0%
+integration but you integrate it between
+ 
+
+ align:start position:0%
+integration but you integrate it between
+zero and some time and between some
+
+ align:start position:0%
+zero and some time and between some
+ 
+
+ align:start position:0%
+zero and some time and between some
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+thickness X subi and your final
+
+ align:start position:0%
+thickness X subi and your final
+ 
+
+ align:start position:0%
+thickness X subi and your final
+thickness or the thickness at any point
+
+ align:start position:0%
+thickness or the thickness at any point
+ 
+
+ align:start position:0%
+thickness or the thickness at any point
+in time x0 so here x0 is the thickness
+
+ align:start position:0%
+in time x0 so here x0 is the thickness
+ 
+
+ align:start position:0%
+in time x0 so here x0 is the thickness
+of the oxide right at the time t and XI
+
+ align:start position:0%
+of the oxide right at the time t and XI
+ 
+
+ align:start position:0%
+of the oxide right at the time t and XI
+is whatever thickness you started with
+
+ align:start position:0%
+is whatever thickness you started with
+ 
+
+ align:start position:0%
+is whatever thickness you started with
+could be zero whatever your thickness
+
+ align:start position:0%
+could be zero whatever your thickness
+ 
+
+ align:start position:0%
+could be zero whatever your thickness
+you started with at the the start of the
+
+ align:start position:0%
+you started with at the the start of the
+ 
+
+ align:start position:0%
+you started with at the the start of the
+oxidation process so by doing that
+
+ align:start position:0%
+oxidation process so by doing that
+ 
+
+ align:start position:0%
+oxidation process so by doing that
+integration you end up with that uh time
+
+ align:start position:0%
+integration you end up with that uh time
+ 
+
+ align:start position:0%
+integration you end up with that uh time
+if this is you can solve for time uh is
+
+ align:start position:0%
+if this is you can solve for time uh is
+ 
+
+ align:start position:0%
+if this is you can solve for time uh is
+equal to as a two- term expression
+
+ align:start position:0%
+equal to as a two- term expression
+ 
+
+ align:start position:0%
+equal to as a two- term expression
+something that involves x squared
+
+ align:start position:0%
+something that involves x squared
+ 
+
+ align:start position:0%
+something that involves x squared
+thickness squared and something that
+
+ align:start position:0%
+thickness squared and something that
+ 
+
+ align:start position:0%
+thickness squared and something that
+involves a linear term thickness to the
+
+ align:start position:0%
+involves a linear term thickness to the
+ 
+
+ align:start position:0%
+involves a linear term thickness to the
+F uh first power so this is the origin
+
+ align:start position:0%
+F uh first power so this is the origin
+ 
+
+ align:start position:0%
+F uh first power so this is the origin
+origin of this parabolic linear model
+
+ align:start position:0%
+origin of this parabolic linear model
+ 
+
+ align:start position:0%
+origin of this parabolic linear model
+here's a parabolic term it goes like the
+
+ align:start position:0%
+here's a parabolic term it goes like the
+ 
+
+ align:start position:0%
+here's a parabolic term it goes like the
+thickness squ here's a linear
+
+ align:start position:0%
+thickness squ here's a linear
+ 
+
+ align:start position:0%
+thickness squ here's a linear
+term and the uh multipliers are B here
+
+ align:start position:0%
+term and the uh multipliers are B here
+ 
+
+ align:start position:0%
+term and the uh multipliers are B here
+this is the multiplier um of the X not
+
+ align:start position:0%
+this is the multiplier um of the X not
+ 
+
+ align:start position:0%
+this is the multiplier um of the X not
+the parabolic term looks like this it's
+
+ align:start position:0%
+the parabolic term looks like this it's
+ 
+
+ align:start position:0%
+the parabolic term looks like this it's
+um it looks like the diffusion
+
+ align:start position:0%
+um it looks like the diffusion
+ 
+
+ align:start position:0%
+um it looks like the diffusion
+coefficient through the oxide times the
+
+ align:start position:0%
+coefficient through the oxide times the
+ 
+
+ align:start position:0%
+coefficient through the oxide times the
+solubility in the oxide C star divided
+
+ align:start position:0%
+solubility in the oxide C star divided
+ 
+
+ align:start position:0%
+solubility in the oxide C star divided
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+N1 so the parabolic process has to do
+
+ align:start position:0%
+N1 so the parabolic process has to do
+ 
+
+ align:start position:0%
+N1 so the parabolic process has to do
+with diffusion through the oxide the
+
+ align:start position:0%
+with diffusion through the oxide the
+ 
+
+ align:start position:0%
+with diffusion through the oxide the
+linear term the term that multiplies X
+
+ align:start position:0%
+linear term the term that multiplies X
+ 
+
+ align:start position:0%
+linear term the term that multiplies X
+notot um can be simplified here to um
+
+ align:start position:0%
+notot um can be simplified here to um
+ 
+
+ align:start position:0%
+notot um can be simplified here to um
+something that looks like C star KAS
+
+ align:start position:0%
+something that looks like C star KAS
+ 
+
+ align:start position:0%
+something that looks like C star KAS
+Subs over N1 and again I'm ignoring this
+
+ align:start position:0%
+Subs over N1 and again I'm ignoring this
+ 
+
+ align:start position:0%
+Subs over N1 and again I'm ignoring this
+one over H because um this is going very
+
+ align:start position:0%
+one over H because um this is going very
+ 
+
+ align:start position:0%
+one over H because um this is going very
+rapidly so H is very large compared to
+
+ align:start position:0%
+rapidly so H is very large compared to
+ 
+
+ align:start position:0%
+rapidly so H is very large compared to
+ques so I can ignore this
+
+ align:start position:0%
+ques so I can ignore this
+ 
+
+ align:start position:0%
+ques so I can ignore this
+term uh so this is the linear rate
+
+ align:start position:0%
+term uh so this is the linear rate
+ 
+
+ align:start position:0%
+term uh so this is the linear rate
+constant which go which tells you
+
+ align:start position:0%
+constant which go which tells you
+ 
+
+ align:start position:0%
+constant which go which tells you
+something about the surface reaction
+
+ align:start position:0%
+something about the surface reaction
+ 
+
+ align:start position:0%
+something about the surface reaction
+rate so linear rate constant has to do
+
+ align:start position:0%
+rate so linear rate constant has to do
+ 
+
+ align:start position:0%
+rate so linear rate constant has to do
+with a reaction parabolic has to do with
+
+ align:start position:0%
+with a reaction parabolic has to do with
+ 
+
+ align:start position:0%
+with a reaction parabolic has to do with
+a diffusion notice that they both depend
+
+ align:start position:0%
+a diffusion notice that they both depend
+ 
+
+ align:start position:0%
+a diffusion notice that they both depend
+however on C star which is the
+
+ align:start position:0%
+however on C star which is the
+ 
+
+ align:start position:0%
+however on C star which is the
+concentration or the solubility of
+
+ align:start position:0%
+concentration or the solubility of
+ 
+
+ align:start position:0%
+concentration or the solubility of
+either the oxygen or the water in the
+
+ align:start position:0%
+either the oxygen or the water in the
+ 
+
+ align:start position:0%
+either the oxygen or the water in the
+oxide
+
+ align:start position:0%
+oxide
+ 
+
+ align:start position:0%
+oxide
+let so let's go on to slide number six
+
+ align:start position:0%
+let so let's go on to slide number six
+ 
+
+ align:start position:0%
+let so let's go on to slide number six
+these rate constants B and B over a have
+
+ align:start position:0%
+these rate constants B and B over a have
+ 
+
+ align:start position:0%
+these rate constants B and B over a have
+some physical meaning we just talked
+
+ align:start position:0%
+some physical meaning we just talked
+ 
+
+ align:start position:0%
+some physical meaning we just talked
+about that diffusion uh of the oxidant
+
+ align:start position:0%
+about that diffusion uh of the oxidant
+ 
+
+ align:start position:0%
+about that diffusion uh of the oxidant
+and interface reaction and we write them
+
+ align:start position:0%
+and interface reaction and we write them
+ 
+
+ align:start position:0%
+and interface reaction and we write them
+uh we find experimentally that we can
+
+ align:start position:0%
+uh we find experimentally that we can
+ 
+
+ align:start position:0%
+uh we find experimentally that we can
+write them as arous relationships
+
+ align:start position:0%
+write them as arous relationships
+ 
+
+ align:start position:0%
+write them as arous relationships
+they're exponentially dependent on e to
+
+ align:start position:0%
+they're exponentially dependent on e to
+ 
+
+ align:start position:0%
+they're exponentially dependent on e to
+the some activation energy uh e the
+
+ align:start position:0%
+the some activation energy uh e the
+ 
+
+ align:start position:0%
+the some activation energy uh e the
+minus E1 over KT or E Theus E2 over KT
+
+ align:start position:0%
+minus E1 over KT or E Theus E2 over KT
+ 
+
+ align:start position:0%
+minus E1 over KT or E Theus E2 over KT
+times a
+
+ align:start position:0%
+times a
+ 
+
+ align:start position:0%
+times a
+prefactor uh the preactor here is C1 uh
+
+ align:start position:0%
+prefactor uh the preactor here is C1 uh
+ 
+
+ align:start position:0%
+prefactor uh the preactor here is C1 uh
+for B and B over a is
+
+ align:start position:0%
+for B and B over a is
+ 
+
+ align:start position:0%
+for B and B over a is
+C2 and these rate constants have been
+
+ align:start position:0%
+C2 and these rate constants have been
+ 
+
+ align:start position:0%
+C2 and these rate constants have been
+studied for many years people have
+
+ align:start position:0%
+studied for many years people have
+ 
+
+ align:start position:0%
+studied for many years people have
+measured them or tried to extract them
+
+ align:start position:0%
+measured them or tried to extract them
+ 
+
+ align:start position:0%
+measured them or tried to extract them
+uh experimentally and this is a chart um
+
+ align:start position:0%
+uh experimentally and this is a chart um
+ 
+
+ align:start position:0%
+uh experimentally and this is a chart um
+uh table I took directly out of your
+
+ align:start position:0%
+uh table I took directly out of your
+ 
+
+ align:start position:0%
+uh table I took directly out of your
+text which shows the ambient so that's
+
+ align:start position:0%
+text which shows the ambient so that's
+ 
+
+ align:start position:0%
+text which shows the ambient so that's
+the type of uh of uh uh gases
+
+ align:start position:0%
+the type of uh of uh uh gases
+ 
+
+ align:start position:0%
+the type of uh of uh uh gases
+environment that you are in the wafer is
+
+ align:start position:0%
+environment that you are in the wafer is
+ 
+
+ align:start position:0%
+environment that you are in the wafer is
+in and the rate constants B and B over a
+
+ align:start position:0%
+in and the rate constants B and B over a
+ 
+
+ align:start position:0%
+in and the rate constants B and B over a
+and how to calculate them so in dry
+
+ align:start position:0%
+and how to calculate them so in dry
+ 
+
+ align:start position:0%
+and how to calculate them so in dry
+oxygen so there's you're flowing O2 in
+
+ align:start position:0%
+oxygen so there's you're flowing O2 in
+ 
+
+ align:start position:0%
+oxygen so there's you're flowing O2 in
+the tube but there's no moisture around
+
+ align:start position:0%
+the tube but there's no moisture around
+ 
+
+ align:start position:0%
+the tube but there's no moisture around
+um to catch calculate the B rate
+
+ align:start position:0%
+um to catch calculate the B rate
+ 
+
+ align:start position:0%
+um to catch calculate the B rate
+constant you need to know C1 and you
+
+ align:start position:0%
+constant you need to know C1 and you
+ 
+
+ align:start position:0%
+constant you need to know C1 and you
+need to know E1 the activation energies
+
+ align:start position:0%
+need to know E1 the activation energies
+ 
+
+ align:start position:0%
+need to know E1 the activation energies
+uh wed O2 they're listed um uh so and
+
+ align:start position:0%
+uh wed O2 they're listed um uh so and
+ 
+
+ align:start position:0%
+uh wed O2 they're listed um uh so and
+and and the and H2O and moisture
+
+ align:start position:0%
+and and the and H2O and moisture
+ 
+
+ align:start position:0%
+and and the and H2O and moisture
+environment so these are by the way just
+
+ align:start position:0%
+environment so these are by the way just
+ 
+
+ align:start position:0%
+environment so these are by the way just
+be careful when you're going to use
+
+ align:start position:0%
+be careful when you're going to use
+ 
+
+ align:start position:0%
+be careful when you're going to use
+these numbers these are for 111 silicon
+
+ align:start position:0%
+these numbers these are for 111 silicon
+ 
+
+ align:start position:0%
+these numbers these are for 111 silicon
+oxidation so that's oxidation of a wafer
+
+ align:start position:0%
+oxidation so that's oxidation of a wafer
+ 
+
+ align:start position:0%
+oxidation so that's oxidation of a wafer
+with orientation surface of 111 at one
+
+ align:start position:0%
+with orientation surface of 111 at one
+ 
+
+ align:start position:0%
+with orientation surface of 111 at one
+atmospheric pressure if you want to know
+
+ align:start position:0%
+atmospheric pressure if you want to know
+ 
+
+ align:start position:0%
+atmospheric pressure if you want to know
+the values for one0 silicon then you
+
+ align:start position:0%
+the values for one0 silicon then you
+ 
+
+ align:start position:0%
+the values for one0 silicon then you
+take the C2 values these B over a the
+
+ align:start position:0%
+take the C2 values these B over a the
+ 
+
+ align:start position:0%
+take the C2 values these B over a the
+rate constants uh and you divide by 1.68
+
+ align:start position:0%
+rate constants uh and you divide by 1.68
+ 
+
+ align:start position:0%
+rate constants uh and you divide by 1.68
+so it's slower for a one z0 interface
+
+ align:start position:0%
+so it's slower for a one z0 interface
+ 
+
+ align:start position:0%
+so it's slower for a one z0 interface
+and if we if you go back and look at
+
+ align:start position:0%
+and if we if you go back and look at
+ 
+
+ align:start position:0%
+and if we if you go back and look at
+your crystallography and look at the
+
+ align:start position:0%
+your crystallography and look at the
+ 
+
+ align:start position:0%
+your crystallography and look at the
+number of atoms per square centimeter it
+
+ align:start position:0%
+number of atoms per square centimeter it
+ 
+
+ align:start position:0%
+number of atoms per square centimeter it
+actually makes some sense because on a
+
+ align:start position:0%
+actually makes some sense because on a
+ 
+
+ align:start position:0%
+actually makes some sense because on a
+111 interface we have the largest number
+
+ align:start position:0%
+111 interface we have the largest number
+ 
+
+ align:start position:0%
+111 interface we have the largest number
+of atoms per square centimeter uh
+
+ align:start position:0%
+of atoms per square centimeter uh
+ 
+
+ align:start position:0%
+of atoms per square centimeter uh
+available uh uh so uh for the oxidation
+
+ align:start position:0%
+available uh uh so uh for the oxidation
+ 
+
+ align:start position:0%
+available uh uh so uh for the oxidation
+so it's going to be the rate constants
+
+ align:start position:0%
+so it's going to be the rate constants
+ 
+
+ align:start position:0%
+so it's going to be the rate constants
+are going to be faster uh but notice um
+
+ align:start position:0%
+are going to be faster uh but notice um
+ 
+
+ align:start position:0%
+are going to be faster uh but notice um
+the activation energy doesn't change uh
+
+ align:start position:0%
+the activation energy doesn't change uh
+ 
+
+ align:start position:0%
+the activation energy doesn't change uh
+as you change orientations it's all for
+
+ align:start position:0%
+as you change orientations it's all for
+ 
+
+ align:start position:0%
+as you change orientations it's all for
+the rate constant B over a the surface
+
+ align:start position:0%
+the rate constant B over a the surface
+ 
+
+ align:start position:0%
+the rate constant B over a the surface
+reaction rate um it all has an
+
+ align:start position:0%
+reaction rate um it all has an
+ 
+
+ align:start position:0%
+reaction rate um it all has an
+activation energy of close to two uh 2
+
+ align:start position:0%
+activation energy of close to two uh 2
+ 
+
+ align:start position:0%
+activation energy of close to two uh 2
+EV uh so the activation energy for boa
+
+ align:start position:0%
+EV uh so the activation energy for boa
+ 
+
+ align:start position:0%
+EV uh so the activation energy for boa
+is roughly constant um it just depends
+
+ align:start position:0%
+is roughly constant um it just depends
+ 
+
+ align:start position:0%
+is roughly constant um it just depends
+on the surface reaction rate for B uh
+
+ align:start position:0%
+on the surface reaction rate for B uh
+ 
+
+ align:start position:0%
+on the surface reaction rate for B uh
+interestingly it uh the activation
+
+ align:start position:0%
+interestingly it uh the activation
+ 
+
+ align:start position:0%
+interestingly it uh the activation
+energy for B varies with the process so
+
+ align:start position:0%
+energy for B varies with the process so
+ 
+
+ align:start position:0%
+energy for B varies with the process so
+depending on whether you're in a dry O2
+
+ align:start position:0%
+depending on whether you're in a dry O2
+ 
+
+ align:start position:0%
+depending on whether you're in a dry O2
+here um you get 1 23 uh EV here this is
+
+ align:start position:0%
+here um you get 1 23 uh EV here this is
+ 
+
+ align:start position:0%
+here um you get 1 23 uh EV here this is
+7 EV and for moisture and for water it's
+
+ align:start position:0%
+7 EV and for moisture and for water it's
+ 
+
+ align:start position:0%
+7 EV and for moisture and for water it's
+78 EV so it actually varies with the
+
+ align:start position:0%
+78 EV so it actually varies with the
+ 
+
+ align:start position:0%
+78 EV so it actually varies with the
+process and that makes some sense
+
+ align:start position:0%
+process and that makes some sense
+ 
+
+ align:start position:0%
+process and that makes some sense
+because what did we say B depends on
+
+ align:start position:0%
+because what did we say B depends on
+ 
+
+ align:start position:0%
+because what did we say B depends on
+depends on the diffusion of this species
+
+ align:start position:0%
+depends on the diffusion of this species
+ 
+
+ align:start position:0%
+depends on the diffusion of this species
+through the oxide well a water molecule
+
+ align:start position:0%
+through the oxide well a water molecule
+ 
+
+ align:start position:0%
+through the oxide well a water molecule
+if that's what's diffusing the oxide is
+
+ align:start position:0%
+if that's what's diffusing the oxide is
+ 
+
+ align:start position:0%
+if that's what's diffusing the oxide is
+going to diffuse at a different rate um
+
+ align:start position:0%
+going to diffuse at a different rate um
+ 
+
+ align:start position:0%
+going to diffuse at a different rate um
+or maybe have a different uh
+
+ align:start position:0%
+or maybe have a different uh
+ 
+
+ align:start position:0%
+or maybe have a different uh
+solubility uh than uh water than the um
+
+ align:start position:0%
+solubility uh than uh water than the um
+ 
+
+ align:start position:0%
+solubility uh than uh water than the um
+dry o than just oxygen molecule so we do
+
+ align:start position:0%
+dry o than just oxygen molecule so we do
+ 
+
+ align:start position:0%
+dry o than just oxygen molecule so we do
+see a difference um in the activation
+
+ align:start position:0%
+see a difference um in the activation
+ 
+
+ align:start position:0%
+see a difference um in the activation
+energy for
+
+ align:start position:0%
+energy for
+ 
+
+ align:start position:0%
+energy for
+B and on slide seven you could obviously
+
+ align:start position:0%
+B and on slide seven you could obviously
+ 
+
+ align:start position:0%
+B and on slide seven you could obviously
+you could do this yourself you just sit
+
+ align:start position:0%
+you could do this yourself you just sit
+ 
+
+ align:start position:0%
+you could do this yourself you just sit
+down with those equations and on a semi
+
+ align:start position:0%
+down with those equations and on a semi
+ 
+
+ align:start position:0%
+down with those equations and on a semi
+log plot so this is a log scale on the
+
+ align:start position:0%
+log plot so this is a log scale on the
+ 
+
+ align:start position:0%
+log plot so this is a log scale on the
+y- AIS and this is a one overt or a
+
+ align:start position:0%
+y- AIS and this is a one overt or a
+ 
+
+ align:start position:0%
+y- AIS and this is a one overt or a
+th000 overt this is a standard arenus
+
+ align:start position:0%
+th000 overt this is a standard arenus
+ 
+
+ align:start position:0%
+th000 overt this is a standard arenus
+plot uh that if you you have to make uh
+
+ align:start position:0%
+plot uh that if you you have to make uh
+ 
+
+ align:start position:0%
+plot uh that if you you have to make uh
+so um on a on a semi log plot uh any
+
+ align:start position:0%
+so um on a on a semi log plot uh any
+ 
+
+ align:start position:0%
+so um on a on a semi log plot uh any
+kind of exponential relationship will
+
+ align:start position:0%
+kind of exponential relationship will
+ 
+
+ align:start position:0%
+kind of exponential relationship will
+appear as a straight line right because
+
+ align:start position:0%
+appear as a straight line right because
+ 
+
+ align:start position:0%
+appear as a straight line right because
+it's log paper
+
+ align:start position:0%
+it's log paper
+ 
+
+ align:start position:0%
+it's log paper
+um and these are the different um
+
+ align:start position:0%
+um and these are the different um
+ 
+
+ align:start position:0%
+um and these are the different um
+constants here we are for a water is the
+
+ align:start position:0%
+constants here we are for a water is the
+ 
+
+ align:start position:0%
+constants here we are for a water is the
+B constant um and uh the uh B over a
+
+ align:start position:0%
+B constant um and uh the uh B over a
+ 
+
+ align:start position:0%
+B constant um and uh the uh B over a
+rather and this is the B constant and um
+
+ align:start position:0%
+rather and this is the B constant and um
+ 
+
+ align:start position:0%
+rather and this is the B constant and um
+these are taken these are for 111 so I
+
+ align:start position:0%
+these are taken these are for 111 so I
+ 
+
+ align:start position:0%
+these are taken these are for 111 so I
+just you just literally plot what values
+
+ align:start position:0%
+just you just literally plot what values
+ 
+
+ align:start position:0%
+just you just literally plot what values
+are on the table one thing you see right
+
+ align:start position:0%
+are on the table one thing you see right
+ 
+
+ align:start position:0%
+are on the table one thing you see right
+off the bat just from this plot these
+
+ align:start position:0%
+off the bat just from this plot these
+ 
+
+ align:start position:0%
+off the bat just from this plot these
+two lines on top that are faster that
+
+ align:start position:0%
+two lines on top that are faster that
+ 
+
+ align:start position:0%
+two lines on top that are faster that
+are larger are for uh oxidation in water
+
+ align:start position:0%
+are larger are for uh oxidation in water
+ 
+
+ align:start position:0%
+are larger are for uh oxidation in water
+vapor as opposed to dry so right off the
+
+ align:start position:0%
+vapor as opposed to dry so right off the
+ 
+
+ align:start position:0%
+vapor as opposed to dry so right off the
+bat you know the rate constants are
+
+ align:start position:0%
+bat you know the rate constants are
+ 
+
+ align:start position:0%
+bat you know the rate constants are
+higher for water than dry so if you want
+
+ align:start position:0%
+higher for water than dry so if you want
+ 
+
+ align:start position:0%
+higher for water than dry so if you want
+to grow faster an oxide you would grow
+
+ align:start position:0%
+to grow faster an oxide you would grow
+ 
+
+ align:start position:0%
+to grow faster an oxide you would grow
+it in a in a moisture environment not
+
+ align:start position:0%
+it in a in a moisture environment not
+ 
+
+ align:start position:0%
+it in a in a moisture environment not
+not in dry O2 and that's typically the
+
+ align:start position:0%
+not in dry O2 and that's typically the
+ 
+
+ align:start position:0%
+not in dry O2 and that's typically the
+case people grow thick oxides using a
+
+ align:start position:0%
+case people grow thick oxides using a
+ 
+
+ align:start position:0%
+case people grow thick oxides using a
+wet environment thin oxides using a dry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment okay let's go just uh go on
+
+ align:start position:0%
+environment okay let's go just uh go on
+ 
+
+ align:start position:0%
+environment okay let's go just uh go on
+to slide number eight and and just
+
+ align:start position:0%
+to slide number eight and and just
+ 
+
+ align:start position:0%
+to slide number eight and and just
+reformulate this you can do some
+
+ align:start position:0%
+reformulate this you can do some
+ 
+
+ align:start position:0%
+reformulate this you can do some
+mathematical manipulations on the law
+
+ align:start position:0%
+mathematical manipulations on the law
+ 
+
+ align:start position:0%
+mathematical manipulations on the law
+the linear parabolic law as I showed it
+
+ align:start position:0%
+the linear parabolic law as I showed it
+ 
+
+ align:start position:0%
+the linear parabolic law as I showed it
+earlier I've just repeated that equation
+
+ align:start position:0%
+earlier I've just repeated that equation
+ 
+
+ align:start position:0%
+earlier I've just repeated that equation
+where on the right hand side we've
+
+ align:start position:0%
+where on the right hand side we've
+ 
+
+ align:start position:0%
+where on the right hand side we've
+solved for T the left hand side is the
+
+ align:start position:0%
+solved for T the left hand side is the
+ 
+
+ align:start position:0%
+solved for T the left hand side is the
+oxide
+
+ align:start position:0%
+oxide
+ 
+
+ align:start position:0%
+oxide
+thickness um there are alternate ways to
+
+ align:start position:0%
+thickness um there are alternate ways to
+ 
+
+ align:start position:0%
+thickness um there are alternate ways to
+express this uh this law and and in fact
+
+ align:start position:0%
+express this uh this law and and in fact
+ 
+
+ align:start position:0%
+express this uh this law and and in fact
+here's a reformulation of it shown in
+
+ align:start position:0%
+here's a reformulation of it shown in
+ 
+
+ align:start position:0%
+here's a reformulation of it shown in
+the second um equation on this slide
+
+ align:start position:0%
+the second um equation on this slide
+ 
+
+ align:start position:0%
+the second um equation on this slide
+what you've seen is what we've done is
+
+ align:start position:0%
+what you've seen is what we've done is
+ 
+
+ align:start position:0%
+what you've seen is what we've done is
+now we've expressing it as x^2 over B
+
+ align:start position:0%
+now we've expressing it as x^2 over B
+ 
+
+ align:start position:0%
+now we've expressing it as x^2 over B
+plus xot / B over a is equal to t plus
+
+ align:start position:0%
+plus xot / B over a is equal to t plus
+ 
+
+ align:start position:0%
+plus xot / B over a is equal to t plus
+to where what we've done is to now is
+
+ align:start position:0%
+to where what we've done is to now is
+ 
+
+ align:start position:0%
+to where what we've done is to now is
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+um as the time that it would have taken
+
+ align:start position:0%
+um as the time that it would have taken
+ 
+
+ align:start position:0%
+um as the time that it would have taken
+the effective time to grow the initial
+
+ align:start position:0%
+the effective time to grow the initial
+ 
+
+ align:start position:0%
+the effective time to grow the initial
+oxide thickness X subi so this is just
+
+ align:start position:0%
+oxide thickness X subi so this is just
+ 
+
+ align:start position:0%
+oxide thickness X subi so this is just
+obtained by mathematical manipulation of
+
+ align:start position:0%
+obtained by mathematical manipulation of
+ 
+
+ align:start position:0%
+obtained by mathematical manipulation of
+the first equation so if you set to
+
+ align:start position:0%
+the first equation so if you set to
+ 
+
+ align:start position:0%
+the first equation so if you set to
+equal to x i the initial squar plus a XI
+
+ align:start position:0%
+equal to x i the initial squar plus a XI
+ 
+
+ align:start position:0%
+equal to x i the initial squar plus a XI
+over B just mathematically you do that
+
+ align:start position:0%
+over B just mathematically you do that
+ 
+
+ align:start position:0%
+over B just mathematically you do that
+then you get a mathematical equence of
+
+ align:start position:0%
+then you get a mathematical equence of
+ 
+
+ align:start position:0%
+then you get a mathematical equence of
+this second equation to the first
+
+ align:start position:0%
+this second equation to the first
+ 
+
+ align:start position:0%
+this second equation to the first
+equation um sometimes you also want to
+
+ align:start position:0%
+equation um sometimes you also want to
+ 
+
+ align:start position:0%
+equation um sometimes you also want to
+explicitly have an equation that Sol
+
+ align:start position:0%
+explicitly have an equation that Sol
+ 
+
+ align:start position:0%
+explicitly have an equation that Sol
+that shows you what x knot is the oxide
+
+ align:start position:0%
+that shows you what x knot is the oxide
+ 
+
+ align:start position:0%
+that shows you what x knot is the oxide
+thickness that's not what's shown here
+
+ align:start position:0%
+thickness that's not what's shown here
+ 
+
+ align:start position:0%
+thickness that's not what's shown here
+on the upper two equations X knot is
+
+ align:start position:0%
+on the upper two equations X knot is
+ 
+
+ align:start position:0%
+on the upper two equations X knot is
+implicit because it appears here in two
+
+ align:start position:0%
+implicit because it appears here in two
+ 
+
+ align:start position:0%
+implicit because it appears here in two
+different terms if you want to solve
+
+ align:start position:0%
+different terms if you want to solve
+ 
+
+ align:start position:0%
+different terms if you want to solve
+explicitly for the oxide thickness you
+
+ align:start position:0%
+explicitly for the oxide thickness you
+ 
+
+ align:start position:0%
+explicitly for the oxide thickness you
+can see this middle equation x knot it
+
+ align:start position:0%
+can see this middle equation x knot it
+ 
+
+ align:start position:0%
+can see this middle equation x knot it
+looks like this it's got a square root
+
+ align:start position:0%
+looks like this it's got a square root
+ 
+
+ align:start position:0%
+looks like this it's got a square root
+uh dependence on time um and uh where
+
+ align:start position:0%
+uh dependence on time um and uh where
+ 
+
+ align:start position:0%
+uh dependence on time um and uh where
+again too has the same uh definition xi^
+
+ align:start position:0%
+again too has the same uh definition xi^
+ 
+
+ align:start position:0%
+again too has the same uh definition xi^
+s just the time to grow the initial
+
+ align:start position:0%
+s just the time to grow the initial
+ 
+
+ align:start position:0%
+s just the time to grow the initial
+oxide the effect of time in the deal
+
+ align:start position:0%
+oxide the effect of time in the deal
+ 
+
+ align:start position:0%
+oxide the effect of time in the deal
+Grove model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's go on to slide number nine um
+
+ align:start position:0%
+okay let's go on to slide number nine um
+ 
+
+ align:start position:0%
+okay let's go on to slide number nine um
+and uh again this reformulation I I'm
+
+ align:start position:0%
+and uh again this reformulation I I'm
+ 
+
+ align:start position:0%
+and uh again this reformulation I I'm
+just repeating the equations from the
+
+ align:start position:0%
+just repeating the equations from the
+ 
+
+ align:start position:0%
+just repeating the equations from the
+previous slides so you don't have to
+
+ align:start position:0%
+previous slides so you don't have to
+ 
+
+ align:start position:0%
+previous slides so you don't have to
+remember them uh again XI and and to
+
+ align:start position:0%
+remember them uh again XI and and to
+ 
+
+ align:start position:0%
+remember them uh again XI and and to
+account for any oxide that was present
+
+ align:start position:0%
+account for any oxide that was present
+ 
+
+ align:start position:0%
+account for any oxide that was present
+at the start of the process okay we you
+
+ align:start position:0%
+at the start of the process okay we you
+ 
+
+ align:start position:0%
+at the start of the process okay we you
+know when you first push the wafer in
+
+ align:start position:0%
+know when you first push the wafer in
+ 
+
+ align:start position:0%
+know when you first push the wafer in
+you might have had other processes that
+
+ align:start position:0%
+you might have had other processes that
+ 
+
+ align:start position:0%
+you might have had other processes that
+have taken place and they might already
+
+ align:start position:0%
+have taken place and they might already
+ 
+
+ align:start position:0%
+have taken place and they might already
+have some oxide uh present there
+
+ align:start position:0%
+have some oxide uh present there
+ 
+
+ align:start position:0%
+have some oxide uh present there
+so we can take this uh we can take uh
+
+ align:start position:0%
+so we can take this uh we can take uh
+ 
+
+ align:start position:0%
+so we can take this uh we can take uh
+this equation and differentiate it and
+
+ align:start position:0%
+this equation and differentiate it and
+ 
+
+ align:start position:0%
+this equation and differentiate it and
+and let's say we're interest interested
+
+ align:start position:0%
+and let's say we're interest interested
+ 
+
+ align:start position:0%
+and let's say we're interest interested
+in the oxidation rate not the absolute
+
+ align:start position:0%
+in the oxidation rate not the absolute
+ 
+
+ align:start position:0%
+in the oxidation rate not the absolute
+thickness versus time but how is the
+
+ align:start position:0%
+thickness versus time but how is the
+ 
+
+ align:start position:0%
+thickness versus time but how is the
+rate changing how how fast is it
+
+ align:start position:0%
+rate changing how how fast is it
+ 
+
+ align:start position:0%
+rate changing how how fast is it
+growing um well this is this is the
+
+ align:start position:0%
+growing um well this is this is the
+ 
+
+ align:start position:0%
+growing um well this is this is the
+oxidation rate by differentiating you
+
+ align:start position:0%
+oxidation rate by differentiating you
+ 
+
+ align:start position:0%
+oxidation rate by differentiating you
+can see it's given by B divided by the
+
+ align:start position:0%
+can see it's given by B divided by the
+ 
+
+ align:start position:0%
+can see it's given by B divided by the
+um this quantity 2x knot plus a so this
+
+ align:start position:0%
+um this quantity 2x knot plus a so this
+ 
+
+ align:start position:0%
+um this quantity 2x knot plus a so this
+gives you an idea of of the rate how how
+
+ align:start position:0%
+gives you an idea of of the rate how how
+ 
+
+ align:start position:0%
+gives you an idea of of the rate how how
+rapidly is it
+
+ align:start position:0%
+rapidly is it
+ 
+
+ align:start position:0%
+rapidly is it
+growing so these equations are very
+
+ align:start position:0%
+growing so these equations are very
+ 
+
+ align:start position:0%
+growing so these equations are very
+general and what they describe as the
+
+ align:start position:0%
+general and what they describe as the
+ 
+
+ align:start position:0%
+general and what they describe as the
+growth kinetics for oxidation when
+
+ align:start position:0%
+growth kinetics for oxidation when
+ 
+
+ align:start position:0%
+growth kinetics for oxidation when
+you're in these falling conditions we
+
+ align:start position:0%
+you're in these falling conditions we
+ 
+
+ align:start position:0%
+you're in these falling conditions we
+have to remind ourselves they it only
+
+ align:start position:0%
+have to remind ourselves they it only
+ 
+
+ align:start position:0%
+have to remind ourselves they it only
+applies for certain you know basic case
+
+ align:start position:0%
+applies for certain you know basic case
+ 
+
+ align:start position:0%
+applies for certain you know basic case
+so this means when it's pler oxidation
+
+ align:start position:0%
+so this means when it's pler oxidation
+ 
+
+ align:start position:0%
+so this means when it's pler oxidation
+so I'm just oxidizing a flat surface
+
+ align:start position:0%
+so I'm just oxidizing a flat surface
+ 
+
+ align:start position:0%
+so I'm just oxidizing a flat surface
+we'll talk next time when you have a
+
+ align:start position:0%
+we'll talk next time when you have a
+ 
+
+ align:start position:0%
+we'll talk next time when you have a
+surface that has structure on it the
+
+ align:start position:0%
+surface that has structure on it the
+ 
+
+ align:start position:0%
+surface that has structure on it the
+equations need to be modified um it's
+
+ align:start position:0%
+equations need to be modified um it's
+ 
+
+ align:start position:0%
+equations need to be modified um it's
+planer and it's unpatterned so this is
+
+ align:start position:0%
+planer and it's unpatterned so this is
+ 
+
+ align:start position:0%
+planer and it's unpatterned so this is
+just an unpatterned surface this assumes
+
+ align:start position:0%
+just an unpatterned surface this assumes
+ 
+
+ align:start position:0%
+just an unpatterned surface this assumes
+that the Silicon is lightly doped that
+
+ align:start position:0%
+that the Silicon is lightly doped that
+ 
+
+ align:start position:0%
+that the Silicon is lightly doped that
+you can use these numbers heavily doped
+
+ align:start position:0%
+you can use these numbers heavily doped
+ 
+
+ align:start position:0%
+you can use these numbers heavily doped
+oxidation we'll talk about next time uh
+
+ align:start position:0%
+oxidation we'll talk about next time uh
+ 
+
+ align:start position:0%
+oxidation we'll talk about next time uh
+a simple ambient such as oxygen dry O2
+
+ align:start position:0%
+a simple ambient such as oxygen dry O2
+ 
+
+ align:start position:0%
+a simple ambient such as oxygen dry O2
+or water is is assumed if you're going
+
+ align:start position:0%
+or water is is assumed if you're going
+ 
+
+ align:start position:0%
+or water is is assumed if you're going
+to add other gases nitrous oxide and
+
+ align:start position:0%
+to add other gases nitrous oxide and
+ 
+
+ align:start position:0%
+to add other gases nitrous oxide and
+other things that people do to grow High
+
+ align:start position:0%
+other things that people do to grow High
+ 
+
+ align:start position:0%
+other things that people do to grow High
+K these particular equations don't apply
+
+ align:start position:0%
+K these particular equations don't apply
+ 
+
+ align:start position:0%
+K these particular equations don't apply
+exactly um and when this also these
+
+ align:start position:0%
+exactly um and when this also these
+ 
+
+ align:start position:0%
+exactly um and when this also these
+equations work when the final oxide
+
+ align:start position:0%
+equations work when the final oxide
+ 
+
+ align:start position:0%
+equations work when the final oxide
+thickness is larger than about 20 nmet
+
+ align:start position:0%
+thickness is larger than about 20 nmet
+ 
+
+ align:start position:0%
+thickness is larger than about 20 nmet
+about 200
+
+ align:start position:0%
+about 200
+ 
+
+ align:start position:0%
+about 200
+anrs they work quite well but um uh so
+
+ align:start position:0%
+anrs they work quite well but um uh so
+ 
+
+ align:start position:0%
+anrs they work quite well but um uh so
+that's a certain number of limitations
+
+ align:start position:0%
+that's a certain number of limitations
+ 
+
+ align:start position:0%
+that's a certain number of limitations
+still very useful because what we're
+
+ align:start position:0%
+still very useful because what we're
+ 
+
+ align:start position:0%
+still very useful because what we're
+going to do from here is now make
+
+ align:start position:0%
+going to do from here is now make
+ 
+
+ align:start position:0%
+going to do from here is now make
+Corrections right off the bat though
+
+ align:start position:0%
+Corrections right off the bat though
+ 
+
+ align:start position:0%
+Corrections right off the bat though
+when when you see this 20 nanometer
+
+ align:start position:0%
+when when you see this 20 nanometer
+ 
+
+ align:start position:0%
+when when you see this 20 nanometer
+number what do you think of I mean gate
+
+ align:start position:0%
+number what do you think of I mean gate
+ 
+
+ align:start position:0%
+number what do you think of I mean gate
+oxides today just from you're reading of
+
+ align:start position:0%
+oxides today just from you're reading of
+ 
+
+ align:start position:0%
+oxides today just from you're reading of
+the itrs and high performance devices
+
+ align:start position:0%
+the itrs and high performance devices
+ 
+
+ align:start position:0%
+the itrs and high performance devices
+how what are they are they less than or
+
+ align:start position:0%
+how what are they are they less than or
+ 
+
+ align:start position:0%
+how what are they are they less than or
+or greater than 20
+
+ align:start position:0%
+or greater than 20
+ 
+
+ align:start position:0%
+or greater than 20
+nanometers less than significantly less
+
+ align:start position:0%
+nanometers less than significantly less
+ 
+
+ align:start position:0%
+nanometers less than significantly less
+than for most high performance devices
+
+ align:start position:0%
+than for most high performance devices
+ 
+
+ align:start position:0%
+than for most high performance devices
+so this tells us right off the bat if we
+
+ align:start position:0%
+so this tells us right off the bat if we
+ 
+
+ align:start position:0%
+so this tells us right off the bat if we
+want to use deal Grove to model a
+
+ align:start position:0%
+want to use deal Grove to model a
+ 
+
+ align:start position:0%
+want to use deal Grove to model a
+standard sort of gate oxide thickness
+
+ align:start position:0%
+standard sort of gate oxide thickness
+ 
+
+ align:start position:0%
+standard sort of gate oxide thickness
+that someone might be growing 100
+
+ align:start position:0%
+that someone might be growing 100
+ 
+
+ align:start position:0%
+that someone might be growing 100
+angstroms or less um it's not going to
+
+ align:start position:0%
+angstroms or less um it's not going to
+ 
+
+ align:start position:0%
+angstroms or less um it's not going to
+be perfect
+
+ align:start position:0%
+be perfect
+ 
+
+ align:start position:0%
+be perfect
+we're going to have to make corrections
+
+ align:start position:0%
+we're going to have to make corrections
+ 
+
+ align:start position:0%
+we're going to have to make corrections
+to this and we'll talk today about those
+
+ align:start position:0%
+to this and we'll talk today about those
+ 
+
+ align:start position:0%
+to this and we'll talk today about those
+thin oxid thin oxidation
+
+ align:start position:0%
+thin oxid thin oxidation
+ 
+
+ align:start position:0%
+thin oxid thin oxidation
+models but let's go on to um slide 10
+
+ align:start position:0%
+models but let's go on to um slide 10
+ 
+
+ align:start position:0%
+models but let's go on to um slide 10
+and again just to make a different way
+
+ align:start position:0%
+and again just to make a different way
+ 
+
+ align:start position:0%
+and again just to make a different way
+of of looking at these same equations
+
+ align:start position:0%
+of of looking at these same equations
+ 
+
+ align:start position:0%
+of of looking at these same equations
+I've repeated them um again at the top
+
+ align:start position:0%
+I've repeated them um again at the top
+ 
+
+ align:start position:0%
+I've repeated them um again at the top
+so we don't have to memorize them but
+
+ align:start position:0%
+so we don't have to memorize them but
+ 
+
+ align:start position:0%
+so we don't have to memorize them but
+what we can do now is to take two
+
+ align:start position:0%
+what we can do now is to take two
+ 
+
+ align:start position:0%
+what we can do now is to take two
+limiting
+
+ align:start position:0%
+limiting
+ 
+
+ align:start position:0%
+limiting
+cases one limiting case I'm going to say
+
+ align:start position:0%
+cases one limiting case I'm going to say
+ 
+
+ align:start position:0%
+cases one limiting case I'm going to say
+is when the oxide is relatively thin so
+
+ align:start position:0%
+is when the oxide is relatively thin so
+ 
+
+ align:start position:0%
+is when the oxide is relatively thin so
+X knot uh is relatively small then it
+
+ align:start position:0%
+X knot uh is relatively small then it
+ 
+
+ align:start position:0%
+X knot uh is relatively small then it
+turns out this term here the linear term
+
+ align:start position:0%
+turns out this term here the linear term
+ 
+
+ align:start position:0%
+turns out this term here the linear term
+xot ID B over a um uh is going to
+
+ align:start position:0%
+xot ID B over a um uh is going to
+ 
+
+ align:start position:0%
+xot ID B over a um uh is going to
+dominate over this xnot squar this this
+
+ align:start position:0%
+dominate over this xnot squar this this
+ 
+
+ align:start position:0%
+dominate over this xnot squar this this
+is going to become a smaller term so we
+
+ align:start position:0%
+is going to become a smaller term so we
+ 
+
+ align:start position:0%
+is going to become a smaller term so we
+can ignore this first term and we end up
+
+ align:start position:0%
+can ignore this first term and we end up
+ 
+
+ align:start position:0%
+can ignore this first term and we end up
+that x is proportional to B over a time
+
+ align:start position:0%
+that x is proportional to B over a time
+ 
+
+ align:start position:0%
+that x is proportional to B over a time
+time so it's essentially in thin oxides
+
+ align:start position:0%
+time so it's essentially in thin oxides
+ 
+
+ align:start position:0%
+time so it's essentially in thin oxides
+we have the uh equation is linear in
+
+ align:start position:0%
+we have the uh equation is linear in
+ 
+
+ align:start position:0%
+we have the uh equation is linear in
+time so just um we have a constant
+
+ align:start position:0%
+time so just um we have a constant
+ 
+
+ align:start position:0%
+time so just um we have a constant
+oxidation rate and the thickness just
+
+ align:start position:0%
+oxidation rate and the thickness just
+ 
+
+ align:start position:0%
+oxidation rate and the thickness just
+increases linearly according to this uh
+
+ align:start position:0%
+increases linearly according to this uh
+ 
+
+ align:start position:0%
+increases linearly according to this uh
+deog Grove model for thicker oxides and
+
+ align:start position:0%
+deog Grove model for thicker oxides and
+ 
+
+ align:start position:0%
+deog Grove model for thicker oxides and
+we'll Define later what we mean by
+
+ align:start position:0%
+we'll Define later what we mean by
+ 
+
+ align:start position:0%
+we'll Define later what we mean by
+thicker but at some point this term this
+
+ align:start position:0%
+thicker but at some point this term this
+ 
+
+ align:start position:0%
+thicker but at some point this term this
+x^ squar over B starts to dominate over
+
+ align:start position:0%
+x^ squar over B starts to dominate over
+ 
+
+ align:start position:0%
+x^ squar over B starts to dominate over
+the linear term we can ignore this
+
+ align:start position:0%
+the linear term we can ignore this
+ 
+
+ align:start position:0%
+the linear term we can ignore this
+linear term for long times or very thick
+
+ align:start position:0%
+linear term for long times or very thick
+ 
+
+ align:start position:0%
+linear term for long times or very thick
+oxides it goes like x^ squ is a constant
+
+ align:start position:0%
+oxides it goes like x^ squ is a constant
+ 
+
+ align:start position:0%
+oxides it goes like x^ squ is a constant
+times T so um it's uh basically a
+
+ align:start position:0%
+times T so um it's uh basically a
+ 
+
+ align:start position:0%
+times T so um it's uh basically a
+parabolic uh term so the oxide thickness
+
+ align:start position:0%
+parabolic uh term so the oxide thickness
+ 
+
+ align:start position:0%
+parabolic uh term so the oxide thickness
+starts uh increasing like the square
+
+ align:start position:0%
+starts uh increasing like the square
+ 
+
+ align:start position:0%
+starts uh increasing like the square
+root of time so initially it's going up
+
+ align:start position:0%
+root of time so initially it's going up
+ 
+
+ align:start position:0%
+root of time so initially it's going up
+linearly and then when it becomes thick
+
+ align:start position:0%
+linearly and then when it becomes thick
+ 
+
+ align:start position:0%
+linearly and then when it becomes thick
+enough starts increasing more like a
+
+ align:start position:0%
+enough starts increasing more like a
+ 
+
+ align:start position:0%
+enough starts increasing more like a
+square root kind of function um and that
+
+ align:start position:0%
+square root kind of function um and that
+ 
+
+ align:start position:0%
+square root kind of function um and that
+point you know it's thick enough that
+
+ align:start position:0%
+point you know it's thick enough that
+ 
+
+ align:start position:0%
+point you know it's thick enough that
+diffusion through the oxide is really
+
+ align:start position:0%
+diffusion through the oxide is really
+ 
+
+ align:start position:0%
+diffusion through the oxide is really
+starting to limit you um mathematically
+
+ align:start position:0%
+starting to limit you um mathematically
+ 
+
+ align:start position:0%
+starting to limit you um mathematically
+if you want to see this if you prefer to
+
+ align:start position:0%
+if you want to see this if you prefer to
+ 
+
+ align:start position:0%
+if you want to see this if you prefer to
+think mathematically you're going to
+
+ align:start position:0%
+think mathematically you're going to
+ 
+
+ align:start position:0%
+think mathematically you're going to
+make yourself a plot this is a actually
+
+ align:start position:0%
+make yourself a plot this is a actually
+ 
+
+ align:start position:0%
+make yourself a plot this is a actually
+a log scale a log log plot log on the Y
+
+ align:start position:0%
+a log scale a log log plot log on the Y
+ 
+
+ align:start position:0%
+a log scale a log log plot log on the Y
+log on the X and it's kind of normalized
+
+ align:start position:0%
+log on the X and it's kind of normalized
+ 
+
+ align:start position:0%
+log on the X and it's kind of normalized
+what it's a plot of is X notot ided a
+
+ align:start position:0%
+what it's a plot of is X notot ided a
+ 
+
+ align:start position:0%
+what it's a plot of is X notot ided a
+over2 so we' sort of normalized uh the
+
+ align:start position:0%
+over2 so we' sort of normalized uh the
+ 
+
+ align:start position:0%
+over2 so we' sort of normalized uh the
+um uh the the Y AIS and t plus to ided
+
+ align:start position:0%
+um uh the the Y AIS and t plus to ided
+ 
+
+ align:start position:0%
+um uh the the Y AIS and t plus to ided
+by this constant a^2 over 4B to make it
+
+ align:start position:0%
+by this constant a^2 over 4B to make it
+ 
+
+ align:start position:0%
+by this constant a^2 over 4B to make it
+in in unitless and what you see this
+
+ align:start position:0%
+in in unitless and what you see this
+ 
+
+ align:start position:0%
+in in unitless and what you see this
+solid line
+
+ align:start position:0%
+solid line
+ 
+
+ align:start position:0%
+solid line
+here is uh equal to a plot of xot 2 plus
+
+ align:start position:0%
+here is uh equal to a plot of xot 2 plus
+ 
+
+ align:start position:0%
+here is uh equal to a plot of xot 2 plus
+a x KN = B * T * t plus T so that's the
+
+ align:start position:0%
+a x KN = B * T * t plus T so that's the
+ 
+
+ align:start position:0%
+a x KN = B * T * t plus T so that's the
+exact deal grow model at short time you
+
+ align:start position:0%
+exact deal grow model at short time you
+ 
+
+ align:start position:0%
+exact deal grow model at short time you
+can see it it approaches uh or low
+
+ align:start position:0%
+can see it it approaches uh or low
+ 
+
+ align:start position:0%
+can see it it approaches uh or low
+thicknesses it approaches this linear uh
+
+ align:start position:0%
+thicknesses it approaches this linear uh
+ 
+
+ align:start position:0%
+thicknesses it approaches this linear uh
+rate constant this linear uh equation
+
+ align:start position:0%
+rate constant this linear uh equation
+ 
+
+ align:start position:0%
+rate constant this linear uh equation
+remember on on a semi log plot this has
+
+ align:start position:0%
+remember on on a semi log plot this has
+ 
+
+ align:start position:0%
+remember on on a semi log plot this has
+a certain slope uh and then it has for
+
+ align:start position:0%
+a certain slope uh and then it has for
+ 
+
+ align:start position:0%
+a certain slope uh and then it has for
+longer timeses much longer higher
+
+ align:start position:0%
+longer timeses much longer higher
+ 
+
+ align:start position:0%
+longer timeses much longer higher
+thicknesses it approaches a straight
+
+ align:start position:0%
+thicknesses it approaches a straight
+ 
+
+ align:start position:0%
+thicknesses it approaches a straight
+line This dash line that has half the
+
+ align:start position:0%
+line This dash line that has half the
+ 
+
+ align:start position:0%
+line This dash line that has half the
+slope again linear here versus square
+
+ align:start position:0%
+slope again linear here versus square
+ 
+
+ align:start position:0%
+slope again linear here versus square
+root has half the
+
+ align:start position:0%
+root has half the
+ 
+
+ align:start position:0%
+root has half the
+slope different way of looking at it I
+
+ align:start position:0%
+slope different way of looking at it I
+ 
+
+ align:start position:0%
+slope different way of looking at it I
+actually like you to think a little more
+
+ align:start position:0%
+actually like you to think a little more
+ 
+
+ align:start position:0%
+actually like you to think a little more
+physically not just look at the
+
+ align:start position:0%
+physically not just look at the
+ 
+
+ align:start position:0%
+physically not just look at the
+equations and say which term is big and
+
+ align:start position:0%
+equations and say which term is big and
+ 
+
+ align:start position:0%
+equations and say which term is big and
+which is small in fact it's much easier
+
+ align:start position:0%
+which is small in fact it's much easier
+ 
+
+ align:start position:0%
+which is small in fact it's much easier
+to remember to limiting cases in a
+
+ align:start position:0%
+to remember to limiting cases in a
+ 
+
+ align:start position:0%
+to remember to limiting cases in a
+physical sense uh and that's what's
+
+ align:start position:0%
+physical sense uh and that's what's
+ 
+
+ align:start position:0%
+physical sense uh and that's what's
+being uh shown on slide 11 so if you
+
+ align:start position:0%
+being uh shown on slide 11 so if you
+ 
+
+ align:start position:0%
+being uh shown on slide 11 so if you
+look at the case of a thin oxide it's
+
+ align:start position:0%
+look at the case of a thin oxide it's
+ 
+
+ align:start position:0%
+look at the case of a thin oxide it's
+it's relatively thin what's happening is
+
+ align:start position:0%
+it's relatively thin what's happening is
+ 
+
+ align:start position:0%
+it's relatively thin what's happening is
+is physically is diffusion this is so
+
+ align:start position:0%
+is physically is diffusion this is so
+ 
+
+ align:start position:0%
+is physically is diffusion this is so
+thin the diffusion process happens very
+
+ align:start position:0%
+thin the diffusion process happens very
+ 
+
+ align:start position:0%
+thin the diffusion process happens very
+rapidly compared to the rate at which
+
+ align:start position:0%
+rapidly compared to the rate at which
+ 
+
+ align:start position:0%
+rapidly compared to the rate at which
+those Mo those atoms can react at the
+
+ align:start position:0%
+those Mo those atoms can react at the
+ 
+
+ align:start position:0%
+those Mo those atoms can react at the
+surface so when it's thin the surface
+
+ align:start position:0%
+surface so when it's thin the surface
+ 
+
+ align:start position:0%
+surface so when it's thin the surface
+reaction is what limits it's the slowest
+
+ align:start position:0%
+reaction is what limits it's the slowest
+ 
+
+ align:start position:0%
+reaction is what limits it's the slowest
+uh step any of these serial processes
+
+ align:start position:0%
+uh step any of these serial processes
+ 
+
+ align:start position:0%
+uh step any of these serial processes
+always end up being limited by the rate
+
+ align:start position:0%
+always end up being limited by the rate
+ 
+
+ align:start position:0%
+always end up being limited by the rate
+limiting step is the slowest step so
+
+ align:start position:0%
+limiting step is the slowest step so
+ 
+
+ align:start position:0%
+limiting step is the slowest step so
+clearly when you're thin getting through
+
+ align:start position:0%
+clearly when you're thin getting through
+ 
+
+ align:start position:0%
+clearly when you're thin getting through
+the oxide takes no time at all uh what's
+
+ align:start position:0%
+the oxide takes no time at all uh what's
+ 
+
+ align:start position:0%
+the oxide takes no time at all uh what's
+limiting you is the rate at which you
+
+ align:start position:0%
+limiting you is the rate at which you
+ 
+
+ align:start position:0%
+limiting you is the rate at which you
+can react um and we know that is um a
+
+ align:start position:0%
+can react um and we know that is um a
+ 
+
+ align:start position:0%
+can react um and we know that is um a
+linear process just depends on K
+
+ align:start position:0%
+linear process just depends on K
+ 
+
+ align:start position:0%
+linear process just depends on K
+Subs okay now let's say when you're
+
+ align:start position:0%
+Subs okay now let's say when you're
+ 
+
+ align:start position:0%
+Subs okay now let's say when you're
+thick if you have a thick oxide well
+
+ align:start position:0%
+thick if you have a thick oxide well
+ 
+
+ align:start position:0%
+thick if you have a thick oxide well
+then it the diffusion process is what's
+
+ align:start position:0%
+then it the diffusion process is what's
+ 
+
+ align:start position:0%
+then it the diffusion process is what's
+rate limiting you uh the reaction uh at
+
+ align:start position:0%
+rate limiting you uh the reaction uh at
+ 
+
+ align:start position:0%
+rate limiting you uh the reaction uh at
+the surface can be relatively fast
+
+ align:start position:0%
+the surface can be relatively fast
+ 
+
+ align:start position:0%
+the surface can be relatively fast
+compared to the diffusion rate um so
+
+ align:start position:0%
+compared to the diffusion rate um so
+ 
+
+ align:start position:0%
+compared to the diffusion rate um so
+diffuses rate limit and that process uh
+
+ align:start position:0%
+diffuses rate limit and that process uh
+ 
+
+ align:start position:0%
+diffuses rate limit and that process uh
+ends up depending uh on on a square has
+
+ align:start position:0%
+ends up depending uh on on a square has
+ 
+
+ align:start position:0%
+ends up depending uh on on a square has
+a square root type uh dependence on time
+
+ align:start position:0%
+a square root type uh dependence on time
+ 
+
+ align:start position:0%
+a square root type uh dependence on time
+um so uh in in uh in both cases though
+
+ align:start position:0%
+um so uh in in uh in both cases though
+ 
+
+ align:start position:0%
+um so uh in in uh in both cases though
+and just for these these little diagrams
+
+ align:start position:0%
+and just for these these little diagrams
+ 
+
+ align:start position:0%
+and just for these these little diagrams
+I drew C star Remember is the solubility
+
+ align:start position:0%
+I drew C star Remember is the solubility
+ 
+
+ align:start position:0%
+I drew C star Remember is the solubility
+of the oxidant and the oxide so in the
+
+ align:start position:0%
+of the oxidant and the oxide so in the
+ 
+
+ align:start position:0%
+of the oxidant and the oxide so in the
+thin case you diffuse very rapidly
+
+ align:start position:0%
+thin case you diffuse very rapidly
+ 
+
+ align:start position:0%
+thin case you diffuse very rapidly
+through you have almost uh no gradient
+
+ align:start position:0%
+through you have almost uh no gradient
+ 
+
+ align:start position:0%
+through you have almost uh no gradient
+uh in in in the oxide you're getting
+
+ align:start position:0%
+uh in in in the oxide you're getting
+ 
+
+ align:start position:0%
+uh in in in the oxide you're getting
+through very rapidly just by virtue of
+
+ align:start position:0%
+through very rapidly just by virtue of
+ 
+
+ align:start position:0%
+through very rapidly just by virtue of
+it so thin in a thick Case C star is a
+
+ align:start position:0%
+it so thin in a thick Case C star is a
+ 
+
+ align:start position:0%
+it so thin in a thick Case C star is a
+solubility that's what you have at the
+
+ align:start position:0%
+solubility that's what you have at the
+ 
+
+ align:start position:0%
+solubility that's what you have at the
+surface um at the interface it's almost
+
+ align:start position:0%
+surface um at the interface it's almost
+ 
+
+ align:start position:0%
+surface um at the interface it's almost
+going to zero because again you're rate
+
+ align:start position:0%
+going to zero because again you're rate
+ 
+
+ align:start position:0%
+going to zero because again you're rate
+limited by the rate of of diffusion you
+
+ align:start position:0%
+limited by the rate of of diffusion you
+ 
+
+ align:start position:0%
+limited by the rate of of diffusion you
+have a large gradient so this this uh
+
+ align:start position:0%
+have a large gradient so this this uh
+ 
+
+ align:start position:0%
+have a large gradient so this this uh
+flux through the oxide is being driven
+
+ align:start position:0%
+flux through the oxide is being driven
+ 
+
+ align:start position:0%
+flux through the oxide is being driven
+by this this
+
+ align:start position:0%
+by this this
+ 
+
+ align:start position:0%
+by this this
+gradient so those are the two limiting
+
+ align:start position:0%
+gradient so those are the two limiting
+ 
+
+ align:start position:0%
+gradient so those are the two limiting
+cases one depends on diffusion the other
+
+ align:start position:0%
+cases one depends on diffusion the other
+ 
+
+ align:start position:0%
+cases one depends on diffusion the other
+is limited by surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction uh slide 12 was just a little
+
+ align:start position:0%
+reaction uh slide 12 was just a little
+ 
+
+ align:start position:0%
+reaction uh slide 12 was just a little
+example of if if you're an
+
+ align:start position:0%
+example of if if you're an
+ 
+
+ align:start position:0%
+example of if if you're an
+experimentalist how do you sit down and
+
+ align:start position:0%
+experimentalist how do you sit down and
+ 
+
+ align:start position:0%
+experimentalist how do you sit down and
+how do people in the old days used to do
+
+ align:start position:0%
+how do people in the old days used to do
+ 
+
+ align:start position:0%
+how do people in the old days used to do
+this well it's pretty simple
+
+ align:start position:0%
+this well it's pretty simple
+ 
+
+ align:start position:0%
+this well it's pretty simple
+experimentally you just do uh oxidize a
+
+ align:start position:0%
+experimentally you just do uh oxidize a
+ 
+
+ align:start position:0%
+experimentally you just do uh oxidize a
+bunch of uh Wafers the same temperature
+
+ align:start position:0%
+bunch of uh Wafers the same temperature
+ 
+
+ align:start position:0%
+bunch of uh Wafers the same temperature
+for different times and you plot the
+
+ align:start position:0%
+for different times and you plot the
+ 
+
+ align:start position:0%
+for different times and you plot the
+oxide thickness is measured versus time
+
+ align:start position:0%
+oxide thickness is measured versus time
+ 
+
+ align:start position:0%
+oxide thickness is measured versus time
+you'll see this linear dependence at
+
+ align:start position:0%
+you'll see this linear dependence at
+ 
+
+ align:start position:0%
+you'll see this linear dependence at
+first and then it'll start to bend over
+
+ align:start position:0%
+first and then it'll start to bend over
+ 
+
+ align:start position:0%
+first and then it'll start to bend over
+where it's square root easy way to do it
+
+ align:start position:0%
+where it's square root easy way to do it
+ 
+
+ align:start position:0%
+where it's square root easy way to do it
+is to plot X um instead X notot instead
+
+ align:start position:0%
+is to plot X um instead X notot instead
+ 
+
+ align:start position:0%
+is to plot X um instead X notot instead
+of as a function of time but T time
+
+ align:start position:0%
+of as a function of time but T time
+ 
+
+ align:start position:0%
+of as a function of time but T time
+divided by X knot and you'll find out
+
+ align:start position:0%
+divided by X knot and you'll find out
+ 
+
+ align:start position:0%
+divided by X knot and you'll find out
+that the slope if you if you just
+
+ align:start position:0%
+that the slope if you if you just
+ 
+
+ align:start position:0%
+that the slope if you if you just
+manipulate those simple linear equations
+
+ align:start position:0%
+manipulate those simple linear equations
+ 
+
+ align:start position:0%
+manipulate those simple linear equations
+the slope is the parameter B and the Y
+
+ align:start position:0%
+the slope is the parameter B and the Y
+ 
+
+ align:start position:0%
+the slope is the parameter B and the Y
+intercept is the parameter minus a so
+
+ align:start position:0%
+intercept is the parameter minus a so
+ 
+
+ align:start position:0%
+intercept is the parameter minus a so
+for the D gr model it's very simple
+
+ align:start position:0%
+for the D gr model it's very simple
+ 
+
+ align:start position:0%
+for the D gr model it's very simple
+experimentally if you do this kind of
+
+ align:start position:0%
+experimentally if you do this kind of
+ 
+
+ align:start position:0%
+experimentally if you do this kind of
+plot uh to extract those two
+
+ align:start position:0%
+plot uh to extract those two
+ 
+
+ align:start position:0%
+plot uh to extract those two
+parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are some actual um calculations of
+
+ align:start position:0%
+these are some actual um calculations of
+ 
+
+ align:start position:0%
+these are some actual um calculations of
+the oxidation rates in dry on on slide
+
+ align:start position:0%
+the oxidation rates in dry on on slide
+ 
+
+ align:start position:0%
+the oxidation rates in dry on on slide
+13 in dry oxygen using the deal Grove
+
+ align:start position:0%
+13 in dry oxygen using the deal Grove
+ 
+
+ align:start position:0%
+13 in dry oxygen using the deal Grove
+model um this is for 10 silicon now so
+
+ align:start position:0%
+model um this is for 10 silicon now so
+ 
+
+ align:start position:0%
+model um this is for 10 silicon now so
+10 silicon is much more likely what
+
+ align:start position:0%
+10 silicon is much more likely what
+ 
+
+ align:start position:0%
+10 silicon is much more likely what
+you're going to be using in a silicon uh
+
+ align:start position:0%
+you're going to be using in a silicon uh
+ 
+
+ align:start position:0%
+you're going to be using in a silicon uh
+silicon manufacturing process or
+
+ align:start position:0%
+silicon manufacturing process or
+ 
+
+ align:start position:0%
+silicon manufacturing process or
+probably in your research so it's a plot
+
+ align:start position:0%
+probably in your research so it's a plot
+ 
+
+ align:start position:0%
+probably in your research so it's a plot
+on the left axis linear scale of oxide
+
+ align:start position:0%
+on the left axis linear scale of oxide
+ 
+
+ align:start position:0%
+on the left axis linear scale of oxide
+thickness as a function of time uh and
+
+ align:start position:0%
+thickness as a function of time uh and
+ 
+
+ align:start position:0%
+thickness as a function of time uh and
+what you do see is um a linear regime
+
+ align:start position:0%
+what you do see is um a linear regime
+ 
+
+ align:start position:0%
+what you do see is um a linear regime
+here say uh for thin when you're at thin
+
+ align:start position:0%
+here say uh for thin when you're at thin
+ 
+
+ align:start position:0%
+here say uh for thin when you're at thin
+oxides say below um below 0.1 microns or
+
+ align:start position:0%
+oxides say below um below 0.1 microns or
+ 
+
+ align:start position:0%
+oxides say below um below 0.1 microns or
+maybe half of that 500 angstroms the
+
+ align:start position:0%
+maybe half of that 500 angstroms the
+ 
+
+ align:start position:0%
+maybe half of that 500 angstroms the
+lines look quite linear uh and then you
+
+ align:start position:0%
+lines look quite linear uh and then you
+ 
+
+ align:start position:0%
+lines look quite linear uh and then you
+start they start bending over so they're
+
+ align:start position:0%
+start they start bending over so they're
+ 
+
+ align:start position:0%
+start they start bending over so they're
+followed by this sort of parabolic
+
+ align:start position:0%
+followed by this sort of parabolic
+ 
+
+ align:start position:0%
+followed by this sort of parabolic
+behavior uh where they they grow less
+
+ align:start position:0%
+behavior uh where they they grow less
+ 
+
+ align:start position:0%
+behavior uh where they they grow less
+rapidly and you can also see look at the
+
+ align:start position:0%
+rapidly and you can also see look at the
+ 
+
+ align:start position:0%
+rapidly and you can also see look at the
+thicknesses uh as we mentioned before
+
+ align:start position:0%
+thicknesses uh as we mentioned before
+ 
+
+ align:start position:0%
+thicknesses uh as we mentioned before
+dry oxides even at high temperatures of
+
+ align:start position:0%
+dry oxides even at high temperatures of
+ 
+
+ align:start position:0%
+dry oxides even at high temperatures of
+1100 which is quite high for a furnace
+
+ align:start position:0%
+1100 which is quite high for a furnace
+ 
+
+ align:start position:0%
+1100 which is quite high for a furnace
+um you're really limited for practical
+
+ align:start position:0%
+um you're really limited for practical
+ 
+
+ align:start position:0%
+um you're really limited for practical
+times you don't want to be leaving the
+
+ align:start position:0%
+times you don't want to be leaving the
+ 
+
+ align:start position:0%
+times you don't want to be leaving the
+wafers in there any more than a few
+
+ align:start position:0%
+wafers in there any more than a few
+ 
+
+ align:start position:0%
+wafers in there any more than a few
+hours 4 hours 6 hours whatever you're
+
+ align:start position:0%
+hours 4 hours 6 hours whatever you're
+ 
+
+ align:start position:0%
+hours 4 hours 6 hours whatever you're
+limited to things on the order of uh a
+
+ align:start position:0%
+limited to things on the order of uh a
+ 
+
+ align:start position:0%
+limited to things on the order of uh a
+thousand 2,000 angstroms would from a
+
+ align:start position:0%
+thousand 2,000 angstroms would from a
+ 
+
+ align:start position:0%
+thousand 2,000 angstroms would from a
+practical point of view where people
+
+ align:start position:0%
+practical point of view where people
+ 
+
+ align:start position:0%
+practical point of view where people
+grow dry oxides um of course you could
+
+ align:start position:0%
+grow dry oxides um of course you could
+ 
+
+ align:start position:0%
+grow dry oxides um of course you could
+leave it in the furnace for days but
+
+ align:start position:0%
+leave it in the furnace for days but
+ 
+
+ align:start position:0%
+leave it in the furnace for days but
+that is not very economical in terms of
+
+ align:start position:0%
+that is not very economical in terms of
+ 
+
+ align:start position:0%
+that is not very economical in terms of
+use of the furnace use of electricity
+
+ align:start position:0%
+use of the furnace use of electricity
+ 
+
+ align:start position:0%
+use of the furnace use of electricity
+and all the resources so if you want to
+
+ align:start position:0%
+and all the resources so if you want to
+ 
+
+ align:start position:0%
+and all the resources so if you want to
+to grow an oxide in this thickness range
+
+ align:start position:0%
+to grow an oxide in this thickness range
+ 
+
+ align:start position:0%
+to grow an oxide in this thickness range
+you use a dry oxide if you want to go
+
+ align:start position:0%
+you use a dry oxide if you want to go
+ 
+
+ align:start position:0%
+you use a dry oxide if you want to go
+well above that you should be going to
+
+ align:start position:0%
+well above that you should be going to
+ 
+
+ align:start position:0%
+well above that you should be going to
+wet oxidation because the oxidation rate
+
+ align:start position:0%
+wet oxidation because the oxidation rate
+ 
+
+ align:start position:0%
+wet oxidation because the oxidation rate
+constant are so much
+
+ align:start position:0%
+constant are so much
+ 
+
+ align:start position:0%
+constant are so much
+higher in fact on the next slide slide
+
+ align:start position:0%
+higher in fact on the next slide slide
+ 
+
+ align:start position:0%
+higher in fact on the next slide slide
+14 you can see the oxidation rate const
+
+ align:start position:0%
+14 you can see the oxidation rate const
+ 
+
+ align:start position:0%
+14 you can see the oxidation rate const
+of the oxidation uh for oxide thickness
+
+ align:start position:0%
+of the oxidation uh for oxide thickness
+ 
+
+ align:start position:0%
+of the oxidation uh for oxide thickness
+versus time for wet uh ambient for
+
+ align:start position:0%
+versus time for wet uh ambient for
+ 
+
+ align:start position:0%
+versus time for wet uh ambient for
+moisture ambient using deal Grove and
+
+ align:start position:0%
+moisture ambient using deal Grove and
+ 
+
+ align:start position:0%
+moisture ambient using deal Grove and
+now look at the time of say two or three
+
+ align:start position:0%
+now look at the time of say two or three
+ 
+
+ align:start position:0%
+now look at the time of say two or three
+hours um instead of growing a thousand
+
+ align:start position:0%
+hours um instead of growing a thousand
+ 
+
+ align:start position:0%
+hours um instead of growing a thousand
+angstroms um or so at 1100 degrees
+
+ align:start position:0%
+angstroms um or so at 1100 degrees
+ 
+
+ align:start position:0%
+angstroms um or so at 1100 degrees
+you're growing
+
+ align:start position:0%
+you're growing
+ 
+
+ align:start position:0%
+you're growing
+Micron um here after about 2 hours at
+
+ align:start position:0%
+Micron um here after about 2 hours at
+ 
+
+ align:start position:0%
+Micron um here after about 2 hours at
+1100° in wet uh wet ambient about a
+
+ align:start position:0%
+1100° in wet uh wet ambient about a
+ 
+
+ align:start position:0%
+1100° in wet uh wet ambient about a
+micron so uh much faster than dry
+
+ align:start position:0%
+micron so uh much faster than dry
+ 
+
+ align:start position:0%
+micron so uh much faster than dry
+oxidation or is a magnitude
+
+ align:start position:0%
+oxidation or is a magnitude
+ 
+
+ align:start position:0%
+oxidation or is a magnitude
+faster uh and the reason as it turns out
+
+ align:start position:0%
+faster uh and the reason as it turns out
+ 
+
+ align:start position:0%
+faster uh and the reason as it turns out
+the physical reason why is that the
+
+ align:start position:0%
+the physical reason why is that the
+ 
+
+ align:start position:0%
+the physical reason why is that the
+solubility C star uh of water vapor is
+
+ align:start position:0%
+solubility C star uh of water vapor is
+ 
+
+ align:start position:0%
+solubility C star uh of water vapor is
+much higher uh than the solubility of
+
+ align:start position:0%
+much higher uh than the solubility of
+ 
+
+ align:start position:0%
+much higher uh than the solubility of
+oxygen of the oxygen molecule uh for
+
+ align:start position:0%
+oxygen of the oxygen molecule uh for
+ 
+
+ align:start position:0%
+oxygen of the oxygen molecule uh for
+various reasons just because of the
+
+ align:start position:0%
+various reasons just because of the
+ 
+
+ align:start position:0%
+various reasons just because of the
+configuration of the molecule and the
+
+ align:start position:0%
+configuration of the molecule and the
+ 
+
+ align:start position:0%
+configuration of the molecule and the
+size of the interstitial spaces water
+
+ align:start position:0%
+size of the interstitial spaces water
+ 
+
+ align:start position:0%
+size of the interstitial spaces water
+vapor is just easier to get in there um
+
+ align:start position:0%
+vapor is just easier to get in there um
+ 
+
+ align:start position:0%
+vapor is just easier to get in there um
+so it has a much higher solubility so
+
+ align:start position:0%
+so it has a much higher solubility so
+ 
+
+ align:start position:0%
+so it has a much higher solubility so
+that whole um concentration can be
+
+ align:start position:0%
+that whole um concentration can be
+ 
+
+ align:start position:0%
+that whole um concentration can be
+elevated and you can oxidize it at a
+
+ align:start position:0%
+elevated and you can oxidize it at a
+ 
+
+ align:start position:0%
+elevated and you can oxidize it at a
+much faster rate so you need a thick
+
+ align:start position:0%
+much faster rate so you need a thick
+ 
+
+ align:start position:0%
+much faster rate so you need a thick
+oxide you use Mo uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moisture Yeah question real all of the
+
+ align:start position:0%
+moisture Yeah question real all of the
+ 
+
+ align:start position:0%
+moisture Yeah question real all of the
+all of the side um
+
+ align:start position:0%
+all of the side um
+ 
+
+ align:start position:0%
+all of the side um
+doesn't it uh okay so the question is is
+
+ align:start position:0%
+doesn't it uh okay so the question is is
+ 
+
+ align:start position:0%
+doesn't it uh okay so the question is is
+is going back to let's say um slide uh
+
+ align:start position:0%
+is going back to let's say um slide uh
+ 
+
+ align:start position:0%
+is going back to let's say um slide uh
+11 uh maybe of these limiting cases what
+
+ align:start position:0%
+11 uh maybe of these limiting cases what
+ 
+
+ align:start position:0%
+11 uh maybe of these limiting cases what
+happens in in a real case uh if you have
+
+ align:start position:0%
+happens in in a real case uh if you have
+ 
+
+ align:start position:0%
+happens in in a real case uh if you have
+an oxident diffusing through the oxide
+
+ align:start position:0%
+an oxident diffusing through the oxide
+ 
+
+ align:start position:0%
+an oxident diffusing through the oxide
+and uh does it all react is there any
+
+ align:start position:0%
+and uh does it all react is there any
+ 
+
+ align:start position:0%
+and uh does it all react is there any
+unreacted uh species at the interface uh
+
+ align:start position:0%
+unreacted uh species at the interface uh
+ 
+
+ align:start position:0%
+unreacted uh species at the interface uh
+basically it does have to react now uh
+
+ align:start position:0%
+basically it does have to react now uh
+ 
+
+ align:start position:0%
+basically it does have to react now uh
+um and then if if the reaction rate is
+
+ align:start position:0%
+um and then if if the reaction rate is
+ 
+
+ align:start position:0%
+um and then if if the reaction rate is
+what's limiting you um then uh then
+
+ align:start position:0%
+what's limiting you um then uh then
+ 
+
+ align:start position:0%
+what's limiting you um then uh then
+you're you're sort of in this regime but
+
+ align:start position:0%
+you're you're sort of in this regime but
+ 
+
+ align:start position:0%
+you're you're sort of in this regime but
+there can there will be a certain amount
+
+ align:start position:0%
+there can there will be a certain amount
+ 
+
+ align:start position:0%
+there can there will be a certain amount
+of oxidant that doesn't react um and
+
+ align:start position:0%
+of oxidant that doesn't react um and
+ 
+
+ align:start position:0%
+of oxidant that doesn't react um and
+that can lead to uh perhaps excess uh
+
+ align:start position:0%
+that can lead to uh perhaps excess uh
+ 
+
+ align:start position:0%
+that can lead to uh perhaps excess uh
+charges and things like that some of the
+
+ align:start position:0%
+charges and things like that some of the
+ 
+
+ align:start position:0%
+charges and things like that some of the
+more realistic as aspects of the ox
+
+ align:start position:0%
+more realistic as aspects of the ox
+ 
+
+ align:start position:0%
+more realistic as aspects of the ox
+oxidation process that you're left over
+
+ align:start position:0%
+oxidation process that you're left over
+ 
+
+ align:start position:0%
+oxidation process that you're left over
+so it can affect the um uh the quality
+
+ align:start position:0%
+so it can affect the um uh the quality
+ 
+
+ align:start position:0%
+so it can affect the um uh the quality
+oxide to a certain extent and what you
+
+ align:start position:0%
+oxide to a certain extent and what you
+ 
+
+ align:start position:0%
+oxide to a certain extent and what you
+generally find is that wet oxides uh you
+
+ align:start position:0%
+generally find is that wet oxides uh you
+ 
+
+ align:start position:0%
+generally find is that wet oxides uh you
+don't see a whole lot of people growing
+
+ align:start position:0%
+don't see a whole lot of people growing
+ 
+
+ align:start position:0%
+don't see a whole lot of people growing
+gate oxides by wet well because they
+
+ align:start position:0%
+gate oxides by wet well because they
+ 
+
+ align:start position:0%
+gate oxides by wet well because they
+want thinner but even in the old days
+
+ align:start position:0%
+want thinner but even in the old days
+ 
+
+ align:start position:0%
+want thinner but even in the old days
+when a gate oxide was thicker uh 500
+
+ align:start position:0%
+when a gate oxide was thicker uh 500
+ 
+
+ align:start position:0%
+when a gate oxide was thicker uh 500
+anrs or whatever he didn't see people
+
+ align:start position:0%
+anrs or whatever he didn't see people
+ 
+
+ align:start position:0%
+anrs or whatever he didn't see people
+growing them in a wet ambient uh and the
+
+ align:start position:0%
+growing them in a wet ambient uh and the
+ 
+
+ align:start position:0%
+growing them in a wet ambient uh and the
+oxidation ratees a lot faster the
+
+ align:start position:0%
+oxidation ratees a lot faster the
+ 
+
+ align:start position:0%
+oxidation ratees a lot faster the
+quality of the oxide the the number of
+
+ align:start position:0%
+quality of the oxide the the number of
+ 
+
+ align:start position:0%
+quality of the oxide the the number of
+interface States and things like that
+
+ align:start position:0%
+interface States and things like that
+ 
+
+ align:start position:0%
+interface States and things like that
+tends to to be higher for a wet oxide um
+
+ align:start position:0%
+tends to to be higher for a wet oxide um
+ 
+
+ align:start position:0%
+tends to to be higher for a wet oxide um
+so uh typically um what you do if you're
+
+ align:start position:0%
+so uh typically um what you do if you're
+ 
+
+ align:start position:0%
+so uh typically um what you do if you're
+trying to grow a gate oxide is you grow
+
+ align:start position:0%
+trying to grow a gate oxide is you grow
+ 
+
+ align:start position:0%
+trying to grow a gate oxide is you grow
+it dry or if you want to make it um
+
+ align:start position:0%
+it dry or if you want to make it um
+ 
+
+ align:start position:0%
+it dry or if you want to make it um
+thick and you have practical limitations
+
+ align:start position:0%
+thick and you have practical limitations
+ 
+
+ align:start position:0%
+thick and you have practical limitations
+you go a dry step a wet step and then a
+
+ align:start position:0%
+you go a dry step a wet step and then a
+ 
+
+ align:start position:0%
+you go a dry step a wet step and then a
+dry Step at the end so the interface was
+
+ align:start position:0%
+dry Step at the end so the interface was
+ 
+
+ align:start position:0%
+dry Step at the end so the interface was
+always grown in a dry step to try to
+
+ align:start position:0%
+always grown in a dry step to try to
+ 
+
+ align:start position:0%
+always grown in a dry step to try to
+reduce the interface uh State density um
+
+ align:start position:0%
+reduce the interface uh State density um
+ 
+
+ align:start position:0%
+reduce the interface uh State density um
+so if you need an oxide gate oxide
+
+ align:start position:0%
+so if you need an oxide gate oxide
+ 
+
+ align:start position:0%
+so if you need an oxide gate oxide
+that's a th a you do what they call a
+
+ align:start position:0%
+that's a th a you do what they call a
+ 
+
+ align:start position:0%
+that's a th a you do what they call a
+dry wet dry um so it does matter the
+
+ align:start position:0%
+dry wet dry um so it does matter the
+ 
+
+ align:start position:0%
+dry wet dry um so it does matter the
+oxidation rate being too high is not the
+
+ align:start position:0%
+oxidation rate being too high is not the
+ 
+
+ align:start position:0%
+oxidation rate being too high is not the
+greatest thing in the world for in terms
+
+ align:start position:0%
+greatest thing in the world for in terms
+ 
+
+ align:start position:0%
+greatest thing in the world for in terms
+of the device properties I think there
+
+ align:start position:0%
+of the device properties I think there
+ 
+
+ align:start position:0%
+of the device properties I think there
+was there a hand in the back or did I
+
+ align:start position:0%
+was there a hand in the back or did I
+ 
+
+ align:start position:0%
+was there a hand in the back or did I
+missed question
+
+ align:start position:0%
+missed question
+ 
+
+ align:start position:0%
+missed question
+okay okay good so let's go on so those
+
+ align:start position:0%
+okay okay good so let's go on so those
+ 
+
+ align:start position:0%
+okay okay good so let's go on so those
+are the wet oxide kinetics let's go on
+
+ align:start position:0%
+are the wet oxide kinetics let's go on
+ 
+
+ align:start position:0%
+are the wet oxide kinetics let's go on
+to slide number 15 and just show some
+
+ align:start position:0%
+to slide number 15 and just show some
+ 
+
+ align:start position:0%
+to slide number 15 and just show some
+examples uh now right off the bat
+
+ align:start position:0%
+examples uh now right off the bat
+ 
+
+ align:start position:0%
+examples uh now right off the bat
+unfortunately um showing an example
+
+ align:start position:0%
+unfortunately um showing an example
+ 
+
+ align:start position:0%
+unfortunately um showing an example
+that's to which the deal Grove model
+
+ align:start position:0%
+that's to which the deal Grove model
+ 
+
+ align:start position:0%
+that's to which the deal Grove model
+doesn't doesn't perfectly apply but
+
+ align:start position:0%
+doesn't doesn't perfectly apply but
+ 
+
+ align:start position:0%
+doesn't doesn't perfectly apply but
+we'll apply it anyway and we'll next
+
+ align:start position:0%
+we'll apply it anyway and we'll next
+ 
+
+ align:start position:0%
+we'll apply it anyway and we'll next
+time we'll talk about why it's not
+
+ align:start position:0%
+time we'll talk about why it's not
+ 
+
+ align:start position:0%
+time we'll talk about why it's not
+perfect but there is a process called um
+
+ align:start position:0%
+perfect but there is a process called um
+ 
+
+ align:start position:0%
+perfect but there is a process called um
+uh just to make this a little more
+
+ align:start position:0%
+uh just to make this a little more
+ 
+
+ align:start position:0%
+uh just to make this a little more
+interesting called recess
+
+ align:start position:0%
+interesting called recess
+ 
+
+ align:start position:0%
+interesting called recess
+loose uh local oxidation which can be
+
+ align:start position:0%
+loose uh local oxidation which can be
+ 
+
+ align:start position:0%
+loose uh local oxidation which can be
+used to provide this lateral isolation
+
+ align:start position:0%
+used to provide this lateral isolation
+ 
+
+ align:start position:0%
+used to provide this lateral isolation
+between device a and device B um we need
+
+ align:start position:0%
+between device a and device B um we need
+ 
+
+ align:start position:0%
+between device a and device B um we need
+to grow an oxide uh here and uh it
+
+ align:start position:0%
+to grow an oxide uh here and uh it
+ 
+
+ align:start position:0%
+to grow an oxide uh here and uh it
+results in a more planer surface than
+
+ align:start position:0%
+results in a more planer surface than
+ 
+
+ align:start position:0%
+results in a more planer surface than
+standard Locos remember standard Locos
+
+ align:start position:0%
+standard Locos remember standard Locos
+ 
+
+ align:start position:0%
+standard Locos remember standard Locos
+look like this um we have a very not
+
+ align:start position:0%
+look like this um we have a very not
+ 
+
+ align:start position:0%
+look like this um we have a very not
+when we're done and you strip off this
+
+ align:start position:0%
+when we're done and you strip off this
+ 
+
+ align:start position:0%
+when we're done and you strip off this
+nitrite up in the upper right you have a
+
+ align:start position:0%
+nitrite up in the upper right you have a
+ 
+
+ align:start position:0%
+nitrite up in the upper right you have a
+very nonplanar surface uh introduced um
+
+ align:start position:0%
+very nonplanar surface uh introduced um
+ 
+
+ align:start position:0%
+very nonplanar surface uh introduced um
+you've got this this region up here
+
+ align:start position:0%
+you've got this this region up here
+ 
+
+ align:start position:0%
+you've got this this region up here
+where the oxide pushed up uh and so the
+
+ align:start position:0%
+where the oxide pushed up uh and so the
+ 
+
+ align:start position:0%
+where the oxide pushed up uh and so the
+surface is not very planer recess losis
+
+ align:start position:0%
+surface is not very planer recess losis
+ 
+
+ align:start position:0%
+surface is not very planer recess losis
+the basis basic idea is you etch a
+
+ align:start position:0%
+the basis basic idea is you etch a
+ 
+
+ align:start position:0%
+the basis basic idea is you etch a
+trench first so here I've etched in the
+
+ align:start position:0%
+trench first so here I've etched in the
+ 
+
+ align:start position:0%
+trench first so here I've etched in the
+Silicon um around the Silicon nitrate
+
+ align:start position:0%
+Silicon um around the Silicon nitrate
+ 
+
+ align:start position:0%
+Silicon um around the Silicon nitrate
+I've etched a half Micron deep
+
+ align:start position:0%
+I've etched a half Micron deep
+ 
+
+ align:start position:0%
+I've etched a half Micron deep
+trench uh and now we assume I'm going to
+
+ align:start position:0%
+trench uh and now we assume I'm going to
+ 
+
+ align:start position:0%
+trench uh and now we assume I'm going to
+subject that wafer to Thermal oxidation
+
+ align:start position:0%
+subject that wafer to Thermal oxidation
+ 
+
+ align:start position:0%
+subject that wafer to Thermal oxidation
+well on the left and the right side of
+
+ align:start position:0%
+well on the left and the right side of
+ 
+
+ align:start position:0%
+well on the left and the right side of
+the trench um uh that should say silicon
+
+ align:start position:0%
+the trench um uh that should say silicon
+ 
+
+ align:start position:0%
+the trench um uh that should say silicon
+uh silicon nitride sorry this this left
+
+ align:start position:0%
+uh silicon nitride sorry this this left
+ 
+
+ align:start position:0%
+uh silicon nitride sorry this this left
+and right side should both be silicon
+
+ align:start position:0%
+and right side should both be silicon
+ 
+
+ align:start position:0%
+and right side should both be silicon
+nitrate there's no oxidation taking
+
+ align:start position:0%
+nitrate there's no oxidation taking
+ 
+
+ align:start position:0%
+nitrate there's no oxidation taking
+place so maybe correct this hand out on
+
+ align:start position:0%
+place so maybe correct this hand out on
+ 
+
+ align:start position:0%
+place so maybe correct this hand out on
+the right where it's pointing to S2 that
+
+ align:start position:0%
+the right where it's pointing to S2 that
+ 
+
+ align:start position:0%
+the right where it's pointing to S2 that
+should say silicon
+
+ align:start position:0%
+should say silicon
+ 
+
+ align:start position:0%
+should say silicon
+nitrite uh si3 and4 so we're only
+
+ align:start position:0%
+nitrite uh si3 and4 so we're only
+ 
+
+ align:start position:0%
+nitrite uh si3 and4 so we're only
+oxidizing we're assuming in this this
+
+ align:start position:0%
+oxidizing we're assuming in this this
+ 
+
+ align:start position:0%
+oxidizing we're assuming in this this
+trench region now this schematic is
+
+ align:start position:0%
+trench region now this schematic is
+ 
+
+ align:start position:0%
+trench region now this schematic is
+highly schematic it's not including any
+
+ align:start position:0%
+highly schematic it's not including any
+ 
+
+ align:start position:0%
+highly schematic it's not including any
+birds beak effects which we'll talk
+
+ align:start position:0%
+birds beak effects which we'll talk
+ 
+
+ align:start position:0%
+birds beak effects which we'll talk
+about where they originate from or any
+
+ align:start position:0%
+about where they originate from or any
+ 
+
+ align:start position:0%
+about where they originate from or any
+two-dimensional oxidation we're going to
+
+ align:start position:0%
+two-dimensional oxidation we're going to
+ 
+
+ align:start position:0%
+two-dimensional oxidation we're going to
+do a very simple calculation of how long
+
+ align:start position:0%
+do a very simple calculation of how long
+ 
+
+ align:start position:0%
+do a very simple calculation of how long
+would it take to fill that to make a
+
+ align:start position:0%
+would it take to fill that to make a
+ 
+
+ align:start position:0%
+would it take to fill that to make a
+planer surf Sur uh assuming I was half
+
+ align:start position:0%
+planer surf Sur uh assuming I was half
+ 
+
+ align:start position:0%
+planer surf Sur uh assuming I was half
+Micron uh down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there is in between yeah it's just
+
+ align:start position:0%
+yeah there is in between yeah it's just
+ 
+
+ align:start position:0%
+yeah there is in between yeah it's just
+the arrow got Mis uh displaced this
+
+ align:start position:0%
+the arrow got Mis uh displaced this
+ 
+
+ align:start position:0%
+the arrow got Mis uh displaced this
+arrow is actually pointing to the top
+
+ align:start position:0%
+arrow is actually pointing to the top
+ 
+
+ align:start position:0%
+arrow is actually pointing to the top
+region which is the Silicon nitride
+
+ align:start position:0%
+region which is the Silicon nitride
+ 
+
+ align:start position:0%
+region which is the Silicon nitride
+there is as was just pointed out uh by
+
+ align:start position:0%
+there is as was just pointed out uh by
+ 
+
+ align:start position:0%
+there is as was just pointed out uh by
+someone in the class here there uh this
+
+ align:start position:0%
+someone in the class here there uh this
+ 
+
+ align:start position:0%
+someone in the class here there uh this
+hatched region is meant to represent the
+
+ align:start position:0%
+hatched region is meant to represent the
+ 
+
+ align:start position:0%
+hatched region is meant to represent the
+sio2 what they call the um padox or the
+
+ align:start position:0%
+sio2 what they call the um padox or the
+ 
+
+ align:start position:0%
+sio2 what they call the um padox or the
+pado oxide they always stress that's
+
+ align:start position:0%
+pado oxide they always stress that's
+ 
+
+ align:start position:0%
+pado oxide they always stress that's
+induced by the nitride so so there is in
+
+ align:start position:0%
+induced by the nitride so so there is in
+ 
+
+ align:start position:0%
+induced by the nitride so so there is in
+fact a thin pad oxide underneath the
+
+ align:start position:0%
+fact a thin pad oxide underneath the
+ 
+
+ align:start position:0%
+fact a thin pad oxide underneath the
+Silicon nitride but what's preventing
+
+ align:start position:0%
+Silicon nitride but what's preventing
+ 
+
+ align:start position:0%
+Silicon nitride but what's preventing
+the oxidation from taking place is this
+
+ align:start position:0%
+the oxidation from taking place is this
+ 
+
+ align:start position:0%
+the oxidation from taking place is this
+silicon nitride Ox si2 itself won't
+
+ align:start position:0%
+silicon nitride Ox si2 itself won't
+ 
+
+ align:start position:0%
+silicon nitride Ox si2 itself won't
+prevent oxidation the oxide will oxidant
+
+ align:start position:0%
+prevent oxidation the oxide will oxidant
+ 
+
+ align:start position:0%
+prevent oxidation the oxide will oxidant
+will diffuse right through it the nice
+
+ align:start position:0%
+will diffuse right through it the nice
+ 
+
+ align:start position:0%
+will diffuse right through it the nice
+thing about silicon nitride is that it's
+
+ align:start position:0%
+thing about silicon nitride is that it's
+ 
+
+ align:start position:0%
+thing about silicon nitride is that it's
+hard to get Ox uh oxygen and moisture to
+
+ align:start position:0%
+hard to get Ox uh oxygen and moisture to
+ 
+
+ align:start position:0%
+hard to get Ox uh oxygen and moisture to
+diffuse through it so it can act as a
+
+ align:start position:0%
+diffuse through it so it can act as a
+ 
+
+ align:start position:0%
+diffuse through it so it can act as a
+mask or as a blocking layer um so you
+
+ align:start position:0%
+mask or as a blocking layer um so you
+ 
+
+ align:start position:0%
+mask or as a blocking layer um so you
+don't oxidize uh underneath it the first
+
+ align:start position:0%
+don't oxidize uh underneath it the first
+ 
+
+ align:start position:0%
+don't oxidize uh underneath it the first
+wor so this oxide that's shown here
+
+ align:start position:0%
+wor so this oxide that's shown here
+ 
+
+ align:start position:0%
+wor so this oxide that's shown here
+underneath it happened before the
+
+ align:start position:0%
+underneath it happened before the
+ 
+
+ align:start position:0%
+underneath it happened before the
+nitrate was put
+
+ align:start position:0%
+nitrate was put
+ 
+
+ align:start position:0%
+nitrate was put
+down okay good
+
+ align:start position:0%
+down okay good
+ 
+
+ align:start position:0%
+down okay good
+point so let's go on to slide 15 and and
+
+ align:start position:0%
+point so let's go on to slide 15 and and
+ 
+
+ align:start position:0%
+point so let's go on to slide 15 and and
+here's just an example uh of a question
+
+ align:start position:0%
+here's just an example uh of a question
+ 
+
+ align:start position:0%
+here's just an example uh of a question
+uh so we're assuming we've edged half
+
+ align:start position:0%
+uh so we're assuming we've edged half
+ 
+
+ align:start position:0%
+uh so we're assuming we've edged half
+Micron down into the wafer below the
+
+ align:start position:0%
+Micron down into the wafer below the
+ 
+
+ align:start position:0%
+Micron down into the wafer below the
+original surface prior to
+
+ align:start position:0%
+original surface prior to
+ 
+
+ align:start position:0%
+original surface prior to
+oxidizing and a simple question might be
+
+ align:start position:0%
+oxidizing and a simple question might be
+ 
+
+ align:start position:0%
+oxidizing and a simple question might be
+how long do I have to put it in the
+
+ align:start position:0%
+how long do I have to put it in the
+ 
+
+ align:start position:0%
+how long do I have to put it in the
+furnace at a th000 degrees assuming uh
+
+ align:start position:0%
+furnace at a th000 degrees assuming uh
+ 
+
+ align:start position:0%
+furnace at a th000 degrees assuming uh
+water water oxidation in H2O to produce
+
+ align:start position:0%
+water water oxidation in H2O to produce
+ 
+
+ align:start position:0%
+water water oxidation in H2O to produce
+a planer surface again we're going to
+
+ align:start position:0%
+a planer surface again we're going to
+ 
+
+ align:start position:0%
+a planer surface again we're going to
+ignore any of the bird's beak effects or
+
+ align:start position:0%
+ignore any of the bird's beak effects or
+ 
+
+ align:start position:0%
+ignore any of the bird's beak effects or
+the stress effects that we know are
+
+ align:start position:0%
+the stress effects that we know are
+ 
+
+ align:start position:0%
+the stress effects that we know are
+there we'll talk about those next time
+
+ align:start position:0%
+there we'll talk about those next time
+ 
+
+ align:start position:0%
+there we'll talk about those next time
+so but Ju Just to make it a little uh
+
+ align:start position:0%
+so but Ju Just to make it a little uh
+ 
+
+ align:start position:0%
+so but Ju Just to make it a little uh
+more interesting we want to fill this up
+
+ align:start position:0%
+more interesting we want to fill this up
+ 
+
+ align:start position:0%
+more interesting we want to fill this up
+to the surface the original surface and
+
+ align:start position:0%
+to the surface the original surface and
+ 
+
+ align:start position:0%
+to the surface the original surface and
+and then make it
+
+ align:start position:0%
+and then make it
+ 
+
+ align:start position:0%
+and then make it
+planer um so we have to be a little
+
+ align:start position:0%
+planer um so we have to be a little
+ 
+
+ align:start position:0%
+planer um so we have to be a little
+careful in doing this because remember
+
+ align:start position:0%
+careful in doing this because remember
+ 
+
+ align:start position:0%
+careful in doing this because remember
+as I'm growing this oxide right here I'm
+
+ align:start position:0%
+as I'm growing this oxide right here I'm
+ 
+
+ align:start position:0%
+as I'm growing this oxide right here I'm
+consuming the Silicon underneath it so
+
+ align:start position:0%
+consuming the Silicon underneath it so
+ 
+
+ align:start position:0%
+consuming the Silicon underneath it so
+you're consuming silicon underneath it
+
+ align:start position:0%
+you're consuming silicon underneath it
+ 
+
+ align:start position:0%
+you're consuming silicon underneath it
+uh but the oxide is also growing up at
+
+ align:start position:0%
+uh but the oxide is also growing up at
+ 
+
+ align:start position:0%
+uh but the oxide is also growing up at
+the same time so it's going it's kind of
+
+ align:start position:0%
+the same time so it's going it's kind of
+ 
+
+ align:start position:0%
+the same time so it's going it's kind of
+starting here very thin and it's kind of
+
+ align:start position:0%
+starting here very thin and it's kind of
+ 
+
+ align:start position:0%
+starting here very thin and it's kind of
+going like this at some point it'll just
+
+ align:start position:0%
+going like this at some point it'll just
+ 
+
+ align:start position:0%
+going like this at some point it'll just
+flat or close to being almost flat uh
+
+ align:start position:0%
+flat or close to being almost flat uh
+ 
+
+ align:start position:0%
+flat or close to being almost flat uh
+with the original
+
+ align:start position:0%
+with the original
+ 
+
+ align:start position:0%
+with the original
+surface so how we figure this out well
+
+ align:start position:0%
+surface so how we figure this out well
+ 
+
+ align:start position:0%
+surface so how we figure this out well
+there there's a um you can make yourself
+
+ align:start position:0%
+there there's a um you can make yourself
+ 
+
+ align:start position:0%
+there there's a um you can make yourself
+a little schematic diagram as shown here
+
+ align:start position:0%
+a little schematic diagram as shown here
+ 
+
+ align:start position:0%
+a little schematic diagram as shown here
+in color in the lower left and in a in a
+
+ align:start position:0%
+in color in the lower left and in a in a
+ 
+
+ align:start position:0%
+in color in the lower left and in a in a
+rough sense for every Micron of silicon
+
+ align:start position:0%
+rough sense for every Micron of silicon
+ 
+
+ align:start position:0%
+rough sense for every Micron of silicon
+I consume so I'm going to as you start
+
+ align:start position:0%
+I consume so I'm going to as you start
+ 
+
+ align:start position:0%
+I consume so I'm going to as you start
+oxidizing I'm going to start bringing
+
+ align:start position:0%
+oxidizing I'm going to start bringing
+ 
+
+ align:start position:0%
+oxidizing I'm going to start bringing
+this trench Point lower every Micron I
+
+ align:start position:0%
+this trench Point lower every Micron I
+ 
+
+ align:start position:0%
+this trench Point lower every Micron I
+go down uh 2 and a half microns or 2.2
+
+ align:start position:0%
+go down uh 2 and a half microns or 2.2
+ 
+
+ align:start position:0%
+go down uh 2 and a half microns or 2.2
+I'm sorry microns of silicon is gr of of
+
+ align:start position:0%
+I'm sorry microns of silicon is gr of of
+ 
+
+ align:start position:0%
+I'm sorry microns of silicon is gr of of
+silicon dioxide
+
+ align:start position:0%
+silicon dioxide
+ 
+
+ align:start position:0%
+silicon dioxide
+S2 um so um you can write this sort of
+
+ align:start position:0%
+S2 um so um you can write this sort of
+ 
+
+ align:start position:0%
+S2 um so um you can write this sort of
+mathematically if I say why is the
+
+ align:start position:0%
+mathematically if I say why is the
+ 
+
+ align:start position:0%
+mathematically if I say why is the
+thickness of the Silicon that was
+
+ align:start position:0%
+thickness of the Silicon that was
+ 
+
+ align:start position:0%
+thickness of the Silicon that was
+consumed then 2.2 * Y is X knot that's
+
+ align:start position:0%
+consumed then 2.2 * Y is X knot that's
+ 
+
+ align:start position:0%
+consumed then 2.2 * Y is X knot that's
+the thickness of the
+
+ align:start position:0%
+the thickness of the
+ 
+
+ align:start position:0%
+the thickness of the
+si2 okay so that's just due to the
+
+ align:start position:0%
+si2 okay so that's just due to the
+ 
+
+ align:start position:0%
+si2 okay so that's just due to the
+volume expansion when you grow oxide so
+
+ align:start position:0%
+volume expansion when you grow oxide so
+ 
+
+ align:start position:0%
+volume expansion when you grow oxide so
+we can we can have that as one uh one
+
+ align:start position:0%
+we can we can have that as one uh one
+ 
+
+ align:start position:0%
+we can we can have that as one uh one
+equation that describes what's going
+
+ align:start position:0%
+equation that describes what's going
+ 
+
+ align:start position:0%
+equation that describes what's going
+on on slide
+
+ align:start position:0%
+on on slide
+ 
+
+ align:start position:0%
+on on slide
+17 um so we we remember that but then we
+
+ align:start position:0%
+17 um so we we remember that but then we
+ 
+
+ align:start position:0%
+17 um so we we remember that but then we
+also know um that the total thickness of
+
+ align:start position:0%
+also know um that the total thickness of
+ 
+
+ align:start position:0%
+also know um that the total thickness of
+oxide grown in order to satisfy this
+
+ align:start position:0%
+oxide grown in order to satisfy this
+ 
+
+ align:start position:0%
+oxide grown in order to satisfy this
+requirement that we fill the trench well
+
+ align:start position:0%
+requirement that we fill the trench well
+ 
+
+ align:start position:0%
+requirement that we fill the trench well
+we want to know a specific ta case where
+
+ align:start position:0%
+we want to know a specific ta case where
+ 
+
+ align:start position:0%
+we want to know a specific ta case where
+X knot is equal to um half Micron which
+
+ align:start position:0%
+X knot is equal to um half Micron which
+ 
+
+ align:start position:0%
+X knot is equal to um half Micron which
+is the original trench depth plus Y
+
+ align:start position:0%
+is the original trench depth plus Y
+ 
+
+ align:start position:0%
+is the original trench depth plus Y
+which is the thickness of silicon
+
+ align:start position:0%
+which is the thickness of silicon
+ 
+
+ align:start position:0%
+which is the thickness of silicon
+consumed so that's just by looking at
+
+ align:start position:0%
+consumed so that's just by looking at
+ 
+
+ align:start position:0%
+consumed so that's just by looking at
+this geometry so the distance from here
+
+ align:start position:0%
+this geometry so the distance from here
+ 
+
+ align:start position:0%
+this geometry so the distance from here
+to here is half Micron that was my
+
+ align:start position:0%
+to here is half Micron that was my
+ 
+
+ align:start position:0%
+to here is half Micron that was my
+original trench plus the Silicon is
+
+ align:start position:0%
+original trench plus the Silicon is
+ 
+
+ align:start position:0%
+original trench plus the Silicon is
+going to get consumed down a little bit
+
+ align:start position:0%
+going to get consumed down a little bit
+ 
+
+ align:start position:0%
+going to get consumed down a little bit
+um and that we're calling the variable y
+
+ align:start position:0%
+um and that we're calling the variable y
+ 
+
+ align:start position:0%
+um and that we're calling the variable y
+we don't know that number yet so we have
+
+ align:start position:0%
+we don't know that number yet so we have
+ 
+
+ align:start position:0%
+we don't know that number yet so we have
+two equations
+
+ align:start position:0%
+two equations
+ 
+
+ align:start position:0%
+two equations
+here uh this x equals 0.5 Micron plus Y
+
+ align:start position:0%
+here uh this x equals 0.5 Micron plus Y
+ 
+
+ align:start position:0%
+here uh this x equals 0.5 Micron plus Y
+and we also have the constraint that 2.2
+
+ align:start position:0%
+and we also have the constraint that 2.2
+ 
+
+ align:start position:0%
+and we also have the constraint that 2.2
+* Y is X knot uh and that's just from
+
+ align:start position:0%
+* Y is X knot uh and that's just from
+ 
+
+ align:start position:0%
+* Y is X knot uh and that's just from
+the volume expansion that we know so if
+
+ align:start position:0%
+the volume expansion that we know so if
+ 
+
+ align:start position:0%
+the volume expansion that we know so if
+we can we can simply now just equate
+
+ align:start position:0%
+we can we can simply now just equate
+ 
+
+ align:start position:0%
+we can we can simply now just equate
+these two equations we have two
+
+ align:start position:0%
+these two equations we have two
+ 
+
+ align:start position:0%
+these two equations we have two
+equations uh and we're going to um uh
+
+ align:start position:0%
+equations uh and we're going to um uh
+ 
+
+ align:start position:0%
+equations uh and we're going to um uh
+set X notot in equation one equal x not
+
+ align:start position:0%
+set X notot in equation one equal x not
+ 
+
+ align:start position:0%
+set X notot in equation one equal x not
+in equation 2 uh and then you can simply
+
+ align:start position:0%
+in equation 2 uh and then you can simply
+ 
+
+ align:start position:0%
+in equation 2 uh and then you can simply
+solve for y so y turns out to be about4
+
+ align:start position:0%
+solve for y so y turns out to be about4
+ 
+
+ align:start position:0%
+solve for y so y turns out to be about4
+Micron so that says we need to consume
+
+ align:start position:0%
+Micron so that says we need to consume
+ 
+
+ align:start position:0%
+Micron so that says we need to consume
+about4 microns in order to just fill the
+
+ align:start position:0%
+about4 microns in order to just fill the
+ 
+
+ align:start position:0%
+about4 microns in order to just fill the
+trench up to the original
+
+ align:start position:0%
+trench up to the original
+ 
+
+ align:start position:0%
+trench up to the original
+surface so I'm going to actually go down
+
+ align:start position:0%
+surface so I'm going to actually go down
+ 
+
+ align:start position:0%
+surface so I'm going to actually go down
+here from the original trench depth I'm
+
+ align:start position:0%
+here from the original trench depth I'm
+ 
+
+ align:start position:0%
+here from the original trench depth I'm
+actually going to consume 04 microns
+
+ align:start position:0%
+actually going to consume 04 microns
+ 
+
+ align:start position:0%
+actually going to consume 04 microns
+down into the wafer so xnot then the
+
+ align:start position:0%
+down into the wafer so xnot then the
+ 
+
+ align:start position:0%
+down into the wafer so xnot then the
+oxide thickness must be two and a half
+
+ align:start position:0%
+oxide thickness must be two and a half
+ 
+
+ align:start position:0%
+oxide thickness must be two and a half
+2.2 times that so it's about 0.9 microns
+
+ align:start position:0%
+2.2 times that so it's about 0.9 microns
+ 
+
+ align:start position:0%
+2.2 times that so it's about 0.9 microns
+so we really have the answer we know we
+
+ align:start position:0%
+so we really have the answer we know we
+ 
+
+ align:start position:0%
+so we really have the answer we know we
+need to grow at 1,000 de up .9 microns
+
+ align:start position:0%
+need to grow at 1,000 de up .9 microns
+ 
+
+ align:start position:0%
+need to grow at 1,000 de up .9 microns
+when we're told we can do it in a wet
+
+ align:start position:0%
+when we're told we can do it in a wet
+ 
+
+ align:start position:0%
+when we're told we can do it in a wet
+ambient so you can calculate being B
+
+ align:start position:0%
+ambient so you can calculate being B
+ 
+
+ align:start position:0%
+ambient so you can calculate being B
+over a using the table uh in table 6.2
+
+ align:start position:0%
+over a using the table uh in table 6.2
+ 
+
+ align:start position:0%
+over a using the table uh in table 6.2
+of your text um so you know this is the
+
+ align:start position:0%
+of your text um so you know this is the
+ 
+
+ align:start position:0%
+of your text um so you know this is the
+deal Grove
+
+ align:start position:0%
+deal Grove
+ 
+
+ align:start position:0%
+deal Grove
+equation um you can just calculate B and
+
+ align:start position:0%
+equation um you can just calculate B and
+ 
+
+ align:start position:0%
+equation um you can just calculate B and
+B over a and solve for the time or if
+
+ align:start position:0%
+B over a and solve for the time or if
+ 
+
+ align:start position:0%
+B over a and solve for the time or if
+you want to go on the next slide I'll
+
+ align:start position:0%
+you want to go on the next slide I'll
+ 
+
+ align:start position:0%
+you want to go on the next slide I'll
+show you use the
+
+ align:start position:0%
+show you use the
+ 
+
+ align:start position:0%
+show you use the
+graph so on slide 18 these are just the
+
+ align:start position:0%
+graph so on slide 18 these are just the
+ 
+
+ align:start position:0%
+graph so on slide 18 these are just the
+oxidation kinetics or oxide thickness
+
+ align:start position:0%
+oxidation kinetics or oxide thickness
+ 
+
+ align:start position:0%
+oxidation kinetics or oxide thickness
+versus time in a wet ambient and I I was
+
+ align:start position:0%
+versus time in a wet ambient and I I was
+ 
+
+ align:start position:0%
+versus time in a wet ambient and I I was
+told we were at a th000 de so that's
+
+ align:start position:0%
+told we were at a th000 de so that's
+ 
+
+ align:start position:0%
+told we were at a th000 de so that's
+this line right here um and we know we
+
+ align:start position:0%
+this line right here um and we know we
+ 
+
+ align:start position:0%
+this line right here um and we know we
+need to grow a point M Micron so that's
+
+ align:start position:0%
+need to grow a point M Micron so that's
+ 
+
+ align:start position:0%
+need to grow a point M Micron so that's
+this uh black line horizontal line and
+
+ align:start position:0%
+this uh black line horizontal line and
+ 
+
+ align:start position:0%
+this uh black line horizontal line and
+you can get it roughly here it's just
+
+ align:start position:0%
+you can get it roughly here it's just
+ 
+
+ align:start position:0%
+you can get it roughly here it's just
+3.8 or so hours depending on how
+
+ align:start position:0%
+3.8 or so hours depending on how
+ 
+
+ align:start position:0%
+3.8 or so hours depending on how
+accurately you can read off the gra off
+
+ align:start position:0%
+accurately you can read off the gra off
+ 
+
+ align:start position:0%
+accurately you can read off the gra off
+the plot if you want to get a little
+
+ align:start position:0%
+the plot if you want to get a little
+ 
+
+ align:start position:0%
+the plot if you want to get a little
+more accurate you go ahead and calculate
+
+ align:start position:0%
+more accurate you go ahead and calculate
+ 
+
+ align:start position:0%
+more accurate you go ahead and calculate
+B and B over a and plug in the equation
+
+ align:start position:0%
+B and B over a and plug in the equation
+ 
+
+ align:start position:0%
+B and B over a and plug in the equation
+but you always check the plot that way
+
+ align:start position:0%
+but you always check the plot that way
+ 
+
+ align:start position:0%
+but you always check the plot that way
+you have you're sure you have a sanity
+
+ align:start position:0%
+you have you're sure you have a sanity
+ 
+
+ align:start position:0%
+you have you're sure you have a sanity
+check that you made didn't make some uh
+
+ align:start position:0%
+check that you made didn't make some uh
+ 
+
+ align:start position:0%
+check that you made didn't make some uh
+calculator mistake or type in the wrong
+
+ align:start position:0%
+calculator mistake or type in the wrong
+ 
+
+ align:start position:0%
+calculator mistake or type in the wrong
+number okay so that's that seems like a
+
+ align:start position:0%
+number okay so that's that seems like a
+ 
+
+ align:start position:0%
+number okay so that's that seems like a
+reasonable um reasonable example of how
+
+ align:start position:0%
+reasonable um reasonable example of how
+ 
+
+ align:start position:0%
+reasonable um reasonable example of how
+you would do um a simple calculation
+
+ align:start position:0%
+you would do um a simple calculation
+ 
+
+ align:start position:0%
+you would do um a simple calculation
+so let's go on now to slide 19 so that
+
+ align:start position:0%
+so let's go on now to slide 19 so that
+ 
+
+ align:start position:0%
+so let's go on now to slide 19 so that
+was a deal Grove model immediately at
+
+ align:start position:0%
+was a deal Grove model immediately at
+ 
+
+ align:start position:0%
+was a deal Grove model immediately at
+the same time deal and Grove published
+
+ align:start position:0%
+the same time deal and Grove published
+ 
+
+ align:start position:0%
+the same time deal and Grove published
+it um they realized that there was a
+
+ align:start position:0%
+it um they realized that there was a
+ 
+
+ align:start position:0%
+it um they realized that there was a
+major problem with the model even when
+
+ align:start position:0%
+major problem with the model even when
+ 
+
+ align:start position:0%
+major problem with the model even when
+it was first proposed um it doesn't
+
+ align:start position:0%
+it was first proposed um it doesn't
+ 
+
+ align:start position:0%
+it was first proposed um it doesn't
+correctly model what they knew to be the
+
+ align:start position:0%
+correctly model what they knew to be the
+ 
+
+ align:start position:0%
+correctly model what they knew to be the
+thin oxide growth kinetics and you can
+
+ align:start position:0%
+thin oxide growth kinetics and you can
+ 
+
+ align:start position:0%
+thin oxide growth kinetics and you can
+see that in this plot this is a plot I
+
+ align:start position:0%
+see that in this plot this is a plot I
+ 
+
+ align:start position:0%
+see that in this plot this is a plot I
+took out of Andy Grove's um book which
+
+ align:start position:0%
+took out of Andy Grove's um book which
+ 
+
+ align:start position:0%
+took out of Andy Grove's um book which
+published quite some time ago but still
+
+ align:start position:0%
+published quite some time ago but still
+ 
+
+ align:start position:0%
+published quite some time ago but still
+a famous book um oxide thickness in
+
+ align:start position:0%
+a famous book um oxide thickness in
+ 
+
+ align:start position:0%
+a famous book um oxide thickness in
+microns as a function of time uh this
+
+ align:start position:0%
+microns as a function of time uh this
+ 
+
+ align:start position:0%
+microns as a function of time uh this
+was this is for a dry oxide grown at 700
+
+ align:start position:0%
+was this is for a dry oxide grown at 700
+ 
+
+ align:start position:0%
+was this is for a dry oxide grown at 700
+very low temperature um and these little
+
+ align:start position:0%
+very low temperature um and these little
+ 
+
+ align:start position:0%
+very low temperature um and these little
+bullets or these open symbols are what
+
+ align:start position:0%
+bullets or these open symbols are what
+ 
+
+ align:start position:0%
+bullets or these open symbols are what
+they measured as the oxide thickness um
+
+ align:start position:0%
+they measured as the oxide thickness um
+ 
+
+ align:start position:0%
+they measured as the oxide thickness um
+and in fact um what they noticed is um
+
+ align:start position:0%
+and in fact um what they noticed is um
+ 
+
+ align:start position:0%
+and in fact um what they noticed is um
+uh that the the model itself which would
+
+ align:start position:0%
+uh that the the model itself which would
+ 
+
+ align:start position:0%
+uh that the the model itself which would
+be in this range um dry the dry oxides
+
+ align:start position:0%
+be in this range um dry the dry oxides
+ 
+
+ align:start position:0%
+be in this range um dry the dry oxides
+grow much faster uh for thicknesses
+
+ align:start position:0%
+grow much faster uh for thicknesses
+ 
+
+ align:start position:0%
+grow much faster uh for thicknesses
+below about um uh 20 nmet or 02 microns
+
+ align:start position:0%
+below about um uh 20 nmet or 02 microns
+ 
+
+ align:start position:0%
+below about um uh 20 nmet or 02 microns
+than predicted by the linear parabolic
+
+ align:start position:0%
+than predicted by the linear parabolic
+ 
+
+ align:start position:0%
+than predicted by the linear parabolic
+uh uh uh model so the linear parabolic
+
+ align:start position:0%
+uh uh uh model so the linear parabolic
+ 
+
+ align:start position:0%
+uh uh uh model so the linear parabolic
+model would have had them you know sort
+
+ align:start position:0%
+model would have had them you know sort
+ 
+
+ align:start position:0%
+model would have had them you know sort
+of going like this and here these oxides
+
+ align:start position:0%
+of going like this and here these oxides
+ 
+
+ align:start position:0%
+of going like this and here these oxides
+are already going up much faster so a
+
+ align:start position:0%
+are already going up much faster so a
+ 
+
+ align:start position:0%
+are already going up much faster so a
+rapid initial oxidation phase which do
+
+ align:start position:0%
+rapid initial oxidation phase which do
+ 
+
+ align:start position:0%
+rapid initial oxidation phase which do
+not take into account when you have a
+
+ align:start position:0%
+not take into account when you have a
+ 
+
+ align:start position:0%
+not take into account when you have a
+linear model in the beginning and then a
+
+ align:start position:0%
+linear model in the beginning and then a
+ 
+
+ align:start position:0%
+linear model in the beginning and then a
+parabolic model so uh people knew right
+
+ align:start position:0%
+parabolic model so uh people knew right
+ 
+
+ align:start position:0%
+parabolic model so uh people knew right
+off that this this really wasn't going
+
+ align:start position:0%
+off that this this really wasn't going
+ 
+
+ align:start position:0%
+off that this this really wasn't going
+to model the initial oxidation kinetics
+
+ align:start position:0%
+to model the initial oxidation kinetics
+ 
+
+ align:start position:0%
+to model the initial oxidation kinetics
+uh very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so if we can go on to slide 20 then
+
+ align:start position:0%
+well so if we can go on to slide 20 then
+ 
+
+ align:start position:0%
+well so if we can go on to slide 20 then
+um since that time there's been a number
+
+ align:start position:0%
+um since that time there's been a number
+ 
+
+ align:start position:0%
+um since that time there's been a number
+of people have uh uh made suggestions to
+
+ align:start position:0%
+of people have uh uh made suggestions to
+ 
+
+ align:start position:0%
+of people have uh uh made suggestions to
+explain why the initial kinetics are
+
+ align:start position:0%
+explain why the initial kinetics are
+ 
+
+ align:start position:0%
+explain why the initial kinetics are
+faster than what deal and growth uh
+
+ align:start position:0%
+faster than what deal and growth uh
+ 
+
+ align:start position:0%
+faster than what deal and growth uh
+model would predict uh there isn't
+
+ align:start position:0%
+model would predict uh there isn't
+ 
+
+ align:start position:0%
+model would predict uh there isn't
+really one model that's widely uh
+
+ align:start position:0%
+really one model that's widely uh
+ 
+
+ align:start position:0%
+really one model that's widely uh
+totally always accepted um there's a
+
+ align:start position:0%
+totally always accepted um there's a
+ 
+
+ align:start position:0%
+totally always accepted um there's a
+couple of them that that are used in
+
+ align:start position:0%
+couple of them that that are used in
+ 
+
+ align:start position:0%
+couple of them that that are used in
+simulators today so if you go to the
+
+ align:start position:0%
+simulators today so if you go to the
+ 
+
+ align:start position:0%
+simulators today so if you go to the
+Supreme 4 manual and you read up about
+
+ align:start position:0%
+Supreme 4 manual and you read up about
+ 
+
+ align:start position:0%
+Supreme 4 manual and you read up about
+what thin oxide models are available for
+
+ align:start position:0%
+what thin oxide models are available for
+ 
+
+ align:start position:0%
+what thin oxide models are available for
+you to use in your numerical simulations
+
+ align:start position:0%
+you to use in your numerical simulations
+ 
+
+ align:start position:0%
+you to use in your numerical simulations
+here's an example of three of
+
+ align:start position:0%
+here's an example of three of
+ 
+
+ align:start position:0%
+here's an example of three of
+them uh there's the rean model uh Han
+
+ align:start position:0%
+them uh there's the rean model uh Han
+ 
+
+ align:start position:0%
+them uh there's the rean model uh Han
+and Helms and the massud model um so I
+
+ align:start position:0%
+and Helms and the massud model um so I
+ 
+
+ align:start position:0%
+and Helms and the massud model um so I
+want to go through these three they're
+
+ align:start position:0%
+want to go through these three they're
+ 
+
+ align:start position:0%
+want to go through these three they're
+maybe um maybe the most popular or well
+
+ align:start position:0%
+maybe um maybe the most popular or well
+ 
+
+ align:start position:0%
+maybe um maybe the most popular or well
+known of all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proposals so on slide 21 we have the
+
+ align:start position:0%
+proposals so on slide 21 we have the
+ 
+
+ align:start position:0%
+proposals so on slide 21 we have the
+raceman model um and uh this uh they
+
+ align:start position:0%
+raceman model um and uh this uh they
+ 
+
+ align:start position:0%
+raceman model um and uh this uh they
+they actually proposed a relatively
+
+ align:start position:0%
+they actually proposed a relatively
+ 
+
+ align:start position:0%
+they actually proposed a relatively
+simple power law but it's it seems in
+
+ align:start position:0%
+simple power law but it's it seems in
+ 
+
+ align:start position:0%
+simple power law but it's it seems in
+some people regarded as more of a
+
+ align:start position:0%
+some people regarded as more of a
+ 
+
+ align:start position:0%
+some people regarded as more of a
+mathematical fit uh that quote unquote
+
+ align:start position:0%
+mathematical fit uh that quote unquote
+ 
+
+ align:start position:0%
+mathematical fit uh that quote unquote
+fits the data for dry O2 over a wide
+
+ align:start position:0%
+fits the data for dry O2 over a wide
+ 
+
+ align:start position:0%
+fits the data for dry O2 over a wide
+range of thicknesses and so their power
+
+ align:start position:0%
+range of thicknesses and so their power
+ 
+
+ align:start position:0%
+range of thicknesses and so their power
+law um is actually looks different from
+
+ align:start position:0%
+law um is actually looks different from
+ 
+
+ align:start position:0%
+law um is actually looks different from
+the deal Grove model they say the oxide
+
+ align:start position:0%
+the deal Grove model they say the oxide
+ 
+
+ align:start position:0%
+the deal Grove model they say the oxide
+thickness X not is some constant a Time
+
+ align:start position:0%
+thickness X not is some constant a Time
+ 
+
+ align:start position:0%
+thickness X not is some constant a Time
+t plus ti ti is the initial oxide um
+
+ align:start position:0%
+t plus ti ti is the initial oxide um
+ 
+
+ align:start position:0%
+t plus ti ti is the initial oxide um
+thickness or time equivalent to uh
+
+ align:start position:0%
+thickness or time equivalent to uh
+ 
+
+ align:start position:0%
+thickness or time equivalent to uh
+corresponding to uh the initial oxide to
+
+ align:start position:0%
+corresponding to uh the initial oxide to
+ 
+
+ align:start position:0%
+corresponding to uh the initial oxide to
+the B
+
+ align:start position:0%
+the B
+ 
+
+ align:start position:0%
+the B
+power um or you can uh you know
+
+ align:start position:0%
+power um or you can uh you know
+ 
+
+ align:start position:0%
+power um or you can uh you know
+rearrange it so it looks something like
+
+ align:start position:0%
+rearrange it so it looks something like
+ 
+
+ align:start position:0%
+rearrange it so it looks something like
+this in terms of A and B uh
+
+ align:start position:0%
+this in terms of A and B uh
+ 
+
+ align:start position:0%
+this in terms of A and B uh
+look at this compared to deal Grove you
+
+ align:start position:0%
+look at this compared to deal Grove you
+ 
+
+ align:start position:0%
+look at this compared to deal Grove you
+can see it is actually um it is actually
+
+ align:start position:0%
+can see it is actually um it is actually
+ 
+
+ align:start position:0%
+can see it is actually um it is actually
+uh quite different um although they
+
+ align:start position:0%
+uh quite different um although they
+ 
+
+ align:start position:0%
+uh quite different um although they
+still have a couple of constants they
+
+ align:start position:0%
+still have a couple of constants they
+ 
+
+ align:start position:0%
+still have a couple of constants they
+have a little a a lowercase a and a
+
+ align:start position:0%
+have a little a a lowercase a and a
+ 
+
+ align:start position:0%
+have a little a a lowercase a and a
+lowercase b uh for a given set of
+
+ align:start position:0%
+lowercase b uh for a given set of
+ 
+
+ align:start position:0%
+lowercase b uh for a given set of
+process conditions so similar to deal
+
+ align:start position:0%
+process conditions so similar to deal
+ 
+
+ align:start position:0%
+process conditions so similar to deal
+Grove you have two constants they're
+
+ align:start position:0%
+Grove you have two constants they're
+ 
+
+ align:start position:0%
+Grove you have two constants they're
+different numbers um this actually works
+
+ align:start position:0%
+different numbers um this actually works
+ 
+
+ align:start position:0%
+different numbers um this actually works
+the fit mathematically fits better in
+
+ align:start position:0%
+the fit mathematically fits better in
+ 
+
+ align:start position:0%
+the fit mathematically fits better in
+the thin oxide regime um the problem is
+
+ align:start position:0%
+the thin oxide regime um the problem is
+ 
+
+ align:start position:0%
+the thin oxide regime um the problem is
+it's not as it's not as uh appealing in
+
+ align:start position:0%
+it's not as it's not as uh appealing in
+ 
+
+ align:start position:0%
+it's not as it's not as uh appealing in
+sense of it's not as quite as simple
+
+ align:start position:0%
+sense of it's not as quite as simple
+ 
+
+ align:start position:0%
+sense of it's not as quite as simple
+deal Grove uh but they their physical uh
+
+ align:start position:0%
+deal Grove uh but they their physical uh
+ 
+
+ align:start position:0%
+deal Grove uh but they their physical uh
+reasoning was that the interface
+
+ align:start position:0%
+reasoning was that the interface
+ 
+
+ align:start position:0%
+reasoning was that the interface
+reaction controls the oxidation process
+
+ align:start position:0%
+reaction controls the oxidation process
+ 
+
+ align:start position:0%
+reaction controls the oxidation process
+at all times this is what they thought
+
+ align:start position:0%
+at all times this is what they thought
+ 
+
+ align:start position:0%
+at all times this is what they thought
+um but they believe that this volume
+
+ align:start position:0%
+um but they believe that this volume
+ 
+
+ align:start position:0%
+um but they believe that this volume
+expansion the need for the volume
+
+ align:start position:0%
+expansion the need for the volume
+ 
+
+ align:start position:0%
+expansion the need for the volume
+expansion and and the flow of the oxide
+
+ align:start position:0%
+expansion and and the flow of the oxide
+ 
+
+ align:start position:0%
+expansion and and the flow of the oxide
+the interface control the the um growth
+
+ align:start position:0%
+the interface control the the um growth
+ 
+
+ align:start position:0%
+the interface control the the um growth
+uh kinetics the rate and a and b were
+
+ align:start position:0%
+uh kinetics the rate and a and b were
+ 
+
+ align:start position:0%
+uh kinetics the rate and a and b were
+believed to be some time dependent flow
+
+ align:start position:0%
+believed to be some time dependent flow
+ 
+
+ align:start position:0%
+believed to be some time dependent flow
+parameters for the oxide so uh not as
+
+ align:start position:0%
+parameters for the oxide so uh not as
+ 
+
+ align:start position:0%
+parameters for the oxide so uh not as
+obvious or as simple appealing as the
+
+ align:start position:0%
+obvious or as simple appealing as the
+ 
+
+ align:start position:0%
+obvious or as simple appealing as the
+simple deal Grove model but but they
+
+ align:start position:0%
+simple deal Grove model but but they
+ 
+
+ align:start position:0%
+simple deal Grove model but but they
+also uh found that mathematically it
+
+ align:start position:0%
+also uh found that mathematically it
+ 
+
+ align:start position:0%
+also uh found that mathematically it
+just makes a better
+
+ align:start position:0%
+just makes a better
+ 
+
+ align:start position:0%
+just makes a better
+fit so people do um sometimes use this
+
+ align:start position:0%
+fit so people do um sometimes use this
+ 
+
+ align:start position:0%
+fit so people do um sometimes use this
+type of model and and then fit their own
+
+ align:start position:0%
+type of model and and then fit their own
+ 
+
+ align:start position:0%
+type of model and and then fit their own
+data with their own A and B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants so that's the the reesman
+
+ align:start position:0%
+constants so that's the the reesman
+ 
+
+ align:start position:0%
+constants so that's the the reesman
+model um H and Helms came along and got
+
+ align:start position:0%
+model um H and Helms came along and got
+ 
+
+ align:start position:0%
+model um H and Helms came along and got
+uh uh additional data and they actually
+
+ align:start position:0%
+uh uh additional data and they actually
+ 
+
+ align:start position:0%
+uh uh additional data and they actually
+said this they actually said that there
+
+ align:start position:0%
+said this they actually said that there
+ 
+
+ align:start position:0%
+said this they actually said that there
+are two in parallel a couple of
+
+ align:start position:0%
+are two in parallel a couple of
+ 
+
+ align:start position:0%
+are two in parallel a couple of
+different oxidation processes taking
+
+ align:start position:0%
+different oxidation processes taking
+ 
+
+ align:start position:0%
+different oxidation processes taking
+place um uh in the model so perhaps they
+
+ align:start position:0%
+place um uh in the model so perhaps they
+ 
+
+ align:start position:0%
+place um uh in the model so perhaps they
+said not only o2 molecules but oxygen
+
+ align:start position:0%
+said not only o2 molecules but oxygen
+ 
+
+ align:start position:0%
+said not only o2 molecules but oxygen
+atoms can diffuse through the oxide
+
+ align:start position:0%
+atoms can diffuse through the oxide
+ 
+
+ align:start position:0%
+atoms can diffuse through the oxide
+maybe in
+
+ align:start position:0%
+maybe in
+ 
+
+ align:start position:0%
+maybe in
+parallel or maybe there's diffusion of
+
+ align:start position:0%
+parallel or maybe there's diffusion of
+ 
+
+ align:start position:0%
+parallel or maybe there's diffusion of
+oxygen vacancies and so you have
+
+ align:start position:0%
+oxygen vacancies and so you have
+ 
+
+ align:start position:0%
+oxygen vacancies and so you have
+something diffusing in and something
+
+ align:start position:0%
+something diffusing in and something
+ 
+
+ align:start position:0%
+something diffusing in and something
+else diffusing out and nevertheless they
+
+ align:start position:0%
+else diffusing out and nevertheless they
+ 
+
+ align:start position:0%
+else diffusing out and nevertheless they
+said there are two species that you need
+
+ align:start position:0%
+said there are two species that you need
+ 
+
+ align:start position:0%
+said there are two species that you need
+to take into account uh and these can
+
+ align:start position:0%
+to take into account uh and these can
+ 
+
+ align:start position:0%
+to take into account uh and these can
+cause re and they have Associated
+
+ align:start position:0%
+cause re and they have Associated
+ 
+
+ align:start position:0%
+cause re and they have Associated
+reactions uh at the interfaces so it
+
+ align:start position:0%
+reactions uh at the interfaces so it
+ 
+
+ align:start position:0%
+reactions uh at the interfaces so it
+looks very much like deal Grove fact
+
+ align:start position:0%
+looks very much like deal Grove fact
+ 
+
+ align:start position:0%
+looks very much like deal Grove fact
+this is deal Grove if you express deal
+
+ align:start position:0%
+this is deal Grove if you express deal
+ 
+
+ align:start position:0%
+this is deal Grove if you express deal
+Grove remember in terms of an oxidation
+
+ align:start position:0%
+Grove remember in terms of an oxidation
+ 
+
+ align:start position:0%
+Grove remember in terms of an oxidation
+rate it's just B / 2 X plus a this looks
+
+ align:start position:0%
+rate it's just B / 2 X plus a this looks
+ 
+
+ align:start position:0%
+rate it's just B / 2 X plus a this looks
+a lot like deal grow but they've added a
+
+ align:start position:0%
+a lot like deal grow but they've added a
+ 
+
+ align:start position:0%
+a lot like deal grow but they've added a
+second term and this this second term
+
+ align:start position:0%
+second term and this this second term
+ 
+
+ align:start position:0%
+second term and this this second term
+here is to correspond to that second
+
+ align:start position:0%
+here is to correspond to that second
+ 
+
+ align:start position:0%
+here is to correspond to that second
+oxidation uh oxidation process happening
+
+ align:start position:0%
+oxidation uh oxidation process happening
+ 
+
+ align:start position:0%
+oxidation uh oxidation process happening
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+parallel and they proposed that all rate
+
+ align:start position:0%
+parallel and they proposed that all rate
+ 
+
+ align:start position:0%
+parallel and they proposed that all rate
+constants would be of an arous type
+
+ align:start position:0%
+constants would be of an arous type
+ 
+
+ align:start position:0%
+constants would be of an arous type
+nature based on the data that they they
+
+ align:start position:0%
+nature based on the data that they they
+ 
+
+ align:start position:0%
+nature based on the data that they they
+fit uh it's just like deal Grove but in
+
+ align:start position:0%
+fit uh it's just like deal Grove but in
+ 
+
+ align:start position:0%
+fit uh it's just like deal Grove but in
+fact they um so you say well you double
+
+ align:start position:0%
+fact they um so you say well you double
+ 
+
+ align:start position:0%
+fact they um so you say well you double
+you should double the number of
+
+ align:start position:0%
+you should double the number of
+ 
+
+ align:start position:0%
+you should double the number of
+constants on Deal Grove so instead of
+
+ align:start position:0%
+constants on Deal Grove so instead of
+ 
+
+ align:start position:0%
+constants on Deal Grove so instead of
+two you should have four in fact what
+
+ align:start position:0%
+two you should have four in fact what
+ 
+
+ align:start position:0%
+two you should have four in fact what
+they found they only really needed three
+
+ align:start position:0%
+they found they only really needed three
+ 
+
+ align:start position:0%
+they found they only really needed three
+parameters to fit the data so they
+
+ align:start position:0%
+parameters to fit the data so they
+ 
+
+ align:start position:0%
+parameters to fit the data so they
+needed a B1 associated with this process
+
+ align:start position:0%
+needed a B1 associated with this process
+ 
+
+ align:start position:0%
+needed a B1 associated with this process
+uh and a B2 associated with this process
+
+ align:start position:0%
+uh and a B2 associated with this process
+ 
+
+ align:start position:0%
+uh and a B2 associated with this process
+and B2 over A2 so they found A1 equal to
+
+ align:start position:0%
+and B2 over A2 so they found A1 equal to
+ 
+
+ align:start position:0%
+and B2 over A2 so they found A1 equal to
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+zero so those of you who are
+
+ align:start position:0%
+zero so those of you who are
+ 
+
+ align:start position:0%
+zero so those of you who are
+skeptical uh in the audience will say
+
+ align:start position:0%
+skeptical uh in the audience will say
+ 
+
+ align:start position:0%
+skeptical uh in the audience will say
+well okay The Grove had two uh two
+
+ align:start position:0%
+well okay The Grove had two uh two
+ 
+
+ align:start position:0%
+well okay The Grove had two uh two
+parameters and Han and Helms have three
+
+ align:start position:0%
+parameters and Han and Helms have three
+ 
+
+ align:start position:0%
+parameters and Han and Helms have three
+so you can if you add more and more
+
+ align:start position:0%
+so you can if you add more and more
+ 
+
+ align:start position:0%
+so you can if you add more and more
+parameters to a fit you can always do a
+
+ align:start position:0%
+parameters to a fit you can always do a
+ 
+
+ align:start position:0%
+parameters to a fit you can always do a
+better job mathematically of fitting
+
+ align:start position:0%
+better job mathematically of fitting
+ 
+
+ align:start position:0%
+better job mathematically of fitting
+data everybody kind of knows that from
+
+ align:start position:0%
+data everybody kind of knows that from
+ 
+
+ align:start position:0%
+data everybody kind of knows that from
+your mathematical experience so you
+
+ align:start position:0%
+your mathematical experience so you
+ 
+
+ align:start position:0%
+your mathematical experience so you
+could be skeptical and say all right
+
+ align:start position:0%
+could be skeptical and say all right
+ 
+
+ align:start position:0%
+could be skeptical and say all right
+they just add another constant and and
+
+ align:start position:0%
+they just add another constant and and
+ 
+
+ align:start position:0%
+they just add another constant and and
+perhaps that's true because the truth is
+
+ align:start position:0%
+perhaps that's true because the truth is
+ 
+
+ align:start position:0%
+perhaps that's true because the truth is
+there isn't really
+
+ align:start position:0%
+there isn't really
+ 
+
+ align:start position:0%
+there isn't really
+any you know definitive data saying what
+
+ align:start position:0%
+any you know definitive data saying what
+ 
+
+ align:start position:0%
+any you know definitive data saying what
+the species are that are diffusing
+
+ align:start position:0%
+the species are that are diffusing
+ 
+
+ align:start position:0%
+the species are that are diffusing
+through there um but nevertheless they
+
+ align:start position:0%
+through there um but nevertheless they
+ 
+
+ align:start position:0%
+through there um but nevertheless they
+did come up with a model that's
+
+ align:start position:0%
+did come up with a model that's
+ 
+
+ align:start position:0%
+did come up with a model that's
+reasonably simple that does a better job
+
+ align:start position:0%
+reasonably simple that does a better job
+ 
+
+ align:start position:0%
+reasonably simple that does a better job
+in the thin oxide uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kinetics so actually let's compare these
+
+ align:start position:0%
+kinetics so actually let's compare these
+ 
+
+ align:start position:0%
+kinetics so actually let's compare these
+two models uh just on slide 23 with a
+
+ align:start position:0%
+two models uh just on slide 23 with a
+ 
+
+ align:start position:0%
+two models uh just on slide 23 with a
+deal Grove model
+
+ align:start position:0%
+deal Grove model
+ 
+
+ align:start position:0%
+deal Grove model
+so the x-axis here is oxide thickness
+
+ align:start position:0%
+so the x-axis here is oxide thickness
+ 
+
+ align:start position:0%
+so the x-axis here is oxide thickness
+and microns um and this is th uh I'm
+
+ align:start position:0%
+and microns um and this is th uh I'm
+ 
+
+ align:start position:0%
+and microns um and this is th uh I'm
+sorry the y axis is thickness the x-axis
+
+ align:start position:0%
+sorry the y axis is thickness the x-axis
+ 
+
+ align:start position:0%
+sorry the y axis is thickness the x-axis
+this time and this is plotted for um
+
+ align:start position:0%
+this time and this is plotted for um
+ 
+
+ align:start position:0%
+this time and this is plotted for um
+atmospheric pressure dry O2 at
+
+ align:start position:0%
+atmospheric pressure dry O2 at
+ 
+
+ align:start position:0%
+atmospheric pressure dry O2 at
+800° and so let's look at the the the
+
+ align:start position:0%
+800° and so let's look at the the the
+ 
+
+ align:start position:0%
+800° and so let's look at the the the
+different models this line right here
+
+ align:start position:0%
+different models this line right here
+ 
+
+ align:start position:0%
+different models this line right here
+unfortunately they're all the same color
+
+ align:start position:0%
+unfortunately they're all the same color
+ 
+
+ align:start position:0%
+unfortunately they're all the same color
+I apologize but you can sort of see
+
+ align:start position:0%
+I apologize but you can sort of see
+ 
+
+ align:start position:0%
+I apologize but you can sort of see
+where the arrow is pointing to the rean
+
+ align:start position:0%
+where the arrow is pointing to the rean
+ 
+
+ align:start position:0%
+where the arrow is pointing to the rean
+model um look something like this H and
+
+ align:start position:0%
+model um look something like this H and
+ 
+
+ align:start position:0%
+model um look something like this H and
+Helms amazingly you know different
+
+ align:start position:0%
+Helms amazingly you know different
+ 
+
+ align:start position:0%
+Helms amazingly you know different
+mathematical equations but they look
+
+ align:start position:0%
+mathematical equations but they look
+ 
+
+ align:start position:0%
+mathematical equations but they look
+pretty darn close they're not exactly on
+
+ align:start position:0%
+pretty darn close they're not exactly on
+ 
+
+ align:start position:0%
+pretty darn close they're not exactly on
+top of each other in this thin oxide
+
+ align:start position:0%
+top of each other in this thin oxide
+ 
+
+ align:start position:0%
+top of each other in this thin oxide
+machinee but they're pretty darn close
+
+ align:start position:0%
+machinee but they're pretty darn close
+ 
+
+ align:start position:0%
+machinee but they're pretty darn close
+uh the deal Grove model with t equals
+
+ align:start position:0%
+uh the deal Grove model with t equals
+ 
+
+ align:start position:0%
+uh the deal Grove model with t equals
+Zer looks like this and withal equals 8
+
+ align:start position:0%
+Zer looks like this and withal equals 8
+ 
+
+ align:start position:0%
+Zer looks like this and withal equals 8
+looks like that doesn't actually
+
+ align:start position:0%
+looks like that doesn't actually
+ 
+
+ align:start position:0%
+looks like that doesn't actually
+approach e either one of them very well
+
+ align:start position:0%
+approach e either one of them very well
+ 
+
+ align:start position:0%
+approach e either one of them very well
+until you get into the thicker regime up
+
+ align:start position:0%
+until you get into the thicker regime up
+ 
+
+ align:start position:0%
+until you get into the thicker regime up
+here um but in this thin regime say
+
+ align:start position:0%
+here um but in this thin regime say
+ 
+
+ align:start position:0%
+here um but in this thin regime say
+below 200 angstroms or 02 microns uh
+
+ align:start position:0%
+below 200 angstroms or 02 microns uh
+ 
+
+ align:start position:0%
+below 200 angstroms or 02 microns uh
+deal Grove doesn't really approach
+
+ align:start position:0%
+deal Grove doesn't really approach
+ 
+
+ align:start position:0%
+deal Grove doesn't really approach
+either one and and Han and Helms and
+
+ align:start position:0%
+either one and and Han and Helms and
+ 
+
+ align:start position:0%
+either one and and Han and Helms and
+Raisman do actually approach the data
+
+ align:start position:0%
+Raisman do actually approach the data
+ 
+
+ align:start position:0%
+Raisman do actually approach the data
+quite quite well they will converge
+
+ align:start position:0%
+quite quite well they will converge
+ 
+
+ align:start position:0%
+quite quite well they will converge
+though when you get oxides thicker than
+
+ align:start position:0%
+though when you get oxides thicker than
+ 
+
+ align:start position:0%
+though when you get oxides thicker than
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+angstroms there's one more model that
+
+ align:start position:0%
+angstroms there's one more model that
+ 
+
+ align:start position:0%
+angstroms there's one more model that
+people actually uh are very uh are very
+
+ align:start position:0%
+people actually uh are very uh are very
+ 
+
+ align:start position:0%
+people actually uh are very uh are very
+fond of and I'll talk about that now
+
+ align:start position:0%
+fond of and I'll talk about that now
+ 
+
+ align:start position:0%
+fond of and I'll talk about that now
+that's shown on slide 24 this was the um
+
+ align:start position:0%
+that's shown on slide 24 this was the um
+ 
+
+ align:start position:0%
+that's shown on slide 24 this was the um
+the massud model this was published
+
+ align:start position:0%
+the massud model this was published
+ 
+
+ align:start position:0%
+the massud model this was published
+quite some time ago at the
+
+ align:start position:0%
+quite some time ago at the
+ 
+
+ align:start position:0%
+quite some time ago at the
+electrochemical society and the nice
+
+ align:start position:0%
+electrochemical society and the nice
+ 
+
+ align:start position:0%
+electrochemical society and the nice
+thing about H the neat thing about uh
+
+ align:start position:0%
+thing about H the neat thing about uh
+ 
+
+ align:start position:0%
+thing about H the neat thing about uh
+Mass's experiment was they actually
+
+ align:start position:0%
+Mass's experiment was they actually
+ 
+
+ align:start position:0%
+Mass's experiment was they actually
+measured in in
+
+ align:start position:0%
+measured in in
+ 
+
+ align:start position:0%
+measured in in
+situ you know in the furnace they
+
+ align:start position:0%
+situ you know in the furnace they
+ 
+
+ align:start position:0%
+situ you know in the furnace they
+actually measured the thickness uh of
+
+ align:start position:0%
+actually measured the thickness uh of
+ 
+
+ align:start position:0%
+actually measured the thickness uh of
+the oxide growing as a function of time
+
+ align:start position:0%
+the oxide growing as a function of time
+ 
+
+ align:start position:0%
+the oxide growing as a function of time
+so the other people like deal Grove and
+
+ align:start position:0%
+so the other people like deal Grove and
+ 
+
+ align:start position:0%
+so the other people like deal Grove and
+and Han and Helms all those people you
+
+ align:start position:0%
+and Han and Helms all those people you
+ 
+
+ align:start position:0%
+and Han and Helms all those people you
+know they put a couple wafers in and
+
+ align:start position:0%
+know they put a couple wafers in and
+ 
+
+ align:start position:0%
+know they put a couple wafers in and
+take them out you know put them in for
+
+ align:start position:0%
+take them out you know put them in for
+ 
+
+ align:start position:0%
+take them out you know put them in for
+different amounts of time and so they
+
+ align:start position:0%
+different amounts of time and so they
+ 
+
+ align:start position:0%
+different amounts of time and so they
+get a few certain data points you know
+
+ align:start position:0%
+get a few certain data points you know
+ 
+
+ align:start position:0%
+get a few certain data points you know
+how many Wafers can you put in maybe
+
+ align:start position:0%
+how many Wafers can you put in maybe
+ 
+
+ align:start position:0%
+how many Wafers can you put in maybe
+five or 10 in an experiment so you can't
+
+ align:start position:0%
+five or 10 in an experiment so you can't
+ 
+
+ align:start position:0%
+five or 10 in an experiment so you can't
+really measure the kinetics in in great
+
+ align:start position:0%
+really measure the kinetics in in great
+ 
+
+ align:start position:0%
+really measure the kinetics in in great
+detail uh if you're just pushing pulling
+
+ align:start position:0%
+detail uh if you're just pushing pulling
+ 
+
+ align:start position:0%
+detail uh if you're just pushing pulling
+Wafers out of the furnace and just
+
+ align:start position:0%
+Wafers out of the furnace and just
+ 
+
+ align:start position:0%
+Wafers out of the furnace and just
+measuring them outside what massud
+
+ align:start position:0%
+measuring them outside what massud
+ 
+
+ align:start position:0%
+measuring them outside what massud
+decided to do to study the very thin
+
+ align:start position:0%
+decided to do to study the very thin
+ 
+
+ align:start position:0%
+decided to do to study the very thin
+regime
+
+ align:start position:0%
+regime
+ 
+
+ align:start position:0%
+regime
+uh was actually set up and it was
+
+ align:start position:0%
+uh was actually set up and it was
+ 
+
+ align:start position:0%
+uh was actually set up and it was
+non-trivial he had a diffusion furnace
+
+ align:start position:0%
+non-trivial he had a diffusion furnace
+ 
+
+ align:start position:0%
+non-trivial he had a diffusion furnace
+had special Windows placed into it where
+
+ align:start position:0%
+had special Windows placed into it where
+ 
+
+ align:start position:0%
+had special Windows placed into it where
+he could put laser beam so you could put
+
+ align:start position:0%
+he could put laser beam so you could put
+ 
+
+ align:start position:0%
+he could put laser beam so you could put
+a laser beam coming in laser beam coming
+
+ align:start position:0%
+a laser beam coming in laser beam coming
+ 
+
+ align:start position:0%
+a laser beam coming in laser beam coming
+out and he could do insitu measurements
+
+ align:start position:0%
+out and he could do insitu measurements
+ 
+
+ align:start position:0%
+out and he could do insitu measurements
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+ellipsometry um of the oxidate oxide out
+
+ align:start position:0%
+ellipsometry um of the oxidate oxide out
+ 
+
+ align:start position:0%
+ellipsometry um of the oxidate oxide out
+as it was growing in the tube it doesn't
+
+ align:start position:0%
+as it was growing in the tube it doesn't
+ 
+
+ align:start position:0%
+as it was growing in the tube it doesn't
+you it doesn't sound like a big deal but
+
+ align:start position:0%
+you it doesn't sound like a big deal but
+ 
+
+ align:start position:0%
+you it doesn't sound like a big deal but
+it turns out it's it's pretty uh
+
+ align:start position:0%
+it turns out it's it's pretty uh
+ 
+
+ align:start position:0%
+it turns out it's it's pretty uh
+challenging because there's all kinds of
+
+ align:start position:0%
+challenging because there's all kinds of
+ 
+
+ align:start position:0%
+challenging because there's all kinds of
+thermal expansion going on and the wafer
+
+ align:start position:0%
+thermal expansion going on and the wafer
+ 
+
+ align:start position:0%
+thermal expansion going on and the wafer
+has to sit still and not move while this
+
+ align:start position:0%
+has to sit still and not move while this
+ 
+
+ align:start position:0%
+has to sit still and not move while this
+laser comes in hits and bounces off
+
+ align:start position:0%
+laser comes in hits and bounces off
+ 
+
+ align:start position:0%
+laser comes in hits and bounces off
+because in ellip omry the angle of
+
+ align:start position:0%
+because in ellip omry the angle of
+ 
+
+ align:start position:0%
+because in ellip omry the angle of
+incidence is very important and all that
+
+ align:start position:0%
+incidence is very important and all that
+ 
+
+ align:start position:0%
+incidence is very important and all that
+so designing the equipment was like a
+
+ align:start position:0%
+so designing the equipment was like a
+ 
+
+ align:start position:0%
+so designing the equipment was like a
+huge part of this PhD faces uh but it
+
+ align:start position:0%
+huge part of this PhD faces uh but it
+ 
+
+ align:start position:0%
+huge part of this PhD faces uh but it
+the nice thing is it did produce a lot
+
+ align:start position:0%
+the nice thing is it did produce a lot
+ 
+
+ align:start position:0%
+the nice thing is it did produce a lot
+of data look at all these data points
+
+ align:start position:0%
+of data look at all these data points
+ 
+
+ align:start position:0%
+of data look at all these data points
+they're all basically give you a nice
+
+ align:start position:0%
+they're all basically give you a nice
+ 
+
+ align:start position:0%
+they're all basically give you a nice
+looking curve instead of one point here
+
+ align:start position:0%
+looking curve instead of one point here
+ 
+
+ align:start position:0%
+looking curve instead of one point here
+one here and one here uh he published um
+
+ align:start position:0%
+one here and one here uh he published um
+ 
+
+ align:start position:0%
+one here and one here uh he published um
+measured Inu measured oxidation rates
+
+ align:start position:0%
+measured Inu measured oxidation rates
+ 
+
+ align:start position:0%
+measured Inu measured oxidation rates
+now this is the rate so this is not the
+
+ align:start position:0%
+now this is the rate so this is not the
+ 
+
+ align:start position:0%
+now this is the rate so this is not the
+thickness this is angstroms per
+
+ align:start position:0%
+thickness this is angstroms per
+ 
+
+ align:start position:0%
+thickness this is angstroms per
+minute uh as a function of the thickness
+
+ align:start position:0%
+minute uh as a function of the thickness
+ 
+
+ align:start position:0%
+minute uh as a function of the thickness
+grown and indeed look below 200
+
+ align:start position:0%
+grown and indeed look below 200
+ 
+
+ align:start position:0%
+grown and indeed look below 200
+angstroms um all these rates are much
+
+ align:start position:0%
+angstroms um all these rates are much
+ 
+
+ align:start position:0%
+angstroms um all these rates are much
+larger than they are uh where they they
+
+ align:start position:0%
+larger than they are uh where they they
+ 
+
+ align:start position:0%
+larger than they are uh where they they
+they reach steady state they reach
+
+ align:start position:0%
+they reach steady state they reach
+ 
+
+ align:start position:0%
+they reach steady state they reach
+smaller uh rates and these are at three
+
+ align:start position:0%
+smaller uh rates and these are at three
+ 
+
+ align:start position:0%
+smaller uh rates and these are at three
+different temperatures 800 900 and a
+
+ align:start position:0%
+different temperatures 800 900 and a
+ 
+
+ align:start position:0%
+different temperatures 800 900 and a
+th000 and in the thin oxide regime the
+
+ align:start position:0%
+th000 and in the thin oxide regime the
+ 
+
+ align:start position:0%
+th000 and in the thin oxide regime the
+rate itself appears to be going up
+
+ align:start position:0%
+rate itself appears to be going up
+ 
+
+ align:start position:0%
+rate itself appears to be going up
+exponentially uh as you get to thinner
+
+ align:start position:0%
+exponentially uh as you get to thinner
+ 
+
+ align:start position:0%
+exponentially uh as you get to thinner
+and thinner which are shorter and
+
+ align:start position:0%
+and thinner which are shorter and
+ 
+
+ align:start position:0%
+and thinner which are shorter and
+shorter times so interestingly initially
+
+ align:start position:0%
+shorter times so interestingly initially
+ 
+
+ align:start position:0%
+shorter times so interestingly initially
+it appears to be in fact an exponential
+
+ align:start position:0%
+it appears to be in fact an exponential
+ 
+
+ align:start position:0%
+it appears to be in fact an exponential
+process with time so it's growing very
+
+ align:start position:0%
+process with time so it's growing very
+ 
+
+ align:start position:0%
+process with time so it's growing very
+rapidly uh and then it starts to
+
+ align:start position:0%
+rapidly uh and then it starts to
+ 
+
+ align:start position:0%
+rapidly uh and then it starts to
+converge to a process that looks going
+
+ align:start position:0%
+converge to a process that looks going
+ 
+
+ align:start position:0%
+converge to a process that looks going
+to look more linear and then eventually
+
+ align:start position:0%
+to look more linear and then eventually
+ 
+
+ align:start position:0%
+to look more linear and then eventually
+parabolic only with that kind of special
+
+ align:start position:0%
+parabolic only with that kind of special
+ 
+
+ align:start position:0%
+parabolic only with that kind of special
+apparatus could one get enough data
+
+ align:start position:0%
+apparatus could one get enough data
+ 
+
+ align:start position:0%
+apparatus could one get enough data
+point density to really see that though
+
+ align:start position:0%
+point density to really see that though
+ 
+
+ align:start position:0%
+point density to really see that though
+so this is probably the most um
+
+ align:start position:0%
+so this is probably the most um
+ 
+
+ align:start position:0%
+so this is probably the most um
+extensive experimental study that has
+
+ align:start position:0%
+extensive experimental study that has
+ 
+
+ align:start position:0%
+extensive experimental study that has
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+done um and what he did was he took deal
+
+ align:start position:0%
+done um and what he did was he took deal
+ 
+
+ align:start position:0%
+done um and what he did was he took deal
+grow just as it as it came right out of
+
+ align:start position:0%
+grow just as it as it came right out of
+ 
+
+ align:start position:0%
+grow just as it as it came right out of
+the box and added one more term but the
+
+ align:start position:0%
+the box and added one more term but the
+ 
+
+ align:start position:0%
+the box and added one more term but the
+term was exponential in
+
+ align:start position:0%
+term was exponential in
+ 
+
+ align:start position:0%
+term was exponential in
+thickness so the oxidation rate had the
+
+ align:start position:0%
+thickness so the oxidation rate had the
+ 
+
+ align:start position:0%
+thickness so the oxidation rate had the
+deal Grove B / 2x KN plus a plus a term
+
+ align:start position:0%
+deal Grove B / 2x KN plus a plus a term
+ 
+
+ align:start position:0%
+deal Grove B / 2x KN plus a plus a term
+that went like C * exponential of minus
+
+ align:start position:0%
+that went like C * exponential of minus
+ 
+
+ align:start position:0%
+that went like C * exponential of minus
+x l so what is this this mathematically
+
+ align:start position:0%
+x l so what is this this mathematically
+ 
+
+ align:start position:0%
+x l so what is this this mathematically
+this is a decaying exponential when L
+
+ align:start position:0%
+this is a decaying exponential when L
+ 
+
+ align:start position:0%
+this is a decaying exponential when L
+gets very large L is much greater than
+
+ align:start position:0%
+gets very large L is much greater than
+ 
+
+ align:start position:0%
+gets very large L is much greater than
+200 angstroms this this number goes away
+
+ align:start position:0%
+200 angstroms this this number goes away
+ 
+
+ align:start position:0%
+200 angstroms this this number goes away
+right you can always make it go go uh go
+
+ align:start position:0%
+right you can always make it go go uh go
+ 
+
+ align:start position:0%
+right you can always make it go go uh go
+go to be very small compared to this
+
+ align:start position:0%
+go to be very small compared to this
+ 
+
+ align:start position:0%
+go to be very small compared to this
+term so he wanted it all converge to
+
+ align:start position:0%
+term so he wanted it all converge to
+ 
+
+ align:start position:0%
+term so he wanted it all converge to
+deal growth at thick enough oxides but
+
+ align:start position:0%
+deal growth at thick enough oxides but
+ 
+
+ align:start position:0%
+deal growth at thick enough oxides but
+for thin oxides this is going to
+
+ align:start position:0%
+for thin oxides this is going to
+ 
+
+ align:start position:0%
+for thin oxides this is going to
+dominate this C
+
+ align:start position:0%
+dominate this C
+ 
+
+ align:start position:0%
+dominate this C
+term uh and he in order to do that he
+
+ align:start position:0%
+term uh and he in order to do that he
+ 
+
+ align:start position:0%
+term uh and he in order to do that he
+had to choose L to be a certain number
+
+ align:start position:0%
+had to choose L to be a certain number
+ 
+
+ align:start position:0%
+had to choose L to be a certain number
+so that had the right Decay length and
+
+ align:start position:0%
+so that had the right Decay length and
+ 
+
+ align:start position:0%
+so that had the right Decay length and
+and L he found experimentally should be
+
+ align:start position:0%
+and L he found experimentally should be
+ 
+
+ align:start position:0%
+and L he found experimentally should be
+about 7 nmet so that the second term
+
+ align:start position:0%
+about 7 nmet so that the second term
+ 
+
+ align:start position:0%
+about 7 nmet so that the second term
+will Decay rapidly enough uh by the time
+
+ align:start position:0%
+will Decay rapidly enough uh by the time
+ 
+
+ align:start position:0%
+will Decay rapidly enough uh by the time
+you get to um 20 nmet or
+
+ align:start position:0%
+you get to um 20 nmet or
+ 
+
+ align:start position:0%
+you get to um 20 nmet or
+so um in fact this this model does agree
+
+ align:start position:0%
+so um in fact this this model does agree
+ 
+
+ align:start position:0%
+so um in fact this this model does agree
+very well mathematically with
+
+ align:start position:0%
+very well mathematically with
+ 
+
+ align:start position:0%
+very well mathematically with
+experimental data um it's actually very
+
+ align:start position:0%
+experimental data um it's actually very
+ 
+
+ align:start position:0%
+experimental data um it's actually very
+easy to implement in simulators like
+
+ align:start position:0%
+easy to implement in simulators like
+ 
+
+ align:start position:0%
+easy to implement in simulators like
+Supreme 4 and so you will it it has been
+
+ align:start position:0%
+Supreme 4 and so you will it it has been
+ 
+
+ align:start position:0%
+Supreme 4 and so you will it it has been
+found to be implemented in Supreme 4 and
+
+ align:start position:0%
+found to be implemented in Supreme 4 and
+ 
+
+ align:start position:0%
+found to be implemented in Supreme 4 and
+um uh in terms of physical explanations
+
+ align:start position:0%
+um uh in terms of physical explanations
+ 
+
+ align:start position:0%
+um uh in terms of physical explanations
+there's there's a few that have come out
+
+ align:start position:0%
+there's there's a few that have come out
+ 
+
+ align:start position:0%
+there's there's a few that have come out
+but none has really been clearly
+
+ align:start position:0%
+but none has really been clearly
+ 
+
+ align:start position:0%
+but none has really been clearly
+identified as being the right reason uh
+
+ align:start position:0%
+identified as being the right reason uh
+ 
+
+ align:start position:0%
+identified as being the right reason uh
+so for now we use it as sort of a
+
+ align:start position:0%
+so for now we use it as sort of a
+ 
+
+ align:start position:0%
+so for now we use it as sort of a
+mathematical model or an empirical
+
+ align:start position:0%
+mathematical model or an empirical
+ 
+
+ align:start position:0%
+mathematical model or an empirical
+relation um it's very handy and it can
+
+ align:start position:0%
+relation um it's very handy and it can
+ 
+
+ align:start position:0%
+relation um it's very handy and it can
+be reasonably accurate so it's appealing
+
+ align:start position:0%
+be reasonably accurate so it's appealing
+ 
+
+ align:start position:0%
+be reasonably accurate so it's appealing
+in that sense in terms of the physics
+
+ align:start position:0%
+in that sense in terms of the physics
+ 
+
+ align:start position:0%
+in that sense in terms of the physics
+and the chemistry it's not completely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obvious okay so those are the three thin
+
+ align:start position:0%
+obvious okay so those are the three thin
+ 
+
+ align:start position:0%
+obvious okay so those are the three thin
+oxide models and and hopefully you'll
+
+ align:start position:0%
+oxide models and and hopefully you'll
+ 
+
+ align:start position:0%
+oxide models and and hopefully you'll
+get a chance to study some of those a
+
+ align:start position:0%
+get a chance to study some of those a
+ 
+
+ align:start position:0%
+get a chance to study some of those a
+little bit more in in one of your
+
+ align:start position:0%
+little bit more in in one of your
+ 
+
+ align:start position:0%
+little bit more in in one of your
+homework problems um so now let's let's
+
+ align:start position:0%
+homework problems um so now let's let's
+ 
+
+ align:start position:0%
+homework problems um so now let's let's
+let VAR something else all we varied so
+
+ align:start position:0%
+let VAR something else all we varied so
+ 
+
+ align:start position:0%
+let VAR something else all we varied so
+far is the following we varied the
+
+ align:start position:0%
+far is the following we varied the
+ 
+
+ align:start position:0%
+far is the following we varied the
+ambient uh we said it could be dry O2 or
+
+ align:start position:0%
+ambient uh we said it could be dry O2 or
+ 
+
+ align:start position:0%
+ambient uh we said it could be dry O2 or
+water and temperature what else can you
+
+ align:start position:0%
+water and temperature what else can you
+ 
+
+ align:start position:0%
+water and temperature what else can you
+vary well it it turns out people often
+
+ align:start position:0%
+vary well it it turns out people often
+ 
+
+ align:start position:0%
+vary well it it turns out people often
+do vary the pressure um that is the
+
+ align:start position:0%
+do vary the pressure um that is the
+ 
+
+ align:start position:0%
+do vary the pressure um that is the
+partial pressure of the oxidant if you
+
+ align:start position:0%
+partial pressure of the oxidant if you
+ 
+
+ align:start position:0%
+partial pressure of the oxidant if you
+want to grow a very thin oxide and yet
+
+ align:start position:0%
+want to grow a very thin oxide and yet
+ 
+
+ align:start position:0%
+want to grow a very thin oxide and yet
+you want to grow at a higher temperature
+
+ align:start position:0%
+you want to grow at a higher temperature
+ 
+
+ align:start position:0%
+you want to grow at a higher temperature
+because you want to get different uh
+
+ align:start position:0%
+because you want to get different uh
+ 
+
+ align:start position:0%
+because you want to get different uh
+electrical quality of the interface you
+
+ align:start position:0%
+electrical quality of the interface you
+ 
+
+ align:start position:0%
+electrical quality of the interface you
+can't grow too fast so you might want to
+
+ align:start position:0%
+can't grow too fast so you might want to
+ 
+
+ align:start position:0%
+can't grow too fast so you might want to
+slow it down by diluting you can just
+
+ align:start position:0%
+slow it down by diluting you can just
+ 
+
+ align:start position:0%
+slow it down by diluting you can just
+take the oxygen and flow mostly nitrogen
+
+ align:start position:0%
+take the oxygen and flow mostly nitrogen
+ 
+
+ align:start position:0%
+take the oxygen and flow mostly nitrogen
+and have oxygen flow be a very small
+
+ align:start position:0%
+and have oxygen flow be a very small
+ 
+
+ align:start position:0%
+and have oxygen flow be a very small
+fraction of the gas stream that's a way
+
+ align:start position:0%
+fraction of the gas stream that's a way
+ 
+
+ align:start position:0%
+fraction of the gas stream that's a way
+of diluting the uh the gas stream and
+
+ align:start position:0%
+of diluting the uh the gas stream and
+ 
+
+ align:start position:0%
+of diluting the uh the gas stream and
+growing at lower partial
+
+ align:start position:0%
+growing at lower partial
+ 
+
+ align:start position:0%
+growing at lower partial
+pressures so um just as a reminder um
+
+ align:start position:0%
+pressures so um just as a reminder um
+ 
+
+ align:start position:0%
+pressures so um just as a reminder um
+what it deal grow predicts that the
+
+ align:start position:0%
+what it deal grow predicts that the
+ 
+
+ align:start position:0%
+what it deal grow predicts that the
+oxide growth rate should be directly
+
+ align:start position:0%
+oxide growth rate should be directly
+ 
+
+ align:start position:0%
+oxide growth rate should be directly
+proportional to the pressure of the
+
+ align:start position:0%
+proportional to the pressure of the
+ 
+
+ align:start position:0%
+proportional to the pressure of the
+oxygen C star uh effectively you can
+
+ align:start position:0%
+oxygen C star uh effectively you can
+ 
+
+ align:start position:0%
+oxygen C star uh effectively you can
+think of it um should depend on PG where
+
+ align:start position:0%
+think of it um should depend on PG where
+ 
+
+ align:start position:0%
+think of it um should depend on PG where
+PG is the bulk gas pressure um so um
+
+ align:start position:0%
+PG is the bulk gas pressure um so um
+ 
+
+ align:start position:0%
+PG is the bulk gas pressure um so um
+basically if I were to um lower the gas
+
+ align:start position:0%
+basically if I were to um lower the gas
+ 
+
+ align:start position:0%
+basically if I were to um lower the gas
+pressure um you would expect that you
+
+ align:start position:0%
+pressure um you would expect that you
+ 
+
+ align:start position:0%
+pressure um you would expect that you
+could lower the oxidation rate so just
+
+ align:start position:0%
+could lower the oxidation rate so just
+ 
+
+ align:start position:0%
+could lower the oxidation rate so just
+uh to be a little more specific we go on
+
+ align:start position:0%
+uh to be a little more specific we go on
+ 
+
+ align:start position:0%
+uh to be a little more specific we go on
+to slide
+
+ align:start position:0%
+to slide
+ 
+
+ align:start position:0%
+to slide
+27 what people have found though is it's
+
+ align:start position:0%
+27 what people have found though is it's
+ 
+
+ align:start position:0%
+27 what people have found though is it's
+not completely linear um experimentally
+
+ align:start position:0%
+not completely linear um experimentally
+ 
+
+ align:start position:0%
+not completely linear um experimentally
+if you lower the partial pressure of the
+
+ align:start position:0%
+if you lower the partial pressure of the
+ 
+
+ align:start position:0%
+if you lower the partial pressure of the
+oxidant um in fact B and B over a do
+
+ align:start position:0%
+oxidant um in fact B and B over a do
+ 
+
+ align:start position:0%
+oxidant um in fact B and B over a do
+scale like P where P would be the
+
+ align:start position:0%
+scale like P where P would be the
+ 
+
+ align:start position:0%
+scale like P where P would be the
+partial pressure
+
+ align:start position:0%
+partial pressure
+ 
+
+ align:start position:0%
+partial pressure
+um for uh for water
+
+ align:start position:0%
+um for uh for water
+ 
+
+ align:start position:0%
+um for uh for water
+oxidation and the rate constant B does
+
+ align:start position:0%
+oxidation and the rate constant B does
+ 
+
+ align:start position:0%
+oxidation and the rate constant B does
+scale like the pressure um uh for um dry
+
+ align:start position:0%
+scale like the pressure um uh for um dry
+ 
+
+ align:start position:0%
+scale like the pressure um uh for um dry
+O2 the one rate constant that's
+
+ align:start position:0%
+O2 the one rate constant that's
+ 
+
+ align:start position:0%
+O2 the one rate constant that's
+anomalous is the linear rate constant
+
+ align:start position:0%
+anomalous is the linear rate constant
+ 
+
+ align:start position:0%
+anomalous is the linear rate constant
+the B over a for um dry O2 doesn't go
+
+ align:start position:0%
+the B over a for um dry O2 doesn't go
+ 
+
+ align:start position:0%
+the B over a for um dry O2 doesn't go
+quite like exactly like pressure it goes
+
+ align:start position:0%
+quite like exactly like pressure it goes
+ 
+
+ align:start position:0%
+quite like exactly like pressure it goes
+like P to the N where n is close to one
+
+ align:start position:0%
+like P to the N where n is close to one
+ 
+
+ align:start position:0%
+like P to the N where n is close to one
+but not really one it's somewhere
+
+ align:start position:0%
+but not really one it's somewhere
+ 
+
+ align:start position:0%
+but not really one it's somewhere
+between 0.5 so it's a parallel between
+
+ align:start position:0%
+between 0.5 so it's a parallel between
+ 
+
+ align:start position:0%
+between 0.5 so it's a parallel between
+05 and
+
+ align:start position:0%
+05 and
+ 
+
+ align:start position:0%
+05 and
+one so this suggests that at least for
+
+ align:start position:0%
+one so this suggests that at least for
+ 
+
+ align:start position:0%
+one so this suggests that at least for
+oxid you know case of s maybe has some
+
+ align:start position:0%
+oxid you know case of s maybe has some
+ 
+
+ align:start position:0%
+oxid you know case of s maybe has some
+dependence on pressure uh that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonlinear so these are some empirical
+
+ align:start position:0%
+nonlinear so these are some empirical
+ 
+
+ align:start position:0%
+nonlinear so these are some empirical
+models that people that you'll find in
+
+ align:start position:0%
+models that people that you'll find in
+ 
+
+ align:start position:0%
+models that people that you'll find in
+Supreme 4 for example the linear rate
+
+ align:start position:0%
+Supreme 4 for example the linear rate
+ 
+
+ align:start position:0%
+Supreme 4 for example the linear rate
+constant may depend um may go like some
+
+ align:start position:0%
+constant may depend um may go like some
+ 
+
+ align:start position:0%
+constant may depend um may go like some
+some number B over a to the I uh times
+
+ align:start position:0%
+some number B over a to the I uh times
+ 
+
+ align:start position:0%
+some number B over a to the I uh times
+pressure uh where I here refers to the
+
+ align:start position:0%
+pressure uh where I here refers to the
+ 
+
+ align:start position:0%
+pressure uh where I here refers to the
+values intrinsic values at one
+
+ align:start position:0%
+values intrinsic values at one
+ 
+
+ align:start position:0%
+values intrinsic values at one
+atmosphere um n here might be 7 to 08
+
+ align:start position:0%
+atmosphere um n here might be 7 to 08
+ 
+
+ align:start position:0%
+atmosphere um n here might be 7 to 08
+and you notice uh you specify the
+
+ align:start position:0%
+and you notice uh you specify the
+ 
+
+ align:start position:0%
+and you notice uh you specify the
+pressure p so maybe you say at half an
+
+ align:start position:0%
+pressure p so maybe you say at half an
+ 
+
+ align:start position:0%
+pressure p so maybe you say at half an
+atmosphere or a tenth of an atmosphere
+
+ align:start position:0%
+atmosphere or a tenth of an atmosphere
+ 
+
+ align:start position:0%
+atmosphere or a tenth of an atmosphere
+um so but we're not changing think of it
+
+ align:start position:0%
+um so but we're not changing think of it
+ 
+
+ align:start position:0%
+um so but we're not changing think of it
+this way you're not actually changing
+
+ align:start position:0%
+this way you're not actually changing
+ 
+
+ align:start position:0%
+this way you're not actually changing
+the pressure in the tube the pressure of
+
+ align:start position:0%
+the pressure in the tube the pressure of
+ 
+
+ align:start position:0%
+the pressure in the tube the pressure of
+of all the gas in the tube is still an
+
+ align:start position:0%
+of all the gas in the tube is still an
+ 
+
+ align:start position:0%
+of all the gas in the tube is still an
+atmosphere what we're doing is we're
+
+ align:start position:0%
+atmosphere what we're doing is we're
+ 
+
+ align:start position:0%
+atmosphere what we're doing is we're
+flowing mostly nitrogen and we're
+
+ align:start position:0%
+flowing mostly nitrogen and we're
+ 
+
+ align:start position:0%
+flowing mostly nitrogen and we're
+putting a small amount of uh oxygen in
+
+ align:start position:0%
+putting a small amount of uh oxygen in
+ 
+
+ align:start position:0%
+putting a small amount of uh oxygen in
+in the gas stream so that's say I wanted
+
+ align:start position:0%
+in the gas stream so that's say I wanted
+ 
+
+ align:start position:0%
+in the gas stream so that's say I wanted
+to oxidize at half an atmosphere oh I
+
+ align:start position:0%
+to oxidize at half an atmosphere oh I
+ 
+
+ align:start position:0%
+to oxidize at half an atmosphere oh I
+just cut the flow I'd use equal flows of
+
+ align:start position:0%
+just cut the flow I'd use equal flows of
+ 
+
+ align:start position:0%
+just cut the flow I'd use equal flows of
+nitrogen and oxygen so we're we're
+
+ align:start position:0%
+nitrogen and oxygen so we're we're
+ 
+
+ align:start position:0%
+nitrogen and oxygen so we're we're
+diluting uh the the pressure basically
+
+ align:start position:0%
+diluting uh the the pressure basically
+ 
+
+ align:start position:0%
+diluting uh the the pressure basically
+we're diluting the oxiden in the gas
+
+ align:start position:0%
+we're diluting the oxiden in the gas
+ 
+
+ align:start position:0%
+we're diluting the oxiden in the gas
+stream so here's an example suppose I
+
+ align:start position:0%
+stream so here's an example suppose I
+ 
+
+ align:start position:0%
+stream so here's an example suppose I
+dilute it by a factor of 10 to
+
+ align:start position:0%
+dilute it by a factor of 10 to
+ 
+
+ align:start position:0%
+dilute it by a factor of 10 to
+one so I'm flowing a th SCCM of uh inert
+
+ align:start position:0%
+one so I'm flowing a th SCCM of uh inert
+ 
+
+ align:start position:0%
+one so I'm flowing a th SCCM of uh inert
+gas like argon or nitrogen and uh I'm
+
+ align:start position:0%
+gas like argon or nitrogen and uh I'm
+ 
+
+ align:start position:0%
+gas like argon or nitrogen and uh I'm
+I'm flowing only 100 secm of oxygen dro2
+
+ align:start position:0%
+I'm flowing only 100 secm of oxygen dro2
+ 
+
+ align:start position:0%
+I'm flowing only 100 secm of oxygen dro2
+um this is what we would get as the
+
+ align:start position:0%
+um this is what we would get as the
+ 
+
+ align:start position:0%
+um this is what we would get as the
+oxide thickness uh versus
+
+ align:start position:0%
+oxide thickness uh versus
+ 
+
+ align:start position:0%
+oxide thickness uh versus
+time and uh the solid lines were if you
+
+ align:start position:0%
+time and uh the solid lines were if you
+ 
+
+ align:start position:0%
+time and uh the solid lines were if you
+were to do the very Brute Force simple
+
+ align:start position:0%
+were to do the very Brute Force simple
+ 
+
+ align:start position:0%
+were to do the very Brute Force simple
+simple uh idea that it was all scaled
+
+ align:start position:0%
+simple uh idea that it was all scaled
+ 
+
+ align:start position:0%
+simple uh idea that it was all scaled
+like P and uh you know it's just down
+
+ align:start position:0%
+like P and uh you know it's just down
+ 
+
+ align:start position:0%
+like P and uh you know it's just down
+these uh the the um rate constants are
+
+ align:start position:0%
+these uh the the um rate constants are
+ 
+
+ align:start position:0%
+these uh the the um rate constants are
+down by a factor of P where P here would
+
+ align:start position:0%
+down by a factor of P where P here would
+ 
+
+ align:start position:0%
+down by a factor of P where P here would
+be a 1/10th the pressure of atmospheric
+
+ align:start position:0%
+be a 1/10th the pressure of atmospheric
+ 
+
+ align:start position:0%
+be a 1/10th the pressure of atmospheric
+pressure the dash line is where you use
+
+ align:start position:0%
+pressure the dash line is where you use
+ 
+
+ align:start position:0%
+pressure the dash line is where you use
+a little bit more sophisticated model
+
+ align:start position:0%
+a little bit more sophisticated model
+ 
+
+ align:start position:0%
+a little bit more sophisticated model
+where in fact um the B parameter scales
+
+ align:start position:0%
+where in fact um the B parameter scales
+ 
+
+ align:start position:0%
+where in fact um the B parameter scales
+like pressure but the B over a parameter
+
+ align:start position:0%
+like pressure but the B over a parameter
+ 
+
+ align:start position:0%
+like pressure but the B over a parameter
+scales like pressure to point8 so just
+
+ align:start position:0%
+scales like pressure to point8 so just
+ 
+
+ align:start position:0%
+scales like pressure to point8 so just
+slightly so in fact the kinetics would
+
+ align:start position:0%
+slightly so in fact the kinetics would
+ 
+
+ align:start position:0%
+slightly so in fact the kinetics would
+be slightly faster the oxide would be
+
+ align:start position:0%
+be slightly faster the oxide would be
+ 
+
+ align:start position:0%
+be slightly faster the oxide would be
+growing slightly faster than you would
+
+ align:start position:0%
+growing slightly faster than you would
+ 
+
+ align:start position:0%
+growing slightly faster than you would
+have predicted using very simple
+
+ align:start position:0%
+have predicted using very simple
+ 
+
+ align:start position:0%
+have predicted using very simple
+dependence on just saying it depends uh
+
+ align:start position:0%
+dependence on just saying it depends uh
+ 
+
+ align:start position:0%
+dependence on just saying it depends uh
+strictly on P um so it gives you a
+
+ align:start position:0%
+strictly on P um so it gives you a
+ 
+
+ align:start position:0%
+strictly on P um so it gives you a
+little bit more accuracy using some of
+
+ align:start position:0%
+little bit more accuracy using some of
+ 
+
+ align:start position:0%
+little bit more accuracy using some of
+these uh more empirical
+
+ align:start position:0%
+these uh more empirical
+ 
+
+ align:start position:0%
+these uh more empirical
+models but again if you what the idea
+
+ align:start position:0%
+models but again if you what the idea
+ 
+
+ align:start position:0%
+models but again if you what the idea
+here is you need if for some reason we
+
+ align:start position:0%
+here is you need if for some reason we
+ 
+
+ align:start position:0%
+here is you need if for some reason we
+need to control the oxidation rate
+
+ align:start position:0%
+need to control the oxidation rate
+ 
+
+ align:start position:0%
+need to control the oxidation rate
+better you want to slow it down you just
+
+ align:start position:0%
+better you want to slow it down you just
+ 
+
+ align:start position:0%
+better you want to slow it down you just
+dilute the oxygen in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furnace whoops oh I just showed some
+
+ align:start position:0%
+furnace whoops oh I just showed some
+ 
+
+ align:start position:0%
+furnace whoops oh I just showed some
+specific examples here of trying to read
+
+ align:start position:0%
+specific examples here of trying to read
+ 
+
+ align:start position:0%
+specific examples here of trying to read
+off what difference would be you'd make
+
+ align:start position:0%
+off what difference would be you'd make
+ 
+
+ align:start position:0%
+off what difference would be you'd make
+an error of about a thou 100 angstroms
+
+ align:start position:0%
+an error of about a thou 100 angstroms
+ 
+
+ align:start position:0%
+an error of about a thou 100 angstroms
+uh if you use the simple uh assumption
+
+ align:start position:0%
+uh if you use the simple uh assumption
+ 
+
+ align:start position:0%
+uh if you use the simple uh assumption
+compared to what's a little bit more
+
+ align:start position:0%
+compared to what's a little bit more
+ 
+
+ align:start position:0%
+compared to what's a little bit more
+accurate um here at a th000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+um okay so let me let me just skip
+
+ align:start position:0%
+um okay so let me let me just skip
+ 
+
+ align:start position:0%
+um okay so let me let me just skip
+through that's uh the standard kinetics
+
+ align:start position:0%
+through that's uh the standard kinetics
+ 
+
+ align:start position:0%
+through that's uh the standard kinetics
+um on slide 29 uh let's go on to slide
+
+ align:start position:0%
+um on slide 29 uh let's go on to slide
+ 
+
+ align:start position:0%
+um on slide 29 uh let's go on to slide
+30 then okay so what I just talked about
+
+ align:start position:0%
+30 then okay so what I just talked about
+ 
+
+ align:start position:0%
+30 then okay so what I just talked about
+was trying to dilute the oxidation the
+
+ align:start position:0%
+was trying to dilute the oxidation the
+ 
+
+ align:start position:0%
+was trying to dilute the oxidation the
+oxidant so you can grow slower at a
+
+ align:start position:0%
+oxidant so you can grow slower at a
+ 
+
+ align:start position:0%
+oxidant so you can grow slower at a
+given temperature um on slide 30 we're
+
+ align:start position:0%
+given temperature um on slide 30 we're
+ 
+
+ align:start position:0%
+given temperature um on slide 30 we're
+doing just the opposite now it it's not
+
+ align:start position:0%
+doing just the opposite now it it's not
+ 
+
+ align:start position:0%
+doing just the opposite now it it's not
+so easy to do from um a physical point
+
+ align:start position:0%
+so easy to do from um a physical point
+ 
+
+ align:start position:0%
+so easy to do from um a physical point
+of view but you can imagine growing at
+
+ align:start position:0%
+of view but you can imagine growing at
+ 
+
+ align:start position:0%
+of view but you can imagine growing at
+higher than one pressure um let's say
+
+ align:start position:0%
+higher than one pressure um let's say
+ 
+
+ align:start position:0%
+higher than one pressure um let's say
+you know the pressure tells you what it
+
+ align:start position:0%
+you know the pressure tells you what it
+ 
+
+ align:start position:0%
+you know the pressure tells you what it
+tells you the number of atoms or
+
+ align:start position:0%
+tells you the number of atoms or
+ 
+
+ align:start position:0%
+tells you the number of atoms or
+molecules you know species hitting the
+
+ align:start position:0%
+molecules you know species hitting the
+ 
+
+ align:start position:0%
+molecules you know species hitting the
+the surface per unit time right so if I
+
+ align:start position:0%
+the surface per unit time right so if I
+ 
+
+ align:start position:0%
+the surface per unit time right so if I
+double that pressure I can double the
+
+ align:start position:0%
+double that pressure I can double the
+ 
+
+ align:start position:0%
+double that pressure I can double the
+amount there uh hitting that surface I
+
+ align:start position:0%
+amount there uh hitting that surface I
+ 
+
+ align:start position:0%
+amount there uh hitting that surface I
+can double the flux to the surface so
+
+ align:start position:0%
+can double the flux to the surface so
+ 
+
+ align:start position:0%
+can double the flux to the surface so
+you expect the growth rate to go up uh
+
+ align:start position:0%
+you expect the growth rate to go up uh
+ 
+
+ align:start position:0%
+you expect the growth rate to go up uh
+it's just you know not in your intuition
+
+ align:start position:0%
+it's just you know not in your intuition
+ 
+
+ align:start position:0%
+it's just you know not in your intuition
+of how I could do that here you have a
+
+ align:start position:0%
+of how I could do that here you have a
+ 
+
+ align:start position:0%
+of how I could do that here you have a
+tube uh that's made of quartz I have it
+
+ align:start position:0%
+tube uh that's made of quartz I have it
+ 
+
+ align:start position:0%
+tube uh that's made of quartz I have it
+open to on both ends to the ambient and
+
+ align:start position:0%
+open to on both ends to the ambient and
+ 
+
+ align:start position:0%
+open to on both ends to the ambient and
+I'm flowing some gas SW how you going to
+
+ align:start position:0%
+I'm flowing some gas SW how you going to
+ 
+
+ align:start position:0%
+I'm flowing some gas SW how you going to
+get a higher pressure we're all at
+
+ align:start position:0%
+get a higher pressure we're all at
+ 
+
+ align:start position:0%
+get a higher pressure we're all at
+atmospheric pressure doesn't work but
+
+ align:start position:0%
+atmospheric pressure doesn't work but
+ 
+
+ align:start position:0%
+atmospheric pressure doesn't work but
+you can do it you can build a system
+
+ align:start position:0%
+you can do it you can build a system
+ 
+
+ align:start position:0%
+you can do it you can build a system
+where outside that quartz tube there's a
+
+ align:start position:0%
+where outside that quartz tube there's a
+ 
+
+ align:start position:0%
+where outside that quartz tube there's a
+big envelope made of stainless steel
+
+ align:start position:0%
+big envelope made of stainless steel
+ 
+
+ align:start position:0%
+big envelope made of stainless steel
+like a divers tank right if you take
+
+ align:start position:0%
+like a divers tank right if you take
+ 
+
+ align:start position:0%
+like a divers tank right if you take
+they have training tanks for deep sea
+
+ align:start position:0%
+they have training tanks for deep sea
+ 
+
+ align:start position:0%
+they have training tanks for deep sea
+divers they put these guys in these
+
+ align:start position:0%
+divers they put these guys in these
+ 
+
+ align:start position:0%
+divers they put these guys in these
+tanks they seal it up like a submarine
+
+ align:start position:0%
+tanks they seal it up like a submarine
+ 
+
+ align:start position:0%
+tanks they seal it up like a submarine
+and they can stuff more and more gas in
+
+ align:start position:0%
+and they can stuff more and more gas in
+ 
+
+ align:start position:0%
+and they can stuff more and more gas in
+there and you can increase the pressure
+
+ align:start position:0%
+there and you can increase the pressure
+ 
+
+ align:start position:0%
+there and you can increase the pressure
+on the diver um so that's EX exactly
+
+ align:start position:0%
+on the diver um so that's EX exactly
+ 
+
+ align:start position:0%
+on the diver um so that's EX exactly
+what people do with high press oxidation
+
+ align:start position:0%
+what people do with high press oxidation
+ 
+
+ align:start position:0%
+what people do with high press oxidation
+it's a very special type of equipment
+
+ align:start position:0%
+it's a very special type of equipment
+ 
+
+ align:start position:0%
+it's a very special type of equipment
+it's not something you're going to find
+
+ align:start position:0%
+it's not something you're going to find
+ 
+
+ align:start position:0%
+it's not something you're going to find
+in the standard Fab they are available
+
+ align:start position:0%
+in the standard Fab they are available
+ 
+
+ align:start position:0%
+in the standard Fab they are available
+though they've been commercially made
+
+ align:start position:0%
+though they've been commercially made
+ 
+
+ align:start position:0%
+though they've been commercially made
+and people call it hyox a high pressure
+
+ align:start position:0%
+and people call it hyox a high pressure
+ 
+
+ align:start position:0%
+and people call it hyox a high pressure
+oxidation system so here's an example of
+
+ align:start position:0%
+oxidation system so here's an example of
+ 
+
+ align:start position:0%
+oxidation system so here's an example of
+how the kinetics would would go up and
+
+ align:start position:0%
+how the kinetics would would go up and
+ 
+
+ align:start position:0%
+how the kinetics would would go up and
+this I took from uh mayor and LA's book
+
+ align:start position:0%
+this I took from uh mayor and LA's book
+ 
+
+ align:start position:0%
+this I took from uh mayor and LA's book
+1990 what they're showing here is on a
+
+ align:start position:0%
+1990 what they're showing here is on a
+ 
+
+ align:start position:0%
+1990 what they're showing here is on a
+on a log plot here a semi log so it's
+
+ align:start position:0%
+on a log plot here a semi log so it's
+ 
+
+ align:start position:0%
+on a log plot here a semi log so it's
+log on the Y linear on uh on the X oxide
+
+ align:start position:0%
+log on the Y linear on uh on the X oxide
+ 
+
+ align:start position:0%
+log on the Y linear on uh on the X oxide
+thickness versus time
+
+ align:start position:0%
+thickness versus time
+ 
+
+ align:start position:0%
+thickness versus time
+and this is 10 in Steam and uh they're
+
+ align:start position:0%
+and this is 10 in Steam and uh they're
+ 
+
+ align:start position:0%
+and this is 10 in Steam and uh they're
+looking at versus temperature I'm sorry
+
+ align:start position:0%
+looking at versus temperature I'm sorry
+ 
+
+ align:start position:0%
+looking at versus temperature I'm sorry
+looking at a couple different curves
+
+ align:start position:0%
+looking at a couple different curves
+ 
+
+ align:start position:0%
+looking at a couple different curves
+here at different pressure so an
+
+ align:start position:0%
+here at different pressure so an
+ 
+
+ align:start position:0%
+here at different pressure so an
+atmospheric pressure it looks like this
+
+ align:start position:0%
+atmospheric pressure it looks like this
+ 
+
+ align:start position:0%
+atmospheric pressure it looks like this
+at five pressure uh five atmospheres or
+
+ align:start position:0%
+at five pressure uh five atmospheres or
+ 
+
+ align:start position:0%
+at five pressure uh five atmospheres or
+10 atmospheres uh it looks like this
+
+ align:start position:0%
+10 atmospheres uh it looks like this
+ 
+
+ align:start position:0%
+10 atmospheres uh it looks like this
+here we are 20 atmospheres look how much
+
+ align:start position:0%
+here we are 20 atmospheres look how much
+ 
+
+ align:start position:0%
+here we are 20 atmospheres look how much
+faster we can grow um so um this can be
+
+ align:start position:0%
+faster we can grow um so um this can be
+ 
+
+ align:start position:0%
+faster we can grow um so um this can be
+used to increase the oxidation grate at
+
+ align:start position:0%
+used to increase the oxidation grate at
+ 
+
+ align:start position:0%
+used to increase the oxidation grate at
+low temperatures if you need to grow a
+
+ align:start position:0%
+low temperatures if you need to grow a
+ 
+
+ align:start position:0%
+low temperatures if you need to grow a
+thick oxide thermally you need to have
+
+ align:start position:0%
+thick oxide thermally you need to have
+ 
+
+ align:start position:0%
+thick oxide thermally you need to have
+the properties of a thermal oxide which
+
+ align:start position:0%
+the properties of a thermal oxide which
+ 
+
+ align:start position:0%
+the properties of a thermal oxide which
+are quite unique its density is well
+
+ align:start position:0%
+are quite unique its density is well
+ 
+
+ align:start position:0%
+are quite unique its density is well
+defined um it has much better electrical
+
+ align:start position:0%
+defined um it has much better electrical
+ 
+
+ align:start position:0%
+defined um it has much better electrical
+properties than you would get by
+
+ align:start position:0%
+properties than you would get by
+ 
+
+ align:start position:0%
+properties than you would get by
+depositing an oxide it actually consumes
+
+ align:start position:0%
+depositing an oxide it actually consumes
+ 
+
+ align:start position:0%
+depositing an oxide it actually consumes
+silicon which is not true of a deposited
+
+ align:start position:0%
+silicon which is not true of a deposited
+ 
+
+ align:start position:0%
+silicon which is not true of a deposited
+oxide then you have to go to a hypox
+
+ align:start position:0%
+oxide then you have to go to a hypox
+ 
+
+ align:start position:0%
+oxide then you have to go to a hypox
+process or let's say you have some
+
+ align:start position:0%
+process or let's say you have some
+ 
+
+ align:start position:0%
+process or let's say you have some
+structure on the surf on the surface
+
+ align:start position:0%
+structure on the surf on the surface
+ 
+
+ align:start position:0%
+structure on the surf on the surface
+like silic and geranium or some material
+
+ align:start position:0%
+like silic and geranium or some material
+ 
+
+ align:start position:0%
+like silic and geranium or some material
+that can't go to a high temperature
+
+ align:start position:0%
+that can't go to a high temperature
+ 
+
+ align:start position:0%
+that can't go to a high temperature
+because it'll it'll it'll cause the
+
+ align:start position:0%
+because it'll it'll it'll cause the
+ 
+
+ align:start position:0%
+because it'll it'll it'll cause the
+material to diffuse or to relax or you
+
+ align:start position:0%
+material to diffuse or to relax or you
+ 
+
+ align:start position:0%
+material to diffuse or to relax or you
+have you're trying to limit the amount
+
+ align:start position:0%
+have you're trying to limit the amount
+ 
+
+ align:start position:0%
+have you're trying to limit the amount
+of diffusion in the substrate well and
+
+ align:start position:0%
+of diffusion in the substrate well and
+ 
+
+ align:start position:0%
+of diffusion in the substrate well and
+you need to grow a thick oxide you can
+
+ align:start position:0%
+you need to grow a thick oxide you can
+ 
+
+ align:start position:0%
+you need to grow a thick oxide you can
+do it in a high machine uh at 800 where
+
+ align:start position:0%
+do it in a high machine uh at 800 where
+ 
+
+ align:start position:0%
+do it in a high machine uh at 800 where
+you never would be able to do you know
+
+ align:start position:0%
+you never would be able to do you know
+ 
+
+ align:start position:0%
+you never would be able to do you know
+grow a half a micron at 800 but you can
+
+ align:start position:0%
+grow a half a micron at 800 but you can
+ 
+
+ align:start position:0%
+grow a half a micron at 800 but you can
+do it in hyox at 20 atmospher so for
+
+ align:start position:0%
+do it in hyox at 20 atmospher so for
+ 
+
+ align:start position:0%
+do it in hyox at 20 atmospher so for
+materials that are and processes that
+
+ align:start position:0%
+materials that are and processes that
+ 
+
+ align:start position:0%
+materials that are and processes that
+are getting limited by temperature and
+
+ align:start position:0%
+are getting limited by temperature and
+ 
+
+ align:start position:0%
+are getting limited by temperature and
+they have to go lower and lower in
+
+ align:start position:0%
+they have to go lower and lower in
+ 
+
+ align:start position:0%
+they have to go lower and lower in
+temperature hpox is away of uh of
+
+ align:start position:0%
+temperature hpox is away of uh of
+ 
+
+ align:start position:0%
+temperature hpox is away of uh of
+increase in the oxidation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate so in fact here's some data uh
+
+ align:start position:0%
+rate so in fact here's some data uh
+ 
+
+ align:start position:0%
+rate so in fact here's some data uh
+shown on slide
+
+ align:start position:0%
+shown on slide
+ 
+
+ align:start position:0%
+shown on slide
+31 um on hyox I took from Simon z uh in
+
+ align:start position:0%
+31 um on hyox I took from Simon z uh in
+ 
+
+ align:start position:0%
+31 um on hyox I took from Simon z uh in
+Z's book and what it shows is the
+
+ align:start position:0%
+Z's book and what it shows is the
+ 
+
+ align:start position:0%
+Z's book and what it shows is the
+measurements of the on the y- axis the
+
+ align:start position:0%
+measurements of the on the y- axis the
+ 
+
+ align:start position:0%
+measurements of the on the y- axis the
+parabolic rate constant so this is the B
+
+ align:start position:0%
+parabolic rate constant so this is the B
+ 
+
+ align:start position:0%
+parabolic rate constant so this is the B
+parameter as a function of one th overt
+
+ align:start position:0%
+parameter as a function of one th overt
+ 
+
+ align:start position:0%
+parameter as a function of one th overt
+so it's a semilog kind of arous
+
+ align:start position:0%
+so it's a semilog kind of arous
+ 
+
+ align:start position:0%
+so it's a semilog kind of arous
+plot um in Steam and this applies to a
+
+ align:start position:0%
+plot um in Steam and this applies to a
+ 
+
+ align:start position:0%
+plot um in Steam and this applies to a
+couple different it's been measured for
+
+ align:start position:0%
+couple different it's been measured for
+ 
+
+ align:start position:0%
+couple different it's been measured for
+a couple different orientations uh of
+
+ align:start position:0%
+a couple different orientations uh of
+ 
+
+ align:start position:0%
+a couple different orientations uh of
+silicon and what you see here is this
+
+ align:start position:0%
+silicon and what you see here is this
+ 
+
+ align:start position:0%
+silicon and what you see here is this
+this solid line uh which has an act two
+
+ align:start position:0%
+this solid line uh which has an act two
+ 
+
+ align:start position:0%
+this solid line uh which has an act two
+different activation energies there seem
+
+ align:start position:0%
+different activation energies there seem
+ 
+
+ align:start position:0%
+different activation energies there seem
+to be a break point here somewhere
+
+ align:start position:0%
+to be a break point here somewhere
+ 
+
+ align:start position:0%
+to be a break point here somewhere
+around 950 degrees but um AC activation
+
+ align:start position:0%
+around 950 degrees but um AC activation
+ 
+
+ align:start position:0%
+around 950 degrees but um AC activation
+energy close to one electron volt this
+
+ align:start position:0%
+energy close to one electron volt this
+ 
+
+ align:start position:0%
+energy close to one electron volt this
+is the this is the B parameter here at
+
+ align:start position:0%
+is the this is the B parameter here at
+ 
+
+ align:start position:0%
+is the this is the B parameter here at
+five 10 15 and 20
+
+ align:start position:0%
+five 10 15 and 20
+ 
+
+ align:start position:0%
+five 10 15 and 20
+atmospheres um this is what the B
+
+ align:start position:0%
+atmospheres um this is what the B
+ 
+
+ align:start position:0%
+atmospheres um this is what the B
+parameter goes up by and in fact I mark
+
+ align:start position:0%
+parameter goes up by and in fact I mark
+ 
+
+ align:start position:0%
+parameter goes up by and in fact I mark
+this blue line which is at 800° and in
+
+ align:start position:0%
+this blue line which is at 800° and in
+ 
+
+ align:start position:0%
+this blue line which is at 800° and in
+fact I'm reading off the chart here uh
+
+ align:start position:0%
+fact I'm reading off the chart here uh
+ 
+
+ align:start position:0%
+fact I'm reading off the chart here uh
+the B parameter is almost exactly a
+
+ align:start position:0%
+the B parameter is almost exactly a
+ 
+
+ align:start position:0%
+the B parameter is almost exactly a
+factor of 20 faster uh at 20 atmospheres
+
+ align:start position:0%
+factor of 20 faster uh at 20 atmospheres
+ 
+
+ align:start position:0%
+factor of 20 faster uh at 20 atmospheres
+than it is um at one atmosphere so we
+
+ align:start position:0%
+than it is um at one atmosphere so we
+ 
+
+ align:start position:0%
+than it is um at one atmosphere so we
+can go up um to uh 20 times the
+
+ align:start position:0%
+can go up um to uh 20 times the
+ 
+
+ align:start position:0%
+can go up um to uh 20 times the
+oxidation rate at 20 atmospheres at 800°
+
+ align:start position:0%
+oxidation rate at 20 atmospheres at 800°
+ 
+
+ align:start position:0%
+oxidation rate at 20 atmospheres at 800°
+so it does scale reasonably well this
+
+ align:start position:0%
+so it does scale reasonably well this
+ 
+
+ align:start position:0%
+so it does scale reasonably well this
+parameter does uh with uh pressure at
+
+ align:start position:0%
+parameter does uh with uh pressure at
+ 
+
+ align:start position:0%
+parameter does uh with uh pressure at
+higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressures um on slide 32 I'm actually
+
+ align:start position:0%
+pressures um on slide 32 I'm actually
+ 
+
+ align:start position:0%
+pressures um on slide 32 I'm actually
+showing you remember I said um you can
+
+ align:start position:0%
+showing you remember I said um you can
+ 
+
+ align:start position:0%
+showing you remember I said um you can
+build this complex diver tank looking
+
+ align:start position:0%
+build this complex diver tank looking
+ 
+
+ align:start position:0%
+build this complex diver tank looking
+thing with a great big steel uh vacuum
+
+ align:start position:0%
+thing with a great big steel uh vacuum
+ 
+
+ align:start position:0%
+thing with a great big steel uh vacuum
+system that can hold the pressure and
+
+ align:start position:0%
+system that can hold the pressure and
+ 
+
+ align:start position:0%
+system that can hold the pressure and
+pressurization system um I've taken this
+
+ align:start position:0%
+pressurization system um I've taken this
+ 
+
+ align:start position:0%
+pressurization system um I've taken this
+from Simon Z's book he actually talks
+
+ align:start position:0%
+from Simon Z's book he actually talks
+ 
+
+ align:start position:0%
+from Simon Z's book he actually talks
+about how you would do um a hpox run if
+
+ align:start position:0%
+about how you would do um a hpox run if
+ 
+
+ align:start position:0%
+about how you would do um a hpox run if
+you had such a thing just so you can
+
+ align:start position:0%
+you had such a thing just so you can
+ 
+
+ align:start position:0%
+you had such a thing just so you can
+think about it what what happens is the
+
+ align:start position:0%
+think about it what what happens is the
+ 
+
+ align:start position:0%
+think about it what what happens is the
+Wafers um get loaded here at atmospheric
+
+ align:start position:0%
+Wafers um get loaded here at atmospheric
+ 
+
+ align:start position:0%
+Wafers um get loaded here at atmospheric
+pressure down here this solid uh bar it
+
+ align:start position:0%
+pressure down here this solid uh bar it
+ 
+
+ align:start position:0%
+pressure down here this solid uh bar it
+means you're at atmospheric pressure
+
+ align:start position:0%
+means you're at atmospheric pressure
+ 
+
+ align:start position:0%
+means you're at atmospheric pressure
+obviously you can't pump up the diver
+
+ align:start position:0%
+obviously you can't pump up the diver
+ 
+
+ align:start position:0%
+obviously you can't pump up the diver
+tank until uh the the hatch is closed so
+
+ align:start position:0%
+tank until uh the the hatch is closed so
+ 
+
+ align:start position:0%
+tank until uh the the hatch is closed so
+you load them in atmospheric pressure uh
+
+ align:start position:0%
+you load them in atmospheric pressure uh
+ 
+
+ align:start position:0%
+you load them in atmospheric pressure uh
+and you uh have a ceiling step and here
+
+ align:start position:0%
+and you uh have a ceiling step and here
+ 
+
+ align:start position:0%
+and you uh have a ceiling step and here
+you're starting to increase the pressure
+
+ align:start position:0%
+you're starting to increase the pressure
+ 
+
+ align:start position:0%
+you're starting to increase the pressure
+um again using O2 um you do some purging
+
+ align:start position:0%
+um again using O2 um you do some purging
+ 
+
+ align:start position:0%
+um again using O2 um you do some purging
+and then it's some point what you do is
+
+ align:start position:0%
+and then it's some point what you do is
+ 
+
+ align:start position:0%
+and then it's some point what you do is
+you bring the shell uh this outside
+
+ align:start position:0%
+you bring the shell uh this outside
+ 
+
+ align:start position:0%
+you bring the shell uh this outside
+steel shell and the tube up together in
+
+ align:start position:0%
+steel shell and the tube up together in
+ 
+
+ align:start position:0%
+steel shell and the tube up together in
+pressure and you go up to say 10
+
+ align:start position:0%
+pressure and you go up to say 10
+ 
+
+ align:start position:0%
+pressure and you go up to say 10
+atmospheres um you do your um so you're
+
+ align:start position:0%
+atmospheres um you do your um so you're
+ 
+
+ align:start position:0%
+atmospheres um you do your um so you're
+pressurizing uh in moisture and then you
+
+ align:start position:0%
+pressurizing uh in moisture and then you
+ 
+
+ align:start position:0%
+pressurizing uh in moisture and then you
+you do your oxidation then you
+
+ align:start position:0%
+you do your oxidation then you
+ 
+
+ align:start position:0%
+you do your oxidation then you
+depressurize um and bring it down to
+
+ align:start position:0%
+depressurize um and bring it down to
+ 
+
+ align:start position:0%
+depressurize um and bring it down to
+atmospheric pressure and unload so it's
+
+ align:start position:0%
+atmospheric pressure and unload so it's
+ 
+
+ align:start position:0%
+atmospheric pressure and unload so it's
+perfectly possible to do this obviously
+
+ align:start position:0%
+perfectly possible to do this obviously
+ 
+
+ align:start position:0%
+perfectly possible to do this obviously
+if you try to do it with a quartz tube
+
+ align:start position:0%
+if you try to do it with a quartz tube
+ 
+
+ align:start position:0%
+if you try to do it with a quartz tube
+and put end caps on it pressurize it of
+
+ align:start position:0%
+and put end caps on it pressurize it of
+ 
+
+ align:start position:0%
+and put end caps on it pressurize it of
+course the quartz would explode all over
+
+ align:start position:0%
+course the quartz would explode all over
+ 
+
+ align:start position:0%
+course the quartz would explode all over
+so because it's not a strong material
+
+ align:start position:0%
+so because it's not a strong material
+ 
+
+ align:start position:0%
+so because it's not a strong material
+but if you um you know you have the
+
+ align:start position:0%
+but if you um you know you have the
+ 
+
+ align:start position:0%
+but if you um you know you have the
+stainless steel shroud all around it
+
+ align:start position:0%
+stainless steel shroud all around it
+ 
+
+ align:start position:0%
+stainless steel shroud all around it
+then the differential pressure across
+
+ align:start position:0%
+then the differential pressure across
+ 
+
+ align:start position:0%
+then the differential pressure across
+the quartz is is very close to zero or
+
+ align:start position:0%
+the quartz is is very close to zero or
+ 
+
+ align:start position:0%
+the quartz is is very close to zero or
+it can be uh just maybe one atmosphere
+
+ align:start position:0%
+it can be uh just maybe one atmosphere
+ 
+
+ align:start position:0%
+it can be uh just maybe one atmosphere
+we know it can withstand one atmosphere
+
+ align:start position:0%
+we know it can withstand one atmosphere
+ 
+
+ align:start position:0%
+we know it can withstand one atmosphere
+but that way you you keep the quartz
+
+ align:start position:0%
+but that way you you keep the quartz
+ 
+
+ align:start position:0%
+but that way you you keep the quartz
+from uh exploding all over the place so
+
+ align:start position:0%
+from uh exploding all over the place so
+ 
+
+ align:start position:0%
+from uh exploding all over the place so
+it's a special piece of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equipment okay so then let's go on to
+
+ align:start position:0%
+equipment okay so then let's go on to
+ 
+
+ align:start position:0%
+equipment okay so then let's go on to
+slide 33 so high poox you can do low
+
+ align:start position:0%
+slide 33 so high poox you can do low
+ 
+
+ align:start position:0%
+slide 33 so high poox you can do low
+pressures you can do high pressures if
+
+ align:start position:0%
+pressures you can do high pressures if
+ 
+
+ align:start position:0%
+pressures you can do high pressures if
+you have the right equipment um it turns
+
+ align:start position:0%
+you have the right equipment um it turns
+ 
+
+ align:start position:0%
+you have the right equipment um it turns
+out simple oxidation also isn't always
+
+ align:start position:0%
+out simple oxidation also isn't always
+ 
+
+ align:start position:0%
+out simple oxidation also isn't always
+done just with oxygen or water vapor um
+
+ align:start position:0%
+done just with oxygen or water vapor um
+ 
+
+ align:start position:0%
+done just with oxygen or water vapor um
+small concentrations of certain other
+
+ align:start position:0%
+small concentrations of certain other
+ 
+
+ align:start position:0%
+small concentrations of certain other
+species are often added for example HCL
+
+ align:start position:0%
+species are often added for example HCL
+ 
+
+ align:start position:0%
+species are often added for example HCL
+is sometimes added to the O2 um because
+
+ align:start position:0%
+is sometimes added to the O2 um because
+ 
+
+ align:start position:0%
+is sometimes added to the O2 um because
+it turns out people are found by adding
+
+ align:start position:0%
+it turns out people are found by adding
+ 
+
+ align:start position:0%
+it turns out people are found by adding
+that they can reduce oxide defect
+
+ align:start position:0%
+that they can reduce oxide defect
+ 
+
+ align:start position:0%
+that they can reduce oxide defect
+densities uh or they can reduce
+
+ align:start position:0%
+densities uh or they can reduce
+ 
+
+ align:start position:0%
+densities uh or they can reduce
+contamination levels HCL we know in the
+
+ align:start position:0%
+contamination levels HCL we know in the
+ 
+
+ align:start position:0%
+contamination levels HCL we know in the
+liquid form HCL is very good at um uh
+
+ align:start position:0%
+liquid form HCL is very good at um uh
+ 
+
+ align:start position:0%
+liquid form HCL is very good at um uh
+etching off metals from the surface so
+
+ align:start position:0%
+etching off metals from the surface so
+ 
+
+ align:start position:0%
+etching off metals from the surface so
+perhaps it has a similar role uh when
+
+ align:start position:0%
+perhaps it has a similar role uh when
+ 
+
+ align:start position:0%
+perhaps it has a similar role uh when
+it's in the Vapor face so sometimes
+
+ align:start position:0%
+it's in the Vapor face so sometimes
+ 
+
+ align:start position:0%
+it's in the Vapor face so sometimes
+people add a small am of HCL to the
+
+ align:start position:0%
+people add a small am of HCL to the
+ 
+
+ align:start position:0%
+people add a small am of HCL to the
+furnace um it can produce chlorine which
+
+ align:start position:0%
+furnace um it can produce chlorine which
+ 
+
+ align:start position:0%
+furnace um it can produce chlorine which
+can react with maybe Trace
+
+ align:start position:0%
+can react with maybe Trace
+ 
+
+ align:start position:0%
+can react with maybe Trace
+Metals um by this this kind of process
+
+ align:start position:0%
+Metals um by this this kind of process
+ 
+
+ align:start position:0%
+Metals um by this this kind of process
+that's shown here so it's not unusual to
+
+ align:start position:0%
+that's shown here so it's not unusual to
+ 
+
+ align:start position:0%
+that's shown here so it's not unusual to
+see in manufacturing processes oxidation
+
+ align:start position:0%
+see in manufacturing processes oxidation
+ 
+
+ align:start position:0%
+see in manufacturing processes oxidation
+in not just O2 but HCL O2 plus
+
+ align:start position:0%
+in not just O2 but HCL O2 plus
+ 
+
+ align:start position:0%
+in not just O2 but HCL O2 plus
+HCL um so these uh these bullets here in
+
+ align:start position:0%
+HCL um so these uh these bullets here in
+ 
+
+ align:start position:0%
+HCL um so these uh these bullets here in
+the middle of the slide there's just
+
+ align:start position:0%
+the middle of the slide there's just
+ 
+
+ align:start position:0%
+the middle of the slide there's just
+some generic kind of observations that
+
+ align:start position:0%
+some generic kind of observations that
+ 
+
+ align:start position:0%
+some generic kind of observations that
+have been made on these different
+
+ align:start position:0%
+have been made on these different
+ 
+
+ align:start position:0%
+have been made on these different
+ambients uh well we know we just studied
+
+ align:start position:0%
+ambients uh well we know we just studied
+ 
+
+ align:start position:0%
+ambients uh well we know we just studied
+in Deal Grove we know in detail that you
+
+ align:start position:0%
+in Deal Grove we know in detail that you
+ 
+
+ align:start position:0%
+in Deal Grove we know in detail that you
+can get 20 to 50 times faster um than
+
+ align:start position:0%
+can get 20 to 50 times faster um than
+ 
+
+ align:start position:0%
+can get 20 to 50 times faster um than
+dry O2 just by putting in in wet O2 in
+
+ align:start position:0%
+dry O2 just by putting in in wet O2 in
+ 
+
+ align:start position:0%
+dry O2 just by putting in in wet O2 in
+in Steam so we know that um 3% chlorine
+
+ align:start position:0%
+in Steam so we know that um 3% chlorine
+ 
+
+ align:start position:0%
+in Steam so we know that um 3% chlorine
+in the ambient can increase the growth
+
+ align:start position:0%
+in the ambient can increase the growth
+ 
+
+ align:start position:0%
+in the ambient can increase the growth
+rate by 20 to 30% so also HCL is a way
+
+ align:start position:0%
+rate by 20 to 30% so also HCL is a way
+ 
+
+ align:start position:0%
+rate by 20 to 30% so also HCL is a way
+of at a at a low temperature is boosting
+
+ align:start position:0%
+of at a at a low temperature is boosting
+ 
+
+ align:start position:0%
+of at a at a low temperature is boosting
+the growth rate the name of the game
+
+ align:start position:0%
+the growth rate the name of the game
+ 
+
+ align:start position:0%
+the growth rate the name of the game
+these days is keep the dopin from moving
+
+ align:start position:0%
+these days is keep the dopin from moving
+ 
+
+ align:start position:0%
+these days is keep the dopin from moving
+but keep the growth rate high enough to
+
+ align:start position:0%
+but keep the growth rate high enough to
+ 
+
+ align:start position:0%
+but keep the growth rate high enough to
+be to be give you a reasonable thickness
+
+ align:start position:0%
+be to be give you a reasonable thickness
+ 
+
+ align:start position:0%
+be to be give you a reasonable thickness
+so you can add a little chlorine to
+
+ align:start position:0%
+so you can add a little chlorine to
+ 
+
+ align:start position:0%
+so you can add a little chlorine to
+speed up the growth rate
+
+ align:start position:0%
+speed up the growth rate
+ 
+
+ align:start position:0%
+speed up the growth rate
+you can also add nf3 another U commonly
+
+ align:start position:0%
+you can also add nf3 another U commonly
+ 
+
+ align:start position:0%
+you can also add nf3 another U commonly
+used species a small amount of that will
+
+ align:start position:0%
+used species a small amount of that will
+ 
+
+ align:start position:0%
+used species a small amount of that will
+increase the growth rate by two to three
+
+ align:start position:0%
+increase the growth rate by two to three
+ 
+
+ align:start position:0%
+increase the growth rate by two to three
+times um again this is adding in a lot
+
+ align:start position:0%
+times um again this is adding in a lot
+ 
+
+ align:start position:0%
+times um again this is adding in a lot
+of new chemistry and there's no way in
+
+ align:start position:0%
+of new chemistry and there's no way in
+ 
+
+ align:start position:0%
+of new chemistry and there's no way in
+an abono in a first principal sense to
+
+ align:start position:0%
+an abono in a first principal sense to
+ 
+
+ align:start position:0%
+an abono in a first principal sense to
+really calculate what those rates are so
+
+ align:start position:0%
+really calculate what those rates are so
+ 
+
+ align:start position:0%
+really calculate what those rates are so
+in in simulators like Supreme 4 if you
+
+ align:start position:0%
+in in simulators like Supreme 4 if you
+ 
+
+ align:start position:0%
+in in simulators like Supreme 4 if you
+go sit down and tell it oh I want to
+
+ align:start position:0%
+go sit down and tell it oh I want to
+ 
+
+ align:start position:0%
+go sit down and tell it oh I want to
+grow an oxide in chlorine and oxygen it
+
+ align:start position:0%
+grow an oxide in chlorine and oxygen it
+ 
+
+ align:start position:0%
+grow an oxide in chlorine and oxygen it
+doesn't simulate the chemical reaction
+
+ align:start position:0%
+doesn't simulate the chemical reaction
+ 
+
+ align:start position:0%
+doesn't simulate the chemical reaction
+and all the kinetics and come on spit
+
+ align:start position:0%
+and all the kinetics and come on spit
+ 
+
+ align:start position:0%
+and all the kinetics and come on spit
+out a number it has a lookup table of B
+
+ align:start position:0%
+out a number it has a lookup table of B
+ 
+
+ align:start position:0%
+out a number it has a lookup table of B
+and Bay values that have been measured
+
+ align:start position:0%
+and Bay values that have been measured
+ 
+
+ align:start position:0%
+and Bay values that have been measured
+in the literature for commonly used
+
+ align:start position:0%
+in the literature for commonly used
+ 
+
+ align:start position:0%
+in the literature for commonly used
+ambients like chlorine and maybe nf3 and
+
+ align:start position:0%
+ambients like chlorine and maybe nf3 and
+ 
+
+ align:start position:0%
+ambients like chlorine and maybe nf3 and
+a few others so it looks up in the table
+
+ align:start position:0%
+a few others so it looks up in the table
+ 
+
+ align:start position:0%
+a few others so it looks up in the table
+uh what B over A and B should be um uh
+
+ align:start position:0%
+uh what B over A and B should be um uh
+ 
+
+ align:start position:0%
+uh what B over A and B should be um uh
+as a function of the pressure here this
+
+ align:start position:0%
+as a function of the pressure here this
+ 
+
+ align:start position:0%
+as a function of the pressure here this
+pressure Delta or Kai these are some
+
+ align:start position:0%
+pressure Delta or Kai these are some
+ 
+
+ align:start position:0%
+pressure Delta or Kai these are some
+functions of the concentration of this
+
+ align:start position:0%
+functions of the concentration of this
+ 
+
+ align:start position:0%
+functions of the concentration of this
+additional uh species that's in the
+
+ align:start position:0%
+additional uh species that's in the
+ 
+
+ align:start position:0%
+additional uh species that's in the
+furnace could it be HCL or whatever and
+
+ align:start position:0%
+furnace could it be HCL or whatever and
+ 
+
+ align:start position:0%
+furnace could it be HCL or whatever and
+they've been determined very empirically
+
+ align:start position:0%
+they've been determined very empirically
+ 
+
+ align:start position:0%
+they've been determined very empirically
+so don't expect first principles models
+
+ align:start position:0%
+so don't expect first principles models
+ 
+
+ align:start position:0%
+so don't expect first principles models
+but maybe some mathematical models would
+
+ align:start position:0%
+but maybe some mathematical models would
+ 
+
+ align:start position:0%
+but maybe some mathematical models would
+be in Supreme for different ambients but
+
+ align:start position:0%
+be in Supreme for different ambients but
+ 
+
+ align:start position:0%
+be in Supreme for different ambients but
+again they've all been calibrated
+
+ align:start position:0%
+again they've all been calibrated
+ 
+
+ align:start position:0%
+again they've all been calibrated
+somebody's experiment so you know they
+
+ align:start position:0%
+somebody's experiment so you know they
+ 
+
+ align:start position:0%
+somebody's experiment so you know they
+may not exactly agree with your
+
+ align:start position:0%
+may not exactly agree with your
+ 
+
+ align:start position:0%
+may not exactly agree with your
+experiment you might have to calibrate
+
+ align:start position:0%
+experiment you might have to calibrate
+ 
+
+ align:start position:0%
+experiment you might have to calibrate
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yourself uh here's an interesting
+
+ align:start position:0%
+yourself uh here's an interesting
+ 
+
+ align:start position:0%
+yourself uh here's an interesting
+example on slide uh
+
+ align:start position:0%
+example on slide uh
+ 
+
+ align:start position:0%
+example on slide uh
+34 these are some kinetics in um HCL has
+
+ align:start position:0%
+34 these are some kinetics in um HCL has
+ 
+
+ align:start position:0%
+34 these are some kinetics in um HCL has
+been used for quite a while it's it's
+
+ align:start position:0%
+been used for quite a while it's it's
+ 
+
+ align:start position:0%
+been used for quite a while it's it's
+even my old fashioned now something
+
+ align:start position:0%
+even my old fashioned now something
+ 
+
+ align:start position:0%
+even my old fashioned now something
+that's a little bit newer is people
+
+ align:start position:0%
+that's a little bit newer is people
+ 
+
+ align:start position:0%
+that's a little bit newer is people
+oxidizing an Ambience like n o n2o and
+
+ align:start position:0%
+oxidizing an Ambience like n o n2o and
+ 
+
+ align:start position:0%
+oxidizing an Ambience like n o n2o and
+even implanting nitrogen remember we
+
+ align:start position:0%
+even implanting nitrogen remember we
+ 
+
+ align:start position:0%
+even implanting nitrogen remember we
+talked about oxy nitrides um are the
+
+ align:start position:0%
+talked about oxy nitrides um are the
+ 
+
+ align:start position:0%
+talked about oxy nitrides um are the
+first form of high K uh oxy nitride
+
+ align:start position:0%
+first form of high K uh oxy nitride
+ 
+
+ align:start position:0%
+first form of high K uh oxy nitride
+which is a mixture of silicon oxygen and
+
+ align:start position:0%
+which is a mixture of silicon oxygen and
+ 
+
+ align:start position:0%
+which is a mixture of silicon oxygen and
+nitrogen has a higher dialectric
+
+ align:start position:0%
+nitrogen has a higher dialectric
+ 
+
+ align:start position:0%
+nitrogen has a higher dialectric
+constant you can make it a little bit
+
+ align:start position:0%
+constant you can make it a little bit
+ 
+
+ align:start position:0%
+constant you can make it a little bit
+thicker and so you get less gate leakage
+
+ align:start position:0%
+thicker and so you get less gate leakage
+ 
+
+ align:start position:0%
+thicker and so you get less gate leakage
+so gate oxides of oxy nitride were very
+
+ align:start position:0%
+so gate oxides of oxy nitride were very
+ 
+
+ align:start position:0%
+so gate oxides of oxy nitride were very
+popular for people are popular for
+
+ align:start position:0%
+popular for people are popular for
+ 
+
+ align:start position:0%
+popular for people are popular for
+people to study but um here's an example
+
+ align:start position:0%
+people to study but um here's an example
+ 
+
+ align:start position:0%
+people to study but um here's an example
+of trying to fabricate an oxy nitride
+
+ align:start position:0%
+of trying to fabricate an oxy nitride
+ 
+
+ align:start position:0%
+of trying to fabricate an oxy nitride
+where the kinetics are really crazy
+
+ align:start position:0%
+where the kinetics are really crazy
+ 
+
+ align:start position:0%
+where the kinetics are really crazy
+they're not at all linear parabolic and
+
+ align:start position:0%
+they're not at all linear parabolic and
+ 
+
+ align:start position:0%
+they're not at all linear parabolic and
+uh in fact this is a plot here on the y
+
+ align:start position:0%
+uh in fact this is a plot here on the y
+ 
+
+ align:start position:0%
+uh in fact this is a plot here on the y
+axis is oxide thickness uh or oxy
+
+ align:start position:0%
+axis is oxide thickness uh or oxy
+ 
+
+ align:start position:0%
+axis is oxide thickness uh or oxy
+nitrite thickness if you want as a
+
+ align:start position:0%
+nitrite thickness if you want as a
+ 
+
+ align:start position:0%
+nitrite thickness if you want as a
+function of the nitrogen
+
+ align:start position:0%
+function of the nitrogen
+ 
+
+ align:start position:0%
+function of the nitrogen
+dose um so here the the substrate was
+
+ align:start position:0%
+dose um so here the the substrate was
+ 
+
+ align:start position:0%
+dose um so here the the substrate was
+implanted first with nitrogen and we'll
+
+ align:start position:0%
+implanted first with nitrogen and we'll
+ 
+
+ align:start position:0%
+implanted first with nitrogen and we'll
+talk about ion implantation to a certain
+
+ align:start position:0%
+talk about ion implantation to a certain
+ 
+
+ align:start position:0%
+talk about ion implantation to a certain
+number of atoms per square
+
+ align:start position:0%
+number of atoms per square
+ 
+
+ align:start position:0%
+number of atoms per square
+centimeter and they're plotting the
+
+ align:start position:0%
+centimeter and they're plotting the
+ 
+
+ align:start position:0%
+centimeter and they're plotting the
+oxide thickness here uh at different
+
+ align:start position:0%
+oxide thickness here uh at different
+ 
+
+ align:start position:0%
+oxide thickness here uh at different
+times so say for 25 minutes as a
+
+ align:start position:0%
+times so say for 25 minutes as a
+ 
+
+ align:start position:0%
+times so say for 25 minutes as a
+function of of dose uh um and you can
+
+ align:start position:0%
+function of of dose uh um and you can
+ 
+
+ align:start position:0%
+function of of dose uh um and you can
+see depending on how the dose how much
+
+ align:start position:0%
+see depending on how the dose how much
+ 
+
+ align:start position:0%
+see depending on how the dose how much
+of nitrogen you implanted the thickness
+
+ align:start position:0%
+of nitrogen you implanted the thickness
+ 
+
+ align:start position:0%
+of nitrogen you implanted the thickness
+actually um can go down so the the
+
+ align:start position:0%
+actually um can go down so the the
+ 
+
+ align:start position:0%
+actually um can go down so the the
+oxidation rate can depend on exactly
+
+ align:start position:0%
+oxidation rate can depend on exactly
+ 
+
+ align:start position:0%
+oxidation rate can depend on exactly
+what is at that surface was it silicon
+
+ align:start position:0%
+what is at that surface was it silicon
+ 
+
+ align:start position:0%
+what is at that surface was it silicon
+Pure or was it silicon that had been on
+
+ align:start position:0%
+Pure or was it silicon that had been on
+ 
+
+ align:start position:0%
+Pure or was it silicon that had been on
+implanted with something um so uh this
+
+ align:start position:0%
+implanted with something um so uh this
+ 
+
+ align:start position:0%
+implanted with something um so uh this
+needs a very a qualitatively very
+
+ align:start position:0%
+needs a very a qualitatively very
+ 
+
+ align:start position:0%
+needs a very a qualitatively very
+different model from deal Grove because
+
+ align:start position:0%
+different model from deal Grove because
+ 
+
+ align:start position:0%
+different model from deal Grove because
+you need to specify something that the
+
+ align:start position:0%
+you need to specify something that the
+ 
+
+ align:start position:0%
+you need to specify something that the
+deal Grove doesn't even treat deal Grove
+
+ align:start position:0%
+deal Grove doesn't even treat deal Grove
+ 
+
+ align:start position:0%
+deal Grove doesn't even treat deal Grove
+assumed you had a perfectly pure silicon
+
+ align:start position:0%
+assumed you had a perfectly pure silicon
+ 
+
+ align:start position:0%
+assumed you had a perfectly pure silicon
+wafer that you were oxidizing with just
+
+ align:start position:0%
+wafer that you were oxidizing with just
+ 
+
+ align:start position:0%
+wafer that you were oxidizing with just
+silicon atoms in it once you start
+
+ align:start position:0%
+silicon atoms in it once you start
+ 
+
+ align:start position:0%
+silicon atoms in it once you start
+implanting nitrogen or some other
+
+ align:start position:0%
+implanting nitrogen or some other
+ 
+
+ align:start position:0%
+implanting nitrogen or some other
+species all bets are off you're not
+
+ align:start position:0%
+species all bets are off you're not
+ 
+
+ align:start position:0%
+species all bets are off you're not
+going to widely find uh simulators that
+
+ align:start position:0%
+going to widely find uh simulators that
+ 
+
+ align:start position:0%
+going to widely find uh simulators that
+can support this type of model if you
+
+ align:start position:0%
+can support this type of model if you
+ 
+
+ align:start position:0%
+can support this type of model if you
+want to do this you're going to have to
+
+ align:start position:0%
+want to do this you're going to have to
+ 
+
+ align:start position:0%
+want to do this you're going to have to
+model it yourself um by taking data from
+
+ align:start position:0%
+model it yourself um by taking data from
+ 
+
+ align:start position:0%
+model it yourself um by taking data from
+the literature and fitting it um or or
+
+ align:start position:0%
+the literature and fitting it um or or
+ 
+
+ align:start position:0%
+the literature and fitting it um or or
+maybe doing your own
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiments um so let's look at um slide
+
+ align:start position:0%
+experiments um so let's look at um slide
+ 
+
+ align:start position:0%
+experiments um so let's look at um slide
+35 there's another parameter we need to
+
+ align:start position:0%
+35 there's another parameter we need to
+ 
+
+ align:start position:0%
+35 there's another parameter we need to
+vary or we can you can imagine varying
+
+ align:start position:0%
+vary or we can you can imagine varying
+ 
+
+ align:start position:0%
+vary or we can you can imagine varying
+and this is a relatively simple one and
+
+ align:start position:0%
+and this is a relatively simple one and
+ 
+
+ align:start position:0%
+and this is a relatively simple one and
+that's the orientation of the crystal
+
+ align:start position:0%
+that's the orientation of the crystal
+ 
+
+ align:start position:0%
+that's the orientation of the crystal
+the face of the crystal that you're
+
+ align:start position:0%
+the face of the crystal that you're
+ 
+
+ align:start position:0%
+the face of the crystal that you're
+oxidizing um we know that the B
+
+ align:start position:0%
+oxidizing um we know that the B
+ 
+
+ align:start position:0%
+oxidizing um we know that the B
+parameter which depends on the diffusion
+
+ align:start position:0%
+parameter which depends on the diffusion
+ 
+
+ align:start position:0%
+parameter which depends on the diffusion
+through the oxide is independent of
+
+ align:start position:0%
+through the oxide is independent of
+ 
+
+ align:start position:0%
+through the oxide is independent of
+orientation B over a which is the the
+
+ align:start position:0%
+orientation B over a which is the the
+ 
+
+ align:start position:0%
+orientation B over a which is the the
+the the reaction rate at the at the
+
+ align:start position:0%
+the the reaction rate at the at the
+ 
+
+ align:start position:0%
+the the reaction rate at the at the
+inter phase of course it's going to
+
+ align:start position:0%
+inter phase of course it's going to
+ 
+
+ align:start position:0%
+inter phase of course it's going to
+depend on the number of atoms available
+
+ align:start position:0%
+depend on the number of atoms available
+ 
+
+ align:start position:0%
+depend on the number of atoms available
+per square centimeter to react uh so it
+
+ align:start position:0%
+per square centimeter to react uh so it
+ 
+
+ align:start position:0%
+per square centimeter to react uh so it
+does depend on orientation so and these
+
+ align:start position:0%
+does depend on orientation so and these
+ 
+
+ align:start position:0%
+does depend on orientation so and these
+are the dependencies just to give you
+
+ align:start position:0%
+are the dependencies just to give you
+ 
+
+ align:start position:0%
+are the dependencies just to give you
+rough numbers or our relationship 111 is
+
+ align:start position:0%
+rough numbers or our relationship 111 is
+ 
+
+ align:start position:0%
+rough numbers or our relationship 111 is
+the fastest it has the greatest number
+
+ align:start position:0%
+the fastest it has the greatest number
+ 
+
+ align:start position:0%
+the fastest it has the greatest number
+of atoms per square centimeter one one0
+
+ align:start position:0%
+of atoms per square centimeter one one0
+ 
+
+ align:start position:0%
+of atoms per square centimeter one one0
+is second and the slowest is one z
+
+ align:start position:0%
+is second and the slowest is one z
+ 
+
+ align:start position:0%
+is second and the slowest is one z
+z and in fact these are the
+
+ align:start position:0%
+z and in fact these are the
+ 
+
+ align:start position:0%
+z and in fact these are the
+relationships um if we take the 111
+
+ align:start position:0%
+relationships um if we take the 111
+ 
+
+ align:start position:0%
+relationships um if we take the 111
+rates uh and we divide them uh by 1.68
+
+ align:start position:0%
+rates uh and we divide them uh by 1.68
+ 
+
+ align:start position:0%
+rates uh and we divide them uh by 1.68
+we get the 10 rates uh and the
+
+ align:start position:0%
+we get the 10 rates uh and the
+ 
+
+ align:start position:0%
+we get the 10 rates uh and the
+relationship between 1 one0 is in
+
+ align:start position:0%
+relationship between 1 one0 is in
+ 
+
+ align:start position:0%
+relationship between 1 one0 is in
+between and again it's related to the
+
+ align:start position:0%
+between and again it's related to the
+ 
+
+ align:start position:0%
+between and again it's related to the
+Silicon Atomic density the number of
+
+ align:start position:0%
+Silicon Atomic density the number of
+ 
+
+ align:start position:0%
+Silicon Atomic density the number of
+atoms per square centimeter that are
+
+ align:start position:0%
+atoms per square centimeter that are
+ 
+
+ align:start position:0%
+atoms per square centimeter that are
+available and you can believe that
+
+ align:start position:0%
+available and you can believe that
+ 
+
+ align:start position:0%
+available and you can believe that
+because in order to have the surface
+
+ align:start position:0%
+because in order to have the surface
+ 
+
+ align:start position:0%
+because in order to have the surface
+reaction take place silicon silicon
+
+ align:start position:0%
+reaction take place silicon silicon
+ 
+
+ align:start position:0%
+reaction take place silicon silicon
+bonds have to be broken
+
+ align:start position:0%
+bonds have to be broken
+ 
+
+ align:start position:0%
+bonds have to be broken
+um so and the number of atoms available
+
+ align:start position:0%
+um so and the number of atoms available
+ 
+
+ align:start position:0%
+um so and the number of atoms available
+is is going to be uh important in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case uh slide 36 um is an interesting
+
+ align:start position:0%
+case uh slide 36 um is an interesting
+ 
+
+ align:start position:0%
+case uh slide 36 um is an interesting
+example of how um even you might say
+
+ align:start position:0%
+example of how um even you might say
+ 
+
+ align:start position:0%
+example of how um even you might say
+well I only use 10 Wafers what do I care
+
+ align:start position:0%
+well I only use 10 Wafers what do I care
+ 
+
+ align:start position:0%
+well I only use 10 Wafers what do I care
+about oxidation on 11 Z well you will
+
+ align:start position:0%
+about oxidation on 11 Z well you will
+ 
+
+ align:start position:0%
+about oxidation on 11 Z well you will
+care because you often um etch a trench
+
+ align:start position:0%
+care because you often um etch a trench
+ 
+
+ align:start position:0%
+care because you often um etch a trench
+and then need to oxidize the trench and
+
+ align:start position:0%
+and then need to oxidize the trench and
+ 
+
+ align:start position:0%
+and then need to oxidize the trench and
+of course the trench has different
+
+ align:start position:0%
+of course the trench has different
+ 
+
+ align:start position:0%
+of course the trench has different
+orientations of its walls so this
+
+ align:start position:0%
+orientations of its walls so this
+ 
+
+ align:start position:0%
+orientations of its walls so this
+particular this is a um a Supreme four
+
+ align:start position:0%
+particular this is a um a Supreme four
+ 
+
+ align:start position:0%
+particular this is a um a Supreme four
+simulation of a trench that was uh
+
+ align:start position:0%
+simulation of a trench that was uh
+ 
+
+ align:start position:0%
+simulation of a trench that was uh
+etched into a 10 wafer so 10 means what
+
+ align:start position:0%
+etched into a 10 wafer so 10 means what
+ 
+
+ align:start position:0%
+etched into a 10 wafer so 10 means what
+it means the surface of this
+
+ align:start position:0%
+it means the surface of this
+ 
+
+ align:start position:0%
+it means the surface of this
+wafer this plane at the very surface is
+
+ align:start position:0%
+wafer this plane at the very surface is
+ 
+
+ align:start position:0%
+wafer this plane at the very surface is
+is is 10 the 10 direction or1 is
+
+ align:start position:0%
+is is 10 the 10 direction or1 is
+ 
+
+ align:start position:0%
+is is 10 the 10 direction or1 is
+pointing up but if once I start itching
+
+ align:start position:0%
+pointing up but if once I start itching
+ 
+
+ align:start position:0%
+pointing up but if once I start itching
+into it the planes that I expose will be
+
+ align:start position:0%
+into it the planes that I expose will be
+ 
+
+ align:start position:0%
+into it the planes that I expose will be
+different orientations right depending
+
+ align:start position:0%
+different orientations right depending
+ 
+
+ align:start position:0%
+different orientations right depending
+on how I design my trench if I etch into
+
+ align:start position:0%
+on how I design my trench if I etch into
+ 
+
+ align:start position:0%
+on how I design my trench if I etch into
+the crystal so for example um I edch a
+
+ align:start position:0%
+the crystal so for example um I edch a
+ 
+
+ align:start position:0%
+the crystal so for example um I edch a
+trench here down into the crystal the
+
+ align:start position:0%
+trench here down into the crystal the
+ 
+
+ align:start position:0%
+trench here down into the crystal the
+bottom face is one z0 because the bottom
+
+ align:start position:0%
+bottom face is one z0 because the bottom
+ 
+
+ align:start position:0%
+bottom face is one z0 because the bottom
+face is the same as as the top face the
+
+ align:start position:0%
+face is the same as as the top face the
+ 
+
+ align:start position:0%
+face is the same as as the top face the
+face of the wafer uh but the side wall
+
+ align:start position:0%
+face of the wafer uh but the side wall
+ 
+
+ align:start position:0%
+face of the wafer uh but the side wall
+this face right here the sidewall that
+
+ align:start position:0%
+this face right here the sidewall that
+ 
+
+ align:start position:0%
+this face right here the sidewall that
+I've exposed depending on how I oriented
+
+ align:start position:0%
+I've exposed depending on how I oriented
+ 
+
+ align:start position:0%
+I've exposed depending on how I oriented
+this trench which is um assumed to be uh
+
+ align:start position:0%
+this trench which is um assumed to be uh
+ 
+
+ align:start position:0%
+this trench which is um assumed to be uh
+square or rectangular the sidewall face
+
+ align:start position:0%
+square or rectangular the sidewall face
+ 
+
+ align:start position:0%
+square or rectangular the sidewall face
+could be a one one
+
+ align:start position:0%
+could be a one one
+ 
+
+ align:start position:0%
+could be a one one
+Z depending on how I orent it with
+
+ align:start position:0%
+Z depending on how I orent it with
+ 
+
+ align:start position:0%
+Z depending on how I orent it with
+respect to the flat um so um the you can
+
+ align:start position:0%
+respect to the flat um so um the you can
+ 
+
+ align:start position:0%
+respect to the flat um so um the you can
+immediately expect a different oxidation
+
+ align:start position:0%
+immediately expect a different oxidation
+ 
+
+ align:start position:0%
+immediately expect a different oxidation
+rate on this face right here from the
+
+ align:start position:0%
+rate on this face right here from the
+ 
+
+ align:start position:0%
+rate on this face right here from the
+oxidation on the bottom
+
+ align:start position:0%
+oxidation on the bottom
+ 
+
+ align:start position:0%
+oxidation on the bottom
+um and this is an example of a
+
+ align:start position:0%
+um and this is an example of a
+ 
+
+ align:start position:0%
+um and this is an example of a
+simulation that was done uh 30 minutes
+
+ align:start position:0%
+simulation that was done uh 30 minutes
+ 
+
+ align:start position:0%
+simulation that was done uh 30 minutes
+in 900 900 degrees C in water and you
+
+ align:start position:0%
+in 900 900 degrees C in water and you
+ 
+
+ align:start position:0%
+in 900 900 degrees C in water and you
+see the thicker oxide That Grew on the
+
+ align:start position:0%
+see the thicker oxide That Grew on the
+ 
+
+ align:start position:0%
+see the thicker oxide That Grew on the
+sidewall that's pretty much in this bulk
+
+ align:start position:0%
+sidewall that's pretty much in this bulk
+ 
+
+ align:start position:0%
+sidewall that's pretty much in this bulk
+region of the sidewall that's entirely
+
+ align:start position:0%
+region of the sidewall that's entirely
+ 
+
+ align:start position:0%
+region of the sidewall that's entirely
+due to the fact that it's a different
+
+ align:start position:0%
+due to the fact that it's a different
+ 
+
+ align:start position:0%
+due to the fact that it's a different
+orientation so this simulator took that
+
+ align:start position:0%
+orientation so this simulator took that
+ 
+
+ align:start position:0%
+orientation so this simulator took that
+into account it's a little bit thicker
+
+ align:start position:0%
+into account it's a little bit thicker
+ 
+
+ align:start position:0%
+into account it's a little bit thicker
+here than it is on the
+
+ align:start position:0%
+here than it is on the
+ 
+
+ align:start position:0%
+here than it is on the
+bottom what is this this weird looking
+
+ align:start position:0%
+bottom what is this this weird looking
+ 
+
+ align:start position:0%
+bottom what is this this weird looking
+Corner effect that's not orientation so
+
+ align:start position:0%
+Corner effect that's not orientation so
+ 
+
+ align:start position:0%
+Corner effect that's not orientation so
+much this actually shows a
+
+ align:start position:0%
+much this actually shows a
+ 
+
+ align:start position:0%
+much this actually shows a
+two-dimensional effect we'll we'll talk
+
+ align:start position:0%
+two-dimensional effect we'll we'll talk
+ 
+
+ align:start position:0%
+two-dimensional effect we'll we'll talk
+about next time which is a stress effect
+
+ align:start position:0%
+about next time which is a stress effect
+ 
+
+ align:start position:0%
+about next time which is a stress effect
+when you're oxidizing a corner again the
+
+ align:start position:0%
+when you're oxidizing a corner again the
+ 
+
+ align:start position:0%
+when you're oxidizing a corner again the
+oxide has to expand in a corner it's a
+
+ align:start position:0%
+oxide has to expand in a corner it's a
+ 
+
+ align:start position:0%
+oxide has to expand in a corner it's a
+little bit hard to do some expansion
+
+ align:start position:0%
+little bit hard to do some expansion
+ 
+
+ align:start position:0%
+little bit hard to do some expansion
+where it's going to turn out the
+
+ align:start position:0%
+where it's going to turn out the
+ 
+
+ align:start position:0%
+where it's going to turn out the
+oxidation rate in in these sharp Corners
+
+ align:start position:0%
+oxidation rate in in these sharp Corners
+ 
+
+ align:start position:0%
+oxidation rate in in these sharp Corners
+it's going to end up being slower due to
+
+ align:start position:0%
+it's going to end up being slower due to
+ 
+
+ align:start position:0%
+it's going to end up being slower due to
+stress so that was Tak account into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulation so let me just summarize what
+
+ align:start position:0%
+simulation so let me just summarize what
+ 
+
+ align:start position:0%
+simulation so let me just summarize what
+we have from today um the basic growth
+
+ align:start position:0%
+we have from today um the basic growth
+ 
+
+ align:start position:0%
+we have from today um the basic growth
+Mech mechanism is transport through the
+
+ align:start position:0%
+Mech mechanism is transport through the
+ 
+
+ align:start position:0%
+Mech mechanism is transport through the
+oxide by diffusion and then chemical
+
+ align:start position:0%
+oxide by diffusion and then chemical
+ 
+
+ align:start position:0%
+oxide by diffusion and then chemical
+reaction at the interface as opposed to
+
+ align:start position:0%
+reaction at the interface as opposed to
+ 
+
+ align:start position:0%
+reaction at the interface as opposed to
+the Silicon doesn't come out of lattice
+
+ align:start position:0%
+the Silicon doesn't come out of lattice
+ 
+
+ align:start position:0%
+the Silicon doesn't come out of lattice
+and go up to the surface um we generally
+
+ align:start position:0%
+and go up to the surface um we generally
+ 
+
+ align:start position:0%
+and go up to the surface um we generally
+have a linear parabolic law when we have
+
+ align:start position:0%
+have a linear parabolic law when we have
+ 
+
+ align:start position:0%
+have a linear parabolic law when we have
+planer oxidation next time we're going
+
+ align:start position:0%
+planer oxidation next time we're going
+ 
+
+ align:start position:0%
+planer oxidation next time we're going
+to see there are a lot of different
+
+ align:start position:0%
+to see there are a lot of different
+ 
+
+ align:start position:0%
+to see there are a lot of different
+cases where it's non-planar and it's not
+
+ align:start position:0%
+cases where it's non-planar and it's not
+ 
+
+ align:start position:0%
+cases where it's non-planar and it's not
+just simple linear
+
+ align:start position:0%
+just simple linear
+ 
+
+ align:start position:0%
+just simple linear
+parabolic um the deal grow model isn't
+
+ align:start position:0%
+parabolic um the deal grow model isn't
+ 
+
+ align:start position:0%
+parabolic um the deal grow model isn't
+uh completely accurate in the thin oxide
+
+ align:start position:0%
+uh completely accurate in the thin oxide
+ 
+
+ align:start position:0%
+uh completely accurate in the thin oxide
+regime but it can be corrected by using
+
+ align:start position:0%
+regime but it can be corrected by using
+ 
+
+ align:start position:0%
+regime but it can be corrected by using
+uh Han and Helms or rein or you can use
+
+ align:start position:0%
+uh Han and Helms or rein or you can use
+ 
+
+ align:start position:0%
+uh Han and Helms or rein or you can use
+massud then they all can be designed to
+
+ align:start position:0%
+massud then they all can be designed to
+ 
+
+ align:start position:0%
+massud then they all can be designed to
+converge to deal grow for when you're at
+
+ align:start position:0%
+converge to deal grow for when you're at
+ 
+
+ align:start position:0%
+converge to deal grow for when you're at
+uh thinner at thicker oxide say above
+
+ align:start position:0%
+uh thinner at thicker oxide say above
+ 
+
+ align:start position:0%
+uh thinner at thicker oxide say above
+200 anrs and the growth rate varies with
+
+ align:start position:0%
+200 anrs and the growth rate varies with
+ 
+
+ align:start position:0%
+200 anrs and the growth rate varies with
+orientation 111 is the fastest and 10 uh
+
+ align:start position:0%
+orientation 111 is the fastest and 10 uh
+ 
+
+ align:start position:0%
+orientation 111 is the fastest and 10 uh
+being the
+
+ align:start position:0%
+being the
+ 
+
+ align:start position:0%
+being the
+slowest so that's mostly what I wanted
+
+ align:start position:0%
+slowest so that's mostly what I wanted
+ 
+
+ align:start position:0%
+slowest so that's mostly what I wanted
+to cover for today I have a couple
+
+ align:start position:0%
+to cover for today I have a couple
+ 
+
+ align:start position:0%
+to cover for today I have a couple
+things for you though um your
+
+ align:start position:0%
+things for you though um your
+ 
+
+ align:start position:0%
+things for you though um your
+homework is um going back so you can
+
+ align:start position:0%
+homework is um going back so you can
+ 
+
+ align:start position:0%
+homework is um going back so you can
+come up and grab your homework it's been
+
+ align:start position:0%
+come up and grab your homework it's been
+ 
+
+ align:start position:0%
+come up and grab your homework it's been
+graded uh up here homework number one
+
+ align:start position:0%
+graded uh up here homework number one
+ 
+
+ align:start position:0%
+graded uh up here homework number one
+and the solutions are also up front so
+
+ align:start position:0%
+and the solutions are also up front so
+ 
+
+ align:start position:0%
+and the solutions are also up front so
+if you can come on up and take the
+
+ align:start position:0%
+if you can come on up and take the
+ 
+
+ align:start position:0%
+if you can come on up and take the
+homework and the solutions uh from
+
+ align:start position:0%
+homework and the solutions uh from
+ 
+
+ align:start position:0%
+homework and the solutions uh from
+homework number one that's good if if
+
+ align:start position:0%
+homework number one that's good if if
+ 
+
+ align:start position:0%
+homework number one that's good if if
+you weren't here last time you didn't
+
+ align:start position:0%
+you weren't here last time you didn't
+ 
+
+ align:start position:0%
+you weren't here last time you didn't
+get to see the Intel wafer I'm going to
+
+ align:start position:0%
+get to see the Intel wafer I'm going to
+ 
+
+ align:start position:0%
+get to see the Intel wafer I'm going to
+hand it back after today so you're
+
+ align:start position:0%
+hand it back after today so you're
+ 
+
+ align:start position:0%
+hand it back after today so you're
+welcome to take a look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it oh these are not in any particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order what I need for strain on the what
+
+ align:start position:0%
+order what I need for strain on the what
+ 
+
+ align:start position:0%
+order what I need for strain on the what
+people extracted The Strain silicon yeah
+
+ align:start position:0%
+people extracted The Strain silicon yeah
+ 
+
+ align:start position:0%
+people extracted The Strain silicon yeah
+people tried Jeff tried um this pretty
+
+ align:start position:0%
+people tried Jeff tried um this pretty
+ 
+
+ align:start position:0%
+people tried Jeff tried um this pretty
+darn
+
+ align:start position:0%
+darn
+ 
+
+ align:start position:0%
+darn
+close you know a change of 1% in the
+
+ align:start position:0%
+close you know a change of 1% in the
+ 
+
+ align:start position:0%
+close you know a change of 1% in the
+last C now cuz I really haven't changed
+
+ align:start position:0%
+last C now cuz I really haven't changed
+ 
+
+ align:start position:0%
+last C now cuz I really haven't changed
+the the number of atoms per square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+centimeter what does change is as soon
+
+ align:start position:0%
+centimeter what does change is as soon
+ 
+
+ align:start position:0%
+centimeter what does change is as soon
+as you hit the SL and geranium oxidation
+
+ align:start position:0%
+as you hit the SL and geranium oxidation
+ 
+
+ align:start position:0%
+as you hit the SL and geranium oxidation
+rate goes way up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
\ No newline at end of file
diff --git a/Lgacew5BjDI.txt b/Lgacew5BjDI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e4a633b87d812a78f3082c80d07723ff1595c049
--- /dev/null
+++ b/Lgacew5BjDI.txt
@@ -0,0 +1,403 @@
+align:start position:0%
+ 
+so we looked at the formal definition of
+
+ align:start position:0%
+so we looked at the formal definition of
+ 
+
+ align:start position:0%
+so we looked at the formal definition of
+what it means for a sequence to converge
+
+ align:start position:0%
+what it means for a sequence to converge
+ 
+
+ align:start position:0%
+what it means for a sequence to converge
+but as a practical matter how can we
+
+ align:start position:0%
+but as a practical matter how can we
+ 
+
+ align:start position:0%
+but as a practical matter how can we
+tell whether a given sequence converges
+
+ align:start position:0%
+tell whether a given sequence converges
+ 
+
+ align:start position:0%
+tell whether a given sequence converges
+or not there are two criteria that are
+
+ align:start position:0%
+or not there are two criteria that are
+ 
+
+ align:start position:0%
+or not there are two criteria that are
+the most commonly used for that purpose
+
+ align:start position:0%
+the most commonly used for that purpose
+ 
+
+ align:start position:0%
+the most commonly used for that purpose
+and it's useful to be aware of them the
+
+ align:start position:0%
+and it's useful to be aware of them the
+ 
+
+ align:start position:0%
+and it's useful to be aware of them the
+first one deals with the case where we
+
+ align:start position:0%
+first one deals with the case where we
+ 
+
+ align:start position:0%
+first one deals with the case where we
+have a sequence of numbers that keep
+
+ align:start position:0%
+have a sequence of numbers that keep
+ 
+
+ align:start position:0%
+have a sequence of numbers that keep
+increasing or at least they do not go
+
+ align:start position:0%
+increasing or at least they do not go
+ 
+
+ align:start position:0%
+increasing or at least they do not go
+down in that case those numbers may go
+
+ align:start position:0%
+down in that case those numbers may go
+ 
+
+ align:start position:0%
+down in that case those numbers may go
+up forever without any bound so if you
+
+ align:start position:0%
+up forever without any bound so if you
+ 
+
+ align:start position:0%
+up forever without any bound so if you
+look at any particular value there's
+
+ align:start position:0%
+look at any particular value there's
+ 
+
+ align:start position:0%
+look at any particular value there's
+going to be a time at which the sequence
+
+ align:start position:0%
+going to be a time at which the sequence
+ 
+
+ align:start position:0%
+going to be a time at which the sequence
+has exceeded that value in that case we
+
+ align:start position:0%
+has exceeded that value in that case we
+ 
+
+ align:start position:0%
+has exceeded that value in that case we
+say that the sequence converges to
+
+ align:start position:0%
+say that the sequence converges to
+ 
+
+ align:start position:0%
+say that the sequence converges to
+infinity but if this is not the case if
+
+ align:start position:0%
+infinity but if this is not the case if
+ 
+
+ align:start position:0%
+infinity but if this is not the case if
+it does not converge to infinity which
+
+ align:start position:0%
+it does not converge to infinity which
+ 
+
+ align:start position:0%
+it does not converge to infinity which
+means that the entries of the sequence
+
+ align:start position:0%
+means that the entries of the sequence
+ 
+
+ align:start position:0%
+means that the entries of the sequence
+are bounded they do not grow arbitrarily
+
+ align:start position:0%
+are bounded they do not grow arbitrarily
+ 
+
+ align:start position:0%
+are bounded they do not grow arbitrarily
+large then in that case it is guaranteed
+
+ align:start position:0%
+large then in that case it is guaranteed
+ 
+
+ align:start position:0%
+large then in that case it is guaranteed
+that the sequence would converge to a
+
+ align:start position:0%
+that the sequence would converge to a
+ 
+
+ align:start position:0%
+that the sequence would converge to a
+certain number this is not something
+
+ align:start position:0%
+certain number this is not something
+ 
+
+ align:start position:0%
+certain number this is not something
+that we will attempt to prove but it is
+
+ align:start position:0%
+that we will attempt to prove but it is
+ 
+
+ align:start position:0%
+that we will attempt to prove but it is
+a useful fact to know another way of
+
+ align:start position:0%
+a useful fact to know another way of
+ 
+
+ align:start position:0%
+a useful fact to know another way of
+establishing convergence is to derive
+
+ align:start position:0%
+establishing convergence is to derive
+ 
+
+ align:start position:0%
+establishing convergence is to derive
+some bounds on the distance of our
+
+ align:start position:0%
+some bounds on the distance of our
+ 
+
+ align:start position:0%
+some bounds on the distance of our
+sequence from the number that we suspect
+
+ align:start position:0%
+sequence from the number that we suspect
+ 
+
+ align:start position:0%
+sequence from the number that we suspect
+to be the limit if that distance becomes
+
+ align:start position:0%
+to be the limit if that distance becomes
+ 
+
+ align:start position:0%
+to be the limit if that distance becomes
+smaller and smaller if we can manage to
+
+ align:start position:0%
+smaller and smaller if we can manage to
+ 
+
+ align:start position:0%
+smaller and smaller if we can manage to
+bound that distance by a certain number
+
+ align:start position:0%
+bound that distance by a certain number
+ 
+
+ align:start position:0%
+bound that distance by a certain number
+and that number goes down to zero then
+
+ align:start position:0%
+and that number goes down to zero then
+ 
+
+ align:start position:0%
+and that number goes down to zero then
+it is guaranteed that since this
+
+ align:start position:0%
+it is guaranteed that since this
+ 
+
+ align:start position:0%
+it is guaranteed that since this
+distance goes down to zero that the
+
+ align:start position:0%
+distance goes down to zero that the
+ 
+
+ align:start position:0%
+distance goes down to zero that the
+sequence ái converges to a and there's a
+
+ align:start position:0%
+sequence ái converges to a and there's a
+ 
+
+ align:start position:0%
+sequence ái converges to a and there's a
+variation of this argument which is the
+
+ align:start position:0%
+variation of this argument which is the
+ 
+
+ align:start position:0%
+variation of this argument which is the
+so-called sandwich argument and it goes
+
+ align:start position:0%
+so-called sandwich argument and it goes
+ 
+
+ align:start position:0%
+so-called sandwich argument and it goes
+as follows if we have a certain sequence
+
+ align:start position:0%
+as follows if we have a certain sequence
+ 
+
+ align:start position:0%
+as follows if we have a certain sequence
+that converges to some number a and we
+
+ align:start position:0%
+that converges to some number a and we
+ 
+
+ align:start position:0%
+that converges to some number a and we
+have another sequence that converges to
+
+ align:start position:0%
+have another sequence that converges to
+ 
+
+ align:start position:0%
+have another sequence that converges to
+that same number
+
+ align:start position:0%
+that same number
+ 
+
+ align:start position:0%
+that same number
+and our sequence is somewhere in between
+
+ align:start position:0%
+and our sequence is somewhere in between
+ 
+
+ align:start position:0%
+and our sequence is somewhere in between
+then our sequence must also converge to
+
+ align:start position:0%
+then our sequence must also converge to
+ 
+
+ align:start position:0%
+then our sequence must also converge to
+that particular number a so these are
+
+ align:start position:0%
+that particular number a so these are
+ 
+
+ align:start position:0%
+that particular number a so these are
+the usual ways of quickly saying
+
+ align:start position:0%
+the usual ways of quickly saying
+ 
+
+ align:start position:0%
+the usual ways of quickly saying
+something about the convergence of a
+
+ align:start position:0%
+something about the convergence of a
+ 
+
+ align:start position:0%
+something about the convergence of a
+given sequence and we will be often
+
+ align:start position:0%
+given sequence and we will be often
+ 
+
+ align:start position:0%
+given sequence and we will be often
+using this type of argument in this
+
+ align:start position:0%
+using this type of argument in this
+ 
+
+ align:start position:0%
+using this type of argument in this
+class but without making a big fuss
+
+ align:start position:0%
+class but without making a big fuss
+ 
+
+ align:start position:0%
+class but without making a big fuss
+about them or without even referring to
+
+ align:start position:0%
+about them or without even referring to
+ 
+
+ align:start position:0%
+about them or without even referring to
+these facts in an explicit manner
\ No newline at end of file
diff --git a/Lm8WHM0glHE.txt b/Lm8WHM0glHE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61c2a661a9df7c8b36f7a07ad801a2ce13fd23e5
--- /dev/null
+++ b/Lm8WHM0glHE.txt
@@ -0,0 +1,1731 @@
+align:start position:0%
+ 
+I think fun is an very important part to
+
+ align:start position:0%
+I think fun is an very important part to
+ 
+
+ align:start position:0%
+I think fun is an very important part to
+life in general and in particular work
+
+ align:start position:0%
+life in general and in particular work
+ 
+
+ align:start position:0%
+life in general and in particular work
+maybe not so common to view it that way
+
+ align:start position:0%
+maybe not so common to view it that way
+ 
+
+ align:start position:0%
+maybe not so common to view it that way
+but I think if you have fun if you enjoy
+
+ align:start position:0%
+but I think if you have fun if you enjoy
+ 
+
+ align:start position:0%
+but I think if you have fun if you enjoy
+if you're passionate about what you do
+
+ align:start position:0%
+if you're passionate about what you do
+ 
+
+ align:start position:0%
+if you're passionate about what you do
+then you'll do it well and you'll be
+
+ align:start position:0%
+then you'll do it well and you'll be
+ 
+
+ align:start position:0%
+then you'll do it well and you'll be
+super productive and people will love
+
+ align:start position:0%
+super productive and people will love
+ 
+
+ align:start position:0%
+super productive and people will love
+you for it um and so my guiding
+
+ align:start position:0%
+you for it um and so my guiding
+ 
+
+ align:start position:0%
+you for it um and so my guiding
+principle in in the research that I do
+
+ align:start position:0%
+principle in in the research that I do
+ 
+
+ align:start position:0%
+principle in in the research that I do
+has been to uh to always pursue to what
+
+ align:start position:0%
+has been to uh to always pursue to what
+ 
+
+ align:start position:0%
+has been to uh to always pursue to what
+I view as fun and sometimes it's things
+
+ align:start position:0%
+I view as fun and sometimes it's things
+ 
+
+ align:start position:0%
+I view as fun and sometimes it's things
+that are very relatable as fun like
+
+ align:start position:0%
+that are very relatable as fun like
+ 
+
+ align:start position:0%
+that are very relatable as fun like
+games and puzzles uh sometimes it's more
+
+ align:start position:0%
+games and puzzles uh sometimes it's more
+ 
+
+ align:start position:0%
+games and puzzles uh sometimes it's more
+obscure things but I personally find
+
+ align:start position:0%
+obscure things but I personally find
+ 
+
+ align:start position:0%
+obscure things but I personally find
+them really fun and maybe they're more
+
+ align:start position:0%
+them really fun and maybe they're more
+ 
+
+ align:start position:0%
+them really fun and maybe they're more
+practical um and so it's also nice to
+
+ align:start position:0%
+practical um and so it's also nice to
+ 
+
+ align:start position:0%
+practical um and so it's also nice to
+have a mixture but in teaching I think I
+
+ align:start position:0%
+have a mixture but in teaching I think I
+ 
+
+ align:start position:0%
+have a mixture but in teaching I think I
+mean I think learning should also be fun
+
+ align:start position:0%
+mean I think learning should also be fun
+ 
+
+ align:start position:0%
+mean I think learning should also be fun
+my dad raised me this way when he was
+
+ align:start position:0%
+my dad raised me this way when he was
+ 
+
+ align:start position:0%
+my dad raised me this way when he was
+homeschooling me and uh that always you
+
+ align:start position:0%
+homeschooling me and uh that always you
+ 
+
+ align:start position:0%
+homeschooling me and uh that always you
+should uh learn what you're curious
+
+ align:start position:0%
+should uh learn what you're curious
+ 
+
+ align:start position:0%
+should uh learn what you're curious
+about and uh so conversely as a teacher
+
+ align:start position:0%
+about and uh so conversely as a teacher
+ 
+
+ align:start position:0%
+about and uh so conversely as a teacher
+I want to make uh material really
+
+ align:start position:0%
+I want to make uh material really
+ 
+
+ align:start position:0%
+I want to make uh material really
+interesting and intriguing and just fun
+
+ align:start position:0%
+interesting and intriguing and just fun
+ 
+
+ align:start position:0%
+interesting and intriguing and just fun
+to learn about because I think students
+
+ align:start position:0%
+to learn about because I think students
+ 
+
+ align:start position:0%
+to learn about because I think students
+will be more excited and engage more
+
+ align:start position:0%
+will be more excited and engage more
+ 
+
+ align:start position:0%
+will be more excited and engage more
+with the material if they enjoy it seems
+
+ align:start position:0%
+with the material if they enjoy it seems
+ 
+
+ align:start position:0%
+with the material if they enjoy it seems
+natural um and so in this class I really
+
+ align:start position:0%
+natural um and so in this class I really
+ 
+
+ align:start position:0%
+natural um and so in this class I really
+tried to bring lots of fun examples I
+
+ align:start position:0%
+tried to bring lots of fun examples I
+ 
+
+ align:start position:0%
+tried to bring lots of fun examples I
+mean maybe there are some more uh
+
+ align:start position:0%
+mean maybe there are some more uh
+ 
+
+ align:start position:0%
+mean maybe there are some more uh
+serious problems that people have proved
+
+ align:start position:0%
+serious problems that people have proved
+ 
+
+ align:start position:0%
+serious problems that people have proved
+hard and then there's more entertaining
+
+ align:start position:0%
+hard and then there's more entertaining
+ 
+
+ align:start position:0%
+hard and then there's more entertaining
+problems that people have proved hard so
+
+ align:start position:0%
+problems that people have proved hard so
+ 
+
+ align:start position:0%
+problems that people have proved hard so
+I would I mean I often cover both but
+
+ align:start position:0%
+I would I mean I often cover both but
+ 
+
+ align:start position:0%
+I would I mean I often cover both but
+given the choice I'd prefer the one
+
+ align:start position:0%
+given the choice I'd prefer the one
+ 
+
+ align:start position:0%
+given the choice I'd prefer the one
+that's more entertaining and something
+
+ align:start position:0%
+that's more entertaining and something
+ 
+
+ align:start position:0%
+that's more entertaining and something
+that people can relate to like yeah I
+
+ align:start position:0%
+that people can relate to like yeah I
+ 
+
+ align:start position:0%
+that people can relate to like yeah I
+played that video game and it was really
+
+ align:start position:0%
+played that video game and it was really
+ 
+
+ align:start position:0%
+played that video game and it was really
+tough and now we can actually prove that
+
+ align:start position:0%
+tough and now we can actually prove that
+ 
+
+ align:start position:0%
+tough and now we can actually prove that
+it's tough then that's that makes it
+
+ align:start position:0%
+it's tough then that's that makes it
+ 
+
+ align:start position:0%
+it's tough then that's that makes it
+exciting um and so it's really nice I
+
+ align:start position:0%
+exciting um and so it's really nice I
+ 
+
+ align:start position:0%
+exciting um and so it's really nice I
+mean I view teaching as kind of a
+
+ align:start position:0%
+mean I view teaching as kind of a
+ 
+
+ align:start position:0%
+mean I view teaching as kind of a
+entertainment of sorts U I think it's
+
+ align:start position:0%
+entertainment of sorts U I think it's
+ 
+
+ align:start position:0%
+entertainment of sorts U I think it's
+nice to have that as a goal and if
+
+ align:start position:0%
+nice to have that as a goal and if
+ 
+
+ align:start position:0%
+nice to have that as a goal and if
+people are entertained they'll be
+
+ align:start position:0%
+people are entertained they'll be
+ 
+
+ align:start position:0%
+people are entertained they'll be
+engaged and they'll learn the material
+
+ align:start position:0%
+engaged and they'll learn the material
+ 
+
+ align:start position:0%
+engaged and they'll learn the material
+and they'll care more deeply about it
+
+ align:start position:0%
+and they'll care more deeply about it
+ 
+
+ align:start position:0%
+and they'll care more deeply about it
+and hopefully do research in the field
+
+ align:start position:0%
+and hopefully do research in the field
+ 
+
+ align:start position:0%
+and hopefully do research in the field
+and and all that I mean when I was
+
+ align:start position:0%
+and and all that I mean when I was
+ 
+
+ align:start position:0%
+and and all that I mean when I was
+younger when I was a graduate student uh
+
+ align:start position:0%
+younger when I was a graduate student uh
+ 
+
+ align:start position:0%
+younger when I was a graduate student uh
+a lot of my more senior colleagues other
+
+ align:start position:0%
+a lot of my more senior colleagues other
+ 
+
+ align:start position:0%
+a lot of my more senior colleagues other
+professors would uh warn me that it was
+
+ align:start position:0%
+professors would uh warn me that it was
+ 
+
+ align:start position:0%
+professors would uh warn me that it was
+maybe dangerous to do to pursue fun
+
+ align:start position:0%
+maybe dangerous to do to pursue fun
+ 
+
+ align:start position:0%
+maybe dangerous to do to pursue fun
+things that people would not view it as
+
+ align:start position:0%
+things that people would not view it as
+ 
+
+ align:start position:0%
+things that people would not view it as
+serious and maybe you won't get a job
+
+ align:start position:0%
+serious and maybe you won't get a job
+ 
+
+ align:start position:0%
+serious and maybe you won't get a job
+when you graduate um and I kind of
+
+ align:start position:0%
+when you graduate um and I kind of
+ 
+
+ align:start position:0%
+when you graduate um and I kind of
+ignored those
+
+ align:start position:0%
+ignored those
+ 
+
+ align:start position:0%
+ignored those
+people and uh it was it was a bit of a
+
+ align:start position:0%
+people and uh it was it was a bit of a
+ 
+
+ align:start position:0%
+people and uh it was it was a bit of a
+bold bold guess but um it worked out
+
+ align:start position:0%
+bold bold guess but um it worked out
+ 
+
+ align:start position:0%
+bold bold guess but um it worked out
+well for me and later those same people
+
+ align:start position:0%
+well for me and later those same people
+ 
+
+ align:start position:0%
+well for me and later those same people
+apologized for making that suggestion um
+
+ align:start position:0%
+apologized for making that suggestion um
+ 
+
+ align:start position:0%
+apologized for making that suggestion um
+I think again if if you're if you do
+
+ align:start position:0%
+I think again if if you're if you do
+ 
+
+ align:start position:0%
+I think again if if you're if you do
+things you're pass about you'll do them
+
+ align:start position:0%
+things you're pass about you'll do them
+ 
+
+ align:start position:0%
+things you're pass about you'll do them
+really well and you'll be very
+
+ align:start position:0%
+really well and you'll be very
+ 
+
+ align:start position:0%
+really well and you'll be very
+productive and so you can make up for
+
+ align:start position:0%
+productive and so you can make up for
+ 
+
+ align:start position:0%
+productive and so you can make up for
+the topics being more recreational by uh
+
+ align:start position:0%
+the topics being more recreational by uh
+ 
+
+ align:start position:0%
+the topics being more recreational by uh
+showing that they're really powerful and
+
+ align:start position:0%
+showing that they're really powerful and
+ 
+
+ align:start position:0%
+showing that they're really powerful and
+really deep mathematically um and that's
+
+ align:start position:0%
+really deep mathematically um and that's
+ 
+
+ align:start position:0%
+really deep mathematically um and that's
+turned out to work for me um since being
+
+ align:start position:0%
+turned out to work for me um since being
+ 
+
+ align:start position:0%
+turned out to work for me um since being
+at MIT it was again like uh you know
+
+ align:start position:0%
+at MIT it was again like uh you know
+ 
+
+ align:start position:0%
+at MIT it was again like uh you know
+will I get tenure is uh will people
+
+ align:start position:0%
+will I get tenure is uh will people
+ 
+
+ align:start position:0%
+will I get tenure is uh will people
+appreciate the fun side of things and I
+
+ align:start position:0%
+appreciate the fun side of things and I
+ 
+
+ align:start position:0%
+appreciate the fun side of things and I
+do lots of serious things in addition to
+
+ align:start position:0%
+do lots of serious things in addition to
+ 
+
+ align:start position:0%
+do lots of serious things in addition to
+lots of fun things but uh it worked out
+
+ align:start position:0%
+lots of fun things but uh it worked out
+ 
+
+ align:start position:0%
+lots of fun things but uh it worked out
+I got tenure and uh um in fact I think
+
+ align:start position:0%
+I got tenure and uh um in fact I think
+ 
+
+ align:start position:0%
+I got tenure and uh um in fact I think
+it was it's an important part of who I
+
+ align:start position:0%
+it was it's an important part of who I
+ 
+
+ align:start position:0%
+it was it's an important part of who I
+am one one analogy is to Martin Gardner
+
+ align:start position:0%
+am one one analogy is to Martin Gardner
+ 
+
+ align:start position:0%
+am one one analogy is to Martin Gardner
+uh he's sort of an idol of mine I never
+
+ align:start position:0%
+uh he's sort of an idol of mine I never
+ 
+
+ align:start position:0%
+uh he's sort of an idol of mine I never
+got to meet him although we corresponded
+
+ align:start position:0%
+got to meet him although we corresponded
+ 
+
+ align:start position:0%
+got to meet him although we corresponded
+a little bit um and he is called the
+
+ align:start position:0%
+a little bit um and he is called the
+ 
+
+ align:start position:0%
+a little bit um and he is called the
+father of recreational mathematics he
+
+ align:start position:0%
+father of recreational mathematics he
+ 
+
+ align:start position:0%
+father of recreational mathematics he
+wrote a column for Scientific American
+
+ align:start position:0%
+wrote a column for Scientific American
+ 
+
+ align:start position:0%
+wrote a column for Scientific American
+for decades and it really influenced a
+
+ align:start position:0%
+for decades and it really influenced a
+ 
+
+ align:start position:0%
+for decades and it really influenced a
+lot of uh present day mathematicians and
+
+ align:start position:0%
+lot of uh present day mathematicians and
+ 
+
+ align:start position:0%
+lot of uh present day mathematicians and
+computer scientists to get into the
+
+ align:start position:0%
+computer scientists to get into the
+ 
+
+ align:start position:0%
+computer scientists to get into the
+field because they read this column and
+
+ align:start position:0%
+field because they read this column and
+ 
+
+ align:start position:0%
+field because they read this column and
+it's talking about open problems but in
+
+ align:start position:0%
+it's talking about open problems but in
+ 
+
+ align:start position:0%
+it's talking about open problems but in
+a very accessible way he wasn't really a
+
+ align:start position:0%
+a very accessible way he wasn't really a
+ 
+
+ align:start position:0%
+a very accessible way he wasn't really a
+mathematician he just learned from
+
+ align:start position:0%
+mathematician he just learned from
+ 
+
+ align:start position:0%
+mathematician he just learned from
+mathematicians that he knew and wrote
+
+ align:start position:0%
+mathematicians that he knew and wrote
+ 
+
+ align:start position:0%
+mathematicians that he knew and wrote
+about the cool problems very accessible
+
+ align:start position:0%
+about the cool problems very accessible
+ 
+
+ align:start position:0%
+about the cool problems very accessible
+problems and fun problems uh that people
+
+ align:start position:0%
+problems and fun problems uh that people
+ 
+
+ align:start position:0%
+problems and fun problems uh that people
+were working on and what kind of
+
+ align:start position:0%
+were working on and what kind of
+ 
+
+ align:start position:0%
+were working on and what kind of
+solutions they had um and so Martin
+
+ align:start position:0%
+solutions they had um and so Martin
+ 
+
+ align:start position:0%
+solutions they had um and so Martin
+Gardner is kind of a model although I do
+
+ align:start position:0%
+Gardner is kind of a model although I do
+ 
+
+ align:start position:0%
+Gardner is kind of a model although I do
+it more in the teaching side than in the
+
+ align:start position:0%
+it more in the teaching side than in the
+ 
+
+ align:start position:0%
+it more in the teaching side than in the
+writing side of a way to engage new
+
+ align:start position:0%
+writing side of a way to engage new
+ 
+
+ align:start position:0%
+writing side of a way to engage new
+people into the field um get people
+
+ align:start position:0%
+people into the field um get people
+ 
+
+ align:start position:0%
+people into the field um get people
+excited about science and technology and
+
+ align:start position:0%
+excited about science and technology and
+ 
+
+ align:start position:0%
+excited about science and technology and
+Mathematics um and I think MIT appre
+
+ align:start position:0%
+Mathematics um and I think MIT appre
+ 
+
+ align:start position:0%
+Mathematics um and I think MIT appre
+appreciates that a lot uh that by
+
+ align:start position:0%
+appreciates that a lot uh that by
+ 
+
+ align:start position:0%
+appreciates that a lot uh that by
+working on fun problems you can reach a
+
+ align:start position:0%
+working on fun problems you can reach a
+ 
+
+ align:start position:0%
+working on fun problems you can reach a
+broad audience you know when we prove
+
+ align:start position:0%
+broad audience you know when we prove
+ 
+
+ align:start position:0%
+broad audience you know when we prove
+Super Mario Brothers is EMP complete all
+
+ align:start position:0%
+Super Mario Brothers is EMP complete all
+ 
+
+ align:start position:0%
+Super Mario Brothers is EMP complete all
+the newspapers were covering it like wow
+
+ align:start position:0%
+the newspapers were covering it like wow
+ 
+
+ align:start position:0%
+the newspapers were covering it like wow
+Hard Nintendo games really are hard and
+
+ align:start position:0%
+Hard Nintendo games really are hard and
+ 
+
+ align:start position:0%
+Hard Nintendo games really are hard and
+you know mathematicians proed this thing
+
+ align:start position:0%
+you know mathematicians proed this thing
+ 
+
+ align:start position:0%
+you know mathematicians proed this thing
+everyone knew sounds funny and so it's
+
+ align:start position:0%
+everyone knew sounds funny and so it's
+ 
+
+ align:start position:0%
+everyone knew sounds funny and so it's
+makes for good good press um and I think
+
+ align:start position:0%
+makes for good good press um and I think
+ 
+
+ align:start position:0%
+makes for good good press um and I think
+people are intrigued by oh what does
+
+ align:start position:0%
+people are intrigued by oh what does
+ 
+
+ align:start position:0%
+people are intrigued by oh what does
+that mean then they can go and read the
+
+ align:start position:0%
+that mean then they can go and read the
+ 
+
+ align:start position:0%
+that mean then they can go and read the
+paper and or take this class and it
+
+ align:start position:0%
+paper and or take this class and it
+ 
+
+ align:start position:0%
+paper and or take this class and it
+covers why how do you prove something
+
+ align:start position:0%
+covers why how do you prove something
+ 
+
+ align:start position:0%
+covers why how do you prove something
+like that and how do you actually and
+
+ align:start position:0%
+like that and how do you actually and
+ 
+
+ align:start position:0%
+like that and how do you actually and
+it's really fun to prove prove that
+
+ align:start position:0%
+it's really fun to prove prove that
+ 
+
+ align:start position:0%
+it's really fun to prove prove that
+Super Mario Brothers is hard you
+
+ align:start position:0%
+Super Mario Brothers is hard you
+ 
+
+ align:start position:0%
+Super Mario Brothers is hard you
+basically construct little levels that
+
+ align:start position:0%
+basically construct little levels that
+ 
+
+ align:start position:0%
+basically construct little levels that
+that build a computer so you build a
+
+ align:start position:0%
+that build a computer so you build a
+ 
+
+ align:start position:0%
+that build a computer so you build a
+Super Mario Brothers level that
+
+ align:start position:0%
+Super Mario Brothers level that
+ 
+
+ align:start position:0%
+Super Mario Brothers level that
+represents an entire computer and that's
+
+ align:start position:0%
+represents an entire computer and that's
+ 
+
+ align:start position:0%
+represents an entire computer and that's
+that's a fun thing to do and I think it
+
+ align:start position:0%
+that's a fun thing to do and I think it
+ 
+
+ align:start position:0%
+that's a fun thing to do and I think it
+can get a lot of people excited about
+
+ align:start position:0%
+can get a lot of people excited about
+ 
+
+ align:start position:0%
+can get a lot of people excited about
+computer science um when I first came to
+
+ align:start position:0%
+computer science um when I first came to
+ 
+
+ align:start position:0%
+computer science um when I first came to
+MIT I I Ed this as a principle to get
+
+ align:start position:0%
+MIT I I Ed this as a principle to get
+ 
+
+ align:start position:0%
+MIT I I Ed this as a principle to get
+new graduate students started so they're
+
+ align:start position:0%
+new graduate students started so they're
+ 
+
+ align:start position:0%
+new graduate students started so they're
+look they're trying to find a problem to
+
+ align:start position:0%
+look they're trying to find a problem to
+ 
+
+ align:start position:0%
+look they're trying to find a problem to
+solve they don't really know what
+
+ align:start position:0%
+solve they don't really know what
+ 
+
+ align:start position:0%
+solve they don't really know what
+they're interested in so often I'll
+
+ align:start position:0%
+they're interested in so often I'll
+ 
+
+ align:start position:0%
+they're interested in so often I'll
+suggest a game or a puzzle hey let's
+
+ align:start position:0%
+suggest a game or a puzzle hey let's
+ 
+
+ align:start position:0%
+suggest a game or a puzzle hey let's
+prove this hard one of the first ones
+
+ align:start position:0%
+prove this hard one of the first ones
+ 
+
+ align:start position:0%
+prove this hard one of the first ones
+was Tetris that was done with two MIT
+
+ align:start position:0%
+was Tetris that was done with two MIT
+ 
+
+ align:start position:0%
+was Tetris that was done with two MIT
+students uh back in 2003 I think just
+
+ align:start position:0%
+students uh back in 2003 I think just
+ 
+
+ align:start position:0%
+students uh back in 2003 I think just
+after I started I was like you I've
+
+ align:start position:0%
+after I started I was like you I've
+ 
+
+ align:start position:0%
+after I started I was like you I've
+always been curious about Tetris it
+
+ align:start position:0%
+always been curious about Tetris it
+ 
+
+ align:start position:0%
+always been curious about Tetris it
+seems really tricky um and then together
+
+ align:start position:0%
+seems really tricky um and then together
+ 
+
+ align:start position:0%
+seems really tricky um and then together
+we we proved that it was hard and that
+
+ align:start position:0%
+we we proved that it was hard and that
+ 
+
+ align:start position:0%
+we we proved that it was hard and that
+was their first paper and it got them
+
+ align:start position:0%
+was their first paper and it got them
+ 
+
+ align:start position:0%
+was their first paper and it got them
+kind of psyched up and ready to solve
+
+ align:start position:0%
+kind of psyched up and ready to solve
+ 
+
+ align:start position:0%
+kind of psyched up and ready to solve
+more problems you know they don't do
+
+ align:start position:0%
+more problems you know they don't do
+ 
+
+ align:start position:0%
+more problems you know they don't do
+hardness of games anymore uh but it was
+
+ align:start position:0%
+hardness of games anymore uh but it was
+ 
+
+ align:start position:0%
+hardness of games anymore uh but it was
+like a nice warmup to build their
+
+ align:start position:0%
+like a nice warmup to build their
+ 
+
+ align:start position:0%
+like a nice warmup to build their
+confidence and show that they can do
+
+ align:start position:0%
+confidence and show that they can do
+ 
+
+ align:start position:0%
+confidence and show that they can do
+this uh so I think a lot of these
+
+ align:start position:0%
+this uh so I think a lot of these
+ 
+
+ align:start position:0%
+this uh so I think a lot of these
+problems are it's hardness make easy you
+
+ align:start position:0%
+problems are it's hardness make easy you
+ 
+
+ align:start position:0%
+problems are it's hardness make easy you
+it becomes quite accessible uh one of
+
+ align:start position:0%
+it becomes quite accessible uh one of
+ 
+
+ align:start position:0%
+it becomes quite accessible uh one of
+the things that really made me happy
+
+ align:start position:0%
+the things that really made me happy
+ 
+
+ align:start position:0%
+the things that really made me happy
+about this class is I I have teach a lot
+
+ align:start position:0%
+about this class is I I have teach a lot
+ 
+
+ align:start position:0%
+about this class is I I have teach a lot
+of advanced Theory classes and each one
+
+ align:start position:0%
+of advanced Theory classes and each one
+ 
+
+ align:start position:0%
+of advanced Theory classes and each one
+of them has a final project at the end
+
+ align:start position:0%
+of them has a final project at the end
+ 
+
+ align:start position:0%
+of them has a final project at the end
+and this class uh also had a final
+
+ align:start position:0%
+and this class uh also had a final
+ 
+
+ align:start position:0%
+and this class uh also had a final
+project and there many types you can do
+
+ align:start position:0%
+project and there many types you can do
+ 
+
+ align:start position:0%
+project and there many types you can do
+uh but the type I'm always most excited
+
+ align:start position:0%
+uh but the type I'm always most excited
+ 
+
+ align:start position:0%
+uh but the type I'm always most excited
+about is solve an open problem and in
+
+ align:start position:0%
+about is solve an open problem and in
+ 
+
+ align:start position:0%
+about is solve an open problem and in
+this hardness proof class uh most of the
+
+ align:start position:0%
+this hardness proof class uh most of the
+ 
+
+ align:start position:0%
+this hardness proof class uh most of the
+students solved an open problem compared
+
+ align:start position:0%
+students solved an open problem compared
+ 
+
+ align:start position:0%
+students solved an open problem compared
+to any other class I've taught or seen
+
+ align:start position:0%
+to any other class I've taught or seen
+ 
+
+ align:start position:0%
+to any other class I've taught or seen
+um many more students solved open
+
+ align:start position:0%
+um many more students solved open
+ 
+
+ align:start position:0%
+um many more students solved open
+problems because they a lot of them are
+
+ align:start position:0%
+problems because they a lot of them are
+ 
+
+ align:start position:0%
+problems because they a lot of them are
+relatively accessible you can take a
+
+ align:start position:0%
+relatively accessible you can take a
+ 
+
+ align:start position:0%
+relatively accessible you can take a
+game or a puzzle that just you like
+
+ align:start position:0%
+game or a puzzle that just you like
+ 
+
+ align:start position:0%
+game or a puzzle that just you like
+playing and you have expertise in but no
+
+ align:start position:0%
+playing and you have expertise in but no
+ 
+
+ align:start position:0%
+playing and you have expertise in but no
+one else has tried to analyze
+
+ align:start position:0%
+one else has tried to analyze
+ 
+
+ align:start position:0%
+one else has tried to analyze
+mathematically and now suddenly you can
+
+ align:start position:0%
+mathematically and now suddenly you can
+ 
+
+ align:start position:0%
+mathematically and now suddenly you can
+bring these new tools to it and uh prove
+
+ align:start position:0%
+bring these new tools to it and uh prove
+ 
+
+ align:start position:0%
+bring these new tools to it and uh prove
+your result and write it paper fun is
+
+ align:start position:0%
+your result and write it paper fun is
+ 
+
+ align:start position:0%
+your result and write it paper fun is
+like the hook that gets you excited
+
+ align:start position:0%
+like the hook that gets you excited
+ 
+
+ align:start position:0%
+like the hook that gets you excited
+about the the research the problems the
+
+ align:start position:0%
+about the the research the problems the
+ 
+
+ align:start position:0%
+about the the research the problems the
+and the material so uh you know we
+
+ align:start position:0%
+and the material so uh you know we
+ 
+
+ align:start position:0%
+and the material so uh you know we
+analyze a lot of uh games and puzzles
+
+ align:start position:0%
+analyze a lot of uh games and puzzles
+ 
+
+ align:start position:0%
+analyze a lot of uh games and puzzles
+and most of them to kind of keep it
+
+ align:start position:0%
+and most of them to kind of keep it
+ 
+
+ align:start position:0%
+and most of them to kind of keep it
+interesting we analyze real world games
+
+ align:start position:0%
+interesting we analyze real world games
+ 
+
+ align:start position:0%
+interesting we analyze real world games
+and puzzles like video games that people
+
+ align:start position:0%
+and puzzles like video games that people
+ 
+
+ align:start position:0%
+and puzzles like video games that people
+play um and one example is Super Mario
+
+ align:start position:0%
+play um and one example is Super Mario
+ 
+
+ align:start position:0%
+play um and one example is Super Mario
+Brothers where we can prove that it's NP
+
+ align:start position:0%
+Brothers where we can prove that it's NP
+ 
+
+ align:start position:0%
+Brothers where we can prove that it's NP
+hard to figure out whether you can solve
+
+ align:start position:0%
+hard to figure out whether you can solve
+ 
+
+ align:start position:0%
+hard to figure out whether you can solve
+a given level so there's no good
+
+ align:start position:0%
+a given level so there's no good
+ 
+
+ align:start position:0%
+a given level so there's no good
+algorithm to given a Super Mario
+
+ align:start position:0%
+algorithm to given a Super Mario
+ 
+
+ align:start position:0%
+algorithm to given a Super Mario
+Brothers level figure out how to solve
+
+ align:start position:0%
+Brothers level figure out how to solve
+ 
+
+ align:start position:0%
+Brothers level figure out how to solve
+it um this I guess becomes particularly
+
+ align:start position:0%
+it um this I guess becomes particularly
+ 
+
+ align:start position:0%
+it um this I guess becomes particularly
+relevant uh once you can make your own
+
+ align:start position:0%
+relevant uh once you can make your own
+ 
+
+ align:start position:0%
+relevant uh once you can make your own
+custom levels so with the the upcoming
+
+ align:start position:0%
+custom levels so with the the upcoming
+ 
+
+ align:start position:0%
+custom levels so with the the upcoming
+release of Super Mario Maker uh now
+
+ align:start position:0%
+release of Super Mario Maker uh now
+ 
+
+ align:start position:0%
+release of Super Mario Maker uh now
+people can actually build their own
+
+ align:start position:0%
+people can actually build their own
+ 
+
+ align:start position:0%
+people can actually build their own
+levels uh this will be really fun from a
+
+ align:start position:0%
+levels uh this will be really fun from a
+ 
+
+ align:start position:0%
+levels uh this will be really fun from a
+research perspective because we can take
+
+ align:start position:0%
+research perspective because we can take
+ 
+
+ align:start position:0%
+research perspective because we can take
+all the levels that we've designed we
+
+ align:start position:0%
+all the levels that we've designed we
+ 
+
+ align:start position:0%
+all the levels that we've designed we
+when we design them we just arrange them
+
+ align:start position:0%
+when we design them we just arrange them
+ 
+
+ align:start position:0%
+when we design them we just arrange them
+as pixel art so that you can see the
+
+ align:start position:0%
+as pixel art so that you can see the
+ 
+
+ align:start position:0%
+as pixel art so that you can see the
+level but you can't actually experience
+
+ align:start position:0%
+level but you can't actually experience
+ 
+
+ align:start position:0%
+level but you can't actually experience
+the level um and in order to actually
+
+ align:start position:0%
+the level um and in order to actually
+ 
+
+ align:start position:0%
+the level um and in order to actually
+experience the level you'd have to
+
+ align:start position:0%
+experience the level you'd have to
+ 
+
+ align:start position:0%
+experience the level you'd have to
+modify the ROM of the game and it's very
+
+ align:start position:0%
+modify the ROM of the game and it's very
+ 
+
+ align:start position:0%
+modify the ROM of the game and it's very
+tricky and technically uh annoying and
+
+ align:start position:0%
+tricky and technically uh annoying and
+ 
+
+ align:start position:0%
+tricky and technically uh annoying and
+maybe also illegal to do that um Super
+
+ align:start position:0%
+maybe also illegal to do that um Super
+ 
+
+ align:start position:0%
+maybe also illegal to do that um Super
+Mario Maker suddenly Mak makes it
+
+ align:start position:0%
+Mario Maker suddenly Mak makes it
+ 
+
+ align:start position:0%
+Mario Maker suddenly Mak makes it
+accessible that everyone can make custom
+
+ align:start position:0%
+accessible that everyone can make custom
+ 
+
+ align:start position:0%
+accessible that everyone can make custom
+levels I think it also makes the results
+
+ align:start position:0%
+levels I think it also makes the results
+ 
+
+ align:start position:0%
+levels I think it also makes the results
+more relevant it says hey if you
+
+ align:start position:0%
+more relevant it says hey if you
+ 
+
+ align:start position:0%
+more relevant it says hey if you
+download a new level figuring out how to
+
+ align:start position:0%
+download a new level figuring out how to
+ 
+
+ align:start position:0%
+download a new level figuring out how to
+solve it is going to be a real Challenge
+
+ align:start position:0%
+solve it is going to be a real Challenge
+ 
+
+ align:start position:0%
+solve it is going to be a real Challenge
+and I think this is a big reason why
+
+ align:start position:0%
+and I think this is a big reason why
+ 
+
+ align:start position:0%
+and I think this is a big reason why
+people find video games fun uh because
+
+ align:start position:0%
+people find video games fun uh because
+ 
+
+ align:start position:0%
+people find video games fun uh because
+they find them challenging I think if a
+
+ align:start position:0%
+they find them challenging I think if a
+ 
+
+ align:start position:0%
+they find them challenging I think if a
+game is too easy there are exceptions
+
+ align:start position:0%
+game is too easy there are exceptions
+ 
+
+ align:start position:0%
+game is too easy there are exceptions
+but if a game is too easy it gets boring
+
+ align:start position:0%
+but if a game is too easy it gets boring
+ 
+
+ align:start position:0%
+but if a game is too easy it gets boring
+pretty quickly um and when there's this
+
+ align:start position:0%
+pretty quickly um and when there's this
+ 
+
+ align:start position:0%
+pretty quickly um and when there's this
+nice uh when you can set the difficulty
+
+ align:start position:0%
+nice uh when you can set the difficulty
+ 
+
+ align:start position:0%
+nice uh when you can set the difficulty
+of the problem so it's not impossible
+
+ align:start position:0%
+of the problem so it's not impossible
+ 
+
+ align:start position:0%
+of the problem so it's not impossible
+but at least it's a big challenge to to
+
+ align:start position:0%
+but at least it's a big challenge to to
+ 
+
+ align:start position:0%
+but at least it's a big challenge to to
+solve it um I think that's where you get
+
+ align:start position:0%
+solve it um I think that's where you get
+ 
+
+ align:start position:0%
+solve it um I think that's where you get
+The Sweet Spot in having fun and this
+
+ align:start position:0%
+The Sweet Spot in having fun and this
+ 
+
+ align:start position:0%
+The Sweet Spot in having fun and this
+whole area of hardness proofs gives you
+
+ align:start position:0%
+whole area of hardness proofs gives you
+ 
+
+ align:start position:0%
+whole area of hardness proofs gives you
+a mathematical way of analyzing games
+
+ align:start position:0%
+a mathematical way of analyzing games
+ 
+
+ align:start position:0%
+a mathematical way of analyzing games
+and puzzles to show yeah they are really
+
+ align:start position:0%
+and puzzles to show yeah they are really
+ 
+
+ align:start position:0%
+and puzzles to show yeah they are really
+challenging they're hard even for
+
+ align:start position:0%
+challenging they're hard even for
+ 
+
+ align:start position:0%
+challenging they're hard even for
+computers to solve them so for humans it
+
+ align:start position:0%
+computers to solve them so for humans it
+ 
+
+ align:start position:0%
+computers to solve them so for humans it
+could be also really challenging
\ No newline at end of file
diff --git a/Lo_LSZ_R1w4.txt b/Lo_LSZ_R1w4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a73847b98e61118cc397b8074d235fbdfeed5c1
--- /dev/null
+++ b/Lo_LSZ_R1w4.txt
@@ -0,0 +1,9640 @@
+align:start position:0%
+ 
+we have to finish
+
+ align:start position:0%
+we have to finish
+ 
+
+ align:start position:0%
+we have to finish
+our discussion of evolution and then
+
+ align:start position:0%
+our discussion of evolution and then
+ 
+
+ align:start position:0%
+our discussion of evolution and then
+we'll start talking about
+
+ align:start position:0%
+we'll start talking about
+ 
+
+ align:start position:0%
+we'll start talking about
+anatomy
+
+ align:start position:0%
+anatomy
+ 
+
+ align:start position:0%
+anatomy
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the function of the notochord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know that's a good question why did
+
+ align:start position:0%
+you know that's a good question why did
+ 
+
+ align:start position:0%
+you know that's a good question why did
+it evolve in the first place
+
+ align:start position:0%
+it evolve in the first place
+ 
+
+ align:start position:0%
+it evolve in the first place
+it gives the body some rigidity you know
+
+ align:start position:0%
+it gives the body some rigidity you know
+ 
+
+ align:start position:0%
+it gives the body some rigidity you know
+and but you know i'd be all i'd just be
+
+ align:start position:0%
+and but you know i'd be all i'd just be
+ 
+
+ align:start position:0%
+and but you know i'd be all i'd just be
+making it up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the animal what would it be like
+
+ align:start position:0%
+what is the animal what would it be like
+ 
+
+ align:start position:0%
+what is the animal what would it be like
+if it didn't have the notochord it would
+
+ align:start position:0%
+if it didn't have the notochord it would
+ 
+
+ align:start position:0%
+if it didn't have the notochord it would
+be a a worm
+
+ align:start position:0%
+be a a worm
+ 
+
+ align:start position:0%
+be a a worm
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+and it looks like a worm when it first
+
+ align:start position:0%
+and it looks like a worm when it first
+ 
+
+ align:start position:0%
+and it looks like a worm when it first
+evolves but it's a chordate it's got a
+
+ align:start position:0%
+evolves but it's a chordate it's got a
+ 
+
+ align:start position:0%
+evolves but it's a chordate it's got a
+notochord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can say a lot more than that about it
+
+ align:start position:0%
+we can say a lot more than that about it
+ 
+
+ align:start position:0%
+we can say a lot more than that about it
+its roles it plays
+
+ align:start position:0%
+its roles it plays
+ 
+
+ align:start position:0%
+its roles it plays
+clear roles in the evolution of the
+
+ align:start position:0%
+clear roles in the evolution of the
+ 
+
+ align:start position:0%
+clear roles in the evolution of the
+brain or inductive influences from an
+
+ align:start position:0%
+brain or inductive influences from an
+ 
+
+ align:start position:0%
+brain or inductive influences from an
+autocard that affect the overlying
+
+ align:start position:0%
+autocard that affect the overlying
+ 
+
+ align:start position:0%
+autocard that affect the overlying
+nervous system and we'll talk about that
+
+ align:start position:0%
+nervous system and we'll talk about that
+ 
+
+ align:start position:0%
+nervous system and we'll talk about that
+when we talk about development
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's just go back a little bit
+
+ align:start position:0%
+okay let's just go back a little bit
+ 
+
+ align:start position:0%
+okay let's just go back a little bit
+we're talking about evolution of the
+
+ align:start position:0%
+we're talking about evolution of the
+ 
+
+ align:start position:0%
+we're talking about evolution of the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+we looked at the
+
+ align:start position:0%
+we looked at the
+ 
+
+ align:start position:0%
+we looked at the
+simplest possible neural tube in a
+
+ align:start position:0%
+simplest possible neural tube in a
+ 
+
+ align:start position:0%
+simplest possible neural tube in a
+chordate in amphioxus
+
+ align:start position:0%
+chordate in amphioxus
+ 
+
+ align:start position:0%
+chordate in amphioxus
+and we talked about the evolution of
+
+ align:start position:0%
+and we talked about the evolution of
+ 
+
+ align:start position:0%
+and we talked about the evolution of
+forward locomotion
+
+ align:start position:0%
+forward locomotion
+ 
+
+ align:start position:0%
+forward locomotion
+that led to the
+
+ align:start position:0%
+that led to the
+ 
+
+ align:start position:0%
+that led to the
+need for head receptors as head
+
+ align:start position:0%
+need for head receptors as head
+ 
+
+ align:start position:0%
+need for head receptors as head
+receptors evolved they led to an
+
+ align:start position:0%
+receptors evolved they led to an
+ 
+
+ align:start position:0%
+receptors evolved they led to an
+enlargement of the anterior ends we call
+
+ align:start position:0%
+enlargement of the anterior ends we call
+ 
+
+ align:start position:0%
+enlargement of the anterior ends we call
+that the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there were expansions of
+
+ align:start position:0%
+there were expansions of
+ 
+
+ align:start position:0%
+there were expansions of
+structures in the brain that received
+
+ align:start position:0%
+structures in the brain that received
+ 
+
+ align:start position:0%
+structures in the brain that received
+inputs from the head receptors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give me an example of inputs that come
+
+ align:start position:0%
+give me an example of inputs that come
+ 
+
+ align:start position:0%
+give me an example of inputs that come
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+through a cranial nerve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather than a spinal nerve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vision yes
+
+ align:start position:0%
+vision yes
+ 
+
+ align:start position:0%
+vision yes
+v1
+
+ align:start position:0%
+v1
+ 
+
+ align:start position:0%
+v1
+what's the one that comes in most
+
+ align:start position:0%
+what's the one that comes in most
+ 
+
+ align:start position:0%
+what's the one that comes in most
+anterior way up at the rostral line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well factory you see it here
+
+ align:start position:0%
+well factory you see it here
+ 
+
+ align:start position:0%
+well factory you see it here
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's where we'll start today
+
+ align:start position:0%
+and that's where we'll start today
+ 
+
+ align:start position:0%
+and that's where we'll start today
+the forebrain
+
+ align:start position:0%
+the forebrain
+ 
+
+ align:start position:0%
+the forebrain
+expanded initially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're talking about forebrain not the
+
+ align:start position:0%
+we're talking about forebrain not the
+ 
+
+ align:start position:0%
+we're talking about forebrain not the
+whole brain because of the influence of
+
+ align:start position:0%
+whole brain because of the influence of
+ 
+
+ align:start position:0%
+whole brain because of the influence of
+olfaction and the importance of
+
+ align:start position:0%
+olfaction and the importance of
+ 
+
+ align:start position:0%
+olfaction and the importance of
+olfaction
+
+ align:start position:0%
+olfaction
+ 
+
+ align:start position:0%
+olfaction
+or approach and avoidance functions
+
+ align:start position:0%
+or approach and avoidance functions
+ 
+
+ align:start position:0%
+or approach and avoidance functions
+feeding mating behavior predator
+
+ align:start position:0%
+feeding mating behavior predator
+ 
+
+ align:start position:0%
+feeding mating behavior predator
+avoidance so forth
+
+ align:start position:0%
+avoidance so forth
+ 
+
+ align:start position:0%
+avoidance so forth
+the links to the local motor system were
+
+ align:start position:0%
+the links to the local motor system were
+ 
+
+ align:start position:0%
+the links to the local motor system were
+not made by direct connections initially
+
+ align:start position:0%
+not made by direct connections initially
+ 
+
+ align:start position:0%
+not made by direct connections initially
+they were made through links through the
+
+ align:start position:0%
+they were made through links through the
+ 
+
+ align:start position:0%
+they were made through links through the
+midbrain
+
+ align:start position:0%
+midbrain
+ 
+
+ align:start position:0%
+midbrain
+we know we're guessing that from studies
+
+ align:start position:0%
+we know we're guessing that from studies
+ 
+
+ align:start position:0%
+we know we're guessing that from studies
+of primitive
+
+ align:start position:0%
+of primitive
+ 
+
+ align:start position:0%
+of primitive
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+primitive vertebrates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what we're showing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i added those words at the top
+
+ align:start position:0%
+i added those words at the top
+ 
+
+ align:start position:0%
+i added those words at the top
+the expansions continue then with the
+
+ align:start position:0%
+the expansions continue then with the
+ 
+
+ align:start position:0%
+the expansions continue then with the
+development of structures in between
+
+ align:start position:0%
+development of structures in between
+ 
+
+ align:start position:0%
+development of structures in between
+sensory and motor structures
+
+ align:start position:0%
+sensory and motor structures
+ 
+
+ align:start position:0%
+sensory and motor structures
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+various functions
+
+ align:start position:0%
+various functions
+ 
+
+ align:start position:0%
+various functions
+maintaining stabilities stability in
+
+ align:start position:0%
+maintaining stabilities stability in
+ 
+
+ align:start position:0%
+maintaining stabilities stability in
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+approach and avoidance functions and
+
+ align:start position:0%
+approach and avoidance functions and
+ 
+
+ align:start position:0%
+approach and avoidance functions and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+led to the evolution of these
+
+ align:start position:0%
+led to the evolution of these
+ 
+
+ align:start position:0%
+led to the evolution of these
+specialized structures particularly in
+
+ align:start position:0%
+specialized structures particularly in
+ 
+
+ align:start position:0%
+specialized structures particularly in
+the midbrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+showing here the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fish with an expanded midbrain as well
+
+ align:start position:0%
+fish with an expanded midbrain as well
+ 
+
+ align:start position:0%
+fish with an expanded midbrain as well
+as cerebellum important the midbrain was
+
+ align:start position:0%
+as cerebellum important the midbrain was
+ 
+
+ align:start position:0%
+as cerebellum important the midbrain was
+connected to the cerebellum
+
+ align:start position:0%
+connected to the cerebellum
+ 
+
+ align:start position:0%
+connected to the cerebellum
+for coordinating
+
+ align:start position:0%
+for coordinating
+ 
+
+ align:start position:0%
+for coordinating
+movements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the midbrain expanded with the
+
+ align:start position:0%
+and the midbrain expanded with the
+ 
+
+ align:start position:0%
+and the midbrain expanded with the
+evolution of distance receptors
+
+ align:start position:0%
+evolution of distance receptors
+ 
+
+ align:start position:0%
+evolution of distance receptors
+other than olfaction the olfaction could
+
+ align:start position:0%
+other than olfaction the olfaction could
+ 
+
+ align:start position:0%
+other than olfaction the olfaction could
+be called a distance receptor but
+
+ align:start position:0%
+be called a distance receptor but
+ 
+
+ align:start position:0%
+be called a distance receptor but
+the real distance receptors are
+
+ align:start position:0%
+the real distance receptors are
+ 
+
+ align:start position:0%
+the real distance receptors are
+division and audition which has many
+
+ align:start position:0%
+division and audition which has many
+ 
+
+ align:start position:0%
+division and audition which has many
+advantages for
+
+ align:start position:0%
+advantages for
+ 
+
+ align:start position:0%
+advantages for
+speed sensory acuity
+
+ align:start position:0%
+speed sensory acuity
+ 
+
+ align:start position:0%
+speed sensory acuity
+early warning
+
+ align:start position:0%
+early warning
+ 
+
+ align:start position:0%
+early warning
+and for anticipating things that are
+
+ align:start position:0%
+and for anticipating things that are
+ 
+
+ align:start position:0%
+and for anticipating things that are
+about to happen
+
+ align:start position:0%
+about to happen
+ 
+
+ align:start position:0%
+about to happen
+so when that evolved on the motor side
+
+ align:start position:0%
+so when that evolved on the motor side
+ 
+
+ align:start position:0%
+so when that evolved on the motor side
+you have to be able to turn the
+
+ align:start position:0%
+you have to be able to turn the
+ 
+
+ align:start position:0%
+you have to be able to turn the
+receptors
+
+ align:start position:0%
+receptors
+ 
+
+ align:start position:0%
+receptors
+which means
+
+ align:start position:0%
+which means
+ 
+
+ align:start position:0%
+which means
+orienting movements
+
+ align:start position:0%
+orienting movements
+ 
+
+ align:start position:0%
+orienting movements
+and the midbrain became particularly
+
+ align:start position:0%
+and the midbrain became particularly
+ 
+
+ align:start position:0%
+and the midbrain became particularly
+important for that and i'm showing here
+
+ align:start position:0%
+important for that and i'm showing here
+ 
+
+ align:start position:0%
+important for that and i'm showing here
+in the picture
+
+ align:start position:0%
+in the picture
+ 
+
+ align:start position:0%
+in the picture
+fibers coming from the eye coming into
+
+ align:start position:0%
+fibers coming from the eye coming into
+ 
+
+ align:start position:0%
+fibers coming from the eye coming into
+the midbrain
+
+ align:start position:0%
+the midbrain
+ 
+
+ align:start position:0%
+the midbrain
+it's interesting the eye did not evolve
+
+ align:start position:0%
+it's interesting the eye did not evolve
+ 
+
+ align:start position:0%
+it's interesting the eye did not evolve
+initially from the midbrain it
+
+ align:start position:0%
+initially from the midbrain it
+ 
+
+ align:start position:0%
+initially from the midbrain it
+originated as an out pouching of the
+
+ align:start position:0%
+originated as an out pouching of the
+ 
+
+ align:start position:0%
+originated as an out pouching of the
+twin brain
+
+ align:start position:0%
+twin brain
+ 
+
+ align:start position:0%
+twin brain
+and probably played even more
+
+ align:start position:0%
+and probably played even more
+ 
+
+ align:start position:0%
+and probably played even more
+had more primitive functions initially
+
+ align:start position:0%
+had more primitive functions initially
+ 
+
+ align:start position:0%
+had more primitive functions initially
+coordinating activity with the day night
+
+ align:start position:0%
+coordinating activity with the day night
+ 
+
+ align:start position:0%
+coordinating activity with the day night
+cycle just detecting light
+
+ align:start position:0%
+cycle just detecting light
+ 
+
+ align:start position:0%
+cycle just detecting light
+but once the connection to the midbrain
+
+ align:start position:0%
+but once the connection to the midbrain
+ 
+
+ align:start position:0%
+but once the connection to the midbrain
+was formed then it took on
+
+ align:start position:0%
+was formed then it took on
+ 
+
+ align:start position:0%
+was formed then it took on
+the role
+
+ align:start position:0%
+the role
+ 
+
+ align:start position:0%
+the role
+that required an expansion
+
+ align:start position:0%
+that required an expansion
+ 
+
+ align:start position:0%
+that required an expansion
+the sensory analyzers of the midbrain
+
+ align:start position:0%
+the sensory analyzers of the midbrain
+ 
+
+ align:start position:0%
+the sensory analyzers of the midbrain
+tectum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the midbrain then became the major
+
+ align:start position:0%
+and the midbrain then became the major
+ 
+
+ align:start position:0%
+and the midbrain then became the major
+we could call it a sentinel detecting
+
+ align:start position:0%
+we could call it a sentinel detecting
+ 
+
+ align:start position:0%
+we could call it a sentinel detecting
+predators
+
+ align:start position:0%
+predators
+ 
+
+ align:start position:0%
+predators
+it also played an important role in
+
+ align:start position:0%
+it also played an important role in
+ 
+
+ align:start position:0%
+it also played an important role in
+orienting and feeding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then finally my fifth stage here
+
+ align:start position:0%
+okay then finally my fifth stage here
+ 
+
+ align:start position:0%
+okay then finally my fifth stage here
+expansion of the forebrain again
+
+ align:start position:0%
+expansion of the forebrain again
+ 
+
+ align:start position:0%
+expansion of the forebrain again
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+not because of olfaction anymore
+
+ align:start position:0%
+not because of olfaction anymore
+ 
+
+ align:start position:0%
+not because of olfaction anymore
+but because non-olfactory systems
+
+ align:start position:0%
+but because non-olfactory systems
+ 
+
+ align:start position:0%
+but because non-olfactory systems
+invaded the end brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they did so not just they initially
+
+ align:start position:0%
+and they did so not just they initially
+ 
+
+ align:start position:0%
+and they did so not just they initially
+invaded the corpus triatum
+
+ align:start position:0%
+invaded the corpus triatum
+ 
+
+ align:start position:0%
+invaded the corpus triatum
+very important structure in
+
+ align:start position:0%
+very important structure in
+ 
+
+ align:start position:0%
+very important structure in
+plasticity of habit formation and so
+
+ align:start position:0%
+plasticity of habit formation and so
+ 
+
+ align:start position:0%
+plasticity of habit formation and so
+forth important in
+
+ align:start position:0%
+forth important in
+ 
+
+ align:start position:0%
+forth important in
+both feeding approach and avoidance
+
+ align:start position:0%
+both feeding approach and avoidance
+ 
+
+ align:start position:0%
+both feeding approach and avoidance
+functions and feeding and predator
+
+ align:start position:0%
+functions and feeding and predator
+ 
+
+ align:start position:0%
+functions and feeding and predator
+avoidance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then something very interesting
+
+ align:start position:0%
+but then something very interesting
+ 
+
+ align:start position:0%
+but then something very interesting
+happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the corpus triatum was not a cortical
+
+ align:start position:0%
+the corpus triatum was not a cortical
+ 
+
+ align:start position:0%
+the corpus triatum was not a cortical
+structure was not a layered structure at
+
+ align:start position:0%
+structure was not a layered structure at
+ 
+
+ align:start position:0%
+structure was not a layered structure at
+the surface of the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like the cortex of the olfactory system
+
+ align:start position:0%
+like the cortex of the olfactory system
+ 
+
+ align:start position:0%
+like the cortex of the olfactory system
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+but when that cortex was began to be
+
+ align:start position:0%
+but when that cortex was began to be
+ 
+
+ align:start position:0%
+but when that cortex was began to be
+invaded by these other sensory systems
+
+ align:start position:0%
+invaded by these other sensory systems
+ 
+
+ align:start position:0%
+invaded by these other sensory systems
+vision and audition and
+
+ align:start position:0%
+vision and audition and
+ 
+
+ align:start position:0%
+vision and audition and
+somatic sensation
+
+ align:start position:0%
+somatic sensation
+ 
+
+ align:start position:0%
+somatic sensation
+it led to a great expansion of the
+
+ align:start position:0%
+it led to a great expansion of the
+ 
+
+ align:start position:0%
+it led to a great expansion of the
+forebrain the end at the end brain part
+
+ align:start position:0%
+forebrain the end at the end brain part
+ 
+
+ align:start position:0%
+forebrain the end at the end brain part
+of the forebrain very rustled into the
+
+ align:start position:0%
+of the forebrain very rustled into the
+ 
+
+ align:start position:0%
+of the forebrain very rustled into the
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm showing here
+
+ align:start position:0%
+and i'm showing here
+ 
+
+ align:start position:0%
+and i'm showing here
+a projection from
+
+ align:start position:0%
+a projection from
+ 
+
+ align:start position:0%
+a projection from
+the tectum
+
+ align:start position:0%
+the tectum
+ 
+
+ align:start position:0%
+the tectum
+carrying visual and auditory information
+
+ align:start position:0%
+carrying visual and auditory information
+ 
+
+ align:start position:0%
+carrying visual and auditory information
+into the forebrain through the tween
+
+ align:start position:0%
+into the forebrain through the tween
+ 
+
+ align:start position:0%
+into the forebrain through the tween
+brain i show a connection there in the
+
+ align:start position:0%
+brain i show a connection there in the
+ 
+
+ align:start position:0%
+brain i show a connection there in the
+twin brain then a connection into the
+
+ align:start position:0%
+twin brain then a connection into the
+ 
+
+ align:start position:0%
+twin brain then a connection into the
+end brain now that kind of connection
+
+ align:start position:0%
+end brain now that kind of connection
+ 
+
+ align:start position:0%
+end brain now that kind of connection
+initially went into the corpus triadon
+
+ align:start position:0%
+initially went into the corpus triadon
+ 
+
+ align:start position:0%
+initially went into the corpus triadon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i mention here that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what was happening on the motor side but
+
+ align:start position:0%
+what was happening on the motor side but
+ 
+
+ align:start position:0%
+what was happening on the motor side but
+that didn't happen so much until the end
+
+ align:start position:0%
+that didn't happen so much until the end
+ 
+
+ align:start position:0%
+that didn't happen so much until the end
+brain expanded
+
+ align:start position:0%
+brain expanded
+ 
+
+ align:start position:0%
+brain expanded
+i mentioned this before elaboration of
+
+ align:start position:0%
+i mentioned this before elaboration of
+ 
+
+ align:start position:0%
+i mentioned this before elaboration of
+other things that were going on
+
+ align:start position:0%
+other things that were going on
+ 
+
+ align:start position:0%
+other things that were going on
+elaboration of complex programs for goal
+
+ align:start position:0%
+elaboration of complex programs for goal
+ 
+
+ align:start position:0%
+elaboration of complex programs for goal
+directed activities
+
+ align:start position:0%
+directed activities
+ 
+
+ align:start position:0%
+directed activities
+the so-called fixed action patterns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i put a red star here it probably
+
+ align:start position:0%
+if i put a red star here it probably
+ 
+
+ align:start position:0%
+if i put a red star here it probably
+means i've changed the slide a little
+
+ align:start position:0%
+means i've changed the slide a little
+ 
+
+ align:start position:0%
+means i've changed the slide a little
+bit since you have your printout
+
+ align:start position:0%
+bit since you have your printout
+ 
+
+ align:start position:0%
+bit since you have your printout
+i probably added here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this phrase the great mammalian
+
+ align:start position:0%
+this phrase the great mammalian
+ 
+
+ align:start position:0%
+this phrase the great mammalian
+elaborations just to stress that
+
+ align:start position:0%
+elaborations just to stress that
+ 
+
+ align:start position:0%
+elaborations just to stress that
+the additions to the brain that happen
+
+ align:start position:0%
+the additions to the brain that happen
+ 
+
+ align:start position:0%
+the additions to the brain that happen
+for reward driven learning and habit
+
+ align:start position:0%
+for reward driven learning and habit
+ 
+
+ align:start position:0%
+for reward driven learning and habit
+formation the corpus triatum
+
+ align:start position:0%
+formation the corpus triatum
+ 
+
+ align:start position:0%
+formation the corpus triatum
+which was closely linked to neocortex
+
+ align:start position:0%
+which was closely linked to neocortex
+ 
+
+ align:start position:0%
+which was closely linked to neocortex
+was something that happened in mammals
+
+ align:start position:0%
+was something that happened in mammals
+ 
+
+ align:start position:0%
+was something that happened in mammals
+especially because of the evolution of
+
+ align:start position:0%
+especially because of the evolution of
+ 
+
+ align:start position:0%
+especially because of the evolution of
+neocortex okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yes there's certainly reward
+
+ align:start position:0%
+oh yes there's certainly reward
+ 
+
+ align:start position:0%
+oh yes there's certainly reward
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+in non-mammalian animals also
+
+ align:start position:0%
+in non-mammalian animals also
+ 
+
+ align:start position:0%
+in non-mammalian animals also
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it was the expansion of the neocortex
+
+ align:start position:0%
+it was the expansion of the neocortex
+ 
+
+ align:start position:0%
+it was the expansion of the neocortex
+which elaborated the possibilities of
+
+ align:start position:0%
+which elaborated the possibilities of
+ 
+
+ align:start position:0%
+which elaborated the possibilities of
+input to those structures that led to
+
+ align:start position:0%
+input to those structures that led to
+ 
+
+ align:start position:0%
+input to those structures that led to
+the biggest expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question he asked me if
+
+ align:start position:0%
+that's a good question he asked me if
+ 
+
+ align:start position:0%
+that's a good question he asked me if
+non-mammals go for things like cocaine
+
+ align:start position:0%
+non-mammals go for things like cocaine
+ 
+
+ align:start position:0%
+non-mammals go for things like cocaine
+which is a
+
+ align:start position:0%
+which is a
+ 
+
+ align:start position:0%
+which is a
+these kinds of addictions are
+
+ align:start position:0%
+these kinds of addictions are
+ 
+
+ align:start position:0%
+these kinds of addictions are
+you could say they're
+
+ align:start position:0%
+you could say they're
+ 
+
+ align:start position:0%
+you could say they're
+acquired pathologies of the reward
+
+ align:start position:0%
+acquired pathologies of the reward
+ 
+
+ align:start position:0%
+acquired pathologies of the reward
+system the motivational system
+
+ align:start position:0%
+system the motivational system
+ 
+
+ align:start position:0%
+system the motivational system
+it's a good question i'm not sure but i
+
+ align:start position:0%
+it's a good question i'm not sure but i
+ 
+
+ align:start position:0%
+it's a good question i'm not sure but i
+would guess they probably do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what systems
+
+ align:start position:0%
+okay so what systems
+ 
+
+ align:start position:0%
+okay so what systems
+evolved to modulate
+
+ align:start position:0%
+evolved to modulate
+ 
+
+ align:start position:0%
+evolved to modulate
+other brand systems and resp
+
+ align:start position:0%
+other brand systems and resp
+ 
+
+ align:start position:0%
+other brand systems and resp
+for motivational control visceral and
+
+ align:start position:0%
+for motivational control visceral and
+ 
+
+ align:start position:0%
+for motivational control visceral and
+social needs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are the structures that you should
+
+ align:start position:0%
+these are the structures that you should
+ 
+
+ align:start position:0%
+these are the structures that you should
+think of there i put them in blue here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are the functions we're talking
+
+ align:start position:0%
+these are the functions we're talking
+ 
+
+ align:start position:0%
+these are the functions we're talking
+about control of motivation elaboration
+
+ align:start position:0%
+about control of motivation elaboration
+ 
+
+ align:start position:0%
+about control of motivation elaboration
+of hierarchies of goals and
+
+ align:start position:0%
+of hierarchies of goals and
+ 
+
+ align:start position:0%
+of hierarchies of goals and
+communication of
+
+ align:start position:0%
+communication of
+ 
+
+ align:start position:0%
+communication of
+needs to other members of the species
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the main structures that evolved
+
+ align:start position:0%
+and the main structures that evolved
+ 
+
+ align:start position:0%
+and the main structures that evolved
+here were the hypothalamus
+
+ align:start position:0%
+here were the hypothalamus
+ 
+
+ align:start position:0%
+here were the hypothalamus
+which were connected to the lower
+
+ align:start position:0%
+which were connected to the lower
+ 
+
+ align:start position:0%
+which were connected to the lower
+structures that did that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then the structures in the end brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we're most closely connected to the
+
+ align:start position:0%
+that we're most closely connected to the
+ 
+
+ align:start position:0%
+that we're most closely connected to the
+hypothalamus and we call those
+
+ align:start position:0%
+hypothalamus and we call those
+ 
+
+ align:start position:0%
+hypothalamus and we call those
+structures the limbic system of the
+
+ align:start position:0%
+structures the limbic system of the
+ 
+
+ align:start position:0%
+structures the limbic system of the
+forebrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then along with that of the further
+
+ align:start position:0%
+and then along with that of the further
+ 
+
+ align:start position:0%
+and then along with that of the further
+elaboration of the end brain and this
+
+ align:start position:0%
+elaboration of the end brain and this
+ 
+
+ align:start position:0%
+elaboration of the end brain and this
+happened really only with neocortex
+
+ align:start position:0%
+happened really only with neocortex
+ 
+
+ align:start position:0%
+happened really only with neocortex
+systems for anticipating
+
+ align:start position:0%
+systems for anticipating
+ 
+
+ align:start position:0%
+systems for anticipating
+and predicting things on the sensory
+
+ align:start position:0%
+and predicting things on the sensory
+ 
+
+ align:start position:0%
+and predicting things on the sensory
+side images that could simulate objects
+
+ align:start position:0%
+side images that could simulate objects
+ 
+
+ align:start position:0%
+side images that could simulate objects
+and events on the motor side planning of
+
+ align:start position:0%
+and events on the motor side planning of
+ 
+
+ align:start position:0%
+and events on the motor side planning of
+actions these were non-reflex functions
+
+ align:start position:0%
+actions these were non-reflex functions
+ 
+
+ align:start position:0%
+actions these were non-reflex functions
+that i talked about at the end of the
+
+ align:start position:0%
+that i talked about at the end of the
+ 
+
+ align:start position:0%
+that i talked about at the end of the
+introductory lectures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here
+
+ align:start position:0%
+and here
+ 
+
+ align:start position:0%
+and here
+it was the neocortex that played the
+
+ align:start position:0%
+it was the neocortex that played the
+ 
+
+ align:start position:0%
+it was the neocortex that played the
+primary role in fact at these higher
+
+ align:start position:0%
+primary role in fact at these higher
+ 
+
+ align:start position:0%
+primary role in fact at these higher
+functions cognitive functions
+
+ align:start position:0%
+functions cognitive functions
+ 
+
+ align:start position:0%
+functions cognitive functions
+the structures that expanded the most in
+
+ align:start position:0%
+the structures that expanded the most in
+ 
+
+ align:start position:0%
+the structures that expanded the most in
+the neocortex where the
+
+ align:start position:0%
+the neocortex where the
+ 
+
+ align:start position:0%
+the neocortex where the
+so-called association areas those are
+
+ align:start position:0%
+so-called association areas those are
+ 
+
+ align:start position:0%
+so-called association areas those are
+the areas that in us
+
+ align:start position:0%
+the areas that in us
+ 
+
+ align:start position:0%
+the areas that in us
+occupy the largest part of our neocortex
+
+ align:start position:0%
+occupy the largest part of our neocortex
+ 
+
+ align:start position:0%
+occupy the largest part of our neocortex
+along with that all parts of the
+
+ align:start position:0%
+along with that all parts of the
+ 
+
+ align:start position:0%
+along with that all parts of the
+neocortex are connected the corpus
+
+ align:start position:0%
+neocortex are connected the corpus
+ 
+
+ align:start position:0%
+neocortex are connected the corpus
+triadom
+
+ align:start position:0%
+triadom
+ 
+
+ align:start position:0%
+triadom
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the parts that get those connections
+
+ align:start position:0%
+and the parts that get those connections
+ 
+
+ align:start position:0%
+and the parts that get those connections
+from the cortex have expanded also so
+
+ align:start position:0%
+from the cortex have expanded also so
+ 
+
+ align:start position:0%
+from the cortex have expanded also so
+it's not just one thing that expands
+
+ align:start position:0%
+it's not just one thing that expands
+ 
+
+ align:start position:0%
+it's not just one thing that expands
+many things expand in parallel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and before that the end brain of the of
+
+ align:start position:0%
+and before that the end brain of the of
+ 
+
+ align:start position:0%
+and before that the end brain of the of
+the animals leading to mammals was
+
+ align:start position:0%
+the animals leading to mammals was
+ 
+
+ align:start position:0%
+the animals leading to mammals was
+dominated by olfaction the paleocortex
+
+ align:start position:0%
+dominated by olfaction the paleocortex
+ 
+
+ align:start position:0%
+dominated by olfaction the paleocortex
+and more ancient parts of the corpus
+
+ align:start position:0%
+and more ancient parts of the corpus
+ 
+
+ align:start position:0%
+and more ancient parts of the corpus
+tree atom and you can see that by
+
+ align:start position:0%
+tree atom and you can see that by
+ 
+
+ align:start position:0%
+tree atom and you can see that by
+looking at the brains
+
+ align:start position:0%
+looking at the brains
+ 
+
+ align:start position:0%
+looking at the brains
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+of various species
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm showing here this expansion of
+
+ align:start position:0%
+and i'm showing here this expansion of
+ 
+
+ align:start position:0%
+and i'm showing here this expansion of
+the in-brain
+
+ align:start position:0%
+the in-brain
+ 
+
+ align:start position:0%
+the in-brain
+i put here a picture based on brains of
+
+ align:start position:0%
+i put here a picture based on brains of
+ 
+
+ align:start position:0%
+i put here a picture based on brains of
+fish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+showing the smaller end brain little
+
+ align:start position:0%
+showing the smaller end brain little
+ 
+
+ align:start position:0%
+showing the smaller end brain little
+tween brain
+
+ align:start position:0%
+tween brain
+ 
+
+ align:start position:0%
+tween brain
+and then a larger brain stem
+
+ align:start position:0%
+and then a larger brain stem
+ 
+
+ align:start position:0%
+and then a larger brain stem
+midbrain and hindbrain
+
+ align:start position:0%
+midbrain and hindbrain
+ 
+
+ align:start position:0%
+midbrain and hindbrain
+larger than the end brain but then
+
+ align:start position:0%
+larger than the end brain but then
+ 
+
+ align:start position:0%
+larger than the end brain but then
+in mammals
+
+ align:start position:0%
+in mammals
+ 
+
+ align:start position:0%
+in mammals
+you have the evolution of neocortex
+
+ align:start position:0%
+you have the evolution of neocortex
+ 
+
+ align:start position:0%
+you have the evolution of neocortex
+that's the structure that's
+
+ align:start position:0%
+that's the structure that's
+ 
+
+ align:start position:0%
+that's the structure that's
+pretty much unique with mammals although
+
+ align:start position:0%
+pretty much unique with mammals although
+ 
+
+ align:start position:0%
+pretty much unique with mammals although
+higher birds
+
+ align:start position:0%
+higher birds
+ 
+
+ align:start position:0%
+higher birds
+also have structures like neocortex
+
+ align:start position:0%
+also have structures like neocortex
+ 
+
+ align:start position:0%
+also have structures like neocortex
+but it doesn't have the same structure
+
+ align:start position:0%
+but it doesn't have the same structure
+ 
+
+ align:start position:0%
+but it doesn't have the same structure
+as the neocortex of mammals
+
+ align:start position:0%
+as the neocortex of mammals
+ 
+
+ align:start position:0%
+as the neocortex of mammals
+okay but they do have
+
+ align:start position:0%
+okay but they do have
+ 
+
+ align:start position:0%
+okay but they do have
+they have structures we don't have that
+
+ align:start position:0%
+they have structures we don't have that
+ 
+
+ align:start position:0%
+they have structures we don't have that
+that are similarly connected
+
+ align:start position:0%
+that are similarly connected
+ 
+
+ align:start position:0%
+that are similarly connected
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the relative size of structures i'm
+
+ align:start position:0%
+the relative size of structures i'm
+ 
+
+ align:start position:0%
+the relative size of structures i'm
+showing here would be
+
+ align:start position:0%
+showing here would be
+ 
+
+ align:start position:0%
+showing here would be
+well in proportion about the brain of a
+
+ align:start position:0%
+well in proportion about the brain of a
+ 
+
+ align:start position:0%
+well in proportion about the brain of a
+rodent
+
+ align:start position:0%
+rodent
+ 
+
+ align:start position:0%
+rodent
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is just
+
+ align:start position:0%
+so this is just
+ 
+
+ align:start position:0%
+so this is just
+earlier expansion of the cortex and then
+
+ align:start position:0%
+earlier expansion of the cortex and then
+ 
+
+ align:start position:0%
+earlier expansion of the cortex and then
+i'm showing here along with it
+
+ align:start position:0%
+i'm showing here along with it
+ 
+
+ align:start position:0%
+i'm showing here along with it
+expanded the cerebellum
+
+ align:start position:0%
+expanded the cerebellum
+ 
+
+ align:start position:0%
+expanded the cerebellum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+parts the more lateral parts of the
+
+ align:start position:0%
+parts the more lateral parts of the
+ 
+
+ align:start position:0%
+parts the more lateral parts of the
+cerebellum
+
+ align:start position:0%
+cerebellum
+ 
+
+ align:start position:0%
+cerebellum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and also i'm not showing here at all the
+
+ align:start position:0%
+and also i'm not showing here at all the
+ 
+
+ align:start position:0%
+and also i'm not showing here at all the
+neostriatum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now before we go to a more
+
+ align:start position:0%
+okay now before we go to a more
+ 
+
+ align:start position:0%
+okay now before we go to a more
+systematic coverage of neuroanatomy
+
+ align:start position:0%
+systematic coverage of neuroanatomy
+ 
+
+ align:start position:0%
+systematic coverage of neuroanatomy
+let's just talk a little bit about
+
+ align:start position:0%
+let's just talk a little bit about
+ 
+
+ align:start position:0%
+let's just talk a little bit about
+what's happening to the brain evolution
+
+ align:start position:0%
+what's happening to the brain evolution
+ 
+
+ align:start position:0%
+what's happening to the brain evolution
+if we just look at the weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+we don't have the heaviest brains
+
+ align:start position:0%
+we don't have the heaviest brains
+ 
+
+ align:start position:0%
+we don't have the heaviest brains
+the heaviest brains are in animals that
+
+ align:start position:0%
+the heaviest brains are in animals that
+ 
+
+ align:start position:0%
+the heaviest brains are in animals that
+are larger than us especially much
+
+ align:start position:0%
+are larger than us especially much
+ 
+
+ align:start position:0%
+are larger than us especially much
+larger like whales
+
+ align:start position:0%
+larger like whales
+ 
+
+ align:start position:0%
+larger like whales
+elephants
+
+ align:start position:0%
+elephants
+ 
+
+ align:start position:0%
+elephants
+if you look at here brainwave is on the
+
+ align:start position:0%
+if you look at here brainwave is on the
+ 
+
+ align:start position:0%
+if you look at here brainwave is on the
+coordinate here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see we here have at the top the blue
+
+ align:start position:0%
+see we here have at the top the blue
+ 
+
+ align:start position:0%
+see we here have at the top the blue
+whale
+
+ align:start position:0%
+whale
+ 
+
+ align:start position:0%
+whale
+also the elephant
+
+ align:start position:0%
+also the elephant
+ 
+
+ align:start position:0%
+also the elephant
+uh the porpoise and here's modern humans
+
+ align:start position:0%
+uh the porpoise and here's modern humans
+ 
+
+ align:start position:0%
+uh the porpoise and here's modern humans
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but if we were it's plotted here on a
+
+ align:start position:0%
+but if we were it's plotted here on a
+ 
+
+ align:start position:0%
+but if we were it's plotted here on a
+against body weight
+
+ align:start position:0%
+against body weight
+ 
+
+ align:start position:0%
+against body weight
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and if you look at that graph
+
+ align:start position:0%
+and if you look at that graph
+ 
+
+ align:start position:0%
+and if you look at that graph
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll see that
+
+ align:start position:0%
+you'll see that
+ 
+
+ align:start position:0%
+you'll see that
+humans are the furthest from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this line here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in proportion to body weight
+
+ align:start position:0%
+in proportion to body weight
+ 
+
+ align:start position:0%
+in proportion to body weight
+the brain is larger than humans okay
+
+ align:start position:0%
+the brain is larger than humans okay
+ 
+
+ align:start position:0%
+the brain is larger than humans okay
+there are actually a few exceptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+porpoises are
+
+ align:start position:0%
+porpoises are
+ 
+
+ align:start position:0%
+porpoises are
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+very close to us partly because they
+
+ align:start position:0%
+very close to us partly because they
+ 
+
+ align:start position:0%
+very close to us partly because they
+don't have limbs
+
+ align:start position:0%
+don't have limbs
+ 
+
+ align:start position:0%
+don't have limbs
+so their spinal cords don't have the
+
+ align:start position:0%
+so their spinal cords don't have the
+ 
+
+ align:start position:0%
+so their spinal cords don't have the
+enlargements
+
+ align:start position:0%
+enlargements
+ 
+
+ align:start position:0%
+enlargements
+with the extra neurons supporting the
+
+ align:start position:0%
+with the extra neurons supporting the
+ 
+
+ align:start position:0%
+with the extra neurons supporting the
+limbs okay so that distorts that picture
+
+ align:start position:0%
+limbs okay so that distorts that picture
+ 
+
+ align:start position:0%
+limbs okay so that distorts that picture
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+there are some little rodent-like
+
+ align:start position:0%
+there are some little rodent-like
+ 
+
+ align:start position:0%
+there are some little rodent-like
+animals that have a pretty high brand
+
+ align:start position:0%
+animals that have a pretty high brand
+ 
+
+ align:start position:0%
+animals that have a pretty high brand
+body weight ratio but we don't talk much
+
+ align:start position:0%
+body weight ratio but we don't talk much
+ 
+
+ align:start position:0%
+body weight ratio but we don't talk much
+about them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here if you look at the various animal
+
+ align:start position:0%
+here if you look at the various animal
+ 
+
+ align:start position:0%
+here if you look at the various animal
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+on this that kind of graph
+
+ align:start position:0%
+on this that kind of graph
+ 
+
+ align:start position:0%
+on this that kind of graph
+you'll see that the mammals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are different
+
+ align:start position:0%
+are different
+ 
+
+ align:start position:0%
+are different
+although there's overlap with
+
+ align:start position:0%
+although there's overlap with
+ 
+
+ align:start position:0%
+although there's overlap with
+birds and other animals
+
+ align:start position:0%
+birds and other animals
+ 
+
+ align:start position:0%
+birds and other animals
+and the more primitive vertebrates
+
+ align:start position:0%
+and the more primitive vertebrates
+ 
+
+ align:start position:0%
+and the more primitive vertebrates
+are the furthest to the
+
+ align:start position:0%
+are the furthest to the
+ 
+
+ align:start position:0%
+are the furthest to the
+lower right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we know some of the factors that
+
+ align:start position:0%
+now we know some of the factors that
+ 
+
+ align:start position:0%
+now we know some of the factors that
+affect brain size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not just intelligence
+
+ align:start position:0%
+not just intelligence
+ 
+
+ align:start position:0%
+not just intelligence
+by a long shot
+
+ align:start position:0%
+by a long shot
+ 
+
+ align:start position:0%
+by a long shot
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i'll say a little bit more about that
+
+ align:start position:0%
+i'll say a little bit more about that
+ 
+
+ align:start position:0%
+i'll say a little bit more about that
+in a minute here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+these terms the notochord
+
+ align:start position:0%
+these terms the notochord
+ 
+
+ align:start position:0%
+these terms the notochord
+you see it spelled in both these ways
+
+ align:start position:0%
+you see it spelled in both these ways
+ 
+
+ align:start position:0%
+you see it spelled in both these ways
+the h or without the h and i'll accept
+
+ align:start position:0%
+the h or without the h and i'll accept
+ 
+
+ align:start position:0%
+the h or without the h and i'll accept
+either one
+
+ align:start position:0%
+either one
+ 
+
+ align:start position:0%
+either one
+but the first one is actually the
+
+ align:start position:0%
+but the first one is actually the
+ 
+
+ align:start position:0%
+but the first one is actually the
+supposedly the proper one
+
+ align:start position:0%
+supposedly the proper one
+ 
+
+ align:start position:0%
+supposedly the proper one
+but don't spell spinal cord with the h
+
+ align:start position:0%
+but don't spell spinal cord with the h
+ 
+
+ align:start position:0%
+but don't spell spinal cord with the h
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only the it is a cord
+
+ align:start position:0%
+only the it is a cord
+ 
+
+ align:start position:0%
+only the it is a cord
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say a little bit about the
+
+ align:start position:0%
+let's say a little bit about the
+ 
+
+ align:start position:0%
+let's say a little bit about the
+relationship of
+
+ align:start position:0%
+relationship of
+ 
+
+ align:start position:0%
+relationship of
+development or ontogeny the development
+
+ align:start position:0%
+development or ontogeny the development
+ 
+
+ align:start position:0%
+development or ontogeny the development
+of the individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comparing that to uh
+
+ align:start position:0%
+comparing that to uh
+ 
+
+ align:start position:0%
+comparing that to uh
+difference in species phylogeny
+
+ align:start position:0%
+difference in species phylogeny
+ 
+
+ align:start position:0%
+difference in species phylogeny
+we want to know whether development can
+
+ align:start position:0%
+we want to know whether development can
+ 
+
+ align:start position:0%
+we want to know whether development can
+tell us anything about evolution we
+
+ align:start position:0%
+tell us anything about evolution we
+ 
+
+ align:start position:0%
+tell us anything about evolution we
+there's a popular phrase that ontogeny
+
+ align:start position:0%
+there's a popular phrase that ontogeny
+ 
+
+ align:start position:0%
+there's a popular phrase that ontogeny
+recaps capitulates phylogeny what does
+
+ align:start position:0%
+recaps capitulates phylogeny what does
+ 
+
+ align:start position:0%
+recaps capitulates phylogeny what does
+that mean
+
+ align:start position:0%
+that mean
+ 
+
+ align:start position:0%
+that mean
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what it means is that the earlier the
+
+ align:start position:0%
+what it means is that the earlier the
+ 
+
+ align:start position:0%
+what it means is that the earlier the
+stage of embryonic development the
+
+ align:start position:0%
+stage of embryonic development the
+ 
+
+ align:start position:0%
+stage of embryonic development the
+greater the resemblance of different
+
+ align:start position:0%
+greater the resemblance of different
+ 
+
+ align:start position:0%
+greater the resemblance of different
+species okay
+
+ align:start position:0%
+species okay
+ 
+
+ align:start position:0%
+species okay
+so if you take say the brain of a pig or
+
+ align:start position:0%
+so if you take say the brain of a pig or
+ 
+
+ align:start position:0%
+so if you take say the brain of a pig or
+the brain of a monkey compared to the
+
+ align:start position:0%
+the brain of a monkey compared to the
+ 
+
+ align:start position:0%
+the brain of a monkey compared to the
+brain of humans at very early stages of
+
+ align:start position:0%
+brain of humans at very early stages of
+ 
+
+ align:start position:0%
+brain of humans at very early stages of
+development they all look the same
+
+ align:start position:0%
+development they all look the same
+ 
+
+ align:start position:0%
+development they all look the same
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as you get later
+
+ align:start position:0%
+as you get later
+ 
+
+ align:start position:0%
+as you get later
+you get more and more divergence okay
+
+ align:start position:0%
+you get more and more divergence okay
+ 
+
+ align:start position:0%
+you get more and more divergence okay
+let's look at the pictures from
+
+ align:start position:0%
+let's look at the pictures from
+ 
+
+ align:start position:0%
+let's look at the pictures from
+romanus
+
+ align:start position:0%
+romanus
+ 
+
+ align:start position:0%
+romanus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+here he's showing
+
+ align:start position:0%
+here he's showing
+ 
+
+ align:start position:0%
+here he's showing
+at a very early stage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fish salamander a tortoise chick a hog a
+
+ align:start position:0%
+fish salamander a tortoise chick a hog a
+ 
+
+ align:start position:0%
+fish salamander a tortoise chick a hog a
+calf a rabbit and a human
+
+ align:start position:0%
+calf a rabbit and a human
+ 
+
+ align:start position:0%
+calf a rabbit and a human
+we see very similar
+
+ align:start position:0%
+we see very similar
+ 
+
+ align:start position:0%
+we see very similar
+appearances
+
+ align:start position:0%
+appearances
+ 
+
+ align:start position:0%
+appearances
+in all these different vertebrates
+
+ align:start position:0%
+in all these different vertebrates
+ 
+
+ align:start position:0%
+in all these different vertebrates
+in early stages
+
+ align:start position:0%
+in early stages
+ 
+
+ align:start position:0%
+in early stages
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+middle stages
+
+ align:start position:0%
+middle stages
+ 
+
+ align:start position:0%
+middle stages
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+you see that already the fish and the
+
+ align:start position:0%
+you see that already the fish and the
+ 
+
+ align:start position:0%
+you see that already the fish and the
+salamander looking very different
+
+ align:start position:0%
+salamander looking very different
+ 
+
+ align:start position:0%
+salamander looking very different
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the reptile here
+
+ align:start position:0%
+the reptile here
+ 
+
+ align:start position:0%
+the reptile here
+the bird
+
+ align:start position:0%
+the bird
+ 
+
+ align:start position:0%
+the bird
+and all the mammals still look pretty
+
+ align:start position:0%
+and all the mammals still look pretty
+ 
+
+ align:start position:0%
+and all the mammals still look pretty
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+there are some small differences
+
+ align:start position:0%
+there are some small differences
+ 
+
+ align:start position:0%
+there are some small differences
+beginning to appear
+
+ align:start position:0%
+beginning to appear
+ 
+
+ align:start position:0%
+beginning to appear
+and then when we get much later in
+
+ align:start position:0%
+and then when we get much later in
+ 
+
+ align:start position:0%
+and then when we get much later in
+development and we're still here pretty
+
+ align:start position:0%
+development and we're still here pretty
+ 
+
+ align:start position:0%
+development and we're still here pretty
+early in gestation for humans
+
+ align:start position:0%
+early in gestation for humans
+ 
+
+ align:start position:0%
+early in gestation for humans
+we see more differences
+
+ align:start position:0%
+we see more differences
+ 
+
+ align:start position:0%
+we see more differences
+right now if we had a monkey in there or
+
+ align:start position:0%
+right now if we had a monkey in there or
+ 
+
+ align:start position:0%
+right now if we had a monkey in there or
+an ape
+
+ align:start position:0%
+an ape
+ 
+
+ align:start position:0%
+an ape
+we would say that this stage the human
+
+ align:start position:0%
+we would say that this stage the human
+ 
+
+ align:start position:0%
+we would say that this stage the human
+still looks pretty much the same it's
+
+ align:start position:0%
+still looks pretty much the same it's
+ 
+
+ align:start position:0%
+still looks pretty much the same it's
+these primates
+
+ align:start position:0%
+these primates
+ 
+
+ align:start position:0%
+these primates
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it seems that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they diverge later in development if
+
+ align:start position:0%
+they diverge later in development if
+ 
+
+ align:start position:0%
+they diverge later in development if
+they diverge later in evolution that's
+
+ align:start position:0%
+they diverge later in evolution that's
+ 
+
+ align:start position:0%
+they diverge later in evolution that's
+the correlation that seems to hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's just to remind you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my outline of high priority behavioral
+
+ align:start position:0%
+my outline of high priority behavioral
+ 
+
+ align:start position:0%
+my outline of high priority behavioral
+demands
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's based only mainly on
+
+ align:start position:0%
+uh it's based only mainly on
+ 
+
+ align:start position:0%
+uh it's based only mainly on
+studies of evolution and behavior
+
+ align:start position:0%
+studies of evolution and behavior
+ 
+
+ align:start position:0%
+studies of evolution and behavior
+comparative studies of behavior
+
+ align:start position:0%
+comparative studies of behavior
+ 
+
+ align:start position:0%
+comparative studies of behavior
+and i've correlated that with changes in
+
+ align:start position:0%
+and i've correlated that with changes in
+ 
+
+ align:start position:0%
+and i've correlated that with changes in
+anatomy
+
+ align:start position:0%
+anatomy
+ 
+
+ align:start position:0%
+anatomy
+i emphasize that it's speculative here
+
+ align:start position:0%
+i emphasize that it's speculative here
+ 
+
+ align:start position:0%
+i emphasize that it's speculative here
+but it is based on a lot of information
+
+ align:start position:0%
+but it is based on a lot of information
+ 
+
+ align:start position:0%
+but it is based on a lot of information
+and i support it with illustrations from
+
+ align:start position:0%
+and i support it with illustrations from
+ 
+
+ align:start position:0%
+and i support it with illustrations from
+comparative anatomy
+
+ align:start position:0%
+comparative anatomy
+ 
+
+ align:start position:0%
+comparative anatomy
+so these are the various stages we've
+
+ align:start position:0%
+so these are the various stages we've
+ 
+
+ align:start position:0%
+so these are the various stages we've
+already reviewed that today so i won't
+
+ align:start position:0%
+already reviewed that today so i won't
+ 
+
+ align:start position:0%
+already reviewed that today so i won't
+go over this now
+
+ align:start position:0%
+go over this now
+ 
+
+ align:start position:0%
+go over this now
+i just want to remind you that we have
+
+ align:start position:0%
+i just want to remind you that we have
+ 
+
+ align:start position:0%
+i just want to remind you that we have
+these data that i showed you before that
+
+ align:start position:0%
+these data that i showed you before that
+ 
+
+ align:start position:0%
+these data that i showed you before that
+show the importance of
+
+ align:start position:0%
+show the importance of
+ 
+
+ align:start position:0%
+show the importance of
+relative size
+
+ align:start position:0%
+relative size
+ 
+
+ align:start position:0%
+relative size
+or specialized functions
+
+ align:start position:0%
+or specialized functions
+ 
+
+ align:start position:0%
+or specialized functions
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+the expansions of the hindbrain here
+
+ align:start position:0%
+the expansions of the hindbrain here
+ 
+
+ align:start position:0%
+the expansions of the hindbrain here
+with specialized taste functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in these fish
+
+ align:start position:0%
+in these fish
+ 
+
+ align:start position:0%
+in these fish
+but i just want to mention some other
+
+ align:start position:0%
+but i just want to mention some other
+ 
+
+ align:start position:0%
+but i just want to mention some other
+specializations so you want
+
+ align:start position:0%
+specializations so you want
+ 
+
+ align:start position:0%
+specializations so you want
+assume that it's only these fish that
+
+ align:start position:0%
+assume that it's only these fish that
+ 
+
+ align:start position:0%
+assume that it's only these fish that
+give us this
+
+ align:start position:0%
+give us this
+ 
+
+ align:start position:0%
+give us this
+some fish have electro reception we
+
+ align:start position:0%
+some fish have electro reception we
+ 
+
+ align:start position:0%
+some fish have electro reception we
+don't have that but they some as many
+
+ align:start position:0%
+don't have that but they some as many
+ 
+
+ align:start position:0%
+don't have that but they some as many
+fish have this they can detect
+
+ align:start position:0%
+fish have this they can detect
+ 
+
+ align:start position:0%
+fish have this they can detect
+disturbances in the electric field that
+
+ align:start position:0%
+disturbances in the electric field that
+ 
+
+ align:start position:0%
+disturbances in the electric field that
+they generate around their body with the
+
+ align:start position:0%
+they generate around their body with the
+ 
+
+ align:start position:0%
+they generate around their body with the
+electric organs
+
+ align:start position:0%
+electric organs
+ 
+
+ align:start position:0%
+electric organs
+in the mormon fish this has led to an
+
+ align:start position:0%
+in the mormon fish this has led to an
+ 
+
+ align:start position:0%
+in the mormon fish this has led to an
+enormous expansion of cerebellum so if
+
+ align:start position:0%
+enormous expansion of cerebellum so if
+ 
+
+ align:start position:0%
+enormous expansion of cerebellum so if
+you open the skull you see a cerebellum
+
+ align:start position:0%
+you open the skull you see a cerebellum
+ 
+
+ align:start position:0%
+you open the skull you see a cerebellum
+it covers everything it's it's like when
+
+ align:start position:0%
+it covers everything it's it's like when
+ 
+
+ align:start position:0%
+it covers everything it's it's like when
+you open a human skull you see is the
+
+ align:start position:0%
+you open a human skull you see is the
+ 
+
+ align:start position:0%
+you open a human skull you see is the
+neocortex okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we still don't fully understand
+
+ align:start position:0%
+we still don't fully understand
+ 
+
+ align:start position:0%
+we still don't fully understand
+exactly what the cerebellum is doing
+
+ align:start position:0%
+exactly what the cerebellum is doing
+ 
+
+ align:start position:0%
+exactly what the cerebellum is doing
+in those animals or even in us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we have some ideas about it
+
+ align:start position:0%
+that we have some ideas about it
+ 
+
+ align:start position:0%
+that we have some ideas about it
+if you take
+
+ align:start position:0%
+if you take
+ 
+
+ align:start position:0%
+if you take
+let's look at another specialization
+
+ align:start position:0%
+let's look at another specialization
+ 
+
+ align:start position:0%
+let's look at another specialization
+what is a pit viper it's a snake
+
+ align:start position:0%
+what is a pit viper it's a snake
+ 
+
+ align:start position:0%
+what is a pit viper it's a snake
+that has a specialized pit organ
+
+ align:start position:0%
+that has a specialized pit organ
+ 
+
+ align:start position:0%
+that has a specialized pit organ
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+on its
+
+ align:start position:0%
+on its
+ 
+
+ align:start position:0%
+on its
+head okay
+
+ align:start position:0%
+head okay
+ 
+
+ align:start position:0%
+head okay
+means it it has infrared detectors those
+
+ align:start position:0%
+means it it has infrared detectors those
+ 
+
+ align:start position:0%
+means it it has infrared detectors those
+pin organs
+
+ align:start position:0%
+pin organs
+ 
+
+ align:start position:0%
+pin organs
+so in total darkness
+
+ align:start position:0%
+so in total darkness
+ 
+
+ align:start position:0%
+so in total darkness
+a snake can detect your presence or the
+
+ align:start position:0%
+a snake can detect your presence or the
+ 
+
+ align:start position:0%
+a snake can detect your presence or the
+presence of anything warm
+
+ align:start position:0%
+presence of anything warm
+ 
+
+ align:start position:0%
+presence of anything warm
+okay because it can detect infrared
+
+ align:start position:0%
+okay because it can detect infrared
+ 
+
+ align:start position:0%
+okay because it can detect infrared
+radiation
+
+ align:start position:0%
+radiation
+ 
+
+ align:start position:0%
+radiation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have to we can do that too but
+
+ align:start position:0%
+and we have to we can do that too but
+ 
+
+ align:start position:0%
+and we have to we can do that too but
+only if we invent a machine to do it
+
+ align:start position:0%
+only if we invent a machine to do it
+ 
+
+ align:start position:0%
+only if we invent a machine to do it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+bats and corpuses
+
+ align:start position:0%
+bats and corpuses
+ 
+
+ align:start position:0%
+bats and corpuses
+have echolocation so that's another
+
+ align:start position:0%
+have echolocation so that's another
+ 
+
+ align:start position:0%
+have echolocation so that's another
+specialized sense that's led to an
+
+ align:start position:0%
+specialized sense that's led to an
+ 
+
+ align:start position:0%
+specialized sense that's led to an
+expansion in their auditory system in
+
+ align:start position:0%
+expansion in their auditory system in
+ 
+
+ align:start position:0%
+expansion in their auditory system in
+midbrain
+
+ align:start position:0%
+midbrain
+ 
+
+ align:start position:0%
+midbrain
+controlling orientation movements
+
+ align:start position:0%
+controlling orientation movements
+ 
+
+ align:start position:0%
+controlling orientation movements
+they also have expanded there are some
+
+ align:start position:0%
+they also have expanded there are some
+ 
+
+ align:start position:0%
+they also have expanded there are some
+studies of
+
+ align:start position:0%
+studies of
+ 
+
+ align:start position:0%
+studies of
+bat and neocortex from expanded auditory
+
+ align:start position:0%
+bat and neocortex from expanded auditory
+ 
+
+ align:start position:0%
+bat and neocortex from expanded auditory
+regions in the neocortex as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+primates
+
+ align:start position:0%
+primates
+ 
+
+ align:start position:0%
+primates
+what's characteristic most
+
+ align:start position:0%
+what's characteristic most
+ 
+
+ align:start position:0%
+what's characteristic most
+characteristic the primase vision
+
+ align:start position:0%
+characteristic the primase vision
+ 
+
+ align:start position:0%
+characteristic the primase vision
+high visual acuity
+
+ align:start position:0%
+high visual acuity
+ 
+
+ align:start position:0%
+high visual acuity
+learned object recognition that's led to
+
+ align:start position:0%
+learned object recognition that's led to
+ 
+
+ align:start position:0%
+learned object recognition that's led to
+expansion of visual cortical areas if
+
+ align:start position:0%
+expansion of visual cortical areas if
+ 
+
+ align:start position:0%
+expansion of visual cortical areas if
+you look at the brain of a barista's
+
+ align:start position:0%
+you look at the brain of a barista's
+ 
+
+ align:start position:0%
+you look at the brain of a barista's
+monkey
+
+ align:start position:0%
+monkey
+ 
+
+ align:start position:0%
+monkey
+i mean it looks like more than half of
+
+ align:start position:0%
+i mean it looks like more than half of
+ 
+
+ align:start position:0%
+i mean it looks like more than half of
+the brain is occupied by areas related
+
+ align:start position:0%
+the brain is occupied by areas related
+ 
+
+ align:start position:0%
+the brain is occupied by areas related
+to vision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in rodents the comparable thing would be
+
+ align:start position:0%
+in rodents the comparable thing would be
+ 
+
+ align:start position:0%
+in rodents the comparable thing would be
+representation of the whiskers their
+
+ align:start position:0%
+representation of the whiskers their
+ 
+
+ align:start position:0%
+representation of the whiskers their
+face the debris okay
+
+ align:start position:0%
+face the debris okay
+ 
+
+ align:start position:0%
+face the debris okay
+they have specialized somatosensory
+
+ align:start position:0%
+they have specialized somatosensory
+ 
+
+ align:start position:0%
+they have specialized somatosensory
+systems and they're frequently studied
+
+ align:start position:0%
+systems and they're frequently studied
+ 
+
+ align:start position:0%
+systems and they're frequently studied
+in neuroscience because of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are other examples
+
+ align:start position:0%
+so there are other examples
+ 
+
+ align:start position:0%
+so there are other examples
+i'll mention some a few other behavioral
+
+ align:start position:0%
+i'll mention some a few other behavioral
+ 
+
+ align:start position:0%
+i'll mention some a few other behavioral
+specializations these are all correlated
+
+ align:start position:0%
+specializations these are all correlated
+ 
+
+ align:start position:0%
+specializations these are all correlated
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+elaborations in the brain
+
+ align:start position:0%
+elaborations in the brain
+ 
+
+ align:start position:0%
+elaborations in the brain
+the hand we mentioned vision in the
+
+ align:start position:0%
+the hand we mentioned vision in the
+ 
+
+ align:start position:0%
+the hand we mentioned vision in the
+primates but also they have specialized
+
+ align:start position:0%
+primates but also they have specialized
+ 
+
+ align:start position:0%
+primates but also they have specialized
+hands okay
+
+ align:start position:0%
+hands okay
+ 
+
+ align:start position:0%
+hands okay
+but so do raccoons
+
+ align:start position:0%
+but so do raccoons
+ 
+
+ align:start position:0%
+but so do raccoons
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and humans of course especially which
+
+ align:start position:0%
+and humans of course especially which
+ 
+
+ align:start position:0%
+and humans of course especially which
+requires a lot of tactile acuity and
+
+ align:start position:0%
+requires a lot of tactile acuity and
+ 
+
+ align:start position:0%
+requires a lot of tactile acuity and
+fine motor control both
+
+ align:start position:0%
+fine motor control both
+ 
+
+ align:start position:0%
+fine motor control both
+and these lead to expansions are
+
+ align:start position:0%
+and these lead to expansions are
+ 
+
+ align:start position:0%
+and these lead to expansions are
+correlated with expansions in the
+
+ align:start position:0%
+correlated with expansions in the
+ 
+
+ align:start position:0%
+correlated with expansions in the
+somatic sensory motor cortex and in the
+
+ align:start position:0%
+somatic sensory motor cortex and in the
+ 
+
+ align:start position:0%
+somatic sensory motor cortex and in the
+cerebellar hemispheres connected with
+
+ align:start position:0%
+cerebellar hemispheres connected with
+ 
+
+ align:start position:0%
+cerebellar hemispheres connected with
+those areas of the hemispheres
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other animals have this this monkey
+
+ align:start position:0%
+other animals have this this monkey
+ 
+
+ align:start position:0%
+other animals have this this monkey
+also has a special specialized tail a
+
+ align:start position:0%
+also has a special specialized tail a
+ 
+
+ align:start position:0%
+also has a special specialized tail a
+prehensile tail
+
+ align:start position:0%
+prehensile tail
+ 
+
+ align:start position:0%
+prehensile tail
+and he's got something we don't have at
+
+ align:start position:0%
+and he's got something we don't have at
+ 
+
+ align:start position:0%
+and he's got something we don't have at
+all expanded tail representations and
+
+ align:start position:0%
+all expanded tail representations and
+ 
+
+ align:start position:0%
+all expanded tail representations and
+sensory and motor cortex
+
+ align:start position:0%
+sensory and motor cortex
+ 
+
+ align:start position:0%
+sensory and motor cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+for both the motor control of that tail
+
+ align:start position:0%
+for both the motor control of that tail
+ 
+
+ align:start position:0%
+for both the motor control of that tail
+and the sensory
+
+ align:start position:0%
+and the sensory
+ 
+
+ align:start position:0%
+and the sensory
+detection with the tail
+
+ align:start position:0%
+detection with the tail
+ 
+
+ align:start position:0%
+detection with the tail
+the glabrous specialized global skin
+
+ align:start position:0%
+the glabrous specialized global skin
+ 
+
+ align:start position:0%
+the glabrous specialized global skin
+like the skin of our
+
+ align:start position:0%
+like the skin of our
+ 
+
+ align:start position:0%
+like the skin of our
+fingers and palm than he has on his tail
+
+ align:start position:0%
+fingers and palm than he has on his tail
+ 
+
+ align:start position:0%
+fingers and palm than he has on his tail
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spider monkeys
+
+ align:start position:0%
+spider monkeys
+ 
+
+ align:start position:0%
+spider monkeys
+never seen a movie of spider monkey in
+
+ align:start position:0%
+never seen a movie of spider monkey in
+ 
+
+ align:start position:0%
+never seen a movie of spider monkey in
+the way they use their tail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they use their tail like we use their
+
+ align:start position:0%
+they use their tail like we use their
+ 
+
+ align:start position:0%
+they use their tail like we use their
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+when they go through the trees they're
+
+ align:start position:0%
+when they go through the trees they're
+ 
+
+ align:start position:0%
+when they go through the trees they're
+using their hands too
+
+ align:start position:0%
+using their hands too
+ 
+
+ align:start position:0%
+using their hands too
+using the tail and the hands okay
+
+ align:start position:0%
+using the tail and the hands okay
+ 
+
+ align:start position:0%
+using the tail and the hands okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they can when they touch things with the
+
+ align:start position:0%
+they can when they touch things with the
+ 
+
+ align:start position:0%
+they can when they touch things with the
+tail they can be it's like we touching
+
+ align:start position:0%
+tail they can be it's like we touching
+ 
+
+ align:start position:0%
+tail they can be it's like we touching
+with our hands they can they have good
+
+ align:start position:0%
+with our hands they can they have good
+ 
+
+ align:start position:0%
+with our hands they can they have good
+acuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i just want to point out here that
+
+ align:start position:0%
+and i just want to point out here that
+ 
+
+ align:start position:0%
+and i just want to point out here that
+in humans
+
+ align:start position:0%
+in humans
+ 
+
+ align:start position:0%
+in humans
+language is a specialization and that's
+
+ align:start position:0%
+language is a specialization and that's
+ 
+
+ align:start position:0%
+language is a specialization and that's
+led to expansions also or it's
+
+ align:start position:0%
+led to expansions also or it's
+ 
+
+ align:start position:0%
+led to expansions also or it's
+correlated with expansions
+
+ align:start position:0%
+correlated with expansions
+ 
+
+ align:start position:0%
+correlated with expansions
+of the polymodel association cortex the
+
+ align:start position:0%
+of the polymodel association cortex the
+ 
+
+ align:start position:0%
+of the polymodel association cortex the
+parietal temporal and frontal lobes it's
+
+ align:start position:0%
+parietal temporal and frontal lobes it's
+ 
+
+ align:start position:0%
+parietal temporal and frontal lobes it's
+also led to hemispheric specialization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there may be other reasons though that
+
+ align:start position:0%
+there may be other reasons though that
+ 
+
+ align:start position:0%
+there may be other reasons though that
+lead to hemispheric specialization okay
+
+ align:start position:0%
+lead to hemispheric specialization okay
+ 
+
+ align:start position:0%
+lead to hemispheric specialization okay
+and finally
+
+ align:start position:0%
+and finally
+ 
+
+ align:start position:0%
+and finally
+i don't know if you'll hear about this
+
+ align:start position:0%
+i don't know if you'll hear about this
+ 
+
+ align:start position:0%
+i don't know if you'll hear about this
+in other classes but
+
+ align:start position:0%
+in other classes but
+ 
+
+ align:start position:0%
+in other classes but
+the elaborate social organization and
+
+ align:start position:0%
+the elaborate social organization and
+ 
+
+ align:start position:0%
+the elaborate social organization and
+planning and problem solving that you
+
+ align:start position:0%
+planning and problem solving that you
+ 
+
+ align:start position:0%
+planning and problem solving that you
+have in social animals social mammals
+
+ align:start position:0%
+have in social animals social mammals
+ 
+
+ align:start position:0%
+have in social animals social mammals
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has a representation in the brain
+
+ align:start position:0%
+that has a representation in the brain
+ 
+
+ align:start position:0%
+that has a representation in the brain
+two especially
+
+ align:start position:0%
+two especially
+ 
+
+ align:start position:0%
+two especially
+prefrontal neocortical areas in the
+
+ align:start position:0%
+prefrontal neocortical areas in the
+ 
+
+ align:start position:0%
+prefrontal neocortical areas in the
+primates okay
+
+ align:start position:0%
+primates okay
+ 
+
+ align:start position:0%
+primates okay
+is huge in us
+
+ align:start position:0%
+is huge in us
+ 
+
+ align:start position:0%
+is huge in us
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a lot of it has to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planning and
+
+ align:start position:0%
+planning and
+ 
+
+ align:start position:0%
+planning and
+problem solving
+
+ align:start position:0%
+problem solving
+ 
+
+ align:start position:0%
+problem solving
+anticipating what we're going to do
+
+ align:start position:0%
+anticipating what we're going to do
+ 
+
+ align:start position:0%
+anticipating what we're going to do
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because females are so good at that i
+
+ align:start position:0%
+because females are so good at that i
+ 
+
+ align:start position:0%
+because females are so good at that i
+would probably say the female brain
+
+ align:start position:0%
+would probably say the female brain
+ 
+
+ align:start position:0%
+would probably say the female brain
+expanded first and the male had to catch
+
+ align:start position:0%
+expanded first and the male had to catch
+ 
+
+ align:start position:0%
+expanded first and the male had to catch
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+okay okay sorry but there are more women
+
+ align:start position:0%
+okay okay sorry but there are more women
+ 
+
+ align:start position:0%
+okay okay sorry but there are more women
+in this class i've got to say a few
+
+ align:start position:0%
+in this class i've got to say a few
+ 
+
+ align:start position:0%
+in this class i've got to say a few
+things like that it's probably true okay
+
+ align:start position:0%
+things like that it's probably true okay
+ 
+
+ align:start position:0%
+things like that it's probably true okay
+there is actually a theory of brain
+
+ align:start position:0%
+there is actually a theory of brain
+ 
+
+ align:start position:0%
+there is actually a theory of brain
+evolution that
+
+ align:start position:0%
+evolution that
+ 
+
+ align:start position:0%
+evolution that
+takes that view
+
+ align:start position:0%
+takes that view
+ 
+
+ align:start position:0%
+takes that view
+okay let's now start talking about going
+
+ align:start position:0%
+okay let's now start talking about going
+ 
+
+ align:start position:0%
+okay let's now start talking about going
+back to brain connections okay
+
+ align:start position:0%
+back to brain connections okay
+ 
+
+ align:start position:0%
+back to brain connections okay
+let's talk about basic subdivisions of
+
+ align:start position:0%
+let's talk about basic subdivisions of
+ 
+
+ align:start position:0%
+let's talk about basic subdivisions of
+the brain basic types of neurons we
+
+ align:start position:0%
+the brain basic types of neurons we
+ 
+
+ align:start position:0%
+the brain basic types of neurons we
+introduced that before
+
+ align:start position:0%
+introduced that before
+ 
+
+ align:start position:0%
+introduced that before
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+basic channels of conduction of sensory
+
+ align:start position:0%
+basic channels of conduction of sensory
+ 
+
+ align:start position:0%
+basic channels of conduction of sensory
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+through and into the brain
+
+ align:start position:0%
+through and into the brain
+ 
+
+ align:start position:0%
+through and into the brain
+and then i'll give you an overview of
+
+ align:start position:0%
+and then i'll give you an overview of
+ 
+
+ align:start position:0%
+and then i'll give you an overview of
+the cephalic structures
+
+ align:start position:0%
+the cephalic structures
+ 
+
+ align:start position:0%
+the cephalic structures
+and finally we'll talk about the
+
+ align:start position:0%
+and finally we'll talk about the
+ 
+
+ align:start position:0%
+and finally we'll talk about the
+specialized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connections that evolve with
+
+ align:start position:0%
+connections that evolve with
+ 
+
+ align:start position:0%
+connections that evolve with
+the elaboration of neocortex
+
+ align:start position:0%
+the elaboration of neocortex
+ 
+
+ align:start position:0%
+the elaboration of neocortex
+in the mammals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to use
+
+ align:start position:0%
+i'm going to use
+ 
+
+ align:start position:0%
+i'm going to use
+the shmo brain for this
+
+ align:start position:0%
+the shmo brain for this
+ 
+
+ align:start position:0%
+the shmo brain for this
+so i'll have to tell you what a schmoo
+
+ align:start position:0%
+so i'll have to tell you what a schmoo
+ 
+
+ align:start position:0%
+so i'll have to tell you what a schmoo
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+and then we'll identify the basic
+
+ align:start position:0%
+and then we'll identify the basic
+ 
+
+ align:start position:0%
+and then we'll identify the basic
+structures and learn that some
+
+ align:start position:0%
+structures and learn that some
+ 
+
+ align:start position:0%
+structures and learn that some
+definitions
+
+ align:start position:0%
+definitions
+ 
+
+ align:start position:0%
+definitions
+here's a shmuel here the corner
+
+ align:start position:0%
+here's a shmuel here the corner
+ 
+
+ align:start position:0%
+here's a shmuel here the corner
+i got this he's very cute
+
+ align:start position:0%
+i got this he's very cute
+ 
+
+ align:start position:0%
+i got this he's very cute
+little animal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he evolved in the brain of
+
+ align:start position:0%
+he evolved in the brain of
+ 
+
+ align:start position:0%
+he evolved in the brain of
+al cap was a cartoonist
+
+ align:start position:0%
+al cap was a cartoonist
+ 
+
+ align:start position:0%
+al cap was a cartoonist
+in chicago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this describes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people used to read this every every
+
+ align:start position:0%
+people used to read this every every
+ 
+
+ align:start position:0%
+people used to read this every every
+time he published a
+
+ align:start position:0%
+time he published a
+ 
+
+ align:start position:0%
+time he published a
+little cartoon series in the chicago
+
+ align:start position:0%
+little cartoon series in the chicago
+ 
+
+ align:start position:0%
+little cartoon series in the chicago
+newspapers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's just to remind you a little bit
+
+ align:start position:0%
+and it's just to remind you a little bit
+ 
+
+ align:start position:0%
+and it's just to remind you a little bit
+about shmuel because he loves all cars 9
+
+ align:start position:0%
+about shmuel because he loves all cars 9
+ 
+
+ align:start position:0%
+about shmuel because he loves all cars 9
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+instinctively and without fail no matter
+
+ align:start position:0%
+instinctively and without fail no matter
+ 
+
+ align:start position:0%
+instinctively and without fail no matter
+what well you can read these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're also serious gosh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the schmooze is sort of serious too
+
+ align:start position:0%
+well the schmooze is sort of serious too
+ 
+
+ align:start position:0%
+well the schmooze is sort of serious too
+but he also makes you laugh
+
+ align:start position:0%
+but he also makes you laugh
+ 
+
+ align:start position:0%
+but he also makes you laugh
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is it it's a pedagogical device
+
+ align:start position:0%
+so what is it it's a pedagogical device
+ 
+
+ align:start position:0%
+so what is it it's a pedagogical device
+of course it was invented by nauta
+
+ align:start position:0%
+of course it was invented by nauta
+ 
+
+ align:start position:0%
+of course it was invented by nauta
+the great neuroanatomist who finished
+
+ align:start position:0%
+the great neuroanatomist who finished
+ 
+
+ align:start position:0%
+the great neuroanatomist who finished
+his career here at mit
+
+ align:start position:0%
+his career here at mit
+ 
+
+ align:start position:0%
+his career here at mit
+he invented it to illustrate some basic
+
+ align:start position:0%
+he invented it to illustrate some basic
+ 
+
+ align:start position:0%
+he invented it to illustrate some basic
+principles
+
+ align:start position:0%
+principles
+ 
+
+ align:start position:0%
+principles
+of the anatomical organization of the
+
+ align:start position:0%
+of the anatomical organization of the
+ 
+
+ align:start position:0%
+of the anatomical organization of the
+brain of animals
+
+ align:start position:0%
+brain of animals
+ 
+
+ align:start position:0%
+brain of animals
+suggested to be ancestral to mammals
+
+ align:start position:0%
+suggested to be ancestral to mammals
+ 
+
+ align:start position:0%
+suggested to be ancestral to mammals
+the first move could represent a
+
+ align:start position:0%
+the first move could represent a
+ 
+
+ align:start position:0%
+the first move could represent a
+generalized amphibian brain he usually
+
+ align:start position:0%
+generalized amphibian brain he usually
+ 
+
+ align:start position:0%
+generalized amphibian brain he usually
+described it that way it was based on
+
+ align:start position:0%
+described it that way it was based on
+ 
+
+ align:start position:0%
+described it that way it was based on
+the work of c judson herrick
+
+ align:start position:0%
+the work of c judson herrick
+ 
+
+ align:start position:0%
+the work of c judson herrick
+okay an american comparative anatomist
+
+ align:start position:0%
+okay an american comparative anatomist
+ 
+
+ align:start position:0%
+okay an american comparative anatomist
+and then more recent anatomical studies
+
+ align:start position:0%
+and then more recent anatomical studies
+ 
+
+ align:start position:0%
+and then more recent anatomical studies
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+studies of connections that herrick did
+
+ align:start position:0%
+studies of connections that herrick did
+ 
+
+ align:start position:0%
+studies of connections that herrick did
+not know so well because he didn't use
+
+ align:start position:0%
+not know so well because he didn't use
+ 
+
+ align:start position:0%
+not know so well because he didn't use
+experimental studies to study
+
+ align:start position:0%
+experimental studies to study
+ 
+
+ align:start position:0%
+experimental studies to study
+connections the way nada and his
+
+ align:start position:0%
+connections the way nada and his
+ 
+
+ align:start position:0%
+connections the way nada and his
+students did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why do we study primitive why do i
+
+ align:start position:0%
+now why do we study primitive why do i
+ 
+
+ align:start position:0%
+now why do we study primitive why do i
+introduce the brain by talking about
+
+ align:start position:0%
+introduce the brain by talking about
+ 
+
+ align:start position:0%
+introduce the brain by talking about
+primitive brains why don't i just
+
+ align:start position:0%
+primitive brains why don't i just
+ 
+
+ align:start position:0%
+primitive brains why don't i just
+save time and go right to the human
+
+ align:start position:0%
+save time and go right to the human
+ 
+
+ align:start position:0%
+save time and go right to the human
+brain like they do in medical school
+
+ align:start position:0%
+brain like they do in medical school
+ 
+
+ align:start position:0%
+brain like they do in medical school
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well you'll find that you'll appreciate
+
+ align:start position:0%
+well you'll find that you'll appreciate
+ 
+
+ align:start position:0%
+well you'll find that you'll appreciate
+more and more
+
+ align:start position:0%
+more and more
+ 
+
+ align:start position:0%
+more and more
+why i do that as we go on
+
+ align:start position:0%
+why i do that as we go on
+ 
+
+ align:start position:0%
+why i do that as we go on
+but it's also relevant because
+
+ align:start position:0%
+but it's also relevant because
+ 
+
+ align:start position:0%
+but it's also relevant because
+not only helps you learn but it's we
+
+ align:start position:0%
+not only helps you learn but it's we
+ 
+
+ align:start position:0%
+not only helps you learn but it's we
+still have all those
+
+ align:start position:0%
+still have all those
+ 
+
+ align:start position:0%
+still have all those
+parts
+
+ align:start position:0%
+parts
+ 
+
+ align:start position:0%
+parts
+because when the brain evolved we don't
+
+ align:start position:0%
+because when the brain evolved we don't
+ 
+
+ align:start position:0%
+because when the brain evolved we don't
+just throw things out and replace it
+
+ align:start position:0%
+just throw things out and replace it
+ 
+
+ align:start position:0%
+just throw things out and replace it
+with something new we just add
+
+ align:start position:0%
+with something new we just add
+ 
+
+ align:start position:0%
+with something new we just add
+to what we had before
+
+ align:start position:0%
+to what we had before
+ 
+
+ align:start position:0%
+to what we had before
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+very little is discarded i mean there
+
+ align:start position:0%
+very little is discarded i mean there
+ 
+
+ align:start position:0%
+very little is discarded i mean there
+are some things that get harnessed
+
+ align:start position:0%
+are some things that get harnessed
+ 
+
+ align:start position:0%
+are some things that get harnessed
+that might get smaller
+
+ align:start position:0%
+that might get smaller
+ 
+
+ align:start position:0%
+that might get smaller
+but basically we keep everything so you
+
+ align:start position:0%
+but basically we keep everything so you
+ 
+
+ align:start position:0%
+but basically we keep everything so you
+still have that
+
+ align:start position:0%
+still have that
+ 
+
+ align:start position:0%
+still have that
+ancestral brain the core of your human
+
+ align:start position:0%
+ancestral brain the core of your human
+ 
+
+ align:start position:0%
+ancestral brain the core of your human
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that little note you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crawling in the slime of the swamp or
+
+ align:start position:0%
+crawling in the slime of the swamp or
+ 
+
+ align:start position:0%
+crawling in the slime of the swamp or
+you might find in your basement
+
+ align:start position:0%
+you might find in your basement
+ 
+
+ align:start position:0%
+you might find in your basement
+has connections in his brain that you
+
+ align:start position:0%
+has connections in his brain that you
+ 
+
+ align:start position:0%
+has connections in his brain that you
+also have in yours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when we get very angry we probably
+
+ align:start position:0%
+and when we get very angry we probably
+ 
+
+ align:start position:0%
+and when we get very angry we probably
+use those a lot more
+
+ align:start position:0%
+use those a lot more
+ 
+
+ align:start position:0%
+use those a lot more
+okay let's
+
+ align:start position:0%
+okay let's
+ 
+
+ align:start position:0%
+okay let's
+first give you the outline here this is
+
+ align:start position:0%
+first give you the outline here this is
+ 
+
+ align:start position:0%
+first give you the outline here this is
+my outline of shmu1
+
+ align:start position:0%
+my outline of shmu1
+ 
+
+ align:start position:0%
+my outline of shmu1
+and here are the subdivisions i want you
+
+ align:start position:0%
+and here are the subdivisions i want you
+ 
+
+ align:start position:0%
+and here are the subdivisions i want you
+to know all of these
+
+ align:start position:0%
+to know all of these
+ 
+
+ align:start position:0%
+to know all of these
+they're very basic you know some of them
+
+ align:start position:0%
+they're very basic you know some of them
+ 
+
+ align:start position:0%
+they're very basic you know some of them
+already it shows the spinal cord here at
+
+ align:start position:0%
+already it shows the spinal cord here at
+ 
+
+ align:start position:0%
+already it shows the spinal cord here at
+the caudal end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you see at the rostral in the
+
+ align:start position:0%
+here you see at the rostral in the
+ 
+
+ align:start position:0%
+here you see at the rostral in the
+olfactory bulb
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the midbrain
+
+ align:start position:0%
+here's the midbrain
+ 
+
+ align:start position:0%
+here's the midbrain
+sorry the hindbrain in the midbrain in
+
+ align:start position:0%
+sorry the hindbrain in the midbrain in
+ 
+
+ align:start position:0%
+sorry the hindbrain in the midbrain in
+the hindbrain i've shown the cerebellum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the brain brain the little bumps
+
+ align:start position:0%
+in the brain brain the little bumps
+ 
+
+ align:start position:0%
+in the brain brain the little bumps
+there represent the tectum of the
+
+ align:start position:0%
+there represent the tectum of the
+ 
+
+ align:start position:0%
+there represent the tectum of the
+midbrain
+
+ align:start position:0%
+midbrain
+ 
+
+ align:start position:0%
+midbrain
+the more anterior one is often called
+
+ align:start position:0%
+the more anterior one is often called
+ 
+
+ align:start position:0%
+the more anterior one is often called
+the optic tectum that's where those
+
+ align:start position:0%
+the optic tectum that's where those
+ 
+
+ align:start position:0%
+the optic tectum that's where those
+visual connections go and this is all
+
+ align:start position:0%
+visual connections go and this is all
+ 
+
+ align:start position:0%
+visual connections go and this is all
+forebrain
+
+ align:start position:0%
+forebrain
+ 
+
+ align:start position:0%
+forebrain
+and i've got it divided into different
+
+ align:start position:0%
+and i've got it divided into different
+ 
+
+ align:start position:0%
+and i've got it divided into different
+parts here
+
+ align:start position:0%
+parts here
+ 
+
+ align:start position:0%
+parts here
+the lower part here's the more caudal
+
+ align:start position:0%
+the lower part here's the more caudal
+ 
+
+ align:start position:0%
+the lower part here's the more caudal
+parts between brain and i've got the two
+
+ align:start position:0%
+parts between brain and i've got the two
+ 
+
+ align:start position:0%
+parts between brain and i've got the two
+major divisions here thalamus and
+
+ align:start position:0%
+major divisions here thalamus and
+ 
+
+ align:start position:0%
+major divisions here thalamus and
+hypothalamus there are a couple other
+
+ align:start position:0%
+hypothalamus there are a couple other
+ 
+
+ align:start position:0%
+hypothalamus there are a couple other
+divisions too
+
+ align:start position:0%
+divisions too
+ 
+
+ align:start position:0%
+divisions too
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we know most about the two largest
+
+ align:start position:0%
+but we know most about the two largest
+ 
+
+ align:start position:0%
+but we know most about the two largest
+parts the thalamus and the hypothalamus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the end brain
+
+ align:start position:0%
+and then the end brain
+ 
+
+ align:start position:0%
+and then the end brain
+corpus triadum subcortical structure
+
+ align:start position:0%
+corpus triadum subcortical structure
+ 
+
+ align:start position:0%
+corpus triadum subcortical structure
+other subcortical
+
+ align:start position:0%
+other subcortical
+ 
+
+ align:start position:0%
+other subcortical
+parts of the
+
+ align:start position:0%
+parts of the
+ 
+
+ align:start position:0%
+parts of the
+connected with that we call limbic
+
+ align:start position:0%
+connected with that we call limbic
+ 
+
+ align:start position:0%
+connected with that we call limbic
+because they're connected to the
+
+ align:start position:0%
+because they're connected to the
+ 
+
+ align:start position:0%
+because they're connected to the
+hypothalamus they're sort of at the
+
+ align:start position:0%
+hypothalamus they're sort of at the
+ 
+
+ align:start position:0%
+hypothalamus they're sort of at the
+fringes of the hemispheres
+
+ align:start position:0%
+fringes of the hemispheres
+ 
+
+ align:start position:0%
+fringes of the hemispheres
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cortical structures
+
+ align:start position:0%
+cortical structures
+ 
+
+ align:start position:0%
+cortical structures
+related to olfaction
+
+ align:start position:0%
+related to olfaction
+ 
+
+ align:start position:0%
+related to olfaction
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what we call limbic cortex
+
+ align:start position:0%
+what we call limbic cortex
+ 
+
+ align:start position:0%
+what we call limbic cortex
+some of that
+
+ align:start position:0%
+some of that
+ 
+
+ align:start position:0%
+some of that
+that cortex that is not just olfactory
+
+ align:start position:0%
+that cortex that is not just olfactory
+ 
+
+ align:start position:0%
+that cortex that is not just olfactory
+but connected to hypothalamus
+
+ align:start position:0%
+but connected to hypothalamus
+ 
+
+ align:start position:0%
+but connected to hypothalamus
+there's no neocortex in schmuwan okay
+
+ align:start position:0%
+there's no neocortex in schmuwan okay
+ 
+
+ align:start position:0%
+there's no neocortex in schmuwan okay
+now in the most primitive amphibians
+
+ align:start position:0%
+now in the most primitive amphibians
+ 
+
+ align:start position:0%
+now in the most primitive amphibians
+that this is based on
+
+ align:start position:0%
+that this is based on
+ 
+
+ align:start position:0%
+that this is based on
+there is very little anything that looks
+
+ align:start position:0%
+there is very little anything that looks
+ 
+
+ align:start position:0%
+there is very little anything that looks
+like neocortex
+
+ align:start position:0%
+like neocortex
+ 
+
+ align:start position:0%
+like neocortex
+there's a little bit of cortex they call
+
+ align:start position:0%
+there's a little bit of cortex they call
+ 
+
+ align:start position:0%
+there's a little bit of cortex they call
+general cortex that's probably the
+
+ align:start position:0%
+general cortex that's probably the
+ 
+
+ align:start position:0%
+general cortex that's probably the
+predecessor of it
+
+ align:start position:0%
+predecessor of it
+ 
+
+ align:start position:0%
+predecessor of it
+and here i've shown
+
+ align:start position:0%
+and here i've shown
+ 
+
+ align:start position:0%
+and here i've shown
+some of the basic connections
+
+ align:start position:0%
+some of the basic connections
+ 
+
+ align:start position:0%
+some of the basic connections
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+a mishmash to you at the moment
+
+ align:start position:0%
+a mishmash to you at the moment
+ 
+
+ align:start position:0%
+a mishmash to you at the moment
+but it won't as we
+
+ align:start position:0%
+but it won't as we
+ 
+
+ align:start position:0%
+but it won't as we
+proceed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here i'm showing you what
+
+ align:start position:0%
+now here i'm showing you what
+ 
+
+ align:start position:0%
+now here i'm showing you what
+the actual neural tube
+
+ align:start position:0%
+the actual neural tube
+ 
+
+ align:start position:0%
+the actual neural tube
+looks like although i've exaggerated
+
+ align:start position:0%
+looks like although i've exaggerated
+ 
+
+ align:start position:0%
+looks like although i've exaggerated
+thickness of the
+
+ align:start position:0%
+thickness of the
+ 
+
+ align:start position:0%
+thickness of the
+spinal cord
+
+ align:start position:0%
+spinal cord
+ 
+
+ align:start position:0%
+spinal cord
+and brain stem a bit here
+
+ align:start position:0%
+and brain stem a bit here
+ 
+
+ align:start position:0%
+and brain stem a bit here
+remember it's a tube
+
+ align:start position:0%
+remember it's a tube
+ 
+
+ align:start position:0%
+remember it's a tube
+it's a tube that then expands more in
+
+ align:start position:0%
+it's a tube that then expands more in
+ 
+
+ align:start position:0%
+it's a tube that then expands more in
+some regions than others and on the
+
+ align:start position:0%
+some regions than others and on the
+ 
+
+ align:start position:0%
+some regions than others and on the
+right here i've shown the cross sections
+
+ align:start position:0%
+right here i've shown the cross sections
+ 
+
+ align:start position:0%
+right here i've shown the cross sections
+of these various levels there's a cross
+
+ align:start position:0%
+of these various levels there's a cross
+ 
+
+ align:start position:0%
+of these various levels there's a cross
+section through the
+
+ align:start position:0%
+section through the
+ 
+
+ align:start position:0%
+section through the
+the embryonic spinal cord
+
+ align:start position:0%
+the embryonic spinal cord
+ 
+
+ align:start position:0%
+the embryonic spinal cord
+and the embryonic hindbrain the
+
+ align:start position:0%
+and the embryonic hindbrain the
+ 
+
+ align:start position:0%
+and the embryonic hindbrain the
+embryonic midbrain
+
+ align:start position:0%
+embryonic midbrain
+ 
+
+ align:start position:0%
+embryonic midbrain
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+you see the twin brain and brain here
+
+ align:start position:0%
+you see the twin brain and brain here
+ 
+
+ align:start position:0%
+you see the twin brain and brain here
+the tween brain has this heart shape in
+
+ align:start position:0%
+the tween brain has this heart shape in
+ 
+
+ align:start position:0%
+the tween brain has this heart shape in
+its cross section
+
+ align:start position:0%
+its cross section
+ 
+
+ align:start position:0%
+its cross section
+and then the
+
+ align:start position:0%
+and then the
+ 
+
+ align:start position:0%
+and then the
+membrane with a corpus triadon below the
+
+ align:start position:0%
+membrane with a corpus triadon below the
+ 
+
+ align:start position:0%
+membrane with a corpus triadon below the
+ventricle
+
+ align:start position:0%
+ventricle
+ 
+
+ align:start position:0%
+ventricle
+and the cortex above okay
+
+ align:start position:0%
+and the cortex above okay
+ 
+
+ align:start position:0%
+and the cortex above okay
+and i'm showing here
+
+ align:start position:0%
+and i'm showing here
+ 
+
+ align:start position:0%
+and i'm showing here
+again the basic subdivisions which i
+
+ align:start position:0%
+again the basic subdivisions which i
+ 
+
+ align:start position:0%
+again the basic subdivisions which i
+would like you to learn there and i've
+
+ align:start position:0%
+would like you to learn there and i've
+ 
+
+ align:start position:0%
+would like you to learn there and i've
+given you the both the english
+
+ align:start position:0%
+given you the both the english
+ 
+
+ align:start position:0%
+given you the both the english
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the greek names
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll keep repeating these i'll
+
+ align:start position:0%
+so we'll keep repeating these i'll
+ 
+
+ align:start position:0%
+so we'll keep repeating these i'll
+mention this i don't expect you to like
+
+ align:start position:0%
+mention this i don't expect you to like
+ 
+
+ align:start position:0%
+mention this i don't expect you to like
+to learn it instantly
+
+ align:start position:0%
+to learn it instantly
+ 
+
+ align:start position:0%
+to learn it instantly
+and i will repeat this a number of times
+
+ align:start position:0%
+and i will repeat this a number of times
+ 
+
+ align:start position:0%
+and i will repeat this a number of times
+to try to get you to relax a little bit
+
+ align:start position:0%
+to try to get you to relax a little bit
+ 
+
+ align:start position:0%
+to try to get you to relax a little bit
+neuroanatomy takes a little time to
+
+ align:start position:0%
+neuroanatomy takes a little time to
+ 
+
+ align:start position:0%
+neuroanatomy takes a little time to
+acquire you have to get it repeatedly
+
+ align:start position:0%
+acquire you have to get it repeatedly
+ 
+
+ align:start position:0%
+acquire you have to get it repeatedly
+and so i will go over things repeatedly
+
+ align:start position:0%
+and so i will go over things repeatedly
+ 
+
+ align:start position:0%
+and so i will go over things repeatedly
+in the class you'll also do some
+
+ align:start position:0%
+in the class you'll also do some
+ 
+
+ align:start position:0%
+in the class you'll also do some
+readings
+
+ align:start position:0%
+readings
+ 
+
+ align:start position:0%
+readings
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+don't get too frustrated with yourself
+
+ align:start position:0%
+don't get too frustrated with yourself
+ 
+
+ align:start position:0%
+don't get too frustrated with yourself
+when you have trouble remembering it
+
+ align:start position:0%
+when you have trouble remembering it
+ 
+
+ align:start position:0%
+when you have trouble remembering it
+because it's like you can connect it
+
+ align:start position:0%
+because it's like you can connect it
+ 
+
+ align:start position:0%
+because it's like you can connect it
+with if it takes on more meaning to you
+
+ align:start position:0%
+with if it takes on more meaning to you
+ 
+
+ align:start position:0%
+with if it takes on more meaning to you
+when you know a little bit more about
+
+ align:start position:0%
+when you know a little bit more about
+ 
+
+ align:start position:0%
+when you know a little bit more about
+connections about function
+
+ align:start position:0%
+connections about function
+ 
+
+ align:start position:0%
+connections about function
+and it'll grow on you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then we'll look at where these
+
+ align:start position:0%
+okay then we'll look at where these
+ 
+
+ align:start position:0%
+okay then we'll look at where these
+things are in the brain let's talk a
+
+ align:start position:0%
+things are in the brain let's talk a
+ 
+
+ align:start position:0%
+things are in the brain let's talk a
+little bit about the primary sensory
+
+ align:start position:0%
+little bit about the primary sensory
+ 
+
+ align:start position:0%
+little bit about the primary sensory
+neurons in different animals
+
+ align:start position:0%
+neurons in different animals
+ 
+
+ align:start position:0%
+neurons in different animals
+this is a picture from ramonica hall
+
+ align:start position:0%
+this is a picture from ramonica hall
+ 
+
+ align:start position:0%
+this is a picture from ramonica hall
+showing primary sensory neurons
+
+ align:start position:0%
+showing primary sensory neurons
+ 
+
+ align:start position:0%
+showing primary sensory neurons
+that carry input from the body surface
+
+ align:start position:0%
+that carry input from the body surface
+ 
+
+ align:start position:0%
+that carry input from the body surface
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in various species here
+
+ align:start position:0%
+in various species here
+ 
+
+ align:start position:0%
+in various species here
+here he has a sensory cell in the
+
+ align:start position:0%
+here he has a sensory cell in the
+ 
+
+ align:start position:0%
+here he has a sensory cell in the
+earthworm that goes to a sensory
+
+ align:start position:0%
+earthworm that goes to a sensory
+ 
+
+ align:start position:0%
+earthworm that goes to a sensory
+ganglion in the earthworm and notice
+
+ align:start position:0%
+ganglion in the earthworm and notice
+ 
+
+ align:start position:0%
+ganglion in the earthworm and notice
+that the the primary sensory neuron is
+
+ align:start position:0%
+that the the primary sensory neuron is
+ 
+
+ align:start position:0%
+that the the primary sensory neuron is
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the surface epithelium of the body
+
+ align:start position:0%
+the surface epithelium of the body
+ 
+
+ align:start position:0%
+the surface epithelium of the body
+surface okay
+
+ align:start position:0%
+surface okay
+ 
+
+ align:start position:0%
+surface okay
+this is the epithelium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the derivative of the ectoderm the
+
+ align:start position:0%
+the derivative of the ectoderm the
+ 
+
+ align:start position:0%
+the derivative of the ectoderm the
+surface layer the embryo the entire
+
+ align:start position:0%
+surface layer the embryo the entire
+ 
+
+ align:start position:0%
+surface layer the embryo the entire
+nervous system in fact is the derivative
+
+ align:start position:0%
+nervous system in fact is the derivative
+ 
+
+ align:start position:0%
+nervous system in fact is the derivative
+of the ectoderm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here he shows the sensory cell in the
+
+ align:start position:0%
+here he shows the sensory cell in the
+ 
+
+ align:start position:0%
+here he shows the sensory cell in the
+mollusk which is similar but
+
+ align:start position:0%
+mollusk which is similar but
+ 
+
+ align:start position:0%
+mollusk which is similar but
+the cell body now
+
+ align:start position:0%
+the cell body now
+ 
+
+ align:start position:0%
+the cell body now
+has moved deep to the surface
+
+ align:start position:0%
+has moved deep to the surface
+ 
+
+ align:start position:0%
+has moved deep to the surface
+but it's still connected with the
+
+ align:start position:0%
+but it's still connected with the
+ 
+
+ align:start position:0%
+but it's still connected with the
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+okay so now it's become
+
+ align:start position:0%
+okay so now it's become
+ 
+
+ align:start position:0%
+okay so now it's become
+a bipolar neuron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the input side
+
+ align:start position:0%
+with the input side
+ 
+
+ align:start position:0%
+with the input side
+at the surface and then the output side
+
+ align:start position:0%
+at the surface and then the output side
+ 
+
+ align:start position:0%
+at the surface and then the output side
+here in the sensor in the ganglion or
+
+ align:start position:0%
+here in the sensor in the ganglion or
+ 
+
+ align:start position:0%
+here in the sensor in the ganglion or
+central nervous system
+
+ align:start position:0%
+central nervous system
+ 
+
+ align:start position:0%
+central nervous system
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then he gets to vertebrates here
+
+ align:start position:0%
+and then he gets to vertebrates here
+ 
+
+ align:start position:0%
+and then he gets to vertebrates here
+and he's showing a sensory cell that a
+
+ align:start position:0%
+and he's showing a sensory cell that a
+ 
+
+ align:start position:0%
+and he's showing a sensory cell that a
+lower fish here which is still a bipolar
+
+ align:start position:0%
+lower fish here which is still a bipolar
+ 
+
+ align:start position:0%
+lower fish here which is still a bipolar
+neuron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receiving inputs from the surface
+
+ align:start position:0%
+receiving inputs from the surface
+ 
+
+ align:start position:0%
+receiving inputs from the surface
+carrying it into the central nervous
+
+ align:start position:0%
+carrying it into the central nervous
+ 
+
+ align:start position:0%
+carrying it into the central nervous
+system the neural tube now because now
+
+ align:start position:0%
+system the neural tube now because now
+ 
+
+ align:start position:0%
+system the neural tube now because now
+we're invertebrates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're all chordates
+
+ align:start position:0%
+we're all chordates
+ 
+
+ align:start position:0%
+we're all chordates
+okay and then finally
+
+ align:start position:0%
+okay and then finally
+ 
+
+ align:start position:0%
+okay and then finally
+in amphibians reptiles birds and mammals
+
+ align:start position:0%
+in amphibians reptiles birds and mammals
+ 
+
+ align:start position:0%
+in amphibians reptiles birds and mammals
+the sensory cells innervating the body
+
+ align:start position:0%
+the sensory cells innervating the body
+ 
+
+ align:start position:0%
+the sensory cells innervating the body
+surface are have this
+
+ align:start position:0%
+surface are have this
+ 
+
+ align:start position:0%
+surface are have this
+we call it a pseudo-unipolar shape okay
+
+ align:start position:0%
+we call it a pseudo-unipolar shape okay
+ 
+
+ align:start position:0%
+we call it a pseudo-unipolar shape okay
+with the cell body off to the side
+
+ align:start position:0%
+with the cell body off to the side
+ 
+
+ align:start position:0%
+with the cell body off to the side
+dendritic part of the cell is out here
+
+ align:start position:0%
+dendritic part of the cell is out here
+ 
+
+ align:start position:0%
+dendritic part of the cell is out here
+and then the axon
+
+ align:start position:0%
+and then the axon
+ 
+
+ align:start position:0%
+and then the axon
+goes into the central nervous system
+
+ align:start position:0%
+goes into the central nervous system
+ 
+
+ align:start position:0%
+goes into the central nervous system
+this way
+
+ align:start position:0%
+this way
+ 
+
+ align:start position:0%
+this way
+so these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the outlines here show what we would
+
+ align:start position:0%
+the outlines here show what we would
+ 
+
+ align:start position:0%
+the outlines here show what we would
+call a peripheral
+
+ align:start position:0%
+call a peripheral
+ 
+
+ align:start position:0%
+call a peripheral
+ganglion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collections of those kinds of cells
+
+ align:start position:0%
+collections of those kinds of cells
+ 
+
+ align:start position:0%
+collections of those kinds of cells
+okay so now let's go back
+
+ align:start position:0%
+okay so now let's go back
+ 
+
+ align:start position:0%
+okay so now let's go back
+to the shmu brain now where the primary
+
+ align:start position:0%
+to the shmu brain now where the primary
+ 
+
+ align:start position:0%
+to the shmu brain now where the primary
+sensory neurons i've shown
+
+ align:start position:0%
+sensory neurons i've shown
+ 
+
+ align:start position:0%
+sensory neurons i've shown
+just three of them here
+
+ align:start position:0%
+just three of them here
+ 
+
+ align:start position:0%
+just three of them here
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+an example only one
+
+ align:start position:0%
+an example only one
+ 
+
+ align:start position:0%
+an example only one
+showing a cell that would be in the
+
+ align:start position:0%
+showing a cell that would be in the
+ 
+
+ align:start position:0%
+showing a cell that would be in the
+dorsal root ganglia
+
+ align:start position:0%
+dorsal root ganglia
+ 
+
+ align:start position:0%
+dorsal root ganglia
+in one of the dorsal root ganglia
+
+ align:start position:0%
+in one of the dorsal root ganglia
+ 
+
+ align:start position:0%
+in one of the dorsal root ganglia
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+next to the spinal cord
+
+ align:start position:0%
+next to the spinal cord
+ 
+
+ align:start position:0%
+next to the spinal cord
+so it's through the unipolar in shape
+
+ align:start position:0%
+so it's through the unipolar in shape
+ 
+
+ align:start position:0%
+so it's through the unipolar in shape
+it has its
+
+ align:start position:0%
+it has its
+ 
+
+ align:start position:0%
+it has its
+dendritic endings out here in the skin
+
+ align:start position:0%
+dendritic endings out here in the skin
+ 
+
+ align:start position:0%
+dendritic endings out here in the skin
+the axon starts there
+
+ align:start position:0%
+the axon starts there
+ 
+
+ align:start position:0%
+the axon starts there
+goes into the central nervous system
+
+ align:start position:0%
+goes into the central nervous system
+ 
+
+ align:start position:0%
+goes into the central nervous system
+where it connects with secondary sensory
+
+ align:start position:0%
+where it connects with secondary sensory
+ 
+
+ align:start position:0%
+where it connects with secondary sensory
+neurons okay
+
+ align:start position:0%
+neurons okay
+ 
+
+ align:start position:0%
+neurons okay
+here's another one this would be
+
+ align:start position:0%
+here's another one this would be
+ 
+
+ align:start position:0%
+here's another one this would be
+in the auditory or vestibular system and
+
+ align:start position:0%
+in the auditory or vestibular system and
+ 
+
+ align:start position:0%
+in the auditory or vestibular system and
+noted that it knows note that it has a
+
+ align:start position:0%
+noted that it knows note that it has a
+ 
+
+ align:start position:0%
+noted that it knows note that it has a
+bipolar shape there are many fewer of
+
+ align:start position:0%
+bipolar shape there are many fewer of
+ 
+
+ align:start position:0%
+bipolar shape there are many fewer of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+okay but the in the auditory system we
+
+ align:start position:0%
+okay but the in the auditory system we
+ 
+
+ align:start position:0%
+okay but the in the auditory system we
+have bipolar neurons
+
+ align:start position:0%
+have bipolar neurons
+ 
+
+ align:start position:0%
+have bipolar neurons
+the sensory endodendric and
+
+ align:start position:0%
+the sensory endodendric and
+ 
+
+ align:start position:0%
+the sensory endodendric and
+out in the cochlea
+
+ align:start position:0%
+out in the cochlea
+ 
+
+ align:start position:0%
+out in the cochlea
+or in the vestibular canals okay
+
+ align:start position:0%
+or in the vestibular canals okay
+ 
+
+ align:start position:0%
+or in the vestibular canals okay
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+the action potential has to go by the
+
+ align:start position:0%
+the action potential has to go by the
+ 
+
+ align:start position:0%
+the action potential has to go by the
+cell body it sort of jumps over it
+
+ align:start position:0%
+cell body it sort of jumps over it
+ 
+
+ align:start position:0%
+cell body it sort of jumps over it
+and the axon then continues into the
+
+ align:start position:0%
+and the axon then continues into the
+ 
+
+ align:start position:0%
+and the axon then continues into the
+central nervous system where you have
+
+ align:start position:0%
+central nervous system where you have
+ 
+
+ align:start position:0%
+central nervous system where you have
+the cochlear nuclei and the vestibular
+
+ align:start position:0%
+the cochlear nuclei and the vestibular
+ 
+
+ align:start position:0%
+the cochlear nuclei and the vestibular
+nuclei the secondary sensory cells of
+
+ align:start position:0%
+nuclei the secondary sensory cells of
+ 
+
+ align:start position:0%
+nuclei the secondary sensory cells of
+that those systems
+
+ align:start position:0%
+that those systems
+ 
+
+ align:start position:0%
+that those systems
+and finally here i show
+
+ align:start position:0%
+and finally here i show
+ 
+
+ align:start position:0%
+and finally here i show
+another primary sensory neuron on the
+
+ align:start position:0%
+another primary sensory neuron on the
+ 
+
+ align:start position:0%
+another primary sensory neuron on the
+olfactory an olfactory neuron an example
+
+ align:start position:0%
+olfactory an olfactory neuron an example
+ 
+
+ align:start position:0%
+olfactory an olfactory neuron an example
+of one olfactory and a note
+
+ align:start position:0%
+of one olfactory and a note
+ 
+
+ align:start position:0%
+of one olfactory and a note
+is just like the sensor all the sensory
+
+ align:start position:0%
+is just like the sensor all the sensory
+ 
+
+ align:start position:0%
+is just like the sensor all the sensory
+cells in the worm okay
+
+ align:start position:0%
+cells in the worm okay
+ 
+
+ align:start position:0%
+cells in the worm okay
+the cell body is insert at the surface
+
+ align:start position:0%
+the cell body is insert at the surface
+ 
+
+ align:start position:0%
+the cell body is insert at the surface
+and the epithelial layer
+
+ align:start position:0%
+and the epithelial layer
+ 
+
+ align:start position:0%
+and the epithelial layer
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+in the mucosal factory mucosal lining
+
+ align:start position:0%
+in the mucosal factory mucosal lining
+ 
+
+ align:start position:0%
+in the mucosal factory mucosal lining
+our nasal passages
+
+ align:start position:0%
+our nasal passages
+ 
+
+ align:start position:0%
+our nasal passages
+then it has a little dendritic part here
+
+ align:start position:0%
+then it has a little dendritic part here
+ 
+
+ align:start position:0%
+then it has a little dendritic part here
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+in a mucus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over these
+
+ align:start position:0%
+over these
+ 
+
+ align:start position:0%
+over these
+cells response to molecules dissolved in
+
+ align:start position:0%
+cells response to molecules dissolved in
+ 
+
+ align:start position:0%
+cells response to molecules dissolved in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+substance
+
+ align:start position:0%
+substance
+ 
+
+ align:start position:0%
+substance
+those molecules that trigger action
+
+ align:start position:0%
+those molecules that trigger action
+ 
+
+ align:start position:0%
+those molecules that trigger action
+potentials will the action potential
+
+ align:start position:0%
+potentials will the action potential
+ 
+
+ align:start position:0%
+potentials will the action potential
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+through the primary olfactory neurons
+
+ align:start position:0%
+through the primary olfactory neurons
+ 
+
+ align:start position:0%
+through the primary olfactory neurons
+axon into the brain part of the brain
+
+ align:start position:0%
+axon into the brain part of the brain
+ 
+
+ align:start position:0%
+axon into the brain part of the brain
+here we call the olfactory bulb where it
+
+ align:start position:0%
+here we call the olfactory bulb where it
+ 
+
+ align:start position:0%
+here we call the olfactory bulb where it
+contacts secondary sensory cells of the
+
+ align:start position:0%
+contacts secondary sensory cells of the
+ 
+
+ align:start position:0%
+contacts secondary sensory cells of the
+olfactory system okay so three examples
+
+ align:start position:0%
+olfactory system okay so three examples
+ 
+
+ align:start position:0%
+olfactory system okay so three examples
+of primary sensory neurons
+
+ align:start position:0%
+of primary sensory neurons
+ 
+
+ align:start position:0%
+of primary sensory neurons
+the secondary sensory neurons are the
+
+ align:start position:0%
+the secondary sensory neurons are the
+ 
+
+ align:start position:0%
+the secondary sensory neurons are the
+ones that get input to it
+
+ align:start position:0%
+ones that get input to it
+ 
+
+ align:start position:0%
+ones that get input to it
+everything else is an interneuron
+
+ align:start position:0%
+everything else is an interneuron
+ 
+
+ align:start position:0%
+everything else is an interneuron
+and of course we want to understand how
+
+ align:start position:0%
+and of course we want to understand how
+ 
+
+ align:start position:0%
+and of course we want to understand how
+are those interneurons connected what
+
+ align:start position:0%
+are those interneurons connected what
+ 
+
+ align:start position:0%
+are those interneurons connected what
+kind of systems do they form
+
+ align:start position:0%
+kind of systems do they form
+ 
+
+ align:start position:0%
+kind of systems do they form
+the only exception that we don't call
+
+ align:start position:0%
+the only exception that we don't call
+ 
+
+ align:start position:0%
+the only exception that we don't call
+interneuron here is the motor neuron and
+
+ align:start position:0%
+interneuron here is the motor neuron and
+ 
+
+ align:start position:0%
+interneuron here is the motor neuron and
+i'm showing it here in the little black
+
+ align:start position:0%
+i'm showing it here in the little black
+ 
+
+ align:start position:0%
+i'm showing it here in the little black
+triangles
+
+ align:start position:0%
+triangles
+ 
+
+ align:start position:0%
+triangles
+that you see in the
+
+ align:start position:0%
+that you see in the
+ 
+
+ align:start position:0%
+that you see in the
+ventral part
+
+ align:start position:0%
+ventral part
+ 
+
+ align:start position:0%
+ventral part
+of the brain in the spinal cord
+
+ align:start position:0%
+of the brain in the spinal cord
+ 
+
+ align:start position:0%
+of the brain in the spinal cord
+but also
+
+ align:start position:0%
+but also
+ 
+
+ align:start position:0%
+but also
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+hind brain and in the midbrain
+
+ align:start position:0%
+hind brain and in the midbrain
+ 
+
+ align:start position:0%
+hind brain and in the midbrain
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+where there are collections of these
+
+ align:start position:0%
+where there are collections of these
+ 
+
+ align:start position:0%
+where there are collections of these
+motor neurons motor neurons are defined
+
+ align:start position:0%
+motor neurons motor neurons are defined
+ 
+
+ align:start position:0%
+motor neurons motor neurons are defined
+as the neurons with an axon that goes
+
+ align:start position:0%
+as the neurons with an axon that goes
+ 
+
+ align:start position:0%
+as the neurons with an axon that goes
+out of the central nervous system
+
+ align:start position:0%
+out of the central nervous system
+ 
+
+ align:start position:0%
+out of the central nervous system
+okay and we have two kinds
+
+ align:start position:0%
+okay and we have two kinds
+ 
+
+ align:start position:0%
+okay and we have two kinds
+of motor neurons there and i've shown
+
+ align:start position:0%
+of motor neurons there and i've shown
+ 
+
+ align:start position:0%
+of motor neurons there and i've shown
+the two kinds
+
+ align:start position:0%
+the two kinds
+ 
+
+ align:start position:0%
+the two kinds
+here one type the axon goes to muscle
+
+ align:start position:0%
+here one type the axon goes to muscle
+ 
+
+ align:start position:0%
+here one type the axon goes to muscle
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+just striated muscle cells i've shown
+
+ align:start position:0%
+just striated muscle cells i've shown
+ 
+
+ align:start position:0%
+just striated muscle cells i've shown
+depicted the striations there to
+
+ align:start position:0%
+depicted the striations there to
+ 
+
+ align:start position:0%
+depicted the striations there to
+indicate a particular kind of muscle
+
+ align:start position:0%
+indicate a particular kind of muscle
+ 
+
+ align:start position:0%
+indicate a particular kind of muscle
+cell it's not a smooth muscle
+
+ align:start position:0%
+cell it's not a smooth muscle
+ 
+
+ align:start position:0%
+cell it's not a smooth muscle
+the other kind of motor neuron connects
+
+ align:start position:0%
+the other kind of motor neuron connects
+ 
+
+ align:start position:0%
+the other kind of motor neuron connects
+with a ganglion
+
+ align:start position:0%
+with a ganglion
+ 
+
+ align:start position:0%
+with a ganglion
+so we call it a preganglionic motor
+
+ align:start position:0%
+so we call it a preganglionic motor
+ 
+
+ align:start position:0%
+so we call it a preganglionic motor
+neuron
+
+ align:start position:0%
+neuron
+ 
+
+ align:start position:0%
+neuron
+of the autonomic nervous system the
+
+ align:start position:0%
+of the autonomic nervous system the
+ 
+
+ align:start position:0%
+of the autonomic nervous system the
+autonomic nervous system innervates
+
+ align:start position:0%
+autonomic nervous system innervates
+ 
+
+ align:start position:0%
+autonomic nervous system innervates
+smooth muscles and glands
+
+ align:start position:0%
+smooth muscles and glands
+ 
+
+ align:start position:0%
+smooth muscles and glands
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so there the connection is different it
+
+ align:start position:0%
+so there the connection is different it
+ 
+
+ align:start position:0%
+so there the connection is different it
+goes through a relay in a peripheral
+
+ align:start position:0%
+goes through a relay in a peripheral
+ 
+
+ align:start position:0%
+goes through a relay in a peripheral
+ganglion
+
+ align:start position:0%
+ganglion
+ 
+
+ align:start position:0%
+ganglion
+of the autonomic nervous system
+
+ align:start position:0%
+of the autonomic nervous system
+ 
+
+ align:start position:0%
+of the autonomic nervous system
+and then those cells
+
+ align:start position:0%
+and then those cells
+ 
+
+ align:start position:0%
+and then those cells
+in those ganglia connect to smooth
+
+ align:start position:0%
+in those ganglia connect to smooth
+ 
+
+ align:start position:0%
+in those ganglia connect to smooth
+muscle and gland tissue
+
+ align:start position:0%
+muscle and gland tissue
+ 
+
+ align:start position:0%
+muscle and gland tissue
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so two kinds of motor neurons
+
+ align:start position:0%
+so two kinds of motor neurons
+ 
+
+ align:start position:0%
+so two kinds of motor neurons
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we've defined now
+
+ align:start position:0%
+okay so we've defined now
+ 
+
+ align:start position:0%
+okay so we've defined now
+the subdivisions the primary sensory
+
+ align:start position:0%
+the subdivisions the primary sensory
+ 
+
+ align:start position:0%
+the subdivisions the primary sensory
+neurons secondary sensory neurons
+
+ align:start position:0%
+neurons secondary sensory neurons
+ 
+
+ align:start position:0%
+neurons secondary sensory neurons
+interneurons of the great intermediate
+
+ align:start position:0%
+interneurons of the great intermediate
+ 
+
+ align:start position:0%
+interneurons of the great intermediate
+net
+
+ align:start position:0%
+net
+ 
+
+ align:start position:0%
+net
+two kinds of motor neurons
+
+ align:start position:0%
+two kinds of motor neurons
+ 
+
+ align:start position:0%
+two kinds of motor neurons
+cranial nerves
+
+ align:start position:0%
+cranial nerves
+ 
+
+ align:start position:0%
+cranial nerves
+one and eight
+
+ align:start position:0%
+one and eight
+ 
+
+ align:start position:0%
+one and eight
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cranial nerve one you generally the
+
+ align:start position:0%
+cranial nerve one you generally the
+ 
+
+ align:start position:0%
+cranial nerve one you generally the
+cranial nerves are the nerves coming in
+
+ align:start position:0%
+cranial nerves are the nerves coming in
+ 
+
+ align:start position:0%
+cranial nerves are the nerves coming in
+the head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry in the head that come into the
+
+ align:start position:0%
+sorry in the head that come into the
+ 
+
+ align:start position:0%
+sorry in the head that come into the
+brain above the spinal cord and they're
+
+ align:start position:0%
+brain above the spinal cord and they're
+ 
+
+ align:start position:0%
+brain above the spinal cord and they're
+numbered from rostral claddle
+
+ align:start position:0%
+numbered from rostral claddle
+ 
+
+ align:start position:0%
+numbered from rostral claddle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+quite a few of them well over 20 in fact
+
+ align:start position:0%
+quite a few of them well over 20 in fact
+ 
+
+ align:start position:0%
+quite a few of them well over 20 in fact
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+there's only 12 major ones in humans and
+
+ align:start position:0%
+there's only 12 major ones in humans and
+ 
+
+ align:start position:0%
+there's only 12 major ones in humans and
+so we usually think of just 12 cranial
+
+ align:start position:0%
+so we usually think of just 12 cranial
+ 
+
+ align:start position:0%
+so we usually think of just 12 cranial
+nerves
+
+ align:start position:0%
+nerves
+ 
+
+ align:start position:0%
+nerves
+the first one the rostral one is the
+
+ align:start position:0%
+the first one the rostral one is the
+ 
+
+ align:start position:0%
+the first one the rostral one is the
+olfactory
+
+ align:start position:0%
+olfactory
+ 
+
+ align:start position:0%
+olfactory
+the eighth one
+
+ align:start position:0%
+the eighth one
+ 
+
+ align:start position:0%
+the eighth one
+is the auditory distributor
+
+ align:start position:0%
+is the auditory distributor
+ 
+
+ align:start position:0%
+is the auditory distributor
+okay and those are the only ones i'm
+
+ align:start position:0%
+okay and those are the only ones i'm
+ 
+
+ align:start position:0%
+okay and those are the only ones i'm
+showing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is why
+
+ align:start position:0%
+which is why
+ 
+
+ align:start position:0%
+which is why
+i put it here to be identified in the
+
+ align:start position:0%
+i put it here to be identified in the
+ 
+
+ align:start position:0%
+i put it here to be identified in the
+shrew brain here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now what happens to the input when it
+
+ align:start position:0%
+so now what happens to the input when it
+ 
+
+ align:start position:0%
+so now what happens to the input when it
+comes in and here we're going to focus
+
+ align:start position:0%
+comes in and here we're going to focus
+ 
+
+ align:start position:0%
+comes in and here we're going to focus
+on spinal cord initially
+
+ align:start position:0%
+on spinal cord initially
+ 
+
+ align:start position:0%
+on spinal cord initially
+but the other sensory systems have
+
+ align:start position:0%
+but the other sensory systems have
+ 
+
+ align:start position:0%
+but the other sensory systems have
+similar channels of conduction
+
+ align:start position:0%
+similar channels of conduction
+ 
+
+ align:start position:0%
+similar channels of conduction
+in every case we can talk about a local
+
+ align:start position:0%
+in every case we can talk about a local
+ 
+
+ align:start position:0%
+in every case we can talk about a local
+reflex channel
+
+ align:start position:0%
+reflex channel
+ 
+
+ align:start position:0%
+reflex channel
+cerebellar channel
+
+ align:start position:0%
+cerebellar channel
+ 
+
+ align:start position:0%
+cerebellar channel
+and leniscal channels plural okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're gonna
+
+ align:start position:0%
+and we're gonna
+ 
+
+ align:start position:0%
+and we're gonna
+learn all these terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll first talk about segmental
+
+ align:start position:0%
+we'll first talk about segmental
+ 
+
+ align:start position:0%
+we'll first talk about segmental
+reflexes
+
+ align:start position:0%
+reflexes
+ 
+
+ align:start position:0%
+reflexes
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll define
+
+ align:start position:0%
+and we'll define
+ 
+
+ align:start position:0%
+and we'll define
+dermatome and myotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here would be the we could call it also
+
+ align:start position:0%
+here would be the we could call it also
+ 
+
+ align:start position:0%
+here would be the we could call it also
+a local reflex channel we can follow
+
+ align:start position:0%
+a local reflex channel we can follow
+ 
+
+ align:start position:0%
+a local reflex channel we can follow
+input through a primary sensory neuron
+
+ align:start position:0%
+input through a primary sensory neuron
+ 
+
+ align:start position:0%
+input through a primary sensory neuron
+in the shmu brain here
+
+ align:start position:0%
+in the shmu brain here
+ 
+
+ align:start position:0%
+in the shmu brain here
+context secondary sensory cells and some
+
+ align:start position:0%
+context secondary sensory cells and some
+ 
+
+ align:start position:0%
+context secondary sensory cells and some
+of those have fairly short connections
+
+ align:start position:0%
+of those have fairly short connections
+ 
+
+ align:start position:0%
+of those have fairly short connections
+through interneurons reaching motor
+
+ align:start position:0%
+through interneurons reaching motor
+ 
+
+ align:start position:0%
+through interneurons reaching motor
+neurons
+
+ align:start position:0%
+neurons
+ 
+
+ align:start position:0%
+neurons
+now that all happens within one segment
+
+ align:start position:0%
+now that all happens within one segment
+ 
+
+ align:start position:0%
+now that all happens within one segment
+of the spinal cord the segment being
+
+ align:start position:0%
+of the spinal cord the segment being
+ 
+
+ align:start position:0%
+of the spinal cord the segment being
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+as the area connected with one spinal
+
+ align:start position:0%
+as the area connected with one spinal
+ 
+
+ align:start position:0%
+as the area connected with one spinal
+nerve one dorsal root
+
+ align:start position:0%
+nerve one dorsal root
+ 
+
+ align:start position:0%
+nerve one dorsal root
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's about 32 segments in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cord and if that then goes from sensory
+
+ align:start position:0%
+cord and if that then goes from sensory
+ 
+
+ align:start position:0%
+cord and if that then goes from sensory
+to motor within one segment contacts the
+
+ align:start position:0%
+to motor within one segment contacts the
+ 
+
+ align:start position:0%
+to motor within one segment contacts the
+motor neuron we would call a segmental
+
+ align:start position:0%
+motor neuron we would call a segmental
+ 
+
+ align:start position:0%
+motor neuron we would call a segmental
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+okay or local reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it comes in at one segment here but
+
+ align:start position:0%
+if it comes in at one segment here but
+ 
+
+ align:start position:0%
+if it comes in at one segment here but
+the output through interneurons connects
+
+ align:start position:0%
+the output through interneurons connects
+ 
+
+ align:start position:0%
+the output through interneurons connects
+with other segments in the chord
+
+ align:start position:0%
+with other segments in the chord
+ 
+
+ align:start position:0%
+with other segments in the chord
+then we would call it an intersegmental
+
+ align:start position:0%
+then we would call it an intersegmental
+ 
+
+ align:start position:0%
+then we would call it an intersegmental
+reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if it involves these long axons
+
+ align:start position:0%
+but if it involves these long axons
+ 
+
+ align:start position:0%
+but if it involves these long axons
+going up into the brain the liministical
+
+ align:start position:0%
+going up into the brain the liministical
+ 
+
+ align:start position:0%
+going up into the brain the liministical
+channels
+
+ align:start position:0%
+channels
+ 
+
+ align:start position:0%
+channels
+before it comes back
+
+ align:start position:0%
+before it comes back
+ 
+
+ align:start position:0%
+before it comes back
+if we're going to call it still a reflex
+
+ align:start position:0%
+if we're going to call it still a reflex
+ 
+
+ align:start position:0%
+if we're going to call it still a reflex
+we would call it a suprasegmental reflex
+
+ align:start position:0%
+we would call it a suprasegmental reflex
+ 
+
+ align:start position:0%
+we would call it a suprasegmental reflex
+okay because it involves conduction
+
+ align:start position:0%
+okay because it involves conduction
+ 
+
+ align:start position:0%
+okay because it involves conduction
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+supra
+
+ align:start position:0%
+supra
+ 
+
+ align:start position:0%
+supra
+above the segments of the spinal cord
+
+ align:start position:0%
+above the segments of the spinal cord
+ 
+
+ align:start position:0%
+above the segments of the spinal cord
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+if we're dealing with
+
+ align:start position:0%
+if we're dealing with
+ 
+
+ align:start position:0%
+if we're dealing with
+one dorsal root here
+
+ align:start position:0%
+one dorsal root here
+ 
+
+ align:start position:0%
+one dorsal root here
+which is a collection of axons of course
+
+ align:start position:0%
+which is a collection of axons of course
+ 
+
+ align:start position:0%
+which is a collection of axons of course
+coming through one spinal nerve
+
+ align:start position:0%
+coming through one spinal nerve
+ 
+
+ align:start position:0%
+coming through one spinal nerve
+those axons originate on the body
+
+ align:start position:0%
+those axons originate on the body
+ 
+
+ align:start position:0%
+those axons originate on the body
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+from just a limited
+
+ align:start position:0%
+from just a limited
+ 
+
+ align:start position:0%
+from just a limited
+part of the skin and we call the skin
+
+ align:start position:0%
+part of the skin and we call the skin
+ 
+
+ align:start position:0%
+part of the skin and we call the skin
+innervated by one
+
+ align:start position:0%
+innervated by one
+ 
+
+ align:start position:0%
+innervated by one
+spinal nerve we call it a dermatome and
+
+ align:start position:0%
+spinal nerve we call it a dermatome and
+ 
+
+ align:start position:0%
+spinal nerve we call it a dermatome and
+this is a dermatomal map
+
+ align:start position:0%
+this is a dermatomal map
+ 
+
+ align:start position:0%
+this is a dermatomal map
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+showing
+
+ align:start position:0%
+showing
+ 
+
+ align:start position:0%
+showing
+usually there's no
+
+ align:start position:0%
+usually there's no
+ 
+
+ align:start position:0%
+usually there's no
+first cervical segment
+
+ align:start position:0%
+first cervical segment
+ 
+
+ align:start position:0%
+first cervical segment
+dorsal root we start with c2 to c8
+
+ align:start position:0%
+dorsal root we start with c2 to c8
+ 
+
+ align:start position:0%
+dorsal root we start with c2 to c8
+and then the thoracic segments t1
+
+ align:start position:0%
+and then the thoracic segments t1
+ 
+
+ align:start position:0%
+and then the thoracic segments t1
+through 12
+
+ align:start position:0%
+through 12
+ 
+
+ align:start position:0%
+through 12
+5 lumbar segments and five sacral
+
+ align:start position:0%
+5 lumbar segments and five sacral
+ 
+
+ align:start position:0%
+5 lumbar segments and five sacral
+segments okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually because
+
+ align:start position:0%
+usually because
+ 
+
+ align:start position:0%
+usually because
+because the gel segments are not even
+
+ align:start position:0%
+because the gel segments are not even
+ 
+
+ align:start position:0%
+because the gel segments are not even
+indicated on these dermatol maps because
+
+ align:start position:0%
+indicated on these dermatol maps because
+ 
+
+ align:start position:0%
+indicated on these dermatol maps because
+they're not very large or important
+
+ align:start position:0%
+they're not very large or important
+ 
+
+ align:start position:0%
+they're not very large or important
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we put the human in a quadruped
+
+ align:start position:0%
+if we put the human in a quadruped
+ 
+
+ align:start position:0%
+if we put the human in a quadruped
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+we can see
+
+ align:start position:0%
+we can see
+ 
+
+ align:start position:0%
+we can see
+why those dermatomes are the way they
+
+ align:start position:0%
+why those dermatomes are the way they
+ 
+
+ align:start position:0%
+why those dermatomes are the way they
+are because in early development of
+
+ align:start position:0%
+are because in early development of
+ 
+
+ align:start position:0%
+are because in early development of
+course the limbs are very short and
+
+ align:start position:0%
+course the limbs are very short and
+ 
+
+ align:start position:0%
+course the limbs are very short and
+stubby when these things first develop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the body is segmented the same way
+
+ align:start position:0%
+so the body is segmented the same way
+ 
+
+ align:start position:0%
+so the body is segmented the same way
+the spinal cord is segmented if we look
+
+ align:start position:0%
+the spinal cord is segmented if we look
+ 
+
+ align:start position:0%
+the spinal cord is segmented if we look
+at it this way okay now why
+
+ align:start position:0%
+at it this way okay now why
+ 
+
+ align:start position:0%
+at it this way okay now why
+do we start the map with the c2
+
+ align:start position:0%
+do we start the map with the c2
+ 
+
+ align:start position:0%
+do we start the map with the c2
+innervation here
+
+ align:start position:0%
+innervation here
+ 
+
+ align:start position:0%
+innervation here
+in the middle of the head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+everything else is cranial nerve that's
+
+ align:start position:0%
+everything else is cranial nerve that's
+ 
+
+ align:start position:0%
+everything else is cranial nerve that's
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so the cranial nerves they'll
+
+ align:start position:0%
+okay so the cranial nerves they'll
+ 
+
+ align:start position:0%
+okay so the cranial nerves they'll
+innovate the face primarily the fifth
+
+ align:start position:0%
+innovate the face primarily the fifth
+ 
+
+ align:start position:0%
+innovate the face primarily the fifth
+cranial nerve
+
+ align:start position:0%
+cranial nerve
+ 
+
+ align:start position:0%
+cranial nerve
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+although the cranial nerves too but the
+
+ align:start position:0%
+although the cranial nerves too but the
+ 
+
+ align:start position:0%
+although the cranial nerves too but the
+skin
+
+ align:start position:0%
+skin
+ 
+
+ align:start position:0%
+skin
+is the skin surface of the
+
+ align:start position:0%
+is the skin surface of the
+ 
+
+ align:start position:0%
+is the skin surface of the
+face their forehead and face is the
+
+ align:start position:0%
+face their forehead and face is the
+ 
+
+ align:start position:0%
+face their forehead and face is the
+fifth cranial nerve
+
+ align:start position:0%
+fifth cranial nerve
+ 
+
+ align:start position:0%
+fifth cranial nerve
+then we have the
+
+ align:start position:0%
+then we have the
+ 
+
+ align:start position:0%
+then we have the
+cervical segments okay
+
+ align:start position:0%
+cervical segments okay
+ 
+
+ align:start position:0%
+cervical segments okay
+then the thoracic
+
+ align:start position:0%
+then the thoracic
+ 
+
+ align:start position:0%
+then the thoracic
+the lumbar and the sacral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+with this kind of map if you look at the
+
+ align:start position:0%
+with this kind of map if you look at the
+ 
+
+ align:start position:0%
+with this kind of map if you look at the
+dermatomes
+
+ align:start position:0%
+dermatomes
+ 
+
+ align:start position:0%
+dermatomes
+then we know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the caudal mouse part is right around
+
+ align:start position:0%
+the caudal mouse part is right around
+ 
+
+ align:start position:0%
+the caudal mouse part is right around
+the anus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the very tail end okay
+
+ align:start position:0%
+the very tail end okay
+ 
+
+ align:start position:0%
+the very tail end okay
+and the reason for these
+
+ align:start position:0%
+and the reason for these
+ 
+
+ align:start position:0%
+and the reason for these
+funny ways divided up in the legs and
+
+ align:start position:0%
+funny ways divided up in the legs and
+ 
+
+ align:start position:0%
+funny ways divided up in the legs and
+arms
+
+ align:start position:0%
+arms
+ 
+
+ align:start position:0%
+arms
+is because of the way those nerves grew
+
+ align:start position:0%
+is because of the way those nerves grew
+ 
+
+ align:start position:0%
+is because of the way those nerves grew
+into in development okay but basically
+
+ align:start position:0%
+into in development okay but basically
+ 
+
+ align:start position:0%
+into in development okay but basically
+they follow the dermatomal pattern that
+
+ align:start position:0%
+they follow the dermatomal pattern that
+ 
+
+ align:start position:0%
+they follow the dermatomal pattern that
+you see here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the innovation of adjacent dorsal
+
+ align:start position:0%
+now the innovation of adjacent dorsal
+ 
+
+ align:start position:0%
+now the innovation of adjacent dorsal
+roots here and here they
+
+ align:start position:0%
+roots here and here they
+ 
+
+ align:start position:0%
+roots here and here they
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cartoon here on the right they're
+
+ align:start position:0%
+cartoon here on the right they're
+ 
+
+ align:start position:0%
+cartoon here on the right they're
+showing
+
+ align:start position:0%
+showing
+ 
+
+ align:start position:0%
+showing
+they only show a single axon
+
+ align:start position:0%
+they only show a single axon
+ 
+
+ align:start position:0%
+they only show a single axon
+in each they're showing up a single
+
+ align:start position:0%
+in each they're showing up a single
+ 
+
+ align:start position:0%
+in each they're showing up a single
+peripheral nerve that may enter several
+
+ align:start position:0%
+peripheral nerve that may enter several
+ 
+
+ align:start position:0%
+peripheral nerve that may enter several
+spinal nerves so it goes in through
+
+ align:start position:0%
+spinal nerves so it goes in through
+ 
+
+ align:start position:0%
+spinal nerves so it goes in through
+several different dorsal roots
+
+ align:start position:0%
+several different dorsal roots
+ 
+
+ align:start position:0%
+several different dorsal roots
+that's what they're showing there
+
+ align:start position:0%
+that's what they're showing there
+ 
+
+ align:start position:0%
+that's what they're showing there
+and they show that
+
+ align:start position:0%
+and they show that
+ 
+
+ align:start position:0%
+and they show that
+out in the periphery it can come there
+
+ align:start position:0%
+out in the periphery it can come there
+ 
+
+ align:start position:0%
+out in the periphery it can come there
+are there is some overlap okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the way these innervate but it's a
+
+ align:start position:0%
+of the way these innervate but it's a
+ 
+
+ align:start position:0%
+of the way these innervate but it's a
+limited amount of overlap now how do
+
+ align:start position:0%
+limited amount of overlap now how do
+ 
+
+ align:start position:0%
+limited amount of overlap now how do
+those things how were they mapped
+
+ align:start position:0%
+those things how were they mapped
+ 
+
+ align:start position:0%
+those things how were they mapped
+well there was two major methods
+
+ align:start position:0%
+well there was two major methods
+ 
+
+ align:start position:0%
+well there was two major methods
+first of all the regions that become
+
+ align:start position:0%
+first of all the regions that become
+ 
+
+ align:start position:0%
+first of all the regions that become
+hypersensitive when a single spinal root
+
+ align:start position:0%
+hypersensitive when a single spinal root
+ 
+
+ align:start position:0%
+hypersensitive when a single spinal root
+is irritated
+
+ align:start position:0%
+is irritated
+ 
+
+ align:start position:0%
+is irritated
+of course you could stimulate it
+
+ align:start position:0%
+of course you could stimulate it
+ 
+
+ align:start position:0%
+of course you could stimulate it
+electrically but we usually don't
+
+ align:start position:0%
+electrically but we usually don't
+ 
+
+ align:start position:0%
+electrically but we usually don't
+experiment like that with human beings
+
+ align:start position:0%
+experiment like that with human beings
+ 
+
+ align:start position:0%
+experiment like that with human beings
+but we don't have to because they have
+
+ align:start position:0%
+but we don't have to because they have
+ 
+
+ align:start position:0%
+but we don't have to because they have
+problems with backs like
+
+ align:start position:0%
+problems with backs like
+ 
+
+ align:start position:0%
+problems with backs like
+inevitable discs can
+
+ align:start position:0%
+inevitable discs can
+ 
+
+ align:start position:0%
+inevitable discs can
+slip and herniate and put pressure on a
+
+ align:start position:0%
+slip and herniate and put pressure on a
+ 
+
+ align:start position:0%
+slip and herniate and put pressure on a
+dorsal root
+
+ align:start position:0%
+dorsal root
+ 
+
+ align:start position:0%
+dorsal root
+they can even transect another dorsal
+
+ align:start position:0%
+they can even transect another dorsal
+ 
+
+ align:start position:0%
+they can even transect another dorsal
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+usually they cause initially just
+
+ align:start position:0%
+usually they cause initially just
+ 
+
+ align:start position:0%
+usually they cause initially just
+irritation
+
+ align:start position:0%
+irritation
+ 
+
+ align:start position:0%
+irritation
+and then we can map the area of the body
+
+ align:start position:0%
+and then we can map the area of the body
+ 
+
+ align:start position:0%
+and then we can map the area of the body
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+shows the irritation
+
+ align:start position:0%
+shows the irritation
+ 
+
+ align:start position:0%
+shows the irritation
+the irritation of course results in
+
+ align:start position:0%
+the irritation of course results in
+ 
+
+ align:start position:0%
+the irritation of course results in
+action potential so it gives us feeling
+
+ align:start position:0%
+action potential so it gives us feeling
+ 
+
+ align:start position:0%
+action potential so it gives us feeling
+like it's coming from the skin like if
+
+ align:start position:0%
+like it's coming from the skin like if
+ 
+
+ align:start position:0%
+like it's coming from the skin like if
+we hit
+
+ align:start position:0%
+we hit
+ 
+
+ align:start position:0%
+we hit
+we hit a nerve which we you can hit a
+
+ align:start position:0%
+we hit a nerve which we you can hit a
+ 
+
+ align:start position:0%
+we hit a nerve which we you can hit a
+nerve in your elbow because it's very
+
+ align:start position:0%
+nerve in your elbow because it's very
+ 
+
+ align:start position:0%
+nerve in your elbow because it's very
+close to the surface there
+
+ align:start position:0%
+close to the surface there
+ 
+
+ align:start position:0%
+close to the surface there
+so that's why we call it the funny bone
+
+ align:start position:0%
+so that's why we call it the funny bone
+ 
+
+ align:start position:0%
+so that's why we call it the funny bone
+we can we can actually disturb it and
+
+ align:start position:0%
+we can we can actually disturb it and
+ 
+
+ align:start position:0%
+we can we can actually disturb it and
+fire action potentials there that would
+
+ align:start position:0%
+fire action potentials there that would
+ 
+
+ align:start position:0%
+fire action potentials there that would
+that's similar to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to this method of mapping a dermatome so
+
+ align:start position:0%
+to this method of mapping a dermatome so
+ 
+
+ align:start position:0%
+to this method of mapping a dermatome so
+we can map the hypersensitive regions we
+
+ align:start position:0%
+we can map the hypersensitive regions we
+ 
+
+ align:start position:0%
+we can map the hypersensitive regions we
+can also look at
+
+ align:start position:0%
+can also look at
+ 
+
+ align:start position:0%
+can also look at
+what happens in the rare cases where
+
+ align:start position:0%
+what happens in the rare cases where
+ 
+
+ align:start position:0%
+what happens in the rare cases where
+there's a severance of adjacent spinal
+
+ align:start position:0%
+there's a severance of adjacent spinal
+ 
+
+ align:start position:0%
+there's a severance of adjacent spinal
+nerves if there's a one nerve remaining
+
+ align:start position:0%
+nerves if there's a one nerve remaining
+ 
+
+ align:start position:0%
+nerves if there's a one nerve remaining
+and sort of as an island we'll see an
+
+ align:start position:0%
+and sort of as an island we'll see an
+ 
+
+ align:start position:0%
+and sort of as an island we'll see an
+area of remaining sensibility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's how these were mapped and
+
+ align:start position:0%
+so that's how these were mapped and
+ 
+
+ align:start position:0%
+so that's how these were mapped and
+sometimes we talk about a myotome also
+
+ align:start position:0%
+sometimes we talk about a myotome also
+ 
+
+ align:start position:0%
+sometimes we talk about a myotome also
+the corresponding muscles of the ventral
+
+ align:start position:0%
+the corresponding muscles of the ventral
+ 
+
+ align:start position:0%
+the corresponding muscles of the ventral
+root the same segment and there's a
+
+ align:start position:0%
+root the same segment and there's a
+ 
+
+ align:start position:0%
+root the same segment and there's a
+pretty good correspondence between the
+
+ align:start position:0%
+pretty good correspondence between the
+ 
+
+ align:start position:0%
+pretty good correspondence between the
+position of the dermatomes and myotones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i my timing was perfect today we're
+
+ align:start position:0%
+i my timing was perfect today we're
+ 
+
+ align:start position:0%
+i my timing was perfect today we're
+right at the end of the hour
\ No newline at end of file
diff --git a/MK3DduTjcrA.txt b/MK3DduTjcrA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eef17a34a81e6b892bd93a542348f57ead25a5e6
--- /dev/null
+++ b/MK3DduTjcrA.txt
@@ -0,0 +1,99 @@
+To illustrate how linear
+optimization works in revenue
+
+management, let us consider
+a simple example --
+
+a flight from New
+York to Los Angeles.
+
+In this flight, there are
+two types of economy fares,
+
+Early Bird fares that cost
+$238, and Last Minute fares
+
+that cost $617.
+
+In this flight, a
+Boeing 757 is used
+
+that has 166 economy seats.
+
+Demand for these prices
+has been forecasted
+
+using analytics tools,
+looking at historical data
+
+and incorporating
+models like time
+
+series or linear regression.
+
+Clearly, forecasts have
+errors, and therefore, we
+
+need to assess the
+sensitivity of our decisions
+
+to these errors.
+
+To illustrate the use
+of linear optimization,
+
+we assume that demand has
+already been forecasted.
+
+We'll illustrate how our
+decisions on how many discount
+
+seats to sell vary as the
+demand forecasts vary.
+
+If the demand for
+regular seats is
+
+50, and for discounted
+fares is 150,
+
+and the capacity is 166 seats,
+then the optimal allocation
+
+is going to be to sell
+the 50 seats to satisfy
+
+the regular demand, and then
+we allocate the remaining 116
+
+seats to the
+discounted fare class.
+
+If the regular demand
+increases to 100 seats,
+
+then we allocate these 100 seats
+to these customers, and only
+
+66 seats to discounted
+fare customers.
+
+Finally, if the regular
+demand increases to 200,
+
+then we allocate all of
+our capacity, 166 seats,
+
+to these customers.
+
+While this seems
+simple, what happens
+
+if we have 100 flights with
+connections in tens of fares?
+
+We'll next see how to formulate
+the problem mathematically
+
+and solve it in a systematic
+way, using linear optimization.
\ No newline at end of file
diff --git a/MWcO8ZTOQQQ.txt b/MWcO8ZTOQQQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b2c963fac59b27f656d545fb23493808d9829e59
--- /dev/null
+++ b/MWcO8ZTOQQQ.txt
@@ -0,0 +1,2611 @@
+align:start position:0%
+ 
+in this segment we look into the
+
+ align:start position:0%
+in this segment we look into the
+ 
+
+ align:start position:0%
+in this segment we look into the
+probability that the sum of N
+
+ align:start position:0%
+probability that the sum of N
+ 
+
+ align:start position:0%
+probability that the sum of N
+independent identically distributed
+
+ align:start position:0%
+independent identically distributed
+ 
+
+ align:start position:0%
+independent identically distributed
+random variables takes an abnormally
+
+ align:start position:0%
+random variables takes an abnormally
+ 
+
+ align:start position:0%
+random variables takes an abnormally
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+value we will get an upper bound on this
+
+ align:start position:0%
+value we will get an upper bound on this
+ 
+
+ align:start position:0%
+value we will get an upper bound on this
+quantity which is known as hings
+
+ align:start position:0%
+quantity which is known as hings
+ 
+
+ align:start position:0%
+quantity which is known as hings
+inequality this is an upper bound that
+
+ align:start position:0%
+inequality this is an upper bound that
+ 
+
+ align:start position:0%
+inequality this is an upper bound that
+applies to a special case although the
+
+ align:start position:0%
+applies to a special case although the
+ 
+
+ align:start position:0%
+applies to a special case although the
+method actually generalizes here is the
+
+ align:start position:0%
+method actually generalizes here is the
+ 
+
+ align:start position:0%
+method actually generalizes here is the
+special case that we will consider the
+
+ align:start position:0%
+special case that we will consider the
+ 
+
+ align:start position:0%
+special case that we will consider the
+random variables the XIs are equally
+
+ align:start position:0%
+random variables the XIs are equally
+ 
+
+ align:start position:0%
+random variables the XIs are equally
+likely to take the values minus one and
+
+ align:start position:0%
+likely to take the values minus one and
+ 
+
+ align:start position:0%
+likely to take the values minus one and
++ one with equal
+
+ align:start position:0%
++ one with equal
+ 
+
+ align:start position:0%
++ one with equal
+probability and we're interested in the
+
+ align:start position:0%
+probability and we're interested in the
+ 
+
+ align:start position:0%
+probability and we're interested in the
+random variable which is the sum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X's what do we know about this random
+
+ align:start position:0%
+X's what do we know about this random
+ 
+
+ align:start position:0%
+X's what do we know about this random
+variable well the expected value of each
+
+ align:start position:0%
+variable well the expected value of each
+ 
+
+ align:start position:0%
+variable well the expected value of each
+one of the XIs is equal to zero because
+
+ align:start position:0%
+one of the XIs is equal to zero because
+ 
+
+ align:start position:0%
+one of the XIs is equal to zero because
+the distribution is symmetric and also
+
+ align:start position:0%
+the distribution is symmetric and also
+ 
+
+ align:start position:0%
+the distribution is symmetric and also
+the distance of XI from the mean has
+
+ align:start position:0%
+the distance of XI from the mean has
+ 
+
+ align:start position:0%
+the distance of XI from the mean has
+always magnitude one and for this reason
+
+ align:start position:0%
+always magnitude one and for this reason
+ 
+
+ align:start position:0%
+always magnitude one and for this reason
+the variance of the x i is equal to one
+
+ align:start position:0%
+the variance of the x i is equal to one
+ 
+
+ align:start position:0%
+the variance of the x i is equal to one
+for this reason the random variable y
+
+ align:start position:0%
+for this reason the random variable y
+ 
+
+ align:start position:0%
+for this reason the random variable y
+has a mean of
+
+ align:start position:0%
+has a mean of
+ 
+
+ align:start position:0%
+has a mean of
+zero and a variance equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n now what do we know about the random
+
+ align:start position:0%
+n now what do we know about the random
+ 
+
+ align:start position:0%
+n now what do we know about the random
+variable y by the center limit theorem y
+
+ align:start position:0%
+variable y by the center limit theorem y
+ 
+
+ align:start position:0%
+variable y by the center limit theorem y
+has an approximately nor normal
+
+ align:start position:0%
+has an approximately nor normal
+ 
+
+ align:start position:0%
+has an approximately nor normal
+distribution the distribution is
+
+ align:start position:0%
+distribution the distribution is
+ 
+
+ align:start position:0%
+distribution the distribution is
+centered at
+
+ align:start position:0%
+centered at
+ 
+
+ align:start position:0%
+centered at
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+also the random variable y over square
+
+ align:start position:0%
+also the random variable y over square
+ 
+
+ align:start position:0%
+also the random variable y over square
+otk of n this is a standardized random
+
+ align:start position:0%
+otk of n this is a standardized random
+ 
+
+ align:start position:0%
+otk of n this is a standardized random
+variable so it's approximately normal
+
+ align:start position:0%
+variable so it's approximately normal
+ 
+
+ align:start position:0%
+variable so it's approximately normal
+and so the probability that this number
+
+ align:start position:0%
+and so the probability that this number
+ 
+
+ align:start position:0%
+and so the probability that this number
+is larger than or equal to some a is
+
+ align:start position:0%
+is larger than or equal to some a is
+ 
+
+ align:start position:0%
+is larger than or equal to some a is
+approximately 1 minus the cumulative of
+
+ align:start position:0%
+approximately 1 minus the cumulative of
+ 
+
+ align:start position:0%
+approximately 1 minus the cumulative of
+the standard normal so F here stands for
+
+ align:start position:0%
+the standard normal so F here stands for
+ 
+
+ align:start position:0%
+the standard normal so F here stands for
+the standard normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CDF what does this tell us it tells us
+
+ align:start position:0%
+CDF what does this tell us it tells us
+ 
+
+ align:start position:0%
+CDF what does this tell us it tells us
+that if we take somewhere here the
+
+ align:start position:0%
+that if we take somewhere here the
+ 
+
+ align:start position:0%
+that if we take somewhere here the
+number Square < TK of n *
+
+ align:start position:0%
+number Square < TK of n *
+ 
+
+ align:start position:0%
+number Square < TK of n *
+a then this probability down here in the
+
+ align:start position:0%
+a then this probability down here in the
+ 
+
+ align:start position:0%
+a then this probability down here in the
+tail is approximately constant no matter
+
+ align:start position:0%
+tail is approximately constant no matter
+ 
+
+ align:start position:0%
+tail is approximately constant no matter
+what n is and this particular tells us
+
+ align:start position:0%
+what n is and this particular tells us
+ 
+
+ align:start position:0%
+what n is and this particular tells us
+that values of the order of square root
+
+ align:start position:0%
+that values of the order of square root
+ 
+
+ align:start position:0%
+that values of the order of square root
+n are fairly likely to
+
+ align:start position:0%
+n are fairly likely to
+ 
+
+ align:start position:0%
+n are fairly likely to
+occur however what we're interested in
+
+ align:start position:0%
+occur however what we're interested in
+ 
+
+ align:start position:0%
+occur however what we're interested in
+here is not being larger than square
+
+ align:start position:0%
+here is not being larger than square
+ 
+
+ align:start position:0%
+here is not being larger than square
+root n * a we're interested in being
+
+ align:start position:0%
+root n * a we're interested in being
+ 
+
+ align:start position:0%
+root n * a we're interested in being
+larger than n * a so we're talking about
+
+ align:start position:0%
+larger than n * a so we're talking about
+ 
+
+ align:start position:0%
+larger than n * a so we're talking about
+what happens further down in the tail of
+
+ align:start position:0%
+what happens further down in the tail of
+ 
+
+ align:start position:0%
+what happens further down in the tail of
+the distribution so if we take here n *
+
+ align:start position:0%
+the distribution so if we take here n *
+ 
+
+ align:start position:0%
+the distribution so if we take here n *
+a we're looking at this prob probability
+
+ align:start position:0%
+a we're looking at this prob probability
+ 
+
+ align:start position:0%
+a we're looking at this prob probability
+down here and we want to ask how small
+
+ align:start position:0%
+down here and we want to ask how small
+ 
+
+ align:start position:0%
+down here and we want to ask how small
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+probability well we have chfs in
+
+ align:start position:0%
+probability well we have chfs in
+ 
+
+ align:start position:0%
+probability well we have chfs in
+equality and chf's inequality tells us
+
+ align:start position:0%
+equality and chf's inequality tells us
+ 
+
+ align:start position:0%
+equality and chf's inequality tells us
+that the probability of Y being larger
+
+ align:start position:0%
+that the probability of Y being larger
+ 
+
+ align:start position:0%
+that the probability of Y being larger
+than a certain number is less than or
+
+ align:start position:0%
+than a certain number is less than or
+ 
+
+ align:start position:0%
+than a certain number is less than or
+equal to the variance of Y divided by
+
+ align:start position:0%
+equal to the variance of Y divided by
+ 
+
+ align:start position:0%
+equal to the variance of Y divided by
+the square of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number and in this case since the
+
+ align:start position:0%
+number and in this case since the
+ 
+
+ align:start position:0%
+number and in this case since the
+variance is n this is 1 / n a s
+
+ align:start position:0%
+variance is n this is 1 / n a s
+ 
+
+ align:start position:0%
+variance is n this is 1 / n a s
+so CH Bish's inequality tells us that
+
+ align:start position:0%
+so CH Bish's inequality tells us that
+ 
+
+ align:start position:0%
+so CH Bish's inequality tells us that
+this probability goes to zero and it
+
+ align:start position:0%
+this probability goes to zero and it
+ 
+
+ align:start position:0%
+this probability goes to zero and it
+goes to zero at least as fast as 1 / n
+
+ align:start position:0%
+goes to zero at least as fast as 1 / n
+ 
+
+ align:start position:0%
+goes to zero at least as fast as 1 / n
+goes to zero however it turns out that
+
+ align:start position:0%
+goes to zero however it turns out that
+ 
+
+ align:start position:0%
+goes to zero however it turns out that
+this is extremely conservative herting
+
+ align:start position:0%
+this is extremely conservative herting
+ 
+
+ align:start position:0%
+this is extremely conservative herting
+inequality which we are going to
+
+ align:start position:0%
+inequality which we are going to
+ 
+
+ align:start position:0%
+inequality which we are going to
+establish tells us something much
+
+ align:start position:0%
+establish tells us something much
+ 
+
+ align:start position:0%
+establish tells us something much
+stronger it tells us that this tail
+
+ align:start position:0%
+stronger it tells us that this tail
+ 
+
+ align:start position:0%
+stronger it tells us that this tail
+probability down here Falls
+
+ align:start position:0%
+probability down here Falls
+ 
+
+ align:start position:0%
+probability down here Falls
+exponentially with
+
+ align:start position:0%
+exponentially with
+ 
+
+ align:start position:0%
+exponentially with
+n so this is what we want to show and
+
+ align:start position:0%
+n so this is what we want to show and
+ 
+
+ align:start position:0%
+n so this is what we want to show and
+let us get started to see how the
+
+ align:start position:0%
+let us get started to see how the
+ 
+
+ align:start position:0%
+let us get started to see how the
+derivation
+
+ align:start position:0%
+derivation
+ 
+
+ align:start position:0%
+derivation
+goes the derivation relies on a
+
+ align:start position:0%
+goes the derivation relies on a
+ 
+
+ align:start position:0%
+goes the derivation relies on a
+beautiful
+
+ align:start position:0%
+beautiful
+ 
+
+ align:start position:0%
+beautiful
+trick instead of looking at this event
+
+ align:start position:0%
+trick instead of looking at this event
+ 
+
+ align:start position:0%
+trick instead of looking at this event
+here we're going to look at the
+
+ align:start position:0%
+here we're going to look at the
+ 
+
+ align:start position:0%
+here we're going to look at the
+following equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+event let us fix some number
+
+ align:start position:0%
+event let us fix some number
+ 
+
+ align:start position:0%
+event let us fix some number
+s we're going to leave the choice of s
+
+ align:start position:0%
+s we're going to leave the choice of s
+ 
+
+ align:start position:0%
+s we're going to leave the choice of s
+free for now
+
+ align:start position:0%
+free for now
+ 
+
+ align:start position:0%
+free for now
+it is only that we're going to assume
+
+ align:start position:0%
+it is only that we're going to assume
+ 
+
+ align:start position:0%
+it is only that we're going to assume
+that s is a positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number and throughout we're also
+
+ align:start position:0%
+number and throughout we're also
+ 
+
+ align:start position:0%
+number and throughout we're also
+assuming that a is also a positive
+
+ align:start position:0%
+assuming that a is also a positive
+ 
+
+ align:start position:0%
+assuming that a is also a positive
+number now we look at this quantity and
+
+ align:start position:0%
+number now we look at this quantity and
+ 
+
+ align:start position:0%
+number now we look at this quantity and
+the event that this quantity is larger
+
+ align:start position:0%
+the event that this quantity is larger
+ 
+
+ align:start position:0%
+the event that this quantity is larger
+than or equal to e to the s n *
+
+ align:start position:0%
+than or equal to e to the s n *
+ 
+
+ align:start position:0%
+than or equal to e to the s n *
+a now this sum is larger than or equal
+
+ align:start position:0%
+a now this sum is larger than or equal
+ 
+
+ align:start position:0%
+a now this sum is larger than or equal
+to na a if and only if this quantity is
+
+ align:start position:0%
+to na a if and only if this quantity is
+ 
+
+ align:start position:0%
+to na a if and only if this quantity is
+larger than or equal to e to the S NA a
+
+ align:start position:0%
+larger than or equal to e to the S NA a
+ 
+
+ align:start position:0%
+larger than or equal to e to the S NA a
+this is because A and S are both
+
+ align:start position:0%
+this is because A and S are both
+ 
+
+ align:start position:0%
+this is because A and S are both
+positive so the direction of the
+
+ align:start position:0%
+positive so the direction of the
+ 
+
+ align:start position:0%
+positive so the direction of the
+inequalities does not get reversed and
+
+ align:start position:0%
+inequalities does not get reversed and
+ 
+
+ align:start position:0%
+inequalities does not get reversed and
+also because the exponential function is
+
+ align:start position:0%
+also because the exponential function is
+ 
+
+ align:start position:0%
+also because the exponential function is
+monotonic so this event is the same as
+
+ align:start position:0%
+monotonic so this event is the same as
+ 
+
+ align:start position:0%
+monotonic so this event is the same as
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+event so we will try to say something
+
+ align:start position:0%
+event so we will try to say something
+ 
+
+ align:start position:0%
+event so we will try to say something
+about the probability of this event how
+
+ align:start position:0%
+about the probability of this event how
+ 
+
+ align:start position:0%
+about the probability of this event how
+are we going to do it we will use the
+
+ align:start position:0%
+are we going to do it we will use the
+ 
+
+ align:start position:0%
+are we going to do it we will use the
+mark of inequality where Z is the random
+
+ align:start position:0%
+mark of inequality where Z is the random
+ 
+
+ align:start position:0%
+mark of inequality where Z is the random
+variable that appears here so by Mark of
+
+ align:start position:0%
+variable that appears here so by Mark of
+ 
+
+ align:start position:0%
+variable that appears here so by Mark of
+inequality this probability is less than
+
+ align:start position:0%
+inequality this probability is less than
+ 
+
+ align:start position:0%
+inequality this probability is less than
+or equal to the expected value of the
+
+ align:start position:0%
+or equal to the expected value of the
+ 
+
+ align:start position:0%
+or equal to the expected value of the
+random variable that we are dealing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with divided by this value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the exponential of a sum we can
+
+ align:start position:0%
+now the exponential of a sum we can
+ 
+
+ align:start position:0%
+now the exponential of a sum we can
+Factor it as a product of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponentials and then we use the
+
+ align:start position:0%
+exponentials and then we use the
+ 
+
+ align:start position:0%
+exponentials and then we use the
+assumption that the X's are
+
+ align:start position:0%
+assumption that the X's are
+ 
+
+ align:start position:0%
+assumption that the X's are
+independent since the X's are
+
+ align:start position:0%
+independent since the X's are
+ 
+
+ align:start position:0%
+independent since the X's are
+independent e to the sx1 is independent
+
+ align:start position:0%
+independent e to the sx1 is independent
+ 
+
+ align:start position:0%
+independent e to the sx1 is independent
+from e to the sx2 and so on and so we
+
+ align:start position:0%
+from e to the sx2 and so on and so we
+ 
+
+ align:start position:0%
+from e to the sx2 and so on and so we
+have the expected value of a product of
+
+ align:start position:0%
+have the expected value of a product of
+ 
+
+ align:start position:0%
+have the expected value of a product of
+independent random variables and so this
+
+ align:start position:0%
+independent random variables and so this
+ 
+
+ align:start position:0%
+independent random variables and so this
+is equal to the product of the
+
+ align:start position:0%
+is equal to the product of the
+ 
+
+ align:start position:0%
+is equal to the product of the
+expectations so we are going to multiply
+
+ align:start position:0%
+expectations so we are going to multiply
+ 
+
+ align:start position:0%
+expectations so we are going to multiply
+the expected value of e to the S
+
+ align:start position:0%
+the expected value of e to the S
+ 
+
+ align:start position:0%
+the expected value of e to the S
+X1 with the expected value of e to the
+
+ align:start position:0%
+X1 with the expected value of e to the
+ 
+
+ align:start position:0%
+X1 with the expected value of e to the
+sx2 and so on but because all the XIs
+
+ align:start position:0%
+sx2 and so on but because all the XIs
+ 
+
+ align:start position:0%
+sx2 and so on but because all the XIs
+are identically distributed the terms
+
+ align:start position:0%
+are identically distributed the terms
+ 
+
+ align:start position:0%
+are identically distributed the terms
+that we get are all the same so we get
+
+ align:start position:0%
+that we get are all the same so we get
+ 
+
+ align:start position:0%
+that we get are all the same so we get
+this term to the nth power divided Again
+
+ align:start position:0%
+this term to the nth power divided Again
+ 
+
+ align:start position:0%
+this term to the nth power divided Again
+by e to the SN
+
+ align:start position:0%
+by e to the SN
+ 
+
+ align:start position:0%
+by e to the SN
+a or we can write this in more
+
+ align:start position:0%
+a or we can write this in more
+ 
+
+ align:start position:0%
+a or we can write this in more
+suggestive form as
+
+ align:start position:0%
+suggestive form as
+ 
+
+ align:start position:0%
+suggestive form as
+follows it's the expected value of e to
+
+ align:start position:0%
+follows it's the expected value of e to
+ 
+
+ align:start position:0%
+follows it's the expected value of e to
+the S
+
+ align:start position:0%
+the S
+ 
+
+ align:start position:0%
+the S
+X1 divided by e to the sa a all that to
+
+ align:start position:0%
+X1 divided by e to the sa a all that to
+ 
+
+ align:start position:0%
+X1 divided by e to the sa a all that to
+the nth power so think of that as being
+
+ align:start position:0%
+the nth power so think of that as being
+ 
+
+ align:start position:0%
+the nth power so think of that as being
+some number raw to the nth
+
+ align:start position:0%
+some number raw to the nth
+ 
+
+ align:start position:0%
+some number raw to the nth
+power when is this bound going to be
+
+ align:start position:0%
+power when is this bound going to be
+ 
+
+ align:start position:0%
+power when is this bound going to be
+interesting it's going to be interesting
+
+ align:start position:0%
+interesting it's going to be interesting
+ 
+
+ align:start position:0%
+interesting it's going to be interesting
+if raow is less than one because in that
+
+ align:start position:0%
+if raow is less than one because in that
+ 
+
+ align:start position:0%
+if raow is less than one because in that
+case this bound Falls exponentially with
+
+ align:start position:0%
+case this bound Falls exponentially with
+ 
+
+ align:start position:0%
+case this bound Falls exponentially with
+n and so this probability in particular
+
+ align:start position:0%
+n and so this probability in particular
+ 
+
+ align:start position:0%
+n and so this probability in particular
+will fall exponentially with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n the key here is that we have freedom
+
+ align:start position:0%
+n the key here is that we have freedom
+ 
+
+ align:start position:0%
+n the key here is that we have freedom
+to choose s for any value of s we obtain
+
+ align:start position:0%
+to choose s for any value of s we obtain
+ 
+
+ align:start position:0%
+to choose s for any value of s we obtain
+an upper bound we're going to choose s
+
+ align:start position:0%
+an upper bound we're going to choose s
+ 
+
+ align:start position:0%
+an upper bound we're going to choose s
+so that we get the most informative or a
+
+ align:start position:0%
+so that we get the most informative or a
+ 
+
+ align:start position:0%
+so that we get the most informative or a
+most powerful upper
+
+ align:start position:0%
+most powerful upper
+ 
+
+ align:start position:0%
+most powerful upper
+bound so let us continue to see what we
+
+ align:start position:0%
+bound so let us continue to see what we
+ 
+
+ align:start position:0%
+bound so let us continue to see what we
+can do first let us write down what this
+
+ align:start position:0%
+can do first let us write down what this
+ 
+
+ align:start position:0%
+can do first let us write down what this
+expected value
+
+ align:start position:0%
+expected value
+ 
+
+ align:start position:0%
+expected value
+is since
+
+ align:start position:0%
+is since
+ 
+
+ align:start position:0%
+is since
+X1 takes values minus one or+ one with
+
+ align:start position:0%
+X1 takes values minus one or+ one with
+ 
+
+ align:start position:0%
+X1 takes values minus one or+ one with
+equal probability this expectation is
+
+ align:start position:0%
+equal probability this expectation is
+ 
+
+ align:start position:0%
+equal probability this expectation is
+the following with probability 1 12 X1
+
+ align:start position:0%
+the following with probability 1 12 X1
+ 
+
+ align:start position:0%
+the following with probability 1 12 X1
+takes the value of one and so this
+
+ align:start position:0%
+takes the value of one and so this
+ 
+
+ align:start position:0%
+takes the value of one and so this
+random variable is e to the S and with
+
+ align:start position:0%
+random variable is e to the S and with
+ 
+
+ align:start position:0%
+random variable is e to the S and with
+probability 1/2 it takes the value minus
+
+ align:start position:0%
+probability 1/2 it takes the value minus
+ 
+
+ align:start position:0%
+probability 1/2 it takes the value minus
+one in which case this random variable
+
+ align:start position:0%
+one in which case this random variable
+ 
+
+ align:start position:0%
+one in which case this random variable
+is e to the minus s so this is the
+
+ align:start position:0%
+is e to the minus s so this is the
+ 
+
+ align:start position:0%
+is e to the minus s so this is the
+expectation in the numerator and we
+
+ align:start position:0%
+expectation in the numerator and we
+ 
+
+ align:start position:0%
+expectation in the numerator and we
+write again the term in the
+
+ align:start position:0%
+write again the term in the
+ 
+
+ align:start position:0%
+write again the term in the
+denominator and we have all this to the
+
+ align:start position:0%
+denominator and we have all this to the
+ 
+
+ align:start position:0%
+denominator and we have all this to the
+power n if we can choose s so that this
+
+ align:start position:0%
+power n if we can choose s so that this
+ 
+
+ align:start position:0%
+power n if we can choose s so that this
+quantity is less than one we will have
+
+ align:start position:0%
+quantity is less than one we will have
+ 
+
+ align:start position:0%
+quantity is less than one we will have
+achieved our
+
+ align:start position:0%
+achieved our
+ 
+
+ align:start position:0%
+achieved our
+objective can we do
+
+ align:start position:0%
+objective can we do
+ 
+
+ align:start position:0%
+objective can we do
+that let's see let's look at the
+
+ align:start position:0%
+that let's see let's look at the
+ 
+
+ align:start position:0%
+that let's see let's look at the
+numerator as a function of
+
+ align:start position:0%
+numerator as a function of
+ 
+
+ align:start position:0%
+numerator as a function of
+s when s is equal to zero we have 1 + 1/
+
+ align:start position:0%
+s when s is equal to zero we have 1 + 1/
+ 
+
+ align:start position:0%
+s when s is equal to zero we have 1 + 1/
+by2 that gives us
+
+ align:start position:0%
+by2 that gives us
+ 
+
+ align:start position:0%
+by2 that gives us
+1 and then as s moves away from zero
+
+ align:start position:0%
+1 and then as s moves away from zero
+ 
+
+ align:start position:0%
+1 and then as s moves away from zero
+this function will have this kind of
+
+ align:start position:0%
+this function will have this kind of
+ 
+
+ align:start position:0%
+this function will have this kind of
+shape and it is symmet ATC around zero
+
+ align:start position:0%
+shape and it is symmet ATC around zero
+ 
+
+ align:start position:0%
+shape and it is symmet ATC around zero
+because we have an S and A minus s
+
+ align:start position:0%
+because we have an S and A minus s
+ 
+
+ align:start position:0%
+because we have an S and A minus s
+here in particular the derivative of
+
+ align:start position:0%
+here in particular the derivative of
+ 
+
+ align:start position:0%
+here in particular the derivative of
+this function is 0 at 0o let's look at
+
+ align:start position:0%
+this function is 0 at 0o let's look at
+ 
+
+ align:start position:0%
+this function is 0 at 0o let's look at
+the denominator term the denominator
+
+ align:start position:0%
+the denominator term the denominator
+ 
+
+ align:start position:0%
+the denominator term the denominator
+term is an
+
+ align:start position:0%
+term is an
+ 
+
+ align:start position:0%
+term is an
+exponential a is a positive number so
+
+ align:start position:0%
+exponential a is a positive number so
+ 
+
+ align:start position:0%
+exponential a is a positive number so
+it's an exponential that has a shape of
+
+ align:start position:0%
+it's an exponential that has a shape of
+ 
+
+ align:start position:0%
+it's an exponential that has a shape of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind the important thing to notice is
+
+ align:start position:0%
+kind the important thing to notice is
+ 
+
+ align:start position:0%
+kind the important thing to notice is
+that this exponential has a positive
+
+ align:start position:0%
+that this exponential has a positive
+ 
+
+ align:start position:0%
+that this exponential has a positive
+derivative at
+
+ align:start position:0%
+derivative at
+ 
+
+ align:start position:0%
+derivative at
+zero what does that tell us that at
+
+ align:start position:0%
+zero what does that tell us that at
+ 
+
+ align:start position:0%
+zero what does that tell us that at
+least in the vicinity of
+
+ align:start position:0%
+least in the vicinity of
+ 
+
+ align:start position:0%
+least in the vicinity of
+zero this term the denominator is going
+
+ align:start position:0%
+zero this term the denominator is going
+ 
+
+ align:start position:0%
+zero this term the denominator is going
+to be larger than the numerator term and
+
+ align:start position:0%
+to be larger than the numerator term and
+ 
+
+ align:start position:0%
+to be larger than the numerator term and
+that implies that in the vicinity of
+
+ align:start position:0%
+that implies that in the vicinity of
+ 
+
+ align:start position:0%
+that implies that in the vicinity of
+zero this fraction is going to be less
+
+ align:start position:0%
+zero this fraction is going to be less
+ 
+
+ align:start position:0%
+zero this fraction is going to be less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+one and we will have achieved our goal
+
+ align:start position:0%
+one and we will have achieved our goal
+ 
+
+ align:start position:0%
+one and we will have achieved our goal
+of an exponentially decay G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound so the conclusion is that for
+
+ align:start position:0%
+bound so the conclusion is that for
+ 
+
+ align:start position:0%
+bound so the conclusion is that for
+small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s we have that raw is less than
+
+ align:start position:0%
+s we have that raw is less than
+ 
+
+ align:start position:0%
+s we have that raw is less than
+one now we would like to get an explicit
+
+ align:start position:0%
+one now we would like to get an explicit
+ 
+
+ align:start position:0%
+one now we would like to get an explicit
+value for raw and we will do that by
+
+ align:start position:0%
+value for raw and we will do that by
+ 
+
+ align:start position:0%
+value for raw and we will do that by
+fixing a specific value for S it turns
+
+ align:start position:0%
+fixing a specific value for S it turns
+ 
+
+ align:start position:0%
+fixing a specific value for S it turns
+out that if we set s to be equal to a
+
+ align:start position:0%
+out that if we set s to be equal to a
+ 
+
+ align:start position:0%
+out that if we set s to be equal to a
+then the bound that we get is going to
+
+ align:start position:0%
+then the bound that we get is going to
+ 
+
+ align:start position:0%
+then the bound that we get is going to
+be that this probability here is less
+
+ align:start position:0%
+be that this probability here is less
+ 
+
+ align:start position:0%
+be that this probability here is less
+than or equal to e to Theus N A
+
+ align:start position:0%
+than or equal to e to Theus N A
+ 
+
+ align:start position:0%
+than or equal to e to Theus N A
+2 over
+
+ align:start position:0%
+2 over
+ 
+
+ align:start position:0%
+2 over
+2 and this is the hefting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound at this point you may just
+
+ align:start position:0%
+bound at this point you may just
+ 
+
+ align:start position:0%
+bound at this point you may just
+pause or if you're curious you can
+
+ align:start position:0%
+pause or if you're curious you can
+ 
+
+ align:start position:0%
+pause or if you're curious you can
+continue with this video to see the
+
+ align:start position:0%
+continue with this video to see the
+ 
+
+ align:start position:0%
+continue with this video to see the
+algebraic manipulations involved in
+
+ align:start position:0%
+algebraic manipulations involved in
+ 
+
+ align:start position:0%
+algebraic manipulations involved in
+order to show that this expression is
+
+ align:start position:0%
+order to show that this expression is
+ 
+
+ align:start position:0%
+order to show that this expression is
+less than or equal to that
+
+ align:start position:0%
+less than or equal to that
+ 
+
+ align:start position:0%
+less than or equal to that
+expression but before going there I
+
+ align:start position:0%
+expression but before going there I
+ 
+
+ align:start position:0%
+expression but before going there I
+would like to make a general comment
+
+ align:start position:0%
+would like to make a general comment
+ 
+
+ align:start position:0%
+would like to make a general comment
+even if the X's had a different
+
+ align:start position:0%
+even if the X's had a different
+ 
+
+ align:start position:0%
+even if the X's had a different
+distribution but with zero mean the
+
+ align:start position:0%
+distribution but with zero mean the
+ 
+
+ align:start position:0%
+distribution but with zero mean the
+derivation up to this point would go
+
+ align:start position:0%
+derivation up to this point would go
+ 
+
+ align:start position:0%
+derivation up to this point would go
+through here you would have a somewhat
+
+ align:start position:0%
+through here you would have a somewhat
+ 
+
+ align:start position:0%
+through here you would have a somewhat
+different expression for the expected
+
+ align:start position:0%
+different expression for the expected
+ 
+
+ align:start position:0%
+different expression for the expected
+value of e to the s
+
+ align:start position:0%
+value of e to the s
+ 
+
+ align:start position:0%
+value of e to the s
+X1 however it turns out that the
+
+ align:start position:0%
+X1 however it turns out that the
+ 
+
+ align:start position:0%
+X1 however it turns out that the
+expression that you get here will always
+
+ align:start position:0%
+expression that you get here will always
+ 
+
+ align:start position:0%
+expression that you get here will always
+have this property that it has a zero
+
+ align:start position:0%
+have this property that it has a zero
+ 
+
+ align:start position:0%
+have this property that it has a zero
+derivative this is a consequence of the
+
+ align:start position:0%
+derivative this is a consequence of the
+ 
+
+ align:start position:0%
+derivative this is a consequence of the
+assumption that we assumed zero mean and
+
+ align:start position:0%
+assumption that we assumed zero mean and
+ 
+
+ align:start position:0%
+assumption that we assumed zero mean and
+because of that we will still have a
+
+ align:start position:0%
+because of that we will still have a
+ 
+
+ align:start position:0%
+because of that we will still have a
+picture of this kind and so this
+
+ align:start position:0%
+picture of this kind and so this
+ 
+
+ align:start position:0%
+picture of this kind and so this
+fraction will always be less than one
+
+ align:start position:0%
+fraction will always be less than one
+ 
+
+ align:start position:0%
+fraction will always be less than one
+when we choose s to be suitably small
+
+ align:start position:0%
+when we choose s to be suitably small
+ 
+
+ align:start position:0%
+when we choose s to be suitably small
+and so this is going to give us a
+
+ align:start position:0%
+and so this is going to give us a
+ 
+
+ align:start position:0%
+and so this is going to give us a
+results for more General distributions
+
+ align:start position:0%
+results for more General distributions
+ 
+
+ align:start position:0%
+results for more General distributions
+and that more General result is known as
+
+ align:start position:0%
+and that more General result is known as
+ 
+
+ align:start position:0%
+and that more General result is known as
+the churn of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound however we will not develop in
+
+ align:start position:0%
+bound however we will not develop in
+ 
+
+ align:start position:0%
+bound however we will not develop in
+this video the churn of bounds in its
+
+ align:start position:0%
+this video the churn of bounds in its
+ 
+
+ align:start position:0%
+this video the churn of bounds in its
+greater generality we will just stay
+
+ align:start position:0%
+greater generality we will just stay
+ 
+
+ align:start position:0%
+greater generality we will just stay
+with heing inequality that gives us the
+
+ align:start position:0%
+with heing inequality that gives us the
+ 
+
+ align:start position:0%
+with heing inequality that gives us the
+basic idea and what we will do next will
+
+ align:start position:0%
+basic idea and what we will do next will
+ 
+
+ align:start position:0%
+basic idea and what we will do next will
+be to derive this
+
+ align:start position:0%
+be to derive this
+ 
+
+ align:start position:0%
+be to derive this
+inequality so I'm carrying over what we
+
+ align:start position:0%
+inequality so I'm carrying over what we
+ 
+
+ align:start position:0%
+inequality so I'm carrying over what we
+figured out in the previous slide
+
+ align:start position:0%
+figured out in the previous slide
+ 
+
+ align:start position:0%
+figured out in the previous slide
+and this is the quantity here that we
+
+ align:start position:0%
+and this is the quantity here that we
+ 
+
+ align:start position:0%
+and this is the quantity here that we
+wish to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound we will look at the numerator term
+
+ align:start position:0%
+bound we will look at the numerator term
+ 
+
+ align:start position:0%
+bound we will look at the numerator term
+and we're going to use a tailor series
+
+ align:start position:0%
+and we're going to use a tailor series
+ 
+
+ align:start position:0%
+and we're going to use a tailor series
+for the exponential
+
+ align:start position:0%
+for the exponential
+ 
+
+ align:start position:0%
+for the exponential
+function remember the tailor series for
+
+ align:start position:0%
+function remember the tailor series for
+ 
+
+ align:start position:0%
+function remember the tailor series for
+the exponential function takes this form
+
+ align:start position:0%
+the exponential function takes this form
+ 
+
+ align:start position:0%
+the exponential function takes this form
+and using that we have 12 e to the S +
+
+ align:start position:0%
+and using that we have 12 e to the S +
+ 
+
+ align:start position:0%
+and using that we have 12 e to the S +
+e- S is equal to the
+
+ align:start position:0%
+e- S is equal to the
+ 
+
+ align:start position:0%
+e- S is equal to the
+following we first first write the
+
+ align:start position:0%
+following we first first write the
+ 
+
+ align:start position:0%
+following we first first write the
+tailor series for e to the S I'm just
+
+ align:start position:0%
+tailor series for e to the S I'm just
+ 
+
+ align:start position:0%
+tailor series for e to the S I'm just
+copying from here it's 1 + S + s^ 2 / 2
+
+ align:start position:0%
+copying from here it's 1 + S + s^ 2 / 2
+ 
+
+ align:start position:0%
+copying from here it's 1 + S + s^ 2 / 2
+factorial plus s Cub over 3
+
+ align:start position:0%
+factorial plus s Cub over 3
+ 
+
+ align:start position:0%
+factorial plus s Cub over 3
+factorial and we continue
+
+ align:start position:0%
+factorial and we continue
+ 
+
+ align:start position:0%
+factorial and we continue
+similarly and then for the term e to the
+
+ align:start position:0%
+similarly and then for the term e to the
+ 
+
+ align:start position:0%
+similarly and then for the term e to the
+minus s we have a similar expansion
+
+ align:start position:0%
+minus s we have a similar expansion
+ 
+
+ align:start position:0%
+minus s we have a similar expansion
+except that we put a minus s in the
+
+ align:start position:0%
+except that we put a minus s in the
+ 
+
+ align:start position:0%
+except that we put a minus s in the
+place of s now minus s s is the same as
+
+ align:start position:0%
+place of s now minus s s is the same as
+ 
+
+ align:start position:0%
+place of s now minus s s is the same as
+s squ with a plus
+
+ align:start position:0%
+s squ with a plus
+ 
+
+ align:start position:0%
+s squ with a plus
+sign but for S Cub when we have minus s
+
+ align:start position:0%
+sign but for S Cub when we have minus s
+ 
+
+ align:start position:0%
+sign but for S Cub when we have minus s
+this becomes Min - s cub and so on and
+
+ align:start position:0%
+this becomes Min - s cub and so on and
+ 
+
+ align:start position:0%
+this becomes Min - s cub and so on and
+so we see that in this expansion here we
+
+ align:start position:0%
+so we see that in this expansion here we
+ 
+
+ align:start position:0%
+so we see that in this expansion here we
+will alternate between positive and
+
+ align:start position:0%
+will alternate between positive and
+ 
+
+ align:start position:0%
+will alternate between positive and
+negative signs this means that all the
+
+ align:start position:0%
+negative signs this means that all the
+ 
+
+ align:start position:0%
+negative signs this means that all the
+odd power terms will cancel each other
+
+ align:start position:0%
+odd power terms will cancel each other
+ 
+
+ align:start position:0%
+odd power terms will cancel each other
+but the even power terms Will
+
+ align:start position:0%
+but the even power terms Will
+ 
+
+ align:start position:0%
+but the even power terms Will
+Survive so what we obtain is
+
+ align:start position:0%
+Survive so what we obtain is
+ 
+
+ align:start position:0%
+Survive so what we obtain is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sum of all those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms but we only have the even power
+
+ align:start position:0%
+terms but we only have the even power
+ 
+
+ align:start position:0%
+terms but we only have the even power
+terms so we have powers of the form 2 I
+
+ align:start position:0%
+terms so we have powers of the form 2 I
+ 
+
+ align:start position:0%
+terms so we have powers of the form 2 I
+these are the even
+
+ align:start position:0%
+these are the even
+ 
+
+ align:start position:0%
+these are the even
+integers and in the denominators we will
+
+ align:start position:0%
+integers and in the denominators we will
+ 
+
+ align:start position:0%
+integers and in the denominators we will
+always have the factorial of whatever
+
+ align:start position:0%
+always have the factorial of whatever
+ 
+
+ align:start position:0%
+always have the factorial of whatever
+exponent we have at the top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let us get a bound on this term in
+
+ align:start position:0%
+now let us get a bound on this term in
+ 
+
+ align:start position:0%
+now let us get a bound on this term in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+denominator 2 I
+
+ align:start position:0%
+denominator 2 I
+ 
+
+ align:start position:0%
+denominator 2 I
+factorial is 1 * 2 * 3 all the way up to
+
+ align:start position:0%
+factorial is 1 * 2 * 3 all the way up to
+ 
+
+ align:start position:0%
+factorial is 1 * 2 * 3 all the way up to
+I and then we continue I + 1 I + 2 all
+
+ align:start position:0%
+I and then we continue I + 1 I + 2 all
+ 
+
+ align:start position:0%
+I and then we continue I + 1 I + 2 all
+the way up to 2
+
+ align:start position:0%
+the way up to 2
+ 
+
+ align:start position:0%
+the way up to 2
+I and what we have is first I factorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then each one of these terms is
+
+ align:start position:0%
+but then each one of these terms is
+ 
+
+ align:start position:0%
+but then each one of these terms is
+larger than or equal to two and we have
+
+ align:start position:0%
+larger than or equal to two and we have
+ 
+
+ align:start position:0%
+larger than or equal to two and we have
+I such terms and this gives us this
+
+ align:start position:0%
+I such terms and this gives us this
+ 
+
+ align:start position:0%
+I such terms and this gives us this
+inequality so we're going to use this
+
+ align:start position:0%
+inequality so we're going to use this
+ 
+
+ align:start position:0%
+inequality so we're going to use this
+substitution here because this term is
+
+ align:start position:0%
+substitution here because this term is
+ 
+
+ align:start position:0%
+substitution here because this term is
+in the denominator the direction of the
+
+ align:start position:0%
+in the denominator the direction of the
+ 
+
+ align:start position:0%
+in the denominator the direction of the
+inequality is going to be reversed and
+
+ align:start position:0%
+inequality is going to be reversed and
+ 
+
+ align:start position:0%
+inequality is going to be reversed and
+we obtain this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we can rewrite this by taking this
+
+ align:start position:0%
+now we can rewrite this by taking this
+ 
+
+ align:start position:0%
+now we can rewrite this by taking this
+term 2 to the I and combining it with
+
+ align:start position:0%
+term 2 to the I and combining it with
+ 
+
+ align:start position:0%
+term 2 to the I and combining it with
+the other term in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerator and what we have is s² / 2 all
+
+ align:start position:0%
+numerator and what we have is s² / 2 all
+ 
+
+ align:start position:0%
+numerator and what we have is s² / 2 all
+of that to the ice power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now does this expression look
+
+ align:start position:0%
+now does this expression look
+ 
+
+ align:start position:0%
+now does this expression look
+familiar it is of exactly the same form
+
+ align:start position:0%
+familiar it is of exactly the same form
+ 
+
+ align:start position:0%
+familiar it is of exactly the same form
+as this expansion but instead of s we
+
+ align:start position:0%
+as this expansion but instead of s we
+ 
+
+ align:start position:0%
+as this expansion but instead of s we
+now have S squ over 2 therefore this is
+
+ align:start position:0%
+now have S squ over 2 therefore this is
+ 
+
+ align:start position:0%
+now have S squ over 2 therefore this is
+equal to e to the
+
+ align:start position:0%
+equal to e to the
+ 
+
+ align:start position:0%
+equal to e to the
+s² /
+
+ align:start position:0%
+s² /
+ 
+
+ align:start position:0%
+s² /
+2 so we managed to
+
+ align:start position:0%
+2 so we managed to
+ 
+
+ align:start position:0%
+2 so we managed to
+bound this term using now this bound we
+
+ align:start position:0%
+bound this term using now this bound we
+ 
+
+ align:start position:0%
+bound this term using now this bound we
+go back to this
+
+ align:start position:0%
+go back to this
+ 
+
+ align:start position:0%
+go back to this
+inequality and we have that this is less
+
+ align:start position:0%
+inequality and we have that this is less
+ 
+
+ align:start position:0%
+inequality and we have that this is less
+than or equal
+
+ align:start position:0%
+than or equal
+ 
+
+ align:start position:0%
+than or equal
+to in the numerator we have e to the
+
+ align:start position:0%
+to in the numerator we have e to the
+ 
+
+ align:start position:0%
+to in the numerator we have e to the
+s² over two in the denominator we have e
+
+ align:start position:0%
+s² over two in the denominator we have e
+ 
+
+ align:start position:0%
+s² over two in the denominator we have e
+to the sa
+
+ align:start position:0%
+to the sa
+ 
+
+ align:start position:0%
+to the sa
+a and all that is raised to the nth
+
+ align:start position:0%
+a and all that is raised to the nth
+ 
+
+ align:start position:0%
+a and all that is raised to the nth
+power or another way to write this is e
+
+ align:start position:0%
+power or another way to write this is e
+ 
+
+ align:start position:0%
+power or another way to write this is e
+to the s² /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 minus
+
+ align:start position:0%
+2 minus
+ 
+
+ align:start position:0%
+2 minus
+sa and all that to the nth
+
+ align:start position:0%
+sa and all that to the nth
+ 
+
+ align:start position:0%
+sa and all that to the nth
+power and now if I choose s equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a what I obtain here is going to be e to
+
+ align:start position:0%
+a what I obtain here is going to be e to
+ 
+
+ align:start position:0%
+a what I obtain here is going to be e to
+the a^ 2 / 2 - a^ 2 that leaves me me
+
+ align:start position:0%
+the a^ 2 / 2 - a^ 2 that leaves me me
+ 
+
+ align:start position:0%
+the a^ 2 / 2 - a^ 2 that leaves me me
+with e to the minus a^ 2 / 2 and then I
+
+ align:start position:0%
+with e to the minus a^ 2 / 2 and then I
+ 
+
+ align:start position:0%
+with e to the minus a^ 2 / 2 and then I
+take this factor of n as well and the
+
+ align:start position:0%
+take this factor of n as well and the
+ 
+
+ align:start position:0%
+take this factor of n as well and the
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+conclusion is that this quantity becomes
+
+ align:start position:0%
+conclusion is that this quantity becomes
+ 
+
+ align:start position:0%
+conclusion is that this quantity becomes
+equal to this
+
+ align:start position:0%
+equal to this
+ 
+
+ align:start position:0%
+equal to this
+term and so we have completed the
+
+ align:start position:0%
+term and so we have completed the
+ 
+
+ align:start position:0%
+term and so we have completed the
+derivation that this expression is less
+
+ align:start position:0%
+derivation that this expression is less
+ 
+
+ align:start position:0%
+derivation that this expression is less
+than or equal to this quantity when we
+
+ align:start position:0%
+than or equal to this quantity when we
+ 
+
+ align:start position:0%
+than or equal to this quantity when we
+choose s equal to a and this is heing
+
+ align:start position:0%
+choose s equal to a and this is heing
+ 
+
+ align:start position:0%
+choose s equal to a and this is heing
+inequality
\ No newline at end of file
diff --git a/MuNpOg4W7jk.txt b/MuNpOg4W7jk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..214a13d3c27b68b40b2213a388bb6873f41c5aa1
--- /dev/null
+++ b/MuNpOg4W7jk.txt
@@ -0,0 +1,16427 @@
+align:start position:0%
+ 
+I'm going to talk about building the
+
+ align:start position:0%
+I'm going to talk about building the
+ 
+
+ align:start position:0%
+I'm going to talk about building the
+health system so that technology or
+
+ align:start position:0%
+health system so that technology or
+ 
+
+ align:start position:0%
+health system so that technology or
+platforms again some jargon that I I
+
+ align:start position:0%
+platforms again some jargon that I I
+ 
+
+ align:start position:0%
+platforms again some jargon that I I
+really learned
+
+ align:start position:0%
+really learned
+ 
+
+ align:start position:0%
+really learned
+um from people with trainings like some
+
+ align:start position:0%
+um from people with trainings like some
+ 
+
+ align:start position:0%
+um from people with trainings like some
+of those in this room how can we use
+
+ align:start position:0%
+of those in this room how can we use
+ 
+
+ align:start position:0%
+of those in this room how can we use
+those platforms to innovate or you know
+
+ align:start position:0%
+those platforms to innovate or you know
+ 
+
+ align:start position:0%
+those platforms to innovate or you know
+you've heard all the Expressions since
+
+ align:start position:0%
+you've heard all the Expressions since
+ 
+
+ align:start position:0%
+you've heard all the Expressions since
+then leapfrog leapfrog Innovations
+
+ align:start position:0%
+then leapfrog leapfrog Innovations
+ 
+
+ align:start position:0%
+then leapfrog leapfrog Innovations
+disruptive Innovations
+
+ align:start position:0%
+disruptive Innovations
+ 
+
+ align:start position:0%
+disruptive Innovations
+one of the ways that that can work is to
+
+ align:start position:0%
+one of the ways that that can work is to
+ 
+
+ align:start position:0%
+one of the ways that that can work is to
+not have systems and systems advice you
+
+ align:start position:0%
+not have systems and systems advice you
+ 
+
+ align:start position:0%
+not have systems and systems advice you
+can build around another is to have
+
+ align:start position:0%
+can build around another is to have
+ 
+
+ align:start position:0%
+can build around another is to have
+decent elastic ones so I'm going to talk
+
+ align:start position:0%
+decent elastic ones so I'm going to talk
+ 
+
+ align:start position:0%
+decent elastic ones so I'm going to talk
+about that part how do you deliver
+
+ align:start position:0%
+about that part how do you deliver
+ 
+
+ align:start position:0%
+about that part how do you deliver
+Services what how do you what is Health
+
+ align:start position:0%
+Services what how do you what is Health
+ 
+
+ align:start position:0%
+Services what how do you what is Health
+System strengthening and I would like to
+
+ align:start position:0%
+System strengthening and I would like to
+ 
+
+ align:start position:0%
+System strengthening and I would like to
+end fairly early so that this can be a
+
+ align:start position:0%
+end fairly early so that this can be a
+ 
+
+ align:start position:0%
+end fairly early so that this can be a
+good discussion for for me as well and
+
+ align:start position:0%
+good discussion for for me as well and
+ 
+
+ align:start position:0%
+good discussion for for me as well and
+and my colleagues are here too in
+
+ align:start position:0%
+and my colleagues are here too in
+ 
+
+ align:start position:0%
+and my colleagues are here too in
+addition to Hamish Renee and their team
+
+ align:start position:0%
+addition to Hamish Renee and their team
+ 
+
+ align:start position:0%
+addition to Hamish Renee and their team
+with me today is Claire Pierre who's
+
+ align:start position:0%
+with me today is Claire Pierre who's
+ 
+
+ align:start position:0%
+with me today is Claire Pierre who's
+worked at an I.T and Health Systems in
+
+ align:start position:0%
+worked at an I.T and Health Systems in
+ 
+
+ align:start position:0%
+worked at an I.T and Health Systems in
+Cambridge Massachusetts and in uh in
+
+ align:start position:0%
+Cambridge Massachusetts and in uh in
+ 
+
+ align:start position:0%
+Cambridge Massachusetts and in uh in
+Haiti and Emily bonson
+
+ align:start position:0%
+Haiti and Emily bonson
+ 
+
+ align:start position:0%
+Haiti and Emily bonson
+um who is
+
+ align:start position:0%
+um who is
+ 
+
+ align:start position:0%
+um who is
+anyway I'm her right hand let's put it
+
+ align:start position:0%
+anyway I'm her right hand let's put it
+ 
+
+ align:start position:0%
+anyway I'm her right hand let's put it
+that way so I want to talk a little bit
+
+ align:start position:0%
+that way so I want to talk a little bit
+ 
+
+ align:start position:0%
+that way so I want to talk a little bit
+about basic health design
+
+ align:start position:0%
+about basic health design
+ 
+
+ align:start position:0%
+about basic health design
+um and and we'll be focusing on Haiti
+
+ align:start position:0%
+um and and we'll be focusing on Haiti
+ 
+
+ align:start position:0%
+um and and we'll be focusing on Haiti
+and Rwanda however in each of these
+
+ align:start position:0%
+and Rwanda however in each of these
+ 
+
+ align:start position:0%
+and Rwanda however in each of these
+sites we've tried to use
+
+ align:start position:0%
+sites we've tried to use
+ 
+
+ align:start position:0%
+sites we've tried to use
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+information technology and other
+
+ align:start position:0%
+information technology and other
+ 
+
+ align:start position:0%
+information technology and other
+Technologies to again LeapFrog now
+
+ align:start position:0%
+Technologies to again LeapFrog now
+ 
+
+ align:start position:0%
+Technologies to again LeapFrog now
+that's a lot easier in a place where
+
+ align:start position:0%
+that's a lot easier in a place where
+ 
+
+ align:start position:0%
+that's a lot easier in a place where
+there's stable electricity
+
+ align:start position:0%
+there's stable electricity
+ 
+
+ align:start position:0%
+there's stable electricity
+which is to say a lot of the places we
+
+ align:start position:0%
+which is to say a lot of the places we
+ 
+
+ align:start position:0%
+which is to say a lot of the places we
+work actually do have stable electricity
+
+ align:start position:0%
+work actually do have stable electricity
+ 
+
+ align:start position:0%
+work actually do have stable electricity
+uh Russia the United States
+
+ align:start position:0%
+uh Russia the United States
+ 
+
+ align:start position:0%
+uh Russia the United States
+um or Urban Peru the other sites however
+
+ align:start position:0%
+um or Urban Peru the other sites however
+ 
+
+ align:start position:0%
+um or Urban Peru the other sites however
+have very disrupted electrical supply so
+
+ align:start position:0%
+have very disrupted electrical supply so
+ 
+
+ align:start position:0%
+have very disrupted electrical supply so
+for example Rwanda in 2004 2005 was
+
+ align:start position:0%
+for example Rwanda in 2004 2005 was
+ 
+
+ align:start position:0%
+for example Rwanda in 2004 2005 was
+about five percent on the grid Haiti is
+
+ align:start position:0%
+about five percent on the grid Haiti is
+ 
+
+ align:start position:0%
+about five percent on the grid Haiti is
+a shockingly low number for the Americas
+
+ align:start position:0%
+a shockingly low number for the Americas
+ 
+
+ align:start position:0%
+a shockingly low number for the Americas
+we had a lot of challenges so when I say
+
+ align:start position:0%
+we had a lot of challenges so when I say
+ 
+
+ align:start position:0%
+we had a lot of challenges so when I say
+build systems I literally mean build
+
+ align:start position:0%
+build systems I literally mean build
+ 
+
+ align:start position:0%
+build systems I literally mean build
+systems and this is as simple a diagram
+
+ align:start position:0%
+systems and this is as simple a diagram
+ 
+
+ align:start position:0%
+systems and this is as simple a diagram
+as I could I could come up with
+
+ align:start position:0%
+as I could I could come up with
+ 
+
+ align:start position:0%
+as I could I could come up with
+um as as Hamish said Partners in Health
+
+ align:start position:0%
+um as as Hamish said Partners in Health
+ 
+
+ align:start position:0%
+um as as Hamish said Partners in Health
+is is focused on three he didn't say
+
+ align:start position:0%
+is is focused on three he didn't say
+ 
+
+ align:start position:0%
+is is focused on three he didn't say
+this way but let me say it this way
+
+ align:start position:0%
+this way but let me say it this way
+ 
+
+ align:start position:0%
+this way but let me say it this way
+three levels of care community-based
+
+ align:start position:0%
+three levels of care community-based
+ 
+
+ align:start position:0%
+three levels of care community-based
+care which is done largely with
+
+ align:start position:0%
+care which is done largely with
+ 
+
+ align:start position:0%
+care which is done largely with
+community health workers community
+
+ align:start position:0%
+community health workers community
+ 
+
+ align:start position:0%
+community health workers community
+health workers who we that usually call
+
+ align:start position:0%
+health workers who we that usually call
+ 
+
+ align:start position:0%
+health workers who we that usually call
+accommodernators people who are
+
+ align:start position:0%
+accommodernators people who are
+ 
+
+ align:start position:0%
+accommodernators people who are
+accompanying their neighbors with
+
+ align:start position:0%
+accompanying their neighbors with
+ 
+
+ align:start position:0%
+accompanying their neighbors with
+chronic illness they provide the natural
+
+ align:start position:0%
+chronic illness they provide the natural
+ 
+
+ align:start position:0%
+chronic illness they provide the natural
+human Network to amplify a lot of the
+
+ align:start position:0%
+human Network to amplify a lot of the
+ 
+
+ align:start position:0%
+human Network to amplify a lot of the
+technological innovation that is being
+
+ align:start position:0%
+technological innovation that is being
+ 
+
+ align:start position:0%
+technological innovation that is being
+developed now so if you if you hear
+
+ align:start position:0%
+developed now so if you if you hear
+ 
+
+ align:start position:0%
+developed now so if you if you hear
+about a point of use diagnostic or
+
+ align:start position:0%
+about a point of use diagnostic or
+ 
+
+ align:start position:0%
+about a point of use diagnostic or
+therapeutic
+
+ align:start position:0%
+therapeutic
+ 
+
+ align:start position:0%
+therapeutic
+you know I've heard story after story
+
+ align:start position:0%
+you know I've heard story after story
+ 
+
+ align:start position:0%
+you know I've heard story after story
+about what's coming on the Pike it's
+
+ align:start position:0%
+about what's coming on the Pike it's
+ 
+
+ align:start position:0%
+about what's coming on the Pike it's
+hard to imagine those Technologies being
+
+ align:start position:0%
+hard to imagine those Technologies being
+ 
+
+ align:start position:0%
+hard to imagine those Technologies being
+rolled out effectively equitably
+
+ align:start position:0%
+rolled out effectively equitably
+ 
+
+ align:start position:0%
+rolled out effectively equitably
+especially those most vulnerable and in
+
+ align:start position:0%
+especially those most vulnerable and in
+ 
+
+ align:start position:0%
+especially those most vulnerable and in
+rural regions without community health
+
+ align:start position:0%
+rural regions without community health
+ 
+
+ align:start position:0%
+rural regions without community health
+workers that would be one argument a
+
+ align:start position:0%
+workers that would be one argument a
+ 
+
+ align:start position:0%
+workers that would be one argument a
+second is that the CUNY health workers
+
+ align:start position:0%
+second is that the CUNY health workers
+ 
+
+ align:start position:0%
+second is that the CUNY health workers
+should not be called upon to provide
+
+ align:start position:0%
+should not be called upon to provide
+ 
+
+ align:start position:0%
+should not be called upon to provide
+services that are you know beyond their
+
+ align:start position:0%
+services that are you know beyond their
+ 
+
+ align:start position:0%
+services that are you know beyond their
+or anyone's means for example there is a
+
+ align:start position:0%
+or anyone's means for example there is a
+ 
+
+ align:start position:0%
+or anyone's means for example there is a
+romanticization in international Health
+
+ align:start position:0%
+romanticization in international Health
+ 
+
+ align:start position:0%
+romanticization in international Health
+what used to be called International
+
+ align:start position:0%
+what used to be called International
+ 
+
+ align:start position:0%
+what used to be called International
+Health in the 70s and 80s a
+
+ align:start position:0%
+Health in the 70s and 80s a
+ 
+
+ align:start position:0%
+Health in the 70s and 80s a
+romanticization of the capacity of
+
+ align:start position:0%
+romanticization of the capacity of
+ 
+
+ align:start position:0%
+romanticization of the capacity of
+community health workers to solve
+
+ align:start position:0%
+community health workers to solve
+ 
+
+ align:start position:0%
+community health workers to solve
+problems which is really hidden
+
+ align:start position:0%
+problems which is really hidden
+ 
+
+ align:start position:0%
+problems which is really hidden
+enthusiasm for spending very little
+
+ align:start position:0%
+enthusiasm for spending very little
+ 
+
+ align:start position:0%
+enthusiasm for spending very little
+money in resource poor settings
+
+ align:start position:0%
+money in resource poor settings
+ 
+
+ align:start position:0%
+money in resource poor settings
+and one day people will go back to
+
+ align:start position:0%
+and one day people will go back to
+ 
+
+ align:start position:0%
+and one day people will go back to
+analyze uh you know how this ideology
+
+ align:start position:0%
+analyze uh you know how this ideology
+ 
+
+ align:start position:0%
+analyze uh you know how this ideology
+work but let me give an example when you
+
+ align:start position:0%
+work but let me give an example when you
+ 
+
+ align:start position:0%
+work but let me give an example when you
+hear that traditional birth attendance
+
+ align:start position:0%
+hear that traditional birth attendance
+ 
+
+ align:start position:0%
+hear that traditional birth attendance
+can very much reduce maternal mortality
+
+ align:start position:0%
+can very much reduce maternal mortality
+ 
+
+ align:start position:0%
+can very much reduce maternal mortality
+just skipping the blood banks the
+
+ align:start position:0%
+just skipping the blood banks the
+ 
+
+ align:start position:0%
+just skipping the blood banks the
+cesarean section of modern obstetrics I
+
+ align:start position:0%
+cesarean section of modern obstetrics I
+ 
+
+ align:start position:0%
+cesarean section of modern obstetrics I
+would ask you all to be very suspicious
+
+ align:start position:0%
+would ask you all to be very suspicious
+ 
+
+ align:start position:0%
+would ask you all to be very suspicious
+of such claims because I don't think
+
+ align:start position:0%
+of such claims because I don't think
+ 
+
+ align:start position:0%
+of such claims because I don't think
+there's adequate evidence to prove that
+
+ align:start position:0%
+there's adequate evidence to prove that
+ 
+
+ align:start position:0%
+there's adequate evidence to prove that
+to prove that true so the first thing
+
+ align:start position:0%
+to prove that true so the first thing
+ 
+
+ align:start position:0%
+to prove that true so the first thing
+that we've done in some settings uh is
+
+ align:start position:0%
+that we've done in some settings uh is
+ 
+
+ align:start position:0%
+that we've done in some settings uh is
+to actually build Health Centers now
+
+ align:start position:0%
+to actually build Health Centers now
+ 
+
+ align:start position:0%
+to actually build Health Centers now
+health centers in in the jargon that
+
+ align:start position:0%
+health centers in in the jargon that
+ 
+
+ align:start position:0%
+health centers in in the jargon that
+we're using and developing
+
+ align:start position:0%
+we're using and developing
+ 
+
+ align:start position:0%
+we're using and developing
+are usually nurse-led programs but
+
+ align:start position:0%
+are usually nurse-led programs but
+ 
+
+ align:start position:0%
+are usually nurse-led programs but
+nurses are also rare just as rare in the
+
+ align:start position:0%
+nurses are also rare just as rare in the
+ 
+
+ align:start position:0%
+nurses are also rare just as rare in the
+developing World in rural regions as our
+
+ align:start position:0%
+developing World in rural regions as our
+ 
+
+ align:start position:0%
+developing World in rural regions as our
+doctors
+
+ align:start position:0%
+doctors
+ 
+
+ align:start position:0%
+doctors
+senior managers
+
+ align:start position:0%
+senior managers
+ 
+
+ align:start position:0%
+senior managers
+Etc so that's but that's a often the
+
+ align:start position:0%
+Etc so that's but that's a often the
+ 
+
+ align:start position:0%
+Etc so that's but that's a often the
+first step so it's Health Center
+
+ align:start position:0%
+first step so it's Health Center
+ 
+
+ align:start position:0%
+first step so it's Health Center
+enriched
+
+ align:start position:0%
+enriched
+ 
+
+ align:start position:0%
+enriched
+and then finally some fraction of the
+
+ align:start position:0%
+and then finally some fraction of the
+ 
+
+ align:start position:0%
+and then finally some fraction of the
+care that would be delivered in any of
+
+ align:start position:0%
+care that would be delivered in any of
+ 
+
+ align:start position:0%
+care that would be delivered in any of
+the settings where where Hamish and and
+
+ align:start position:0%
+the settings where where Hamish and and
+ 
+
+ align:start position:0%
+the settings where where Hamish and and
+I and others have worked would be
+
+ align:start position:0%
+I and others have worked would be
+ 
+
+ align:start position:0%
+I and others have worked would be
+incomplete without
+
+ align:start position:0%
+incomplete without
+ 
+
+ align:start position:0%
+incomplete without
+hospitals it just doesn't work that way
+
+ align:start position:0%
+hospitals it just doesn't work that way
+ 
+
+ align:start position:0%
+hospitals it just doesn't work that way
+you know you could manage very
+
+ align:start position:0%
+you know you could manage very
+ 
+
+ align:start position:0%
+you know you could manage very
+effectively I believe you can manage
+
+ align:start position:0%
+effectively I believe you can manage
+ 
+
+ align:start position:0%
+effectively I believe you can manage
+most chronic infectious disease
+
+ align:start position:0%
+most chronic infectious disease
+ 
+
+ align:start position:0%
+most chronic infectious disease
+um and I'll say this in front of Leo and
+
+ align:start position:0%
+um and I'll say this in front of Leo and
+ 
+
+ align:start position:0%
+um and I'll say this in front of Leo and
+see if he buys this most chronic
+
+ align:start position:0%
+see if he buys this most chronic
+ 
+
+ align:start position:0%
+see if he buys this most chronic
+infectious disease I think can be best
+
+ align:start position:0%
+infectious disease I think can be best
+ 
+
+ align:start position:0%
+infectious disease I think can be best
+managed
+
+ align:start position:0%
+managed
+ 
+
+ align:start position:0%
+managed
+in a hospital in a clinic setting or
+
+ align:start position:0%
+in a hospital in a clinic setting or
+ 
+
+ align:start position:0%
+in a hospital in a clinic setting or
+community-based setting
+
+ align:start position:0%
+community-based setting
+ 
+
+ align:start position:0%
+community-based setting
+take HIV disease there's more seats up
+
+ align:start position:0%
+take HIV disease there's more seats up
+ 
+
+ align:start position:0%
+take HIV disease there's more seats up
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the highest standard of care for
+
+ align:start position:0%
+the the highest standard of care for
+ 
+
+ align:start position:0%
+the the highest standard of care for
+AIDS is probably community-based care
+
+ align:start position:0%
+AIDS is probably community-based care
+ 
+
+ align:start position:0%
+AIDS is probably community-based care
+first of all that's the way you deliver
+
+ align:start position:0%
+first of all that's the way you deliver
+ 
+
+ align:start position:0%
+first of all that's the way you deliver
+a therapeutic on a daily basis second of
+
+ align:start position:0%
+a therapeutic on a daily basis second of
+ 
+
+ align:start position:0%
+a therapeutic on a daily basis second of
+all you also are reducing risk of
+
+ align:start position:0%
+all you also are reducing risk of
+ 
+
+ align:start position:0%
+all you also are reducing risk of
+exposure to the leading opportunistic
+
+ align:start position:0%
+exposure to the leading opportunistic
+ 
+
+ align:start position:0%
+exposure to the leading opportunistic
+infection uh killing people with HIV in
+
+ align:start position:0%
+infection uh killing people with HIV in
+ 
+
+ align:start position:0%
+infection uh killing people with HIV in
+the places we work which is tuberculosis
+
+ align:start position:0%
+the places we work which is tuberculosis
+ 
+
+ align:start position:0%
+the places we work which is tuberculosis
+and a lot of that happens at the
+
+ align:start position:0%
+and a lot of that happens at the
+ 
+
+ align:start position:0%
+and a lot of that happens at the
+institutional level so community-based
+
+ align:start position:0%
+institutional level so community-based
+ 
+
+ align:start position:0%
+institutional level so community-based
+care is better in many ways however
+
+ align:start position:0%
+care is better in many ways however
+ 
+
+ align:start position:0%
+care is better in many ways however
+people have complications you know
+
+ align:start position:0%
+people have complications you know
+ 
+
+ align:start position:0%
+people have complications you know
+whether they
+
+ align:start position:0%
+whether they
+ 
+
+ align:start position:0%
+whether they
+you know people have broken bones and
+
+ align:start position:0%
+you know people have broken bones and
+ 
+
+ align:start position:0%
+you know people have broken bones and
+obstructed labor and acute pneumonia and
+
+ align:start position:0%
+obstructed labor and acute pneumonia and
+ 
+
+ align:start position:0%
+obstructed labor and acute pneumonia and
+you know again these and of course
+
+ align:start position:0%
+you know again these and of course
+ 
+
+ align:start position:0%
+you know again these and of course
+any kind of complication of pregnancy
+
+ align:start position:0%
+any kind of complication of pregnancy
+ 
+
+ align:start position:0%
+any kind of complication of pregnancy
+these are really best managed in a
+
+ align:start position:0%
+these are really best managed in a
+ 
+
+ align:start position:0%
+these are really best managed in a
+hospital so this is what I'm talking
+
+ align:start position:0%
+hospital so this is what I'm talking
+ 
+
+ align:start position:0%
+hospital so this is what I'm talking
+about when I'm saying Health System
+
+ align:start position:0%
+about when I'm saying Health System
+ 
+
+ align:start position:0%
+about when I'm saying Health System
+strengthening there are these three uh
+
+ align:start position:0%
+strengthening there are these three uh
+ 
+
+ align:start position:0%
+strengthening there are these three uh
+components again as they say at MIT it's
+
+ align:start position:0%
+components again as they say at MIT it's
+ 
+
+ align:start position:0%
+components again as they say at MIT it's
+not rocket science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words we can do this part
+
+ align:start position:0%
+in other words we can do this part
+ 
+
+ align:start position:0%
+in other words we can do this part
+without you guys
+
+ align:start position:0%
+without you guys
+ 
+
+ align:start position:0%
+without you guys
+so there's a lot we can't do without you
+
+ align:start position:0%
+so there's a lot we can't do without you
+ 
+
+ align:start position:0%
+so there's a lot we can't do without you
+guys and I'll show you what I mean first
+
+ align:start position:0%
+guys and I'll show you what I mean first
+ 
+
+ align:start position:0%
+guys and I'll show you what I mean first
+of all uh and the hay majority said this
+
+ align:start position:0%
+of all uh and the hay majority said this
+ 
+
+ align:start position:0%
+of all uh and the hay majority said this
+and I've used these pictures before at
+
+ align:start position:0%
+and I've used these pictures before at
+ 
+
+ align:start position:0%
+and I've used these pictures before at
+MIT
+
+ align:start position:0%
+MIT
+ 
+
+ align:start position:0%
+MIT
+um to actually this is not an unusual uh
+
+ align:start position:0%
+um to actually this is not an unusual uh
+ 
+
+ align:start position:0%
+um to actually this is not an unusual uh
+clinical story it's pretty much the kind
+
+ align:start position:0%
+clinical story it's pretty much the kind
+ 
+
+ align:start position:0%
+clinical story it's pretty much the kind
+of patient I I see all the time young
+
+ align:start position:0%
+of patient I I see all the time young
+ 
+
+ align:start position:0%
+of patient I I see all the time young
+person with HIV disease and another
+
+ align:start position:0%
+person with HIV disease and another
+ 
+
+ align:start position:0%
+person with HIV disease and another
+problem in this case he's got two he's
+
+ align:start position:0%
+problem in this case he's got two he's
+ 
+
+ align:start position:0%
+problem in this case he's got two he's
+got tuberculosis and and uh probably in
+
+ align:start position:0%
+got tuberculosis and and uh probably in
+ 
+
+ align:start position:0%
+got tuberculosis and and uh probably in
+addition and malnutrition just due to
+
+ align:start position:0%
+addition and malnutrition just due to
+ 
+
+ align:start position:0%
+addition and malnutrition just due to
+those wasting consumptive diseases
+
+ align:start position:0%
+those wasting consumptive diseases
+ 
+
+ align:start position:0%
+those wasting consumptive diseases
+um it's hard to tell in settings of food
+
+ align:start position:0%
+um it's hard to tell in settings of food
+ 
+
+ align:start position:0%
+um it's hard to tell in settings of food
+insecurity you know how to a portion
+
+ align:start position:0%
+insecurity you know how to a portion
+ 
+
+ align:start position:0%
+insecurity you know how to a portion
+responsibility for someone's wasting is
+
+ align:start position:0%
+responsibility for someone's wasting is
+ 
+
+ align:start position:0%
+responsibility for someone's wasting is
+it the disease or the lack of ready
+
+ align:start position:0%
+it the disease or the lack of ready
+ 
+
+ align:start position:0%
+it the disease or the lack of ready
+access to food anyway he this this
+
+ align:start position:0%
+access to food anyway he this this
+ 
+
+ align:start position:0%
+access to food anyway he this this
+patient whose name is Joseph who's of
+
+ align:start position:0%
+patient whose name is Joseph who's of
+ 
+
+ align:start position:0%
+patient whose name is Joseph who's of
+course given me permission to use his
+
+ align:start position:0%
+course given me permission to use his
+ 
+
+ align:start position:0%
+course given me permission to use his
+images and to broadcast them across the
+
+ align:start position:0%
+images and to broadcast them across the
+ 
+
+ align:start position:0%
+images and to broadcast them across the
+world I we've already done that when Jim
+
+ align:start position:0%
+world I we've already done that when Jim
+ 
+
+ align:start position:0%
+world I we've already done that when Jim
+Kim who some of you may have heard of
+
+ align:start position:0%
+Kim who some of you may have heard of
+ 
+
+ align:start position:0%
+Kim who some of you may have heard of
+um was at the World Health Organization
+
+ align:start position:0%
+um was at the World Health Organization
+ 
+
+ align:start position:0%
+um was at the World Health Organization
+he said send me pictures before and
+
+ align:start position:0%
+he said send me pictures before and
+ 
+
+ align:start position:0%
+he said send me pictures before and
+after pictures this is before the
+
+ align:start position:0%
+after pictures this is before the
+ 
+
+ align:start position:0%
+after pictures this is before the
+establishment of some of the big AIDS
+
+ align:start position:0%
+establishment of some of the big AIDS
+ 
+
+ align:start position:0%
+establishment of some of the big AIDS
+treatment and integrated prevention and
+
+ align:start position:0%
+treatment and integrated prevention and
+ 
+
+ align:start position:0%
+treatment and integrated prevention and
+Care programs
+
+ align:start position:0%
+Care programs
+ 
+
+ align:start position:0%
+Care programs
+um I sent him these two pictures uh and
+
+ align:start position:0%
+um I sent him these two pictures uh and
+ 
+
+ align:start position:0%
+um I sent him these two pictures uh and
+many other before and after pictures and
+
+ align:start position:0%
+many other before and after pictures and
+ 
+
+ align:start position:0%
+many other before and after pictures and
+he used these doing this glossy brochure
+
+ align:start position:0%
+he used these doing this glossy brochure
+ 
+
+ align:start position:0%
+he used these doing this glossy brochure
+and I said you know I'd like a copy of
+
+ align:start position:0%
+and I said you know I'd like a copy of
+ 
+
+ align:start position:0%
+and I said you know I'd like a copy of
+that for Joseph so I gave it to Joseph
+
+ align:start position:0%
+that for Joseph so I gave it to Joseph
+ 
+
+ align:start position:0%
+that for Joseph so I gave it to Joseph
+and think he would be very impressed
+
+ align:start position:0%
+and think he would be very impressed
+ 
+
+ align:start position:0%
+and think he would be very impressed
+with that and he just looked at and said
+
+ align:start position:0%
+with that and he just looked at and said
+ 
+
+ align:start position:0%
+with that and he just looked at and said
+yeah I'm a star
+
+ align:start position:0%
+yeah I'm a star
+ 
+
+ align:start position:0%
+yeah I'm a star
+uh he later went by the way he later
+
+ align:start position:0%
+uh he later went by the way he later
+ 
+
+ align:start position:0%
+uh he later went by the way he later
+went to one of these giant AIDS meetings
+
+ align:start position:0%
+went to one of these giant AIDS meetings
+ 
+
+ align:start position:0%
+went to one of these giant AIDS meetings
+how many of you have ever been to one of
+
+ align:start position:0%
+how many of you have ever been to one of
+ 
+
+ align:start position:0%
+how many of you have ever been to one of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+things is beyond there some of you if
+
+ align:start position:0%
+things is beyond there some of you if
+ 
+
+ align:start position:0%
+things is beyond there some of you if
+it's what 10 15 000 people anyway I went
+
+ align:start position:0%
+it's what 10 15 000 people anyway I went
+ 
+
+ align:start position:0%
+it's what 10 15 000 people anyway I went
+to one from
+
+ align:start position:0%
+to one from
+ 
+
+ align:start position:0%
+to one from
+from Rwanda directly to I think it was
+
+ align:start position:0%
+from Rwanda directly to I think it was
+ 
+
+ align:start position:0%
+from Rwanda directly to I think it was
+Toronto it was definitely Canada
+
+ align:start position:0%
+Toronto it was definitely Canada
+ 
+
+ align:start position:0%
+Toronto it was definitely Canada
+all those Canadian cities look alike to
+
+ align:start position:0%
+all those Canadian cities look alike to
+ 
+
+ align:start position:0%
+all those Canadian cities look alike to
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+and uh and he came from Haiti this guy
+
+ align:start position:0%
+and uh and he came from Haiti this guy
+ 
+
+ align:start position:0%
+and uh and he came from Haiti this guy
+and it was uh
+
+ align:start position:0%
+and it was uh
+ 
+
+ align:start position:0%
+and it was uh
+I learned that one of the Cardinal rules
+
+ align:start position:0%
+I learned that one of the Cardinal rules
+ 
+
+ align:start position:0%
+I learned that one of the Cardinal rules
+of the public I learned many when you
+
+ align:start position:0%
+of the public I learned many when you
+ 
+
+ align:start position:0%
+of the public I learned many when you
+take someone from rural Haiti and
+
+ align:start position:0%
+take someone from rural Haiti and
+ 
+
+ align:start position:0%
+take someone from rural Haiti and
+they've not been to a place like Toronto
+
+ align:start position:0%
+they've not been to a place like Toronto
+ 
+
+ align:start position:0%
+they've not been to a place like Toronto
+for you know there are some things that
+
+ align:start position:0%
+for you know there are some things that
+ 
+
+ align:start position:0%
+for you know there are some things that
+I know all about like be careful on the
+
+ align:start position:0%
+I know all about like be careful on the
+ 
+
+ align:start position:0%
+I know all about like be careful on the
+escalators this uh the card for your
+
+ align:start position:0%
+escalators this uh the card for your
+ 
+
+ align:start position:0%
+escalators this uh the card for your
+hotel room door works Etc but I did
+
+ align:start position:0%
+hotel room door works Etc but I did
+ 
+
+ align:start position:0%
+hotel room door works Etc but I did
+learn a one of the important things in
+
+ align:start position:0%
+learn a one of the important things in
+ 
+
+ align:start position:0%
+learn a one of the important things in
+public health that we should all know is
+
+ align:start position:0%
+public health that we should all know is
+ 
+
+ align:start position:0%
+public health that we should all know is
+you just should not give anyone keys to
+
+ align:start position:0%
+you just should not give anyone keys to
+ 
+
+ align:start position:0%
+you just should not give anyone keys to
+the mini bar
+
+ align:start position:0%
+the mini bar
+ 
+
+ align:start position:0%
+the mini bar
+so anyway the of funding has gone up
+
+ align:start position:0%
+so anyway the of funding has gone up
+ 
+
+ align:start position:0%
+so anyway the of funding has gone up
+very substantially as we know this is
+
+ align:start position:0%
+very substantially as we know this is
+ 
+
+ align:start position:0%
+very substantially as we know this is
+vertical funding is that bad that it's
+
+ align:start position:0%
+vertical funding is that bad that it's
+ 
+
+ align:start position:0%
+vertical funding is that bad that it's
+going to be broadcast to Taipei my
+
+ align:start position:0%
+going to be broadcast to Taipei my
+ 
+
+ align:start position:0%
+going to be broadcast to Taipei my
+little jokes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the amount of funding has gone up in
+
+ align:start position:0%
+the the amount of funding has gone up in
+ 
+
+ align:start position:0%
+the the amount of funding has gone up in
+part as a way of countering a lack of
+
+ align:start position:0%
+part as a way of countering a lack of
+ 
+
+ align:start position:0%
+part as a way of countering a lack of
+really intelligent response uh to a
+
+ align:start position:0%
+really intelligent response uh to a
+ 
+
+ align:start position:0%
+really intelligent response uh to a
+novel epidemic so that's always going to
+
+ align:start position:0%
+novel epidemic so that's always going to
+ 
+
+ align:start position:0%
+novel epidemic so that's always going to
+be the case and I think it's not
+
+ align:start position:0%
+be the case and I think it's not
+ 
+
+ align:start position:0%
+be the case and I think it's not
+unrelated to the question you're asking
+
+ align:start position:0%
+unrelated to the question you're asking
+ 
+
+ align:start position:0%
+unrelated to the question you're asking
+this class how can we use new technology
+
+ align:start position:0%
+this class how can we use new technology
+ 
+
+ align:start position:0%
+this class how can we use new technology
+uh to promote Health Equity but also how
+
+ align:start position:0%
+uh to promote Health Equity but also how
+ 
+
+ align:start position:0%
+uh to promote Health Equity but also how
+do we take on new problems and there was
+
+ align:start position:0%
+do we take on new problems and there was
+ 
+
+ align:start position:0%
+do we take on new problems and there was
+it's not as if we we've ever lived
+
+ align:start position:0%
+it's not as if we we've ever lived
+ 
+
+ align:start position:0%
+it's not as if we we've ever lived
+through the stunning changes that went
+
+ align:start position:0%
+through the stunning changes that went
+ 
+
+ align:start position:0%
+through the stunning changes that went
+occurred at the epidemiologic change
+
+ align:start position:0%
+occurred at the epidemiologic change
+ 
+
+ align:start position:0%
+occurred at the epidemiologic change
+that occurred at the end of the 20th
+
+ align:start position:0%
+that occurred at the end of the 20th
+ 
+
+ align:start position:0%
+that occurred at the end of the 20th
+century where you had the leading
+
+ align:start position:0%
+century where you had the leading
+ 
+
+ align:start position:0%
+century where you had the leading
+infectious killer of adults tuberculosis
+
+ align:start position:0%
+infectious killer of adults tuberculosis
+ 
+
+ align:start position:0%
+infectious killer of adults tuberculosis
+persisting and then joined to another
+
+ align:start position:0%
+persisting and then joined to another
+ 
+
+ align:start position:0%
+persisting and then joined to another
+killer in Synergy which is HIV and it
+
+ align:start position:0%
+killer in Synergy which is HIV and it
+ 
+
+ align:start position:0%
+killer in Synergy which is HIV and it
+surpassed TB as leading infectious clear
+
+ align:start position:0%
+surpassed TB as leading infectious clear
+ 
+
+ align:start position:0%
+surpassed TB as leading infectious clear
+of the adults in the world today young
+
+ align:start position:0%
+of the adults in the world today young
+ 
+
+ align:start position:0%
+of the adults in the world today young
+adults and they were linked together and
+
+ align:start position:0%
+adults and they were linked together and
+ 
+
+ align:start position:0%
+adults and they were linked together and
+they were invading especially southern
+
+ align:start position:0%
+they were invading especially southern
+ 
+
+ align:start position:0%
+they were invading especially southern
+Africa I would say that's where it was I
+
+ align:start position:0%
+Africa I would say that's where it was I
+ 
+
+ align:start position:0%
+Africa I would say that's where it was I
+mean all over the world in every urban
+
+ align:start position:0%
+mean all over the world in every urban
+ 
+
+ align:start position:0%
+mean all over the world in every urban
+area there are huge outbreaks or large
+
+ align:start position:0%
+area there are huge outbreaks or large
+ 
+
+ align:start position:0%
+area there are huge outbreaks or large
+outbreaks of TB and HIV but this burden
+
+ align:start position:0%
+outbreaks of TB and HIV but this burden
+ 
+
+ align:start position:0%
+outbreaks of TB and HIV but this burden
+of disease was especially enormous
+
+ align:start position:0%
+of disease was especially enormous
+ 
+
+ align:start position:0%
+of disease was especially enormous
+southern Africa and at the same time you
+
+ align:start position:0%
+southern Africa and at the same time you
+ 
+
+ align:start position:0%
+southern Africa and at the same time you
+have a third anybody here an
+
+ align:start position:0%
+have a third anybody here an
+ 
+
+ align:start position:0%
+have a third anybody here an
+anthropologist there's actually several
+
+ align:start position:0%
+anthropologist there's actually several
+ 
+
+ align:start position:0%
+anthropologist there's actually several
+anthropologists at MIT
+
+ align:start position:0%
+anthropologists at MIT
+ 
+
+ align:start position:0%
+anthropologists at MIT
+there was a third collision and that was
+
+ align:start position:0%
+there was a third collision and that was
+ 
+
+ align:start position:0%
+there was a third collision and that was
+with a therapeutic regime
+
+ align:start position:0%
+with a therapeutic regime
+ 
+
+ align:start position:0%
+with a therapeutic regime
+like this Collision didn't occur in the
+
+ align:start position:0%
+like this Collision didn't occur in the
+ 
+
+ align:start position:0%
+like this Collision didn't occur in the
+late 19th century but in the late 20th
+
+ align:start position:0%
+late 19th century but in the late 20th
+ 
+
+ align:start position:0%
+late 19th century but in the late 20th
+century so it also meant that for a
+
+ align:start position:0%
+century so it also meant that for a
+ 
+
+ align:start position:0%
+century so it also meant that for a
+while in any case we had to during uh
+
+ align:start position:0%
+while in any case we had to during uh
+ 
+
+ align:start position:0%
+while in any case we had to during uh
+this period of time we had to say well
+
+ align:start position:0%
+this period of time we had to say well
+ 
+
+ align:start position:0%
+this period of time we had to say well
+what do we how do we treat these people
+
+ align:start position:0%
+what do we how do we treat these people
+ 
+
+ align:start position:0%
+what do we how do we treat these people
+and You Heard lots of arguments you know
+
+ align:start position:0%
+and You Heard lots of arguments you know
+ 
+
+ align:start position:0%
+and You Heard lots of arguments you know
+uh that wasn't sustainable or cost
+
+ align:start position:0%
+uh that wasn't sustainable or cost
+ 
+
+ align:start position:0%
+uh that wasn't sustainable or cost
+effective but you really in the end had
+
+ align:start position:0%
+effective but you really in the end had
+ 
+
+ align:start position:0%
+effective but you really in the end had
+three collisions HIV TV and therapeutic
+
+ align:start position:0%
+three collisions HIV TV and therapeutic
+ 
+
+ align:start position:0%
+three collisions HIV TV and therapeutic
+regimes in other words treatment for
+
+ align:start position:0%
+regimes in other words treatment for
+ 
+
+ align:start position:0%
+regimes in other words treatment for
+tuberculosis and HIV which would lead to
+
+ align:start position:0%
+tuberculosis and HIV which would lead to
+ 
+
+ align:start position:0%
+tuberculosis and HIV which would lead to
+more complex problems like drug
+
+ align:start position:0%
+more complex problems like drug
+ 
+
+ align:start position:0%
+more complex problems like drug
+resistant disease
+
+ align:start position:0%
+resistant disease
+ 
+
+ align:start position:0%
+resistant disease
+and then if one of them is Airborne as
+
+ align:start position:0%
+and then if one of them is Airborne as
+ 
+
+ align:start position:0%
+and then if one of them is Airborne as
+is the case with TB and this is a very
+
+ align:start position:0%
+is the case with TB and this is a very
+ 
+
+ align:start position:0%
+is the case with TB and this is a very
+to use the jargon for my field medical
+
+ align:start position:0%
+to use the jargon for my field medical
+ 
+
+ align:start position:0%
+to use the jargon for my field medical
+anthropology this is an incredibly
+
+ align:start position:0%
+anthropology this is an incredibly
+ 
+
+ align:start position:0%
+anthropology this is an incredibly
+biosocially complex set of problems now
+
+ align:start position:0%
+biosocially complex set of problems now
+ 
+
+ align:start position:0%
+biosocially complex set of problems now
+that's not what I'm going to focus on
+
+ align:start position:0%
+that's not what I'm going to focus on
+ 
+
+ align:start position:0%
+that's not what I'm going to focus on
+today I'm just going to say the
+
+ align:start position:0%
+today I'm just going to say the
+ 
+
+ align:start position:0%
+today I'm just going to say the
+platforms that you build to answer those
+
+ align:start position:0%
+platforms that you build to answer those
+ 
+
+ align:start position:0%
+platforms that you build to answer those
+questions that I disposed are the very
+
+ align:start position:0%
+questions that I disposed are the very
+ 
+
+ align:start position:0%
+questions that I disposed are the very
+same ones that need new technologies to
+
+ align:start position:0%
+same ones that need new technologies to
+ 
+
+ align:start position:0%
+same ones that need new technologies to
+promote good outcomes but also just to
+
+ align:start position:0%
+promote good outcomes but also just to
+ 
+
+ align:start position:0%
+promote good outcomes but also just to
+manage you know and I'll show you some
+
+ align:start position:0%
+manage you know and I'll show you some
+ 
+
+ align:start position:0%
+manage you know and I'll show you some
+examples so
+
+ align:start position:0%
+examples so
+ 
+
+ align:start position:0%
+examples so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+some of you know that um
+
+ align:start position:0%
+some of you know that um
+ 
+
+ align:start position:0%
+some of you know that um
+and I I think uh Leo and others should
+
+ align:start position:0%
+and I I think uh Leo and others should
+ 
+
+ align:start position:0%
+and I I think uh Leo and others should
+be proud of this that a group of Harvard
+
+ align:start position:0%
+be proud of this that a group of Harvard
+ 
+
+ align:start position:0%
+be proud of this that a group of Harvard
+faculty got together I mean people look
+
+ align:start position:0%
+faculty got together I mean people look
+ 
+
+ align:start position:0%
+faculty got together I mean people look
+at this they Harvard consensus statement
+
+ align:start position:0%
+at this they Harvard consensus statement
+ 
+
+ align:start position:0%
+at this they Harvard consensus statement
+is such a thing possible
+
+ align:start position:0%
+is such a thing possible
+ 
+
+ align:start position:0%
+is such a thing possible
+but we got together and not just Harvard
+
+ align:start position:0%
+but we got together and not just Harvard
+ 
+
+ align:start position:0%
+but we got together and not just Harvard
+faculty but Jeff Sachs was here then and
+
+ align:start position:0%
+faculty but Jeff Sachs was here then and
+ 
+
+ align:start position:0%
+faculty but Jeff Sachs was here then and
+a lot of infectious disease doctors uh
+
+ align:start position:0%
+a lot of infectious disease doctors uh
+ 
+
+ align:start position:0%
+a lot of infectious disease doctors uh
+and some economists and public health
+
+ align:start position:0%
+and some economists and public health
+ 
+
+ align:start position:0%
+and some economists and public health
+figures and said you know we really need
+
+ align:start position:0%
+figures and said you know we really need
+ 
+
+ align:start position:0%
+figures and said you know we really need
+to abandon this idea that we have to
+
+ align:start position:0%
+to abandon this idea that we have to
+ 
+
+ align:start position:0%
+to abandon this idea that we have to
+choose between prevention and Care a
+
+ align:start position:0%
+choose between prevention and Care a
+ 
+
+ align:start position:0%
+choose between prevention and Care a
+noxious idea we have to have integrated
+
+ align:start position:0%
+noxious idea we have to have integrated
+ 
+
+ align:start position:0%
+noxious idea we have to have integrated
+prevention and care for HIV and we have
+
+ align:start position:0%
+prevention and care for HIV and we have
+ 
+
+ align:start position:0%
+prevention and care for HIV and we have
+to acknowledge the complexity of the
+
+ align:start position:0%
+to acknowledge the complexity of the
+ 
+
+ align:start position:0%
+to acknowledge the complexity of the
+epidemic so we wrote that together and
+
+ align:start position:0%
+epidemic so we wrote that together and
+ 
+
+ align:start position:0%
+epidemic so we wrote that together and
+and we were really pushing for something
+
+ align:start position:0%
+and we were really pushing for something
+ 
+
+ align:start position:0%
+and we were really pushing for something
+this is a policy piece and we were
+
+ align:start position:0%
+this is a policy piece and we were
+ 
+
+ align:start position:0%
+this is a policy piece and we were
+pushing of course for the creation of
+
+ align:start position:0%
+pushing of course for the creation of
+ 
+
+ align:start position:0%
+pushing of course for the creation of
+multilateral or bilateral programs that
+
+ align:start position:0%
+multilateral or bilateral programs that
+ 
+
+ align:start position:0%
+multilateral or bilateral programs that
+would fund much more ambitious responses
+
+ align:start position:0%
+would fund much more ambitious responses
+ 
+
+ align:start position:0%
+would fund much more ambitious responses
+to these ranking health problems and
+
+ align:start position:0%
+to these ranking health problems and
+ 
+
+ align:start position:0%
+to these ranking health problems and
+those became pepfar and and first the
+
+ align:start position:0%
+those became pepfar and and first the
+ 
+
+ align:start position:0%
+those became pepfar and and first the
+global fund I guess and then that far
+
+ align:start position:0%
+global fund I guess and then that far
+ 
+
+ align:start position:0%
+global fund I guess and then that far
+and then this failure of imagination
+
+ align:start position:0%
+and then this failure of imagination
+ 
+
+ align:start position:0%
+and then this failure of imagination
+which was I believe caused by a
+
+ align:start position:0%
+which was I believe caused by a
+ 
+
+ align:start position:0%
+which was I believe caused by a
+socialization for scarcity was was
+
+ align:start position:0%
+socialization for scarcity was was
+ 
+
+ align:start position:0%
+socialization for scarcity was was
+countered by resources and that that
+
+ align:start position:0%
+countered by resources and that that
+ 
+
+ align:start position:0%
+countered by resources and that that
+opened up the space to build the
+
+ align:start position:0%
+opened up the space to build the
+ 
+
+ align:start position:0%
+opened up the space to build the
+platforms that I'll describe and also
+
+ align:start position:0%
+platforms that I'll describe and also
+ 
+
+ align:start position:0%
+platforms that I'll describe and also
+created an acute need for better
+
+ align:start position:0%
+created an acute need for better
+ 
+
+ align:start position:0%
+created an acute need for better
+management of information and
+
+ align:start position:0%
+management of information and
+ 
+
+ align:start position:0%
+management of information and
+now the I will skip over this I told you
+
+ align:start position:0%
+now the I will skip over this I told you
+ 
+
+ align:start position:0%
+now the I will skip over this I told you
+we talk about accompaniment but we have
+
+ align:start position:0%
+we talk about accompaniment but we have
+ 
+
+ align:start position:0%
+we talk about accompaniment but we have
+good reason to believe that this is the
+
+ align:start position:0%
+good reason to believe that this is the
+ 
+
+ align:start position:0%
+good reason to believe that this is the
+highest standard of care because we've
+
+ align:start position:0%
+highest standard of care because we've
+ 
+
+ align:start position:0%
+highest standard of care because we've
+been taking care of people in so-called
+
+ align:start position:0%
+been taking care of people in so-called
+ 
+
+ align:start position:0%
+been taking care of people in so-called
+resource core settings as you're just
+
+ align:start position:0%
+resource core settings as you're just
+ 
+
+ align:start position:0%
+resource core settings as you're just
+you determining using in this class
+
+ align:start position:0%
+you determining using in this class
+ 
+
+ align:start position:0%
+you determining using in this class
+um who are still a decade later or more
+
+ align:start position:0%
+um who are still a decade later or more
+ 
+
+ align:start position:0%
+um who are still a decade later or more
+doing very well like this is another
+
+ align:start position:0%
+doing very well like this is another
+ 
+
+ align:start position:0%
+doing very well like this is another
+patient of mine first at home dying of
+
+ align:start position:0%
+patient of mine first at home dying of
+ 
+
+ align:start position:0%
+patient of mine first at home dying of
+AIDS and then 10 years later at Sanders
+
+ align:start position:0%
+AIDS and then 10 years later at Sanders
+ 
+
+ align:start position:0%
+AIDS and then 10 years later at Sanders
+Theater at Harvard giving a talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a doctor or nurse or Community
+
+ align:start position:0%
+for a doctor or nurse or Community
+ 
+
+ align:start position:0%
+for a doctor or nurse or Community
+Health program as you might imagine or
+
+ align:start position:0%
+Health program as you might imagine or
+ 
+
+ align:start position:0%
+Health program as you might imagine or
+anyone right to have a family member
+
+ align:start position:0%
+anyone right to have a family member
+ 
+
+ align:start position:0%
+anyone right to have a family member
+who comes back from the dead as the
+
+ align:start position:0%
+who comes back from the dead as the
+ 
+
+ align:start position:0%
+who comes back from the dead as the
+nation say it's very gratifying and when
+
+ align:start position:0%
+nation say it's very gratifying and when
+ 
+
+ align:start position:0%
+nation say it's very gratifying and when
+this happens over and over and over
+
+ align:start position:0%
+this happens over and over and over
+ 
+
+ align:start position:0%
+this happens over and over and over
+again you have a lot of satisfaction but
+
+ align:start position:0%
+again you have a lot of satisfaction but
+ 
+
+ align:start position:0%
+again you have a lot of satisfaction but
+you also have a huge challenge of
+
+ align:start position:0%
+you also have a huge challenge of
+ 
+
+ align:start position:0%
+you also have a huge challenge of
+managing uh information and that
+
+ align:start position:0%
+managing uh information and that
+ 
+
+ align:start position:0%
+managing uh information and that
+challenge occurs at each of the three
+
+ align:start position:0%
+challenge occurs at each of the three
+ 
+
+ align:start position:0%
+challenge occurs at each of the three
+levels that I mentioned at the community
+
+ align:start position:0%
+levels that I mentioned at the community
+ 
+
+ align:start position:0%
+levels that I mentioned at the community
+level for the community health worker or
+
+ align:start position:0%
+level for the community health worker or
+ 
+
+ align:start position:0%
+level for the community health worker or
+a company nature at the clinic level
+
+ align:start position:0%
+a company nature at the clinic level
+ 
+
+ align:start position:0%
+a company nature at the clinic level
+where care should be coordinated not in
+
+ align:start position:0%
+where care should be coordinated not in
+ 
+
+ align:start position:0%
+where care should be coordinated not in
+the hospital and then but finally at the
+
+ align:start position:0%
+the hospital and then but finally at the
+ 
+
+ align:start position:0%
+the hospital and then but finally at the
+hospital how do you track people who do
+
+ align:start position:0%
+hospital how do you track people who do
+ 
+
+ align:start position:0%
+hospital how do you track people who do
+have complications and do get sick again
+
+ align:start position:0%
+have complications and do get sick again
+ 
+
+ align:start position:0%
+have complications and do get sick again
+actually this guy later got does can
+
+ align:start position:0%
+actually this guy later got does can
+ 
+
+ align:start position:0%
+actually this guy later got does can
+anyone guess okay he's been treated now
+
+ align:start position:0%
+anyone guess okay he's been treated now
+ 
+
+ align:start position:0%
+anyone guess okay he's been treated now
+for a smear positive TB and for HIV and
+
+ align:start position:0%
+for a smear positive TB and for HIV and
+ 
+
+ align:start position:0%
+for a smear positive TB and for HIV and
+he's doing well what what do you think
+
+ align:start position:0%
+he's doing well what what do you think
+ 
+
+ align:start position:0%
+he's doing well what what do you think
+now the new and deadly the people in
+
+ align:start position:0%
+now the new and deadly the people in
+ 
+
+ align:start position:0%
+now the new and deadly the people in
+southern Africa know this what's the new
+
+ align:start position:0%
+southern Africa know this what's the new
+ 
+
+ align:start position:0%
+southern Africa know this what's the new
+and deadly
+
+ align:start position:0%
+and deadly
+ 
+
+ align:start position:0%
+and deadly
+complication
+
+ align:start position:0%
+complication
+ 
+
+ align:start position:0%
+complication
+MDR so he got MDR
+
+ align:start position:0%
+MDR so he got MDR
+ 
+
+ align:start position:0%
+MDR so he got MDR
+but may I ask who said that yeah so um
+
+ align:start position:0%
+but may I ask who said that yeah so um
+ 
+
+ align:start position:0%
+but may I ask who said that yeah so um
+that's you know in other words we used
+
+ align:start position:0%
+that's you know in other words we used
+ 
+
+ align:start position:0%
+that's you know in other words we used
+to believe
+
+ align:start position:0%
+to believe
+ 
+
+ align:start position:0%
+to believe
+in the 40s and 50s now I personally was
+
+ align:start position:0%
+in the 40s and 50s now I personally was
+ 
+
+ align:start position:0%
+in the 40s and 50s now I personally was
+not around in the 40s so I didn't
+
+ align:start position:0%
+not around in the 40s so I didn't
+ 
+
+ align:start position:0%
+not around in the 40s so I didn't
+personally believe anything in the 40s
+
+ align:start position:0%
+personally believe anything in the 40s
+ 
+
+ align:start position:0%
+personally believe anything in the 40s
+but we used to believe as they say
+
+ align:start position:0%
+but we used to believe as they say
+ 
+
+ align:start position:0%
+but we used to believe as they say
+magisterial magisteri in medicine that
+
+ align:start position:0%
+magisterial magisteri in medicine that
+ 
+
+ align:start position:0%
+magisterial magisteri in medicine that
+you couldn't get tuberculosis twice
+
+ align:start position:0%
+you couldn't get tuberculosis twice
+ 
+
+ align:start position:0%
+you couldn't get tuberculosis twice
+but we didn't have the Diagnostics
+
+ align:start position:0%
+but we didn't have the Diagnostics
+ 
+
+ align:start position:0%
+but we didn't have the Diagnostics
+molecular Diagnostics to show that that
+
+ align:start position:0%
+molecular Diagnostics to show that that
+ 
+
+ align:start position:0%
+molecular Diagnostics to show that that
+was a false idea you can and do get
+
+ align:start position:0%
+was a false idea you can and do get
+ 
+
+ align:start position:0%
+was a false idea you can and do get
+tuberculosis multiple times you can have
+
+ align:start position:0%
+tuberculosis multiple times you can have
+ 
+
+ align:start position:0%
+tuberculosis multiple times you can have
+even have multiple infections at the
+
+ align:start position:0%
+even have multiple infections at the
+ 
+
+ align:start position:0%
+even have multiple infections at the
+same time and then we said well once you
+
+ align:start position:0%
+same time and then we said well once you
+ 
+
+ align:start position:0%
+same time and then we said well once you
+treat someone for the TB
+
+ align:start position:0%
+treat someone for the TB
+ 
+
+ align:start position:0%
+treat someone for the TB
+they're they're good because they have
+
+ align:start position:0%
+they're they're good because they have
+ 
+
+ align:start position:0%
+they're they're good because they have
+natural immunity that also wasn't true
+
+ align:start position:0%
+natural immunity that also wasn't true
+ 
+
+ align:start position:0%
+natural immunity that also wasn't true
+so this problem that Joseph had and
+
+ align:start position:0%
+so this problem that Joseph had and
+ 
+
+ align:start position:0%
+so this problem that Joseph had and
+already survived that is his second bout
+
+ align:start position:0%
+already survived that is his second bout
+ 
+
+ align:start position:0%
+already survived that is his second bout
+with TB MDR TV is going to happen more
+
+ align:start position:0%
+with TB MDR TV is going to happen more
+ 
+
+ align:start position:0%
+with TB MDR TV is going to happen more
+and more and more and so again the
+
+ align:start position:0%
+and more and more and so again the
+ 
+
+ align:start position:0%
+and more and more and so again the
+complexity of this and Hamish mentioned
+
+ align:start position:0%
+complexity of this and Hamish mentioned
+ 
+
+ align:start position:0%
+complexity of this and Hamish mentioned
+some of our work in Peru the complexity
+
+ align:start position:0%
+some of our work in Peru the complexity
+ 
+
+ align:start position:0%
+some of our work in Peru the complexity
+of this is just astounding you have
+
+ align:start position:0%
+of this is just astounding you have
+ 
+
+ align:start position:0%
+of this is just astounding you have
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+drugs you have if you know you're
+
+ align:start position:0%
+drugs you have if you know you're
+ 
+
+ align:start position:0%
+drugs you have if you know you're
+talking sometimes about 10 or 15 drugs a
+
+ align:start position:0%
+talking sometimes about 10 or 15 drugs a
+ 
+
+ align:start position:0%
+talking sometimes about 10 or 15 drugs a
+day you have not as he said thousands of
+
+ align:start position:0%
+day you have not as he said thousands of
+ 
+
+ align:start position:0%
+day you have not as he said thousands of
+patients I'll show you how many tens of
+
+ align:start position:0%
+patients I'll show you how many tens of
+ 
+
+ align:start position:0%
+patients I'll show you how many tens of
+thousands we're talking about and you
+
+ align:start position:0%
+thousands we're talking about and you
+ 
+
+ align:start position:0%
+thousands we're talking about and you
+have to manage uh the the complexity for
+
+ align:start position:0%
+have to manage uh the the complexity for
+ 
+
+ align:start position:0%
+have to manage uh the the complexity for
+every patient but also the complexity of
+
+ align:start position:0%
+every patient but also the complexity of
+ 
+
+ align:start position:0%
+every patient but also the complexity of
+the program
+
+ align:start position:0%
+the program
+ 
+
+ align:start position:0%
+the program
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and at the same time
+
+ align:start position:0%
+and at the same time
+ 
+
+ align:start position:0%
+and at the same time
+we have to strengthen Health Systems now
+
+ align:start position:0%
+we have to strengthen Health Systems now
+ 
+
+ align:start position:0%
+we have to strengthen Health Systems now
+what does that mean I already told you
+
+ align:start position:0%
+what does that mean I already told you
+ 
+
+ align:start position:0%
+what does that mean I already told you
+that we're getting an influx of vertical
+
+ align:start position:0%
+that we're getting an influx of vertical
+ 
+
+ align:start position:0%
+that we're getting an influx of vertical
+money focused on AIDS but with that
+
+ align:start position:0%
+money focused on AIDS but with that
+ 
+
+ align:start position:0%
+money focused on AIDS but with that
+money we have to make it do several
+
+ align:start position:0%
+money we have to make it do several
+ 
+
+ align:start position:0%
+money we have to make it do several
+things at once one is to strengthen
+
+ align:start position:0%
+things at once one is to strengthen
+ 
+
+ align:start position:0%
+things at once one is to strengthen
+community-based care right but the other
+
+ align:start position:0%
+community-based care right but the other
+ 
+
+ align:start position:0%
+community-based care right but the other
+is to build all those levels those three
+
+ align:start position:0%
+is to build all those levels those three
+ 
+
+ align:start position:0%
+is to build all those levels those three
+levels of of care including hospitals so
+
+ align:start position:0%
+levels of of care including hospitals so
+ 
+
+ align:start position:0%
+levels of of care including hospitals so
+we developed I think along with others
+
+ align:start position:0%
+we developed I think along with others
+ 
+
+ align:start position:0%
+we developed I think along with others
+but this language of Health System
+
+ align:start position:0%
+but this language of Health System
+ 
+
+ align:start position:0%
+but this language of Health System
+strengthening does describe what it is
+
+ align:start position:0%
+strengthening does describe what it is
+ 
+
+ align:start position:0%
+strengthening does describe what it is
+we were doing with the AIDS money we
+
+ align:start position:0%
+we were doing with the AIDS money we
+ 
+
+ align:start position:0%
+we were doing with the AIDS money we
+received in uh especially after 2003 and
+
+ align:start position:0%
+received in uh especially after 2003 and
+ 
+
+ align:start position:0%
+received in uh especially after 2003 and
+this is an example of a place
+
+ align:start position:0%
+this is an example of a place
+ 
+
+ align:start position:0%
+this is an example of a place
+before and after now it is by the way
+
+ align:start position:0%
+before and after now it is by the way
+ 
+
+ align:start position:0%
+before and after now it is by the way
+all uh solar powered as well
+
+ align:start position:0%
+all uh solar powered as well
+ 
+
+ align:start position:0%
+all uh solar powered as well
+and although the the person who
+
+ align:start position:0%
+and although the the person who
+ 
+
+ align:start position:0%
+and although the the person who
+um set up that system in Haitian with us
+
+ align:start position:0%
+um set up that system in Haitian with us
+ 
+
+ align:start position:0%
+um set up that system in Haitian with us
+in Rwanda and elsewhere died in the
+
+ align:start position:0%
+in Rwanda and elsewhere died in the
+ 
+
+ align:start position:0%
+in Rwanda and elsewhere died in the
+earthquake but you know we've made a lot
+
+ align:start position:0%
+earthquake but you know we've made a lot
+ 
+
+ align:start position:0%
+earthquake but you know we've made a lot
+of progress on other leapfrogging
+
+ align:start position:0%
+of progress on other leapfrogging
+ 
+
+ align:start position:0%
+of progress on other leapfrogging
+Technologies including how to power
+
+ align:start position:0%
+Technologies including how to power
+ 
+
+ align:start position:0%
+Technologies including how to power
+these hospitals and we learned how to
+
+ align:start position:0%
+these hospitals and we learned how to
+ 
+
+ align:start position:0%
+these hospitals and we learned how to
+make better hospitals this one was a few
+
+ align:start position:0%
+make better hospitals this one was a few
+ 
+
+ align:start position:0%
+make better hospitals this one was a few
+years later
+
+ align:start position:0%
+years later
+ 
+
+ align:start position:0%
+years later
+um actually a hospital redo in 2003 the
+
+ align:start position:0%
+um actually a hospital redo in 2003 the
+ 
+
+ align:start position:0%
+um actually a hospital redo in 2003 the
+first place that we used Global fund
+
+ align:start position:0%
+first place that we used Global fund
+ 
+
+ align:start position:0%
+first place that we used Global fund
+money this is an 80.
+
+ align:start position:0%
+money this is an 80.
+ 
+
+ align:start position:0%
+money this is an 80.
+um and then we just rebuilt it again
+
+ align:start position:0%
+um and then we just rebuilt it again
+ 
+
+ align:start position:0%
+um and then we just rebuilt it again
+from scratch and I'll talk a little bit
+
+ align:start position:0%
+from scratch and I'll talk a little bit
+ 
+
+ align:start position:0%
+from scratch and I'll talk a little bit
+more about that at the end now this
+
+ align:start position:0%
+more about that at the end now this
+ 
+
+ align:start position:0%
+more about that at the end now this
+model of three levels of intervention
+
+ align:start position:0%
+model of three levels of intervention
+ 
+
+ align:start position:0%
+model of three levels of intervention
+public-private Partnerships you know I
+
+ align:start position:0%
+public-private Partnerships you know I
+ 
+
+ align:start position:0%
+public-private Partnerships you know I
+could I could go on this I don't even
+
+ align:start position:0%
+could I could go on this I don't even
+ 
+
+ align:start position:0%
+could I could go on this I don't even
+know if model is the right word that is
+
+ align:start position:0%
+know if model is the right word that is
+ 
+
+ align:start position:0%
+know if model is the right word that is
+we also want to strengthen wood shell
+
+ align:start position:0%
+we also want to strengthen wood shell
+ 
+
+ align:start position:0%
+we also want to strengthen wood shell
+systems the Public Health Systems
+
+ align:start position:0%
+systems the Public Health Systems
+ 
+
+ align:start position:0%
+systems the Public Health Systems
+because those were the weakest now there
+
+ align:start position:0%
+because those were the weakest now there
+ 
+
+ align:start position:0%
+because those were the weakest now there
+are some places where people are not at
+
+ align:start position:0%
+are some places where people are not at
+ 
+
+ align:start position:0%
+are some places where people are not at
+all sanguine about doing that and are
+
+ align:start position:0%
+all sanguine about doing that and are
+ 
+
+ align:start position:0%
+all sanguine about doing that and are
+going to stick with the private sector
+
+ align:start position:0%
+going to stick with the private sector
+ 
+
+ align:start position:0%
+going to stick with the private sector
+but in general in Latin America and
+
+ align:start position:0%
+but in general in Latin America and
+ 
+
+ align:start position:0%
+but in general in Latin America and
+Africa the places where I work most or
+
+ align:start position:0%
+Africa the places where I work most or
+ 
+
+ align:start position:0%
+Africa the places where I work most or
+to say nothing of Siberia this is a good
+
+ align:start position:0%
+to say nothing of Siberia this is a good
+ 
+
+ align:start position:0%
+to say nothing of Siberia this is a good
+the idea to strengthen the public sector
+
+ align:start position:0%
+the idea to strengthen the public sector
+ 
+
+ align:start position:0%
+the idea to strengthen the public sector
+and in general I'm not saying we have to
+
+ align:start position:0%
+and in general I'm not saying we have to
+ 
+
+ align:start position:0%
+and in general I'm not saying we have to
+be ideological about it is there some
+
+ align:start position:0%
+be ideological about it is there some
+ 
+
+ align:start position:0%
+be ideological about it is there some
+I'm glad I'm getting a weekly update
+
+ align:start position:0%
+I'm glad I'm getting a weekly update
+ 
+
+ align:start position:0%
+I'm glad I'm getting a weekly update
+call on TV I told you Hamish that I love
+
+ align:start position:0%
+call on TV I told you Hamish that I love
+ 
+
+ align:start position:0%
+call on TV I told you Hamish that I love
+technology but not that much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodbye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as if you were ever on those weekly
+
+ align:start position:0%
+as if you were ever on those weekly
+ 
+
+ align:start position:0%
+as if you were ever on those weekly
+update calls now I'll I'll be ready when
+
+ align:start position:0%
+update calls now I'll I'll be ready when
+ 
+
+ align:start position:0%
+update calls now I'll I'll be ready when
+it comes back so from the Dominican
+
+ align:start position:0%
+it comes back so from the Dominican
+ 
+
+ align:start position:0%
+it comes back so from the Dominican
+border
+
+ align:start position:0%
+border
+ 
+
+ align:start position:0%
+border
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um to the coast and so many of you have
+
+ align:start position:0%
+um to the coast and so many of you have
+ 
+
+ align:start position:0%
+um to the coast and so many of you have
+been to this this part of the world we
+
+ align:start position:0%
+been to this this part of the world we
+ 
+
+ align:start position:0%
+been to this this part of the world we
+followed this model more or less and
+
+ align:start position:0%
+followed this model more or less and
+ 
+
+ align:start position:0%
+followed this model more or less and
+started serving uh uh a lot of people
+
+ align:start position:0%
+started serving uh uh a lot of people
+ 
+
+ align:start position:0%
+started serving uh uh a lot of people
+how many people well this is this is I
+
+ align:start position:0%
+how many people well this is this is I
+ 
+
+ align:start position:0%
+how many people well this is this is I
+just pulled this yesterday from the PIH
+
+ align:start position:0%
+just pulled this yesterday from the PIH
+ 
+
+ align:start position:0%
+just pulled this yesterday from the PIH
+report annual report
+
+ align:start position:0%
+report annual report
+ 
+
+ align:start position:0%
+report annual report
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and there's this helpful part the
+
+ align:start position:0%
+and there's this helpful part the
+ 
+
+ align:start position:0%
+and there's this helpful part the
+margins in fact
+
+ align:start position:0%
+margins in fact
+ 
+
+ align:start position:0%
+margins in fact
+whoever made this I didn't I wish I
+
+ align:start position:0%
+whoever made this I didn't I wish I
+ 
+
+ align:start position:0%
+whoever made this I didn't I wish I
+could claim to have made this nice
+
+ align:start position:0%
+could claim to have made this nice
+ 
+
+ align:start position:0%
+could claim to have made this nice
+report but this is very helpful
+
+ align:start position:0%
+report but this is very helpful
+ 
+
+ align:start position:0%
+report but this is very helpful
+certainly helpful when you contemplate
+
+ align:start position:0%
+certainly helpful when you contemplate
+ 
+
+ align:start position:0%
+certainly helpful when you contemplate
+information technology and managing
+
+ align:start position:0%
+information technology and managing
+ 
+
+ align:start position:0%
+information technology and managing
+systems when you start reaching this
+
+ align:start position:0%
+systems when you start reaching this
+ 
+
+ align:start position:0%
+systems when you start reaching this
+scale and this is more patients served
+
+ align:start position:0%
+scale and this is more patients served
+ 
+
+ align:start position:0%
+scale and this is more patients served
+I'm not going to talk about quality of
+
+ align:start position:0%
+I'm not going to talk about quality of
+ 
+
+ align:start position:0%
+I'm not going to talk about quality of
+care today although I believe the
+
+ align:start position:0%
+care today although I believe the
+ 
+
+ align:start position:0%
+care today although I believe the
+programmatic care like creativity is
+
+ align:start position:0%
+programmatic care like creativity is
+ 
+
+ align:start position:0%
+programmatic care like creativity is
+very good as I said but this is many
+
+ align:start position:0%
+very good as I said but this is many
+ 
+
+ align:start position:0%
+very good as I said but this is many
+more probably than the big hospitals in
+
+ align:start position:0%
+more probably than the big hospitals in
+ 
+
+ align:start position:0%
+more probably than the big hospitals in
+Boston where I train Leo train
+
+ align:start position:0%
+Boston where I train Leo train
+ 
+
+ align:start position:0%
+Boston where I train Leo train
+um this is a huge huge scale now you'll
+
+ align:start position:0%
+um this is a huge huge scale now you'll
+ 
+
+ align:start position:0%
+um this is a huge huge scale now you'll
+hear people talk about scale that
+
+ align:start position:0%
+hear people talk about scale that
+ 
+
+ align:start position:0%
+hear people talk about scale that
+involves hundreds of millions of
+
+ align:start position:0%
+involves hundreds of millions of
+ 
+
+ align:start position:0%
+involves hundreds of millions of
+patients and
+
+ align:start position:0%
+patients and
+ 
+
+ align:start position:0%
+patients and
+I'm sure that happens now and again but
+
+ align:start position:0%
+I'm sure that happens now and again but
+ 
+
+ align:start position:0%
+I'm sure that happens now and again but
+it's really we're we're still struggling
+
+ align:start position:0%
+it's really we're we're still struggling
+ 
+
+ align:start position:0%
+it's really we're we're still struggling
+to get there
+
+ align:start position:0%
+to get there
+ 
+
+ align:start position:0%
+to get there
+and I I train some of you were involved
+
+ align:start position:0%
+and I I train some of you were involved
+ 
+
+ align:start position:0%
+and I I train some of you were involved
+in the the uh the creation of the
+
+ align:start position:0%
+in the the uh the creation of the
+ 
+
+ align:start position:0%
+in the the uh the creation of the
+Brigham electronic medical record and
+
+ align:start position:0%
+Brigham electronic medical record and
+ 
+
+ align:start position:0%
+Brigham electronic medical record and
+you know I I was lucky enough to be in
+
+ align:start position:0%
+you know I I was lucky enough to be in
+ 
+
+ align:start position:0%
+you know I I was lucky enough to be in
+that first cohort of American doctors
+
+ align:start position:0%
+that first cohort of American doctors
+ 
+
+ align:start position:0%
+that first cohort of American doctors
+who became accustomed to having
+
+ align:start position:0%
+who became accustomed to having
+ 
+
+ align:start position:0%
+who became accustomed to having
+electronic medical record but the real
+
+ align:start position:0%
+electronic medical record but the real
+ 
+
+ align:start position:0%
+electronic medical record but the real
+the way I got the idea to push this
+
+ align:start position:0%
+the way I got the idea to push this
+ 
+
+ align:start position:0%
+the way I got the idea to push this
+forward in Haiti and to recruit Hamish
+
+ align:start position:0%
+forward in Haiti and to recruit Hamish
+ 
+
+ align:start position:0%
+forward in Haiti and to recruit Hamish
+which I did
+
+ align:start position:0%
+which I did
+ 
+
+ align:start position:0%
+which I did
+was actually getting on board a plane do
+
+ align:start position:0%
+was actually getting on board a plane do
+ 
+
+ align:start position:0%
+was actually getting on board a plane do
+you remember this
+
+ align:start position:0%
+you remember this
+ 
+
+ align:start position:0%
+you remember this
+every time that you go to the American
+
+ align:start position:0%
+every time that you go to the American
+ 
+
+ align:start position:0%
+every time that you go to the American
+Airlines and believe me I have I I would
+
+ align:start position:0%
+Airlines and believe me I have I I would
+ 
+
+ align:start position:0%
+Airlines and believe me I have I I would
+put George Clooney to shame
+
+ align:start position:0%
+put George Clooney to shame
+ 
+
+ align:start position:0%
+put George Clooney to shame
+um they you they can't print out the
+
+ align:start position:0%
+um they you they can't print out the
+ 
+
+ align:start position:0%
+um they you they can't print out the
+boarding pass
+
+ align:start position:0%
+boarding pass
+ 
+
+ align:start position:0%
+boarding pass
+if they don't have the right information
+
+ align:start position:0%
+if they don't have the right information
+ 
+
+ align:start position:0%
+if they don't have the right information
+in in there and it's programmed that
+
+ align:start position:0%
+in in there and it's programmed that
+ 
+
+ align:start position:0%
+in in there and it's programmed that
+they code they wrote or stole I don't
+
+ align:start position:0%
+they code they wrote or stole I don't
+ 
+
+ align:start position:0%
+they code they wrote or stole I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+but this was uh something that American
+
+ align:start position:0%
+but this was uh something that American
+ 
+
+ align:start position:0%
+but this was uh something that American
+Airline used not as open source but they
+
+ align:start position:0%
+Airline used not as open source but they
+ 
+
+ align:start position:0%
+Airline used not as open source but they
+developed their own software you know
+
+ align:start position:0%
+developed their own software you know
+ 
+
+ align:start position:0%
+developed their own software you know
+some of you will know the name of it I
+
+ align:start position:0%
+some of you will know the name of it I
+ 
+
+ align:start position:0%
+some of you will know the name of it I
+certainly remember the name of it and if
+
+ align:start position:0%
+certainly remember the name of it and if
+ 
+
+ align:start position:0%
+certainly remember the name of it and if
+you don't have all the right information
+
+ align:start position:0%
+you don't have all the right information
+ 
+
+ align:start position:0%
+you don't have all the right information
+it won't print the boarding pass how
+
+ align:start position:0%
+it won't print the boarding pass how
+ 
+
+ align:start position:0%
+it won't print the boarding pass how
+many times have you seen this so my
+
+ align:start position:0%
+many times have you seen this so my
+ 
+
+ align:start position:0%
+many times have you seen this so my
+frustration was goading I already told
+
+ align:start position:0%
+frustration was goading I already told
+ 
+
+ align:start position:0%
+frustration was goading I already told
+you I'm a specialist at guilt tripping
+
+ align:start position:0%
+you I'm a specialist at guilt tripping
+ 
+
+ align:start position:0%
+you I'm a specialist at guilt tripping
+but I couldn't manage to Guilt Trip
+
+ align:start position:0%
+but I couldn't manage to Guilt Trip
+ 
+
+ align:start position:0%
+but I couldn't manage to Guilt Trip
+people into making sure that every time
+
+ align:start position:0%
+people into making sure that every time
+ 
+
+ align:start position:0%
+people into making sure that every time
+a patient came in to Clinic they were
+
+ align:start position:0%
+a patient came in to Clinic they were
+ 
+
+ align:start position:0%
+a patient came in to Clinic they were
+weighed does this ring any bells and you
+
+ align:start position:0%
+weighed does this ring any bells and you
+ 
+
+ align:start position:0%
+weighed does this ring any bells and you
+know I thought well that's what doctor
+
+ align:start position:0%
+know I thought well that's what doctor
+ 
+
+ align:start position:0%
+know I thought well that's what doctor
+pay if they don't weigh the patient
+
+ align:start position:0%
+pay if they don't weigh the patient
+ 
+
+ align:start position:0%
+pay if they don't weigh the patient
+although people do that now they call it
+
+ align:start position:0%
+although people do that now they call it
+ 
+
+ align:start position:0%
+although people do that now they call it
+they call that
+
+ align:start position:0%
+they call that
+ 
+
+ align:start position:0%
+they call that
+yeah exactly I just call it you know
+
+ align:start position:0%
+yeah exactly I just call it you know
+ 
+
+ align:start position:0%
+yeah exactly I just call it you know
+good old-fashioned Catholic punishment
+
+ align:start position:0%
+good old-fashioned Catholic punishment
+ 
+
+ align:start position:0%
+good old-fashioned Catholic punishment
+but it didn't it didn't work on a
+
+ align:start position:0%
+but it didn't it didn't work on a
+ 
+
+ align:start position:0%
+but it didn't it didn't work on a
+systems level right let's do it if we're
+
+ align:start position:0%
+systems level right let's do it if we're
+ 
+
+ align:start position:0%
+systems level right let's do it if we're
+going to go around to each clinic and
+
+ align:start position:0%
+going to go around to each clinic and
+ 
+
+ align:start position:0%
+going to go around to each clinic and
+you know try and shame the nurses of
+
+ align:start position:0%
+you know try and shame the nurses of
+ 
+
+ align:start position:0%
+you know try and shame the nurses of
+course not doesn't work but
+
+ align:start position:0%
+course not doesn't work but
+ 
+
+ align:start position:0%
+course not doesn't work but
+um we asked hey Mission Darius to
+
+ align:start position:0%
+um we asked hey Mission Darius to
+ 
+
+ align:start position:0%
+um we asked hey Mission Darius to
+rewrite our code so that you couldn't
+
+ align:start position:0%
+rewrite our code so that you couldn't
+ 
+
+ align:start position:0%
+rewrite our code so that you couldn't
+prescribe if the patient wasn't right it
+
+ align:start position:0%
+prescribe if the patient wasn't right it
+ 
+
+ align:start position:0%
+prescribe if the patient wasn't right it
+would just give you like a message like
+
+ align:start position:0%
+would just give you like a message like
+ 
+
+ align:start position:0%
+would just give you like a message like
+I just got about the TV meeting now this
+
+ align:start position:0%
+I just got about the TV meeting now this
+ 
+
+ align:start position:0%
+I just got about the TV meeting now this
+was quite a while ago before this had
+
+ align:start position:0%
+was quite a while ago before this had
+ 
+
+ align:start position:0%
+was quite a while ago before this had
+ever been seen remember this is an area
+
+ align:start position:0%
+ever been seen remember this is an area
+ 
+
+ align:start position:0%
+ever been seen remember this is an area
+these are areas of the world where
+
+ align:start position:0%
+these are areas of the world where
+ 
+
+ align:start position:0%
+these are areas of the world where
+there's no electricity so we also had to
+
+ align:start position:0%
+there's no electricity so we also had to
+ 
+
+ align:start position:0%
+there's no electricity so we also had to
+generate the electricity put in place a
+
+ align:start position:0%
+generate the electricity put in place a
+ 
+
+ align:start position:0%
+generate the electricity put in place a
+satellite hookup
+
+ align:start position:0%
+satellite hookup
+ 
+
+ align:start position:0%
+satellite hookup
+so that it could be automatic up Uplink
+
+ align:start position:0%
+so that it could be automatic up Uplink
+ 
+
+ align:start position:0%
+so that it could be automatic up Uplink
+of this information
+
+ align:start position:0%
+of this information
+ 
+
+ align:start position:0%
+of this information
+and actually build the hospitals I mean
+
+ align:start position:0%
+and actually build the hospitals I mean
+ 
+
+ align:start position:0%
+and actually build the hospitals I mean
+that's an unusual set of Demands again I
+
+ align:start position:0%
+that's an unusual set of Demands again I
+ 
+
+ align:start position:0%
+that's an unusual set of Demands again I
+just called that building a platform as
+
+ align:start position:0%
+just called that building a platform as
+ 
+
+ align:start position:0%
+just called that building a platform as
+if it were easy if I'm on service at the
+
+ align:start position:0%
+if it were easy if I'm on service at the
+ 
+
+ align:start position:0%
+if it were easy if I'm on service at the
+Brigham as an infectious disease doctor
+
+ align:start position:0%
+Brigham as an infectious disease doctor
+ 
+
+ align:start position:0%
+Brigham as an infectious disease doctor
+and think that a patient should have a
+
+ align:start position:0%
+and think that a patient should have a
+ 
+
+ align:start position:0%
+and think that a patient should have a
+brain biopsy to find out what's going on
+
+ align:start position:0%
+brain biopsy to find out what's going on
+ 
+
+ align:start position:0%
+brain biopsy to find out what's going on
+in some infection or supposed infection
+
+ align:start position:0%
+in some infection or supposed infection
+ 
+
+ align:start position:0%
+in some infection or supposed infection
+then I don't have to build the operating
+
+ align:start position:0%
+then I don't have to build the operating
+ 
+
+ align:start position:0%
+then I don't have to build the operating
+room and put in the electricity at the
+
+ align:start position:0%
+room and put in the electricity at the
+ 
+
+ align:start position:0%
+room and put in the electricity at the
+Brigham it's all done
+
+ align:start position:0%
+Brigham it's all done
+ 
+
+ align:start position:0%
+Brigham it's all done
+I don't have to do the surgery or
+
+ align:start position:0%
+I don't have to do the surgery or
+ 
+
+ align:start position:0%
+I don't have to do the surgery or
+anything like that either but this is
+
+ align:start position:0%
+anything like that either but this is
+ 
+
+ align:start position:0%
+anything like that either but this is
+what I mean by building a platform in a
+
+ align:start position:0%
+what I mean by building a platform in a
+ 
+
+ align:start position:0%
+what I mean by building a platform in a
+rural area now here's
+
+ align:start position:0%
+rural area now here's
+ 
+
+ align:start position:0%
+rural area now here's
+just back to what you're doing in this
+
+ align:start position:0%
+just back to what you're doing in this
+ 
+
+ align:start position:0%
+just back to what you're doing in this
+class we knew way before and again
+
+ align:start position:0%
+class we knew way before and again
+ 
+
+ align:start position:0%
+class we knew way before and again
+thanks to American Airlines and those
+
+ align:start position:0%
+thanks to American Airlines and those
+ 
+
+ align:start position:0%
+thanks to American Airlines and those
+boarding passes
+
+ align:start position:0%
+boarding passes
+ 
+
+ align:start position:0%
+boarding passes
+we knew way before this e helped
+
+ align:start position:0%
+we knew way before this e helped
+ 
+
+ align:start position:0%
+we knew way before this e helped
+uh I'm not going to say craze because I
+
+ align:start position:0%
+uh I'm not going to say craze because I
+ 
+
+ align:start position:0%
+uh I'm not going to say craze because I
+think it would be better if it were a
+
+ align:start position:0%
+think it would be better if it were a
+ 
+
+ align:start position:0%
+think it would be better if it were a
+craze we knew a long time before that
+
+ align:start position:0%
+craze we knew a long time before that
+ 
+
+ align:start position:0%
+craze we knew a long time before that
+that we needed this kind of assistance
+
+ align:start position:0%
+that we needed this kind of assistance
+ 
+
+ align:start position:0%
+that we needed this kind of assistance
+again that's why we recruited Hamish and
+
+ align:start position:0%
+again that's why we recruited Hamish and
+ 
+
+ align:start position:0%
+again that's why we recruited Hamish and
+started a health informatics team and
+
+ align:start position:0%
+started a health informatics team and
+ 
+
+ align:start position:0%
+started a health informatics team and
+then later tried to develop these open
+
+ align:start position:0%
+then later tried to develop these open
+ 
+
+ align:start position:0%
+then later tried to develop these open
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh systems that could manage this kind
+
+ align:start position:0%
+uh systems that could manage this kind
+ 
+
+ align:start position:0%
+uh systems that could manage this kind
+of collect complexity but we also knew
+
+ align:start position:0%
+of collect complexity but we also knew
+ 
+
+ align:start position:0%
+of collect complexity but we also knew
+early on that we there's no way have you
+
+ align:start position:0%
+early on that we there's no way have you
+ 
+
+ align:start position:0%
+early on that we there's no way have you
+ever seen a uh a file room in a hospital
+
+ align:start position:0%
+ever seen a uh a file room in a hospital
+ 
+
+ align:start position:0%
+ever seen a uh a file room in a hospital
+yeah it's pretty sad we still have them
+
+ align:start position:0%
+yeah it's pretty sad we still have them
+ 
+
+ align:start position:0%
+yeah it's pretty sad we still have them
+everywhere that we work the paper files
+
+ align:start position:0%
+everywhere that we work the paper files
+ 
+
+ align:start position:0%
+everywhere that we work the paper files
+which you know if you have seeing
+
+ align:start position:0%
+which you know if you have seeing
+ 
+
+ align:start position:0%
+which you know if you have seeing
+patients with a chronic disease they
+
+ align:start position:0%
+patients with a chronic disease they
+ 
+
+ align:start position:0%
+patients with a chronic disease they
+come back many times right it's not the
+
+ align:start position:0%
+come back many times right it's not the
+ 
+
+ align:start position:0%
+come back many times right it's not the
+same as managing you know a fracture or
+
+ align:start position:0%
+same as managing you know a fracture or
+ 
+
+ align:start position:0%
+same as managing you know a fracture or
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+a childbirth right the patients come
+
+ align:start position:0%
+a childbirth right the patients come
+ 
+
+ align:start position:0%
+a childbirth right the patients come
+back with chronic disease every month
+
+ align:start position:0%
+back with chronic disease every month
+ 
+
+ align:start position:0%
+back with chronic disease every month
+and then you have to do what you have to
+
+ align:start position:0%
+and then you have to do what you have to
+ 
+
+ align:start position:0%
+and then you have to do what you have to
+find their chart
+
+ align:start position:0%
+find their chart
+ 
+
+ align:start position:0%
+find their chart
+and again A lot of people are nodding
+
+ align:start position:0%
+and again A lot of people are nodding
+ 
+
+ align:start position:0%
+and again A lot of people are nodding
+because they've known how how hopelessly
+
+ align:start position:0%
+because they've known how how hopelessly
+ 
+
+ align:start position:0%
+because they've known how how hopelessly
+outdated the system is uh and probably
+
+ align:start position:0%
+outdated the system is uh and probably
+ 
+
+ align:start position:0%
+outdated the system is uh and probably
+was you know a hundred years ago but now
+
+ align:start position:0%
+was you know a hundred years ago but now
+ 
+
+ align:start position:0%
+was you know a hundred years ago but now
+we have Alternatives so that's where
+
+ align:start position:0%
+we have Alternatives so that's where
+ 
+
+ align:start position:0%
+we have Alternatives so that's where
+we're trying to go uh and why we need
+
+ align:start position:0%
+we're trying to go uh and why we need
+ 
+
+ align:start position:0%
+we're trying to go uh and why we need
+more help not unless so now we we took
+
+ align:start position:0%
+more help not unless so now we we took
+ 
+
+ align:start position:0%
+more help not unless so now we we took
+this system this platform to Rwanda
+
+ align:start position:0%
+this system this platform to Rwanda
+ 
+
+ align:start position:0%
+this system this platform to Rwanda
+and also to Malawi this tutu and uh and
+
+ align:start position:0%
+and also to Malawi this tutu and uh and
+ 
+
+ align:start position:0%
+and also to Malawi this tutu and uh and
+through partner organizations to other
+
+ align:start position:0%
+through partner organizations to other
+ 
+
+ align:start position:0%
+through partner organizations to other
+settings but this same model we did with
+
+ align:start position:0%
+settings but this same model we did with
+ 
+
+ align:start position:0%
+settings but this same model we did with
+the Clinton Foundation
+
+ align:start position:0%
+the Clinton Foundation
+ 
+
+ align:start position:0%
+the Clinton Foundation
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh what was designed to fill in this
+
+ align:start position:0%
+uh what was designed to fill in this
+ 
+
+ align:start position:0%
+uh what was designed to fill in this
+empty space in rural regions
+
+ align:start position:0%
+empty space in rural regions
+ 
+
+ align:start position:0%
+empty space in rural regions
+and the go arm means Governor Rwanda CF
+
+ align:start position:0%
+and the go arm means Governor Rwanda CF
+ 
+
+ align:start position:0%
+and the go arm means Governor Rwanda CF
+Foundation PIH we are Mo by that time
+
+ align:start position:0%
+Foundation PIH we are Mo by that time
+ 
+
+ align:start position:0%
+Foundation PIH we are Mo by that time
+was to build a local sister organization
+
+ align:start position:0%
+was to build a local sister organization
+ 
+
+ align:start position:0%
+was to build a local sister organization
+so some of you here have worked with the
+
+ align:start position:0%
+so some of you here have worked with the
+ 
+
+ align:start position:0%
+so some of you here have worked with the
+sister organizations whether in Peru or
+
+ align:start position:0%
+sister organizations whether in Peru or
+ 
+
+ align:start position:0%
+sister organizations whether in Peru or
+Haiti or Wonderland that's the idea is
+
+ align:start position:0%
+Haiti or Wonderland that's the idea is
+ 
+
+ align:start position:0%
+Haiti or Wonderland that's the idea is
+You're Building local capacity but by
+
+ align:start position:0%
+You're Building local capacity but by
+ 
+
+ align:start position:0%
+You're Building local capacity but by
+then in 2004 2005 we had one hopes
+
+ align:start position:0%
+then in 2004 2005 we had one hopes
+ 
+
+ align:start position:0%
+then in 2004 2005 we had one hopes
+learned enough about the limitations of
+
+ align:start position:0%
+learned enough about the limitations of
+ 
+
+ align:start position:0%
+learned enough about the limitations of
+our past
+
+ align:start position:0%
+our past
+ 
+
+ align:start position:0%
+our past
+uh platforms and could build new ones
+
+ align:start position:0%
+uh platforms and could build new ones
+ 
+
+ align:start position:0%
+uh platforms and could build new ones
+but that's why actually Hamish and
+
+ align:start position:0%
+but that's why actually Hamish and
+ 
+
+ align:start position:0%
+but that's why actually Hamish and
+Darius and others actually spent a lot
+
+ align:start position:0%
+Darius and others actually spent a lot
+ 
+
+ align:start position:0%
+Darius and others actually spent a lot
+of time moved to Rwanda with us to
+
+ align:start position:0%
+of time moved to Rwanda with us to
+ 
+
+ align:start position:0%
+of time moved to Rwanda with us to
+create the system a little bit more
+
+ align:start position:0%
+create the system a little bit more
+ 
+
+ align:start position:0%
+create the system a little bit more
+rapidly uh than it had happened in Haiti
+
+ align:start position:0%
+rapidly uh than it had happened in Haiti
+ 
+
+ align:start position:0%
+rapidly uh than it had happened in Haiti
+where it happened organically or Peru
+
+ align:start position:0%
+where it happened organically or Peru
+ 
+
+ align:start position:0%
+where it happened organically or Peru
+could we start the right way from the
+
+ align:start position:0%
+could we start the right way from the
+ 
+
+ align:start position:0%
+could we start the right way from the
+beginning now the answer to that is
+
+ align:start position:0%
+beginning now the answer to that is
+ 
+
+ align:start position:0%
+beginning now the answer to that is
+still no we're still not there but we I
+
+ align:start position:0%
+still no we're still not there but we I
+ 
+
+ align:start position:0%
+still no we're still not there but we I
+think we've made a lot of progress and
+
+ align:start position:0%
+think we've made a lot of progress and
+ 
+
+ align:start position:0%
+think we've made a lot of progress and
+I'm hoping that
+
+ align:start position:0%
+I'm hoping that
+ 
+
+ align:start position:0%
+I'm hoping that
+um Hamish and maybe Claire will have
+
+ align:start position:0%
+um Hamish and maybe Claire will have
+ 
+
+ align:start position:0%
+um Hamish and maybe Claire will have
+some ideas too so this is what we did we
+
+ align:start position:0%
+some ideas too so this is what we did we
+ 
+
+ align:start position:0%
+some ideas too so this is what we did we
+went to a rural area and we did the same
+
+ align:start position:0%
+went to a rural area and we did the same
+ 
+
+ align:start position:0%
+went to a rural area and we did the same
+three things we did delivered Services
+
+ align:start position:0%
+three things we did delivered Services
+ 
+
+ align:start position:0%
+three things we did delivered Services
+which are largely Clinical Services we
+
+ align:start position:0%
+which are largely Clinical Services we
+ 
+
+ align:start position:0%
+which are largely Clinical Services we
+train local people capacity building and
+
+ align:start position:0%
+train local people capacity building and
+ 
+
+ align:start position:0%
+train local people capacity building and
+we built the systems again this was
+
+ align:start position:0%
+we built the systems again this was
+ 
+
+ align:start position:0%
+we built the systems again this was
+literally rebuilding infrastructure or
+
+ align:start position:0%
+literally rebuilding infrastructure or
+ 
+
+ align:start position:0%
+literally rebuilding infrastructure or
+building and of course we saw the same
+
+ align:start position:0%
+building and of course we saw the same
+ 
+
+ align:start position:0%
+building and of course we saw the same
+kind of effects on patients as we did in
+
+ align:start position:0%
+kind of effects on patients as we did in
+ 
+
+ align:start position:0%
+kind of effects on patients as we did in
+Haiti or anywhere else you know where
+
+ align:start position:0%
+Haiti or anywhere else you know where
+ 
+
+ align:start position:0%
+Haiti or anywhere else you know where
+you go and actually deliver high quality
+
+ align:start position:0%
+you go and actually deliver high quality
+ 
+
+ align:start position:0%
+you go and actually deliver high quality
+and I say community based care to people
+
+ align:start position:0%
+and I say community based care to people
+ 
+
+ align:start position:0%
+and I say community based care to people
+with chronic wasting diseases you have
+
+ align:start position:0%
+with chronic wasting diseases you have
+ 
+
+ align:start position:0%
+with chronic wasting diseases you have
+the same response and I remember one of
+
+ align:start position:0%
+the same response and I remember one of
+ 
+
+ align:start position:0%
+the same response and I remember one of
+the things that struck me in working in
+
+ align:start position:0%
+the things that struck me in working in
+ 
+
+ align:start position:0%
+the things that struck me in working in
+Africa even as late as 2005 2006 and
+
+ align:start position:0%
+Africa even as late as 2005 2006 and
+ 
+
+ align:start position:0%
+Africa even as late as 2005 2006 and
+again I've mentioned the countries I
+
+ align:start position:0%
+again I've mentioned the countries I
+ 
+
+ align:start position:0%
+again I've mentioned the countries I
+mean is that people often did not were
+
+ align:start position:0%
+mean is that people often did not were
+ 
+
+ align:start position:0%
+mean is that people often did not were
+skeptical that we would see the same
+
+ align:start position:0%
+skeptical that we would see the same
+ 
+
+ align:start position:0%
+skeptical that we would see the same
+results in rural Rwanda as we had in
+
+ align:start position:0%
+results in rural Rwanda as we had in
+ 
+
+ align:start position:0%
+results in rural Rwanda as we had in
+Haiti and that wasn't true of course we
+
+ align:start position:0%
+Haiti and that wasn't true of course we
+ 
+
+ align:start position:0%
+Haiti and that wasn't true of course we
+did see the same results but I
+
+ align:start position:0%
+did see the same results but I
+ 
+
+ align:start position:0%
+did see the same results but I
+understand after many years of hearing
+
+ align:start position:0%
+understand after many years of hearing
+ 
+
+ align:start position:0%
+understand after many years of hearing
+well there's medications but we can't
+
+ align:start position:0%
+well there's medications but we can't
+ 
+
+ align:start position:0%
+well there's medications but we can't
+get them to you it's not cost effective
+
+ align:start position:0%
+get them to you it's not cost effective
+ 
+
+ align:start position:0%
+get them to you it's not cost effective
+it's too complicated they were pretty
+
+ align:start position:0%
+it's too complicated they were pretty
+ 
+
+ align:start position:0%
+it's too complicated they were pretty
+skeptical when we showed up that this
+
+ align:start position:0%
+skeptical when we showed up that this
+ 
+
+ align:start position:0%
+skeptical when we showed up that this
+was actually going to work I was
+
+ align:start position:0%
+was actually going to work I was
+ 
+
+ align:start position:0%
+was actually going to work I was
+actually in a Princeton
+
+ align:start position:0%
+actually in a Princeton
+ 
+
+ align:start position:0%
+actually in a Princeton
+uh in in that year maybe 2004 giving a
+
+ align:start position:0%
+uh in in that year maybe 2004 giving a
+ 
+
+ align:start position:0%
+uh in in that year maybe 2004 giving a
+talk and it was full of very
+
+ align:start position:0%
+talk and it was full of very
+ 
+
+ align:start position:0%
+talk and it was full of very
+self-confident young people I'll tell
+
+ align:start position:0%
+self-confident young people I'll tell
+ 
+
+ align:start position:0%
+self-confident young people I'll tell
+you that
+
+ align:start position:0%
+you that
+ 
+
+ align:start position:0%
+you that
+hopefully you guys are more modest at
+
+ align:start position:0%
+hopefully you guys are more modest at
+ 
+
+ align:start position:0%
+hopefully you guys are more modest at
+MIT as nerds tend to be but anyway so
+
+ align:start position:0%
+MIT as nerds tend to be but anyway so
+ 
+
+ align:start position:0%
+MIT as nerds tend to be but anyway so
+we're in The Deco lab to Taipei I don't
+
+ align:start position:0%
+we're in The Deco lab to Taipei I don't
+ 
+
+ align:start position:0%
+we're in The Deco lab to Taipei I don't
+know if that's good so we're in this big
+
+ align:start position:0%
+know if that's good so we're in this big
+ 
+
+ align:start position:0%
+know if that's good so we're in this big
+Auditorium and someone says oh you're
+
+ align:start position:0%
+Auditorium and someone says oh you're
+ 
+
+ align:start position:0%
+Auditorium and someone says oh you're
+never going to make this model work in
+
+ align:start position:0%
+never going to make this model work in
+ 
+
+ align:start position:0%
+never going to make this model work in
+Rwanda and I said oh really and this is
+
+ align:start position:0%
+Rwanda and I said oh really and this is
+ 
+
+ align:start position:0%
+Rwanda and I said oh really and this is
+someone that looked to me to be all I'm
+
+ align:start position:0%
+someone that looked to me to be all I'm
+ 
+
+ align:start position:0%
+someone that looked to me to be all I'm
+about 22 years old
+
+ align:start position:0%
+about 22 years old
+ 
+
+ align:start position:0%
+about 22 years old
+and I said really why is that and they
+
+ align:start position:0%
+and I said really why is that and they
+ 
+
+ align:start position:0%
+and I said really why is that and they
+said well you know this history of
+
+ align:start position:0%
+said well you know this history of
+ 
+
+ align:start position:0%
+said well you know this history of
+violence and Division and and started he
+
+ align:start position:0%
+violence and Division and and started he
+ 
+
+ align:start position:0%
+violence and Division and and started he
+started with a he of course started
+
+ align:start position:0%
+started with a he of course started
+ 
+
+ align:start position:0%
+started with a he of course started
+naming the different ethnicities and I
+
+ align:start position:0%
+naming the different ethnicities and I
+ 
+
+ align:start position:0%
+naming the different ethnicities and I
+said well we'll see you know we'll see
+
+ align:start position:0%
+said well we'll see you know we'll see
+ 
+
+ align:start position:0%
+said well we'll see you know we'll see
+how it works it actually worked even
+
+ align:start position:0%
+how it works it actually worked even
+ 
+
+ align:start position:0%
+how it works it actually worked even
+better in Rwanda this model of
+
+ align:start position:0%
+better in Rwanda this model of
+ 
+
+ align:start position:0%
+better in Rwanda this model of
+community-based care and linked to
+
+ align:start position:0%
+community-based care and linked to
+ 
+
+ align:start position:0%
+community-based care and linked to
+Health Centers and then on to hospitals
+
+ align:start position:0%
+Health Centers and then on to hospitals
+ 
+
+ align:start position:0%
+Health Centers and then on to hospitals
+this guy I I will my medical colleagues
+
+ align:start position:0%
+this guy I I will my medical colleagues
+ 
+
+ align:start position:0%
+this guy I I will my medical colleagues
+have heard me made this to make this
+
+ align:start position:0%
+have heard me made this to make this
+ 
+
+ align:start position:0%
+have heard me made this to make this
+joke before but I'll try I'm going to do
+
+ align:start position:0%
+joke before but I'll try I'm going to do
+ 
+
+ align:start position:0%
+joke before but I'll try I'm going to do
+it again he goes from looking like
+
+ align:start position:0%
+it again he goes from looking like
+ 
+
+ align:start position:0%
+it again he goes from looking like
+Skeletor to kneading Lipitor so that to
+
+ align:start position:0%
+Skeletor to kneading Lipitor so that to
+ 
+
+ align:start position:0%
+Skeletor to kneading Lipitor so that to
+me is a really successful intervention
+
+ align:start position:0%
+me is a really successful intervention
+ 
+
+ align:start position:0%
+me is a really successful intervention
+but this time around we actually worked
+
+ align:start position:0%
+but this time around we actually worked
+ 
+
+ align:start position:0%
+but this time around we actually worked
+with Hamish and team to try and develop
+
+ align:start position:0%
+with Hamish and team to try and develop
+ 
+
+ align:start position:0%
+with Hamish and team to try and develop
+this from the get-go so I mean I could
+
+ align:start position:0%
+this from the get-go so I mean I could
+ 
+
+ align:start position:0%
+this from the get-go so I mean I could
+be wrong but this is a picture from
+
+ align:start position:0%
+be wrong but this is a picture from
+ 
+
+ align:start position:0%
+be wrong but this is a picture from
+Rwanda right
+
+ align:start position:0%
+Rwanda right
+ 
+
+ align:start position:0%
+Rwanda right
+and uh it is definitely one I can tell
+
+ align:start position:0%
+and uh it is definitely one I can tell
+ 
+
+ align:start position:0%
+and uh it is definitely one I can tell
+by the table actually more than my
+
+ align:start position:0%
+by the table actually more than my
+ 
+
+ align:start position:0%
+by the table actually more than my
+colleague where we put in place for high
+
+ align:start position:0%
+colleague where we put in place for high
+ 
+
+ align:start position:0%
+colleague where we put in place for high
+high-speed internet access
+
+ align:start position:0%
+high-speed internet access
+ 
+
+ align:start position:0%
+high-speed internet access
+and started working on a locally adapted
+
+ align:start position:0%
+and started working on a locally adapted
+ 
+
+ align:start position:0%
+and started working on a locally adapted
+Community electronic medical record
+
+ align:start position:0%
+Community electronic medical record
+ 
+
+ align:start position:0%
+Community electronic medical record
+right then and there now again that was
+
+ align:start position:0%
+right then and there now again that was
+ 
+
+ align:start position:0%
+right then and there now again that was
+how did you put it diplomatically that I
+
+ align:start position:0%
+how did you put it diplomatically that I
+ 
+
+ align:start position:0%
+how did you put it diplomatically that I
+was prodding you or
+
+ align:start position:0%
+was prodding you or
+ 
+
+ align:start position:0%
+was prodding you or
+I was annoying this team
+
+ align:start position:0%
+I was annoying this team
+ 
+
+ align:start position:0%
+I was annoying this team
+thank you because on the program side is
+
+ align:start position:0%
+thank you because on the program side is
+ 
+
+ align:start position:0%
+thank you because on the program side is
+the doctors and nurses do we want to
+
+ align:start position:0%
+the doctors and nurses do we want to
+ 
+
+ align:start position:0%
+the doctors and nurses do we want to
+immediate
+
+ align:start position:0%
+immediate
+ 
+
+ align:start position:0%
+immediate
+not gratification we wanted immediate
+
+ align:start position:0%
+not gratification we wanted immediate
+ 
+
+ align:start position:0%
+not gratification we wanted immediate
+results stock management patient
+
+ align:start position:0%
+results stock management patient
+ 
+
+ align:start position:0%
+results stock management patient
+management it just was because our goal
+
+ align:start position:0%
+management it just was because our goal
+ 
+
+ align:start position:0%
+management it just was because our goal
+in going to Rwanda was take what we'd
+
+ align:start position:0%
+in going to Rwanda was take what we'd
+ 
+
+ align:start position:0%
+in going to Rwanda was take what we'd
+done in 20 years in Haiti and do it in
+
+ align:start position:0%
+done in 20 years in Haiti and do it in
+ 
+
+ align:start position:0%
+done in 20 years in Haiti and do it in
+five in Rwanda
+
+ align:start position:0%
+five in Rwanda
+ 
+
+ align:start position:0%
+five in Rwanda
+that was an explicit goal we didn't
+
+ align:start position:0%
+that was an explicit goal we didn't
+ 
+
+ align:start position:0%
+that was an explicit goal we didn't
+really know much about strategic
+
+ align:start position:0%
+really know much about strategic
+ 
+
+ align:start position:0%
+really know much about strategic
+planning or how to use language like
+
+ align:start position:0%
+planning or how to use language like
+ 
+
+ align:start position:0%
+planning or how to use language like
+that but that's what we said in the
+
+ align:start position:0%
+that but that's what we said in the
+ 
+
+ align:start position:0%
+that but that's what we said in the
+beginning that we would go
+
+ align:start position:0%
+beginning that we would go
+ 
+
+ align:start position:0%
+beginning that we would go
+uh you know somebody out of at the
+
+ align:start position:0%
+uh you know somebody out of at the
+ 
+
+ align:start position:0%
+uh you know somebody out of at the
+business school Sloan how to write a
+
+ align:start position:0%
+business school Sloan how to write a
+ 
+
+ align:start position:0%
+business school Sloan how to write a
+case about this that was our strategy so
+
+ align:start position:0%
+case about this that was our strategy so
+ 
+
+ align:start position:0%
+case about this that was our strategy so
+what's your strategy we wanna the answer
+
+ align:start position:0%
+what's your strategy we wanna the answer
+ 
+
+ align:start position:0%
+what's your strategy we wanna the answer
+was to to go to do what we did in 20
+
+ align:start position:0%
+was to to go to do what we did in 20
+ 
+
+ align:start position:0%
+was to to go to do what we did in 20
+years in Haiti in five years because
+
+ align:start position:0%
+years in Haiti in five years because
+ 
+
+ align:start position:0%
+years in Haiti in five years because
+it's a country that's much more
+
+ align:start position:0%
+it's a country that's much more
+ 
+
+ align:start position:0%
+it's a country that's much more
+organized
+
+ align:start position:0%
+organized
+ 
+
+ align:start position:0%
+organized
+um and this was again not in the 90s
+
+ align:start position:0%
+um and this was again not in the 90s
+ 
+
+ align:start position:0%
+um and this was again not in the 90s
+it's just 2005. and I think uh people on
+
+ align:start position:0%
+it's just 2005. and I think uh people on
+ 
+
+ align:start position:0%
+it's just 2005. and I think uh people on
+the Rwanda team feel that that we have
+
+ align:start position:0%
+the Rwanda team feel that that we have
+ 
+
+ align:start position:0%
+the Rwanda team feel that that we have
+succeeded and we could not have done it
+
+ align:start position:0%
+succeeded and we could not have done it
+ 
+
+ align:start position:0%
+succeeded and we could not have done it
+without struggling with some of these
+
+ align:start position:0%
+without struggling with some of these
+ 
+
+ align:start position:0%
+without struggling with some of these
+uh issues of the you know how to manage
+
+ align:start position:0%
+uh issues of the you know how to manage
+ 
+
+ align:start position:0%
+uh issues of the you know how to manage
+information we also had help expert help
+
+ align:start position:0%
+information we also had help expert help
+ 
+
+ align:start position:0%
+information we also had help expert help
+but we didn't have
+
+ align:start position:0%
+but we didn't have
+ 
+
+ align:start position:0%
+but we didn't have
+uh 20 years ago in Haiti and who were
+
+ align:start position:0%
+uh 20 years ago in Haiti and who were
+ 
+
+ align:start position:0%
+uh 20 years ago in Haiti and who were
+they this is in Rwanda but these are not
+
+ align:start position:0%
+they this is in Rwanda but these are not
+ 
+
+ align:start position:0%
+they this is in Rwanda but these are not
+rwandans these are our Haitian
+
+ align:start position:0%
+rwandans these are our Haitian
+ 
+
+ align:start position:0%
+rwandans these are our Haitian
+colleagues who went with us to Rwanda
+
+ align:start position:0%
+colleagues who went with us to Rwanda
+ 
+
+ align:start position:0%
+colleagues who went with us to Rwanda
+and were very credible mentors for the
+
+ align:start position:0%
+and were very credible mentors for the
+ 
+
+ align:start position:0%
+and were very credible mentors for the
+training that went on
+
+ align:start position:0%
+training that went on
+ 
+
+ align:start position:0%
+training that went on
+so uh some of you made it no Dr Leon has
+
+ align:start position:0%
+so uh some of you made it no Dr Leon has
+ 
+
+ align:start position:0%
+so uh some of you made it no Dr Leon has
+worked with us for 20 years he's a very
+
+ align:start position:0%
+worked with us for 20 years he's a very
+ 
+
+ align:start position:0%
+worked with us for 20 years he's a very
+good teacher of course because he's a
+
+ align:start position:0%
+good teacher of course because he's a
+ 
+
+ align:start position:0%
+good teacher of course because he's a
+teacher as was the entire Haitian team
+
+ align:start position:0%
+teacher as was the entire Haitian team
+ 
+
+ align:start position:0%
+teacher as was the entire Haitian team
+that went there they've actually done
+
+ align:start position:0%
+that went there they've actually done
+ 
+
+ align:start position:0%
+that went there they've actually done
+the work they're not Cruising Into A an
+
+ align:start position:0%
+the work they're not Cruising Into A an
+ 
+
+ align:start position:0%
+the work they're not Cruising Into A an
+urban hotel to you have a two-day long
+
+ align:start position:0%
+urban hotel to you have a two-day long
+ 
+
+ align:start position:0%
+urban hotel to you have a two-day long
+Workshop these are people who went and
+
+ align:start position:0%
+Workshop these are people who went and
+ 
+
+ align:start position:0%
+Workshop these are people who went and
+lived with us
+
+ align:start position:0%
+lived with us
+ 
+
+ align:start position:0%
+lived with us
+uh in Rwanda from Haiti with real
+
+ align:start position:0%
+uh in Rwanda from Haiti with real
+ 
+
+ align:start position:0%
+uh in Rwanda from Haiti with real
+credible experience to share so that
+
+ align:start position:0%
+credible experience to share so that
+ 
+
+ align:start position:0%
+credible experience to share so that
+part went I think quite well
+
+ align:start position:0%
+part went I think quite well
+ 
+
+ align:start position:0%
+part went I think quite well
+um and then finally you have to have a
+
+ align:start position:0%
+um and then finally you have to have a
+ 
+
+ align:start position:0%
+um and then finally you have to have a
+there there you have to be able to
+
+ align:start position:0%
+there there you have to be able to
+ 
+
+ align:start position:0%
+there there you have to be able to
+deliver the resources somewhere that is
+
+ align:start position:0%
+deliver the resources somewhere that is
+ 
+
+ align:start position:0%
+deliver the resources somewhere that is
+not appalling and we were sent to a an
+
+ align:start position:0%
+not appalling and we were sent to a an
+ 
+
+ align:start position:0%
+not appalling and we were sent to a an
+abandoned hospital and again some of you
+
+ align:start position:0%
+abandoned hospital and again some of you
+ 
+
+ align:start position:0%
+abandoned hospital and again some of you
+have been there it looked like you might
+
+ align:start position:0%
+have been there it looked like you might
+ 
+
+ align:start position:0%
+have been there it looked like you might
+imagine looked like it had been
+
+ align:start position:0%
+imagine looked like it had been
+ 
+
+ align:start position:0%
+imagine looked like it had been
+abandoned
+
+ align:start position:0%
+abandoned
+ 
+
+ align:start position:0%
+abandoned
+and we had to rebuild that as well
+
+ align:start position:0%
+and we had to rebuild that as well
+ 
+
+ align:start position:0%
+and we had to rebuild that as well
+although later we found that the best
+
+ align:start position:0%
+although later we found that the best
+ 
+
+ align:start position:0%
+although later we found that the best
+health system design was when we could
+
+ align:start position:0%
+health system design was when we could
+ 
+
+ align:start position:0%
+health system design was when we could
+build from scratch and not have to redo
+
+ align:start position:0%
+build from scratch and not have to redo
+ 
+
+ align:start position:0%
+build from scratch and not have to redo
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that little cross that's an X
+
+ align:start position:0%
+that little cross that's an X
+ 
+
+ align:start position:0%
+that little cross that's an X
+I thought you were a Scottish I thought
+
+ align:start position:0%
+I thought you were a Scottish I thought
+ 
+
+ align:start position:0%
+I thought you were a Scottish I thought
+you were Scottish
+
+ align:start position:0%
+you were Scottish
+ 
+
+ align:start position:0%
+you were Scottish
+I thought you were going to say
+
+ align:start position:0%
+I thought you were going to say
+ 
+
+ align:start position:0%
+I thought you were going to say
+something constructive too but
+
+ align:start position:0%
+something constructive too but
+ 
+
+ align:start position:0%
+something constructive too but
+so you know and then as the years went
+
+ align:start position:0%
+so you know and then as the years went
+ 
+
+ align:start position:0%
+so you know and then as the years went
+by they were at that time in 2004 there
+
+ align:start position:0%
+by they were at that time in 2004 there
+ 
+
+ align:start position:0%
+by they were at that time in 2004 there
+were four of 30 districts that had no
+
+ align:start position:0%
+were four of 30 districts that had no
+ 
+
+ align:start position:0%
+were four of 30 districts that had no
+District hospitals at all we were
+
+ align:start position:0%
+District hospitals at all we were
+ 
+
+ align:start position:0%
+District hospitals at all we were
+assigned to three of the four at our
+
+ align:start position:0%
+assigned to three of the four at our
+ 
+
+ align:start position:0%
+assigned to three of the four at our
+request
+
+ align:start position:0%
+request
+ 
+
+ align:start position:0%
+request
+he said we'd really rather go to a place
+
+ align:start position:0%
+he said we'd really rather go to a place
+ 
+
+ align:start position:0%
+he said we'd really rather go to a place
+where you know that where there's the
+
+ align:start position:0%
+where you know that where there's the
+ 
+
+ align:start position:0%
+where you know that where there's the
+greatest need but also where you could
+
+ align:start position:0%
+greatest need but also where you could
+ 
+
+ align:start position:0%
+greatest need but also where you could
+show that this is more than possible in
+
+ align:start position:0%
+show that this is more than possible in
+ 
+
+ align:start position:0%
+show that this is more than possible in
+a setting like this again without
+
+ align:start position:0%
+a setting like this again without
+ 
+
+ align:start position:0%
+a setting like this again without
+electricity this this is uh in butara in
+
+ align:start position:0%
+electricity this this is uh in butara in
+ 
+
+ align:start position:0%
+electricity this this is uh in butara in
+the North
+
+ align:start position:0%
+the North
+ 
+
+ align:start position:0%
+the North
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+don't look Hamish ignore the little
+
+ align:start position:0%
+don't look Hamish ignore the little
+ 
+
+ align:start position:0%
+don't look Hamish ignore the little
+beeps and blurbs
+
+ align:start position:0%
+beeps and blurbs
+ 
+
+ align:start position:0%
+beeps and blurbs
+and there's no there was no electricity
+
+ align:start position:0%
+and there's no there was no electricity
+ 
+
+ align:start position:0%
+and there's no there was no electricity
+there either and this is probably about
+
+ align:start position:0%
+there either and this is probably about
+ 
+
+ align:start position:0%
+there either and this is probably about
+400 500 000 people without a hospital so
+
+ align:start position:0%
+400 500 000 people without a hospital so
+ 
+
+ align:start position:0%
+400 500 000 people without a hospital so
+we went into the health center and uh
+
+ align:start position:0%
+we went into the health center and uh
+ 
+
+ align:start position:0%
+we went into the health center and uh
+and transformed it into a hospital with
+
+ align:start position:0%
+and transformed it into a hospital with
+ 
+
+ align:start position:0%
+and transformed it into a hospital with
+the ministry of course
+
+ align:start position:0%
+the ministry of course
+ 
+
+ align:start position:0%
+the ministry of course
+um and then we built another one uh this
+
+ align:start position:0%
+um and then we built another one uh this
+ 
+
+ align:start position:0%
+um and then we built another one uh this
+time to our own specifications some of
+
+ align:start position:0%
+time to our own specifications some of
+ 
+
+ align:start position:0%
+time to our own specifications some of
+you have probably heard from a group
+
+ align:start position:0%
+you have probably heard from a group
+ 
+
+ align:start position:0%
+you have probably heard from a group
+with actually some MIT involvement as
+
+ align:start position:0%
+with actually some MIT involvement as
+ 
+
+ align:start position:0%
+with actually some MIT involvement as
+well called mass at that point this
+
+ align:start position:0%
+well called mass at that point this
+ 
+
+ align:start position:0%
+well called mass at that point this
+group had informed but it's a design
+
+ align:start position:0%
+group had informed but it's a design
+ 
+
+ align:start position:0%
+group had informed but it's a design
+let's see Architects but also some
+
+ align:start position:0%
+let's see Architects but also some
+ 
+
+ align:start position:0%
+let's see Architects but also some
+Engineers who are working on social
+
+ align:start position:0%
+Engineers who are working on social
+ 
+
+ align:start position:0%
+Engineers who are working on social
+justice projects and they were born
+
+ align:start position:0%
+justice projects and they were born
+ 
+
+ align:start position:0%
+justice projects and they were born
+really in the process of if I can say
+
+ align:start position:0%
+really in the process of if I can say
+ 
+
+ align:start position:0%
+really in the process of if I can say
+that I think they say it quite a bit
+
+ align:start position:0%
+that I think they say it quite a bit
+ 
+
+ align:start position:0%
+that I think they say it quite a bit
+they were really born out of doing this
+
+ align:start position:0%
+they were really born out of doing this
+ 
+
+ align:start position:0%
+they were really born out of doing this
+uh work with us Moana and you can see
+
+ align:start position:0%
+uh work with us Moana and you can see
+ 
+
+ align:start position:0%
+uh work with us Moana and you can see
+that looks like I I say that looks like
+
+ align:start position:0%
+that looks like I I say that looks like
+ 
+
+ align:start position:0%
+that looks like I I say that looks like
+a you know artist rendering that's a
+
+ align:start position:0%
+a you know artist rendering that's a
+ 
+
+ align:start position:0%
+a you know artist rendering that's a
+photograph that's what the hospital
+
+ align:start position:0%
+photograph that's what the hospital
+ 
+
+ align:start position:0%
+photograph that's what the hospital
+really looks like it's a very beautiful
+
+ align:start position:0%
+really looks like it's a very beautiful
+ 
+
+ align:start position:0%
+really looks like it's a very beautiful
+Hospital
+
+ align:start position:0%
+Hospital
+ 
+
+ align:start position:0%
+Hospital
+now and just for the data at the bottom
+
+ align:start position:0%
+now and just for the data at the bottom
+ 
+
+ align:start position:0%
+now and just for the data at the bottom
+people ask a lot in fact the last time I
+
+ align:start position:0%
+people ask a lot in fact the last time I
+ 
+
+ align:start position:0%
+people ask a lot in fact the last time I
+gave a talk here at MIT uh I was
+
+ align:start position:0%
+gave a talk here at MIT uh I was
+ 
+
+ align:start position:0%
+gave a talk here at MIT uh I was
+practically assailed with questions
+
+ align:start position:0%
+practically assailed with questions
+ 
+
+ align:start position:0%
+practically assailed with questions
+about sustainability
+
+ align:start position:0%
+about sustainability
+ 
+
+ align:start position:0%
+about sustainability
+and uh I was trying to figure out who
+
+ align:start position:0%
+and uh I was trying to figure out who
+ 
+
+ align:start position:0%
+and uh I was trying to figure out who
+which Professor was responsible for that
+
+ align:start position:0%
+which Professor was responsible for that
+ 
+
+ align:start position:0%
+which Professor was responsible for that
+but couldn't
+
+ align:start position:0%
+but couldn't
+ 
+
+ align:start position:0%
+but couldn't
+you know the idea is that you work in
+
+ align:start position:0%
+you know the idea is that you work in
+ 
+
+ align:start position:0%
+you know the idea is that you work in
+the public sector for a number of
+
+ align:start position:0%
+the public sector for a number of
+ 
+
+ align:start position:0%
+the public sector for a number of
+reasons one as Hamish said referring to
+
+ align:start position:0%
+reasons one as Hamish said referring to
+ 
+
+ align:start position:0%
+reasons one as Hamish said referring to
+some other uh work of of mine which I
+
+ align:start position:0%
+some other uh work of of mine which I
+ 
+
+ align:start position:0%
+some other uh work of of mine which I
+kind of forget about is that when you're
+
+ align:start position:0%
+kind of forget about is that when you're
+ 
+
+ align:start position:0%
+kind of forget about is that when you're
+thinking about a right space model
+
+ align:start position:0%
+thinking about a right space model
+ 
+
+ align:start position:0%
+thinking about a right space model
+who confers the right to something like
+
+ align:start position:0%
+who confers the right to something like
+ 
+
+ align:start position:0%
+who confers the right to something like
+the right to Health Care the right to
+
+ align:start position:0%
+the right to Health Care the right to
+ 
+
+ align:start position:0%
+the right to Health Care the right to
+education to the public sector so
+
+ align:start position:0%
+education to the public sector so
+ 
+
+ align:start position:0%
+education to the public sector so
+working with the public sector has that
+
+ align:start position:0%
+working with the public sector has that
+ 
+
+ align:start position:0%
+working with the public sector has that
+Advantage as well and then getting the
+
+ align:start position:0%
+Advantage as well and then getting the
+ 
+
+ align:start position:0%
+Advantage as well and then getting the
+scale any kind of scale I I believe that
+
+ align:start position:0%
+scale any kind of scale I I believe that
+ 
+
+ align:start position:0%
+scale any kind of scale I I believe that
+the notion of scale as we
+
+ align:start position:0%
+the notion of scale as we
+ 
+
+ align:start position:0%
+the notion of scale as we
+anthropologists would say has been
+
+ align:start position:0%
+anthropologists would say has been
+ 
+
+ align:start position:0%
+anthropologists would say has been
+somewhat fetishized people talk about
+
+ align:start position:0%
+somewhat fetishized people talk about
+ 
+
+ align:start position:0%
+somewhat fetishized people talk about
+scale all the time and you're never
+
+ align:start position:0%
+scale all the time and you're never
+ 
+
+ align:start position:0%
+scale all the time and you're never
+quite sure what they mean at least in
+
+ align:start position:0%
+quite sure what they mean at least in
+ 
+
+ align:start position:0%
+quite sure what they mean at least in
+public health but you know because
+
+ align:start position:0%
+public health but you know because
+ 
+
+ align:start position:0%
+public health but you know because
+they're always having a national scale
+
+ align:start position:0%
+they're always having a national scale
+ 
+
+ align:start position:0%
+they're always having a national scale
+but there are also subunits of the
+
+ align:start position:0%
+but there are also subunits of the
+ 
+
+ align:start position:0%
+but there are also subunits of the
+nation in this case the district that
+
+ align:start position:0%
+nation in this case the district that
+ 
+
+ align:start position:0%
+nation in this case the district that
+are all they're important to work with
+
+ align:start position:0%
+are all they're important to work with
+ 
+
+ align:start position:0%
+are all they're important to work with
+and that's what we've done mostly is
+
+ align:start position:0%
+and that's what we've done mostly is
+ 
+
+ align:start position:0%
+and that's what we've done mostly is
+work the district level so that's the
+
+ align:start position:0%
+work the district level so that's the
+ 
+
+ align:start position:0%
+work the district level so that's the
+model replicated uh with with the same
+
+ align:start position:0%
+model replicated uh with with the same
+ 
+
+ align:start position:0%
+model replicated uh with with the same
+challenges that we'd seen in Haiti and
+
+ align:start position:0%
+challenges that we'd seen in Haiti and
+ 
+
+ align:start position:0%
+challenges that we'd seen in Haiti and
+elsewhere
+
+ align:start position:0%
+elsewhere
+ 
+
+ align:start position:0%
+elsewhere
+but a little bit more of a head start I
+
+ align:start position:0%
+but a little bit more of a head start I
+ 
+
+ align:start position:0%
+but a little bit more of a head start I
+would say and
+
+ align:start position:0%
+would say and
+ 
+
+ align:start position:0%
+would say and
+now let me just give you some outcomes
+
+ align:start position:0%
+now let me just give you some outcomes
+ 
+
+ align:start position:0%
+now let me just give you some outcomes
+and then uh
+
+ align:start position:0%
+and then uh
+ 
+
+ align:start position:0%
+and then uh
+open this up for the discussion
+
+ align:start position:0%
+open this up for the discussion
+ 
+
+ align:start position:0%
+open this up for the discussion
+first of all Rwanda we had bet heavily
+
+ align:start position:0%
+first of all Rwanda we had bet heavily
+ 
+
+ align:start position:0%
+first of all Rwanda we had bet heavily
+as as we decided in 2004 we bet heavily
+
+ align:start position:0%
+as as we decided in 2004 we bet heavily
+ 
+
+ align:start position:0%
+as as we decided in 2004 we bet heavily
+on Rwanda being a good place
+
+ align:start position:0%
+on Rwanda being a good place
+ 
+
+ align:start position:0%
+on Rwanda being a good place
+to bring the scale of rural Health
+
+ align:start position:0%
+to bring the scale of rural Health
+ 
+
+ align:start position:0%
+to bring the scale of rural Health
+Project The Glenn Foundation has been
+
+ align:start position:0%
+Project The Glenn Foundation has been
+ 
+
+ align:start position:0%
+Project The Glenn Foundation has been
+heavily honored pardons in health and
+
+ align:start position:0%
+heavily honored pardons in health and
+ 
+
+ align:start position:0%
+heavily honored pardons in health and
+better and I think we were right because
+
+ align:start position:0%
+better and I think we were right because
+ 
+
+ align:start position:0%
+better and I think we were right because
+at that time I can tell you there wasn't
+
+ align:start position:0%
+at that time I can tell you there wasn't
+ 
+
+ align:start position:0%
+at that time I can tell you there wasn't
+a lot of enthusiasm among some of my
+
+ align:start position:0%
+a lot of enthusiasm among some of my
+ 
+
+ align:start position:0%
+a lot of enthusiasm among some of my
+circles on the rights
+
+ align:start position:0%
+circles on the rights
+ 
+
+ align:start position:0%
+circles on the rights
+side for working there but happily we've
+
+ align:start position:0%
+side for working there but happily we've
+ 
+
+ align:start position:0%
+side for working there but happily we've
+made our own assessment and we said that
+
+ align:start position:0%
+made our own assessment and we said that
+ 
+
+ align:start position:0%
+made our own assessment and we said that
+this would be really Forward Thinking
+
+ align:start position:0%
+this would be really Forward Thinking
+ 
+
+ align:start position:0%
+this would be really Forward Thinking
+people to work with on the district
+
+ align:start position:0%
+people to work with on the district
+ 
+
+ align:start position:0%
+people to work with on the district
+level and on the national level and in
+
+ align:start position:0%
+level and on the national level and in
+ 
+
+ align:start position:0%
+level and on the national level and in
+fact that the director of the national
+
+ align:start position:0%
+fact that the director of the national
+ 
+
+ align:start position:0%
+fact that the director of the national
+AIDS program who has been to speak here
+
+ align:start position:0%
+AIDS program who has been to speak here
+ 
+
+ align:start position:0%
+AIDS program who has been to speak here
+before uh Agnes Ben aguahu
+
+ align:start position:0%
+before uh Agnes Ben aguahu
+ 
+
+ align:start position:0%
+before uh Agnes Ben aguahu
+has since gone from director of the
+
+ align:start position:0%
+has since gone from director of the
+ 
+
+ align:start position:0%
+has since gone from director of the
+national AIDS program to the um the lead
+
+ align:start position:0%
+national AIDS program to the um the lead
+ 
+
+ align:start position:0%
+national AIDS program to the um the lead
+technical position in the ministry to
+
+ align:start position:0%
+technical position in the ministry to
+ 
+
+ align:start position:0%
+technical position in the ministry to
+the minister of health so we've got to
+
+ align:start position:0%
+the minister of health so we've got to
+ 
+
+ align:start position:0%
+the minister of health so we've got to
+grow we've been able to grow with her
+
+ align:start position:0%
+grow we've been able to grow with her
+ 
+
+ align:start position:0%
+grow we've been able to grow with her
+and this is what she's done along with
+
+ align:start position:0%
+and this is what she's done along with
+ 
+
+ align:start position:0%
+and this is what she's done along with
+many as she would be cooked at that I
+
+ align:start position:0%
+many as she would be cooked at that I
+ 
+
+ align:start position:0%
+many as she would be cooked at that I
+don't think has been done anywhere and
+
+ align:start position:0%
+don't think has been done anywhere and
+ 
+
+ align:start position:0%
+don't think has been done anywhere and
+that is universal access almost to
+
+ align:start position:0%
+that is universal access almost to
+ 
+
+ align:start position:0%
+that is universal access almost to
+antiretro viral care and there's a lot
+
+ align:start position:0%
+antiretro viral care and there's a lot
+ 
+
+ align:start position:0%
+antiretro viral care and there's a lot
+of talk in 2004 about whether it's a
+
+ align:start position:0%
+of talk in 2004 about whether it's a
+ 
+
+ align:start position:0%
+of talk in 2004 about whether it's a
+small number of patients in in
+
+ align:start position:0%
+small number of patients in in
+ 
+
+ align:start position:0%
+small number of patients in in
+sub-Saharan getting care but it was more
+
+ align:start position:0%
+sub-Saharan getting care but it was more
+ 
+
+ align:start position:0%
+sub-Saharan getting care but it was more
+like a tiny number than a small number I
+
+ align:start position:0%
+like a tiny number than a small number I
+ 
+
+ align:start position:0%
+like a tiny number than a small number I
+have in all these years of doing this
+
+ align:start position:0%
+have in all these years of doing this
+ 
+
+ align:start position:0%
+have in all these years of doing this
+work I've never seen
+
+ align:start position:0%
+work I've never seen
+ 
+
+ align:start position:0%
+work I've never seen
+someone living in a rural area of Africa
+
+ align:start position:0%
+someone living in a rural area of Africa
+ 
+
+ align:start position:0%
+someone living in a rural area of Africa
+and in poverty
+
+ align:start position:0%
+and in poverty
+ 
+
+ align:start position:0%
+and in poverty
+except for
+
+ align:start position:0%
+except for
+ 
+
+ align:start position:0%
+except for
+sites that have come up with uh pepfar
+
+ align:start position:0%
+sites that have come up with uh pepfar
+ 
+
+ align:start position:0%
+sites that have come up with uh pepfar
+or the global fund I had never seen
+
+ align:start position:0%
+or the global fund I had never seen
+ 
+
+ align:start position:0%
+or the global fund I had never seen
+anybody on care
+
+ align:start position:0%
+anybody on care
+ 
+
+ align:start position:0%
+anybody on care
+I saw people know there's knew their
+
+ align:start position:0%
+I saw people know there's knew their
+ 
+
+ align:start position:0%
+I saw people know there's knew their
+status you know there's CD4 accounts but
+
+ align:start position:0%
+status you know there's CD4 accounts but
+ 
+
+ align:start position:0%
+status you know there's CD4 accounts but
+they weren't getting medicines or if
+
+ align:start position:0%
+they weren't getting medicines or if
+ 
+
+ align:start position:0%
+they weren't getting medicines or if
+they had they had received them only
+
+ align:start position:0%
+they had they had received them only
+ 
+
+ align:start position:0%
+they had they had received them only
+irregularly by paying some astronomical
+
+ align:start position:0%
+irregularly by paying some astronomical
+ 
+
+ align:start position:0%
+irregularly by paying some astronomical
+some for them uh and and so this is a
+
+ align:start position:0%
+some for them uh and and so this is a
+ 
+
+ align:start position:0%
+some for them uh and and so this is a
+huge achievement and Rwanda is not I
+
+ align:start position:0%
+huge achievement and Rwanda is not I
+ 
+
+ align:start position:0%
+huge achievement and Rwanda is not I
+mean it is post-conflict it was very
+
+ align:start position:0%
+mean it is post-conflict it was very
+ 
+
+ align:start position:0%
+mean it is post-conflict it was very
+poor still very poor but it was very
+
+ align:start position:0%
+poor still very poor but it was very
+ 
+
+ align:start position:0%
+poor still very poor but it was very
+poor back then and to go from zero to
+
+ align:start position:0%
+poor back then and to go from zero to
+ 
+
+ align:start position:0%
+poor back then and to go from zero to
+now I think they're up to a hundred
+
+ align:start position:0%
+now I think they're up to a hundred
+ 
+
+ align:start position:0%
+now I think they're up to a hundred
+thousand people that's pretty much
+
+ align:start position:0%
+thousand people that's pretty much
+ 
+
+ align:start position:0%
+thousand people that's pretty much
+complete coverage now they're looking
+
+ align:start position:0%
+complete coverage now they're looking
+ 
+
+ align:start position:0%
+complete coverage now they're looking
+with active case finding for others who
+
+ align:start position:0%
+with active case finding for others who
+ 
+
+ align:start position:0%
+with active case finding for others who
+need care
+
+ align:start position:0%
+need care
+ 
+
+ align:start position:0%
+need care
+I don't want to overstate this but if
+
+ align:start position:0%
+I don't want to overstate this but if
+ 
+
+ align:start position:0%
+I don't want to overstate this but if
+you get to 90 000 you're probably
+
+ align:start position:0%
+you get to 90 000 you're probably
+ 
+
+ align:start position:0%
+you get to 90 000 you're probably
+talking about 85 percent of all people
+
+ align:start position:0%
+talking about 85 percent of all people
+ 
+
+ align:start position:0%
+talking about 85 percent of all people
+living with HIV who need uh who need
+
+ align:start position:0%
+living with HIV who need uh who need
+ 
+
+ align:start position:0%
+living with HIV who need uh who need
+Care acutely on therapy now we have not
+
+ align:start position:0%
+Care acutely on therapy now we have not
+ 
+
+ align:start position:0%
+Care acutely on therapy now we have not
+worked uh in all those sites of course
+
+ align:start position:0%
+worked uh in all those sites of course
+ 
+
+ align:start position:0%
+worked uh in all those sites of course
+Hamish has concerned himself with the
+
+ align:start position:0%
+Hamish has concerned himself with the
+ 
+
+ align:start position:0%
+Hamish has concerned himself with the
+national program as have I I have worked
+
+ align:start position:0%
+national program as have I I have worked
+ 
+
+ align:start position:0%
+national program as have I I have worked
+along with a lot of my colleagues in
+
+ align:start position:0%
+along with a lot of my colleagues in
+ 
+
+ align:start position:0%
+along with a lot of my colleagues in
+three of those four districts without a
+
+ align:start position:0%
+three of those four districts without a
+ 
+
+ align:start position:0%
+three of those four districts without a
+uh without a district hospital but
+
+ align:start position:0%
+uh without a district hospital but
+ 
+
+ align:start position:0%
+uh without a district hospital but
+through the electronic medical record
+
+ align:start position:0%
+through the electronic medical record
+ 
+
+ align:start position:0%
+through the electronic medical record
+through e-health through policy
+
+ align:start position:0%
+through e-health through policy
+ 
+
+ align:start position:0%
+through e-health through policy
+discussion debates and a later a
+
+ align:start position:0%
+discussion debates and a later a
+ 
+
+ align:start position:0%
+discussion debates and a later a
+training center that we built in this
+
+ align:start position:0%
+training center that we built in this
+ 
+
+ align:start position:0%
+training center that we built in this
+rural region the first place we went
+
+ align:start position:0%
+rural region the first place we went
+ 
+
+ align:start position:0%
+rural region the first place we went
+we've also participated we feel in a
+
+ align:start position:0%
+we've also participated we feel in a
+ 
+
+ align:start position:0%
+we've also participated we feel in a
+stunning reversal of Fortune uh in
+
+ align:start position:0%
+stunning reversal of Fortune uh in
+ 
+
+ align:start position:0%
+stunning reversal of Fortune uh in
+Rwanda and let me just give you some
+
+ align:start position:0%
+Rwanda and let me just give you some
+ 
+
+ align:start position:0%
+Rwanda and let me just give you some
+numbers first of all when you integrate
+
+ align:start position:0%
+numbers first of all when you integrate
+ 
+
+ align:start position:0%
+numbers first of all when you integrate
+these programs and this is language from
+
+ align:start position:0%
+these programs and this is language from
+ 
+
+ align:start position:0%
+these programs and this is language from
+Julio Fring the dean of Harvard school
+
+ align:start position:0%
+Julio Fring the dean of Harvard school
+ 
+
+ align:start position:0%
+Julio Fring the dean of Harvard school
+public health who is Minister of health
+
+ align:start position:0%
+public health who is Minister of health
+ 
+
+ align:start position:0%
+public health who is Minister of health
+and in Mexico is actually visited Us in
+
+ align:start position:0%
+and in Mexico is actually visited Us in
+ 
+
+ align:start position:0%
+and in Mexico is actually visited Us in
+Rwanda
+
+ align:start position:0%
+Rwanda
+ 
+
+ align:start position:0%
+Rwanda
+um when you integrate with uh again I
+
+ align:start position:0%
+um when you integrate with uh again I
+ 
+
+ align:start position:0%
+um when you integrate with uh again I
+showed you an AIDS program a vertical
+
+ align:start position:0%
+showed you an AIDS program a vertical
+ 
+
+ align:start position:0%
+showed you an AIDS program a vertical
+program same for a family planning
+
+ align:start position:0%
+program same for a family planning
+ 
+
+ align:start position:0%
+program same for a family planning
+program it would be a vertical program
+
+ align:start position:0%
+program it would be a vertical program
+ 
+
+ align:start position:0%
+program it would be a vertical program
+or a tuberculosis program when you can
+
+ align:start position:0%
+or a tuberculosis program when you can
+ 
+
+ align:start position:0%
+or a tuberculosis program when you can
+integrate that into a health system
+
+ align:start position:0%
+integrate that into a health system
+ 
+
+ align:start position:0%
+integrate that into a health system
+strengthening model
+
+ align:start position:0%
+strengthening model
+ 
+
+ align:start position:0%
+strengthening model
+you can have impacts far beyond you know
+
+ align:start position:0%
+you can have impacts far beyond you know
+ 
+
+ align:start position:0%
+you can have impacts far beyond you know
+what the intervention is designed or the
+
+ align:start position:0%
+what the intervention is designed or the
+ 
+
+ align:start position:0%
+what the intervention is designed or the
+vertical intervention is designed to do
+
+ align:start position:0%
+vertical intervention is designed to do
+ 
+
+ align:start position:0%
+vertical intervention is designed to do
+and that's what I think we see happening
+
+ align:start position:0%
+and that's what I think we see happening
+ 
+
+ align:start position:0%
+and that's what I think we see happening
+in uh in Rwanda so looking at child
+
+ align:start position:0%
+in uh in Rwanda so looking at child
+ 
+
+ align:start position:0%
+in uh in Rwanda so looking at child
+mortality and maternal mortality and
+
+ align:start position:0%
+mortality and maternal mortality and
+ 
+
+ align:start position:0%
+mortality and maternal mortality and
+juvenile mortality this is again a
+
+ align:start position:0%
+juvenile mortality this is again a
+ 
+
+ align:start position:0%
+juvenile mortality this is again a
+stunning reversal on the national level
+
+ align:start position:0%
+stunning reversal on the national level
+ 
+
+ align:start position:0%
+stunning reversal on the national level
+and uh it's actually been wonderful to
+
+ align:start position:0%
+and uh it's actually been wonderful to
+ 
+
+ align:start position:0%
+and uh it's actually been wonderful to
+be part of Rwanda during this time this
+
+ align:start position:0%
+be part of Rwanda during this time this
+ 
+
+ align:start position:0%
+be part of Rwanda during this time this
+past decade because trust me after 1994
+
+ align:start position:0%
+past decade because trust me after 1994
+ 
+
+ align:start position:0%
+past decade because trust me after 1994
+there are a lot of people who are only
+
+ align:start position:0%
+there are a lot of people who are only
+ 
+
+ align:start position:0%
+there are a lot of people who are only
+too happy to write off Rwanda as a
+
+ align:start position:0%
+too happy to write off Rwanda as a
+ 
+
+ align:start position:0%
+too happy to write off Rwanda as a
+chance as a place where recovery could
+
+ align:start position:0%
+chance as a place where recovery could
+ 
+
+ align:start position:0%
+chance as a place where recovery could
+occur and many other maimed States and
+
+ align:start position:0%
+occur and many other maimed States and
+ 
+
+ align:start position:0%
+occur and many other maimed States and
+weak states have still struggled and and
+
+ align:start position:0%
+weak states have still struggled and and
+ 
+
+ align:start position:0%
+weak states have still struggled and and
+I've seen that in Haiti but Rwanda
+
+ align:start position:0%
+I've seen that in Haiti but Rwanda
+ 
+
+ align:start position:0%
+I've seen that in Haiti but Rwanda
+really did turn things around glad to
+
+ align:start position:0%
+really did turn things around glad to
+ 
+
+ align:start position:0%
+really did turn things around glad to
+talk about that
+
+ align:start position:0%
+talk about that
+ 
+
+ align:start position:0%
+talk about that
+we made our contribution there as I said
+
+ align:start position:0%
+we made our contribution there as I said
+ 
+
+ align:start position:0%
+we made our contribution there as I said
+with the ministry and the Clinton
+
+ align:start position:0%
+with the ministry and the Clinton
+ 
+
+ align:start position:0%
+with the ministry and the Clinton
+foundation and many other parties and
+
+ align:start position:0%
+foundation and many other parties and
+ 
+
+ align:start position:0%
+foundation and many other parties and
+then uh set off to other settings
+
+ align:start position:0%
+then uh set off to other settings
+ 
+
+ align:start position:0%
+then uh set off to other settings
+and again rural Africa this is part of
+
+ align:start position:0%
+and again rural Africa this is part of
+ 
+
+ align:start position:0%
+and again rural Africa this is part of
+initiative we called in 2004 there were
+
+ align:start position:0%
+initiative we called in 2004 there were
+ 
+
+ align:start position:0%
+initiative we called in 2004 there were
+a late AIDS initiative that Clinton
+
+ align:start position:0%
+a late AIDS initiative that Clinton
+ 
+
+ align:start position:0%
+a late AIDS initiative that Clinton
+launched that year
+
+ align:start position:0%
+launched that year
+ 
+
+ align:start position:0%
+launched that year
+and it was pretty much the same thing
+
+ align:start position:0%
+and it was pretty much the same thing
+ 
+
+ align:start position:0%
+and it was pretty much the same thing
+now let me close by talking a little bit
+
+ align:start position:0%
+now let me close by talking a little bit
+ 
+
+ align:start position:0%
+now let me close by talking a little bit
+about two things one is conscious
+
+ align:start position:0%
+about two things one is conscious
+ 
+
+ align:start position:0%
+about two things one is conscious
+attempts to
+
+ align:start position:0%
+attempts to
+ 
+
+ align:start position:0%
+attempts to
+tackle this challenge of Information
+
+ align:start position:0%
+tackle this challenge of Information
+ 
+
+ align:start position:0%
+tackle this challenge of Information
+Technology and outsystem striking and
+
+ align:start position:0%
+Technology and outsystem striking and
+ 
+
+ align:start position:0%
+Technology and outsystem striking and
+the other is as you might imagine what
+
+ align:start position:0%
+the other is as you might imagine what
+ 
+
+ align:start position:0%
+the other is as you might imagine what
+is what are some things that we didn't
+
+ align:start position:0%
+is what are some things that we didn't
+ 
+
+ align:start position:0%
+is what are some things that we didn't
+plan for and uh I could I'm not going to
+
+ align:start position:0%
+plan for and uh I could I'm not going to
+ 
+
+ align:start position:0%
+plan for and uh I could I'm not going to
+say couldn't but there are some
+
+ align:start position:0%
+say couldn't but there are some
+ 
+
+ align:start position:0%
+say couldn't but there are some
+contingencies that that happened in
+
+ align:start position:0%
+contingencies that that happened in
+ 
+
+ align:start position:0%
+contingencies that that happened in
+Haiti recently as you all know that we
+
+ align:start position:0%
+Haiti recently as you all know that we
+ 
+
+ align:start position:0%
+Haiti recently as you all know that we
+were unprepared for and uh I'd like to
+
+ align:start position:0%
+were unprepared for and uh I'd like to
+ 
+
+ align:start position:0%
+were unprepared for and uh I'd like to
+open up some of our some reflection on
+
+ align:start position:0%
+open up some of our some reflection on
+ 
+
+ align:start position:0%
+open up some of our some reflection on
+how it could be and can be useful there
+
+ align:start position:0%
+how it could be and can be useful there
+ 
+
+ align:start position:0%
+how it could be and can be useful there
+now we've developed along with many
+
+ align:start position:0%
+now we've developed along with many
+ 
+
+ align:start position:0%
+now we've developed along with many
+partners this ghd online platform which
+
+ align:start position:0%
+partners this ghd online platform which
+ 
+
+ align:start position:0%
+partners this ghd online platform which
+we'd love to make sure it gets improved
+
+ align:start position:0%
+we'd love to make sure it gets improved
+ 
+
+ align:start position:0%
+we'd love to make sure it gets improved
+and used that's another thing about uh
+
+ align:start position:0%
+and used that's another thing about uh
+ 
+
+ align:start position:0%
+and used that's another thing about uh
+we're just saying Hamish and I were
+
+ align:start position:0%
+we're just saying Hamish and I were
+ 
+
+ align:start position:0%
+we're just saying Hamish and I were
+quite skeptical 10 years ago about what
+
+ align:start position:0%
+quite skeptical 10 years ago about what
+ 
+
+ align:start position:0%
+quite skeptical 10 years ago about what
+he used to what he calls telemedicine
+
+ align:start position:0%
+he used to what he calls telemedicine
+ 
+
+ align:start position:0%
+he used to what he calls telemedicine
+and it's just that it was so much
+
+ align:start position:0%
+and it's just that it was so much
+ 
+
+ align:start position:0%
+and it's just that it was so much
+disgust but so little implemented right
+
+ align:start position:0%
+disgust but so little implemented right
+ 
+
+ align:start position:0%
+disgust but so little implemented right
+so you go to the places I work there's
+
+ align:start position:0%
+so you go to the places I work there's
+ 
+
+ align:start position:0%
+so you go to the places I work there's
+no electricity there's certainly not
+
+ align:start position:0%
+no electricity there's certainly not
+ 
+
+ align:start position:0%
+no electricity there's certainly not
+going to be telementin but again you
+
+ align:start position:0%
+going to be telementin but again you
+ 
+
+ align:start position:0%
+going to be telementin but again you
+know now you know we have to revise that
+
+ align:start position:0%
+know now you know we have to revise that
+ 
+
+ align:start position:0%
+know now you know we have to revise that
+because with new technologies including
+
+ align:start position:0%
+because with new technologies including
+ 
+
+ align:start position:0%
+because with new technologies including
+Broadband access and Rural reaches you
+
+ align:start position:0%
+Broadband access and Rural reaches you
+ 
+
+ align:start position:0%
+Broadband access and Rural reaches you
+can imagine a much more robust platform
+
+ align:start position:0%
+can imagine a much more robust platform
+ 
+
+ align:start position:0%
+can imagine a much more robust platform
+to use that much abused word uh in using
+
+ align:start position:0%
+to use that much abused word uh in using
+ 
+
+ align:start position:0%
+to use that much abused word uh in using
+telemedicine but also
+
+ align:start position:0%
+telemedicine but also
+ 
+
+ align:start position:0%
+telemedicine but also
+um this this platform again which should
+
+ align:start position:0%
+um this this platform again which should
+ 
+
+ align:start position:0%
+um this this platform again which should
+be linked to other efforts as you can
+
+ align:start position:0%
+be linked to other efforts as you can
+ 
+
+ align:start position:0%
+be linked to other efforts as you can
+see there's lots of members in a lot of
+
+ align:start position:0%
+see there's lots of members in a lot of
+ 
+
+ align:start position:0%
+see there's lots of members in a lot of
+countries and a lot of them are ngos
+
+ align:start position:0%
+countries and a lot of them are ngos
+ 
+
+ align:start position:0%
+countries and a lot of them are ngos
+hospitals academics
+
+ align:start position:0%
+hospitals academics
+ 
+
+ align:start position:0%
+hospitals academics
+and and this platform is again open
+
+ align:start position:0%
+and and this platform is again open
+ 
+
+ align:start position:0%
+and and this platform is again open
+source this is I bet you I learned that
+
+ align:start position:0%
+source this is I bet you I learned that
+ 
+
+ align:start position:0%
+source this is I bet you I learned that
+term from Hamish and Darius
+
+ align:start position:0%
+term from Hamish and Darius
+ 
+
+ align:start position:0%
+term from Hamish and Darius
+I had no idea what that meant probably
+
+ align:start position:0%
+I had no idea what that meant probably
+ 
+
+ align:start position:0%
+I had no idea what that meant probably
+10 years ago and it was a bit of a you
+
+ align:start position:0%
+10 years ago and it was a bit of a you
+ 
+
+ align:start position:0%
+10 years ago and it was a bit of a you
+know struggle for us I was looking for
+
+ align:start position:0%
+know struggle for us I was looking for
+ 
+
+ align:start position:0%
+know struggle for us I was looking for
+expedience and saying no speed it up
+
+ align:start position:0%
+expedience and saying no speed it up
+ 
+
+ align:start position:0%
+expedience and saying no speed it up
+speed it up
+
+ align:start position:0%
+speed it up
+ 
+
+ align:start position:0%
+speed it up
+um and uh but I think the purists were
+
+ align:start position:0%
+um and uh but I think the purists were
+ 
+
+ align:start position:0%
+um and uh but I think the purists were
+saying the open source part is really
+
+ align:start position:0%
+saying the open source part is really
+ 
+
+ align:start position:0%
+saying the open source part is really
+important if some of this code we will
+
+ align:start position:0%
+important if some of this code we will
+ 
+
+ align:start position:0%
+important if some of this code we will
+take us a long time to rewrite but we
+
+ align:start position:0%
+take us a long time to rewrite but we
+ 
+
+ align:start position:0%
+take us a long time to rewrite but we
+should do it ourselves so that we can
+
+ align:start position:0%
+should do it ourselves so that we can
+ 
+
+ align:start position:0%
+should do it ourselves so that we can
+say this is an open medical record
+
+ align:start position:0%
+say this is an open medical record
+ 
+
+ align:start position:0%
+say this is an open medical record
+system problem and uh so I'll just say
+
+ align:start position:0%
+system problem and uh so I'll just say
+ 
+
+ align:start position:0%
+system problem and uh so I'll just say
+publicly thank you for that teaching
+
+ align:start position:0%
+publicly thank you for that teaching
+ 
+
+ align:start position:0%
+publicly thank you for that teaching
+now the contingencies I want to close
+
+ align:start position:0%
+now the contingencies I want to close
+ 
+
+ align:start position:0%
+now the contingencies I want to close
+with is uh and again Claire Pierre and
+
+ align:start position:0%
+with is uh and again Claire Pierre and
+ 
+
+ align:start position:0%
+with is uh and again Claire Pierre and
+many of you have been nominating to help
+
+ align:start position:0%
+many of you have been nominating to help
+ 
+
+ align:start position:0%
+many of you have been nominating to help
+eclair Pierre actually live through a
+
+ align:start position:0%
+eclair Pierre actually live through a
+ 
+
+ align:start position:0%
+eclair Pierre actually live through a
+lot of this uh with me and and I'm glad
+
+ align:start position:0%
+lot of this uh with me and and I'm glad
+ 
+
+ align:start position:0%
+lot of this uh with me and and I'm glad
+she's here but it was a very uh
+
+ align:start position:0%
+she's here but it was a very uh
+ 
+
+ align:start position:0%
+she's here but it was a very uh
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+time as you might imagine it's after
+
+ align:start position:0%
+time as you might imagine it's after
+ 
+
+ align:start position:0%
+time as you might imagine it's after
+January 10th and this is the uh the
+
+ align:start position:0%
+January 10th and this is the uh the
+ 
+
+ align:start position:0%
+January 10th and this is the uh the
+nursing school the main nursing school
+
+ align:start position:0%
+nursing school the main nursing school
+ 
+
+ align:start position:0%
+nursing school the main nursing school
+and this is 4 53 in the afternoon so
+
+ align:start position:0%
+and this is 4 53 in the afternoon so
+ 
+
+ align:start position:0%
+and this is 4 53 in the afternoon so
+when you think about health system
+
+ align:start position:0%
+when you think about health system
+ 
+
+ align:start position:0%
+when you think about health system
+strengthening there's the three levels I
+
+ align:start position:0%
+strengthening there's the three levels I
+ 
+
+ align:start position:0%
+strengthening there's the three levels I
+talked about community-based Care
+
+ align:start position:0%
+talked about community-based Care
+ 
+
+ align:start position:0%
+talked about community-based Care
+Health Centers and hospitals but there
+
+ align:start position:0%
+Health Centers and hospitals but there
+ 
+
+ align:start position:0%
+Health Centers and hospitals but there
+have to be people in there delivering
+
+ align:start position:0%
+have to be people in there delivering
+ 
+
+ align:start position:0%
+have to be people in there delivering
+services and the loss of a generation uh
+
+ align:start position:0%
+services and the loss of a generation uh
+ 
+
+ align:start position:0%
+services and the loss of a generation uh
+or I mean everybody in the second year
+
+ align:start position:0%
+or I mean everybody in the second year
+ 
+
+ align:start position:0%
+or I mean everybody in the second year
+class perished and their teachers did
+
+ align:start position:0%
+class perished and their teachers did
+ 
+
+ align:start position:0%
+class perished and their teachers did
+too pretty much the laws of a huge
+
+ align:start position:0%
+too pretty much the laws of a huge
+ 
+
+ align:start position:0%
+too pretty much the laws of a huge
+number of health professionals just in
+
+ align:start position:0%
+number of health professionals just in
+ 
+
+ align:start position:0%
+number of health professionals just in
+one day you know again people weren't
+
+ align:start position:0%
+one day you know again people weren't
+ 
+
+ align:start position:0%
+one day you know again people weren't
+prepared for this and rebuilding Haiti
+
+ align:start position:0%
+prepared for this and rebuilding Haiti
+ 
+
+ align:start position:0%
+prepared for this and rebuilding Haiti
+actually means rebuilding it all those
+
+ align:start position:0%
+actually means rebuilding it all those
+ 
+
+ align:start position:0%
+actually means rebuilding it all those
+three levels uh including the tertiary
+
+ align:start position:0%
+three levels uh including the tertiary
+ 
+
+ align:start position:0%
+three levels uh including the tertiary
+Medical Center level
+
+ align:start position:0%
+Medical Center level
+ 
+
+ align:start position:0%
+Medical Center level
+film
+
+ align:start position:0%
+film
+ 
+
+ align:start position:0%
+film
+and then of course I say of course hey
+
+ align:start position:0%
+and then of course I say of course hey
+ 
+
+ align:start position:0%
+and then of course I say of course hey
+the the earthquake was followed
+
+ align:start position:0%
+the the earthquake was followed
+ 
+
+ align:start position:0%
+the the earthquake was followed
+temporarily by A cholerate outbreak
+
+ align:start position:0%
+temporarily by A cholerate outbreak
+ 
+
+ align:start position:0%
+temporarily by A cholerate outbreak
+which you know some people call a
+
+ align:start position:0%
+which you know some people call a
+ 
+
+ align:start position:0%
+which you know some people call a
+secondary Spike immortality but it
+
+ align:start position:0%
+secondary Spike immortality but it
+ 
+
+ align:start position:0%
+secondary Spike immortality but it
+wasn't really related so much the
+
+ align:start position:0%
+wasn't really related so much the
+ 
+
+ align:start position:0%
+wasn't really related so much the
+earthquake as the terribly weak water
+
+ align:start position:0%
+earthquake as the terribly weak water
+ 
+
+ align:start position:0%
+earthquake as the terribly weak water
+system so I'm saying this is a
+
+ align:start position:0%
+system so I'm saying this is a
+ 
+
+ align:start position:0%
+system so I'm saying this is a
+limitation of Health System design
+
+ align:start position:0%
+limitation of Health System design
+ 
+
+ align:start position:0%
+limitation of Health System design
+because it actually occurred and I gave
+
+ align:start position:0%
+because it actually occurred and I gave
+ 
+
+ align:start position:0%
+because it actually occurred and I gave
+a talk about this at MIT last year this
+
+ align:start position:0%
+a talk about this at MIT last year this
+ 
+
+ align:start position:0%
+a talk about this at MIT last year this
+epidemic occurred right in the area
+
+ align:start position:0%
+epidemic occurred right in the area
+ 
+
+ align:start position:0%
+epidemic occurred right in the area
+where we had been working for such a
+
+ align:start position:0%
+where we had been working for such a
+ 
+
+ align:start position:0%
+where we had been working for such a
+long time so it's pretty humbling
+
+ align:start position:0%
+long time so it's pretty humbling
+ 
+
+ align:start position:0%
+long time so it's pretty humbling
+reminder that building Health Systems
+
+ align:start position:0%
+reminder that building Health Systems
+ 
+
+ align:start position:0%
+reminder that building Health Systems
+has to be linked to other systems
+
+ align:start position:0%
+has to be linked to other systems
+ 
+
+ align:start position:0%
+has to be linked to other systems
+water and sanitation education food
+
+ align:start position:0%
+water and sanitation education food
+ 
+
+ align:start position:0%
+water and sanitation education food
+security at the very least shelter I
+
+ align:start position:0%
+security at the very least shelter I
+ 
+
+ align:start position:0%
+security at the very least shelter I
+would throw in there too and of course
+
+ align:start position:0%
+would throw in there too and of course
+ 
+
+ align:start position:0%
+would throw in there too and of course
+why not add jobs
+
+ align:start position:0%
+why not add jobs
+ 
+
+ align:start position:0%
+why not add jobs
+I tried doing that with the global funds
+
+ align:start position:0%
+I tried doing that with the global funds
+ 
+
+ align:start position:0%
+I tried doing that with the global funds
+with Grant I would say oh no we can't
+
+ align:start position:0%
+with Grant I would say oh no we can't
+ 
+
+ align:start position:0%
+with Grant I would say oh no we can't
+have just an AIDS program you have to
+
+ align:start position:0%
+have just an AIDS program you have to
+ 
+
+ align:start position:0%
+have just an AIDS program you have to
+have a women's health program they said
+
+ align:start position:0%
+have a women's health program they said
+ 
+
+ align:start position:0%
+have a women's health program they said
+women's health program this is not the
+
+ align:start position:0%
+women's health program this is not the
+ 
+
+ align:start position:0%
+women's health program this is not the
+global fund for Women's Health that's
+
+ align:start position:0%
+global fund for Women's Health that's
+ 
+
+ align:start position:0%
+global fund for Women's Health that's
+well how are we going to do prevention
+
+ align:start position:0%
+well how are we going to do prevention
+ 
+
+ align:start position:0%
+well how are we going to do prevention
+of mother to child transmission without
+
+ align:start position:0%
+of mother to child transmission without
+ 
+
+ align:start position:0%
+of mother to child transmission without
+thinking about the moms too and don't we
+
+ align:start position:0%
+thinking about the moms too and don't we
+ 
+
+ align:start position:0%
+thinking about the moms too and don't we
+want to promote Family Planning anyway
+
+ align:start position:0%
+want to promote Family Planning anyway
+ 
+
+ align:start position:0%
+want to promote Family Planning anyway
+so I'm kind of a pro at that too
+
+ align:start position:0%
+so I'm kind of a pro at that too
+ 
+
+ align:start position:0%
+so I'm kind of a pro at that too
+broadening the Mandate of others without
+
+ align:start position:0%
+broadening the Mandate of others without
+ 
+
+ align:start position:0%
+broadening the Mandate of others without
+their knowing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway so this is squarely within my
+
+ align:start position:0%
+anyway so this is squarely within my
+ 
+
+ align:start position:0%
+anyway so this is squarely within my
+remed right infectious disease epidemic
+
+ align:start position:0%
+remed right infectious disease epidemic
+ 
+
+ align:start position:0%
+remed right infectious disease epidemic
+and we've been trying and again I'll be
+
+ align:start position:0%
+and we've been trying and again I'll be
+ 
+
+ align:start position:0%
+and we've been trying and again I'll be
+glad to talk about this if anyone's
+
+ align:start position:0%
+glad to talk about this if anyone's
+ 
+
+ align:start position:0%
+glad to talk about this if anyone's
+interested we've been trying to respond
+
+ align:start position:0%
+interested we've been trying to respond
+ 
+
+ align:start position:0%
+interested we've been trying to respond
+obviously with by reinforcing water and
+
+ align:start position:0%
+obviously with by reinforcing water and
+ 
+
+ align:start position:0%
+obviously with by reinforcing water and
+sanitation but we've said wait a second
+
+ align:start position:0%
+sanitation but we've said wait a second
+ 
+
+ align:start position:0%
+sanitation but we've said wait a second
+we've been here a long time and we've
+
+ align:start position:0%
+we've been here a long time and we've
+ 
+
+ align:start position:0%
+we've been here a long time and we've
+failed
+
+ align:start position:0%
+failed
+ 
+
+ align:start position:0%
+failed
+um we don't have a lot of confidence
+
+ align:start position:0%
+um we don't have a lot of confidence
+ 
+
+ align:start position:0%
+um we don't have a lot of confidence
+that it you know a bunch of usaid
+
+ align:start position:0%
+that it you know a bunch of usaid
+ 
+
+ align:start position:0%
+that it you know a bunch of usaid
+contractors are going to come in and
+
+ align:start position:0%
+contractors are going to come in and
+ 
+
+ align:start position:0%
+contractors are going to come in and
+solve all these problems we've been
+
+ align:start position:0%
+solve all these problems we've been
+ 
+
+ align:start position:0%
+solve all these problems we've been
+working here for decades we've heard all
+
+ align:start position:0%
+working here for decades we've heard all
+ 
+
+ align:start position:0%
+working here for decades we've heard all
+this before we have to think of new
+
+ align:start position:0%
+this before we have to think of new
+ 
+
+ align:start position:0%
+this before we have to think of new
+technologies again back to the theme of
+
+ align:start position:0%
+technologies again back to the theme of
+ 
+
+ align:start position:0%
+technologies again back to the theme of
+this course not just to count the number
+
+ align:start position:0%
+this course not just to count the number
+ 
+
+ align:start position:0%
+this course not just to count the number
+of people affected like Jon Snow did but
+
+ align:start position:0%
+of people affected like Jon Snow did but
+ 
+
+ align:start position:0%
+of people affected like Jon Snow did but
+to prevent uh infection as he did by
+
+ align:start position:0%
+to prevent uh infection as he did by
+ 
+
+ align:start position:0%
+to prevent uh infection as he did by
+taking the handle off the Broad Street
+
+ align:start position:0%
+taking the handle off the Broad Street
+ 
+
+ align:start position:0%
+taking the handle off the Broad Street
+Department and so you know I think
+
+ align:start position:0%
+Department and so you know I think
+ 
+
+ align:start position:0%
+Department and so you know I think
+Hamish worked on this I believe others
+
+ align:start position:0%
+Hamish worked on this I believe others
+ 
+
+ align:start position:0%
+Hamish worked on this I believe others
+have as well working with
+
+ align:start position:0%
+have as well working with
+ 
+
+ align:start position:0%
+have as well working with
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+key manager and disaster relief outfits
+
+ align:start position:0%
+key manager and disaster relief outfits
+ 
+
+ align:start position:0%
+key manager and disaster relief outfits
+to try and find out where this epidemic
+
+ align:start position:0%
+to try and find out where this epidemic
+ 
+
+ align:start position:0%
+to try and find out where this epidemic
+was going and uh and to do what was our
+
+ align:start position:0%
+was going and uh and to do what was our
+ 
+
+ align:start position:0%
+was going and uh and to do what was our
+job to do at the very least which was
+
+ align:start position:0%
+job to do at the very least which was
+ 
+
+ align:start position:0%
+job to do at the very least which was
+reduce what's called case fatality rate
+
+ align:start position:0%
+reduce what's called case fatality rate
+ 
+
+ align:start position:0%
+reduce what's called case fatality rate
+the number of people sick who actually
+
+ align:start position:0%
+the number of people sick who actually
+ 
+
+ align:start position:0%
+the number of people sick who actually
+got I'm happy to tell you I think in Mir
+
+ align:start position:0%
+got I'm happy to tell you I think in Mir
+ 
+
+ align:start position:0%
+got I'm happy to tell you I think in Mir
+ballet now which I'm going to return to
+
+ align:start position:0%
+ballet now which I'm going to return to
+ 
+
+ align:start position:0%
+ballet now which I'm going to return to
+him in a second uh I don't think we've
+
+ align:start position:0%
+him in a second uh I don't think we've
+ 
+
+ align:start position:0%
+him in a second uh I don't think we've
+had any cholera deaths recently so we
+
+ align:start position:0%
+had any cholera deaths recently so we
+ 
+
+ align:start position:0%
+had any cholera deaths recently so we
+have a lot of Cholera but the staff
+
+ align:start position:0%
+have a lot of Cholera but the staff
+ 
+
+ align:start position:0%
+have a lot of Cholera but the staff
+there has been trained uh to deliver the
+
+ align:start position:0%
+there has been trained uh to deliver the
+ 
+
+ align:start position:0%
+there has been trained uh to deliver the
+make the diagnosis live with care and
+
+ align:start position:0%
+make the diagnosis live with care and
+ 
+
+ align:start position:0%
+make the diagnosis live with care and
+that's a good thing but it's still not
+
+ align:start position:0%
+that's a good thing but it's still not
+ 
+
+ align:start position:0%
+that's a good thing but it's still not
+going to get rid of Cholera from the
+
+ align:start position:0%
+going to get rid of Cholera from the
+ 
+
+ align:start position:0%
+going to get rid of Cholera from the
+island so we have to do this long-term
+
+ align:start position:0%
+island so we have to do this long-term
+ 
+
+ align:start position:0%
+island so we have to do this long-term
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+um and we also have to I I think I
+
+ align:start position:0%
+um and we also have to I I think I
+ 
+
+ align:start position:0%
+um and we also have to I I think I
+skipped one slide because I didn't want
+
+ align:start position:0%
+skipped one slide because I didn't want
+ 
+
+ align:start position:0%
+skipped one slide because I didn't want
+to go on too long but we've also
+
+ align:start position:0%
+to go on too long but we've also
+ 
+
+ align:start position:0%
+to go on too long but we've also
+launched a an integrated prevention CARE
+
+ align:start position:0%
+launched a an integrated prevention CARE
+ 
+
+ align:start position:0%
+launched a an integrated prevention CARE
+program that includes
+
+ align:start position:0%
+program that includes
+ 
+
+ align:start position:0%
+program that includes
+a vaccination I may have thrown that
+
+ align:start position:0%
+a vaccination I may have thrown that
+ 
+
+ align:start position:0%
+a vaccination I may have thrown that
+thrown that back in but back to this
+
+ align:start position:0%
+thrown that back in but back to this
+ 
+
+ align:start position:0%
+thrown that back in but back to this
+model right again not rocket science
+
+ align:start position:0%
+model right again not rocket science
+ 
+
+ align:start position:0%
+model right again not rocket science
+um I'd argue that you know 20 years from
+
+ align:start position:0%
+um I'd argue that you know 20 years from
+ 
+
+ align:start position:0%
+um I'd argue that you know 20 years from
+now when people are writing books about
+
+ align:start position:0%
+now when people are writing books about
+ 
+
+ align:start position:0%
+now when people are writing books about
+health system striking they'll basically
+
+ align:start position:0%
+health system striking they'll basically
+ 
+
+ align:start position:0%
+health system striking they'll basically
+just describe this community-based Care
+
+ align:start position:0%
+just describe this community-based Care
+ 
+
+ align:start position:0%
+just describe this community-based Care
+on Center enrich Hospital link and
+
+ align:start position:0%
+on Center enrich Hospital link and
+ 
+
+ align:start position:0%
+on Center enrich Hospital link and
+there'll be better language for it new
+
+ align:start position:0%
+there'll be better language for it new
+ 
+
+ align:start position:0%
+there'll be better language for it new
+jargon and hopefully new research posts
+
+ align:start position:0%
+jargon and hopefully new research posts
+ 
+
+ align:start position:0%
+jargon and hopefully new research posts
+and new contracts we usaid but
+
+ align:start position:0%
+and new contracts we usaid but
+ 
+
+ align:start position:0%
+and new contracts we usaid but
+I'm kidding but this is the basic model
+
+ align:start position:0%
+I'm kidding but this is the basic model
+ 
+
+ align:start position:0%
+I'm kidding but this is the basic model
+and again it's not rocket science
+
+ align:start position:0%
+and again it's not rocket science
+ 
+
+ align:start position:0%
+and again it's not rocket science
+now we also considered very strongly
+
+ align:start position:0%
+now we also considered very strongly
+ 
+
+ align:start position:0%
+now we also considered very strongly
+what should be our signal effort post
+
+ align:start position:0%
+what should be our signal effort post
+ 
+
+ align:start position:0%
+what should be our signal effort post
+earthquake in Haiti
+
+ align:start position:0%
+earthquake in Haiti
+ 
+
+ align:start position:0%
+earthquake in Haiti
+and um we were already building yet
+
+ align:start position:0%
+and um we were already building yet
+ 
+
+ align:start position:0%
+and um we were already building yet
+another Community Hospital in this town
+
+ align:start position:0%
+another Community Hospital in this town
+ 
+
+ align:start position:0%
+another Community Hospital in this town
+nearby which I happen to be working in
+
+ align:start position:0%
+nearby which I happen to be working in
+ 
+
+ align:start position:0%
+nearby which I happen to be working in
+in 1983 as in the year between college
+
+ align:start position:0%
+in 1983 as in the year between college
+ 
+
+ align:start position:0%
+in 1983 as in the year between college
+and medical school and so I was pretty
+
+ align:start position:0%
+and medical school and so I was pretty
+ 
+
+ align:start position:0%
+and medical school and so I was pretty
+excited about building a community
+
+ align:start position:0%
+excited about building a community
+ 
+
+ align:start position:0%
+excited about building a community
+hospital in nearby they but after the
+
+ align:start position:0%
+hospital in nearby they but after the
+ 
+
+ align:start position:0%
+hospital in nearby they but after the
+earthquake
+
+ align:start position:0%
+earthquake
+ 
+
+ align:start position:0%
+earthquake
+we went back to the drawing board
+
+ align:start position:0%
+we went back to the drawing board
+ 
+
+ align:start position:0%
+we went back to the drawing board
+literally I say we we this time we took
+
+ align:start position:0%
+literally I say we we this time we took
+ 
+
+ align:start position:0%
+literally I say we we this time we took
+this over to real professionals
+
+ align:start position:0%
+this over to real professionals
+ 
+
+ align:start position:0%
+this over to real professionals
+to redesign the hospital again I said we
+
+ align:start position:0%
+to redesign the hospital again I said we
+ 
+
+ align:start position:0%
+to redesign the hospital again I said we
+had a pretty good community-based design
+
+ align:start position:0%
+had a pretty good community-based design
+ 
+
+ align:start position:0%
+had a pretty good community-based design
+Health Centers we were doing okay
+
+ align:start position:0%
+Health Centers we were doing okay
+ 
+
+ align:start position:0%
+Health Centers we were doing okay
+although I still think a lot of them are
+
+ align:start position:0%
+although I still think a lot of them are
+ 
+
+ align:start position:0%
+although I still think a lot of them are
+dangerous as far as musical infections
+
+ align:start position:0%
+dangerous as far as musical infections
+ 
+
+ align:start position:0%
+dangerous as far as musical infections
+go especially in southern Africa but our
+
+ align:start position:0%
+go especially in southern Africa but our
+ 
+
+ align:start position:0%
+go especially in southern Africa but our
+weak point some of us felt was still the
+
+ align:start position:0%
+weak point some of us felt was still the
+ 
+
+ align:start position:0%
+weak point some of us felt was still the
+quality of the design and construction
+
+ align:start position:0%
+quality of the design and construction
+ 
+
+ align:start position:0%
+quality of the design and construction
+of the hospitals
+
+ align:start position:0%
+of the hospitals
+ 
+
+ align:start position:0%
+of the hospitals
+and then throw on top of that the
+
+ align:start position:0%
+and then throw on top of that the
+ 
+
+ align:start position:0%
+and then throw on top of that the
+earthquake in Haiti and the you know the
+
+ align:start position:0%
+earthquake in Haiti and the you know the
+ 
+
+ align:start position:0%
+earthquake in Haiti and the you know the
+destruction of the medical
+
+ align:start position:0%
+destruction of the medical
+ 
+
+ align:start position:0%
+destruction of the medical
+infrastructure the training
+
+ align:start position:0%
+infrastructure the training
+ 
+
+ align:start position:0%
+infrastructure the training
+infrastructure rather in the capital
+
+ align:start position:0%
+infrastructure rather in the capital
+ 
+
+ align:start position:0%
+infrastructure rather in the capital
+city because that's where all of it was
+
+ align:start position:0%
+city because that's where all of it was
+ 
+
+ align:start position:0%
+city because that's where all of it was
+happening 95
+
+ align:start position:0%
+happening 95
+ 
+
+ align:start position:0%
+happening 95
+and then the loss also of 20 probably of
+
+ align:start position:0%
+and then the loss also of 20 probably of
+ 
+
+ align:start position:0%
+and then the loss also of 20 probably of
+the house Professionals in the
+
+ align:start position:0%
+the house Professionals in the
+ 
+
+ align:start position:0%
+the house Professionals in the
+earthquake of the practicing health
+
+ align:start position:0%
+earthquake of the practicing health
+ 
+
+ align:start position:0%
+earthquake of the practicing health
+professionals
+
+ align:start position:0%
+professionals
+ 
+
+ align:start position:0%
+professionals
+so this is block loss or maiming let's
+
+ align:start position:0%
+so this is block loss or maiming let's
+ 
+
+ align:start position:0%
+so this is block loss or maiming let's
+say so this is a calls for system
+
+ align:start position:0%
+say so this is a calls for system
+ 
+
+ align:start position:0%
+say so this is a calls for system
+redesign right
+
+ align:start position:0%
+redesign right
+ 
+
+ align:start position:0%
+redesign right
+and when President Clinton started
+
+ align:start position:0%
+and when President Clinton started
+ 
+
+ align:start position:0%
+and when President Clinton started
+talking about build back better build
+
+ align:start position:0%
+talking about build back better build
+ 
+
+ align:start position:0%
+talking about build back better build
+back better you know we're asking what
+
+ align:start position:0%
+back better you know we're asking what
+ 
+
+ align:start position:0%
+back better you know we're asking what
+does that mean and we thought this is
+
+ align:start position:0%
+does that mean and we thought this is
+ 
+
+ align:start position:0%
+does that mean and we thought this is
+what it means we're not going to take
+
+ align:start position:0%
+what it means we're not going to take
+ 
+
+ align:start position:0%
+what it means we're not going to take
+shortcuts this time on construction
+
+ align:start position:0%
+shortcuts this time on construction
+ 
+
+ align:start position:0%
+shortcuts this time on construction
+and that means obviously things like
+
+ align:start position:0%
+and that means obviously things like
+ 
+
+ align:start position:0%
+and that means obviously things like
+building code this this hospital was
+
+ align:start position:0%
+building code this this hospital was
+ 
+
+ align:start position:0%
+building code this this hospital was
+designed to California earthquake
+
+ align:start position:0%
+designed to California earthquake
+ 
+
+ align:start position:0%
+designed to California earthquake
+standards and Beyond but also how are we
+
+ align:start position:0%
+standards and Beyond but also how are we
+ 
+
+ align:start position:0%
+standards and Beyond but also how are we
+going to power it if it's going to be a
+
+ align:start position:0%
+going to power it if it's going to be a
+ 
+
+ align:start position:0%
+going to power it if it's going to be a
+medical center rather than a community
+
+ align:start position:0%
+medical center rather than a community
+ 
+
+ align:start position:0%
+medical center rather than a community
+hospital you know we're going to go back
+
+ align:start position:0%
+hospital you know we're going to go back
+ 
+
+ align:start position:0%
+hospital you know we're going to go back
+in and then put in the Solar so we've
+
+ align:start position:0%
+in and then put in the Solar so we've
+ 
+
+ align:start position:0%
+in and then put in the Solar so we've
+been doing that as I mentioned the our
+
+ align:start position:0%
+been doing that as I mentioned the our
+ 
+
+ align:start position:0%
+been doing that as I mentioned the our
+chief partner the implementer died in
+
+ align:start position:0%
+chief partner the implementer died in
+ 
+
+ align:start position:0%
+chief partner the implementer died in
+the earthquake in American but we had we
+
+ align:start position:0%
+the earthquake in American but we had we
+ 
+
+ align:start position:0%
+the earthquake in American but we had we
+knew we had to do something very
+
+ align:start position:0%
+knew we had to do something very
+ 
+
+ align:start position:0%
+knew we had to do something very
+different and so we we redesigned the
+
+ align:start position:0%
+different and so we we redesigned the
+ 
+
+ align:start position:0%
+different and so we we redesigned the
+hospital
+
+ align:start position:0%
+hospital
+ 
+
+ align:start position:0%
+hospital
+and built it I say we I didn't do any
+
+ align:start position:0%
+and built it I say we I didn't do any
+ 
+
+ align:start position:0%
+and built it I say we I didn't do any
+heavy lifting but we've actually managed
+
+ align:start position:0%
+heavy lifting but we've actually managed
+ 
+
+ align:start position:0%
+heavy lifting but we've actually managed
+to get and I hear I always try to make a
+
+ align:start position:0%
+to get and I hear I always try to make a
+ 
+
+ align:start position:0%
+to get and I hear I always try to make a
+tribute to one of my former students uh
+
+ align:start position:0%
+tribute to one of my former students uh
+ 
+
+ align:start position:0%
+tribute to one of my former students uh
+David Walton who is the Project Director
+
+ align:start position:0%
+David Walton who is the Project Director
+ 
+
+ align:start position:0%
+David Walton who is the Project Director
+but also to uh former Construction
+
+ align:start position:0%
+but also to uh former Construction
+ 
+
+ align:start position:0%
+but also to uh former Construction
+Company magnet who started a
+
+ align:start position:0%
+Company magnet who started a
+ 
+
+ align:start position:0%
+Company magnet who started a
+construction company here in
+
+ align:start position:0%
+construction company here in
+ 
+
+ align:start position:0%
+construction company here in
+Massachusetts when he was 22 years old
+
+ align:start position:0%
+Massachusetts when he was 22 years old
+ 
+
+ align:start position:0%
+Massachusetts when he was 22 years old
+his name's Jim and Sarah built a big
+
+ align:start position:0%
+his name's Jim and Sarah built a big
+ 
+
+ align:start position:0%
+his name's Jim and Sarah built a big
+company uh sold it and then since the
+
+ align:start position:0%
+company uh sold it and then since the
+ 
+
+ align:start position:0%
+company uh sold it and then since the
+earthquake has basically been down in
+
+ align:start position:0%
+earthquake has basically been down in
+ 
+
+ align:start position:0%
+earthquake has basically been down in
+Hades and some of you if you ever get to
+
+ align:start position:0%
+Hades and some of you if you ever get to
+ 
+
+ align:start position:0%
+Hades and some of you if you ever get to
+meet him he's a very quiet somewhat
+
+ align:start position:0%
+meet him he's a very quiet somewhat
+ 
+
+ align:start position:0%
+meet him he's a very quiet somewhat
+Gruff but terrific guy
+
+ align:start position:0%
+Gruff but terrific guy
+ 
+
+ align:start position:0%
+Gruff but terrific guy
+and together they put together a team
+
+ align:start position:0%
+and together they put together a team
+ 
+
+ align:start position:0%
+and together they put together a team
+that has people from all over from the
+
+ align:start position:0%
+that has people from all over from the
+ 
+
+ align:start position:0%
+that has people from all over from the
+United States Dominican Republicans
+
+ align:start position:0%
+United States Dominican Republicans
+ 
+
+ align:start position:0%
+United States Dominican Republicans
+especially Haiti and built this really
+
+ align:start position:0%
+especially Haiti and built this really
+ 
+
+ align:start position:0%
+especially Haiti and built this really
+terrific hospital so I'm gonna I'm gonna
+
+ align:start position:0%
+terrific hospital so I'm gonna I'm gonna
+ 
+
+ align:start position:0%
+terrific hospital so I'm gonna I'm gonna
+stop here and open it up for discussion
+
+ align:start position:0%
+stop here and open it up for discussion
+ 
+
+ align:start position:0%
+stop here and open it up for discussion
+with the summary point that there it in
+
+ align:start position:0%
+with the summary point that there it in
+ 
+
+ align:start position:0%
+with the summary point that there it in
+order for you guys and those of you who
+
+ align:start position:0%
+order for you guys and those of you who
+ 
+
+ align:start position:0%
+order for you guys and those of you who
+are interested in technology not all of
+
+ align:start position:0%
+are interested in technology not all of
+ 
+
+ align:start position:0%
+are interested in technology not all of
+you are actually going to generate the
+
+ align:start position:0%
+you are actually going to generate the
+ 
+
+ align:start position:0%
+you are actually going to generate the
+technology but for those who are
+
+ align:start position:0%
+technology but for those who are
+ 
+
+ align:start position:0%
+technology but for those who are
+interested in technology and how it
+
+ align:start position:0%
+interested in technology and how it
+ 
+
+ align:start position:0%
+interested in technology and how it
+works remember that you need it there
+
+ align:start position:0%
+works remember that you need it there
+ 
+
+ align:start position:0%
+works remember that you need it there
+there to a platform that is built and
+
+ align:start position:0%
+there to a platform that is built and
+ 
+
+ align:start position:0%
+there to a platform that is built and
+sometimes that platform is already
+
+ align:start position:0%
+sometimes that platform is already
+ 
+
+ align:start position:0%
+sometimes that platform is already
+halfway there three quarters of the way
+
+ align:start position:0%
+halfway there three quarters of the way
+ 
+
+ align:start position:0%
+halfway there three quarters of the way
+there but sometimes it's almost absent
+
+ align:start position:0%
+there but sometimes it's almost absent
+ 
+
+ align:start position:0%
+there but sometimes it's almost absent
+completely and that's where I hope
+
+ align:start position:0%
+completely and that's where I hope
+ 
+
+ align:start position:0%
+completely and that's where I hope
+people like me come in who are not on
+
+ align:start position:0%
+people like me come in who are not on
+ 
+
+ align:start position:0%
+people like me come in who are not on
+The Cutting Edge in terms of Technology
+
+ align:start position:0%
+The Cutting Edge in terms of Technology
+ 
+
+ align:start position:0%
+The Cutting Edge in terms of Technology
+development or new tools but we're in a
+
+ align:start position:0%
+development or new tools but we're in a
+ 
+
+ align:start position:0%
+development or new tools but we're in a
+way in The Cutting Edge of Delta system
+
+ align:start position:0%
+way in The Cutting Edge of Delta system
+ 
+
+ align:start position:0%
+way in The Cutting Edge of Delta system
+design merely because we're going back
+
+ align:start position:0%
+design merely because we're going back
+ 
+
+ align:start position:0%
+design merely because we're going back
+saying well you can't really skip over
+
+ align:start position:0%
+saying well you can't really skip over
+ 
+
+ align:start position:0%
+saying well you can't really skip over
+that step you actually do have to have
+
+ align:start position:0%
+that step you actually do have to have
+ 
+
+ align:start position:0%
+that step you actually do have to have
+hospitals and health centers and
+
+ align:start position:0%
+hospitals and health centers and
+ 
+
+ align:start position:0%
+hospitals and health centers and
+community health workers so thank you
+
+ align:start position:0%
+community health workers so thank you
+ 
+
+ align:start position:0%
+community health workers so thank you
+very much I look forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you Paul really appreciate it so I
+
+ align:start position:0%
+thank you Paul really appreciate it so I
+ 
+
+ align:start position:0%
+thank you Paul really appreciate it so I
+went over a little bit um we're plenty
+
+ align:start position:0%
+went over a little bit um we're plenty
+ 
+
+ align:start position:0%
+went over a little bit um we're plenty
+of time actually so that's no problem
+
+ align:start position:0%
+of time actually so that's no problem
+ 
+
+ align:start position:0%
+of time actually so that's no problem
+um a couple of things first of all um
+
+ align:start position:0%
+um a couple of things first of all um
+ 
+
+ align:start position:0%
+um a couple of things first of all um
+we'd like to get some questions or
+
+ align:start position:0%
+we'd like to get some questions or
+ 
+
+ align:start position:0%
+we'd like to get some questions or
+comments from the students in the class
+
+ align:start position:0%
+comments from the students in the class
+ 
+
+ align:start position:0%
+comments from the students in the class
+first of all that's all right
+
+ align:start position:0%
+first of all that's all right
+ 
+
+ align:start position:0%
+first of all that's all right
+um and I know you have a few ideas that
+
+ align:start position:0%
+um and I know you have a few ideas that
+ 
+
+ align:start position:0%
+um and I know you have a few ideas that
+you would like to ask Paul about
+
+ align:start position:0%
+you would like to ask Paul about
+ 
+
+ align:start position:0%
+you would like to ask Paul about
+um just a couple of quick comments about
+
+ align:start position:0%
+um just a couple of quick comments about
+ 
+
+ align:start position:0%
+um just a couple of quick comments about
+certain things that we've discussed in
+
+ align:start position:0%
+certain things that we've discussed in
+ 
+
+ align:start position:0%
+certain things that we've discussed in
+the lecture we wanted us about open
+
+ align:start position:0%
+the lecture we wanted us about open
+ 
+
+ align:start position:0%
+the lecture we wanted us about open
+source in addition to making software
+
+ align:start position:0%
+source in addition to making software
+ 
+
+ align:start position:0%
+source in addition to making software
+available to other organizations and
+
+ align:start position:0%
+available to other organizations and
+ 
+
+ align:start position:0%
+available to other organizations and
+countries one of the things that we keep
+
+ align:start position:0%
+countries one of the things that we keep
+ 
+
+ align:start position:0%
+countries one of the things that we keep
+going back to is the fact that there are
+
+ align:start position:0%
+going back to is the fact that there are
+ 
+
+ align:start position:0%
+going back to is the fact that there are
+differences and there are different
+
+ align:start position:0%
+differences and there are different
+ 
+
+ align:start position:0%
+differences and there are different
+requirements and different
+
+ align:start position:0%
+requirements and different
+ 
+
+ align:start position:0%
+requirements and different
+customizations that are required in each
+
+ align:start position:0%
+customizations that are required in each
+ 
+
+ align:start position:0%
+customizations that are required in each
+different country and as the sort of
+
+ align:start position:0%
+different country and as the sort of
+ 
+
+ align:start position:0%
+different country and as the sort of
+provide very little very nature of the
+
+ align:start position:0%
+provide very little very nature of the
+ 
+
+ align:start position:0%
+provide very little very nature of the
+environment you're working by using open
+
+ align:start position:0%
+environment you're working by using open
+ 
+
+ align:start position:0%
+environment you're working by using open
+source we give control and Leadership
+
+ align:start position:0%
+source we give control and Leadership
+ 
+
+ align:start position:0%
+source we give control and Leadership
+and ability to actually manage this
+
+ align:start position:0%
+and ability to actually manage this
+ 
+
+ align:start position:0%
+and ability to actually manage this
+project to people working in different
+
+ align:start position:0%
+project to people working in different
+ 
+
+ align:start position:0%
+project to people working in different
+countries and that's particularly true
+
+ align:start position:0%
+countries and that's particularly true
+ 
+
+ align:start position:0%
+countries and that's particularly true
+in Rwanda where we've trained other
+
+ align:start position:0%
+in Rwanda where we've trained other
+ 
+
+ align:start position:0%
+in Rwanda where we've trained other
+people who around with program
+
+ align:start position:0%
+people who around with program
+ 
+
+ align:start position:0%
+people who around with program
+assistance so I think in addition to the
+
+ align:start position:0%
+assistance so I think in addition to the
+ 
+
+ align:start position:0%
+assistance so I think in addition to the
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+um almost like you know human rights
+
+ align:start position:0%
+um almost like you know human rights
+ 
+
+ align:start position:0%
+um almost like you know human rights
+approach of making these Technologies
+
+ align:start position:0%
+approach of making these Technologies
+ 
+
+ align:start position:0%
+approach of making these Technologies
+available and really empowering people
+
+ align:start position:0%
+available and really empowering people
+ 
+
+ align:start position:0%
+available and really empowering people
+it's also really essential to allow them
+
+ align:start position:0%
+it's also really essential to allow them
+ 
+
+ align:start position:0%
+it's also really essential to allow them
+to be adapted to the real needs on the
+
+ align:start position:0%
+to be adapted to the real needs on the
+ 
+
+ align:start position:0%
+to be adapted to the real needs on the
+ground rather than something that looks
+
+ align:start position:0%
+ground rather than something that looks
+ 
+
+ align:start position:0%
+ground rather than something that looks
+similar such as you know the
+
+ align:start position:0%
+similar such as you know the
+ 
+
+ align:start position:0%
+similar such as you know the
+requirements of hating Rwanda which are
+
+ align:start position:0%
+requirements of hating Rwanda which are
+ 
+
+ align:start position:0%
+requirements of hating Rwanda which are
+superficious and there are many things
+
+ align:start position:0%
+superficious and there are many things
+ 
+
+ align:start position:0%
+superficious and there are many things
+are the same but actually are not quite
+
+ align:start position:0%
+are the same but actually are not quite
+ 
+
+ align:start position:0%
+are the same but actually are not quite
+the same and the other comment I just
+
+ align:start position:0%
+the same and the other comment I just
+ 
+
+ align:start position:0%
+the same and the other comment I just
+make about the collar outbreak that I
+
+ align:start position:0%
+make about the collar outbreak that I
+ 
+
+ align:start position:0%
+make about the collar outbreak that I
+know that there's many people in the MIT
+
+ align:start position:0%
+know that there's many people in the MIT
+ 
+
+ align:start position:0%
+know that there's many people in the MIT
+and the Boston Community who've been
+
+ align:start position:0%
+and the Boston Community who've been
+ 
+
+ align:start position:0%
+and the Boston Community who've been
+looking at the question of how do we
+
+ align:start position:0%
+looking at the question of how do we
+ 
+
+ align:start position:0%
+looking at the question of how do we
+actually understand and measure what's
+
+ align:start position:0%
+actually understand and measure what's
+ 
+
+ align:start position:0%
+actually understand and measure what's
+going on there and so Paul commented
+
+ align:start position:0%
+going on there and so Paul commented
+ 
+
+ align:start position:0%
+going on there and so Paul commented
+about some of these issues and you know
+
+ align:start position:0%
+about some of these issues and you know
+ 
+
+ align:start position:0%
+about some of these issues and you know
+in one of the slides and I know that
+
+ align:start position:0%
+in one of the slides and I know that
+ 
+
+ align:start position:0%
+in one of the slides and I know that
+many people here have been interested in
+
+ align:start position:0%
+many people here have been interested in
+ 
+
+ align:start position:0%
+many people here have been interested in
+that question and they've been looking
+
+ align:start position:0%
+that question and they've been looking
+ 
+
+ align:start position:0%
+that question and they've been looking
+at a whole range of different ways that
+
+ align:start position:0%
+at a whole range of different ways that
+ 
+
+ align:start position:0%
+at a whole range of different ways that
+we can look at the
+
+ align:start position:0%
+we can look at the
+ 
+
+ align:start position:0%
+we can look at the
+um what's going on which communities
+
+ align:start position:0%
+um what's going on which communities
+ 
+
+ align:start position:0%
+um what's going on which communities
+have good Water Supplies how can we even
+
+ align:start position:0%
+have good Water Supplies how can we even
+ 
+
+ align:start position:0%
+have good Water Supplies how can we even
+track which pumps are actually
+
+ align:start position:0%
+track which pumps are actually
+ 
+
+ align:start position:0%
+track which pumps are actually
+functioning using cell phone connections
+
+ align:start position:0%
+functioning using cell phone connections
+ 
+
+ align:start position:0%
+functioning using cell phone connections
+to those how do we overload that with
+
+ align:start position:0%
+to those how do we overload that with
+ 
+
+ align:start position:0%
+to those how do we overload that with
+social networks and actually manage to
+
+ align:start position:0%
+social networks and actually manage to
+ 
+
+ align:start position:0%
+social networks and actually manage to
+track the cholera outbreak through those
+
+ align:start position:0%
+track the cholera outbreak through those
+ 
+
+ align:start position:0%
+track the cholera outbreak through those
+as well so I think there's a lot of
+
+ align:start position:0%
+as well so I think there's a lot of
+ 
+
+ align:start position:0%
+as well so I think there's a lot of
+areas where there's overlap but I will
+
+ align:start position:0%
+areas where there's overlap but I will
+ 
+
+ align:start position:0%
+areas where there's overlap but I will
+not take over this ad just first of all
+
+ align:start position:0%
+not take over this ad just first of all
+ 
+
+ align:start position:0%
+not take over this ad just first of all
+just like to say
+
+ align:start position:0%
+just like to say
+ 
+
+ align:start position:0%
+just like to say
+um doing the students in the class have
+
+ align:start position:0%
+um doing the students in the class have
+ 
+
+ align:start position:0%
+um doing the students in the class have
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes please if you don't mind introducing
+
+ align:start position:0%
+yes please if you don't mind introducing
+ 
+
+ align:start position:0%
+yes please if you don't mind introducing
+yourself just in the hopes that I will
+
+ align:start position:0%
+yourself just in the hopes that I will
+ 
+
+ align:start position:0%
+yourself just in the hopes that I will
+stay in touch with some of you my name
+
+ align:start position:0%
+stay in touch with some of you my name
+ 
+
+ align:start position:0%
+stay in touch with some of you my name
+is Sherry Ward and and they engage
+
+ align:start position:0%
+is Sherry Ward and and they engage
+ 
+
+ align:start position:0%
+is Sherry Ward and and they engage
+program over at the Harvard School of
+
+ align:start position:0%
+program over at the Harvard School of
+ 
+
+ align:start position:0%
+program over at the Harvard School of
+global Health in the global Health
+
+ align:start position:0%
+global Health in the global Health
+ 
+
+ align:start position:0%
+global Health in the global Health
+Department thank you for coming thank
+
+ align:start position:0%
+Department thank you for coming thank
+ 
+
+ align:start position:0%
+Department thank you for coming thank
+you and I also wanted to say thank you I
+
+ align:start position:0%
+you and I also wanted to say thank you I
+ 
+
+ align:start position:0%
+you and I also wanted to say thank you I
+heard you speak in mayor Blair and in
+
+ align:start position:0%
+heard you speak in mayor Blair and in
+ 
+
+ align:start position:0%
+heard you speak in mayor Blair and in
+January did I did I cry or not
+
+ align:start position:0%
+January did I did I cry or not
+ 
+
+ align:start position:0%
+January did I did I cry or not
+oh that was very emotional but it really
+
+ align:start position:0%
+oh that was very emotional but it really
+ 
+
+ align:start position:0%
+oh that was very emotional but it really
+affected the way I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well thank you for coming all the way to
+
+ align:start position:0%
+well thank you for coming all the way to
+ 
+
+ align:start position:0%
+well thank you for coming all the way to
+Haiti to hear it
+
+ align:start position:0%
+Haiti to hear it
+ 
+
+ align:start position:0%
+Haiti to hear it
+thank you um another question is what
+
+ align:start position:0%
+thank you um another question is what
+ 
+
+ align:start position:0%
+thank you um another question is what
+has been your experience with any M
+
+ align:start position:0%
+has been your experience with any M
+ 
+
+ align:start position:0%
+has been your experience with any M
+Health technology and either yourself or
+
+ align:start position:0%
+Health technology and either yourself or
+ 
+
+ align:start position:0%
+Health technology and either yourself or
+with Partners in Health that was very
+
+ align:start position:0%
+with Partners in Health that was very
+ 
+
+ align:start position:0%
+with Partners in Health that was very
+successful that you felt made a big
+
+ align:start position:0%
+successful that you felt made a big
+ 
+
+ align:start position:0%
+successful that you felt made a big
+difference in patient outcomes and why
+
+ align:start position:0%
+difference in patient outcomes and why
+ 
+
+ align:start position:0%
+difference in patient outcomes and why
+do you feel that those specific programs
+
+ align:start position:0%
+do you feel that those specific programs
+ 
+
+ align:start position:0%
+do you feel that those specific programs
+well I'm going to tell you again for as
+
+ align:start position:0%
+well I'm going to tell you again for as
+ 
+
+ align:start position:0%
+well I'm going to tell you again for as
+the as The Outsider and then ask Hamish
+
+ align:start position:0%
+the as The Outsider and then ask Hamish
+ 
+
+ align:start position:0%
+the as The Outsider and then ask Hamish
+to to comment on that the outsider
+
+ align:start position:0%
+to to comment on that the outsider
+ 
+
+ align:start position:0%
+to to comment on that the outsider
+meaning The Insider clinically
+
+ align:start position:0%
+meaning The Insider clinically
+ 
+
+ align:start position:0%
+meaning The Insider clinically
+um I would if I had to choose one uh
+
+ align:start position:0%
+um I would if I had to choose one uh
+ 
+
+ align:start position:0%
+um I would if I had to choose one uh
+leaving aside the electronic medical
+
+ align:start position:0%
+leaving aside the electronic medical
+ 
+
+ align:start position:0%
+leaving aside the electronic medical
+record you said M mobile right it would
+
+ align:start position:0%
+record you said M mobile right it would
+ 
+
+ align:start position:0%
+record you said M mobile right it would
+be the cell phone uh the use of cell
+
+ align:start position:0%
+be the cell phone uh the use of cell
+ 
+
+ align:start position:0%
+be the cell phone uh the use of cell
+phones by community health workers in
+
+ align:start position:0%
+phones by community health workers in
+ 
+
+ align:start position:0%
+phones by community health workers in
+Peru to manage complex uh pharmacopoeia
+
+ align:start position:0%
+Peru to manage complex uh pharmacopoeia
+ 
+
+ align:start position:0%
+Peru to manage complex uh pharmacopoeia
+you know these these regimens that are
+
+ align:start position:0%
+you know these these regimens that are
+ 
+
+ align:start position:0%
+you know these these regimens that are
+sometimes I have 10 12 15 medications
+
+ align:start position:0%
+sometimes I have 10 12 15 medications
+ 
+
+ align:start position:0%
+sometimes I have 10 12 15 medications
+and I would say that that is probably a
+
+ align:start position:0%
+and I would say that that is probably a
+ 
+
+ align:start position:0%
+and I would say that that is probably a
+and my colleagues are doing that in
+
+ align:start position:0%
+and my colleagues are doing that in
+ 
+
+ align:start position:0%
+and my colleagues are doing that in
+Mexico in Rwanda now in Haiti but the
+
+ align:start position:0%
+Mexico in Rwanda now in Haiti but the
+ 
+
+ align:start position:0%
+Mexico in Rwanda now in Haiti but the
+Peruvian
+
+ align:start position:0%
+Peruvian
+ 
+
+ align:start position:0%
+Peruvian
+it looks to me that they're really the
+
+ align:start position:0%
+it looks to me that they're really the
+ 
+
+ align:start position:0%
+it looks to me that they're really the
+community health workers really can't
+
+ align:start position:0%
+community health workers really can't
+ 
+
+ align:start position:0%
+community health workers really can't
+work without it and in their handheld
+
+ align:start position:0%
+work without it and in their handheld
+ 
+
+ align:start position:0%
+work without it and in their handheld
+devices am I right or not
+
+ align:start position:0%
+devices am I right or not
+ 
+
+ align:start position:0%
+devices am I right or not
+I mean actually Mexico in particular
+
+ align:start position:0%
+I mean actually Mexico in particular
+ 
+
+ align:start position:0%
+I mean actually Mexico in particular
+Davenport Services work looking at um
+
+ align:start position:0%
+Davenport Services work looking at um
+ 
+
+ align:start position:0%
+Davenport Services work looking at um
+how you can simplify prescribing of such
+
+ align:start position:0%
+how you can simplify prescribing of such
+ 
+
+ align:start position:0%
+how you can simplify prescribing of such
+medications and providing that support
+
+ align:start position:0%
+medications and providing that support
+ 
+
+ align:start position:0%
+medications and providing that support
+is probably the most advanced one that
+
+ align:start position:0%
+is probably the most advanced one that
+ 
+
+ align:start position:0%
+is probably the most advanced one that
+we're being looking at I mean I think
+
+ align:start position:0%
+we're being looking at I mean I think
+ 
+
+ align:start position:0%
+we're being looking at I mean I think
+there there's a huge amount of energy in
+
+ align:start position:0%
+there there's a huge amount of energy in
+ 
+
+ align:start position:0%
+there there's a huge amount of energy in
+NF at this point and many people looking
+
+ align:start position:0%
+NF at this point and many people looking
+ 
+
+ align:start position:0%
+NF at this point and many people looking
+at different ways we can use it I would
+
+ align:start position:0%
+at different ways we can use it I would
+ 
+
+ align:start position:0%
+at different ways we can use it I would
+say that we we've had specific benefits
+
+ align:start position:0%
+say that we we've had specific benefits
+ 
+
+ align:start position:0%
+say that we we've had specific benefits
+the other thing to improve actually is
+
+ align:start position:0%
+the other thing to improve actually is
+ 
+
+ align:start position:0%
+the other thing to improve actually is
+the Palm Pilots before that's what I
+
+ align:start position:0%
+the Palm Pilots before that's what I
+ 
+
+ align:start position:0%
+the Palm Pilots before that's what I
+mean handheld devices and be able to
+
+ align:start position:0%
+mean handheld devices and be able to
+ 
+
+ align:start position:0%
+mean handheld devices and be able to
+collect that data and improve quality if
+
+ align:start position:0%
+collect that data and improve quality if
+ 
+
+ align:start position:0%
+collect that data and improve quality if
+it's also access the lab data I know
+
+ align:start position:0%
+it's also access the lab data I know
+ 
+
+ align:start position:0%
+it's also access the lab data I know
+that their app is also interested in
+
+ align:start position:0%
+that their app is also interested in
+ 
+
+ align:start position:0%
+that their app is also interested in
+this question how do we actually get the
+
+ align:start position:0%
+this question how do we actually get the
+ 
+
+ align:start position:0%
+this question how do we actually get the
+lab data from the from the market maybe
+
+ align:start position:0%
+lab data from the from the market maybe
+ 
+
+ align:start position:0%
+lab data from the from the market maybe
+the remote car from the patients back to
+
+ align:start position:0%
+the remote car from the patients back to
+ 
+
+ align:start position:0%
+the remote car from the patients back to
+the clinician's caring for those
+
+ align:start position:0%
+the clinician's caring for those
+ 
+
+ align:start position:0%
+the clinician's caring for those
+patients and that's thinking pushes I
+
+ align:start position:0%
+patients and that's thinking pushes I
+ 
+
+ align:start position:0%
+patients and that's thinking pushes I
+mean going forward there's the big
+
+ align:start position:0%
+mean going forward there's the big
+ 
+
+ align:start position:0%
+mean going forward there's the big
+question this is actually one that I'm
+
+ align:start position:0%
+question this is actually one that I'm
+ 
+
+ align:start position:0%
+question this is actually one that I'm
+very interested in
+
+ align:start position:0%
+very interested in
+ 
+
+ align:start position:0%
+very interested in
+um two grand national forecast we talked
+
+ align:start position:0%
+um two grand national forecast we talked
+ 
+
+ align:start position:0%
+um two grand national forecast we talked
+about in the class looking at text
+
+ align:start position:0%
+about in the class looking at text
+ 
+
+ align:start position:0%
+about in the class looking at text
+message reminders for patients to take
+
+ align:start position:0%
+message reminders for patients to take
+ 
+
+ align:start position:0%
+message reminders for patients to take
+their HIV medications and show them that
+
+ align:start position:0%
+their HIV medications and show them that
+ 
+
+ align:start position:0%
+their HIV medications and show them that
+there was a benefit of that but at the
+
+ align:start position:0%
+there was a benefit of that but at the
+ 
+
+ align:start position:0%
+there was a benefit of that but at the
+same time
+
+ align:start position:0%
+same time
+ 
+
+ align:start position:0%
+same time
+food to my knowledge and I think we're
+
+ align:start position:0%
+food to my knowledge and I think we're
+ 
+
+ align:start position:0%
+food to my knowledge and I think we're
+still trying to map this out this is not
+
+ align:start position:0%
+still trying to map this out this is not
+ 
+
+ align:start position:0%
+still trying to map this out this is not
+as effective as a community healthcare
+
+ align:start position:0%
+as effective as a community healthcare
+ 
+
+ align:start position:0%
+as effective as a community healthcare
+worker plus do that and so there's a big
+
+ align:start position:0%
+worker plus do that and so there's a big
+ 
+
+ align:start position:0%
+worker plus do that and so there's a big
+interesting question that we have not
+
+ align:start position:0%
+interesting question that we have not
+ 
+
+ align:start position:0%
+interesting question that we have not
+resolved is how well does the company
+
+ align:start position:0%
+resolved is how well does the company
+ 
+
+ align:start position:0%
+resolved is how well does the company
+internal model function in different
+
+ align:start position:0%
+internal model function in different
+ 
+
+ align:start position:0%
+internal model function in different
+environments relative to the phone and I
+
+ align:start position:0%
+environments relative to the phone and I
+ 
+
+ align:start position:0%
+environments relative to the phone and I
+I believe that the New Hampshire worker
+
+ align:start position:0%
+I believe that the New Hampshire worker
+ 
+
+ align:start position:0%
+I believe that the New Hampshire worker
+is actually much more effective
+
+ align:start position:0%
+is actually much more effective
+ 
+
+ align:start position:0%
+is actually much more effective
+approach however there's also the
+
+ align:start position:0%
+approach however there's also the
+ 
+
+ align:start position:0%
+approach however there's also the
+questions of how you organize that so
+
+ align:start position:0%
+questions of how you organize that so
+ 
+
+ align:start position:0%
+questions of how you organize that so
+there's a big interesting question in
+
+ align:start position:0%
+there's a big interesting question in
+ 
+
+ align:start position:0%
+there's a big interesting question in
+the public health aspect which I think
+
+ align:start position:0%
+the public health aspect which I think
+ 
+
+ align:start position:0%
+the public health aspect which I think
+is going to be one of the important
+
+ align:start position:0%
+is going to be one of the important
+ 
+
+ align:start position:0%
+is going to be one of the important
+things going forward in the next couple
+
+ align:start position:0%
+things going forward in the next couple
+ 
+
+ align:start position:0%
+things going forward in the next couple
+of years if I could just add to that
+
+ align:start position:0%
+of years if I could just add to that
+ 
+
+ align:start position:0%
+of years if I could just add to that
+back to the question of comparing some
+
+ align:start position:0%
+back to the question of comparing some
+ 
+
+ align:start position:0%
+back to the question of comparing some
+of the neat gadgetry that has been
+
+ align:start position:0%
+of the neat gadgetry that has been
+ 
+
+ align:start position:0%
+of the neat gadgetry that has been
+Advanced by MIT specifically one of them
+
+ align:start position:0%
+Advanced by MIT specifically one of them
+ 
+
+ align:start position:0%
+Advanced by MIT specifically one of them
+I remember was
+
+ align:start position:0%
+I remember was
+ 
+
+ align:start position:0%
+I remember was
+a a urine strip to test isoniazide
+
+ align:start position:0%
+a a urine strip to test isoniazide
+ 
+
+ align:start position:0%
+a a urine strip to test isoniazide
+levels in the blood to see if you were
+
+ align:start position:0%
+levels in the blood to see if you were
+ 
+
+ align:start position:0%
+levels in the blood to see if you were
+actually complying with your regimen for
+
+ align:start position:0%
+actually complying with your regimen for
+ 
+
+ align:start position:0%
+actually complying with your regimen for
+tuberculosis and I was saying okay then
+
+ align:start position:0%
+tuberculosis and I was saying okay then
+ 
+
+ align:start position:0%
+tuberculosis and I was saying okay then
+you feed the strip into a cool little
+
+ align:start position:0%
+you feed the strip into a cool little
+ 
+
+ align:start position:0%
+you feed the strip into a cool little
+handout machine and but you could have
+
+ align:start position:0%
+handout machine and but you could have
+ 
+
+ align:start position:0%
+handout machine and but you could have
+given someone a job to be the community
+
+ align:start position:0%
+given someone a job to be the community
+ 
+
+ align:start position:0%
+given someone a job to be the community
+health worker and visit the patron and
+
+ align:start position:0%
+health worker and visit the patron and
+ 
+
+ align:start position:0%
+health worker and visit the patron and
+accompaniment so this is another I I
+
+ align:start position:0%
+accompaniment so this is another I I
+ 
+
+ align:start position:0%
+accompaniment so this is another I I
+don't want to sound like a Luddite I
+
+ align:start position:0%
+don't want to sound like a Luddite I
+ 
+
+ align:start position:0%
+don't want to sound like a Luddite I
+believe that it's the technical term
+
+ align:start position:0%
+believe that it's the technical term
+ 
+
+ align:start position:0%
+believe that it's the technical term
+remember for Ned blood and if I don't
+
+ align:start position:0%
+remember for Ned blood and if I don't
+ 
+
+ align:start position:0%
+remember for Ned blood and if I don't
+even know if he was a real person but
+
+ align:start position:0%
+even know if he was a real person but
+ 
+
+ align:start position:0%
+even know if he was a real person but
+trying to slow down in your peeps trying
+
+ align:start position:0%
+trying to slow down in your peeps trying
+ 
+
+ align:start position:0%
+trying to slow down in your peeps trying
+to slow down the Industrial Revolution
+
+ align:start position:0%
+to slow down the Industrial Revolution
+ 
+
+ align:start position:0%
+to slow down the Industrial Revolution
+on the contrary I'm not I'm just saying
+
+ align:start position:0%
+on the contrary I'm not I'm just saying
+ 
+
+ align:start position:0%
+on the contrary I'm not I'm just saying
+we need to learn how to measure
+
+ align:start position:0%
+we need to learn how to measure
+ 
+
+ align:start position:0%
+we need to learn how to measure
+especially you know at the school public
+
+ align:start position:0%
+especially you know at the school public
+ 
+
+ align:start position:0%
+especially you know at the school public
+out there in an economics Department
+
+ align:start position:0%
+out there in an economics Department
+ 
+
+ align:start position:0%
+out there in an economics Department
+this the positive impact of actually
+
+ align:start position:0%
+this the positive impact of actually
+ 
+
+ align:start position:0%
+this the positive impact of actually
+reducing unemployment
+
+ align:start position:0%
+reducing unemployment
+ 
+
+ align:start position:0%
+reducing unemployment
+and then community health workers are
+
+ align:start position:0%
+and then community health workers are
+ 
+
+ align:start position:0%
+and then community health workers are
+Far and Away the largest
+
+ align:start position:0%
+Far and Away the largest
+ 
+
+ align:start position:0%
+Far and Away the largest
+fraction of workers at partisan Health
+
+ align:start position:0%
+fraction of workers at partisan Health
+ 
+
+ align:start position:0%
+fraction of workers at partisan Health
+which is counts probably fifteen
+
+ align:start position:0%
+which is counts probably fifteen
+ 
+
+ align:start position:0%
+which is counts probably fifteen
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+employees and most of them have never
+
+ align:start position:0%
+employees and most of them have never
+ 
+
+ align:start position:0%
+employees and most of them have never
+had a job before so there's this
+
+ align:start position:0%
+had a job before so there's this
+ 
+
+ align:start position:0%
+had a job before so there's this
+virtuous social cycle that gets started
+
+ align:start position:0%
+virtuous social cycle that gets started
+ 
+
+ align:start position:0%
+virtuous social cycle that gets started
+just by using human labor when you can
+
+ align:start position:0%
+just by using human labor when you can
+ 
+
+ align:start position:0%
+just by using human labor when you can
+and you want to never fail to integrate
+
+ align:start position:0%
+and you want to never fail to integrate
+ 
+
+ align:start position:0%
+and you want to never fail to integrate
+new technology at the same time that you
+
+ align:start position:0%
+new technology at the same time that you
+ 
+
+ align:start position:0%
+new technology at the same time that you
+would learn how to Value positively
+
+ align:start position:0%
+would learn how to Value positively
+ 
+
+ align:start position:0%
+would learn how to Value positively
+giving a job to Community Health program
+
+ align:start position:0%
+giving a job to Community Health program
+ 
+
+ align:start position:0%
+giving a job to Community Health program
+which by the way still as I said
+
+ align:start position:0%
+which by the way still as I said
+ 
+
+ align:start position:0%
+which by the way still as I said
+delivers a better service but also has
+
+ align:start position:0%
+delivers a better service but also has
+ 
+
+ align:start position:0%
+delivers a better service but also has
+these other things we need to learn how
+
+ align:start position:0%
+these other things we need to learn how
+ 
+
+ align:start position:0%
+these other things we need to learn how
+to study I mean something that we're
+
+ align:start position:0%
+to study I mean something that we're
+ 
+
+ align:start position:0%
+to study I mean something that we're
+doing a lot at the moment yeah just
+
+ align:start position:0%
+doing a lot at the moment yeah just
+ 
+
+ align:start position:0%
+doing a lot at the moment yeah just
+looking at how the really effective
+
+ align:start position:0%
+looking at how the really effective
+ 
+
+ align:start position:0%
+looking at how the really effective
+community health care worker programs
+
+ align:start position:0%
+community health care worker programs
+ 
+
+ align:start position:0%
+community health care worker programs
+and the training and the way that those
+
+ align:start position:0%
+and the training and the way that those
+ 
+
+ align:start position:0%
+and the training and the way that those
+have been set up and managed can be
+
+ align:start position:0%
+have been set up and managed can be
+ 
+
+ align:start position:0%
+have been set up and managed can be
+linked to these mobile appliances and
+
+ align:start position:0%
+linked to these mobile appliances and
+ 
+
+ align:start position:0%
+linked to these mobile appliances and
+that's in Reliance in particular we've
+
+ align:start position:0%
+that's in Reliance in particular we've
+ 
+
+ align:start position:0%
+that's in Reliance in particular we've
+got a 40 000 community healthcare
+
+ align:start position:0%
+got a 40 000 community healthcare
+ 
+
+ align:start position:0%
+got a 40 000 community healthcare
+workers hard by the government and being
+
+ align:start position:0%
+workers hard by the government and being
+ 
+
+ align:start position:0%
+workers hard by the government and being
+trained they are working really hard on
+
+ align:start position:0%
+trained they are working really hard on
+ 
+
+ align:start position:0%
+trained they are working really hard on
+how we can actually look at using
+
+ align:start position:0%
+how we can actually look at using
+ 
+
+ align:start position:0%
+how we can actually look at using
+initiative text messaging rapid SMS but
+
+ align:start position:0%
+initiative text messaging rapid SMS but
+ 
+
+ align:start position:0%
+initiative text messaging rapid SMS but
+you know other than that can we actually
+
+ align:start position:0%
+you know other than that can we actually
+ 
+
+ align:start position:0%
+you know other than that can we actually
+build on the phones with both of those
+
+ align:start position:0%
+build on the phones with both of those
+ 
+
+ align:start position:0%
+build on the phones with both of those
+things the the community the employment
+
+ align:start position:0%
+things the the community the employment
+ 
+
+ align:start position:0%
+things the the community the employment
+that people could really get into the
+
+ align:start position:0%
+that people could really get into the
+ 
+
+ align:start position:0%
+that people could really get into the
+patient's homes but also linking that so
+
+ align:start position:0%
+patient's homes but also linking that so
+ 
+
+ align:start position:0%
+patient's homes but also linking that so
+that you can for example Ensure if
+
+ align:start position:0%
+that you can for example Ensure if
+ 
+
+ align:start position:0%
+that you can for example Ensure if
+somebody has TV and it wasn't known when
+
+ align:start position:0%
+somebody has TV and it wasn't known when
+ 
+
+ align:start position:0%
+somebody has TV and it wasn't known when
+they were in the clinic that you can get
+
+ align:start position:0%
+they were in the clinic that you can get
+ 
+
+ align:start position:0%
+they were in the clinic that you can get
+that message to your healthcare worker
+
+ align:start position:0%
+that message to your healthcare worker
+ 
+
+ align:start position:0%
+that message to your healthcare worker
+and bring them into you know for further
+
+ align:start position:0%
+and bring them into you know for further
+ 
+
+ align:start position:0%
+and bring them into you know for further
+treatment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another question yes please
+
+ align:start position:0%
+another question yes please
+ 
+
+ align:start position:0%
+another question yes please
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say I've been reading a lot of her books
+
+ align:start position:0%
+say I've been reading a lot of her books
+ 
+
+ align:start position:0%
+say I've been reading a lot of her books
+oh don't say needless to say stay away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've been following your words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and I'm grateful to be here
+
+ align:start position:0%
+here and I'm grateful to be here
+ 
+
+ align:start position:0%
+here and I'm grateful to be here
+my first husband
+
+ align:start position:0%
+my first husband
+ 
+
+ align:start position:0%
+my first husband
+throughout this class in my anthropology
+
+ align:start position:0%
+throughout this class in my anthropology
+ 
+
+ align:start position:0%
+throughout this class in my anthropology
+studies how to Major and maintain
+
+ align:start position:0%
+studies how to Major and maintain
+ 
+
+ align:start position:0%
+studies how to Major and maintain
+quality of care in those settings when
+
+ align:start position:0%
+quality of care in those settings when
+ 
+
+ align:start position:0%
+quality of care in those settings when
+the priority is in giving access and in
+
+ align:start position:0%
+the priority is in giving access and in
+ 
+
+ align:start position:0%
+the priority is in giving access and in
+maintaining sustainability so the Health
+
+ align:start position:0%
+maintaining sustainability so the Health
+ 
+
+ align:start position:0%
+maintaining sustainability so the Health
+Care system
+
+ align:start position:0%
+Care system
+ 
+
+ align:start position:0%
+Care system
+animating to maintain um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+earlier but I was wondering yeah well um
+
+ align:start position:0%
+earlier but I was wondering yeah well um
+ 
+
+ align:start position:0%
+earlier but I was wondering yeah well um
+first of all this is a it's not that I
+
+ align:start position:0%
+first of all this is a it's not that I
+ 
+
+ align:start position:0%
+first of all this is a it's not that I
+didn't want to talk about it it's just
+
+ align:start position:0%
+didn't want to talk about it it's just
+ 
+
+ align:start position:0%
+didn't want to talk about it it's just
+such a humbling topic
+
+ align:start position:0%
+such a humbling topic
+ 
+
+ align:start position:0%
+such a humbling topic
+um the quality issue so again we were
+
+ align:start position:0%
+um the quality issue so again we were
+ 
+
+ align:start position:0%
+um the quality issue so again we were
+moving towards scale but I would say the
+
+ align:start position:0%
+moving towards scale but I would say the
+ 
+
+ align:start position:0%
+moving towards scale but I would say the
+main reason that our organization
+
+ align:start position:0%
+main reason that our organization
+ 
+
+ align:start position:0%
+main reason that our organization
+is in 25 countries but rather only in 12
+
+ align:start position:0%
+is in 25 countries but rather only in 12
+ 
+
+ align:start position:0%
+is in 25 countries but rather only in 12
+and isn't trying to claim Nationwide
+
+ align:start position:0%
+and isn't trying to claim Nationwide
+ 
+
+ align:start position:0%
+and isn't trying to claim Nationwide
+coverage
+
+ align:start position:0%
+coverage
+ 
+
+ align:start position:0%
+coverage
+is because of uh I hope a humility about
+
+ align:start position:0%
+is because of uh I hope a humility about
+ 
+
+ align:start position:0%
+is because of uh I hope a humility about
+quality we don't believe that it's that
+
+ align:start position:0%
+quality we don't believe that it's that
+ 
+
+ align:start position:0%
+quality we don't believe that it's that
+easy to just go in and fit it with the
+
+ align:start position:0%
+easy to just go in and fit it with the
+ 
+
+ align:start position:0%
+easy to just go in and fit it with the
+policy and and suddenly the quality of
+
+ align:start position:0%
+policy and and suddenly the quality of
+ 
+
+ align:start position:0%
+policy and and suddenly the quality of
+care changes on a national level
+
+ align:start position:0%
+care changes on a national level
+ 
+
+ align:start position:0%
+care changes on a national level
+sometimes you know but it's usually a
+
+ align:start position:0%
+sometimes you know but it's usually a
+ 
+
+ align:start position:0%
+sometimes you know but it's usually a
+mix of resources human and and other
+
+ align:start position:0%
+mix of resources human and and other
+ 
+
+ align:start position:0%
+mix of resources human and and other
+kinds of capital and then the
+
+ align:start position:0%
+kinds of capital and then the
+ 
+
+ align:start position:0%
+kinds of capital and then the
+implementation so we're very focused on
+
+ align:start position:0%
+implementation so we're very focused on
+ 
+
+ align:start position:0%
+implementation so we're very focused on
+implementation and even with that Focus
+
+ align:start position:0%
+implementation and even with that Focus
+ 
+
+ align:start position:0%
+implementation and even with that Focus
+I would say that we you know we've had a
+
+ align:start position:0%
+I would say that we you know we've had a
+ 
+
+ align:start position:0%
+I would say that we you know we've had a
+you know a big quality problem with
+
+ align:start position:0%
+you know a big quality problem with
+ 
+
+ align:start position:0%
+you know a big quality problem with
+scale just like everybody else so that's
+
+ align:start position:0%
+scale just like everybody else so that's
+ 
+
+ align:start position:0%
+scale just like everybody else so that's
+what we're struggling you ask me what
+
+ align:start position:0%
+what we're struggling you ask me what
+ 
+
+ align:start position:0%
+what we're struggling you ask me what
+measures okay
+
+ align:start position:0%
+measures okay
+ 
+
+ align:start position:0%
+measures okay
+um there there most of them are proxy
+
+ align:start position:0%
+um there there most of them are proxy
+ 
+
+ align:start position:0%
+um there there most of them are proxy
+measures like I mentioned one right I
+
+ align:start position:0%
+measures like I mentioned one right I
+ 
+
+ align:start position:0%
+measures like I mentioned one right I
+said I didn't really say it but I'm
+
+ align:start position:0%
+said I didn't really say it but I'm
+ 
+
+ align:start position:0%
+said I didn't really say it but I'm
+going to say it now
+
+ align:start position:0%
+going to say it now
+ 
+
+ align:start position:0%
+going to say it now
+just look when you're looking at
+
+ align:start position:0%
+just look when you're looking at
+ 
+
+ align:start position:0%
+just look when you're looking at
+outcomes
+
+ align:start position:0%
+outcomes
+ 
+
+ align:start position:0%
+outcomes
+of HIV and TB care you obviously have
+
+ align:start position:0%
+of HIV and TB care you obviously have
+ 
+
+ align:start position:0%
+of HIV and TB care you obviously have
+you can use viral load right for HIV for
+
+ align:start position:0%
+you can use viral load right for HIV for
+ 
+
+ align:start position:0%
+you can use viral load right for HIV for
+TB you can use smear my Cosby microscopy
+
+ align:start position:0%
+TB you can use smear my Cosby microscopy
+ 
+
+ align:start position:0%
+TB you can use smear my Cosby microscopy
+or some of the new diagnosis but you can
+
+ align:start position:0%
+or some of the new diagnosis but you can
+ 
+
+ align:start position:0%
+or some of the new diagnosis but you can
+all just also just weigh the patients
+
+ align:start position:0%
+all just also just weigh the patients
+ 
+
+ align:start position:0%
+all just also just weigh the patients
+so again a proxy measure for quality of
+
+ align:start position:0%
+so again a proxy measure for quality of
+ 
+
+ align:start position:0%
+so again a proxy measure for quality of
+services is if they gain 20 pounds
+
+ align:start position:0%
+services is if they gain 20 pounds
+ 
+
+ align:start position:0%
+services is if they gain 20 pounds
+you know like Joseph did and and John
+
+ align:start position:0%
+you know like Joseph did and and John
+ 
+
+ align:start position:0%
+you know like Joseph did and and John
+that was the name of the other guy
+
+ align:start position:0%
+that was the name of the other guy
+ 
+
+ align:start position:0%
+that was the name of the other guy
+then that's a pretty good proxy measure
+
+ align:start position:0%
+then that's a pretty good proxy measure
+ 
+
+ align:start position:0%
+then that's a pretty good proxy measure
+it's inexpensive and it can be sent in
+
+ align:start position:0%
+it's inexpensive and it can be sent in
+ 
+
+ align:start position:0%
+it's inexpensive and it can be sent in
+by a mobile technology now let me just I
+
+ align:start position:0%
+by a mobile technology now let me just I
+ 
+
+ align:start position:0%
+by a mobile technology now let me just I
+can go through this like for Diabetes
+
+ align:start position:0%
+can go through this like for Diabetes
+ 
+
+ align:start position:0%
+can go through this like for Diabetes
+Care well hemoglobin A1c is is one
+
+ align:start position:0%
+Care well hemoglobin A1c is is one
+ 
+
+ align:start position:0%
+Care well hemoglobin A1c is is one
+measure right so you can imagine again a
+
+ align:start position:0%
+measure right so you can imagine again a
+ 
+
+ align:start position:0%
+measure right so you can imagine again a
+hand this time I would actually say it'd
+
+ align:start position:0%
+hand this time I would actually say it'd
+ 
+
+ align:start position:0%
+hand this time I would actually say it'd
+be better to have a handheld device that
+
+ align:start position:0%
+be better to have a handheld device that
+ 
+
+ align:start position:0%
+be better to have a handheld device that
+could actually be introduced a fingers
+
+ align:start position:0%
+could actually be introduced a fingers
+ 
+
+ align:start position:0%
+could actually be introduced a fingers
+thick is painful some of you know but
+
+ align:start position:0%
+thick is painful some of you know but
+ 
+
+ align:start position:0%
+thick is painful some of you know but
+get a sample that is able to tell you
+
+ align:start position:0%
+get a sample that is able to tell you
+ 
+
+ align:start position:0%
+get a sample that is able to tell you
+well what's the blood sugar and what's
+
+ align:start position:0%
+well what's the blood sugar and what's
+ 
+
+ align:start position:0%
+well what's the blood sugar and what's
+the hemoglobin m1c is there proxies of
+
+ align:start position:0%
+the hemoglobin m1c is there proxies of
+ 
+
+ align:start position:0%
+the hemoglobin m1c is there proxies of
+quality you could use as people at this
+
+ align:start position:0%
+quality you could use as people at this
+ 
+
+ align:start position:0%
+quality you could use as people at this
+institution have are sort of the pros
+
+ align:start position:0%
+institution have are sort of the pros
+ 
+
+ align:start position:0%
+institution have are sort of the pros
+now in random you know randomized Trials
+
+ align:start position:0%
+now in random you know randomized Trials
+ 
+
+ align:start position:0%
+now in random you know randomized Trials
+of positive social outcomes they're
+
+ align:start position:0%
+of positive social outcomes they're
+ 
+
+ align:start position:0%
+of positive social outcomes they're
+using you are using those who do that
+
+ align:start position:0%
+using you are using those who do that
+ 
+
+ align:start position:0%
+using you are using those who do that
+we're proxy measures so I found there's
+
+ align:start position:0%
+we're proxy measures so I found there's
+ 
+
+ align:start position:0%
+we're proxy measures so I found there's
+a long list of them and even in a
+
+ align:start position:0%
+a long list of them and even in a
+ 
+
+ align:start position:0%
+a long list of them and even in a
+setting where you wouldn't easily have
+
+ align:start position:0%
+setting where you wouldn't easily have
+ 
+
+ align:start position:0%
+setting where you wouldn't easily have
+access to a lab or you wouldn't have
+
+ align:start position:0%
+access to a lab or you wouldn't have
+ 
+
+ align:start position:0%
+access to a lab or you wouldn't have
+access to uh you know a researcher who
+
+ align:start position:0%
+access to uh you know a researcher who
+ 
+
+ align:start position:0%
+access to uh you know a researcher who
+is registering things is using
+
+ align:start position:0%
+is registering things is using
+ 
+
+ align:start position:0%
+is registering things is using
+questionnaire you still if you have this
+
+ align:start position:0%
+questionnaire you still if you have this
+ 
+
+ align:start position:0%
+questionnaire you still if you have this
+network this platform you still have
+
+ align:start position:0%
+network this platform you still have
+ 
+
+ align:start position:0%
+network this platform you still have
+your community health workers and they
+
+ align:start position:0%
+your community health workers and they
+ 
+
+ align:start position:0%
+your community health workers and they
+can manage quite a bit of
+
+ align:start position:0%
+can manage quite a bit of
+ 
+
+ align:start position:0%
+can manage quite a bit of
+complexity in terms of reporting if
+
+ align:start position:0%
+complexity in terms of reporting if
+ 
+
+ align:start position:0%
+complexity in terms of reporting if
+they're supported fully so I think for
+
+ align:start position:0%
+they're supported fully so I think for
+ 
+
+ align:start position:0%
+they're supported fully so I think for
+each of these problems you can find
+
+ align:start position:0%
+each of these problems you can find
+ 
+
+ align:start position:0%
+each of these problems you can find
+proxy measures for Quality now I would
+
+ align:start position:0%
+proxy measures for Quality now I would
+ 
+
+ align:start position:0%
+proxy measures for Quality now I would
+add in and I'm just learning about this
+
+ align:start position:0%
+add in and I'm just learning about this
+ 
+
+ align:start position:0%
+add in and I'm just learning about this
+uh Julia Frank your boss is he has a
+
+ align:start position:0%
+uh Julia Frank your boss is he has a
+ 
+
+ align:start position:0%
+uh Julia Frank your boss is he has a
+mentor I think at University of Michigan
+
+ align:start position:0%
+mentor I think at University of Michigan
+ 
+
+ align:start position:0%
+mentor I think at University of Michigan
+I had a mentor who's sort of the father
+
+ align:start position:0%
+I had a mentor who's sort of the father
+ 
+
+ align:start position:0%
+I had a mentor who's sort of the father
+of quality improvement from the 70s and
+
+ align:start position:0%
+of quality improvement from the 70s and
+ 
+
+ align:start position:0%
+of quality improvement from the 70s and
+80s wrote a paper evidently in Milbank
+
+ align:start position:0%
+80s wrote a paper evidently in Milbank
+ 
+
+ align:start position:0%
+80s wrote a paper evidently in Milbank
+quarterly in 1960 something Julio Frank
+
+ align:start position:0%
+quarterly in 1960 something Julio Frank
+ 
+
+ align:start position:0%
+quarterly in 1960 something Julio Frank
+just told me this and he not earlier but
+
+ align:start position:0%
+just told me this and he not earlier but
+ 
+
+ align:start position:0%
+just told me this and he not earlier but
+his mentor one of them said that there
+
+ align:start position:0%
+his mentor one of them said that there
+ 
+
+ align:start position:0%
+his mentor one of them said that there
+are many kinds of quality there's
+
+ align:start position:0%
+are many kinds of quality there's
+ 
+
+ align:start position:0%
+are many kinds of quality there's
+technical technically confident quality
+
+ align:start position:0%
+technical technically confident quality
+ 
+
+ align:start position:0%
+technical technically confident quality
+the least we could do but there's also
+
+ align:start position:0%
+the least we could do but there's also
+ 
+
+ align:start position:0%
+the least we could do but there's also
+respect for the rights of the person the
+
+ align:start position:0%
+respect for the rights of the person the
+ 
+
+ align:start position:0%
+respect for the rights of the person the
+so-called client patient and uh you know
+
+ align:start position:0%
+so-called client patient and uh you know
+ 
+
+ align:start position:0%
+so-called client patient and uh you know
+what about the Dignity of the
+
+ align:start position:0%
+what about the Dignity of the
+ 
+
+ align:start position:0%
+what about the Dignity of the
+surroundings in which the care is
+
+ align:start position:0%
+surroundings in which the care is
+ 
+
+ align:start position:0%
+surroundings in which the care is
+delivered like we've focused a lot on
+
+ align:start position:0%
+delivered like we've focused a lot on
+ 
+
+ align:start position:0%
+delivered like we've focused a lot on
+them and Julio has been helping us yeah
+
+ align:start position:0%
+them and Julio has been helping us yeah
+ 
+
+ align:start position:0%
+them and Julio has been helping us yeah
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is tough wow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example I think you're looking at
+
+ align:start position:0%
+for example I think you're looking at
+ 
+
+ align:start position:0%
+for example I think you're looking at
+the entire care coverage a lot of the
+
+ align:start position:0%
+the entire care coverage a lot of the
+ 
+
+ align:start position:0%
+the entire care coverage a lot of the
+programs and increasing use of that I
+
+ align:start position:0%
+programs and increasing use of that I
+ 
+
+ align:start position:0%
+programs and increasing use of that I
+would say it has been covered that
+
+ align:start position:0%
+would say it has been covered that
+ 
+
+ align:start position:0%
+would say it has been covered that
+incentivizing women through vouchers and
+
+ align:start position:0%
+incentivizing women through vouchers and
+ 
+
+ align:start position:0%
+incentivizing women through vouchers and
+cash transfers
+
+ align:start position:0%
+cash transfers
+ 
+
+ align:start position:0%
+cash transfers
+from a technology example how would you
+
+ align:start position:0%
+from a technology example how would you
+ 
+
+ align:start position:0%
+from a technology example how would you
+use technology to to get people and say
+
+ align:start position:0%
+use technology to to get people and say
+ 
+
+ align:start position:0%
+use technology to to get people and say
+to find you something like ANC yeah well
+
+ align:start position:0%
+to find you something like ANC yeah well
+ 
+
+ align:start position:0%
+to find you something like ANC yeah well
+first of all I'm glad you asked me first
+
+ align:start position:0%
+first of all I'm glad you asked me first
+ 
+
+ align:start position:0%
+first of all I'm glad you asked me first
+of all but first of all I think there's
+
+ align:start position:0%
+of all but first of all I think there's
+ 
+
+ align:start position:0%
+of all but first of all I think there's
+a right track and a wrong track and the
+
+ align:start position:0%
+a right track and a wrong track and the
+ 
+
+ align:start position:0%
+a right track and a wrong track and the
+right track is the cash transfer part
+
+ align:start position:0%
+right track is the cash transfer part
+ 
+
+ align:start position:0%
+right track is the cash transfer part
+the wrong track is trying to you know
+
+ align:start position:0%
+the wrong track is trying to you know
+ 
+
+ align:start position:0%
+the wrong track is trying to you know
+then again this is I have a colleague
+
+ align:start position:0%
+then again this is I have a colleague
+ 
+
+ align:start position:0%
+then again this is I have a colleague
+here and I'll see how she thinks I do
+
+ align:start position:0%
+here and I'll see how she thinks I do
+ 
+
+ align:start position:0%
+here and I'll see how she thinks I do
+there's so little knowledge in public
+
+ align:start position:0%
+there's so little knowledge in public
+ 
+
+ align:start position:0%
+there's so little knowledge in public
+health of how
+
+ align:start position:0%
+health of how
+ 
+
+ align:start position:0%
+health of how
+structural problems poverty gender
+
+ align:start position:0%
+structural problems poverty gender
+ 
+
+ align:start position:0%
+structural problems poverty gender
+inequality travel Transportation
+
+ align:start position:0%
+inequality travel Transportation
+ 
+
+ align:start position:0%
+inequality travel Transportation
+whatever there's very very limited
+
+ align:start position:0%
+whatever there's very very limited
+ 
+
+ align:start position:0%
+whatever there's very very limited
+understanding of how those things
+
+ align:start position:0%
+understanding of how those things
+ 
+
+ align:start position:0%
+understanding of how those things
+determine agency the ability to choose
+
+ align:start position:0%
+determine agency the ability to choose
+ 
+
+ align:start position:0%
+determine agency the ability to choose
+so I would say the wrong way is to try
+
+ align:start position:0%
+so I would say the wrong way is to try
+ 
+
+ align:start position:0%
+so I would say the wrong way is to try
+and get people to Value things when we
+
+ align:start position:0%
+and get people to Value things when we
+ 
+
+ align:start position:0%
+and get people to Value things when we
+don't have evidence that they don't
+
+ align:start position:0%
+don't have evidence that they don't
+ 
+
+ align:start position:0%
+don't have evidence that they don't
+value them but we have evidence of is
+
+ align:start position:0%
+value them but we have evidence of is
+ 
+
+ align:start position:0%
+value them but we have evidence of is
+their inability to access them
+
+ align:start position:0%
+their inability to access them
+ 
+
+ align:start position:0%
+their inability to access them
+so this is It's a somewhat subtle point
+
+ align:start position:0%
+so this is It's a somewhat subtle point
+ 
+
+ align:start position:0%
+so this is It's a somewhat subtle point
+but I think cognitive approaches
+
+ align:start position:0%
+but I think cognitive approaches
+ 
+
+ align:start position:0%
+but I think cognitive approaches
+um to for example the promotion of of
+
+ align:start position:0%
+um to for example the promotion of of
+ 
+
+ align:start position:0%
+um to for example the promotion of of
+ANC
+
+ align:start position:0%
+ANC
+ 
+
+ align:start position:0%
+ANC
+um that is exhorting poor women to do
+
+ align:start position:0%
+um that is exhorting poor women to do
+ 
+
+ align:start position:0%
+um that is exhorting poor women to do
+what you want I think they're fraudulent
+
+ align:start position:0%
+what you want I think they're fraudulent
+ 
+
+ align:start position:0%
+what you want I think they're fraudulent
+and I also think they're heavily funded
+
+ align:start position:0%
+and I also think they're heavily funded
+ 
+
+ align:start position:0%
+and I also think they're heavily funded
+for a reason
+
+ align:start position:0%
+for a reason
+ 
+
+ align:start position:0%
+for a reason
+because what they do and yeah I want to
+
+ align:start position:0%
+because what they do and yeah I want to
+ 
+
+ align:start position:0%
+because what they do and yeah I want to
+see how you think I'm doing what they do
+
+ align:start position:0%
+see how you think I'm doing what they do
+ 
+
+ align:start position:0%
+see how you think I'm doing what they do
+what these approaches do is to move the
+
+ align:start position:0%
+what these approaches do is to move the
+ 
+
+ align:start position:0%
+what these approaches do is to move the
+locus of the problem into the head of
+
+ align:start position:0%
+locus of the problem into the head of
+ 
+
+ align:start position:0%
+locus of the problem into the head of
+the mother and out of her conditions
+
+ align:start position:0%
+the mother and out of her conditions
+ 
+
+ align:start position:0%
+the mother and out of her conditions
+right they're saying we have to make you
+
+ align:start position:0%
+right they're saying we have to make you
+ 
+
+ align:start position:0%
+right they're saying we have to make you
+value this because you don't value it
+
+ align:start position:0%
+value this because you don't value it
+ 
+
+ align:start position:0%
+value this because you don't value it
+what's the subject is you don't know
+
+ align:start position:0%
+what's the subject is you don't know
+ 
+
+ align:start position:0%
+what's the subject is you don't know
+you're not able to value and a NATO care
+
+ align:start position:0%
+you're not able to value and a NATO care
+ 
+
+ align:start position:0%
+you're not able to value and a NATO care
+but actually we don't have data for that
+
+ align:start position:0%
+but actually we don't have data for that
+ 
+
+ align:start position:0%
+but actually we don't have data for that
+but we have data forces that show that
+
+ align:start position:0%
+but we have data forces that show that
+ 
+
+ align:start position:0%
+but we have data forces that show that
+they don't there are barriers user fees
+
+ align:start position:0%
+they don't there are barriers user fees
+ 
+
+ align:start position:0%
+they don't there are barriers user fees
+transport you know who's going to
+
+ align:start position:0%
+transport you know who's going to
+ 
+
+ align:start position:0%
+transport you know who's going to
+babysit the other kids so when we and a
+
+ align:start position:0%
+babysit the other kids so when we and a
+ 
+
+ align:start position:0%
+babysit the other kids so when we and a
+lot of anthropologists would call those
+
+ align:start position:0%
+lot of anthropologists would call those
+ 
+
+ align:start position:0%
+lot of anthropologists would call those
+structural constraints as opposed to
+
+ align:start position:0%
+structural constraints as opposed to
+ 
+
+ align:start position:0%
+structural constraints as opposed to
+cultural or cognitive now here's the
+
+ align:start position:0%
+cultural or cognitive now here's the
+ 
+
+ align:start position:0%
+cultural or cognitive now here's the
+scam in my view and I guess that might
+
+ align:start position:0%
+scam in my view and I guess that might
+ 
+
+ align:start position:0%
+scam in my view and I guess that might
+as well know I'm transubmitting this
+
+ align:start position:0%
+as well know I'm transubmitting this
+ 
+
+ align:start position:0%
+as well know I'm transubmitting this
+around the world is that the idea that
+
+ align:start position:0%
+around the world is that the idea that
+ 
+
+ align:start position:0%
+around the world is that the idea that
+these are really the problems of poor
+
+ align:start position:0%
+these are really the problems of poor
+ 
+
+ align:start position:0%
+these are really the problems of poor
+people is really good for us people like
+
+ align:start position:0%
+people is really good for us people like
+ 
+
+ align:start position:0%
+people is really good for us people like
+you and me who go to places like
+
+ align:start position:0%
+you and me who go to places like
+ 
+
+ align:start position:0%
+you and me who go to places like
+Brandeis and Harvard because then we get
+
+ align:start position:0%
+Brandeis and Harvard because then we get
+ 
+
+ align:start position:0%
+Brandeis and Harvard because then we get
+a job afterwards if we can yell at poor
+
+ align:start position:0%
+a job afterwards if we can yell at poor
+ 
+
+ align:start position:0%
+a job afterwards if we can yell at poor
+ladies and tell them what to do right
+
+ align:start position:0%
+ladies and tell them what to do right
+ 
+
+ align:start position:0%
+ladies and tell them what to do right
+and we'll get funded for that for years
+
+ align:start position:0%
+and we'll get funded for that for years
+ 
+
+ align:start position:0%
+and we'll get funded for that for years
+and years and we'll even be able to
+
+ align:start position:0%
+and years and we'll even be able to
+ 
+
+ align:start position:0%
+and years and we'll even be able to
+repeat the cycle and do research on that
+
+ align:start position:0%
+repeat the cycle and do research on that
+ 
+
+ align:start position:0%
+repeat the cycle and do research on that
+as if we didn't already know that
+
+ align:start position:0%
+as if we didn't already know that
+ 
+
+ align:start position:0%
+as if we didn't already know that
+animatal care was good
+
+ align:start position:0%
+animatal care was good
+ 
+
+ align:start position:0%
+animatal care was good
+right so I think
+
+ align:start position:0%
+right so I think
+ 
+
+ align:start position:0%
+right so I think
+um you know how we use technology back
+
+ align:start position:0%
+um you know how we use technology back
+ 
+
+ align:start position:0%
+um you know how we use technology back
+to the point of your question in in
+
+ align:start position:0%
+to the point of your question in in
+ 
+
+ align:start position:0%
+to the point of your question in in
+something like making people value
+
+ align:start position:0%
+something like making people value
+ 
+
+ align:start position:0%
+something like making people value
+these good things that we believe in
+
+ align:start position:0%
+these good things that we believe in
+ 
+
+ align:start position:0%
+these good things that we believe in
+include cash transfers and even having
+
+ align:start position:0%
+include cash transfers and even having
+ 
+
+ align:start position:0%
+include cash transfers and even having
+for fan unconditional cash transfers
+
+ align:start position:0%
+for fan unconditional cash transfers
+ 
+
+ align:start position:0%
+for fan unconditional cash transfers
+because after all poor people have been
+
+ align:start position:0%
+because after all poor people have been
+ 
+
+ align:start position:0%
+because after all poor people have been
+making unconditional cash transfers to
+
+ align:start position:0%
+making unconditional cash transfers to
+ 
+
+ align:start position:0%
+making unconditional cash transfers to
+us for many centuries
+
+ align:start position:0%
+us for many centuries
+ 
+
+ align:start position:0%
+us for many centuries
+right you with me
+
+ align:start position:0%
+right you with me
+ 
+
+ align:start position:0%
+right you with me
+um so I think using those Technologies
+
+ align:start position:0%
+um so I think using those Technologies
+ 
+
+ align:start position:0%
+um so I think using those Technologies
+to transfer resources rather than just
+
+ align:start position:0%
+to transfer resources rather than just
+ 
+
+ align:start position:0%
+to transfer resources rather than just
+reminders and I I'll be looking forward
+
+ align:start position:0%
+reminders and I I'll be looking forward
+ 
+
+ align:start position:0%
+reminders and I I'll be looking forward
+to seeing the results of those studies
+
+ align:start position:0%
+to seeing the results of those studies
+ 
+
+ align:start position:0%
+to seeing the results of those studies
+but um you know reminders are one thing
+
+ align:start position:0%
+but um you know reminders are one thing
+ 
+
+ align:start position:0%
+but um you know reminders are one thing
+exploitations I'm calling them but just
+
+ align:start position:0%
+exploitations I'm calling them but just
+ 
+
+ align:start position:0%
+exploitations I'm calling them but just
+link these Technologies a little bit to
+
+ align:start position:0%
+link these Technologies a little bit to
+ 
+
+ align:start position:0%
+link these Technologies a little bit to
+removing barriers like for example if
+
+ align:start position:0%
+removing barriers like for example if
+ 
+
+ align:start position:0%
+removing barriers like for example if
+you if you look at structural barriers
+
+ align:start position:0%
+you if you look at structural barriers
+ 
+
+ align:start position:0%
+you if you look at structural barriers
+to care again I mentioned transport have
+
+ align:start position:0%
+to care again I mentioned transport have
+ 
+
+ align:start position:0%
+to care again I mentioned transport have
+the voucher go all the way out to the
+
+ align:start position:0%
+the voucher go all the way out to the
+ 
+
+ align:start position:0%
+the voucher go all the way out to the
+woman you know move the analog care to
+
+ align:start position:0%
+woman you know move the analog care to
+ 
+
+ align:start position:0%
+woman you know move the analog care to
+her or bring her to the Animal Care and
+
+ align:start position:0%
+her or bring her to the Animal Care and
+ 
+
+ align:start position:0%
+her or bring her to the Animal Care and
+again think about all these structural
+
+ align:start position:0%
+again think about all these structural
+ 
+
+ align:start position:0%
+again think about all these structural
+problems who's going to take care of the
+
+ align:start position:0%
+problems who's going to take care of the
+ 
+
+ align:start position:0%
+problems who's going to take care of the
+other kids how is she going to get there
+
+ align:start position:0%
+other kids how is she going to get there
+ 
+
+ align:start position:0%
+other kids how is she going to get there
+is there going to be a long line is
+
+ align:start position:0%
+is there going to be a long line is
+ 
+
+ align:start position:0%
+is there going to be a long line is
+there a hidden fee is there an open user
+
+ align:start position:0%
+there a hidden fee is there an open user
+ 
+
+ align:start position:0%
+there a hidden fee is there an open user
+view right because you find out people
+
+ align:start position:0%
+view right because you find out people
+ 
+
+ align:start position:0%
+view right because you find out people
+say we don't have any user fees and then
+
+ align:start position:0%
+say we don't have any user fees and then
+ 
+
+ align:start position:0%
+say we don't have any user fees and then
+you go and do research and there are
+
+ align:start position:0%
+you go and do research and there are
+ 
+
+ align:start position:0%
+you go and do research and there are
+user fees they may be hidden they may
+
+ align:start position:0%
+user fees they may be hidden they may
+ 
+
+ align:start position:0%
+user fees they may be hidden they may
+not so that's just my own personal take
+
+ align:start position:0%
+not so that's just my own personal take
+ 
+
+ align:start position:0%
+not so that's just my own personal take
+on that now I I don't go out to a
+
+ align:start position:0%
+on that now I I don't go out to a
+ 
+
+ align:start position:0%
+on that now I I don't go out to a
+conference on you know how to make women
+
+ align:start position:0%
+conference on you know how to make women
+ 
+
+ align:start position:0%
+conference on you know how to make women
+value into Nano care and say this stuff
+
+ align:start position:0%
+value into Nano care and say this stuff
+ 
+
+ align:start position:0%
+value into Nano care and say this stuff
+actually I don't go to those conferences
+
+ align:start position:0%
+actually I don't go to those conferences
+ 
+
+ align:start position:0%
+actually I don't go to those conferences
+anymore because I think they're a bit of
+
+ align:start position:0%
+anymore because I think they're a bit of
+ 
+
+ align:start position:0%
+anymore because I think they're a bit of
+a as I said a fraud
+
+ align:start position:0%
+a as I said a fraud
+ 
+
+ align:start position:0%
+a as I said a fraud
+so actually there's a question from
+
+ align:start position:0%
+so actually there's a question from
+ 
+
+ align:start position:0%
+so actually there's a question from
+Lauren who's when I got students who
+
+ align:start position:0%
+Lauren who's when I got students who
+ 
+
+ align:start position:0%
+Lauren who's when I got students who
+unfortunately can't be here today which
+
+ align:start position:0%
+unfortunately can't be here today which
+ 
+
+ align:start position:0%
+unfortunately can't be here today which
+I think is is very relevant um and it
+
+ align:start position:0%
+I think is is very relevant um and it
+ 
+
+ align:start position:0%
+I think is is very relevant um and it
+relates also to something that last
+
+ align:start position:0%
+relates also to something that last
+ 
+
+ align:start position:0%
+relates also to something that last
+weekend when I was in Haiti we were
+
+ align:start position:0%
+weekend when I was in Haiti we were
+ 
+
+ align:start position:0%
+weekend when I was in Haiti we were
+looking at our system which does very
+
+ align:start position:0%
+looking at our system which does very
+ 
+
+ align:start position:0%
+looking at our system which does very
+close to what Paul was describing the
+
+ align:start position:0%
+close to what Paul was describing the
+ 
+
+ align:start position:0%
+close to what Paul was describing the
+American Airlines where each patient is
+
+ align:start position:0%
+American Airlines where each patient is
+ 
+
+ align:start position:0%
+American Airlines where each patient is
+registered it only took you 10 years
+
+ align:start position:0%
+registered it only took you 10 years
+ 
+
+ align:start position:0%
+registered it only took you 10 years
+and you know for some good reasons
+
+ align:start position:0%
+and you know for some good reasons
+ 
+
+ align:start position:0%
+and you know for some good reasons
+um and to print out an ID card actually
+
+ align:start position:0%
+um and to print out an ID card actually
+ 
+
+ align:start position:0%
+um and to print out an ID card actually
+plastic idea on it and so each patient
+
+ align:start position:0%
+plastic idea on it and so each patient
+ 
+
+ align:start position:0%
+plastic idea on it and so each patient
+visits back and we can see we can come
+
+ align:start position:0%
+visits back and we can see we can come
+ 
+
+ align:start position:0%
+visits back and we can see we can come
+back and we can see the same person can
+
+ align:start position:0%
+back and we can see the same person can
+ 
+
+ align:start position:0%
+back and we can see the same person can
+only get to the lab data and so on so
+
+ align:start position:0%
+only get to the lab data and so on so
+ 
+
+ align:start position:0%
+only get to the lab data and so on so
+it's a very important foundational
+
+ align:start position:0%
+it's a very important foundational
+ 
+
+ align:start position:0%
+it's a very important foundational
+component which we hope to really be
+
+ align:start position:0%
+component which we hope to really be
+ 
+
+ align:start position:0%
+component which we hope to really be
+able to scale up in the new ballet
+
+ align:start position:0%
+able to scale up in the new ballet
+ 
+
+ align:start position:0%
+able to scale up in the new ballet
+hospital as a critical First Step
+
+ align:start position:0%
+hospital as a critical First Step
+ 
+
+ align:start position:0%
+hospital as a critical First Step
+um but it also introduces and kind of
+
+ align:start position:0%
+um but it also introduces and kind of
+ 
+
+ align:start position:0%
+um but it also introduces and kind of
+furthers one of the questions that we
+
+ align:start position:0%
+furthers one of the questions that we
+ 
+
+ align:start position:0%
+furthers one of the questions that we
+often get which is what are the
+
+ align:start position:0%
+often get which is what are the
+ 
+
+ align:start position:0%
+often get which is what are the
+quickoffs between collecting personal
+
+ align:start position:0%
+quickoffs between collecting personal
+ 
+
+ align:start position:0%
+quickoffs between collecting personal
+data in information systems and the
+
+ align:start position:0%
+data in information systems and the
+ 
+
+ align:start position:0%
+data in information systems and the
+potential risks or perceived risks that
+
+ align:start position:0%
+potential risks or perceived risks that
+ 
+
+ align:start position:0%
+potential risks or perceived risks that
+they pose to the patients and then the
+
+ align:start position:0%
+they pose to the patients and then the
+ 
+
+ align:start position:0%
+they pose to the patients and then the
+question of how to improve access to
+
+ align:start position:0%
+question of how to improve access to
+ 
+
+ align:start position:0%
+question of how to improve access to
+care and it seems like bit of attention
+
+ align:start position:0%
+care and it seems like bit of attention
+ 
+
+ align:start position:0%
+care and it seems like bit of attention
+there so Largemouth actually asked a
+
+ align:start position:0%
+there so Largemouth actually asked a
+ 
+
+ align:start position:0%
+there so Largemouth actually asked a
+question about that I don't know if
+
+ align:start position:0%
+question about that I don't know if
+ 
+
+ align:start position:0%
+question about that I don't know if
+she's listening now or is just going to
+
+ align:start position:0%
+she's listening now or is just going to
+ 
+
+ align:start position:0%
+she's listening now or is just going to
+hear this later but
+
+ align:start position:0%
+hear this later but
+ 
+
+ align:start position:0%
+hear this later but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is a a problem that I've again I'm
+
+ align:start position:0%
+this is a a problem that I've again I'm
+ 
+
+ align:start position:0%
+this is a a problem that I've again I'm
+going to use a little uh political
+
+ align:start position:0%
+going to use a little uh political
+ 
+
+ align:start position:0%
+going to use a little uh political
+economic notion here
+
+ align:start position:0%
+economic notion here
+ 
+
+ align:start position:0%
+economic notion here
+the the times I've heard that question
+
+ align:start position:0%
+the the times I've heard that question
+ 
+
+ align:start position:0%
+the the times I've heard that question
+most has not been in settings of great
+
+ align:start position:0%
+most has not been in settings of great
+ 
+
+ align:start position:0%
+most has not been in settings of great
+rural privation from our patients it's
+
+ align:start position:0%
+rural privation from our patients it's
+ 
+
+ align:start position:0%
+rural privation from our patients it's
+more from our staff interestingly right
+
+ align:start position:0%
+more from our staff interestingly right
+ 
+
+ align:start position:0%
+more from our staff interestingly right
+um and so the primary again this is a
+
+ align:start position:0%
+um and so the primary again this is a
+ 
+
+ align:start position:0%
+um and so the primary again this is a
+gross generalization but I think it's
+
+ align:start position:0%
+gross generalization but I think it's
+ 
+
+ align:start position:0%
+gross generalization but I think it's
+true nonetheless gross meaning Grand
+
+ align:start position:0%
+true nonetheless gross meaning Grand
+ 
+
+ align:start position:0%
+true nonetheless gross meaning Grand
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the privacy concerns are tightly time
+
+ align:start position:0%
+the privacy concerns are tightly time
+ 
+
+ align:start position:0%
+the privacy concerns are tightly time
+tied to class aspirations right so a lot
+
+ align:start position:0%
+tied to class aspirations right so a lot
+ 
+
+ align:start position:0%
+tied to class aspirations right so a lot
+of the people were serving AIDS is kind
+
+ align:start position:0%
+of the people were serving AIDS is kind
+ 
+
+ align:start position:0%
+of the people were serving AIDS is kind
+of just the latest problem to show up in
+
+ align:start position:0%
+of just the latest problem to show up in
+ 
+
+ align:start position:0%
+of just the latest problem to show up in
+their lives you know some of the people
+
+ align:start position:0%
+their lives you know some of the people
+ 
+
+ align:start position:0%
+their lives you know some of the people
+you've met in reality and their primary
+
+ align:start position:0%
+you've met in reality and their primary
+ 
+
+ align:start position:0%
+you've met in reality and their primary
+concern is access back to the second
+
+ align:start position:0%
+concern is access back to the second
+ 
+
+ align:start position:0%
+concern is access back to the second
+part of her question is how can we get
+
+ align:start position:0%
+part of her question is how can we get
+ 
+
+ align:start position:0%
+part of her question is how can we get
+care I remember being told in uh again
+
+ align:start position:0%
+care I remember being told in uh again
+ 
+
+ align:start position:0%
+care I remember being told in uh again
+here that when you go to Rwanda there's
+
+ align:start position:0%
+here that when you go to Rwanda there's
+ 
+
+ align:start position:0%
+here that when you go to Rwanda there's
+so much secrecy no one's going to know
+
+ align:start position:0%
+so much secrecy no one's going to know
+ 
+
+ align:start position:0%
+so much secrecy no one's going to know
+their status or tell you their status I
+
+ align:start position:0%
+their status or tell you their status I
+ 
+
+ align:start position:0%
+their status or tell you their status I
+went in 2004 out to community meetings
+
+ align:start position:0%
+went in 2004 out to community meetings
+ 
+
+ align:start position:0%
+went in 2004 out to community meetings
+the year before we started some months
+
+ align:start position:0%
+the year before we started some months
+ 
+
+ align:start position:0%
+the year before we started some months
+before in a village where you know in
+
+ align:start position:0%
+before in a village where you know in
+ 
+
+ align:start position:0%
+before in a village where you know in
+the city this might happen in the
+
+ align:start position:0%
+the city this might happen in the
+ 
+
+ align:start position:0%
+the city this might happen in the
+village in the rural area say well how
+
+ align:start position:0%
+village in the rural area say well how
+ 
+
+ align:start position:0%
+village in the rural area say well how
+many of you have HIV and it all rest
+
+ align:start position:0%
+many of you have HIV and it all rest
+ 
+
+ align:start position:0%
+many of you have HIV and it all rest
+their hand and how many of you know your
+
+ align:start position:0%
+their hand and how many of you know your
+ 
+
+ align:start position:0%
+their hand and how many of you know your
+C4 count they'd be going 262 84. and
+
+ align:start position:0%
+C4 count they'd be going 262 84. and
+ 
+
+ align:start position:0%
+C4 count they'd be going 262 84. and
+these are very public for us you know
+
+ align:start position:0%
+these are very public for us you know
+ 
+
+ align:start position:0%
+these are very public for us you know
+and so I would just say we have to be
+
+ align:start position:0%
+and so I would just say we have to be
+ 
+
+ align:start position:0%
+and so I would just say we have to be
+very careful to respect that question
+
+ align:start position:0%
+very careful to respect that question
+ 
+
+ align:start position:0%
+very careful to respect that question
+how to protect privacy
+
+ align:start position:0%
+how to protect privacy
+ 
+
+ align:start position:0%
+how to protect privacy
+but it's still not fundamentally related
+
+ align:start position:0%
+but it's still not fundamentally related
+ 
+
+ align:start position:0%
+but it's still not fundamentally related
+to it's not the on the top five uh
+
+ align:start position:0%
+to it's not the on the top five uh
+ 
+
+ align:start position:0%
+to it's not the on the top five uh
+barriers back to your question uh to
+
+ align:start position:0%
+barriers back to your question uh to
+ 
+
+ align:start position:0%
+barriers back to your question uh to
+access in the rural regions uh oh even I
+
+ align:start position:0%
+access in the rural regions uh oh even I
+ 
+
+ align:start position:0%
+access in the rural regions uh oh even I
+think in the urban regions it's in the
+
+ align:start position:0%
+think in the urban regions it's in the
+ 
+
+ align:start position:0%
+think in the urban regions it's in the
+maybe top 15 as a barrier itself now
+
+ align:start position:0%
+maybe top 15 as a barrier itself now
+ 
+
+ align:start position:0%
+maybe top 15 as a barrier itself now
+that doesn't mean we don't have an
+
+ align:start position:0%
+that doesn't mean we don't have an
+ 
+
+ align:start position:0%
+that doesn't mean we don't have an
+obligation to take this very seriously
+
+ align:start position:0%
+obligation to take this very seriously
+ 
+
+ align:start position:0%
+obligation to take this very seriously
+as I know you and your team have with a
+
+ align:start position:0%
+as I know you and your team have with a
+ 
+
+ align:start position:0%
+as I know you and your team have with a
+unique patient identifiers and sign-in
+
+ align:start position:0%
+unique patient identifiers and sign-in
+ 
+
+ align:start position:0%
+unique patient identifiers and sign-in
+code so you can't log on the system in
+
+ align:start position:0%
+code so you can't log on the system in
+ 
+
+ align:start position:0%
+code so you can't log on the system in
+Haiti unless you use your user ID just
+
+ align:start position:0%
+Haiti unless you use your user ID just
+ 
+
+ align:start position:0%
+Haiti unless you use your user ID just
+like at the Brigham you know and so your
+
+ align:start position:0%
+like at the Brigham you know and so your
+ 
+
+ align:start position:0%
+like at the Brigham you know and so your
+electronic fingerprint if you're going
+
+ align:start position:0%
+electronic fingerprint if you're going
+ 
+
+ align:start position:0%
+electronic fingerprint if you're going
+into someone's medical record is there
+
+ align:start position:0%
+into someone's medical record is there
+ 
+
+ align:start position:0%
+into someone's medical record is there
+but again I think that's just uh that
+
+ align:start position:0%
+but again I think that's just uh that
+ 
+
+ align:start position:0%
+but again I think that's just uh that
+that's us being responsible
+
+ align:start position:0%
+that's us being responsible
+ 
+
+ align:start position:0%
+that's us being responsible
+um to you know to have not a double
+
+ align:start position:0%
+um to you know to have not a double
+ 
+
+ align:start position:0%
+um to you know to have not a double
+standard care in Haiti uh and Rwanda
+
+ align:start position:0%
+standard care in Haiti uh and Rwanda
+ 
+
+ align:start position:0%
+standard care in Haiti uh and Rwanda
+Malawi et cetera but again that the
+
+ align:start position:0%
+Malawi et cetera but again that the
+ 
+
+ align:start position:0%
+Malawi et cetera but again that the
+concern comes largely from has come more
+
+ align:start position:0%
+concern comes largely from has come more
+ 
+
+ align:start position:0%
+concern comes largely from has come more
+from our employees than who also I mean
+
+ align:start position:0%
+from our employees than who also I mean
+ 
+
+ align:start position:0%
+from our employees than who also I mean
+our employees with HIV than from the
+
+ align:start position:0%
+our employees with HIV than from the
+ 
+
+ align:start position:0%
+our employees with HIV than from the
+patients who we've been seeing in these
+
+ align:start position:0%
+patients who we've been seeing in these
+ 
+
+ align:start position:0%
+patients who we've been seeing in these
+first years and I think that's an
+
+ align:start position:0%
+first years and I think that's an
+ 
+
+ align:start position:0%
+first years and I think that's an
+interesting I mean an anthropologist
+
+ align:start position:0%
+interesting I mean an anthropologist
+ 
+
+ align:start position:0%
+interesting I mean an anthropologist
+ought to go in and talk about how some
+
+ align:start position:0%
+ought to go in and talk about how some
+ 
+
+ align:start position:0%
+ought to go in and talk about how some
+people have these aspirations where
+
+ align:start position:0%
+people have these aspirations where
+ 
+
+ align:start position:0%
+people have these aspirations where
+suddenly for the first time in their
+
+ align:start position:0%
+suddenly for the first time in their
+ 
+
+ align:start position:0%
+suddenly for the first time in their
+lives HIV comes along to spoil their
+
+ align:start position:0%
+lives HIV comes along to spoil their
+ 
+
+ align:start position:0%
+lives HIV comes along to spoil their
+aspirations whereas other people have
+
+ align:start position:0%
+aspirations whereas other people have
+ 
+
+ align:start position:0%
+aspirations whereas other people have
+been living a lifetime of disappointment
+
+ align:start position:0%
+been living a lifetime of disappointment
+ 
+
+ align:start position:0%
+been living a lifetime of disappointment
+and you know that again this is the
+
+ align:start position:0%
+and you know that again this is the
+ 
+
+ align:start position:0%
+and you know that again this is the
+latest thing to come in and spoil
+
+ align:start position:0%
+latest thing to come in and spoil
+ 
+
+ align:start position:0%
+latest thing to come in and spoil
+aspirations that were set though to
+
+ align:start position:0%
+aspirations that were set though to
+ 
+
+ align:start position:0%
+aspirations that were set though to
+start with because of so many so much
+
+ align:start position:0%
+start with because of so many so much
+ 
+
+ align:start position:0%
+start with because of so many so much
+unfairness again lack of access to
+
+ align:start position:0%
+unfairness again lack of access to
+ 
+
+ align:start position:0%
+unfairness again lack of access to
+school primary even Primary School to a
+
+ align:start position:0%
+school primary even Primary School to a
+ 
+
+ align:start position:0%
+school primary even Primary School to a
+job to family planning to you know on
+
+ align:start position:0%
+job to family planning to you know on
+ 
+
+ align:start position:0%
+job to family planning to you know on
+and on the list codes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to open it up to other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I mean I please yes sir there's a
+
+ align:start position:0%
+yeah I mean I please yes sir there's a
+ 
+
+ align:start position:0%
+yeah I mean I please yes sir there's a
+snake also from the School of Public
+
+ align:start position:0%
+snake also from the School of Public
+ 
+
+ align:start position:0%
+snake also from the School of Public
+Health so I've got the question
+
+ align:start position:0%
+Health so I've got the question
+ 
+
+ align:start position:0%
+Health so I've got the question
+um to you about uh using the human
+
+ align:start position:0%
+um to you about uh using the human
+ 
+
+ align:start position:0%
+um to you about uh using the human
+rights framework yeah in what you do and
+
+ align:start position:0%
+rights framework yeah in what you do and
+ 
+
+ align:start position:0%
+rights framework yeah in what you do and
+the status of Technology within that so
+
+ align:start position:0%
+the status of Technology within that so
+ 
+
+ align:start position:0%
+the status of Technology within that so
+given the rise of mhealth Kelly medicine
+
+ align:start position:0%
+given the rise of mhealth Kelly medicine
+ 
+
+ align:start position:0%
+given the rise of mhealth Kelly medicine
+um you too with the telemedicine and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh do you think that it is inherent
+
+ align:start position:0%
+um uh do you think that it is inherent
+ 
+
+ align:start position:0%
+um uh do you think that it is inherent
+in the right to health technology is
+
+ align:start position:0%
+in the right to health technology is
+ 
+
+ align:start position:0%
+in the right to health technology is
+included within that or do you think
+
+ align:start position:0%
+included within that or do you think
+ 
+
+ align:start position:0%
+included within that or do you think
+there is an on-the-ground tangible
+
+ align:start position:0%
+there is an on-the-ground tangible
+ 
+
+ align:start position:0%
+there is an on-the-ground tangible
+important role the separate right the
+
+ align:start position:0%
+important role the separate right the
+ 
+
+ align:start position:0%
+important role the separate right the
+right to enjoy the benefits of
+
+ align:start position:0%
+right to enjoy the benefits of
+ 
+
+ align:start position:0%
+right to enjoy the benefits of
+scientific progress what do you think
+
+ align:start position:0%
+scientific progress what do you think
+ 
+
+ align:start position:0%
+scientific progress what do you think
+that's now that I have given that
+
+ align:start position:0%
+that's now that I have given that
+ 
+
+ align:start position:0%
+that's now that I have given that
+technology is so Central to help today
+
+ align:start position:0%
+technology is so Central to help today
+ 
+
+ align:start position:0%
+technology is so Central to help today
+well I mean I would I would say that it
+
+ align:start position:0%
+well I mean I would I would say that it
+ 
+
+ align:start position:0%
+well I mean I would I would say that it
+is possible to exploit multiple
+
+ align:start position:0%
+is possible to exploit multiple
+ 
+
+ align:start position:0%
+is possible to exploit multiple
+Frameworks at the same time and I I'm
+
+ align:start position:0%
+Frameworks at the same time and I I'm
+ 
+
+ align:start position:0%
+Frameworks at the same time and I I'm
+also kind of a pro at that right so
+
+ align:start position:0%
+also kind of a pro at that right so
+ 
+
+ align:start position:0%
+also kind of a pro at that right so
+three big Frameworks when the right
+
+ align:start position:0%
+three big Frameworks when the right
+ 
+
+ align:start position:0%
+three big Frameworks when the right
+space framework which I find very useful
+
+ align:start position:0%
+space framework which I find very useful
+ 
+
+ align:start position:0%
+space framework which I find very useful
+uh another would be the public goods for
+
+ align:start position:0%
+uh another would be the public goods for
+ 
+
+ align:start position:0%
+uh another would be the public goods for
+public health framework which the public
+
+ align:start position:0%
+public health framework which the public
+ 
+
+ align:start position:0%
+public health framework which the public
+health people as you know develop this
+
+ align:start position:0%
+health people as you know develop this
+ 
+
+ align:start position:0%
+health people as you know develop this
+they're comfortable with it it doesn't
+
+ align:start position:0%
+they're comfortable with it it doesn't
+ 
+
+ align:start position:0%
+they're comfortable with it it doesn't
+you'll find a lot of people in public
+
+ align:start position:0%
+you'll find a lot of people in public
+ 
+
+ align:start position:0%
+you'll find a lot of people in public
+health who are uncomfortable with the
+
+ align:start position:0%
+health who are uncomfortable with the
+ 
+
+ align:start position:0%
+health who are uncomfortable with the
+right space probes they think it sounds
+
+ align:start position:0%
+right space probes they think it sounds
+ 
+
+ align:start position:0%
+right space probes they think it sounds
+real or you know I get I get that and
+
+ align:start position:0%
+real or you know I get I get that and
+ 
+
+ align:start position:0%
+real or you know I get I get that and
+then third how are we gonna which is
+
+ align:start position:0%
+then third how are we gonna which is
+ 
+
+ align:start position:0%
+then third how are we gonna which is
+kind of the economics development
+
+ align:start position:0%
+kind of the economics development
+ 
+
+ align:start position:0%
+kind of the economics development
+framework how will we break the cycle of
+
+ align:start position:0%
+framework how will we break the cycle of
+ 
+
+ align:start position:0%
+framework how will we break the cycle of
+poverty disease if we don't invest in
+
+ align:start position:0%
+poverty disease if we don't invest in
+ 
+
+ align:start position:0%
+poverty disease if we don't invest in
+these new technologies so I think either
+
+ align:start position:0%
+these new technologies so I think either
+ 
+
+ align:start position:0%
+these new technologies so I think either
+way you look at it
+
+ align:start position:0%
+way you look at it
+ 
+
+ align:start position:0%
+way you look at it
+these Frameworks lead to the same thing
+
+ align:start position:0%
+these Frameworks lead to the same thing
+ 
+
+ align:start position:0%
+these Frameworks lead to the same thing
+which is valuing
+
+ align:start position:0%
+which is valuing
+ 
+
+ align:start position:0%
+which is valuing
+uh scientific progress as the basis of a
+
+ align:start position:0%
+uh scientific progress as the basis of a
+ 
+
+ align:start position:0%
+uh scientific progress as the basis of a
+lot of these interventions I think
+
+ align:start position:0%
+lot of these interventions I think
+ 
+
+ align:start position:0%
+lot of these interventions I think
+that's a healthy thing to do so whether
+
+ align:start position:0%
+that's a healthy thing to do so whether
+ 
+
+ align:start position:0%
+that's a healthy thing to do so whether
+we say well you know just the right to
+
+ align:start position:0%
+we say well you know just the right to
+ 
+
+ align:start position:0%
+we say well you know just the right to
+Health Care will drag in the right to
+
+ align:start position:0%
+Health Care will drag in the right to
+ 
+
+ align:start position:0%
+Health Care will drag in the right to
+technological advance I think that's
+
+ align:start position:0%
+technological advance I think that's
+ 
+
+ align:start position:0%
+technological advance I think that's
+true because all of the Technologies
+
+ align:start position:0%
+true because all of the Technologies
+ 
+
+ align:start position:0%
+true because all of the Technologies
+we're talking about that I've spoken
+
+ align:start position:0%
+we're talking about that I've spoken
+ 
+
+ align:start position:0%
+we're talking about that I've spoken
+about today each of them is a post-mid
+
+ align:start position:0%
+about today each of them is a post-mid
+ 
+
+ align:start position:0%
+about today each of them is a post-mid
+20th century development antivirus
+
+ align:start position:0%
+20th century development antivirus
+ 
+
+ align:start position:0%
+20th century development antivirus
+antibiotics Diagnostics and the maladies
+
+ align:start position:0%
+antibiotics Diagnostics and the maladies
+ 
+
+ align:start position:0%
+antibiotics Diagnostics and the maladies
+themselves right they've changed at the
+
+ align:start position:0%
+themselves right they've changed at the
+ 
+
+ align:start position:0%
+themselves right they've changed at the
+genetic level drug resistant TV drug
+
+ align:start position:0%
+genetic level drug resistant TV drug
+ 
+
+ align:start position:0%
+genetic level drug resistant TV drug
+resistant HIV drug assistance staph
+
+ align:start position:0%
+resistant HIV drug assistance staph
+ 
+
+ align:start position:0%
+resistant HIV drug assistance staph
+aureus blah blah blah they've all
+
+ align:start position:0%
+aureus blah blah blah they've all
+ 
+
+ align:start position:0%
+aureus blah blah blah they've all
+um I guess blah blah is not really good
+
+ align:start position:0%
+um I guess blah blah is not really good
+ 
+
+ align:start position:0%
+um I guess blah blah is not really good
+to broadcast internationally you know
+
+ align:start position:0%
+to broadcast internationally you know
+ 
+
+ align:start position:0%
+to broadcast internationally you know
+what I mean so I think that that model
+
+ align:start position:0%
+what I mean so I think that that model
+ 
+
+ align:start position:0%
+what I mean so I think that that model
+is still robust say look if you want to
+
+ align:start position:0%
+is still robust say look if you want to
+ 
+
+ align:start position:0%
+is still robust say look if you want to
+if you want to talk about the right to
+
+ align:start position:0%
+if you want to talk about the right to
+ 
+
+ align:start position:0%
+if you want to talk about the right to
+health care you're going to have to talk
+
+ align:start position:0%
+health care you're going to have to talk
+ 
+
+ align:start position:0%
+health care you're going to have to talk
+about the right to access a new
+
+ align:start position:0%
+about the right to access a new
+ 
+
+ align:start position:0%
+about the right to access a new
+technology now at the same time does it
+
+ align:start position:0%
+technology now at the same time does it
+ 
+
+ align:start position:0%
+technology now at the same time does it
+weaken or strengthen the argument
+
+ align:start position:0%
+weaken or strengthen the argument
+ 
+
+ align:start position:0%
+weaken or strengthen the argument
+because this is really about an argument
+
+ align:start position:0%
+because this is really about an argument
+ 
+
+ align:start position:0%
+because this is really about an argument
+right a pitch for using these
+
+ align:start position:0%
+right a pitch for using these
+ 
+
+ align:start position:0%
+right a pitch for using these
+developments to promote health and
+
+ align:start position:0%
+developments to promote health and
+ 
+
+ align:start position:0%
+developments to promote health and
+well-being among people have been cut
+
+ align:start position:0%
+well-being among people have been cut
+ 
+
+ align:start position:0%
+well-being among people have been cut
+out of scientific progress I think it's
+
+ align:start position:0%
+out of scientific progress I think it's
+ 
+
+ align:start position:0%
+out of scientific progress I think it's
+also helpful to have people think about
+
+ align:start position:0%
+also helpful to have people think about
+ 
+
+ align:start position:0%
+also helpful to have people think about
+the digital divide you know what the
+
+ align:start position:0%
+the digital divide you know what the
+ 
+
+ align:start position:0%
+the digital divide you know what the
+cost of not having access to these new
+
+ align:start position:0%
+cost of not having access to these new
+ 
+
+ align:start position:0%
+cost of not having access to these new
+technologies is in a right space
+
+ align:start position:0%
+technologies is in a right space
+ 
+
+ align:start position:0%
+technologies is in a right space
+framework as well I think it's
+
+ align:start position:0%
+framework as well I think it's
+ 
+
+ align:start position:0%
+framework as well I think it's
+complementary rather than corrosive or
+
+ align:start position:0%
+complementary rather than corrosive or
+ 
+
+ align:start position:0%
+complementary rather than corrosive or
+um so I would actually say that we're
+
+ align:start position:0%
+um so I would actually say that we're
+ 
+
+ align:start position:0%
+um so I would actually say that we're
+working together like if we get the I.T
+
+ align:start position:0%
+working together like if we get the I.T
+ 
+
+ align:start position:0%
+working together like if we get the I.T
+nerds together with us as the health
+
+ align:start position:0%
+nerds together with us as the health
+ 
+
+ align:start position:0%
+nerds together with us as the health
+providers it's a very powerful thing
+
+ align:start position:0%
+providers it's a very powerful thing
+ 
+
+ align:start position:0%
+providers it's a very powerful thing
+itns you could move for one or two more
+
+ align:start position:0%
+itns you could move for one or two more
+ 
+
+ align:start position:0%
+itns you could move for one or two more
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+am I am I yes please and then can we
+
+ align:start position:0%
+am I am I yes please and then can we
+ 
+
+ align:start position:0%
+am I am I yes please and then can we
+just at least take these three because
+
+ align:start position:0%
+just at least take these three because
+ 
+
+ align:start position:0%
+just at least take these three because
+they're all in a little triangle and I
+
+ align:start position:0%
+they're all in a little triangle and I
+ 
+
+ align:start position:0%
+they're all in a little triangle and I
+said so
+
+ align:start position:0%
+said so
+ 
+
+ align:start position:0%
+said so
+I'll try to speed it up
+
+ align:start position:0%
+I'll try to speed it up
+ 
+
+ align:start position:0%
+I'll try to speed it up
+I'm Gene Gilman with the security
+
+ align:start position:0%
+I'm Gene Gilman with the security
+ 
+
+ align:start position:0%
+I'm Gene Gilman with the security
+studies program at MIT and I have a
+
+ align:start position:0%
+studies program at MIT and I have a
+ 
+
+ align:start position:0%
+studies program at MIT and I have a
+question about surveillance and how do
+
+ align:start position:0%
+question about surveillance and how do
+ 
+
+ align:start position:0%
+question about surveillance and how do
+you think about certain disease
+
+ align:start position:0%
+you think about certain disease
+ 
+
+ align:start position:0%
+you think about certain disease
+surveillance yeah we've had a great
+
+ align:start position:0%
+surveillance yeah we've had a great
+ 
+
+ align:start position:0%
+surveillance yeah we've had a great
+controversy about h5n1 and that
+
+ align:start position:0%
+controversy about h5n1 and that
+ 
+
+ align:start position:0%
+controversy about h5n1 and that
+researches at least the Wisconsin aspect
+
+ align:start position:0%
+researches at least the Wisconsin aspect
+ 
+
+ align:start position:0%
+researches at least the Wisconsin aspect
+of it is to be published in nature in
+
+ align:start position:0%
+of it is to be published in nature in
+ 
+
+ align:start position:0%
+of it is to be published in nature in
+Italy and the Science magazine will also
+
+ align:start position:0%
+Italy and the Science magazine will also
+ 
+
+ align:start position:0%
+Italy and the Science magazine will also
+be published in the rottenham result and
+
+ align:start position:0%
+be published in the rottenham result and
+ 
+
+ align:start position:0%
+be published in the rottenham result and
+both of the
+
+ align:start position:0%
+both of the
+ 
+
+ align:start position:0%
+both of the
+academies of researchers have said that
+
+ align:start position:0%
+academies of researchers have said that
+ 
+
+ align:start position:0%
+academies of researchers have said that
+they're doing this research which is to
+
+ align:start position:0%
+they're doing this research which is to
+ 
+
+ align:start position:0%
+they're doing this research which is to
+actually jump ahead of nature that would
+
+ align:start position:0%
+actually jump ahead of nature that would
+ 
+
+ align:start position:0%
+actually jump ahead of nature that would
+host
+
+ align:start position:0%
+host
+ 
+
+ align:start position:0%
+host
+host responses to avian flu h5n1 they
+
+ align:start position:0%
+host responses to avian flu h5n1 they
+ 
+
+ align:start position:0%
+host responses to avian flu h5n1 they
+both said that what they want to do is
+
+ align:start position:0%
+both said that what they want to do is
+ 
+
+ align:start position:0%
+both said that what they want to do is
+create mechanisms for improved
+
+ align:start position:0%
+create mechanisms for improved
+ 
+
+ align:start position:0%
+create mechanisms for improved
+surveillance so I'm asking you about
+
+ align:start position:0%
+surveillance so I'm asking you about
+ 
+
+ align:start position:0%
+surveillance so I'm asking you about
+surveillance because there are these
+
+ align:start position:0%
+surveillance because there are these
+ 
+
+ align:start position:0%
+surveillance because there are these
+platforms that you have established and
+
+ align:start position:0%
+platforms that you have established and
+ 
+
+ align:start position:0%
+platforms that you have established and
+that you're looking at are they also
+
+ align:start position:0%
+that you're looking at are they also
+ 
+
+ align:start position:0%
+that you're looking at are they also
+good modalities for for surveillance
+
+ align:start position:0%
+good modalities for for surveillance
+ 
+
+ align:start position:0%
+good modalities for for surveillance
+which is a huge problem if you look at
+
+ align:start position:0%
+which is a huge problem if you look at
+ 
+
+ align:start position:0%
+which is a huge problem if you look at
+Avian Influenza
+
+ align:start position:0%
+Avian Influenza
+ 
+
+ align:start position:0%
+Avian Influenza
+um and then I guess
+
+ align:start position:0%
+um and then I guess
+ 
+
+ align:start position:0%
+um and then I guess
+um I think behind behind that question I
+
+ align:start position:0%
+um I think behind behind that question I
+ 
+
+ align:start position:0%
+um I think behind behind that question I
+think would it's going to be a larger
+
+ align:start position:0%
+think would it's going to be a larger
+ 
+
+ align:start position:0%
+think would it's going to be a larger
+question about
+
+ align:start position:0%
+question about
+ 
+
+ align:start position:0%
+question about
+um which has already been echoed here is
+
+ align:start position:0%
+um which has already been echoed here is
+ 
+
+ align:start position:0%
+um which has already been echoed here is
+our are we bringing people into the 21st
+
+ align:start position:0%
+our are we bringing people into the 21st
+ 
+
+ align:start position:0%
+our are we bringing people into the 21st
+century and are this is very futuristic
+
+ align:start position:0%
+century and are this is very futuristic
+ 
+
+ align:start position:0%
+century and are this is very futuristic
+this is a true called in question please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um no I just I I guess it's this this
+
+ align:start position:0%
+um no I just I I guess it's this this
+ 
+
+ align:start position:0%
+um no I just I I guess it's this this
+whole issue of where is basic science
+
+ align:start position:0%
+whole issue of where is basic science
+ 
+
+ align:start position:0%
+whole issue of where is basic science
+relative to what you're doing and I know
+
+ align:start position:0%
+relative to what you're doing and I know
+ 
+
+ align:start position:0%
+relative to what you're doing and I know
+you think of this in the treatment mode
+
+ align:start position:0%
+you think of this in the treatment mode
+ 
+
+ align:start position:0%
+you think of this in the treatment mode
+yeah the way people are looking at it
+
+ align:start position:0%
+yeah the way people are looking at it
+ 
+
+ align:start position:0%
+yeah the way people are looking at it
+now is there a surveillance level but I
+
+ align:start position:0%
+now is there a surveillance level but I
+ 
+
+ align:start position:0%
+now is there a surveillance level but I
+can throw you the general questions
+
+ align:start position:0%
+can throw you the general questions
+ 
+
+ align:start position:0%
+can throw you the general questions
+where is the link between basic science
+
+ align:start position:0%
+where is the link between basic science
+ 
+
+ align:start position:0%
+where is the link between basic science
+and treatment as it impacts your project
+
+ align:start position:0%
+and treatment as it impacts your project
+ 
+
+ align:start position:0%
+and treatment as it impacts your project
+yeah can I start with the second part
+
+ align:start position:0%
+yeah can I start with the second part
+ 
+
+ align:start position:0%
+yeah can I start with the second part
+and go back to surveillance because you
+
+ align:start position:0%
+and go back to surveillance because you
+ 
+
+ align:start position:0%
+and go back to surveillance because you
+know there are multiple regimens of
+
+ align:start position:0%
+know there are multiple regimens of
+ 
+
+ align:start position:0%
+know there are multiple regimens of
+surveillance as you well know but back
+
+ align:start position:0%
+surveillance as you well know but back
+ 
+
+ align:start position:0%
+surveillance as you well know but back
+to the the basic science question I
+
+ align:start position:0%
+to the the basic science question I
+ 
+
+ align:start position:0%
+to the the basic science question I
+would argue that
+
+ align:start position:0%
+would argue that
+ 
+
+ align:start position:0%
+would argue that
+we in no example is more powerful than
+
+ align:start position:0%
+we in no example is more powerful than
+ 
+
+ align:start position:0%
+we in no example is more powerful than
+AIDS and in 30 years
+
+ align:start position:0%
+AIDS and in 30 years
+ 
+
+ align:start position:0%
+AIDS and in 30 years
+only 30 years that you
+
+ align:start position:0%
+only 30 years that you
+ 
+
+ align:start position:0%
+only 30 years that you
+can go from a new
+
+ align:start position:0%
+can go from a new
+ 
+
+ align:start position:0%
+can go from a new
+uh syndrome and you know at least in
+
+ align:start position:0%
+uh syndrome and you know at least in
+ 
+
+ align:start position:0%
+uh syndrome and you know at least in
+this part of the world and certainly
+
+ align:start position:0%
+this part of the world and certainly
+ 
+
+ align:start position:0%
+this part of the world and certainly
+newly described identify the pathogen
+
+ align:start position:0%
+newly described identify the pathogen
+ 
+
+ align:start position:0%
+newly described identify the pathogen
+learn how to Stage diagnose and Stage
+
+ align:start position:0%
+learn how to Stage diagnose and Stage
+ 
+
+ align:start position:0%
+learn how to Stage diagnose and Stage
+the disease with great reliability
+
+ align:start position:0%
+the disease with great reliability
+ 
+
+ align:start position:0%
+the disease with great reliability
+and then have a fairly reasonable
+
+ align:start position:0%
+and then have a fairly reasonable
+ 
+
+ align:start position:0%
+and then have a fairly reasonable
+treatment regimen developed uh
+
+ align:start position:0%
+treatment regimen developed uh
+ 
+
+ align:start position:0%
+treatment regimen developed uh
+suppressive chronic but still pretty
+
+ align:start position:0%
+suppressive chronic but still pretty
+ 
+
+ align:start position:0%
+suppressive chronic but still pretty
+pretty good I mean look at certainly
+
+ align:start position:0%
+pretty good I mean look at certainly
+ 
+
+ align:start position:0%
+pretty good I mean look at certainly
+looks good to me as a doctor
+
+ align:start position:0%
+looks good to me as a doctor
+ 
+
+ align:start position:0%
+looks good to me as a doctor
+all that has happened in 30 years and
+
+ align:start position:0%
+all that has happened in 30 years and
+ 
+
+ align:start position:0%
+all that has happened in 30 years and
+it's all database I mean it's all built
+
+ align:start position:0%
+it's all database I mean it's all built
+ 
+
+ align:start position:0%
+it's all database I mean it's all built
+on basic science laboratory research the
+
+ align:start position:0%
+on basic science laboratory research the
+ 
+
+ align:start position:0%
+on basic science laboratory research the
+legit the Therapeutics the Diagnostics
+
+ align:start position:0%
+legit the Therapeutics the Diagnostics
+ 
+
+ align:start position:0%
+legit the Therapeutics the Diagnostics
+so I think that is a pretty powerful
+
+ align:start position:0%
+so I think that is a pretty powerful
+ 
+
+ align:start position:0%
+so I think that is a pretty powerful
+example of how you can link uh
+
+ align:start position:0%
+example of how you can link uh
+ 
+
+ align:start position:0%
+example of how you can link uh
+scientific development to a great need
+
+ align:start position:0%
+scientific development to a great need
+ 
+
+ align:start position:0%
+scientific development to a great need
+again I mentioned already the leading
+
+ align:start position:0%
+again I mentioned already the leading
+ 
+
+ align:start position:0%
+again I mentioned already the leading
+infectious killer of young adults in the
+
+ align:start position:0%
+infectious killer of young adults in the
+ 
+
+ align:start position:0%
+infectious killer of young adults in the
+world and the huge killer of children as
+
+ align:start position:0%
+world and the huge killer of children as
+ 
+
+ align:start position:0%
+world and the huge killer of children as
+well and elderly people I mean it's just
+
+ align:start position:0%
+well and elderly people I mean it's just
+ 
+
+ align:start position:0%
+well and elderly people I mean it's just
+the and then there's the indirect cost
+
+ align:start position:0%
+the and then there's the indirect cost
+ 
+
+ align:start position:0%
+the and then there's the indirect cost
+to the elderly and the um who are not
+
+ align:start position:0%
+to the elderly and the um who are not
+ 
+
+ align:start position:0%
+to the elderly and the um who are not
+infected but are affected so I think
+
+ align:start position:0%
+infected but are affected so I think
+ 
+
+ align:start position:0%
+infected but are affected so I think
+it's a good story for science for basic
+
+ align:start position:0%
+it's a good story for science for basic
+ 
+
+ align:start position:0%
+it's a good story for science for basic
+science and that it also gets back to
+
+ align:start position:0%
+science and that it also gets back to
+ 
+
+ align:start position:0%
+science and that it also gets back to
+the surveillance question because I
+
+ align:start position:0%
+the surveillance question because I
+ 
+
+ align:start position:0%
+the surveillance question because I
+remember you know
+
+ align:start position:0%
+remember you know
+ 
+
+ align:start position:0%
+remember you know
+um some of the things indeed I wrote
+
+ align:start position:0%
+um some of the things indeed I wrote
+ 
+
+ align:start position:0%
+um some of the things indeed I wrote
+about this in the 80s
+
+ align:start position:0%
+about this in the 80s
+ 
+
+ align:start position:0%
+about this in the 80s
+about the negative aspects of
+
+ align:start position:0%
+about the negative aspects of
+ 
+
+ align:start position:0%
+about the negative aspects of
+surveillance of HIV and there are a lot
+
+ align:start position:0%
+surveillance of HIV and there are a lot
+ 
+
+ align:start position:0%
+surveillance of HIV and there are a lot
+of people writing about that in 80s
+
+ align:start position:0%
+of people writing about that in 80s
+ 
+
+ align:start position:0%
+of people writing about that in 80s
+because you really you know we really
+
+ align:start position:0%
+because you really you know we really
+ 
+
+ align:start position:0%
+because you really you know we really
+didn't have a good therapeutic strategy
+
+ align:start position:0%
+didn't have a good therapeutic strategy
+ 
+
+ align:start position:0%
+didn't have a good therapeutic strategy
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+but we did have the people did have the
+
+ align:start position:0%
+but we did have the people did have the
+ 
+
+ align:start position:0%
+but we did have the people did have the
+ability to discriminate against people
+
+ align:start position:0%
+ability to discriminate against people
+ 
+
+ align:start position:0%
+ability to discriminate against people
+with living or living with HIV in the
+
+ align:start position:0%
+with living or living with HIV in the
+ 
+
+ align:start position:0%
+with living or living with HIV in the
+workplace and in housing questions in
+
+ align:start position:0%
+workplace and in housing questions in
+ 
+
+ align:start position:0%
+workplace and in housing questions in
+this country and in all kinds of ways in
+
+ align:start position:0%
+this country and in all kinds of ways in
+ 
+
+ align:start position:0%
+this country and in all kinds of ways in
+other settings too so the negative
+
+ align:start position:0%
+other settings too so the negative
+ 
+
+ align:start position:0%
+other settings too so the negative
+aspects of surveillance are also out
+
+ align:start position:0%
+aspects of surveillance are also out
+ 
+
+ align:start position:0%
+aspects of surveillance are also out
+there I don't know which one you were
+
+ align:start position:0%
+there I don't know which one you were
+ 
+
+ align:start position:0%
+there I don't know which one you were
+leaning on Gene but in terms of
+
+ align:start position:0%
+leaning on Gene but in terms of
+ 
+
+ align:start position:0%
+leaning on Gene but in terms of
+surveillance to serve as important as
+
+ align:start position:0%
+surveillance to serve as important as
+ 
+
+ align:start position:0%
+surveillance to serve as important as
+opposed to to discipline
+
+ align:start position:0%
+opposed to to discipline
+ 
+
+ align:start position:0%
+opposed to to discipline
+um these platforms offer great potential
+
+ align:start position:0%
+um these platforms offer great potential
+ 
+
+ align:start position:0%
+um these platforms offer great potential
+and well I think one of the again one of
+
+ align:start position:0%
+and well I think one of the again one of
+ 
+
+ align:start position:0%
+and well I think one of the again one of
+the smart things for us to do to show
+
+ align:start position:0%
+the smart things for us to do to show
+ 
+
+ align:start position:0%
+the smart things for us to do to show
+how surveillance of an epidemic is a
+
+ align:start position:0%
+how surveillance of an epidemic is a
+ 
+
+ align:start position:0%
+how surveillance of an epidemic is a
+good thing is to link that to service
+
+ align:start position:0%
+good thing is to link that to service
+ 
+
+ align:start position:0%
+good thing is to link that to service
+like with cholera do you want to count
+
+ align:start position:0%
+like with cholera do you want to count
+ 
+
+ align:start position:0%
+like with cholera do you want to count
+call our victims or do we want to
+
+ align:start position:0%
+call our victims or do we want to
+ 
+
+ align:start position:0%
+call our victims or do we want to
+eradicate cholera from the island of
+
+ align:start position:0%
+eradicate cholera from the island of
+ 
+
+ align:start position:0%
+eradicate cholera from the island of
+Hispaniola and develop a stockpile for
+
+ align:start position:0%
+Hispaniola and develop a stockpile for
+ 
+
+ align:start position:0%
+Hispaniola and develop a stockpile for
+the world we want the latter and we want
+
+ align:start position:0%
+the world we want the latter and we want
+ 
+
+ align:start position:0%
+the world we want the latter and we want
+to count cholera cases so that we can
+
+ align:start position:0%
+to count cholera cases so that we can
+ 
+
+ align:start position:0%
+to count cholera cases so that we can
+build better budgets and better
+
+ align:start position:0%
+build better budgets and better
+ 
+
+ align:start position:0%
+build better budgets and better
+interventions and raise resources to
+
+ align:start position:0%
+interventions and raise resources to
+ 
+
+ align:start position:0%
+interventions and raise resources to
+save lives but we also want to do it uh
+
+ align:start position:0%
+save lives but we also want to do it uh
+ 
+
+ align:start position:0%
+save lives but we also want to do it uh
+you know to eradicate disease so for to
+
+ align:start position:0%
+you know to eradicate disease so for to
+ 
+
+ align:start position:0%
+you know to eradicate disease so for to
+the extent I'm back to the general Point
+
+ align:start position:0%
+the extent I'm back to the general Point
+ 
+
+ align:start position:0%
+the extent I'm back to the general Point
+here about surveillance stop looking at
+
+ align:start position:0%
+here about surveillance stop looking at
+ 
+
+ align:start position:0%
+here about surveillance stop looking at
+your cell phone watch a good time
+
+ align:start position:0%
+your cell phone watch a good time
+ 
+
+ align:start position:0%
+your cell phone watch a good time
+so you know I think the promise of good
+
+ align:start position:0%
+so you know I think the promise of good
+ 
+
+ align:start position:0%
+so you know I think the promise of good
+surveillance uh is is it comes out of
+
+ align:start position:0%
+surveillance uh is is it comes out of
+ 
+
+ align:start position:0%
+surveillance uh is is it comes out of
+these platforms and that the net good is
+
+ align:start position:0%
+these platforms and that the net good is
+ 
+
+ align:start position:0%
+these platforms and that the net good is
+going to be huge we also just have to
+
+ align:start position:0%
+going to be huge we also just have to
+ 
+
+ align:start position:0%
+going to be huge we also just have to
+link that back to the rights questions
+
+ align:start position:0%
+link that back to the rights questions
+ 
+
+ align:start position:0%
+link that back to the rights questions
+that were mentioned already and the
+
+ align:start position:0%
+that were mentioned already and the
+ 
+
+ align:start position:0%
+that were mentioned already and the
+right of it to access is the biggest one
+
+ align:start position:0%
+right of it to access is the biggest one
+ 
+
+ align:start position:0%
+right of it to access is the biggest one
+among them
+
+ align:start position:0%
+among them
+ 
+
+ align:start position:0%
+among them
+so we've actually got um like five
+
+ align:start position:0%
+so we've actually got um like five
+ 
+
+ align:start position:0%
+so we've actually got um like five
+minutes and there is a class after this
+
+ align:start position:0%
+minutes and there is a class after this
+ 
+
+ align:start position:0%
+minutes and there is a class after this
+so I think what I'll do is just a quick
+
+ align:start position:0%
+so I think what I'll do is just a quick
+ 
+
+ align:start position:0%
+so I think what I'll do is just a quick
+announcement and then one more question
+
+ align:start position:0%
+announcement and then one more question
+ 
+
+ align:start position:0%
+announcement and then one more question
+so just for next week for the class um
+
+ align:start position:0%
+so just for next week for the class um
+ 
+
+ align:start position:0%
+so just for next week for the class um
+we actually have the class project
+
+ align:start position:0%
+we actually have the class project
+ 
+
+ align:start position:0%
+we actually have the class project
+presentation so we're looking forward to
+
+ align:start position:0%
+presentation so we're looking forward to
+ 
+
+ align:start position:0%
+presentation so we're looking forward to
+that and other people are interested in
+
+ align:start position:0%
+that and other people are interested in
+ 
+
+ align:start position:0%
+that and other people are interested in
+welcome to come and join that
+
+ align:start position:0%
+welcome to come and join that
+ 
+
+ align:start position:0%
+welcome to come and join that
+um uh as I said there is another class
+
+ align:start position:0%
+um uh as I said there is another class
+ 
+
+ align:start position:0%
+um uh as I said there is another class
+coming in so in the Buckeyes we need to
+
+ align:start position:0%
+coming in so in the Buckeyes we need to
+ 
+
+ align:start position:0%
+coming in so in the Buckeyes we need to
+and to leave the room but everything
+
+ align:start position:0%
+and to leave the room but everything
+ 
+
+ align:start position:0%
+and to leave the room but everything
+sounds like to use that last time for at
+
+ align:start position:0%
+sounds like to use that last time for at
+ 
+
+ align:start position:0%
+sounds like to use that last time for at
+least one more question everything that
+
+ align:start position:0%
+least one more question everything that
+ 
+
+ align:start position:0%
+least one more question everything that
+sounds better with the Scottish Burr
+
+ align:start position:0%
+sounds better with the Scottish Burr
+ 
+
+ align:start position:0%
+sounds better with the Scottish Burr
+like get out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'll stick around outside by
+
+ align:start position:0%
+and then I'll stick around outside by
+ 
+
+ align:start position:0%
+and then I'll stick around outside by
+the way if I might so sorry
+
+ align:start position:0%
+the way if I might so sorry
+ 
+
+ align:start position:0%
+the way if I might so sorry
+I'm curious if there was an optimal mix
+
+ align:start position:0%
+I'm curious if there was an optimal mix
+ 
+
+ align:start position:0%
+I'm curious if there was an optimal mix
+of the number of participants in the
+
+ align:start position:0%
+of the number of participants in the
+ 
+
+ align:start position:0%
+of the number of participants in the
+process so the physician the first the
+
+ align:start position:0%
+process so the physician the first the
+ 
+
+ align:start position:0%
+process so the physician the first the
+community healthcare presentation that's
+
+ align:start position:0%
+community healthcare presentation that's
+ 
+
+ align:start position:0%
+community healthcare presentation that's
+a great question is there where where
+
+ align:start position:0%
+a great question is there where where
+ 
+
+ align:start position:0%
+a great question is there where where
+the the software do you try to engage
+
+ align:start position:0%
+the the software do you try to engage
+ 
+
+ align:start position:0%
+the the software do you try to engage
+the whole Community because it's a
+
+ align:start position:0%
+the whole Community because it's a
+ 
+
+ align:start position:0%
+the whole Community because it's a
+community-based pro if you engage the
+
+ align:start position:0%
+community-based pro if you engage the
+ 
+
+ align:start position:0%
+community-based pro if you engage the
+whole community
+
+ align:start position:0%
+whole community
+ 
+
+ align:start position:0%
+whole community
+where does it stop before it comes
+
+ align:start position:0%
+where does it stop before it comes
+ 
+
+ align:start position:0%
+where does it stop before it comes
+becomes like an issue like here where
+
+ align:start position:0%
+becomes like an issue like here where
+ 
+
+ align:start position:0%
+becomes like an issue like here where
+there's so many participants in the
+
+ align:start position:0%
+there's so many participants in the
+ 
+
+ align:start position:0%
+there's so many participants in the
+process like third-party Healthcare
+
+ align:start position:0%
+process like third-party Healthcare
+ 
+
+ align:start position:0%
+process like third-party Healthcare
+managers
+
+ align:start position:0%
+managers
+ 
+
+ align:start position:0%
+managers
+it's a great question I I will say given
+
+ align:start position:0%
+it's a great question I I will say given
+ 
+
+ align:start position:0%
+it's a great question I I will say given
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um threats that I just received from
+
+ align:start position:0%
+um threats that I just received from
+ 
+
+ align:start position:0%
+um threats that I just received from
+your divorce director that of all my
+
+ align:start position:0%
+your divorce director that of all my
+ 
+
+ align:start position:0%
+your divorce director that of all my
+co-workers who are working on this
+
+ align:start position:0%
+co-workers who are working on this
+ 
+
+ align:start position:0%
+co-workers who are working on this
+question are the ideal structure how
+
+ align:start position:0%
+question are the ideal structure how
+ 
+
+ align:start position:0%
+question are the ideal structure how
+many health workers
+
+ align:start position:0%
+many health workers
+ 
+
+ align:start position:0%
+many health workers
+um to nurses to doctors how do they fit
+
+ align:start position:0%
+um to nurses to doctors how do they fit
+ 
+
+ align:start position:0%
+um to nurses to doctors how do they fit
+in with a larger community of people
+
+ align:start position:0%
+in with a larger community of people
+ 
+
+ align:start position:0%
+in with a larger community of people
+living in HIV women's groups Community
+
+ align:start position:0%
+living in HIV women's groups Community
+ 
+
+ align:start position:0%
+living in HIV women's groups Community
+groups how they fit in with the ministry
+
+ align:start position:0%
+groups how they fit in with the ministry
+ 
+
+ align:start position:0%
+groups how they fit in with the ministry
+it's actually there's quite a number of
+
+ align:start position:0%
+it's actually there's quite a number of
+ 
+
+ align:start position:0%
+it's actually there's quite a number of
+us in Rwanda working on this project and
+
+ align:start position:0%
+us in Rwanda working on this project and
+ 
+
+ align:start position:0%
+us in Rwanda working on this project and
+Michael Rich my wife plenty of people
+
+ align:start position:0%
+Michael Rich my wife plenty of people
+ 
+
+ align:start position:0%
+Michael Rich my wife plenty of people
+were working really on this question
+
+ align:start position:0%
+were working really on this question
+ 
+
+ align:start position:0%
+were working really on this question
+what's this what should it look like
+
+ align:start position:0%
+what's this what should it look like
+ 
+
+ align:start position:0%
+what's this what should it look like
+I think that that's going to lead to a
+
+ align:start position:0%
+I think that that's going to lead to a
+ 
+
+ align:start position:0%
+I think that that's going to lead to a
+great efflorescence of you know
+
+ align:start position:0%
+great efflorescence of you know
+ 
+
+ align:start position:0%
+great efflorescence of you know
+knowledge and and its review and
+
+ align:start position:0%
+knowledge and and its review and
+ 
+
+ align:start position:0%
+knowledge and and its review and
+publication but I can connect you to all
+
+ align:start position:0%
+publication but I can connect you to all
+ 
+
+ align:start position:0%
+publication but I can connect you to all
+that right now and they've already
+
+ align:start position:0%
+that right now and they've already
+ 
+
+ align:start position:0%
+that right now and they've already
+started I think to publish them stuff
+
+ align:start position:0%
+started I think to publish them stuff
+ 
+
+ align:start position:0%
+started I think to publish them stuff
+from the door stoop Grant I don't know
+
+ align:start position:0%
+from the door stoop Grant I don't know
+ 
+
+ align:start position:0%
+from the door stoop Grant I don't know
+if that's true
+
+ align:start position:0%
+if that's true
+ 
+
+ align:start position:0%
+if that's true
+um but as far as third party payers in
+
+ align:start position:0%
+um but as far as third party payers in
+ 
+
+ align:start position:0%
+um but as far as third party payers in
+the complexities that we've seen in
+
+ align:start position:0%
+the complexities that we've seen in
+ 
+
+ align:start position:0%
+the complexities that we've seen in
+resource non-poor settings non-resource
+
+ align:start position:0%
+resource non-poor settings non-resource
+ 
+
+ align:start position:0%
+resource non-poor settings non-resource
+course settings sorry we're starting to
+
+ align:start position:0%
+course settings sorry we're starting to
+ 
+
+ align:start position:0%
+course settings sorry we're starting to
+see that in Haiti too I mean that that
+
+ align:start position:0%
+see that in Haiti too I mean that that
+ 
+
+ align:start position:0%
+see that in Haiti too I mean that that
+challenge for example this new hospital
+
+ align:start position:0%
+challenge for example this new hospital
+ 
+
+ align:start position:0%
+challenge for example this new hospital
+we're building looking at Dr Pierre
+
+ align:start position:0%
+we're building looking at Dr Pierre
+ 
+
+ align:start position:0%
+we're building looking at Dr Pierre
+we're going to suddenly for the first
+
+ align:start position:0%
+we're going to suddenly for the first
+ 
+
+ align:start position:0%
+we're going to suddenly for the first
+time in our history the 200 000 insured
+
+ align:start position:0%
+time in our history the 200 000 insured
+ 
+
+ align:start position:0%
+time in our history the 200 000 insured
+families in Haiti out of the 11 million
+
+ align:start position:0%
+families in Haiti out of the 11 million
+ 
+
+ align:start position:0%
+families in Haiti out of the 11 million
+uninsured are going to be coming to us
+
+ align:start position:0%
+uninsured are going to be coming to us
+ 
+
+ align:start position:0%
+uninsured are going to be coming to us
+with actually the ability to reimburse
+
+ align:start position:0%
+with actually the ability to reimburse
+ 
+
+ align:start position:0%
+with actually the ability to reimburse
+us I mean it's going to be a novel
+
+ align:start position:0%
+us I mean it's going to be a novel
+ 
+
+ align:start position:0%
+us I mean it's going to be a novel
+experience let me tell you so we're also
+
+ align:start position:0%
+experience let me tell you so we're also
+ 
+
+ align:start position:0%
+experience let me tell you so we're also
+going to have to take on that kind of
+
+ align:start position:0%
+going to have to take on that kind of
+ 
+
+ align:start position:0%
+going to have to take on that kind of
+complexity to moving forward in Rwanda
+
+ align:start position:0%
+complexity to moving forward in Rwanda
+ 
+
+ align:start position:0%
+complexity to moving forward in Rwanda
+that was sort of pushed on us with a
+
+ align:start position:0%
+that was sort of pushed on us with a
+ 
+
+ align:start position:0%
+that was sort of pushed on us with a
+mutual system and insurance system there
+
+ align:start position:0%
+mutual system and insurance system there
+ 
+
+ align:start position:0%
+mutual system and insurance system there
+was also community-based but I think we
+
+ align:start position:0%
+was also community-based but I think we
+ 
+
+ align:start position:0%
+was also community-based but I think we
+have to we're going to have to get
+
+ align:start position:0%
+have to we're going to have to get
+ 
+
+ align:start position:0%
+have to we're going to have to get
+stronger at this in those settings with
+
+ align:start position:0%
+stronger at this in those settings with
+ 
+
+ align:start position:0%
+stronger at this in those settings with
+there aren't many formal structures like
+
+ align:start position:0%
+there aren't many formal structures like
+ 
+
+ align:start position:0%
+there aren't many formal structures like
+that and then see if you can apply
+
+ align:start position:0%
+that and then see if you can apply
+ 
+
+ align:start position:0%
+that and then see if you can apply
+lessons here or from here and going
+
+ align:start position:0%
+lessons here or from here and going
+ 
+
+ align:start position:0%
+lessons here or from here and going
+forward well anyway thank you all very
+
+ align:start position:0%
+forward well anyway thank you all very
+ 
+
+ align:start position:0%
+forward well anyway thank you all very
+much and I'll Stick Around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay thanks
\ No newline at end of file
diff --git a/OT04cEdpK-M.txt b/OT04cEdpK-M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1e107d107c2a1e5d5669f267f29a6312c3fcaf1b
--- /dev/null
+++ b/OT04cEdpK-M.txt
@@ -0,0 +1,8519 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+hello welcome to the first lecture in
+
+ align:start position:0%
+hello welcome to the first lecture in
+ 
+
+ align:start position:0%
+hello welcome to the first lecture in
+the last topic of this class so we we'll
+
+ align:start position:0%
+the last topic of this class so we we'll
+ 
+
+ align:start position:0%
+the last topic of this class so we we'll
+spend this lecture and the next lecture
+
+ align:start position:0%
+spend this lecture and the next lecture
+ 
+
+ align:start position:0%
+spend this lecture and the next lecture
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+modulation modulation like sampling is
+
+ align:start position:0%
+modulation modulation like sampling is
+ 
+
+ align:start position:0%
+modulation modulation like sampling is
+an excellent illustration of the power
+
+ align:start position:0%
+an excellent illustration of the power
+ 
+
+ align:start position:0%
+an excellent illustration of the power
+of thinking about signals in terms of
+
+ align:start position:0%
+of thinking about signals in terms of
+ 
+
+ align:start position:0%
+of thinking about signals in terms of
+their 4A transforms we'll see just like
+
+ align:start position:0%
+their 4A transforms we'll see just like
+ 
+
+ align:start position:0%
+their 4A transforms we'll see just like
+we saw in sampling that a problem that
+
+ align:start position:0%
+we saw in sampling that a problem that
+ 
+
+ align:start position:0%
+we saw in sampling that a problem that
+was potentially very complicated to
+
+ align:start position:0%
+was potentially very complicated to
+ 
+
+ align:start position:0%
+was potentially very complicated to
+understand sampling was very easy when
+
+ align:start position:0%
+understand sampling was very easy when
+ 
+
+ align:start position:0%
+understand sampling was very easy when
+you thought about it in the 48 domain
+
+ align:start position:0%
+you thought about it in the 48 domain
+ 
+
+ align:start position:0%
+you thought about it in the 48 domain
+and precisely the same thing happens
+
+ align:start position:0%
+and precisely the same thing happens
+ 
+
+ align:start position:0%
+and precisely the same thing happens
+with modulation which is precisely the
+
+ align:start position:0%
+with modulation which is precisely the
+ 
+
+ align:start position:0%
+with modulation which is precisely the
+reason we're talking about it now
+
+ align:start position:0%
+reason we're talking about it now
+ 
+
+ align:start position:0%
+reason we're talking about it now
+so I'll talk about modulation in the
+
+ align:start position:0%
+so I'll talk about modulation in the
+ 
+
+ align:start position:0%
+so I'll talk about modulation in the
+context of a communication
+
+ align:start position:0%
+context of a communication
+ 
+
+ align:start position:0%
+context of a communication
+system that's just for convenience in
+
+ align:start position:0%
+system that's just for convenience in
+ 
+
+ align:start position:0%
+system that's just for convenience in
+fact modulation is used in lots of other
+
+ align:start position:0%
+fact modulation is used in lots of other
+ 
+
+ align:start position:0%
+fact modulation is used in lots of other
+places in fact next time in the next
+
+ align:start position:0%
+places in fact next time in the next
+ 
+
+ align:start position:0%
+places in fact next time in the next
+lecture I'll show you an application of
+
+ align:start position:0%
+lecture I'll show you an application of
+ 
+
+ align:start position:0%
+lecture I'll show you an application of
+modulation from my research group where
+
+ align:start position:0%
+modulation from my research group where
+ 
+
+ align:start position:0%
+modulation from my research group where
+we use modulation to improve the
+
+ align:start position:0%
+we use modulation to improve the
+ 
+
+ align:start position:0%
+we use modulation to improve the
+resolution of an optical
+
+ align:start position:0%
+resolution of an optical
+ 
+
+ align:start position:0%
+resolution of an optical
+microscope nothing whatever to do with
+
+ align:start position:0%
+microscope nothing whatever to do with
+ 
+
+ align:start position:0%
+microscope nothing whatever to do with
+Communications but it's still the
+
+ align:start position:0%
+Communications but it's still the
+ 
+
+ align:start position:0%
+Communications but it's still the
+optical microscope the enhancement to
+
+ align:start position:0%
+optical microscope the enhancement to
+ 
+
+ align:start position:0%
+optical microscope the enhancement to
+resolution that we U achieve is directly
+
+ align:start position:0%
+resolution that we U achieve is directly
+ 
+
+ align:start position:0%
+resolution that we U achieve is directly
+based on the principles that I start to
+
+ align:start position:0%
+based on the principles that I start to
+ 
+
+ align:start position:0%
+based on the principles that I start to
+describe
+
+ align:start position:0%
+describe
+ 
+
+ align:start position:0%
+describe
+today so I'll talk about uh modulation
+
+ align:start position:0%
+today so I'll talk about uh modulation
+ 
+
+ align:start position:0%
+today so I'll talk about uh modulation
+today in the context of communications
+
+ align:start position:0%
+today in the context of communications
+ 
+
+ align:start position:0%
+today in the context of communications
+probably the most convenient easiest to
+
+ align:start position:0%
+probably the most convenient easiest to
+ 
+
+ align:start position:0%
+probably the most convenient easiest to
+think about communication system to all
+
+ align:start position:0%
+think about communication system to all
+ 
+
+ align:start position:0%
+think about communication system to all
+of us being humans is speech okay that
+
+ align:start position:0%
+of us being humans is speech okay that
+ 
+
+ align:start position:0%
+of us being humans is speech okay that
+we use speech for communication all the
+
+ align:start position:0%
+we use speech for communication all the
+ 
+
+ align:start position:0%
+we use speech for communication all the
+time it's very easy to think about how
+
+ align:start position:0%
+time it's very easy to think about how
+ 
+
+ align:start position:0%
+time it's very easy to think about how
+communication works as a how speech
+
+ align:start position:0%
+communication works as a how speech
+ 
+
+ align:start position:0%
+communication works as a how speech
+works as a communication medium somebody
+
+ align:start position:0%
+works as a communication medium somebody
+ 
+
+ align:start position:0%
+works as a communication medium somebody
+talks somebody listen
+
+ align:start position:0%
+talks somebody listen
+ 
+
+ align:start position:0%
+talks somebody listen
+one of the first ways of thinking about
+
+ align:start position:0%
+one of the first ways of thinking about
+ 
+
+ align:start position:0%
+one of the first ways of thinking about
+it as a um technological uh feat was the
+
+ align:start position:0%
+it as a um technological uh feat was the
+ 
+
+ align:start position:0%
+it as a um technological uh feat was the
+telephone the idea being that you
+
+ align:start position:0%
+telephone the idea being that you
+ 
+
+ align:start position:0%
+telephone the idea being that you
+convert the sound that I'm emitting when
+
+ align:start position:0%
+convert the sound that I'm emitting when
+ 
+
+ align:start position:0%
+convert the sound that I'm emitting when
+I'm speaking by a microphone into an
+
+ align:start position:0%
+I'm speaking by a microphone into an
+ 
+
+ align:start position:0%
+I'm speaking by a microphone into an
+electrical representation that gets shot
+
+ align:start position:0%
+electrical representation that gets shot
+ 
+
+ align:start position:0%
+electrical representation that gets shot
+down a
+
+ align:start position:0%
+down a
+ 
+
+ align:start position:0%
+down a
+wire then at the other end you take the
+
+ align:start position:0%
+wire then at the other end you take the
+ 
+
+ align:start position:0%
+wire then at the other end you take the
+electrical P the electrical signal
+
+ align:start position:0%
+electrical P the electrical signal
+ 
+
+ align:start position:0%
+electrical P the electrical signal
+that's coming down the wire and turn it
+
+ align:start position:0%
+that's coming down the wire and turn it
+ 
+
+ align:start position:0%
+that's coming down the wire and turn it
+back into a sound that's the principle
+
+ align:start position:0%
+back into a sound that's the principle
+ 
+
+ align:start position:0%
+back into a sound that's the principle
+of um of a telephone works very well
+
+ align:start position:0%
+of um of a telephone works very well
+ 
+
+ align:start position:0%
+of um of a telephone works very well
+modulation comes up when we start to
+
+ align:start position:0%
+modulation comes up when we start to
+ 
+
+ align:start position:0%
+modulation comes up when we start to
+think about how would we um generalize
+
+ align:start position:0%
+think about how would we um generalize
+ 
+
+ align:start position:0%
+think about how would we um generalize
+this notion for wireless communication
+
+ align:start position:0%
+this notion for wireless communication
+ 
+
+ align:start position:0%
+this notion for wireless communication
+in particular if we do cell phone
+
+ align:start position:0%
+in particular if we do cell phone
+ 
+
+ align:start position:0%
+in particular if we do cell phone
+communication cell phones
+
+ align:start position:0%
+communication cell phones
+ 
+
+ align:start position:0%
+communication cell phones
+transmit the signal that is picked up
+
+ align:start position:0%
+transmit the signal that is picked up
+ 
+
+ align:start position:0%
+transmit the signal that is picked up
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+microphone that signal gets converted
+
+ align:start position:0%
+microphone that signal gets converted
+ 
+
+ align:start position:0%
+microphone that signal gets converted
+into electromagnetic signals That's the
+
+ align:start position:0%
+into electromagnetic signals That's the
+ 
+
+ align:start position:0%
+into electromagnetic signals That's the
+basis by which cell phones communicate
+
+ align:start position:0%
+basis by which cell phones communicate
+ 
+
+ align:start position:0%
+basis by which cell phones communicate
+with the cell tower the towers May
+
+ align:start position:0%
+with the cell tower the towers May
+ 
+
+ align:start position:0%
+with the cell tower the towers May
+communicate with other Towers via a lot
+
+ align:start position:0%
+communicate with other Towers via a lot
+ 
+
+ align:start position:0%
+communicate with other Towers via a lot
+of different kinds of Technologies I'm
+
+ align:start position:0%
+of different kinds of Technologies I'm
+ 
+
+ align:start position:0%
+of different kinds of Technologies I'm
+ignoring those for now but the
+
+ align:start position:0%
+ignoring those for now but the
+ 
+
+ align:start position:0%
+ignoring those for now but the
+communication between the phone and the
+
+ align:start position:0%
+communication between the phone and the
+ 
+
+ align:start position:0%
+communication between the phone and the
+tower is via electromagnetic
+
+ align:start position:0%
+tower is via electromagnetic
+ 
+
+ align:start position:0%
+tower is via electromagnetic
+waves and there's an interesting thing
+
+ align:start position:0%
+waves and there's an interesting thing
+ 
+
+ align:start position:0%
+waves and there's an interesting thing
+that happens when you try to recode the
+
+ align:start position:0%
+that happens when you try to recode the
+ 
+
+ align:start position:0%
+that happens when you try to recode the
+signal that would have been perfectly
+
+ align:start position:0%
+signal that would have been perfectly
+ 
+
+ align:start position:0%
+signal that would have been perfectly
+happy running down the copper wire when
+
+ align:start position:0%
+happy running down the copper wire when
+ 
+
+ align:start position:0%
+happy running down the copper wire when
+you try to recode that signal into an
+
+ align:start position:0%
+you try to recode that signal into an
+ 
+
+ align:start position:0%
+you try to recode that signal into an
+electromagnetic wave and that has to do
+
+ align:start position:0%
+electromagnetic wave and that has to do
+ 
+
+ align:start position:0%
+electromagnetic wave and that has to do
+with basic physics of electromagnetics
+
+ align:start position:0%
+with basic physics of electromagnetics
+ 
+
+ align:start position:0%
+with basic physics of electromagnetics
+waves which I'm sure you all know and so
+
+ align:start position:0%
+waves which I'm sure you all know and so
+ 
+
+ align:start position:0%
+waves which I'm sure you all know and so
+uh I'll just remind you of one simple
+
+ align:start position:0%
+uh I'll just remind you of one simple
+ 
+
+ align:start position:0%
+uh I'll just remind you of one simple
+idea so for efficient transmission from
+
+ align:start position:0%
+idea so for efficient transmission from
+ 
+
+ align:start position:0%
+idea so for efficient transmission from
+an electrical representation to an
+
+ align:start position:0%
+an electrical representation to an
+ 
+
+ align:start position:0%
+an electrical representation to an
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+wave first off that that U transduction
+
+ align:start position:0%
+wave first off that that U transduction
+ 
+
+ align:start position:0%
+wave first off that that U transduction
+is mediated by something we call an
+
+ align:start position:0%
+is mediated by something we call an
+ 
+
+ align:start position:0%
+is mediated by something we call an
+antenna antennas will take an electrical
+
+ align:start position:0%
+antenna antennas will take an electrical
+ 
+
+ align:start position:0%
+antenna antennas will take an electrical
+signal and convert it into an
+
+ align:start position:0%
+signal and convert it into an
+ 
+
+ align:start position:0%
+signal and convert it into an
+electromagnetic wave and vice
+
+ align:start position:0%
+electromagnetic wave and vice
+ 
+
+ align:start position:0%
+electromagnetic wave and vice
+versa but the efficiency with which an
+
+ align:start position:0%
+versa but the efficiency with which an
+ 
+
+ align:start position:0%
+versa but the efficiency with which an
+antenna
+
+ align:start position:0%
+antenna
+ 
+
+ align:start position:0%
+antenna
+works has to do uh among other things
+
+ align:start position:0%
+works has to do uh among other things
+ 
+
+ align:start position:0%
+works has to do uh among other things
+with its
+
+ align:start position:0%
+with its
+ 
+
+ align:start position:0%
+with its
+size it's very difficult by which I mean
+
+ align:start position:0%
+size it's very difficult by which I mean
+ 
+
+ align:start position:0%
+size it's very difficult by which I mean
+it takes lots of
+
+ align:start position:0%
+it takes lots of
+ 
+
+ align:start position:0%
+it takes lots of
+power to transmit a signal to transform
+
+ align:start position:0%
+power to transmit a signal to transform
+ 
+
+ align:start position:0%
+power to transmit a signal to transform
+a signal from an electrical
+
+ align:start position:0%
+a signal from an electrical
+ 
+
+ align:start position:0%
+a signal from an electrical
+representation to an enm representation
+
+ align:start position:0%
+representation to an enm representation
+ 
+
+ align:start position:0%
+representation to an enm representation
+if the antenna is smaller is
+
+ align:start position:0%
+if the antenna is smaller is
+ 
+
+ align:start position:0%
+if the antenna is smaller is
+significantly smaller than the
+
+ align:start position:0%
+significantly smaller than the
+ 
+
+ align:start position:0%
+significantly smaller than the
+wavelength of
+
+ align:start position:0%
+wavelength of
+ 
+
+ align:start position:0%
+wavelength of
+Interest okay so um it's not that you
+
+ align:start position:0%
+Interest okay so um it's not that you
+ 
+
+ align:start position:0%
+Interest okay so um it's not that you
+can't do it is that it takes lots of
+
+ align:start position:0%
+can't do it is that it takes lots of
+ 
+
+ align:start position:0%
+can't do it is that it takes lots of
+power so if you don't want to burn a lot
+
+ align:start position:0%
+power so if you don't want to burn a lot
+ 
+
+ align:start position:0%
+power so if you don't want to burn a lot
+of power do doing that transformation
+
+ align:start position:0%
+of power do doing that transformation
+ 
+
+ align:start position:0%
+of power do doing that transformation
+then you need to make an antenna that's
+
+ align:start position:0%
+then you need to make an antenna that's
+ 
+
+ align:start position:0%
+then you need to make an antenna that's
+roughly the size of the wavelength that
+
+ align:start position:0%
+roughly the size of the wavelength that
+ 
+
+ align:start position:0%
+roughly the size of the wavelength that
+you're trying to to uh transmit as an
+
+ align:start position:0%
+you're trying to to uh transmit as an
+ 
+
+ align:start position:0%
+you're trying to to uh transmit as an
+electromagnetic wave okay so if we were
+
+ align:start position:0%
+electromagnetic wave okay so if we were
+ 
+
+ align:start position:0%
+electromagnetic wave okay so if we were
+thinking about this kind of a scheme for
+
+ align:start position:0%
+thinking about this kind of a scheme for
+ 
+
+ align:start position:0%
+thinking about this kind of a scheme for
+the communication of voice we've talked
+
+ align:start position:0%
+the communication of voice we've talked
+ 
+
+ align:start position:0%
+the communication of voice we've talked
+about voice many times telephone quality
+
+ align:start position:0%
+about voice many times telephone quality
+ 
+
+ align:start position:0%
+about voice many times telephone quality
+voice is usually defined to be
+
+ align:start position:0%
+voice is usually defined to be
+ 
+
+ align:start position:0%
+voice is usually defined to be
+frequencies between about 200 htz and
+
+ align:start position:0%
+frequencies between about 200 htz and
+ 
+
+ align:start position:0%
+frequencies between about 200 htz and
+about 3 khz if I had a signal that was
+
+ align:start position:0%
+about 3 khz if I had a signal that was
+ 
+
+ align:start position:0%
+about 3 khz if I had a signal that was
+composed of those kinds of frequencies
+
+ align:start position:0%
+composed of those kinds of frequencies
+ 
+
+ align:start position:0%
+composed of those kinds of frequencies
+how big should I make the
+
+ align:start position:0%
+how big should I make the
+ 
+
+ align:start position:0%
+how big should I make the
+antenna to get efficient coupling
+
+ align:start position:0%
+antenna to get efficient coupling
+ 
+
+ align:start position:0%
+antenna to get efficient coupling
+between the electrical representation in
+
+ align:start position:0%
+between the electrical representation in
+ 
+
+ align:start position:0%
+between the electrical representation in
+the cell phone and the electromagnetic
+
+ align:start position:0%
+the cell phone and the electromagnetic
+ 
+
+ align:start position:0%
+the cell phone and the electromagnetic
+wave that the cell phone wants to launch
+
+ align:start position:0%
+wave that the cell phone wants to launch
+ 
+
+ align:start position:0%
+wave that the cell phone wants to launch
+to get to the cell tower so look at your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighbor okay that involves turning your
+
+ align:start position:0%
+neighbor okay that involves turning your
+ 
+
+ align:start position:0%
+neighbor okay that involves turning your
+head say hello and figure out how long
+
+ align:start position:0%
+head say hello and figure out how long
+ 
+
+ align:start position:0%
+head say hello and figure out how long
+should the antenna be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay does everybody have an answer
+
+ align:start position:0%
+okay does everybody have an answer
+ 
+
+ align:start position:0%
+okay does everybody have an answer
+raise your hand if you don't have an
+
+ align:start position:0%
+raise your hand if you don't have an
+ 
+
+ align:start position:0%
+raise your hand if you don't have an
+answer H how do you like that for a
+
+ align:start position:0%
+answer H how do you like that for a
+ 
+
+ align:start position:0%
+answer H how do you like that for a
+switch of a raise your hand if you don't
+
+ align:start position:0%
+switch of a raise your hand if you don't
+ 
+
+ align:start position:0%
+switch of a raise your hand if you don't
+have an answer ah you all have answers
+
+ align:start position:0%
+have an answer ah you all have answers
+ 
+
+ align:start position:0%
+have an answer ah you all have answers
+okay so what's how big should the Anna
+
+ align:start position:0%
+okay so what's how big should the Anna
+ 
+
+ align:start position:0%
+okay so what's how big should the Anna
+be antenna be one two three four or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+answer okay very good so the answer is
+
+ align:start position:0%
+answer okay very good so the answer is
+ 
+
+ align:start position:0%
+answer okay very good so the answer is
+really big right so uh you think about
+
+ align:start position:0%
+really big right so uh you think about
+ 
+
+ align:start position:0%
+really big right so uh you think about
+um the relationship between
+
+ align:start position:0%
+um the relationship between
+ 
+
+ align:start position:0%
+um the relationship between
+wavelength and distance so you can think
+
+ align:start position:0%
+wavelength and distance so you can think
+ 
+
+ align:start position:0%
+wavelength and distance so you can think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um the relationship is given by speed
+
+ align:start position:0%
+um the relationship is given by speed
+ 
+
+ align:start position:0%
+um the relationship is given by speed
+the speed of a wave is the wavelength
+
+ align:start position:0%
+the speed of a wave is the wavelength
+ 
+
+ align:start position:0%
+the speed of a wave is the wavelength
+how long it goes per
+
+ align:start position:0%
+how long it goes per
+ 
+
+ align:start position:0%
+how long it goes per
+cycle times the number of cycles per
+
+ align:start position:0%
+cycle times the number of cycles per
+ 
+
+ align:start position:0%
+cycle times the number of cycles per
+second F so that LE so you can solve
+
+ align:start position:0%
+second F so that LE so you can solve
+ 
+
+ align:start position:0%
+second F so that LE so you can solve
+that expression to find out the
+
+ align:start position:0%
+that expression to find out the
+ 
+
+ align:start position:0%
+that expression to find out the
+wavelength in terms of the speed which
+
+ align:start position:0%
+wavelength in terms of the speed which
+ 
+
+ align:start position:0%
+wavelength in terms of the speed which
+for an electromagnetic wave is the speed
+
+ align:start position:0%
+for an electromagnetic wave is the speed
+ 
+
+ align:start position:0%
+for an electromagnetic wave is the speed
+of of light uh 3 * 10 e
+
+ align:start position:0%
+of of light uh 3 * 10 e
+ 
+
+ align:start position:0%
+of of light uh 3 * 10 e
+m/s the hardest one to launch is the
+
+ align:start position:0%
+m/s the hardest one to launch is the
+ 
+
+ align:start position:0%
+m/s the hardest one to launch is the
+lowest
+
+ align:start position:0%
+lowest
+ 
+
+ align:start position:0%
+lowest
+frequency right that will take the
+
+ align:start position:0%
+frequency right that will take the
+ 
+
+ align:start position:0%
+frequency right that will take the
+biggest antenna so the lowest frequency
+
+ align:start position:0%
+biggest antenna so the lowest frequency
+ 
+
+ align:start position:0%
+biggest antenna so the lowest frequency
+in teleph in um in telephone quality
+
+ align:start position:0%
+in teleph in um in telephone quality
+ 
+
+ align:start position:0%
+in teleph in um in telephone quality
+speech is 200 Hertz so we get about uh
+
+ align:start position:0%
+speech is 200 Hertz so we get about uh
+ 
+
+ align:start position:0%
+speech is 200 Hertz so we get about uh
+1,500
+
+ align:start position:0%
+1,500
+ 
+
+ align:start position:0%
+1,500
+kilometers okay kind of big okay kind of
+
+ align:start position:0%
+kilometers okay kind of big okay kind of
+ 
+
+ align:start position:0%
+kilometers okay kind of big okay kind of
+useless right if you were thinking about
+
+ align:start position:0%
+useless right if you were thinking about
+ 
+
+ align:start position:0%
+useless right if you were thinking about
+trying to make cellular communication
+
+ align:start position:0%
+trying to make cellular communication
+ 
+
+ align:start position:0%
+trying to make cellular communication
+and your antenna actually had to
+
+ align:start position:0%
+and your antenna actually had to
+ 
+
+ align:start position:0%
+and your antenna actually had to
+be500 kilometers right that just isn't
+
+ align:start position:0%
+be500 kilometers right that just isn't
+ 
+
+ align:start position:0%
+be500 kilometers right that just isn't
+going to work right okay so what do we
+
+ align:start position:0%
+going to work right okay so what do we
+ 
+
+ align:start position:0%
+going to work right okay so what do we
+do we obviously don't do this right
+
+ align:start position:0%
+do we obviously don't do this right
+ 
+
+ align:start position:0%
+do we obviously don't do this right
+uh so the answer is that you would need
+
+ align:start position:0%
+uh so the answer is that you would need
+ 
+
+ align:start position:0%
+uh so the answer is that you would need
+an antenna hundreds of miles in
+
+ align:start position:0%
+an antenna hundreds of miles in
+ 
+
+ align:start position:0%
+an antenna hundreds of miles in
+length so what frequency should you be
+
+ align:start position:0%
+length so what frequency should you be
+ 
+
+ align:start position:0%
+length so what frequency should you be
+using if you wanted to build a phone
+
+ align:start position:0%
+using if you wanted to build a phone
+ 
+
+ align:start position:0%
+using if you wanted to build a phone
+that kind of fit in your hand kind of 10
+
+ align:start position:0%
+that kind of fit in your hand kind of 10
+ 
+
+ align:start position:0%
+that kind of fit in your hand kind of 10
+centimeters or
+
+ align:start position:0%
+centimeters or
+ 
+
+ align:start position:0%
+centimeters or
+so what would be the frequency what in
+
+ align:start position:0%
+so what would be the frequency what in
+ 
+
+ align:start position:0%
+so what would be the frequency what in
+what would be the interesting range of
+
+ align:start position:0%
+what would be the interesting range of
+ 
+
+ align:start position:0%
+what would be the interesting range of
+frequencies that you would want to use
+
+ align:start position:0%
+frequencies that you would want to use
+ 
+
+ align:start position:0%
+frequencies that you would want to use
+for such a device
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answer
+
+ align:start position:0%
+and the answer
+ 
+
+ align:start position:0%
+and the answer
+is of course so the answer is you go to
+
+ align:start position:0%
+is of course so the answer is you go to
+ 
+
+ align:start position:0%
+is of course so the answer is you go to
+the bottom one it's bigger than a
+
+ align:start position:0%
+the bottom one it's bigger than a
+ 
+
+ align:start position:0%
+the bottom one it's bigger than a
+gigahertz and it's just running the the
+
+ align:start position:0%
+gigahertz and it's just running the the
+ 
+
+ align:start position:0%
+gigahertz and it's just running the the
+same expression in the other direction
+
+ align:start position:0%
+same expression in the other direction
+ 
+
+ align:start position:0%
+same expression in the other direction
+so you think about um uh the frequency
+
+ align:start position:0%
+so you think about um uh the frequency
+ 
+
+ align:start position:0%
+so you think about um uh the frequency
+that you would like would be the speed
+
+ align:start position:0%
+that you would like would be the speed
+ 
+
+ align:start position:0%
+that you would like would be the speed
+of light divided by the wavelength if
+
+ align:start position:0%
+of light divided by the wavelength if
+ 
+
+ align:start position:0%
+of light divided by the wavelength if
+you wanted the wavelength to be 10 cm
+
+ align:start position:0%
+you wanted the wavelength to be 10 cm
+ 
+
+ align:start position:0%
+you wanted the wavelength to be 10 cm
+then you would end up with a a frequency
+
+ align:start position:0%
+then you would end up with a a frequency
+ 
+
+ align:start position:0%
+then you would end up with a a frequency
+on the order of gigahertz and it
+
+ align:start position:0%
+on the order of gigahertz and it
+ 
+
+ align:start position:0%
+on the order of gigahertz and it
+shouldn't come as a surprise to you then
+
+ align:start position:0%
+shouldn't come as a surprise to you then
+ 
+
+ align:start position:0%
+shouldn't come as a surprise to you then
+that that's what we use in C
+
+ align:start position:0%
+that that's what we use in C
+ 
+
+ align:start position:0%
+that that's what we use in C
+Communications so a modern cell phone
+
+ align:start position:0%
+Communications so a modern cell phone
+ 
+
+ align:start position:0%
+Communications so a modern cell phone
+uses 2.1 uh Mega uh
+
+ align:start position:0%
+uses 2.1 uh Mega uh
+ 
+
+ align:start position:0%
+uses 2.1 uh Mega uh
+gahz so uh the point is that what when
+
+ align:start position:0%
+gahz so uh the point is that what when
+ 
+
+ align:start position:0%
+gahz so uh the point is that what when
+we're thinking
+
+ align:start position:0%
+we're thinking
+ 
+
+ align:start position:0%
+we're thinking
+about uh how we would like to use the
+
+ align:start position:0%
+about uh how we would like to use the
+ 
+
+ align:start position:0%
+about uh how we would like to use the
+electromagnetic spectrum for
+
+ align:start position:0%
+electromagnetic spectrum for
+ 
+
+ align:start position:0%
+electromagnetic spectrum for
+communications tasks that spectrum is
+
+ align:start position:0%
+communications tasks that spectrum is
+ 
+
+ align:start position:0%
+communications tasks that spectrum is
+not necessarily well matched to the
+
+ align:start position:0%
+not necessarily well matched to the
+ 
+
+ align:start position:0%
+not necessarily well matched to the
+communications problem of interest you
+
+ align:start position:0%
+communications problem of interest you
+ 
+
+ align:start position:0%
+communications problem of interest you
+might think that that cellular example
+
+ align:start position:0%
+might think that that cellular example
+ 
+
+ align:start position:0%
+might think that that cellular example
+is an exception in fact that's the rule
+
+ align:start position:0%
+is an exception in fact that's the rule
+ 
+
+ align:start position:0%
+is an exception in fact that's the rule
+if you try to have a signal of Interest
+
+ align:start position:0%
+if you try to have a signal of Interest
+ 
+
+ align:start position:0%
+if you try to have a signal of Interest
+transmitted over a medium or stored on
+
+ align:start position:0%
+transmitted over a medium or stored on
+ 
+
+ align:start position:0%
+transmitted over a medium or stored on
+some sort of a medium it is generally
+
+ align:start position:0%
+some sort of a medium it is generally
+ 
+
+ align:start position:0%
+some sort of a medium it is generally
+the case that there's a matching problem
+
+ align:start position:0%
+the case that there's a matching problem
+ 
+
+ align:start position:0%
+the case that there's a matching problem
+that the characteristics of the medium
+
+ align:start position:0%
+that the characteristics of the medium
+ 
+
+ align:start position:0%
+that the characteristics of the medium
+don't match the characteristics of the
+
+ align:start position:0%
+don't match the characteristics of the
+ 
+
+ align:start position:0%
+don't match the characteristics of the
+message and so uh part of communications
+
+ align:start position:0%
+message and so uh part of communications
+ 
+
+ align:start position:0%
+message and so uh part of communications
+engineering is trying to come up with a
+
+ align:start position:0%
+engineering is trying to come up with a
+ 
+
+ align:start position:0%
+engineering is trying to come up with a
+coding
+
+ align:start position:0%
+coding
+ 
+
+ align:start position:0%
+coding
+scheme that matches the mess the
+
+ align:start position:0%
+scheme that matches the mess the
+ 
+
+ align:start position:0%
+scheme that matches the mess the
+characteristics of the message to the
+
+ align:start position:0%
+characteristics of the message to the
+ 
+
+ align:start position:0%
+characteristics of the message to the
+characteristics of the
+
+ align:start position:0%
+characteristics of the
+ 
+
+ align:start position:0%
+characteristics of the
+medium um and so what I'm going to do
+
+ align:start position:0%
+medium um and so what I'm going to do
+ 
+
+ align:start position:0%
+medium um and so what I'm going to do
+today is talk about uh some matching
+
+ align:start position:0%
+today is talk about uh some matching
+ 
+
+ align:start position:0%
+today is talk about uh some matching
+schemes based on
+
+ align:start position:0%
+schemes based on
+ 
+
+ align:start position:0%
+schemes based on
+modulation so we just saw that if we
+
+ align:start position:0%
+modulation so we just saw that if we
+ 
+
+ align:start position:0%
+modulation so we just saw that if we
+wanted to do cellular communication of
+
+ align:start position:0%
+wanted to do cellular communication of
+ 
+
+ align:start position:0%
+wanted to do cellular communication of
+voice voice might have a spectrum
+
+ align:start position:0%
+voice voice might have a spectrum
+ 
+
+ align:start position:0%
+voice voice might have a spectrum
+represented by by uh this magnitude
+
+ align:start position:0%
+represented by by uh this magnitude
+ 
+
+ align:start position:0%
+represented by by uh this magnitude
+function X where the bandwidth is on the
+
+ align:start position:0%
+function X where the bandwidth is on the
+ 
+
+ align:start position:0%
+function X where the bandwidth is on the
+order of a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kilohertz but we might want to transmit
+
+ align:start position:0%
+kilohertz but we might want to transmit
+ 
+
+ align:start position:0%
+kilohertz but we might want to transmit
+a signal that has the same information
+
+ align:start position:0%
+a signal that has the same information
+ 
+
+ align:start position:0%
+a signal that has the same information
+however we would like the frequencies to
+
+ align:start position:0%
+however we would like the frequencies to
+ 
+
+ align:start position:0%
+however we would like the frequencies to
+be up around 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gigahertz which of these coding schemes
+
+ align:start position:0%
+gigahertz which of these coding schemes
+ 
+
+ align:start position:0%
+gigahertz which of these coding schemes
+y as a function of
+
+ align:start position:0%
+y as a function of
+ 
+
+ align:start position:0%
+y as a function of
+X achieves this transformation take the
+
+ align:start position:0%
+X achieves this transformation take the
+ 
+
+ align:start position:0%
+X achieves this transformation take the
+stuff that you have at a low frequency
+
+ align:start position:0%
+stuff that you have at a low frequency
+ 
+
+ align:start position:0%
+stuff that you have at a low frequency
+in a low frequency range and shift it to
+
+ align:start position:0%
+in a low frequency range and shift it to
+ 
+
+ align:start position:0%
+in a low frequency range and shift it to
+a high frequency range what would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do the obvious answer is to stare blind
+
+ align:start position:0%
+do the obvious answer is to stare blind
+ 
+
+ align:start position:0%
+do the obvious answer is to stare blind
+with a blank face toward and it it'll
+
+ align:start position:0%
+with a blank face toward and it it'll
+ 
+
+ align:start position:0%
+with a blank face toward and it it'll
+definitely come to you
+
+ align:start position:0%
+definitely come to you
+ 
+
+ align:start position:0%
+definitely come to you
+right you don't want to talk to somebody
+
+ align:start position:0%
+right you don't want to talk to somebody
+ 
+
+ align:start position:0%
+right you don't want to talk to somebody
+else right that would give it away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the relationship between X of
+
+ align:start position:0%
+so what's the relationship between X of
+ 
+
+ align:start position:0%
+so what's the relationship between X of
+T and Y of t uh is it relation 1 2 3 4
+
+ align:start position:0%
+T and Y of t uh is it relation 1 2 3 4
+ 
+
+ align:start position:0%
+T and Y of t uh is it relation 1 2 3 4
+or none of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+above okay it's about 80% correct um so
+
+ align:start position:0%
+above okay it's about 80% correct um so
+ 
+
+ align:start position:0%
+above okay it's about 80% correct um so
+how do I think about it so if I have so
+
+ align:start position:0%
+how do I think about it so if I have so
+ 
+
+ align:start position:0%
+how do I think about it so if I have so
+let's see I've got I want to figure out
+
+ align:start position:0%
+let's see I've got I want to figure out
+ 
+
+ align:start position:0%
+let's see I've got I want to figure out
+a relationship between the 4A transform
+
+ align:start position:0%
+a relationship between the 4A transform
+ 
+
+ align:start position:0%
+a relationship between the 4A transform
+of Y and X okay so I want if I knew if I
+
+ align:start position:0%
+of Y and X okay so I want if I knew if I
+ 
+
+ align:start position:0%
+of Y and X okay so I want if I knew if I
+wanted to figure out the 4A transform of
+
+ align:start position:0%
+wanted to figure out the 4A transform of
+ 
+
+ align:start position:0%
+wanted to figure out the 4A transform of
+Y right so I would integrate y of
+
+ align:start position:0%
+Y right so I would integrate y of
+ 
+
+ align:start position:0%
+Y right so I would integrate y of
+T eus J Omega T DT right that looks kind
+
+ align:start position:0%
+T eus J Omega T DT right that looks kind
+ 
+
+ align:start position:0%
+T eus J Omega T DT right that looks kind
+of right and Y would be X of T let's say
+
+ align:start position:0%
+of right and Y would be X of T let's say
+ 
+
+ align:start position:0%
+of right and Y would be X of T let's say
+let's try the first one X of t e to the
+
+ align:start position:0%
+let's try the first one X of t e to the
+ 
+
+ align:start position:0%
+let's try the first one X of t e to the
+J Omega c t e minus J Omega T DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's almost the 48 transform of
+
+ align:start position:0%
+well that's almost the 48 transform of
+ 
+
+ align:start position:0%
+well that's almost the 48 transform of
+X right all I've done is shifted
+
+ align:start position:0%
+X right all I've done is shifted
+ 
+
+ align:start position:0%
+X right all I've done is shifted
+Omega so that's in fact that's the same
+
+ align:start position:0%
+Omega so that's in fact that's the same
+ 
+
+ align:start position:0%
+Omega so that's in fact that's the same
+as X of J Omega minus Omega C right and
+
+ align:start position:0%
+as X of J Omega minus Omega C right and
+ 
+
+ align:start position:0%
+as X of J Omega minus Omega C right and
+that's what I wanted to do right so the
+
+ align:start position:0%
+that's what I wanted to do right so the
+ 
+
+ align:start position:0%
+that's what I wanted to do right so the
+idea is that if you multiply by this
+
+ align:start position:0%
+idea is that if you multiply by this
+ 
+
+ align:start position:0%
+idea is that if you multiply by this
+complex exponential
+
+ align:start position:0%
+complex exponential
+ 
+
+ align:start position:0%
+complex exponential
+the effect of that multiplication in
+
+ align:start position:0%
+the effect of that multiplication in
+ 
+
+ align:start position:0%
+the effect of that multiplication in
+time is to shift
+
+ align:start position:0%
+time is to shift
+ 
+
+ align:start position:0%
+time is to shift
+frequencies can somebody say that to me
+
+ align:start position:0%
+frequencies can somebody say that to me
+ 
+
+ align:start position:0%
+frequencies can somebody say that to me
+say the same transformation but in
+
+ align:start position:0%
+say the same transformation but in
+ 
+
+ align:start position:0%
+say the same transformation but in
+slightly different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words guess that was kind of
+
+ align:start position:0%
+words guess that was kind of
+ 
+
+ align:start position:0%
+words guess that was kind of
+big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes expon time multiply by exponential
+
+ align:start position:0%
+yes expon time multiply by exponential
+ 
+
+ align:start position:0%
+yes expon time multiply by exponential
+in time should correspond to
+
+ align:start position:0%
+in time should correspond to
+ 
+
+ align:start position:0%
+in time should correspond to
+so generally a multiplication in time
+
+ align:start position:0%
+so generally a multiplication in time
+ 
+
+ align:start position:0%
+so generally a multiplication in time
+corresponds
+
+ align:start position:0%
+corresponds
+ 
+
+ align:start position:0%
+corresponds
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+convolution so you could equivalently
+
+ align:start position:0%
+convolution so you could equivalently
+ 
+
+ align:start position:0%
+convolution so you could equivalently
+instead of saying it shifted in
+
+ align:start position:0%
+instead of saying it shifted in
+ 
+
+ align:start position:0%
+instead of saying it shifted in
+frequency you could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it got
+
+ align:start position:0%
+say it got
+ 
+
+ align:start position:0%
+say it got
+convolved with the Delta
+
+ align:start position:0%
+convolved with the Delta
+ 
+
+ align:start position:0%
+convolved with the Delta
+function so a different way of saying
+
+ align:start position:0%
+function so a different way of saying
+ 
+
+ align:start position:0%
+function so a different way of saying
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+thing would be that you think about
+
+ align:start position:0%
+thing would be that you think about
+ 
+
+ align:start position:0%
+thing would be that you think about
+convolving with the Delta function in
+
+ align:start position:0%
+convolving with the Delta function in
+ 
+
+ align:start position:0%
+convolving with the Delta function in
+frequency okay same same thing okay now
+
+ align:start position:0%
+frequency okay same same thing okay now
+ 
+
+ align:start position:0%
+frequency okay same same thing okay now
+we don't actually do this right when
+
+ align:start position:0%
+we don't actually do this right when
+ 
+
+ align:start position:0%
+we don't actually do this right when
+we're doing the cell phone thing we
+
+ align:start position:0%
+we're doing the cell phone thing we
+ 
+
+ align:start position:0%
+we're doing the cell phone thing we
+don't actually multiply by e to the J
+
+ align:start position:0%
+don't actually multiply by e to the J
+ 
+
+ align:start position:0%
+don't actually multiply by e to the J
+Omega C anyone know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why this is kind of the simplest way
+
+ align:start position:0%
+why this is kind of the simplest way
+ 
+
+ align:start position:0%
+why this is kind of the simplest way
+that you could imagine of taking
+
+ align:start position:0%
+that you could imagine of taking
+ 
+
+ align:start position:0%
+that you could imagine of taking
+frequency content centered near zero and
+
+ align:start position:0%
+frequency content centered near zero and
+ 
+
+ align:start position:0%
+frequency content centered near zero and
+turning it into frequency content
+
+ align:start position:0%
+turning it into frequency content
+ 
+
+ align:start position:0%
+turning it into frequency content
+centered near Omega C but that's not
+
+ align:start position:0%
+centered near Omega C but that's not
+ 
+
+ align:start position:0%
+centered near Omega C but that's not
+what we really do why don't we really do
+
+ align:start position:0%
+what we really do why don't we really do
+ 
+
+ align:start position:0%
+what we really do why don't we really do
+that exactly we don't really do it
+
+ align:start position:0%
+that exactly we don't really do it
+ 
+
+ align:start position:0%
+that exactly we don't really do it
+because the signal is not
+
+ align:start position:0%
+because the signal is not
+ 
+
+ align:start position:0%
+because the signal is not
+real right so how do you know the signal
+
+ align:start position:0%
+real right so how do you know the signal
+ 
+
+ align:start position:0%
+real right so how do you know the signal
+is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real so if the signal had been real the
+
+ align:start position:0%
+real so if the signal had been real the
+ 
+
+ align:start position:0%
+real so if the signal had been real the
+48 transform would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+been if the signal had been real the 4A
+
+ align:start position:0%
+been if the signal had been real the 4A
+ 
+
+ align:start position:0%
+been if the signal had been real the 4A
+transform would have
+
+ align:start position:0%
+transform would have
+ 
+
+ align:start position:0%
+transform would have
+been X of J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega if the signal had been real the 4A
+
+ align:start position:0%
+Omega if the signal had been real the 4A
+ 
+
+ align:start position:0%
+Omega if the signal had been real the 4A
+transform would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+been some kind of symmetry right how do
+
+ align:start position:0%
+been some kind of symmetry right how do
+ 
+
+ align:start position:0%
+been some kind of symmetry right how do
+I see symmetry in that expression
+
+ align:start position:0%
+I see symmetry in that expression
+ 
+
+ align:start position:0%
+I see symmetry in that expression
+conjugate conjugate symmetry how do I
+
+ align:start position:0%
+conjugate conjugate symmetry how do I
+ 
+
+ align:start position:0%
+conjugate conjugate symmetry how do I
+see conjugate symmetry in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expression well I can you know this is
+
+ align:start position:0%
+expression well I can you know this is
+ 
+
+ align:start position:0%
+expression well I can you know this is
+post t plus J sin Omega
+
+ align:start position:0%
+post t plus J sin Omega
+ 
+
+ align:start position:0%
+post t plus J sin Omega
+T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if this is a real signal then
+
+ align:start position:0%
+right so if this is a real signal then
+ 
+
+ align:start position:0%
+right so if this is a real signal then
+it gives rise to something here that is
+
+ align:start position:0%
+it gives rise to something here that is
+ 
+
+ align:start position:0%
+it gives rise to something here that is
+symmetric the cosine terms are all
+
+ align:start position:0%
+symmetric the cosine terms are all
+ 
+
+ align:start position:0%
+symmetric the cosine terms are all
+symmetric about the
+
+ align:start position:0%
+symmetric about the
+ 
+
+ align:start position:0%
+symmetric about the
+origin and it has an imaginary part that
+
+ align:start position:0%
+origin and it has an imaginary part that
+ 
+
+ align:start position:0%
+origin and it has an imaginary part that
+is antisymmetric about the origin right
+
+ align:start position:0%
+is antisymmetric about the origin right
+ 
+
+ align:start position:0%
+is antisymmetric about the origin right
+because you add together a bunch of
+
+ align:start position:0%
+because you add together a bunch of
+ 
+
+ align:start position:0%
+because you add together a bunch of
+cosin you can't get anything that's
+
+ align:start position:0%
+cosin you can't get anything that's
+ 
+
+ align:start position:0%
+cosin you can't get anything that's
+anything other than symmetric about the
+
+ align:start position:0%
+anything other than symmetric about the
+ 
+
+ align:start position:0%
+anything other than symmetric about the
+origin you add together a bunch of of
+
+ align:start position:0%
+origin you add together a bunch of of
+ 
+
+ align:start position:0%
+origin you add together a bunch of of
+signs you can't get anything except
+
+ align:start position:0%
+signs you can't get anything except
+ 
+
+ align:start position:0%
+signs you can't get anything except
+something that is anti- symmetric about
+
+ align:start position:0%
+something that is anti- symmetric about
+ 
+
+ align:start position:0%
+something that is anti- symmetric about
+the origin okay so you know this thing
+
+ align:start position:0%
+the origin okay so you know this thing
+ 
+
+ align:start position:0%
+the origin okay so you know this thing
+has to be um so a real signal would have
+
+ align:start position:0%
+has to be um so a real signal would have
+ 
+
+ align:start position:0%
+has to be um so a real signal would have
+had conjugate
+
+ align:start position:0%
+had conjugate
+ 
+
+ align:start position:0%
+had conjugate
+symmetry the real part would have been
+
+ align:start position:0%
+symmetry the real part would have been
+ 
+
+ align:start position:0%
+symmetry the real part would have been
+symmetric the imaginary part would be
+
+ align:start position:0%
+symmetric the imaginary part would be
+ 
+
+ align:start position:0%
+symmetric the imaginary part would be
+anti- symmetric and you can see that
+
+ align:start position:0%
+anti- symmetric and you can see that
+ 
+
+ align:start position:0%
+anti- symmetric and you can see that
+this is not conjugate symmetric right
+
+ align:start position:0%
+this is not conjugate symmetric right
+ 
+
+ align:start position:0%
+this is not conjugate symmetric right
+okay everybody knows what I'm talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about conjugate symmetry would mean that
+
+ align:start position:0%
+about conjugate symmetry would mean that
+ 
+
+ align:start position:0%
+about conjugate symmetry would mean that
+the real part of the signal is symmetric
+
+ align:start position:0%
+the real part of the signal is symmetric
+ 
+
+ align:start position:0%
+the real part of the signal is symmetric
+about the origin which means that if
+
+ align:start position:0%
+about the origin which means that if
+ 
+
+ align:start position:0%
+about the origin which means that if
+this is supposed to represent a real
+
+ align:start position:0%
+this is supposed to represent a real
+ 
+
+ align:start position:0%
+this is supposed to represent a real
+signal then there should have been a
+
+ align:start position:0%
+signal then there should have been a
+ 
+
+ align:start position:0%
+signal then there should have been a
+reflection over here to make it
+
+ align:start position:0%
+reflection over here to make it
+ 
+
+ align:start position:0%
+reflection over here to make it
+symmetric about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+origin it was symmetric but I shifted it
+
+ align:start position:0%
+origin it was symmetric but I shifted it
+ 
+
+ align:start position:0%
+origin it was symmetric but I shifted it
+by a complex number I shifted it by Co
+
+ align:start position:0%
+by a complex number I shifted it by Co
+ 
+
+ align:start position:0%
+by a complex number I shifted it by Co
+Omega C plus J sin Omega C so I
+
+ align:start position:0%
+Omega C plus J sin Omega C so I
+ 
+
+ align:start position:0%
+Omega C plus J sin Omega C so I
+generated by that multiplication I
+
+ align:start position:0%
+generated by that multiplication I
+ 
+
+ align:start position:0%
+generated by that multiplication I
+generated a complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number so the signal so so uh this
+
+ align:start position:0%
+number so the signal so so uh this
+ 
+
+ align:start position:0%
+number so the signal so so uh this
+signal was complex valued and not
+
+ align:start position:0%
+signal was complex valued and not
+ 
+
+ align:start position:0%
+signal was complex valued and not
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+symmetric okay so the point is trying to
+
+ align:start position:0%
+symmetric okay so the point is trying to
+ 
+
+ align:start position:0%
+symmetric okay so the point is trying to
+get you to remember the kinds of things
+
+ align:start position:0%
+get you to remember the kinds of things
+ 
+
+ align:start position:0%
+get you to remember the kinds of things
+that we're supposed to know about 48
+
+ align:start position:0%
+that we're supposed to know about 48
+ 
+
+ align:start position:0%
+that we're supposed to know about 48
+transforms right so uh by shifting with
+
+ align:start position:0%
+transforms right so uh by shifting with
+ 
+
+ align:start position:0%
+transforms right so uh by shifting with
+a a um complex exponential we wreck the
+
+ align:start position:0%
+a a um complex exponential we wreck the
+ 
+
+ align:start position:0%
+a a um complex exponential we wreck the
+realness of the original signal the real
+
+ align:start position:0%
+realness of the original signal the real
+ 
+
+ align:start position:0%
+realness of the original signal the real
+re original signal would have been
+
+ align:start position:0%
+re original signal would have been
+ 
+
+ align:start position:0%
+re original signal would have been
+conjugate symmetric in
+
+ align:start position:0%
+conjugate symmetric in
+ 
+
+ align:start position:0%
+conjugate symmetric in
+frequency but the wrecking of it gave
+
+ align:start position:0%
+frequency but the wrecking of it gave
+ 
+
+ align:start position:0%
+frequency but the wrecking of it gave
+rise to a signal that was no longer
+
+ align:start position:0%
+rise to a signal that was no longer
+ 
+
+ align:start position:0%
+rise to a signal that was no longer
+conjugate symmetric in
+
+ align:start position:0%
+conjugate symmetric in
+ 
+
+ align:start position:0%
+conjugate symmetric in
+frequency okay so we don't really
+
+ align:start position:0%
+frequency okay so we don't really
+ 
+
+ align:start position:0%
+frequency okay so we don't really
+modulate this
+
+ align:start position:0%
+modulate this
+ 
+
+ align:start position:0%
+modulate this
+way but we do the obvious extension what
+
+ align:start position:0%
+way but we do the obvious extension what
+ 
+
+ align:start position:0%
+way but we do the obvious extension what
+we would uh do is modulate with a cosine
+
+ align:start position:0%
+we would uh do is modulate with a cosine
+ 
+
+ align:start position:0%
+we would uh do is modulate with a cosine
+wave okay so now if instead of
+
+ align:start position:0%
+wave okay so now if instead of
+ 
+
+ align:start position:0%
+wave okay so now if instead of
+multiplying by a complex exponential I
+
+ align:start position:0%
+multiplying by a complex exponential I
+ 
+
+ align:start position:0%
+multiplying by a complex exponential I
+multiply by the cosine Omega CT by oil's
+
+ align:start position:0%
+multiply by the cosine Omega CT by oil's
+ 
+
+ align:start position:0%
+multiply by the cosine Omega CT by oil's
+expression I can think about that as
+
+ align:start position:0%
+expression I can think about that as
+ 
+
+ align:start position:0%
+expression I can think about that as
+being uh the sum of two uh components
+
+ align:start position:0%
+being uh the sum of two uh components
+ 
+
+ align:start position:0%
+being uh the sum of two uh components
+one at plus Omega C and one at minus
+
+ align:start position:0%
+one at plus Omega C and one at minus
+ 
+
+ align:start position:0%
+one at plus Omega C and one at minus
+Omega C and now when I do the
+
+ align:start position:0%
+Omega C and now when I do the
+ 
+
+ align:start position:0%
+Omega C and now when I do the
+convolution I get a signal that is
+
+ align:start position:0%
+convolution I get a signal that is
+ 
+
+ align:start position:0%
+convolution I get a signal that is
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+symmetric right so when I convolve this
+
+ align:start position:0%
+symmetric right so when I convolve this
+ 
+
+ align:start position:0%
+symmetric right so when I convolve this
+with this one this one gives me a copy
+
+ align:start position:0%
+with this one this one gives me a copy
+ 
+
+ align:start position:0%
+with this one this one gives me a copy
+of this here and when I convolve this
+
+ align:start position:0%
+of this here and when I convolve this
+ 
+
+ align:start position:0%
+of this here and when I convolve this
+with this one this one gives me a copy
+
+ align:start position:0%
+with this one this one gives me a copy
+ 
+
+ align:start position:0%
+with this one this one gives me a copy
+of this one down here so now the
+
+ align:start position:0%
+of this one down here so now the
+ 
+
+ align:start position:0%
+of this one down here so now the
+resulting signal
+
+ align:start position:0%
+resulting signal
+ 
+
+ align:start position:0%
+resulting signal
+which I know by construction if this was
+
+ align:start position:0%
+which I know by construction if this was
+ 
+
+ align:start position:0%
+which I know by construction if this was
+real and this was real then that's
+
+ align:start position:0%
+real and this was real then that's
+ 
+
+ align:start position:0%
+real and this was real then that's
+real right I know by construction that
+
+ align:start position:0%
+real right I know by construction that
+ 
+
+ align:start position:0%
+real right I know by construction that
+this signal must have been real but I
+
+ align:start position:0%
+this signal must have been real but I
+ 
+
+ align:start position:0%
+this signal must have been real but I
+can also see it in the transform because
+
+ align:start position:0%
+can also see it in the transform because
+ 
+
+ align:start position:0%
+can also see it in the transform because
+I can see now that there's a symmetry
+
+ align:start position:0%
+I can see now that there's a symmetry
+ 
+
+ align:start position:0%
+I can see now that there's a symmetry
+that is consistent with it being
+
+ align:start position:0%
+that is consistent with it being
+ 
+
+ align:start position:0%
+that is consistent with it being
+conjugate symmetric yes somebody had a
+
+ align:start position:0%
+conjugate symmetric yes somebody had a
+ 
+
+ align:start position:0%
+conjugate symmetric yes somebody had a
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+okay uh okay so that's what we mean by
+
+ align:start position:0%
+okay uh okay so that's what we mean by
+ 
+
+ align:start position:0%
+okay uh okay so that's what we mean by
+modulation this is modulation modulation
+
+ align:start position:0%
+modulation this is modulation modulation
+ 
+
+ align:start position:0%
+modulation this is modulation modulation
+just is a fancy word that means
+
+ align:start position:0%
+just is a fancy word that means
+ 
+
+ align:start position:0%
+just is a fancy word that means
+multiply so what we're going to do is is
+
+ align:start position:0%
+multiply so what we're going to do is is
+ 
+
+ align:start position:0%
+multiply so what we're going to do is is
+multiply the signal by a carrier the
+
+ align:start position:0%
+multiply the signal by a carrier the
+ 
+
+ align:start position:0%
+multiply the signal by a carrier the
+carrier is going to be a signal that
+
+ align:start position:0%
+carrier is going to be a signal that
+ 
+
+ align:start position:0%
+carrier is going to be a signal that
+carries the message through the medium
+
+ align:start position:0%
+carries the message through the medium
+ 
+
+ align:start position:0%
+carries the message through the medium
+okay the carrier is chosen so that it
+
+ align:start position:0%
+okay the carrier is chosen so that it
+ 
+
+ align:start position:0%
+okay the carrier is chosen so that it
+goes efficiently through the
+
+ align:start position:0%
+goes efficiently through the
+ 
+
+ align:start position:0%
+goes efficiently through the
+medium and then the carrier carries the
+
+ align:start position:0%
+medium and then the carrier carries the
+ 
+
+ align:start position:0%
+medium and then the carrier carries the
+message through the medium so we think
+
+ align:start position:0%
+message through the medium so we think
+ 
+
+ align:start position:0%
+message through the medium so we think
+about this as
+
+ align:start position:0%
+about this as
+ 
+
+ align:start position:0%
+about this as
+modulation and we want to be familiar
+
+ align:start position:0%
+modulation and we want to be familiar
+ 
+
+ align:start position:0%
+modulation and we want to be familiar
+with going back and forth between time
+
+ align:start position:0%
+with going back and forth between time
+ 
+
+ align:start position:0%
+with going back and forth between time
+and frequency you can also think about
+
+ align:start position:0%
+and frequency you can also think about
+ 
+
+ align:start position:0%
+and frequency you can also think about
+the result of modulation in time so if
+
+ align:start position:0%
+the result of modulation in time so if
+ 
+
+ align:start position:0%
+the result of modulation in time so if
+this were my message which is intended
+
+ align:start position:0%
+this were my message which is intended
+ 
+
+ align:start position:0%
+this were my message which is intended
+to be represented as a low
+
+ align:start position:0%
+to be represented as a low
+ 
+
+ align:start position:0%
+to be represented as a low
+frequency and this is my carrier which
+
+ align:start position:0%
+frequency and this is my carrier which
+ 
+
+ align:start position:0%
+frequency and this is my carrier which
+is intended to be represented as a
+
+ align:start position:0%
+is intended to be represented as a
+ 
+
+ align:start position:0%
+is intended to be represented as a
+higher frequency then when I modulate it
+
+ align:start position:0%
+higher frequency then when I modulate it
+ 
+
+ align:start position:0%
+higher frequency then when I modulate it
+I get a modulated signal by which I mean
+
+ align:start position:0%
+I get a modulated signal by which I mean
+ 
+
+ align:start position:0%
+I get a modulated signal by which I mean
+this is called amplitude
+
+ align:start position:0%
+this is called amplitude
+ 
+
+ align:start position:0%
+this is called amplitude
+modulation the amplitude of the carrier
+
+ align:start position:0%
+modulation the amplitude of the carrier
+ 
+
+ align:start position:0%
+modulation the amplitude of the carrier
+is modulated by the message that's all
+
+ align:start position:0%
+is modulated by the message that's all
+ 
+
+ align:start position:0%
+is modulated by the message that's all
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+mean so you can see that the transform
+
+ align:start position:0%
+mean so you can see that the transform
+ 
+
+ align:start position:0%
+mean so you can see that the transform
+this transformation which has the
+
+ align:start position:0%
+this transformation which has the
+ 
+
+ align:start position:0%
+this transformation which has the
+property of moving the information from
+
+ align:start position:0%
+property of moving the information from
+ 
+
+ align:start position:0%
+property of moving the information from
+a low frequency that's hard to transmit
+
+ align:start position:0%
+a low frequency that's hard to transmit
+ 
+
+ align:start position:0%
+a low frequency that's hard to transmit
+to a high frequency that is easy to
+
+ align:start position:0%
+to a high frequency that is easy to
+ 
+
+ align:start position:0%
+to a high frequency that is easy to
+transmit that has the effect of U uh
+
+ align:start position:0%
+transmit that has the effect of U uh
+ 
+
+ align:start position:0%
+transmit that has the effect of U uh
+doing a very particular dist uh U uh
+
+ align:start position:0%
+doing a very particular dist uh U uh
+ 
+
+ align:start position:0%
+doing a very particular dist uh U uh
+pattern to the time domain
+
+ align:start position:0%
+pattern to the time domain
+ 
+
+ align:start position:0%
+pattern to the time domain
+waveform okay now it would be completely
+
+ align:start position:0%
+waveform okay now it would be completely
+ 
+
+ align:start position:0%
+waveform okay now it would be completely
+useless as a communication scheme if it
+
+ align:start position:0%
+useless as a communication scheme if it
+ 
+
+ align:start position:0%
+useless as a communication scheme if it
+weren't easy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invert so imagine that I have this
+
+ align:start position:0%
+invert so imagine that I have this
+ 
+
+ align:start position:0%
+invert so imagine that I have this
+signal and what I'd like to do is
+
+ align:start position:0%
+signal and what I'd like to do is
+ 
+
+ align:start position:0%
+signal and what I'd like to do is
+recover X
+
+ align:start position:0%
+recover X
+ 
+
+ align:start position:0%
+recover X
+what should I do to recover X the
+
+ align:start position:0%
+what should I do to recover X the
+ 
+
+ align:start position:0%
+what should I do to recover X the
+original message so the idea is I have
+
+ align:start position:0%
+original message so the idea is I have
+ 
+
+ align:start position:0%
+original message so the idea is I have
+an original message in my available in
+
+ align:start position:0%
+an original message in my available in
+ 
+
+ align:start position:0%
+an original message in my available in
+my cell phone it gets modulated so that
+
+ align:start position:0%
+my cell phone it gets modulated so that
+ 
+
+ align:start position:0%
+my cell phone it gets modulated so that
+it can be launched into electromagnetic
+
+ align:start position:0%
+it can be launched into electromagnetic
+ 
+
+ align:start position:0%
+it can be launched into electromagnetic
+waves the electromagnetic waves go to a
+
+ align:start position:0%
+waves the electromagnetic waves go to a
+ 
+
+ align:start position:0%
+waves the electromagnetic waves go to a
+receiver uh thousands of miles away and
+
+ align:start position:0%
+receiver uh thousands of miles away and
+ 
+
+ align:start position:0%
+receiver uh thousands of miles away and
+now the idea is to reconstruct my
+
+ align:start position:0%
+now the idea is to reconstruct my
+ 
+
+ align:start position:0%
+now the idea is to reconstruct my
+original signal x what would I do what
+
+ align:start position:0%
+original signal x what would I do what
+ 
+
+ align:start position:0%
+original signal x what would I do what
+kind of a system would I use to recover
+
+ align:start position:0%
+kind of a system would I use to recover
+ 
+
+ align:start position:0%
+kind of a system would I use to recover
+X from y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry you need divide out the you
+
+ align:start position:0%
+I'm sorry you need divide out the you
+ 
+
+ align:start position:0%
+I'm sorry you need divide out the you
+could divide out the cosine so you could
+
+ align:start position:0%
+could divide out the cosine so you could
+ 
+
+ align:start position:0%
+could divide out the cosine so you could
+you could take uh X of T cosine Omega CT
+
+ align:start position:0%
+you could take uh X of T cosine Omega CT
+ 
+
+ align:start position:0%
+you could take uh X of T cosine Omega CT
+times something uh what do I want to say
+
+ align:start position:0%
+times something uh what do I want to say
+ 
+
+ align:start position:0%
+times something uh what do I want to say
+a of
+
+ align:start position:0%
+a of
+ 
+
+ align:start position:0%
+a of
+T designed so that this times this is
+
+ align:start position:0%
+T designed so that this times this is
+ 
+
+ align:start position:0%
+T designed so that this times this is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+right that's kind of ugly anybody see
+
+ align:start position:0%
+right that's kind of ugly anybody see
+ 
+
+ align:start position:0%
+right that's kind of ugly anybody see
+anything ugly about that
+
+ align:start position:0%
+anything ugly about that
+ 
+
+ align:start position:0%
+anything ugly about that
+yeah shift it back the other way you
+
+ align:start position:0%
+yeah shift it back the other way you
+ 
+
+ align:start position:0%
+yeah shift it back the other way you
+could also shift it back the other way
+
+ align:start position:0%
+could also shift it back the other way
+ 
+
+ align:start position:0%
+could also shift it back the other way
+so before we do that why is this
+
+ align:start position:0%
+so before we do that why is this
+ 
+
+ align:start position:0%
+so before we do that why is this
+ugly the zeros right so if we wanted to
+
+ align:start position:0%
+ugly the zeros right so if we wanted to
+ 
+
+ align:start position:0%
+ugly the zeros right so if we wanted to
+take a signal that looks like a a cosine
+
+ align:start position:0%
+take a signal that looks like a a cosine
+ 
+
+ align:start position:0%
+take a signal that looks like a a cosine
+wave and multiply it by some signal that
+
+ align:start position:0%
+wave and multiply it by some signal that
+ 
+
+ align:start position:0%
+wave and multiply it by some signal that
+generates one right that's not too hard
+
+ align:start position:0%
+generates one right that's not too hard
+ 
+
+ align:start position:0%
+generates one right that's not too hard
+to do here right you would do that with
+
+ align:start position:0%
+to do here right you would do that with
+ 
+
+ align:start position:0%
+to do here right you would do that with
+something like this but it becomes very
+
+ align:start position:0%
+something like this but it becomes very
+ 
+
+ align:start position:0%
+something like this but it becomes very
+hard to do here so you would end up
+
+ align:start position:0%
+hard to do here so you would end up
+ 
+
+ align:start position:0%
+hard to do here so you would end up
+making some signal that does some
+
+ align:start position:0%
+making some signal that does some
+ 
+
+ align:start position:0%
+making some signal that does some
+awful right so it would periodically be
+
+ align:start position:0%
+awful right so it would periodically be
+ 
+
+ align:start position:0%
+awful right so it would periodically be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+mess right but you can do what you said
+
+ align:start position:0%
+mess right but you can do what you said
+ 
+
+ align:start position:0%
+mess right but you can do what you said
+an alternative would be to multiply it
+
+ align:start position:0%
+an alternative would be to multiply it
+ 
+
+ align:start position:0%
+an alternative would be to multiply it
+by another
+
+ align:start position:0%
+by another
+ 
+
+ align:start position:0%
+by another
+cosine which in the frequency domain is
+
+ align:start position:0%
+cosine which in the frequency domain is
+ 
+
+ align:start position:0%
+cosine which in the frequency domain is
+easy to think about it would just shift
+
+ align:start position:0%
+easy to think about it would just shift
+ 
+
+ align:start position:0%
+easy to think about it would just shift
+it back right so convolve with a pair of
+
+ align:start position:0%
+it back right so convolve with a pair of
+ 
+
+ align:start position:0%
+it back right so convolve with a pair of
+impulses to move something that was at
+
+ align:start position:0%
+impulses to move something that was at
+ 
+
+ align:start position:0%
+impulses to move something that was at
+DC out to some high frequency convolve
+
+ align:start position:0%
+DC out to some high frequency convolve
+ 
+
+ align:start position:0%
+DC out to some high frequency convolve
+again to take the thing that was high
+
+ align:start position:0%
+again to take the thing that was high
+ 
+
+ align:start position:0%
+again to take the thing that was high
+frequency and bring it back to DC and
+
+ align:start position:0%
+frequency and bring it back to DC and
+ 
+
+ align:start position:0%
+frequency and bring it back to DC and
+you can think about that in either uh
+
+ align:start position:0%
+you can think about that in either uh
+ 
+
+ align:start position:0%
+you can think about that in either uh
+frequency or time it's easy to think
+
+ align:start position:0%
+frequency or time it's easy to think
+ 
+
+ align:start position:0%
+frequency or time it's easy to think
+about it in time if you think about it
+
+ align:start position:0%
+about it in time if you think about it
+ 
+
+ align:start position:0%
+about it in time if you think about it
+in time here we've got the product of
+
+ align:start position:0%
+in time here we've got the product of
+ 
+
+ align:start position:0%
+in time here we've got the product of
+two cosiness but the product of two
+
+ align:start position:0%
+two cosiness but the product of two
+ 
+
+ align:start position:0%
+two cosiness but the product of two
+cosiness is just half plus half the
+
+ align:start position:0%
+cosiness is just half plus half the
+ 
+
+ align:start position:0%
+cosiness is just half plus half the
+cosine of
+
+ align:start position:0%
+cosine of
+ 
+
+ align:start position:0%
+cosine of
+double well that's good right why is
+
+ align:start position:0%
+double well that's good right why is
+ 
+
+ align:start position:0%
+double well that's good right why is
+that good well you can if you multiply X
+
+ align:start position:0%
+that good well you can if you multiply X
+ 
+
+ align:start position:0%
+that good well you can if you multiply X
+of T by this this is a super high
+
+ align:start position:0%
+of T by this this is a super high
+ 
+
+ align:start position:0%
+of T by this this is a super high
+frequency if Omega C was a high
+
+ align:start position:0%
+frequency if Omega C was a high
+ 
+
+ align:start position:0%
+frequency if Omega C was a high
+frequency two Omega C is even higher
+
+ align:start position:0%
+frequency two Omega C is even higher
+ 
+
+ align:start position:0%
+frequency two Omega C is even higher
+so what you could do is remove x * half
+
+ align:start position:0%
+so what you could do is remove x * half
+ 
+
+ align:start position:0%
+so what you could do is remove x * half
+Co 2 Omega CT with a low pass filter
+
+ align:start position:0%
+Co 2 Omega CT with a low pass filter
+ 
+
+ align:start position:0%
+Co 2 Omega CT with a low pass filter
+right since Omega C is such a high
+
+ align:start position:0%
+right since Omega C is such a high
+ 
+
+ align:start position:0%
+right since Omega C is such a high
+frequency and that would just leave you
+
+ align:start position:0%
+frequency and that would just leave you
+ 
+
+ align:start position:0%
+frequency and that would just leave you
+with half the message which would be
+
+ align:start position:0%
+with half the message which would be
+ 
+
+ align:start position:0%
+with half the message which would be
+easy then to
+
+ align:start position:0%
+easy then to
+ 
+
+ align:start position:0%
+easy then to
+reconstruct because what you would do is
+
+ align:start position:0%
+reconstruct because what you would do is
+ 
+
+ align:start position:0%
+reconstruct because what you would do is
+just put it through a low pass filter
+
+ align:start position:0%
+just put it through a low pass filter
+ 
+
+ align:start position:0%
+just put it through a low pass filter
+and then multiply by two you can
+
+ align:start position:0%
+and then multiply by two you can
+ 
+
+ align:start position:0%
+and then multiply by two you can
+similarly think about the same thing in
+
+ align:start position:0%
+similarly think about the same thing in
+ 
+
+ align:start position:0%
+similarly think about the same thing in
+frequency if I took Y and convolved it
+
+ align:start position:0%
+frequency if I took Y and convolved it
+ 
+
+ align:start position:0%
+frequency if I took Y and convolved it
+If I multiply In Time by another cosine
+
+ align:start position:0%
+If I multiply In Time by another cosine
+ 
+
+ align:start position:0%
+If I multiply In Time by another cosine
+wave that second cosine wave is a pair
+
+ align:start position:0%
+wave that second cosine wave is a pair
+ 
+
+ align:start position:0%
+wave that second cosine wave is a pair
+of impulses one minus Omega C and one
+
+ align:start position:0%
+of impulses one minus Omega C and one
+ 
+
+ align:start position:0%
+of impulses one minus Omega C and one
+Omega C and now when I convolve the Y
+
+ align:start position:0%
+Omega C and now when I convolve the Y
+ 
+
+ align:start position:0%
+Omega C and now when I convolve the Y
+signal this one uh shifts these two
+
+ align:start position:0%
+signal this one uh shifts these two
+ 
+
+ align:start position:0%
+signal this one uh shifts these two
+up and this one shifts these two down
+
+ align:start position:0%
+up and this one shifts these two down
+ 
+
+ align:start position:0%
+up and this one shifts these two down
+and two of them land on top of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other and uh but each of these was only
+
+ align:start position:0%
+other and uh but each of these was only
+ 
+
+ align:start position:0%
+other and uh but each of these was only
+of height one
+
+ align:start position:0%
+of height one
+ 
+
+ align:start position:0%
+of height one
+half right so by Oiler expression I
+
+ align:start position:0%
+half right so by Oiler expression I
+ 
+
+ align:start position:0%
+half right so by Oiler expression I
+um cosine of something was half e to the
+
+ align:start position:0%
+um cosine of something was half e to the
+ 
+
+ align:start position:0%
+um cosine of something was half e to the
+whatever plus half e to the whatever so
+
+ align:start position:0%
+whatever plus half e to the whatever so
+ 
+
+ align:start position:0%
+whatever plus half e to the whatever so
+I got halves on each of those
+
+ align:start position:0%
+I got halves on each of those
+ 
+
+ align:start position:0%
+I got halves on each of those
+amplitudes so uh the result is then that
+
+ align:start position:0%
+amplitudes so uh the result is then that
+ 
+
+ align:start position:0%
+amplitudes so uh the result is then that
+I have to multiply the low frequency
+
+ align:start position:0%
+I have to multiply the low frequency
+ 
+
+ align:start position:0%
+I have to multiply the low frequency
+part by a factor of two to undo the the
+
+ align:start position:0%
+part by a factor of two to undo the the
+ 
+
+ align:start position:0%
+part by a factor of two to undo the the
+halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so this kind of a scheme is
+
+ align:start position:0%
+okay okay so this kind of a scheme is
+ 
+
+ align:start position:0%
+okay okay so this kind of a scheme is
+especially
+
+ align:start position:0%
+especially
+ 
+
+ align:start position:0%
+especially
+nice because you can scramble together
+
+ align:start position:0%
+nice because you can scramble together
+ 
+
+ align:start position:0%
+nice because you can scramble together
+multiple messages and still get them
+
+ align:start position:0%
+multiple messages and still get them
+ 
+
+ align:start position:0%
+multiple messages and still get them
+separated at the
+
+ align:start position:0%
+separated at the
+ 
+
+ align:start position:0%
+separated at the
+destination if you imagine
+
+ align:start position:0%
+destination if you imagine
+ 
+
+ align:start position:0%
+destination if you imagine
+having uh three similar
+
+ align:start position:0%
+having uh three similar
+ 
+
+ align:start position:0%
+having uh three similar
+transmitters that use their own Omega C
+
+ align:start position:0%
+transmitters that use their own Omega C
+ 
+
+ align:start position:0%
+transmitters that use their own Omega C
+so the first one uses Omega 1 Omega 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+omega3 so if each one of the
+
+ align:start position:0%
+omega3 so if each one of the
+ 
+
+ align:start position:0%
+omega3 so if each one of the
+transmitters had their own
+
+ align:start position:0%
+transmitters had their own
+ 
+
+ align:start position:0%
+transmitters had their own
+frequency and if the frequencies were
+
+ align:start position:0%
+frequency and if the frequencies were
+ 
+
+ align:start position:0%
+frequency and if the frequencies were
+far enough apart and if the frequencies
+
+ align:start position:0%
+far enough apart and if the frequencies
+ 
+
+ align:start position:0%
+far enough apart and if the frequencies
+were all big compared to the message
+
+ align:start position:0%
+were all big compared to the message
+ 
+
+ align:start position:0%
+were all big compared to the message
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+then you could combine them all and
+
+ align:start position:0%
+then you could combine them all and
+ 
+
+ align:start position:0%
+then you could combine them all and
+select out the one of
+
+ align:start position:0%
+select out the one of
+ 
+
+ align:start position:0%
+select out the one of
+Interest by tuning the
+
+ align:start position:0%
+Interest by tuning the
+ 
+
+ align:start position:0%
+Interest by tuning the
+receiver by
+
+ align:start position:0%
+receiver by
+ 
+
+ align:start position:0%
+receiver by
+choosing the demodulation frequency so
+
+ align:start position:0%
+choosing the demodulation frequency so
+ 
+
+ align:start position:0%
+choosing the demodulation frequency so
+now if the receiver chose Omega C equals
+
+ align:start position:0%
+now if the receiver chose Omega C equals
+ 
+
+ align:start position:0%
+now if the receiver chose Omega C equals
+Omega 1 you would decode message one if
+
+ align:start position:0%
+Omega 1 you would decode message one if
+ 
+
+ align:start position:0%
+Omega 1 you would decode message one if
+Omega C were Omega 2 You' decode message
+
+ align:start position:0%
+Omega C were Omega 2 You' decode message
+ 
+
+ align:start position:0%
+Omega C were Omega 2 You' decode message
+two and that's the principle uh and
+
+ align:start position:0%
+two and that's the principle uh and
+ 
+
+ align:start position:0%
+two and that's the principle uh and
+that's because the medium Works
+
+ align:start position:0%
+that's because the medium Works
+ 
+
+ align:start position:0%
+that's because the medium Works
+approximately linearly
+
+ align:start position:0%
+approximately linearly
+ 
+
+ align:start position:0%
+approximately linearly
+so if you launch multiple waves into the
+
+ align:start position:0%
+so if you launch multiple waves into the
+ 
+
+ align:start position:0%
+so if you launch multiple waves into the
+air you um
+
+ align:start position:0%
+air you um
+ 
+
+ align:start position:0%
+air you um
+uh I don't want to get too much into
+
+ align:start position:0%
+uh I don't want to get too much into
+ 
+
+ align:start position:0%
+uh I don't want to get too much into
+electromagnetic Theory so the presence
+
+ align:start position:0%
+electromagnetic Theory so the presence
+ 
+
+ align:start position:0%
+electromagnetic Theory so the presence
+of the antennas distort it from
+
+ align:start position:0%
+of the antennas distort it from
+ 
+
+ align:start position:0%
+of the antennas distort it from
+linearity but once the antennas are all
+
+ align:start position:0%
+linearity but once the antennas are all
+ 
+
+ align:start position:0%
+linearity but once the antennas are all
+there then it's a perfectly linear
+
+ align:start position:0%
+there then it's a perfectly linear
+ 
+
+ align:start position:0%
+there then it's a perfectly linear
+system and the sum of what gets into and
+
+ align:start position:0%
+system and the sum of what gets into and
+ 
+
+ align:start position:0%
+system and the sum of what gets into and
+the the thing that gets into the uh air
+
+ align:start position:0%
+the the thing that gets into the uh air
+ 
+
+ align:start position:0%
+the the thing that gets into the uh air
+as a result of a sum is the sum of the
+
+ align:start position:0%
+as a result of a sum is the sum of the
+ 
+
+ align:start position:0%
+as a result of a sum is the sum of the
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+parts so uh the idea then is Illustrated
+
+ align:start position:0%
+parts so uh the idea then is Illustrated
+ 
+
+ align:start position:0%
+parts so uh the idea then is Illustrated
+here if I had
+
+ align:start position:0%
+here if I had
+ 
+
+ align:start position:0%
+here if I had
+uh three different messages represented
+
+ align:start position:0%
+uh three different messages represented
+ 
+
+ align:start position:0%
+uh three different messages represented
+by different style
+
+ align:start position:0%
+by different style
+ 
+
+ align:start position:0%
+by different style
+houses and each one of the messages was
+
+ align:start position:0%
+houses and each one of the messages was
+ 
+
+ align:start position:0%
+houses and each one of the messages was
+at a different frequency Omega 1 Omega 2
+
+ align:start position:0%
+at a different frequency Omega 1 Omega 2
+ 
+
+ align:start position:0%
+at a different frequency Omega 1 Omega 2
+omega3 by tuning the Omega C of the
+
+ align:start position:0%
+omega3 by tuning the Omega C of the
+ 
+
+ align:start position:0%
+omega3 by tuning the Omega C of the
+receiver if I put Omega C at Omega one
+
+ align:start position:0%
+receiver if I put Omega C at Omega one
+ 
+
+ align:start position:0%
+receiver if I put Omega C at Omega one
+that would uh convolution of this one
+
+ align:start position:0%
+that would uh convolution of this one
+ 
+
+ align:start position:0%
+that would uh convolution of this one
+would suck this one up to
+
+ align:start position:0%
+would suck this one up to
+ 
+
+ align:start position:0%
+would suck this one up to
+here and by this one would lower that
+
+ align:start position:0%
+here and by this one would lower that
+ 
+
+ align:start position:0%
+here and by this one would lower that
+one down to there you get overlap of the
+
+ align:start position:0%
+one down to there you get overlap of the
+ 
+
+ align:start position:0%
+one down to there you get overlap of the
+of the lowest frequency p pair and so if
+
+ align:start position:0%
+of the lowest frequency p pair and so if
+ 
+
+ align:start position:0%
+of the lowest frequency p pair and so if
+you built a low pass filter of exactly
+
+ align:start position:0%
+you built a low pass filter of exactly
+ 
+
+ align:start position:0%
+you built a low pass filter of exactly
+the right width you would decode message
+
+ align:start position:0%
+the right width you would decode message
+ 
+
+ align:start position:0%
+the right width you would decode message
+one where if you just change the
+
+ align:start position:0%
+one where if you just change the
+ 
+
+ align:start position:0%
+one where if you just change the
+frequency of the
+
+ align:start position:0%
+frequency of the
+ 
+
+ align:start position:0%
+frequency of the
+demodulator if you make the demodulation
+
+ align:start position:0%
+demodulator if you make the demodulation
+ 
+
+ align:start position:0%
+demodulator if you make the demodulation
+frequency now be Omega 2 now the effect
+
+ align:start position:0%
+frequency now be Omega 2 now the effect
+ 
+
+ align:start position:0%
+frequency now be Omega 2 now the effect
+of Shifting that different amount means
+
+ align:start position:0%
+of Shifting that different amount means
+ 
+
+ align:start position:0%
+of Shifting that different amount means
+that the low pass filter recovers the
+
+ align:start position:0%
+that the low pass filter recovers the
+ 
+
+ align:start position:0%
+that the low pass filter recovers the
+message two rather than message
+
+ align:start position:0%
+message two rather than message
+ 
+
+ align:start position:0%
+message two rather than message
+one okay so that's the idea and in fact
+
+ align:start position:0%
+one okay so that's the idea and in fact
+ 
+
+ align:start position:0%
+one okay so that's the idea and in fact
+so that's the idea that we use in
+
+ align:start position:0%
+so that's the idea that we use in
+ 
+
+ align:start position:0%
+so that's the idea that we use in
+commercial AM radio and that was in fact
+
+ align:start position:0%
+commercial AM radio and that was in fact
+ 
+
+ align:start position:0%
+commercial AM radio and that was in fact
+a revolutionary
+
+ align:start position:0%
+a revolutionary
+ 
+
+ align:start position:0%
+a revolutionary
+idea that enabled people to think about
+
+ align:start position:0%
+idea that enabled people to think about
+ 
+
+ align:start position:0%
+idea that enabled people to think about
+for the first time a communication
+
+ align:start position:0%
+for the first time a communication
+ 
+
+ align:start position:0%
+for the first time a communication
+system that did a lot of things that
+
+ align:start position:0%
+system that did a lot of things that
+ 
+
+ align:start position:0%
+system that did a lot of things that
+were very different from previous
+
+ align:start position:0%
+were very different from previous
+ 
+
+ align:start position:0%
+were very different from previous
+communication systems in particular it
+
+ align:start position:0%
+communication systems in particular it
+ 
+
+ align:start position:0%
+communication systems in particular it
+went at the speed of
+
+ align:start position:0%
+went at the speed of
+ 
+
+ align:start position:0%
+went at the speed of
+light even more importantly or at least
+
+ align:start position:0%
+light even more importantly or at least
+ 
+
+ align:start position:0%
+light even more importantly or at least
+as important is the fact that it was a
+
+ align:start position:0%
+as important is the fact that it was a
+ 
+
+ align:start position:0%
+as important is the fact that it was a
+broadcast system so broadcast was uh an
+
+ align:start position:0%
+broadcast system so broadcast was uh an
+ 
+
+ align:start position:0%
+broadcast system so broadcast was uh an
+idea that was championed by David
+
+ align:start position:0%
+idea that was championed by David
+ 
+
+ align:start position:0%
+idea that was championed by David
+snof sarof was a
+
+ align:start position:0%
+snof sarof was a
+ 
+
+ align:start position:0%
+snof sarof was a
+Visionary he was the the person who was
+
+ align:start position:0%
+Visionary he was the the person who was
+ 
+
+ align:start position:0%
+Visionary he was the the person who was
+very excited about the idea of broadcast
+
+ align:start position:0%
+very excited about the idea of broadcast
+ 
+
+ align:start position:0%
+very excited about the idea of broadcast
+which is a little ironic because he got
+
+ align:start position:0%
+which is a little ironic because he got
+ 
+
+ align:start position:0%
+which is a little ironic because he got
+his start with Marone Mar anybody ever
+
+ align:start position:0%
+his start with Marone Mar anybody ever
+ 
+
+ align:start position:0%
+his start with Marone Mar anybody ever
+hear
+
+ align:start position:0%
+hear
+ 
+
+ align:start position:0%
+hear
+Marone good good you're supposed to have
+
+ align:start position:0%
+Marone good good you're supposed to have
+ 
+
+ align:start position:0%
+Marone good good you're supposed to have
+heard of Marone okay so he so sof got
+
+ align:start position:0%
+heard of Marone okay so he so sof got
+ 
+
+ align:start position:0%
+heard of Marone okay so he so sof got
+his start this is sof this is Marone uh
+
+ align:start position:0%
+his start this is sof this is Marone uh
+ 
+
+ align:start position:0%
+his start this is sof this is Marone uh
+sof got his start with Marone Marone
+
+ align:start position:0%
+sof got his start with Marone Marone
+ 
+
+ align:start position:0%
+sof got his start with Marone Marone
+made his
+
+ align:start position:0%
+made his
+ 
+
+ align:start position:0%
+made his
+mint with wireless telegraphy anybody
+
+ align:start position:0%
+mint with wireless telegraphy anybody
+ 
+
+ align:start position:0%
+mint with wireless telegraphy anybody
+hear ever hear of telegraphy of course
+
+ align:start position:0%
+hear ever hear of telegraphy of course
+ 
+
+ align:start position:0%
+hear ever hear of telegraphy of course
+not uh so telegraphy this that's
+
+ align:start position:0%
+not uh so telegraphy this that's
+ 
+
+ align:start position:0%
+not uh so telegraphy this that's
+Telegraph right shake your heads yes
+
+ align:start position:0%
+Telegraph right shake your heads yes
+ 
+
+ align:start position:0%
+Telegraph right shake your heads yes
+it's ancient I realize so Marone made
+
+ align:start position:0%
+it's ancient I realize so Marone made
+ 
+
+ align:start position:0%
+it's ancient I realize so Marone made
+his fortune with wireless telegraphy
+
+ align:start position:0%
+his fortune with wireless telegraphy
+ 
+
+ align:start position:0%
+his fortune with wireless telegraphy
+telegraphy was what we call point to
+
+ align:start position:0%
+telegraphy was what we call point to
+ 
+
+ align:start position:0%
+telegraphy was what we call point to
+point the idea in telegraphy was
+
+ align:start position:0%
+point the idea in telegraphy was
+ 
+
+ align:start position:0%
+point the idea in telegraphy was
+precisely the same as the idea aide of
+
+ align:start position:0%
+precisely the same as the idea aide of
+ 
+
+ align:start position:0%
+precisely the same as the idea aide of
+the US Post
+
+ align:start position:0%
+the US Post
+ 
+
+ align:start position:0%
+the US Post
+Office except it was at the speed of
+
+ align:start position:0%
+Office except it was at the speed of
+ 
+
+ align:start position:0%
+Office except it was at the speed of
+light or not quite the speed of light so
+
+ align:start position:0%
+light or not quite the speed of light so
+ 
+
+ align:start position:0%
+light or not quite the speed of light so
+the idea in the post office is you take
+
+ align:start position:0%
+the idea in the post office is you take
+ 
+
+ align:start position:0%
+the idea in the post office is you take
+a sheet of
+
+ align:start position:0%
+a sheet of
+ 
+
+ align:start position:0%
+a sheet of
+paper and do something to it that makes
+
+ align:start position:0%
+paper and do something to it that makes
+ 
+
+ align:start position:0%
+paper and do something to it that makes
+it magically appear at somebody else's
+
+ align:start position:0%
+it magically appear at somebody else's
+ 
+
+ align:start position:0%
+it magically appear at somebody else's
+place okay so point a communicated to
+
+ align:start position:0%
+place okay so point a communicated to
+ 
+
+ align:start position:0%
+place okay so point a communicated to
+point B telegraphy was precisely the
+
+ align:start position:0%
+point B telegraphy was precisely the
+ 
+
+ align:start position:0%
+point B telegraphy was precisely the
+same you take your sheet of paper to the
+
+ align:start position:0%
+same you take your sheet of paper to the
+ 
+
+ align:start position:0%
+same you take your sheet of paper to the
+telegraph office and somebody who's very
+
+ align:start position:0%
+telegraph office and somebody who's very
+ 
+
+ align:start position:0%
+telegraph office and somebody who's very
+skilled with with their hands or
+
+ align:start position:0%
+skilled with with their hands or
+ 
+
+ align:start position:0%
+skilled with with their hands or
+specifically with their
+
+ align:start position:0%
+specifically with their
+ 
+
+ align:start position:0%
+specifically with their
+finger uh would do something that caused
+
+ align:start position:0%
+finger uh would do something that caused
+ 
+
+ align:start position:0%
+finger uh would do something that caused
+that piece of paper to be regenerated
+
+ align:start position:0%
+that piece of paper to be regenerated
+ 
+
+ align:start position:0%
+that piece of paper to be regenerated
+hundreds of miles
+
+ align:start position:0%
+hundreds of miles
+ 
+
+ align:start position:0%
+hundreds of miles
+away then that piece of paper got
+
+ align:start position:0%
+away then that piece of paper got
+ 
+
+ align:start position:0%
+away then that piece of paper got
+delivered so message went from point A
+
+ align:start position:0%
+delivered so message went from point A
+ 
+
+ align:start position:0%
+delivered so message went from point A
+to point B okay so telegraphy came long
+
+ align:start position:0%
+to point B okay so telegraphy came long
+ 
+
+ align:start position:0%
+to point B okay so telegraphy came long
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+Marone and it was a revolution in how
+
+ align:start position:0%
+Marone and it was a revolution in how
+ 
+
+ align:start position:0%
+Marone and it was a revolution in how
+you do Communications but it was point
+
+ align:start position:0%
+you do Communications but it was point
+ 
+
+ align:start position:0%
+you do Communications but it was point
+to point one person sent one message to
+
+ align:start position:0%
+to point one person sent one message to
+ 
+
+ align:start position:0%
+to point one person sent one message to
+one person um
+
+ align:start position:0%
+one person um
+ 
+
+ align:start position:0%
+one person um
+um sarof got his uh start in newspaper
+
+ align:start position:0%
+um sarof got his uh start in newspaper
+ 
+
+ align:start position:0%
+um sarof got his uh start in newspaper
+business he was a uh Russian immigrant
+
+ align:start position:0%
+business he was a uh Russian immigrant
+ 
+
+ align:start position:0%
+business he was a uh Russian immigrant
+impoverished and had a a newspaper route
+
+ align:start position:0%
+impoverished and had a a newspaper route
+ 
+
+ align:start position:0%
+impoverished and had a a newspaper route
+as a kid and he was so ambitious uh
+
+ align:start position:0%
+as a kid and he was so ambitious uh
+ 
+
+ align:start position:0%
+as a kid and he was so ambitious uh
+newspapers are
+
+ align:start position:0%
+newspapers are
+ 
+
+ align:start position:0%
+newspapers are
+broadcast the idea in pointto point and
+
+ align:start position:0%
+broadcast the idea in pointto point and
+ 
+
+ align:start position:0%
+broadcast the idea in pointto point and
+broadcast are very different in
+
+ align:start position:0%
+broadcast are very different in
+ 
+
+ align:start position:0%
+broadcast are very different in
+broadcast you're allowed to spend a
+
+ align:start position:0%
+broadcast you're allowed to spend a
+ 
+
+ align:start position:0%
+broadcast you're allowed to spend a
+fortune on the transmitter the printing
+
+ align:start position:0%
+fortune on the transmitter the printing
+ 
+
+ align:start position:0%
+fortune on the transmitter the printing
+press but not on the thing that the
+
+ align:start position:0%
+press but not on the thing that the
+ 
+
+ align:start position:0%
+press but not on the thing that the
+individuals get the individuals get
+
+ align:start position:0%
+individuals get the individuals get
+ 
+
+ align:start position:0%
+individuals get the individuals get
+newsprint so the paper and the ink have
+
+ align:start position:0%
+newsprint so the paper and the ink have
+ 
+
+ align:start position:0%
+newsprint so the paper and the ink have
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+cheap the printing press doesn't Okay so
+
+ align:start position:0%
+cheap the printing press doesn't Okay so
+ 
+
+ align:start position:0%
+cheap the printing press doesn't Okay so
+that was sof's
+
+ align:start position:0%
+that was sof's
+ 
+
+ align:start position:0%
+that was sof's
+background uh but so he was interested
+
+ align:start position:0%
+background uh but so he was interested
+ 
+
+ align:start position:0%
+background uh but so he was interested
+as a kid in broadcast in newspaper but
+
+ align:start position:0%
+as a kid in broadcast in newspaper but
+ 
+
+ align:start position:0%
+as a kid in broadcast in newspaper but
+then he got his reputation working for
+
+ align:start position:0%
+then he got his reputation working for
+ 
+
+ align:start position:0%
+then he got his reputation working for
+Marone in Wireless te telegraphy Marone
+
+ align:start position:0%
+Marone in Wireless te telegraphy Marone
+ 
+
+ align:start position:0%
+Marone in Wireless te telegraphy Marone
+the inventor of radio thought of a way
+
+ align:start position:0%
+the inventor of radio thought of a way
+ 
+
+ align:start position:0%
+the inventor of radio thought of a way
+of doing point-to-point
+
+ align:start position:0%
+of doing point-to-point
+ 
+
+ align:start position:0%
+of doing point-to-point
+telegraphy wirelessly via radio radio
+
+ align:start position:0%
+telegraphy wirelessly via radio radio
+ 
+
+ align:start position:0%
+telegraphy wirelessly via radio radio
+telegraphy and he sold it to um uh
+
+ align:start position:0%
+telegraphy and he sold it to um uh
+ 
+
+ align:start position:0%
+telegraphy and he sold it to um uh
+ships and stof made his reputation
+
+ align:start position:0%
+ships and stof made his reputation
+ 
+
+ align:start position:0%
+ships and stof made his reputation
+because he was the guy operating the
+
+ align:start position:0%
+because he was the guy operating the
+ 
+
+ align:start position:0%
+because he was the guy operating the
+radio telegraphy system at the Marone
+
+ align:start position:0%
+radio telegraphy system at the Marone
+ 
+
+ align:start position:0%
+radio telegraphy system at the Marone
+system at the Marone company when the
+
+ align:start position:0%
+system at the Marone company when the
+ 
+
+ align:start position:0%
+system at the Marone company when the
+Titanic
+
+ align:start position:0%
+Titanic
+ 
+
+ align:start position:0%
+Titanic
+sank uh everybody know about the Titanic
+
+ align:start position:0%
+sank uh everybody know about the Titanic
+ 
+
+ align:start position:0%
+sank uh everybody know about the Titanic
+right big ship
+
+ align:start position:0%
+right big ship
+ 
+
+ align:start position:0%
+right big ship
+sank um Mark uh so sarof uh stayed uh at
+
+ align:start position:0%
+sank um Mark uh so sarof uh stayed uh at
+ 
+
+ align:start position:0%
+sank um Mark uh so sarof uh stayed uh at
+the snof was known as an amazing uh
+
+ align:start position:0%
+the snof was known as an amazing uh
+ 
+
+ align:start position:0%
+the snof was known as an amazing uh
+telegraphy operator and he stayed at the
+
+ align:start position:0%
+telegraphy operator and he stayed at the
+ 
+
+ align:start position:0%
+telegraphy operator and he stayed at the
+station for 72 consecutive hours getting
+
+ align:start position:0%
+station for 72 consecutive hours getting
+ 
+
+ align:start position:0%
+station for 72 consecutive hours getting
+emergency messages from the Titanic
+
+ align:start position:0%
+emergency messages from the Titanic
+ 
+
+ align:start position:0%
+emergency messages from the Titanic
+telling everybody everything that he
+
+ align:start position:0%
+telling everybody everything that he
+ 
+
+ align:start position:0%
+telling everybody everything that he
+could trying to tell them the situation
+
+ align:start position:0%
+could trying to tell them the situation
+ 
+
+ align:start position:0%
+could trying to tell them the situation
+whose family was in good shape whose
+
+ align:start position:0%
+whose family was in good shape whose
+ 
+
+ align:start position:0%
+whose family was in good shape whose
+family was not in good shape it had an
+
+ align:start position:0%
+family was not in good shape it had an
+ 
+
+ align:start position:0%
+family was not in good shape it had an
+enormous
+
+ align:start position:0%
+enormous
+ 
+
+ align:start position:0%
+enormous
+impact big enough that Congress made a
+
+ align:start position:0%
+impact big enough that Congress made a
+ 
+
+ align:start position:0%
+impact big enough that Congress made a
+law saying that every ship had to have
+
+ align:start position:0%
+law saying that every ship had to have
+ 
+
+ align:start position:0%
+law saying that every ship had to have
+wireless telegraphy now that made Marone
+
+ align:start position:0%
+wireless telegraphy now that made Marone
+ 
+
+ align:start position:0%
+wireless telegraphy now that made Marone
+extremely rich and it uh indirectly made
+
+ align:start position:0%
+extremely rich and it uh indirectly made
+ 
+
+ align:start position:0%
+extremely rich and it uh indirectly made
+sarof extremely rich too sarof then got
+
+ align:start position:0%
+sarof extremely rich too sarof then got
+ 
+
+ align:start position:0%
+sarof extremely rich too sarof then got
+very interested in uh
+
+ align:start position:0%
+very interested in uh
+ 
+
+ align:start position:0%
+very interested in uh
+extending the idea of radio which then
+
+ align:start position:0%
+extending the idea of radio which then
+ 
+
+ align:start position:0%
+extending the idea of radio which then
+was pointto point to
+
+ align:start position:0%
+was pointto point to
+ 
+
+ align:start position:0%
+was pointto point to
+broadcast so the idea was to somehow he
+
+ align:start position:0%
+broadcast so the idea was to somehow he
+ 
+
+ align:start position:0%
+broadcast so the idea was to somehow he
+called it a radio music box somehow it
+
+ align:start position:0%
+called it a radio music box somehow it
+ 
+
+ align:start position:0%
+called it a radio music box somehow it
+was supposed to be like a newspaper but
+
+ align:start position:0%
+was supposed to be like a newspaper but
+ 
+
+ align:start position:0%
+was supposed to be like a newspaper but
+at the speed of light so the idea was to
+
+ align:start position:0%
+at the speed of light so the idea was to
+ 
+
+ align:start position:0%
+at the speed of light so the idea was to
+somehow make Mass
+
+ align:start position:0%
+somehow make Mass
+ 
+
+ align:start position:0%
+somehow make Mass
+consumption of radio at the time radio
+
+ align:start position:0%
+consumption of radio at the time radio
+ 
+
+ align:start position:0%
+consumption of radio at the time radio
+was per
+
+ align:start position:0%
+was per
+ 
+
+ align:start position:0%
+was per
+ship point to point so you have the
+
+ align:start position:0%
+ship point to point so you have the
+ 
+
+ align:start position:0%
+ship point to point so you have the
+landbased station talking to ship a or
+
+ align:start position:0%
+landbased station talking to ship a or
+ 
+
+ align:start position:0%
+landbased station talking to ship a or
+the landbased station talking to ship b
+
+ align:start position:0%
+the landbased station talking to ship b
+ 
+
+ align:start position:0%
+the landbased station talking to ship b
+or ship a talking to ship B but it was
+
+ align:start position:0%
+or ship a talking to ship B but it was
+ 
+
+ align:start position:0%
+or ship a talking to ship B but it was
+all point to point sof's idea was let's
+
+ align:start position:0%
+all point to point sof's idea was let's
+ 
+
+ align:start position:0%
+all point to point sof's idea was let's
+make a newspaper out of this the key to
+
+ align:start position:0%
+make a newspaper out of this the key to
+ 
+
+ align:start position:0%
+make a newspaper out of this the key to
+doing that was making a cheap
+
+ align:start position:0%
+doing that was making a cheap
+ 
+
+ align:start position:0%
+doing that was making a cheap
+Receiver right it's like newsprint right
+
+ align:start position:0%
+Receiver right it's like newsprint right
+ 
+
+ align:start position:0%
+Receiver right it's like newsprint right
+the printer can cost a
+
+ align:start position:0%
+the printer can cost a
+ 
+
+ align:start position:0%
+the printer can cost a
+mint the transmitter for radio um uh
+
+ align:start position:0%
+mint the transmitter for radio um uh
+ 
+
+ align:start position:0%
+mint the transmitter for radio um uh
+radio broadcast music is allowed to cost
+
+ align:start position:0%
+radio broadcast music is allowed to cost
+ 
+
+ align:start position:0%
+radio broadcast music is allowed to cost
+a mint but the receivers are not allowed
+
+ align:start position:0%
+a mint but the receivers are not allowed
+ 
+
+ align:start position:0%
+a mint but the receivers are not allowed
+to cost a mint that's like the
+
+ align:start position:0%
+to cost a mint that's like the
+ 
+
+ align:start position:0%
+to cost a mint that's like the
+newsprint so the trick was to make an
+
+ align:start position:0%
+newsprint so the trick was to make an
+ 
+
+ align:start position:0%
+newsprint so the trick was to make an
+inexpensive receiver the problem with
+
+ align:start position:0%
+inexpensive receiver the problem with
+ 
+
+ align:start position:0%
+inexpensive receiver the problem with
+making an inex expensive receiver is
+
+ align:start position:0%
+making an inex expensive receiver is
+ 
+
+ align:start position:0%
+making an inex expensive receiver is
+that the scheme that we just talked
+
+ align:start position:0%
+that the scheme that we just talked
+ 
+
+ align:start position:0%
+that the scheme that we just talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh where you derive the where you decode
+
+ align:start position:0%
+uh where you derive the where you decode
+ 
+
+ align:start position:0%
+uh where you derive the where you decode
+the signal by multiplying a second time
+
+ align:start position:0%
+the signal by multiplying a second time
+ 
+
+ align:start position:0%
+the signal by multiplying a second time
+by multiplying by Co Omega CT Omega C
+
+ align:start position:0%
+by multiplying by Co Omega CT Omega C
+ 
+
+ align:start position:0%
+by multiplying by Co Omega CT Omega C
+chosen to be the frequency that you want
+
+ align:start position:0%
+chosen to be the frequency that you want
+ 
+
+ align:start position:0%
+chosen to be the frequency that you want
+to listen to problem with that that's
+
+ align:start position:0%
+to listen to problem with that that's
+ 
+
+ align:start position:0%
+to listen to problem with that that's
+called synchronous demodulation problem
+
+ align:start position:0%
+called synchronous demodulation problem
+ 
+
+ align:start position:0%
+called synchronous demodulation problem
+with that is that you've got to be
+
+ align:start position:0%
+with that is that you've got to be
+ 
+
+ align:start position:0%
+with that is that you've got to be
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+synchronized if you want to listen to
+
+ align:start position:0%
+synchronized if you want to listen to
+ 
+
+ align:start position:0%
+synchronized if you want to listen to
+the message at Omega 2 Omega C must
+
+ align:start position:0%
+the message at Omega 2 Omega C must
+ 
+
+ align:start position:0%
+the message at Omega 2 Omega C must
+equal Omega 2 not omega 2 +
+
+ align:start position:0%
+equal Omega 2 not omega 2 +
+ 
+
+ align:start position:0%
+equal Omega 2 not omega 2 +
+3 okay so if you want to listen to a
+
+ align:start position:0%
+3 okay so if you want to listen to a
+ 
+
+ align:start position:0%
+3 okay so if you want to listen to a
+particular frequency at a to a
+
+ align:start position:0%
+particular frequency at a to a
+ 
+
+ align:start position:0%
+particular frequency at a to a
+particular message you had to have the
+
+ align:start position:0%
+particular message you had to have the
+ 
+
+ align:start position:0%
+particular message you had to have the
+frequency chosen to match the carrier of
+
+ align:start position:0%
+frequency chosen to match the carrier of
+ 
+
+ align:start position:0%
+frequency chosen to match the carrier of
+the message you wanted to listen
+
+ align:start position:0%
+the message you wanted to listen
+ 
+
+ align:start position:0%
+the message you wanted to listen
+to today that's not so hard the way we
+
+ align:start position:0%
+to today that's not so hard the way we
+ 
+
+ align:start position:0%
+to today that's not so hard the way we
+would make frequencies today is with a
+
+ align:start position:0%
+would make frequencies today is with a
+ 
+
+ align:start position:0%
+would make frequencies today is with a
+crystal crystals are great because the
+
+ align:start position:0%
+crystal crystals are great because the
+ 
+
+ align:start position:0%
+crystal crystals are great because the
+frequencies are determined by the
+
+ align:start position:0%
+frequencies are determined by the
+ 
+
+ align:start position:0%
+frequencies are determined by the
+distances in Crystal lates which are
+
+ align:start position:0%
+distances in Crystal lates which are
+ 
+
+ align:start position:0%
+distances in Crystal lates which are
+determined by nanomechanical processes
+
+ align:start position:0%
+determined by nanomechanical processes
+ 
+
+ align:start position:0%
+determined by nanomechanical processes
+to very precisely and in fact we can
+
+ align:start position:0%
+to very precisely and in fact we can
+ 
+
+ align:start position:0%
+to very precisely and in fact we can
+make crystals with no problem with uh
+
+ align:start position:0%
+make crystals with no problem with uh
+ 
+
+ align:start position:0%
+make crystals with no problem with uh
+frequency resolutions of 10us 7 even 10
+
+ align:start position:0%
+frequency resolutions of 10us 7 even 10
+ 
+
+ align:start position:0%
+frequency resolutions of 10us 7 even 10
+Theus 8 so the errors are very small
+
+ align:start position:0%
+Theus 8 so the errors are very small
+ 
+
+ align:start position:0%
+Theus 8 so the errors are very small
+compared to the U frequencies that we're
+
+ align:start position:0%
+compared to the U frequencies that we're
+ 
+
+ align:start position:0%
+compared to the U frequencies that we're
+trying to generate even that wouldn't be
+
+ align:start position:0%
+trying to generate even that wouldn't be
+ 
+
+ align:start position:0%
+trying to generate even that wouldn't be
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+enough so back then this is uh so sof
+
+ align:start position:0%
+enough so back then this is uh so sof
+ 
+
+ align:start position:0%
+enough so back then this is uh so sof
+was working back in the
+
+ align:start position:0%
+was working back in the
+ 
+
+ align:start position:0%
+was working back in the
+1900s back then they couldn't possibly
+
+ align:start position:0%
+1900s back then they couldn't possibly
+ 
+
+ align:start position:0%
+1900s back then they couldn't possibly
+do 10us 8 Precision they were doing
+
+ align:start position:0%
+do 10us 8 Precision they were doing
+ 
+
+ align:start position:0%
+do 10us 8 Precision they were doing
+something more like 10us 2 precision
+
+ align:start position:0%
+something more like 10us 2 precision
+ 
+
+ align:start position:0%
+something more like 10us 2 precision
+they didn't have a Technology based on
+
+ align:start position:0%
+they didn't have a Technology based on
+ 
+
+ align:start position:0%
+they didn't have a Technology based on
+crystals so
+
+ align:start position:0%
+crystals so
+ 
+
+ align:start position:0%
+crystals so
+um they so it would have been impossible
+
+ align:start position:0%
+um they so it would have been impossible
+ 
+
+ align:start position:0%
+um they so it would have been impossible
+to match even to within a factor of 10
+
+ align:start position:0%
+to match even to within a factor of 10
+ 
+
+ align:start position:0%
+to match even to within a factor of 10
+the minus 3 but even if they could have
+
+ align:start position:0%
+the minus 3 but even if they could have
+ 
+
+ align:start position:0%
+the minus 3 but even if they could have
+matched to within 10 the minus8 which we
+
+ align:start position:0%
+matched to within 10 the minus8 which we
+ 
+
+ align:start position:0%
+matched to within 10 the minus8 which we
+could today even that wouldn't work
+
+ align:start position:0%
+could today even that wouldn't work
+ 
+
+ align:start position:0%
+could today even that wouldn't work
+because not only does the frequency have
+
+ align:start position:0%
+because not only does the frequency have
+ 
+
+ align:start position:0%
+because not only does the frequency have
+to match the phase has to
+
+ align:start position:0%
+to match the phase has to
+ 
+
+ align:start position:0%
+to match the phase has to
+match so if you're multiplying by a CO
+
+ align:start position:0%
+match so if you're multiplying by a CO
+ 
+
+ align:start position:0%
+match so if you're multiplying by a CO
+Omega CT and you want Omega C to be
+
+ align:start position:0%
+Omega CT and you want Omega C to be
+ 
+
+ align:start position:0%
+Omega CT and you want Omega C to be
+Omega 2 it better actually be the cosine
+
+ align:start position:0%
+Omega 2 it better actually be the cosine
+ 
+
+ align:start position:0%
+Omega 2 it better actually be the cosine
+of Omega 2 and not the of Omega 2 and Co
+
+ align:start position:0%
+of Omega 2 and not the of Omega 2 and Co
+ 
+
+ align:start position:0%
+of Omega 2 and not the of Omega 2 and Co
+differ by a phase so the question is
+
+ align:start position:0%
+differ by a phase so the question is
+ 
+
+ align:start position:0%
+differ by a phase so the question is
+what's the effect of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase when you're trying to demodulate a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal so look at your
+
+ align:start position:0%
+signal so look at your
+ 
+
+ align:start position:0%
+signal so look at your
+neighbor what would happen if you tried
+
+ align:start position:0%
+neighbor what would happen if you tried
+ 
+
+ align:start position:0%
+neighbor what would happen if you tried
+to demodulate by precisely the right
+
+ align:start position:0%
+to demodulate by precisely the right
+ 
+
+ align:start position:0%
+to demodulate by precisely the right
+frequency but you were slipped by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what would happen if there was a
+
+ align:start position:0%
+okay so what would happen if there was a
+ 
+
+ align:start position:0%
+okay so what would happen if there was a
+phase shift between this carrier that
+
+ align:start position:0%
+phase shift between this carrier that
+ 
+
+ align:start position:0%
+phase shift between this carrier that
+was modulating the
+
+ align:start position:0%
+was modulating the
+ 
+
+ align:start position:0%
+was modulating the
+signal and the carrier that is
+
+ align:start position:0%
+signal and the carrier that is
+ 
+
+ align:start position:0%
+signal and the carrier that is
+demodulating the signal what would
+
+ align:start position:0%
+demodulating the signal what would
+ 
+
+ align:start position:0%
+demodulating the signal what would
+happen if there's a phase shift of five
+
+ align:start position:0%
+happen if there's a phase shift of five
+ 
+
+ align:start position:0%
+happen if there's a phase shift of five
+between those
+
+ align:start position:0%
+between those
+ 
+
+ align:start position:0%
+between those
+two what's the effect of five not being
+
+ align:start position:0%
+two what's the effect of five not being
+ 
+
+ align:start position:0%
+two what's the effect of five not being
+zero ideally five would be zero right
+
+ align:start position:0%
+zero ideally five would be zero right
+ 
+
+ align:start position:0%
+zero ideally five would be zero right
+ideally five would be zero what would
+
+ align:start position:0%
+ideally five would be zero what would
+ 
+
+ align:start position:0%
+ideally five would be zero what would
+happen if I were not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay you did all that talking and
+
+ align:start position:0%
+zero okay you did all that talking and
+ 
+
+ align:start position:0%
+zero okay you did all that talking and
+you don't
+
+ align:start position:0%
+you don't
+ 
+
+ align:start position:0%
+you don't
+have yes so like the low pass filter yes
+
+ align:start position:0%
+have yes so like the low pass filter yes
+ 
+
+ align:start position:0%
+have yes so like the low pass filter yes
+of like two will not work in like it
+
+ align:start position:0%
+of like two will not work in like it
+ 
+
+ align:start position:0%
+of like two will not work in like it
+will be either it will be a lot smaller
+
+ align:start position:0%
+will be either it will be a lot smaller
+ 
+
+ align:start position:0%
+will be either it will be a lot smaller
+than what you wanted to done like half
+
+ align:start position:0%
+than what you wanted to done like half
+ 
+
+ align:start position:0%
+than what you wanted to done like half
+so that's exactly right so the the
+
+ align:start position:0%
+so that's exactly right so the the
+ 
+
+ align:start position:0%
+so that's exactly right so the the
+effect of fi if you think about uh so
+
+ align:start position:0%
+effect of fi if you think about uh so
+ 
+
+ align:start position:0%
+effect of fi if you think about uh so
+now you have cosine of some omega C and
+
+ align:start position:0%
+now you have cosine of some omega C and
+ 
+
+ align:start position:0%
+now you have cosine of some omega C and
+Co Omega c c but plus 5 so you have Co a
+
+ align:start position:0%
+Co Omega c c but plus 5 so you have Co a
+ 
+
+ align:start position:0%
+Co Omega c c but plus 5 so you have Co a
+CO B right so that gives you uh the co
+
+ align:start position:0%
+CO B right so that gives you uh the co
+ 
+
+ align:start position:0%
+CO B right so that gives you uh the co
+of the difference and the co of the sum
+
+ align:start position:0%
+of the difference and the co of the sum
+ 
+
+ align:start position:0%
+of the difference and the co of the sum
+right the co of the difference was
+
+ align:start position:0%
+right the co of the difference was
+ 
+
+ align:start position:0%
+right the co of the difference was
+supposed to be the co the difference was
+
+ align:start position:0%
+supposed to be the co the difference was
+ 
+
+ align:start position:0%
+supposed to be the co the difference was
+supposed to be zero the co of the
+
+ align:start position:0%
+supposed to be zero the co of the
+ 
+
+ align:start position:0%
+supposed to be zero the co of the
+difference would be the co of zero it
+
+ align:start position:0%
+difference would be the co of zero it
+ 
+
+ align:start position:0%
+difference would be the co of zero it
+should be one and that's where the half
+
+ align:start position:0%
+should be one and that's where the half
+ 
+
+ align:start position:0%
+should be one and that's where the half
+came
+
+ align:start position:0%
+came
+ 
+
+ align:start position:0%
+came
+from but now the difference isn't zero
+
+ align:start position:0%
+from but now the difference isn't zero
+ 
+
+ align:start position:0%
+from but now the difference isn't zero
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+so instead of getting uh a half Co of
+
+ align:start position:0%
+so instead of getting uh a half Co of
+ 
+
+ align:start position:0%
+so instead of getting uh a half Co of
+zero we get half Co of f which means
+
+ align:start position:0%
+zero we get half Co of f which means
+ 
+
+ align:start position:0%
+zero we get half Co of f which means
+that if f is a constant you just get the
+
+ align:start position:0%
+that if f is a constant you just get the
+ 
+
+ align:start position:0%
+that if f is a constant you just get the
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+amplitude but if fi is a slowly varying
+
+ align:start position:0%
+amplitude but if fi is a slowly varying
+ 
+
+ align:start position:0%
+amplitude but if fi is a slowly varying
+signal then uh which it would be even if
+
+ align:start position:0%
+signal then uh which it would be even if
+ 
+
+ align:start position:0%
+signal then uh which it would be even if
+you had a a frequency reliability of one
+
+ align:start position:0%
+you had a a frequency reliability of one
+ 
+
+ align:start position:0%
+you had a a frequency reliability of one
+part in 10 minus
+
+ align:start position:0%
+part in 10 minus
+ 
+
+ align:start position:0%
+part in 10 minus
+7 one way of thinking about that would
+
+ align:start position:0%
+7 one way of thinking about that would
+ 
+
+ align:start position:0%
+7 one way of thinking about that would
+be that there's a slowly varying phase
+
+ align:start position:0%
+be that there's a slowly varying phase
+ 
+
+ align:start position:0%
+be that there's a slowly varying phase
+the effect of the slowly varying phase
+
+ align:start position:0%
+the effect of the slowly varying phase
+ 
+
+ align:start position:0%
+the effect of the slowly varying phase
+would be to make the
+
+ align:start position:0%
+would be to make the
+ 
+
+ align:start position:0%
+would be to make the
+amplitude uh vary with time so we call
+
+ align:start position:0%
+amplitude uh vary with time so we call
+ 
+
+ align:start position:0%
+amplitude uh vary with time so we call
+that fading and it would be a very uh
+
+ align:start position:0%
+that fading and it would be a very uh
+ 
+
+ align:start position:0%
+that fading and it would be a very uh
+distracting thing to have happen so this
+
+ align:start position:0%
+distracting thing to have happen so this
+ 
+
+ align:start position:0%
+distracting thing to have happen so this
+kind of a technology would even be
+
+ align:start position:0%
+kind of a technology would even be
+ 
+
+ align:start position:0%
+kind of a technology would even be
+difficult today when we can match
+
+ align:start position:0%
+difficult today when we can match
+ 
+
+ align:start position:0%
+difficult today when we can match
+frequencies very well it was completely
+
+ align:start position:0%
+frequencies very well it was completely
+ 
+
+ align:start position:0%
+frequencies very well it was completely
+out of the question back in the 1900s
+
+ align:start position:0%
+out of the question back in the 1900s
+ 
+
+ align:start position:0%
+out of the question back in the 1900s
+when they couldn't match frequencies
+
+ align:start position:0%
+when they couldn't match frequencies
+ 
+
+ align:start position:0%
+when they couldn't match frequencies
+that well so the trick was to not only
+
+ align:start position:0%
+that well so the trick was to not only
+ 
+
+ align:start position:0%
+that well so the trick was to not only
+send the message but also send the
+
+ align:start position:0%
+send the message but also send the
+ 
+
+ align:start position:0%
+send the message but also send the
+carrier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so ideally when we first talked about
+
+ align:start position:0%
+so ideally when we first talked about
+ 
+
+ align:start position:0%
+so ideally when we first talked about
+modulation there is no C path all you do
+
+ align:start position:0%
+modulation there is no C path all you do
+ 
+
+ align:start position:0%
+modulation there is no C path all you do
+is you take the signal and you modulate
+
+ align:start position:0%
+is you take the signal and you modulate
+ 
+
+ align:start position:0%
+is you take the signal and you modulate
+it by a carrier and you send that out on
+
+ align:start position:0%
+it by a carrier and you send that out on
+ 
+
+ align:start position:0%
+it by a carrier and you send that out on
+the antenna now instead add on a little
+
+ align:start position:0%
+the antenna now instead add on a little
+ 
+
+ align:start position:0%
+the antenna now instead add on a little
+bit of the
+
+ align:start position:0%
+bit of the
+ 
+
+ align:start position:0%
+bit of the
+carrier that way what's in the air is
+
+ align:start position:0%
+carrier that way what's in the air is
+ 
+
+ align:start position:0%
+carrier that way what's in the air is
+the carrier and the message so now when
+
+ align:start position:0%
+the carrier and the message so now when
+ 
+
+ align:start position:0%
+the carrier and the message so now when
+you receive it somehow if you can
+
+ align:start position:0%
+you receive it somehow if you can
+ 
+
+ align:start position:0%
+you receive it somehow if you can
+receive the carrier you can use the
+
+ align:start position:0%
+receive the carrier you can use the
+ 
+
+ align:start position:0%
+receive the carrier you can use the
+carrier to tell you information about
+
+ align:start position:0%
+carrier to tell you information about
+ 
+
+ align:start position:0%
+carrier to tell you information about
+not only the frequency but also the
+
+ align:start position:0%
+not only the frequency but also the
+ 
+
+ align:start position:0%
+not only the frequency but also the
+phase of the carrier and you can use
+
+ align:start position:0%
+phase of the carrier and you can use
+ 
+
+ align:start position:0%
+phase of the carrier and you can use
+that then to demodulate the message
+
+ align:start position:0%
+that then to demodulate the message
+ 
+
+ align:start position:0%
+that then to demodulate the message
+that's the idea notice that uh adding in
+
+ align:start position:0%
+that's the idea notice that uh adding in
+ 
+
+ align:start position:0%
+that's the idea notice that uh adding in
+a little bit C of the carrier is
+
+ align:start position:0%
+a little bit C of the carrier is
+ 
+
+ align:start position:0%
+a little bit C of the carrier is
+precisely the same as adding a constant
+
+ align:start position:0%
+precisely the same as adding a constant
+ 
+
+ align:start position:0%
+precisely the same as adding a constant
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+message before you modulate
+
+ align:start position:0%
+message before you modulate
+ 
+
+ align:start position:0%
+message before you modulate
+mathematically identical and that gives
+
+ align:start position:0%
+mathematically identical and that gives
+ 
+
+ align:start position:0%
+mathematically identical and that gives
+an easy way of thinking about the effect
+
+ align:start position:0%
+an easy way of thinking about the effect
+ 
+
+ align:start position:0%
+an easy way of thinking about the effect
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+carrier if you think about the message
+
+ align:start position:0%
+carrier if you think about the message
+ 
+
+ align:start position:0%
+carrier if you think about the message
+added to C and if C is big
+
+ align:start position:0%
+added to C and if C is big
+ 
+
+ align:start position:0%
+added to C and if C is big
+enough you can make the carry you can
+
+ align:start position:0%
+enough you can make the carry you can
+ 
+
+ align:start position:0%
+enough you can make the carry you can
+make the message positive
+
+ align:start position:0%
+make the message positive
+ 
+
+ align:start position:0%
+make the message positive
+only you remember before in the previous
+
+ align:start position:0%
+only you remember before in the previous
+ 
+
+ align:start position:0%
+only you remember before in the previous
+illustration uh every time the message
+
+ align:start position:0%
+illustration uh every time the message
+ 
+
+ align:start position:0%
+illustration uh every time the message
+went through zero which might happen
+
+ align:start position:0%
+went through zero which might happen
+ 
+
+ align:start position:0%
+went through zero which might happen
+here the the uh modulated message went
+
+ align:start position:0%
+here the the uh modulated message went
+ 
+
+ align:start position:0%
+here the the uh modulated message went
+through zero also which means that sign
+
+ align:start position:0%
+through zero also which means that sign
+ 
+
+ align:start position:0%
+through zero also which means that sign
+changes were affected by 180° face
+
+ align:start position:0%
+changes were affected by 180° face
+ 
+
+ align:start position:0%
+changes were affected by 180° face
+shifts of the carrier which was kind of
+
+ align:start position:0%
+shifts of the carrier which was kind of
+ 
+
+ align:start position:0%
+shifts of the carrier which was kind of
+a subtle thing so now the message appear
+
+ align:start position:0%
+a subtle thing so now the message appear
+ 
+
+ align:start position:0%
+a subtle thing so now the message appear
+entirely as the positive
+
+ align:start position:0%
+entirely as the positive
+ 
+
+ align:start position:0%
+entirely as the positive
+envelope of the carrier well that's nice
+
+ align:start position:0%
+envelope of the carrier well that's nice
+ 
+
+ align:start position:0%
+envelope of the carrier well that's nice
+because that makes it very easy to
+
+ align:start position:0%
+because that makes it very easy to
+ 
+
+ align:start position:0%
+because that makes it very easy to
+decode in a way that has uh no
+
+ align:start position:0%
+decode in a way that has uh no
+ 
+
+ align:start position:0%
+decode in a way that has uh no
+dependence
+
+ align:start position:0%
+dependence
+ 
+
+ align:start position:0%
+dependence
+whatever on the carrier frequency if the
+
+ align:start position:0%
+whatever on the carrier frequency if the
+ 
+
+ align:start position:0%
+whatever on the carrier frequency if the
+carrier frequency is big enough you can
+
+ align:start position:0%
+carrier frequency is big enough you can
+ 
+
+ align:start position:0%
+carrier frequency is big enough you can
+uh if the frequency of the carrier is
+
+ align:start position:0%
+uh if the frequency of the carrier is
+ 
+
+ align:start position:0%
+uh if the frequency of the carrier is
+sufficiently larger than the maximum
+
+ align:start position:0%
+sufficiently larger than the maximum
+ 
+
+ align:start position:0%
+sufficiently larger than the maximum
+frequency of the message there's a
+
+ align:start position:0%
+frequency of the message there's a
+ 
+
+ align:start position:0%
+frequency of the message there's a
+trivial way to decode such a such a
+
+ align:start position:0%
+trivial way to decode such a such a
+ 
+
+ align:start position:0%
+trivial way to decode such a such a
+system uh with a nonlinear Circuit of
+
+ align:start position:0%
+system uh with a nonlinear Circuit of
+ 
+
+ align:start position:0%
+system uh with a nonlinear Circuit of
+this type what's intended here is that
+
+ align:start position:0%
+this type what's intended here is that
+ 
+
+ align:start position:0%
+this type what's intended here is that
+you take the message that's received
+
+ align:start position:0%
+you take the message that's received
+ 
+
+ align:start position:0%
+you take the message that's received
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+antenna re reconstruct Y which is
+
+ align:start position:0%
+antenna re reconstruct Y which is
+ 
+
+ align:start position:0%
+antenna re reconstruct Y which is
+intended to be the output
+
+ align:start position:0%
+intended to be the output
+ 
+
+ align:start position:0%
+intended to be the output
+message such that if Z the signal on the
+
+ align:start position:0%
+message such that if Z the signal on the
+ 
+
+ align:start position:0%
+message such that if Z the signal on the
+antenna exceeds the current value of the
+
+ align:start position:0%
+antenna exceeds the current value of the
+ 
+
+ align:start position:0%
+antenna exceeds the current value of the
+message the diode comes
+
+ align:start position:0%
+message the diode comes
+ 
+
+ align:start position:0%
+message the diode comes
+on and that makes the Blue Line the
+
+ align:start position:0%
+on and that makes the Blue Line the
+ 
+
+ align:start position:0%
+on and that makes the Blue Line the
+decoded signal rapidly go back up to the
+
+ align:start position:0%
+decoded signal rapidly go back up to the
+ 
+
+ align:start position:0%
+decoded signal rapidly go back up to the
+red line the thing that's coming off the
+
+ align:start position:0%
+red line the thing that's coming off the
+ 
+
+ align:start position:0%
+red line the thing that's coming off the
+antenna
+
+ align:start position:0%
+antenna
+ 
+
+ align:start position:0%
+antenna
+but if the antenna signal shrinks below
+
+ align:start position:0%
+but if the antenna signal shrinks below
+ 
+
+ align:start position:0%
+but if the antenna signal shrinks below
+the Blue Line let the Blue Line
+
+ align:start position:0%
+the Blue Line let the Blue Line
+ 
+
+ align:start position:0%
+the Blue Line let the Blue Line
+discharge because there's a an RC Decay
+
+ align:start position:0%
+discharge because there's a an RC Decay
+ 
+
+ align:start position:0%
+discharge because there's a an RC Decay
+constant so there's a fast attack
+
+ align:start position:0%
+constant so there's a fast attack
+ 
+
+ align:start position:0%
+constant so there's a fast attack
+through the diode so that the blue
+
+ align:start position:0%
+through the diode so that the blue
+ 
+
+ align:start position:0%
+through the diode so that the blue
+quickly goes to the peak value of the
+
+ align:start position:0%
+quickly goes to the peak value of the
+ 
+
+ align:start position:0%
+quickly goes to the peak value of the
+red and slowly decays back towards zero
+
+ align:start position:0%
+red and slowly decays back towards zero
+ 
+
+ align:start position:0%
+red and slowly decays back towards zero
+the result is that if the frequencies
+
+ align:start position:0%
+the result is that if the frequencies
+ 
+
+ align:start position:0%
+the result is that if the frequencies
+the the difference in frequency between
+
+ align:start position:0%
+the the difference in frequency between
+ 
+
+ align:start position:0%
+the the difference in frequency between
+the carrier frequency and the message
+
+ align:start position:0%
+the carrier frequency and the message
+ 
+
+ align:start position:0%
+the carrier frequency and the message
+frequencies is sufficiently large you
+
+ align:start position:0%
+frequencies is sufficiently large you
+ 
+
+ align:start position:0%
+frequencies is sufficiently large you
+can effectively separate the blue from
+
+ align:start position:0%
+can effectively separate the blue from
+ 
+
+ align:start position:0%
+can effectively separate the blue from
+the red with a very simple circuit and
+
+ align:start position:0%
+the red with a very simple circuit and
+ 
+
+ align:start position:0%
+the red with a very simple circuit and
+that's the way they do it or that's the
+
+ align:start position:0%
+that's the way they do it or that's the
+ 
+
+ align:start position:0%
+that's the way they do it or that's the
+way they did it in in u the early 1900s
+
+ align:start position:0%
+way they did it in in u the early 1900s
+ 
+
+ align:start position:0%
+way they did it in in u the early 1900s
+but there's still a problem with that
+
+ align:start position:0%
+but there's still a problem with that
+ 
+
+ align:start position:0%
+but there's still a problem with that
+the problem is that the
+
+ align:start position:0%
+the problem is that the
+ 
+
+ align:start position:0%
+the problem is that the
+messages audio of the type that I'm
+
+ align:start position:0%
+messages audio of the type that I'm
+ 
+
+ align:start position:0%
+messages audio of the type that I'm
+speaking speech is characterized by an
+
+ align:start position:0%
+speaking speech is characterized by an
+ 
+
+ align:start position:0%
+speaking speech is characterized by an
+enormous Peak to average
+
+ align:start position:0%
+enormous Peak to average
+ 
+
+ align:start position:0%
+enormous Peak to average
+ratio the strongest pressures that are
+
+ align:start position:0%
+ratio the strongest pressures that are
+ 
+
+ align:start position:0%
+ratio the strongest pressures that are
+generated by speech are enormously more
+
+ align:start position:0%
+generated by speech are enormously more
+ 
+
+ align:start position:0%
+generated by speech are enormously more
+powerful than the average pressure
+
+ align:start position:0%
+powerful than the average pressure
+ 
+
+ align:start position:0%
+powerful than the average pressure
+that's generated in speech you can see
+
+ align:start position:0%
+that's generated in speech you can see
+ 
+
+ align:start position:0%
+that's generated in speech you can see
+that in this diagram by these Peaks
+
+ align:start position:0%
+that in this diagram by these Peaks
+ 
+
+ align:start position:0%
+that in this diagram by these Peaks
+right there's several things that
+
+ align:start position:0%
+right there's several things that
+ 
+
+ align:start position:0%
+right there's several things that
+generate Peaks Peaks are generated at
+
+ align:start position:0%
+generate Peaks Peaks are generated at
+ 
+
+ align:start position:0%
+generate Peaks Peaks are generated at
+about uh 60 or 70 Hertz by my vocal
+
+ align:start position:0%
+about uh 60 or 70 Hertz by my vocal
+ 
+
+ align:start position:0%
+about uh 60 or 70 Hertz by my vocal
+cords but they're also generated by my
+
+ align:start position:0%
+cords but they're also generated by my
+ 
+
+ align:start position:0%
+cords but they're also generated by my
+lips in plosives right when I do
+
+ align:start position:0%
+lips in plosives right when I do
+ 
+
+ align:start position:0%
+lips in plosives right when I do
+aive there's a sudden jump in the
+
+ align:start position:0%
+aive there's a sudden jump in the
+ 
+
+ align:start position:0%
+aive there's a sudden jump in the
+instantaneous frequency that's not there
+
+ align:start position:0%
+instantaneous frequency that's not there
+ 
+
+ align:start position:0%
+instantaneous frequency that's not there
+on average and for normal speech that
+
+ align:start position:0%
+on average and for normal speech that
+ 
+
+ align:start position:0%
+on average and for normal speech that
+ratio can be as high as 35
+
+ align:start position:0%
+ratio can be as high as 35
+ 
+
+ align:start position:0%
+ratio can be as high as 35
+to1 35 to1 big deal problem is that
+
+ align:start position:0%
+to1 35 to1 big deal problem is that
+ 
+
+ align:start position:0%
+to1 35 to1 big deal problem is that
+power goes like the square of voltage so
+
+ align:start position:0%
+power goes like the square of voltage so
+ 
+
+ align:start position:0%
+power goes like the square of voltage so
+35 to1 becomes a th to one It Takes a
+
+ align:start position:0%
+35 to1 becomes a th to one It Takes a
+ 
+
+ align:start position:0%
+35 to1 becomes a th to one It Takes a
+thousand times more
+
+ align:start position:0%
+thousand times more
+ 
+
+ align:start position:0%
+thousand times more
+energy to code the Peaks than it does to
+
+ align:start position:0%
+energy to code the Peaks than it does to
+ 
+
+ align:start position:0%
+energy to code the Peaks than it does to
+code the average and the problem with
+
+ align:start position:0%
+code the average and the problem with
+ 
+
+ align:start position:0%
+code the average and the problem with
+that is that in this coding scheme that
+
+ align:start position:0%
+that is that in this coding scheme that
+ 
+
+ align:start position:0%
+that is that in this coding scheme that
+we talked
+
+ align:start position:0%
+we talked
+ 
+
+ align:start position:0%
+we talked
+about you have to add a constant that is
+
+ align:start position:0%
+about you have to add a constant that is
+ 
+
+ align:start position:0%
+about you have to add a constant that is
+big enough so that the signal never goes
+
+ align:start position:0%
+big enough so that the signal never goes
+ 
+
+ align:start position:0%
+big enough so that the signal never goes
+negative so the constant that you add
+
+ align:start position:0%
+negative so the constant that you add
+ 
+
+ align:start position:0%
+negative so the constant that you add
+has to go in proportion to the peak
+
+ align:start position:0%
+has to go in proportion to the peak
+ 
+
+ align:start position:0%
+has to go in proportion to the peak
+value so you end up transmitting almost
+
+ align:start position:0%
+value so you end up transmitting almost
+ 
+
+ align:start position:0%
+value so you end up transmitting almost
+all of your
+
+ align:start position:0%
+all of your
+ 
+
+ align:start position:0%
+all of your
+power 1,00 to one by the ratio of 1,00
+
+ align:start position:0%
+power 1,00 to one by the ratio of 1,00
+ 
+
+ align:start position:0%
+power 1,00 to one by the ratio of 1,00
+to one that's the amount of power that
+
+ align:start position:0%
+to one that's the amount of power that
+ 
+
+ align:start position:0%
+to one that's the amount of power that
+gets used to transmit the carrier
+
+ align:start position:0%
+gets used to transmit the carrier
+ 
+
+ align:start position:0%
+gets used to transmit the carrier
+compared to the message well that's a
+
+ align:start position:0%
+compared to the message well that's a
+ 
+
+ align:start position:0%
+compared to the message well that's a
+terrible scheme if what we were trying
+
+ align:start position:0%
+terrible scheme if what we were trying
+ 
+
+ align:start position:0%
+terrible scheme if what we were trying
+to do is point to point imagine your
+
+ align:start position:0%
+to do is point to point imagine your
+ 
+
+ align:start position:0%
+to do is point to point imagine your
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+phone if you had to transmit enough
+
+ align:start position:0%
+phone if you had to transmit enough
+ 
+
+ align:start position:0%
+phone if you had to transmit enough
+power to in the worst case do the
+
+ align:start position:0%
+power to in the worst case do the
+ 
+
+ align:start position:0%
+power to in the worst case do the
+Peaks you would on average be
+
+ align:start position:0%
+Peaks you would on average be
+ 
+
+ align:start position:0%
+Peaks you would on average be
+transmitting power at a thousand times
+
+ align:start position:0%
+transmitting power at a thousand times
+ 
+
+ align:start position:0%
+transmitting power at a thousand times
+the rate that you would necessarily have
+
+ align:start position:0%
+the rate that you would necessarily have
+ 
+
+ align:start position:0%
+the rate that you would necessarily have
+to so that's okay for broadcast so for
+
+ align:start position:0%
+to so that's okay for broadcast so for
+ 
+
+ align:start position:0%
+to so that's okay for broadcast so for
+example WBZ broadcast radio WBZ uses a
+
+ align:start position:0%
+example WBZ broadcast radio WBZ uses a
+ 
+
+ align:start position:0%
+example WBZ broadcast radio WBZ uses a
+50 kilowatt transmitter 50 kilowatts is
+
+ align:start position:0%
+50 kilowatt transmitter 50 kilowatts is
+ 
+
+ align:start position:0%
+50 kilowatt transmitter 50 kilowatts is
+the amount of power that would otherwise
+
+ align:start position:0%
+the amount of power that would otherwise
+ 
+
+ align:start position:0%
+the amount of power that would otherwise
+be sufficient to generate 500 100 W
+
+ align:start position:0%
+be sufficient to generate 500 100 W
+ 
+
+ align:start position:0%
+be sufficient to generate 500 100 W
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+bulbs okay
+
+ align:start position:0%
+bulbs okay
+ 
+
+ align:start position:0%
+bulbs okay
+that's a fair amount of power right
+
+ align:start position:0%
+that's a fair amount of power right
+ 
+
+ align:start position:0%
+that's a fair amount of power right
+imagine the heat that comes off 500 100
+
+ align:start position:0%
+imagine the heat that comes off 500 100
+ 
+
+ align:start position:0%
+imagine the heat that comes off 500 100
+watt light bulbs that's how much power
+
+ align:start position:0%
+watt light bulbs that's how much power
+ 
+
+ align:start position:0%
+watt light bulbs that's how much power
+is being radiated by the
+
+ align:start position:0%
+is being radiated by the
+ 
+
+ align:start position:0%
+is being radiated by the
+antenna for
+
+ align:start position:0%
+antenna for
+ 
+
+ align:start position:0%
+antenna for
+WBZ that power is not necessary to
+
+ align:start position:0%
+WBZ that power is not necessary to
+ 
+
+ align:start position:0%
+WBZ that power is not necessary to
+transmit the average message it's
+
+ align:start position:0%
+transmit the average message it's
+ 
+
+ align:start position:0%
+transmit the average message it's
+necessary to transmit the peak
+
+ align:start position:0%
+necessary to transmit the peak
+ 
+
+ align:start position:0%
+necessary to transmit the peak
+message you can imagine how long your
+
+ align:start position:0%
+message you can imagine how long your
+ 
+
+ align:start position:0%
+message you can imagine how long your
+cell phone battery would last if you
+
+ align:start position:0%
+cell phone battery would last if you
+ 
+
+ align:start position:0%
+cell phone battery would last if you
+were transmitting 50 kilow right it
+
+ align:start position:0%
+were transmitting 50 kilow right it
+ 
+
+ align:start position:0%
+were transmitting 50 kilow right it
+doesn't work right so that's a that's
+
+ align:start position:0%
+doesn't work right so that's a that's
+ 
+
+ align:start position:0%
+doesn't work right so that's a that's
+how the uh broadcast radio takes
+
+ align:start position:0%
+how the uh broadcast radio takes
+ 
+
+ align:start position:0%
+how the uh broadcast radio takes
+advantage of broadcast it makes no sense
+
+ align:start position:0%
+advantage of broadcast it makes no sense
+ 
+
+ align:start position:0%
+advantage of broadcast it makes no sense
+to use this coding scheme for a
+
+ align:start position:0%
+to use this coding scheme for a
+ 
+
+ align:start position:0%
+to use this coding scheme for a
+point-to-point
+
+ align:start position:0%
+point-to-point
+ 
+
+ align:start position:0%
+point-to-point
+system it's fine if what you're trying
+
+ align:start position:0%
+system it's fine if what you're trying
+ 
+
+ align:start position:0%
+system it's fine if what you're trying
+to do is have one transmitter WBZ that
+
+ align:start position:0%
+to do is have one transmitter WBZ that
+ 
+
+ align:start position:0%
+to do is have one transmitter WBZ that
+Services a million listeners that's
+
+ align:start position:0%
+Services a million listeners that's
+ 
+
+ align:start position:0%
+Services a million listeners that's
+fine okay problem with this scheme for
+
+ align:start position:0%
+fine okay problem with this scheme for
+ 
+
+ align:start position:0%
+fine okay problem with this scheme for
+decoding is it still doesn't separate
+
+ align:start position:0%
+decoding is it still doesn't separate
+ 
+
+ align:start position:0%
+decoding is it still doesn't separate
+different channels and the way to fix
+
+ align:start position:0%
+different channels and the way to fix
+ 
+
+ align:start position:0%
+different channels and the way to fix
+that was uh develop by Edward Armstrong
+
+ align:start position:0%
+that was uh develop by Edward Armstrong
+ 
+
+ align:start position:0%
+that was uh develop by Edward Armstrong
+so sof was kind of the Visionary he had
+
+ align:start position:0%
+so sof was kind of the Visionary he had
+ 
+
+ align:start position:0%
+so sof was kind of the Visionary he had
+the idea for broadcast radio he's the
+
+ align:start position:0%
+the idea for broadcast radio he's the
+ 
+
+ align:start position:0%
+the idea for broadcast radio he's the
+the the uh entrepreneurial type who
+
+ align:start position:0%
+the the uh entrepreneurial type who
+ 
+
+ align:start position:0%
+the the uh entrepreneurial type who
+thought of how to do this Armstrong was
+
+ align:start position:0%
+thought of how to do this Armstrong was
+ 
+
+ align:start position:0%
+thought of how to do this Armstrong was
+the technical genius he knew how to do
+
+ align:start position:0%
+the technical genius he knew how to do
+ 
+
+ align:start position:0%
+the technical genius he knew how to do
+it so Armstrong's idea here which we
+
+ align:start position:0%
+it so Armstrong's idea here which we
+ 
+
+ align:start position:0%
+it so Armstrong's idea here which we
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+superod was let's make the signal look
+
+ align:start position:0%
+superod was let's make the signal look
+ 
+
+ align:start position:0%
+superod was let's make the signal look
+like it always come from comes from
+
+ align:start position:0%
+like it always come from comes from
+ 
+
+ align:start position:0%
+like it always come from comes from
+Omega I regardless of what channel it
+
+ align:start position:0%
+Omega I regardless of what channel it
+ 
+
+ align:start position:0%
+Omega I regardless of what channel it
+comes
+
+ align:start position:0%
+comes
+ 
+
+ align:start position:0%
+comes
+from so Omega I the intermediate
+
+ align:start position:0%
+from so Omega I the intermediate
+ 
+
+ align:start position:0%
+from so Omega I the intermediate
+frequency will always take Whatever
+
+ align:start position:0%
+frequency will always take Whatever
+ 
+
+ align:start position:0%
+frequency will always take Whatever
+frequency you're interested in and turn
+
+ align:start position:0%
+frequency you're interested in and turn
+ 
+
+ align:start position:0%
+frequency you're interested in and turn
+it into Omega I and we'll do that by
+
+ align:start position:0%
+it into Omega I and we'll do that by
+ 
+
+ align:start position:0%
+it into Omega I and we'll do that by
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+modulating and the cleverness had to do
+
+ align:start position:0%
+modulating and the cleverness had to do
+ 
+
+ align:start position:0%
+modulating and the cleverness had to do
+with with with a lot of technical
+
+ align:start position:0%
+with with with a lot of technical
+ 
+
+ align:start position:0%
+with with with a lot of technical
+details he worked out a scheme where
+
+ align:start position:0%
+details he worked out a scheme where
+ 
+
+ align:start position:0%
+details he worked out a scheme where
+this modulation was very easy the cut
+
+ align:start position:0%
+this modulation was very easy the cut
+ 
+
+ align:start position:0%
+this modulation was very easy the cut
+off the side bands on the band pass
+
+ align:start position:0%
+off the side bands on the band pass
+ 
+
+ align:start position:0%
+off the side bands on the band pass
+filters didn't have to be very uh steep
+
+ align:start position:0%
+filters didn't have to be very uh steep
+ 
+
+ align:start position:0%
+filters didn't have to be very uh steep
+which made them easy to
+
+ align:start position:0%
+which made them easy to
+ 
+
+ align:start position:0%
+which made them easy to
+implement the sharp bam pass filters
+
+ align:start position:0%
+implement the sharp bam pass filters
+ 
+
+ align:start position:0%
+implement the sharp bam pass filters
+were all at that one intermediate
+
+ align:start position:0%
+were all at that one intermediate
+ 
+
+ align:start position:0%
+were all at that one intermediate
+frequency so he had to generate one very
+
+ align:start position:0%
+frequency so he had to generate one very
+ 
+
+ align:start position:0%
+frequency so he had to generate one very
+sharp band pass filter but that same
+
+ align:start position:0%
+sharp band pass filter but that same
+ 
+
+ align:start position:0%
+sharp band pass filter but that same
+sharp bandwidth uh sharp uh bandpass
+
+ align:start position:0%
+sharp bandwidth uh sharp uh bandpass
+ 
+
+ align:start position:0%
+sharp bandwidth uh sharp uh bandpass
+filter then be used for all the
+
+ align:start position:0%
+filter then be used for all the
+ 
+
+ align:start position:0%
+filter then be used for all the
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+channels so uh the idea then was use a
+
+ align:start position:0%
+channels so uh the idea then was use a
+ 
+
+ align:start position:0%
+channels so uh the idea then was use a
+coarse tunable filter to map the
+
+ align:start position:0%
+coarse tunable filter to map the
+ 
+
+ align:start position:0%
+coarse tunable filter to map the
+frequency of interest to Omega
+
+ align:start position:0%
+frequency of interest to Omega
+ 
+
+ align:start position:0%
+frequency of interest to Omega
+I put that through a very sharp filter
+
+ align:start position:0%
+I put that through a very sharp filter
+ 
+
+ align:start position:0%
+I put that through a very sharp filter
+of which there is exactly one in
+
+ align:start position:0%
+of which there is exactly one in
+ 
+
+ align:start position:0%
+of which there is exactly one in
+receiver and then use this uh decoding
+
+ align:start position:0%
+receiver and then use this uh decoding
+ 
+
+ align:start position:0%
+receiver and then use this uh decoding
+scheme
+
+ align:start position:0%
+scheme
+ 
+
+ align:start position:0%
+scheme
+um to tr to uh
+
+ align:start position:0%
+um to tr to uh
+ 
+
+ align:start position:0%
+um to tr to uh
+demodulate the uh carrier
+
+ align:start position:0%
+demodulate the uh carrier
+ 
+
+ align:start position:0%
+demodulate the uh carrier
+wi okay that's how they did it we would
+
+ align:start position:0%
+wi okay that's how they did it we would
+ 
+
+ align:start position:0%
+wi okay that's how they did it we would
+never do it that
+
+ align:start position:0%
+never do it that
+ 
+
+ align:start position:0%
+never do it that
+way right that's part of the theme of
+
+ align:start position:0%
+way right that's part of the theme of
+ 
+
+ align:start position:0%
+way right that's part of the theme of
+the course we we are interested in
+
+ align:start position:0%
+the course we we are interested in
+ 
+
+ align:start position:0%
+the course we we are interested in
+schemes that let us map continuous time
+
+ align:start position:0%
+schemes that let us map continuous time
+ 
+
+ align:start position:0%
+schemes that let us map continuous time
+to discrete time that sort of thing so
+
+ align:start position:0%
+to discrete time that sort of thing so
+ 
+
+ align:start position:0%
+to discrete time that sort of thing so
+one way we might do it is Implement a
+
+ align:start position:0%
+one way we might do it is Implement a
+ 
+
+ align:start position:0%
+one way we might do it is Implement a
+radio digitally okay so the idea would
+
+ align:start position:0%
+radio digitally okay so the idea would
+ 
+
+ align:start position:0%
+radio digitally okay so the idea would
+be what if you took the antenna put it
+
+ align:start position:0%
+be what if you took the antenna put it
+ 
+
+ align:start position:0%
+be what if you took the antenna put it
+through a
+
+ align:start position:0%
+through a
+ 
+
+ align:start position:0%
+through a
+sampler turn the radio signal which
+
+ align:start position:0%
+sampler turn the radio signal which
+ 
+
+ align:start position:0%
+sampler turn the radio signal which
+contains gazillion number of bands for
+
+ align:start position:0%
+contains gazillion number of bands for
+ 
+
+ align:start position:0%
+contains gazillion number of bands for
+for commercial radio there's 100
+
+ align:start position:0%
+for commercial radio there's 100
+ 
+
+ align:start position:0%
+for commercial radio there's 100
+channels in the frequency band 500 to
+
+ align:start position:0%
+channels in the frequency band 500 to
+ 
+
+ align:start position:0%
+channels in the frequency band 500 to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+khz but just take the whole uh signal
+
+ align:start position:0%
+khz but just take the whole uh signal
+ 
+
+ align:start position:0%
+khz but just take the whole uh signal
+off the antenna turn it into a bunch of
+
+ align:start position:0%
+off the antenna turn it into a bunch of
+ 
+
+ align:start position:0%
+off the antenna turn it into a bunch of
+bits run that through some digital logic
+
+ align:start position:0%
+bits run that through some digital logic
+ 
+
+ align:start position:0%
+bits run that through some digital logic
+that does by Magic picks out the one
+
+ align:start position:0%
+that does by Magic picks out the one
+ 
+
+ align:start position:0%
+that does by Magic picks out the one
+that you're interested in generates a
+
+ align:start position:0%
+that you're interested in generates a
+ 
+
+ align:start position:0%
+that you're interested in generates a
+new stream of bits yd from which you can
+
+ align:start position:0%
+new stream of bits yd from which you can
+ 
+
+ align:start position:0%
+new stream of bits yd from which you can
+do band limited reconstruction so this
+
+ align:start position:0%
+do band limited reconstruction so this
+ 
+
+ align:start position:0%
+do band limited reconstruction so this
+is you know the last two lectures how do
+
+ align:start position:0%
+is you know the last two lectures how do
+ 
+
+ align:start position:0%
+is you know the last two lectures how do
+you do this how you do this now all we
+
+ align:start position:0%
+you do this how you do this now all we
+ 
+
+ align:start position:0%
+you do this how you do this now all we
+do is we put a particular algorithm in
+
+ align:start position:0%
+do is we put a particular algorithm in
+ 
+
+ align:start position:0%
+do is we put a particular algorithm in
+there and we've got a radio that's the
+
+ align:start position:0%
+there and we've got a radio that's the
+ 
+
+ align:start position:0%
+there and we've got a radio that's the
+idea it seems it this is uh oh so the
+
+ align:start position:0%
+idea it seems it this is uh oh so the
+ 
+
+ align:start position:0%
+idea it seems it this is uh oh so the
+key to being able to that is whether or
+
+ align:start position:0%
+key to being able to that is whether or
+ 
+
+ align:start position:0%
+key to being able to that is whether or
+not you can build that
+
+ align:start position:0%
+not you can build that
+ 
+
+ align:start position:0%
+not you can build that
+sampler so what what would be the
+
+ align:start position:0%
+sampler so what what would be the
+ 
+
+ align:start position:0%
+sampler so what what would be the
+required sampling
+
+ align:start position:0%
+required sampling
+ 
+
+ align:start position:0%
+required sampling
+time in order to make a digital
+
+ align:start position:0%
+time in order to make a digital
+ 
+
+ align:start position:0%
+time in order to make a digital
+radio and since I'm running out of time
+
+ align:start position:0%
+radio and since I'm running out of time
+ 
+
+ align:start position:0%
+radio and since I'm running out of time
+uh I I'll just tell you that the
+
+ align:start position:0%
+uh I I'll just tell you that the
+ 
+
+ align:start position:0%
+uh I I'll just tell you that the
+important thing it's sampling it's what
+
+ align:start position:0%
+important thing it's sampling it's what
+ 
+
+ align:start position:0%
+important thing it's sampling it's what
+we did last time the answer is uh you
+
+ align:start position:0%
+we did last time the answer is uh you
+ 
+
+ align:start position:0%
+we did last time the answer is uh you
+need um T so that the sampling frequency
+
+ align:start position:0%
+need um T so that the sampling frequency
+ 
+
+ align:start position:0%
+need um T so that the sampling frequency
+is at least twice the maximum frequency
+
+ align:start position:0%
+is at least twice the maximum frequency
+ 
+
+ align:start position:0%
+is at least twice the maximum frequency
+of the thing that you're trying to
+
+ align:start position:0%
+of the thing that you're trying to
+ 
+
+ align:start position:0%
+of the thing that you're trying to
+code so the the biggest frequency here
+
+ align:start position:0%
+code so the the biggest frequency here
+ 
+
+ align:start position:0%
+code so the the biggest frequency here
+is600 uh
+
+ align:start position:0%
+is600 uh
+ 
+
+ align:start position:0%
+is600 uh
+KZ you need to sample that with Omega
+
+ align:start position:0%
+KZ you need to sample that with Omega
+ 
+
+ align:start position:0%
+KZ you need to sample that with Omega
+sampling more than twice that
+
+ align:start position:0%
+sampling more than twice that
+ 
+
+ align:start position:0%
+sampling more than twice that
+frequency so bigger than 2 pi 1600 khz
+
+ align:start position:0%
+frequency so bigger than 2 pi 1600 khz
+ 
+
+ align:start position:0%
+frequency so bigger than 2 pi 1600 khz
+and if you work that out that leaves a
+
+ align:start position:0%
+and if you work that out that leaves a
+ 
+
+ align:start position:0%
+and if you work that out that leaves a
+sampling time of about a third of a
+
+ align:start position:0%
+sampling time of about a third of a
+ 
+
+ align:start position:0%
+sampling time of about a third of a
+microsc and the point is that that's
+
+ align:start position:0%
+microsc and the point is that that's
+ 
+
+ align:start position:0%
+microsc and the point is that that's
+easy to do these days that's the kind of
+
+ align:start position:0%
+easy to do these days that's the kind of
+ 
+
+ align:start position:0%
+easy to do these days that's the kind of
+part that you get from Digi key for
+
+ align:start position:0%
+part that you get from Digi key for
+ 
+
+ align:start position:0%
+part that you get from Digi key for
+$2 so that's easy so the only thing that
+
+ align:start position:0%
+$2 so that's easy so the only thing that
+ 
+
+ align:start position:0%
+$2 so that's easy so the only thing that
+you need to do is worry about well then
+
+ align:start position:0%
+you need to do is worry about well then
+ 
+
+ align:start position:0%
+you need to do is worry about well then
+how much computation is
+
+ align:start position:0%
+how much computation is
+ 
+
+ align:start position:0%
+how much computation is
+there and that also turns out to be easy
+
+ align:start position:0%
+there and that also turns out to be easy
+ 
+
+ align:start position:0%
+there and that also turns out to be easy
+the principal thing you need to do is
+
+ align:start position:0%
+the principal thing you need to do is
+ 
+
+ align:start position:0%
+the principal thing you need to do is
+make a band pass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+filter the question is how would you
+
+ align:start position:0%
+filter the question is how would you
+ 
+
+ align:start position:0%
+filter the question is how would you
+make a bandpass
+
+ align:start position:0%
+make a bandpass
+ 
+
+ align:start position:0%
+make a bandpass
+filter and here are three possible
+
+ align:start position:0%
+filter and here are three possible
+ 
+
+ align:start position:0%
+filter and here are three possible
+systems for making a band pass filter
+
+ align:start position:0%
+systems for making a band pass filter
+ 
+
+ align:start position:0%
+systems for making a band pass filter
+should I take my my digitized antenna
+
+ align:start position:0%
+should I take my my digitized antenna
+ 
+
+ align:start position:0%
+should I take my my digitized antenna
+signal modulate low pass
+
+ align:start position:0%
+signal modulate low pass
+ 
+
+ align:start position:0%
+signal modulate low pass
+modulate or modulate low pass modulate
+
+ align:start position:0%
+modulate or modulate low pass modulate
+ 
+
+ align:start position:0%
+modulate or modulate low pass modulate
+modulate low pass modulate cosine s
+
+ align:start position:0%
+modulate low pass modulate cosine s
+ 
+
+ align:start position:0%
+modulate low pass modulate cosine s
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+s or put it through a filter that looks
+
+ align:start position:0%
+s or put it through a filter that looks
+ 
+
+ align:start position:0%
+s or put it through a filter that looks
+just like that unit sample response
+
+ align:start position:0%
+just like that unit sample response
+ 
+
+ align:start position:0%
+just like that unit sample response
+except that it's multiplied by Co Omega
+
+ align:start position:0%
+except that it's multiplied by Co Omega
+ 
+
+ align:start position:0%
+except that it's multiplied by Co Omega
+CTN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some number of those
+
+ align:start position:0%
+some number of those
+ 
+
+ align:start position:0%
+some number of those
+work and I'll leave it for you to figure
+
+ align:start position:0%
+work and I'll leave it for you to figure
+ 
+
+ align:start position:0%
+work and I'll leave it for you to figure
+out which of those
+
+ align:start position:0%
+out which of those
+ 
+
+ align:start position:0%
+out which of those
+work okay good to see you have a good
+
+ align:start position:0%
+work okay good to see you have a good
+ 
+
+ align:start position:0%
+work okay good to see you have a good
+day
\ No newline at end of file
diff --git a/Ob9xGBPvr_s.txt b/Ob9xGBPvr_s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f464539ce6d95cc9816e7c00f8cf1cb246a19292
--- /dev/null
+++ b/Ob9xGBPvr_s.txt
@@ -0,0 +1,4007 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So good
+afternoon, once again.
+
+And welcome back to
+Computational Systems Biology,
+
+lecture number seven.
+
+And today we're going
+to put to good use
+
+two things that we have learned.
+
+We've learned how to align high
+throughput reads to genomes.
+
+And we've learned how to take
+a collection of high throughput
+
+reads and assemble a genome.
+
+And today we're going to
+delve into the mysteries
+
+of transcriptional regulation.
+
+And so what I'd like to
+discuss with you today
+
+is a very important
+set of techniques
+
+that allows us to
+elucidate exactly how genes
+
+are regulated.
+
+It's probably the most
+important technique
+
+for allowing us to
+get at that question.
+
+And I'm sure many of you
+are familiar with the idea
+
+of transcriptional
+regulators, which
+
+are proteins that bind in
+a sequence specific way
+
+to the genome and act
+as molecular switches.
+
+And we'll return to
+some aspects of these
+
+when we talk about
+proteomics later in the term.
+
+But suffice to
+say, these proteins
+
+have domains that interact
+in a sequence specific way
+
+with the DNA bases in one
+of the grooves of DNA.
+
+They also typically
+contain a domain
+
+which is an activation
+domain or repression
+
+domain that interacts
+with other proteins that
+
+can cause the genome to fold up.
+
+And it can also help recruit
+the RNA polymerase holoenzyme
+
+to actually turn on
+a gene transcription.
+
+So here we have a
+figure of a collection
+
+of Pit1 molecules
+interacting with the genome.
+
+And of course, there are many
+flavors of genomic regulators.
+
+It's estimated that humans have
+about 2,000 different proteins
+
+that act as these molecular
+switches, some as activators,
+
+some as repressors.
+
+And we're going to be
+talking about, fundamentally,
+
+today the idea of how
+these molecules interact
+
+with the genome and
+control gene expression
+
+through the analysis
+of where they actually
+
+interact with
+specific genome loci.
+
+So if we were to draw a
+picture of how we understand
+
+gene regulation in cartoon
+form, if we have a gene here
+
+with the transcription
+start site
+
+and we can imagine RNA
+molecules being produced off
+
+of this genomic
+template, we know
+
+that there are non-coding
+regions of a gene that
+
+permit for the binding
+of these regulators.
+
+And my definition
+of a gene is all
+
+of the DNA that's required to
+make a specific transcriptive
+
+protein.
+
+So that includes not
+only the coding parts
+
+of the gene but the non-coding,
+regulatory parts as well.
+
+So we can imagine
+out here that there
+
+are a collection of
+regulators, perhaps just
+
+one, that bind to a sequence
+that in turn activate
+
+this gene, producing the RNA
+transcript, which then in turn
+
+this turned into
+another protein.
+
+This protein may
+undergo some sort
+
+of post-translational
+modification
+
+by signaling pathway or other
+mechanism that activates it.
+
+So regulators need
+to be activated
+
+before they could
+bind and some do not.
+
+And this activated regular
+combine to get another gene
+
+and cause another
+RNA to be expressed.
+
+And it may be, in
+the second context,
+
+that we need two
+different proteins to bind
+
+to activate the gene.
+
+And so during the
+course of the term,
+
+we're going to be talking
+about many aspects
+
+of these regulatory networks,
+including things like what
+
+the regulatory code
+of a genome is,
+
+that is where these
+binding sites are
+
+and how they're occupied.
+
+And we'll return to that
+later on in today's lecture.
+
+We'll talk about the dynamics of
+binding of proteins, including
+
+how concentration
+[? they ?] dependent are.
+
+And we'll talk about
+combinatorial control,
+
+whether or not,
+for example, both
+
+of these have to be
+present or just one of them
+
+needs to be present for
+a gene to be transcribed,
+
+and how you can use these
+regulatory sequences
+
+to implement very complex
+computational functions.
+
+But suffice to say, the
+most important thing
+
+that we have to identify
+is the programming
+
+that underlies the
+genome, which includes
+
+these regulatory sequences
+and exactly how they're
+
+occupied by regulatory proteins.
+
+Ideally what we would
+like to be able to do
+
+is to do a single experiment
+that elucidated all
+
+of the regulatory
+sites in the genome
+
+and which ones were
+occupied by which proteins.
+
+But presently, that's
+technically not possible.
+
+So we'll begin today
+with a technique that
+
+allows us to consider
+one protein at a time
+
+and identify where it
+occupies the genome.
+
+Now there are other
+kinds of proteins
+
+that we can identify in terms
+of where they are associated
+
+with the genome that are not
+transcriptional regulators, per
+
+se.
+
+For example, we all
+know that chromatin
+
+is organized on spools
+called nucleosomes.
+
+These nucleosomes are composed
+of eight different histones
+
+that have tails
+on them, and there
+
+can be covalent marks
+put on these tails.
+
+We'll return to this later on
+when we talk about epigenetics.
+
+But I did want to mention today
+that it's possible to identify
+
+where there are histones
+with specific barks that
+
+are present in the
+genome and what
+
+genome sequences they
+are associated with.
+
+So we can look at sequence
+specific regulators.
+
+We could look at a more
+general epigenetic marks,
+
+all using the same technology.
+
+And this slide simply
+recapitulates what we just
+
+talked about over here on the
+left-hand side of the board.
+
+But we want to
+know basically what
+
+and where, in terms of
+these genomic regulators,
+
+what they are and where
+they are in the genome.
+
+And today we're going to assume
+a fairly simple model, which
+
+is that regulars that are
+proximal to a gene, most
+
+probably regulated.
+
+Although we know in
+practice, actually, it
+
+appears that roughly one
+third of the regulators that
+
+are proximal to a gene actually
+skip it and regulate a gene
+
+further down the genome.
+
+It's not really
+understood very well
+
+how the genome
+folds in three space
+
+to allow these transit
+regulatory interactions
+
+to occur.
+
+But I'll just point out to
+you that the simplistic model
+
+that proximal binding
+regulates proximal genes
+
+doesn't always hold,
+especially when
+
+we get into mammals and
+other higher organisms.
+
+And as I mentioned,
+another aspect of this
+
+is that certain
+proteins may need
+
+to be modified to become
+active, and thus there
+
+are signaling pathways.
+
+You can imagine signaling
+pathways responding
+
+to environmental stimuli
+outside of cells.
+
+These signaling
+pathways can interact
+
+with transcriptional
+activators and modify
+
+what targets they
+seek in the genome.
+
+So these sorts of
+regulatory networks
+
+will be talked
+about specifically
+
+in a separate lecture
+later in the term,
+
+but they're
+extraordinarily important.
+
+And a foundational
+aspect of them
+
+is putting together
+the wiring diagram.
+
+And the wiring diagram
+has to do with where
+
+the regulators occupy
+the genome and what
+
+genes those regulators regulate.
+
+And in order to do
+that, we're going
+
+to utilize a
+technique today called
+
+ChIP-seq, which stands for
+chromatin immunoprecipitation
+
+followed by sequencing.
+
+And we can now reliably
+identify where regulars bind
+
+to the genome within
+roughly 10 base pairs.
+
+So the spatial
+resolution has gotten
+
+exceptionally good with high
+throughput sequencing, as we'll
+
+see, which really is a
+fantastic era to be in now,
+
+because this really
+wasn't possible 5
+
+or even 10 years ago.
+
+And so we now have
+the tools to be
+
+able to take apart the
+regulatory occupancy
+
+of the genome and
+discern exactly
+
+where these proteins
+are binding.
+
+The way that this is done,
+as I'll describe the protocol
+
+to you, in general, and then
+I'm going to pause for a second
+
+and see if anybody has any
+questions about the specifics.
+
+But the essential idea is that
+you have a collection of cells.
+
+Typically you need
+a lot of cells.
+
+We're talking 10 million cells.
+
+So for certain
+kinds of marks, you
+
+can get down below a million
+or even to 100,000 cells.
+
+But to get robust signals, you
+need a lot of cells at present.
+
+And all these cells obviously
+have chromosomes inside of them
+
+with proteins that
+are occupying them.
+
+And the essential idea is that
+you take a flash photography
+
+picture of the cell
+while it's alive.
+
+You add a cross linking agent,
+and that cross links proteins
+
+creates bonds
+between the proteins
+
+and the genome, the DNA, where
+those proteins are sitting.
+
+And so you then isolate
+the chromatin material,
+
+and you wind up with pieces
+of DNA with proteins occupying
+
+them, all the proteins.
+
+So not just some of the
+proteins, but all the proteins
+
+are non-selectively
+cross-linked to the genome.
+
+You then can take this
+extract and fragment it.
+
+Typically you fragment
+it by using sonication,
+
+which is mechanical energy,
+which causes the DNA
+
+to break at random locations.
+
+There are more modern
+techniques that we'll
+
+touch on at the end
+of today's lecture
+
+where you could enzymatically
+digest these fragments right
+
+down to where the protein is.
+
+But suffice to say, you get
+small fragments, which you then
+
+can immunopurify
+with an antibody
+
+to a protein of interest.
+
+So one condition of using
+this technology is either A,
+
+you have a good
+antibody to a protein
+
+that you care about
+as regulatory, or B,
+
+you have tagged
+this protein such
+
+that it has a flag tag, myc
+tag, or some other epitope
+
+tag on it which allows
+you to use an antibody
+
+or other purification
+methodology
+
+for that specific tag.
+
+So either you have
+a good antibody
+
+or you have a tag
+on the protein.
+
+One problem with
+tags on proteins
+
+is that they can render
+the proteins nonfunctional.
+
+If they're nonfunctional,
+then, of course,
+
+they're not going to bind
+where they should bind.
+
+And one has to be
+careful about this,
+
+because if you
+introduce a tag and you
+
+have a couple good copies of
+the protein that are untagged
+
+and one copy that
+is tagged, it's
+
+hard to tell whether or not
+the tagged version is actually
+
+doing what you think it does,
+and one has to be careful.
+
+But suffice to say,
+assuming that you
+
+have some way of
+immunopurifying this protein,
+
+you can then use the
+antibodies to simply purify
+
+those fragments that have
+the protein of interest.
+
+After you've purified
+the protein of interest,
+
+you can reverse
+the cross linking,
+
+have a collection of
+fragments which you then
+
+sequence using a high throughput
+sequencing instrument.
+
+Now recall that, in the
+usually applied protocol,
+
+the fragmentation is a random.
+
+So you're going to be sequencing
+both ends of these molecules.
+
+For each one, you probably
+only sequence one end.
+
+You're going to sequence an
+end of these molecules which
+
+gives you a sequence tag that is
+near where the event occurred,
+
+but not exactly at it.
+
+And we're going to
+take those tags,
+
+and if we have our
+genome-- here represented
+
+as this short, horizontal chalk
+line-- we'll take our reads,
+
+and we will align
+them to the genome,
+
+and try and discern
+from those aligned
+
+reads where the original
+proteins were binding.
+
+Now our job is to do the best
+possible alignment or discovery
+
+of where the proteins are
+binding, given this evidence.
+
+So we have a
+collection of evidence
+
+exhibited by the read sequences.
+
+The other thing
+that we will do is
+
+we will take the original
+population of molecules,
+
+and we will sequence
+them as well,
+
+sometimes called the whole cell
+extract sequence, as a control.
+
+And we'll see why we need this
+control a little bit later on.
+
+But this is going to be
+a purified so-called IP
+
+for immunoprecipitate
+fraction, which we'll sequence.
+
+And this will be the whole
+cell extract, which should not
+
+be enriched for any
+particular protein.
+
+Now before I go on, I'd be
+happy to entertain any questions
+
+about the details
+of this protocol,
+
+because it's really important
+that you feel comfortable
+
+with it before we talk about
+the computational analysis
+
+of the output.
+
+So if anybody has
+any questions, now
+
+would be a great time to ask.
+
+Yes.
+
+AUDIENCE: I have more of
+a scientific question.
+
+This assumes that we know
+a transcriptioned factor.
+
+Are there are ways, methods
+to figure out transcription
+
+factors so that you can design
+antibodies to bind to it?
+
+PROFESSOR: So the
+question is, this
+
+assumes that we know the
+regulators that we're
+
+interested in ahead of time.
+
+And is there a de novo
+way of discovering
+
+heretofore unknown regulators
+that are binding to the genome?
+
+The answer to that
+question is sometimes,
+
+as is usually the case.
+
+Later in the term, we'll talk
+about other methodologies
+
+for looking at the regulatory
+occupancy of the genome that
+
+don't depend upon
+immunopurification,
+
+in which case we'll get
+an understanding of what's
+
+going on with the genome at
+the level of knowing what
+
+particular sequences are
+occupied without knowing what's
+
+there.
+
+From the sequence,
+sometimes we can
+
+infer the family of the
+protein that is sitting there.
+
+But in general, the holy grail
+of this, which has not really
+
+fully materialized,
+would be as follows,
+
+which is instead of
+purifying with an antibody
+
+and then sequencing, why not
+purify with a nucleic acid
+
+sequence and then do mass spec,
+to actually take the proteins
+
+off of the DNA, run
+them through mass spec,
+
+and figure out what's there.
+
+And we and others
+have attempted this.
+
+And at times, you
+get good results.
+
+But mass spec is
+improving greatly,
+
+but it's till a fraught
+process with noise.
+
+And there's a paper just
+published in Nature Methods
+
+late last year on something
+called the CRAPome.
+
+Have you heard of
+this paper before?
+
+It is all the junk you get when
+you run mass spec experiments.
+
+And so when you run a
+mass spec experiment,
+
+you can just take all the
+stuff in the CRAPome out of it,
+
+and it actually helps
+you quite a bit.
+
+That gives you an idea what the
+state of the art of mass spec
+
+is.
+
+It's a little bit noisy.
+
+But I think your
+question is great.
+
+I think we need to get there.
+
+We need to get to
+the place where
+
+we can take portions
+of the genome
+
+and run them through
+mass spec and figure out
+
+what is populating it de novo
+without having to know ahead
+
+of time.
+
+Any other questions?
+
+OK.
+
+Great.
+
+So the figure on
+the slide up there
+
+also describes the
+ChIP-seq protocol.
+
+And I'll also say
+that some people
+
+believe this would never work.
+
+They actually thought that
+when you did the purification,
+
+you would just get so
+much background sequence
+
+that when you map
+it to the genome,
+
+you could never discern
+any signal whatsoever.
+
+And so there are lively debates
+about this until somebody
+
+actually made it work,
+and then the argument
+
+was over because it made
+everything else completely
+
+and totally obsolete.
+
+So it wasn't good to be on the
+wrong side of that argument,
+
+I'll tell you that.
+
+I wasn't, but all right.
+
+I was on the right side.
+
+But suffice to say, here's
+a close-up picture of Mr.
+
+Protein-- Ms. Protein-- and what
+happens when there is breakage
+
+around that site,
+followed by sequencing.
+
+And as you can see,
+the little black lines
+
+connecting between the
+protein and the DNA
+
+is supposed to indicate
+contacts sites.
+
+And you can see the little
+yellow arrows are supposed
+
+to indicate breakage sites of
+the DNA that are being caused
+
+by, in this case, mechanical
+breakage through sonication.
+
+And you get reads from
+both strands of the DNA.
+
+Remember that a sequencing
+instrument always
+
+sequences from five
+prime to three prime.
+
+So you're going to get the
+reads on the red strand
+
+and on the blue
+strand, shown here.
+
+And when we do the
+mapping, we know
+
+which strand they're mapped on.
+
+And the profile is
+shown in the lower plot,
+
+showing the density of
+map reads versus distance
+
+from where we believe
+the protein is sitting.
+
+And the tag density refers
+to tags or sequence tags
+
+or reads that are aligned using
+the methodology we discussed
+
+two lectures ago to the genome
+we assembled last lecture.
+
+So the characteristic
+shape shown in this picture
+
+is something that is not
+the same for all proteins.
+
+It is something that varies
+from protein to protein.
+
+And thus, one of the
+things that we'll
+
+want to do during our discovery
+of where these proteins are
+
+binding is always learn the
+shape of the read distribution
+
+that will come out of a
+particular binding event.
+
+So just to show you some
+actual data, so you'll
+
+get a feel for what
+we're talking about,
+
+this is actual data from
+the Oct4 protein, which
+
+is an embryonic regulator,
+pluripotency factor,
+
+binding to the mouse genome
+around the SOCS2 gene.
+
+And you can see the two distinct
+peaks on the upper track,
+
+both the plus strand
+reads and the minus strand
+
+reads, shown in blue
+and red respectively.
+
+Each one of the black and
+white bars at the top--
+
+probably can't be read
+from the back of the room--
+
+but each one of
+those is 1,000 bases,
+
+to give you some idea about
+sort of the scale of the genome
+
+that we're looking at here.
+
+You can see the
+SOCS2 gene below.
+
+The exons are the solid bars.
+
+And then you see the whole
+cell extract channel,
+
+which we talked about earlier.
+
+And the whole cell
+extract channel
+
+is simply giving us a
+background set of reads
+
+that are nonspecific.
+
+And so you might have a set of,
+say, 10 or 20 million reads,
+
+something like that, for when
+these experiments that you map
+
+to the genome and get a
+picture that looks like this.
+
+So now our job is to take the
+read sets that we see here,
+
+genome wide, and
+figure out every place
+
+that the Oct4 protein is
+binding to the genome.
+
+Now there are
+several ways that we
+
+could approach this question.
+
+One way to approach
+the question would
+
+be to simply say,
+where are the peaks?
+
+And so you hear this kind of
+exploration often described
+
+as peak finding.
+
+Where can you find the peaks?
+
+And where is the
+middle of the peak?
+
+Now the problem
+with this approach
+
+is that it works just fine
+when a peak represents
+
+a single binding event.
+
+So imagine that these
+two fingers here
+
+are binding events, and they're
+fairly far apart of the genome.
+
+Now as they come closer and
+closer and closer together,
+
+what will happen is that,
+instead of having two peaks,
+
+we're going to wind up
+having one broad peak.
+
+And thus, there's a
+lot of biology present
+
+in this kind of binding
+of the same protein
+
+proximal to itself.
+
+So we need to be able to take
+these sorts of events that
+
+occur underneath a single
+enrichment, or single peak,
+
+into two separate
+binding events.
+
+And this is shown in the
+next couple of slides,
+
+right where we look at
+what we would expect
+
+from a single event, in terms
+of a read enrichment profile
+
+once it's aligned to the genome.
+
+And we think about a
+possibility that there
+
+are two events, here
+shown in indiscernible
+
+gray and blue and red.
+
+And we note that
+each one of these
+
+will have its own
+specific profile.
+
+And then you can consider
+them to be added together
+
+to get the peak that we observe.
+
+Now one of the reasons this
+additive property works
+
+is that, remember, we're
+working with a large population
+
+of cells, and regulators
+don't always occupy a site.
+
+And thus, what we're looking
+at in terms of the reads
+
+are the sum of all of the
+evidence from all of the cells.
+
+And so even though the proteins
+are close to one another,
+
+we often can find
+an additive effect
+
+between that proximal binding.
+
+So how can we handle this?
+
+Well, what we're
+going to do is we're
+
+going to do two key
+algorithmic things.
+
+We're going to model the spatial
+distribution of the reads that
+
+come out of a specific event,
+as I suggested earlier.
+
+And we're going to keep
+that model up to date.
+
+That is, we can learn that model
+by first running our method
+
+using a common
+distribution of reads,
+
+identify a bunch
+of events that we
+
+think are bindings of a single
+protein, take those events
+
+and use them to build
+a better model of what
+
+the redistribution looks like,
+and then run the algorithm
+
+again.
+
+And with the better
+distribution,
+
+we can do a much better
+job at resolving events out
+
+of multiple events
+out of single peaks.
+
+And the next thing
+we're going to do
+
+is we're going to model the
+genome at a single base pair
+
+level.
+
+So we're going to consider every
+single base as being the center
+
+point of a protein binding
+event, and using that model,
+
+try and sort through how
+we could have observed
+
+the reads that we
+are presented with.
+
+And first, the spatial
+distribution that we build
+
+is going to look
+something like this.
+
+And we consider a
+400 base pair window,
+
+and we learn the
+distribution of reads,
+
+and we build an actual
+empirical distribution.
+
+We don't fit the
+distribution to it,
+
+but rather we can keep an
+exact distribution or histogram
+
+of what we observe, averaged
+over many, many events.
+
+So when we're fitting things,
+we have the best possible
+
+estimate.
+
+Yes.
+
+AUDIENCE: I was just
+trying to remember
+
+to origin of the
+[INAUDIBLE] clearly.
+
+So within the protocol,
+are you sequencing
+
+with the proteins bound
+to these fragments?
+
+PROFESSOR: No.
+
+See, you can't do that.
+
+You have to reverse the
+cross-linking from the DNA.
+
+And then there's
+a step here which
+
+we omitted for simplicity,
+which is, we amplified the DNA.
+
+AUDIENCE: So I was
+just wondering,
+
+if there's no protein, why
+doesn't the polymerase just
+
+read through the whole
+thing from one side?
+
+Why is there a peak?
+
+There seems to be a
+loss of signal right
+
+where the protein is bound.
+
+PROFESSOR: Well, that depends
+upon how long the reads are
+
+and how hard you fragment.
+
+And in fact, that can occur.
+
+But typically,
+we're using fairly
+
+short reads, like
+35 base pair reads.
+
+And we're fragmenting
+the DNA to be,
+
+say, perhaps 200 to
+300 base pairs along.
+
+So we're reading the first 35
+base pairs of the DNA fragment,
+
+but we're not really
+all the way through.
+
+We could read all the
+way through if we wanted,
+
+but there really wouldn't
+be a point to that.
+
+The thing that
+we're observing here
+
+is where the five prime
+end of the readers, where
+
+the leftmost edge
+of the read is.
+
+So even though it might be
+reading all the way through,
+
+we're just seeing
+the left edge of it.
+
+Does that answer your question?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: OK, great.
+
+Any other questions?
+
+Yes, at the back.
+
+AUDIENCE: So to clarify,
+this distribution
+
+that's being shown
+up here on both
+
+the positive and
+negative strand--
+
+PROFESSOR: Yes.
+
+AUDIENCE: This is the position
+of where the reads started,
+
+not the count of the number of
+times that particular base was
+
+shown in the sequencing result.
+
+Is that correct?
+
+PROFESSOR: Let me
+repeat the question.
+
+What we're observing
+in the distribution
+
+is where the read starts
+and not the number of times
+
+that base shows up in
+the sequencing data.
+
+It is the number of reads
+whose five prime position
+
+start at that base.
+
+OK So each read
+only get one count.
+
+Does that help?
+
+OK.
+
+The other thing that we're
+going to do, for simplicity,
+
+is we're going to assume
+that the plus and the minus
+
+strand distributions
+are symmetric.
+
+So we only learn
+one distribution,
+
+and then we flip it to
+do the minus strand.
+
+And that's shown here,
+where we can articulate
+
+this as this empirical
+distribution,
+
+where the probability or
+read given a base position is
+
+described in terms of the
+distance between where we are
+
+considering the binding
+of it may have occurred
+
+and where the read is.
+
+So it's important for us to
+look at this in some detail
+
+so you're comfortable with it.
+
+Here's our genome again.
+
+And let's assume that
+we have a binding
+
+event at base m
+along the genome.
+
+And we have a read here,
+r sub n, at some position.
+
+The probability
+that this read was
+
+caused by this binding event can
+be described as probably a read
+
+n given the fact that
+we're considering
+
+an event at location m.
+
+Now of course, it
+could be that there
+
+are other possible locations
+that have caused this read.
+
+And let us suppose
+that we model all
+
+of those positions along
+the genome as a vector pi.
+
+And each element of pi describes
+the probability or the strength
+
+of a binding event
+having occurred
+
+in a particular location.
+
+So we can now describe the
+probability of a read sub n
+
+given pi is equal
+to the summation
+
+where i equals 1 to big
+M, assuming that there
+
+is 1 to M bases in this
+genome, of a p rn given m pi m,
+
+like this.
+
+So we are mixing together
+here all of the positions
+
+along the genome to try
+and explain this read.
+
+So the probably of the
+read, given this vector
+
+pi, which describes all
+the possible events that
+
+could have created this
+read, is this formulation,
+
+which considers the
+probability of each position
+
+times the probability that an
+event occurred at that position
+
+subject to the constraint
+that all of a pi i's sum to 1.
+
+So we're just assigning
+probability mass
+
+along the genome from whence all
+of the reads originally came.
+
+So this is considering
+a single read, r sub n,
+
+and where that might
+have originated from.
+
+Yes.
+
+AUDIENCE: Does the
+constraint basically state
+
+that only one event occurred
+in this fragment point?
+
+PROFESSOR: The question
+is, does this constraint
+
+imply that only
+one event occurred?
+
+No.
+
+The constraint is
+implying that we're
+
+going to only have one
+unit of probability mass
+
+to assign along the genome which
+will generate all of the reads.
+
+And thus, this vector
+describes the contribution
+
+of each base to the
+reads that we observe.
+
+So let us say
+simplistically that it
+
+might be that there are only
+two events in the genome,
+
+and we had a perfect solution.
+
+Two points in the
+genome, like m1 and m2,
+
+would have 0.5 as
+their values for pi.
+
+And all the other values
+in the genome would be 0.
+
+We're going to try to make
+this as sparse as possible,
+
+as many zeroes as possible.
+
+So only at the places in
+the genome where protein
+
+is actually binding
+will pi i be nonzero.
+
+Does that make sense?
+
+These are great questions.
+
+Yes.
+
+And if people could
+say their names first,
+
+that would be great.
+
+Yes.
+
+AUDIENCE: Sara.
+
+Just to clarify, the pi vector
+is completely empirical?
+
+PROFESSOR: This distribution
+is completely empirical.
+
+Yes, that's right, Sara,
+completely empirical.
+
+I'll also say, just so
+you know, that there
+
+are many ways of doing
+this kind of discovery,
+
+as you might imagine.
+
+The way we're going
+to describe today
+
+was a way that was selected
+as part of the ENCODE 3
+
+pipeline for the
+government's ENCODE project.
+
+And so what I'm going
+to talk about today
+
+is the methodology that's being
+used for the next set of data
+
+for ENCODE 3 followed
+by IDR analysis, which
+
+is also part of ENCODE 3.
+
+So what you're
+hearing about today
+
+is a pipeline that's being
+used that will be published
+
+next year as part of
+the ENCODE project.
+
+These papers, this
+method's been published.
+
+But the analysis of
+all the Encyclopedia
+
+of DNA Elements-- which
+is what Encode stands
+
+for-- the third phase of
+that is utilizing this.
+
+OK, any other questions?
+
+Yes.
+
+AUDIENCE: Does the shape
+of this binding event
+
+tell you anything about the
+topology of the actual protein?
+
+PROFESSOR: It does, actually.
+
+And we'll return to that.
+
+But the shape of this
+binding can tell you
+
+something about the class
+of protein, which is still
+
+an area of active research.
+
+But also note that
+that is a little bit
+
+confounded by the
+fact that when you
+
+have homotypic
+binding, which means
+
+you have these closely
+spaced binding events,
+
+you get these broader peaks.
+
+And so there's a lot
+of research into what
+
+the shapes on the genome mean
+and what biological function
+
+of mechanism they might imply.
+
+Yes.
+
+AUDIENCE: Can you
+explain pi one more time?
+
+PROFESSOR: Yeah, explain
+pi one more time, sure.
+
+So pi is describing
+where there are
+
+binding events along the genome.
+
+So for example, if we just had
+two binding events, m1 and m2,
+
+then pi of m1 would be
+equal to 0.5, and pi of m2
+
+would be equal to 0.5, and
+all the other values of pi
+
+would be 0.
+
+So we're just describing with pi
+where the events are occurring.
+
+That gives us the
+location of the events.
+
+OK?
+
+And you'll see in a moment why
+we articulated it that way.
+
+But that's what pi is doing.
+
+Does that answer your question?
+
+OK.
+
+Any other questions?
+
+Yes.
+
+AUDIENCE: In cases
+when you have two peaks
+
+really close together,
+to a point that there's
+
+some sort of
+[INAUDIBLE] between,
+
+how do you constrain your pi?
+
+PROFESSOR: How do
+you constrain the pi
+
+when you have
+closely spaced peaks?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Well, you
+don't constrain it.
+
+You actually want--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Well, I'm
+going to show you
+
+some actual examples of
+this algorithm running.
+
+So I'm going to give you an
+animation of the algorithm
+
+running, so you can
+actually watch what it does.
+
+And you'll see, first
+it's going to be something
+
+that isn't too pleasant,
+and then we'll fix it.
+
+But the key thing
+here is sparsity.
+
+What we want to do is
+we want to enforce pi
+
+being as sparse as possible
+to explain the data.
+
+One of the common problems
+in any approach to machine
+
+learning is that, with a
+suitably complex model,
+
+you can model anything, but it's
+not necessarily interpretable.
+
+So what we want to do here is
+to make pi as simple as possible
+
+to be able to explain
+the data that we see.
+
+However, if a single event
+cannot explain and observe
+
+redistribution at a particular
+point in the genome,
+
+we'll need to bring
+another event in.
+
+All right, so that is how to
+think about a single read.
+
+And now we can just
+say the probability
+
+of our entire read set
+given pi is quite simple.
+
+It's simply the product
+over all the reads.
+
+Sorry.
+
+Like so.
+
+So this is the probability
+of the entire read set.
+
+So we had this
+previously, which is
+
+the probability
+of a single read.
+
+And we take the product of the
+probability for each individual
+
+read to get the likelihood
+of all the reads.
+
+So now all we need to do to
+solve this problem is this.
+
+We need to say that pi
+is equal to the arg max
+
+pi of P R pi, which gives
+us the maximum likelihood
+
+estimate for pi.
+
+Now it's easy to
+write that down, just
+
+find the setting for
+pi that maximizes
+
+the likelihood of the observed
+reads, and proof, you're done,
+
+because now you've come up
+with a pi that describes where
+
+the binding events
+are along the genome
+
+at single base pair
+solution, assuming
+
+that pi is modeling
+every single base.
+
+Does everybody see that?
+
+Any questions about that?
+
+Yes.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: n is the
+number of reads.
+
+m is a number of
+bases in the genome.
+
+n is the number of reads.
+
+AUDIENCE: The
+length of pi, right?
+
+Is that equal to the
+number of binding events?
+
+Or is it equal to just
+the number of [INAUDIBLE]?
+
+PROFESSOR: The length of pi?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: It's the number
+of bases in the genome,
+
+and hopefully the
+number of bindings
+
+is much, much, much
+smaller than that.
+
+Typical number of binding
+events is 5 to 30,000
+
+across a genome that has
+3 billion bases, something
+
+like that.
+
+So it's much, much smaller.
+
+OK?
+
+So this is what we
+would like to solve.
+
+And another way to look
+at this model, which
+
+it may be somewhat
+more confusing,
+
+is as follows, which is that
+we have these events spread
+
+along the genome.
+
+And we have the reads
+shown on the lower line.
+
+And the events are
+generating the reads.
+
+So this is called
+a generative model,
+
+because the derivation
+of the likelihood
+
+directly follows from, if we
+knew where the events were,
+
+we could exactly
+come up with the best
+
+solution for the
+assignment of pi,
+
+and thus for the likelihood.
+
+So this is what we have
+on the board over here.
+
+But we can solve this directly.
+
+Yes.
+
+Question in the back.
+
+AUDIENCE: Hi.
+
+My name is Eric.
+
+I have a little question.
+
+What is the definition
+of GPS here?
+
+PROFESSOR: Oh, sorry.
+
+Yeah, GPS is the name
+of this algorithm.
+
+I told it to an editor
+and they hated it.
+
+But at any rate, it's called
+the genome positioning system.
+
+[LAUGHTER]
+
+Yeah, so you don't like
+it either, right, Eric?
+
+Oh, well.
+
+But yes, it locates proteins
+on the genome, right?
+
+Yeah.
+
+Good question.
+
+So this is going to be, I
+think, our first introduction
+
+to the EM algorithm
+as a way of solving
+
+complex problems like this.
+
+And here is the
+insight we're going
+
+to use to solve
+this problem, which
+
+is that imagine I
+do the function g.
+
+So g is going to be
+this function that
+
+tells us what reads
+came from which events
+
+and where those events
+are in the genome.
+
+So if you knew g
+exactly, this would
+
+be a really trivial
+problem to solve.
+
+It would tell you, for
+every single read, which
+
+particular binding
+event caused it.
+
+And if we knew that,
+it would be great,
+
+because then we could
+say something like this.
+
+We could say, well, we knew g.
+
+Then the number of reeds created
+by a binding event at location
+
+m would simply be-- it's not a
+very good summation sign here--
+
+we would sum over all the reads
+and count up the number of them
+
+where read n was caused
+by an event at location m.
+
+And we just summed
+up this number.
+
+We'd have the number
+of reads caused
+
+by an event at location m.
+
+Is everybody cool with that?
+
+No.
+
+Do you see the
+definition of there of g
+
+on the overhead projector?
+
+So every time a read
+n comes from event m,
+
+that function is going
+to be equal to 1.
+
+So we just count the
+number of times it's 1.
+
+For a given location
+m, we find out
+
+how many reads came from
+that event-- could be 5,
+
+could be 10, could be 100.
+
+We don't know exactly
+how many were generated
+
+by that particular
+event, but there's
+
+going to be some number.
+
+And we have 10 million reads,
+and we have 100,000 events,
+
+we're going to get
+about 100 reads
+
+per event, something like that.
+
+You can give that kind
+of order of magnitude.
+
+Everybody OK?
+
+Any questions about
+the details of this?
+
+Because the next step is going
+to be causing leaps of faith,
+
+so I want to make sure that
+everybody's on firm ground
+
+before we take
+the leap together.
+
+Yes.
+
+AUDIENCE: So you are
+in forced sparsity yet?
+
+PROFESSOR: I'm not in
+forced sparsity yet.
+
+You like sparsity.
+
+You're going to keep
+me to that, right?
+
+So later on, you'll hold
+me to it, all right?
+
+That's your job.
+
+What's your name?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+That's your job, all right?
+
+Mr. Sparsity.
+
+I like that.
+
+He's been sparse.
+
+I like it.
+
+So if this is the
+number of reads assigned
+
+to a particular
+location, then we
+
+know that pi sub
+m will simply be
+
+n sub m over the summation
+of all of the reads assigned
+
+to all of the events.
+
+And some of these
+are going to be zero.
+
+A lot of them will be zero.
+
+So here, I don't know this
+assignment of reads to events.
+
+It's latent.
+
+It's something I have
+invented which I do not know.
+
+But if I did know it, I'd be
+able to compute pi directly,
+
+like so, because I'd
+be able to figure out
+
+for each location on the genome
+how many reads were there.
+
+And that's how much
+responsibility that location
+
+had for generating
+all of the reads.
+
+Is everybody with me so far?
+
+Any questions at all?
+
+OK.
+
+So remember, this is latent.
+
+We don't know what it
+is, but if we did know,
+
+we'd be in great shape.
+
+So our job now is to estimate g.
+
+And if we could estimate
+g, we can estimate pi.
+
+And once we get a
+better estimate for pi,
+
+I'd like to suggest
+to you we can
+
+get a better estimate for g.
+
+And we can go between
+these two steps.
+
+And so that's what the
+expectation, maximization
+
+algorithm does in the
+lower part here, which
+
+is that the left part is
+estimating gamma, which
+
+is our estimate for g, which is
+looking at the number of reads
+
+that we think are softly
+assigned to a location m
+
+over the total number
+of softly assigned
+
+reads from all locations.
+
+And that gives the fraction of
+a read at n assigned to event m.
+
+So we are computing
+an estimate of g.
+
+But to compute this
+estimate, we have to have pi.
+
+It's telling us where we
+believe that these reads are
+
+coming from.
+
+And once we have gamma,
+which is an estimate,
+
+we can compute pi, just in the
+same way we computed it here,
+
+if we knew g.
+
+So we compute the expectation
+of this latent function, which
+
+we don't know, and
+then we maximize
+
+pi to maximize our likelihood.
+
+And you can derive
+this directly by taking
+
+the log of that likelihood
+probability up there
+
+and maximizing it.
+
+But suffice to say, you wind
+up with this formulation
+
+in the EM framework.
+
+So I can go between these
+two different steps--
+
+the E step, the M step,
+the E step, the M step.
+
+And each time as
+I go through it,
+
+I get a better and better
+approximation for pi,
+
+until I ultimately get it
+within some preset level
+
+of convergence.
+
+And then I'm finished.
+
+I actually can report my pi.
+
+But before I leave the EM
+algorithm, and this formulation
+
+of it, are there
+any questions at all
+
+about what's going on here?
+
+Yes, question in the back.
+
+AUDIENCE: So the solution
+to the EM algorithm
+
+doesn't always [INAUDIBLE]?
+
+PROFESSOR: It gives
+you a solution.
+
+And it is the optimum solution
+given the starting conditions
+
+that we give it.
+
+AUDIENCE: But it depends on
+the starting conditions, right?
+
+PROFESSOR: It does depend
+on the starting conditions.
+
+Any other questions?
+
+Yes, in the back.
+
+AUDIENCE: Is this
+dependent upon you
+
+having discrete binding events?
+
+So if you have a protein that
+has more diffuse localization
+
+across the genome, for
+example, RNA Pol II,
+
+would this model break down?
+
+PROFESSOR: So the
+question is, does this
+
+depend upon you having
+discrete binding events?
+
+What biological assumptions are
+we making in this model about
+
+whether or not a protein is
+actually fixed and welded
+
+to the genome in a
+particular location
+
+or whether or not
+it's drifting around?
+
+And this might be of
+particular interest,
+
+for example, if we're
+looking at histones, which
+
+are known to slide up
+and down the genome,
+
+and we're
+immunoprecipitating them.
+
+What will this give us?
+
+We are making the
+assumption that we're
+
+dealing with proteins that have
+punctate binding properties,
+
+that actually are
+point binding proteins.
+
+And thus what we're going to
+get out of this, as you'll see,
+
+is going to be a
+single location.
+
+There are other methodologies,
+which I won't describe today,
+
+for essentially deconvolving
+the motion of a protein
+
+on the genome and coming
+up with its middle
+
+or mean position while
+allowing it to move.
+
+But today's
+algorithm is designed
+
+for point binding proteins.
+
+Good question, OK?
+
+All right.
+
+So just to be clear,
+what we're going to do
+
+is we're going to
+initialize everything,
+
+such that we'll begin
+by initializing pi
+
+to be 1 over the
+size of the genome.
+
+And at the very end of this,
+the strength of a binding event
+
+will be simply the number of
+reads assigned to that event
+
+by summing up our estimate of g.
+
+And the nice thing about this
+is that because the number
+
+of reads assigned to an
+event, in some sense,
+
+is scaled relative to
+the total number of reads
+
+in the experiment, we can
+algorithmically take our genome
+
+and chop it up into
+independent pieces
+
+and process them
+all in parallel,
+
+which is what this
+methodology does.
+
+All right.
+
+So let's have a
+look at what happens
+
+when we run this algorithm.
+
+So here we are.
+
+This is synthetic data.
+
+I have events planted at
+500 and 550 base pairs.
+
+The x-axis is between
+0 and 1,400 base pairs.
+
+And the y-axis is
+pi from 0 to 1.
+
+So here we go.
+
+It's running.
+
+And this is one base
+pair resolution.
+
+And it is still
+running-- and stop.
+
+Well, we get sort of a
+fuzzy mess there, don't we?
+
+And the reason we're
+getting a fuzzy mess there
+
+is that we have got a lot
+of reads we've created,
+
+and there are a lot of
+different genome positions
+
+that are claiming some
+responsibility for this, which
+
+my friend, Mr. Sparsity,
+doesn't like, right?
+
+We need to clean
+this up somehow.
+
+And let's see what
+happens when we actually
+
+look at actual data.
+
+So here is that original
+data I showed you
+
+for the two Oct4 binding
+events next to the SOCS2 gene.
+
+And I'll run the
+algorithm on these data.
+
+And you can see it
+working away here.
+
+And once again, it's giving
+us a spread of events,
+
+and you can see
+it even beginning
+
+to fill in along where
+there's noise in the genome
+
+and stopped here.
+
+And it's assigning the
+probability mass of pi
+
+all over the place.
+
+It is not sparse at all.
+
+So does anybody
+have any suggestions
+
+for how to fix this?
+
+We've worked all might.
+
+We've got our algorithm running.
+
+We thought it was going
+to be totally great.
+
+When we run it, it gives us
+this unfortunate, smeary kind
+
+of result.
+
+What could we do?
+
+Any ideas at all?
+
+Yes.
+
+AUDIENCE: Add a prior where
+most of the reads are.
+
+PROFESSOR: Add a prior.
+
+You saw the word no
+prior, a little tip off.
+
+Yeah, absolutely, good point.
+
+Add a prior.
+
+So what we're going
+to do is we're
+
+going to try and add a prior
+that's going to prejudice pi
+
+to be 0 to create sparsity.
+
+So we like pi being 0.
+
+So we'll add what's called
+a negative Dirichlet prior,
+
+which looks like this, which is
+the probability of pi there is
+
+proportional to 1 over pi to
+the m raised to the alpha power.
+
+And as pi gets smaller,
+that gets much, much bigger.
+
+And thus, if we add
+this prior, which
+
+happens to be a very
+convenient prior to use,
+
+we can force pi to
+be 0 in many cases.
+
+And when we take that prior
+into account and we compute
+
+the maximum a posteriori
+values for pi,
+
+the update rules
+are very similar,
+
+except that what's
+interesting is
+
+that the rule on the left for
+computing our estimate of g
+
+is identical.
+
+But on the right, what we do
+is we take the number of reads
+
+that we observe at a
+particular location
+
+and we subtract
+alpha from it, which
+
+was that exponent in our prior.
+
+And what that simply means is
+that if you don't have alpha
+
+reads, you're history.
+
+You're going to get eliminated.
+
+So this is going to do something
+called component elimination.
+
+If you don't have
+enough strength,
+
+you're going to
+get zapped to zero.
+
+Now you don't want to do this
+too aggressively early on.
+
+You want to let things sort
+of percolate for a while.
+
+So what this algorithm does
+is it doesn't eliminate
+
+all of the components that don't
+have alpha reads at the outset.
+
+It lets it run for
+a little while.
+
+But it provides you with a way
+of ensuring that components
+
+get eliminated and set to zero
+when they actually don't have
+
+enough support in the read set.
+
+So once again, all
+we're going to do
+
+is we're going to add this prior
+on pi, which we will wind up
+
+multiplying times
+that top equation.
+
+We'll get the joint probability
+of r and pi in this case,
+
+and then we're going to maximize
+it using this EM adaptation.
+
+And when we do so,
+let me show you
+
+what happens to our first
+example that we had.
+
+OK, that's much cleaner, right?
+
+We actually only have
+two events popping out
+
+of this at the right locations.
+
+All right.
+
+So that's looking good.
+
+And the probability is
+summed to 1, which we like.
+
+And then we'll run
+this on the Oct4 data.
+
+And you can see now,
+instead of getting
+
+the mushing around
+those locations, what's
+
+going to happen is that
+most of the probability mass
+
+is going to be absorbed into
+just a couple components
+
+around those binding events.
+
+Now another way to test this
+is to ask whether or not,
+
+if we looked at what we
+believe are closely spaced
+
+homotypic events, in this case,
+for CTCF, with that prior,
+
+we still can recover
+those two events being
+
+next to each other
+in the genome.
+
+And so if we run this, you
+can see it running along here.
+
+Each one of these iterations,
+by the way, is an EM step.
+
+And there you go.
+
+And you can see that
+even from the sparse data
+
+you see above-- that's the
+actual data being used,
+
+all those little bars
+up there, read counts
+
+for the five prime ends of
+the reads-- we can recover
+
+the position of
+those binding events.
+
+Question, yes.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It depends
+upon the number of reads,
+
+but it's somewhere
+around three or four.
+
+I mean, if you look at the
+GPS paper, which I posted,
+
+it tells you how alpha is set.
+
+Yes.
+
+AUDIENCE: Do you use
+wholesale extract data
+
+when you are trying to compute?
+
+PROFESSOR: Question, do we
+use wholesale extract data?
+
+I told you all how
+important it was,
+
+and I haven't
+mentioned it again.
+
+We're about to get to that,
+because that's very important.
+
+I'm glad you asked
+that question.
+
+Yes.
+
+AUDIENCE: It looks like,
+along the genome coordinates,
+
+each event is only
+one base pare,
+
+but binding is usually
+more than one base pair.
+
+So is that the center
+of the binding?
+
+PROFESSOR: Yes.
+
+Well, it's the center of the
+read distribution function.
+
+Whether or not it's the center
+of the binding of the protein,
+
+I really can't tell.
+
+OK, great.
+
+And I'll just point out
+that a power of this method
+
+is its ability to take
+apart piles of reads
+
+like this and to these so-called
+homotypic binding events, where
+
+you can see where the motif is.
+
+And you can see this method will
+take apart that pile of reads
+
+into two independent events,
+whereas other popular methods,
+
+of which there are
+many for analyzing
+
+these type of ChIP-seq
+data, don't take apart
+
+the event into multiple
+events, because most of them
+
+make the assumption
+that one pile of reads
+
+equals one binding event.
+
+Now back to our question
+about wholesale extract.
+
+What happens if you get to
+a part of the genome that
+
+looks like this?
+
+We're going to go
+back to our Oct4 data.
+
+And we have our Oct4 IP
+track, which is above,
+
+and then our wholesale
+extract tract
+
+is down there on the bottom.
+
+What would you say?
+
+Would you say those are
+really Oct4 binding events?
+
+Or do you think something
+else is going on there?
+
+If so, what might it be?
+
+Any ideas about
+what's going on here?
+
+Yes.
+
+AUDIENCE: Regions with a lot
+of repeats in the genome?
+
+PROFESSOR: Regions with
+repeats in the genome?
+
+Yes.
+
+In fact, you can see repeats
+annotated in green right there.
+
+And as you recall from last time
+when we talked about assembly,
+
+it's very difficult
+to actually get
+
+the number of repeat
+elements correct.
+
+And a consequence of that
+is if you underestimate
+
+the number of repeat
+elements in the genome
+
+and you collapse them, when
+you do sequencing of the genome
+
+and you remap it, you're going
+to get regions of the genome
+
+were a lot of reads pile
+up, because they're actually
+
+coming from many different
+places in the genome,
+
+but they only have
+one place to align.
+
+And these towers of
+reads, as they're called,
+
+can create all
+sorts of artifacts.
+
+So in order to judge the
+significant of events,
+
+what we'll do is a
+two-step process.
+
+First, we will run
+our discovery pipeline
+
+and discover where all the
+events are in the IP channel
+
+without regard to the
+wholesale extract channel,
+
+in this particular case.
+
+And then we will
+filter the events
+
+and say which of the events
+are real in view of the data
+
+from the wholesale
+extract channel.
+
+And so the way to
+represent this is
+
+what is the likelihood we
+would have seen those IP reads
+
+at random given the
+wholesale extract channel?
+
+So how can we
+formulate this problem?
+
+Well imagine that we
+take all of the reads
+
+that we see in both channels
+and we add them together.
+
+So we get a total
+number of reads
+
+at a particular
+location in the genome.
+
+If, in fact, they were
+going to occur at random,
+
+we'd be doing a coin flip.
+
+Some reads will go
+on the IP channel.
+
+Some reads will go on the
+wholesale extract channel.
+
+So now we can ask what's the
+probability we observed greater
+
+than a certain number of
+reads on the IP channel
+
+at chance, assuming a
+coin flipping model where
+
+we've added the reads together.
+
+Another way to view that is
+what's the chance that we have
+
+observed less than
+a certain number of
+
+reads in the wholesale
+extract channel
+
+assuming a coin flipping model?
+
+And that will give us a p-value
+under the null hypothesis
+
+that, in fact, there
+is no binding event
+
+and simply what's
+going on is that we
+
+have reads being flipped
+between the two channels out
+
+of a pool of the
+total number of reads.
+
+And if we take that
+approach, we can formulate it
+
+as the binomial in
+the following way.
+
+We can compute a p-value for
+a given binding event using
+
+the data from both
+the IP channel
+
+and from the control channel.
+
+And the way that we do this is
+that we look at the number of
+
+reads assigned to an
+event, because we already
+
+know that number.
+
+We've computed that number.
+
+And we take a similar window
+around the control channel.
+
+We count the number
+of reads in it
+
+and ask whether or not the
+reads in the IP channel
+
+is significantly larger enough
+than the reads in the control
+
+channel to reject the null
+hypothesis that, in fact, they
+
+occurred at random.
+
+So this is the way that
+we compute the p-values
+
+for events.
+
+So once we've computed
+the p-values for events,
+
+we still have our multiple
+hypothesis correction problem,
+
+which is that if we
+have 100,000 events,
+
+we need to set our p-value's
+cut off and appropriate value.
+
+And I think that
+you may have heard
+
+about this before in recitation.
+
+But the way that this
+is done in this system
+
+is to use a
+Benjamini-Hochberg correction.
+
+And the essential idea is that
+we take all of the p-values
+
+and we organize them
+from smallest to largest.
+
+And we're going to take
+a set of the top events,
+
+say 1 through 4, and
+call them significant.
+
+And we call them significant
+under the constraint
+
+that p-value sub i is less
+than or equal to i over n,
+
+where n is the total number
+of events times alpha,
+
+which is our desired
+false discovery rate.
+
+So this allows us
+in a principled way
+
+to select the events
+that we believe
+
+are significant up to a false
+discovery rate, which might be,
+
+for example, 0.05 for
+something that's typically
+
+used for a false discovery rate.
+
+So we've talked about
+how to discover events,
+
+how to judge their
+significance individually,
+
+how to take a ranked list of
+events from a given experiment
+
+and determine which
+ones are significant
+
+up to a desired
+false discovery rate.
+
+The false discovery
+means that, let's say,
+
+that we have 1,000
+events that come out.
+
+If this false
+discovery rate was 0.1,
+
+we would expect 100 of
+them to be false positives.
+
+So it's the fraction
+of positives
+
+that we detect that we
+think are going to be false.
+
+And we can set that to
+be whatever we want.
+
+Now let's talk about the
+analysis of these sort of data.
+
+There's a question up here.
+
+Yes.
+
+AUDIENCE: So this randomness,
+does that correct to the fact
+
+that in your previous slide the
+coin isn't necessarily fair?
+
+PROFESSOR: Oh, the
+null hypothesis
+
+assumed that the coin was fair,
+that reads could either occur.
+
+That in this case, for
+example, that the reads were
+
+either occurring in the control
+channel or in the IP channel
+
+with equal likelihood, assuming
+because they were coming
+
+from the same process, which was
+not related to the IP itself.
+
+They're coming from some
+underlying noise process.
+
+AUDIENCE: So typically
+you'd have some fixed number
+
+of reads, and so in the IP
+channel, the bulk of your reads
+
+was in your peaks.
+
+Then you would have
+fewer in your--
+
+PROFESSOR: So the
+question is, how do you
+
+normalize for the
+number of reads
+
+and how they're being spent?
+
+Because in the IP
+channel, you're
+
+spending the reeds on
+IP enriched events.
+
+In the wholesale
+extract channel,
+
+you're not spending
+the reads on those,
+
+so you have more reads to
+go around for bad things,
+
+so to speak.
+
+So what this algorithm
+does-- which I'm glad
+
+you brought it up-- is it takes
+regions of the genome that
+
+are event free, and it matches
+them up against one another
+
+and fits a model
+against them to be
+
+able to scale the control reads
+so that the number of reads
+
+in the IP and
+extract channel are
+
+the same in the regions
+that are free of events.
+
+And so it matches
+things, so it is 0.5.
+
+OK?
+
+AUDIENCE: Even if wasn't
+0.5, wouldn't this rank list
+
+correct with that?
+
+PROFESSOR: No, it would not.
+
+Let us suppose that we
+made a horrible mistake
+
+and that we let
+these events through
+
+because our p was wrong.
+
+They would have a very
+large number of reads,
+
+and they would be
+very significant.
+
+As a consequence,
+they would float up
+
+to the top of this list
+as having the lowest
+
+p-values, or the
+most significant,
+
+and they would pop through this.
+
+So we would report
+them as binding events,
+
+which is not desirable.
+
+These are all great questions.
+
+Any other questions at all?
+
+So we've talked about this.
+
+The next question you
+might have would be,
+
+you've done two replicates
+of the same chip.
+
+You always want to do two of
+every experiment, if not three
+
+or four.
+
+And I know it's
+expensive, but you
+
+don't know where you are if
+you only do one of something.
+
+Trust me.
+
+So assuming you've done
+two experiments that
+
+were identical ChIP
+experiments, and you
+
+would like to know
+whether or not
+
+the results between those two
+experiments are concordant.
+
+How might you go about
+determining this?
+
+Does anybody have any ideas?
+
+Let me suggest something to you.
+
+Imagine that we
+create two lists-- one
+
+for experiment x and
+one for experiment y.
+
+And we're going to
+put in this list,
+
+in rank order, the
+strongest events
+
+and where they
+occur in the genome.
+
+And let us suppose that we
+are able to match events
+
+across experiments when
+they're in the same location.
+
+So what we'll do is we'll
+say Event one occurs here.
+
+Event 13 occurs here and here.
+
+Event 9 occurs here and here.
+
+Event 10 is matched.
+
+Event 11 occurs here.
+
+Event 57 occurs here.
+
+And these are ranked in
+order of significance.
+
+They're not
+completely concordant,
+
+and they're ranked according
+to the significance
+
+in this particular experiment
+and this particular experiment.
+
+And we would like to
+know whether or not
+
+we think these two
+experiments are
+
+good replicates of one another.
+
+Now the nice thing
+about converting this
+
+into a rank test is
+that we are no longer
+
+sensitive to the number of reads
+or any specific numeric values
+
+represented by each
+one of these events.
+
+We're simply ranking them
+in terms of their importance
+
+and asking whether or not they
+appear to be quite similar.
+
+So one way to do this is simply
+to take a rank correlation,
+
+which is a correlation between
+the ranks of identical events
+
+in the two lists.
+
+And so, for example, imagine
+in the lower right-hand corner
+
+of this slide shows you an
+example of X and Y values,
+
+although there's not really
+a linear relationship
+
+between them, and the Pearson
+correlation coefficient
+
+is 0.88.
+
+If we look at the right
+correlation, which
+
+is defined by the equation
+on the left, which is really
+
+simply the correlation
+between their rank values,
+
+the Spearman correlation
+for rank is 1.
+
+They're perfectly matched.
+
+So if you want to
+consider whether or not
+
+two experiments
+are very similar,
+
+I'd suggest you consider
+rank based tests.
+
+But we can do even
+more than this.
+
+Imagine that we
+would like to know
+
+at what point along
+this list things
+
+are no longer concordant,
+that we would like to consider
+
+all the events that are
+consistent among these two
+
+experiments.
+
+And we assume that there is
+a portion of the experiment
+
+results that are concordant
+and part that is discordant.
+
+And we want to learn
+where the boundary is.
+
+So what we'll do is this.
+
+We will look at the number of
+events that are concordant up
+
+to a particular point.
+
+Let's see here, make sure we
+get the parametrization right.
+
+So if we have lists that
+are n long, psi of n of t
+
+is the number of
+events that are paired
+
+in the top n times t events.
+
+So t is simply the fraction.
+
+If is 0.25, that would
+mean that in the top 25%
+
+of the events, the number
+of events that are paired.
+
+Actually, it's the
+fraction of events.
+
+Sorry.
+
+So assuming that we had perfect
+replicates, what we would see
+
+would be that psi of n of
+t would look like this.
+
+Yes?
+
+AUDIENCE: What is t?
+
+PROFESSOR: t is the
+fraction of the events
+
+that we're considering.
+
+So this t might
+be equal to 0.25.
+
+If this was 10, then this
+would be-- oh, sorry.
+
+I think this t equal 0.5.
+
+If n was equal to 10, this
+would be the first five events.
+
+So t is the fraction.
+
+n is the total number of events.
+
+So if this is t, which
+is the fraction which
+
+goes from 0 to 1, and
+this is psi of n of t,
+
+this would be a perfectly
+matched set of replicates.
+
+A 0.5, 0.5 of the events are
+matched, which is perfect.
+
+Can't do any better than that.
+
+So this is simply
+telling us, as we
+
+take larger and larger
+fractions of our event, what
+
+fraction of them are
+matched up to that point?
+
+Question.
+
+AUDIENCE: So this assumes
+that the rank order
+
+is important for the
+correlation, right?
+
+The higher rank
+they are, we expect
+
+them to be better correlated.
+
+For example, if
+in the middle they
+
+were the best correlated, but
+not the top or bottom in terms
+
+of the ranking, then you
+might have a weird looking--
+
+PROFESSOR: Yeah.
+
+The question is,
+doesn't this assume
+
+that we care most
+about the events
+
+up here, as opposed to
+the events, for example,
+
+in the middle.
+
+And this analysis
+is done to consider
+
+how many of the
+top events we take
+
+that we think are consistent
+across replicates.
+
+So it starts at the top as a
+consequence of that assumption.
+
+This is the definition
+of psi n, which
+
+is the fraction of
+the top events that
+
+are paired in the top events.
+
+It's roughly linear
+from the point
+
+where events are no
+longer reproducible.
+
+And psi prime of n is the
+derivative of that function.
+
+And graphically, if
+we look at these,
+
+we can see that there's
+perfect correspondence
+
+on the left point
+up to some point.
+
+And then the hypothesis of this
+irreproducible discovery rate
+
+is at that point things
+stop being in correspondence
+
+because you've hit the noise
+part of the event population.
+
+and you get to junk.
+
+And as soon as you get to
+junk, things fall apart.
+
+And what this
+methodology does is
+
+it attempts to fit the
+distribution to both
+
+the correspondence and the
+non-correspondence parts
+
+of the population, and you
+get to set a parameter, which
+
+is the probability that you're
+willing to accept something
+
+that's part of the
+junk population
+
+of the non-correspondence
+population.
+
+And the way this is used, for
+example, in the ENCODE project
+
+is that all ChIP-seq experiments
+are done in parallel.
+
+Event discovery is done
+independently on them.
+
+All of the events from
+each independent experiment
+
+are ranked from 1 to n.
+
+And then IDR is
+done on the results
+
+to figure out
+which of the events
+
+are consistent
+across replicates.
+
+And obviously, if you've
+had a very bad replicate,
+
+you get a very small number
+of events, if any at all.
+
+But if you have good
+replicates, then you
+
+get a large number of events.
+
+A secondary question is, imagine
+you had processing algorithm A
+
+and processing algorithm B.
+It might be that processing
+
+algorithm A typically
+gave you more reproducible
+
+events than processing algorithm
+B, that whenever you ran A,
+
+you could get much
+further down this curve
+
+before things fell apart.
+
+Does that mean that A is
+necessarily better, or not?
+
+What do you think?
+
+Would you always pick algorithm
+A if that was the case?
+
+Any insight on this?
+
+Yes?
+
+AUDIENCE: No, probably,
+because there's
+
+experimental
+considerations to it.
+
+PROFESSOR: Yeah.
+
+I would go with [INAUDIBLE]
+experimental considerations.
+
+But the reason
+you might not pick
+
+it is it might be that if
+algorithm A always gave you
+
+the same wrong answers
+in the same order,
+
+it would score perfectly
+on this, right?
+
+It doesn't mean that it's right.
+
+It just means it's consistent.
+
+So for example, it could
+be calling all the towers
+
+as events, and it
+could always give you,
+
+for every experiment,
+the same results.
+
+In fact, one
+interesting thing to do
+
+is to run this kind of analysis
+against your experiment,
+
+and an outlier shouldn't
+match your experiment.
+
+It should fail.
+
+It's always good to
+run negative controls
+
+when you're doing data analysis.
+
+So this IDR analysis
+simply allows
+
+you to pick alpha, which is
+the probability of the rate
+
+of repairs for the
+irreproducible part
+
+of the mixture that
+you're willing to accept.
+
+And the way this is
+used is, as I said,
+
+is that here you see
+different ways of analyzing
+
+ChIP-seq data.
+
+And the little
+vertical tick mark
+
+indicates how many
+peaks they get
+
+before they can't go
+any further because they
+
+hit the IDR bound alpha.
+
+And some methodologies can
+produce far more events
+
+consistently than
+other methods can.
+
+So that's just something
+for you to keep in mind.
+
+And I will not have time to
+present all the rest of this.
+
+But I did want to point
+out one thing to you, which
+
+is that the methodology
+we talked about today
+
+is able to resolve
+where things are
+
+in the genome at exceptional
+spatial resolution,
+
+within 20 base
+pairs genome wide.
+
+And it's always run genome wide
+at single base pair solution.
+
+And it can do
+things like compute
+
+for pairs of
+transcription factors
+
+that have been profiled
+using ChIP-seq,
+
+the spacing between them for
+spacings that are significant.
+
+And so you can see
+that we're beginning
+
+to understand the regulatory
+grammar of the genome in terms
+
+of the way factors
+organize together
+
+and they interact to implement
+the combinatorial switches
+
+that' we've talked about.
+
+That's it for today.
+
+You guys have been
+totally great.
+
+We'll see you on
+Tuesday for RNA-seq.
+
+And have a great
+weekend until then.
\ No newline at end of file
diff --git a/P7a4bjE6Crk.txt b/P7a4bjE6Crk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..68fc319d73daddf79133139495f25864acad1a21
--- /dev/null
+++ b/P7a4bjE6Crk.txt
@@ -0,0 +1,2372 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOHN TSITSIKLIS: So today we're
+going to finish with the
+
+core material of this class.
+
+That is the material that has to
+do with probability theory
+
+in general.
+
+And then for the rest of the
+semester we're going to look
+
+at some special types of models,
+talk about inference.
+
+Well, there's also going to
+be a small module of core
+
+material coming later.
+
+But today we're basically
+finishing chapter four.
+
+And what we're going to do is
+we're going to look at a
+
+somewhat familiar concept, the
+concept of the conditional
+
+expectation.
+
+But we're going to look at it
+from a slightly different
+
+angle, from a slightly more
+sophisticated angle.
+
+And together with the
+conditional expectation we
+
+will also talk about conditional
+variances.
+
+It's something that we're going
+to denote this way.
+
+And we're going to see what they
+are, and there are some
+
+subtle concepts that
+are involved here.
+
+And we're going to apply some
+of the tools we're going to
+
+develop to deal with a special
+type of situation in which
+
+we're adding random variables.
+
+But we're adding a random number
+of random variables.
+
+OK, so let's start talking
+about conditional
+
+expectations.
+
+I guess you know
+what they are.
+
+Suppose we are in the discrete
+the world. xy, or discrete
+
+random variables.
+
+We defined the conditional
+expectation of x given that I
+
+told you the value of the
+random variable y.
+
+And the way we define it is the
+same way as an ordinary
+
+expectation, except that we're
+using the conditional PMF.
+
+So we're using the probabilities
+that apply to
+
+the new universe where we are
+told the value of the random
+
+variable y.
+
+So this is still a familiar
+concept so far.
+
+If we're dealing with the
+continuous random variable x
+
+the formula is the same, except
+that here we have an
+
+integral, and we have to use
+the conditional density
+
+function of x.
+
+Now what I'm going to do, I want
+to introduce it gently
+
+through the example that we
+talked about last time.
+
+So last time we talked about
+having a stick that has a
+
+certain length.
+
+And we take that stick, and we
+break it at some point that we
+
+choose uniformly at random.
+
+And let's denote why the place
+where we chose to break it.
+
+Having chosen y, then
+we're left with a
+
+piece of the stick.
+
+And I'm going to choose a place
+to break it once more
+
+uniformly at random
+between 0 and y.
+
+So this is the second place at
+which we are going to break
+
+it, and we call that place x.
+
+OK, so what's the conditional
+expectation of x if I tell you
+
+the value of y?
+
+I tell you that capital Y
+happens to take a specific
+
+numerical value.
+
+So this capital Y is now a
+specific numerical value, x is
+
+chosen uniformly over
+this range.
+
+So the expected value of x is
+going to be half of this range
+
+between 0 and y.
+
+So the conditional expectation
+is little y over 2.
+
+The important thing to realize
+here is that this
+
+quantity is a number.
+
+I told you that the random
+variable took a certain
+
+numerical value,
+let's say 3.5.
+
+And then you tell me given that
+the random variable took
+
+the numerical value 3.5 the
+expected value of x is 1.75.
+
+So this is an equality
+between numbers.
+
+On the other hand, before you
+do the experiment you don't
+
+know what y is going
+to turn out to be.
+
+So this little y is the
+numerical value that has been
+
+observed when you start doing
+the experiments and you
+
+observe the value of capital
+Y. So in some sense this
+
+quantity is not known ahead of
+time, it is random itself.
+
+So maybe we can start thinking
+of it as a random variable.
+
+So to put it differently, before
+we do the experiment I
+
+ask you what's the expected
+value of x given y?
+
+You're going to answer me well
+I don't know, it depends on
+
+what y is going to
+turn out to be.
+
+So the expected value of x given
+y itself can be viewed
+
+as a random variable, because
+it depends on the random
+
+variable capital Y.
+
+So hidden here there's some kind
+of statement about random
+
+variables instead of numbers.
+
+And that statement about
+random variables, we
+
+write it this way.
+
+By thinking of the expected
+value, the conditional
+
+expectation, as a random
+variable instead of a number.
+
+It's a random variable when we
+do not specify a specific
+
+number, but we think of it
+as an abstract object.
+
+The expected value of x given
+the random variable y is the
+
+random variable y over 2 no
+matter what capital Y
+
+turns out to be.
+
+So we turn and take a statement
+that deals with
+
+equality of two numbers, and we
+make it a statement that's
+
+an equality between two
+random variables.
+
+OK so this is clearly a random
+variable because
+
+capital Y is random.
+
+What exactly is this object?
+
+I didn't yet define it
+for you formally.
+
+So let's now give the formal
+definition of this object
+
+that's going to be
+denoted this way.
+
+The conditional expectation of
+x given the random variable y
+
+is a random variable.
+
+Which random variable is it?
+
+It's the random variable that
+takes this specific numerical
+
+value whenever capital Y happens
+to take the specific
+
+numerical value little y.
+
+In particular, this is a random
+variable, which is a
+
+function of the random variable
+capital Y. In this
+
+instance, it's given by a simple
+formula in terms of
+
+capital Y. In other situations
+it might be a
+
+more complicated formula.
+
+So again, to summarize,
+it's a random.
+
+The conditional expectation can
+be thought of as a random
+
+variable instead of something
+that's just a number.
+
+So in any specific context when
+you're given the value of
+
+capital Y the conditional
+expectation becomes a number.
+
+This is the realized value
+of this random variable.
+
+But before the experiment
+starts, before you know what
+
+capital Y is going to be, all
+that you can say is that the
+
+conditional expectation is going
+to be 1/2 of whatever
+
+capital Y turns out to be.
+
+This is a pretty subtle concept,
+it's an abstraction,
+
+but it's a useful abstraction.
+
+And we're going to see
+today how to use it.
+
+All right, I have made the point
+that the conditional
+
+expectation, the random variable
+that takes these
+
+numerical values is
+a random variable.
+
+If it is a random variable
+this means that it has an
+
+expectation of its own.
+
+So let's start thinking what
+the expectation of the
+
+conditional expectation is
+going to turn out to be.
+
+OK, so the conditional
+expectation is a random
+
+variable, and in general it's
+some function of the random
+
+variable y that we
+are observing.
+
+In terms of numerical values if
+capital Y happens to take a
+
+specific numerical value then
+the conditional expectation
+
+also takes a specific numerical
+value, and we use
+
+the same function
+to evaluate it.
+
+The difference here is that this
+is an equality of random
+
+variables, this is an equality
+between numbers.
+
+Now if we want to calculate
+the expected value of the
+
+conditional expectation we're
+basically talking about the
+
+expected value of a function
+of a random variable.
+
+And we know how to calculate
+expected values of a function.
+
+If we are in the discrete case,
+for example, this would
+
+be a sum over all y's of the
+function who's expected value
+
+we're taking times the
+probability that y takes on a
+
+specific numerical value.
+
+OK, but let's remember
+what g is.
+
+So g is the numerical value
+of the conditional
+
+expectation of x with y.
+
+And now when you see this
+expression you recognize it.
+
+This is the expression
+that we get in the
+
+total expectation theorem.
+
+Did I miss something?
+
+Yes, in the total expectation
+theorem to find the expected
+
+value of x, we divide the world
+into different scenarios
+
+depending on what y happens.
+
+We calculate the expectation
+in each one of the possible
+
+worlds, and we take the
+weighted average.
+
+So this is a formula that you
+have seen before, and you
+
+recognize that this is the
+expected value of x.
+
+So this is a longer, more
+detailed derivation of what I
+
+had written up here, but the
+important thing to keep in
+
+mind is the moral of the
+story, the punchline.
+
+The expected value of the
+conditional expectation is the
+
+expectation itself.
+
+So this is just our total
+expectation theorem, but
+
+written in more abstract
+notation.
+
+And it comes handy to have this
+more abstract notation,
+
+as as we're going to
+see in a while.
+
+OK, we can apply this to
+our stick example.
+
+If we want to find the expected
+value of x how much
+
+of the stick is left
+at the end?
+
+We can calculate it using this
+law of iterated expectations.
+
+It's the expected value of the
+conditional expectation.
+
+We know that the conditional
+expectation is y over 2.
+
+So expected value of y is l over
+2, because y is uniform
+
+so we get l over 4.
+
+So this gives us the same answer
+that we derived last
+
+time in a rather long way.
+
+All right, now that we have
+mastered conditional
+
+expectations, let's raise the
+bar a little more and talk
+
+about conditional variances.
+
+So the conditional expectation
+is the mean value, or the
+
+expected value, in a conditional
+universe where
+
+you're told the value of y.
+
+In that same conditional
+universe you can talk about
+
+the conditional distribution
+of x, which has a mean--
+
+the conditional expectation--
+
+but the conditional
+distribution of
+
+x also has a variance.
+
+So we can talk about the
+variance of x in that
+
+conditional universe.
+
+The conditional variance as a
+number is the natural thing.
+
+It's the variance of x, except
+that all the calculations are
+
+done in the conditional
+universe.
+
+In the conditional universe the
+expected value of x is the
+
+conditional expectation.
+
+This is the distance from the
+mean in the conditional
+
+universe squared.
+
+And we take the average value
+of the squared distance, but
+
+calculate it again using the
+probabilities that apply in
+
+the conditional universe.
+
+This is an equality
+between numbers.
+
+I tell you the value of y, once
+you know that value for y
+
+you can go ahead and plot the
+conditional distribution of x.
+
+And for that conditional
+distribution you can calculate
+
+the number which is the
+variance of x in that
+
+conditional universe.
+
+So now let's repeat the mental
+gymnastics from the previous
+
+slide, and abstract things, and
+define a random variable--
+
+the conditional variance.
+
+And it's going to be a random
+variable because we leave the
+
+numerical value of capital
+Y unspecified.
+
+So ahead of time we don't know
+what capital Y is going to be,
+
+and because of that we don't
+know ahead of time what the
+
+conditional variance
+is going to be.
+
+So before the experiment starts
+if I ask you what's the
+
+conditional variance of x?
+
+You're going to tell me well I
+don't know, It depends on what
+
+y is going to turn out to be.
+
+It's going to be something
+that depends on y.
+
+So it's a random variable,
+which is a function of y.
+
+So more precisely, the
+conditional variance when
+
+written in this notation just
+with capital letters, is a
+
+random variable.
+
+It's a random variable whose
+value is completely determined
+
+once you learned the value of
+capital Y. And it takes a
+
+specific numerical value.
+
+If capital Y happens to get a
+realization that's a specific
+
+number, then the variance also
+becomes a specific number.
+
+And it's just a conditional
+variance of y
+
+over x in that universe.
+
+All right, OK, so let's continue
+what we did in the
+
+previous slide.
+
+We had the law of iterated
+expectations.
+
+That told us that expected
+value of a conditional
+
+expectation is the unconditional
+expectation.
+
+Is there a similar rule that
+might apply in this context?
+
+So you might guess that the
+variance of x could be found
+
+by taking the expected value of
+the conditional variance.
+
+It turns out that this
+is not true.
+
+There is a formula for the
+variance in terms of
+
+conditional quantities.
+
+But the formula is a little
+more complicated.
+
+If involves two terms
+instead of one.
+
+So we're going to go
+quickly through the
+
+derivation of this formula.
+
+And then, through examples
+we'll try to get some
+
+interpretation of what the
+different terms here
+
+correspond to.
+
+All right, so let's try
+to prove this formula.
+
+And the proof is sort of a
+useful exercise to make sure
+
+you understand all the symbols
+that are involved in here.
+
+So the proof is not difficult,
+it's 4 and 1/2 lines of
+
+algebra, of just writing
+down formulas.
+
+But the challenge is to make
+sure that at each point you
+
+understand what each one
+of the objects is.
+
+So we go into formula for
+the variance affects.
+
+We know in general that the
+variance of x has this nice
+
+expression that we often
+use to calculate it.
+
+The expected value of the
+squared of the random variable
+
+minus the mean squared.
+
+This formula, for the variances,
+of course it should
+
+apply to conditional
+universes.
+
+I mean it's a general formula
+about variances.
+
+If we put ourselves in a
+conditional universe where the
+
+random variable y is given to us
+the same math should work.
+
+So we should have a similar
+formula for
+
+the conditional variances.
+
+It's just the same formula,
+but applied to
+
+the conditional universe.
+
+The variance of x in the
+conditional universe is the
+
+expected value of x squared--
+
+in the conditional universe--
+
+minus the mean of x-- in the
+conditional universe--
+
+squared.
+
+So this formula looks fine.
+
+Now let's take expected
+values of both sides.
+
+Remember the conditional
+variance is a random variable,
+
+because its value depends on
+whatever realization we get
+
+for capital Y. So we can
+take expectations here.
+
+We get the expected value
+of the variance.
+
+Then we have the expected
+value of a conditional
+
+expectation.
+
+Here we use the fact that
+we discussed before.
+
+The expected value of a
+conditional expectation is the
+
+same as the unconditional
+expectation.
+
+So this term becomes this.
+
+And finally, here we just have
+some weird looking random
+
+variable, and we take the
+expected value of it.
+
+All right, now we need to do
+something about this term.
+
+Let's use the same
+rule up here to
+
+write down this variance.
+
+So variance of an expectation,
+that's kind of strange, but
+
+you remember that the
+conditional expectation is
+
+random, because y is random.
+
+So this thing is a random
+variable, so
+
+this thing has a variance.
+
+What is the variance
+of this thing?
+
+It's the expected value of the
+thing squared minus the square
+
+of the expected value
+of the thing.
+
+Now what's the expected
+value of that thing?
+
+By the law of iterated
+expectations, once more, the
+
+expected value of this thing
+is the unconditional
+
+expectation.
+
+And that's why here I put the
+unconditional expectation.
+
+So I'm using again this general
+rule about how to
+
+calculate variances, and I'm
+applying it to calculate the
+
+variance of the conditional
+expectation.
+
+And now you notice that if you
+add these two expressions c
+
+and d we get this plus
+that, which is this.
+
+It's equal to--
+
+these two terms cancel, we're
+left with this minus that,
+
+which is the variance of x.
+
+And that's the end
+of the proof.
+
+This one of those proofs that
+do not convey any intuition.
+
+This, as I said, it's a useful
+proof to go through just to
+
+make sure you understand
+the symbols.
+
+It starts to get pretty
+confusing, and a little bit on
+
+the abstract side.
+
+So it's good to understand
+what's going on.
+
+Now there is intuition behind
+this formula, some of which is
+
+better left for later
+in the class when
+
+we talk about inference.
+
+The idea is that the conditional
+expectation you
+
+can interpret it as an estimate
+of the random
+
+variable that you
+are trying to--
+
+an estimate of x based on
+measurements of y, you can
+
+think of these variances as
+having something to do with an
+
+estimation error.
+
+And once you start thinking in
+those terms an interpretation
+
+will come about.
+
+But again as I said this is
+better left for when we start
+
+talking about inference.
+
+Nevertheless, we're going to get
+some intuition about all
+
+these formulas by considering
+a baby example where we're
+
+going to apply the law of
+iterated expectations, and the
+
+law of total variance.
+
+So the baby example is that we
+do this beautiful experiment
+
+of giving a quiz to a class
+consisting of many sections.
+
+And we're interested in
+two random variables.
+
+So we have a number of students,
+and they're all
+
+allocated to sections.
+
+The experiment is that I pick
+a student at random, and I
+
+look at two random variables.
+
+One is the quiz score of the
+randomly selected student, and
+
+the other random variable is
+the section number of the
+
+student that I have selected.
+
+We're given some statistics
+about the two sections.
+
+Section one has 10 students,
+section two has 20 students.
+
+The quiz average in section
+one was 90.
+
+Quiz average in section
+two was 60.
+
+What's the expected
+value of x?
+
+What's the expected quiz score
+if I pick a student at random?
+
+Well, each student has the same
+
+probability of being selected.
+
+I'm making that assumption
+out of the 30 students.
+
+I need to add the quiz scores
+of all of the students.
+
+So I need to add the quiz scores
+in section one, which
+
+is 90 times 10.
+
+I need to add the quiz scores
+in that section,
+
+which is 60 times 20.
+
+And we find that the overall
+average was 70.
+
+So this is the usual
+unconditional expectation.
+
+Let's look at the conditional
+expectation, and let's look at
+
+the elementary version
+where we're talking
+
+about numerical values.
+
+If I tell you that the randomly
+selected student was
+
+in section one what's the
+expected value of the quiz
+
+score of that student?
+
+Well, given this information,
+we're picking a random student
+
+uniformly from that section in
+which the average was 90.
+
+The expected value of the
+score of that student
+
+is going to be 90.
+
+So given the specific value of
+y, the specific section, the
+
+conditional expectation or the
+expected value of the quiz
+
+score is a specific number,
+the number 90.
+
+Similarly for the second section
+the expected value is
+
+60, that's the average score
+in the second section.
+
+This is the elementary
+version.
+
+What about the abstract
+version?
+
+In the abstract version the
+conditional expectation is a
+
+random variable because
+it depends.
+
+In which section is the
+student that I picked?
+
+And with probability 1/3, I'm
+going to pick a student in the
+
+first section, in which case
+the conditional expectation
+
+will be 90, and with probability
+2/3 I'm going to
+
+pick a student in the
+second section.
+
+And in that case the conditional
+expectation will
+
+take the value of 60.
+
+So this illustrates the idea
+that the conditional
+
+expectation is a random
+variable.
+
+Depending on what y is going
+to be, the conditional
+
+expectation is going to be one
+or the other value with
+
+certain probabilities.
+
+Now that we have the
+distribution of the
+
+conditional expectation
+we can calculate the
+
+expected value of it.
+
+And the expected value of such a
+random variable is 1/3 times
+
+90, plus 2/3 times 60, and
+it comes out to equal 70.
+
+Which miraculously is the same
+number that we got up there.
+
+So this tells you that you can
+calculate the overall average
+
+in a large class by taking the
+averages in each one of the
+
+sections and weighing each one
+of the sections according to
+
+the number of students
+that it has.
+
+So this section had 90 students
+but only 1/3 of the
+
+students, so it gets
+a weight of 1/3.
+
+So the law of iterated
+expectations, once more, is
+
+nothing too complicated.
+
+It's just that you can calculate
+overall class
+
+average by looking
+at the section
+
+averages and combine them.
+
+Now since the conditional
+expectation is a random
+
+variable, of course it has
+a variance of it's own.
+
+So let's calculate
+the variance.
+
+How do we calculate variances?
+
+We look at all the possible
+numerical values of this
+
+random variable, which
+are 90 and 60.
+
+We look at the difference of
+those possible numerical
+
+values from the mean of this
+random variable, and the mean
+
+of that random variable, we
+found that's it's 70.
+
+And then we weight the different
+possible numerical
+
+values according to their
+probabilities.
+
+So with probability 1/3 the
+conditional expectation is 90,
+
+which is 20 away
+from the mean.
+
+And we get this squared
+distance.
+
+With probability 2/3 the
+conditional expectation is 60,
+
+which is 10 away from the
+mean, has this squared
+
+distance and gets weighed
+by 2/3, which is the
+
+probability of 60.
+
+So you do the numbers, and you
+get the value for the variance
+
+equal to 200.
+
+All right, so now we want to
+move towards using that more
+
+complicated formula involving
+the conditional variances.
+
+OK, suppose someone goes and
+calculates the variance of the
+
+quiz scores inside each
+one of the sections.
+
+So someone gives us these two
+pieces of information.
+
+In section one we take the
+differences from the mean in
+
+that section, and let's say that
+the various turns out to
+
+be a number equal
+to 10 similarly
+
+in the second section.
+
+So these are the variances
+of the quiz scores inside
+
+individual sections.
+
+The variance in one conditional
+universe, the
+
+variance in the other
+conditional universe.
+
+So if I pick a student in
+section one and I don't tell
+
+you anything more about the
+student, what's the variance
+
+of the random score
+of that student?
+
+The variance is 10.
+
+I know why, but I don't
+know the student.
+
+So the score is still a random
+variable in that universe.
+
+It has a variance, and
+that's the variance.
+
+Similarly, in the other
+universe, the variance of the
+
+quiz scores is this
+number, 20.
+
+Once more, this is an equality
+between numbers.
+
+I have fixed the specific
+value of y.
+
+So I put myself in a specific
+universe, I can calculate the
+
+variance in that specific
+universe.
+
+If I don't specify a numerical
+value for capital Y, and say I
+
+don't know what Y is going to
+be, it's going to be random.
+
+Then what kind of section
+variance I'm going to get
+
+itself will be random.
+
+With probability 1/3, I pick a
+student in the first section
+
+in which case the conditional
+variance given what I have
+
+picked is going to be 10.
+
+Or with probability 2/3 I pick
+y equal to 2, and I place
+
+myself in that universe.
+
+And in that universe the
+conditional variance is 20.
+
+So you see again from here that
+the conditional variance
+
+is a random variable that takes
+different values with
+
+certain probabilities.
+
+And which value it takes depends
+on the realization of
+
+the random variable capital Y.
+So this happens if capital Y
+
+is one, this happens if capital
+Y is equal to 2.
+
+Once you have something
+of this form--
+
+a random variable that takes
+values with certain
+
+probabilities--
+
+then you can certainly calculate
+the expected value
+
+of that random variable.
+
+Don't get intimidated by the
+fact that this random
+
+variable, it's something that's
+described by a string
+
+of eight symbols, or
+seven, instead of
+
+just a single letter.
+
+Think of this whole string of
+symbols there as just being a
+
+random variable.
+
+You could call it z for example,
+use one letter.
+
+So z is a random variable that
+takes these two values with
+
+these corresponding
+probabilities.
+
+So we can talk about the
+expected value of Z, which is
+
+going to be 1/3 times 10, 2/3
+times 20, and we get a certain
+
+number from here.
+
+And now we have all the pieces
+to calculate the overall
+
+variance of x.
+
+The formula from the previous
+slide tells us this.
+
+Do we have all the pieces?
+
+The expected value of
+the variance, we
+
+just calculated it.
+
+The variance of the expected
+value, this was the last
+
+calculation in the
+previous slide.
+
+We did get a number for
+it, it was 200.
+
+You add the two, you find
+the total variance.
+
+Now the useful piece of this
+exercise is to try to
+
+interpret these two numbers,
+and see what they mean.
+
+The variance of x given y for
+a specific y is the variance
+
+inside section one.
+
+This is the variance
+inside section two.
+
+The expected value is some
+kind of average of the
+
+variances inside individual
+sections.
+
+So this term tells us
+something about the
+
+variability of this course,
+how widely spread they are
+
+within individual sections.
+
+So we have three sections, and
+this course happens to be--
+
+OK, let's say the sections
+are really different.
+
+So here you have undergraduates
+and here you
+
+have post-doctoral students.
+
+And these are the quiz scores,
+that's section one, section
+
+two, section three.
+
+Here's the mean of the
+first section.
+
+And the variance has something
+to do with the spread.
+
+The variance in the second
+section has something to do
+
+with the spread, similarly
+with the third spread.
+
+And the expected value of the
+conditional variances is some
+
+weighted average of the three
+variances that we get from
+
+individual sections.
+
+So variability within sections
+definitely contributes
+
+something to the overall
+variability of this course.
+
+But if you ask me about the
+variability over the entire
+
+class there's a second effect.
+
+That has to do with the fact
+that different sections are
+
+very different from
+each other.
+
+That these courses here are far
+away from those scores.
+
+And this term is the one
+that does the job.
+
+This one looks at the expected
+values inside each section,
+
+and these expected values are
+this, this, and that.
+
+And asks a question how widely
+spread are they?
+
+It asks how different from
+each other are the means
+
+inside individual sections?
+
+And in this picture it would be
+a large number because the
+
+difference section means
+are quite different.
+
+So the story that this formula
+is telling us is that the
+
+overall variability of the quiz
+scores consists of two
+
+factors that can be quantified
+and added.
+
+One factor is how much
+variability is there inside
+
+individual sections?
+
+And the other factor is how
+different are the sections
+
+from each other?
+
+Both effects contribute
+to the overall
+
+variability of this course.
+
+Let's continue with just one
+more numerical example.
+
+Just to get the hang of doing
+these kinds of calculations,
+
+and apply this formula to do a
+divide and conquer calculation
+
+of the variance of a
+random variable.
+
+Just for variety now we're going
+to take a continuous
+
+random variable.
+
+Somebody gives you a PDF if this
+form, and they ask you
+
+for the variance.
+
+And you say oh that's too
+complicated, I don't want to
+
+do integrals.
+
+Can I divide and conquer?
+
+And you say OK, let me do
+the following trick.
+
+Let me define a random
+variable, y.
+
+Which takes the value 1 if x
+falls in here, and takes the
+
+value 2 if x falls in
+the second interval.
+
+And let me try to work in the
+conditional world where things
+
+might be easier, and then
+add things up to
+
+get the overall variance.
+
+So I have defined y this
+particular way.
+
+In this example y becomes
+a function of x.
+
+y is completely determined
+by x.
+
+And I'm going to calculate the
+overall variance by trying to
+
+calculate all of the terms
+that are involved here.
+
+So let's start calculating.
+
+First observation is that this
+event has probability 1/3, and
+
+this event has probability
+2/3.
+
+The expected value of x given
+that we are in this universe
+
+is 1/2, because we
+have a uniform
+
+distribution from 0 to 1.
+
+Here we have a uniform
+distribution from 1 to 2, so
+
+the conditional expectation of
+x in that universe is 3/2.
+
+How about conditional
+variances?
+
+In the world who are y is equal
+to 1 x has a uniform
+
+distribution on a
+unit interval.
+
+What's the variance of x?
+
+By now you've probably seen that
+formula, it's 1 over 12.
+
+1 over 12 is the variance of a
+uniform distribution over a
+
+unit interval.
+
+When y is equal to 2 the
+variance is again 1 over 12.
+
+Because in this instance again
+x has a uniform distribution
+
+over an interval
+of unit length.
+
+What's the overall expected
+value of x?
+
+The way you find the overall
+expected value is to consider
+
+the different numerical values
+of the conditional
+
+expectation.
+
+And weigh them according
+to their probabilities.
+
+So with probability 1/3
+the conditional
+
+expectation is 1/2.
+
+And with probability
+2/3 the conditional
+
+expectation is 3 over 2.
+
+And this turns out
+to be 7 over 6.
+
+So this is the advance work
+we need to do, now let's
+
+calculate a few things here.
+
+What's the variance of the
+expected value of x given y?
+
+Expected value of x given y is
+a random variable that takes
+
+these two values with
+these probabilities.
+
+So to find the variance we
+consider the probability that
+
+the expected value takes the
+numerical value of 1/2 minus
+
+the mean of the conditional
+expectation.
+
+What's the mean of the
+conditional expectation?
+
+It's the unconditional
+expectation.
+
+So it's 7 over 6.
+
+We just did that calculation.
+
+So I'm putting here that number,
+7 over 6 squared.
+
+And then there's a second term
+with probability 2/3, the
+
+conditional expectation takes
+this value of 3 over 2, which
+
+is so much away from the mean,
+and we get this contribution.
+
+So this way we have calculated
+the variance of the
+
+conditional expectation,
+this is this term.
+
+What is this?
+
+Any guesses what
+this number is?
+
+It's 1 over 12, why?
+
+The conditional variance just
+happened in this example to be
+
+1 over 12 no matter what.
+
+So the conditional variance
+is a deterministic random
+
+variable that takes
+a constant value.
+
+So the expected value of
+this random variable
+
+is just 1 over 12.
+
+So we got the two pieces that we
+need, and so we do have the
+
+overall variance of the
+random variable x.
+
+So this was just an academic
+example in order to get the
+
+hang of how to manipulate
+various quantities.
+
+Now let's use what we have
+learned and the tools that we
+
+have to do something a little
+more interesting.
+
+OK, so by now you're all in
+love with probabilities.
+
+So over the weekend you're going
+to bookstores to buy
+
+probability books.
+
+So you're going to visit a
+random number bookstores, and
+
+at each one of the bookstores
+you're going to spend a random
+
+amount of money.
+
+So let n be the number of stores
+that you are visiting.
+
+So n is an integer--
+
+non-negative random variable--
+
+and perhaps you know
+the distribution
+
+of that random variable.
+
+Each time that you walk into a
+store your mind is clear from
+
+whatever you did before, and you
+just buy a random number
+
+of books that has nothing to
+do with how many books you
+
+bought earlier on the day.
+
+It has nothing to do with
+how many stores you are
+
+visiting, and so on.
+
+So each time you enter as a
+brand new person, and buy a
+
+random number of books,
+and spend a
+
+random amount of money.
+
+So what I'm saying, more
+precisely, is that I'm making
+
+the following assumptions.
+
+That for each store i--
+
+if you end up visiting
+the i-th store--
+
+the amount of money that you
+spend is a random variable
+
+that has a certain
+distribution.
+
+That distribution is the same
+for each store, and the xi's
+
+from store to store are
+independent from each other.
+
+And furthermore, the xi's are
+all independent of n.
+
+So how much I'm spending at the
+store-- once I get in--
+
+has nothing to do with how
+many stores I'm visiting.
+
+So this is the setting that
+we're going to look at.
+
+y is the total amount of money
+that you did spend.
+
+It's the sum of how much you
+spent in the stores, but the
+
+index goes up to capital N.
+And what's the twist here?
+
+It's that we're dealing with the
+sum of independent random
+
+variables except that how many
+random variables we have is
+
+not given to us ahead of time,
+but it is chosen at random.
+
+So it's a sum of a random number
+of random variables.
+
+We would like to calculate some
+quantities that have to
+
+do with y, in particular the
+expected value of y, or the
+
+variance of y.
+
+How do we go about it?
+
+OK, we know something about the
+linearity of expectations.
+
+That expectation of a sum is the
+sum of the expectations.
+
+But we have used that rule only
+in the case where it's
+
+the sum of a fixed number
+of random variables.
+
+So expected value of x plus y
+plus z is expectation of x,
+
+plus expectation of y, plus
+expectation of z.
+
+We know this for a fixed number
+of random variables.
+
+We don't know it, or how it
+would work for the case of a
+
+random number.
+
+Well, if we know something
+about the case for fixed
+
+random variables let's transport
+ourselves to a
+
+conditional universe where the
+number of random variables
+
+we're summing is fixed.
+
+So let's try to break the
+problem divide and conquer by
+
+conditioning on the different
+possible values of the number
+
+of bookstores that
+we're visiting.
+
+So let's work in the conditional
+universe, find the
+
+conditional expectation in this
+universe, and then use
+
+our law of iterated expectations
+to see what
+
+happens more generally.
+
+If I told you that I visited
+exactly little n stores, where
+
+little n now is a number,
+let's say 10.
+
+Then the amount of money you're
+spending is x1 plus x2
+
+all the way up to x10 given
+that we visited 10 stores.
+
+So what I have done here is that
+I've replaced the capital
+
+N with little n, and I can do
+this because I'm now in the
+
+conditional universe
+where I know that
+
+capital N is little n.
+
+Now little n is fixed.
+
+We have assumed that n is
+independent from the xi's.
+
+So in this universe of a fixed
+n this information here
+
+doesn't tell me anything new
+about the values of the x's.
+
+If you're conditioning random
+variables that are independent
+
+from the random variables you
+are interested in, the
+
+conditioning has no effect,
+and so it can be dropped.
+
+So in this conditional universe
+where you visit
+
+exactly 10 stores the expected
+amount of money you're
+
+spending is the expectation of
+the amount of money spent in
+
+10 stores, which is the sum of
+the expected amount of money
+
+in each store.
+
+Each one of these is the same
+number, because the random
+
+variables have identical
+distributions.
+
+So it's n times the expected
+value of money you spent in a
+
+typical store.
+
+This is almost obvious without
+doing it formally.
+
+If I'm telling you that you're
+visiting 10 stores, what you
+
+expect to spend is 10 times the
+amount you expect to spend
+
+in each store individually.
+
+Now let's take this equality
+here and rewrite it in our
+
+abstract notation, in terms
+of random variables.
+
+This is an equality
+between numbers.
+
+Expected value of y given that
+you visit 10 stores is 10
+
+times this particular number.
+
+Let's translate it into
+random variables.
+
+In random variable notation,
+the expected value of money
+
+you're spending given the
+number of stores--
+
+but without telling you
+a specific number--
+
+is whatever that number of
+stores turns out to be times
+
+the expected value of x.
+
+So this is a random variable
+that takes this as a numerical
+
+value whenever capital
+N happens to be
+
+equal to little n.
+
+This is a random variable, which
+by definition takes this
+
+numerical value whenever
+capital N is
+
+equal to little n.
+
+So no matter what capital N
+happens to be what specific
+
+value, little n, it takes
+this is equal to that.
+
+Therefore the value of this
+random variable is going to be
+
+equal to that random variable.
+
+So as random variables, these
+two random variables are equal
+
+to each other.
+
+And now we use the law of
+iterated expectations.
+
+The law of iterated expectations
+tells us that the
+
+overall expected value of y is
+the expected value of the
+
+conditional expectation.
+
+We have a formula for the
+conditional expectation.
+
+It's n times expected
+value of x.
+
+Now the expected value
+of x is a number.
+
+Expected value of something
+random times a number is
+
+expected value of the
+random variable
+
+times the number itself.
+
+We can take a number outside
+the expectation.
+
+So expected value of
+x gets pulled out.
+
+And that's the conclusion,
+that overall the expected
+
+amount of money you're going to
+spend is equal to how many
+
+stores you expect to visit on
+the average, and how much
+
+money you expect to spend on
+each one on the average.
+
+You might have guessed that
+this is the answer.
+
+If you expect to visit 10
+stores, and you expect to
+
+spend $100 on each store, then
+yes, you expect to spend
+
+$1,000 today.
+
+You're not going to impress your
+Harvard friends if you
+
+tell them that story.
+
+It's one of the cases where
+reasoning, on the average,
+
+does give you the plausible
+answer.
+
+But you will be able to impress
+your Harvard friends
+
+if you tell them that I can
+actually calculate the
+
+variance of how much
+I can spend.
+
+And we're going to work by
+applying this formula that we
+
+have, and the difficulty is
+basically sorting out all
+
+those terms here, and
+what they mean.
+
+So let's start with this term.
+
+So the expected value of y given
+that you're visiting n
+
+stores is n times the
+expected value of x.
+
+That's what we did in
+the previous slide.
+
+So this thing is a random
+variable, it has a variance.
+
+What is the variance?
+
+Is the variance of n times
+the expected value of x.
+
+Remember expected value
+of x is a number.
+
+So we're dealing with the
+variance of n times a number.
+
+What happens when you
+multiply a random
+
+variable by a constant?
+
+The variance becomes the
+previous variance times the
+
+constant squared.
+
+So the variance of this is the
+variance of n times the square
+
+of that constant that
+we had here.
+
+So this tells us the variance
+of the expected
+
+value of y given n.
+
+This is the part of the
+variability of how much money
+
+you're spending, which is
+attributed to the randomness,
+
+or the variability, in
+the number of stores
+
+that you are visiting.
+
+So the interpretation of the
+two terms is there's
+
+randomness in how much you're
+going to spend, and this is
+
+attributed to the randomness
+in the number of stores
+
+together with the randomness
+inside individual stores.
+
+Well, after I tell you how many
+stores you're visiting.
+
+So now let's deal with this
+term-- the variance inside
+
+individual stores.
+
+Let's take it slow.
+
+If I tell you that you're
+visiting exactly little n
+
+stores, then y is how much
+money you spent in those
+
+little n stores.
+
+You're dealing with the sum of
+little n random variables.
+
+What is the variance
+of the sum of
+
+little n random variables?
+
+It's the sum of their
+variances.
+
+So each store contributes a
+variance of x, and you're
+
+adding over little n stores.
+
+That's the variance of money
+spent if I tell you
+
+the number of stores.
+
+Now let's translate this into
+random variable notation.
+
+This is a random variable that
+takes this numerical value
+
+whenever capital N is
+equal to little n.
+
+This is a random variable that
+takes this numerical value
+
+whenever capital N is
+equal to little n.
+
+This is equal to that.
+
+Therefore, these two are always
+equal, no matter what
+
+happens to y.
+
+So we have an equality here
+between random variables.
+
+Now we take expectations
+of both.
+
+Expected value of the variance
+is expected value of this.
+
+OK it may look confusing to
+think of the expected value of
+
+the variance here, but the
+variance of x is a number, not
+
+a random variable.
+
+You think of it as a constant.
+
+So its expected value of n times
+a constant gives us the
+
+expected value of n times
+the constant itself.
+
+So now we got the second term
+as well, and now we put
+
+everything together, this plus
+that to get an expression for
+
+the overall variance of y.
+
+Which again, as I said before,
+the overall variability in y
+
+has to do with the variability
+of how much you spent inside
+
+the typical store.
+
+And the variability in
+the number of stores
+
+that you are visiting.
+
+OK, so this is it for today.
+
+We'll change subjects quite
+radically from next time.
\ No newline at end of file
diff --git a/PGnLAx8e4Gk.txt b/PGnLAx8e4Gk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c9c620e1d2eae786c70a562a1118f0389e03db0f
--- /dev/null
+++ b/PGnLAx8e4Gk.txt
@@ -0,0 +1,3497 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu
+
+MEHRAN KARDAR: OK, let's start.
+
+So in this class,
+we focused mostly
+
+on having some slab of material
+and having some configuration
+
+of some kind of a field inside.
+
+And we said that,
+basically, we are
+
+going to be interested
+close to, let's say,
+
+phase transition and some
+quantity that changes
+
+at the phase transition.
+
+We are interested in figuring
+out the singularities
+
+associated with that.
+
+And we can coarse grain.
+
+Once we have coarse grained, we
+have the field m, potentially
+
+a vector, that is characterized
+throughout this material.
+
+So it's a field
+that's function of x.
+
+And by integrating out over
+a lot of degrees of freedom,
+
+we can focus on the
+probability of finding
+
+different configurations
+of this field.
+
+And this probability
+we constructed
+
+on the basis of a number
+of simple assumptions
+
+such as locality, which
+implied that we would write
+
+this probability as a
+product of contributions
+
+of different parts, which in the
+exponent becomes an integral.
+
+And then we would put
+within this all kinds
+
+of things that are consistent
+with the symmetries
+
+of the problem.
+
+So if, for example,
+this is a field that
+
+is invariant on
+the rotations, we
+
+would be having terms such as
+m squared, m to the fourth,
+
+and so forth.
+
+But the interesting thing
+was that, of course,
+
+there is some interaction
+with the neighborhoods.
+
+Those neighborhood interactions
+we can, in the continuum limit,
+
+inclement by putting terms that
+are proportional to radiant
+
+of m and so forth.
+
+So there is a lot
+of things that you
+
+could put consistent
+with symmetry
+
+and presumably be as
+general as possible.
+
+You could have
+this and the terms
+
+in this coefficients
+of this expansion would
+
+be these phenomenological
+parameters characterizing
+
+this probability,
+function of all kinds
+
+of microscopic
+degrees of freedom,
+
+as well as microscopic
+constraints
+
+such as temperature,
+pressures, et cetera.
+
+Now the question that we have
+is if I start with a system,
+
+let's say a configuration
+where everybody's pointing up
+
+or some other configuration
+that is not the equilibrium
+
+configuration, how
+does the probability
+
+evolve to become
+something like this?
+
+Now we are interested
+therefore in m
+
+that is a function
+of position and time.
+
+And since I want to use t for
+time, this coefficient of m
+
+squared that we were
+previously calling t,
+
+I will indicate by r, OK?
+
+There are various types
+of dynamics that you
+
+can look at for this problem.
+
+I will look at the class
+that is dissipative.
+
+And its inspiration
+is the Brownian motion
+
+that we discussed
+last time where
+
+we saw that when you put
+a particle in a fluid
+
+to a very good approximation
+when the fluid is viscous,
+
+it is the velocity that is
+proportional to the force
+
+and you can't ignore inertial
+effects such as mass times
+
+acceleration and you
+write an equation
+
+that is linear in position.
+
+Velocity is the
+linear derivative
+
+of position, which
+is the variable that
+
+is of interest to you.
+
+So here the variable that
+is of interest to us,
+
+is this magnetization that is
+changing as a function of time.
+
+And the equation
+that we write down
+
+is the derivative of this
+field with respect to time.
+
+And again, for the
+Brownian motion,
+
+the velocity was
+proportional to the force.
+
+The constant of proportionality
+was some kind of a mobility
+
+that you would
+have in the fluid.
+
+So continuing with
+that inspiration,
+
+let's put some kind
+of a mobility here.
+
+I should really put a
+vector field here, but just
+
+for convenience, let's
+just focus on one component
+
+and see what happens.
+
+Now what is the force?
+
+Presumably, each
+location individually
+
+feels some kind of a force.
+
+And typically when we had the
+Brownian particle, the force
+
+we were getting
+from the derivative
+
+of the potential with
+respect to the [? aviation ?]
+
+of the position, the field
+that we are interested.
+
+So the analog of our
+potential is the energy
+
+that we have over here,
+and in the same sense
+
+that we want this effective
+potential, if you like,
+
+to govern the
+equilibrium behavior--
+
+and again, recall that for the
+case of the Brownian particle,
+
+eventually the probability was
+related to the potential by e
+
+to the minus beta v. This
+is the analog of beta v, now
+
+considered in the entire field.
+
+So the analog of the force is
+a derivative of this beta H,
+
+so this would be our beta H
+with respect to the variable
+
+that I'm trying to change.
+
+And since I don't have just
+one variable, but a field,
+
+the analog of the derivative
+becomes this functional
+
+derivative.
+
+And in the same sense that
+the Brownian particle,
+
+the Brownian motion,
+is trying to pull you
+
+towards the minimum
+of the potential,
+
+this is an equation that,
+if I kind of stop over here,
+
+tries to put the particle
+towards the minimum
+
+of this beta H.
+
+Now the reason that the Brownian
+particle didn't go and stick
+
+at one position, which was
+the minimum, but fluctuated,
+
+was of course, that we
+added the random force.
+
+So there is some kind of an
+analog of a random force that
+
+we can put either in front of
+[? mu ?] or imagine that if we
+
+added it to [? mu, ?]
+and we put it over here.
+
+Now for the case of
+the Brownian particle,
+
+the assumption was that if
+I evaluate eta at some time,
+
+and eta at another
+time t2 and t1,
+
+that this was related to 2D
+delta function t1 minus t2.
+
+Now of course here, at each
+location, I have a noise term.
+
+So this noise carries
+an index, which
+
+indicates the position, which
+is, of course, a vector in D
+
+dimension in principal.
+
+And there is no reason to
+imagine that the noise here
+
+that comes from all kinds of
+microscopic degrees of freedom
+
+that we have
+integrated out should
+
+have correlation with the
+noise at some other point.
+
+So the simplest assumption is
+to also put the delta function
+
+in the positions, OK?
+
+So if I take this beta
+H that I have over there
+
+and take the functional
+derivative, what do I get?
+
+I will get that the m of xt by
+dt is the function of-- oops,
+
+and I forgot to put a
+the minus sign here.
+
+The force is minus
+the potential,
+
+and this is basically
+going down the gradient,
+
+so I need to put that.
+
+So I have to take a
+derivative of this.
+
+First of all I can take
+a derivative with respect
+
+to m itself.
+
+I will get minus rm.
+
+Well, actually, let's
+put the minus out front.
+
+And then I will get
+the derivative of m
+
+to the fourth, which is
+[? 4umq, ?] all kinds of terms
+
+like this.
+
+Then the terms that come
+from the derivatives
+
+and taking the derivative
+with respect to gradient
+
+will give me K
+times the gradient.
+
+But then in the
+functional derivative,
+
+I have to take
+another derivative,
+
+converting this to minus
+K log Gaussian of m.
+
+And then I would have
+L the fourth derivative
+
+from the next term and so forth.
+
+And on top of
+everything else, I will
+
+have the noise who's statistics
+I have indicated above.
+
+So this entity,
+this equation, came
+
+from the Landau-Ginzburg
+model, and it
+
+is called a time dependent
+Landau-Ginzburg equation.
+
+And so would be the analog of
+the Brownian type of equation,
+
+now for an entire field.
+
+Now we're going to have
+a lot of difficulty
+
+in the short amount of time
+that is left to us to deal
+
+with this nonlinear
+equation, so we
+
+are going to do the same
+thing that we did in order
+
+to capture the properties
+of the Landau-Ginzburg model
+
+qualitatively.
+
+Which is to ignore
+nonlinearities,
+
+so it's a kind of Gaussian
+version of the model.
+
+So what we did
+was we linearized.
+
+AUDIENCE: Question.
+
+MEHRAN KARDAR: Yes?
+
+AUDIENCE: Why does the
+sign in front of the K term
+
+change relative to the others?
+
+MEHRAN KARDAR: OK, so when you
+have the function 0 of a field
+
+gradient, et
+cetera, you can show
+
+that the functional
+derivative, the first term
+
+is the ordinary
+type of derivative.
+
+And then if you think about the
+variations that are carrying m
+
+and with the gradient and you
+write it as m plus delta m
+
+and then make sure that you
+take the delta m outside,
+
+you need to do an integration
+by part that changes the sign.
+
+And the next term
+would be the gradient
+
+of the phi by the [? grad ?]
+m, and the next term
+
+would be log [INAUDIBLE]
+of [INAUDIBLE] gradient
+
+of m squared and so forth.
+
+It alternates and so by
+explicitly calculating
+
+the difference of
+two functionals
+
+with this integration evaluated
+at m and m plus delta m
+
+and pulling out everything
+that is proportional to delta m
+
+you can prove these expressions.
+
+So we linearize this equation,
+which I've already done that.
+
+I cross out the mq term and
+any other nonlinear terms,
+
+so I only keep the linear term.
+
+And then I do a
+Fourier transform.
+
+So basically I switch from
+the position representation
+
+to the Fourier transform that's
+called m tilde of q, I think.
+
+x is replaced with q.
+
+And then the equation
+for the field m linears.
+
+The form separates out
+into independent equations
+
+for the components that
+are characterized by q.
+
+So the Fourier transform of the
+left hand side is just this.
+
+Fourier transform of
+the right hand side
+
+will give me minus mu
+r plus K q squared.
+
+The derivative of [INAUDIBLE]
+will give me a minus q squared.
+
+The derivative of the next term
+L q to the forth, et cetera.
+
+And I've only kept
+the linear term,
+
+so I have m tilde of q and t.
+
+And then I have the
+Fourier transforms
+
+of the noise eta of x and t.
+
+They [? call it ?] eta
+tilde of q [? m. ?]
+
+So you can see that
+each mode satisfy
+
+a separate linear equation.
+
+So this equation is
+actually very easy
+
+to solve for any linear
+equation m tilde of q and t.
+
+If I didn't have the
+noise, so I would
+
+start with some value
+at t [? close ?] to 0,
+
+and that value would
+decay exponentially
+
+in the characteristic time
+that I will call tao of q.
+
+And 1 over tao of q is
+simply this mu r plus K q2
+
+and so forth.
+
+Now once you have noise,
+essentially each one
+
+of these noises acts like
+an initial condition.
+
+And so the full
+answer is an integral
+
+over all of these noises from
+0 tilde time t of interest.
+
+Dt prime the noise that
+occurs at a time t prime,
+
+and the noise that occurs at
+time t [? trime ?] relaxes
+
+with this into the minus
+t minus t prime tao of q.
+
+So that's the solution to
+that linear noisy equations,
+
+basically [? sequencing ?]
+[INAUDIBLE].
+
+So one of the things
+that we now see
+
+is that essentially the
+different Fourier components
+
+of the field.
+
+Each one of them
+is independently
+
+relaxing to something,
+and each one of them
+
+has a characteristic
+relaxation time.
+
+As I go towards smaller
+and smaller values of q,
+
+this rate becomes smaller,
+and the relaxation time
+
+becomes larger.
+
+So essentially shortwave
+wavelength modes
+
+that correspond to large
+q, they relax first.
+
+Longer wavelength modes
+will relax later on.
+
+And you can see that the largest
+relaxation time, tao max,
+
+corresponds to q equals to 0
+is simply 1 over [? nu ?] r.
+
+So I can pluck this to a
+max as a function of r,
+
+and again in this theory,
+the Gaussian theory,
+
+we saw only makes sense as
+long as all is positive.
+
+So I have to look only
+on the positive axis.
+
+And I find that
+the relaxation time
+
+for the entire system for
+the longest wavelength
+
+actually diverges
+as r goes to 0.
+
+And recall that r,
+in our perspective,
+
+is really something that is
+proportional to T minus Tc.
+
+So basically we find that
+as we are approaching
+
+the critical point,
+the time it takes
+
+for the entirety of the
+system or the longest
+
+wavelength [? modes ?] to relax
+diverges as 1 over T minus Tc.
+
+There's an exponent that
+shows this, so called,
+
+critical slowing down.
+
+Yes?
+
+AUDIENCE: In principal,
+why couldn't you
+
+have that r becomes negative
+if you restrict your range of q
+
+to be outside of some value
+and not go arbitrarily
+
+close to the origin.
+
+MEHRAN KARDAR: You could, but
+what's the physics of that?
+
+See.
+
+AUDIENCE: I'm wondering if
+there is or is that not needed.
+
+MEHRAN KARDAR: No.
+
+OK, so the physics of that could
+be that you have a system that
+
+has some finite size, [? l. ?]
+Then the largest q that you
+
+could have [? or ?] the smallest
+q that you could have would be
+
+the [? 1/l. ?] So in principal,
+for that you can go slightly
+
+negative.
+
+You still cannot go too negative
+because ultimately this will
+
+overcome that.
+
+But again, we are
+interested in singularities
+
+that we kind of know arise
+in the limit of [INAUDIBLE].
+
+I also recall, there is a
+time that we see as diverging
+
+as r goes to 0.
+
+Of course, we identified
+before a correlation length
+
+from balancing these two terms,
+and the correlation length
+
+is square root of K over r,
+which is again proportional
+
+to T minus Tc and diverges
+with a square root singularity.
+
+So we can see that this
+tao max is actually related
+
+to the psi squared over Nu K.
+
+And it is also
+related towards this.
+
+We can see that our tao of
+q, basically, if q is large
+
+such that qc is larger than
+1 and the characteristic time
+
+is going to be 1 over [? nu ?] K
+times the inverse of q squared.
+
+And the inverse of q is
+something like a wavelength.
+
+Whereas, ultimately, this
+saturates for qc what is less
+
+than 1 [? long ?] wavelengths
+to c squared over [? nu ?] K.
+
+So basically you see
+things at very short range,
+
+at length scales that are
+much less than the correlation
+
+length of the system, that
+the characteristic time will
+
+depend on the length scale that
+you are looking at squared.
+
+Now you have seen times
+scaling as length squared
+
+from diffusion, so
+essentially this
+
+is some kind of a
+manifestation of diffusion,
+
+but as you perturb the system,
+let's say at short distances,
+
+there's some equilibrium system.
+
+Let's say we do some
+perturbation to it
+
+at some point, and
+that perturbation
+
+will start to expand
+diffusively until it reaches
+
+the size of the correlation
+length, at which point
+
+it stops because essentially
+correlation length is
+
+an individual block that doesn't
+know about individual blocks,
+
+so the influence does not last.
+
+So quite generally,
+what you find--
+
+so we solved the
+linearized version
+
+of the Landau-Ginzburg
+model, but we
+
+know that, say, the critical
+behaviors for the divergence
+
+of the correlation length
+that is predicted here
+
+is not correct in
+three dimensions,
+
+things get modified.
+
+So these kind of exponents
+that come from diffusion also
+
+gets modified.
+
+And quite generally, you
+find that the relaxation time
+
+of a mode of wavelength q
+is going to behave something
+
+like wavelength,
+which is 1 over q,
+
+rather than squared
+as some exponent z.
+
+And then there is some
+function of the product
+
+of the wavelength
+you are looking at
+
+and the correlation length
+so that you will cross over
+
+from one behavior
+to another behavior
+
+as you are looking
+at length scales that
+
+are smaller than the
+correlation length
+
+or larger than the
+correlation length.
+
+And to get what
+this exponent z is,
+
+you have to do study
+of the nonlinear model
+
+in the same sense
+that, in order to get
+
+the correction to the
+exponent [? nu ?],
+
+we had to do epsilon expansion.
+
+You have to do
+something similar,
+
+and you'll fine that
+at higher changes,
+
+it goes like some correction
+that does not actually
+
+start at order of epsilon but
+at order of epsilon squared.
+
+But there's essentially
+some modification
+
+of the qualitative
+behavior that we
+
+can ascribe to the fusion
+of independent modes
+
+exists quite generally
+and universal exponents
+
+different from [? to ?]
+will emerge from that.
+
+Now it turns out that this
+is not the end of the story
+
+because we have seen
+that the same probability
+
+distribution can describe
+a lot of different systems.
+
+Let's say the focus on
+the case of n equals to 1.
+
+So then this Landau-Ginzburg
+that I described
+
+for you can describe,
+let's say, the Ising model,
+
+which describes
+magnetizations that lie
+
+along the particular direction.
+
+So that it can also describe
+liquid gas phenomena
+
+where the order parameter is
+the difference in density,
+
+if you like, between
+the liquid and the gas.
+
+Yet another example
+that it describes
+
+is the mixing of an alloy.
+
+So let's, for example, imagine
+brass that has a composition
+
+x that goes between 0 and 1.
+
+On one end, let's say
+you have entirely copper
+
+and on the other and
+you have entirely zinc.
+
+And so this is how you
+make brass as an alloy.
+
+And what my other axis
+is is the temperature.
+
+What you find is that there
+is some kind of phase diagram
+
+such that you get a nice
+mixture of copper and zinc
+
+only if you are at
+high temperatures,
+
+whereas if you are
+at low temperature,
+
+you basically will
+separate into chunks
+
+that are rich copper and
+chunks that are rich in zinc.
+
+And you'll have a
+critical demixing
+
+point, which has exactly the
+same properties as the Ising
+
+model.
+
+For example, this curve
+will be characterized
+
+with an exponent
+beta, which would
+
+be the beta of the Ising mode.
+
+And in particular, if I
+were to take someplace
+
+in the vicinity of this and
+try to write down a probability
+
+distribution, that
+probability distribution
+
+would be exactly what
+I have over there where
+
+m is, let's say, the difference
+between the two types of alloys
+
+that I have compared to
+each other over here.
+
+So this is related to 2x minus
+1 or something like that.
+
+So as you go across your piece
+of material close to here,
+
+there will be
+compositional variations
+
+that are described by that.
+
+So the question is, I know
+exactly what the probability
+
+distribution is for this system
+to be an equilibrium given
+
+this choice of m.
+
+Again, with some set of
+parameters, R, U, et cetera.
+
+The question is-- is the
+dynamics again described
+
+by the same equation?
+
+And the answer is no.
+
+The same probability
+of distribution
+
+can describe-- or
+can be obtained
+
+with very different dynamics.
+
+And in particular,
+what is happening
+
+in the system is that, if
+I integrate this quantity m
+
+across the system, I will
+get the total number of 1
+
+minus the other, which
+is what is given to you,
+
+and it does not change
+as a function of time.
+
+d by dt of this quantity is 0.
+
+It cannot change.
+
+OK.
+
+Whereas the equation that
+I have written over here,
+
+in principle, locally, I
+can, by adding the noise
+
+or by bringing things
+from the neighborhood,
+
+I can change the value of m.
+
+I cannot do that.
+
+So this process of the
+relaxation that would go
+
+on in data graphs cannot be
+described by the time dependent
+
+on the Landau-Ginzburg
+equation because you have this
+
+conservation here.
+
+OK.
+
+So what should we do?
+
+Well, when things are
+conserved, like, say,
+
+as the gas particles
+move in this fluid,
+
+and if I'm interested in
+the number of particles
+
+in some cube, then the
+change in the number
+
+of particles in some
+cube in this room
+
+is related to the gradient
+of the current that
+
+goes into that place.
+
+So the appropriate way of
+writing an equation that
+
+describes, let's say, the
+magnetization changing
+
+as a function of time.
+
+Given that you have
+a conservation,
+
+though, is to write it
+as minus the gradient
+
+of some kind of a current.
+
+So this j is some
+kind of a current,
+
+and these would be vectors.
+
+This is a current
+of the particles
+
+moving into the system.
+
+Now, in systems that
+are dissipative,
+
+currents are related to the
+gradient of some density
+
+through the diffusion
+constant, et cetera.
+
+So it kind of makes sense to
+imagine that this current is
+
+the gradient of something that
+is trying-- or more precisely,
+
+minus the gradient
+of something that
+
+tries to bring the system
+to be, more or less,
+
+in its equilibrium state.
+
+Equilibrium state, as we said,
+is determined by this data H,
+
+and we want to push
+it in that direction.
+
+So we put our data
+H by dm over here,
+
+and we put some kind
+of a U over here.
+
+Of course, I would
+have to add some kind
+
+of a conserved
+random current also,
+
+which is the analog of
+this non-conserved noise
+
+that I add over initially.
+
+OK.
+
+Now, the conservative version
+of the equation, you can see,
+
+you have two more
+derivatives with respect
+
+to what we had before.
+
+And so once I-- OK.
+
+So if we do something like
+this, dm by dt is mu C.
+
+And then I would
+have [INAUDIBLE]
+
+plus of R, rather
+than by itself.
+
+Actually, it would be the plus
+then of something like R m
+
+plus 4 U m cubed, and so forth.
+
+And we are going to
+ignore this kind of term.
+
+And then there would
+be high order terms
+
+that would show up minus
+k the fourth derivative,
+
+and so forth.
+
+And then there may be some
+kind of a conserved noise
+
+that I have to put outside.
+
+OK.
+
+So when I fully transform
+this equation, what do I get?
+
+I will get that dm by dt is--
+let's say in the full space,
+
+until there is a
+function of qnt is minus
+
+U C. Because of this plus, then
+there's an additional factor
+
+of q squared.
+
+And then I have R
+plus kq squared plus L
+
+cubed to the fourth, et cetera.
+
+And then I will have a
+fully transformed version
+
+of this conserved noise.
+
+OK.
+
+You can see that the difference
+between this equation
+
+and the previous equation is
+that all of the relaxation
+
+times will have an additional
+factor of q squared.
+
+And so eventually, this shortest
+relaxation time actually
+
+will glow like the size
+of the system squared.
+
+Whereas previously,
+it was saturated
+
+at the correlation length.
+
+And because you will
+have this conservation,
+
+though, you have to
+rearrange a lot of particles
+
+keeping their numbers constant.
+
+You have a much harder time
+of relaxing the system.
+
+All of the relaxation
+times, as we see,
+
+grow correspondingly
+and become higher.
+
+OK.
+
+So indeed, for this class, one
+can show that z starts with 4,
+
+and then there
+will be corrections
+
+that would modify that.
+
+So the-- yes?
+
+AUDIENCE: How do we
+define or how do we
+
+do a realization of the
+conserved noise, conserved
+
+current-- conserved
+noise in the room?
+
+MEHRAN KARDAR: OK.
+
+AUDIENCE: So it has some
+kind of like correlation--
+
+self-correlation
+properties, I suppose,
+
+because, if current
+flowing out of some region,
+
+doesn't it want to go in?
+
+MEHRAN KARDAR: If
+I go back here,
+
+I have a good idea of what is
+happening because all I need,
+
+in order to ensure conservation,
+is that the m by dt
+
+is the gradient of something.
+
+AUDIENCE: OK.
+
+MEHRAN KARDAR: So I can put
+whatever I want over here.
+
+AUDIENCE: So if it's a scalar
+or an [INAUDIBLE] field?
+
+MEHRAN KARDAR: Yes.
+
+As long as it is sitting
+under the gradient--
+
+AUDIENCE: OK.
+
+MEHRAN KARDAR: --it will be OK,
+which means this quantity here
+
+that I'm calling a to
+z has a gradient in it.
+
+And if you wait for
+about five minutes,
+
+we'll show that, because
+of that in full space,
+
+rather than having--
+well, I'll describe
+
+the difference between
+non-conserved and conserved
+
+noise in fully space.
+
+It's much easier.
+
+OK.
+
+So actually, as far as what I
+have discussed so far, which
+
+is relaxation, I don't
+really need the noise
+
+because I can forget the noise.
+
+And all I have
+said-- and I forgot
+
+the n tilde-- is that I
+have a linear equation that
+
+relaxes your variable to 0.
+
+I can immediately read
+off for the correlation,
+
+then this-- a correlation times
+what I need the noise for it
+
+so that, ultimately, I don't go
+to the medium is the potential,
+
+but I go to this
+pro-rated distribution.
+
+So let's see what we have to
+do in order to achieve that.
+
+For simplicity, let's
+take this equation.
+
+Although I can take the
+corresponding one for that.
+
+And let's calculate-- because
+of the presence of this noise,
+
+if I run the same system
+at different times,
+
+I will have different
+realizations of the noise
+
+than if I had run many
+versions of the system because
+
+of the realizations of noise.
+
+It's quantity and tilde
+would be different.
+
+It would satisfy some kind
+of a pro-rated distribution.
+
+So what I want to do is
+to calculate averages,
+
+such as the average of m tilde.
+
+Let's say, q1 at time T
+with m tilde q2 at time t.
+
+And you can see already
+from this equation
+
+that, if I forget the part
+that comes from the noise,
+
+whatever initial
+condition that I have
+
+will eventually decay to 0.
+
+So the thing that
+agitates and gives
+
+some kind of a randomness to
+this really comes from this.
+
+So let's imagine
+that we have looked
+
+at times that are
+sufficiently long so
+
+that the influence of
+the initial condition
+
+has died down.
+
+I don't want to
+write the other term.
+
+I could do it, but it's kind
+of boring to include it.
+
+So let's forget that and
+focus on the integral.
+
+0 to t.
+
+Now, if I multiply two
+of these quantities,
+
+I will have two
+integrals over t prime.
+
+All right.
+
+Each one of them would decay
+with the corresponding tau
+
+of q.
+
+In one case, tau of q1.
+
+In the other case, tau of q2.
+
+Coming from these things.
+
+And the noise, q1 at time
+to 1 prime, and noise q2
+
+at time [? t2 prime. ?]
+
+OK.
+
+Now if I average over
+the noise, then I
+
+have to do an average over here.
+
+OK.
+
+Now, one thing that I forgot to
+mention right at the beginning
+
+is that, of course,
+the average of this
+
+we are going to set to 0.
+
+It's the very least
+that is important.
+
+Right?
+
+So if I do that,
+clearly, the average
+
+of one of these in
+full space would
+
+be 0 also because the full q is
+related to the real space delta
+
+just by an integral.
+
+So if the average of
+the integral is 0,
+
+the average of this is 0.
+
+So it turns out that, when
+you look at the average of two
+
+of them-- and it's a
+very simple exercise
+
+to just rewrite these things
+in terms of 8 of x and t.
+
+8 of x and t applied
+average that you have.
+
+And we find that the things that
+are uncorrelated in real space
+
+also are uncoordinated
+in full space.
+
+And so the variance
+of this quantity
+
+is 2d delta 1 prime
+minus [? d2 prime. ?]
+
+And then you have the analog
+of the function in full space,
+
+which always carries the
+solution of a factor of 2 pi
+
+to the d.
+
+And it becomes a sum
+of the q's, as we've
+
+seen many times before.
+
+OK.
+
+So because of this
+delta function,
+
+this delta integral
+becomes one integral.
+
+So I have the integral 0 to t.
+
+The 2t prime I can
+write as just 1t prime,
+
+and these two factors
+merge into one.
+
+It comes into minus t minus
+t prime over tau of q,
+
+except that I get
+multiplied by a factor 2
+
+since I have two of them.
+
+And outside of the integral,
+I will have this factor of 2d,
+
+and then 2 pi to the d delta
+function with 1 plus 2.
+
+OK.
+
+Now, we are really
+interested-- and I already
+
+kind of hinted at
+that in the limit
+
+where time becomes very large.
+
+In the limit, where time
+becomes a very large,
+
+essentially, I need to calculate
+the limit of this integral
+
+as time becomes very large.
+
+And as time grows
+to very large, this
+
+is just the integral
+from 0 to infinity.
+
+And the integral is going
+to give me 2 over tau of q.
+
+Essentially, you can see that
+integrating at the upper end
+
+will give me just 0.
+
+Integrating at the
+smaller end, it
+
+will be exponentially
+small as it
+
+goes to infinity as a
+factor of 2 over tau.
+
+OK.
+
+Yes?
+
+AUDIENCE: Are you
+assuming or-- yeah.
+
+Are you assuming that
+tau of q is even in q
+
+to be able to combine to--
+
+MEHRAN KARDAR: Yes.
+
+AUDIENCE: --2 tau?
+
+So-- OK.
+
+MEHRAN KARDAR: I'm thinking
+of the tau of q's that we've
+
+calculated over here.
+
+AUDIENCE: OK.
+
+MEHRAN KARDAR: OK.
+
+Yes?
+
+AUDIENCE: The e
+times the [INAUDIBLE]
+
+do the equation of something?
+
+Right?
+
+MEHRAN KARDAR: At this stage, I
+am focusing on this expression
+
+over here, where a is not.
+
+But I will come to
+that expression also.
+
+So for the time being, this
+d is just the same constant
+
+as we have over here.
+
+OK?
+
+So you can see that
+the final answer
+
+is going to be d
+over tau of q 2 pi
+
+to the d delta
+function q1 plus q2.
+
+And if I use the value of tau
+of q that I have, tau of q
+
+is mu R plus kq squared,
+which becomes d over mu R
+
+plus kq squared and so forth.
+
+2 pi to the d delta
+function q1 plus q2.
+
+So essentially, if I take this
+linearized time dependent line
+
+of Landau-Ginzburg equation,
+run it for a very long time,
+
+and look at the
+correlations of the field,
+
+I see that the
+correlations of the field,
+
+at the limit of long times,
+satisfy this expression.
+
+Now, what do I know if
+I look at the top line
+
+that I have for the
+probability of distribution?
+
+I can go and express that
+probability of distribution
+
+in full mode.
+
+In the linear
+version, I immediately
+
+get that the probability
+of m tilde of q
+
+is proportional to a
+product over different q's,
+
+e to the minus R
+plus kq squared,
+
+et cetera, and tilde
+of q squared over 2.
+
+All right.
+
+So when I look at the
+equilibrium linear
+
+as Landau-Ginzburg, I can
+see that, if I calculate
+
+the average of m of
+q1, m of q2, then
+
+this is an equilibrium average.
+
+What I would get is 2 pi
+to the d delta function
+
+of q1 plus q2 because, clearly,
+the different q's are recovered
+
+from each other.
+
+And for the particular value of
+q, what I will get is 1 over R
+
+plus kq squared and so forth.
+
+Yes?
+
+AUDIENCE: So isn't the 2
+over tau-- [INAUDIBLE]?
+
+MEHRAN KARDAR: Yes.
+
+Over 2.
+
+Yeah.
+
+OK.
+
+OK.
+
+I changed because I
+had 2d cancels the 2.
+
+I would have to put
+here tau of q over 2.
+
+I had 2d times tau of q over 2.
+
+So it's d tau.
+
+And inverse of tau, I
+have everything correct.
+
+OK.
+
+So if you make an even number
+of errors, the answer comes up.
+
+OK.
+
+But you can now
+compare this expression
+
+that comes from equilibrium
+and this expression that
+
+comes from the long time
+limit of this noisy equation.
+
+OK So we want to
+choose our noise
+
+so that the stochastic
+dynamics gives the same value
+
+as equilibrium, just like we
+did for the case of a Brownian
+
+particular where you have some
+kind of an Einstein equation
+
+that was relating the strength
+of the noise and the mobility.
+
+And we see that here
+all I need to do
+
+is to ensure that d over
+mu should be equal to 1.
+
+OK.
+
+Now, the thing is that,
+if I am doing this,
+
+I, in principle, can have a
+different noise for each q,
+
+and compensate by different
+mobility for each q.
+
+And I would get the same answer.
+
+So in the non-conserved version
+of this time dependent dynamics
+
+that you wrote down,
+the d was a constant
+
+and the mu was a constant.
+
+Whereas, if you want to get
+the same equilibrium result out
+
+of the conserved dynamics,
+you can see that, essentially,
+
+what we previously had as
+mu became something that
+
+is proportional to q squared.
+
+So essentially, here, this
+becomes mu C q squared.
+
+So clearly, in order
+to get the same answer,
+
+I have to put my noise to be
+proportional to q squared also.
+
+And we can see that this kind of
+conserved noise that I put over
+
+here achieves that
+because, as I said,
+
+this conserved noise is the
+gradient of something, which
+
+means that, when I go to
+fully space, if it be q,
+
+it will be proportional to q.
+
+And when I take its
+variants, it's variants
+
+will be proportional
+to q squared.
+
+Anything precisely canceled.
+
+But you can see
+that you also-- this
+
+had a physical explanation in
+terms of a conservation law.
+
+In principle, you can cook
+up all kinds of b of q and mu
+
+of q.
+
+As long as this equality is
+satisfied, you will have,
+
+for these linear
+stochastic equations,
+
+the guarantee that you would
+always get the same equilibrium
+
+result.
+
+Because if you wait
+for this dynamics
+
+to settle down after long times,
+you will get to the answer.
+
+Yes?
+
+AUDIENCE: I wonder how general
+is this result for stochastic
+
+[INAUDIBLE]?
+
+MEHRAN KARDAR: OK.
+
+AUDIENCE: But what I--
+
+MEHRAN KARDAR: So
+what I showed you
+
+was with for linearized version,
+and the only thing that I
+
+calculated was the variance.
+
+And I showed that the
+variances were the same.
+
+And if I have a Gaussian
+problem of distribution,
+
+the variance is
+completely categorizable
+
+with distribution.
+
+So this is safe.
+
+But we are truly interested
+in the more general
+
+non-Gaussian probability
+of distribution.
+
+So the question really is-- if
+I keep the full non-linearity
+
+in this story, would
+I be able to show
+
+that the probability
+of distribution that
+
+will be characterized
+by all kinds of moments
+
+eventually has the
+same behavior as that.
+
+AUDIENCE: Mm-hmm.
+
+MEHRAN KARDAR: And the
+answer is, in fact, yes.
+
+There's a procedure that
+relies on converting
+
+this equation-- sorry.
+
+One equation that
+governs the evolution
+
+of the full probability
+as a function of time.
+
+Right?
+
+So basically, I can start
+with a an initial probability
+
+and see how this probability
+evolves as a function of time.
+
+And this is sometimes
+called a master equation.
+
+Sometimes, called a
+[INAUDIBLE] equation.
+
+And we did cover, in fact,
+this in-- next spring
+
+in the statistical
+physics and biology,
+
+we spent some time talking
+about these things.
+
+So you can come back to the
+third version of this class.
+
+And one can ensure that,
+with appropriate choice
+
+of the noise, the asymptotic
+solution for this probability
+
+distribution is
+whatever Landau-Ginzburg
+
+or other probability
+distribution
+
+that you need most.
+
+AUDIENCE: So is this
+true if we assume
+
+Landau-Ginzburg potential
+for how resistant?
+
+MEHRAN KARDAR: Yes.
+
+AUDIENCE: OK.
+
+Maybe this is not a very
+good-stated question,
+
+but is there kind of like
+an even more general level?
+
+MEHRAN KARDAR: I'll
+come to that, sure.
+
+But currently, the way
+that I set up the problem
+
+was that we know some
+complicated equilibrium
+
+force that exist-- form of
+the probability that exist.
+
+And these kinds of
+linear-- these kinds
+
+of stochastic linear
+or non-linear evolution
+
+equations-- generally
+called non- [INAUDIBLE]
+
+equations-- one can show that,
+with the appropriate choice
+
+of the noise, we'll be able
+to asymptotically reproduce
+
+the probability of
+distribution that we knew.
+
+But now, the question
+is, of course, you
+
+don't know the probability
+of distribution.
+
+And I'll say a few
+words about that.
+
+AUDIENCE: OK.
+
+Thank you.
+
+MEHRAN KARDAR: Anything else?
+
+OK.
+
+So the lesson of this
+part is that the field
+
+of dynamic or critical phenomena
+is quite rich, much richer
+
+than the corresponding
+equilibrium critical phenomena
+
+because the same
+equilibrium state can
+
+be obtained by various
+different types of dynamics.
+
+And I explained to you
+just one conservation law,
+
+but there could be
+some combination
+
+of conservation of energy,
+conservation of something.
+
+So there is a whole listing of
+different universality classes
+
+that people have targeted
+for the dynamics.
+
+But not all of this
+was assuming that you
+
+know what the ultimate answer
+is because, in all cases,
+
+the equations that
+we're writing are
+
+dependent on some kind of a
+gradient descent conserved
+
+or non-conserved around
+something that corresponded
+
+to the log of probability
+of distribution
+
+that we eventually want to put.
+
+And maybe you don't
+know that, and so
+
+let me give you a particular
+example in the context of,
+
+let's say, surface
+interface fluctuations.
+
+Starting from things that
+you know and then building
+
+to something that
+maybe you don't.
+
+Let's first with the
+case of a soap bubble.
+
+So we take some kind of
+a circle or whatever,
+
+and we put a soap
+bubble on top of it.
+
+And in this case, the
+energy of the formation--
+
+the cost of the formation
+comes from surface tension.
+
+And let's say, the
+cost of the deformation
+
+is the changing area
+times some sigma.
+
+So I neglect the
+contribution that
+
+comes from the flat surface,
+and see if I make a deformation.
+
+If I make a deformation, I have
+changed the area of the spin.
+
+So there is a cost that is
+proportion to the surface
+
+tension times the
+change in area.
+
+Change in area locally
+is the square root of 1
+
+plus the gradient
+of a height profile.
+
+So what I can do is I can define
+at each point on the surface
+
+how much it has changed its
+height from being perfectly
+
+flat.
+
+So h equals to 0 is flat.
+
+Local area is the integral
+dx dy of square root of 1
+
+plus gradient of h
+squared, minus 1.
+
+That corresponds to the flat.
+
+And so then you expand that.
+
+The first term is going to
+be the integral gradient of h
+
+squared.
+
+So this is the analog of
+what we had over there, only
+
+the first term.
+
+So you would say that the
+equation that you would write
+
+down for this would be
+all to some constant mu
+
+proportional to the
+variations of this,
+
+which will give me something
+like sigma Laplacian of h.
+
+But because of the particles
+from the air constantly
+
+bombarding the
+surface, there will
+
+be some noise that
+depends on where
+
+you are on the surface in time.
+
+And this is the
+non-conserved version.
+
+And you can from
+this very quickly get
+
+that the expectation value
+of h tilde of q squared
+
+is going to be proportional
+to something like D
+
+over mu sigma q squared,
+because of this q squared.
+
+And if you ask how
+much fluctuations you
+
+have in real space--
+so that typical scale
+
+of the fluctuations
+in real space--
+
+will come from integrating
+1 over q squared.
+
+And it's going to be
+our usual things that
+
+have this logarithmic
+dependence, so there will
+
+be something that ultimately
+will go logarithmically
+
+with the size of the system.
+
+The constant of
+proportionality will be
+
+proportional to kt over sigma.
+
+So you have to choose your D
+and mu to correspond to this.
+
+But basically, a soap
+film, as an example
+
+of all kinds of Goldstone
+mode-like things
+
+that we have seen.
+
+It's a 2-dimensional entity.
+
+We will have logarithmic
+fluctuations-- not very big,
+
+but ultimately, at
+large enough distances,
+
+it will have fluctuations.
+
+So that was non-conserved.
+
+I can imagine that,
+rather than this,
+
+I have the case of
+a surface of a pool.
+
+So here I have some
+depth of water,
+
+and then there's the surface
+of the pool of water.
+
+And the difference between this
+case and the previous case--
+
+both of them can be described
+by a height function.
+
+The difference is that
+if I ignore evaporation
+
+and condensation, the
+total mass of water
+
+is going to be conserved.
+
+So I would need to have divided
+t of the integral dx d qx
+
+h of x and t to be 0.
+
+So this would go into
+the conserved variety.
+
+And while, if I create a
+ripple on the surface of this
+
+compared to the surface of
+that, the relaxation time
+
+through this
+dissipative dynamics
+
+would be much longer in this
+case as opposed to that case.
+
+Ultimately, if I wait
+sufficiently long time,
+
+both of them would have
+exactly the same fluctuations.
+
+That is, you would go
+logarithmically with the length
+
+scale over which [INAUDIBLE].
+
+OK, so now let's look at
+another system that fluctuates.
+
+And I don't know what
+the final answer is.
+
+That was the question,
+maybe, that you asked.
+
+The example that I will
+give is the following--
+
+so suppose that
+you have a surface.
+
+And then you have a
+rain of sticky materials
+
+that falls down on top of it.
+
+So this material will come down.
+
+You'll have something like this.
+
+And then as time
+goes on, there will
+
+be more material that will come,
+more material that will come,
+
+more material that will come.
+
+So there, because the particles
+are raining down randomly
+
+at different points, there
+will be a stochastic process
+
+that is going on.
+
+So you can try to
+characterize the system
+
+in terms of a height that
+changes as a function of t
+
+and as a function of position.
+
+And there could be all kinds
+of microscopic things going on,
+
+like maybe these
+are particles that
+
+are representing some kind
+of a deposition process.
+
+And then they come, they
+stick in a particular way.
+
+Maybe they can slide
+on the surface.
+
+We can imagine all kinds of
+microscopic degrees of freedom
+
+and things that we can put.
+
+But you say, well, can
+I change my perspective,
+
+and try to describe the
+system the same way that we
+
+did for the case of
+coarse grading and going
+
+from without the
+microscopic details
+
+to describe the phenomenological
+Landau-Ginzburg equation?
+
+And so you say, OK, there
+is a height that is growing.
+
+And what I will write
+down is an equation
+
+that is very similar
+to the equations
+
+that I had written before.
+
+Now I'm going to follow
+the same kind of reasoning
+
+that we did in the construction
+of this Landau-Ginzburg model,
+
+is we said that this weight
+is going to depend on all
+
+kinds of things that
+relate to this height
+
+that I don't quite know.
+
+So let's imagine that there
+is some kind of a function
+
+of the height itself.
+
+And potentially, just
+like we did over there,
+
+the gradient of the height,
+five derivatives of the height,
+
+et cetera.
+
+And then I will start to
+make an expansion of this
+
+in the same spirit that I did
+for the Landau-Ginzburg Model,
+
+except that when I was doing
+the Landau-Ginzburg Model,
+
+I was doing the expansion
+at the level of looking
+
+at the probability distribution
+and the log of the probability.
+
+Here I'm making the expansion
+at the level of an equation that
+
+governs the dynamics.
+
+Of course, in this
+particular system,
+
+that's not the end of story,
+because the change in height
+
+is also governed by this random
+addition of the particles.
+
+So there is some
+function that changes
+
+as a function of
+position and time,
+
+depending on whether,
+at that time,
+
+a particle was dropped down.
+
+I can always take
+the average of this
+
+to be 0, and put that average
+into the expansion of this
+
+starting from a constant.
+
+Basically, if I just
+have a single point
+
+and I randomly drop particles
+at that single point,
+
+there will be an
+average growth velocity,
+
+an average addition
+to the height,
+
+that averages over here.
+
+But there will be fluctuations
+that are going [INAUDIBLE].
+
+OK but the constant
+is the first term
+
+in an expansion such as this.
+
+And you can start thinking,
+OK, what next order?
+
+Can I put something
+like alpha h?
+
+Potentially-- depends
+on your system--
+
+but if the system is invariant
+whether you started from here
+
+or whether you started from
+there-- something like gravity,
+
+for example, is not
+important-- you say, OK,
+
+I cannot have any function of
+h if my dynamics will proceed
+
+exactly the same way if I
+were to translate this surface
+
+to some further up
+or further down.
+
+If I see that there's no change
+in future dynamics on average,
+
+then the dynamic
+cannot depend on this.
+
+OK, so we've got rid of that.
+
+And any function
+of h-- can I put
+
+something that is
+proportional to gradient of h?
+
+Maybe for something I can,
+but for h itself I cannot,
+
+because h is a scalar gradient.
+
+If h is a vector, I
+can't set something
+
+that is a scalar equal to a
+vector, so I can't have this.
+
+Yes?
+
+AUDIENCE: Couldn't
+you, in principle,
+
+make your constant term in
+front of the gradient also
+
+a vector and [INAUDIBLE]?
+
+MEHRAN KARDAR: You could.
+
+So there's a whole set
+of different systems
+
+that you can be thinking about.
+
+Right now, I want to focus
+on the simplest system, which
+
+is a scalar field, so
+that my equation can
+
+be as simple as
+possible, but still we
+
+will see it has
+sufficient complication.
+
+So you can see that
+if I don't have them,
+
+the next order term
+that I can have
+
+would be something
+like a Laplacian.
+
+So this kind of diffusion
+equation, you can see,
+
+has to emerge as a low-order
+expansion of something
+
+like this.
+
+And this is the ubiquity of the
+diffusion equation appearing
+
+all over the place.
+
+And then you could
+have terms that
+
+would be of the order of
+the fourth derivative,
+
+and so forth.
+
+There's nothing wrong with that.
+
+And then, if you
+think about it, you'll
+
+see that there is one
+interesting possibility that
+
+is not allowed for
+that system, but is
+
+allowed for this system, which
+is something that is a scalar.
+
+It's the gradient of h squared.
+
+Now I could not have added this
+term for the case of the soap
+
+bubble for the
+following reason--
+
+that if I reverse the
+soap bubble so that h
+
+becomes minus h, the dynamics
+would proceed exactly
+
+as before.
+
+So the soap bubble has a
+symmetry of h going to minus h,
+
+and so that symmetry should
+be preserved in the equation.
+
+This term breaks that symmetry
+because the left-hand side
+
+is odd in h, whereas the
+right-hand side of this term
+
+would be even in h.
+
+But for the case of the growing
+surface-- and you've seen
+
+things that are growing.
+
+And typically, if I
+give you something
+
+that has grown like the
+tree trunk, for example,
+
+and if I take the
+picture of a part of it,
+
+and you don't see where the
+center is, where the end is,
+
+you can immediately
+tell from the way
+
+that the shape of this
+object is, that it is growing
+
+in some particular direction.
+
+So for growth systems, that
+symmetry does not exist.
+
+You are allowed to have
+this term, and so forth.
+
+Now the interesting
+thing about this term
+
+is that there is no beta
+h that you can write down
+
+that is local-- some
+function of h such
+
+that if you take a functional
+derivative with respect to h,
+
+it will reproduce that
+term-- just does not exist.
+
+So you can see that
+somehow immediately,
+
+as soon as we liberate ourselves
+from writing equations that
+
+came from functional
+derivative of something,
+
+but potentially have
+physical significance,
+
+we can write down new terms.
+
+So this is actually--
+also, you can do
+
+this, even for two particles.
+
+A potential v of x1 and x2 will
+have some kind of derivatives.
+
+But if you write
+dynamical equations,
+
+there are dynamical
+equations that
+
+allow you to rotate
+1 x from x1 to x2.
+
+That kind of term
+will never come
+
+from taking the derivative.
+
+So fine.
+
+So this is a candidate
+equation that
+
+is obtained in this context--
+something that is grown.
+
+We say we are not
+interested in it's
+
+coming from some
+underlying weight,
+
+but presumably,
+this system still,
+
+if I look at it at
+long times, will
+
+have some kind of fluctuations.
+
+All the fluctuations of
+this growing surface,
+
+like the fluctuations
+of the soap bubble,
+
+and they have this
+logarithmic dependence.
+
+You have a question?
+
+AUDIENCE: So why doesn't that
+term-- what if I put in h times
+
+that term that we want
+to appear and then I
+
+vary with respect to h?
+
+A term like what we want to pop
+out together with other terms?
+
+MEHRAN KARDAR: Yeah,
+but those other terms,
+
+what do you want
+to do with them?
+
+AUDIENCE: Well, maybe they're
+not acceptable [INAUDIBLE]?
+
+MEHRAN KARDAR: So you're
+saying why not have a term that
+
+is h gradient of h squared?
+
+Functional derivative of that
+is gradient of h squared.
+
+And then you have a term
+that is h Laplacian-- it's
+
+a gradient of,
+sorry, gradient of h.
+
+And then you expand this.
+
+Among the terms that
+you would generate
+
+would be a term that
+is h, a Laplacian of h.
+
+This term violates
+this condition
+
+that we had over here.
+
+And you cannot separate
+this term from that term.
+
+So what you
+describe, you already
+
+see at the level over here.
+
+It violates translation of
+symmetry in [? nature ?].
+
+And you can play around
+with other functions.
+
+You come to the same conclusion.
+
+OK, so the question is, well,
+you added some term here.
+
+If I look at this surface
+that has grown at large time,
+
+does it have the same
+fluctuations as we had before?
+
+So a simple way
+to ascertain that
+
+is to do the same kind
+of dimensional analysis
+
+which, for the Landau-Ginzburg,
+was a prelude to doing
+
+renormalization.
+
+So we did things like
+epsilon expansion, et cetera.
+
+But to calculate that there
+was a critical dimension of 4,
+
+all we needed to do
+was to rescale x and m,
+
+and we would
+immediately see that mu
+
+goes to mu, b to the 4
+minus D or something--
+
+D minus 4, for example.
+
+So we can do the
+same thing here.
+
+We can always move
+to a frame that
+
+is moving with the
+average velocity,
+
+so that we are focusing
+on the fluctuations.
+
+So we can basically
+ignore this term.
+
+I'm going to rescale
+x by a factor of b.
+
+I'm going to rescale time by
+a factor of b to something
+
+to the z.
+
+And this z is kind
+of indicative of what
+
+we've seen before-- that somehow
+in these dynamical phenomena,
+
+the scaling of time and space
+are related to some exponent.
+
+But there's also
+an exponent that
+
+characterizes how
+the fluctuations in h
+
+grow if I look at systems
+that are larger and larger.
+
+In particular, if I had
+solved that equation,
+
+rather than for a soap
+bubble in two dimensions,
+
+for a line-- for a string that
+I was pulling so that I had
+
+line tension-- the
+one-dimensional version of it,
+
+the one-dimensional version of
+an integral of 1 over q squared
+
+would be something
+that would grow
+
+with the size of the system.
+
+So there I would have a
+chi of 1/2, for example,
+
+in one dimension.
+
+So this is the general thing.
+
+And then I would say that
+the first equation, dhy dt,
+
+gets a factor of
+b to the chi minus
+
+z, because h scaled
+by a factor of chi,
+
+t scaled by a factor of z,
+the term sigma Laplacian of h
+
+gets a factor of b
+to the chi minus 2
+
+from the two derivatives here--
+sorry, the z and the 2 look
+
+kind of the same.
+
+This is a z.
+
+This is a 2.
+
+And then the term
+that is proportional
+
+to this non-linearity that
+I wrote down-- actually, it
+
+is very easy, maybe worthwhile,
+to show that sigma to the 4th
+
+goes with a factor of
+b to the chi minus 4.
+
+It is always down by a factor of
+two scalings in b with respect
+
+to a Laplacian-- the
+same reason that when
+
+we were doing the
+Landau-Ginzburg.
+
+We could terminate the series
+at order of gradient squared,
+
+because higher-order
+derivatives were irrelevant.
+
+They were scaling to 0.
+
+But this term grows
+like b to the 2 chi,
+
+because it's h squared, minus 2,
+because there's two gradients.
+
+Now thinking about
+the scaling of eta
+
+takes a little bit of thought,
+because what we have-- we
+
+said that the average
+of eta goes to 0.
+
+The average of eta at
+two different locations
+
+and two different times--
+it is these particles that
+
+are raining down--
+they're uncorrelated
+
+at different times.
+
+They're uncorrelated
+at different positions.
+
+There's some kind
+of variance here,
+
+but that's not important to us.
+
+If I rescale t by a factor
+of b, delta of bt-- sorry,
+
+if I scale t by a factor of b
+to the z, delta of b to the zx
+
+will get a factor
+of b to the minus z.
+
+This will get a factor
+of b to the minus d.
+
+But the noise, eta,
+is half of that.
+
+So what I will have is b to
+the minus z plus d over 2 times
+
+eta on the rescalings
+that I have indicated.
+
+I get rid of this term.
+
+So this-- divide by
+b to the chi minus z.
+
+So then this becomes bh y dt
+is sigma b to the z minus 2.
+
+Maybe I'll write it in
+red-- b to the z minus 2.
+
+This becomes sigma to the
+4, b to the z minus 4.
+
+And then lambda over 2.
+
+This is Laplacian of h.
+
+This, for derivative of
+h, this is Laplacian of h.
+
+This term becomes b to the chi
+plus z minus 2, gradient of h
+
+squared.
+
+And the final term becomes b to
+the chi minus d minus z over 2.
+
+AUDIENCE: [INAUDIBLE]?
+
+MEHRAN KARDAR: b to the
+minus chi-- you're right.
+
+And then, actually, this I-- no?
+
+Minus chi minus d over 2
+minus d over 2 [INAUDIBLE],
+
+That's fine.
+
+So I can make this
+equation to be invariant.
+
+So I want to find
+out what happens
+
+to this system if I find
+some kind of an equation,
+
+or some kind of behavior
+that is scale invariant.
+
+You can see that immediately,
+my choice for the first term
+
+has to be z equals to 2.
+
+So basically, it
+says that as long
+
+as you're governed by
+something that is diffusive,
+
+so that when you go to Fourier
+space, you have q squared,
+
+your relaxation times
+are going to have
+
+this diffusive character,
+where time is distance squared.
+
+Actually, you can see that
+immediately from the equation
+
+that this diffusion time
+goes like distance squared.
+
+So this is just a
+statement of that.
+
+Now, it is the noise that
+causes the fluctuations.
+
+And if I haven't made
+some simple error,
+
+you will find that the
+coefficient of the noise term
+
+becomes scale invariant,
+provided that I choose it
+
+to be z minus d over 2 for chi.
+
+And since my z was
+2, I'm forced to have
+
+chi to be 2 minus d over 2.
+
+And let's see if it
+makes sense to us.
+
+So if I have a surface such
+as the case of the soap bubble
+
+in two dimensions, chi is 0.
+
+And 0 is actually
+this limiting case
+
+that would also be a logarithm.
+
+If I go to the case of d equals
+to 1-- like pulling a line
+
+and having the line fluctuate--
+then I have 2 minus 1
+
+over 2, which is
+1/2, which means
+
+that, because of
+thermal fluctuations,
+
+this line will look
+like it a random walk.
+
+You go a distance x.
+
+The fluctuations
+in height will go
+
+like the square root of that.
+
+OK?
+
+So all of that is fine.
+
+You would have done
+exactly the same answer
+
+if you had just gotten a
+kind of scaling such as this
+
+for the case of
+the Gaussian Model
+
+without the nonlinearities.
+
+But for the Gaussian
+Model with nonlinearities,
+
+we could also then estimate
+whether the nonlinearity u
+
+is relevant.
+
+So here we see that the
+coefficient of our nonlinearity
+
+is lambda, is
+governed by something
+
+that is chi plus z minus 2.
+
+And our chi is 2 minus z over 2.
+
+z minus 2 is 0.
+
+So whether or not this
+nonlinearity is relevant,
+
+we can see depends
+on whether you're
+
+above or below two dimensions.
+
+So when you are
+below two dimensions,
+
+this nonlinearity is relevant.
+
+And you will certainly
+have different types
+
+of scaling phenomena
+then what you
+
+predict by the case of the
+diffusion equation plus noise.
+
+Of course, the
+interesting case is
+
+when you are at the
+marginal dimension of 2.
+
+Now, in terms of when you do
+proper renormalization group
+
+with this nonlinearity,
+you will find that,
+
+unlike the nonlinearity of
+the Landau-Ginzburg, which
+
+is marginally irrelevant
+in four dimensions.
+
+du by dl was minus u
+squared, this lambda
+
+is marginally relevant.
+
+d lambda by dl is proportional
+to plus lambda squared.
+
+It is relevant marginality--
+marginally relevant.
+
+And actually, the
+epsilon expansion
+
+gives you no information about
+what's happening in the system.
+
+So people have then done
+numerical simulations.
+
+And they find that there
+is a roughness that
+
+is characterized by an exponent,
+say something like 0.4.
+
+So that when you look at
+some surface that is grown,
+
+is much, much rougher than
+the surface of a soap bubble
+
+or what's happening on
+the surface of the pond.
+
+And the key to all of this is
+that we wrote down equations
+
+on the basis of
+this generalization
+
+on symmetry that we had
+learned, now applied
+
+to this dynamical
+system, did an expansion,
+
+found one first term.
+
+And we found it to be relevant.
+
+And is actually not
+that often that you
+
+find something that is
+relevant, because then it
+
+is a reason to celebrate.
+
+Because most of the time,
+things are irrelevant,
+
+and you end up with boring
+diffusion equations.
+
+So find something
+that is relevant.
+
+And that's my last
+message to you.
\ No newline at end of file
diff --git a/Q-nk311H-Fw.txt b/Q-nk311H-Fw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e3ee3dc9f3602c04c78ba66b925606d747d4141c
--- /dev/null
+++ b/Q-nk311H-Fw.txt
@@ -0,0 +1,1291 @@
+align:start position:0%
+ 
+visualization is a crucial step for
+
+ align:start position:0%
+visualization is a crucial step for
+ 
+
+ align:start position:0%
+visualization is a crucial step for
+initial data exploration
+
+ align:start position:0%
+initial data exploration
+ 
+
+ align:start position:0%
+initial data exploration
+it helps us discern relationships
+
+ align:start position:0%
+it helps us discern relationships
+ 
+
+ align:start position:0%
+it helps us discern relationships
+patterns and outliers this video will
+
+ align:start position:0%
+patterns and outliers this video will
+ 
+
+ align:start position:0%
+patterns and outliers this video will
+give us a starting point on how to make
+
+ align:start position:0%
+give us a starting point on how to make
+ 
+
+ align:start position:0%
+give us a starting point on how to make
+plots on our but more advanced and way
+
+ align:start position:0%
+plots on our but more advanced and way
+ 
+
+ align:start position:0%
+plots on our but more advanced and way
+cooler visualization tips will be given
+
+ align:start position:0%
+cooler visualization tips will be given
+ 
+
+ align:start position:0%
+cooler visualization tips will be given
+in week eight of this class let us first
+
+ align:start position:0%
+in week eight of this class let us first
+ 
+
+ align:start position:0%
+in week eight of this class let us first
+create a scatter plot with protein on
+
+ align:start position:0%
+create a scatter plot with protein on
+ 
+
+ align:start position:0%
+create a scatter plot with protein on
+the x-axis and fat on the y-axis to do
+
+ align:start position:0%
+the x-axis and fat on the y-axis to do
+ 
+
+ align:start position:0%
+the x-axis and fat on the y-axis to do
+this we can use the plot function in R
+
+ align:start position:0%
+this we can use the plot function in R
+ 
+
+ align:start position:0%
+this we can use the plot function in R
+and give it as a first input the protein
+
+ align:start position:0%
+and give it as a first input the protein
+ 
+
+ align:start position:0%
+and give it as a first input the protein
+factor on the x-axis and as a second
+
+ align:start position:0%
+factor on the x-axis and as a second
+ 
+
+ align:start position:0%
+factor on the x-axis and as a second
+input the total fat vector on the y-axis
+
+ align:start position:0%
+input the total fat vector on the y-axis
+ 
+
+ align:start position:0%
+input the total fat vector on the y-axis
+and now pressing enter in new window
+
+ align:start position:0%
+and now pressing enter in new window
+ 
+
+ align:start position:0%
+and now pressing enter in new window
+pops up if you are on a PC the new
+
+ align:start position:0%
+pops up if you are on a PC the new
+ 
+
+ align:start position:0%
+pops up if you are on a PC the new
+window is called our graphics and if you
+
+ align:start position:0%
+window is called our graphics and if you
+ 
+
+ align:start position:0%
+window is called our graphics and if you
+are on a Mac it is called quartz the
+
+ align:start position:0%
+are on a Mac it is called quartz the
+ 
+
+ align:start position:0%
+are on a Mac it is called quartz the
+plot has a very interesting triangular
+
+ align:start position:0%
+plot has a very interesting triangular
+ 
+
+ align:start position:0%
+plot has a very interesting triangular
+shape it looks like foods that are
+
+ align:start position:0%
+shape it looks like foods that are
+ 
+
+ align:start position:0%
+shape it looks like foods that are
+higher in protein are typically lower in
+
+ align:start position:0%
+higher in protein are typically lower in
+ 
+
+ align:start position:0%
+higher in protein are typically lower in
+fat and vice versa now looking at the
+
+ align:start position:0%
+fat and vice versa now looking at the
+ 
+
+ align:start position:0%
+fat and vice versa now looking at the
+aesthetics of the graph we realize the
+
+ align:start position:0%
+aesthetics of the graph we realize the
+ 
+
+ align:start position:0%
+aesthetics of the graph we realize the
+argives default names for the x axis and
+
+ align:start position:0%
+argives default names for the x axis and
+ 
+
+ align:start position:0%
+argives default names for the x axis and
+the y axis using the vector dollar
+
+ align:start position:0%
+the y axis using the vector dollar
+ 
+
+ align:start position:0%
+the y axis using the vector dollar
+notation we can modify these labels by
+
+ align:start position:0%
+notation we can modify these labels by
+ 
+
+ align:start position:0%
+notation we can modify these labels by
+adding more arguments to the plot
+
+ align:start position:0%
+adding more arguments to the plot
+ 
+
+ align:start position:0%
+adding more arguments to the plot
+function to go back to the our console
+
+ align:start position:0%
+function to go back to the our console
+ 
+
+ align:start position:0%
+function to go back to the our console
+you can simply switch windows using the
+
+ align:start position:0%
+you can simply switch windows using the
+ 
+
+ align:start position:0%
+you can simply switch windows using the
+ctrl tab if you are on a Windows machine
+
+ align:start position:0%
+ctrl tab if you are on a Windows machine
+ 
+
+ align:start position:0%
+ctrl tab if you are on a Windows machine
+on a Mac the windows are not overlaid by
+
+ align:start position:0%
+on a Mac the windows are not overlaid by
+ 
+
+ align:start position:0%
+on a Mac the windows are not overlaid by
+default so accessing the console should
+
+ align:start position:0%
+default so accessing the console should
+ 
+
+ align:start position:0%
+default so accessing the console should
+be easy ok now let's use the up arrow to
+
+ align:start position:0%
+be easy ok now let's use the up arrow to
+ 
+
+ align:start position:0%
+be easy ok now let's use the up arrow to
+go back to our plot function and at the
+
+ align:start position:0%
+go back to our plot function and at the
+ 
+
+ align:start position:0%
+go back to our plot function and at the
+argument X lab equal protein and that
+
+ align:start position:0%
+argument X lab equal protein and that
+ 
+
+ align:start position:0%
+argument X lab equal protein and that
+gives us the label of the x axis then y
+
+ align:start position:0%
+gives us the label of the x axis then y
+ 
+
+ align:start position:0%
+gives us the label of the x axis then y
+iLab equals fat and this gives us the
+
+ align:start position:0%
+iLab equals fat and this gives us the
+ 
+
+ align:start position:0%
+iLab equals fat and this gives us the
+label to the y axis and let's add a
+
+ align:start position:0%
+label to the y axis and let's add a
+ 
+
+ align:start position:0%
+label to the y axis and let's add a
+title to the plot using the argument
+
+ align:start position:0%
+title to the plot using the argument
+ 
+
+ align:start position:0%
+title to the plot using the argument
+main say the title is protein versus fat
+
+ align:start position:0%
+main say the title is protein versus fat
+ 
+
+ align:start position:0%
+main say the title is protein versus fat
+and let's change the color to red and
+
+ align:start position:0%
+and let's change the color to red and
+ 
+
+ align:start position:0%
+and let's change the color to red and
+remember to put quotation marks around
+
+ align:start position:0%
+remember to put quotation marks around
+ 
+
+ align:start position:0%
+remember to put quotation marks around
+the values of all these arguments and
+
+ align:start position:0%
+the values of all these arguments and
+ 
+
+ align:start position:0%
+the values of all these arguments and
+now pressing enter going back to the
+
+ align:start position:0%
+now pressing enter going back to the
+ 
+
+ align:start position:0%
+now pressing enter going back to the
+graphics window we see that our made all
+
+ align:start position:0%
+graphics window we see that our made all
+ 
+
+ align:start position:0%
+graphics window we see that our made all
+the modifications we requested another
+
+ align:start position:0%
+the modifications we requested another
+ 
+
+ align:start position:0%
+the modifications we requested another
+way we can visualize our data is by
+
+ align:start position:0%
+way we can visualize our data is by
+ 
+
+ align:start position:0%
+way we can visualize our data is by
+plotting histogram
+
+ align:start position:0%
+plotting histogram
+ 
+
+ align:start position:0%
+plotting histogram
+we can do this using the histogram
+
+ align:start position:0%
+we can do this using the histogram
+ 
+
+ align:start position:0%
+we can do this using the histogram
+function in our but note that this
+
+ align:start position:0%
+function in our but note that this
+ 
+
+ align:start position:0%
+function in our but note that this
+function now only takes one variable as
+
+ align:start position:0%
+function now only takes one variable as
+ 
+
+ align:start position:0%
+function now only takes one variable as
+an input because the y-axis should have
+
+ align:start position:0%
+an input because the y-axis should have
+ 
+
+ align:start position:0%
+an input because the y-axis should have
+the frequencies so let's go back to our
+
+ align:start position:0%
+the frequencies so let's go back to our
+ 
+
+ align:start position:0%
+the frequencies so let's go back to our
+console and create a histogram of
+
+ align:start position:0%
+console and create a histogram of
+ 
+
+ align:start position:0%
+console and create a histogram of
+vitamin C for instance so we're gonna
+
+ align:start position:0%
+vitamin C for instance so we're gonna
+ 
+
+ align:start position:0%
+vitamin C for instance so we're gonna
+use the piston or histogram and then the
+
+ align:start position:0%
+use the piston or histogram and then the
+ 
+
+ align:start position:0%
+use the piston or histogram and then the
+argument that it takes is the vitamin C
+
+ align:start position:0%
+argument that it takes is the vitamin C
+ 
+
+ align:start position:0%
+argument that it takes is the vitamin C
+vector let's label the x-axis as vitamin
+
+ align:start position:0%
+vector let's label the x-axis as vitamin
+ 
+
+ align:start position:0%
+vector let's label the x-axis as vitamin
+C and this is given to us in milligrams
+
+ align:start position:0%
+C and this is given to us in milligrams
+ 
+
+ align:start position:0%
+C and this is given to us in milligrams
+and give it a title say histogram of
+
+ align:start position:0%
+and give it a title say histogram of
+ 
+
+ align:start position:0%
+and give it a title say histogram of
+vitamin C levels hmm even though the
+
+ align:start position:0%
+vitamin C levels hmm even though the
+ 
+
+ align:start position:0%
+vitamin C levels hmm even though the
+maximum vitamin C content is 2,000
+
+ align:start position:0%
+maximum vitamin C content is 2,000
+ 
+
+ align:start position:0%
+maximum vitamin C content is 2,000
+milligrams most of our foods well to be
+
+ align:start position:0%
+milligrams most of our foods well to be
+ 
+
+ align:start position:0%
+milligrams most of our foods well to be
+more precise more than 6,000 of them
+
+ align:start position:0%
+more precise more than 6,000 of them
+ 
+
+ align:start position:0%
+more precise more than 6,000 of them
+have less than 200 milligrams of vitamin
+
+ align:start position:0%
+have less than 200 milligrams of vitamin
+ 
+
+ align:start position:0%
+have less than 200 milligrams of vitamin
+C and the histogram lumps them all
+
+ align:start position:0%
+C and the histogram lumps them all
+ 
+
+ align:start position:0%
+C and the histogram lumps them all
+together in one cell well it would be
+
+ align:start position:0%
+together in one cell well it would be
+ 
+
+ align:start position:0%
+together in one cell well it would be
+nice if we can zoom into this section
+
+ align:start position:0%
+nice if we can zoom into this section
+ 
+
+ align:start position:0%
+nice if we can zoom into this section
+here and get a finer understanding of
+
+ align:start position:0%
+here and get a finer understanding of
+ 
+
+ align:start position:0%
+here and get a finer understanding of
+the data to do this we need to limit the
+
+ align:start position:0%
+the data to do this we need to limit the
+ 
+
+ align:start position:0%
+the data to do this we need to limit the
+x-axis to go from zero to say 100
+
+ align:start position:0%
+x-axis to go from zero to say 100
+ 
+
+ align:start position:0%
+x-axis to go from zero to say 100
+milligrams so let's go back to the
+
+ align:start position:0%
+milligrams so let's go back to the
+ 
+
+ align:start position:0%
+milligrams so let's go back to the
+console and then we're going to add the
+
+ align:start position:0%
+console and then we're going to add the
+ 
+
+ align:start position:0%
+console and then we're going to add the
+argument x lim to limit the x-axis and
+
+ align:start position:0%
+argument x lim to limit the x-axis and
+ 
+
+ align:start position:0%
+argument x lim to limit the x-axis and
+using the combine function or the c
+
+ align:start position:0%
+using the combine function or the c
+ 
+
+ align:start position:0%
+using the combine function or the c
+function we're gonna set the first input
+
+ align:start position:0%
+function we're gonna set the first input
+ 
+
+ align:start position:0%
+function we're gonna set the first input
+to be zero which is the lowest value
+
+ align:start position:0%
+to be zero which is the lowest value
+ 
+
+ align:start position:0%
+to be zero which is the lowest value
+that we want to see on the x-axis and
+
+ align:start position:0%
+that we want to see on the x-axis and
+ 
+
+ align:start position:0%
+that we want to see on the x-axis and
+the second argument is being 100 which
+
+ align:start position:0%
+the second argument is being 100 which
+ 
+
+ align:start position:0%
+the second argument is being 100 which
+is the highest value that we want to see
+
+ align:start position:0%
+is the highest value that we want to see
+ 
+
+ align:start position:0%
+is the highest value that we want to see
+on the x axis and now pressing enter and
+
+ align:start position:0%
+on the x axis and now pressing enter and
+ 
+
+ align:start position:0%
+on the x axis and now pressing enter and
+we can see that our gives us 0 to 100 on
+
+ align:start position:0%
+we can see that our gives us 0 to 100 on
+ 
+
+ align:start position:0%
+we can see that our gives us 0 to 100 on
+the x axis but we only see this one big
+
+ align:start position:0%
+the x axis but we only see this one big
+ 
+
+ align:start position:0%
+the x axis but we only see this one big
+cell it's used that are only zoomed into
+
+ align:start position:0%
+cell it's used that are only zoomed into
+ 
+
+ align:start position:0%
+cell it's used that are only zoomed into
+the area but it didn't break that huge
+
+ align:start position:0%
+the area but it didn't break that huge
+ 
+
+ align:start position:0%
+the area but it didn't break that huge
+cell and this doesn't give us any
+
+ align:start position:0%
+cell and this doesn't give us any
+ 
+
+ align:start position:0%
+cell and this doesn't give us any
+additional information so we really need
+
+ align:start position:0%
+additional information so we really need
+ 
+
+ align:start position:0%
+additional information so we really need
+to break up the cell into smaller pieces
+
+ align:start position:0%
+to break up the cell into smaller pieces
+ 
+
+ align:start position:0%
+to break up the cell into smaller pieces
+and say we want 100 cells and since the
+
+ align:start position:0%
+and say we want 100 cells and since the
+ 
+
+ align:start position:0%
+and say we want 100 cells and since the
+interval goes from 0 to 100 then we
+
+ align:start position:0%
+interval goes from 0 to 100 then we
+ 
+
+ align:start position:0%
+interval goes from 0 to 100 then we
+would expect our to create divisions
+
+ align:start position:0%
+would expect our to create divisions
+ 
+
+ align:start position:0%
+would expect our to create divisions
+that are 1 milligrams in length so let's
+
+ align:start position:0%
+that are 1 milligrams in length so let's
+ 
+
+ align:start position:0%
+that are 1 milligrams in length so let's
+do this let's go back to the console and
+
+ align:start position:0%
+do this let's go back to the console and
+ 
+
+ align:start position:0%
+do this let's go back to the console and
+then we're going to add the argument
+
+ align:start position:0%
+then we're going to add the argument
+ 
+
+ align:start position:0%
+then we're going to add the argument
+rakes equals 100 and this sets the
+
+ align:start position:0%
+rakes equals 100 and this sets the
+ 
+
+ align:start position:0%
+rakes equals 100 and this sets the
+number of cells that we want to see to
+
+ align:start position:0%
+number of cells that we want to see to
+ 
+
+ align:start position:0%
+number of cells that we want to see to
+100 so let's see oh we actually only see
+
+ align:start position:0%
+100 so let's see oh we actually only see
+ 
+
+ align:start position:0%
+100 so let's see oh we actually only see
+5 cells and each cell is 20 milligrams
+
+ align:start position:0%
+5 cells and each cell is 20 milligrams
+ 
+
+ align:start position:0%
+5 cells and each cell is 20 milligrams
+long well what happened we were
+
+ align:start position:0%
+long well what happened we were
+ 
+
+ align:start position:0%
+long well what happened we were
+expecting 100 cells I'll remember that
+
+ align:start position:0%
+expecting 100 cells I'll remember that
+ 
+
+ align:start position:0%
+expecting 100 cells I'll remember that
+the histogram originally went far beyond
+
+ align:start position:0%
+the histogram originally went far beyond
+ 
+
+ align:start position:0%
+the histogram originally went far beyond
+100 milligrams the maximum was 2,000
+
+ align:start position:0%
+100 milligrams the maximum was 2,000
+ 
+
+ align:start position:0%
+100 milligrams the maximum was 2,000
+milligrams and now if we were to divide
+
+ align:start position:0%
+milligrams and now if we were to divide
+ 
+
+ align:start position:0%
+milligrams and now if we were to divide
+the original interval from zero to 2,000
+
+ align:start position:0%
+the original interval from zero to 2,000
+ 
+
+ align:start position:0%
+the original interval from zero to 2,000
+into 100 cells then 2,000 divided by 100
+
+ align:start position:0%
+into 100 cells then 2,000 divided by 100
+ 
+
+ align:start position:0%
+into 100 cells then 2,000 divided by 100
+each cell would be 20 milligrams long
+
+ align:start position:0%
+each cell would be 20 milligrams long
+ 
+
+ align:start position:0%
+each cell would be 20 milligrams long
+and this is exactly what our did it
+
+ align:start position:0%
+and this is exactly what our did it
+ 
+
+ align:start position:0%
+and this is exactly what our did it
+actually divided all the spectrum of
+
+ align:start position:0%
+actually divided all the spectrum of
+ 
+
+ align:start position:0%
+actually divided all the spectrum of
+values from 0 to 2000 into 100 cells and
+
+ align:start position:0%
+values from 0 to 2000 into 100 cells and
+ 
+
+ align:start position:0%
+values from 0 to 2000 into 100 cells and
+not only the spectrum from 0 to 100 but
+
+ align:start position:0%
+not only the spectrum from 0 to 100 but
+ 
+
+ align:start position:0%
+not only the spectrum from 0 to 100 but
+we still want to divide the interval 0
+
+ align:start position:0%
+we still want to divide the interval 0
+ 
+
+ align:start position:0%
+we still want to divide the interval 0
+to 100 into 100 cells each of length one
+
+ align:start position:0%
+to 100 into 100 cells each of length one
+ 
+
+ align:start position:0%
+to 100 into 100 cells each of length one
+milligram and how can we do this well we
+
+ align:start position:0%
+milligram and how can we do this well we
+ 
+
+ align:start position:0%
+milligram and how can we do this well we
+simply need to think in terms of the
+
+ align:start position:0%
+simply need to think in terms of the
+ 
+
+ align:start position:0%
+simply need to think in terms of the
+original interval which was 0 to 2000
+
+ align:start position:0%
+original interval which was 0 to 2000
+ 
+
+ align:start position:0%
+original interval which was 0 to 2000
+and if we were to break it into two
+
+ align:start position:0%
+and if we were to break it into two
+ 
+
+ align:start position:0%
+and if we were to break it into two
+thousand cells then each one will be of
+
+ align:start position:0%
+thousand cells then each one will be of
+ 
+
+ align:start position:0%
+thousand cells then each one will be of
+length 1 milligrams so now we know that
+
+ align:start position:0%
+length 1 milligrams so now we know that
+ 
+
+ align:start position:0%
+length 1 milligrams so now we know that
+actually we needed to set the brakes to
+
+ align:start position:0%
+actually we needed to set the brakes to
+ 
+
+ align:start position:0%
+actually we needed to set the brakes to
+2,000 so let's do this and now we obtain
+
+ align:start position:0%
+2,000 so let's do this and now we obtain
+ 
+
+ align:start position:0%
+2,000 so let's do this and now we obtain
+our refined histogram and we see new
+
+ align:start position:0%
+our refined histogram and we see new
+ 
+
+ align:start position:0%
+our refined histogram and we see new
+information here come up remember our
+
+ align:start position:0%
+information here come up remember our
+ 
+
+ align:start position:0%
+information here come up remember our
+initial conclusion was that more than
+
+ align:start position:0%
+initial conclusion was that more than
+ 
+
+ align:start position:0%
+initial conclusion was that more than
+6,000 foods have less than 200
+
+ align:start position:0%
+6,000 foods have less than 200
+ 
+
+ align:start position:0%
+6,000 foods have less than 200
+milligrams of vitamin C but now that we
+
+ align:start position:0%
+milligrams of vitamin C but now that we
+ 
+
+ align:start position:0%
+milligrams of vitamin C but now that we
+refined our graph we obtained an
+
+ align:start position:0%
+refined our graph we obtained an
+ 
+
+ align:start position:0%
+refined our graph we obtained an
+additional level of information actually
+
+ align:start position:0%
+additional level of information actually
+ 
+
+ align:start position:0%
+additional level of information actually
+more than 5000 of them have less than 1
+
+ align:start position:0%
+more than 5000 of them have less than 1
+ 
+
+ align:start position:0%
+more than 5000 of them have less than 1
+milligrams of vitamin C now a third way
+
+ align:start position:0%
+milligrams of vitamin C now a third way
+ 
+
+ align:start position:0%
+milligrams of vitamin C now a third way
+we can visualize the data is using box
+
+ align:start position:0%
+we can visualize the data is using box
+ 
+
+ align:start position:0%
+we can visualize the data is using box
+plots so let's go back to the console
+
+ align:start position:0%
+plots so let's go back to the console
+ 
+
+ align:start position:0%
+plots so let's go back to the console
+and create a box plot for sugar so the
+
+ align:start position:0%
+and create a box plot for sugar so the
+ 
+
+ align:start position:0%
+and create a box plot for sugar so the
+function we're going to be using is
+
+ align:start position:0%
+function we're going to be using is
+ 
+
+ align:start position:0%
+function we're going to be using is
+simply box plot and similarly to the
+
+ align:start position:0%
+simply box plot and similarly to the
+ 
+
+ align:start position:0%
+simply box plot and similarly to the
+histogram function the box plot function
+
+ align:start position:0%
+histogram function the box plot function
+ 
+
+ align:start position:0%
+histogram function the box plot function
+only takes as an input a single vector
+
+ align:start position:0%
+only takes as an input a single vector
+ 
+
+ align:start position:0%
+only takes as an input a single vector
+and in this case it would be the sugar
+
+ align:start position:0%
+and in this case it would be the sugar
+ 
+
+ align:start position:0%
+and in this case it would be the sugar
+vector and let's create a title that
+
+ align:start position:0%
+vector and let's create a title that
+ 
+
+ align:start position:0%
+vector and let's create a title that
+says box plot of sugar levels
+
+ align:start position:0%
+says box plot of sugar levels
+ 
+
+ align:start position:0%
+says box plot of sugar levels
+and is it the y-axis or the x-axis that
+
+ align:start position:0%
+and is it the y-axis or the x-axis that
+ 
+
+ align:start position:0%
+and is it the y-axis or the x-axis that
+we have to label it as you know the
+
+ align:start position:0%
+we have to label it as you know the
+ 
+
+ align:start position:0%
+we have to label it as you know the
+sugar level so if we're not so sure
+
+ align:start position:0%
+sugar level so if we're not so sure
+ 
+
+ align:start position:0%
+sugar level so if we're not so sure
+let's just plot it and oh this should be
+
+ align:start position:0%
+let's just plot it and oh this should be
+ 
+
+ align:start position:0%
+let's just plot it and oh this should be
+the y-axis so let's go back to the
+
+ align:start position:0%
+the y-axis so let's go back to the
+ 
+
+ align:start position:0%
+the y-axis so let's go back to the
+console and simply set the y label to be
+
+ align:start position:0%
+console and simply set the y label to be
+ 
+
+ align:start position:0%
+console and simply set the y label to be
+sugar in grams and now we have our box
+
+ align:start position:0%
+sugar in grams and now we have our box
+ 
+
+ align:start position:0%
+sugar in grams and now we have our box
+plot with the right labels what is it
+
+ align:start position:0%
+plot with the right labels what is it
+ 
+
+ align:start position:0%
+plot with the right labels what is it
+trying to tell us here it looks a little
+
+ align:start position:0%
+trying to tell us here it looks a little
+ 
+
+ align:start position:0%
+trying to tell us here it looks a little
+bit strange well the average of sugar
+
+ align:start position:0%
+bit strange well the average of sugar
+ 
+
+ align:start position:0%
+bit strange well the average of sugar
+across the data set seems to be pretty
+
+ align:start position:0%
+across the data set seems to be pretty
+ 
+
+ align:start position:0%
+across the data set seems to be pretty
+low it's somewhere around five grams but
+
+ align:start position:0%
+low it's somewhere around five grams but
+ 
+
+ align:start position:0%
+low it's somewhere around five grams but
+we have a lot of outliers with extremely
+
+ align:start position:0%
+we have a lot of outliers with extremely
+ 
+
+ align:start position:0%
+we have a lot of outliers with extremely
+high values of sugar there exist some
+
+ align:start position:0%
+high values of sugar there exist some
+ 
+
+ align:start position:0%
+high values of sugar there exist some
+foods that have almost 100 grams of
+
+ align:start position:0%
+foods that have almost 100 grams of
+ 
+
+ align:start position:0%
+foods that have almost 100 grams of
+sugar in 100 grams while candies are
+
+ align:start position:0%
+sugar in 100 grams while candies are
+ 
+
+ align:start position:0%
+sugar in 100 grams while candies are
+definitely among these foods so we just
+
+ align:start position:0%
+definitely among these foods so we just
+ 
+
+ align:start position:0%
+definitely among these foods so we just
+reviewed three ways in which we can
+
+ align:start position:0%
+reviewed three ways in which we can
+ 
+
+ align:start position:0%
+reviewed three ways in which we can
+visualize our data in week eight we will
+
+ align:start position:0%
+visualize our data in week eight we will
+ 
+
+ align:start position:0%
+visualize our data in week eight we will
+see more advanced visualization tools to
+
+ align:start position:0%
+see more advanced visualization tools to
+ 
+
+ align:start position:0%
+see more advanced visualization tools to
+make more informative plots in our next
+
+ align:start position:0%
+make more informative plots in our next
+ 
+
+ align:start position:0%
+make more informative plots in our next
+video we will see how we can construct
+
+ align:start position:0%
+video we will see how we can construct
+ 
+
+ align:start position:0%
+video we will see how we can construct
+and add new variables to our data set
\ No newline at end of file
diff --git a/QaY9AxkqifQ.txt b/QaY9AxkqifQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3b3ea6f1bce19c3c12eabfb13dff96ef6d42275b
--- /dev/null
+++ b/QaY9AxkqifQ.txt
@@ -0,0 +1,5615 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Today I want to
+make some remarks about
+
+William Barton Rogers.
+
+You were supposed to read an
+essay that I wrote about him,
+
+so I'm not going to go
+into great detail.
+
+I don't want to repeat what I've
+already written in the
+
+essay, but I thought I would hit
+had some high points and
+
+then end up talking a bit about
+this piece that Charles
+
+Eliot wrote called "The New
+Education," because I readily
+
+admit that that is not the
+easiest thing to read and
+
+surely not scintillating
+prose--
+
+you would not want to keep it up
+with you at night and think
+
+you're going to read
+it one AM.
+
+That wouldn't work.
+
+But it's an important essay.
+
+So we'll talk a bit about
+that after I make
+
+my few remarks here.
+
+First thing I want to say is
+that it's hard to believe that
+
+MIT has no full-scale
+history--
+
+history book, that is, a book
+that's been written about the
+
+entire history of MIT.
+
+One does not exist.
+
+As close as we get to it is the
+book you're reading now.
+
+And basically that consists
+primarily of snapshots of
+
+critical moments in the
+institute's history.
+
+I think it's a very good book,
+but it's not a complete
+
+history of the Institute.
+
+And hopefully, someday, someone
+will decide one is
+
+needed and actually write it.
+
+It will take it a lot of work
+because the more I read and
+
+study about this place, the more
+I realize that it has a
+
+very deep and very
+diverse history.
+
+And it will not be an easy book
+to write, in my opinion--
+
+or at least to make it
+a good book, that it
+
+really should be.
+
+But all the great universities
+in the United States have
+
+these histories and MIT is one
+of the few that doesn't.
+
+And I was sort of surprised
+at that.
+
+I must admit, I didn't know a
+thing about the history of MIT
+
+until about two or three years
+ago, when I was asked to write
+
+this essay, and then, all of
+the sudden, I, of course,
+
+started to read as much as I
+could about it in preparing
+
+for the essay that I wrote.
+
+But I was really surprised that
+there's no one big book
+
+you can go to and kind of
+get the story there.
+
+My assignment by the editor of
+the book Moments of Decision,
+
+his name is David Kaiser, and he
+teaches in the STS program,
+
+history of physics.
+
+He's also a physicist.
+
+He has a Ph.D in physics.
+
+And he persuaded me to write
+this essay, which I did
+
+because he was my colleague,
+not because I wanted to, I
+
+must admit.
+
+But I'm glad I did in retrospect
+because I learned a
+
+lot about this place
+and especially
+
+about its early years.
+
+And so what that in mind, I want
+to talk about, well, what
+
+did I learn from this extensive
+reading that I did,
+
+and what did I learn especially
+about William
+
+Barton Rogers the person and the
+significance of his life?
+
+I think it's fair to say from
+the outset that he is a very
+
+significant educator.
+
+In the larger history of
+education, he has to be one of
+
+the more important people
+of the 19th century.
+
+He came of age in the middle
+of America's Industrial
+
+Revolution.
+
+He was born in 1804, so he was
+in his 20s during the 1820s,
+
+right at the very moment when
+the United States was really
+
+beginning to experience
+factory systems, the
+
+mechanization of production,
+the advent of railroads--
+
+it was the moment.
+
+It was the right moment to be
+in the country, to see these
+
+changes taking place.
+
+And he saw them, and he was
+very, very interested in them,
+
+though he always considered
+himself to be a scientist.
+
+He was initially educated by
+his father, primarily, at
+
+William and Mary.
+
+His father was an academician.
+
+And he initially called himself
+a natural philosopher,
+
+which would be a 19th
+century word for
+
+a physicist, basically.
+
+Natural philosophy--
+
+interesting name.
+
+But technology in those days,
+interestingly, was also
+
+referred to as "the useful
+arts." The word technology, in
+
+the 1820s, I don't even know
+if it had appeared in the
+
+United States at that point.
+
+But in any case, it was a very
+new word to the lexicon and it
+
+was rarely used until we had
+the founding of this place,
+
+the Massachusetts Institute
+of Technology.
+
+It's very interesting that
+he chose that word.
+
+If I could go back and interview
+Rogers, that would
+
+be one of the questions I'd want
+to ask him, is why did
+
+you choose the word technology,
+not Massachusetts
+
+Institute of Useful Arts, or
+some more contemporary
+
+expression that was used,
+frankly, more often than the
+
+word technology was, by 1860.
+
+In any cases here he is.
+
+He's a young man during
+the 1820s.
+
+His first job out of college
+was to teach in a small
+
+private school in Baltimore
+Maryland.
+
+And it's in Baltimore that he
+comes in contact with some of
+
+the really famous railroad
+engineers of
+
+the early 19th century.
+
+All of these guys were West
+Point-trained people.
+
+They were army engineers who had
+been basically seconded to
+
+the Baltimore and Ohio
+Railroad, a private
+
+corporation, to initiate surveys
+and construction of
+
+this privately owned railroad.
+
+Talk about government in.
+
+It's a great example, in which,
+here, the federal
+
+government is actually sending
+its own personnel to a private
+
+corporation to get
+the job started.
+
+And so he meets people like
+William Gibbs McNeill and
+
+George Washington Whistler,
+who, actually,
+
+are brothers in law.
+
+Whistler is the more interesting
+of-- well, more
+
+historically interesting
+of the two.
+
+They're both important engineers
+because his son
+
+became a very famous artist,
+James McNeill Abbott Whistler,
+
+is George Washington's son.
+
+And the famous portrait,
+Whistler's mother, that sits
+
+in the Louvre in Paris is of
+George Washington's wife, who
+
+was a McNeill as a young lady.
+
+So here you have these engineers
+in Baltimore
+
+interacting with this young
+teacher because he got
+
+interested in railroads and
+wanted to give a lecture about
+
+the building of this new steam
+powered railroad out of
+
+Baltimore westward toward
+the Ohio River.
+
+And he started borrowing models
+from these engineers to
+
+illustrate his lectures with.
+
+They were building very
+interesting and fairly, not
+
+large scale models--
+
+but I've seen some of them,
+they currently exist in
+
+Russia, they're found in a
+museum in St. Petersburg--
+
+of the type of bridges that were
+being built on the B&O
+
+railroad, and the types of
+locomotives and rolling stock.
+
+A locomotive would be maybe that
+long, a 440, that wide,
+
+it's this high, fairly
+sizable model.
+
+But he was borrowing these
+models to give lectures with
+
+and, in the process, began to
+get interested in railroads,
+
+and especially because his
+brothers, two of his brothers,
+
+actually worked for McNeill.
+
+Once they left the B&O, McNeill
+came north to the
+
+Boston area to build a railroad
+that, basically, is
+
+now part of the Northeast
+corridor.
+
+It's the road between Boston
+and Providence--
+
+and did the surveys on that,
+even those these two young
+
+were basically interested in
+geology, McNeill hired them to
+
+help with the survey team,
+and then, on the side, he
+
+encouraged them to do geological
+explorations of the
+
+area, which they did.
+
+And they loved it.
+
+And they got to really admire
+these army engineers, so much
+
+so that they really seriously
+thought about becoming
+
+engineers themselves.
+
+That didn't happen, primarily
+because they felt that army
+
+engineers had such an inroad
+into the engineering business
+
+at that time, they were really
+the only serious engineers in
+
+the United States, were these
+West Point trained people,
+
+that they didn't think they had
+much of a chance getting
+
+the good jobs compared to what
+Whistler, and McNeill, and
+
+others were getting as a result
+of their connection
+
+with the Army.
+
+Both Whistler and McNeill left
+the Army in the 1830s and
+
+became private, consulting
+engineers.
+
+And Whistler went on to engineer
+not only the Western
+
+branch of what became the Boston
+and Albany railroad,
+
+which was the first major
+railroad to go over a serious
+
+mountain chain, the Berkshire
+mountains.
+
+If you drive west on the Mass
+Pike and go up over the
+
+Berkshires toward Albany, New
+York, you're going exactly
+
+through the area that Whistler
+ran a railroad through during
+
+the mid 1830s, late 1830s--
+
+serious elevations there.
+
+And he did it.
+
+He got a lot of attention
+for doing it.
+
+And one of the groups that paid
+attention to him were
+
+these Russian engineers that
+were sent to the United States
+
+by Tsar, I think
+it's Nicholas.
+
+It's either Nicholas or
+Alexander, but, in
+
+any case, he was--
+
+DAVID KAISER: Weren't they all
+Nicholas or Alexander?
+
+PROFESSOR: Nicholas and
+Alexander, you've got to be
+
+one or the other.
+
+I can't be far wrong
+on that one.
+
+But in any case, he was hired by
+the tsar to go to Russia to
+
+engineer what is now called the
+Moscow and St. Petersburg
+
+Railroad, which he did.
+
+He died in Russia, of
+cholera, in 1849.
+
+But his body was brought back
+to the United States and
+
+buried down in Stonington,
+Connecticut.
+
+I have visited his grave.
+
+And I can attest that George
+Washington Whistler now lies
+
+in Stonington, Connecticut.
+
+But he was a great engineer, and
+he was an important here.
+
+He had a lot of influence on
+Rogers and his brothers.
+
+And as a result of that, as I
+said, they both contemplated
+
+engineering careers but then
+backed away and decided, no,
+
+we are really educators.
+
+We're interested in this new
+field called geology.
+
+Both William Barton and his
+brother Henry Darwin Rogers
+
+became very, very eminent
+geologists.
+
+In fact, Henry, his younger
+brother, actually got an
+
+appointment at the University
+of Glasgow as a chaired
+
+professor there during the--
+
+I think it was during the
+late 1840s, early 1850s.
+
+And it's in the process of
+experiencing these things with
+
+these new railroads and
+industrial ventures that
+
+really begins to turn his head
+toward these "useful arts" and
+
+to think about how are they
+related to the sorts of
+
+scientific interests
+that he has.
+
+The other experience that he had
+that's very important in
+
+all this was that when he was
+teaching at the University of
+
+Virginia in the 1830s he was
+appointed the head of the
+
+state Geological Survey, and
+I've written about that in the
+
+essay, in which she had a
+miserable time because of the
+
+political interest that were
+vying with one another.
+
+He conducted the survey.
+
+He completed it, but the results
+of the survey, which
+
+were important, were never
+published because the
+
+legislature was bickering
+among themselves--
+
+sounds familiar--
+
+about the costs, whether it was
+a worthwhile project, the
+
+whole thing you might imagine.
+
+But in any case, Rogers was
+disgusted with Virginia.
+
+Surely, by the late '40s, he was
+really disgusted with the
+
+whole state legislature and
+political process there.
+
+But in conducting these surveys
+from one end of the
+
+state to the other, and in those
+days, Virginia included
+
+the current state of West
+Virginia, not just the current
+
+state of Virginia.
+
+It was a big state.
+
+He got interested, basically,
+in things like mountain
+
+formations and very much
+interested in where mineral
+
+deposits were located and
+things like that.
+
+But the big problem was finding
+assistants that could
+
+help him conduct the sort of
+geological work that he needed
+
+to do in order to finish up the
+survey and make a report.
+
+And that was another stimulus
+toward his interest in trying
+
+to do something with combining
+science with the useful arts.
+
+So those are, I would say, two
+critical moments during the
+
+1830s in which he really began
+to begin to think about
+
+establishing some sort of what
+we would call a Polytechnic
+
+Institute, or Institute
+of Technology.
+
+He and his brother both started
+talking about this as
+
+early as 1829 in Baltimore.
+
+But then it got continued
+throughout the 1830s and well
+
+into the 1840s.
+
+And that's really how the whole
+idea of what this place
+
+is about got started.
+
+Rogers also saw, through these
+years, that there was a crying
+
+need for people to do
+engineering work and meet what
+
+he referred to as the "wants
+of the age." This was the
+
+great field, the open field--
+
+lots of jobs and possibilities
+for advancement.
+
+And he saw that, and,
+again, it stimulated
+
+his interest in education.
+
+So as a result of this, he
+develops a plan for a
+
+Polytechnic Institute, the first
+draft of which, I think,
+
+was written as early as 1829.
+
+And then over the next 30 years
+he and his brother sort
+
+of elaborate on this plan
+about how would
+
+they organize it?
+
+What disciplines would
+be included?
+
+But the key, I think, the key
+idea that they developed over
+
+these years was trying to
+combine, trying to develop an
+
+educational system that would
+combine science with the
+
+useful arts, make them relevant
+to one another and
+
+especially inform the useful
+arts about what science could
+
+reveal to them-- the
+understandings of chemistry,
+
+or physics, or whatever.
+
+And of courses, as you've read,
+the finality of this
+
+comes in 1861, when he receives
+a charter from the
+
+state of Massachusetts to
+establish what is called the
+
+Massachusetts Institute
+of Technology.
+
+Now in that, he'd had to
+do a lot of lobbying.
+
+He had learned how to work with
+politicians through that
+
+miserable Virginia experience.
+
+I think it made him
+a wiser man--
+
+maybe a cagier person in terms
+of learning how to work with
+
+politicians or to get
+around the obstacles
+
+they put in this way.
+
+It's during the early questions
+about the charter
+
+for MIT, for example, that the
+governor of Massachusetts, who
+
+was a Harvard graduate, first
+proposed the idea of, why
+
+create this MIT as a
+separate institute?
+
+Why not combine it
+with Harvard?
+
+It's one of those early
+questions about, well, why not
+
+combine it with Harvard rather
+than make it a separate
+
+institution?
+
+Rogers resisted that throughout
+this entire life.
+
+And there were several other
+attempts made during his
+
+lifetime to try to merge
+MIT with Harvard.
+
+But it began very early.
+
+And it began first with the
+government of Massachusetts,
+
+who would like to have
+seen that sort of
+
+combination put together.
+
+But once they got the charter,
+the big challenge then was to
+
+try to get the place going.
+
+And the problem was that he got
+his charter in April 1861,
+
+and what happens in
+1861, in April?
+
+Civil War.
+
+And so a war breaks out.
+
+It makes it difficult for him
+to raise money, basically--
+
+very difficult to raise money.
+
+And some scholars who have
+studied the history of MIT
+
+think that maybe it was a good
+thing that there was a war, in
+
+terms of his interest, because
+it gave him time to complete
+
+this plans and to work the
+political process in a way
+
+that allowed him to
+eventually get the
+
+Institute started in 1865.
+
+There may be some truth to that,
+but I think the real
+
+problem that he faced
+1861 was money.
+
+And that was a problem MIT was
+going to face for the next
+
+four years or so.
+
+MIT was always running in the
+red, basically, well into the
+
+late 1890s and probably
+beyond that.
+
+I just haven't studied that
+much beyond the fiscal
+
+situation beyond the 1890s.
+
+But in any case, he
+got his charter.
+
+He has to hire faculty.
+
+He has to choose and acquire a
+site to initiate classes in.
+
+He has to raise this money.
+
+There are a lot of things that
+have to be accomplished.
+
+And I think one of the big
+godsends of the period was
+
+that there was a law
+passed in 1862.
+
+It was a federal law, part of
+the Lincoln administration's
+
+political agenda called the
+Morrill Land Grant Act.
+
+And I remember reading about
+this when I was your age and
+
+being totally bored by it.
+
+But it turns out that that is
+a very important piece of
+
+legislation because it led to
+the establishment of what we
+
+call the land grant university
+system in this country.
+
+All the big state universities,
+basically, are
+
+related to that land
+grant act.
+
+Some very directly, and others
+less so, but, nonetheless,
+
+most of them--
+
+Texas A&M, Penn State, Ohio
+State, Michigan State,
+
+Wisconsin, Berkeley, you know,
+you can go across the country
+
+and almost choose.
+
+In every state, there's at least
+one institution that was
+
+founded under the Morrill Act.
+
+Well, that Morrill Act
+was passed in 1862.
+
+And basically, what it said
+was that for each
+
+congressional representative
+that you had in the US
+
+Congress, the state would get
+30,000 acres of land, which it
+
+in turn could convert into
+script and sell the script, or
+
+the rights to the land, as
+a way of raising money to
+
+establish agricultural
+mechanical colleges within the
+
+state boundaries--
+
+A&Ms, if you want to
+call them that.
+
+So Massachusetts, I think,
+had 10 congressional
+
+representatives and
+two US Senators.
+
+So it got a fairly sizable chunk
+of land in the Midwest.
+
+If I'm not mistaken, it was out
+in the area of northern
+
+Iowa, southern Minnesota, in
+that area, where a lot of this
+
+land was located.
+
+People in Minnesota and Iowa,
+by the way, were not happy
+
+that the federal government was
+giving away land in their
+
+states to states that had
+nothing to do with them.
+
+You can imagine how people in
+Minnesota must've felt about
+
+this huge chunk of land going
+to New York State, or
+
+Massachusetts, or wherever.
+
+But in any case, that converted
+into substantial
+
+funds that were used to found
+not only MIT but also the
+
+University of Massachusetts
+at Amherst.
+
+And basically, MIT got a
+third of those monies
+
+over a 30 year period.
+
+It was given to them
+in increments.
+
+They got a sizable amount of
+money, well over $300,000.
+
+That may not sound like much
+today, but if you convert it
+
+into 2008 dollars, it's
+a big hunk of money.
+
+I don't know but I've--
+
+DAVID KAISER: Well, it would
+put you through MIT today.
+
+PROFESSOR: It would put
+you through MIT today.
+
+That's a good way to put it.
+
+Yeah, so it's a sizable
+amount of money.
+
+DAVID KAISER: Plus a
+couple vacations.
+
+PROFESSOR: But probably just as
+important as the grant from
+
+the state itself, which
+consisted not only of money,
+
+but also of land, over
+in the Back Bay--
+
+MIT was first established not
+here, where we are today, but
+
+over in the Back Bay
+near Copley Square.
+
+If you're familiar with that
+area, the original building
+
+was very close, block or two,
+from Copley Square.
+
+And it stayed there until
+1916, pretty much.
+
+But in any case, the money for
+all that came from the state
+
+of Massachusetts.
+
+So the state was important
+in all this.
+
+Without the state, I would, in
+fact, question whether private
+
+donors would have stepped
+forward to donate money to MIT
+
+because they weren't sure
+about its future.
+
+But when the state began to
+invest in MIT, that sort of
+
+gave a signal that, yeah,
+MIT's got a future.
+
+I'm going to pony up some money
+and give --and one of
+
+the big donations that came very
+soon after MIT got the
+
+state funds was a donation that
+I begin my essay with,
+
+this doctor--
+
+what's his name--
+
+DAVID KAISER: Walker?
+
+PROFESSOR: What is it?
+
+DAVID KAISER: Walker.
+
+PROFESSOR: Walker, yes.
+
+William Walker, a physician who
+had invested in industry
+
+in this state.
+
+This was a leading
+industrial state.
+
+And he ponied up $60,000--
+
+a lot of money for a private
+individual in those days.
+
+DAVID KAISER: On the last
+day before the--
+
+PROFESSOR: In the last day,
+yeah, so it was an iffy
+
+proposition from
+the beginning.
+
+And Rogers, I think one of his
+great skills was as a, in a
+
+way, small p politician,
+a lobbyist.
+
+He was very effective at
+lobbying people, and raising
+
+funds, and keeping this
+institution going from one
+
+year, literally, one
+year to another.
+
+Because every year, as I said,
+it was running on the red.
+
+But he made it go.
+
+DAVID KAISER: Something about
+Back Bay, too-- because maybe
+
+not everybody knows that
+what is now Back
+
+Bay was once a Bay.
+
+PROFESSOR: Absolutely.
+
+DAVID KAISER: And I hadn't
+really remembered until I was
+
+reading the reading last night
+that part of the initial
+
+interest was--
+
+they filled in the Back Bay to
+make what is now Back Bay,
+
+which was a huge engineering
+project in and of itself.
+
+And then there was interest
+in using that land for
+
+educational purposes, which
+Rogers then sort of satisfied
+
+to some degree.
+
+PROFESSOR: Right.
+
+And I think I mentioned in the
+essay that the initial
+
+proposal was not just for an
+industrial school, MIT, but
+
+was also for a natural history
+museum and a society of arts.
+
+It was a 3 part combination that
+was initially proposed.
+
+And eventually, of course,
+MIT was the
+
+one that really lasted.
+
+And the other two sort of
+slipped by the wayside.
+
+But in any case, that's the
+story of the beginning
+
+because, I think, in the early
+days, if I'm not mistaken,
+
+that one of the early courses
+at MIT was in mining and,
+
+what's the other--
+
+DAVID KAISER: Metallurgy.
+
+PROFESSOR: Mining
+and metallurgy.
+
+And in those days, geology
+would've been
+
+lumped into that area.
+
+And then later, it becomes--
+
+yeah, yeah.
+
+Now, I can't absolutely
+swear that's the
+
+case, but that's my--
+
+what would say say, an
+educated guess, I
+
+guess, would be.
+
+So to look at Rogers and just
+say, OK, what are some of the
+
+important points to remember
+about him?
+
+One is, he's a good lobbyist.
+
+He keeps the place going.
+
+He keeps the vision alive, OK?
+
+And secondly, there's
+the vision itself.
+
+You see it on the great
+seal of MIT.
+
+You know, interestingly, if
+you look at the seal, it's
+
+interesting.
+
+It says mens et manus--
+
+mind and hand.
+
+Science and the useful arts,
+another way to think of it.
+
+But clearly, that vision of the
+combination of science and
+
+the useful arts was there
+from day one.
+
+And that seal was actually
+approved in 1864, if I'm not
+
+mistaken Rogers was on the
+committee that, you know,
+
+approved that seal.
+
+And he obviously played a role,
+I mean, I think his
+
+vision is sort of stamped,
+literally, into the seal
+
+itself, of what this place
+was going to be.
+
+One curious thing about that
+seal, however, I'll
+
+point it out now.
+
+It's not original with me, but
+a colleague of mine, years
+
+ago, pointed it out to me,
+and I have thought
+
+about it ever since--
+
+was that when you look at this
+seal, you have a craftsman, or
+
+an industrial worker, and a
+scholar, OK, the scientist and
+
+the useful arts standing next
+to a pedestal, and then the
+
+words mens et manus below,
+and the date of
+
+the founding of MIT.
+
+The interesting thing though is
+that, in Rogers' vision he
+
+wanted to combine, he wanted
+each of them, science and
+
+useful arts, to inform
+one another.
+
+That was the special thing,
+the idea that he had.
+
+This was a new way of
+educating people.
+
+And yet these figures, science
+and engineering, or science
+
+and useful arts, they have their
+backs turned to each
+
+other, as if they're not
+conversing at all.
+
+Curious.
+
+I don't know it if was for
+aesthetic purposes or what,
+
+but from a didactic point of
+view, they should have been
+
+facing each other, and having
+discussions, and interacting.
+
+Clearly, they're not
+doing anything.
+
+They're sort of both in
+their own worlds.
+
+And that's an interesting
+comment, I think, just on the
+
+seal, not necessarily about
+Rogers' vision.
+
+But he has this important idea
+about the combination of the
+
+two, which is very important.
+
+And in the essay, I put a lot of
+emphasis on the importance
+
+of laboratory education there,
+in which students are not just
+
+being given lectures and
+demonstrations by the
+
+professor using the apparatus,
+but, in fact, they're allowed
+
+to go in and perform experiments
+themselves using
+
+the apparatus.
+
+One of the reasons why MIT was
+constantly in financial
+
+difficulty was the need to
+maintain the laboratories that
+
+were so critical to the
+education of its students.
+
+Laboratories are very expensive,
+to this day
+
+probably the most expensive
+item in the MIT budget, I
+
+would think-- one of the
+most expensive ones.
+
+Look around us at these new
+buildings that are going up
+
+just in the biological sciences
+and think of the
+
+expense that has been
+invested in them.
+
+And it was no less true
+in the 19th century.
+
+And it had a special meaning for
+Rogers because he wanted
+
+students to be immersed in that
+experimental process and
+
+not just lookers-on.
+
+He wanted them involved
+in the process.
+
+And I think that's one of the
+really distinctive things
+
+about MIT, then and today.
+
+I keep thinking that vision of
+1861, 1864, of Rogers can be
+
+seen in the UROP projects.
+
+And several of you have written
+in your reflections
+
+about this today--
+
+different programs that exist at
+MIT that have that sort of
+
+active involvement of students
+that, in the days of the
+
+1860s, just didn't exist at
+other places, or surely not to
+
+any extent like it did at MIT.
+
+The other thing that Rogers
+had was an eye for talent.
+
+Every great leader needs to
+surround themselves with
+
+capable people.
+
+And the more capable,
+the better.
+
+And Rogers, I don't know if
+you want to call it good
+
+fortune or just the ability to
+spot people and hire them.
+
+But he hired a very
+talented staff.
+
+I think there were something
+like 20 professors, maybe not
+
+even 20, by 1870, five years
+after classes started.
+
+But at least half of them were
+very, very competent people.
+
+And two of the most important
+were a guy named Francis
+
+Storer, S-T-O-R-E-R, and
+somewhat younger guy, but not
+
+a lot younger, Charles Eliot,
+both of whom were chemists,
+
+both of whom were Harvard
+educated, and, it turns out,
+
+both of whom were
+brothers in law.
+
+Storer married Eliot's sister.
+
+And Storer came to MIT first.
+
+He was one of the first faculty
+hired at MIT, to set
+
+up a chemistry department
+here.
+
+And then Eliot, who was studying
+in Germany, was hired
+
+like in 1867 to come in and
+fill out that enterprise.
+
+And they end up building
+one of the first really
+
+experimental research oriented
+laboratories in the United
+
+States, academic, anyway.
+
+And they also are the first to
+write textbooks for the study
+
+of chemistry, and chemical
+experiments, and things like--
+
+two very famous textbooks that
+were published during the
+
+early, well, the late 1860s
+and early 1870s.
+
+So they're important people.
+
+Now the interesting thing is
+that Eliot was at MIT a very
+
+short period of time.
+
+He came and '67 and he
+left in '69 to become
+
+President of Harvard.
+
+And interestingly, it's Eliot
+who really initiates all these
+
+attempts to merge Harvard
+with MIT.
+
+The essay that you read today
+called, "The New Education,"
+
+same guy, Charles Eliot, the
+author is Charles Eliot.
+
+He wrote that while he was at
+MIT, but the same year that
+
+essay was published, he becomes
+president of Harvard.
+
+And immediately, he starts
+making overtures to William
+
+Rogers about, come
+on, Bill, let's--
+
+I don't know if they'd
+call him Bill.
+
+I've often wondered, what did
+they call William-- did
+
+William Rogers have
+a nickname?
+
+We had a reunion over in
+Burton-Conner about two or
+
+three weeks ago, and they
+had this big cut
+
+out picture of Rogers.
+
+And one of the students from
+Burton-Conner came over and
+
+clipped a little ID badge on
+him saying, "Billy." But I
+
+can't imagine, William Rogers,
+does not strike me that you
+
+would walk up and call
+him Billy Rogers.
+
+I don't know if he had
+a nickname or not.
+
+But in any case, Eliot liked--
+
+DAVID KAISER: Mr. Rogers.
+
+PROFESSOR: Pardon?
+
+Mr. Rogers, that would
+even be better.
+
+Yeah, Mr. Rogers.
+
+DAVID KAISER: And they called
+MIT Mr. Rogers' neighborhood.
+
+PROFESSOR: Well, you're
+just full of neat
+
+observations today.
+
+DAVID KAISER: That's
+my job, [INAUDIBLE]
+
+PROFESSOR: That's good.
+
+That's good.
+
+You remind me of Waldorf over
+and-- you know, the muppets up
+
+in the balcony?
+
+DAVID KAISER: [LAUGHS]
+
+PROFESSOR: You're
+Waldorf today.
+
+Anyway, Eliot really liked
+what he saw at MIT.
+
+He clearly thinks that MIT
+is the core of this "new
+
+education." This is where
+the action was at.
+
+And he tried very hard during
+his presidential years at
+
+Harvard-- and he was president
+of Harvard for at, what, 35
+
+years or so?
+
+A long time.
+
+Never happened.
+
+But that was one of his
+fondest wishes.
+
+And he was one of these early
+hires that William Barton
+
+Rogers made here.
+
+Clearly, he had sold Eliot
+on the MIT vision.
+
+There were others.
+
+Edward Pickering, like Eliot and
+Storer, established a very
+
+famous lab in physics here.
+
+And he was literally Rogers
+successor as the teacher of
+
+physics at MIT--
+
+again, another Harvard
+graduate.
+
+All these early professors are
+pretty much Harvard graduates
+
+who came to MIT and then, like
+Storer and Eliot, often left
+
+MIT to go back to Harvard,
+interestingly.
+
+I don't know exactly why.
+
+Eliot was a very persuasive
+person, but I'm sure Harvard
+
+could shake a lot more money in
+their faces, too, in terms
+
+of salaries and things
+like that.
+
+That's probably important,
+an important attraction.
+
+So Pickering, as I recollect,
+also returned to Harvard at
+
+one point in this career.
+
+But he was a very important
+laboratory builder here at MIT
+
+that established, again, the MIT
+model for spreading this
+
+new vision of education
+around the country.
+
+And then finally, in
+architecture, another Harvard
+
+graduate, William Ware,
+establishes the Department of
+
+Architecture at MIT.
+
+It's the first in the country,
+and very successful, very much
+
+oriented towards this hands on,
+laboratory oriented design
+
+process in architecture.
+
+He was at MIT for
+about 15 years.
+
+And then he leaves to go to
+Columbia and establish a
+
+similar school at Columbia.
+
+He's considered the leading
+educator in architecture of
+
+the late 19th century.
+
+So you have here, in this
+early faculty, some very
+
+interesting and significant
+people.
+
+And I think the important thing,
+for the purposes of our
+
+discussion today, is that
+Rogers hired these guys.
+
+He had an eye for talent.
+
+And there's nothing like having
+great talent around you
+
+to build a great institution.
+
+And that was underway
+by the 1870s.
+
+People were actually writing to
+Rogers by the 1870s, like,
+
+within five years of the
+founding of this place,
+
+saying, MIT is making
+itself heard.
+
+And that reputation continues
+to gain momentum throughout
+
+the decades of the late
+19th century.
+
+So much so that in the paper
+that I wrote, I refer to
+
+Francis Amasa Walker, who was
+the third president of MIT
+
+making his annual report in
+1894, in which he comes out
+
+and says, basically, thanks
+to the founders of this
+
+Institute, and especially to
+William Rogers, the battle of
+
+"the new education" " has won.
+
+Well, the new education meant
+that MIT had now become the
+
+great model of this new way of
+educating people toward a more
+
+integrated curriculum built
+around science and
+
+engineering.
+
+That was a new model.
+
+And when you look around the
+country today, virtually every
+
+major university has sort of
+bought in to that model.
+
+Even a number of small colleges
+have, but especially
+
+large state universities--
+
+very much influenced by
+this MIT approach.
+
+Now the final point to be made
+about Rogers, I think, is that
+
+he's one of the country's
+first geologists,
+
+professional geologist.
+
+He's one of the founders
+of the field
+
+in the United States.
+
+He is also a founder of the
+American Association for the
+
+Advancement of Science.
+
+He's not and he's not on the
+inside of that operation, but
+
+he's definitely consulted about
+it, is an early member,
+
+and plays a role in it.
+
+But he is an important geologist
+in the history of
+
+science in this country.
+
+And he's also an early defender
+of Charles Darwin.
+
+Darwin's Origins of Species,
+the famous book on
+
+evolutionary theory, was
+published in 1859.
+
+And Rogers was one of the first
+in the Boston area to
+
+embrace that theory,
+and defend it, and
+
+argue that it had--
+
+from his geological perspective
+
+was a viable theory.
+
+He was opposed, very vigorously,
+by a zoologist
+
+from Harvard named Louis
+Agassiz, who, in more than one
+
+time, tried to do in Rogers,
+both as a geologist and as the
+
+founder of MIT.
+
+But, again Rogers had staying
+power and was able to make its
+
+way through all these crises.
+
+But I think as a geologist, he
+often gets forgotten in that
+
+area, even though he
+was an important
+
+contributor to that field.
+
+Now what are the take
+home points of the
+
+essay that I wrote.
+
+I'll give you three.
+
+One is obvious.
+
+It's the sustainability of
+Rogers' vision for MIT--
+
+the mens et manus theme.
+
+The idea of combining, bringing
+together science and
+
+the useful arts.
+
+It's a remarkable continuity,
+if you ask me.
+
+I think it's something that has
+maintained itself right up
+
+to the present.
+
+That's amazing.
+
+This place is 150 years old, and
+yet the founding vision of
+
+the place still informs
+it in many ways.
+
+Now that doesn't mean there
+haven't been changes.
+
+There surely have been.
+
+And we'll see them
+during the term.
+
+But that basic concept has
+maintained itself.
+
+That's amazing to me.
+
+Another thing that's important
+to note here is the role of
+
+the state in the founding of
+MIT, the fact that the state
+
+of Massachusetts, funded by
+the federal government,
+
+basically, put up a lot of the
+real seed bed money that was
+
+used to get this
+place started.
+
+And then that, in turn,
+attracted private
+
+donations to MIT.
+
+But as late as the 1890s, MIT
+was petitioning the state of
+
+Massachusetts for increments of
+$25,000 a year, simply to
+
+try to support the building of
+labs and stuff like that.
+
+So Massachusetts have a long
+history of involvement with
+
+MIT, even though this was
+supposedly a "private
+
+corporation." It's curious.
+
+It's a land grant school that
+is a private corporation.
+
+Not many were like that.
+
+Most were state universities
+that were state controlled and
+
+did not have this word
+corporation.
+
+You might have been a member of
+the board of trustees, but
+
+you were not a member
+of the corporation
+
+like we have today.
+
+So again the state is
+important here.
+
+And then finally, just about
+MIT's significance, it's the
+
+new education that's
+important.
+
+It's a new breed of cat that's
+being developed here, and it's
+
+one that had legs.
+
+It's probably had, I suppose,
+this sounds so much like a
+
+homer lecture, but
+it is, in a way.
+
+I'm enthusiastic about
+the history of MIT.
+
+Maybe it's because I haven't
+learned enough about it yet.
+
+But the vision for MIT
+had an impact.
+
+It made impacts elsewhere.
+
+It continues to have that.
+
+We'll talk about, later in the
+term, about how the MIT model
+
+is now being exported to
+Singapore, and to India, and
+
+all over the world.
+
+So it's had enormous,
+enormous impact.
+
+And that's not something
+to be sneezed at.
+
+And it's really why Charles
+Eliot wrote that essay called
+
+"The New Education," was to
+point out, this is something
+
+new and different.
+
+This is worth attending to.
+
+And he does a survey of all
+these various schools and says
+
+the real place where the
+action is is MIT.
+
+That's 1869.
+
+Within months, he was going to
+become president of Harvard
+
+and, as I said, made numerous
+attempts to try to bring MIT
+
+into the Harvard fold,
+unsuccessfully.
+
+So David suggested that's
+my remarks, OK.
+
+Brilliant.
+
+Aren't they?
+
+Eli, you thought they were
+pretty good, huh?
+
+That's good.
+
+I know all these people.
+
+So you're wondering, why is he
+talking to them, you know?
+
+Anyway, David suggested, before
+the class started, that
+
+we take a closer look at
+Eliot's piece "The New
+
+Education." I debated about
+whether we should have you
+
+read this or not because,
+frankly, it's pretty boring.
+
+It's not an easy
+piece to read.
+
+It's written in a very stilted,
+19th century style.
+
+And yet it's says things, if you
+can make your way through
+
+it, it does say things,
+I think, that are
+
+important to note.
+
+And so, this is basically
+Charles Eliot's take on the
+
+state of education, higher
+education, in the United
+
+States circa 1869.
+
+That's really what this
+essay is about.
+
+And the big distinction he makes
+is that he talks about
+
+how there are basically three
+different types of higher
+
+education institutions
+in the United States.
+
+There are the classical colleges
+that teach Latin and
+
+Greek, mathematics, the typical
+curriculum aimed at
+
+cultivating an educated
+gentleman for society.
+
+That's where gentlemanly
+people went.
+
+Ladies, I'm sorry, were not
+admitted to those schools in
+
+those days.
+
+Most women, in those days, if
+they went to college at all,
+
+and many of them did
+not, went to--
+
+my grandmother, who went to one
+of these college called
+
+state teachers institutes, or
+educational institutes.
+
+But rarely would you see women
+on the campus of Yale.
+
+I don't even know
+if Yale admitted
+
+women, did they in the--?
+
+DAVID KAISER: 1969.
+
+PROFESSOR: Wow.
+
+See?
+
+It's a good--
+
+OK.
+
+Well, Harvard had Radcliffe.
+
+So they're next door neighbors,
+but there's this
+
+divorce that exists.
+
+Now, interestingly, Rogers,
+from day one, said we will
+
+admit women to this place.
+
+A very, very small
+number came.
+
+And most of those who did come
+were called special students.
+
+They were not regular students
+like you are but rather
+
+special students who were part
+time, basically, part time
+
+students, women who were working
+in the area who wanted
+
+to take a chemistry class or
+something, could enroll here.
+
+But for it's day, that was quite
+a revolutionary and open
+
+minded thing to do, I think.
+
+But he was very open to that.
+
+He was very much a reformer,
+I think.
+
+He was involved in the
+abolitionist movement.
+
+And David pointed out today that
+one of his friends from
+
+Virginia, a guy named Edmund
+Ruffin, was actually one of
+
+the first to fire the
+Confederate cannons on Fort
+
+Sumter in 1861.
+
+So here's this man coming out
+of Virginia who was imbued
+
+with this slave oriented ethos
+that's pervaded Virginia prior
+
+to the Civil War, who was open
+minded enough to see the
+
+problems and downright evils of
+slavery, resist them, and,
+
+eventually, remove himself
+from the South
+
+and come to New England.
+
+That's one of the reasons
+he moved here.
+
+He was just so sick of the
+violent society that Virginia
+
+had become by the 1850s,
+especially around slavery.
+
+A lot of his problems came
+from that direction.
+
+Well, when Eliot writes about
+"The New Education," he
+
+doesn't use that phrase
+a lot in here.
+
+You really have to
+kind of look--
+
+he may have mentioned the term
+new education or some variant
+
+of it maybe three or four times
+in the entire essay.
+
+It's not something he's
+pounding away at.
+
+But he's making as interesting
+comparisons, first, between
+
+these three kinds of
+institutions that are trying
+
+to organize educational
+framework around the useful
+
+arts and science.
+
+And he argues that two of them
+are just abject failures,
+
+basically, there are schools
+like the Lawrence School at
+
+Harvard, or the Sheffield
+School at Yale, or the
+
+Chandler School at Dartmouth,
+that make the attempt but can
+
+never quite achieve what is
+needed to be done because
+
+their faculty come from
+the school itself.
+
+And as a result, the faculty
+loyalties and the degree of
+
+involvement in these new
+ways of educating
+
+students is never complete.
+
+It's always sort of
+a halfway process.
+
+And that's something that
+bothered Eliot a great deal,
+
+especially about Harvard because
+the Lawrence School
+
+was heavily endowed
+for its day.
+
+And yet it had really had a
+sort of a meager record of
+
+turning out students who
+were well educated
+
+in the useful arts.
+
+And so that's a problem.
+
+There are other types of
+colleges that he talks about
+
+with reference to the useful
+arts, smaller schools like
+
+Union College up in Schenectady,
+New York or Brown
+
+University down in Providence.
+
+And basically, the argument is
+somewhat similar there, is
+
+that it's hard to introduce this
+new concept of combining
+
+useful arts and science in
+environments that have been
+
+completely oriented toward
+the classical education
+
+up until that time.
+
+It's very difficult
+to do that.
+
+And as a result, he says, it's
+really to the third type of
+
+school, the RPIs, the MITs, are
+the two main ones where
+
+this model is more likely
+to succeed.
+
+And there, he says that RPI's
+been quite successful at it.
+
+It's really the first civilian
+engineering school founded in
+
+the United States.
+
+It dates to 1824.
+
+And RPI is basically a place
+that trains civil engineers.
+
+It does not get into mechanical
+engineering or
+
+metallurgical engineering,
+things like that.
+
+It's strictly oriented toward
+civil engineering-- by the
+
+time the Civil War,
+very successful.
+
+But it's really to MIT
+that he looks.
+
+And he says now here is the
+model because it's so open to
+
+educating not only civil
+engineers but mechanical
+
+engineers, architects,
+metallurgical engineers--
+
+MIT has a menu by the late 1860s
+that no other school
+
+really has.
+
+And so that is, I think,
+a distinctive
+
+comment that he makes.
+
+But basically, I read this,
+and for me the takeaway is
+
+that Eliot loves MIT.
+
+He sees MIT as the new direction
+for higher education
+
+and that's doing something
+different than any other place
+
+has ever done.
+
+It's a good question.
+
+The interesting thing, I wanted
+to note, here, though
+
+is that on page 216 near the
+end, yeah, he's talking about
+
+RPI and MIT, but he makes no
+reference to the US Military
+
+Academy, which is arguably the
+first engineering school in
+
+the United States.
+
+It's modeled after the French
+Ecole Polytechnique--
+
+except for a footnote at
+the bottom of 216.
+
+Did you see this note?
+
+He says the United States Naval
+and military academies
+
+are not referred to at length
+because-- they're not refer to
+
+at all, basically, because
+access to them is not free.
+
+A thoroughly vicious system
+blah, blah, blah.
+
+He does not like the
+military academies.
+
+But he completely erases
+them from the essay.
+
+Did you have your hand up?
+
+AUDIENCE: Um, not really.
+
+PROFESSOR: Huh?
+
+AUDIENCE: No.
+
+PROFESSOR: Oh OK, I thought
+you were waving your hand
+
+going, I object!
+
+He's just anti-militarist,
+or something.
+
+But those are important
+places--
+
+especially West Point.
+
+In fact, I think I say it in my
+essay, that the president
+
+of Brown University, Francis
+Wayland, made a comment in the
+
+1850s that West Point had
+trained more engineers then
+
+all the other colleges in the
+United States put together.
+
+Well, that says something.
+
+It's not a big school.
+
+And it also tells you about the
+need for more engineers in
+
+the country because West
+Point could not produce
+
+all of these people.
+
+Hence the reason why MIT became
+so important by the
+
+later decades of the
+19th century.
+
+And where did early MIT
+graduates go to work?
+
+Many of them went
+to railroads.
+
+That was the big industry
+after the Civil War.
+
+And many of them go into the
+railroad industry as managers,
+
+engineers, railroad builders.
+
+Many go into chemical industries
+that are beginning
+
+to emerge during this
+period too.
+
+It's interesting, for example,
+that the du Pont family sends
+
+the best and brightest of their
+family, of young people,
+
+up here to get educated.
+
+Pierre du Pont, one of
+the really important
+
+industrialists of the early 20th
+century, is a graduate of
+
+MIT class of 1890.
+
+And there were other du Ponts
+that came here, too, but he's
+
+probably the most important.
+
+And Arthur D. Little, famous
+AD Little Laboratories.
+
+I don't know if they're still,
+are they still in operation?
+
+Private research laboratories
+in chemistry?
+
+DAVID KAISER: I belive AD Little
+is still in operation
+
+but they sold off
+the R&D lab--
+
+PROFESSOR: They did, OK.
+
+DAVID KAISER: To an MIT
+alum, actually, Kenan
+
+Sahin, owns it now.
+
+And it's got a different name.
+
+PROFESSOR: Oh, he did?
+
+OK.
+
+Well, there's a list of very
+eminent engineers, chemists,
+
+applied scientists that are
+coming out of MIT by the 1890s
+
+that go on to really play a
+big role in the commercial
+
+development and
+industrialization of the
+
+United States in the
+20th century.
+
+So MIT has had an impact.
+
+I don't know if you want to
+say any more about Charles
+
+Eliot's piece here.
+
+DAVID KAISER: I would
+read through little
+
+bit of it in detail.
+
+PROFESSOR: Go ahead.
+
+DAVID KAISER: How many people
+brought the piece
+
+[INTERPOSING VOICES]
+
+PROFESSOR: Can you get it
+off the scholar site?
+
+DAVID KAISER: If you have it,
+maybe pull it out because it's
+
+sort of worth, I think, reading
+parts of it in some
+
+detail because, first of all,
+it's a good exercise in what
+
+we call close reading,
+were how you--
+
+I mean, the language
+a little foreign.
+
+It's not very foreign, but
+what's being said between the
+
+lines, or what's he assuming
+that people are saying.
+
+And I think some of it is
+relevant to both what
+
+[? Rowe ?] was saying, and
+even to MIT today.
+
+I'm sorry?
+
+It is on Stellar, yeah, so
+if you have a laptop
+
+you can find it.
+
+You know, he starts out
+with this line--
+
+"what can I do with my boy?"
+Which is very interesting.
+
+I mean, obviously it's only
+boys and men that he's
+
+addressed like [? Rowe ?]
+mentioned, that was the
+
+language of the day, up until
+a couple of decades ago.
+
+But, sort of addressed to the
+parents, and of if you read
+
+down a little bit, this is what
+a parent might say, I
+
+want to give my boy practical
+education.
+
+One that will prepare him better
+than I was prepared to
+
+follow my business, or any
+other active calling.
+
+And I like that phrase active
+calling, because implied there
+
+is there are passive callings.
+
+I wonder what he means by
+a non active calling.
+
+I would guess he would mean the
+clergy, or probably law,
+
+and he comes back to
+them a little bit.
+
+And then he says this is a
+problem that everyone has, but
+
+the difficulty presses more
+heavily-- still in the first
+
+paragraph--
+
+on the thoughtful American
+than on the European.
+
+And so he's making a distinction
+that the
+
+conditions of this country are
+special, in some way, for this
+
+kind of education.
+
+It's not the modern phrase of
+old Europe, there are special
+
+things here, because the
+American is free to choose, in
+
+a way, a way of life for himself
+and his children.
+
+And then--
+
+a couple lines down-- in the
+face of prodigious material
+
+resources of a vast and new
+territory, he is more fully
+
+awake then the European can be
+to the gravity and urgency of
+
+the problem.
+
+Also a really interesting way to
+start out at the beginning,
+
+that there are special things
+about this country.
+
+That's not a new idea, American
+exceptionalism, is
+
+what historians call it.
+
+But, the conditions here are
+different than in Europe.
+
+Partly because of the huge
+size of the place.
+
+Partly because of the huge
+amount of resources.
+
+And that makes the American
+more fully awake.
+
+And yet, he has fewer options
+than any other, except
+
+possibly the English, of
+solving the problem.
+
+And then on the next column,
+he refers to implicitly
+
+particularly the French
+engineering schools.
+
+For more than a generation the
+government schools of arts and
+
+trades, arts and manufactures,
+bridges and highways--
+
+one of the famous French
+engineering school is Ponts Et
+
+Chaussees, the school of
+bridges and highways--
+
+Ecole Des Mines--
+
+another famous French
+engineering school--
+
+mines, agriculture, and commerce
+have introduced
+
+hundreds of well trained
+young men.
+
+They begin as subalterns,
+basically low people on the
+
+totem pole, but soon become the
+commission's officers of
+
+the army, and of industry.
+
+Which is interesting too, what
+is the problem that the
+
+European engineering schools
+are feeding?
+
+They don't have vast territory
+remaining, they don't have
+
+vast resources in their
+countries, where are all those
+
+engineers going, if in the US
+they're going out west?
+
+Into the colonies.
+
+It's a problem of maintaining
+the empire.
+
+He doesn't talk too much about,
+he does use the word
+
+empire in there, but in a way
+he's sort of arguing that
+
+America has its own empire
+right here, and French
+
+particularly, German, English,
+they're all building railroads
+
+in the colonies, a little
+bit more in
+
+the later 19th century.
+
+PROFESSOR: Think, for example,
+the British and India, huge,
+
+huge, and that's only a
+part of the British
+
+empire in that period.
+
+It's a huge empire.
+
+DAVID KAISER: Then he this
+great line, The American
+
+people are fighting
+the wilderness,
+
+physical and moral.
+
+Which is funny, it's also
+interesting, this is four
+
+years after the Civil War.
+
+In fact, most of the stuff we've
+been reading, relatively
+
+recent, doesn't mention
+the war in here.
+
+You have a country that just
+lost the better part of a
+
+million people.
+
+The South has been destroyed to
+a large degree by the war.
+
+The young people's population
+has been destroyed.
+
+I don't know, what was the
+population of the US in the
+
+time of the Civil War?
+
+PROFESSOR: I want to say it's
+around six million maybe?
+
+DAVID KAISER: So six million,
+even if you lost six--
+
+PROFESSOR: I'm not sure.
+
+DAVID KAISER: --hundred thousand
+people out of that.
+
+10% of the population.
+
+Extend that out today, that's
+like you having a civil war
+
+where you are losing tens
+of millions of people.
+
+Nobody would have been
+unaffected, and he doesn't
+
+mention it in this piece,
+which is also very
+
+interesting.
+
+PROFESSOR: I know one thing,
+the South lost 25% of it's
+
+younger men during that war.
+
+25%--
+
+DAVID KAISER: That's huge.
+
+PROFESSOR: --that's a big,
+big, [INAUDIBLE]
+
+DAVID KAISER: The American
+people are fighting the
+
+wilderness, physical
+and moral.
+
+So, you wonder what that,
+physical wilderness is
+
+obvious, moral probably is
+referring to the, I would
+
+imagine, the Western
+wars and--
+
+PROFESSOR: Yeah.
+
+DAVID KAISER: --fighting the--
+
+PROFESSOR: Indians.
+
+DAVID KAISER: --Native
+Americans there.
+
+And that's his vision
+of the battle.
+
+At the same time, trying to work
+out the awful problem of
+
+self government.
+
+So he's tying these basic ideas
+about education to both
+
+the physical state of the
+country, and also the
+
+ideological and government
+state of the country.
+
+PROFESSOR: One thing to note
+in all that is that William
+
+Tecumseh Sherman was a very
+famous Civil War general, he's
+
+the one that burned Atlanta,
+and did the famous march to
+
+the sea, was asked during the
+1870's, what he thought about
+
+the quote "Indian problem"
+Here's this movement west, and
+
+the part of white settlers.
+
+He says, nothing to worry
+about, we're building
+
+railroads in the West and that's
+driving a stake into
+
+the heart of the American
+Indian, or
+
+something like that.
+
+That was going to do them in,
+is the engineering of these
+
+new railroad technologies, is
+just going to overwhelm them,
+
+and it did basically.
+
+DAVID KAISER: So down in the
+bottom of that column he talks
+
+about all these frustrations,
+but he knows the greatness of
+
+the material prizes to be won.
+
+So it's not an appeal for moral
+elevation necessarily,
+
+or this and that.
+
+It's an appeal for material
+prizes, which is very much on
+
+the mind of Americans,
+since the founding
+
+On the next page, just
+interesting phrases on the top
+
+left, on 204, These old ways
+have trained some boys well,
+
+for the life of 50 or 100 years
+ago, And the American
+
+will not believe that they are
+applicable to his son.
+
+For the reason that the kind of
+man which he wants a son to
+
+make, did not exist in all
+the world 50 years ago.
+
+This was 1869, and somebody
+mentioned in one of their
+
+response papers that they
+appreciated, from the reading,
+
+how close the revolution still
+was, in that most of the
+
+fathers of these people would
+have been directly involved in
+
+it, which is correct.
+
+So, 50 or 100 years ago
+there's been all this
+
+political upheaval and America
+was a very agrarian society,
+
+but everywhere was, and he's
+really referring to what we
+
+now call the Industrial
+Revolution there.
+
+Entirely new kind of people
+are required.
+
+Then also down in that column,
+I think this is very
+
+interesting too, it requires
+courage to quit the beaten
+
+paths in which the great
+majority of well educated men
+
+have walked, and still walk.
+
+So he's basically saying, and
+you even still hear this to
+
+some degree today, the MIT
+graduates especially if
+
+they're successful, will enter
+a world where everyone knows
+
+Latin and Greek.
+
+Everyone knows different
+kinds of history.
+
+Everyone is going to be
+extremely well versed in
+
+theology, and these other
+things, and MIT graduates, for
+
+the most part, won't be.
+
+But he refers to it as courage
+to go into that world with
+
+this new kind of training,
+because it will be so rare, it
+
+certainly was rare
+at the time.
+
+Frankly, it's still rare, as
+you'll find what you graduate.
+
+And that he talks about
+a special kind of
+
+courage that's required.
+
+And down at the end or that
+paragraph, even more, a boy
+
+who was brought up in a
+different way suffers
+
+somewhat, both in youth and
+in manhood, from the mere
+
+singularity of his education,
+though it may have been better
+
+than the common.
+
+I found that really interesting
+to read.
+
+I never thought about this
+kind of education as
+
+courageous, or the kind of
+people who are educated, as
+
+taking that on.
+
+Because you will be an anomaly,
+you may not be if you
+
+go work for a very highly
+technical corporation in the
+
+engineering part.
+
+But, most corporations, even
+the very highly technical
+
+ones, as you rise up the people
+are less and less
+
+engineering educated, not
+to mention in the
+
+general social world.
+
+Then he talks a little bit about
+the organization that
+
+Roe mentioned on the
+next column.
+
+A large number of professors
+trained in the existing
+
+methods, hold firm possession
+and transmit the traditions
+
+they inherited.
+
+And I just thought that was an
+interesting word, inherited.
+
+Because again, he's kind of
+trying to overthrow European
+
+model of inheritance, comes back
+to that in a minute, and
+
+again the American model
+is one of earning it.
+
+And he talks here about how
+stodgy these old systems are,
+
+backed by the reputation of
+their authors and the capital
+
+of their publishers.
+
+Steadily fed by schools whose
+masters are inspired, these
+
+are the older schools, and
+all the so-called learned
+
+professions, I love that
+kind of language.
+
+Again, I think that's really a
+dig at, probably, both the
+
+clergy and the legal
+profession, maybe
+
+some others as well.
+
+Also, makes a distinction
+between, it's an interesting
+
+thing about, that none of the
+MIT founders have any problem
+
+teaching languages.
+
+Which is interesting because one
+of the few things that was
+
+required then, that's not
+required now, which I'm not
+
+sure is the greatest idea, but
+it's the living languages
+
+versus dead languages.
+
+Especially, then if you don't
+read French and German, you
+
+can't read engineering
+literature basically.
+
+It's not so true today.
+
+German was, for many years, the
+real classic engineering
+
+literature.
+
+But just not Latin and Greek.
+
+And then there's a great line on
+the top of the 205 where he
+
+talks about, again, the
+old style educators.
+
+To have been a school master or
+college professor 30 years
+
+ago only too often makes a man
+an unsafe witness in matters
+
+of education.
+
+It Is just a great metaphor.
+
+There are flanges on his mental
+wheels which will fit
+
+only one gauge.
+
+What is that a reference to?
+
+It's a railroad analogy.
+
+So he's using these sort of
+technical analogies to make
+
+his point about the education.
+
+Then he talks here, again, also
+sort of a dis at the kind
+
+of great professor model
+of education.
+
+In no country is so little
+attention paid by parents and
+
+students to the reputation of
+teachers for genius and deep
+
+learning as in our
+own country.
+
+Faradays, Rumfords,
+and Cuviers--
+
+these are the famous European
+professors--
+
+would get very few pupils here
+if they're teachings were
+
+unmethodical and objectless.
+
+If, in short, they taught under
+a bad general system.
+
+Spasmodic and ill-directed
+genius cannot compete in the
+
+American community with
+methodical, careful, teaching
+
+by less inspired men.
+
+Very interesting argument
+to make.
+
+I'm not sure if everyone would
+agree with that today
+
+necessarily, but obviously we
+don't want to have spasmodic
+
+and ill-directed directed
+genius in
+
+front of the classroom.
+
+But, it really is very much
+an argument about order in
+
+education and sort of focus
+on what's empirical.
+
+And I think that's a really
+important component of a lot
+
+of the background here, we
+haven't said anything about
+
+the Enlightenment yet,
+in this class.
+
+Anybody heard that
+phrase before?
+
+Usually associated with the 18th
+century, late 17th, most
+
+of the 18th century, into
+the early 19th.
+
+But, one of the great focuses
+of the Enlightenment is
+
+empirical learning, not just
+theorizing, not just the sort
+
+of platonic philosophy of
+working as the ancients
+
+through a set of reasoned
+arguments, but, actually
+
+gathering data from the world.
+
+Now, what's interesting about
+that, is there's sort of a
+
+split that you observe where
+if you look at someone like
+
+Louis Agassiz who Roe has
+mentioned, the great Harvard
+
+natural history professor at
+the time, very much an
+
+enlightenment empiricist, in the
+sense of Natural History.
+
+Has anybody been over to
+the Harvard Natural
+
+History Museum lately?
+
+What kind of a museum is it?
+
+AUDIENCE: It has
+a lot of rocks.
+
+DAVID KAISER: OK,
+a lot of rocks.
+
+What else?
+
+AUDIENCE: [INAUDIBLE]
+
+DAVID KAISER: What?
+
+Animals.
+
+It's a kind of, old-fashioned,
+glass case museum.
+
+Right?
+
+Very typical, not what you'd
+find, I was just at the
+
+Natural History Museum in New
+York, which is used to be that
+
+kind of museum, and still has
+pieces of it, but is a very
+
+different kind of museum.
+
+But the Harvard museums are sort
+of lovely and wonderful
+
+in this way, but there's cases
+and cases of specimens,
+
+whether they're , plants, or
+stuffed animals, what's the
+
+correct word?
+
+Taxidermy.
+
+I brought my daughter there
+actually, she liked the
+
+stuffed animals.
+
+Animals, plants, geological
+specimens, and that's very
+
+much the kind of natural
+historical world that Louis
+
+Agassiz represented.
+
+There, the empirical philosophy
+was one of
+
+collecting, ordering the
+collection, everything's very
+
+carefully labeled.
+
+Very carefully name with a
+very fancy Latin name.
+
+Often then numbered, drawers and
+drawers, taking the world
+
+classifying it, putting
+it into a hierarchy.
+
+You're familiar with the
+Linnaean hierarchy of the
+
+natural world.
+
+Very much an enlightenment
+practice, but slightly more,
+
+kind of, 18th century version
+of it that Agassiz, sort of,
+
+still represents into
+the 19th century.
+
+Rogers, in his reaction against
+that, is in a way,
+
+kind of even further, more
+radical enlightenment.
+
+What's different about the kind
+of world that he would
+
+think about?
+
+Let me give you an example that
+maybe you could set off.
+
+I was reading last night an
+example of a student who said,
+
+when I went to work for
+Louis Agassiz at
+
+Harvard as a student.
+
+Basically, he locked me in a
+room with 500 tortoise shells
+
+and no supporting anything, and
+my job was to discern the
+
+inherent truth of nature that
+was collected in those
+
+tortoise shells.
+
+What's the kind of world, the
+way that Rogers and an MIT
+
+approach to that problem
+might use?
+
+It's also very empirical,
+collecting
+
+information from the world.
+
+So it's not that what
+he's reacting
+
+against is not empirical.
+
+Well first of all, intervention
+by active
+
+experiments.
+
+You're not just collecting the
+world and putting it in glass
+
+cases, you're often physically
+out in it, collectors were
+
+doing that too, but your making
+changes to it, putting
+
+things on, and also enhancing
+your senses by using
+
+instruments.
+
+He was a great fan, Rogers, of
+new kinds of instrumentation
+
+and the uses of these kinds
+of instruments.
+
+They might be spectroscopes,
+spectrographs, or obviously
+
+microscopes, but other kinds
+of photometers and things.
+
+And a much more kind of, you
+might call it high-tech in a
+
+way, but also very active
+intervention in the world of
+
+nature, the physical world, the
+things you're going into.
+
+It's not a world of collecting
+and classifying, and
+
+discerning this inherent
+underlying truth from.
+
+It's a world of very active,
+and again, as much for the
+
+students as for the researchers
+in his world.
+
+Which says something about
+why he was such
+
+an admirer of Darwin.
+
+Yeah, very much so.
+
+PROFESSOR: It's a world
+that's evolving.
+
+DAVID KAISER: There's a nice
+story, which we haven't really
+
+told about, when Rogers finally
+gets the charter for
+
+MIT, and the war starts.
+
+And Massachusetts gives him
+one year to come up with
+
+$100,000, which is then later
+extended to two years and he
+
+almost doesn't make it except
+for this big gift from
+
+[? Walker ?].
+
+And so he's figured, OK great,
+now I'm off and running, I've
+
+got all this time, the war is
+probably going to delay our
+
+plans a minute I can just
+go raise money.
+
+And the governor comes back to
+him and says, oh, and by the
+
+way, I would really like
+you to become the
+
+inspector of gas in Boston.
+
+And gas, at the time, is the
+new high tech way to light
+
+your home, and it's a
+technological systems, there
+
+are pipes being run under
+the streets in the city.
+
+But it's very dangerous,
+because as still
+
+today, gas is explosive.
+
+Probably every few months, a
+house in the Boston area blows
+
+up because of a gas leak.
+
+And Rogers says, no way,
+I can't take the
+
+time out to do this.
+
+This is crazy.
+
+And the governor calls him in
+for a one on one, and we don't
+
+really know what was said,
+but he walks out of there
+
+convinced that he's
+going to do it.
+
+So he takes on this job.
+
+And soon he finds that the
+instruments that he's been
+
+given to inspect the gas,
+probably the quality of the
+
+gas, and different chemical
+composition of it, and the
+
+different illuminating
+capabilities, and maybe
+
+measure leaks and things
+for safety, are
+
+inadequate for him.
+
+So he re-engineers, and
+re-designs a number of the
+
+instruments.
+
+And then he begins to see that
+this is actually a very
+
+valuable thing for him because
+he uses the states money to
+
+buy the latest instrumentation.
+
+He has very close contact with
+industry, and it gives him
+
+insight into what the latest
+kinds of instrumentation
+
+should be that the students at
+MIT, that he would then buy
+
+for the laboratories as
+they're outfitting
+
+laboratories.
+
+And it's a nice little story,
+partly because of the kind of
+
+ethos of presidents of MIT doing
+national service, or in
+
+that case they service, which is
+something we'll talk about
+
+later, starts at
+the beginning.
+
+But also because it gets him
+out in the world, get him
+
+involved, and he's very much
+a fan of instrumentation.
+
+Even though you think about
+geology in the 1830's and '40s
+
+is not a ton of instrumentation
+associated
+
+with that, although certainly
+there is in surveying.
+
+It gives you the sense of him as
+not simply a scientist, but
+
+also quite a tinkerer.
+
+A couple other things to point
+out in Elliott essay.
+
+I found it interesting because
+I actually went to Yale as an
+
+undergrad, and studied
+engineering.
+
+So, I could see why he thought
+that was all the wrong model,
+
+although he praises
+it a little bit.
+
+But, at Yale the school he was
+writing about, The Sheffield
+
+Scientific School, which was
+a very famous science and
+
+engineering school, doesn't
+exist anymore.
+
+It was closed down by the Yale
+faculty in the 1950s.
+
+So, it sort of supports his case
+that, that kind of model
+
+and The Lawrence Scientific
+School doesn't existent at
+
+Harvard either anymore, that
+that kind of model is the
+
+wrong model, and not really
+destined survive as a second
+
+class citizen there.
+
+But there are a couple other
+interesting pieces I
+
+want to point out.
+
+He talks on page 215 about, and
+this a good reminder, 216
+
+on the bottom and the left,
+he says, when the American
+
+University emerges, it will
+not be a copy of foreign
+
+institutions or a
+hotbed plant.
+
+But the slow and natural
+outgrowth of American social
+
+and political habits.
+
+An expression of the average
+aims and ambitions of the
+
+better educated classes.
+
+That's interesting because you
+think we've been spending all
+
+of our time you're talking
+about the emergence of an
+
+American university, and the
+whole issue vis a vis Harvard.
+
+What is he referring to there?
+
+Well, it's worth keeping in
+mind that everything we've
+
+been talking about, so far, is
+really about college teaching.
+
+Harvard College is still Harvard
+College at the time.
+
+I don't know when they changed
+their name to Harvard
+
+University.
+
+He says the American college
+is an institution without a
+
+parallel, the American
+University future tense, will
+
+be equally original.
+
+MIT is not a university then
+either, some people think it
+
+isn't today, but I don't think
+that's really right.
+
+But what's the difference
+between a college and
+
+university?
+
+Simple crude distinction.
+
+AUDIENCE: [INAUDIBLE]
+have more colleges.
+
+DAVID KAISER: Sorry?
+
+AUDIENCE: Universities have
+[? several ?] colleges.
+
+DAVID KAISER: Some
+do, not all.
+
+Graduate education.
+
+So that's actually the first,
+does anybody know what the
+
+first university is in
+the United States?
+
+Johns Hopkins actually.
+
+And it's founded late 19th,
+early 20th century.
+
+Where you really have the idea
+that there's research and
+
+graduate education, combined
+with a college.
+
+So it's just worth keeping
+that in mind, as we move
+
+forward in time, and MIT does
+become a university.
+
+I mean if you read rankings,
+everybody thinks of it as a
+
+university.
+
+There are people here still who
+say, no it's a technical
+
+institute, it's not
+a university.
+
+I don't think there's really
+too much to be argued for
+
+that, but arguably MIT only
+really became our university,
+
+in that sense, about
+20 years ago.
+
+It's not an old thing.
+
+But the graduate model, the
+American University that he is
+
+referring to, is really still
+40 years away when he's
+
+writing this in 1869.
+
+Then I just thought there was a
+great passage on 218, on the
+
+right column, which also
+have an amazing,
+
+and truly MIT metaphor.
+
+People who think vaguely about
+the difference between a good
+
+college and a good Polytechnic
+school are apt to say, that
+
+the aim of the college course is
+to make a rounded man, with
+
+all his faculties impartially
+developed.
+
+While it is to express object of
+a technical course to make
+
+a one sided man, the mere
+
+engineer, chemist, or architect.
+
+Two truths are supported in
+this form of statement.
+
+First, faculties are
+not given by God.
+
+Sorry, two truths
+are suppressed
+
+in this form statement.
+
+He was arguing against it.
+
+First, faculties are not given
+by God impartially, to each
+
+round soul a little
+of each power.
+
+As if the soul were a pill,
+which must contain it's due
+
+proportion of many variance
+ingredients.
+
+To reason about the average
+human mind as if it were a
+
+globe, to be expanded
+symmetrically from a center
+
+outward, is to be betrayed
+by metaphor.
+
+Then I love this.
+
+A cutting tool, a drill, or an
+auger would be a juster symbol
+
+of the mind.
+
+If there's not a great
+MIT statement, I
+
+think it's that one.
+
+PROFESSOR: That's good.
+
+DAVID KAISER: The natural, best,
+and particular quality
+
+of everybody's mind
+should be sacredly
+
+regarded in his education.
+
+The division of mental labor,
+which is essential in
+
+civilized communities, in order
+that knowledge may grow
+
+and society improve, demands
+this regard to peculiar
+
+constitution of each mind,
+so on and so forth.
+
+But I think, in some way, that's
+also a nice statement
+
+of the case for MIT, in
+an intellectual sense.
+
+That, not everybody agrees with
+it by any stretch, but
+
+that the model of the mind is
+the cutting tool, or the
+
+drill, or the auger.
+
+Those of you, all of you, who
+are here as undergrads could
+
+probably feel maybe your mind
+as being expected to behave
+
+that way on a regular basis,
+honed finely and sharpened.
+
+So, I sort of thought
+it was worth going
+
+through some of this.
+
+It is a difficult
+piece to read.
+
+It's written in this, sort of,
+19th century English which can
+
+be hard to read, but it's
+actually a very rich piece,
+
+and he's got a very strong
+opinions, and some of them I
+
+think are still valuable.
+
+I did exactly what he thought
+was a bad idea.
+
+Which was I did both a literary
+education and
+
+engineering education
+at the same time.
+
+And given that there's only 24
+hours a day, it's very hard.
+
+I always my students it's not
+hard to do a double major,
+
+it's just twice the work.
+
+Which is sort of true, but
+inevitably there are
+
+compromises on either side.
+
+And the question is, what's
+the benefit versus what's
+
+lost, I think it probably
+depends on the individual and
+
+what you see.
+
+I think in all this
+conversation, right, don't
+
+forget that the people who run
+this world are still more
+
+Harvard graduates that
+MIT graduates.
+
+OK.
+
+There is something about that
+model, you go over to Harvard
+
+and you see Teddy Roosevelt,
+and Franklin Roosevelt, and
+
+John F Kennedy, and any number
+of US presidents who have been
+
+Harvard graduates.
+
+And any number of Harvard
+graduates who are in Congress,
+
+and the Senate, and the Supreme
+Court, at any given
+
+time, far out way, and even
+arguably at the top echelons
+
+of corporations,
+MIT graduates.
+
+And it is worth thinking about
+why that is, and why it hasn't
+
+been different in the last
+150 years, that way.
+
+So what we're reading is the
+argument of the people who
+
+founded MIT, and there's
+no question that in the
+
+scientific and technological
+world MIT graduates have been
+
+great leaders, and actually in
+other countries they are more
+
+likely to be found as presidents
+or top political
+
+leaders than they are
+in this country.
+
+There are many other countries
+where engineering is a much
+
+higher prestige profession,
+relatively
+
+speaking, than it is here.
+
+And there's reasons for
+that, historically.
+
+Even in France, for example,
+the polytechnic graduates
+
+really are the people who
+populate the upper echelons of
+
+the government.
+
+That may be changing now
+in the last 20 years.
+
+But it has not been changing
+dramatically.
+
+And so there's a lot of
+reasons for that.
+
+And it's a whole other
+conversation to have.
+
+But it is interesting to think
+about what it really takes to
+
+train people to be leaders and
+how well are we doing at that?
+
+Or how well does Eliot's
+model do that?
+
+I think the general principle
+of it really does go back to
+
+the beginning.
+
+There has always been a fair
+amount of English history,
+
+management sort of stuff,
+languages, again.
+
+Languages, were considered,
+frankly, they probably should
+
+still be considered, a core part
+of a technical education.
+
+Because we go around as MIT
+saying we're training global
+
+leaders and to do that and not
+have a language requirement
+
+for the undergraduates is a
+little bit missing the mark.
+
+That's my opinion.
+
+And I'm not someone who's good
+with languages at all.
+
+But many colleges have language
+requirements, and it
+
+probably would be, as someone
+pointed out, more Chinese than
+
+German today.
+
+That's fine.
+
+That's the way the
+world is going.
+
+But whatever people
+took would surely
+
+benefit them in the world.
+
+But the actual school of
+humanities and social sciences
+
+was founded in 1949.
+
+We just celebrated, well just,
+10 years ago, we celebrated
+
+the 50th anniversary
+of the school.
+
+And the actual eight courses,
+I believe, dates from then.
+
+And that was a product, and
+we'll come across this, and
+
+we'll read the report that the
+so-called Lewis Commission
+
+wrote at the end of World War
+II, which really did a lot of
+
+introspection about what kind
+of place is MIT becoming.
+
+There's all this military
+research, there's all this big
+
+time research on campus.
+
+What do we really owe
+our students?
+
+And you all know that you have
+eight required HASS courses.
+
+That's quite a bit larger than
+most comparable technical
+
+institutions like Caltech
+and RPI, Georgia Tech.
+
+It's usually lower.
+
+Certainly overseas at technical
+institutions it's
+
+close to zero.
+
+And so it is a much bigger
+component of it and arguably
+
+why MIT can consider itself now
+among the top ranks of the
+
+universities.
+
+If you asked people at MIT
+20 years ago, who are our
+
+competitors?
+
+They'd say Caltech, Georgia
+Tech, RPI, The Royal
+
+Institute, ETH in Zurich
+and so on.
+
+Now, people will say Harvard,
+Yale, Stanford, Princeton.
+
+And that's really only in the
+last 20 years that I know as
+
+we compete for undergraduates,
+most students who say no to
+
+MIT as undergrads,
+where do they go?
+
+AUDIENCE: [INAUDIBLE]
+
+Harvard?
+
+DAVID KAISER: No, Stanford is
+the place where you lose the
+
+most people to.
+
+So that's a good measure of who
+you think you're competing
+
+against when you accept the
+student, and they say no,
+
+where are they going?
+
+Far fewer do we lose
+to Caltech or
+
+RPI or Georgia Tech.
+
+That's true--
+
+AUDIENCE: Does that also
+have to do with
+
+the size of the school?
+
+Like Stanford is a larger
+school than Caltech.
+
+DAVID KAISER: It may well.
+
+But Stanford is a very different
+place from Caltech.
+
+And so Caltech is a very small
+college, as you know.
+
+It's really, still is, in
+many ways a college.
+
+Other questions?
+
+Comments from the reading?
+
+AUDIENCE: [INAUDIBLE] you
+mentioned before that
+
+[INAUDIBLE] college
+and universities.
+
+So how did graduate education
+work for people in the 19th
+
+century here, or how did
+it work in Europe?
+
+Was there a lot of advanced
+degrees [? conferred?]
+
+in physics or what not?
+
+DAVID KAISER: Well, up into the
+1920's, certainly in the
+
+sciences, if you wanted to get a
+Ph.D, you went to Germany or
+
+to Europe in general, England,
+France as well.
+
+And so if you look at the MIT
+faculty in the sciences in the
+
+teens and '20s, most of them
+would probably have European
+
+educations at the
+graduate level.
+
+That was not just because of
+what programs were available
+
+but also because
+of the quality.
+
+It was really the German
+universities in physics that
+
+were the main thing.
+
+That begin to change during
+the decades before the
+
+second World War.
+
+Not least when a lot of European
+professors came here.
+
+But PhDs in engineering, I mean
+you don't even see them--
+
+MIT did not--
+
+I know Vannevar Bush, who
+graduated with a Ph.D in 1916,
+
+I believe, that was MIT's fifth
+Ph.D in engineering.
+
+So a 20th century phenomena
+to be sure.
+
+And, again, engineering was
+considered a useful art.
+
+A Ph.D was considered a high,
+scholarly calling.
+
+And there was a lot of ferment
+in and around I want to say
+
+1890 to 1905 or so.
+
+University of Chicago
+was big in that.
+
+They hired--
+
+it was in Worcester, Clark
+University used to have all
+
+these famous people.
+
+Robert Goddard was there
+for a while and so on.
+
+And now it's sort of a little
+university in a way.
+
+Why?
+
+Because the University of
+Chicago came in with a lot of
+
+money and hired away all their
+people around 1910, I believe.
+
+So it's very much a 20th
+century thing.
+
+PROFESSOR: I was thinking about
+Warren Lewis who is the
+
+author of the report David
+referred to that established
+
+the humanities requirement
+at MIT.
+
+He was a chemical engineer.
+
+And he joined the MIT faculty
+around 1910, 1911 after doing
+
+his Ph.D in Germany.
+
+And so he's right at the
+borderline, I think.
+
+And he's very much responsible,
+in a way, for not
+
+just revolutionizing
+undergraduate education after
+
+World War II but also being
+involved in the establishment
+
+of doctoral programs at MIT.
+
+After the arrival of Karl
+Compton which is 1930 that--
+
+Compton is a physicist who came
+to MIT from Princeton and
+
+comes out of a background at
+which doctoral education is
+
+important to him.
+
+And so he supports that.
+
+And then it really grows, I
+think, during his presidency
+
+and then beyond.
+
+But Lewis is a really
+interesting person.
+
+To think that here's a chemical
+engineer who is
+
+talking so strongly about the
+need for humanities education
+
+at a technical university,
+basically, or a technical
+
+institute is very interesting.
+
+His granddaughter is a
+colleague of ours.
+
+And I think she's coming to
+give a talk about him.
+
+He's extremely interesting, he's
+one of these key people
+
+at MIT in the 20th century
+that had his
+
+hand on a lot of things.
+
+DAVID KAISER: You would not find
+MIT faculty mostly having
+
+PhDs until probably
+also about 1920.
+
+Arthur Kennelly is either the
+first or one of the first
+
+electrical engineering
+professors here and really
+
+kind of founds the department.
+
+He was Bush's advisor.
+
+Where did he come from?
+
+He worked in Thomas
+Edison's lab.
+
+I don't believe he had a Ph.D.
+And Edison really started this
+
+model of industrial research
+around the 1890s.
+
+And that was what brought
+people back in.
+
+PROFESSOR: Is that it begins to
+happen after World War II
+
+mainly because so much
+important research
+
+was going on here.
+
+And big laboratories were
+established after World War II
+
+or during and after World War
+II that would have enhanced
+
+graduate education.
+
+And as a result, when
+you're educating the
+
+best, you hire them.
+
+I think that's how it happened,
+especially in the
+
+School of Engineering which has
+had a fairly long track
+
+record of hiring its own.
+
+If you're producing the best,
+you try to hire the best.
+
+And so I would guess, it's
+a guess, I don't have the
+
+answer, but I would guess that
+it's right after World War II
+
+that you begin to see it.
+
+DAVID KAISER: So I would give
+you a different answer.
+
+I would guess that
+it was earlier.
+
+Because, again, if you read
+all the stuff like in
+
+Elliott's piece about why the
+institution not only needs to
+
+be what it is, but it needs
+to be autonomous.
+
+I often think of it as a kind
+of sign of MIT's arrogance
+
+like nobody else in the
+world is good enough.
+
+So we have to hire
+our own students.
+
+But you read this sort of stuff,
+and you see it's part
+
+of the culture in that when
+they're on the cutting edge of
+
+either a field or just generally
+of the types of
+
+teaching that you're doing then
+you really, it's very
+
+hard to find people from
+elsewhere who are doing that.
+
+PROFESSOR: So, you would say
+it's during the Compton years
+
+starting in the '30s
+or there abouts?
+
+Or even before that?
+
+DAVID KAISER: I would imagine
+it's before that with hiring
+
+instructors.
+
+Not sure about that.
+
+PROFESSOR: That's interesting.
+
+DAVID KAISER: Obviously,
+it's not so early on.
+
+But I bet as soon as they become
+the right age, it's
+
+something that gets done.
+
+It can't be something that's
+done that often without some
+
+traditions behind it.
+
+A lot of universities
+won't do it at all.
+
+Although, here, I was talking to
+someone in Economics, they
+
+won't hire their own graduates
+on the faculty until they've
+
+gone away for a year or
+two, and then they
+
+will hire them back.
+
+So, they have a rule that you
+cannot come out of your Ph.D
+
+and join the faculty.
+
+But you go somewhere else for
+a little while and then you
+
+can come right back.
+
+And many of their faculty
+have PhDs from here.
+
+PROFESSOR: Not a bad rule.
+
+Not to my knowledge.
+
+I don't think there is
+a big difference.
+
+It's basically a play on the
+same word, technic but
+
+preceded by poly means many.
+
+Basically, it's perhaps
+a reference to a
+
+more diverse approach.
+
+I don't know.
+
+You're asking good questions.
+
+I don't have the answers.
+
+DAVID KAISER: I think it's
+just what you said.
+
+I think polytechnic, especially
+at this time, has a
+
+little more European
+connotation.
+
+The French schools really are,
+they are called polytechnique.
+
+And they have a certain
+way of being that.
+
+West Point was modeled after
+much of, but probably not so
+
+all of, in that they're
+very connected in
+
+the political system.
+
+And there's a very sort of well
+understood hierarchy for
+
+the alumni to go through and run
+the big bureaucracies and
+
+the government.
+
+And there are polytechnic
+schools in this country.
+
+There's California Polytechnic,
+there's Brooklyn
+
+Polytechnic.
+
+And I think it's really
+those are not--
+
+there's no meaningful
+distinction from them from MIT
+
+or Caltech.
+
+It's a kind of term,
+connotation.
+
+PROFESSOR: The other thing
+that's relevant to that is
+
+that Rogers, Charles Eliot,
+William Ware in architecture
+
+all spent time in Europe,
+especially in France during
+
+the founding years of MIT, late
+'60s early '70s, looking
+
+at European universities and, to
+a degree, German technical
+
+institutes.
+
+And so they're influenced by
+these European organizational
+
+models, if you want
+to call it that.
+
+They don't copy them directly.
+
+But they surely are looking
+and trying to find niches
+
+where certain parts of the
+French educational system fit
+
+in to the MIT model and
+stuff like that.
+
+They're borrowing.
+
+They're definitely borrowing
+ideas as they should.
+
+And so those influences are
+very much in evidence
+
+especially during
+the early years.
+
+DAVID KAISER: It's worth
+mentioning a phrase that may
+
+come up which is technocrat.
+
+Has anybody ever heard
+that phrase?
+
+PROFESSOR: Technocrat.
+
+DAVID KAISER: You'll hear it
+used from time to time.
+
+And, again, technocracy is a
+sort of funny social movement
+
+from the '20s.
+
+It's not quite worth
+talking about.
+
+But people do talk about
+technocrats when they're
+
+technically trained people who
+are in high positions of
+
+bureaucracies of one kind or
+another and bring a sort of
+
+technical mentality to running
+a large organization.
+
+And, again, in France, the
+technocratic tradition is a
+
+very old tradition where the
+leaders of the polytechnic go
+
+into the UN, they go into the
+various civil bureaucracies,
+
+and it's the big government
+institutions are very much run
+
+by people with technical
+backgrounds.
+
+It's just not a tradition
+in the US that has
+
+been nearly so much.
+
+And so we'll come across it when
+we talk about the '60s
+
+like Robert McNamara who ran
+the Pentagon during the
+
+Vietnam War is not an MIT
+
+graduate, he's not an engineer.
+
+But he was a very technical
+person, very mathematical.
+
+He was a sort of prototype
+technocrat.
+
+But most leaders of the Pentagon
+are not technical,
+
+most of them are political in
+background and have very
+
+different kinds of skills and
+approaches to the world.
+
+Robert Seamans, who we'll talk
+about as well, who was an MIT
+
+graduate and kind of led the
+chief engineer on the Apollo
+
+program and Secretary of the
+Air Force and the first
+
+Secretary of the Energy was
+much more in a kind of
+
+technocratic role where he had
+this kind of background.
+
+And so you'll see some of
+it in the US setting
+
+but not that much.
+
+Whereas, again, the
+polytechniques and the English
+
+system doesn't really work
+that way either.
+
+They have their own civil
+service system and engineers
+
+are not particularly high up.
+
+PROFESSOR: Seamans is one of
+these MIT trained engineers,
+
+comes from an old New England
+family as I understand it, but
+
+who really reached in
+the higher echelon.
+
+He wasn't a politician, but he
+ran a number of agencies and
+
+really was a person of
+considerable influence.
+
+He's only been dead, what?
+
+Three years, four years?
+
+DAVID KAISER: One or two.
+
+Has anyone heard that name?
+
+Robert Seamans?
+
+PROFESSOR: Robert
+Seamans, aero?
+
+DAVID KAISER: We'll
+come across him.
+
+PROFESSOR: I'm so sorry he's
+not still alive to come and
+
+visit this class because
+he was quite--
+
+DAVID KAISER: He's an
+interesting story.
+
+You know we haven't also
+mentioned huge issue of social
+
+class between Harvard and MIT.
+
+And all of this stuff that we're
+reading has buried in it
+
+the sort of MIT attitude that
+Harvard is for elites, and the
+
+Harvard attitude that MIT
+is for vocational
+
+middle class workers.
+
+And that runs throughout
+all this history.
+
+And Seamans came from this very
+old New England family,
+
+comes from a family on
+the North Shore.
+
+And he went to Harvard as an
+undergrad, in fact he was
+
+classmates with John
+F. Kennedy.
+
+And I think he maybe took one
+course, or he had a friend who
+
+was doing something at MIT,
+and he got really
+
+interested in MIT.
+
+And he wanted to come here
+for graduate school.
+
+And he writes in his memoirs
+about how his parents said,
+
+no, no, no, fine boys from our
+background don't go to MIT,
+
+that's not what they do.
+
+Go, study science at Harvard.
+
+And he rebelled against that and
+really said, no I really
+
+want to go to MIT.
+
+And he did amazingly
+well here.
+
+But when time came for him to
+advance in his career, he was
+
+certainly helped by the fact
+that he had this advanced
+
+social background when he
+went back to Washington.
+
+And, again, he was rubbing
+elbows with JFK and all the
+
+senior leadership during
+that period.
+
+And he was socially very
+well suited for it.
+
+So he was a little
+bit unusual as an
+
+engineer during that period.
+
+PROFESSOR: About every 20 years,
+there's a discussion
+
+that pops up in the MIT
+community about why doesn't
+
+MIT have as many CEOs as Harvard
+or Princeton or--
+
+and a lot of it centers around
+what David has just said is
+
+that if you look at the social
+backgrounds of CEO's, the
+
+majority of them come out of
+backgrounds like Seamans.
+
+They come out of well-to-do,
+socially placed families.
+
+And so there's this generational
+movement that you
+
+went to Harvard, and you're from
+an old family, and you
+
+have an interest in the company,
+you become the CEO at
+
+some point.
+
+I think there's a lot
+of truth to that.
+
+And MIT, I think, has been
+more of a place that has
+
+attracted socially mobile
+students from middle class
+
+backgrounds, sometimes working
+class backgrounds,
+
+oftentimes, I think.
+
+And which is one of the great
+things about the place, I
+
+think, is that--
+
+DAVID KAISER: The fraction of
+our students who are the first
+
+generation of their family
+to go to college, even
+
+today, is very high.
+
+A lot of children
+of immigrants--
+
+PROFESSOR: I think there's a
+very old cultural influence
+
+involved in all of this in the
+sense that during the 19th
+
+century when we're talking about
+the founding of MIT, one
+
+of the tensions of that period
+in the academic world was
+
+between what groups we'll call
+Ancients versus Moderns.
+
+And the Moderns would be the
+type of school like MIT that
+
+was emphasizing science and
+engineering as opposed to the
+
+Ancients, which were the old
+classical colleges teaching
+
+Greek and Latin and all the
+classics and literature and
+
+things like that.
+
+There was a lot of
+tension there.
+
+And it also had class
+implications that you were
+
+educating people on the classics
+to be gentlemen and
+
+ladies and things like that.
+
+Whereas people coming to the
+MIT were people that were
+
+going to go out in the world
+and engineer that world or
+
+pursue science in that world.
+
+It was a much more utilitarian
+oriented disposition, I think,
+
+which is very American in
+many ways because early
+
+sociologists, I guess you could
+call them, people like
+
+Alexis de Tocqueville, who
+visited the United States in
+
+the 1830's and wrote a very
+famous treatise called
+
+Democracy in America, asks a
+lot of questions about what
+
+makes the United States
+what it is.
+
+Why is it different
+from Europe?
+
+That's one interesting questions
+he's asking.
+
+One of the answers he gives is
+that these Americans are so
+
+utilitarian oriented.
+
+They are very oriented towards
+things that work, things that
+
+are put to work in society.
+
+Where as you don't see as
+much of that in Europe.
+
+That was one of his most
+important statements about the
+
+difference between Europe and
+the United States, is
+
+Americans like utility.
+
+They like things that work.
+
+They like to get out and tinker
+around with stuff.
+
+He also talks about literacy
+in the United States being
+
+higher than it is in Europe.
+
+And that being a more literate
+nation meant that the United
+
+States was more apt to be
+inventive and pursue areas of
+
+engineering and science
+that others would be
+
+less involved with.
+
+DAVID KAISER: It arguably is.
+
+Which I'm not so
+sure, German--
+
+PROFESSOR: Maybe.
+
+DAVID KAISER: I'm not so sure.
+
+Where it is also is very much
+in developing countries even
+
+in the Middle East and lots of
+places where MIT has had an
+
+influence actually setting
+up engineering schools.
+
+But I'll give you one example,
+a lot of wealthy American
+
+families, they send their
+brightest kid to Harvard and
+
+may become a lawyer or other
+place and become a lawyer.
+
+I used to spend a lot
+of time in Turkey.
+
+And I worked with some people
+who were very wealthy and ran
+
+a lot of big international
+trading which is an old
+
+Turkish kind of profession.
+
+And these were the very
+few, very elite
+
+families in that country.
+
+And the people who were my age
+who were really the ones
+
+running and soon to inherit
+the business, they had all
+
+gone to American engineering
+schools and
+
+gotten American MBA's.
+
+That was their education.
+
+And I was once at a conference,
+and I sat next to
+
+a guy who was a deputy oil
+minister from Iran, which I
+
+don't meet a lot of
+Iranian government
+
+officials in my work.
+
+And I was sort of like, this
+will be an interesting
+
+conversation with the two of
+us are going to talk about.
+
+And he was like, you're
+from MIT?
+
+I went to the Iranian Institute
+of Technology, it
+
+was all founded on
+MIT's principles.
+
+And he was incredibly pleased
+to meet someone from MIT.
+
+And sort of like a lot of the
+Iranian technocratic class, as
+
+it were, were trained
+as engineers.
+
+And, again, it has a lot to do
+with when countries got on the
+
+steep part of the development
+curve.
+
+And if it was after World War
+II, engineering is generally a
+
+pretty high status thing
+in the field.
+
+If they're older countries, it's
+going to be less so and
+
+more political or financially
+oriented.
+
+That's a broad generalization,
+but it's probably not that--
+
+PROFESSOR: It's interesting.
+
+DAVID KAISER: I have one story
+that maybe we should end with
+
+which was, I went to Yale as an
+undergraduate, and I was a
+
+middle class kid.
+
+And I remember going
+to graduation--
+
+has anybody here been
+to one of the MIT
+
+commencements, by the way?
+
+You'll all go in
+a couple years.
+
+PROFESSOR: I hope you do.
+
+DAVID KAISER: Hopefully,
+you'll all go.
+
+So when I graduated from Yale,
+it was a beautiful May day,
+
+and it had the feeling of
+sort of a garden party.
+
+Everybody was incredibly well
+dressed and sort of very
+
+polite and well behaved
+with the big hats on.
+
+And you had the sense that these
+families had been to
+
+Yale graduations many
+times in the past.
+
+And it was very sort
+of contained.
+
+And the clapping was
+sort of like this.
+
+When you go as faculty or as
+students too to an MIT
+
+graduation, you march down
+Memorial Drive in all the
+
+regalia, and there's somebody
+in the front with the
+
+processional.
+
+And you don't really see any of
+the parents or any of the
+
+audience until you turn off
+of Memorial Drive into the
+
+Killian Court, right in
+the center there.
+
+And it has this feeling,
+you feel like
+
+you're at a rock show.
+
+I mean the parents are
+just over the top.
+
+And there's hundreds of them
+outside the gate because they
+
+only get two tickets per grad,
+but they bring like 15 people
+
+and cousins and aunts and uncles
+and grandparents and
+
+everything.
+
+And you really have the sense
+that it's like a huge
+
+celebration.
+
+And, to me, that always
+represents that kind of
+
+different social standing where
+it's a really big deal
+
+for families when their kids
+graduate from MIT whether
+
+they're immigrants
+or not because--
+
+but it sort of represents
+something.
+
+Sometimes that's a pressure that
+the students carry, which
+
+is not so easy.
+
+But it really represents
+something.
+
+And it's a big celebration.
+
+It's not nearly as much
+something that generations of
+
+Smiths have done for all these
+years, and it's been expected,
+
+and we're so proud of
+you, kind of thing.
+
+And you'll see when
+you graduate, it
+
+really feels that way.
+
+There's 10,000 people there.
+
+And they're just sort of like
+coming out of the woodwork and
+
+climbing up the trees
+and everything.
+
+And it's a very--
+
+to me that's the kind of
+ultimate MIT moment where--
+
+it's nice as a faculty member,
+you remember like what we were
+
+working for all these years and
+I'm sure students as well.
+
+PROFESSOR: Yeah, it's a good
+time, you'll enjoy it.
+
+Alex will go up to get his
+diploma, or whoever, and
+
+you'll hear people
+shouting from the
+
+audience, that's my Alex.
+
+And then other students are
+going, ah Alex, way to go,
+
+blah, blah.
+
+It's all very exciting.
+
+DAVID KAISER: And they read
+every single name of the 2,000
+
+or so people who graduate,
+which itself is quite an
+
+accomplishment of logistics
+to make that work.
+
+PROFESSOR: You'll have your
+hand shaken either by the
+
+President of the Provost.
+
+Isn't that they hand
+out every degree?
+
+So, it's pretty cool.
+
+When I went to Ohio State, there
+were like, I don't know,
+
+5,000 people on the
+football stadium.
+
+They are all down on the field
+and the President gets up, and
+
+said, I hereby declare
+you Bachelor of Art.
+
+Boom.
+
+And that was done.
+
+And everybody goes, OK, let's
+get the hell out of here.
+
+It's very, very different.
\ No newline at end of file
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+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so today is our
+
+ align:start position:0%
+ocw.mit.edu all right so today is our
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so today is our
+third and probably final lecture on
+
+ align:start position:0%
+third and probably final lecture on
+ 
+
+ align:start position:0%
+third and probably final lecture on
+approximation algorithms we're going to
+
+ align:start position:0%
+approximation algorithms we're going to
+ 
+
+ align:start position:0%
+approximation algorithms we're going to
+do take a sort of different approach to
+
+ align:start position:0%
+do take a sort of different approach to
+ 
+
+ align:start position:0%
+do take a sort of different approach to
+proving inapproximability uh to
+
+ align:start position:0%
+proving inapproximability uh to
+ 
+
+ align:start position:0%
+proving inapproximability uh to
+optimization problems uh called Gap
+
+ align:start position:0%
+optimization problems uh called Gap
+ 
+
+ align:start position:0%
+optimization problems uh called Gap
+problems and we'll think about Gap
+
+ align:start position:0%
+problems and we'll think about Gap
+ 
+
+ align:start position:0%
+problems and we'll think about Gap
+preserving reductions we will prove
+
+ align:start position:0%
+preserving reductions we will prove
+ 
+
+ align:start position:0%
+preserving reductions we will prove
+along the way optimal lower bound on Max
+
+ align:start position:0%
+along the way optimal lower bound on Max
+ 
+
+ align:start position:0%
+along the way optimal lower bound on Max
+3at and other fun things so let's start
+
+ align:start position:0%
+3at and other fun things so let's start
+ 
+
+ align:start position:0%
+3at and other fun things so let's start
+with what a gap problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is I haven't actually seen a generic of
+
+ align:start position:0%
+is I haven't actually seen a generic of
+ 
+
+ align:start position:0%
+is I haven't actually seen a generic of
+this so this is new terminology but I
+
+ align:start position:0%
+this so this is new terminology but I
+ 
+
+ align:start position:0%
+this so this is new terminology but I
+think helpful
+
+ align:start position:0%
+think helpful
+ 
+
+ align:start position:0%
+think helpful
+um a gap problem is a is a way of
+
+ align:start position:0%
+um a gap problem is a is a way of
+ 
+
+ align:start position:0%
+um a gap problem is a is a way of
+converting a optimization problem into a
+
+ align:start position:0%
+converting a optimization problem into a
+ 
+
+ align:start position:0%
+converting a optimization problem into a
+decision problem now we already know one
+
+ align:start position:0%
+decision problem now we already know one
+ 
+
+ align:start position:0%
+decision problem now we already know one
+way to do that if you have an NPO
+
+ align:start position:0%
+way to do that if you have an NPO
+ 
+
+ align:start position:0%
+way to do that if you have an NPO
+optimization problem you convert it into
+
+ align:start position:0%
+optimization problem you convert it into
+ 
+
+ align:start position:0%
+optimization problem you convert it into
+the obvious decision problem which is
+
+ align:start position:0%
+the obvious decision problem which is
+ 
+
+ align:start position:0%
+the obvious decision problem which is
+opt at most K uh for the uh minimization
+
+ align:start position:0%
+opt at most K uh for the uh minimization
+ 
+
+ align:start position:0%
+opt at most K uh for the uh minimization
+problem uh that is MP complete but we
+
+ align:start position:0%
+problem uh that is MP complete but we
+ 
+
+ align:start position:0%
+problem uh that is MP complete but we
+want to get something useful from an
+
+ align:start position:0%
+want to get something useful from an
+ 
+
+ align:start position:0%
+want to get something useful from an
+approximability standpoint and and so
+
+ align:start position:0%
+approximability standpoint and and so
+ 
+
+ align:start position:0%
+approximability standpoint and and so
+the idea is here's a different
+
+ align:start position:0%
+the idea is here's a different
+ 
+
+ align:start position:0%
+the idea is here's a different
+problem instead of just deciding whether
+
+ align:start position:0%
+problem instead of just deciding whether
+ 
+
+ align:start position:0%
+problem instead of just deciding whether
+opt is at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+uh we want to distinguish
+
+ align:start position:0%
+uh we want to distinguish
+ 
+
+ align:start position:0%
+uh we want to distinguish
+between uh opt being at most K
+
+ align:start position:0%
+between uh opt being at most K
+ 
+
+ align:start position:0%
+between uh opt being at most K
+versus opt being at least K Over
+
+ align:start position:0%
+versus opt being at least K Over
+ 
+
+ align:start position:0%
+versus opt being at least K Over
+C for some value C and the analogy here
+
+ align:start position:0%
+C for some value C and the analogy here
+ 
+
+ align:start position:0%
+C for some value C and the analogy here
+is with c approxim algorithm C does not
+
+ align:start position:0%
+is with c approxim algorithm C does not
+ 
+
+ align:start position:0%
+is with c approxim algorithm C does not
+have to be constant despite the name uh
+
+ align:start position:0%
+have to be constant despite the name uh
+ 
+
+ align:start position:0%
+have to be constant despite the name uh
+could be a function of n maybe it's log
+
+ align:start position:0%
+could be a function of n maybe it's log
+ 
+
+ align:start position:0%
+could be a function of n maybe it's log
+n maybe it's n the Epsilon
+
+ align:start position:0%
+n maybe it's n the Epsilon
+ 
+
+ align:start position:0%
+n maybe it's n the Epsilon
+whatever uh so for minimization problem
+
+ align:start position:0%
+whatever uh so for minimization problem
+ 
+
+ align:start position:0%
+whatever uh so for minimization problem
+normally uh did I get this the right way
+
+ align:start position:0%
+normally uh did I get this the right way
+ 
+
+ align:start position:0%
+normally uh did I get this the right way
+sorry that should be C *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k for minimization and for
+
+ align:start position:0%
+k for minimization and for
+ 
+
+ align:start position:0%
+k for minimization and for
+maximization it's going to be the
+
+ align:start position:0%
+maximization it's going to be the
+ 
+
+ align:start position:0%
+maximization it's going to be the
+reverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think I'm going to use strict
+
+ align:start position:0%
+and I think I'm going to use strict
+ 
+
+ align:start position:0%
+and I think I'm going to use strict
+inequality here
+
+ align:start position:0%
+inequality here
+ 
+
+ align:start position:0%
+inequality here
+also okay so minimization there's a gap
+
+ align:start position:0%
+also okay so minimization there's a gap
+ 
+
+ align:start position:0%
+also okay so minimization there's a gap
+here between K and C * K we're imagining
+
+ align:start position:0%
+here between K and C * K we're imagining
+ 
+
+ align:start position:0%
+here between K and C * K we're imagining
+here C is bigger than
+
+ align:start position:0%
+here C is bigger than
+ 
+
+ align:start position:0%
+here C is bigger than
+one uh so distinguishing between being
+
+ align:start position:0%
+one uh so distinguishing between being
+ 
+
+ align:start position:0%
+one uh so distinguishing between being
+less than K being uh at least C * K
+
+ align:start position:0%
+less than K being uh at least C * K
+ 
+
+ align:start position:0%
+less than K being uh at least C * K
+leaves uh a ho and uh the point is you
+
+ align:start position:0%
+leaves uh a ho and uh the point is you
+ 
+
+ align:start position:0%
+leaves uh a ho and uh the point is you
+are promised that your input you have a
+
+ align:start position:0%
+are promised that your input you have a
+ 
+
+ align:start position:0%
+are promised that your input you have a
+question um the second one should it
+
+ align:start position:0%
+question um the second one should it
+ 
+
+ align:start position:0%
+question um the second one should it
+really be C
+
+ align:start position:0%
+really be C
+ 
+
+ align:start position:0%
+really be C
+okay uh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no thank
+
+ align:start position:0%
+no thank
+ 
+
+ align:start position:0%
+no thank
+you c and k sound the same so it's
+
+ align:start position:0%
+you c and k sound the same so it's
+ 
+
+ align:start position:0%
+you c and k sound the same so it's
+always easy to mix them up um cool so
+
+ align:start position:0%
+always easy to mix them up um cool so
+ 
+
+ align:start position:0%
+always easy to mix them up um cool so
+the idea is that you're so in both cases
+
+ align:start position:0%
+the idea is that you're so in both cases
+ 
+
+ align:start position:0%
+the idea is that you're so in both cases
+there's a ratio Gap here of c um and the
+
+ align:start position:0%
+there's a ratio Gap here of c um and the
+ 
+
+ align:start position:0%
+there's a ratio Gap here of c um and the
+idea is that you're promised that your
+
+ align:start position:0%
+idea is that you're promised that your
+ 
+
+ align:start position:0%
+idea is that you're promised that your
+input falls into one of these two
+
+ align:start position:0%
+input falls into one of these two
+ 
+
+ align:start position:0%
+input falls into one of these two
+categories what does it mean to
+
+ align:start position:0%
+categories what does it mean to
+ 
+
+ align:start position:0%
+categories what does it mean to
+distinguish I mean I tell you up front
+
+ align:start position:0%
+distinguish I mean I tell you up front
+ 
+
+ align:start position:0%
+distinguish I mean I tell you up front
+the input either has this property or
+
+ align:start position:0%
+the input either has this property or
+ 
+
+ align:start position:0%
+the input either has this property or
+this property and I want you to decide
+
+ align:start position:0%
+this property and I want you to decide
+ 
+
+ align:start position:0%
+this property and I want you to decide
+which one it is and we'll call these yes
+
+ align:start position:0%
+which one it is and we'll call these yes
+ 
+
+ align:start position:0%
+which one it is and we'll call these yes
+instances and these no
+
+ align:start position:0%
+instances and these no
+ 
+
+ align:start position:0%
+instances and these no
+instances uh normally with the decision
+
+ align:start position:0%
+instances uh normally with the decision
+ 
+
+ align:start position:0%
+instances uh normally with the decision
+problem the no instance is that opt is
+
+ align:start position:0%
+problem the no instance is that opt is
+ 
+
+ align:start position:0%
+problem the no instance is that opt is
+just one bigger or one smaller now we
+
+ align:start position:0%
+just one bigger or one smaller now we
+ 
+
+ align:start position:0%
+just one bigger or one smaller now we
+have a big gap between the no instances
+
+ align:start position:0%
+have a big gap between the no instances
+ 
+
+ align:start position:0%
+have a big gap between the no instances
+and the yes instances we're told that
+
+ align:start position:0%
+and the yes instances we're told that
+ 
+
+ align:start position:0%
+and the yes instances we're told that
+that's true this is called Promise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and effectively what that means
+
+ align:start position:0%
+problem and effectively what that means
+ 
+
+ align:start position:0%
+problem and effectively what that means
+is if you're trying to come up with an
+
+ align:start position:0%
+is if you're trying to come up with an
+ 
+
+ align:start position:0%
+is if you're trying to come up with an
+algorithm to solve this decision problem
+
+ align:start position:0%
+algorithm to solve this decision problem
+ 
+
+ align:start position:0%
+algorithm to solve this decision problem
+you don't care what the algorithm does
+
+ align:start position:0%
+you don't care what the algorithm does
+ 
+
+ align:start position:0%
+you don't care what the algorithm does
+if opt happens to fall in between can
+
+ align:start position:0%
+if opt happens to fall in between can
+ 
+
+ align:start position:0%
+if opt happens to fall in between can
+the algorithm can do whatever it want it
+
+ align:start position:0%
+the algorithm can do whatever it want it
+ 
+
+ align:start position:0%
+the algorithm can do whatever it want it
+can output digits of pi in the middle uh
+
+ align:start position:0%
+can output digits of pi in the middle uh
+ 
+
+ align:start position:0%
+can output digits of pi in the middle uh
+as long as when opt is uh most K or
+
+ align:start position:0%
+as long as when opt is uh most K or
+ 
+
+ align:start position:0%
+as long as when opt is uh most K or
+greater than or equal to K it outputs
+
+ align:start position:0%
+greater than or equal to K it outputs
+ 
+
+ align:start position:0%
+greater than or equal to K it outputs
+yes and when opt is at least a factor C
+
+ align:start position:0%
+yes and when opt is at least a factor C
+ 
+
+ align:start position:0%
+yes and when opt is at least a factor C
+away from that it outputs
+
+ align:start position:0%
+away from that it outputs
+ 
+
+ align:start position:0%
+away from that it outputs
+no okay so that's an easier
+
+ align:start position:0%
+no okay so that's an easier
+ 
+
+ align:start position:0%
+no okay so that's an easier
+problem uh and the cool thing
+
+ align:start position:0%
+problem uh and the cool thing
+ 
+
+ align:start position:0%
+problem uh and the cool thing
+is if the C Gap version of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem is NP hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so is C approximating your original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem okay so this really is in direct
+
+ align:start position:0%
+problem okay so this really is in direct
+ 
+
+ align:start position:0%
+problem okay so this really is in direct
+analogy to C approximation and so this
+
+ align:start position:0%
+analogy to C approximation and so this
+ 
+
+ align:start position:0%
+analogy to C approximation and so this
+lets us think about an empty hardness
+
+ align:start position:0%
+lets us think about an empty hardness
+ 
+
+ align:start position:0%
+lets us think about an empty hardness
+for decision problem and prove an
+
+ align:start position:0%
+for decision problem and prove an
+ 
+
+ align:start position:0%
+for decision problem and prove an
+inapproximability result this is nice
+
+ align:start position:0%
+inapproximability result this is nice
+ 
+
+ align:start position:0%
+inapproximability result this is nice
+because in the last two lectures we were
+
+ align:start position:0%
+because in the last two lectures we were
+ 
+
+ align:start position:0%
+because in the last two lectures we were
+having to keep track keep track of a lot
+
+ align:start position:0%
+having to keep track keep track of a lot
+ 
+
+ align:start position:0%
+having to keep track keep track of a lot
+more in just defining what
+
+ align:start position:0%
+more in just defining what
+ 
+
+ align:start position:0%
+more in just defining what
+inapproximability meant and uh apx
+
+ align:start position:0%
+inapproximability meant and uh apx
+ 
+
+ align:start position:0%
+inapproximability meant and uh apx
+hardness and so on here it's kind of
+
+ align:start position:0%
+hardness and so on here it's kind of
+ 
+
+ align:start position:0%
+hardness and so on here it's kind of
+back to regular NP hardness now the
+
+ align:start position:0%
+back to regular NP hardness now the
+ 
+
+ align:start position:0%
+back to regular NP hardness now the
+techniques are completely different in
+
+ align:start position:0%
+techniques are completely different in
+ 
+
+ align:start position:0%
+techniques are completely different in
+this world than our older NP hardness
+
+ align:start position:0%
+this world than our older NP hardness
+ 
+
+ align:start position:0%
+this world than our older NP hardness
+proofs but still it's kind of comforting
+
+ align:start position:0%
+proofs but still it's kind of comforting
+ 
+
+ align:start position:0%
+proofs but still it's kind of comforting
+to be back in decision
+
+ align:start position:0%
+to be back in decision
+ 
+
+ align:start position:0%
+to be back in decision
+land uh
+
+ align:start position:0%
+land uh
+ 
+
+ align:start position:0%
+land uh
+cool so uh
+
+ align:start position:0%
+cool so uh
+ 
+
+ align:start position:0%
+cool so uh
+because of this
+
+ align:start position:0%
+because of this
+ 
+
+ align:start position:0%
+because of this
+implication in previous lectures we were
+
+ align:start position:0%
+implication in previous lectures we were
+ 
+
+ align:start position:0%
+implication in previous lectures we were
+just worried about proving
+
+ align:start position:0%
+just worried about proving
+ 
+
+ align:start position:0%
+just worried about proving
+inapproximability
+
+ align:start position:0%
+inapproximability
+ 
+
+ align:start position:0%
+inapproximability
+um but today we're going to be thinking
+
+ align:start position:0%
+um but today we're going to be thinking
+ 
+
+ align:start position:0%
+um but today we're going to be thinking
+about proving that Gap problems are NP
+
+ align:start position:0%
+about proving that Gap problems are NP
+ 
+
+ align:start position:0%
+about proving that Gap problems are NP
+hard or some other kind of hardness um
+
+ align:start position:0%
+hard or some other kind of hardness um
+ 
+
+ align:start position:0%
+hard or some other kind of hardness um
+this is a stronger type of result so in
+
+ align:start position:0%
+this is a stronger type of result so in
+ 
+
+ align:start position:0%
+this is a stronger type of result so in
+general in approximability is kind of
+
+ align:start position:0%
+general in approximability is kind of
+ 
+
+ align:start position:0%
+general in approximability is kind of
+what you care about from the algorithmic
+
+ align:start position:0%
+what you care about from the algorithmic
+ 
+
+ align:start position:0%
+what you care about from the algorithmic
+standpoint but Gap results saying that
+
+ align:start position:0%
+standpoint but Gap results saying that
+ 
+
+ align:start position:0%
+standpoint but Gap results saying that
+hey your problem is hard even if you
+
+ align:start position:0%
+hey your problem is hard even if you
+ 
+
+ align:start position:0%
+hey your problem is hard even if you
+have this huge gap between uh the yes
+
+ align:start position:0%
+have this huge gap between uh the yes
+ 
+
+ align:start position:0%
+have this huge gap between uh the yes
+instances and the no instances that's
+
+ align:start position:0%
+instances and the no instances that's
+ 
+
+ align:start position:0%
+instances and the no instances that's
+also sort of of independent interest
+
+ align:start position:0%
+also sort of of independent interest
+ 
+
+ align:start position:0%
+also sort of of independent interest
+more about the structure of the problem
+
+ align:start position:0%
+more about the structure of the problem
+ 
+
+ align:start position:0%
+more about the structure of the problem
+uh but one implies the other so this is
+
+ align:start position:0%
+uh but one implies the other so this is
+ 
+
+ align:start position:0%
+uh but one implies the other so this is
+the stronger type of thing to go
+
+ align:start position:0%
+the stronger type of thing to go
+ 
+
+ align:start position:0%
+the stronger type of thing to go
+for uh the other the Practical reason to
+
+ align:start position:0%
+for uh the other the Practical reason to
+ 
+
+ align:start position:0%
+for uh the other the Practical reason to
+care about this stuff is that Gap uh
+
+ align:start position:0%
+care about this stuff is that Gap uh
+ 
+
+ align:start position:0%
+care about this stuff is that Gap uh
+this Gap idea lets you get stronger in
+
+ align:start position:0%
+this Gap idea lets you get stronger in
+ 
+
+ align:start position:0%
+this Gap idea lets you get stronger in
+approximability results the the factor C
+
+ align:start position:0%
+approximability results the the factor C
+ 
+
+ align:start position:0%
+approximability results the the factor C
+you get by thinking about gaps in
+
+ align:start position:0%
+you get by thinking about gaps in
+ 
+
+ align:start position:0%
+you get by thinking about gaps in
+practice seems to be larger than the
+
+ align:start position:0%
+practice seems to be larger than the
+ 
+
+ align:start position:0%
+practice seems to be larger than the
+gaps you get by um L reductions and
+
+ align:start position:0%
+gaps you get by um L reductions and
+ 
+
+ align:start position:0%
+gaps you get by um L reductions and
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so let me tell you about one other type
+
+ align:start position:0%
+so let me tell you about one other type
+ 
+
+ align:start position:0%
+so let me tell you about one other type
+of Gap problem this is a standard
+
+ align:start position:0%
+of Gap problem this is a standard
+ 
+
+ align:start position:0%
+of Gap problem this is a standard
+one a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precise uh consider Max sat pick your
+
+ align:start position:0%
+precise uh consider Max sat pick your
+ 
+
+ align:start position:0%
+precise uh consider Max sat pick your
+favorite version of maxat or Max CSP was
+
+ align:start position:0%
+favorite version of maxat or Max CSP was
+ 
+
+ align:start position:0%
+favorite version of maxat or Max CSP was
+the general form where you could have
+
+ align:start position:0%
+the general form where you could have
+ 
+
+ align:start position:0%
+the general form where you could have
+any type of clause uh instead of just a
+
+ align:start position:0%
+any type of clause uh instead of just a
+ 
+
+ align:start position:0%
+any type of clause uh instead of just a
+c Gap we will Define slightly more
+
+ align:start position:0%
+c Gap we will Define slightly more
+ 
+
+ align:start position:0%
+c Gap we will Define slightly more
+precisely an AB gap which is to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distinguish
+
+ align:start position:0%
+distinguish
+ 
+
+ align:start position:0%
+distinguish
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh opt is less than a times the number
+
+ align:start position:0%
+uh opt is less than a times the number
+ 
+
+ align:start position:0%
+uh opt is less than a times the number
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Clauses and opt is at least B times the
+
+ align:start position:0%
+Clauses and opt is at least B times the
+ 
+
+ align:start position:0%
+Clauses and opt is at least B times the
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Clauses okay so uh whereas here sort of
+
+ align:start position:0%
+Clauses okay so uh whereas here sort of
+ 
+
+ align:start position:0%
+Clauses okay so uh whereas here sort of
+everything was relative to some put K
+
+ align:start position:0%
+everything was relative to some put K
+ 
+
+ align:start position:0%
+everything was relative to some put K
+that you want to decide about here
+
+ align:start position:0%
+that you want to decide about here
+ 
+
+ align:start position:0%
+that you want to decide about here
+there's uh with sat there's a kind of
+
+ align:start position:0%
+there's uh with sat there's a kind of
+ 
+
+ align:start position:0%
+there's uh with sat there's a kind of
+absolute notion of what you'd like to
+
+ align:start position:0%
+absolute notion of what you'd like to
+ 
+
+ align:start position:0%
+absolute notion of what you'd like to
+achieve which is that you satisfy
+
+ align:start position:0%
+achieve which is that you satisfy
+ 
+
+ align:start position:0%
+achieve which is that you satisfy
+everything all clauses are true so
+
+ align:start position:0%
+everything all clauses are true so
+ 
+
+ align:start position:0%
+everything all clauses are true so
+typically we'll think about B being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh and so you're distinguishing
+
+ align:start position:0%
+one uh and so you're distinguishing
+ 
+
+ align:start position:0%
+one uh and so you're distinguishing
+between a satisfiable instance where all
+
+ align:start position:0%
+between a satisfiable instance where all
+ 
+
+ align:start position:0%
+between a satisfiable instance where all
+clauses are satisfied and something
+
+ align:start position:0%
+clauses are satisfied and something
+ 
+
+ align:start position:0%
+clauses are satisfied and something
+that's very unsatisfiable there's some
+
+ align:start position:0%
+that's very unsatisfiable there's some
+ 
+
+ align:start position:0%
+that's very unsatisfiable there's some
+uh usually constant fraction uh
+
+ align:start position:0%
+uh usually constant fraction uh
+ 
+
+ align:start position:0%
+uh usually constant fraction uh
+unsatisfiable
+
+ align:start position:0%
+unsatisfiable
+ 
+
+ align:start position:0%
+unsatisfiable
+Clauses okay so that lets us be this is
+
+ align:start position:0%
+Clauses okay so that lets us be this is
+ 
+
+ align:start position:0%
+Clauses okay so that lets us be this is
+we need need this level of precision uh
+
+ align:start position:0%
+we need need this level of precision uh
+ 
+
+ align:start position:0%
+we need need this level of precision uh
+thinking about when you're WR up against
+
+ align:start position:0%
+thinking about when you're WR up against
+ 
+
+ align:start position:0%
+thinking about when you're WR up against
+100% satisfied versus like 1% satisfied
+
+ align:start position:0%
+100% satisfied versus like 1% satisfied
+ 
+
+ align:start position:0%
+100% satisfied versus like 1% satisfied
+or something like that or 1%
+
+ align:start position:0%
+or something like that or 1%
+ 
+
+ align:start position:0%
+or something like that or 1%
+satisfiable okay uh do we use the same
+
+ align:start position:0%
+satisfiable okay uh do we use the same
+ 
+
+ align:start position:0%
+satisfiable okay uh do we use the same
+notation for one ER or only for the ones
+
+ align:start position:0%
+notation for one ER or only for the ones
+ 
+
+ align:start position:0%
+notation for one ER or only for the ones
+problem like the maximum number of ones
+
+ align:start position:0%
+problem like the maximum number of ones
+ 
+
+ align:start position:0%
+problem like the maximum number of ones
+I haven't seen it but yeah it's a good
+
+ align:start position:0%
+I haven't seen it but yeah it's a good
+ 
+
+ align:start position:0%
+I haven't seen it but yeah it's a good
+question s certainly valid to do it for
+
+ align:start position:0%
+question s certainly valid to do it for
+ 
+
+ align:start position:0%
+question s certainly valid to do it for
+uh we will see it for one other type of
+
+ align:start position:0%
+uh we will see it for one other type of
+ 
+
+ align:start position:0%
+uh we will see it for one other type of
+problem I mean for any problem if you
+
+ align:start position:0%
+problem I mean for any problem if you
+ 
+
+ align:start position:0%
+problem I mean for any problem if you
+can Define some absolute notion of how
+
+ align:start position:0%
+can Define some absolute notion of how
+ 
+
+ align:start position:0%
+can Define some absolute notion of how
+much you'd like to get you can always
+
+ align:start position:0%
+much you'd like to get you can always
+ 
+
+ align:start position:0%
+much you'd like to get you can always
+measure relative to that and Define a
+
+ align:start position:0%
+measure relative to that and Define a
+ 
+
+ align:start position:0%
+measure relative to that and Define a
+this kind of ab Gap
+
+ align:start position:0%
+this kind of ab Gap
+ 
+
+ align:start position:0%
+this kind of ab Gap
+problem cool uh all right so how do we
+
+ align:start position:0%
+problem cool uh all right so how do we
+ 
+
+ align:start position:0%
+problem cool uh all right so how do we
+get these
+
+ align:start position:0%
+get these
+ 
+
+ align:start position:0%
+get these
+gaps uh there's two well maybe three
+
+ align:start position:0%
+gaps uh there's two well maybe three
+ 
+
+ align:start position:0%
+gaps uh there's two well maybe three
+ways I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in general we're going to use
+
+ align:start position:0%
+uh in general we're going to use
+ 
+
+ align:start position:0%
+uh in general we're going to use
+reductions like always uh and you could
+
+ align:start position:0%
+reductions like always uh and you could
+ 
+
+ align:start position:0%
+reductions like always uh and you could
+start from no Gap and make a gap or
+
+ align:start position:0%
+start from no Gap and make a gap or
+ 
+
+ align:start position:0%
+start from no Gap and make a gap or
+start from from a gap of additive one
+
+ align:start position:0%
+start from from a gap of additive one
+ 
+
+ align:start position:0%
+start from from a gap of additive one
+and turn it into a big multiplicative
+
+ align:start position:0%
+and turn it into a big multiplicative
+ 
+
+ align:start position:0%
+and turn it into a big multiplicative
+Gap that will be Gap producing
+
+ align:start position:0%
+Gap that will be Gap producing
+ 
+
+ align:start position:0%
+Gap that will be Gap producing
+reductions you could start with some Gap
+
+ align:start position:0%
+reductions you could start with some Gap
+ 
+
+ align:start position:0%
+reductions you could start with some Gap
+and then make it bigger that's a gap
+
+ align:start position:0%
+and then make it bigger that's a gap
+ 
+
+ align:start position:0%
+and then make it bigger that's a gap
+amplifying reduction or you could just
+
+ align:start position:0%
+amplifying reduction or you could just
+ 
+
+ align:start position:0%
+amplifying reduction or you could just
+start with a gap and try to preserve it
+
+ align:start position:0%
+start with a gap and try to preserve it
+ 
+
+ align:start position:0%
+start with a gap and try to preserve it
+that would be Gap preserving reductions
+
+ align:start position:0%
+that would be Gap preserving reductions
+ 
+
+ align:start position:0%
+that would be Gap preserving reductions
+in general if you once you have some Gap
+
+ align:start position:0%
+in general if you once you have some Gap
+ 
+
+ align:start position:0%
+in general if you once you have some Gap
+you try to keep it or make it bigger to
+
+ align:start position:0%
+you try to keep it or make it bigger to
+ 
+
+ align:start position:0%
+you try to keep it or make it bigger to
+get stronger hardness for your problem
+
+ align:start position:0%
+get stronger hardness for your problem
+ 
+
+ align:start position:0%
+get stronger hardness for your problem
+um so the idea with a gap producing
+
+ align:start position:0%
+um so the idea with a gap producing
+ 
+
+ align:start position:0%
+um so the idea with a gap producing
+reduction is that you have no assumption
+
+ align:start position:0%
+reduction is that you have no assumption
+ 
+
+ align:start position:0%
+reduction is that you have no assumption
+about your starting problem in general
+
+ align:start position:0%
+about your starting problem in general
+ 
+
+ align:start position:0%
+about your starting problem in general
+reduction we're going from some problem
+
+ align:start position:0%
+reduction we're going from some problem
+ 
+
+ align:start position:0%
+reduction we're going from some problem
+a to some problem B and what we would
+
+ align:start position:0%
+a to some problem B and what we would
+ 
+
+ align:start position:0%
+a to some problem B and what we would
+like is that the output instance uh to
+
+ align:start position:0%
+like is that the output instance uh to
+ 
+
+ align:start position:0%
+like is that the output instance uh to
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+B uh the output of the reduction
+
+ align:start position:0%
+B uh the output of the reduction
+ 
+
+ align:start position:0%
+B uh the output of the reduction
+has uh let's say opt equal to K or uh
+
+ align:start position:0%
+has uh let's say opt equal to K or uh
+ 
+
+ align:start position:0%
+has uh let's say opt equal to K or uh
+for a minimization problem opt bigger
+
+ align:start position:0%
+for a minimization problem opt bigger
+ 
+
+ align:start position:0%
+for a minimization problem opt bigger
+than C * k
+
+ align:start position:0%
+than C * k
+ 
+
+ align:start position:0%
+than C * k
+and for a maximization problem opt less
+
+ align:start position:0%
+and for a maximization problem opt less
+ 
+
+ align:start position:0%
+and for a maximization problem opt less
+than K Over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C uh so that's just saying we have a gap
+
+ align:start position:0%
+C uh so that's just saying we have a gap
+ 
+
+ align:start position:0%
+C uh so that's just saying we have a gap
+in the output we assume nothing about
+
+ align:start position:0%
+in the output we assume nothing about
+ 
+
+ align:start position:0%
+in the output we assume nothing about
+the input instance that would be a gap
+
+ align:start position:0%
+the input instance that would be a gap
+ 
+
+ align:start position:0%
+the input instance that would be a gap
+producing reduction now we have seen
+
+ align:start position:0%
+producing reduction now we have seen
+ 
+
+ align:start position:0%
+producing reduction now we have seen
+some of these
+
+ align:start position:0%
+some of these
+ 
+
+ align:start position:0%
+some of these
+before um or at least mention them one
+
+ align:start position:0%
+before um or at least mention them one
+ 
+
+ align:start position:0%
+before um or at least mention them one
+of them this is from lecture three I
+
+ align:start position:0%
+of them this is from lecture three I
+ 
+
+ align:start position:0%
+of them this is from lecture three I
+think for Tetris we proved MP hardness
+
+ align:start position:0%
+think for Tetris we proved MP hardness
+ 
+
+ align:start position:0%
+think for Tetris we proved MP hardness
+which was this three partition reduction
+
+ align:start position:0%
+which was this three partition reduction
+ 
+
+ align:start position:0%
+which was this three partition reduction
+and the idea is that if you could
+
+ align:start position:0%
+and the idea is that if you could
+ 
+
+ align:start position:0%
+and the idea is that if you could
+satisfy that and open this thing then
+
+ align:start position:0%
+satisfy that and open this thing then
+ 
+
+ align:start position:0%
+satisfy that and open this thing then
+you could get a zillion points down here
+
+ align:start position:0%
+you could get a zillion points down here
+ 
+
+ align:start position:0%
+you could get a zillion points down here
+here uh and most of the instances down
+
+ align:start position:0%
+here uh and most of the instances down
+ 
+
+ align:start position:0%
+here uh and most of the instances down
+here we squeeze this down to like an N
+
+ align:start position:0%
+here we squeeze this down to like an N
+ 
+
+ align:start position:0%
+here we squeeze this down to like an N
+the Epsilon that's still hard and so n
+
+ align:start position:0%
+the Epsilon that's still hard and so n
+ 
+
+ align:start position:0%
+the Epsilon that's still hard and so n
+1us Epsilon of the instances down here
+
+ align:start position:0%
+1us Epsilon of the instances down here
+ 
+
+ align:start position:0%
+1us Epsilon of the instances down here
+uh and you know you're given a ton of
+
+ align:start position:0%
+uh and you know you're given a ton of
+ 
+
+ align:start position:0%
+uh and you know you're given a ton of
+pieces uh to fill into space get lots of
+
+ align:start position:0%
+pieces uh to fill into space get lots of
+ 
+
+ align:start position:0%
+pieces uh to fill into space get lots of
+points if the answer was no here then
+
+ align:start position:0%
+points if the answer was no here then
+ 
+
+ align:start position:0%
+points if the answer was no here then
+you won't get those points and so opt is
+
+ align:start position:0%
+you won't get those points and so opt is
+ 
+
+ align:start position:0%
+you won't get those points and so opt is
+very small at most say n to the Epsilon
+
+ align:start position:0%
+very small at most say n to the Epsilon
+ 
+
+ align:start position:0%
+very small at most say n to the Epsilon
+uh if you can solve this instance we
+
+ align:start position:0%
+uh if you can solve this instance we
+ 
+
+ align:start position:0%
+uh if you can solve this instance we
+have a yes instance in the input then we
+
+ align:start position:0%
+have a yes instance in the input then we
+ 
+
+ align:start position:0%
+have a yes instance in the input then we
+get uh like end points so the Gap there
+
+ align:start position:0%
+get uh like end points so the Gap there
+ 
+
+ align:start position:0%
+get uh like end points so the Gap there
+is n the 1us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon so Tetris the tetris reduction
+
+ align:start position:0%
+Epsilon so Tetris the tetris reduction
+ 
+
+ align:start position:0%
+Epsilon so Tetris the tetris reduction
+we assumed nothing about the three
+
+ align:start position:0%
+we assumed nothing about the three
+ 
+
+ align:start position:0%
+we assumed nothing about the three
+partition instance it was just yes or no
+
+ align:start position:0%
+partition instance it was just yes or no
+ 
+
+ align:start position:0%
+partition instance it was just yes or no
+and we produced an instance that had a a
+
+ align:start position:0%
+and we produced an instance that had a a
+ 
+
+ align:start position:0%
+and we produced an instance that had a a
+gap of n 1 minus Epsilon we could set
+
+ align:start position:0%
+gap of n 1 minus Epsilon we could set
+ 
+
+ align:start position:0%
+gap of n 1 minus Epsilon we could set
+Epsilon to any constant we want bigger
+
+ align:start position:0%
+Epsilon to any constant we want bigger
+ 
+
+ align:start position:0%
+Epsilon to any constant we want bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+zero okay uh we also mentioned another
+
+ align:start position:0%
+zero okay uh we also mentioned another
+ 
+
+ align:start position:0%
+zero okay uh we also mentioned another
+such reduction and in general for a lot
+
+ align:start position:0%
+such reduction and in general for a lot
+ 
+
+ align:start position:0%
+such reduction and in general for a lot
+of games and puzzles you can do this
+
+ align:start position:0%
+of games and puzzles you can do this
+ 
+
+ align:start position:0%
+of games and puzzles you can do this
+it's sort of an All or Nothing deal and
+
+ align:start position:0%
+it's sort of an All or Nothing deal and
+ 
+
+ align:start position:0%
+it's sort of an All or Nothing deal and
+GAP producing reduction is a way to
+
+ align:start position:0%
+GAP producing reduction is a way to
+ 
+
+ align:start position:0%
+GAP producing reduction is a way to
+formalize
+
+ align:start position:0%
+formalize
+ 
+
+ align:start position:0%
+formalize
+that uh another problem we talked about
+
+ align:start position:0%
+that uh another problem we talked about
+ 
+
+ align:start position:0%
+that uh another problem we talked about
+last class I believe was non-metric tsp
+
+ align:start position:0%
+last class I believe was non-metric tsp
+ 
+
+ align:start position:0%
+last class I believe was non-metric tsp
+I just give you uh complete graph every
+
+ align:start position:0%
+I just give you uh complete graph every
+ 
+
+ align:start position:0%
+I just give you uh complete graph every
+Edge has some number on it that's the
+
+ align:start position:0%
+Edge has some number on it that's the
+ 
+
+ align:start position:0%
+Edge has some number on it that's the
+length of that edge you want to find a
+
+ align:start position:0%
+length of that edge you want to find a
+ 
+
+ align:start position:0%
+length of that edge you want to find a
+tsp tour of minimum total length this is
+
+ align:start position:0%
+tsp tour of minimum total length this is
+ 
+
+ align:start position:0%
+tsp tour of minimum total length this is
+really hard to approximate because uh
+
+ align:start position:0%
+really hard to approximate because uh
+ 
+
+ align:start position:0%
+really hard to approximate because uh
+depending on your model you can use uh
+
+ align:start position:0%
+depending on your model you can use uh
+ 
+
+ align:start position:0%
+depending on your model you can use uh
+let's say Edge
+
+ align:start position:0%
+let's say Edge
+ 
+
+ align:start position:0%
+let's say Edge
+weights in uh to be really annoying
+
+ align:start position:0%
+weights in uh to be really annoying
+ 
+
+ align:start position:0%
+weights in uh to be really annoying
+would be 0 comma 1 and if I'm given a
+
+ align:start position:0%
+would be 0 comma 1 and if I'm given a
+ 
+
+ align:start position:0%
+would be 0 comma 1 and if I'm given a
+hamiltonicity instance wherever there's
+
+ align:start position:0%
+hamiltonicity instance wherever there's
+ 
+
+ align:start position:0%
+hamiltonicity instance wherever there's
+an edge I put a weight of zero wherever
+
+ align:start position:0%
+an edge I put a weight of zero wherever
+ 
+
+ align:start position:0%
+an edge I put a weight of zero wherever
+there's not an edge I put weight of one
+
+ align:start position:0%
+there's not an edge I put weight of one
+ 
+
+ align:start position:0%
+there's not an edge I put weight of one
+and then if the input graph was
+
+ align:start position:0%
+and then if the input graph was
+ 
+
+ align:start position:0%
+and then if the input graph was
+hamiltonian as a yes instance then the
+
+ align:start position:0%
+hamiltonian as a yes instance then the
+ 
+
+ align:start position:0%
+hamiltonian as a yes instance then the
+output thing will have a tour of length
+
+ align:start position:0%
+output thing will have a tour of length
+ 
+
+ align:start position:0%
+output thing will have a tour of length
+zero and if the input was not
+
+ align:start position:0%
+zero and if the input was not
+ 
+
+ align:start position:0%
+zero and if the input was not
+hamiltonian then the output will have
+
+ align:start position:0%
+hamiltonian then the output will have
+ 
+
+ align:start position:0%
+hamiltonian then the output will have
+weight n ratio between n and zero is
+
+ align:start position:0%
+weight n ratio between n and zero is
+ 
+
+ align:start position:0%
+weight n ratio between n and zero is
+Infinity so this is an infinite Gap
+
+ align:start position:0%
+Infinity so this is an infinite Gap
+ 
+
+ align:start position:0%
+Infinity so this is an infinite Gap
+creation if you allow weights of zero if
+
+ align:start position:0%
+creation if you allow weights of zero if
+ 
+
+ align:start position:0%
+creation if you allow weights of zero if
+you say Zero's cheating uh which we did
+
+ align:start position:0%
+you say Zero's cheating uh which we did
+ 
+
+ align:start position:0%
+you say Zero's cheating uh which we did
+uh and some papers do uh you can instead
+
+ align:start position:0%
+uh and some papers do uh you can instead
+ 
+
+ align:start position:0%
+uh and some papers do uh you can instead
+do one and Infinity uh where Infinity is
+
+ align:start position:0%
+do one and Infinity uh where Infinity is
+ 
+
+ align:start position:0%
+do one and Infinity uh where Infinity is
+the largest rep uh representable number
+
+ align:start position:0%
+the largest rep uh representable number
+ 
+
+ align:start position:0%
+the largest rep uh representable number
+so that's going to be something like 2
+
+ align:start position:0%
+so that's going to be something like 2
+ 
+
+ align:start position:0%
+so that's going to be something like 2
+to the N if you allow usual binary
+
+ align:start position:0%
+to the N if you allow usual binary
+ 
+
+ align:start position:0%
+to the N if you allow usual binary
+encodings of numbers uh if you if you
+
+ align:start position:0%
+encodings of numbers uh if you if you
+ 
+
+ align:start position:0%
+encodings of numbers uh if you if you
+don't the the PB case then that would be
+
+ align:start position:0%
+don't the the PB case then that would be
+ 
+
+ align:start position:0%
+don't the the PB case then that would be
+you know end to some constant but you
+
+ align:start position:0%
+you know end to some constant but you
+ 
+
+ align:start position:0%
+you know end to some constant but you
+get a big gap in any case right so you
+
+ align:start position:0%
+get a big gap in any case right so you
+ 
+
+ align:start position:0%
+get a big gap in any case right so you
+get some Gap equals
+
+ align:start position:0%
+get some Gap equals
+ 
+
+ align:start position:0%
+get some Gap equals
+huge okay so these are kind of trivial
+
+ align:start position:0%
+huge okay so these are kind of trivial
+ 
+
+ align:start position:0%
+huge okay so these are kind of trivial
+senses of inapproximability but hey
+
+ align:start position:0%
+senses of inapproximability but hey
+ 
+
+ align:start position:0%
+senses of inapproximability but hey
+that's one way to do it um what we're
+
+ align:start position:0%
+that's one way to do it um what we're
+ 
+
+ align:start position:0%
+that's one way to do it um what we're
+going to talk about today are uh other
+
+ align:start position:0%
+going to talk about today are uh other
+ 
+
+ align:start position:0%
+going to talk about today are uh other
+known ways to get Gap production uh that
+
+ align:start position:0%
+known ways to get Gap production uh that
+ 
+
+ align:start position:0%
+known ways to get Gap production uh that
+are really cool and more broadly useful
+
+ align:start position:0%
+are really cool and more broadly useful
+ 
+
+ align:start position:0%
+are really cool and more broadly useful
+this is useful when you have a sort of
+
+ align:start position:0%
+this is useful when you have a sort of
+ 
+
+ align:start position:0%
+this is useful when you have a sort of
+All or Nothing problem a lot of the time
+
+ align:start position:0%
+All or Nothing problem a lot of the time
+ 
+
+ align:start position:0%
+All or Nothing problem a lot of the time
+it's not so clear there's a constant
+
+ align:start position:0%
+it's not so clear there's a constant
+ 
+
+ align:start position:0%
+it's not so clear there's a constant
+Factor approximation uh so some giant
+
+ align:start position:0%
+Factor approximation uh so some giant
+ 
+
+ align:start position:0%
+Factor approximation uh so some giant
+Gap like this isn't going to be possible
+
+ align:start position:0%
+Gap like this isn't going to be possible
+ 
+
+ align:start position:0%
+Gap like this isn't going to be possible
+but still gaps are
+
+ align:start position:0%
+but still gaps are
+ 
+
+ align:start position:0%
+but still gaps are
+possible uh
+
+ align:start position:0%
+possible uh
+ 
+
+ align:start position:0%
+possible uh
+now uh an important part of the story
+
+ align:start position:0%
+now uh an important part of the story
+ 
+
+ align:start position:0%
+now uh an important part of the story
+here is the the PCP theorem so this is
+
+ align:start position:0%
+here is the the PCP theorem so this is
+ 
+
+ align:start position:0%
+here is the the PCP theorem so this is
+not about drugs this is
+
+ align:start position:0%
+not about drugs this is
+ 
+
+ align:start position:0%
+not about drugs this is
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh another complexity
+
+ align:start position:0%
+uh another complexity
+ 
+
+ align:start position:0%
+uh another complexity
+class um and the complexity class is
+
+ align:start position:0%
+class um and the complexity class is
+ 
+
+ align:start position:0%
+class um and the complexity class is
+normally written PCP of order log n
+
+ align:start position:0%
+normally written PCP of order log n
+ 
+
+ align:start position:0%
+normally written PCP of order log n
+comma order one I'm going to simplify
+
+ align:start position:0%
+comma order one I'm going to simplify
+ 
+
+ align:start position:0%
+comma order one I'm going to simplify
+this to just PCP as the class the other
+
+ align:start position:0%
+this to just PCP as the class the other
+ 
+
+ align:start position:0%
+this to just PCP as the class the other
+Notions make sense here although
+
+ align:start position:0%
+Notions make sense here although
+ 
+
+ align:start position:0%
+Notions make sense here although
+parameters don't turn out to matter too
+
+ align:start position:0%
+parameters don't turn out to matter too
+ 
+
+ align:start position:0%
+parameters don't turn out to matter too
+much and it's rather lengthy to write
+
+ align:start position:0%
+much and it's rather lengthy to write
+ 
+
+ align:start position:0%
+much and it's rather lengthy to write
+that every time so I'm just going to
+
+ align:start position:0%
+that every time so I'm just going to
+ 
+
+ align:start position:0%
+that every time so I'm just going to
+write PCP uh let me first tell you what
+
+ align:start position:0%
+write PCP uh let me first tell you what
+ 
+
+ align:start position:0%
+write PCP uh let me first tell you what
+this class is about uh briefly and then
+
+ align:start position:0%
+this class is about uh briefly and then
+ 
+
+ align:start position:0%
+this class is about uh briefly and then
+we'll see why it's directly related to
+
+ align:start position:0%
+we'll see why it's directly related to
+ 
+
+ align:start position:0%
+we'll see why it's directly related to
+Gap problems and where a lot of these
+
+ align:start position:0%
+Gap problems and where a lot of these
+ 
+
+ align:start position:0%
+Gap problems and where a lot of these
+Gap producing reductions come from so uh
+
+ align:start position:0%
+Gap producing reductions come from so uh
+ 
+
+ align:start position:0%
+Gap producing reductions come from so uh
+PCP stands for probabilistically
+
+ align:start position:0%
+PCP stands for probabilistically
+ 
+
+ align:start position:0%
+PCP stands for probabilistically
+checkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof the checkable proof refers to uh
+
+ align:start position:0%
+proof the checkable proof refers to uh
+ 
+
+ align:start position:0%
+proof the checkable proof refers to uh
+NP NP every yes instance has a checkable
+
+ align:start position:0%
+NP NP every yes instance has a checkable
+ 
+
+ align:start position:0%
+NP NP every yes instance has a checkable
+proof that the answer is yes uh
+
+ align:start position:0%
+proof that the answer is yes uh
+ 
+
+ align:start position:0%
+proof that the answer is yes uh
+probabilistically checkable means you
+
+ align:start position:0%
+probabilistically checkable means you
+ 
+
+ align:start position:0%
+probabilistically checkable means you
+can check it even faster with high
+
+ align:start position:0%
+can check it even faster with high
+ 
+
+ align:start position:0%
+can check it even faster with high
+probability so normally to check a proof
+
+ align:start position:0%
+probability so normally to check a proof
+ 
+
+ align:start position:0%
+probability so normally to check a proof
+we take polinomial time in NP
+
+ align:start position:0%
+we take polinomial time in NP
+ 
+
+ align:start position:0%
+we take polinomial time in NP
+uh here we want to achieve like constant
+
+ align:start position:0%
+uh here we want to achieve like constant
+ 
+
+ align:start position:0%
+uh here we want to achieve like constant
+time that's the main idea that can't be
+
+ align:start position:0%
+time that's the main idea that can't be
+ 
+
+ align:start position:0%
+time that's the main idea that can't be
+done perfectly but you can do it
+
+ align:start position:0%
+done perfectly but you can do it
+ 
+
+ align:start position:0%
+done perfectly but you can do it
+correctly with high probability so in
+
+ align:start position:0%
+correctly with high probability so in
+ 
+
+ align:start position:0%
+correctly with high probability so in
+general in a problem in PCP has
+
+ align:start position:0%
+general in a problem in PCP has
+ 
+
+ align:start position:0%
+general in a problem in PCP has
+certificates of polinomial length just
+
+ align:start position:0%
+certificates of polinomial length just
+ 
+
+ align:start position:0%
+certificates of polinomial length just
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NP and we have an algorithm for checking
+
+ align:start position:0%
+NP and we have an algorithm for checking
+ 
+
+ align:start position:0%
+NP and we have an algorithm for checking
+certificates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+given uh
+
+ align:start position:0%
+given uh
+ 
+
+ align:start position:0%
+given uh
+certificate and it's given uh order log
+
+ align:start position:0%
+certificate and it's given uh order log
+ 
+
+ align:start position:0%
+certificate and it's given uh order log
+n Bits of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Randomness that's what this first
+
+ align:start position:0%
+Randomness that's what this first
+ 
+
+ align:start position:0%
+Randomness that's what this first
+parameter refers to is how much
+
+ align:start position:0%
+parameter refers to is how much
+ 
+
+ align:start position:0%
+parameter refers to is how much
+Randomness the algorithm's given so we
+
+ align:start position:0%
+Randomness the algorithm's given so we
+ 
+
+ align:start position:0%
+Randomness the algorithm's given so we
+restrict the amount of Randomness to
+
+ align:start position:0%
+restrict the amount of Randomness to
+ 
+
+ align:start position:0%
+restrict the amount of Randomness to
+fairly small
+
+ align:start position:0%
+fairly small
+ 
+
+ align:start position:0%
+fairly small
+amount and it should tell you whether
+
+ align:start position:0%
+amount and it should tell you whether
+ 
+
+ align:start position:0%
+amount and it should tell you whether
+the instance is a yes instance or a no
+
+ align:start position:0%
+the instance is a yes instance or a no
+ 
+
+ align:start position:0%
+the instance is a yes instance or a no
+instance uh in some sense if you're
+
+ align:start position:0%
+instance uh in some sense if you're
+ 
+
+ align:start position:0%
+instance uh in some sense if you're
+given the right certificate so uh in
+
+ align:start position:0%
+given the right certificate so uh in
+ 
+
+ align:start position:0%
+given the right certificate so uh in
+particular if the instance was the S
+
+ align:start position:0%
+particular if the instance was the S
+ 
+
+ align:start position:0%
+particular if the instance was the S
+instance so this is back to decision
+
+ align:start position:0%
+instance so this is back to decision
+ 
+
+ align:start position:0%
+instance so this is back to decision
+problems right just like NP there's no
+
+ align:start position:0%
+problems right just like NP there's no
+ 
+
+ align:start position:0%
+problems right just like NP there's no
+optimization here but we're going to
+
+ align:start position:0%
+optimization here but we're going to
+ 
+
+ align:start position:0%
+optimization here but we're going to
+apply this to Gap problems and that will
+
+ align:start position:0%
+apply this to Gap problems and that will
+ 
+
+ align:start position:0%
+apply this to Gap problems and that will
+relate us to
+
+ align:start position:0%
+relate us to
+ 
+
+ align:start position:0%
+relate us to
+optimization uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say uh there's no error on yes
+
+ align:start position:0%
+let's say uh there's no error on yes
+ 
+
+ align:start position:0%
+let's say uh there's no error on yes
+inst instances although you could relax
+
+ align:start position:0%
+inst instances although you could relax
+ 
+
+ align:start position:0%
+inst instances although you could relax
+that it won't make a big difference so
+
+ align:start position:0%
+that it won't make a big difference so
+ 
+
+ align:start position:0%
+that it won't make a big difference so
+if you give if you have a yes instance
+
+ align:start position:0%
+if you give if you have a yes instance
+ 
+
+ align:start position:0%
+if you give if you have a yes instance
+and you give the right certificate so
+
+ align:start position:0%
+and you give the right certificate so
+ 
+
+ align:start position:0%
+and you give the right certificate so
+this is for some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certificate uh the algorithm is
+
+ align:start position:0%
+certificate uh the algorithm is
+ 
+
+ align:start position:0%
+certificate uh the algorithm is
+guaranteed to say yes so no error there
+
+ align:start position:0%
+guaranteed to say yes so no error there
+ 
+
+ align:start position:0%
+guaranteed to say yes so no error there
+uh where we add some slack is if there's
+
+ align:start position:0%
+uh where we add some slack is if there's
+ 
+
+ align:start position:0%
+uh where we add some slack is if there's
+a no
+
+ align:start position:0%
+a no
+ 
+
+ align:start position:0%
+a no
+instance now normally in NP for a no
+
+ align:start position:0%
+instance now normally in NP for a no
+ 
+
+ align:start position:0%
+instance now normally in NP for a no
+instance there is no correct
+
+ align:start position:0%
+instance there is no correct
+ 
+
+ align:start position:0%
+instance there is no correct
+certificate uh now the algorithm will
+
+ align:start position:0%
+certificate uh now the algorithm will
+ 
+
+ align:start position:0%
+certificate uh now the algorithm will
+sometimes say yes even if we give it the
+
+ align:start position:0%
+sometimes say yes even if we give it the
+ 
+
+ align:start position:0%
+sometimes say yes even if we give it the
+wrong certificate uh there is no right
+
+ align:start position:0%
+wrong certificate uh there is no right
+ 
+
+ align:start position:0%
+wrong certificate uh there is no right
+certificate but it will say so with some
+
+ align:start position:0%
+certificate but it will say so with some
+ 
+
+ align:start position:0%
+certificate but it will say so with some
+uh at most constant
+
+ align:start position:0%
+uh at most constant
+ 
+
+ align:start position:0%
+uh at most constant
+probability so let's say the
+
+ align:start position:0%
+probability so let's say the
+ 
+
+ align:start position:0%
+probability so let's say the
+probability that the
+
+ align:start position:0%
+probability that the
+ 
+
+ align:start position:0%
+probability that the
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+no is at least some
+
+ align:start position:0%
+no is at least some
+ 
+
+ align:start position:0%
+no is at least some
+constant presumably less than one
+
+ align:start position:0%
+constant presumably less than one
+ 
+
+ align:start position:0%
+constant presumably less than one
+uh if it's one then that's
+
+ align:start position:0%
+uh if it's one then that's
+ 
+
+ align:start position:0%
+uh if it's one then that's
+NP uh if it's a half that would be fine
+
+ align:start position:0%
+NP uh if it's a half that would be fine
+ 
+
+ align:start position:0%
+NP uh if it's a half that would be fine
+a tenth a 100th though they'll all be
+
+ align:start position:0%
+a tenth a 100th though they'll all be
+ 
+
+ align:start position:0%
+a tenth a 100th though they'll all be
+the same uh because once you have such
+
+ align:start position:0%
+the same uh because once you have such
+ 
+
+ align:start position:0%
+the same uh because once you have such
+an algorithm that achieves some constant
+
+ align:start position:0%
+an algorithm that achieves some constant
+ 
+
+ align:start position:0%
+an algorithm that achieves some constant
+probability you can apply it uh log 1
+
+ align:start position:0%
+probability you can apply it uh log 1
+ 
+
+ align:start position:0%
+probability you can apply it uh log 1
+over Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times and uh we reduce the
+
+ align:start position:0%
+times and uh we reduce the
+ 
+
+ align:start position:0%
+times and uh we reduce the
+error to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon the probability error goes to
+
+ align:start position:0%
+Epsilon the probability error goes to
+ 
+
+ align:start position:0%
+Epsilon the probability error goes to
+Epsilon if we just repeat this log 1
+
+ align:start position:0%
+Epsilon if we just repeat this log 1
+ 
+
+ align:start position:0%
+Epsilon if we just repeat this log 1
+over Epsilon times so in constant
+
+ align:start position:0%
+over Epsilon times so in constant
+ 
+
+ align:start position:0%
+over Epsilon times so in constant
+time uh so it didn't say uh the order
+
+ align:start position:0%
+time uh so it didn't say uh the order
+ 
+
+ align:start position:0%
+time uh so it didn't say uh the order
+one here refers to the running time of
+
+ align:start position:0%
+one here refers to the running time of
+ 
+
+ align:start position:0%
+one here refers to the running time of
+the algorithm so this is an order one
+
+ align:start position:0%
+the algorithm so this is an order one
+ 
+
+ align:start position:0%
+the algorithm so this is an order one
+time algorithm so the point is the
+
+ align:start position:0%
+time algorithm so the point is the
+ 
+
+ align:start position:0%
+time algorithm so the point is the
+algorithm super fast and still in
+
+ align:start position:0%
+algorithm super fast and still in
+ 
+
+ align:start position:0%
+algorithm super fast and still in
+constant time for constant Epsilon you
+
+ align:start position:0%
+constant time for constant Epsilon you
+ 
+
+ align:start position:0%
+constant time for constant Epsilon you
+can get arbitrarily small error
+
+ align:start position:0%
+can get arbitrarily small error
+ 
+
+ align:start position:0%
+can get arbitrarily small error
+probability uh say one in 100 or one in
+
+ align:start position:0%
+probability uh say one in 100 or one in
+ 
+
+ align:start position:0%
+probability uh say one in 100 or one in
+a million and uh
+
+ align:start position:0%
+a million and uh
+ 
+
+ align:start position:0%
+a million and uh
+it's still pretty good and you're
+
+ align:start position:0%
+it's still pretty good and you're
+ 
+
+ align:start position:0%
+it's still pretty good and you're
+checking your proof super super fast
+
+ align:start position:0%
+checking your proof super super fast
+ 
+
+ align:start position:0%
+checking your proof super super fast
+question why is there a limit on the
+
+ align:start position:0%
+question why is there a limit on the
+ 
+
+ align:start position:0%
+question why is there a limit on the
+randomness
+
+ align:start position:0%
+randomness
+ 
+
+ align:start position:0%
+randomness
+uh this limit on Randomness is not
+
+ align:start position:0%
+uh this limit on Randomness is not
+ 
+
+ align:start position:0%
+uh this limit on Randomness is not
+strictly necessary uh for example n Bits
+
+ align:start position:0%
+strictly necessary uh for example n Bits
+ 
+
+ align:start position:0%
+strictly necessary uh for example n Bits
+of Randomness turn out not to help you
+
+ align:start position:0%
+of Randomness turn out not to help you
+ 
+
+ align:start position:0%
+of Randomness turn out not to help you
+that was proved later but uh we're going
+
+ align:start position:0%
+that was proved later but uh we're going
+ 
+
+ align:start position:0%
+that was proved later but uh we're going
+to use this in a moment it will help us
+
+ align:start position:0%
+to use this in a moment it will help us
+ 
+
+ align:start position:0%
+to use this in a moment it will help us
+uh simulate this algorithm without
+
+ align:start position:0%
+uh simulate this algorithm without
+ 
+
+ align:start position:0%
+uh simulate this algorithm without
+Randomness basically yeah the verifier
+
+ align:start position:0%
+Randomness basically yeah the verifier
+ 
+
+ align:start position:0%
+Randomness basically yeah the verifier
+runs in constant time can even read all
+
+ align:start position:0%
+runs in constant time can even read all
+ 
+
+ align:start position:0%
+runs in constant time can even read all
+his r uh so this is constant time in a
+
+ align:start position:0%
+his r uh so this is constant time in a
+ 
+
+ align:start position:0%
+his r uh so this is constant time in a
+model of computation where you can read
+
+ align:start position:0%
+model of computation where you can read
+ 
+
+ align:start position:0%
+model of computation where you can read
+log n Bits in one step so your word
+
+ align:start position:0%
+log n Bits in one step so your word
+ 
+
+ align:start position:0%
+log n Bits in one step so your word
+let's say is log n Bits long so you have
+
+ align:start position:0%
+let's say is log n Bits long so you have
+ 
+
+ align:start position:0%
+let's say is log n Bits long so you have
+enough time to read the randomness
+
+ align:start position:0%
+enough time to read the randomness
+ 
+
+ align:start position:0%
+enough time to read the randomness
+obviously you don't have time to read
+
+ align:start position:0%
+obviously you don't have time to read
+ 
+
+ align:start position:0%
+obviously you don't have time to read
+the certificate because that has
+
+ align:start position:0%
+the certificate because that has
+ 
+
+ align:start position:0%
+the certificate because that has
+polinomial length uh but yeah constant
+
+ align:start position:0%
+polinomial length uh but yeah constant
+ 
+
+ align:start position:0%
+polinomial length uh but yeah constant
+time cool other questions so that is the
+
+ align:start position:0%
+time cool other questions so that is the
+ 
+
+ align:start position:0%
+time cool other questions so that is the
+definition of PCP now let me relate it
+
+ align:start position:0%
+definition of PCP now let me relate it
+ 
+
+ align:start position:0%
+definition of PCP now let me relate it
+to Gap problems
+
+ align:start position:0%
+to Gap problems
+ 
+
+ align:start position:0%
+to Gap problems
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say uh first claim is that if we look at
+
+ align:start position:0%
+say uh first claim is that if we look at
+ 
+
+ align:start position:0%
+say uh first claim is that if we look at
+this uh Gap sat problem where b equals 1
+
+ align:start position:0%
+this uh Gap sat problem where b equals 1
+ 
+
+ align:start position:0%
+this uh Gap sat problem where b equals 1
+and a is some constant presumably less
+
+ align:start position:0%
+and a is some constant presumably less
+ 
+
+ align:start position:0%
+and a is some constant presumably less
+than one uh then in fact that should be
+
+ align:start position:0%
+than one uh then in fact that should be
+ 
+
+ align:start position:0%
+than one uh then in fact that should be
+less than one why don't I write uh
+
+ align:start position:0%
+less than one why don't I write uh
+ 
+
+ align:start position:0%
+less than one why don't I write uh
+strictly less than one here this is a
+
+ align:start position:0%
+strictly less than one here this is a
+ 
+
+ align:start position:0%
+strictly less than one here this is a
+constant less than one then uh I claim
+
+ align:start position:0%
+constant less than one then uh I claim
+ 
+
+ align:start position:0%
+constant less than one then uh I claim
+that problem is in
+
+ align:start position:0%
+that problem is in
+ 
+
+ align:start position:0%
+that problem is in
+PCP that there is a probabilistically
+
+ align:start position:0%
+PCP that there is a probabilistically
+ 
+
+ align:start position:0%
+PCP that there is a probabilistically
+checkable proof for this instance namely
+
+ align:start position:0%
+checkable proof for this instance namely
+ 
+
+ align:start position:0%
+checkable proof for this instance namely
+it's a satisfying variable assignment
+
+ align:start position:0%
+it's a satisfying variable assignment
+ 
+
+ align:start position:0%
+it's a satisfying variable assignment
+again it's this instance either has the
+
+ align:start position:0%
+again it's this instance either has the
+ 
+
+ align:start position:0%
+again it's this instance either has the
+prop when in yes instance all of the
+
+ align:start position:0%
+prop when in yes instance all of the
+ 
+
+ align:start position:0%
+prop when in yes instance all of the
+entire thing is satisfiable so just like
+
+ align:start position:0%
+entire thing is satisfiable so just like
+ 
+
+ align:start position:0%
+entire thing is satisfiable so just like
+before uh I can have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certificate just like an
+
+ align:start position:0%
+certificate just like an
+ 
+
+ align:start position:0%
+certificate just like an
+NP satisfying assignment to the
+
+ align:start position:0%
+NP satisfying assignment to the
+ 
+
+ align:start position:0%
+NP satisfying assignment to the
+variables is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good in the no instance now I know let's
+
+ align:start position:0%
+good in the no instance now I know let's
+ 
+
+ align:start position:0%
+good in the no instance now I know let's
+say h most half of the things are
+
+ align:start position:0%
+say h most half of the things are
+ 
+
+ align:start position:0%
+say h most half of the things are
+satisfied if this was one
+
+ align:start position:0%
+satisfied if this was one
+ 
+
+ align:start position:0%
+satisfied if this was one
+half um and so what is my algorithm
+
+ align:start position:0%
+half um and so what is my algorithm
+ 
+
+ align:start position:0%
+half um and so what is my algorithm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+do uh in order to get some constant prob
+
+ align:start position:0%
+do uh in order to get some constant prob
+ 
+
+ align:start position:0%
+do uh in order to get some constant prob
+at most constant probability of failure
+
+ align:start position:0%
+at most constant probability of failure
+ 
+
+ align:start position:0%
+at most constant probability of failure
+it's going to choose a random clause and
+
+ align:start position:0%
+it's going to choose a random clause and
+ 
+
+ align:start position:0%
+it's going to choose a random clause and
+check that it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfied
+
+ align:start position:0%
+satisfied
+ 
+
+ align:start position:0%
+satisfied
+uh uniform random so I've got log n Bits
+
+ align:start position:0%
+uh uniform random so I've got log n Bits
+ 
+
+ align:start position:0%
+uh uniform random so I've got log n Bits
+let's say there are n clauses
+
+ align:start position:0%
+let's say there are n clauses
+ 
+
+ align:start position:0%
+let's say there are n clauses
+so I can choose one of them at random by
+
+ align:start position:0%
+so I can choose one of them at random by
+ 
+
+ align:start position:0%
+so I can choose one of them at random by
+flipping login coins and then uh check
+
+ align:start position:0%
+flipping login coins and then uh check
+ 
+
+ align:start position:0%
+flipping login coins and then uh check
+so that involves this is three SATs so
+
+ align:start position:0%
+so that involves this is three SATs so
+ 
+
+ align:start position:0%
+so that involves this is three SATs so
+it only involves three variables I check
+
+ align:start position:0%
+it only involves three variables I check
+ 
+
+ align:start position:0%
+it only involves three variables I check
+those three variable value assignments
+
+ align:start position:0%
+those three variable value assignments
+ 
+
+ align:start position:0%
+those three variable value assignments
+in my certificate just R by random
+
+ align:start position:0%
+in my certificate just R by random
+ 
+
+ align:start position:0%
+in my certificate just R by random
+access into the certificate uh in
+
+ align:start position:0%
+access into the certificate uh in
+ 
+
+ align:start position:0%
+access into the certificate uh in
+constant time I determine whether that
+
+ align:start position:0%
+constant time I determine whether that
+ 
+
+ align:start position:0%
+constant time I determine whether that
+Clause is satisfied if this Clause is
+
+ align:start position:0%
+Clause is satisfied if this Clause is
+ 
+
+ align:start position:0%
+Clause is satisfied if this Clause is
+satisfied algorithm returns yes
+
+ align:start position:0%
+satisfied algorithm returns yes
+ 
+
+ align:start position:0%
+satisfied algorithm returns yes
+otherwise return no now if it was a
+
+ align:start position:0%
+otherwise return no now if it was a
+ 
+
+ align:start position:0%
+otherwise return no now if it was a
+satisfying assignment the algorithm will
+
+ align:start position:0%
+satisfying assignment the algorithm will
+ 
+
+ align:start position:0%
+satisfying assignment the algorithm will
+always say yes so that's good uh if it
+
+ align:start position:0%
+always say yes so that's good uh if it
+ 
+
+ align:start position:0%
+always say yes so that's good uh if it
+wasn't if it was not satisfiable we know
+
+ align:start position:0%
+wasn't if it was not satisfiable we know
+ 
+
+ align:start position:0%
+wasn't if it was not satisfiable we know
+that let's say at most half of the
+
+ align:start position:0%
+that let's say at most half of the
+ 
+
+ align:start position:0%
+that let's say at most half of the
+Clauses are
+
+ align:start position:0%
+Clauses are
+ 
+
+ align:start position:0%
+Clauses are
+satisable which means in every
+
+ align:start position:0%
+satisable which means in every
+ 
+
+ align:start position:0%
+satisable which means in every
+certificate uh the algorithm will say no
+
+ align:start position:0%
+certificate uh the algorithm will say no
+ 
+
+ align:start position:0%
+certificate uh the algorithm will say no
+at least half the time and half is
+
+ align:start position:0%
+at least half the time and half is
+ 
+
+ align:start position:0%
+at least half the time and half is
+whatever that conston
+
+ align:start position:0%
+whatever that conston
+ 
+
+ align:start position:0%
+whatever that conston
+is uh so that
+
+ align:start position:0%
+is uh so that
+ 
+
+ align:start position:0%
+is uh so that
+means uh the
+
+ align:start position:0%
+means uh the
+ 
+
+ align:start position:0%
+means uh the
+probability that the algorithm is
+
+ align:start position:0%
+probability that the algorithm is
+ 
+
+ align:start position:0%
+probability that the algorithm is
+wrong is uh less than one over the gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever that ratio
+
+ align:start position:0%
+whatever that ratio
+ 
+
+ align:start position:0%
+whatever that ratio
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+cool yeah so does this group not then
+
+ align:start position:0%
+cool yeah so does this group not then
+ 
+
+ align:start position:0%
+cool yeah so does this group not then
+hold not hold done for General CNF so
+
+ align:start position:0%
+hold not hold done for General CNF so
+ 
+
+ align:start position:0%
+hold not hold done for General CNF so
+for General CNF you we will uh let me
+
+ align:start position:0%
+for General CNF you we will uh let me
+ 
+
+ align:start position:0%
+for General CNF you we will uh let me
+tell you the PCP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem is that NP equals
+
+ align:start position:0%
+theorem is that NP equals
+ 
+
+ align:start position:0%
+theorem is that NP equals
+PCP this is proofed so all problems are
+
+ align:start position:0%
+PCP this is proofed so all problems are
+ 
+
+ align:start position:0%
+PCP this is proofed so all problems are
+in PCP but this is some motivation for
+
+ align:start position:0%
+in PCP but this is some motivation for
+ 
+
+ align:start position:0%
+in PCP but this is some motivation for
+where this class came from
+
+ align:start position:0%
+where this class came from
+ 
+
+ align:start position:0%
+where this class came from
+yeah okay uh I'm not going to prove this
+
+ align:start position:0%
+yeah okay uh I'm not going to prove this
+ 
+
+ align:start position:0%
+yeah okay uh I'm not going to prove this
+theorem uh the original proof is super
+
+ align:start position:0%
+theorem uh the original proof is super
+ 
+
+ align:start position:0%
+theorem uh the original proof is super
+long since then there have been
+
+ align:start position:0%
+long since then there have been
+ 
+
+ align:start position:0%
+long since then there have been
+relatively short proofs I think the
+
+ align:start position:0%
+relatively short proofs I think the
+ 
+
+ align:start position:0%
+relatively short proofs I think the
+shortest proof currently is two pages
+
+ align:start position:0%
+shortest proof currently is two pages
+ 
+
+ align:start position:0%
+shortest proof currently is two pages
+long still not going to prove it um
+
+ align:start position:0%
+long still not going to prove it um
+ 
+
+ align:start position:0%
+long still not going to prove it um
+because it's a bit aside the point uh to
+
+ align:start position:0%
+because it's a bit aside the point uh to
+ 
+
+ align:start position:0%
+because it's a bit aside the point uh to
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+extent it does use reductions and GAP
+
+ align:start position:0%
+extent it does use reductions and GAP
+ 
+
+ align:start position:0%
+extent it does use reductions and GAP
+Gap amplification but it's a technical
+
+ align:start position:0%
+Gap amplification but it's a technical
+ 
+
+ align:start position:0%
+Gap amplification but it's a technical
+to prove it let's
+
+ align:start position:0%
+to prove it let's
+ 
+
+ align:start position:0%
+to prove it let's
+say uh but I will give you some more
+
+ align:start position:0%
+say uh but I will give you some more
+ 
+
+ align:start position:0%
+say uh but I will give you some more
+motivation for why it's true true uh so
+
+ align:start position:0%
+motivation for why it's true true uh so
+ 
+
+ align:start position:0%
+motivation for why it's true true uh so
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so here's one
+
+ align:start position:0%
+um so here's one
+ 
+
+ align:start position:0%
+um so here's one
+claim uh
+
+ align:start position:0%
+claim uh
+ 
+
+ align:start position:0%
+claim uh
+if order
+
+ align:start position:0%
+if order
+ 
+
+ align:start position:0%
+if order
+one change this
+
+ align:start position:0%
+one change this
+ 
+
+ align:start position:0%
+one change this
+notation if less than one comma 1 Gap
+
+ align:start position:0%
+notation if less than one comma 1 Gap
+ 
+
+ align:start position:0%
+notation if less than one comma 1 Gap
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set is M hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then NP equals
+
+ align:start position:0%
+then NP equals
+ 
+
+ align:start position:0%
+then NP equals
+PCP so we know that this is true but
+
+ align:start position:0%
+PCP so we know that this is true but
+ 
+
+ align:start position:0%
+PCP so we know that this is true but
+before we know that uh here um so we
+
+ align:start position:0%
+before we know that uh here um so we
+ 
+
+ align:start position:0%
+before we know that uh here um so we
+just proved that this thing is in PCP uh
+
+ align:start position:0%
+just proved that this thing is in PCP uh
+ 
+
+ align:start position:0%
+just proved that this thing is in PCP uh
+and if
+
+ align:start position:0%
+and if
+ 
+
+ align:start position:0%
+and if
+furthermore this problem uh we're going
+
+ align:start position:0%
+furthermore this problem uh we're going
+ 
+
+ align:start position:0%
+furthermore this problem uh we're going
+to prove this is NP hard that's the
+
+ align:start position:0%
+to prove this is NP hard that's the
+ 
+
+ align:start position:0%
+to prove this is NP hard that's the
+motivation um if you believe that it's
+
+ align:start position:0%
+motivation um if you believe that it's
+ 
+
+ align:start position:0%
+motivation um if you believe that it's
+NP hard then we know all problems in NP
+
+ align:start position:0%
+NP hard then we know all problems in NP
+ 
+
+ align:start position:0%
+NP hard then we know all problems in NP
+can reduce to this thing and then that
+
+ align:start position:0%
+can reduce to this thing and then that
+ 
+
+ align:start position:0%
+can reduce to this thing and then that
+thing is in PCP so that tells us that
+
+ align:start position:0%
+thing is in PCP so that tells us that
+ 
+
+ align:start position:0%
+thing is in PCP so that tells us that
+all problems in NP you can convert them
+
+ align:start position:0%
+all problems in NP you can convert them
+ 
+
+ align:start position:0%
+all problems in NP you can convert them
+into less than one comma one Gap 3at and
+
+ align:start position:0%
+into less than one comma one Gap 3at and
+ 
+
+ align:start position:0%
+into less than one comma one Gap 3at and
+then uh get a PCP algorithm for them so
+
+ align:start position:0%
+then uh get a PCP algorithm for them so
+ 
+
+ align:start position:0%
+then uh get a PCP algorithm for them so
+that would be one way to prove the PCP
+
+ align:start position:0%
+that would be one way to prove the PCP
+ 
+
+ align:start position:0%
+that would be one way to prove the PCP
+theorem uh in fact the reverse is also
+
+ align:start position:0%
+theorem uh in fact the reverse is also
+ 
+
+ align:start position:0%
+theorem uh in fact the reverse is also
+true and this is sort of more directly
+
+ align:start position:0%
+true and this is sort of more directly
+ 
+
+ align:start position:0%
+true and this is sort of more directly
+useful to us uh
+
+ align:start position:0%
+useful to us uh
+ 
+
+ align:start position:0%
+useful to us uh
+if let's
+
+ align:start position:0%
+if let's
+ 
+
+ align:start position:0%
+if let's
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+threat is in PCP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the Gap version of threet is NP
+
+ align:start position:0%
+then the Gap version of threet is NP
+ 
+
+ align:start position:0%
+then the Gap version of threet is NP
+heart okay this is interesting because
+
+ align:start position:0%
+heart okay this is interesting because
+ 
+
+ align:start position:0%
+heart okay this is interesting because
+uh this is true because NP equals PCP in
+
+ align:start position:0%
+uh this is true because NP equals PCP in
+ 
+
+ align:start position:0%
+uh this is true because NP equals PCP in
+particular threat is in
+
+ align:start position:0%
+particular threat is in
+ 
+
+ align:start position:0%
+particular threat is in
+PCP uh and so we're going to be able to
+
+ align:start position:0%
+PCP uh and so we're going to be able to
+ 
+
+ align:start position:0%
+PCP uh and so we're going to be able to
+conclude by a very short argument that
+
+ align:start position:0%
+conclude by a very short argument that
+ 
+
+ align:start position:0%
+conclude by a very short argument that
+the Gap version of threet is also NP
+
+ align:start position:0%
+the Gap version of threet is also NP
+ 
+
+ align:start position:0%
+the Gap version of threet is also NP
+hard and this proves constant factor in
+
+ align:start position:0%
+hard and this proves constant factor in
+ 
+
+ align:start position:0%
+hard and this proves constant factor in
+approximability of threet we will see a
+
+ align:start position:0%
+approximability of threet we will see a
+ 
+
+ align:start position:0%
+approximability of threet we will see a
+tighter constant in a little bit but
+
+ align:start position:0%
+tighter constant in a little bit but
+ 
+
+ align:start position:0%
+tighter constant in a little bit but
+this will be our first first s
+
+ align:start position:0%
+this will be our first first s
+ 
+
+ align:start position:0%
+this will be our first first s
+bound um and this is a very general kind
+
+ align:start position:0%
+bound um and this is a very general kind
+ 
+
+ align:start position:0%
+bound um and this is a very general kind
+of algorithm it's kind of cool uh so
+
+ align:start position:0%
+of algorithm it's kind of cool uh so
+ 
+
+ align:start position:0%
+of algorithm it's kind of cool uh so
+suppose uh so PCP is easy for The Gap
+
+ align:start position:0%
+suppose uh so PCP is easy for The Gap
+ 
+
+ align:start position:0%
+suppose uh so PCP is easy for The Gap
+version of threat but Suppose there was
+
+ align:start position:0%
+version of threat but Suppose there was
+ 
+
+ align:start position:0%
+version of threat but Suppose there was
+a probabilistically checkable proof uh
+
+ align:start position:0%
+a probabilistically checkable proof uh
+ 
+
+ align:start position:0%
+a probabilistically checkable proof uh
+for just straight up threet when you're
+
+ align:start position:0%
+for just straight up threet when you're
+ 
+
+ align:start position:0%
+for just straight up threet when you're
+not given any Gap bound which is true it
+
+ align:start position:0%
+not given any Gap bound which is true it
+ 
+
+ align:start position:0%
+not given any Gap bound which is true it
+does exist um so we're going to use that
+
+ align:start position:0%
+does exist um so we're going to use that
+ 
+
+ align:start position:0%
+does exist um so we're going to use that
+algorithm and we're going to do a gap
+
+ align:start position:0%
+algorithm and we're going to do a gap
+ 
+
+ align:start position:0%
+algorithm and we're going to do a gap
+preserving reduction
+
+ align:start position:0%
+preserving reduction
+ 
+
+ align:start position:0%
+preserving reduction
+so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say uh the PCP algorithm we're given
+
+ align:start position:0%
+say uh the PCP algorithm we're given
+ 
+
+ align:start position:0%
+say uh the PCP algorithm we're given
+because we're looking at PCP log n comma
+
+ align:start position:0%
+because we're looking at PCP log n comma
+ 
+
+ align:start position:0%
+because we're looking at PCP log n comma
+order one runs in constant time constant
+
+ align:start position:0%
+order one runs in constant time constant
+ 
+
+ align:start position:0%
+order one runs in constant time constant
+time algorithm can't do very much uh in
+
+ align:start position:0%
+time algorithm can't do very much uh in
+ 
+
+ align:start position:0%
+time algorithm can't do very much uh in
+particular I can write the algorithm and
+
+ align:start position:0%
+particular I can write the algorithm and
+ 
+
+ align:start position:0%
+particular I can write the algorithm and
+as a constant size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula okay it's really a distribution
+
+ align:start position:0%
+formula okay it's really a distribution
+ 
+
+ align:start position:0%
+formula okay it's really a distribution
+over such formulas defined by the log n
+
+ align:start position:0%
+over such formulas defined by the log n
+ 
+
+ align:start position:0%
+over such formulas defined by the log n
+random bits uh but let's say it's a
+
+ align:start position:0%
+random bits uh but let's say it's a
+ 
+
+ align:start position:0%
+random bits uh but let's say it's a
+random variable where at each for each
+
+ align:start position:0%
+random variable where at each for each
+ 
+
+ align:start position:0%
+random variable where at each for each
+possible random choice is a constant
+
+ align:start position:0%
+possible random choice is a constant
+ 
+
+ align:start position:0%
+possible random choice is a constant
+size formula uh that evaluates to true
+
+ align:start position:0%
+size formula uh that evaluates to true
+ 
+
+ align:start position:0%
+size formula uh that evaluates to true
+or false corresponding to whether the
+
+ align:start position:0%
+or false corresponding to whether the
+ 
+
+ align:start position:0%
+or false corresponding to whether the
+algorithm says yes or no we know we can
+
+ align:start position:0%
+algorithm says yes or no we know we can
+ 
+
+ align:start position:0%
+algorithm says yes or no we know we can
+convert algorithms to formulas if
+
+ align:start position:0%
+convert algorithms to formulas if
+ 
+
+ align:start position:0%
+convert algorithms to formulas if
+they're if they're short amount of
+
+ align:start position:0%
+they're if they're short amount of
+ 
+
+ align:start position:0%
+they're if they're short amount of
+time uh so we can make had a CNF formula
+
+ align:start position:0%
+time uh so we can make had a CNF formula
+ 
+
+ align:start position:0%
+time uh so we can make had a CNF formula
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+not 3 CNF if we want my goal is to uh I
+
+ align:start position:0%
+not 3 CNF if we want my goal is to uh I
+ 
+
+ align:start position:0%
+not 3 CNF if we want my goal is to uh I
+want to reduce threat to the Gap version
+
+ align:start position:0%
+want to reduce threat to the Gap version
+ 
+
+ align:start position:0%
+want to reduce threat to the Gap version
+of threat because threat we know is EMP
+
+ align:start position:0%
+of threat because threat we know is EMP
+ 
+
+ align:start position:0%
+of threat because threat we know is EMP
+hard so if I can reduce it to the Gap
+
+ align:start position:0%
+hard so if I can reduce it to the Gap
+ 
+
+ align:start position:0%
+hard so if I can reduce it to the Gap
+version of threat I'm happy then I know
+
+ align:start position:0%
+version of threat I'm happy then I know
+ 
+
+ align:start position:0%
+version of threat I'm happy then I know
+the Gap version of threet is also hard
+
+ align:start position:0%
+the Gap version of threet is also hard
+ 
+
+ align:start position:0%
+the Gap version of threet is also hard
+so here is my
+
+ align:start position:0%
+so here is my
+ 
+
+ align:start position:0%
+so here is my
+reduction uh I'm going to so I'm given
+
+ align:start position:0%
+reduction uh I'm going to so I'm given
+ 
+
+ align:start position:0%
+reduction uh I'm going to so I'm given
+the threat formula uh and the algorithm
+
+ align:start position:0%
+the threat formula uh and the algorithm
+ 
+
+ align:start position:0%
+the threat formula uh and the algorithm
+evaluates some form formula on it and
+
+ align:start position:0%
+evaluates some form formula on it and
+ 
+
+ align:start position:0%
+evaluates some form formula on it and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+certificate uh what I'm going to
+
+ align:start position:0%
+certificate uh what I'm going to
+ 
+
+ align:start position:0%
+certificate uh what I'm going to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh try all of the random
+
+ align:start position:0%
+is uh try all of the random
+ 
+
+ align:start position:0%
+is uh try all of the random
+choices because there's only log n Bits
+
+ align:start position:0%
+choices because there's only log n Bits
+ 
+
+ align:start position:0%
+choices because there's only log n Bits
+there's only polom many possible choices
+
+ align:start position:0%
+there's only polom many possible choices
+ 
+
+ align:start position:0%
+there's only polom many possible choices
+for those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bits it's order log n as n to some
+
+ align:start position:0%
+bits it's order log n as n to some
+ 
+
+ align:start position:0%
+bits it's order log n as n to some
+constant and I want to take this formula
+
+ align:start position:0%
+constant and I want to take this formula
+ 
+
+ align:start position:0%
+constant and I want to take this formula
+take the conjunction over all of those
+
+ align:start position:0%
+take the conjunction over all of those
+ 
+
+ align:start position:0%
+take the conjunction over all of those
+choices if if the Alm always says
+
+ align:start position:0%
+choices if if the Alm always says
+ 
+
+ align:start position:0%
+choices if if the Alm always says
+yes uh then this formula will be
+
+ align:start position:0%
+yes uh then this formula will be
+ 
+
+ align:start position:0%
+yes uh then this formula will be
+satisfiable so in the yes instance case
+
+ align:start position:0%
+satisfiable so in the yes instance case
+ 
+
+ align:start position:0%
+satisfiable so in the yes instance case
+I get a satisfiable
+
+ align:start position:0%
+I get a satisfiable
+ 
+
+ align:start position:0%
+I get a satisfiable
+formula so
+
+ align:start position:0%
+formula so
+ 
+
+ align:start position:0%
+formula so
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+implies satisfiable 100%
+
+ align:start position:0%
+implies satisfiable 100%
+ 
+
+ align:start position:0%
+implies satisfiable 100%
+satisfiable that corresponds to this
+
+ align:start position:0%
+satisfiable that corresponds to this
+ 
+
+ align:start position:0%
+satisfiable that corresponds to this
+number I want it to be 100% in the yes
+
+ align:start position:0%
+number I want it to be 100% in the yes
+ 
+
+ align:start position:0%
+number I want it to be 100% in the yes
+case um in the no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case uh I know that uh a constant
+
+ align:start position:0%
+case uh I know that uh a constant
+ 
+
+ align:start position:0%
+case uh I know that uh a constant
+fraction of these random choices give a
+
+ align:start position:0%
+fraction of these random choices give a
+ 
+
+ align:start position:0%
+fraction of these random choices give a
+no meaning uh they will not be satisfied
+
+ align:start position:0%
+no meaning uh they will not be satisfied
+ 
+
+ align:start position:0%
+no meaning uh they will not be satisfied
+for any choice any uh certificate I know
+
+ align:start position:0%
+for any choice any uh certificate I know
+ 
+
+ align:start position:0%
+for any choice any uh certificate I know
+that a constant fraction of these terms
+
+ align:start position:0%
+that a constant fraction of these terms
+ 
+
+ align:start position:0%
+that a constant fraction of these terms
+which I'm conjuncting will evaluate to
+
+ align:start position:0%
+which I'm conjuncting will evaluate to
+ 
+
+ align:start position:0%
+which I'm conjuncting will evaluate to
+false because of the definition of PCP
+
+ align:start position:0%
+false because of the definition of PCP
+ 
+
+ align:start position:0%
+false because of the definition of PCP
+that's what probability algorithm saying
+
+ align:start position:0%
+that's what probability algorithm saying
+ 
+
+ align:start position:0%
+that's what probability algorithm saying
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+means um
+
+ align:start position:0%
+means um
+ 
+
+ align:start position:0%
+means um
+so uh let's say
+
+ align:start position:0%
+so uh let's say
+ 
+
+ align:start position:0%
+so uh let's say
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraction of the
+
+ align:start position:0%
+fraction of the
+ 
+
+ align:start position:0%
+fraction of the
+terms are
+
+ align:start position:0%
+terms are
+ 
+
+ align:start position:0%
+terms are
+false the terms are the things we're
+
+ align:start position:0%
+false the terms are the things we're
+ 
+
+ align:start position:0%
+false the terms are the things we're
+conjuncting over uh but each each term
+
+ align:start position:0%
+conjuncting over uh but each each term
+ 
+
+ align:start position:0%
+conjuncting over uh but each each term
+here is a constant size CNF
+
+ align:start position:0%
+here is a constant size CNF
+ 
+
+ align:start position:0%
+here is a constant size CNF
+formula so when I and those together I
+
+ align:start position:0%
+formula so when I and those together I
+ 
+
+ align:start position:0%
+formula so when I and those together I
+really just get one giant and of
+
+ align:start position:0%
+really just get one giant and of
+ 
+
+ align:start position:0%
+really just get one giant and of
+Clauses constant fraction larger than
+
+ align:start position:0%
+Clauses constant fraction larger than
+ 
+
+ align:start position:0%
+Clauses constant fraction larger than
+the number of terms and if a term is
+
+ align:start position:0%
+the number of terms and if a term is
+ 
+
+ align:start position:0%
+the number of terms and if a term is
+false
+
+ align:start position:0%
+false
+ 
+
+ align:start position:0%
+false
+that means at least one of the Clauses
+
+ align:start position:0%
+that means at least one of the Clauses
+ 
+
+ align:start position:0%
+that means at least one of the Clauses
+is false and there's only a constant
+
+ align:start position:0%
+is false and there's only a constant
+ 
+
+ align:start position:0%
+is false and there's only a constant
+number of Clauses in each term so this
+
+ align:start position:0%
+number of Clauses in each term so this
+ 
+
+ align:start position:0%
+number of Clauses in each term so this
+means a constant fraction of the Clauses
+
+ align:start position:0%
+means a constant fraction of the Clauses
+ 
+
+ align:start position:0%
+means a constant fraction of the Clauses
+in that giant con conjunction are also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+false and that is essentially
+
+ align:start position:0%
+false and that is essentially
+ 
+
+ align:start position:0%
+false and that is essentially
+it let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduction uh so in the yes instance I
+
+ align:start position:0%
+reduction uh so in the yes instance I
+ 
+
+ align:start position:0%
+reduction uh so in the yes instance I
+get 100% satisfiable thing in the no
+
+ align:start position:0%
+get 100% satisfiable thing in the no
+ 
+
+ align:start position:0%
+get 100% satisfiable thing in the no
+instance I get some constant strictly
+
+ align:start position:0%
+instance I get some constant strictly
+ 
+
+ align:start position:0%
+instance I get some constant strictly
+less than one satisfiable thing because
+
+ align:start position:0%
+less than one satisfiable thing because
+ 
+
+ align:start position:0%
+less than one satisfiable thing because
+in any solution I get a constant
+
+ align:start position:0%
+in any solution I get a constant
+ 
+
+ align:start position:0%
+in any solution I get a constant
+fraction that turn out to be false
+
+ align:start position:0%
+fraction that turn out to be false
+ 
+
+ align:start position:0%
+fraction that turn out to be false
+constant fraction of the Clauses now
+
+ align:start position:0%
+constant fraction of the Clauses now
+ 
+
+ align:start position:0%
+constant fraction of the Clauses now
+what the constant is you'd have to work
+
+ align:start position:0%
+what the constant is you'd have to work
+ 
+
+ align:start position:0%
+what the constant is you'd have to work
+out things you'd have to know how big
+
+ align:start position:0%
+out things you'd have to know how big
+ 
+
+ align:start position:0%
+out things you'd have to know how big
+your PCP algorithm is but at least we
+
+ align:start position:0%
+your PCP algorithm is but at least we
+ 
+
+ align:start position:0%
+your PCP algorithm is but at least we
+get a constant lower bound proving uh in
+
+ align:start position:0%
+get a constant lower bound proving uh in
+ 
+
+ align:start position:0%
+get a constant lower bound proving uh in
+particular proving there's no P task for
+
+ align:start position:0%
+particular proving there's no P task for
+ 
+
+ align:start position:0%
+particular proving there's no P task for
+Max 3 set this is what you might call a
+
+ align:start position:0%
+Max 3 set this is what you might call a
+ 
+
+ align:start position:0%
+Max 3 set this is what you might call a
+gap amplifying reduction in the sense we
+
+ align:start position:0%
+gap amplifying reduction in the sense we
+ 
+
+ align:start position:0%
+gap amplifying reduction in the sense we
+started with no Gap the the instance of
+
+ align:start position:0%
+started with no Gap the the instance of
+ 
+
+ align:start position:0%
+started with no Gap the the instance of
+three set was either true or false and
+
+ align:start position:0%
+three set was either true or false and
+ 
+
+ align:start position:0%
+three set was either true or false and
+we ended up with something with a
+
+ align:start position:0%
+we ended up with something with a
+ 
+
+ align:start position:0%
+we ended up with something with a
+significant Gap
+
+ align:start position:0%
+significant Gap
+ 
+
+ align:start position:0%
+significant Gap
+um fine uh so what we're going to talk
+
+ align:start position:0%
+um fine uh so what we're going to talk
+ 
+
+ align:start position:0%
+um fine uh so what we're going to talk
+about next is called Gap preserving R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reductions but maybe before I get there
+
+ align:start position:0%
+reductions but maybe before I get there
+ 
+
+ align:start position:0%
+reductions but maybe before I get there
+um what we just showed is that uh the
+
+ align:start position:0%
+um what we just showed is that uh the
+ 
+
+ align:start position:0%
+um what we just showed is that uh the
+PCP theorem is equivalent and in
+
+ align:start position:0%
+PCP theorem is equivalent and in
+ 
+
+ align:start position:0%
+PCP theorem is equivalent and in
+particular we get uh Gap problems being
+
+ align:start position:0%
+particular we get uh Gap problems being
+ 
+
+ align:start position:0%
+particular we get uh Gap problems being
+NP this is why we care about
+
+ align:start position:0%
+NP this is why we care about
+ 
+
+ align:start position:0%
+NP this is why we care about
+pcps um and uh then in general once we
+
+ align:start position:0%
+pcps um and uh then in general once we
+ 
+
+ align:start position:0%
+pcps um and uh then in general once we
+have these kinds of Gap hardness results
+
+ align:start position:0%
+have these kinds of Gap hardness results
+ 
+
+ align:start position:0%
+have these kinds of Gap hardness results
+we convert our when we're thinking about
+
+ align:start position:0%
+we convert our when we're thinking about
+ 
+
+ align:start position:0%
+we convert our when we're thinking about
+reductions from A to B you I mean
+
+ align:start position:0%
+reductions from A to B you I mean
+ 
+
+ align:start position:0%
+reductions from A to B you I mean
+because we know Gap implies
+
+ align:start position:0%
+because we know Gap implies
+ 
+
+ align:start position:0%
+because we know Gap implies
+inapproximability we could say Okay
+
+ align:start position:0%
+inapproximability we could say Okay
+ 
+
+ align:start position:0%
+inapproximability we could say Okay
+threat is in approximable and then do
+
+ align:start position:0%
+threat is in approximable and then do
+ 
+
+ align:start position:0%
+threat is in approximable and then do
+say an L reduction from threat to
+
+ align:start position:0%
+say an L reduction from threat to
+ 
+
+ align:start position:0%
+say an L reduction from threat to
+something else uh the something else is
+
+ align:start position:0%
+something else uh the something else is
+ 
+
+ align:start position:0%
+something else uh the something else is
+therefore inapproximability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how much carries from A to B we can
+
+ align:start position:0%
+and how much carries from A to B we can
+ 
+
+ align:start position:0%
+and how much carries from A to B we can
+think about the Gap directly and this is
+
+ align:start position:0%
+think about the Gap directly and this is
+ 
+
+ align:start position:0%
+think about the Gap directly and this is
+sort of the main approach in this
+
+ align:start position:0%
+sort of the main approach in this
+ 
+
+ align:start position:0%
+sort of the main approach in this
+lecture that I'm trying to demonstrate
+
+ align:start position:0%
+lecture that I'm trying to demonstrate
+ 
+
+ align:start position:0%
+lecture that I'm trying to demonstrate
+is by preserving the Gap directly a well
+
+ align:start position:0%
+is by preserving the Gap directly a well
+ 
+
+ align:start position:0%
+is by preserving the Gap directly a well
+you get new Gap bounds and generally
+
+ align:start position:0%
+you get new Gap bounds and generally
+ 
+
+ align:start position:0%
+you get new Gap bounds and generally
+stronger Gap bounds and then those imply
+
+ align:start position:0%
+stronger Gap bounds and then those imply
+ 
+
+ align:start position:0%
+stronger Gap bounds and then those imply
+in approximability results uh but the
+
+ align:start position:0%
+in approximability results uh but the
+ 
+
+ align:start position:0%
+in approximability results uh but the
+Gap bounds are stronger than the
+
+ align:start position:0%
+Gap bounds are stronger than the
+ 
+
+ align:start position:0%
+Gap bounds are stronger than the
+inapproximability and also they tend to
+
+ align:start position:0%
+inapproximability and also they tend to
+ 
+
+ align:start position:0%
+inapproximability and also they tend to
+give larger constant factors in the uh
+
+ align:start position:0%
+give larger constant factors in the uh
+ 
+
+ align:start position:0%
+give larger constant factors in the uh
+in approximability results so what do we
+
+ align:start position:0%
+in approximability results so what do we
+ 
+
+ align:start position:0%
+in approximability results so what do we
+want out of a gap preserving reduction
+
+ align:start position:0%
+want out of a gap preserving reduction
+ 
+
+ align:start position:0%
+want out of a gap preserving reduction
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+um we have an
+
+ align:start position:0%
+um we have an
+ 
+
+ align:start position:0%
+um we have an
+instance X of a a we convert that into
+
+ align:start position:0%
+instance X of a a we convert that into
+ 
+
+ align:start position:0%
+instance X of a a we convert that into
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+instance X
+
+ align:start position:0%
+instance X
+ 
+
+ align:start position:0%
+instance X
+Prime of some problem
+
+ align:start position:0%
+Prime of some problem
+ 
+
+ align:start position:0%
+Prime of some problem
+B uh we're just going to think about the
+
+ align:start position:0%
+B uh we're just going to think about the
+ 
+
+ align:start position:0%
+B uh we're just going to think about the
+opt of X versus the opt of X
+
+ align:start position:0%
+opt of X versus the opt of X
+ 
+
+ align:start position:0%
+opt of X versus the opt of X
+Prime and what we
+
+ align:start position:0%
+Prime and what we
+ 
+
+ align:start position:0%
+Prime and what we
+want uh for let's say a minimization
+
+ align:start position:0%
+want uh for let's say a minimization
+ 
+
+ align:start position:0%
+want uh for let's say a minimization
+problem is two
+
+ align:start position:0%
+problem is two
+ 
+
+ align:start position:0%
+problem is two
+properties one is that the
+
+ align:start position:0%
+properties one is that the
+ 
+
+ align:start position:0%
+properties one is that the
+opt if the opt of X is at most sum k
+
+ align:start position:0%
+opt if the opt of X is at most sum k
+ 
+
+ align:start position:0%
+opt if the opt of X is at most sum k
+then the opt of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime is at most sum K
+
+ align:start position:0%
+Prime is at most sum K
+ 
+
+ align:start position:0%
+Prime is at most sum K
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversely okay so in general opt may
+
+ align:start position:0%
+conversely okay so in general opt may
+ 
+
+ align:start position:0%
+conversely okay so in general opt may
+not be preserved but let's say uh
+
+ align:start position:0%
+not be preserved but let's say uh
+ 
+
+ align:start position:0%
+not be preserved but let's say uh
+it changes by some prime operation so in
+
+ align:start position:0%
+it changes by some prime operation so in
+ 
+
+ align:start position:0%
+it changes by some prime operation so in
+fact you can think of K and K Prime as
+
+ align:start position:0%
+fact you can think of K and K Prime as
+ 
+
+ align:start position:0%
+fact you can think of K and K Prime as
+uh functions of
+
+ align:start position:0%
+uh functions of
+ 
+
+ align:start position:0%
+uh functions of
+n okay so if I know that opt of X is at
+
+ align:start position:0%
+n okay so if I know that opt of X is at
+ 
+
+ align:start position:0%
+n okay so if I know that opt of X is at
+most some function of n then I get that
+
+ align:start position:0%
+most some function of n then I get that
+ 
+
+ align:start position:0%
+most some function of n then I get that
+opt uh of X Prime is at most some other
+
+ align:start position:0%
+opt uh of X Prime is at most some other
+ 
+
+ align:start position:0%
+opt uh of X Prime is at most some other
+function of n but there's some known
+
+ align:start position:0%
+function of n but there's some known
+ 
+
+ align:start position:0%
+function of n but there's some known
+relation between the two what I care
+
+ align:start position:0%
+relation between the two what I care
+ 
+
+ align:start position:0%
+relation between the two what I care
+about is this Gap C uh should be a c
+
+ align:start position:0%
+about is this Gap C uh should be a c
+ 
+
+ align:start position:0%
+about is this Gap C uh should be a c
+Prime here so this is what this is
+
+ align:start position:0%
+Prime here so this is what this is
+ 
+
+ align:start position:0%
+Prime here so this is what this is
+saying is suppose I had a gap if I know
+
+ align:start position:0%
+saying is suppose I had a gap if I know
+ 
+
+ align:start position:0%
+saying is suppose I had a gap if I know
+that all Solutions are either less than
+
+ align:start position:0%
+that all Solutions are either less than
+ 
+
+ align:start position:0%
+that all Solutions are either less than
+K or more than C * K I want that to be
+
+ align:start position:0%
+K or more than C * K I want that to be
+ 
+
+ align:start position:0%
+K or more than C * K I want that to be
+preserved for some possibly other gap C
+
+ align:start position:0%
+preserved for some possibly other gap C
+ 
+
+ align:start position:0%
+preserved for some possibly other gap C
+Prime in the new problem okay so this is
+
+ align:start position:0%
+Prime in the new problem okay so this is
+ 
+
+ align:start position:0%
+Prime in the new problem okay so this is
+pretty General but this is the sort of
+
+ align:start position:0%
+pretty General but this is the sort of
+ 
+
+ align:start position:0%
+pretty General but this is the sort of
+thing we want to preserve if we had a
+
+ align:start position:0%
+thing we want to preserve if we had a
+ 
+
+ align:start position:0%
+thing we want to preserve if we had a
+gap of C before we get some Gap C Prime
+
+ align:start position:0%
+gap of C before we get some Gap C Prime
+ 
+
+ align:start position:0%
+gap of C before we get some Gap C Prime
+after if C Prime equals c this would be
+
+ align:start position:0%
+after if C Prime equals c this would be
+ 
+
+ align:start position:0%
+after if C Prime equals c this would be
+a perfectly Gap preserving reduction
+
+ align:start position:0%
+a perfectly Gap preserving reduction
+ 
+
+ align:start position:0%
+a perfectly Gap preserving reduction
+maybe we'll lose some constant Factor uh
+
+ align:start position:0%
+maybe we'll lose some constant Factor uh
+ 
+
+ align:start position:0%
+maybe we'll lose some constant Factor uh
+if C Prime is greater than C uh this is
+
+ align:start position:0%
+if C Prime is greater than C uh this is
+ 
+
+ align:start position:0%
+if C Prime is greater than C uh this is
+called Gap Gap amplification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and GAP Gap amplification is essentially
+
+ align:start position:0%
+and GAP Gap amplification is essentially
+ 
+
+ align:start position:0%
+and GAP Gap amplification is essentially
+how the PCP theorem is shown uh
+
+ align:start position:0%
+how the PCP theorem is shown uh
+ 
+
+ align:start position:0%
+how the PCP theorem is shown uh
+by repeatedly growing the Gap until it's
+
+ align:start position:0%
+by repeatedly growing the Gap until it's
+ 
+
+ align:start position:0%
+by repeatedly growing the Gap until it's
+something reasonable um and if you want
+
+ align:start position:0%
+something reasonable um and if you want
+ 
+
+ align:start position:0%
+something reasonable um and if you want
+to say prove that set cover is log n
+
+ align:start position:0%
+to say prove that set cover is log n
+ 
+
+ align:start position:0%
+to say prove that set cover is log n
+hard it's a similar thing where you
+
+ align:start position:0%
+hard it's a similar thing where you
+ 
+
+ align:start position:0%
+hard it's a similar thing where you
+start with a small Gap constant factor
+
+ align:start position:0%
+start with a small Gap constant factor
+ 
+
+ align:start position:0%
+start with a small Gap constant factor
+and then you grow it and you show you
+
+ align:start position:0%
+and then you grow it and you show you
+ 
+
+ align:start position:0%
+and then you grow it and you show you
+can grow it to log n before you run out
+
+ align:start position:0%
+can grow it to log n before you run out
+ 
+
+ align:start position:0%
+can grow it to log n before you run out
+of space to write it in your problem
+
+ align:start position:0%
+of space to write it in your problem
+ 
+
+ align:start position:0%
+of space to write it in your problem
+essentially before your instance gets
+
+ align:start position:0%
+essentially before your instance gets
+ 
+
+ align:start position:0%
+essentially before your instance gets
+more than polinomial uh or if you want
+
+ align:start position:0%
+more than polinomial uh or if you want
+ 
+
+ align:start position:0%
+more than polinomial uh or if you want
+to prove that click can't be solved in
+
+ align:start position:0%
+to prove that click can't be solved in
+ 
+
+ align:start position:0%
+to prove that click can't be solved in
+better than uh whatever n to the one
+
+ align:start position:0%
+better than uh whatever n to the one
+ 
+
+ align:start position:0%
+better than uh whatever n to the one
+minus Epsilon then a similar trick of
+
+ align:start position:0%
+minus Epsilon then a similar trick of
+ 
+
+ align:start position:0%
+minus Epsilon then a similar trick of
+Gap amplification Works those
+
+ align:start position:0%
+Gap amplification Works those
+ 
+
+ align:start position:0%
+Gap amplification Works those
+amplification arguments are involved and
+
+ align:start position:0%
+amplification arguments are involved and
+ 
+
+ align:start position:0%
+amplification arguments are involved and
+so I'm not going to show them here um
+
+ align:start position:0%
+so I'm not going to show them here um
+ 
+
+ align:start position:0%
+so I'm not going to show them here um
+but I will show you an example of a gap
+
+ align:start position:0%
+but I will show you an example of a gap
+ 
+
+ align:start position:0%
+but I will show you an example of a gap
+preserving reduction next unless there
+
+ align:start position:0%
+preserving reduction next unless there
+ 
+
+ align:start position:0%
+preserving reduction next unless there
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions cool so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to
+
+ align:start position:0%
+I'm going to
+ 
+
+ align:start position:0%
+I'm going to
+reduce uh a problem which we have
+
+ align:start position:0%
+reduce uh a problem which we have
+ 
+
+ align:start position:0%
+reduce uh a problem which we have
+mentioned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before this um which is Max exactly
+
+ align:start position:0%
+before this um which is Max exactly
+ 
+
+ align:start position:0%
+before this um which is Max exactly
+three xor and X nor set this is uh
+
+ align:start position:0%
+three xor and X nor set this is uh
+ 
+
+ align:start position:0%
+three xor and X nor set this is uh
+linear equations mod 2 where every term
+
+ align:start position:0%
+linear equations mod 2 where every term
+ 
+
+ align:start position:0%
+linear equations mod 2 where every term
+has exactly sorry every equation has
+
+ align:start position:0%
+has exactly sorry every equation has
+ 
+
+ align:start position:0%
+has exactly sorry every equation has
+exactly three terms right so something
+
+ align:start position:0%
+exactly three terms right so something
+ 
+
+ align:start position:0%
+exactly three terms right so something
+like uh x i x or
+
+ align:start position:0%
+like uh x i x or
+ 
+
+ align:start position:0%
+like uh x i x or
+XJ X or XK equals one or something uh
+
+ align:start position:0%
+XJ X or XK equals one or something uh
+ 
+
+ align:start position:0%
+XJ X or XK equals one or something uh
+you can also have negations
+
+ align:start position:0%
+you can also have negations
+ 
+
+ align:start position:0%
+you can also have negations
+here okay so I have a bunch of equations
+
+ align:start position:0%
+here okay so I have a bunch of equations
+ 
+
+ align:start position:0%
+here okay so I have a bunch of equations
+like that uh I'm going to just tell you
+
+ align:start position:0%
+like that uh I'm going to just tell you
+ 
+
+ align:start position:0%
+like that uh I'm going to just tell you
+a gap bound on this problem and then
+
+ align:start position:0%
+a gap bound on this problem and then
+ 
+
+ align:start position:0%
+a gap bound on this problem and then
+we're going to reduce it to another
+
+ align:start position:0%
+we're going to reduce it to another
+ 
+
+ align:start position:0%
+we're going to reduce it to another
+problem namely Max E3
+
+ align:start position:0%
+problem namely Max E3
+ 
+
+ align:start position:0%
+problem namely Max E3
+set so uh the claim here is this problem
+
+ align:start position:0%
+set so uh the claim here is this problem
+ 
+
+ align:start position:0%
+set so uh the claim here is this problem
+is 12 + Epsilon 1 -
+
+ align:start position:0%
+is 12 + Epsilon 1 -
+ 
+
+ align:start position:0%
+is 12 + Epsilon 1 -
+Epsilon Gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon uh which in particular implies
+
+ align:start position:0%
+Epsilon uh which in particular implies
+ 
+
+ align:start position:0%
+Epsilon uh which in particular implies
+that it is uh 12 minus Epsilon in
+
+ align:start position:0%
+that it is uh 12 minus Epsilon in
+ 
+
+ align:start position:0%
+that it is uh 12 minus Epsilon in
+approximable unless P equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NP uh but this is of course stronger it
+
+ align:start position:0%
+NP uh but this is of course stronger it
+ 
+
+ align:start position:0%
+NP uh but this is of course stronger it
+says uh if you just look at instances
+
+ align:start position:0%
+says uh if you just look at instances
+ 
+
+ align:start position:0%
+says uh if you just look at instances
+where uh say 99% of the uh for of the
+
+ align:start position:0%
+where uh say 99% of the uh for of the
+ 
+
+ align:start position:0%
+where uh say 99% of the uh for of the
+equations are satisfiable
+
+ align:start position:0%
+equations are satisfiable
+ 
+
+ align:start position:0%
+equations are satisfiable
+versus uh when 51% are satisfiable it's
+
+ align:start position:0%
+versus uh when 51% are satisfiable it's
+ 
+
+ align:start position:0%
+versus uh when 51% are satisfiable it's
+empty hard to distinguish between those
+
+ align:start position:0%
+empty hard to distinguish between those
+ 
+
+ align:start position:0%
+empty hard to distinguish between those
+two um why 1/2 here because there is a
+
+ align:start position:0%
+two um why 1/2 here because there is a
+ 
+
+ align:start position:0%
+two um why 1/2 here because there is a
+1/ half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation I've kind of mentioned the
+
+ align:start position:0%
+approximation I've kind of mentioned the
+ 
+
+ align:start position:0%
+approximation I've kind of mentioned the
+general approach for oximation algorithm
+
+ align:start position:0%
+general approach for oximation algorithm
+ 
+
+ align:start position:0%
+general approach for oximation algorithm
+for sat is take a random assignment
+
+ align:start position:0%
+for sat is take a random assignment
+ 
+
+ align:start position:0%
+for sat is take a random assignment
+variable assignment um and in this case
+
+ align:start position:0%
+variable assignment um and in this case
+ 
+
+ align:start position:0%
+variable assignment um and in this case
+because these statements are about a
+
+ align:start position:0%
+because these statements are about a
+ 
+
+ align:start position:0%
+because these statements are about a
+par uh you if you think of XK as random
+
+ align:start position:0%
+par uh you if you think of XK as random
+ 
+
+ align:start position:0%
+par uh you if you think of XK as random
+it doesn't matter what these two are 50%
+
+ align:start position:0%
+it doesn't matter what these two are 50%
+ 
+
+ align:start position:0%
+it doesn't matter what these two are 50%
+probability this will be satisfied and
+
+ align:start position:0%
+probability this will be satisfied and
+ 
+
+ align:start position:0%
+probability this will be satisfied and
+so you can always satisfy at least half
+
+ align:start position:0%
+so you can always satisfy at least half
+ 
+
+ align:start position:0%
+so you can always satisfy at least half
+of the Clauses because a Rand this
+
+ align:start position:0%
+of the Clauses because a Rand this
+ 
+
+ align:start position:0%
+of the Clauses because a Rand this
+randomized algorithm will satisfy half
+
+ align:start position:0%
+randomized algorithm will satisfy half
+ 
+
+ align:start position:0%
+randomized algorithm will satisfy half
+in expectation therefore at least one
+
+ align:start position:0%
+in expectation therefore at least one
+ 
+
+ align:start position:0%
+in expectation therefore at least one
+instance it will do so uh but if you
+
+ align:start position:0%
+instance it will do so uh but if you
+ 
+
+ align:start position:0%
+instance it will do so uh but if you
+allow randomized approximation this is a
+
+ align:start position:0%
+allow randomized approximation this is a
+ 
+
+ align:start position:0%
+allow randomized approximation this is a
+one half approximation or a two
+
+ align:start position:0%
+one half approximation or a two
+ 
+
+ align:start position:0%
+one half approximation or a two
+approximation depending on your
+
+ align:start position:0%
+approximation depending on your
+ 
+
+ align:start position:0%
+approximation depending on your
+perspective uh so this is really tight
+
+ align:start position:0%
+perspective uh so this is really tight
+ 
+
+ align:start position:0%
+perspective uh so this is really tight
+that's good news and this is this is
+
+ align:start position:0%
+that's good news and this is this is
+ 
+
+ align:start position:0%
+that's good news and this is this is
+proved this is essentially a form of the
+
+ align:start position:0%
+proved this is essentially a form of the
+ 
+
+ align:start position:0%
+proved this is essentially a form of the
+PCP theorem um PCP theorem says that uh
+
+ align:start position:0%
+PCP theorem um PCP theorem says that uh
+ 
+
+ align:start position:0%
+PCP theorem um PCP theorem says that uh
+you can there's some
+
+ align:start position:0%
+you can there's some
+ 
+
+ align:start position:0%
+you can there's some
+algorithm and you can prove that in fact
+
+ align:start position:0%
+algorithm and you can prove that in fact
+ 
+
+ align:start position:0%
+algorithm and you can prove that in fact
+there is an algorithm that looks like
+
+ align:start position:0%
+there is an algorithm that looks like
+ 
+
+ align:start position:0%
+there is an algorithm that looks like
+this it's a bunch of uh linear equations
+
+ align:start position:0%
+this it's a bunch of uh linear equations
+ 
+
+ align:start position:0%
+this it's a bunch of uh linear equations
+with three terms per uh equation
+
+ align:start position:0%
+with three terms per uh equation
+ 
+
+ align:start position:0%
+with three terms per uh equation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take that as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given now what I want to show is a
+
+ align:start position:0%
+given now what I want to show is a
+ 
+
+ align:start position:0%
+given now what I want to show is a
+reduction from that problem to Max E3
+
+ align:start position:0%
+reduction from that problem to Max E3
+ 
+
+ align:start position:0%
+reduction from that problem to Max E3
+set so remember Max E3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Set uh you're given CNF where every
+
+ align:start position:0%
+Set uh you're given CNF where every
+ 
+
+ align:start position:0%
+Set uh you're given CNF where every
+Clause has exact three distinct literals
+
+ align:start position:0%
+Clause has exact three distinct literals
+ 
+
+ align:start position:0%
+Clause has exact three distinct literals
+uh you want to maximize the number of
+
+ align:start position:0%
+uh you want to maximize the number of
+ 
+
+ align:start position:0%
+uh you want to maximize the number of
+satisfied things um so this is roughly
+
+ align:start position:0%
+satisfied things um so this is roughly
+ 
+
+ align:start position:0%
+satisfied things um so this is roughly
+the problem we were talking about up
+
+ align:start position:0%
+the problem we were talking about up
+ 
+
+ align:start position:0%
+the problem we were talking about up
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um so first thing I'm going to do is
+
+ align:start position:0%
+um so first thing I'm going to do is
+ 
+
+ align:start position:0%
+um so first thing I'm going to do is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+oh so I I want to reduce this to
+
+ align:start position:0%
+oh so I I want to reduce this to
+ 
+
+ align:start position:0%
+oh so I I want to reduce this to
+that um and this is the reduction and
+
+ align:start position:0%
+that um and this is the reduction and
+ 
+
+ align:start position:0%
+that um and this is the reduction and
+first claim is just that it's an
+
+ align:start position:0%
+first claim is just that it's an
+ 
+
+ align:start position:0%
+first claim is just that it's an
+reduction so that's something we're
+
+ align:start position:0%
+reduction so that's something we're
+ 
+
+ align:start position:0%
+reduction so that's something we're
+familiar with let's think about it that
+
+ align:start position:0%
+familiar with let's think about it that
+ 
+
+ align:start position:0%
+familiar with let's think about it that
+way then we will think about it in a gap
+
+ align:start position:0%
+way then we will think about it in a gap
+ 
+
+ align:start position:0%
+way then we will think about it in a gap
+preserving sense okay so there are two
+
+ align:start position:0%
+preserving sense okay so there are two
+ 
+
+ align:start position:0%
+preserving sense okay so there are two
+types of equations we need to satisfy
+
+ align:start position:0%
+types of equations we need to satisfy
+ 
+
+ align:start position:0%
+types of equations we need to satisfy
+the sort of odd case or the even
+
+ align:start position:0%
+the sort of odd case or the even
+ 
+
+ align:start position:0%
+the sort of odd case or the even
+case um again each of these could be
+
+ align:start position:0%
+case um again each of these could be
+ 
+
+ align:start position:0%
+case um again each of these could be
+negated and I'm just going to double
+
+ align:start position:0%
+negated and I'm just going to double
+ 
+
+ align:start position:0%
+negated and I'm just going to double
+negate means un negated over here so uh
+
+ align:start position:0%
+negate means un negated over here so uh
+ 
+
+ align:start position:0%
+negate means un negated over here so uh
+each equation is going to be replaced
+
+ align:start position:0%
+each equation is going to be replaced
+ 
+
+ align:start position:0%
+each equation is going to be replaced
+with exactly four Clauses in the E3 set
+
+ align:start position:0%
+with exactly four Clauses in the E3 set
+ 
+
+ align:start position:0%
+with exactly four Clauses in the E3 set
+instance um and the idea is as well if I
+
+ align:start position:0%
+instance um and the idea is as well if I
+ 
+
+ align:start position:0%
+instance um and the idea is as well if I
+want them all uh the par of them to be
+
+ align:start position:0%
+want them all uh the par of them to be
+ 
+
+ align:start position:0%
+want them all uh the par of them to be
+odd uh it should be the case that at
+
+ align:start position:0%
+odd uh it should be the case that at
+ 
+
+ align:start position:0%
+odd uh it should be the case that at
+least one of them is true and if you
+
+ align:start position:0%
+least one of them is true and if you
+ 
+
+ align:start position:0%
+least one of them is true and if you
+stare at it long enough also uh when you
+
+ align:start position:0%
+stare at it long enough also uh when you
+ 
+
+ align:start position:0%
+stare at it long enough also uh when you
+put two bars in there I don't want
+
+ align:start position:0%
+put two bars in there I don't want
+ 
+
+ align:start position:0%
+put two bars in there I don't want
+exactly two of them to be true that's
+
+ align:start position:0%
+exactly two of them to be true that's
+ 
+
+ align:start position:0%
+exactly two of them to be true that's
+the parody constraint if this is true uh
+
+ align:start position:0%
+the parody constraint if this is true uh
+ 
+
+ align:start position:0%
+the parody constraint if this is true uh
+all four of these should be true that's
+
+ align:start position:0%
+all four of these should be true that's
+ 
+
+ align:start position:0%
+all four of these should be true that's
+the first claim this by the par of the
+
+ align:start position:0%
+the first claim this by the par of the
+ 
+
+ align:start position:0%
+the first claim this by the par of the
+number of bars on there's either Zero
+
+ align:start position:0%
+number of bars on there's either Zero
+ 
+
+ align:start position:0%
+number of bars on there's either Zero
+Bar or two bars or three positive or uh
+
+ align:start position:0%
+Bar or two bars or three positive or uh
+ 
+
+ align:start position:0%
+Bar or two bars or three positive or uh
+one positive those the two cases and uh
+
+ align:start position:0%
+one positive those the two cases and uh
+ 
+
+ align:start position:0%
+one positive those the two cases and uh
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+situation uh where I want the parity to
+
+ align:start position:0%
+situation uh where I want the parity to
+ 
+
+ align:start position:0%
+situation uh where I want the parity to
+be even even number of truths I have all
+
+ align:start position:0%
+be even even number of truths I have all
+ 
+
+ align:start position:0%
+be even even number of truths I have all
+the even number of truths cases over
+
+ align:start position:0%
+the even number of truths cases over
+ 
+
+ align:start position:0%
+the even number of truths cases over
+here uh here are two of them even and
+
+ align:start position:0%
+here uh here are two of them even and
+ 
+
+ align:start position:0%
+here uh here are two of them even and
+here are none of them
+
+ align:start position:0%
+here are none of them
+ 
+
+ align:start position:0%
+here are none of them
+even okay and again if this is satisfied
+
+ align:start position:0%
+even okay and again if this is satisfied
+ 
+
+ align:start position:0%
+even okay and again if this is satisfied
+then all four of those are satisfied
+
+ align:start position:0%
+then all four of those are satisfied
+ 
+
+ align:start position:0%
+then all four of those are satisfied
+now if these are not
+
+ align:start position:0%
+now if these are not
+ 
+
+ align:start position:0%
+now if these are not
+satisfied uh by the same argument you
+
+ align:start position:0%
+satisfied uh by the same argument you
+ 
+
+ align:start position:0%
+satisfied uh by the same argument you
+can show that at least one of these is
+
+ align:start position:0%
+can show that at least one of these is
+ 
+
+ align:start position:0%
+can show that at least one of these is
+violated but in fact just one will be
+
+ align:start position:0%
+violated but in fact just one will be
+ 
+
+ align:start position:0%
+violated but in fact just one will be
+violated okay so for example um if so
+
+ align:start position:0%
+violated okay so for example um if so
+ 
+
+ align:start position:0%
+violated okay so for example um if so
+this is just a case analysis let's say I
+
+ align:start position:0%
+this is just a case analysis let's say I
+ 
+
+ align:start position:0%
+this is just a case analysis let's say I
+set all of these to be zero and so their
+
+ align:start position:0%
+set all of these to be zero and so their
+ 
+
+ align:start position:0%
+set all of these to be zero and so their
+xor is zero not one so if they're all
+
+ align:start position:0%
+xor is zero not one so if they're all
+ 
+
+ align:start position:0%
+xor is zero not one so if they're all
+false then this will not be satisfied
+
+ align:start position:0%
+false then this will not be satisfied
+ 
+
+ align:start position:0%
+false then this will not be satisfied
+but the other three will
+
+ align:start position:0%
+but the other three will
+ 
+
+ align:start position:0%
+but the other three will
+be um and in general
+
+ align:start position:0%
+be um and in general
+ 
+
+ align:start position:0%
+be um and in general
+because we have for example XI appearing
+
+ align:start position:0%
+because we have for example XI appearing
+ 
+
+ align:start position:0%
+because we have for example XI appearing
+true and false in different cases uh you
+
+ align:start position:0%
+true and false in different cases uh you
+ 
+
+ align:start position:0%
+true and false in different cases uh you
+will satisfy three out of four in when
+
+ align:start position:0%
+will satisfy three out of four in when
+ 
+
+ align:start position:0%
+will satisfy three out of four in when
+on the right when you don't satisfy on
+
+ align:start position:0%
+on the right when you don't satisfy on
+ 
+
+ align:start position:0%
+on the right when you don't satisfy on
+the left so it's uh the difference is
+
+ align:start position:0%
+the left so it's uh the difference is
+ 
+
+ align:start position:0%
+the left so it's uh the difference is
+three versus four when these are
+
+ align:start position:0%
+three versus four when these are
+ 
+
+ align:start position:0%
+three versus four when these are
+satisfied you satisfy four on the right
+
+ align:start position:0%
+satisfied you satisfy four on the right
+ 
+
+ align:start position:0%
+satisfied you satisfy four on the right
+when they're unsatisfied you satisfy
+
+ align:start position:0%
+when they're unsatisfied you satisfy
+ 
+
+ align:start position:0%
+when they're unsatisfied you satisfy
+three on the right that's all I'm
+
+ align:start position:0%
+three on the right that's all I'm
+ 
+
+ align:start position:0%
+three on the right that's all I'm
+claiming
+
+ align:start position:0%
+claiming
+ 
+
+ align:start position:0%
+claiming
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so if the equation is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfied then we get
+
+ align:start position:0%
+satisfied then we get
+ 
+
+ align:start position:0%
+satisfied then we get
+four uh in the three side
+
+ align:start position:0%
+four uh in the three side
+ 
+
+ align:start position:0%
+four uh in the three side
+instance and if it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unsatisfied we turn out to get exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three okay so I want to prove that this
+
+ align:start position:0%
+three okay so I want to prove that this
+ 
+
+ align:start position:0%
+three okay so I want to prove that this
+is an L reduction to prove L reduction
+
+ align:start position:0%
+is an L reduction to prove L reduction
+ 
+
+ align:start position:0%
+is an L reduction to prove L reduction
+we need two things one is that the
+
+ align:start position:0%
+we need two things one is that the
+ 
+
+ align:start position:0%
+we need two things one is that the
+additive Gap if I solve the three set
+
+ align:start position:0%
+additive Gap if I solve the three set
+ 
+
+ align:start position:0%
+additive Gap if I solve the three set
+instance and convert it back into a
+
+ align:start position:0%
+instance and convert it back into a
+ 
+
+ align:start position:0%
+instance and convert it back into a
+corresponding uh solution to Max e3x
+
+ align:start position:0%
+corresponding uh solution to Max e3x
+ 
+
+ align:start position:0%
+corresponding uh solution to Max e3x
+noret which uh I don't change anything
+
+ align:start position:0%
+noret which uh I don't change anything
+ 
+
+ align:start position:0%
+noret which uh I don't change anything
+the variables are just what they were
+
+ align:start position:0%
+the variables are just what they were
+ 
+
+ align:start position:0%
+the variables are just what they were
+before uh that the additive Gap from opt
+
+ align:start position:0%
+before uh that the additive Gap from opt
+ 
+
+ align:start position:0%
+before uh that the additive Gap from opt
+on the right side is is uh most some
+
+ align:start position:0%
+on the right side is is uh most some
+ 
+
+ align:start position:0%
+on the right side is is uh most some
+constant times the additive gap on the
+
+ align:start position:0%
+constant times the additive gap on the
+ 
+
+ align:start position:0%
+constant times the additive gap on the
+left side vice
+
+ align:start position:0%
+left side vice
+ 
+
+ align:start position:0%
+left side vice
+versa uh in this case the Gap is exactly
+
+ align:start position:0%
+versa uh in this case the Gap is exactly
+ 
+
+ align:start position:0%
+versa uh in this case the Gap is exactly
+preserved because uh it's 4 vers three
+
+ align:start position:0%
+preserved because uh it's 4 vers three
+ 
+
+ align:start position:0%
+preserved because uh it's 4 vers three
+over here it's one versus Z over here so
+
+ align:start position:0%
+over here it's one versus Z over here so
+ 
+
+ align:start position:0%
+over here it's one versus Z over here so
+additive Gap remains
+
+ align:start position:0%
+additive Gap remains
+ 
+
+ align:start position:0%
+additive Gap remains
+one and that is
+
+ align:start position:0%
+one and that is
+ 
+
+ align:start position:0%
+one and that is
+called beta I think in uh in L reduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+land so this was property two in the L
+
+ align:start position:0%
+land so this was property two in the L
+ 
+
+ align:start position:0%
+land so this was property two in the L
+reduction uh so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additive error in this case is um
+
+ align:start position:0%
+additive error in this case is um
+ 
+
+ align:start position:0%
+additive error in this case is um
+exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preserved so there's no scale beta
+
+ align:start position:0%
+preserved so there's no scale beta
+ 
+
+ align:start position:0%
+preserved so there's no scale beta
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+one if there's some other gap than four
+
+ align:start position:0%
+one if there's some other gap than four
+ 
+
+ align:start position:0%
+one if there's some other gap than four
+if it was five versus three then the
+
+ align:start position:0%
+if it was five versus three then the
+ 
+
+ align:start position:0%
+if it was five versus three then the
+we'd have beta equal
+
+ align:start position:0%
+we'd have beta equal
+ 
+
+ align:start position:0%
+we'd have beta equal
+two okay then there was the other
+
+ align:start position:0%
+two okay then there was the other
+ 
+
+ align:start position:0%
+two okay then there was the other
+property which is you need to show that
+
+ align:start position:0%
+property which is you need to show that
+ 
+
+ align:start position:0%
+property which is you need to show that
+you don't blow up opt too much we want
+
+ align:start position:0%
+you don't blow up opt too much we want
+ 
+
+ align:start position:0%
+you don't blow up opt too much we want
+the opt on the right hand side to be at
+
+ align:start position:0%
+the opt on the right hand side to be at
+ 
+
+ align:start position:0%
+the opt on the right hand side to be at
+most some constant times opt on the left
+
+ align:start position:0%
+most some constant times opt on the left
+ 
+
+ align:start position:0%
+most some constant times opt on the left
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+side uh this requires a little bit
+
+ align:start position:0%
+side uh this requires a little bit
+ 
+
+ align:start position:0%
+side uh this requires a little bit
+more care because we need to make sure
+
+ align:start position:0%
+more care because we need to make sure
+ 
+
+ align:start position:0%
+more care because we need to make sure
+opt is linear basically we did a lot of
+
+ align:start position:0%
+opt is linear basically we did a lot of
+ 
+
+ align:start position:0%
+opt is linear basically we did a lot of
+these arguments uh last lecture uh
+
+ align:start position:0%
+these arguments uh last lecture uh
+ 
+
+ align:start position:0%
+these arguments uh last lecture uh
+because even when you don't satisfy
+
+ align:start position:0%
+because even when you don't satisfy
+ 
+
+ align:start position:0%
+because even when you don't satisfy
+things you still get points and the
+
+ align:start position:0%
+things you still get points and the
+ 
+
+ align:start position:0%
+things you still get points and the
+difference between zero and three is Big
+
+ align:start position:0%
+difference between zero and three is Big
+ 
+
+ align:start position:0%
+difference between zero and three is Big
+ratio so we want that to not happen too
+
+ align:start position:0%
+ratio so we want that to not happen too
+ 
+
+ align:start position:0%
+ratio so we want that to not happen too
+much and it doesn't happen too much
+
+ align:start position:0%
+much and it doesn't happen too much
+ 
+
+ align:start position:0%
+much and it doesn't happen too much
+because we know uh the left hand side
+
+ align:start position:0%
+because we know uh the left hand side
+ 
+
+ align:start position:0%
+because we know uh the left hand side
+opt is at least half of all the claes so
+
+ align:start position:0%
+opt is at least half of all the claes so
+ 
+
+ align:start position:0%
+opt is at least half of all the claes so
+it's not like there are very many
+
+ align:start position:0%
+it's not like there are very many
+ 
+
+ align:start position:0%
+it's not like there are very many
+unsatisfied Clauses at most half of them
+
+ align:start position:0%
+unsatisfied Clauses at most half of them
+ 
+
+ align:start position:0%
+unsatisfied Clauses at most half of them
+are unsatisfied cu because at least half
+
+ align:start position:0%
+are unsatisfied cu because at least half
+ 
+
+ align:start position:0%
+are unsatisfied cu because at least half
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+satisfiable in the case of opt uh
+
+ align:start position:0%
+satisfiable in the case of opt uh
+ 
+
+ align:start position:0%
+satisfiable in the case of opt uh
+so here's the full
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argument in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general opt for the threat instance is
+
+ align:start position:0%
+general opt for the threat instance is
+ 
+
+ align:start position:0%
+general opt for the threat instance is
+going to be four times all the
+
+ align:start position:0%
+going to be four times all the
+ 
+
+ align:start position:0%
+going to be four times all the
+satisfiable things plus three times all
+
+ align:start position:0%
+satisfiable things plus three times all
+ 
+
+ align:start position:0%
+satisfiable things plus three times all
+the unsatisfiable things this is the
+
+ align:start position:0%
+the unsatisfiable things this is the
+ 
+
+ align:start position:0%
+the unsatisfiable things this is the
+same thing as saying uh the
+
+ align:start position:0%
+same thing as saying uh the
+ 
+
+ align:start position:0%
+same thing as saying uh the
+uh sorry you take three times the number
+
+ align:start position:0%
+uh sorry you take three times the number
+ 
+
+ align:start position:0%
+uh sorry you take three times the number
+of equations every equation gets three
+
+ align:start position:0%
+of equations every equation gets three
+ 
+
+ align:start position:0%
+of equations every equation gets three
+points for free and then if you also
+
+ align:start position:0%
+points for free and then if you also
+ 
+
+ align:start position:0%
+points for free and then if you also
+satisfy them you get one more Point okay
+
+ align:start position:0%
+satisfy them you get one more Point okay
+ 
+
+ align:start position:0%
+satisfy them you get one more Point okay
+so this is an equation on those things
+
+ align:start position:0%
+so this is an equation on those things
+ 
+
+ align:start position:0%
+so this is an equation on those things
+the two Ops and we get plus three times
+
+ align:start position:0%
+the two Ops and we get plus three times
+ 
+
+ align:start position:0%
+the two Ops and we get plus three times
+the number of equations and because
+
+ align:start position:0%
+the number of equations and because
+ 
+
+ align:start position:0%
+the number of equations and because
+there is a 1/2 approximation we know
+
+ align:start position:0%
+there is a 1/2 approximation we know
+ 
+
+ align:start position:0%
+there is a 1/2 approximation we know
+that number of equations uh is at most
+
+ align:start position:0%
+that number of equations uh is at most
+ 
+
+ align:start position:0%
+that number of equations uh is at most
+uh 2 * opt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because opt is at least a half the
+
+ align:start position:0%
+because opt is at least a half the
+ 
+
+ align:start position:0%
+because opt is at least a half the
+number of equations and so this thing is
+
+ align:start position:0%
+number of equations and so this thing is
+ 
+
+ align:start position:0%
+number of equations and so this thing is
+overall at most 6 + 1 7
+
+ align:start position:0%
+overall at most 6 + 1 7
+ 
+
+ align:start position:0%
+overall at most 6 + 1 7
+* opt e3x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nor okay uh and this is the thing called
+
+ align:start position:0%
+nor okay uh and this is the thing called
+ 
+
+ align:start position:0%
+nor okay uh and this is the thing called
+Alpha in L
+
+ align:start position:0%
+Alpha in L
+ 
+
+ align:start position:0%
+Alpha in L
+reduction I wanted to compute these
+
+ align:start position:0%
+reduction I wanted to compute these
+ 
+
+ align:start position:0%
+reduction I wanted to compute these
+explicitly because I want to see how
+
+ align:start position:0%
+explicitly because I want to see how
+ 
+
+ align:start position:0%
+explicitly because I want to see how
+much inapproximability I get because I
+
+ align:start position:0%
+much inapproximability I get because I
+ 
+
+ align:start position:0%
+much inapproximability I get because I
+started with a tight in approximability
+
+ align:start position:0%
+started with a tight in approximability
+ 
+
+ align:start position:0%
+started with a tight in approximability
+Bound of 1 12 minus Epsilon being
+
+ align:start position:0%
+Bound of 1 12 minus Epsilon being
+ 
+
+ align:start position:0%
+Bound of 1 12 minus Epsilon being
+impossible uh whereas 1/2 is possible
+
+ align:start position:0%
+impossible uh whereas 1/2 is possible
+ 
+
+ align:start position:0%
+impossible uh whereas 1/2 is possible
+it's tight up to this very tiny
+
+ align:start position:0%
+it's tight up to this very tiny
+ 
+
+ align:start position:0%
+it's tight up to this very tiny
+arbitrary additive
+
+ align:start position:0%
+arbitrary additive
+ 
+
+ align:start position:0%
+arbitrary additive
+constant uh and over here we're going to
+
+ align:start position:0%
+constant uh and over here we're going to
+ 
+
+ align:start position:0%
+constant uh and over here we're going to
+lose something uh we know from L
+
+ align:start position:0%
+lose something uh we know from L
+ 
+
+ align:start position:0%
+lose something uh we know from L
+reductions if you're inapproximability
+
+ align:start position:0%
+reductions if you're inapproximability
+ 
+
+ align:start position:0%
+reductions if you're inapproximability
+in this case of Max E3 set so what is
+
+ align:start position:0%
+in this case of Max E3 set so what is
+ 
+
+ align:start position:0%
+in this case of Max E3 set so what is
+the factor um if you think of there's uh
+
+ align:start position:0%
+the factor um if you think of there's uh
+ 
+
+ align:start position:0%
+the factor um if you think of there's uh
+one simplif here relative to what I
+
+ align:start position:0%
+one simplif here relative to what I
+ 
+
+ align:start position:0%
+one simplif here relative to what I
+presented before uh a couple lectures
+
+ align:start position:0%
+presented before uh a couple lectures
+ 
+
+ align:start position:0%
+presented before uh a couple lectures
+ago we always thought about 1 plus
+
+ align:start position:0%
+ago we always thought about 1 plus
+ 
+
+ align:start position:0%
+ago we always thought about 1 plus
+Epsilon approximation and how does
+
+ align:start position:0%
+Epsilon approximation and how does
+ 
+
+ align:start position:0%
+Epsilon approximation and how does
+epsilon change um and that works really
+
+ align:start position:0%
+epsilon change um and that works really
+ 
+
+ align:start position:0%
+epsilon change um and that works really
+well for minimization problems for a
+
+ align:start position:0%
+well for minimization problems for a
+ 
+
+ align:start position:0%
+well for minimization problems for a
+maximization problem your approximation
+
+ align:start position:0%
+maximization problem your approximation
+ 
+
+ align:start position:0%
+maximization problem your approximation
+factor is uh more I mean one an
+
+ align:start position:0%
+factor is uh more I mean one an
+ 
+
+ align:start position:0%
+factor is uh more I mean one an
+approximation factor of 1 plus Epsilon
+
+ align:start position:0%
+approximation factor of 1 plus Epsilon
+ 
+
+ align:start position:0%
+approximation factor of 1 plus Epsilon
+means you are at least this thing times
+
+ align:start position:0%
+means you are at least this thing times
+ 
+
+ align:start position:0%
+means you are at least this thing times
+opt and this thing gets awkward to work
+
+ align:start position:0%
+opt and this thing gets awkward to work
+ 
+
+ align:start position:0%
+opt and this thing gets awkward to work
+with uh equivalently with a different
+
+ align:start position:0%
+with uh equivalently with a different
+ 
+
+ align:start position:0%
+with uh equivalently with a different
+notion of Epsilon you can just think of
+
+ align:start position:0%
+notion of Epsilon you can just think of
+ 
+
+ align:start position:0%
+notion of Epsilon you can just think of
+a 1 minus Epsilon approximation and how
+
+ align:start position:0%
+a 1 minus Epsilon approximation and how
+ 
+
+ align:start position:0%
+a 1 minus Epsilon approximation and how
+does epsilon change and in general uh
+
+ align:start position:0%
+does epsilon change and in general uh
+ 
+
+ align:start position:0%
+does epsilon change and in general uh
+for so for maximization problem if you
+
+ align:start position:0%
+for so for maximization problem if you
+ 
+
+ align:start position:0%
+for so for maximization problem if you
+have one minus Epsilon approximation
+
+ align:start position:0%
+have one minus Epsilon approximation
+ 
+
+ align:start position:0%
+have one minus Epsilon approximation
+before the L reduction then afterwards
+
+ align:start position:0%
+before the L reduction then afterwards
+ 
+
+ align:start position:0%
+before the L reduction then afterwards
+you will have a 1 minus Epsilon over
+
+ align:start position:0%
+you will have a 1 minus Epsilon over
+ 
+
+ align:start position:0%
+you will have a 1 minus Epsilon over
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+Beta so for maximization we had one plus
+
+ align:start position:0%
+Beta so for maximization we had one plus
+ 
+
+ align:start position:0%
+Beta so for maximization we had one plus
+Epsilon and then we got 1 plus Epsilon
+
+ align:start position:0%
+Epsilon and then we got 1 plus Epsilon
+ 
+
+ align:start position:0%
+Epsilon and then we got 1 plus Epsilon
+over Alpha Beta with the minuses it also
+
+ align:start position:0%
+over Alpha Beta with the minuses it also
+ 
+
+ align:start position:0%
+over Alpha Beta with the minuses it also
+works out that's a cleaner way to do Max
+
+ align:start position:0%
+works out that's a cleaner way to do Max
+ 
+
+ align:start position:0%
+works out that's a cleaner way to do Max
+Max imization so this was a maximization
+
+ align:start position:0%
+Max imization so this was a maximization
+ 
+
+ align:start position:0%
+Max imization so this was a maximization
+problem we had uh over here Epsilon was
+
+ align:start position:0%
+problem we had uh over here Epsilon was
+ 
+
+ align:start position:0%
+problem we had uh over here Epsilon was
+uh sorry different Notions of Epsilon
+
+ align:start position:0%
+uh sorry different Notions of Epsilon
+ 
+
+ align:start position:0%
+uh sorry different Notions of Epsilon
+here we have one2 in approximability
+
+ align:start position:0%
+here we have one2 in approximability
+ 
+
+ align:start position:0%
+here we have one2 in approximability
+that it 1/2 is also known as 1 minus 1/2
+
+ align:start position:0%
+that it 1/2 is also known as 1 minus 1/2
+ 
+
+ align:start position:0%
+that it 1/2 is also known as 1 minus 1/2
+so Epsilon here is a half um and Alpha
+
+ align:start position:0%
+so Epsilon here is a half um and Alpha
+ 
+
+ align:start position:0%
+so Epsilon here is a half um and Alpha
+was 7 beta was uh 1 and so we just
+
+ align:start position:0%
+was 7 beta was uh 1 and so we just
+ 
+
+ align:start position:0%
+was 7 beta was uh 1 and so we just
+divide by seven so in this case we get
+
+ align:start position:0%
+divide by seven so in this case we get
+ 
+
+ align:start position:0%
+divide by seven so in this case we get
+that Max E3 sat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is 1
+
+ align:start position:0%
+uh is 1
+ 
+
+ align:start position:0%
+uh is 1
+minus uh 12 / 7 which is
+
+ align:start position:0%
+minus uh 12 / 7 which is
+ 
+
+ align:start position:0%
+minus uh 12 / 7 which is
+114th technically there's a minus
+
+ align:start position:0%
+114th technically there's a minus
+ 
+
+ align:start position:0%
+114th technically there's a minus
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+here sorry bad use of bad overuse of
+
+ align:start position:0%
+here sorry bad use of bad overuse of
+ 
+
+ align:start position:0%
+here sorry bad use of bad overuse of
+Epsilon this is again for any Epsilon
+
+ align:start position:0%
+Epsilon this is again for any Epsilon
+ 
+
+ align:start position:0%
+Epsilon this is again for any Epsilon
+greater than zero because uh we had some
+
+ align:start position:0%
+greater than zero because uh we had some
+ 
+
+ align:start position:0%
+greater than zero because uh we had some
+Epsilon greater than zero here slightly
+
+ align:start position:0%
+Epsilon greater than zero here slightly
+ 
+
+ align:start position:0%
+Epsilon greater than zero here slightly
+less than 1/2 is impossible so over here
+
+ align:start position:0%
+less than 1/2 is impossible so over here
+ 
+
+ align:start position:0%
+less than 1/2 is impossible so over here
+we get slightly less than 1 - 1 14th is
+
+ align:start position:0%
+we get slightly less than 1 - 1 14th is
+ 
+
+ align:start position:0%
+we get slightly less than 1 - 1 14th is
+impossible this is
+
+ align:start position:0%
+impossible this is
+ 
+
+ align:start position:0%
+impossible this is
+uh uh 13 over
+
+ align:start position:0%
+uh uh 13 over
+ 
+
+ align:start position:0%
+uh uh 13 over
+14 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon uh which is okay it's a bound uh
+
+ align:start position:0%
+Epsilon uh which is okay it's a bound uh
+ 
+
+ align:start position:0%
+Epsilon uh which is okay it's a bound uh
+but it's not a tight bount the right
+
+ align:start position:0%
+but it's not a tight bount the right
+ 
+
+ align:start position:0%
+but it's not a tight bount the right
+answer for Max 3 set is 78 because if
+
+ align:start position:0%
+answer for Max 3 set is 78 because if
+ 
+
+ align:start position:0%
+answer for Max 3 set is 78 because if
+you take a again a uniform random
+
+ align:start position:0%
+you take a again a uniform random
+ 
+
+ align:start position:0%
+you take a again a uniform random
+assignment every variable flips a coin
+
+ align:start position:0%
+assignment every variable flips a coin
+ 
+
+ align:start position:0%
+assignment every variable flips a coin
+heads or tails true or false
+
+ align:start position:0%
+heads or tails true or false
+ 
+
+ align:start position:0%
+heads or tails true or false
+uh then 7/8 of the Clauses will be
+
+ align:start position:0%
+uh then 7/8 of the Clauses will be
+ 
+
+ align:start position:0%
+uh then 7/8 of the Clauses will be
+satisfied in expectation because if you
+
+ align:start position:0%
+satisfied in expectation because if you
+ 
+
+ align:start position:0%
+satisfied in expectation because if you
+look at a clause if it has exactly three
+
+ align:start position:0%
+look at a clause if it has exactly three
+ 
+
+ align:start position:0%
+look at a clause if it has exactly three
+terms and it's an or of three things you
+
+ align:start position:0%
+terms and it's an or of three things you
+ 
+
+ align:start position:0%
+terms and it's an or of three things you
+just need at least one head to satisfy
+
+ align:start position:0%
+just need at least one head to satisfy
+ 
+
+ align:start position:0%
+just need at least one head to satisfy
+this thing so you get a 50% chance to do
+
+ align:start position:0%
+this thing so you get a 50% chance to do
+ 
+
+ align:start position:0%
+this thing so you get a 50% chance to do
+it in the first time and then a quarter
+
+ align:start position:0%
+it in the first time and then a quarter
+ 
+
+ align:start position:0%
+it in the first time and then a quarter
+chance to do it in the third time and
+
+ align:start position:0%
+chance to do it in the third time and
+ 
+
+ align:start position:0%
+chance to do it in the third time and
+general 78 chance to get it one of the
+
+ align:start position:0%
+general 78 chance to get it one of the
+ 
+
+ align:start position:0%
+general 78 chance to get it one of the
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+times uh 78 is smaller than
+
+ align:start position:0%
+times uh 78 is smaller than
+ 
+
+ align:start position:0%
+times uh 78 is smaller than
+1314 so we're not quite there yet but
+
+ align:start position:0%
+1314 so we're not quite there yet but
+ 
+
+ align:start position:0%
+1314 so we're not quite there yet but
+this reduction will do it if we think
+
+ align:start position:0%
+this reduction will do it if we think
+ 
+
+ align:start position:0%
+this reduction will do it if we think
+about it from the perspective of Gap
+
+ align:start position:0%
+about it from the perspective of Gap
+ 
+
+ align:start position:0%
+about it from the perspective of Gap
+preserving
+
+ align:start position:0%
+preserving
+ 
+
+ align:start position:0%
+preserving
+reductions so from this General L
+
+ align:start position:0%
+reductions so from this General L
+ 
+
+ align:start position:0%
+reductions so from this General L
+reduction black box that we only lose an
+
+ align:start position:0%
+reduction black box that we only lose an
+ 
+
+ align:start position:0%
+reduction black box that we only lose an
+alpha beta Factor yeah we get this bound
+
+ align:start position:0%
+alpha beta Factor yeah we get this bound
+ 
+
+ align:start position:0%
+alpha beta Factor yeah we get this bound
+um but from a gap perspective we can do
+
+ align:start position:0%
+um but from a gap perspective we can do
+ 
+
+ align:start position:0%
+um but from a gap perspective we can do
+better the reason we can do better is uh
+
+ align:start position:0%
+better the reason we can do better is uh
+ 
+
+ align:start position:0%
+better the reason we can do better is uh
+because gaps are always talking about
+
+ align:start position:0%
+because gaps are always talking about
+ 
+
+ align:start position:0%
+because gaps are always talking about
+yes instances where lots of things are
+
+ align:start position:0%
+yes instances where lots of things are
+ 
+
+ align:start position:0%
+yes instances where lots of things are
+satisfied that means we're most of the
+
+ align:start position:0%
+satisfied that means we're most of the
+ 
+
+ align:start position:0%
+satisfied that means we're most of the
+time in the case where we have fours on
+
+ align:start position:0%
+time in the case where we have fours on
+ 
+
+ align:start position:0%
+time in the case where we have fours on
+the right hand side
+
+ align:start position:0%
+the right hand side
+ 
+
+ align:start position:0%
+the right hand side
+or a situation where we have lots of
+
+ align:start position:0%
+or a situation where we have lots of
+ 
+
+ align:start position:0%
+or a situation where we have lots of
+things unsatisfied that means we have
+
+ align:start position:0%
+things unsatisfied that means we have
+ 
+
+ align:start position:0%
+things unsatisfied that means we have
+lots of Threes on the right hand side it
+
+ align:start position:0%
+lots of Threes on the right hand side it
+ 
+
+ align:start position:0%
+lots of Threes on the right hand side it
+lets us get a slightly tighter bound so
+
+ align:start position:0%
+lets us get a slightly tighter bound so
+ 
+
+ align:start position:0%
+lets us get a slightly tighter bound so
+let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all all right so here is a gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+argument about the same reduction what
+
+ align:start position:0%
+argument about the same reduction what
+ 
+
+ align:start position:0%
+argument about the same reduction what
+we're going to claim is that uh 78 minus
+
+ align:start position:0%
+we're going to claim is that uh 78 minus
+ 
+
+ align:start position:0%
+we're going to claim is that uh 78 minus
+Epsilon uh
+
+ align:start position:0%
+Epsilon uh
+ 
+
+ align:start position:0%
+Epsilon uh
+Gap
+
+ align:start position:0%
+Gap
+ 
+
+ align:start position:0%
+Gap
+threat is nty
+
+ align:start position:0%
+threat is nty
+ 
+
+ align:start position:0%
+threat is nty
+hard which implies 78 in approximability
+
+ align:start position:0%
+hard which implies 78 in approximability
+ 
+
+ align:start position:0%
+hard which implies 78 in approximability
+but by looking at it from The Gap
+
+ align:start position:0%
+but by looking at it from The Gap
+ 
+
+ align:start position:0%
+but by looking at it from The Gap
+perspective we will get this stronger
+
+ align:start position:0%
+perspective we will get this stronger
+ 
+
+ align:start position:0%
+perspective we will get this stronger
+bound versus the 13 over 14
+
+ align:start position:0%
+bound versus the 13 over 14
+ 
+
+ align:start position:0%
+bound versus the 13 over 14
+bound so
+
+ align:start position:0%
+bound so
+ 
+
+ align:start position:0%
+bound so
+uh the proof is by a gap preserving
+
+ align:start position:0%
+uh the proof is by a gap preserving
+ 
+
+ align:start position:0%
+uh the proof is by a gap preserving
+reduction namely that reduction from Max
+
+ align:start position:0%
+reduction namely that reduction from Max
+ 
+
+ align:start position:0%
+reduction namely that reduction from Max
+E3 X norat to
+
+ align:start position:0%
+E3 X norat to
+ 
+
+ align:start position:0%
+E3 X norat to
+uh Max 3at E3 sat I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say and so the idea is the following
+
+ align:start position:0%
+say and so the idea is the following
+ 
+
+ align:start position:0%
+say and so the idea is the following
+either we have a yes instance or a no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instance if we have a yes instance
+
+ align:start position:0%
+instance if we have a yes instance
+ 
+
+ align:start position:0%
+instance if we have a yes instance
+uh to
+
+ align:start position:0%
+uh to
+ 
+
+ align:start position:0%
+uh to
+the uh equation problem then we know
+
+ align:start position:0%
+the uh equation problem then we know
+ 
+
+ align:start position:0%
+the uh equation problem then we know
+that uh at least 1us Epsilon of the
+
+ align:start position:0%
+that uh at least 1us Epsilon of the
+ 
+
+ align:start position:0%
+that uh at least 1us Epsilon of the
+uh equations are
+
+ align:start position:0%
+uh equations are
+ 
+
+ align:start position:0%
+uh equations are
+satisfiable okay
+
+ align:start position:0%
+satisfiable okay
+ 
+
+ align:start position:0%
+satisfiable okay
+so we have 1 minus Epsilon let's say m
+
+ align:start position:0%
+so we have 1 minus Epsilon let's say m
+ 
+
+ align:start position:0%
+so we have 1 minus Epsilon let's say m
+is the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations in the no instance case of
+
+ align:start position:0%
+equations in the no instance case of
+ 
+
+ align:start position:0%
+equations in the no instance case of
+course we know uh that not too many are
+
+ align:start position:0%
+course we know uh that not too many are
+ 
+
+ align:start position:0%
+course we know uh that not too many are
+satisfied at most 12 plus Epsilon
+
+ align:start position:0%
+satisfied at most 12 plus Epsilon
+ 
+
+ align:start position:0%
+satisfied at most 12 plus Epsilon
+fraction the equations are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfiable so uh in both cases I want
+
+ align:start position:0%
+satisfiable so uh in both cases I want
+ 
+
+ align:start position:0%
+satisfiable so uh in both cases I want
+to see what that converts into so on in
+
+ align:start position:0%
+to see what that converts into so on in
+ 
+
+ align:start position:0%
+to see what that converts into so on in
+the yes instance we get uh all four of
+
+ align:start position:0%
+the yes instance we get uh all four of
+ 
+
+ align:start position:0%
+the yes instance we get uh all four of
+those things being satisfied
+
+ align:start position:0%
+those things being satisfied
+ 
+
+ align:start position:0%
+those things being satisfied
+so that means we're going to have uh at
+
+ align:start position:0%
+so that means we're going to have uh at
+ 
+
+ align:start position:0%
+so that means we're going to have uh at
+least 1 - Epsilon time M * 4 Clauses
+
+ align:start position:0%
+least 1 - Epsilon time M * 4 Clauses
+ 
+
+ align:start position:0%
+least 1 - Epsilon time M * 4 Clauses
+satisfied we'll also have Epsilon M * 3
+
+ align:start position:0%
+satisfied we'll also have Epsilon M * 3
+ 
+
+ align:start position:0%
+satisfied we'll also have Epsilon M * 3
+those are the uh unsatisfied and maybe
+
+ align:start position:0%
+those are the uh unsatisfied and maybe
+ 
+
+ align:start position:0%
+those are the uh unsatisfied and maybe
+some of them are actually satisfied but
+
+ align:start position:0%
+some of them are actually satisfied but
+ 
+
+ align:start position:0%
+some of them are actually satisfied but
+this is a lower bound on how many
+
+ align:start position:0%
+this is a lower bound on how many
+ 
+
+ align:start position:0%
+this is a lower bound on how many
+Clauses we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get okay on the other hand in this
+
+ align:start position:0%
+get okay on the other hand in this
+ 
+
+ align:start position:0%
+get okay on the other hand in this
+situation where not too many are
+
+ align:start position:0%
+situation where not too many are
+ 
+
+ align:start position:0%
+situation where not too many are
+satisfied that means we get a a tighter
+
+ align:start position:0%
+satisfied that means we get a a tighter
+ 
+
+ align:start position:0%
+satisfied that means we get a a tighter
+upper bound so we have
+
+ align:start position:0%
+upper bound so we have
+ 
+
+ align:start position:0%
+upper bound so we have
+uh 12 plus Epsilon * m * 4 and then
+
+ align:start position:0%
+uh 12 plus Epsilon * m * 4 and then
+ 
+
+ align:start position:0%
+uh 12 plus Epsilon * m * 4 and then
+there's the rest 12 minus
+
+ align:start position:0%
+there's the rest 12 minus
+ 
+
+ align:start position:0%
+there's the rest 12 minus
+Epsilon uh *
+
+ align:start position:0%
+Epsilon uh *
+ 
+
+ align:start position:0%
+Epsilon uh *
+3 and maybe some of these are not
+
+ align:start position:0%
+3 and maybe some of these are not
+ 
+
+ align:start position:0%
+3 and maybe some of these are not
+satisfied but this is an upper bound on
+
+ align:start position:0%
+satisfied but this is an upper bound on
+ 
+
+ align:start position:0%
+satisfied but this is an upper bound on
+how many Clauses are
+
+ align:start position:0%
+how many Clauses are
+ 
+
+ align:start position:0%
+how many Clauses are
+satisfied in the three set instance
+
+ align:start position:0%
+satisfied in the three set instance
+ 
+
+ align:start position:0%
+satisfied in the three set instance
+versus equations in the uh 3x set
+
+ align:start position:0%
+versus equations in the uh 3x set
+ 
+
+ align:start position:0%
+versus equations in the uh 3x set
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+okay now I just want to uh compute these
+
+ align:start position:0%
+okay now I just want to uh compute these
+ 
+
+ align:start position:0%
+okay now I just want to uh compute these
+so everything's time M and over here we
+
+ align:start position:0%
+so everything's time M and over here we
+ 
+
+ align:start position:0%
+so everything's time M and over here we
+have 4 - 4 Epsilon over here we have + 3
+
+ align:start position:0%
+have 4 - 4 Epsilon over here we have + 3
+ 
+
+ align:start position:0%
+have 4 - 4 Epsilon over here we have + 3
+Epsilon so that is 4 -
+
+ align:start position:0%
+Epsilon so that is 4 -
+ 
+
+ align:start position:0%
+Epsilon so that is 4 -
+Epsilon M and here we have again
+
+ align:start position:0%
+Epsilon M and here we have again
+ 
+
+ align:start position:0%
+Epsilon M and here we have again
+everything is times M so we have uh four
+
+ align:start position:0%
+everything is times M so we have uh four
+ 
+
+ align:start position:0%
+everything is times M so we have uh four
+halves also known as
+
+ align:start position:0%
+halves also known as
+ 
+
+ align:start position:0%
+halves also known as
+two uh plus 4 Epsilon
+
+ align:start position:0%
+two uh plus 4 Epsilon
+ 
+
+ align:start position:0%
+two uh plus 4 Epsilon
+uh plus we have three halves uh minus 3
+
+ align:start position:0%
+uh plus we have three halves uh minus 3
+ 
+
+ align:start position:0%
+uh plus we have three halves uh minus 3
+Epsilon so the epsilons add up to plus
+
+ align:start position:0%
+Epsilon so the epsilons add up to plus
+ 
+
+ align:start position:0%
+Epsilon so the epsilons add up to plus
+Epsilon that much I can see 4 Epsilon
+
+ align:start position:0%
+Epsilon that much I can see 4 Epsilon
+ 
+
+ align:start position:0%
+Epsilon that much I can see 4 Epsilon
+minus 3 Epsilon um and then we have four
+
+ align:start position:0%
+minus 3 Epsilon um and then we have four
+ 
+
+ align:start position:0%
+minus 3 Epsilon um and then we have four
+halves plus three Hales also known as
+
+ align:start position:0%
+halves plus three Hales also known as
+ 
+
+ align:start position:0%
+halves plus three Hales also known as
+seven halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay so we had a gap four and we get
+
+ align:start position:0%
+yes okay so we had a gap four and we get
+ 
+
+ align:start position:0%
+yes okay so we had a gap four and we get
+this new Gap after when we have a yes
+
+ align:start position:0%
+this new Gap after when we have a yes
+ 
+
+ align:start position:0%
+this new Gap after when we have a yes
+instance we know that there'll be at
+
+ align:start position:0%
+instance we know that there'll be at
+ 
+
+ align:start position:0%
+instance we know that there'll be at
+least as many Clauses satisfied in the
+
+ align:start position:0%
+least as many Clauses satisfied in the
+ 
+
+ align:start position:0%
+least as many Clauses satisfied in the
+three set and there'll be at most this
+
+ align:start position:0%
+three set and there'll be at most this
+ 
+
+ align:start position:0%
+three set and there'll be at most this
+many in the no instance so what we
+
+ align:start position:0%
+many in the no instance so what we
+ 
+
+ align:start position:0%
+many in the no instance so what we
+proved is uh this bound that
+
+ align:start position:0%
+proved is uh this bound that
+ 
+
+ align:start position:0%
+proved is uh this bound that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh got them in the right order s Hales
+
+ align:start position:0%
+uh got them in the right order s Hales
+ 
+
+ align:start position:0%
+uh got them in the right order s Hales
+is the smaller one 7es plus Epsilon
+
+ align:start position:0%
+is the smaller one 7es plus Epsilon
+ 
+
+ align:start position:0%
+is the smaller one 7es plus Epsilon
+comma 4 minus
+
+ align:start position:0%
+comma 4 minus
+ 
+
+ align:start position:0%
+comma 4 minus
+Epsilon Gap three set
+
+ align:start position:0%
+Epsilon Gap three set
+ 
+
+ align:start position:0%
+Epsilon Gap three set
+E3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set is NP hard because we had NP
+
+ align:start position:0%
+set is NP hard because we had NP
+ 
+
+ align:start position:0%
+set is NP hard because we had NP
+hardness of the of the gap before we did
+
+ align:start position:0%
+hardness of the of the gap before we did
+ 
+
+ align:start position:0%
+hardness of the of the gap before we did
+this Gap preserving reduction which
+
+ align:start position:0%
+this Gap preserving reduction which
+ 
+
+ align:start position:0%
+this Gap preserving reduction which
+ended up with this new Gap uh this being
+
+ align:start position:0%
+ended up with this new Gap uh this being
+ 
+
+ align:start position:0%
+ended up with this new Gap uh this being
+for no instances as being for yes
+
+ align:start position:0%
+for no instances as being for yes
+ 
+
+ align:start position:0%
+for no instances as being for yes
+instances uh and so if we want to this
+
+ align:start position:0%
+instances uh and so if we want to this
+ 
+
+ align:start position:0%
+instances uh and so if we want to this
+is with the comma notation for the yes
+
+ align:start position:0%
+is with the comma notation for the yes
+ 
+
+ align:start position:0%
+is with the comma notation for the yes
+and no how how what fraction is
+
+ align:start position:0%
+and no how how what fraction is
+ 
+
+ align:start position:0%
+and no how how what fraction is
+satisfied uh if you um convert it back
+
+ align:start position:0%
+satisfied uh if you um convert it back
+ 
+
+ align:start position:0%
+satisfied uh if you um convert it back
+into the C Gap notation you just take
+
+ align:start position:0%
+into the C Gap notation you just take
+ 
+
+ align:start position:0%
+into the C Gap notation you just take
+the ratio between these two things and
+
+ align:start position:0%
+the ratio between these two things and
+ 
+
+ align:start position:0%
+the ratio between these two things and
+ignoring the epsilons this is like 4 / 7
+
+ align:start position:0%
+ignoring the epsilons this is like 4 / 7
+ 
+
+ align:start position:0%
+ignoring the epsilons this is like 4 / 7
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+is 78 or 87th depending on which way
+
+ align:start position:0%
+is 78 or 87th depending on which way
+ 
+
+ align:start position:0%
+is 78 or 87th depending on which way
+you're looking uh so we get also
+
+ align:start position:0%
+you're looking uh so we get also
+ 
+
+ align:start position:0%
+you're looking uh so we get also
+78 Gap sorry I guess
+
+ align:start position:0%
+78 Gap sorry I guess
+ 
+
+ align:start position:0%
+78 Gap sorry I guess
+87th the way I was phrasing it
+
+ align:start position:0%
+87th the way I was phrasing it
+ 
+
+ align:start position:0%
+87th the way I was phrasing it
+before uh is also NP heart and so that
+
+ align:start position:0%
+before uh is also NP heart and so that
+ 
+
+ align:start position:0%
+before uh is also NP heart and so that
+proves there's also a minus Epsilon
+
+ align:start position:0%
+proves there's also a minus Epsilon
+ 
+
+ align:start position:0%
+proves there's also a minus Epsilon
+sorry I should have kept those slightly
+
+ align:start position:0%
+sorry I should have kept those slightly
+ 
+
+ align:start position:0%
+sorry I should have kept those slightly
+different Epsilon but minus 2 Epsilon
+
+ align:start position:0%
+different Epsilon but minus 2 Epsilon
+ 
+
+ align:start position:0%
+different Epsilon but minus 2 Epsilon
+whatever um and so this gives us the
+
+ align:start position:0%
+whatever um and so this gives us the
+ 
+
+ align:start position:0%
+whatever um and so this gives us the
+87th is the best approximation Factor we
+
+ align:start position:0%
+87th is the best approximation Factor we
+ 
+
+ align:start position:0%
+87th is the best approximation Factor we
+can hope for yeah uh and the first
+
+ align:start position:0%
+can hope for yeah uh and the first
+ 
+
+ align:start position:0%
+can hope for yeah uh and the first
+notation isn't it the fraction of
+
+ align:start position:0%
+notation isn't it the fraction of
+ 
+
+ align:start position:0%
+notation isn't it the fraction of
+Clauses so between zero and one oh yeah
+
+ align:start position:0%
+Clauses so between zero and one oh yeah
+ 
+
+ align:start position:0%
+Clauses so between zero and one oh yeah
+four is a little funny uh right I needed
+
+ align:start position:0%
+four is a little funny uh right I needed
+ 
+
+ align:start position:0%
+four is a little funny uh right I needed
+to scale um thank you because the number
+
+ align:start position:0%
+to scale um thank you because the number
+ 
+
+ align:start position:0%
+to scale um thank you because the number
+of Clauses in the resulting thing is
+
+ align:start position:0%
+of Clauses in the resulting thing is
+ 
+
+ align:start position:0%
+of Clauses in the resulting thing is
+actually 4 m not M so everything here
+
+ align:start position:0%
+actually 4 m not M so everything here
+ 
+
+ align:start position:0%
+actually 4 m not M so everything here
+needs to be div divided by
+
+ align:start position:0%
+needs to be div divided by
+ 
+
+ align:start position:0%
+needs to be div divided by
+four won't affect the final ratio but
+
+ align:start position:0%
+four won't affect the final ratio but
+ 
+
+ align:start position:0%
+four won't affect the final ratio but
+this should really be over four and over
+
+ align:start position:0%
+this should really be over four and over
+ 
+
+ align:start position:0%
+this should really be over four and over
+four um so also known
+
+ align:start position:0%
+four um so also known
+ 
+
+ align:start position:0%
+four um so also known
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+78 plus Epsilon comma 1us
+
+ align:start position:0%
+78 plus Epsilon comma 1us
+ 
+
+ align:start position:0%
+78 plus Epsilon comma 1us
+Epsilon now it's a little clearer
+
+ align:start position:0%
+Epsilon now it's a little clearer
+ 
+
+ align:start position:0%
+Epsilon now it's a little clearer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool yeah so are there any like see this
+
+ align:start position:0%
+cool yeah so are there any like see this
+ 
+
+ align:start position:0%
+cool yeah so are there any like see this
+piece where we can beat
+
+ align:start position:0%
+piece where we can beat
+ 
+
+ align:start position:0%
+piece where we can beat
+Randomness uh so for Max cut you can
+
+ align:start position:0%
+Randomness uh so for Max cut you can
+ 
+
+ align:start position:0%
+Randomness uh so for Max cut you can
+beat the r Randomness oh cool uh
+
+ align:start position:0%
+beat the r Randomness oh cool uh
+ 
+
+ align:start position:0%
+beat the r Randomness oh cool uh
+Randomness would give you one half the
+
+ align:start position:0%
+Randomness would give you one half the
+ 
+
+ align:start position:0%
+Randomness would give you one half the
+Williamson algorithm gives you like 1
+
+ align:start position:0%
+Williamson algorithm gives you like 1
+ 
+
+ align:start position:0%
+Williamson algorithm gives you like 1
+something so you can beat it by a
+
+ align:start position:0%
+something so you can beat it by a
+ 
+
+ align:start position:0%
+something so you can beat it by a
+constant Factor probably not by more
+
+ align:start position:0%
+constant Factor probably not by more
+ 
+
+ align:start position:0%
+constant Factor probably not by more
+than a constant Factor but yeah Max cut
+
+ align:start position:0%
+than a constant Factor but yeah Max cut
+ 
+
+ align:start position:0%
+than a constant Factor but yeah Max cut
+is an example where you can beat it um I
+
+ align:start position:0%
+is an example where you can beat it um I
+ 
+
+ align:start position:0%
+is an example where you can beat it um I
+think I have the G Williamson bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here Max cut the best approximation is
+
+ align:start position:0%
+here Max cut the best approximation is
+ 
+
+ align:start position:0%
+here Max cut the best approximation is
+0878 which is better than what you get
+
+ align:start position:0%
+0878 which is better than what you get
+ 
+
+ align:start position:0%
+0878 which is better than what you get
+by random which is a half I
+
+ align:start position:0%
+by random which is a half I
+ 
+
+ align:start position:0%
+by random which is a half I
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+cool all
+
+ align:start position:0%
+cool all
+ 
+
+ align:start position:0%
+cool all
+right uh cool so we get optimal Bound
+
+ align:start position:0%
+right uh cool so we get optimal Bound
+ 
+
+ align:start position:0%
+right uh cool so we get optimal Bound
+for Max E3 Set uh assuming an optimal
+
+ align:start position:0%
+for Max E3 Set uh assuming an optimal
+ 
+
+ align:start position:0%
+for Max E3 Set uh assuming an optimal
+pound for e3x nor Set uh which is from
+
+ align:start position:0%
+pound for e3x nor Set uh which is from
+ 
+
+ align:start position:0%
+pound for e3x nor Set uh which is from
+PCP yeah so I'm sorry can you explain to
+
+ align:start position:0%
+PCP yeah so I'm sorry can you explain to
+ 
+
+ align:start position:0%
+PCP yeah so I'm sorry can you explain to
+me again why we don't get this from the
+
+ align:start position:0%
+me again why we don't get this from the
+ 
+
+ align:start position:0%
+me again why we don't get this from the
+L reduction but we do get it from the
+
+ align:start position:0%
+L reduction but we do get it from the
+ 
+
+ align:start position:0%
+L reduction but we do get it from the
+Gap argument even though the reduction
+
+ align:start position:0%
+Gap argument even though the reduction
+ 
+
+ align:start position:0%
+Gap argument even though the reduction
+is the same reduction uh it's just a it
+
+ align:start position:0%
+is the same reduction uh it's just a it
+ 
+
+ align:start position:0%
+is the same reduction uh it's just a it
+lets us give a a tighter argument in
+
+ align:start position:0%
+lets us give a a tighter argument in
+ 
+
+ align:start position:0%
+lets us give a a tighter argument in
+this case by thinking about yes
+
+ align:start position:0%
+this case by thinking about yes
+ 
+
+ align:start position:0%
+this case by thinking about yes
+instances and no instances separately we
+
+ align:start position:0%
+instances and no instances separately we
+ 
+
+ align:start position:0%
+instances and no instances separately we
+get one thing because this reduction is
+
+ align:start position:0%
+get one thing because this reduction is
+ 
+
+ align:start position:0%
+get one thing because this reduction is
+designed to do different things for yes
+
+ align:start position:0%
+designed to do different things for yes
+ 
+
+ align:start position:0%
+designed to do different things for yes
+and no instances whereas the L reduction
+
+ align:start position:0%
+and no instances whereas the L reduction
+ 
+
+ align:start position:0%
+and no instances whereas the L reduction
+just says generically if you satisfy
+
+ align:start position:0%
+just says generically if you satisfy
+ 
+
+ align:start position:0%
+just says generically if you satisfy
+these parameters Alpha and beta you get
+
+ align:start position:0%
+these parameters Alpha and beta you get
+ 
+
+ align:start position:0%
+these parameters Alpha and beta you get
+some an approximability result on the
+
+ align:start position:0%
+some an approximability result on the
+ 
+
+ align:start position:0%
+some an approximability result on the
+output but uh it's conservative it's a
+
+ align:start position:0%
+output but uh it's conservative it's a
+ 
+
+ align:start position:0%
+output but uh it's conservative it's a
+conservative bound if you just use
+
+ align:start position:0%
+conservative bound if you just use
+ 
+
+ align:start position:0%
+conservative bound if you just use
+properties one and two up here that's
+
+ align:start position:0%
+properties one and two up here that's
+ 
+
+ align:start position:0%
+properties one and two up here that's
+the best you could show but by
+
+ align:start position:0%
+the best you could show but by
+ 
+
+ align:start position:0%
+the best you could show but by
+essentially reanalyzing property one uh
+
+ align:start position:0%
+essentially reanalyzing property one uh
+ 
+
+ align:start position:0%
+essentially reanalyzing property one uh
+but thinking separately about yes and no
+
+ align:start position:0%
+but thinking separately about yes and no
+ 
+
+ align:start position:0%
+but thinking separately about yes and no
+instances this held for all instances we
+
+ align:start position:0%
+instances this held for all instances we
+ 
+
+ align:start position:0%
+instances this held for all instances we
+got a bound of seven but in the yes and
+
+ align:start position:0%
+got a bound of seven but in the yes and
+ 
+
+ align:start position:0%
+got a bound of seven but in the yes and
+the no cases you can essentially get a
+
+ align:start position:0%
+the no cases you can essentially get a
+ 
+
+ align:start position:0%
+the no cases you can essentially get a
+slightly tighter constant
+
+ align:start position:0%
+slightly tighter constant
+ 
+
+ align:start position:0%
+slightly tighter constant
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+Cool all right I want to tell you
+
+ align:start position:0%
+Cool all right I want to tell you
+ 
+
+ align:start position:0%
+Cool all right I want to tell you
+about uh another cool problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another Gap hardness that you can get
+
+ align:start position:0%
+another Gap hardness that you can get
+ 
+
+ align:start position:0%
+another Gap hardness that you can get
+out of PCP kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis by some Gap amplification
+
+ align:start position:0%
+analysis by some Gap amplification
+ 
+
+ align:start position:0%
+analysis by some Gap amplification
+essentially uh which is called label
+
+ align:start position:0%
+essentially uh which is called label
+ 
+
+ align:start position:0%
+essentially uh which is called label
+cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh this problem takes a little bit of
+
+ align:start position:0%
+so uh this problem takes a little bit of
+ 
+
+ align:start position:0%
+so uh this problem takes a little bit of
+time to Define uh but there the basic
+
+ align:start position:0%
+time to Define uh but there the basic
+ 
+
+ align:start position:0%
+time to Define uh but there the basic
+point is there are very strong lower
+
+ align:start position:0%
+point is there are very strong lower
+ 
+
+ align:start position:0%
+point is there are very strong lower
+bounds on the approximation Factor so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so you're given a bipartite graph no
+
+ align:start position:0%
+uh so you're given a bipartite graph no
+ 
+
+ align:start position:0%
+uh so you're given a bipartite graph no
+weights
+
+ align:start position:0%
+weights
+ 
+
+ align:start position:0%
+weights
+um the bipartition is
+
+ align:start position:0%
+um the bipartition is
+ 
+
+ align:start position:0%
+um the bipartition is
+a and furthermore a can be divided into
+
+ align:start position:0%
+a and furthermore a can be divided into
+ 
+
+ align:start position:0%
+a and furthermore a can be divided into
+K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chunks and so can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be again these are disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unions and let's say
+
+ align:start position:0%
+unions and let's say
+ 
+
+ align:start position:0%
+unions and let's say
+size of a is n size of B is
+
+ align:start position:0%
+size of a is n size of B is
+ 
+
+ align:start position:0%
+size of a is n size of B is
+n and size of each
+
+ align:start position:0%
+n and size of each
+ 
+
+ align:start position:0%
+n and size of each
+AI is also the
+
+ align:start position:0%
+AI is also the
+ 
+
+ align:start position:0%
+AI is also the
+same you don't have to make these
+
+ align:start position:0%
+same you don't have to make these
+ 
+
+ align:start position:0%
+same you don't have to make these
+assumptions but you can so let's make it
+
+ align:start position:0%
+assumptions but you can so let's make it
+ 
+
+ align:start position:0%
+assumptions but you can so let's make it
+a little bit cleaner so in general uh a
+
+ align:start position:0%
+a little bit cleaner so in general uh a
+ 
+
+ align:start position:0%
+a little bit cleaner so in general uh a
+consists of K groups each of size n over
+
+ align:start position:0%
+consists of K groups each of size n over
+ 
+
+ align:start position:0%
+consists of K groups each of size n over
+k b consists of K groups each of size n
+
+ align:start position:0%
+k b consists of K groups each of size n
+ 
+
+ align:start position:0%
+k b consists of K groups each of size n
+overk so that's our you know we have a
+
+ align:start position:0%
+overk so that's our you know we have a
+ 
+
+ align:start position:0%
+overk so that's our you know we have a
+here with these little groups
+
+ align:start position:0%
+here with these little groups
+ 
+
+ align:start position:0%
+here with these little groups
+we have B these little groups and
+
+ align:start position:0%
+we have B these little groups and
+ 
+
+ align:start position:0%
+we have B these little groups and
+there's some edges between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them in general your goal is to
+
+ align:start position:0%
+them in general your goal is to
+ 
+
+ align:start position:0%
+them in general your goal is to
+choose some subset of a let's call it a
+
+ align:start position:0%
+choose some subset of a let's call it a
+ 
+
+ align:start position:0%
+choose some subset of a let's call it a
+prime and some subset of B call it B
+
+ align:start position:0%
+prime and some subset of B call it B
+ 
+
+ align:start position:0%
+prime and some subset of B call it B
+Prime and uh one other thing I want to
+
+ align:start position:0%
+Prime and uh one other thing I want to
+ 
+
+ align:start position:0%
+Prime and uh one other thing I want to
+talk about is called a super
+
+ align:start position:0%
+talk about is called a super
+ 
+
+ align:start position:0%
+talk about is called a super
+Edge so
+
+ align:start position:0%
+Edge so
+ 
+
+ align:start position:0%
+Edge so
+uh and then I'll say what we want out of
+
+ align:start position:0%
+uh and then I'll say what we want out of
+ 
+
+ align:start position:0%
+uh and then I'll say what we want out of
+these subsets that we choose uh imagine
+
+ align:start position:0%
+these subsets that we choose uh imagine
+ 
+
+ align:start position:0%
+these subsets that we choose uh imagine
+Contracting each of these groups these
+
+ align:start position:0%
+Contracting each of these groups these
+ 
+
+ align:start position:0%
+Contracting each of these groups these
+are there are uh n over K items here and
+
+ align:start position:0%
+are there are uh n over K items here and
+ 
+
+ align:start position:0%
+are there are uh n over K items here and
+there are K different
+
+ align:start position:0%
+there are K different
+ 
+
+ align:start position:0%
+there are K different
+groups imagine Contracting each group to
+
+ align:start position:0%
+groups imagine Contracting each group to
+ 
+
+ align:start position:0%
+groups imagine Contracting each group to
+a single vertex so that here's this is
+
+ align:start position:0%
+a single vertex so that here's this is
+ 
+
+ align:start position:0%
+a single vertex so that here's this is
+A1 this is
+
+ align:start position:0%
+A1 this is
+ 
+
+ align:start position:0%
+A1 this is
+B3 um I want to say that there's a super
+
+ align:start position:0%
+B3 um I want to say that there's a super
+ 
+
+ align:start position:0%
+B3 um I want to say that there's a super
+Edge from the group A1 to the group B3
+
+ align:start position:0%
+Edge from the group A1 to the group B3
+ 
+
+ align:start position:0%
+Edge from the group A1 to the group B3
+because there's at least one Edge
+
+ align:start position:0%
+because there's at least one Edge
+ 
+
+ align:start position:0%
+because there's at least one Edge
+between them if I squashed A1 down to a
+
+ align:start position:0%
+between them if I squashed A1 down to a
+ 
+
+ align:start position:0%
+between them if I squashed A1 down to a
+single vertex B3 down to a single vertex
+
+ align:start position:0%
+single vertex B3 down to a single vertex
+ 
+
+ align:start position:0%
+single vertex B3 down to a single vertex
+I would get an edge between them so a
+
+ align:start position:0%
+I would get an edge between them so a
+ 
+
+ align:start position:0%
+I would get an edge between them so a
+super Edge uh AI b a i BJ I should
+
+ align:start position:0%
+super Edge uh AI b a i BJ I should
+ 
+
+ align:start position:0%
+super Edge uh AI b a i BJ I should
+say uh exists if there's at least one
+
+ align:start position:0%
+say uh exists if there's at least one
+ 
+
+ align:start position:0%
+say uh exists if there's at least one
+Edge in uh AI cross
+
+ align:start position:0%
+Edge in uh AI cross
+ 
+
+ align:start position:0%
+Edge in uh AI cross
+bj at least one Edge connecting those
+
+ align:start position:0%
+bj at least one Edge connecting those
+ 
+
+ align:start position:0%
+bj at least one Edge connecting those
+groups groups and I'm going to call such
+
+ align:start position:0%
+groups groups and I'm going to call such
+ 
+
+ align:start position:0%
+groups groups and I'm going to call such
+a super Edge
+
+ align:start position:0%
+a super Edge
+ 
+
+ align:start position:0%
+a super Edge
+covered by a prime B Prime if uh at
+
+ align:start position:0%
+covered by a prime B Prime if uh at
+ 
+
+ align:start position:0%
+covered by a prime B Prime if uh at
+least one of those edges is in this
+
+ align:start position:0%
+least one of those edges is in this
+ 
+
+ align:start position:0%
+least one of those edges is in this
+chosen set so if there's at least one
+
+ align:start position:0%
+chosen set so if there's at least one
+ 
+
+ align:start position:0%
+chosen set so if there's at least one
+Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry if this uh AI cross BJ these are
+
+ align:start position:0%
+sorry if this uh AI cross BJ these are
+ 
+
+ align:start position:0%
+sorry if this uh AI cross BJ these are
+all the possible edges between those
+
+ align:start position:0%
+all the possible edges between those
+ 
+
+ align:start position:0%
+all the possible edges between those
+groups uh intersects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um a prime cross B
+
+ align:start position:0%
+um a prime cross B
+ 
+
+ align:start position:0%
+um a prime cross B
+Prime and in general I want to cover all
+
+ align:start position:0%
+Prime and in general I want to cover all
+ 
+
+ align:start position:0%
+Prime and in general I want to cover all
+the hyper edges if I can so I would like
+
+ align:start position:0%
+the hyper edges if I can so I would like
+ 
+
+ align:start position:0%
+the hyper edges if I can so I would like
+to have a solution where if there is
+
+ align:start position:0%
+to have a solution where if there is
+ 
+
+ align:start position:0%
+to have a solution where if there is
+some Edge between A1 and B3 then in the
+
+ align:start position:0%
+some Edge between A1 and B3 then in the
+ 
+
+ align:start position:0%
+some Edge between A1 and B3 then in the
+set of vertices I choose a prime and B
+
+ align:start position:0%
+set of vertices I choose a prime and B
+ 
+
+ align:start position:0%
+set of vertices I choose a prime and B
+Prime in the left uh they induce at
+
+ align:start position:0%
+Prime in the left uh they induce at
+ 
+
+ align:start position:0%
+Prime in the left uh they induce at
+least one Edge from A1 to B3 and also
+
+ align:start position:0%
+least one Edge from A1 to B3 and also
+ 
+
+ align:start position:0%
+least one Edge from A1 to B3 and also
+from A2 to B3 because there's a there's
+
+ align:start position:0%
+from A2 to B3 because there's a there's
+ 
+
+ align:start position:0%
+from A2 to B3 because there's a there's
+is an edge that I drew here uh I want
+
+ align:start position:0%
+is an edge that I drew here uh I want
+ 
+
+ align:start position:0%
+is an edge that I drew here uh I want
+ideally to choose the end points of that
+
+ align:start position:0%
+ideally to choose the end points of that
+ 
+
+ align:start position:0%
+ideally to choose the end points of that
+edge or some other Edge that connects
+
+ align:start position:0%
+edge or some other Edge that connects
+ 
+
+ align:start position:0%
+edge or some other Edge that connects
+those two groups yeah so you're choosing
+
+ align:start position:0%
+those two groups yeah so you're choosing
+ 
+
+ align:start position:0%
+those two groups yeah so you're choosing
+subsets a prime of a is there some
+
+ align:start position:0%
+subsets a prime of a is there some
+ 
+
+ align:start position:0%
+subsets a prime of a is there some
+restriction on the subset you choose why
+
+ align:start position:0%
+restriction on the subset you choose why
+ 
+
+ align:start position:0%
+restriction on the subset you choose why
+don't you choose like all of a wait oh
+
+ align:start position:0%
+don't you choose like all of a wait oh
+ 
+
+ align:start position:0%
+don't you choose like all of a wait oh
+okay you're not done yet
+
+ align:start position:0%
+okay you're not done yet
+ 
+
+ align:start position:0%
+okay you're not done yet
+nope that's about half of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition it's a lot to say it's not
+
+ align:start position:0%
+definition it's a lot to say it's not
+ 
+
+ align:start position:0%
+definition it's a lot to say it's not
+that complicated of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem uh so there's two versions it's
+
+ align:start position:0%
+problem uh so there's two versions it's
+ 
+
+ align:start position:0%
+problem uh so there's two versions it's
+part of what makes it longer we'll start
+
+ align:start position:0%
+part of what makes it longer we'll start
+ 
+
+ align:start position:0%
+part of what makes it longer we'll start
+with the maximization version which is
+
+ align:start position:0%
+with the maximization version which is
+ 
+
+ align:start position:0%
+with the maximization version which is
+called Max rep uh so we have two
+
+ align:start position:0%
+called Max rep uh so we have two
+ 
+
+ align:start position:0%
+called Max rep uh so we have two
+constraints on a prime and B
+
+ align:start position:0%
+constraints on a prime and B
+ 
+
+ align:start position:0%
+constraints on a prime and B
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+uh first is that we choose exactly one
+
+ align:start position:0%
+uh first is that we choose exactly one
+ 
+
+ align:start position:0%
+uh first is that we choose exactly one
+vertex from each group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh you know a prime intersect AI
+
+ align:start position:0%
+so uh you know a prime intersect AI
+ 
+
+ align:start position:0%
+so uh you know a prime intersect AI
+equals 1 and B Prime intersect
+
+ align:start position:0%
+equals 1 and B Prime intersect
+ 
+
+ align:start position:0%
+equals 1 and B Prime intersect
+BJ equals 1 for all I and
+
+ align:start position:0%
+BJ equals 1 for all I and
+ 
+
+ align:start position:0%
+BJ equals 1 for all I and
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+okay and then subject to that constraint
+
+ align:start position:0%
+okay and then subject to that constraint
+ 
+
+ align:start position:0%
+okay and then subject to that constraint
+we want to
+
+ align:start position:0%
+we want to
+ 
+
+ align:start position:0%
+we want to
+maximize uh the number of covered super
+
+ align:start position:0%
+maximize uh the number of covered super
+ 
+
+ align:start position:0%
+maximize uh the number of covered super
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay intuition here is that those groups
+
+ align:start position:0%
+okay intuition here is that those groups
+ 
+
+ align:start position:0%
+okay intuition here is that those groups
+are labels and there's really one super
+
+ align:start position:0%
+are labels and there's really one super
+ 
+
+ align:start position:0%
+are labels and there's really one super
+vertex there and you want to choose one
+
+ align:start position:0%
+vertex there and you want to choose one
+ 
+
+ align:start position:0%
+vertex there and you want to choose one
+of those labels to satisfy the instance
+
+ align:start position:0%
+of those labels to satisfy the instance
+ 
+
+ align:start position:0%
+of those labels to satisfy the instance
+so here you're only allowed to choose
+
+ align:start position:0%
+so here you're only allowed to choose
+ 
+
+ align:start position:0%
+so here you're only allowed to choose
+one label per vertex you choose one out
+
+ align:start position:0%
+one label per vertex you choose one out
+ 
+
+ align:start position:0%
+one label per vertex you choose one out
+of each of the groups then uh you'd like
+
+ align:start position:0%
+of each of the groups then uh you'd like
+ 
+
+ align:start position:0%
+of each of the groups then uh you'd like
+to cover as many edges as you can if
+
+ align:start position:0%
+to cover as many edges as you can if
+ 
+
+ align:start position:0%
+to cover as many edges as you can if
+there is an edge uh in the super graph
+
+ align:start position:0%
+there is an edge uh in the super graph
+ 
+
+ align:start position:0%
+there is an edge uh in the super graph
+from AI to BJ you would like to include
+
+ align:start position:0%
+from AI to BJ you would like to include
+ 
+
+ align:start position:0%
+from AI to BJ you would like to include
+an induced Edge like there should
+
+ align:start position:0%
+an induced Edge like there should
+ 
+
+ align:start position:0%
+an induced Edge like there should
+actually be an edge between the label
+
+ align:start position:0%
+actually be an edge between the label
+ 
+
+ align:start position:0%
+actually be an edge between the label
+you assign to Ai and the label you
+
+ align:start position:0%
+you assign to Ai and the label you
+ 
+
+ align:start position:0%
+you assign to Ai and the label you
+assign to BJ so that's this version the
+
+ align:start position:0%
+assign to BJ so that's this version the
+ 
+
+ align:start position:0%
+assign to BJ so that's this version the
+complimentary problem is a minimization
+
+ align:start position:0%
+complimentary problem is a minimization
+ 
+
+ align:start position:0%
+complimentary problem is a minimization
+problem where we switch what is relaxed
+
+ align:start position:0%
+problem where we switch what is relaxed
+ 
+
+ align:start position:0%
+problem where we switch what is relaxed
+what constraint is relaxed and uh what
+
+ align:start position:0%
+what constraint is relaxed and uh what
+ 
+
+ align:start position:0%
+what constraint is relaxed and uh what
+constraint must hold so here we're going
+
+ align:start position:0%
+constraint must hold so here we're going
+ 
+
+ align:start position:0%
+constraint must hold so here we're going
+to allow multiple labels for each super
+
+ align:start position:0%
+to allow multiple labels for each super
+ 
+
+ align:start position:0%
+to allow multiple labels for each super
+vertex multiple vertices to be chosen
+
+ align:start position:0%
+vertex multiple vertices to be chosen
+ 
+
+ align:start position:0%
+vertex multiple vertices to be chosen
+from each
+
+ align:start position:0%
+from each
+ 
+
+ align:start position:0%
+from each
+group uh instead we force that
+
+ align:start position:0%
+group uh instead we force that
+ 
+
+ align:start position:0%
+group uh instead we force that
+everything is covered we want to cover
+
+ align:start position:0%
+everything is covered we want to cover
+ 
+
+ align:start position:0%
+everything is covered we want to cover
+every Super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edge that exists and our goal is to
+
+ align:start position:0%
+Edge that exists and our goal is to
+ 
+
+ align:start position:0%
+Edge that exists and our goal is to
+minimize the size of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets a prime plus b
+
+ align:start position:0%
+sets a prime plus b
+ 
+
+ align:start position:0%
+sets a prime plus b
+Prime okay so this is sort of the Dual
+
+ align:start position:0%
+Prime okay so this is sort of the Dual
+ 
+
+ align:start position:0%
+Prime okay so this is sort of the Dual
+problem uh here we force one label per
+
+ align:start position:0%
+problem uh here we force one label per
+ 
+
+ align:start position:0%
+problem uh here we force one label per
+vertex want to maximize a number of
+
+ align:start position:0%
+vertex want to maximize a number of
+ 
+
+ align:start position:0%
+vertex want to maximize a number of
+covered things here we force everything
+
+ align:start position:0%
+covered things here we force everything
+ 
+
+ align:start position:0%
+covered things here we force everything
+to be covered want to essentially
+
+ align:start position:0%
+to be covered want to essentially
+ 
+
+ align:start position:0%
+to be covered want to essentially
+minimize the number of labels we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assign okay so these problems are both
+
+ align:start position:0%
+assign okay so these problems are both
+ 
+
+ align:start position:0%
+assign okay so these problems are both
+very hard just to build you some more
+
+ align:start position:0%
+very hard just to build you some more
+ 
+
+ align:start position:0%
+very hard just to build you some more
+intuition uh let me show you a
+
+ align:start position:0%
+intuition uh let me show you a
+ 
+
+ align:start position:0%
+intuition uh let me show you a
+puzzle which is basically exactly this
+
+ align:start position:0%
+puzzle which is basically exactly this
+ 
+
+ align:start position:0%
+puzzle which is basically exactly this
+game uh designed by our MIT Professor
+
+ align:start position:0%
+game uh designed by our MIT Professor
+ 
+
+ align:start position:0%
+game uh designed by our MIT Professor
+Dana
+
+ align:start position:0%
+Dana
+ 
+
+ align:start position:0%
+Dana
+movich uh so here's a word
+
+ align:start position:0%
+movich uh so here's a word
+ 
+
+ align:start position:0%
+movich uh so here's a word
+puzzle uh your goal is to put letters
+
+ align:start position:0%
+puzzle uh your goal is to put letters
+ 
+
+ align:start position:0%
+puzzle uh your goal is to put letters
+into each of these boxes this is B and
+
+ align:start position:0%
+into each of these boxes this is B and
+ 
+
+ align:start position:0%
+into each of these boxes this is B and
+this is a uh and such that for example
+
+ align:start position:0%
+this is a uh and such that for example
+ 
+
+ align:start position:0%
+this is a uh and such that for example
+this says animal which means these the
+
+ align:start position:0%
+this says animal which means these the
+ 
+
+ align:start position:0%
+this says animal which means these the
+three things pointed by the Red Arrows
+
+ align:start position:0%
+three things pointed by the Red Arrows
+ 
+
+ align:start position:0%
+three things pointed by the Red Arrows
+those letters should concatenate to form
+
+ align:start position:0%
+those letters should concatenate to form
+ 
+
+ align:start position:0%
+those letters should concatenate to form
+an animal like uh cat bat all right it's
+
+ align:start position:0%
+an animal like uh cat bat all right it's
+ 
+
+ align:start position:0%
+an animal like uh cat bat all right it's
+the example uh so if I write B A and T
+
+ align:start position:0%
+the example uh so if I write B A and T
+ 
+
+ align:start position:0%
+the example uh so if I write B A and T
+animal is satisfied perfectly uh because
+
+ align:start position:0%
+animal is satisfied perfectly uh because
+ 
+
+ align:start position:0%
+animal is satisfied perfectly uh because
+all three letters form a word I get
+
+ align:start position:0%
+all three letters form a word I get
+ 
+
+ align:start position:0%
+all three letters form a word I get
+three points so far okay next let's
+
+ align:start position:0%
+three points so far okay next let's
+ 
+
+ align:start position:0%
+three points so far okay next let's
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+Transportation uh for example cab is a
+
+ align:start position:0%
+Transportation uh for example cab is a
+ 
+
+ align:start position:0%
+Transportation uh for example cab is a
+three-letter word that is transportation
+
+ align:start position:0%
+three-letter word that is transportation
+ 
+
+ align:start position:0%
+three-letter word that is transportation
+I notice there's always three over here
+
+ align:start position:0%
+I notice there's always three over here
+ 
+
+ align:start position:0%
+I notice there's always three over here
+this corresponds to
+
+ align:start position:0%
+this corresponds to
+ 
+
+ align:start position:0%
+this corresponds to
+uh some regularity constraint on the
+
+ align:start position:0%
+uh some regularity constraint on the
+ 
+
+ align:start position:0%
+uh some regularity constraint on the
+bipart graph there's always going to be
+
+ align:start position:0%
+bipart graph there's always going to be
+ 
+
+ align:start position:0%
+bipart graph there's always going to be
+three arrows going from left to right
+
+ align:start position:0%
+three arrows going from left to right
+ 
+
+ align:start position:0%
+three arrows going from left to right
+for every every
+
+ align:start position:0%
+for every every
+ 
+
+ align:start position:0%
+for every every
+group uh so Transportation fine we got
+
+ align:start position:0%
+group uh so Transportation fine we got
+ 
+
+ align:start position:0%
+group uh so Transportation fine we got
+cab uh that uh is happy we happen to
+
+ align:start position:0%
+cab uh that uh is happy we happen to
+ 
+
+ align:start position:0%
+cab uh that uh is happy we happen to
+reuse the a so we get three more points
+
+ align:start position:0%
+reuse the a so we get three more points
+ 
+
+ align:start position:0%
+reuse the a so we get three more points
+total of six uh Furniture uh is we have
+
+ align:start position:0%
+total of six uh Furniture uh is we have
+ 
+
+ align:start position:0%
+total of six uh Furniture uh is we have
+b blank and T left this is going to be a
+
+ align:start position:0%
+b blank and T left this is going to be a
+ 
+
+ align:start position:0%
+b blank and T left this is going to be a
+little harder I don't know of any
+
+ align:start position:0%
+little harder I don't know of any
+ 
+
+ align:start position:0%
+little harder I don't know of any
+furniture that starts with b and ends
+
+ align:start position:0%
+furniture that starts with b and ends
+ 
+
+ align:start position:0%
+furniture that starts with b and ends
+with t and is three letters long uh but
+
+ align:start position:0%
+with t and is three letters long uh but
+ 
+
+ align:start position:0%
+with t and is three letters long uh but
+if you for example write an e here
+
+ align:start position:0%
+if you for example write an e here
+ 
+
+ align:start position:0%
+if you for example write an e here
+that's pretty close to the word bed
+
+ align:start position:0%
+that's pretty close to the word bed
+ 
+
+ align:start position:0%
+that's pretty close to the word bed
+which is Furniture uh so in general of
+
+ align:start position:0%
+which is Furniture uh so in general of
+ 
+
+ align:start position:0%
+which is Furniture uh so in general of
+course each of these words corresponds
+
+ align:start position:0%
+course each of these words corresponds
+ 
+
+ align:start position:0%
+course each of these words corresponds
+to a set of English words uh that's
+
+ align:start position:0%
+to a set of English words uh that's
+ 
+
+ align:start position:0%
+to a set of English words uh that's
+going to be the uh groups on the left so
+
+ align:start position:0%
+going to be the uh groups on the left so
+ 
+
+ align:start position:0%
+going to be the uh groups on the left so
+this AI group for furniture is a set of
+
+ align:start position:0%
+this AI group for furniture is a set of
+ 
+
+ align:start position:0%
+this AI group for furniture is a set of
+all words that are furniture and three
+
+ align:start position:0%
+all words that are furniture and three
+ 
+
+ align:start position:0%
+all words that are furniture and three
+letters long um and then for each such
+
+ align:start position:0%
+letters long um and then for each such
+ 
+
+ align:start position:0%
+letters long um and then for each such
+choice on the left for each such choice
+
+ align:start position:0%
+choice on the left for each such choice
+ 
+
+ align:start position:0%
+choice on the left for each such choice
+on the right you can say is are they
+
+ align:start position:0%
+on the right you can say is are they
+ 
+
+ align:start position:0%
+on the right you can say is are they
+compatible by either putting an edge or
+
+ align:start position:0%
+compatible by either putting an edge or
+ 
+
+ align:start position:0%
+compatible by either putting an edge or
+not um and so this is uh we got two out
+
+ align:start position:0%
+not um and so this is uh we got two out
+ 
+
+ align:start position:0%
+not um and so this is uh we got two out
+of three of these edges these two were
+
+ align:start position:0%
+of three of these edges these two were
+ 
+
+ align:start position:0%
+of three of these edges these two were
+satisfied this one's not so we get two
+
+ align:start position:0%
+satisfied this one's not so we get two
+ 
+
+ align:start position:0%
+satisfied this one's not so we get two
+more points so for a total of
+
+ align:start position:0%
+more points so for a total of
+ 
+
+ align:start position:0%
+more points so for a total of
+eight okay this is for the maximization
+
+ align:start position:0%
+eight okay this is for the maximization
+ 
+
+ align:start position:0%
+eight okay this is for the maximization
+problem minimization is would be
+
+ align:start position:0%
+problem minimization is would be
+ 
+
+ align:start position:0%
+problem minimization is would be
+different uh here's a verb where we
+
+ align:start position:0%
+different uh here's a verb where we
+ 
+
+ align:start position:0%
+different uh here's a verb where we
+almost get to cry CB y so we get two
+
+ align:start position:0%
+almost get to cry CB y so we get two
+ 
+
+ align:start position:0%
+almost get to cry CB y so we get two
+more points um here is another we want a
+
+ align:start position:0%
+more points um here is another we want a
+ 
+
+ align:start position:0%
+more points um here is another we want a
+verb blank a y there are multiple such
+
+ align:start position:0%
+verb blank a y there are multiple such
+ 
+
+ align:start position:0%
+verb blank a y there are multiple such
+verbs uh can think of them and on the
+
+ align:start position:0%
+verbs uh can think of them and on the
+ 
+
+ align:start position:0%
+verbs uh can think of them and on the
+other hand we have a food which is
+
+ align:start position:0%
+other hand we have a food which is
+ 
+
+ align:start position:0%
+other hand we have a food which is
+supposed to be blank
+
+ align:start position:0%
+supposed to be blank
+ 
+
+ align:start position:0%
+supposed to be blank
+ey uh so a pretty good choice would be P
+
+ align:start position:0%
+ey uh so a pretty good choice would be P
+ 
+
+ align:start position:0%
+ey uh so a pretty good choice would be P
+for that top letter then you get pay
+
+ align:start position:0%
+for that top letter then you get pay
+ 
+
+ align:start position:0%
+for that top letter then you get pay
+exactly and almost get P so a total
+
+ align:start position:0%
+exactly and almost get P so a total
+ 
+
+ align:start position:0%
+exactly and almost get P so a total
+score of 15 uh and so this would be a
+
+ align:start position:0%
+score of 15 uh and so this would be a
+ 
+
+ align:start position:0%
+score of 15 uh and so this would be a
+solution to Max rep of cost uh 15 it's
+
+ align:start position:0%
+solution to Max rep of cost uh 15 it's
+ 
+
+ align:start position:0%
+solution to Max rep of cost uh 15 it's
+not the best and if you start at this
+
+ align:start position:0%
+not the best and if you start at this
+ 
+
+ align:start position:0%
+not the best and if you start at this
+example long enough you can actually get
+
+ align:start position:0%
+example long enough you can actually get
+ 
+
+ align:start position:0%
+example long enough you can actually get
+a perfect solution of score 18 where
+
+ align:start position:0%
+a perfect solution of score 18 where
+ 
+
+ align:start position:0%
+a perfect solution of score 18 where
+there are no violations basically in
+
+ align:start position:0%
+there are no violations basically in
+ 
+
+ align:start position:0%
+there are no violations basically in
+particular you do say here and get soy
+
+ align:start position:0%
+particular you do say here and get soy
+ 
+
+ align:start position:0%
+particular you do say here and get soy
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+food uh so so the sets on the right are
+
+ align:start position:0%
+food uh so so the sets on the right are
+ 
+
+ align:start position:0%
+food uh so so the sets on the right are
+26 letters yes the biis here are the
+
+ align:start position:0%
+26 letters yes the biis here are the
+ 
+
+ align:start position:0%
+26 letters yes the biis here are the
+alphabet A through Z and the sets on the
+
+ align:start position:0%
+alphabet A through Z and the sets on the
+ 
+
+ align:start position:0%
+alphabet A through Z and the sets on the
+left are set of words and then you're
+
+ align:start position:0%
+left are set of words and then you're
+ 
+
+ align:start position:0%
+left are set of words and then you're
+going to connect two of them by an edge
+
+ align:start position:0%
+going to connect two of them by an edge
+ 
+
+ align:start position:0%
+going to connect two of them by an edge
+if that
+
+ align:start position:0%
+if that
+ 
+
+ align:start position:0%
+if that
+that in that letter uh happens to match
+
+ align:start position:0%
+that in that letter uh happens to match
+ 
+
+ align:start position:0%
+that in that letter uh happens to match
+on the right the i letter so it's a
+
+ align:start position:0%
+on the right the i letter so it's a
+ 
+
+ align:start position:0%
+on the right the i letter so it's a
+little I mean the mapping is slightly
+
+ align:start position:0%
+little I mean the mapping is slightly
+ 
+
+ align:start position:0%
+little I mean the mapping is slightly
+complicated but this is a particular
+
+ align:start position:0%
+complicated but this is a particular
+ 
+
+ align:start position:0%
+complicated but this is a particular
+instance of Max
+
+ align:start position:0%
+instance of Max
+ 
+
+ align:start position:0%
+instance of Max
+rep okay
+
+ align:start position:0%
+rep okay
+ 
+
+ align:start position:0%
+rep okay
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+um well we get some super extreme
+
+ align:start position:0%
+um well we get some super extreme
+ 
+
+ align:start position:0%
+um well we get some super extreme
+hardness for these problems
+
+ align:start position:0%
+hardness for these problems
+ 
+
+ align:start position:0%
+hardness for these problems
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+let's start with Epsilon comma
+
+ align:start position:0%
+let's start with Epsilon comma
+ 
+
+ align:start position:0%
+let's start with Epsilon comma
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Gap uh Max
+
+ align:start position:0%
+Gap uh Max
+ 
+
+ align:start position:0%
+Gap uh Max
+rep is NP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah so uh what I mean by this is in the
+
+ align:start position:0%
+yeah so uh what I mean by this is in the
+ 
+
+ align:start position:0%
+yeah so uh what I mean by this is in the
+best situation you cover all of the
+
+ align:start position:0%
+best situation you cover all of the
+ 
+
+ align:start position:0%
+best situation you cover all of the
+super edges so the one means 100% of the
+
+ align:start position:0%
+super edges so the one means 100% of the
+ 
+
+ align:start position:0%
+super edges so the one means 100% of the
+super edges are covered
+
+ align:start position:0%
+super edges are covered
+ 
+
+ align:start position:0%
+super edges are covered
+Epsilon means that most Epsilon fraction
+
+ align:start position:0%
+Epsilon means that most Epsilon fraction
+ 
+
+ align:start position:0%
+Epsilon means that most Epsilon fraction
+of them are covered so that problem is
+
+ align:start position:0%
+of them are covered so that problem is
+ 
+
+ align:start position:0%
+of them are covered so that problem is
+empty hard this is a bit stronger than
+
+ align:start position:0%
+empty hard this is a bit stronger than
+ 
+
+ align:start position:0%
+empty hard this is a bit stronger than
+what we had before before we had a
+
+ align:start position:0%
+what we had before before we had a
+ 
+
+ align:start position:0%
+what we had before before we had a
+particular constant comma one or one
+
+ align:start position:0%
+particular constant comma one or one
+ 
+
+ align:start position:0%
+particular constant comma one or one
+minus Epsilon or something uh here for
+
+ align:start position:0%
+minus Epsilon or something uh here for
+ 
+
+ align:start position:0%
+minus Epsilon or something uh here for
+any constant Epsilon this is
+
+ align:start position:0%
+any constant Epsilon this is
+ 
+
+ align:start position:0%
+any constant Epsilon this is
+true and there's a similar result for a
+
+ align:start position:0%
+true and there's a similar result for a
+ 
+
+ align:start position:0%
+true and there's a similar result for a
+Min rep it's just uh from one to one
+
+ align:start position:0%
+Min rep it's just uh from one to one
+ 
+
+ align:start position:0%
+Min rep it's just uh from one to one
+over Epsilon so this means there is no
+
+ align:start position:0%
+over Epsilon so this means there is no
+ 
+
+ align:start position:0%
+over Epsilon so this means there is no
+constant Factor approximation Max rep is
+
+ align:start position:0%
+constant Factor approximation Max rep is
+ 
+
+ align:start position:0%
+constant Factor approximation Max rep is
+not in apx
+
+ align:start position:0%
+not in apx
+ 
+
+ align:start position:0%
+not in apx
+okay but it's worse than that uh we need
+
+ align:start position:0%
+okay but it's worse than that uh we need
+ 
+
+ align:start position:0%
+okay but it's worse than that uh we need
+to assume slightly
+
+ align:start position:0%
+to assume slightly
+ 
+
+ align:start position:0%
+to assume slightly
+more um in general what you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show if you have some constant P or
+
+ align:start position:0%
+show if you have some constant P or
+ 
+
+ align:start position:0%
+show if you have some constant P or
+there is a constant
+
+ align:start position:0%
+there is a constant
+ 
+
+ align:start position:0%
+there is a constant
+P such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you can solve this Gap problem 1
+
+ align:start position:0%
+that if you can solve this Gap problem 1
+ 
+
+ align:start position:0%
+that if you can solve this Gap problem 1
+over P the K so a very tiny fraction of
+
+ align:start position:0%
+over P the K so a very tiny fraction of
+ 
+
+ align:start position:0%
+over P the K so a very tiny fraction of
+things satisfied versus all of the super
+
+ align:start position:0%
+things satisfied versus all of the super
+ 
+
+ align:start position:0%
+things satisfied versus all of the super
+edges covered um
+
+ align:start position:0%
+edges covered um
+ 
+
+ align:start position:0%
+edges covered um
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+NP can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solved in N to the order K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time uh okay so we haven't usually used
+
+ align:start position:0%
+time uh okay so we haven't usually used
+ 
+
+ align:start position:0%
+time uh okay so we haven't usually used
+this class usually we talk about P which
+
+ align:start position:0%
+this class usually we talk about P which
+ 
+
+ align:start position:0%
+this class usually we talk about P which
+is the union of all these for constant K
+
+ align:start position:0%
+is the union of all these for constant K
+ 
+
+ align:start position:0%
+is the union of all these for constant K
+but here K doesn't have to be a constant
+
+ align:start position:0%
+but here K doesn't have to be a constant
+ 
+
+ align:start position:0%
+but here K doesn't have to be a constant
+it could be some function of N and uh in
+
+ align:start position:0%
+it could be some function of N and uh in
+ 
+
+ align:start position:0%
+it could be some function of N and uh in
+particular if P does not equal NP then K
+
+ align:start position:0%
+particular if P does not equal NP then K
+ 
+
+ align:start position:0%
+particular if P does not equal NP then K
+constant is not possible so this result
+
+ align:start position:0%
+constant is not possible so this result
+ 
+
+ align:start position:0%
+constant is not possible so this result
+implies this
+
+ align:start position:0%
+implies this
+ 
+
+ align:start position:0%
+implies this
+result uh but if we let K get bigger
+
+ align:start position:0%
+result uh but if we let K get bigger
+ 
+
+ align:start position:0%
+result uh but if we let K get bigger
+than a
+
+ align:start position:0%
+than a
+ 
+
+ align:start position:0%
+than a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+like log log n or something then we get
+
+ align:start position:0%
+like log log n or something then we get
+ 
+
+ align:start position:0%
+like log log n or something then we get
+some separation between uh well we get a
+
+ align:start position:0%
+some separation between uh well we get a
+ 
+
+ align:start position:0%
+some separation between uh well we get a
+a somewhat weaker statement here we know
+
+ align:start position:0%
+a somewhat weaker statement here we know
+ 
+
+ align:start position:0%
+a somewhat weaker statement here we know
+if P does not equal NP we know that NP
+
+ align:start position:0%
+if P does not equal NP we know that NP
+ 
+
+ align:start position:0%
+if P does not equal NP we know that NP
+is not contained in p uh but if we uh
+
+ align:start position:0%
+is not contained in p uh but if we uh
+ 
+
+ align:start position:0%
+is not contained in p uh but if we uh
+furthermore assume that NP doesn't have
+
+ align:start position:0%
+furthermore assume that NP doesn't have
+ 
+
+ align:start position:0%
+furthermore assume that NP doesn't have
+uh subexponential Solutions and very
+
+ align:start position:0%
+uh subexponential Solutions and very
+ 
+
+ align:start position:0%
+uh subexponential Solutions and very
+subexponential Solutions then we get
+
+ align:start position:0%
+subexponential Solutions then we get
+ 
+
+ align:start position:0%
+subexponential Solutions then we get
+various Gap bounds and inapproximability
+
+ align:start position:0%
+various Gap bounds and inapproximability
+ 
+
+ align:start position:0%
+various Gap bounds and inapproximability
+on Max rep so a reasonable limit for
+
+ align:start position:0%
+on Max rep so a reasonable limit for
+ 
+
+ align:start position:0%
+on Max rep so a reasonable limit for
+example is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's say we assume NP is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in uh n to the poly log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n to the poly log n is usually called
+
+ align:start position:0%
+n to the poly log n is usually called
+ 
+
+ align:start position:0%
+n to the poly log n is usually called
+quasi polinomial it's almost polom you
+
+ align:start position:0%
+quasi polinomial it's almost polom you
+ 
+
+ align:start position:0%
+quasi polinomial it's almost polom you
+know log n is kind of close to constant
+
+ align:start position:0%
+know log n is kind of close to constant
+ 
+
+ align:start position:0%
+know log n is kind of close to constant
+is this is the same as two to the poly
+
+ align:start position:0%
+is this is the same as two to the poly
+ 
+
+ align:start position:0%
+is this is the same as two to the poly
+log n uh n to the poly log n but it's a
+
+ align:start position:0%
+log n uh n to the poly log n but it's a
+ 
+
+ align:start position:0%
+log n uh n to the poly log n but it's a
+little clearer this is obviously closer
+
+ align:start position:0%
+little clearer this is obviously closer
+ 
+
+ align:start position:0%
+little clearer this is obviously closer
+close to polinomial quite far from
+
+ align:start position:0%
+close to polinomial quite far from
+ 
+
+ align:start position:0%
+close to polinomial quite far from
+exponential which is 2 to the N not
+
+ align:start position:0%
+exponential which is 2 to the N not
+ 
+
+ align:start position:0%
+exponential which is 2 to the N not
+polog so very different from exponential
+
+ align:start position:0%
+polog so very different from exponential
+ 
+
+ align:start position:0%
+polog so very different from exponential
+so most almost everyone believes NP is
+
+ align:start position:0%
+so most almost everyone believes NP is
+ 
+
+ align:start position:0%
+so most almost everyone believes NP is
+not does not admit quasi polinomial
+
+ align:start position:0%
+not does not admit quasi polinomial
+ 
+
+ align:start position:0%
+not does not admit quasi polinomial
+Solutions they're all problems in NP
+
+ align:start position:0%
+Solutions they're all problems in NP
+ 
+
+ align:start position:0%
+Solutions they're all problems in NP
+would have to admit that threat for
+
+ align:start position:0%
+would have to admit that threat for
+ 
+
+ align:start position:0%
+would have to admit that threat for
+example people don't think you can do
+
+ align:start position:0%
+example people don't think you can do
+ 
+
+ align:start position:0%
+example people don't think you can do
+better than some constant to the
+
+ align:start position:0%
+better than some constant to the
+ 
+
+ align:start position:0%
+better than some constant to the
+N uh then what do we get when we plug in
+
+ align:start position:0%
+N uh then what do we get when we plug in
+ 
+
+ align:start position:0%
+N uh then what do we get when we plug in
+that value of K
+
+ align:start position:0%
+that value of K
+ 
+
+ align:start position:0%
+that value of K
+uh that there is a No 1 over 2 to the
+
+ align:start position:0%
+uh that there is a No 1 over 2 to the
+ 
+
+ align:start position:0%
+uh that there is a No 1 over 2 to the
+log the 1 - Epsilon
+
+ align:start position:0%
+log the 1 - Epsilon
+ 
+
+ align:start position:0%
+log the 1 - Epsilon
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+approximation or also this the same
+
+ align:start position:0%
+approximation or also this the same
+ 
+
+ align:start position:0%
+approximation or also this the same
+thing Gap is
+
+ align:start position:0%
+thing Gap is
+ 
+
+ align:start position:0%
+thing Gap is
+hard now it's not NP hard uh but it's as
+
+ align:start position:0%
+hard now it's not NP hard uh but it's as
+ 
+
+ align:start position:0%
+hard now it's not NP hard uh but it's as
+hard as this problem if you believe this
+
+ align:start position:0%
+hard as this problem if you believe this
+ 
+
+ align:start position:0%
+hard as this problem if you believe this
+is not true then there will be no
+
+ align:start position:0%
+is not true then there will be no
+ 
+
+ align:start position:0%
+is not true then there will be no
+polinomial time algorithm to solve this
+
+ align:start position:0%
+polinomial time algorithm to solve this
+ 
+
+ align:start position:0%
+polinomial time algorithm to solve this
+Factor Gap Max rep so this is very large
+
+ align:start position:0%
+Factor Gap Max rep so this is very large
+ 
+
+ align:start position:0%
+Factor Gap Max rep so this is very large
+this we've seen this before uh in this
+
+ align:start position:0%
+this we've seen this before uh in this
+ 
+
+ align:start position:0%
+this we've seen this before uh in this
+table of various results near the bottom
+
+ align:start position:0%
+table of various results near the bottom
+ 
+
+ align:start position:0%
+table of various results near the bottom
+there was a lower bound of 2 to the log
+
+ align:start position:0%
+there was a lower bound of 2 to the log
+ 
+
+ align:start position:0%
+there was a lower bound of 2 to the log
+to 1us Epsilon n this is not assuming P
+
+ align:start position:0%
+to 1us Epsilon n this is not assuming P
+ 
+
+ align:start position:0%
+to 1us Epsilon n this is not assuming P
+does not equal NP it's assuming this
+
+ align:start position:0%
+does not equal NP it's assuming this
+ 
+
+ align:start position:0%
+does not equal NP it's assuming this
+statement NP does not have quasi
+
+ align:start position:0%
+statement NP does not have quasi
+ 
+
+ align:start position:0%
+statement NP does not have quasi
+polinomial algorithms and you see here
+
+ align:start position:0%
+polinomial algorithms and you see here
+ 
+
+ align:start position:0%
+polinomial algorithms and you see here
+our friends Max and mrep two versions of
+
+ align:start position:0%
+our friends Max and mrep two versions of
+ 
+
+ align:start position:0%
+our friends Max and mrep two versions of
+label
+
+ align:start position:0%
+label
+ 
+
+ align:start position:0%
+label
+cover so uh I'm not going to prove these
+
+ align:start position:0%
+cover so uh I'm not going to prove these
+ 
+
+ align:start position:0%
+cover so uh I'm not going to prove these
+theorems but again there are PCP style
+
+ align:start position:0%
+theorems but again there are PCP style
+ 
+
+ align:start position:0%
+theorems but again there are PCP style
+arguments with some Gap uh
+
+ align:start position:0%
+arguments with some Gap uh
+ 
+
+ align:start position:0%
+arguments with some Gap uh
+boosting uh but I would say most or a
+
+ align:start position:0%
+boosting uh but I would say most or a
+ 
+
+ align:start position:0%
+boosting uh but I would say most or a
+lot of uh approximation lower bounds in
+
+ align:start position:0%
+lot of uh approximation lower bounds in
+ 
+
+ align:start position:0%
+lot of uh approximation lower bounds in
+the world today start from Max rep or
+
+ align:start position:0%
+the world today start from Max rep or
+ 
+
+ align:start position:0%
+the world today start from Max rep or
+Min rep and reduce to the problem using
+
+ align:start position:0%
+Min rep and reduce to the problem using
+ 
+
+ align:start position:0%
+Min rep and reduce to the problem using
+usually some kind of Gap preserving
+
+ align:start position:0%
+usually some kind of Gap preserving
+ 
+
+ align:start position:0%
+usually some kind of Gap preserving
+reduction maybe they lose the Gap but we
+
+ align:start position:0%
+reduction maybe they lose the Gap but we
+ 
+
+ align:start position:0%
+reduction maybe they lose the Gap but we
+have a such a huge gap to start with
+
+ align:start position:0%
+have a such a huge gap to start with
+ 
+
+ align:start position:0%
+have a such a huge gap to start with
+then even if you lose Gap you still get
+
+ align:start position:0%
+then even if you lose Gap you still get
+ 
+
+ align:start position:0%
+then even if you lose Gap you still get
+pretty good results um so a couple of
+
+ align:start position:0%
+pretty good results um so a couple of
+ 
+
+ align:start position:0%
+pretty good results um so a couple of
+quick examples here on the slides uh
+
+ align:start position:0%
+quick examples here on the slides uh
+ 
+
+ align:start position:0%
+quick examples here on the slides uh
+directed Steiner Forest remember you
+
+ align:start position:0%
+directed Steiner Forest remember you
+ 
+
+ align:start position:0%
+directed Steiner Forest remember you
+have a directed graph and you have uh a
+
+ align:start position:0%
+have a directed graph and you have uh a
+ 
+
+ align:start position:0%
+have a directed graph and you have uh a
+bunch of terminal Pairs and you want to
+
+ align:start position:0%
+bunch of terminal Pairs and you want to
+ 
+
+ align:start position:0%
+bunch of terminal Pairs and you want to
+in particular connect via directed path
+
+ align:start position:0%
+in particular connect via directed path
+ 
+
+ align:start position:0%
+in particular connect via directed path
+uh some AIS and B BJs let's say uh and
+
+ align:start position:0%
+uh some AIS and B BJs let's say uh and
+ 
+
+ align:start position:0%
+uh some AIS and B BJs let's say uh and
+you want to do so by choosing uh the
+
+ align:start position:0%
+you want to do so by choosing uh the
+ 
+
+ align:start position:0%
+you want to do so by choosing uh the
+fewest vertices in this graph so what
+
+ align:start position:0%
+fewest vertices in this graph so what
+ 
+
+ align:start position:0%
+fewest vertices in this graph so what
+I'm going to do if I'm given My
+
+ align:start position:0%
+I'm going to do if I'm given My
+ 
+
+ align:start position:0%
+I'm going to do if I'm given My
+bipartite Graph here uh for Min rep I'm
+
+ align:start position:0%
+bipartite Graph here uh for Min rep I'm
+ 
+
+ align:start position:0%
+bipartite Graph here uh for Min rep I'm
+just going to add to represent that this
+
+ align:start position:0%
+just going to add to represent that this
+ 
+
+ align:start position:0%
+just going to add to represent that this
+is a group I'm going to add a Vertex
+
+ align:start position:0%
+is a group I'm going to add a Vertex
+ 
+
+ align:start position:0%
+is a group I'm going to add a Vertex
+here connect by directed edges here and
+
+ align:start position:0%
+here connect by directed edges here and
+ 
+
+ align:start position:0%
+here connect by directed edges here and
+there's a group down here so I'm going
+
+ align:start position:0%
+there's a group down here so I'm going
+ 
+
+ align:start position:0%
+there's a group down here so I'm going
+to have downward edges down there and
+
+ align:start position:0%
+to have downward edges down there and
+ 
+
+ align:start position:0%
+to have downward edges down there and
+whenever there's a super Edge from say
+
+ align:start position:0%
+whenever there's a super Edge from say
+ 
+
+ align:start position:0%
+whenever there's a super Edge from say
+A2 Capital A2 to Capital B1 then I'm
+
+ align:start position:0%
+A2 Capital A2 to Capital B1 then I'm
+ 
+
+ align:start position:0%
+A2 Capital A2 to Capital B1 then I'm
+going to say in my directed Steiner
+
+ align:start position:0%
+going to say in my directed Steiner
+ 
+
+ align:start position:0%
+going to say in my directed Steiner
+Force problem I want a path from Little
+
+ align:start position:0%
+Force problem I want a path from Little
+ 
+
+ align:start position:0%
+Force problem I want a path from Little
+A2 to little B1 so in general whenever
+
+ align:start position:0%
+A2 to little B1 so in general whenever
+ 
+
+ align:start position:0%
+A2 to little B1 so in general whenever
+there's a super Edge I add that
+
+ align:start position:0%
+there's a super Edge I add that
+ 
+
+ align:start position:0%
+there's a super Edge I add that
+constraint and then any solution to
+
+ align:start position:0%
+constraint and then any solution to
+ 
+
+ align:start position:0%
+constraint and then any solution to
+directed Steiner Forest will exactly be
+
+ align:start position:0%
+directed Steiner Forest will exactly be
+ 
+
+ align:start position:0%
+directed Steiner Forest will exactly be
+a solution to mrep you're just forcing
+
+ align:start position:0%
+a solution to mrep you're just forcing
+ 
+
+ align:start position:0%
+a solution to mrep you're just forcing
+the addition of the AIS and bis but it's
+
+ align:start position:0%
+the addition of the AIS and bis but it's
+ 
+
+ align:start position:0%
+the addition of the AIS and bis but it's
+again an L reduction you're just
+
+ align:start position:0%
+again an L reduction you're just
+ 
+
+ align:start position:0%
+again an L reduction you're just
+offsetting by a fixed additive amount so
+
+ align:start position:0%
+offsetting by a fixed additive amount so
+ 
+
+ align:start position:0%
+offsetting by a fixed additive amount so
+your Gap to opt will be the same and so
+
+ align:start position:0%
+your Gap to opt will be the same and so
+ 
+
+ align:start position:0%
+your Gap to opt will be the same and so
+you get that this problem is just as
+
+ align:start position:0%
+you get that this problem is just as
+ 
+
+ align:start position:0%
+you get that this problem is just as
+hard as mrep it's a
+
+ align:start position:0%
+hard as mrep it's a
+ 
+
+ align:start position:0%
+hard as mrep it's a
+yeah uh and well this is another one
+
+ align:start position:0%
+yeah uh and well this is another one
+ 
+
+ align:start position:0%
+yeah uh and well this is another one
+from set cover you can also show node
+
+ align:start position:0%
+from set cover you can also show node
+ 
+
+ align:start position:0%
+from set cover you can also show node
+white weighted Steiner tree is uh log
+
+ align:start position:0%
+white weighted Steiner tree is uh log
+ 
+
+ align:start position:0%
+white weighted Steiner tree is uh log
+and hard to approximate that's not from
+
+ align:start position:0%
+and hard to approximate that's not from
+ 
+
+ align:start position:0%
+and hard to approximate that's not from
+minra but through in there while we're
+
+ align:start position:0%
+minra but through in there while we're
+ 
+
+ align:start position:0%
+minra but through in there while we're
+on the topic of Steiner trees all right
+
+ align:start position:0%
+on the topic of Steiner trees all right
+ 
+
+ align:start position:0%
+on the topic of Steiner trees all right
+I want to mention one more thing
+
+ align:start position:0%
+I want to mention one more thing
+ 
+
+ align:start position:0%
+I want to mention one more thing
+quickly in my zero minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remaining and that is uh unique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+games so unique games is a special case
+
+ align:start position:0%
+games so unique games is a special case
+ 
+
+ align:start position:0%
+games so unique games is a special case
+of say Max rep or either label cover
+
+ align:start position:0%
+of say Max rep or either label cover
+ 
+
+ align:start position:0%
+of say Max rep or either label cover
+problem where
+
+ align:start position:0%
+problem where
+ 
+
+ align:start position:0%
+problem where
+uh the edges in
+
+ align:start position:0%
+uh the edges in
+ 
+
+ align:start position:0%
+uh the edges in
+AI cross
+
+ align:start position:0%
+AI cross
+ 
+
+ align:start position:0%
+AI cross
+BJ form a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matching okay for every choice on the
+
+ align:start position:0%
+matching okay for every choice on the
+ 
+
+ align:start position:0%
+matching okay for every choice on the
+left there's a unique choice on the
+
+ align:start position:0%
+left there's a unique choice on the
+ 
+
+ align:start position:0%
+left there's a unique choice on the
+right and vice versa that matches
+
+ align:start position:0%
+right and vice versa that matches
+ 
+
+ align:start position:0%
+right and vice versa that matches
+uh well there's at most one choice I
+
+ align:start position:0%
+uh well there's at most one choice I
+ 
+
+ align:start position:0%
+uh well there's at most one choice I
+guess and I think that corresponds to
+
+ align:start position:0%
+guess and I think that corresponds to
+ 
+
+ align:start position:0%
+guess and I think that corresponds to
+these games right if you once you choose
+
+ align:start position:0%
+these games right if you once you choose
+ 
+
+ align:start position:0%
+these games right if you once you choose
+a word over here there's a unique letter
+
+ align:start position:0%
+a word over here there's a unique letter
+ 
+
+ align:start position:0%
+a word over here there's a unique letter
+that matches uh the reverse is not true
+
+ align:start position:0%
+that matches uh the reverse is not true
+ 
+
+ align:start position:0%
+that matches uh the reverse is not true
+so in this problem it's more like a star
+
+ align:start position:0%
+so in this problem it's more like a star
+ 
+
+ align:start position:0%
+so in this problem it's more like a star
+left to right star once you choose this
+
+ align:start position:0%
+left to right star once you choose this
+ 
+
+ align:start position:0%
+left to right star once you choose this
+word uh it's fix what you have to choose
+
+ align:start position:0%
+word uh it's fix what you have to choose
+ 
+
+ align:start position:0%
+word uh it's fix what you have to choose
+on the right side but if you choose a
+
+ align:start position:0%
+on the right side but if you choose a
+ 
+
+ align:start position:0%
+on the right side but if you choose a
+single letter over here it does not
+
+ align:start position:0%
+single letter over here it does not
+ 
+
+ align:start position:0%
+single letter over here it does not
+uniquely determine the word over here so
+
+ align:start position:0%
+uniquely determine the word over here so
+ 
+
+ align:start position:0%
+uniquely determine the word over here so
+unique games is quite a bit stronger you
+
+ align:start position:0%
+unique games is quite a bit stronger you
+ 
+
+ align:start position:0%
+unique games is quite a bit stronger you
+choose either side it forces the other
+
+ align:start position:0%
+choose either side it forces the other
+ 
+
+ align:start position:0%
+choose either side it forces the other
+one if you want to cover that
+
+ align:start position:0%
+one if you want to cover that
+ 
+
+ align:start position:0%
+one if you want to cover that
+edge okay
+
+ align:start position:0%
+edge okay
+ 
+
+ align:start position:0%
+edge okay
+okay so far so good unique games
+
+ align:start position:0%
+okay so far so good unique games
+ 
+
+ align:start position:0%
+okay so far so good unique games
+conjecture is that this special case is
+
+ align:start position:0%
+conjecture is that this special case is
+ 
+
+ align:start position:0%
+conjecture is that this special case is
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+hard unique games
+
+ align:start position:0%
+hard unique games
+ 
+
+ align:start position:0%
+hard unique games
+conjecture is that Epsilon 1 minus
+
+ align:start position:0%
+conjecture is that Epsilon 1 minus
+ 
+
+ align:start position:0%
+conjecture is that Epsilon 1 minus
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+Gap uh unique game is NP
+
+ align:start position:0%
+Gap uh unique game is NP
+ 
+
+ align:start position:0%
+Gap uh unique game is NP
+heart of course there are weaker
+
+ align:start position:0%
+heart of course there are weaker
+ 
+
+ align:start position:0%
+heart of course there are weaker
+versions of this conjecture that don't
+
+ align:start position:0%
+versions of this conjecture that don't
+ 
+
+ align:start position:0%
+versions of this conjecture that don't
+say NP hard maybe assuming some weaker
+
+ align:start position:0%
+say NP hard maybe assuming some weaker
+ 
+
+ align:start position:0%
+say NP hard maybe assuming some weaker
+assumption that there's no polinomial
+
+ align:start position:0%
+assumption that there's no polinomial
+ 
+
+ align:start position:0%
+assumption that there's no polinomial
+time algorithm uh unlike every other
+
+ align:start position:0%
+time algorithm uh unlike every other
+ 
+
+ align:start position:0%
+time algorithm uh unlike every other
+complexity theoretic assumption I have
+
+ align:start position:0%
+complexity theoretic assumption I have
+ 
+
+ align:start position:0%
+complexity theoretic assumption I have
+mentioned in this class this one is a
+
+ align:start position:0%
+mentioned in this class this one is a
+ 
+
+ align:start position:0%
+mentioned in this class this one is a
+subject of much debate not everyone
+
+ align:start position:0%
+subject of much debate not everyone
+ 
+
+ align:start position:0%
+subject of much debate not everyone
+believes that is true some people
+
+ align:start position:0%
+believes that is true some people
+ 
+
+ align:start position:0%
+believes that is true some people
+believe that is false uh many people
+
+ align:start position:0%
+believe that is false uh many people
+ 
+
+ align:start position:0%
+believe that is false uh many people
+believe or basically people don't know
+
+ align:start position:0%
+believe or basically people don't know
+ 
+
+ align:start position:0%
+believe or basically people don't know
+it's a short answer there's uh there's
+
+ align:start position:0%
+it's a short answer there's uh there's
+ 
+
+ align:start position:0%
+it's a short answer there's uh there's
+some somewhat scary evidence that it's
+
+ align:start position:0%
+some somewhat scary evidence that it's
+ 
+
+ align:start position:0%
+some somewhat scary evidence that it's
+not true there are slightly stronger
+
+ align:start position:0%
+not true there are slightly stronger
+ 
+
+ align:start position:0%
+not true there are slightly stronger
+forms of this that are definitely not
+
+ align:start position:0%
+forms of this that are definitely not
+ 
+
+ align:start position:0%
+forms of this that are definitely not
+true uh which I won't get into there is
+
+ align:start position:0%
+true uh which I won't get into there is
+ 
+
+ align:start position:0%
+true uh which I won't get into there is
+a subexponential algorithm for this
+
+ align:start position:0%
+a subexponential algorithm for this
+ 
+
+ align:start position:0%
+a subexponential algorithm for this
+problem but uh it's still up in the air
+
+ align:start position:0%
+problem but uh it's still up in the air
+ 
+
+ align:start position:0%
+problem but uh it's still up in the air
+uh a lot of people like to assume that
+
+ align:start position:0%
+uh a lot of people like to assume that
+ 
+
+ align:start position:0%
+uh a lot of people like to assume that
+this is true because it makes life uh a
+
+ align:start position:0%
+this is true because it makes life uh a
+ 
+
+ align:start position:0%
+this is true because it makes life uh a
+lot more beautiful uh especially from a
+
+ align:start position:0%
+lot more beautiful uh especially from a
+ 
+
+ align:start position:0%
+lot more beautiful uh especially from a
+an approximability standpoint so for
+
+ align:start position:0%
+an approximability standpoint so for
+ 
+
+ align:start position:0%
+an approximability standpoint so for
+example Max the best approximation
+
+ align:start position:0%
+example Max the best approximation
+ 
+
+ align:start position:0%
+example Max the best approximation
+algorithm is 0.94 zero if you assume
+
+ align:start position:0%
+algorithm is 0.94 zero if you assume
+ 
+
+ align:start position:0%
+algorithm is 0.94 zero if you assume
+unique games you can prove a matching
+
+ align:start position:0%
+unique games you can prove a matching
+ 
+
+ align:start position:0%
+unique games you can prove a matching
+lower bound that was Max two set for Max
+
+ align:start position:0%
+lower bound that was Max two set for Max
+ 
+
+ align:start position:0%
+lower bound that was Max two set for Max
+cut uh as was mentioned 878 is the best
+
+ align:start position:0%
+cut uh as was mentioned 878 is the best
+ 
+
+ align:start position:0%
+cut uh as was mentioned 878 is the best
+upper Bound by Gman williamon Williamson
+
+ align:start position:0%
+upper Bound by Gman williamon Williamson
+ 
+
+ align:start position:0%
+upper Bound by Gman williamon Williamson
+this uh if you assume unique games then
+
+ align:start position:0%
+this uh if you assume unique games then
+ 
+
+ align:start position:0%
+this uh if you assume unique games then
+that's also so tight there's a matching
+
+ align:start position:0%
+that's also so tight there's a matching
+ 
+
+ align:start position:0%
+that's also so tight there's a matching
+uh this minus Epsilon or plus Epsilon in
+
+ align:start position:0%
+uh this minus Epsilon or plus Epsilon in
+ 
+
+ align:start position:0%
+uh this minus Epsilon or plus Epsilon in
+approximability
+
+ align:start position:0%
+approximability
+ 
+
+ align:start position:0%
+approximability
+result um and vertex cover two you
+
+ align:start position:0%
+result um and vertex cover two you
+ 
+
+ align:start position:0%
+result um and vertex cover two you
+probably know how to do two if you
+
+ align:start position:0%
+probably know how to do two if you
+ 
+
+ align:start position:0%
+probably know how to do two if you
+assume unique games uh two is the right
+
+ align:start position:0%
+assume unique games uh two is the right
+ 
+
+ align:start position:0%
+assume unique games uh two is the right
+answer if you don't assume anything the
+
+ align:start position:0%
+answer if you don't assume anything the
+ 
+
+ align:start position:0%
+answer if you don't assume anything the
+best we know how to prove using all of
+
+ align:start position:0%
+best we know how to prove using all of
+ 
+
+ align:start position:0%
+best we know how to prove using all of
+this stuff is
+
+ align:start position:0%
+this stuff is
+ 
+
+ align:start position:0%
+this stuff is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+857 versus
+
+ align:start position:0%
+857 versus
+ 
+
+ align:start position:0%
+857 versus
+0.5 so uh it's nice to assume unique
+
+ align:start position:0%
+0.5 so uh it's nice to assume unique
+ 
+
+ align:start position:0%
+0.5 so uh it's nice to assume unique
+games is true
+
+ align:start position:0%
+games is true
+ 
+
+ align:start position:0%
+games is true
+um very cool result is if you look at
+
+ align:start position:0%
+um very cool result is if you look at
+ 
+
+ align:start position:0%
+um very cool result is if you look at
+over all the different CSP problems that
+
+ align:start position:0%
+over all the different CSP problems that
+ 
+
+ align:start position:0%
+over all the different CSP problems that
+we've seen all the Mac CSP problems and
+
+ align:start position:0%
+we've seen all the Mac CSP problems and
+ 
+
+ align:start position:0%
+we've seen all the Mac CSP problems and
+you try to solve it using a particular
+
+ align:start position:0%
+you try to solve it using a particular
+ 
+
+ align:start position:0%
+you try to solve it using a particular
+kind of semi-definite programming uh
+
+ align:start position:0%
+kind of semi-definite programming uh
+ 
+
+ align:start position:0%
+kind of semi-definite programming uh
+there's an STP
+
+ align:start position:0%
+there's an STP
+ 
+
+ align:start position:0%
+there's an STP
+relaxation if you don't know stps ignore
+
+ align:start position:0%
+relaxation if you don't know stps ignore
+ 
+
+ align:start position:0%
+relaxation if you don't know stps ignore
+the sentence uh there's an STP
+
+ align:start position:0%
+the sentence uh there's an STP
+ 
+
+ align:start position:0%
+the sentence uh there's an STP
+relaxation of all CSP problems you do
+
+ align:start position:0%
+relaxation of all CSP problems you do
+ 
+
+ align:start position:0%
+relaxation of all CSP problems you do
+the sort of obvious thing uh and that
+
+ align:start position:0%
+the sort of obvious thing uh and that
+ 
+
+ align:start position:0%
+the sort of obvious thing uh and that
+STP will have an integrality Gap and if
+
+ align:start position:0%
+STP will have an integrality Gap and if
+ 
+
+ align:start position:0%
+STP will have an integrality Gap and if
+you believe unique games conjecture then
+
+ align:start position:0%
+you believe unique games conjecture then
+ 
+
+ align:start position:0%
+you believe unique games conjecture then
+that integrality Gap equals the
+
+ align:start position:0%
+that integrality Gap equals the
+ 
+
+ align:start position:0%
+that integrality Gap equals the
+approximability
+
+ align:start position:0%
+approximability
+ 
+
+ align:start position:0%
+approximability
+factor one for one and so in this sense
+
+ align:start position:0%
+factor one for one and so in this sense
+ 
+
+ align:start position:0%
+factor one for one and so in this sense
+if you're trying to solve any CSP
+
+ align:start position:0%
+if you're trying to solve any CSP
+ 
+
+ align:start position:0%
+if you're trying to solve any CSP
+problem semi-definite programming is the
+
+ align:start position:0%
+problem semi-definite programming is the
+ 
+
+ align:start position:0%
+problem semi-definite programming is the
+ultimate tool for all approximation
+
+ align:start position:0%
+ultimate tool for all approximation
+ 
+
+ align:start position:0%
+ultimate tool for all approximation
+algorithms uh because if there's a gap
+
+ align:start position:0%
+algorithms uh because if there's a gap
+ 
+
+ align:start position:0%
+algorithms uh because if there's a gap
+in the sdp you can prove an
+
+ align:start position:0%
+in the sdp you can prove an
+ 
+
+ align:start position:0%
+in the sdp you can prove an
+inapproximability result of that minus
+
+ align:start position:0%
+inapproximability result of that minus
+ 
+
+ align:start position:0%
+inapproximability result of that minus
+Epsilon so this is amazingly powerful
+
+ align:start position:0%
+Epsilon so this is amazingly powerful
+ 
+
+ align:start position:0%
+Epsilon so this is amazingly powerful
+the only catch is we don't know whether
+
+ align:start position:0%
+the only catch is we don't know whether
+ 
+
+ align:start position:0%
+the only catch is we don't know whether
+unique games conjecture is true and for
+
+ align:start position:0%
+unique games conjecture is true and for
+ 
+
+ align:start position:0%
+unique games conjecture is true and for
+that reason I'm not going to spend more
+
+ align:start position:0%
+that reason I'm not going to spend more
+ 
+
+ align:start position:0%
+that reason I'm not going to spend more
+time on it but uh this gives you a
+
+ align:start position:0%
+time on it but uh this gives you a
+ 
+
+ align:start position:0%
+time on it but uh this gives you a
+flavor of this this side the field the
+
+ align:start position:0%
+flavor of this this side the field the
+ 
+
+ align:start position:0%
+flavor of this this side the field the
+Gap Gap preservation
+
+ align:start position:0%
+Gap Gap preservation
+ 
+
+ align:start position:0%
+Gap Gap preservation
+approximation any final
+
+ align:start position:0%
+approximation any final
+ 
+
+ align:start position:0%
+approximation any final
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah uh it's it's fine for a problem to
+
+ align:start position:0%
+yeah uh it's it's fine for a problem to
+ 
+
+ align:start position:0%
+yeah uh it's it's fine for a problem to
+be slightly
+
+ align:start position:0%
+be slightly
+ 
+
+ align:start position:0%
+be slightly
+subexponential it's like 2 to the N to
+
+ align:start position:0%
+subexponential it's like 2 to the N to
+ 
+
+ align:start position:0%
+subexponential it's like 2 to the N to
+to the Epsilon or something so when you
+
+ align:start position:0%
+to the Epsilon or something so when you
+ 
+
+ align:start position:0%
+to the Epsilon or something so when you
+when you do an NP reduction you can blow
+
+ align:start position:0%
+when you do an NP reduction you can blow
+ 
+
+ align:start position:0%
+when you do an NP reduction you can blow
+things up by a polinomial factor and so
+
+ align:start position:0%
+things up by a polinomial factor and so
+ 
+
+ align:start position:0%
+things up by a polinomial factor and so
+so that n to the Epsilon becomes n again
+
+ align:start position:0%
+so that n to the Epsilon becomes n again
+ 
+
+ align:start position:0%
+so that n to the Epsilon becomes n again
+so even if you start from threat where
+
+ align:start position:0%
+so even if you start from threat where
+ 
+
+ align:start position:0%
+so even if you start from threat where
+we don't believe there's a
+
+ align:start position:0%
+we don't believe there's a
+ 
+
+ align:start position:0%
+we don't believe there's a
+subexponential thing uh when you reduce
+
+ align:start position:0%
+subexponential thing uh when you reduce
+ 
+
+ align:start position:0%
+subexponential thing uh when you reduce
+to this you might end up putting it uh
+
+ align:start position:0%
+to this you might end up putting it uh
+ 
+
+ align:start position:0%
+to this you might end up putting it uh
+you you lose that polinomial factor and
+
+ align:start position:0%
+you you lose that polinomial factor and
+ 
+
+ align:start position:0%
+you you lose that polinomial factor and
+so it's not a contradiction yeah bit
+
+ align:start position:0%
+so it's not a contradiction yeah bit
+ 
+
+ align:start position:0%
+so it's not a contradiction yeah bit
+subtle
+
+ align:start position:0%
+subtle
+ 
+
+ align:start position:0%
+subtle
+but cool see you Thursday
\ No newline at end of file
diff --git a/RITcQMokTJs.txt b/RITcQMokTJs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0fe098e5e68e765487ea84a374ccea20c05162b1
--- /dev/null
+++ b/RITcQMokTJs.txt
@@ -0,0 +1,3450 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Good afternoon.
+
+The title here is the
+topic for our class today.
+
+We want to discuss formally
+the derivation Optical Bloch
+
+Equations, but usually
+when I teach you something,
+
+I have a general concept in mind
+and the concept right now here
+
+is, how can we get from unitary
+time evolution of a quantum
+
+system to rate
+equations anticipation.
+
+And this is sort of the
+subject of master equation
+
+open system dynamics, and
+this cartoon sort of tells you
+
+what you want to do.
+
+We have a total system, which is
+one part we are interested in,
+
+and the other one, often it has
+many, many degrees of freedom,
+
+and we don't want to
+keep track of them.
+
+But they have one Hamiltonian.
+
+But we are only interested in
+how our atomic system evolves,
+
+and we want to find
+an equation, which
+
+is no longer a
+Schrodinger equation.
+
+How does an initial density
+matrix describing our system
+
+develop with time?
+
+And as we will see, in general,
+it follows a master equation,
+
+and we want to discuss
+what are general principles
+
+of such equations.
+
+But it's very important
+here is that we are not
+
+keeping track of what
+happens in the environment,
+
+and that's associated here with
+a little bucket or trash can.
+
+Every result photons
+or such are measured,
+
+the environment is constantly
+projected on a measurement
+
+basis, and therefore,
+re-introduce probabilistic
+
+element into the part
+we don't observe mainly
+
+the part which
+characterizes the atoms.
+
+So for that we need the
+formalism of density matrix,
+
+and that's where
+we want to start.
+
+At the end of last
+lecture, I reminded you
+
+that the density
+matrix can always
+
+be written as an
+ensemble where you
+
+say you have a certain
+probability for certain rate
+
+function.
+
+This is always possible,
+but it is not unique.
+
+So each of you could actually
+create the same density matrix
+
+by preparing a number
+of quantum states
+
+with a certain
+probability and saying
+
+this is my density matrix.
+
+And also each of you has
+prepared different quantum
+
+states.
+
+If you sum them up
+in that same way,
+
+you get the same density matrix
+and therefore, all observables
+
+or measurements you will do
+on your ensemble in the future
+
+will be identical because
+the density matrix is
+
+a full description
+of the system.
+
+So at that level, it may
+look sort of very trivial
+
+that we have
+different unraveling.
+
+Unraveling means you
+look microscopically
+
+what is behind the
+density matrix,
+
+but in your homework
+assignment, you
+
+will all show that you can have
+a system which have very, very
+
+different dissipation
+mechanisms,
+
+but they're described
+by the same equation.
+
+So therefore, it's
+physically not possible
+
+to distinguish by just measuring
+the density matrix what
+
+causes a dissipation.
+
+Of course, if you know
+what causes a dissipation,
+
+fluctuating fields
+or collisions,
+
+you know more than the
+density matrix knows.
+
+Any questions about density
+matrix or the agenda
+
+we want to go through today?
+
+Just a quick reminder and
+since this was covered in 8421,
+
+and most of you know about
+it, I pre-wrote the slides.
+
+The density matrix
+is a time evolution.
+
+There is one which is sort
+trivial and covered in more
+
+elementary takes, and this
+is the Hamiltonian evolution,
+
+and I'm sure you've seen it.
+
+The time evolution, the
+unitary time evolution
+
+involves the commutative
+of the Hamiltonian
+
+with a density matrix,
+and later on, we
+
+want to specialize including
+dissipation, including
+
+the environment to the evolution
+of a tool evolutionary system
+
+driven by a monochromatic field
+
+And this the famous
+Jaynes-Cummings Hamiltonian,
+
+and we can characterize this
+system by a density matrix,
+
+but will be very important
+is that we distinguish
+
+between populations,
+the diagonal parts,
+
+and the coherences.
+
+And if you simply put
+this density matrix
+
+into this equation, you find the
+time evolution of the system,
+
+and we will refer to
+that result later on.
+
+Many of you have
+seen it in 8421.
+
+we can parametrize
+the density matrix
+
+for the two-level system.
+
+So we can parametrize
+the densities
+
+of the two-level system
+by a local vector,
+
+r, which is defined
+by this equation.
+
+And then the equation
+of motion is simply
+
+the rotation of a Bloch
+vector on the Bloch sphere,
+
+and it has a
+rotational axis, which
+
+is given by-- the
+undriven system
+
+rotates around the z-axis.
+
+This is just e to
+the i omega naught
+
+t, the normal evolution
+of the free system.
+
+But if you divide it with
+a monochromatic field
+
+rotation over the x-axis
+and the x-axis, of course,
+
+can take your two-level system,
+and flip it from the ground
+
+to the excited state.
+
+So it's just a reminder of the
+simple unitary time evolution,
+
+but now we want to add
+dissipation on top of it.
+
+And what I've decided
+that before I discuss
+
+with you Optical Bloch Equation
+and master equation in general,
+
+I want to give you
+a very simple model.
+
+I really like
+simple models which
+
+capture the essence of what
+you are going to discuss.
+
+So what I want to use is I
+want to use a beam splitter
+
+model I formulated for photons,
+but it would also immediately
+
+apply to atoms.
+
+And this model, what
+I like about it,
+
+it has all the ingredients
+of integration of the master
+
+equation we'll do later
+on without the kind
+
+of many indices and
+summations and integration,
+
+but it captures every single
+bit of what is important.
+
+And I usually like to present
+exactly solvable, simple models
+
+where you get it, and
+then I can go a little bit
+
+faster for the
+general derivation
+
+because you know exactly what
+the more complicated equations,
+
+what they are doing.
+
+So in other words, what I
+want to derive for you is
+
+we want to have the
+following situation.
+
+We have a beam splitter,
+and we know everything
+
+about beam splitters
+because we talked about them
+
+in the first part of
+the course, and we
+
+have a wave function,
+which is the input,
+
+and this is a photon.
+
+And we want to understand
+after the beam splitter,
+
+how has the system evolved.
+
+In general, it will
+be a density matrix,
+
+and what you want
+to find out is,
+
+what is the equation
+for the density matrix.
+
+Maybe this density matrix goes
+through the next beam splitter
+
+and then we want to know
+what comes out of it.
+
+And all we have to
+apply is the formalism
+
+we developed for the beam
+splitter earlier in the course.
+
+Of course, the beam
+splitter is not as harmless
+
+as it looks like.
+
+There is another part
+and another part one here
+
+brings in the environment,
+and for the environment,
+
+we will use the vacuum.
+
+That's the simplest environment.
+
+It's actually
+important environment
+
+because it is the environment
+we will use all the time when
+
+we discuss spontaneous emission.
+
+We send photons into the
+nirvana, into the vacuum
+
+and they disappear, and
+this is our modified.
+
+But the other one which
+is often not so explicit.
+
+If you send your
+photons away, you're
+
+not keeping track
+of what happens,
+
+but you could as well
+perform a measurement,
+
+and this is what we put in here.
+
+We say those photons
+hit a bucket or detector
+
+and measure them,
+we observe them.
+
+There's nothing else
+we do with them,
+
+so we can as well measure them,
+and this being immediately
+
+lead to the equation
+for the density matrix.
+
+So this is what you
+want to discuss,
+
+and it will have all
+the ingredients later
+
+on in a mathematically
+simple form
+
+for the derivation
+of master equation.
+
+So let's consider a
+similar photon for that.
+
+So the wave function,
+this is superposition
+
+of no photon and 1 photon,
+and the coefficients
+
+are alpha and beta.
+
+And just for
+simplifying notation,
+
+I pick alpha and
+beta to be real.
+
+So what do we expect to
+happen at the beam splitter?
+
+Well, there's a probability
+that the photon gets reflected.
+
+Probability to
+reflect the photon
+
+and therefore to
+observe the photon.
+
+This probability is, of course,
+beta square-- the probability
+
+that we have a photon to
+begin with-- and then the beam
+
+splitter, remember we
+categorized the beam
+
+splitter with angle
+sine theta cosine theta.
+
+Sine theta was the
+reflection amplitude,
+
+cosine theta, the
+transmission amplitude.
+
+So this probability,
+which I call P1
+
+is the probability for
+reflection and for measurement.
+
+And now naively you
+would think what
+
+happens after the system
+has passed through the beam
+
+splitter, with a probability of
+P1, we've measured the photon.
+
+We know for sure there
+is no photon left.
+
+The system is in
+the vacuum state,
+
+but then you would say,
+well, maybe with probability
+
+1 minus P1, we have
+not measured anything.
+
+Nothing has happened
+to the wave function,
+
+and that means the wave
+function just continuous.
+
+Well as we will
+see, this is wrong.
+
+We are missing something.
+
+What we are actually missing
+is that if you measure nothing,
+
+the wave function is not sine.
+
+The possibility that we could
+have measured something,
+
+changes the wave function.
+
+I will comment on that in much
+more detail in a few lectures
+
+down the road when
+I derive for you
+
+quantum Monte Carlo
+wave function.
+
+I will have a wonderful
+discussions with you
+
+about how does non-observation
+change a wave function.
+
+So we will talk about
+the physics behind it
+
+in some more detail.
+
+Right now, I don't want to
+get into this discussion.
+
+I simply want to use our
+beam splitter equation,
+
+so we can just take the beam
+splitter equation and apply it.
+
+So our output state
+is obtained by taking
+
+the operator for
+our beam splitter,
+
+and maybe you remember that the
+propagation for beam splitter
+
+was discovered by
+an operator, which
+
+had a dagger b dagger
+a in the exponent.
+
+a and b are the two input nodes.
+
+And the angle of
+the beam splitter,
+
+which interpolates between
+0% and 100% reflection
+
+transmission is theta.
+
+And we're now looking
+for the output
+
+state of the total system.
+
+We're not performing
+the measurement yet,
+
+and this is now acting on
+the total system, which
+
+is the cross product
+of our photon system,
+
+of our system of interest.
+
+And the other
+input, which we call
+
+the environment or
+the vacuum, is 0.
+
+Well, look a few weeks
+back, we have done that all.
+
+The output state is, well,
+there was a probability, alpha,
+
+that we had no photon
+in the state psi.
+
+And if we have no
+photon in the state psi
+
+and no photon in the vacuum,
+this is the state 0, 0.
+
+What I denote here
+with this second place
+
+is the environment.
+
+And now we have one photon.
+
+We have exactly one photon
+with the amplitude beta,
+
+and this photon is split
+with cosine theta transmitted
+
+and with phi theta reflected.
+
+If you transmit
+it, we have 1, 0.
+
+If we reflect it, we have 0, 1.
+
+And again, this is
+the environment,
+
+and here is a photon
+in the environment.
+
+So let me just be
+clear that this
+
+is where the
+environment comes in.
+
+It is a vacuum
+state, and here, this
+
+is the output part
+for the environment.
+
+This is where we
+do the measurement.
+
+And I don't think it matters.
+
+I haven't really told you
+which is mode A, which
+
+is mode B. It doesn't
+matter, but one, let's say
+
+the environment is
+mode B, and the system
+
+evolves in mode
+A. As you can see,
+
+I'm using a new
+program, which has
+
+some nicer features in
+terms of handwriting,
+
+but it is a little bit
+rough in scrolling,
+
+so I sometimes have to
+scroll back and forth.
+
+So what is our output?
+
+Now, we have two possibilities.
+
+The environment is 0,
+or the environment is 1,
+
+and we perform a measurement.
+
+So we have to now go into a
+probabilistic description.
+
+So with probability P1, we
+have done a measurement,
+
+and our output state is
+now the vacuum state.
+
+With probability 1
+minus P1, we have not
+
+detected anything in the
+vacuum, and therefore, our state
+
+of the system is alpha 0
+plus beta cosine theta 1.
+
+Is alpha 0, so it is not beta 1
+as naively would have assumed.
+
+It's not the original state.
+
+There is a cosine theta
+factor, which we got exactly
+
+from the beam splitter from
+the unitary evolution provided
+
+by the beam splitter.
+
+And since these state
+is no longer normalized,
+
+I have to normalize
+it by alpha squared
+
+plus beta square
+cosine square theta.
+
+So now we have done our
+measurement probability P1
+
+to detect the photon.
+
+This projects the system
+into the vacuum state
+
+with the probability 1 minus P1.
+
+We have that state.
+
+Just one second.
+
+Scroll in the pictures.
+
+Write that down.
+
+In fact, millions
+that our system is now
+
+described by a density
+matrix with probability P1
+
+and 1 minus 1 minus P1.
+
+With probability P1, we
+are in the vacuum state,
+
+and with probability
+1 minus P1, we
+
+are in that state, the
+denormalized state psi
+
+naught, which I just hold down.
+
+Question?
+
+AUDIENCE: Have you
+considered theta
+
+to be some like a dynamical
+phase evolution system.
+
+It's very low order
+like when you expand it
+
+the first time it looks almost
+identical to [INAUDIBLE]
+
+quantum effect maybe.
+
+The environment is measuring the
+state in some way, and I mean,
+
+it's the lowest order now.
+
+PROFESSOR: Yeah, I Quite
+agree that random 0 is just
+
+an example of it.
+
+Pretty much, it's all the same.
+
+Yeah.
+
+What we do here is, I
+like the beam splitter
+
+because the beam splitter
+provides an exact formulation
+
+of the measurement process.
+
+You really can use
+a beam splitter
+
+to discuss what
+happens fundamentally
+
+when you perform a measurement.
+
+And the beams splitter is one
+typical implementation of that,
+
+but it has all the
+features you'll
+
+find in any measurement system.
+
+And especially what
+you observe here,
+
+let me just emphasizes is,
+the fact that we you do not
+
+make a measurement
+is changing the way
+
+function from the initial wave
+function psi to psi naught,
+
+we have a factor of
+cosine theta here.
+
+And that's also very general.
+
+A measurement perturbs,
+modifies your wave function
+
+no matter what the outcome
+of the measurement is.
+
+So let me write
+it down because we
+
+want to take it
+to the next level.
+
+So we have now found in terms of
+the beam splitter, angle theta,
+
+and the parameters of the
+initial state, alpha beta.
+
+We found the density matrix
+after the beam splitter.
+
+Yes.
+
+So what is the next step?
+
+Our goal is to derive the
+master equation for the density
+
+matrix, the time evolution
+of the density matrix.
+
+So since we want to
+discuss the time evolution,
+
+we want to find a
+differential equation.
+
+So what we want
+to figure out is,
+
+what is the difference
+between the output density
+
+matrix and the input
+density matrix.
+
+The input was, of
+course, pure state
+
+characterized by the matrix
+population alpha squared
+
+and beta squared of diagonal
+matrix element of alpha beta.
+
+The difference between
+the density matrix
+
+is can just calculate
+the difference.
+
+You can simplify
+things by applying
+
+some trigonometric
+identities, so this
+
+is an exact result,
+cosine theta minus 1.
+
+Here we have alpha beta
+cosine theta minus 1,
+
+and on the diagonal,
+we have cosine
+
+2 theta minus 1 divided by 2.
+
+Anyway this is an
+intermediate result.
+
+We're interested in the
+differential equation.
+
+We want to sort of find out
+what happens when we observe,
+
+when we have the density
+matrix interacting
+
+with the environment
+all the time.
+
+And this can be simulated
+by beam splitters
+
+by using many beam splitters
+with a small degree
+
+of reflection.
+
+So we want to simplify
+this result now
+
+for the case of many beam
+splitters, and each of them
+
+has a small tipping
+angle, theta,
+
+and for later convenience, I
+defined theta to be gamma times
+
+delta t over 2.
+
+That's just my
+definition of theta.
+
+So what we have in mind now is
+that we start with the system
+
+psi, and we have many such beam
+splitters with an infinitesimal
+
+tipping angle.
+
+Each beam splitter has the
+vacuum at its input state.
+
+And we always perform
+the measurement.
+
+If I take the
+equation above, which
+
+I know you can't see anymore,
+we find a differential equation
+
+for the density matrix, which is
+we find an infinitesimal change
+
+delta over the density
+matrix, which looks like this.
+
+So all I've done is, I've
+used the equation above,
+
+and I've done a Taylor expansion
+in the small angle theta.
+
+And the reason why I brought
+in the square root, well,
+
+we get cosine theta.
+
+The first order Taylor expansion
+or the lowest order Taylor
+
+expansion from cosine is
+1 minus theta squared.
+
+So I get the square
+root squared.
+
+So I get gamma,
+which appears here,
+
+and then I divide by delta t.
+
+So this is just an exact
+mathematical expression,
+
+and the next step is to form
+a differential equation.
+
+But before I do that, I want
+to emphasize the two features
+
+we are using here.
+
+They sort of enter
+automatically,
+
+but these are the
+two big assumptions
+
+we make when we derive
+a master equation.
+
+The first one is that we
+always have a vacuum state
+
+as the input.
+
+So in other words,
+the environment
+
+is always in the same state,
+which is a vacuum state,
+
+and this is sort of called
+a Bohr approximation.
+
+What it means is that we
+do a measurement here,
+
+but the vacuum is not changing.
+
+In other words, we are
+not overloading the vacuum
+
+with so many photons
+that suddenly the vacuum
+
+Is no longer in
+the vacuum state.
+
+Or in the case of
+spontaneous emission,
+
+the vacuum can just take as many
+photons as you dumping into it.
+
+They disappear so quickly that
+for all practical purposes,
+
+the environment stays
+in the vacuum state.
+
+So this is called the
+Bohr approximation.
+
+The environment is not changing.
+
+It has enough capacity you to
+be modified by the measurement
+
+process.
+
+And the second thing
+which is related
+
+is, the vacuum is always
+in the same state,
+
+and there are no correlations
+from here to here to here,
+
+there is no memory effect.
+
+Everything is
+completely uncorrelated.
+
+So the environment
+is uncorrelated.
+
+It has no memory.
+
+It's correlation function
+is a delta function,
+
+and this is called
+Markov approximation.
+
+So these are the two
+effects which are important.
+
+One is no memory
+for the environment,
+
+Delta function correlation,
+Markov approximation,
+
+and the two, of
+course, are related
+
+in the environment is all
+of this in the same state.
+
+So remember this is a change
+for the density matrix,
+
+and alpha beta where
+the original parameters
+
+of the density matrix
+for the input state.
+
+So I can now rewrite everything
+as a differential equation.
+
+The density matrix
+has a derivative
+
+for the diagonal matrix
+elements and for the coherences.
+
+Here we have plus gamma.
+
+Here we have minus
+gamma 0, 1, 1,
+
+makes sense because
+we conserve the trace.
+
+We have unity probability
+that we have a stellar system.
+
+And therefore the two
+diagonal matrix elements,
+
+the population, the sum of
+them cannot change with time.
+
+And for the coherence,
+we have gamma over 2.
+
+And if you're familiar with
+Optical Bloch Equations, which
+
+we derive next, we
+can say that these
+
+means if 0 is the ground state
+that the ground state changes
+
+because-- call it spontaneous
+emission from the excited
+
+state.
+
+This equation would say that
+the excited state decays
+
+with the rate gamma,
+and sometimes you
+
+may have wondered about
+that there are factors
+
+of two appearing,
+which also appears here
+
+that when the excited state
+decays with a rate gamma,
+
+we have a factor here
+for the coherences, which
+
+is gamma over 2.
+
+So what we have
+accomplished in contrast
+
+to let's say Einstein's
+equation with the Einstein
+
+a and b coefficient,
+which lead to rate
+
+equations for the population,
+we have now a new feature.
+
+We have an the equation
+for the coherences,
+
+and we find a decay
+of the coherences
+
+with half the rate as a
+decay of the population.
+
+Questions?
+
+So if you want you could rewrite
+this model for photon, which
+
+goes through beam splitters,
+undergoes measurement.
+
+You can rewrite it from
+atomic wave function
+
+and you measure
+whether the atomics
+
+in the excited and ground
+state and the equation
+
+for the measurement
+performed on the atom
+
+is exactly as the equation by
+which the beam splitter acts
+
+on the photon state.
+
+So what I've shown
+here it's very
+
+specific for a single
+photon because I
+
+could use simple
+equations, but everything
+
+is what you find in a much
+more general situation.
+
+So before I give you the
+general derivation of the master
+
+equation, let me talk
+about what we have learned
+
+from this example and what
+the general procedure is.
+
+The first thing is our goal
+is to find a differential
+
+equation for the density
+matrix of the system.
+
+I just remember.
+
+There was one thing
+I wanted to mention.
+
+In the previous derivation
+with the beam splitter,
+
+I started with a purer
+state, and the purer state
+
+developed into a
+statistical mixture,
+
+and this statistical
+mixture would then
+
+transform the next
+beam splitter into
+
+another statistical mixture.
+
+I derived the differential
+equation for you
+
+for the first state
+from the pure state
+
+to the statistical mixture.
+
+But if you would
+spend a few minutes,
+
+you could immediately
+show that you
+
+can start with an
+elementary density matrix,
+
+look how it evolves
+through the beam splitter,
+
+and you get exactly the
+same differential equation.
+
+So the general procedure is,
+we want a differential equation
+
+how the density matrix
+evolves with time.
+
+And this will be obtained
+by finding an operator which
+
+acts on the initial
+density matrix.
+
+This operator is not
+a unitary operator
+
+because we are
+performing measurements
+
+through the environment,
+even if you don't actually
+
+perform them.
+
+Once we dump something
+into the environment,
+
+it's out of our
+control and anybody
+
+could go and perform
+a measurement,
+
+and so we should assume
+that this measurement has
+
+been taken.
+
+It's one of those
+quantum mechanical things
+
+that you don't even have to
+care whether somebody does it.
+
+The environment does it for you.
+
+So this operator is called
+a Liouvillian operator.
+
+It's sometimes called--
+and I haven't really
+
+traced down why-- it's called
+sometimes super operator.
+
+I know what
+superconductivity is,
+
+but I don't know what the super
+powers of this operator are,
+
+but that's just a name
+which you will find.
+
+The second thing
+which we have used
+
+is that the evolution
+of this system
+
+can be obtained from the time
+evolution of the total system
+
+by performing a trace over
+the degrees of freedom
+
+of the environment.
+
+This was exactly
+what we actually
+
+did when we said the system
+continues with probability P
+
+naught in one state
+and probability
+
+P1 in the other state.
+
+The operation which lead
+to this density matrix
+
+was exactly the partial trace.
+
+So this is the second
+general feature
+
+which we have to implement.
+
+Thirdly, if we could
+do one and two exactly,
+
+we would have an
+exact formulation
+
+for a small part
+of a quantum system
+
+no matter how complicated
+the environment is.
+
+In practice, we can
+solve the equations only
+
+when we make
+simplifying assumptions
+
+about the environment.
+
+One is, it is large,
+and more important,
+
+therefore, it's unchanging, and
+this is the Bohr approximation.
+
+And the second feature is,
+it has a short correlation
+
+time, tau c.
+
+In the beam splitter, I
+have made the assumption
+
+that there is no correlation
+between different beam
+
+splitters in the
+derivation, which
+
+I want to walk you through.
+
+Right now, you
+will see explicitly
+
+where the correlation
+times enter.
+
+And this is called the
+Markov approximation.
+
+And finally, this is number
+four, the whole possibility
+
+to derive a master
+equation hinges on the fact
+
+that we have different
+time scales which
+
+are very different.
+
+We are interested in the
+evolution of our system.
+
+We want to know how it relaxes,
+and this is on a time scale
+
+1 over gamma.
+
+So we call this slow.
+
+We are interested
+in the variation
+
+of our system, the atomic
+system or the photon state,
+
+which passes through
+the beam splitter,
+
+and this time scale
+has to be much slower
+
+than the fluctuations
+of the environment.
+
+So therefore, if the
+environment has fluctuations,
+
+which in the beam
+splitter model where
+
+assumed to be 0, it was
+delta function of time,
+
+if that correlation time is
+much smaller than the time
+
+it takes for the system
+to relax and to evolve,
+
+that opens a window
+delta t, and this
+
+is the time scale of
+the master equation.
+
+Just to give you one example
+for the spontaneous emission,
+
+the correlation
+time, tau c, would
+
+be the time it takes the photon
+to disappear from the atom.
+
+And the photon has
+disappeared from the atom
+
+when it is one wavelengths away.
+
+So typically, the
+correlation time
+
+f the vacuum for
+spontaneous emission
+
+is one cycle of the
+optical frequency.
+
+It's very, very fast.
+
+Whereas typical decay times
+of the excited states,
+
+a nano second.
+
+It's six orders of
+magnitude slower,
+
+and this is what we describe.
+
+But on a time scale
+of a femtosecond
+
+of one optical cycle, the photon
+has not detached from the atom
+
+and it could go actually
+back to the atom.
+
+During that time, we talked
+a little bit about it
+
+when we did this diagrammatic
+discussions of resonance
+
+scattering for very,
+very early times.
+
+You don't have exponential
+decay because you cannot do
+
+the approximations where
+we approximated the kernel
+
+by something which was
+completely energy dependent.
+
+And so what happens
+at such short times,
+
+we encounter here again
+in such short times,
+
+we will not have a simple
+description of the system.
+
+So the last point,
+let me summarize.
+
+Our goal is that we describe the
+density matrix of the system,
+
+and we want to find
+the Liouville operator
+
+or some matrix which acts on it.
+
+And because we will integrate
+over time steps, which
+
+are larger than the
+correlation time of the system,
+
+we can also call it, it will
+be a coarse-grained evolution.
+
+Any questions about that?
+
+I really like the discussion,
+the derivation of the master
+
+equation, how it is presented
+in atom-photon indirection.
+
+But it is presented
+on more than 50 pages
+
+with many, many equations.
+
+So after giving you all
+of the principles, all
+
+of the concepts, I
+want to go with you now
+
+over those equations
+and point out how
+
+the principles, which we
+encountered with the beam
+
+splitter, how they
+are now implemented
+
+in a very general context.
+
+I will not be able to give you
+all of the mathematical aspects
+
+of it, but I think by now you
+know that the book atom-photon
+
+interactions are
+actually wonderful.
+
+You can get a lot of conception
+information out of it
+
+by looking at the equations
+without understanding
+
+every technical detail.
+
+So I would really encourage
+you, if there is something which
+
+piques your interest and I
+hope there will be things which
+
+you'll find very interesting,
+that you go to the book
+
+and read it.
+
+So I'm exactly following
+that actually I
+
+used copies of the book.
+
+So we have a
+Hamiltonian, which is
+
+describing the atomic system.
+
+It describes the reservoir and
+then there is an interaction.
+
+We keep it very general here,
+but you may always think well,
+
+the atom is your favorite
+two-level system.
+
+The environment is
+maybe the vacuum
+
+with all its possible
+modes, and the interaction
+
+is the dipole interaction
+or the a dot p interaction.
+
+So we start out
+with an equation,
+
+which is nothing else
+than Schrodinger's
+
+equation for the density matrix.
+
+The time derivation
+of the density matrix
+
+is commutative
+with the Hamilton.
+
+But it is often useful and
+you've seen it many times,
+
+to go to the interaction
+representation,
+
+that the time dependence
+due to the unperturbed part
+
+of the operator is absorbed
+in a unitary transformation,
+
+so therefore, this density
+matrix in the interaction
+
+representation evolves not with,
+h, because h naught is taken
+
+care of, it only involves due
+to the coupling between the two
+
+systems, between the
+system and the environment.
+
+So now this equation, we are
+interested in a time step delta
+
+t.
+
+And this time step,
+delta t remember,
+
+we want to coarse
+grain, will be larger
+
+than the correlation
+time of the reservoir,
+
+and you will see exactly
+where it comes about.
+
+So we want to now do one of
+those coarse-grain steps.
+
+We take this equation and
+we integrate from time t
+
+to time t plus delta t.
+
+So this is exact here.
+
+But now we want to iterate,
+and that means the following.
+
+We have expressed the time
+step in the density matrix
+
+by having the
+density matrix there.
+
+But now we can do in a
+first-order perturbation
+
+theory, we can do one step and
+we get the second order result
+
+by plugging the first order
+result into this equation.
+
+It's the same we have seen
+with our diagrams and such.
+
+We have an exact equation.
+
+It's useless unless we do
+something, and what we do is,
+
+we realize that
+we can iterate it
+
+because the part we don't
+know involves one more
+
+occurrence of the
+interaction potential.
+
+And when you plug the nth
+order solution in here,
+
+you get the n plus
+first order solution.
+
+And this is exactly
+what is done here.
+
+And I skipped a
+few equations here.
+
+This is what he's
+done here, number one.
+
+And number two is, we are
+interested in the system,
+
+not in the reservoir,
+so therefore we
+
+perform the trace
+over the reservoir.
+
+And the trace of the reservoir
+for the photon beam splitter
+
+mend, we say we have
+two possible states,
+
+we detect a photon or not.
+
+And for the system, we
+have now a density matrix
+
+which is probability P naught
+in one state, probability
+
+P1 in the other state.
+
+And this is exactly what the
+operator partial trace does.
+
+Remember also I want
+to really make sure
+
+that you recognize
+all the structures.
+
+The time evolution of a density
+matrix was a commutator with h,
+
+but in the interaction picture,
+it's a commutator with v.
+
+But since we are putting the
+first order result in here,
+
+the second order result
+is now the commutator
+
+of v with the
+commutator of v and o.
+
+It's just we have
+iterated one more time.
+
+So the sigma tilde, the
+density matrix for our system,
+
+tilde means in the
+interaction picture
+
+is now the partial
+trace over the reservoir
+
+of the total density matrix.
+
+Tilde means in the
+interaction picture.
+
+And the important part
+here is that it is exact.
+
+We have not done any
+approximation here.
+
+Any questions?
+
+Of course, now we have to
+make approximations because we
+
+cannot solve an interactive
+problem exactly.
+
+The first one is-- and what
+do we want to do in the end?
+
+We want to keep the
+first non-trivial term
+
+but to the extent possible, we
+want to factorize everything.
+
+We want to get rid of the
+entanglement of the environment
+
+in the system and only get
+sort of the minimum which
+
+is provided by the coupling.
+
+So this evolves as follows.
+
+The interaction we assume is
+a product of two operators.
+
+One operator acts on
+the system, one operator
+
+acts on the environment.
+
+So this could be the dipole
+acting on the atom, the vacuum
+
+field, e, interacting
+with the environment
+
+or it could be p dot a.
+
+Or maybe your system has
+a magnetic moment, m,
+
+and the environment consists
+of fluctuating magnetic fields.
+
+So we'll pretty much find
+in every kind of measurement
+
+that a measurement involves
+the product of two operators.
+
+One is an operator
+for your system
+
+and one is an operator for the
+reservoir of the environment.
+
+And so this is one
+thing we want to use,
+
+and now there is one
+thing which the moment we
+
+will set in our equations,
+there is one thing
+
+which will naturally appear.
+
+Let me scroll back.
+
+What we have here is the
+interaction operator, v,
+
+at two different times.
+
+So this means if something
+happens at different times
+
+and we integrate over times.
+
+This is a correlation function,
+a correlation function
+
+between v at the time t prime
+and the time t double prime
+
+and since the reservoir
+part of this interaction
+
+is the operator, r, so
+what we have here now is,
+
+we have a correlation
+between the operator, r,
+
+at two times, which
+characterizes the environment.
+
+And now comes an
+important approximation.
+
+You remember I said we want to
+assume that the environment has
+
+a very short correlation time.
+
+Whenever a photon is emitted,
+it appears dramatically fast.
+
+It disappears in
+one optical cycle,
+
+and the environment
+is sort of reset,
+
+it's back in the vacuum state.
+
+So this is now expressed here
+that this product over which
+
+we take the partial trace has
+a very short coherence time.
+
+And the fact is
+now the following.
+
+We are integrating over a
+coarse-grained step delta t,
+
+but this correlation function
+goes to 0 in a very short time.
+
+So therefore it will
+not contribute a lot.
+
+Let me write that down.
+
+What we are going to approximate
+is our total density matrix
+
+is now approximately
+factorizing in a density matrix
+
+describing the atomic system.
+
+Well, we describe
+the atomic system
+
+when we trace out
+the environment.
+
+We describe the environment when
+we trace out the atomic part.
+
+And if we now form
+the direct product,
+
+we are back to the
+total system, but we
+
+have factorized the total
+density matrix into two parts.
+
+What we neglect here is a part
+which cannot be factorized
+
+which is the
+correlated part of it.
+
+But what happens is, since we
+are integrating over time steps
+
+delta t and the
+correlation decay
+
+in a very, very short
+time, the result is
+
+that this complicated part,
+which we could never calculate,
+
+is smaller than the first
+part by the ratio of the time
+
+where the correlations
+contribute over the time delta
+
+t, the time step we
+are going to take.
+
+So this is a very
+critical assumption.
+
+There is a whole page
+or two in the book where
+
+an photon-atom
+interaction they discuss
+
+the validity of this
+assumption, but I've given you
+
+the physical motivation that we
+indicate over much larger time,
+
+and if this time is large
+and the correlation is
+
+lost for short time,
+they only contribute
+
+with this small
+parameter to the result.
+
+So in other words,
+this means after-- we
+
+have an interaction between
+the environment and the system.
+
+We write it down
+in second order,
+
+but the second
+order result is now
+
+we evaluated by
+factorizing the density
+
+matrix into our system
+in the reservoir.
+
+So that means in that sense
+if you factorize something,
+
+it looks as if it's
+not interacting,
+
+but the trick is the same.
+
+You write down something
+to first and second order,
+
+and once you have factored
+out the important physics,
+
+now you can evaluate
+the expression
+
+by using an approximation,
+which is now the approximation
+
+that the density
+matrix factorizes.
+
+So with that, this
+is the approximation
+
+that we have made that the
+correlation time is very short.
+
+And now we have a
+differential equation
+
+for the density matrix
+sigma, which describes
+
+or atomic system.
+
+We have traced out the
+degrees of the reservoir.
+
+And now we want to insert B.17.
+
+You probably don't
+remember what B.17 is.
+
+It says that the
+interaction operator
+
+is a product of a, the
+operator a for the atoms
+
+and r for the reservoir.
+
+So the reservoir part, tau
+prime tau double prime,
+
+gives a correlation function.
+
+This is the correlation
+function between the operator,
+
+r, at two different
+times and the part
+
+which acts on our system, the a
+part, is explicitly kept here.
+
+So this is now a
+general master equation.
+
+It tells us the time
+evolution of the density
+
+matrix in this form.
+
+It looks very
+complicated, but this
+
+is because it's very general.
+
+In order to bring it
+into an easier form,
+
+we want to now introduce a basis
+of states, energy eigenstates
+
+of the unperturbed
+system, and write down
+
+all of these operator into
+such a basis of states.
+
+But anyway you saw here how
+we had an exact equation,
+
+and the main
+approximation we made
+
+is that the operator
+acting on the environment
+
+has a very short
+correlation time.
+
+Any questions?
+
+Well, you're only
+a few minutes away
+
+from producing this result
+to Fermi's golden rule, which
+
+you have known for
+a long, long time.
+
+It's just we have made
+very general assumptions.
+
+You see sort of how the
+assumptions propagate,
+
+but now if you write it down
+for an energy eigenbasis,
+
+you will immediately see
+results you have probably
+
+known since your childhood.
+
+So we want to have
+energy eigenstates
+
+of the atomic
+operators, so this is
+
+sort of ground and
+excited state if you
+
+think about a two-level system.
+
+The previous equation,
+I have to go back to it.
+
+Our previous equation is
+a differential equation
+
+for the density matrix here,
+and here is the density matrix.
+
+So now we formulate
+this equation
+
+into an energy eigenbasis,
+and what do we get?
+
+Well, we get an equation
+for the matrix elements,
+
+and what matrix
+elements are important?
+
+diagonal matrix elements
+which are population
+
+of diagonal matrix elements
+which are coherences.
+
+So we pretty much
+take this equation,
+
+use the energy
+eigenbasis and look,
+
+what do we get for
+the populations
+
+and what do we get
+for the coherences.
+
+So the structure is
+now the following.
+
+That we have our
+matrix elements ab.
+
+There is one part which looks
+like a unitary time evolution.
+
+This is what comes from
+the Hamilton operator.
+
+This is sort of the-- we'll
+see that in a moment--
+
+but this is the time
+evolution without relaxation
+
+and now we have
+something here which
+
+are generalized
+relaxation coefficients.
+
+And you will find if
+you go further above
+
+that those relaxation
+coefficients are directly
+
+related to the correlation
+function of the reservoir.
+
+So we can now specify what
+happens between populations.
+
+Population means that we
+have a differential equation,
+
+let's say between
+sigma aa the puller,
+
+and sigma cc, so we
+have a rate coefficient
+
+which connects the
+population in state A
+
+with the population in state C.
+
+And if you take this expression,
+you find several things.
+
+Well, you find
+Fermi's golden rule,
+
+in a generalized
+way-- that's always
+
+nice-- you find
+Fermi's golden rule.
+
+When you integrate over time,
+you often get data function,
+
+and you expect to get a
+delta function because
+
+of energy conservation.
+
+So you get that, of
+course, naturally.
+
+Secondly, we have second
+order matrix element,
+
+which you know from
+Fermi's golden rule,
+
+but now we have the
+following situation
+
+that the matrix element
+in Fermi's golden rule
+
+may actually depend on the
+state, mu, of the environment.
+
+So you have maybe 10
+different possibilities
+
+for the environment,
+and Fermi's golden rule
+
+gives you spontaneous
+emission, which
+
+is different for
+those 10 states.
+
+And naturally, since we have
+performed the partial trace
+
+over the environment,
+we have all those rates
+
+weighted with the probability
+that the environment
+
+is in one of those states.
+
+So what you find here is
+a simple generalization
+
+of Fermi's golden rule.
+
+And if you look at the
+off-diagonal matrix elements,
+
+for instance, you
+want to know what
+
+is this rate, what is the rate
+coefficient, which gives you
+
+the time derivative
+of the coherence,
+
+and it's multiplied
+with the coherence.
+
+You'll find now that in general,
+this rate coefficient has
+
+a damping term, but it may
+also have an imaginary term.
+
+And I hope you remember when we
+played with diagrams, that we
+
+had something similar.
+
+There was something which we
+called the radiative shift.
+
+I called it the AC stock
+effect of a single photon,
+
+and here it is a
+level shift which
+
+comes because the environment
+interacts with your system
+
+and it shifts the
+levels a little bit.
+
+So in addition to
+just relaxation,
+
+spontaneous emission,
+and damping,
+
+there is also a dispersive
+part, a level shift,
+
+and it has exactly
+the same structure.
+
+Let me add that delta
+ab is the difference
+
+between the shift of state
+b and the shift of state a.
+
+And those shifts have
+exactly the same structure.
+
+You have to take the principle
+part of something which
+
+has 1 over the
+difference of energies,
+
+and we discussed that
+this has to be understood
+
+by somewhere adding an
+infinitesimal imaginary part
+
+and doing the right thing
+with complex function.
+
+It's actually related to
+Laplace time difference
+
+between Laplace transformation
+and Fourier transformation.
+
+So anyway what I find
+sort of beautiful
+
+is that we started with
+a most general situation.
+
+We perform the partial trace.
+
+We made one assumption of
+short correlation times,
+
+and a lot of things we have
+known about quantum system
+
+just pops out in a
+very general form here.
+
+Any questions about so far?
+
+Well, the coherences are,
+of course, more interesting
+
+than the population.
+
+Coherence is always something
+physicists get excited about it
+
+because it captures
+something which goes often
+
+beyond classical
+system that we have
+
+quantum mechanical coherences.
+
+And what happens is the
+coefficient here, which
+
+provides the damping
+of the coherence,
+
+just comes out of the
+formalism, has two parts.
+
+And one part is
+an adiabatic part
+
+and the other one is
+a non-adiabatic part.
+
+Well, and that makes sense.
+
+If you have two quantum
+states and there
+
+is a coherence, some
+phase between the two,
+
+the phase can get lost if you
+do a transition between the two
+
+states or one state undergoes
+a collision and is quenched.
+
+So you definitely have one
+part which is due to the fact
+
+that the quantum states
+or the population
+
+changes, and you find that there
+is this state-changing part,
+
+which is pretty much
+the sum of all the rate
+
+coefficient leading
+out of state,
+
+leading to the decay
+of state a and leading
+
+to the decay of state b.
+
+In other words, if you have
+a two-level system, which
+
+has a coherence and you
+have decay of the excited
+
+state and decay of
+the ground state,
+
+you would expect that those
+decay terms appear also
+
+in the decay of the coherence
+between the two levels
+
+and they do, and they appear
+with the correct factor of 1/2.
+
+But there is another possibility
+and this is the following.
+
+You can have no [INAUDIBLE] of
+the population of the state,
+
+but you can still
+lose the coherence.
+
+The model you
+should maybe make is
+
+that you have spin
+up, spin down.
+
+You are not perturbing
+the populations
+
+in spin up and spin
+down, but the environment
+
+provides fluctuating
+magnetic field.
+
+Then due to the
+fluctuating magnetic field,
+
+you no longer can keep
+track of the phase,
+
+and that means in
+your identity matrix
+
+the off-diagonal
+matrix elements decay.
+
+And we find that here this
+is the second part which
+
+in this book is called
+the adiabatic part,
+
+and the physics behind it
+is now pure de-phasing.
+
+So it's an independent
+way for coherences
+
+to decay independent of the
+decay of the population.
+
+Questions?
+
+Collin.
+
+AUDIENCE: Where does the
+Markov approximation come in?
+
+PROFESSOR: The Markov
+approximation is, so to speak,
+
+the delta function
+approximation,
+
+which would say that-- I mean,
+I introduced the correlation
+
+function between the
+reservoir operator
+
+and said the correlation time
+tau c is very, very short.
+
+The Markov approximation
+would actually
+
+state that it would actually
+say in a more radical way
+
+the correlation time is 0.
+
+And the Bohr
+approximation, the fact
+
+that the reservoir
+is unchanged came
+
+in when we said
+the total density
+
+matrix for the second order
+expression just factorizes.
+
+It factorizes into
+the environment,
+
+which is just this density
+matrix of the environment.
+
+It's not changed by the
+interaction with the system.
+
+And this is the
+Bohr approximation.
+
+We just use the same expression
+for the reservoir independent
+
+of the measurements
+the reservoir has done.
+
+Other questions?
+
+Yes, Nancy.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: This is
+something very general.
+
+Thank you actually
+for the question.
+
+Whenever we have some
+damping of the population,
+
+the coherence is only
+damped with a factor of 1/2.
+
+One way to explain it
+in a very simple way
+
+is, that if you have an
+amplitude alpha excited
+
+and alpha ground, the
+population in the excited state
+
+is this squared.
+
+So you sometimes make the
+model that the amplitude decays
+
+with gamma over 2,
+but the population
+
+is-- because you take the
+product, decays with gamma.
+
+So you would say alpha
+e and alpha g both decay
+
+with half the rate,
+but the probability
+
+is for the total rate,
+and the coherence
+
+is the product of
+the amplitudes.
+
+So therefore when you
+look at the coherence,
+
+this decays with 1/2 gamma e.
+
+This decays with 1/2 gamma g,
+and this is what you get here,
+
+1/2 gamma in state a,
+1/2 gamma in state b.
+
+Whereas the probability
+to be in this state
+
+decays with twice that because
+the probability is squared.
+
+So you find that pretty much
+in any quantum mechanically
+
+corrects derivation,
+which you do
+
+about the decay of
+population coherences.
+
+Other questions?
+
+So we have done two things.
+
+We have done the very,
+very simple derivation
+
+using the beam splitter
+model where you may not even
+
+notice where I did the Markov
+approximation because I jumped
+
+from beam splitter
+to beam splitter
+
+and left all the
+correlations behind.
+
+Here in the most
+general calculation,
+
+you have seen exactly
+where it enters,
+
+but maybe now you have the
+full forest in front of you,
+
+and you don't recognize
+the trees anymore.
+
+So let me wrap up this
+lecture by now focusing
+
+on the system we want
+to discuss further on,
+
+namely a two-level system
+interacting with a vacuum
+
+through spontaneous emission.
+
+But I also want to make
+some generalizations.
+
+I want to give you some
+generalizations about what
+
+kind of environments are
+possible in quantum physics.
+
+Let me just see how I do that.
+
+So this part I actually owe to
+Professor [? Ikschuan ?] who
+
+wonderfully compiled that.
+
+So what I want to
+do now is, I want
+
+to call your attention
+to the operator
+
+form which, is rather unique.
+
+Remember when we did second
+order perturbation theory,
+
+we had sort of the
+commutator of v
+
+with the commutator
+of v and rho.
+
+This came from iterating
+the exact equation of motion
+
+for the density matrix.
+
+And you want to specialize that
+now to Jaynes-Cummings model.
+
+I mean, in the end, at
+least in this course,
+
+we always come back to
+the Jaynes-Cummings model
+
+because it captures a lot
+of what we want to explore.
+
+So the Jaynes-Cummings model in
+the rotating wave approximation
+
+is very simple.
+
+It raises the atom from
+ground to excited state
+
+and destroys a photon,
+or it does the opposite.
+
+So this is our
+simple interaction
+
+between our system,
+the two-level atom
+
+and our reservoir which is just
+the vacuum of all the modes.
+
+And you, again, recognize
+what I said in general.
+
+You usually always
+find it by linear form,
+
+an operator which
+acts on the modes,
+
+on the reservoir on the
+vacuum, and an operator which
+
+acts on the vacuum.
+
+Now, we want to make
+the explicit assumption
+
+that the initial state of the
+reservoir is the vacuum state.
+
+It's empty.
+
+And I want to show you
+what is the structure
+
+of the operators we obtain.
+
+And so if you put
+v into here, you
+
+have first the commutator with
+rho, which I write down here,
+
+and then we have to take
+another commutator with v.
+
+And the result of
+that is the following,
+
+that when it comes
+to relaxation pauses,
+
+based on the general
+structure of the time
+
+evolution of quantum mechanics,
+we have this double commutator.
+
+And the operator which, couples
+our system to the environment
+
+is erasing and
+lower an operator.
+
+I mean, the atom because it
+interacts with the environment
+
+either absolves the photon
+or emits the photon.
+
+But those operators, sigma
+plus and sigma minus,
+
+appear now always as
+products because we
+
+have two occurrences
+of the interaction,
+
+v. But if you look at the
+double commutator structure,
+
+the operator sigma plus
+sigma minus appears.
+
+This is just the
+general structure
+
+of this double
+commutator appears
+
+to the left side of the
+atomic density matrix
+
+to the right side of the
+atomic density matrix
+
+and then there is the coarse
+term where the atomic density
+
+matrix is in the
+middle of the two.
+
+So this is actually
+something which
+
+is very general
+and very important
+
+in the theory of
+open quantum system.
+
+What I'm discussing with you now
+is this famous Lindblad form.
+
+And the story goes like that.
+
+You want to know what are
+possible environments, not just
+
+empty vacuum.
+
+You can have fluctuating fields.
+
+You can have, you name it.
+
+But if you are saying that
+your environment interacts
+
+with your system
+through an operator,
+
+and our operator is now the
+operator sigma minus, which
+
+is a spontaneous emission,
+you need heavy t.
+
+The mathematical structure
+of a valid quantum field
+
+remains that if your system
+interacts with an environment
+
+by emitting a
+photon sigma minus,
+
+this is now the structure
+of the master equation.
+
+This is the structure of the
+time evolution of the density
+
+matrix.
+
+So the operator
+sigma minus and its
+
+and its Hermitian conjugate
+sigma plus, all of this
+
+have to appear in
+this combination.
+
+Yes, Collin.
+
+AUDIENCE: This is still
+in my interaction picture.
+
+Right?
+
+There's no dynamical
+phase evolution
+
+that we put back in there.
+
+PROFESSOR: Yeah.
+
+OK.
+
+What we do in general if the
+system is driven by a laser
+
+beam, for instance,
+Rabi oscillation,
+
+we simply add up the dynamics
+of the Rabi oscillation
+
+of the unitary time evolution
+to the time evolution
+
+done by the reservoir.
+
+AUDIENCE: So this form is always
+in the interaction picture?
+
+PROFESSOR: Well, this
+is, you would say,
+
+this form is what is
+the relaxation provided
+
+by the environment.
+
+And if you drive the
+system in addition
+
+with the coherent field,
+unitary time evolution,
+
+you would add it to it.
+
+So in other words,
+what I'm telling
+
+you here is that this is
+the general structure,
+
+and if you have a
+system which interacts
+
+with an environment in
+five different ways,
+
+with a dipole wand, with a
+magnetic moment and such,
+
+you have maybe five
+interaction terms
+
+and then you have to perform
+the sum over five operators,
+
+and here one of them is
+a sigma minus operator.
+
+So in other words,
+if you want to know
+
+what is the whole world of
+possibilities for quantum
+
+system to relax and dissipate
+with an environment,
+
+you can pretty much
+take any operator which
+
+acts on your system,
+but then put it
+
+into this so-called
+Lindblad form
+
+and you have a
+possible environment.
+
+And I mentioned
+I think last week
+
+that people are now in
+our field actively working
+
+on environmental engineering.
+
+They want to expose a system
+to an artificial environment
+
+and hope the system is
+not relaxing, let's say,
+
+to a broken ground state, but
+to a fancy correlated state.
+
+So what this Lindblad form,
+if the operators appears
+
+in this way, what it
+insures is the following.
+
+Just imagine if we
+have an equation,
+
+a derivative of
+the density matrix,
+
+which depends on
+the density matrix,
+
+you could write down a
+differential equation and say
+
+is it possible?
+
+Well, it has to be consistent
+with quantum physics.
+
+You have certain requirements.
+
+One requirement is that
+rho, the density matrix,
+
+always has to be
+the density matrix.
+
+The trace equal 1
+has to be conserved.
+
+A density matrix always must
+have non-negative eigenvalues,
+
+otherwise, what
+you write down, it
+
+might be a nice differential
+equation, but quantum
+
+mechanically, it's nonsense.
+
+But now there is one more
+thing, which is also necessary.
+
+This time evolution of the
+system's density matrix
+
+must come from a unitary time
+evolution of a bigger system.
+
+So you must be able to extend
+your system into a bigger
+
+system, which is
+now the environment,
+
+and this whole system must
+follow a Schrodinger equation
+
+with a Hamilton as a
+unitary time evolution.
+
+And this is where
+it's restrictive.
+
+You cannot just write down a
+differential equation and hope
+
+that this will fill
+some requirement,
+
+and what people have shown is
+under very general assumptions,
+
+it is the Lindblad form
+which allows for it.
+
+So some operator always
+has to appear in this form.
+
+So often in this
+Lindblad form, you
+
+have an operator, which is
+called a jump operator, which
+
+is responsible for
+the measurement, which
+
+the environment
+does on your system.
+
+The jump operator is
+here, the operator
+
+which takes the atom from the
+excited to the ground state.
+
+With that you need a photon,
+and the photon can be measured.
+
+So often you can describe a
+system by a jump operator,
+
+and if the jump operator is
+put into this Lindblad form,
+
+then you have a valid master
+equation for your system.
+
+So let me wrap up.
+
+If you take now the definition
+of the raising and lowering
+
+operator, and you take the
+form I showed you, the Lindblad
+
+form, you'll find now
+this differential equation
+
+for your two-level system.
+
+And this is one part of
+the Optical Bloch Equation.
+
+Now, coming to
+Collin's question,
+
+if you include
+the time evolution
+
+of the classical field,
+this is a coherent evolution
+
+of the Bloch vector,
+which I showed
+
+at the beginning of
+the class, and we
+
+add this and what I wrote down
+at the beginning of the class.
+
+Then we find the famous
+Optical Bloch Equations
+
+in the Jaynes-Cummings model.
+
+So these are now the
+Optical Bloch Equations,
+
+and I hope you enjoy now after
+this complicated discussion,
+
+how simple they are.
+
+And it is this simple
+set of equations,
+
+which will be used in
+the rest of the course
+
+to describe the time
+evolution of the system.
+
+Just because I did
+some generalizations
+
+about the Lindblad equation,
+I copied that into the lecture
+
+notes from Wikipedia,
+and probably now you
+
+sort of understand what is the
+most general Lindblad equation.
+
+It has a Hamiltonian
+part and then it
+
+has jump operators like
+you sigma minus operator,
+
+but it has to come in
+the form that the jump
+
+operator and its complex
+conjugate, emission. conjugate,
+
+is on the left side, on the
+right side, and left and right
+
+of your density matrix.
+
+So this is the generalization
+I've mentioned.
+
+Yeah. with that I think with
+that we've derived the master
+
+equation, and on
+Wednesday, we will
+
+look at rather simple solutions,
+transient and steady-state
+
+solution of the
+Optical Bloch Equation.
+
+Any questions?
+
+One reminder about the
+schedule, this week
+
+we have a lecture on
+Friday because I will not
+
+be on town next
+week on Wednesday.
+
+And of course, you know today
+in a week, next week on Monday.
+
+It's [INAUDIBLE] day.
+
+So we have three
+classes this week,
+
+no class the following week,
+and then the normal schedule
+
+for the rest of the semester.
\ No newline at end of file
diff --git a/RUjePzTQfQg.txt b/RUjePzTQfQg.txt
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--- /dev/null
+++ b/RUjePzTQfQg.txt
@@ -0,0 +1,7683 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
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+the following content is provided by MIT
+ 
+
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+the following content is provided by MIT
+open courseware under a Creative Commons
+
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+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
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+license additional information about our
+ 
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+license additional information about our
+license and MIT open courseware in
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+license and MIT open courseware in
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+
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+license and MIT open courseware in
+general is available at
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+
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+ 
+ocw.mit.edu all right today uh we're
+
+ align:start position:0%
+ocw.mit.edu all right today uh we're
+ 
+
+ align:start position:0%
+ocw.mit.edu all right today uh we're
+going to start on a topic that's one of
+
+ align:start position:0%
+going to start on a topic that's one of
+ 
+
+ align:start position:0%
+going to start on a topic that's one of
+the harder topics that we cover this
+
+ align:start position:0%
+the harder topics that we cover this
+ 
+
+ align:start position:0%
+the harder topics that we cover this
+semester we going to start talking about
+
+ align:start position:0%
+semester we going to start talking about
+ 
+
+ align:start position:0%
+semester we going to start talking about
+um molecular orbital Theory
+
+ align:start position:0%
+um molecular orbital Theory
+ 
+
+ align:start position:0%
+um molecular orbital Theory
+so this is a quantum mechanical
+
+ align:start position:0%
+so this is a quantum mechanical
+ 
+
+ align:start position:0%
+so this is a quantum mechanical
+description of the wave functions in a
+
+ align:start position:0%
+description of the wave functions in a
+ 
+
+ align:start position:0%
+description of the wave functions in a
+molecule and we're going to use
+
+ align:start position:0%
+molecule and we're going to use
+ 
+
+ align:start position:0%
+molecule and we're going to use
+molecular orbital Theory to uh look at
+
+ align:start position:0%
+molecular orbital Theory to uh look at
+ 
+
+ align:start position:0%
+molecular orbital Theory to uh look at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bonding in datomic molecules that's what
+
+ align:start position:0%
+bonding in datomic molecules that's what
+ 
+
+ align:start position:0%
+bonding in datomic molecules that's what
+we'll do for the rest of today we'll
+
+ align:start position:0%
+we'll do for the rest of today we'll
+ 
+
+ align:start position:0%
+we'll do for the rest of today we'll
+look solely at diatomic
+
+ align:start position:0%
+look solely at diatomic
+ 
+
+ align:start position:0%
+look solely at diatomic
+molecules and we'll look mostly at
+
+ align:start position:0%
+molecules and we'll look mostly at
+ 
+
+ align:start position:0%
+molecules and we'll look mostly at
+homonuclear diatomic molecules at the
+
+ align:start position:0%
+homonuclear diatomic molecules at the
+ 
+
+ align:start position:0%
+homonuclear diatomic molecules at the
+end we'll look at one heteronuclear
+
+ align:start position:0%
+end we'll look at one heteronuclear
+ 
+
+ align:start position:0%
+end we'll look at one heteronuclear
+datomic
+
+ align:start position:0%
+datomic
+ 
+
+ align:start position:0%
+datomic
+molecule and then on um and then on
+
+ align:start position:0%
+molecule and then on um and then on
+ 
+
+ align:start position:0%
+molecule and then on um and then on
+Monday we're actually going to use a
+
+ align:start position:0%
+Monday we're actually going to use a
+ 
+
+ align:start position:0%
+Monday we're actually going to use a
+different kind of approach to look at
+
+ align:start position:0%
+different kind of approach to look at
+ 
+
+ align:start position:0%
+different kind of approach to look at
+the chemical bonding in molecules that
+
+ align:start position:0%
+the chemical bonding in molecules that
+ 
+
+ align:start position:0%
+the chemical bonding in molecules that
+are larger than datomic all right so
+
+ align:start position:0%
+are larger than datomic all right so
+ 
+
+ align:start position:0%
+are larger than datomic all right so
+we're going to use molecular orbital
+
+ align:start position:0%
+we're going to use molecular orbital
+ 
+
+ align:start position:0%
+we're going to use molecular orbital
+theory for these diatomic
+
+ align:start position:0%
+theory for these diatomic
+ 
+
+ align:start position:0%
+theory for these diatomic
+molecules and then on Monday we'll go a
+
+ align:start position:0%
+molecules and then on Monday we'll go a
+ 
+
+ align:start position:0%
+molecules and then on Monday we'll go a
+little bit further we'll look at big ger
+
+ align:start position:0%
+little bit further we'll look at big ger
+ 
+
+ align:start position:0%
+little bit further we'll look at big ger
+molecules and we're going to use
+
+ align:start position:0%
+molecules and we're going to use
+ 
+
+ align:start position:0%
+molecules and we're going to use
+something else we're going to use veence
+
+ align:start position:0%
+something else we're going to use veence
+ 
+
+ align:start position:0%
+something else we're going to use veence
+Bond Theory and hybridization ideas all
+
+ align:start position:0%
+Bond Theory and hybridization ideas all
+ 
+
+ align:start position:0%
+Bond Theory and hybridization ideas all
+right but today we're going to deal with
+
+ align:start position:0%
+right but today we're going to deal with
+ 
+
+ align:start position:0%
+right but today we're going to deal with
+these datomic molecules the molecular
+
+ align:start position:0%
+these datomic molecules the molecular
+ 
+
+ align:start position:0%
+these datomic molecules the molecular
+orbital approach all right so here
+
+ align:start position:0%
+orbital approach all right so here
+ 
+
+ align:start position:0%
+orbital approach all right so here
+goes we're going to start talking about
+
+ align:start position:0%
+goes we're going to start talking about
+ 
+
+ align:start position:0%
+goes we're going to start talking about
+hydrogen as we usually do when we start
+
+ align:start position:0%
+hydrogen as we usually do when we start
+ 
+
+ align:start position:0%
+hydrogen as we usually do when we start
+talking about chemical
+
+ align:start position:0%
+talking about chemical
+ 
+
+ align:start position:0%
+talking about chemical
+bonding so I'm going to represent my
+
+ align:start position:0%
+bonding so I'm going to represent my
+ 
+
+ align:start position:0%
+bonding so I'm going to represent my
+hydrogen atom here by this nucleus here
+
+ align:start position:0%
+hydrogen atom here by this nucleus here
+ 
+
+ align:start position:0%
+hydrogen atom here by this nucleus here
+a this is is going to be hydrogen atom a
+
+ align:start position:0%
+a this is is going to be hydrogen atom a
+ 
+
+ align:start position:0%
+a this is is going to be hydrogen atom a
+and I'm going to represent the wave
+
+ align:start position:0%
+and I'm going to represent the wave
+ 
+
+ align:start position:0%
+and I'm going to represent the wave
+function of that hydrogen atom by a
+
+ align:start position:0%
+function of that hydrogen atom by a
+ 
+
+ align:start position:0%
+function of that hydrogen atom by a
+circle right because after all the 1 s
+
+ align:start position:0%
+circle right because after all the 1 s
+ 
+
+ align:start position:0%
+circle right because after all the 1 s
+wave function in hydrogen is spherically
+
+ align:start position:0%
+wave function in hydrogen is spherically
+ 
+
+ align:start position:0%
+wave function in hydrogen is spherically
+symmetric so I'm going to represented by
+
+ align:start position:0%
+symmetric so I'm going to represented by
+ 
+
+ align:start position:0%
+symmetric so I'm going to represented by
+a circle around the nucleus so this is
+
+ align:start position:0%
+a circle around the nucleus so this is
+ 
+
+ align:start position:0%
+a circle around the nucleus so this is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+1s and then I'm going to of course have
+
+ align:start position:0%
+1s and then I'm going to of course have
+ 
+
+ align:start position:0%
+1s and then I'm going to of course have
+a second hydrogen atom represented here
+
+ align:start position:0%
+a second hydrogen atom represented here
+ 
+
+ align:start position:0%
+a second hydrogen atom represented here
+by this nucleus b in a circle around it
+
+ align:start position:0%
+by this nucleus b in a circle around it
+ 
+
+ align:start position:0%
+by this nucleus b in a circle around it
+because that wave function is
+
+ align:start position:0%
+because that wave function is
+ 
+
+ align:start position:0%
+because that wave function is
+spherically
+
+ align:start position:0%
+spherically
+ 
+
+ align:start position:0%
+spherically
+symmetric and what I'm going to do in
+
+ align:start position:0%
+symmetric and what I'm going to do in
+ 
+
+ align:start position:0%
+symmetric and what I'm going to do in
+this molecular orbital Theory approach
+
+ align:start position:0%
+this molecular orbital Theory approach
+ 
+
+ align:start position:0%
+this molecular orbital Theory approach
+is that I'm going to take these two wave
+
+ align:start position:0%
+is that I'm going to take these two wave
+ 
+
+ align:start position:0%
+is that I'm going to take these two wave
+functions and I'm going to bring them a
+
+ align:start position:0%
+functions and I'm going to bring them a
+ 
+
+ align:start position:0%
+functions and I'm going to bring them a
+distance of the bond length apart so in
+
+ align:start position:0%
+distance of the bond length apart so in
+ 
+
+ align:start position:0%
+distance of the bond length apart so in
+other words I'm going to take those two
+
+ align:start position:0%
+other words I'm going to take those two
+ 
+
+ align:start position:0%
+other words I'm going to take those two
+hydrogen atoms and I'm going to put the
+
+ align:start position:0%
+hydrogen atoms and I'm going to put the
+ 
+
+ align:start position:0%
+hydrogen atoms and I'm going to put the
+two nuclei here a A and
+
+ align:start position:0%
+two nuclei here a A and
+ 
+
+ align:start position:0%
+two nuclei here a A and
+B at a distance of a bond length apart
+
+ align:start position:0%
+B at a distance of a bond length apart
+ 
+
+ align:start position:0%
+B at a distance of a bond length apart
+and I'm going to let these two wave
+
+ align:start position:0%
+and I'm going to let these two wave
+ 
+
+ align:start position:0%
+and I'm going to let these two wave
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+overlap right and these are wave
+
+ align:start position:0%
+overlap right and these are wave
+ 
+
+ align:start position:0%
+overlap right and these are wave
+functions and what we learned a few
+
+ align:start position:0%
+functions and what we learned a few
+ 
+
+ align:start position:0%
+functions and what we learned a few
+weeks ago is that waves constructively
+
+ align:start position:0%
+weeks ago is that waves constructively
+ 
+
+ align:start position:0%
+weeks ago is that waves constructively
+interfere or destructively interfere
+
+ align:start position:0%
+interfere or destructively interfere
+ 
+
+ align:start position:0%
+interfere or destructively interfere
+what we're going to do first here is
+
+ align:start position:0%
+what we're going to do first here is
+ 
+
+ align:start position:0%
+what we're going to do first here is
+we're going to let these two waves
+
+ align:start position:0%
+we're going to let these two waves
+ 
+
+ align:start position:0%
+we're going to let these two waves
+constructively interfere where they
+
+ align:start position:0%
+constructively interfere where they
+ 
+
+ align:start position:0%
+constructively interfere where they
+overlap all right so when we do that
+
+ align:start position:0%
+overlap all right so when we do that
+ 
+
+ align:start position:0%
+overlap all right so when we do that
+this part of the wave function here is
+
+ align:start position:0%
+this part of the wave function here is
+ 
+
+ align:start position:0%
+this part of the wave function here is
+going to constructively interfere with
+
+ align:start position:0%
+going to constructively interfere with
+ 
+
+ align:start position:0%
+going to constructively interfere with
+this part of this wave
+
+ align:start position:0%
+this part of this wave
+ 
+
+ align:start position:0%
+this part of this wave
+function and then the sum of those two
+
+ align:start position:0%
+function and then the sum of those two
+ 
+
+ align:start position:0%
+function and then the sum of those two
+is going to look something like this
+
+ align:start position:0%
+is going to look something like this
+ 
+
+ align:start position:0%
+is going to look something like this
+right where now there's this
+
+ align:start position:0%
+right where now there's this
+ 
+
+ align:start position:0%
+right where now there's this
+constructive interference between these
+
+ align:start position:0%
+constructive interference between these
+ 
+
+ align:start position:0%
+constructive interference between these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+nuclei right there's a lot of wave
+
+ align:start position:0%
+nuclei right there's a lot of wave
+ 
+
+ align:start position:0%
+nuclei right there's a lot of wave
+function right here because we
+
+ align:start position:0%
+function right here because we
+ 
+
+ align:start position:0%
+function right here because we
+superimposed those two wave functions
+
+ align:start position:0%
+superimposed those two wave functions
+ 
+
+ align:start position:0%
+superimposed those two wave functions
+each from one hydrogen atom and so
+
+ align:start position:0%
+each from one hydrogen atom and so
+ 
+
+ align:start position:0%
+each from one hydrogen atom and so
+there's constructive interference here
+
+ align:start position:0%
+there's constructive interference here
+ 
+
+ align:start position:0%
+there's constructive interference here
+there's a lot of wave function right
+
+ align:start position:0%
+there's a lot of wave function right
+ 
+
+ align:start position:0%
+there's a lot of wave function right
+there and in so doing what we're going
+
+ align:start position:0%
+there and in so doing what we're going
+ 
+
+ align:start position:0%
+there and in so doing what we're going
+to call this resultant wave function
+
+ align:start position:0%
+to call this resultant wave function
+ 
+
+ align:start position:0%
+to call this resultant wave function
+here we're going to call that the
+
+ align:start position:0%
+here we're going to call that the
+ 
+
+ align:start position:0%
+here we're going to call that the
+molecular wave function or the molecular
+
+ align:start position:0%
+molecular wave function or the molecular
+ 
+
+ align:start position:0%
+molecular wave function or the molecular
+orbital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and how we got it was simply a
+
+ align:start position:0%
+right and how we got it was simply a
+ 
+
+ align:start position:0%
+right and how we got it was simply a
+linear combination of atomic orbitals
+
+ align:start position:0%
+linear combination of atomic orbitals
+ 
+
+ align:start position:0%
+linear combination of atomic orbitals
+right this is a linear combination of
+
+ align:start position:0%
+right this is a linear combination of
+ 
+
+ align:start position:0%
+right this is a linear combination of
+atomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals we just brought those two atoms
+
+ align:start position:0%
+orbitals we just brought those two atoms
+ 
+
+ align:start position:0%
+orbitals we just brought those two atoms
+close enough so that their wave
+
+ align:start position:0%
+close enough so that their wave
+ 
+
+ align:start position:0%
+close enough so that their wave
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+overlapped constructive interference and
+
+ align:start position:0%
+overlapped constructive interference and
+ 
+
+ align:start position:0%
+overlapped constructive interference and
+the result is a molecular wave
+
+ align:start position:0%
+the result is a molecular wave
+ 
+
+ align:start position:0%
+the result is a molecular wave
+function now we're going to give that
+
+ align:start position:0%
+function now we're going to give that
+ 
+
+ align:start position:0%
+function now we're going to give that
+molecular wave function a name we're
+
+ align:start position:0%
+molecular wave function a name we're
+ 
+
+ align:start position:0%
+molecular wave function a name we're
+going to call it a sigma wave function
+
+ align:start position:0%
+going to call it a sigma wave function
+ 
+
+ align:start position:0%
+going to call it a sigma wave function
+the sigma designates the symmetry of
+
+ align:start position:0%
+the sigma designates the symmetry of
+ 
+
+ align:start position:0%
+the sigma designates the symmetry of
+that wave function with respect to the
+
+ align:start position:0%
+that wave function with respect to the
+ 
+
+ align:start position:0%
+that wave function with respect to the
+bond axis this is the bond axis right
+
+ align:start position:0%
+bond axis this is the bond axis right
+ 
+
+ align:start position:0%
+bond axis this is the bond axis right
+here the sigma represents the fact that
+
+ align:start position:0%
+here the sigma represents the fact that
+ 
+
+ align:start position:0%
+here the sigma represents the fact that
+this is cylindrically symmetric about
+
+ align:start position:0%
+this is cylindrically symmetric about
+ 
+
+ align:start position:0%
+this is cylindrically symmetric about
+the molecular Bond axis that's what that
+
+ align:start position:0%
+the molecular Bond axis that's what that
+ 
+
+ align:start position:0%
+the molecular Bond axis that's what that
+Sigma means and we're going to call this
+
+ align:start position:0%
+Sigma means and we're going to call this
+ 
+
+ align:start position:0%
+Sigma means and we're going to call this
+a sigma 1s orbital it's a sigma 1s
+
+ align:start position:0%
+a sigma 1s orbital it's a sigma 1s
+ 
+
+ align:start position:0%
+a sigma 1s orbital it's a sigma 1s
+orbital because this was a linear
+
+ align:start position:0%
+orbital because this was a linear
+ 
+
+ align:start position:0%
+orbital because this was a linear
+combination of two 1s Atomic
+
+ align:start position:0%
+combination of two 1s Atomic
+ 
+
+ align:start position:0%
+combination of two 1s Atomic
+orbitals
+
+ align:start position:0%
+orbitals
+ 
+
+ align:start position:0%
+orbitals
+okay all right but now what I want to do
+
+ align:start position:0%
+okay all right but now what I want to do
+ 
+
+ align:start position:0%
+okay all right but now what I want to do
+is I want to remind you that the
+
+ align:start position:0%
+is I want to remind you that the
+ 
+
+ align:start position:0%
+is I want to remind you that the
+physically significant part of this wave
+
+ align:start position:0%
+physically significant part of this wave
+ 
+
+ align:start position:0%
+physically significant part of this wave
+function was actually the wave function
+
+ align:start position:0%
+function was actually the wave function
+ 
+
+ align:start position:0%
+function was actually the wave function
+Square squared remember that we talked
+
+ align:start position:0%
+Square squared remember that we talked
+ 
+
+ align:start position:0%
+Square squared remember that we talked
+about taking the wave function squaring
+
+ align:start position:0%
+about taking the wave function squaring
+ 
+
+ align:start position:0%
+about taking the wave function squaring
+it and that interpretation is a
+
+ align:start position:0%
+it and that interpretation is a
+ 
+
+ align:start position:0%
+it and that interpretation is a
+probability density that was what was
+
+ align:start position:0%
+probability density that was what was
+ 
+
+ align:start position:0%
+probability density that was what was
+critical to our understanding of where
+
+ align:start position:0%
+critical to our understanding of where
+ 
+
+ align:start position:0%
+critical to our understanding of where
+the electrons are in a molecule so
+
+ align:start position:0%
+the electrons are in a molecule so
+ 
+
+ align:start position:0%
+the electrons are in a molecule so
+that's what we're going to do here we're
+
+ align:start position:0%
+that's what we're going to do here we're
+ 
+
+ align:start position:0%
+that's what we're going to do here we're
+going to take this Sigma 1s molecular
+
+ align:start position:0%
+going to take this Sigma 1s molecular
+ 
+
+ align:start position:0%
+going to take this Sigma 1s molecular
+wave function
+
+ align:start position:0%
+wave function
+ 
+
+ align:start position:0%
+wave function
+now and we're going to square it and
+
+ align:start position:0%
+now and we're going to square it and
+ 
+
+ align:start position:0%
+now and we're going to square it and
+that's then proportional to or
+
+ align:start position:0%
+that's then proportional to or
+ 
+
+ align:start position:0%
+that's then proportional to or
+interpreted as a probability density
+
+ align:start position:0%
+interpreted as a probability density
+ 
+
+ align:start position:0%
+interpreted as a probability density
+I'll just abbreviate that by P but this
+
+ align:start position:0%
+I'll just abbreviate that by P but this
+ 
+
+ align:start position:0%
+I'll just abbreviate that by P but this
+is a probability density remember not a
+
+ align:start position:0%
+is a probability density remember not a
+ 
+
+ align:start position:0%
+is a probability density remember not a
+probability all
+
+ align:start position:0%
+probability all
+ 
+
+ align:start position:0%
+probability all
+right okay well if that's the case then
+
+ align:start position:0%
+right okay well if that's the case then
+ 
+
+ align:start position:0%
+right okay well if that's the case then
+I can multiply this out right because
+
+ align:start position:0%
+I can multiply this out right because
+ 
+
+ align:start position:0%
+I can multiply this out right because
+Sigma 1 s right here that Sigma 1 s
+
+ align:start position:0%
+Sigma 1 s right here that Sigma 1 s
+ 
+
+ align:start position:0%
+Sigma 1 s right here that Sigma 1 s
+is really equal to this linear
+
+ align:start position:0%
+is really equal to this linear
+ 
+
+ align:start position:0%
+is really equal to this linear
+combination of 1sa 1sb that's Sigma
+
+ align:start position:0%
+combination of 1sa 1sb that's Sigma
+ 
+
+ align:start position:0%
+combination of 1sa 1sb that's Sigma
+1s so let me take 1sa + 1
+
+ align:start position:0%
+1s so let me take 1sa + 1
+ 
+
+ align:start position:0%
+1s so let me take 1sa + 1
+SB multiply it by
+
+ align:start position:0%
+SB multiply it by
+ 
+
+ align:start position:0%
+SB multiply it by
+1sa plus
+
+ align:start position:0%
+1sa plus
+ 
+
+ align:start position:0%
+1sa plus
+1sb all right that's what Sigma 1s is
+
+ align:start position:0%
+1sb all right that's what Sigma 1s is
+ 
+
+ align:start position:0%
+1sb all right that's what Sigma 1s is
+I'm just going to multiply this out and
+
+ align:start position:0%
+I'm just going to multiply this out and
+ 
+
+ align:start position:0%
+I'm just going to multiply this out and
+when I do that I'm going to get
+
+ align:start position:0%
+when I do that I'm going to get
+ 
+
+ align:start position:0%
+when I do that I'm going to get
+1sa SAR plus 1 1 SB 2 + 2 * 1s a 1
+
+ align:start position:0%
+1sa SAR plus 1 1 SB 2 + 2 * 1s a 1
+ 
+
+ align:start position:0%
+1sa SAR plus 1 1 SB 2 + 2 * 1s a 1
+SB right that's my probability
+
+ align:start position:0%
+SB right that's my probability
+ 
+
+ align:start position:0%
+SB right that's my probability
+density now to make this a little bit
+
+ align:start position:0%
+density now to make this a little bit
+ 
+
+ align:start position:0%
+density now to make this a little bit
+more real for you let's plot it so I'm
+
+ align:start position:0%
+more real for you let's plot it so I'm
+ 
+
+ align:start position:0%
+more real for you let's plot it so I'm
+going to plot the probability
+
+ align:start position:0%
+going to plot the probability
+ 
+
+ align:start position:0%
+going to plot the probability
+density as a function of the position
+
+ align:start position:0%
+density as a function of the position
+ 
+
+ align:start position:0%
+density as a function of the position
+along the bond axis so in this case
+
+ align:start position:0%
+along the bond axis so in this case
+ 
+
+ align:start position:0%
+along the bond axis so in this case
+here the uh nucleus a is here
+
+ align:start position:0%
+here the uh nucleus a is here
+ 
+
+ align:start position:0%
+here the uh nucleus a is here
+and the nucleus B is there all right so
+
+ align:start position:0%
+and the nucleus B is there all right so
+ 
+
+ align:start position:0%
+and the nucleus B is there all right so
+we have a molecule now I'm just going to
+
+ align:start position:0%
+we have a molecule now I'm just going to
+ 
+
+ align:start position:0%
+we have a molecule now I'm just going to
+plot the probability density as a
+
+ align:start position:0%
+plot the probability density as a
+ 
+
+ align:start position:0%
+plot the probability density as a
+function of the position along the
+
+ align:start position:0%
+function of the position along the
+ 
+
+ align:start position:0%
+function of the position along the
+internuclear axis and what's it going to
+
+ align:start position:0%
+internuclear axis and what's it going to
+ 
+
+ align:start position:0%
+internuclear axis and what's it going to
+look like well it's going to look like
+
+ align:start position:0%
+look like well it's going to look like
+ 
+
+ align:start position:0%
+look like well it's going to look like
+this going to look something like that
+
+ align:start position:0%
+this going to look something like that
+ 
+
+ align:start position:0%
+this going to look something like that
+all right where the probability density
+
+ align:start position:0%
+all right where the probability density
+ 
+
+ align:start position:0%
+all right where the probability density
+is the highest right at nucleus a and
+
+ align:start position:0%
+is the highest right at nucleus a and
+ 
+
+ align:start position:0%
+is the highest right at nucleus a and
+the probability density is the highest
+
+ align:start position:0%
+the probability density is the highest
+ 
+
+ align:start position:0%
+the probability density is the highest
+right at nucleus B cuz Hey after all you
+
+ align:start position:0%
+right at nucleus B cuz Hey after all you
+ 
+
+ align:start position:0%
+right at nucleus B cuz Hey after all you
+know the wave function any wave function
+
+ align:start position:0%
+know the wave function any wave function
+ 
+
+ align:start position:0%
+know the wave function any wave function
+a w s wave function the highest value of
+
+ align:start position:0%
+a w s wave function the highest value of
+ 
+
+ align:start position:0%
+a w s wave function the highest value of
+that wave function is right at R is
+
+ align:start position:0%
+that wave function is right at R is
+ 
+
+ align:start position:0%
+that wave function is right at R is
+equal to zero or right at the nucleus
+
+ align:start position:0%
+equal to zero or right at the nucleus
+ 
+
+ align:start position:0%
+equal to zero or right at the nucleus
+all right so that's what that
+
+ align:start position:0%
+all right so that's what that
+ 
+
+ align:start position:0%
+all right so that's what that
+probability density looks like and I've
+
+ align:start position:0%
+probability density looks like and I've
+ 
+
+ align:start position:0%
+probability density looks like and I've
+just uh been informed here that the
+
+ align:start position:0%
+just uh been informed here that the
+ 
+
+ align:start position:0%
+just uh been informed here that the
+xeroxing on that particular figure
+
+ align:start position:0%
+xeroxing on that particular figure
+ 
+
+ align:start position:0%
+xeroxing on that particular figure
+didn't uh turn out so well all right but
+
+ align:start position:0%
+didn't uh turn out so well all right but
+ 
+
+ align:start position:0%
+didn't uh turn out so well all right but
+that's uh what it should read if you
+
+ align:start position:0%
+that's uh what it should read if you
+ 
+
+ align:start position:0%
+that's uh what it should read if you
+can't read it very
+
+ align:start position:0%
+can't read it very
+ 
+
+ align:start position:0%
+can't read it very
+well all right but the reason I PLO this
+
+ align:start position:0%
+well all right but the reason I PLO this
+ 
+
+ align:start position:0%
+well all right but the reason I PLO this
+here is to contrast it with the
+
+ align:start position:0%
+here is to contrast it with the
+ 
+
+ align:start position:0%
+here is to contrast it with the
+following suppose I take just one
+
+ align:start position:0%
+following suppose I take just one
+ 
+
+ align:start position:0%
+following suppose I take just one
+hydrogen atom and the other hydrogen
+
+ align:start position:0%
+hydrogen atom and the other hydrogen
+ 
+
+ align:start position:0%
+hydrogen atom and the other hydrogen
+atom but I take those wave functions and
+
+ align:start position:0%
+atom but I take those wave functions and
+ 
+
+ align:start position:0%
+atom but I take those wave functions and
+I just Square them and then I add them
+
+ align:start position:0%
+I just Square them and then I add them
+ 
+
+ align:start position:0%
+I just Square them and then I add them
+up all right so suppose I take a
+
+ align:start position:0%
+up all right so suppose I take a
+ 
+
+ align:start position:0%
+up all right so suppose I take a
+hydrogen atom with its wave function 1sa
+
+ align:start position:0%
+hydrogen atom with its wave function 1sa
+ 
+
+ align:start position:0%
+hydrogen atom with its wave function 1sa
+I Square
+
+ align:start position:0%
+I Square
+ 
+
+ align:start position:0%
+I Square
+it and then I take another wave function
+
+ align:start position:0%
+it and then I take another wave function
+ 
+
+ align:start position:0%
+it and then I take another wave function
+for another hydrogen atom 1sb I Square
+
+ align:start position:0%
+for another hydrogen atom 1sb I Square
+ 
+
+ align:start position:0%
+for another hydrogen atom 1sb I Square
+it and I add those two up in this case
+
+ align:start position:0%
+it and I add those two up in this case
+ 
+
+ align:start position:0%
+it and I add those two up in this case
+what that's doing is taking two hydrogen
+
+ align:start position:0%
+what that's doing is taking two hydrogen
+ 
+
+ align:start position:0%
+what that's doing is taking two hydrogen
+atoms and just taking their wave
+
+ align:start position:0%
+atoms and just taking their wave
+ 
+
+ align:start position:0%
+atoms and just taking their wave
+function and squaring them in this
+
+ align:start position:0%
+function and squaring them in this
+ 
+
+ align:start position:0%
+function and squaring them in this
+particular case what I haven't done is I
+
+ align:start position:0%
+particular case what I haven't done is I
+ 
+
+ align:start position:0%
+particular case what I haven't done is I
+haven't allowed any interference to
+
+ align:start position:0%
+haven't allowed any interference to
+ 
+
+ align:start position:0%
+haven't allowed any interference to
+happen I haven't allowed the wave
+
+ align:start position:0%
+happen I haven't allowed the wave
+ 
+
+ align:start position:0%
+happen I haven't allowed the wave
+functions to constructively interfere
+
+ align:start position:0%
+functions to constructively interfere
+ 
+
+ align:start position:0%
+functions to constructively interfere
+right I didn't add up these wave
+
+ align:start position:0%
+right I didn't add up these wave
+ 
+
+ align:start position:0%
+right I didn't add up these wave
+functions first before I squared them I
+
+ align:start position:0%
+functions first before I squared them I
+ 
+
+ align:start position:0%
+functions first before I squared them I
+squared them and then I added them up
+
+ align:start position:0%
+squared them and then I added them up
+ 
+
+ align:start position:0%
+squared them and then I added them up
+that's different than taking those wave
+
+ align:start position:0%
+that's different than taking those wave
+ 
+
+ align:start position:0%
+that's different than taking those wave
+functions letting them constructively
+
+ align:start position:0%
+functions letting them constructively
+ 
+
+ align:start position:0%
+functions letting them constructively
+interfere and then squaring
+
+ align:start position:0%
+interfere and then squaring
+ 
+
+ align:start position:0%
+interfere and then squaring
+them and you can see the difference is
+
+ align:start position:0%
+them and you can see the difference is
+ 
+
+ align:start position:0%
+them and you can see the difference is
+when I plot this sum and compare it to
+
+ align:start position:0%
+when I plot this sum and compare it to
+ 
+
+ align:start position:0%
+when I plot this sum and compare it to
+that sum right so I'm going to plot now
+
+ align:start position:0%
+that sum right so I'm going to plot now
+ 
+
+ align:start position:0%
+that sum right so I'm going to plot now
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+sum when I do that it's going to look
+
+ align:start position:0%
+sum when I do that it's going to look
+ 
+
+ align:start position:0%
+sum when I do that it's going to look
+well it's going to look pretty much like
+
+ align:start position:0%
+well it's going to look pretty much like
+ 
+
+ align:start position:0%
+well it's going to look pretty much like
+this but then right at the center right
+
+ align:start position:0%
+this but then right at the center right
+ 
+
+ align:start position:0%
+this but then right at the center right
+here hey the probability
+
+ align:start position:0%
+here hey the probability
+ 
+
+ align:start position:0%
+here hey the probability
+density right for this case for two
+
+ align:start position:0%
+density right for this case for two
+ 
+
+ align:start position:0%
+density right for this case for two
+hydrogen atoms which are now nonbonded
+
+ align:start position:0%
+hydrogen atoms which are now nonbonded
+ 
+
+ align:start position:0%
+hydrogen atoms which are now nonbonded
+they're non-bonded because I didn't let
+
+ align:start position:0%
+they're non-bonded because I didn't let
+ 
+
+ align:start position:0%
+they're non-bonded because I didn't let
+those two wave functions constructively
+
+ align:start position:0%
+those two wave functions constructively
+ 
+
+ align:start position:0%
+those two wave functions constructively
+interfere the result is that this
+
+ align:start position:0%
+interfere the result is that this
+ 
+
+ align:start position:0%
+interfere the result is that this
+probability density right in the center
+
+ align:start position:0%
+probability density right in the center
+ 
+
+ align:start position:0%
+probability density right in the center
+here hey that probability density is
+
+ align:start position:0%
+here hey that probability density is
+ 
+
+ align:start position:0%
+here hey that probability density is
+less than what it would be if I let
+
+ align:start position:0%
+less than what it would be if I let
+ 
+
+ align:start position:0%
+less than what it would be if I let
+those two hydrogen atom wave functions
+
+ align:start position:0%
+those two hydrogen atom wave functions
+ 
+
+ align:start position:0%
+those two hydrogen atom wave functions
+constructively
+
+ align:start position:0%
+constructively
+ 
+
+ align:start position:0%
+constructively
+interfere and that's the key in this
+
+ align:start position:0%
+interfere and that's the key in this
+ 
+
+ align:start position:0%
+interfere and that's the key in this
+chemical bond is this term right here
+
+ align:start position:0%
+chemical bond is this term right here
+ 
+
+ align:start position:0%
+chemical bond is this term right here
+it's this term that makes all of the
+
+ align:start position:0%
+it's this term that makes all of the
+ 
+
+ align:start position:0%
+it's this term that makes all of the
+difference this is our constructive
+
+ align:start position:0%
+difference this is our constructive
+ 
+
+ align:start position:0%
+difference this is our constructive
+interference this is the extra
+
+ align:start position:0%
+interference this is the extra
+ 
+
+ align:start position:0%
+interference this is the extra
+density that we get because those two
+
+ align:start position:0%
+density that we get because those two
+ 
+
+ align:start position:0%
+density that we get because those two
+wave functions have constructively
+
+ align:start position:0%
+wave functions have constructively
+ 
+
+ align:start position:0%
+wave functions have constructively
+interfered that's what gives me this
+
+ align:start position:0%
+interfered that's what gives me this
+ 
+
+ align:start position:0%
+interfered that's what gives me this
+pile up of elect electron density right
+
+ align:start position:0%
+pile up of elect electron density right
+ 
+
+ align:start position:0%
+pile up of elect electron density right
+in the center here this is the glue in
+
+ align:start position:0%
+in the center here this is the glue in
+ 
+
+ align:start position:0%
+in the center here this is the glue in
+this chemical bond okay make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so we have formed now a molecular
+
+ align:start position:0%
+okay so we have formed now a molecular
+ 
+
+ align:start position:0%
+okay so we have formed now a molecular
+wave function by this linear combination
+
+ align:start position:0%
+wave function by this linear combination
+ 
+
+ align:start position:0%
+wave function by this linear combination
+of atomic wave
+
+ align:start position:0%
+of atomic wave
+ 
+
+ align:start position:0%
+of atomic wave
+functions now what happens to the energy
+
+ align:start position:0%
+functions now what happens to the energy
+ 
+
+ align:start position:0%
+functions now what happens to the energy
+when we do
+
+ align:start position:0%
+when we do
+ 
+
+ align:start position:0%
+when we do
+that well you can imagine what happens
+
+ align:start position:0%
+that well you can imagine what happens
+ 
+
+ align:start position:0%
+that well you can imagine what happens
+to the energy the energy goes down we're
+
+ align:start position:0%
+to the energy the energy goes down we're
+ 
+
+ align:start position:0%
+to the energy the energy goes down we're
+going to form a new molecular state so
+
+ align:start position:0%
+going to form a new molecular state so
+ 
+
+ align:start position:0%
+going to form a new molecular state so
+let's draw energy level diagram all
+
+ align:start position:0%
+let's draw energy level diagram all
+ 
+
+ align:start position:0%
+let's draw energy level diagram all
+right so energy going up
+
+ align:start position:0%
+right so energy going up
+ 
+
+ align:start position:0%
+right so energy going up
+here and let me represent here by these
+
+ align:start position:0%
+here and let me represent here by these
+ 
+
+ align:start position:0%
+here and let me represent here by these
+two lines the energy
+
+ align:start position:0%
+two lines the energy
+ 
+
+ align:start position:0%
+two lines the energy
+levels of the separated hydrogen atoms
+
+ align:start position:0%
+levels of the separated hydrogen atoms
+ 
+
+ align:start position:0%
+levels of the separated hydrogen atoms
+so I'm going to call this the 1s State
+
+ align:start position:0%
+so I'm going to call this the 1s State
+ 
+
+ align:start position:0%
+so I'm going to call this the 1s State
+on atom a the 1s State on atom B hey
+
+ align:start position:0%
+on atom a the 1s State on atom B hey
+ 
+
+ align:start position:0%
+on atom a the 1s State on atom B hey
+they're at the same energy they're two
+
+ align:start position:0%
+they're at the same energy they're two
+ 
+
+ align:start position:0%
+they're at the same energy they're two
+hydrogen atoms you can't P them
+
+ align:start position:0%
+hydrogen atoms you can't P them
+ 
+
+ align:start position:0%
+hydrogen atoms you can't P them
+apart and each one of them has an
+
+ align:start position:0%
+apart and each one of them has an
+ 
+
+ align:start position:0%
+apart and each one of them has an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+once we allow those two wave functions
+
+ align:start position:0%
+once we allow those two wave functions
+ 
+
+ align:start position:0%
+once we allow those two wave functions
+to constructively interfere we're going
+
+ align:start position:0%
+to constructively interfere we're going
+ 
+
+ align:start position:0%
+to constructively interfere we're going
+to produce a new state we're going to
+
+ align:start position:0%
+to produce a new state we're going to
+ 
+
+ align:start position:0%
+to produce a new state we're going to
+call that state Sigma 1s and that state
+
+ align:start position:0%
+call that state Sigma 1s and that state
+ 
+
+ align:start position:0%
+call that state Sigma 1s and that state
+is going to be lower in energy
+
+ align:start position:0%
+is going to be lower in energy
+ 
+
+ align:start position:0%
+is going to be lower in energy
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+than the two states from the individual
+
+ align:start position:0%
+than the two states from the individual
+ 
+
+ align:start position:0%
+than the two states from the individual
+hydrogen atoms and that's good because
+
+ align:start position:0%
+hydrogen atoms and that's good because
+ 
+
+ align:start position:0%
+hydrogen atoms and that's good because
+if it's lower in energy hey we got these
+
+ align:start position:0%
+if it's lower in energy hey we got these
+ 
+
+ align:start position:0%
+if it's lower in energy hey we got these
+two hydrogen atoms stuck together right
+
+ align:start position:0%
+two hydrogen atoms stuck together right
+ 
+
+ align:start position:0%
+two hydrogen atoms stuck together right
+we formed a chemical bond these two
+
+ align:start position:0%
+we formed a chemical bond these two
+ 
+
+ align:start position:0%
+we formed a chemical bond these two
+hydrogen atoms aren't going to fly apart
+
+ align:start position:0%
+hydrogen atoms aren't going to fly apart
+ 
+
+ align:start position:0%
+hydrogen atoms aren't going to fly apart
+that's what we wanted to
+
+ align:start position:0%
+that's what we wanted to
+ 
+
+ align:start position:0%
+that's what we wanted to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+okay and therefore those two electrons
+
+ align:start position:0%
+okay and therefore those two electrons
+ 
+
+ align:start position:0%
+okay and therefore those two electrons
+here one for me hydrogen atom are
+
+ align:start position:0%
+here one for me hydrogen atom are
+ 
+
+ align:start position:0%
+here one for me hydrogen atom are
+sitting now in this new molecular state
+
+ align:start position:0%
+sitting now in this new molecular state
+ 
+
+ align:start position:0%
+sitting now in this new molecular state
+that we are calling Sigma 1s and the
+
+ align:start position:0%
+that we are calling Sigma 1s and the
+ 
+
+ align:start position:0%
+that we are calling Sigma 1s and the
+wave function then that describes the
+
+ align:start position:0%
+wave function then that describes the
+ 
+
+ align:start position:0%
+wave function then that describes the
+electrons in that state is a sigma 1s
+
+ align:start position:0%
+electrons in that state is a sigma 1s
+ 
+
+ align:start position:0%
+electrons in that state is a sigma 1s
+molecular wave
+
+ align:start position:0%
+molecular wave
+ 
+
+ align:start position:0%
+molecular wave
+function okay that's great everything
+
+ align:start position:0%
+function okay that's great everything
+ 
+
+ align:start position:0%
+function okay that's great everything
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+cool except now that uh you know these
+
+ align:start position:0%
+cool except now that uh you know these
+ 
+
+ align:start position:0%
+cool except now that uh you know these
+are waves so not only can waves
+
+ align:start position:0%
+are waves so not only can waves
+ 
+
+ align:start position:0%
+are waves so not only can waves
+constructively interfere but hey they
+
+ align:start position:0%
+constructively interfere but hey they
+ 
+
+ align:start position:0%
+constructively interfere but hey they
+can destructively interfere too all
+
+ align:start position:0%
+can destructively interfere too all
+ 
+
+ align:start position:0%
+can destructively interfere too all
+right so we got to take care of that
+
+ align:start position:0%
+right so we got to take care of that
+ 
+
+ align:start position:0%
+right so we got to take care of that
+case now the case of destructive uh
+
+ align:start position:0%
+case now the case of destructive uh
+ 
+
+ align:start position:0%
+case now the case of destructive uh
+interference so let's uh let's do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right in this case what's going to
+
+ align:start position:0%
+all right in this case what's going to
+ 
+
+ align:start position:0%
+all right in this case what's going to
+happen well again we have our 1s a wave
+
+ align:start position:0%
+happen well again we have our 1s a wave
+ 
+
+ align:start position:0%
+happen well again we have our 1s a wave
+function and our 1 SB W
+
+ align:start position:0%
+function and our 1 SB W
+ 
+
+ align:start position:0%
+function and our 1 SB W
+function and now when I'm going to bring
+
+ align:start position:0%
+function and now when I'm going to bring
+ 
+
+ align:start position:0%
+function and now when I'm going to bring
+these two together to the equilibrium
+
+ align:start position:0%
+these two together to the equilibrium
+ 
+
+ align:start position:0%
+these two together to the equilibrium
+Bond length AB here what's going to
+
+ align:start position:0%
+Bond length AB here what's going to
+ 
+
+ align:start position:0%
+Bond length AB here what's going to
+happen is in destructive
+
+ align:start position:0%
+happen is in destructive
+ 
+
+ align:start position:0%
+happen is in destructive
+interference this wave function is going
+
+ align:start position:0%
+interference this wave function is going
+ 
+
+ align:start position:0%
+interference this wave function is going
+to cancel this part of the wave
+
+ align:start position:0%
+to cancel this part of the wave
+ 
+
+ align:start position:0%
+to cancel this part of the wave
+function right when these overlap and I
+
+ align:start position:0%
+function right when these overlap and I
+ 
+
+ align:start position:0%
+function right when these overlap and I
+take this minus sign here or I'm
+
+ align:start position:0%
+take this minus sign here or I'm
+ 
+
+ align:start position:0%
+take this minus sign here or I'm
+superimposing two wave functions with
+
+ align:start position:0%
+superimposing two wave functions with
+ 
+
+ align:start position:0%
+superimposing two wave functions with
+different sign we're going to have
+
+ align:start position:0%
+different sign we're going to have
+ 
+
+ align:start position:0%
+different sign we're going to have
+destructive interference and the result
+
+ align:start position:0%
+destructive interference and the result
+ 
+
+ align:start position:0%
+destructive interference and the result
+is that the molecular wave function is
+
+ align:start position:0%
+is that the molecular wave function is
+ 
+
+ align:start position:0%
+is that the molecular wave function is
+going to kind of look like like
+
+ align:start position:0%
+going to kind of look like like
+ 
+
+ align:start position:0%
+going to kind of look like like
+this okay right in the center here hey
+
+ align:start position:0%
+this okay right in the center here hey
+ 
+
+ align:start position:0%
+this okay right in the center here hey
+there's going to be a node there's a
+
+ align:start position:0%
+there's going to be a node there's a
+ 
+
+ align:start position:0%
+there's going to be a node there's a
+node because this part of the wave
+
+ align:start position:0%
+node because this part of the wave
+ 
+
+ align:start position:0%
+node because this part of the wave
+function exactly cancel this part of the
+
+ align:start position:0%
+function exactly cancel this part of the
+ 
+
+ align:start position:0%
+function exactly cancel this part of the
+wave function hey there's no wave
+
+ align:start position:0%
+wave function hey there's no wave
+ 
+
+ align:start position:0%
+wave function hey there's no wave
+function right
+
+ align:start position:0%
+function right
+ 
+
+ align:start position:0%
+function right
+there all right because we have
+
+ align:start position:0%
+there all right because we have
+ 
+
+ align:start position:0%
+there all right because we have
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+interference how are we going to label
+
+ align:start position:0%
+interference how are we going to label
+ 
+
+ align:start position:0%
+interference how are we going to label
+this wave function well we're also going
+
+ align:start position:0%
+this wave function well we're also going
+ 
+
+ align:start position:0%
+this wave function well we're also going
+to call it a sigma wave function it's
+
+ align:start position:0%
+to call it a sigma wave function it's
+ 
+
+ align:start position:0%
+to call it a sigma wave function it's
+Sigma that's a symmetry because it's
+
+ align:start position:0%
+Sigma that's a symmetry because it's
+ 
+
+ align:start position:0%
+Sigma that's a symmetry because it's
+cylindrically symmetric around the
+
+ align:start position:0%
+cylindrically symmetric around the
+ 
+
+ align:start position:0%
+cylindrically symmetric around the
+axis right but because it is a linear
+
+ align:start position:0%
+axis right but because it is a linear
+ 
+
+ align:start position:0%
+axis right but because it is a linear
+combination
+
+ align:start position:0%
+combination
+ 
+
+ align:start position:0%
+combination
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+that is a consequence of destructive
+
+ align:start position:0%
+that is a consequence of destructive
+ 
+
+ align:start position:0%
+that is a consequence of destructive
+interference I'm going to call this
+
+ align:start position:0%
+interference I'm going to call this
+ 
+
+ align:start position:0%
+interference I'm going to call this
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+star Sigma star
+
+ align:start position:0%
+star Sigma star
+ 
+
+ align:start position:0%
+star Sigma star
+1s and I'm going to call that Sigma star
+
+ align:start position:0%
+1s and I'm going to call that Sigma star
+ 
+
+ align:start position:0%
+1s and I'm going to call that Sigma star
+1s that's an anti-bonding
+
+ align:start position:0%
+1s that's an anti-bonding
+ 
+
+ align:start position:0%
+1s that's an anti-bonding
+orbital or an anti antibonding wave
+
+ align:start position:0%
+orbital or an anti antibonding wave
+ 
+
+ align:start position:0%
+orbital or an anti antibonding wave
+function okay now how do I know that
+
+ align:start position:0%
+function okay now how do I know that
+ 
+
+ align:start position:0%
+function okay now how do I know that
+well let's um let's also calculate the
+
+ align:start position:0%
+well let's um let's also calculate the
+ 
+
+ align:start position:0%
+well let's um let's also calculate the
+probability density here for Sigma 1s
+
+ align:start position:0%
+probability density here for Sigma 1s
+ 
+
+ align:start position:0%
+probability density here for Sigma 1s
+star hey that's going to be uh that's
+
+ align:start position:0%
+star hey that's going to be uh that's
+ 
+
+ align:start position:0%
+star hey that's going to be uh that's
+going to be interesting so we got P
+
+ align:start position:0%
+going to be interesting so we got P
+ 
+
+ align:start position:0%
+going to be interesting so we got P
+probability density Sigma 1 s star
+
+ align:start position:0%
+probability density Sigma 1 s star
+ 
+
+ align:start position:0%
+probability density Sigma 1 s star
+Square it right so I have now a one s a
+
+ align:start position:0%
+Square it right so I have now a one s a
+ 
+
+ align:start position:0%
+Square it right so I have now a one s a
+- 1
+
+ align:start position:0%
+- 1
+ 
+
+ align:start position:0%
+- 1
+SB time 1s
+
+ align:start position:0%
+SB time 1s
+ 
+
+ align:start position:0%
+SB time 1s
+Aus 1
+
+ align:start position:0%
+Aus 1
+ 
+
+ align:start position:0%
+Aus 1
+SB multiply that out so I get
+
+ align:start position:0%
+SB multiply that out so I get
+ 
+
+ align:start position:0%
+SB multiply that out so I get
+1sa quty squared plus 1
+
+ align:start position:0%
+1sa quty squared plus 1
+ 
+
+ align:start position:0%
+1sa quty squared plus 1
+sban squar minus 2 * 1s
+
+ align:start position:0%
+sban squar minus 2 * 1s
+ 
+
+ align:start position:0%
+sban squar minus 2 * 1s
+a * 1 SB hey I'm now going to plot this
+
+ align:start position:0%
+a * 1 SB hey I'm now going to plot this
+ 
+
+ align:start position:0%
+a * 1 SB hey I'm now going to plot this
+on my graph here all right so this is
+
+ align:start position:0%
+on my graph here all right so this is
+ 
+
+ align:start position:0%
+on my graph here all right so this is
+what I'm plotting right on my graph of
+
+ align:start position:0%
+what I'm plotting right on my graph of
+ 
+
+ align:start position:0%
+what I'm plotting right on my graph of
+the probability density when I do that
+
+ align:start position:0%
+the probability density when I do that
+ 
+
+ align:start position:0%
+the probability density when I do that
+well okay way out here right on one end
+
+ align:start position:0%
+well okay way out here right on one end
+ 
+
+ align:start position:0%
+well okay way out here right on one end
+of the molecule probability density is
+
+ align:start position:0%
+of the molecule probability density is
+ 
+
+ align:start position:0%
+of the molecule probability density is
+pretty low probability density goes to a
+
+ align:start position:0%
+pretty low probability density goes to a
+ 
+
+ align:start position:0%
+pretty low probability density goes to a
+maximum right at the nucleus and then it
+
+ align:start position:0%
+maximum right at the nucleus and then it
+ 
+
+ align:start position:0%
+maximum right at the nucleus and then it
+plummets right and right at the center
+
+ align:start position:0%
+plummets right and right at the center
+ 
+
+ align:start position:0%
+plummets right and right at the center
+here right at the center here the
+
+ align:start position:0%
+here right at the center here the
+ 
+
+ align:start position:0%
+here right at the center here the
+probability density is zero because the
+
+ align:start position:0%
+probability density is zero because the
+ 
+
+ align:start position:0%
+probability density is zero because the
+wave function's zero because we had
+
+ align:start position:0%
+wave function's zero because we had
+ 
+
+ align:start position:0%
+wave function's zero because we had
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+interference okay hey I want you to
+
+ align:start position:0%
+interference okay hey I want you to
+ 
+
+ align:start position:0%
+interference okay hey I want you to
+notice something probability density
+
+ align:start position:0%
+notice something probability density
+ 
+
+ align:start position:0%
+notice something probability density
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+zero it is even lower than this case
+
+ align:start position:0%
+zero it is even lower than this case
+ 
+
+ align:start position:0%
+zero it is even lower than this case
+this case which is just the sum of two
+
+ align:start position:0%
+this case which is just the sum of two
+ 
+
+ align:start position:0%
+this case which is just the sum of two
+hydrogen atoms their wave function
+
+ align:start position:0%
+hydrogen atoms their wave function
+ 
+
+ align:start position:0%
+hydrogen atoms their wave function
+squared in the case when the two
+
+ align:start position:0%
+squared in the case when the two
+ 
+
+ align:start position:0%
+squared in the case when the two
+hydrogen atoms aren't interacting the
+
+ align:start position:0%
+hydrogen atoms aren't interacting the
+ 
+
+ align:start position:0%
+hydrogen atoms aren't interacting the
+probability density is some finite value
+
+ align:start position:0%
+probability density is some finite value
+ 
+
+ align:start position:0%
+probability density is some finite value
+but in the case of this antibonding
+
+ align:start position:0%
+but in the case of this antibonding
+ 
+
+ align:start position:0%
+but in the case of this antibonding
+state right the probability density is
+
+ align:start position:0%
+state right the probability density is
+ 
+
+ align:start position:0%
+state right the probability density is
+zero Goose zip NADA all of the other
+
+ align:start position:0%
+zero Goose zip NADA all of the other
+ 
+
+ align:start position:0%
+zero Goose zip NADA all of the other
+things right there's nothing there this
+
+ align:start position:0%
+things right there's nothing there this
+ 
+
+ align:start position:0%
+things right there's nothing there this
+state here that we're forming it's
+
+ align:start position:0%
+state here that we're forming it's
+ 
+
+ align:start position:0%
+state here that we're forming it's
+antibonding it's not even nonbonding
+
+ align:start position:0%
+antibonding it's not even nonbonding
+ 
+
+ align:start position:0%
+antibonding it's not even nonbonding
+non-bonding right it's got more electron
+
+ align:start position:0%
+non-bonding right it's got more electron
+ 
+
+ align:start position:0%
+non-bonding right it's got more electron
+density the microphone
+
+ align:start position:0%
+density the microphone
+ 
+
+ align:start position:0%
+density the microphone
+here all right all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right non-bonding has more electron
+
+ align:start position:0%
+right non-bonding has more electron
+ 
+
+ align:start position:0%
+right non-bonding has more electron
+density than antibonding hey this is
+
+ align:start position:0%
+density than antibonding hey this is
+ 
+
+ align:start position:0%
+density than antibonding hey this is
+anti bonding against
+
+ align:start position:0%
+anti bonding against
+ 
+
+ align:start position:0%
+anti bonding against
+bonding okay that's the kind of state we
+
+ align:start position:0%
+bonding okay that's the kind of state we
+ 
+
+ align:start position:0%
+bonding okay that's the kind of state we
+just formed by destructive
+
+ align:start position:0%
+just formed by destructive
+ 
+
+ align:start position:0%
+just formed by destructive
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+so where do you think in an energy
+
+ align:start position:0%
+so where do you think in an energy
+ 
+
+ align:start position:0%
+so where do you think in an energy
+diagram where do you think the sigma One
+
+ align:start position:0%
+diagram where do you think the sigma One
+ 
+
+ align:start position:0%
+diagram where do you think the sigma One
+S Star level is well you can imagine
+
+ align:start position:0%
+S Star level is well you can imagine
+ 
+
+ align:start position:0%
+S Star level is well you can imagine
+where it is it's increased in energy
+
+ align:start position:0%
+where it is it's increased in energy
+ 
+
+ align:start position:0%
+where it is it's increased in energy
+it's up here Sigma 1 s
+
+ align:start position:0%
+it's up here Sigma 1 s
+ 
+
+ align:start position:0%
+it's up here Sigma 1 s
+star and it turns out that the amount of
+
+ align:start position:0%
+star and it turns out that the amount of
+ 
+
+ align:start position:0%
+star and it turns out that the amount of
+energy above the energy for the two
+
+ align:start position:0%
+energy above the energy for the two
+ 
+
+ align:start position:0%
+energy above the energy for the two
+separated hydrogen atoms that this state
+
+ align:start position:0%
+separated hydrogen atoms that this state
+ 
+
+ align:start position:0%
+separated hydrogen atoms that this state
+lies is about equal to the amount of
+
+ align:start position:0%
+lies is about equal to the amount of
+ 
+
+ align:start position:0%
+lies is about equal to the amount of
+energy below the separated atoms that
+
+ align:start position:0%
+energy below the separated atoms that
+ 
+
+ align:start position:0%
+energy below the separated atoms that
+this state lies these two energies are
+
+ align:start position:0%
+this state lies these two energies are
+ 
+
+ align:start position:0%
+this state lies these two energies are
+about equivalent all right
+
+ align:start position:0%
+about equivalent all right
+ 
+
+ align:start position:0%
+about equivalent all right
+so we now have a bonding state or a
+
+ align:start position:0%
+so we now have a bonding state or a
+ 
+
+ align:start position:0%
+so we now have a bonding state or a
+bonding orbital we now have an
+
+ align:start position:0%
+bonding orbital we now have an
+ 
+
+ align:start position:0%
+bonding orbital we now have an
+antibonding state or an anti-bonding
+
+ align:start position:0%
+antibonding state or an anti-bonding
+ 
+
+ align:start position:0%
+antibonding state or an anti-bonding
+orbital
+
+ align:start position:0%
+orbital
+ 
+
+ align:start position:0%
+orbital
+okay now when do we use that
+
+ align:start position:0%
+okay now when do we use that
+ 
+
+ align:start position:0%
+okay now when do we use that
+anti-bonding orbital well we're going to
+
+ align:start position:0%
+anti-bonding orbital well we're going to
+ 
+
+ align:start position:0%
+anti-bonding orbital well we're going to
+see in a moment but one case would be if
+
+ align:start position:0%
+see in a moment but one case would be if
+ 
+
+ align:start position:0%
+see in a moment but one case would be if
+we had an excited state of a hydrogen
+
+ align:start position:0%
+we had an excited state of a hydrogen
+ 
+
+ align:start position:0%
+we had an excited state of a hydrogen
+molecule hey in an excited state what we
+
+ align:start position:0%
+molecule hey in an excited state what we
+ 
+
+ align:start position:0%
+molecule hey in an excited state what we
+could do is we could take one of these
+
+ align:start position:0%
+could do is we could take one of these
+ 
+
+ align:start position:0%
+could do is we could take one of these
+electrons my Eraser is kind of wet here
+
+ align:start position:0%
+electrons my Eraser is kind of wet here
+ 
+
+ align:start position:0%
+electrons my Eraser is kind of wet here
+so it's not
+
+ align:start position:0%
+so it's not
+ 
+
+ align:start position:0%
+so it's not
+erasing let me try
+
+ align:start position:0%
+erasing let me try
+ 
+
+ align:start position:0%
+erasing let me try
+this I could take one of these electrons
+
+ align:start position:0%
+this I could take one of these electrons
+ 
+
+ align:start position:0%
+this I could take one of these electrons
+here right and populate it and put it in
+
+ align:start position:0%
+here right and populate it and put it in
+ 
+
+ align:start position:0%
+here right and populate it and put it in
+this state that's the first excited
+
+ align:start position:0%
+this state that's the first excited
+ 
+
+ align:start position:0%
+this state that's the first excited
+state of H2 not H
+
+ align:start position:0%
+state of H2 not H
+ 
+
+ align:start position:0%
+state of H2 not H
+H2 a second excited state would be take
+
+ align:start position:0%
+H2 a second excited state would be take
+ 
+
+ align:start position:0%
+H2 a second excited state would be take
+hey this is a permanent chalk once it
+
+ align:start position:0%
+hey this is a permanent chalk once it
+ 
+
+ align:start position:0%
+hey this is a permanent chalk once it
+gets wet all right the second uh excited
+
+ align:start position:0%
+gets wet all right the second uh excited
+ 
+
+ align:start position:0%
+gets wet all right the second uh excited
+state will be taking that second
+
+ align:start position:0%
+state will be taking that second
+ 
+
+ align:start position:0%
+state will be taking that second
+electron and promoting it to this
+
+ align:start position:0%
+electron and promoting it to this
+ 
+
+ align:start position:0%
+electron and promoting it to this
+anti-bonding state that would be the
+
+ align:start position:0%
+anti-bonding state that would be the
+ 
+
+ align:start position:0%
+anti-bonding state that would be the
+second excited state of molecular
+
+ align:start position:0%
+second excited state of molecular
+ 
+
+ align:start position:0%
+second excited state of molecular
+hydrogen now I got to tell you if you
+
+ align:start position:0%
+hydrogen now I got to tell you if you
+ 
+
+ align:start position:0%
+hydrogen now I got to tell you if you
+have these kinds of excited states of
+
+ align:start position:0%
+have these kinds of excited states of
+ 
+
+ align:start position:0%
+have these kinds of excited states of
+molecular hydrogen molecular hydrogen
+
+ align:start position:0%
+molecular hydrogen molecular hydrogen
+ 
+
+ align:start position:0%
+molecular hydrogen molecular hydrogen
+doesn't stick around right it's going to
+
+ align:start position:0%
+doesn't stick around right it's going to
+ 
+
+ align:start position:0%
+doesn't stick around right it's going to
+fall
+
+ align:start position:0%
+fall
+ 
+
+ align:start position:0%
+fall
+apart okay but the ground state
+
+ align:start position:0%
+apart okay but the ground state
+ 
+
+ align:start position:0%
+apart okay but the ground state
+configuration of H2
+
+ align:start position:0%
+configuration of H2
+ 
+
+ align:start position:0%
+configuration of H2
+has these two electrons here in the
+
+ align:start position:0%
+has these two electrons here in the
+ 
+
+ align:start position:0%
+has these two electrons here in the
+sigma 1s
+
+ align:start position:0%
+sigma 1s
+ 
+
+ align:start position:0%
+sigma 1s
+State I also just want to point out here
+
+ align:start position:0%
+State I also just want to point out here
+ 
+
+ align:start position:0%
+State I also just want to point out here
+what the significance physically is of
+
+ align:start position:0%
+what the significance physically is of
+ 
+
+ align:start position:0%
+what the significance physically is of
+the separation in energy between the
+
+ align:start position:0%
+the separation in energy between the
+ 
+
+ align:start position:0%
+the separation in energy between the
+hydrogen atom States and the molecular
+
+ align:start position:0%
+hydrogen atom States and the molecular
+ 
+
+ align:start position:0%
+hydrogen atom States and the molecular
+hydrogen State all right here's the
+
+ align:start position:0%
+hydrogen State all right here's the
+ 
+
+ align:start position:0%
+hydrogen State all right here's the
+significance remember we drew a uh
+
+ align:start position:0%
+significance remember we drew a uh
+ 
+
+ align:start position:0%
+significance remember we drew a uh
+an energy of interaction for molecular
+
+ align:start position:0%
+an energy of interaction for molecular
+ 
+
+ align:start position:0%
+an energy of interaction for molecular
+hydrogen we talked about the
+
+ align:start position:0%
+hydrogen we talked about the
+ 
+
+ align:start position:0%
+hydrogen we talked about the
+general principles in the general
+
+ align:start position:0%
+general principles in the general
+ 
+
+ align:start position:0%
+general principles in the general
+attractions and repulsions that take
+
+ align:start position:0%
+attractions and repulsions that take
+ 
+
+ align:start position:0%
+attractions and repulsions that take
+place in every chemical bond and the
+
+ align:start position:0%
+place in every chemical bond and the
+ 
+
+ align:start position:0%
+place in every chemical bond and the
+result was a curve that kind of looked
+
+ align:start position:0%
+result was a curve that kind of looked
+ 
+
+ align:start position:0%
+result was a curve that kind of looked
+like this where this is hydrogen two
+
+ align:start position:0%
+like this where this is hydrogen two
+ 
+
+ align:start position:0%
+like this where this is hydrogen two
+separated hydrogen atoms this is of
+
+ align:start position:0%
+separated hydrogen atoms this is of
+ 
+
+ align:start position:0%
+separated hydrogen atoms this is of
+course equilibrium Bond length of H2 the
+
+ align:start position:0%
+course equilibrium Bond length of H2 the
+ 
+
+ align:start position:0%
+course equilibrium Bond length of H2 the
+molecules bonded here everywhere where
+
+ align:start position:0%
+molecules bonded here everywhere where
+ 
+
+ align:start position:0%
+molecules bonded here everywhere where
+this energy is lower than the separated
+
+ align:start position:0%
+this energy is lower than the separated
+ 
+
+ align:start position:0%
+this energy is lower than the separated
+hydrogen atom limit okay well the
+
+ align:start position:0%
+hydrogen atom limit okay well the
+ 
+
+ align:start position:0%
+hydrogen atom limit okay well the
+physical significance here of this
+
+ align:start position:0%
+physical significance here of this
+ 
+
+ align:start position:0%
+physical significance here of this
+energy lowering of this state is well
+
+ align:start position:0%
+energy lowering of this state is well
+ 
+
+ align:start position:0%
+energy lowering of this state is well
+you know this is essentially Delta e
+
+ align:start position:0%
+you know this is essentially Delta e
+ 
+
+ align:start position:0%
+you know this is essentially Delta e
+subd right this is essentially the bond
+
+ align:start position:0%
+subd right this is essentially the bond
+ 
+
+ align:start position:0%
+subd right this is essentially the bond
+strength of molecular hydrogen that's
+
+ align:start position:0%
+strength of molecular hydrogen that's
+ 
+
+ align:start position:0%
+strength of molecular hydrogen that's
+what that is
+
+ align:start position:0%
+what that is
+ 
+
+ align:start position:0%
+what that is
+physically
+
+ align:start position:0%
+physically
+ 
+
+ align:start position:0%
+physically
+okay right this energy from here here
+
+ align:start position:0%
+okay right this energy from here here
+ 
+
+ align:start position:0%
+okay right this energy from here here
+that's what it's going to take to pull
+
+ align:start position:0%
+that's what it's going to take to pull
+ 
+
+ align:start position:0%
+that's what it's going to take to pull
+the hydrogen atoms apart the bond
+
+ align:start position:0%
+the hydrogen atoms apart the bond
+ 
+
+ align:start position:0%
+the hydrogen atoms apart the bond
+energy okay
+
+ align:start position:0%
+energy okay
+ 
+
+ align:start position:0%
+energy okay
+so we took care of hydrogen we have two
+
+ align:start position:0%
+so we took care of hydrogen we have two
+ 
+
+ align:start position:0%
+so we took care of hydrogen we have two
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+States bonding antibonding for the
+
+ align:start position:0%
+States bonding antibonding for the
+ 
+
+ align:start position:0%
+States bonding antibonding for the
+ground state hydrogen both electrons are
+
+ align:start position:0%
+ground state hydrogen both electrons are
+ 
+
+ align:start position:0%
+ground state hydrogen both electrons are
+in that bonding
+
+ align:start position:0%
+in that bonding
+ 
+
+ align:start position:0%
+in that bonding
+state so now let's walk across the
+
+ align:start position:0%
+state so now let's walk across the
+ 
+
+ align:start position:0%
+state so now let's walk across the
+periodic
+
+ align:start position:0%
+periodic
+ 
+
+ align:start position:0%
+periodic
+table let's um oh okay one other thing
+
+ align:start position:0%
+table let's um oh okay one other thing
+ 
+
+ align:start position:0%
+table let's um oh okay one other thing
+if you were asked to write the electron
+
+ align:start position:0%
+if you were asked to write the electron
+ 
+
+ align:start position:0%
+if you were asked to write the electron
+configuration of molecular hydrogen in
+
+ align:start position:0%
+configuration of molecular hydrogen in
+ 
+
+ align:start position:0%
+configuration of molecular hydrogen in
+the ground state what would you do well
+
+ align:start position:0%
+the ground state what would you do well
+ 
+
+ align:start position:0%
+the ground state what would you do well
+the electron configuration of molecular
+
+ align:start position:0%
+the electron configuration of molecular
+ 
+
+ align:start position:0%
+the electron configuration of molecular
+hydrogen then the way we would write it
+
+ align:start position:0%
+hydrogen then the way we would write it
+ 
+
+ align:start position:0%
+hydrogen then the way we would write it
+is Sigma
+
+ align:start position:0%
+is Sigma
+ 
+
+ align:start position:0%
+is Sigma
+1s2 meaning two electrons in the sigma
+
+ align:start position:0%
+1s2 meaning two electrons in the sigma
+ 
+
+ align:start position:0%
+1s2 meaning two electrons in the sigma
+1s State and just to be complete here
+
+ align:start position:0%
+1s State and just to be complete here
+ 
+
+ align:start position:0%
+1s State and just to be complete here
+you could write this antibonding state
+
+ align:start position:0%
+you could write this antibonding state
+ 
+
+ align:start position:0%
+you could write this antibonding state
+as Sigma 1est star with zero electrons
+
+ align:start position:0%
+as Sigma 1est star with zero electrons
+ 
+
+ align:start position:0%
+as Sigma 1est star with zero electrons
+in it all right that would be the
+
+ align:start position:0%
+in it all right that would be the
+ 
+
+ align:start position:0%
+in it all right that would be the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+configuration okay well now what we're
+
+ align:start position:0%
+configuration okay well now what we're
+ 
+
+ align:start position:0%
+configuration okay well now what we're
+going to want to do is to write the um
+
+ align:start position:0%
+going to want to do is to write the um
+ 
+
+ align:start position:0%
+going to want to do is to write the um
+electron configuration for the next
+
+ align:start position:0%
+electron configuration for the next
+ 
+
+ align:start position:0%
+electron configuration for the next
+molecule as we walk across the periodic
+
+ align:start position:0%
+molecule as we walk across the periodic
+ 
+
+ align:start position:0%
+molecule as we walk across the periodic
+table the next diatomic molecule hey the
+
+ align:start position:0%
+table the next diatomic molecule hey the
+ 
+
+ align:start position:0%
+table the next diatomic molecule hey the
+next diatomic molecule is going to be
+
+ align:start position:0%
+next diatomic molecule is going to be
+ 
+
+ align:start position:0%
+next diatomic molecule is going to be
+helium 2 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so where are the electrons in the
+
+ align:start position:0%
+okay so where are the electrons in the
+ 
+
+ align:start position:0%
+okay so where are the electrons in the
+case of helium
+
+ align:start position:0%
+case of helium
+ 
+
+ align:start position:0%
+case of helium
+2 well in the case of
+
+ align:start position:0%
+2 well in the case of
+ 
+
+ align:start position:0%
+2 well in the case of
+helium
+
+ align:start position:0%
+helium
+ 
+
+ align:start position:0%
+helium
+each helium atom brings in two electrons
+
+ align:start position:0%
+each helium atom brings in two electrons
+ 
+
+ align:start position:0%
+each helium atom brings in two electrons
+each helium atom has an electron has two
+
+ align:start position:0%
+each helium atom has an electron has two
+ 
+
+ align:start position:0%
+each helium atom has an electron has two
+electrons here in the 1s state so I'm
+
+ align:start position:0%
+electrons here in the 1s state so I'm
+ 
+
+ align:start position:0%
+electrons here in the 1s state so I'm
+now drawing this for helium all right
+
+ align:start position:0%
+now drawing this for helium all right
+ 
+
+ align:start position:0%
+now drawing this for helium all right
+and the way we draw this correlation
+
+ align:start position:0%
+and the way we draw this correlation
+ 
+
+ align:start position:0%
+and the way we draw this correlation
+diagram as it's called is following the
+
+ align:start position:0%
+diagram as it's called is following the
+ 
+
+ align:start position:0%
+diagram as it's called is following the
+sou bow principle that we had for
+
+ align:start position:0%
+sou bow principle that we had for
+ 
+
+ align:start position:0%
+sou bow principle that we had for
+filling Atomic
+
+ align:start position:0%
+filling Atomic
+ 
+
+ align:start position:0%
+filling Atomic
+States right that is we take the states
+
+ align:start position:0%
+States right that is we take the states
+ 
+
+ align:start position:0%
+States right that is we take the states
+we order them in terms of their energy
+
+ align:start position:0%
+we order them in terms of their energy
+ 
+
+ align:start position:0%
+we order them in terms of their energy
+lowest energy at the bottom next highest
+
+ align:start position:0%
+lowest energy at the bottom next highest
+ 
+
+ align:start position:0%
+lowest energy at the bottom next highest
+energy and then we start to put
+
+ align:start position:0%
+energy and then we start to put
+ 
+
+ align:start position:0%
+energy and then we start to put
+electrons in those States one at a
+
+ align:start position:0%
+electrons in those States one at a
+ 
+
+ align:start position:0%
+electrons in those States one at a
+time until we starting at the bottom
+
+ align:start position:0%
+time until we starting at the bottom
+ 
+
+ align:start position:0%
+time until we starting at the bottom
+starting at the lowest energy until we
+
+ align:start position:0%
+starting at the lowest energy until we
+ 
+
+ align:start position:0%
+starting at the lowest energy until we
+run out of electrons so that's what
+
+ align:start position:0%
+run out of electrons so that's what
+ 
+
+ align:start position:0%
+run out of electrons so that's what
+we're going to do for helium all right
+
+ align:start position:0%
+we're going to do for helium all right
+ 
+
+ align:start position:0%
+we're going to do for helium all right
+so what's going to happen two of these
+
+ align:start position:0%
+so what's going to happen two of these
+ 
+
+ align:start position:0%
+so what's going to happen two of these
+electrons are going to be in the bonding
+
+ align:start position:0%
+electrons are going to be in the bonding
+ 
+
+ align:start position:0%
+electrons are going to be in the bonding
+State and then two of these electrons
+
+ align:start position:0%
+State and then two of these electrons
+ 
+
+ align:start position:0%
+State and then two of these electrons
+are going to be in the antibonding state
+
+ align:start position:0%
+are going to be in the antibonding state
+ 
+
+ align:start position:0%
+are going to be in the antibonding state
+and so the electron configuration here
+
+ align:start position:0%
+and so the electron configuration here
+ 
+
+ align:start position:0%
+and so the electron configuration here
+for helium is 1
+
+ align:start position:0%
+for helium is 1
+ 
+
+ align:start position:0%
+for helium is 1
+S2 Sigma 1 s star 2 that's the electron
+
+ align:start position:0%
+S2 Sigma 1 s star 2 that's the electron
+ 
+
+ align:start position:0%
+S2 Sigma 1 s star 2 that's the electron
+configuration for helium
+
+ align:start position:0%
+configuration for helium
+ 
+
+ align:start position:0%
+configuration for helium
+dimer all right but hey this is
+
+ align:start position:0%
+dimer all right but hey this is
+ 
+
+ align:start position:0%
+dimer all right but hey this is
+interesting because
+
+ align:start position:0%
+interesting because
+ 
+
+ align:start position:0%
+interesting because
+look we have now in this molecular state
+
+ align:start position:0%
+look we have now in this molecular state
+ 
+
+ align:start position:0%
+look we have now in this molecular state
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+electrons that um are at an energy that
+
+ align:start position:0%
+electrons that um are at an energy that
+ 
+
+ align:start position:0%
+electrons that um are at an energy that
+is lower than the two separated helium
+
+ align:start position:0%
+is lower than the two separated helium
+ 
+
+ align:start position:0%
+is lower than the two separated helium
+atom limit and two electrons that are
+
+ align:start position:0%
+atom limit and two electrons that are
+ 
+
+ align:start position:0%
+atom limit and two electrons that are
+higher hey it seems like there wasn't a
+
+ align:start position:0%
+higher hey it seems like there wasn't a
+ 
+
+ align:start position:0%
+higher hey it seems like there wasn't a
+an overall stabilization of this
+
+ align:start position:0%
+an overall stabilization of this
+ 
+
+ align:start position:0%
+an overall stabilization of this
+molecule right because we have one state
+
+ align:start position:0%
+molecule right because we have one state
+ 
+
+ align:start position:0%
+molecule right because we have one state
+that is lower in
+
+ align:start position:0%
+that is lower in
+ 
+
+ align:start position:0%
+that is lower in
+energy and another state that is higher
+
+ align:start position:0%
+energy and another state that is higher
+ 
+
+ align:start position:0%
+energy and another state that is higher
+in energy by the same amount so the
+
+ align:start position:0%
+in energy by the same amount so the
+ 
+
+ align:start position:0%
+in energy by the same amount so the
+overall is hey
+
+ align:start position:0%
+overall is hey
+ 
+
+ align:start position:0%
+overall is hey
+Zippo okay and indeed that is the case
+
+ align:start position:0%
+Zippo okay and indeed that is the case
+ 
+
+ align:start position:0%
+Zippo okay and indeed that is the case
+so uh we've got a tool for uh
+
+ align:start position:0%
+so uh we've got a tool for uh
+ 
+
+ align:start position:0%
+so uh we've got a tool for uh
+counting um or for telling
+
+ align:start position:0%
+counting um or for telling
+ 
+
+ align:start position:0%
+counting um or for telling
+how strong the bond is and that tool is
+
+ align:start position:0%
+how strong the bond is and that tool is
+ 
+
+ align:start position:0%
+how strong the bond is and that tool is
+called the bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order the bond order is defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as2 the
+
+ align:start position:0%
+as2 the
+ 
+
+ align:start position:0%
+as2 the
+number of bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons minus the number of
+
+ align:start position:0%
+electrons minus the number of
+ 
+
+ align:start position:0%
+electrons minus the number of
+anti-bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons all right so in the case of
+
+ align:start position:0%
+electrons all right so in the case of
+ 
+
+ align:start position:0%
+electrons all right so in the case of
+helium 2 we've got two bonding electrons
+
+ align:start position:0%
+helium 2 we've got two bonding electrons
+ 
+
+ align:start position:0%
+helium 2 we've got two bonding electrons
+and two anti-bonding electrons hey in
+
+ align:start position:0%
+and two anti-bonding electrons hey in
+ 
+
+ align:start position:0%
+and two anti-bonding electrons hey in
+the case of helium 2 the bond order here
+
+ align:start position:0%
+the case of helium 2 the bond order here
+ 
+
+ align:start position:0%
+the case of helium 2 the bond order here
+is equal to zero when you have a bond
+
+ align:start position:0%
+is equal to zero when you have a bond
+ 
+
+ align:start position:0%
+is equal to zero when you have a bond
+order equal to zero what that means is
+
+ align:start position:0%
+order equal to zero what that means is
+ 
+
+ align:start position:0%
+order equal to zero what that means is
+that you have no
+
+ align:start position:0%
+that you have no
+ 
+
+ align:start position:0%
+that you have no
+bond all right and indeed that is the
+
+ align:start position:0%
+bond all right and indeed that is the
+ 
+
+ align:start position:0%
+bond all right and indeed that is the
+case helium
+
+ align:start position:0%
+case helium
+ 
+
+ align:start position:0%
+case helium
+2 has no bond between them okay now
+
+ align:start position:0%
+2 has no bond between them okay now
+ 
+
+ align:start position:0%
+2 has no bond between them okay now
+accurately speaking helium 2 does have a
+
+ align:start position:0%
+accurately speaking helium 2 does have a
+ 
+
+ align:start position:0%
+accurately speaking helium 2 does have a
+bond between them right uh helium 2 was
+
+ align:start position:0%
+bond between them right uh helium 2 was
+ 
+
+ align:start position:0%
+bond between them right uh helium 2 was
+discovered so to speak in
+
+ align:start position:0%
+discovered so to speak in
+ 
+
+ align:start position:0%
+discovered so to speak in
+1993 and it was made under really very
+
+ align:start position:0%
+1993 and it was made under really very
+ 
+
+ align:start position:0%
+1993 and it was made under really very
+special conditions and the bond
+
+ align:start position:0%
+special conditions and the bond
+ 
+
+ align:start position:0%
+special conditions and the bond
+strength here of helium 2 is a whopping
+
+ align:start position:0%
+strength here of helium 2 is a whopping
+ 
+
+ align:start position:0%
+strength here of helium 2 is a whopping
+0.01 kilj per mole that's for helium too
+
+ align:start position:0%
+0.01 kilj per mole that's for helium too
+ 
+
+ align:start position:0%
+0.01 kilj per mole that's for helium too
+right whereas for example the bond
+
+ align:start position:0%
+right whereas for example the bond
+ 
+
+ align:start position:0%
+right whereas for example the bond
+strength in hydrogen is
+
+ align:start position:0%
+strength in hydrogen is
+ 
+
+ align:start position:0%
+strength in hydrogen is
+432 K per
+
+ align:start position:0%
+432 K per
+ 
+
+ align:start position:0%
+432 K per
+mole so you can see how weak a bond that
+
+ align:start position:0%
+mole so you can see how weak a bond that
+ 
+
+ align:start position:0%
+mole so you can see how weak a bond that
+is effectively this is no bond at all
+
+ align:start position:0%
+is effectively this is no bond at all
+ 
+
+ align:start position:0%
+is effectively this is no bond at all
+all right practically speaking and so
+
+ align:start position:0%
+all right practically speaking and so
+ 
+
+ align:start position:0%
+all right practically speaking and so
+molecular orbital Theory really gets it
+
+ align:start position:0%
+molecular orbital Theory really gets it
+ 
+
+ align:start position:0%
+molecular orbital Theory really gets it
+right in the sense that it tells you hey
+
+ align:start position:0%
+right in the sense that it tells you hey
+ 
+
+ align:start position:0%
+right in the sense that it tells you hey
+there's no bond here
+
+ align:start position:0%
+there's no bond here
+ 
+
+ align:start position:0%
+there's no bond here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay great
+
+ align:start position:0%
+okay great
+ 
+
+ align:start position:0%
+okay great
+all right so now um what we're going to
+
+ align:start position:0%
+all right so now um what we're going to
+ 
+
+ align:start position:0%
+all right so now um what we're going to
+do is we're going to keep marching
+
+ align:start position:0%
+do is we're going to keep marching
+ 
+
+ align:start position:0%
+do is we're going to keep marching
+across the periodic table actually we've
+
+ align:start position:0%
+across the periodic table actually we've
+ 
+
+ align:start position:0%
+across the periodic table actually we've
+got to go down one row now and um let's
+
+ align:start position:0%
+got to go down one row now and um let's
+ 
+
+ align:start position:0%
+got to go down one row now and um let's
+uh look at the electron configuration
+
+ align:start position:0%
+uh look at the electron configuration
+ 
+
+ align:start position:0%
+uh look at the electron configuration
+for lithium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dier all
+
+ align:start position:0%
+dier all
+ 
+
+ align:start position:0%
+dier all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now if we're going to bring together two
+
+ align:start position:0%
+now if we're going to bring together two
+ 
+
+ align:start position:0%
+now if we're going to bring together two
+lithium
+
+ align:start position:0%
+lithium
+ 
+
+ align:start position:0%
+lithium
+atoms lithium has two electrons uh that
+
+ align:start position:0%
+atoms lithium has two electrons uh that
+ 
+
+ align:start position:0%
+atoms lithium has two electrons uh that
+are in the 1s State and one electron
+
+ align:start position:0%
+are in the 1s State and one electron
+ 
+
+ align:start position:0%
+are in the 1s State and one electron
+each in a 2s
+
+ align:start position:0%
+each in a 2s
+ 
+
+ align:start position:0%
+each in a 2s
+State and let me put them in all right
+
+ align:start position:0%
+State and let me put them in all right
+ 
+
+ align:start position:0%
+State and let me put them in all right
+so those are the electron configurations
+
+ align:start position:0%
+so those are the electron configurations
+ 
+
+ align:start position:0%
+so those are the electron configurations
+for the two separated lithium
+
+ align:start position:0%
+for the two separated lithium
+ 
+
+ align:start position:0%
+for the two separated lithium
+atoms so how do we write this electron
+
+ align:start position:0%
+atoms so how do we write this electron
+ 
+
+ align:start position:0%
+atoms so how do we write this electron
+configuration well again we follow the
+
+ align:start position:0%
+configuration well again we follow the
+ 
+
+ align:start position:0%
+configuration well again we follow the
+albow principle we put two electrons
+
+ align:start position:0%
+albow principle we put two electrons
+ 
+
+ align:start position:0%
+albow principle we put two electrons
+here two electrons here but now since
+
+ align:start position:0%
+here two electrons here but now since
+ 
+
+ align:start position:0%
+here two electrons here but now since
+we've got these 2 s electrons what we're
+
+ align:start position:0%
+we've got these 2 s electrons what we're
+ 
+
+ align:start position:0%
+we've got these 2 s electrons what we're
+going to have to do is to form molecular
+
+ align:start position:0%
+going to have to do is to form molecular
+ 
+
+ align:start position:0%
+going to have to do is to form molecular
+States molecular
+
+ align:start position:0%
+States molecular
+ 
+
+ align:start position:0%
+States molecular
+orbitals between these 2s Atomic
+
+ align:start position:0%
+orbitals between these 2s Atomic
+ 
+
+ align:start position:0%
+orbitals between these 2s Atomic
+orbitals and the 2s Atomic
+
+ align:start position:0%
+orbitals and the 2s Atomic
+ 
+
+ align:start position:0%
+orbitals and the 2s Atomic
+orbitals form these molecular states in
+
+ align:start position:0%
+orbitals form these molecular states in
+ 
+
+ align:start position:0%
+orbitals form these molecular states in
+the same way that the 1s Atomic orbitals
+
+ align:start position:0%
+the same way that the 1s Atomic orbitals
+ 
+
+ align:start position:0%
+the same way that the 1s Atomic orbitals
+do hey they're all spherically symmetric
+
+ align:start position:0%
+do hey they're all spherically symmetric
+ 
+
+ align:start position:0%
+do hey they're all spherically symmetric
+all right so they formed these orbitals
+
+ align:start position:0%
+all right so they formed these orbitals
+ 
+
+ align:start position:0%
+all right so they formed these orbitals
+in absolutely the same way and so you
+
+ align:start position:0%
+in absolutely the same way and so you
+ 
+
+ align:start position:0%
+in absolutely the same way and so you
+get a sigma 2s bonding State and a sigma
+
+ align:start position:0%
+get a sigma 2s bonding State and a sigma
+ 
+
+ align:start position:0%
+get a sigma 2s bonding State and a sigma
+2s Star antibonding
+
+ align:start position:0%
+2s Star antibonding
+ 
+
+ align:start position:0%
+2s Star antibonding
+State so if you want to write the
+
+ align:start position:0%
+State so if you want to write the
+ 
+
+ align:start position:0%
+State so if you want to write the
+correlation diagram as this called as
+
+ align:start position:0%
+correlation diagram as this called as
+ 
+
+ align:start position:0%
+correlation diagram as this called as
+it's called for lithium 2 you take all
+
+ align:start position:0%
+it's called for lithium 2 you take all
+ 
+
+ align:start position:0%
+it's called for lithium 2 you take all
+of lithium's electrons and you now put
+
+ align:start position:0%
+of lithium's electrons and you now put
+ 
+
+ align:start position:0%
+of lithium's electrons and you now put
+it in the lowest energy State put it in
+
+ align:start position:0%
+it in the lowest energy State put it in
+ 
+
+ align:start position:0%
+it in the lowest energy State put it in
+the next highest energy State and put it
+
+ align:start position:0%
+the next highest energy State and put it
+ 
+
+ align:start position:0%
+the next highest energy State and put it
+in the next highest energy State that's
+
+ align:start position:0%
+in the next highest energy State that's
+ 
+
+ align:start position:0%
+in the next highest energy State that's
+the correlation diagram we ran out of
+
+ align:start position:0%
+the correlation diagram we ran out of
+ 
+
+ align:start position:0%
+the correlation diagram we ran out of
+electrons we had six six electrons total
+
+ align:start position:0%
+electrons we had six six electrons total
+ 
+
+ align:start position:0%
+electrons we had six six electrons total
+so the electron configuration written
+
+ align:start position:0%
+so the electron configuration written
+ 
+
+ align:start position:0%
+so the electron configuration written
+here is this Sigma 1 S2 Sigma 1 s star
+
+ align:start position:0%
+here is this Sigma 1 S2 Sigma 1 s star
+ 
+
+ align:start position:0%
+here is this Sigma 1 S2 Sigma 1 s star
+to Sigma 2
+
+ align:start position:0%
+to Sigma 2
+ 
+
+ align:start position:0%
+to Sigma 2
+S2 all right what's the bond order here
+
+ align:start position:0%
+S2 all right what's the bond order here
+ 
+
+ align:start position:0%
+S2 all right what's the bond order here
+hey let's calculate it we have two four
+
+ align:start position:0%
+hey let's calculate it we have two four
+ 
+
+ align:start position:0%
+hey let's calculate it we have two four
+bonding electrons we got two
+
+ align:start position:0%
+bonding electrons we got two
+ 
+
+ align:start position:0%
+bonding electrons we got two
+anti-bonding electrons 4 - 2 / 2 is 1
+
+ align:start position:0%
+anti-bonding electrons 4 - 2 / 2 is 1
+ 
+
+ align:start position:0%
+anti-bonding electrons 4 - 2 / 2 is 1
+all right we got bond order of one that
+
+ align:start position:0%
+all right we got bond order of one that
+ 
+
+ align:start position:0%
+all right we got bond order of one that
+means we got a single bond that bond
+
+ align:start position:0%
+means we got a single bond that bond
+ 
+
+ align:start position:0%
+means we got a single bond that bond
+strength is 105 K per mole that's a
+
+ align:start position:0%
+strength is 105 K per mole that's a
+ 
+
+ align:start position:0%
+strength is 105 K per mole that's a
+single Bond it's a weak single Bond but
+
+ align:start position:0%
+single Bond it's a weak single Bond but
+ 
+
+ align:start position:0%
+single Bond it's a weak single Bond but
+that's a single Bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay what about
+
+ align:start position:0%
+okay okay what about
+ 
+
+ align:start position:0%
+okay okay what about
+brillium let's make brillium to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry how did these two get up here okay
+
+ align:start position:0%
+sorry how did these two get up here okay
+ 
+
+ align:start position:0%
+sorry how did these two get up here okay
+these electrons right are the electrons
+
+ align:start position:0%
+these electrons right are the electrons
+ 
+
+ align:start position:0%
+these electrons right are the electrons
+on the atom so the lithium atom has two
+
+ align:start position:0%
+on the atom so the lithium atom has two
+ 
+
+ align:start position:0%
+on the atom so the lithium atom has two
+1s electrons and one 2s electron
+
+ align:start position:0%
+1s electrons and one 2s electron
+ 
+
+ align:start position:0%
+1s electrons and one 2s electron
+okay and this is the energy ordering for
+
+ align:start position:0%
+okay and this is the energy ordering for
+ 
+
+ align:start position:0%
+okay and this is the energy ordering for
+the atomic States in lithium okay the
+
+ align:start position:0%
+the atomic States in lithium okay the
+ 
+
+ align:start position:0%
+the atomic States in lithium okay the
+molecular state for um lithium here or
+
+ align:start position:0%
+molecular state for um lithium here or
+ 
+
+ align:start position:0%
+molecular state for um lithium here or
+the sigma 2s state it is higher in
+
+ align:start position:0%
+the sigma 2s state it is higher in
+ 
+
+ align:start position:0%
+the sigma 2s state it is higher in
+energy than the sigma 1s star this is
+
+ align:start position:0%
+energy than the sigma 1s star this is
+ 
+
+ align:start position:0%
+energy than the sigma 1s star this is
+the correct level ordering of the
+
+ align:start position:0%
+the correct level ordering of the
+ 
+
+ align:start position:0%
+the correct level ordering of the
+energies of these states okay I didn't
+
+ align:start position:0%
+energies of these states okay I didn't
+ 
+
+ align:start position:0%
+energies of these states okay I didn't
+clearly explain that to you all right
+
+ align:start position:0%
+clearly explain that to you all right
+ 
+
+ align:start position:0%
+clearly explain that to you all right
+does that make sense yeah okay all
+
+ align:start position:0%
+does that make sense yeah okay all
+ 
+
+ align:start position:0%
+does that make sense yeah okay all
+right okay so now we'll uh go to
+
+ align:start position:0%
+right okay so now we'll uh go to
+ 
+
+ align:start position:0%
+right okay so now we'll uh go to
+brillium
+
+ align:start position:0%
+brillium
+ 
+
+ align:start position:0%
+brillium
+dier and now we got two 2s
+
+ align:start position:0%
+dier and now we got two 2s
+ 
+
+ align:start position:0%
+dier and now we got two 2s
+electrons so again what do we do we put
+
+ align:start position:0%
+electrons so again what do we do we put
+ 
+
+ align:start position:0%
+electrons so again what do we do we put
+two of the electrons in the lowest
+
+ align:start position:0%
+two of the electrons in the lowest
+ 
+
+ align:start position:0%
+two of the electrons in the lowest
+energy state two in the next highest
+
+ align:start position:0%
+energy state two in the next highest
+ 
+
+ align:start position:0%
+energy state two in the next highest
+energy state two in the next highest
+
+ align:start position:0%
+energy state two in the next highest
+ 
+
+ align:start position:0%
+energy state two in the next highest
+energy State and another two in the next
+
+ align:start position:0%
+energy State and another two in the next
+ 
+
+ align:start position:0%
+energy State and another two in the next
+highest energy State the El
+
+ align:start position:0%
+highest energy State the El
+ 
+
+ align:start position:0%
+highest energy State the El
+configuration here brillium dier one
+
+ align:start position:0%
+configuration here brillium dier one
+ 
+
+ align:start position:0%
+configuration here brillium dier one
+Sigma 1 S2 Sigma 1
+
+ align:start position:0%
+Sigma 1 S2 Sigma 1
+ 
+
+ align:start position:0%
+Sigma 1 S2 Sigma 1
+sar2 Sigma 2 S2 Sigma 2 s star 2 oh the
+
+ align:start position:0%
+sar2 Sigma 2 S2 Sigma 2 s star 2 oh the
+ 
+
+ align:start position:0%
+sar2 Sigma 2 S2 Sigma 2 s star 2 oh the
+two's cut off here but there's a two
+
+ align:start position:0%
+two's cut off here but there's a two
+ 
+
+ align:start position:0%
+two's cut off here but there's a two
+okay all right what's the bond
+
+ align:start position:0%
+okay all right what's the bond
+ 
+
+ align:start position:0%
+okay all right what's the bond
+order zero there's no bond here in
+
+ align:start position:0%
+order zero there's no bond here in
+ 
+
+ align:start position:0%
+order zero there's no bond here in
+brillium two now again there is a very
+
+ align:start position:0%
+brillium two now again there is a very
+ 
+
+ align:start position:0%
+brillium two now again there is a very
+weak Bond it's 9 K per mole but for all
+
+ align:start position:0%
+weak Bond it's 9 K per mole but for all
+ 
+
+ align:start position:0%
+weak Bond it's 9 K per mole but for all
+practical purposes there is no bond
+
+ align:start position:0%
+practical purposes there is no bond
+ 
+
+ align:start position:0%
+practical purposes there is no bond
+between gillium 2 and this molecular
+
+ align:start position:0%
+between gillium 2 and this molecular
+ 
+
+ align:start position:0%
+between gillium 2 and this molecular
+orbital approach gets that
+
+ align:start position:0%
+orbital approach gets that
+ 
+
+ align:start position:0%
+orbital approach gets that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay okay well NOW Boron hey boron has
+
+ align:start position:0%
+okay okay well NOW Boron hey boron has
+ 
+
+ align:start position:0%
+okay okay well NOW Boron hey boron has
+got a p electron in the atomic uh
+
+ align:start position:0%
+got a p electron in the atomic uh
+ 
+
+ align:start position:0%
+got a p electron in the atomic uh
+configuration so now what we've got to
+
+ align:start position:0%
+configuration so now what we've got to
+ 
+
+ align:start position:0%
+configuration so now what we've got to
+do is we've got to look at the
+
+ align:start position:0%
+do is we've got to look at the
+ 
+
+ align:start position:0%
+do is we've got to look at the
+constructive and destructive
+
+ align:start position:0%
+constructive and destructive
+ 
+
+ align:start position:0%
+constructive and destructive
+interference between these P wave
+
+ align:start position:0%
+interference between these P wave
+ 
+
+ align:start position:0%
+interference between these P wave
+functions all right so we got to do that
+
+ align:start position:0%
+functions all right so we got to do that
+ 
+
+ align:start position:0%
+functions all right so we got to do that
+we got to make molecular States we've
+
+ align:start position:0%
+we got to make molecular States we've
+ 
+
+ align:start position:0%
+we got to make molecular States we've
+got to let the P wve functions the P
+
+ align:start position:0%
+got to let the P wve functions the P
+ 
+
+ align:start position:0%
+got to let the P wve functions the P
+Atomic wave functions constructively and
+
+ align:start position:0%
+Atomic wave functions constructively and
+ 
+
+ align:start position:0%
+Atomic wave functions constructively and
+destructively interfere to make a new
+
+ align:start position:0%
+destructively interfere to make a new
+ 
+
+ align:start position:0%
+destructively interfere to make a new
+molecular wave function all right you
+
+ align:start position:0%
+molecular wave function all right you
+ 
+
+ align:start position:0%
+molecular wave function all right you
+ready here's how we do it here's the 2p
+
+ align:start position:0%
+ready here's how we do it here's the 2p
+ 
+
+ align:start position:0%
+ready here's how we do it here's the 2p
+X wave function or the 2p y wave
+
+ align:start position:0%
+X wave function or the 2p y wave
+ 
+
+ align:start position:0%
+X wave function or the 2p y wave
+function they look the same right one is
+
+ align:start position:0%
+function they look the same right one is
+ 
+
+ align:start position:0%
+function they look the same right one is
+just an X Dimension one is in the Y
+
+ align:start position:0%
+just an X Dimension one is in the Y
+ 
+
+ align:start position:0%
+just an X Dimension one is in the Y
+Dimension they got a noal plane right
+
+ align:start position:0%
+Dimension they got a noal plane right
+ 
+
+ align:start position:0%
+Dimension they got a noal plane right
+here all right what we're going to do is
+
+ align:start position:0%
+here all right what we're going to do is
+ 
+
+ align:start position:0%
+here all right what we're going to do is
+we're going to take that wave function
+
+ align:start position:0%
+we're going to take that wave function
+ 
+
+ align:start position:0%
+we're going to take that wave function
+over it lap it with the same wave
+
+ align:start position:0%
+over it lap it with the same wave
+ 
+
+ align:start position:0%
+over it lap it with the same wave
+function 2px or 2py from another
+
+ align:start position:0%
+function 2px or 2py from another
+ 
+
+ align:start position:0%
+function 2px or 2py from another
+atom we're going to bring these two
+
+ align:start position:0%
+atom we're going to bring these two
+ 
+
+ align:start position:0%
+atom we're going to bring these two
+within the equilibrium Bond length we're
+
+ align:start position:0%
+within the equilibrium Bond length we're
+ 
+
+ align:start position:0%
+within the equilibrium Bond length we're
+going to let this part of the wave
+
+ align:start position:0%
+going to let this part of the wave
+ 
+
+ align:start position:0%
+going to let this part of the wave
+function overlap with this part of the
+
+ align:start position:0%
+function overlap with this part of the
+ 
+
+ align:start position:0%
+function overlap with this part of the
+wave function and this part of the wave
+
+ align:start position:0%
+wave function and this part of the wave
+ 
+
+ align:start position:0%
+wave function and this part of the wave
+function overlap with this and we're
+
+ align:start position:0%
+function overlap with this and we're
+ 
+
+ align:start position:0%
+function overlap with this and we're
+going to treat constructive interference
+
+ align:start position:0%
+going to treat constructive interference
+ 
+
+ align:start position:0%
+going to treat constructive interference
+first and the result is a wave function
+
+ align:start position:0%
+first and the result is a wave function
+ 
+
+ align:start position:0%
+first and the result is a wave function
+that kind of looks like this okay in the
+
+ align:start position:0%
+that kind of looks like this okay in the
+ 
+
+ align:start position:0%
+that kind of looks like this okay in the
+center right here we got a lot of wave
+
+ align:start position:0%
+center right here we got a lot of wave
+ 
+
+ align:start position:0%
+center right here we got a lot of wave
+function because right here we have
+
+ align:start position:0%
+function because right here we have
+ 
+
+ align:start position:0%
+function because right here we have
+constructive
+
+ align:start position:0%
+constructive
+ 
+
+ align:start position:0%
+constructive
+interference in the center here we got a
+
+ align:start position:0%
+interference in the center here we got a
+ 
+
+ align:start position:0%
+interference in the center here we got a
+lot of wave
+
+ align:start position:0%
+lot of wave
+ 
+
+ align:start position:0%
+lot of wave
+function however right along the
+
+ align:start position:0%
+function however right along the
+ 
+
+ align:start position:0%
+function however right along the
+internuclear axis we got a nodal
+
+ align:start position:0%
+internuclear axis we got a nodal
+ 
+
+ align:start position:0%
+internuclear axis we got a nodal
+plane well we got a noal plane there
+
+ align:start position:0%
+plane well we got a noal plane there
+ 
+
+ align:start position:0%
+plane well we got a noal plane there
+because hey we had a noal plane in the
+
+ align:start position:0%
+because hey we had a noal plane in the
+ 
+
+ align:start position:0%
+because hey we had a noal plane in the
+atomic wave functions to begin with so
+
+ align:start position:0%
+atomic wave functions to begin with so
+ 
+
+ align:start position:0%
+atomic wave functions to begin with so
+that noal plane is maintained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we try this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+okay now this molecular wave function
+
+ align:start position:0%
+okay now this molecular wave function
+ 
+
+ align:start position:0%
+okay now this molecular wave function
+here it's going to have a different name
+
+ align:start position:0%
+here it's going to have a different name
+ 
+
+ align:start position:0%
+here it's going to have a different name
+because it has a different symmetry
+
+ align:start position:0%
+because it has a different symmetry
+ 
+
+ align:start position:0%
+because it has a different symmetry
+right this way function is not
+
+ align:start position:0%
+right this way function is not
+ 
+
+ align:start position:0%
+right this way function is not
+cylindrically symmetric around the bond
+
+ align:start position:0%
+cylindrically symmetric around the bond
+ 
+
+ align:start position:0%
+cylindrically symmetric around the bond
+axis there's wave function above the
+
+ align:start position:0%
+axis there's wave function above the
+ 
+
+ align:start position:0%
+axis there's wave function above the
+bond axis and wave function below the
+
+ align:start position:0%
+bond axis and wave function below the
+ 
+
+ align:start position:0%
+bond axis and wave function below the
+bond axis right but not on the sides
+
+ align:start position:0%
+bond axis right but not on the sides
+ 
+
+ align:start position:0%
+bond axis right but not on the sides
+here it's not cylindrically symmetric so
+
+ align:start position:0%
+here it's not cylindrically symmetric so
+ 
+
+ align:start position:0%
+here it's not cylindrically symmetric so
+we got a new name for it it's a pi wave
+
+ align:start position:0%
+we got a new name for it it's a pi wave
+ 
+
+ align:start position:0%
+we got a new name for it it's a pi wave
+function and we're going to call it Pi 2
+
+ align:start position:0%
+function and we're going to call it Pi 2
+ 
+
+ align:start position:0%
+function and we're going to call it Pi 2
+PX or Pi 2
+
+ align:start position:0%
+PX or Pi 2
+ 
+
+ align:start position:0%
+PX or Pi 2
+py all
+
+ align:start position:0%
+py all
+ 
+
+ align:start position:0%
+py all
+right okay it's going to be a bonding
+
+ align:start position:0%
+right okay it's going to be a bonding
+ 
+
+ align:start position:0%
+right okay it's going to be a bonding
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+function and of course since it's a
+
+ align:start position:0%
+function and of course since it's a
+ 
+
+ align:start position:0%
+function and of course since it's a
+bonding wave function if we look at an
+
+ align:start position:0%
+bonding wave function if we look at an
+ 
+
+ align:start position:0%
+bonding wave function if we look at an
+energy level diagram right the pi 2px
+
+ align:start position:0%
+energy level diagram right the pi 2px
+ 
+
+ align:start position:0%
+energy level diagram right the pi 2px
+and Pi 2py are going to be lower in
+
+ align:start position:0%
+and Pi 2py are going to be lower in
+ 
+
+ align:start position:0%
+and Pi 2py are going to be lower in
+energy than the atomic wave functions
+
+ align:start position:0%
+energy than the atomic wave functions
+ 
+
+ align:start position:0%
+energy than the atomic wave functions
+just like this and since the 2px and the
+
+ align:start position:0%
+just like this and since the 2px and the
+ 
+
+ align:start position:0%
+just like this and since the 2px and the
+2py in the atomic states are at the same
+
+ align:start position:0%
+2py in the atomic states are at the same
+ 
+
+ align:start position:0%
+2py in the atomic states are at the same
+energy right the pi 2px and Pi 2py hey
+
+ align:start position:0%
+energy right the pi 2px and Pi 2py hey
+ 
+
+ align:start position:0%
+energy right the pi 2px and Pi 2py hey
+they're going to be at the same energy
+
+ align:start position:0%
+they're going to be at the same energy
+ 
+
+ align:start position:0%
+they're going to be at the same energy
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+okay make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense okay let's do
+
+ align:start position:0%
+sense okay let's do
+ 
+
+ align:start position:0%
+sense okay let's do
+Boron Boron two boron has got one p
+
+ align:start position:0%
+Boron Boron two boron has got one p
+ 
+
+ align:start position:0%
+Boron Boron two boron has got one p
+electron it also has some s and uh s
+
+ align:start position:0%
+electron it also has some s and uh s
+ 
+
+ align:start position:0%
+electron it also has some s and uh s
+electrons right the S states are down
+
+ align:start position:0%
+electrons right the S states are down
+ 
+
+ align:start position:0%
+electrons right the S states are down
+here I didn't draw them in on this
+
+ align:start position:0%
+here I didn't draw them in on this
+ 
+
+ align:start position:0%
+here I didn't draw them in on this
+diagram I'm just treating right here the
+
+ align:start position:0%
+diagram I'm just treating right here the
+ 
+
+ align:start position:0%
+diagram I'm just treating right here the
+2px
+
+ align:start position:0%
+2px
+ 
+
+ align:start position:0%
+2px
+electron so what happens well what
+
+ align:start position:0%
+electron so what happens well what
+ 
+
+ align:start position:0%
+electron so what happens well what
+happens is we're going to fill each one
+
+ align:start position:0%
+happens is we're going to fill each one
+ 
+
+ align:start position:0%
+happens is we're going to fill each one
+of these states with these P
+
+ align:start position:0%
+of these states with these P
+ 
+
+ align:start position:0%
+of these states with these P
+electrons now we're going to use Hunt's
+
+ align:start position:0%
+electrons now we're going to use Hunt's
+ 
+
+ align:start position:0%
+electrons now we're going to use Hunt's
+rule again remember Hunt's rule it says
+
+ align:start position:0%
+rule again remember Hunt's rule it says
+ 
+
+ align:start position:0%
+rule again remember Hunt's rule it says
+that when you have states that are
+
+ align:start position:0%
+that when you have states that are
+ 
+
+ align:start position:0%
+that when you have states that are
+degenerate that have the same
+
+ align:start position:0%
+degenerate that have the same
+ 
+
+ align:start position:0%
+degenerate that have the same
+energy the electrons fill such that one
+
+ align:start position:0%
+energy the electrons fill such that one
+ 
+
+ align:start position:0%
+energy the electrons fill such that one
+electron goes in each state before you
+
+ align:start position:0%
+electron goes in each state before you
+ 
+
+ align:start position:0%
+electron goes in each state before you
+can put a second electron in either one
+
+ align:start position:0%
+can put a second electron in either one
+ 
+
+ align:start position:0%
+can put a second electron in either one
+of those States right so that's what we
+
+ align:start position:0%
+of those States right so that's what we
+ 
+
+ align:start position:0%
+of those States right so that's what we
+did one electron has to go here one
+
+ align:start position:0%
+did one electron has to go here one
+ 
+
+ align:start position:0%
+did one electron has to go here one
+electron has to go here you can't put
+
+ align:start position:0%
+electron has to go here you can't put
+ 
+
+ align:start position:0%
+electron has to go here you can't put
+two electrons in one of these states and
+
+ align:start position:0%
+two electrons in one of these states and
+ 
+
+ align:start position:0%
+two electrons in one of these states and
+leave the other one empty that's not the
+
+ align:start position:0%
+leave the other one empty that's not the
+ 
+
+ align:start position:0%
+leave the other one empty that's not the
+lowest energy configuration and you got
+
+ align:start position:0%
+lowest energy configuration and you got
+ 
+
+ align:start position:0%
+lowest energy configuration and you got
+to put those electrons in with parallel
+
+ align:start position:0%
+to put those electrons in with parallel
+ 
+
+ align:start position:0%
+to put those electrons in with parallel
+spins not opposite spins that's not the
+
+ align:start position:0%
+spins not opposite spins that's not the
+ 
+
+ align:start position:0%
+spins not opposite spins that's not the
+lowest energy
+
+ align:start position:0%
+lowest energy
+ 
+
+ align:start position:0%
+lowest energy
+configuration all right so that's the
+
+ align:start position:0%
+configuration all right so that's the
+ 
+
+ align:start position:0%
+configuration all right so that's the
+electron configuration here for Boron 2
+
+ align:start position:0%
+electron configuration here for Boron 2
+ 
+
+ align:start position:0%
+electron configuration here for Boron 2
+one Sigma 1 S2 Sigma 1 star 2 Sigma 2 S2
+
+ align:start position:0%
+one Sigma 1 S2 Sigma 1 star 2 Sigma 2 S2
+ 
+
+ align:start position:0%
+one Sigma 1 S2 Sigma 1 star 2 Sigma 2 S2
+Sigma 2 Star 2 and now Pi 2 px1 pi 2 px1
+
+ align:start position:0%
+Sigma 2 Star 2 and now Pi 2 px1 pi 2 px1
+ 
+
+ align:start position:0%
+Sigma 2 Star 2 and now Pi 2 px1 pi 2 px1
+hey let's calculate the bond order here
+
+ align:start position:0%
+hey let's calculate the bond order here
+ 
+
+ align:start position:0%
+hey let's calculate the bond order here
+the bond order is 2 four five six
+
+ align:start position:0%
+the bond order is 2 four five six
+ 
+
+ align:start position:0%
+the bond order is 2 four five six
+bonding electrons two four hey four
+
+ align:start position:0%
+bonding electrons two four hey four
+ 
+
+ align:start position:0%
+bonding electrons two four hey four
+antibonding electrons 6 - 4 over 2 is 1
+
+ align:start position:0%
+antibonding electrons 6 - 4 over 2 is 1
+ 
+
+ align:start position:0%
+antibonding electrons 6 - 4 over 2 is 1
+we got a single Bond 200 9 KJ per mole
+
+ align:start position:0%
+we got a single Bond 200 9 KJ per mole
+ 
+
+ align:start position:0%
+we got a single Bond 200 9 KJ per mole
+hey that's a pretty good single Bond
+
+ align:start position:0%
+hey that's a pretty good single Bond
+ 
+
+ align:start position:0%
+hey that's a pretty good single Bond
+pretty strong single Bond okay that's
+
+ align:start position:0%
+pretty strong single Bond okay that's
+ 
+
+ align:start position:0%
+pretty strong single Bond okay that's
+Boron
+
+ align:start position:0%
+Boron
+ 
+
+ align:start position:0%
+Boron
+to let's do carbon well carbon has got
+
+ align:start position:0%
+to let's do carbon well carbon has got
+ 
+
+ align:start position:0%
+to let's do carbon well carbon has got
+two 2p
+
+ align:start position:0%
+two 2p
+ 
+
+ align:start position:0%
+two 2p
+electrons so we follow the albow
+
+ align:start position:0%
+electrons so we follow the albow
+ 
+
+ align:start position:0%
+electrons so we follow the albow
+principle hey Carbon 2 all four of those
+
+ align:start position:0%
+principle hey Carbon 2 all four of those
+ 
+
+ align:start position:0%
+principle hey Carbon 2 all four of those
+electrons then are going to go into
+
+ align:start position:0%
+electrons then are going to go into
+ 
+
+ align:start position:0%
+electrons then are going to go into
+these pi 2px and Pi 2py
+
+ align:start position:0%
+these pi 2px and Pi 2py
+ 
+
+ align:start position:0%
+these pi 2px and Pi 2py
+States and here's our elect
+
+ align:start position:0%
+States and here's our elect
+ 
+
+ align:start position:0%
+States and here's our elect
+configuration we keep going here's the
+
+ align:start position:0%
+configuration we keep going here's the
+ 
+
+ align:start position:0%
+configuration we keep going here's the
+pi 2 px2 pi 2
+
+ align:start position:0%
+pi 2 px2 pi 2
+ 
+
+ align:start position:0%
+pi 2 px2 pi 2
+py2 okay let's calculate the bond order
+
+ align:start position:0%
+py2 okay let's calculate the bond order
+ 
+
+ align:start position:0%
+py2 okay let's calculate the bond order
+bond order number of bonding electrons 2
+
+ align:start position:0%
+bond order number of bonding electrons 2
+ 
+
+ align:start position:0%
+bond order number of bonding electrons 2
+4 6 eight bonding
+
+ align:start position:0%
+4 6 eight bonding
+ 
+
+ align:start position:0%
+4 6 eight bonding
+electrons number of anti-bonding
+
+ align:start position:0%
+electrons number of anti-bonding
+ 
+
+ align:start position:0%
+electrons number of anti-bonding
+electrons 2 4 8 - 4 is 4 / 2 bond order
+
+ align:start position:0%
+electrons 2 4 8 - 4 is 4 / 2 bond order
+ 
+
+ align:start position:0%
+electrons 2 4 8 - 4 is 4 / 2 bond order
+is two and we have a double bond right
+
+ align:start position:0%
+is two and we have a double bond right
+ 
+
+ align:start position:0%
+is two and we have a double bond right
+hey let's look and see how strong that
+
+ align:start position:0%
+hey let's look and see how strong that
+ 
+
+ align:start position:0%
+hey let's look and see how strong that
+double bond is 599 K per mole hey that's
+
+ align:start position:0%
+double bond is 599 K per mole hey that's
+ 
+
+ align:start position:0%
+double bond is 599 K per mole hey that's
+a pretty good double bond remember the
+
+ align:start position:0%
+a pretty good double bond remember the
+ 
+
+ align:start position:0%
+a pretty good double bond remember the
+double bond is shorter the double bond
+
+ align:start position:0%
+double bond is shorter the double bond
+ 
+
+ align:start position:0%
+double bond is shorter the double bond
+is stronger right our single Bonds were
+
+ align:start position:0%
+is stronger right our single Bonds were
+ 
+
+ align:start position:0%
+is stronger right our single Bonds were
+at 300 400 KJ this is almost 600 K
+
+ align:start position:0%
+at 300 400 KJ this is almost 600 K
+ 
+
+ align:start position:0%
+at 300 400 KJ this is almost 600 K
+that's a strong
+
+ align:start position:0%
+that's a strong
+ 
+
+ align:start position:0%
+that's a strong
+bond all
+
+ align:start position:0%
+bond all
+ 
+
+ align:start position:0%
+bond all
+right and this molecular orbital picture
+
+ align:start position:0%
+right and this molecular orbital picture
+ 
+
+ align:start position:0%
+right and this molecular orbital picture
+tells you that youve got this double
+
+ align:start position:0%
+tells you that youve got this double
+ 
+
+ align:start position:0%
+tells you that youve got this double
+bond here all right by virtue of this
+
+ align:start position:0%
+bond here all right by virtue of this
+ 
+
+ align:start position:0%
+bond here all right by virtue of this
+bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay uh but I'm just about to treat
+
+ align:start position:0%
+yes okay uh but I'm just about to treat
+ 
+
+ align:start position:0%
+yes okay uh but I'm just about to treat
+the 2pz all right I'll tell you what our
+
+ align:start position:0%
+the 2pz all right I'll tell you what our
+ 
+
+ align:start position:0%
+the 2pz all right I'll tell you what our
+convention is good question okay okay
+
+ align:start position:0%
+convention is good question okay okay
+ 
+
+ align:start position:0%
+convention is good question okay okay
+here comes the 2pz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the 2 pz Atomic orbitals by
+
+ align:start position:0%
+the 2 pz Atomic orbitals by
+ 
+
+ align:start position:0%
+the 2 pz Atomic orbitals by
+convention the two pz Atomic orbitals
+
+ align:start position:0%
+convention the two pz Atomic orbitals
+ 
+
+ align:start position:0%
+convention the two pz Atomic orbitals
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+put along the internuclear bond
+
+ align:start position:0%
+put along the internuclear bond
+ 
+
+ align:start position:0%
+put along the internuclear bond
+axis so in the case of the constructive
+
+ align:start position:0%
+axis so in the case of the constructive
+ 
+
+ align:start position:0%
+axis so in the case of the constructive
+interference of the two
+
+ align:start position:0%
+interference of the two
+ 
+
+ align:start position:0%
+interference of the two
+pz
+
+ align:start position:0%
+pz
+ 
+
+ align:start position:0%
+pz
+electrons all right in that case these
+
+ align:start position:0%
+electrons all right in that case these
+ 
+
+ align:start position:0%
+electrons all right in that case these
+two P wave functions look like this they
+
+ align:start position:0%
+two P wave functions look like this they
+ 
+
+ align:start position:0%
+two P wave functions look like this they
+were no longer coming in you know
+
+ align:start position:0%
+were no longer coming in you know
+ 
+
+ align:start position:0%
+were no longer coming in you know
+parallel to each other now they're
+
+ align:start position:0%
+parallel to each other now they're
+ 
+
+ align:start position:0%
+parallel to each other now they're
+coming in head
+
+ align:start position:0%
+coming in head
+ 
+
+ align:start position:0%
+coming in head
+on all
+
+ align:start position:0%
+on all
+ 
+
+ align:start position:0%
+on all
+right so that's our convention the 2 pz
+
+ align:start position:0%
+right so that's our convention the 2 pz
+ 
+
+ align:start position:0%
+right so that's our convention the 2 pz
+is going to be along the bond Axis Three
+
+ align:start position:0%
+is going to be along the bond Axis Three
+ 
+
+ align:start position:0%
+is going to be along the bond Axis Three
+pz is going to be along the bond
+
+ align:start position:0%
+pz is going to be along the bond
+ 
+
+ align:start position:0%
+pz is going to be along the bond
+axis all right so we're going to bring
+
+ align:start position:0%
+axis all right so we're going to bring
+ 
+
+ align:start position:0%
+axis all right so we're going to bring
+these two Atomic wave functions in we're
+
+ align:start position:0%
+these two Atomic wave functions in we're
+ 
+
+ align:start position:0%
+these two Atomic wave functions in we're
+going to let this part overlap with that
+
+ align:start position:0%
+going to let this part overlap with that
+ 
+
+ align:start position:0%
+going to let this part overlap with that
+part and the result is a wave function
+
+ align:start position:0%
+part and the result is a wave function
+ 
+
+ align:start position:0%
+part and the result is a wave function
+that looks like this lots of electron
+
+ align:start position:0%
+that looks like this lots of electron
+ 
+
+ align:start position:0%
+that looks like this lots of electron
+density or wave function right in
+
+ align:start position:0%
+density or wave function right in
+ 
+
+ align:start position:0%
+density or wave function right in
+between the two
+
+ align:start position:0%
+between the two
+ 
+
+ align:start position:0%
+between the two
+nuclei here's a node right here's a node
+
+ align:start position:0%
+nuclei here's a node right here's a node
+ 
+
+ align:start position:0%
+nuclei here's a node right here's a node
+well these are nodes because there were
+
+ align:start position:0%
+well these are nodes because there were
+ 
+
+ align:start position:0%
+well these are nodes because there were
+nodes in the atomic wave functions to
+
+ align:start position:0%
+nodes in the atomic wave functions to
+ 
+
+ align:start position:0%
+nodes in the atomic wave functions to
+begin with we're going to call this wave
+
+ align:start position:0%
+begin with we're going to call this wave
+ 
+
+ align:start position:0%
+begin with we're going to call this wave
+function the sigma 2pz it's Sigma
+
+ align:start position:0%
+function the sigma 2pz it's Sigma
+ 
+
+ align:start position:0%
+function the sigma 2pz it's Sigma
+because it's symmetric around the
+
+ align:start position:0%
+because it's symmetric around the
+ 
+
+ align:start position:0%
+because it's symmetric around the
+internuclear bond axis right so that's
+
+ align:start position:0%
+internuclear bond axis right so that's
+ 
+
+ align:start position:0%
+internuclear bond axis right so that's
+the Symmetry call that
+
+ align:start position:0%
+the Symmetry call that
+ 
+
+ align:start position:0%
+the Symmetry call that
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+okay now what happens
+
+ align:start position:0%
+okay now what happens
+ 
+
+ align:start position:0%
+okay now what happens
+here it turns out that this Sigma state
+
+ align:start position:0%
+here it turns out that this Sigma state
+ 
+
+ align:start position:0%
+here it turns out that this Sigma state
+is a little higher in energy than the pi
+
+ align:start position:0%
+is a little higher in energy than the pi
+ 
+
+ align:start position:0%
+is a little higher in energy than the pi
+states in the next molecule there's
+
+ align:start position:0%
+states in the next molecule there's
+ 
+
+ align:start position:0%
+states in the next molecule there's
+going to be some exceptions here in a
+
+ align:start position:0%
+going to be some exceptions here in a
+ 
+
+ align:start position:0%
+going to be some exceptions here in a
+moment all right so
+
+ align:start position:0%
+moment all right so
+ 
+
+ align:start position:0%
+moment all right so
+nitrogen nitrogen has one electron in
+
+ align:start position:0%
+nitrogen nitrogen has one electron in
+ 
+
+ align:start position:0%
+nitrogen nitrogen has one electron in
+each one of the P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States let's use the albow principle to
+
+ align:start position:0%
+States let's use the albow principle to
+ 
+
+ align:start position:0%
+States let's use the albow principle to
+fill them up well there it is two here
+
+ align:start position:0%
+fill them up well there it is two here
+ 
+
+ align:start position:0%
+fill them up well there it is two here
+two here two there right the electron
+
+ align:start position:0%
+two here two there right the electron
+ 
+
+ align:start position:0%
+two here two there right the electron
+configuration is the 1 S's and the pi 2
+
+ align:start position:0%
+configuration is the 1 S's and the pi 2
+ 
+
+ align:start position:0%
+configuration is the 1 S's and the pi 2
+px2 pi 2 py2 and now Sigma 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pz2 let's calculate the bond order in
+
+ align:start position:0%
+pz2 let's calculate the bond order in
+ 
+
+ align:start position:0%
+pz2 let's calculate the bond order in
+molecular nit nen well it's the number
+
+ align:start position:0%
+molecular nit nen well it's the number
+ 
+
+ align:start position:0%
+molecular nit nen well it's the number
+of bonding electrons 2 4 6 8
+
+ align:start position:0%
+of bonding electrons 2 4 6 8
+ 
+
+ align:start position:0%
+of bonding electrons 2 4 6 8
+10 minus the number of antibonding
+
+ align:start position:0%
+10 minus the number of antibonding
+ 
+
+ align:start position:0%
+10 minus the number of antibonding
+electrons 2 4 10 - 4 is 6 / 2 bond order
+
+ align:start position:0%
+electrons 2 4 10 - 4 is 6 / 2 bond order
+ 
+
+ align:start position:0%
+electrons 2 4 10 - 4 is 6 / 2 bond order
+three and hey this means we got a triple
+
+ align:start position:0%
+three and hey this means we got a triple
+ 
+
+ align:start position:0%
+three and hey this means we got a triple
+bond and boy this better be a whole lot
+
+ align:start position:0%
+bond and boy this better be a whole lot
+ 
+
+ align:start position:0%
+bond and boy this better be a whole lot
+stronger and it is if you look at the
+
+ align:start position:0%
+stronger and it is if you look at the
+ 
+
+ align:start position:0%
+stronger and it is if you look at the
+bond energy in molecular nitrogen it's a
+
+ align:start position:0%
+bond energy in molecular nitrogen it's a
+ 
+
+ align:start position:0%
+bond energy in molecular nitrogen it's a
+whopping 941
+
+ align:start position:0%
+whopping 941
+ 
+
+ align:start position:0%
+whopping 941
+kles per mole we got a triple bond this
+
+ align:start position:0%
+kles per mole we got a triple bond this
+ 
+
+ align:start position:0%
+kles per mole we got a triple bond this
+is a strong bond this is a short
+
+ align:start position:0%
+is a strong bond this is a short
+ 
+
+ align:start position:0%
+is a strong bond this is a short
+Bond
+
+ align:start position:0%
+Bond
+ 
+
+ align:start position:0%
+Bond
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+now next one's going to be molecular
+
+ align:start position:0%
+now next one's going to be molecular
+ 
+
+ align:start position:0%
+now next one's going to be molecular
+oxygen and so now we've taken care of
+
+ align:start position:0%
+oxygen and so now we've taken care of
+ 
+
+ align:start position:0%
+oxygen and so now we've taken care of
+all of the wave functions the molecular
+
+ align:start position:0%
+all of the wave functions the molecular
+ 
+
+ align:start position:0%
+all of the wave functions the molecular
+wave functions that we can form from the
+
+ align:start position:0%
+wave functions that we can form from the
+ 
+
+ align:start position:0%
+wave functions that we can form from the
+2p Atomic wave functions using
+
+ align:start position:0%
+2p Atomic wave functions using
+ 
+
+ align:start position:0%
+2p Atomic wave functions using
+constructive interference it's now time
+
+ align:start position:0%
+constructive interference it's now time
+ 
+
+ align:start position:0%
+constructive interference it's now time
+to form form some molecular wave
+
+ align:start position:0%
+to form form some molecular wave
+ 
+
+ align:start position:0%
+to form form some molecular wave
+functions using destructive interference
+
+ align:start position:0%
+functions using destructive interference
+ 
+
+ align:start position:0%
+functions using destructive interference
+let's do that let's go back to 2px and
+
+ align:start position:0%
+let's do that let's go back to 2px and
+ 
+
+ align:start position:0%
+let's do that let's go back to 2px and
+2py okay they're the ones that come in
+
+ align:start position:0%
+2py okay they're the ones that come in
+ 
+
+ align:start position:0%
+2py okay they're the ones that come in
+parallel to each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other all right so as we bring them in
+
+ align:start position:0%
+other all right so as we bring them in
+ 
+
+ align:start position:0%
+other all right so as we bring them in
+and we're going to go destructively
+
+ align:start position:0%
+and we're going to go destructively
+ 
+
+ align:start position:0%
+and we're going to go destructively
+inter we're going to do a destructive
+
+ align:start position:0%
+inter we're going to do a destructive
+ 
+
+ align:start position:0%
+inter we're going to do a destructive
+interference this part of the wave
+
+ align:start position:0%
+interference this part of the wave
+ 
+
+ align:start position:0%
+interference this part of the wave
+function is going to destructively
+
+ align:start position:0%
+function is going to destructively
+ 
+
+ align:start position:0%
+function is going to destructively
+interfere with this part this part
+
+ align:start position:0%
+interfere with this part this part
+ 
+
+ align:start position:0%
+interfere with this part this part
+constructively interferes with that part
+
+ align:start position:0%
+constructively interferes with that part
+ 
+
+ align:start position:0%
+constructively interferes with that part
+hey the result is something that looks
+
+ align:start position:0%
+hey the result is something that looks
+ 
+
+ align:start position:0%
+hey the result is something that looks
+like this we got another Mo node right
+
+ align:start position:0%
+like this we got another Mo node right
+ 
+
+ align:start position:0%
+like this we got another Mo node right
+along wrong here the
+
+ align:start position:0%
+along wrong here the
+ 
+
+ align:start position:0%
+along wrong here the
+center that's a node because of this
+
+ align:start position:0%
+center that's a node because of this
+ 
+
+ align:start position:0%
+center that's a node because of this
+destructive interference we got another
+
+ align:start position:0%
+destructive interference we got another
+ 
+
+ align:start position:0%
+destructive interference we got another
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+here where the plane of the molecular
+
+ align:start position:0%
+here where the plane of the molecular
+ 
+
+ align:start position:0%
+here where the plane of the molecular
+axis is that's because these 2p wave
+
+ align:start position:0%
+axis is that's because these 2p wave
+ 
+
+ align:start position:0%
+axis is that's because these 2p wave
+functions had nodes in them to begin
+
+ align:start position:0%
+functions had nodes in them to begin
+ 
+
+ align:start position:0%
+functions had nodes in them to begin
+with right so that's what our wave
+
+ align:start position:0%
+with right so that's what our wave
+ 
+
+ align:start position:0%
+with right so that's what our wave
+function looks like it's got some wave
+
+ align:start position:0%
+function looks like it's got some wave
+ 
+
+ align:start position:0%
+function looks like it's got some wave
+function in this quadrant and this
+
+ align:start position:0%
+function in this quadrant and this
+ 
+
+ align:start position:0%
+function in this quadrant and this
+quadrant and this quadrant and this
+
+ align:start position:0%
+quadrant and this quadrant and this
+ 
+
+ align:start position:0%
+quadrant and this quadrant and this
+quadrant this is another Pi wave
+
+ align:start position:0%
+quadrant this is another Pi wave
+ 
+
+ align:start position:0%
+quadrant this is another Pi wave
+function because it's not symmetric
+
+ align:start position:0%
+function because it's not symmetric
+ 
+
+ align:start position:0%
+function because it's not symmetric
+around this Bond
+
+ align:start position:0%
+around this Bond
+ 
+
+ align:start position:0%
+around this Bond
+axis it is a anti-bonding orbital it's
+
+ align:start position:0%
+axis it is a anti-bonding orbital it's
+ 
+
+ align:start position:0%
+axis it is a anti-bonding orbital it's
+Pi
+
+ align:start position:0%
+Pi
+ 
+
+ align:start position:0%
+Pi
+star because this was formed as a result
+
+ align:start position:0%
+star because this was formed as a result
+ 
+
+ align:start position:0%
+star because this was formed as a result
+of destructive interference so we have a
+
+ align:start position:0%
+of destructive interference so we have a
+ 
+
+ align:start position:0%
+of destructive interference so we have a
+pi star 2px and a pi star 2py let's put
+
+ align:start position:0%
+pi star 2px and a pi star 2py let's put
+ 
+
+ align:start position:0%
+pi star 2px and a pi star 2py let's put
+those on an energy level diagram if
+
+ align:start position:0%
+those on an energy level diagram if
+ 
+
+ align:start position:0%
+those on an energy level diagram if
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+antibonding the energies are above those
+
+ align:start position:0%
+antibonding the energies are above those
+ 
+
+ align:start position:0%
+antibonding the energies are above those
+of the atomic States all right now let's
+
+ align:start position:0%
+of the atomic States all right now let's
+ 
+
+ align:start position:0%
+of the atomic States all right now let's
+write the electron configuration for O2
+
+ align:start position:0%
+write the electron configuration for O2
+ 
+
+ align:start position:0%
+write the electron configuration for O2
+here it comes there's the four 2p
+
+ align:start position:0%
+here it comes there's the four 2p
+ 
+
+ align:start position:0%
+here it comes there's the four 2p
+electrons for each oxygen atom we're
+
+ align:start position:0%
+electrons for each oxygen atom we're
+ 
+
+ align:start position:0%
+electrons for each oxygen atom we're
+going to put two of them in the sigma 2p
+
+ align:start position:0%
+going to put two of them in the sigma 2p
+ 
+
+ align:start position:0%
+going to put two of them in the sigma 2p
+Z 2 in the pi 2p x 2 in the pi 2py and
+
+ align:start position:0%
+Z 2 in the pi 2p x 2 in the pi 2py and
+ 
+
+ align:start position:0%
+Z 2 in the pi 2p x 2 in the pi 2py and
+then we're going to f follow Hunt's Rule
+
+ align:start position:0%
+then we're going to f follow Hunt's Rule
+ 
+
+ align:start position:0%
+then we're going to f follow Hunt's Rule
+and we're going to put one electron in
+
+ align:start position:0%
+and we're going to put one electron in
+ 
+
+ align:start position:0%
+and we're going to put one electron in
+the pi star 2px and one in the pi star
+
+ align:start position:0%
+the pi star 2px and one in the pi star
+ 
+
+ align:start position:0%
+the pi star 2px and one in the pi star
+2py we didn't put them both in the pi
+
+ align:start position:0%
+2py we didn't put them both in the pi
+ 
+
+ align:start position:0%
+2py we didn't put them both in the pi
+star 2px or both in the par Pi star 2py
+
+ align:start position:0%
+star 2px or both in the par Pi star 2py
+ 
+
+ align:start position:0%
+star 2px or both in the par Pi star 2py
+and we put them in with parallel spins
+
+ align:start position:0%
+and we put them in with parallel spins
+ 
+
+ align:start position:0%
+and we put them in with parallel spins
+not opposite
+
+ align:start position:0%
+not opposite
+ 
+
+ align:start position:0%
+not opposite
+spins thank you you're going to ask me a
+
+ align:start position:0%
+spins thank you you're going to ask me a
+ 
+
+ align:start position:0%
+spins thank you you're going to ask me a
+question get to lower
+
+ align:start position:0%
+question get to lower
+ 
+
+ align:start position:0%
+question get to lower
+good question I wanted you to notice
+
+ align:start position:0%
+good question I wanted you to notice
+ 
+
+ align:start position:0%
+good question I wanted you to notice
+that hey here's a change when we get to
+
+ align:start position:0%
+that hey here's a change when we get to
+ 
+
+ align:start position:0%
+that hey here's a change when we get to
+Z equal 8 what
+
+ align:start position:0%
+Z equal 8 what
+ 
+
+ align:start position:0%
+Z equal 8 what
+happens what happens is that they want
+
+ align:start position:0%
+happens what happens is that they want
+ 
+
+ align:start position:0%
+happens what happens is that they want
+to make this tough for you and what's
+
+ align:start position:0%
+to make this tough for you and what's
+ 
+
+ align:start position:0%
+to make this tough for you and what's
+happened is that this Sigma 2pz has
+
+ align:start position:0%
+happened is that this Sigma 2pz has
+ 
+
+ align:start position:0%
+happened is that this Sigma 2pz has
+dropped in energy compared to the pi 2px
+
+ align:start position:0%
+dropped in energy compared to the pi 2px
+ 
+
+ align:start position:0%
+dropped in energy compared to the pi 2px
+and Pi 2
+
+ align:start position:0%
+and Pi 2
+ 
+
+ align:start position:0%
+and Pi 2
+py at Z equal 8 the energy ordering
+
+ align:start position:0%
+py at Z equal 8 the energy ordering
+ 
+
+ align:start position:0%
+py at Z equal 8 the energy ordering
+flips at Z equal 7 for nitrogen Pi 2px
+
+ align:start position:0%
+flips at Z equal 7 for nitrogen Pi 2px
+ 
+
+ align:start position:0%
+flips at Z equal 7 for nitrogen Pi 2px
+Pi 2py is lower in energy than Sigma
+
+ align:start position:0%
+Pi 2py is lower in energy than Sigma
+ 
+
+ align:start position:0%
+Pi 2py is lower in energy than Sigma
+2pz but for Z equal 8 oxygen and
+
+ align:start position:0%
+2pz but for Z equal 8 oxygen and
+ 
+
+ align:start position:0%
+2pz but for Z equal 8 oxygen and
+above the energy ordering flips right
+
+ align:start position:0%
+above the energy ordering flips right
+ 
+
+ align:start position:0%
+above the energy ordering flips right
+Sigma is lower in energy than the pi
+
+ align:start position:0%
+Sigma is lower in energy than the pi
+ 
+
+ align:start position:0%
+Sigma is lower in energy than the pi
+that is something you have to know it
+
+ align:start position:0%
+that is something you have to know it
+ 
+
+ align:start position:0%
+that is something you have to know it
+has to do with the fact that
+
+ align:start position:0%
+has to do with the fact that
+ 
+
+ align:start position:0%
+has to do with the fact that
+the sigma 2ps has much more electron
+
+ align:start position:0%
+the sigma 2ps has much more electron
+ 
+
+ align:start position:0%
+the sigma 2ps has much more electron
+density in between the two
+
+ align:start position:0%
+density in between the two
+ 
+
+ align:start position:0%
+density in between the two
+nuclei that electron
+
+ align:start position:0%
+nuclei that electron
+ 
+
+ align:start position:0%
+nuclei that electron
+density is so high that when the nuclear
+
+ align:start position:0%
+density is so high that when the nuclear
+ 
+
+ align:start position:0%
+density is so high that when the nuclear
+charge is that of
+
+ align:start position:0%
+charge is that of
+ 
+
+ align:start position:0%
+charge is that of
+nitrogen plus 7e the nuclear charge
+
+ align:start position:0%
+nitrogen plus 7e the nuclear charge
+ 
+
+ align:start position:0%
+nitrogen plus 7e the nuclear charge
+actually isn't large enough to support
+
+ align:start position:0%
+actually isn't large enough to support
+ 
+
+ align:start position:0%
+actually isn't large enough to support
+all that electron density right but when
+
+ align:start position:0%
+all that electron density right but when
+ 
+
+ align:start position:0%
+all that electron density right but when
+you get to Z equal 8 it is and those
+
+ align:start position:0%
+you get to Z equal 8 it is and those
+ 
+
+ align:start position:0%
+you get to Z equal 8 it is and those
+energy levels FL
+
+ align:start position:0%
+energy levels FL
+ 
+
+ align:start position:0%
+energy levels FL
+it's an exception right I mean it's a
+
+ align:start position:0%
+it's an exception right I mean it's a
+ 
+
+ align:start position:0%
+it's an exception right I mean it's a
+change right there it is one that you
+
+ align:start position:0%
+change right there it is one that you
+ 
+
+ align:start position:0%
+change right there it is one that you
+have to know
+
+ align:start position:0%
+have to know
+ 
+
+ align:start position:0%
+have to know
+okay okay here's the electron
+
+ align:start position:0%
+okay okay here's the electron
+ 
+
+ align:start position:0%
+okay okay here's the electron
+configuration for molecular
+
+ align:start position:0%
+configuration for molecular
+ 
+
+ align:start position:0%
+configuration for molecular
+nitrogen if we go and we calculate here
+
+ align:start position:0%
+nitrogen if we go and we calculate here
+ 
+
+ align:start position:0%
+nitrogen if we go and we calculate here
+the bond order what will you find is the
+
+ align:start position:0%
+the bond order what will you find is the
+ 
+
+ align:start position:0%
+the bond order what will you find is the
+bond order is
+
+ align:start position:0%
+bond order is
+ 
+
+ align:start position:0%
+bond order is
+two that means we got a double bond and
+
+ align:start position:0%
+two that means we got a double bond and
+ 
+
+ align:start position:0%
+two that means we got a double bond and
+that bond strength is 494 K per mole
+
+ align:start position:0%
+that bond strength is 494 K per mole
+ 
+
+ align:start position:0%
+that bond strength is 494 K per mole
+okay so now we've got to make one more
+
+ align:start position:0%
+okay so now we've got to make one more
+ 
+
+ align:start position:0%
+okay so now we've got to make one more
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+orbital and that other molecular orbital
+
+ align:start position:0%
+orbital and that other molecular orbital
+ 
+
+ align:start position:0%
+orbital and that other molecular orbital
+is between the two pz states and it's
+
+ align:start position:0%
+is between the two pz states and it's
+ 
+
+ align:start position:0%
+is between the two pz states and it's
+going to be destructive
+
+ align:start position:0%
+going to be destructive
+ 
+
+ align:start position:0%
+going to be destructive
+interference so when these this part of
+
+ align:start position:0%
+interference so when these this part of
+ 
+
+ align:start position:0%
+interference so when these this part of
+the wave function overlaps with this
+
+ align:start position:0%
+the wave function overlaps with this
+ 
+
+ align:start position:0%
+the wave function overlaps with this
+part of the wave function we're going to
+
+ align:start position:0%
+part of the wave function we're going to
+ 
+
+ align:start position:0%
+part of the wave function we're going to
+cancel some wave function right and the
+
+ align:start position:0%
+cancel some wave function right and the
+ 
+
+ align:start position:0%
+cancel some wave function right and the
+result is that we're going to have a
+
+ align:start position:0%
+result is that we're going to have a
+ 
+
+ align:start position:0%
+result is that we're going to have a
+node right here in the center these are
+
+ align:start position:0%
+node right here in the center these are
+ 
+
+ align:start position:0%
+node right here in the center these are
+the two nuclei here's our nodal plane
+
+ align:start position:0%
+the two nuclei here's our nodal plane
+ 
+
+ align:start position:0%
+the two nuclei here's our nodal plane
+hey we've got a nodal plane right here
+
+ align:start position:0%
+hey we've got a nodal plane right here
+ 
+
+ align:start position:0%
+hey we've got a nodal plane right here
+anyway and one here from the atomic wave
+
+ align:start position:0%
+anyway and one here from the atomic wave
+ 
+
+ align:start position:0%
+anyway and one here from the atomic wave
+functions this wave function is a
+
+ align:start position:0%
+functions this wave function is a
+ 
+
+ align:start position:0%
+functions this wave function is a
+antibinding wave function it's Sigma
+
+ align:start position:0%
+antibinding wave function it's Sigma
+ 
+
+ align:start position:0%
+antibinding wave function it's Sigma
+star 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pz and if you look at the energy level
+
+ align:start position:0%
+pz and if you look at the energy level
+ 
+
+ align:start position:0%
+pz and if you look at the energy level
+diagram its energy that antibonding
+
+ align:start position:0%
+diagram its energy that antibonding
+ 
+
+ align:start position:0%
+diagram its energy that antibonding
+state is higher in energy than Sigma Pi
+
+ align:start position:0%
+state is higher in energy than Sigma Pi
+ 
+
+ align:start position:0%
+state is higher in energy than Sigma Pi
+2 PX and Sigma Pi 2
+
+ align:start position:0%
+2 PX and Sigma Pi 2
+ 
+
+ align:start position:0%
+2 PX and Sigma Pi 2
+py and so if we go to write the electron
+
+ align:start position:0%
+py and so if we go to write the electron
+ 
+
+ align:start position:0%
+py and so if we go to write the electron
+configuration for neon two well all of
+
+ align:start position:0%
+configuration for neon two well all of
+ 
+
+ align:start position:0%
+configuration for neon two well all of
+the bonding and anti-bonding states are
+
+ align:start position:0%
+the bonding and anti-bonding states are
+ 
+
+ align:start position:0%
+the bonding and anti-bonding states are
+filled the bond order in Neon 2 is zero
+
+ align:start position:0%
+filled the bond order in Neon 2 is zero
+ 
+
+ align:start position:0%
+filled the bond order in Neon 2 is zero
+right there is no bond for all practical
+
+ align:start position:0%
+right there is no bond for all practical
+ 
+
+ align:start position:0%
+right there is no bond for all practical
+purposes in Neon 2
\ No newline at end of file
diff --git a/TSjJlJJ2aoI.txt b/TSjJlJJ2aoI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f90ef5225f4852ac7fadb5d6dfbccb926e0c6c37
--- /dev/null
+++ b/TSjJlJJ2aoI.txt
@@ -0,0 +1,3206 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: And to
+this purpose, we
+
+need to calculate
+some thermodynamics.
+
+And we usually do that
+in statistical mechanics
+
+by calculating for some kind
+of a partition function.
+
+And we saw last
+time that it would
+
+be useful to calculate this
+grand partition function, which
+
+is the ensemble
+where you specify
+
+the temperature, the chemical
+potential, and the volume
+
+of the gas.
+
+And in this ensemble,
+your task is
+
+to look at within
+this box of volume V
+
+the possibility of there
+being any number of particles.
+
+So you have to sum over all
+possible N particle states.
+
+The contribution of
+each N particle states
+
+is exponentially related
+to the number of particles
+
+through the chemical potential.
+
+And then given that you are in
+a segment that has N particles,
+
+you have to look at all
+possible configurations
+
+of those particles
+and integrate over
+
+all of those possibilities.
+
+And that amounts to calculating
+the partition function.
+
+So for the partition function
+of an N particle system,
+
+you have to integrate
+over all of the momenta.
+
+Integration over each
+component of the momentum
+
+gives you a factor of 1 over
+lambda, where lambda again
+
+was related to the mass of
+the particle and temperature
+
+through this formula
+with h what we
+
+use to make these integrations
+over pq combinations
+
+dimensionless.
+
+There are 3N such integrations.
+
+So that's a contribution
+from the momenta.
+
+And then we have to
+do the integration
+
+over all of the coordinates.
+
+And as long as these
+particles are identical,
+
+we decided to divide by
+the number of permutations.
+
+Because we cannot
+tear them apart.
+
+So having done that, I need to
+now integrate over all of the N
+
+particles spanning
+a box of size V
+
+so the integration
+is within the box.
+
+And when I have
+interactions, then I
+
+have to worry about the
+Boltzmann weight that
+
+comes from the interaction.
+
+So here I should really
+put some kind of e
+
+to the minus beta times
+the interaction U.
+
+And what we did was we
+said that let's assume
+
+that this interaction comes
+from pairs of particles.
+
+And so this U is the sum
+over all possible pairs
+
+of particles, which
+when exponentiated
+
+will then give you a product
+over all possible pairs j, k
+
+and a factor that is related
+to the potential interaction
+
+between these.
+
+And we found it useful
+to write that factor as 1
+
+plus fjk, where this fjk
+stood for e to the minus
+
+beta of V qj minus qk minus 1.
+
+So basically if I
+add the 1 to that,
+
+I just get the exponentiated
+interaction potential.
+
+And then I have a
+forum such as this.
+
+So basically, this
+is the quantity
+
+that we wanted to compute.
+
+And so then we said,
+well, let's imagine
+
+expanding these factors of
+1 plus f1, 2, 1 plus f1, 3,
+
+1 plus f2, 3, all
+of these factors,
+
+and organize them according to
+the powers of f that they have.
+
+So the leading term would
+be taking 1 from everybody.
+
+So that would give
+me V to the N, which
+
+would be the 0-th
+order partition
+
+function, the
+non-interacting system.
+
+And then I would start
+to get corrections
+
+where there's order of f
+integrated, order of f squared
+
+integrated, all kinds of things.
+
+And that being a somewhat
+difficult object to look at,
+
+we said, let's imagine
+graphically what we would get.
+
+And the typical contribution
+that we would get to this
+
+would involve having to iterate
+over all of these N particles.
+
+So we have to somehow imagine
+that we have particles 1 to N.
+
+And then for a particular term,
+we either pick 1's-- and there
+
+will be some points that are
+not connected to any f that is
+
+integrated.
+
+There will be a bunch of
+things that will be connected
+
+to things where there
+are pair of f's.
+
+There will be things
+later on maybe
+
+where there are triplets of
+f, and so forth and so on.
+
+And then we said that when
+I do the integrations that
+
+correspond to this,
+what do I get?
+
+I will get the contribution
+that comes from one particle
+
+by itself integrated.
+
+Let's call that b1
+to the power of n1.
+
+I will get the contribution
+from this pair integrated.
+
+I will get b2 to
+the power of n2.
+
+I will get the contributions
+from these entities.
+
+And in general, I said,
+well, OK, somewhere in this,
+
+I will get bl to
+the power of nl.
+
+Now of course, I have
+a big constraint here
+
+that is that the
+sum over l of lnl
+
+has to be the total
+number of points 1 to n.
+
+So however I partition this,
+I will have for each graph
+
+that particular
+constraint acting.
+
+We said that clearly there's a
+lot of graphs and combinations
+
+that give you precisely
+this same factor.
+
+But all I had to do was
+to sort of rearrange
+
+the numbers and
+ordering, et cetera,
+
+and I would get all of this.
+
+So it would be very nice
+if I could figure out
+
+what the overall
+factor is out here.
+
+So we said that the factor is
+something like N factorial.
+
+Because what I can do is I can
+permute all of these numbers,
+
+and I would get
+exactly the same thing.
+
+But then I have to make sure
+that I don't over count.
+
+And not over counting
+required me to divide
+
+by the number of
+permutations that I
+
+have within each subgroup.
+
+So I have bl to the power of n.
+
+I have l factorial
+to the power of nl.
+
+And then I have the change.
+
+Let's say this is
+1, 2, this is 3, 4.
+
+I could have called one of
+them 3, 4, the other one 1, 2.
+
+So basically I will have nl
+factorial from the permutations
+
+within each.
+
+But I would have gotten exactly
+the same numerical factor
+
+out front if I had
+the same configuration
+
+but I had this diagram.
+
+I would have gotten
+exactly the same factor.
+
+I would call the
+contribution to this b3.
+
+I didn't say
+currently what b3 is.
+
+I would have gotten
+exactly the same factor.
+
+So maybe then what I
+did was to sort of group
+
+all of those things
+that would come
+
+with the same numerical factor
+into this [INAUDIBLE] sum
+
+that I call bl.
+
+So I call bl to be the sum
+over all l-particle clusters.
+
+And then, of course
+here, I have to sum over
+
+all configurations
+of nl that are
+
+consistent with this constraint
+that I have to put up there.
+
+So the rest of it
+then was algebra.
+
+We said that if I
+constrain the total number,
+
+it's difficult for me to do.
+
+That's why I didn't go and
+calculate the partition
+
+function and switch to the
+grand partition function.
+
+Because in the grand
+partition, I can essentially
+
+make this N that constrains
+the values of these nl's
+
+to be all over the place.
+
+And therefore summing over
+things with nl unconstrained
+
+is equivalent to summing over
+terms with nl constrained,
+
+and then summing over whatever
+the final constraint is.
+
+So once I did that, I was
+liberated from this constraint.
+
+I could do the sum for each
+value of nl separately.
+
+And the thing nicely
+broke up into pieces.
+
+And so then what I
+could do is I could
+
+show that each term
+in the sum, there
+
+would be a product over
+different contributions l.
+
+For each l, I could sum over
+nl running from 0 to infinity.
+
+I had the 1 over nl
+factorial from out here.
+
+I had an e to the
+beta mu divided
+
+by lambda cubed from the
+combination of these things
+
+raised to the
+power of lnl, which
+
+is how big N would
+have been composed.
+
+So I would have here lnl.
+
+And I also had an l factorial
+raised to the power of nl.
+
+So I can write things
+in this fashion.
+
+So this thing then
+became the same thing
+
+as an exponential of a sum over
+l running from 1 to infinity.
+
+1 over l factorial,
+of if you like
+
+e to the beta mu over lambda
+cubed to the power of l 1
+
+over l factorial.
+
+And then I had bl.
+
+So it was this very nice
+result somehow summing
+
+over all kinds of things, and
+then taking the logarithm.
+
+The logarithm
+really depends only
+
+on the contributions
+of single clusters.
+
+And again, the
+reason it had to be
+
+that way is because
+the ultimate thing
+
+that I calculated
+in this ensemble
+
+is that the answer
+should be e to the beta V
+
+times the pressure.
+
+And so the expression that
+we have over here better
+
+have terms which are all
+proportional to volume.
+
+Sorry, they're all made
+extensive by proportionality
+
+to volume.
+
+And indeed, when I do the
+integrations over a single any
+
+cluster, there is one degree
+of freedom, if you like,
+
+associated with the center
+of mass of the cluster that
+
+can go and explore
+the entire volume.
+
+And so all of these things are
+in fact in the large end limit
+
+proportional to V and
+something that I call bl bar.
+
+So once I divide by this
+volume, the final outcome
+
+of my calculation is
+that I can calculate
+
+the pressure of
+an interacting gas
+
+by summing over a series whose
+terms are this e to the beta mu
+
+over lambda cubed raised to
+the power of l bl bar divided
+
+by l factorial.
+
+OK, this is correct, but not
+particularly illuminating.
+
+Because the thing that we said
+we have some intuition for
+
+is that the pressure
+of a gas-- let's
+
+say if I look at it
+in terms of beta P,
+
+actually P is the density
+times kt, which is 1 over beta,
+
+if you like, or nkT.
+
+It doesn't matter.
+
+And then there will
+be corrections.
+
+There will be a term that
+is order of n squared.
+
+There will be a term
+that is order of n cubed.
+
+And there are
+these coefficients,
+
+which are functions
+of temperature,
+
+that are called the
+virial coefficient.
+
+And this is a virial expansion.
+
+Essentially what
+it is is a fitting
+
+of the form of the
+pressure of the gas
+
+as a function of density.
+
+In the very low density limit
+you get ideal gas result.
+
+And presumably because
+of these interactions,
+
+you will get corrections
+that presumably also
+
+know about the
+potential that went
+
+into the construction of all
+of these b bars, et cetera.
+
+So how do we relate these things
+that are, say, experimentally
+
+accessible to this expansion
+that we have over here?
+
+And the reason it is
+not obvious immediately
+
+is because this is an expansion
+in chemical potential,
+
+whereas over here,
+I have density.
+
+So what do I do?
+
+Well, I realize that the density
+can be obtained as follows.
+
+In the grand canonical ensemble,
+the number of particles
+
+is in principal a
+random variable.
+
+But that random variable
+is governed by this e
+
+to the beta mu N that
+controls how many you have.
+
+And if I take the log of
+Q with respect to beta mu,
+
+I will generate
+the average number,
+
+which in the
+thermodynamic limit we
+
+expect to be the same thing
+as what we thermodynamically
+
+would call the number.
+
+And this log Q we just
+established is beta PV.
+
+So what we have here is
+the derivative of beta VP
+
+with respect to beta mu.
+
+And if I do this at
+constant temperature,
+
+the betas disappear.
+
+This is the same
+thing as V dP by d
+
+mu at constant temperature.
+
+But also I can take the
+derivative right here.
+
+So what happens?
+
+I will find that the
+density which is N over V,
+
+is the derivative of this
+expression with respect
+
+to beta mu.
+
+I go and I find that
+there's a beta mu.
+
+If I take a derivative of
+this with respect to beta mu,
+
+really it's exponential
+of beta mu l.
+
+The derivative of it will
+give me l e to the beta mu l.
+
+So what I get is a sum
+over l e to the beta mu
+
+over lambda cubed.
+
+l gets repeated.
+
+And then I will
+have l times this.
+
+So I will have vl bar divided
+by l minus 1 factorial.
+
+So the series for
+density is very
+
+much like the
+series for pressure,
+
+except that you replace 1
+over l factorial with 1 over l
+
+minus 1 factorial.
+
+So now my task is clear.
+
+What I should do
+is I should solve
+
+given a particular
+density for what mu is.
+
+Once I have mu as a
+function of density,
+
+I can substitute it back here.
+
+And I will have pressure
+as a function of density.
+
+Of course it's clear that
+the right variable to look at
+
+is not mu, but x, which is e to
+the beta mu over lambda cubed.
+
+This actually has a name.
+
+It's sometimes called fugacity.
+
+So the second
+equation is telling me
+
+that the density I can write in
+terms of the fugacity as a sum
+
+over l x to the l bl bar divided
+by l minus 1 factorial, which
+
+if I were to sort of
+write in its full details,
+
+it starts with b1 bar x
+plus b2 bar x squared.
+
+Because there I have 0 factorial
+or 1 factorial respectively.
+
+The next term will be
+b3 bar over 2 x cubed.
+
+And this will go on and on.
+
+Also, let me remind
+you what b1 bar is.
+
+b1 bar, for every
+one of these b1 bars,
+
+I have to divide by 1
+over V because of this V.
+
+And then I have to do the
+integration that corresponds
+
+to the one cluster, which is
+essentially one cluster going
+
+over the entirety of space,
+which will give me V.
+
+So this is in fact 1.
+
+So basically this
+coefficient here is 1.
+
+And then I will have
+the corrections.
+
+So you say, well, I have
+n as a function of x.
+
+I want x as a function of n.
+
+And I say, OK, that's
+not that difficult.
+
+I will write that x
+equals n minus b2 bar
+
+x squared minus b3 bar x
+cubed over 2, and so forth.
+
+And I have now x.
+
+Maybe a few of
+you are skeptical.
+
+Some of you don't
+seem to be bothered.
+
+OK, so my claim is
+that this is indeed
+
+a systematic way of solving
+a series in which when
+
+the density goes to 0, you
+expect x to also go to 0.
+
+And to lowest order, x will
+be of the order of density.
+
+And these will be higher
+order powers in density.
+
+So to get a systematic series
+in density, all you need to do
+
+is to sort of work with a
+series such as this keeping
+
+in mind what order you
+have solved things to.
+
+So I claim that to
+lowest order, this really
+
+just says that x is n.
+
+And then there are corrections
+that are order of n squared.
+
+And to get the next order
+term, all I need to do
+
+is to substitute the lower
+order in this equation.
+
+So basically if I substitute
+x equals n in this equation,
+
+I will get n minus b2 n square.
+
+If I substitute x over n here,
+it will be a higher order term.
+
+And I claim that this
+is the correct result
+
+to order of n cubed.
+
+And then to get the
+result to order of n
+
+cubed, I substitute this back
+into the original equation.
+
+So I start with n minus
+b2 bar, the square
+
+of the previous solution
+at the right order.
+
+So squaring this, I will
+get n squared minus twice
+
+b2 bar n cubed.
+
+And the next term that would
+be the square of this, which
+
+is order of n to the
+fourth, I don't write down.
+
+And then I have
+minus b3 bar over 2,
+
+the cube of the
+previous solution.
+
+And at the right
+order that I have,
+
+that's the same thing
+as b3 bar over 2 n cubed
+
+and order of n to the fourth.
+
+And all I really need
+to do at this order
+
+is to recognize that
+I have two terms that
+
+are order of n cubed.
+
+Putting them together, I have
+n minus b2 bar n squared.
+
+And then I have
+plus 2b2 bar squared
+
+minus b3 bar over 2 n cubed
+and order of n to the fourth.
+
+So now we erase this.
+
+OK, so now I have solved for
+x in a power series in n.
+
+All I need to do
+is to substitute
+
+in the power series for p.
+
+So let's write that down.
+
+The power series for
+beta p is b1 bar times
+
+the density b2 bar
+squared over 2 density
+
+square, b3 bar over
+3 factorial, which
+
+is 6 n cubed, and so forth.
+
+But I only calculated
+things to order of n cubed.
+
+Also, b1 bar is the
+same thing as 1.
+
+So basically that's what
+I should be working with.
+
+And so all I need to do
+is to substitute-- oops,
+
+except that these are all x's.
+
+The series here
+for beta p that I
+
+have is in powers
+of this quantity x.
+
+And it is x that I had
+calculated as a function of n.
+
+To the order that I calculated,
+it is n minus b2n squared.
+
+And then I have 2b2
+squared minus b3 over b3.
+
+Somehow this sounds
+incorrect to me.
+
+Nope, that's fine.
+
+Because here I have 2.
+
+So that's correct.
+
+b3 over 2 n cubed--
+so essentially,
+
+I just substituted for x here.
+
+The next order
+term is going to be
+
+b2 over 2 times the square of x.
+
+The square of x will give
+me a term that is n squared,
+
+a term that is from
+here 2b2n cubed.
+
+Order of n to the fourth I
+haven't calculated correctly.
+
+Order of n cubed
+I have b3 over 6.
+
+And just x cubed is the same
+thing as n cubed to this order.
+
+And I have not calculated
+anything at the next order.
+
+So let's see what we have.
+
+We have n.
+
+At the next order, there are
+two terms that are n squared.
+
+There is this term,
+and there is that term.
+
+Putting them together, I will
+get minus b2 over 2 n squared.
+
+At the next order, at
+the order of n cubed,
+
+I have a bunch of terms.
+
+First of all, there
+is this 2b2 squared.
+
+But then multiplying this with
+this will subtract one b2.
+
+So I'm going to be
+left with b2 squared.
+
+And then I have minus 1/2 b3.
+
+So that's one term.
+
+And then I have plus 1/6 b3.
+
+Minus 1/2 plus 1/6 is minus 1/3.
+
+So this is minus
+b3 over 3 n cubed.
+
+And I haven't calculated
+order of n to the fourth.
+
+And this is the formula for BP.
+
+So lowest order, I have
+the ideal gas result.
+
+Actually, let me,
+for simplicity,
+
+define the virial
+coefficients in this fashion.
+
+The second order, I will
+get a correction B2,
+
+which is minus 1/2 of b2 bar.
+
+So this is minus 1/2
+of the diagram that
+
+corresponds to essentially
+one of these lines
+
+that I have up here.
+
+And so what is it?
+
+It is minus 1/2 the integral
+over the relative coordinate
+
+of e to the minus
+beta v as a function
+
+of the relative
+coordinate minus 1.
+
+Now earlier, we had in fact
+calculated this result directly
+
+through the partition function.
+
+I did a calculation in which
+I calculated the first term
+
+in the other way of
+looking at things,
+
+in the cumulant expansion,
+as a function of expansions
+
+in the potential.
+
+We saw that there
+was a term that all
+
+was order of density squared.
+
+We summed all of the
+terms to get this factor.
+
+And there was precisely
+a factor of minus 1/2
+
+as a correction to
+pressure once we
+
+took the derivative of
+the partition function
+
+with respect to volume.
+
+OK, so the thing that is new is
+really the next order term, B3,
+
+which is b2 squared
+minus b3 bar over 3.
+
+OK, so what is that?
+
+Diagrammatically,
+B2 was this factor
+
+that we calculated above and
+is the square of this pair.
+
+And then I have to subtract
+from that 1/3 of whatever
+
+goes into B3.
+
+Now remember, we said that B3,
+I have to pick three points
+
+and make sure I link them
+in all possible ways.
+
+So the diagrams that go into
+B3, one of them is this.
+
+But then there are
+three other ways
+
+of making a linked object,
+which is these things.
+
+We also saw that if
+I were to calculate
+
+the contribution of any
+one of these objects,
+
+I can very easily choose
+to measure my coordinates
+
+with respect to, say, the
+point that is at their apex.
+
+And then I would
+have one variable
+
+which is this distance,
+one variable which
+
+is that distance.
+
+And independently,
+each one of them
+
+would give me the factor
+that I calculated before.
+
+In essence, all of these one
+particle reducible graphs
+
+give a contribution,
+which is the product
+
+of these single line graphs.
+
+There are three of them.
+
+Minus 1/3 precisely
+cancels that.
+
+And so the calculation that
+goes into the third virial
+
+coefficient ultimately will
+only depend on this one graph.
+
+And we had anticipated
+this before.
+
+When we were doing
+things previously
+
+using the expansion of
+the partition function,
+
+we saw that in this
+cumulant expansion,
+
+only the cumulants
+were appearing.
+
+And for calculation
+of the cumulants,
+
+I had to do lots
+of subtractions.
+
+And those subtractions
+were genetically
+
+removing these one
+particle reducible graphs.
+
+And this continues
+to all orders.
+
+And the general formula is
+that the l-th contribution here
+
+will be a factor of l minus 1
+over l factorial, which is not
+
+so difficult to get by
+following the procedures
+
+that I have described over here,
+and then the part of bl that
+
+is one particle irreducible.
+
+So this is the
+eventual result for how
+
+you would be able, given some
+particular form of the two body
+
+interaction, to calculate
+an expansion for pressure
+
+in powers of density, how the
+coefficients of that expansion
+
+are related to properties
+of this potential
+
+through this
+diagrammatic expansion.
+
+So this is formally correct.
+
+And then the next question
+is, is it practical?
+
+Is it useful?
+
+So we need to start computing
+things to see something
+
+about the usefulness of this
+series for some particular type
+
+of potential.
+
+So we are going to look
+at the kind of potential
+
+that I already
+described for you.
+
+That is, if I look at two
+particles in a gas that
+
+are separated by
+an amount r-- let's
+
+imagine the potential
+only depends
+
+on the relative distance, not
+orientation or anything else.
+
+We said that basically,
+at large distances,
+
+the potential is attractive
+because of van der Waals.
+
+At short distances, the
+potential is repulsive.
+
+And so you have a general
+form such as this.
+
+Now, if I want to
+do calculations,
+
+it would be useful for
+me to have something
+
+that I can do
+calculations exactly
+
+with and get an estimate.
+
+So what I'm going to do is
+to replace that potential,
+
+essentially, with a hard wall.
+
+So my approximation to the
+potential is that my v of r
+
+is infinite for
+distances, separations
+
+that are less than some r0.
+
+So basically, I define
+some kind of r0,
+
+which is the-- if you think
+of them as billiard balls,
+
+it's related to the closest
+distance of approach.
+
+This potential at
+large distances
+
+has typical van der
+Waals form, by which
+
+I mean it falls off as
+a function of separation
+
+with the sixth power.
+
+It is attractive.
+
+So I put a minus sign here.
+
+In order to make sure that I
+get eventually the dimensions
+
+right, the coefficient that goes
+here I write as r0 with a u0
+
+up here such that if I assume
+that the potential is precisely
+
+this for all r that are
+greater than r0, then
+
+I'm replacing the
+actual potential
+
+by something like this.
+
+And the minimum
+depth of potential
+
+will occur at this cusp
+over here at minus u0.
+
+So why did I do that?
+
+Because now I can
+calculate with that
+
+what the second
+virial coefficient is.
+
+So what is B2?
+
+B2 is minus 1/2 the integral
+of relative potential.
+
+Now this integral
+will take two parts
+
+from these two
+different contributions.
+
+One part is when I'm in the
+regime where the particles are
+
+excluded, the
+potential is infinity.
+
+And there, f is simply minus 1.
+
+So that minus 1 then gets
+integrated from 0 to r,
+
+giving me the volume
+that is excluded.
+
+So what I will get
+here is a minus 1
+
+times the excluded volume.
+
+That's the first part, where
+the volume is, of course,
+
+4 pi over 3 r0 cubed for
+the volume of the sphere.
+
+And then I have to
+add the part where
+
+I go from f0 all
+the way to infinity.
+
+The potential is
+vertically symmetric.
+
+So d cubed r becomes
+4 pi r squared dr.
+
+And I have to integrate
+e to the minus
+
+beta times the attractive
+part of the potential.
+
+So it's beta u0 r0 over
+r to the sixth minus 1.
+
+So what I will do,
+I will additionally
+
+assume that I'm in the
+range of parameters
+
+where this beta u0
+is much less than 1,
+
+that is, at temperatures
+that are higher
+
+compared to the depth of
+this potential converted
+
+to units of kT.
+
+And if that is the case,
+then I can expand this.
+
+And the expansion
+to the lowest order
+
+will simply give me beta u0
+r0 over r to the sixth power.
+
+And I will ignore
+higher order terms.
+
+So this, if you like, is
+order of beta u0 squared.
+
+Now, having done that, then the
+second integral becomes simple.
+
+Because I have to
+integrate r squared
+
+divided by r to the fourth,
+which is r to the minus 4.
+
+Integral of r to the minus
+4 gives me r to the minus 3.
+
+And then there's a factor of
+minus 1/3 from the integration.
+
+It has to be evaluated
+between 0 and infinity.
+
+And so the final answer,
+then, for B2 is minus 1/2.
+
+I have minus 4 pi over 3 r0
+cubed from the excluded volume
+
+part.
+
+From here, I will get a 4
+pi beta u0 r0 to the sixth.
+
+And then I will get this
+factor of r the minus 3
+
+over 3 evaluated
+between infinity,
+
+which gives me 0 and r0.
+
+So you can see that with
+this potential, actually
+
+both terms are proportional
+to 4 pi r0 cubed over 3.
+
+And so I can write the
+answer as minus omega over 2
+
+where I have defined omega
+to be this 4 pi r0 cubed
+
+over 3, which is
+the excluded volume.
+
+Basically, it's the volume that
+is excluded from exploration
+
+when you have two particles.
+
+Because their center of mass
+cannot come as close as r0.
+
+So that 1/2 appears here as 1.
+
+Because I already
+took care of that.
+
+This rest of the coefficients
+are proportional to this
+
+except with a factor
+of minus beta u0.
+
+So I get minus beta u0.
+
+So this is your second
+virial coefficient for this.
+
+AUDIENCE: It should
+be positive out front.
+
+PROFESSOR: Pardon?
+
+AUDIENCE: It should be positive
+out front, [INAUDIBLE]?
+
+PROFESSOR: Yes, because
+there was a minus,
+
+and there's a minus.
+
+There's a plus.
+
+Let's keep that.
+
+So what we have
+so far, we've said
+
+that beta times the pressure
+starts with ideal gas behavior
+
+n.
+
+And then I have the
+next correction,
+
+which is this B2
+multiplying n squared.
+
+So I will have n squared
+times this coefficient
+
+that I have calculated for
+this type of gas, which
+
+is omega over 2 1 minus beta u0.
+
+And presumably there are
+higher order terms in this.
+
+So whenever you see
+something like this,
+
+then you have to
+start thinking about,
+
+is this a good expansion?
+
+So let's think about
+how this expansion could
+
+have become problematic.
+
+Actually, there is already one
+thing that I should have noted
+
+and I didn't, which is short
+versus long range potential.
+
+Now, it was nice
+for this potential
+
+that I got an answer
+that was in the form
+
+that I could write
+down, factor out omega.
+
+You can say, well,
+would you have always
+
+been able to do something
+similar to that?
+
+Because you see,
+ultimately what this
+
+says is that in order for all
+of these terms in this expansion
+
+to be dimensionally correct,
+the next term is a density,
+
+has dimensions of
+inverse volume,
+
+density squared
+compared to this.
+
+So it should be compensated
+by some factor of volume.
+
+And we can see that
+this factor of volume
+
+came from something
+that was of the order
+
+of this size of the
+molecule, this r0.
+
+OK, so it's interesting.
+
+It says that it's really
+the short-range part
+
+of the potential that seems
+to be setting the correction.
+
+Now, where did that come from?
+
+Well, there was one
+place that I had
+
+to do an integration
+over the potential.
+
+And I found that
+the integration was
+
+dominated by the lower range.
+
+That was over here.
+
+Where would this
+become difficult?
+
+AUDIENCE: In a small box?
+
+PROFESSOR: In a
+small box, but we
+
+are always taking the
+thermodynamic limit
+
+where V goes to infinity.
+
+AUDIENCE: Or inverse square log?
+
+PROFESSOR: Inverse square
+log, yes, that's right.
+
+So who says that this
+integral should converge?
+
+I'm doing an integral d cubed
+r, something like v of r.
+
+And convergence was the
+reason why this integral
+
+was dominated by short distance.
+
+If this potential goes
+like 1 over r cubed,
+
+then it will logarithmically
+depend on the size of the box.
+
+For Coulomb interaction,
+1/r potential
+
+you can't even think about it.
+
+It's just too divergent.
+
+So this expansion will
+fail for potentials
+
+that have tails that
+are decaying as 1
+
+over r cubed or even slower.
+
+Fortunately, that's not
+the case for van der Waals'
+
+potential and
+typical potentials.
+
+But if you have a plasma,
+you have to worry about this.
+
+And that's why I was
+also saying last time
+
+that the typical expansions
+that you have to do for plasmas
+
+are different.
+
+So given that we are
+dominated by the short range,
+
+what is the correction
+that I've obtained
+
+compared to the first term?
+
+So essentially, I have
+calculated a second order term
+
+that is of the order of this
+divided by the first order
+
+term and pressure
+that was density.
+
+And we find that this is
+of the order of n omega.
+
+How many particles are within
+the range of interaction?
+
+And this would be
+kind of like the ratio
+
+of the density of liquid
+to the density of gas.
+
+Because the density of
+liquid would be related-- oh,
+
+it's the other way around.
+
+The density of liquid
+would be 1 over the volume
+
+that one particle occupies.
+
+So the density of liquid
+would go in the denominator.
+
+The density of gas is this
+n that I have over here.
+
+And again, for the
+gas in this room,
+
+this ratio is of the order
+of 10 to the minus 3.
+
+And we are safe.
+
+But if I were to
+start compressing this
+
+so that I go to higher
+and higher densities,
+
+ultimately I say that this
+second order term becomes
+
+of the order of the
+first order term.
+
+And then perturbation
+doesn't make sense.
+
+Naturally, the reason for
+that is I haven't calculated.
+
+But typically what you
+find is that if you
+
+go to higher and
+higher order terms
+
+in the series, in most cases,
+but clearly not in all cases,
+
+the ratio of successive
+terms is more or less
+
+set by the ratio
+of the first terms.
+
+It has to be
+dimensionally correct.
+
+And we've established that
+the typical dimension that
+
+is controlling everything is
+the volume of the particle.
+
+So this expansion will fail
+for long range potentials,
+
+for going to
+liquid-like densities.
+
+But also I made
+another thing, which
+
+is that I assumed that that
+could expand this exponential.
+
+And then in principle,
+there are other difficulties
+
+that could arise if this
+condition that I wrote here
+
+is violated.
+
+If beta u0 is greater than 1,
+then this coefficient by itself
+
+becomes large exponentially.
+
+And then you would expect that
+higher order terms will also
+
+get more factors of this
+exponential and potential.
+
+And things will blow up on you.
+
+So it will also
+have difficulties
+
+at low temperatures for
+attractive potentials.
+
+Again, the reason
+for that is obvious.
+
+If you have an
+attractive potential,
+
+you go to low
+enough temperature,
+
+and the ground state is
+everybody sticking together--
+
+looks nothing like a gas, looks
+like a solid or something.
+
+So these are the
+kind of limitations
+
+that one has in this series.
+
+OK, let's be brave
+and do some more
+
+rearrangements of this equation.
+
+So I have that to
+this order, beta P
+
+is n plus n squared
+this excluded
+
+volume over 2 1 minus beta u0.
+
+And then there's higher
+order terms of course.
+
+And then I notice that there are
+two terms on this equation that
+
+are proportional to beta.
+
+And I say, why not put
+both of them together?
+
+So I will have beta.
+
+Bring that term to
+this side, and it
+
+becomes P plus n
+squared omega over 2 u0.
+
+And then what is left
+on the other side?
+
+Let's factor out the n.
+
+I expect this to be a series in
+higher and higher powers of n.
+
+And the first
+correction to 1 comes
+
+from here, which
+is n omega over 2.
+
+And I expect there to
+be higher order terms.
+
+Now again, to order of n squared
+that I have calculated things
+
+correctly, this
+expression is no different
+
+from the following expression--
+1 minus n omega over 2.
+
+Again, there will be
+higher order terms in n.
+
+But the order of n squared,
+both of these equations,
+
+expressions, are equivalent.
+
+So if I now ignore
+higher order terms,
+
+this whole thing is equivalent
+to P plus n squared u--
+
+well, let's write this in
+the following fashion-- p
+
+plus u0 omega over 2 N over
+V, which is density squared.
+
+And actually this side, if
+I were to multiply by V,
+
+what do I get?
+
+This becomes numerator
+V, denominator V minus N
+
+omega over 2.
+
+Let's multiply by V
+minus N omega over 2.
+
+And the right-hand
+side will be--
+
+AUDIENCE: Is that where
+it should be there?
+
+PROFESSOR: What happened?
+
+AUDIENCE: This one, [INAUDIBLE].
+
+PROFESSOR: Yes, so if I multiply
+this, which is N over V, by V,
+
+I will get N,
+good, which removes
+
+the difficulty that I had.
+
+Because now I multiply by kT.
+
+And the left hand
+side disappears.
+
+And on the right hand
+side, I will get NkT.
+
+So we'll spend some
+time on this equation
+
+that you will likely recognize
+as the van der Waals equation.
+
+I kind of justify it by
+rearranging this series.
+
+But van der Waals
+himself, of course,
+
+had a different way
+of justifying it,
+
+which is that basically if
+we think about the ideal gas,
+
+and you have particles that are
+moving within some volume V,
+
+if you have excluded
+volume interactions,
+
+then some of this volume
+is no longer available.
+
+And so maybe what
+you should do is
+
+you should reduce the
+volume by an amount that
+
+is proportional to the
+number of particles.
+
+This factor of 1/2 is
+actually very interesting.
+
+Because it is correct.
+
+And I see that a
+number of people
+
+in well known
+journals, et cetera,
+
+write that the excluded
+volume should be essentially
+
+n times the volume that is
+excluded around each particle.
+
+It's not that.
+
+It is 1/2 of that.
+
+And I'll leave you
+to mull on that.
+
+Because we will
+justify it later on.
+
+But in the meantime,
+you can think
+
+about why the factor
+of 1/2 is there.
+
+The other issue
+is that-- so there
+
+has to be a correction
+to the volume.
+
+And the kind of
+hand-waving statement
+
+that you make about the
+correction to pressure
+
+is that if you think about the
+particle that is in the middle,
+
+it is being attracted by
+everybody, whereas when
+
+it comes to the surface, it
+is really being attracted
+
+by things that are
+half of the space.
+
+So there is an
+effective potential
+
+that the particles feel
+from the collective action
+
+of all the others, which
+is slightly less steep when
+
+you approach the boundaries.
+
+And therefore, you can either
+think that because of this,
+
+there's less density that
+you have at the boundary.
+
+Less density will give
+you less pressure.
+
+Or if you have a
+particle that is
+
+kind of moving
+towards the wall, it
+
+is being pulled
+back so it doesn't
+
+hit the wall as strongly
+as you would expect,
+
+that would give the
+pressure of the ideal gas.
+
+So there is a pressure that
+has to be reduced related
+
+to the strength of the
+potential and something that
+
+has to do with all of
+the other particles.
+
+And there's density
+squared will appear there.
+
+We will have a more full
+justification of this equation
+
+later on.
+
+But for the time being, let's
+sort of sit with this equation
+
+and think about its
+consequences for awhile.
+
+Because the thing that
+we would like to do
+
+is we have come from a
+perspective of looking
+
+at the ideal gas and how the
+pressure of the ideal gas
+
+starts to get corrected
+because of the interactions.
+
+Of course, things
+become interesting
+
+when you go to the dense limit.
+
+And then the gas becomes
+something like a liquid.
+
+And you have transitions
+and things like that.
+
+So really, it's the other limit,
+the dense, highly interacting
+
+limited that is interesting.
+
+And to get that, we
+have few choices.
+
+Either I have to somehow sum
+many, many terms in the series,
+
+which will be very difficult,
+and we can't do that,
+
+or you can make some kind of
+approximation, rearrangement,
+
+and a guess.
+
+And this is what the van der
+Waals equation is based on.
+
+I made the guess here
+by somewhat rearranging
+
+and re-summing the
+terms in this series.
+
+But I will give you shortly
+a different justification
+
+that is more transparent
+and tells you immediately
+
+what the limitations are.
+
+But basically that's
+why we are going
+
+to spend some time
+with this equation.
+
+Because ultimately, we
+are hoping to transition
+
+from the weakly interacting
+case to the strongly interacting
+
+case.
+
+Yes.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: No, no,
+no, no, omega was
+
+defined as the volume
+excluded around one particle.
+
+So if you're thinking
+about billiard balls,
+
+r0 is the diameter.
+
+It's not the radius.
+
+And 4 pi over 3 r0 cubed
+is 8 times the diameter
+
+of a single billiard ball.
+
+So the correction that
+we get, if you like,
+
+is 4 times the volume of
+a billiard ball multiplied
+
+by the number of billiard balls.
+
+Where was I?
+
+OK, so what this equation
+gives you, the van der Waals,
+
+is an expression for
+how the pressure behaves
+
+as a function of volume.
+
+Actually, it would be nicer
+if we were to sort of replace
+
+this by volume per
+particle, which
+
+would be the inverse density.
+
+But you can use
+one or the other.
+
+It doesn't matter.
+
+Now, what you find is
+that there is, first
+
+of all, a limitation
+to the volume.
+
+So basically, none
+of your cares are
+
+going to go to volumes that
+are lower than n omega over 2.
+
+So basically there's a barrier
+here that occurs over here.
+
+But if you go to
+the other limit,
+
+where you go to large volumes,
+you can ignore terms like this.
+
+And then you get back the
+kind of ideal gas behavior.
+
+So basically, in
+one limit, where
+
+you are either at
+high temperatures--
+
+and at high temperatures,
+essentially, the correction
+
+here will also be negligible.
+
+Or you are at high
+values of the volume.
+
+You get isotherms that are
+very much like the isotherms
+
+that you have for the
+ideal gas, except that
+
+rather than asymptote
+to 0, PV going like NkT,
+
+you asymptote to
+this excluded volume.
+
+So this is for high T, T large.
+
+T larger than what?
+
+Well essentially,
+what happens is
+
+that if I look at the pressure,
+I can write it in this fashion
+
+also.
+
+It is NkT divided by V
+minus N omega over 2.
+
+So that's the term that
+dominates at high temperature.
+
+It's proportional to kT.
+
+But then there's the subtraction
+u0 omega over 2 N/V squared.
+
+And again, this term is not
+so important at large volume.
+
+Because at large
+volume, this 1/V
+
+is more dominant than
+1 over V squared.
+
+But as you go to
+lower temperatures
+
+and intermediate volumes,
+then essentially you
+
+have potentially a correction
+that falls off as minus 1
+
+over V squared.
+
+And so this correction that
+falls off as 1 over V squared
+
+can potentially
+modify your curve,
+
+bring it down, and then give
+it a structure such as this.
+
+So this is T less than.
+
+And clearly, between these
+two types of behavior,
+
+where there is
+monotonic behavior
+
+or non-monotonic
+behavior, there has
+
+to be a limiting curve that,
+let's say, does something
+
+like this, comes tangentially
+to the horizontal axis,
+
+and then goes on like this.
+
+So this would be
+for T equals Tc.
+
+This is T greater than
+Tc, T less than Tc.
+
+OK, so that's fine,
+except that now we
+
+have encountered the difficulty.
+
+Because one of the things
+that we had established
+
+for thermodynamic stability
+was that delta P delta
+
+V had to be negative.
+
+And the ideal gas
+curve and portions
+
+of this curve which
+have a negative slope
+
+are all consistent with this.
+
+But this portion over here
+where dP by dV is positive,
+
+it kind of violates
+the condition
+
+that the compressibility
+kappa T, which is minus 1/V dV
+
+by dP at constant temperature,
+better be positive.
+
+And so clearly, the expression
+that one gets through this van
+
+der Waals equation
+has a limitation.
+
+And the most
+natural way about it
+
+is to say, well, the
+question that you wrote down
+
+is clearly incorrect.
+
+That's certainly true.
+
+Also, this equation
+is incorrect,
+
+except that this
+kind of reminds us
+
+with what actually happens if I
+look at the isotherms of a gas,
+
+such as gas in this
+room, or something that
+
+is more familiar, such as water.
+
+What you find is that
+at high temperatures,
+
+you indeed have curves
+that look like this.
+
+But at low temperatures,
+you liquidify.
+
+And what you have is
+a zone of coexistence,
+
+let's say something
+like this, by which I
+
+mean that the
+isotherm that you draw
+
+has a portion that
+lives in the gas phase
+
+and is a slightly modified
+version of the ideal gas.
+
+But then it has a
+portion that corresponds
+
+to the more or less
+incompressible liquid.
+
+Although this has clearly still
+some finite compressibility.
+
+And then in between, there is a
+region where if you have a box,
+
+part of your box would be
+liquid, and part of your box
+
+would be gas.
+
+And as you compress the box,
+the proportion of liquid and gas
+
+will change.
+
+And this happens for
+T less than some Tc.
+
+And once more, there
+is a curve that kind of
+
+looks like this at some
+intermediate temperature Tc.
+
+So you look at the
+comparison, you say, well,
+
+as long as I stay
+above Tc-- of course
+
+I don't expect this equation
+to give the right numbers
+
+for what Tc or whatever is.
+
+But qualitatively, I get
+topologies and behaviors
+
+at that T greater
+than Tc all the way up
+
+to Tc are not very different.
+
+But at T less than
+Tc, they also signal
+
+that something bad is happening.
+
+And somehow, the original
+description has to be modified.
+
+And so the thing that Maxwell
+and van der Waals and company
+
+did was to somehow convert
+this incorrect set of equations
+
+to something that
+resembles this.
+
+So let's see how they
+managed to do this.
+
+Actually, this may not be a
+bad thing to keep in mind.
+
+Let's have a
+thermodynamic-- well,
+
+I kind of emphasize that there
+is thermodynamic reason for why
+
+this is not valid.
+
+Always there's a
+corresponding reason
+
+if you look at things
+from the perspective
+
+of statistical mechanics.
+
+So it may be useful
+to sort of think
+
+about what's happening
+from that perspective.
+
+Let's imagine that we are in
+this grand canonical ensemble.
+
+In the grand canonical ensemble,
+the number of particles,
+
+as we discussed, is not fixed.
+
+But the mean number of particles
+is given by the expressions
+
+that we saw over
+here, is related
+
+to the pressure through dP by
+d mu at constant temperature.
+
+But there are fluctuations.
+
+So you would say that the
+fluctuations are related
+
+by taking a second
+derivative of this object.
+
+Because clearly, q, if I were to
+expand it in powers of beta mu,
+
+will generate
+various moments of n.
+
+Log of q will
+generate cumulants.
+
+So the variance would
+be one more derivative.
+
+And so that will
+amount to taking
+
+a derivative of the
+first derivative, which
+
+was the number itself.
+
+So I will get this to be
+dN by d mu at constant T,
+
+except that there's an
+additional factor of kT.
+
+So maybe I will write
+this carefully enough.
+
+I have d2 log Q with
+respect to beta mu squared
+
+will give me N squared.
+
+Now, the first derivative with
+respect to beta mu of log Q
+
+gave me the mean, which I'm
+actually thinking of as N
+
+itself.
+
+And then there's
+this factor of beta.
+
+So this is really kT dN by d mu.
+
+All of these are done
+at constant temperature.
+
+So the statistical
+analog of stability
+
+really comes down to
+variances being positive.
+
+So my claim is that this
+variance being positive
+
+is related to this
+stability condition.
+
+Let me do that in the
+following fashion.
+
+I divide these two expressions.
+
+I will get the average
+of N squared divided
+
+by average of N, which is really
+N, so the variance over N.
+
+I have kT.
+
+And then I have the ratio
+of two of these derivatives.
+
+And the reason I
+wanted to do that ratio
+
+was to get rid of the d mu.
+
+Because d mu is not so nice.
+
+If I take the ratio of
+those two derivatives,
+
+I will get dN by
+dP at constant T.
+
+But what I really wanted was
+to say something about dV
+
+by dP at constant T
+rather than dN by dP.
+
+So what I'm going to do is to
+somehow convert this dN by dP
+
+into dN by dV,
+and then dV by dP.
+
+And actually to do that, I
+need to use the chain rule.
+
+So this will be T,
+P. This will be T, N.
+
+And the chain rule will give
+me an additional minus sign.
+
+So this is a reminder of
+how your partial derivatives
+
+and the chain rule goes.
+
+Finally, dN by dV is none
+other than the density N/V.
+
+At constant temperature, N
+and V will be proportional.
+
+And what I have here
+is 1/V dV by dP,
+
+which is the compressibility.
+
+So the whole thing here
+is NkT times kappa of T.
+
+And so this being positive,
+this positivity of the variance,
+
+is-- the thermodynamic
+analog of it
+
+was from the stability,
+and something such as this.
+
+The statistical analog of
+it is that the probability
+
+distribution that I'm looking at
+in the grand canonical ensemble
+
+as a function of N has to be
+peaked around some region.
+
+The variance around
+that peak better
+
+be positive so that I'm looking
+in the vicinity of a maximum.
+
+If it was negative,
+it means that I'm
+
+looking in the
+vicinity of a minimum.
+
+And I'm looking at the
+least likely configuration.
+
+So it cannot be allowed.
+
+So that's the
+statistical reason.
+
+OK, now I want to use
+that in connection
+
+with what we have
+over here and see
+
+what I can learn about this.
+
+I said that I wrote two
+expressions and divided them,
+
+because I didn't want to deal
+with the chemical potential.
+
+But let me redefine that
+and say the following,
+
+that N is V dP by
+d mu at constant T.
+
+And maybe I will start to
+gain some idea about chemical
+
+potential if I
+rearrange this as d mu
+
+is V/N dP along this surface
+of constant P at constant T.
+
+And then I can calculate
+mu as a function of P
+
+at some particular
+temperature minus mu
+
+at some reference point by
+integrating from the reference
+
+point to the
+pressure of interest
+
+the quantity V/N dP prime
+where V of P prime I
+
+take from this curve.
+
+So this curve gives me
+P as a function of V.
+
+But I can invert it and think
+of V as a function of P,
+
+put it here, and see what is
+happening with the chemical
+
+potential if I walk along
+one of these trajectories.
+
+And in particular, let's
+kind of draw one of these
+
+curves that I am
+unhappy with that
+
+have this kind of
+form in general
+
+and calculate what happens
+to the chemical potential
+
+if I, let's say, pick
+this reference point
+
+A, and the corresponding
+pressure PA,
+
+and go along this curve, which
+corresponds to some temperature
+
+T that is less than this
+instability temperature,
+
+and track the shape of
+the chemical potential.
+
+So this formula says that the
+change in chemical potential we
+
+obtained by calculating
+V-- divide by N,
+
+but our N is fixed--
+as a function of P,
+
+and integrating as
+you go up in pressure.
+
+So essentially, I'm calculating
+the integral starting
+
+from point A as I
+go under this curve.
+
+So let's plot as a result
+of that integration how
+
+that chemical potential at
+P minus PA is going to look
+
+like as I go in P beyond PA.
+
+So at PA, that's my reference.
+
+The chemical potential
+is some value.
+
+As I go up and up, because
+of this area of this curve,
+
+I keep adding to the
+chemical potential
+
+until I reach the maximum
+here at this point C.
+
+So there is some curve that goes
+from this A to some point C.
+
+Now, the thing is that when I
+continue going along this curve
+
+down this potential all the way
+to the bottom of this, which
+
+I will call D, my
+DP's are negative.
+
+So I start subtracting
+from what I had before.
+
+And so then the curve
+starts to go down.
+
+So all the way to
+D, I'm proceeding
+
+in the opposite direction.
+
+Once I hit D, I start going all
+the way to the end of the curve
+
+however far I want to go.
+
+And I'm adding
+some positive area.
+
+So the next part I also have a
+variation in chemical potential
+
+that goes like this.
+
+So you ask, well, if I give
+you what the temperature is
+
+and what the pressure
+is-- and I have told you
+
+what the temperature
+and pressure are--
+
+I should be able to calculate
+the chemical potential.
+
+It's an intensive
+function of the other two
+
+intensive functions.
+
+And this curve tells me
+that, except that there
+
+are regions where I don't
+know which one to pick.
+
+There are regions where
+it's obvious there's
+
+one value of the
+chemical potential.
+
+But there is in between,
+because of this instability,
+
+three possible values.
+
+And typically, if
+you have systems--
+
+think about different chemicals
+that can go between each other.
+
+And there are potentials for
+chemical transformations.
+
+You say, go and pick the
+lowest chemical potential.
+
+The system will evolve
+onto the condition that
+
+has the lowest
+chemical potential.
+
+So that says that when you
+have a situation such as this,
+
+you really have to
+pick the lowest one.
+
+And so you have to bail out on
+your first curve at the point
+
+B, and on your second curve at
+a point E, where on this curve
+
+B and E are such that when
+you integrate this BDP all
+
+the way from B to E, you will
+get 0, which means that you
+
+have to find points B and E
+such that the integral here
+
+is the same as
+the integral here.
+
+And this is the so-called
+Maxwell construction.
+
+So what that means is that
+originally I was telling you
+
+over here that there is some
+portion of the curve that
+
+violates all kinds
+of thermodynamics.
+
+And you should not access it.
+
+And this other argument that
+we are pursuing here says that
+
+actually the regions that you
+cannot access are beyond that.
+
+There's a portion that
+extends in this direction,
+
+and a portion that
+extends in that direction.
+
+And really there's a portion
+that you can access up to here,
+
+and a portion that you
+can access up to here.
+
+And maybe you
+should sort of then
+
+join them by a straight
+line and make an analog
+
+with what we have over there.
+
+Now, in another thing,
+another way of looking at this
+
+is that the green portion
+is certainly unstable,
+
+violates all kinds of
+thermodynamic conditions.
+
+And people argue that
+these other portions that
+
+have the right slope are
+in some sense metastable.
+
+So this would be a
+stable equilibrium.
+
+This would be an
+unstable equilibrium.
+
+And a metastable equilibrium
+is that you are at a minimum,
+
+but there's a deeper
+minimum somewhere else.
+
+And the picture is that if
+you manage to take your gas
+
+and put additional
+pressure on it,
+
+there is a region where there
+is a coexistence with the liquid
+
+which is better in terms
+of free energy, et cetera.
+
+But there could be some
+kind of a kinetic barrier,
+
+like nucleation or whatever,
+that prevents you to go there.
+
+And this again is something
+that is experimentally observed.
+
+If you try to rapidly
+pressurize a gas,
+
+you could sometimes avoid
+and not make your transition
+
+to the liquid state
+at the right pressure.
+
+But if you were to do
+things sufficiently slowly,
+
+you would ultimately
+reach this point
+
+that corresponds to
+the true equilibrium
+
+pressure of making
+this transition.
+
+Now, the thing is that
+somehow this whole story
+
+is not very satisfactory.
+
+I started with
+some rearrangement
+
+of some perturbative to
+arrive at this equation.
+
+This equation has
+this unstable portion.
+
+And somehow I'm trying to relate
+something that makes absolutely
+
+no thermodynamic
+sense and try to gain
+
+from it some idea about what is
+happening in a real liquid gas
+
+system.
+
+So it would be
+good if all of this
+
+could be more formally
+described within a framework
+
+where all of the approximations,
+et cetera, are clear,
+
+and we know what's going on.
+
+And so next time,
+we will do that.
+
+We will essentially developed a
+much more systematic formalism
+
+for calculating the properties
+of an interacting gas,
+
+and see that we get this, and
+we also understand why it fails.
\ No newline at end of file
diff --git a/TiHHz3sKDbY.txt b/TiHHz3sKDbY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7910b393ff6723fd7b79e4807df5dcfcd901bd9e
--- /dev/null
+++ b/TiHHz3sKDbY.txt
@@ -0,0 +1,12099 @@
+align:start position:0%
+ 
+good afternoon so um we
+
+ align:start position:0%
+good afternoon so um we
+ 
+
+ align:start position:0%
+good afternoon so um we
+spent our last lecture laying out some
+
+ align:start position:0%
+spent our last lecture laying out some
+ 
+
+ align:start position:0%
+spent our last lecture laying out some
+of the basic foundations making a couple
+
+ align:start position:0%
+of the basic foundations making a couple
+ 
+
+ align:start position:0%
+of the basic foundations making a couple
+of definitions I want to quickly recap
+
+ align:start position:0%
+of definitions I want to quickly recap
+ 
+
+ align:start position:0%
+of definitions I want to quickly recap
+the most important concepts and
+
+ align:start position:0%
+the most important concepts and
+ 
+
+ align:start position:0%
+the most important concepts and
+definitions and then maybe blunt I kind
+
+ align:start position:0%
+definitions and then maybe blunt I kind
+ 
+
+ align:start position:0%
+definitions and then maybe blunt I kind
+of want to get through these definitions
+
+ align:start position:0%
+of want to get through these definitions
+ 
+
+ align:start position:0%
+of want to get through these definitions
+which I think are it's important to do
+
+ align:start position:0%
+which I think are it's important to do
+ 
+
+ align:start position:0%
+which I think are it's important to do
+them precisely but
+
+ align:start position:0%
+them precisely but
+ 
+
+ align:start position:0%
+them precisely but
+there's nothing significantly
+
+ align:start position:0%
+there's nothing significantly
+ 
+
+ align:start position:0%
+there's nothing significantly
+challenging about them we just need to
+
+ align:start position:0%
+challenging about them we just need to
+ 
+
+ align:start position:0%
+challenging about them we just need to
+make sure they are defined very
+
+ align:start position:0%
+make sure they are defined very
+ 
+
+ align:start position:0%
+make sure they are defined very
+precisely so now that you've kind of
+
+ align:start position:0%
+precisely so now that you've kind of
+ 
+
+ align:start position:0%
+precisely so now that you've kind of
+seen the style of these things I would
+
+ align:start position:0%
+seen the style of these things I would
+ 
+
+ align:start position:0%
+seen the style of these things I would
+like to sort of move through the next
+
+ align:start position:0%
+like to sort of move through the next
+ 
+
+ align:start position:0%
+like to sort of move through the next
+batch of these definitions quickly
+
+ align:start position:0%
+batch of these definitions quickly
+ 
+
+ align:start position:0%
+batch of these definitions quickly
+enough that we can start to move into
+
+ align:start position:0%
+enough that we can start to move into
+ 
+
+ align:start position:0%
+enough that we can start to move into
+more interesting material so a quick
+
+ align:start position:0%
+more interesting material so a quick
+ 
+
+ align:start position:0%
+more interesting material so a quick
+recap and my apologies my daughter has
+
+ align:start position:0%
+recap and my apologies my daughter has
+ 
+
+ align:start position:0%
+recap and my apologies my daughter has
+some kind of a virus that I am
+
+ align:start position:0%
+some kind of a virus that I am
+ 
+
+ align:start position:0%
+some kind of a virus that I am
+desperately trying to make sure
+
+ align:start position:0%
+desperately trying to make sure
+ 
+
+ align:start position:0%
+desperately trying to make sure
+I do not catch and so I will be
+
+ align:start position:0%
+I do not catch and so I will be
+ 
+
+ align:start position:0%
+I do not catch and so I will be
+hydrating during this lecture so I just
+
+ align:start position:0%
+hydrating during this lecture so I just
+ 
+
+ align:start position:0%
+hydrating during this lecture so I just
+want to recap some of the most important
+
+ align:start position:0%
+want to recap some of the most important
+ 
+
+ align:start position:0%
+want to recap some of the most important
+cop since we went over so this whole
+
+ align:start position:0%
+cop since we went over so this whole
+ 
+
+ align:start position:0%
+cop since we went over so this whole
+class is essentially a study in
+
+ align:start position:0%
+class is essentially a study in
+ 
+
+ align:start position:0%
+class is essentially a study in
+space-time okay we're gonna later we're
+
+ align:start position:0%
+space-time okay we're gonna later we're
+ 
+
+ align:start position:0%
+space-time okay we're gonna later we're
+going to connect space-time to gravity
+
+ align:start position:0%
+going to connect space-time to gravity
+ 
+
+ align:start position:0%
+going to connect space-time to gravity
+and general relativity is going to
+
+ align:start position:0%
+and general relativity is going to
+ 
+
+ align:start position:0%
+and general relativity is going to
+become the relativistic theory of
+
+ align:start position:0%
+become the relativistic theory of
+ 
+
+ align:start position:0%
+become the relativistic theory of
+gravity so we began with a fairly
+
+ align:start position:0%
+gravity so we began with a fairly
+ 
+
+ align:start position:0%
+gravity so we began with a fairly
+mathematical definition space-time is a
+
+ align:start position:0%
+mathematical definition space-time is a
+ 
+
+ align:start position:0%
+mathematical definition space-time is a
+manifold of events that is endowed with
+
+ align:start position:0%
+manifold of events that is endowed with
+ 
+
+ align:start position:0%
+manifold of events that is endowed with
+a metric manifold for our purposes is
+
+ align:start position:0%
+a metric manifold for our purposes is
+ 
+
+ align:start position:0%
+a metric manifold for our purposes is
+essentially just a set in which we
+
+ align:start position:0%
+essentially just a set in which we
+ 
+
+ align:start position:0%
+essentially just a set in which we
+understand how different members of the
+
+ align:start position:0%
+understand how different members of the
+ 
+
+ align:start position:0%
+understand how different members of the
+set are connected to each other events
+
+ align:start position:0%
+set are connected to each other events
+ 
+
+ align:start position:0%
+set are connected to each other events
+are really just when and where something
+
+ align:start position:0%
+are really just when and where something
+ 
+
+ align:start position:0%
+are really just when and where something
+happens we haven't precisely defined
+
+ align:start position:0%
+happens we haven't precisely defined
+ 
+
+ align:start position:0%
+happens we haven't precisely defined
+metric yet we will soon okay but
+
+ align:start position:0%
+metric yet we will soon okay but
+ 
+
+ align:start position:0%
+metric yet we will soon okay but
+intuitively disregard it as some kind of
+
+ align:start position:0%
+intuitively disregard it as some kind of
+ 
+
+ align:start position:0%
+intuitively disregard it as some kind of
+a mathematical object that gives me a
+
+ align:start position:0%
+a mathematical object that gives me a
+ 
+
+ align:start position:0%
+a mathematical object that gives me a
+notion of distance between these events
+
+ align:start position:0%
+notion of distance between these events
+ 
+
+ align:start position:0%
+notion of distance between these events
+I was tried and I will continue to try
+
+ align:start position:0%
+I was tried and I will continue to try
+ 
+
+ align:start position:0%
+I was tried and I will continue to try
+to be very careful to make a distinction
+
+ align:start position:0%
+to be very careful to make a distinction
+ 
+
+ align:start position:0%
+to be very careful to make a distinction
+between geometric objects that live in
+
+ align:start position:0%
+between geometric objects that live in
+ 
+
+ align:start position:0%
+between geometric objects that live in
+the manifold the events themselves with
+
+ align:start position:0%
+the manifold the events themselves with
+ 
+
+ align:start position:0%
+the manifold the events themselves with
+things like a displacement vector
+
+ align:start position:0%
+things like a displacement vector
+ 
+
+ align:start position:0%
+things like a displacement vector
+between two events other vectors which I
+
+ align:start position:0%
+between two events other vectors which I
+ 
+
+ align:start position:0%
+between two events other vectors which I
+will recap the definition of in just a
+
+ align:start position:0%
+will recap the definition of in just a
+ 
+
+ align:start position:0%
+will recap the definition of in just a
+moment they have an existence and sort
+
+ align:start position:0%
+moment they have an existence and sort
+ 
+
+ align:start position:0%
+moment they have an existence and sort
+of a reality to them that is deeper and
+
+ align:start position:0%
+of a reality to them that is deeper and
+ 
+
+ align:start position:0%
+of a reality to them that is deeper and
+more fundamental than the representation
+
+ align:start position:0%
+more fundamental than the representation
+ 
+
+ align:start position:0%
+more fundamental than the representation
+of that object okay so when I state the
+
+ align:start position:0%
+of that object okay so when I state the
+ 
+
+ align:start position:0%
+of that object okay so when I state the
+displacement vector is Delta X Delta Y
+
+ align:start position:0%
+displacement vector is Delta X Delta Y
+ 
+
+ align:start position:0%
+displacement vector is Delta X Delta Y
+delta T Delta X Delta Y Delta Z that is
+
+ align:start position:0%
+delta T Delta X Delta Y Delta Z that is
+ 
+
+ align:start position:0%
+delta T Delta X Delta Y Delta Z that is
+according to observer oh and when I
+
+ align:start position:0%
+according to observer oh and when I
+ 
+
+ align:start position:0%
+according to observer oh and when I
+write that down I will be very clear for
+
+ align:start position:0%
+write that down I will be very clear for
+ 
+
+ align:start position:0%
+write that down I will be very clear for
+as much as possible I will occasionally
+
+ align:start position:0%
+as much as possible I will occasionally
+ 
+
+ align:start position:0%
+as much as possible I will occasionally
+screw this up but I will try to write
+
+ align:start position:0%
+screw this up but I will try to write
+ 
+
+ align:start position:0%
+screw this up but I will try to write
+this down without using an equal sign
+
+ align:start position:0%
+this down without using an equal sign
+ 
+
+ align:start position:0%
+this down without using an equal sign
+okay equal sign implies a degree of
+
+ align:start position:0%
+okay equal sign implies a degree of
+ 
+
+ align:start position:0%
+okay equal sign implies a degree of
+reality that I do not want to impart to
+
+ align:start position:0%
+reality that I do not want to impart to
+ 
+
+ align:start position:0%
+reality that I do not want to impart to
+that representation so an equal dot with
+
+ align:start position:0%
+that representation so an equal dot with
+ 
+
+ align:start position:0%
+that representation so an equal dot with
+a little oh here that's my personal
+
+ align:start position:0%
+a little oh here that's my personal
+ 
+
+ align:start position:0%
+a little oh here that's my personal
+notation for Delta X is represented by
+
+ align:start position:0%
+notation for Delta X is represented by
+ 
+
+ align:start position:0%
+notation for Delta X is represented by
+these components according to observer
+
+ align:start position:0%
+these components according to observer
+ 
+
+ align:start position:0%
+these components according to observer
+oh and for shorthand I will sometimes
+
+ align:start position:0%
+oh and for shorthand I will sometimes
+ 
+
+ align:start position:0%
+oh and for shorthand I will sometimes
+just write this by the collection of
+
+ align:start position:0%
+just write this by the collection of
+ 
+
+ align:start position:0%
+just write this by the collection of
+indices Delta X alpha a different
+
+ align:start position:0%
+indices Delta X alpha a different
+ 
+
+ align:start position:0%
+indices Delta X alpha a different
+observer Oh bar will represent their
+
+ align:start position:0%
+observer Oh bar will represent their
+ 
+
+ align:start position:0%
+observer Oh bar will represent their
+that they will represent this this
+
+ align:start position:0%
+that they will represent this this
+ 
+
+ align:start position:0%
+that they will represent this this
+vector using it's the exact same
+
+ align:start position:0%
+vector using it's the exact same
+ 
+
+ align:start position:0%
+vector using it's the exact same
+geometric object they all agree that
+
+ align:start position:0%
+geometric object they all agree that
+ 
+
+ align:start position:0%
+geometric object they all agree that
+it's this displacement between two
+
+ align:start position:0%
+it's this displacement between two
+ 
+
+ align:start position:0%
+it's this displacement between two
+physical events in space-time but they
+
+ align:start position:0%
+physical events in space-time but they
+ 
+
+ align:start position:0%
+physical events in space-time but they
+assign different coordinates to it they
+
+ align:start position:0%
+assign different coordinates to it they
+ 
+
+ align:start position:0%
+assign different coordinates to it they
+give a different representation to it
+
+ align:start position:0%
+give a different representation to it
+ 
+
+ align:start position:0%
+give a different representation to it
+and we find that representation using a
+
+ align:start position:0%
+and we find that representation using a
+ 
+
+ align:start position:0%
+and we find that representation using a
+Lorentz transformation okay and I'm not
+
+ align:start position:0%
+Lorentz transformation okay and I'm not
+ 
+
+ align:start position:0%
+Lorentz transformation okay and I'm not
+gonna write explicitly the Lorentz
+
+ align:start position:0%
+gonna write explicitly the Lorentz
+ 
+
+ align:start position:0%
+gonna write explicitly the Lorentz
+transformation matrix lambda I gave it
+
+ align:start position:0%
+transformation matrix lambda I gave it
+ 
+
+ align:start position:0%
+transformation matrix lambda I gave it
+in the last lecture and I'm assuming
+
+ align:start position:0%
+in the last lecture and I'm assuming
+ 
+
+ align:start position:0%
+in the last lecture and I'm assuming
+you're all experts in special relativity
+
+ align:start position:0%
+you're all experts in special relativity
+ 
+
+ align:start position:0%
+you're all experts in special relativity
+and I don't need to go over that so I
+
+ align:start position:0%
+and I don't need to go over that so I
+ 
+
+ align:start position:0%
+and I don't need to go over that so I
+will then using this sort of the
+
+ align:start position:0%
+will then using this sort of the
+ 
+
+ align:start position:0%
+will then using this sort of the
+prototype the general notion of a vector
+
+ align:start position:0%
+prototype the general notion of a vector
+ 
+
+ align:start position:0%
+prototype the general notion of a vector
+in space-time which we will often call a
+
+ align:start position:0%
+in space-time which we will often call a
+ 
+
+ align:start position:0%
+in space-time which we will often call a
+for vector for the obvious reason that
+
+ align:start position:0%
+for vector for the obvious reason that
+ 
+
+ align:start position:0%
+for vector for the obvious reason that
+it has four components I'm gonna treat
+
+ align:start position:0%
+it has four components I'm gonna treat
+ 
+
+ align:start position:0%
+it has four components I'm gonna treat
+that as any quartet of numbers that has
+
+ align:start position:0%
+that as any quartet of numbers that has
+ 
+
+ align:start position:0%
+that as any quartet of numbers that has
+transformation properties just like the
+
+ align:start position:0%
+transformation properties just like the
+ 
+
+ align:start position:0%
+transformation properties just like the
+displacement factor I just went over so
+
+ align:start position:0%
+displacement factor I just went over so
+ 
+
+ align:start position:0%
+displacement factor I just went over so
+if there's some quantity a that has time
+
+ align:start position:0%
+if there's some quantity a that has time
+ 
+
+ align:start position:0%
+if there's some quantity a that has time
+like an X or Y and a Z component as long
+
+ align:start position:0%
+like an X or Y and a Z component as long
+ 
+
+ align:start position:0%
+like an X or Y and a Z component as long
+as a different observer for reasons
+
+ align:start position:0%
+as a different observer for reasons
+ 
+
+ align:start position:0%
+as a different observer for reasons
+having to do with the underlying physics
+
+ align:start position:0%
+having to do with the underlying physics
+ 
+
+ align:start position:0%
+having to do with the underlying physics
+of whatever the heck this a is as long
+
+ align:start position:0%
+of whatever the heck this a is as long
+ 
+
+ align:start position:0%
+of whatever the heck this a is as long
+as that different observer relates their
+
+ align:start position:0%
+as that different observer relates their
+ 
+
+ align:start position:0%
+as that different observer relates their
+components to observer OHS components
+
+ align:start position:0%
+components to observer OHS components
+ 
+
+ align:start position:0%
+components to observer OHS components
+via Lorentz transformation you got
+
+ align:start position:0%
+via Lorentz transformation you got
+ 
+
+ align:start position:0%
+via Lorentz transformation you got
+yourself a four vector okay any random
+
+ align:start position:0%
+yourself a four vector okay any random
+ 
+
+ align:start position:0%
+yourself a four vector okay any random
+set of four numbers that ain't a four
+
+ align:start position:0%
+set of four numbers that ain't a four
+ 
+
+ align:start position:0%
+set of four numbers that ain't a four
+vector ah you need to have some physics
+
+ align:start position:0%
+vector ah you need to have some physics
+ 
+
+ align:start position:0%
+vector ah you need to have some physics
+associated with it and the physics has
+
+ align:start position:0%
+associated with it and the physics has
+ 
+
+ align:start position:0%
+associated with it and the physics has
+to tell it that it's a thing that's
+
+ align:start position:0%
+to tell it that it's a thing that's
+ 
+
+ align:start position:0%
+to tell it that it's a thing that's
+related by Lorentz transformation
+
+ align:start position:0%
+related by Lorentz transformation
+ 
+
+ align:start position:0%
+related by Lorentz transformation
+alright
+
+ align:start position:0%
+alright
+ 
+
+ align:start position:0%
+alright
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to pick up this discussion by
+
+ align:start position:0%
+I want to pick up this discussion by
+ 
+
+ align:start position:0%
+I want to pick up this discussion by
+introducing four particularly important
+
+ align:start position:0%
+introducing four particularly important
+ 
+
+ align:start position:0%
+introducing four particularly important
+and special vectors which to be honest
+
+ align:start position:0%
+and special vectors which to be honest
+ 
+
+ align:start position:0%
+and special vectors which to be honest
+we're not going to use too much beyond
+
+ align:start position:0%
+we're not going to use too much beyond
+ 
+
+ align:start position:0%
+we're not going to use too much beyond
+some of this the first couple weeks or
+
+ align:start position:0%
+some of this the first couple weeks or
+ 
+
+ align:start position:0%
+some of this the first couple weeks or
+so of the course but they're very useful
+
+ align:start position:0%
+so of the course but they're very useful
+ 
+
+ align:start position:0%
+so of the course but they're very useful
+and one should often bear in mind even
+
+ align:start position:0%
+and one should often bear in mind even
+ 
+
+ align:start position:0%
+and one should often bear in mind even
+later in the course and they've sort of
+
+ align:start position:0%
+later in the course and they've sort of
+ 
+
+ align:start position:0%
+later in the course and they've sort of
+disappeared that they're kind of they're
+
+ align:start position:0%
+disappeared that they're kind of they're
+ 
+
+ align:start position:0%
+disappeared that they're kind of they're
+coming along for the ride secret like
+
+ align:start position:0%
+coming along for the ride secret like
+ 
+
+ align:start position:0%
+coming along for the ride secret like
+these are basis vectors okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I go into frame Oh just gonna pick
+
+ align:start position:0%
+so if I go into frame Oh just gonna pick
+ 
+
+ align:start position:0%
+so if I go into frame Oh just gonna pick
+some particular reference frame I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+immediately write down for special
+
+ align:start position:0%
+immediately write down for special
+ 
+
+ align:start position:0%
+immediately write down for special
+vectors so
+
+ align:start position:0%
+vectors so
+ 
+
+ align:start position:0%
+vectors so
+remember this is a Cartesian type of
+
+ align:start position:0%
+remember this is a Cartesian type of
+ 
+
+ align:start position:0%
+remember this is a Cartesian type of
+coordinate system so I'm going to
+
+ align:start position:0%
+coordinate system so I'm going to
+ 
+
+ align:start position:0%
+coordinate system so I'm going to
+introduce easy
+
+ align:start position:0%
+introduce easy
+ 
+
+ align:start position:0%
+introduce easy
+Rho I'm
+
+ align:start position:0%
+Rho I'm
+ 
+
+ align:start position:0%
+Rho I'm
+gonna represent this by just the number
+
+ align:start position:0%
+gonna represent this by just the number
+ 
+
+ align:start position:0%
+gonna represent this by just the number
+one and the time like slot and zero
+
+ align:start position:0%
+one and the time like slot and zero
+ 
+
+ align:start position:0%
+one and the time like slot and zero
+everywhere else e 1
+
+ align:start position:0%
+everywhere else e 1
+ 
+
+ align:start position:0%
+everywhere else e 1
+or e X if you prefer I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gonna write that down like so and
+
+ align:start position:0%
+gonna write that down like so and
+ 
+
+ align:start position:0%
+gonna write that down like so and
+you can kind of see where I'm going with
+
+ align:start position:0%
+you can kind of see where I'm going with
+ 
+
+ align:start position:0%
+you can kind of see where I'm going with
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+analogy if you've all seen unit vectors
+
+ align:start position:0%
+analogy if you've all seen unit vectors
+ 
+
+ align:start position:0%
+analogy if you've all seen unit vectors
+in other classes hopefully this is
+
+ align:start position:0%
+in other classes hopefully this is
+ 
+
+ align:start position:0%
+in other classes hopefully this is
+fairly obvious what I'm doing okay I'm
+
+ align:start position:0%
+fairly obvious what I'm doing okay I'm
+ 
+
+ align:start position:0%
+fairly obvious what I'm doing okay I'm
+just picking out a set of you know
+
+ align:start position:0%
+just picking out a set of you know
+ 
+
+ align:start position:0%
+just picking out a set of you know
+little dimensionless simple quantities
+
+ align:start position:0%
+little dimensionless simple quantities
+ 
+
+ align:start position:0%
+little dimensionless simple quantities
+that point along the preferred
+
+ align:start position:0%
+that point along the preferred
+ 
+
+ align:start position:0%
+that point along the preferred
+directions that I've set up in this
+
+ align:start position:0%
+directions that I've set up in this
+ 
+
+ align:start position:0%
+directions that I've set up in this
+inertial reference frame a compact way
+
+ align:start position:0%
+inertial reference frame a compact way
+ 
+
+ align:start position:0%
+inertial reference frame a compact way
+of writing this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice I have four of these vectors and
+
+ align:start position:0%
+notice I have four of these vectors and
+ 
+
+ align:start position:0%
+notice I have four of these vectors and
+these vectors each have four components
+
+ align:start position:0%
+these vectors each have four components
+ 
+
+ align:start position:0%
+these vectors each have four components
+and so what I can say is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta component of unit vector E alpha is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+represented according to observer oh by
+
+ align:start position:0%
+represented according to observer oh by
+ 
+
+ align:start position:0%
+represented according to observer oh by
+Delta alpha beta the Kronecker Delta
+
+ align:start position:0%
+Delta alpha beta the Kronecker Delta
+ 
+
+ align:start position:0%
+Delta alpha beta the Kronecker Delta
+okay if
+
+ align:start position:0%
+okay if
+ 
+
+ align:start position:0%
+okay if
+you're not familiar with this one I'm
+
+ align:start position:0%
+you're not familiar with this one I'm
+ 
+
+ align:start position:0%
+you're not familiar with this one I'm
+usually reluctant to send you to
+
+ align:start position:0%
+usually reluctant to send you to
+ 
+
+ align:start position:0%
+usually reluctant to send you to
+Wikipedia but in this case wiki
+
+ align:start position:0%
+Wikipedia but in this case wiki
+ 
+
+ align:start position:0%
+Wikipedia but in this case wiki
+the Kronecker Delta yeah
+
+ align:start position:0%
+the Kronecker Delta yeah
+ 
+
+ align:start position:0%
+the Kronecker Delta yeah
+so that that kind of what that does just
+
+ align:start position:0%
+so that that kind of what that does just
+ 
+
+ align:start position:0%
+so that that kind of what that does just
+emphasize is that at least in by the way
+
+ align:start position:0%
+emphasize is that at least in by the way
+ 
+
+ align:start position:0%
+emphasize is that at least in by the way
+I should put little O's underneath all
+
+ align:start position:0%
+I should put little O's underneath all
+ 
+
+ align:start position:0%
+I should put little O's underneath all
+of these things because I have chosen
+
+ align:start position:0%
+of these things because I have chosen
+ 
+
+ align:start position:0%
+of these things because I have chosen
+this according to observer OHS
+
+ align:start position:0%
+this according to observer OHS
+ 
+
+ align:start position:0%
+this according to observer OHS
+representation so this is just saying
+
+ align:start position:0%
+representation so this is just saying
+ 
+
+ align:start position:0%
+representation so this is just saying
+that according to observer oh these are
+
+ align:start position:0%
+that according to observer oh these are
+ 
+
+ align:start position:0%
+that according to observer oh these are
+four very special vectors the utility of
+
+ align:start position:0%
+four very special vectors the utility of
+ 
+
+ align:start position:0%
+four very special vectors the utility of
+these things back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be honest thing okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the utility of doing this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if I now want to write the vector a
+
+ align:start position:0%
+that if I now want to write the vector a
+ 
+
+ align:start position:0%
+that if I now want to write the vector a
+as a geometric object I can combine the
+
+ align:start position:0%
+as a geometric object I can combine the
+ 
+
+ align:start position:0%
+as a geometric object I can combine the
+components that observer o uses with the
+
+ align:start position:0%
+components that observer o uses with the
+ 
+
+ align:start position:0%
+components that observer o uses with the
+basis vectors that observer o uses and I
+
+ align:start position:0%
+basis vectors that observer o uses and I
+ 
+
+ align:start position:0%
+basis vectors that observer o uses and I
+can sum them all together I can put them
+
+ align:start position:0%
+can sum them all together I can put them
+ 
+
+ align:start position:0%
+can sum them all together I can put them
+together and then I've got the it's not
+
+ align:start position:0%
+together and then I've got the it's not
+ 
+
+ align:start position:0%
+together and then I've got the it's not
+a representation that's the damn vector
+
+ align:start position:0%
+a representation that's the damn vector
+ 
+
+ align:start position:0%
+a representation that's the damn vector
+okay I put it all together using sort of
+
+ align:start position:0%
+okay I put it all together using sort of
+ 
+
+ align:start position:0%
+okay I put it all together using sort of
+an internally consistent set of numbers
+
+ align:start position:0%
+an internally consistent set of numbers
+ 
+
+ align:start position:0%
+an internally consistent set of numbers
+and basis vectors and so
+
+ align:start position:0%
+and basis vectors and so
+ 
+
+ align:start position:0%
+and basis vectors and so
+I am free to say this
+
+ align:start position:0%
+I am free to say this
+ 
+
+ align:start position:0%
+I am free to say this
+where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I actually use an actual equal sign okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might stop and think well but those
+
+ align:start position:0%
+you might stop and think well but those
+ 
+
+ align:start position:0%
+you might stop and think well but those
+aren't the components that observer Oh
+
+ align:start position:0%
+aren't the components that observer Oh
+ 
+
+ align:start position:0%
+aren't the components that observer Oh
+bar is it would use and you're right
+
+ align:start position:0%
+bar is it would use and you're right
+ 
+
+ align:start position:0%
+bar is it would use and you're right
+observer Oh bar would not use those
+
+ align:start position:0%
+observer Oh bar would not use those
+ 
+
+ align:start position:0%
+observer Oh bar would not use those
+components they would also not use those
+
+ align:start position:0%
+components they would also not use those
+ 
+
+ align:start position:0%
+components they would also not use those
+basis vectors we're gonna talk about how
+
+ align:start position:0%
+basis vectors we're gonna talk about how
+ 
+
+ align:start position:0%
+basis vectors we're gonna talk about how
+those things change but observer Oh bar
+
+ align:start position:0%
+those things change but observer Oh bar
+ 
+
+ align:start position:0%
+those things change but observer Oh bar
+does agree that if they were handed owes
+
+ align:start position:0%
+does agree that if they were handed owes
+ 
+
+ align:start position:0%
+does agree that if they were handed owes
+components in those basis vectors this
+
+ align:start position:0%
+components in those basis vectors this
+ 
+
+ align:start position:0%
+components in those basis vectors this
+would give me a complete representation
+
+ align:start position:0%
+would give me a complete representation
+ 
+
+ align:start position:0%
+would give me a complete representation
+of what the vector is okay so
+
+ align:start position:0%
+of what the vector is okay so
+ 
+
+ align:start position:0%
+of what the vector is okay so
+again I'm really harping on this sort of
+
+ align:start position:0%
+again I'm really harping on this sort of
+ 
+
+ align:start position:0%
+again I'm really harping on this sort of
+distinction between the geometric object
+
+ align:start position:0%
+distinction between the geometric object
+ 
+
+ align:start position:0%
+distinction between the geometric object
+and the representation this is the
+
+ align:start position:0%
+and the representation this is the
+ 
+
+ align:start position:0%
+and the representation this is the
+geometric object we can take advantage
+
+ align:start position:0%
+geometric object we can take advantage
+ 
+
+ align:start position:0%
+geometric object we can take advantage
+of this okay
+
+ align:start position:0%
+of this okay
+ 
+
+ align:start position:0%
+of this okay
+the fact that that combination of things
+
+ align:start position:0%
+the fact that that combination of things
+ 
+
+ align:start position:0%
+the fact that that combination of things
+is the geometric object is a tool that
+
+ align:start position:0%
+is the geometric object is a tool that
+ 
+
+ align:start position:0%
+is the geometric object is a tool that
+I'm gonna now it's a fact that I'm going
+
+ align:start position:0%
+I'm gonna now it's a fact that I'm going
+ 
+
+ align:start position:0%
+I'm gonna now it's a fact that I'm going
+to exploit in order to figure out how my
+
+ align:start position:0%
+to exploit in order to figure out how my
+ 
+
+ align:start position:0%
+to exploit in order to figure out how my
+basis vectors transform when I change
+
+ align:start position:0%
+basis vectors transform when I change
+ 
+
+ align:start position:0%
+basis vectors transform when I change
+reference frames so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just repeat what I wrote up there ah
+
+ align:start position:0%
+we just repeat what I wrote up there ah
+ 
+
+ align:start position:0%
+we just repeat what I wrote up there ah
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+whoops
+
+ align:start position:0%
+whoops
+ 
+
+ align:start position:0%
+whoops
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point for just a slight editorial
+
+ align:start position:0%
+point for just a slight editorial
+ 
+
+ align:start position:0%
+point for just a slight editorial
+comment um when you're talking and
+
+ align:start position:0%
+comment um when you're talking and
+ 
+
+ align:start position:0%
+comment um when you're talking and
+writing and there are millions of little
+
+ align:start position:0%
+writing and there are millions of little
+ 
+
+ align:start position:0%
+writing and there are millions of little
+subscripts and indices sometimes the
+
+ align:start position:0%
+subscripts and indices sometimes the
+ 
+
+ align:start position:0%
+subscripts and indices sometimes the
+brain and the appendages get out of sync
+
+ align:start position:0%
+brain and the appendages get out of sync
+ 
+
+ align:start position:0%
+brain and the appendages get out of sync
+with one another I caught that one I
+
+ align:start position:0%
+with one another I caught that one I
+ 
+
+ align:start position:0%
+with one another I caught that one I
+don't always okay so if you see
+
+ align:start position:0%
+don't always okay so if you see
+ 
+
+ align:start position:0%
+don't always okay so if you see
+something like that and you kind of go
+
+ align:start position:0%
+something like that and you kind of go
+ 
+
+ align:start position:0%
+something like that and you kind of go
+umm why did that alpha magically turn
+
+ align:start position:0%
+umm why did that alpha magically turn
+ 
+
+ align:start position:0%
+umm why did that alpha magically turn
+into a beta it's probably a mistake
+
+ align:start position:0%
+into a beta it's probably a mistake
+ 
+
+ align:start position:0%
+into a beta it's probably a mistake
+please call it out okay all right so
+
+ align:start position:0%
+please call it out okay all right so
+ 
+
+ align:start position:0%
+please call it out okay all right so
+this is how I build this geometric
+
+ align:start position:0%
+this is how I build this geometric
+ 
+
+ align:start position:0%
+this is how I build this geometric
+object using the components and the
+
+ align:start position:0%
+object using the components and the
+ 
+
+ align:start position:0%
+object using the components and the
+basis vectors as measured by O as used
+
+ align:start position:0%
+basis vectors as measured by O as used
+ 
+
+ align:start position:0%
+basis vectors as measured by O as used
+by observer oh let's now write out what
+
+ align:start position:0%
+by observer oh let's now write out what
+ 
+
+ align:start position:0%
+by observer oh let's now write out what
+they would be if they were measured by a
+
+ align:start position:0%
+they would be if they were measured by a
+ 
+
+ align:start position:0%
+they would be if they were measured by a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+observer and o'Barr okay
+
+ align:start position:0%
+observer and o'Barr okay
+ 
+
+ align:start position:0%
+observer and o'Barr okay
+I know how to get components the barred
+
+ align:start position:0%
+I know how to get components the barred
+ 
+
+ align:start position:0%
+I know how to get components the barred
+components from the unbarred components
+
+ align:start position:0%
+components from the unbarred components
+ 
+
+ align:start position:0%
+components from the unbarred components
+I don't yet know how to get the unbarred
+
+ align:start position:0%
+I don't yet know how to get the unbarred
+ 
+
+ align:start position:0%
+I don't yet know how to get the unbarred
+Basin to be the bard basis vectors and
+
+ align:start position:0%
+Basin to be the bard basis vectors and
+ 
+
+ align:start position:0%
+Basin to be the bard basis vectors and
+the unbarred basis vectors but I know
+
+ align:start position:0%
+the unbarred basis vectors but I know
+ 
+
+ align:start position:0%
+the unbarred basis vectors but I know
+that whatever they exist and that once I
+
+ align:start position:0%
+that whatever they exist and that once I
+ 
+
+ align:start position:0%
+that whatever they exist and that once I
+know what they are this equation is true
+
+ align:start position:0%
+know what they are this equation is true
+ 
+
+ align:start position:0%
+know what they are this equation is true
+okay these are just two different ways
+
+ align:start position:0%
+okay these are just two different ways
+ 
+
+ align:start position:0%
+okay these are just two different ways
+of writing this geometric object which
+
+ align:start position:0%
+of writing this geometric object which
+ 
+
+ align:start position:0%
+of writing this geometric object which
+every observer agrees has this existence
+
+ align:start position:0%
+every observer agrees has this existence
+ 
+
+ align:start position:0%
+every observer agrees has this existence
+that transcends the representation so
+
+ align:start position:0%
+that transcends the representation so
+ 
+
+ align:start position:0%
+that transcends the representation so
+let's rewrite what I've got on the
+
+ align:start position:0%
+let's rewrite what I've got on the
+ 
+
+ align:start position:0%
+let's rewrite what I've got on the
+right-hand side of the the rightmost
+
+ align:start position:0%
+right-hand side of the the rightmost
+ 
+
+ align:start position:0%
+right-hand side of the the rightmost
+equal sign here I'm gonna write this as
+
+ align:start position:0%
+equal sign here I'm gonna write this as
+ 
+
+ align:start position:0%
+equal sign here I'm gonna write this as
+lambda
+
+ align:start position:0%
+lambda
+ 
+
+ align:start position:0%
+lambda
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+bar beta
+
+ align:start position:0%
+bar beta
+ 
+
+ align:start position:0%
+bar beta
+a beta and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then now I'm going to use a trick which
+
+ align:start position:0%
+then now I'm going to use a trick which
+ 
+
+ align:start position:0%
+then now I'm going to use a trick which
+is what the tonight units much a trick
+
+ align:start position:0%
+is what the tonight units much a trick
+ 
+
+ align:start position:0%
+is what the tonight units much a trick
+but just gonna use a fact that is great
+
+ align:start position:0%
+but just gonna use a fact that is great
+ 
+
+ align:start position:0%
+but just gonna use a fact that is great
+when you're working in index notation
+
+ align:start position:0%
+when you're working in index notation
+ 
+
+ align:start position:0%
+when you're working in index notation
+okay so often when students first
+
+ align:start position:0%
+okay so often when students first
+ 
+
+ align:start position:0%
+okay so often when students first
+encounter this kind of notation your
+
+ align:start position:0%
+encounter this kind of notation your
+ 
+
+ align:start position:0%
+encounter this kind of notation your
+instinct is to try to write everything
+
+ align:start position:0%
+instinct is to try to write everything
+ 
+
+ align:start position:0%
+instinct is to try to write everything
+out using matrices and things like row
+
+ align:start position:0%
+out using matrices and things like row
+ 
+
+ align:start position:0%
+out using matrices and things like row
+vectors and column vectors okay it's a
+
+ align:start position:0%
+vectors and column vectors okay it's a
+ 
+
+ align:start position:0%
+vectors and column vectors okay it's a
+natural thing to do I urge you to get
+
+ align:start position:0%
+natural thing to do I urge you to get
+ 
+
+ align:start position:0%
+natural thing to do I urge you to get
+over that
+
+ align:start position:0%
+over that
+ 
+
+ align:start position:0%
+over that
+if I get some bandwidth for that I'm
+
+ align:start position:0%
+if I get some bandwidth for that I'm
+ 
+
+ align:start position:0%
+if I get some bandwidth for that I'm
+gonna write up a set of notes this
+
+ align:start position:0%
+gonna write up a set of notes this
+ 
+
+ align:start position:0%
+gonna write up a set of notes this
+weekend showing how one can translate at
+
+ align:start position:0%
+weekend showing how one can translate at
+ 
+
+ align:start position:0%
+weekend showing how one can translate at
+least two by two objects and one that to
+
+ align:start position:0%
+least two by two objects and one that to
+ 
+
+ align:start position:0%
+least two by two objects and one that to
+index objects and one ending objects in
+
+ align:start position:0%
+index objects and one ending objects in
+ 
+
+ align:start position:0%
+index objects and one ending objects in
+a consistent way between matrices
+
+ align:start position:0%
+a consistent way between matrices
+ 
+
+ align:start position:0%
+a consistent way between matrices
+and row vectors and column vectors but
+
+ align:start position:0%
+and row vectors and column vectors but
+ 
+
+ align:start position:0%
+and row vectors and column vectors but
+we're rapidly going to start getting
+
+ align:start position:0%
+we're rapidly going to start getting
+ 
+
+ align:start position:0%
+we're rapidly going to start getting
+into objects that are bigger than that
+
+ align:start position:0%
+into objects that are bigger than that
+ 
+
+ align:start position:0%
+into objects that are bigger than that
+for which trying to represent them in
+
+ align:start position:0%
+for which trying to represent them in
+ 
+
+ align:start position:0%
+for which trying to represent them in
+matrix like form gets untenable okay and
+
+ align:start position:0%
+matrix like form gets untenable okay and
+ 
+
+ align:start position:0%
+matrix like form gets untenable okay and
+a little while we're gonna have a three
+
+ align:start position:0%
+a little while we're gonna have a three
+ 
+
+ align:start position:0%
+a little while we're gonna have a three
+indexed object since we don't have
+
+ align:start position:0%
+indexed object since we don't have
+ 
+
+ align:start position:0%
+indexed object since we don't have
+three-dimensional chalkboards making
+
+ align:start position:0%
+three-dimensional chalkboards making
+ 
+
+ align:start position:0%
+three-dimensional chalkboards making
+this sort of matrix representation that
+
+ align:start position:0%
+this sort of matrix representation that
+ 
+
+ align:start position:0%
+this sort of matrix representation that
+is challenging soon after that we'll
+
+ align:start position:0%
+is challenging soon after that we'll
+ 
+
+ align:start position:0%
+is challenging soon after that we'll
+have four index objects and we'll
+
+ align:start position:0%
+have four index objects and we'll
+ 
+
+ align:start position:0%
+have four index objects and we'll
+occasionally need to take derivatives of
+
+ align:start position:0%
+occasionally need to take derivatives of
+ 
+
+ align:start position:0%
+occasionally need to take derivatives of
+that for an index object giving us a 5
+
+ align:start position:0%
+that for an index object giving us a 5
+ 
+
+ align:start position:0%
+that for an index object giving us a 5
+index object at that point the ability
+
+ align:start position:0%
+index object at that point the ability
+ 
+
+ align:start position:0%
+index object at that point the ability
+to sort of treat them like matrices is
+
+ align:start position:0%
+to sort of treat them like matrices is
+ 
+
+ align:start position:0%
+to sort of treat them like matrices is
+hopeless so really you should just be
+
+ align:start position:0%
+hopeless so really you should just be
+ 
+
+ align:start position:0%
+hopeless so really you should just be
+thinking of this as ordinary
+
+ align:start position:0%
+thinking of this as ordinary
+ 
+
+ align:start position:0%
+thinking of this as ordinary
+multiplication of the numbers that are
+
+ align:start position:0%
+multiplication of the numbers that are
+ 
+
+ align:start position:0%
+multiplication of the numbers that are
+represented by these components as
+
+ align:start position:0%
+represented by these components as
+ 
+
+ align:start position:0%
+represented by these components as
+written out here and an ordinary
+
+ align:start position:0%
+written out here and an ordinary
+ 
+
+ align:start position:0%
+written out here and an ordinary
+multiplication like this I can swap the
+
+ align:start position:0%
+multiplication like this I can swap the
+ 
+
+ align:start position:0%
+multiplication like this I can swap the
+order of I
+
+ align:start position:0%
+order of I
+ 
+
+ align:start position:0%
+order of I
+can just go ahead and swap the order of
+
+ align:start position:0%
+can just go ahead and swap the order of
+ 
+
+ align:start position:0%
+can just go ahead and swap the order of
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+very easily here so I'm gonna do is move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm doing sorry about that I misread my
+
+ align:start position:0%
+I'm doing sorry about that I misread my
+ 
+
+ align:start position:0%
+I'm doing sorry about that I misread my
+notes I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just gonna move the a on to the other
+
+ align:start position:0%
+just gonna move the a on to the other
+ 
+
+ align:start position:0%
+just gonna move the a on to the other
+side of my lambda oops
+
+ align:start position:0%
+side of my lambda oops
+ 
+
+ align:start position:0%
+side of my lambda oops
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then I'm going to use the fact that beta
+
+ align:start position:0%
+then I'm going to use the fact that beta
+ 
+
+ align:start position:0%
+then I'm going to use the fact that beta
+on my right-hand side is a dummy index
+
+ align:start position:0%
+on my right-hand side is a dummy index
+ 
+
+ align:start position:0%
+on my right-hand side is a dummy index
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in that final expression I wrote down
+
+ align:start position:0%
+in that final expression I wrote down
+ 
+
+ align:start position:0%
+in that final expression I wrote down
+over there beta is a dummy index and I'm
+
+ align:start position:0%
+over there beta is a dummy index and I'm
+ 
+
+ align:start position:0%
+over there beta is a dummy index and I'm
+free to adjust it to put it into a form
+
+ align:start position:0%
+free to adjust it to put it into a form
+ 
+
+ align:start position:0%
+free to adjust it to put it into a form
+that's more convenient for me so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's begin let me just write where I've
+
+ align:start position:0%
+let's begin let me just write where I've
+ 
+
+ align:start position:0%
+let's begin let me just write where I've
+got this equation right now over there
+
+ align:start position:0%
+got this equation right now over there
+ 
+
+ align:start position:0%
+got this equation right now over there
+so P alpha a alpha e alpha equals what
+
+ align:start position:0%
+so P alpha a alpha e alpha equals what
+ 
+
+ align:start position:0%
+so P alpha a alpha e alpha equals what
+I've got then is component a beta
+
+ align:start position:0%
+I've got then is component a beta
+ 
+
+ align:start position:0%
+I've got then is component a beta
+lambda bar beta mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar that so I'm gonna remap my dummy
+
+ align:start position:0%
+bar that so I'm gonna remap my dummy
+ 
+
+ align:start position:0%
+bar that so I'm gonna remap my dummy
+index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+reason I did that is I can now move this
+
+ align:start position:0%
+reason I did that is I can now move this
+ 
+
+ align:start position:0%
+reason I did that is I can now move this
+to the other side and factor out the a
+
+ align:start position:0%
+to the other side and factor out the a
+ 
+
+ align:start position:0%
+to the other side and factor out the a
+alpha okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see that I hope so see what I did was I
+
+ align:start position:0%
+see that I hope so see what I did was I
+ 
+
+ align:start position:0%
+see that I hope so see what I did was I
+arranged this so that I've isolated
+
+ align:start position:0%
+arranged this so that I've isolated
+ 
+
+ align:start position:0%
+arranged this so that I've isolated
+essentially only the transformation of
+
+ align:start position:0%
+essentially only the transformation of
+ 
+
+ align:start position:0%
+essentially only the transformation of
+the basis factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this equation has to hold no matter what
+
+ align:start position:0%
+this equation has to hold no matter what
+ 
+
+ align:start position:0%
+this equation has to hold no matter what
+vector I am working with right it's got
+
+ align:start position:0%
+vector I am working with right it's got
+ 
+
+ align:start position:0%
+vector I am working with right it's got
+a hold for an arbitrary a alpha so the
+
+ align:start position:0%
+a hold for an arbitrary a alpha so the
+ 
+
+ align:start position:0%
+a hold for an arbitrary a alpha so the
+only way that can happen
+
+ align:start position:0%
+only way that can happen
+ 
+
+ align:start position:0%
+only way that can happen
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means that my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation of basis vectors Oh basil
+
+ align:start position:0%
+transformation of basis vectors Oh basil
+ 
+
+ align:start position:0%
+transformation of basis vectors Oh basil
+wah that looks like this now
+
+ align:start position:0%
+wah that looks like this now
+ 
+
+ align:start position:0%
+wah that looks like this now
+in first inspection you're going to go
+
+ align:start position:0%
+in first inspection you're going to go
+ 
+
+ align:start position:0%
+in first inspection you're going to go
+ah that's exactly what we got for the
+
+ align:start position:0%
+ah that's exactly what we got for the
+ 
+
+ align:start position:0%
+ah that's exactly what we got for the
+components of the four vector caution
+
+ align:start position:0%
+components of the four vector caution
+ 
+
+ align:start position:0%
+components of the four vector caution
+and remind you it's actually on the
+
+ align:start position:0%
+and remind you it's actually on the
+ 
+
+ align:start position:0%
+and remind you it's actually on the
+board over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the
+
+ align:start position:0%
+okay the
+ 
+
+ align:start position:0%
+okay the
+bard component is playing a different
+
+ align:start position:0%
+bard component is playing a different
+ 
+
+ align:start position:0%
+bard component is playing a different
+role than the bard basis vector here
+
+ align:start position:0%
+role than the bard basis vector here
+ 
+
+ align:start position:0%
+role than the bard basis vector here
+okay if you want to get the bard basis
+
+ align:start position:0%
+okay if you want to get the bard basis
+ 
+
+ align:start position:0%
+okay if you want to get the bard basis
+vector from the unbarred basis factor
+
+ align:start position:0%
+vector from the unbarred basis factor
+ 
+
+ align:start position:0%
+vector from the unbarred basis factor
+you need to work with the inverse of
+
+ align:start position:0%
+you need to work with the inverse of
+ 
+
+ align:start position:0%
+you need to work with the inverse of
+this matrix that's what this is telling
+
+ align:start position:0%
+this matrix that's what this is telling
+ 
+
+ align:start position:0%
+this matrix that's what this is telling
+us here okay all
+
+ align:start position:0%
+us here okay all
+ 
+
+ align:start position:0%
+us here okay all
+that being said if you're just working
+
+ align:start position:0%
+that being said if you're just working
+ 
+
+ align:start position:0%
+that being said if you're just working
+through this and you're got you know
+
+ align:start position:0%
+through this and you're got you know
+ 
+
+ align:start position:0%
+through this and you're got you know
+your components set up and you're sort
+
+ align:start position:0%
+your components set up and you're sort
+ 
+
+ align:start position:0%
+your components set up and you're sort
+of hacking through it the algorithm for
+
+ align:start position:0%
+of hacking through it the algorithm for
+ 
+
+ align:start position:0%
+of hacking through it the algorithm for
+you to follow is actually simple really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all we're doing is lining up the indices
+
+ align:start position:0%
+all we're doing is lining up the indices
+ 
+
+ align:start position:0%
+all we're doing is lining up the indices
+we're summing over the ones that are
+
+ align:start position:0%
+we're summing over the ones that are
+ 
+
+ align:start position:0%
+we're summing over the ones that are
+repeated and requiring that those that
+
+ align:start position:0%
+repeated and requiring that those that
+ 
+
+ align:start position:0%
+repeated and requiring that those that
+are on both the left-hand side and the
+
+ align:start position:0%
+are on both the left-hand side and the
+ 
+
+ align:start position:0%
+are on both the left-hand side and the
+right-hand side appear and equal one
+
+ align:start position:0%
+right-hand side appear and equal one
+ 
+
+ align:start position:0%
+right-hand side appear and equal one
+another or
+
+ align:start position:0%
+another or
+ 
+
+ align:start position:0%
+another or
+there's an old professor mind like to
+
+ align:start position:0%
+there's an old professor mind like to
+ 
+
+ align:start position:0%
+there's an old professor mind like to
+say about 12 times a lecture line up the
+
+ align:start position:0%
+say about 12 times a lecture line up the
+ 
+
+ align:start position:0%
+say about 12 times a lecture line up the
+indices so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's essentially we're doing okay in
+
+ align:start position:0%
+that's essentially we're doing okay in
+ 
+
+ align:start position:0%
+that's essentially we're doing okay in
+this case I line up you know if I have
+
+ align:start position:0%
+this case I line up you know if I have
+ 
+
+ align:start position:0%
+this case I line up you know if I have
+my Lorentz transformation matrix with
+
+ align:start position:0%
+my Lorentz transformation matrix with
+ 
+
+ align:start position:0%
+my Lorentz transformation matrix with
+the bharden X up top and the unbarred
+
+ align:start position:0%
+the bharden X up top and the unbarred
+ 
+
+ align:start position:0%
+the bharden X up top and the unbarred
+down below boom I'll add the indices and
+
+ align:start position:0%
+down below boom I'll add the indices and
+ 
+
+ align:start position:0%
+down below boom I'll add the indices and
+that tells me what the unbarred basis
+
+ align:start position:0%
+that tells me what the unbarred basis
+ 
+
+ align:start position:0%
+that tells me what the unbarred basis
+components are from the bard once and
+
+ align:start position:0%
+components are from the bard once and
+ 
+
+ align:start position:0%
+components are from the bard once and
+vice versa for the components so
+
+ align:start position:0%
+vice versa for the components so
+ 
+
+ align:start position:0%
+vice versa for the components so
+with that basically as I just said that
+
+ align:start position:0%
+with that basically as I just said that
+ 
+
+ align:start position:0%
+with that basically as I just said that
+tells me if I actually want to get this
+
+ align:start position:0%
+tells me if I actually want to get this
+ 
+
+ align:start position:0%
+tells me if I actually want to get this
+guy given this guy I need to work with
+
+ align:start position:0%
+guy given this guy I need to work with
+ 
+
+ align:start position:0%
+guy given this guy I need to work with
+the inverse but
+
+ align:start position:0%
+the inverse but
+ 
+
+ align:start position:0%
+the inverse but
+there's a high so everyone in the back
+
+ align:start position:0%
+there's a high so everyone in the back
+ 
+
+ align:start position:0%
+there's a high so everyone in the back
+and see it so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+again is one of those places where you
+
+ align:start position:0%
+again is one of those places where you
+ 
+
+ align:start position:0%
+again is one of those places where you
+might be tempted right out
+
+ align:start position:0%
+might be tempted right out
+ 
+
+ align:start position:0%
+might be tempted right out
+of matrix and do a matrix inversion but
+
+ align:start position:0%
+of matrix and do a matrix inversion but
+ 
+
+ align:start position:0%
+of matrix and do a matrix inversion but
+before you do that remember this is
+
+ align:start position:0%
+before you do that remember this is
+ 
+
+ align:start position:0%
+before you do that remember this is
+physics okay the inverse is going to be
+
+ align:start position:0%
+physics okay the inverse is going to be
+ 
+
+ align:start position:0%
+physics okay the inverse is going to be
+the inverse matrix is going to be the
+
+ align:start position:0%
+the inverse matrix is going to be the
+ 
+
+ align:start position:0%
+the inverse matrix is going to be the
+one that does at least for certain
+
+ align:start position:0%
+one that does at least for certain
+ 
+
+ align:start position:0%
+one that does at least for certain
+quantities you know what what the what
+
+ align:start position:0%
+quantities you know what what the what
+ 
+
+ align:start position:0%
+quantities you know what what the what
+the Lorentz transformation does that it
+
+ align:start position:0%
+the Lorentz transformation does that it
+ 
+
+ align:start position:0%
+the Lorentz transformation does that it
+relates objects if I'm at rest if I
+
+ align:start position:0%
+relates objects if I'm at rest if I
+ 
+
+ align:start position:0%
+relates objects if I'm at rest if I
+consider myself at rest it tells me
+
+ align:start position:0%
+consider myself at rest it tells me
+ 
+
+ align:start position:0%
+consider myself at rest it tells me
+about things according to a frame that
+
+ align:start position:0%
+about things according to a frame that
+ 
+
+ align:start position:0%
+about things according to a frame that
+is moving with respect to me the inverse
+
+ align:start position:0%
+is moving with respect to me the inverse
+ 
+
+ align:start position:0%
+is moving with respect to me the inverse
+matrix does the opposite it would say to
+
+ align:start position:0%
+matrix does the opposite it would say to
+ 
+
+ align:start position:0%
+matrix does the opposite it would say to
+that person being at rest what the what
+
+ align:start position:0%
+that person being at rest what the what
+ 
+
+ align:start position:0%
+that person being at rest what the what
+is the matrix that tells them about
+
+ align:start position:0%
+is the matrix that tells them about
+ 
+
+ align:start position:0%
+is the matrix that tells them about
+things according to me and they see me
+
+ align:start position:0%
+things according to me and they see me
+ 
+
+ align:start position:0%
+things according to me and they see me
+moving with the exact same velocity but
+
+ align:start position:0%
+moving with the exact same velocity but
+ 
+
+ align:start position:0%
+moving with the exact same velocity but
+in the opposite direction so
+
+ align:start position:0%
+in the opposite direction so
+ 
+
+ align:start position:0%
+in the opposite direction so
+to get the inverse matrix to get the
+
+ align:start position:0%
+to get the inverse matrix to get the
+ 
+
+ align:start position:0%
+to get the inverse matrix to get the
+inverse Lorentz transformation what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we end up doing is we just reverse the
+
+ align:start position:0%
+we end up doing is we just reverse the
+ 
+
+ align:start position:0%
+we end up doing is we just reverse the
+velocity okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I have just wrote down for you and
+
+ align:start position:0%
+so I have just wrote down for you and
+ 
+
+ align:start position:0%
+so I have just wrote down for you and
+it's worth bearing in mind every one of
+
+ align:start position:0%
+it's worth bearing in mind every one of
+ 
+
+ align:start position:0%
+it's worth bearing in mind every one of
+these lambdas that it's there they are
+
+ align:start position:0%
+these lambdas that it's there they are
+ 
+
+ align:start position:0%
+these lambdas that it's there they are
+really functions right so my e alpha
+
+ align:start position:0%
+really functions right so my e alpha
+ 
+
+ align:start position:0%
+really functions right so my e alpha
+that I wrote down over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm gonna use an under tilde to denote a
+
+ align:start position:0%
+I'm gonna use an under tilde to denote a
+ 
+
+ align:start position:0%
+I'm gonna use an under tilde to denote a
+three factor okay
+
+ align:start position:0%
+three factor okay
+ 
+
+ align:start position:0%
+three factor okay
+in money for textbooks it's written with
+
+ align:start position:0%
+in money for textbooks it's written with
+ 
+
+ align:start position:0%
+in money for textbooks it's written with
+a boldface but that's hard to do on a
+
+ align:start position:0%
+a boldface but that's hard to do on a
+ 
+
+ align:start position:0%
+a boldface but that's hard to do on a
+blackboard okay so if I want to go the
+
+ align:start position:0%
+blackboard okay so if I want to go the
+ 
+
+ align:start position:0%
+blackboard okay so if I want to go the
+other direction well I just need to move
+
+ align:start position:0%
+other direction well I just need to move
+ 
+
+ align:start position:0%
+other direction well I just need to move
+the have the inverse transformation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I have that bear in mind I mean
+
+ align:start position:0%
+and I have that bear in mind I mean
+ 
+
+ align:start position:0%
+and I have that bear in mind I mean
+those are really the exact same matrices
+
+ align:start position:0%
+those are really the exact same matrices
+ 
+
+ align:start position:0%
+those are really the exact same matrices
+okay in terms of the function that I'm
+
+ align:start position:0%
+okay in terms of the function that I'm
+ 
+
+ align:start position:0%
+okay in terms of the function that I'm
+working with here I'm just flipping
+
+ align:start position:0%
+working with here I'm just flipping
+ 
+
+ align:start position:0%
+working with here I'm just flipping
+around the direction we're to get these
+
+ align:start position:0%
+around the direction we're to get these
+ 
+
+ align:start position:0%
+around the direction we're to get these
+things out okay so as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I said you might be tempted just to go
+
+ align:start position:0%
+I said you might be tempted just to go
+ 
+
+ align:start position:0%
+I said you might be tempted just to go
+ahead and do the
+
+ align:start position:0%
+ahead and do the
+ 
+
+ align:start position:0%
+ahead and do the
+matrix inversion let
+
+ align:start position:0%
+matrix inversion let
+ 
+
+ align:start position:0%
+matrix inversion let
+me just do a quick calculation to show
+
+ align:start position:0%
+me just do a quick calculation to show
+ 
+
+ align:start position:0%
+me just do a quick calculation to show
+you that that would work okay
+
+ align:start position:0%
+you that that would work okay
+ 
+
+ align:start position:0%
+you that that would work okay
+and the reason I'm doing this is I just
+
+ align:start position:0%
+and the reason I'm doing this is I just
+ 
+
+ align:start position:0%
+and the reason I'm doing this is I just
+want to quickly step through a
+
+ align:start position:0%
+want to quickly step through a
+ 
+
+ align:start position:0%
+want to quickly step through a
+particular step which is again sort of
+
+ align:start position:0%
+particular step which is again sort of
+ 
+
+ align:start position:0%
+particular step which is again sort of
+in the spirit of swatting mosquitoes
+
+ align:start position:0%
+in the spirit of swatting mosquitoes
+ 
+
+ align:start position:0%
+in the spirit of swatting mosquitoes
+with sledgehammers it's the kind of
+
+ align:start position:0%
+with sledgehammers it's the kind of
+ 
+
+ align:start position:0%
+with sledgehammers it's the kind of
+analysis that you're going to sort of
+
+ align:start position:0%
+analysis that you're going to sort of
+ 
+
+ align:start position:0%
+analysis that you're going to sort of
+have to do off to the side and now and
+
+ align:start position:0%
+have to do off to the side and now and
+ 
+
+ align:start position:0%
+have to do off to the side and now and
+again so
+
+ align:start position:0%
+again so
+ 
+
+ align:start position:0%
+again so
+given that I
+
+ align:start position:0%
+given that I
+ 
+
+ align:start position:0%
+given that I
+know a Alpha is let's see let's use beta
+
+ align:start position:0%
+know a Alpha is let's see let's use beta
+ 
+
+ align:start position:0%
+know a Alpha is let's see let's use beta
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+bar the
+
+ align:start position:0%
+bar the
+ 
+
+ align:start position:0%
+bar the
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+bar but I now know that I could write
+
+ align:start position:0%
+bar but I now know that I could write
+ 
+
+ align:start position:0%
+bar but I now know that I could write
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy as lambda she's a gamma beta
+
+ align:start position:0%
+guy as lambda she's a gamma beta
+ 
+
+ align:start position:0%
+guy as lambda she's a gamma beta
+bar minus
+
+ align:start position:0%
+bar minus
+ 
+
+ align:start position:0%
+bar minus
+V you
+
+ align:start position:0%
+V you
+ 
+
+ align:start position:0%
+V you
+have a direction now you look at that
+
+ align:start position:0%
+have a direction now you look at that
+ 
+
+ align:start position:0%
+have a direction now you look at that
+and you go oh look I'm actually summing
+
+ align:start position:0%
+and you go oh look I'm actually summing
+ 
+
+ align:start position:0%
+and you go oh look I'm actually summing
+over the betas there let's gather my
+
+ align:start position:0%
+over the betas there let's gather my
+ 
+
+ align:start position:0%
+over the betas there let's gather my
+terms a little bit differently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice I have unbarred basis vectors
+
+ align:start position:0%
+notice I have unbarred basis vectors
+ 
+
+ align:start position:0%
+notice I have unbarred basis vectors
+over here on the Left unbarred ones over
+
+ align:start position:0%
+over here on the Left unbarred ones over
+ 
+
+ align:start position:0%
+over here on the Left unbarred ones over
+here on the right a bunch of junk in
+
+ align:start position:0%
+here on the right a bunch of junk in
+ 
+
+ align:start position:0%
+here on the right a bunch of junk in
+these braces here in the middle the only
+
+ align:start position:0%
+these braces here in the middle the only
+ 
+
+ align:start position:0%
+these braces here in the middle the only
+way for that to work is if after summing
+
+ align:start position:0%
+way for that to work is if after summing
+ 
+
+ align:start position:0%
+way for that to work is if after summing
+over beta that bunch of junk is in
+
+ align:start position:0%
+over beta that bunch of junk is in
+ 
+
+ align:start position:0%
+over beta that bunch of junk is in
+matrix language we would say it's the
+
+ align:start position:0%
+matrix language we would say it's the
+ 
+
+ align:start position:0%
+matrix language we would say it's the
+identity matrix okay in component
+
+ align:start position:0%
+identity matrix okay in component
+ 
+
+ align:start position:0%
+identity matrix okay in component
+notation we're gonna call it the
+
+ align:start position:0%
+notation we're gonna call it the
+ 
+
+ align:start position:0%
+notation we're gonna call it the
+Kronecker Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a little aside if I started with the
+
+ align:start position:0%
+as a little aside if I started with the
+ 
+
+ align:start position:0%
+as a little aside if I started with the
+bard on the left side and the unbarred
+
+ align:start position:0%
+bard on the left side and the unbarred
+ 
+
+ align:start position:0%
+bard on the left side and the unbarred
+in the right hand side and did a similar
+
+ align:start position:0%
+in the right hand side and did a similar
+ 
+
+ align:start position:0%
+in the right hand side and did a similar
+analysis it would take you at this point
+
+ align:start position:0%
+analysis it would take you at this point
+ 
+
+ align:start position:0%
+analysis it would take you at this point
+now that you are all fully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expert in this kind of index
+
+ align:start position:0%
+expert in this kind of index
+ 
+
+ align:start position:0%
+expert in this kind of index
+manipulation it
+
+ align:start position:0%
+manipulation it
+ 
+
+ align:start position:0%
+manipulation it
+should take you no more than about a
+
+ align:start position:0%
+should take you no more than about a
+ 
+
+ align:start position:0%
+should take you no more than about a
+minute to demonstrate to yourself that
+
+ align:start position:0%
+minute to demonstrate to yourself that
+ 
+
+ align:start position:0%
+minute to demonstrate to yourself that
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+can get a chronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or Delta on the bard indices in a
+
+ align:start position:0%
+or Delta on the bard indices in a
+ 
+
+ align:start position:0%
+or Delta on the bard indices in a
+similar way just by using them in a
+
+ align:start position:0%
+similar way just by using them in a
+ 
+
+ align:start position:0%
+similar way just by using them in a
+slightly different order okay alright so
+
+ align:start position:0%
+slightly different order okay alright so
+ 
+
+ align:start position:0%
+slightly different order okay alright so
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+all still basically just formalism so
+
+ align:start position:0%
+all still basically just formalism so
+ 
+
+ align:start position:0%
+all still basically just formalism so
+I'm gonna start now doing a little bit
+
+ align:start position:0%
+I'm gonna start now doing a little bit
+ 
+
+ align:start position:0%
+I'm gonna start now doing a little bit
+of formalism that will
+
+ align:start position:0%
+of formalism that will
+ 
+
+ align:start position:0%
+of formalism that will
+very quickly sag into physics we can all
+
+ align:start position:0%
+very quickly sag into physics we can all
+ 
+
+ align:start position:0%
+very quickly sag into physics we can all
+take a deep sigh of relief and go ah
+
+ align:start position:0%
+take a deep sigh of relief and go ah
+ 
+
+ align:start position:0%
+take a deep sigh of relief and go ah
+okay something you can imagine measuring
+
+ align:start position:0%
+okay something you can imagine measuring
+ 
+
+ align:start position:0%
+okay something you can imagine measuring
+so that's nice so
+
+ align:start position:0%
+so that's nice so
+ 
+
+ align:start position:0%
+so that's nice so
+I have
+
+ align:start position:0%
+I have
+ 
+
+ align:start position:0%
+I have
+introduced four vectors I have
+
+ align:start position:0%
+introduced four vectors I have
+ 
+
+ align:start position:0%
+introduced four vectors I have
+introduced the basis vectors and their
+
+ align:start position:0%
+introduced the basis vectors and their
+ 
+
+ align:start position:0%
+introduced the basis vectors and their
+components I've really done anything
+
+ align:start position:0%
+components I've really done anything
+ 
+
+ align:start position:0%
+components I've really done anything
+with them yet so
+
+ align:start position:0%
+with them yet so
+ 
+
+ align:start position:0%
+with them yet so
+before we start doing things with them
+
+ align:start position:0%
+before we start doing things with them
+ 
+
+ align:start position:0%
+before we start doing things with them
+let's think about some operations that
+
+ align:start position:0%
+let's think about some operations that
+ 
+
+ align:start position:0%
+let's think about some operations that
+we can do with four vectors so the first
+
+ align:start position:0%
+we can do with four vectors so the first
+ 
+
+ align:start position:0%
+we can do with four vectors so the first
+one which I would like to introduce is a
+
+ align:start position:0%
+one which I would like to introduce is a
+ 
+
+ align:start position:0%
+one which I would like to introduce is a
+scalar product to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motivate the scalar product that I'm
+
+ align:start position:0%
+motivate the scalar product that I'm
+ 
+
+ align:start position:0%
+motivate the scalar product that I'm
+going to define in the same way that I
+
+ align:start position:0%
+going to define in the same way that I
+ 
+
+ align:start position:0%
+going to define in the same way that I
+defined for vectors as a quartet of
+
+ align:start position:0%
+defined for vectors as a quartet of
+ 
+
+ align:start position:0%
+defined for vectors as a quartet of
+numbers whose transformation properties
+
+ align:start position:0%
+numbers whose transformation properties
+ 
+
+ align:start position:0%
+numbers whose transformation properties
+are based on the transformation
+
+ align:start position:0%
+are based on the transformation
+ 
+
+ align:start position:0%
+are based on the transformation
+properties of the displacement I'm going
+
+ align:start position:0%
+properties of the displacement I'm going
+ 
+
+ align:start position:0%
+properties of the displacement I'm going
+to motivate a general scalar product
+
+ align:start position:0%
+to motivate a general scalar product
+ 
+
+ align:start position:0%
+to motivate a general scalar product
+between four vectors by a similar kind
+
+ align:start position:0%
+between four vectors by a similar kind
+ 
+
+ align:start position:0%
+between four vectors by a similar kind
+of quantity that is constructed from the
+
+ align:start position:0%
+of quantity that is constructed from the
+ 
+
+ align:start position:0%
+of quantity that is constructed from the
+displacement so let me recall a result
+
+ align:start position:0%
+displacement so let me recall a result
+ 
+
+ align:start position:0%
+displacement so let me recall a result
+that I hope is familiar from special
+
+ align:start position:0%
+that I hope is familiar from special
+ 
+
+ align:start position:0%
+that I hope is familiar from special
+relativity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+working in units where the speed of
+
+ align:start position:0%
+working in units where the speed of
+ 
+
+ align:start position:0%
+working in units where the speed of
+light is one you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are hopefully all familiar at the fact
+
+ align:start position:0%
+are hopefully all familiar at the fact
+ 
+
+ align:start position:0%
+are hopefully all familiar at the fact
+that this quantity is something that is
+
+ align:start position:0%
+that this quantity is something that is
+ 
+
+ align:start position:0%
+that this quantity is something that is
+invariance to all observers I really I
+
+ align:start position:0%
+invariance to all observers I really I
+ 
+
+ align:start position:0%
+invariance to all observers I really I
+did not use a represented by symbol
+
+ align:start position:0%
+did not use a represented by symbol
+ 
+
+ align:start position:0%
+did not use a represented by symbol
+there because no matter whose Delta T
+
+ align:start position:0%
+there because no matter whose Delta T
+ 
+
+ align:start position:0%
+there because no matter whose Delta T
+Delta X Delta Y Delta Z I use there they
+
+ align:start position:0%
+Delta X Delta Y Delta Z I use there they
+ 
+
+ align:start position:0%
+Delta X Delta Y Delta Z I use there they
+will all agree on the Delta s squared
+
+ align:start position:0%
+will all agree on the Delta s squared
+ 
+
+ align:start position:0%
+will all agree on the Delta s squared
+that comes out of us okay if I want to
+
+ align:start position:0%
+that comes out of us okay if I want to
+ 
+
+ align:start position:0%
+that comes out of us okay if I want to
+actually want me to write a few things
+
+ align:start position:0%
+actually want me to write a few things
+ 
+
+ align:start position:0%
+actually want me to write a few things
+down before I even think more so this is
+
+ align:start position:0%
+down before I even think more so this is
+ 
+
+ align:start position:0%
+down before I even think more so this is
+an invariant this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the same different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way it is the same in all Lorentz frames
+
+ align:start position:0%
+way it is the same in all Lorentz frames
+ 
+
+ align:start position:0%
+way it is the same in all Lorentz frames
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pick some observer get their delta T
+
+ align:start position:0%
+pick some observer get their delta T
+ 
+
+ align:start position:0%
+pick some observer get their delta T
+Delta X etc assemble
+
+ align:start position:0%
+Delta X etc assemble
+ 
+
+ align:start position:0%
+Delta X etc assemble
+Delta s squared pick a different
+
+ align:start position:0%
+Delta s squared pick a different
+ 
+
+ align:start position:0%
+Delta s squared pick a different
+observer do de Lorentz transformation
+
+ align:start position:0%
+observer do de Lorentz transformation
+ 
+
+ align:start position:0%
+observer do de Lorentz transformation
+assemble their delta T prime Delta X
+
+ align:start position:0%
+assemble their delta T prime Delta X
+ 
+
+ align:start position:0%
+assemble their delta T prime Delta X
+prime etc make that boom they all agree
+
+ align:start position:0%
+prime etc make that boom they all agree
+ 
+
+ align:start position:0%
+prime etc make that boom they all agree
+so we're going to use this to say you
+
+ align:start position:0%
+so we're going to use this to say you
+ 
+
+ align:start position:0%
+so we're going to use this to say you
+know what I'm gonna call that the
+
+ align:start position:0%
+know what I'm gonna call that the
+ 
+
+ align:start position:0%
+know what I'm gonna call that the
+inner product of the displacement vector
+
+ align:start position:0%
+inner product of the displacement vector
+ 
+
+ align:start position:0%
+inner product of the displacement vector
+with itself so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to call this Delta
+
+ align:start position:0%
+I'm going to call this Delta
+ 
+
+ align:start position:0%
+I'm going to call this Delta
+X dot it into Delta X ok so what this
+
+ align:start position:0%
+X dot it into Delta X ok so what this
+ 
+
+ align:start position:0%
+X dot it into Delta X ok so what this
+means is that built into my scalar
+
+ align:start position:0%
+means is that built into my scalar
+ 
+
+ align:start position:0%
+means is that built into my scalar
+product so
+
+ align:start position:0%
+product so
+ 
+
+ align:start position:0%
+product so
+if I write this as a particular observer
+
+ align:start position:0%
+if I write this as a particular observer
+ 
+
+ align:start position:0%
+if I write this as a particular observer
+would compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the scalar product that I'm going to
+
+ align:start position:0%
+is the scalar product that I'm going to
+ 
+
+ align:start position:0%
+is the scalar product that I'm going to
+define with respect to the displacement
+
+ align:start position:0%
+define with respect to the displacement
+ 
+
+ align:start position:0%
+define with respect to the displacement
+factor and this is usually the point
+
+ align:start position:0%
+factor and this is usually the point
+ 
+
+ align:start position:0%
+factor and this is usually the point
+where somebody in the class is thinking
+
+ align:start position:0%
+where somebody in the class is thinking
+ 
+
+ align:start position:0%
+where somebody in the class is thinking
+why is there a minus sign in front of
+
+ align:start position:0%
+why is there a minus sign in front of
+ 
+
+ align:start position:0%
+why is there a minus sign in front of
+the time like piece I can't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer that all I can say is that
+
+ align:start position:0%
+answer that all I can say is that
+ 
+
+ align:start position:0%
+answer that all I can say is that
+appears to be more than appears to be
+
+ align:start position:0%
+appears to be more than appears to be
+ 
+
+ align:start position:0%
+appears to be more than appears to be
+there's a whole freaking buttload of
+
+ align:start position:0%
+there's a whole freaking buttload of
+ 
+
+ align:start position:0%
+there's a whole freaking buttload of
+evidence it says how nature is assembled
+
+ align:start position:0%
+evidence it says how nature is assembled
+ 
+
+ align:start position:0%
+evidence it says how nature is assembled
+okay it's connected to the fact so the
+
+ align:start position:0%
+okay it's connected to the fact so the
+ 
+
+ align:start position:0%
+okay it's connected to the fact so the
+fact that all of my spatial directions
+
+ align:start position:0%
+fact that all of my spatial directions
+ 
+
+ align:start position:0%
+fact that all of my spatial directions
+are sort of entually the same sign but
+
+ align:start position:0%
+are sort of entually the same sign but
+ 
+
+ align:start position:0%
+are sort of entually the same sign but
+my time light direction is moving it has
+
+ align:start position:0%
+my time light direction is moving it has
+ 
+
+ align:start position:0%
+my time light direction is moving it has
+a different sign it's connected to the
+
+ align:start position:0%
+a different sign it's connected to the
+ 
+
+ align:start position:0%
+a different sign it's connected to the
+fact that I can easily move left and
+
+ align:start position:0%
+fact that I can easily move left and
+ 
+
+ align:start position:0%
+fact that I can easily move left and
+right front and back a little bit of
+
+ align:start position:0%
+right front and back a little bit of
+ 
+
+ align:start position:0%
+right front and back a little bit of
+effort I can move up and down but I
+
+ align:start position:0%
+effort I can move up and down but I
+ 
+
+ align:start position:0%
+effort I can move up and down but I
+cannot say oh crap I left my phone at
+
+ align:start position:0%
+cannot say oh crap I left my phone at
+ 
+
+ align:start position:0%
+cannot say oh crap I left my phone at
+home I'll go back fifteen minutes and
+
+ align:start position:0%
+home I'll go back fifteen minutes and
+ 
+
+ align:start position:0%
+home I'll go back fifteen minutes and
+pick it up right you cannot move back
+
+ align:start position:0%
+pick it up right you cannot move back
+ 
+
+ align:start position:0%
+pick it up right you cannot move back
+and forth in time time actually which is
+
+ align:start position:0%
+and forth in time time actually which is
+ 
+
+ align:start position:0%
+and forth in time time actually which is
+the time light component of this thing
+
+ align:start position:0%
+the time light component of this thing
+ 
+
+ align:start position:0%
+the time light component of this thing
+it enters into the geometry in a
+
+ align:start position:0%
+it enters into the geometry in a
+ 
+
+ align:start position:0%
+it enters into the geometry in a
+fundamentally different way from the
+
+ align:start position:0%
+fundamentally different way from the
+ 
+
+ align:start position:0%
+fundamentally different way from the
+spatial things and that's reflected in
+
+ align:start position:0%
+spatial things and that's reflected in
+ 
+
+ align:start position:0%
+spatial things and that's reflected in
+that minus sign anything
+
+ align:start position:0%
+that minus sign anything
+ 
+
+ align:start position:0%
+that minus sign anything
+deeper than that let's
+
+ align:start position:0%
+deeper than that let's
+ 
+
+ align:start position:0%
+deeper than that let's
+just say that we're probably not likely
+
+ align:start position:0%
+just say that we're probably not likely
+ 
+
+ align:start position:0%
+just say that we're probably not likely
+to get very far at that conversation
+
+ align:start position:0%
+to get very far at that conversation
+ 
+
+ align:start position:0%
+to get very far at that conversation
+depending on what kind of muscle
+
+ align:start position:0%
+depending on what kind of muscle
+ 
+
+ align:start position:0%
+depending on what kind of muscle
+relaxants you enjoy using on the weekend
+
+ align:start position:0%
+relaxants you enjoy using on the weekend
+ 
+
+ align:start position:0%
+relaxants you enjoy using on the weekend
+you might have some fun conversations
+
+ align:start position:0%
+you might have some fun conversations
+ 
+
+ align:start position:0%
+you might have some fun conversations
+about it but it is not something that
+
+ align:start position:0%
+about it but it is not something that
+ 
+
+ align:start position:0%
+about it but it is not something that
+you're really going to get very far with
+
+ align:start position:0%
+you're really going to get very far with
+ 
+
+ align:start position:0%
+you're really going to get very far with
+you just kind of have to accept it it's
+
+ align:start position:0%
+you just kind of have to accept it it's
+ 
+
+ align:start position:0%
+you just kind of have to accept it it's
+part of the built in geometry of nature
+
+ align:start position:0%
+part of the built in geometry of nature
+ 
+
+ align:start position:0%
+part of the built in geometry of nature
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this I am defining as the inner
+
+ align:start position:0%
+so this I am defining as the inner
+ 
+
+ align:start position:0%
+so this I am defining as the inner
+product with the of the displacement
+
+ align:start position:0%
+product with the of the displacement
+ 
+
+ align:start position:0%
+product with the of the displacement
+vector with itself i define vectors as
+
+ align:start position:0%
+vector with itself i define vectors as
+ 
+
+ align:start position:0%
+vector with itself i define vectors as
+having the same transformation property
+
+ align:start position:0%
+having the same transformation property
+ 
+
+ align:start position:0%
+having the same transformation property
+as the displacement vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can similarly define an inner product of
+
+ align:start position:0%
+can similarly define an inner product of
+ 
+
+ align:start position:0%
+can similarly define an inner product of
+a four vector with itself another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board a dot
+
+ align:start position:0%
+board a dot
+ 
+
+ align:start position:0%
+board a dot
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going to define this or rather I will
+
+ align:start position:0%
+going to define this or rather I will
+ 
+
+ align:start position:0%
+going to define this or rather I will
+say it is represented according to
+
+ align:start position:0%
+say it is represented according to
+ 
+
+ align:start position:0%
+say it is represented according to
+observer o as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus a0
+
+ align:start position:0%
+minus a0
+ 
+
+ align:start position:0%
+minus a0
+squared plus
+
+ align:start position:0%
+squared plus
+ 
+
+ align:start position:0%
+squared plus
+a1 squared plus
+
+ align:start position:0%
+a1 squared plus
+ 
+
+ align:start position:0%
+a1 squared plus
+a2 squared plus a3
+
+ align:start position:0%
+a2 squared plus a3
+ 
+
+ align:start position:0%
+a2 squared plus a3
+squared okay
+
+ align:start position:0%
+squared okay
+ 
+
+ align:start position:0%
+squared okay
+I realize there can be a little bit of
+
+ align:start position:0%
+I realize there can be a little bit of
+ 
+
+ align:start position:0%
+I realize there can be a little bit of
+ambiguity in the way I'm writing it here
+
+ align:start position:0%
+ambiguity in the way I'm writing it here
+ 
+
+ align:start position:0%
+ambiguity in the way I'm writing it here
+I you just have to if you ever confused
+
+ align:start position:0%
+I you just have to if you ever confused
+ 
+
+ align:start position:0%
+I you just have to if you ever confused
+just ask for clarification about whether
+
+ align:start position:0%
+just ask for clarification about whether
+ 
+
+ align:start position:0%
+just ask for clarification about whether
+I'm raising something to a power or
+
+ align:start position:0%
+I'm raising something to a power or
+ 
+
+ align:start position:0%
+I'm raising something to a power or
+whether it's an index label contacts
+
+ align:start position:0%
+whether it's an index label contacts
+ 
+
+ align:start position:0%
+whether it's an index label contacts
+usually makes it clear handwriting
+
+ align:start position:0%
+usually makes it clear handwriting
+ 
+
+ align:start position:0%
+usually makes it clear handwriting
+sometimes excuse contacts
+
+ align:start position:0%
+sometimes excuse contacts
+ 
+
+ align:start position:0%
+sometimes excuse contacts
+though the reason why I'm doing this and
+
+ align:start position:0%
+though the reason why I'm doing this and
+ 
+
+ align:start position:0%
+though the reason why I'm doing this and
+a real benefit of this is that whatever
+
+ align:start position:0%
+a real benefit of this is that whatever
+ 
+
+ align:start position:0%
+a real benefit of this is that whatever
+this quantity is because a has the same
+
+ align:start position:0%
+this quantity is because a has the same
+ 
+
+ align:start position:0%
+this quantity is because a has the same
+transformation properties of the
+
+ align:start position:0%
+transformation properties of the
+ 
+
+ align:start position:0%
+transformation properties of the
+displacement this must be a Lorentz
+
+ align:start position:0%
+displacement this must be a Lorentz
+ 
+
+ align:start position:0%
+displacement this must be a Lorentz
+invariant as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the underlying mathematics of Lorentz
+
+ align:start position:0%
+the underlying mathematics of Lorentz
+ 
+
+ align:start position:0%
+the underlying mathematics of Lorentz
+transformation doesn't care that I wrote
+
+ align:start position:0%
+transformation doesn't care that I wrote
+ 
+
+ align:start position:0%
+transformation doesn't care that I wrote
+a zero instead of Delta X here it
+
+ align:start position:0%
+a zero instead of Delta X here it
+ 
+
+ align:start position:0%
+a zero instead of Delta X here it
+doesn't care that I wrote a 1 instead of
+
+ align:start position:0%
+doesn't care that I wrote a 1 instead of
+ 
+
+ align:start position:0%
+doesn't care that I wrote a 1 instead of
+Delta X 1 etc okay it just knows that
+
+ align:start position:0%
+Delta X 1 etc okay it just knows that
+ 
+
+ align:start position:0%
+Delta X 1 etc okay it just knows that
+it's a thing that goes into that slot of
+
+ align:start position:0%
+it's a thing that goes into that slot of
+ 
+
+ align:start position:0%
+it's a thing that goes into that slot of
+Lorentz transformation so all observers
+
+ align:start position:0%
+Lorentz transformation so all observers
+ 
+
+ align:start position:0%
+Lorentz transformation so all observers
+this is how I represent it according to
+
+ align:start position:0%
+this is how I represent it according to
+ 
+
+ align:start position:0%
+this is how I represent it according to
+observer oh but all observers agree on
+
+ align:start position:0%
+observer oh but all observers agree on
+ 
+
+ align:start position:0%
+observer oh but all observers agree on
+that form um and as a consequence this
+
+ align:start position:0%
+that form um and as a consequence this
+ 
+
+ align:start position:0%
+that form um and as a consequence this
+is gonna be something that we exploit a
+
+ align:start position:0%
+is gonna be something that we exploit a
+ 
+
+ align:start position:0%
+is gonna be something that we exploit a
+lot ok even when we move beyond the sort
+
+ align:start position:0%
+lot ok even when we move beyond the sort
+ 
+
+ align:start position:0%
+lot ok even when we move beyond the sort
+of the simple geometry of special
+
+ align:start position:0%
+of the simple geometry of special
+ 
+
+ align:start position:0%
+of the simple geometry of special
+relativity a generalization of this will
+
+ align:start position:0%
+relativity a generalization of this will
+ 
+
+ align:start position:0%
+relativity a generalization of this will
+be extremely important for not an
+
+ align:start position:0%
+be extremely important for not an
+ 
+
+ align:start position:0%
+be extremely important for not an
+exaggeration to say everything so
+
+ align:start position:0%
+exaggeration to say everything so
+ 
+
+ align:start position:0%
+exaggeration to say everything so
+a little bit of terminology so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a dot
+
+ align:start position:0%
+if a dot
+ 
+
+ align:start position:0%
+if a dot
+a is negative and depending upon which
+
+ align:start position:0%
+a is negative and depending upon which
+ 
+
+ align:start position:0%
+a is negative and depending upon which
+is bigger a zero squared or the some of
+
+ align:start position:0%
+is bigger a zero squared or the some of
+ 
+
+ align:start position:0%
+is bigger a zero squared or the some of
+the other ones could very well be
+
+ align:start position:0%
+the other ones could very well be
+ 
+
+ align:start position:0%
+the other ones could very well be
+negative we say that a is a time like
+
+ align:start position:0%
+negative we say that a is a time like
+ 
+
+ align:start position:0%
+negative we say that a is a time like
+vector ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's traces back to the fact that if
+
+ align:start position:0%
+there's traces back to the fact that if
+ 
+
+ align:start position:0%
+there's traces back to the fact that if
+a were the displacement vector if the
+
+ align:start position:0%
+a were the displacement vector if the
+ 
+
+ align:start position:0%
+a were the displacement vector if the
+displacement the invariant interval were
+
+ align:start position:0%
+displacement the invariant interval were
+ 
+
+ align:start position:0%
+displacement the invariant interval were
+negative that would tell me that the two
+
+ align:start position:0%
+negative that would tell me that the two
+ 
+
+ align:start position:0%
+negative that would tell me that the two
+events which are the beginning in the
+
+ align:start position:0%
+events which are the beginning in the
+ 
+
+ align:start position:0%
+events which are the beginning in the
+end of the interval I could find a frame
+
+ align:start position:0%
+end of the interval I could find a frame
+ 
+
+ align:start position:0%
+end of the interval I could find a frame
+at which they are at the exact same
+
+ align:start position:0%
+at which they are at the exact same
+ 
+
+ align:start position:0%
+at which they are at the exact same
+location and are only separated in time
+
+ align:start position:0%
+location and are only separated in time
+ 
+
+ align:start position:0%
+location and are only separated in time
+ok in the same way this is basically
+
+ align:start position:0%
+ok in the same way this is basically
+ 
+
+ align:start position:0%
+ok in the same way this is basically
+saying that I can find a frame where
+
+ align:start position:0%
+saying that I can find a frame where
+ 
+
+ align:start position:0%
+saying that I can find a frame where
+this vector points parallel to observer
+
+ align:start position:0%
+this vector points parallel to observer
+ 
+
+ align:start position:0%
+this vector points parallel to observer
+at some observers time axis this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is positive a is
+
+ align:start position:0%
+is positive a is
+ 
+
+ align:start position:0%
+is positive a is
+spaced
+
+ align:start position:0%
+spaced
+ 
+
+ align:start position:0%
+spaced
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything I just said about time like
+
+ align:start position:0%
+everything I just said about time like
+ 
+
+ align:start position:0%
+everything I just said about time like
+lather rinse repeat but replace time
+
+ align:start position:0%
+lather rinse repeat but replace time
+ 
+
+ align:start position:0%
+lather rinse repeat but replace time
+with space good and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a dot a equals zero we
+
+ align:start position:0%
+if a dot a equals zero we
+ 
+
+ align:start position:0%
+if a dot a equals zero we
+say a is there's two words that are
+
+ align:start position:0%
+say a is there's two words that are
+ 
+
+ align:start position:0%
+say a is there's two words that are
+commonly used lights
+
+ align:start position:0%
+commonly used lights
+ 
+
+ align:start position:0%
+commonly used lights
+like or
+
+ align:start position:0%
+like or
+ 
+
+ align:start position:0%
+like or
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+null
+
+ align:start position:0%
+null
+ 
+
+ align:start position:0%
+null
+just traces back obviously to the zero
+
+ align:start position:0%
+just traces back obviously to the zero
+ 
+
+ align:start position:0%
+just traces back obviously to the zero
+light like is because this is a vector
+
+ align:start position:0%
+light like is because this is a vector
+ 
+
+ align:start position:0%
+light like is because this is a vector
+that could lie tangent to the trajectory
+
+ align:start position:0%
+that could lie tangent to the trajectory
+ 
+
+ align:start position:0%
+that could lie tangent to the trajectory
+that a light beam follows in space in
+
+ align:start position:0%
+that a light beam follows in space in
+ 
+
+ align:start position:0%
+that a light beam follows in space in
+space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+get some clean shock so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far I've only talked about this inner
+
+ align:start position:0%
+so far I've only talked about this inner
+ 
+
+ align:start position:0%
+so far I've only talked about this inner
+product this scalar product oh and by
+
+ align:start position:0%
+product this scalar product oh and by
+ 
+
+ align:start position:0%
+product this scalar product oh and by
+the way so with this we will often I'll
+
+ align:start position:0%
+the way so with this we will often I'll
+ 
+
+ align:start position:0%
+the way so with this we will often I'll
+use inner product and scalar product
+
+ align:start position:0%
+use inner product and scalar product
+ 
+
+ align:start position:0%
+use inner product and scalar product
+somewhat
+
+ align:start position:0%
+somewhat
+ 
+
+ align:start position:0%
+somewhat
+interchangeably but this allows me to
+
+ align:start position:0%
+interchangeably but this allows me to
+ 
+
+ align:start position:0%
+interchangeably but this allows me to
+reiterate a point I made in Tuesday's
+
+ align:start position:0%
+reiterate a point I made in Tuesday's
+ 
+
+ align:start position:0%
+reiterate a point I made in Tuesday's
+lecture when I say scalar scalar refers
+
+ align:start position:0%
+lecture when I say scalar scalar refers
+ 
+
+ align:start position:0%
+lecture when I say scalar scalar refers
+to a quantity which is it doesn't many
+
+ align:start position:0%
+to a quantity which is it doesn't many
+ 
+
+ align:start position:0%
+to a quantity which is it doesn't many
+components associated with it so in that
+
+ align:start position:0%
+components associated with it so in that
+ 
+
+ align:start position:0%
+components associated with it so in that
+sense it's familiar from your your
+
+ align:start position:0%
+sense it's familiar from your your
+ 
+
+ align:start position:0%
+sense it's familiar from your your
+intuition of you know not a vector but
+
+ align:start position:0%
+intuition of you know not a vector but
+ 
+
+ align:start position:0%
+intuition of you know not a vector but
+it has a deeper meaning in this course
+
+ align:start position:0%
+it has a deeper meaning in this course
+ 
+
+ align:start position:0%
+it has a deeper meaning in this course
+because I also want to be something that
+
+ align:start position:0%
+because I also want to be something that
+ 
+
+ align:start position:0%
+because I also want to be something that
+is invariant between reference frames so
+
+ align:start position:0%
+is invariant between reference frames so
+ 
+
+ align:start position:0%
+is invariant between reference frames so
+a dot a is the scalar product gives me a
+
+ align:start position:0%
+a dot a is the scalar product gives me a
+ 
+
+ align:start position:0%
+a dot a is the scalar product gives me a
+quantity that all observers agree on now
+
+ align:start position:0%
+quantity that all observers agree on now
+ 
+
+ align:start position:0%
+quantity that all observers agree on now
+I've only done scalar products of
+
+ align:start position:0%
+I've only done scalar products of
+ 
+
+ align:start position:0%
+I've only done scalar products of
+vectors and the displacement factor with
+
+ align:start position:0%
+vectors and the displacement factor with
+ 
+
+ align:start position:0%
+vectors and the displacement factor with
+themselves so a more general notion if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have vectors a and B then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will define the inner product between
+
+ align:start position:0%
+I will define the inner product between
+ 
+
+ align:start position:0%
+I will define the inner product between
+them as observed by oh that's
+
+ align:start position:0%
+them as observed by oh that's
+ 
+
+ align:start position:0%
+them as observed by oh that's
+constructed by observer oh rather like
+
+ align:start position:0%
+constructed by observer oh rather like
+ 
+
+ align:start position:0%
+constructed by observer oh rather like
+so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not hard to convince yourself given
+
+ align:start position:0%
+it's not hard to convince yourself given
+ 
+
+ align:start position:0%
+it's not hard to convince yourself given
+everything we've done so far that this
+
+ align:start position:0%
+everything we've done so far that this
+ 
+
+ align:start position:0%
+everything we've done so far that this
+quantity must also be invariant I'll
+
+ align:start position:0%
+quantity must also be invariant I'll
+ 
+
+ align:start position:0%
+quantity must also be invariant I'll
+sketch a really quick proof let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define let's say we have two four
+
+ align:start position:0%
+define let's say we have two four
+ 
+
+ align:start position:0%
+define let's say we have two four
+vectors a and Bing they're
+
+ align:start position:0%
+vectors a and Bing they're
+ 
+
+ align:start position:0%
+vectors a and Bing they're
+some by the linearity rules that apply
+
+ align:start position:0%
+some by the linearity rules that apply
+ 
+
+ align:start position:0%
+some by the linearity rules that apply
+to these vectors must also be a vector
+
+ align:start position:0%
+to these vectors must also be a vector
+ 
+
+ align:start position:0%
+to these vectors must also be a vector
+and so if I compute C
+
+ align:start position:0%
+and so if I compute C
+ 
+
+ align:start position:0%
+and so if I compute C
+dot C this is an invariant with
+
+ align:start position:0%
+dot C this is an invariant with
+ 
+
+ align:start position:0%
+dot C this is an invariant with
+a little bit of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit of labour that
+
+ align:start position:0%
+a little bit of labour that
+ 
+
+ align:start position:0%
+a little bit of labour that
+basically boils down to middle school
+
+ align:start position:0%
+basically boils down to middle school
+ 
+
+ align:start position:0%
+basically boils down to middle school
+algebra you can show that C dot C is a
+
+ align:start position:0%
+algebra you can show that C dot C is a
+ 
+
+ align:start position:0%
+algebra you can show that C dot C is a
+plus B dot B plus twice a dot B this is
+
+ align:start position:0%
+plus B dot B plus twice a dot B this is
+ 
+
+ align:start position:0%
+plus B dot B plus twice a dot B this is
+invariant this is invariant this is
+
+ align:start position:0%
+invariant this is invariant this is
+ 
+
+ align:start position:0%
+invariant this is invariant this is
+invariant and so this must be invariant
+
+ align:start position:0%
+invariant and so this must be invariant
+ 
+
+ align:start position:0%
+invariant and so this must be invariant
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is really useful for us okay
+
+ align:start position:0%
+this is really useful for us okay
+ 
+
+ align:start position:0%
+this is really useful for us okay
+because we now have a way now I've
+
+ align:start position:0%
+because we now have a way now I've
+ 
+
+ align:start position:0%
+because we now have a way now I've
+introduced these objects these geometric
+
+ align:start position:0%
+introduced these objects these geometric
+ 
+
+ align:start position:0%
+introduced these objects these geometric
+objects these four vectors we are going
+
+ align:start position:0%
+objects these four vectors we are going
+ 
+
+ align:start position:0%
+objects these four vectors we are going
+to use them in this class to describe
+
+ align:start position:0%
+to use them in this class to describe
+ 
+
+ align:start position:0%
+to use them in this class to describe
+quantities that are of interest to the
+
+ align:start position:0%
+quantities that are of interest to the
+ 
+
+ align:start position:0%
+quantities that are of interest to the
+physicist who wants to make measurements
+
+ align:start position:0%
+physicist who wants to make measurements
+ 
+
+ align:start position:0%
+physicist who wants to make measurements
+in space-time we've now learned what
+
+ align:start position:0%
+in space-time we've now learned what
+ 
+
+ align:start position:0%
+in space-time we've now learned what
+other things when you're doing stuff in
+
+ align:start position:0%
+other things when you're doing stuff in
+ 
+
+ align:start position:0%
+other things when you're doing stuff in
+relativity have to be careful who is
+
+ align:start position:0%
+relativity have to be careful who is
+ 
+
+ align:start position:0%
+relativity have to be careful who is
+measuring what okay what are the
+
+ align:start position:0%
+measuring what okay what are the
+ 
+
+ align:start position:0%
+measuring what okay what are the
+compounds that for vector as seen by
+
+ align:start position:0%
+compounds that for vector as seen by
+ 
+
+ align:start position:0%
+compounds that for vector as seen by
+this observer what about their friend
+
+ align:start position:0%
+this observer what about their friend
+ 
+
+ align:start position:0%
+this observer what about their friend
+who's jogging through the room and 3/4
+
+ align:start position:0%
+who's jogging through the room and 3/4
+ 
+
+ align:start position:0%
+who's jogging through the room and 3/4
+beetle light what about their friend
+
+ align:start position:0%
+beetle light what about their friend
+ 
+
+ align:start position:0%
+beetle light what about their friend
+who's dragging at 2/3 P lettin you know
+
+ align:start position:0%
+who's dragging at 2/3 P lettin you know
+ 
+
+ align:start position:0%
+who's dragging at 2/3 P lettin you know
+direction you know you have all these
+
+ align:start position:0%
+direction you know you have all these
+ 
+
+ align:start position:0%
+direction you know you have all these
+really annoying calculations that you
+
+ align:start position:0%
+really annoying calculations that you
+ 
+
+ align:start position:0%
+really annoying calculations that you
+can and sometimes have to do this gives
+
+ align:start position:0%
+can and sometimes have to do this gives
+ 
+
+ align:start position:0%
+can and sometimes have to do this gives
+us a way to get certain things that are
+
+ align:start position:0%
+us a way to get certain things that are
+ 
+
+ align:start position:0%
+us a way to get certain things that are
+invariant out of the situation that
+
+ align:start position:0%
+invariant out of the situation that
+ 
+
+ align:start position:0%
+invariant out of the situation that
+everyone is going to agree on and
+
+ align:start position:0%
+everyone is going to agree on and
+ 
+
+ align:start position:0%
+everyone is going to agree on and
+variance are our friends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+earlier today earlier in today's lecture
+
+ align:start position:0%
+earlier today earlier in today's lecture
+ 
+
+ align:start position:0%
+earlier today earlier in today's lecture
+I talked about how I can write my four
+
+ align:start position:0%
+I talked about how I can write my four
+ 
+
+ align:start position:0%
+I talked about how I can write my four
+vectors using the basis factors so
+
+ align:start position:0%
+vectors using the basis factors so
+ 
+
+ align:start position:0%
+vectors using the basis factors so
+another way of writing this so know what
+
+ align:start position:0%
+another way of writing this so know what
+ 
+
+ align:start position:0%
+another way of writing this so know what
+sort of annoying is every time I've
+
+ align:start position:0%
+sort of annoying is every time I've
+ 
+
+ align:start position:0%
+sort of annoying is every time I've
+actually written out the inner product I
+
+ align:start position:0%
+actually written out the inner product I
+ 
+
+ align:start position:0%
+actually written out the inner product I
+have used them represented by symbol I
+
+ align:start position:0%
+have used them represented by symbol I
+ 
+
+ align:start position:0%
+have used them represented by symbol I
+don't want that I want to have equal
+
+ align:start position:0%
+don't want that I want to have equal
+ 
+
+ align:start position:0%
+don't want that I want to have equal
+symbols in there damn it so let's
+
+ align:start position:0%
+symbols in there damn it so let's
+ 
+
+ align:start position:0%
+symbols in there damn it so let's
+take advantage of the fact that a big
+
+ align:start position:0%
+take advantage of the fact that a big
+ 
+
+ align:start position:0%
+take advantage of the fact that a big
+I know how to expand a and B using
+
+ align:start position:0%
+I know how to expand a and B using
+ 
+
+ align:start position:0%
+I know how to expand a and B using
+components and basis vectors and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again using the index notation I can
+
+ align:start position:0%
+again using the index notation I can
+ 
+
+ align:start position:0%
+again using the index notation I can
+just pull everything out and rearrange
+
+ align:start position:0%
+just pull everything out and rearrange
+ 
+
+ align:start position:0%
+just pull everything out and rearrange
+this a little bit whenever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get down to a point like this we now
+
+ align:start position:0%
+you get down to a point like this we now
+ 
+
+ align:start position:0%
+you get down to a point like this we now
+get to do what every mathematician loves
+
+ align:start position:0%
+get to do what every mathematician loves
+ 
+
+ align:start position:0%
+get to do what every mathematician loves
+to do give something a name I'm going to
+
+ align:start position:0%
+to do give something a name I'm going to
+ 
+
+ align:start position:0%
+to do give something a name I'm going to
+define the inner product of basis vector
+
+ align:start position:0%
+define the inner product of basis vector
+ 
+
+ align:start position:0%
+define the inner product of basis vector
+a with basis vector B to
+
+ align:start position:0%
+a with basis vector B to
+ 
+
+ align:start position:0%
+a with basis vector B to
+be a to index tensor ada alpha beta
+
+ align:start position:0%
+be a to index tensor ada alpha beta
+ 
+
+ align:start position:0%
+be a to index tensor ada alpha beta
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lovely about this is this is a totally
+
+ align:start position:0%
+lovely about this is this is a totally
+ 
+
+ align:start position:0%
+lovely about this is this is a totally
+frame invariant quantity we know that
+
+ align:start position:0%
+frame invariant quantity we know that
+ 
+
+ align:start position:0%
+frame invariant quantity we know that
+and so I've now found a way to write
+
+ align:start position:0%
+and so I've now found a way to write
+ 
+
+ align:start position:0%
+and so I've now found a way to write
+this using the components as something
+
+ align:start position:0%
+this using the components as something
+ 
+
+ align:start position:0%
+this using the components as something
+that gives me a result that is totally
+
+ align:start position:0%
+that gives me a result that is totally
+ 
+
+ align:start position:0%
+that gives me a result that is totally
+frame invariant now when you hack
+
+ align:start position:0%
+frame invariant now when you hack
+ 
+
+ align:start position:0%
+frame invariant now when you hack
+through a little of the algebra of this
+
+ align:start position:0%
+through a little of the algebra of this
+ 
+
+ align:start position:0%
+through a little of the algebra of this
+what you'll find is that the components
+
+ align:start position:0%
+what you'll find is that the components
+ 
+
+ align:start position:0%
+what you'll find is that the components
+of this metric oh shoot it out loud the
+
+ align:start position:0%
+of this metric oh shoot it out loud the
+ 
+
+ align:start position:0%
+of this metric oh shoot it out loud the
+components of this tensor which I will
+
+ align:start position:0%
+components of this tensor which I will
+ 
+
+ align:start position:0%
+components of this tensor which I will
+pretend you didn't hear me say that the
+
+ align:start position:0%
+pretend you didn't hear me say that the
+ 
+
+ align:start position:0%
+pretend you didn't hear me say that the
+compliance of this tensor has the
+
+ align:start position:0%
+compliance of this tensor has the
+ 
+
+ align:start position:0%
+compliance of this tensor has the
+following components I just
+
+ align:start position:0%
+following components I just
+ 
+
+ align:start position:0%
+following components I just
+answered or had the following values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is as I unfortunately gave away the plot
+
+ align:start position:0%
+is as I unfortunately gave away the plot
+ 
+
+ align:start position:0%
+is as I unfortunately gave away the plot
+this is in fact the metric that I set at
+
+ align:start position:0%
+this is in fact the metric that I set at
+ 
+
+ align:start position:0%
+this is in fact the metric that I set at
+the beginning is the quantity that I
+
+ align:start position:0%
+the beginning is the quantity that I
+ 
+
+ align:start position:0%
+the beginning is the quantity that I
+must associate with space-time in order
+
+ align:start position:0%
+must associate with space-time in order
+ 
+
+ align:start position:0%
+must associate with space-time in order
+for there to be a notion of distance
+
+ align:start position:0%
+for there to be a notion of distance
+ 
+
+ align:start position:0%
+for there to be a notion of distance
+between events I haven't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really said what a tensor is carefully
+
+ align:start position:0%
+really said what a tensor is carefully
+ 
+
+ align:start position:0%
+really said what a tensor is carefully
+yet I'm gonna make a more formal
+
+ align:start position:0%
+yet I'm gonna make a more formal
+ 
+
+ align:start position:0%
+yet I'm gonna make a more formal
+definition of this in just a moment but
+
+ align:start position:0%
+definition of this in just a moment but
+ 
+
+ align:start position:0%
+definition of this in just a moment but
+this is your first example of one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the way in which this actually
+
+ align:start position:0%
+and so the way in which this actually
+ 
+
+ align:start position:0%
+and so the way in which this actually
+gives me a notion of distance it's
+
+ align:start position:0%
+gives me a notion of distance it's
+ 
+
+ align:start position:0%
+gives me a notion of distance it's
+through this that I wrote down right
+
+ align:start position:0%
+through this that I wrote down right
+ 
+
+ align:start position:0%
+through this that I wrote down right
+here okay if I have two events in
+
+ align:start position:0%
+here okay if I have two events in
+ 
+
+ align:start position:0%
+here okay if I have two events in
+space-time that are
+
+ align:start position:0%
+space-time that are
+ 
+
+ align:start position:0%
+space-time that are
+separated by a displacement Delta X the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta s squared which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I obtained from this thing is
+
+ align:start position:0%
+I obtained from this thing is
+ 
+
+ align:start position:0%
+I obtained from this thing is
+fundamentally the notion of distance
+
+ align:start position:0%
+fundamentally the notion of distance
+ 
+
+ align:start position:0%
+fundamentally the notion of distance
+between those two events that I use and
+
+ align:start position:0%
+between those two events that I use and
+ 
+
+ align:start position:0%
+between those two events that I use and
+notice it's a little less normal of a
+
+ align:start position:0%
+notice it's a little less normal of a
+ 
+
+ align:start position:0%
+notice it's a little less normal of a
+distance than you're used to when you do
+
+ align:start position:0%
+distance than you're used to when you do
+ 
+
+ align:start position:0%
+distance than you're used to when you do
+sort of ordinary Euclidean geometry this
+
+ align:start position:0%
+sort of ordinary Euclidean geometry this
+ 
+
+ align:start position:0%
+sort of ordinary Euclidean geometry this
+is a distance whose square can be
+
+ align:start position:0%
+is a distance whose square can be
+ 
+
+ align:start position:0%
+is a distance whose square can be
+negative okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we like to say is that when you're
+
+ align:start position:0%
+what we like to say is that when you're
+ 
+
+ align:start position:0%
+what we like to say is that when you're
+working in special relativity you know
+
+ align:start position:0%
+working in special relativity you know
+ 
+
+ align:start position:0%
+working in special relativity you know
+that these are not it's not necessarily
+
+ align:start position:0%
+that these are not it's not necessarily
+ 
+
+ align:start position:0%
+that these are not it's not necessarily
+positive the distance between two events
+
+ align:start position:0%
+positive the distance between two events
+ 
+
+ align:start position:0%
+positive the distance between two events
+is not necessarily positive distance
+
+ align:start position:0%
+is not necessarily positive distance
+ 
+
+ align:start position:0%
+is not necessarily positive distance
+squared it's not necessarily positive
+
+ align:start position:0%
+squared it's not necessarily positive
+ 
+
+ align:start position:0%
+squared it's not necessarily positive
+definite okay if it's negative though it
+
+ align:start position:0%
+definite okay if it's negative though it
+ 
+
+ align:start position:0%
+definite okay if it's negative though it
+just means you know it sort of dominated
+
+ align:start position:0%
+just means you know it sort of dominated
+ 
+
+ align:start position:0%
+just means you know it sort of dominated
+by the time interval between them okay
+
+ align:start position:0%
+by the time interval between them okay
+ 
+
+ align:start position:0%
+by the time interval between them okay
+if it's positive you know it's dominated
+
+ align:start position:0%
+if it's positive you know it's dominated
+ 
+
+ align:start position:0%
+if it's positive you know it's dominated
+by the space interval between them if
+
+ align:start position:0%
+by the space interval between them if
+ 
+
+ align:start position:0%
+by the space interval between them if
+it's zero well you actually know you
+
+ align:start position:0%
+it's zero well you actually know you
+ 
+
+ align:start position:0%
+it's zero well you actually know you
+it's actually a little bit confusing at
+
+ align:start position:0%
+it's actually a little bit confusing at
+ 
+
+ align:start position:0%
+it's actually a little bit confusing at
+that point they could be in fact you
+
+ align:start position:0%
+that point they could be in fact you
+ 
+
+ align:start position:0%
+that point they could be in fact you
+know very widely separated in both space
+
+ align:start position:0%
+know very widely separated in both space
+ 
+
+ align:start position:0%
+know very widely separated in both space
+and time but in such a way that a light
+
+ align:start position:0%
+and time but in such a way that a light
+ 
+
+ align:start position:0%
+and time but in such a way that a light
+being could connect them okay so there's
+
+ align:start position:0%
+being could connect them okay so there's
+ 
+
+ align:start position:0%
+being could connect them okay so there's
+a lot of information encoded in that now
+
+ align:start position:0%
+a lot of information encoded in that now
+ 
+
+ align:start position:0%
+a lot of information encoded in that now
+as we move forward a second
+
+ align:start position:0%
+as we move forward a second
+ 
+
+ align:start position:0%
+as we move forward a second
+as we move forward we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gonna upgrade this okay so right now our
+
+ align:start position:0%
+gonna upgrade this okay so right now our
+ 
+
+ align:start position:0%
+gonna upgrade this okay so right now our
+metric is just this simple matrix of
+
+ align:start position:0%
+metric is just this simple matrix of
+ 
+
+ align:start position:0%
+metric is just this simple matrix of
+minus one zeros and ones one
+
+ align:start position:0%
+minus one zeros and ones one
+ 
+
+ align:start position:0%
+minus one zeros and ones one
+of the things that we're going to do is
+
+ align:start position:0%
+of the things that we're going to do is
+ 
+
+ align:start position:0%
+of the things that we're going to do is
+sort of a warm-up exercise so the more
+
+ align:start position:0%
+sort of a warm-up exercise so the more
+ 
+
+ align:start position:0%
+sort of a warm-up exercise so the more
+complicated things we're going to do
+
+ align:start position:0%
+complicated things we're going to do
+ 
+
+ align:start position:0%
+complicated things we're going to do
+later is we're gonna move away from
+
+ align:start position:0%
+later is we're gonna move away from
+ 
+
+ align:start position:0%
+later is we're gonna move away from
+special relativity and Cartesian
+
+ align:start position:0%
+special relativity and Cartesian
+ 
+
+ align:start position:0%
+special relativity and Cartesian
+coordinate it in polar coordinates
+
+ align:start position:0%
+coordinate it in polar coordinates
+ 
+
+ align:start position:0%
+coordinate it in polar coordinates
+that's gonna be kind of like a warm-up
+
+ align:start position:0%
+that's gonna be kind of like a warm-up
+ 
+
+ align:start position:0%
+that's gonna be kind of like a warm-up
+zone and so when we do that this we're
+
+ align:start position:0%
+zone and so when we do that this we're
+ 
+
+ align:start position:0%
+zone and so when we do that this we're
+always going to reserve Etta for the the
+
+ align:start position:0%
+always going to reserve Etta for the the
+ 
+
+ align:start position:0%
+always going to reserve Etta for the the
+metric of special relativity when I'm
+
+ align:start position:0%
+metric of special relativity when I'm
+ 
+
+ align:start position:0%
+metric of special relativity when I'm
+working in Cartesian coordinates okay
+
+ align:start position:0%
+working in Cartesian coordinates okay
+ 
+
+ align:start position:0%
+working in Cartesian coordinates okay
+just it's a great symbol to have for
+
+ align:start position:0%
+just it's a great symbol to have for
+ 
+
+ align:start position:0%
+just it's a great symbol to have for
+that and it's it's a useful thing to
+
+ align:start position:0%
+that and it's it's a useful thing to
+ 
+
+ align:start position:0%
+that and it's it's a useful thing to
+always have that definition in mind I
+
+ align:start position:0%
+always have that definition in mind I
+ 
+
+ align:start position:0%
+always have that definition in mind I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+continue to do special relativity but
+
+ align:start position:0%
+continue to do special relativity but
+ 
+
+ align:start position:0%
+continue to do special relativity but
+then working in coordinates that are you
+
+ align:start position:0%
+then working in coordinates that are you
+ 
+
+ align:start position:0%
+then working in coordinates that are you
+know spherical like or polar like or
+
+ align:start position:0%
+know spherical like or polar like or
+ 
+
+ align:start position:0%
+know spherical like or polar like or
+something like that then this is gonna
+
+ align:start position:0%
+something like that then this is gonna
+ 
+
+ align:start position:0%
+something like that then this is gonna
+become a function okay and what that is
+
+ align:start position:0%
+become a function okay and what that is
+ 
+
+ align:start position:0%
+become a function okay and what that is
+going to mean is that things like my
+
+ align:start position:0%
+going to mean is that things like my
+ 
+
+ align:start position:0%
+going to mean is that things like my
+little basis vectors are gonna have more
+
+ align:start position:0%
+little basis vectors are gonna have more
+ 
+
+ align:start position:0%
+little basis vectors are gonna have more
+complicated behavior ah later in the
+
+ align:start position:0%
+complicated behavior ah later in the
+ 
+
+ align:start position:0%
+complicated behavior ah later in the
+course we will then show that when
+
+ align:start position:0%
+course we will then show that when
+ 
+
+ align:start position:0%
+course we will then show that when
+gravity enters into the picture
+
+ align:start position:0%
+gravity enters into the picture
+ 
+
+ align:start position:0%
+gravity enters into the picture
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+the essence of gravity is going to be
+
+ align:start position:0%
+the essence of gravity is going to be
+ 
+
+ align:start position:0%
+the essence of gravity is going to be
+encoded in this thing as well in a way
+
+ align:start position:0%
+encoded in this thing as well in a way
+ 
+
+ align:start position:0%
+encoded in this thing as well in a way
+where again it's gonna be a function
+
+ align:start position:0%
+where again it's gonna be a function
+ 
+
+ align:start position:0%
+where again it's gonna be a function
+it's gonna vary as a function of space
+
+ align:start position:0%
+it's gonna vary as a function of space
+ 
+
+ align:start position:0%
+it's gonna vary as a function of space
+and time and the dynamics of gravity
+
+ align:start position:0%
+and time and the dynamics of gravity
+ 
+
+ align:start position:0%
+and time and the dynamics of gravity
+will be buried in that sort of funny
+
+ align:start position:0%
+will be buried in that sort of funny
+ 
+
+ align:start position:0%
+will be buried in that sort of funny
+that it really does just sort of start
+
+ align:start position:0%
+that it really does just sort of start
+ 
+
+ align:start position:0%
+that it really does just sort of start
+out I mean if you take that thing and
+
+ align:start position:0%
+out I mean if you take that thing and
+ 
+
+ align:start position:0%
+out I mean if you take that thing and
+you set delta T equals zero this is just
+
+ align:start position:0%
+you set delta T equals zero this is just
+ 
+
+ align:start position:0%
+you set delta T equals zero this is just
+the bloody Pythagorean theorem okay that
+
+ align:start position:0%
+the bloody Pythagorean theorem okay that
+ 
+
+ align:start position:0%
+the bloody Pythagorean theorem okay that
+is all this is put
+
+ align:start position:0%
+is all this is put
+ 
+
+ align:start position:0%
+is all this is put
+time back in and it's sort of is the
+
+ align:start position:0%
+time back in and it's sort of is the
+ 
+
+ align:start position:0%
+time back in and it's sort of is the
+generalization of Pythagoras to
+
+ align:start position:0%
+generalization of Pythagoras to
+ 
+
+ align:start position:0%
+generalization of Pythagoras to
+space-time and in fact we're going to
+
+ align:start position:0%
+space-time and in fact we're going to
+ 
+
+ align:start position:0%
+space-time and in fact we're going to
+take advantage of that and sort of
+
+ align:start position:0%
+take advantage of that and sort of
+ 
+
+ align:start position:0%
+take advantage of that and sort of
+define a geometry that looks like this
+
+ align:start position:0%
+define a geometry that looks like this
+ 
+
+ align:start position:0%
+define a geometry that looks like this
+as being flat in the same way that a
+
+ align:start position:0%
+as being flat in the same way that a
+ 
+
+ align:start position:0%
+as being flat in the same way that a
+board is flat and the Pythagorean
+
+ align:start position:0%
+board is flat and the Pythagorean
+ 
+
+ align:start position:0%
+board is flat and the Pythagorean
+theorem works perfectly on it then
+
+ align:start position:0%
+theorem works perfectly on it then
+ 
+
+ align:start position:0%
+theorem works perfectly on it then
+we're gonna start thinking about what
+
+ align:start position:0%
+we're gonna start thinking about what
+ 
+
+ align:start position:0%
+we're gonna start thinking about what
+happens when it becomes curved then you
+
+ align:start position:0%
+happens when it becomes curved then you
+ 
+
+ align:start position:0%
+happens when it becomes curved then you
+start thinking about things like what is
+
+ align:start position:0%
+start thinking about things like what is
+ 
+
+ align:start position:0%
+start thinking about things like what is
+the geometry on the surface of a sphere
+
+ align:start position:0%
+the geometry on the surface of a sphere
+ 
+
+ align:start position:0%
+the geometry on the surface of a sphere
+look like okay that's just sort of
+
+ align:start position:0%
+look like okay that's just sort of
+ 
+
+ align:start position:0%
+look like okay that's just sort of
+pointing ahead so I just throw that out
+
+ align:start position:0%
+pointing ahead so I just throw that out
+ 
+
+ align:start position:0%
+pointing ahead so I just throw that out
+you so that you get ready for some of
+
+ align:start position:0%
+you so that you get ready for some of
+ 
+
+ align:start position:0%
+you so that you get ready for some of
+the concepts that we will we'll be
+
+ align:start position:0%
+the concepts that we will we'll be
+ 
+
+ align:start position:0%
+the concepts that we will we'll be
+talking about soon so let me write this
+
+ align:start position:0%
+talking about soon so let me write this
+ 
+
+ align:start position:0%
+talking about soon so let me write this
+actually in terms of differentials sort
+
+ align:start position:0%
+actually in terms of differentials sort
+ 
+
+ align:start position:0%
+actually in terms of differentials sort
+of useful for what I want to say next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little differential if I have two
+
+ align:start position:0%
+a little differential if I have two
+ 
+
+ align:start position:0%
+a little differential if I have two
+events in space-time that are very close
+
+ align:start position:0%
+events in space-time that are very close
+ 
+
+ align:start position:0%
+events in space-time that are very close
+to one another I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can write them like so and what I've
+
+ align:start position:0%
+can write them like so and what I've
+ 
+
+ align:start position:0%
+can write them like so and what I've
+essentially done here is written DX
+
+ align:start position:0%
+essentially done here is written DX
+ 
+
+ align:start position:0%
+essentially done here is written DX
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+alpha e alpha ah before
+
+ align:start position:0%
+alpha e alpha ah before
+ 
+
+ align:start position:0%
+alpha e alpha ah before
+I get into some more sort of a couple of
+
+ align:start position:0%
+I get into some more sort of a couple of
+ 
+
+ align:start position:0%
+I get into some more sort of a couple of
+important physically important for
+
+ align:start position:0%
+important physically important for
+ 
+
+ align:start position:0%
+important physically important for
+vectors reason I did this is I want to
+
+ align:start position:0%
+vectors reason I did this is I want to
+ 
+
+ align:start position:0%
+vectors reason I did this is I want to
+make an important point about some
+
+ align:start position:0%
+make an important point about some
+ 
+
+ align:start position:0%
+make an important point about some
+notation and terminology that is used if
+
+ align:start position:0%
+notation and terminology that is used if
+ 
+
+ align:start position:0%
+notation and terminology that is used if
+it is the case that the displacement
+
+ align:start position:0%
+it is the case that the displacement
+ 
+
+ align:start position:0%
+it is the case that the displacement
+vector is related to the differentials
+
+ align:start position:0%
+vector is related to the differentials
+ 
+
+ align:start position:0%
+vector is related to the differentials
+of your coordinates like so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that e alpha
+
+ align:start position:0%
+say that e alpha
+ 
+
+ align:start position:0%
+say that e alpha
+is a coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis vector
+
+ align:start position:0%
+basis vector
+ 
+
+ align:start position:0%
+basis vector
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it does is it
+
+ align:start position:0%
+it does is it
+ 
+
+ align:start position:0%
+it does is it
+transforms a differential of your
+
+ align:start position:0%
+transforms a differential of your
+ 
+
+ align:start position:0%
+transforms a differential of your
+coordinate into a differential of a
+
+ align:start position:0%
+coordinate into a differential of a
+ 
+
+ align:start position:0%
+coordinate into a differential of a
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+vector in space-time now you may be
+
+ align:start position:0%
+vector in space-time now you may be
+ 
+
+ align:start position:0%
+vector in space-time now you may be
+thinking to yourself okay well what
+
+ align:start position:0%
+thinking to yourself okay well what
+ 
+
+ align:start position:0%
+thinking to yourself okay well what
+other kind can their big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is where my little spiel there a
+
+ align:start position:0%
+this is where my little spiel there a
+ 
+
+ align:start position:0%
+this is where my little spiel there a
+second ago about how we're gonna start
+
+ align:start position:0%
+second ago about how we're gonna start
+ 
+
+ align:start position:0%
+second ago about how we're gonna start
+looking at more complicated complicated
+
+ align:start position:0%
+looking at more complicated complicated
+ 
+
+ align:start position:0%
+looking at more complicated complicated
+things it's going to become important so
+
+ align:start position:0%
+things it's going to become important so
+ 
+
+ align:start position:0%
+things it's going to become important so
+when we're working in a Cartesian like
+
+ align:start position:0%
+when we're working in a Cartesian like
+ 
+
+ align:start position:0%
+when we're working in a Cartesian like
+coordinate system the fact that this is
+
+ align:start position:0%
+coordinate system the fact that this is
+ 
+
+ align:start position:0%
+coordinate system the fact that this is
+what we call a coordinate basis vector
+
+ align:start position:0%
+what we call a coordinate basis vector
+ 
+
+ align:start position:0%
+what we call a coordinate basis vector
+isn't very interesting suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was working in some kind of a
+
+ align:start position:0%
+I was working in some kind of a
+ 
+
+ align:start position:0%
+I was working in some kind of a
+curvilinear coordinate system okay
+
+ align:start position:0%
+curvilinear coordinate system okay
+ 
+
+ align:start position:0%
+curvilinear coordinate system okay
+circle coordinates and let's just focus
+
+ align:start position:0%
+circle coordinates and let's just focus
+ 
+
+ align:start position:0%
+circle coordinates and let's just focus
+on three space for a second so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I have write out a sort of analogous
+
+ align:start position:0%
+if I have write out a sort of analogous
+ 
+
+ align:start position:0%
+if I have write out a sort of analogous
+equation and
+
+ align:start position:0%
+equation and
+ 
+
+ align:start position:0%
+equation and
+curvilinear
+
+ align:start position:0%
+curvilinear
+ 
+
+ align:start position:0%
+curvilinear
+coordinates okay
+
+ align:start position:0%
+coordinates okay
+ 
+
+ align:start position:0%
+coordinates okay
+so here's the three space version of
+
+ align:start position:0%
+so here's the three space version of
+ 
+
+ align:start position:0%
+so here's the three space version of
+that now let's imagine that I equals 1
+
+ align:start position:0%
+that now let's imagine that I equals 1
+ 
+
+ align:start position:0%
+that now let's imagine that I equals 1
+corresponds to radius I equals 2 is
+
+ align:start position:0%
+corresponds to radius I equals 2 is
+ 
+
+ align:start position:0%
+corresponds to radius I equals 2 is
+Theta I equals 3 is Phi then
+
+ align:start position:0%
+Theta I equals 3 is Phi then
+ 
+
+ align:start position:0%
+Theta I equals 3 is Phi then
+this would be dr ER plus d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta D theta plus
+
+ align:start position:0%
+theta D theta plus
+ 
+
+ align:start position:0%
+theta D theta plus
+D Phi D Phi does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that disturb you at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this has two dimensions of lengths these
+
+ align:start position:0%
+this has two dimensions of lengths these
+ 
+
+ align:start position:0%
+this has two dimensions of lengths these
+have the dimensions of of angle in
+
+ align:start position:0%
+have the dimensions of of angle in
+ 
+
+ align:start position:0%
+have the dimensions of of angle in
+order for this to work er must be
+
+ align:start position:0%
+order for this to work er must be
+ 
+
+ align:start position:0%
+order for this to work er must be
+dimensionless data must have the
+
+ align:start position:0%
+dimensionless data must have the
+ 
+
+ align:start position:0%
+dimensionless data must have the
+dimensions of length D Phi must have the
+
+ align:start position:0%
+dimensions of length D Phi must have the
+ 
+
+ align:start position:0%
+dimensions of length D Phi must have the
+dimensions of length this is
+
+ align:start position:0%
+dimensions of length this is
+ 
+
+ align:start position:0%
+dimensions of length this is
+the form of a base this is what a
+
+ align:start position:0%
+the form of a base this is what a
+ 
+
+ align:start position:0%
+the form of a base this is what a
+coordinate basis looks like when I am
+
+ align:start position:0%
+coordinate basis looks like when I am
+ 
+
+ align:start position:0%
+coordinate basis looks like when I am
+dealing with well well we're gonna use
+
+ align:start position:0%
+dealing with well well we're gonna use
+ 
+
+ align:start position:0%
+dealing with well well we're gonna use
+this a lot in this thing so this is I
+
+ align:start position:0%
+this a lot in this thing so this is I
+ 
+
+ align:start position:0%
+this a lot in this thing so this is I
+introduce this right now because you are
+
+ align:start position:0%
+introduce this right now because you are
+ 
+
+ align:start position:0%
+introduce this right now because you are
+all probably looking at that and some
+
+ align:start position:0%
+all probably looking at that and some
+ 
+
+ align:start position:0%
+all probably looking at that and some
+small part of you inside is weeping
+
+ align:start position:0%
+small part of you inside is weeping
+ 
+
+ align:start position:0%
+small part of you inside is weeping
+because what you want me to write down
+
+ align:start position:0%
+because what you want me to write down
+ 
+
+ align:start position:0%
+because what you want me to write down
+is this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this looks like something you're used to
+
+ align:start position:0%
+this looks like something you're used to
+ 
+
+ align:start position:0%
+this looks like something you're used to
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I throw this out here right now just
+
+ align:start position:0%
+I throw this out here right now just
+ 
+
+ align:start position:0%
+I throw this out here right now just
+because I want to make sure you're aware
+
+ align:start position:0%
+because I want to make sure you're aware
+ 
+
+ align:start position:0%
+because I want to make sure you're aware
+that there are some equations and some
+
+ align:start position:0%
+that there are some equations and some
+ 
+
+ align:start position:0%
+that there are some equations and some
+foundational stuff you guys have been
+
+ align:start position:0%
+foundational stuff you guys have been
+ 
+
+ align:start position:0%
+foundational stuff you guys have been
+doing over the years particularly they
+
+ align:start position:0%
+doing over the years particularly they
+ 
+
+ align:start position:0%
+doing over the years particularly they
+shows up a lot when you've done a em out
+
+ align:start position:0%
+shows up a lot when you've done a em out
+ 
+
+ align:start position:0%
+shows up a lot when you've done a em out
+of a textbook like Purcell or Griffiths
+
+ align:start position:0%
+of a textbook like Purcell or Griffiths
+ 
+
+ align:start position:0%
+of a textbook like Purcell or Griffiths
+or Jackson because
+
+ align:start position:0%
+or Jackson because
+ 
+
+ align:start position:0%
+or Jackson because
+there's some derivative operators which
+
+ align:start position:0%
+there's some derivative operators which
+ 
+
+ align:start position:0%
+there's some derivative operators which
+are assuming that your basis factors are
+
+ align:start position:0%
+are assuming that your basis factors are
+ 
+
+ align:start position:0%
+are assuming that your basis factors are
+what we call orthonormal so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my e I hat here it
+
+ align:start position:0%
+my e I hat here it
+ 
+
+ align:start position:0%
+my e I hat here it
+is an orthonormal basis and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal basis is defined such that
+
+ align:start position:0%
+orthonormal basis is defined such that
+ 
+
+ align:start position:0%
+orthonormal basis is defined such that
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot product of any two members of this
+
+ align:start position:0%
+dot product of any two members of this
+ 
+
+ align:start position:0%
+dot product of any two members of this
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives me back the Kronecker Delta okay
+
+ align:start position:0%
+gives me back the Kronecker Delta okay
+ 
+
+ align:start position:0%
+gives me back the Kronecker Delta okay
+that is not necessarily the case when I
+
+ align:start position:0%
+that is not necessarily the case when I
+ 
+
+ align:start position:0%
+that is not necessarily the case when I
+work with a coordinate basis our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis has er
+
+ align:start position:0%
+basis has er
+ 
+
+ align:start position:0%
+basis has er
+er
+
+ align:start position:0%
+er
+ 
+
+ align:start position:0%
+er
+equals one yeah nice but when I do Ethan
+
+ align:start position:0%
+equals one yeah nice but when I do Ethan
+ 
+
+ align:start position:0%
+equals one yeah nice but when I do Ethan
+is ADA I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R squared he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+535 will be R squared sine squared theta
+
+ align:start position:0%
+535 will be R squared sine squared theta
+ 
+
+ align:start position:0%
+535 will be R squared sine squared theta
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what I'm gonna do when I start
+
+ align:start position:0%
+what I'm gonna do when I start
+ 
+
+ align:start position:0%
+what I'm gonna do when I start
+generalizing these things I'm gonna
+
+ align:start position:0%
+generalizing these things I'm gonna
+ 
+
+ align:start position:0%
+generalizing these things I'm gonna
+change my you know this this thing which
+
+ align:start position:0%
+change my you know this this thing which
+ 
+
+ align:start position:0%
+change my you know this this thing which
+I defined up here yeah
+
+ align:start position:0%
+I defined up here yeah
+ 
+
+ align:start position:0%
+I defined up here yeah
+yeah right here so when I said ADA alpha
+
+ align:start position:0%
+yeah right here so when I said ADA alpha
+ 
+
+ align:start position:0%
+yeah right here so when I said ADA alpha
+beta is e alpha D beta and I made it
+
+ align:start position:0%
+beta is e alpha D beta and I made it
+ 
+
+ align:start position:0%
+beta is e alpha D beta and I made it
+this thing I'm gonna generalize this and
+
+ align:start position:0%
+this thing I'm gonna generalize this and
+ 
+
+ align:start position:0%
+this thing I'm gonna generalize this and
+say at the dot product of any two basis
+
+ align:start position:0%
+say at the dot product of any two basis
+ 
+
+ align:start position:0%
+say at the dot product of any two basis
+vectors it gives me a more general
+
+ align:start position:0%
+vectors it gives me a more general
+ 
+
+ align:start position:0%
+vectors it gives me a more general
+notion of a metric tensor and the values
+
+ align:start position:0%
+notion of a metric tensor and the values
+ 
+
+ align:start position:0%
+notion of a metric tensor and the values
+in the metric tensor may be functions
+
+ align:start position:0%
+in the metric tensor may be functions
+ 
+
+ align:start position:0%
+in the metric tensor may be functions
+like this okay right
+
+ align:start position:0%
+like this okay right
+ 
+
+ align:start position:0%
+like this okay right
+now throw that out there you know this
+
+ align:start position:0%
+now throw that out there you know this
+ 
+
+ align:start position:0%
+now throw that out there you know this
+might be sort of like just like a peak
+
+ align:start position:0%
+might be sort of like just like a peak
+ 
+
+ align:start position:0%
+might be sort of like just like a peak
+of the horrors that lie ahead okay we're
+
+ align:start position:0%
+of the horrors that lie ahead okay we're
+ 
+
+ align:start position:0%
+of the horrors that lie ahead okay we're
+not gonna worry about this too much just
+
+ align:start position:0%
+not gonna worry about this too much just
+ 
+
+ align:start position:0%
+not gonna worry about this too much just
+yet but I want you to be prepared for
+
+ align:start position:0%
+yet but I want you to be prepared for
+ 
+
+ align:start position:0%
+yet but I want you to be prepared for
+this in particular it's really useful to
+
+ align:start position:0%
+this in particular it's really useful to
+ 
+
+ align:start position:0%
+this in particular it's really useful to
+have this notion of a coordinate basis
+
+ align:start position:0%
+have this notion of a coordinate basis
+ 
+
+ align:start position:0%
+have this notion of a coordinate basis
+versus an orthonormal basis in your head
+
+ align:start position:0%
+versus an orthonormal basis in your head
+ 
+
+ align:start position:0%
+versus an orthonormal basis in your head
+okay we're going to start defining some
+
+ align:start position:0%
+okay we're going to start defining some
+ 
+
+ align:start position:0%
+okay we're going to start defining some
+derivative operations soon in fact
+
+ align:start position:0%
+derivative operations soon in fact
+ 
+
+ align:start position:0%
+derivative operations soon in fact
+probably won't get to them today but
+
+ align:start position:0%
+probably won't get to them today but
+ 
+
+ align:start position:0%
+probably won't get to them today but
+they will be present when we start doing
+
+ align:start position:0%
+they will be present when we start doing
+ 
+
+ align:start position:0%
+they will be present when we start doing
+a lecture 3 and there's a couple results
+
+ align:start position:0%
+a lecture 3 and there's a couple results
+ 
+
+ align:start position:0%
+a lecture 3 and there's a couple results
+that come up where everyone's sort of
+
+ align:start position:0%
+that come up where everyone's sort of
+ 
+
+ align:start position:0%
+that come up where everyone's sort of
+like wait I knew that the divergence had
+
+ align:start position:0%
+like wait I knew that the divergence had
+ 
+
+ align:start position:0%
+like wait I knew that the divergence had
+a factor of R on that derivative there
+
+ align:start position:0%
+a factor of R on that derivative there
+ 
+
+ align:start position:0%
+a factor of R on that derivative there
+where'd it go okay it's because we're
+
+ align:start position:0%
+where'd it go okay it's because we're
+ 
+
+ align:start position:0%
+where'd it go okay it's because we're
+not working in an orthonormal basis all
+
+ align:start position:0%
+not working in an orthonormal basis all
+ 
+
+ align:start position:0%
+not working in an orthonormal basis all
+right I'm
+
+ align:start position:0%
+right I'm
+ 
+
+ align:start position:0%
+right I'm
+a little sick of math so let's do a
+
+ align:start position:0%
+a little sick of math so let's do a
+ 
+
+ align:start position:0%
+a little sick of math so let's do a
+little fist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far the actual only physical
+
+ align:start position:0%
+so far the actual only physical
+ 
+
+ align:start position:0%
+so far the actual only physical
+four-vector
+
+ align:start position:0%
+four-vector
+ 
+
+ align:start position:0%
+four-vector
+that I've introduced is a displacement
+
+ align:start position:0%
+that I've introduced is a displacement
+ 
+
+ align:start position:0%
+that I've introduced is a displacement
+factor from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the displacement factor it's really easy
+
+ align:start position:0%
+the displacement factor it's really easy
+ 
+
+ align:start position:0%
+the displacement factor it's really easy
+to make and apply the first and simplest
+
+ align:start position:0%
+to make and apply the first and simplest
+ 
+
+ align:start position:0%
+to make and apply the first and simplest
+important for brach four-vector which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is known as the floor velocity this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tells me the rate of displacement of an
+
+ align:start position:0%
+tells me the rate of displacement of an
+ 
+
+ align:start position:0%
+tells me the rate of displacement of an
+observer as this person moves through
+
+ align:start position:0%
+observer as this person moves through
+ 
+
+ align:start position:0%
+observer as this person moves through
+space time per
+
+ align:start position:0%
+space time per
+ 
+
+ align:start position:0%
+space time per
+unit and we're going to be careful about
+
+ align:start position:0%
+unit and we're going to be careful about
+ 
+
+ align:start position:0%
+unit and we're going to be careful about
+this in this class D
+
+ align:start position:0%
+this in this class D
+ 
+
+ align:start position:0%
+this in this class D
+tau is the time interval
+
+ align:start position:0%
+tau is the time interval
+ 
+
+ align:start position:0%
+tau is the time interval
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+measured
+
+ align:start position:0%
+measured
+ 
+
+ align:start position:0%
+measured
+along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the trajectory of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observer with four velocity U in
+
+ align:start position:0%
+observer with four velocity U in
+ 
+
+ align:start position:0%
+observer with four velocity U in
+other words it's a very long-winded way
+
+ align:start position:0%
+other words it's a very long-winded way
+ 
+
+ align:start position:0%
+other words it's a very long-winded way
+of saying it it's an interval of proper
+
+ align:start position:0%
+of saying it it's an interval of proper
+ 
+
+ align:start position:0%
+of saying it it's an interval of proper
+time in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+English the word property and it sounds
+
+ align:start position:0%
+English the word property and it sounds
+ 
+
+ align:start position:0%
+English the word property and it sounds
+very like whoo I don't want to use
+
+ align:start position:0%
+very like whoo I don't want to use
+ 
+
+ align:start position:0%
+very like whoo I don't want to use
+improper time I better use that but this
+
+ align:start position:0%
+improper time I better use that but this
+ 
+
+ align:start position:0%
+improper time I better use that but this
+actually I think it comes from French it
+
+ align:start position:0%
+actually I think it comes from French it
+ 
+
+ align:start position:0%
+actually I think it comes from French it
+just refers to the fact that it's one's
+
+ align:start position:0%
+just refers to the fact that it's one's
+ 
+
+ align:start position:0%
+just refers to the fact that it's one's
+own time
+
+ align:start position:0%
+own time
+ 
+
+ align:start position:0%
+own time
+apparently in German people say eigen
+
+ align:start position:0%
+apparently in German people say eigen
+ 
+
+ align:start position:0%
+apparently in German people say eigen
+site so you know there's a couple of
+
+ align:start position:0%
+site so you know there's a couple of
+ 
+
+ align:start position:0%
+site so you know there's a couple of
+different words for a minute so but
+
+ align:start position:0%
+different words for a minute so but
+ 
+
+ align:start position:0%
+different words for a minute so but
+proper time is what we use in
+
+ align:start position:0%
+proper time is what we use in
+ 
+
+ align:start position:0%
+proper time is what we use in
+special relativity if we see someone
+
+ align:start position:0%
+special relativity if we see someone
+ 
+
+ align:start position:0%
+special relativity if we see someone
+going by with constant velocity a
+
+ align:start position:0%
+going by with constant velocity a
+ 
+
+ align:start position:0%
+going by with constant velocity a
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+observer who sees you know we're here in
+
+ align:start position:0%
+observer who sees you know we're here in
+ 
+
+ align:start position:0%
+observer who sees you know we're here in
+the room someone comes through therefore
+
+ align:start position:0%
+the room someone comes through therefore
+ 
+
+ align:start position:0%
+the room someone comes through therefore
+velocity is U we would see therefore
+
+ align:start position:0%
+velocity is U we would see therefore
+ 
+
+ align:start position:0%
+velocity is U we would see therefore
+velocity to have the components gamma
+
+ align:start position:0%
+velocity to have the components gamma
+ 
+
+ align:start position:0%
+velocity to have the components gamma
+gamma V okay where gamma I'll remind you
+
+ align:start position:0%
+gamma V okay where gamma I'll remind you
+ 
+
+ align:start position:0%
+gamma V okay where gamma I'll remind you
+is the special relativistic Lorentz
+
+ align:start position:0%
+is the special relativistic Lorentz
+ 
+
+ align:start position:0%
+is the special relativistic Lorentz
+factor and
+
+ align:start position:0%
+factor and
+ 
+
+ align:start position:0%
+factor and
+I'll remind you again we've set speed of
+
+ align:start position:0%
+I'll remind you again we've set speed of
+ 
+
+ align:start position:0%
+I'll remind you again we've set speed of
+light to one a very
+
+ align:start position:0%
+light to one a very
+ 
+
+ align:start position:0%
+light to one a very
+useful thing which we're actually going
+
+ align:start position:0%
+useful thing which we're actually going
+ 
+
+ align:start position:0%
+useful thing which we're actually going
+to take advantage of quite a bit is that
+
+ align:start position:0%
+to take advantage of quite a bit is that
+ 
+
+ align:start position:0%
+to take advantage of quite a bit is that
+in the rest frame of you
+
+ align:start position:0%
+in the rest frame of you
+ 
+
+ align:start position:0%
+in the rest frame of you
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the rest frame of you or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should say the observer who's for
+
+ align:start position:0%
+I should say the observer who's for
+ 
+
+ align:start position:0%
+I should say the observer who's for
+velocity is you okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just have one in a time like direction
+
+ align:start position:0%
+just have one in a time like direction
+ 
+
+ align:start position:0%
+just have one in a time like direction
+see if you want to put your factors back
+
+ align:start position:0%
+see if you want to put your factors back
+ 
+
+ align:start position:0%
+see if you want to put your factors back
+into there and that's basically saying
+
+ align:start position:0%
+into there and that's basically saying
+ 
+
+ align:start position:0%
+into there and that's basically saying
+that the person is standing still but
+
+ align:start position:0%
+that the person is standing still but
+ 
+
+ align:start position:0%
+that the person is standing still but
+moving through time okay because
+
+ align:start position:0%
+moving through time okay because
+ 
+
+ align:start position:0%
+moving through time okay because
+you are always moving through time all
+
+ align:start position:0%
+you are always moving through time all
+ 
+
+ align:start position:0%
+you are always moving through time all
+right ah from the floor velocity for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an observer who has a foreign object I
+
+ align:start position:0%
+an observer who has a foreign object I
+ 
+
+ align:start position:0%
+an observer who has a foreign object I
+should say who has some mass we can
+
+ align:start position:0%
+should say who has some mass we can
+ 
+
+ align:start position:0%
+should say who has some mass we can
+easily define the for momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where this em is known as the rest mass
+
+ align:start position:0%
+where this em is known as the rest mass
+ 
+
+ align:start position:0%
+where this em is known as the rest mass
+of this object worth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a bit of description here you will often
+
+ align:start position:0%
+a bit of description here you will often
+ 
+
+ align:start position:0%
+a bit of description here you will often
+see particularly in some older textbooks
+
+ align:start position:0%
+see particularly in some older textbooks
+ 
+
+ align:start position:0%
+see particularly in some older textbooks
+that discuss special relativity people
+
+ align:start position:0%
+that discuss special relativity people
+ 
+
+ align:start position:0%
+that discuss special relativity people
+like to talk about the relativistic mass
+
+ align:start position:0%
+like to talk about the relativistic mass
+ 
+
+ align:start position:0%
+like to talk about the relativistic mass
+okay and that comes from the fact that
+
+ align:start position:0%
+okay and that comes from the fact that
+ 
+
+ align:start position:0%
+okay and that comes from the fact that
+if I write out what this thing looks
+
+ align:start position:0%
+if I write out what this thing looks
+ 
+
+ align:start position:0%
+if I write out what this thing looks
+like according to some particular
+
+ align:start position:0%
+like according to some particular
+ 
+
+ align:start position:0%
+like according to some particular
+observer you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have this gamma M entering into both of
+
+ align:start position:0%
+have this gamma M entering into both of
+ 
+
+ align:start position:0%
+have this gamma M entering into both of
+the complex and so older textbooks often
+
+ align:start position:0%
+the complex and so older textbooks often
+ 
+
+ align:start position:0%
+the complex and so older textbooks often
+call gamma M the relativistic mass
+
+ align:start position:0%
+call gamma M the relativistic mass
+ 
+
+ align:start position:0%
+call gamma M the relativistic mass
+that's not really the way people have
+
+ align:start position:0%
+that's not really the way people have
+ 
+
+ align:start position:0%
+that's not really the way people have
+over the course of the past couple
+
+ align:start position:0%
+over the course of the past couple
+ 
+
+ align:start position:0%
+over the course of the past couple
+decades they've moved away from that and
+
+ align:start position:0%
+decades they've moved away from that and
+ 
+
+ align:start position:0%
+decades they've moved away from that and
+it's just more useful to focus on the
+
+ align:start position:0%
+it's just more useful to focus on the
+ 
+
+ align:start position:0%
+it's just more useful to focus on the
+rest mass is the only really meaningful
+
+ align:start position:0%
+rest mass is the only really meaningful
+ 
+
+ align:start position:0%
+rest mass is the only really meaningful
+mass because as we'll see in a moment
+
+ align:start position:0%
+mass because as we'll see in a moment
+ 
+
+ align:start position:0%
+mass because as we'll see in a moment
+it's a Lorentz invariant okay we'll see
+
+ align:start position:0%
+it's a Lorentz invariant okay we'll see
+ 
+
+ align:start position:0%
+it's a Lorentz invariant okay we'll see
+wow that is in literally about three
+
+ align:start position:0%
+wow that is in literally about three
+ 
+
+ align:start position:0%
+wow that is in literally about three
+minutes and so what we're instead going
+
+ align:start position:0%
+minutes and so what we're instead going
+ 
+
+ align:start position:0%
+minutes and so what we're instead going
+to say is that as seen by some
+
+ align:start position:0%
+to say is that as seen by some
+ 
+
+ align:start position:0%
+to say is that as seen by some
+particular observer this
+
+ align:start position:0%
+particular observer this
+ 
+
+ align:start position:0%
+particular observer this
+has a time light component that is the
+
+ align:start position:0%
+has a time light component that is the
+ 
+
+ align:start position:0%
+has a time light component that is the
+energy that that observer would measure
+
+ align:start position:0%
+energy that that observer would measure
+ 
+
+ align:start position:0%
+energy that that observer would measure
+and a space set of space like compliance
+
+ align:start position:0%
+and a space set of space like compliance
+ 
+
+ align:start position:0%
+and a space set of space like compliance
+that are the momentum that that observer
+
+ align:start position:0%
+that are the momentum that that observer
+ 
+
+ align:start position:0%
+that are the momentum that that observer
+will measure so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we get a bit of important physics
+
+ align:start position:0%
+where we get a bit of important physics
+ 
+
+ align:start position:0%
+where we get a bit of important physics
+out of all this stuff is by coupling
+
+ align:start position:0%
+out of all this stuff is by coupling
+ 
+
+ align:start position:0%
+out of all this stuff is by coupling
+these two four vectors to the scalar
+
+ align:start position:0%
+these two four vectors to the scalar
+ 
+
+ align:start position:0%
+these two four vectors to the scalar
+product that we made up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one if you do you dot you
+
+ align:start position:0%
+the first one if you do you dot you
+ 
+
+ align:start position:0%
+the first one if you do you dot you
+queen to any observer that's it's going
+
+ align:start position:0%
+queen to any observer that's it's going
+ 
+
+ align:start position:0%
+queen to any observer that's it's going
+to be minus gamma squared plus
+
+ align:start position:0%
+to be minus gamma squared plus
+ 
+
+ align:start position:0%
+to be minus gamma squared plus
+gamma squared V squared and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+about twenty seconds worth of analysis
+
+ align:start position:0%
+about twenty seconds worth of analysis
+ 
+
+ align:start position:0%
+about twenty seconds worth of analysis
+you can find that this is always equal
+
+ align:start position:0%
+you can find that this is always equal
+ 
+
+ align:start position:0%
+you can find that this is always equal
+to minus
+
+ align:start position:0%
+to minus
+ 
+
+ align:start position:0%
+to minus
+one actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's an even trickier way to do this
+
+ align:start position:0%
+there's an even trickier way to do this
+ 
+
+ align:start position:0%
+there's an even trickier way to do this
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+I evaluate this in the rest frame of the
+
+ align:start position:0%
+I evaluate this in the rest frame of the
+ 
+
+ align:start position:0%
+I evaluate this in the rest frame of the
+observer who's for velocity is U well in
+
+ align:start position:0%
+observer who's for velocity is U well in
+ 
+
+ align:start position:0%
+observer who's for velocity is U well in
+the rest frame V is 0 and gamma is one
+
+ align:start position:0%
+the rest frame V is 0 and gamma is one
+ 
+
+ align:start position:0%
+the rest frame V is 0 and gamma is one
+and I get minus one and this is an
+
+ align:start position:0%
+and I get minus one and this is an
+ 
+
+ align:start position:0%
+and I get minus one and this is an
+invariant so whatever I get in that
+
+ align:start position:0%
+invariant so whatever I get in that
+ 
+
+ align:start position:0%
+invariant so whatever I get in that
+particular frame must be obtained in all
+
+ align:start position:0%
+particular frame must be obtained in all
+ 
+
+ align:start position:0%
+particular frame must be obtained in all
+frames that's a trick we're gonna use
+
+ align:start position:0%
+frames that's a trick we're gonna use
+ 
+
+ align:start position:0%
+frames that's a trick we're gonna use
+over and over and over again sometimes
+
+ align:start position:0%
+over and over and over again sometimes
+ 
+
+ align:start position:0%
+over and over and over again sometimes
+you can identify you know you get some
+
+ align:start position:0%
+you can identify you know you get some
+ 
+
+ align:start position:0%
+you can identify you know you get some
+kind of god-awful expression that just
+
+ align:start position:0%
+kind of god-awful expression that just
+ 
+
+ align:start position:0%
+kind of god-awful expression that just
+makes you want to vomit but then you go
+
+ align:start position:0%
+makes you want to vomit but then you go
+ 
+
+ align:start position:0%
+makes you want to vomit but then you go
+wait a minute what would this look like
+
+ align:start position:0%
+wait a minute what would this look like
+ 
+
+ align:start position:0%
+wait a minute what would this look like
+in frame blah blah blah you sort of
+
+ align:start position:0%
+in frame blah blah blah you sort of
+ 
+
+ align:start position:0%
+in frame blah blah blah you sort of
+think about some particular frame and in
+
+ align:start position:0%
+think about some particular frame and in
+ 
+
+ align:start position:0%
+think about some particular frame and in
+that frame it may simplify and if it
+
+ align:start position:0%
+that frame it may simplify and if it
+ 
+
+ align:start position:0%
+that frame it may simplify and if it
+does and it's a frame invariant quantity
+
+ align:start position:0%
+does and it's a frame invariant quantity
+ 
+
+ align:start position:0%
+does and it's a frame invariant quantity
+Mazel Tov you have just basically won
+
+ align:start position:0%
+Mazel Tov you have just basically won
+ 
+
+ align:start position:0%
+Mazel Tov you have just basically won
+the lottery you've got this all taken
+
+ align:start position:0%
+the lottery you've got this all taken
+ 
+
+ align:start position:0%
+the lottery you've got this all taken
+care of go on with your life so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for velocity has a scalar prior to
+
+ align:start position:0%
+for velocity has a scalar prior to
+ 
+
+ align:start position:0%
+for velocity has a scalar prior to
+itself that is always minus one okay how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the for momentum well the for
+
+ align:start position:0%
+about the for momentum well the for
+ 
+
+ align:start position:0%
+about the for momentum well the for
+momentum is just for velocity x max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's just minus M squared but we also
+
+ align:start position:0%
+that's just minus M squared but we also
+ 
+
+ align:start position:0%
+that's just minus M squared but we also
+know it's related to these two other
+
+ align:start position:0%
+know it's related to these two other
+ 
+
+ align:start position:0%
+know it's related to these two other
+quantities which are important in
+
+ align:start position:0%
+quantities which are important in
+ 
+
+ align:start position:0%
+quantities which are important in
+physics this is related to the energy
+
+ align:start position:0%
+physics this is related to the energy
+ 
+
+ align:start position:0%
+physics this is related to the energy
+into the momentum so this is also equal
+
+ align:start position:0%
+into the momentum so this is also equal
+ 
+
+ align:start position:0%
+into the momentum so this is also equal
+to minus e squared plus so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the ordinary three the
+
+ align:start position:0%
+this is the ordinary three the
+ 
+
+ align:start position:0%
+this is the ordinary three the
+magnitude of the three vector part of
+
+ align:start position:0%
+magnitude of the three vector part of
+ 
+
+ align:start position:0%
+magnitude of the three vector part of
+this thing as measured by the observer
+
+ align:start position:0%
+this thing as measured by the observer
+ 
+
+ align:start position:0%
+this thing as measured by the observer
+who who breaks up the floor momentum in
+
+ align:start position:0%
+who who breaks up the floor momentum in
+ 
+
+ align:start position:0%
+who who breaks up the floor momentum in
+this way so what this means is I can
+
+ align:start position:0%
+this way so what this means is I can
+ 
+
+ align:start position:0%
+this way so what this means is I can
+manipulate this guy around a little bit
+
+ align:start position:0%
+manipulate this guy around a little bit
+ 
+
+ align:start position:0%
+manipulate this guy around a little bit
+here anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who works in particle physics is
+
+ align:start position:0%
+who works in particle physics is
+ 
+
+ align:start position:0%
+who works in particle physics is
+presumably familiar with this equation
+
+ align:start position:0%
+presumably familiar with this equation
+ 
+
+ align:start position:0%
+presumably familiar with this equation
+sometimes it appears with the piece
+
+ align:start position:0%
+sometimes it appears with the piece
+ 
+
+ align:start position:0%
+sometimes it appears with the piece
+where it moved on to the other side if
+
+ align:start position:0%
+where it moved on to the other side if
+ 
+
+ align:start position:0%
+where it moved on to the other side if
+it looks a little bit unfamiliar to you
+
+ align:start position:0%
+it looks a little bit unfamiliar to you
+ 
+
+ align:start position:0%
+it looks a little bit unfamiliar to you
+let me put some factors of C back in
+
+ align:start position:0%
+let me put some factors of C back in
+ 
+
+ align:start position:0%
+let me put some factors of C back in
+this so
+
+ align:start position:0%
+this so
+ 
+
+ align:start position:0%
+this so
+remember we have set C equal to one when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+you put it back in that's
+
+ align:start position:0%
+you put it back in that's
+ 
+
+ align:start position:0%
+you put it back in that's
+what this is so it drops out of this in
+
+ align:start position:0%
+what this is so it drops out of this in
+ 
+
+ align:start position:0%
+what this is so it drops out of this in
+a very very simple way one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the uses of this and many
+
+ align:start position:0%
+of the uses of this and many
+ 
+
+ align:start position:0%
+of the uses of this and many
+of you have done exercises presumably in
+
+ align:start position:0%
+of you have done exercises presumably in
+ 
+
+ align:start position:0%
+of you have done exercises presumably in
+some previous study that does this and
+
+ align:start position:0%
+some previous study that does this and
+ 
+
+ align:start position:0%
+some previous study that does this and
+ob8 one
+
+ align:start position:0%
+ob8 one
+ 
+
+ align:start position:0%
+ob8 one
+exercise on the pset that was just
+
+ align:start position:0%
+exercise on the pset that was just
+ 
+
+ align:start position:0%
+exercise on the pset that was just
+posted where you exploit this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a key bit of physics the reason why we
+
+ align:start position:0%
+a key bit of physics the reason why we
+ 
+
+ align:start position:0%
+a key bit of physics the reason why we
+care about for momentum is it's in one
+
+ align:start position:0%
+care about for momentum is it's in one
+ 
+
+ align:start position:0%
+care about for momentum is it's in one
+mathematical object allows us to combine
+
+ align:start position:0%
+mathematical object allows us to combine
+ 
+
+ align:start position:0%
+mathematical object allows us to combine
+conservation of energy and conservation
+
+ align:start position:0%
+conservation of energy and conservation
+ 
+
+ align:start position:0%
+conservation of energy and conservation
+of momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conservation of 4-momentum puts
+
+ align:start position:0%
+conservation of 4-momentum puts
+ 
+
+ align:start position:0%
+conservation of 4-momentum puts
+both conservation of energy and
+
+ align:start position:0%
+both conservation of energy and
+ 
+
+ align:start position:0%
+both conservation of energy and
+conservation of momentum into one
+
+ align:start position:0%
+conservation of momentum into one
+ 
+
+ align:start position:0%
+conservation of momentum into one
+mathematical object so if I have n
+
+ align:start position:0%
+mathematical object so if I have n
+ 
+
+ align:start position:0%
+mathematical object so if I have n
+particles that interact then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total for momentum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conserved in the interaction okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah
+
+ align:start position:0%
+so yeah
+ 
+
+ align:start position:0%
+so yeah
+we talked a little bit more about this
+
+ align:start position:0%
+we talked a little bit more about this
+ 
+
+ align:start position:0%
+we talked a little bit more about this
+and then just sort of quickly move on so
+
+ align:start position:0%
+and then just sort of quickly move on so
+ 
+
+ align:start position:0%
+and then just sort of quickly move on so
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+combining this with the fact that we are
+
+ align:start position:0%
+combining this with the fact that we are
+ 
+
+ align:start position:0%
+combining this with the fact that we are
+free to change our reference frames
+
+ align:start position:0%
+free to change our reference frames
+ 
+
+ align:start position:0%
+free to change our reference frames
+often it gives us a trick that allows us
+
+ align:start position:0%
+often it gives us a trick that allows us
+ 
+
+ align:start position:0%
+often it gives us a trick that allows us
+to really simplify a lot of analysis so
+
+ align:start position:0%
+to really simplify a lot of analysis so
+ 
+
+ align:start position:0%
+to really simplify a lot of analysis so
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have n particles that are sort of
+
+ align:start position:0%
+I have n particles that are sort of
+ 
+
+ align:start position:0%
+I have n particles that are sort of
+swarming around and doing some horrible
+
+ align:start position:0%
+swarming around and doing some horrible
+ 
+
+ align:start position:0%
+swarming around and doing some horrible
+horrible bit of business but
+
+ align:start position:0%
+horrible bit of business but
+ 
+
+ align:start position:0%
+horrible bit of business but
+I need to study and I need to have a
+
+ align:start position:0%
+I need to study and I need to have a
+ 
+
+ align:start position:0%
+I need to study and I need to have a
+good understanding of we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can often vastly simplify our algebra by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choosing a special and very convenient
+
+ align:start position:0%
+choosing a special and very convenient
+ 
+
+ align:start position:0%
+choosing a special and very convenient
+frame of reference in which to do our
+
+ align:start position:0%
+frame of reference in which to do our
+ 
+
+ align:start position:0%
+frame of reference in which to do our
+analysis choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the center of momentum frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is the frame in which that
+
+ align:start position:0%
+this is the frame in which that
+ 
+
+ align:start position:0%
+this is the frame in which that
+pea tote socio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+em center of momentum has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero spatial momentum okay in that frame
+
+ align:start position:0%
+zero spatial momentum okay in that frame
+ 
+
+ align:start position:0%
+zero spatial momentum okay in that frame
+you have just as much momentum going to
+
+ align:start position:0%
+you have just as much momentum going to
+ 
+
+ align:start position:0%
+you have just as much momentum going to
+the left as going to the right just as
+
+ align:start position:0%
+the left as going to the right just as
+ 
+
+ align:start position:0%
+the left as going to the right just as
+much going forward is going backwards as
+
+ align:start position:0%
+much going forward is going backwards as
+ 
+
+ align:start position:0%
+much going forward is going backwards as
+much going up is going down and so this
+
+ align:start position:0%
+much going up is going down and so this
+ 
+
+ align:start position:0%
+much going up is going down and so this
+tends out to be so it the classic
+
+ align:start position:0%
+tends out to be so it the classic
+ 
+
+ align:start position:0%
+tends out to be so it the classic
+example of where this is really useful
+
+ align:start position:0%
+example of where this is really useful
+ 
+
+ align:start position:0%
+example of where this is really useful
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+you are studying particle
+
+ align:start position:0%
+you are studying particle
+ 
+
+ align:start position:0%
+you are studying particle
+collisions and you're looking at things
+
+ align:start position:0%
+collisions and you're looking at things
+ 
+
+ align:start position:0%
+collisions and you're looking at things
+like the production of new particles so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imagine you've got particle
+
+ align:start position:0%
+imagine you've got particle
+ 
+
+ align:start position:0%
+imagine you've got particle
+a with some four momentum PA coming in
+
+ align:start position:0%
+a with some four momentum PA coming in
+ 
+
+ align:start position:0%
+a with some four momentum PA coming in
+like this particle B's got some four
+
+ align:start position:0%
+like this particle B's got some four
+ 
+
+ align:start position:0%
+like this particle B's got some four
+momentum coming in like this these
+
+ align:start position:0%
+momentum coming in like this these
+ 
+
+ align:start position:0%
+momentum coming in like this these
+guys collide and they do so I work in
+
+ align:start position:0%
+guys collide and they do so I work in
+ 
+
+ align:start position:0%
+guys collide and they do so I work in
+the center of momentum frame I might
+
+ align:start position:0%
+the center of momentum frame I might
+ 
+
+ align:start position:0%
+the center of momentum frame I might
+want to just calculate the energy at
+
+ align:start position:0%
+want to just calculate the energy at
+ 
+
+ align:start position:0%
+want to just calculate the energy at
+which they just happen to produce some
+
+ align:start position:0%
+which they just happen to produce some
+ 
+
+ align:start position:0%
+which they just happen to produce some
+new pair
+
+ align:start position:0%
+new pair
+ 
+
+ align:start position:0%
+new pair
+of particles at rest that we like to
+
+ align:start position:0%
+of particles at rest that we like to
+ 
+
+ align:start position:0%
+of particles at rest that we like to
+find the threshold for this particular
+
+ align:start position:0%
+find the threshold for this particular
+ 
+
+ align:start position:0%
+find the threshold for this particular
+creation process okay so you're they're
+
+ align:start position:0%
+creation process okay so you're they're
+ 
+
+ align:start position:0%
+creation process okay so you're they're
+gonna play with one problem on the piece
+
+ align:start position:0%
+gonna play with one problem on the piece
+ 
+
+ align:start position:0%
+gonna play with one problem on the piece
+that it's kind of like that let's
+
+ align:start position:0%
+that it's kind of like that let's
+ 
+
+ align:start position:0%
+that it's kind of like that let's
+see I think I will do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all the dot products that I have been
+
+ align:start position:0%
+all the dot products that I have been
+ 
+
+ align:start position:0%
+all the dot products that I have been
+talking about so far have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+been a dot product of a four vector with
+
+ align:start position:0%
+been a dot product of a four vector with
+ 
+
+ align:start position:0%
+been a dot product of a four vector with
+itself okay I did you dot into you I did
+
+ align:start position:0%
+itself okay I did you dot into you I did
+ 
+
+ align:start position:0%
+itself okay I did you dot into you I did
+P dotted into P I invented a frame in
+
+ align:start position:0%
+P dotted into P I invented a frame in
+ 
+
+ align:start position:0%
+P dotted into P I invented a frame in
+which P has a particularly simple form
+
+ align:start position:0%
+which P has a particularly simple form
+ 
+
+ align:start position:0%
+which P has a particularly simple form
+and then when you actually do some the
+
+ align:start position:0%
+and then when you actually do some the
+ 
+
+ align:start position:0%
+and then when you actually do some the
+analysis you would probably take that P
+
+ align:start position:0%
+analysis you would probably take that P
+ 
+
+ align:start position:0%
+analysis you would probably take that P
+tote and dot it into itself I haven't
+
+ align:start position:0%
+tote and dot it into itself I haven't
+ 
+
+ align:start position:0%
+tote and dot it into itself I haven't
+done anything that looks at you know the
+
+ align:start position:0%
+done anything that looks at you know the
+ 
+
+ align:start position:0%
+done anything that looks at you know the
+crossing between these two things okay
+
+ align:start position:0%
+crossing between these two things okay
+ 
+
+ align:start position:0%
+crossing between these two things okay
+dotting one into the other need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to go through a very useful result that
+
+ align:start position:0%
+to go through a very useful result that
+ 
+
+ align:start position:0%
+to go through a very useful result that
+follows by combining P with you they're
+
+ align:start position:0%
+follows by combining P with you they're
+ 
+
+ align:start position:0%
+follows by combining P with you they're
+very specific notion of P in a very
+
+ align:start position:0%
+very specific notion of P in a very
+ 
+
+ align:start position:0%
+very specific notion of P in a very
+specific notion of you so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's let key be
+
+ align:start position:0%
+let's let key be
+ 
+
+ align:start position:0%
+let's let key be
+the full row mentum of a particle I'll
+
+ align:start position:0%
+the full row mentum of a particle I'll
+ 
+
+ align:start position:0%
+the full row mentum of a particle I'll
+call it egg let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let you be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the four velocity not
+
+ align:start position:0%
+the four velocity not
+ 
+
+ align:start position:0%
+the four velocity not
+of a but the four velocity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observer oh ok
+
+ align:start position:0%
+observer oh ok
+ 
+
+ align:start position:0%
+observer oh ok
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so particle a might be a muon that was
+
+ align:start position:0%
+so particle a might be a muon that was
+ 
+
+ align:start position:0%
+so particle a might be a muon that was
+creating upper atmosphere and it's
+
+ align:start position:0%
+creating upper atmosphere and it's
+ 
+
+ align:start position:0%
+creating upper atmosphere and it's
+crashing through our room right now
+
+ align:start position:0%
+crashing through our room right now
+ 
+
+ align:start position:0%
+crashing through our room right now
+observer Oh might be you're hyperactive
+
+ align:start position:0%
+observer Oh might be you're hyperactive
+ 
+
+ align:start position:0%
+observer Oh might be you're hyperactive
+friend who is jogging through the room
+
+ align:start position:0%
+friend who is jogging through the room
+ 
+
+ align:start position:0%
+friend who is jogging through the room
+and half the speed of light question
+
+ align:start position:0%
+and half the speed of light question
+ 
+
+ align:start position:0%
+and half the speed of light question
+I want to ask is what does
+
+ align:start position:0%
+I want to ask is what does
+ 
+
+ align:start position:0%
+I want to ask is what does
+Oh measure as the energy of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the naive way to do this which I will
+
+ align:start position:0%
+the naive way to do this which I will
+ 
+
+ align:start position:0%
+the naive way to do this which I will
+emphasize is not wrong okay what you
+
+ align:start position:0%
+emphasize is not wrong okay what you
+ 
+
+ align:start position:0%
+emphasize is not wrong okay what you
+might do is sort of go okay well we're
+
+ align:start position:0%
+might do is sort of go okay well we're
+ 
+
+ align:start position:0%
+might do is sort of go okay well we're
+sitting here this room is our laboratory
+
+ align:start position:0%
+sitting here this room is our laboratory
+ 
+
+ align:start position:0%
+sitting here this room is our laboratory
+I've measured this thing in my lab so I
+
+ align:start position:0%
+I've measured this thing in my lab so I
+ 
+
+ align:start position:0%
+I've measured this thing in my lab so I
+know P as I measure it I can see oh ja
+
+ align:start position:0%
+know P as I measure it I can see oh ja
+ 
+
+ align:start position:0%
+know P as I measure it I can see oh ja
+ghing by so I know O's for velocity as I
+
+ align:start position:0%
+ghing by so I know O's for velocity as I
+ 
+
+ align:start position:0%
+ghing by so I know O's for velocity as I
+measure it so what I should do is figure
+
+ align:start position:0%
+measure it so what I should do is figure
+ 
+
+ align:start position:0%
+measure it so what I should do is figure
+out the Lorentz transformation that
+
+ align:start position:0%
+out the Lorentz transformation that
+ 
+
+ align:start position:0%
+out the Lorentz transformation that
+takes me into the rest frame of oh once
+
+ align:start position:0%
+takes me into the rest frame of oh once
+ 
+
+ align:start position:0%
+takes me into the rest frame of oh once
+I have that Lorentz transformation I'll
+
+ align:start position:0%
+I have that Lorentz transformation I'll
+ 
+
+ align:start position:0%
+I have that Lorentz transformation I'll
+do I'll apply that Lorentz
+
+ align:start position:0%
+do I'll apply that Lorentz
+ 
+
+ align:start position:0%
+do I'll apply that Lorentz
+transformation to the four vector ki
+
+ align:start position:0%
+transformation to the four vector ki
+ 
+
+ align:start position:0%
+transformation to the four vector ki
+boom that will give me that energy okay
+
+ align:start position:0%
+boom that will give me that energy okay
+ 
+
+ align:start position:0%
+boom that will give me that energy okay
+that will work that will absolutely work
+
+ align:start position:0%
+that will work that will absolutely work
+ 
+
+ align:start position:0%
+that will work that will absolutely work
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's an easier way to do it so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one thing you should note is that
+
+ align:start position:0%
+one thing you should note is that
+ 
+
+ align:start position:0%
+one thing you should note is that
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+represents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that for velocity as
+
+ align:start position:0%
+that for velocity as
+ 
+
+ align:start position:0%
+that for velocity as
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+energy there
+
+ align:start position:0%
+energy there
+ 
+
+ align:start position:0%
+energy there
+was at the four momentum as an energy
+
+ align:start position:0%
+was at the four momentum as an energy
+ 
+
+ align:start position:0%
+was at the four momentum as an energy
+and a three momentum in particular
+
+ align:start position:0%
+and a three momentum in particular
+ 
+
+ align:start position:0%
+and a three momentum in particular
+though they represent it as the energy
+
+ align:start position:0%
+though they represent it as the energy
+ 
+
+ align:start position:0%
+though they represent it as the energy
+that they would measure and the four
+
+ align:start position:0%
+that they would measure and the four
+ 
+
+ align:start position:0%
+that they would measure and the four
+moment to me the three momentum that
+
+ align:start position:0%
+moment to me the three momentum that
+ 
+
+ align:start position:0%
+moment to me the three momentum that
+they would measure so that means P
+
+ align:start position:0%
+they would measure so that means P
+ 
+
+ align:start position:0%
+they would measure so that means P
+as seen
+
+ align:start position:0%
+as seen
+ 
+
+ align:start position:0%
+as seen
+by Oh is e according to oh and P
+
+ align:start position:0%
+by Oh is e according to oh and P
+ 
+
+ align:start position:0%
+by Oh is e according to oh and P
+according to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+eeeh cornea Oh is what we want and I
+
+ align:start position:0%
+eeeh cornea Oh is what we want and I
+ 
+
+ align:start position:0%
+eeeh cornea Oh is what we want and I
+just told you a moment ago you know if
+
+ align:start position:0%
+just told you a moment ago you know if
+ 
+
+ align:start position:0%
+just told you a moment ago you know if
+you have peeing your own reference frame
+
+ align:start position:0%
+you have peeing your own reference frame
+ 
+
+ align:start position:0%
+you have peeing your own reference frame
+and you have you and your own reference
+
+ align:start position:0%
+and you have you and your own reference
+ 
+
+ align:start position:0%
+and you have you and your own reference
+frame you can do this whole math let's
+
+ align:start position:0%
+frame you can do this whole math let's
+ 
+
+ align:start position:0%
+frame you can do this whole math let's
+Lorentz transformations and get it out
+
+ align:start position:0%
+Lorentz transformations and get it out
+ 
+
+ align:start position:0%
+Lorentz transformations and get it out
+but you also know that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ozone reference frame o represents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore velocity as one
+
+ align:start position:0%
+therefore velocity as one
+ 
+
+ align:start position:0%
+therefore velocity as one
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the time light Direction zero in the
+
+ align:start position:0%
+the time light Direction zero in the
+ 
+
+ align:start position:0%
+the time light Direction zero in the
+spatial direction so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what this means is if I go into o's
+
+ align:start position:0%
+what this means is if I go into o's
+ 
+
+ align:start position:0%
+what this means is if I go into o's
+reference frame if I go into their
+
+ align:start position:0%
+reference frame if I go into their
+ 
+
+ align:start position:0%
+reference frame if I go into their
+inertial reference frame notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if I take the dot product of P and
+
+ align:start position:0%
+that if I take the dot product of P and
+ 
+
+ align:start position:0%
+that if I take the dot product of P and
+you I get e times 1 and P times 0 so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is just negative it's exactly no
+
+ align:start position:0%
+that is just negative it's exactly no
+ 
+
+ align:start position:0%
+that is just negative it's exactly no
+it's exactly what I want module a minus
+
+ align:start position:0%
+it's exactly what I want module a minus
+ 
+
+ align:start position:0%
+it's exactly what I want module a minus
+sign and so you go okay well I'll flip
+
+ align:start position:0%
+sign and so you go okay well I'll flip
+ 
+
+ align:start position:0%
+sign and so you go okay well I'll flip
+my minus sign around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you think okay great but that's new
+
+ align:start position:0%
+and you think okay great but that's new
+ 
+
+ align:start position:0%
+and you think okay great but that's new
+I did that using those Quan DS that's
+
+ align:start position:0%
+I did that using those Quan DS that's
+ 
+
+ align:start position:0%
+I did that using those Quan DS that's
+written down the O's reference frame and
+
+ align:start position:0%
+written down the O's reference frame and
+ 
+
+ align:start position:0%
+written down the O's reference frame and
+then you go holy crap that's an
+
+ align:start position:0%
+then you go holy crap that's an
+ 
+
+ align:start position:0%
+then you go holy crap that's an
+invariant scalar product I'm done mic
+
+ align:start position:0%
+invariant scalar product I'm done mic
+ 
+
+ align:start position:0%
+invariant scalar product I'm done mic
+drop leave the room what this means is
+
+ align:start position:0%
+drop leave the room what this means is
+ 
+
+ align:start position:0%
+drop leave the room what this means is
+you start with P as you measure it you
+
+ align:start position:0%
+you start with P as you measure it you
+ 
+
+ align:start position:0%
+you start with P as you measure it you
+as you measure it take the scalar
+
+ align:start position:0%
+as you measure it take the scalar
+ 
+
+ align:start position:0%
+as you measure it take the scalar
+product between the two of them boom the
+
+ align:start position:0%
+product between the two of them boom the
+ 
+
+ align:start position:0%
+product between the two of them boom the
+answer you want pops out no nonsense of
+
+ align:start position:0%
+answer you want pops out no nonsense of
+ 
+
+ align:start position:0%
+answer you want pops out no nonsense of
+Lorentz transformations none of that
+
+ align:start position:0%
+Lorentz transformations none of that
+ 
+
+ align:start position:0%
+Lorentz transformations none of that
+garbage needs to happen you just take
+
+ align:start position:0%
+garbage needs to happen you just take
+ 
+
+ align:start position:0%
+garbage needs to happen you just take
+the inner product and you've got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that sort of says in words you know no
+
+ align:start position:0%
+that sort of says in words you know no
+ 
+
+ align:start position:0%
+that sort of says in words you know no
+matter what representation you choose to
+
+ align:start position:0%
+matter what representation you choose to
+ 
+
+ align:start position:0%
+matter what representation you choose to
+write down P and un take the dot product
+
+ align:start position:0%
+write down P and un take the dot product
+ 
+
+ align:start position:0%
+write down P and un take the dot product
+Rena two of them throw in a minus sign
+
+ align:start position:0%
+Rena two of them throw in a minus sign
+ 
+
+ align:start position:0%
+Rena two of them throw in a minus sign
+you've got the energy of the particle
+
+ align:start position:0%
+you've got the energy of the particle
+ 
+
+ align:start position:0%
+you've got the energy of the particle
+with P as measured by the observer with
+
+ align:start position:0%
+with P as measured by the observer with
+ 
+
+ align:start position:0%
+with P as measured by the observer with
+you it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of late in the hour the
+
+ align:start position:0%
+sort of late in the hour the
+ 
+
+ align:start position:0%
+sort of late in the hour the
+hour and a half I should say so let me
+
+ align:start position:0%
+hour and a half I should say so let me
+ 
+
+ align:start position:0%
+hour and a half I should say so let me
+just sort of emphasize there are
+
+ align:start position:0%
+just sort of emphasize there are
+ 
+
+ align:start position:0%
+just sort of emphasize there are
+occasional moments in this class where
+
+ align:start position:0%
+occasional moments in this class where
+ 
+
+ align:start position:0%
+occasional moments in this class where
+if you're dozing off a little bit I
+
+ align:start position:0%
+if you're dozing off a little bit I
+ 
+
+ align:start position:0%
+if you're dozing off a little bit I
+suggest you pop up and tattoo this into
+
+ align:start position:0%
+suggest you pop up and tattoo this into
+ 
+
+ align:start position:0%
+suggest you pop up and tattoo this into
+a neuron somewhere this is one of those
+
+ align:start position:0%
+a neuron somewhere this is one of those
+ 
+
+ align:start position:0%
+a neuron somewhere this is one of those
+moments okay this is web result that
+
+ align:start position:0%
+moments okay this is web result that
+ 
+
+ align:start position:0%
+moments okay this is web result that
+we're going to use over and over and
+
+ align:start position:0%
+we're going to use over and over and
+ 
+
+ align:start position:0%
+we're going to use over and over and
+over again because this holds isn't just
+
+ align:start position:0%
+over again because this holds isn't just
+ 
+
+ align:start position:0%
+over again because this holds isn't just
+a special relativity okay we are
+
+ align:start position:0%
+a special relativity okay we are
+ 
+
+ align:start position:0%
+a special relativity okay we are
+actually when we start talking about
+
+ align:start position:0%
+actually when we start talking about
+ 
+
+ align:start position:0%
+actually when we start talking about
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+of things near black holes there's only
+
+ align:start position:0%
+of things near black holes there's only
+ 
+
+ align:start position:0%
+of things near black holes there's only
+a place where I basically at that point
+
+ align:start position:0%
+a place where I basically at that point
+ 
+
+ align:start position:0%
+a place where I basically at that point
+to say well I'm just gonna use the fact
+
+ align:start position:0%
+to say well I'm just gonna use the fact
+ 
+
+ align:start position:0%
+to say well I'm just gonna use the fact
+that the observer measures an energy
+
+ align:start position:0%
+that the observer measures an energy
+ 
+
+ align:start position:0%
+that the observer measures an energy
+that is given by and I'm gonna write
+
+ align:start position:0%
+that is given by and I'm gonna write
+ 
+
+ align:start position:0%
+that is given by and I'm gonna write
+down that okay the dot product that
+
+ align:start position:0%
+down that okay the dot product that
+ 
+
+ align:start position:0%
+down that okay the dot product that
+involves a little bit more complicated
+
+ align:start position:0%
+involves a little bit more complicated
+ 
+
+ align:start position:0%
+involves a little bit more complicated
+because my metric is hairier but it's
+
+ align:start position:0%
+because my metric is hairier but it's
+ 
+
+ align:start position:0%
+because my metric is hairier but it's
+the exact same physical concept okay let
+
+ align:start position:0%
+the exact same physical concept okay let
+ 
+
+ align:start position:0%
+the exact same physical concept okay let
+me just do one more and then I'm gonna
+
+ align:start position:0%
+me just do one more and then I'm gonna
+ 
+
+ align:start position:0%
+me just do one more and then I'm gonna
+talk without getting into the math about
+
+ align:start position:0%
+talk without getting into the math about
+ 
+
+ align:start position:0%
+talk without getting into the math about
+what I will start with on Tuesday last
+
+ align:start position:0%
+what I will start with on Tuesday last
+ 
+
+ align:start position:0%
+what I will start with on Tuesday last
+for velocity which I was probably useful
+
+ align:start position:0%
+for velocity which I was probably useful
+ 
+
+ align:start position:0%
+for velocity which I was probably useful
+for us to quickly talk about is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we've been doing we
+
+ align:start position:0%
+we've been doing we
+ 
+
+ align:start position:0%
+we've been doing we
+talked a lot about for velocity that
+
+ align:start position:0%
+talked a lot about for velocity that
+ 
+
+ align:start position:0%
+talked a lot about for velocity that
+is just one piece we're not talking
+
+ align:start position:0%
+is just one piece we're not talking
+ 
+
+ align:start position:0%
+is just one piece we're not talking
+about sort of the kinematics of bodies
+
+ align:start position:0%
+about sort of the kinematics of bodies
+ 
+
+ align:start position:0%
+about sort of the kinematics of bodies
+moving in space-time you need more
+
+ align:start position:0%
+moving in space-time you need more
+ 
+
+ align:start position:0%
+moving in space-time you need more
+information than its velocity sometimes
+
+ align:start position:0%
+information than its velocity sometimes
+ 
+
+ align:start position:0%
+information than its velocity sometimes
+things are moving around there's
+
+ align:start position:0%
+things are moving around there's
+ 
+
+ align:start position:0%
+things are moving around there's
+additional additional
+
+ align:start position:0%
+additional additional
+ 
+
+ align:start position:0%
+additional additional
+forces acting on them and so we also
+
+ align:start position:0%
+forces acting on them and so we also
+ 
+
+ align:start position:0%
+forces acting on them and so we also
+care about the for acceleration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is what I get when I take the
+
+ align:start position:0%
+this is what I get when I take the
+ 
+
+ align:start position:0%
+this is what I get when I take the
+derivative with respect to proper time
+
+ align:start position:0%
+derivative with respect to proper time
+ 
+
+ align:start position:0%
+derivative with respect to proper time
+of the four-velocity okay so will there
+
+ align:start position:0%
+of the four-velocity okay so will there
+ 
+
+ align:start position:0%
+of the four-velocity okay so will there
+be some homework exercises that use this
+
+ align:start position:0%
+be some homework exercises that use this
+ 
+
+ align:start position:0%
+be some homework exercises that use this
+the main thing which I want to emphasize
+
+ align:start position:0%
+the main thing which I want to emphasize
+ 
+
+ align:start position:0%
+the main thing which I want to emphasize
+to sort of conclude our calculations for
+
+ align:start position:0%
+to sort of conclude our calculations for
+ 
+
+ align:start position:0%
+to sort of conclude our calculations for
+today is that when I talk about a four
+
+ align:start position:0%
+today is that when I talk about a four
+ 
+
+ align:start position:0%
+today is that when I talk about a four
+velocity of acceleration this has an
+
+ align:start position:0%
+velocity of acceleration this has an
+ 
+
+ align:start position:0%
+velocity of acceleration this has an
+extremely important property it is
+
+ align:start position:0%
+extremely important property it is
+ 
+
+ align:start position:0%
+extremely important property it is
+always the case that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a dotted
+
+ align:start position:0%
+a dotted
+ 
+
+ align:start position:0%
+a dotted
+into u equals
+
+ align:start position:0%
+into u equals
+ 
+
+ align:start position:0%
+into u equals
+zero if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're used to sort of three-dimensional
+
+ align:start position:0%
+you're used to sort of three-dimensional
+ 
+
+ align:start position:0%
+you're used to sort of three-dimensional
+intuition that may seem weird okay any
+
+ align:start position:0%
+intuition that may seem weird okay any
+ 
+
+ align:start position:0%
+intuition that may seem weird okay any
+time you see a car accelerate from a
+
+ align:start position:0%
+time you see a car accelerate from a
+ 
+
+ align:start position:0%
+time you see a car accelerate from a
+stopped education
+
+ align:start position:0%
+stopped education
+ 
+
+ align:start position:0%
+stopped education
+which is acceleration is clearly not
+
+ align:start position:0%
+which is acceleration is clearly not
+ 
+
+ align:start position:0%
+which is acceleration is clearly not
+orthogonal to its velocity okay but the
+
+ align:start position:0%
+orthogonal to its velocity okay but the
+ 
+
+ align:start position:0%
+orthogonal to its velocity okay but the
+issue here is this is not a spatial dot
+
+ align:start position:0%
+issue here is this is not a spatial dot
+ 
+
+ align:start position:0%
+issue here is this is not a spatial dot
+product this is a space-time dot product
+
+ align:start position:0%
+product this is a space-time dot product
+ 
+
+ align:start position:0%
+product this is a space-time dot product
+and so your intuition has to go out the
+
+ align:start position:0%
+and so your intuition has to go out the
+ 
+
+ align:start position:0%
+and so your intuition has to go out the
+window because of that it's very simple
+
+ align:start position:0%
+window because of that it's very simple
+ 
+
+ align:start position:0%
+window because of that it's very simple
+to prove this remember u dot u equals
+
+ align:start position:0%
+to prove this remember u dot u equals
+ 
+
+ align:start position:0%
+to prove this remember u dot u equals
+minus one so D of U dot u D tau which is
+
+ align:start position:0%
+minus one so D of U dot u D tau which is
+ 
+
+ align:start position:0%
+minus one so D of U dot u D tau which is
+just two u
+
+ align:start position:0%
+just two u
+ 
+
+ align:start position:0%
+just two u
+dot a is the
+
+ align:start position:0%
+dot a is the
+ 
+
+ align:start position:0%
+dot a is the
+derivative of minus one which
+
+ align:start position:0%
+derivative of minus one which
+ 
+
+ align:start position:0%
+derivative of minus one which
+is zero okay
+
+ align:start position:0%
+is zero okay
+ 
+
+ align:start position:0%
+is zero okay
+so this is something that we will
+
+ align:start position:0%
+so this is something that we will
+ 
+
+ align:start position:0%
+so this is something that we will
+exploit if you want to describe the
+
+ align:start position:0%
+exploit if you want to describe the
+ 
+
+ align:start position:0%
+exploit if you want to describe the
+relativistic kinematics of an
+
+ align:start position:0%
+relativistic kinematics of an
+ 
+
+ align:start position:0%
+relativistic kinematics of an
+accelerating body this
+
+ align:start position:0%
+accelerating body this
+ 
+
+ align:start position:0%
+accelerating body this
+is a great thing that we can use to
+
+ align:start position:0%
+is a great thing that we can use to
+ 
+
+ align:start position:0%
+is a great thing that we can use to
+exploit you'll often need a little bit
+
+ align:start position:0%
+exploit you'll often need a little bit
+ 
+
+ align:start position:0%
+exploit you'll often need a little bit
+more information okay we have to give
+
+ align:start position:0%
+more information okay we have to give
+ 
+
+ align:start position:0%
+more information okay we have to give
+you as a bit of additional information
+
+ align:start position:0%
+you as a bit of additional information
+ 
+
+ align:start position:0%
+you as a bit of additional information
+some knowledge about what the
+
+ align:start position:0%
+some knowledge about what the
+ 
+
+ align:start position:0%
+some knowledge about what the
+orientation the acceleration is and
+
+ align:start position:0%
+orientation the acceleration is and
+ 
+
+ align:start position:0%
+orientation the acceleration is and
+things like that okay so there are
+
+ align:start position:0%
+things like that okay so there are
+ 
+
+ align:start position:0%
+things like that okay so there are
+whenever you are given getting just a
+
+ align:start position:0%
+whenever you are given getting just a
+ 
+
+ align:start position:0%
+whenever you are given getting just a
+second ever you're given any kind of
+
+ align:start position:0%
+second ever you're given any kind of
+ 
+
+ align:start position:0%
+second ever you're given any kind of
+differential quantity like this it's not
+
+ align:start position:0%
+differential quantity like this it's not
+ 
+
+ align:start position:0%
+differential quantity like this it's not
+enough to know it's like the
+
+ align:start position:0%
+enough to know it's like the
+ 
+
+ align:start position:0%
+enough to know it's like the
+acceleration of loss you have to also
+
+ align:start position:0%
+acceleration of loss you have to also
+ 
+
+ align:start position:0%
+acceleration of loss you have to also
+have boundary conditions okay and that
+
+ align:start position:0%
+have boundary conditions okay and that
+ 
+
+ align:start position:0%
+have boundary conditions okay and that
+sort of tells you like what the initial
+
+ align:start position:0%
+sort of tells you like what the initial
+ 
+
+ align:start position:0%
+sort of tells you like what the initial
+direction is question
+
+ align:start position:0%
+direction is question
+ 
+
+ align:start position:0%
+direction is question
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+time is the proper time yes that's
+
+ align:start position:0%
+time is the proper time yes that's
+ 
+
+ align:start position:0%
+time is the proper time yes that's
+right so you can still define a proper
+
+ align:start position:0%
+right so you can still define a proper
+ 
+
+ align:start position:0%
+right so you can still define a proper
+time for an accelerating observer it
+
+ align:start position:0%
+time for an accelerating observer it
+ 
+
+ align:start position:0%
+time for an accelerating observer it
+will not relate hold
+
+ align:start position:0%
+will not relate hold
+ 
+
+ align:start position:0%
+will not relate hold
+that thought you're gonna play with this
+
+ align:start position:0%
+that thought you're gonna play with this
+ 
+
+ align:start position:0%
+that thought you're gonna play with this
+a little bit more on a future problem
+
+ align:start position:0%
+a little bit more on a future problem
+ 
+
+ align:start position:0%
+a little bit more on a future problem
+set I mean that the key thing is that
+
+ align:start position:0%
+set I mean that the key thing is that
+ 
+
+ align:start position:0%
+set I mean that the key thing is that
+the way if you have an accelerated
+
+ align:start position:0%
+the way if you have an accelerated
+ 
+
+ align:start position:0%
+the way if you have an accelerated
+observer an interval of proper time as
+
+ align:start position:0%
+observer an interval of proper time as
+ 
+
+ align:start position:0%
+observer an interval of proper time as
+compared to an interval of time for you
+
+ align:start position:0%
+compared to an interval of time for you
+ 
+
+ align:start position:0%
+compared to an interval of time for you
+know someone in a restroom that sees
+
+ align:start position:0%
+know someone in a restroom that sees
+ 
+
+ align:start position:0%
+know someone in a restroom that sees
+this person accelerate away the
+
+ align:start position:0%
+this person accelerate away the
+ 
+
+ align:start position:0%
+this person accelerate away the
+the the conversion between the intervals
+
+ align:start position:0%
+the the conversion between the intervals
+ 
+
+ align:start position:0%
+the the conversion between the intervals
+of time the to measure it evolves okay
+
+ align:start position:0%
+of time the to measure it evolves okay
+ 
+
+ align:start position:0%
+of time the to measure it evolves okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know let's say you're in this room
+
+ align:start position:0%
+you know let's say you're in this room
+ 
+
+ align:start position:0%
+you know let's say you're in this room
+with me in fact it turns out that if you
+
+ align:start position:0%
+with me in fact it turns out that if you
+ 
+
+ align:start position:0%
+with me in fact it turns out that if you
+accelerate at 1 J for a year you get to
+
+ align:start position:0%
+accelerate at 1 J for a year you get to
+ 
+
+ align:start position:0%
+accelerate at 1 J for a year you get to
+very close to the speed of light okay so
+
+ align:start position:0%
+very close to the speed of light okay so
+ 
+
+ align:start position:0%
+very close to the speed of light okay so
+let's say that you were in a rocket ship
+
+ align:start position:0%
+let's say that you were in a rocket ship
+ 
+
+ align:start position:0%
+let's say that you were in a rocket ship
+right now that launched at with an
+
+ align:start position:0%
+right now that launched at with an
+ 
+
+ align:start position:0%
+right now that launched at with an
+acceleration of G initially you and I
+
+ align:start position:0%
+acceleration of G initially you and I
+ 
+
+ align:start position:0%
+acceleration of G initially you and I
+synchronize
+
+ align:start position:0%
+synchronize
+ 
+
+ align:start position:0%
+synchronize
+our watches and so an interval of a
+
+ align:start position:0%
+our watches and so an interval of a
+ 
+
+ align:start position:0%
+our watches and so an interval of a
+second to me is the same as a second to
+
+ align:start position:0%
+second to me is the same as a second to
+ 
+
+ align:start position:0%
+second to me is the same as a second to
+you half a year later you're moving at
+
+ align:start position:0%
+you half a year later you're moving at
+ 
+
+ align:start position:0%
+you half a year later you're moving at
+something like half the speed of light
+
+ align:start position:0%
+something like half the speed of light
+ 
+
+ align:start position:0%
+something like half the speed of light
+and I will see a noticeable time delay
+
+ align:start position:0%
+and I will see a noticeable time delay
+ 
+
+ align:start position:0%
+and I will see a noticeable time delay
+your interval of an integral of a second
+
+ align:start position:0%
+your interval of an integral of a second
+ 
+
+ align:start position:0%
+your interval of an integral of a second
+as you measure it looks long compared to
+
+ align:start position:0%
+as you measure it looks long compared to
+ 
+
+ align:start position:0%
+as you measure it looks long compared to
+me oh you're six months later you're
+
+ align:start position:0%
+me oh you're six months later you're
+ 
+
+ align:start position:0%
+me oh you're six months later you're
+actually quite close to the speed of
+
+ align:start position:0%
+actually quite close to the speed of
+ 
+
+ align:start position:0%
+actually quite close to the speed of
+light and it gets dilated even more okay
+
+ align:start position:0%
+light and it gets dilated even more okay
+ 
+
+ align:start position:0%
+light and it gets dilated even more okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+last thing which I'm going to say and
+
+ align:start position:0%
+last thing which I'm going to say and
+ 
+
+ align:start position:0%
+last thing which I'm going to say and
+I'm not gonna get into too much detail
+
+ align:start position:0%
+I'm not gonna get into too much detail
+ 
+
+ align:start position:0%
+I'm not gonna get into too much detail
+with this yet is we're gonna begin next
+
+ align:start position:0%
+with this yet is we're gonna begin next
+ 
+
+ align:start position:0%
+with this yet is we're gonna begin next
+time by making
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit more formal some of the
+
+ align:start position:0%
+a little bit more formal some of the
+ 
+
+ align:start position:0%
+a little bit more formal some of the
+notions that go around so if we just
+
+ align:start position:0%
+notions that go around so if we just
+ 
+
+ align:start position:0%
+notions that go around so if we just
+talked about we've introduced some
+
+ align:start position:0%
+talked about we've introduced some
+ 
+
+ align:start position:0%
+talked about we've introduced some
+physics and some vectors I've given you
+
+ align:start position:0%
+physics and some vectors I've given you
+ 
+
+ align:start position:0%
+physics and some vectors I've given you
+guys one tensor so far the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metric tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I'm gonna give you in fact I will write
+
+ align:start position:0%
+I'm gonna give you in fact I will write
+ 
+
+ align:start position:0%
+I'm gonna give you in fact I will write
+down a very precise definition of this
+
+ align:start position:0%
+down a very precise definition of this
+ 
+
+ align:start position:0%
+down a very precise definition of this
+right now and we'll pick it up from
+
+ align:start position:0%
+right now and we'll pick it up from
+ 
+
+ align:start position:0%
+right now and we'll pick it up from
+there on Tuesday basic ideas so you guys
+
+ align:start position:0%
+there on Tuesday basic ideas so you guys
+ 
+
+ align:start position:0%
+there on Tuesday basic ideas so you guys
+have seen the 1/10 you've seen so far is
+
+ align:start position:0%
+have seen the 1/10 you've seen so far is
+ 
+
+ align:start position:0%
+have seen the 1/10 you've seen so far is
+the metric tensor and what the metric is
+
+ align:start position:0%
+the metric tensor and what the metric is
+ 
+
+ align:start position:0%
+the metric tensor and what the metric is
+is it sort of a mathematical object that
+
+ align:start position:0%
+is it sort of a mathematical object that
+ 
+
+ align:start position:0%
+is it sort of a mathematical object that
+I put in a pair of four vectors and it
+
+ align:start position:0%
+I put in a pair of four vectors and it
+ 
+
+ align:start position:0%
+I put in a pair of four vectors and it
+spits out a quantity that is a Lorentz
+
+ align:start position:0%
+spits out a quantity that is a Lorentz
+ 
+
+ align:start position:0%
+spits out a quantity that is a Lorentz
+invariant scalar okay that characterizes
+
+ align:start position:0%
+invariant scalar okay that characterizes
+ 
+
+ align:start position:0%
+invariant scalar okay that characterizes
+what we call the inner product of those
+
+ align:start position:0%
+what we call the inner product of those
+ 
+
+ align:start position:0%
+what we call the inner product of those
+two four vectors more
+
+ align:start position:0%
+two four vectors more
+ 
+
+ align:start position:0%
+two four vectors more
+generally I'm going to define a tensor
+
+ align:start position:0%
+generally I'm going to define a tensor
+ 
+
+ align:start position:0%
+generally I'm going to define a tensor
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type zero n as
+
+ align:start position:0%
+type zero n as
+ 
+
+ align:start position:0%
+type zero n as
+a function
+
+ align:start position:0%
+a function
+ 
+
+ align:start position:0%
+a function
+or mapping of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n for
+
+ align:start position:0%
+n for
+ 
+
+ align:start position:0%
+n for
+vectors into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lorentz
+
+ align:start position:0%
+Lorentz
+ 
+
+ align:start position:0%
+Lorentz
+invariant scalars which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is linear in each
+
+ align:start position:0%
+is linear in each
+ 
+
+ align:start position:0%
+is linear in each
+of its and arguments so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will pick it up here on Tuesday is
+
+ align:start position:0%
+I will pick it up here on Tuesday is
+ 
+
+ align:start position:0%
+I will pick it up here on Tuesday is
+only just say in words the metric is a
+
+ align:start position:0%
+only just say in words the metric is a
+ 
+
+ align:start position:0%
+only just say in words the metric is a
+zero two tensor I put in two four
+
+ align:start position:0%
+zero two tensor I put in two four
+ 
+
+ align:start position:0%
+zero two tensor I put in two four
+vectors it spits out a Lorentz invariant
+
+ align:start position:0%
+vectors it spits out a Lorentz invariant
+ 
+
+ align:start position:0%
+vectors it spits out a Lorentz invariant
+scalar we're going to before too long I
+
+ align:start position:0%
+scalar we're going to before too long I
+ 
+
+ align:start position:0%
+scalar we're going to before too long I
+come up with a couple of things that
+
+ align:start position:0%
+come up with a couple of things that
+ 
+
+ align:start position:0%
+come up with a couple of things that
+involve three real vectors see me three
+
+ align:start position:0%
+involve three real vectors see me three
+ 
+
+ align:start position:0%
+involve three real vectors see me three
+four vectors too many numbers they're a
+
+ align:start position:0%
+four vectors too many numbers they're a
+ 
+
+ align:start position:0%
+four vectors too many numbers they're a
+trio of four vectors which it then maps
+
+ align:start position:0%
+trio of four vectors which it then maps
+ 
+
+ align:start position:0%
+trio of four vectors which it then maps
+to a Lorentz invariant scale some of
+
+ align:start position:0%
+to a Lorentz invariant scale some of
+ 
+
+ align:start position:0%
+to a Lorentz invariant scale some of
+them will take in four four vectors and
+
+ align:start position:0%
+them will take in four four vectors and
+ 
+
+ align:start position:0%
+them will take in four four vectors and
+produce a Lorentz invariant scalar
+
+ align:start position:0%
+produce a Lorentz invariant scalar
+ 
+
+ align:start position:0%
+produce a Lorentz invariant scalar
+notice I wrote this in a sort of funny
+
+ align:start position:0%
+notice I wrote this in a sort of funny
+ 
+
+ align:start position:0%
+notice I wrote this in a sort of funny
+way the zero end sort of begs were there
+
+ align:start position:0%
+way the zero end sort of begs were there
+ 
+
+ align:start position:0%
+way the zero end sort of begs were there
+to be sort of a n zero okay to do that I
+
+ align:start position:0%
+to be sort of a n zero okay to do that I
+ 
+
+ align:start position:0%
+to be sort of a n zero okay to do that I
+have to introduce a dual an object that
+
+ align:start position:0%
+have to introduce a dual an object that
+ 
+
+ align:start position:0%
+have to introduce a dual an object that
+is sort of dual to a vector okay we're
+
+ align:start position:0%
+is sort of dual to a vector okay we're
+ 
+
+ align:start position:0%
+is sort of dual to a vector okay we're
+going to talk about that those are
+
+ align:start position:0%
+going to talk about that those are
+ 
+
+ align:start position:0%
+going to talk about that those are
+objects called one forms which actually
+
+ align:start position:0%
+objects called one forms which actually
+ 
+
+ align:start position:0%
+objects called one forms which actually
+happened to be a species of vector we're
+
+ align:start position:0%
+happened to be a species of vector we're
+ 
+
+ align:start position:0%
+happened to be a species of vector we're
+actually going to then learn that the
+
+ align:start position:0%
+actually going to then learn that the
+ 
+
+ align:start position:0%
+actually going to then learn that the
+vector is itself a tensor and so we will
+
+ align:start position:0%
+vector is itself a tensor and so we will
+ 
+
+ align:start position:0%
+vector is itself a tensor and so we will
+make a very general classification of
+
+ align:start position:0%
+make a very general classification of
+ 
+
+ align:start position:0%
+make a very general classification of
+these things and we'll see that vectors
+
+ align:start position:0%
+these things and we'll see that vectors
+ 
+
+ align:start position:0%
+these things and we'll see that vectors
+are just a subset of these tensors and
+
+ align:start position:0%
+are just a subset of these tensors and
+ 
+
+ align:start position:0%
+are just a subset of these tensors and
+at last we'll sort of have all the
+
+ align:start position:0%
+at last we'll sort of have all the
+ 
+
+ align:start position:0%
+at last we'll sort of have all the
+mathematics in place we can sort of lose
+
+ align:start position:0%
+mathematics in place we can sort of lose
+ 
+
+ align:start position:0%
+mathematics in place we can sort of lose
+some of these distinctions and just life
+
+ align:start position:0%
+some of these distinctions and just life
+ 
+
+ align:start position:0%
+some of these distinctions and just life
+goes on and we can start actually doing
+
+ align:start position:0%
+goes on and we can start actually doing
+ 
+
+ align:start position:0%
+goes on and we can start actually doing
+some physics with these all right I will
+
+ align:start position:0%
+some physics with these all right I will
+ 
+
+ align:start position:0%
+some physics with these all right I will
+pick it up there on Tuesday
\ No newline at end of file
diff --git a/Ttezuzs39nk.txt b/Ttezuzs39nk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..707b045207b1639883dc4fd22074c7919f600f36
--- /dev/null
+++ b/Ttezuzs39nk.txt
@@ -0,0 +1,3274 @@
+Good morning,
+everyone.
+
+Glad you are all here bright
+and early.
+
+I'm counting the days till the
+TA's outnumber the students.
+
+They'll show up.
+We return to a familiar story.
+
+This is part two,
+the Empire Strikes Back.
+
+So last time,
+our adversary,
+
+the graph, came to us with a
+problem.
+
+We have a source,
+and we had a directed graph,
+
+and we had weights on the
+edges, and they were all
+
+nonnegative.
+And there was happiness.
+
+And we triumphed over the
+Empire by designing Dijkstra's
+
+algorithm, and very efficiently
+finding single source shortest
+
+paths, shortest path weight from
+s to every other vertex.
+
+Today, however,
+the Death Star has a new trick
+
+up its sleeve,
+and we have negative weights,
+
+potentially.
+And we're going to have to
+
+somehow deal with,
+in particular,
+
+negative weight cycles.
+And we saw that when we have a
+
+negative weight cycle,
+we can just keep going around,
+
+and around, and around,
+and go back in time farther,
+
+and farther,
+and farther.
+
+And we can get to be
+arbitrarily far back in the
+
+past.
+And so there's no shortest
+
+path, because whatever path you
+take you can get a shorter one.
+
+So we want to address that
+issue today, and we're going to
+
+come up with a new algorithm
+actually simpler than Dijkstra,
+
+but not as fast,
+called the Bellman-Ford
+
+algorithm.
+And, it's going to allow
+
+negative weights,
+and in some sense allow
+
+negative weight cycles,
+although maybe not as much as
+
+you might hope.
+We have to leave room for a
+
+sequel, of course.
+OK, so the Bellman-Ford
+
+algorithm, invented by two guys,
+as you might expect,
+
+it computes the shortest path
+weights.
+
+So, it makes no assumption
+about the weights.
+
+Weights are arbitrary,
+and it's going to compute the
+
+shortest path weights.
+So, remember this notation:
+
+delta of s, v is the weight of
+the shortest path from s to v.
+
+s was called a source vertex.
+And, we want to compute these
+
+weights for all vertices,
+little v.
+
+The claim is that computing
+from s to everywhere is no
+
+harder than computing s to a
+particular location.
+
+So, we're going to do for all
+them.
+
+It's still going to be the case
+here.
+
+And, it allows negative
+weights.
+
+And this is the good case,
+but there's an alternative,
+
+which is that Bellman-Ford may
+just say, oops,
+
+there's a negative weight
+cycle.
+
+And in that case it will just
+say so.
+
+So, they say a negative weight
+cycle exists.
+
+Therefore, some of these deltas
+are minus infinity.
+
+And that seems weird.
+So, Bellman-Ford as we'll
+
+present it today is intended for
+the case, but there are no
+
+negative weights cycles,
+which is more intuitive.
+
+It sort of allows them,
+but it will just report them.
+
+In that case,
+it will not give you delta
+
+values.
+You can change the algorithm to
+
+give you delta values in that
+case, but we are not going to
+
+see it here.
+So, in exercise,
+
+after you see the algorithm,
+exercise is:
+
+compute these deltas in all
+cases.
+
+So, it's not hard to do.
+But we don't have time for it
+
+here.
+So, here's the algorithm.
+
+It's pretty straightforward.
+As I said, it's easier than
+
+Dijkstra.
+It's a relaxation algorithm.
+
+So the main thing that it does
+is relax edges just like
+
+Dijkstra.
+So, we'll be able to use a lot
+
+of dilemmas from Dijkstra.
+And proof of correctness will
+
+be three times shorter because
+the first two thirds we already
+
+have from Dijkstra.
+But I'm jumping ahead a bit.
+
+So, the first part is
+initialization.
+
+Again, d of v will represent
+the estimated distance from s to
+
+v.
+And we're going to be updating
+
+those estimates as the algorithm
+goes along.
+
+And initially,
+d of s is zero,
+
+which now may not be the right
+answer conceivably.
+
+Everyone else is infinity,
+which is certainly an upper
+
+bound.
+OK, these are both upper bounds
+
+on the true distance.
+So that's fine.
+
+That's initialization just like
+before.
+
+And now we have a main loop
+which happens v minus one times.
+
+We're not actually going to use
+the index i.
+
+It's just a counter.
+
+And we're just going to look at
+every edge and relax it.
+
+It's a very simple idea.
+If you learn about relaxation,
+
+this is the first thing you
+might try.
+
+The question is when do you
+stop.
+
+It's sort of like I have this
+friend to what he was like six
+
+years old he would claim,
+oh, I know how to spell banana.
+
+I just don't know when to stop.
+OK, same thing with relaxation.
+
+This is our relaxation step
+just as before.
+
+We look at the edge;
+we see whether it violates the
+
+triangle inequality according to
+our current estimates we know
+
+the distance from s to v should
+be at most distance from s to
+
+plus the weight of that edge
+from u to v.
+
+If it isn't,
+we set it equal.
+
+We've proved that this is
+always an OK thing to do.
+
+We never violate,
+I mean, these d of v's never
+
+get too small if we do a bunch
+of relaxations.
+
+So, the idea is you take every
+edge.
+
+You relax it.
+I don't care which order.
+
+Just relax every edge,
+one each.
+
+And that do that V minus one
+times.
+
+The claim is that that should
+be enough if you have no
+
+negative weights cycles.
+So, if there's a negative
+
+weight cycle,
+we need to figure it out.
+
+And, we'll do that in a fairly
+straightforward way,
+
+which is we're going to do
+exactly the same thing.
+
+So this is outside before loop
+here.
+
+We'll have the same four loops
+for each edge in our graph.
+
+We'll try to relax it.
+And if you can relax it,
+
+the claim is that there has to
+be a negative weight cycle.
+
+So this is the main thing that
+needs proof.
+
+OK, and that's the algorithm.
+So the claim is that at the
+
+ends we should have d of v,
+let's see, L's so to speak.
+
+d of v equals delta of s comma
+v for every vertex,
+
+v.
+If we don't find a negative
+
+weight cycle according to this
+rule, that we should have all
+
+the shortest path weights.
+That's the claim.
+
+Now, the first question is,
+in here, the running time is
+
+very easy to analyze.
+So let's start with the running
+
+time.
+We can compare it to Dijkstra,
+
+which is over here.
+What is the running time of
+
+this algorithm?
+V times E, exactly.
+
+OK, I'm going to assume,
+because it's pretty reasonable,
+
+that V and E are both positive.
+Then it's V times E.
+
+So, this is a little bit
+slower, or a fair amount slower,
+
+than Dijkstra's algorithm.
+There it is:
+
+E plus V log V is essentially,
+ignoring the logs is pretty
+
+much linear time.
+Here we have something that's
+
+at least quadratic in V,
+assuming your graph is
+
+connected.
+So, it's slower,
+
+but it's going to handle these
+negative weights.
+
+Dijkstra can't handle negative
+weights at all.
+
+So, let's do an example,
+make it clear why you might
+
+hope this algorithm works.
+And then we'll prove that it
+
+works, of course.
+But the proof will be pretty
+
+easy.
+So, I'm going to draw a graph
+
+that has negative weights,
+but no negative weight cycles
+
+so that I get an interesting
+answer.
+
+Good.
+The other thing I need in order
+
+to make the output of this
+algorithm well defined,
+
+it depends in which order you
+visit the edges.
+
+So I'm going to assign an
+arbitrary order to these edges.
+
+I could just ask you for an
+order, but to be consistent with
+
+the notes, I'll put an ordering
+on it.
+
+Let's say I put number four,
+say that's the fourth edge I'll
+
+visit.
+It doesn't matter.
+
+But it will affect what happens
+during the algorithm for a
+
+particular graph.
+
+Do they get them all?
+One, two, three,
+
+four, five, six,
+seven, eight,
+
+OK.
+And my source is going to be A.
+
+And, that's it.
+So, I want to run this
+
+algorithm.
+I'm just going to initialize
+
+everything.
+So, I set the estimates for s
+
+to be zero, and everyone else to
+be infinity.
+
+And to give me some notion of
+time, over here I'm going to
+
+draw or write down what all of
+these d values are as the
+
+algorithm proceeds because I'm
+going to start crossing them out
+
+and rewriting them that the
+figure will get a little bit
+
+messier.
+But we can keep track of it
+
+over here.
+It's initially zero and
+
+infinities.
+Yeah?
+
+It doesn't matter.
+So, for the algorithm you can
+
+go to the edges in a different
+order every time if you want.
+
+We'll prove that,
+but here I'm going to go
+
+through the same order every
+time.
+
+Good question.
+It turns out it doesn't matter
+
+here.
+OK, so here's the starting
+
+point.
+Now I'm going to relax every
+
+edge.
+So, there's going to be a lot
+
+of edges here that don't do
+anything.
+
+I try to relax n minus one.
+I'd say, well,
+
+I know how to get from s to B
+with weight infinity.
+
+Infinity plus two I can get to
+from s to E.
+
+Well, infinity plus two is not
+much better than infinity.
+
+OK, so I don't do anything,
+don't update this to infinity.
+
+I mean, infinity plus two
+sounds even worse.
+
+But infinity plus two is
+infinity.
+
+OK, that's the edge number one.
+So, no relaxation edge number
+
+two, same deal as number three,
+same deal, edge number four we
+
+start to get something
+interesting because I have a
+
+finite value here that says I
+can get from A to B using a
+
+total weight of minus one.
+So that seems good.
+
+I'll write down minus one here,
+and update B to minus one.
+
+The rest stay the same.
+So, I'm just going to keep
+
+doing this over and over.
+That was edge number four.
+
+Number five,
+we also get a relaxation.
+
+Four is better than infinity.
+So, c gets a number of four.
+
+Then we get to edge number six.
+That's infinity plus five is
+
+worse than four.
+OK, so no relaxation there.
+
+Edge number seven is
+interesting because I have a
+
+finite value here minus one plus
+the weight of this edge,
+
+which is three.
+That's a total of two,
+
+which is actually better than
+four.
+
+So, this route,
+A, B, c is actually better than
+
+the route I just found a second
+ago.
+
+So, this is now a two.
+This is all happening in one
+
+iteration of the main loop.
+We actually found two good
+
+paths to c.
+We found one better than the
+
+other.
+OK, and that was edge number
+
+seven, and edge number eight is
+over here.
+
+It doesn't matter.
+OK, so that was round one of
+
+this outer loop,
+so, the first value of i.
+
+i equals one.
+OK, now we continue.
+
+Just keep going.
+So, we start with edge number
+
+one.
+Now, minus one plus two is one.
+
+That's better than infinity.
+It'll start speeding up.
+
+It's repetitive.
+It's actually not too much
+
+longer until we're done.
+Number two, this is an infinity
+
+so we don't do anything.
+Number three:
+
+minus one plus two is one;
+better than infinity.
+
+This is vertex d,
+and it's number three.
+
+Number four we've already done.
+Nothing changed.
+
+Number five:
+this is where we see the path
+
+four again, but that's worse
+than two.
+
+So, we don't update anything.
+Number six: one plus five is
+
+six, which is bigger than two,
+so no good.
+
+Go around this way.
+Number seven:
+
+same deal.
+Number eight is interesting.
+
+So, we have a weight of one
+here, a weight of minus three
+
+here.
+So, the total is minus two,
+
+which is better than one.
+So, that was d.
+
+And, I believe that's it.
+So that was definitely the end
+
+of that round.
+So, it's I plus two because we
+
+just looked at the eighth edge.
+And, I'll cheat and check.
+
+Indeed, that is the last thing
+that happens.
+
+We can check the couple of
+outgoing edges from d because
+
+that's the only one whose value
+just changed.
+
+And, there are no more
+relaxations possible.
+
+So, that was in two rounds.
+The claim is we got all the
+
+shortest path weights.
+The algorithm would actually
+
+loop four times to guarantee
+correctness because we have five
+
+vertices here and one less than
+that.
+
+So, in fact,
+in the execution here there are
+
+two more blank rounds at the
+bottom.
+
+Nothing happens.
+But, what the hell?
+
+OK, so that is Bellman-Ford.
+I mean, it's certainly not
+
+doing anything wrong.
+The question is,
+
+why is it guaranteed to
+converge in V minus one steps
+
+unless there is a negative
+weight cycle?
+
+Question?
+
+Right, so that's an
+optimization.
+
+If you discover a whole round,
+and nothing happens,
+
+so you can keep track of that
+in the algorithm thing,
+
+you can stop.
+In the worst case,
+
+it won't make a difference.
+But in practice,
+
+you probably want to do that.
+Yeah?
+
+Good question.
+All right, so some simple
+
+observations,
+I mean, we're only doing
+
+relaxation.
+So, we can use a lot of our
+
+analysis from before.
+In particular,
+
+the d values are only
+decreasing monotonically.
+
+As we cross out values here,
+we are always making it
+
+smaller, which is good.
+Another nifty thing about this
+
+algorithm is that you can run it
+even in a distributed system.
+
+If this is some actual network,
+some computer network,
+
+and these are machines,
+and they're communicating by
+
+these links, I mean,
+it's a purely local thing.
+
+Relaxation is a local thing.
+You don't need any global
+
+strategy, and you're asking
+about, can we do a different
+
+order in each step?
+Well, yeah, you could just keep
+
+relaxing edges,
+and keep relaxing edges,
+
+and just keep going for the
+entire lifetime of the network.
+
+And eventually,
+you will find shortest paths.
+
+So, this algorithm is
+guaranteed to finish in V rounds
+
+in a distributed system.
+It might be more asynchronous.
+
+And, it's a little harder to
+analyze.
+
+But it will still work
+eventually.
+
+It's guaranteed to converge.
+And so, Bellman-Ford is used in
+
+the Internet for finding
+shortest paths.
+
+OK, so let's finally prove that
+it works.
+
+This should only take a couple
+of boards.
+
+So let's suppose we have a
+graph and some edge weights that
+
+have no negative weight cycles.
+Then the claim is that we
+
+terminate with the correct
+answer.
+
+So, Bellman-Ford terminates
+with all of these d of v values
+
+set to the delta values for
+every vertex.
+
+OK, the proof is going to be
+pretty immediate using the
+
+lemmas that we had from before
+if you remember them.
+
+So, we're just going to look at
+every vertex separately.
+
+So, I'll call the vertex v.
+The claim is that this holds by
+
+the end of the algorithm.
+So, remember what we need to
+
+prove is that at some point,
+d of v equals delta of s comma
+
+v because we know it decreases
+monotonically,
+
+and we know that it never gets
+any smaller than the correct
+
+value because relaxations are
+always safe.
+
+So, we just need to show at
+some point this holds,
+
+and that it will hold at the
+end.
+
+So, by monotonicity of the d
+values, and by correctness part
+
+one, which was that the d of v's
+are always greater than or equal
+
+to the deltas,
+we only need to show that at
+
+some point we have equality.
+
+So that's our goal.
+So what we're going to do is
+
+just look at v,
+and the shortest path to v,
+
+and see what happens to the
+algorithm relative to that path.
+
+So, I'm going to name the path.
+Let's call it p.
+
+It starts at vertex v_0 and
+goes to v_1, v_2,
+
+whatever, and ends at v_k.
+And, this is not just any
+
+shortest path,
+but it's one that starts at s.
+
+So, v_0's s,
+and it ends at v.
+
+So, I'm going to give a couple
+of names to s and v so I can
+
+talk about the path more
+uniformly.
+
+So, this is a shortest path
+from s to v.
+
+Now, I also want it to be not
+just any shortest path from s to
+
+v, but among all shortest paths
+from s to v I want it to be one
+
+with the fewest possible edges.
+
+OK, so shortest here means in
+terms of the total weight of the
+
+path.
+Subject to being shortest in
+
+weight, I wanted to also be
+shortest in the number of edges.
+
+And, the reason I want that is
+to be able to conclude that p is
+
+a simple path,
+meaning that it doesn't repeat
+
+any vertices.
+Now, can anyone tell me why I
+
+need to assume that the number
+of edges is the smallest
+
+possible in order to guarantee
+that p is simple?
+
+The claim is that not all
+shortest paths are necessarily
+
+simple.
+Yeah?
+
+Right, I can have a zero weight
+cycle, exactly.
+
+So, we are hoping,
+I mean, in fact in the theorem
+
+here, we're assuming that there
+are no negative weight cycles.
+
+But there might be zero weight
+cycles still.
+
+As a zero weight cycle,
+you can put that in the middle
+
+of any shortest path to make it
+arbitrarily long,
+
+repeat vertices over and over.
+That's going to be annoying.
+
+What I want is that p is
+simple.
+
+And, I can guarantee that
+essentially by shortcutting.
+
+If ever I take a zero weight
+cycle, I throw it away.
+
+And this is one mathematical
+way of doing that.
+
+OK, now what else do we know
+about this shortest path?
+
+Well, we know that subpaths are
+shortest paths are shortest
+
+paths.
+That's optimal substructure.
+
+So, we know what the shortest
+path from s to v_i is sort of
+
+inductively.
+It's the shortest path,
+
+I mean, it's the weight of that
+path, which is,
+
+in particular,
+the shortest path from s to v
+
+minus one plus the weight of the
+last edge, v minus one to v_i.
+
+So, this is by optimal
+substructure as we proved last
+
+time.
+OK, and I think that's pretty
+
+much the warm-up.
+So, I want to sort of do this
+
+inductively in I,
+start out with v zero,
+
+and go up to v_k.
+So, the first question is,
+
+what is d of v_0,
+which is s?
+
+What is d of the source?
+Well, certainly at the
+
+beginning of the algorithm,
+it's zero.
+
+So, let's say equals zero
+initially because that's what we
+
+set it to.
+And it only goes down from
+
+there.
+So, it certainly,
+
+at most, zero.
+The real question is,
+
+what is delta of s comma v_0.
+What is the shortest path
+
+weight from s to s?
+It has to be zero,
+
+otherwise you have a negative
+weight cycle,
+
+exactly.
+My favorite answer,
+
+zero.
+So, if we had another path from
+
+s to s, I mean,
+that is a cycle.
+
+So, it's got to be zero.
+So, these are actually equal at
+
+the beginning of the algorithm,
+which is great.
+
+That means they will be for all
+time because we just argued up
+
+here, only goes down,
+never can get too small.
+
+So, we have d of v_0 set to the
+right thing.
+
+Great: good for the base case
+of the induction.
+
+Of course, what we really care
+about is v_k,
+
+which is v.
+So, let's talk about the v_i
+
+inductively, and then we will
+get v_k as a result.
+
+So, yeah, let's do it by
+induction.
+
+That's more fun.
+
+Let's say that d of v_i is
+equal to delta of s v_i after I
+
+rounds of the algorithm.
+So, this is actually referring
+
+to the I that is in the
+algorithm here.
+
+These are rounds.
+So, one round is an entire
+
+execution of all the edges,
+relaxation of all the edges.
+
+So, this is certainly true for
+I equals zero.
+
+We just proved that.
+After zero rounds,
+
+at the beginning of the
+algorithm, d of v_0 equals delta
+
+of s, v_0.
+OK, so now, that's not really
+
+what I wanted,
+but OK, fine.
+
+Now we'll prove it for d of v_i
+plus one.
+
+Generally, I recommend you
+assume something.
+
+In fact, why don't I follow my
+own advice and change it?
+
+It's usually nicer to think of
+induction as recursion.
+
+So, you assume that this is
+true, let's say,
+
+for j less than the i that you
+care about, and then you prove
+
+it for d of v_i.
+It's usually a lot easier to
+
+think about it that way.
+In particular,
+
+you can use strong induction
+for all less than i.
+
+Here, we're only going to need
+it for one less.
+
+We have some relation between I
+and I minus one here in terms of
+
+the deltas.
+And so, we want to argue
+
+something about the d values.
+OK, well, let's think about
+
+what's going on here.
+We know that,
+
+let's say, after I minus one
+rounds, we have this inductive
+
+hypothesis, d of v_i minus one
+equals delta of s v_i minus one.
+
+And, we want to conclude that
+after i rounds,
+
+so we have one more round to do
+this.
+
+We want to conclude that d of
+v_i has the right answer,
+
+delta of s comma v_i.
+Does that look familiar at all?
+
+So we want to relax every edge
+in this round.
+
+In particular,
+at some point,
+
+we have to relax the edge from
+v_i minus one to v_i.
+
+We know that this path consists
+of edges.
+
+That's the definition of a
+path.
+
+So, during the i'th round,
+we relax every edge.
+
+So, we better relax v_i minus
+one v_i.
+
+And, what happens then?
+It's a test of memory.
+
+Quick, the Death Star is
+approaching.
+
+So, if we have the correct
+value for v_i minus one,
+
+that we relax an outgoing edge
+from there, and that edge is an
+
+edge of the shortest path from s
+to v_i.
+
+What do we know?
+d of v_i becomes the correct
+
+value, delta of s comma v_i.
+This was called correctness
+
+lemma last time.
+One of the things we proved
+
+about Dijkstra's algorithm,
+but it was really just a fact
+
+about relaxation.
+And it was a pretty simple
+
+proof.
+And it comes from this fact.
+
+We know the shortest path
+weight is this.
+
+So, certainly d of v_i was at
+least this big,
+
+and let's suppose it's greater,
+or otherwise we were done.
+
+We know d of v_i minus one is
+set to this.
+
+And so, this is exactly the
+condition that's being checked
+
+in the relaxation step.
+And, the d of v_i value will be
+
+greater than this,
+let's suppose.
+
+And then, we'll set it equal to
+this.
+
+And that's exactly d of s v_i.
+So, when we relax that edge,
+
+we've got to set it to the
+right value.
+
+So, this is the end of the
+proof, right?
+
+It's very simple.
+The point is,
+
+you look at your shortest path.
+Here it is.
+
+And if we assume there's no
+negative weight cycles,
+
+this has the correct value
+initially.
+
+d of s is going to be zero.
+After the first round,
+
+you've got to relax this edge.
+And then you get the right
+
+value for that vertex.
+After the second round,
+
+you've got to relax this edge,
+which gets you the right d
+
+value for this vertex and so on.
+And so, no matter which
+
+shortest path you take,
+you can apply this analysis.
+
+And you know that by,
+if the length of this path,
+
+here we assumed it was k edges,
+then after k rounds you've got
+
+to be done.
+OK, so this was not actually
+
+the end of the proof.
+Sorry.
+
+So this means after k rounds,
+we have the right answer for
+
+v_k, which is v.
+So, the only question is how
+
+big could k be?
+And, it better be the right
+
+answer, at most,
+v minus one is the claim by the
+
+algorithm that you only need to
+do v minus one steps.
+
+And indeed, the number of edges
+in a simple path in a graph is,
+
+at most, the number of vertices
+minus one.
+
+k is, at most,
+v minus one because p is
+
+simple.
+So, that's why we had to assume
+
+that it wasn't just any shortest
+path.
+
+It had to be a simple one so it
+didn't repeat any vertices.
+
+So there are,
+at most, V vertices in the
+
+path, so at most,
+V minus one edges in the path.
+
+OK, and that's all there is to
+Bellman-Ford.
+
+So: pretty simple in
+correctness.
+
+Of course, we're using a lot of
+the lemmas that we proved last
+
+time, which makes it easier.
+OK, a consequence of this
+
+theorem, or of this proof is
+that if Bellman-Ford fails to
+
+converge, and that's what the
+algorithm is checking is whether
+
+this relaxation still requires
+work after these d minus one
+
+steps.
+Right, the end of this
+
+algorithm is run another round,
+a V'th round,
+
+see whether anything changes.
+So, we'll say that the
+
+algorithm fails to converge
+after V minus one steps or
+
+rounds.
+Then, there has to be a
+
+negative weight cycle.
+OK, this is just a
+
+contrapositive of what we
+proved.
+
+We proved that if you assume
+there's no negative weight
+
+cycle, then we know that d of s
+is zero, and then all this
+
+argument says is you've got to
+converge after v minus one
+
+rounds.
+There can't be anything left to
+
+do once you've reached the
+shortest path weights because
+
+you're going monotonically;
+you can never hit the bottom.
+
+You can never go to the floor.
+So, if you fail to converge
+
+somehow after V minus one
+rounds, you've got to have
+
+violated the assumption.
+The only assumption we made was
+
+there's no negative weight
+cycle.
+
+So, this tells us that
+Bellman-Ford is actually
+
+correct.
+When it says that there is a
+
+negative weight cycle,
+it indeed means it.
+
+It's true.
+OK, and you can modify
+
+Bellman-Ford in that case to
+sort of run a little longer,
+
+and find where all the minus
+infinities are.
+
+And that is,
+in some sense,
+
+one of the things you have to
+do in your problem set,
+
+I believe.
+So, I won't cover it here.
+
+But, it's a good exercise in
+any case to figure out how you
+
+would find where the minus
+infinities are.
+
+What are all the vertices
+reachable from negative weight
+
+cycle?
+Those are the ones that have
+
+minus infinities.
+OK, so you might say,
+
+well, that was awfully fast.
+Actually, it's not over yet.
+
+The episode is not yet ended.
+We're going to use Bellman-Ford
+
+to solve the even bigger and
+greater shortest path problems.
+
+And in the remainder of today's
+lecture, we will see it applied
+
+to a more general problem,
+in some sense,
+
+called linear programming.
+And the next lecture,
+
+we'll really use it to do some
+amazing stuff with all pairs
+
+shortest paths.
+Let's go over here.
+
+So, our goal,
+although it won't be obvious
+
+today, is to be able to compute
+the shortest paths between every
+
+pair of vertices,
+which we could certainly do at
+
+this point just by running
+Bellman-Ford v times.
+
+OK, but we want to do better
+than that, of course.
+
+And, that will be the climax of
+the trilogy.
+
+OK, today we just discovered
+who Luke's father is.
+
+So, it turns out the father of
+shortest paths is linear
+
+programming.
+Actually, simultaneously the
+
+father and the mother because
+programs do not have gender.
+
+OK, my father likes to say,
+we both took improv comedy
+
+lessons so we have degrees in
+improvisation.
+
+And he said,
+you know, we went to improv
+
+classes in order to learn how to
+make our humor better.
+
+And, the problem is,
+it didn't actually make our
+
+humor better.
+It just made us less afraid to
+
+use it.
+[LAUGHTER] So,
+
+you are subjected to all this
+improv humor.
+
+I didn't see the connection of
+Luke's father,
+
+but there you go.
+OK, so, linear programming is a
+
+very general problem,
+a very big tool.
+
+Has anyone seen linear
+programming before?
+
+OK, one person.
+And, I'm sure you will,
+
+at some time in your life,
+do anything vaguely computing
+
+optimization related,
+linear programming comes up at
+
+some point.
+It's a very useful tool.
+
+You're given a matrix and two
+vectors: not too exciting yet.
+
+What you want to do is find a
+vector.
+
+This is a very dry description.
+We'll see what makes it so
+
+interesting in a moment.
+
+So, you want to maximize some
+objective, and you have some
+
+constraints.
+And they're all linear.
+
+So, the objective is a linear
+function in the variables x,
+
+and your constraints are a
+bunch of linear constraints,
+
+inequality constraints,
+that's one makes an
+
+interesting.
+It's not just solving a linear
+
+system as you've seen in linear
+algebra, or whatever.
+
+Or, of course,
+it could be that there is no
+
+such x.
+OK: vaguely familiar you might
+
+think to the theorem about
+Bellman-Ford.
+
+And, we'll show that there's
+some kind of connection here
+
+that either you want to find
+something, or show that it
+
+doesn't exist.
+Well, that's still a pretty
+
+vague connection,
+but I also want to maximize
+
+something, or are sort of
+minimize the shortest paths,
+
+OK, somewhat similar.
+We have these constraints.
+
+So, yeah.
+This may be intuitive to you,
+
+I don't know.
+I prefer a more geometric
+
+picture, and I will try to draw
+such a geometric picture,
+
+and I've never tried to do this
+on a blackboard,
+
+so it should be interesting.
+I think I'm going to fail
+
+miserably.
+It sort of looks like a
+
+dodecahedron,
+right?
+
+Sort of, kind of,
+not really.
+
+A bit rough on the bottom,
+OK.
+
+So, if you have a bunch of
+linear constraints,
+
+this is supposed to be in 3-D.
+Now I labeled it.
+
+It's now in 3-D.
+Good.
+
+So, you have these linear
+constraints.
+
+That turns out to define
+hyperplanes in n dimensions.
+
+OK, so you have this base here
+that's three-dimensional space.
+
+So, n equals three.
+And, these hyperplanes,
+
+if you're looking at one side
+of the hyperplane,
+
+that's the less than or equal
+to, if you take the
+
+intersection,
+you get some convex polytope or
+
+polyhedron.
+In 3-D, you might get a
+
+dodecahedron or whatever.
+And, your goal,
+
+you have some objective vector
+c, let's say,
+
+up.
+Suppose that's the c vector.
+
+Your goal is to find the
+highest point in this polytope.
+
+So here, it's maybe this one.
+OK, this is the target.
+
+This is the optimal,
+x.
+
+That is the geometric view.
+If you prefer the algebraic
+
+view, you want to maximize the c
+transpose times x.
+
+So, this is m.
+This is n.
+
+Check out the dimensions work
+out.
+
+So that's saying you want to
+maximize the dot product.
+
+You want to maximize the extent
+to which x is in the direction
+
+c.
+And, you want to maximize that
+
+subject to some constraints,
+which looks something like
+
+this, maybe.
+So, this is A,
+
+and it's m by n.
+You want to multiply it by,
+
+it should be something of
+height n.
+
+That's x.
+Let me put x down here,
+
+n by one.
+And, it should be less than or
+
+equal to something of this
+height, which is B,
+
+the right hand side.
+OK, that's the algebraic view,
+
+which is to check out all the
+dimensions are working out.
+
+But, you can read these off in
+each row here,
+
+when multiplied by this column,
+gives you one value here.
+
+And as just a linear
+constraints on all the x sides.
+
+So, you want to maximize this
+linear function of x_1 up to x_n
+
+subject to these constraints,
+OK?
+
+Pretty simple,
+but pretty powerful in general.
+
+So, it turns out that with,
+you can formulate a huge number
+
+of problems such as shortest
+paths as a linear program.
+
+So, it's a general tool.
+And in this class,
+
+we will not cover any
+algorithms for solving linear
+
+programming.
+It's a bit tricky.
+
+I'll just mention that they are
+out there.
+
+So, there's many efficient
+algorithms, and lots of code
+
+that does this.
+It's a very practical setup.
+
+So, lots of algorithms to solve
+LP's, linear programs.
+
+Linear programming is usually
+called LP.
+
+And, I'll mention a few of
+them.
+
+There's the simplex algorithm.
+This is one of the first.
+
+I think it is the first,
+the ellipsoid algorithm.
+
+There's interior point methods,
+and there's random sampling.
+
+I'll just say a little bit
+about each of these because
+
+we're not going to talk about
+any of them in depth.
+
+The simplex algorithm,
+this is, I mean,
+
+one of the first algorithms in
+the world in some sense,
+
+certainly one of the most
+popular.
+
+It's still used today.
+Almost all linear programming
+
+code uses the simplex algorithm.
+It happens to run an
+
+exponential time in the
+worst-case, so it's actually
+
+pretty bad theoretically.
+But in practice,
+
+it works really well.
+And there is some recent work
+
+that tries to understand this.
+It's still exponential in the
+
+worst case.
+But, it's practical.
+
+There's actually an open
+problem whether there exists a
+
+variation of simplex that runs
+in polynomial time.
+
+But, I won't go into that.
+That's a major open problem in
+
+this area of linear programming.
+The ellipsoid algorithm was the
+
+first algorithm to solve linear
+programming in polynomial time.
+
+So, for a long time,
+people didn't know.
+
+Around this time,
+people started realizing
+
+polynomial time is a good thing.
+That happened around the late
+
+60s.
+Polynomial time is good.
+
+And, the ellipsoid algorithm is
+the first one to do it.
+
+It's a very general algorithm,
+and very powerful,
+
+theoretically:
+completely impractical.
+
+But, it's cool.
+It lets you do things like you
+
+can solve a linear program that
+has exponentially many
+
+constraints in polynomial time.
+You've got all sorts of crazy
+
+things.
+So, I'll just say it's
+
+polynomial time.
+I can't say something nice
+
+about it; don't say it at all.
+It's impractical.
+
+Interior point methods are sort
+of the mixture.
+
+They run in polynomial time.
+You can guarantee that.
+
+And, they are also pretty
+practical, and there's sort of
+
+this competition these days
+about whether simplex or
+
+interior point is better.
+And, I don't know what it is
+
+today but a few years ago they
+were neck and neck.
+
+And, random sampling is a brand
+new approach.
+
+This is just from a couple
+years ago by two MIT professors,
+
+Dimitris Bertsimas and Santosh
+Vempala, I guess the other is in
+
+applied math.
+So, just to show you,
+
+there's active work in this
+area.
+
+People are still finding new
+ways to solve linear programs.
+
+This is completely randomized,
+and very simple,
+
+and very general.
+It hasn't been implemented,
+
+so we don't know how practical
+it is yet.
+
+But, it has potential.
+OK: pretty neat.
+
+OK, we're going to look at a
+somewhat simpler version of
+
+linear programming.
+The first restriction we are
+
+going to make is actually not
+much of a restriction.
+
+But, nonetheless we will
+consider it, it's a little bit
+
+easier to think about.
+So here, we had some polytope
+
+we wanted to maximize some
+objective.
+
+In a feasibility problem,
+I just want to know,
+
+is the polytope empty?
+Can you find any point in that
+
+polytope?
+Can you find any set of values,
+
+x, that satisfy these
+constraints?
+
+OK, so there's no objective.
+c, just find x such that AX is
+
+less than or equal to B.
+OK, it turns out you can prove
+
+a very general theorem that if
+you can solve linear
+
+feasibility, you can also solve
+linear programming.
+
+We won't prove that here,
+but this is actually no easier
+
+than the original problem even
+though it feels easier,
+
+and it's easier to think about.
+I was just saying actually no
+
+easier than LP.
+OK, the next restriction we're
+
+going to make is a real
+restriction.
+
+And it simplifies the problem
+quite a bit.
+
+And that's to look at different
+constraints.
+
+And, if all this seemed a bit
+abstract so far,
+
+we will now ground ourselves
+little bit.
+
+A system of different
+constraints is a linear
+
+feasibility problem.
+So, it's an LP where there's no
+
+objective.
+And, it's with a restriction,
+
+so, where each row of the
+matrix, so, the matrix,
+
+A, has one one,
+and it has one minus one,
+
+and everything else in the row
+is zero.
+
+OK, in other words,
+each constraint has its very
+
+simple form.
+It involves two variables and
+
+some number.
+So, we have something like x_j
+
+minus x_i is less than or equal
+to w_ij.
+
+So, this is just a number.
+These are two variables.
+
+There's a minus sign,
+no values up here,
+
+no coefficients,
+no other of the X_k's appear,
+
+just two of them.
+And, you have a bunch of
+
+constraints of this form,
+one per row of the matrix.
+
+Geometrically,
+I haven't thought about what
+
+this means.
+I think it means the
+
+hyperplanes are pretty simple.
+Sorry I can't do better than
+
+that.
+It's a little hard to see this
+
+in high dimensions.
+But, it will start to
+
+correspond to something we've
+seen, namely the board that its
+
+next to, very shortly.
+OK, so let's do a very quick
+
+example mainly to have something
+to point at.
+
+Here's a very simple system of
+difference constraints --
+
+-- OK, and a solution.
+Why not?
+
+It's not totally trivial to
+solve this, but here's a
+
+solution.
+And the only thing to check is
+
+that each of these constraints
+is satisfied.
+
+x_1 minus x_2 is three,
+which is less than or equal to
+
+three, and so on.
+There could be negative values.
+
+There could be positive values.
+It doesn't matter.
+
+I'd like to transform this
+system of difference constraints
+
+into a graph because we know a
+lot about graphs.
+
+So, we're going to call this
+the constraint graph.
+
+And, it's going to represent
+these constraints.
+
+How'd I do it?
+Well, I take every constraint,
+
+which in general looks like
+this, and I convert it into an
+
+edge.
+OK, so if I write it as x_j
+
+minus x_i is less than or equal
+to some w_ij,
+
+w seems suggestive of weights.
+That's exactly why I called it
+
+w.
+I'm going to make that an edge
+
+from v_i to v_j.
+So, the order flips a little
+
+bit.
+And, the weight of that edge is
+
+w_ij.
+So, just do that.
+
+Make n vertices.
+So, you have the number of
+
+vertices equals n.
+The number of edges equals the
+
+number of constraints,
+which is m, the height of the
+
+matrix, and just transform.
+So, for example,
+
+here we have three variables.
+So, we have three vertices,
+
+v_1, v_2, v_3.
+We have x_1 minus x_2.
+
+So, we have an edge from v_2 to
+v_1 of weight three.
+
+We have x_2 minus x_3.
+So, we have an edge from v_3 to
+
+v_2 of weight minus two.
+And, we have x_1 minus x_3.
+
+So, we have an edge from v_3 to
+v_1 of weight two.
+
+I hope I got the directions
+right.
+
+Yep.
+So, there it is,
+
+a graph: currently no obvious
+connection to shortest paths,
+
+right?
+But in fact,
+
+this constraint is closely
+related to shortest paths.
+
+So let me just rewrite it.
+You could say,
+
+well, an x_j is less than or
+equal to x_i plus w_ij.
+
+Or, you could think of it as
+d[j] less than or equal to d[i]
+
+plus w_ij.
+This is a conceptual balloon.
+
+Look awfully familiar?
+A lot like the triangle
+
+inequality, a lot like
+relaxation.
+
+So, there's a very close
+connection between these two
+
+problems as we will now prove.
+
+So, we're going to have two
+theorems.
+
+And, they're going to look
+similar to the correctness of
+
+Bellman-Ford in that they talk
+about negative weight cycles.
+
+Here we go.
+It turns out,
+
+I mean, we have this constraint
+graph.
+
+It can have negative weights.
+It can have positive weights.
+
+It turns out what matters is if
+you have a negative weight
+
+cycle.
+So, the first thing to prove is
+
+that if you have a negative
+weight cycle that something bad
+
+happens.
+OK, what could happen bad?
+
+Well, we're just trying to
+satisfy this system of
+
+constraints.
+So, the bad thing is that there
+
+might not be any solution.
+These constraints may be
+
+infeasible.
+And that's the claim.
+
+The claim is that this is
+actually an if and only if.
+
+But first we'll proved the if.
+If you have a negative weight
+
+cycle, you're doomed.
+The difference constraints are
+
+unsatisfiable.
+That's a more intuitive way to
+
+say it.
+In the LP world,
+
+they call it infeasible.
+But unsatisfiable makes a lot
+
+more sense.
+There's no way to assign the
+
+x_i's in order to satisfy all
+the constraints simultaneously.
+
+So, let's just take a look.
+Consider a negative weight
+
+cycle.
+It starts at some vertex,
+
+goes through some vertices,
+and at some point comes back.
+
+I don't care whether it repeats
+vertices, just as long as this
+
+cycle, from v_1 to v_1 is a
+negative weight cycle strictly
+
+negative weight.
+
+OK, and what I'm going to do is
+just write down all the
+
+constraints.
+Each of these edges corresponds
+
+to a constraint,
+which must be in the set of
+
+constraints because we had that
+graph.
+
+So, these are all edges.
+Let's look at what they give
+
+us.
+So, we have an edge from v_1 to
+
+v_2.
+That corresponds to x_2 minus
+
+x_1 is, at most,
+something, w_12.
+
+Then we have x_3 minus x_2.
+That's the weight w_23,
+
+and so on.
+And eventually we get up to
+
+something like x_k minus
+x_(k-1).
+
+That's this edge:
+w_(k-1),k , and lastly we have
+
+this edge, which wraps around.
+So, it's x_1 minus x_k,
+
+w_k1 if I've got the signs
+right.
+
+Good, so here's a bunch of
+constraints.
+
+What do you suggest I do with
+them?
+
+Anything interesting about
+these constraints,
+
+say, the left hand sides?
+Sorry?
+
+It sounded like the right word.
+What was it?
+
+Telescopes, yes,
+good.
+
+Everything cancels.
+If I added these up,
+
+there's an x_2 and a minus x_2.
+There's a minus x_1 and an x_1.
+
+There's a minus XK and an XK.
+Everything here cancels if I
+
+add up the left hand sides.
+So, what happens if I add up
+
+the right hand sides?
+Over here I get zero,
+
+my favorite answer.
+And over here,
+
+we get all the weights of all
+the edges in the negative weight
+
+cycle, which is the weight of
+the cycle, which is negative.
+
+So, zero is strictly less than
+zero: contradiction.
+
+Contradiction:
+wait a minute,
+
+we didn't assume anything that
+was false.
+
+So, it's not really a
+contradiction in the
+
+mathematical sense.
+We didn't contradict the world.
+
+We just said that these
+constraints are contradictory.
+
+In other words,
+if you pick any values of the
+
+x_i's, there is no way that
+these can all be true because
+
+that you would get a
+contradiction.
+
+So, it's impossible for these
+things to be satisfied by some
+
+real x_i's.
+So, these must be
+
+unsatisfiable.
+Let's say there's no satisfying
+
+assignment, a little more
+precise, x_1 up to x_m,
+
+no weights.
+Can we satisfy those
+
+constraints?
+Because they add up to zero on
+
+the left-hand side,
+and negative on the right-hand
+
+side.
+OK, so that's an easy proof.
+
+The reverse direction will be
+only slightly harder.
+
+OK, so, cool.
+We have this connection.
+
+So motivation is,
+suppose you'd want to solve
+
+these difference constraints.
+And we'll see one such
+
+application.
+I Googled around for difference
+
+constraints.
+There is a fair number of
+
+papers that care about
+difference constraints.
+
+And, they all use shortest
+paths to solve them.
+
+So, if we can prove a
+connection between shortest
+
+paths, which we know how to
+compute, and difference
+
+constraints, then we'll have
+something cool.
+
+And, next class will see even
+more applications of difference
+
+constraints.
+It turns out they're really
+
+useful for all pairs shortest
+paths.
+
+OK, but for now let's just
+prove this equivalence and
+
+finish it off.
+So, the reverse direction is if
+
+there's no negative weight cycle
+in this constraint graph,
+
+then the system better be
+satisfiable.
+
+The claim is that these
+negative weight cycles are the
+
+only barriers for finding a
+solution to these difference
+
+constraints.
+I have this feeling somewhere
+
+here.
+I had to talk about the
+
+constraint graph.
+Good.
+
+Satisfied, good.
+So, here we're going to see a
+
+technique that is very useful
+when thinking about shortest
+
+paths.
+And, it's a bit hard to guess,
+
+especially if you haven't seen
+it before.
+
+This is useful in problem sets,
+and in quizzes,
+
+and finals, and everything.
+So, keep this in mind.
+
+I mean, I'm using it to prove
+this rather simple theorem,
+
+but the idea of changing the
+graph, so I'm going to call this
+
+constraint graph G.
+Changing the graph is a very
+
+powerful idea.
+So, we're going to add a new
+
+vertex, s, or source,
+use the source,
+
+Luke, and we're going to add a
+bunch of edges from s because
+
+being a source,
+it better be connected to some
+
+things.
+So, we are going to add a zero
+
+weight edge, or weight zero edge
+from s to everywhere,
+
+so, to every other vertex in
+the constraint graph.
+
+Those vertices are called v_i,
+v_1 up to v_n.
+
+So, I have my constraint graph.
+But I'll copy this one so I can
+
+change it.
+It's always good to backup your
+
+work before you make changes,
+right?
+
+So now, I want to add a new
+vertex, s, over here,
+
+my new source.
+I just take my constraint
+
+graph, whatever it looks like,
+add in weight zero edges to all
+
+the other vertices.
+Simple enough.
+
+Now, what did I do?
+What did you do?
+
+Well, I have a candidate source
+now which can reach all the
+
+vertices.
+So, shortest path from s,
+
+hopefully, well,
+paths from s exist.
+
+I can get from s to everywhere
+in weight at most zero.
+
+OK, maybe less.
+Could it be less?
+
+Well, you know,
+like v_2, I can get to it by
+
+zero minus two.
+So, that's less than zero.
+
+So I've got to be a little
+careful.
+
+What if there's a negative
+weight cycle?
+
+Oh no?
+Then there wouldn't be any
+
+shortest paths.
+Fortunately,
+
+we assume that there's no
+negative weight cycle in the
+
+original graph.
+And if you think about it,
+
+if there's no negative weight
+cycle in the original graph,
+
+we add an edge from s to
+everywhere else.
+
+We're not making any new
+negative weight cycles because
+
+you can start at s and go
+somewhere at a cost of zero,
+
+which doesn't affect any
+weights.
+
+And then, you are forced to
+stay in the old graph.
+
+So, there can't be any new
+negative weight cycles.
+
+So, the modified graph has no
+negative weight cycles.
+
+That's good because it also has
+paths from s,
+
+and therefore it also has
+shortest paths from s.
+
+The modified graph has no
+negative weight because it
+
+didn't before.
+And, it has paths from s.
+
+There's a path from s to every
+vertex.
+
+There may not have been before.
+Before, I couldn't get from v_2
+
+to v_3, for example.
+Well, that's still true.
+
+But from s I can get to
+everywhere.
+
+So, that means that this graph,
+this modified graph,
+
+has shortest paths.
+Shortest paths exist from s.
+
+In other words,
+if I took all the shortest path
+
+weights, like I ran Bellman-Ford
+from s, then,
+
+I would get a bunch of finite
+numbers, d of v,
+
+for every value,
+for every vertex.
+
+That seems like a good idea.
+Let's do it.
+
+So, shortest paths exist.
+Let's just assign x_i to be the
+
+shortest path weight from s to
+v_i.
+
+Why not?
+That's a good choice for a
+
+number, the shortest path weight
+from s to v_i.
+
+This is finite because it's
+less than infinity,
+
+and it's greater than minus
+infinity, so,
+
+some finite number.
+That's what we need to do in
+
+order to satisfy these
+constraints.
+
+The claim is that this is a
+satisfying assignment.
+
+Why?
+Triangle inequality.
+
+Somewhere here we wrote
+triangle inequality.
+
+This looks a lot like the
+triangle inequality.
+
+In fact, I think that's the end
+of the proof.
+
+Let's see here.
+What we want to be true with
+
+this assignment is that x_j
+minus x_i is less than or equal
+
+to w_ij whenever ij is an edge.
+Or, let's say v_i,
+
+v_j, for every such constraint,
+so, for v_i,
+
+v_j in the edge set.
+OK, so what is this true?
+
+Well, let's just expand it out.
+So, x_i is this delta,
+
+and x_j is some other delta.
+So, we have delta of s,
+
+vj minus delta of s_vi.
+And, on the right-hand side,
+
+well, w_ij, that was the weight
+of the edge from I to J.
+
+So, this is the weight of v_i
+to v_j.
+
+OK, I will rewrite this
+slightly.
+
+Delta s, vj is less than or
+equal to delta s,
+
+vi plus w of v_i,
+v_j.
+
+And that's the triangle
+inequality more or less.
+
+The shortest path from s to v_j
+is, at most, shortest path from
+
+s to v_i plus a particular path
+from v_i to v_j,
+
+namely the single edge v_i to
+v_j.
+
+This could only be longer than
+the shortest path.
+
+And so, that makes the
+right-hand side bigger,
+
+which makes this inequality
+more true, meaning it was true
+
+before.
+And now it's still true.
+
+And, that proves it.
+This is true.
+
+And, these were all equivalent
+statements.
+
+This we know to be true by
+triangle inequality.
+
+Therefore, these constraints
+are all satisfied.
+
+Magic.
+I'm so excited here.
+
+So, we've proved that having a
+negative weight cycle is exactly
+
+when these system of difference
+constraints are unsatisfiable.
+
+So, if we want to satisfy them,
+if we want to find the right
+
+answer to x, we run
+Bellman-Ford.
+
+Either it says,
+oh, no negative weight cycle.
+
+Then you are hosed.
+Then, there is no solution.
+
+But that's the best you could
+hope to know.
+
+Otherwise, it says,
+oh, there was no negative
+
+weight cycle,
+and here are your shortest path
+
+weights.
+You just plug them in,
+
+and bam, you have your x_i's
+that satisfy the constraints.
+
+Awesome.
+Now, it wasn't just any graph.
+
+I mean, we started with
+constraints, algebra,
+
+we converted it into a graph by
+this transform.
+
+Then we added a source vertex,
+s.
+
+So, I mean, we had to build a
+graph to solve our problem,
+
+very powerful idea.
+Cool.
+
+This is the idea of reduction.
+You can reduce the problem you
+
+want to solve into some problem
+you know how to solve.
+
+You know how to solve shortest
+paths when there are no negative
+
+weight cycles,
+or find out that there is a
+
+negative weight cycle by
+Bellman-Ford.
+
+So, now we know how to solve
+difference constraints.
+
+It turns out you can do even
+more.
+
+Bellman-Ford does a little bit
+more than just solve these
+
+constraints.
+But first let me write down
+
+what I've been jumping up and
+down about.
+
+The corollary is you can use
+Bellman-Ford.
+
+I mean, you make this graph.
+Then you apply Bellman-Ford,
+
+and it will solve your system
+of difference constraints.
+
+So, let me put in some numbers
+here.
+
+You have m difference
+constraints.
+
+And, you have n variables.
+And, it will solve them in
+
+order m times n time.
+Actually, these numbers go up
+
+slightly because we are adding n
+edges, and we're adding one
+
+vertex, but assuming all of
+these numbers are nontrivial,
+
+m is at least n.
+It's order MN time.
+
+OK, trying to avoid cases where
+some of them are close to zero.
+
+Good.
+So, some other facts,
+
+that's what I just said.
+And we'll leave these as
+
+exercises because they're not
+too essential.
+
+The main thing we need is this.
+But, some other cool facts is
+
+that Bellman-Ford actually
+optimizes some objective
+
+functions.
+So, we are saying it's just a
+
+feasibility problem.
+We just want to know whether
+
+these constraints are
+satisfiable.
+
+In fact, you can add a
+particular objective function.
+
+So, you can't give it an
+arbitrary objective function,
+
+but here's one of interest.
+x_1 plus x_2 plus x_n,
+
+OK, but not just that.
+We have some constraints.
+
+OK, this is a linear program.
+I want to maximize the sum of
+
+the x_i's subject to all the
+x_i's being nonpositive and the
+
+difference constraints.
+So, this we had before.
+
+This is fine.
+We noticed at some point you
+
+could get from s to everywhere
+with cost, at most,
+
+zero.
+So, we know that in this
+
+assignment all of the x_i's are
+negative.
+
+That's not necessary,
+but it's true when you run
+
+Bellman-Ford.
+So if you solve your system
+
+using Bellman-Ford,
+which is no less general than
+
+anything else,
+you happen to get nonpositive
+
+x_i's.
+And so, subject to that
+
+constraint, it actually makes
+them is close to zero as
+
+possible in the L1 norm.
+In the sum of these values,
+
+it tries to make the sum as
+close to zero,
+
+it tries to make the values as
+small as possible in absolute
+
+value in this sense.
+OK, it does more than that.
+
+It cooks, it cleans,
+it finds shortest paths.
+
+It also minimizes the spread,
+the maximum over all i of x_i
+
+minus the minimum over all i of
+x_i.
+
+So, I mean, if you have your
+real line, and here are the
+
+x_i's wherever they are.
+It minimizes this distance.
+
+And zero is somewhere over
+here.
+
+So, it tries to make the x_i's
+as compact as possible.
+
+This is actually the L infinity
+norm, if you know stuff about
+
+norms from your linear algebra
+class.
+
+OK, this is the L1 norm.
+I think it minimizes every LP
+
+norm.
+Good, so let's use this for
+
+something.
+Yeah, let's solve a real
+
+problem, and then we'll be done
+for today.
+
+Next class we'll see the really
+cool stuff, the really cool
+
+application of all of this.
+For now, and we'll see a cool
+
+but relatively simple
+application, which is VLSI
+
+layout.
+We talked a little bit about
+
+VLSI way back and divide and
+conquer.
+
+You have a bunch of chips,
+or you want to arrange them,
+
+and minimize some objectives.
+So, here's a particular,
+
+tons of problems that come out
+of VLSI layout.
+
+Here's one of them.
+You have a bunch of features of
+
+an integrated circuit.
+You want to somehow arrange
+
+them on your circuit without
+putting any two of them too
+
+close to each other.
+You have some minimum
+
+separation like at least they
+should not get top of each
+
+other.
+Probably, you also need some
+
+separation to put wires in
+between, and so on,
+
+so, without putting any two
+features too close together.
+
+OK, so just to give you an
+idea, so I have some objects and
+
+I'm going to be a little bit
+vague about how this works.
+
+You have some features.
+This is stuff,
+
+some chips, whatever.
+We don't really care what their
+
+shapes look like.
+I just want to be able to move
+
+them around so that the gap at
+any point, so let me just think
+
+about this gap.
+This gap should be at least
+
+some delta.
+Or, I don't want to use delta.
+
+Let's say epsilon,
+good, small number.
+
+So, I just need some separation
+between all of my parts.
+
+And for this problem,
+I'm going to be pretty simple,
+
+just say that the parts are
+only allowed to slide
+
+horizontally.
+So, it's a one-dimensional
+
+problem.
+These objects are in 2-d,
+
+or whatever,
+but I can only slide them an x
+
+coordinate.
+So, to model that,
+
+I'm going to look at the left
+edge of every part and say,
+
+well, these two left edges
+should be at least some
+
+separation.
+So, I think of it as whatever
+
+the distance is plus some
+epsilon.
+
+But, you know,
+if you have some funky 2-d
+
+shapes you have to compute,
+well, this is a little bit too
+
+close because these come into
+alignment.
+
+But, there's some constraint,
+well, for any two pieces,
+
+I could figure out how close
+they can get.
+
+They should get no closer.
+So, I'm going to call this x_1.
+
+I'll call this x_2.
+So, we have some constraint
+
+like x_2 minus x_1 is at least d
+plus epsilon,
+
+or whatever you compute that
+weight to be.
+
+OK, so for every pair of
+pieces, I can do this,
+
+compute some constraint on how
+far apart they have to be.
+
+And, now I'd like to assign
+these x coordinates.
+
+Right now, I'm assuming they're
+just variables.
+
+I want to slide these pieces
+around horizontally in order to
+
+compactify them as much as
+possible so they fit in the
+
+smallest chip that I can make
+because it costs money,
+
+and time, and everything,
+and power, everything.
+
+You always want your chip
+small.
+
+So, Bellman-Ford does that.
+All right, so Bellman-Ford
+
+solves these constraints because
+it's just a bunch of difference
+
+constraints.
+And we know that they are
+
+solvable because you could
+spread all the pieces out
+
+arbitrarily far.
+And, it minimizes the spread,
+
+minimizes the size of the chip
+I need, a max of x_i minus the
+
+min of x_i.
+So, this is it maximizes
+
+compactness, or minimizes size
+of the chip.
+
+OK, this is a one-dimensional
+problem, so it may seem a little
+
+artificial, but the two
+dimensional problem is really
+
+hard to solve.
+And this is,
+
+in fact, the best you can do
+with a nice polynomial time
+
+algorithm.
+There are other applications if
+
+you're scheduling events in,
+like, a multimedia environment,
+
+and you want to guarantee that
+this audio plays at least two
+
+seconds after this video,
+but then there are things that
+
+are playing at the same time,
+and they have to be within some
+
+gap of each other,
+so, lots of papers about using
+
+Bellman-Ford,
+solve difference constraints to
+
+enable multimedia environments.
+OK, so there you go.
+
+And next class we'll see more
+applications of Bellman-Ford to
+
+all pairs shortest paths.
+Questions?
+
+Great.
\ No newline at end of file
diff --git a/Tw1k46ywN6E.txt b/Tw1k46ywN6E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6f5f457bfaa20a4adba56d435864cf855a5c60d1
--- /dev/null
+++ b/Tw1k46ywN6E.txt
@@ -0,0 +1,13109 @@
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+ocw.mit.edu all right good morning
+
+ align:start position:0%
+ocw.mit.edu all right good morning
+ 
+
+ align:start position:0%
+ocw.mit.edu all right good morning
+everyone thanks for coming on quiz day I
+
+ align:start position:0%
+everyone thanks for coming on quiz day I
+ 
+
+ align:start position:0%
+everyone thanks for coming on quiz day I
+have to have someone to throw frisbees
+
+ align:start position:0%
+have to have someone to throw frisbees
+ 
+
+ align:start position:0%
+have to have someone to throw frisbees
+to you know Empty Chairs uh would be
+
+ align:start position:0%
+to you know Empty Chairs uh would be
+ 
+
+ align:start position:0%
+to you know Empty Chairs uh would be
+difficult uh so we're going to be doing
+
+ align:start position:0%
+difficult uh so we're going to be doing
+ 
+
+ align:start position:0%
+difficult uh so we're going to be doing
+dynamic programming a notion you've
+
+ align:start position:0%
+dynamic programming a notion you've
+ 
+
+ align:start position:0%
+dynamic programming a notion you've
+learned uh in
+
+ align:start position:0%
+learned uh in
+ 
+
+ align:start position:0%
+learned uh in
+66 we look at three different examples
+
+ align:start position:0%
+66 we look at three different examples
+ 
+
+ align:start position:0%
+66 we look at three different examples
+today the first one is uh really at the
+
+ align:start position:0%
+today the first one is uh really at the
+ 
+
+ align:start position:0%
+today the first one is uh really at the
+level of6 a cute little problem on
+
+ align:start position:0%
+level of6 a cute little problem on
+ 
+
+ align:start position:0%
+level of6 a cute little problem on
+finding the longest palindromic sequence
+
+ align:start position:0%
+finding the longest palindromic sequence
+ 
+
+ align:start position:0%
+finding the longest palindromic sequence
+um inside of a longer sequence sometimes
+
+ align:start position:0%
+um inside of a longer sequence sometimes
+ 
+
+ align:start position:0%
+um inside of a longer sequence sometimes
+it's called longest palindromic
+
+ align:start position:0%
+it's called longest palindromic
+ 
+
+ align:start position:0%
+it's called longest palindromic
+subsequence and uh as we'll talk about a
+
+ align:start position:0%
+subsequence and uh as we'll talk about a
+ 
+
+ align:start position:0%
+subsequence and uh as we'll talk about a
+subsequence means that uh it can be
+
+ align:start position:0%
+subsequence means that uh it can be
+ 
+
+ align:start position:0%
+subsequence means that uh it can be
+non-contiguous so you could uh you could
+
+ align:start position:0%
+non-contiguous so you could uh you could
+ 
+
+ align:start position:0%
+non-contiguous so you could uh you could
+skip uh letters uh in a sequence of
+
+ align:start position:0%
+skip uh letters uh in a sequence of
+ 
+
+ align:start position:0%
+skip uh letters uh in a sequence of
+letters uh and it it it would you would
+
+ align:start position:0%
+letters uh and it it it would you would
+ 
+
+ align:start position:0%
+letters uh and it it it would you would
+still have a subsequence corresponding
+
+ align:start position:0%
+still have a subsequence corresponding
+ 
+
+ align:start position:0%
+still have a subsequence corresponding
+to that don't have to be contiguous and
+
+ align:start position:0%
+to that don't have to be contiguous and
+ 
+
+ align:start position:0%
+to that don't have to be contiguous and
+then uh we'll raise the stakes a little
+
+ align:start position:0%
+then uh we'll raise the stakes a little
+ 
+
+ align:start position:0%
+then uh we'll raise the stakes a little
+bit so each of these uh problems uh gets
+
+ align:start position:0%
+bit so each of these uh problems uh gets
+ 
+
+ align:start position:0%
+bit so each of these uh problems uh gets
+progressively more complicated more
+
+ align:start position:0%
+progressively more complicated more
+ 
+
+ align:start position:0%
+progressively more complicated more
+sophisticated and you'll probably see uh
+
+ align:start position:0%
+sophisticated and you'll probably see uh
+ 
+
+ align:start position:0%
+sophisticated and you'll probably see uh
+uh problems here at least alternating
+
+ align:start position:0%
+uh problems here at least alternating
+ 
+
+ align:start position:0%
+uh problems here at least alternating
+coin game that are
+
+ align:start position:0%
+coin game that are
+ 
+
+ align:start position:0%
+coin game that are
+beyond6 uh in the sense that it wasn't
+
+ align:start position:0%
+beyond6 uh in the sense that it wasn't
+ 
+
+ align:start position:0%
+beyond6 uh in the sense that it wasn't
+covered those kinds of Notions weren't
+
+ align:start position:0%
+covered those kinds of Notions weren't
+ 
+
+ align:start position:0%
+covered those kinds of Notions weren't
+covered
+
+ align:start position:0%
+covered
+ 
+
+ align:start position:0%
+covered
+in6 so just in terms of review I wrote
+
+ align:start position:0%
+in6 so just in terms of review I wrote
+ 
+
+ align:start position:0%
+in6 so just in terms of review I wrote
+this up here because I don't want to
+
+ align:start position:0%
+this up here because I don't want to
+ 
+
+ align:start position:0%
+this up here because I don't want to
+spend a whole lot of time on it uh this
+
+ align:start position:0%
+spend a whole lot of time on it uh this
+ 
+
+ align:start position:0%
+spend a whole lot of time on it uh this
+is something that uh you should have
+
+ align:start position:0%
+is something that uh you should have
+ 
+
+ align:start position:0%
+is something that uh you should have
+some familiarity with uh by
+
+ align:start position:0%
+some familiarity with uh by
+ 
+
+ align:start position:0%
+some familiarity with uh by
+I from the recitation for example that
+
+ align:start position:0%
+I from the recitation for example that
+ 
+
+ align:start position:0%
+I from the recitation for example that
+you had on Friday and from dou six
+
+ align:start position:0%
+you had on Friday and from dou six
+ 
+
+ align:start position:0%
+you had on Friday and from dou six
+dynamic programming is this wonderful
+
+ align:start position:0%
+dynamic programming is this wonderful
+ 
+
+ align:start position:0%
+dynamic programming is this wonderful
+Hammer it's a an algorithmic technique
+
+ align:start position:0%
+Hammer it's a an algorithmic technique
+ 
+
+ align:start position:0%
+Hammer it's a an algorithmic technique
+that you can use to solve problems that
+
+ align:start position:0%
+that you can use to solve problems that
+ 
+
+ align:start position:0%
+that you can use to solve problems that
+you know look exponential in complexity
+
+ align:start position:0%
+you know look exponential in complexity
+ 
+
+ align:start position:0%
+you know look exponential in complexity
+but if you can find this Optimum
+
+ align:start position:0%
+but if you can find this Optimum
+ 
+
+ align:start position:0%
+but if you can find this Optimum
+substructure associated with the the
+
+ align:start position:0%
+substructure associated with the the
+ 
+
+ align:start position:0%
+substructure associated with the the
+problem and its connection to its sub
+
+ align:start position:0%
+problem and its connection to its sub
+ 
+
+ align:start position:0%
+problem and its connection to its sub
+problems and if you can characterize
+
+ align:start position:0%
+problems and if you can characterize
+ 
+
+ align:start position:0%
+problems and if you can characterize
+that then you can do a recursive
+
+ align:start position:0%
+that then you can do a recursive
+ 
+
+ align:start position:0%
+that then you can do a recursive
+decomposition of the problem where you
+
+ align:start position:0%
+decomposition of the problem where you
+ 
+
+ align:start position:0%
+decomposition of the problem where you
+show that you can construct
+
+ align:start position:0%
+show that you can construct
+ 
+
+ align:start position:0%
+show that you can construct
+the optimum solution from the sub
+
+ align:start position:0%
+the optimum solution from the sub
+ 
+
+ align:start position:0%
+the optimum solution from the sub
+problems and that's really the the key
+
+ align:start position:0%
+problems and that's really the the key
+ 
+
+ align:start position:0%
+problems and that's really the the key
+step really in dynamic programming is uh
+
+ align:start position:0%
+step really in dynamic programming is uh
+ 
+
+ align:start position:0%
+step really in dynamic programming is uh
+step two you know once you've made this
+
+ align:start position:0%
+step two you know once you've made this
+ 
+
+ align:start position:0%
+step two you know once you've made this
+characterization where you write this
+
+ align:start position:0%
+characterization where you write this
+ 
+
+ align:start position:0%
+characterization where you write this
+recurrence out that relates the optimal
+
+ align:start position:0%
+recurrence out that relates the optimal
+ 
+
+ align:start position:0%
+recurrence out that relates the optimal
+value of a bigger problem to the optimal
+
+ align:start position:0%
+value of a bigger problem to the optimal
+ 
+
+ align:start position:0%
+value of a bigger problem to the optimal
+values of sub problems and um you
+
+ align:start position:0%
+values of sub problems and um you
+ 
+
+ align:start position:0%
+values of sub problems and um you
+compute the value of the optimal
+
+ align:start position:0%
+compute the value of the optimal
+ 
+
+ align:start position:0%
+compute the value of the optimal
+solution uh through uh a recursive memo
+
+ align:start position:0%
+solution uh through uh a recursive memo
+ 
+
+ align:start position:0%
+solution uh through uh a recursive memo
+memorize or recursive
+
+ align:start position:0%
+memorize or recursive
+ 
+
+ align:start position:0%
+memorize or recursive
+memorization and uh that memorization is
+
+ align:start position:0%
+memorization and uh that memorization is
+ 
+
+ align:start position:0%
+memorization and uh that memorization is
+really what gives you the
+
+ align:start position:0%
+really what gives you the
+ 
+
+ align:start position:0%
+really what gives you the
+efficient algorithm because you don't
+
+ align:start position:0%
+efficient algorithm because you don't
+ 
+
+ align:start position:0%
+efficient algorithm because you don't
+repeat the solution of sub problems you
+
+ align:start position:0%
+repeat the solution of sub problems you
+ 
+
+ align:start position:0%
+repeat the solution of sub problems you
+can also do this in an iterative fashion
+
+ align:start position:0%
+can also do this in an iterative fashion
+ 
+
+ align:start position:0%
+can also do this in an iterative fashion
+essentially you're going to be Computing
+
+ align:start position:0%
+essentially you're going to be Computing
+ 
+
+ align:start position:0%
+essentially you're going to be Computing
+things bottom up U you might want to
+
+ align:start position:0%
+things bottom up U you might want to
+ 
+
+ align:start position:0%
+things bottom up U you might want to
+think about it as top down when you
+
+ align:start position:0%
+think about it as top down when you
+ 
+
+ align:start position:0%
+think about it as top down when you
+write your recurrence But ultimately
+
+ align:start position:0%
+write your recurrence But ultimately
+ 
+
+ align:start position:0%
+write your recurrence But ultimately
+when you actually execute the program
+
+ align:start position:0%
+when you actually execute the program
+ 
+
+ align:start position:0%
+when you actually execute the program
+you'll be Computing things bottom up and
+
+ align:start position:0%
+you'll be Computing things bottom up and
+ 
+
+ align:start position:0%
+you'll be Computing things bottom up and
+you'll be checking the memo table to see
+
+ align:start position:0%
+you'll be checking the memo table to see
+ 
+
+ align:start position:0%
+you'll be checking the memo table to see
+if you've actually solved this problem
+
+ align:start position:0%
+if you've actually solved this problem
+ 
+
+ align:start position:0%
+if you've actually solved this problem
+before and uh that would be the
+
+ align:start position:0%
+before and uh that would be the
+ 
+
+ align:start position:0%
+before and uh that would be the
+recursive memoi case which in some sense
+
+ align:start position:0%
+recursive memoi case which in some sense
+ 
+
+ align:start position:0%
+recursive memoi case which in some sense
+is a little bit easier to think about
+
+ align:start position:0%
+is a little bit easier to think about
+ 
+
+ align:start position:0%
+is a little bit easier to think about
+and translates directly from the
+
+ align:start position:0%
+and translates directly from the
+ 
+
+ align:start position:0%
+and translates directly from the
+recurrence uh but the other way to do it
+
+ align:start position:0%
+recurrence uh but the other way to do it
+ 
+
+ align:start position:0%
+recurrence uh but the other way to do it
+is to do it iteratively and uh we'll
+
+ align:start position:0%
+is to do it iteratively and uh we'll
+ 
+
+ align:start position:0%
+is to do it iteratively and uh we'll
+take a look for this first problem as to
+
+ align:start position:0%
+take a look for this first problem as to
+ 
+
+ align:start position:0%
+take a look for this first problem as to
+how you would do the two different ways
+
+ align:start position:0%
+how you would do the two different ways
+ 
+
+ align:start position:0%
+how you would do the two different ways
+um at least from a conceptual standpoint
+
+ align:start position:0%
+um at least from a conceptual standpoint
+ 
+
+ align:start position:0%
+um at least from a conceptual standpoint
+uh even though I might not write out the
+
+ align:start position:0%
+uh even though I might not write out the
+ 
+
+ align:start position:0%
+uh even though I might not write out the
+code of for each of those cases so a
+
+ align:start position:0%
+code of for each of those cases so a
+ 
+
+ align:start position:0%
+code of for each of those cases so a
+couple of choices here recurs in memo wi
+
+ align:start position:0%
+couple of choices here recurs in memo wi
+ 
+
+ align:start position:0%
+couple of choices here recurs in memo wi
+or um
+
+ align:start position:0%
+or um
+ 
+
+ align:start position:0%
+or um
+essentially do it tively and the smaller
+
+ align:start position:0%
+essentially do it tively and the smaller
+ 
+
+ align:start position:0%
+essentially do it tively and the smaller
+sub problems would have to get computed
+
+ align:start position:0%
+sub problems would have to get computed
+ 
+
+ align:start position:0%
+sub problems would have to get computed
+first in both uh approaches uh the one
+
+ align:start position:0%
+first in both uh approaches uh the one
+ 
+
+ align:start position:0%
+first in both uh approaches uh the one
+thing that uh sometimes we don't spend a
+
+ align:start position:0%
+thing that uh sometimes we don't spend a
+ 
+
+ align:start position:0%
+thing that uh sometimes we don't spend a
+whole lot of time on is this last step
+
+ align:start position:0%
+whole lot of time on is this last step
+ 
+
+ align:start position:0%
+whole lot of time on is this last step
+which is getting the exact solution so a
+
+ align:start position:0%
+which is getting the exact solution so a
+ 
+
+ align:start position:0%
+which is getting the exact solution so a
+lot of the time you stop with saying I
+
+ align:start position:0%
+lot of the time you stop with saying I
+ 
+
+ align:start position:0%
+lot of the time you stop with saying I
+can compute the value of the optim
+
+ align:start position:0%
+can compute the value of the optim
+ 
+
+ align:start position:0%
+can compute the value of the optim
+Optimum solution the value of in terms
+
+ align:start position:0%
+Optimum solution the value of in terms
+ 
+
+ align:start position:0%
+Optimum solution the value of in terms
+of the length of the longest pal
+
+ align:start position:0%
+of the length of the longest pal
+ 
+
+ align:start position:0%
+of the length of the longest pal
+sequence is seven or nine but what is
+
+ align:start position:0%
+sequence is seven or nine but what is
+ 
+
+ align:start position:0%
+sequence is seven or nine but what is
+that sequence or subsequence that
+
+ align:start position:0%
+that sequence or subsequence that
+ 
+
+ align:start position:0%
+that sequence or subsequence that
+requires some additional coding some
+
+ align:start position:0%
+requires some additional coding some
+ 
+
+ align:start position:0%
+requires some additional coding some
+additional uh accounting some uh uh the
+
+ align:start position:0%
+additional uh accounting some uh uh the
+ 
+
+ align:start position:0%
+additional uh accounting some uh uh the
+construction of this optimal solution
+
+ align:start position:0%
+construction of this optimal solution
+ 
+
+ align:start position:0%
+construction of this optimal solution
+typically requires some back tracing and
+
+ align:start position:0%
+typically requires some back tracing and
+ 
+
+ align:start position:0%
+typically requires some back tracing and
+some uh information to
+
+ align:start position:0%
+some uh information to
+ 
+
+ align:start position:0%
+some uh information to
+be keep kept track of during the
+
+ align:start position:0%
+be keep kept track of during the
+ 
+
+ align:start position:0%
+be keep kept track of during the
+recursion memoized step or during the
+
+ align:start position:0%
+recursion memoized step or during the
+ 
+
+ align:start position:0%
+recursion memoized step or during the
+iterative step right so that's something
+
+ align:start position:0%
+iterative step right so that's something
+ 
+
+ align:start position:0%
+iterative step right so that's something
+to keep in mind you're not quite done
+
+ align:start position:0%
+to keep in mind you're not quite done
+ 
+
+ align:start position:0%
+to keep in mind you're not quite done
+once you found the value of the optimum
+
+ align:start position:0%
+once you found the value of the optimum
+ 
+
+ align:start position:0%
+once you found the value of the optimum
+solution and more often than not you
+
+ align:start position:0%
+solution and more often than not you
+ 
+
+ align:start position:0%
+solution and more often than not you
+want the solution right so we'll talk
+
+ align:start position:0%
+want the solution right so we'll talk
+ 
+
+ align:start position:0%
+want the solution right so we'll talk
+about that as well a little bit but
+
+ align:start position:0%
+about that as well a little bit but
+ 
+
+ align:start position:0%
+about that as well a little bit but
+let's just dive in and uh look
+
+ align:start position:0%
+let's just dive in and uh look
+ 
+
+ align:start position:0%
+let's just dive in and uh look
+at this cute little
+
+ align:start position:0%
+at this cute little
+ 
+
+ align:start position:0%
+at this cute little
+problem of uh longest Palam dromic
+
+ align:start position:0%
+problem of uh longest Palam dromic
+ 
+
+ align:start position:0%
+problem of uh longest Palam dromic
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+and palindromes of course read the
+
+ align:start position:0%
+and palindromes of course read the
+ 
+
+ align:start position:0%
+and palindromes of course read the
+same front to back or back to front
+
+ align:start position:0%
+same front to back or back to front
+ 
+
+ align:start position:0%
+same front to back or back to front
+radar is a palindrome uh just as a
+
+ align:start position:0%
+radar is a palindrome uh just as a
+ 
+
+ align:start position:0%
+radar is a palindrome uh just as a
+trivial example a single letter is a
+
+ align:start position:0%
+trivial example a single letter is a
+ 
+
+ align:start position:0%
+trivial example a single letter is a
+palindrome U maybe I should have used u
+
+ align:start position:0%
+palindrome U maybe I should have used u
+ 
+
+ align:start position:0%
+palindrome U maybe I should have used u
+a since that's actually a word uh but uh
+
+ align:start position:0%
+a since that's actually a word uh but uh
+ 
+
+ align:start position:0%
+a since that's actually a word uh but uh
+you know here I got BB and that's not
+
+ align:start position:0%
+you know here I got BB and that's not
+ 
+
+ align:start position:0%
+you know here I got BB and that's not
+definitely not a word um at least not a
+
+ align:start position:0%
+definitely not a word um at least not a
+ 
+
+ align:start position:0%
+definitely not a word um at least not a
+word
+
+ align:start position:0%
+word
+ 
+
+ align:start position:0%
+word
+that acronym maybe um rder is a
+
+ align:start position:0%
+that acronym maybe um rder is a
+ 
+
+ align:start position:0%
+that acronym maybe um rder is a
+palindrome
+
+ align:start position:0%
+palindrome
+ 
+
+ align:start position:0%
+palindrome
+able was I I saw Elba right that's a
+
+ align:start position:0%
+able was I I saw Elba right that's a
+ 
+
+ align:start position:0%
+able was I I saw Elba right that's a
+palindrome and that's of course not a
+
+ align:start position:0%
+palindrome and that's of course not a
+ 
+
+ align:start position:0%
+palindrome and that's of course not a
+single word but it's a famous palindrome
+
+ align:start position:0%
+single word but it's a famous palindrome
+ 
+
+ align:start position:0%
+single word but it's a famous palindrome
+uh days of Napoleon uh but what we're
+
+ align:start position:0%
+uh days of Napoleon uh but what we're
+ 
+
+ align:start position:0%
+uh days of Napoleon uh but what we're
+trying to do here is uh given that we
+
+ align:start position:0%
+trying to do here is uh given that we
+ 
+
+ align:start position:0%
+trying to do here is uh given that we
+have uh this notion of a palindrome we'd
+
+ align:start position:0%
+have uh this notion of a palindrome we'd
+ 
+
+ align:start position:0%
+have uh this notion of a palindrome we'd
+like to discover palindromes
+
+ align:start position:0%
+like to discover palindromes
+ 
+
+ align:start position:0%
+like to discover palindromes
+inside longer words or longer sequences
+
+ align:start position:0%
+inside longer words or longer sequences
+ 
+
+ align:start position:0%
+inside longer words or longer sequences
+so what we have is a
+
+ align:start position:0%
+so what we have is a
+ 
+
+ align:start position:0%
+so what we have is a
+string and we'll call it
+
+ align:start position:0%
+string and we'll call it
+ 
+
+ align:start position:0%
+string and we'll call it
+X1 through n n greater than or equal to
+
+ align:start position:0%
+X1 through n n greater than or equal to
+ 
+
+ align:start position:0%
+X1 through n n greater than or equal to
+1 and we want to find the
+
+ align:start position:0%
+1 and we want to find the
+ 
+
+ align:start position:0%
+1 and we want to find the
+longest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+palindrome
+
+ align:start position:0%
+palindrome
+ 
+
+ align:start position:0%
+palindrome
+that is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence and so here's an example to
+
+ align:start position:0%
+subsequence and so here's an example to
+ 
+
+ align:start position:0%
+subsequence and so here's an example to
+get you guys warmed up we'll have a
+
+ align:start position:0%
+get you guys warmed up we'll have a
+ 
+
+ align:start position:0%
+get you guys warmed up we'll have a
+couple of puzzles here in a
+
+ align:start position:0%
+couple of puzzles here in a
+ 
+
+ align:start position:0%
+couple of puzzles here in a
+second so character
+
+ align:start position:0%
+second so character
+ 
+
+ align:start position:0%
+second so character
+and you want to find the longest
+
+ align:start position:0%
+and you want to find the longest
+ 
+
+ align:start position:0%
+and you want to find the longest
+palindrome and so you go I'll pick C
+
+ align:start position:0%
+palindrome and so you go I'll pick C
+ 
+
+ align:start position:0%
+palindrome and so you go I'll pick C
+I'll skip H I'll pick a I'll pick R A
+
+ align:start position:0%
+I'll skip H I'll pick a I'll pick R A
+ 
+
+ align:start position:0%
+I'll skip H I'll pick a I'll pick R A
+and C
+
+ align:start position:0%
+and C
+ 
+
+ align:start position:0%
+and C
+and carak which I guess is not a word
+
+ align:start position:0%
+and carak which I guess is not a word
+ 
+
+ align:start position:0%
+and carak which I guess is not a word
+either but uh it's uh it's the
+
+ align:start position:0%
+either but uh it's uh it's the
+ 
+
+ align:start position:0%
+either but uh it's uh it's the
+longest palindrome that corresponds to a
+
+ align:start position:0%
+longest palindrome that corresponds to a
+ 
+
+ align:start position:0%
+longest palindrome that corresponds to a
+subsequence of character right so uh the
+
+ align:start position:0%
+subsequence of character right so uh the
+ 
+
+ align:start position:0%
+subsequence of character right so uh the
+game here as you can see is to pick the
+
+ align:start position:0%
+game here as you can see is to pick the
+ 
+
+ align:start position:0%
+game here as you can see is to pick the
+letters
+
+ align:start position:0%
+letters
+ 
+
+ align:start position:0%
+letters
+that I form the palindrome and drop the
+
+ align:start position:0%
+that I form the palindrome and drop the
+ 
+
+ align:start position:0%
+that I form the palindrome and drop the
+ones that don't okay and we're going to
+
+ align:start position:0%
+ones that don't okay and we're going to
+ 
+
+ align:start position:0%
+ones that don't okay and we're going to
+have to use dynamic programming uh to do
+
+ align:start position:0%
+have to use dynamic programming uh to do
+ 
+
+ align:start position:0%
+have to use dynamic programming uh to do
+this uh the
+
+ align:start position:0%
+this uh the
+ 
+
+ align:start position:0%
+this uh the
+answer will be greater than or one in
+
+ align:start position:0%
+answer will be greater than or one in
+ 
+
+ align:start position:0%
+answer will be greater than or one in
+length because we've defined a single
+
+ align:start position:0%
+length because we've defined a single
+ 
+
+ align:start position:0%
+length because we've defined a single
+letter as a palindrome right so it has
+
+ align:start position:0%
+letter as a palindrome right so it has
+ 
+
+ align:start position:0%
+letter as a palindrome right so it has
+to be if you have one letter in the
+
+ align:start position:0%
+to be if you have one letter in the
+ 
+
+ align:start position:0%
+to be if you have one letter in the
+input well you just pick that letter but
+
+ align:start position:0%
+input well you just pick that letter but
+ 
+
+ align:start position:0%
+input well you just pick that letter but
+regardless of how many letters you have
+
+ align:start position:0%
+regardless of how many letters you have
+ 
+
+ align:start position:0%
+regardless of how many letters you have
+on the input greater than equal to one
+
+ align:start position:0%
+on the input greater than equal to one
+ 
+
+ align:start position:0%
+on the input greater than equal to one
+you know that you're going to get at
+
+ align:start position:0%
+you know that you're going to get at
+ 
+
+ align:start position:0%
+you know that you're going to get at
+least a a onlet palindrome at the
+
+ align:start position:0%
+least a a onlet palindrome at the
+ 
+
+ align:start position:0%
+least a a onlet palindrome at the
+output uh so here we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go let's say I have under and this is
+
+ align:start position:0%
+go let's say I have under and this is
+ 
+
+ align:start position:0%
+go let's say I have under and this is
+thanks to Eric
+
+ align:start position:0%
+thanks to Eric
+ 
+
+ align:start position:0%
+thanks to Eric
+here got a couple of nice words
+
+ align:start position:0%
+here got a couple of nice words
+ 
+
+ align:start position:0%
+here got a couple of nice words
+underqualified
+
+ align:start position:0%
+underqualified
+ 
+
+ align:start position:0%
+underqualified
+the person who gets me the longest
+
+ align:start position:0%
+the person who gets me the longest
+ 
+
+ align:start position:0%
+the person who gets me the longest
+palindrome Vin of Frisbee and if you
+
+ align:start position:0%
+palindrome Vin of Frisbee and if you
+ 
+
+ align:start position:0%
+palindrome Vin of Frisbee and if you
+want to code dynamic programming the
+
+ align:start position:0%
+want to code dynamic programming the
+ 
+
+ align:start position:0%
+want to code dynamic programming the
+next two minutes and run it on your
+
+ align:start position:0%
+next two minutes and run it on your
+ 
+
+ align:start position:0%
+next two minutes and run it on your
+laptops that's perfectly fine with me
+
+ align:start position:0%
+laptops that's perfectly fine with me
+ 
+
+ align:start position:0%
+laptops that's perfectly fine with me
+that's not cheating okay so
+
+ align:start position:0%
+that's not cheating okay so
+ 
+
+ align:start position:0%
+that's not cheating okay so
+underqualified
+
+ align:start position:0%
+underqualified
+ 
+
+ align:start position:0%
+underqualified
+so U is a palr so we got that right so
+
+ align:start position:0%
+so U is a palr so we got that right so
+ 
+
+ align:start position:0%
+so U is a palr so we got that right so
+one letter for
+
+ align:start position:0%
+one letter for
+ 
+
+ align:start position:0%
+one letter for
+sure what else what's the longest
+
+ align:start position:0%
+sure what else what's the longest
+ 
+
+ align:start position:0%
+sure what else what's the longest
+palindrome shout it out go go ahead
+
+ align:start position:0%
+palindrome shout it out go go ahead
+ 
+
+ align:start position:0%
+palindrome shout it out go go ahead
+Shout It
+
+ align:start position:0%
+Shout It
+ 
+
+ align:start position:0%
+Shout It
+Out Dei well that was quick deified
+
+ align:start position:0%
+Out Dei well that was quick deified
+ 
+
+ align:start position:0%
+Out Dei well that was quick deified
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+right well defi to make is is to make
+
+ align:start position:0%
+right well defi to make is is to make
+ 
+
+ align:start position:0%
+right well defi to make is is to make
+somebody u a a Dy so uh that was you
+
+ align:start position:0%
+somebody u a a Dy so uh that was you
+ 
+
+ align:start position:0%
+somebody u a a Dy so uh that was you
+couple couple of you
+
+ align:start position:0%
+couple couple of you
+ 
+
+ align:start position:0%
+couple couple of you
+guys uh do you have a frisbe yet all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right this is a little bit
+
+ align:start position:0%
+right all right this is a little bit
+ 
+
+ align:start position:0%
+right all right this is a little bit
+more difficult I tried this on my on my
+
+ align:start position:0%
+more difficult I tried this on my on my
+ 
+
+ align:start position:0%
+more difficult I tried this on my on my
+daughter yesterday so I know it's a
+
+ align:start position:0%
+daughter yesterday so I know it's a
+ 
+
+ align:start position:0%
+daughter yesterday so I know it's a
+little more difficult
+
+ align:start position:0%
+little more difficult
+ 
+
+ align:start position:0%
+little more difficult
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+turbo ventilator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we'll call that a
+
+ align:start position:0%
+right we'll call that a
+ 
+
+ align:start position:0%
+right we'll call that a
+word right turbo ventilator right yell
+
+ align:start position:0%
+word right turbo ventilator right yell
+ 
+
+ align:start position:0%
+word right turbo ventilator right yell
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out sorry rotor okay well that's five
+
+ align:start position:0%
+out sorry rotor okay well that's five
+ 
+
+ align:start position:0%
+out sorry rotor okay well that's five
+can anybody beat that
+
+ align:start position:0%
+can anybody beat that
+ 
+
+ align:start position:0%
+can anybody beat that
+Rotator so Rotator Rotator right so r o
+
+ align:start position:0%
+Rotator so Rotator Rotator right so r o
+ 
+
+ align:start position:0%
+Rotator so Rotator Rotator right so r o
+t a t o r
+
+ align:start position:0%
+t a t o r
+ 
+
+ align:start position:0%
+t a t o r
+Rotator all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who is the
+
+ align:start position:0%
+who is the
+ 
+
+ align:start position:0%
+who is the
+Rotator all right could you you already
+
+ align:start position:0%
+Rotator all right could you you already
+ 
+
+ align:start position:0%
+Rotator all right could you you already
+have one I I want to throw this one
+
+ align:start position:0%
+have one I I want to throw this one
+ 
+
+ align:start position:0%
+have one I I want to throw this one
+right um good practice with the quiz
+
+ align:start position:0%
+right um good practice with the quiz
+ 
+
+ align:start position:0%
+right um good practice with the quiz
+guys good practice with the quiz no no
+
+ align:start position:0%
+guys good practice with the quiz no no
+ 
+
+ align:start position:0%
+guys good practice with the quiz no no
+no these quiz jokes never go over well
+
+ align:start position:0%
+no these quiz jokes never go over well
+ 
+
+ align:start position:0%
+no these quiz jokes never go over well
+you know I've been teaching for 27 years
+
+ align:start position:0%
+you know I've been teaching for 27 years
+ 
+
+ align:start position:0%
+you know I've been teaching for 27 years
+and I still haven't learned that you
+
+ align:start position:0%
+and I still haven't learned that you
+ 
+
+ align:start position:0%
+and I still haven't learned that you
+don't joke about
+
+ align:start position:0%
+don't joke about
+ 
+
+ align:start position:0%
+don't joke about
+exams but I so nothing like this on the
+
+ align:start position:0%
+exams but I so nothing like this on the
+ 
+
+ align:start position:0%
+exams but I so nothing like this on the
+quiz I don't want you studying the
+
+ align:start position:0%
+quiz I don't want you studying the
+ 
+
+ align:start position:0%
+quiz I don't want you studying the
+thesaurus as opposed to the textbook for
+
+ align:start position:0%
+thesaurus as opposed to the textbook for
+ 
+
+ align:start position:0%
+thesaurus as opposed to the textbook for
+the for the next few hours okay nothing
+
+ align:start position:0%
+the for the next few hours okay nothing
+ 
+
+ align:start position:0%
+the for the next few hours okay nothing
+like this on the quiz all right um those
+
+ align:start position:0%
+like this on the quiz all right um those
+ 
+
+ align:start position:0%
+like this on the quiz all right um those
+of you who are missing
+
+ align:start position:0%
+of you who are missing
+ 
+
+ align:start position:0%
+of you who are missing
+python who loves 66 and python uh let's
+
+ align:start position:0%
+python who loves 66 and python uh let's
+ 
+
+ align:start position:0%
+python who loves 66 and python uh let's
+let's talk about uh uh how you would
+
+ align:start position:0%
+let's talk about uh uh how you would
+ 
+
+ align:start position:0%
+let's talk about uh uh how you would
+actually solve this using dynamic
+
+ align:start position:0%
+actually solve this using dynamic
+ 
+
+ align:start position:0%
+actually solve this using dynamic
+programming uh and so what we want is Li
+
+ align:start position:0%
+programming uh and so what we want is Li
+ 
+
+ align:start position:0%
+programming uh and so what we want is Li
+J which is the length
+
+ align:start position:0%
+J which is the length
+ 
+
+ align:start position:0%
+J which is the length
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+longest palindromic uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence for XI
+
+ align:start position:0%
+subsequence for XI
+ 
+
+ align:start position:0%
+subsequence for XI
+J and we're going to have I less than or
+
+ align:start position:0%
+J and we're going to have I less than or
+ 
+
+ align:start position:0%
+J and we're going to have I less than or
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J so so that's essentially what we'd
+
+ align:start position:0%
+J so so that's essentially what we'd
+ 
+
+ align:start position:0%
+J so so that's essentially what we'd
+like to uh compute and essentially when
+
+ align:start position:0%
+like to uh compute and essentially when
+ 
+
+ align:start position:0%
+like to uh compute and essentially when
+I've set this
+
+ align:start position:0%
+I've set this
+ 
+
+ align:start position:0%
+I've set this
+here I when I have Li J I have
+
+ align:start position:0%
+here I when I have Li J I have
+ 
+
+ align:start position:0%
+here I when I have Li J I have
+decomposed the overall problem into sub
+
+ align:start position:0%
+decomposed the overall problem into sub
+ 
+
+ align:start position:0%
+decomposed the overall problem into sub
+problems and it's kind of Fairly obvious
+
+ align:start position:0%
+problems and it's kind of Fairly obvious
+ 
+
+ align:start position:0%
+problems and it's kind of Fairly obvious
+in this case because I'm going to have
+
+ align:start position:0%
+in this case because I'm going to have
+ 
+
+ align:start position:0%
+in this case because I'm going to have
+to go in order right I mean that's the
+
+ align:start position:0%
+to go in order right I mean that's the
+ 
+
+ align:start position:0%
+to go in order right I mean that's the
+constraint a subsequence does maintain
+
+ align:start position:0%
+constraint a subsequence does maintain
+ 
+
+ align:start position:0%
+constraint a subsequence does maintain
+the ordering constraint it's not like I
+
+ align:start position:0%
+the ordering constraint it's not like I
+ 
+
+ align:start position:0%
+the ordering constraint it's not like I
+can invert these letters right that
+
+ align:start position:0%
+can invert these letters right that
+ 
+
+ align:start position:0%
+can invert these letters right that
+would be a different problem if I
+
+ align:start position:0%
+would be a different problem if I
+ 
+
+ align:start position:0%
+would be a different problem if I
+allowed you to do that so um I'm going
+
+ align:start position:0%
+allowed you to do that so um I'm going
+ 
+
+ align:start position:0%
+allowed you to do that so um I'm going
+to start somewhere and I'm going to end
+
+ align:start position:0%
+to start somewhere and I'm going to end
+ 
+
+ align:start position:0%
+to start somewhere and I'm going to end
+somewhere and I want to have a non-null
+
+ align:start position:0%
+somewhere and I want to have a non-null
+ 
+
+ align:start position:0%
+somewhere and I want to have a non-null
+subsequence so I'm going to have I less
+
+ align:start position:0%
+subsequence so I'm going to have I less
+ 
+
+ align:start position:0%
+subsequence so I'm going to have I less
+than or equal to J I'm good with I being
+
+ align:start position:0%
+than or equal to J I'm good with I being
+ 
+
+ align:start position:0%
+than or equal to J I'm good with I being
+equal to J because I still have one
+
+ align:start position:0%
+equal to J because I still have one
+ 
+
+ align:start position:0%
+equal to J because I still have one
+letter and well that happens to be a
+
+ align:start position:0%
+letter and well that happens to be a
+ 
+
+ align:start position:0%
+letter and well that happens to be a
+palindrome and it'll have a length of
+
+ align:start position:0%
+palindrome and it'll have a length of
+ 
+
+ align:start position:0%
+palindrome and it'll have a length of
+one right so that's my li
+
+ align:start position:0%
+one right so that's my li
+ 
+
+ align:start position:0%
+one right so that's my li
+J and what I want to do is uh Define a a
+
+ align:start position:0%
+J and what I want to do is uh Define a a
+ 
+
+ align:start position:0%
+J and what I want to do is uh Define a a
+recursive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm that computes Li right so U
+
+ align:start position:0%
+algorithm that computes Li right so U
+ 
+
+ align:start position:0%
+algorithm that computes Li right so U
+we'll just try and figure out what the
+
+ align:start position:0%
+we'll just try and figure out what the
+ 
+
+ align:start position:0%
+we'll just try and figure out what the
+recurrence looks like and then we can
+
+ align:start position:0%
+recurrence looks like and then we can
+ 
+
+ align:start position:0%
+recurrence looks like and then we can
+talk about uh memorization or iteration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if I equals equals
+
+ align:start position:0%
+if I equals equals
+ 
+
+ align:start position:0%
+if I equals equals
+J then I'm going to return one because I
+
+ align:start position:0%
+J then I'm going to return one because I
+ 
+
+ align:start position:0%
+J then I'm going to return one because I
+know that that's a palindrome right by
+
+ align:start position:0%
+know that that's a palindrome right by
+ 
+
+ align:start position:0%
+know that that's a palindrome right by
+default so that's
+
+ align:start position:0%
+default so that's
+ 
+
+ align:start position:0%
+default so that's
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+and um what do you think the next check
+
+ align:start position:0%
+and um what do you think the next check
+ 
+
+ align:start position:0%
+and um what do you think the next check
+should be if if I look at this x
+
+ align:start position:0%
+should be if if I look at this x
+ 
+
+ align:start position:0%
+should be if if I look at this x
+sequence and I've have I as the starting
+
+ align:start position:0%
+sequence and I've have I as the starting
+ 
+
+ align:start position:0%
+sequence and I've have I as the starting
+point in J as the next uh Point what do
+
+ align:start position:0%
+point in J as the next uh Point what do
+ 
+
+ align:start position:0%
+point in J as the next uh Point what do
+you think the next check is going to be
+
+ align:start position:0%
+you think the next check is going to be
+ 
+
+ align:start position:0%
+you think the next check is going to be
+once I have if I is not equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J uh sorry what was that again if x
+
+ align:start position:0%
+J uh sorry what was that again if x
+ 
+
+ align:start position:0%
+J uh sorry what was that again if x
+IAL beautiful you're just checking to
+
+ align:start position:0%
+IAL beautiful you're just checking to
+ 
+
+ align:start position:0%
+IAL beautiful you're just checking to
+see uh you're you're just checking to
+
+ align:start position:0%
+see uh you're you're just checking to
+ 
+
+ align:start position:0%
+see uh you're you're just checking to
+see whether uh uh the two end points are
+
+ align:start position:0%
+see whether uh uh the two end points are
+ 
+
+ align:start position:0%
+see whether uh uh the two end points are
+equal or not because if they're equal uh
+
+ align:start position:0%
+equal or not because if they're equal uh
+ 
+
+ align:start position:0%
+equal or not because if they're equal uh
+then you can uh essentially uh grab
+
+ align:start position:0%
+then you can uh essentially uh grab
+ 
+
+ align:start position:0%
+then you can uh essentially uh grab
+those letters and uh say that you're
+
+ align:start position:0%
+those letters and uh say that you're
+ 
+
+ align:start position:0%
+those letters and uh say that you're
+going to be looking at a
+
+ align:start position:0%
+going to be looking at a
+ 
+
+ align:start position:0%
+going to be looking at a
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+subsequence that uh is going to uh get
+
+ align:start position:0%
+subsequence that uh is going to uh get
+ 
+
+ align:start position:0%
+subsequence that uh is going to uh get
+you a palindrome and you're going to be
+
+ align:start position:0%
+you a palindrome and you're going to be
+ 
+
+ align:start position:0%
+you a palindrome and you're going to be
+able to add these two letters that are
+
+ align:start position:0%
+able to add these two letters that are
+ 
+
+ align:start position:0%
+able to add these two letters that are
+equal on either side of the computed
+
+ align:start position:0%
+equal on either side of the computed
+ 
+
+ align:start position:0%
+equal on either side of the computed
+palindrome from the subsequence right so
+
+ align:start position:0%
+palindrome from the subsequence right so
+ 
+
+ align:start position:0%
+palindrome from the subsequence right so
+if x of
+
+ align:start position:0%
+if x of
+ 
+
+ align:start position:0%
+if x of
+I um equals equals x of
+
+ align:start position:0%
+I um equals equals x of
+ 
+
+ align:start position:0%
+I um equals equals x of
+J then uh I'm going
+
+ align:start position:0%
+J then uh I'm going
+ 
+
+ align:start position:0%
+J then uh I'm going
+to say if
+
+ align:start position:0%
+to say if
+ 
+
+ align:start position:0%
+to say if
+I + 1al equal J I'm going to go ahead
+
+ align:start position:0%
+I + 1al equal J I'm going to go ahead
+ 
+
+ align:start position:0%
+I + 1al equal J I'm going to go ahead
+and return
+
+ align:start position:0%
+and return
+ 
+
+ align:start position:0%
+and return
+two because uh at that point I'm I'm
+
+ align:start position:0%
+two because uh at that point I'm I'm
+ 
+
+ align:start position:0%
+two because uh at that point I'm I'm
+done there's no nothing else to do um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else I'm going to return
+
+ align:start position:0%
+else I'm going to return
+ 
+
+ align:start position:0%
+else I'm going to return
+2+ L of I + 1 Jus one right so I'm going
+
+ align:start position:0%
+2+ L of I + 1 Jus one right so I'm going
+ 
+
+ align:start position:0%
+2+ L of I + 1 Jus one right so I'm going
+to look inside and got these two letters
+
+ align:start position:0%
+to look inside and got these two letters
+ 
+
+ align:start position:0%
+to look inside and got these two letters
+on either side that are equal so I can
+
+ align:start position:0%
+on either side that are equal so I can
+ 
+
+ align:start position:0%
+on either side that are equal so I can
+always uh prepend to the palindrome I
+
+ align:start position:0%
+always uh prepend to the palindrome I
+ 
+
+ align:start position:0%
+always uh prepend to the palindrome I
+got from here the letter and then a pen
+
+ align:start position:0%
+got from here the letter and then a pen
+ 
+
+ align:start position:0%
+got from here the letter and then a pen
+the same letter and I got two plus
+
+ align:start position:0%
+the same letter and I got two plus
+ 
+
+ align:start position:0%
+the same letter and I got two plus
+whatever value I got from this quantity
+
+ align:start position:0%
+whatever value I got from this quantity
+ 
+
+ align:start position:0%
+whatever value I got from this quantity
+here all right so so so far uh it's uh
+
+ align:start position:0%
+here all right so so so far uh it's uh
+ 
+
+ align:start position:0%
+here all right so so so far uh it's uh
+not really particularly interesting from
+
+ align:start position:0%
+not really particularly interesting from
+ 
+
+ align:start position:0%
+not really particularly interesting from
+a standpoint of constructing the optimum
+
+ align:start position:0%
+a standpoint of constructing the optimum
+ 
+
+ align:start position:0%
+a standpoint of constructing the optimum
+solution but this last line that we have
+
+ align:start position:0%
+solution but this last line that we have
+ 
+
+ align:start position:0%
+solution but this last line that we have
+here where we have the case that the two
+
+ align:start position:0%
+here where we have the case that the two
+ 
+
+ align:start position:0%
+here where we have the case that the two
+letters are not equal is the most
+
+ align:start position:0%
+letters are not equal is the most
+ 
+
+ align:start position:0%
+letters are not equal is the most
+interesting line of code that's the most
+
+ align:start position:0%
+interesting line of code that's the most
+ 
+
+ align:start position:0%
+interesting line of code that's the most
+interesting aspect of this algorithm
+
+ align:start position:0%
+interesting aspect of this algorithm
+ 
+
+ align:start position:0%
+interesting aspect of this algorithm
+right so someone want to tell me what
+
+ align:start position:0%
+right so someone want to tell me what
+ 
+
+ align:start position:0%
+right so someone want to tell me what
+this line is going to be out here yeah
+
+ align:start position:0%
+this line is going to be out here yeah
+ 
+
+ align:start position:0%
+this line is going to be out here yeah
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead beautiful that's exactly right so
+
+ align:start position:0%
+ahead beautiful that's exactly right so
+ 
+
+ align:start position:0%
+ahead beautiful that's exactly right so
+what you're going to do is you're going
+
+ align:start position:0%
+what you're going to do is you're going
+ 
+
+ align:start position:0%
+what you're going to do is you're going
+to say I need to look at two different
+
+ align:start position:0%
+to say I need to look at two different
+ 
+
+ align:start position:0%
+to say I need to look at two different
+sub problems and I need to evaluate both
+
+ align:start position:0%
+sub problems and I need to evaluate both
+ 
+
+ align:start position:0%
+sub problems and I need to evaluate both
+of the sub
+
+ align:start position:0%
+of the sub
+ 
+
+ align:start position:0%
+of the sub
+problems uh and the first sub problem is
+
+ align:start position:0%
+problems uh and the first sub problem is
+ 
+
+ align:start position:0%
+problems uh and the first sub problem is
+I'm going to since these two letters are
+
+ align:start position:0%
+I'm going to since these two letters are
+ 
+
+ align:start position:0%
+I'm going to since these two letters are
+different I'm going to have to drop one
+
+ align:start position:0%
+different I'm going to have to drop one
+ 
+
+ align:start position:0%
+different I'm going to have to drop one
+of them okay and I'm going to look
+
+ align:start position:0%
+of them okay and I'm going to look
+ 
+
+ align:start position:0%
+of them okay and I'm going to look
+inside I'm going to say I in this case
+
+ align:start position:0%
+inside I'm going to say I in this case
+ 
+
+ align:start position:0%
+inside I'm going to say I in this case
+I'm going to drop the i letter and I'm
+
+ align:start position:0%
+I'm going to drop the i letter and I'm
+ 
+
+ align:start position:0%
+I'm going to drop the i letter and I'm
+going to get l i + 1 J and in the second
+
+ align:start position:0%
+going to get l i + 1 J and in the second
+ 
+
+ align:start position:0%
+going to get l i + 1 J and in the second
+case I'm going to drop the jth letter
+
+ align:start position:0%
+case I'm going to drop the jth letter
+ 
+
+ align:start position:0%
+case I'm going to drop the jth letter
+and I'm going to get i j minus
+
+ align:start position:0%
+and I'm going to get i j minus
+ 
+
+ align:start position:0%
+and I'm going to get i j minus
+one and that's it so it's a a Max and
+
+ align:start position:0%
+one and that's it so it's a a Max and
+ 
+
+ align:start position:0%
+one and that's it so it's a a Max and
+there's nothing that's being added here
+
+ align:start position:0%
+there's nothing that's being added here
+ 
+
+ align:start position:0%
+there's nothing that's being added here
+because those two letters one of them
+
+ align:start position:0%
+because those two letters one of them
+ 
+
+ align:start position:0%
+because those two letters one of them
+had to get
+
+ align:start position:0%
+had to get
+ 
+
+ align:start position:0%
+had to get
+dropped they weren't equal so one of
+
+ align:start position:0%
+dropped they weren't equal so one of
+ 
+
+ align:start position:0%
+dropped they weren't equal so one of
+them had to get dropped so you're not
+
+ align:start position:0%
+them had to get dropped so you're not
+ 
+
+ align:start position:0%
+them had to get dropped so you're not
+adding anything to this right so uh so
+
+ align:start position:0%
+adding anything to this right so uh so
+ 
+
+ align:start position:0%
+adding anything to this right so uh so
+that's good and at this point you're
+
+ align:start position:0%
+that's good and at this point you're
+ 
+
+ align:start position:0%
+that's good and at this point you're
+kind of done right
+
+ align:start position:0%
+kind of done right
+ 
+
+ align:start position:0%
+kind of done right
+um whoops oh nice catch but you did drop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something uh all right so uh the the
+
+ align:start position:0%
+something uh all right so uh the the
+ 
+
+ align:start position:0%
+something uh all right so uh the the
+thing that we've done here is gotten to
+
+ align:start position:0%
+thing that we've done here is gotten to
+ 
+
+ align:start position:0%
+thing that we've done here is gotten to
+U step three right so just to be clear
+
+ align:start position:0%
+U step three right so just to be clear
+ 
+
+ align:start position:0%
+U step three right so just to be clear
+we're not done done in terms of this
+
+ align:start position:0%
+we're not done done in terms of this
+ 
+
+ align:start position:0%
+we're not done done in terms of this
+chart here because uh we don't have the
+
+ align:start position:0%
+chart here because uh we don't have the
+ 
+
+ align:start position:0%
+chart here because uh we don't have the
+code there that corresponds
+
+ align:start position:0%
+code there that corresponds
+ 
+
+ align:start position:0%
+code there that corresponds
+to actually
+
+ align:start position:0%
+to actually
+ 
+
+ align:start position:0%
+to actually
+Computing uh the sequence right so it's
+
+ align:start position:0%
+Computing uh the sequence right so it's
+ 
+
+ align:start position:0%
+Computing uh the sequence right so it's
+not that hard I'm I'm not going to go
+
+ align:start position:0%
+not that hard I'm I'm not going to go
+ 
+
+ align:start position:0%
+not that hard I'm I'm not going to go
+over uh the code here I I'll you can
+
+ align:start position:0%
+over uh the code here I I'll you can
+ 
+
+ align:start position:0%
+over uh the code here I I'll you can
+certainly U look at it in the notes uh
+
+ align:start position:0%
+certainly U look at it in the notes uh
+ 
+
+ align:start position:0%
+certainly U look at it in the notes uh
+but uh you need a little bit of uh
+
+ align:start position:0%
+but uh you need a little bit of uh
+ 
+
+ align:start position:0%
+but uh you need a little bit of uh
+tracing backwards in this uh recursion
+
+ align:start position:0%
+tracing backwards in this uh recursion
+ 
+
+ align:start position:0%
+tracing backwards in this uh recursion
+to actually compute things what is the
+
+ align:start position:0%
+to actually compute things what is the
+ 
+
+ align:start position:0%
+to actually compute things what is the
+complexity of what I wrote up there
+
+ align:start position:0%
+complexity of what I wrote up there
+ 
+
+ align:start position:0%
+complexity of what I wrote up there
+though yeah s Theta n Square do people
+
+ align:start position:0%
+though yeah s Theta n Square do people
+ 
+
+ align:start position:0%
+though yeah s Theta n Square do people
+agree that the complexity is Theta n
+
+ align:start position:0%
+agree that the complexity is Theta n
+ 
+
+ align:start position:0%
+agree that the complexity is Theta n
+square or is this gentleman an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimist is this is the complexity Theta
+
+ align:start position:0%
+optimist is this is the complexity Theta
+ 
+
+ align:start position:0%
+optimist is this is the complexity Theta
+n Square tell me why the complexity is
+
+ align:start position:0%
+n Square tell me why the complexity is
+ 
+
+ align:start position:0%
+n Square tell me why the complexity is
+Theta n Square because each sub problem
+
+ align:start position:0%
+Theta n Square because each sub problem
+ 
+
+ align:start position:0%
+Theta n Square because each sub problem
+is that that code right there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely but if you actually
+
+ align:start position:0%
+absolutely but if you actually
+ 
+
+ align:start position:0%
+absolutely but if you actually
+implemented this code and you ran it and
+
+ align:start position:0%
+implemented this code and you ran it and
+ 
+
+ align:start position:0%
+implemented this code and you ran it and
+N was a was a was 100 how long would you
+
+ align:start position:0%
+N was a was a was 100 how long would you
+ 
+
+ align:start position:0%
+N was a was a was 100 how long would you
+wait for this code to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete look at it what's
+
+ align:start position:0%
+complete look at it what's
+ 
+
+ align:start position:0%
+complete look at it what's
+missing the cash exactly well you fixed
+
+ align:start position:0%
+missing the cash exactly well you fixed
+ 
+
+ align:start position:0%
+missing the cash exactly well you fixed
+U your own little error there it was a
+
+ align:start position:0%
+U your own little error there it was a
+ 
+
+ align:start position:0%
+U your own little error there it was a
+trick question okay so there's no
+
+ align:start position:0%
+trick question okay so there's no
+ 
+
+ align:start position:0%
+trick question okay so there's no
+recursion I'm sorry there's recursion
+
+ align:start position:0%
+recursion I'm sorry there's recursion
+ 
+
+ align:start position:0%
+recursion I'm sorry there's recursion
+here but no memorization right so this
+
+ align:start position:0%
+here but no memorization right so this
+ 
+
+ align:start position:0%
+here but no memorization right so this
+is exponential complexity right you will
+
+ align:start position:0%
+is exponential complexity right you will
+ 
+
+ align:start position:0%
+is exponential complexity right you will
+recur in fact the recurrence for that is
+
+ align:start position:0%
+recur in fact the recurrence for that is
+ 
+
+ align:start position:0%
+recur in fact the recurrence for that is
+something like T of n equal 1 if n equal
+
+ align:start position:0%
+something like T of n equal 1 if n equal
+ 
+
+ align:start position:0%
+something like T of n equal 1 if n equal
+1 and 2 T nus 1 if n greater than 1 and
+
+ align:start position:0%
+1 and 2 T nus 1 if n greater than 1 and
+ 
+
+ align:start position:0%
+1 and 2 T nus 1 if n greater than 1 and
+this would be 2 to n minus1 in
+
+ align:start position:0%
+this would be 2 to n minus1 in
+ 
+
+ align:start position:0%
+this would be 2 to n minus1 in
+complexity right now there's a single
+
+ align:start position:0%
+complexity right now there's a single
+ 
+
+ align:start position:0%
+complexity right now there's a single
+line of code and you all know this that
+
+ align:start position:0%
+line of code and you all know this that
+ 
+
+ align:start position:0%
+line of code and you all know this that
+would fix this right and that single
+
+ align:start position:0%
+would fix this right and that single
+ 
+
+ align:start position:0%
+would fix this right and that single
+line of code is simply something that
+
+ align:start position:0%
+line of code is simply something that
+ 
+
+ align:start position:0%
+line of code is simply something that
+says right
+
+ align:start position:0%
+says right
+ 
+
+ align:start position:0%
+says right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+look at the LI J and I'm writing this
+
+ align:start position:0%
+look at the LI J and I'm writing this
+ 
+
+ align:start position:0%
+look at the LI J and I'm writing this
+differently I'm I'm I I'm calling this
+
+ align:start position:0%
+differently I'm I'm I I'm calling this
+ 
+
+ align:start position:0%
+differently I'm I'm I I'm calling this
+now a 2d array right so that's why I
+
+ align:start position:0%
+now a 2d array right so that's why I
+ 
+
+ align:start position:0%
+now a 2d array right so that's why I
+have the Open brackets and closed
+
+ align:start position:0%
+have the Open brackets and closed
+ 
+
+ align:start position:0%
+have the Open brackets and closed
+brackets so I'm overloading L here but
+
+ align:start position:0%
+brackets so I'm overloading L here but
+ 
+
+ align:start position:0%
+brackets so I'm overloading L here but
+it's a 2d array that is going to
+
+ align:start position:0%
+it's a 2d array that is going to
+ 
+
+ align:start position:0%
+it's a 2d array that is going to
+essentially be a cache for uh the sub
+
+ align:start position:0%
+essentially be a cache for uh the sub
+ 
+
+ align:start position:0%
+essentially be a cache for uh the sub
+problem solution values okay and then if
+
+ align:start position:0%
+problem solution values okay and then if
+ 
+
+ align:start position:0%
+problem solution values okay and then if
+you want to do the the back tracing to
+
+ align:start position:0%
+you want to do the the back tracing to
+ 
+
+ align:start position:0%
+you want to do the the back tracing to
+actually compute the solution you can
+
+ align:start position:0%
+actually compute the solution you can
+ 
+
+ align:start position:0%
+actually compute the solution you can
+certainly have that as an additional
+
+ align:start position:0%
+certainly have that as an additional
+ 
+
+ align:start position:0%
+certainly have that as an additional
+record that's uh connected to this very
+
+ align:start position:0%
+record that's uh connected to this very
+ 
+
+ align:start position:0%
+record that's uh connected to this very
+same value but that's uh implementation
+
+ align:start position:0%
+same value but that's uh implementation
+ 
+
+ align:start position:0%
+same value but that's uh implementation
+and we won't really go there so look at
+
+ align:start position:0%
+and we won't really go there so look at
+ 
+
+ align:start position:0%
+and we won't really go there so look at
+Li and don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurse if Li already computed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's important to remember
+
+ align:start position:0%
+okay so that's important to remember
+ 
+
+ align:start position:0%
+okay so that's important to remember
+right now if you actually put that uh
+
+ align:start position:0%
+right now if you actually put that uh
+ 
+
+ align:start position:0%
+right now if you actually put that uh
+the cache look up hash table look up
+
+ align:start position:0%
+the cache look up hash table look up
+ 
+
+ align:start position:0%
+the cache look up hash table look up
+array look up what whatever you want to
+
+ align:start position:0%
+array look up what whatever you want to
+ 
+
+ align:start position:0%
+array look up what whatever you want to
+call it out there then what you said is
+
+ align:start position:0%
+call it out there then what you said is
+ 
+
+ align:start position:0%
+call it out there then what you said is
+exactly correct right so our um our uh
+
+ align:start position:0%
+exactly correct right so our um our uh
+ 
+
+ align:start position:0%
+exactly correct right so our um our uh
+formula for computing the complexity of
+
+ align:start position:0%
+formula for computing the complexity of
+ 
+
+ align:start position:0%
+formula for computing the complexity of
+a DP that you've seen a bunch of times
+
+ align:start position:0%
+a DP that you've seen a bunch of times
+ 
+
+ align:start position:0%
+a DP that you've seen a bunch of times
+and I mentioned in the very first
+
+ align:start position:0%
+and I mentioned in the very first
+ 
+
+ align:start position:0%
+and I mentioned in the very first
+lecture as well is number of sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+time to
+
+ align:start position:0%
+time to
+ 
+
+ align:start position:0%
+time to
+solve each sub
+
+ align:start position:0%
+solve each sub
+ 
+
+ align:start position:0%
+solve each sub
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+assuming are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given that smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones are solved or a look is order one
+
+ align:start position:0%
+ones are solved or a look is order one
+ 
+
+ align:start position:0%
+ones are solved or a look is order one
+so look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up now you could say the hash table look
+
+ align:start position:0%
+up now you could say the hash table look
+ 
+
+ align:start position:0%
+up now you could say the hash table look
+up is order one on average etc etc so um
+
+ align:start position:0%
+up is order one on average etc etc so um
+ 
+
+ align:start position:0%
+up is order one on average etc etc so um
+what actually happens in the worst case
+
+ align:start position:0%
+what actually happens in the worst case
+ 
+
+ align:start position:0%
+what actually happens in the worst case
+in this particular case and in most DPS
+
+ align:start position:0%
+in this particular case and in most DPS
+ 
+
+ align:start position:0%
+in this particular case and in most DPS
+uh you can uh do things like uh perfect
+
+ align:start position:0%
+uh you can uh do things like uh perfect
+ 
+
+ align:start position:0%
+uh you can uh do things like uh perfect
+hashing or something that's even simpler
+
+ align:start position:0%
+hashing or something that's even simpler
+ 
+
+ align:start position:0%
+hashing or something that's even simpler
+in this case it's just a 2d array
+
+ align:start position:0%
+in this case it's just a 2d array
+ 
+
+ align:start position:0%
+in this case it's just a 2d array
+there's not going to be any collisions
+
+ align:start position:0%
+there's not going to be any collisions
+ 
+
+ align:start position:0%
+there's not going to be any collisions
+if you just use I andj as the indices to
+
+ align:start position:0%
+if you just use I andj as the indices to
+ 
+
+ align:start position:0%
+if you just use I andj as the indices to
+the array so you will definitely get a
+
+ align:start position:0%
+the array so you will definitely get a
+ 
+
+ align:start position:0%
+the array so you will definitely get a
+an order one look up uh in in this case
+
+ align:start position:0%
+an order one look up uh in in this case
+ 
+
+ align:start position:0%
+an order one look up uh in in this case
+and most problems we look at uh in 046
+
+ align:start position:0%
+and most problems we look at uh in 046
+ 
+
+ align:start position:0%
+and most problems we look at uh in 046
+so if you just do that computation which
+
+ align:start position:0%
+so if you just do that computation which
+ 
+
+ align:start position:0%
+so if you just do that computation which
+uh my friend over here just described
+
+ align:start position:0%
+uh my friend over here just described
+ 
+
+ align:start position:0%
+uh my friend over here just described
+you do get your Theta n Square because
+
+ align:start position:0%
+you do get your Theta n Square because
+ 
+
+ align:start position:0%
+you do get your Theta n Square because
+you have Theta n Square sub problems and
+
+ align:start position:0%
+you have Theta n Square sub problems and
+ 
+
+ align:start position:0%
+you have Theta n Square sub problems and
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+uh time to solve each sub problem
+
+ align:start position:0%
+uh time to solve each sub problem
+ 
+
+ align:start position:0%
+uh time to solve each sub problem
+given that the smaller ones are solved
+
+ align:start position:0%
+given that the smaller ones are solved
+ 
+
+ align:start position:0%
+given that the smaller ones are solved
+um is uh is is simply going to be a
+
+ align:start position:0%
+um is uh is is simply going to be a
+ 
+
+ align:start position:0%
+um is uh is is simply going to be a
+computation of a of a Max and an
+
+ align:start position:0%
+computation of a of a Max and an
+ 
+
+ align:start position:0%
+computation of a of a Max and an
+addition right so all of that is is
+
+ align:start position:0%
+addition right so all of that is is
+ 
+
+ align:start position:0%
+addition right so all of that is is
+Theta one right because you're not
+
+ align:start position:0%
+Theta one right because you're not
+ 
+
+ align:start position:0%
+Theta one right because you're not
+counting the recursive calls okay so uh
+
+ align:start position:0%
+counting the recursive calls okay so uh
+ 
+
+ align:start position:0%
+counting the recursive calls okay so uh
+this is our first example I'm I'm uh
+
+ align:start position:0%
+this is our first example I'm I'm uh
+ 
+
+ align:start position:0%
+this is our first example I'm I'm uh
+done with it uh any questions about it
+
+ align:start position:0%
+done with it uh any questions about it
+ 
+
+ align:start position:0%
+done with it uh any questions about it
+any questions about DP in
+
+ align:start position:0%
+any questions about DP in
+ 
+
+ align:start position:0%
+any questions about DP in
+general all right good uh so little bit
+
+ align:start position:0%
+general all right good uh so little bit
+ 
+
+ align:start position:0%
+general all right good uh so little bit
+of review there
+
+ align:start position:0%
+of review there
+ 
+
+ align:start position:0%
+of review there
+uh not a particularly complicated
+
+ align:start position:0%
+uh not a particularly complicated
+ 
+
+ align:start position:0%
+uh not a particularly complicated
+question uh let's uh go to a different
+
+ align:start position:0%
+question uh let's uh go to a different
+ 
+
+ align:start position:0%
+question uh let's uh go to a different
+question corresponding to Optimal binary
+
+ align:start position:0%
+question corresponding to Optimal binary
+ 
+
+ align:start position:0%
+question corresponding to Optimal binary
+search trees it's a very different
+
+ align:start position:0%
+search trees it's a very different
+ 
+
+ align:start position:0%
+search trees it's a very different
+question I I don't think I need this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anymore and it's kind of cute in its own
+
+ align:start position:0%
+anymore and it's kind of cute in its own
+ 
+
+ align:start position:0%
+anymore and it's kind of cute in its own
+way one of the things that's interesting
+
+ align:start position:0%
+way one of the things that's interesting
+ 
+
+ align:start position:0%
+way one of the things that's interesting
+about this question
+
+ align:start position:0%
+about this question
+ 
+
+ align:start position:0%
+about this question
+is is it seems like a greedy algorithm
+
+ align:start position:0%
+is is it seems like a greedy algorithm
+ 
+
+ align:start position:0%
+is is it seems like a greedy algorithm
+should work and we'll talk about that in
+
+ align:start position:0%
+should work and we'll talk about that in
+ 
+
+ align:start position:0%
+should work and we'll talk about that in
+as to why the greedy algorithm you know
+
+ align:start position:0%
+as to why the greedy algorithm you know
+ 
+
+ align:start position:0%
+as to why the greedy algorithm you know
+doesn't quite work so it's kind of
+
+ align:start position:0%
+doesn't quite work so it's kind of
+ 
+
+ align:start position:0%
+doesn't quite work so it's kind of
+similar to the interval scheduling and
+
+ align:start position:0%
+similar to the interval scheduling and
+ 
+
+ align:start position:0%
+similar to the interval scheduling and
+the weighted interval scheduling problem
+
+ align:start position:0%
+the weighted interval scheduling problem
+ 
+
+ align:start position:0%
+the weighted interval scheduling problem
+that we had back in February where the
+
+ align:start position:0%
+that we had back in February where the
+ 
+
+ align:start position:0%
+that we had back in February where the
+regular interval scheduling problem
+
+ align:start position:0%
+regular interval scheduling problem
+ 
+
+ align:start position:0%
+regular interval scheduling problem
+greedy worked earliest finish time
+
+ align:start position:0%
+greedy worked earliest finish time
+ 
+
+ align:start position:0%
+greedy worked earliest finish time
+worked uh but when it came to weights we
+
+ align:start position:0%
+worked uh but when it came to weights we
+ 
+
+ align:start position:0%
+worked uh but when it came to weights we
+had to
+
+ align:start position:0%
+had to
+ 
+
+ align:start position:0%
+had to
+graduate um to dynamic programming so um
+
+ align:start position:0%
+graduate um to dynamic programming so um
+ 
+
+ align:start position:0%
+graduate um to dynamic programming so um
+here's our second problem optimal bsts
+
+ align:start position:0%
+here's our second problem optimal bsts
+ 
+
+ align:start position:0%
+here's our second problem optimal bsts
+right so what is an optimal
+
+ align:start position:0%
+right so what is an optimal
+ 
+
+ align:start position:0%
+right so what is an optimal
+bstd um we have a bunch of
+
+ align:start position:0%
+bstd um we have a bunch of
+ 
+
+ align:start position:0%
+bstd um we have a bunch of
+keys that we want to store in the BST K1
+
+ align:start position:0%
+keys that we want to store in the BST K1
+ 
+
+ align:start position:0%
+keys that we want to store in the BST K1
+through KNN and um we'll assume that the
+
+ align:start position:0%
+through KNN and um we'll assume that the
+ 
+
+ align:start position:0%
+through KNN and um we'll assume that the
+way this is set up is that K1 is less
+
+ align:start position:0%
+way this is set up is that K1 is less
+ 
+
+ align:start position:0%
+way this is set up is that K1 is less
+than K2 da d da less than KNN and just
+
+ align:start position:0%
+than K2 da d da less than KNN and just
+ 
+
+ align:start position:0%
+than K2 da d da less than KNN and just
+to make our life easier in our examples
+
+ align:start position:0%
+to make our life easier in our examples
+ 
+
+ align:start position:0%
+to make our life easier in our examples
+I we'll just assume that Ki equals
+
+ align:start position:0%
+I we'll just assume that Ki equals
+ 
+
+ align:start position:0%
+I we'll just assume that Ki equals
+I um that's not necessarily required for
+
+ align:start position:0%
+I um that's not necessarily required for
+ 
+
+ align:start position:0%
+I um that's not necessarily required for
+anything we're going to do next is just
+
+ align:start position:0%
+anything we're going to do next is just
+ 
+
+ align:start position:0%
+anything we're going to do next is just
+for the sake of examples and keeping
+
+ align:start position:0%
+for the sake of examples and keeping
+ 
+
+ align:start position:0%
+for the sake of examples and keeping
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+manageable so I got a bunch of keys and
+
+ align:start position:0%
+manageable so I got a bunch of keys and
+ 
+
+ align:start position:0%
+manageable so I got a bunch of keys and
+clearly there are many different binary
+
+ align:start position:0%
+clearly there are many different binary
+ 
+
+ align:start position:0%
+clearly there are many different binary
+search trees that uh can come uh whether
+
+ align:start position:0%
+search trees that uh can come uh whether
+ 
+
+ align:start position:0%
+search trees that uh can come uh whether
+they're balanced or unbalanced many
+
+ align:start position:0%
+they're balanced or unbalanced many
+ 
+
+ align:start position:0%
+they're balanced or unbalanced many
+different binary search trees can be
+
+ align:start position:0%
+different binary search trees can be
+ 
+
+ align:start position:0%
+different binary search trees can be
+consistent with uh a given set of keys
+
+ align:start position:0%
+consistent with uh a given set of keys
+ 
+
+ align:start position:0%
+consistent with uh a given set of keys
+right if I choose the root to be uh KNN
+
+ align:start position:0%
+right if I choose the root to be uh KNN
+ 
+
+ align:start position:0%
+right if I choose the root to be uh KNN
+then I'm going to get this horribly
+
+ align:start position:0%
+then I'm going to get this horribly
+ 
+
+ align:start position:0%
+then I'm going to get this horribly
+unbalanced tree right if I chose the
+
+ align:start position:0%
+unbalanced tree right if I chose the
+ 
+
+ align:start position:0%
+unbalanced tree right if I chose the
+root to be somewhere in the middle then
+
+ align:start position:0%
+root to be somewhere in the middle then
+ 
+
+ align:start position:0%
+root to be somewhere in the middle then
+I'm going to get something that looks a
+
+ align:start position:0%
+I'm going to get something that looks a
+ 
+
+ align:start position:0%
+I'm going to get something that looks a
+little better at least at the top level
+
+ align:start position:0%
+little better at least at the top level
+ 
+
+ align:start position:0%
+little better at least at the top level
+but again if I messed it up at the next
+
+ align:start position:0%
+but again if I messed it up at the next
+ 
+
+ align:start position:0%
+but again if I messed it up at the next
+level I'd get something that's
+
+ align:start position:0%
+level I'd get something that's
+ 
+
+ align:start position:0%
+level I'd get something that's
+unbalanced right so there's clearly many
+
+ align:start position:0%
+unbalanced right so there's clearly many
+ 
+
+ align:start position:0%
+unbalanced right so there's clearly many
+different bsts uh I'm not talking about
+
+ align:start position:0%
+different bsts uh I'm not talking about
+ 
+
+ align:start position:0%
+different bsts uh I'm not talking about
+balanced bsts here but we're going to
+
+ align:start position:0%
+balanced bsts here but we're going to
+ 
+
+ align:start position:0%
+balanced bsts here but we're going to
+Define an optimality Criterion that's a
+
+ align:start position:0%
+Define an optimality Criterion that's a
+ 
+
+ align:start position:0%
+Define an optimality Criterion that's a
+little bit different from balanced bsts
+
+ align:start position:0%
+little bit different from balanced bsts
+ 
+
+ align:start position:0%
+little bit different from balanced bsts
+because it's going to have this
+
+ align:start position:0%
+because it's going to have this
+ 
+
+ align:start position:0%
+because it's going to have this
+additional cost function associated with
+
+ align:start position:0%
+additional cost function associated with
+ 
+
+ align:start position:0%
+additional cost function associated with
+it that corresponds to the weight of the
+
+ align:start position:0%
+it that corresponds to the weight of the
+ 
+
+ align:start position:0%
+it that corresponds to the weight of the
+keys okay so what is that well I'm going
+
+ align:start position:0%
+keys okay so what is that well I'm going
+ 
+
+ align:start position:0%
+keys okay so what is that well I'm going
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+weights um associated with each of these
+
+ align:start position:0%
+weights um associated with each of these
+ 
+
+ align:start position:0%
+weights um associated with each of these
+Keys corresponding to W1 through WN and
+
+ align:start position:0%
+Keys corresponding to W1 through WN and
+ 
+
+ align:start position:0%
+Keys corresponding to W1 through WN and
+um the easiest way to uh motivate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you to think that um these weights are
+
+ align:start position:0%
+you to think that um these weights are
+ 
+
+ align:start position:0%
+you to think that um these weights are
+an interesting addition to this problem
+
+ align:start position:0%
+an interesting addition to this problem
+ 
+
+ align:start position:0%
+an interesting addition to this problem
+is to think about these weights as being
+
+ align:start position:0%
+is to think about these weights as being
+ 
+
+ align:start position:0%
+is to think about these weights as being
+search probabilities so what you have
+
+ align:start position:0%
+search probabilities so what you have
+ 
+
+ align:start position:0%
+search probabilities so what you have
+for argument sake is a is a static
+
+ align:start position:0%
+for argument sake is a is a static
+ 
+
+ align:start position:0%
+for argument sake is a is a static
+structure that you've created uh and I
+
+ align:start position:0%
+structure that you've created uh and I
+ 
+
+ align:start position:0%
+structure that you've created uh and I
+mean you could modify it there's nothing
+
+ align:start position:0%
+mean you could modify it there's nothing
+ 
+
+ align:start position:0%
+mean you could modify it there's nothing
+that stopping you from doing that but
+
+ align:start position:0%
+that stopping you from doing that but
+ 
+
+ align:start position:0%
+that stopping you from doing that but
+let's just pretend for now that it's a
+
+ align:start position:0%
+let's just pretend for now that it's a
+ 
+
+ align:start position:0%
+let's just pretend for now that it's a
+static structure corresponding to this
+
+ align:start position:0%
+static structure corresponding to this
+ 
+
+ align:start position:0%
+static structure corresponding to this
+BST has a particular structure and um
+
+ align:start position:0%
+BST has a particular structure and um
+ 
+
+ align:start position:0%
+BST has a particular structure and um
+chances are you're going to be searching
+
+ align:start position:0%
+chances are you're going to be searching
+ 
+
+ align:start position:0%
+chances are you're going to be searching
+for some keys more frequently than
+
+ align:start position:0%
+for some keys more frequently than
+ 
+
+ align:start position:0%
+for some keys more frequently than
+others and the wi tell you what the
+
+ align:start position:0%
+others and the wi tell you what the
+ 
+
+ align:start position:0%
+others and the wi tell you what the
+probabilities are in terms of searching
+
+ align:start position:0%
+probabilities are in terms of searching
+ 
+
+ align:start position:0%
+probabilities are in terms of searching
+for a particular key Ki right so you can
+
+ align:start position:0%
+for a particular key Ki right so you can
+ 
+
+ align:start position:0%
+for a particular key Ki right so you can
+imagine and we won't have this here that
+
+ align:start position:0%
+imagine and we won't have this here that
+ 
+
+ align:start position:0%
+imagine and we won't have this here that
+uh you take the wi all sum up to one if
+
+ align:start position:0%
+uh you take the wi all sum up to one if
+ 
+
+ align:start position:0%
+uh you take the wi all sum up to one if
+you want to think of them as
+
+ align:start position:0%
+you want to think of them as
+ 
+
+ align:start position:0%
+you want to think of them as
+probabilities or you can just I'm just
+
+ align:start position:0%
+probabilities or you can just I'm just
+ 
+
+ align:start position:0%
+probabilities or you can just I'm just
+going to give you numbers I don't want
+
+ align:start position:0%
+going to give you numbers I don't want
+ 
+
+ align:start position:0%
+going to give you numbers I don't want
+to deal with fractions no don't
+
+ align:start position:0%
+to deal with fractions no don't
+ 
+
+ align:start position:0%
+to deal with fractions no don't
+particularly like fractions uh so uh you
+
+ align:start position:0%
+particularly like fractions uh so uh you
+ 
+
+ align:start position:0%
+particularly like fractions uh so uh you
+can imagine that each probability
+
+ align:start position:0%
+can imagine that each probability
+ 
+
+ align:start position:0%
+can imagine that each probability
+corresponds to a wi divided by the sum
+
+ align:start position:0%
+corresponds to a wi divided by the sum
+ 
+
+ align:start position:0%
+corresponds to a wi divided by the sum
+of all of the wi if you want all of the
+
+ align:start position:0%
+of all of the wi if you want all of the
+ 
+
+ align:start position:0%
+of all of the wi if you want all of the
+probabilities to sum up to one okay but
+
+ align:start position:0%
+probabilities to sum up to one okay but
+ 
+
+ align:start position:0%
+probabilities to sum up to one okay but
+so think of them as search probabilities
+
+ align:start position:0%
+so think of them as search probabilities
+ 
+
+ align:start position:0%
+so think of them as search probabilities
+because then you'll see what the point
+
+ align:start position:0%
+because then you'll see what the point
+ 
+
+ align:start position:0%
+because then you'll see what the point
+of this exercise is uh and the point of
+
+ align:start position:0%
+of this exercise is uh and the point of
+ 
+
+ align:start position:0%
+of this exercise is uh and the point of
+this exercise is to
+
+ align:start position:0%
+this exercise is to
+ 
+
+ align:start position:0%
+this exercise is to
+find the BST T so we're actually
+
+ align:start position:0%
+find the BST T so we're actually
+ 
+
+ align:start position:0%
+find the BST T so we're actually
+constructing a binary search Tre here so
+
+ align:start position:0%
+constructing a binary search Tre here so
+ 
+
+ align:start position:0%
+constructing a binary search Tre here so
+it's a little more interesting than than
+
+ align:start position:0%
+it's a little more interesting than than
+ 
+
+ align:start position:0%
+it's a little more interesting than than
+a subsequence for example it has a
+
+ align:start position:0%
+a subsequence for example it has a
+ 
+
+ align:start position:0%
+a subsequence for example it has a
+richer structure associated with it
+
+ align:start position:0%
+richer structure associated with it
+ 
+
+ align:start position:0%
+richer structure associated with it
+there are an exponential number of
+
+ align:start position:0%
+there are an exponential number of
+ 
+
+ align:start position:0%
+there are an exponential number of
+possible binary search trees that are
+
+ align:start position:0%
+possible binary search trees that are
+ 
+
+ align:start position:0%
+possible binary search trees that are
+associated with a given set of n keys
+
+ align:start position:0%
+associated with a given set of n keys
+ 
+
+ align:start position:0%
+associated with a given set of n keys
+that are all you know binary searches
+
+ align:start position:0%
+that are all you know binary searches
+ 
+
+ align:start position:0%
+that are all you know binary searches
+they're consistent unbalanced balanced
+
+ align:start position:0%
+they're consistent unbalanced balanced
+ 
+
+ align:start position:0%
+they're consistent unbalanced balanced
+you know unbalanced in one way versus
+
+ align:start position:0%
+you know unbalanced in one way versus
+ 
+
+ align:start position:0%
+you know unbalanced in one way versus
+another way etc etc
+
+ align:start position:0%
+another way etc etc
+ 
+
+ align:start position:0%
+another way etc etc
+so we want to find a binary sech stre T
+
+ align:start position:0%
+so we want to find a binary sech stre T
+ 
+
+ align:start position:0%
+so we want to find a binary sech stre T
+that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimizes um
+
+ align:start position:0%
+minimizes um
+ 
+
+ align:start position:0%
+minimizes um
+Sigma I = 1 through n obviously we're
+
+ align:start position:0%
+Sigma I = 1 through n obviously we're
+ 
+
+ align:start position:0%
+Sigma I = 1 through n obviously we're
+going to have this wi that's the the
+
+ align:start position:0%
+going to have this wi that's the the
+ 
+
+ align:start position:0%
+going to have this wi that's the the
+game here uh
+
+ align:start position:0%
+game here uh
+ 
+
+ align:start position:0%
+game here uh
+depth uh in the T So this depth is for
+
+ align:start position:0%
+depth uh in the T So this depth is for
+ 
+
+ align:start position:0%
+depth uh in the T So this depth is for
+the T what is the depth of the node um
+
+ align:start position:0%
+the T what is the depth of the node um
+ 
+
+ align:start position:0%
+the T what is the depth of the node um
+and K of I + one
+
+ align:start position:0%
+and K of I + one
+ 
+
+ align:start position:0%
+and K of I + one
+okay um and I'll explain exactly what
+
+ align:start position:0%
+okay um and I'll explain exactly what
+ 
+
+ align:start position:0%
+okay um and I'll explain exactly what
+this is and I tell you what precisely
+
+ align:start position:0%
+this is and I tell you what precisely
+ 
+
+ align:start position:0%
+this is and I tell you what precisely
+the depth is uh but roughly speaking uh
+
+ align:start position:0%
+the depth is uh but roughly speaking uh
+ 
+
+ align:start position:0%
+the depth is uh but roughly speaking uh
+the depth of the root not roughly
+
+ align:start position:0%
+the depth of the root not roughly
+ 
+
+ align:start position:0%
+the depth of the root not roughly
+speaking the depth of the root is zero
+
+ align:start position:0%
+speaking the depth of the root is zero
+ 
+
+ align:start position:0%
+speaking the depth of the root is zero
+okay uh and uh the the depth of one
+
+ align:start position:0%
+okay uh and uh the the depth of one
+ 
+
+ align:start position:0%
+okay uh and uh the the depth of one
+below the root is one and so on and so
+
+ align:start position:0%
+below the root is one and so on and so
+ 
+
+ align:start position:0%
+below the root is one and so on and so
+forth um and so as you can see what you
+
+ align:start position:0%
+forth um and so as you can see what you
+ 
+
+ align:start position:0%
+forth um and so as you can see what you
+want to do is collect uh in roughly
+
+ align:start position:0%
+want to do is collect uh in roughly
+ 
+
+ align:start position:0%
+want to do is collect uh in roughly
+speaking you want to collect the high
+
+ align:start position:0%
+speaking you want to collect the high
+ 
+
+ align:start position:0%
+speaking you want to collect the high
+weight nodes to have L depth right if wi
+
+ align:start position:0%
+weight nodes to have L depth right if wi
+ 
+
+ align:start position:0%
+weight nodes to have L depth right if wi
+is high you want the the multiplicative
+
+ align:start position:0%
+is high you want the the multiplicative
+ 
+
+ align:start position:0%
+is high you want the the multiplicative
+Factor corresponding to depth T of that
+
+ align:start position:0%
+Factor corresponding to depth T of that
+ 
+
+ align:start position:0%
+Factor corresponding to depth T of that
+node I the I node to be to be small and
+
+ align:start position:0%
+node I the I node to be to be small and
+ 
+
+ align:start position:0%
+node I the I node to be to be small and
+if wi is small then you don't mind the
+
+ align:start position:0%
+if wi is small then you don't mind the
+ 
+
+ align:start position:0%
+if wi is small then you don't mind the
+depth uh number to be higher uh you only
+
+ align:start position:0%
+depth uh number to be higher uh you only
+ 
+
+ align:start position:0%
+depth uh number to be higher uh you only
+have a certain number of a low depth
+
+ align:start position:0%
+have a certain number of a low depth
+ 
+
+ align:start position:0%
+have a certain number of a low depth
+nodes you only have one node of depth
+
+ align:start position:0%
+nodes you only have one node of depth
+ 
+
+ align:start position:0%
+nodes you only have one node of depth
+zero and you have two nodes of depth uh
+
+ align:start position:0%
+zero and you have two nodes of depth uh
+ 
+
+ align:start position:0%
+zero and you have two nodes of depth uh
+uh one which means that you only have
+
+ align:start position:0%
+uh one which means that you only have
+ 
+
+ align:start position:0%
+uh one which means that you only have
+one node where that quantity there is
+
+ align:start position:0%
+one node where that quantity there is
+ 
+
+ align:start position:0%
+one node where that quantity there is
+going to be one right because you're
+
+ align:start position:0%
+going to be one right because you're
+ 
+
+ align:start position:0%
+going to be one right because you're
+doing 0 plus one and you have two nodes
+
+ align:start position:0%
+doing 0 plus one and you have two nodes
+ 
+
+ align:start position:0%
+doing 0 plus one and you have two nodes
+where the quantity is going to be two um
+
+ align:start position:0%
+where the quantity is going to be two um
+ 
+
+ align:start position:0%
+where the quantity is going to be two um
+and so on and so forth so you have some
+
+ align:start position:0%
+and so on and so forth so you have some
+ 
+
+ align:start position:0%
+and so on and so forth so you have some
+room here to play with corresponding to
+
+ align:start position:0%
+room here to play with corresponding to
+ 
+
+ align:start position:0%
+room here to play with corresponding to
+the BST structure and you want to
+
+ align:start position:0%
+the BST structure and you want to
+ 
+
+ align:start position:0%
+the BST structure and you want to
+minimize that quantity okay um any
+
+ align:start position:0%
+minimize that quantity okay um any
+ 
+
+ align:start position:0%
+minimize that quantity okay um any
+questions so
+
+ align:start position:0%
+questions so
+ 
+
+ align:start position:0%
+questions so
+far all right good um so uh the search
+
+ align:start position:0%
+far all right good um so uh the search
+ 
+
+ align:start position:0%
+far all right good um so uh the search
+probabilities would be an example so I
+
+ align:start position:0%
+probabilities would be an example so I
+ 
+
+ align:start position:0%
+probabilities would be an example so I
+in terms of a more concrete application
+
+ align:start position:0%
+in terms of a more concrete application
+ 
+
+ align:start position:0%
+in terms of a more concrete application
+you could imagine you had a a
+
+ align:start position:0%
+you could imagine you had a a
+ 
+
+ align:start position:0%
+you could imagine you had a a
+dictionary English to French French to
+
+ align:start position:0%
+dictionary English to French French to
+ 
+
+ align:start position:0%
+dictionary English to French French to
+English what have you and um there're
+
+ align:start position:0%
+English what have you and um there're
+ 
+
+ align:start position:0%
+English what have you and um there're
+obviously words that are more common
+
+ align:start position:0%
+obviously words that are more common
+ 
+
+ align:start position:0%
+obviously words that are more common
+let's say in uh uh common speech than
+
+ align:start position:0%
+let's say in uh uh common speech than
+ 
+
+ align:start position:0%
+let's say in uh uh common speech than
+others and you do want to do the
+
+ align:start position:0%
+others and you do want to do the
+ 
+
+ align:start position:0%
+others and you do want to do the
+translation uh in a dynamic way using
+
+ align:start position:0%
+translation uh in a dynamic way using
+ 
+
+ align:start position:0%
+translation uh in a dynamic way using
+this data structure and you could
+
+ align:start position:0%
+this data structure and you could
+ 
+
+ align:start position:0%
+this data structure and you could
+imagine that in this case the uh the
+
+ align:start position:0%
+imagine that in this case the uh the
+ 
+
+ align:start position:0%
+imagine that in this case the uh the
+search probability of a word is
+
+ align:start position:0%
+search probability of a word is
+ 
+
+ align:start position:0%
+search probability of a word is
+associated with the uh occurrence of the
+
+ align:start position:0%
+associated with the uh occurrence of the
+ 
+
+ align:start position:0%
+associated with the uh occurrence of the
+word the uh the number of times uh over
+
+ align:start position:0%
+word the uh the number of times uh over
+ 
+
+ align:start position:0%
+word the uh the number of times uh over
+some normalized uh uh number of words
+
+ align:start position:0%
+some normalized uh uh number of words
+ 
+
+ align:start position:0%
+some normalized uh uh number of words
+that this particular word occurs and
+
+ align:start position:0%
+that this particular word occurs and
+ 
+
+ align:start position:0%
+that this particular word occurs and
+that would be the that would be the
+
+ align:start position:0%
+that would be the that would be the
+ 
+
+ align:start position:0%
+that would be the that would be the
+weight so it makes sense to create a
+
+ align:start position:0%
+weight so it makes sense to create a
+ 
+
+ align:start position:0%
+weight so it makes sense to create a
+structure that minimizes that function
+
+ align:start position:0%
+structure that minimizes that function
+ 
+
+ align:start position:0%
+structure that minimizes that function
+because it would minimize the expected
+
+ align:start position:0%
+because it would minimize the expected
+ 
+
+ align:start position:0%
+because it would minimize the expected
+search cost when you want to take this
+
+ align:start position:0%
+search cost when you want to take this
+ 
+
+ align:start position:0%
+search cost when you want to take this
+entire uh essay for example and and
+
+ align:start position:0%
+entire uh essay for example and and
+ 
+
+ align:start position:0%
+entire uh essay for example and and
+convert it from English to French or
+
+ align:start position:0%
+convert it from English to French or
+ 
+
+ align:start position:0%
+convert it from English to French or
+vice versa okay so this can if if these
+
+ align:start position:0%
+vice versa okay so this can if if these
+ 
+
+ align:start position:0%
+vice versa okay so this can if if these
+are search probabilities then this would
+
+ align:start position:0%
+are search probabilities then this would
+ 
+
+ align:start position:0%
+are search probabilities then this would
+minimize this cost function here would
+
+ align:start position:0%
+minimize this cost function here would
+ 
+
+ align:start position:0%
+minimize this cost function here would
+minimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expected search
+
+ align:start position:0%
+expected search
+ 
+
+ align:start position:0%
+expected search
+cost right
+
+ align:start position:0%
+cost right
+ 
+
+ align:start position:0%
+cost right
+um make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense okay so uh that's the definition
+
+ align:start position:0%
+sense okay so uh that's the definition
+ 
+
+ align:start position:0%
+sense okay so uh that's the definition
+of the problem um and uh now we have to
+
+ align:start position:0%
+of the problem um and uh now we have to
+ 
+
+ align:start position:0%
+of the problem um and uh now we have to
+talk about um why this is complicated
+
+ align:start position:0%
+talk about um why this is complicated
+ 
+
+ align:start position:0%
+talk about um why this is complicated
+why uh this uh requires uh dynamic
+
+ align:start position:0%
+why uh this uh requires uh dynamic
+ 
+
+ align:start position:0%
+why uh this uh requires uh dynamic
+programming uh why can't we um just do
+
+ align:start position:0%
+programming uh why can't we um just do
+ 
+
+ align:start position:0%
+programming uh why can't we um just do
+something fairly straightforward uh like
+
+ align:start position:0%
+something fairly straightforward uh like
+ 
+
+ align:start position:0%
+something fairly straightforward uh like
+a like a grey
+
+ align:start position:0%
+a like a grey
+ 
+
+ align:start position:0%
+a like a grey
+algorithm and so let's look into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that let me give you a really good sense
+
+ align:start position:0%
+that let me give you a really good sense
+ 
+
+ align:start position:0%
+that let me give you a really good sense
+for what's going on here with respect to
+
+ align:start position:0%
+for what's going on here with respect to
+ 
+
+ align:start position:0%
+for what's going on here with respect to
+this cost function that may be a little
+
+ align:start position:0%
+this cost function that may be a little
+ 
+
+ align:start position:0%
+this cost function that may be a little
+abstract by giving you a couple of
+
+ align:start position:0%
+abstract by giving you a couple of
+ 
+
+ align:start position:0%
+abstract by giving you a couple of
+concrete examples uh first off we got
+
+ align:start position:0%
+concrete examples uh first off we got
+ 
+
+ align:start position:0%
+concrete examples uh first off we got
+exponentially many trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential in
+
+ align:start position:0%
+exponential in
+ 
+
+ align:start position:0%
+exponential in
+N let's say that n equals 2 so the
+
+ align:start position:0%
+N let's say that n equals 2 so the
+ 
+
+ align:start position:0%
+N let's say that n equals 2 so the
+number of nodes is two then remember
+
+ align:start position:0%
+number of nodes is two then remember
+ 
+
+ align:start position:0%
+number of nodes is two then remember
+that I'm assuming that the kis Are all
+
+ align:start position:0%
+that I'm assuming that the kis Are all
+ 
+
+ align:start position:0%
+that I'm assuming that the kis Are all
+uh eyes that's the one and two would be
+
+ align:start position:0%
+uh eyes that's the one and two would be
+ 
+
+ align:start position:0%
+uh eyes that's the one and two would be
+uh the K is for uh Nal 2 and 1 2 3 for
+
+ align:start position:0%
+uh the K is for uh Nal 2 and 1 2 3 for
+ 
+
+ align:start position:0%
+uh the K is for uh Nal 2 and 1 2 3 for
+uh K Nal 3 Etc so I could have a tree
+
+ align:start position:0%
+uh K Nal 3 Etc so I could have a tree
+ 
+
+ align:start position:0%
+uh K Nal 3 Etc so I could have a tree
+that looks like that and I could have a
+
+ align:start position:0%
+that looks like that and I could have a
+ 
+
+ align:start position:0%
+that looks like that and I could have a
+tree that looks like this that's it um n
+
+ align:start position:0%
+tree that looks like this that's it um n
+ 
+
+ align:start position:0%
+tree that looks like this that's it um n
+equals 2 I got two trees right so in
+
+ align:start position:0%
+equals 2 I got two trees right so in
+ 
+
+ align:start position:0%
+equals 2 I got two trees right so in
+this case my cost function is W1 + 2
+
+ align:start position:0%
+this case my cost function is W1 + 2
+ 
+
+ align:start position:0%
+this case my cost function is W1 + 2
+W2 and in this case my cost function is
+
+ align:start position:0%
+W2 and in this case my cost function is
+ 
+
+ align:start position:0%
+W2 and in this case my cost function is
+2 W1 + W2 okay um just to be
+
+ align:start position:0%
+2 W1 + W2 okay um just to be
+ 
+
+ align:start position:0%
+2 W1 + W2 okay um just to be
+clear um what this is is the
+
+ align:start position:0%
+clear um what this is is the
+ 
+
+ align:start position:0%
+clear um what this is is the
+uh is is um the K right and it's also
+
+ align:start position:0%
+uh is is um the K right and it's also
+ 
+
+ align:start position:0%
+uh is is um the K right and it's also
+the I so the numbers that you see inside
+
+ align:start position:0%
+the I so the numbers that you see inside
+ 
+
+ align:start position:0%
+the I so the numbers that you see inside
+those are the I numbers which happen to
+
+ align:start position:0%
+those are the I numbers which happen to
+ 
+
+ align:start position:0%
+those are the I numbers which happen to
+be equal to the Ki numbers okay and the
+
+ align:start position:0%
+be equal to the Ki numbers okay and the
+ 
+
+ align:start position:0%
+be equal to the Ki numbers okay and the
+weight itself would be the wi so I put
+
+ align:start position:0%
+weight itself would be the wi so I put
+ 
+
+ align:start position:0%
+weight itself would be the wi so I put
+W1 here and the reason it only gets
+
+ align:start position:0%
+W1 here and the reason it only gets
+ 
+
+ align:start position:0%
+W1 here and the reason it only gets
+multiplied by one is because the depth
+
+ align:start position:0%
+multiplied by one is because the depth
+ 
+
+ align:start position:0%
+multiplied by one is because the depth
+here is zero and I add one to it the
+
+ align:start position:0%
+here is zero and I add one to it the
+ 
+
+ align:start position:0%
+here is zero and I add one to it the
+depth here is one and I add one to it
+
+ align:start position:0%
+depth here is one and I add one to it
+ 
+
+ align:start position:0%
+depth here is one and I add one to it
+which is why I have a two out here okay
+
+ align:start position:0%
+which is why I have a two out here okay
+ 
+
+ align:start position:0%
+which is why I have a two out here okay
+um being a little uh
+
+ align:start position:0%
+um being a little uh
+ 
+
+ align:start position:0%
+um being a little uh
+pedantic here and pointing things out
+
+ align:start position:0%
+pedantic here and pointing things out
+ 
+
+ align:start position:0%
+pedantic here and pointing things out
+because you're going to start seeing
+
+ align:start position:0%
+because you're going to start seeing
+ 
+
+ align:start position:0%
+because you're going to start seeing
+some equations that are a little more
+
+ align:start position:0%
+some equations that are a little more
+ 
+
+ align:start position:0%
+some equations that are a little more
+complicated than this and I don't want
+
+ align:start position:0%
+complicated than this and I don't want
+ 
+
+ align:start position:0%
+complicated than this and I don't want
+you to get confused as to what the
+
+ align:start position:0%
+you to get confused as to what the
+ 
+
+ align:start position:0%
+you to get confused as to what the
+weight is and what the key number is and
+
+ align:start position:0%
+weight is and what the key number is and
+ 
+
+ align:start position:0%
+weight is and what the key number is and
+what the depth is there's three things
+
+ align:start position:0%
+what the depth is there's three things
+ 
+
+ align:start position:0%
+what the depth is there's three things
+going on here okay so over here you see
+
+ align:start position:0%
+going on here okay so over here you see
+ 
+
+ align:start position:0%
+going on here okay so over here you see
+that um I got I'm looking at W1 here
+
+ align:start position:0%
+that um I got I'm looking at W1 here
+ 
+
+ align:start position:0%
+that um I got I'm looking at W1 here
+which is this key right so the the one
+
+ align:start position:0%
+which is this key right so the the one
+ 
+
+ align:start position:0%
+which is this key right so the the one
+corresponds to the one and and this has
+
+ align:start position:0%
+corresponds to the one and and this has
+ 
+
+ align:start position:0%
+corresponds to the one and and this has
+a depth of one so I put a two in here
+
+ align:start position:0%
+a depth of one so I put a two in here
+ 
+
+ align:start position:0%
+a depth of one so I put a two in here
+and so on okay so so far so good um
+
+ align:start position:0%
+and so on okay so so far so good um
+ 
+
+ align:start position:0%
+and so on okay so so far so good um
+when you get to n equals 3 uh you you
+
+ align:start position:0%
+when you get to n equals 3 uh you you
+ 
+
+ align:start position:0%
+when you get to n equals 3 uh you you
+start getting well you have you have at
+
+ align:start position:0%
+start getting well you have you have at
+ 
+
+ align:start position:0%
+start getting well you have you have at
+this point you have u 1 2 3 4 five you
+
+ align:start position:0%
+this point you have u 1 2 3 4 five you
+ 
+
+ align:start position:0%
+this point you have u 1 2 3 4 five you
+got five
+
+ align:start position:0%
+got five
+ 
+
+ align:start position:0%
+got five
+trees uh and uh the trees look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I'll draw them really quickly just
+
+ align:start position:0%
+this I'll draw them really quickly just
+ 
+
+ align:start position:0%
+this I'll draw them really quickly just
+to get a sense of the variety here but I
+
+ align:start position:0%
+to get a sense of the variety here but I
+ 
+
+ align:start position:0%
+to get a sense of the variety here but I
+won't write the equations down for um
+
+ align:start position:0%
+won't write the equations down for um
+ 
+
+ align:start position:0%
+won't write the equations down for um
+all of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you go so those are the the five
+
+ align:start position:0%
+there you go so those are the the five
+ 
+
+ align:start position:0%
+there you go so those are the the five
+binary trees associated with n equals 3
+
+ align:start position:0%
+binary trees associated with n equals 3
+ 
+
+ align:start position:0%
+binary trees associated with n equals 3
+right the binary search trees um and U
+
+ align:start position:0%
+right the binary search trees um and U
+ 
+
+ align:start position:0%
+right the binary search trees um and U
+this is this is kind of cool uh it's
+
+ align:start position:0%
+this is this is kind of cool uh it's
+ 
+
+ align:start position:0%
+this is this is kind of cool uh it's
+nice and balanced you know the other
+
+ align:start position:0%
+nice and balanced you know the other
+ 
+
+ align:start position:0%
+nice and balanced you know the other
+ones aren't um and I'm not I'm not uh um
+
+ align:start position:0%
+ones aren't um and I'm not I'm not uh um
+ 
+
+ align:start position:0%
+ones aren't um and I'm not I'm not uh um
+looking at U or do should I should I
+
+ align:start position:0%
+looking at U or do should I should I
+ 
+
+ align:start position:0%
+looking at U or do should I should I
+have another one here I guess I should
+
+ align:start position:0%
+have another one here I guess I should
+ 
+
+ align:start position:0%
+have another one here I guess I should
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a oh no no so I'm not doing
+
+ align:start position:0%
+this is a oh no no so I'm not doing
+ 
+
+ align:start position:0%
+this is a oh no no so I'm not doing
+mirrors uh and so so there is there are
+
+ align:start position:0%
+mirrors uh and so so there is there are
+ 
+
+ align:start position:0%
+mirrors uh and so so there is there are
+a bunch of other trees that have the
+
+ align:start position:0%
+a bunch of other trees that have the
+ 
+
+ align:start position:0%
+a bunch of other trees that have the
+same equation associated with two no
+
+ align:start position:0%
+same equation associated with two no
+ 
+
+ align:start position:0%
+same equation associated with two no
+that's that's not true because uh these
+
+ align:start position:0%
+that's that's not true because uh these
+ 
+
+ align:start position:0%
+that's that's not true because uh these
+are it I I I was going to say that you
+
+ align:start position:0%
+are it I I I was going to say that you
+ 
+
+ align:start position:0%
+are it I I I was going to say that you
+could put three in here but that would
+
+ align:start position:0%
+could put three in here but that would
+ 
+
+ align:start position:0%
+could put three in here but that would
+be a binary search tree right so this
+
+ align:start position:0%
+be a binary search tree right so this
+ 
+
+ align:start position:0%
+be a binary search tree right so this
+this is it uh and we got a bunch of
+
+ align:start position:0%
+this is it uh and we got a bunch of
+ 
+
+ align:start position:0%
+this is it uh and we got a bunch of
+trees this this one would be uh 2 W1 +
+
+ align:start position:0%
+trees this this one would be uh 2 W1 +
+ 
+
+ align:start position:0%
+trees this this one would be uh 2 W1 +
+W2 + 2 W3
+
+ align:start position:0%
+W2 + 2 W3
+ 
+
+ align:start position:0%
+W2 + 2 W3
+by the same process that I used to show
+
+ align:start position:0%
+by the same process that I used to show
+ 
+
+ align:start position:0%
+by the same process that I used to show
+you the W1 + 2 W2 for the N equals 2
+
+ align:start position:0%
+you the W1 + 2 W2 for the N equals 2
+ 
+
+ align:start position:0%
+you the W1 + 2 W2 for the N equals 2
+case you just go off and that's the
+
+ align:start position:0%
+case you just go off and that's the
+ 
+
+ align:start position:0%
+case you just go off and that's the
+equation and so your goal here in an
+
+ align:start position:0%
+equation and so your goal here in an
+ 
+
+ align:start position:0%
+equation and so your goal here in an
+algorithm clearly this is not the
+
+ align:start position:0%
+algorithm clearly this is not the
+ 
+
+ align:start position:0%
+algorithm clearly this is not the
+algorithm you want to enumerate all the
+
+ align:start position:0%
+algorithm you want to enumerate all the
+ 
+
+ align:start position:0%
+algorithm you want to enumerate all the
+exponentially many trees compute the
+
+ align:start position:0%
+exponentially many trees compute the
+ 
+
+ align:start position:0%
+exponentially many trees compute the
+equations for each of those trees and
+
+ align:start position:0%
+equations for each of those trees and
+ 
+
+ align:start position:0%
+equations for each of those trees and
+pick the minimum right I mean that would
+
+ align:start position:0%
+pick the minimum right I mean that would
+ 
+
+ align:start position:0%
+pick the minimum right I mean that would
+work but it would take exponential time
+
+ align:start position:0%
+work but it would take exponential time
+ 
+
+ align:start position:0%
+work but it would take exponential time
+right so uh so but that's what you have
+
+ align:start position:0%
+right so uh so but that's what you have
+ 
+
+ align:start position:0%
+right so uh so but that's what you have
+to do now that's the the goal you
+
+ align:start position:0%
+to do now that's the the goal you
+ 
+
+ align:start position:0%
+to do now that's the the goal you
+absolutely want the best possible tree
+
+ align:start position:0%
+absolutely want the best possible tree
+ 
+
+ align:start position:0%
+absolutely want the best possible tree
+that has for the given wi that you're
+
+ align:start position:0%
+that has for the given wi that you're
+ 
+
+ align:start position:0%
+that has for the given wi that you're
+going to be assigned as constants you do
+
+ align:start position:0%
+going to be assigned as constants you do
+ 
+
+ align:start position:0%
+going to be assigned as constants you do
+want to find the one uh uh threee that
+
+ align:start position:0%
+want to find the one uh uh threee that
+ 
+
+ align:start position:0%
+want to find the one uh uh threee that
+has the minimum sum uh and you want to
+
+ align:start position:0%
+has the minimum sum uh and you want to
+ 
+
+ align:start position:0%
+has the minimum sum uh and you want to
+do that for arbitary n and you want to
+
+ align:start position:0%
+do that for arbitary n and you want to
+ 
+
+ align:start position:0%
+do that for arbitary n and you want to
+do that in polinomial time okay so uh
+
+ align:start position:0%
+do that in polinomial time okay so uh
+ 
+
+ align:start position:0%
+do that in polinomial time okay so uh
+the first thing that you do when you
+
+ align:start position:0%
+the first thing that you do when you
+ 
+
+ align:start position:0%
+the first thing that you do when you
+have something like this
+
+ align:start position:0%
+have something like this
+ 
+
+ align:start position:0%
+have something like this
+is f about the fact that uh we're in a
+
+ align:start position:0%
+is f about the fact that uh we're in a
+ 
+
+ align:start position:0%
+is f about the fact that uh we're in a
+dynamic programming lecture or a dynamic
+
+ align:start position:0%
+dynamic programming lecture or a dynamic
+ 
+
+ align:start position:0%
+dynamic programming lecture or a dynamic
+programming module of this class when
+
+ align:start position:0%
+programming module of this class when
+ 
+
+ align:start position:0%
+programming module of this class when
+you see a problem like this so in the
+
+ align:start position:0%
+you see a problem like this so in the
+ 
+
+ align:start position:0%
+you see a problem like this so in the
+real world uh you want to think about
+
+ align:start position:0%
+real world uh you want to think about
+ 
+
+ align:start position:0%
+real world uh you want to think about
+whether a greedy algorithm would work or
+
+ align:start position:0%
+whether a greedy algorithm would work or
+ 
+
+ align:start position:0%
+whether a greedy algorithm would work or
+not um and uh you don't want to go off
+
+ align:start position:0%
+not um and uh you don't want to go off
+ 
+
+ align:start position:0%
+not um and uh you don't want to go off
+and build this Dynamic program solution
+
+ align:start position:0%
+and build this Dynamic program solution
+ 
+
+ align:start position:0%
+and build this Dynamic program solution
+uh which is chances are going to be in
+
+ align:start position:0%
+uh which is chances are going to be in
+ 
+
+ align:start position:0%
+uh which is chances are going to be in
+more in more uh uh inefficient than a
+
+ align:start position:0%
+more in more uh uh inefficient than a
+ 
+
+ align:start position:0%
+more in more uh uh inefficient than a
+greedy solution which if it produces the
+
+ align:start position:0%
+greedy solution which if it produces the
+ 
+
+ align:start position:0%
+greedy solution which if it produces the
+optimum answer um is the best way to go
+
+ align:start position:0%
+optimum answer um is the best way to go
+ 
+
+ align:start position:0%
+optimum answer um is the best way to go
+so um an obvious greedy solution would
+
+ align:start position:0%
+so um an obvious greedy solution would
+ 
+
+ align:start position:0%
+so um an obvious greedy solution would
+be to pick K of R in
+
+ align:start position:0%
+be to pick K of R in
+ 
+
+ align:start position:0%
+be to pick K of R in
+some greedy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fashion and what is the obvious way of
+
+ align:start position:0%
+fashion and what is the obvious way of
+ 
+
+ align:start position:0%
+fashion and what is the obvious way of
+picking K of R uh to try and get a
+
+ align:start position:0%
+picking K of R uh to try and get a
+ 
+
+ align:start position:0%
+picking K of R uh to try and get a
+greedy solution that at least attempts
+
+ align:start position:0%
+greedy solution that at least attempts
+ 
+
+ align:start position:0%
+greedy solution that at least attempts
+to minimize that cost function that we
+
+ align:start position:0%
+to minimize that cost function that we
+ 
+
+ align:start position:0%
+to minimize that cost function that we
+have there high highest weight right so
+
+ align:start position:0%
+have there high highest weight right so
+ 
+
+ align:start position:0%
+have there high highest weight right so
+just pick K of R to be highest weight
+
+ align:start position:0%
+just pick K of R to be highest weight
+ 
+
+ align:start position:0%
+just pick K of R to be highest weight
+because that goes back to what I said
+
+ align:start position:0%
+because that goes back to what I said
+ 
+
+ align:start position:0%
+because that goes back to what I said
+about if wi is high you
+
+ align:start position:0%
+about if wi is high you
+ 
+
+ align:start position:0%
+about if wi is high you
+want uh this value here to be small
+
+ align:start position:0%
+want uh this value here to be small
+ 
+
+ align:start position:0%
+want uh this value here to be small
+right so that's essentially your greedy
+
+ align:start position:0%
+right so that's essentially your greedy
+ 
+
+ align:start position:0%
+right so that's essentially your greedy
+heuristic so K of R should be picked in
+
+ align:start position:0%
+heuristic so K of R should be picked in
+ 
+
+ align:start position:0%
+heuristic so K of R should be picked in
+a in a greedy fashion so what you do is
+
+ align:start position:0%
+a in a greedy fashion so what you do is
+ 
+
+ align:start position:0%
+a in a greedy fashion so what you do is
+you pick K of r as the root in this
+
+ align:start position:0%
+you pick K of r as the root in this
+ 
+
+ align:start position:0%
+you pick K of r as the root in this
+particular problem and you could
+
+ align:start position:0%
+particular problem and you could
+ 
+
+ align:start position:0%
+particular problem and you could
+certainly apply this greedy technique
+
+ align:start position:0%
+certainly apply this greedy technique
+ 
+
+ align:start position:0%
+certainly apply this greedy technique
+recursively okay so you do that for
+
+ align:start position:0%
+recursively okay so you do that for
+ 
+
+ align:start position:0%
+recursively okay so you do that for
+every sub problem that you find because
+
+ align:start position:0%
+every sub problem that you find because
+ 
+
+ align:start position:0%
+every sub problem that you find because
+when you do this choice of the the root
+
+ align:start position:0%
+when you do this choice of the the root
+ 
+
+ align:start position:0%
+when you do this choice of the the root
+for KR in the current problem that you
+
+ align:start position:0%
+for KR in the current problem that you
+ 
+
+ align:start position:0%
+for KR in the current problem that you
+have you immediately split the keys into
+
+ align:start position:0%
+have you immediately split the keys into
+ 
+
+ align:start position:0%
+have you immediately split the keys into
+two sets right the sets that have to go
+
+ align:start position:0%
+two sets right the sets that have to go
+ 
+
+ align:start position:0%
+two sets right the sets that have to go
+on the left hand side of KR and the sets
+
+ align:start position:0%
+on the left hand side of KR and the sets
+ 
+
+ align:start position:0%
+on the left hand side of KR and the sets
+that have to go on the right hand side
+
+ align:start position:0%
+that have to go on the right hand side
+ 
+
+ align:start position:0%
+that have to go on the right hand side
+of KR right so in this case you know
+
+ align:start position:0%
+of KR right so in this case you know
+ 
+
+ align:start position:0%
+of KR right so in this case you know
+that you're going to have uh a a bunch
+
+ align:start position:0%
+that you're going to have uh a a bunch
+ 
+
+ align:start position:0%
+that you're going to have uh a a bunch
+of keys here that correspond to
+
+ align:start position:0%
+of keys here that correspond to
+ 
+
+ align:start position:0%
+of keys here that correspond to
+KI to
+
+ align:start position:0%
+KI to
+ 
+
+ align:start position:0%
+KI to
+KR and over here um you're going to have
+
+ align:start position:0%
+KR and over here um you're going to have
+ 
+
+ align:start position:0%
+KR and over here um you're going to have
+or KR minus one I should say because you
+
+ align:start position:0%
+or KR minus one I should say because you
+ 
+
+ align:start position:0%
+or KR minus one I should say because you
+already have KR out there and the keys
+
+ align:start position:0%
+already have KR out there and the keys
+ 
+
+ align:start position:0%
+already have KR out there and the keys
+here are going to be KR + one to uh KJ
+
+ align:start position:0%
+here are going to be KR + one to uh KJ
+ 
+
+ align:start position:0%
+here are going to be KR + one to uh KJ
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+overall uh I'm going to say that um e
+
+ align:start position:0%
+overall uh I'm going to say that um e
+ 
+
+ align:start position:0%
+overall uh I'm going to say that um e
+j um
+
+ align:start position:0%
+j um
+ 
+
+ align:start position:0%
+j um
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+cost of the
+
+ align:start position:0%
+cost of the
+ 
+
+ align:start position:0%
+cost of the
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+BST on Ki
+
+ align:start position:0%
+BST on Ki
+ 
+
+ align:start position:0%
+BST on Ki
+k i +
+
+ align:start position:0%
+k i +
+ 
+
+ align:start position:0%
+k i +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um all the
+
+ align:start position:0%
+um all the
+ 
+
+ align:start position:0%
+um all the
+way to
+
+ align:start position:0%
+way to
+ 
+
+ align:start position:0%
+way to
+KJ okay so um I'm kind of already
+
+ align:start position:0%
+KJ okay so um I'm kind of already
+ 
+
+ align:start position:0%
+KJ okay so um I'm kind of already
+setting myself up here for uh dynamic
+
+ align:start position:0%
+setting myself up here for uh dynamic
+ 
+
+ align:start position:0%
+setting myself up here for uh dynamic
+programming but it also makes sense in
+
+ align:start position:0%
+programming but it also makes sense in
+ 
+
+ align:start position:0%
+programming but it also makes sense in
+the case of a of a greedy algorithm
+
+ align:start position:0%
+the case of a of a greedy algorithm
+ 
+
+ align:start position:0%
+the case of a of a greedy algorithm
+where this greedy heuristic is going to
+
+ align:start position:0%
+where this greedy heuristic is going to
+ 
+
+ align:start position:0%
+where this greedy heuristic is going to
+be applied recursively okay so initially
+
+ align:start position:0%
+be applied recursively okay so initially
+ 
+
+ align:start position:0%
+be applied recursively okay so initially
+you're going to have uh
+
+ align:start position:0%
+you're going to have uh
+ 
+
+ align:start position:0%
+you're going to have uh
+e1n right so if you want to compute
+
+ align:start position:0%
+e1n right so if you want to compute
+ 
+
+ align:start position:0%
+e1n right so if you want to compute
+e1n which is the cost of the optimal BST
+
+ align:start position:0%
+e1n which is the cost of the optimal BST
+ 
+
+ align:start position:0%
+e1n which is the cost of the optimal BST
+on the original problem all right all
+
+ align:start position:0%
+on the original problem all right all
+ 
+
+ align:start position:0%
+on the original problem all right all
+the way from one to n you're going to
+
+ align:start position:0%
+the way from one to n you're going to
+ 
+
+ align:start position:0%
+the way from one to n you're going to
+look at it and you're going to say uh I
+
+ align:start position:0%
+look at it and you're going to say uh I
+ 
+
+ align:start position:0%
+look at it and you're going to say uh I
+have a bunch of keys here of a different
+
+ align:start position:0%
+have a bunch of keys here of a different
+ 
+
+ align:start position:0%
+have a bunch of keys here of a different
+weights that correspond to K1 through
+
+ align:start position:0%
+weights that correspond to K1 through
+ 
+
+ align:start position:0%
+weights that correspond to K1 through
+KNN I'm going to pick the KR that
+
+ align:start position:0%
+KNN I'm going to pick the KR that
+ 
+
+ align:start position:0%
+KNN I'm going to pick the KR that
+corresponds to the maximum weight and
+
+ align:start position:0%
+corresponds to the maximum weight and
+ 
+
+ align:start position:0%
+corresponds to the maximum weight and
+I'm going to use that as the root node
+
+ align:start position:0%
+I'm going to use that as the root node
+ 
+
+ align:start position:0%
+I'm going to use that as the root node
+and I'm going to stick that up there and
+
+ align:start position:0%
+and I'm going to stick that up there and
+ 
+
+ align:start position:0%
+and I'm going to stick that up there and
+uh the reason I did that uh is because
+
+ align:start position:0%
+uh the reason I did that uh is because
+ 
+
+ align:start position:0%
+uh the reason I did that uh is because
+I'm I believe that this greedy heuristic
+
+ align:start position:0%
+I'm I believe that this greedy heuristic
+ 
+
+ align:start position:0%
+I'm I believe that this greedy heuristic
+is going to work where this maximum
+
+ align:start position:0%
+is going to work where this maximum
+ 
+
+ align:start position:0%
+is going to work where this maximum
+weight node should have the the absolute
+
+ align:start position:0%
+weight node should have the the absolute
+ 
+
+ align:start position:0%
+weight node should have the the absolute
+minimum depth okay so I stick that up
+
+ align:start position:0%
+minimum depth okay so I stick that up
+ 
+
+ align:start position:0%
+minimum depth okay so I stick that up
+there and then my BST invariant tells me
+
+ align:start position:0%
+there and then my BST invariant tells me
+ 
+
+ align:start position:0%
+there and then my BST invariant tells me
+that Ki through KR minus1 remember these
+
+ align:start position:0%
+that Ki through KR minus1 remember these
+ 
+
+ align:start position:0%
+that Ki through KR minus1 remember these
+are sorted right and they go uh in
+
+ align:start position:0%
+are sorted right and they go uh in
+ 
+
+ align:start position:0%
+are sorted right and they go uh in
+increasing order as I have up here uh
+
+ align:start position:0%
+increasing order as I have up here uh
+ 
+
+ align:start position:0%
+increasing order as I have up here uh
+you're going to have those on the left
+
+ align:start position:0%
+you're going to have those on the left
+ 
+
+ align:start position:0%
+you're going to have those on the left
+and you have going to have those on the
+
+ align:start position:0%
+and you have going to have those on the
+ 
+
+ align:start position:0%
+and you have going to have those on the
+right and then you got to go solve this
+
+ align:start position:0%
+right and then you got to go solve this
+ 
+
+ align:start position:0%
+right and then you got to go solve this
+problem and you can certainly apply the
+
+ align:start position:0%
+problem and you can certainly apply the
+ 
+
+ align:start position:0%
+problem and you can certainly apply the
+greedy heuristic to solve this problem
+
+ align:start position:0%
+greedy heuristic to solve this problem
+ 
+
+ align:start position:0%
+greedy heuristic to solve this problem
+right you could go essentially uh find
+
+ align:start position:0%
+right you could go essentially uh find
+ 
+
+ align:start position:0%
+right you could go essentially uh find
+the K uh that uh has the highest weight
+
+ align:start position:0%
+the K uh that uh has the highest weight
+ 
+
+ align:start position:0%
+the K uh that uh has the highest weight
+so you look at wi through w r minus one
+
+ align:start position:0%
+so you look at wi through w r minus one
+ 
+
+ align:start position:0%
+so you look at wi through w r minus one
+and you find the the K that has the
+
+ align:start position:0%
+and you find the the K that has the
+ 
+
+ align:start position:0%
+and you find the the K that has the
+highest weight right so you're not going
+
+ align:start position:0%
+highest weight right so you're not going
+ 
+
+ align:start position:0%
+highest weight right so you're not going
+Midway here it's quite possible that KR
+
+ align:start position:0%
+Midway here it's quite possible that KR
+ 
+
+ align:start position:0%
+Midway here it's quite possible that KR
+is K of n okay it just happens to be KR
+
+ align:start position:0%
+is K of n okay it just happens to be KR
+ 
+
+ align:start position:0%
+is K of n okay it just happens to be KR
+is K of n so so that means that uh uh
+
+ align:start position:0%
+is K of n so so that means that uh uh
+ 
+
+ align:start position:0%
+is K of n so so that means that uh uh
+you have the highest weight node up here
+
+ align:start position:0%
+you have the highest weight node up here
+ 
+
+ align:start position:0%
+you have the highest weight node up here
+but it's also the the biggest key so all
+
+ align:start position:0%
+but it's also the the biggest key so all
+ 
+
+ align:start position:0%
+but it's also the the biggest key so all
+of the nodes are going to be on the left
+
+ align:start position:0%
+of the nodes are going to be on the left
+ 
+
+ align:start position:0%
+of the nodes are going to be on the left
+so this greedy heuristic and now you're
+
+ align:start position:0%
+so this greedy heuristic and now you're
+ 
+
+ align:start position:0%
+so this greedy heuristic and now you're
+starting to see maybe there's a problem
+
+ align:start position:0%
+starting to see maybe there's a problem
+ 
+
+ align:start position:0%
+starting to see maybe there's a problem
+here because uh if you have a situation
+
+ align:start position:0%
+here because uh if you have a situation
+ 
+
+ align:start position:0%
+here because uh if you have a situation
+where uh the the highest weight node is
+
+ align:start position:0%
+where uh the the highest weight node is
+ 
+
+ align:start position:0%
+where uh the the highest weight node is
+also the largest node you're going to
+
+ align:start position:0%
+also the largest node you're going to
+ 
+
+ align:start position:0%
+also the largest node you're going to
+get a pretty unbalanced tree okay so I
+
+ align:start position:0%
+get a pretty unbalanced tree okay so I
+ 
+
+ align:start position:0%
+get a pretty unbalanced tree okay so I
+can tell you that greedy doesn't work
+
+ align:start position:0%
+can tell you that greedy doesn't work
+ 
+
+ align:start position:0%
+can tell you that greedy doesn't work
+and U uh when I gave this lecture I
+
+ align:start position:0%
+and U uh when I gave this lecture I
+ 
+
+ align:start position:0%
+and U uh when I gave this lecture I
+think it was a couple of years ago I I
+
+ align:start position:0%
+think it was a couple of years ago I I
+ 
+
+ align:start position:0%
+think it was a couple of years ago I I
+made that statement and U uh this uh uh
+
+ align:start position:0%
+made that statement and U uh this uh uh
+ 
+
+ align:start position:0%
+made that statement and U uh this uh uh
+annoying student asked me for an example
+
+ align:start position:0%
+annoying student asked me for an example
+ 
+
+ align:start position:0%
+annoying student asked me for an example
+okay and I couldn't come up with one and
+
+ align:start position:0%
+okay and I couldn't come up with one and
+ 
+
+ align:start position:0%
+okay and I couldn't come up with one and
+so I kind of bailed on it went on uh
+
+ align:start position:0%
+so I kind of bailed on it went on uh
+ 
+
+ align:start position:0%
+so I kind of bailed on it went on uh
+completely dissatisfied of course and by
+
+ align:start position:0%
+completely dissatisfied of course and by
+ 
+
+ align:start position:0%
+completely dissatisfied of course and by
+the end of uh the lecture uh the same
+
+ align:start position:0%
+the end of uh the lecture uh the same
+ 
+
+ align:start position:0%
+the end of uh the lecture uh the same
+student came up with a counter example
+
+ align:start position:0%
+student came up with a counter example
+ 
+
+ align:start position:0%
+student came up with a counter example
+right so I'm going to have to put that
+
+ align:start position:0%
+right so I'm going to have to put that
+ 
+
+ align:start position:0%
+right so I'm going to have to put that
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+and uh thank the student who sent me
+
+ align:start position:0%
+and uh thank the student who sent me
+ 
+
+ align:start position:0%
+and uh thank the student who sent me
+a email about
+
+ align:start position:0%
+a email about
+ 
+
+ align:start position:0%
+a email about
+it and so here's a concrete example it
+
+ align:start position:0%
+it and so here's a concrete example it
+ 
+
+ align:start position:0%
+it and so here's a concrete example it
+turns out I was trying to get a three-
+
+ align:start position:0%
+turns out I was trying to get a three-
+ 
+
+ align:start position:0%
+turns out I was trying to get a three-
+Noe example for a few minutes and uh
+
+ align:start position:0%
+Noe example for a few minutes and uh
+ 
+
+ align:start position:0%
+Noe example for a few minutes and uh
+fail it it's it's it's uh I think
+
+ align:start position:0%
+fail it it's it's it's uh I think
+ 
+
+ align:start position:0%
+fail it it's it's it's uh I think
+impossible I haven't proved this to to
+
+ align:start position:0%
+impossible I haven't proved this to to
+ 
+
+ align:start position:0%
+impossible I haven't proved this to to
+find a three Noe example with arbitrary
+
+ align:start position:0%
+find a three Noe example with arbitrary
+ 
+
+ align:start position:0%
+find a three Noe example with arbitrary
+weights for which the greedy algorithm
+
+ align:start position:0%
+weights for which the greedy algorithm
+ 
+
+ align:start position:0%
+weights for which the greedy algorithm
+fails
+
+ align:start position:0%
+fails
+ 
+
+ align:start position:0%
+fails
+okay but four nodes it fails okay so
+
+ align:start position:0%
+okay but four nodes it fails okay so
+ 
+
+ align:start position:0%
+okay but four nodes it fails okay so
+that's the good news um so
+
+ align:start position:0%
+that's the good news um so
+ 
+
+ align:start position:0%
+that's the good news um so
+here's here's the
+
+ align:start position:0%
+here's here's the
+ 
+
+ align:start position:0%
+here's here's the
+example thanks to Nick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Davis and it looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops so I claim that the greedy
+
+ align:start position:0%
+oops so I claim that the greedy
+ 
+
+ align:start position:0%
+oops so I claim that the greedy
+algorithm for the problem that is given
+
+ align:start position:0%
+algorithm for the problem that is given
+ 
+
+ align:start position:0%
+algorithm for the problem that is given
+to me uh would
+
+ align:start position:0%
+to me uh would
+ 
+
+ align:start position:0%
+to me uh would
+produce this uh BST right and uh the
+
+ align:start position:0%
+produce this uh BST right and uh the
+ 
+
+ align:start position:0%
+produce this uh BST right and uh the
+reason reason for that uh is simple uh
+
+ align:start position:0%
+reason reason for that uh is simple uh
+ 
+
+ align:start position:0%
+reason reason for that uh is simple uh
+the highest weight node happens to be
+
+ align:start position:0%
+the highest weight node happens to be
+ 
+
+ align:start position:0%
+the highest weight node happens to be
+node two which has a weight of 10 so I
+
+ align:start position:0%
+node two which has a weight of 10 so I
+ 
+
+ align:start position:0%
+node two which has a weight of 10 so I
+would pick that and I'd stick that up
+
+ align:start position:0%
+would pick that and I'd stick that up
+ 
+
+ align:start position:0%
+would pick that and I'd stick that up
+here which means of course that I'm
+
+ align:start position:0%
+here which means of course that I'm
+ 
+
+ align:start position:0%
+here which means of course that I'm
+going to have to have one on this side
+
+ align:start position:0%
+going to have to have one on this side
+ 
+
+ align:start position:0%
+going to have to have one on this side
+and I'm going to have to have four and
+
+ align:start position:0%
+and I'm going to have to have four and
+ 
+
+ align:start position:0%
+and I'm going to have to have four and
+three on the other side and since four
+
+ align:start position:0%
+three on the other side and since four
+ 
+
+ align:start position:0%
+three on the other side and since four
+has a higher weight uh than three I'd
+
+ align:start position:0%
+has a higher weight uh than three I'd
+ 
+
+ align:start position:0%
+has a higher weight uh than three I'd
+pick that first and then three would
+
+ align:start position:0%
+pick that first and then three would
+ 
+
+ align:start position:0%
+pick that first and then three would
+have to go over here okay so if I go do
+
+ align:start position:0%
+have to go over here okay so if I go do
+ 
+
+ align:start position:0%
+have to go over here okay so if I go do
+the math um the cost is going to be 1 *
+
+ align:start position:0%
+the math um the cost is going to be 1 *
+ 
+
+ align:start position:0%
+the math um the cost is going to be 1 *
+2 and I'll explain what these numbers
+
+ align:start position:0%
+2 and I'll explain what these numbers
+ 
+
+ align:start position:0%
+2 and I'll explain what these numbers
+are I did tell you it was going to get a
+
+ align:start position:0%
+are I did tell you it was going to get a
+ 
+
+ align:start position:0%
+are I did tell you it was going to get a
+little uh cluttered here with uh with
+
+ align:start position:0%
+little uh cluttered here with uh with
+ 
+
+ align:start position:0%
+little uh cluttered here with uh with
+lots of numbers but if you keep that
+
+ align:start position:0%
+lots of numbers but if you keep that
+ 
+
+ align:start position:0%
+lots of numbers but if you keep that
+equation in mind then this should all
+
+ align:start position:0%
+equation in mind then this should all
+ 
+
+ align:start position:0%
+equation in mind then this should all
+work out um so what do I have here um
+
+ align:start position:0%
+work out um so what do I have here um
+ 
+
+ align:start position:0%
+work out um so what do I have here um
+I'm just Computing this is
+
+ align:start position:0%
+I'm just Computing this is
+ 
+
+ align:start position:0%
+I'm just Computing this is
+W1 so you you see the first numbers in
+
+ align:start position:0%
+W1 so you you see the first numbers in
+ 
+
+ align:start position:0%
+W1 so you you see the first numbers in
+each of these are the are the weights uh
+
+ align:start position:0%
+each of these are the are the weights uh
+ 
+
+ align:start position:0%
+each of these are the are the weights uh
+and so this would be W2 and Etc and you
+
+ align:start position:0%
+and so this would be W2 and Etc and you
+ 
+
+ align:start position:0%
+and so this would be W2 and Etc and you
+can see that this is at
+
+ align:start position:0%
+can see that this is at
+ 
+
+ align:start position:0%
+can see that this is at
+depth one which means I have to have two
+
+ align:start position:0%
+depth one which means I have to have two
+ 
+
+ align:start position:0%
+depth one which means I have to have two
+here because I'm adding one to the depth
+
+ align:start position:0%
+here because I'm adding one to the depth
+ 
+
+ align:start position:0%
+here because I'm adding one to the depth
+so I have 1 * 2 10 * 1 because that's at
+
+ align:start position:0%
+so I have 1 * 2 10 * 1 because that's at
+ 
+
+ align:start position:0%
+so I have 1 * 2 10 * 1 because that's at
+the root 9 * 2 Etc and um I get I get 54
+
+ align:start position:0%
+the root 9 * 2 Etc and um I get I get 54
+ 
+
+ align:start position:0%
+the root 9 * 2 Etc and um I get I get 54
+right it turns out the optimum tree you
+
+ align:start position:0%
+right it turns out the optimum tree you
+ 
+
+ align:start position:0%
+right it turns out the optimum tree you
+can do you can do better than that if
+
+ align:start position:0%
+can do you can do better than that if
+ 
+
+ align:start position:0%
+can do you can do better than that if
+you pick
+
+ align:start position:0%
+you pick
+ 
+
+ align:start position:0%
+you pick
+three um and you
+
+ align:start position:0%
+three um and you
+ 
+
+ align:start position:0%
+three um and you
+go like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what you have here is the cost =
+
+ align:start position:0%
+and so what you have here is the cost =
+ 
+
+ align:start position:0%
+and so what you have here is the cost =
+1 * 3 + 10 * 2 + 8 * 1 + 9 * 2 and
+
+ align:start position:0%
+1 * 3 + 10 * 2 + 8 * 1 + 9 * 2 and
+ 
+
+ align:start position:0%
+1 * 3 + 10 * 2 + 8 * 1 + 9 * 2 and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so I'll let you look at that um the
+
+ align:start position:0%
+okay so I'll let you look at that um the
+ 
+
+ align:start position:0%
+okay so I'll let you look at that um the
+bottom line is I it because of the way
+
+ align:start position:0%
+bottom line is I it because of the way
+ 
+
+ align:start position:0%
+bottom line is I it because of the way
+the weights are set up here uh you
+
+ align:start position:0%
+the weights are set up here uh you
+ 
+
+ align:start position:0%
+the weights are set up here uh you
+really want to use the top three
+
+ align:start position:0%
+really want to use the top three
+ 
+
+ align:start position:0%
+really want to use the top three
+spots uh for which have the the minimum
+
+ align:start position:0%
+spots uh for which have the the minimum
+ 
+
+ align:start position:0%
+spots uh for which have the the minimum
+depth uh for the highest weight nodes
+
+ align:start position:0%
+depth uh for the highest weight nodes
+ 
+
+ align:start position:0%
+depth uh for the highest weight nodes
+right and so you can see that I could
+
+ align:start position:0%
+right and so you can see that I could
+ 
+
+ align:start position:0%
+right and so you can see that I could
+make this uh these weights uh arbitrary
+
+ align:start position:0%
+make this uh these weights uh arbitrary
+ 
+
+ align:start position:0%
+make this uh these weights uh arbitrary
+obviously and I could break a greedy
+
+ align:start position:0%
+obviously and I could break a greedy
+ 
+
+ align:start position:0%
+obviously and I could break a greedy
+algorithm as this little example shows
+
+ align:start position:0%
+algorithm as this little example shows
+ 
+
+ align:start position:0%
+algorithm as this little example shows
+right so we got no recurse here we got
+
+ align:start position:0%
+right so we got no recurse here we got
+ 
+
+ align:start position:0%
+right so we got no recurse here we got
+to do some more work we're going to have
+
+ align:start position:0%
+to do some more work we're going to have
+ 
+
+ align:start position:0%
+to do some more work we're going to have
+to use DP to solve this problem the good
+
+ align:start position:0%
+to use DP to solve this problem the good
+ 
+
+ align:start position:0%
+to use DP to solve this problem the good
+news is DP does solve this problem
+
+ align:start position:0%
+news is DP does solve this problem
+ 
+
+ align:start position:0%
+news is DP does solve this problem
+okay um so let Let's uh let's take a
+
+ align:start position:0%
+okay um so let Let's uh let's take a
+ 
+
+ align:start position:0%
+okay um so let Let's uh let's take a
+look at the decomposition and as with
+
+ align:start position:0%
+look at the decomposition and as with
+ 
+
+ align:start position:0%
+look at the decomposition and as with
+anything else uh the key is uh the the
+
+ align:start position:0%
+anything else uh the key is uh the the
+ 
+
+ align:start position:0%
+anything else uh the key is uh the the
+step that corresponds to breaking up the
+
+ align:start position:0%
+step that corresponds to breaking up the
+ 
+
+ align:start position:0%
+step that corresponds to breaking up the
+original problem into two parts uh or
+
+ align:start position:0%
+original problem into two parts uh or
+ 
+
+ align:start position:0%
+original problem into two parts uh or
+more uh that that essentially give you
+
+ align:start position:0%
+more uh that that essentially give you
+ 
+
+ align:start position:0%
+more uh that that essentially give you
+this sort of decomposition and uh we
+
+ align:start position:0%
+this sort of decomposition and uh we
+ 
+
+ align:start position:0%
+this sort of decomposition and uh we
+don't quite know so this is really the
+
+ align:start position:0%
+don't quite know so this is really the
+ 
+
+ align:start position:0%
+don't quite know so this is really the
+key question here we don't quite know
+
+ align:start position:0%
+key question here we don't quite know
+ 
+
+ align:start position:0%
+key question here we don't quite know
+what the root node is going to be so
+
+ align:start position:0%
+what the root node is going to be so
+ 
+
+ align:start position:0%
+what the root node is going to be so
+what is what do we do when we don't know
+
+ align:start position:0%
+what is what do we do when we don't know
+ 
+
+ align:start position:0%
+what is what do we do when we don't know
+what to do
+
+ align:start position:0%
+what to do
+ 
+
+ align:start position:0%
+what to do
+do right what do we do in DP when we
+
+ align:start position:0%
+do right what do we do in DP when we
+ 
+
+ align:start position:0%
+do right what do we do in DP when we
+don't know what to do this is a very
+
+ align:start position:0%
+don't know what to do this is a very
+ 
+
+ align:start position:0%
+don't know what to do this is a very
+profound
+
+ align:start position:0%
+profound
+ 
+
+ align:start position:0%
+profound
+question what do you do you guess and
+
+ align:start position:0%
+question what do you do you guess and
+ 
+
+ align:start position:0%
+question what do you do you guess and
+not only do you guess you guess all
+
+ align:start position:0%
+not only do you guess you guess all
+ 
+
+ align:start position:0%
+not only do you guess you guess all
+outcomes you you you say is it going to
+
+ align:start position:0%
+outcomes you you you say is it going to
+ 
+
+ align:start position:0%
+outcomes you you you say is it going to
+come up heads is it going to come up
+
+ align:start position:0%
+come up heads is it going to come up
+ 
+
+ align:start position:0%
+come up heads is it going to come up
+Tails I'll guess both you have a die
+
+ align:start position:0%
+Tails I'll guess both you have a die
+ 
+
+ align:start position:0%
+Tails I'll guess both you have a die
+it's going to get roll a one 2 3 four 5
+
+ align:start position:0%
+it's going to get roll a one 2 3 four 5
+ 
+
+ align:start position:0%
+it's going to get roll a one 2 3 four 5
+six guess them all right so if you're
+
+ align:start position:0%
+six guess them all right so if you're
+ 
+
+ align:start position:0%
+six guess them all right so if you're
+going to have to guess that the root
+
+ align:start position:0%
+going to have to guess that the root
+ 
+
+ align:start position:0%
+going to have to guess that the root
+node could be any of the any of the keys
+
+ align:start position:0%
+node could be any of the any of the keys
+ 
+
+ align:start position:0%
+node could be any of the any of the keys
+right and it's still I mean there's
+
+ align:start position:0%
+right and it's still I mean there's
+ 
+
+ align:start position:0%
+right and it's still I mean there's
+there's a linear number of guesses there
+
+ align:start position:0%
+there's a linear number of guesses there
+ 
+
+ align:start position:0%
+there's a linear number of guesses there
+that's the good news it's going to stay
+
+ align:start position:0%
+that's the good news it's going to stay
+ 
+
+ align:start position:0%
+that's the good news it's going to stay
+polinomial time okay so we're going to
+
+ align:start position:0%
+polinomial time okay so we're going to
+ 
+
+ align:start position:0%
+polinomial time okay so we're going to
+have to guess and once you do that guess
+
+ align:start position:0%
+have to guess and once you do that guess
+ 
+
+ align:start position:0%
+have to guess and once you do that guess
+it turns out that decomposition that you
+
+ align:start position:0%
+it turns out that decomposition that you
+ 
+
+ align:start position:0%
+it turns out that decomposition that you
+see up there um is exactly what we want
+
+ align:start position:0%
+see up there um is exactly what we want
+ 
+
+ align:start position:0%
+see up there um is exactly what we want
+it's just that the greedy algorithm
+
+ align:start position:0%
+it's just that the greedy algorithm
+ 
+
+ align:start position:0%
+it's just that the greedy algorithm
+didn't bother with all of these
+
+ align:start position:0%
+didn't bother with all of these
+ 
+
+ align:start position:0%
+didn't bother with all of these
+different guesses and the DP is
+
+ align:start position:0%
+different guesses and the DP is
+ 
+
+ align:start position:0%
+different guesses and the DP is
+different from the greedy algorithm
+
+ align:start position:0%
+different from the greedy algorithm
+ 
+
+ align:start position:0%
+different from the greedy algorithm
+because um it's going to do each of
+
+ align:start position:0%
+because um it's going to do each of
+ 
+
+ align:start position:0%
+because um it's going to do each of
+those guesses and he going to pick the
+
+ align:start position:0%
+those guesses and he going to pick the
+ 
+
+ align:start position:0%
+those guesses and he going to pick the
+best one
+
+ align:start position:0%
+best one
+ 
+
+ align:start position:0%
+best one
+that comes out of all of those guesses
+
+ align:start position:0%
+that comes out of all of those guesses
+ 
+
+ align:start position:0%
+that comes out of all of those guesses
+right so it's really not that different
+
+ align:start position:0%
+right so it's really not that different
+ 
+
+ align:start position:0%
+right so it's really not that different
+from greedy right so um we'll keep that
+
+ align:start position:0%
+from greedy right so um we'll keep that
+ 
+
+ align:start position:0%
+from greedy right so um we'll keep that
+up there I leave that here let's go over
+
+ align:start position:0%
+up there I leave that here let's go over
+ 
+
+ align:start position:0%
+up there I leave that here let's go over
+here so the recursion here is not going
+
+ align:start position:0%
+here so the recursion here is not going
+ 
+
+ align:start position:0%
+here so the recursion here is not going
+to be that uh hard once you have gotten
+
+ align:start position:0%
+to be that uh hard once you have gotten
+ 
+
+ align:start position:0%
+to be that uh hard once you have gotten
+the inside that you just have to go make
+
+ align:start position:0%
+the inside that you just have to go make
+ 
+
+ align:start position:0%
+the inside that you just have to go make
+a linear number of guesses corresponding
+
+ align:start position:0%
+a linear number of guesses corresponding
+ 
+
+ align:start position:0%
+a linear number of guesses corresponding
+to the root node for your particular sub
+
+ align:start position:0%
+to the root node for your particular sub
+ 
+
+ align:start position:0%
+to the root node for your particular sub
+problem and obviously this happens
+
+ align:start position:0%
+problem and obviously this happens
+ 
+
+ align:start position:0%
+problem and obviously this happens
+recursively
+
+ align:start position:0%
+recursively
+ 
+
+ align:start position:0%
+recursively
+okay so there's a little subtlety here
+
+ align:start position:0%
+okay so there's a little subtlety here
+ 
+
+ align:start position:0%
+okay so there's a little subtlety here
+that I'll point out with respect to
+
+ align:start position:0%
+that I'll point out with respect to
+ 
+
+ align:start position:0%
+that I'll point out with respect to
+writing these equations out right so
+
+ align:start position:0%
+writing these equations out right so
+ 
+
+ align:start position:0%
+writing these equations out right so
+what I have here just to be clear is
+
+ align:start position:0%
+what I have here just to be clear is
+ 
+
+ align:start position:0%
+what I have here just to be clear is
+what I wrote up there even when I was
+
+ align:start position:0%
+what I wrote up there even when I was
+ 
+
+ align:start position:0%
+what I wrote up there even when I was
+talking about the greedy algorithm I uh
+
+ align:start position:0%
+talking about the greedy algorithm I uh
+ 
+
+ align:start position:0%
+talking about the greedy algorithm I uh
+had the sub problems defined so the
+
+ align:start position:0%
+had the sub problems defined so the
+ 
+
+ align:start position:0%
+had the sub problems defined so the
+original problem is E1 through n uh the
+
+ align:start position:0%
+original problem is E1 through n uh the
+ 
+
+ align:start position:0%
+original problem is E1 through n uh the
+sub problems correspond to uh e
+
+ align:start position:0%
+sub problems correspond to uh e
+ 
+
+ align:start position:0%
+sub problems correspond to uh e
+j and given a sub problem once I make a
+
+ align:start position:0%
+j and given a sub problem once I make a
+ 
+
+ align:start position:0%
+j and given a sub problem once I make a
+root choice I get two sub problems that
+
+ align:start position:0%
+root choice I get two sub problems that
+ 
+
+ align:start position:0%
+root choice I get two sub problems that
+result from the root Choice okay and
+
+ align:start position:0%
+result from the root Choice okay and
+ 
+
+ align:start position:0%
+result from the root Choice okay and
+each of those two sub problems is going
+
+ align:start position:0%
+each of those two sub problems is going
+ 
+
+ align:start position:0%
+each of those two sub problems is going
+to be something and this is something to
+
+ align:start position:0%
+to be something and this is something to
+ 
+
+ align:start position:0%
+to be something and this is something to
+keep in mind as we write these equations
+
+ align:start position:0%
+keep in mind as we write these equations
+ 
+
+ align:start position:0%
+keep in mind as we write these equations
+out they're going to be one level below
+
+ align:start position:0%
+out they're going to be one level below
+ 
+
+ align:start position:0%
+out they're going to be one level below
+the root okay so keep in mind that the
+
+ align:start position:0%
+the root okay so keep in mind that the
+ 
+
+ align:start position:0%
+the root okay so keep in mind that the
+original e j sub problem corresponded to
+
+ align:start position:0%
+original e j sub problem corresponded to
+ 
+
+ align:start position:0%
+original e j sub problem corresponded to
+this level uh but the e i r minus one
+
+ align:start position:0%
+this level uh but the e i r minus one
+ 
+
+ align:start position:0%
+this level uh but the e i r minus one
+problem uh and the e r + one J problem
+
+ align:start position:0%
+problem uh and the e r + one J problem
+ 
+
+ align:start position:0%
+problem uh and the e r + one J problem
+are at one level below okay so keep that
+
+ align:start position:0%
+are at one level below okay so keep that
+ 
+
+ align:start position:0%
+are at one level below okay so keep that
+in mind as we write these equations
+
+ align:start position:0%
+in mind as we write these equations
+ 
+
+ align:start position:0%
+in mind as we write these equations
+out um and so uh what I want to do here
+
+ align:start position:0%
+out um and so uh what I want to do here
+ 
+
+ align:start position:0%
+out um and so uh what I want to do here
+is just write the recurrence and after
+
+ align:start position:0%
+is just write the recurrence and after
+ 
+
+ align:start position:0%
+is just write the recurrence and after
+that Things become fairly mechanical the
+
+ align:start position:0%
+that Things become fairly mechanical the
+ 
+
+ align:start position:0%
+that Things become fairly mechanical the
+fun is in the recurrence right so I got
+
+ align:start position:0%
+fun is in the recurrence right so I got
+ 
+
+ align:start position:0%
+fun is in the recurrence right so I got
+wi if I equals
+
+ align:start position:0%
+wi if I equals
+ 
+
+ align:start position:0%
+wi if I equals
+J right so I'm at this level and uh if I
+
+ align:start position:0%
+J right so I'm at this level and uh if I
+ 
+
+ align:start position:0%
+J right so I'm at this level and uh if I
+just have one node left then um at that
+
+ align:start position:0%
+just have one node left then um at that
+ 
+
+ align:start position:0%
+just have one node left then um at that
+level uh I'm going to pay uh the the
+
+ align:start position:0%
+level uh I'm going to pay uh the the
+ 
+
+ align:start position:0%
+level uh I'm going to pay uh the the
+weight associated with that node uh and
+
+ align:start position:0%
+weight associated with that node uh and
+ 
+
+ align:start position:0%
+weight associated with that node uh and
+I'm going to have to do a certain amount
+
+ align:start position:0%
+I'm going to have to do a certain amount
+ 
+
+ align:start position:0%
+I'm going to have to do a certain amount
+of um um of of multiplication here with
+
+ align:start position:0%
+of um um of of multiplication here with
+ 
+
+ align:start position:0%
+of um um of of multiplication here with
+respect to the depth but I'm just
+
+ align:start position:0%
+respect to the depth but I'm just
+ 
+
+ align:start position:0%
+respect to the depth but I'm just
+talking about EIG as the sub problem
+
+ align:start position:0%
+talking about EIG as the sub problem
+ 
+
+ align:start position:0%
+talking about EIG as the sub problem
+weight just focusing in on that problem
+
+ align:start position:0%
+weight just focusing in on that problem
+ 
+
+ align:start position:0%
+weight just focusing in on that problem
+so if I only have one node it's the root
+
+ align:start position:0%
+so if I only have one node it's the root
+ 
+
+ align:start position:0%
+so if I only have one node it's the root
+node and that weight is going to be wi
+
+ align:start position:0%
+node and that weight is going to be wi
+ 
+
+ align:start position:0%
+node and that weight is going to be wi
+because the root node has depth of zero
+
+ align:start position:0%
+because the root node has depth of zero
+ 
+
+ align:start position:0%
+because the root node has depth of zero
+and I'm going to add one to it right so
+
+ align:start position:0%
+and I'm going to add one to it right so
+ 
+
+ align:start position:0%
+and I'm going to add one to it right so
+for that sub problem I got I got wi all
+
+ align:start position:0%
+for that sub problem I got I got wi all
+ 
+
+ align:start position:0%
+for that sub problem I got I got wi all
+right keep that in mind because that's
+
+ align:start position:0%
+right keep that in mind because that's
+ 
+
+ align:start position:0%
+right keep that in mind because that's
+the only subtlety here with respect to
+
+ align:start position:0%
+the only subtlety here with respect to
+ 
+
+ align:start position:0%
+the only subtlety here with respect to
+these equations making sure that our
+
+ align:start position:0%
+these equations making sure that our
+ 
+
+ align:start position:0%
+these equations making sure that our
+actual cost function that we're
+
+ align:start position:0%
+actual cost function that we're
+ 
+
+ align:start position:0%
+actual cost function that we're
+Computing has the correct uh depth uh
+
+ align:start position:0%
+Computing has the correct uh depth uh
+ 
+
+ align:start position:0%
+Computing has the correct uh depth uh
+multipli cant associated with it okay so
+
+ align:start position:0%
+multipli cant associated with it okay so
+ 
+
+ align:start position:0%
+multipli cant associated with it okay so
+um then we have our linear guessing um
+
+ align:start position:0%
+um then we have our linear guessing um
+ 
+
+ align:start position:0%
+um then we have our linear guessing um
+and uh oh I I I might have said Max at
+
+ align:start position:0%
+and uh oh I I I might have said Max at
+ 
+
+ align:start position:0%
+and uh oh I I I might have said Max at
+some point uh we want to get the the the
+
+ align:start position:0%
+some point uh we want to get the the the
+ 
+
+ align:start position:0%
+some point uh we want to get the the the
+min here and I had min minimize here so
+
+ align:start position:0%
+min here and I had min minimize here so
+ 
+
+ align:start position:0%
+min here and I had min minimize here so
+I think I'd wrote things down correct
+
+ align:start position:0%
+I think I'd wrote things down correct
+ 
+
+ align:start position:0%
+I think I'd wrote things down correct
+but at some point I think I might have
+
+ align:start position:0%
+but at some point I think I might have
+ 
+
+ align:start position:0%
+but at some point I think I might have
+said we want to maximize cost uh uh but
+
+ align:start position:0%
+said we want to maximize cost uh uh but
+ 
+
+ align:start position:0%
+said we want to maximize cost uh uh but
+we do want to minimize cost here
+
+ align:start position:0%
+we do want to minimize cost here
+ 
+
+ align:start position:0%
+we do want to minimize cost here
+corresponding to the uh the search
+
+ align:start position:0%
+corresponding to the uh the search
+ 
+
+ align:start position:0%
+corresponding to the uh the search
+expected search so we're doing a linear
+
+ align:start position:0%
+expected search so we're doing a linear
+ 
+
+ align:start position:0%
+expected search so we're doing a linear
+and uh we're doing a A Min and we're
+
+ align:start position:0%
+and uh we're doing a A Min and we're
+ 
+
+ align:start position:0%
+and uh we're doing a A Min and we're
+going to go off and uh look at each of
+
+ align:start position:0%
+going to go off and uh look at each of
+ 
+
+ align:start position:0%
+going to go off and uh look at each of
+the different uh nodes as being the root
+
+ align:start position:0%
+the different uh nodes as being the root
+ 
+
+ align:start position:0%
+the different uh nodes as being the root
+just like we discussed okay um and what
+
+ align:start position:0%
+just like we discussed okay um and what
+ 
+
+ align:start position:0%
+just like we discussed okay um and what
+I'm going to do here is I'm going to
+
+ align:start position:0%
+I'm going to do here is I'm going to
+ 
+
+ align:start position:0%
+I'm going to do here is I'm going to
+Simply say first that I'm going to look
+
+ align:start position:0%
+Simply say first that I'm going to look
+ 
+
+ align:start position:0%
+Simply say first that I'm going to look
+at e r minus one which corresponds to
+
+ align:start position:0%
+at e r minus one which corresponds to
+ 
+
+ align:start position:0%
+at e r minus one which corresponds to
+this um and I'm going
+
+ align:start position:0%
+this um and I'm going
+ 
+
+ align:start position:0%
+this um and I'm going
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+have plus e of r + 1 comma
+
+ align:start position:0%
+have plus e of r + 1 comma
+ 
+
+ align:start position:0%
+have plus e of r + 1 comma
+J okay and I at this
+
+ align:start position:0%
+J okay and I at this
+ 
+
+ align:start position:0%
+J okay and I at this
+point I
+
+ align:start position:0%
+point I
+ 
+
+ align:start position:0%
+point I
+I don't quite have what I want because I
+
+ align:start position:0%
+I don't quite have what I want because I
+ 
+
+ align:start position:0%
+I don't quite have what I want because I
+haven't actually taken into account the
+
+ align:start position:0%
+haven't actually taken into account the
+ 
+
+ align:start position:0%
+haven't actually taken into account the
+fact that uh the the depth of the EI
+
+ align:start position:0%
+fact that uh the the depth of the EI
+ 
+
+ align:start position:0%
+fact that uh the the depth of the EI
+rus1 and the r+1 J is one more than the
+
+ align:start position:0%
+rus1 and the r+1 J is one more than the
+ 
+
+ align:start position:0%
+rus1 and the r+1 J is one more than the
+eii J right so it's it's one more than
+
+ align:start position:0%
+eii J right so it's it's one more than
+ 
+
+ align:start position:0%
+eii J right so it's it's one more than
+that right and I also haven't taken into
+
+ align:start position:0%
+that right and I also haven't taken into
+ 
+
+ align:start position:0%
+that right and I also haven't taken into
+account the fact that in this case um I
+
+ align:start position:0%
+account the fact that in this case um I
+ 
+
+ align:start position:0%
+account the fact that in this case um I
+definitely need to add a wi as well
+
+ align:start position:0%
+definitely need to add a wi as well
+ 
+
+ align:start position:0%
+definitely need to add a wi as well
+right because I the root node is part of
+
+ align:start position:0%
+right because I the root node is part of
+ 
+
+ align:start position:0%
+right because I the root node is part of
+my solution in both cases in one case it
+
+ align:start position:0%
+my solution in both cases in one case it
+ 
+
+ align:start position:0%
+my solution in both cases in one case it
+ended my solution uh the top case but in
+
+ align:start position:0%
+ended my solution uh the top case but in
+ 
+
+ align:start position:0%
+ended my solution uh the top case but in
+this case it's also the root node as you
+
+ align:start position:0%
+this case it's also the root node as you
+ 
+
+ align:start position:0%
+this case it's also the root node as you
+can see over on the left and I got to
+
+ align:start position:0%
+can see over on the left and I got to
+ 
+
+ align:start position:0%
+can see over on the left and I got to
+add that in there so I definitely need
+
+ align:start position:0%
+add that in there so I definitely need
+ 
+
+ align:start position:0%
+add that in there so I definitely need
+to add a wi here okay and what else do I
+
+ align:start position:0%
+to add a wi here okay and what else do I
+ 
+
+ align:start position:0%
+to add a wi here okay and what else do I
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+add uh from a from from a standpoint of
+
+ align:start position:0%
+add uh from a from from a standpoint of
+ 
+
+ align:start position:0%
+add uh from a from from a standpoint of
+the weights what other weights do I need
+
+ align:start position:0%
+the weights what other weights do I need
+ 
+
+ align:start position:0%
+the weights what other weights do I need
+to add uh to uh to this line yeah go
+
+ align:start position:0%
+to add uh to uh to this line yeah go
+ 
+
+ align:start position:0%
+to add uh to uh to this line yeah go
+ahead first of all should be
+
+ align:start position:0%
+ahead first of all should be
+ 
+
+ align:start position:0%
+ahead first of all should be
+R uh first of all that should be a WR
+
+ align:start position:0%
+R uh first of all that should be a WR
+ 
+
+ align:start position:0%
+R uh first of all that should be a WR
+you're exactly correct you want add and
+
+ align:start position:0%
+you're exactly correct you want add and
+ 
+
+ align:start position:0%
+you're exactly correct you want add and
+you want to add all the weights right uh
+
+ align:start position:0%
+you want to add all the weights right uh
+ 
+
+ align:start position:0%
+you want to add all the weights right uh
+and uh you're exactly right um I have
+
+ align:start position:0%
+and uh you're exactly right um I have
+ 
+
+ align:start position:0%
+and uh you're exactly right um I have
+two more frisbees but I need to use them
+
+ align:start position:0%
+two more frisbees but I need to use them
+ 
+
+ align:start position:0%
+two more frisbees but I need to use them
+for something else okay so you get one
+
+ align:start position:0%
+for something else okay so you get one
+ 
+
+ align:start position:0%
+for something else okay so you get one
+next time right or um do I have more
+
+ align:start position:0%
+next time right or um do I have more
+ 
+
+ align:start position:0%
+next time right or um do I have more
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+that no no I these are precious frisbees
+
+ align:start position:0%
+that no no I these are precious frisbees
+ 
+
+ align:start position:0%
+that no no I these are precious frisbees
+here you know sorry man you
+
+ align:start position:0%
+here you know sorry man you
+ 
+
+ align:start position:0%
+here you know sorry man you
+know um so and you you corrected me too
+
+ align:start position:0%
+know um so and you you corrected me too
+ 
+
+ align:start position:0%
+know um so and you you corrected me too
+sh you know shoot this is this is sad um
+
+ align:start position:0%
+sh you know shoot this is this is sad um
+ 
+
+ align:start position:0%
+sh you know shoot this is this is sad um
+uh so that needed to be a WRR okay uh
+
+ align:start position:0%
+uh so that needed to be a WRR okay uh
+ 
+
+ align:start position:0%
+uh so that needed to be a WRR okay uh
+but you also need to add all of the
+
+ align:start position:0%
+but you also need to add all of the
+ 
+
+ align:start position:0%
+but you also need to add all of the
+nodes that are in here because there one
+
+ align:start position:0%
+nodes that are in here because there one
+ 
+
+ align:start position:0%
+nodes that are in here because there one
+one more level right and now you see why
+
+ align:start position:0%
+one more level right and now you see why
+ 
+
+ align:start position:0%
+one more level right and now you see why
+I made the mistake right I don't usually
+
+ align:start position:0%
+I made the mistake right I don't usually
+ 
+
+ align:start position:0%
+I made the mistake right I don't usually
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+mistakes but what I really want actually
+
+ align:start position:0%
+mistakes but what I really want actually
+ 
+
+ align:start position:0%
+mistakes but what I really want actually
+it's more like you know I don't know a
+
+ align:start position:0%
+it's more like you know I don't know a
+ 
+
+ align:start position:0%
+it's more like you know I don't know a
+few per lecture you know constant order
+
+ align:start position:0%
+few per lecture you know constant order
+ 
+
+ align:start position:0%
+few per lecture you know constant order
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+mistakes right and I'm going to say this
+
+ align:start position:0%
+mistakes right and I'm going to say this
+ 
+
+ align:start position:0%
+mistakes right and I'm going to say this
+is W comma J all right where wi comma J
+
+ align:start position:0%
+is W comma J all right where wi comma J
+ 
+
+ align:start position:0%
+is W comma J all right where wi comma J
+is simply the sum of all of the weights
+
+ align:start position:0%
+is simply the sum of all of the weights
+ 
+
+ align:start position:0%
+is simply the sum of all of the weights
+from I to J okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and this makes perfect sense because
+
+ align:start position:0%
+so and this makes perfect sense because
+ 
+
+ align:start position:0%
+so and this makes perfect sense because
+the nice thing is that I don't even need
+
+ align:start position:0%
+the nice thing is that I don't even need
+ 
+
+ align:start position:0%
+the nice thing is that I don't even need
+to put an r in there all right so it's
+
+ align:start position:0%
+to put an r in there all right so it's
+ 
+
+ align:start position:0%
+to put an r in there all right so it's
+uh I I could choose I put particular R
+
+ align:start position:0%
+uh I I could choose I put particular R
+ 
+
+ align:start position:0%
+uh I I could choose I put particular R
+WR R will be in there but all of the
+
+ align:start position:0%
+WR R will be in there but all of the
+ 
+
+ align:start position:0%
+WR R will be in there but all of the
+other nodes are going to be in there
+
+ align:start position:0%
+other nodes are going to be in there
+ 
+
+ align:start position:0%
+other nodes are going to be in there
+anyway right so it doesn't really matter
+
+ align:start position:0%
+anyway right so it doesn't really matter
+ 
+
+ align:start position:0%
+anyway right so it doesn't really matter
+what the r selection is corresponding to
+
+ align:start position:0%
+what the r selection is corresponding to
+ 
+
+ align:start position:0%
+what the r selection is corresponding to
+this term here though I will put it
+
+ align:start position:0%
+this term here though I will put it
+ 
+
+ align:start position:0%
+this term here though I will put it
+inside the uh the the the minimization
+
+ align:start position:0%
+inside the uh the the the minimization
+ 
+
+ align:start position:0%
+inside the uh the the the minimization
+uh this bracket here is closed with that
+
+ align:start position:0%
+uh this bracket here is closed with that
+ 
+
+ align:start position:0%
+uh this bracket here is closed with that
+but you can pull that out because that
+
+ align:start position:0%
+but you can pull that out because that
+ 
+
+ align:start position:0%
+but you can pull that out because that
+doesn't depend on R right it's it's just
+
+ align:start position:0%
+doesn't depend on R right it's it's just
+ 
+
+ align:start position:0%
+doesn't depend on R right it's it's just
+going to be there uh uh for all of the
+
+ align:start position:0%
+going to be there uh uh for all of the
+ 
+
+ align:start position:0%
+going to be there uh uh for all of the
+cases all of the guesses all right so
+
+ align:start position:0%
+cases all of the guesses all right so
+ 
+
+ align:start position:0%
+cases all of the guesses all right so
+that's it that's uh that's our
+
+ align:start position:0%
+that's it that's uh that's our
+ 
+
+ align:start position:0%
+that's it that's uh that's our
+recurrence relationship corresponding to
+
+ align:start position:0%
+recurrence relationship corresponding to
+ 
+
+ align:start position:0%
+recurrence relationship corresponding to
+uh the DP for this particular
+
+ align:start position:0%
+uh the DP for this particular
+ 
+
+ align:start position:0%
+uh the DP for this particular
+problem um you can go figure out what
+
+ align:start position:0%
+problem um you can go figure out what
+ 
+
+ align:start position:0%
+problem um you can go figure out what
+the complexity is and I I have other
+
+ align:start position:0%
+the complexity is and I I have other
+ 
+
+ align:start position:0%
+the complexity is and I I have other
+things to do so we'll move on uh but you
+
+ align:start position:0%
+things to do so we'll move on uh but you
+ 
+
+ align:start position:0%
+things to do so we'll move on uh but you
+can do the same things and these are
+
+ align:start position:0%
+can do the same things and these are
+ 
+
+ align:start position:0%
+can do the same things and these are
+fairly mechanical at this point to go
+
+ align:start position:0%
+fairly mechanical at this point to go
+ 
+
+ align:start position:0%
+fairly mechanical at this point to go
+write code for it trace the solution to
+
+ align:start position:0%
+write code for it trace the solution to
+ 
+
+ align:start position:0%
+write code for it trace the solution to
+get the optimum binary search Tre uh y y
+
+ align:start position:0%
+get the optimum binary search Tre uh y y
+ 
+
+ align:start position:0%
+get the optimum binary search Tre uh y y
+y right uh any questions about this
+
+ align:start position:0%
+y right uh any questions about this
+ 
+
+ align:start position:0%
+y right uh any questions about this
+equation or anything else do people get
+
+ align:start position:0%
+equation or anything else do people get
+ 
+
+ align:start position:0%
+equation or anything else do people get
+that yeah go ahead what is the depth so
+
+ align:start position:0%
+that yeah go ahead what is the depth so
+ 
+
+ align:start position:0%
+that yeah go ahead what is the depth so
+um the depth is getting added by the
+
+ align:start position:0%
+um the depth is getting added by the
+ 
+
+ align:start position:0%
+um the depth is getting added by the
+weights um so basically what's happening
+
+ align:start position:0%
+weights um so basically what's happening
+ 
+
+ align:start position:0%
+weights um so basically what's happening
+is that um as I go deeper into the
+
+ align:start position:0%
+is that um as I go deeper into the
+ 
+
+ align:start position:0%
+is that um as I go deeper into the
+recursion I'm adding the weights and
+
+ align:start position:0%
+recursion I'm adding the weights and
+ 
+
+ align:start position:0%
+recursion I'm adding the weights and
+potentially multiple times depending on
+
+ align:start position:0%
+potentially multiple times depending on
+ 
+
+ align:start position:0%
+potentially multiple times depending on
+the depth right so if you really think
+
+ align:start position:0%
+the depth right so if you really think
+ 
+
+ align:start position:0%
+the depth right so if you really think
+about it this wi
+
+ align:start position:0%
+about it this wi
+ 
+
+ align:start position:0%
+about it this wi
+J added all of these weights but when
+
+ align:start position:0%
+J added all of these weights but when
+ 
+
+ align:start position:0%
+J added all of these weights but when
+you go into this recursion into the EI
+
+ align:start position:0%
+you go into this recursion into the EI
+ 
+
+ align:start position:0%
+you go into this recursion into the EI
+of Rus one well you're going to see I to
+
+ align:start position:0%
+of Rus one well you're going to see I to
+ 
+
+ align:start position:0%
+of Rus one well you're going to see I to
+Rus one in the next level of recursion
+
+ align:start position:0%
+Rus one in the next level of recursion
+ 
+
+ align:start position:0%
+Rus one in the next level of recursion
+so you would have added you know the
+
+ align:start position:0%
+so you would have added you know the
+ 
+
+ align:start position:0%
+so you would have added you know the
+weight again right so it's not the case
+
+ align:start position:0%
+weight again right so it's not the case
+ 
+
+ align:start position:0%
+weight again right so it's not the case
+that the weights are only appearing once
+
+ align:start position:0%
+that the weights are only appearing once
+ 
+
+ align:start position:0%
+that the weights are only appearing once
+they're in fact appearing this many
+
+ align:start position:0%
+they're in fact appearing this many
+ 
+
+ align:start position:0%
+they're in fact appearing this many
+times right so that's what's kind of
+
+ align:start position:0%
+times right so that's what's kind of
+ 
+
+ align:start position:0%
+times right so that's what's kind of
+cute about this right the way the way we
+
+ align:start position:0%
+cute about this right the way the way we
+ 
+
+ align:start position:0%
+cute about this right the way the way we
+wrote it
+
+ align:start position:0%
+wrote it
+ 
+
+ align:start position:0%
+wrote it
+okay uh any other
+
+ align:start position:0%
+okay uh any other
+ 
+
+ align:start position:0%
+okay uh any other
+questions all right good so uh we're
+
+ align:start position:0%
+questions all right good so uh we're
+ 
+
+ align:start position:0%
+questions all right good so uh we're
+done with that so one last example um
+
+ align:start position:0%
+done with that so one last example um
+ 
+
+ align:start position:0%
+done with that so one last example um
+this is again a little bit different uh
+
+ align:start position:0%
+this is again a little bit different uh
+ 
+
+ align:start position:0%
+this is again a little bit different uh
+from uh the examples of DP we've looked
+
+ align:start position:0%
+from uh the examples of DP we've looked
+ 
+
+ align:start position:0%
+from uh the examples of DP we've looked
+at up until now because it's it's a game
+
+ align:start position:0%
+at up until now because it's it's a game
+ 
+
+ align:start position:0%
+at up until now because it's it's a game
+and you have an opponent and U you have
+
+ align:start position:0%
+and you have an opponent and U you have
+ 
+
+ align:start position:0%
+and you have an opponent and U you have
+to figure out what the opponent is going
+
+ align:start position:0%
+to figure out what the opponent is going
+ 
+
+ align:start position:0%
+to figure out what the opponent is going
+to do uh and you know try to try to
+
+ align:start position:0%
+to do uh and you know try to try to
+ 
+
+ align:start position:0%
+to do uh and you know try to try to
+win uh I guess you suppose you could try
+
+ align:start position:0%
+win uh I guess you suppose you could try
+ 
+
+ align:start position:0%
+win uh I guess you suppose you could try
+to lose as well but um let's assume here
+
+ align:start position:0%
+to lose as well but um let's assume here
+ 
+
+ align:start position:0%
+to lose as well but um let's assume here
+same thing with minimization and
+
+ align:start position:0%
+same thing with minimization and
+ 
+
+ align:start position:0%
+same thing with minimization and
+maximization uh most of the time you can
+
+ align:start position:0%
+maximization uh most of the time you can
+ 
+
+ align:start position:0%
+maximization uh most of the time you can
+U invert these cost functions and DP
+
+ align:start position:0%
+U invert these cost functions and DP
+ 
+
+ align:start position:0%
+U invert these cost functions and DP
+will still work but let's assume here
+
+ align:start position:0%
+will still work but let's assume here
+ 
+
+ align:start position:0%
+will still work but let's assume here
+that you want to win this game right so
+
+ align:start position:0%
+that you want to win this game right so
+ 
+
+ align:start position:0%
+that you want to win this game right so
+uh so the game is an alternating coins
+
+ align:start position:0%
+uh so the game is an alternating coins
+ 
+
+ align:start position:0%
+uh so the game is an alternating coins
+game
+
+ align:start position:0%
+game
+ 
+
+ align:start position:0%
+game
+where we have a row of n
+
+ align:start position:0%
+where we have a row of n
+ 
+
+ align:start position:0%
+where we have a row of n
+coins um of
+
+ align:start position:0%
+coins um of
+ 
+
+ align:start position:0%
+coins um of
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+V1 through VN um these are not
+
+ align:start position:0%
+V1 through VN um these are not
+ 
+
+ align:start position:0%
+V1 through VN um these are not
+necessarily in any particular order uh
+
+ align:start position:0%
+necessarily in any particular order uh
+ 
+
+ align:start position:0%
+necessarily in any particular order uh
+it and N is
+
+ align:start position:0%
+it and N is
+ 
+
+ align:start position:0%
+it and N is
+even and um uh the goal here is uh
+
+ align:start position:0%
+even and um uh the goal here is uh
+ 
+
+ align:start position:0%
+even and um uh the goal here is uh
+select the outer coins so uh select uh
+
+ align:start position:0%
+select the outer coins so uh select uh
+ 
+
+ align:start position:0%
+select the outer coins so uh select uh
+either the
+
+ align:start position:0%
+either the
+ 
+
+ align:start position:0%
+either the
+first or
+
+ align:start position:0%
+first or
+ 
+
+ align:start position:0%
+first or
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+coin uh from the
+
+ align:start position:0%
+coin uh from the
+ 
+
+ align:start position:0%
+coin uh from the
+row and then the uh opponent Place
+
+ align:start position:0%
+row and then the uh opponent Place
+ 
+
+ align:start position:0%
+row and then the uh opponent Place
+remove permanently but add it to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value and receive the value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I need two
+
+ align:start position:0%
+all right so I need two
+ 
+
+ align:start position:0%
+all right so I need two
+volunteers to play this game and uh you
+
+ align:start position:0%
+volunteers to play this game and uh you
+ 
+
+ align:start position:0%
+volunteers to play this game and uh you
+want to maximize the value the winner
+
+ align:start position:0%
+want to maximize the value the winner
+ 
+
+ align:start position:0%
+want to maximize the value the winner
+gets a blue
+
+ align:start position:0%
+gets a blue
+ 
+
+ align:start position:0%
+gets a blue
+frisbee the loser gets a purple frisbee
+
+ align:start position:0%
+frisbee the loser gets a purple frisbee
+ 
+
+ align:start position:0%
+frisbee the loser gets a purple frisbee
+because blue is greater than
+
+ align:start position:0%
+because blue is greater than
+ 
+
+ align:start position:0%
+because blue is greater than
+purple and and you might ask why is that
+
+ align:start position:0%
+purple and and you might ask why is that
+ 
+
+ align:start position:0%
+purple and and you might ask why is that
+well if you went to a
+
+ align:start position:0%
+well if you went to a
+ 
+
+ align:start position:0%
+well if you went to a
+beach and you saw water this color you
+
+ align:start position:0%
+beach and you saw water this color you
+ 
+
+ align:start position:0%
+beach and you saw water this color you
+went to another Beach and you saw water
+
+ align:start position:0%
+went to another Beach and you saw water
+ 
+
+ align:start position:0%
+went to another Beach and you saw water
+this color which beach would you pick
+
+ align:start position:0%
+this color which beach would you pick
+ 
+
+ align:start position:0%
+this color which beach would you pick
+right this is cuml this is Boston Harbor
+
+ align:start position:0%
+right this is cuml this is Boston Harbor
+ 
+
+ align:start position:0%
+right this is cuml this is Boston Harbor
+right right so blue is greater than
+
+ align:start position:0%
+right right so blue is greater than
+ 
+
+ align:start position:0%
+right right so blue is greater than
+purple right don't use this proof
+
+ align:start position:0%
+purple right don't use this proof
+ 
+
+ align:start position:0%
+purple right don't use this proof
+technique in the quiz all right so do I
+
+ align:start position:0%
+technique in the quiz all right so do I
+ 
+
+ align:start position:0%
+technique in the quiz all right so do I
+have a couple of volunteers to play this
+
+ align:start position:0%
+have a couple of volunteers to play this
+ 
+
+ align:start position:0%
+have a couple of volunteers to play this
+game two of them over there or are you
+
+ align:start position:0%
+game two of them over there or are you
+ 
+
+ align:start position:0%
+game two of them over there or are you
+were waving for him yeah I I see one you
+
+ align:start position:0%
+were waving for him yeah I I see one you
+ 
+
+ align:start position:0%
+were waving for him yeah I I see one you
+can come down another
+
+ align:start position:0%
+can come down another
+ 
+
+ align:start position:0%
+can come down another
+volunteer right y over there right all
+
+ align:start position:0%
+volunteer right y over there right all
+ 
+
+ align:start position:0%
+volunteer right y over there right all
+right you don't get your fris PES yet so
+
+ align:start position:0%
+right you don't get your fris PES yet so
+ 
+
+ align:start position:0%
+right you don't get your fris PES yet so
+um we going to make this really fair
+
+ align:start position:0%
+um we going to make this really fair
+ 
+
+ align:start position:0%
+um we going to make this really fair
+right uh what's your name Josiah Josiah
+
+ align:start position:0%
+right uh what's your name Josiah Josiah
+ 
+
+ align:start position:0%
+right uh what's your name Josiah Josiah
+Tessa Tessa Josiah uh and Tessa I'm
+
+ align:start position:0%
+Tessa Tessa Josiah uh and Tessa I'm
+ 
+
+ align:start position:0%
+Tessa Tessa Josiah uh and Tessa I'm
+going to write out uh a bunch of it's
+
+ align:start position:0%
+going to write out uh a bunch of it's
+ 
+
+ align:start position:0%
+going to write out uh a bunch of it's
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+a a fairly short game
+
+ align:start position:0%
+a a fairly short game
+ 
+
+ align:start position:0%
+a a fairly short game
+okay and we're going to be really fair
+
+ align:start position:0%
+okay and we're going to be really fair
+ 
+
+ align:start position:0%
+okay and we're going to be really fair
+and we're going to flip a coin to decide
+
+ align:start position:0%
+and we're going to flip a coin to decide
+ 
+
+ align:start position:0%
+and we're going to flip a coin to decide
+whether Josiah goes first you can pick
+
+ align:start position:0%
+whether Josiah goes first you can pick
+ 
+
+ align:start position:0%
+whether Josiah goes first you can pick
+heads or tails uh and or whether Tesla
+
+ align:start position:0%
+heads or tails uh and or whether Tesla
+ 
+
+ align:start position:0%
+heads or tails uh and or whether Tesla
+goes first and you can actually if you
+
+ align:start position:0%
+goes first and you can actually if you
+ 
+
+ align:start position:0%
+goes first and you can actually if you
+win you can let her go first if you want
+
+ align:start position:0%
+win you can let her go first if you want
+ 
+
+ align:start position:0%
+win you can let her go first if you want
+but you get to choose all right so pick
+
+ align:start position:0%
+but you get to choose all right so pick
+ 
+
+ align:start position:0%
+but you get to choose all right so pick
+heads that's heads all right do you want
+
+ align:start position:0%
+heads that's heads all right do you want
+ 
+
+ align:start position:0%
+heads that's heads all right do you want
+to go first or do you want to let Tessa
+
+ align:start position:0%
+to go first or do you want to let Tessa
+ 
+
+ align:start position:0%
+to go first or do you want to let Tessa
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first you should go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first all right so um Tessa you get to
+
+ align:start position:0%
+first all right so um Tessa you get to
+ 
+
+ align:start position:0%
+first all right so um Tessa you get to
+go first okay um six six okay so uh
+
+ align:start position:0%
+go first okay um six six okay so uh
+ 
+
+ align:start position:0%
+go first okay um six six okay so uh
+let's just say uh t Okay uh so you get
+
+ align:start position:0%
+let's just say uh t Okay uh so you get
+ 
+
+ align:start position:0%
+let's just say uh t Okay uh so you get
+to choose uh either 25 or four Josiah
+
+ align:start position:0%
+to choose uh either 25 or four Josiah
+ 
+
+ align:start position:0%
+to choose uh either 25 or four Josiah
+well I think I take 25 you think you'll
+
+ align:start position:0%
+well I think I take 25 you think you'll
+ 
+
+ align:start position:0%
+well I think I take 25 you think you'll
+take 25 okay so that's J all right so
+
+ align:start position:0%
+take 25 okay so that's J all right so
+ 
+
+ align:start position:0%
+take 25 okay so that's J all right so
+it's it's now down to four and 19 over
+
+ align:start position:0%
+it's it's now down to four and 19 over
+ 
+
+ align:start position:0%
+it's it's now down to four and 19 over
+here because those are gone so you're
+
+ align:start position:0%
+here because those are gone so you're
+ 
+
+ align:start position:0%
+here because those are gone so you're
+turn again okay um can I take a minute
+
+ align:start position:0%
+turn again okay um can I take a minute
+ 
+
+ align:start position:0%
+turn again okay um can I take a minute
+or should I just uh well you can take
+
+ align:start position:0%
+or should I just uh well you can take
+ 
+
+ align:start position:0%
+or should I just uh well you can take
+you can take uh 30 seconds okay
+
+ align:start position:0%
+you can take uh 30 seconds okay
+ 
+
+ align:start position:0%
+you can take uh 30 seconds okay
+right 19 19 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right PA
+
+ align:start position:0%
+all right PA
+ 
+
+ align:start position:0%
+all right PA
+four all
+
+ align:start position:0%
+four all
+ 
+
+ align:start position:0%
+four all
+right and 42 all right 42 this is one
+
+ align:start position:0%
+right and 42 all right 42 this is one
+ 
+
+ align:start position:0%
+right and 42 all right 42 this is one
+strange game all right all right now we
+
+ align:start position:0%
+strange game all right all right now we
+ 
+
+ align:start position:0%
+strange game all right all right now we
+get to add up the numbers this is going
+
+ align:start position:0%
+get to add up the numbers this is going
+ 
+
+ align:start position:0%
+get to add up the numbers this is going
+to be tight right 4 + 39 is 43 43 + 25
+
+ align:start position:0%
+to be tight right 4 + 39 is 43 43 + 25
+ 
+
+ align:start position:0%
+to be tight right 4 + 39 is 43 43 + 25
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+68 um 42 + 19 is uh 61 61 + 6 is
+
+ align:start position:0%
+68 um 42 + 19 is uh 61 61 + 6 is
+ 
+
+ align:start position:0%
+68 um 42 + 19 is uh 61 61 + 6 is
+67 oo all right well you get frisbees
+
+ align:start position:0%
+67 oo all right well you get frisbees
+ 
+
+ align:start position:0%
+67 oo all right well you get frisbees
+right all right well uh blue for you
+
+ align:start position:0%
+right all right well uh blue for you
+ 
+
+ align:start position:0%
+right all right well uh blue for you
+right I mean you can give her blue if
+
+ align:start position:0%
+right I mean you can give her blue if
+ 
+
+ align:start position:0%
+right I mean you can give her blue if
+you like yeah you prefer purple right
+
+ align:start position:0%
+you like yeah you prefer purple right
+ 
+
+ align:start position:0%
+you like yeah you prefer purple right
+thanks okay good job
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um no offenses intended to Josiah and
+
+ align:start position:0%
+um no offenses intended to Josiah and
+ 
+
+ align:start position:0%
+um no offenses intended to Josiah and
+Tessa but that was a classic example of
+
+ align:start position:0%
+Tessa but that was a classic example of
+ 
+
+ align:start position:0%
+Tessa but that was a classic example of
+how not to play the game okay first off
+
+ align:start position:0%
+how not to play the game okay first off
+ 
+
+ align:start position:0%
+how not to play the game okay first off
+Josiah could have won uh regardless of
+
+ align:start position:0%
+Josiah could have won uh regardless of
+ 
+
+ align:start position:0%
+Josiah could have won uh regardless of
+the coins that were up there regardless
+
+ align:start position:0%
+the coins that were up there regardless
+ 
+
+ align:start position:0%
+the coins that were up there regardless
+of the values of the coins if he chosen
+
+ align:start position:0%
+of the values of the coins if he chosen
+ 
+
+ align:start position:0%
+of the values of the coins if he chosen
+to go first right so this game the
+
+ align:start position:0%
+to go first right so this game the
+ 
+
+ align:start position:0%
+to go first right so this game the
+person who goes first is guaranteed to
+
+ align:start position:0%
+person who goes first is guaranteed to
+ 
+
+ align:start position:0%
+person who goes first is guaranteed to
+not lose and by that I mean you uh uh
+
+ align:start position:0%
+not lose and by that I mean you uh uh
+ 
+
+ align:start position:0%
+not lose and by that I mean you uh uh
+may have a situation where you can have
+
+ align:start position:0%
+may have a situation where you can have
+ 
+
+ align:start position:0%
+may have a situation where you can have
+a tie in terms of the values but you're
+
+ align:start position:0%
+a tie in terms of the values but you're
+ 
+
+ align:start position:0%
+a tie in terms of the values but you're
+guaranteed to not lose all right so now
+
+ align:start position:0%
+guaranteed to not lose all right so now
+ 
+
+ align:start position:0%
+guaranteed to not lose all right so now
+he ended up winning anyway because there
+
+ align:start position:0%
+he ended up winning anyway because there
+ 
+
+ align:start position:0%
+he ended up winning anyway because there
+were other errors
+
+ align:start position:0%
+were other errors
+ 
+
+ align:start position:0%
+were other errors
+made uh in in in during this and I don't
+
+ align:start position:0%
+made uh in in in during this and I don't
+ 
+
+ align:start position:0%
+made uh in in in during this and I don't
+have the time to enumerate all of them
+
+ align:start position:0%
+have the time to enumerate all of them
+ 
+
+ align:start position:0%
+have the time to enumerate all of them
+okay so we're just going to go move on
+
+ align:start position:0%
+okay so we're just going to go move on
+ 
+
+ align:start position:0%
+okay so we're just going to go move on
+and uh do the right thing all
+
+ align:start position:0%
+and uh do the right thing all
+ 
+
+ align:start position:0%
+and uh do the right thing all
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me first tell you outside of DP
+
+ align:start position:0%
+so let me first tell you outside of DP
+ 
+
+ align:start position:0%
+so let me first tell you outside of DP
+just in case you play this game over
+
+ align:start position:0%
+just in case you play this game over
+ 
+
+ align:start position:0%
+just in case you play this game over
+spring break or
+
+ align:start position:0%
+spring break or
+ 
+
+ align:start position:0%
+spring break or
+something how you can uh win this game
+
+ align:start position:0%
+something how you can uh win this game
+ 
+
+ align:start position:0%
+something how you can uh win this game
+uh without having to compute you know
+
+ align:start position:0%
+uh without having to compute you know
+ 
+
+ align:start position:0%
+uh without having to compute you know
+complicated recursive memorization DP
+
+ align:start position:0%
+complicated recursive memorization DP
+ 
+
+ align:start position:0%
+complicated recursive memorization DP
+programs right for this case Okay so
+
+ align:start position:0%
+programs right for this case Okay so
+ 
+
+ align:start position:0%
+programs right for this case Okay so
+let's say I have V1 V2 V3 all the way to
+
+ align:start position:0%
+let's say I have V1 V2 V3 all the way to
+ 
+
+ align:start position:0%
+let's say I have V1 V2 V3 all the way to
+VN minus one and VN and remember n is
+
+ align:start position:0%
+VN minus one and VN and remember n is
+ 
+
+ align:start position:0%
+VN minus one and VN and remember n is
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+right so you got to Pick n n/2 coins uh
+
+ align:start position:0%
+right so you got to Pick n n/2 coins uh
+ 
+
+ align:start position:0%
+right so you got to Pick n n/2 coins uh
+if you're the first player and n/ two if
+
+ align:start position:0%
+if you're the first player and n/ two if
+ 
+
+ align:start position:0%
+if you're the first player and n/ two if
+you're the second
+
+ align:start position:0%
+you're the second
+ 
+
+ align:start position:0%
+you're the second
+player um so what the what the first
+
+ align:start position:0%
+player um so what the what the first
+ 
+
+ align:start position:0%
+player um so what the what the first
+player
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does um is simply
+
+ align:start position:0%
+does um is simply
+ 
+
+ align:start position:0%
+does um is simply
+compute V1 take the odd numbers and uh n
+
+ align:start position:0%
+compute V1 take the odd numbers and uh n
+ 
+
+ align:start position:0%
+compute V1 take the odd numbers and uh n
+is even so you got VN minus1 being odd
+
+ align:start position:0%
+is even so you got VN minus1 being odd
+ 
+
+ align:start position:0%
+is even so you got VN minus1 being odd
+compute V1 + V3 all the way to VN minus
+
+ align:start position:0%
+compute V1 + V3 all the way to VN minus
+ 
+
+ align:start position:0%
+compute V1 + V3 all the way to VN minus
+one and compare
+
+ align:start position:0%
+one and compare
+ 
+
+ align:start position:0%
+one and compare
+that with uh the even positions V2 plus
+
+ align:start position:0%
+that with uh the even positions V2 plus
+ 
+
+ align:start position:0%
+that with uh the even positions V2 plus
+V4 all the way to VN so in this
+
+ align:start position:0%
+V4 all the way to VN so in this
+ 
+
+ align:start position:0%
+V4 all the way to VN so in this
+particular instance
+
+ align:start position:0%
+particular instance
+ 
+
+ align:start position:0%
+particular instance
+um uh Josiah who went second uh uh but
+
+ align:start position:0%
+um uh Josiah who went second uh uh but
+ 
+
+ align:start position:0%
+um uh Josiah who went second uh uh but
+if you just if you just look at the odd
+
+ align:start position:0%
+if you just if you just look at the odd
+ 
+
+ align:start position:0%
+if you just if you just look at the odd
+positions which is in fact what he ended
+
+ align:start position:0%
+positions which is in fact what he ended
+ 
+
+ align:start position:0%
+positions which is in fact what he ended
+up picking it was 4 + 39 plus 25 which
+
+ align:start position:0%
+up picking it was 4 + 39 plus 25 which
+ 
+
+ align:start position:0%
+up picking it was 4 + 39 plus 25 which
+was 68 and so you can do this
+
+ align:start position:0%
+was 68 and so you can do this
+ 
+
+ align:start position:0%
+was 68 and so you can do this
+computation beforehand you compute this
+
+ align:start position:0%
+computation beforehand you compute this
+ 
+
+ align:start position:0%
+computation beforehand you compute this
+to be 68 in our case compare that with
+
+ align:start position:0%
+to be 68 in our case compare that with
+ 
+
+ align:start position:0%
+to be 68 in our case compare that with
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+67 okay and uh you don't give up your
+
+ align:start position:0%
+67 okay and uh you don't give up your
+ 
+
+ align:start position:0%
+67 okay and uh you don't give up your
+your uh your first player Advantage so
+
+ align:start position:0%
+your uh your first player Advantage so
+ 
+
+ align:start position:0%
+your uh your first player Advantage so
+you're going with the first player but
+
+ align:start position:0%
+you're going with the first player but
+ 
+
+ align:start position:0%
+you're going with the first player but
+now you say I know that I can set this
+
+ align:start position:0%
+now you say I know that I can set this
+ 
+
+ align:start position:0%
+now you say I know that I can set this
+up and that wasn't the order that he did
+
+ align:start position:0%
+up and that wasn't the order that he did
+ 
+
+ align:start position:0%
+up and that wasn't the order that he did
+this but I know I can set this up so I I
+
+ align:start position:0%
+this but I know I can set this up so I I
+ 
+
+ align:start position:0%
+this but I know I can set this up so I I
+always have a chance to get V1 V3 V5 Etc
+
+ align:start position:0%
+always have a chance to get V1 V3 V5 Etc
+ 
+
+ align:start position:0%
+always have a chance to get V1 V3 V5 Etc
+because let's just say that uh uh the
+
+ align:start position:0%
+because let's just say that uh uh the
+ 
+
+ align:start position:0%
+because let's just say that uh uh the
+first player Josiah started first and he
+
+ align:start position:0%
+first player Josiah started first and he
+ 
+
+ align:start position:0%
+first player Josiah started first and he
+decided in this case that the odd values
+
+ align:start position:0%
+decided in this case that the odd values
+ 
+
+ align:start position:0%
+decided in this case that the odd values
+are the ones that win right so you'll
+
+ align:start position:0%
+are the ones that win right so you'll
+ 
+
+ align:start position:0%
+are the ones that win right so you'll
+pick he he pick let's say he picks V1 uh
+
+ align:start position:0%
+pick he he pick let's say he picks V1 uh
+ 
+
+ align:start position:0%
+pick he he pick let's say he picks V1 uh
+at this point Tessa sees V2 through VN
+
+ align:start position:0%
+at this point Tessa sees V2 through VN
+ 
+
+ align:start position:0%
+at this point Tessa sees V2 through VN
+right so he's just looking at to that
+
+ align:start position:0%
+right so he's just looking at to that
+ 
+
+ align:start position:0%
+right so he's just looking at to that
+now Tessa could either pick V2 or she
+
+ align:start position:0%
+now Tessa could either pick V2 or she
+ 
+
+ align:start position:0%
+now Tessa could either pick V2 or she
+could pick VN in that case uh jiia who's
+
+ align:start position:0%
+could pick VN in that case uh jiia who's
+ 
+
+ align:start position:0%
+could pick VN in that case uh jiia who's
+the first player could pick V3 or VN
+
+ align:start position:0%
+the first player could pick V3 or VN
+ 
+
+ align:start position:0%
+the first player could pick V3 or VN
+minus one and stick with his rule of
+
+ align:start position:0%
+minus one and stick with his rule of
+ 
+
+ align:start position:0%
+minus one and stick with his rule of
+picking the odd coins all right so
+
+ align:start position:0%
+picking the odd coins all right so
+ 
+
+ align:start position:0%
+picking the odd coins all right so
+regardless of what Tessa does I the
+
+ align:start position:0%
+regardless of what Tessa does I the
+ 
+
+ align:start position:0%
+regardless of what Tessa does I the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+player jessiah could pick odd if odd was
+
+ align:start position:0%
+player jessiah could pick odd if odd was
+ 
+
+ align:start position:0%
+player jessiah could pick odd if odd was
+the way to go or if the values were such
+
+ align:start position:0%
+the way to go or if the values were such
+ 
+
+ align:start position:0%
+the way to go or if the values were such
+that even were were the way to go he
+
+ align:start position:0%
+that even were were the way to go he
+ 
+
+ align:start position:0%
+that even were were the way to go he
+could go even okay so no reason for the
+
+ align:start position:0%
+could go even okay so no reason for the
+ 
+
+ align:start position:0%
+could go even okay so no reason for the
+first player to lose uh but uh let's
+
+ align:start position:0%
+first player to lose uh but uh let's
+ 
+
+ align:start position:0%
+first player to lose uh but uh let's
+just say that um you're a nasty person
+
+ align:start position:0%
+just say that um you're a nasty person
+ 
+
+ align:start position:0%
+just say that um you're a nasty person
+right Michael Jordan
+
+ align:start position:0%
+right Michael Jordan
+ 
+
+ align:start position:0%
+right Michael Jordan
+nasty you want to just crush your
+
+ align:start position:0%
+nasty you want to just crush your
+ 
+
+ align:start position:0%
+nasty you want to just crush your
+opponent you you want to make sure they
+
+ align:start position:0%
+opponent you you want to make sure they
+ 
+
+ align:start position:0%
+opponent you you want to make sure they
+never want to play you again okay so now
+
+ align:start position:0%
+never want to play you again okay so now
+ 
+
+ align:start position:0%
+never want to play you again okay so now
+you have a a a a maximization problem
+
+ align:start position:0%
+you have a a a a maximization problem
+ 
+
+ align:start position:0%
+you have a a a a maximization problem
+right so this is clearly not DP you
+
+ align:start position:0%
+right so this is clearly not DP you
+ 
+
+ align:start position:0%
+right so this is clearly not DP you
+don't need DP to add up a bunch of
+
+ align:start position:0%
+don't need DP to add up a bunch of
+ 
+
+ align:start position:0%
+don't need DP to add up a bunch of
+numbers uh but let's say that you want
+
+ align:start position:0%
+numbers uh but let's say that you want
+ 
+
+ align:start position:0%
+numbers uh but let's say that you want
+to given a set of coins V1 through uh VN
+
+ align:start position:0%
+to given a set of coins V1 through uh VN
+ 
+
+ align:start position:0%
+to given a set of coins V1 through uh VN
+uh you want a strategy a dynamic
+
+ align:start position:0%
+uh you want a strategy a dynamic
+ 
+
+ align:start position:0%
+uh you want a strategy a dynamic
+strategy that U uh gives you the maximum
+
+ align:start position:0%
+strategy that U uh gives you the maximum
+ 
+
+ align:start position:0%
+strategy that U uh gives you the maximum
+value right um this odd versus even is a
+
+ align:start position:0%
+value right um this odd versus even is a
+ 
+
+ align:start position:0%
+value right um this odd versus even is a
+bit constraining because you're stuck to
+
+ align:start position:0%
+bit constraining because you're stuck to
+ 
+
+ align:start position:0%
+bit constraining because you're stuck to
+these positions and it's good to be uh
+
+ align:start position:0%
+these positions and it's good to be uh
+ 
+
+ align:start position:0%
+these positions and it's good to be uh
+in that situation if you just want to
+
+ align:start position:0%
+in that situation if you just want to
+ 
+
+ align:start position:0%
+in that situation if you just want to
+win and you don't care how you win right
+
+ align:start position:0%
+win and you don't care how you win right
+ 
+
+ align:start position:0%
+win and you don't care how you win right
+but if you want to maximize then it's a
+
+ align:start position:0%
+but if you want to maximize then it's a
+ 
+
+ align:start position:0%
+but if you want to maximize then it's a
+more complicated problem right and so we
+
+ align:start position:0%
+more complicated problem right and so we
+ 
+
+ align:start position:0%
+more complicated problem right and so we
+have to talk about how you would do uh
+
+ align:start position:0%
+have to talk about how you would do uh
+ 
+
+ align:start position:0%
+have to talk about how you would do uh
+something that would uh give maybe it
+
+ align:start position:0%
+something that would uh give maybe it
+ 
+
+ align:start position:0%
+something that would uh give maybe it
+would be V1 and V4 and something else
+
+ align:start position:0%
+would be V1 and V4 and something else
+ 
+
+ align:start position:0%
+would be V1 and V4 and something else
+depends on the values how would you get
+
+ align:start position:0%
+depends on the values how would you get
+ 
+
+ align:start position:0%
+depends on the values how would you get
+to a situation if you're the first
+
+ align:start position:0%
+to a situation if you're the first
+ 
+
+ align:start position:0%
+to a situation if you're the first
+player we just stick with you're the
+
+ align:start position:0%
+player we just stick with you're the
+ 
+
+ align:start position:0%
+player we just stick with you're the
+first player you know you can't lose
+
+ align:start position:0%
+first player you know you can't lose
+ 
+
+ align:start position:0%
+first player you know you can't lose
+using this strategy but not only do you
+
+ align:start position:0%
+using this strategy but not only do you
+ 
+
+ align:start position:0%
+using this strategy but not only do you
+want to not lose you want to get as many
+
+ align:start position:0%
+want to not lose you want to get as many
+ 
+
+ align:start position:0%
+want to not lose you want to get as many
+coins as possible let's say this is
+
+ align:start position:0%
+coins as possible let's say this is
+ 
+
+ align:start position:0%
+coins as possible let's say this is
+money you know more money is better uh
+
+ align:start position:0%
+money you know more money is better uh
+ 
+
+ align:start position:0%
+money you know more money is better uh
+and uh that's your goal okay so uh so
+
+ align:start position:0%
+and uh that's your goal okay so uh so
+ 
+
+ align:start position:0%
+and uh that's your goal okay so uh so
+people understand that a little
+
+ align:start position:0%
+people understand that a little
+ 
+
+ align:start position:0%
+people understand that a little
+U little trick there with a I guess a
+
+ align:start position:0%
+U little trick there with a I guess a
+ 
+
+ align:start position:0%
+U little trick there with a I guess a
+greedy algorithm you can you can think
+
+ align:start position:0%
+greedy algorithm you can you can think
+ 
+
+ align:start position:0%
+greedy algorithm you can you can think
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+or it's not really a even something that
+
+ align:start position:0%
+or it's not really a even something that
+ 
+
+ align:start position:0%
+or it's not really a even something that
+you might want to call an algorithm
+
+ align:start position:0%
+you might want to call an algorithm
+ 
+
+ align:start position:0%
+you might want to call an algorithm
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+computation and our goal now is to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximize the amount of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assuming you move
+
+ align:start position:0%
+assuming you move
+ 
+
+ align:start position:0%
+assuming you move
+first and so this is going to be a
+
+ align:start position:0%
+first and so this is going to be a
+ 
+
+ align:start position:0%
+first and so this is going to be a
+little bit different uh from all of the
+
+ align:start position:0%
+little bit different uh from all of the
+ 
+
+ align:start position:0%
+little bit different uh from all of the
+other problems we looked at because we
+
+ align:start position:0%
+other problems we looked at because we
+ 
+
+ align:start position:0%
+other problems we looked at because we
+have to now think about what the
+
+ align:start position:0%
+have to now think about what the
+ 
+
+ align:start position:0%
+have to now think about what the
+opponent would do right and there's
+
+ align:start position:0%
+opponent would do right and there's
+ 
+
+ align:start position:0%
+opponent would do right and there's
+going to be a sequence of moves here
+
+ align:start position:0%
+going to be a sequence of moves here
+ 
+
+ align:start position:0%
+going to be a sequence of moves here
+right you're going to move first so that
+
+ align:start position:0%
+right you're going to move first so that
+ 
+
+ align:start position:0%
+right you're going to move first so that
+one is easy you got the whole problem uh
+
+ align:start position:0%
+one is easy you got the whole problem uh
+ 
+
+ align:start position:0%
+one is easy you got the whole problem uh
+but now you have to say um the opponent
+
+ align:start position:0%
+but now you have to say um the opponent
+ 
+
+ align:start position:0%
+but now you have to say um the opponent
+is going to move uh and pick a coin and
+
+ align:start position:0%
+is going to move uh and pick a coin and
+ 
+
+ align:start position:0%
+is going to move uh and pick a coin and
+then you have to think of your sub
+
+ align:start position:0%
+then you have to think of your sub
+ 
+
+ align:start position:0%
+then you have to think of your sub
+problems as the potential uh rows of
+
+ align:start position:0%
+problems as the potential uh rows of
+ 
+
+ align:start position:0%
+problems as the potential uh rows of
+coins that are going to be different
+
+ align:start position:0%
+coins that are going to be different
+ 
+
+ align:start position:0%
+coins that are going to be different
+depending on what the opponent does
+
+ align:start position:0%
+depending on what the opponent does
+ 
+
+ align:start position:0%
+depending on what the opponent does
+right and through this process you have
+
+ align:start position:0%
+right and through this process you have
+ 
+
+ align:start position:0%
+right and through this process you have
+to maximize the value right so it's a
+
+ align:start position:0%
+to maximize the value right so it's a
+ 
+
+ align:start position:0%
+to maximize the value right so it's a
+it's really pretty different from the
+
+ align:start position:0%
+it's really pretty different from the
+ 
+
+ align:start position:0%
+it's really pretty different from the
+other couple of examples that uh that we
+
+ align:start position:0%
+other couple of examples that uh that we
+ 
+
+ align:start position:0%
+other couple of examples that uh that we
+looked
+
+ align:start position:0%
+looked
+ 
+
+ align:start position:0%
+looked
+at um so we're going to have to do a
+
+ align:start position:0%
+at um so we're going to have to do a
+ 
+
+ align:start position:0%
+at um so we're going to have to do a
+little bit of setup before we get to the
+
+ align:start position:0%
+little bit of setup before we get to the
+ 
+
+ align:start position:0%
+little bit of setup before we get to the
+point where we can write something like
+
+ align:start position:0%
+point where we can write something like
+ 
+
+ align:start position:0%
+point where we can write something like
+this which is uh the solution to our to
+
+ align:start position:0%
+this which is uh the solution to our to
+ 
+
+ align:start position:0%
+this which is uh the solution to our to
+our DP and so let me do that set up but
+
+ align:start position:0%
+our DP and so let me do that set up but
+ 
+
+ align:start position:0%
+our DP and so let me do that set up but
+it's not super complicated and part of
+
+ align:start position:0%
+it's not super complicated and part of
+ 
+
+ align:start position:0%
+it's not super complicated and part of
+this is going to look kind of the same
+
+ align:start position:0%
+this is going to look kind of the same
+ 
+
+ align:start position:0%
+this is going to look kind of the same
+as previous problems we've looked at um
+
+ align:start position:0%
+as previous problems we've looked at um
+ 
+
+ align:start position:0%
+as previous problems we've looked at um
+so VI J is the max value
+
+ align:start position:0%
+so VI J is the max value
+ 
+
+ align:start position:0%
+so VI J is the max value
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+can definitely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+win
+
+ align:start position:0%
+win
+ 
+
+ align:start position:0%
+win
+if it is our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turn and only
+
+ align:start position:0%
+turn and only
+ 
+
+ align:start position:0%
+turn and only
+coins VI through VJ I
+
+ align:start position:0%
+coins VI through VJ I
+ 
+
+ align:start position:0%
+coins VI through VJ I
+remain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so we have VI I
+
+ align:start position:0%
+okay and so we have VI I
+ 
+
+ align:start position:0%
+okay and so we have VI I
+then there's only one coin
+
+ align:start position:0%
+then there's only one coin
+ 
+
+ align:start position:0%
+then there's only one coin
+left and you just pick
+
+ align:start position:0%
+left and you just pick
+ 
+
+ align:start position:0%
+left and you just pick
+I right now uh you need this you might
+
+ align:start position:0%
+I right now uh you need this you might
+ 
+
+ align:start position:0%
+I right now uh you need this you might
+say well but that's never going to
+
+ align:start position:0%
+say well but that's never going to
+ 
+
+ align:start position:0%
+say well but that's never going to
+happen uh if there's an even number of
+
+ align:start position:0%
+happen uh if there's an even number of
+ 
+
+ align:start position:0%
+happen uh if there's an even number of
+coins and I'm playing first uh because
+
+ align:start position:0%
+coins and I'm playing first uh because
+ 
+
+ align:start position:0%
+coins and I'm playing first uh because
+the other uh player is going to be at
+
+ align:start position:0%
+the other uh player is going to be at
+ 
+
+ align:start position:0%
+the other uh player is going to be at
+the end of the the the the is going to
+
+ align:start position:0%
+the end of the the the the is going to
+ 
+
+ align:start position:0%
+the end of the the the the is going to
+be the person who picks the last coin
+
+ align:start position:0%
+be the person who picks the last coin
+ 
+
+ align:start position:0%
+be the person who picks the last coin
+but we need to characterize VII is
+
+ align:start position:0%
+but we need to characterize VII is
+ 
+
+ align:start position:0%
+but we need to characterize VII is
+because we need to model what the other
+
+ align:start position:0%
+because we need to model what the other
+ 
+
+ align:start position:0%
+because we need to model what the other
+players going to do right so we can't
+
+ align:start position:0%
+players going to do right so we can't
+ 
+
+ align:start position:0%
+players going to do right so we can't
+just say that we're going to be looking
+
+ align:start position:0%
+just say that we're going to be looking
+ 
+
+ align:start position:0%
+just say that we're going to be looking
+at even number of coins in terms of the
+
+ align:start position:0%
+at even number of coins in terms of the
+ 
+
+ align:start position:0%
+at even number of coins in terms of the
+row of coins that uh you you look at
+
+ align:start position:0%
+row of coins that uh you you look at
+ 
+
+ align:start position:0%
+row of coins that uh you you look at
+which is true that when you get to move
+
+ align:start position:0%
+which is true that when you get to move
+ 
+
+ align:start position:0%
+which is true that when you get to move
+you only see an even number of coins if
+
+ align:start position:0%
+you only see an even number of coins if
+ 
+
+ align:start position:0%
+you only see an even number of coins if
+you're the first player but you do have
+
+ align:start position:0%
+you're the first player but you do have
+ 
+
+ align:start position:0%
+you're the first player but you do have
+to model what the opponent does so we
+
+ align:start position:0%
+to model what the opponent does so we
+ 
+
+ align:start position:0%
+to model what the opponent does so we
+need the VII
+
+ align:start position:0%
+need the VII
+ 
+
+ align:start position:0%
+need the VII
+okay um and what you you might see of
+
+ align:start position:0%
+okay um and what you you might see of
+ 
+
+ align:start position:0%
+okay um and what you you might see of
+course uh is a board that looks like VI
+
+ align:start position:0%
+course uh is a board that looks like VI
+ 
+
+ align:start position:0%
+course uh is a board that looks like VI
+I +
+
+ align:start position:0%
+I +
+ 
+
+ align:start position:0%
+I +
+one uh and I mean it might um
+
+ align:start position:0%
+one uh and I mean it might um
+ 
+
+ align:start position:0%
+one uh and I mean it might um
+be for some arbitrary eye right so
+
+ align:start position:0%
+be for some arbitrary eye right so
+ 
+
+ align:start position:0%
+be for some arbitrary eye right so
+that's why I have it up there but
+
+ align:start position:0%
+that's why I have it up there but
+ 
+
+ align:start position:0%
+that's why I have it up there but
+remember that you're only picking coins
+
+ align:start position:0%
+remember that you're only picking coins
+ 
+
+ align:start position:0%
+remember that you're only picking coins
+on the outside so it's not like you're
+
+ align:start position:0%
+on the outside so it's not like you're
+ 
+
+ align:start position:0%
+on the outside so it's not like you're
+going to have a gap Ian you're not going
+
+ align:start position:0%
+going to have a gap Ian you're not going
+ 
+
+ align:start position:0%
+going to have a gap Ian you're not going
+to have V3 left and V7 left right
+
+ align:start position:0%
+to have V3 left and V7 left right
+ 
+
+ align:start position:0%
+to have V3 left and V7 left right
+there's no way that's going to happen
+
+ align:start position:0%
+there's no way that's going to happen
+ 
+
+ align:start position:0%
+there's no way that's going to happen
+you're just going to keep shrinking
+
+ align:start position:0%
+you're just going to keep shrinking
+ 
+
+ align:start position:0%
+you're just going to keep shrinking
+taking things from the left or the right
+
+ align:start position:0%
+taking things from the left or the right
+ 
+
+ align:start position:0%
+taking things from the left or the right
+right so it's going to be I and I + one
+
+ align:start position:0%
+right so it's going to be I and I + one
+ 
+
+ align:start position:0%
+right so it's going to be I and I + one
+right that Mak sense um and so in this
+
+ align:start position:0%
+right that Mak sense um and so in this
+ 
+
+ align:start position:0%
+right that Mak sense um and so in this
+case what would you pick VI and I +
+
+ align:start position:0%
+case what would you pick VI and I +
+ 
+
+ align:start position:0%
+case what would you pick VI and I +
+one you just pick the max right because
+
+ align:start position:0%
+one you just pick the max right because
+ 
+
+ align:start position:0%
+one you just pick the max right because
+that end of this either you did it right
+
+ align:start position:0%
+that end of this either you did it right
+ 
+
+ align:start position:0%
+that end of this either you did it right
+or you did it wrong either way you're
+
+ align:start position:0%
+or you did it wrong either way you're
+ 
+
+ align:start position:0%
+or you did it wrong either way you're
+going to improve your situation by
+
+ align:start position:0%
+going to improve your situation by
+ 
+
+ align:start position:0%
+going to improve your situation by
+picking the max of VI or VI + 1 right so
+
+ align:start position:0%
+picking the max of VI or VI + 1 right so
+ 
+
+ align:start position:0%
+picking the max of VI or VI + 1 right so
+there's no two things about it so here
+
+ align:start position:0%
+there's no two things about it so here
+ 
+
+ align:start position:0%
+there's no two things about it so here
+you're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pick the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two um and you might have U VI i+ plus
+
+ align:start position:0%
+two um and you might have U VI i+ plus
+ 
+
+ align:start position:0%
+two um and you might have U VI i+ plus
+two which is an an odd number of coins
+
+ align:start position:0%
+two which is an an odd number of coins
+ 
+
+ align:start position:0%
+two which is an an odd number of coins
+that um that your opponent might see uh
+
+ align:start position:0%
+that um that your opponent might see uh
+ 
+
+ align:start position:0%
+that um that your opponent might see uh
+it gets more complicated uh for Vi and
+
+ align:start position:0%
+it gets more complicated uh for Vi and
+ 
+
+ align:start position:0%
+it gets more complicated uh for Vi and
+i+ 2 we're going to have to uh now start
+
+ align:start position:0%
+i+ 2 we're going to have to uh now start
+ 
+
+ align:start position:0%
+i+ 2 we're going to have to uh now start
+thinking in more general terms as to
+
+ align:start position:0%
+thinking in more general terms as to
+ 
+
+ align:start position:0%
+thinking in more general terms as to
+what the different moves are right but
+
+ align:start position:0%
+what the different moves are right but
+ 
+
+ align:start position:0%
+what the different moves are right but
+we got the base cases here all I did
+
+ align:start position:0%
+we got the base cases here all I did
+ 
+
+ align:start position:0%
+we got the base cases here all I did
+here was take care of the base case or a
+
+ align:start position:0%
+here was take care of the base case or a
+ 
+
+ align:start position:0%
+here was take care of the base case or a
+couple of Base cases associated with um
+
+ align:start position:0%
+couple of Base cases associated with um
+ 
+
+ align:start position:0%
+couple of Base cases associated with um
+a single coin which is what your
+
+ align:start position:0%
+a single coin which is what your
+ 
+
+ align:start position:0%
+a single coin which is what your
+opponent will see and pick or two coins
+
+ align:start position:0%
+opponent will see and pick or two coins
+ 
+
+ align:start position:0%
+opponent will see and pick or two coins
+which is your last move
+
+ align:start position:0%
+which is your last move
+ 
+
+ align:start position:0%
+which is your last move
+okay so with all with DP of course you
+
+ align:start position:0%
+okay so with all with DP of course you
+ 
+
+ align:start position:0%
+okay so with all with DP of course you
+always have to go down to your base case
+
+ align:start position:0%
+always have to go down to your base case
+ 
+
+ align:start position:0%
+always have to go down to your base case
+right and that's when things become
+
+ align:start position:0%
+right and that's when things become
+ 
+
+ align:start position:0%
+right and that's when things become
+easy um so let's talk about we have to
+
+ align:start position:0%
+easy um so let's talk about we have to
+ 
+
+ align:start position:0%
+easy um so let's talk about we have to
+talk about two things and put U our
+
+ align:start position:0%
+talk about two things and put U our
+ 
+
+ align:start position:0%
+talk about two things and put U our
+recurrence
+
+ align:start position:0%
+recurrence
+ 
+
+ align:start position:0%
+recurrence
+together the two things we have to talk
+
+ align:start position:0%
+together the two things we have to talk
+ 
+
+ align:start position:0%
+together the two things we have to talk
+about are what you do when you
+
+ align:start position:0%
+about are what you do when you
+ 
+
+ align:start position:0%
+about are what you do when you
+move um and that's actually fairly easy
+
+ align:start position:0%
+move um and that's actually fairly easy
+ 
+
+ align:start position:0%
+move um and that's actually fairly easy
+and the second thing is what uh the
+
+ align:start position:0%
+and the second thing is what uh the
+ 
+
+ align:start position:0%
+and the second thing is what uh the
+model of the opponent looks like uh when
+
+ align:start position:0%
+model of the opponent looks like uh when
+ 
+
+ align:start position:0%
+model of the opponent looks like uh when
+uh you're waiting for um uh him or her
+
+ align:start position:0%
+uh you're waiting for um uh him or her
+ 
+
+ align:start position:0%
+uh you're waiting for um uh him or her
+to move so let's take a look at your
+
+ align:start position:0%
+to move so let's take a look at your
+ 
+
+ align:start position:0%
+to move so let's take a look at your
+move and I got
+
+ align:start position:0%
+move and I got
+ 
+
+ align:start position:0%
+move and I got
+V1 let's look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VI let say VJ here dot do dot VN right
+
+ align:start position:0%
+VI let say VJ here dot do dot VN right
+ 
+
+ align:start position:0%
+VI let say VJ here dot do dot VN right
+so that's the the what you see uh and
+
+ align:start position:0%
+so that's the the what you see uh and
+ 
+
+ align:start position:0%
+so that's the the what you see uh and
+you're looking at I and
+
+ align:start position:0%
+you're looking at I and
+ 
+
+ align:start position:0%
+you're looking at I and
+J and at this point you're you're seeing
+
+ align:start position:0%
+J and at this point you're you're seeing
+ 
+
+ align:start position:0%
+J and at this point you're you're seeing
+all those other coins the outer coins
+
+ align:start position:0%
+all those other coins the outer coins
+ 
+
+ align:start position:0%
+all those other coins the outer coins
+have disappeared
+
+ align:start position:0%
+have disappeared
+ 
+
+ align:start position:0%
+have disappeared
+uh into people's pockets uh and you're
+
+ align:start position:0%
+uh into people's pockets uh and you're
+ 
+
+ align:start position:0%
+uh into people's pockets uh and you're
+looking at this uh
+
+ align:start position:0%
+looking at this uh
+ 
+
+ align:start position:0%
+looking at this uh
+interval so I'm going to write out what
+
+ align:start position:0%
+interval so I'm going to write out what
+ 
+
+ align:start position:0%
+interval so I'm going to write out what
+VI should be and keep in mind that we
+
+ align:start position:0%
+VI should be and keep in mind that we
+ 
+
+ align:start position:0%
+VI should be and keep in mind that we
+want to um uh maximize the amount of
+
+ align:start position:0%
+want to um uh maximize the amount of
+ 
+
+ align:start position:0%
+want to um uh maximize the amount of
+money and we want to say that we should
+
+ align:start position:0%
+money and we want to say that we should
+ 
+
+ align:start position:0%
+money and we want to say that we should
+be able to definitely win this amount of
+
+ align:start position:0%
+be able to definitely win this amount of
+ 
+
+ align:start position:0%
+be able to definitely win this amount of
+money right regardless of what the
+
+ align:start position:0%
+money right regardless of what the
+ 
+
+ align:start position:0%
+money right regardless of what the
+opponent
+
+ align:start position:0%
+opponent
+ 
+
+ align:start position:0%
+opponent
+does so um I want to do a a Max
+
+ align:start position:0%
+does so um I want to do a a Max
+ 
+
+ align:start position:0%
+does so um I want to do a a Max
+obviously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um I have two choices here I can
+
+ align:start position:0%
+and um I have two choices here I can
+ 
+
+ align:start position:0%
+and um I have two choices here I can
+pick VI or I can pick VJ right so it's
+
+ align:start position:0%
+pick VI or I can pick VJ right so it's
+ 
+
+ align:start position:0%
+pick VI or I can pick VJ right so it's
+not like there's a lot of choices here
+
+ align:start position:0%
+not like there's a lot of choices here
+ 
+
+ align:start position:0%
+not like there's a lot of choices here
+right so if I pick VI uh then let me go
+
+ align:start position:0%
+right so if I pick VI uh then let me go
+ 
+
+ align:start position:0%
+right so if I pick VI uh then let me go
+ahead and say I pick VI
+
+ align:start position:0%
+ahead and say I pick VI
+ 
+
+ align:start position:0%
+ahead and say I pick VI
+here and here I'd pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VJ and uh whoops let me draw this a
+
+ align:start position:0%
+VJ and uh whoops let me draw this a
+ 
+
+ align:start position:0%
+VJ and uh whoops let me draw this a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+better so I got to fill in uh these two
+
+ align:start position:0%
+better so I got to fill in uh these two
+ 
+
+ align:start position:0%
+better so I got to fill in uh these two
+uh uh arguments
+
+ align:start position:0%
+uh uh arguments
+ 
+
+ align:start position:0%
+uh uh arguments
+to to my
+
+ align:start position:0%
+to to my
+ 
+
+ align:start position:0%
+to to my
+Max right so um this is
+
+ align:start position:0%
+Max right so um this is
+ 
+
+ align:start position:0%
+Max right so um this is
+easy I'm going to have a plus VI here
+
+ align:start position:0%
+easy I'm going to have a plus VI here
+ 
+
+ align:start position:0%
+easy I'm going to have a plus VI here
+going to have a plus VJ
+
+ align:start position:0%
+going to have a plus VJ
+ 
+
+ align:start position:0%
+going to have a plus VJ
+here right so because I picked the
+
+ align:start position:0%
+here right so because I picked the
+ 
+
+ align:start position:0%
+here right so because I picked the
+appropriate value um and um now this is
+
+ align:start position:0%
+appropriate value um and um now this is
+ 
+
+ align:start position:0%
+appropriate value um and um now this is
+also not that uh difficult uh what
+
+ align:start position:0%
+also not that uh difficult uh what
+ 
+
+ align:start position:0%
+also not that uh difficult uh what
+exactly happens what can I put in
+
+ align:start position:0%
+exactly happens what can I put in
+ 
+
+ align:start position:0%
+exactly happens what can I put in
+here if I pick
+
+ align:start position:0%
+here if I pick
+ 
+
+ align:start position:0%
+here if I pick
+VI yeah VI + one to J so the range
+
+ align:start position:0%
+VI yeah VI + one to J so the range
+ 
+
+ align:start position:0%
+VI yeah VI + one to J so the range
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+uh I + 1 J so I got uh uh I I have to be
+
+ align:start position:0%
+uh I + 1 J so I got uh uh I I have to be
+ 
+
+ align:start position:0%
+uh I + 1 J so I got uh uh I I have to be
+a little careful here in terms of uh uh
+
+ align:start position:0%
+a little careful here in terms of uh uh
+ 
+
+ align:start position:0%
+a little careful here in terms of uh uh
+whether um I can argue that it's
+
+ align:start position:0%
+whether um I can argue that it's
+ 
+
+ align:start position:0%
+whether um I can argue that it's
+actually the V that I put in here so the
+
+ align:start position:0%
+actually the V that I put in here so the
+ 
+
+ align:start position:0%
+actually the V that I put in here so the
+subtlety here is simply that uh uh that
+
+ align:start position:0%
+subtlety here is simply that uh uh that
+ 
+
+ align:start position:0%
+subtlety here is simply that uh uh that
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+vi + one J is not something that I see
+
+ align:start position:0%
+vi + one J is not something that I see
+ 
+
+ align:start position:0%
+vi + one J is not something that I see
+in front of me
+
+ align:start position:0%
+in front of me
+ 
+
+ align:start position:0%
+in front of me
+okay this is the complication VI + 1j is
+
+ align:start position:0%
+okay this is the complication VI + 1j is
+ 
+
+ align:start position:0%
+okay this is the complication VI + 1j is
+never a board that I see in front of me
+
+ align:start position:0%
+never a board that I see in front of me
+ 
+
+ align:start position:0%
+never a board that I see in front of me
+whereas VI was a board that I saw in
+
+ align:start position:0%
+whereas VI was a board that I saw in
+ 
+
+ align:start position:0%
+whereas VI was a board that I saw in
+front of me right so I have to model uh
+
+ align:start position:0%
+front of me right so I have to model uh
+ 
+
+ align:start position:0%
+front of me right so I have to model uh
+the the boards that I see in front of me
+
+ align:start position:0%
+the the boards that I see in front of me
+ 
+
+ align:start position:0%
+the the boards that I see in front of me
+because those are the boards that I have
+
+ align:start position:0%
+because those are the boards that I have
+ 
+
+ align:start position:0%
+because those are the boards that I have
+control over that I can maximize right I
+
+ align:start position:0%
+control over that I can maximize right I
+ 
+
+ align:start position:0%
+control over that I can maximize right I
+the the I need I cannot put vij vi+ 1j
+
+ align:start position:0%
+the the I need I cannot put vij vi+ 1j
+ 
+
+ align:start position:0%
+the the I need I cannot put vij vi+ 1j
+in there simply because I I don't quite
+
+ align:start position:0%
+in there simply because I I don't quite
+ 
+
+ align:start position:0%
+in there simply because I I don't quite
+know what that is because I what I get
+
+ align:start position:0%
+know what that is because I what I get
+ 
+
+ align:start position:0%
+know what that is because I what I get
+eventually is not something I control
+
+ align:start position:0%
+eventually is not something I control
+ 
+
+ align:start position:0%
+eventually is not something I control
+right it's going to be the the the board
+
+ align:start position:0%
+right it's going to be the the the board
+ 
+
+ align:start position:0%
+right it's going to be the the the board
+after my opponent has moved all right so
+
+ align:start position:0%
+after my opponent has moved all right so
+ 
+
+ align:start position:0%
+after my opponent has moved all right so
+all I'm going to do is I'm going to say
+
+ align:start position:0%
+all I'm going to do is I'm going to say
+ 
+
+ align:start position:0%
+all I'm going to do is I'm going to say
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+range um
+
+ align:start position:0%
+range um
+ 
+
+ align:start position:0%
+range um
+becomes range
+
+ align:start position:0%
+becomes range
+ 
+
+ align:start position:0%
+becomes range
+is um I + 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J um and I'm going to say something else
+
+ align:start position:0%
+J um and I'm going to say something else
+ 
+
+ align:start position:0%
+J um and I'm going to say something else
+in a second here the range is uh
+
+ align:start position:0%
+in a second here the range is uh
+ 
+
+ align:start position:0%
+in a second here the range is uh
+i j minus
+
+ align:start position:0%
+i j minus
+ 
+
+ align:start position:0%
+i j minus
+one okay and in both of these
+
+ align:start position:0%
+one okay and in both of these
+ 
+
+ align:start position:0%
+one okay and in both of these
+cases the opponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves so in order to actually write out
+
+ align:start position:0%
+moves so in order to actually write out
+ 
+
+ align:start position:0%
+moves so in order to actually write out
+my DP I'm going to have to now U look at
+
+ align:start position:0%
+my DP I'm going to have to now U look at
+ 
+
+ align:start position:0%
+my DP I'm going to have to now U look at
+the worst case
+
+ align:start position:0%
+the worst case
+ 
+
+ align:start position:0%
+the worst case
+situation in terms of the board I get
+
+ align:start position:0%
+situation in terms of the board I get
+ 
+
+ align:start position:0%
+situation in terms of the board I get
+back because the only times I'm adding
+
+ align:start position:0%
+back because the only times I'm adding
+ 
+
+ align:start position:0%
+back because the only times I'm adding
+values is when I see a board in front of
+
+ align:start position:0%
+values is when I see a board in front of
+ 
+
+ align:start position:0%
+values is when I see a board in front of
+me and pick a coin and I'm going to have
+
+ align:start position:0%
+me and pick a coin and I'm going to have
+ 
+
+ align:start position:0%
+me and pick a coin and I'm going to have
+to say now the opponent is going to see
+
+ align:start position:0%
+to say now the opponent is going to see
+ 
+
+ align:start position:0%
+to say now the opponent is going to see
+an i + 1
+
+ align:start position:0%
+an i + 1
+ 
+
+ align:start position:0%
+an i + 1
+J and or or an i minus one i j minus one
+
+ align:start position:0%
+J and or or an i minus one i j minus one
+ 
+
+ align:start position:0%
+J and or or an i minus one i j minus one
+excuse me and might do something and I'm
+
+ align:start position:0%
+excuse me and might do something and I'm
+ 
+
+ align:start position:0%
+excuse me and might do something and I'm
+going to get something back let's assume
+
+ align:start position:0%
+going to get something back let's assume
+ 
+
+ align:start position:0%
+going to get something back let's assume
+that I I'm going to assume that the
+
+ align:start position:0%
+that I I'm going to assume that the
+ 
+
+ align:start position:0%
+that I I'm going to assume that the
+opponent is just as smart as I am knows
+
+ align:start position:0%
+opponent is just as smart as I am knows
+ 
+
+ align:start position:0%
+opponent is just as smart as I am knows
+DP taking 6046 etc etc and uh I still
+
+ align:start position:0%
+DP taking 6046 etc etc and uh I still
+ 
+
+ align:start position:0%
+DP taking 6046 etc etc and uh I still
+want to get the maximum value that I can
+
+ align:start position:0%
+want to get the maximum value that I can
+ 
+
+ align:start position:0%
+want to get the maximum value that I can
+definitely win okay um and so uh we need
+
+ align:start position:0%
+definitely win okay um and so uh we need
+ 
+
+ align:start position:0%
+definitely win okay um and so uh we need
+to look inside of that a little bit and
+
+ align:start position:0%
+to look inside of that a little bit and
+ 
+
+ align:start position:0%
+to look inside of that a little bit and
+it's not that hard if you just make the
+
+ align:start position:0%
+it's not that hard if you just make the
+ 
+
+ align:start position:0%
+it's not that hard if you just make the
+assumption that I just did which is uh
+
+ align:start position:0%
+assumption that I just did which is uh
+ 
+
+ align:start position:0%
+assumption that I just did which is uh
+the opponent um is going
+
+ align:start position:0%
+the opponent um is going
+ 
+
+ align:start position:0%
+the opponent um is going
+to uh I mean might not necessarily do
+
+ align:start position:0%
+to uh I mean might not necessarily do
+ 
+
+ align:start position:0%
+to uh I mean might not necessarily do
+the right thing but you have to assume
+
+ align:start position:0%
+the right thing but you have to assume
+ 
+
+ align:start position:0%
+the right thing but you have to assume
+that uh the opponent knows it just as
+
+ align:start position:0%
+that uh the opponent knows it just as
+ 
+
+ align:start position:0%
+that uh the opponent knows it just as
+much as you do and is going to try and
+
+ align:start position:0%
+much as you do and is going to try and
+ 
+
+ align:start position:0%
+much as you do and is going to try and
+um uh uh do as well as possible okay so
+
+ align:start position:0%
+um uh uh do as well as possible okay so
+ 
+
+ align:start position:0%
+um uh uh do as well as possible okay so
+uh let's do that that's the last thing
+
+ align:start position:0%
+uh let's do that that's the last thing
+ 
+
+ align:start position:0%
+uh let's do that that's the last thing
+that we have to do here and uh it's just
+
+ align:start position:0%
+that we have to do here and uh it's just
+ 
+
+ align:start position:0%
+that we have to do here and uh it's just
+one uh more equation so so here's the
+
+ align:start position:0%
+one uh more equation so so here's the
+ 
+
+ align:start position:0%
+one uh more equation so so here's the
+solution we now have a v i + 1 J sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem with the opponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picking
+
+ align:start position:0%
+picking
+ 
+
+ align:start position:0%
+picking
+and um the simple observation is that we
+
+ align:start position:0%
+and um the simple observation is that we
+ 
+
+ align:start position:0%
+and um the simple observation is that we
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guaranteed the
+
+ align:start position:0%
+guaranteed the
+ 
+
+ align:start position:0%
+guaranteed the
+men of v i + 1 Jus
+
+ align:start position:0%
+men of v i + 1 Jus
+ 
+
+ align:start position:0%
+men of v i + 1 Jus
+1 or v i + 2
+
+ align:start position:0%
+1 or v i + 2
+ 
+
+ align:start position:0%
+1 or v i + 2
+J in this
+
+ align:start position:0%
+J in this
+ 
+
+ align:start position:0%
+J in this
+case um the opponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picks VJ and in this case the opponent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picks VI +
+
+ align:start position:0%
+picks VI +
+ 
+
+ align:start position:0%
+picks VI +
+1 right and you're you're guaranteed the
+
+ align:start position:0%
+1 right and you're you're guaranteed the
+ 
+
+ align:start position:0%
+1 right and you're you're guaranteed the
+minimum of these two because the
+
+ align:start position:0%
+minimum of these two because the
+ 
+
+ align:start position:0%
+minimum of these two because the
+opponent can only pick one coin right so
+
+ align:start position:0%
+opponent can only pick one coin right so
+ 
+
+ align:start position:0%
+opponent can only pick one coin right so
+that's the the simple observation that
+
+ align:start position:0%
+that's the the simple observation that
+ 
+
+ align:start position:0%
+that's the the simple observation that
+lets you jump
+
+ align:start position:0%
+lets you jump
+ 
+
+ align:start position:0%
+lets you jump
+ahead uh to your next move which is
+
+ align:start position:0%
+ahead uh to your next move which is
+ 
+
+ align:start position:0%
+ahead uh to your next move which is
+really what uh the DP is interested in
+
+ align:start position:0%
+really what uh the DP is interested in
+ 
+
+ align:start position:0%
+really what uh the DP is interested in
+uh because uh that's the only time that
+
+ align:start position:0%
+uh because uh that's the only time that
+ 
+
+ align:start position:0%
+uh because uh that's the only time that
+you're actually executing something in
+
+ align:start position:0%
+you're actually executing something in
+ 
+
+ align:start position:0%
+you're actually executing something in
+terms of picking coins from the board
+
+ align:start position:0%
+terms of picking coins from the board
+ 
+
+ align:start position:0%
+terms of picking coins from the board
+and adding to your value right but we
+
+ align:start position:0%
+and adding to your value right but we
+ 
+
+ align:start position:0%
+and adding to your value right but we
+did did have to model that as to what uh
+
+ align:start position:0%
+did did have to model that as to what uh
+ 
+
+ align:start position:0%
+did did have to model that as to what uh
+the maximum value was that you could win
+
+ align:start position:0%
+the maximum value was that you could win
+ 
+
+ align:start position:0%
+the maximum value was that you could win
+uh jumping ahead of this move and you
+
+ align:start position:0%
+uh jumping ahead of this move and you
+ 
+
+ align:start position:0%
+uh jumping ahead of this move and you
+have have the the Min here because
+
+ align:start position:0%
+have have the the Min here because
+ 
+
+ align:start position:0%
+have have the the Min here because
+you're assuming that uh this is a
+
+ align:start position:0%
+you're assuming that uh this is a
+ 
+
+ align:start position:0%
+you're assuming that uh this is a
+definite guarantee right that's what we
+
+ align:start position:0%
+definite guarantee right that's what we
+ 
+
+ align:start position:0%
+definite guarantee right that's what we
+want uh it's possible that uh the
+
+ align:start position:0%
+want uh it's possible that uh the
+ 
+
+ align:start position:0%
+want uh it's possible that uh the
+opponent plays uh um a different game
+
+ align:start position:0%
+opponent plays uh um a different game
+ 
+
+ align:start position:0%
+opponent plays uh um a different game
+from uh the one that um we think he or
+
+ align:start position:0%
+from uh the one that um we think he or
+ 
+
+ align:start position:0%
+from uh the one that um we think he or
+she is going to play which maximizes his
+
+ align:start position:0%
+she is going to play which maximizes his
+ 
+
+ align:start position:0%
+she is going to play which maximizes his
+or her value but the men is a guarantee
+
+ align:start position:0%
+or her value but the men is a guarantee
+ 
+
+ align:start position:0%
+or her value but the men is a guarantee
+okay so now that you've made this
+
+ align:start position:0%
+okay so now that you've made this
+ 
+
+ align:start position:0%
+okay so now that you've made this
+observation uh it turns out we just have
+
+ align:start position:0%
+observation uh it turns out we just have
+ 
+
+ align:start position:0%
+observation uh it turns out we just have
+to take that and uh uh we we we'll we'll
+
+ align:start position:0%
+to take that and uh uh we we we'll we'll
+ 
+
+ align:start position:0%
+to take that and uh uh we we we'll we'll
+be done right so let's see uh let me
+
+ align:start position:0%
+be done right so let's see uh let me
+ 
+
+ align:start position:0%
+be done right so let's see uh let me
+erase this so
+
+ align:start position:0%
+erase this so
+ 
+
+ align:start position:0%
+erase this so
+last set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations and it's just plugging in that
+
+ align:start position:0%
+equations and it's just plugging in that
+ 
+
+ align:start position:0%
+equations and it's just plugging in that
+observation into what I wrote
+
+ align:start position:0%
+observation into what I wrote
+ 
+
+ align:start position:0%
+observation into what I wrote
+before so we have V
+
+ align:start position:0%
+before so we have V
+ 
+
+ align:start position:0%
+before so we have V
+J equals Max this is the outer Max that
+
+ align:start position:0%
+J equals Max this is the outer Max that
+ 
+
+ align:start position:0%
+J equals Max this is the outer Max that
+I had up there already so that's the
+
+ align:start position:0%
+I had up there already so that's the
+ 
+
+ align:start position:0%
+I had up there already so that's the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+Max um and put this giant brackets here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and inside I I'm going to plug in this
+
+ align:start position:0%
+and inside I I'm going to plug in this
+ 
+
+ align:start position:0%
+and inside I I'm going to plug in this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+minim uh which is something that
+
+ align:start position:0%
+minim uh which is something that
+ 
+
+ align:start position:0%
+minim uh which is something that
+corresponds to the the the value that I
+
+ align:start position:0%
+corresponds to the the the value that I
+ 
+
+ align:start position:0%
+corresponds to the the the value that I
+would win in the worst case after the
+
+ align:start position:0%
+would win in the worst case after the
+ 
+
+ align:start position:0%
+would win in the worst case after the
+opponent plays the best possible move
+
+ align:start position:0%
+opponent plays the best possible move
+ 
+
+ align:start position:0%
+opponent plays the best possible move
+and that would be VI I +
+
+ align:start position:0%
+and that would be VI I +
+ 
+
+ align:start position:0%
+and that would be VI I +
+1 Jus
+
+ align:start position:0%
+1 Jus
+ 
+
+ align:start position:0%
+1 Jus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+comma we I + 2 J plus VI this VI is the
+
+ align:start position:0%
+comma we I + 2 J plus VI this VI is the
+ 
+
+ align:start position:0%
+comma we I + 2 J plus VI this VI is the
+same as this one up
+
+ align:start position:0%
+same as this one up
+ 
+
+ align:start position:0%
+same as this one up
+here um and you got a plus VJ here and I
+
+ align:start position:0%
+here um and you got a plus VJ here and I
+ 
+
+ align:start position:0%
+here um and you got a plus VJ here and I
+didn't actually do this but in terms of
+
+ align:start position:0%
+didn't actually do this but in terms of
+ 
+
+ align:start position:0%
+didn't actually do this but in terms of
+writing out what the opponent would do
+
+ align:start position:0%
+writing out what the opponent would do
+ 
+
+ align:start position:0%
+writing out what the opponent would do
+in the other sub problem case but it's
+
+ align:start position:0%
+in the other sub problem case but it's
+ 
+
+ align:start position:0%
+in the other sub problem case but it's
+really pretty straightforward uh you um
+
+ align:start position:0%
+really pretty straightforward uh you um
+ 
+
+ align:start position:0%
+really pretty straightforward uh you um
+have a problem that corresponds to uh
+
+ align:start position:0%
+have a problem that corresponds to uh
+ 
+
+ align:start position:0%
+have a problem that corresponds to uh
+the i j minus one problem and the
+
+ align:start position:0%
+the i j minus one problem and the
+ 
+
+ align:start position:0%
+the i j minus one problem and the
+opponent could pick the I or could pick
+
+ align:start position:0%
+opponent could pick the I or could pick
+ 
+
+ align:start position:0%
+opponent could pick the I or could pick
+the J minus one if the opponent picks
+
+ align:start position:0%
+the J minus one if the opponent picks
+ 
+
+ align:start position:0%
+the J minus one if the opponent picks
+the J minus one you get um v i j minus 2
+
+ align:start position:0%
+the J minus one you get um v i j minus 2
+ 
+
+ align:start position:0%
+the J minus one you get um v i j minus 2
+and you need to take the Min of that and
+
+ align:start position:0%
+and you need to take the Min of that and
+ 
+
+ align:start position:0%
+and you need to take the Min of that and
+the other case where the opponent picks
+
+ align:start position:0%
+the other case where the opponent picks
+ 
+
+ align:start position:0%
+the other case where the opponent picks
+I in which case you get I + 1 J minus
+
+ align:start position:0%
+I in which case you get I + 1 J minus
+ 
+
+ align:start position:0%
+I in which case you get I + 1 J minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay and that's our DP that's that's R
+
+ align:start position:0%
+okay and that's our DP that's that's R
+ 
+
+ align:start position:0%
+okay and that's our DP that's that's R
+DP okay so the big difference here was
+
+ align:start position:0%
+DP okay so the big difference here was
+ 
+
+ align:start position:0%
+DP okay so the big difference here was
+the modeling that you had to do in the
+
+ align:start position:0%
+the modeling that you had to do in the
+ 
+
+ align:start position:0%
+the modeling that you had to do in the
+middle we didn't actually have to do
+
+ align:start position:0%
+middle we didn't actually have to do
+ 
+
+ align:start position:0%
+middle we didn't actually have to do
+that in any of the DPS we've
+
+ align:start position:0%
+that in any of the DPS we've
+ 
+
+ align:start position:0%
+that in any of the DPS we've
+covered uh in 046 at least uh up until
+
+ align:start position:0%
+covered uh in 046 at least uh up until
+ 
+
+ align:start position:0%
+covered uh in 046 at least uh up until
+this point um before we talk about
+
+ align:start position:0%
+this point um before we talk about
+ 
+
+ align:start position:0%
+this point um before we talk about
+complexity I that should just take a
+
+ align:start position:0%
+complexity I that should just take a
+ 
+
+ align:start position:0%
+complexity I that should just take a
+minute people buy that see that good so
+
+ align:start position:0%
+minute people buy that see that good so
+ 
+
+ align:start position:0%
+minute people buy that see that good so
+uh with all of these problems the
+
+ align:start position:0%
+uh with all of these problems the
+ 
+
+ align:start position:0%
+uh with all of these problems the
+complexities are fairly straightforward
+
+ align:start position:0%
+complexities are fairly straightforward
+ 
+
+ align:start position:0%
+complexities are fairly straightforward
+to compute I the complexity here is
+
+ align:start position:0%
+to compute I the complexity here is
+ 
+
+ align:start position:0%
+to compute I the complexity here is
+simply again as before the number of sub
+
+ align:start position:0%
+simply again as before the number of sub
+ 
+
+ align:start position:0%
+simply again as before the number of sub
+problems times the time it it it takes
+
+ align:start position:0%
+problems times the time it it it takes
+ 
+
+ align:start position:0%
+problems times the time it it it takes
+to solve a sub problem uh you can see
+
+ align:start position:0%
+to solve a sub problem uh you can see
+ 
+
+ align:start position:0%
+to solve a sub problem uh you can see
+here that these are all constant time
+
+ align:start position:0%
+here that these are all constant time
+ 
+
+ align:start position:0%
+here that these are all constant time
+operations so assuming that the the the
+
+ align:start position:0%
+operations so assuming that the the the
+ 
+
+ align:start position:0%
+operations so assuming that the the the
+the vs have been computed it's Theta one
+
+ align:start position:0%
+the vs have been computed it's Theta one
+ 
+
+ align:start position:0%
+the vs have been computed it's Theta one
+time to compute a sub problem so that's
+
+ align:start position:0%
+time to compute a sub problem so that's
+ 
+
+ align:start position:0%
+time to compute a sub problem so that's
+your Theta 1 and U as before there
+
+ align:start position:0%
+your Theta 1 and U as before there
+ 
+
+ align:start position:0%
+your Theta 1 and U as before there
+are N squ Sub problems uh sorry let's
+
+ align:start position:0%
+are N squ Sub problems uh sorry let's
+ 
+
+ align:start position:0%
+are N squ Sub problems uh sorry let's
+just do number of sub
+
+ align:start position:0%
+just do number of sub
+ 
+
+ align:start position:0%
+just do number of sub
+problems times Theta 1 which is Theta n
+
+ align:start position:0%
+problems times Theta 1 which is Theta n
+ 
+
+ align:start position:0%
+problems times Theta 1 which is Theta n
+squ
+
+ align:start position:0%
+squ
+ 
+
+ align:start position:0%
+squ
+all right so that was good all right so
+
+ align:start position:0%
+all right so that was good all right so
+ 
+
+ align:start position:0%
+all right so that was good all right so
+uh good luck for the quiz uh and um
+
+ align:start position:0%
+uh good luck for the quiz uh and um
+ 
+
+ align:start position:0%
+uh good luck for the quiz uh and um
+don't worry too much about it uh see you
+
+ align:start position:0%
+don't worry too much about it uh see you
+ 
+
+ align:start position:0%
+don't worry too much about it uh see you
+guys next week
\ No newline at end of file
diff --git a/U1JYwHcFfso.txt b/U1JYwHcFfso.txt
new file mode 100644
index 0000000000000000000000000000000000000000..225b2e023affb464157790f848f0e625cca541c5
--- /dev/null
+++ b/U1JYwHcFfso.txt
@@ -0,0 +1,9323 @@
+align:start position:0%
+ 
+all right welcome back to data
+
+ align:start position:0%
+all right welcome back to data
+ 
+
+ align:start position:0%
+all right welcome back to data
+structures land today we continue and
+
+ align:start position:0%
+structures land today we continue and
+ 
+
+ align:start position:0%
+structures land today we continue and
+complete our segment on binary trees so
+
+ align:start position:0%
+complete our segment on binary trees so
+ 
+
+ align:start position:0%
+complete our segment on binary trees so
+this is part two if you missed part one
+
+ align:start position:0%
+this is part two if you missed part one
+ 
+
+ align:start position:0%
+this is part two if you missed part one
+go back and watch part one um last time
+
+ align:start position:0%
+go back and watch part one um last time
+ 
+
+ align:start position:0%
+go back and watch part one um last time
+we talked about binary trees in general
+
+ align:start position:0%
+we talked about binary trees in general
+ 
+
+ align:start position:0%
+we talked about binary trees in general
+uh we had uh each node stored an item uh
+
+ align:start position:0%
+uh we had uh each node stored an item uh
+ 
+
+ align:start position:0%
+uh we had uh each node stored an item uh
+which and also a left pointer and a
+
+ align:start position:0%
+which and also a left pointer and a
+ 
+
+ align:start position:0%
+which and also a left pointer and a
+right pointer to other nodes and a
+
+ align:start position:0%
+right pointer to other nodes and a
+ 
+
+ align:start position:0%
+right pointer to other nodes and a
+parent pointer to another node uh this
+
+ align:start position:0%
+parent pointer to another node uh this
+ 
+
+ align:start position:0%
+parent pointer to another node uh this
+was an example of a tree B and C or A's
+
+ align:start position:0%
+was an example of a tree B and C or A's
+ 
+
+ align:start position:0%
+was an example of a tree B and C or A's
+children a is the parent of B and C and
+
+ align:start position:0%
+children a is the parent of B and C and
+ 
+
+ align:start position:0%
+children a is the parent of B and C and
+also the root of the entire tree we
+
+ align:start position:0%
+also the root of the entire tree we
+ 
+
+ align:start position:0%
+also the root of the entire tree we
+defined the height of a node we didn't
+
+ align:start position:0%
+defined the height of a node we didn't
+ 
+
+ align:start position:0%
+defined the height of a node we didn't
+use this too much yet but we're going to
+
+ align:start position:0%
+use this too much yet but we're going to
+ 
+
+ align:start position:0%
+use this too much yet but we're going to
+use it a lot today so remember the
+
+ align:start position:0%
+use it a lot today so remember the
+ 
+
+ align:start position:0%
+use it a lot today so remember the
+height is as drawn in red here um height
+
+ align:start position:0%
+height is as drawn in red here um height
+ 
+
+ align:start position:0%
+height is as drawn in red here um height
+of the node is the length of the longest
+
+ align:start position:0%
+of the node is the length of the longest
+ 
+
+ align:start position:0%
+of the node is the length of the longest
+downward path counting edges so B for
+
+ align:start position:0%
+downward path counting edges so B for
+ 
+
+ align:start position:0%
+downward path counting edges so B for
+example has a length two path so we
+
+ align:start position:0%
+example has a length two path so we
+ 
+
+ align:start position:0%
+example has a length two path so we
+write a two here you can also think of
+
+ align:start position:0%
+write a two here you can also think of
+ 
+
+ align:start position:0%
+write a two here you can also think of
+it is if you just live within the sub
+
+ align:start position:0%
+it is if you just live within the sub
+ 
+
+ align:start position:0%
+it is if you just live within the sub
+tree rooted at b b's subtree uh then uh
+
+ align:start position:0%
+tree rooted at b b's subtree uh then uh
+ 
+
+ align:start position:0%
+tree rooted at b b's subtree uh then uh
+what is the maximum depth of those nodes
+
+ align:start position:0%
+what is the maximum depth of those nodes
+ 
+
+ align:start position:0%
+what is the maximum depth of those nodes
+if you prefer to think about it that way
+
+ align:start position:0%
+if you prefer to think about it that way
+ 
+
+ align:start position:0%
+if you prefer to think about it that way
+either way is fine um and in particular
+
+ align:start position:0%
+either way is fine um and in particular
+ 
+
+ align:start position:0%
+either way is fine um and in particular
+we distinguished H the height of the
+
+ align:start position:0%
+we distinguished H the height of the
+ 
+
+ align:start position:0%
+we distinguished H the height of the
+root node as the height of the entire
+
+ align:start position:0%
+root node as the height of the entire
+ 
+
+ align:start position:0%
+root node as the height of the entire
+tree and what we achieved last time was
+
+ align:start position:0%
+tree and what we achieved last time was
+ 
+
+ align:start position:0%
+tree and what we achieved last time was
+basically all of our operations ran in
+
+ align:start position:0%
+basically all of our operations ran in
+ 
+
+ align:start position:0%
+basically all of our operations ran in
+order H time so um we had subtree insert
+
+ align:start position:0%
+order H time so um we had subtree insert
+ 
+
+ align:start position:0%
+order H time so um we had subtree insert
+subtree delete subtree first and last we
+
+ align:start position:0%
+subtree delete subtree first and last we
+ 
+
+ align:start position:0%
+subtree delete subtree first and last we
+could compute the predecessor and
+
+ align:start position:0%
+could compute the predecessor and
+ 
+
+ align:start position:0%
+could compute the predecessor and
+successor of a node all in order H time
+
+ align:start position:0%
+successor of a node all in order H time
+ 
+
+ align:start position:0%
+successor of a node all in order H time
+so as long as H was small uh we were
+
+ align:start position:0%
+so as long as H was small uh we were
+ 
+
+ align:start position:0%
+so as long as H was small uh we were
+happy um and remember what does
+
+ align:start position:0%
+happy um and remember what does
+ 
+
+ align:start position:0%
+happy um and remember what does
+predecessor and successor mean it's
+
+ align:start position:0%
+predecessor and successor mean it's
+ 
+
+ align:start position:0%
+predecessor and successor mean it's
+talking about an implicit order in the
+
+ align:start position:0%
+talking about an implicit order in the
+ 
+
+ align:start position:0%
+talking about an implicit order in the
+tree which is what we call traversal
+
+ align:start position:0%
+tree which is what we call traversal
+ 
+
+ align:start position:0%
+tree which is what we call traversal
+order which is defined recursively as
+
+ align:start position:0%
+order which is defined recursively as
+ 
+
+ align:start position:0%
+order which is defined recursively as
+recursively Traverse left sub tree then
+
+ align:start position:0%
+recursively Traverse left sub tree then
+ 
+
+ align:start position:0%
+recursively Traverse left sub tree then
+output the root then recursively
+
+ align:start position:0%
+output the root then recursively
+ 
+
+ align:start position:0%
+output the root then recursively
+Traverse the right sub tree so in this
+
+ align:start position:0%
+Traverse the right sub tree so in this
+ 
+
+ align:start position:0%
+Traverse the right sub tree so in this
+example the traversal order is f is the
+
+ align:start position:0%
+example the traversal order is f is the
+ 
+
+ align:start position:0%
+example the traversal order is f is the
+if you go all the way left that was the
+
+ align:start position:0%
+if you go all the way left that was the
+ 
+
+ align:start position:0%
+if you go all the way left that was the
+first in the traversal order uh then we
+
+ align:start position:0%
+first in the traversal order uh then we
+ 
+
+ align:start position:0%
+first in the traversal order uh then we
+have right make some space here uh then
+
+ align:start position:0%
+have right make some space here uh then
+ 
+
+ align:start position:0%
+have right make some space here uh then
+we have D then we have
+
+ align:start position:0%
+we have D then we have
+ 
+
+ align:start position:0%
+we have D then we have
+B then we do the right sub tree of B
+
+ align:start position:0%
+B then we do the right sub tree of B
+ 
+
+ align:start position:0%
+B then we do the right sub tree of B
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+e then we have the root because we
+
+ align:start position:0%
+e then we have the root because we
+ 
+
+ align:start position:0%
+e then we have the root because we
+finished the left sub tree of the root
+
+ align:start position:0%
+finished the left sub tree of the root
+ 
+
+ align:start position:0%
+finished the left sub tree of the root
+so that's a and then we have
+
+ align:start position:0%
+so that's a and then we have
+ 
+
+ align:start position:0%
+so that's a and then we have
+C okay so there's an implicit linear
+
+ align:start position:0%
+C okay so there's an implicit linear
+ 
+
+ align:start position:0%
+C okay so there's an implicit linear
+order encoded by this tree and the whole
+
+ align:start position:0%
+order encoded by this tree and the whole
+ 
+
+ align:start position:0%
+order encoded by this tree and the whole
+point of binary trees is that we can
+
+ align:start position:0%
+point of binary trees is that we can
+ 
+
+ align:start position:0%
+point of binary trees is that we can
+efficiently update the tree uh much
+
+ align:start position:0%
+efficiently update the tree uh much
+ 
+
+ align:start position:0%
+efficiently update the tree uh much
+faster than we could explicitly write
+
+ align:start position:0%
+faster than we could explicitly write
+ 
+
+ align:start position:0%
+faster than we could explicitly write
+down an order in an array or something
+
+ align:start position:0%
+down an order in an array or something
+ 
+
+ align:start position:0%
+down an order in an array or something
+like that so binary trees let us quickly
+
+ align:start position:0%
+like that so binary trees let us quickly
+ 
+
+ align:start position:0%
+like that so binary trees let us quickly
+Now quickly is not so quick right now
+
+ align:start position:0%
+Now quickly is not so quick right now
+ 
+
+ align:start position:0%
+Now quickly is not so quick right now
+because everything is order H and in the
+
+ align:start position:0%
+because everything is order H and in the
+ 
+
+ align:start position:0%
+because everything is order H and in the
+worst case h is linear because we could
+
+ align:start position:0%
+worst case h is linear because we could
+ 
+
+ align:start position:0%
+worst case h is linear because we could
+have a tree like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this but today we're going to make we're
+
+ align:start position:0%
+this but today we're going to make we're
+ 
+
+ align:start position:0%
+this but today we're going to make we're
+going to guarantee that H is log n and
+
+ align:start position:0%
+going to guarantee that H is log n and
+ 
+
+ align:start position:0%
+going to guarantee that H is log n and
+so the goal of today is to take all of
+
+ align:start position:0%
+so the goal of today is to take all of
+ 
+
+ align:start position:0%
+so the goal of today is to take all of
+these operations that run in order H
+
+ align:start position:0%
+these operations that run in order H
+ 
+
+ align:start position:0%
+these operations that run in order H
+time and get them to run in order log n
+
+ align:start position:0%
+time and get them to run in order log n
+ 
+
+ align:start position:0%
+time and get them to run in order log n
+time just by modifying the data
+
+ align:start position:0%
+time just by modifying the data
+ 
+
+ align:start position:0%
+time just by modifying the data
+structure we've already seen so we've
+
+ align:start position:0%
+structure we've already seen so we've
+ 
+
+ align:start position:0%
+structure we've already seen so we've
+done a lot of the hard work just a
+
+ align:start position:0%
+done a lot of the hard work just a
+ 
+
+ align:start position:0%
+done a lot of the hard work just a
+little bit more work we need to do today
+
+ align:start position:0%
+little bit more work we need to do today
+ 
+
+ align:start position:0%
+little bit more work we need to do today
+in something called AVL trees or height
+
+ align:start position:0%
+in something called AVL trees or height
+ 
+
+ align:start position:0%
+in something called AVL trees or height
+balance okay but before we get there I
+
+ align:start position:0%
+balance okay but before we get there I
+ 
+
+ align:start position:0%
+balance okay but before we get there I
+want to talk a little bit more at the
+
+ align:start position:0%
+want to talk a little bit more at the
+ 
+
+ align:start position:0%
+want to talk a little bit more at the
+very end of last leure we talked about
+
+ align:start position:0%
+very end of last leure we talked about
+ 
+
+ align:start position:0%
+very end of last leure we talked about
+once you have these subtree operations
+
+ align:start position:0%
+once you have these subtree operations
+ 
+
+ align:start position:0%
+once you have these subtree operations
+so I can insert and delete into subtree
+
+ align:start position:0%
+so I can insert and delete into subtree
+ 
+
+ align:start position:0%
+so I can insert and delete into subtree
+um how do I actually use that to solve
+
+ align:start position:0%
+um how do I actually use that to solve
+ 
+
+ align:start position:0%
+um how do I actually use that to solve
+the problems that we care about in this
+
+ align:start position:0%
+the problems that we care about in this
+ 
+
+ align:start position:0%
+the problems that we care about in this
+class which are sequence data structure
+
+ align:start position:0%
+class which are sequence data structure
+ 
+
+ align:start position:0%
+class which are sequence data structure
+and set data structure so um we talked
+
+ align:start position:0%
+and set data structure so um we talked
+ 
+
+ align:start position:0%
+and set data structure so um we talked
+mostly about the set data structure last
+
+ align:start position:0%
+mostly about the set data structure last
+ 
+
+ align:start position:0%
+mostly about the set data structure last
+time so in general we're going to Define
+
+ align:start position:0%
+time so in general we're going to Define
+ 
+
+ align:start position:0%
+time so in general we're going to Define
+what traversal order we maintain by a
+
+ align:start position:0%
+what traversal order we maintain by a
+ 
+
+ align:start position:0%
+what traversal order we maintain by a
+binary tree and so for a set um because
+
+ align:start position:0%
+binary tree and so for a set um because
+ 
+
+ align:start position:0%
+binary tree and so for a set um because
+we're for the set interface we're
+
+ align:start position:0%
+we're for the set interface we're
+ 
+
+ align:start position:0%
+we're for the set interface we're
+interested in doing
+
+ align:start position:0%
+interested in doing
+ 
+
+ align:start position:0%
+interested in doing
+uh queries like find next and find
+
+ align:start position:0%
+uh queries like find next and find
+ 
+
+ align:start position:0%
+uh queries like find next and find
+previous given a key if it's not there
+
+ align:start position:0%
+previous given a key if it's not there
+ 
+
+ align:start position:0%
+previous given a key if it's not there
+tell me the previous one or the next one
+
+ align:start position:0%
+tell me the previous one or the next one
+ 
+
+ align:start position:0%
+tell me the previous one or the next one
+this is something we could do with
+
+ align:start position:0%
+this is something we could do with
+ 
+
+ align:start position:0%
+this is something we could do with
+binary search and so the the big cool
+
+ align:start position:0%
+binary search and so the the big cool
+ 
+
+ align:start position:0%
+binary search and so the the big cool
+thing that binary trees let us do if we
+
+ align:start position:0%
+thing that binary trees let us do if we
+ 
+
+ align:start position:0%
+thing that binary trees let us do if we
+let the traversal order always be uh all
+
+ align:start position:0%
+let the traversal order always be uh all
+ 
+
+ align:start position:0%
+let the traversal order always be uh all
+of the items stored in increasing key
+
+ align:start position:0%
+of the items stored in increasing key
+ 
+
+ align:start position:0%
+of the items stored in increasing key
+order then we are effectively
+
+ align:start position:0%
+order then we are effectively
+ 
+
+ align:start position:0%
+order then we are effectively
+maintaining the items in
+
+ align:start position:0%
+maintaining the items in
+ 
+
+ align:start position:0%
+maintaining the items in
+order in in the traversal order sense
+
+ align:start position:0%
+order in in the traversal order sense
+ 
+
+ align:start position:0%
+order in in the traversal order sense
+again we're not explicitly maintaining
+
+ align:start position:0%
+again we're not explicitly maintaining
+ 
+
+ align:start position:0%
+again we're not explicitly maintaining
+them in order but up here we're
+
+ align:start position:0%
+them in order but up here we're
+ 
+
+ align:start position:0%
+them in order but up here we're
+maintaining a tree that that represents
+
+ align:start position:0%
+maintaining a tree that that represents
+ 
+
+ align:start position:0%
+maintaining a tree that that represents
+items in key order and so this lets us
+
+ align:start position:0%
+items in key order and so this lets us
+ 
+
+ align:start position:0%
+items in key order and so this lets us
+do uh a sub tree find operation which
+
+ align:start position:0%
+do uh a sub tree find operation which
+ 
+
+ align:start position:0%
+do uh a sub tree find operation which
+you could easily use to implement find
+
+ align:start position:0%
+you could easily use to implement find
+ 
+
+ align:start position:0%
+you could easily use to implement find
+and find previous and so on um as
+
+ align:start position:0%
+and find previous and so on um as
+ 
+
+ align:start position:0%
+and find previous and so on um as
+follows we start at the root of the tree
+
+ align:start position:0%
+follows we start at the root of the tree
+ 
+
+ align:start position:0%
+follows we start at the root of the tree
+so we could say node equals root
+
+ align:start position:0%
+so we could say node equals root
+ 
+
+ align:start position:0%
+so we could say node equals root
+initially and then we can recursively
+
+ align:start position:0%
+initially and then we can recursively
+ 
+
+ align:start position:0%
+initially and then we can recursively
+search for a key K as follows we check
+
+ align:start position:0%
+search for a key K as follows we check
+ 
+
+ align:start position:0%
+search for a key K as follows we check
+well if the item at the root has a key
+
+ align:start position:0%
+well if the item at the root has a key
+ 
+
+ align:start position:0%
+well if the item at the root has a key
+that's bigger than K let me draw a
+
+ align:start position:0%
+that's bigger than K let me draw a
+ 
+
+ align:start position:0%
+that's bigger than K let me draw a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+uh so we're at some node
+
+ align:start position:0%
+uh so we're at some node
+ 
+
+ align:start position:0%
+uh so we're at some node
+here this is a
+
+ align:start position:0%
+here this is a
+ 
+
+ align:start position:0%
+here this is a
+node and it has a left sub tree and a
+
+ align:start position:0%
+node and it has a left sub tree and a
+ 
+
+ align:start position:0%
+node and it has a left sub tree and a
+right sub tree and there's some
+
+ align:start position:0%
+right sub tree and there's some
+ 
+
+ align:start position:0%
+right sub tree and there's some
+item with some key so if the key we're
+
+ align:start position:0%
+item with some key so if the key we're
+ 
+
+ align:start position:0%
+item with some key so if the key we're
+looking for is less than the nodes item
+
+ align:start position:0%
+looking for is less than the nodes item
+ 
+
+ align:start position:0%
+looking for is less than the nodes item
+that means it's down here in the left
+
+ align:start position:0%
+that means it's down here in the left
+ 
+
+ align:start position:0%
+that means it's down here in the left
+sub tree and so we recurse on node. left
+
+ align:start position:0%
+sub tree and so we recurse on node. left
+ 
+
+ align:start position:0%
+sub tree and so we recurse on node. left
+if they're equal that means that this
+
+ align:start position:0%
+if they're equal that means that this
+ 
+
+ align:start position:0%
+if they're equal that means that this
+item is the item we're looking for so we
+
+ align:start position:0%
+item is the item we're looking for so we
+ 
+
+ align:start position:0%
+item is the item we're looking for so we
+can just turn it or the node depending
+
+ align:start position:0%
+can just turn it or the node depending
+ 
+
+ align:start position:0%
+can just turn it or the node depending
+on what you're looking for and if the
+
+ align:start position:0%
+on what you're looking for and if the
+ 
+
+ align:start position:0%
+on what you're looking for and if the
+key in here is greater than the key
+
+ align:start position:0%
+key in here is greater than the key
+ 
+
+ align:start position:0%
+key in here is greater than the key
+we're looking for then we'll recurse to
+
+ align:start position:0%
+we're looking for then we'll recurse to
+ 
+
+ align:start position:0%
+we're looking for then we'll recurse to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right this if you think about it a
+
+ align:start position:0%
+right this if you think about it a
+ 
+
+ align:start position:0%
+right this if you think about it a
+little bit this is exactly binary search
+
+ align:start position:0%
+little bit this is exactly binary search
+ 
+
+ align:start position:0%
+little bit this is exactly binary search
+on an array it just happens to be on a
+
+ align:start position:0%
+on an array it just happens to be on a
+ 
+
+ align:start position:0%
+on an array it just happens to be on a
+tree instead if you think of an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+array um like this B where does binary
+
+ align:start position:0%
+array um like this B where does binary
+ 
+
+ align:start position:0%
+array um like this B where does binary
+stretch do it first looks at the key in
+
+ align:start position:0%
+stretch do it first looks at the key in
+ 
+
+ align:start position:0%
+stretch do it first looks at the key in
+the middle I'm going to draw that as the
+
+ align:start position:0%
+the middle I'm going to draw that as the
+ 
+
+ align:start position:0%
+the middle I'm going to draw that as the
+root uh and then uh it recurses either
+
+ align:start position:0%
+root uh and then uh it recurses either
+ 
+
+ align:start position:0%
+root uh and then uh it recurses either
+on the left chunk which I will draw
+
+ align:start position:0%
+on the left chunk which I will draw
+ 
+
+ align:start position:0%
+on the left chunk which I will draw
+recursively or on the right
+
+ align:start position:0%
+recursively or on the right
+ 
+
+ align:start position:0%
+recursively or on the right
+chunk and so if you happen to have a
+
+ align:start position:0%
+chunk and so if you happen to have a
+ 
+
+ align:start position:0%
+chunk and so if you happen to have a
+perfect binary tree like this one it is
+
+ align:start position:0%
+perfect binary tree like this one it is
+ 
+
+ align:start position:0%
+perfect binary tree like this one it is
+simulating exactly uh binary search in
+
+ align:start position:0%
+simulating exactly uh binary search in
+ 
+
+ align:start position:0%
+simulating exactly uh binary search in
+this array but this we're going to be
+
+ align:start position:0%
+this array but this we're going to be
+ 
+
+ align:start position:0%
+this array but this we're going to be
+able to maintain dynamically not perfect
+
+ align:start position:0%
+able to maintain dynamically not perfect
+ 
+
+ align:start position:0%
+able to maintain dynamically not perfect
+anymore but close uh whereas this we
+
+ align:start position:0%
+anymore but close uh whereas this we
+ 
+
+ align:start position:0%
+anymore but close uh whereas this we
+could not maintain in sorted order okay
+
+ align:start position:0%
+could not maintain in sorted order okay
+ 
+
+ align:start position:0%
+could not maintain in sorted order okay
+so uh this is like a generalization of
+
+ align:start position:0%
+so uh this is like a generalization of
+ 
+
+ align:start position:0%
+so uh this is like a generalization of
+binary search to work on trees instead
+
+ align:start position:0%
+binary search to work on trees instead
+ 
+
+ align:start position:0%
+binary search to work on trees instead
+of on arrays and for this reason set
+
+ align:start position:0%
+of on arrays and for this reason set
+ 
+
+ align:start position:0%
+of on arrays and for this reason set
+binary trees are called binary search
+
+ align:start position:0%
+binary trees are called binary search
+ 
+
+ align:start position:0%
+binary trees are called binary search
+trees because they are the tree version
+
+ align:start position:0%
+trees because they are the tree version
+ 
+
+ align:start position:0%
+trees because they are the tree version
+of binary search so there's many
+
+ align:start position:0%
+of binary search so there's many
+ 
+
+ align:start position:0%
+of binary search so there's many
+equivalent names so binary search tree
+
+ align:start position:0%
+equivalent names so binary search tree
+ 
+
+ align:start position:0%
+equivalent names so binary search tree
+is another name for set binary tree and
+
+ align:start position:0%
+is another name for set binary tree and
+ 
+
+ align:start position:0%
+is another name for set binary tree and
+the key thing that makes this algorithm
+
+ align:start position:0%
+the key thing that makes this algorithm
+ 
+
+ align:start position:0%
+the key thing that makes this algorithm
+work is so-called binary search tree
+
+ align:start position:0%
+work is so-called binary search tree
+ 
+
+ align:start position:0%
+work is so-called binary search tree
+property which is um all the keys in the
+
+ align:start position:0%
+property which is um all the keys in the
+ 
+
+ align:start position:0%
+property which is um all the keys in the
+left sub tree of a node are less than uh
+
+ align:start position:0%
+left sub tree of a node are less than uh
+ 
+
+ align:start position:0%
+left sub tree of a node are less than uh
+the root and all or of that node and
+
+ align:start position:0%
+the root and all or of that node and
+ 
+
+ align:start position:0%
+the root and all or of that node and
+that key that key is less than all the
+
+ align:start position:0%
+that key that key is less than all the
+ 
+
+ align:start position:0%
+that key that key is less than all the
+keys in the right sub tree and this is
+
+ align:start position:0%
+keys in the right sub tree and this is
+ 
+
+ align:start position:0%
+keys in the right sub tree and this is
+true recursively all the way down
+
+ align:start position:0%
+true recursively all the way down
+ 
+
+ align:start position:0%
+true recursively all the way down
+and so that's that's how you prove that
+
+ align:start position:0%
+and so that's that's how you prove that
+ 
+
+ align:start position:0%
+and so that's that's how you prove that
+this algorithm is correct by this
+
+ align:start position:0%
+this algorithm is correct by this
+ 
+
+ align:start position:0%
+this algorithm is correct by this
+property why is this true because uh if
+
+ align:start position:0%
+property why is this true because uh if
+ 
+
+ align:start position:0%
+property why is this true because uh if
+we can maintain traversal order to be
+
+ align:start position:0%
+we can maintain traversal order to be
+ 
+
+ align:start position:0%
+we can maintain traversal order to be
+increasing key then that's exactly what
+
+ align:start position:0%
+increasing key then that's exactly what
+ 
+
+ align:start position:0%
+increasing key then that's exactly what
+traversal order means it tells you all
+
+ align:start position:0%
+traversal order means it tells you all
+ 
+
+ align:start position:0%
+traversal order means it tells you all
+the things in the left sub tree come
+
+ align:start position:0%
+the things in the left sub tree come
+ 
+
+ align:start position:0%
+the things in the left sub tree come
+before the root which come before all
+
+ align:start position:0%
+before the root which come before all
+ 
+
+ align:start position:0%
+before the root which come before all
+the things in the right sub tree so uh
+
+ align:start position:0%
+the things in the right sub tree so uh
+ 
+
+ align:start position:0%
+the things in the right sub tree so uh
+this property implies this
+
+ align:start position:0%
+this property implies this
+ 
+
+ align:start position:0%
+this property implies this
+one and how do you maintain things in
+
+ align:start position:0%
+one and how do you maintain things in
+ 
+
+ align:start position:0%
+one and how do you maintain things in
+increasing key order it's pretty easy uh
+
+ align:start position:0%
+increasing key order it's pretty easy uh
+ 
+
+ align:start position:0%
+increasing key order it's pretty easy uh
+if you want to insert an item where does
+
+ align:start position:0%
+if you want to insert an item where does
+ 
+
+ align:start position:0%
+if you want to insert an item where does
+it belong well you do this search to
+
+ align:start position:0%
+it belong well you do this search to
+ 
+
+ align:start position:0%
+it belong well you do this search to
+find where it would belong if it was
+
+ align:start position:0%
+find where it would belong if it was
+ 
+
+ align:start position:0%
+find where it would belong if it was
+there if it's there you can overwrite
+
+ align:start position:0%
+there if it's there you can overwrite
+ 
+
+ align:start position:0%
+there if it's there you can overwrite
+the values stored with that key if it's
+
+ align:start position:0%
+the values stored with that key if it's
+ 
+
+ align:start position:0%
+the values stored with that key if it's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+um this search will fall off the tree at
+
+ align:start position:0%
+um this search will fall off the tree at
+ 
+
+ align:start position:0%
+um this search will fall off the tree at
+some point and that's where you insert
+
+ align:start position:0%
+some point and that's where you insert
+ 
+
+ align:start position:0%
+some point and that's where you insert
+your uh a new node in your tree okay
+
+ align:start position:0%
+your uh a new node in your tree okay
+ 
+
+ align:start position:0%
+your uh a new node in your tree okay
+that was discovered in recitation so I
+
+ align:start position:0%
+that was discovered in recitation so I
+ 
+
+ align:start position:0%
+that was discovered in recitation so I
+don't want to dwell on it what I want to
+
+ align:start position:0%
+don't want to dwell on it what I want to
+ 
+
+ align:start position:0%
+don't want to dwell on it what I want to
+focus on today is the other application
+
+ align:start position:0%
+focus on today is the other application
+ 
+
+ align:start position:0%
+focus on today is the other application
+how do we this is for representing a set
+
+ align:start position:0%
+how do we this is for representing a set
+ 
+
+ align:start position:0%
+how do we this is for representing a set
+which is relatively easy uh a CH
+
+ align:start position:0%
+which is relatively easy uh a CH
+ 
+
+ align:start position:0%
+which is relatively easy uh a CH
+we sort of set ourselves up for but we
+
+ align:start position:0%
+we sort of set ourselves up for but we
+ 
+
+ align:start position:0%
+we sort of set ourselves up for but we
+need a little more work is to make
+
+ align:start position:0%
+need a little more work is to make
+ 
+
+ align:start position:0%
+need a little more work is to make
+sequence binary
+
+ align:start position:0%
+sequence binary
+ 
+
+ align:start position:0%
+sequence binary
+trees so suppose I have a binary tree
+
+ align:start position:0%
+trees so suppose I have a binary tree
+ 
+
+ align:start position:0%
+trees so suppose I have a binary tree
+and what I would like mentioned at the
+
+ align:start position:0%
+and what I would like mentioned at the
+ 
+
+ align:start position:0%
+and what I would like mentioned at the
+end of last time is that I want the
+
+ align:start position:0%
+end of last time is that I want the
+ 
+
+ align:start position:0%
+end of last time is that I want the
+traversal order of my tree to be the
+
+ align:start position:0%
+traversal order of my tree to be the
+ 
+
+ align:start position:0%
+traversal order of my tree to be the
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+order the order that I'm trying to
+
+ align:start position:0%
+order the order that I'm trying to
+ 
+
+ align:start position:0%
+order the order that I'm trying to
+represent that's changed by operations
+
+ align:start position:0%
+represent that's changed by operations
+ 
+
+ align:start position:0%
+represent that's changed by operations
+like insert
+
+ align:start position:0%
+like insert
+ 
+
+ align:start position:0%
+like insert
+at and so I just like to do the same
+
+ align:start position:0%
+at and so I just like to do the same
+ 
+
+ align:start position:0%
+at and so I just like to do the same
+thing but now I have to think about how
+
+ align:start position:0%
+thing but now I have to think about how
+ 
+
+ align:start position:0%
+thing but now I have to think about how
+do I do a search how do I do insert at
+
+ align:start position:0%
+do I do a search how do I do insert at
+ 
+
+ align:start position:0%
+do I do a search how do I do insert at
+that sort of thing and here is an
+
+ align:start position:0%
+that sort of thing and here is an
+ 
+
+ align:start position:0%
+that sort of thing and here is an
+algorithm for what I would like to work
+
+ align:start position:0%
+algorithm for what I would like to work
+ 
+
+ align:start position:0%
+algorithm for what I would like to work
+but it's not going to quite work yet so
+
+ align:start position:0%
+but it's not going to quite work yet so
+ 
+
+ align:start position:0%
+but it's not going to quite work yet so
+suppose I give you a sub tree so
+
+ align:start position:0%
+suppose I give you a sub tree so
+ 
+
+ align:start position:0%
+suppose I give you a sub tree so
+specified by a node so there's all the
+
+ align:start position:0%
+specified by a node so there's all the
+ 
+
+ align:start position:0%
+specified by a node so there's all the
+descendants of that node and I'd like to
+
+ align:start position:0%
+descendants of that node and I'd like to
+ 
+
+ align:start position:0%
+descendants of that node and I'd like to
+know what is in the traversal order of
+
+ align:start position:0%
+know what is in the traversal order of
+ 
+
+ align:start position:0%
+know what is in the traversal order of
+that subtree which starts here and ends
+
+ align:start position:0%
+that subtree which starts here and ends
+ 
+
+ align:start position:0%
+that subtree which starts here and ends
+here and the root will be somewhere in
+
+ align:start position:0%
+here and the root will be somewhere in
+ 
+
+ align:start position:0%
+here and the root will be somewhere in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+middle give me the
+
+ align:start position:0%
+middle give me the
+ 
+
+ align:start position:0%
+middle give me the
+node so this if I ask I equals z i want
+
+ align:start position:0%
+node so this if I ask I equals z i want
+ 
+
+ align:start position:0%
+node so this if I ask I equals z i want
+to get this leftmost descendant if I ask
+
+ align:start position:0%
+to get this leftmost descendant if I ask
+ 
+
+ align:start position:0%
+to get this leftmost descendant if I ask
+for I equals the size of the tree minus
+
+ align:start position:0%
+for I equals the size of the tree minus
+ 
+
+ align:start position:0%
+for I equals the size of the tree minus
+one I want to get The rightmost
+
+ align:start position:0%
+one I want to get The rightmost
+ 
+
+ align:start position:0%
+one I want to get The rightmost
+Descendant that was the first and last
+
+ align:start position:0%
+Descendant that was the first and last
+ 
+
+ align:start position:0%
+Descendant that was the first and last
+in the sub tree that we talked about but
+
+ align:start position:0%
+in the sub tree that we talked about but
+ 
+
+ align:start position:0%
+in the sub tree that we talked about but
+we don't we know how to find the first
+
+ align:start position:0%
+we don't we know how to find the first
+ 
+
+ align:start position:0%
+we don't we know how to find the first
+and last just walk left or walk right
+
+ align:start position:0%
+and last just walk left or walk right
+ 
+
+ align:start position:0%
+and last just walk left or walk right
+but we don't know how to find the I
+
+ align:start position:0%
+but we don't know how to find the I
+ 
+
+ align:start position:0%
+but we don't know how to find the I
+node in order H time is the goal right
+
+ align:start position:0%
+node in order H time is the goal right
+ 
+
+ align:start position:0%
+node in order H time is the goal right
+now not log in and the idea is well it
+
+ align:start position:0%
+now not log in and the idea is well it
+ 
+
+ align:start position:0%
+now not log in and the idea is well it
+seems like size
+
+ align:start position:0%
+seems like size
+ 
+
+ align:start position:0%
+seems like size
+matters sorry if you heard otherwise um
+
+ align:start position:0%
+matters sorry if you heard otherwise um
+ 
+
+ align:start position:0%
+matters sorry if you heard otherwise um
+so in particular I I mentioned size when
+
+ align:start position:0%
+so in particular I I mentioned size when
+ 
+
+ align:start position:0%
+so in particular I I mentioned size when
+I was talking about the the last node in
+
+ align:start position:0%
+I was talking about the the last node in
+ 
+
+ align:start position:0%
+I was talking about the the last node in
+the sequence that the index of that node
+
+ align:start position:0%
+the sequence that the index of that node
+ 
+
+ align:start position:0%
+the sequence that the index of that node
+is size of this subtree minus one so
+
+ align:start position:0%
+is size of this subtree minus one so
+ 
+
+ align:start position:0%
+is size of this subtree minus one so
+let's define the size of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node to be uh the number of nodes in its
+
+ align:start position:0%
+node to be uh the number of nodes in its
+ 
+
+ align:start position:0%
+node to be uh the number of nodes in its
+sub tree we're calling that subtree
+
+ align:start position:0%
+sub tree we're calling that subtree
+ 
+
+ align:start position:0%
+sub tree we're calling that subtree
+paren
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node okay including the node
+
+ align:start position:0%
+node okay including the node
+ 
+
+ align:start position:0%
+node okay including the node
+itself so if I somehow knew the size
+
+ align:start position:0%
+itself so if I somehow knew the size
+ 
+
+ align:start position:0%
+itself so if I somehow knew the size
+this seems important for understanding
+
+ align:start position:0%
+this seems important for understanding
+ 
+
+ align:start position:0%
+this seems important for understanding
+indexes let's just assume that I knew
+
+ align:start position:0%
+indexes let's just assume that I knew
+ 
+
+ align:start position:0%
+indexes let's just assume that I knew
+that magically in constant
+
+ align:start position:0%
+that magically in constant
+ 
+
+ align:start position:0%
+that magically in constant
+time okay uh then I claim that the size
+
+ align:start position:0%
+time okay uh then I claim that the size
+ 
+
+ align:start position:0%
+time okay uh then I claim that the size
+of the left sub tree so why don't I
+
+ align:start position:0%
+of the left sub tree so why don't I
+ 
+
+ align:start position:0%
+of the left sub tree so why don't I
+expand this diagram a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so we we have node as
+
+ align:start position:0%
+bit so we we have node as
+ 
+
+ align:start position:0%
+bit so we we have node as
+before but we have a left sub tree and a
+
+ align:start position:0%
+before but we have a left sub tree and a
+ 
+
+ align:start position:0%
+before but we have a left sub tree and a
+right sub tree so this node here is
+
+ align:start position:0%
+right sub tree so this node here is
+ 
+
+ align:start position:0%
+right sub tree so this node here is
+node. left this node here is node. right
+
+ align:start position:0%
+node. left this node here is node. right
+ 
+
+ align:start position:0%
+node. left this node here is node. right
+they might not exist but let's ignore
+
+ align:start position:0%
+they might not exist but let's ignore
+ 
+
+ align:start position:0%
+they might not exist but let's ignore
+those exceptional cases for now let's
+
+ align:start position:0%
+those exceptional cases for now let's
+ 
+
+ align:start position:0%
+those exceptional cases for now let's
+suppose we knew not only the size of
+
+ align:start position:0%
+suppose we knew not only the size of
+ 
+
+ align:start position:0%
+suppose we knew not only the size of
+node but we knew the size of node. left
+
+ align:start position:0%
+node but we knew the size of node. left
+ 
+
+ align:start position:0%
+node but we knew the size of node. left
+so that is the size of this tree on the
+
+ align:start position:0%
+so that is the size of this tree on the
+ 
+
+ align:start position:0%
+so that is the size of this tree on the
+left I'm going to call that NL so let's
+
+ align:start position:0%
+left I'm going to call that NL so let's
+ 
+
+ align:start position:0%
+left I'm going to call that NL so let's
+suppose that there are NL nodes down
+
+ align:start position:0%
+suppose that there are NL nodes down
+ 
+
+ align:start position:0%
+suppose that there are NL nodes down
+here why I claim that lets me do the
+
+ align:start position:0%
+here why I claim that lets me do the
+ 
+
+ align:start position:0%
+here why I claim that lets me do the
+equivalent of a binary
+
+ align:start position:0%
+equivalent of a binary
+ 
+
+ align:start position:0%
+equivalent of a binary
+search cuz I'm looking for some index I
+
+ align:start position:0%
+search cuz I'm looking for some index I
+ 
+
+ align:start position:0%
+search cuz I'm looking for some index I
+and if I is less than NL then I know
+
+ align:start position:0%
+and if I is less than NL then I know
+ 
+
+ align:start position:0%
+and if I is less than NL then I know
+that it must be down here for example if
+
+ align:start position:0%
+that it must be down here for example if
+ 
+
+ align:start position:0%
+that it must be down here for example if
+I equals z it's going to be in the left
+
+ align:start position:0%
+I equals z it's going to be in the left
+ 
+
+ align:start position:0%
+I equals z it's going to be in the left
+sub tree as long as NL is greater than
+
+ align:start position:0%
+sub tree as long as NL is greater than
+ 
+
+ align:start position:0%
+sub tree as long as NL is greater than
+zero right so uh that's exactly this
+
+ align:start position:0%
+zero right so uh that's exactly this
+ 
+
+ align:start position:0%
+zero right so uh that's exactly this
+check if I is less than NL I'm going to
+
+ align:start position:0%
+check if I is less than NL I'm going to
+ 
+
+ align:start position:0%
+check if I is less than NL I'm going to
+recurse to the left call subt tree at of
+
+ align:start position:0%
+recurse to the left call subt tree at of
+ 
+
+ align:start position:0%
+recurse to the left call subt tree at of
+no do left comma
+
+ align:start position:0%
+no do left comma
+ 
+
+ align:start position:0%
+no do left comma
+I that's what's written here um if I
+
+ align:start position:0%
+I that's what's written here um if I
+ 
+
+ align:start position:0%
+I that's what's written here um if I
+equals NL
+
+ align:start position:0%
+equals NL
+ 
+
+ align:start position:0%
+equals NL
+if you think about it for a second so NL
+
+ align:start position:0%
+if you think about it for a second so NL
+ 
+
+ align:start position:0%
+if you think about it for a second so NL
+is the number of nodes here and so that
+
+ align:start position:0%
+is the number of nodes here and so that
+ 
+
+ align:start position:0%
+is the number of nodes here and so that
+means this node has index NL the index
+
+ align:start position:0%
+means this node has index NL the index
+ 
+
+ align:start position:0%
+means this node has index NL the index
+of this node is NL and so if I equals
+
+ align:start position:0%
+of this node is NL and so if I equals
+ 
+
+ align:start position:0%
+of this node is NL and so if I equals
+the if the one index we're looking for
+
+ align:start position:0%
+the if the one index we're looking for
+ 
+
+ align:start position:0%
+the if the one index we're looking for
+is that one then we just return this
+
+ align:start position:0%
+is that one then we just return this
+ 
+
+ align:start position:0%
+is that one then we just return this
+node we're
+
+ align:start position:0%
+node we're
+ 
+
+ align:start position:0%
+node we're
+done and otherwise I is greater than NL
+
+ align:start position:0%
+done and otherwise I is greater than NL
+ 
+
+ align:start position:0%
+done and otherwise I is greater than NL
+and that means that the node we're
+
+ align:start position:0%
+and that means that the node we're
+ 
+
+ align:start position:0%
+and that means that the node we're
+looking for is in the right sub tree
+
+ align:start position:0%
+looking for is in the right sub tree
+ 
+
+ align:start position:0%
+looking for is in the right sub tree
+because it comes after the root again
+
+ align:start position:0%
+because it comes after the root again
+ 
+
+ align:start position:0%
+because it comes after the root again
+that's what it means that's what
+
+ align:start position:0%
+that's what it means that's what
+ 
+
+ align:start position:0%
+that's what it means that's what
+traversal order means so if we Define it
+
+ align:start position:0%
+traversal order means so if we Define it
+ 
+
+ align:start position:0%
+traversal order means so if we Define it
+to be sequence order
+
+ align:start position:0%
+to be sequence order
+ 
+
+ align:start position:0%
+to be sequence order
+uh then we know all the things that come
+
+ align:start position:0%
+uh then we know all the things that come
+ 
+
+ align:start position:0%
+uh then we know all the things that come
+after this node which is index NL must
+
+ align:start position:0%
+after this node which is index NL must
+ 
+
+ align:start position:0%
+after this node which is index NL must
+be over here now when we recurse down
+
+ align:start position:0%
+be over here now when we recurse down
+ 
+
+ align:start position:0%
+be over here now when we recurse down
+here our numbering system changes
+
+ align:start position:0%
+here our numbering system changes
+ 
+
+ align:start position:0%
+here our numbering system changes
+because out in for node zero is here and
+
+ align:start position:0%
+because out in for node zero is here and
+ 
+
+ align:start position:0%
+because out in for node zero is here and
+then for node. right Zer is here so we
+
+ align:start position:0%
+then for node. right Zer is here so we
+ 
+
+ align:start position:0%
+then for node. right Zer is here so we
+need to do a little bit of subtraction
+
+ align:start position:0%
+need to do a little bit of subtraction
+ 
+
+ align:start position:0%
+need to do a little bit of subtraction
+here which is when we recurse to the
+
+ align:start position:0%
+here which is when we recurse to the
+ 
+
+ align:start position:0%
+here which is when we recurse to the
+right we take IUS NL minus one minus NL
+
+ align:start position:0%
+right we take IUS NL minus one minus NL
+ 
+
+ align:start position:0%
+right we take IUS NL minus one minus NL
+for these guys minus one for the root
+
+ align:start position:0%
+for these guys minus one for the root
+ 
+
+ align:start position:0%
+for these guys minus one for the root
+node um and that will give us the index
+
+ align:start position:0%
+node um and that will give us the index
+ 
+
+ align:start position:0%
+node um and that will give us the index
+we're looking for within this sub
+
+ align:start position:0%
+we're looking for within this sub
+ 
+
+ align:start position:0%
+we're looking for within this sub
+okay so it's my point is this algorithm
+
+ align:start position:0%
+okay so it's my point is this algorithm
+ 
+
+ align:start position:0%
+okay so it's my point is this algorithm
+is basically the same as this algorithm
+
+ align:start position:0%
+is basically the same as this algorithm
+ 
+
+ align:start position:0%
+is basically the same as this algorithm
+but this one uses keys because we're
+
+ align:start position:0%
+but this one uses keys because we're
+ 
+
+ align:start position:0%
+but this one uses keys because we're
+dealing with a set and in sets we assume
+
+ align:start position:0%
+dealing with a set and in sets we assume
+ 
+
+ align:start position:0%
+dealing with a set and in sets we assume
+items have keys over here we items don't
+
+ align:start position:0%
+items have keys over here we items don't
+ 
+
+ align:start position:0%
+items have keys over here we items don't
+have to have keys in fact we're not
+
+ align:start position:0%
+have to have keys in fact we're not
+ 
+
+ align:start position:0%
+have to have keys in fact we're not
+touching the items at all we're just
+
+ align:start position:0%
+touching the items at all we're just
+ 
+
+ align:start position:0%
+touching the items at all we're just
+asking what is the I item in my sequence
+
+ align:start position:0%
+asking what is the I item in my sequence
+ 
+
+ align:start position:0%
+asking what is the I item in my sequence
+which is the same thing as what is the I
+
+ align:start position:0%
+which is the same thing as what is the I
+ 
+
+ align:start position:0%
+which is the same thing as what is the I
+item in my traversal order which is the
+
+ align:start position:0%
+item in my traversal order which is the
+ 
+
+ align:start position:0%
+item in my traversal order which is the
+same thing as asking what is the I node
+
+ align:start position:0%
+same thing as asking what is the I node
+ 
+
+ align:start position:0%
+same thing as asking what is the I node
+in the traversal order and this
+
+ align:start position:0%
+in the traversal order and this
+ 
+
+ align:start position:0%
+in the traversal order and this
+algorithm gives it to you exactly the
+
+ align:start position:0%
+algorithm gives it to you exactly the
+ 
+
+ align:start position:0%
+algorithm gives it to you exactly the
+same way
+
+ align:start position:0%
+same way
+ 
+
+ align:start position:0%
+same way
+in order H
+
+ align:start position:0%
+in order H
+ 
+
+ align:start position:0%
+in order H
+time okay now I'm not going to show you
+
+ align:start position:0%
+time okay now I'm not going to show you
+ 
+
+ align:start position:0%
+time okay now I'm not going to show you
+all the operations but you can use subt
+
+ align:start position:0%
+all the operations but you can use subt
+ 
+
+ align:start position:0%
+all the operations but you can use subt
+tree at to
+
+ align:start position:0%
+tree at to
+ 
+
+ align:start position:0%
+tree at to
+implement uh get at and set at you just
+
+ align:start position:0%
+implement uh get at and set at you just
+ 
+
+ align:start position:0%
+implement uh get at and set at you just
+find the appropriate node and return the
+
+ align:start position:0%
+find the appropriate node and return the
+ 
+
+ align:start position:0%
+find the appropriate node and return the
+item or modify the item uh or you can
+
+ align:start position:0%
+item or modify the item uh or you can
+ 
+
+ align:start position:0%
+item or modify the item uh or you can
+use it to most crucially you can use it
+
+ align:start position:0%
+use it to most crucially you can use it
+ 
+
+ align:start position:0%
+use it to most crucially you can use it
+to do insert at and delete at this is a
+
+ align:start position:0%
+to do insert at and delete at this is a
+ 
+
+ align:start position:0%
+to do insert at and delete at this is a
+new thing we've never been able to do
+
+ align:start position:0%
+new thing we've never been able to do
+ 
+
+ align:start position:0%
+new thing we've never been able to do
+before uh what do you do just like over
+
+ align:start position:0%
+before uh what do you do just like over
+ 
+
+ align:start position:0%
+before uh what do you do just like over
+here if I'm trying to insert an item I
+
+ align:start position:0%
+here if I'm trying to insert an item I
+ 
+
+ align:start position:0%
+here if I'm trying to insert an item I
+search for that item over here uh so if
+
+ align:start position:0%
+search for that item over here uh so if
+ 
+
+ align:start position:0%
+search for that item over here uh so if
+I'm trying to insert at I for example I
+
+ align:start position:0%
+I'm trying to insert at I for example I
+ 
+
+ align:start position:0%
+I'm trying to insert at I for example I
+look for I and then
+
+ align:start position:0%
+look for I and then
+ 
+
+ align:start position:0%
+look for I and then
+uh for insert at I I want to add a new
+
+ align:start position:0%
+uh for insert at I I want to add a new
+ 
+
+ align:start position:0%
+uh for insert at I I want to add a new
+item just before that one and
+
+ align:start position:0%
+item just before that one and
+ 
+
+ align:start position:0%
+item just before that one and
+conveniently we already have I didn't
+
+ align:start position:0%
+conveniently we already have I didn't
+ 
+
+ align:start position:0%
+conveniently we already have I didn't
+mention but we have a subtree insert we
+
+ align:start position:0%
+mention but we have a subtree insert we
+ 
+
+ align:start position:0%
+mention but we have a subtree insert we
+had two versions before and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after I think we cover it
+
+ align:start position:0%
+after I think we cover it
+ 
+
+ align:start position:0%
+after I think we cover it
+after which is success before use
+
+ align:start position:0%
+after which is success before use
+ 
+
+ align:start position:0%
+after which is success before use
+predecessor uh but we can just call
+
+ align:start position:0%
+predecessor uh but we can just call
+ 
+
+ align:start position:0%
+predecessor uh but we can just call
+subtree insert before at that node and
+
+ align:start position:0%
+subtree insert before at that node and
+ 
+
+ align:start position:0%
+subtree insert before at that node and
+boom we will have added a new item just
+
+ align:start position:0%
+boom we will have added a new item just
+ 
+
+ align:start position:0%
+boom we will have added a new item just
+before it um and great so magically
+
+ align:start position:0%
+before it um and great so magically
+ 
+
+ align:start position:0%
+before it um and great so magically
+somehow uh we have inserted in the
+
+ align:start position:0%
+somehow uh we have inserted in the
+ 
+
+ align:start position:0%
+somehow uh we have inserted in the
+middle of the sequence and all of the
+
+ align:start position:0%
+middle of the sequence and all of the
+ 
+
+ align:start position:0%
+middle of the sequence and all of the
+indices update because I'm not storing
+
+ align:start position:0%
+indices update because I'm not storing
+ 
+
+ align:start position:0%
+indices update because I'm not storing
+indices instead I'm to search for an
+
+ align:start position:0%
+indices instead I'm to search for an
+ 
+
+ align:start position:0%
+indices instead I'm to search for an
+item at index I I'm using the search
+
+ align:start position:0%
+item at index I I'm using the search
+ 
+
+ align:start position:0%
+item at index I I'm using the search
+algorithm but
+
+ align:start position:0%
+algorithm but
+ 
+
+ align:start position:0%
+algorithm but
+there's a problem what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem this seems a little too good to
+
+ align:start position:0%
+problem this seems a little too good to
+ 
+
+ align:start position:0%
+problem this seems a little too good to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+true I insert in the middle of this tree
+
+ align:start position:0%
+true I insert in the middle of this tree
+ 
+
+ align:start position:0%
+true I insert in the middle of this tree
+and then somehow I can magically search
+
+ align:start position:0%
+and then somehow I can magically search
+ 
+
+ align:start position:0%
+and then somehow I can magically search
+and still find the I item even though
+
+ align:start position:0%
+and still find the I item even though
+ 
+
+ align:start position:0%
+and still find the I item even though
+all the indices to the right of that
+
+ align:start position:0%
+all the indices to the right of that
+ 
+
+ align:start position:0%
+all the indices to the right of that
+item incremented by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it's almost true question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer yeah
+
+ align:start position:0%
+answer yeah
+ 
+
+ align:start position:0%
+answer yeah
+because we have to update the SI because
+
+ align:start position:0%
+because we have to update the SI because
+ 
+
+ align:start position:0%
+because we have to update the SI because
+we have to update the sizes right I
+
+ align:start position:0%
+we have to update the sizes right I
+ 
+
+ align:start position:0%
+we have to update the sizes right I
+didn't say how do I compute the size of
+
+ align:start position:0%
+didn't say how do I compute the size of
+ 
+
+ align:start position:0%
+didn't say how do I compute the size of
+the left sub tree so that is the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topic we're almost done this this will
+
+ align:start position:0%
+topic we're almost done this this will
+ 
+
+ align:start position:0%
+topic we're almost done this this will
+actually work it's really quite awesome
+
+ align:start position:0%
+actually work it's really quite awesome
+ 
+
+ align:start position:0%
+actually work it's really quite awesome
+but uh for it to work we need something
+
+ align:start position:0%
+but uh for it to work we need something
+ 
+
+ align:start position:0%
+but uh for it to work we need something
+called sub tree
+
+ align:start position:0%
+called sub tree
+ 
+
+ align:start position:0%
+called sub tree
+augmentation which I'll talk about
+
+ align:start position:0%
+augmentation which I'll talk about
+ 
+
+ align:start position:0%
+augmentation which I'll talk about
+generally and then we'll apply it to
+
+ align:start position:0%
+generally and then we'll apply it to
+ 
+
+ align:start position:0%
+generally and then we'll apply it to
+size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea with subtree augmentation is
+
+ align:start position:0%
+so the idea with subtree augmentation is
+ 
+
+ align:start position:0%
+so the idea with subtree augmentation is
+that uh each node in our binary tree uh
+
+ align:start position:0%
+that uh each node in our binary tree uh
+ 
+
+ align:start position:0%
+that uh each node in our binary tree uh
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+store uh constant number of extra
+
+ align:start position:0%
+store uh constant number of extra
+ 
+
+ align:start position:0%
+store uh constant number of extra
+Fields why
+
+ align:start position:0%
+Fields why
+ 
+
+ align:start position:0%
+Fields why
+not and in particular if these fields
+
+ align:start position:0%
+not and in particular if these fields
+ 
+
+ align:start position:0%
+not and in particular if these fields
+are of a particular type or maybe I'll
+
+ align:start position:0%
+are of a particular type or maybe I'll
+ 
+
+ align:start position:0%
+are of a particular type or maybe I'll
+call them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties I'm going to define a a
+
+ align:start position:0%
+properties I'm going to define a a
+ 
+
+ align:start position:0%
+properties I'm going to define a a
+subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property uh to be something that can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computed from the
+
+ align:start position:0%
+computed from the
+ 
+
+ align:start position:0%
+computed from the
+properties of the nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+children so I should say this is of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node so children are node. left and no.
+
+ align:start position:0%
+node so children are node. left and no.
+ 
+
+ align:start position:0%
+node so children are node. left and no.
+right uh you can also access constant
+
+ align:start position:0%
+right uh you can also access constant
+ 
+
+ align:start position:0%
+right uh you can also access constant
+amount of other stuff for example the
+
+ align:start position:0%
+amount of other stuff for example the
+ 
+
+ align:start position:0%
+amount of other stuff for example the
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+itself uh but the point of a subtree
+
+ align:start position:0%
+itself uh but the point of a subtree
+ 
+
+ align:start position:0%
+itself uh but the point of a subtree
+property is it's downward looking if I
+
+ align:start position:0%
+property is it's downward looking if I
+ 
+
+ align:start position:0%
+property is it's downward looking if I
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and I want to compute some property
+
+ align:start position:0%
+and I want to compute some property
+ 
+
+ align:start position:0%
+and I want to compute some property
+about it call it uh we want to store P
+
+ align:start position:0%
+about it call it uh we want to store P
+ 
+
+ align:start position:0%
+about it call it uh we want to store P
+of the node and suppose we already know
+
+ align:start position:0%
+of the node and suppose we already know
+ 
+
+ align:start position:0%
+of the node and suppose we already know
+p over here the property computed for
+
+ align:start position:0%
+p over here the property computed for
+ 
+
+ align:start position:0%
+p over here the property computed for
+the left subtree or for the left node
+
+ align:start position:0%
+the left subtree or for the left node
+ 
+
+ align:start position:0%
+the left subtree or for the left node
+and we already know the property for the
+
+ align:start position:0%
+and we already know the property for the
+ 
+
+ align:start position:0%
+and we already know the property for the
+right node then uh what I'd like is for
+
+ align:start position:0%
+right node then uh what I'd like is for
+ 
+
+ align:start position:0%
+right node then uh what I'd like is for
+this to be computable in constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so I can compute P of this node
+
+ align:start position:0%
+time so I can compute P of this node
+ 
+
+ align:start position:0%
+time so I can compute P of this node
+given P of the left node and P of the
+
+ align:start position:0%
+given P of the left node and P of the
+ 
+
+ align:start position:0%
+given P of the left node and P of the
+right node that's a sub tree property
+
+ align:start position:0%
+right node that's a sub tree property
+ 
+
+ align:start position:0%
+right node that's a sub tree property
+now in
+
+ align:start position:0%
+now in
+ 
+
+ align:start position:0%
+now in
+particular size is a sub tree
+
+ align:start position:0%
+particular size is a sub tree
+ 
+
+ align:start position:0%
+particular size is a sub tree
+property why
+
+ align:start position:0%
+property why
+ 
+
+ align:start position:0%
+property why
+because I can write this kind of
+
+ align:start position:0%
+because I can write this kind of
+ 
+
+ align:start position:0%
+because I can write this kind of
+recurrence uh node.
+
+ align:start position:0%
+recurrence uh node.
+ 
+
+ align:start position:0%
+recurrence uh node.
+size equals no do left do
+
+ align:start position:0%
+size equals no do left do
+ 
+
+ align:start position:0%
+size equals no do left do
+size is very tedious to
+
+ align:start position:0%
+size is very tedious to
+ 
+
+ align:start position:0%
+size is very tedious to
+write plus no do right. size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus one thank
+
+ align:start position:0%
+plus one thank
+ 
+
+ align:start position:0%
+plus one thank
+you size of the sub of the entire sub
+
+ align:start position:0%
+you size of the sub of the entire sub
+ 
+
+ align:start position:0%
+you size of the sub of the entire sub
+tree here called node um is the size of
+
+ align:start position:0%
+tree here called node um is the size of
+ 
+
+ align:start position:0%
+tree here called node um is the size of
+the left sub tree plus the size of the
+
+ align:start position:0%
+the left sub tree plus the size of the
+ 
+
+ align:start position:0%
+the left sub tree plus the size of the
+right sub tree plus one for that node
+
+ align:start position:0%
+right sub tree plus one for that node
+ 
+
+ align:start position:0%
+right sub tree plus one for that node
+itself okay so this is an update rule
+
+ align:start position:0%
+itself okay so this is an update rule
+ 
+
+ align:start position:0%
+itself okay so this is an update rule
+takes constant time to evaluate it's two
+
+ align:start position:0%
+takes constant time to evaluate it's two
+ 
+
+ align:start position:0%
+takes constant time to evaluate it's two
+additions sorry my T's look kind of like
+
+ align:start position:0%
+additions sorry my T's look kind of like
+ 
+
+ align:start position:0%
+additions sorry my T's look kind of like
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signs make the pluses a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger okay so we're summing those three
+
+ align:start position:0%
+bigger okay so we're summing those three
+ 
+
+ align:start position:0%
+bigger okay so we're summing those three
+things boom we can get node do size so I
+
+ align:start position:0%
+things boom we can get node do size so I
+ 
+
+ align:start position:0%
+things boom we can get node do size so I
+claim that uh if as long as my property
+
+ align:start position:0%
+claim that uh if as long as my property
+ 
+
+ align:start position:0%
+claim that uh if as long as my property
+has this feature I can maintain it
+
+ align:start position:0%
+has this feature I can maintain it
+ 
+
+ align:start position:0%
+has this feature I can maintain it
+dynamically as I'm changing the
+
+ align:start position:0%
+dynamically as I'm changing the
+ 
+
+ align:start position:0%
+dynamically as I'm changing the
+tree okay now this is a little bit of a
+
+ align:start position:0%
+tree okay now this is a little bit of a
+ 
+
+ align:start position:0%
+tree okay now this is a little bit of a
+forward reference because we haven't
+
+ align:start position:0%
+forward reference because we haven't
+ 
+
+ align:start position:0%
+forward reference because we haven't
+said exactly how we're going to change
+
+ align:start position:0%
+said exactly how we're going to change
+ 
+
+ align:start position:0%
+said exactly how we're going to change
+the tree yet but uh question if um no SI
+
+ align:start position:0%
+the tree yet but uh question if um no SI
+ 
+
+ align:start position:0%
+the tree yet but uh question if um no SI
+is recursive yeah how is it happen would
+
+ align:start position:0%
+is recursive yeah how is it happen would
+ 
+
+ align:start position:0%
+is recursive yeah how is it happen would
+okay why is this okay good question so
+
+ align:start position:0%
+okay why is this okay good question so
+ 
+
+ align:start position:0%
+okay why is this okay good question so
+one natural way you can think of this as
+
+ align:start position:0%
+one natural way you can think of this as
+ 
+
+ align:start position:0%
+one natural way you can think of this as
+a recursion which gives you a recursive
+
+ align:start position:0%
+a recursion which gives you a recursive
+ 
+
+ align:start position:0%
+a recursion which gives you a recursive
+algorithm uh so I wrote but I didn't
+
+ align:start position:0%
+algorithm uh so I wrote but I didn't
+ 
+
+ align:start position:0%
+algorithm uh so I wrote but I didn't
+write it but I could have written size
+
+ align:start position:0%
+write it but I could have written size
+ 
+
+ align:start position:0%
+write it but I could have written size
+of node equals this size of node. left
+
+ align:start position:0%
+of node equals this size of node. left
+ 
+
+ align:start position:0%
+of node equals this size of node. left
+plus and that would give you a linear
+
+ align:start position:0%
+plus and that would give you a linear
+ 
+
+ align:start position:0%
+plus and that would give you a linear
+time algorithm to count the size and if
+
+ align:start position:0%
+time algorithm to count the size and if
+ 
+
+ align:start position:0%
+time algorithm to count the size and if
+you don't have any information that
+
+ align:start position:0%
+you don't have any information that
+ 
+
+ align:start position:0%
+you don't have any information that
+is what you would do and that would be
+
+ align:start position:0%
+is what you would do and that would be
+ 
+
+ align:start position:0%
+is what you would do and that would be
+very painful so that would would make
+
+ align:start position:0%
+very painful so that would would make
+ 
+
+ align:start position:0%
+very painful so that would would make
+this algorithm really slow if I'm
+
+ align:start position:0%
+this algorithm really slow if I'm
+ 
+
+ align:start position:0%
+this algorithm really slow if I'm
+calling sizes a recursive function it's
+
+ align:start position:0%
+calling sizes a recursive function it's
+ 
+
+ align:start position:0%
+calling sizes a recursive function it's
+bad uh what I'm instead doing is storing
+
+ align:start position:0%
+bad uh what I'm instead doing is storing
+ 
+
+ align:start position:0%
+bad uh what I'm instead doing is storing
+the sizes on every single
+
+ align:start position:0%
+the sizes on every single
+ 
+
+ align:start position:0%
+the sizes on every single
+node okay and precomputing this so in
+
+ align:start position:0%
+node okay and precomputing this so in
+ 
+
+ align:start position:0%
+node okay and precomputing this so in
+fact I'm going to Define uh size of node
+
+ align:start position:0%
+fact I'm going to Define uh size of node
+ 
+
+ align:start position:0%
+fact I'm going to Define uh size of node
+in so this is the definition
+
+ align:start position:0%
+in so this is the definition
+ 
+
+ align:start position:0%
+in so this is the definition
+mathematically but the algorithm for
+
+ align:start position:0%
+mathematically but the algorithm for
+ 
+
+ align:start position:0%
+mathematically but the algorithm for
+this function is just going to be return
+
+ align:start position:0%
+this function is just going to be return
+ 
+
+ align:start position:0%
+this function is just going to be return
+node. size okay so that's constant time
+
+ align:start position:0%
+node. size okay so that's constant time
+ 
+
+ align:start position:0%
+node. size okay so that's constant time
+so I the challenge now is I have to keep
+
+ align:start position:0%
+so I the challenge now is I have to keep
+ 
+
+ align:start position:0%
+so I the challenge now is I have to keep
+these sizes up to dat no matter what I
+
+ align:start position:0%
+these sizes up to dat no matter what I
+ 
+
+ align:start position:0%
+these sizes up to dat no matter what I
+do to the tree and you could look back
+
+ align:start position:0%
+do to the tree and you could look back
+ 
+
+ align:start position:0%
+do to the tree and you could look back
+at last lecture and see okay what were
+
+ align:start position:0%
+at last lecture and see okay what were
+ 
+
+ align:start position:0%
+at last lecture and see okay what were
+all the changes that I did in a tree uh
+
+ align:start position:0%
+all the changes that I did in a tree uh
+ 
+
+ align:start position:0%
+all the changes that I did in a tree uh
+we only did changes during insert and
+
+ align:start position:0%
+we only did changes during insert and
+ 
+
+ align:start position:0%
+we only did changes during insert and
+delete and I will just claim to you when
+
+ align:start position:0%
+delete and I will just claim to you when
+ 
+
+ align:start position:0%
+delete and I will just claim to you when
+we did uh insert and
+
+ align:start position:0%
+we did uh insert and
+ 
+
+ align:start position:0%
+we did uh insert and
+delete what they ended up
+
+ align:start position:0%
+delete what they ended up
+ 
+
+ align:start position:0%
+delete what they ended up
+doing uh in the
+
+ align:start position:0%
+doing uh in the
+ 
+
+ align:start position:0%
+doing uh in the
+end they add or
+
+ align:start position:0%
+end they add or
+ 
+
+ align:start position:0%
+end they add or
+remove a leaf of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree okay remember Leaf was a node with
+
+ align:start position:0%
+tree okay remember Leaf was a node with
+ 
+
+ align:start position:0%
+tree okay remember Leaf was a node with
+no children um so let's just think about
+
+ align:start position:0%
+no children um so let's just think about
+ 
+
+ align:start position:0%
+no children um so let's just think about
+if I add a new Leaf in a tree here's a
+
+ align:start position:0%
+if I add a new Leaf in a tree here's a
+ 
+
+ align:start position:0%
+if I add a new Leaf in a tree here's a
+tree suppose I add a leaf here which sub
+
+ align:start position:0%
+tree suppose I add a leaf here which sub
+ 
+
+ align:start position:0%
+tree suppose I add a leaf here which sub
+trees
+
+ align:start position:0%
+trees
+ 
+
+ align:start position:0%
+trees
+change well which sub trees contain that
+
+ align:start position:0%
+change well which sub trees contain that
+ 
+
+ align:start position:0%
+change well which sub trees contain that
+node it it is its own new sub tree then
+
+ align:start position:0%
+node it it is its own new sub tree then
+ 
+
+ align:start position:0%
+node it it is its own new sub tree then
+its parents it's in it's in its parents
+
+ align:start position:0%
+its parents it's in it's in its parents
+ 
+
+ align:start position:0%
+its parents it's in it's in its parents
+sub tree and its grandparents sub tree
+
+ align:start position:0%
+sub tree and its grandparents sub tree
+ 
+
+ align:start position:0%
+sub tree and its grandparents sub tree
+and and the overall sub tree okay in
+
+ align:start position:0%
+and and the overall sub tree okay in
+ 
+
+ align:start position:0%
+and and the overall sub tree okay in
+general these nodes are called the
+
+ align:start position:0%
+general these nodes are called the
+ 
+
+ align:start position:0%
+general these nodes are called the
+ancestors of this node that we added and
+
+ align:start position:0%
+ancestors of this node that we added and
+ 
+
+ align:start position:0%
+ancestors of this node that we added and
+those are the ones that update this sub
+
+ align:start position:0%
+those are the ones that update this sub
+ 
+
+ align:start position:0%
+those are the ones that update this sub
+tree over here didn't change it didn't
+
+ align:start position:0%
+tree over here didn't change it didn't
+ 
+
+ align:start position:0%
+tree over here didn't change it didn't
+change size and because it's a sub tree
+
+ align:start position:0%
+change size and because it's a sub tree
+ 
+
+ align:start position:0%
+change size and because it's a sub tree
+property no subtree property will change
+
+ align:start position:0%
+property no subtree property will change
+ 
+
+ align:start position:0%
+property no subtree property will change
+over here because the sub tree was
+
+ align:start position:0%
+over here because the sub tree was
+ 
+
+ align:start position:0%
+over here because the sub tree was
+untouched okay so
+
+ align:start position:0%
+untouched okay so
+ 
+
+ align:start position:0%
+untouched okay so
+um when I touch this guy I just have to
+
+ align:start position:0%
+um when I touch this guy I just have to
+ 
+
+ align:start position:0%
+um when I touch this guy I just have to
+update the sub tree property here update
+
+ align:start position:0%
+update the sub tree property here update
+ 
+
+ align:start position:0%
+update the sub tree property here update
+the subtree property here update the
+
+ align:start position:0%
+the subtree property here update the
+ 
+
+ align:start position:0%
+the subtree property here update the
+subtree property here how many of these
+
+ align:start position:0%
+subtree property here how many of these
+ 
+
+ align:start position:0%
+subtree property here how many of these
+are there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah H I'll say order H to be safe but I
+
+ align:start position:0%
+yeah H I'll say order H to be safe but I
+ 
+
+ align:start position:0%
+yeah H I'll say order H to be safe but I
+think it's exactly H um so also when I
+
+ align:start position:0%
+think it's exactly H um so also when I
+ 
+
+ align:start position:0%
+think it's exactly H um so also when I
+remove a leaf the same thing if I remove
+
+ align:start position:0%
+remove a leaf the same thing if I remove
+ 
+
+ align:start position:0%
+remove a leaf the same thing if I remove
+this Leaf then the the sub trees that
+
+ align:start position:0%
+this Leaf then the the sub trees that
+ 
+
+ align:start position:0%
+this Leaf then the the sub trees that
+change are exactly its former
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ancestors
+
+ align:start position:0%
+ancestors
+ 
+
+ align:start position:0%
+ancestors
+uh cool so
+
+ align:start position:0%
+uh cool so
+ 
+
+ align:start position:0%
+uh cool so
+um we're going to update those order
+
+ align:start position:0%
+um we're going to update those order
+ 
+
+ align:start position:0%
+um we're going to update those order
+H uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ancestors um in
+
+ align:start position:0%
+ancestors um in
+ 
+
+ align:start position:0%
+ancestors um in
+order up the
+
+ align:start position:0%
+order up the
+ 
+
+ align:start position:0%
+order up the
+tree so what do I mean by update I mean
+
+ align:start position:0%
+tree so what do I mean by update I mean
+ 
+
+ align:start position:0%
+tree so what do I mean by update I mean
+apply this rule for sub for size it's
+
+ align:start position:0%
+apply this rule for sub for size it's
+ 
+
+ align:start position:0%
+apply this rule for sub for size it's
+this rule but for in general the subtree
+
+ align:start position:0%
+this rule but for in general the subtree
+ 
+
+ align:start position:0%
+this rule but for in general the subtree
+property gives me an update rule that
+
+ align:start position:0%
+property gives me an update rule that
+ 
+
+ align:start position:0%
+property gives me an update rule that
+takes constant time and so I'm going to
+
+ align:start position:0%
+takes constant time and so I'm going to
+ 
+
+ align:start position:0%
+takes constant time and so I'm going to
+apply that update rule to this node
+
+ align:start position:0%
+apply that update rule to this node
+ 
+
+ align:start position:0%
+apply that update rule to this node
+which will fix whatever property is
+
+ align:start position:0%
+which will fix whatever property is
+ 
+
+ align:start position:0%
+which will fix whatever property is
+stored in there maybe there's more than
+
+ align:start position:0%
+stored in there maybe there's more than
+ 
+
+ align:start position:0%
+stored in there maybe there's more than
+one property and then I'll apply it to
+
+ align:start position:0%
+one property and then I'll apply it to
+ 
+
+ align:start position:0%
+one property and then I'll apply it to
+this node and because this is already
+
+ align:start position:0%
+this node and because this is already
+ 
+
+ align:start position:0%
+this node and because this is already
+correct by induction and this is already
+
+ align:start position:0%
+correct by induction and this is already
+ 
+
+ align:start position:0%
+correct by induction and this is already
+correct because I didn't touch this
+
+ align:start position:0%
+correct because I didn't touch this
+ 
+
+ align:start position:0%
+correct because I didn't touch this
+subre it's unchanged then I can update
+
+ align:start position:0%
+subre it's unchanged then I can update
+ 
+
+ align:start position:0%
+subre it's unchanged then I can update
+the value at this node the property at
+
+ align:start position:0%
+the value at this node the property at
+ 
+
+ align:start position:0%
+the value at this node the property at
+this node in constant time then I update
+
+ align:start position:0%
+this node in constant time then I update
+ 
+
+ align:start position:0%
+this node in constant time then I update
+this one and because this one is already
+
+ align:start position:0%
+this one and because this one is already
+ 
+
+ align:start position:0%
+this one and because this one is already
+correct by induction and this one is
+
+ align:start position:0%
+correct by induction and this one is
+ 
+
+ align:start position:0%
+correct by induction and this one is
+already correct because this sub tree is
+
+ align:start position:0%
+already correct because this sub tree is
+ 
+
+ align:start position:0%
+already correct because this sub tree is
+unchanged I can update the property
+
+ align:start position:0%
+unchanged I can update the property
+ 
+
+ align:start position:0%
+unchanged I can update the property
+correctly here in constant time okay so
+
+ align:start position:0%
+correctly here in constant time okay so
+ 
+
+ align:start position:0%
+correctly here in constant time okay so
+when I make a change in order H time
+
+ align:start position:0%
+when I make a change in order H time
+ 
+
+ align:start position:0%
+when I make a change in order H time
+because I'm making H calls to this
+
+ align:start position:0%
+because I'm making H calls to this
+ 
+
+ align:start position:0%
+because I'm making H calls to this
+constant time algorithm I can update a
+
+ align:start position:0%
+constant time algorithm I can update a
+ 
+
+ align:start position:0%
+constant time algorithm I can update a
+constant number of sub tree
+
+ align:start position:0%
+constant number of sub tree
+ 
+
+ align:start position:0%
+constant number of sub tree
+properties this is very powerful data
+
+ align:start position:0%
+properties this is very powerful data
+ 
+
+ align:start position:0%
+properties this is very powerful data
+structure argumentation is super useful
+
+ align:start position:0%
+structure argumentation is super useful
+ 
+
+ align:start position:0%
+structure argumentation is super useful
+you will use it on your problem set we
+
+ align:start position:0%
+you will use it on your problem set we
+ 
+
+ align:start position:0%
+you will use it on your problem set we
+will use it again
+
+ align:start position:0%
+will use it again
+ 
+
+ align:start position:0%
+will use it again
+today let me give you some examples of
+
+ align:start position:0%
+today let me give you some examples of
+ 
+
+ align:start position:0%
+today let me give you some examples of
+sub tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties they could would be uh common
+
+ align:start position:0%
+properties they could would be uh common
+ 
+
+ align:start position:0%
+properties they could would be uh common
+ones are like the sum or the product or
+
+ align:start position:0%
+ones are like the sum or the product or
+ 
+
+ align:start position:0%
+ones are like the sum or the product or
+the Min or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+max or sum of squares or all sorts of
+
+ align:start position:0%
+max or sum of squares or all sorts of
+ 
+
+ align:start position:0%
+max or sum of squares or all sorts of
+things of
+
+ align:start position:0%
+things of
+ 
+
+ align:start position:0%
+things of
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feature of every node in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree okay in fact
+
+ align:start position:0%
+subtree okay in fact
+ 
+
+ align:start position:0%
+subtree okay in fact
+uh sub tree size is an example of such a
+
+ align:start position:0%
+uh sub tree size is an example of such a
+ 
+
+ align:start position:0%
+uh sub tree size is an example of such a
+thing it is the sum over all nodes in
+
+ align:start position:0%
+thing it is the sum over all nodes in
+ 
+
+ align:start position:0%
+thing it is the sum over all nodes in
+the sub tree of the value one okay
+
+ align:start position:0%
+the sub tree of the value one okay
+ 
+
+ align:start position:0%
+the sub tree of the value one okay
+that's another way to say count the
+
+ align:start position:0%
+that's another way to say count the
+ 
+
+ align:start position:0%
+that's another way to say count the
+number of nodes okay but you could also
+
+ align:start position:0%
+number of nodes okay but you could also
+ 
+
+ align:start position:0%
+number of nodes okay but you could also
+say what's the sum of the keys in these
+
+ align:start position:0%
+say what's the sum of the keys in these
+ 
+
+ align:start position:0%
+say what's the sum of the keys in these
+nodes or you could say what's the
+
+ align:start position:0%
+nodes or you could say what's the
+ 
+
+ align:start position:0%
+nodes or you could say what's the
+maximum key in these nodes or you could
+
+ align:start position:0%
+maximum key in these nodes or you could
+ 
+
+ align:start position:0%
+maximum key in these nodes or you could
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+uh um what is the
+
+ align:start position:0%
+uh um what is the
+ 
+
+ align:start position:0%
+uh um what is the
+maximum value in these notes you can
+
+ align:start position:0%
+maximum value in these notes you can
+ 
+
+ align:start position:0%
+maximum value in these notes you can
+take any property it doesn't have to be
+
+ align:start position:0%
+take any property it doesn't have to be
+ 
+
+ align:start position:0%
+take any property it doesn't have to be
+key it doesn't have to be anything in
+
+ align:start position:0%
+key it doesn't have to be anything in
+ 
+
+ align:start position:0%
+key it doesn't have to be anything in
+particular it's very powerful you can
+
+ align:start position:0%
+particular it's very powerful you can
+ 
+
+ align:start position:0%
+particular it's very powerful you can
+take all sums products and Main maintain
+
+ align:start position:0%
+take all sums products and Main maintain
+ 
+
+ align:start position:0%
+take all sums products and Main maintain
+them as long as they're downward looking
+
+ align:start position:0%
+them as long as they're downward looking
+ 
+
+ align:start position:0%
+them as long as they're downward looking
+as long as you're only thinking about
+
+ align:start position:0%
+as long as you're only thinking about
+ 
+
+ align:start position:0%
+as long as you're only thinking about
+the sub
+
+ align:start position:0%
+the sub
+ 
+
+ align:start position:0%
+the sub
+tree okay uh some examples of things you
+
+ align:start position:0%
+tree okay uh some examples of things you
+ 
+
+ align:start position:0%
+tree okay uh some examples of things you
+cannot
+
+ align:start position:0%
+cannot
+ 
+
+ align:start position:0%
+cannot
+maintain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+not a nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+index so if you get a little bit too
+
+ align:start position:0%
+index so if you get a little bit too
+ 
+
+ align:start position:0%
+index so if you get a little bit too
+excited about augmentation you might
+
+ align:start position:0%
+excited about augmentation you might
+ 
+
+ align:start position:0%
+excited about augmentation you might
+think oh it could do everything right I
+
+ align:start position:0%
+think oh it could do everything right I
+ 
+
+ align:start position:0%
+think oh it could do everything right I
+needed to support subtree at or let's
+
+ align:start position:0%
+needed to support subtree at or let's
+ 
+
+ align:start position:0%
+needed to support subtree at or let's
+just say uh get at globally I wanted to
+
+ align:start position:0%
+just say uh get at globally I wanted to
+ 
+
+ align:start position:0%
+just say uh get at globally I wanted to
+know what is the I node in my tree well
+
+ align:start position:0%
+know what is the I node in my tree well
+ 
+
+ align:start position:0%
+know what is the I node in my tree well
+I'll just use data structure
+
+ align:start position:0%
+I'll just use data structure
+ 
+
+ align:start position:0%
+I'll just use data structure
+augumentation and store in every node
+
+ align:start position:0%
+augumentation and store in every node
+ 
+
+ align:start position:0%
+augumentation and store in every node
+what is its index zero through n minus
+
+ align:start position:0%
+what is its index zero through n minus
+ 
+
+ align:start position:0%
+what is its index zero through n minus
+one I can't maintain that efficiently
+
+ align:start position:0%
+one I can't maintain that efficiently
+ 
+
+ align:start position:0%
+one I can't maintain that efficiently
+because if I insert at the beginning of
+
+ align:start position:0%
+because if I insert at the beginning of
+ 
+
+ align:start position:0%
+because if I insert at the beginning of
+my traversal order then all the indices
+
+ align:start position:0%
+my traversal order then all the indices
+ 
+
+ align:start position:0%
+my traversal order then all the indices
+change right so that that's an example
+
+ align:start position:0%
+change right so that that's an example
+ 
+
+ align:start position:0%
+change right so that that's an example
+of a of a edit so if I insert a new Noe
+
+ align:start position:0%
+of a of a edit so if I insert a new Noe
+ 
+
+ align:start position:0%
+of a of a edit so if I insert a new Noe
+over here so this guy's index was Zero
+
+ align:start position:0%
+over here so this guy's index was Zero
+ 
+
+ align:start position:0%
+over here so this guy's index was Zero
+now it's one this guy's index was one
+
+ align:start position:0%
+now it's one this guy's index was one
+ 
+
+ align:start position:0%
+now it's one this guy's index was one
+now it's two this was two two now it's
+
+ align:start position:0%
+now it's two this was two two now it's
+ 
+
+ align:start position:0%
+now it's two this was two two now it's
+three and so on every node changes its
+
+ align:start position:0%
+three and so on every node changes its
+ 
+
+ align:start position:0%
+three and so on every node changes its
+index index is not a subtree property
+
+ align:start position:0%
+index index is not a subtree property
+ 
+
+ align:start position:0%
+index index is not a subtree property
+and that's why we can't maintain it
+
+ align:start position:0%
+and that's why we can't maintain it
+ 
+
+ align:start position:0%
+and that's why we can't maintain it
+because it depends on all of the nodes
+
+ align:start position:0%
+because it depends on all of the nodes
+ 
+
+ align:start position:0%
+because it depends on all of the nodes
+in the tree or it depends on all the
+
+ align:start position:0%
+in the tree or it depends on all the
+ 
+
+ align:start position:0%
+in the tree or it depends on all the
+nodes to its left all the predecessors
+
+ align:start position:0%
+nodes to its left all the predecessors
+ 
+
+ align:start position:0%
+nodes to its left all the predecessors
+so for example this guy's index depends
+
+ align:start position:0%
+so for example this guy's index depends
+ 
+
+ align:start position:0%
+so for example this guy's index depends
+on how many nodes are over here on the
+
+ align:start position:0%
+on how many nodes are over here on the
+ 
+
+ align:start position:0%
+on how many nodes are over here on the
+left which is not in the sub tree of
+
+ align:start position:0%
+left which is not in the sub tree of
+ 
+
+ align:start position:0%
+left which is not in the sub tree of
+that Noe so that's where you have to be
+
+ align:start position:0%
+that Noe so that's where you have to be
+ 
+
+ align:start position:0%
+that Noe so that's where you have to be
+careful don't use Global properties of
+
+ align:start position:0%
+careful don't use Global properties of
+ 
+
+ align:start position:0%
+careful don't use Global properties of
+the tree you can only use
+
+ align:start position:0%
+the tree you can only use
+ 
+
+ align:start position:0%
+the tree you can only use
+subtree sub tree
+
+ align:start position:0%
+subtree sub tree
+ 
+
+ align:start position:0%
+subtree sub tree
+properties okay another example is uh
+
+ align:start position:0%
+properties okay another example is uh
+ 
+
+ align:start position:0%
+properties okay another example is uh
+depth depth is annoying to
+
+ align:start position:0%
+depth depth is annoying to
+ 
+
+ align:start position:0%
+depth depth is annoying to
+maintain uh but it's not obvious why yet
+
+ align:start position:0%
+maintain uh but it's not obvious why yet
+ 
+
+ align:start position:0%
+maintain uh but it's not obvious why yet
+we will see that in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment okay the rest of today is about
+
+ align:start position:0%
+moment okay the rest of today is about
+ 
+
+ align:start position:0%
+moment okay the rest of today is about
+going from order H to order log n which
+
+ align:start position:0%
+going from order H to order log n which
+ 
+
+ align:start position:0%
+going from order H to order log n which
+is what this slide is showing us so at
+
+ align:start position:0%
+is what this slide is showing us so at
+ 
+
+ align:start position:0%
+is what this slide is showing us so at
+this point you should believe that we
+
+ align:start position:0%
+this point you should believe that we
+ 
+
+ align:start position:0%
+this point you should believe that we
+can do all of the sequence data
+
+ align:start position:0%
+can do all of the sequence data
+ 
+
+ align:start position:0%
+can do all of the sequence data
+structure operations in order H time
+
+ align:start position:0%
+structure operations in order H time
+ 
+
+ align:start position:0%
+structure operations in order H time
+except for build and iterate which take
+
+ align:start position:0%
+except for build and iterate which take
+ 
+
+ align:start position:0%
+except for build and iterate which take
+linear time uh and that we can do all of
+
+ align:start position:0%
+linear time uh and that we can do all of
+ 
+
+ align:start position:0%
+linear time uh and that we can do all of
+the set operations in order H time
+
+ align:start position:0%
+the set operations in order H time
+ 
+
+ align:start position:0%
+the set operations in order H time
+except build and iterate which Take N
+
+ align:start position:0%
+except build and iterate which Take N
+ 
+
+ align:start position:0%
+except build and iterate which Take N
+log n and n respectively and our goal is
+
+ align:start position:0%
+log n and n respectively and our goal is
+ 
+
+ align:start position:0%
+log n and n respectively and our goal is
+to now
+
+ align:start position:0%
+to now
+ 
+
+ align:start position:0%
+to now
+bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh H by log n we know it's possible at
+
+ align:start position:0%
+uh H by log n we know it's possible at
+ 
+
+ align:start position:0%
+uh H by log n we know it's possible at
+some level because there are
+
+ align:start position:0%
+some level because there are
+ 
+
+ align:start position:0%
+some level because there are
+trees that have logarithmic height
+
+ align:start position:0%
+trees that have logarithmic height
+ 
+
+ align:start position:0%
+trees that have logarithmic height
+that's like this Perfect Tree
+
+ align:start position:0%
+that's like this Perfect Tree
+ 
+
+ align:start position:0%
+that's like this Perfect Tree
+here but we also know we have to be
+
+ align:start position:0%
+here but we also know we have to be
+ 
+
+ align:start position:0%
+here but we also know we have to be
+careful because there are some bad trees
+
+ align:start position:0%
+careful because there are some bad trees
+ 
+
+ align:start position:0%
+careful because there are some bad trees
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain so
+
+ align:start position:0%
+chain so
+ 
+
+ align:start position:0%
+chain so
+um if H equals log n we call this a
+
+ align:start position:0%
+um if H equals log n we call this a
+ 
+
+ align:start position:0%
+um if H equals log n we call this a
+balanced binary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree there are many balanced binary
+
+ align:start position:0%
+tree there are many balanced binary
+ 
+
+ align:start position:0%
+tree there are many balanced binary
+trees in the world maybe a dozen or
+
+ align:start position:0%
+trees in the world maybe a dozen or
+ 
+
+ align:start position:0%
+trees in the world maybe a dozen or
+two a lot of different data structures
+
+ align:start position:0%
+two a lot of different data structures
+ 
+
+ align:start position:0%
+two a lot of different data structures
+question hi you um you said like not to
+
+ align:start position:0%
+question hi you um you said like not to
+ 
+
+ align:start position:0%
+question hi you um you said like not to
+think about things on a global level
+
+ align:start position:0%
+think about things on a global level
+ 
+
+ align:start position:0%
+think about things on a global level
+think of them at a sub level can you
+
+ align:start position:0%
+think of them at a sub level can you
+ 
+
+ align:start position:0%
+think of them at a sub level can you
+explain what
+
+ align:start position:0%
+explain what
+ 
+
+ align:start position:0%
+explain what
+that okay what does it mean for property
+
+ align:start position:0%
+that okay what does it mean for property
+ 
+
+ align:start position:0%
+that okay what does it mean for property
+to be uh local to a sub tree versus
+
+ align:start position:0%
+to be uh local to a sub tree versus
+ 
+
+ align:start position:0%
+to be uh local to a sub tree versus
+global the best answer is this
+
+ align:start position:0%
+global the best answer is this
+ 
+
+ align:start position:0%
+global the best answer is this
+definition but that's maybe not the most
+
+ align:start position:0%
+definition but that's maybe not the most
+ 
+
+ align:start position:0%
+definition but that's maybe not the most
+intuitive definition this is what I mean
+
+ align:start position:0%
+intuitive definition this is what I mean
+ 
+
+ align:start position:0%
+intuitive definition this is what I mean
+something that can be computed just
+
+ align:start position:0%
+something that can be computed just
+ 
+
+ align:start position:0%
+something that can be computed just
+knowing information about your left and
+
+ align:start position:0%
+knowing information about your left and
+ 
+
+ align:start position:0%
+knowing information about your left and
+right children that is the meaning of
+
+ align:start position:0%
+right children that is the meaning of
+ 
+
+ align:start position:0%
+right children that is the meaning of
+subre property and those are the only
+
+ align:start position:0%
+subre property and those are the only
+ 
+
+ align:start position:0%
+subre property and those are the only
+things you're allowed to maintain
+
+ align:start position:0%
+things you're allowed to maintain
+ 
+
+ align:start position:0%
+things you're allowed to maintain
+because those are the only
+
+ align:start position:0%
+because those are the only
+ 
+
+ align:start position:0%
+because those are the only
+things uh that are easy to update by
+
+ align:start position:0%
+things uh that are easy to update by
+ 
+
+ align:start position:0%
+things uh that are easy to update by
+walking up this path and the contrast is
+
+ align:start position:0%
+walking up this path and the contrast is
+ 
+
+ align:start position:0%
+walking up this path and the contrast is
+that a global property like
+
+ align:start position:0%
+that a global property like
+ 
+
+ align:start position:0%
+that a global property like
+index I it's Global in particular
+
+ align:start position:0%
+index I it's Global in particular
+ 
+
+ align:start position:0%
+index I it's Global in particular
+because I can do one change add one no
+
+ align:start position:0%
+because I can do one change add one no
+ 
+
+ align:start position:0%
+because I can do one change add one no
+node and all of the nodes properties
+
+ align:start position:0%
+node and all of the nodes properties
+ 
+
+ align:start position:0%
+node and all of the nodes properties
+change so that's an extreme example of
+
+ align:start position:0%
+change so that's an extreme example of
+ 
+
+ align:start position:0%
+change so that's an extreme example of
+global we want this very particular
+
+ align:start position:0%
+global we want this very particular
+ 
+
+ align:start position:0%
+global we want this very particular
+notion of
+
+ align:start position:0%
+notion of
+ 
+
+ align:start position:0%
+notion of
+local uh because that's what we can
+
+ align:start position:0%
+local uh because that's what we can
+ 
+
+ align:start position:0%
+local uh because that's what we can
+actually afford to recompute hopefully
+
+ align:start position:0%
+actually afford to recompute hopefully
+ 
+
+ align:start position:0%
+actually afford to recompute hopefully
+that clarifies
+
+ align:start position:0%
+that clarifies
+ 
+
+ align:start position:0%
+that clarifies
+yeah doesn't size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're right that if we added oh no
+
+ align:start position:0%
+you're right that if we added oh no
+ 
+
+ align:start position:0%
+you're right that if we added oh no
+let's okay let's think about that if we
+
+ align:start position:0%
+let's okay let's think about that if we
+ 
+
+ align:start position:0%
+let's okay let's think about that if we
+added a new parent to the tree this is
+
+ align:start position:0%
+added a new parent to the tree this is
+ 
+
+ align:start position:0%
+added a new parent to the tree this is
+not something that we've ever done um
+
+ align:start position:0%
+not something that we've ever done um
+ 
+
+ align:start position:0%
+not something that we've ever done um
+but even if we did that which sub trees
+
+ align:start position:0%
+but even if we did that which sub trees
+ 
+
+ align:start position:0%
+but even if we did that which sub trees
+change only this
+
+ align:start position:0%
+change only this
+ 
+
+ align:start position:0%
+change only this
+one right this node it's it's a new
+
+ align:start position:0%
+one right this node it's it's a new
+ 
+
+ align:start position:0%
+one right this node it's it's a new
+totally new sub tree but the sub tree of
+
+ align:start position:0%
+totally new sub tree but the sub tree of
+ 
+
+ align:start position:0%
+totally new sub tree but the sub tree of
+this node is completely unchanged
+
+ align:start position:0%
+this node is completely unchanged
+ 
+
+ align:start position:0%
+this node is completely unchanged
+because sub trees are always downward
+
+ align:start position:0%
+because sub trees are always downward
+ 
+
+ align:start position:0%
+because sub trees are always downward
+looking if I added a new root um I
+
+ align:start position:0%
+looking if I added a new root um I
+ 
+
+ align:start position:0%
+looking if I added a new root um I
+didn't change any sub except for one so
+
+ align:start position:0%
+didn't change any sub except for one so
+ 
+
+ align:start position:0%
+didn't change any sub except for one so
+size is a sube property now there are I
+
+ align:start position:0%
+size is a sube property now there are I
+ 
+
+ align:start position:0%
+size is a sube property now there are I
+mean I can completely redraw the tree
+
+ align:start position:0%
+mean I can completely redraw the tree
+ 
+
+ align:start position:0%
+mean I can completely redraw the tree
+and that's an operation that requires
+
+ align:start position:0%
+and that's an operation that requires
+ 
+
+ align:start position:0%
+and that's an operation that requires
+everything to be recomputed okay so it
+
+ align:start position:0%
+everything to be recomputed okay so it
+ 
+
+ align:start position:0%
+everything to be recomputed okay so it
+is limited exactly what I'm allowed to
+
+ align:start position:0%
+is limited exactly what I'm allowed to
+ 
+
+ align:start position:0%
+is limited exactly what I'm allowed to
+do in the tree but I claim everything
+
+ align:start position:0%
+do in the tree but I claim everything
+ 
+
+ align:start position:0%
+do in the tree but I claim everything
+will do last class and today uh we can
+
+ align:start position:0%
+will do last class and today uh we can
+ 
+
+ align:start position:0%
+will do last class and today uh we can
+afford this
+
+ align:start position:0%
+afford this
+ 
+
+ align:start position:0%
+afford this
+augmentation so it's a feature not of
+
+ align:start position:0%
+augmentation so it's a feature not of
+ 
+
+ align:start position:0%
+augmentation so it's a feature not of
+all binary trees necessarily but the
+
+ align:start position:0%
+all binary trees necessarily but the
+ 
+
+ align:start position:0%
+all binary trees necessarily but the
+ones that we would cover
+
+ align:start position:0%
+ones that we would cover
+ 
+
+ align:start position:0%
+ones that we would cover
+yeah what is a
+
+ align:start position:0%
+yeah what is a
+ 
+
+ align:start position:0%
+yeah what is a
+Min binary binary tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay let's uh this will make a
+
+ align:start position:0%
+yeah okay let's uh this will make a
+ 
+
+ align:start position:0%
+yeah okay let's uh this will make a
+little more sense in a moment when I say
+
+ align:start position:0%
+little more sense in a moment when I say
+ 
+
+ align:start position:0%
+little more sense in a moment when I say
+what we're actually going to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees we
+
+ align:start position:0%
+trees we
+ 
+
+ align:start position:0%
+trees we
+uh we need a new tool for manipulating a
+
+ align:start position:0%
+uh we need a new tool for manipulating a
+ 
+
+ align:start position:0%
+uh we need a new tool for manipulating a
+tree what we've done so far we've done
+
+ align:start position:0%
+tree what we've done so far we've done
+ 
+
+ align:start position:0%
+tree what we've done so far we've done
+some swapping of items and we did adding
+
+ align:start position:0%
+some swapping of items and we did adding
+ 
+
+ align:start position:0%
+some swapping of items and we did adding
+removing a leaf that's not enough we're
+
+ align:start position:0%
+removing a leaf that's not enough we're
+ 
+
+ align:start position:0%
+removing a leaf that's not enough we're
+going to need something else to let us
+
+ align:start position:0%
+going to need something else to let us
+ 
+
+ align:start position:0%
+going to need something else to let us
+guarantee logarithmic
+
+ align:start position:0%
+guarantee logarithmic
+ 
+
+ align:start position:0%
+guarantee logarithmic
+height and that's something else is
+
+ align:start position:0%
+height and that's something else is
+ 
+
+ align:start position:0%
+height and that's something else is
+called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation what does this something else
+
+ align:start position:0%
+rotation what does this something else
+ 
+
+ align:start position:0%
+rotation what does this something else
+need to do this is just a tool for
+
+ align:start position:0%
+need to do this is just a tool for
+ 
+
+ align:start position:0%
+need to do this is just a tool for
+rebalancing the tree so it should not
+
+ align:start position:0%
+rebalancing the tree so it should not
+ 
+
+ align:start position:0%
+rebalancing the tree so it should not
+change the data that's represented by
+
+ align:start position:0%
+change the data that's represented by
+ 
+
+ align:start position:0%
+change the data that's represented by
+the tree what is the data represented by
+
+ align:start position:0%
+the tree what is the data represented by
+ 
+
+ align:start position:0%
+the tree what is the data represented by
+the tree traversal order traversal order
+
+ align:start position:0%
+the tree traversal order traversal order
+ 
+
+ align:start position:0%
+the tree traversal order traversal order
+is sacran where not allowed to touch it
+
+ align:start position:0%
+is sacran where not allowed to touch it
+ 
+
+ align:start position:0%
+is sacran where not allowed to touch it
+it's already defined two different ways
+
+ align:start position:0%
+it's already defined two different ways
+ 
+
+ align:start position:0%
+it's already defined two different ways
+depending on whether you're using a set
+
+ align:start position:0%
+depending on whether you're using a set
+ 
+
+ align:start position:0%
+depending on whether you're using a set
+or sequence so we want to modify the
+
+ align:start position:0%
+or sequence so we want to modify the
+ 
+
+ align:start position:0%
+or sequence so we want to modify the
+tree in a way that doesn't modify the
+
+ align:start position:0%
+tree in a way that doesn't modify the
+ 
+
+ align:start position:0%
+tree in a way that doesn't modify the
+traversal order so this we're exploiting
+
+ align:start position:0%
+traversal order so this we're exploiting
+ 
+
+ align:start position:0%
+traversal order so this we're exploiting
+redundancy if you wrote down the
+
+ align:start position:0%
+redundancy if you wrote down the
+ 
+
+ align:start position:0%
+redundancy if you wrote down the
+traversal order in an array there's
+
+ align:start position:0%
+traversal order in an array there's
+ 
+
+ align:start position:0%
+traversal order in an array there's
+exactly one representation of a given
+
+ align:start position:0%
+exactly one representation of a given
+ 
+
+ align:start position:0%
+exactly one representation of a given
+order but in a tree there's many
+
+ align:start position:0%
+order but in a tree there's many
+ 
+
+ align:start position:0%
+order but in a tree there's many
+representations it could be a long line
+
+ align:start position:0%
+representations it could be a long line
+ 
+
+ align:start position:0%
+representations it could be a long line
+it could be a balanced thing they could
+
+ align:start position:0%
+it could be a balanced thing they could
+ 
+
+ align:start position:0%
+it could be a balanced thing they could
+represent the exact same order on the
+
+ align:start position:0%
+represent the exact same order on the
+ 
+
+ align:start position:0%
+represent the exact same order on the
+nodes if you label them right okay in
+
+ align:start position:0%
+nodes if you label them right okay in
+ 
+
+ align:start position:0%
+nodes if you label them right okay in
+fact they're exponentially many
+
+ align:start position:0%
+fact they're exponentially many
+ 
+
+ align:start position:0%
+fact they're exponentially many
+different representations of the same
+
+ align:start position:0%
+different representations of the same
+ 
+
+ align:start position:0%
+different representations of the same
+thing and we're going to exploit that
+
+ align:start position:0%
+thing and we're going to exploit that
+ 
+
+ align:start position:0%
+thing and we're going to exploit that
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+order and Define this is just a thing
+
+ align:start position:0%
+order and Define this is just a thing
+ 
+
+ align:start position:0%
+order and Define this is just a thing
+you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know me label a x b y
+
+ align:start position:0%
+know me label a x b y
+ 
+
+ align:start position:0%
+know me label a x b y
+c you can tell I've drawn this diagram
+
+ align:start position:0%
+c you can tell I've drawn this diagram
+ 
+
+ align:start position:0%
+c you can tell I've drawn this diagram
+before many many times this is a very
+
+ align:start position:0%
+before many many times this is a very
+ 
+
+ align:start position:0%
+before many many times this is a very
+powerful tool in all tree data
+
+ align:start position:0%
+powerful tool in all tree data
+ 
+
+ align:start position:0%
+powerful tool in all tree data
+structures which are most of data
+
+ align:start position:0%
+structures which are most of data
+ 
+
+ align:start position:0%
+structures which are most of data
+structures uh and they are called right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate of Y and left rotate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x uh so if I have this tree which I'm
+
+ align:start position:0%
+x uh so if I have this tree which I'm
+ 
+
+ align:start position:0%
+x uh so if I have this tree which I'm
+just blackboxing some of the sub into
+
+ align:start position:0%
+just blackboxing some of the sub into
+ 
+
+ align:start position:0%
+just blackboxing some of the sub into
+little triangles if I have a node and it
+
+ align:start position:0%
+little triangles if I have a node and it
+ 
+
+ align:start position:0%
+little triangles if I have a node and it
+it has a left child then I'm allowed to
+
+ align:start position:0%
+it has a left child then I'm allowed to
+ 
+
+ align:start position:0%
+it has a left child then I'm allowed to
+right rotate this Edge which means take
+
+ align:start position:0%
+right rotate this Edge which means take
+ 
+
+ align:start position:0%
+right rotate this Edge which means take
+this Edge and go like this 90 Dees kind
+
+ align:start position:0%
+this Edge and go like this 90 Dees kind
+ 
+
+ align:start position:0%
+this Edge and go like this 90 Dees kind
+of uh or you could just think of it as
+
+ align:start position:0%
+of uh or you could just think of it as
+ 
+
+ align:start position:0%
+of uh or you could just think of it as
+rewriting it this way now you might also
+
+ align:start position:0%
+rewriting it this way now you might also
+ 
+
+ align:start position:0%
+rewriting it this way now you might also
+keep in track of the parent pointer
+
+ align:start position:0%
+keep in track of the parent pointer
+ 
+
+ align:start position:0%
+keep in track of the parent pointer
+parent pointer uh moves around before
+
+ align:start position:0%
+parent pointer uh moves around before
+ 
+
+ align:start position:0%
+parent pointer uh moves around before
+this was the parent of Y now it's the
+
+ align:start position:0%
+this was the parent of Y now it's the
+ 
+
+ align:start position:0%
+this was the parent of Y now it's the
+parent of
+
+ align:start position:0%
+parent of
+ 
+
+ align:start position:0%
+parent of
+X okay so we X and Y are switching
+
+ align:start position:0%
+X okay so we X and Y are switching
+ 
+
+ align:start position:0%
+X okay so we X and Y are switching
+places but if we we couldn't just swap
+
+ align:start position:0%
+places but if we we couldn't just swap
+ 
+
+ align:start position:0%
+places but if we we couldn't just swap
+these items around that would change
+
+ align:start position:0%
+these items around that would change
+ 
+
+ align:start position:0%
+these items around that would change
+traversal order in this picture X comes
+
+ align:start position:0%
+traversal order in this picture X comes
+ 
+
+ align:start position:0%
+traversal order in this picture X comes
+before y because X is in the left sub
+
+ align:start position:0%
+before y because X is in the left sub
+ 
+
+ align:start position:0%
+before y because X is in the left sub
+tree of Y in traversal order and over
+
+ align:start position:0%
+tree of Y in traversal order and over
+ 
+
+ align:start position:0%
+tree of Y in traversal order and over
+here now Y is in the right sub tree of X
+
+ align:start position:0%
+here now Y is in the right sub tree of X
+ 
+
+ align:start position:0%
+here now Y is in the right sub tree of X
+so it comes after X so in both cases X
+
+ align:start position:0%
+so it comes after X so in both cases X
+ 
+
+ align:start position:0%
+so it comes after X so in both cases X
+comes before Y and indeed in all of
+
+ align:start position:0%
+comes before Y and indeed in all of
+ 
+
+ align:start position:0%
+comes before Y and indeed in all of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+pictures uh the traversal order I mean
+
+ align:start position:0%
+pictures uh the traversal order I mean
+ 
+
+ align:start position:0%
+pictures uh the traversal order I mean
+not just for X and Y but also for a b
+
+ align:start position:0%
+not just for X and Y but also for a b
+ 
+
+ align:start position:0%
+not just for X and Y but also for a b
+and c the traversal order is consistent
+
+ align:start position:0%
+and c the traversal order is consistent
+ 
+
+ align:start position:0%
+and c the traversal order is consistent
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+a uh x b
+
+ align:start position:0%
+a uh x b
+ 
+
+ align:start position:0%
+a uh x b
+y c where when I write a triangle I mean
+
+ align:start position:0%
+y c where when I write a triangle I mean
+ 
+
+ align:start position:0%
+y c where when I write a triangle I mean
+recursively the traversal order of all
+
+ align:start position:0%
+recursively the traversal order of all
+ 
+
+ align:start position:0%
+recursively the traversal order of all
+the things in the Triangle so if you
+
+ align:start position:0%
+the things in the Triangle so if you
+ 
+
+ align:start position:0%
+the things in the Triangle so if you
+just apply the traversal order algorithm
+
+ align:start position:0%
+just apply the traversal order algorithm
+ 
+
+ align:start position:0%
+just apply the traversal order algorithm
+here versus here you get the same output
+
+ align:start position:0%
+here versus here you get the same output
+ 
+
+ align:start position:0%
+here versus here you get the same output
+which means these these operations
+
+ align:start position:0%
+which means these these operations
+ 
+
+ align:start position:0%
+which means these these operations
+preserve traversal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order great so this is a thing that we
+
+ align:start position:0%
+order great so this is a thing that we
+ 
+
+ align:start position:0%
+order great so this is a thing that we
+can do in a tree that won't affect any
+
+ align:start position:0%
+can do in a tree that won't affect any
+ 
+
+ align:start position:0%
+can do in a tree that won't affect any
+of the stuff we've done so far it's a
+
+ align:start position:0%
+of the stuff we've done so far it's a
+ 
+
+ align:start position:0%
+of the stuff we've done so far it's a
+tool that we can used to rebalance
+
+ align:start position:0%
+tool that we can used to rebalance
+ 
+
+ align:start position:0%
+tool that we can used to rebalance
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+um you know how deep things are in the
+
+ align:start position:0%
+um you know how deep things are in the
+ 
+
+ align:start position:0%
+um you know how deep things are in the
+tree changes our problem with this
+
+ align:start position:0%
+tree changes our problem with this
+ 
+
+ align:start position:0%
+tree changes our problem with this
+linear tree is that there are some nodes
+
+ align:start position:0%
+linear tree is that there are some nodes
+ 
+
+ align:start position:0%
+linear tree is that there are some nodes
+of linear depth we want to get rid of
+
+ align:start position:0%
+of linear depth we want to get rid of
+ 
+
+ align:start position:0%
+of linear depth we want to get rid of
+those how we could take these edges and
+
+ align:start position:0%
+those how we could take these edges and
+ 
+
+ align:start position:0%
+those how we could take these edges and
+start rotating them up if you look at
+
+ align:start position:0%
+start rotating them up if you look at
+ 
+
+ align:start position:0%
+start rotating them up if you look at
+depths um you know in this picture A and
+
+ align:start position:0%
+depths um you know in this picture A and
+ 
+
+ align:start position:0%
+depths um you know in this picture A and
+B are deeper than C and in this picture
+
+ align:start position:0%
+B are deeper than C and in this picture
+ 
+
+ align:start position:0%
+B are deeper than C and in this picture
+uh B and C are deeper than a so you know
+
+ align:start position:0%
+uh B and C are deeper than a so you know
+ 
+
+ align:start position:0%
+uh B and C are deeper than a so you know
+there a trade-off this one moved up this
+
+ align:start position:0%
+there a trade-off this one moved up this
+ 
+
+ align:start position:0%
+there a trade-off this one moved up this
+one moved down this one stayed at the
+
+ align:start position:0%
+one moved down this one stayed at the
+ 
+
+ align:start position:0%
+one moved down this one stayed at the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+depth so hopefully if if a is too deep
+
+ align:start position:0%
+depth so hopefully if if a is too deep
+ 
+
+ align:start position:0%
+depth so hopefully if if a is too deep
+and C is too shallow uh they can trade
+
+ align:start position:0%
+and C is too shallow uh they can trade
+ 
+
+ align:start position:0%
+and C is too shallow uh they can trade
+off like this okay it may sound
+
+ align:start position:0%
+off like this okay it may sound
+ 
+
+ align:start position:0%
+off like this okay it may sound
+difficult but in fact there's a pretty
+
+ align:start position:0%
+difficult but in fact there's a pretty
+ 
+
+ align:start position:0%
+difficult but in fact there's a pretty
+simple way uh which are called AVL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees uh that maintain balance in a
+
+ align:start position:0%
+trees uh that maintain balance in a
+ 
+
+ align:start position:0%
+trees uh that maintain balance in a
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+way called height balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is uh if we take the
+
+ align:start position:0%
+this is uh if we take the
+ 
+
+ align:start position:0%
+this is uh if we take the
+height of no dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left uh actually I'd prefer
+
+ align:start position:0%
+left uh actually I'd prefer
+ 
+
+ align:start position:0%
+left uh actually I'd prefer
+to no do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+minus height of node do left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this thing is called um
+
+ align:start position:0%
+so this thing is called um
+ 
+
+ align:start position:0%
+so this thing is called um
+skew of the
+
+ align:start position:0%
+skew of the
+ 
+
+ align:start position:0%
+skew of the
+node I want this to always be minus1 0
+
+ align:start position:0%
+node I want this to always be minus1 0
+ 
+
+ align:start position:0%
+node I want this to always be minus1 0
+or plus
+
+ align:start position:0%
+or plus
+ 
+
+ align:start position:0%
+or plus
+one okay so this is saying that if I
+
+ align:start position:0%
+one okay so this is saying that if I
+ 
+
+ align:start position:0%
+one okay so this is saying that if I
+have any node and I look if it's left
+
+ align:start position:0%
+have any node and I look if it's left
+ 
+
+ align:start position:0%
+have any node and I look if it's left
+sube and it's right sub tree I measure
+
+ align:start position:0%
+sube and it's right sub tree I measure
+ 
+
+ align:start position:0%
+sube and it's right sub tree I measure
+their heights remember that's downward
+
+ align:start position:0%
+their heights remember that's downward
+ 
+
+ align:start position:0%
+their heights remember that's downward
+dist to maximum distance to a leaf I
+
+ align:start position:0%
+dist to maximum distance to a leaf I
+ 
+
+ align:start position:0%
+dist to maximum distance to a leaf I
+measure the height of this tree maximum
+
+ align:start position:0%
+measure the height of this tree maximum
+ 
+
+ align:start position:0%
+measure the height of this tree maximum
+height I measure the maximum height of
+
+ align:start position:0%
+height I measure the maximum height of
+ 
+
+ align:start position:0%
+height I measure the maximum height of
+this sube I want these to be within one
+
+ align:start position:0%
+this sube I want these to be within one
+ 
+
+ align:start position:0%
+this sube I want these to be within one
+of each other maybe ideally they're
+
+ align:start position:0%
+of each other maybe ideally they're
+ 
+
+ align:start position:0%
+of each other maybe ideally they're
+equal that would be the perfect case but
+
+ align:start position:0%
+equal that would be the perfect case but
+ 
+
+ align:start position:0%
+equal that would be the perfect case but
+let's let them differ by one so maybe
+
+ align:start position:0%
+let's let them differ by one so maybe
+ 
+
+ align:start position:0%
+let's let them differ by one so maybe
+this is K and this is k + one or maybe
+
+ align:start position:0%
+this is K and this is k + one or maybe
+ 
+
+ align:start position:0%
+this is K and this is k + one or maybe
+this is K and this is K minus one what's
+
+ align:start position:0%
+this is K and this is K minus one what's
+ 
+
+ align:start position:0%
+this is K and this is K minus one what's
+the in this picture what is the height
+
+ align:start position:0%
+the in this picture what is the height
+ 
+
+ align:start position:0%
+the in this picture what is the height
+of this node it's good
+
+ align:start position:0%
+of this node it's good
+ 
+
+ align:start position:0%
+of this node it's good
+practice k+ 2
+
+ align:start position:0%
+practice k+ 2
+ 
+
+ align:start position:0%
+practice k+ 2
+good what's the longest path from this
+
+ align:start position:0%
+good what's the longest path from this
+ 
+
+ align:start position:0%
+good what's the longest path from this
+node to a leaf well it could go through
+
+ align:start position:0%
+node to a leaf well it could go through
+ 
+
+ align:start position:0%
+node to a leaf well it could go through
+this sub tree and that would be length
+
+ align:start position:0%
+this sub tree and that would be length
+ 
+
+ align:start position:0%
+this sub tree and that would be length
+k+ 1 cuz it's K in here plus one for
+
+ align:start position:0%
+k+ 1 cuz it's K in here plus one for
+ 
+
+ align:start position:0%
+k+ 1 cuz it's K in here plus one for
+this Edge or it could be through here
+
+ align:start position:0%
+this Edge or it could be through here
+ 
+
+ align:start position:0%
+this Edge or it could be through here
+and that's k+ 1 plus one so the biggest
+
+ align:start position:0%
+and that's k+ 1 plus one so the biggest
+ 
+
+ align:start position:0%
+and that's k+ 1 plus one so the biggest
+is to go to the right so the height if I
+
+ align:start position:0%
+is to go to the right so the height if I
+ 
+
+ align:start position:0%
+is to go to the right so the height if I
+told you the height of these sub trees
+
+ align:start position:0%
+told you the height of these sub trees
+ 
+
+ align:start position:0%
+told you the height of these sub trees
+we can derive the height of this note
+
+ align:start position:0%
+we can derive the height of this note
+ 
+
+ align:start position:0%
+we can derive the height of this note
+we're going to use that a lot in a
+
+ align:start position:0%
+we're going to use that a lot in a
+ 
+
+ align:start position:0%
+we're going to use that a lot in a
+moment so first claim is that if I could
+
+ align:start position:0%
+moment so first claim is that if I could
+ 
+
+ align:start position:0%
+moment so first claim is that if I could
+maintain height balance then I
+
+ align:start position:0%
+maintain height balance then I
+ 
+
+ align:start position:0%
+maintain height balance then I
+can uh I will guarantee that H equals
+
+ align:start position:0%
+can uh I will guarantee that H equals
+ 
+
+ align:start position:0%
+can uh I will guarantee that H equals
+log n so in other words height balance
+
+ align:start position:0%
+log n so in other words height balance
+ 
+
+ align:start position:0%
+log n so in other words height balance
+implies
+
+ align:start position:0%
+implies
+ 
+
+ align:start position:0%
+implies
+balance so let's prove that
+
+ align:start position:0%
+balance so let's prove that
+ 
+
+ align:start position:0%
+balance so let's prove that
+first quickly and then the interesting
+
+ align:start position:0%
+first quickly and then the interesting
+ 
+
+ align:start position:0%
+first quickly and then the interesting
+part is how do we actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove or how do we actually maintain the
+
+ align:start position:0%
+prove or how do we actually maintain the
+ 
+
+ align:start position:0%
+prove or how do we actually maintain the
+balance property we're going to do that
+
+ align:start position:0%
+balance property we're going to do that
+ 
+
+ align:start position:0%
+balance property we're going to do that
+using rotations but how is a big
+
+ align:start position:0%
+using rotations but how is a big
+ 
+
+ align:start position:0%
+using rotations but how is a big
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so why does height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balance imply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balance so uh what this is saying is
+
+ align:start position:0%
+balance so uh what this is saying is
+ 
+
+ align:start position:0%
+balance so uh what this is saying is
+that all height balanc trees have
+
+ align:start position:0%
+that all height balanc trees have
+ 
+
+ align:start position:0%
+that all height balanc trees have
+logarithmic
+
+ align:start position:0%
+logarithmic
+ 
+
+ align:start position:0%
+logarithmic
+height so what I'd like to think about
+
+ align:start position:0%
+height so what I'd like to think about
+ 
+
+ align:start position:0%
+height so what I'd like to think about
+is sort of the Le least balanced height
+
+ align:start position:0%
+is sort of the Le least balanced height
+ 
+
+ align:start position:0%
+is sort of the Le least balanced height
+balanced tree uh the least balanced one
+
+ align:start position:0%
+balanced tree uh the least balanced one
+ 
+
+ align:start position:0%
+balanced tree uh the least balanced one
+is going to have at every node a
+
+ align:start position:0%
+is going to have at every node a
+ 
+
+ align:start position:0%
+is going to have at every node a
+mismatch the the left let's say the left
+
+ align:start position:0%
+mismatch the the left let's say the left
+ 
+
+ align:start position:0%
+mismatch the the left let's say the left
+sube is shallower than the right subtree
+
+ align:start position:0%
+sube is shallower than the right subtree
+ 
+
+ align:start position:0%
+sube is shallower than the right subtree
+by one and recursively all the way down
+
+ align:start position:0%
+by one and recursively all the way down
+ 
+
+ align:start position:0%
+by one and recursively all the way down
+so every node has a a Gap
+
+ align:start position:0%
+so every node has a a Gap
+ 
+
+ align:start position:0%
+so every node has a a Gap
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh what do we call it uh a skew of
+
+ align:start position:0%
+uh what do we call it uh a skew of
+ 
+
+ align:start position:0%
+uh what do we call it uh a skew of
+one okay which I'm going to write I'm
+
+ align:start position:0%
+one okay which I'm going to write I'm
+ 
+
+ align:start position:0%
+one okay which I'm going to write I'm
+going to introduce some notation I'll
+
+ align:start position:0%
+going to introduce some notation I'll
+ 
+
+ align:start position:0%
+going to introduce some notation I'll
+write a descending rightward Arrow if
+
+ align:start position:0%
+write a descending rightward Arrow if
+ 
+
+ align:start position:0%
+write a descending rightward Arrow if
+this one is is higher than the left sub
+
+ align:start position:0%
+this one is is higher than the left sub
+ 
+
+ align:start position:0%
+this one is is higher than the left sub
+tree uh so the easy way to think about
+
+ align:start position:0%
+tree uh so the easy way to think about
+ 
+
+ align:start position:0%
+tree uh so the easy way to think about
+this is this is sort of the our worst
+
+ align:start position:0%
+this is this is sort of the our worst
+ 
+
+ align:start position:0%
+this is this is sort of the our worst
+case this is going to be the the fewest
+
+ align:start position:0%
+case this is going to be the the fewest
+ 
+
+ align:start position:0%
+case this is going to be the the fewest
+nodes for the maximum depth let's just
+
+ align:start position:0%
+nodes for the maximum depth let's just
+ 
+
+ align:start position:0%
+nodes for the maximum depth let's just
+count how many nodes are in this
+
+ align:start position:0%
+count how many nodes are in this
+ 
+
+ align:start position:0%
+count how many nodes are in this
+tree I'm going to write that as a
+
+ align:start position:0%
+tree I'm going to write that as a
+ 
+
+ align:start position:0%
+tree I'm going to write that as a
+recurrence um which is the number of
+
+ align:start position:0%
+recurrence um which is the number of
+ 
+
+ align:start position:0%
+recurrence um which is the number of
+nodes in a tree of height
+
+ align:start position:0%
+nodes in a tree of height
+ 
+
+ align:start position:0%
+nodes in a tree of height
+H so if this whole tree has height h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H uh as we said in this picture if I
+
+ align:start position:0%
+H uh as we said in this picture if I
+ 
+
+ align:start position:0%
+H uh as we said in this picture if I
+just subtract two from all these numbers
+
+ align:start position:0%
+just subtract two from all these numbers
+ 
+
+ align:start position:0%
+just subtract two from all these numbers
+then this one has height uh H minus 2
+
+ align:start position:0%
+then this one has height uh H minus 2
+ 
+
+ align:start position:0%
+then this one has height uh H minus 2
+and this one has height H minus
+
+ align:start position:0%
+and this one has height H minus
+ 
+
+ align:start position:0%
+and this one has height H minus
+one okay so how many nodes are in here
+
+ align:start position:0%
+one okay so how many nodes are in here
+ 
+
+ align:start position:0%
+one okay so how many nodes are in here
+well this is a recurrence I'm going to
+
+ align:start position:0%
+well this is a recurrence I'm going to
+ 
+
+ align:start position:0%
+well this is a recurrence I'm going to
+write so this will be N Sub h-2 this
+
+ align:start position:0%
+write so this will be N Sub h-2 this
+ 
+
+ align:start position:0%
+write so this will be N Sub h-2 this
+will be N Sub
+
+ align:start position:0%
+will be N Sub
+ 
+
+ align:start position:0%
+will be N Sub
+hus1 and then I just count how many
+
+ align:start position:0%
+hus1 and then I just count how many
+ 
+
+ align:start position:0%
+hus1 and then I just count how many
+nodes are in this picture
+
+ align:start position:0%
+nodes are in this picture
+ 
+
+ align:start position:0%
+nodes are in this picture
+it is n subh -1 plus n subh - 2 + 1 or
+
+ align:start position:0%
+it is n subh -1 plus n subh - 2 + 1 or
+ 
+
+ align:start position:0%
+it is n subh -1 plus n subh - 2 + 1 or
+this note now you might ask what is NH
+
+ align:start position:0%
+this note now you might ask what is NH
+ 
+
+ align:start position:0%
+this note now you might ask what is NH
+or recurrence for uh but it is the
+
+ align:start position:0%
+or recurrence for uh but it is the
+ 
+
+ align:start position:0%
+or recurrence for uh but it is the
+number of nodes in this sort of worst
+
+ align:start position:0%
+number of nodes in this sort of worst
+ 
+
+ align:start position:0%
+number of nodes in this sort of worst
+case uh for if the worst case has total
+
+ align:start position:0%
+case uh for if the worst case has total
+ 
+
+ align:start position:0%
+case uh for if the worst case has total
+height H so you can also think of it as
+
+ align:start position:0%
+height H so you can also think of it as
+ 
+
+ align:start position:0%
+height H so you can also think of it as
+what is the minimum number of nodes I
+
+ align:start position:0%
+what is the minimum number of nodes I
+ 
+
+ align:start position:0%
+what is the minimum number of nodes I
+could have in an AVL tree which is a
+
+ align:start position:0%
+could have in an AVL tree which is a
+ 
+
+ align:start position:0%
+could have in an AVL tree which is a
+height balance tree uh that has height h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a height balanced
+
+ align:start position:0%
+in a height balanced
+ 
+
+ align:start position:0%
+in a height balanced
+tree okay so now I just need to solve
+
+ align:start position:0%
+tree okay so now I just need to solve
+ 
+
+ align:start position:0%
+tree okay so now I just need to solve
+this recurrence this recurrence look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+is it's like Fibonacci numbers if I
+
+ align:start position:0%
+is it's like Fibonacci numbers if I
+ 
+
+ align:start position:0%
+is it's like Fibonacci numbers if I
+remove the plus one it's Fibonacci and
+
+ align:start position:0%
+remove the plus one it's Fibonacci and
+ 
+
+ align:start position:0%
+remove the plus one it's Fibonacci and
+if you happen to know the Fibonacci
+
+ align:start position:0%
+if you happen to know the Fibonacci
+ 
+
+ align:start position:0%
+if you happen to know the Fibonacci
+numbers grow as like a golden ratio to
+
+ align:start position:0%
+numbers grow as like a golden ratio to
+ 
+
+ align:start position:0%
+numbers grow as like a golden ratio to
+the N then we know that this is
+
+ align:start position:0%
+the N then we know that this is
+ 
+
+ align:start position:0%
+the N then we know that this is
+exponential which is what we want
+
+ align:start position:0%
+exponential which is what we want
+ 
+
+ align:start position:0%
+exponential which is what we want
+because if NH is exponential in h that
+
+ align:start position:0%
+because if NH is exponential in h that
+ 
+
+ align:start position:0%
+because if NH is exponential in h that
+means H is logarithmic in N because log
+
+ align:start position:0%
+means H is logarithmic in N because log
+ 
+
+ align:start position:0%
+means H is logarithmic in N because log
+is inverse of exponential okay but maybe
+
+ align:start position:0%
+is inverse of exponential okay but maybe
+ 
+
+ align:start position:0%
+is inverse of exponential okay but maybe
+you don't know about Fibonacci numbers
+
+ align:start position:0%
+you don't know about Fibonacci numbers
+ 
+
+ align:start position:0%
+you don't know about Fibonacci numbers
+and uh so we can still uh easily show
+
+ align:start position:0%
+and uh so we can still uh easily show
+ 
+
+ align:start position:0%
+and uh so we can still uh easily show
+that this is exponential as follows I
+
+ align:start position:0%
+that this is exponential as follows I
+ 
+
+ align:start position:0%
+that this is exponential as follows I
+want to prove that it's at least an
+
+ align:start position:0%
+want to prove that it's at least an
+ 
+
+ align:start position:0%
+want to prove that it's at least an
+exponential because that gives me that H
+
+ align:start position:0%
+exponential because that gives me that H
+ 
+
+ align:start position:0%
+exponential because that gives me that H
+is at most
+
+ align:start position:0%
+is at most
+ 
+
+ align:start position:0%
+is at most
+logarithmic um so we need a lower bound
+
+ align:start position:0%
+logarithmic um so we need a lower bound
+ 
+
+ align:start position:0%
+logarithmic um so we need a lower bound
+and so we have these two terms which are
+
+ align:start position:0%
+and so we have these two terms which are
+ 
+
+ align:start position:0%
+and so we have these two terms which are
+hard to compare n subh minus 1 and N Sub
+
+ align:start position:0%
+hard to compare n subh minus 1 and N Sub
+ 
+
+ align:start position:0%
+hard to compare n subh minus 1 and N Sub
+hus 2 it's kind of ugly uh but if we're
+
+ align:start position:0%
+hus 2 it's kind of ugly uh but if we're
+ 
+
+ align:start position:0%
+hus 2 it's kind of ugly uh but if we're
+allowed to be sloppy and we'll see if
+
+ align:start position:0%
+allowed to be sloppy and we'll see if
+ 
+
+ align:start position:0%
+allowed to be sloppy and we'll see if
+we're not too sloppy and still get an
+
+ align:start position:0%
+we're not too sloppy and still get an
+ 
+
+ align:start position:0%
+we're not too sloppy and still get an
+exponential answer um let's just make
+
+ align:start position:0%
+exponential answer um let's just make
+ 
+
+ align:start position:0%
+exponential answer um let's just make
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+equal uh like
+
+ align:start position:0%
+equal uh like
+ 
+
+ align:start position:0%
+equal uh like
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so this is a true statement in fact
+
+ align:start position:0%
+um so this is a true statement in fact
+ 
+
+ align:start position:0%
+um so this is a true statement in fact
+strictly greater than uh why because so
+
+ align:start position:0%
+strictly greater than uh why because so
+ 
+
+ align:start position:0%
+strictly greater than uh why because so
+I removed the plus one that should only
+
+ align:start position:0%
+I removed the plus one that should only
+ 
+
+ align:start position:0%
+I removed the plus one that should only
+make something smaller and um I replaced
+
+ align:start position:0%
+make something smaller and um I replaced
+ 
+
+ align:start position:0%
+make something smaller and um I replaced
+n subh minus1 with n subh minus 2 here
+
+ align:start position:0%
+n subh minus1 with n subh minus 2 here
+ 
+
+ align:start position:0%
+n subh minus1 with n subh minus 2 here
+I'm implic using a fact which is obvious
+
+ align:start position:0%
+I'm implic using a fact which is obvious
+ 
+
+ align:start position:0%
+I'm implic using a fact which is obvious
+by induction that uh this tree on height
+
+ align:start position:0%
+by induction that uh this tree on height
+ 
+
+ align:start position:0%
+by induction that uh this tree on height
+if I take this tree versus this tree
+
+ align:start position:0%
+if I take this tree versus this tree
+ 
+
+ align:start position:0%
+if I take this tree versus this tree
+this one has more nodes than this one
+
+ align:start position:0%
+this one has more nodes than this one
+ 
+
+ align:start position:0%
+this one has more nodes than this one
+right if I have larger height this
+
+ align:start position:0%
+right if I have larger height this
+ 
+
+ align:start position:0%
+right if I have larger height this
+construction is going to build a bigger
+
+ align:start position:0%
+construction is going to build a bigger
+ 
+
+ align:start position:0%
+construction is going to build a bigger
+tree at least as big doesn't need even
+
+ align:start position:0%
+tree at least as big doesn't need even
+ 
+
+ align:start position:0%
+tree at least as big doesn't need even
+need to be strictly bigger so certainly
+
+ align:start position:0%
+need to be strictly bigger so certainly
+ 
+
+ align:start position:0%
+need to be strictly bigger so certainly
+n subh minus one is greater than or
+
+ align:start position:0%
+n subh minus one is greater than or
+ 
+
+ align:start position:0%
+n subh minus one is greater than or
+equal to n subh minus 2 now this is 2 *
+
+ align:start position:0%
+equal to n subh minus 2 now this is 2 *
+ 
+
+ align:start position:0%
+equal to n subh minus 2 now this is 2 *
+n subus 2 and this is an easy recurrence
+
+ align:start position:0%
+n subus 2 and this is an easy recurrence
+ 
+
+ align:start position:0%
+n subus 2 and this is an easy recurrence
+this is just powers of two right I keep
+
+ align:start position:0%
+this is just powers of two right I keep
+ 
+
+ align:start position:0%
+this is just powers of two right I keep
+multiplying by two and subtracting two
+
+ align:start position:0%
+multiplying by two and subtracting two
+ 
+
+ align:start position:0%
+multiplying by two and subtracting two
+from H so this solves to 2 to the h 2
+
+ align:start position:0%
+from H so this solves to 2 to the h 2
+ 
+
+ align:start position:0%
+from H so this solves to 2 to the h 2
+maybe with a floor or something okay but
+
+ align:start position:0%
+maybe with a floor or something okay but
+ 
+
+ align:start position:0%
+maybe with a floor or something okay but
+uh it is I'm using a base case here
+
+ align:start position:0%
+uh it is I'm using a base case here
+ 
+
+ align:start position:0%
+uh it is I'm using a base case here
+which is N Sub 0al
+
+ align:start position:0%
+which is N Sub 0al
+ 
+
+ align:start position:0%
+which is N Sub 0al
+1 uh maybe it's a ceiling then but the
+
+ align:start position:0%
+1 uh maybe it's a ceiling then but the
+ 
+
+ align:start position:0%
+1 uh maybe it's a ceiling then but the
+point is this is exponential so this
+
+ align:start position:0%
+point is this is exponential so this
+ 
+
+ align:start position:0%
+point is this is exponential so this
+implies that the height is always at
+
+ align:start position:0%
+implies that the height is always at
+ 
+
+ align:start position:0%
+implies that the height is always at
+most 2 * log
+
+ align:start position:0%
+most 2 * log
+ 
+
+ align:start position:0%
+most 2 * log
+n uh this two corresponds to this to if
+
+ align:start position:0%
+n uh this two corresponds to this to if
+ 
+
+ align:start position:0%
+n uh this two corresponds to this to if
+you just invert this formula this was
+
+ align:start position:0%
+you just invert this formula this was
+ 
+
+ align:start position:0%
+you just invert this formula this was
+number of nodes is going to be at
+
+ align:start position:0%
+number of nodes is going to be at
+ 
+
+ align:start position:0%
+number of nodes is going to be at
+least uh 2 the H2 and so H is at most to
+
+ align:start position:0%
+least uh 2 the H2 and so H is at most to
+ 
+
+ align:start position:0%
+least uh 2 the H2 and so H is at most to
+log n so it's not log n that would be
+
+ align:start position:0%
+log n so it's not log n that would be
+ 
+
+ align:start position:0%
+log n so it's not log n that would be
+perfect but it's within a factor of two
+
+ align:start position:0%
+perfect but it's within a factor of two
+ 
+
+ align:start position:0%
+perfect but it's within a factor of two
+of log n so AVL trees are always quite
+
+ align:start position:0%
+of log n so AVL trees are always quite
+ 
+
+ align:start position:0%
+of log n so AVL trees are always quite
+balanced number of levels is at most
+
+ align:start position:0%
+balanced number of levels is at most
+ 
+
+ align:start position:0%
+balanced number of levels is at most
+double what you need to store end nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great we're left with the main Magic
+
+ align:start position:0%
+great we're left with the main Magic
+ 
+
+ align:start position:0%
+great we're left with the main Magic
+not domain magic that's different uh and
+
+ align:start position:0%
+not domain magic that's different uh and
+ 
+
+ align:start position:0%
+not domain magic that's different uh and
+let's see we're going to use subt tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+augmentation keep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that big remaining challenge is how do
+
+ align:start position:0%
+that big remaining challenge is how do
+ 
+
+ align:start position:0%
+that big remaining challenge is how do
+we maintain this height balance property
+
+ align:start position:0%
+we maintain this height balance property
+ 
+
+ align:start position:0%
+we maintain this height balance property
+using rotations we have all the
+
+ align:start position:0%
+using rotations we have all the
+ 
+
+ align:start position:0%
+using rotations we have all the
+ingredients lined up for us we have sub
+
+ align:start position:0%
+ingredients lined up for us we have sub
+ 
+
+ align:start position:0%
+ingredients lined up for us we have sub
+Tre
+
+ align:start position:0%
+Tre
+ 
+
+ align:start position:0%
+Tre
+augmentation what does that let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do that's relevant to AVL trees well it
+
+ align:start position:0%
+do that's relevant to AVL trees well it
+ 
+
+ align:start position:0%
+do that's relevant to AVL trees well it
+lets me store
+
+ align:start position:0%
+lets me store
+ 
+
+ align:start position:0%
+lets me store
+height right I need to be able to
+
+ align:start position:0%
+height right I need to be able to
+ 
+
+ align:start position:0%
+height right I need to be able to
+compute the height of a
+
+ align:start position:0%
+compute the height of a
+ 
+
+ align:start position:0%
+compute the height of a
+node that in general takes linear time
+
+ align:start position:0%
+node that in general takes linear time
+ 
+
+ align:start position:0%
+node that in general takes linear time
+because I have to look at all the
+
+ align:start position:0%
+because I have to look at all the
+ 
+
+ align:start position:0%
+because I have to look at all the
+downward paths all the leaves within
+
+ align:start position:0%
+downward paths all the leaves within
+ 
+
+ align:start position:0%
+downward paths all the leaves within
+that sub tree but height is a sub tree
+
+ align:start position:0%
+that sub tree but height is a sub tree
+ 
+
+ align:start position:0%
+that sub tree but height is a sub tree
+property so uh
+
+ align:start position:0%
+property so uh
+ 
+
+ align:start position:0%
+property so uh
+yes height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+because uh let me just write it here
+
+ align:start position:0%
+because uh let me just write it here
+ 
+
+ align:start position:0%
+because uh let me just write it here
+node.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+height equals 1 + Max of node. left.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+height and no do right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+height and of Max let me put this in a
+
+ align:start position:0%
+height and of Max let me put this in a
+ 
+
+ align:start position:0%
+height and of Max let me put this in a
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+this equation or I guess it's an
+
+ align:start position:0%
+this equation or I guess it's an
+ 
+
+ align:start position:0%
+this equation or I guess it's an
+assignment operation this is a
+
+ align:start position:0%
+assignment operation this is a
+ 
+
+ align:start position:0%
+assignment operation this is a
+one is the thing we've been doing over
+
+ align:start position:0%
+one is the thing we've been doing over
+ 
+
+ align:start position:0%
+one is the thing we've been doing over
+and over when I said what is the height
+
+ align:start position:0%
+and over when I said what is the height
+ 
+
+ align:start position:0%
+and over when I said what is the height
+of this node you just figured that out
+
+ align:start position:0%
+of this node you just figured that out
+ 
+
+ align:start position:0%
+of this node you just figured that out
+right you took the height of the left
+
+ align:start position:0%
+right you took the height of the left
+ 
+
+ align:start position:0%
+right you took the height of the left
+sub tree maxed with the height of the
+
+ align:start position:0%
+sub tree maxed with the height of the
+ 
+
+ align:start position:0%
+sub tree maxed with the height of the
+right sub tree and added one for to
+
+ align:start position:0%
+right sub tree and added one for to
+ 
+
+ align:start position:0%
+right sub tree and added one for to
+count for these edges okay so this is a
+
+ align:start position:0%
+count for these edges okay so this is a
+ 
+
+ align:start position:0%
+count for these edges okay so this is a
+general update rule it matches this
+
+ align:start position:0%
+general update rule it matches this
+ 
+
+ align:start position:0%
+general update rule it matches this
+subtree property pattern if I have the
+
+ align:start position:0%
+subtree property pattern if I have the
+ 
+
+ align:start position:0%
+subtree property pattern if I have the
+property of left and right I can compute
+
+ align:start position:0%
+property of left and right I can compute
+ 
+
+ align:start position:0%
+property of left and right I can compute
+it for node
+
+ align:start position:0%
+it for node
+ 
+
+ align:start position:0%
+it for node
+and this takes constant time to do and
+
+ align:start position:0%
+and this takes constant time to do and
+ 
+
+ align:start position:0%
+and this takes constant time to do and
+so it's a sub tree property and so I can
+
+ align:start position:0%
+so it's a sub tree property and so I can
+ 
+
+ align:start position:0%
+so it's a sub tree property and so I can
+maintain through all the things I'm
+
+ align:start position:0%
+maintain through all the things I'm
+ 
+
+ align:start position:0%
+maintain through all the things I'm
+doing the height of every node oh by the
+
+ align:start position:0%
+doing the height of every node oh by the
+ 
+
+ align:start position:0%
+doing the height of every node oh by the
+way whenever I do a rotation I'm also
+
+ align:start position:0%
+way whenever I do a rotation I'm also
+ 
+
+ align:start position:0%
+way whenever I do a rotation I'm also
+going to have to update my sube
+
+ align:start position:0%
+going to have to update my sube
+ 
+
+ align:start position:0%
+going to have to update my sube
+properties when I rotate this Edge a
+
+ align:start position:0%
+properties when I rotate this Edge a
+ 
+
+ align:start position:0%
+properties when I rotate this Edge a
+does not change B does not change C does
+
+ align:start position:0%
+does not change B does not change C does
+ 
+
+ align:start position:0%
+does not change B does not change C does
+not change so that's good but X's sub
+
+ align:start position:0%
+not change so that's good but X's sub
+ 
+
+ align:start position:0%
+not change so that's good but X's sub
+tree changes it now has why it didn't
+
+ align:start position:0%
+tree changes it now has why it didn't
+ 
+
+ align:start position:0%
+tree changes it now has why it didn't
+before so we're going to have to also uh
+
+ align:start position:0%
+before so we're going to have to also uh
+ 
+
+ align:start position:0%
+before so we're going to have to also uh
+update the augmentation here
+
+ align:start position:0%
+update the augmentation here
+ 
+
+ align:start position:0%
+update the augmentation here
+Y and we're going to have to update the
+
+ align:start position:0%
+Y and we're going to have to update the
+ 
+
+ align:start position:0%
+Y and we're going to have to update the
+augmentation in
+
+ align:start position:0%
+augmentation in
+ 
+
+ align:start position:0%
+augmentation in
+X and we're going to have to update the
+
+ align:start position:0%
+X and we're going to have to update the
+ 
+
+ align:start position:0%
+X and we're going to have to update the
+augmentation of all of the ancestors of
+
+ align:start position:0%
+augmentation of all of the ancestors of
+ 
+
+ align:start position:0%
+augmentation of all of the ancestors of
+X eventually um so rotation is locally
+
+ align:start position:0%
+X eventually um so rotation is locally
+ 
+
+ align:start position:0%
+X eventually um so rotation is locally
+just changing a constant number of
+
+ align:start position:0%
+just changing a constant number of
+ 
+
+ align:start position:0%
+just changing a constant number of
+pointers so I usually think of rotations
+
+ align:start position:0%
+pointers so I usually think of rotations
+ 
+
+ align:start position:0%
+pointers so I usually think of rotations
+as taking constant
+
+ align:start position:0%
+as taking constant
+ 
+
+ align:start position:0%
+as taking constant
+time uh but eventually we will have to
+
+ align:start position:0%
+time uh but eventually we will have to
+ 
+
+ align:start position:0%
+time uh but eventually we will have to
+do this is constant time
+
+ align:start position:0%
+do this is constant time
+ 
+
+ align:start position:0%
+do this is constant time
+locally
+
+ align:start position:0%
+locally
+ 
+
+ align:start position:0%
+locally
+uh but we will need to up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh H
+
+ align:start position:0%
+uh H
+ 
+
+ align:start position:0%
+uh H
+ancestors in order to store all of keep
+
+ align:start position:0%
+ancestors in order to store all of keep
+ 
+
+ align:start position:0%
+ancestors in order to store all of keep
+all of our augmentations up to date okay
+
+ align:start position:0%
+all of our augmentations up to date okay
+ 
+
+ align:start position:0%
+all of our augmentations up to date okay
+we'll worry about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later all right so great now we have the
+
+ align:start position:0%
+later all right so great now we have the
+ 
+
+ align:start position:0%
+later all right so great now we have the
+height of all the nodes we can compute
+
+ align:start position:0%
+height of all the nodes we can compute
+ 
+
+ align:start position:0%
+height of all the nodes we can compute
+the SK skew of all the nodes cool uh we
+
+ align:start position:0%
+the SK skew of all the nodes cool uh we
+ 
+
+ align:start position:0%
+the SK skew of all the nodes cool uh we
+have this rotation operation and we want
+
+ align:start position:0%
+have this rotation operation and we want
+ 
+
+ align:start position:0%
+have this rotation operation and we want
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+maintain
+
+ align:start position:0%
+maintain
+ 
+
+ align:start position:0%
+maintain
+uh this height balance property height
+
+ align:start position:0%
+uh this height balance property height
+ 
+
+ align:start position:0%
+uh this height balance property height
+of left node left and right of every
+
+ align:start position:0%
+of left node left and right of every
+ 
+
+ align:start position:0%
+of left node left and right of every
+node is within is plus or minus one or
+
+ align:start position:0%
+node is within is plus or minus one or
+ 
+
+ align:start position:0%
+node is within is plus or minus one or
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+cool so uh I said over here
+
+ align:start position:0%
+cool so uh I said over here
+ 
+
+ align:start position:0%
+cool so uh I said over here
+somewhere whenever we so the only things
+
+ align:start position:0%
+somewhere whenever we so the only things
+ 
+
+ align:start position:0%
+somewhere whenever we so the only things
+that change the tree are when we insert
+
+ align:start position:0%
+that change the tree are when we insert
+ 
+
+ align:start position:0%
+that change the tree are when we insert
+or delete a new node and it and the way
+
+ align:start position:0%
+or delete a new node and it and the way
+ 
+
+ align:start position:0%
+or delete a new node and it and the way
+that we implemented those so far is to
+
+ align:start position:0%
+that we implemented those so far is to
+ 
+
+ align:start position:0%
+that we implemented those so far is to
+add or remove a leaf so we should still
+
+ align:start position:0%
+add or remove a leaf so we should still
+ 
+
+ align:start position:0%
+add or remove a leaf so we should still
+be thinking about adding or removing a
+
+ align:start position:0%
+be thinking about adding or removing a
+ 
+
+ align:start position:0%
+be thinking about adding or removing a
+leaf the problem is when I add a new
+
+ align:start position:0%
+leaf the problem is when I add a new
+ 
+
+ align:start position:0%
+leaf the problem is when I add a new
+Leaf
+
+ align:start position:0%
+Leaf
+ 
+
+ align:start position:0%
+Leaf
+now maybe this tree is higher than it
+
+ align:start position:0%
+now maybe this tree is higher than it
+ 
+
+ align:start position:0%
+now maybe this tree is higher than it
+used to be so um some node here may no
+
+ align:start position:0%
+used to be so um some node here may no
+ 
+
+ align:start position:0%
+used to be so um some node here may no
+longer be height balanced but because
+
+ align:start position:0%
+longer be height balanced but because
+ 
+
+ align:start position:0%
+longer be height balanced but because
+height is a subtree property the only
+
+ align:start position:0%
+height is a subtree property the only
+ 
+
+ align:start position:0%
+height is a subtree property the only
+nodes we need to check are the ones up
+
+ align:start position:0%
+nodes we need to check are the ones up
+ 
+
+ align:start position:0%
+nodes we need to check are the ones up
+this ancestor path so and there's only
+
+ align:start position:0%
+this ancestor path so and there's only
+ 
+
+ align:start position:0%
+this ancestor path so and there's only
+log n of them because now height is log
+
+ align:start position:0%
+log n of them because now height is log
+ 
+
+ align:start position:0%
+log n of them because now height is log
+n that's what we just proved as long as
+
+ align:start position:0%
+n that's what we just proved as long as
+ 
+
+ align:start position:0%
+n that's what we just proved as long as
+we have this property now we right now
+
+ align:start position:0%
+we have this property now we right now
+ 
+
+ align:start position:0%
+we have this property now we right now
+don't have it for like maybe these few
+
+ align:start position:0%
+don't have it for like maybe these few
+ 
+
+ align:start position:0%
+don't have it for like maybe these few
+notes but it will be it was log n before
+
+ align:start position:0%
+notes but it will be it was log n before
+ 
+
+ align:start position:0%
+notes but it will be it was log n before
+it's at most log n 2 log n plus one
+
+ align:start position:0%
+it's at most log n 2 log n plus one
+ 
+
+ align:start position:0%
+it's at most log n 2 log n plus one
+right now cuz we just added a Noe
+
+ align:start position:0%
+right now cuz we just added a Noe
+ 
+
+ align:start position:0%
+right now cuz we just added a Noe
+so what I want to do is check all of
+
+ align:start position:0%
+so what I want to do is check all of
+ 
+
+ align:start position:0%
+so what I want to do is check all of
+these ancestor nodes in sequence from
+
+ align:start position:0%
+these ancestor nodes in sequence from
+ 
+
+ align:start position:0%
+these ancestor nodes in sequence from
+bottom up and find one that's out of
+
+ align:start position:0%
+bottom up and find one that's out of
+ 
+
+ align:start position:0%
+bottom up and find one that's out of
+balance so let's take the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+lowest uh outof balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node I'm going to call that X now
+
+ align:start position:0%
+node I'm going to call that X now
+ 
+
+ align:start position:0%
+node I'm going to call that X now
+because we just inserted or deleted a
+
+ align:start position:0%
+because we just inserted or deleted a
+ 
+
+ align:start position:0%
+because we just inserted or deleted a
+single leaf it's only out of balance by
+
+ align:start position:0%
+single leaf it's only out of balance by
+ 
+
+ align:start position:0%
+single leaf it's only out of balance by
+one right because we only changed height
+
+ align:start position:0%
+one right because we only changed height
+ 
+
+ align:start position:0%
+one right because we only changed height
+one height went up by one or one height
+
+ align:start position:0%
+one height went up by one or one height
+ 
+
+ align:start position:0%
+one height went up by one or one height
+went down by one and before all of our
+
+ align:start position:0%
+went down by one and before all of our
+ 
+
+ align:start position:0%
+went down by one and before all of our
+SKS were plus or minus one or zero so
+
+ align:start position:0%
+SKS were plus or minus one or zero so
+ 
+
+ align:start position:0%
+SKS were plus or minus one or zero so
+now it's going the bad case is when it's
+
+ align:start position:0%
+now it's going the bad case is when it's
+ 
+
+ align:start position:0%
+now it's going the bad case is when it's
+plus or minus two if it happens to still
+
+ align:start position:0%
+plus or minus two if it happens to still
+ 
+
+ align:start position:0%
+plus or minus two if it happens to still
+be in this range for all the nodes we're
+
+ align:start position:0%
+be in this range for all the nodes we're
+ 
+
+ align:start position:0%
+be in this range for all the nodes we're
+happy but if it's outside this range
+
+ align:start position:0%
+happy but if it's outside this range
+ 
+
+ align:start position:0%
+happy but if it's outside this range
+it's only going to be out by one uh so
+
+ align:start position:0%
+it's only going to be out by one uh so
+ 
+
+ align:start position:0%
+it's only going to be out by one uh so
+this means the
+
+ align:start position:0%
+this means the
+ 
+
+ align:start position:0%
+this means the
+skew is in plus 2 orus
+
+ align:start position:0%
+skew is in plus 2 orus
+ 
+
+ align:start position:0%
+skew is in plus 2 orus
+2 and let's say that it's two by
+
+ align:start position:0%
+2 and let's say that it's two by
+ 
+
+ align:start position:0%
+2 and let's say that it's two by
+symmetry so um my picture
+
+ align:start position:0%
+symmetry so um my picture
+ 
+
+ align:start position:0%
+symmetry so um my picture
+is I'm going to draw double right
+
+ align:start position:0%
+is I'm going to draw double right
+ 
+
+ align:start position:0%
+is I'm going to draw double right
+arrow to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this sub tree is two higher than
+
+ align:start position:0%
+that this sub tree is two higher than
+ 
+
+ align:start position:0%
+that this sub tree is two higher than
+this sub tree okay so that's bad and we
+
+ align:start position:0%
+this sub tree okay so that's bad and we
+ 
+
+ align:start position:0%
+this sub tree okay so that's bad and we
+want to fix it the obvious thing to do
+
+ align:start position:0%
+want to fix it the obvious thing to do
+ 
+
+ align:start position:0%
+want to fix it the obvious thing to do
+is to rotate this Edge because that'll
+
+ align:start position:0%
+is to rotate this Edge because that'll
+ 
+
+ align:start position:0%
+is to rotate this Edge because that'll
+make this this is
+
+ align:start position:0%
+make this this is
+ 
+
+ align:start position:0%
+make this this is
+too this is too high and this is too low
+
+ align:start position:0%
+too this is too high and this is too low
+ 
+
+ align:start position:0%
+too this is too high and this is too low
+so if we rotate this should go down by
+
+ align:start position:0%
+so if we rotate this should go down by
+ 
+
+ align:start position:0%
+so if we rotate this should go down by
+one and this should go up by one and
+
+ align:start position:0%
+one and this should go up by one and
+ 
+
+ align:start position:0%
+one and this should go up by one and
+that works most of the
+
+ align:start position:0%
+that works most of the
+ 
+
+ align:start position:0%
+that works most of the
+time so case
+
+ align:start position:0%
+time so case
+ 
+
+ align:start position:0%
+time so case
+one is that
+
+ align:start position:0%
+one is that
+ 
+
+ align:start position:0%
+one is that
+skew of Y what is y I want y to be the
+
+ align:start position:0%
+skew of Y what is y I want y to be the
+ 
+
+ align:start position:0%
+skew of Y what is y I want y to be the
+right child of X because we have
+
+ align:start position:0%
+right child of X because we have
+ 
+
+ align:start position:0%
+right child of X because we have
+positive skew we know there is a right
+
+ align:start position:0%
+positive skew we know there is a right
+ 
+
+ align:start position:0%
+positive skew we know there is a right
+child now uh because this was the lowest
+
+ align:start position:0%
+child now uh because this was the lowest
+ 
+
+ align:start position:0%
+child now uh because this was the lowest
+bad we know that Y is actually good it's
+
+ align:start position:0%
+bad we know that Y is actually good it's
+ 
+
+ align:start position:0%
+bad we know that Y is actually good it's
+either right heavy or even the two sub
+
+ align:start position:0%
+either right heavy or even the two sub
+ 
+
+ align:start position:0%
+either right heavy or even the two sub
+trees have the same height or left heavy
+
+ align:start position:0%
+trees have the same height or left heavy
+ 
+
+ align:start position:0%
+trees have the same height or left heavy
+the easy
+
+ align:start position:0%
+the easy
+ 
+
+ align:start position:0%
+the easy
+cases uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are when skew of Y is either one or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero which I will draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so double right arrow let's
+
+ align:start position:0%
+all right so double right arrow let's
+ 
+
+ align:start position:0%
+all right so double right arrow let's
+say single right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arrow so this uh I'm just going to add
+
+ align:start position:0%
+arrow so this uh I'm just going to add
+ 
+
+ align:start position:0%
+arrow so this uh I'm just going to add
+some labels here to make this picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistent uh k + one K plus two I'm
+
+ align:start position:0%
+consistent uh k + one K plus two I'm
+ 
+
+ align:start position:0%
+consistent uh k + one K plus two I'm
+writing the heights so this is an
+
+ align:start position:0%
+writing the heights so this is an
+ 
+
+ align:start position:0%
+writing the heights so this is an
+example where C is is taller than b
+
+ align:start position:0%
+example where C is is taller than b
+ 
+
+ align:start position:0%
+example where C is is taller than b
+uh B A and B are the same height and
+
+ align:start position:0%
+uh B A and B are the same height and
+ 
+
+ align:start position:0%
+uh B A and B are the same height and
+then if you compute the heights up here
+
+ align:start position:0%
+then if you compute the heights up here
+ 
+
+ align:start position:0%
+then if you compute the heights up here
+indeed uh this one is right leaning this
+
+ align:start position:0%
+indeed uh this one is right leaning this
+ 
+
+ align:start position:0%
+indeed uh this one is right leaning this
+one is doubly right leaning this one has
+
+ align:start position:0%
+one is doubly right leaning this one has
+ 
+
+ align:start position:0%
+one is doubly right leaning this one has
+height K plus one this one has height K
+
+ align:start position:0%
+height K plus one this one has height K
+ 
+
+ align:start position:0%
+height K plus one this one has height K
+minus one that's bad but if we do this
+
+ align:start position:0%
+minus one that's bad but if we do this
+ 
+
+ align:start position:0%
+minus one that's bad but if we do this
+right rotation on X we get exactly what
+
+ align:start position:0%
+right rotation on X we get exactly what
+ 
+
+ align:start position:0%
+right rotation on X we get exactly what
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want so I'm just going to copy the
+
+ align:start position:0%
+want so I'm just going to copy the
+ 
+
+ align:start position:0%
+want so I'm just going to copy the
+labels on ABC we have k minus1 k minus
+
+ align:start position:0%
+labels on ABC we have k minus1 k minus
+ 
+
+ align:start position:0%
+labels on ABC we have k minus1 k minus
+one and K and then recompute that means
+
+ align:start position:0%
+one and K and then recompute that means
+ 
+
+ align:start position:0%
+one and K and then recompute that means
+this guy has height K this one has
+
+ align:start position:0%
+this guy has height K this one has
+ 
+
+ align:start position:0%
+this guy has height K this one has
+height k + 1 and now all the nodes in
+
+ align:start position:0%
+height k + 1 and now all the nodes in
+ 
+
+ align:start position:0%
+height k + 1 and now all the nodes in
+this picture that I've highlighted A and
+
+ align:start position:0%
+this picture that I've highlighted A and
+ 
+
+ align:start position:0%
+this picture that I've highlighted A and
+C haven't changed they were height
+
+ align:start position:0%
+C haven't changed they were height
+ 
+
+ align:start position:0%
+C haven't changed they were height
+balanced before they still are um but
+
+ align:start position:0%
+balanced before they still are um but
+ 
+
+ align:start position:0%
+balanced before they still are um but
+now X and Y X wasn't height balanced
+
+ align:start position:0%
+now X and Y X wasn't height balanced
+ 
+
+ align:start position:0%
+now X and Y X wasn't height balanced
+before y was now both X and Y are height
+
+ align:start position:0%
+before y was now both X and Y are height
+ 
+
+ align:start position:0%
+before y was now both X and Y are height
+balanced okay that's case one in case
+
+ align:start position:0%
+balanced okay that's case one in case
+ 
+
+ align:start position:0%
+balanced okay that's case one in case
+two the SK of Y is flat which means that
+
+ align:start position:0%
+two the SK of Y is flat which means that
+ 
+
+ align:start position:0%
+two the SK of Y is flat which means that
+this is a k and this is a k and this is
+
+ align:start position:0%
+this is a k and this is a k and this is
+ 
+
+ align:start position:0%
+this is a k and this is a k and this is
+a k + one and this this is a K plus 2
+
+ align:start position:0%
+a k + one and this this is a K plus 2
+ 
+
+ align:start position:0%
+a k + one and this this is a K plus 2
+okay but still all the nodes are
+
+ align:start position:0%
+okay but still all the nodes are
+ 
+
+ align:start position:0%
+okay but still all the nodes are
+balanced height balanced they're still
+
+ align:start position:0%
+balanced height balanced they're still
+ 
+
+ align:start position:0%
+balanced height balanced they're still
+plus or minus one so those are the easy
+
+ align:start position:0%
+plus or minus one so those are the easy
+ 
+
+ align:start position:0%
+plus or minus one so those are the easy
+cases unfortunately there is a hard
+
+ align:start position:0%
+cases unfortunately there is a hard
+ 
+
+ align:start position:0%
+cases unfortunately there is a hard
+case case three but there's only one and
+
+ align:start position:0%
+case case three but there's only one and
+ 
+
+ align:start position:0%
+case case three but there's only one and
+it's not that much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder so it's when skew of Y is minus
+
+ align:start position:0%
+harder so it's when skew of Y is minus
+ 
+
+ align:start position:0%
+harder so it's when skew of Y is minus
+one in this case we need to look at the
+
+ align:start position:0%
+one in this case we need to look at the
+ 
+
+ align:start position:0%
+one in this case we need to look at the
+left child of Y
+
+ align:start position:0%
+left child of Y
+ 
+
+ align:start position:0%
+left child of Y
+uh okay and to be alphabetical I'm going
+
+ align:start position:0%
+uh okay and to be alphabetical I'm going
+ 
+
+ align:start position:0%
+uh okay and to be alphabetical I'm going
+to rename this to
+
+ align:start position:0%
+to rename this to
+ 
+
+ align:start position:0%
+to rename this to
+Z sorry so this one again is double
+
+ align:start position:0%
+Z sorry so this one again is double
+ 
+
+ align:start position:0%
+Z sorry so this one again is double
+right arrow this one is now left
+
+ align:start position:0%
+right arrow this one is now left
+ 
+
+ align:start position:0%
+right arrow this one is now left
+arrow and this is letter Y and so we
+
+ align:start position:0%
+arrow and this is letter Y and so we
+ 
+
+ align:start position:0%
+arrow and this is letter Y and so we
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+b c and d potential sub trees hanging
+
+ align:start position:0%
+b c and d potential sub trees hanging
+ 
+
+ align:start position:0%
+b c and d potential sub trees hanging
+off of them and I'm going to label the
+
+ align:start position:0%
+off of them and I'm going to label the
+ 
+
+ align:start position:0%
+off of them and I'm going to label the
+heights of these things these are each K
+
+ align:start position:0%
+heights of these things these are each K
+ 
+
+ align:start position:0%
+heights of these things these are each K
+minus one or K minus 2 this one's K
+
+ align:start position:0%
+minus one or K minus 2 this one's K
+ 
+
+ align:start position:0%
+minus one or K minus 2 this one's K
+minus one and now compute the inside so
+
+ align:start position:0%
+minus one and now compute the inside so
+ 
+
+ align:start position:0%
+minus one and now compute the inside so
+this is going to be height k for this to
+
+ align:start position:0%
+this is going to be height k for this to
+ 
+
+ align:start position:0%
+this is going to be height k for this to
+be uh left leaning so this is k + 1 and
+
+ align:start position:0%
+be uh left leaning so this is k + 1 and
+ 
+
+ align:start position:0%
+be uh left leaning so this is k + 1 and
+this is k + 2 okay but the problem is
+
+ align:start position:0%
+this is k + 2 okay but the problem is
+ 
+
+ align:start position:0%
+this is k + 2 okay but the problem is
+this is two higher than this the height
+
+ align:start position:0%
+this is two higher than this the height
+ 
+
+ align:start position:0%
+this is two higher than this the height
+of Z is two higher than the height of a
+
+ align:start position:0%
+of Z is two higher than the height of a
+ 
+
+ align:start position:0%
+of Z is two higher than the height of a
+in this case if I do this rotation
+
+ align:start position:0%
+in this case if I do this rotation
+ 
+
+ align:start position:0%
+in this case if I do this rotation
+things get worse actually I'll just tell
+
+ align:start position:0%
+things get worse actually I'll just tell
+ 
+
+ align:start position:0%
+things get worse actually I'll just tell
+you the right thing to
+
+ align:start position:0%
+you the right thing to
+ 
+
+ align:start position:0%
+you the right thing to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+is this is the one thing you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+memorize and let me draw the result you
+
+ align:start position:0%
+memorize and let me draw the result you
+ 
+
+ align:start position:0%
+memorize and let me draw the result you
+can also just think of it as redrawing
+
+ align:start position:0%
+can also just think of it as redrawing
+ 
+
+ align:start position:0%
+can also just think of it as redrawing
+the tree like this uh but it's easier
+
+ align:start position:0%
+the tree like this uh but it's easier
+ 
+
+ align:start position:0%
+the tree like this uh but it's easier
+from an analysis perspective to think
+
+ align:start position:0%
+from an analysis perspective to think
+ 
+
+ align:start position:0%
+from an analysis perspective to think
+about it is two rotations so then we can
+
+ align:start position:0%
+about it is two rotations so then we can
+ 
+
+ align:start position:0%
+about it is two rotations so then we can
+just reduce as long as we know rotations
+
+ align:start position:0%
+just reduce as long as we know rotations
+ 
+
+ align:start position:0%
+just reduce as long as we know rotations
+work then we know that this thing works
+
+ align:start position:0%
+work then we know that this thing works
+ 
+
+ align:start position:0%
+work then we know that this thing works
+Works meaning it preserves traversal
+
+ align:start position:0%
+Works meaning it preserves traversal
+ 
+
+ align:start position:0%
+Works meaning it preserves traversal
+order and we can maintain all the
+
+ align:start position:0%
+order and we can maintain all the
+ 
+
+ align:start position:0%
+order and we can maintain all the
+augmentations so now if I copy over
+
+ align:start position:0%
+augmentations so now if I copy over
+ 
+
+ align:start position:0%
+augmentations so now if I copy over
+these labels the height labels I have K
+
+ align:start position:0%
+these labels the height labels I have K
+ 
+
+ align:start position:0%
+these labels the height labels I have K
+minus one I have for these two guys K
+
+ align:start position:0%
+minus one I have for these two guys K
+ 
+
+ align:start position:0%
+minus one I have for these two guys K
+minus one or k minus 2 biggest one is
+
+ align:start position:0%
+minus one or k minus 2 biggest one is
+ 
+
+ align:start position:0%
+minus one or k minus 2 biggest one is
+Kus one this is K minus one and so this
+
+ align:start position:0%
+Kus one this is K minus one and so this
+ 
+
+ align:start position:0%
+Kus one this is K minus one and so this
+will be K this will be K this will be k
+
+ align:start position:0%
+will be K this will be K this will be k
+ 
+
+ align:start position:0%
+will be K this will be K this will be k
++ one and lo and behold we have a nice
+
+ align:start position:0%
++ one and lo and behold we have a nice
+ 
+
+ align:start position:0%
++ one and lo and behold we have a nice
+height balanc Tree in all three cases
+
+ align:start position:0%
+height balanc Tree in all three cases
+ 
+
+ align:start position:0%
+height balanc Tree in all three cases
+for this one node now this was the low
+
+ align:start position:0%
+for this one node now this was the low
+ 
+
+ align:start position:0%
+for this one node now this was the low
+node once we update this one it could be
+
+ align:start position:0%
+node once we update this one it could be
+ 
+
+ align:start position:0%
+node once we update this one it could be
+that um we changed the height of the
+
+ align:start position:0%
+that um we changed the height of the
+ 
+
+ align:start position:0%
+that um we changed the height of the
+root before it was k + 2 now it's k+ one
+
+ align:start position:0%
+root before it was k + 2 now it's k+ one
+ 
+
+ align:start position:0%
+root before it was k + 2 now it's k+ one
+or sometimes we keep it the same like
+
+ align:start position:0%
+or sometimes we keep it the same like
+ 
+
+ align:start position:0%
+or sometimes we keep it the same like
+over in this case uh and so now we have
+
+ align:start position:0%
+over in this case uh and so now we have
+ 
+
+ align:start position:0%
+over in this case uh and so now we have
+to check the parent maybe the parent is
+
+ align:start position:0%
+to check the parent maybe the parent is
+ 
+
+ align:start position:0%
+to check the parent maybe the parent is
+out of balance we just keep walking up
+
+ align:start position:0%
+out of balance we just keep walking up
+ 
+
+ align:start position:0%
+out of balance we just keep walking up
+the node and also maintain all the
+
+ align:start position:0%
+the node and also maintain all the
+ 
+
+ align:start position:0%
+the node and also maintain all the
+augmentations as we go then we'll keep
+
+ align:start position:0%
+augmentations as we go then we'll keep
+ 
+
+ align:start position:0%
+augmentations as we go then we'll keep
+track of height and subtree size if we
+
+ align:start position:0%
+track of height and subtree size if we
+ 
+
+ align:start position:0%
+track of height and subtree size if we
+want them or any other augmentations and
+
+ align:start position:0%
+want them or any other augmentations and
+ 
+
+ align:start position:0%
+want them or any other augmentations and
+after order H operations we will have
+
+ align:start position:0%
+after order H operations we will have
+ 
+
+ align:start position:0%
+after order H operations we will have
+restored the height balance property
+
+ align:start position:0%
+restored the height balance property
+ 
+
+ align:start position:0%
+restored the height balance property
+which means all the way through H equals
+
+ align:start position:0%
+which means all the way through H equals
+ 
+
+ align:start position:0%
+which means all the way through H equals
+order log n and so all of our operations
+
+ align:start position:0%
+order log n and so all of our operations
+ 
+
+ align:start position:0%
+order log n and so all of our operations
+now are magically order log n
\ No newline at end of file
diff --git a/UP--RL-YKhE.txt b/UP--RL-YKhE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..856510c2a2a94223f75d125ed0128c7f2fca6bbf
--- /dev/null
+++ b/UP--RL-YKhE.txt
@@ -0,0 +1,10363 @@
+align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+next we will so we we're switching away
+
+ align:start position:0%
+next we will so we we're switching away
+ 
+
+ align:start position:0%
+next we will so we we're switching away
+from metric basis and we talk about
+
+ align:start position:0%
+from metric basis and we talk about
+ 
+
+ align:start position:0%
+from metric basis and we talk about
+differentiation.
+
+ align:start position:0%
+differentiation.
+ 
+
+ align:start position:0%
+differentiation.
+So if we have a function
+
+ align:start position:0%
+So if we have a function
+ 
+
+ align:start position:0%
+So if we have a function
+uh on R say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and then we say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh that x that f is differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0. If the limit here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the limit uh f ofx minus f of x0 if
+
+ align:start position:0%
+if the limit uh f ofx minus f of x0 if
+ 
+
+ align:start position:0%
+if the limit uh f ofx minus f of x0 if
+the divided by x - x0 if this limit here
+
+ align:start position:0%
+the divided by x - x0 if this limit here
+ 
+
+ align:start position:0%
+the divided by x - x0 if this limit here
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if this limit here exists
+
+ align:start position:0%
+um if this limit here exists
+ 
+
+ align:start position:0%
+um if this limit here exists
+as x go to x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here This here this quotient here
+
+ align:start position:0%
+this here This here this quotient here
+ 
+
+ align:start position:0%
+this here This here this quotient here
+is usually called the difference quotion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's always of course when you form
+
+ align:start position:0%
+and it's always of course when you form
+ 
+
+ align:start position:0%
+and it's always of course when you form
+this different quotient it's always
+
+ align:start position:0%
+this different quotient it's always
+ 
+
+ align:start position:0%
+this different quotient it's always
+assumed obviously that x is not equal to
+
+ align:start position:0%
+assumed obviously that x is not equal to
+ 
+
+ align:start position:0%
+assumed obviously that x is not equal to
+x0 so that the denominator makes sense
+
+ align:start position:0%
+x0 so that the denominator makes sense
+ 
+
+ align:start position:0%
+x0 so that the denominator makes sense
+right so if this limit here as x go to
+
+ align:start position:0%
+right so if this limit here as x go to
+ 
+
+ align:start position:0%
+right so if this limit here as x go to
+x0 if this exists then we say that the
+
+ align:start position:0%
+x0 if this exists then we say that the
+ 
+
+ align:start position:0%
+x0 if this exists then we say that the
+function f is differentiable at x0 and
+
+ align:start position:0%
+function f is differentiable at x0 and
+ 
+
+ align:start position:0%
+function f is differentiable at x0 and
+the limit is called the derivative of f
+
+ align:start position:0%
+the limit is called the derivative of f
+ 
+
+ align:start position:0%
+the limit is called the derivative of f
+at x0 and this is how it's denoted.
+
+ align:start position:0%
+at x0 and this is how it's denoted.
+ 
+
+ align:start position:0%
+at x0 and this is how it's denoted.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now
+
+ align:start position:0%
+So now
+ 
+
+ align:start position:0%
+So now
+the simplest possible example of this
+
+ align:start position:0%
+the simplest possible example of this
+ 
+
+ align:start position:0%
+the simplest possible example of this
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+uh that suppose that you're looking at a
+
+ align:start position:0%
+uh that suppose that you're looking at a
+ 
+
+ align:start position:0%
+uh that suppose that you're looking at a
+function that is constant. of f is equal
+
+ align:start position:0%
+function that is constant. of f is equal
+ 
+
+ align:start position:0%
+function that is constant. of f is equal
+to f for some constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh then if you're looking at this
+
+ align:start position:0%
+uh then if you're looking at this
+ 
+
+ align:start position:0%
+uh then if you're looking at this
+difference quotient so f of x - f of x0
+
+ align:start position:0%
+difference quotient so f of x - f of x0
+ 
+
+ align:start position:0%
+difference quotient so f of x - f of x0
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+well the value at any point is c so this
+
+ align:start position:0%
+well the value at any point is c so this
+ 
+
+ align:start position:0%
+well the value at any point is c so this
+here is c minus c / X - Y X 0 and so the
+
+ align:start position:0%
+here is c minus c / X - Y X 0 and so the
+ 
+
+ align:start position:0%
+here is c minus c / X - Y X 0 and so the
+denominator is zero. So this whole thing
+
+ align:start position:0%
+denominator is zero. So this whole thing
+ 
+
+ align:start position:0%
+denominator is zero. So this whole thing
+is zero and so of course the limit this
+
+ align:start position:0%
+is zero and so of course the limit this
+ 
+
+ align:start position:0%
+is zero and so of course the limit this
+is zero for each X
+
+ align:start position:0%
+is zero for each X
+ 
+
+ align:start position:0%
+is zero for each X
+and also it takes zero. So in particular
+
+ align:start position:0%
+and also it takes zero. So in particular
+ 
+
+ align:start position:0%
+and also it takes zero. So in particular
+of course the limit here exist. So the
+
+ align:start position:0%
+of course the limit here exist. So the
+ 
+
+ align:start position:0%
+of course the limit here exist. So the
+limit here of the different quotient
+
+ align:start position:0%
+limit here of the different quotient
+ 
+
+ align:start position:0%
+limit here of the different quotient
+uh exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's equal to zero right because
+
+ align:start position:0%
+and it's equal to zero right because
+ 
+
+ align:start position:0%
+and it's equal to zero right because
+it's zero for all x for a given x0.
+
+ align:start position:0%
+it's zero for all x for a given x0.
+ 
+
+ align:start position:0%
+it's zero for all x for a given x0.
+So that would be like the simplest
+
+ align:start position:0%
+So that would be like the simplest
+ 
+
+ align:start position:0%
+So that would be like the simplest
+possible example. The second simplest
+
+ align:start position:0%
+possible example. The second simplest
+ 
+
+ align:start position:0%
+possible example. The second simplest
+example, second most simple example
+
+ align:start position:0%
+example, second most simple example
+ 
+
+ align:start position:0%
+example, second most simple example
+would be that you're looking at a linear
+
+ align:start position:0%
+would be that you're looking at a linear
+ 
+
+ align:start position:0%
+would be that you're looking at a linear
+function. So let's say that f ofx is
+
+ align:start position:0%
+function. So let's say that f ofx is
+ 
+
+ align:start position:0%
+function. So let's say that f ofx is
+equal to x, right? In this case, the
+
+ align:start position:0%
+equal to x, right? In this case, the
+ 
+
+ align:start position:0%
+equal to x, right? In this case, the
+difference quotient.
+
+ align:start position:0%
+difference quotient.
+ 
+
+ align:start position:0%
+difference quotient.
+So the difference quotient here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this here is x.
+
+ align:start position:0%
+well this here is x.
+ 
+
+ align:start position:0%
+well this here is x.
+This here is x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this here is for each x and x0. This
+
+ align:start position:0%
+So this here is for each x and x0. This
+ 
+
+ align:start position:0%
+So this here is for each x and x0. This
+is one. So the limit of course in this
+
+ align:start position:0%
+is one. So the limit of course in this
+ 
+
+ align:start position:0%
+is one. So the limit of course in this
+case also exist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The limit here exist and it's equal to
+
+ align:start position:0%
+The limit here exist and it's equal to
+ 
+
+ align:start position:0%
+The limit here exist and it's equal to
+to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So in this case, so in this case
+
+ align:start position:0%
+Right? So in this case, so in this case
+ 
+
+ align:start position:0%
+Right? So in this case, so in this case
+f is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at all points and the derivative at all
+
+ align:start position:0%
+at all points and the derivative at all
+ 
+
+ align:start position:0%
+at all points and the derivative at all
+points is equal to zero. In this case, f
+
+ align:start position:0%
+points is equal to zero. In this case, f
+ 
+
+ align:start position:0%
+points is equal to zero. In this case, f
+here is also differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the derivative at all points is
+
+ align:start position:0%
+and the derivative at all points is
+ 
+
+ align:start position:0%
+and the derivative at all points is
+equal to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now in general how do we
+
+ align:start position:0%
+Okay. So now in general how do we
+ 
+
+ align:start position:0%
+Okay. So now in general how do we
+compute the so how do we compute the
+
+ align:start position:0%
+compute the so how do we compute the
+ 
+
+ align:start position:0%
+compute the so how do we compute the
+derivative of a function?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh how how do we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for that there are some some basic
+
+ align:start position:0%
+and for that there are some some basic
+ 
+
+ align:start position:0%
+and for that there are some some basic
+uh laws how to compute it. So there's
+
+ align:start position:0%
+uh laws how to compute it. So there's
+ 
+
+ align:start position:0%
+uh laws how to compute it. So there's
+these laws
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the sum rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what's usually called the liess rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the quotient rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then uh also the chain rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now let me uh look at the first three
+
+ align:start position:0%
+Now let me uh look at the first three
+ 
+
+ align:start position:0%
+Now let me uh look at the first three
+rules first.
+
+ align:start position:0%
+rules first.
+ 
+
+ align:start position:0%
+rules first.
+So um
+
+ align:start position:0%
+So um
+ 
+
+ align:start position:0%
+So um
+I have uh two functions f and g they are
+
+ align:start position:0%
+I have uh two functions f and g they are
+ 
+
+ align:start position:0%
+I have uh two functions f and g they are
+defined say on r but it could have been
+
+ align:start position:0%
+defined say on r but it could have been
+ 
+
+ align:start position:0%
+defined say on r but it could have been
+a subset of r
+
+ align:start position:0%
+a subset of r
+ 
+
+ align:start position:0%
+a subset of r
+uh and uh I'm assuming that that they
+
+ align:start position:0%
+uh and uh I'm assuming that that they
+ 
+
+ align:start position:0%
+uh and uh I'm assuming that that they
+are both
+
+ align:start position:0%
+are both
+ 
+
+ align:start position:0%
+are both
+and both
+
+ align:start position:0%
+and both
+ 
+
+ align:start position:0%
+and both
+right actually I need we'll need one
+
+ align:start position:0%
+right actually I need we'll need one
+ 
+
+ align:start position:0%
+right actually I need we'll need one
+okay so both Um
+
+ align:start position:0%
+okay so both Um
+ 
+
+ align:start position:0%
+okay so both Um
+f and g are differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0.
+
+ align:start position:0%
+at x0.
+ 
+
+ align:start position:0%
+at x0.
+Then we have the following. So we have
+
+ align:start position:0%
+Then we have the following. So we have
+ 
+
+ align:start position:0%
+Then we have the following. So we have
+the following lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh one is we have that. So one and this
+
+ align:start position:0%
+uh one is we have that. So one and this
+ 
+
+ align:start position:0%
+uh one is we have that. So one and this
+is really the sum rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We have that the sum here f plus g. So
+
+ align:start position:0%
+We have that the sum here f plus g. So
+ 
+
+ align:start position:0%
+We have that the sum here f plus g. So
+the sum of these two functions this is
+
+ align:start position:0%
+the sum of these two functions this is
+ 
+
+ align:start position:0%
+the sum of these two functions this is
+the function that is just in x is just a
+
+ align:start position:0%
+the function that is just in x is just a
+ 
+
+ align:start position:0%
+the function that is just in x is just a
+sum of f ofx and g of x. We have that
+
+ align:start position:0%
+sum of f ofx and g of x. We have that
+ 
+
+ align:start position:0%
+sum of f ofx and g of x. We have that
+this function here
+
+ align:start position:0%
+this function here
+ 
+
+ align:start position:0%
+this function here
+f + g is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+and the derivative f + g. The derivative
+
+ align:start position:0%
+and the derivative f + g. The derivative
+ 
+
+ align:start position:0%
+and the derivative f + g. The derivative
+of this nx0 is just a sum of the
+
+ align:start position:0%
+of this nx0 is just a sum of the
+ 
+
+ align:start position:0%
+of this nx0 is just a sum of the
+derivative.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me let me prove this one here right
+
+ align:start position:0%
+let me let me prove this one here right
+ 
+
+ align:start position:0%
+let me let me prove this one here right
+away. So let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's prove this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have the sum. So uh we we will we
+
+ align:start position:0%
+So we have the sum. So uh we we will we
+ 
+
+ align:start position:0%
+So we have the sum. So uh we we will we
+are going to look at so we form the
+
+ align:start position:0%
+are going to look at so we form the
+ 
+
+ align:start position:0%
+are going to look at so we form the
+difference. So form the difference
+
+ align:start position:0%
+difference. So form the difference
+ 
+
+ align:start position:0%
+difference. So form the difference
+quotion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So f + g
+
+ align:start position:0%
+So f + g
+ 
+
+ align:start position:0%
+So f + g
+at x - f + g
+
+ align:start position:0%
+at x - f + g
+ 
+
+ align:start position:0%
+at x - f + g
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+right so now what is this? So this here
+
+ align:start position:0%
+right so now what is this? So this here
+ 
+
+ align:start position:0%
+right so now what is this? So this here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh this is just f of x plus g of x
+
+ align:start position:0%
+uh this is just f of x plus g of x
+ 
+
+ align:start position:0%
+uh this is just f of x plus g of x
+minus and then f of x0 plus g of x0
+
+ align:start position:0%
+minus and then f of x0 plus g of x0
+ 
+
+ align:start position:0%
+minus and then f of x0 plus g of x0
+and then divided by x - x0 right
+
+ align:start position:0%
+and then divided by x - x0 right
+ 
+
+ align:start position:0%
+and then divided by x - x0 right
+and so then you can split this up into
+
+ align:start position:0%
+and so then you can split this up into
+ 
+
+ align:start position:0%
+and so then you can split this up into
+two. You can write this difference
+
+ align:start position:0%
+two. You can write this difference
+ 
+
+ align:start position:0%
+two. You can write this difference
+quotion as if you split it up. If you
+
+ align:start position:0%
+quotion as if you split it up. If you
+ 
+
+ align:start position:0%
+quotion as if you split it up. If you
+collect the fs in a nominator.
+
+ align:start position:0%
+collect the fs in a nominator.
+ 
+
+ align:start position:0%
+collect the fs in a nominator.
+So I just collect the fs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then afterwards I collect the and I
+
+ align:start position:0%
+and then afterwards I collect the and I
+ 
+
+ align:start position:0%
+and then afterwards I collect the and I
+put it on two different fractions.
+
+ align:start position:0%
+put it on two different fractions.
+ 
+
+ align:start position:0%
+put it on two different fractions.
+Separate them out and then I collect the
+
+ align:start position:0%
+Separate them out and then I collect the
+ 
+
+ align:start position:0%
+Separate them out and then I collect the
+G's.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now you see that because f was
+
+ align:start position:0%
+And now you see that because f was
+ 
+
+ align:start position:0%
+And now you see that because f was
+differentiable at x0 this thing here as
+
+ align:start position:0%
+differentiable at x0 this thing here as
+ 
+
+ align:start position:0%
+differentiable at x0 this thing here as
+x go to x0 this here goes to fprime. So
+
+ align:start position:0%
+x go to x0 this here goes to fprime. So
+ 
+
+ align:start position:0%
+x go to x0 this here goes to fprime. So
+this here goes to f prime of x0. This is
+
+ align:start position:0%
+this here goes to f prime of x0. This is
+ 
+
+ align:start position:0%
+this here goes to f prime of x0. This is
+what this difference quotient here. And
+
+ align:start position:0%
+what this difference quotient here. And
+ 
+
+ align:start position:0%
+what this difference quotient here. And
+this difference quotient goes to g prime
+
+ align:start position:0%
+this difference quotient goes to g prime
+ 
+
+ align:start position:0%
+this difference quotient goes to g prime
+of zero. So you have that indeed it does
+
+ align:start position:0%
+of zero. So you have that indeed it does
+ 
+
+ align:start position:0%
+of zero. So you have that indeed it does
+converge and this is what it converts to
+
+ align:start position:0%
+converge and this is what it converts to
+ 
+
+ align:start position:0%
+converge and this is what it converts to
+right and so this prove that the sum of
+
+ align:start position:0%
+right and so this prove that the sum of
+ 
+
+ align:start position:0%
+right and so this prove that the sum of
+these two functions is also
+
+ align:start position:0%
+these two functions is also
+ 
+
+ align:start position:0%
+these two functions is also
+differentiable and their derivative is
+
+ align:start position:0%
+differentiable and their derivative is
+ 
+
+ align:start position:0%
+differentiable and their derivative is
+the sum of the derivative okay the next
+
+ align:start position:0%
+the sum of the derivative okay the next
+ 
+
+ align:start position:0%
+the sum of the derivative okay the next
+thing we will prove is len rule but
+
+ align:start position:0%
+thing we will prove is len rule but
+ 
+
+ align:start position:0%
+thing we will prove is len rule but
+before that I need to kind of step back
+
+ align:start position:0%
+before that I need to kind of step back
+ 
+
+ align:start position:0%
+before that I need to kind of step back
+and I want to so before proving so the
+
+ align:start position:0%
+and I want to so before proving so the
+ 
+
+ align:start position:0%
+and I want to so before proving so the
+next uh maybe I'll just state it and
+
+ align:start position:0%
+next uh maybe I'll just state it and
+ 
+
+ align:start position:0%
+next uh maybe I'll just state it and
+then we'll go back and we need something
+
+ align:start position:0%
+then we'll go back and we need something
+ 
+
+ align:start position:0%
+then we'll go back and we need something
+The next is what's called liveness rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's all you know you could also call
+
+ align:start position:0%
+So it's all you know you could also call
+ 
+
+ align:start position:0%
+So it's all you know you could also call
+it product rule but it's really quite
+
+ align:start position:0%
+it product rule but it's really quite
+ 
+
+ align:start position:0%
+it product rule but it's really quite
+generally called the lieness rule.
+
+ align:start position:0%
+generally called the lieness rule.
+ 
+
+ align:start position:0%
+generally called the lieness rule.
+And so this is when you looking at the
+
+ align:start position:0%
+And so this is when you looking at the
+ 
+
+ align:start position:0%
+And so this is when you looking at the
+product of these function. So the
+
+ align:start position:0%
+product of these function. So the
+ 
+
+ align:start position:0%
+product of these function. So the
+product function,
+
+ align:start position:0%
+product function,
+ 
+
+ align:start position:0%
+product function,
+the product function is a function in x
+
+ align:start position:0%
+the product function is a function in x
+ 
+
+ align:start position:0%
+the product function is a function in x
+that is just the product of f ofx and g
+
+ align:start position:0%
+that is just the product of f ofx and g
+ 
+
+ align:start position:0%
+that is just the product of f ofx and g
+of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and lightness rule.
+
+ align:start position:0%
+and lightness rule.
+ 
+
+ align:start position:0%
+and lightness rule.
+Lightness rule it say the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if f and g are differentiable at x0
+
+ align:start position:0%
+that if f and g are differentiable at x0
+ 
+
+ align:start position:0%
+that if f and g are differentiable at x0
+then the product of these two function
+
+ align:start position:0%
+then the product of these two function
+ 
+
+ align:start position:0%
+then the product of these two function
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is also differentiable at x0.
+
+ align:start position:0%
+is also differentiable at x0.
+ 
+
+ align:start position:0%
+is also differentiable at x0.
+And the derivative of the product is the
+
+ align:start position:0%
+And the derivative of the product is the
+ 
+
+ align:start position:0%
+And the derivative of the product is the
+derivative of the first function at x0
+
+ align:start position:0%
+derivative of the first function at x0
+ 
+
+ align:start position:0%
+derivative of the first function at x0
+times the value of the second function
+
+ align:start position:0%
+times the value of the second function
+ 
+
+ align:start position:0%
+times the value of the second function
+at x0 plus the uh the symmetric in f and
+
+ align:start position:0%
+at x0 plus the uh the symmetric in f and
+ 
+
+ align:start position:0%
+at x0 plus the uh the symmetric in f and
+g which is the value of f at x0 times
+
+ align:start position:0%
+g which is the value of f at x0 times
+ 
+
+ align:start position:0%
+g which is the value of f at x0 times
+the derivative of g at x0. Right? So the
+
+ align:start position:0%
+the derivative of g at x0. Right? So the
+ 
+
+ align:start position:0%
+the derivative of g at x0. Right? So the
+product is differentiable at x0 also.
+
+ align:start position:0%
+product is differentiable at x0 also.
+ 
+
+ align:start position:0%
+product is differentiable at x0 also.
+And this is what the derivative is. And
+
+ align:start position:0%
+And this is what the derivative is. And
+ 
+
+ align:start position:0%
+And this is what the derivative is. And
+in the notes, I just copied a little bit
+
+ align:start position:0%
+in the notes, I just copied a little bit
+ 
+
+ align:start position:0%
+in the notes, I just copied a little bit
+of thing just for fun from Wikipedia
+
+ align:start position:0%
+of thing just for fun from Wikipedia
+ 
+
+ align:start position:0%
+of thing just for fun from Wikipedia
+about lightnings. That was kind of
+
+ align:start position:0%
+about lightnings. That was kind of
+ 
+
+ align:start position:0%
+about lightnings. That was kind of
+interesting figure and played an
+
+ align:start position:0%
+interesting figure and played an
+ 
+
+ align:start position:0%
+interesting figure and played an
+important role long time ago.
+
+ align:start position:0%
+important role long time ago.
+ 
+
+ align:start position:0%
+important role long time ago.
+Okay. So before I want to prove this,
+
+ align:start position:0%
+Okay. So before I want to prove this,
+ 
+
+ align:start position:0%
+Okay. So before I want to prove this,
+let me step back and let me make an
+
+ align:start position:0%
+let me step back and let me make an
+ 
+
+ align:start position:0%
+let me step back and let me make an
+observation about
+
+ align:start position:0%
+observation about
+ 
+
+ align:start position:0%
+observation about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh what it means to be differentiable at
+
+ align:start position:0%
+uh what it means to be differentiable at
+ 
+
+ align:start position:0%
+uh what it means to be differentiable at
+a point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So So this is the next lemon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have a function f
+
+ align:start position:0%
+So you have a function f
+ 
+
+ align:start position:0%
+So you have a function f
+on r into r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and you assume that um uh f so if
+
+ align:start position:0%
+and and you assume that um uh f so if
+ 
+
+ align:start position:0%
+and and you assume that um uh f so if
+f here is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0. Then I claim that then f here is
+
+ align:start position:0%
+at x0. Then I claim that then f here is
+ 
+
+ align:start position:0%
+at x0. Then I claim that then f here is
+also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0. Okay. Okay. So, so in other
+
+ align:start position:0%
+at x0. Okay. Okay. So, so in other
+ 
+
+ align:start position:0%
+at x0. Okay. Okay. So, so in other
+words, different being differentiable is
+
+ align:start position:0%
+words, different being differentiable is
+ 
+
+ align:start position:0%
+words, different being differentiable is
+stronger than being continuous.
+
+ align:start position:0%
+stronger than being continuous.
+ 
+
+ align:start position:0%
+stronger than being continuous.
+In a minute, we will see an example of
+
+ align:start position:0%
+In a minute, we will see an example of
+ 
+
+ align:start position:0%
+In a minute, we will see an example of
+something that's continuous but not
+
+ align:start position:0%
+something that's continuous but not
+ 
+
+ align:start position:0%
+something that's continuous but not
+differentiable.
+
+ align:start position:0%
+differentiable.
+ 
+
+ align:start position:0%
+differentiable.
+And so
+
+ align:start position:0%
+And so
+ 
+
+ align:start position:0%
+And so
+uh okay so now let's try to prove that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right so I'm assuming that it's
+
+ align:start position:0%
+so right so I'm assuming that it's
+ 
+
+ align:start position:0%
+so right so I'm assuming that it's
+differentiable so this means that
+
+ align:start position:0%
+differentiable so this means that
+ 
+
+ align:start position:0%
+differentiable so this means that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this difference quotient here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here has a limit and that limit is
+
+ align:start position:0%
+this here has a limit and that limit is
+ 
+
+ align:start position:0%
+this here has a limit and that limit is
+the derivative right as x go to x0.
+
+ align:start position:0%
+the derivative right as x go to x0.
+ 
+
+ align:start position:0%
+the derivative right as x go to x0.
+So this means that um that there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there exist delta greater than zero
+
+ align:start position:0%
+uh there exist delta greater than zero
+ 
+
+ align:start position:0%
+uh there exist delta greater than zero
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if x here
+
+ align:start position:0%
+if x here
+ 
+
+ align:start position:0%
+if x here
+uh minus x0
+
+ align:start position:0%
+uh minus x0
+ 
+
+ align:start position:0%
+uh minus x0
+is less than delta
+
+ align:start position:0%
+is less than delta
+ 
+
+ align:start position:0%
+is less than delta
+right of course I'm assuming that it's
+
+ align:start position:0%
+right of course I'm assuming that it's
+ 
+
+ align:start position:0%
+right of course I'm assuming that it's
+not equal to x0.
+
+ align:start position:0%
+not equal to x0.
+ 
+
+ align:start position:0%
+not equal to x0.
+If it is less than the difference to uh
+
+ align:start position:0%
+If it is less than the difference to uh
+ 
+
+ align:start position:0%
+If it is less than the difference to uh
+between x and x0 is less than delta,
+
+ align:start position:0%
+between x and x0 is less than delta,
+ 
+
+ align:start position:0%
+between x and x0 is less than delta,
+then this difference quotient here then
+
+ align:start position:0%
+then this difference quotient here then
+ 
+
+ align:start position:0%
+then this difference quotient here then
+f of x - f
+
+ align:start position:0%
+f of x - f
+ 
+
+ align:start position:0%
+f of x - f
+of x0
+
+ align:start position:0%
+of x0
+ 
+
+ align:start position:0%
+of x0
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+- frime of x0. this thing here have to
+
+ align:start position:0%
+- frime of x0. this thing here have to
+ 
+
+ align:start position:0%
+- frime of x0. this thing here have to
+be less than one right I mean this is
+
+ align:start position:0%
+be less than one right I mean this is
+ 
+
+ align:start position:0%
+be less than one right I mean this is
+just using that this limit exists and
+
+ align:start position:0%
+just using that this limit exists and
+ 
+
+ align:start position:0%
+just using that this limit exists and
+I'm sort of using in place of epsilon
+
+ align:start position:0%
+I'm sort of using in place of epsilon
+ 
+
+ align:start position:0%
+I'm sort of using in place of epsilon
+I'm using one right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+now so this means just multiplying over
+
+ align:start position:0%
+now so this means just multiplying over
+ 
+
+ align:start position:0%
+now so this means just multiplying over
+and And multiplying over you get that f
+
+ align:start position:0%
+and And multiplying over you get that f
+ 
+
+ align:start position:0%
+and And multiplying over you get that f
+ofx
+
+ align:start position:0%
+ofx
+ 
+
+ align:start position:0%
+ofx
+minus f of x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh minus
+
+ align:start position:0%
+uh minus
+ 
+
+ align:start position:0%
+uh minus
+frime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh of x0
+
+ align:start position:0%
+uh of x0
+ 
+
+ align:start position:0%
+uh of x0
+this thing here
+
+ align:start position:0%
+this thing here
+ 
+
+ align:start position:0%
+this thing here
+uh times I'm I'm multiplying both sides.
+
+ align:start position:0%
+uh times I'm I'm multiplying both sides.
+ 
+
+ align:start position:0%
+uh times I'm I'm multiplying both sides.
+So I'm multiplying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both sides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh by
+
+ align:start position:0%
+uh by
+ 
+
+ align:start position:0%
+uh by
+uh x - x0. This is a positive thing,
+
+ align:start position:0%
+uh x - x0. This is a positive thing,
+ 
+
+ align:start position:0%
+uh x - x0. This is a positive thing,
+right? So I'm multiplying both sync by
+
+ align:start position:0%
+right? So I'm multiplying both sync by
+ 
+
+ align:start position:0%
+right? So I'm multiplying both sync by
+that. So then I get this thing here x -
+
+ align:start position:0%
+that. So then I get this thing here x -
+ 
+
+ align:start position:0%
+that. So then I get this thing here x -
+x0.
+
+ align:start position:0%
+x0.
+ 
+
+ align:start position:0%
+x0.
+Uh and then I get less less strictly
+
+ align:start position:0%
+Uh and then I get less less strictly
+ 
+
+ align:start position:0%
+Uh and then I get less less strictly
+less than x - x0, right? Because this
+
+ align:start position:0%
+less than x - x0, right? Because this
+ 
+
+ align:start position:0%
+less than x - x0, right? Because this
+here is strictly positive.
+
+ align:start position:0%
+here is strictly positive.
+ 
+
+ align:start position:0%
+here is strictly positive.
+because x is not equal to x0. So I have
+
+ align:start position:0%
+because x is not equal to x0. So I have
+ 
+
+ align:start position:0%
+because x is not equal to x0. So I have
+that and so I get that. So I now I just
+
+ align:start position:0%
+that and so I get that. So I now I just
+ 
+
+ align:start position:0%
+that and so I get that. So I now I just
+split it up. So I have that f ofx - f of
+
+ align:start position:0%
+split it up. So I have that f ofx - f of
+ 
+
+ align:start position:0%
+split it up. So I have that f ofx - f of
+x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is now less than
+
+ align:start position:0%
+is now less than
+ 
+
+ align:start position:0%
+is now less than
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+plus frime of x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time uh x - x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is just the triangle
+
+ align:start position:0%
+right this is just the triangle
+ 
+
+ align:start position:0%
+right this is just the triangle
+inequality that we've used many times
+
+ align:start position:0%
+inequality that we've used many times
+ 
+
+ align:start position:0%
+inequality that we've used many times
+just on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so now you see that um that if you
+
+ align:start position:0%
+and so now you see that um that if you
+ 
+
+ align:start position:0%
+and so now you see that um that if you
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um so given
+
+ align:start position:0%
+um so given
+ 
+
+ align:start position:0%
+um so given
+so now if you so now and this here of
+
+ align:start position:0%
+so now if you so now and this here of
+ 
+
+ align:start position:0%
+so now if you so now and this here of
+course I can also write
+
+ align:start position:0%
+course I can also write
+ 
+
+ align:start position:0%
+course I can also write
+uh like this
+
+ align:start position:0%
+uh like this
+ 
+
+ align:start position:0%
+uh like this
+sorry I can just factor this out and I
+
+ align:start position:0%
+sorry I can just factor this out and I
+ 
+
+ align:start position:0%
+sorry I can just factor this out and I
+can write it as 1 + frime of x0
+
+ align:start position:0%
+can write it as 1 + frime of x0
+ 
+
+ align:start position:0%
+can write it as 1 + frime of x0
+like this fine and so now if I want this
+
+ align:start position:0%
+like this fine and so now if I want this
+ 
+
+ align:start position:0%
+like this fine and so now if I want this
+thing here so so now you can if you were
+
+ align:start position:0%
+thing here so so now you can if you were
+ 
+
+ align:start position:0%
+thing here so so now you can if you were
+to right so now you want to prove that f
+
+ align:start position:0%
+to right so now you want to prove that f
+ 
+
+ align:start position:0%
+to right so now you want to prove that f
+is continuous at x0 so you want this
+
+ align:start position:0%
+is continuous at x0 so you want this
+ 
+
+ align:start position:0%
+is continuous at x0 so you want this
+here to be less than some given epsilon
+
+ align:start position:0%
+here to be less than some given epsilon
+ 
+
+ align:start position:0%
+here to be less than some given epsilon
+So given epsilon
+
+ align:start position:0%
+So given epsilon
+ 
+
+ align:start position:0%
+So given epsilon
+epsilon greater than zero
+
+ align:start position:0%
+epsilon greater than zero
+ 
+
+ align:start position:0%
+epsilon greater than zero
+you uh let
+
+ align:start position:0%
+you uh let
+ 
+
+ align:start position:0%
+you uh let
+delta 1 be like the minimum
+
+ align:start position:0%
+delta 1 be like the minimum
+ 
+
+ align:start position:0%
+delta 1 be like the minimum
+of uh if you let said
+
+ align:start position:0%
+of uh if you let said
+ 
+
+ align:start position:0%
+of uh if you let said
+delta 1 to be the minimum of the delta
+
+ align:start position:0%
+delta 1 to be the minimum of the delta
+ 
+
+ align:start position:0%
+delta 1 to be the minimum of the delta
+that I already chose. So then I have
+
+ align:start position:0%
+that I already chose. So then I have
+ 
+
+ align:start position:0%
+that I already chose. So then I have
+this inequality
+
+ align:start position:0%
+this inequality
+ 
+
+ align:start position:0%
+this inequality
+and then um and then uh epsilon
+
+ align:start position:0%
+and then um and then uh epsilon
+ 
+
+ align:start position:0%
+and then um and then uh epsilon
+uh over 1 + frime of x0
+
+ align:start position:0%
+uh over 1 + frime of x0
+ 
+
+ align:start position:0%
+uh over 1 + frime of x0
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so if I make delta
+
+ align:start position:0%
+so if I make delta
+ 
+
+ align:start position:0%
+so if I make delta
+I choose delta like this then I have
+
+ align:start position:0%
+I choose delta like this then I have
+ 
+
+ align:start position:0%
+I choose delta like this then I have
+this inequality
+
+ align:start position:0%
+this inequality
+ 
+
+ align:start position:0%
+this inequality
+I fill in that so now I'm assuming that
+
+ align:start position:0%
+I fill in that so now I'm assuming that
+ 
+
+ align:start position:0%
+I fill in that so now I'm assuming that
+this thing here is less than delta 1.
+
+ align:start position:0%
+this thing here is less than delta 1.
+ 
+
+ align:start position:0%
+this thing here is less than delta 1.
+So again I have this inequality because
+
+ align:start position:0%
+So again I have this inequality because
+ 
+
+ align:start position:0%
+So again I have this inequality because
+it's less than delta. So then uh when I
+
+ align:start position:0%
+it's less than delta. So then uh when I
+ 
+
+ align:start position:0%
+it's less than delta. So then uh when I
+fill in here delta 1
+
+ align:start position:0%
+fill in here delta 1
+ 
+
+ align:start position:0%
+fill in here delta 1
+for this then I see that this thing here
+
+ align:start position:0%
+for this then I see that this thing here
+ 
+
+ align:start position:0%
+for this then I see that this thing here
+times this is less than epsilon.
+
+ align:start position:0%
+times this is less than epsilon.
+ 
+
+ align:start position:0%
+times this is less than epsilon.
+This here
+
+ align:start position:0%
+This here
+ 
+
+ align:start position:0%
+This here
+holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+is less than delta 1 right again because
+
+ align:start position:0%
+is less than delta 1 right again because
+ 
+
+ align:start position:0%
+is less than delta 1 right again because
+if it's less than delta 1 it's less than
+
+ align:start position:0%
+if it's less than delta 1 it's less than
+ 
+
+ align:start position:0%
+if it's less than delta 1 it's less than
+delta so I have this inequality and then
+
+ align:start position:0%
+delta so I have this inequality and then
+ 
+
+ align:start position:0%
+delta so I have this inequality and then
+I can use that delta 1 since is less
+
+ align:start position:0%
+I can use that delta 1 since is less
+ 
+
+ align:start position:0%
+I can use that delta 1 since is less
+than this
+
+ align:start position:0%
+than this
+ 
+
+ align:start position:0%
+than this
+and then I get this inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this prove right so this is
+
+ align:start position:0%
+okay so this prove right so this is
+ 
+
+ align:start position:0%
+okay so this prove right so this is
+really what we want to prove right we
+
+ align:start position:0%
+really what we want to prove right we
+ 
+
+ align:start position:0%
+really what we want to prove right we
+want to prove that if it's
+
+ align:start position:0%
+want to prove that if it's
+ 
+
+ align:start position:0%
+want to prove that if it's
+differentiable then it's also continuous
+
+ align:start position:0%
+differentiable then it's also continuous
+ 
+
+ align:start position:0%
+differentiable then it's also continuous
+and the continuity here I I proved it
+
+ align:start position:0%
+and the continuity here I I proved it
+ 
+
+ align:start position:0%
+and the continuity here I I proved it
+you know with you know epsilon or delta
+
+ align:start position:0%
+you know with you know epsilon or delta
+ 
+
+ align:start position:0%
+you know with you know epsilon or delta
+that you really should prove it like
+
+ align:start position:0%
+that you really should prove it like
+ 
+
+ align:start position:0%
+that you really should prove it like
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now let's look at some examples so this
+
+ align:start position:0%
+now let's look at some examples so this
+ 
+
+ align:start position:0%
+now let's look at some examples so this
+means that if a function is
+
+ align:start position:0%
+means that if a function is
+ 
+
+ align:start position:0%
+means that if a function is
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+then it's continuous
+
+ align:start position:0%
+then it's continuous
+ 
+
+ align:start position:0%
+then it's continuous
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me give you an example
+
+ align:start position:0%
+Let me give you an example
+ 
+
+ align:start position:0%
+Let me give you an example
+uh of a function that is so let me give
+
+ align:start position:0%
+uh of a function that is so let me give
+ 
+
+ align:start position:0%
+uh of a function that is so let me give
+you a few three examples.
+
+ align:start position:0%
+you a few three examples.
+ 
+
+ align:start position:0%
+you a few three examples.
+The first example is maybe the simplest
+
+ align:start position:0%
+The first example is maybe the simplest
+ 
+
+ align:start position:0%
+The first example is maybe the simplest
+one um that so this is the function f
+
+ align:start position:0%
+one um that so this is the function f
+ 
+
+ align:start position:0%
+one um that so this is the function f
+ofx that is equal to the absolute value
+
+ align:start position:0%
+ofx that is equal to the absolute value
+ 
+
+ align:start position:0%
+ofx that is equal to the absolute value
+of of x. So f here is defined on r into
+
+ align:start position:0%
+of of x. So f here is defined on r into
+ 
+
+ align:start position:0%
+of of x. So f here is defined on r into
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's just the absolute value and so
+
+ align:start position:0%
+and it's just the absolute value and so
+ 
+
+ align:start position:0%
+and it's just the absolute value and so
+I well the absolute value here so we've
+
+ align:start position:0%
+I well the absolute value here so we've
+ 
+
+ align:start position:0%
+I well the absolute value here so we've
+seen before so f here is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's continuous at all points right uh
+
+ align:start position:0%
+it's continuous at all points right uh
+ 
+
+ align:start position:0%
+it's continuous at all points right uh
+in particular of course at zero right
+
+ align:start position:0%
+in particular of course at zero right
+ 
+
+ align:start position:0%
+in particular of course at zero right
+but if you now form the difference
+
+ align:start position:0%
+but if you now form the difference
+ 
+
+ align:start position:0%
+but if you now form the difference
+quotient, right? Suppose that x here is
+
+ align:start position:0%
+quotient, right? Suppose that x here is
+ 
+
+ align:start position:0%
+quotient, right? Suppose that x here is
+bigger than zero. And now look at the
+
+ align:start position:0%
+bigger than zero. And now look at the
+ 
+
+ align:start position:0%
+bigger than zero. And now look at the
+difference quotient. So the difference
+
+ align:start position:0%
+difference quotient. So the difference
+ 
+
+ align:start position:0%
+difference quotient. So the difference
+quotient uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at uh at x0 equal to zero. If you're
+
+ align:start position:0%
+at uh at x0 equal to zero. If you're
+ 
+
+ align:start position:0%
+at uh at x0 equal to zero. If you're
+looking at that difference quotient and
+
+ align:start position:0%
+looking at that difference quotient and
+ 
+
+ align:start position:0%
+looking at that difference quotient and
+and you at the you first look at where x
+
+ align:start position:0%
+and you at the you first look at where x
+ 
+
+ align:start position:0%
+and you at the you first look at where x
+is positive if x is positive then uh f
+
+ align:start position:0%
+is positive if x is positive then uh f
+ 
+
+ align:start position:0%
+is positive if x is positive then uh f
+ofx minus f of 0 x - 0 this difference
+
+ align:start position:0%
+ofx minus f of 0 x - 0 this difference
+ 
+
+ align:start position:0%
+ofx minus f of 0 x - 0 this difference
+quotient here if x is positive then this
+
+ align:start position:0%
+quotient here if x is positive then this
+ 
+
+ align:start position:0%
+quotient here if x is positive then this
+thing here is just x. So this is x - 0
+
+ align:start position:0%
+thing here is just x. So this is x - 0
+ 
+
+ align:start position:0%
+thing here is just x. So this is x - 0
+x - 0. So this here is one right this
+
+ align:start position:0%
+x - 0. So this here is one right this
+ 
+
+ align:start position:0%
+x - 0. So this here is one right this
+difference quotient is one. This is when
+
+ align:start position:0%
+difference quotient is one. This is when
+ 
+
+ align:start position:0%
+difference quotient is one. This is when
+x is positive. When x is negative
+
+ align:start position:0%
+x is positive. When x is negative
+ 
+
+ align:start position:0%
+x is positive. When x is negative
+then the then f ofx
+
+ align:start position:0%
+then the then f ofx
+ 
+
+ align:start position:0%
+then the then f ofx
+if x is negative then the absolute value
+
+ align:start position:0%
+if x is negative then the absolute value
+ 
+
+ align:start position:0%
+if x is negative then the absolute value
+is minus x
+
+ align:start position:0%
+is minus x
+ 
+
+ align:start position:0%
+is minus x
+right. So the difference quotient here f
+
+ align:start position:0%
+right. So the difference quotient here f
+ 
+
+ align:start position:0%
+right. So the difference quotient here f
+ofx minus uh f of 0 which is zero x - 0.
+
+ align:start position:0%
+ofx minus uh f of 0 which is zero x - 0.
+ 
+
+ align:start position:0%
+ofx minus uh f of 0 which is zero x - 0.
+This here is just - x
+
+ align:start position:0%
+This here is just - x
+ 
+
+ align:start position:0%
+This here is just - x
+/ x.
+
+ align:start position:0%
+/ x.
+ 
+
+ align:start position:0%
+/ x.
+But this thing here is minus one.
+
+ align:start position:0%
+But this thing here is minus one.
+ 
+
+ align:start position:0%
+But this thing here is minus one.
+So for all if you are if you're looking
+
+ align:start position:0%
+So for all if you are if you're looking
+ 
+
+ align:start position:0%
+So for all if you are if you're looking
+at the difference quotient
+
+ align:start position:0%
+at the difference quotient
+ 
+
+ align:start position:0%
+at the difference quotient
+and you uh that comes from looking at
+
+ align:start position:0%
+and you uh that comes from looking at
+ 
+
+ align:start position:0%
+and you uh that comes from looking at
+the derivative as zero. Then when you
+
+ align:start position:0%
+the derivative as zero. Then when you
+ 
+
+ align:start position:0%
+the derivative as zero. Then when you
+approach zero from the right then the
+
+ align:start position:0%
+approach zero from the right then the
+ 
+
+ align:start position:0%
+approach zero from the right then the
+difference quotient is one. When you
+
+ align:start position:0%
+difference quotient is one. When you
+ 
+
+ align:start position:0%
+difference quotient is one. When you
+approach it from the sorry uh yeah from
+
+ align:start position:0%
+approach it from the sorry uh yeah from
+ 
+
+ align:start position:0%
+approach it from the sorry uh yeah from
+the when you approach it from the left
+
+ align:start position:0%
+the when you approach it from the left
+ 
+
+ align:start position:0%
+the when you approach it from the left
+then the difference quotient is minus
+
+ align:start position:0%
+then the difference quotient is minus
+ 
+
+ align:start position:0%
+then the difference quotient is minus
+one. So it doesn't have a limit right.
+
+ align:start position:0%
+one. So it doesn't have a limit right.
+ 
+
+ align:start position:0%
+one. So it doesn't have a limit right.
+It has a limit from the right from the
+
+ align:start position:0%
+It has a limit from the right from the
+ 
+
+ align:start position:0%
+It has a limit from the right from the
+left but it doesn't have a limit if you
+
+ align:start position:0%
+left but it doesn't have a limit if you
+ 
+
+ align:start position:0%
+left but it doesn't have a limit if you
+don't restrict where it's coming from.
+
+ align:start position:0%
+don't restrict where it's coming from.
+ 
+
+ align:start position:0%
+don't restrict where it's coming from.
+So this function here
+
+ align:start position:0%
+So this function here
+ 
+
+ align:start position:0%
+So this function here
+uh is not differentiable. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So okay. So this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So
+
+ align:start position:0%
+right. So
+ 
+
+ align:start position:0%
+right. So
+so this so this is so so we did this
+
+ align:start position:0%
+so this so this is so so we did this
+ 
+
+ align:start position:0%
+so this so this is so so we did this
+earlier in the class. So if you take
+
+ align:start position:0%
+earlier in the class. So if you take
+ 
+
+ align:start position:0%
+earlier in the class. So if you take
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that the difference quotient here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this thing here is converging to to
+
+ align:start position:0%
+that this thing here is converging to to
+ 
+
+ align:start position:0%
+that this thing here is converging to to
+some number say a right. This here means
+
+ align:start position:0%
+some number say a right. This here means
+ 
+
+ align:start position:0%
+some number say a right. This here means
+that for all for all epsilon greater
+
+ align:start position:0%
+that for all for all epsilon greater
+ 
+
+ align:start position:0%
+that for all for all epsilon greater
+than zero there exist a delta greater
+
+ align:start position:0%
+than zero there exist a delta greater
+ 
+
+ align:start position:0%
+than zero there exist a delta greater
+than zero such that
+
+ align:start position:0%
+than zero such that
+ 
+
+ align:start position:0%
+than zero such that
+if x - x0
+
+ align:start position:0%
+if x - x0
+ 
+
+ align:start position:0%
+if x - x0
+is less than delta
+
+ align:start position:0%
+is less than delta
+ 
+
+ align:start position:0%
+is less than delta
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+x is is assumed to be different from x0.
+
+ align:start position:0%
+x is is assumed to be different from x0.
+ 
+
+ align:start position:0%
+x is is assumed to be different from x0.
+If you have that then this difference
+
+ align:start position:0%
+If you have that then this difference
+ 
+
+ align:start position:0%
+If you have that then this difference
+quotient here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus this a
+
+ align:start position:0%
+minus this a
+ 
+
+ align:start position:0%
+minus this a
+is supposed to be less than epsilon.
+
+ align:start position:0%
+is supposed to be less than epsilon.
+ 
+
+ align:start position:0%
+is supposed to be less than epsilon.
+And so that's is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. And so you see again in this
+
+ align:start position:0%
+okay. And so you see again in this
+ 
+
+ align:start position:0%
+okay. And so you see again in this
+example that we just looked at where uh
+
+ align:start position:0%
+example that we just looked at where uh
+ 
+
+ align:start position:0%
+example that we just looked at where uh
+in the example that we just looked at
+
+ align:start position:0%
+in the example that we just looked at
+ 
+
+ align:start position:0%
+in the example that we just looked at
+where uh so in the example
+
+ align:start position:0%
+where uh so in the example
+ 
+
+ align:start position:0%
+where uh so in the example
+where f ofx was equal to the absolute
+
+ align:start position:0%
+where f ofx was equal to the absolute
+ 
+
+ align:start position:0%
+where f ofx was equal to the absolute
+value of fx
+
+ align:start position:0%
+value of fx
+ 
+
+ align:start position:0%
+value of fx
+the if you were graphing it then this
+
+ align:start position:0%
+the if you were graphing it then this
+ 
+
+ align:start position:0%
+the if you were graphing it then this
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+right and we saw that the difference
+
+ align:start position:0%
+right and we saw that the difference
+ 
+
+ align:start position:0%
+right and we saw that the difference
+quotion when you approach it over here,
+
+ align:start position:0%
+quotion when you approach it over here,
+ 
+
+ align:start position:0%
+quotion when you approach it over here,
+difference quotient was one. When you
+
+ align:start position:0%
+difference quotient was one. When you
+ 
+
+ align:start position:0%
+difference quotient was one. When you
+approach it over here, the difference
+
+ align:start position:0%
+approach it over here, the difference
+ 
+
+ align:start position:0%
+approach it over here, the difference
+quotient is minus one. So if you take a
+
+ align:start position:0%
+quotient is minus one. So if you take a
+ 
+
+ align:start position:0%
+quotient is minus one. So if you take a
+little any little interval around zero,
+
+ align:start position:0%
+little any little interval around zero,
+ 
+
+ align:start position:0%
+little any little interval around zero,
+then there the difference quotient could
+
+ align:start position:0%
+then there the difference quotient could
+ 
+
+ align:start position:0%
+then there the difference quotient could
+be either minus one or one, right? But
+
+ align:start position:0%
+be either minus one or one, right? But
+ 
+
+ align:start position:0%
+be either minus one or one, right? But
+even however small you make this little
+
+ align:start position:0%
+even however small you make this little
+ 
+
+ align:start position:0%
+even however small you make this little
+interval, it's not like that it converts
+
+ align:start position:0%
+interval, it's not like that it converts
+ 
+
+ align:start position:0%
+interval, it's not like that it converts
+to some number because it has it it is
+
+ align:start position:0%
+to some number because it has it it is
+ 
+
+ align:start position:0%
+to some number because it has it it is
+both you know they're both uh cases
+
+ align:start position:0%
+both you know they're both uh cases
+ 
+
+ align:start position:0%
+both you know they're both uh cases
+where it's one and cases where it's
+
+ align:start position:0%
+where it's one and cases where it's
+ 
+
+ align:start position:0%
+where it's one and cases where it's
+minus one.
+
+ align:start position:0%
+minus one.
+ 
+
+ align:start position:0%
+minus one.
+Okay. So that's that's like the first
+
+ align:start position:0%
+Okay. So that's that's like the first
+ 
+
+ align:start position:0%
+Okay. So that's that's like the first
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+and again you know of a function that is
+
+ align:start position:0%
+and again you know of a function that is
+ 
+
+ align:start position:0%
+and again you know of a function that is
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+but it's it's not differentiable as at
+
+ align:start position:0%
+but it's it's not differentiable as at
+ 
+
+ align:start position:0%
+but it's it's not differentiable as at
+zero. In this case it was a zero.
+
+ align:start position:0%
+zero. In this case it was a zero.
+ 
+
+ align:start position:0%
+zero. In this case it was a zero.
+Um and maybe a little bit more
+
+ align:start position:0%
+Um and maybe a little bit more
+ 
+
+ align:start position:0%
+Um and maybe a little bit more
+interesting example along the same line
+
+ align:start position:0%
+interesting example along the same line
+ 
+
+ align:start position:0%
+interesting example along the same line
+uh is uh the following.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um if I so this is again a function
+
+ align:start position:0%
+So um if I so this is again a function
+ 
+
+ align:start position:0%
+So um if I so this is again a function
+on r into r
+
+ align:start position:0%
+on r into r
+ 
+
+ align:start position:0%
+on r into r
+and I said f ofx = x * sin of 1 /x. This
+
+ align:start position:0%
+and I said f ofx = x * sin of 1 /x. This
+ 
+
+ align:start position:0%
+and I said f ofx = x * sin of 1 /x. This
+here is not really defined at zero. So I
+
+ align:start position:0%
+here is not really defined at zero. So I
+ 
+
+ align:start position:0%
+here is not really defined at zero. So I
+need to define it also at zero. So when
+
+ align:start position:0%
+need to define it also at zero. So when
+ 
+
+ align:start position:0%
+need to define it also at zero. So when
+x is equal to zero then I just set it
+
+ align:start position:0%
+x is equal to zero then I just set it
+ 
+
+ align:start position:0%
+x is equal to zero then I just set it
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+to to zero and otherwise I set it equal
+
+ align:start position:0%
+to to zero and otherwise I set it equal
+ 
+
+ align:start position:0%
+to to zero and otherwise I set it equal
+to x * sin 1 /x okay
+
+ align:start position:0%
+to x * sin 1 /x okay
+ 
+
+ align:start position:0%
+to x * sin 1 /x okay
+and so the thing is that this function
+
+ align:start position:0%
+and so the thing is that this function
+ 
+
+ align:start position:0%
+and so the thing is that this function
+here so f here is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular it's continuous at x at at
+
+ align:start position:0%
+in particular it's continuous at x at at
+ 
+
+ align:start position:0%
+in particular it's continuous at x at at
+when at at zero it's continuous
+
+ align:start position:0%
+when at at zero it's continuous
+ 
+
+ align:start position:0%
+when at at zero it's continuous
+continuous it's actually continuous
+
+ align:start position:0%
+continuous it's actually continuous
+ 
+
+ align:start position:0%
+continuous it's actually continuous
+everywhere but but it's mostly
+
+ align:start position:0%
+everywhere but but it's mostly
+ 
+
+ align:start position:0%
+everywhere but but it's mostly
+interested in it at zero the graph of
+
+ align:start position:0%
+interested in it at zero the graph of
+ 
+
+ align:start position:0%
+interested in it at zero the graph of
+this to remember that sine function sine
+
+ align:start position:0%
+this to remember that sine function sine
+ 
+
+ align:start position:0%
+this to remember that sine function sine
+function looks like this that at zero
+
+ align:start position:0%
+function looks like this that at zero
+ 
+
+ align:start position:0%
+function looks like this that at zero
+um at zero
+
+ align:start position:0%
+um at zero
+ 
+
+ align:start position:0%
+um at zero
+at pi
+
+ align:start position:0%
+at pi
+ 
+
+ align:start position:0%
+at pi
+at 2 pi
+
+ align:start position:0%
+at 2 pi
+ 
+
+ align:start position:0%
+at 2 pi
+at 3 pi and so on at all of these
+
+ align:start position:0%
+at 3 pi and so on at all of these
+ 
+
+ align:start position:0%
+at 3 pi and so on at all of these
+by at all integer multiples also for the
+
+ align:start position:0%
+by at all integer multiples also for the
+ 
+
+ align:start position:0%
+by at all integer multiples also for the
+negative ones at all integer multiple of
+
+ align:start position:0%
+negative ones at all integer multiple of
+ 
+
+ align:start position:0%
+negative ones at all integer multiple of
+pi sign function vanishes
+
+ align:start position:0%
+pi sign function vanishes
+ 
+
+ align:start position:0%
+pi sign function vanishes
+and in between here it is at pi / two it
+
+ align:start position:0%
+and in between here it is at pi / two it
+ 
+
+ align:start position:0%
+and in between here it is at pi / two it
+achieves its maximum which is one and so
+
+ align:start position:0%
+achieves its maximum which is one and so
+ 
+
+ align:start position:0%
+achieves its maximum which is one and so
+the function looks like this
+
+ align:start position:0%
+the function looks like this
+ 
+
+ align:start position:0%
+the function looks like this
+so this here is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's how a sign function looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now if you're looking at sine of
+
+ align:start position:0%
+And so now if you're looking at sine of
+ 
+
+ align:start position:0%
+And so now if you're looking at sine of
+1 /x that's going to be a function as
+
+ align:start position:0%
+1 /x that's going to be a function as
+ 
+
+ align:start position:0%
+1 /x that's going to be a function as
+you're going down. So this is so if
+
+ align:start position:0%
+you're going down. So this is so if
+ 
+
+ align:start position:0%
+you're going down. So this is so if
+you're looking at this here was sine of
+
+ align:start position:0%
+you're looking at this here was sine of
+ 
+
+ align:start position:0%
+you're looking at this here was sine of
+x but if you're looking at sine of one
+
+ align:start position:0%
+x but if you're looking at sine of one
+ 
+
+ align:start position:0%
+x but if you're looking at sine of one
+of x as x go to zero this here becomes
+
+ align:start position:0%
+of x as x go to zero this here becomes
+ 
+
+ align:start position:0%
+of x as x go to zero this here becomes
+very large. So this means that as you're
+
+ align:start position:0%
+very large. So this means that as you're
+ 
+
+ align:start position:0%
+very large. So this means that as you're
+going to zero it go very rapidly through
+
+ align:start position:0%
+going to zero it go very rapidly through
+ 
+
+ align:start position:0%
+going to zero it go very rapidly through
+these periods where it goes where it's
+
+ align:start position:0%
+these periods where it goes where it's
+ 
+
+ align:start position:0%
+these periods where it goes where it's
+oscillates between minus1 and one the
+
+ align:start position:0%
+oscillates between minus1 and one the
+ 
+
+ align:start position:0%
+oscillates between minus1 and one the
+value here is minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so as you it will look like this
+
+ align:start position:0%
+and so as you it will look like this
+ 
+
+ align:start position:0%
+and so as you it will look like this
+that uh it will again uh if you're
+
+ align:start position:0%
+that uh it will again uh if you're
+ 
+
+ align:start position:0%
+that uh it will again uh if you're
+looking at it will again fluctu it will
+
+ align:start position:0%
+looking at it will again fluctu it will
+ 
+
+ align:start position:0%
+looking at it will again fluctu it will
+fluctuate but it will fluctuate operates
+
+ align:start position:0%
+fluctuate but it will fluctuate operates
+ 
+
+ align:start position:0%
+fluctuate but it will fluctuate operates
+uh much more rapidly. So if this here
+
+ align:start position:0%
+uh much more rapidly. So if this here
+ 
+
+ align:start position:0%
+uh much more rapidly. So if this here
+say was one over pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at one over pi 1 over 1 / pi is the same
+
+ align:start position:0%
+at one over pi 1 over 1 / pi is the same
+ 
+
+ align:start position:0%
+at one over pi 1 over 1 / pi is the same
+as pi there it would be zero and it
+
+ align:start position:0%
+as pi there it would be zero and it
+ 
+
+ align:start position:0%
+as pi there it would be zero and it
+would like fluctuate
+
+ align:start position:0%
+would like fluctuate
+ 
+
+ align:start position:0%
+would like fluctuate
+um it would fluctuate so it would look
+
+ align:start position:0%
+um it would fluctuate so it would look
+ 
+
+ align:start position:0%
+um it would fluctuate so it would look
+like something like this but it would
+
+ align:start position:0%
+like something like this but it would
+ 
+
+ align:start position:0%
+like something like this but it would
+fluctuate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+it and then as you're going way it will
+
+ align:start position:0%
+it and then as you're going way it will
+ 
+
+ align:start position:0%
+it and then as you're going way it will
+fluctuate less less often right so as
+
+ align:start position:0%
+fluctuate less less often right so as
+ 
+
+ align:start position:0%
+fluctuate less less often right so as
+you're going down towards zero it will
+
+ align:start position:0%
+you're going down towards zero it will
+ 
+
+ align:start position:0%
+you're going down towards zero it will
+fluctuate a lot right it always because
+
+ align:start position:0%
+fluctuate a lot right it always because
+ 
+
+ align:start position:0%
+fluctuate a lot right it always because
+sign always is between minus1 and one
+
+ align:start position:0%
+sign always is between minus1 and one
+ 
+
+ align:start position:0%
+sign always is between minus1 and one
+the value here will always between
+
+ align:start position:0%
+the value here will always between
+ 
+
+ align:start position:0%
+the value here will always between
+minus1 and one but as you're going
+
+ align:start position:0%
+minus1 and one but as you're going
+ 
+
+ align:start position:0%
+minus1 and one but as you're going
+towards zero from the right or from the
+
+ align:start position:0%
+towards zero from the right or from the
+ 
+
+ align:start position:0%
+towards zero from the right or from the
+left it's going to fluctuate more and
+
+ align:start position:0%
+left it's going to fluctuate more and
+ 
+
+ align:start position:0%
+left it's going to fluctuate more and
+more right as you're going away from
+
+ align:start position:0%
+more right as you're going away from
+ 
+
+ align:start position:0%
+more right as you're going away from
+zero is fluctuating less and less.
+
+ align:start position:0%
+zero is fluctuating less and less.
+ 
+
+ align:start position:0%
+zero is fluctuating less and less.
+Okay. So, so this is the function I'm
+
+ align:start position:0%
+Okay. So, so this is the function I'm
+ 
+
+ align:start position:0%
+Okay. So, so this is the function I'm
+interested in. And so, but when you
+
+ align:start position:0%
+interested in. And so, but when you
+ 
+
+ align:start position:0%
+interested in. And so, but when you
+multiply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you multiply through by X
+
+ align:start position:0%
+when you multiply through by X
+ 
+
+ align:start position:0%
+when you multiply through by X
+then you see when you multiply through
+
+ align:start position:0%
+then you see when you multiply through
+ 
+
+ align:start position:0%
+then you see when you multiply through
+by X it's fluctuating but it's always
+
+ align:start position:0%
+by X it's fluctuating but it's always
+ 
+
+ align:start position:0%
+by X it's fluctuating but it's always
+fluctuating between minus1 and one. If
+
+ align:start position:0%
+fluctuating between minus1 and one. If
+ 
+
+ align:start position:0%
+fluctuating between minus1 and one. If
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+multiply it by x then as you're going to
+
+ align:start position:0%
+multiply it by x then as you're going to
+ 
+
+ align:start position:0%
+multiply it by x then as you're going to
+zero this hair will squeeze down and it
+
+ align:start position:0%
+zero this hair will squeeze down and it
+ 
+
+ align:start position:0%
+zero this hair will squeeze down and it
+will become the fluctuation will be zero
+
+ align:start position:0%
+will become the fluctuation will be zero
+ 
+
+ align:start position:0%
+will become the fluctuation will be zero
+at zero. So it's easy to see that this
+
+ align:start position:0%
+at zero. So it's easy to see that this
+ 
+
+ align:start position:0%
+at zero. So it's easy to see that this
+function here so is indeed continuous.
+
+ align:start position:0%
+function here so is indeed continuous.
+ 
+
+ align:start position:0%
+function here so is indeed continuous.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+But let's look at the difference
+
+ align:start position:0%
+But let's look at the difference
+ 
+
+ align:start position:0%
+But let's look at the difference
+quotient. So the difference quotient.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if we're looking at the difference
+
+ align:start position:0%
+So if we're looking at the difference
+ 
+
+ align:start position:0%
+So if we're looking at the difference
+quotion, so we're looking at and we just
+
+ align:start position:0%
+quotion, so we're looking at and we just
+ 
+
+ align:start position:0%
+quotion, so we're looking at and we just
+look at the difference quotient at zero.
+
+ align:start position:0%
+look at the difference quotient at zero.
+ 
+
+ align:start position:0%
+look at the difference quotient at zero.
+So this is the difference quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so it's x sin 1 /x. The value at
+
+ align:start position:0%
+and so it's x sin 1 /x. The value at
+ 
+
+ align:start position:0%
+and so it's x sin 1 /x. The value at
+zero by definition was zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so you see that now this here the x
+
+ align:start position:0%
+And so you see that now this here the x
+ 
+
+ align:start position:0%
+And so you see that now this here the x
+this here becomes just x sin 1 /x / x.
+
+ align:start position:0%
+this here becomes just x sin 1 /x / x.
+ 
+
+ align:start position:0%
+this here becomes just x sin 1 /x / x.
+And so you see that this here cancel
+
+ align:start position:0%
+And so you see that this here cancel
+ 
+
+ align:start position:0%
+And so you see that this here cancel
+with that. So you just get sine 1 /x.
+
+ align:start position:0%
+with that. So you just get sine 1 /x.
+ 
+
+ align:start position:0%
+with that. So you just get sine 1 /x.
+And so you see that now as x go to so
+
+ align:start position:0%
+And so you see that now as x go to so
+ 
+
+ align:start position:0%
+And so you see that now as x go to so
+when x here goes to zero
+
+ align:start position:0%
+when x here goes to zero
+ 
+
+ align:start position:0%
+when x here goes to zero
+this here fluctuates. This have
+
+ align:start position:0%
+this here fluctuates. This have
+ 
+
+ align:start position:0%
+this here fluctuates. This have
+fluctuate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus one and one n1
+
+ align:start position:0%
+minus one and one n1
+ 
+
+ align:start position:0%
+minus one and one n1
+but it doesn't have a limit right
+
+ align:start position:0%
+but it doesn't have a limit right
+ 
+
+ align:start position:0%
+but it doesn't have a limit right
+because it's fluctuated y or why not
+
+ align:start position:0%
+because it's fluctuated y or why not
+ 
+
+ align:start position:0%
+because it's fluctuated y or why not
+right. So this is a this is an example
+
+ align:start position:0%
+right. So this is a this is an example
+ 
+
+ align:start position:0%
+right. So this is a this is an example
+again this is another example of a
+
+ align:start position:0%
+again this is another example of a
+ 
+
+ align:start position:0%
+again this is another example of a
+function that is continuous
+
+ align:start position:0%
+function that is continuous
+ 
+
+ align:start position:0%
+function that is continuous
+at zero but not differentiable at zero.
+
+ align:start position:0%
+at zero but not differentiable at zero.
+ 
+
+ align:start position:0%
+at zero but not differentiable at zero.
+It's actually much worse than the
+
+ align:start position:0%
+It's actually much worse than the
+ 
+
+ align:start position:0%
+It's actually much worse than the
+previous the previous one was the
+
+ align:start position:0%
+previous the previous one was the
+ 
+
+ align:start position:0%
+previous the previous one was the
+previous one the example the
+
+ align:start position:0%
+previous one the example the
+ 
+
+ align:start position:0%
+previous one the example the
+previous example that was this example
+
+ align:start position:0%
+previous example that was this example
+ 
+
+ align:start position:0%
+previous example that was this example
+is much more tame. It is not
+
+ align:start position:0%
+is much more tame. It is not
+ 
+
+ align:start position:0%
+is much more tame. It is not
+differentiable at zero but if you were
+
+ align:start position:0%
+differentiable at zero but if you were
+ 
+
+ align:start position:0%
+differentiable at zero but if you were
+restrict to just positive things then
+
+ align:start position:0%
+restrict to just positive things then
+ 
+
+ align:start position:0%
+restrict to just positive things then
+from then it would be differentiable
+
+ align:start position:0%
+from then it would be differentiable
+ 
+
+ align:start position:0%
+from then it would be differentiable
+right if you were you could also define
+
+ align:start position:0%
+right if you were you could also define
+ 
+
+ align:start position:0%
+right if you were you could also define
+derivative. In general when we define
+
+ align:start position:0%
+derivative. In general when we define
+ 
+
+ align:start position:0%
+derivative. In general when we define
+derivative we let it be defined in a
+
+ align:start position:0%
+derivative we let it be defined in a
+ 
+
+ align:start position:0%
+derivative we let it be defined in a
+neighborhood of that point. So on either
+
+ align:start position:0%
+neighborhood of that point. So on either
+ 
+
+ align:start position:0%
+neighborhood of that point. So on either
+side. But if you were considering where
+
+ align:start position:0%
+side. But if you were considering where
+ 
+
+ align:start position:0%
+side. But if you were considering where
+you were allowing the function just to
+
+ align:start position:0%
+you were allowing the function just to
+ 
+
+ align:start position:0%
+you were allowing the function just to
+be defined at this point and then to the
+
+ align:start position:0%
+be defined at this point and then to the
+ 
+
+ align:start position:0%
+be defined at this point and then to the
+right say or to the left then this
+
+ align:start position:0%
+right say or to the left then this
+ 
+
+ align:start position:0%
+right say or to the left then this
+function would be differentiable. Right?
+
+ align:start position:0%
+function would be differentiable. Right?
+ 
+
+ align:start position:0%
+function would be differentiable. Right?
+But the in the in in in this example
+
+ align:start position:0%
+But the in the in in in this example
+ 
+
+ align:start position:0%
+But the in the in in in this example
+here it doesn't matter if you restrict
+
+ align:start position:0%
+here it doesn't matter if you restrict
+ 
+
+ align:start position:0%
+here it doesn't matter if you restrict
+the interval to just to the right or to
+
+ align:start position:0%
+the interval to just to the right or to
+ 
+
+ align:start position:0%
+the interval to just to the right or to
+the left. It's still not differential.
+
+ align:start position:0%
+the left. It's still not differential.
+ 
+
+ align:start position:0%
+the left. It's still not differential.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Right. So this is something about this
+
+ align:start position:0%
+Right. So this is something about this
+ 
+
+ align:start position:0%
+Right. So this is something about this
+example is something about that it
+
+ align:start position:0%
+example is something about that it
+ 
+
+ align:start position:0%
+example is something about that it
+fluctuates wildly
+
+ align:start position:0%
+fluctuates wildly
+ 
+
+ align:start position:0%
+fluctuates wildly
+and that is causing it not to be
+
+ align:start position:0%
+and that is causing it not to be
+ 
+
+ align:start position:0%
+and that is causing it not to be
+differentiable. If it wasn't again if if
+
+ align:start position:0%
+differentiable. If it wasn't again if if
+ 
+
+ align:start position:0%
+differentiable. If it wasn't again if if
+you if you defined it if you didn't have
+
+ align:start position:0%
+you if you defined it if you didn't have
+ 
+
+ align:start position:0%
+you if you defined it if you didn't have
+this kind of the X here is sort of
+
+ align:start position:0%
+this kind of the X here is sort of
+ 
+
+ align:start position:0%
+this kind of the X here is sort of
+serving as some sort of it's dampening
+
+ align:start position:0%
+serving as some sort of it's dampening
+ 
+
+ align:start position:0%
+serving as some sort of it's dampening
+how much it's fluctuating right so if
+
+ align:start position:0%
+how much it's fluctuating right so if
+ 
+
+ align:start position:0%
+how much it's fluctuating right so if
+there wasn't a X here then this function
+
+ align:start position:0%
+there wasn't a X here then this function
+ 
+
+ align:start position:0%
+there wasn't a X here then this function
+wouldn't it would just fluctuate
+
+ align:start position:0%
+wouldn't it would just fluctuate
+ 
+
+ align:start position:0%
+wouldn't it would just fluctuate
+and it wouldn't even be continuous at X0
+
+ align:start position:0%
+and it wouldn't even be continuous at X0
+ 
+
+ align:start position:0%
+and it wouldn't even be continuous at X0
+right but once I put this X on then it
+
+ align:start position:0%
+right but once I put this X on then it
+ 
+
+ align:start position:0%
+right but once I put this X on then it
+becomes continuous if I put another x.
+
+ align:start position:0%
+becomes continuous if I put another x.
+ 
+
+ align:start position:0%
+becomes continuous if I put another x.
+So if I'm looking at
+
+ align:start position:0%
+So if I'm looking at
+ 
+
+ align:start position:0%
+So if I'm looking at
+f ofx = x^2 * sin
+
+ align:start position:0%
+f ofx = x^2 * sin
+ 
+
+ align:start position:0%
+f ofx = x^2 * sin
+1 / x. Suppose I'm looking at this
+
+ align:start position:0%
+1 / x. Suppose I'm looking at this
+ 
+
+ align:start position:0%
+1 / x. Suppose I'm looking at this
+function. So now I have sort of dampened
+
+ align:start position:0%
+function. So now I have sort of dampened
+ 
+
+ align:start position:0%
+function. So now I have sort of dampened
+dampened the fluctuation even more. And
+
+ align:start position:0%
+dampened the fluctuation even more. And
+ 
+
+ align:start position:0%
+dampened the fluctuation even more. And
+so if I again looking at the difference
+
+ align:start position:0%
+so if I again looking at the difference
+ 
+
+ align:start position:0%
+so if I again looking at the difference
+quotient. So so I'm looking at this
+
+ align:start position:0%
+quotient. So so I'm looking at this
+ 
+
+ align:start position:0%
+quotient. So so I'm looking at this
+function maybe I should be more careful.
+
+ align:start position:0%
+function maybe I should be more careful.
+ 
+
+ align:start position:0%
+function maybe I should be more careful.
+So again at zero I need to define it
+
+ align:start position:0%
+So again at zero I need to define it
+ 
+
+ align:start position:0%
+So again at zero I need to define it
+separately. So I define a function
+
+ align:start position:0%
+separately. So I define a function
+ 
+
+ align:start position:0%
+separately. So I define a function
+that is zero at x = 0 and then it is x^2
+
+ align:start position:0%
+that is zero at x = 0 and then it is x^2
+ 
+
+ align:start position:0%
+that is zero at x = 0 and then it is x^2
+* sin 1 /x otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I'm looking at this function then I
+
+ align:start position:0%
+if I'm looking at this function then I
+ 
+
+ align:start position:0%
+if I'm looking at this function then I
+claim that this function is in fact uh
+
+ align:start position:0%
+claim that this function is in fact uh
+ 
+
+ align:start position:0%
+claim that this function is in fact uh
+French at x at zero and so let's look at
+
+ align:start position:0%
+French at x at zero and so let's look at
+ 
+
+ align:start position:0%
+French at x at zero and so let's look at
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So again, I'm looking at the difference
+
+ align:start position:0%
+So again, I'm looking at the difference
+ 
+
+ align:start position:0%
+So again, I'm looking at the difference
+quotient
+
+ align:start position:0%
+quotient
+ 
+
+ align:start position:0%
+quotient
+and the value at zero is zero. So I have
+
+ align:start position:0%
+and the value at zero is zero. So I have
+ 
+
+ align:start position:0%
+and the value at zero is zero. So I have
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so this here is now just x²
+
+ align:start position:0%
+And so this here is now just x²
+ 
+
+ align:start position:0%
+And so this here is now just x²
+sin 1 /x. This thing here is then x. And
+
+ align:start position:0%
+sin 1 /x. This thing here is then x. And
+ 
+
+ align:start position:0%
+sin 1 /x. This thing here is then x. And
+so you see that this difference quotient
+
+ align:start position:0%
+so you see that this difference quotient
+ 
+
+ align:start position:0%
+so you see that this difference quotient
+is just this. But this here does
+
+ align:start position:0%
+is just this. But this here does
+ 
+
+ align:start position:0%
+is just this. But this here does
+converge to zero as x go to zero.
+
+ align:start position:0%
+converge to zero as x go to zero.
+ 
+
+ align:start position:0%
+converge to zero as x go to zero.
+Right? So this function is actually
+
+ align:start position:0%
+Right? So this function is actually
+ 
+
+ align:start position:0%
+Right? So this function is actually
+differentiable. Right? It's fluctuates
+
+ align:start position:0%
+differentiable. Right? It's fluctuates
+ 
+
+ align:start position:0%
+differentiable. Right? It's fluctuates
+but it's it's more mild the way it
+
+ align:start position:0%
+but it's it's more mild the way it
+ 
+
+ align:start position:0%
+but it's it's more mild the way it
+fluctuates.
+
+ align:start position:0%
+fluctuates.
+ 
+
+ align:start position:0%
+fluctuates.
+Okay. Now let me get back to the the
+
+ align:start position:0%
+Okay. Now let me get back to the the
+ 
+
+ align:start position:0%
+Okay. Now let me get back to the the
+rules. So we proved one uh rule that was
+
+ align:start position:0%
+rules. So we proved one uh rule that was
+ 
+
+ align:start position:0%
+rules. So we proved one uh rule that was
+this sum rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then the second rule we're interested in
+
+ align:start position:0%
+Then the second rule we're interested in
+ 
+
+ align:start position:0%
+Then the second rule we're interested in
+is when we're looking at the likeness
+
+ align:start position:0%
+is when we're looking at the likeness
+ 
+
+ align:start position:0%
+is when we're looking at the likeness
+rule. So we're looking at the product of
+
+ align:start position:0%
+rule. So we're looking at the product of
+ 
+
+ align:start position:0%
+rule. So we're looking at the product of
+these two functions and each function is
+
+ align:start position:0%
+these two functions and each function is
+ 
+
+ align:start position:0%
+these two functions and each function is
+assumed to be differentiable
+
+ align:start position:0%
+assumed to be differentiable
+ 
+
+ align:start position:0%
+assumed to be differentiable
+uh at x0 and then we claim that the
+
+ align:start position:0%
+uh at x0 and then we claim that the
+ 
+
+ align:start position:0%
+uh at x0 and then we claim that the
+product function is also differentiable
+
+ align:start position:0%
+product function is also differentiable
+ 
+
+ align:start position:0%
+product function is also differentiable
+at x0 and this is the formula for the
+
+ align:start position:0%
+at x0 and this is the formula for the
+ 
+
+ align:start position:0%
+at x0 and this is the formula for the
+derivative. Right?
+
+ align:start position:0%
+derivative. Right?
+ 
+
+ align:start position:0%
+derivative. Right?
+to prove this one here I need this fact
+
+ align:start position:0%
+to prove this one here I need this fact
+ 
+
+ align:start position:0%
+to prove this one here I need this fact
+that we have now proved that if it is
+
+ align:start position:0%
+that we have now proved that if it is
+ 
+
+ align:start position:0%
+that we have now proved that if it is
+defensible then it's also continuous at
+
+ align:start position:0%
+defensible then it's also continuous at
+ 
+
+ align:start position:0%
+defensible then it's also continuous at
+that point okay so I'm going to use that
+
+ align:start position:0%
+that point okay so I'm going to use that
+ 
+
+ align:start position:0%
+that point okay so I'm going to use that
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now so
+
+ align:start position:0%
+so so now so
+ 
+
+ align:start position:0%
+so so now so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+let's prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh of lightness room.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have uh these two functions. We're
+
+ align:start position:0%
+So we have uh these two functions. We're
+ 
+
+ align:start position:0%
+So we have uh these two functions. We're
+looking at f of x. We form the
+
+ align:start position:0%
+looking at f of x. We form the
+ 
+
+ align:start position:0%
+looking at f of x. We form the
+difference quotient.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the difference quotient x -
+
+ align:start position:0%
+So this is the difference quotient x -
+ 
+
+ align:start position:0%
+So this is the difference quotient x -
+x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I I we do this trick that we've done
+
+ align:start position:0%
+uh I I we do this trick that we've done
+ 
+
+ align:start position:0%
+uh I I we do this trick that we've done
+a bunch of times before when we also
+
+ align:start position:0%
+a bunch of times before when we also
+ 
+
+ align:start position:0%
+a bunch of times before when we also
+looked at products. We had two sequences
+
+ align:start position:0%
+looked at products. We had two sequences
+ 
+
+ align:start position:0%
+looked at products. We had two sequences
+and we looked at the sequence that was
+
+ align:start position:0%
+and we looked at the sequence that was
+ 
+
+ align:start position:0%
+and we looked at the sequence that was
+the product of the these two. Right? So
+
+ align:start position:0%
+the product of the these two. Right? So
+ 
+
+ align:start position:0%
+the product of the these two. Right? So
+if you have just a reminder
+
+ align:start position:0%
+if you have just a reminder
+ 
+
+ align:start position:0%
+if you have just a reminder
+that I mean it's not like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember that if you had a sequence a
+
+ align:start position:0%
+so remember that if you had a sequence a
+ 
+
+ align:start position:0%
+so remember that if you had a sequence a
+n and a sequence bn and you knew that a
+
+ align:start position:0%
+n and a sequence bn and you knew that a
+ 
+
+ align:start position:0%
+n and a sequence bn and you knew that a
+n converts to a and bn converts to b
+
+ align:start position:0%
+n converts to a and bn converts to b
+ 
+
+ align:start position:0%
+n converts to a and bn converts to b
+then the product here converts to a * b.
+
+ align:start position:0%
+then the product here converts to a * b.
+ 
+
+ align:start position:0%
+then the product here converts to a * b.
+Right? So, and when we prove that we use
+
+ align:start position:0%
+Right? So, and when we prove that we use
+ 
+
+ align:start position:0%
+Right? So, and when we prove that we use
+this little trick with that we are uh
+
+ align:start position:0%
+this little trick with that we are uh
+ 
+
+ align:start position:0%
+this little trick with that we are uh
+we're splitting the difference between
+
+ align:start position:0%
+we're splitting the difference between
+ 
+
+ align:start position:0%
+we're splitting the difference between
+this and this. Right? And so I'm going
+
+ align:start position:0%
+this and this. Right? And so I'm going
+ 
+
+ align:start position:0%
+this and this. Right? And so I'm going
+to do exactly the same trick here.
+
+ align:start position:0%
+to do exactly the same trick here.
+ 
+
+ align:start position:0%
+to do exactly the same trick here.
+So I'm looking at this thing here. And
+
+ align:start position:0%
+So I'm looking at this thing here. And
+ 
+
+ align:start position:0%
+So I'm looking at this thing here. And
+so I write this thing here as f ofx * g
+
+ align:start position:0%
+so I write this thing here as f ofx * g
+ 
+
+ align:start position:0%
+so I write this thing here as f ofx * g
+ofx
+
+ align:start position:0%
+ofx
+ 
+
+ align:start position:0%
+ofx
+minus and it doesn't really matter
+
+ align:start position:0%
+minus and it doesn't really matter
+ 
+
+ align:start position:0%
+minus and it doesn't really matter
+you know where you're inserting it. So
+
+ align:start position:0%
+you know where you're inserting it. So
+ 
+
+ align:start position:0%
+you know where you're inserting it. So
+this here it's like splitting the
+
+ align:start position:0%
+this here it's like splitting the
+ 
+
+ align:start position:0%
+this here it's like splitting the
+difference and then I have to add it
+
+ align:start position:0%
+difference and then I have to add it
+ 
+
+ align:start position:0%
+difference and then I have to add it
+again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is certainly the same. I'm just
+
+ align:start position:0%
+So this is certainly the same. I'm just
+ 
+
+ align:start position:0%
+So this is certainly the same. I'm just
+subtracting it and adding it right back.
+
+ align:start position:0%
+subtracting it and adding it right back.
+ 
+
+ align:start position:0%
+subtracting it and adding it right back.
+And now I split this into two. So I
+
+ align:start position:0%
+And now I split this into two. So I
+ 
+
+ align:start position:0%
+And now I split this into two. So I
+write this in here. So I So this uh
+
+ align:start position:0%
+write this in here. So I So this uh
+ 
+
+ align:start position:0%
+write this in here. So I So this uh
+fraction I split into two. And the first
+
+ align:start position:0%
+fraction I split into two. And the first
+ 
+
+ align:start position:0%
+fraction I split into two. And the first
+one I take this one here together. So
+
+ align:start position:0%
+one I take this one here together. So
+ 
+
+ align:start position:0%
+one I take this one here together. So
+and you can factor out f ofx. You can
+
+ align:start position:0%
+and you can factor out f ofx. You can
+ 
+
+ align:start position:0%
+and you can factor out f ofx. You can
+write it like this. f of x - f of x0
+
+ align:start position:0%
+write it like this. f of x - f of x0
+ 
+
+ align:start position:0%
+write it like this. f of x - f of x0
+x - x0 right so this is just right I'm
+
+ align:start position:0%
+x - x0 right so this is just right I'm
+ 
+
+ align:start position:0%
+x - x0 right so this is just right I'm
+just here I'm factoring out the g of x
+
+ align:start position:0%
+just here I'm factoring out the g of x
+ 
+
+ align:start position:0%
+just here I'm factoring out the g of x
+and then I'm left with this this is this
+
+ align:start position:0%
+and then I'm left with this this is this
+ 
+
+ align:start position:0%
+and then I'm left with this this is this
+and this is giving the denominator like
+
+ align:start position:0%
+and this is giving the denominator like
+ 
+
+ align:start position:0%
+and this is giving the denominator like
+that this is this part here and then I
+
+ align:start position:0%
+that this is this part here and then I
+ 
+
+ align:start position:0%
+that this is this part here and then I
+have the other part here but there you
+
+ align:start position:0%
+have the other part here but there you
+ 
+
+ align:start position:0%
+have the other part here but there you
+see that f of x0 is factoring out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I have g of x minus g of x0 x -
+
+ align:start position:0%
+and then I have g of x minus g of x0 x -
+ 
+
+ align:start position:0%
+and then I have g of x minus g of x0 x -
+x0
+
+ align:start position:0%
+x0
+ 
+
+ align:start position:0%
+x0
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+But now you see that as x goes to x0,
+
+ align:start position:0%
+But now you see that as x goes to x0,
+ 
+
+ align:start position:0%
+But now you see that as x goes to x0,
+right? Well, g was continuous at x0,
+
+ align:start position:0%
+right? Well, g was continuous at x0,
+ 
+
+ align:start position:0%
+right? Well, g was continuous at x0,
+right? So this thing here
+
+ align:start position:0%
+right? So this thing here
+ 
+
+ align:start position:0%
+right? So this thing here
+as x go to x0 this thing here goes to g
+
+ align:start position:0%
+as x go to x0 this thing here goes to g
+ 
+
+ align:start position:0%
+as x go to x0 this thing here goes to g
+of x0 right this one here that was
+
+ align:start position:0%
+of x0 right this one here that was
+ 
+
+ align:start position:0%
+of x0 right this one here that was
+because g was continuous because it was
+
+ align:start position:0%
+because g was continuous because it was
+ 
+
+ align:start position:0%
+because g was continuous because it was
+differentiable so it was also continuous
+
+ align:start position:0%
+differentiable so it was also continuous
+ 
+
+ align:start position:0%
+differentiable so it was also continuous
+this here goes to the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the second thing here is this here
+
+ align:start position:0%
+and the second thing here is this here
+ 
+
+ align:start position:0%
+and the second thing here is this here
+is just constant
+
+ align:start position:0%
+is just constant
+ 
+
+ align:start position:0%
+is just constant
+and this here goes to the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+right so we have so what we have proven
+
+ align:start position:0%
+right so we have so what we have proven
+ 
+
+ align:start position:0%
+right so we have so what we have proven
+is this here is as x goes to x0
+
+ align:start position:0%
+is this here is as x goes to x0
+ 
+
+ align:start position:0%
+is this here is as x goes to x0
+so you see that we have proven that the
+
+ align:start position:0%
+so you see that we have proven that the
+ 
+
+ align:start position:0%
+so you see that we have proven that the
+difference this difference quotient here
+
+ align:start position:0%
+difference this difference quotient here
+ 
+
+ align:start position:0%
+difference this difference quotient here
+for the product
+
+ align:start position:0%
+for the product
+ 
+
+ align:start position:0%
+for the product
+has a limit and this is what the limit
+
+ align:start position:0%
+has a limit and this is what the limit
+ 
+
+ align:start position:0%
+has a limit and this is what the limit
+is right and so this means that the
+
+ align:start position:0%
+is right and so this means that the
+ 
+
+ align:start position:0%
+is right and so this means that the
+product is differentiable
+
+ align:start position:0%
+product is differentiable
+ 
+
+ align:start position:0%
+product is differentiable
+and this here is the derivative and
+
+ align:start position:0%
+and this here is the derivative and
+ 
+
+ align:start position:0%
+and this here is the derivative and
+that's exactly the this formula. Okay,
+
+ align:start position:0%
+that's exactly the this formula. Okay,
+ 
+
+ align:start position:0%
+that's exactly the this formula. Okay,
+which was this over here. This formula
+
+ align:start position:0%
+which was this over here. This formula
+ 
+
+ align:start position:0%
+which was this over here. This formula
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, the next thing is that we uh want
+
+ align:start position:0%
+Okay, the next thing is that we uh want
+ 
+
+ align:start position:0%
+Okay, the next thing is that we uh want
+to prove the next rule is like this
+
+ align:start position:0%
+to prove the next rule is like this
+ 
+
+ align:start position:0%
+to prove the next rule is like this
+quotient rule.
+
+ align:start position:0%
+quotient rule.
+ 
+
+ align:start position:0%
+quotient rule.
+So let me prove the quotient rule.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, Leness, right? Less and
+
+ align:start position:0%
+So, Leness, right? Less and
+ 
+
+ align:start position:0%
+So, Leness, right? Less and
+Leness and Newton was the one that was
+
+ align:start position:0%
+Leness and Newton was the one that was
+ 
+
+ align:start position:0%
+Leness and Newton was the one that was
+uh um um responsible for calculus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and so then the next thing I want to
+
+ align:start position:0%
+Uh and so then the next thing I want to
+ 
+
+ align:start position:0%
+Uh and so then the next thing I want to
+prove is this quotion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so again you have these two
+
+ align:start position:0%
+And so again you have these two
+ 
+
+ align:start position:0%
+And so again you have these two
+functions f and g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh they are differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0 and I'm also assuming that g here
+
+ align:start position:0%
+at x0 and I'm also assuming that g here
+ 
+
+ align:start position:0%
+at x0 and I'm also assuming that g here
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+is is not equal to let's just assume
+
+ align:start position:0%
+is is not equal to let's just assume
+ 
+
+ align:start position:0%
+is is not equal to let's just assume
+that g is not equal to zero everywhere
+
+ align:start position:0%
+that g is not equal to zero everywhere
+ 
+
+ align:start position:0%
+that g is not equal to zero everywhere
+is never is is is is different from zero
+
+ align:start position:0%
+is never is is is is different from zero
+ 
+
+ align:start position:0%
+is never is is is is different from zero
+everywhere.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the quotient rule say that if
+
+ align:start position:0%
+And then the quotient rule say that if
+ 
+
+ align:start position:0%
+And then the quotient rule say that if
+you're looking at the quotient here and
+
+ align:start position:0%
+you're looking at the quotient here and
+ 
+
+ align:start position:0%
+you're looking at the quotient here and
+you take the derivative of the so it say
+
+ align:start position:0%
+you take the derivative of the so it say
+ 
+
+ align:start position:0%
+you take the derivative of the so it say
+that if you're looking at the quotient
+
+ align:start position:0%
+that if you're looking at the quotient
+ 
+
+ align:start position:0%
+that if you're looking at the quotient
+here maybe I should so the quotion will
+
+ align:start position:0%
+here maybe I should so the quotion will
+ 
+
+ align:start position:0%
+here maybe I should so the quotion will
+say that that if you're looking at this
+
+ align:start position:0%
+say that that if you're looking at this
+ 
+
+ align:start position:0%
+say that that if you're looking at this
+thing here this now makes sense because
+
+ align:start position:0%
+thing here this now makes sense because
+ 
+
+ align:start position:0%
+thing here this now makes sense because
+g does not vanish
+
+ align:start position:0%
+g does not vanish
+ 
+
+ align:start position:0%
+g does not vanish
+This here is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0. And the derivative
+
+ align:start position:0%
+at x0. And the derivative
+ 
+
+ align:start position:0%
+at x0. And the derivative
+the derivative of this function
+
+ align:start position:0%
+the derivative of this function
+ 
+
+ align:start position:0%
+the derivative of this function
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+is given by the following formula that
+
+ align:start position:0%
+is given by the following formula that
+ 
+
+ align:start position:0%
+is given by the following formula that
+it is the derivative of f at x0 time g
+
+ align:start position:0%
+it is the derivative of f at x0 time g
+ 
+
+ align:start position:0%
+it is the derivative of f at x0 time g
+of x0
+
+ align:start position:0%
+of x0
+ 
+
+ align:start position:0%
+of x0
+minus uh um f at x0 * g prime at x0
+
+ align:start position:0%
+minus uh um f at x0 * g prime at x0
+ 
+
+ align:start position:0%
+minus uh um f at x0 * g prime at x0
+divided by G G² so G of X0 times itself
+
+ align:start position:0%
+divided by G G² so G of X0 times itself
+ 
+
+ align:start position:0%
+divided by G G² so G of X0 times itself
+I'll write that as a square this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here again this here this here is just g
+
+ align:start position:0%
+here again this here this here is just g
+ 
+
+ align:start position:0%
+here again this here this here is just g
+of X0 * G of X0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's try to prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're looking at f ofx f like this at
+
+ align:start position:0%
+So we're looking at f ofx f like this at
+ 
+
+ align:start position:0%
+So we're looking at f ofx f like this at
+x minus. So this is the difference
+
+ align:start position:0%
+x minus. So this is the difference
+ 
+
+ align:start position:0%
+x minus. So this is the difference
+quotient
+
+ align:start position:0%
+quotient
+ 
+
+ align:start position:0%
+quotient
+at x0 divided by x - x0, right? That's
+
+ align:start position:0%
+at x0 divided by x - x0, right? That's
+ 
+
+ align:start position:0%
+at x0 divided by x - x0, right? That's
+the difference quotion. And so written
+
+ align:start position:0%
+the difference quotion. And so written
+ 
+
+ align:start position:0%
+the difference quotion. And so written
+out this is f of x
+
+ align:start position:0%
+out this is f of x
+ 
+
+ align:start position:0%
+out this is f of x
+g of x
+
+ align:start position:0%
+g of x
+ 
+
+ align:start position:0%
+g of x
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+g uh f sorry f of x0
+
+ align:start position:0%
+g uh f sorry f of x0
+ 
+
+ align:start position:0%
+g uh f sorry f of x0
+divided by g of x0
+
+ align:start position:0%
+divided by g of x0
+ 
+
+ align:start position:0%
+divided by g of x0
+x - x0. So let me put this on a with on
+
+ align:start position:0%
+x - x0. So let me put this on a with on
+ 
+
+ align:start position:0%
+x - x0. So let me put this on a with on
+a fraction with a common denominator. So
+
+ align:start position:0%
+a fraction with a common denominator. So
+ 
+
+ align:start position:0%
+a fraction with a common denominator. So
+if I do that then this thing here is
+
+ align:start position:0%
+if I do that then this thing here is
+ 
+
+ align:start position:0%
+if I do that then this thing here is
+right. So then I'm multiplying
+
+ align:start position:0%
+right. So then I'm multiplying
+ 
+
+ align:start position:0%
+right. So then I'm multiplying
+uh by g of x0 both in the denominator
+
+ align:start position:0%
+uh by g of x0 both in the denominator
+ 
+
+ align:start position:0%
+uh by g of x0 both in the denominator
+and denominator here. So I'm getting f
+
+ align:start position:0%
+and denominator here. So I'm getting f
+ 
+
+ align:start position:0%
+and denominator here. So I'm getting f
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+times g of x0
+
+ align:start position:0%
+times g of x0
+ 
+
+ align:start position:0%
+times g of x0
+and then here I'm multiplying by g of x
+
+ align:start position:0%
+and then here I'm multiplying by g of x
+ 
+
+ align:start position:0%
+and then here I'm multiplying by g of x
+in both denominator and denominator. So
+
+ align:start position:0%
+in both denominator and denominator. So
+ 
+
+ align:start position:0%
+in both denominator and denominator. So
+getting this thing here
+
+ align:start position:0%
+getting this thing here
+ 
+
+ align:start position:0%
+getting this thing here
+g of x and then it becomes x - x0
+
+ align:start position:0%
+g of x and then it becomes x - x0
+ 
+
+ align:start position:0%
+g of x and then it becomes x - x0
+and then g of x g of x0
+
+ align:start position:0%
+and then g of x g of x0
+ 
+
+ align:start position:0%
+and then g of x g of x0
+like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now you can write this thing here
+
+ align:start position:0%
+And so now you can write this thing here
+ 
+
+ align:start position:0%
+And so now you can write this thing here
+uh as right. And so now you do the same
+
+ align:start position:0%
+uh as right. And so now you do the same
+ 
+
+ align:start position:0%
+uh as right. And so now you do the same
+trick uh as before.
+
+ align:start position:0%
+trick uh as before.
+ 
+
+ align:start position:0%
+trick uh as before.
+I mean I could have I could have gotten
+
+ align:start position:0%
+I mean I could have I could have gotten
+ 
+
+ align:start position:0%
+I mean I could have I could have gotten
+away uh slightly easier with looking at
+
+ align:start position:0%
+away uh slightly easier with looking at
+ 
+
+ align:start position:0%
+away uh slightly easier with looking at
+a special case of this quotion rule
+
+ align:start position:0%
+a special case of this quotion rule
+ 
+
+ align:start position:0%
+a special case of this quotion rule
+where f was a constant function one. So
+
+ align:start position:0%
+where f was a constant function one. So
+ 
+
+ align:start position:0%
+where f was a constant function one. So
+I could do that first and then the
+
+ align:start position:0%
+I could do that first and then the
+ 
+
+ align:start position:0%
+I could do that first and then the
+general case I could then from get from
+
+ align:start position:0%
+general case I could then from get from
+ 
+
+ align:start position:0%
+general case I could then from get from
+this special case together with the
+
+ align:start position:0%
+this special case together with the
+ 
+
+ align:start position:0%
+this special case together with the
+lens. But I chose to it's most often
+
+ align:start position:0%
+lens. But I chose to it's most often
+ 
+
+ align:start position:0%
+lens. But I chose to it's most often
+they want to do it together anyway. But
+
+ align:start position:0%
+they want to do it together anyway. But
+ 
+
+ align:start position:0%
+they want to do it together anyway. But
+if you have to do it together, you have
+
+ align:start position:0%
+if you have to do it together, you have
+ 
+
+ align:start position:0%
+if you have to do it together, you have
+to use the same trick that we just did.
+
+ align:start position:0%
+to use the same trick that we just did.
+ 
+
+ align:start position:0%
+to use the same trick that we just did.
+So we're using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that over here.
+
+ align:start position:0%
+uh that over here.
+ 
+
+ align:start position:0%
+uh that over here.
+So uh
+
+ align:start position:0%
+So uh
+ 
+
+ align:start position:0%
+So uh
+so f ofx
+
+ align:start position:0%
+so f ofx
+ 
+
+ align:start position:0%
+so f ofx
+g of x0
+
+ align:start position:0%
+g of x0
+ 
+
+ align:start position:0%
+g of x0
+minus uh and then uh f of uh f of x0
+
+ align:start position:0%
+minus uh and then uh f of uh f of x0
+ 
+
+ align:start position:0%
+minus uh and then uh f of uh f of x0
+g of x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus uh f of x0
+
+ align:start position:0%
+plus uh f of x0
+ 
+
+ align:start position:0%
+plus uh f of x0
+g of x0
+
+ align:start position:0%
+g of x0
+ 
+
+ align:start position:0%
+g of x0
+uh minus f(x)
+
+ align:start position:0%
+uh minus f(x)
+ 
+
+ align:start position:0%
+uh minus f(x)
+g of x. So this is again where I'm
+
+ align:start position:0%
+g of x. So this is again where I'm
+ 
+
+ align:start position:0%
+g of x. So this is again where I'm
+subtracting in the denominator something
+
+ align:start position:0%
+subtracting in the denominator something
+ 
+
+ align:start position:0%
+subtracting in the denominator something
+and then I'm adding it back up
+
+ align:start position:0%
+and then I'm adding it back up
+ 
+
+ align:start position:0%
+and then I'm adding it back up
+immediately.
+
+ align:start position:0%
+immediately.
+ 
+
+ align:start position:0%
+immediately.
+So I have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now uh if you do that then you
+
+ align:start position:0%
+And so now uh if you do that then you
+ 
+
+ align:start position:0%
+And so now uh if you do that then you
+see that. So now you can and now you
+
+ align:start position:0%
+see that. So now you can and now you
+ 
+
+ align:start position:0%
+see that. So now you can and now you
+split it up again into two fractions.
+
+ align:start position:0%
+split it up again into two fractions.
+ 
+
+ align:start position:0%
+split it up again into two fractions.
+So we split it up
+
+ align:start position:0%
+So we split it up
+ 
+
+ align:start position:0%
+So we split it up
+and so this thing here this thing here
+
+ align:start position:0%
+and so this thing here this thing here
+ 
+
+ align:start position:0%
+and so this thing here this thing here
+but there you see that there's a g of x0
+
+ align:start position:0%
+but there you see that there's a g of x0
+ 
+
+ align:start position:0%
+but there you see that there's a g of x0
+that factor out. So this is equal to g
+
+ align:start position:0%
+that factor out. So this is equal to g
+ 
+
+ align:start position:0%
+that factor out. So this is equal to g
+of x0 and then you have f ofx minus f of
+
+ align:start position:0%
+of x0 and then you have f ofx minus f of
+ 
+
+ align:start position:0%
+of x0 and then you have f ofx minus f of
+x0
+
+ align:start position:0%
+x0
+ 
+
+ align:start position:0%
+x0
+and then x - x0
+
+ align:start position:0%
+and then x - x0
+ 
+
+ align:start position:0%
+and then x - x0
+g of x
+
+ align:start position:0%
+g of x
+ 
+
+ align:start position:0%
+g of x
+g of x0 like that.
+
+ align:start position:0%
+g of x0 like that.
+ 
+
+ align:start position:0%
+g of x0 like that.
+And for the second one, see that there
+
+ align:start position:0%
+And for the second one, see that there
+ 
+
+ align:start position:0%
+And for the second one, see that there
+you there you also have something that's
+
+ align:start position:0%
+you there you also have something that's
+ 
+
+ align:start position:0%
+you there you also have something that's
+factor out. And this is f of x0
+
+ align:start position:0%
+factor out. And this is f of x0
+ 
+
+ align:start position:0%
+factor out. And this is f of x0
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+And you're getting g of u of x0
+
+ align:start position:0%
+And you're getting g of u of x0
+ 
+
+ align:start position:0%
+And you're getting g of u of x0
+minus g of x
+
+ align:start position:0%
+minus g of x
+ 
+
+ align:start position:0%
+minus g of x
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+um x - x0.
+
+ align:start position:0%
+um x - x0.
+ 
+
+ align:start position:0%
+um x - x0.
+uh g of x
+
+ align:start position:0%
+uh g of x
+ 
+
+ align:start position:0%
+uh g of x
+g of x here like that.
+
+ align:start position:0%
+g of x here like that.
+ 
+
+ align:start position:0%
+g of x here like that.
+And now okay so now I can make this
+
+ align:start position:0%
+And now okay so now I can make this
+ 
+
+ align:start position:0%
+And now okay so now I can make this
+looks nicer. I can this one here cancel
+
+ align:start position:0%
+looks nicer. I can this one here cancel
+ 
+
+ align:start position:0%
+looks nicer. I can this one here cancel
+with that.
+
+ align:start position:0%
+with that.
+ 
+
+ align:start position:0%
+with that.
+And so I can write this thing here as 1
+
+ align:start position:0%
+And so I can write this thing here as 1
+ 
+
+ align:start position:0%
+And so I can write this thing here as 1
+/ g of x
+
+ align:start position:0%
+/ g of x
+ 
+
+ align:start position:0%
+/ g of x
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+- f of x0
+
+ align:start position:0%
+- f of x0
+ 
+
+ align:start position:0%
+- f of x0
+/ x - x0. So this take care of this.
+
+ align:start position:0%
+/ x - x0. So this take care of this.
+ 
+
+ align:start position:0%
+/ x - x0. So this take care of this.
+Here I can um here I can um I will write
+
+ align:start position:0%
+Here I can um here I can um I will write
+ 
+
+ align:start position:0%
+Here I can um here I can um I will write
+it as I will take this one here out. So
+
+ align:start position:0%
+it as I will take this one here out. So
+ 
+
+ align:start position:0%
+it as I will take this one here out. So
+I'll write it as f of x0
+
+ align:start position:0%
+I'll write it as f of x0
+ 
+
+ align:start position:0%
+I'll write it as f of x0
+g of x
+
+ align:start position:0%
+g of x
+ 
+
+ align:start position:0%
+g of x
+time g of x0.
+
+ align:start position:0%
+time g of x0.
+ 
+
+ align:start position:0%
+time g of x0.
+And then I'm left with this thing here.
+
+ align:start position:0%
+And then I'm left with this thing here.
+ 
+
+ align:start position:0%
+And then I'm left with this thing here.
+And what I don't love about this thing
+
+ align:start position:0%
+And what I don't love about this thing
+ 
+
+ align:start position:0%
+And what I don't love about this thing
+here is it's not quite the difference
+
+ align:start position:0%
+here is it's not quite the difference
+ 
+
+ align:start position:0%
+here is it's not quite the difference
+quotient because the order of these two
+
+ align:start position:0%
+quotient because the order of these two
+ 
+
+ align:start position:0%
+quotient because the order of these two
+is wrong. So I switch the order. But if
+
+ align:start position:0%
+is wrong. So I switch the order. But if
+ 
+
+ align:start position:0%
+is wrong. So I switch the order. But if
+I switch the order then I have to
+
+ align:start position:0%
+I switch the order then I have to
+ 
+
+ align:start position:0%
+I switch the order then I have to
+pick up a minus sign. So I get minus
+
+ align:start position:0%
+pick up a minus sign. So I get minus
+ 
+
+ align:start position:0%
+pick up a minus sign. So I get minus
+here. And now it is g of x
+
+ align:start position:0%
+here. And now it is g of x
+ 
+
+ align:start position:0%
+here. And now it is g of x
+g of x0
+
+ align:start position:0%
+g of x0
+ 
+
+ align:start position:0%
+g of x0
+x - x0 like that.
+
+ align:start position:0%
+x - x0 like that.
+ 
+
+ align:start position:0%
+x - x0 like that.
+Okay. And now you see that as x so as x
+
+ align:start position:0%
+Okay. And now you see that as x so as x
+ 
+
+ align:start position:0%
+Okay. And now you see that as x so as x
+goes to x0
+
+ align:start position:0%
+goes to x0
+ 
+
+ align:start position:0%
+goes to x0
+so now as x
+
+ align:start position:0%
+so now as x
+ 
+
+ align:start position:0%
+so now as x
+goes to x0
+
+ align:start position:0%
+goes to x0
+ 
+
+ align:start position:0%
+goes to x0
+well this one here the function was
+
+ align:start position:0%
+well this one here the function was
+ 
+
+ align:start position:0%
+well this one here the function was
+differentiable so it's also continuous.
+
+ align:start position:0%
+differentiable so it's also continuous.
+ 
+
+ align:start position:0%
+differentiable so it's also continuous.
+So this goes to 1 / g of x0.
+
+ align:start position:0%
+So this goes to 1 / g of x0.
+ 
+
+ align:start position:0%
+So this goes to 1 / g of x0.
+This one here just goes to the
+
+ align:start position:0%
+This one here just goes to the
+ 
+
+ align:start position:0%
+This one here just goes to the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+at x0.
+
+ align:start position:0%
+at x0.
+ 
+
+ align:start position:0%
+at x0.
+This one here goes to again because the
+
+ align:start position:0%
+This one here goes to again because the
+ 
+
+ align:start position:0%
+This one here goes to again because the
+function is continuous. This goes to
+
+ align:start position:0%
+function is continuous. This goes to
+ 
+
+ align:start position:0%
+function is continuous. This goes to
+minus f of x0
+
+ align:start position:0%
+minus f of x0
+ 
+
+ align:start position:0%
+minus f of x0
+and then it's what I wrote before as d²
+
+ align:start position:0%
+and then it's what I wrote before as d²
+ 
+
+ align:start position:0%
+and then it's what I wrote before as d²
+is d of x0 * itself.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then this in here goes to the
+
+ align:start position:0%
+And then this in here goes to the
+ 
+
+ align:start position:0%
+And then this in here goes to the
+derivative of x0 at zero.
+
+ align:start position:0%
+derivative of x0 at zero.
+ 
+
+ align:start position:0%
+derivative of x0 at zero.
+Right? And now I can if I want to I can
+
+ align:start position:0%
+Right? And now I can if I want to I can
+ 
+
+ align:start position:0%
+Right? And now I can if I want to I can
+rewrite this in here. If I want to put
+
+ align:start position:0%
+rewrite this in here. If I want to put
+ 
+
+ align:start position:0%
+rewrite this in here. If I want to put
+it back on a common denominator, then I
+
+ align:start position:0%
+it back on a common denominator, then I
+ 
+
+ align:start position:0%
+it back on a common denominator, then I
+have to multiply in the nominator and
+
+ align:start position:0%
+have to multiply in the nominator and
+ 
+
+ align:start position:0%
+have to multiply in the nominator and
+denominator by g of x0. If I do this, I
+
+ align:start position:0%
+denominator by g of x0. If I do this, I
+ 
+
+ align:start position:0%
+denominator by g of x0. If I do this, I
+get f prime of x0 g of x0
+
+ align:start position:0%
+get f prime of x0 g of x0
+ 
+
+ align:start position:0%
+get f prime of x0 g of x0
+and then I get g^2 of x0 in the
+
+ align:start position:0%
+and then I get g^2 of x0 in the
+ 
+
+ align:start position:0%
+and then I get g^2 of x0 in the
+denominator. And then here it's just
+
+ align:start position:0%
+denominator. And then here it's just
+ 
+
+ align:start position:0%
+denominator. And then here it's just
+those two minus f of x0
+
+ align:start position:0%
+those two minus f of x0
+ 
+
+ align:start position:0%
+those two minus f of x0
+g prime of x0.
+
+ align:start position:0%
+g prime of x0.
+ 
+
+ align:start position:0%
+g prime of x0.
+And so you see that this here is exactly
+
+ align:start position:0%
+And so you see that this here is exactly
+ 
+
+ align:start position:0%
+And so you see that this here is exactly
+this formula here this this quotion rule
+
+ align:start position:0%
+this formula here this this quotion rule
+ 
+
+ align:start position:0%
+this formula here this this quotion rule
+right. So this proof that if you take
+
+ align:start position:0%
+right. So this proof that if you take
+ 
+
+ align:start position:0%
+right. So this proof that if you take
+two functions the the one you have in
+
+ align:start position:0%
+two functions the the one you have in
+ 
+
+ align:start position:0%
+two functions the the one you have in
+the denominator if that is non vanishing
+
+ align:start position:0%
+the denominator if that is non vanishing
+ 
+
+ align:start position:0%
+the denominator if that is non vanishing
+so you can form the quotient and if each
+
+ align:start position:0%
+so you can form the quotient and if each
+ 
+
+ align:start position:0%
+so you can form the quotient and if each
+of these two functions is differentiable
+
+ align:start position:0%
+of these two functions is differentiable
+ 
+
+ align:start position:0%
+of these two functions is differentiable
+then the quotient is also differentiable
+
+ align:start position:0%
+then the quotient is also differentiable
+ 
+
+ align:start position:0%
+then the quotient is also differentiable
+and this is the formula for the
+
+ align:start position:0%
+and this is the formula for the
+ 
+
+ align:start position:0%
+and this is the formula for the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+right so now why is this already really
+
+ align:start position:0%
+right so now why is this already really
+ 
+
+ align:start position:0%
+right so now why is this already really
+really useful
+
+ align:start position:0%
+really useful
+ 
+
+ align:start position:0%
+really useful
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so We calculated
+
+ align:start position:0%
+so We calculated
+ 
+
+ align:start position:0%
+so We calculated
+we already we calculated so we started
+
+ align:start position:0%
+we already we calculated so we started
+ 
+
+ align:start position:0%
+we already we calculated so we started
+with the example of where f is a
+
+ align:start position:0%
+with the example of where f is a
+ 
+
+ align:start position:0%
+with the example of where f is a
+constant right and we saw that it's
+
+ align:start position:0%
+constant right and we saw that it's
+ 
+
+ align:start position:0%
+constant right and we saw that it's
+differentiable and the derivative is
+
+ align:start position:0%
+differentiable and the derivative is
+ 
+
+ align:start position:0%
+differentiable and the derivative is
+zero. Then the second example we had was
+
+ align:start position:0%
+zero. Then the second example we had was
+ 
+
+ align:start position:0%
+zero. Then the second example we had was
+where the function was x and we saw that
+
+ align:start position:0%
+where the function was x and we saw that
+ 
+
+ align:start position:0%
+where the function was x and we saw that
+it was differentiable and the derivative
+
+ align:start position:0%
+it was differentiable and the derivative
+ 
+
+ align:start position:0%
+it was differentiable and the derivative
+is one. Right? If you now take um if you
+
+ align:start position:0%
+is one. Right? If you now take um if you
+ 
+
+ align:start position:0%
+is one. Right? If you now take um if you
+now take ax
+
+ align:start position:0%
+now take ax
+ 
+
+ align:start position:0%
+now take ax
+times uh right so let's just take ax as
+
+ align:start position:0%
+times uh right so let's just take ax as
+ 
+
+ align:start position:0%
+times uh right so let's just take ax as
+the next example
+
+ align:start position:0%
+the next example
+ 
+
+ align:start position:0%
+the next example
+this is like a constant function times
+
+ align:start position:0%
+this is like a constant function times
+ 
+
+ align:start position:0%
+this is like a constant function times
+this function so light rule sorry if f
+
+ align:start position:0%
+this function so light rule sorry if f
+ 
+
+ align:start position:0%
+this function so light rule sorry if f
+ofx is equal to a * x where a is a
+
+ align:start position:0%
+ofx is equal to a * x where a is a
+ 
+
+ align:start position:0%
+ofx is equal to a * x where a is a
+constant lightn will say that the
+
+ align:start position:0%
+constant lightn will say that the
+ 
+
+ align:start position:0%
+constant lightn will say that the
+product of two differentiable functions
+
+ align:start position:0%
+product of two differentiable functions
+ 
+
+ align:start position:0%
+product of two differentiable functions
+is differentiable and the derivative of
+
+ align:start position:0%
+is differentiable and the derivative of
+ 
+
+ align:start position:0%
+is differentiable and the derivative of
+This is the derivative of that, but the
+
+ align:start position:0%
+This is the derivative of that, but the
+ 
+
+ align:start position:0%
+This is the derivative of that, but the
+derivative of that does a constant
+
+ align:start position:0%
+derivative of that does a constant
+ 
+
+ align:start position:0%
+derivative of that does a constant
+function. So that's zero. So I don't
+
+ align:start position:0%
+function. So that's zero. So I don't
+ 
+
+ align:start position:0%
+function. So that's zero. So I don't
+really have to think about that. So it's
+
+ align:start position:0%
+really have to think about that. So it's
+ 
+
+ align:start position:0%
+really have to think about that. So it's
+just the a times the derivative of the
+
+ align:start position:0%
+just the a times the derivative of the
+ 
+
+ align:start position:0%
+just the a times the derivative of the
+second function, but that's one. So this
+
+ align:start position:0%
+second function, but that's one. So this
+ 
+
+ align:start position:0%
+second function, but that's one. So this
+here is the derivative of that.
+
+ align:start position:0%
+here is the derivative of that.
+ 
+
+ align:start position:0%
+here is the derivative of that.
+Right? So and the next example would be
+
+ align:start position:0%
+Right? So and the next example would be
+ 
+
+ align:start position:0%
+Right? So and the next example would be
+that you're looking at a x plus say b f
+
+ align:start position:0%
+that you're looking at a x plus say b f
+ 
+
+ align:start position:0%
+that you're looking at a x plus say b f
+of x is equal to this. Then you can use
+
+ align:start position:0%
+of x is equal to this. Then you can use
+ 
+
+ align:start position:0%
+of x is equal to this. Then you can use
+the sum
+
+ align:start position:0%
+the sum
+ 
+
+ align:start position:0%
+the sum
+plus you know we know what each of these
+
+ align:start position:0%
+plus you know we know what each of these
+ 
+
+ align:start position:0%
+plus you know we know what each of these
+is. So you get that this one here is
+
+ align:start position:0%
+is. So you get that this one here is
+ 
+
+ align:start position:0%
+is. So you get that this one here is
+also differentiable and the derivative
+
+ align:start position:0%
+also differentiable and the derivative
+ 
+
+ align:start position:0%
+also differentiable and the derivative
+of this function here is also just a and
+
+ align:start position:0%
+of this function here is also just a and
+ 
+
+ align:start position:0%
+of this function here is also just a and
+and you can continue like this that if
+
+ align:start position:0%
+and you can continue like this that if
+ 
+
+ align:start position:0%
+and you can continue like this that if
+you take
+
+ align:start position:0%
+you take
+ 
+
+ align:start position:0%
+you take
+um if you use if you now have a polomial
+
+ align:start position:0%
+um if you use if you now have a polomial
+ 
+
+ align:start position:0%
+um if you use if you now have a polomial
+suppose you take a to the power n so f
+
+ align:start position:0%
+suppose you take a to the power n so f
+ 
+
+ align:start position:0%
+suppose you take a to the power n so f
+of sorry uh if f of x is x to the^ n
+
+ align:start position:0%
+of sorry uh if f of x is x to the^ n
+ 
+
+ align:start position:0%
+of sorry uh if f of x is x to the^ n
+then you can think about this thing here
+
+ align:start position:0%
+then you can think about this thing here
+ 
+
+ align:start position:0%
+then you can think about this thing here
+as x * X * X * X
+
+ align:start position:0%
+as x * X * X * X
+ 
+
+ align:start position:0%
+as x * X * X * X
+and you can use the lieness rule right
+
+ align:start position:0%
+and you can use the lieness rule right
+ 
+
+ align:start position:0%
+and you can use the lieness rule right
+and so if you use the leness rule so you
+
+ align:start position:0%
+and so if you use the leness rule so you
+ 
+
+ align:start position:0%
+and so if you use the leness rule so you
+just do it first in the case where f ofx
+
+ align:start position:0%
+just do it first in the case where f ofx
+ 
+
+ align:start position:0%
+just do it first in the case where f ofx
+is equal to x^2 you can think about this
+
+ align:start position:0%
+is equal to x^2 you can think about this
+ 
+
+ align:start position:0%
+is equal to x^2 you can think about this
+as x * x these are two differentiable
+
+ align:start position:0%
+as x * x these are two differentiable
+ 
+
+ align:start position:0%
+as x * x these are two differentiable
+functions so the derivative here is now
+
+ align:start position:0%
+functions so the derivative here is now
+ 
+
+ align:start position:0%
+functions so the derivative here is now
+the derivative of this so that's 1 times
+
+ align:start position:0%
+the derivative of this so that's 1 times
+ 
+
+ align:start position:0%
+the derivative of this so that's 1 times
+the other function plus you keep this
+
+ align:start position:0%
+the other function plus you keep this
+ 
+
+ align:start position:0%
+the other function plus you keep this
+one here and you take the derivative of
+
+ align:start position:0%
+one here and you take the derivative of
+ 
+
+ align:start position:0%
+one here and you take the derivative of
+that. So this is this. So this is 2 * x,
+
+ align:start position:0%
+that. So this is this. So this is 2 * x,
+ 
+
+ align:start position:0%
+that. So this is this. So this is 2 * x,
+right? And so if you take this function
+
+ align:start position:0%
+right? And so if you take this function
+ 
+
+ align:start position:0%
+right? And so if you take this function
+here using lightness rule,
+
+ align:start position:0%
+here using lightness rule,
+ 
+
+ align:start position:0%
+here using lightness rule,
+in this case the derivative it's
+
+ align:start position:0%
+in this case the derivative it's
+ 
+
+ align:start position:0%
+in this case the derivative it's
+differentiable and the derivative
+
+ align:start position:0%
+differentiable and the derivative
+ 
+
+ align:start position:0%
+differentiable and the derivative
+is uh n * x ^ nus one. Right?
+
+ align:start position:0%
+is uh n * x ^ nus one. Right?
+ 
+
+ align:start position:0%
+is uh n * x ^ nus one. Right?
+So that's so so and and in fact find
+
+ align:start position:0%
+So that's so so and and in fact find
+ 
+
+ align:start position:0%
+So that's so so and and in fact find
+even more generally
+
+ align:start position:0%
+even more generally
+ 
+
+ align:start position:0%
+even more generally
+you know just using the sum and the
+
+ align:start position:0%
+you know just using the sum and the
+ 
+
+ align:start position:0%
+you know just using the sum and the
+likeness rule if you take any
+
+ align:start position:0%
+likeness rule if you take any
+ 
+
+ align:start position:0%
+likeness rule if you take any
+if you take any polomium a n x n + a n
+
+ align:start position:0%
+if you take any polomium a n x n + a n
+ 
+
+ align:start position:0%
+if you take any polomium a n x n + a n
+-1 x n minus one
+
+ align:start position:0%
+-1 x n minus one
+ 
+
+ align:start position:0%
+-1 x n minus one
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+the last sign is being a constant. If
+
+ align:start position:0%
+the last sign is being a constant. If
+ 
+
+ align:start position:0%
+the last sign is being a constant. If
+you take a polinomial like this just
+
+ align:start position:0%
+you take a polinomial like this just
+ 
+
+ align:start position:0%
+you take a polinomial like this just
+using the lieness rule and the sum rule
+
+ align:start position:0%
+using the lieness rule and the sum rule
+ 
+
+ align:start position:0%
+using the lieness rule and the sum rule
+using those repeatedly
+
+ align:start position:0%
+using those repeatedly
+ 
+
+ align:start position:0%
+using those repeatedly
+we know that this here is differentiable
+
+ align:start position:0%
+we know that this here is differentiable
+ 
+
+ align:start position:0%
+we know that this here is differentiable
+and the derivative is just like the sum
+
+ align:start position:0%
+and the derivative is just like the sum
+ 
+
+ align:start position:0%
+and the derivative is just like the sum
+of the derivative of these. So this is
+
+ align:start position:0%
+of the derivative of these. So this is
+ 
+
+ align:start position:0%
+of the derivative of these. So this is
+going to be a n * n * x ^ n -1
+
+ align:start position:0%
+going to be a n * n * x ^ n -1
+ 
+
+ align:start position:0%
+going to be a n * n * x ^ n -1
++ n -1 * a n -1 x n - 2
+
+ align:start position:0%
++ n -1 * a n -1 x n - 2
+ 
+
+ align:start position:0%
++ n -1 * a n -1 x n - 2
+and then the this one here the
+
+ align:start position:0%
+and then the this one here the
+ 
+
+ align:start position:0%
+and then the this one here the
+derivative is zero. So the last one
+
+ align:start position:0%
+derivative is zero. So the last one
+ 
+
+ align:start position:0%
+derivative is zero. So the last one
+you're getting something non-trivial for
+
+ align:start position:0%
+you're getting something non-trivial for
+ 
+
+ align:start position:0%
+you're getting something non-trivial for
+is a one
+
+ align:start position:0%
+is a one
+ 
+
+ align:start position:0%
+is a one
+right. So this is just using sum and
+
+ align:start position:0%
+right. So this is just using sum and
+ 
+
+ align:start position:0%
+right. So this is just using sum and
+license room.
+
+ align:start position:0%
+license room.
+ 
+
+ align:start position:0%
+license room.
+And so this is just using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum
+
+ align:start position:0%
+the sum
+ 
+
+ align:start position:0%
+the sum
+plus lightness room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repeatedly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now likewise if you take a
+
+ align:start position:0%
+Okay. Now likewise if you take a
+ 
+
+ align:start position:0%
+Okay. Now likewise if you take a
+rational function so meaning that if you
+
+ align:start position:0%
+rational function so meaning that if you
+ 
+
+ align:start position:0%
+rational function so meaning that if you
+take something if f ofx
+
+ align:start position:0%
+take something if f ofx
+ 
+
+ align:start position:0%
+take something if f ofx
+is equal to some polomium
+
+ align:start position:0%
+is equal to some polomium
+ 
+
+ align:start position:0%
+is equal to some polomium
+a polomial
+
+ align:start position:0%
+a polomial
+ 
+
+ align:start position:0%
+a polomial
+so it's called p
+
+ align:start position:0%
+so it's called p
+ 
+
+ align:start position:0%
+so it's called p
+of x divided by uh q of x. So where this
+
+ align:start position:0%
+of x divided by uh q of x. So where this
+ 
+
+ align:start position:0%
+of x divided by uh q of x. So where this
+here is a polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and and so is that right? So now you
+
+ align:start position:0%
+and and and so is that right? So now you
+ 
+
+ align:start position:0%
+and and and so is that right? So now you
+can use the uh the quotient rule right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the quotient rule will tell you that
+
+ align:start position:0%
+So the quotient rule will tell you that
+ 
+
+ align:start position:0%
+So the quotient rule will tell you that
+as long as you are looking at point
+
+ align:start position:0%
+as long as you are looking at point
+ 
+
+ align:start position:0%
+as long as you are looking at point
+where this here does not vanish. So then
+
+ align:start position:0%
+where this here does not vanish. So then
+ 
+
+ align:start position:0%
+where this here does not vanish. So then
+the quotient here is also differentiable
+
+ align:start position:0%
+the quotient here is also differentiable
+ 
+
+ align:start position:0%
+the quotient here is also differentiable
+and it gives you a formula for the
+
+ align:start position:0%
+and it gives you a formula for the
+ 
+
+ align:start position:0%
+and it gives you a formula for the
+derivative in terms of the derivative of
+
+ align:start position:0%
+derivative in terms of the derivative of
+ 
+
+ align:start position:0%
+derivative in terms of the derivative of
+each of these two and each of those two
+
+ align:start position:0%
+each of these two and each of those two
+ 
+
+ align:start position:0%
+each of these two and each of those two
+they can be calculated like that.
+
+ align:start position:0%
+they can be calculated like that.
+ 
+
+ align:start position:0%
+they can be calculated like that.
+So you see it's already already now we
+
+ align:start position:0%
+So you see it's already already now we
+ 
+
+ align:start position:0%
+So you see it's already already now we
+have like quite the derivative of a lot
+
+ align:start position:0%
+have like quite the derivative of a lot
+ 
+
+ align:start position:0%
+have like quite the derivative of a lot
+of functions right we have of all
+
+ align:start position:0%
+of functions right we have of all
+ 
+
+ align:start position:0%
+of functions right we have of all
+function and of all rational functions
+
+ align:start position:0%
+function and of all rational functions
+ 
+
+ align:start position:0%
+function and of all rational functions
+rational functions again are clos
+
+ align:start position:0%
+rational functions again are clos
+ 
+
+ align:start position:0%
+rational functions again are clos
+by other polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now the next rule uh that we want to
+
+ align:start position:0%
+so now the next rule uh that we want to
+ 
+
+ align:start position:0%
+so now the next rule uh that we want to
+talk about is the the chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what is the chain rule?
+
+ align:start position:0%
+So what is the chain rule?
+ 
+
+ align:start position:0%
+So what is the chain rule?
+So the chain rule is a little bit
+
+ align:start position:0%
+So the chain rule is a little bit
+ 
+
+ align:start position:0%
+So the chain rule is a little bit
+different from those three rules here
+
+ align:start position:0%
+different from those three rules here
+ 
+
+ align:start position:0%
+different from those three rules here
+and and it is where you take the
+
+ align:start position:0%
+and and it is where you take the
+ 
+
+ align:start position:0%
+and and it is where you take the
+composition of functions.
+
+ align:start position:0%
+composition of functions.
+ 
+
+ align:start position:0%
+composition of functions.
+So the next is the chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again this is about
+
+ align:start position:0%
+and again this is about
+ 
+
+ align:start position:0%
+and again this is about
+composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of functions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I have a function f that goes
+
+ align:start position:0%
+Okay. So I have a function f that goes
+ 
+
+ align:start position:0%
+Okay. So I have a function f that goes
+say from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that it goes from some interval a to
+
+ align:start position:0%
+say that it goes from some interval a to
+ 
+
+ align:start position:0%
+say that it goes from some interval a to
+b into another interval from c to d
+
+ align:start position:0%
+b into another interval from c to d
+ 
+
+ align:start position:0%
+b into another interval from c to d
+and then I have a function g
+
+ align:start position:0%
+and then I have a function g
+ 
+
+ align:start position:0%
+and then I have a function g
+that goes from this interval here
+
+ align:start position:0%
+that goes from this interval here
+ 
+
+ align:start position:0%
+that goes from this interval here
+into r
+
+ align:start position:0%
+into r
+ 
+
+ align:start position:0%
+into r
+because g is defined you So like
+
+ align:start position:0%
+because g is defined you So like
+ 
+
+ align:start position:0%
+because g is defined you So like
+whatever the the image of of of F always
+
+ align:start position:0%
+whatever the the image of of of F always
+ 
+
+ align:start position:0%
+whatever the the image of of of F always
+if it's in this set this is where G is
+
+ align:start position:0%
+if it's in this set this is where G is
+ 
+
+ align:start position:0%
+if it's in this set this is where G is
+defined then you have that uh you can
+
+ align:start position:0%
+defined then you have that uh you can
+ 
+
+ align:start position:0%
+defined then you have that uh you can
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+if you take some X in here. So if X here
+
+ align:start position:0%
+if you take some X in here. So if X here
+ 
+
+ align:start position:0%
+if you take some X in here. So if X here
+is in A to B then this here makes sense
+
+ align:start position:0%
+is in A to B then this here makes sense
+ 
+
+ align:start position:0%
+is in A to B then this here makes sense
+and this is now an element here. So this
+
+ align:start position:0%
+and this is now an element here. So this
+ 
+
+ align:start position:0%
+and this is now an element here. So this
+is where G is defined. So this here
+
+ align:start position:0%
+is where G is defined. So this here
+ 
+
+ align:start position:0%
+is where G is defined. So this here
+makes sense, right? And this is now what
+
+ align:start position:0%
+makes sense, right? And this is now what
+ 
+
+ align:start position:0%
+makes sense, right? And this is now what
+we call the composition. And we write it
+
+ align:start position:0%
+we call the composition. And we write it
+ 
+
+ align:start position:0%
+we call the composition. And we write it
+like this. It's important to write it in
+
+ align:start position:0%
+like this. It's important to write it in
+ 
+
+ align:start position:0%
+like this. It's important to write it in
+the correct order.
+
+ align:start position:0%
+the correct order.
+ 
+
+ align:start position:0%
+the correct order.
+And so this is the composition function.
+
+ align:start position:0%
+And so this is the composition function.
+ 
+
+ align:start position:0%
+And so this is the composition function.
+Okay. And uh and the thing is that this
+
+ align:start position:0%
+Okay. And uh and the thing is that this
+ 
+
+ align:start position:0%
+Okay. And uh and the thing is that this
+so right. So now the chain rule is the
+
+ align:start position:0%
+so right. So now the chain rule is the
+ 
+
+ align:start position:0%
+so right. So now the chain rule is the
+following.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the chain rule is a following
+
+ align:start position:0%
+So the chain rule is a following
+ 
+
+ align:start position:0%
+So the chain rule is a following
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and uh g
+
+ align:start position:0%
+and uh g
+ 
+
+ align:start position:0%
+and uh g
+is differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at y0 where y0 is equal to the value of
+
+ align:start position:0%
+at y0 where y0 is equal to the value of
+ 
+
+ align:start position:0%
+at y0 where y0 is equal to the value of
+f at x0.
+
+ align:start position:0%
+f at x0.
+ 
+
+ align:start position:0%
+f at x0.
+Then the composition then the
+
+ align:start position:0%
+Then the composition then the
+ 
+
+ align:start position:0%
+Then the composition then the
+composition of these two functions is
+
+ align:start position:0%
+composition of these two functions is
+ 
+
+ align:start position:0%
+composition of these two functions is
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+at x0. And the derivative is equal to
+
+ align:start position:0%
+at x0. And the derivative is equal to
+ 
+
+ align:start position:0%
+at x0. And the derivative is equal to
+the derivative of g at y0 times the
+
+ align:start position:0%
+the derivative of g at y0 times the
+ 
+
+ align:start position:0%
+the derivative of g at y0 times the
+derivative of f at x0. So this is the
+
+ align:start position:0%
+derivative of f at x0. So this is the
+ 
+
+ align:start position:0%
+derivative of f at x0. So this is the
+chain rule, right? The chain rule say
+
+ align:start position:0%
+chain rule, right? The chain rule say
+ 
+
+ align:start position:0%
+chain rule, right? The chain rule say
+that the composition is also
+
+ align:start position:0%
+that the composition is also
+ 
+
+ align:start position:0%
+that the composition is also
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+at x0. And this is the formula for the
+
+ align:start position:0%
+at x0. And this is the formula for the
+ 
+
+ align:start position:0%
+at x0. And this is the formula for the
+derivative.
+
+ align:start position:0%
+derivative.
+ 
+
+ align:start position:0%
+derivative.
+Okay, let's try to prove that. Uh and so
+
+ align:start position:0%
+Okay, let's try to prove that. Uh and so
+ 
+
+ align:start position:0%
+Okay, let's try to prove that. Uh and so
+that we in this case it's useful to
+
+ align:start position:0%
+that we in this case it's useful to
+ 
+
+ align:start position:0%
+that we in this case it's useful to
+divide up to two to two cases.
+
+ align:start position:0%
+divide up to two to two cases.
+ 
+
+ align:start position:0%
+divide up to two to two cases.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the two cases to divide up to. So
+
+ align:start position:0%
+and the two cases to divide up to. So
+ 
+
+ align:start position:0%
+and the two cases to divide up to. So
+let me just look at the look at the
+
+ align:start position:0%
+let me just look at the look at the
+ 
+
+ align:start position:0%
+let me just look at the look at the
+special case first and then once we
+
+ align:start position:0%
+special case first and then once we
+ 
+
+ align:start position:0%
+special case first and then once we
+understand that it's would be clear the
+
+ align:start position:0%
+understand that it's would be clear the
+ 
+
+ align:start position:0%
+understand that it's would be clear the
+general case would be clear. So let's
+
+ align:start position:0%
+general case would be clear. So let's
+ 
+
+ align:start position:0%
+general case would be clear. So let's
+make one assumption. So let's try to
+
+ align:start position:0%
+make one assumption. So let's try to
+ 
+
+ align:start position:0%
+make one assumption. So let's try to
+prove it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and but we assume first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to assume that the derivative
+
+ align:start position:0%
+I'm going to assume that the derivative
+ 
+
+ align:start position:0%
+I'm going to assume that the derivative
+at x0 is not equal to zero. So I'm
+
+ align:start position:0%
+at x0 is not equal to zero. So I'm
+ 
+
+ align:start position:0%
+at x0 is not equal to zero. So I'm
+assuming that first. What does this
+
+ align:start position:0%
+assuming that first. What does this
+ 
+
+ align:start position:0%
+assuming that first. What does this
+guarantee me? Well, remember that the
+
+ align:start position:0%
+guarantee me? Well, remember that the
+ 
+
+ align:start position:0%
+guarantee me? Well, remember that the
+derivative is the limit of this
+
+ align:start position:0%
+derivative is the limit of this
+ 
+
+ align:start position:0%
+derivative is the limit of this
+difference quotient,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? So this is this is the limit.
+
+ align:start position:0%
+right? So this is this is the limit.
+ 
+
+ align:start position:0%
+right? So this is this is the limit.
+If this here is not equal to zero,
+
+ align:start position:0%
+If this here is not equal to zero,
+ 
+
+ align:start position:0%
+If this here is not equal to zero,
+this means that when x is very close to
+
+ align:start position:0%
+this means that when x is very close to
+ 
+
+ align:start position:0%
+this means that when x is very close to
+x0, this thing here
+
+ align:start position:0%
+x0, this thing here
+ 
+
+ align:start position:0%
+x0, this thing here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+very close to this thing that is not
+
+ align:start position:0%
+very close to this thing that is not
+ 
+
+ align:start position:0%
+very close to this thing that is not
+equal to zero. But then it means that if
+
+ align:start position:0%
+equal to zero. But then it means that if
+ 
+
+ align:start position:0%
+equal to zero. But then it means that if
+you are very close to x0, f ofx cannot
+
+ align:start position:0%
+you are very close to x0, f ofx cannot
+ 
+
+ align:start position:0%
+you are very close to x0, f ofx cannot
+be equal to. So if you have this here,
+
+ align:start position:0%
+be equal to. So if you have this here,
+ 
+
+ align:start position:0%
+be equal to. So if you have this here,
+this implies that f ofx
+
+ align:start position:0%
+this implies that f ofx
+ 
+
+ align:start position:0%
+this implies that f ofx
+is not equal to x0
+
+ align:start position:0%
+is not equal to x0
+ 
+
+ align:start position:0%
+is not equal to x0
+for sorry is not equal to f of x0
+
+ align:start position:0%
+for sorry is not equal to f of x0
+ 
+
+ align:start position:0%
+for sorry is not equal to f of x0
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+x sufficiently closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close to x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm always assuming of course that x is
+
+ align:start position:0%
+I'm always assuming of course that x is
+ 
+
+ align:start position:0%
+I'm always assuming of course that x is
+not But x is not equal to right.
+
+ align:start position:0%
+not But x is not equal to right.
+ 
+
+ align:start position:0%
+not But x is not equal to right.
+So, so I'm going to first make this
+
+ align:start position:0%
+So, so I'm going to first make this
+ 
+
+ align:start position:0%
+So, so I'm going to first make this
+assumption. And if I make this
+
+ align:start position:0%
+assumption. And if I make this
+ 
+
+ align:start position:0%
+assumption. And if I make this
+assumption, what I get out of it is that
+
+ align:start position:0%
+assumption, what I get out of it is that
+ 
+
+ align:start position:0%
+assumption, what I get out of it is that
+this thing here is not equal to that.
+
+ align:start position:0%
+this thing here is not equal to that.
+ 
+
+ align:start position:0%
+this thing here is not equal to that.
+Why is this useful? Because now I can
+
+ align:start position:0%
+Why is this useful? Because now I can
+ 
+
+ align:start position:0%
+Why is this useful? Because now I can
+actually look at this difference and I
+
+ align:start position:0%
+actually look at this difference and I
+ 
+
+ align:start position:0%
+actually look at this difference and I
+can divide by it. Okay.
+
+ align:start position:0%
+can divide by it. Okay.
+ 
+
+ align:start position:0%
+can divide by it. Okay.
+So, I'm going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to just to make things a
+
+ align:start position:0%
+I'm going to just to make things a
+ 
+
+ align:start position:0%
+I'm going to just to make things a
+little bit clearer.
+
+ align:start position:0%
+little bit clearer.
+ 
+
+ align:start position:0%
+little bit clearer.
+So I have my function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this here is is this f and here I
+
+ align:start position:0%
+So this here is is this f and here I
+ 
+
+ align:start position:0%
+So this here is is this f and here I
+have g.
+
+ align:start position:0%
+have g.
+ 
+
+ align:start position:0%
+have g.
+Here I have x0.
+
+ align:start position:0%
+Here I have x0.
+ 
+
+ align:start position:0%
+Here I have x0.
+But under f it's taken to this which is
+
+ align:start position:0%
+But under f it's taken to this which is
+ 
+
+ align:start position:0%
+But under f it's taken to this which is
+f of x0. But this I also will denote by
+
+ align:start position:0%
+f of x0. But this I also will denote by
+ 
+
+ align:start position:0%
+f of x0. But this I also will denote by
+y z right. So I'm denoting just to make
+
+ align:start position:0%
+y z right. So I'm denoting just to make
+ 
+
+ align:start position:0%
+y z right. So I'm denoting just to make
+clear y0 is just the value here.
+
+ align:start position:0%
+clear y0 is just the value here.
+ 
+
+ align:start position:0%
+clear y0 is just the value here.
+And then I will use uh for I will I will
+
+ align:start position:0%
+And then I will use uh for I will I will
+ 
+
+ align:start position:0%
+And then I will use uh for I will I will
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+I will denote by y. Okay.
+
+ align:start position:0%
+I will denote by y. Okay.
+ 
+
+ align:start position:0%
+I will denote by y. Okay.
+So now I'm looking at the difference
+
+ align:start position:0%
+So now I'm looking at the difference
+ 
+
+ align:start position:0%
+So now I'm looking at the difference
+quotient. So I'm looking at f of sorry
+
+ align:start position:0%
+quotient. So I'm looking at f of sorry
+ 
+
+ align:start position:0%
+quotient. So I'm looking at f of sorry
+I'm looking at g of f of x minus uh g of
+
+ align:start position:0%
+I'm looking at g of f of x minus uh g of
+ 
+
+ align:start position:0%
+I'm looking at g of f of x minus uh g of
+f of x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh x - x0 that's what I'm supposed to
+
+ align:start position:0%
+uh x - x0 that's what I'm supposed to
+ 
+
+ align:start position:0%
+uh x - x0 that's what I'm supposed to
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+and I'm can write this thing here
+
+ align:start position:0%
+and I'm can write this thing here
+ 
+
+ align:start position:0%
+and I'm can write this thing here
+as g of y because this here I also call
+
+ align:start position:0%
+as g of y because this here I also call
+ 
+
+ align:start position:0%
+as g of y because this here I also call
+y right so you can write it like this g
+
+ align:start position:0%
+y right so you can write it like this g
+ 
+
+ align:start position:0%
+y right so you can write it like this g
+of y 0
+
+ align:start position:0%
+of y 0
+ 
+
+ align:start position:0%
+of y 0
+and then I will write it as y - y 0 but
+
+ align:start position:0%
+and then I will write it as y - y 0 but
+ 
+
+ align:start position:0%
+and then I will write it as y - y 0 but
+I didn't have this in the denominator up
+
+ align:start position:0%
+I didn't have this in the denominator up
+ 
+
+ align:start position:0%
+I didn't have this in the denominator up
+here so I have to multiply it back on
+
+ align:start position:0%
+here so I have to multiply it back on
+ 
+
+ align:start position:0%
+here so I have to multiply it back on
+and then I still have to divide by like
+
+ align:start position:0%
+and then I still have to divide by like
+ 
+
+ align:start position:0%
+and then I still have to divide by like
+like that right so I can write it like
+
+ align:start position:0%
+like that right so I can write it like
+ 
+
+ align:start position:0%
+like that right so I can write it like
+this this here I'm happy with we'll get
+
+ align:start position:0%
+this this here I'm happy with we'll get
+ 
+
+ align:start position:0%
+this this here I'm happy with we'll get
+to this in just a taken, but I'm happy
+
+ align:start position:0%
+to this in just a taken, but I'm happy
+ 
+
+ align:start position:0%
+to this in just a taken, but I'm happy
+with this expression. The other one I
+
+ align:start position:0%
+with this expression. The other one I
+ 
+
+ align:start position:0%
+with this expression. The other one I
+really want to put it back in in terms
+
+ align:start position:0%
+really want to put it back in in terms
+ 
+
+ align:start position:0%
+really want to put it back in in terms
+of f. So I'm writing this thing here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this thing here, I really want to
+
+ align:start position:0%
+And this thing here, I really want to
+ 
+
+ align:start position:0%
+And this thing here, I really want to
+put it back in in terms of f. So if I do
+
+ align:start position:0%
+put it back in in terms of f. So if I do
+ 
+
+ align:start position:0%
+put it back in in terms of f. So if I do
+that, I write it as f ofx - f of x0
+
+ align:start position:0%
+that, I write it as f ofx - f of x0
+ 
+
+ align:start position:0%
+that, I write it as f ofx - f of x0
+x - x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But now you see that as um as x go to
+
+ align:start position:0%
+But now you see that as um as x go to
+ 
+
+ align:start position:0%
+But now you see that as um as x go to
+x0, right?
+
+ align:start position:0%
+x0, right?
+ 
+
+ align:start position:0%
+x0, right?
+Well, as x go to x0 the because the
+
+ align:start position:0%
+Well, as x go to x0 the because the
+ 
+
+ align:start position:0%
+Well, as x go to x0 the because the
+function f was continuous at x0 it means
+
+ align:start position:0%
+function f was continuous at x0 it means
+ 
+
+ align:start position:0%
+function f was continuous at x0 it means
+that if x go to x0 then the value at x
+
+ align:start position:0%
+that if x go to x0 then the value at x
+ 
+
+ align:start position:0%
+that if x go to x0 then the value at x
+which is y will go to the value at x0.
+
+ align:start position:0%
+which is y will go to the value at x0.
+ 
+
+ align:start position:0%
+which is y will go to the value at x0.
+So when when
+
+ align:start position:0%
+So when when
+ 
+
+ align:start position:0%
+So when when
+x goes to x0
+
+ align:start position:0%
+x goes to x0
+ 
+
+ align:start position:0%
+x goes to x0
+we have that y goes to y0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this means that this thing here this
+
+ align:start position:0%
+so this means that this thing here this
+ 
+
+ align:start position:0%
+so this means that this thing here this
+here converge right that's just because
+
+ align:start position:0%
+here converge right that's just because
+ 
+
+ align:start position:0%
+here converge right that's just because
+the function f is differentiable so this
+
+ align:start position:0%
+the function f is differentiable so this
+ 
+
+ align:start position:0%
+the function f is differentiable so this
+here will converge to the derivative so
+
+ align:start position:0%
+here will converge to the derivative so
+ 
+
+ align:start position:0%
+here will converge to the derivative so
+this the the second factor here is
+
+ align:start position:0%
+this the the second factor here is
+ 
+
+ align:start position:0%
+this the the second factor here is
+converging to fprime at x0. The first
+
+ align:start position:0%
+converging to fprime at x0. The first
+ 
+
+ align:start position:0%
+converging to fprime at x0. The first
+factor is but now you see that we just
+
+ align:start position:0%
+factor is but now you see that we just
+ 
+
+ align:start position:0%
+factor is but now you see that we just
+argued that y goes to y0. So this is
+
+ align:start position:0%
+argued that y goes to y0. So this is
+ 
+
+ align:start position:0%
+argued that y goes to y0. So this is
+also a difference quotient, but it's a
+
+ align:start position:0%
+also a difference quotient, but it's a
+ 
+
+ align:start position:0%
+also a difference quotient, but it's a
+difference quotient for g. And since y
+
+ align:start position:0%
+difference quotient for g. And since y
+ 
+
+ align:start position:0%
+difference quotient for g. And since y
+goes to y z, this difference quotient
+
+ align:start position:0%
+goes to y z, this difference quotient
+ 
+
+ align:start position:0%
+goes to y z, this difference quotient
+here goes to the derivative of g at at y
+
+ align:start position:0%
+here goes to the derivative of g at at y
+ 
+
+ align:start position:0%
+here goes to the derivative of g at at y
+z.
+
+ align:start position:0%
+z.
+ 
+
+ align:start position:0%
+z.
+Right? But that's exactly the formula
+
+ align:start position:0%
+Right? But that's exactly the formula
+ 
+
+ align:start position:0%
+Right? But that's exactly the formula
+that we wanted to prove except that we
+
+ align:start position:0%
+that we wanted to prove except that we
+ 
+
+ align:start position:0%
+that we wanted to prove except that we
+made one assumption that the derivative
+
+ align:start position:0%
+made one assumption that the derivative
+ 
+
+ align:start position:0%
+made one assumption that the derivative
+of f
+
+ align:start position:0%
+of f
+ 
+
+ align:start position:0%
+of f
+at x0 was not equal to zero. We made
+
+ align:start position:0%
+at x0 was not equal to zero. We made
+ 
+
+ align:start position:0%
+at x0 was not equal to zero. We made
+that assumption only so that this number
+
+ align:start position:0%
+that assumption only so that this number
+ 
+
+ align:start position:0%
+that assumption only so that this number
+here was not equal to zero. Right? And
+
+ align:start position:0%
+here was not equal to zero. Right? And
+ 
+
+ align:start position:0%
+here was not equal to zero. Right? And
+so we could kind of divide by it.
+
+ align:start position:0%
+so we could kind of divide by it.
+ 
+
+ align:start position:0%
+so we could kind of divide by it.
+Right? But actually otherwise
+
+ align:start position:0%
+Right? But actually otherwise
+ 
+
+ align:start position:0%
+Right? But actually otherwise
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right if if you for some reason if y was
+
+ align:start position:0%
+right if if you for some reason if y was
+ 
+
+ align:start position:0%
+right if if you for some reason if y was
+not equal to y z
+
+ align:start position:0%
+not equal to y z
+ 
+
+ align:start position:0%
+not equal to y z
+but right then this formula here would
+
+ align:start position:0%
+but right then this formula here would
+ 
+
+ align:start position:0%
+but right then this formula here would
+still hold right so it's only the the
+
+ align:start position:0%
+still hold right so it's only the the
+ 
+
+ align:start position:0%
+still hold right so it's only the the
+the possibility
+
+ align:start position:0%
+the possibility
+ 
+
+ align:start position:0%
+the possibility
+that uh that y could be equal to y z but
+
+ align:start position:0%
+that uh that y could be equal to y z but
+ 
+
+ align:start position:0%
+that uh that y could be equal to y z but
+now you see that if you We're just
+
+ align:start position:0%
+now you see that if you We're just
+ 
+
+ align:start position:0%
+now you see that if you We're just
+looking at the difference quotient g of
+
+ align:start position:0%
+looking at the difference quotient g of
+ 
+
+ align:start position:0%
+looking at the difference quotient g of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+g of uh of y
+
+ align:start position:0%
+g of uh of y
+ 
+
+ align:start position:0%
+g of uh of y
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+sorry uh g of f ofx
+
+ align:start position:0%
+sorry uh g of f ofx
+ 
+
+ align:start position:0%
+sorry uh g of f ofx
+minus.
+
+ align:start position:0%
+minus.
+ 
+
+ align:start position:0%
+minus.
+So this is the difference quotion that
+
+ align:start position:0%
+So this is the difference quotion that
+ 
+
+ align:start position:0%
+So this is the difference quotion that
+is the one we really have to look at for
+
+ align:start position:0%
+is the one we really have to look at for
+ 
+
+ align:start position:0%
+is the one we really have to look at for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+for the composition right and this is
+
+ align:start position:0%
+for the composition right and this is
+ 
+
+ align:start position:0%
+for the composition right and this is
+what we also called this here is what we
+
+ align:start position:0%
+what we also called this here is what we
+ 
+
+ align:start position:0%
+what we also called this here is what we
+call this thing here is what we called
+
+ align:start position:0%
+call this thing here is what we called
+ 
+
+ align:start position:0%
+call this thing here is what we called
+y0 this thing here is what we call y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the only case we haven't dealt with
+
+ align:start position:0%
+and the only case we haven't dealt with
+ 
+
+ align:start position:0%
+and the only case we haven't dealt with
+is where f prime
+
+ align:start position:0%
+is where f prime
+ 
+
+ align:start position:0%
+is where f prime
+of zero is equal to zero and
+
+ align:start position:0%
+of zero is equal to zero and
+ 
+
+ align:start position:0%
+of zero is equal to zero and
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is equal to y z right this here again
+
+ align:start position:0%
+is equal to y z right this here again
+ 
+
+ align:start position:0%
+is equal to y z right this here again
+was f of x and this here was equal to f
+
+ align:start position:0%
+was f of x and this here was equal to f
+ 
+
+ align:start position:0%
+was f of x and this here was equal to f
+of x0 so this only this case here we
+
+ align:start position:0%
+of x0 so this only this case here we
+ 
+
+ align:start position:0%
+of x0 so this only this case here we
+haven't dealt with right
+
+ align:start position:0%
+haven't dealt with right
+ 
+
+ align:start position:0%
+haven't dealt with right
+but you see that if If you if it h if it
+
+ align:start position:0%
+but you see that if If you if it h if it
+ 
+
+ align:start position:0%
+but you see that if If you if it h if it
+so happened that f ofx was equal to f of
+
+ align:start position:0%
+so happened that f ofx was equal to f of
+ 
+
+ align:start position:0%
+so happened that f ofx was equal to f of
+z then this difference quotient here the
+
+ align:start position:0%
+z then this difference quotient here the
+ 
+
+ align:start position:0%
+z then this difference quotient here the
+d the denominator would trivially be
+
+ align:start position:0%
+d the denominator would trivially be
+ 
+
+ align:start position:0%
+d the denominator would trivially be
+zero right and so you want to prove we
+
+ align:start position:0%
+zero right and so you want to prove we
+ 
+
+ align:start position:0%
+zero right and so you want to prove we
+have that if this here was not equal to
+
+ align:start position:0%
+have that if this here was not equal to
+ 
+
+ align:start position:0%
+have that if this here was not equal to
+zero then we have that this is
+
+ align:start position:0%
+zero then we have that this is
+ 
+
+ align:start position:0%
+zero then we have that this is
+converging to the to the derivative
+
+ align:start position:0%
+converging to the to the derivative
+ 
+
+ align:start position:0%
+converging to the to the derivative
+and the only case we have to look at
+
+ align:start position:0%
+and the only case we have to look at
+ 
+
+ align:start position:0%
+and the only case we have to look at
+where this derivative is zero. So we
+
+ align:start position:0%
+where this derivative is zero. So we
+ 
+
+ align:start position:0%
+where this derivative is zero. So we
+want we are claiming that so the only
+
+ align:start position:0%
+want we are claiming that so the only
+ 
+
+ align:start position:0%
+want we are claiming that so the only
+case we're left with that we haven't
+
+ align:start position:0%
+case we're left with that we haven't
+ 
+
+ align:start position:0%
+case we're left with that we haven't
+dealt with is first of all where the
+
+ align:start position:0%
+dealt with is first of all where the
+ 
+
+ align:start position:0%
+dealt with is first of all where the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+so let's see so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just write down here clearly the
+
+ align:start position:0%
+let me just write down here clearly the
+ 
+
+ align:start position:0%
+let me just write down here clearly the
+remaining case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remaining case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the main cases that the derivative at
+
+ align:start position:0%
+So the main cases that the derivative at
+ 
+
+ align:start position:0%
+So the main cases that the derivative at
+x0 is zero. Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And and we have already observed that if
+
+ align:start position:0%
+And and we have already observed that if
+ 
+
+ align:start position:0%
+And and we have already observed that if
+the derivative is zero but
+
+ align:start position:0%
+the derivative is zero but
+ 
+
+ align:start position:0%
+the derivative is zero but
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+y is not equal to y z. If this is the
+
+ align:start position:0%
+y is not equal to y z. If this is the
+ 
+
+ align:start position:0%
+y is not equal to y z. If this is the
+case then actually g of f ofx
+
+ align:start position:0%
+case then actually g of f ofx
+ 
+
+ align:start position:0%
+case then actually g of f ofx
+minus g
+
+ align:start position:0%
+minus g
+ 
+
+ align:start position:0%
+minus g
+of f of x0.
+
+ align:start position:0%
+of f of x0.
+ 
+
+ align:start position:0%
+of f of x0.
+This thing here
+
+ align:start position:0%
+This thing here
+ 
+
+ align:start position:0%
+This thing here
+still converge in this case here where
+
+ align:start position:0%
+still converge in this case here where
+ 
+
+ align:start position:0%
+still converge in this case here where
+this is the case. This here still
+
+ align:start position:0%
+this is the case. This here still
+ 
+
+ align:start position:0%
+this is the case. This here still
+converts to zero. Right? So, so we still
+
+ align:start position:0%
+converts to zero. Right? So, so we still
+ 
+
+ align:start position:0%
+converts to zero. Right? So, so we still
+have the chain rule
+
+ align:start position:0%
+have the chain rule
+ 
+
+ align:start position:0%
+have the chain rule
+in that case if this here was not the
+
+ align:start position:0%
+in that case if this here was not the
+ 
+
+ align:start position:0%
+in that case if this here was not the
+case. The only thing we have to worry
+
+ align:start position:0%
+case. The only thing we have to worry
+ 
+
+ align:start position:0%
+case. The only thing we have to worry
+about is what if y was equal to y z. But
+
+ align:start position:0%
+about is what if y was equal to y z. But
+ 
+
+ align:start position:0%
+about is what if y was equal to y z. But
+if y was equal to y z when we're looking
+
+ align:start position:0%
+if y was equal to y z when we're looking
+ 
+
+ align:start position:0%
+if y was equal to y z when we're looking
+at the difference quotient, this is the
+
+ align:start position:0%
+at the difference quotient, this is the
+ 
+
+ align:start position:0%
+at the difference quotient, this is the
+difference quotion after all. And so in
+
+ align:start position:0%
+difference quotion after all. And so in
+ 
+
+ align:start position:0%
+difference quotion after all. And so in
+that case, this thing here is y z. This
+
+ align:start position:0%
+that case, this thing here is y z. This
+ 
+
+ align:start position:0%
+that case, this thing here is y z. This
+is y z. But in that case the difference
+
+ align:start position:0%
+is y z. But in that case the difference
+ 
+
+ align:start position:0%
+is y z. But in that case the difference
+quotion is actually zero already. So of
+
+ align:start position:0%
+quotion is actually zero already. So of
+ 
+
+ align:start position:0%
+quotion is actually zero already. So of
+course it's it's going to be very close
+
+ align:start position:0%
+course it's it's going to be very close
+ 
+
+ align:start position:0%
+course it's it's going to be very close
+to zero right it's actually is zero
+
+ align:start position:0%
+to zero right it's actually is zero
+ 
+
+ align:start position:0%
+to zero right it's actually is zero
+right you see that the remaining case
+
+ align:start position:0%
+right you see that the remaining case
+ 
+
+ align:start position:0%
+right you see that the remaining case
+that's sort of trivial
+
+ align:start position:0%
+that's sort of trivial
+ 
+
+ align:start position:0%
+that's sort of trivial
+but we wanted to first exclude it
+
+ align:start position:0%
+but we wanted to first exclude it
+ 
+
+ align:start position:0%
+but we wanted to first exclude it
+because we wanted to be able to divide
+
+ align:start position:0%
+because we wanted to be able to divide
+ 
+
+ align:start position:0%
+because we wanted to be able to divide
+by this difference right and then once
+
+ align:start position:0%
+by this difference right and then once
+ 
+
+ align:start position:0%
+by this difference right and then once
+we have seen that under that assumption
+
+ align:start position:0%
+we have seen that under that assumption
+ 
+
+ align:start position:0%
+we have seen that under that assumption
+it was it was you know we got the
+
+ align:start position:0%
+it was it was you know we got the
+ 
+
+ align:start position:0%
+it was it was you know we got the
+formula we wanted then we go back and
+
+ align:start position:0%
+formula we wanted then we go back and
+ 
+
+ align:start position:0%
+formula we wanted then we go back and
+then we say that not only you know the
+
+ align:start position:0%
+then we say that not only you know the
+ 
+
+ align:start position:0%
+then we say that not only you know the
+the the the the remaining issue was well
+
+ align:start position:0%
+the the the the remaining issue was well
+ 
+
+ align:start position:0%
+the the the the remaining issue was well
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+was the case where the derivative was
+
+ align:start position:0%
+was the case where the derivative was
+ 
+
+ align:start position:0%
+was the case where the derivative was
+zero but in fact um you the only case
+
+ align:start position:0%
+zero but in fact um you the only case
+ 
+
+ align:start position:0%
+zero but in fact um you the only case
+that was potentially a problem was when
+
+ align:start position:0%
+that was potentially a problem was when
+ 
+
+ align:start position:0%
+that was potentially a problem was when
+y was equal to y zero but for that it's
+
+ align:start position:0%
+y was equal to y zero but for that it's
+ 
+
+ align:start position:0%
+y was equal to y zero but for that it's
+the difference quotient was was actually
+
+ align:start position:0%
+the difference quotient was was actually
+ 
+
+ align:start position:0%
+the difference quotient was was actually
+trivial zero okay so that's the the
+
+ align:start position:0%
+trivial zero okay so that's the the
+ 
+
+ align:start position:0%
+trivial zero okay so that's the the
+chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and so we only have a few minutes
+
+ align:start position:0%
+Um, and so we only have a few minutes
+ 
+
+ align:start position:0%
+Um, and so we only have a few minutes
+left. Uh, and I won't quite be able to
+
+ align:start position:0%
+left. Uh, and I won't quite be able to
+ 
+
+ align:start position:0%
+left. Uh, and I won't quite be able to
+get through all of the stuff. Uh, but I
+
+ align:start position:0%
+get through all of the stuff. Uh, but I
+ 
+
+ align:start position:0%
+get through all of the stuff. Uh, but I
+can get through one more lema.
+
+ align:start position:0%
+can get through one more lema.
+ 
+
+ align:start position:0%
+can get through one more lema.
+And so, and then I'll pick up from from
+
+ align:start position:0%
+And so, and then I'll pick up from from
+ 
+
+ align:start position:0%
+And so, and then I'll pick up from from
+here uh, next time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the notes are already posted but but
+
+ align:start position:0%
+uh the notes are already posted but but
+ 
+
+ align:start position:0%
+uh the notes are already posted but but
+so the last bit of the notes we'll do
+
+ align:start position:0%
+so the last bit of the notes we'll do
+ 
+
+ align:start position:0%
+so the last bit of the notes we'll do
+next time.
+
+ align:start position:0%
+next time.
+ 
+
+ align:start position:0%
+next time.
+So so the following lema here.
+
+ align:start position:0%
+So so the following lema here.
+ 
+
+ align:start position:0%
+So so the following lema here.
+So if you have a function
+
+ align:start position:0%
+So if you have a function
+ 
+
+ align:start position:0%
+So if you have a function
+say from R to R
+
+ align:start position:0%
+say from R to R
+ 
+
+ align:start position:0%
+say from R to R
+and you have that X here X0 is a local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+max
+
+ align:start position:0%
+max
+ 
+
+ align:start position:0%
+max
+or min.
+
+ align:start position:0%
+or min.
+ 
+
+ align:start position:0%
+or min.
+So f is a function from r to r that is
+
+ align:start position:0%
+So f is a function from r to r that is
+ 
+
+ align:start position:0%
+So f is a function from r to r that is
+that is differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And uh x0 is a local max or local min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for f.
+
+ align:start position:0%
+for f.
+ 
+
+ align:start position:0%
+for f.
+then uh then
+
+ align:start position:0%
+then uh then
+ 
+
+ align:start position:0%
+then uh then
+the derivative
+
+ align:start position:0%
+the derivative
+ 
+
+ align:start position:0%
+the derivative
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+is equal to zero. Okay,
+
+ align:start position:0%
+is equal to zero. Okay,
+ 
+
+ align:start position:0%
+is equal to zero. Okay,
+let me remind you what a local max and
+
+ align:start position:0%
+let me remind you what a local max and
+ 
+
+ align:start position:0%
+let me remind you what a local max and
+local min is. So if you take a function
+
+ align:start position:0%
+local min is. So if you take a function
+ 
+
+ align:start position:0%
+local min is. So if you take a function
+so a local max similar for a local min
+
+ align:start position:0%
+so a local max similar for a local min
+ 
+
+ align:start position:0%
+so a local max similar for a local min
+if you have a function here you have
+
+ align:start position:0%
+if you have a function here you have
+ 
+
+ align:start position:0%
+if you have a function here you have
+here x0 a local max means that in a
+
+ align:start position:0%
+here x0 a local max means that in a
+ 
+
+ align:start position:0%
+here x0 a local max means that in a
+neighborhood of x this point then the
+
+ align:start position:0%
+neighborhood of x this point then the
+ 
+
+ align:start position:0%
+neighborhood of x this point then the
+value at x0 is the maximum. So local max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+that they exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta greater than zero such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that if you're looking at the
+
+ align:start position:0%
+um that if you're looking at the
+ 
+
+ align:start position:0%
+um that if you're looking at the
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+um to either side of x0 this interval
+
+ align:start position:0%
+um to either side of x0 this interval
+ 
+
+ align:start position:0%
+um to either side of x0 this interval
+and you're looking at uh at f here
+
+ align:start position:0%
+and you're looking at uh at f here
+ 
+
+ align:start position:0%
+and you're looking at uh at f here
+restricted to this subset then uh then
+
+ align:start position:0%
+restricted to this subset then uh then
+ 
+
+ align:start position:0%
+restricted to this subset then uh then
+uh x0 is a local max is a max. So this
+
+ align:start position:0%
+uh x0 is a local max is a max. So this
+ 
+
+ align:start position:0%
+uh x0 is a local max is a max. So this
+means that f ofx zero is equal to the
+
+ align:start position:0%
+means that f ofx zero is equal to the
+ 
+
+ align:start position:0%
+means that f ofx zero is equal to the
+max
+
+ align:start position:0%
+max
+ 
+
+ align:start position:0%
+max
+of f where x here is in this little
+
+ align:start position:0%
+of f where x here is in this little
+ 
+
+ align:start position:0%
+of f where x here is in this little
+interval here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oops. Like that.
+
+ align:start position:0%
+Oops. Like that.
+ 
+
+ align:start position:0%
+Oops. Like that.
+Right. So it's it may not be right. So,
+
+ align:start position:0%
+Right. So it's it may not be right. So,
+ 
+
+ align:start position:0%
+Right. So it's it may not be right. So,
+so the idea is that it's just the
+
+ align:start position:0%
+so the idea is that it's just the
+ 
+
+ align:start position:0%
+so the idea is that it's just the
+function may look like this and this
+
+ align:start position:0%
+function may look like this and this
+ 
+
+ align:start position:0%
+function may look like this and this
+here is x0. So, you see that in a
+
+ align:start position:0%
+here is x0. So, you see that in a
+ 
+
+ align:start position:0%
+here is x0. So, you see that in a
+neighborhood like this, it looks like
+
+ align:start position:0%
+neighborhood like this, it looks like
+ 
+
+ align:start position:0%
+neighborhood like this, it looks like
+that you have that this x0 is a maximum,
+
+ align:start position:0%
+that you have that this x0 is a maximum,
+ 
+
+ align:start position:0%
+that you have that this x0 is a maximum,
+but there might even be somewhere else
+
+ align:start position:0%
+but there might even be somewhere else
+ 
+
+ align:start position:0%
+but there might even be somewhere else
+where the value is much higher. Right?
+
+ align:start position:0%
+where the value is much higher. Right?
+ 
+
+ align:start position:0%
+where the value is much higher. Right?
+So, that's a local maximum and similarly
+
+ align:start position:0%
+So, that's a local maximum and similarly
+ 
+
+ align:start position:0%
+So, that's a local maximum and similarly
+for a local minimum. Okay? And so I
+
+ align:start position:0%
+for a local minimum. Okay? And so I
+ 
+
+ align:start position:0%
+for a local minimum. Okay? And so I
+won't be able to to actually prove this
+
+ align:start position:0%
+won't be able to to actually prove this
+ 
+
+ align:start position:0%
+won't be able to to actually prove this
+lema. We we'll prove that next time. Uh
+
+ align:start position:0%
+lema. We we'll prove that next time. Uh
+ 
+
+ align:start position:0%
+lema. We we'll prove that next time. Uh
+and then once we have that lema, we
+
+ align:start position:0%
+and then once we have that lema, we
+ 
+
+ align:start position:0%
+and then once we have that lema, we
+prove what's called roles theorem. And
+
+ align:start position:0%
+prove what's called roles theorem. And
+ 
+
+ align:start position:0%
+prove what's called roles theorem. And
+then we will use it to prove the mean
+
+ align:start position:0%
+then we will use it to prove the mean
+ 
+
+ align:start position:0%
+then we will use it to prove the mean
+battle theorem. But so but I'll do that
+
+ align:start position:0%
+battle theorem. But so but I'll do that
+ 
+
+ align:start position:0%
+battle theorem. But so but I'll do that
+next time, but it's actually in the
+
+ align:start position:0%
+next time, but it's actually in the
+ 
+
+ align:start position:0%
+next time, but it's actually in the
+notes that I I posted already.
\ No newline at end of file
diff --git a/UZQGn1L2CzQ.txt b/UZQGn1L2CzQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..262fb93f31925dd5238ae33407d49e35b2efcdfe
--- /dev/null
+++ b/UZQGn1L2CzQ.txt
@@ -0,0 +1,1795 @@
+align:start position:0%
+ 
+hi everyone I'm Lan welcome back to
+
+ align:start position:0%
+hi everyone I'm Lan welcome back to
+ 
+
+ align:start position:0%
+hi everyone I'm Lan welcome back to
+recitation in recent lectures we have
+
+ align:start position:0%
+recitation in recent lectures we have
+ 
+
+ align:start position:0%
+recitation in recent lectures we have
+studied the properties of the
+
+ align:start position:0%
+studied the properties of the
+ 
+
+ align:start position:0%
+studied the properties of the
+determinant and we also derived the
+
+ align:start position:0%
+determinant and we also derived the
+ 
+
+ align:start position:0%
+determinant and we also derived the
+formula to computed today we're going to
+
+ align:start position:0%
+formula to computed today we're going to
+ 
+
+ align:start position:0%
+formula to computed today we're going to
+put what we learned into practice by
+
+ align:start position:0%
+put what we learned into practice by
+ 
+
+ align:start position:0%
+put what we learned into practice by
+considering these two
+
+ align:start position:0%
+considering these two
+ 
+
+ align:start position:0%
+considering these two
+examples so we want to find out the
+
+ align:start position:0%
+examples so we want to find out the
+ 
+
+ align:start position:0%
+examples so we want to find out the
+determinants of these two 5x five
+
+ align:start position:0%
+determinants of these two 5x five
+ 
+
+ align:start position:0%
+determinants of these two 5x five
+matrices and and as you can see Matrix a
+
+ align:start position:0%
+matrices and and as you can see Matrix a
+ 
+
+ align:start position:0%
+matrices and and as you can see Matrix a
+has X along this diagonal and in the
+
+ align:start position:0%
+has X along this diagonal and in the
+ 
+
+ align:start position:0%
+has X along this diagonal and in the
+first four rows y to the right of X
+
+ align:start position:0%
+first four rows y to the right of X
+ 
+
+ align:start position:0%
+first four rows y to the right of X
+except for the last row and zero entries
+
+ align:start position:0%
+except for the last row and zero entries
+ 
+
+ align:start position:0%
+except for the last row and zero entries
+everywhere else and Matrix B also has X
+
+ align:start position:0%
+everywhere else and Matrix B also has X
+ 
+
+ align:start position:0%
+everywhere else and Matrix B also has X
+along this diagonal and Y everywhere
+
+ align:start position:0%
+along this diagonal and Y everywhere
+ 
+
+ align:start position:0%
+along this diagonal and Y everywhere
+else okay before starting let me help
+
+ align:start position:0%
+else okay before starting let me help
+ 
+
+ align:start position:0%
+else okay before starting let me help
+you review what you can do to compute
+
+ align:start position:0%
+you review what you can do to compute
+ 
+
+ align:start position:0%
+you review what you can do to compute
+determinants of course you can carry out
+
+ align:start position:0%
+determinants of course you can carry out
+ 
+
+ align:start position:0%
+determinants of course you can carry out
+elimination to transform your original
+
+ align:start position:0%
+elimination to transform your original
+ 
+
+ align:start position:0%
+elimination to transform your original
+Matrix into upper triangular
+
+ align:start position:0%
+Matrix into upper triangular
+ 
+
+ align:start position:0%
+Matrix into upper triangular
+Matrix or you can use this big summation
+
+ align:start position:0%
+Matrix or you can use this big summation
+ 
+
+ align:start position:0%
+Matrix or you can use this big summation
+formula another choice would be you can
+
+ align:start position:0%
+formula another choice would be you can
+ 
+
+ align:start position:0%
+formula another choice would be you can
+do it by co-actors namely you can expand
+
+ align:start position:0%
+do it by co-actors namely you can expand
+ 
+
+ align:start position:0%
+do it by co-actors namely you can expand
+your original Matrix along any row or
+
+ align:start position:0%
+your original Matrix along any row or
+ 
+
+ align:start position:0%
+your original Matrix along any row or
+any column and then the determinant is
+
+ align:start position:0%
+any column and then the determinant is
+ 
+
+ align:start position:0%
+any column and then the determinant is
+simply given by the dotproduct of that
+
+ align:start position:0%
+simply given by the dotproduct of that
+ 
+
+ align:start position:0%
+simply given by the dotproduct of that
+row or that column with its
+
+ align:start position:0%
+row or that column with its
+ 
+
+ align:start position:0%
+row or that column with its
+co-actors okay why don't you pause the
+
+ align:start position:0%
+co-actors okay why don't you pause the
+ 
+
+ align:start position:0%
+co-actors okay why don't you pause the
+video now and try to work on them
+
+ align:start position:0%
+video now and try to work on them
+ 
+
+ align:start position:0%
+video now and try to work on them
+yourself whenever you're ready I'll come
+
+ align:start position:0%
+yourself whenever you're ready I'll come
+ 
+
+ align:start position:0%
+yourself whenever you're ready I'll come
+back and show you my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way okay I hope you just had some fun
+
+ align:start position:0%
+way okay I hope you just had some fun
+ 
+
+ align:start position:0%
+way okay I hope you just had some fun
+with these two problems now let's tackle
+
+ align:start position:0%
+with these two problems now let's tackle
+ 
+
+ align:start position:0%
+with these two problems now let's tackle
+them together um let's look at Matrix a
+
+ align:start position:0%
+them together um let's look at Matrix a
+ 
+
+ align:start position:0%
+them together um let's look at Matrix a
+first as you can see there are a lot of
+
+ align:start position:0%
+first as you can see there are a lot of
+ 
+
+ align:start position:0%
+first as you can see there are a lot of
+zero entries in Matrix a so perhaps per
+
+ align:start position:0%
+zero entries in Matrix a so perhaps per
+ 
+
+ align:start position:0%
+zero entries in Matrix a so perhaps per
+you don't need elimination to introduce
+
+ align:start position:0%
+you don't need elimination to introduce
+ 
+
+ align:start position:0%
+you don't need elimination to introduce
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+zeros um furthermore we observe this
+
+ align:start position:0%
+zeros um furthermore we observe this
+ 
+
+ align:start position:0%
+zeros um furthermore we observe this
+pattern of a and you notice that if I
+
+ align:start position:0%
+pattern of a and you notice that if I
+ 
+
+ align:start position:0%
+pattern of a and you notice that if I
+cover the last row and the First Column
+
+ align:start position:0%
+cover the last row and the First Column
+ 
+
+ align:start position:0%
+cover the last row and the First Column
+so if this column and this row not here
+
+ align:start position:0%
+so if this column and this row not here
+ 
+
+ align:start position:0%
+so if this column and this row not here
+what is left over is simply a 4x4 lower
+
+ align:start position:0%
+what is left over is simply a 4x4 lower
+ 
+
+ align:start position:0%
+what is left over is simply a 4x4 lower
+triangular
+
+ align:start position:0%
+triangular
+ 
+
+ align:start position:0%
+triangular
+Matrix and similarly if you cover the
+
+ align:start position:0%
+Matrix and similarly if you cover the
+ 
+
+ align:start position:0%
+Matrix and similarly if you cover the
+First Column and the first row
+
+ align:start position:0%
+First Column and the first row
+ 
+
+ align:start position:0%
+First Column and the first row
+what is left over here is simply a 4x4
+
+ align:start position:0%
+what is left over here is simply a 4x4
+ 
+
+ align:start position:0%
+what is left over here is simply a 4x4
+upper triangular
+
+ align:start position:0%
+upper triangular
+ 
+
+ align:start position:0%
+upper triangular
+Matrix this is telling us that we should
+
+ align:start position:0%
+Matrix this is telling us that we should
+ 
+
+ align:start position:0%
+Matrix this is telling us that we should
+calculate the determinant of a by the
+
+ align:start position:0%
+calculate the determinant of a by the
+ 
+
+ align:start position:0%
+calculate the determinant of a by the
+third method so we should expand along
+
+ align:start position:0%
+third method so we should expand along
+ 
+
+ align:start position:0%
+third method so we should expand along
+the First Column of a and we calculate
+
+ align:start position:0%
+the First Column of a and we calculate
+ 
+
+ align:start position:0%
+the First Column of a and we calculate
+the co-actors let's do it
+
+ align:start position:0%
+the co-actors let's do it
+ 
+
+ align:start position:0%
+the co-actors let's do it
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so determinant of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is equal to the one one entry of a
+
+ align:start position:0%
+a is equal to the one one entry of a
+ 
+
+ align:start position:0%
+a is equal to the one one entry of a
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+x times the co-actor of that spot which
+
+ align:start position:0%
+x times the co-actor of that spot which
+ 
+
+ align:start position:0%
+x times the co-actor of that spot which
+is the determinant of the left over 4x4
+
+ align:start position:0%
+is the determinant of the left over 4x4
+ 
+
+ align:start position:0%
+is the determinant of the left over 4x4
+Matrix Matrix and it's upper triangular
+
+ align:start position:0%
+Matrix Matrix and it's upper triangular
+ 
+
+ align:start position:0%
+Matrix Matrix and it's upper triangular
+so it's determinant is simply given by X
+
+ align:start position:0%
+so it's determinant is simply given by X
+ 
+
+ align:start position:0%
+so it's determinant is simply given by X
+to the^
+
+ align:start position:0%
+to the^
+ 
+
+ align:start position:0%
+to the^
+4 right plus the only other non Zero
+
+ align:start position:0%
+4 right plus the only other non Zero
+ 
+
+ align:start position:0%
+4 right plus the only other non Zero
+Entry in that column is the Y at the
+
+ align:start position:0%
+Entry in that column is the Y at the
+ 
+
+ align:start position:0%
+Entry in that column is the Y at the
+very bottom so you put y
+
+ align:start position:0%
+very bottom so you put y
+ 
+
+ align:start position:0%
+very bottom so you put y
+here and you multiply y by the co-actor
+
+ align:start position:0%
+here and you multiply y by the co-actor
+ 
+
+ align:start position:0%
+here and you multiply y by the co-actor
+of that spot which is a determinant of
+
+ align:start position:0%
+of that spot which is a determinant of
+ 
+
+ align:start position:0%
+of that spot which is a determinant of
+the left left over 4x4 Matrix again in
+
+ align:start position:0%
+the left left over 4x4 Matrix again in
+ 
+
+ align:start position:0%
+the left left over 4x4 Matrix again in
+this case it's lower triangular and it's
+
+ align:start position:0%
+this case it's lower triangular and it's
+ 
+
+ align:start position:0%
+this case it's lower triangular and it's
+determinant is y to the^ 4 so I have a y
+
+ align:start position:0%
+determinant is y to the^ 4 so I have a y
+ 
+
+ align:start position:0%
+determinant is y to the^ 4 so I have a y
+to the^ 4 here but not quite in
+
+ align:start position:0%
+to the^ 4 here but not quite in
+ 
+
+ align:start position:0%
+to the^ 4 here but not quite in
+principle there should be another Factor
+
+ align:start position:0%
+principle there should be another Factor
+ 
+
+ align:start position:0%
+principle there should be another Factor
+here indicating the sign and the sign
+
+ align:start position:0%
+here indicating the sign and the sign
+ 
+
+ align:start position:0%
+here indicating the sign and the sign
+in this case well because Y is the the
+
+ align:start position:0%
+in this case well because Y is the the
+ 
+
+ align:start position:0%
+in this case well because Y is the the
+entry in the fifth row in the First
+
+ align:start position:0%
+entry in the fifth row in the First
+ 
+
+ align:start position:0%
+entry in the fifth row in the First
+Column so this Factor should be -1 to
+
+ align:start position:0%
+Column so this Factor should be -1 to
+ 
+
+ align:start position:0%
+Column so this Factor should be -1 to
+the power 5 + 1 and of course it's just
+
+ align:start position:0%
+the power 5 + 1 and of course it's just
+ 
+
+ align:start position:0%
+the power 5 + 1 and of course it's just
+one so the determinant of a is simply
+
+ align:start position:0%
+one so the determinant of a is simply
+ 
+
+ align:start position:0%
+one so the determinant of a is simply
+equal to x to the 5ifth power plus y to
+
+ align:start position:0%
+equal to x to the 5ifth power plus y to
+ 
+
+ align:start position:0%
+equal to x to the 5ifth power plus y to
+the fifth power did you get the correct
+
+ align:start position:0%
+the fifth power did you get the correct
+ 
+
+ align:start position:0%
+the fifth power did you get the correct
+answer well the determinant of a is not
+
+ align:start position:0%
+answer well the determinant of a is not
+ 
+
+ align:start position:0%
+answer well the determinant of a is not
+too bad because a has a lot of zero
+
+ align:start position:0%
+too bad because a has a lot of zero
+ 
+
+ align:start position:0%
+too bad because a has a lot of zero
+entries now let's look at the
+
+ align:start position:0%
+entries now let's look at the
+ 
+
+ align:start position:0%
+entries now let's look at the
+determinant of Matrix B I have another
+
+ align:start position:0%
+determinant of Matrix B I have another
+ 
+
+ align:start position:0%
+determinant of Matrix B I have another
+copy of B here so B also has a very
+
+ align:start position:0%
+copy of B here so B also has a very
+ 
+
+ align:start position:0%
+copy of B here so B also has a very
+clear structure it has X along this
+
+ align:start position:0%
+clear structure it has X along this
+ 
+
+ align:start position:0%
+clear structure it has X along this
+diagonal and Y everywhere else but in
+
+ align:start position:0%
+diagonal and Y everywhere else but in
+ 
+
+ align:start position:0%
+diagonal and Y everywhere else but in
+general b does not have any Zero Entry
+
+ align:start position:0%
+general b does not have any Zero Entry
+ 
+
+ align:start position:0%
+general b does not have any Zero Entry
+so perhaps our first step should be
+
+ align:start position:0%
+so perhaps our first step should be
+ 
+
+ align:start position:0%
+so perhaps our first step should be
+carrying out elimination to introduce
+
+ align:start position:0%
+carrying out elimination to introduce
+ 
+
+ align:start position:0%
+carrying out elimination to introduce
+zero entries into Matrix
+
+ align:start position:0%
+zero entries into Matrix
+ 
+
+ align:start position:0%
+zero entries into Matrix
+B of course you can do it by the regular
+
+ align:start position:0%
+B of course you can do it by the regular
+ 
+
+ align:start position:0%
+B of course you can do it by the regular
+routine you start with the first row
+
+ align:start position:0%
+routine you start with the first row
+ 
+
+ align:start position:0%
+routine you start with the first row
+find the pivot and you eliminate the
+
+ align:start position:0%
+find the pivot and you eliminate the
+ 
+
+ align:start position:0%
+find the pivot and you eliminate the
+second row and the third row and so on
+
+ align:start position:0%
+second row and the third row and so on
+ 
+
+ align:start position:0%
+second row and the third row and so on
+so forth but in this case there's a
+
+ align:start position:0%
+so forth but in this case there's a
+ 
+
+ align:start position:0%
+so forth but in this case there's a
+shortcut if you compare two rows that
+
+ align:start position:0%
+shortcut if you compare two rows that
+ 
+
+ align:start position:0%
+shortcut if you compare two rows that
+are next to each other for example if
+
+ align:start position:0%
+are next to each other for example if
+ 
+
+ align:start position:0%
+are next to each other for example if
+you compare the fourth row and the fifth
+
+ align:start position:0%
+you compare the fourth row and the fifth
+ 
+
+ align:start position:0%
+you compare the fourth row and the fifth
+row you notice that they have a lot of
+
+ align:start position:0%
+row you notice that they have a lot of
+ 
+
+ align:start position:0%
+row you notice that they have a lot of
+entries in common and they're only
+
+ align:start position:0%
+entries in common and they're only
+ 
+
+ align:start position:0%
+entries in common and they're only
+different at these two spots right so
+
+ align:start position:0%
+different at these two spots right so
+ 
+
+ align:start position:0%
+different at these two spots right so
+imagine if I subtract the fourth row
+
+ align:start position:0%
+imagine if I subtract the fourth row
+ 
+
+ align:start position:0%
+imagine if I subtract the fourth row
+from the fifth row so if I do the
+
+ align:start position:0%
+from the fifth row so if I do the
+ 
+
+ align:start position:0%
+from the fifth row so if I do the
+following corporate uh
+
+ align:start position:0%
+following corporate uh
+ 
+
+ align:start position:0%
+following corporate uh
+operation so I
+
+ align:start position:0%
+operation so I
+ 
+
+ align:start position:0%
+operation so I
+subtract this this Row from the last row
+
+ align:start position:0%
+subtract this this Row from the last row
+ 
+
+ align:start position:0%
+subtract this this Row from the last row
+then the new fifth row should become the
+
+ align:start position:0%
+then the new fifth row should become the
+ 
+
+ align:start position:0%
+then the new fifth row should become the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+so this rule will become 0 0 0 y -
+
+ align:start position:0%
+so this rule will become 0 0 0 y -
+ 
+
+ align:start position:0%
+so this rule will become 0 0 0 y -
+x X -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y you see just by this simple operation
+
+ align:start position:0%
+y you see just by this simple operation
+ 
+
+ align:start position:0%
+y you see just by this simple operation
+I have introduced three zero entries at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once and it's similar with the fourth
+
+ align:start position:0%
+once and it's similar with the fourth
+ 
+
+ align:start position:0%
+once and it's similar with the fourth
+row and the third row they have common
+
+ align:start position:0%
+row and the third row they have common
+ 
+
+ align:start position:0%
+row and the third row they have common
+entries here here and here so you
+
+ align:start position:0%
+entries here here and here so you
+ 
+
+ align:start position:0%
+entries here here and here so you
+subtract the third row from the fourth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row you update the fourth row to 0 0 y -
+
+ align:start position:0%
+row you update the fourth row to 0 0 y -
+ 
+
+ align:start position:0%
+row you update the fourth row to 0 0 y -
+x X - y 0 again three zero entries and
+
+ align:start position:0%
+x X - y 0 again three zero entries and
+ 
+
+ align:start position:0%
+x X - y 0 again three zero entries and
+same thing happened to the third second
+
+ align:start position:0%
+same thing happened to the third second
+ 
+
+ align:start position:0%
+same thing happened to the third second
+row and the third row so you subtract
+
+ align:start position:0%
+row and the third row so you subtract
+ 
+
+ align:start position:0%
+row and the third row so you subtract
+the second row from the third row and
+
+ align:start position:0%
+the second row from the third row and
+ 
+
+ align:start position:0%
+the second row from the third row and
+you your new third row will become
+
+ align:start position:0%
+you your new third row will become
+ 
+
+ align:start position:0%
+you your new third row will become
+0 y - x X - y 0
+
+ align:start position:0%
+0 y - x X - y 0
+ 
+
+ align:start position:0%
+0 y - x X - y 0
+0 finally you subtract the first row
+
+ align:start position:0%
+0 finally you subtract the first row
+ 
+
+ align:start position:0%
+0 finally you subtract the first row
+from the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row and then you update the second row
+
+ align:start position:0%
+row and then you update the second row
+ 
+
+ align:start position:0%
+row and then you update the second row
+to y -
+
+ align:start position:0%
+to y -
+ 
+
+ align:start position:0%
+to y -
+x X - y 0 0 zero let's keep the first
+
+ align:start position:0%
+x X - y 0 0 zero let's keep the first
+ 
+
+ align:start position:0%
+x X - y 0 0 zero let's keep the first
+row unchanged so I'm going to copy it
+
+ align:start position:0%
+row unchanged so I'm going to copy it
+ 
+
+ align:start position:0%
+row unchanged so I'm going to copy it
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right by row elimination we have
+
+ align:start position:0%
+all right by row elimination we have
+ 
+
+ align:start position:0%
+all right by row elimination we have
+introduced many zero entries to Matrix B
+
+ align:start position:0%
+introduced many zero entries to Matrix B
+ 
+
+ align:start position:0%
+introduced many zero entries to Matrix B
+is there anything else that I can take
+
+ align:start position:0%
+is there anything else that I can take
+ 
+
+ align:start position:0%
+is there anything else that I can take
+advantage
+
+ align:start position:0%
+advantage
+ 
+
+ align:start position:0%
+advantage
+of um let's observe the pattern of this
+
+ align:start position:0%
+of um let's observe the pattern of this
+ 
+
+ align:start position:0%
+of um let's observe the pattern of this
+new Matrix as you can see in each row
+
+ align:start position:0%
+new Matrix as you can see in each row
+ 
+
+ align:start position:0%
+new Matrix as you can see in each row
+you have two nonzero entries except the
+
+ align:start position:0%
+you have two nonzero entries except the
+ 
+
+ align:start position:0%
+you have two nonzero entries except the
+first row and they're only different by
+
+ align:start position:0%
+first row and they're only different by
+ 
+
+ align:start position:0%
+first row and they're only different by
+a sign so if somehow you can figure out
+
+ align:start position:0%
+a sign so if somehow you can figure out
+ 
+
+ align:start position:0%
+a sign so if somehow you can figure out
+a way to sum them up you will get even
+
+ align:start position:0%
+a way to sum them up you will get even
+ 
+
+ align:start position:0%
+a way to sum them up you will get even
+more zero entries so let's do it that's
+
+ align:start position:0%
+more zero entries so let's do it that's
+ 
+
+ align:start position:0%
+more zero entries so let's do it that's
+going to involve the operations on
+
+ align:start position:0%
+going to involve the operations on
+ 
+
+ align:start position:0%
+going to involve the operations on
+column so here is how I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I'm going to keep the last column
+
+ align:start position:0%
+it I'm going to keep the last column
+ 
+
+ align:start position:0%
+it I'm going to keep the last column
+unchanged so the last column is y 0 0 0
+
+ align:start position:0%
+unchanged so the last column is y 0 0 0
+ 
+
+ align:start position:0%
+unchanged so the last column is y 0 0 0
+x - y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I will do is I will add a copy of
+
+ align:start position:0%
+what I will do is I will add a copy of
+ 
+
+ align:start position:0%
+what I will do is I will add a copy of
+the last column to the fourth column so
+
+ align:start position:0%
+the last column to the fourth column so
+ 
+
+ align:start position:0%
+the last column to the fourth column so
+this is what I'm going to do add one
+
+ align:start position:0%
+this is what I'm going to do add one
+ 
+
+ align:start position:0%
+this is what I'm going to do add one
+copy of the last
+
+ align:start position:0%
+copy of the last
+ 
+
+ align:start position:0%
+copy of the last
+column to the fourth column now the new
+
+ align:start position:0%
+column to the fourth column now the new
+ 
+
+ align:start position:0%
+column to the fourth column now the new
+fourth column will become 2
+
+ align:start position:0%
+fourth column will become 2
+ 
+
+ align:start position:0%
+fourth column will become 2
+y 0 0 x - y
+
+ align:start position:0%
+y 0 0 x - y
+ 
+
+ align:start position:0%
+y 0 0 x - y
+z as you can see by doing this
+
+ align:start position:0%
+z as you can see by doing this
+ 
+
+ align:start position:0%
+z as you can see by doing this
+I have killed the spot so I have
+
+ align:start position:0%
+I have killed the spot so I have
+ 
+
+ align:start position:0%
+I have killed the spot so I have
+introduced one more Zero Entry into my
+
+ align:start position:0%
+introduced one more Zero Entry into my
+ 
+
+ align:start position:0%
+introduced one more Zero Entry into my
+fourth
+
+ align:start position:0%
+fourth
+ 
+
+ align:start position:0%
+fourth
+column if you continue you may want to
+
+ align:start position:0%
+column if you continue you may want to
+ 
+
+ align:start position:0%
+column if you continue you may want to
+add the fourth column to the third
+
+ align:start position:0%
+add the fourth column to the third
+ 
+
+ align:start position:0%
+add the fourth column to the third
+column let's see what will happen if you
+
+ align:start position:0%
+column let's see what will happen if you
+ 
+
+ align:start position:0%
+column let's see what will happen if you
+do that so if you add the fourth
+
+ align:start position:0%
+do that so if you add the fourth
+ 
+
+ align:start position:0%
+do that so if you add the fourth
+column to the third
+
+ align:start position:0%
+column to the third
+ 
+
+ align:start position:0%
+column to the third
+column then what should appear here is 2
+
+ align:start position:0%
+column then what should appear here is 2
+ 
+
+ align:start position:0%
+column then what should appear here is 2
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+0 x - y 0 y -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x okay but in this new third column you
+
+ align:start position:0%
+x okay but in this new third column you
+ 
+
+ align:start position:0%
+x okay but in this new third column you
+still have two zero entries which is the
+
+ align:start position:0%
+still have two zero entries which is the
+ 
+
+ align:start position:0%
+still have two zero entries which is the
+same as the original third column so
+
+ align:start position:0%
+same as the original third column so
+ 
+
+ align:start position:0%
+same as the original third column so
+although you've killed this spot but
+
+ align:start position:0%
+although you've killed this spot but
+ 
+
+ align:start position:0%
+although you've killed this spot but
+you've introduced a new nonzero entry so
+
+ align:start position:0%
+you've introduced a new nonzero entry so
+ 
+
+ align:start position:0%
+you've introduced a new nonzero entry so
+is there a way that we can kill the spot
+
+ align:start position:0%
+is there a way that we can kill the spot
+ 
+
+ align:start position:0%
+is there a way that we can kill the spot
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+you may have noticed that if you add a
+
+ align:start position:0%
+you may have noticed that if you add a
+ 
+
+ align:start position:0%
+you may have noticed that if you add a
+copy of the fifth column to this column
+
+ align:start position:0%
+copy of the fifth column to this column
+ 
+
+ align:start position:0%
+copy of the fifth column to this column
+again then this spot will have been
+
+ align:start position:0%
+again then this spot will have been
+ 
+
+ align:start position:0%
+again then this spot will have been
+killed right so let's do it if I add
+
+ align:start position:0%
+killed right so let's do it if I add
+ 
+
+ align:start position:0%
+killed right so let's do it if I add
+this column to this one I'm going to
+
+ align:start position:0%
+this column to this one I'm going to
+ 
+
+ align:start position:0%
+this column to this one I'm going to
+just update it here then the first entry
+
+ align:start position:0%
+just update it here then the first entry
+ 
+
+ align:start position:0%
+just update it here then the first entry
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+become 3
+
+ align:start position:0%
+become 3
+ 
+
+ align:start position:0%
+become 3
+y these are
+
+ align:start position:0%
+y these are
+ 
+
+ align:start position:0%
+y these are
+unchanged and the last spot becomes zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it reflects here as you are adding a
+
+ align:start position:0%
+it reflects here as you are adding a
+ 
+
+ align:start position:0%
+it reflects here as you are adding a
+copy of the fourth column and a copy of
+
+ align:start position:0%
+copy of the fourth column and a copy of
+ 
+
+ align:start position:0%
+copy of the fourth column and a copy of
+the fifth column to the third
+
+ align:start position:0%
+the fifth column to the third
+ 
+
+ align:start position:0%
+the fifth column to the third
+column now you've got the idea and you
+
+ align:start position:0%
+column now you've got the idea and you
+ 
+
+ align:start position:0%
+column now you've got the idea and you
+continue what do you do with the second
+
+ align:start position:0%
+continue what do you do with the second
+ 
+
+ align:start position:0%
+continue what do you do with the second
+column this time you will have to
+
+ align:start position:0%
+column this time you will have to
+ 
+
+ align:start position:0%
+column this time you will have to
+add a copy of the third column a copy of
+
+ align:start position:0%
+add a copy of the third column a copy of
+ 
+
+ align:start position:0%
+add a copy of the third column a copy of
+the fifth fourth column and the copy of
+
+ align:start position:0%
+the fifth fourth column and the copy of
+ 
+
+ align:start position:0%
+the fifth fourth column and the copy of
+the fifth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+column so you update the second column
+
+ align:start position:0%
+column so you update the second column
+ 
+
+ align:start position:0%
+column so you update the second column
+to be 4
+
+ align:start position:0%
+to be 4
+ 
+
+ align:start position:0%
+to be 4
+y x -
+
+ align:start position:0%
+y x -
+ 
+
+ align:start position:0%
+y x -
+y0 z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z eventually what you will do to the
+
+ align:start position:0%
+z eventually what you will do to the
+ 
+
+ align:start position:0%
+z eventually what you will do to the
+First Column would be you add everything
+
+ align:start position:0%
+First Column would be you add everything
+ 
+
+ align:start position:0%
+First Column would be you add everything
+to the four the first column
+
+ align:start position:0%
+to the four the first column
+ 
+
+ align:start position:0%
+to the four the first column
+so a copy of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each then the First Column will become
+
+ align:start position:0%
+each then the First Column will become
+ 
+
+ align:start position:0%
+each then the First Column will become
+so I don't have enough spot here so make
+
+ align:start position:0%
+so I don't have enough spot here so make
+ 
+
+ align:start position:0%
+so I don't have enough spot here so make
+it here x + 4
+
+ align:start position:0%
+it here x + 4
+ 
+
+ align:start position:0%
+it here x + 4
+y then everything
+
+ align:start position:0%
+y then everything
+ 
+
+ align:start position:0%
+y then everything
+else is
+
+ align:start position:0%
+else is
+ 
+
+ align:start position:0%
+else is
+zero this is fun and the result is
+
+ align:start position:0%
+zero this is fun and the result is
+ 
+
+ align:start position:0%
+zero this is fun and the result is
+really nice this is is wonderful because
+
+ align:start position:0%
+really nice this is is wonderful because
+ 
+
+ align:start position:0%
+really nice this is is wonderful because
+this is simply our triangular Matrix now
+
+ align:start position:0%
+this is simply our triangular Matrix now
+ 
+
+ align:start position:0%
+this is simply our triangular Matrix now
+you tell me what is the determinant of B
+
+ align:start position:0%
+you tell me what is the determinant of B
+ 
+
+ align:start position:0%
+you tell me what is the determinant of B
+the determinant of
+
+ align:start position:0%
+the determinant of
+ 
+
+ align:start position:0%
+the determinant of
+B is the
+
+ align:start position:0%
+B is the
+ 
+
+ align:start position:0%
+B is the
+determinant of this upper triangular
+
+ align:start position:0%
+determinant of this upper triangular
+ 
+
+ align:start position:0%
+determinant of this upper triangular
+Matrix so you simply multiply everything
+
+ align:start position:0%
+Matrix so you simply multiply everything
+ 
+
+ align:start position:0%
+Matrix so you simply multiply everything
+together that's x + 4
+
+ align:start position:0%
+together that's x + 4
+ 
+
+ align:start position:0%
+together that's x + 4
+y time x -
+
+ align:start position:0%
+y time x -
+ 
+
+ align:start position:0%
+y time x -
+y to the fourth
+
+ align:start position:0%
+y to the fourth
+ 
+
+ align:start position:0%
+y to the fourth
+power okay
+
+ align:start position:0%
+power okay
+ 
+
+ align:start position:0%
+power okay
+so I hope you enjoy these two
+
+ align:start position:0%
+so I hope you enjoy these two
+ 
+
+ align:start position:0%
+so I hope you enjoy these two
+examples maybe your method is different
+
+ align:start position:0%
+examples maybe your method is different
+ 
+
+ align:start position:0%
+examples maybe your method is different
+from mine but at least these two
+
+ align:start position:0%
+from mine but at least these two
+ 
+
+ align:start position:0%
+from mine but at least these two
+examples teach us that you can be
+
+ align:start position:0%
+examples teach us that you can be
+ 
+
+ align:start position:0%
+examples teach us that you can be
+flexible in combining methods in
+
+ align:start position:0%
+flexible in combining methods in
+ 
+
+ align:start position:0%
+flexible in combining methods in
+calculating determinants thanks for
+
+ align:start position:0%
+calculating determinants thanks for
+ 
+
+ align:start position:0%
+calculating determinants thanks for
+watching and I'm looking forward to see
+
+ align:start position:0%
+watching and I'm looking forward to see
+ 
+
+ align:start position:0%
+watching and I'm looking forward to see
+you soon
\ No newline at end of file
diff --git a/UzDqh-1Koyc.txt b/UzDqh-1Koyc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..00785164fbb34d14b980638817f012a348c178c8
--- /dev/null
+++ b/UzDqh-1Koyc.txt
@@ -0,0 +1,8171 @@
+align:start position:0%
+ 
+but um back to Mo Theory which is where
+
+ align:start position:0%
+but um back to Mo Theory which is where
+ 
+
+ align:start position:0%
+but um back to Mo Theory which is where
+what we talked about uh last Friday and
+
+ align:start position:0%
+what we talked about uh last Friday and
+ 
+
+ align:start position:0%
+what we talked about uh last Friday and
+and there were sort of two last things I
+
+ align:start position:0%
+and there were sort of two last things I
+ 
+
+ align:start position:0%
+and there were sort of two last things I
+wanted to to mention now uh related to
+
+ align:start position:0%
+wanted to to mention now uh related to
+ 
+
+ align:start position:0%
+wanted to to mention now uh related to
+ml Theory before moving on to the topic
+
+ align:start position:0%
+ml Theory before moving on to the topic
+ 
+
+ align:start position:0%
+ml Theory before moving on to the topic
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+hybridization um um now before I do that
+
+ align:start position:0%
+hybridization um um now before I do that
+ 
+
+ align:start position:0%
+hybridization um um now before I do that
+you know I'm going to use a couple of
+
+ align:start position:0%
+you know I'm going to use a couple of
+ 
+
+ align:start position:0%
+you know I'm going to use a couple of
+videos today and I'm I'm not going to
+
+ align:start position:0%
+videos today and I'm I'm not going to
+ 
+
+ align:start position:0%
+videos today and I'm I'm not going to
+show you this one but I just want to
+
+ align:start position:0%
+show you this one but I just want to
+ 
+
+ align:start position:0%
+show you this one but I just want to
+mention there's lots of videos that help
+
+ align:start position:0%
+mention there's lots of videos that help
+ 
+
+ align:start position:0%
+mention there's lots of videos that help
+you know animate this stuff right so
+
+ align:start position:0%
+you know animate this stuff right so
+ 
+
+ align:start position:0%
+you know animate this stuff right so
+like this is what you know so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like bonding molecular
+
+ align:start position:0%
+like bonding molecular
+ 
+
+ align:start position:0%
+like bonding molecular
+orbital combination of two an anti
+
+ align:start position:0%
+orbital combination of two an anti
+ 
+
+ align:start position:0%
+orbital combination of two an anti
+antibonding we talk about this last
+
+ align:start position:0%
+antibonding we talk about this last
+ 
+
+ align:start position:0%
+antibonding we talk about this last
+Friday but look at this
+
+ align:start position:0%
+Friday but look at this
+ 
+
+ align:start position:0%
+Friday but look at this
+animation I couldn't do that on the
+
+ align:start position:0%
+animation I couldn't do that on the
+ 
+
+ align:start position:0%
+animation I couldn't do that on the
+board watch this molecular orbitals
+
+ align:start position:0%
+board watch this molecular orbitals
+ 
+
+ align:start position:0%
+board watch this molecular orbitals
+formed by the combination of two 1s
+
+ align:start position:0%
+formed by the combination of two 1s
+ 
+
+ align:start position:0%
+formed by the combination of two 1s
+orbitals are called Sigma
+
+ align:start position:0%
+orbitals are called Sigma
+ 
+
+ align:start position:0%
+orbitals are called Sigma
+1s and Sig star
+
+ align:start position:0%
+1s and Sig star
+ 
+
+ align:start position:0%
+1s and Sig star
+1s kind of remembering stuff now right
+
+ align:start position:0%
+1s kind of remembering stuff now right
+ 
+
+ align:start position:0%
+1s kind of remembering stuff now right
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+Friday oh look at
+
+ align:start position:0%
+Friday oh look at
+ 
+
+ align:start position:0%
+Friday oh look at
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+original that's that kind of Animation
+
+ align:start position:0%
+original that's that kind of Animation
+ 
+
+ align:start position:0%
+original that's that kind of Animation
+that you just can't you know I can't
+
+ align:start position:0%
+that you just can't you know I can't
+ 
+
+ align:start position:0%
+that you just can't you know I can't
+animate the bonding and antibonding well
+
+ align:start position:0%
+animate the bonding and antibonding well
+ 
+
+ align:start position:0%
+animate the bonding and antibonding well
+I kind of can with my hands but but
+
+ align:start position:0%
+I kind of can with my hands but but
+ 
+
+ align:start position:0%
+I kind of can with my hands but but
+there it is and there's lots and lots of
+
+ align:start position:0%
+there it is and there's lots and lots of
+ 
+
+ align:start position:0%
+there it is and there's lots and lots of
+those kinds of videos I'll show you a
+
+ align:start position:0%
+those kinds of videos I'll show you a
+ 
+
+ align:start position:0%
+those kinds of videos I'll show you a
+couple today related to hybridization
+
+ align:start position:0%
+couple today related to hybridization
+ 
+
+ align:start position:0%
+couple today related to hybridization
+because it really does help see these 3D
+
+ align:start position:0%
+because it really does help see these 3D
+ 
+
+ align:start position:0%
+because it really does help see these 3D
+orbitals right in their full shape and
+
+ align:start position:0%
+orbitals right in their full shape and
+ 
+
+ align:start position:0%
+orbitals right in their full shape and
+what's happening so I highly recommend
+
+ align:start position:0%
+what's happening so I highly recommend
+ 
+
+ align:start position:0%
+what's happening so I highly recommend
+if especially if you're having like some
+
+ align:start position:0%
+if especially if you're having like some
+ 
+
+ align:start position:0%
+if especially if you're having like some
+conceptual uh uh questions related to
+
+ align:start position:0%
+conceptual uh uh questions related to
+ 
+
+ align:start position:0%
+conceptual uh uh questions related to
+stuff we talked about Friday and today
+
+ align:start position:0%
+stuff we talked about Friday and today
+ 
+
+ align:start position:0%
+stuff we talked about Friday and today
+uh take a look at some of those videos
+
+ align:start position:0%
+uh take a look at some of those videos
+ 
+
+ align:start position:0%
+uh take a look at some of those videos
+now where we left off uh on Friday um
+
+ align:start position:0%
+now where we left off uh on Friday um
+ 
+
+ align:start position:0%
+now where we left off uh on Friday um
+before I get to nitrous Nitric oxide
+
+ align:start position:0%
+before I get to nitrous Nitric oxide
+ 
+
+ align:start position:0%
+before I get to nitrous Nitric oxide
+which has all those different uses in
+
+ align:start position:0%
+which has all those different uses in
+ 
+
+ align:start position:0%
+which has all those different uses in
+the world um and many more um we left
+
+ align:start position:0%
+the world um and many more um we left
+ 
+
+ align:start position:0%
+the world um and many more um we left
+off with the the the homonuclear dimers
+
+ align:start position:0%
+off with the the the homonuclear dimers
+ 
+
+ align:start position:0%
+off with the the the homonuclear dimers
+that's what we were doing on Friday
+
+ align:start position:0%
+that's what we were doing on Friday
+ 
+
+ align:start position:0%
+that's what we were doing on Friday
+right how do the atomic orbitals come
+
+ align:start position:0%
+right how do the atomic orbitals come
+ 
+
+ align:start position:0%
+right how do the atomic orbitals come
+together to make orbitals that are
+
+ align:start position:0%
+together to make orbitals that are
+ 
+
+ align:start position:0%
+together to make orbitals that are
+molecular MOS right um and and we did it
+
+ align:start position:0%
+molecular MOS right um and and we did it
+ 
+
+ align:start position:0%
+molecular MOS right um and and we did it
+for for dimers that have the same atom
+
+ align:start position:0%
+for for dimers that have the same atom
+ 
+
+ align:start position:0%
+for for dimers that have the same atom
+right and so here so we did nitrogen N2
+
+ align:start position:0%
+right and so here so we did nitrogen N2
+ 
+
+ align:start position:0%
+right and so here so we did nitrogen N2
+and we did O2 right and so let's do that
+
+ align:start position:0%
+and we did O2 right and so let's do that
+ 
+
+ align:start position:0%
+and we did O2 right and so let's do that
+on the board and then because now we're
+
+ align:start position:0%
+on the board and then because now we're
+ 
+
+ align:start position:0%
+on the board and then because now we're
+going to start with one that has n and O
+
+ align:start position:0%
+going to start with one that has n and O
+ 
+
+ align:start position:0%
+going to start with one that has n and O
+heteronuclear dier right two different
+
+ align:start position:0%
+heteronuclear dier right two different
+ 
+
+ align:start position:0%
+heteronuclear dier right two different
+atoms but if I had the same one remember
+
+ align:start position:0%
+atoms but if I had the same one remember
+ 
+
+ align:start position:0%
+atoms but if I had the same one remember
+this is what it would look like right so
+
+ align:start position:0%
+this is what it would look like right so
+ 
+
+ align:start position:0%
+this is what it would look like right so
+here here would be say
+
+ align:start position:0%
+here here would be say
+ 
+
+ align:start position:0%
+here here would be say
+N2 would you know I'm going to just
+
+ align:start position:0%
+N2 would you know I'm going to just
+ 
+
+ align:start position:0%
+N2 would you know I'm going to just
+stick with the veence so the the
+
+ align:start position:0%
+stick with the veence so the the
+ 
+
+ align:start position:0%
+stick with the veence so the the
+2s for a nitrogen atom and the
+
+ align:start position:0%
+2s for a nitrogen atom and the
+ 
+
+ align:start position:0%
+2s for a nitrogen atom and the
+2p would have remember Hun's rule right
+
+ align:start position:0%
+2p would have remember Hun's rule right
+ 
+
+ align:start position:0%
+2p would have remember Hun's rule right
+okay so that's what the 2p would look
+
+ align:start position:0%
+okay so that's what the 2p would look
+ 
+
+ align:start position:0%
+okay so that's what the 2p would look
+like and then over here we would have
+
+ align:start position:0%
+like and then over here we would have
+ 
+
+ align:start position:0%
+like and then over here we would have
+uh the other atom This Is How We Roll
+
+ align:start position:0%
+uh the other atom This Is How We Roll
+ 
+
+ align:start position:0%
+uh the other atom This Is How We Roll
+when we talk about MOS and we'd have the
+
+ align:start position:0%
+when we talk about MOS and we'd have the
+ 
+
+ align:start position:0%
+when we talk about MOS and we'd have the
+2s over here and this is how we start
+
+ align:start position:0%
+2s over here and this is how we start
+ 
+
+ align:start position:0%
+2s over here and this is how we start
+these are my AOS for the two nitrogen
+
+ align:start position:0%
+these are my AOS for the two nitrogen
+ 
+
+ align:start position:0%
+these are my AOS for the two nitrogen
+atoms right this is what we did we're
+
+ align:start position:0%
+atoms right this is what we did we're
+ 
+
+ align:start position:0%
+atoms right this is what we did we're
+just getting back in the mood uh because
+
+ align:start position:0%
+just getting back in the mood uh because
+ 
+
+ align:start position:0%
+just getting back in the mood uh because
+we had the long weekend and when we make
+
+ align:start position:0%
+we had the long weekend and when we make
+ 
+
+ align:start position:0%
+we had the long weekend and when we make
+the OS remember we have all those sort
+
+ align:start position:0%
+the OS remember we have all those sort
+ 
+
+ align:start position:0%
+the OS remember we have all those sort
+of things that we talked about in terms
+
+ align:start position:0%
+of things that we talked about in terms
+ 
+
+ align:start position:0%
+of things that we talked about in terms
+of how these um this difference between
+
+ align:start position:0%
+of how these um this difference between
+ 
+
+ align:start position:0%
+of how these um this difference between
+the bonding and the anti-bonding orbital
+
+ align:start position:0%
+the bonding and the anti-bonding orbital
+ 
+
+ align:start position:0%
+the bonding and the anti-bonding orbital
+right uh is related to the the overlap
+
+ align:start position:0%
+right uh is related to the the overlap
+ 
+
+ align:start position:0%
+right uh is related to the the overlap
+and the same symmetry of the two AOS
+
+ align:start position:0%
+and the same symmetry of the two AOS
+ 
+
+ align:start position:0%
+and the same symmetry of the two AOS
+that come together we talked about that
+
+ align:start position:0%
+that come together we talked about that
+ 
+
+ align:start position:0%
+that come together we talked about that
+the more overlap the biggest this Delta
+
+ align:start position:0%
+the more overlap the biggest this Delta
+ 
+
+ align:start position:0%
+the more overlap the biggest this Delta
+gun typ right and then we also so that
+
+ align:start position:0%
+gun typ right and then we also so that
+ 
+
+ align:start position:0%
+gun typ right and then we also so that
+would be filled this would be filled
+
+ align:start position:0%
+would be filled this would be filled
+ 
+
+ align:start position:0%
+would be filled this would be filled
+right Sigma 2 s Sigma ah Sigma star 2s
+
+ align:start position:0%
+right Sigma 2 s Sigma ah Sigma star 2s
+ 
+
+ align:start position:0%
+right Sigma 2 s Sigma ah Sigma star 2s
+right uh and then for nitrogen we also
+
+ align:start position:0%
+right uh and then for nitrogen we also
+ 
+
+ align:start position:0%
+right uh and then for nitrogen we also
+talked about how oh boy these are
+
+ align:start position:0%
+talked about how oh boy these are
+ 
+
+ align:start position:0%
+talked about how oh boy these are
+reversed right see I'm I'm now already
+
+ align:start position:0%
+reversed right see I'm I'm now already
+ 
+
+ align:start position:0%
+reversed right see I'm I'm now already
+backwards twice which is not what I want
+
+ align:start position:0%
+backwards twice which is not what I want
+ 
+
+ align:start position:0%
+backwards twice which is not what I want
+okay and this was but this is the weird
+
+ align:start position:0%
+okay and this was but this is the weird
+ 
+
+ align:start position:0%
+okay and this was but this is the weird
+thing about nitrogen because if we go to
+
+ align:start position:0%
+thing about nitrogen because if we go to
+ 
+
+ align:start position:0%
+thing about nitrogen because if we go to
+oxygen then the way it goes is you know
+
+ align:start position:0%
+oxygen then the way it goes is you know
+ 
+
+ align:start position:0%
+oxygen then the way it goes is you know
+you got your 2s and
+
+ align:start position:0%
+you got your 2s and
+ 
+
+ align:start position:0%
+you got your 2s and
+oxygen okay and in oxygen you've got
+
+ align:start position:0%
+oxygen okay and in oxygen you've got
+ 
+
+ align:start position:0%
+oxygen okay and in oxygen you've got
+your your six veence electrons in the
+
+ align:start position:0%
+your your six veence electrons in the
+ 
+
+ align:start position:0%
+your your six veence electrons in the
+2p and over here you've also got the
+
+ align:start position:0%
+2p and over here you've also got the
+ 
+
+ align:start position:0%
+2p and over here you've also got the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+okay and you've also got the 2s and but
+
+ align:start position:0%
+okay and you've also got the 2s and but
+ 
+
+ align:start position:0%
+okay and you've also got the 2s and but
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxygen okay so those are the sigma Sigma
+
+ align:start position:0%
+oxygen okay so those are the sigma Sigma
+ 
+
+ align:start position:0%
+oxygen okay so those are the sigma Sigma
+star but for oxygen we go to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ordering that
+
+ align:start position:0%
+ordering that
+ 
+
+ align:start position:0%
+ordering that
+we usually have which is that remember
+
+ align:start position:0%
+we usually have which is that remember
+ 
+
+ align:start position:0%
+we usually have which is that remember
+those Pi
+
+ align:start position:0%
+those Pi
+ 
+
+ align:start position:0%
+those Pi
+orbitals have and this isn't necessarily
+
+ align:start position:0%
+orbitals have and this isn't necessarily
+ 
+
+ align:start position:0%
+orbitals have and this isn't necessarily
+drawn to scale but those Pi or right so
+
+ align:start position:0%
+drawn to scale but those Pi or right so
+ 
+
+ align:start position:0%
+drawn to scale but those Pi or right so
+this is Sigma Sigma star and these are
+
+ align:start position:0%
+this is Sigma Sigma star and these are
+ 
+
+ align:start position:0%
+this is Sigma Sigma star and these are
+the pi orbitals pi and Pi Star
+
+ align:start position:0%
+the pi orbitals pi and Pi Star
+ 
+
+ align:start position:0%
+the pi orbitals pi and Pi Star
+right Sigma
+
+ align:start position:0%
+right Sigma
+ 
+
+ align:start position:0%
+right Sigma
+P Sigma P right 2 p 2s Sigma this would
+
+ align:start position:0%
+P Sigma P right 2 p 2s Sigma this would
+ 
+
+ align:start position:0%
+P Sigma P right 2 p 2s Sigma this would
+be Sigma s Sigma 2s Sigma 2 s star Sigma
+
+ align:start position:0%
+be Sigma s Sigma 2s Sigma 2 s star Sigma
+ 
+
+ align:start position:0%
+be Sigma s Sigma 2s Sigma 2 s star Sigma
+2 p if you want to be exact about it
+
+ align:start position:0%
+2 p if you want to be exact about it
+ 
+
+ align:start position:0%
+2 p if you want to be exact about it
+Sigma 2 p star pix Pi y pix star Pi y
+
+ align:start position:0%
+Sigma 2 p star pix Pi y pix star Pi y
+ 
+
+ align:start position:0%
+Sigma 2 p star pix Pi y pix star Pi y
+star we talked about all this on Friday
+
+ align:start position:0%
+star we talked about all this on Friday
+ 
+
+ align:start position:0%
+star we talked about all this on Friday
+I'm just getting us back in the mood but
+
+ align:start position:0%
+I'm just getting us back in the mood but
+ 
+
+ align:start position:0%
+I'm just getting us back in the mood but
+the but the way we left off was that
+
+ align:start position:0%
+the but the way we left off was that
+ 
+
+ align:start position:0%
+the but the way we left off was that
+these are okay so for if I fill these
+
+ align:start position:0%
+these are okay so for if I fill these
+ 
+
+ align:start position:0%
+these are okay so for if I fill these
+all up now right remember we do the mo
+
+ align:start position:0%
+all up now right remember we do the mo
+ 
+
+ align:start position:0%
+all up now right remember we do the mo
+filling then we'd have this and this and
+
+ align:start position:0%
+filling then we'd have this and this and
+ 
+
+ align:start position:0%
+filling then we'd have this and this and
+O now hold on Yep this and there and
+
+ align:start position:0%
+O now hold on Yep this and there and
+ 
+
+ align:start position:0%
+O now hold on Yep this and there and
+there for oxygen and then over here
+
+ align:start position:0%
+there for oxygen and then over here
+ 
+
+ align:start position:0%
+there for oxygen and then over here
+we're filling them up we got those are
+
+ align:start position:0%
+we're filling them up we got those are
+ 
+
+ align:start position:0%
+we're filling them up we got those are
+filled those are filled and this is
+
+ align:start position:0%
+filled those are filled and this is
+ 
+
+ align:start position:0%
+filled those are filled and this is
+filled filled for nitrogen remember I
+
+ align:start position:0%
+filled filled for nitrogen remember I
+ 
+
+ align:start position:0%
+filled filled for nitrogen remember I
+showed the movie pouring liquid oxygen
+
+ align:start position:0%
+showed the movie pouring liquid oxygen
+ 
+
+ align:start position:0%
+showed the movie pouring liquid oxygen
+pouring liquid nitrogen oxygen has
+
+ align:start position:0%
+pouring liquid nitrogen oxygen has
+ 
+
+ align:start position:0%
+pouring liquid nitrogen oxygen has
+unpaired
+
+ align:start position:0%
+unpaired
+ 
+
+ align:start position:0%
+unpaired
+electrons which means it's
+
+ align:start position:0%
+electrons which means it's
+ 
+
+ align:start position:0%
+electrons which means it's
+paramagnetic it has unpaired electrons
+
+ align:start position:0%
+paramagnetic it has unpaired electrons
+ 
+
+ align:start position:0%
+paramagnetic it has unpaired electrons
+the O2 dier this is O2 these are Theos
+
+ align:start position:0%
+the O2 dier this is O2 these are Theos
+ 
+
+ align:start position:0%
+the O2 dier this is O2 these are Theos
+of o2 these are the atoms these are
+
+ align:start position:0%
+of o2 these are the atoms these are
+ 
+
+ align:start position:0%
+of o2 these are the atoms these are
+Theos of N2 N2 doesn't have any unpaired
+
+ align:start position:0%
+Theos of N2 N2 doesn't have any unpaired
+ 
+
+ align:start position:0%
+Theos of N2 N2 doesn't have any unpaired
+electrons so it's not paramagnetic um
+
+ align:start position:0%
+electrons so it's not paramagnetic um
+ 
+
+ align:start position:0%
+electrons so it's not paramagnetic um
+but the thing that we left off on that's
+
+ align:start position:0%
+but the thing that we left off on that's
+ 
+
+ align:start position:0%
+but the thing that we left off on that's
+what I'm saying is that these two switch
+
+ align:start position:0%
+what I'm saying is that these two switch
+ 
+
+ align:start position:0%
+what I'm saying is that these two switch
+order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for those diers for lithium through
+
+ align:start position:0%
+for those diers for lithium through
+ 
+
+ align:start position:0%
+for those diers for lithium through
+nitrogen those two switch over and we
+
+ align:start position:0%
+nitrogen those two switch over and we
+ 
+
+ align:start position:0%
+nitrogen those two switch over and we
+talk about that on Friday the reason is
+
+ align:start position:0%
+talk about that on Friday the reason is
+ 
+
+ align:start position:0%
+talk about that on Friday the reason is
+because for those atoms these uh
+
+ align:start position:0%
+because for those atoms these uh
+ 
+
+ align:start position:0%
+because for those atoms these uh
+Sigma these Sigma uh uh P orbitals can
+
+ align:start position:0%
+Sigma these Sigma uh uh P orbitals can
+ 
+
+ align:start position:0%
+Sigma these Sigma uh uh P orbitals can
+mix in with the sigma s orbitals and so
+
+ align:start position:0%
+mix in with the sigma s orbitals and so
+ 
+
+ align:start position:0%
+mix in with the sigma s orbitals and so
+you get more because remember the more
+
+ align:start position:0%
+you get more because remember the more
+ 
+
+ align:start position:0%
+you get more because remember the more
+overlap the greater the energy right the
+
+ align:start position:0%
+overlap the greater the energy right the
+ 
+
+ align:start position:0%
+overlap the greater the energy right the
+greater that Delta between bonding and
+
+ align:start position:0%
+greater that Delta between bonding and
+ 
+
+ align:start position:0%
+greater that Delta between bonding and
+antibonding right so the more mixing you
+
+ align:start position:0%
+antibonding right so the more mixing you
+ 
+
+ align:start position:0%
+antibonding right so the more mixing you
+have the more spread you get and it's so
+
+ align:start position:0%
+have the more spread you get and it's so
+ 
+
+ align:start position:0%
+have the more spread you get and it's so
+much that for those diers you you push
+
+ align:start position:0%
+much that for those diers you you push
+ 
+
+ align:start position:0%
+much that for those diers you you push
+the orbital up okay that's all what we
+
+ align:start position:0%
+the orbital up okay that's all what we
+ 
+
+ align:start position:0%
+the orbital up okay that's all what we
+talked about Friday now I got one of
+
+ align:start position:0%
+talked about Friday now I got one of
+ 
+
+ align:start position:0%
+talked about Friday now I got one of
+each and I wanted these on the board so
+
+ align:start position:0%
+each and I wanted these on the board so
+ 
+
+ align:start position:0%
+each and I wanted these on the board so
+that you can see them as we now take one
+
+ align:start position:0%
+that you can see them as we now take one
+ 
+
+ align:start position:0%
+that you can see them as we now take one
+atom from one side and one from the
+
+ align:start position:0%
+atom from one side and one from the
+ 
+
+ align:start position:0%
+atom from one side and one from the
+other it's
+
+ align:start position:0%
+other it's
+ 
+
+ align:start position:0%
+other it's
+actually kind of what you expect you
+
+ align:start position:0%
+actually kind of what you expect you
+ 
+
+ align:start position:0%
+actually kind of what you expect you
+just have to have one thing in mind when
+
+ align:start position:0%
+just have to have one thing in mind when
+ 
+
+ align:start position:0%
+just have to have one thing in mind when
+you think about n o so if this is n okay
+
+ align:start position:0%
+you think about n o so if this is n okay
+ 
+
+ align:start position:0%
+you think about n o so if this is n okay
+over here and we're going to put uh 2 s
+
+ align:start position:0%
+over here and we're going to put uh 2 s
+ 
+
+ align:start position:0%
+over here and we're going to put uh 2 s
+there and 2 p there here here here here
+
+ align:start position:0%
+there and 2 p there here here here here
+ 
+
+ align:start position:0%
+there and 2 p there here here here here
+there's my n atom and now I've got o
+
+ align:start position:0%
+there's my n atom and now I've got o
+ 
+
+ align:start position:0%
+there's my n atom and now I've got o
+over here so I've got my but now see the
+
+ align:start position:0%
+over here so I've got my but now see the
+ 
+
+ align:start position:0%
+over here so I've got my but now see the
+thing is O is more Electro negative and
+
+ align:start position:0%
+thing is O is more Electro negative and
+ 
+
+ align:start position:0%
+thing is O is more Electro negative and
+the way this works for a heteronuclear
+
+ align:start position:0%
+the way this works for a heteronuclear
+ 
+
+ align:start position:0%
+the way this works for a heteronuclear
+dimer is
+
+ align:start position:0%
+dimer is
+ 
+
+ align:start position:0%
+dimer is
+let's write this on the board so for a
+
+ align:start position:0%
+let's write this on the board so for a
+ 
+
+ align:start position:0%
+let's write this on the board so for a
+hetero nuclear that means that the two
+
+ align:start position:0%
+hetero nuclear that means that the two
+ 
+
+ align:start position:0%
+hetero nuclear that means that the two
+atoms are different okay but for a
+
+ align:start position:0%
+atoms are different okay but for a
+ 
+
+ align:start position:0%
+atoms are different okay but for a
+heteronuclear
+
+ align:start position:0%
+heteronuclear
+ 
+
+ align:start position:0%
+heteronuclear
+dimer um the bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+os are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closer in
+
+ align:start position:0%
+closer in
+ 
+
+ align:start position:0%
+closer in
+energy to the more electronegative atom
+
+ align:start position:0%
+energy to the more electronegative atom
+ 
+
+ align:start position:0%
+energy to the more electronegative atom
+electr
+
+ align:start position:0%
+electr
+ 
+
+ align:start position:0%
+electr
+NE
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atom atom so what that means is that if
+
+ align:start position:0%
+atom atom so what that means is that if
+ 
+
+ align:start position:0%
+atom atom so what that means is that if
+I draw so if I draw my oxygen levels but
+
+ align:start position:0%
+I draw so if I draw my oxygen levels but
+ 
+
+ align:start position:0%
+I draw so if I draw my oxygen levels but
+you know this right you know this also
+
+ align:start position:0%
+you know this right you know this also
+ 
+
+ align:start position:0%
+you know this right you know this also
+from all the the work we did on
+
+ align:start position:0%
+from all the the work we did on
+ 
+
+ align:start position:0%
+from all the the work we did on
+atoms right you know a little something
+
+ align:start position:0%
+atoms right you know a little something
+ 
+
+ align:start position:0%
+atoms right you know a little something
+about remember this axis is
+
+ align:start position:0%
+about remember this axis is
+ 
+
+ align:start position:0%
+about remember this axis is
+energy this axis is energy right
+
+ align:start position:0%
+energy this axis is energy right
+ 
+
+ align:start position:0%
+energy this axis is energy right
+and so if this is 2s for oxygen and then
+
+ align:start position:0%
+and so if this is 2s for oxygen and then
+ 
+
+ align:start position:0%
+and so if this is 2s for oxygen and then
+the two PS are going to be sort of like
+
+ align:start position:0%
+the two PS are going to be sort of like
+ 
+
+ align:start position:0%
+the two PS are going to be sort of like
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay and we'll fill them up thinking
+
+ align:start position:0%
+okay and we'll fill them up thinking
+ 
+
+ align:start position:0%
+okay and we'll fill them up thinking
+about Huns rule well now what we're
+
+ align:start position:0%
+about Huns rule well now what we're
+ 
+
+ align:start position:0%
+about Huns rule well now what we're
+going to have is that those the MOs for
+
+ align:start position:0%
+going to have is that those the MOs for
+ 
+
+ align:start position:0%
+going to have is that those the MOs for
+the N
+
+ align:start position:0%
+the N
+ 
+
+ align:start position:0%
+the N
+molecule are going to come closer
+
+ align:start position:0%
+molecule are going to come closer
+ 
+
+ align:start position:0%
+molecule are going to come closer
+they're going to come further down from
+
+ align:start position:0%
+they're going to come further down from
+ 
+
+ align:start position:0%
+they're going to come further down from
+that side right than they come from that
+
+ align:start position:0%
+that side right than they come from that
+ 
+
+ align:start position:0%
+that side right than they come from that
+side you see that there's an asymmetry I
+
+ align:start position:0%
+side you see that there's an asymmetry I
+ 
+
+ align:start position:0%
+side you see that there's an asymmetry I
+made it kind of subtle I made it kind
+
+ align:start position:0%
+made it kind of subtle I made it kind
+ 
+
+ align:start position:0%
+made it kind of subtle I made it kind
+and why is this curved that's not good
+
+ align:start position:0%
+and why is this curved that's not good
+ 
+
+ align:start position:0%
+and why is this curved that's not good
+what's going on here there's a little
+
+ align:start position:0%
+what's going on here there's a little
+ 
+
+ align:start position:0%
+what's going on here there's a little
+bit of an asymmetry here
+
+ align:start position:0%
+bit of an asymmetry here
+ 
+
+ align:start position:0%
+bit of an asymmetry here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so so this is lower
+
+ align:start position:0%
+so so this is lower
+ 
+
+ align:start position:0%
+so so this is lower
+down these are lower down right so when
+
+ align:start position:0%
+down these are lower down right so when
+ 
+
+ align:start position:0%
+down these are lower down right so when
+you draw your orbitals now oh man I'm
+
+ align:start position:0%
+you draw your orbitals now oh man I'm
+ 
+
+ align:start position:0%
+you draw your orbitals now oh man I'm
+going to draw this a little bit
+
+ align:start position:0%
+going to draw this a little bit
+ 
+
+ align:start position:0%
+going to draw this a little bit
+lower right
+
+ align:start position:0%
+lower right
+ 
+
+ align:start position:0%
+lower right
+so now when you draw them you see that
+
+ align:start position:0%
+so now when you draw them you see that
+ 
+
+ align:start position:0%
+so now when you draw them you see that
+bonding orbital is going to be
+
+ align:start position:0%
+bonding orbital is going to be
+ 
+
+ align:start position:0%
+bonding orbital is going to be
+closer you see this is a bonding orbital
+
+ align:start position:0%
+closer you see this is a bonding orbital
+ 
+
+ align:start position:0%
+closer you see this is a bonding orbital
+still it's still bonding right it's a
+
+ align:start position:0%
+still it's still bonding right it's a
+ 
+
+ align:start position:0%
+still it's still bonding right it's a
+it's going to be a a sigma P Sigma 2 p
+
+ align:start position:0%
+it's going to be a a sigma P Sigma 2 p
+ 
+
+ align:start position:0%
+it's going to be a a sigma P Sigma 2 p
+but it's closer and energy to the more
+
+ align:start position:0%
+but it's closer and energy to the more
+ 
+
+ align:start position:0%
+but it's closer and energy to the more
+electronegative levels you see that
+
+ align:start position:0%
+electronegative levels you see that
+ 
+
+ align:start position:0%
+electronegative levels you see that
+right so it's not symmetric
+
+ align:start position:0%
+right so it's not symmetric
+ 
+
+ align:start position:0%
+right so it's not symmetric
+anymore okay and then the same would
+
+ align:start position:0%
+anymore okay and then the same would
+ 
+
+ align:start position:0%
+anymore okay and then the same would
+happen with these guys right they'd be
+
+ align:start position:0%
+happen with these guys right they'd be
+ 
+
+ align:start position:0%
+happen with these guys right they'd be
+closer in energy
+
+ align:start position:0%
+closer in energy
+ 
+
+ align:start position:0%
+closer in energy
+to the yeah they would be closer and I'm
+
+ align:start position:0%
+to the yeah they would be closer and I'm
+ 
+
+ align:start position:0%
+to the yeah they would be closer and I'm
+not leaving myself enough room here
+
+ align:start position:0%
+not leaving myself enough room here
+ 
+
+ align:start position:0%
+not leaving myself enough room here
+that's why I've got some videos they do
+
+ align:start position:0%
+that's why I've got some videos they do
+ 
+
+ align:start position:0%
+that's why I've got some videos they do
+it better
+
+ align:start position:0%
+it better
+ 
+
+ align:start position:0%
+it better
+right okay we'll leave that one there
+
+ align:start position:0%
+right okay we'll leave that one there
+ 
+
+ align:start position:0%
+right okay we'll leave that one there
+it's a little bit
+
+ align:start position:0%
+it's a little bit
+ 
+
+ align:start position:0%
+it's a little bit
+better not much but a little
+
+ align:start position:0%
+better not much but a little
+ 
+
+ align:start position:0%
+better not much but a little
+bit so the B now oh by the way it for no
+
+ align:start position:0%
+bit so the B now oh by the way it for no
+ 
+
+ align:start position:0%
+bit so the B now oh by the way it for no
+o let's talk about Mo for a second cuz
+
+ align:start position:0%
+o let's talk about Mo for a second cuz
+ 
+
+ align:start position:0%
+o let's talk about Mo for a second cuz
+there's another thing that's important
+
+ align:start position:0%
+there's another thing that's important
+ 
+
+ align:start position:0%
+there's another thing that's important
+that we talk about which is bond order
+
+ align:start position:0%
+that we talk about which is bond order
+ 
+
+ align:start position:0%
+that we talk about which is bond order
+and you know so the bond oh electron
+
+ align:start position:0%
+and you know so the bond oh electron
+ 
+
+ align:start position:0%
+and you know so the bond oh electron
+configuration is another thing right so
+
+ align:start position:0%
+configuration is another thing right so
+ 
+
+ align:start position:0%
+configuration is another thing right so
+like the the
+
+ align:start position:0%
+like the the
+ 
+
+ align:start position:0%
+like the the
+configuration we can write this
+
+ align:start position:0%
+configuration we can write this
+ 
+
+ align:start position:0%
+configuration we can write this
+out right so the configuration of say O2
+
+ align:start position:0%
+out right so the configuration of say O2
+ 
+
+ align:start position:0%
+out right so the configuration of say O2
+would be Sigma 2s right you're just
+
+ align:start position:0%
+would be Sigma 2s right you're just
+ 
+
+ align:start position:0%
+would be Sigma 2s right you're just
+filling them up with two electrons Sigma
+
+ align:start position:0%
+filling them up with two electrons Sigma
+ 
+
+ align:start position:0%
+filling them up with two electrons Sigma
+star 2s with two electrons Sigma 2
+
+ align:start position:0%
+star 2s with two electrons Sigma 2
+ 
+
+ align:start position:0%
+star 2s with two electrons Sigma 2
+p with two electrons pi
+
+ align:start position:0%
+p with two electrons pi
+ 
+
+ align:start position:0%
+p with two electrons pi
+2 p with four electrons and then Pi 2 p
+
+ align:start position:0%
+2 p with four electrons and then Pi 2 p
+ 
+
+ align:start position:0%
+2 p with four electrons and then Pi 2 p
+star with two electrons that's how that
+
+ align:start position:0%
+star with two electrons that's how that
+ 
+
+ align:start position:0%
+star with two electrons that's how that
+looks it's a little bit messy but I hope
+
+ align:start position:0%
+looks it's a little bit messy but I hope
+ 
+
+ align:start position:0%
+looks it's a little bit messy but I hope
+you can read it that's just reading up
+
+ align:start position:0%
+you can read it that's just reading up
+ 
+
+ align:start position:0%
+you can read it that's just reading up
+right it's the electron configuration of
+
+ align:start position:0%
+right it's the electron configuration of
+ 
+
+ align:start position:0%
+right it's the electron configuration of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+MOs just like we would write the SPD
+
+ align:start position:0%
+MOs just like we would write the SPD
+ 
+
+ align:start position:0%
+MOs just like we would write the SPD
+electron configuration of atoms but this
+
+ align:start position:0%
+electron configuration of atoms but this
+ 
+
+ align:start position:0%
+electron configuration of atoms but this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+molecule now sometimes you might you
+
+ align:start position:0%
+molecule now sometimes you might you
+ 
+
+ align:start position:0%
+molecule now sometimes you might you
+know some say there's a convention we
+
+ align:start position:0%
+know some say there's a convention we
+ 
+
+ align:start position:0%
+know some say there's a convention we
+use which is that the pz is the sigma ah
+
+ align:start position:0%
+use which is that the pz is the sigma ah
+ 
+
+ align:start position:0%
+use which is that the pz is the sigma ah
+nobody can agree on so different
+
+ align:start position:0%
+nobody can agree on so different
+ 
+
+ align:start position:0%
+nobody can agree on so different
+textbooks say PX P but we were saying P
+
+ align:start position:0%
+textbooks say PX P but we were saying P
+ 
+
+ align:start position:0%
+textbooks say PX P but we were saying P
+if pz is Sigma then this would be like a
+
+ align:start position:0%
+if pz is Sigma then this would be like a
+ 
+
+ align:start position:0%
+if pz is Sigma then this would be like a
+sigma 2
+
+ align:start position:0%
+sigma 2
+ 
+
+ align:start position:0%
+sigma 2
+pz right and and you might if you really
+
+ align:start position:0%
+pz right and and you might if you really
+ 
+
+ align:start position:0%
+pz right and and you might if you really
+want to write this you know you might
+
+ align:start position:0%
+want to write this you know you might
+ 
+
+ align:start position:0%
+want to write this you know you might
+write that that's Pi 2 PX if you really
+
+ align:start position:0%
+write that that's Pi 2 PX if you really
+ 
+
+ align:start position:0%
+write that that's Pi 2 PX if you really
+want to keep track of it there's two
+
+ align:start position:0%
+want to keep track of it there's two
+ 
+
+ align:start position:0%
+want to keep track of it there's two
+orbitals in there you didn't fill one
+
+ align:start position:0%
+orbitals in there you didn't fill one
+ 
+
+ align:start position:0%
+orbitals in there you didn't fill one
+orbital with four electrons right so
+
+ align:start position:0%
+orbital with four electrons right so
+ 
+
+ align:start position:0%
+orbital with four electrons right so
+this would be Pi 2 PX and pi 2 py for
+
+ align:start position:0%
+this would be Pi 2 PX and pi 2 py for
+ 
+
+ align:start position:0%
+this would be Pi 2 PX and pi 2 py for
+right that's what's happening in there
+
+ align:start position:0%
+right that's what's happening in there
+ 
+
+ align:start position:0%
+right that's what's happening in there
+okay but the other thing you can see
+
+ align:start position:0%
+okay but the other thing you can see
+ 
+
+ align:start position:0%
+okay but the other thing you can see
+from the bond from this this filling is
+
+ align:start position:0%
+from the bond from this this filling is
+ 
+
+ align:start position:0%
+from the bond from this this filling is
+also the bond order right and so for the
+
+ align:start position:0%
+also the bond order right and so for the
+ 
+
+ align:start position:0%
+also the bond order right and so for the
+bond order
+
+ align:start position:0%
+bond order
+ 
+
+ align:start position:0%
+bond order
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+order here you would have a half times
+
+ align:start position:0%
+order here you would have a half times
+ 
+
+ align:start position:0%
+order here you would have a half times
+and it's all of the remember the bond is
+
+ align:start position:0%
+and it's all of the remember the bond is
+ 
+
+ align:start position:0%
+and it's all of the remember the bond is
+all of the bonding electrons minus
+
+ align:start position:0%
+all of the bonding electrons minus
+ 
+
+ align:start position:0%
+all of the bonding electrons minus
+antibinding electrons divided by two
+
+ align:start position:0%
+antibinding electrons divided by two
+ 
+
+ align:start position:0%
+antibinding electrons divided by two
+right and and if it's zero it's not a
+
+ align:start position:0%
+right and and if it's zero it's not a
+ 
+
+ align:start position:0%
+right and and if it's zero it's not a
+stable molecule if it's greater than
+
+ align:start position:0%
+stable molecule if it's greater than
+ 
+
+ align:start position:0%
+stable molecule if it's greater than
+zero stable and the higher the bond
+
+ align:start position:0%
+zero stable and the higher the bond
+ 
+
+ align:start position:0%
+zero stable and the higher the bond
+order the higher the bond strength right
+
+ align:start position:0%
+order the higher the bond strength right
+ 
+
+ align:start position:0%
+order the higher the bond strength right
+so that's also from Friday and so this
+
+ align:start position:0%
+so that's also from Friday and so this
+ 
+
+ align:start position:0%
+so that's also from Friday and so this
+is 2 - 2 + 4 - 2 and so you get
+
+ align:start position:0%
+is 2 - 2 + 4 - 2 and so you get
+ 
+
+ align:start position:0%
+is 2 - 2 + 4 - 2 and so you get
+two nope I missed a
+
+ align:start position:0%
+two nope I missed a
+ 
+
+ align:start position:0%
+two nope I missed a
+two + 2 + 4 -
+
+ align:start position:0%
+two + 2 + 4 -
+ 
+
+ align:start position:0%
+two + 2 + 4 -
+2 2 - 2 that kind of cancels out right +
+
+ align:start position:0%
+2 2 - 2 that kind of cancels out right +
+ 
+
+ align:start position:0%
+2 2 - 2 that kind of cancels out right +
+2 + 4 - 2 all divided by two so the the
+
+ align:start position:0%
+2 + 4 - 2 all divided by two so the the
+ 
+
+ align:start position:0%
+2 + 4 - 2 all divided by two so the the
+bond order for oxy now the bond order
+
+ align:start position:0%
+bond order for oxy now the bond order
+ 
+
+ align:start position:0%
+bond order for oxy now the bond order
+for no
+
+ align:start position:0%
+for no
+ 
+
+ align:start position:0%
+for no
+o bond order for no
+
+ align:start position:0%
+o bond order for no
+ 
+
+ align:start position:0%
+o bond order for no
+o is going to be uh 2.5 well it's kind
+
+ align:start position:0%
+o is going to be uh 2.5 well it's kind
+ 
+
+ align:start position:0%
+o is going to be uh 2.5 well it's kind
+of interesting now you can see okay so n
+
+ align:start position:0%
+of interesting now you can see okay so n
+ 
+
+ align:start position:0%
+of interesting now you can see okay so n
+o is stronger uh more strongly bound
+
+ align:start position:0%
+o is stronger uh more strongly bound
+ 
+
+ align:start position:0%
+o is stronger uh more strongly bound
+than O2 less strongly bound than N2 and
+
+ align:start position:0%
+than O2 less strongly bound than N2 and
+ 
+
+ align:start position:0%
+than O2 less strongly bound than N2 and
+it's kind of interesting how can I make
+
+ align:start position:0%
+it's kind of interesting how can I make
+ 
+
+ align:start position:0%
+it's kind of interesting how can I make
+n o a stronger a more strongly bound
+
+ align:start position:0%
+n o a stronger a more strongly bound
+ 
+
+ align:start position:0%
+n o a stronger a more strongly bound
+molecule well I can take an electron
+
+ align:start position:0%
+molecule well I can take an electron
+ 
+
+ align:start position:0%
+molecule well I can take an electron
+away which is a little bit
+
+ align:start position:0%
+away which is a little bit
+ 
+
+ align:start position:0%
+away which is a little bit
+counterintuitive right because for no
+
+ align:start position:0%
+counterintuitive right because for no
+ 
+
+ align:start position:0%
+counterintuitive right because for no
+O+ the bond order goes up because the
+
+ align:start position:0%
+O+ the bond order goes up because the
+ 
+
+ align:start position:0%
+O+ the bond order goes up because the
+electron that I've taken away was in an
+
+ align:start position:0%
+electron that I've taken away was in an
+ 
+
+ align:start position:0%
+electron that I've taken away was in an
+anti-bonding orbital right so no o plus
+
+ align:start position:0%
+anti-bonding orbital right so no o plus
+ 
+
+ align:start position:0%
+anti-bonding orbital right so no o plus
+actually has a stronger Bond than n o
+
+ align:start position:0%
+actually has a stronger Bond than n o
+ 
+
+ align:start position:0%
+actually has a stronger Bond than n o
+even though it has one less electron you
+
+ align:start position:0%
+even though it has one less electron you
+ 
+
+ align:start position:0%
+even though it has one less electron you
+get this all from just looking at which
+
+ align:start position:0%
+get this all from just looking at which
+ 
+
+ align:start position:0%
+get this all from just looking at which
+electrons are occupying which orbitals
+
+ align:start position:0%
+electrons are occupying which orbitals
+ 
+
+ align:start position:0%
+electrons are occupying which orbitals
+ah on in this case you had in this very
+
+ align:start position:0%
+ah on in this case you had in this very
+ 
+
+ align:start position:0%
+ah on in this case you had in this very
+much not drawn to scale oh boy figure
+
+ align:start position:0%
+much not drawn to scale oh boy figure
+ 
+
+ align:start position:0%
+much not drawn to scale oh boy figure
+right what you had was one up
+
+ align:start position:0%
+right what you had was one up
+ 
+
+ align:start position:0%
+right what you had was one up
+there so if I take that out my bond
+
+ align:start position:0%
+there so if I take that out my bond
+ 
+
+ align:start position:0%
+there so if I take that out my bond
+order increases right okay all
+
+ align:start position:0%
+order increases right okay all
+ 
+
+ align:start position:0%
+order increases right okay all
+right and the last point I wanted to
+
+ align:start position:0%
+right and the last point I wanted to
+ 
+
+ align:start position:0%
+right and the last point I wanted to
+make about Mo Theory before we talk
+
+ align:start position:0%
+make about Mo Theory before we talk
+ 
+
+ align:start position:0%
+make about Mo Theory before we talk
+about hybridization is with one other
+
+ align:start position:0%
+about hybridization is with one other
+ 
+
+ align:start position:0%
+about hybridization is with one other
+example and that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HCL okay so for htl you got something
+
+ align:start position:0%
+HCL okay so for htl you got something
+ 
+
+ align:start position:0%
+HCL okay so for htl you got something
+else happening that's important so we
+
+ align:start position:0%
+else happening that's important so we
+ 
+
+ align:start position:0%
+else happening that's important so we
+just talked about electro negativity
+
+ align:start position:0%
+just talked about electro negativity
+ 
+
+ align:start position:0%
+just talked about electro negativity
+driving where the you know that this is
+
+ align:start position:0%
+driving where the you know that this is
+ 
+
+ align:start position:0%
+driving where the you know that this is
+tilted okay fine and now we got the fact
+
+ align:start position:0%
+tilted okay fine and now we got the fact
+ 
+
+ align:start position:0%
+tilted okay fine and now we got the fact
+that chlorine comes into the situation
+
+ align:start position:0%
+that chlorine comes into the situation
+ 
+
+ align:start position:0%
+that chlorine comes into the situation
+you know it's like chlorine is like hey
+
+ align:start position:0%
+you know it's like chlorine is like hey
+ 
+
+ align:start position:0%
+you know it's like chlorine is like hey
+I got seven electrons right and hydrogen
+
+ align:start position:0%
+I got seven electrons right and hydrogen
+ 
+
+ align:start position:0%
+I got seven electrons right and hydrogen
+is like hey I got
+
+ align:start position:0%
+is like hey I got
+ 
+
+ align:start position:0%
+is like hey I got
+one so how does this work right so this
+
+ align:start position:0%
+one so how does this work right so this
+ 
+
+ align:start position:0%
+one so how does this work right so this
+gets to what was brought up uh Friday
+
+ align:start position:0%
+gets to what was brought up uh Friday
+ 
+
+ align:start position:0%
+gets to what was brought up uh Friday
+which is there's another type of Mo and
+
+ align:start position:0%
+which is there's another type of Mo and
+ 
+
+ align:start position:0%
+which is there's another type of Mo and
+it's not bonding and it's not
+
+ align:start position:0%
+it's not bonding and it's not
+ 
+
+ align:start position:0%
+it's not bonding and it's not
+anti-bonding it's
+
+ align:start position:0%
+anti-bonding it's
+ 
+
+ align:start position:0%
+anti-bonding it's
+nonbonding that is not the same as
+
+ align:start position:0%
+nonbonding that is not the same as
+ 
+
+ align:start position:0%
+nonbonding that is not the same as
+antibonding non-bonding doesn't take
+
+ align:start position:0%
+antibonding non-bonding doesn't take
+ 
+
+ align:start position:0%
+antibonding non-bonding doesn't take
+sides it just is because the way this
+
+ align:start position:0%
+sides it just is because the way this
+ 
+
+ align:start position:0%
+sides it just is because the way this
+works is you know hydrogen comes at this
+
+ align:start position:0%
+works is you know hydrogen comes at this
+ 
+
+ align:start position:0%
+works is you know hydrogen comes at this
+okay so hydrogen's up here with its 1 s
+
+ align:start position:0%
+okay so hydrogen's up here with its 1 s
+ 
+
+ align:start position:0%
+okay so hydrogen's up here with its 1 s
+chlorine is you know let's say over here
+
+ align:start position:0%
+chlorine is you know let's say over here
+ 
+
+ align:start position:0%
+chlorine is you know let's say over here
+it's got 3 S filled and it's got uh
+
+ align:start position:0%
+it's got 3 S filled and it's got uh
+ 
+
+ align:start position:0%
+it's got 3 S filled and it's got uh
+let's draw these you know here okay
+
+ align:start position:0%
+let's draw these you know here okay
+ 
+
+ align:start position:0%
+let's draw these you know here okay
+3 p and chlorine got seven electrons in
+
+ align:start position:0%
+3 p and chlorine got seven electrons in
+ 
+
+ align:start position:0%
+3 p and chlorine got seven electrons in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+3p do they do they all come together and
+
+ align:start position:0%
+3p do they do they all come together and
+ 
+
+ align:start position:0%
+3p do they do they all come together and
+formos no they can't because there's
+
+ align:start position:0%
+formos no they can't because there's
+ 
+
+ align:start position:0%
+formos no they can't because there's
+only one on this side right so this one
+
+ align:start position:0%
+only one on this side right so this one
+ 
+
+ align:start position:0%
+only one on this side right so this one
+orbital will form let me ah let me make
+
+ align:start position:0%
+orbital will form let me ah let me make
+ 
+
+ align:start position:0%
+orbital will form let me ah let me make
+myself enough space so I'm going to
+
+ align:start position:0%
+myself enough space so I'm going to
+ 
+
+ align:start position:0%
+myself enough space so I'm going to
+exaggerate this a little bit so this one
+
+ align:start position:0%
+exaggerate this a little bit so this one
+ 
+
+ align:start position:0%
+exaggerate this a little bit so this one
+orbital will will
+
+ align:start position:0%
+orbital will will
+ 
+
+ align:start position:0%
+orbital will will
+form a sigma Bond Sigma uh 3 p Sigma 3p
+
+ align:start position:0%
+form a sigma Bond Sigma uh 3 p Sigma 3p
+ 
+
+ align:start position:0%
+form a sigma Bond Sigma uh 3 p Sigma 3p
+bond this would be a sigma 3p star now
+
+ align:start position:0%
+bond this would be a sigma 3p star now
+ 
+
+ align:start position:0%
+bond this would be a sigma 3p star now
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+exactly what we've already done right
+
+ align:start position:0%
+exactly what we've already done right
+ 
+
+ align:start position:0%
+exactly what we've already done right
+the the sigma
+
+ align:start position:0%
+the the sigma
+ 
+
+ align:start position:0%
+the the sigma
+but but oh there's something a little
+
+ align:start position:0%
+but but oh there's something a little
+ 
+
+ align:start position:0%
+but but oh there's something a little
+interesting about this one right because
+
+ align:start position:0%
+interesting about this one right because
+ 
+
+ align:start position:0%
+interesting about this one right because
+it's an
+
+ align:start position:0%
+it's an
+ 
+
+ align:start position:0%
+it's an
+S it's an S but that's okay because the
+
+ align:start position:0%
+S it's an S but that's okay because the
+ 
+
+ align:start position:0%
+S it's an S but that's okay because the
+S can talk to a sigma P this we talking
+
+ align:start position:0%
+S can talk to a sigma P this we talking
+ 
+
+ align:start position:0%
+S can talk to a sigma P this we talking
+about this the S can talk to this that's
+
+ align:start position:0%
+about this the S can talk to this that's
+ 
+
+ align:start position:0%
+about this the S can talk to this that's
+okay cuz it's
+
+ align:start position:0%
+okay cuz it's
+ 
+
+ align:start position:0%
+okay cuz it's
+aligned right now but these guys don't
+
+ align:start position:0%
+aligned right now but these guys don't
+ 
+
+ align:start position:0%
+aligned right now but these guys don't
+have anyone to talk to they don't so
+
+ align:start position:0%
+have anyone to talk to they don't so
+ 
+
+ align:start position:0%
+have anyone to talk to they don't so
+they can't make their Pi orbitals they
+
+ align:start position:0%
+they can't make their Pi orbitals they
+ 
+
+ align:start position:0%
+they can't make their Pi orbitals they
+can't do that and so they just stay
+
+ align:start position:0%
+can't do that and so they just stay
+ 
+
+ align:start position:0%
+can't do that and so they just stay
+there these stay there exactly at the
+
+ align:start position:0%
+there these stay there exactly at the
+ 
+
+ align:start position:0%
+there these stay there exactly at the
+same place they're not doing anything
+
+ align:start position:0%
+same place they're not doing anything
+ 
+
+ align:start position:0%
+same place they're not doing anything
+different they're just hanging out those
+
+ align:start position:0%
+different they're just hanging out those
+ 
+
+ align:start position:0%
+different they're just hanging out those
+electrons are non-bonding so these are
+
+ align:start position:0%
+electrons are non-bonding so these are
+ 
+
+ align:start position:0%
+electrons are non-bonding so these are
+not these are not Pi orbitals
+
+ align:start position:0%
+not these are not Pi orbitals
+ 
+
+ align:start position:0%
+not these are not Pi orbitals
+Sigma and Pi are special names they
+
+ align:start position:0%
+Sigma and Pi are special names they
+ 
+
+ align:start position:0%
+Sigma and Pi are special names they
+refer to these orbitals that of the of
+
+ align:start position:0%
+refer to these orbitals that of the of
+ 
+
+ align:start position:0%
+refer to these orbitals that of the of
+the molecule that involve the lcao the
+
+ align:start position:0%
+the molecule that involve the lcao the
+ 
+
+ align:start position:0%
+the molecule that involve the lcao the
+linear combination of the atomic
+
+ align:start position:0%
+linear combination of the atomic
+ 
+
+ align:start position:0%
+linear combination of the atomic
+orbitals these do
+
+ align:start position:0%
+orbitals these do
+ 
+
+ align:start position:0%
+orbitals these do
+not n b n
+
+ align:start position:0%
+not n b n
+ 
+
+ align:start position:0%
+not n b n
+b that's what we'll call them just to be
+
+ align:start position:0%
+b that's what we'll call them just to be
+ 
+
+ align:start position:0%
+b that's what we'll call them just to be
+very clear just to be very clear now
+
+ align:start position:0%
+very clear just to be very clear now
+ 
+
+ align:start position:0%
+very clear just to be very clear now
+they're filled they're filled and they
+
+ align:start position:0%
+they're filled they're filled and they
+ 
+
+ align:start position:0%
+they're filled they're filled and they
+do not count count in the bond order by
+
+ align:start position:0%
+do not count count in the bond order by
+ 
+
+ align:start position:0%
+do not count count in the bond order by
+the way this is also a
+
+ align:start position:0%
+the way this is also a
+ 
+
+ align:start position:0%
+the way this is also a
+nonbonding
+
+ align:start position:0%
+nonbonding
+ 
+
+ align:start position:0%
+nonbonding
+orbital that's a non-bonding
+
+ align:start position:0%
+orbital that's a non-bonding
+ 
+
+ align:start position:0%
+orbital that's a non-bonding
+orbital nonbonding orbitals these are
+
+ align:start position:0%
+orbital nonbonding orbitals these are
+ 
+
+ align:start position:0%
+orbital nonbonding orbitals these are
+not going to count so in the bond
+
+ align:start position:0%
+not going to count so in the bond
+ 
+
+ align:start position:0%
+not going to count so in the bond
+order you only have you have 12 * 2 - 0
+
+ align:start position:0%
+order you only have you have 12 * 2 - 0
+ 
+
+ align:start position:0%
+order you only have you have 12 * 2 - 0
+equals 1 these do not participate in
+
+ align:start position:0%
+equals 1 these do not participate in
+ 
+
+ align:start position:0%
+equals 1 these do not participate in
+bonding I got to fill this two electrons
+
+ align:start position:0%
+bonding I got to fill this two electrons
+ 
+
+ align:start position:0%
+bonding I got to fill this two electrons
+are in that
+
+ align:start position:0%
+are in that
+ 
+
+ align:start position:0%
+are in that
+one okay so that's another example of
+
+ align:start position:0%
+one okay so that's another example of
+ 
+
+ align:start position:0%
+one okay so that's another example of
+something that happens in these Mo
+
+ align:start position:0%
+something that happens in these Mo
+ 
+
+ align:start position:0%
+something that happens in these Mo
+diagrams one of them brought too many
+
+ align:start position:0%
+diagrams one of them brought too many
+ 
+
+ align:start position:0%
+diagrams one of them brought too many
+electrons to the party and so there's no
+
+ align:start position:0%
+electrons to the party and so there's no
+ 
+
+ align:start position:0%
+electrons to the party and so there's no
+one to to to to talk to but it's okay
+
+ align:start position:0%
+one to to to to talk to but it's okay
+ 
+
+ align:start position:0%
+one to to to to talk to but it's okay
+they're just going to stay there and
+
+ align:start position:0%
+they're just going to stay there and
+ 
+
+ align:start position:0%
+they're just going to stay there and
+wait maybe something else will come
+
+ align:start position:0%
+wait maybe something else will come
+ 
+
+ align:start position:0%
+wait maybe something else will come
+along right okay now that is right there
+
+ align:start position:0%
+along right okay now that is right there
+ 
+
+ align:start position:0%
+along right okay now that is right there
+what I just drew look at that 2 p 2s and
+
+ align:start position:0%
+what I just drew look at that 2 p 2s and
+ 
+
+ align:start position:0%
+what I just drew look at that 2 p 2s and
+you get this thing right oh that's a
+
+ align:start position:0%
+you get this thing right oh that's a
+ 
+
+ align:start position:0%
+you get this thing right oh that's a
+beautiful molecular orbital between okay
+
+ align:start position:0%
+beautiful molecular orbital between okay
+ 
+
+ align:start position:0%
+beautiful molecular orbital between okay
+fine it was a 1s and a and a 3p but you
+
+ align:start position:0%
+fine it was a 1s and a and a 3p but you
+ 
+
+ align:start position:0%
+fine it was a 1s and a and a 3p but you
+get the point it was a p oriented along
+
+ align:start position:0%
+get the point it was a p oriented along
+ 
+
+ align:start position:0%
+get the point it was a p oriented along
+the axis with Sigma symmetry that means
+
+ align:start position:0%
+the axis with Sigma symmetry that means
+ 
+
+ align:start position:0%
+the axis with Sigma symmetry that means
+if I look along the axis sorry
+
+ align:start position:0%
+if I look along the axis sorry
+ 
+
+ align:start position:0%
+if I look along the axis sorry
+cylindrical symmetry Sigma means if I
+
+ align:start position:0%
+cylindrical symmetry Sigma means if I
+ 
+
+ align:start position:0%
+cylindrical symmetry Sigma means if I
+look around the axis everything's the
+
+ align:start position:0%
+look around the axis everything's the
+ 
+
+ align:start position:0%
+look around the axis everything's the
+same in a circle
+
+ align:start position:0%
+same in a circle
+ 
+
+ align:start position:0%
+same in a circle
+right right so but and so that's a nice
+
+ align:start position:0%
+right right so but and so that's a nice
+ 
+
+ align:start position:0%
+right right so but and so that's a nice
+Sigma orbital between two different
+
+ align:start position:0%
+Sigma orbital between two different
+ 
+
+ align:start position:0%
+Sigma orbital between two different
+atoms M Mo Theory but see the other
+
+ align:start position:0%
+atoms M Mo Theory but see the other
+ 
+
+ align:start position:0%
+atoms M Mo Theory but see the other
+thing that can happen that is something
+
+ align:start position:0%
+thing that can happen that is something
+ 
+
+ align:start position:0%
+thing that can happen that is something
+that I want you to know today
+
+ align:start position:0%
+that I want you to know today
+ 
+
+ align:start position:0%
+that I want you to know today
+is that orbitals on the exact same atom
+
+ align:start position:0%
+is that orbitals on the exact same atom
+ 
+
+ align:start position:0%
+is that orbitals on the exact same atom
+can also do this they can also do this
+
+ align:start position:0%
+can also do this they can also do this
+ 
+
+ align:start position:0%
+can also do this they can also do this
+they can
+
+ align:start position:0%
+they can
+ 
+
+ align:start position:0%
+they can
+combine to form a new
+
+ align:start position:0%
+combine to form a new
+ 
+
+ align:start position:0%
+combine to form a new
+orbital SP same atom forms an SP orbital
+
+ align:start position:0%
+orbital SP same atom forms an SP orbital
+ 
+
+ align:start position:0%
+orbital SP same atom forms an SP orbital
+it's called a hybrid orbital right so
+
+ align:start position:0%
+it's called a hybrid orbital right so
+ 
+
+ align:start position:0%
+it's called a hybrid orbital right so
+we're going to give a couple of examples
+
+ align:start position:0%
+we're going to give a couple of examples
+ 
+
+ align:start position:0%
+we're going to give a couple of examples
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+hybridization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hybridization and give a CLE couple
+
+ align:start position:0%
+hybridization and give a CLE couple
+ 
+
+ align:start position:0%
+hybridization and give a CLE couple
+examples then my why this matters so
+
+ align:start position:0%
+examples then my why this matters so
+ 
+
+ align:start position:0%
+examples then my why this matters so
+this is when two or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+AOS that are similar in
+
+ align:start position:0%
+AOS that are similar in
+ 
+
+ align:start position:0%
+AOS that are similar in
+energy similar they're not the same but
+
+ align:start position:0%
+energy similar they're not the same but
+ 
+
+ align:start position:0%
+energy similar they're not the same but
+they're close you you know you can't
+
+ align:start position:0%
+they're close you you know you can't
+ 
+
+ align:start position:0%
+they're close you you know you can't
+hybridize if one level's way up here and
+
+ align:start position:0%
+hybridize if one level's way up here and
+ 
+
+ align:start position:0%
+hybridize if one level's way up here and
+the other level's way down there but if
+
+ align:start position:0%
+the other level's way down there but if
+ 
+
+ align:start position:0%
+the other level's way down there but if
+they're close to
+
+ align:start position:0%
+they're close to
+ 
+
+ align:start position:0%
+they're close to
+s2p then those
+
+ align:start position:0%
+s2p then those
+ 
+
+ align:start position:0%
+s2p then those
+orbitals can combine
+
+ align:start position:0%
+orbitals can combine
+ 
+
+ align:start position:0%
+orbitals can combine
+and what they do is they combine to form
+
+ align:start position:0%
+and what they do is they combine to form
+ 
+
+ align:start position:0%
+and what they do is they combine to form
+and this is critical
+
+ align:start position:0%
+and this is critical
+ 
+
+ align:start position:0%
+and this is critical
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals properly oriented this is
+
+ align:start position:0%
+orbitals properly oriented this is
+ 
+
+ align:start position:0%
+orbitals properly oriented this is
+really important that's why I'm writing
+
+ align:start position:0%
+really important that's why I'm writing
+ 
+
+ align:start position:0%
+really important that's why I'm writing
+it all out properly not property
+
+ align:start position:0%
+it all out properly not property
+ 
+
+ align:start position:0%
+it all out properly not property
+properly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oriented to form bonds all this this is
+
+ align:start position:0%
+oriented to form bonds all this this is
+ 
+
+ align:start position:0%
+oriented to form bonds all this this is
+such a big a big deal to form
+
+ align:start position:0%
+such a big a big deal to form
+ 
+
+ align:start position:0%
+such a big a big deal to form
+bonds it's the last word there but I did
+
+ align:start position:0%
+bonds it's the last word there but I did
+ 
+
+ align:start position:0%
+bonds it's the last word there but I did
+it all caps to emphasize because that's
+
+ align:start position:0%
+it all caps to emphasize because that's
+ 
+
+ align:start position:0%
+it all caps to emphasize because that's
+what this is all about you see because
+
+ align:start position:0%
+what this is all about you see because
+ 
+
+ align:start position:0%
+what this is all about you see because
+now let's take an
+
+ align:start position:0%
+now let's take an
+ 
+
+ align:start position:0%
+now let's take an
+example I'm going to take an example of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methane who brings what to the party
+
+ align:start position:0%
+methane who brings what to the party
+ 
+
+ align:start position:0%
+methane who brings what to the party
+okay I got H I got four H's H 1 s h 1 s
+
+ align:start position:0%
+okay I got H I got four H's H 1 s h 1 s
+ 
+
+ align:start position:0%
+okay I got H I got four H's H 1 s h 1 s
+h 1 s okay this is definitely getting
+
+ align:start position:0%
+h 1 s okay this is definitely getting
+ 
+
+ align:start position:0%
+h 1 s okay this is definitely getting
+repetitive I'm H
+
+ align:start position:0%
+repetitive I'm H
+ 
+
+ align:start position:0%
+repetitive I'm H
+1s but I did it there they are and they
+
+ align:start position:0%
+1s but I did it there they are and they
+ 
+
+ align:start position:0%
+1s but I did it there they are and they
+come and they're like hey carbon what
+
+ align:start position:0%
+come and they're like hey carbon what
+ 
+
+ align:start position:0%
+come and they're like hey carbon what
+you got and the carbon is like okay hold
+
+ align:start position:0%
+you got and the carbon is like okay hold
+ 
+
+ align:start position:0%
+you got and the carbon is like okay hold
+up I got my 2s that's here and I got my
+
+ align:start position:0%
+up I got my 2s that's here and I got my
+ 
+
+ align:start position:0%
+up I got my 2s that's here and I got my
+all my two PS and what are we to do what
+
+ align:start position:0%
+all my two PS and what are we to do what
+ 
+
+ align:start position:0%
+all my two PS and what are we to do what
+are we to do how can these four
+
+ align:start position:0%
+are we to do how can these four
+ 
+
+ align:start position:0%
+are we to do how can these four
+hydrogens come and bond with the carbon
+
+ align:start position:0%
+hydrogens come and bond with the carbon
+ 
+
+ align:start position:0%
+hydrogens come and bond with the carbon
+given that it looks at least like the
+
+ align:start position:0%
+given that it looks at least like the
+ 
+
+ align:start position:0%
+given that it looks at least like the
+carbon isn't bringing the kind you know
+
+ align:start position:0%
+carbon isn't bringing the kind you know
+ 
+
+ align:start position:0%
+carbon isn't bringing the kind you know
+how is it going to do this and also and
+
+ align:start position:0%
+how is it going to do this and also and
+ 
+
+ align:start position:0%
+how is it going to do this and also and
+this is critical this is why I wrote it
+
+ align:start position:0%
+this is critical this is why I wrote it
+ 
+
+ align:start position:0%
+this is critical this is why I wrote it
+here properly oriented to form bonds you
+
+ align:start position:0%
+here properly oriented to form bonds you
+ 
+
+ align:start position:0%
+here properly oriented to form bonds you
+see because this Taps into what we
+
+ align:start position:0%
+see because this Taps into what we
+ 
+
+ align:start position:0%
+see because this Taps into what we
+learned with
+
+ align:start position:0%
+learned with
+ 
+
+ align:start position:0%
+learned with
+vasper it it does because Vesper says
+
+ align:start position:0%
+vasper it it does because Vesper says
+ 
+
+ align:start position:0%
+vasper it it does because Vesper says
+you got to not repel Oh no you're
+
+ align:start position:0%
+you got to not repel Oh no you're
+ 
+
+ align:start position:0%
+you got to not repel Oh no you're
+repelling but try to minimize it that's
+
+ align:start position:0%
+repelling but try to minimize it that's
+ 
+
+ align:start position:0%
+repelling but try to minimize it that's
+what's at the core of
+
+ align:start position:0%
+what's at the core of
+ 
+
+ align:start position:0%
+what's at the core of
+Vesper so what this system sees is a way
+
+ align:start position:0%
+Vesper so what this system sees is a way
+ 
+
+ align:start position:0%
+Vesper so what this system sees is a way
+out and by we out I mean a we to
+
+ align:start position:0%
+out and by we out I mean a we to
+ 
+
+ align:start position:0%
+out and by we out I mean a we to
+happiness and by a we to happiness I I
+
+ align:start position:0%
+happiness and by a we to happiness I I
+ 
+
+ align:start position:0%
+happiness and by a we to happiness I I
+mean a we to lower energy where all four
+
+ align:start position:0%
+mean a we to lower energy where all four
+ 
+
+ align:start position:0%
+mean a we to lower energy where all four
+of these can bond to the carbon atom if
+
+ align:start position:0%
+of these can bond to the carbon atom if
+ 
+
+ align:start position:0%
+of these can bond to the carbon atom if
+it has four same bonds if it had four
+
+ align:start position:0%
+it has four same bonds if it had four
+ 
+
+ align:start position:0%
+it has four same bonds if it had four
+same bonds then it can Orient them
+
+ align:start position:0%
+same bonds then it can Orient them
+ 
+
+ align:start position:0%
+same bonds then it can Orient them
+tetrahedrally and make Vesper happy
+
+ align:start position:0%
+tetrahedrally and make Vesper happy
+ 
+
+ align:start position:0%
+tetrahedrally and make Vesper happy
+minimize repulsions
+
+ align:start position:0%
+minimize repulsions
+ 
+
+ align:start position:0%
+minimize repulsions
+right and you get your methane molecule
+
+ align:start position:0%
+right and you get your methane molecule
+ 
+
+ align:start position:0%
+right and you get your methane molecule
+so what ends up happening is this carbon
+
+ align:start position:0%
+so what ends up happening is this carbon
+ 
+
+ align:start position:0%
+so what ends up happening is this carbon
+atom says hold up you4 hydrogen's you
+
+ align:start position:0%
+atom says hold up you4 hydrogen's you
+ 
+
+ align:start position:0%
+atom says hold up you4 hydrogen's you
+wait there I'm just going to go into the
+
+ align:start position:0%
+wait there I'm just going to go into the
+ 
+
+ align:start position:0%
+wait there I'm just going to go into the
+back and do a little
+
+ align:start position:0%
+back and do a little
+ 
+
+ align:start position:0%
+back and do a little
+reorganization and I'm going to come in
+
+ align:start position:0%
+reorganization and I'm going to come in
+ 
+
+ align:start position:0%
+reorganization and I'm going to come in
+it with I'm going to say well if I had
+
+ align:start position:0%
+it with I'm going to say well if I had
+ 
+
+ align:start position:0%
+it with I'm going to say well if I had
+if my carbon
+
+ align:start position:0%
+if my carbon
+ 
+
+ align:start position:0%
+if my carbon
+atom comes at comes at it with four
+
+ align:start position:0%
+atom comes at comes at it with four
+ 
+
+ align:start position:0%
+atom comes at comes at it with four
+equal orbitals that look like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are called
+
+ align:start position:0%
+those are called
+ 
+
+ align:start position:0%
+those are called
+sp3 because I took all three p orbitals
+
+ align:start position:0%
+sp3 because I took all three p orbitals
+ 
+
+ align:start position:0%
+sp3 because I took all three p orbitals
+and I mixed them up with my S orbital
+
+ align:start position:0%
+and I mixed them up with my S orbital
+ 
+
+ align:start position:0%
+and I mixed them up with my S orbital
+and I
+
+ align:start position:0%
+and I
+ 
+
+ align:start position:0%
+and I
+formed equivalent
+
+ align:start position:0%
+formed equivalent
+ 
+
+ align:start position:0%
+formed equivalent
+orbitals now carbon comes out of the
+
+ align:start position:0%
+orbitals now carbon comes out of the
+ 
+
+ align:start position:0%
+orbitals now carbon comes out of the
+back room and it's like hydrogens I'm
+
+ align:start position:0%
+back room and it's like hydrogens I'm
+ 
+
+ align:start position:0%
+back room and it's like hydrogens I'm
+ready I can make a a minimum energy V
+
+ align:start position:0%
+ready I can make a a minimum energy V
+ 
+
+ align:start position:0%
+ready I can make a a minimum energy V
+and and I can follow Vesper and we can
+
+ align:start position:0%
+and and I can follow Vesper and we can
+ 
+
+ align:start position:0%
+and and I can follow Vesper and we can
+have all have very very low energy
+
+ align:start position:0%
+have all have very very low energy
+ 
+
+ align:start position:0%
+have all have very very low energy
+compared to whatever else I could have
+
+ align:start position:0%
+compared to whatever else I could have
+ 
+
+ align:start position:0%
+compared to whatever else I could have
+done if I stuck like
+
+ align:start position:0%
+done if I stuck like
+ 
+
+ align:start position:0%
+done if I stuck like
+that what I'm really talking about okay
+
+ align:start position:0%
+that what I'm really talking about okay
+ 
+
+ align:start position:0%
+that what I'm really talking about okay
+you might know Carbon you know it
+
+ align:start position:0%
+you might know Carbon you know it
+ 
+
+ align:start position:0%
+you might know Carbon you know it
+doesn't go into the back room it doesn't
+
+ align:start position:0%
+doesn't go into the back room it doesn't
+ 
+
+ align:start position:0%
+doesn't go into the back room it doesn't
+but what is it doing it's nothing more
+
+ align:start position:0%
+but what is it doing it's nothing more
+ 
+
+ align:start position:0%
+but what is it doing it's nothing more
+than solving its fringer equation that's
+
+ align:start position:0%
+than solving its fringer equation that's
+ 
+
+ align:start position:0%
+than solving its fringer equation that's
+what this is all about you just changed
+
+ align:start position:0%
+what this is all about you just changed
+ 
+
+ align:start position:0%
+what this is all about you just changed
+the boundary conditions you and so what
+
+ align:start position:0%
+the boundary conditions you and so what
+ 
+
+ align:start position:0%
+the boundary conditions you and so what
+happened that's all hybridization is
+
+ align:start position:0%
+happened that's all hybridization is
+ 
+
+ align:start position:0%
+happened that's all hybridization is
+you're solving the Shar equation all the
+
+ align:start position:0%
+you're solving the Shar equation all the
+ 
+
+ align:start position:0%
+you're solving the Shar equation all the
+time we are always solving the sh
+
+ align:start position:0%
+time we are always solving the sh
+ 
+
+ align:start position:0%
+time we are always solving the sh
+equation all the time and in this case
+
+ align:start position:0%
+equation all the time and in this case
+ 
+
+ align:start position:0%
+equation all the time and in this case
+carbon said well how can I solve it and
+
+ align:start position:0%
+carbon said well how can I solve it and
+ 
+
+ align:start position:0%
+carbon said well how can I solve it and
+minimize my energy with the four
+
+ align:start position:0%
+minimize my energy with the four
+ 
+
+ align:start position:0%
+minimize my energy with the four
+hydrogens this gives you the lowest
+
+ align:start position:0%
+hydrogens this gives you the lowest
+ 
+
+ align:start position:0%
+hydrogens this gives you the lowest
+energy because
+
+ align:start position:0%
+energy because
+ 
+
+ align:start position:0%
+energy because
+now oh I got a movie now I can make
+
+ align:start position:0%
+now oh I got a movie now I can make
+ 
+
+ align:start position:0%
+now oh I got a movie now I can make
+those see so I have a I have a picture
+
+ align:start position:0%
+those see so I have a I have a picture
+ 
+
+ align:start position:0%
+those see so I have a I have a picture
+here s and those three and it says how
+
+ align:start position:0%
+here s and those three and it says how
+ 
+
+ align:start position:0%
+here s and those three and it says how
+can I do it and minimize repulsions this
+
+ align:start position:0%
+can I do it and minimize repulsions this
+ 
+
+ align:start position:0%
+can I do it and minimize repulsions this
+is how three equivalent four equivalent
+
+ align:start position:0%
+is how three equivalent four equivalent
+ 
+
+ align:start position:0%
+is how three equivalent four equivalent
+orbitals to make it sp3 and this is
+
+ align:start position:0%
+orbitals to make it sp3 and this is
+ 
+
+ align:start position:0%
+orbitals to make it sp3 and this is
+where I think a movie helps I'm going to
+
+ align:start position:0%
+where I think a movie helps I'm going to
+ 
+
+ align:start position:0%
+where I think a movie helps I'm going to
+play this it's like a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+longal is a shap converging at the
+
+ align:start position:0%
+longal is a shap converging at the
+ 
+
+ align:start position:0%
+longal is a shap converging at the
+nucleus there's the two s so there are
+
+ align:start position:0%
+nucleus there's the two s so there are
+ 
+
+ align:start position:0%
+nucleus there's the two s so there are
+the three 2p orbitals however when
+
+ align:start position:0%
+the three 2p orbitals however when
+ 
+
+ align:start position:0%
+the three 2p orbitals however when
+hybridization occurs the S and P
+
+ align:start position:0%
+hybridization occurs the S and P
+ 
+
+ align:start position:0%
+hybridization occurs the S and P
+orbitals cease to exist they don't cease
+
+ align:start position:0%
+orbitals cease to exist they don't cease
+ 
+
+ align:start position:0%
+orbitals cease to exist they don't cease
+to exist that they just didn't ex it's a
+
+ align:start position:0%
+to exist that they just didn't ex it's a
+ 
+
+ align:start position:0%
+to exist that they just didn't ex it's a
+new boundary condition you're solving
+
+ align:start position:0%
+new boundary condition you're solving
+ 
+
+ align:start position:0%
+new boundary condition you're solving
+the equation right so just to keep that
+
+ align:start position:0%
+the equation right so just to keep that
+ 
+
+ align:start position:0%
+the equation right so just to keep that
+straight right and the two sp3 orbitals
+
+ align:start position:0%
+straight right and the two sp3 orbitals
+ 
+
+ align:start position:0%
+straight right and the two sp3 orbitals
+have an entire different shape that's
+
+ align:start position:0%
+have an entire different shape that's
+ 
+
+ align:start position:0%
+have an entire different shape that's
+true we can see that orbital
+
+ align:start position:0%
+true we can see that orbital
+ 
+
+ align:start position:0%
+true we can see that orbital
+hybridization explains the vcpr
+
+ align:start position:0%
+hybridization explains the vcpr
+ 
+
+ align:start position:0%
+hybridization explains the vcpr
+placement of carbon's four veence
+
+ align:start position:0%
+placement of carbon's four veence
+ 
+
+ align:start position:0%
+placement of carbon's four veence
+electrons since all four 2sp3 orbitals
+
+ align:start position:0%
+electrons since all four 2sp3 orbitals
+ 
+
+ align:start position:0%
+electrons since all four 2sp3 orbitals
+are equivalent each 2sp3 orbital repels
+
+ align:start position:0%
+are equivalent each 2sp3 orbital repels
+ 
+
+ align:start position:0%
+are equivalent each 2sp3 orbital repels
+the others with equal force resulting in
+
+ align:start position:0%
+the others with equal force resulting in
+ 
+
+ align:start position:0%
+the others with equal force resulting in
+identical Bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angles the carbon atom only hybridizes
+
+ align:start position:0%
+angles the carbon atom only hybridizes
+ 
+
+ align:start position:0%
+angles the carbon atom only hybridizes
+when it is in a bonding situation here
+
+ align:start position:0%
+when it is in a bonding situation here
+ 
+
+ align:start position:0%
+when it is in a bonding situation here
+four hydrogen atoms bond to carbon by
+
+ align:start position:0%
+four hydrogen atoms bond to carbon by
+ 
+
+ align:start position:0%
+four hydrogen atoms bond to carbon by
+overlapping their or orbitals with
+
+ align:start position:0%
+overlapping their or orbitals with
+ 
+
+ align:start position:0%
+overlapping their or orbitals with
+carbon's hybrid
+
+ align:start position:0%
+carbon's hybrid
+ 
+
+ align:start position:0%
+carbon's hybrid
+orbitals so what would be the reason for
+
+ align:start position:0%
+orbitals so what would be the reason for
+ 
+
+ align:start position:0%
+orbitals so what would be the reason for
+this if we go back and see that both
+
+ align:start position:0%
+this if we go back and see that both
+ 
+
+ align:start position:0%
+this if we go back and see that both
+carbon and hydrogen have unpaired
+
+ align:start position:0%
+carbon and hydrogen have unpaired
+ 
+
+ align:start position:0%
+carbon and hydrogen have unpaired
+electrons the overlap allows the
+
+ align:start position:0%
+electrons the overlap allows the
+ 
+
+ align:start position:0%
+electrons the overlap allows the
+electrons to pair and thus go to a lower
+
+ align:start position:0%
+electrons to pair and thus go to a lower
+ 
+
+ align:start position:0%
+electrons to pair and thus go to a lower
+potential energy oh that's such a
+
+ align:start position:0%
+potential energy oh that's such a
+ 
+
+ align:start position:0%
+potential energy oh that's such a
+beautiful place to stop lower potential
+
+ align:start position:0%
+beautiful place to stop lower potential
+ 
+
+ align:start position:0%
+beautiful place to stop lower potential
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+happier that's what this is all about
+
+ align:start position:0%
+happier that's what this is all about
+ 
+
+ align:start position:0%
+happier that's what this is all about
+okay so I I you know like I said you can
+
+ align:start position:0%
+okay so I I you know like I said you can
+ 
+
+ align:start position:0%
+okay so I I you know like I said you can
+see now the difference right if you just
+
+ align:start position:0%
+see now the difference right if you just
+ 
+
+ align:start position:0%
+see now the difference right if you just
+watch is one minute long and I think it
+
+ align:start position:0%
+watch is one minute long and I think it
+ 
+
+ align:start position:0%
+watch is one minute long and I think it
+really brings it to life so if you if
+
+ align:start position:0%
+really brings it to life so if you if
+ 
+
+ align:start position:0%
+really brings it to life so if you if
+you're again want to see this a little
+
+ align:start position:0%
+you're again want to see this a little
+ 
+
+ align:start position:0%
+you're again want to see this a little
+bit more conceptually these movies are
+
+ align:start position:0%
+bit more conceptually these movies are
+ 
+
+ align:start position:0%
+bit more conceptually these movies are
+good I have one more uh movie I'll show
+
+ align:start position:0%
+good I have one more uh movie I'll show
+ 
+
+ align:start position:0%
+good I have one more uh movie I'll show
+you that's like a minute long um okay
+
+ align:start position:0%
+you that's like a minute long um okay
+ 
+
+ align:start position:0%
+you that's like a minute long um okay
+now the thing is so what we just did is
+
+ align:start position:0%
+now the thing is so what we just did is
+ 
+
+ align:start position:0%
+now the thing is so what we just did is
+we did carbon hybridizes to sp3 it's
+
+ align:start position:0%
+we did carbon hybridizes to sp3 it's
+ 
+
+ align:start position:0%
+we did carbon hybridizes to sp3 it's
+called sp3 because you're bringing three
+
+ align:start position:0%
+called sp3 because you're bringing three
+ 
+
+ align:start position:0%
+called sp3 because you're bringing three
+p orbitals and mixing them with s to
+
+ align:start position:0%
+p orbitals and mixing them with s to
+ 
+
+ align:start position:0%
+p orbitals and mixing them with s to
+form four and that allowed it to do this
+
+ align:start position:0%
+form four and that allowed it to do this
+ 
+
+ align:start position:0%
+form four and that allowed it to do this
+but you see if I had ethane which is
+
+ align:start position:0%
+but you see if I had ethane which is
+ 
+
+ align:start position:0%
+but you see if I had ethane which is
+c2h6 it's the same thing now because
+
+ align:start position:0%
+c2h6 it's the same thing now because
+ 
+
+ align:start position:0%
+c2h6 it's the same thing now because
+basically what's happening a carbon atom
+
+ align:start position:0%
+basically what's happening a carbon atom
+ 
+
+ align:start position:0%
+basically what's happening a carbon atom
+comes into the system of ethane and it
+
+ align:start position:0%
+comes into the system of ethane and it
+ 
+
+ align:start position:0%
+comes into the system of ethane and it
+says I need four bonds that are kind of
+
+ align:start position:0%
+says I need four bonds that are kind of
+ 
+
+ align:start position:0%
+says I need four bonds that are kind of
+you know equivalent is all right I got
+
+ align:start position:0%
+you know equivalent is all right I got
+ 
+
+ align:start position:0%
+you know equivalent is all right I got
+to give one to each hydrogen and I got
+
+ align:start position:0%
+to give one to each hydrogen and I got
+ 
+
+ align:start position:0%
+to give one to each hydrogen and I got
+to give one to that other carbon over
+
+ align:start position:0%
+to give one to that other carbon over
+ 
+
+ align:start position:0%
+to give one to that other carbon over
+there and by doing that it can minimize
+
+ align:start position:0%
+there and by doing that it can minimize
+ 
+
+ align:start position:0%
+there and by doing that it can minimize
+its energy it can minimize repulsions it
+
+ align:start position:0%
+its energy it can minimize repulsions it
+ 
+
+ align:start position:0%
+its energy it can minimize repulsions it
+can be the happiest molecule it can be
+
+ align:start position:0%
+can be the happiest molecule it can be
+ 
+
+ align:start position:0%
+can be the happiest molecule it can be
+but to do that carbon must have these
+
+ align:start position:0%
+but to do that carbon must have these
+ 
+
+ align:start position:0%
+but to do that carbon must have these
+four equivalent Sigma like bonds it must
+
+ align:start position:0%
+four equivalent Sigma like bonds it must
+ 
+
+ align:start position:0%
+four equivalent Sigma like bonds it must
+be able to form those four equivalent so
+
+ align:start position:0%
+be able to form those four equivalent so
+ 
+
+ align:start position:0%
+be able to form those four equivalent so
+so that's very similar to methane except
+
+ align:start position:0%
+so that's very similar to methane except
+ 
+
+ align:start position:0%
+so that's very similar to methane except
+that in this so also ethane will be sp3
+
+ align:start position:0%
+that in this so also ethane will be sp3
+ 
+
+ align:start position:0%
+that in this so also ethane will be sp3
+hybridized it will have sp3 hybridized
+
+ align:start position:0%
+hybridized it will have sp3 hybridized
+ 
+
+ align:start position:0%
+hybridized it will have sp3 hybridized
+orbitals but then and you know it's
+
+ align:start position:0%
+orbitals but then and you know it's
+ 
+
+ align:start position:0%
+orbitals but then and you know it's
+coming right so ethane has C2 H6 but
+
+ align:start position:0%
+coming right so ethane has C2 H6 but
+ 
+
+ align:start position:0%
+coming right so ethane has C2 H6 but
+what if
+
+ align:start position:0%
+what if
+ 
+
+ align:start position:0%
+what if
+now I've got ethylene I think I have
+
+ align:start position:0%
+now I've got ethylene I think I have
+ 
+
+ align:start position:0%
+now I've got ethylene I think I have
+maybe I have a picture of it do I have a
+
+ align:start position:0%
+maybe I have a picture of it do I have a
+ 
+
+ align:start position:0%
+maybe I have a picture of it do I have a
+picture of it yeah oh there it is
+
+ align:start position:0%
+picture of it yeah oh there it is
+ 
+
+ align:start position:0%
+picture of it yeah oh there it is
+ethylene ethylene is used this this tiny
+
+ align:start position:0%
+ethylene ethylene is used this this tiny
+ 
+
+ align:start position:0%
+ethylene ethylene is used this this tiny
+molecule with two carbons and four
+
+ align:start position:0%
+molecule with two carbons and four
+ 
+
+ align:start position:0%
+molecule with two carbons and four
+hydrogens instead of six this is used in
+
+ align:start position:0%
+hydrogens instead of six this is used in
+ 
+
+ align:start position:0%
+hydrogens instead of six this is used in
+so many applications I can't possibly
+
+ align:start position:0%
+so many applications I can't possibly
+ 
+
+ align:start position:0%
+so many applications I can't possibly
+list them it polyethylene is a polymer
+
+ align:start position:0%
+list them it polyethylene is a polymer
+ 
+
+ align:start position:0%
+list them it polyethylene is a polymer
+made out of this as a base we will
+
+ align:start position:0%
+made out of this as a base we will
+ 
+
+ align:start position:0%
+made out of this as a base we will
+polymerize this a little bit later in
+
+ align:start position:0%
+polymerize this a little bit later in
+ 
+
+ align:start position:0%
+polymerize this a little bit later in
+the semester when we talk about polymers
+
+ align:start position:0%
+the semester when we talk about polymers
+ 
+
+ align:start position:0%
+the semester when we talk about polymers
+it's also used in the back of your
+
+ align:start position:0%
+it's also used in the back of your
+ 
+
+ align:start position:0%
+it's also used in the back of your
+supermarket in case you didn't know that
+
+ align:start position:0%
+supermarket in case you didn't know that
+ 
+
+ align:start position:0%
+supermarket in case you didn't know that
+very soon actually kind of almost nowish
+
+ align:start position:0%
+very soon actually kind of almost nowish
+ 
+
+ align:start position:0%
+very soon actually kind of almost nowish
+most of the fruit we get will be super
+
+ align:start position:0%
+most of the fruit we get will be super
+ 
+
+ align:start position:0%
+most of the fruit we get will be super
+green when it gets here and then they
+
+ align:start position:0%
+green when it gets here and then they
+ 
+
+ align:start position:0%
+green when it gets here and then they
+use ethylene to actually induce uh uh
+
+ align:start position:0%
+use ethylene to actually induce uh uh
+ 
+
+ align:start position:0%
+use ethylene to actually induce uh uh
+sadly the ripeness doesn't taste as good
+
+ align:start position:0%
+sadly the ripeness doesn't taste as good
+ 
+
+ align:start position:0%
+sadly the ripeness doesn't taste as good
+but anyway okay now but for
+
+ align:start position:0%
+but anyway okay now but for
+ 
+
+ align:start position:0%
+but anyway okay now but for
+ethylene you've got a different
+
+ align:start position:0%
+ethylene you've got a different
+ 
+
+ align:start position:0%
+ethylene you've got a different
+situation because for ethylene each
+
+ align:start position:0%
+situation because for ethylene each
+ 
+
+ align:start position:0%
+situation because for ethylene each
+carbon atom needs three bonds
+
+ align:start position:0%
+carbon atom needs three bonds
+ 
+
+ align:start position:0%
+carbon atom needs three bonds
+each carbon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atom needs three equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonds and it can do that too so so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c2h4 each carbon atom needs three
+
+ align:start position:0%
+c2h4 each carbon atom needs three
+ 
+
+ align:start position:0%
+c2h4 each carbon atom needs three
+equivalent bonds and it can do that if
+
+ align:start position:0%
+equivalent bonds and it can do that if
+ 
+
+ align:start position:0%
+equivalent bonds and it can do that if
+it hybridizes in the SP2 hybridization
+
+ align:start position:0%
+it hybridizes in the SP2 hybridization
+ 
+
+ align:start position:0%
+it hybridizes in the SP2 hybridization
+so let's draw that right so these are
+
+ align:start position:0%
+so let's draw that right so these are
+ 
+
+ align:start position:0%
+so let's draw that right so these are
+the original orbitals of carbon and they
+
+ align:start position:0%
+the original orbitals of carbon and they
+ 
+
+ align:start position:0%
+the original orbitals of carbon and they
+will go
+
+ align:start position:0%
+will go
+ 
+
+ align:start position:0%
+will go
+to three SP2
+
+ align:start position:0%
+to three SP2
+ 
+
+ align:start position:0%
+to three SP2
+orbitals notice I can put one electron
+
+ align:start position:0%
+orbitals notice I can put one electron
+ 
+
+ align:start position:0%
+orbitals notice I can put one electron
+in each ready for action ready for
+
+ align:start position:0%
+in each ready for action ready for
+ 
+
+ align:start position:0%
+in each ready for action ready for
+bonding one electron in each of these
+
+ align:start position:0%
+bonding one electron in each of these
+ 
+
+ align:start position:0%
+bonding one electron in each of these
+equivalent hybrid orbitals SP2 and I've
+
+ align:start position:0%
+equivalent hybrid orbitals SP2 and I've
+ 
+
+ align:start position:0%
+equivalent hybrid orbitals SP2 and I've
+got one left over oh ho oh one left
+
+ align:start position:0%
+got one left over oh ho oh one left
+ 
+
+ align:start position:0%
+got one left over oh ho oh one left
+over but you the one left over is a p
+
+ align:start position:0%
+over but you the one left over is a p
+ 
+
+ align:start position:0%
+over but you the one left over is a p
+orbital that didn't get in on the
+
+ align:start position:0%
+orbital that didn't get in on the
+ 
+
+ align:start position:0%
+orbital that didn't get in on the
+hybridization but that's
+
+ align:start position:0%
+hybridization but that's
+ 
+
+ align:start position:0%
+hybridization but that's
+okay that's okay these are P right so
+
+ align:start position:0%
+okay that's okay these are P right so
+ 
+
+ align:start position:0%
+okay that's okay these are P right so
+this is s and this is p 2s 2 2 p and
+
+ align:start position:0%
+this is s and this is p 2s 2 2 p and
+ 
+
+ align:start position:0%
+this is s and this is p 2s 2 2 p and
+that's a p orbital right there those are
+
+ align:start position:0%
+that's a p orbital right there those are
+ 
+
+ align:start position:0%
+that's a p orbital right there those are
+my hybrids and that's a 2p orbital um
+
+ align:start position:0%
+my hybrids and that's a 2p orbital um
+ 
+
+ align:start position:0%
+my hybrids and that's a 2p orbital um
+this is there's another 2p orbital on
+
+ align:start position:0%
+this is there's another 2p orbital on
+ 
+
+ align:start position:0%
+this is there's another 2p orbital on
+the other carbon also got left out now I
+
+ align:start position:0%
+the other carbon also got left out now I
+ 
+
+ align:start position:0%
+the other carbon also got left out now I
+only needed three because you see I form
+
+ align:start position:0%
+only needed three because you see I form
+ 
+
+ align:start position:0%
+only needed three because you see I form
+this nice spatially maximized to
+
+ align:start position:0%
+this nice spatially maximized to
+ 
+
+ align:start position:0%
+this nice spatially maximized to
+minimize repulsion right separation
+
+ align:start position:0%
+minimize repulsion right separation
+ 
+
+ align:start position:0%
+minimize repulsion right separation
+maximized to minimize repulsion so it's
+
+ align:start position:0%
+maximized to minimize repulsion so it's
+ 
+
+ align:start position:0%
+maximized to minimize repulsion so it's
+a planer oh but it's planer for another
+
+ align:start position:0%
+a planer oh but it's planer for another
+ 
+
+ align:start position:0%
+a planer oh but it's planer for another
+reason because each of these carbon
+
+ align:start position:0%
+reason because each of these carbon
+ 
+
+ align:start position:0%
+reason because each of these carbon
+atoms has a p orbital and we know that
+
+ align:start position:0%
+atoms has a p orbital and we know that
+ 
+
+ align:start position:0%
+atoms has a p orbital and we know that
+2p orbitals can form a pi Bond right and
+
+ align:start position:0%
+2p orbitals can form a pi Bond right and
+ 
+
+ align:start position:0%
+2p orbitals can form a pi Bond right and
+I have a picture of that that's exactly
+
+ align:start position:0%
+I have a picture of that that's exactly
+ 
+
+ align:start position:0%
+I have a picture of that that's exactly
+what they do so so this is the
+
+ align:start position:0%
+what they do so so this is the
+ 
+
+ align:start position:0%
+what they do so so this is the
+sigma the hybrid orbitals are Sigma
+
+ align:start position:0%
+sigma the hybrid orbitals are Sigma
+ 
+
+ align:start position:0%
+sigma the hybrid orbitals are Sigma
+right because they're along the axis and
+
+ align:start position:0%
+right because they're along the axis and
+ 
+
+ align:start position:0%
+right because they're along the axis and
+look at them if I look down this axis I
+
+ align:start position:0%
+look at them if I look down this axis I
+ 
+
+ align:start position:0%
+look at them if I look down this axis I
+can draw a circle and there's full
+
+ align:start position:0%
+can draw a circle and there's full
+ 
+
+ align:start position:0%
+can draw a circle and there's full
+cylindrical symmetry right but I've got
+
+ align:start position:0%
+cylindrical symmetry right but I've got
+ 
+
+ align:start position:0%
+cylindrical symmetry right but I've got
+this left over p orbital here on each
+
+ align:start position:0%
+this left over p orbital here on each
+ 
+
+ align:start position:0%
+this left over p orbital here on each
+carbon atom that's that one there and
+
+ align:start position:0%
+carbon atom that's that one there and
+ 
+
+ align:start position:0%
+carbon atom that's that one there and
+and I didn't need it to do this but it's
+
+ align:start position:0%
+and I didn't need it to do this but it's
+ 
+
+ align:start position:0%
+and I didn't need it to do this but it's
+still there and so it forms a bond it
+
+ align:start position:0%
+still there and so it forms a bond it
+ 
+
+ align:start position:0%
+still there and so it forms a bond it
+forms a bond right it forms a pi
+
+ align:start position:0%
+forms a bond right it forms a pi
+ 
+
+ align:start position:0%
+forms a bond right it forms a pi
+Bond so that P
+
+ align:start position:0%
+Bond so that P
+ 
+
+ align:start position:0%
+Bond so that P
+with the p from the other one forms a pi
+
+ align:start position:0%
+with the p from the other one forms a pi
+ 
+
+ align:start position:0%
+with the p from the other one forms a pi
+and a pi Star right in Theos and you you
+
+ align:start position:0%
+and a pi Star right in Theos and you you
+ 
+
+ align:start position:0%
+and a pi Star right in Theos and you you
+occupy the pi with the two electrons and
+
+ align:start position:0%
+occupy the pi with the two electrons and
+ 
+
+ align:start position:0%
+occupy the pi with the two electrons and
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+bond so so in this you've got uh you've
+
+ align:start position:0%
+bond so so in this you've got uh you've
+ 
+
+ align:start position:0%
+bond so so in this you've got uh you've
+got a bond from this uh that's above or
+
+ align:start position:0%
+got a bond from this uh that's above or
+ 
+
+ align:start position:0%
+got a bond from this uh that's above or
+below in in you know in this orientation
+
+ align:start position:0%
+below in in you know in this orientation
+ 
+
+ align:start position:0%
+below in in you know in this orientation
+it's above or below the plane and you've
+
+ align:start position:0%
+it's above or below the plane and you've
+ 
+
+ align:start position:0%
+it's above or below the plane and you've
+got a bond from this so you've got a
+
+ align:start position:0%
+got a bond from this so you've got a
+ 
+
+ align:start position:0%
+got a bond from this so you've got a
+double bond that's exactly what we know
+
+ align:start position:0%
+double bond that's exactly what we know
+ 
+
+ align:start position:0%
+double bond that's exactly what we know
+already but we know so much more now we
+
+ align:start position:0%
+already but we know so much more now we
+ 
+
+ align:start position:0%
+already but we know so much more now we
+know so much more because because now we
+
+ align:start position:0%
+know so much more because because now we
+ 
+
+ align:start position:0%
+know so much more because because now we
+know that it's not just two you know two
+
+ align:start position:0%
+know that it's not just two you know two
+ 
+
+ align:start position:0%
+know that it's not just two you know two
+bonds and four electrons we know that
+
+ align:start position:0%
+bonds and four electrons we know that
+ 
+
+ align:start position:0%
+bonds and four electrons we know that
+they have shape to them we know that
+
+ align:start position:0%
+they have shape to them we know that
+ 
+
+ align:start position:0%
+they have shape to them we know that
+they have structure to them and we know
+
+ align:start position:0%
+they have structure to them and we know
+ 
+
+ align:start position:0%
+they have structure to them and we know
+that those bonds are
+
+ align:start position:0%
+that those bonds are
+ 
+
+ align:start position:0%
+that those bonds are
+different these are Pi bonds and that's
+
+ align:start position:0%
+different these are Pi bonds and that's
+ 
+
+ align:start position:0%
+different these are Pi bonds and that's
+a sigma Bond right and you also know why
+
+ align:start position:0%
+a sigma Bond right and you also know why
+ 
+
+ align:start position:0%
+a sigma Bond right and you also know why
+this molecule stays planer because if I
+
+ align:start position:0%
+this molecule stays planer because if I
+ 
+
+ align:start position:0%
+this molecule stays planer because if I
+try to twist it then those P orbitals
+
+ align:start position:0%
+try to twist it then those P orbitals
+ 
+
+ align:start position:0%
+try to twist it then those P orbitals
+won't align right it's like a little
+
+ align:start position:0%
+won't align right it's like a little
+ 
+
+ align:start position:0%
+won't align right it's like a little
+spring if I if I try to twist it it's
+
+ align:start position:0%
+spring if I if I try to twist it it's
+ 
+
+ align:start position:0%
+spring if I if I try to twist it it's
+going to go right back because it's
+
+ align:start position:0%
+going to go right back because it's
+ 
+
+ align:start position:0%
+going to go right back because it's
+minimum in energy is when these things
+
+ align:start position:0%
+minimum in energy is when these things
+ 
+
+ align:start position:0%
+minimum in energy is when these things
+can maximize their overlap right so
+
+ align:start position:0%
+can maximize their overlap right so
+ 
+
+ align:start position:0%
+can maximize their overlap right so
+that's going to stay
+
+ align:start position:0%
+that's going to stay
+ 
+
+ align:start position:0%
+that's going to stay
+planer
+
+ align:start position:0%
+planer
+ 
+
+ align:start position:0%
+planer
+okay now and so so for this case you've
+
+ align:start position:0%
+okay now and so so for this case you've
+ 
+
+ align:start position:0%
+okay now and so so for this case you've
+got a double
+
+ align:start position:0%
+got a double
+ 
+
+ align:start position:0%
+got a double
+bond so this is
+
+ align:start position:0%
+bond so this is
+ 
+
+ align:start position:0%
+bond so this is
+uh double bond and I think I have a
+
+ align:start position:0%
+uh double bond and I think I have a
+ 
+
+ align:start position:0%
+uh double bond and I think I have a
+little carbon carbon double bond and I
+
+ align:start position:0%
+little carbon carbon double bond and I
+ 
+
+ align:start position:0%
+little carbon carbon double bond and I
+think I've got a video to show this cuz
+
+ align:start position:0%
+think I've got a video to show this cuz
+ 
+
+ align:start position:0%
+think I've got a video to show this cuz
+I I this is another case where you know
+
+ align:start position:0%
+I I this is another case where you know
+ 
+
+ align:start position:0%
+I I this is another case where you know
+again I just want to make sure you guys
+
+ align:start position:0%
+again I just want to make sure you guys
+ 
+
+ align:start position:0%
+again I just want to make sure you guys
+get the intuition here and I thought
+
+ align:start position:0%
+get the intuition here and I thought
+ 
+
+ align:start position:0%
+get the intuition here and I thought
+this was a pretty cool animation of SP2
+
+ align:start position:0%
+this was a pretty cool animation of SP2
+ 
+
+ align:start position:0%
+this was a pretty cool animation of SP2
+so I'll play it for a minute b 1 2s and
+
+ align:start position:0%
+so I'll play it for a minute b 1 2s and
+ 
+
+ align:start position:0%
+so I'll play it for a minute b 1 2s and
+two of the 2p orbitals hybridize
+
+ align:start position:0%
+two of the 2p orbitals hybridize
+ 
+
+ align:start position:0%
+two of the 2p orbitals hybridize
+consequently this hybridization is
+
+ align:start position:0%
+consequently this hybridization is
+ 
+
+ align:start position:0%
+consequently this hybridization is
+termed as SP2 hybridization look at that
+
+ align:start position:0%
+termed as SP2 hybridization look at that
+ 
+
+ align:start position:0%
+termed as SP2 hybridization look at that
+the hybridization leads to the formation
+
+ align:start position:0%
+the hybridization leads to the formation
+ 
+
+ align:start position:0%
+the hybridization leads to the formation
+of three equ energic SP2 hybrid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals as you can see each SP2 hybrid
+
+ align:start position:0%
+orbitals as you can see each SP2 hybrid
+ 
+
+ align:start position:0%
+orbitals as you can see each SP2 hybrid
+orbital is bilobed one loob bigger than
+
+ align:start position:0%
+orbital is bilobed one loob bigger than
+ 
+
+ align:start position:0%
+orbital is bilobed one loob bigger than
+the other the half filled p orbital
+
+ align:start position:0%
+the other the half filled p orbital
+ 
+
+ align:start position:0%
+the other the half filled p orbital
+which was not involved in
+
+ align:start position:0%
+which was not involved in
+ 
+
+ align:start position:0%
+which was not involved in
+hybridization lies at right angles to
+
+ align:start position:0%
+hybridization lies at right angles to
+ 
+
+ align:start position:0%
+hybridization lies at right angles to
+the plane of the equilateral
+
+ align:start position:0%
+the plane of the equilateral
+ 
+
+ align:start position:0%
+the plane of the equilateral
+triangle now let us understand how this
+
+ align:start position:0%
+triangle now let us understand how this
+ 
+
+ align:start position:0%
+triangle now let us understand how this
+hybridized state results in the
+
+ align:start position:0%
+hybridized state results in the
+ 
+
+ align:start position:0%
+hybridized state results in the
+formation of a double
+
+ align:start position:0%
+formation of a double
+ 
+
+ align:start position:0%
+formation of a double
+bond for this imagine a similar SP2
+
+ align:start position:0%
+bond for this imagine a similar SP2
+ 
+
+ align:start position:0%
+bond for this imagine a similar SP2
+hybridized carbon atom approaching this
+
+ align:start position:0%
+hybridized carbon atom approaching this
+ 
+
+ align:start position:0%
+hybridized carbon atom approaching this
+carbon atom
+
+ align:start position:0%
+carbon atom
+ 
+
+ align:start position:0%
+carbon atom
+as these atoms come closer an orbital
+
+ align:start position:0%
+as these atoms come closer an orbital
+ 
+
+ align:start position:0%
+as these atoms come closer an orbital
+overlap takes place along the inter
+
+ align:start position:0%
+overlap takes place along the inter
+ 
+
+ align:start position:0%
+overlap takes place along the inter
+nuclear axis this bond is called a sigma
+
+ align:start position:0%
+nuclear axis this bond is called a sigma
+ 
+
+ align:start position:0%
+nuclear axis this bond is called a sigma
+Bond at this stage the unhybridized P
+
+ align:start position:0%
+Bond at this stage the unhybridized P
+ 
+
+ align:start position:0%
+Bond at this stage the unhybridized P
+orbitals which lie above and below the
+
+ align:start position:0%
+orbitals which lie above and below the
+ 
+
+ align:start position:0%
+orbitals which lie above and below the
+plane of the sigma Bond also come very
+
+ align:start position:0%
+plane of the sigma Bond also come very
+ 
+
+ align:start position:0%
+plane of the sigma Bond also come very
+close to each other and overlap
+
+ align:start position:0%
+close to each other and overlap
+ 
+
+ align:start position:0%
+close to each other and overlap
+laterally resulting in the formation of
+
+ align:start position:0%
+laterally resulting in the formation of
+ 
+
+ align:start position:0%
+laterally resulting in the formation of
+a pi bond between the two carbon atoms
+
+ align:start position:0%
+a pi bond between the two carbon atoms
+ 
+
+ align:start position:0%
+a pi bond between the two carbon atoms
+all right okay so the
+
+ align:start position:0%
+all right okay so the
+ 
+
+ align:start position:0%
+all right okay so the
+thought about it I watched that movie of
+
+ align:start position:0%
+thought about it I watched that movie of
+ 
+
+ align:start position:0%
+thought about it I watched that movie of
+course many times over the weekend and I
+
+ align:start position:0%
+course many times over the weekend and I
+ 
+
+ align:start position:0%
+course many times over the weekend and I
+thought about can I animate you know the
+
+ align:start position:0%
+thought about can I animate you know the
+ 
+
+ align:start position:0%
+thought about can I animate you know the
+electrons like that and do the and I I
+
+ align:start position:0%
+electrons like that and do the and I I
+ 
+
+ align:start position:0%
+electrons like that and do the and I I
+think I could but I don't know that it
+
+ align:start position:0%
+think I could but I don't know that it
+ 
+
+ align:start position:0%
+think I could but I don't know that it
+would be a good use of our time so I
+
+ align:start position:0%
+would be a good use of our time so I
+ 
+
+ align:start position:0%
+would be a good use of our time so I
+thought that they did a pretty good job
+
+ align:start position:0%
+thought that they did a pretty good job
+ 
+
+ align:start position:0%
+thought that they did a pretty good job
+of of bringing it to life now this is a
+
+ align:start position:0%
+of of bringing it to life now this is a
+ 
+
+ align:start position:0%
+of of bringing it to life now this is a
+great time for me uh to tell you about
+
+ align:start position:0%
+great time for me uh to tell you about
+ 
+
+ align:start position:0%
+great time for me uh to tell you about
+my why this matters and of course the
+
+ align:start position:0%
+my why this matters and of course the
+ 
+
+ align:start position:0%
+my why this matters and of course the
+SP2 carbon atom matters because of
+
+ align:start position:0%
+SP2 carbon atom matters because of
+ 
+
+ align:start position:0%
+SP2 carbon atom matters because of
+drinking
+
+ align:start position:0%
+drinking
+ 
+
+ align:start position:0%
+drinking
+water of course
+
+ align:start position:0%
+water of course
+ 
+
+ align:start position:0%
+water of course
+um and you know this is a well in in a
+
+ align:start position:0%
+um and you know this is a well in in a
+ 
+
+ align:start position:0%
+um and you know this is a well in in a
+district in India where more than 50% of
+
+ align:start position:0%
+district in India where more than 50% of
+ 
+
+ align:start position:0%
+district in India where more than 50% of
+the wells exceed The Who limits for
+
+ align:start position:0%
+the wells exceed The Who limits for
+ 
+
+ align:start position:0%
+the wells exceed The Who limits for
+arsenic by around a factor of five um uh
+
+ align:start position:0%
+arsenic by around a factor of five um uh
+ 
+
+ align:start position:0%
+arsenic by around a factor of five um uh
+1.8 billion people in the world drink
+
+ align:start position:0%
+1.8 billion people in the world drink
+ 
+
+ align:start position:0%
+1.8 billion people in the world drink
+Fally contaminated water on a daily
+
+ align:start position:0%
+Fally contaminated water on a daily
+ 
+
+ align:start position:0%
+Fally contaminated water on a daily
+basis 600 million people boil their
+
+ align:start position:0%
+basis 600 million people boil their
+ 
+
+ align:start position:0%
+basis 600 million people boil their
+water in the world um boiling doesn't
+
+ align:start position:0%
+water in the world um boiling doesn't
+ 
+
+ align:start position:0%
+water in the world um boiling doesn't
+help as arsenic though arsenic just
+
+ align:start position:0%
+help as arsenic though arsenic just
+ 
+
+ align:start position:0%
+help as arsenic though arsenic just
+stays in in the boiled water it kills
+
+ align:start position:0%
+stays in in the boiled water it kills
+ 
+
+ align:start position:0%
+stays in in the boiled water it kills
+bacteria but it doesn't help with toxic
+
+ align:start position:0%
+bacteria but it doesn't help with toxic
+ 
+
+ align:start position:0%
+bacteria but it doesn't help with toxic
+uh toxic elements um if you look at the
+
+ align:start position:0%
+uh toxic elements um if you look at the
+ 
+
+ align:start position:0%
+uh toxic elements um if you look at the
+world as a whole and you look at sort of
+
+ align:start position:0%
+world as a whole and you look at sort of
+ 
+
+ align:start position:0%
+world as a whole and you look at sort of
+where there are water uh U you Water
+
+ align:start position:0%
+where there are water uh U you Water
+ 
+
+ align:start position:0%
+where there are water uh U you Water
+Crisis where the Water Crisis is at this
+
+ align:start position:0%
+Crisis where the Water Crisis is at this
+ 
+
+ align:start position:0%
+Crisis where the Water Crisis is at this
+level it's it's a little over three and
+
+ align:start position:0%
+level it's it's a little over three and
+ 
+
+ align:start position:0%
+level it's it's a little over three and
+a half billion people um and in those
+
+ align:start position:0%
+a half billion people um and in those
+ 
+
+ align:start position:0%
+a half billion people um and in those
+countries almost 185 or so countries um
+
+ align:start position:0%
+countries almost 185 or so countries um
+ 
+
+ align:start position:0%
+countries almost 185 or so countries um
+where this is a serious problem if you
+
+ align:start position:0%
+where this is a serious problem if you
+ 
+
+ align:start position:0%
+where this is a serious problem if you
+look at the cause of disease and the
+
+ align:start position:0%
+look at the cause of disease and the
+ 
+
+ align:start position:0%
+look at the cause of disease and the
+cause of death in those count 70 to 80%
+
+ align:start position:0%
+cause of death in those count 70 to 80%
+ 
+
+ align:start position:0%
+cause of death in those count 70 to 80%
+of all disease and almost 30% of all
+
+ align:start position:0%
+of all disease and almost 30% of all
+ 
+
+ align:start position:0%
+of all disease and almost 30% of all
+death can be attributed to the water
+
+ align:start position:0%
+death can be attributed to the water
+ 
+
+ align:start position:0%
+death can be attributed to the water
+quality right so uh when I talk about
+
+ align:start position:0%
+quality right so uh when I talk about
+ 
+
+ align:start position:0%
+quality right so uh when I talk about
+water as a problem I really mean it's a
+
+ align:start position:0%
+water as a problem I really mean it's a
+ 
+
+ align:start position:0%
+water as a problem I really mean it's a
+serious problem it's a problem of life
+
+ align:start position:0%
+serious problem it's a problem of life
+ 
+
+ align:start position:0%
+serious problem it's a problem of life
+or death um now uh this is to get fresh
+
+ align:start position:0%
+or death um now uh this is to get fresh
+ 
+
+ align:start position:0%
+or death um now uh this is to get fresh
+drinking water if you look at the planet
+
+ align:start position:0%
+drinking water if you look at the planet
+ 
+
+ align:start position:0%
+drinking water if you look at the planet
+and you say well where is the water on
+
+ align:start position:0%
+and you say well where is the water on
+ 
+
+ align:start position:0%
+and you say well where is the water on
+this planet where is the water on this
+
+ align:start position:0%
+this planet where is the water on this
+ 
+
+ align:start position:0%
+this planet where is the water on this
+planet I like this picture because um
+
+ align:start position:0%
+planet I like this picture because um
+ 
+
+ align:start position:0%
+planet I like this picture because um
+we consume water volumetrically not in
+
+ align:start position:0%
+we consume water volumetrically not in
+ 
+
+ align:start position:0%
+we consume water volumetrically not in
+an area right we use water as a volume
+
+ align:start position:0%
+an area right we use water as a volume
+ 
+
+ align:start position:0%
+an area right we use water as a volume
+and this is the water we have on this
+
+ align:start position:0%
+and this is the water we have on this
+ 
+
+ align:start position:0%
+and this is the water we have on this
+precious Planet as a
+
+ align:start position:0%
+precious Planet as a
+ 
+
+ align:start position:0%
+precious Planet as a
+volume this bubble here is all of the
+
+ align:start position:0%
+volume this bubble here is all of the
+ 
+
+ align:start position:0%
+volume this bubble here is all of the
+ocean water right it's about 70 it's
+
+ align:start position:0%
+ocean water right it's about 70 it's
+ 
+
+ align:start position:0%
+ocean water right it's about 70 it's
+about 97% of all the water that bubble
+
+ align:start position:0%
+about 97% of all the water that bubble
+ 
+
+ align:start position:0%
+about 97% of all the water that bubble
+there is fresh water that is
+
+ align:start position:0%
+there is fresh water that is
+ 
+
+ align:start position:0%
+there is fresh water that is
+inaccessible right it's frozen and this
+
+ align:start position:0%
+inaccessible right it's frozen and this
+ 
+
+ align:start position:0%
+inaccessible right it's frozen and this
+one here you can't really see it there
+
+ align:start position:0%
+one here you can't really see it there
+ 
+
+ align:start position:0%
+one here you can't really see it there
+is another dot there that's less than 1%
+
+ align:start position:0%
+is another dot there that's less than 1%
+ 
+
+ align:start position:0%
+is another dot there that's less than 1%
+of the world's water that is our
+
+ align:start position:0%
+of the world's water that is our
+ 
+
+ align:start position:0%
+of the world's water that is our
+drinking water ecosystem that is what we
+
+ align:start position:0%
+drinking water ecosystem that is what we
+ 
+
+ align:start position:0%
+drinking water ecosystem that is what we
+are destroying um and but see so what
+
+ align:start position:0%
+are destroying um and but see so what
+ 
+
+ align:start position:0%
+are destroying um and but see so what
+okay so there's a lot of things we can
+
+ align:start position:0%
+okay so there's a lot of things we can
+ 
+
+ align:start position:0%
+okay so there's a lot of things we can
+try to do about this right uh one of the
+
+ align:start position:0%
+try to do about this right uh one of the
+ 
+
+ align:start position:0%
+try to do about this right uh one of the
+things we can try to do is to see if we
+
+ align:start position:0%
+things we can try to do is to see if we
+ 
+
+ align:start position:0%
+things we can try to do is to see if we
+can tap into this in a way that's more
+
+ align:start position:0%
+can tap into this in a way that's more
+ 
+
+ align:start position:0%
+can tap into this in a way that's more
+affordable and more efficient because
+
+ align:start position:0%
+affordable and more efficient because
+ 
+
+ align:start position:0%
+affordable and more efficient because
+there's a lot of water here right and
+
+ align:start position:0%
+there's a lot of water here right and
+ 
+
+ align:start position:0%
+there's a lot of water here right and
+use that um but the problem is if you
+
+ align:start position:0%
+use that um but the problem is if you
+ 
+
+ align:start position:0%
+use that um but the problem is if you
+look at the cost of desalination today
+
+ align:start position:0%
+look at the cost of desalination today
+ 
+
+ align:start position:0%
+look at the cost of desalination today
+as opposed to the C that's if you look
+
+ align:start position:0%
+as opposed to the C that's if you look
+ 
+
+ align:start position:0%
+as opposed to the C that's if you look
+at the cost of that as opposed to just
+
+ align:start position:0%
+at the cost of that as opposed to just
+ 
+
+ align:start position:0%
+at the cost of that as opposed to just
+digging water out of a well like the one
+
+ align:start position:0%
+digging water out of a well like the one
+ 
+
+ align:start position:0%
+digging water out of a well like the one
+I just showed you in India it's over a
+
+ align:start position:0%
+I just showed you in India it's over a
+ 
+
+ align:start position:0%
+I just showed you in India it's over a
+factor of 10 right still and and in fact
+
+ align:start position:0%
+factor of 10 right still and and in fact
+ 
+
+ align:start position:0%
+factor of 10 right still and and in fact
+one of the the big issues with
+
+ align:start position:0%
+one of the the big issues with
+ 
+
+ align:start position:0%
+one of the the big issues with
+desalination isn't just the the total
+
+ align:start position:0%
+desalination isn't just the the total
+ 
+
+ align:start position:0%
+desalination isn't just the the total
+cost or the operating cost but the
+
+ align:start position:0%
+cost or the operating cost but the
+ 
+
+ align:start position:0%
+cost or the operating cost but the
+capital cost how do you build this plant
+
+ align:start position:0%
+capital cost how do you build this plant
+ 
+
+ align:start position:0%
+capital cost how do you build this plant
+in the first place right um and so it
+
+ align:start position:0%
+in the first place right um and so it
+ 
+
+ align:start position:0%
+in the first place right um and so it
+takes too much
+
+ align:start position:0%
+takes too much
+ 
+
+ align:start position:0%
+takes too much
+money if you look at the the thing
+
+ align:start position:0%
+money if you look at the the thing
+ 
+
+ align:start position:0%
+money if you look at the the thing
+that's at the heart of desalination it's
+
+ align:start position:0%
+that's at the heart of desalination it's
+ 
+
+ align:start position:0%
+that's at the heart of desalination it's
+a filter right it's a filter and I
+
+ align:start position:0%
+a filter right it's a filter and I
+ 
+
+ align:start position:0%
+a filter right it's a filter and I
+talked about this in my last why this
+
+ align:start position:0%
+talked about this in my last why this
+ 
+
+ align:start position:0%
+talked about this in my last why this
+matters when I talked about separations
+
+ align:start position:0%
+matters when I talked about separations
+ 
+
+ align:start position:0%
+matters when I talked about separations
+and I promise that in my next why this
+
+ align:start position:0%
+and I promise that in my next why this
+ 
+
+ align:start position:0%
+and I promise that in my next why this
+matter I talk about water right which is
+
+ align:start position:0%
+matter I talk about water right which is
+ 
+
+ align:start position:0%
+matter I talk about water right which is
+what I'm doing um if you look at a
+
+ align:start position:0%
+what I'm doing um if you look at a
+ 
+
+ align:start position:0%
+what I'm doing um if you look at a
+diesel plant this is one of the world's
+
+ align:start position:0%
+diesel plant this is one of the world's
+ 
+
+ align:start position:0%
+diesel plant this is one of the world's
+largest this is a plant called the
+
+ align:start position:0%
+largest this is a plant called the
+ 
+
+ align:start position:0%
+largest this is a plant called the
+hadera plant in Israel um and you look
+
+ align:start position:0%
+hadera plant in Israel um and you look
+ 
+
+ align:start position:0%
+hadera plant in Israel um and you look
+at what their costs are that remember
+
+ align:start position:0%
+at what their costs are that remember
+ 
+
+ align:start position:0%
+at what their costs are that remember
+the cost is half of that cost almost
+
+ align:start position:0%
+the cost is half of that cost almost
+ 
+
+ align:start position:0%
+the cost is half of that cost almost
+half of the cost is in Just Energy and
+
+ align:start position:0%
+half of the cost is in Just Energy and
+ 
+
+ align:start position:0%
+half of the cost is in Just Energy and
+almost all of that energy is in pushing
+
+ align:start position:0%
+almost all of that energy is in pushing
+ 
+
+ align:start position:0%
+almost all of that energy is in pushing
+salt water through a filter through a
+
+ align:start position:0%
+salt water through a filter through a
+ 
+
+ align:start position:0%
+salt water through a filter through a
+membrane
+
+ align:start position:0%
+membrane
+ 
+
+ align:start position:0%
+membrane
+uh that's called a reverse osmosis
+
+ align:start position:0%
+uh that's called a reverse osmosis
+ 
+
+ align:start position:0%
+uh that's called a reverse osmosis
+membrane because you're going against
+
+ align:start position:0%
+membrane because you're going against
+ 
+
+ align:start position:0%
+membrane because you're going against
+the osmotic
+
+ align:start position:0%
+the osmotic
+ 
+
+ align:start position:0%
+the osmotic
+pressure um and if you look at the
+
+ align:start position:0%
+pressure um and if you look at the
+ 
+
+ align:start position:0%
+pressure um and if you look at the
+membrane itself this is a picture of it
+
+ align:start position:0%
+membrane itself this is a picture of it
+ 
+
+ align:start position:0%
+membrane itself this is a picture of it
+it's actually very small layer on top of
+
+ align:start position:0%
+it's actually very small layer on top of
+ 
+
+ align:start position:0%
+it's actually very small layer on top of
+this active layer um that does all the
+
+ align:start position:0%
+this active layer um that does all the
+ 
+
+ align:start position:0%
+this active layer um that does all the
+work it's not a very good design in fact
+
+ align:start position:0%
+work it's not a very good design in fact
+ 
+
+ align:start position:0%
+work it's not a very good design in fact
+membranes for
+
+ align:start position:0%
+membranes for
+ 
+
+ align:start position:0%
+membranes for
+desalination are pretty bad right uh uh
+
+ align:start position:0%
+desalination are pretty bad right uh uh
+ 
+
+ align:start position:0%
+desalination are pretty bad right uh uh
+they kind of do everything worse than
+
+ align:start position:0%
+they kind of do everything worse than
+ 
+
+ align:start position:0%
+they kind of do everything worse than
+they should except that they work which
+
+ align:start position:0%
+they should except that they work which
+ 
+
+ align:start position:0%
+they should except that they work which
+is good and they're cheap dollar square
+
+ align:start position:0%
+is good and they're cheap dollar square
+ 
+
+ align:start position:0%
+is good and they're cheap dollar square
+foot but but see they're very they take
+
+ align:start position:0%
+foot but but see they're very they take
+ 
+
+ align:start position:0%
+foot but but see they're very they take
+much more energy than you
+
+ align:start position:0%
+much more energy than you
+ 
+
+ align:start position:0%
+much more energy than you
+need they foul up very easily and then
+
+ align:start position:0%
+need they foul up very easily and then
+ 
+
+ align:start position:0%
+need they foul up very easily and then
+that means stuff gets kind of you know
+
+ align:start position:0%
+that means stuff gets kind of you know
+ 
+
+ align:start position:0%
+that means stuff gets kind of you know
+stuck in them and then you can't take it
+
+ align:start position:0%
+stuck in them and then you can't take it
+ 
+
+ align:start position:0%
+stuck in them and then you can't take it
+out you can't clean them look these
+
+ align:start position:0%
+out you can't clean them look these
+ 
+
+ align:start position:0%
+out you can't clean them look these
+these polyamide membranes which is the
+
+ align:start position:0%
+these polyamide membranes which is the
+ 
+
+ align:start position:0%
+these polyamide membranes which is the
+same polymer used in these membranes for
+
+ align:start position:0%
+same polymer used in these membranes for
+ 
+
+ align:start position:0%
+same polymer used in these membranes for
+50 years haven't changed the
+
+ align:start position:0%
+50 years haven't changed the
+ 
+
+ align:start position:0%
+50 years haven't changed the
+material those polyamide membranes are
+
+ align:start position:0%
+material those polyamide membranes are
+ 
+
+ align:start position:0%
+material those polyamide membranes are
+destroyed by chlorine so even in a Dell
+
+ align:start position:0%
+destroyed by chlorine so even in a Dell
+ 
+
+ align:start position:0%
+destroyed by chlorine so even in a Dell
+plant in a Dell plant if you have
+
+ align:start position:0%
+plant in a Dell plant if you have
+ 
+
+ align:start position:0%
+plant in a Dell plant if you have
+drinking water in your feed
+
+ align:start position:0%
+drinking water in your feed
+ 
+
+ align:start position:0%
+drinking water in your feed
+stream drinking water has six parts per
+
+ align:start position:0%
+stream drinking water has six parts per
+ 
+
+ align:start position:0%
+stream drinking water has six parts per
+million chlorine that's not much they
+
+ align:start position:0%
+million chlorine that's not much they
+ 
+
+ align:start position:0%
+million chlorine that's not much they
+still will go through the cost to remove
+
+ align:start position:0%
+still will go through the cost to remove
+ 
+
+ align:start position:0%
+still will go through the cost to remove
+it they will remove it from the feed why
+
+ align:start position:0%
+it they will remove it from the feed why
+ 
+
+ align:start position:0%
+it they will remove it from the feed why
+because if you leave that little amount
+
+ align:start position:0%
+because if you leave that little amount
+ 
+
+ align:start position:0%
+because if you leave that little amount
+of chlorine in the feed these membranes
+
+ align:start position:0%
+of chlorine in the feed these membranes
+ 
+
+ align:start position:0%
+of chlorine in the feed these membranes
+get destroyed by the way there's 40,000
+
+ align:start position:0%
+get destroyed by the way there's 40,000
+ 
+
+ align:start position:0%
+get destroyed by the way there's 40,000
+of these membranes in this plant each
+
+ align:start position:0%
+of these membranes in this plant each
+ 
+
+ align:start position:0%
+of these membranes in this plant each
+one is 2 meters long and 40 sare meters
+
+ align:start position:0%
+one is 2 meters long and 40 sare meters
+ 
+
+ align:start position:0%
+one is 2 meters long and 40 sare meters
+of area so so these are so
+
+ align:start position:0%
+of area so so these are so
+ 
+
+ align:start position:0%
+of area so so these are so
+delicate that you can't really clean
+
+ align:start position:0%
+delicate that you can't really clean
+ 
+
+ align:start position:0%
+delicate that you can't really clean
+them well and that's part of what the
+
+ align:start position:0%
+them well and that's part of what the
+ 
+
+ align:start position:0%
+them well and that's part of what the
+cost of a plant involves right that's
+
+ align:start position:0%
+cost of a plant involves right that's
+ 
+
+ align:start position:0%
+cost of a plant involves right that's
+part of what the cost of a plant
+
+ align:start position:0%
+part of what the cost of a plant
+ 
+
+ align:start position:0%
+part of what the cost of a plant
+involves now um this would be like a
+
+ align:start position:0%
+involves now um this would be like a
+ 
+
+ align:start position:0%
+involves now um this would be like a
+plant right you have sea water coming in
+
+ align:start position:0%
+plant right you have sea water coming in
+ 
+
+ align:start position:0%
+plant right you have sea water coming in
+and you know and then you've got your
+
+ align:start position:0%
+and you know and then you've got your
+ 
+
+ align:start position:0%
+and you know and then you've got your
+membrane module that's taking the salt
+
+ align:start position:0%
+membrane module that's taking the salt
+ 
+
+ align:start position:0%
+membrane module that's taking the salt
+out of the water and then the product
+
+ align:start position:0%
+out of the water and then the product
+ 
+
+ align:start position:0%
+out of the water and then the product
+water but because this this filter is so
+
+ align:start position:0%
+water but because this this filter is so
+ 
+
+ align:start position:0%
+water but because this this filter is so
+delicate there's the picture because
+
+ align:start position:0%
+delicate there's the picture because
+ 
+
+ align:start position:0%
+delicate there's the picture because
+that filter is so delicate you actually
+
+ align:start position:0%
+that filter is so delicate you actually
+ 
+
+ align:start position:0%
+that filter is so delicate you actually
+have to add a whole lot more to the
+
+ align:start position:0%
+have to add a whole lot more to the
+ 
+
+ align:start position:0%
+have to add a whole lot more to the
+plant so much of a desel plant is built
+
+ align:start position:0%
+plant so much of a desel plant is built
+ 
+
+ align:start position:0%
+plant so much of a desel plant is built
+around essentially protecting this
+
+ align:start position:0%
+around essentially protecting this
+ 
+
+ align:start position:0%
+around essentially protecting this
+membrane so that's cost that's cost
+
+ align:start position:0%
+membrane so that's cost that's cost
+ 
+
+ align:start position:0%
+membrane so that's cost that's cost
+right a better membrane could change
+
+ align:start position:0%
+right a better membrane could change
+ 
+
+ align:start position:0%
+right a better membrane could change
+this but like I said the membrane oh
+
+ align:start position:0%
+this but like I said the membrane oh
+ 
+
+ align:start position:0%
+this but like I said the membrane oh
+there it is you can't you can't Snapchat
+
+ align:start position:0%
+there it is you can't you can't Snapchat
+ 
+
+ align:start position:0%
+there it is you can't you can't Snapchat
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+that Snapchat what is it that people do
+
+ align:start position:0%
+that Snapchat what is it that people do
+ 
+
+ align:start position:0%
+that Snapchat what is it that people do
+today not Snapchat yeah Snapchat yeah
+
+ align:start position:0%
+today not Snapchat yeah Snapchat yeah
+ 
+
+ align:start position:0%
+today not Snapchat yeah Snapchat yeah
+okay thank you you can't Snapchat on
+
+ align:start position:0%
+okay thank you you can't Snapchat on
+ 
+
+ align:start position:0%
+okay thank you you can't Snapchat on
+that that's what I
+
+ align:start position:0%
+that that's what I
+ 
+
+ align:start position:0%
+that that's what I
+meant I know it's not my space but I
+
+ align:start position:0%
+meant I know it's not my space but I
+ 
+
+ align:start position:0%
+meant I know it's not my space but I
+don't know but anyway um uh this is like
+
+ align:start position:0%
+don't know but anyway um uh this is like
+ 
+
+ align:start position:0%
+don't know but anyway um uh this is like
+you know when I look at at at at
+
+ align:start position:0%
+you know when I look at at at at
+ 
+
+ align:start position:0%
+you know when I look at at at at
+membranes today as a material SCI
+
+ align:start position:0%
+membranes today as a material SCI
+ 
+
+ align:start position:0%
+membranes today as a material SCI
+science is materials chemist all the
+
+ align:start position:0%
+science is materials chemist all the
+ 
+
+ align:start position:0%
+science is materials chemist all the
+memb is I think that's what it looks
+
+ align:start position:0%
+memb is I think that's what it looks
+ 
+
+ align:start position:0%
+memb is I think that's what it looks
+like why doesn't have to be the case we
+
+ align:start position:0%
+like why doesn't have to be the case we
+ 
+
+ align:start position:0%
+like why doesn't have to be the case we
+can do so much
+
+ align:start position:0%
+can do so much
+ 
+
+ align:start position:0%
+can do so much
+better and and so okay energy and cost
+
+ align:start position:0%
+better and and so okay energy and cost
+ 
+
+ align:start position:0%
+better and and so okay energy and cost
+goes into pre-treatment secondary
+
+ align:start position:0%
+goes into pre-treatment secondary
+ 
+
+ align:start position:0%
+goes into pre-treatment secondary
+treatment and this is where this comes
+
+ align:start position:0%
+treatment and this is where this comes
+ 
+
+ align:start position:0%
+treatment and this is where this comes
+back this beautiful
+
+ align:start position:0%
+back this beautiful
+ 
+
+ align:start position:0%
+back this beautiful
+material that we have now understood
+
+ align:start position:0%
+material that we have now understood
+ 
+
+ align:start position:0%
+material that we have now understood
+more than we did before because remember
+
+ align:start position:0%
+more than we did before because remember
+ 
+
+ align:start position:0%
+more than we did before because remember
+before I showed you graphine and I
+
+ align:start position:0%
+before I showed you graphine and I
+ 
+
+ align:start position:0%
+before I showed you graphine and I
+showed you no I showed you
+
+ align:start position:0%
+showed you no I showed you
+ 
+
+ align:start position:0%
+showed you no I showed you
+Benzene and we talked about it as a
+
+ align:start position:0%
+Benzene and we talked about it as a
+ 
+
+ align:start position:0%
+Benzene and we talked about it as a
+Lewis resonance structure remember right
+
+ align:start position:0%
+Lewis resonance structure remember right
+ 
+
+ align:start position:0%
+Lewis resonance structure remember right
+a leis resonance structure to help
+
+ align:start position:0%
+a leis resonance structure to help
+ 
+
+ align:start position:0%
+a leis resonance structure to help
+explain how it LO you know gra graphing
+
+ align:start position:0%
+explain how it LO you know gra graphing
+ 
+
+ align:start position:0%
+explain how it LO you know gra graphing
+does not have alternating bonds remember
+
+ align:start position:0%
+does not have alternating bonds remember
+ 
+
+ align:start position:0%
+does not have alternating bonds remember
+that's what we talked about before it's
+
+ align:start position:0%
+that's what we talked about before it's
+ 
+
+ align:start position:0%
+that's what we talked about before it's
+a Lewis resonant
+
+ align:start position:0%
+a Lewis resonant
+ 
+
+ align:start position:0%
+a Lewis resonant
+structure so it lowers its energy by
+
+ align:start position:0%
+structure so it lowers its energy by
+ 
+
+ align:start position:0%
+structure so it lowers its energy by
+having two sets of structures that have
+
+ align:start position:0%
+having two sets of structures that have
+ 
+
+ align:start position:0%
+having two sets of structures that have
+sort of alternating bonds we talked
+
+ align:start position:0%
+sort of alternating bonds we talked
+ 
+
+ align:start position:0%
+sort of alternating bonds we talked
+about it in the context of benzene but
+
+ align:start position:0%
+about it in the context of benzene but
+ 
+
+ align:start position:0%
+about it in the context of benzene but
+see now you know so much more you know
+
+ align:start position:0%
+see now you know so much more you know
+ 
+
+ align:start position:0%
+see now you know so much more you know
+so much more because now you know why
+
+ align:start position:0%
+so much more because now you know why
+ 
+
+ align:start position:0%
+so much more because now you know why
+graphing is so special
+
+ align:start position:0%
+graphing is so special
+ 
+
+ align:start position:0%
+graphing is so special
+you know why graphine is so special it
+
+ align:start position:0%
+you know why graphine is so special it
+ 
+
+ align:start position:0%
+you know why graphine is so special it
+actually is the
+
+ align:start position:0%
+actually is the
+ 
+
+ align:start position:0%
+actually is the
+hybridization it's the hybridization
+
+ align:start position:0%
+hybridization it's the hybridization
+ 
+
+ align:start position:0%
+hybridization it's the hybridization
+because on top and on the bottom of a
+
+ align:start position:0%
+because on top and on the bottom of a
+ 
+
+ align:start position:0%
+because on top and on the bottom of a
+single atom of of a single sheet of
+
+ align:start position:0%
+single atom of of a single sheet of
+ 
+
+ align:start position:0%
+single atom of of a single sheet of
+graphine you've got piie bonding all the
+
+ align:start position:0%
+graphine you've got piie bonding all the
+ 
+
+ align:start position:0%
+graphine you've got piie bonding all the
+way those Pi bonds are going across the
+
+ align:start position:0%
+way those Pi bonds are going across the
+ 
+
+ align:start position:0%
+way those Pi bonds are going across the
+whole surface and those electrons are
+
+ align:start position:0%
+whole surface and those electrons are
+ 
+
+ align:start position:0%
+whole surface and those electrons are
+critical those electrons that occupy
+
+ align:start position:0%
+critical those electrons that occupy
+ 
+
+ align:start position:0%
+critical those electrons that occupy
+those P orbitals are critical to the the
+
+ align:start position:0%
+those P orbitals are critical to the the
+ 
+
+ align:start position:0%
+those P orbitals are critical to the the
+the very special properties that
+
+ align:start position:0%
+the very special properties that
+ 
+
+ align:start position:0%
+the very special properties that
+graphine has right so you now know the
+
+ align:start position:0%
+graphine has right so you now know the
+ 
+
+ align:start position:0%
+graphine has right so you now know the
+secret it's SP2 hybridization and you
+
+ align:start position:0%
+secret it's SP2 hybridization and you
+ 
+
+ align:start position:0%
+secret it's SP2 hybridization and you
+know this has allowed us uh this is you
+
+ align:start position:0%
+know this has allowed us uh this is you
+ 
+
+ align:start position:0%
+know this has allowed us uh this is you
+might tell I'm kind of passionate about
+
+ align:start position:0%
+might tell I'm kind of passionate about
+ 
+
+ align:start position:0%
+might tell I'm kind of passionate about
+this problem um partly I'm passionate
+
+ align:start position:0%
+this problem um partly I'm passionate
+ 
+
+ align:start position:0%
+this problem um partly I'm passionate
+about a lot of problems but also we
+
+ align:start position:0%
+about a lot of problems but also we
+ 
+
+ align:start position:0%
+about a lot of problems but also we
+happen to work on this and we have been
+
+ align:start position:0%
+happen to work on this and we have been
+ 
+
+ align:start position:0%
+happen to work on this and we have been
+developing this this is like the
+
+ align:start position:0%
+developing this this is like the
+ 
+
+ align:start position:0%
+developing this this is like the
+ultimate membrane I can soak this in
+
+ align:start position:0%
+ultimate membrane I can soak this in
+ 
+
+ align:start position:0%
+ultimate membrane I can soak this in
+chlorine overnight I can put it in
+
+ align:start position:0%
+chlorine overnight I can put it in
+ 
+
+ align:start position:0%
+chlorine overnight I can put it in
+Negative PH Solutions I can heat it up
+
+ align:start position:0%
+Negative PH Solutions I can heat it up
+ 
+
+ align:start position:0%
+Negative PH Solutions I can heat it up
+it doesn't
+
+ align:start position:0%
+it doesn't
+ 
+
+ align:start position:0%
+it doesn't
+degrade and we have figured out how to
+
+ align:start position:0%
+degrade and we have figured out how to
+ 
+
+ align:start position:0%
+degrade and we have figured out how to
+poke holes in it at just the right size
+
+ align:start position:0%
+poke holes in it at just the right size
+ 
+
+ align:start position:0%
+poke holes in it at just the right size
+or to stitch it together so that maybe
+
+ align:start position:0%
+or to stitch it together so that maybe
+ 
+
+ align:start position:0%
+or to stitch it together so that maybe
+you can filter particles by the flow in
+
+ align:start position:0%
+you can filter particles by the flow in
+ 
+
+ align:start position:0%
+you can filter particles by the flow in
+between these sheets
+
+ align:start position:0%
+between these sheets
+ 
+
+ align:start position:0%
+between these sheets
+right and this material as a membrane is
+
+ align:start position:0%
+right and this material as a membrane is
+ 
+
+ align:start position:0%
+right and this material as a membrane is
+so promising that uh we've actually
+
+ align:start position:0%
+so promising that uh we've actually
+ 
+
+ align:start position:0%
+so promising that uh we've actually
+started to commercialize it as of the
+
+ align:start position:0%
+started to commercialize it as of the
+ 
+
+ align:start position:0%
+started to commercialize it as of the
+last year right and I think this is
+
+ align:start position:0%
+last year right and I think this is
+ 
+
+ align:start position:0%
+last year right and I think this is
+really going to make a big difference in
+
+ align:start position:0%
+really going to make a big difference in
+ 
+
+ align:start position:0%
+really going to make a big difference in
+a lot of um a lot of areas why because
+
+ align:start position:0%
+a lot of um a lot of areas why because
+ 
+
+ align:start position:0%
+a lot of um a lot of areas why because
+of SP2 hybridization that is why that is
+
+ align:start position:0%
+of SP2 hybridization that is why that is
+ 
+
+ align:start position:0%
+of SP2 hybridization that is why that is
+why this is such a special material okay
+
+ align:start position:0%
+why this is such a special material okay
+ 
+
+ align:start position:0%
+why this is such a special material okay
+that's my why this matters now uh oh we
+
+ align:start position:0%
+that's my why this matters now uh oh we
+ 
+
+ align:start position:0%
+that's my why this matters now uh oh we
+did c2h6 there it is we did C2 H4 there
+
+ align:start position:0%
+did c2h6 there it is we did C2 H4 there
+ 
+
+ align:start position:0%
+did c2h6 there it is we did C2 H4 there
+it is look at that extra P Bond not
+
+ align:start position:0%
+it is look at that extra P Bond not
+ 
+
+ align:start position:0%
+it is look at that extra P Bond not
+anamated this time and of course you can
+
+ align:start position:0%
+anamated this time and of course you can
+ 
+
+ align:start position:0%
+anamated this time and of course you can
+go on and you could do c2h2 and you can
+
+ align:start position:0%
+go on and you could do c2h2 and you can
+ 
+
+ align:start position:0%
+go on and you could do c2h2 and you can
+imagine what happens in this case is is
+
+ align:start position:0%
+imagine what happens in this case is is
+ 
+
+ align:start position:0%
+imagine what happens in this case is is
+what you would expect is what you would
+
+ align:start position:0%
+what you would expect is what you would
+ 
+
+ align:start position:0%
+what you would expect is what you would
+expect because now I've only got see
+
+ align:start position:0%
+expect because now I've only got see
+ 
+
+ align:start position:0%
+expect because now I've only got see
+each of these carbon
+
+ align:start position:0%
+each of these carbon
+ 
+
+ align:start position:0%
+each of these carbon
+atoms only needs two Sigma bonds one to
+
+ align:start position:0%
+atoms only needs two Sigma bonds one to
+ 
+
+ align:start position:0%
+atoms only needs two Sigma bonds one to
+the hydrogen and one to the other carbon
+
+ align:start position:0%
+the hydrogen and one to the other carbon
+ 
+
+ align:start position:0%
+the hydrogen and one to the other carbon
+so it's only going to grab one it's only
+
+ align:start position:0%
+so it's only going to grab one it's only
+ 
+
+ align:start position:0%
+so it's only going to grab one it's only
+only going to hybridize to make those
+
+ align:start position:0%
+only going to hybridize to make those
+ 
+
+ align:start position:0%
+only going to hybridize to make those
+two equivalent Sigma bonds only going to
+
+ align:start position:0%
+two equivalent Sigma bonds only going to
+ 
+
+ align:start position:0%
+two equivalent Sigma bonds only going to
+hybridize with one of the P electrons so
+
+ align:start position:0%
+hybridize with one of the P electrons so
+ 
+
+ align:start position:0%
+hybridize with one of the P electrons so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+SP that's s hybridization but notice
+
+ align:start position:0%
+SP that's s hybridization but notice
+ 
+
+ align:start position:0%
+SP that's s hybridization but notice
+that in C2 H2 you know now I've got um
+
+ align:start position:0%
+that in C2 H2 you know now I've got um
+ 
+
+ align:start position:0%
+that in C2 H2 you know now I've got um
+two P orbitals left
+
+ align:start position:0%
+two P orbitals left
+ 
+
+ align:start position:0%
+two P orbitals left
+over on each carbon atom and so you can
+
+ align:start position:0%
+over on each carbon atom and so you can
+ 
+
+ align:start position:0%
+over on each carbon atom and so you can
+imagine that with these two P orbitals
+
+ align:start position:0%
+imagine that with these two P orbitals
+ 
+
+ align:start position:0%
+imagine that with these two P orbitals
+well you you know this already right
+
+ align:start position:0%
+well you you know this already right
+ 
+
+ align:start position:0%
+well you you know this already right
+when when we talked about P orbitals we
+
+ align:start position:0%
+when when we talked about P orbitals we
+ 
+
+ align:start position:0%
+when when we talked about P orbitals we
+talked
+
+ align:start position:0%
+talked
+ 
+
+ align:start position:0%
+talked
+about how you know you might you know
+
+ align:start position:0%
+about how you know you might you know
+ 
+
+ align:start position:0%
+about how you know you might you know
+you've got this right
+
+ align:start position:0%
+you've got this right
+ 
+
+ align:start position:0%
+you've got this right
+a okay that's supposed to come like out
+
+ align:start position:0%
+a okay that's supposed to come like out
+ 
+
+ align:start position:0%
+a okay that's supposed to come like out
+of the plane and into the plane they're
+
+ align:start position:0%
+of the plane and into the plane they're
+ 
+
+ align:start position:0%
+of the plane and into the plane they're
+orthogonal they're orthogonal right and
+
+ align:start position:0%
+orthogonal they're orthogonal right and
+ 
+
+ align:start position:0%
+orthogonal they're orthogonal right and
+so so two of them are coming at the
+
+ align:start position:0%
+so so two of them are coming at the
+ 
+
+ align:start position:0%
+so so two of them are coming at the
+other atom one is like this and the
+
+ align:start position:0%
+other atom one is like this and the
+ 
+
+ align:start position:0%
+other atom one is like this and the
+other is like that and the and then the
+
+ align:start position:0%
+other is like that and the and then the
+ 
+
+ align:start position:0%
+other is like that and the and then the
+other Adam has one like this and one
+
+ align:start position:0%
+other Adam has one like this and one
+ 
+
+ align:start position:0%
+other Adam has one like this and one
+well it might not at first but then when
+
+ align:start position:0%
+well it might not at first but then when
+ 
+
+ align:start position:0%
+well it might not at first but then when
+it sees those it's like hey wait a
+
+ align:start position:0%
+it sees those it's like hey wait a
+ 
+
+ align:start position:0%
+it sees those it's like hey wait a
+second if I do this we can pie Bond
+
+ align:start position:0%
+second if I do this we can pie Bond
+ 
+
+ align:start position:0%
+second if I do this we can pie Bond
+but the other ones are like this and
+
+ align:start position:0%
+but the other ones are like this and
+ 
+
+ align:start position:0%
+but the other ones are like this and
+they piie bond and so you get a carbon
+
+ align:start position:0%
+they piie bond and so you get a carbon
+ 
+
+ align:start position:0%
+they piie bond and so you get a carbon
+carbon triple bond right you get a
+
+ align:start position:0%
+carbon triple bond right you get a
+ 
+
+ align:start position:0%
+carbon triple bond right you get a
+carbon carbon triple bond for C uh 2h2
+
+ align:start position:0%
+carbon carbon triple bond for C uh 2h2
+ 
+
+ align:start position:0%
+carbon carbon triple bond for C uh 2h2
+with SP hybridization now it's not oh
+
+ align:start position:0%
+with SP hybridization now it's not oh
+ 
+
+ align:start position:0%
+with SP hybridization now it's not oh
+there it is right okay forms py Bond
+
+ align:start position:0%
+there it is right okay forms py Bond
+ 
+
+ align:start position:0%
+there it is right okay forms py Bond
+Network form Sigma B networ it's not
+
+ align:start position:0%
+Network form Sigma B networ it's not
+ 
+
+ align:start position:0%
+Network form Sigma B networ it's not
+just carbon that hybridizes it's not
+
+ align:start position:0%
+just carbon that hybridizes it's not
+ 
+
+ align:start position:0%
+just carbon that hybridizes it's not
+carbon is a classic example but you know
+
+ align:start position:0%
+carbon is a classic example but you know
+ 
+
+ align:start position:0%
+carbon is a classic example but you know
+if you look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be2 it's the same thing B H2 well be be
+
+ align:start position:0%
+be2 it's the same thing B H2 well be be
+ 
+
+ align:start position:0%
+be2 it's the same thing B H2 well be be
+starts with an
+
+ align:start position:0%
+starts with an
+ 
+
+ align:start position:0%
+starts with an
+un start can I raise this up be starts
+
+ align:start position:0%
+un start can I raise this up be starts
+ 
+
+ align:start position:0%
+un start can I raise this up be starts
+with orbitals that don't look like
+
+ align:start position:0%
+with orbitals that don't look like
+ 
+
+ align:start position:0%
+with orbitals that don't look like
+they're going to give me the equivalent
+
+ align:start position:0%
+they're going to give me the equivalent
+ 
+
+ align:start position:0%
+they're going to give me the equivalent
+two Sigma bonds be starts with
+
+ align:start position:0%
+two Sigma bonds be starts with
+ 
+
+ align:start position:0%
+two Sigma bonds be starts with
+these s electrons filt
+
+ align:start position:0%
+these s electrons filt
+ 
+
+ align:start position:0%
+these s electrons filt
+right but if be had something more like
+
+ align:start position:0%
+right but if be had something more like
+ 
+
+ align:start position:0%
+right but if be had something more like
+this if it had an SP electron in each of
+
+ align:start position:0%
+this if it had an SP electron in each of
+ 
+
+ align:start position:0%
+this if it had an SP electron in each of
+those orbitals well now when I see the
+
+ align:start position:0%
+those orbitals well now when I see the
+ 
+
+ align:start position:0%
+those orbitals well now when I see the
+two H orbitals the two 1sh
+
+ align:start position:0%
+two H orbitals the two 1sh
+ 
+
+ align:start position:0%
+two H orbitals the two 1sh
+orbitals coming at me I can form those
+
+ align:start position:0%
+orbitals coming at me I can form those
+ 
+
+ align:start position:0%
+orbitals coming at me I can form those
+equivalent bonds so be2 will also
+
+ align:start position:0%
+equivalent bonds so be2 will also
+ 
+
+ align:start position:0%
+equivalent bonds so be2 will also
+hybridize to make that
+
+ align:start position:0%
+hybridize to make that
+ 
+
+ align:start position:0%
+hybridize to make that
+molecule and all sorts of other things
+
+ align:start position:0%
+molecule and all sorts of other things
+ 
+
+ align:start position:0%
+molecule and all sorts of other things
+the D orbitals can get in on the action
+
+ align:start position:0%
+the D orbitals can get in on the action
+ 
+
+ align:start position:0%
+the D orbitals can get in on the action
+right so here's sf6 which we talked
+
+ align:start position:0%
+right so here's sf6 which we talked
+ 
+
+ align:start position:0%
+right so here's sf6 which we talked
+about we drew this Le structure
+
+ align:start position:0%
+about we drew this Le structure
+ 
+
+ align:start position:0%
+about we drew this Le structure
+took a long time to draw those loone
+
+ align:start position:0%
+took a long time to draw those loone
+ 
+
+ align:start position:0%
+took a long time to draw those loone
+pairs but now you know that the way this
+
+ align:start position:0%
+pairs but now you know that the way this
+ 
+
+ align:start position:0%
+pairs but now you know that the way this
+actually works because those are
+
+ align:start position:0%
+actually works because those are
+ 
+
+ align:start position:0%
+actually works because those are
+equivalent bonds so the only way this
+
+ align:start position:0%
+equivalent bonds so the only way this
+ 
+
+ align:start position:0%
+equivalent bonds so the only way this
+can work is if I form hybrid
+
+ align:start position:0%
+can work is if I form hybrid
+ 
+
+ align:start position:0%
+can work is if I form hybrid
+orbitals right right but they didn't
+
+ align:start position:0%
+orbitals right right but they didn't
+ 
+
+ align:start position:0%
+orbitals right right but they didn't
+have to be equivalent bonds until we
+
+ align:start position:0%
+have to be equivalent bonds until we
+ 
+
+ align:start position:0%
+have to be equivalent bonds until we
+learned about Vesper and it said no I
+
+ align:start position:0%
+learned about Vesper and it said no I
+ 
+
+ align:start position:0%
+learned about Vesper and it said no I
+want to maximize my separation to
+
+ align:start position:0%
+want to maximize my separation to
+ 
+
+ align:start position:0%
+want to maximize my separation to
+minimize repulsions and so then we know
+
+ align:start position:0%
+minimize repulsions and so then we know
+ 
+
+ align:start position:0%
+minimize repulsions and so then we know
+that if there are equivalent bonds the
+
+ align:start position:0%
+that if there are equivalent bonds the
+ 
+
+ align:start position:0%
+that if there are equivalent bonds the
+energy of the system will be lower right
+
+ align:start position:0%
+energy of the system will be lower right
+ 
+
+ align:start position:0%
+energy of the system will be lower right
+right and and and so that that's uh you
+
+ align:start position:0%
+right and and and so that that's uh you
+ 
+
+ align:start position:0%
+right and and and so that that's uh you
+know that's that's going to have to take
+
+ align:start position:0%
+know that's that's going to have to take
+ 
+
+ align:start position:0%
+know that's that's going to have to take
+some D orbitals and create these hybrid
+
+ align:start position:0%
+some D orbitals and create these hybrid
+ 
+
+ align:start position:0%
+some D orbitals and create these hybrid
+orbitals look they're beautiful because
+
+ align:start position:0%
+orbitals look they're beautiful because
+ 
+
+ align:start position:0%
+orbitals look they're beautiful because
+now this thing from The sulfur this
+
+ align:start position:0%
+now this thing from The sulfur this
+ 
+
+ align:start position:0%
+now this thing from The sulfur this
+thing can say hey I can take six of you
+
+ align:start position:0%
+thing can say hey I can take six of you
+ 
+
+ align:start position:0%
+thing can say hey I can take six of you
+and I can be equivalent bonding to all
+
+ align:start position:0%
+and I can be equivalent bonding to all
+ 
+
+ align:start position:0%
+and I can be equivalent bonding to all
+of you that's what hybridization is okay
+
+ align:start position:0%
+of you that's what hybridization is okay
+ 
+
+ align:start position:0%
+of you that's what hybridization is okay
+it's it's written right up there we're
+
+ align:start position:0%
+it's it's written right up there we're
+ 
+
+ align:start position:0%
+it's it's written right up there we're
+just keeping on saying the same thing
+
+ align:start position:0%
+just keeping on saying the same thing
+ 
+
+ align:start position:0%
+just keeping on saying the same thing
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+um I think that I'm I got very excited
+
+ align:start position:0%
+um I think that I'm I got very excited
+ 
+
+ align:start position:0%
+um I think that I'm I got very excited
+about the water so I have to throw some
+
+ align:start position:0%
+about the water so I have to throw some
+ 
+
+ align:start position:0%
+about the water so I have to throw some
+T-shirts out um and and now I where do I
+
+ align:start position:0%
+T-shirts out um and and now I where do I
+ 
+
+ align:start position:0%
+T-shirts out um and and now I where do I
+where do I okay I don't go there I don't
+
+ align:start position:0%
+where do I okay I don't go there I don't
+ 
+
+ align:start position:0%
+where do I okay I don't go there I don't
+go there I got to
+
+ align:start position:0%
+go there I got to
+ 
+
+ align:start position:0%
+go there I got to
+go back there and back there and oh
+
+ align:start position:0%
+go back there and back there and oh
+ 
+
+ align:start position:0%
+go back there and back there and oh
+that's very loud okay and right there
+
+ align:start position:0%
+that's very loud okay and right there
+ 
+
+ align:start position:0%
+that's very loud okay and right there
+and right
+
+ align:start position:0%
+and right
+ 
+
+ align:start position:0%
+and right
+there see you guys on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Friday for
\ No newline at end of file
diff --git a/WXIU2tK4qtc.txt b/WXIU2tK4qtc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a8b6069bcf5f165ddf44d31a219815ee897901b
--- /dev/null
+++ b/WXIU2tK4qtc.txt
@@ -0,0 +1,1635 @@
+align:start position:0%
+ 
+in this segment we developed the
+
+ align:start position:0%
+in this segment we developed the
+ 
+
+ align:start position:0%
+in this segment we developed the
+inclusion exclusion formula which is a
+
+ align:start position:0%
+inclusion exclusion formula which is a
+ 
+
+ align:start position:0%
+inclusion exclusion formula which is a
+beautiful generalization of a formula
+
+ align:start position:0%
+beautiful generalization of a formula
+ 
+
+ align:start position:0%
+beautiful generalization of a formula
+that we have seen before let us look at
+
+ align:start position:0%
+that we have seen before let us look at
+ 
+
+ align:start position:0%
+that we have seen before let us look at
+this formula and remind ourselves what
+
+ align:start position:0%
+this formula and remind ourselves what
+ 
+
+ align:start position:0%
+this formula and remind ourselves what
+it sells if we have two sets a 1 and a 2
+
+ align:start position:0%
+it sells if we have two sets a 1 and a 2
+ 
+
+ align:start position:0%
+it sells if we have two sets a 1 and a 2
+and we're interested in the probability
+
+ align:start position:0%
+and we're interested in the probability
+ 
+
+ align:start position:0%
+and we're interested in the probability
+of their union how can we find it we
+
+ align:start position:0%
+of their union how can we find it we
+ 
+
+ align:start position:0%
+of their union how can we find it we
+take the probability of the first set we
+
+ align:start position:0%
+take the probability of the first set we
+ 
+
+ align:start position:0%
+take the probability of the first set we
+add to 8 the probability of the second
+
+ align:start position:0%
+add to 8 the probability of the second
+ 
+
+ align:start position:0%
+add to 8 the probability of the second
+set but then we realize that by doing so
+
+ align:start position:0%
+set but then we realize that by doing so
+ 
+
+ align:start position:0%
+set but then we realize that by doing so
+we have double counted this part of the
+
+ align:start position:0%
+we have double counted this part of the
+ 
+
+ align:start position:0%
+we have double counted this part of the
+diagram and so we need to correct for
+
+ align:start position:0%
+diagram and so we need to correct for
+ 
+
+ align:start position:0%
+diagram and so we need to correct for
+that and we need to subtract the
+
+ align:start position:0%
+that and we need to subtract the
+ 
+
+ align:start position:0%
+that and we need to subtract the
+probability of this intersection and
+
+ align:start position:0%
+probability of this intersection and
+ 
+
+ align:start position:0%
+probability of this intersection and
+that's how this formula comes about can
+
+ align:start position:0%
+that's how this formula comes about can
+ 
+
+ align:start position:0%
+that's how this formula comes about can
+we generalize this thinking let's say to
+
+ align:start position:0%
+we generalize this thinking let's say to
+ 
+
+ align:start position:0%
+we generalize this thinking let's say to
+the case of three events suppose that we
+
+ align:start position:0%
+the case of three events suppose that we
+ 
+
+ align:start position:0%
+the case of three events suppose that we
+have three events a1 a2 and a3 and we
+
+ align:start position:0%
+have three events a1 a2 and a3 and we
+ 
+
+ align:start position:0%
+have three events a1 a2 and a3 and we
+want to calculate the probability of
+
+ align:start position:0%
+want to calculate the probability of
+ 
+
+ align:start position:0%
+want to calculate the probability of
+their union we first start by adding the
+
+ align:start position:0%
+their union we first start by adding the
+ 
+
+ align:start position:0%
+their union we first start by adding the
+probabilities of the different sets but
+
+ align:start position:0%
+probabilities of the different sets but
+ 
+
+ align:start position:0%
+probabilities of the different sets but
+then we realize that for example this
+
+ align:start position:0%
+then we realize that for example this
+ 
+
+ align:start position:0%
+then we realize that for example this
+part of the diagram has been counted
+
+ align:start position:0%
+part of the diagram has been counted
+ 
+
+ align:start position:0%
+part of the diagram has been counted
+twice it shows up once inside the
+
+ align:start position:0%
+twice it shows up once inside the
+ 
+
+ align:start position:0%
+twice it shows up once inside the
+probability of a1 and once inside the
+
+ align:start position:0%
+probability of a1 and once inside the
+ 
+
+ align:start position:0%
+probability of a1 and once inside the
+probability of a2 so for this reason we
+
+ align:start position:0%
+probability of a2 so for this reason we
+ 
+
+ align:start position:0%
+probability of a2 so for this reason we
+need to make a correction and we need to
+
+ align:start position:0%
+need to make a correction and we need to
+ 
+
+ align:start position:0%
+need to make a correction and we need to
+subtract the probability of this
+
+ align:start position:0%
+subtract the probability of this
+ 
+
+ align:start position:0%
+subtract the probability of this
+intersection similarly subtract the
+
+ align:start position:0%
+intersection similarly subtract the
+ 
+
+ align:start position:0%
+intersection similarly subtract the
+probability of that intersection and of
+
+ align:start position:0%
+probability of that intersection and of
+ 
+
+ align:start position:0%
+probability of that intersection and of
+this one so we subtract the
+
+ align:start position:0%
+this one so we subtract the
+ 
+
+ align:start position:0%
+this one so we subtract the
+probabilities of these intersections but
+
+ align:start position:0%
+probabilities of these intersections but
+ 
+
+ align:start position:0%
+probabilities of these intersections but
+actually the intersections are not just
+
+ align:start position:0%
+actually the intersections are not just
+ 
+
+ align:start position:0%
+actually the intersections are not just
+what I drew here the intersections also
+
+ align:start position:0%
+what I drew here the intersections also
+ 
+
+ align:start position:0%
+what I drew here the intersections also
+involve this part so now let us focus on
+
+ align:start position:0%
+involve this part so now let us focus on
+ 
+
+ align:start position:0%
+involve this part so now let us focus on
+this part of the diagram here a typical
+
+ align:start position:0%
+this part of the diagram here a typical
+ 
+
+ align:start position:0%
+this part of the diagram here a typical
+element that belongs to all three of the
+
+ align:start position:0%
+element that belongs to all three of the
+ 
+
+ align:start position:0%
+element that belongs to all three of the
+sets will show up once here once here
+
+ align:start position:0%
+sets will show up once here once here
+ 
+
+ align:start position:0%
+sets will show up once here once here
+and once there but it will also show up
+
+ align:start position:0%
+and once there but it will also show up
+ 
+
+ align:start position:0%
+and once there but it will also show up
+in all of these intersections and so it
+
+ align:start position:0%
+in all of these intersections and so it
+ 
+
+ align:start position:0%
+in all of these intersections and so it
+shows up three times with the plus sign
+
+ align:start position:0%
+shows up three times with the plus sign
+ 
+
+ align:start position:0%
+shows up three times with the plus sign
+three times with a minus sign which
+
+ align:start position:0%
+three times with a minus sign which
+ 
+
+ align:start position:0%
+three times with a minus sign which
+means that these elements will not
+
+ align:start position:0%
+means that these elements will not
+ 
+
+ align:start position:0%
+means that these elements will not
+counted at all in order to count them we
+
+ align:start position:0%
+counted at all in order to count them we
+ 
+
+ align:start position:0%
+counted at all in order to count them we
+need to add one more term which is the
+
+ align:start position:0%
+need to add one more term which is the
+ 
+
+ align:start position:0%
+need to add one more term which is the
+probability of the three-way
+
+ align:start position:0%
+probability of the three-way
+ 
+
+ align:start position:0%
+probability of the three-way
+intersection so this is the formula for
+
+ align:start position:0%
+intersection so this is the formula for
+ 
+
+ align:start position:0%
+intersection so this is the formula for
+the probability of the union of three
+
+ align:start position:0%
+the probability of the union of three
+ 
+
+ align:start position:0%
+the probability of the union of three
+events it has a rationale similar to
+
+ align:start position:0%
+events it has a rationale similar to
+ 
+
+ align:start position:0%
+events it has a rationale similar to
+this formula and you can convince
+
+ align:start position:0%
+this formula and you can convince
+ 
+
+ align:start position:0%
+this formula and you can convince
+yourself that it is a correct formula by
+
+ align:start position:0%
+yourself that it is a correct formula by
+ 
+
+ align:start position:0%
+yourself that it is a correct formula by
+just looking at the different pieces of
+
+ align:start position:0%
+just looking at the different pieces of
+ 
+
+ align:start position:0%
+just looking at the different pieces of
+this diagram and make sure that each one
+
+ align:start position:0%
+this diagram and make sure that each one
+ 
+
+ align:start position:0%
+this diagram and make sure that each one
+of them is accounted properly but
+
+ align:start position:0%
+of them is accounted properly but
+ 
+
+ align:start position:0%
+of them is accounted properly but
+instead of working in terms of such a
+
+ align:start position:0%
+instead of working in terms of such a
+ 
+
+ align:start position:0%
+instead of working in terms of such a
+picture let us think about a more formal
+
+ align:start position:0%
+picture let us think about a more formal
+ 
+
+ align:start position:0%
+picture let us think about a more formal
+derivation and the formal derivation
+
+ align:start position:0%
+derivation and the formal derivation
+ 
+
+ align:start position:0%
+derivation and the formal derivation
+we'll use a beautiful trick namely
+
+ align:start position:0%
+we'll use a beautiful trick namely
+ 
+
+ align:start position:0%
+we'll use a beautiful trick namely
+indicator functions so here is the
+
+ align:start position:0%
+indicator functions so here is the
+ 
+
+ align:start position:0%
+indicator functions so here is the
+formula that we want to establish and
+
+ align:start position:0%
+formula that we want to establish and
+ 
+
+ align:start position:0%
+formula that we want to establish and
+let us remind ourselves what indicator
+
+ align:start position:0%
+let us remind ourselves what indicator
+ 
+
+ align:start position:0%
+let us remind ourselves what indicator
+functions are 20 set or event we can
+
+ align:start position:0%
+functions are 20 set or event we can
+ 
+
+ align:start position:0%
+functions are 20 set or event we can
+associate an indicator function let's
+
+ align:start position:0%
+associate an indicator function let's
+ 
+
+ align:start position:0%
+associate an indicator function let's
+say that this is the set a I we are
+
+ align:start position:0%
+say that this is the set a I we are
+ 
+
+ align:start position:0%
+say that this is the set a I we are
+going to associate an indicator function
+
+ align:start position:0%
+going to associate an indicator function
+ 
+
+ align:start position:0%
+going to associate an indicator function
+call it X I which is equal to 1 when the
+
+ align:start position:0%
+call it X I which is equal to 1 when the
+ 
+
+ align:start position:0%
+call it X I which is equal to 1 when the
+outcome is inside this set and it's
+
+ align:start position:0%
+outcome is inside this set and it's
+ 
+
+ align:start position:0%
+outcome is inside this set and it's
+going to be zero when the outcome is
+
+ align:start position:0%
+going to be zero when the outcome is
+ 
+
+ align:start position:0%
+going to be zero when the outcome is
+outside what is the indicator function
+
+ align:start position:0%
+outside what is the indicator function
+ 
+
+ align:start position:0%
+outside what is the indicator function
+of the complement the indicator function
+
+ align:start position:0%
+of the complement the indicator function
+ 
+
+ align:start position:0%
+of the complement the indicator function
+of the complement is 1 minus the
+
+ align:start position:0%
+of the complement is 1 minus the
+ 
+
+ align:start position:0%
+of the complement is 1 minus the
+indicator of the event why is this if
+
+ align:start position:0%
+indicator of the event why is this if
+ 
+
+ align:start position:0%
+indicator of the event why is this if
+the outcome is in the complement then X
+
+ align:start position:0%
+the outcome is in the complement then X
+ 
+
+ align:start position:0%
+the outcome is in the complement then X
+I is equal to 0 and this expression is
+
+ align:start position:0%
+I is equal to 0 and this expression is
+ 
+
+ align:start position:0%
+I is equal to 0 and this expression is
+equal to 1 on the other hand if the
+
+ align:start position:0%
+equal to 1 on the other hand if the
+ 
+
+ align:start position:0%
+equal to 1 on the other hand if the
+outcome is inside a I then the indicator
+
+ align:start position:0%
+outcome is inside a I then the indicator
+ 
+
+ align:start position:0%
+outcome is inside a I then the indicator
+function will be equal to 1 and this
+
+ align:start position:0%
+function will be equal to 1 and this
+ 
+
+ align:start position:0%
+function will be equal to 1 and this
+quantity is going to be equal to 0 if we
+
+ align:start position:0%
+quantity is going to be equal to 0 if we
+ 
+
+ align:start position:0%
+quantity is going to be equal to 0 if we
+have the intersection of two events AI
+
+ align:start position:0%
+have the intersection of two events AI
+ 
+
+ align:start position:0%
+have the intersection of two events AI
+and AJ what is their indicator function
+
+ align:start position:0%
+and AJ what is their indicator function
+ 
+
+ align:start position:0%
+and AJ what is their indicator function
+it is X I times XJ this expression is
+
+ align:start position:0%
+it is X I times XJ this expression is
+ 
+
+ align:start position:0%
+it is X I times XJ this expression is
+equal to 1 if and only if X I is equal
+
+ align:start position:0%
+equal to 1 if and only if X I is equal
+ 
+
+ align:start position:0%
+equal to 1 if and only if X I is equal
+to 1 and XJ is equal to 1 which happens
+
+ align:start position:0%
+to 1 and XJ is equal to 1 which happens
+ 
+
+ align:start position:0%
+to 1 and XJ is equal to 1 which happens
+if and only if the outcome is inside AI
+
+ align:start position:0%
+if and only if the outcome is inside AI
+ 
+
+ align:start position:0%
+if and only if the outcome is inside AI
+and also inside AJ
+
+ align:start position:0%
+and also inside AJ
+ 
+
+ align:start position:0%
+and also inside AJ
+now what about the indicator of the
+
+ align:start position:0%
+now what about the indicator of the
+ 
+
+ align:start position:0%
+now what about the indicator of the
+intersection of the complements while
+
+ align:start position:0%
+intersection of the complements while
+ 
+
+ align:start position:0%
+intersection of the complements while
+it's an intersection so the Associated
+
+ align:start position:0%
+it's an intersection so the Associated
+ 
+
+ align:start position:0%
+it's an intersection so the Associated
+indicator function is going to be the
+
+ align:start position:0%
+indicator function is going to be the
+ 
+
+ align:start position:0%
+indicator function is going to be the
+product of the indicator function of the
+
+ align:start position:0%
+product of the indicator function of the
+ 
+
+ align:start position:0%
+product of the indicator function of the
+first set which is 1 minus X I times the
+
+ align:start position:0%
+first set which is 1 minus X I times the
+ 
+
+ align:start position:0%
+first set which is 1 minus X I times the
+indicator function of the second set
+
+ align:start position:0%
+indicator function of the second set
+ 
+
+ align:start position:0%
+indicator function of the second set
+which is 1 minus XJ and finally what is
+
+ align:start position:0%
+which is 1 minus XJ and finally what is
+ 
+
+ align:start position:0%
+which is 1 minus XJ and finally what is
+the indicator function of this event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we remember the Morgan's laws the
+
+ align:start position:0%
+here we remember the Morgan's laws the
+ 
+
+ align:start position:0%
+here we remember the Morgan's laws the
+Morgan's laws tell us that the
+
+ align:start position:0%
+Morgan's laws tell us that the
+ 
+
+ align:start position:0%
+Morgan's laws tell us that the
+complement of this set the complement of
+
+ align:start position:0%
+complement of this set the complement of
+ 
+
+ align:start position:0%
+complement of this set the complement of
+a union is the intersection of the
+
+ align:start position:0%
+a union is the intersection of the
+ 
+
+ align:start position:0%
+a union is the intersection of the
+complements so this event here is the
+
+ align:start position:0%
+complements so this event here is the
+ 
+
+ align:start position:0%
+complements so this event here is the
+complement of that event and therefore
+
+ align:start position:0%
+complement of that event and therefore
+ 
+
+ align:start position:0%
+complement of that event and therefore
+the Associated indicator function is
+
+ align:start position:0%
+the Associated indicator function is
+ 
+
+ align:start position:0%
+the Associated indicator function is
+going to be 1 minus this expression and
+
+ align:start position:0%
+going to be 1 minus this expression and
+ 
+
+ align:start position:0%
+going to be 1 minus this expression and
+if we were dealing with more than two
+
+ align:start position:0%
+if we were dealing with more than two
+ 
+
+ align:start position:0%
+if we were dealing with more than two
+sets and here we had for example 3-way
+
+ align:start position:0%
+sets and here we had for example 3-way
+ 
+
+ align:start position:0%
+sets and here we had for example 3-way
+intersections you would get the product
+
+ align:start position:0%
+intersections you would get the product
+ 
+
+ align:start position:0%
+intersections you would get the product
+of three terms and if we had a 3-way
+
+ align:start position:0%
+of three terms and if we had a 3-way
+ 
+
+ align:start position:0%
+of three terms and if we had a 3-way
+union we would get a similar expression
+
+ align:start position:0%
+union we would get a similar expression
+ 
+
+ align:start position:0%
+union we would get a similar expression
+except that here we would have again a
+
+ align:start position:0%
+except that here we would have again a
+ 
+
+ align:start position:0%
+except that here we would have again a
+product of three terms instead of two so
+
+ align:start position:0%
+product of three terms instead of two so
+ 
+
+ align:start position:0%
+product of three terms instead of two so
+now let us put to use what we have done
+
+ align:start position:0%
+now let us put to use what we have done
+ 
+
+ align:start position:0%
+now let us put to use what we have done
+so far we are interested in the
+
+ align:start position:0%
+so far we are interested in the
+ 
+
+ align:start position:0%
+so far we are interested in the
+probability that the outcome falls in
+
+ align:start position:0%
+probability that the outcome falls in
+ 
+
+ align:start position:0%
+probability that the outcome falls in
+the union of three sets now an important
+
+ align:start position:0%
+the union of three sets now an important
+ 
+
+ align:start position:0%
+the union of three sets now an important
+fact to remember is that the probability
+
+ align:start position:0%
+fact to remember is that the probability
+ 
+
+ align:start position:0%
+fact to remember is that the probability
+of an event is the same as the expected
+
+ align:start position:0%
+of an event is the same as the expected
+ 
+
+ align:start position:0%
+of an event is the same as the expected
+value of the indicator of that event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is because the indicator is equal
+
+ align:start position:0%
+this is because the indicator is equal
+ 
+
+ align:start position:0%
+this is because the indicator is equal
+to one if and only if the outcome
+
+ align:start position:0%
+to one if and only if the outcome
+ 
+
+ align:start position:0%
+to one if and only if the outcome
+happens to be inside that set and so the
+
+ align:start position:0%
+happens to be inside that set and so the
+ 
+
+ align:start position:0%
+happens to be inside that set and so the
+contribution that we get to the
+
+ align:start position:0%
+contribution that we get to the
+ 
+
+ align:start position:0%
+contribution that we get to the
+expectation is 1 times the probability
+
+ align:start position:0%
+expectation is 1 times the probability
+ 
+
+ align:start position:0%
+expectation is 1 times the probability
+that the indicator is
+
+ align:start position:0%
+that the indicator is
+ 
+
+ align:start position:0%
+that the indicator is
+which is just this probability now the
+
+ align:start position:0%
+which is just this probability now the
+ 
+
+ align:start position:0%
+which is just this probability now the
+indicator of a three-way union is going
+
+ align:start position:0%
+indicator of a three-way union is going
+ 
+
+ align:start position:0%
+indicator of a three-way union is going
+to be by what we just discussed one - a
+
+ align:start position:0%
+to be by what we just discussed one - a
+ 
+
+ align:start position:0%
+to be by what we just discussed one - a
+product of this kind but now with three
+
+ align:start position:0%
+product of this kind but now with three
+ 
+
+ align:start position:0%
+product of this kind but now with three
+terms let us now calculate this
+
+ align:start position:0%
+terms let us now calculate this
+ 
+
+ align:start position:0%
+terms let us now calculate this
+expectation by expanding the product
+
+ align:start position:0%
+expectation by expanding the product
+ 
+
+ align:start position:0%
+expectation by expanding the product
+involved we have this first term then
+
+ align:start position:0%
+involved we have this first term then
+ 
+
+ align:start position:0%
+involved we have this first term then
+when we multiply those three terms
+
+ align:start position:0%
+when we multiply those three terms
+ 
+
+ align:start position:0%
+when we multiply those three terms
+together we're going to get a bunch of
+
+ align:start position:0%
+together we're going to get a bunch of
+ 
+
+ align:start position:0%
+together we're going to get a bunch of
+contributions one contribution with a
+
+ align:start position:0%
+contributions one contribution with a
+ 
+
+ align:start position:0%
+contributions one contribution with a
+minus sign is 1 times 1 times 1 another
+
+ align:start position:0%
+minus sign is 1 times 1 times 1 another
+ 
+
+ align:start position:0%
+minus sign is 1 times 1 times 1 another
+contribution would be minus - that's a
+
+ align:start position:0%
+contribution would be minus - that's a
+ 
+
+ align:start position:0%
+contribution would be minus - that's a
+plus X 1 times 1 times 1 and similarly
+
+ align:start position:0%
+plus X 1 times 1 times 1 and similarly
+ 
+
+ align:start position:0%
+plus X 1 times 1 times 1 and similarly
+we get a contribution of X 2 and X 3 and
+
+ align:start position:0%
+we get a contribution of X 2 and X 3 and
+ 
+
+ align:start position:0%
+we get a contribution of X 2 and X 3 and
+then we have a contribution such as X 1
+
+ align:start position:0%
+then we have a contribution such as X 1
+ 
+
+ align:start position:0%
+then we have a contribution such as X 1
+times X 2 times 1 and if you look at the
+
+ align:start position:0%
+times X 2 times 1 and if you look at the
+ 
+
+ align:start position:0%
+times X 2 times 1 and if you look at the
+minus signs there are 3 minus is
+
+ align:start position:0%
+minus signs there are 3 minus is
+ 
+
+ align:start position:0%
+minus signs there are 3 minus is
+involved so overall it's going to be a
+
+ align:start position:0%
+involved so overall it's going to be a
+ 
+
+ align:start position:0%
+involved so overall it's going to be a
+minus minus x1 times x2 and then there
+
+ align:start position:0%
+minus minus x1 times x2 and then there
+ 
+
+ align:start position:0%
+minus minus x1 times x2 and then there
+is going to be similar terms such as x1
+
+ align:start position:0%
+is going to be similar terms such as x1
+ 
+
+ align:start position:0%
+is going to be similar terms such as x1
+x3 and x2 x3 and finally there's going
+
+ align:start position:0%
+x3 and x2 x3 and finally there's going
+ 
+
+ align:start position:0%
+x3 and x2 x3 and finally there's going
+to be a term x1 times x2 times x3
+
+ align:start position:0%
+to be a term x1 times x2 times x3
+ 
+
+ align:start position:0%
+to be a term x1 times x2 times x3
+there's a total of 4 minus signs
+
+ align:start position:0%
+there's a total of 4 minus signs
+ 
+
+ align:start position:0%
+there's a total of 4 minus signs
+involved so everything shows up in the
+
+ align:start position:0%
+involved so everything shows up in the
+ 
+
+ align:start position:0%
+involved so everything shows up in the
+end with a plus sign so the probability
+
+ align:start position:0%
+end with a plus sign so the probability
+ 
+
+ align:start position:0%
+end with a plus sign so the probability
+of this event is equal to the
+
+ align:start position:0%
+of this event is equal to the
+ 
+
+ align:start position:0%
+of this event is equal to the
+expectation of this random variable here
+
+ align:start position:0%
+expectation of this random variable here
+ 
+
+ align:start position:0%
+expectation of this random variable here
+we notice that the ones cancel out the
+
+ align:start position:0%
+we notice that the ones cancel out the
+ 
+
+ align:start position:0%
+we notice that the ones cancel out the
+expected value of x1 for an indicator
+
+ align:start position:0%
+expected value of x1 for an indicator
+ 
+
+ align:start position:0%
+expected value of x1 for an indicator
+variable is just the probability of that
+
+ align:start position:0%
+variable is just the probability of that
+ 
+
+ align:start position:0%
+variable is just the probability of that
+event and we get this term the expected
+
+ align:start position:0%
+event and we get this term the expected
+ 
+
+ align:start position:0%
+event and we get this term the expected
+value of x2 and x3 give us these terms
+
+ align:start position:0%
+value of x2 and x3 give us these terms
+ 
+
+ align:start position:0%
+value of x2 and x3 give us these terms
+the expected value of x1 times x2 this
+
+ align:start position:0%
+the expected value of x1 times x2 this
+ 
+
+ align:start position:0%
+the expected value of x1 times x2 this
+is the indicator random variable of the
+
+ align:start position:0%
+is the indicator random variable of the
+ 
+
+ align:start position:0%
+is the indicator random variable of the
+intersection so the expected value of
+
+ align:start position:0%
+intersection so the expected value of
+ 
+
+ align:start position:0%
+intersection so the expected value of
+this term is just the probability of the
+
+ align:start position:0%
+this term is just the probability of the
+ 
+
+ align:start position:0%
+this term is just the probability of the
+intersection of a1 and a2
+
+ align:start position:0%
+intersection of a1 and a2
+ 
+
+ align:start position:0%
+intersection of a1 and a2
+and similarly these terms here give rise
+
+ align:start position:0%
+and similarly these terms here give rise
+ 
+
+ align:start position:0%
+and similarly these terms here give rise
+to those two terms here finally x1 times
+
+ align:start position:0%
+to those two terms here finally x1 times
+ 
+
+ align:start position:0%
+to those two terms here finally x1 times
+x2 times x3 is the indicator variable
+
+ align:start position:0%
+x2 times x3 is the indicator variable
+ 
+
+ align:start position:0%
+x2 times x3 is the indicator variable
+for the event a 1 intersection a 2
+
+ align:start position:0%
+for the event a 1 intersection a 2
+ 
+
+ align:start position:0%
+for the event a 1 intersection a 2
+intersection a 3 therefore the expected
+
+ align:start position:0%
+intersection a 3 therefore the expected
+ 
+
+ align:start position:0%
+intersection a 3 therefore the expected
+value of this term is equal to this
+
+ align:start position:0%
+value of this term is equal to this
+ 
+
+ align:start position:0%
+value of this term is equal to this
+probability and therefore we have
+
+ align:start position:0%
+probability and therefore we have
+ 
+
+ align:start position:0%
+probability and therefore we have
+established exactly the formula that we
+
+ align:start position:0%
+established exactly the formula that we
+ 
+
+ align:start position:0%
+established exactly the formula that we
+wanted to establish now this derivation
+
+ align:start position:0%
+wanted to establish now this derivation
+ 
+
+ align:start position:0%
+wanted to establish now this derivation
+that we carried out here there's nothing
+
+ align:start position:0%
+that we carried out here there's nothing
+ 
+
+ align:start position:0%
+that we carried out here there's nothing
+special about the case of three we could
+
+ align:start position:0%
+special about the case of three we could
+ 
+
+ align:start position:0%
+special about the case of three we could
+have the union of many more events we
+
+ align:start position:0%
+have the union of many more events we
+ 
+
+ align:start position:0%
+have the union of many more events we
+would just have here the product of more
+
+ align:start position:0%
+would just have here the product of more
+ 
+
+ align:start position:0%
+would just have here the product of more
+terms and we would need to carry out the
+
+ align:start position:0%
+terms and we would need to carry out the
+ 
+
+ align:start position:0%
+terms and we would need to carry out the
+multiplication and we would get cross
+
+ align:start position:0%
+multiplication and we would get cross
+ 
+
+ align:start position:0%
+multiplication and we would get cross
+terms of all types involving just one of
+
+ align:start position:0%
+terms of all types involving just one of
+ 
+
+ align:start position:0%
+terms of all types involving just one of
+the indicator variables or products of
+
+ align:start position:0%
+the indicator variables or products of
+ 
+
+ align:start position:0%
+the indicator variables or products of
+two indicator variables or products of
+
+ align:start position:0%
+two indicator variables or products of
+ 
+
+ align:start position:0%
+two indicator variables or products of
+three indicator variables and so on and
+
+ align:start position:0%
+three indicator variables and so on and
+ 
+
+ align:start position:0%
+three indicator variables and so on and
+after you carry out this exercise and
+
+ align:start position:0%
+after you carry out this exercise and
+ 
+
+ align:start position:0%
+after you carry out this exercise and
+keep track of the various terms you end
+
+ align:start position:0%
+keep track of the various terms you end
+ 
+
+ align:start position:0%
+keep track of the various terms you end
+up with this general version of what is
+
+ align:start position:0%
+up with this general version of what is
+ 
+
+ align:start position:0%
+up with this general version of what is
+called the inclusion exclusion formula
+
+ align:start position:0%
+called the inclusion exclusion formula
+ 
+
+ align:start position:0%
+called the inclusion exclusion formula
+so the probability of a union is there's
+
+ align:start position:0%
+so the probability of a union is there's
+ 
+
+ align:start position:0%
+so the probability of a union is there's
+the sum of the probabilities but then
+
+ align:start position:0%
+the sum of the probabilities but then
+ 
+
+ align:start position:0%
+the sum of the probabilities but then
+you subtract all possible probabilities
+
+ align:start position:0%
+you subtract all possible probabilities
+ 
+
+ align:start position:0%
+you subtract all possible probabilities
+of two-way intersections then we add
+
+ align:start position:0%
+of two-way intersections then we add
+ 
+
+ align:start position:0%
+of two-way intersections then we add
+probabilities of 3-way intersections
+
+ align:start position:0%
+probabilities of 3-way intersections
+ 
+
+ align:start position:0%
+probabilities of 3-way intersections
+then you subtract probabilities of
+
+ align:start position:0%
+then you subtract probabilities of
+ 
+
+ align:start position:0%
+then you subtract probabilities of
+four-way intersections and you keep
+
+ align:start position:0%
+four-way intersections and you keep
+ 
+
+ align:start position:0%
+four-way intersections and you keep
+going this way alternating signs until
+
+ align:start position:0%
+going this way alternating signs until
+ 
+
+ align:start position:0%
+going this way alternating signs until
+you get to the last term which is the
+
+ align:start position:0%
+you get to the last term which is the
+ 
+
+ align:start position:0%
+you get to the last term which is the
+probability of the intersection of all
+
+ align:start position:0%
+probability of the intersection of all
+ 
+
+ align:start position:0%
+probability of the intersection of all
+the events involved and this exponent
+
+ align:start position:0%
+the events involved and this exponent
+ 
+
+ align:start position:0%
+the events involved and this exponent
+here of n minus 1 is the exponent that
+
+ align:start position:0%
+here of n minus 1 is the exponent that
+ 
+
+ align:start position:0%
+here of n minus 1 is the exponent that
+you need so that the last term has the
+
+ align:start position:0%
+you need so that the last term has the
+ 
+
+ align:start position:0%
+you need so that the last term has the
+correct sign so for example if n is
+
+ align:start position:0%
+correct sign so for example if n is
+ 
+
+ align:start position:0%
+correct sign so for example if n is
+equal to 3 the exponent would be 2 so
+
+ align:start position:0%
+equal to 3 the exponent would be 2 so
+ 
+
+ align:start position:0%
+equal to 3 the exponent would be 2 so
+this could be a plus sign which is
+
+ align:start position:0%
+this could be a plus sign which is
+ 
+
+ align:start position:0%
+this could be a plus sign which is
+consistent with what we got here so this
+
+ align:start position:0%
+consistent with what we got here so this
+ 
+
+ align:start position:0%
+consistent with what we got here so this
+is a formula that is quite useful when
+
+ align:start position:0%
+is a formula that is quite useful when
+ 
+
+ align:start position:0%
+is a formula that is quite useful when
+you want to calculate probabilities of
+
+ align:start position:0%
+you want to calculate probabilities of
+ 
+
+ align:start position:0%
+you want to calculate probabilities of
+unions of events but also this
+
+ align:start position:0%
+unions of events but also this
+ 
+
+ align:start position:0%
+unions of events but also this
+derivation using
+
+ align:start position:0%
+derivation using
+ 
+
+ align:start position:0%
+derivation using
+indicator functions is quite beautiful
\ No newline at end of file
diff --git a/XX7ePR21Ook.txt b/XX7ePR21Ook.txt
new file mode 100644
index 0000000000000000000000000000000000000000..22d801cb6813589a3fdec684d78ec14a75c38647
--- /dev/null
+++ b/XX7ePR21Ook.txt
@@ -0,0 +1,11770 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit M opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so let's get
+
+ align:start position:0%
+ocw.mit.edu so let's get
+ 
+
+ align:start position:0%
+ocw.mit.edu so let's get
+ready um if good you should receive some
+
+ align:start position:0%
+ready um if good you should receive some
+ 
+
+ align:start position:0%
+ready um if good you should receive some
+handouts so the TA are walking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around so you should slowly get those um
+
+ align:start position:0%
+around so you should slowly get those um
+ 
+
+ align:start position:0%
+around so you should slowly get those um
+this is the second lecture on number
+
+ align:start position:0%
+this is the second lecture on number
+ 
+
+ align:start position:0%
+this is the second lecture on number
+Theory and we're going to cover a lot of
+
+ align:start position:0%
+Theory and we're going to cover a lot of
+ 
+
+ align:start position:0%
+Theory and we're going to cover a lot of
+stuff and actually we're going to start
+
+ align:start position:0%
+stuff and actually we're going to start
+ 
+
+ align:start position:0%
+stuff and actually we're going to start
+with uh um encryption which is an
+
+ align:start position:0%
+with uh um encryption which is an
+ 
+
+ align:start position:0%
+with uh um encryption which is an
+application of number Theory and we will
+
+ align:start position:0%
+application of number Theory and we will
+ 
+
+ align:start position:0%
+application of number Theory and we will
+take that as a theme throughout the
+
+ align:start position:0%
+take that as a theme throughout the
+ 
+
+ align:start position:0%
+take that as a theme throughout the
+whole lecture and so in this way you can
+
+ align:start position:0%
+whole lecture and so in this way you can
+ 
+
+ align:start position:0%
+whole lecture and so in this way you can
+see how useful number theory is
+
+ align:start position:0%
+see how useful number theory is
+ 
+
+ align:start position:0%
+see how useful number theory is
+um now um encryption
+
+ align:start position:0%
+um now um encryption
+ 
+
+ align:start position:0%
+um now um encryption
+uh yeah what is it so let's first talk
+
+ align:start position:0%
+uh yeah what is it so let's first talk
+ 
+
+ align:start position:0%
+uh yeah what is it so let's first talk
+about that a little bit maybe some of
+
+ align:start position:0%
+about that a little bit maybe some of
+ 
+
+ align:start position:0%
+about that a little bit maybe some of
+you have heard about it but cryptology
+
+ align:start position:0%
+you have heard about it but cryptology
+ 
+
+ align:start position:0%
+you have heard about it but cryptology
+in general is the art of hiding uh
+
+ align:start position:0%
+in general is the art of hiding uh
+ 
+
+ align:start position:0%
+in general is the art of hiding uh
+information and encryption is a very
+
+ align:start position:0%
+information and encryption is a very
+ 
+
+ align:start position:0%
+information and encryption is a very
+useful tool I will only give a very high
+
+ align:start position:0%
+useful tool I will only give a very high
+ 
+
+ align:start position:0%
+useful tool I will only give a very high
+level overview I mean if you really want
+
+ align:start position:0%
+level overview I mean if you really want
+ 
+
+ align:start position:0%
+level overview I mean if you really want
+to know more about this you should do a
+
+ align:start position:0%
+to know more about this you should do a
+ 
+
+ align:start position:0%
+to know more about this you should do a
+class in in in crypto or or or or
+
+ align:start position:0%
+class in in in crypto or or or or
+ 
+
+ align:start position:0%
+class in in in crypto or or or or
+practical
+
+ align:start position:0%
+practical
+ 
+
+ align:start position:0%
+practical
+security um so what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encryption um the idea is usually that
+
+ align:start position:0%
+encryption um the idea is usually that
+ 
+
+ align:start position:0%
+encryption um the idea is usually that
+beforehand um we're going to
+
+ align:start position:0%
+beforehand um we're going to
+ 
+
+ align:start position:0%
+beforehand um we're going to
+share a whole bunch of
+
+ align:start position:0%
+share a whole bunch of
+ 
+
+ align:start position:0%
+share a whole bunch of
+keys so keys
+
+ align:start position:0%
+keys so keys
+ 
+
+ align:start position:0%
+keys so keys
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exchanged uh between a receiver and a
+
+ align:start position:0%
+exchanged uh between a receiver and a
+ 
+
+ align:start position:0%
+exchanged uh between a receiver and a
+sender and the whole idea is that if I
+
+ align:start position:0%
+sender and the whole idea is that if I
+ 
+
+ align:start position:0%
+sender and the whole idea is that if I
+want to transmit like a message to one
+
+ align:start position:0%
+want to transmit like a message to one
+ 
+
+ align:start position:0%
+want to transmit like a message to one
+of you uh well there could be someone in
+
+ align:start position:0%
+of you uh well there could be someone in
+ 
+
+ align:start position:0%
+of you uh well there could be someone in
+the middle who wants to intercept my my
+
+ align:start position:0%
+the middle who wants to intercept my my
+ 
+
+ align:start position:0%
+the middle who wants to intercept my my
+message and wants to find find out what
+
+ align:start position:0%
+message and wants to find find out what
+ 
+
+ align:start position:0%
+message and wants to find find out what
+I'm saying so I do not like this and in
+
+ align:start position:0%
+I'm saying so I do not like this and in
+ 
+
+ align:start position:0%
+I'm saying so I do not like this and in
+order to avoid it I will use encryption
+
+ align:start position:0%
+order to avoid it I will use encryption
+ 
+
+ align:start position:0%
+order to avoid it I will use encryption
+which is some kind of algorithm that
+
+ align:start position:0%
+which is some kind of algorithm that
+ 
+
+ align:start position:0%
+which is some kind of algorithm that
+actually uh
+
+ align:start position:0%
+actually uh
+ 
+
+ align:start position:0%
+actually uh
+transforms um my message M my plain
+
+ align:start position:0%
+transforms um my message M my plain
+ 
+
+ align:start position:0%
+transforms um my message M my plain
+message by using some kind of algorithm
+
+ align:start position:0%
+message by using some kind of algorithm
+ 
+
+ align:start position:0%
+message by using some kind of algorithm
+e some encryption algorithm uh it can be
+
+ align:start position:0%
+e some encryption algorithm uh it can be
+ 
+
+ align:start position:0%
+e some encryption algorithm uh it can be
+a function as well um that uses the keys
+
+ align:start position:0%
+a function as well um that uses the keys
+ 
+
+ align:start position:0%
+a function as well um that uses the keys
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+transform this into an encryption which
+
+ align:start position:0%
+transform this into an encryption which
+ 
+
+ align:start position:0%
+transform this into an encryption which
+we call M Prime here so the plain text
+
+ align:start position:0%
+we call M Prime here so the plain text
+ 
+
+ align:start position:0%
+we call M Prime here so the plain text
+uh has in the clear all the information
+
+ align:start position:0%
+uh has in the clear all the information
+ 
+
+ align:start position:0%
+uh has in the clear all the information
+that I want to convey to one of you for
+
+ align:start position:0%
+that I want to convey to one of you for
+ 
+
+ align:start position:0%
+that I want to convey to one of you for
+example and M Prime is somehow uh a
+
+ align:start position:0%
+example and M Prime is somehow uh a
+ 
+
+ align:start position:0%
+example and M Prime is somehow uh a
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+uh uh well uh mixture of bits uh out of
+
+ align:start position:0%
+uh uh well uh mixture of bits uh out of
+ 
+
+ align:start position:0%
+uh uh well uh mixture of bits uh out of
+which I'm not able to distill any
+
+ align:start position:0%
+which I'm not able to distill any
+ 
+
+ align:start position:0%
+which I'm not able to distill any
+information about the plain text so
+
+ align:start position:0%
+information about the plain text so
+ 
+
+ align:start position:0%
+information about the plain text so
+encryption is a very special kind of
+
+ align:start position:0%
+encryption is a very special kind of
+ 
+
+ align:start position:0%
+encryption is a very special kind of
+thing and we're not going to talk about
+
+ align:start position:0%
+thing and we're not going to talk about
+ 
+
+ align:start position:0%
+thing and we're not going to talk about
+the precise definitions here but we just
+
+ align:start position:0%
+the precise definitions here but we just
+ 
+
+ align:start position:0%
+the precise definitions here but we just
+take the ID into uh this lecture now
+
+ align:start position:0%
+take the ID into uh this lecture now
+ 
+
+ align:start position:0%
+take the ID into uh this lecture now
+decryption is uh transforming the cipher
+
+ align:start position:0%
+decryption is uh transforming the cipher
+ 
+
+ align:start position:0%
+decryption is uh transforming the cipher
+text back into the plain text so we will
+
+ align:start position:0%
+text back into the plain text so we will
+ 
+
+ align:start position:0%
+text back into the plain text so we will
+start with the encryption uh M Prime and
+
+ align:start position:0%
+start with the encryption uh M Prime and
+ 
+
+ align:start position:0%
+start with the encryption uh M Prime and
+we have some kind of decryption
+
+ align:start position:0%
+we have some kind of decryption
+ 
+
+ align:start position:0%
+we have some kind of decryption
+algorithm and again we can make use of
+
+ align:start position:0%
+algorithm and again we can make use of
+ 
+
+ align:start position:0%
+algorithm and again we can make use of
+the keys that we
+
+ align:start position:0%
+the keys that we
+ 
+
+ align:start position:0%
+the keys that we
+exchanged and we transform it back into
+
+ align:start position:0%
+exchanged and we transform it back into
+ 
+
+ align:start position:0%
+exchanged and we transform it back into
+the plain message so only if I know the
+
+ align:start position:0%
+the plain message so only if I know the
+ 
+
+ align:start position:0%
+the plain message so only if I know the
+keys I can actually transform back the
+
+ align:start position:0%
+keys I can actually transform back the
+ 
+
+ align:start position:0%
+keys I can actually transform back the
+encrypted version into the plain
+
+ align:start position:0%
+encrypted version into the plain
+ 
+
+ align:start position:0%
+encrypted version into the plain
+version so well in encryption schemes we
+
+ align:start position:0%
+version so well in encryption schemes we
+ 
+
+ align:start position:0%
+version so well in encryption schemes we
+like both these algorithms to be really
+
+ align:start position:0%
+like both these algorithms to be really
+ 
+
+ align:start position:0%
+like both these algorithms to be really
+really efficient and um the security of
+
+ align:start position:0%
+really efficient and um the security of
+ 
+
+ align:start position:0%
+really efficient and um the security of
+such a scheme well the first kind of
+
+ align:start position:0%
+such a scheme well the first kind of
+ 
+
+ align:start position:0%
+such a scheme well the first kind of
+intuition that we can get is that well
+
+ align:start position:0%
+intuition that we can get is that well
+ 
+
+ align:start position:0%
+intuition that we can get is that well
+if I'm a man in the middle somewhere
+
+ align:start position:0%
+if I'm a man in the middle somewhere
+ 
+
+ align:start position:0%
+if I'm a man in the middle somewhere
+intercepting like an encrypted message M
+
+ align:start position:0%
+intercepting like an encrypted message M
+ 
+
+ align:start position:0%
+intercepting like an encrypted message M
+Prime I should not be able to get any
+
+ align:start position:0%
+Prime I should not be able to get any
+ 
+
+ align:start position:0%
+Prime I should not be able to get any
+information about M if I have no
+
+ align:start position:0%
+information about M if I have no
+ 
+
+ align:start position:0%
+information about M if I have no
+knowledge about those
+
+ align:start position:0%
+knowledge about those
+ 
+
+ align:start position:0%
+knowledge about those
+keys so this is uh uh the example that
+
+ align:start position:0%
+keys so this is uh uh the example that
+ 
+
+ align:start position:0%
+keys so this is uh uh the example that
+we're going to take throughout this
+
+ align:start position:0%
+we're going to take throughout this
+ 
+
+ align:start position:0%
+we're going to take throughout this
+whole uh
+
+ align:start position:0%
+whole uh
+ 
+
+ align:start position:0%
+whole uh
+lecture so let's start with uh a first
+
+ align:start position:0%
+lecture so let's start with uh a first
+ 
+
+ align:start position:0%
+lecture so let's start with uh a first
+um uh possible scheme um churing who
+
+ align:start position:0%
+um uh possible scheme um churing who
+ 
+
+ align:start position:0%
+um uh possible scheme um churing who
+lived like uh around 1900 um I think 36
+
+ align:start position:0%
+lived like uh around 1900 um I think 36
+ 
+
+ align:start position:0%
+lived like uh around 1900 um I think 36
+he was 24 years old and he lived uh till
+
+ align:start position:0%
+he was 24 years old and he lived uh till
+ 
+
+ align:start position:0%
+he was 24 years old and he lived uh till
+about actually I think he was about 54
+
+ align:start position:0%
+about actually I think he was about 54
+ 
+
+ align:start position:0%
+about actually I think he was about 54
+when he died um in any case churing was
+
+ align:start position:0%
+when he died um in any case churing was
+ 
+
+ align:start position:0%
+when he died um in any case churing was
+the one who first originally proposed um
+
+ align:start position:0%
+the one who first originally proposed um
+ 
+
+ align:start position:0%
+the one who first originally proposed um
+to use number theory in cryptography and
+
+ align:start position:0%
+to use number theory in cryptography and
+ 
+
+ align:start position:0%
+to use number theory in cryptography and
+uh before he joined the British army
+
+ align:start position:0%
+uh before he joined the British army
+ 
+
+ align:start position:0%
+uh before he joined the British army
+before the second world war he actually
+
+ align:start position:0%
+before the second world war he actually
+ 
+
+ align:start position:0%
+before the second world war he actually
+um uh proposed a scheme but it got never
+
+ align:start position:0%
+um uh proposed a scheme but it got never
+ 
+
+ align:start position:0%
+um uh proposed a scheme but it got never
+published so here in this class we are
+
+ align:start position:0%
+published so here in this class we are
+ 
+
+ align:start position:0%
+published so here in this class we are
+going to uh try to think about what he
+
+ align:start position:0%
+going to uh try to think about what he
+ 
+
+ align:start position:0%
+going to uh try to think about what he
+could have thought about so we will have
+
+ align:start position:0%
+could have thought about so we will have
+ 
+
+ align:start position:0%
+could have thought about so we will have
+a first scheme uh which we we will call
+
+ align:start position:0%
+a first scheme uh which we we will call
+ 
+
+ align:start position:0%
+a first scheme uh which we we will call
+churing
+
+ align:start position:0%
+churing
+ 
+
+ align:start position:0%
+churing
+code version number
+
+ align:start position:0%
+code version number
+ 
+
+ align:start position:0%
+code version number
+one and uh the whole idea is that we
+
+ align:start position:0%
+one and uh the whole idea is that we
+ 
+
+ align:start position:0%
+one and uh the whole idea is that we
+going to translate a message first of
+
+ align:start position:0%
+going to translate a message first of
+ 
+
+ align:start position:0%
+going to translate a message first of
+all into a prime number uh because we
+
+ align:start position:0%
+all into a prime number uh because we
+ 
+
+ align:start position:0%
+all into a prime number uh because we
+want to use numbers you're here in
+
+ align:start position:0%
+want to use numbers you're here in
+ 
+
+ align:start position:0%
+want to use numbers you're here in
+number Theory class so we want to use
+
+ align:start position:0%
+number Theory class so we want to use
+ 
+
+ align:start position:0%
+number Theory class so we want to use
+some tricks with numbers in order to
+
+ align:start position:0%
+some tricks with numbers in order to
+ 
+
+ align:start position:0%
+some tricks with numbers in order to
+encrypt it so let's do
+
+ align:start position:0%
+encrypt it so let's do
+ 
+
+ align:start position:0%
+encrypt it so let's do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um so for example let's take the word uh
+
+ align:start position:0%
+um so for example let's take the word uh
+ 
+
+ align:start position:0%
+um so for example let's take the word uh
+victory
+
+ align:start position:0%
+victory
+ 
+
+ align:start position:0%
+victory
+uh we can map this into an integer for
+
+ align:start position:0%
+uh we can map this into an integer for
+ 
+
+ align:start position:0%
+uh we can map this into an integer for
+example we could say well m is um 22
+
+ align:start position:0%
+example we could say well m is um 22
+ 
+
+ align:start position:0%
+example we could say well m is um 22
+where I map V to because I know that V
+
+ align:start position:0%
+where I map V to because I know that V
+ 
+
+ align:start position:0%
+where I map V to because I know that V
+is the 22nd letter in the alphabet I
+
+ align:start position:0%
+is the 22nd letter in the alphabet I
+ 
+
+ align:start position:0%
+is the 22nd letter in the alphabet I
+just start with 22 I is the ninth letter
+
+ align:start position:0%
+just start with 22 I is the ninth letter
+ 
+
+ align:start position:0%
+just start with 22 I is the ninth letter
+in the AL in in the alphabet so ient
+
+ align:start position:0%
+in the AL in in the alphabet so ient
+ 
+
+ align:start position:0%
+in the AL in in the alphabet so ient
+09 uh C is the third letter in the
+
+ align:start position:0%
+09 uh C is the third letter in the
+ 
+
+ align:start position:0%
+09 uh C is the third letter in the
+alphabet I append a three 03 I continue
+
+ align:start position:0%
+alphabet I append a three 03 I continue
+ 
+
+ align:start position:0%
+alphabet I append a three 03 I continue
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+and in the end over here I have mapped y
+
+ align:start position:0%
+and in the end over here I have mapped y
+ 
+
+ align:start position:0%
+and in the end over here I have mapped y
+to the 25th letter because it's the 25th
+
+ align:start position:0%
+to the 25th letter because it's the 25th
+ 
+
+ align:start position:0%
+to the 25th letter because it's the 25th
+letter of the alphabet I write 25 it
+
+ align:start position:0%
+letter of the alphabet I write 25 it
+ 
+
+ align:start position:0%
+letter of the alphabet I write 25 it
+turns out I can just add a couple of
+
+ align:start position:0%
+turns out I can just add a couple of
+ 
+
+ align:start position:0%
+turns out I can just add a couple of
+digits more if I specially compute those
+
+ align:start position:0%
+digits more if I specially compute those
+ 
+
+ align:start position:0%
+digits more if I specially compute those
+in this case I could add 13 and then it
+
+ align:start position:0%
+in this case I could add 13 and then it
+ 
+
+ align:start position:0%
+in this case I could add 13 and then it
+changes into a prime
+
+ align:start position:0%
+changes into a prime
+ 
+
+ align:start position:0%
+changes into a prime
+number um now we're not going to talk
+
+ align:start position:0%
+number um now we're not going to talk
+ 
+
+ align:start position:0%
+number um now we're not going to talk
+about why this is and how this can be
+
+ align:start position:0%
+about why this is and how this can be
+ 
+
+ align:start position:0%
+about why this is and how this can be
+done and so on but uh it turns out that
+
+ align:start position:0%
+done and so on but uh it turns out that
+ 
+
+ align:start position:0%
+done and so on but uh it turns out that
+the prime numbers are densely uh
+
+ align:start position:0%
+the prime numbers are densely uh
+ 
+
+ align:start position:0%
+the prime numbers are densely uh
+distributed over the integers and it is
+
+ align:start position:0%
+distributed over the integers and it is
+ 
+
+ align:start position:0%
+distributed over the integers and it is
+really possible to just with a few extra
+
+ align:start position:0%
+really possible to just with a few extra
+ 
+
+ align:start position:0%
+really possible to just with a few extra
+digits uh by selecting them in a smart
+
+ align:start position:0%
+digits uh by selecting them in a smart
+ 
+
+ align:start position:0%
+digits uh by selecting them in a smart
+way to actually create a prime number
+
+ align:start position:0%
+way to actually create a prime number
+ 
+
+ align:start position:0%
+way to actually create a prime number
+and also verify that it is a prime
+
+ align:start position:0%
+and also verify that it is a prime
+ 
+
+ align:start position:0%
+and also verify that it is a prime
+number very efficiently so it's very
+
+ align:start position:0%
+number very efficiently so it's very
+ 
+
+ align:start position:0%
+number very efficiently so it's very
+easy to compute uh to translate such a
+
+ align:start position:0%
+easy to compute uh to translate such a
+ 
+
+ align:start position:0%
+easy to compute uh to translate such a
+word into a prime number so this is how
+
+ align:start position:0%
+word into a prime number so this is how
+ 
+
+ align:start position:0%
+word into a prime number so this is how
+it all starts and just like in an
+
+ align:start position:0%
+it all starts and just like in an
+ 
+
+ align:start position:0%
+it all starts and just like in an
+encryption scheme um beforehand we are
+
+ align:start position:0%
+encryption scheme um beforehand we are
+ 
+
+ align:start position:0%
+encryption scheme um beforehand we are
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+exchange a key so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exchange a secret uh Prime in this
+
+ align:start position:0%
+exchange a secret uh Prime in this
+ 
+
+ align:start position:0%
+exchange a secret uh Prime in this
+example which we call
+
+ align:start position:0%
+example which we call
+ 
+
+ align:start position:0%
+example which we call
+K and the
+
+ align:start position:0%
+K and the
+ 
+
+ align:start position:0%
+K and the
+encryption is very simple we are just
+
+ align:start position:0%
+encryption is very simple we are just
+ 
+
+ align:start position:0%
+encryption is very simple we are just
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+multiply M with K you may wonder why is
+
+ align:start position:0%
+multiply M with K you may wonder why is
+ 
+
+ align:start position:0%
+multiply M with K you may wonder why is
+this such a fantastic ID but let's uh
+
+ align:start position:0%
+this such a fantastic ID but let's uh
+ 
+
+ align:start position:0%
+this such a fantastic ID but let's uh
+let's bear with me so m is this first
+
+ align:start position:0%
+let's bear with me so m is this first
+ 
+
+ align:start position:0%
+let's bear with me so m is this first
+prime number and we multiply it by
+
+ align:start position:0%
+prime number and we multiply it by
+ 
+
+ align:start position:0%
+prime number and we multiply it by
+second prime number and that's going to
+
+ align:start position:0%
+second prime number and that's going to
+ 
+
+ align:start position:0%
+second prime number and that's going to
+be our
+
+ align:start position:0%
+be our
+ 
+
+ align:start position:0%
+be our
+encryption now how do we decrypt that
+
+ align:start position:0%
+encryption now how do we decrypt that
+ 
+
+ align:start position:0%
+encryption now how do we decrypt that
+seems to be pretty straightforward right
+
+ align:start position:0%
+seems to be pretty straightforward right
+ 
+
+ align:start position:0%
+seems to be pretty straightforward right
+how do we do it uh we start off with M
+
+ align:start position:0%
+how do we do it uh we start off with M
+ 
+
+ align:start position:0%
+how do we do it uh we start off with M
+Prime um I know we have exchanged the
+
+ align:start position:0%
+Prime um I know we have exchanged the
+ 
+
+ align:start position:0%
+Prime um I know we have exchanged the
+secret Prime K so if I receive uh from
+
+ align:start position:0%
+secret Prime K so if I receive uh from
+ 
+
+ align:start position:0%
+secret Prime K so if I receive uh from
+you this message this encrypted message
+
+ align:start position:0%
+you this message this encrypted message
+ 
+
+ align:start position:0%
+you this message this encrypted message
+well I know the key K so I just divide
+
+ align:start position:0%
+well I know the key K so I just divide
+ 
+
+ align:start position:0%
+well I know the key K so I just divide
+it by K
+
+ align:start position:0%
+it by K
+ 
+
+ align:start position:0%
+it by K
+well which is MK / K and I get M so
+
+ align:start position:0%
+well which is MK / K and I get M so
+ 
+
+ align:start position:0%
+well which is MK / K and I get M so
+that's pretty
+
+ align:start position:0%
+that's pretty
+ 
+
+ align:start position:0%
+that's pretty
+straightforward now turn it turns out
+
+ align:start position:0%
+straightforward now turn it turns out
+ 
+
+ align:start position:0%
+straightforward now turn it turns out
+actually and I'll will write it up here
+
+ align:start position:0%
+actually and I'll will write it up here
+ 
+
+ align:start position:0%
+actually and I'll will write it up here
+because you need it later that uh it's
+
+ align:start position:0%
+because you need it later that uh it's
+ 
+
+ align:start position:0%
+because you need it later that uh it's
+not so trivial to actually just given an
+
+ align:start position:0%
+not so trivial to actually just given an
+ 
+
+ align:start position:0%
+not so trivial to actually just given an
+M Prime to figure out what m is or
+
+ align:start position:0%
+M Prime to figure out what m is or
+ 
+
+ align:start position:0%
+M Prime to figure out what m is or
+k m Prime is the product of two very
+
+ align:start position:0%
+k m Prime is the product of two very
+ 
+
+ align:start position:0%
+k m Prime is the product of two very
+large prime numbers and uh that turns
+
+ align:start position:0%
+large prime numbers and uh that turns
+ 
+
+ align:start position:0%
+large prime numbers and uh that turns
+out to be a really hard problem up to
+
+ align:start position:0%
+out to be a really hard problem up to
+ 
+
+ align:start position:0%
+out to be a really hard problem up to
+now nobody has really been able to get a
+
+ align:start position:0%
+now nobody has really been able to get a
+ 
+
+ align:start position:0%
+now nobody has really been able to get a
+really efficient algorithm to solve that
+
+ align:start position:0%
+really efficient algorithm to solve that
+ 
+
+ align:start position:0%
+really efficient algorithm to solve that
+so we may think this is secure so let me
+
+ align:start position:0%
+so we may think this is secure so let me
+ 
+
+ align:start position:0%
+so we may think this is secure so let me
+write it down um it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard to
+
+ align:start position:0%
+hard to
+ 
+
+ align:start position:0%
+hard to
+factor a uh product of two large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+primes you will actually need this also
+
+ align:start position:0%
+primes you will actually need this also
+ 
+
+ align:start position:0%
+primes you will actually need this also
+Al when we come to the final encryption
+
+ align:start position:0%
+Al when we come to the final encryption
+ 
+
+ align:start position:0%
+Al when we come to the final encryption
+scheme RSA that we will discuss which is
+
+ align:start position:0%
+scheme RSA that we will discuss which is
+ 
+
+ align:start position:0%
+scheme RSA that we will discuss which is
+widely used um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but something is wrong here though
+
+ align:start position:0%
+so but something is wrong here though
+ 
+
+ align:start position:0%
+so but something is wrong here though
+this seems to be too simple right so
+
+ align:start position:0%
+this seems to be too simple right so
+ 
+
+ align:start position:0%
+this seems to be too simple right so
+what can we do if we have like say
+
+ align:start position:0%
+what can we do if we have like say
+ 
+
+ align:start position:0%
+what can we do if we have like say
+suppose I intercept two encrypted
+
+ align:start position:0%
+suppose I intercept two encrypted
+ 
+
+ align:start position:0%
+suppose I intercept two encrypted
+messages what what can I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose I have uh a first message uh
+
+ align:start position:0%
+so suppose I have uh a first message uh
+ 
+
+ align:start position:0%
+so suppose I have uh a first message uh
+M Prime 1 which is the product of a
+
+ align:start position:0%
+M Prime 1 which is the product of a
+ 
+
+ align:start position:0%
+M Prime 1 which is the product of a
+first plane message times the key K and
+
+ align:start position:0%
+first plane message times the key K and
+ 
+
+ align:start position:0%
+first plane message times the key K and
+I have a second message that is
+
+ align:start position:0%
+I have a second message that is
+ 
+
+ align:start position:0%
+I have a second message that is
+encrypted by using the same key which is
+
+ align:start position:0%
+encrypted by using the same key which is
+ 
+
+ align:start position:0%
+encrypted by using the same key which is
+M2 * K does anybody has an idea what I
+
+ align:start position:0%
+M2 * K does anybody has an idea what I
+ 
+
+ align:start position:0%
+M2 * K does anybody has an idea what I
+could do here yeah
+
+ align:start position:0%
+could do here yeah
+ 
+
+ align:start position:0%
+could do here yeah
+GC yeah you could uh find the
+
+ align:start position:0%
+GC yeah you could uh find the
+ 
+
+ align:start position:0%
+GC yeah you could uh find the
+gcd of uh M1 Prime and
+
+ align:start position:0%
+gcd of uh M1 Prime and
+ 
+
+ align:start position:0%
+gcd of uh M1 Prime and
+M2 Prime um I've intercepted those two
+
+ align:start position:0%
+M2 Prime um I've intercepted those two
+ 
+
+ align:start position:0%
+M2 Prime um I've intercepted those two
+now M1 is a prime number K is a prime
+
+ align:start position:0%
+now M1 is a prime number K is a prime
+ 
+
+ align:start position:0%
+now M1 is a prime number K is a prime
+number M2 is a prime number K is a prime
+
+ align:start position:0%
+number M2 is a prime number K is a prime
+ 
+
+ align:start position:0%
+number M2 is a prime number K is a prime
+number here also right so they are all
+
+ align:start position:0%
+number here also right so they are all
+ 
+
+ align:start position:0%
+number here also right so they are all
+uh relatively prime towards one another
+
+ align:start position:0%
+uh relatively prime towards one another
+ 
+
+ align:start position:0%
+uh relatively prime towards one another
+the gcd of these
+
+ align:start position:0%
+the gcd of these
+ 
+
+ align:start position:0%
+the gcd of these
+two well the greatest common divisor is
+
+ align:start position:0%
+two well the greatest common divisor is
+ 
+
+ align:start position:0%
+two well the greatest common divisor is
+K so just by calculating the gcd of the
+
+ align:start position:0%
+K so just by calculating the gcd of the
+ 
+
+ align:start position:0%
+K so just by calculating the gcd of the
+two encrypted messages I will be able to
+
+ align:start position:0%
+two encrypted messages I will be able to
+ 
+
+ align:start position:0%
+two encrypted messages I will be able to
+figure out what uh K is the key so
+
+ align:start position:0%
+figure out what uh K is the key so
+ 
+
+ align:start position:0%
+figure out what uh K is the key so
+that's uh well if I know the key then I
+
+ align:start position:0%
+that's uh well if I know the key then I
+ 
+
+ align:start position:0%
+that's uh well if I know the key then I
+can do the decryption of any Cipher text
+
+ align:start position:0%
+can do the decryption of any Cipher text
+ 
+
+ align:start position:0%
+can do the decryption of any Cipher text
+any encryption of a message that that I
+
+ align:start position:0%
+any encryption of a message that that I
+ 
+
+ align:start position:0%
+any encryption of a message that that I
+can intercept so this is not
+
+ align:start position:0%
+can intercept so this is not
+ 
+
+ align:start position:0%
+can intercept so this is not
+secure so how can we uh change this can
+
+ align:start position:0%
+secure so how can we uh change this can
+ 
+
+ align:start position:0%
+secure so how can we uh change this can
+we uh create a different kind of uh um
+
+ align:start position:0%
+we uh create a different kind of uh um
+ 
+
+ align:start position:0%
+we uh create a different kind of uh um
+encryption
+
+ align:start position:0%
+encryption
+ 
+
+ align:start position:0%
+encryption
+scheme let's do something much more uh
+
+ align:start position:0%
+scheme let's do something much more uh
+ 
+
+ align:start position:0%
+scheme let's do something much more uh
+difficult and uh and then we will get
+
+ align:start position:0%
+difficult and uh and then we will get
+ 
+
+ align:start position:0%
+difficult and uh and then we will get
+into to modular arithmetic and things
+
+ align:start position:0%
+into to modular arithmetic and things
+ 
+
+ align:start position:0%
+into to modular arithmetic and things
+like that so let's do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so during code version number
+
+ align:start position:0%
+um so during code version number
+ 
+
+ align:start position:0%
+um so during code version number
+two we try to do something much more
+
+ align:start position:0%
+two we try to do something much more
+ 
+
+ align:start position:0%
+two we try to do something much more
+comp complicated than just multiplying
+
+ align:start position:0%
+comp complicated than just multiplying
+ 
+
+ align:start position:0%
+comp complicated than just multiplying
+by Prime so let's do the
+
+ align:start position:0%
+by Prime so let's do the
+ 
+
+ align:start position:0%
+by Prime so let's do the
+following so
+
+ align:start position:0%
+following so
+ 
+
+ align:start position:0%
+following so
+beforehand uh we are going to exchange a
+
+ align:start position:0%
+beforehand uh we are going to exchange a
+ 
+
+ align:start position:0%
+beforehand uh we are going to exchange a
+uh uh not only a secret Prime K but we
+
+ align:start position:0%
+uh uh not only a secret Prime K but we
+ 
+
+ align:start position:0%
+uh uh not only a secret Prime K but we
+also exchange uh a public
+
+ align:start position:0%
+also exchange uh a public
+ 
+
+ align:start position:0%
+also exchange uh a public
+Prime so we
+
+ align:start position:0%
+Prime so we
+ 
+
+ align:start position:0%
+Prime so we
+exchange uh by public we mean that
+
+ align:start position:0%
+exchange uh by public we mean that
+ 
+
+ align:start position:0%
+exchange uh by public we mean that
+anybody can see this Prime it's it's
+
+ align:start position:0%
+anybody can see this Prime it's it's
+ 
+
+ align:start position:0%
+anybody can see this Prime it's it's
+it's common knowledge a public
+
+ align:start position:0%
+it's common knowledge a public
+ 
+
+ align:start position:0%
+it's common knowledge a public
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+p and also uh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+secret
+
+ align:start position:0%
+secret
+ 
+
+ align:start position:0%
+secret
+Prime okay well let's see whether this
+
+ align:start position:0%
+Prime okay well let's see whether this
+ 
+
+ align:start position:0%
+Prime okay well let's see whether this
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+work um we have an encryption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we going to start out exactly the
+
+ align:start position:0%
+well we going to start out exactly the
+ 
+
+ align:start position:0%
+well we going to start out exactly the
+same way um uh oh first of all I should
+
+ align:start position:0%
+same way um uh oh first of all I should
+ 
+
+ align:start position:0%
+same way um uh oh first of all I should
+tell you how a message is represented a
+
+ align:start position:0%
+tell you how a message is represented a
+ 
+
+ align:start position:0%
+tell you how a message is represented a
+message is going to be represented as a
+
+ align:start position:0%
+message is going to be represented as a
+ 
+
+ align:start position:0%
+message is going to be represented as a
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+um m in the range from 0 1 all the way
+
+ align:start position:0%
+um m in the range from 0 1 all the way
+ 
+
+ align:start position:0%
+um m in the range from 0 1 all the way
+to P minus
+
+ align:start position:0%
+to P minus
+ 
+
+ align:start position:0%
+to P minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and we will compute the encryption as
+
+ align:start position:0%
+and we will compute the encryption as
+ 
+
+ align:start position:0%
+and we will compute the encryption as
+follows uh M uh is going to be the
+
+ align:start position:0%
+follows uh M uh is going to be the
+ 
+
+ align:start position:0%
+follows uh M uh is going to be the
+remainder of M * K after dividing out as
+
+ align:start position:0%
+remainder of M * K after dividing out as
+ 
+
+ align:start position:0%
+remainder of M * K after dividing out as
+many multiples of p as possible so
+
+ align:start position:0%
+many multiples of p as possible so
+ 
+
+ align:start position:0%
+many multiples of p as possible so
+notice we do kind of the same thing we
+
+ align:start position:0%
+notice we do kind of the same thing we
+ 
+
+ align:start position:0%
+notice we do kind of the same thing we
+just multiply by K but now we just uh um
+
+ align:start position:0%
+just multiply by K but now we just uh um
+ 
+
+ align:start position:0%
+just multiply by K but now we just uh um
+take the remainder after taking out as
+
+ align:start position:0%
+take the remainder after taking out as
+ 
+
+ align:start position:0%
+take the remainder after taking out as
+many multiples of
+
+ align:start position:0%
+many multiples of
+ 
+
+ align:start position:0%
+many multiples of
+P um well let's see whether we can do
+
+ align:start position:0%
+P um well let's see whether we can do
+ 
+
+ align:start position:0%
+P um well let's see whether we can do
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+decryption it seems to be
+
+ align:start position:0%
+decryption it seems to be
+ 
+
+ align:start position:0%
+decryption it seems to be
+like a next level of complexity so maybe
+
+ align:start position:0%
+like a next level of complexity so maybe
+ 
+
+ align:start position:0%
+like a next level of complexity so maybe
+that will help us here
+
+ align:start position:0%
+that will help us here
+ 
+
+ align:start position:0%
+that will help us here
+right so how would we do decryption well
+
+ align:start position:0%
+right so how would we do decryption well
+ 
+
+ align:start position:0%
+right so how would we do decryption well
+somehow we would like to divide by K but
+
+ align:start position:0%
+somehow we would like to divide by K but
+ 
+
+ align:start position:0%
+somehow we would like to divide by K but
+we cannot really do that right um this
+
+ align:start position:0%
+we cannot really do that right um this
+ 
+
+ align:start position:0%
+we cannot really do that right um this
+does not make any
+
+ align:start position:0%
+does not make any
+ 
+
+ align:start position:0%
+does not make any
+sense so the decryption we have no idea
+
+ align:start position:0%
+sense so the decryption we have no idea
+ 
+
+ align:start position:0%
+sense so the decryption we have no idea
+at this point how to do this and um now
+
+ align:start position:0%
+at this point how to do this and um now
+ 
+
+ align:start position:0%
+at this point how to do this and um now
+we can get into modular arithmetic
+
+ align:start position:0%
+we can get into modular arithmetic
+ 
+
+ align:start position:0%
+we can get into modular arithmetic
+because it turns out that we can sort of
+
+ align:start position:0%
+because it turns out that we can sort of
+ 
+
+ align:start position:0%
+because it turns out that we can sort of
+divide by K there exists a what we call
+
+ align:start position:0%
+divide by K there exists a what we call
+ 
+
+ align:start position:0%
+divide by K there exists a what we call
+multiplicative inverse of k modulo p and
+
+ align:start position:0%
+multiplicative inverse of k modulo p and
+ 
+
+ align:start position:0%
+multiplicative inverse of k modulo p and
+I will explain all those terminology to
+
+ align:start position:0%
+I will explain all those terminology to
+ 
+
+ align:start position:0%
+I will explain all those terminology to
+you and um then we will be able to take
+
+ align:start position:0%
+you and um then we will be able to take
+ 
+
+ align:start position:0%
+you and um then we will be able to take
+M Prime and transform it back to M so we
+
+ align:start position:0%
+M Prime and transform it back to M so we
+ 
+
+ align:start position:0%
+M Prime and transform it back to M so we
+will be able to get a lot of this
+
+ align:start position:0%
+will be able to get a lot of this
+ 
+
+ align:start position:0%
+will be able to get a lot of this
+Machinery um going so let's uh find out
+
+ align:start position:0%
+Machinery um going so let's uh find out
+ 
+
+ align:start position:0%
+Machinery um going so let's uh find out
+how this works uh so first of all last
+
+ align:start position:0%
+how this works uh so first of all last
+ 
+
+ align:start position:0%
+how this works uh so first of all last
+time we saw that um uh we defined A and
+
+ align:start position:0%
+time we saw that um uh we defined A and
+ 
+
+ align:start position:0%
+time we saw that um uh we defined A and
+B to be relative relatively prime so let
+
+ align:start position:0%
+B to be relative relatively prime so let
+ 
+
+ align:start position:0%
+B to be relative relatively prime so let
+me repeat
+
+ align:start position:0%
+me repeat
+ 
+
+ align:start position:0%
+me repeat
+that so A are relatively
+
+ align:start position:0%
+that so A are relatively
+ 
+
+ align:start position:0%
+that so A are relatively
+prime um if and only if that's how we
+
+ align:start position:0%
+prime um if and only if that's how we
+ 
+
+ align:start position:0%
+prime um if and only if that's how we
+defined it if the gcd of A and B is
+
+ align:start position:0%
+defined it if the gcd of A and B is
+ 
+
+ align:start position:0%
+defined it if the gcd of A and B is
+equal to one and in last lecture and in
+
+ align:start position:0%
+equal to one and in last lecture and in
+ 
+
+ align:start position:0%
+equal to one and in last lecture and in
+the recitation got a difference proof I
+
+ align:start position:0%
+the recitation got a difference proof I
+ 
+
+ align:start position:0%
+the recitation got a difference proof I
+think um we proved that
+
+ align:start position:0%
+think um we proved that
+ 
+
+ align:start position:0%
+think um we proved that
+actually uh the gcd of A and B is equal
+
+ align:start position:0%
+actually uh the gcd of A and B is equal
+ 
+
+ align:start position:0%
+actually uh the gcd of A and B is equal
+to the smallest positive linear
+
+ align:start position:0%
+to the smallest positive linear
+ 
+
+ align:start position:0%
+to the smallest positive linear
+combination of a and B so that means
+
+ align:start position:0%
+combination of a and B so that means
+ 
+
+ align:start position:0%
+combination of a and B so that means
+that one in particular is a linear
+
+ align:start position:0%
+that one in particular is a linear
+ 
+
+ align:start position:0%
+that one in particular is a linear
+combination of A and B so there exists
+
+ align:start position:0%
+combination of A and B so there exists
+ 
+
+ align:start position:0%
+combination of A and B so there exists
+inures s and t such that s * a + T * b =
+
+ align:start position:0%
+inures s and t such that s * a + T * b =
+ 
+
+ align:start position:0%
+inures s and t such that s * a + T * b =
+1 it turns out that we can also go the
+
+ align:start position:0%
+1 it turns out that we can also go the
+ 
+
+ align:start position:0%
+1 it turns out that we can also go the
+other way around
+
+ align:start position:0%
+other way around
+ 
+
+ align:start position:0%
+other way around
+because if I can write one as a linear
+
+ align:start position:0%
+because if I can write one as a linear
+ 
+
+ align:start position:0%
+because if I can write one as a linear
+combination of A and B well I cannot get
+
+ align:start position:0%
+combination of A and B well I cannot get
+ 
+
+ align:start position:0%
+combination of A and B well I cannot get
+much lower than that right so that's
+
+ align:start position:0%
+much lower than that right so that's
+ 
+
+ align:start position:0%
+much lower than that right so that's
+really the smallest possible that I can
+
+ align:start position:0%
+really the smallest possible that I can
+ 
+
+ align:start position:0%
+really the smallest possible that I can
+achieve so the gcd must be equal to one
+
+ align:start position:0%
+achieve so the gcd must be equal to one
+ 
+
+ align:start position:0%
+achieve so the gcd must be equal to one
+so this is a property that we will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+um and uh from this property we can
+
+ align:start position:0%
+um and uh from this property we can
+ 
+
+ align:start position:0%
+um and uh from this property we can
+already figure out an interesting
+
+ align:start position:0%
+already figure out an interesting
+ 
+
+ align:start position:0%
+already figure out an interesting
+property so suppose we have a linear
+
+ align:start position:0%
+property so suppose we have a linear
+ 
+
+ align:start position:0%
+property so suppose we have a linear
+combination that looks like this then
+
+ align:start position:0%
+combination that looks like this then
+ 
+
+ align:start position:0%
+combination that looks like this then
+you can imagine that uh sort of that s *
+
+ align:start position:0%
+you can imagine that uh sort of that s *
+ 
+
+ align:start position:0%
+you can imagine that uh sort of that s *
+a is equal to one plus or minus some
+
+ align:start position:0%
+a is equal to one plus or minus some
+ 
+
+ align:start position:0%
+a is equal to one plus or minus some
+linear a multiple of
+
+ align:start position:0%
+linear a multiple of
+ 
+
+ align:start position:0%
+linear a multiple of
+B so it's sort of s * a sort of equal to
+
+ align:start position:0%
+B so it's sort of s * a sort of equal to
+ 
+
+ align:start position:0%
+B so it's sort of s * a sort of equal to
+one you can say up to a multiple of B so
+
+ align:start position:0%
+one you can say up to a multiple of B so
+ 
+
+ align:start position:0%
+one you can say up to a multiple of B so
+um you can see a sort of as an inverse
+
+ align:start position:0%
+um you can see a sort of as an inverse
+ 
+
+ align:start position:0%
+um you can see a sort of as an inverse
+of s because s * a is equal to one sort
+
+ align:start position:0%
+of s because s * a is equal to one sort
+ 
+
+ align:start position:0%
+of s because s * a is equal to one sort
+of so this is what we're going to use
+
+ align:start position:0%
+of so this is what we're going to use
+ 
+
+ align:start position:0%
+of so this is what we're going to use
+this kind of feeling and um in order to
+
+ align:start position:0%
+this kind of feeling and um in order to
+ 
+
+ align:start position:0%
+this kind of feeling and um in order to
+do that we are going to Define uh
+
+ align:start position:0%
+do that we are going to Define uh
+ 
+
+ align:start position:0%
+do that we are going to Define uh
+congruency
+
+ align:start position:0%
+congruency
+ 
+
+ align:start position:0%
+congruency
+um so that's the first definition for
+
+ align:start position:0%
+um so that's the first definition for
+ 
+
+ align:start position:0%
+um so that's the first definition for
+this lecture uh we say X is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+congruent uh to y
+
+ align:start position:0%
+congruent uh to y
+ 
+
+ align:start position:0%
+congruent uh to y
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+n um
+
+ align:start position:0%
+n um
+ 
+
+ align:start position:0%
+n um
+if which we denote as follows x with
+
+ align:start position:0%
+if which we denote as follows x with
+ 
+
+ align:start position:0%
+if which we denote as follows x with
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+bars Y in between brackets mod
+
+ align:start position:0%
+bars Y in between brackets mod
+ 
+
+ align:start position:0%
+bars Y in between brackets mod
+n and uh we say that this is the case uh
+
+ align:start position:0%
+n and uh we say that this is the case uh
+ 
+
+ align:start position:0%
+n and uh we say that this is the case uh
+if um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n divides the difference between X and Y
+
+ align:start position:0%
+n divides the difference between X and Y
+ 
+
+ align:start position:0%
+n divides the difference between X and Y
+so let's just uh let's have a look at
+
+ align:start position:0%
+so let's just uh let's have a look at
+ 
+
+ align:start position:0%
+so let's just uh let's have a look at
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's uh take
+
+ align:start position:0%
+um so let's uh take
+ 
+
+ align:start position:0%
+um so let's uh take
+31 and I'll like to show to you that
+
+ align:start position:0%
+31 and I'll like to show to you that
+ 
+
+ align:start position:0%
+31 and I'll like to show to you that
+this is congruent to
+
+ align:start position:0%
+this is congruent to
+ 
+
+ align:start position:0%
+this is congruent to
+16 modulo between brackets uh five why
+
+ align:start position:0%
+16 modulo between brackets uh five why
+ 
+
+ align:start position:0%
+16 modulo between brackets uh five why
+is this well I take the difference
+
+ align:start position:0%
+is this well I take the difference
+ 
+
+ align:start position:0%
+is this well I take the difference
+between 31 and 16 which is 15 and I know
+
+ align:start position:0%
+between 31 and 16 which is 15 and I know
+ 
+
+ align:start position:0%
+between 31 and 16 which is 15 and I know
+that 15 is three times 5 so five divides
+
+ align:start position:0%
+that 15 is three times 5 so five divides
+ 
+
+ align:start position:0%
+that 15 is three times 5 so five divides
+this difference and then by the
+
+ align:start position:0%
+this difference and then by the
+ 
+
+ align:start position:0%
+this difference and then by the
+definition we can write it like this and
+
+ align:start position:0%
+definition we can write it like this and
+ 
+
+ align:start position:0%
+definition we can write it like this and
+we say that's the definition 31 is
+
+ align:start position:0%
+we say that's the definition 31 is
+ 
+
+ align:start position:0%
+we say that's the definition 31 is
+congruent to 16 modul 5 another example
+
+ align:start position:0%
+congruent to 16 modul 5 another example
+ 
+
+ align:start position:0%
+congruent to 16 modul 5 another example
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um oh no we will stick with this example
+
+ align:start position:0%
+um oh no we will stick with this example
+ 
+
+ align:start position:0%
+um oh no we will stick with this example
+it's pretty clear um so once we have
+
+ align:start position:0%
+it's pretty clear um so once we have
+ 
+
+ align:start position:0%
+it's pretty clear um so once we have
+defined this uh we can continue and uh
+
+ align:start position:0%
+defined this uh we can continue and uh
+ 
+
+ align:start position:0%
+defined this uh we can continue and uh
+talk about this inverse that I was
+
+ align:start position:0%
+talk about this inverse that I was
+ 
+
+ align:start position:0%
+talk about this inverse that I was
+talking about so we like to sort of
+
+ align:start position:0%
+talking about so we like to sort of
+ 
+
+ align:start position:0%
+talking about so we like to sort of
+explain in this encryption scheme uh how
+
+ align:start position:0%
+explain in this encryption scheme uh how
+ 
+
+ align:start position:0%
+explain in this encryption scheme uh how
+we can divide by K actually we would
+
+ align:start position:0%
+we can divide by K actually we would
+ 
+
+ align:start position:0%
+we can divide by K actually we would
+like to multiply by an inverse of K and
+
+ align:start position:0%
+like to multiply by an inverse of K and
+ 
+
+ align:start position:0%
+like to multiply by an inverse of K and
+we're going to use this this framework
+
+ align:start position:0%
+we're going to use this this framework
+ 
+
+ align:start position:0%
+we're going to use this this framework
+so we'll have a new
+
+ align:start position:0%
+so we'll have a new
+ 
+
+ align:start position:0%
+so we'll have a new
+definition that talks about the
+
+ align:start position:0%
+definition that talks about the
+ 
+
+ align:start position:0%
+definition that talks about the
+multiplicative inverse so it's a New
+
+ align:start position:0%
+multiplicative inverse so it's a New
+ 
+
+ align:start position:0%
+multiplicative inverse so it's a New
+Concept
+
+ align:start position:0%
+Concept
+ 
+
+ align:start position:0%
+Concept
+and you'll give a couple of examples so
+
+ align:start position:0%
+and you'll give a couple of examples so
+ 
+
+ align:start position:0%
+and you'll give a couple of examples so
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplicative
+
+ align:start position:0%
+multiplicative
+ 
+
+ align:start position:0%
+multiplicative
+inverse um of
+
+ align:start position:0%
+inverse um of
+ 
+
+ align:start position:0%
+inverse um of
+X modulo
+
+ align:start position:0%
+X modulo
+ 
+
+ align:start position:0%
+X modulo
+N is a a number which we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denote by X and then minus one on top of
+
+ align:start position:0%
+denote by X and then minus one on top of
+ 
+
+ align:start position:0%
+denote by X and then minus one on top of
+here uh it's a number in the interval 0
+
+ align:start position:0%
+here uh it's a number in the interval 0
+ 
+
+ align:start position:0%
+here uh it's a number in the interval 0
+1 all the way up to n minus
+
+ align:start position:0%
+1 all the way up to n minus
+ 
+
+ align:start position:0%
+1 all the way up to n minus
+one uh such
+
+ align:start position:0%
+one uh such
+ 
+
+ align:start position:0%
+one uh such
+that x * X inverse so x times its
+
+ align:start position:0%
+that x * X inverse so x times its
+ 
+
+ align:start position:0%
+that x * X inverse so x times its
+multiplicative inverse is congruent to
+
+ align:start position:0%
+multiplicative inverse is congruent to
+ 
+
+ align:start position:0%
+multiplicative inverse is congruent to
+One
+
+ align:start position:0%
+One
+ 
+
+ align:start position:0%
+One
+modulo n so this is the definition for a
+
+ align:start position:0%
+modulo n so this is the definition for a
+ 
+
+ align:start position:0%
+modulo n so this is the definition for a
+multiplicative inverse so let's have an
+
+ align:start position:0%
+multiplicative inverse so let's have an
+ 
+
+ align:start position:0%
+multiplicative inverse so let's have an
+uh some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples um
+
+ align:start position:0%
+examples um
+ 
+
+ align:start position:0%
+examples um
+so let's do that over
+
+ align:start position:0%
+so let's do that over
+ 
+
+ align:start position:0%
+so let's do that over
+here uh for
+
+ align:start position:0%
+here uh for
+ 
+
+ align:start position:0%
+here uh for
+example we have that uh 2 * 3 which
+
+ align:start position:0%
+example we have that uh 2 * 3 which
+ 
+
+ align:start position:0%
+example we have that uh 2 * 3 which
+equals 6 right is equal to 1 modul
+
+ align:start position:0%
+equals 6 right is equal to 1 modul
+ 
+
+ align:start position:0%
+equals 6 right is equal to 1 modul
+5 why is this well uh 6 minus one is
+
+ align:start position:0%
+5 why is this well uh 6 minus one is
+ 
+
+ align:start position:0%
+5 why is this well uh 6 minus one is
+divisible by five so I know that this is
+
+ align:start position:0%
+divisible by five so I know that this is
+ 
+
+ align:start position:0%
+divisible by five so I know that this is
+congruent to one modul 5 so what does
+
+ align:start position:0%
+congruent to one modul 5 so what does
+ 
+
+ align:start position:0%
+congruent to one modul 5 so what does
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+mean uh well we can say that two is
+
+ align:start position:0%
+mean uh well we can say that two is
+ 
+
+ align:start position:0%
+mean uh well we can say that two is
+actually equal to the multiplicative
+
+ align:start position:0%
+actually equal to the multiplicative
+ 
+
+ align:start position:0%
+actually equal to the multiplicative
+inverse of
+
+ align:start position:0%
+inverse of
+ 
+
+ align:start position:0%
+inverse of
+three modul 5 uh we can also say that uh
+
+ align:start position:0%
+three modul 5 uh we can also say that uh
+ 
+
+ align:start position:0%
+three modul 5 uh we can also say that uh
+right that three is the multiplicative
+
+ align:start position:0%
+right that three is the multiplicative
+ 
+
+ align:start position:0%
+right that three is the multiplicative
+inverse of two modul
+
+ align:start position:0%
+inverse of two modul
+ 
+
+ align:start position:0%
+inverse of two modul
+5 let's have another example uh just to
+
+ align:start position:0%
+5 let's have another example uh just to
+ 
+
+ align:start position:0%
+5 let's have another example uh just to
+make it a little bit more
+
+ align:start position:0%
+make it a little bit more
+ 
+
+ align:start position:0%
+make it a little bit more
+clear we know that 5 * 5 equals 25 and
+
+ align:start position:0%
+clear we know that 5 * 5 equals 25 and
+ 
+
+ align:start position:0%
+clear we know that 5 * 5 equals 25 and
+this is congruent to one modulo uh 6
+
+ align:start position:0%
+this is congruent to one modulo uh 6
+ 
+
+ align:start position:0%
+this is congruent to one modulo uh 6
+because because 25 is 1 + 4 *
+
+ align:start position:0%
+because because 25 is 1 + 4 *
+ 
+
+ align:start position:0%
+because because 25 is 1 + 4 *
+6 so now we see something funny
+
+ align:start position:0%
+6 so now we see something funny
+ 
+
+ align:start position:0%
+6 so now we see something funny
+happening because 5 is actually equal to
+
+ align:start position:0%
+happening because 5 is actually equal to
+ 
+
+ align:start position:0%
+happening because 5 is actually equal to
+its own multiplicative inverse modul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+so so are there any questions about
+
+ align:start position:0%
+so so are there any questions about
+ 
+
+ align:start position:0%
+so so are there any questions about
+these Concepts because these are really
+
+ align:start position:0%
+these Concepts because these are really
+ 
+
+ align:start position:0%
+these Concepts because these are really
+basic for the whole lecture and this is
+
+ align:start position:0%
+basic for the whole lecture and this is
+ 
+
+ align:start position:0%
+basic for the whole lecture and this is
+what you really need to understand if
+
+ align:start position:0%
+what you really need to understand if
+ 
+
+ align:start position:0%
+what you really need to understand if
+you do all the problem sets as well
+
+ align:start position:0%
+you do all the problem sets as well
+ 
+
+ align:start position:0%
+you do all the problem sets as well
+um are there any
+
+ align:start position:0%
+um are there any
+ 
+
+ align:start position:0%
+um are there any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so now we can actually start talking
+
+ align:start position:0%
+so now we can actually start talking
+ 
+
+ align:start position:0%
+so now we can actually start talking
+about this uh uh second version of the
+
+ align:start position:0%
+about this uh uh second version of the
+ 
+
+ align:start position:0%
+about this uh uh second version of the
+touring code that we uh uh
+
+ align:start position:0%
+touring code that we uh uh
+ 
+
+ align:start position:0%
+touring code that we uh uh
+invented um let's have a look at this
+
+ align:start position:0%
+invented um let's have a look at this
+ 
+
+ align:start position:0%
+invented um let's have a look at this
+remainder so let's write it out again
+
+ align:start position:0%
+remainder so let's write it out again
+ 
+
+ align:start position:0%
+remainder so let's write it out again
+the remainder of uh M * K after dividing
+
+ align:start position:0%
+the remainder of uh M * K after dividing
+ 
+
+ align:start position:0%
+the remainder of uh M * K after dividing
+out as many multiples of P well we know
+
+ align:start position:0%
+out as many multiples of P well we know
+ 
+
+ align:start position:0%
+out as many multiples of P well we know
+that this is congruent to M * k modul
+
+ align:start position:0%
+that this is congruent to M * k modul
+ 
+
+ align:start position:0%
+that this is congruent to M * k modul
+p so why is this uh well we just apply
+
+ align:start position:0%
+p so why is this uh well we just apply
+ 
+
+ align:start position:0%
+p so why is this uh well we just apply
+the definition over here we take the
+
+ align:start position:0%
+the definition over here we take the
+ 
+
+ align:start position:0%
+the definition over here we take the
+difference between those two so here we
+
+ align:start position:0%
+difference between those two so here we
+ 
+
+ align:start position:0%
+difference between those two so here we
+have the remainder of M * K after
+
+ align:start position:0%
+have the remainder of M * K after
+ 
+
+ align:start position:0%
+have the remainder of M * K after
+dividing out as many multiples of
+
+ align:start position:0%
+dividing out as many multiples of
+ 
+
+ align:start position:0%
+dividing out as many multiples of
+P um and if we subtract that from M * K
+
+ align:start position:0%
+P um and if we subtract that from M * K
+ 
+
+ align:start position:0%
+P um and if we subtract that from M * K
+well then we have something that is a
+
+ align:start position:0%
+well then we have something that is a
+ 
+
+ align:start position:0%
+well then we have something that is a
+multiple of P because that's what we
+
+ align:start position:0%
+multiple of P because that's what we
+ 
+
+ align:start position:0%
+multiple of P because that's what we
+divided out so so the difference is a
+
+ align:start position:0%
+divided out so so the difference is a
+ 
+
+ align:start position:0%
+divided out so so the difference is a
+multiple of P um so that means that P
+
+ align:start position:0%
+multiple of P um so that means that P
+ 
+
+ align:start position:0%
+multiple of P um so that means that P
+divides the difference and that's a
+
+ align:start position:0%
+divides the difference and that's a
+ 
+
+ align:start position:0%
+divides the difference and that's a
+definition of saying that this remainder
+
+ align:start position:0%
+definition of saying that this remainder
+ 
+
+ align:start position:0%
+definition of saying that this remainder
+is congruent to MK modulo P so this is
+
+ align:start position:0%
+is congruent to MK modulo P so this is
+ 
+
+ align:start position:0%
+is congruent to MK modulo P so this is
+kind of interesting because now um we
+
+ align:start position:0%
+kind of interesting because now um we
+ 
+
+ align:start position:0%
+kind of interesting because now um we
+can rewrite over there uh well not
+
+ align:start position:0%
+can rewrite over there uh well not
+ 
+
+ align:start position:0%
+can rewrite over there uh well not
+really rewrite but we can uh use this to
+
+ align:start position:0%
+really rewrite but we can uh use this to
+ 
+
+ align:start position:0%
+really rewrite but we can uh use this to
+analyze the encryption over here so M
+
+ align:start position:0%
+analyze the encryption over here so M
+ 
+
+ align:start position:0%
+analyze the encryption over here so M
+Prime is equal to this uh remainder and
+
+ align:start position:0%
+Prime is equal to this uh remainder and
+ 
+
+ align:start position:0%
+Prime is equal to this uh remainder and
+we get a beautiful equation we see that
+
+ align:start position:0%
+we get a beautiful equation we see that
+ 
+
+ align:start position:0%
+we get a beautiful equation we see that
+the encryption is congruent to the plain
+
+ align:start position:0%
+the encryption is congruent to the plain
+ 
+
+ align:start position:0%
+the encryption is congruent to the plain
+message times the key modulo P so how do
+
+ align:start position:0%
+message times the key modulo P so how do
+ 
+
+ align:start position:0%
+message times the key modulo P so how do
+I do decryption I can use the
+
+ align:start position:0%
+I do decryption I can use the
+ 
+
+ align:start position:0%
+I do decryption I can use the
+multiplicative inverse of K right so
+
+ align:start position:0%
+multiplicative inverse of K right so
+ 
+
+ align:start position:0%
+multiplicative inverse of K right so
+then I can divide k out
+
+ align:start position:0%
+then I can divide k out
+ 
+
+ align:start position:0%
+then I can divide k out
+so so let's write this out as well so
+
+ align:start position:0%
+so so let's write this out as well so
+ 
+
+ align:start position:0%
+so so let's write this out as well so
+suppose I have a multiplicative inverse
+
+ align:start position:0%
+suppose I have a multiplicative inverse
+ 
+
+ align:start position:0%
+suppose I have a multiplicative inverse
+K to the^ minus one that that is
+
+ align:start position:0%
+K to the^ minus one that that is
+ 
+
+ align:start position:0%
+K to the^ minus one that that is
+congruent to one modulo
+
+ align:start position:0%
+congruent to one modulo
+ 
+
+ align:start position:0%
+congruent to one modulo
+p why do I do this why why am I writing
+
+ align:start position:0%
+p why do I do this why why am I writing
+ 
+
+ align:start position:0%
+p why do I do this why why am I writing
+this out because uh we will see that it
+
+ align:start position:0%
+this out because uh we will see that it
+ 
+
+ align:start position:0%
+this out because uh we will see that it
+is not always possible to have a
+
+ align:start position:0%
+is not always possible to have a
+ 
+
+ align:start position:0%
+is not always possible to have a
+multiplicative inverse that's going to
+
+ align:start position:0%
+multiplicative inverse that's going to
+ 
+
+ align:start position:0%
+multiplicative inverse that's going to
+be really a big problem and that's uh
+
+ align:start position:0%
+be really a big problem and that's uh
+ 
+
+ align:start position:0%
+be really a big problem and that's uh
+where uh all these other um functions
+
+ align:start position:0%
+where uh all these other um functions
+ 
+
+ align:start position:0%
+where uh all these other um functions
+come in the ear toan function and ear
+
+ align:start position:0%
+come in the ear toan function and ear
+ 
+
+ align:start position:0%
+come in the ear toan function and ear
+theorem and so on so it's not really
+
+ align:start position:0%
+theorem and so on so it's not really
+ 
+
+ align:start position:0%
+theorem and so on so it's not really
+always the case we'll give an example in
+
+ align:start position:0%
+always the case we'll give an example in
+ 
+
+ align:start position:0%
+always the case we'll give an example in
+a moment but suppose that we have a
+
+ align:start position:0%
+a moment but suppose that we have a
+ 
+
+ align:start position:0%
+a moment but suppose that we have a
+multiplicative inverse modulo P well
+
+ align:start position:0%
+multiplicative inverse modulo P well
+ 
+
+ align:start position:0%
+multiplicative inverse modulo P well
+then I'm able to easily compute well I
+
+ align:start position:0%
+then I'm able to easily compute well I
+ 
+
+ align:start position:0%
+then I'm able to easily compute well I
+take M Prime I multiply it with K
+
+ align:start position:0%
+take M Prime I multiply it with K
+ 
+
+ align:start position:0%
+take M Prime I multiply it with K
+inverse well this is I'm substituting
+
+ align:start position:0%
+inverse well this is I'm substituting
+ 
+
+ align:start position:0%
+inverse well this is I'm substituting
+for M Prime M *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K time K inverse I still have this left
+
+ align:start position:0%
+K time K inverse I still have this left
+ 
+
+ align:start position:0%
+K time K inverse I still have this left
+now I can say that those that this is
+
+ align:start position:0%
+now I can say that those that this is
+ 
+
+ align:start position:0%
+now I can say that those that this is
+equal to uh 1 modulo
+
+ align:start position:0%
+equal to uh 1 modulo
+ 
+
+ align:start position:0%
+equal to uh 1 modulo
+P so this is equal or is congruent to m
+
+ align:start position:0%
+P so this is equal or is congruent to m
+ 
+
+ align:start position:0%
+P so this is equal or is congruent to m
+modulo p so now we see how we can do
+
+ align:start position:0%
+modulo p so now we see how we can do
+ 
+
+ align:start position:0%
+modulo p so now we see how we can do
+decryption we simply use the
+
+ align:start position:0%
+decryption we simply use the
+ 
+
+ align:start position:0%
+decryption we simply use the
+multiplicative inverse of K and as in
+
+ align:start position:0%
+multiplicative inverse of K and as in
+ 
+
+ align:start position:0%
+multiplicative inverse of K and as in
+the first uh touring code we are able to
+
+ align:start position:0%
+the first uh touring code we are able to
+ 
+
+ align:start position:0%
+the first uh touring code we are able to
+somehow uh divide out so where did I
+
+ align:start position:0%
+somehow uh divide out so where did I
+ 
+
+ align:start position:0%
+somehow uh divide out so where did I
+have it to divide out k i I did it very
+
+ align:start position:0%
+have it to divide out k i I did it very
+ 
+
+ align:start position:0%
+have it to divide out k i I did it very
+differently have a very different
+
+ align:start position:0%
+differently have a very different
+ 
+
+ align:start position:0%
+differently have a very different
+mathematical structure but but uh the
+
+ align:start position:0%
+mathematical structure but but uh the
+ 
+
+ align:start position:0%
+mathematical structure but but uh the
+idea is essentially the same I have a
+
+ align:start position:0%
+idea is essentially the same I have a
+ 
+
+ align:start position:0%
+idea is essentially the same I have a
+multiplicative inverse of K and If I
+
+ align:start position:0%
+multiplicative inverse of K and If I
+ 
+
+ align:start position:0%
+multiplicative inverse of K and If I
+multiply this with the encryption I will
+
+ align:start position:0%
+multiply this with the encryption I will
+ 
+
+ align:start position:0%
+multiply this with the encryption I will
+get the plain message modulo P so am I
+
+ align:start position:0%
+get the plain message modulo P so am I
+ 
+
+ align:start position:0%
+get the plain message modulo P so am I
+finished now is the question well uh I
+
+ align:start position:0%
+finished now is the question well uh I
+ 
+
+ align:start position:0%
+finished now is the question well uh I
+know that m is in the range uh of 01 all
+
+ align:start position:0%
+know that m is in the range uh of 01 all
+ 
+
+ align:start position:0%
+know that m is in the range uh of 01 all
+the way up to P minus
+
+ align:start position:0%
+the way up to P minus
+ 
+
+ align:start position:0%
+the way up to P minus
+one so um this means that I can also
+
+ align:start position:0%
+one so um this means that I can also
+ 
+
+ align:start position:0%
+one so um this means that I can also
+rewrite m s and I use a similar trick as
+
+ align:start position:0%
+rewrite m s and I use a similar trick as
+ 
+
+ align:start position:0%
+rewrite m s and I use a similar trick as
+what I did over here I can rewrite M as
+
+ align:start position:0%
+what I did over here I can rewrite M as
+ 
+
+ align:start position:0%
+what I did over here I can rewrite M as
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+remainder of M Prime * K
+
+ align:start position:0%
+remainder of M Prime * K
+ 
+
+ align:start position:0%
+remainder of M Prime * K
+inverse after dividing out as many
+
+ align:start position:0%
+inverse after dividing out as many
+ 
+
+ align:start position:0%
+inverse after dividing out as many
+copies of p as
+
+ align:start position:0%
+copies of p as
+ 
+
+ align:start position:0%
+copies of p as
+possible so what we did here is to First
+
+ align:start position:0%
+possible so what we did here is to First
+ 
+
+ align:start position:0%
+possible so what we did here is to First
+prove that the difference between those
+
+ align:start position:0%
+prove that the difference between those
+ 
+
+ align:start position:0%
+prove that the difference between those
+two is a multiple of P that's
+
+ align:start position:0%
+two is a multiple of P that's
+ 
+
+ align:start position:0%
+two is a multiple of P that's
+essentially what congruent modulo p
+
+ align:start position:0%
+essentially what congruent modulo p
+ 
+
+ align:start position:0%
+essentially what congruent modulo p
+means that's the definition
+
+ align:start position:0%
+means that's the definition
+ 
+
+ align:start position:0%
+means that's the definition
+so now that I know that the difference
+
+ align:start position:0%
+so now that I know that the difference
+ 
+
+ align:start position:0%
+so now that I know that the difference
+is a multiple of P um and if I know that
+
+ align:start position:0%
+is a multiple of P um and if I know that
+ 
+
+ align:start position:0%
+is a multiple of P um and if I know that
+m is actually in this range up to P
+
+ align:start position:0%
+m is actually in this range up to P
+ 
+
+ align:start position:0%
+m is actually in this range up to P
+minus one I can use what we learned uh
+
+ align:start position:0%
+minus one I can use what we learned uh
+ 
+
+ align:start position:0%
+minus one I can use what we learned uh
+last lecture and what the book was
+
+ align:start position:0%
+last lecture and what the book was
+ 
+
+ align:start position:0%
+last lecture and what the book was
+talking about that the definition of the
+
+ align:start position:0%
+talking about that the definition of the
+ 
+
+ align:start position:0%
+talking about that the definition of the
+remainder of M Prime * K inverse this
+
+ align:start position:0%
+remainder of M Prime * K inverse this
+ 
+
+ align:start position:0%
+remainder of M Prime * K inverse this
+thing after finding out as many copies
+
+ align:start position:0%
+thing after finding out as many copies
+ 
+
+ align:start position:0%
+thing after finding out as many copies
+of p is exactly this plain message M
+
+ align:start position:0%
+of p is exactly this plain message M
+ 
+
+ align:start position:0%
+of p is exactly this plain message M
+okay so now we have the decryption so
+
+ align:start position:0%
+okay so now we have the decryption so
+ 
+
+ align:start position:0%
+okay so now we have the decryption so
+this is decryption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh that sounds great so now of
+
+ align:start position:0%
+and uh that sounds great so now of
+ 
+
+ align:start position:0%
+and uh that sounds great so now of
+course we are wondering uh well if we uh
+
+ align:start position:0%
+course we are wondering uh well if we uh
+ 
+
+ align:start position:0%
+course we are wondering uh well if we uh
+can do this can we also uh attack this
+
+ align:start position:0%
+can do this can we also uh attack this
+ 
+
+ align:start position:0%
+can do this can we also uh attack this
+scheme right can we do something bad
+
+ align:start position:0%
+scheme right can we do something bad
+ 
+
+ align:start position:0%
+scheme right can we do something bad
+with it um well it can be used to break
+
+ align:start position:0%
+with it um well it can be used to break
+ 
+
+ align:start position:0%
+with it um well it can be used to break
+this code but in a slightly more uh
+
+ align:start position:0%
+this code but in a slightly more uh
+ 
+
+ align:start position:0%
+this code but in a slightly more uh
+complicated way
+
+ align:start position:0%
+complicated way
+ 
+
+ align:start position:0%
+complicated way
+um so let's see where I put that
+
+ align:start position:0%
+um so let's see where I put that
+ 
+
+ align:start position:0%
+um so let's see where I put that
+right so what we're going to use now uh
+
+ align:start position:0%
+right so what we're going to use now uh
+ 
+
+ align:start position:0%
+right so what we're going to use now uh
+so when we talk about security and so on
+
+ align:start position:0%
+so when we talk about security and so on
+ 
+
+ align:start position:0%
+so when we talk about security and so on
+uh you can think of all kinds of ways to
+
+ align:start position:0%
+uh you can think of all kinds of ways to
+ 
+
+ align:start position:0%
+uh you can think of all kinds of ways to
+break uh an encryption scheme so we
+
+ align:start position:0%
+break uh an encryption scheme so we
+ 
+
+ align:start position:0%
+break uh an encryption scheme so we
+started out with in the first version
+
+ align:start position:0%
+started out with in the first version
+ 
+
+ align:start position:0%
+started out with in the first version
+well what if I just know the encryption
+
+ align:start position:0%
+well what if I just know the encryption
+ 
+
+ align:start position:0%
+well what if I just know the encryption
+and then um well I cannot know anything
+
+ align:start position:0%
+and then um well I cannot know anything
+ 
+
+ align:start position:0%
+and then um well I cannot know anything
+about the pl Tech simply because I know
+
+ align:start position:0%
+about the pl Tech simply because I know
+ 
+
+ align:start position:0%
+about the pl Tech simply because I know
+it's very hard to factor to factor a
+
+ align:start position:0%
+it's very hard to factor to factor a
+ 
+
+ align:start position:0%
+it's very hard to factor to factor a
+product of two large primes then I said
+
+ align:start position:0%
+product of two large primes then I said
+ 
+
+ align:start position:0%
+product of two large primes then I said
+but I can know a little bit more as an
+
+ align:start position:0%
+but I can know a little bit more as an
+ 
+
+ align:start position:0%
+but I can know a little bit more as an
+adversary suppose I have a plane message
+
+ align:start position:0%
+adversary suppose I have a plane message
+ 
+
+ align:start position:0%
+adversary suppose I have a plane message
+together with a uh um encrypted message
+
+ align:start position:0%
+together with a uh um encrypted message
+ 
+
+ align:start position:0%
+together with a uh um encrypted message
+well then I could do this gcd trick and
+
+ align:start position:0%
+well then I could do this gcd trick and
+ 
+
+ align:start position:0%
+well then I could do this gcd trick and
+figure out and break the scheme and now
+
+ align:start position:0%
+figure out and break the scheme and now
+ 
+
+ align:start position:0%
+figure out and break the scheme and now
+we're going to do something similar and
+
+ align:start position:0%
+we're going to do something similar and
+ 
+
+ align:start position:0%
+we're going to do something similar and
+we say well suppose
+
+ align:start position:0%
+we say well suppose
+ 
+
+ align:start position:0%
+we say well suppose
+um uh that I do not know two encryptions
+
+ align:start position:0%
+um uh that I do not know two encryptions
+ 
+
+ align:start position:0%
+um uh that I do not know two encryptions
+but I know uh a plain message and an
+
+ align:start position:0%
+but I know uh a plain message and an
+ 
+
+ align:start position:0%
+but I know uh a plain message and an
+corresponding encrypted message message
+
+ align:start position:0%
+corresponding encrypted message message
+ 
+
+ align:start position:0%
+corresponding encrypted message message
+so if I know such a pair which is I mean
+
+ align:start position:0%
+so if I know such a pair which is I mean
+ 
+
+ align:start position:0%
+so if I know such a pair which is I mean
+in practice such such type of
+
+ align:start position:0%
+in practice such such type of
+ 
+
+ align:start position:0%
+in practice such such type of
+information will be leaked um then in
+
+ align:start position:0%
+information will be leaked um then in
+ 
+
+ align:start position:0%
+information will be leaked um then in
+this case I can break it so we call this
+
+ align:start position:0%
+this case I can break it so we call this
+ 
+
+ align:start position:0%
+this case I can break it so we call this
+the known uh plain text
+
+ align:start position:0%
+the known uh plain text
+ 
+
+ align:start position:0%
+the known uh plain text
+attack and
+
+ align:start position:0%
+attack and
+ 
+
+ align:start position:0%
+attack and
+um it assumes that uh we know as an
+
+ align:start position:0%
+um it assumes that uh we know as an
+ 
+
+ align:start position:0%
+um it assumes that uh we know as an
+adversary I
+
+ align:start position:0%
+adversary I
+ 
+
+ align:start position:0%
+adversary I
+know a a message a plain
+
+ align:start position:0%
+know a a message a plain
+ 
+
+ align:start position:0%
+know a a message a plain
+message m
+
+ align:start position:0%
+message m
+ 
+
+ align:start position:0%
+message m
+and also an encryption of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+message
+
+ align:start position:0%
+message
+ 
+
+ align:start position:0%
+message
+um M Prime and M Prime according to this
+
+ align:start position:0%
+um M Prime and M Prime according to this
+ 
+
+ align:start position:0%
+um M Prime and M Prime according to this
+scheme is the remainder of M * K after
+
+ align:start position:0%
+scheme is the remainder of M * K after
+ 
+
+ align:start position:0%
+scheme is the remainder of M * K after
+dividing out as many multiples of p as
+
+ align:start position:0%
+dividing out as many multiples of p as
+ 
+
+ align:start position:0%
+dividing out as many multiples of p as
+possible now we saw um now suppose I
+
+ align:start position:0%
+possible now we saw um now suppose I
+ 
+
+ align:start position:0%
+possible now we saw um now suppose I
+know these two I'm going to show to you
+
+ align:start position:0%
+know these two I'm going to show to you
+ 
+
+ align:start position:0%
+know these two I'm going to show to you
+how to break it so let's have a look M
+
+ align:start position:0%
+how to break it so let's have a look M
+ 
+
+ align:start position:0%
+how to break it so let's have a look M
+uh the the encryption M Prime here is
+
+ align:start position:0%
+uh the the encryption M Prime here is
+ 
+
+ align:start position:0%
+uh the the encryption M Prime here is
+congruent to M * k modulo p you just
+
+ align:start position:0%
+congruent to M * k modulo p you just
+ 
+
+ align:start position:0%
+congruent to M * k modulo p you just
+proved it over
+
+ align:start position:0%
+proved it over
+ 
+
+ align:start position:0%
+proved it over
+here and uh what do we know we know that
+
+ align:start position:0%
+here and uh what do we know we know that
+ 
+
+ align:start position:0%
+here and uh what do we know we know that
+P is a public Prime I know
+
+ align:start position:0%
+P is a public Prime I know
+ 
+
+ align:start position:0%
+P is a public Prime I know
+P since it's a prime I know that the gcd
+
+ align:start position:0%
+P since it's a prime I know that the gcd
+ 
+
+ align:start position:0%
+P since it's a prime I know that the gcd
+of M and P equals
+
+ align:start position:0%
+of M and P equals
+ 
+
+ align:start position:0%
+of M and P equals
+one so these two are relatively prime so
+
+ align:start position:0%
+one so these two are relatively prime so
+ 
+
+ align:start position:0%
+one so these two are relatively prime so
+now if they're relatively prime time and
+
+ align:start position:0%
+now if they're relatively prime time and
+ 
+
+ align:start position:0%
+now if they're relatively prime time and
+that's what we wrote up here we know
+
+ align:start position:0%
+that's what we wrote up here we know
+ 
+
+ align:start position:0%
+that's what we wrote up here we know
+that there exists this linear
+
+ align:start position:0%
+that there exists this linear
+ 
+
+ align:start position:0%
+that there exists this linear
+combination of uh in this case uh M and
+
+ align:start position:0%
+combination of uh in this case uh M and
+ 
+
+ align:start position:0%
+combination of uh in this case uh M and
+M and P uh that is equal to
+
+ align:start position:0%
+M and P uh that is equal to
+ 
+
+ align:start position:0%
+M and P uh that is equal to
+one and in this way we can figure out
+
+ align:start position:0%
+one and in this way we can figure out
+ 
+
+ align:start position:0%
+one and in this way we can figure out
+how to compute uh the inverse the
+
+ align:start position:0%
+how to compute uh the inverse the
+ 
+
+ align:start position:0%
+how to compute uh the inverse the
+multiplicative inverse of
+
+ align:start position:0%
+multiplicative inverse of
+ 
+
+ align:start position:0%
+multiplicative inverse of
+M so that's what we're going to do so we
+
+ align:start position:0%
+M so that's what we're going to do so we
+ 
+
+ align:start position:0%
+M so that's what we're going to do so we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+compute um the multiplicative
+
+ align:start position:0%
+compute um the multiplicative
+ 
+
+ align:start position:0%
+compute um the multiplicative
+inverse uh such that M * m inverse is
+
+ align:start position:0%
+inverse uh such that M * m inverse is
+ 
+
+ align:start position:0%
+inverse uh such that M * m inverse is
+congruent to one
+
+ align:start position:0%
+congruent to one
+ 
+
+ align:start position:0%
+congruent to one
+modulo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p so now we can do the next step uh so
+
+ align:start position:0%
+p so now we can do the next step uh so
+ 
+
+ align:start position:0%
+p so now we can do the next step uh so
+what could I do next so let's see if I
+
+ align:start position:0%
+what could I do next so let's see if I
+ 
+
+ align:start position:0%
+what could I do next so let's see if I
+have such an
+
+ align:start position:0%
+have such an
+ 
+
+ align:start position:0%
+have such an
+inverse then I can take my uh encrypted
+
+ align:start position:0%
+inverse then I can take my uh encrypted
+ 
+
+ align:start position:0%
+inverse then I can take my uh encrypted
+uh message that I have as an attacker
+
+ align:start position:0%
+uh message that I have as an attacker
+ 
+
+ align:start position:0%
+uh message that I have as an attacker
+which is M Prime
+
+ align:start position:0%
+which is M Prime
+ 
+
+ align:start position:0%
+which is M Prime
+time um I Know M and since P was public
+
+ align:start position:0%
+time um I Know M and since P was public
+ 
+
+ align:start position:0%
+time um I Know M and since P was public
+I can compute this multiplicative
+
+ align:start position:0%
+I can compute this multiplicative
+ 
+
+ align:start position:0%
+I can compute this multiplicative
+inverse so I can just compute
+
+ align:start position:0%
+inverse so I can just compute
+ 
+
+ align:start position:0%
+inverse so I can just compute
+this uh product and I know that this is
+
+ align:start position:0%
+this uh product and I know that this is
+ 
+
+ align:start position:0%
+this uh product and I know that this is
+actually equal to well K * m * m inverse
+
+ align:start position:0%
+actually equal to well K * m * m inverse
+ 
+
+ align:start position:0%
+actually equal to well K * m * m inverse
+this is again equal to congruent to one
+
+ align:start position:0%
+this is again equal to congruent to one
+ 
+
+ align:start position:0%
+this is again equal to congruent to one
+modul p so this is equal to K
+
+ align:start position:0%
+modul p so this is equal to K
+ 
+
+ align:start position:0%
+modul p so this is equal to K
+modul so now all of a sudden I know k
+
+ align:start position:0%
+modul so now all of a sudden I know k
+ 
+
+ align:start position:0%
+modul so now all of a sudden I know k
+modulo P because I know those two so if
+
+ align:start position:0%
+modulo P because I know those two so if
+ 
+
+ align:start position:0%
+modulo P because I know those two so if
+I know k i can
+
+ align:start position:0%
+I know k i can
+ 
+
+ align:start position:0%
+I know k i can
+compute its multiplicative inverse so I
+
+ align:start position:0%
+compute its multiplicative inverse so I
+ 
+
+ align:start position:0%
+compute its multiplicative inverse so I
+can compute K inverse uh modulo
+
+ align:start position:0%
+can compute K inverse uh modulo
+ 
+
+ align:start position:0%
+can compute K inverse uh modulo
+p and if I know K inverse again I can
+
+ align:start position:0%
+p and if I know K inverse again I can
+ 
+
+ align:start position:0%
+p and if I know K inverse again I can
+use it to decrypt any other uh encrypted
+
+ align:start position:0%
+use it to decrypt any other uh encrypted
+ 
+
+ align:start position:0%
+use it to decrypt any other uh encrypted
+message that I receive so for all future
+
+ align:start position:0%
+message that I receive so for all future
+ 
+
+ align:start position:0%
+message that I receive so for all future
+encrypted messages I do not need anymore
+
+ align:start position:0%
+encrypted messages I do not need anymore
+ 
+
+ align:start position:0%
+encrypted messages I do not need anymore
+the plain messages I have already used
+
+ align:start position:0%
+the plain messages I have already used
+ 
+
+ align:start position:0%
+the plain messages I have already used
+just by using one plain message
+
+ align:start position:0%
+just by using one plain message
+ 
+
+ align:start position:0%
+just by using one plain message
+encryption pair I have been able to
+
+ align:start position:0%
+encryption pair I have been able to
+ 
+
+ align:start position:0%
+encryption pair I have been able to
+compute the secret key and the whole
+
+ align:start position:0%
+compute the secret key and the whole
+ 
+
+ align:start position:0%
+compute the secret key and the whole
+scheme is broken so security and and
+
+ align:start position:0%
+scheme is broken so security and and
+ 
+
+ align:start position:0%
+scheme is broken so security and and
+it's kind of a
+
+ align:start position:0%
+it's kind of a
+ 
+
+ align:start position:0%
+it's kind of a
+interesting uh sence uh we can always
+
+ align:start position:0%
+interesting uh sence uh we can always
+ 
+
+ align:start position:0%
+interesting uh sence uh we can always
+think of more tricks to break schemes or
+
+ align:start position:0%
+think of more tricks to break schemes or
+ 
+
+ align:start position:0%
+think of more tricks to break schemes or
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+assumptions um that we haven't thought
+
+ align:start position:0%
+assumptions um that we haven't thought
+ 
+
+ align:start position:0%
+assumptions um that we haven't thought
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+before um so now let's Let's uh talk
+
+ align:start position:0%
+before um so now let's Let's uh talk
+ 
+
+ align:start position:0%
+before um so now let's Let's uh talk
+about uh so what did we do
+
+ align:start position:0%
+about uh so what did we do
+ 
+
+ align:start position:0%
+about uh so what did we do
+here um we have been talking about uh
+
+ align:start position:0%
+here um we have been talking about uh
+ 
+
+ align:start position:0%
+here um we have been talking about uh
+about encryption this these two schemes
+
+ align:start position:0%
+about encryption this these two schemes
+ 
+
+ align:start position:0%
+about encryption this these two schemes
+we talked about modular
+
+ align:start position:0%
+we talked about modular
+ 
+
+ align:start position:0%
+we talked about modular
+arithmetic talked about congruence and
+
+ align:start position:0%
+arithmetic talked about congruence and
+ 
+
+ align:start position:0%
+arithmetic talked about congruence and
+also the multiplicative inverse and we
+
+ align:start position:0%
+also the multiplicative inverse and we
+ 
+
+ align:start position:0%
+also the multiplicative inverse and we
+showed how to uh use that to break
+
+ align:start position:0%
+showed how to uh use that to break
+ 
+
+ align:start position:0%
+showed how to uh use that to break
+juring scod version number two so we
+
+ align:start position:0%
+juring scod version number two so we
+ 
+
+ align:start position:0%
+juring scod version number two so we
+need something much more fundamental in
+
+ align:start position:0%
+need something much more fundamental in
+ 
+
+ align:start position:0%
+need something much more fundamental in
+order to create a scheme that is really
+
+ align:start position:0%
+order to create a scheme that is really
+ 
+
+ align:start position:0%
+order to create a scheme that is really
+secure and that's what we're going to do
+
+ align:start position:0%
+secure and that's what we're going to do
+ 
+
+ align:start position:0%
+secure and that's what we're going to do
+now we're going to start off with oil's
+
+ align:start position:0%
+now we're going to start off with oil's
+ 
+
+ align:start position:0%
+now we're going to start off with oil's
+toen function and improve a related
+
+ align:start position:0%
+toen function and improve a related
+ 
+
+ align:start position:0%
+toen function and improve a related
+theorem and with that we will be able to
+
+ align:start position:0%
+theorem and with that we will be able to
+ 
+
+ align:start position:0%
+theorem and with that we will be able to
+actually create uh explain the RSA
+
+ align:start position:0%
+actually create uh explain the RSA
+ 
+
+ align:start position:0%
+actually create uh explain the RSA
+algorithm which is a famous algorithm
+
+ align:start position:0%
+algorithm which is a famous algorithm
+ 
+
+ align:start position:0%
+algorithm which is a famous algorithm
+invented here at MIT in 1977 by uh by
+
+ align:start position:0%
+invented here at MIT in 1977 by uh by
+ 
+
+ align:start position:0%
+invented here at MIT in 1977 by uh by
+reest Shamir and adman and uh they
+
+ align:start position:0%
+reest Shamir and adman and uh they
+ 
+
+ align:start position:0%
+reest Shamir and adman and uh they
+actually also got the touring award for
+
+ align:start position:0%
+actually also got the touring award for
+ 
+
+ align:start position:0%
+actually also got the touring award for
+this a few years ago uh um and it's
+
+ align:start position:0%
+this a few years ago uh um and it's
+ 
+
+ align:start position:0%
+this a few years ago uh um and it's
+widely used uh in in
+
+ align:start position:0%
+widely used uh in in
+ 
+
+ align:start position:0%
+widely used uh in in
+practice but we will be able to actually
+
+ align:start position:0%
+practice but we will be able to actually
+ 
+
+ align:start position:0%
+practice but we will be able to actually
+explain this algorithm with just this
+
+ align:start position:0%
+explain this algorithm with just this
+ 
+
+ align:start position:0%
+explain this algorithm with just this
+fundamental piece of number Theory so
+
+ align:start position:0%
+fundamental piece of number Theory so
+ 
+
+ align:start position:0%
+fundamental piece of number Theory so
+that's really exciting so let's do
+
+ align:start position:0%
+that's really exciting so let's do
+ 
+
+ align:start position:0%
+that's really exciting so let's do
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so we're going to first Define uh
+
+ align:start position:0%
+um so we're going to first Define uh
+ 
+
+ align:start position:0%
+um so we're going to first Define uh
+Oilers toan function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's related to this multiplicative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse this function is uh denoted by F
+
+ align:start position:0%
+inverse this function is uh denoted by F
+ 
+
+ align:start position:0%
+inverse this function is uh denoted by F
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+N
+
+ align:start position:0%
+N
+ 
+
+ align:start position:0%
+N
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+denotes uh the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers number of integers in one 2 3
+
+ align:start position:0%
+integers number of integers in one 2 3
+ 
+
+ align:start position:0%
+integers number of integers in one 2 3
+all the way up to n minus
+
+ align:start position:0%
+all the way up to n minus
+ 
+
+ align:start position:0%
+all the way up to n minus
+one that are relatively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime that are relatively prime to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so well this is uh this just drops out
+
+ align:start position:0%
+so well this is uh this just drops out
+ 
+
+ align:start position:0%
+so well this is uh this just drops out
+of the air you may think but um yeah
+
+ align:start position:0%
+of the air you may think but um yeah
+ 
+
+ align:start position:0%
+of the air you may think but um yeah
+this is a a fundamental quantity and
+
+ align:start position:0%
+this is a a fundamental quantity and
+ 
+
+ align:start position:0%
+this is a a fundamental quantity and
+erish Theorem is what we will try to
+
+ align:start position:0%
+erish Theorem is what we will try to
+ 
+
+ align:start position:0%
+erish Theorem is what we will try to
+prove next but let's give a couple of
+
+ align:start position:0%
+prove next but let's give a couple of
+ 
+
+ align:start position:0%
+prove next but let's give a couple of
+examples about this
+
+ align:start position:0%
+examples about this
+ 
+
+ align:start position:0%
+examples about this
+um just to see how it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works so for example let's take n to be
+
+ align:start position:0%
+works so for example let's take n to be
+ 
+
+ align:start position:0%
+works so for example let's take n to be
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+12 um what would be the value of a
+
+ align:start position:0%
+12 um what would be the value of a
+ 
+
+ align:start position:0%
+12 um what would be the value of a
+erosion function evaluated for
+
+ align:start position:0%
+erosion function evaluated for
+ 
+
+ align:start position:0%
+erosion function evaluated for
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+so if you take 12 we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the following numbers to consider 1 2
+
+ align:start position:0%
+um the following numbers to consider 1 2
+ 
+
+ align:start position:0%
+um the following numbers to consider 1 2
+3 4 5 6 7 8 9 10 11 and 12 so now let's
+
+ align:start position:0%
+3 4 5 6 7 8 9 10 11 and 12 so now let's
+ 
+
+ align:start position:0%
+3 4 5 6 7 8 9 10 11 and 12 so now let's
+have a look you want to count the N the
+
+ align:start position:0%
+have a look you want to count the N the
+ 
+
+ align:start position:0%
+have a look you want to count the N the
+you want to count the integers that are
+
+ align:start position:0%
+you want to count the integers that are
+ 
+
+ align:start position:0%
+you want to count the integers that are
+relatively prime to to
+
+ align:start position:0%
+relatively prime to to
+ 
+
+ align:start position:0%
+relatively prime to to
+12 um well uh one is relatively prime to
+
+ align:start position:0%
+12 um well uh one is relatively prime to
+ 
+
+ align:start position:0%
+12 um well uh one is relatively prime to
+12 why is that because the gcd of 12 and
+
+ align:start position:0%
+12 why is that because the gcd of 12 and
+ 
+
+ align:start position:0%
+12 why is that because the gcd of 12 and
+one is equal to one and that's the
+
+ align:start position:0%
+one is equal to one and that's the
+ 
+
+ align:start position:0%
+one is equal to one and that's the
+definition of being relatively prime so
+
+ align:start position:0%
+definition of being relatively prime so
+ 
+
+ align:start position:0%
+definition of being relatively prime so
+this is a good
+
+ align:start position:0%
+this is a good
+ 
+
+ align:start position:0%
+this is a good
+number H the gcd of 12 and two well both
+
+ align:start position:0%
+number H the gcd of 12 and two well both
+ 
+
+ align:start position:0%
+number H the gcd of 12 and two well both
+are divisible by two and so they're not
+
+ align:start position:0%
+are divisible by two and so they're not
+ 
+
+ align:start position:0%
+are divisible by two and so they're not
+relatively prime because the gcd is at
+
+ align:start position:0%
+relatively prime because the gcd is at
+ 
+
+ align:start position:0%
+relatively prime because the gcd is at
+least two in this case equal to two
+
+ align:start position:0%
+least two in this case equal to two
+ 
+
+ align:start position:0%
+least two in this case equal to two
+three also divides 12 four divides 12
+
+ align:start position:0%
+three also divides 12 four divides 12
+ 
+
+ align:start position:0%
+three also divides 12 four divides 12
+five is relatively prime with respect to
+
+ align:start position:0%
+five is relatively prime with respect to
+ 
+
+ align:start position:0%
+five is relatively prime with respect to
+12 six actually is is dividing 12 as
+
+ align:start position:0%
+12 six actually is is dividing 12 as
+ 
+
+ align:start position:0%
+12 six actually is is dividing 12 as
+well seven is relatively
+
+ align:start position:0%
+well seven is relatively
+ 
+
+ align:start position:0%
+well seven is relatively
+prime and 11 over here as well and all
+
+ align:start position:0%
+prime and 11 over here as well and all
+ 
+
+ align:start position:0%
+prime and 11 over here as well and all
+the others have a greatest common
+
+ align:start position:0%
+the others have a greatest common
+ 
+
+ align:start position:0%
+the others have a greatest common
+divisor that is larger than one so here
+
+ align:start position:0%
+divisor that is larger than one so here
+ 
+
+ align:start position:0%
+divisor that is larger than one so here
+we see that the ELO function in
+
+ align:start position:0%
+we see that the ELO function in
+ 
+
+ align:start position:0%
+we see that the ELO function in
+evaluated in 12 is equal to four there
+
+ align:start position:0%
+evaluated in 12 is equal to four there
+ 
+
+ align:start position:0%
+evaluated in 12 is equal to four there
+are one two three four integers that are
+
+ align:start position:0%
+are one two three four integers that are
+ 
+
+ align:start position:0%
+are one two three four integers that are
+relatively
+
+ align:start position:0%
+relatively
+ 
+
+ align:start position:0%
+relatively
+prime okay so let's have a different one
+
+ align:start position:0%
+prime okay so let's have a different one
+ 
+
+ align:start position:0%
+prime okay so let's have a different one
+say n equals 15 it's a little bit
+
+ align:start position:0%
+say n equals 15 it's a little bit
+ 
+
+ align:start position:0%
+say n equals 15 it's a little bit
+different because here you may think
+
+ align:start position:0%
+different because here you may think
+ 
+
+ align:start position:0%
+different because here you may think
+this is kind of coincidental that 1 5 7
+
+ align:start position:0%
+this is kind of coincidental that 1 5 7
+ 
+
+ align:start position:0%
+this is kind of coincidental that 1 5 7
+and 11 are actually also primes but for
+
+ align:start position:0%
+and 11 are actually also primes but for
+ 
+
+ align:start position:0%
+and 11 are actually also primes but for
+15 it looks a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so let's write out all
+
+ align:start position:0%
+different so let's write out all
+ 
+
+ align:start position:0%
+different so let's write out all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+numbers um again let's have a look well
+
+ align:start position:0%
+numbers um again let's have a look well
+ 
+
+ align:start position:0%
+numbers um again let's have a look well
+one is greatest comma divisor equal to
+
+ align:start position:0%
+one is greatest comma divisor equal to
+ 
+
+ align:start position:0%
+one is greatest comma divisor equal to
+one to with respect to 15 uh two well is
+
+ align:start position:0%
+one to with respect to 15 uh two well is
+ 
+
+ align:start position:0%
+one to with respect to 15 uh two well is
+also relatively prime with respect to 15
+
+ align:start position:0%
+also relatively prime with respect to 15
+ 
+
+ align:start position:0%
+also relatively prime with respect to 15
+three is dividing 15 four yeah four and
+
+ align:start position:0%
+three is dividing 15 four yeah four and
+ 
+
+ align:start position:0%
+three is dividing 15 four yeah four and
+15 have greatest common divisor equal to
+
+ align:start position:0%
+15 have greatest common divisor equal to
+ 
+
+ align:start position:0%
+15 have greatest common divisor equal to
+one so that's relatively prime um five
+
+ align:start position:0%
+one so that's relatively prime um five
+ 
+
+ align:start position:0%
+one so that's relatively prime um five
+is not uh six is not seven is relatively
+
+ align:start position:0%
+is not uh six is not seven is relatively
+ 
+
+ align:start position:0%
+is not uh six is not seven is relatively
+prime eight again this is only divisible
+
+ align:start position:0%
+prime eight again this is only divisible
+ 
+
+ align:start position:0%
+prime eight again this is only divisible
+by Power of Two And this has no power of
+
+ align:start position:0%
+by Power of Two And this has no power of
+ 
+
+ align:start position:0%
+by Power of Two And this has no power of
+two in it uh 9 10 uh are this one is
+
+ align:start position:0%
+two in it uh 9 10 uh are this one is
+ 
+
+ align:start position:0%
+two in it uh 9 10 uh are this one is
+divisible by five divisible by three 11
+
+ align:start position:0%
+divisible by five divisible by three 11
+ 
+
+ align:start position:0%
+divisible by five divisible by three 11
+is again relatively prime and then we
+
+ align:start position:0%
+is again relatively prime and then we
+ 
+
+ align:start position:0%
+is again relatively prime and then we
+have 13 is relatively prime as well and
+
+ align:start position:0%
+have 13 is relatively prime as well and
+ 
+
+ align:start position:0%
+have 13 is relatively prime as well and
+14 as well because this is 2 * 7 and
+
+ align:start position:0%
+14 as well because this is 2 * 7 and
+ 
+
+ align:start position:0%
+14 as well because this is 2 * 7 and
+this is 3 * 5 so how many do we see now
+
+ align:start position:0%
+this is 3 * 5 so how many do we see now
+ 
+
+ align:start position:0%
+this is 3 * 5 so how many do we see now
+1 2 3 four five six seven eight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the O toci function evaluated in 15
+
+ align:start position:0%
+so the O toci function evaluated in 15
+ 
+
+ align:start position:0%
+so the O toci function evaluated in 15
+is actually equal to
+
+ align:start position:0%
+is actually equal to
+ 
+
+ align:start position:0%
+is actually equal to
+8 now it turns out that uh this uh
+
+ align:start position:0%
+8 now it turns out that uh this uh
+ 
+
+ align:start position:0%
+8 now it turns out that uh this uh
+function has really nice properties and
+
+ align:start position:0%
+function has really nice properties and
+ 
+
+ align:start position:0%
+function has really nice properties and
+you can uh easily calculate if you know
+
+ align:start position:0%
+you can uh easily calculate if you know
+ 
+
+ align:start position:0%
+you can uh easily calculate if you know
+its uh if you know the decomposition of
+
+ align:start position:0%
+its uh if you know the decomposition of
+ 
+
+ align:start position:0%
+its uh if you know the decomposition of
+n into its primes and powers of primes
+
+ align:start position:0%
+n into its primes and powers of primes
+ 
+
+ align:start position:0%
+n into its primes and powers of primes
+you can easily compute uh this
+
+ align:start position:0%
+you can easily compute uh this
+ 
+
+ align:start position:0%
+you can easily compute uh this
+number F of
+
+ align:start position:0%
+number F of
+ 
+
+ align:start position:0%
+number F of
+n um
+
+ align:start position:0%
+n um
+ 
+
+ align:start position:0%
+n um
+now you will be able to find this in the
+
+ align:start position:0%
+now you will be able to find this in the
+ 
+
+ align:start position:0%
+now you will be able to find this in the
+book you should read it and also problem
+
+ align:start position:0%
+book you should read it and also problem
+ 
+
+ align:start position:0%
+book you should read it and also problem
+set talks about
+
+ align:start position:0%
+set talks about
+ 
+
+ align:start position:0%
+set talks about
+this but for now let's just uh uh talk
+
+ align:start position:0%
+this but for now let's just uh uh talk
+ 
+
+ align:start position:0%
+this but for now let's just uh uh talk
+about this as an abstract notion because
+
+ align:start position:0%
+about this as an abstract notion because
+ 
+
+ align:start position:0%
+about this as an abstract notion because
+that's all that we will use in this
+
+ align:start position:0%
+that's all that we will use in this
+ 
+
+ align:start position:0%
+that's all that we will use in this
+lecture but you will have a few
+
+ align:start position:0%
+lecture but you will have a few
+ 
+
+ align:start position:0%
+lecture but you will have a few
+exercises that talk about Computing this
+
+ align:start position:0%
+exercises that talk about Computing this
+ 
+
+ align:start position:0%
+exercises that talk about Computing this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um let's talk about the ENT function uh
+
+ align:start position:0%
+um let's talk about the ENT function uh
+ 
+
+ align:start position:0%
+um let's talk about the ENT function uh
+and ear theorem so let me use
+
+ align:start position:0%
+and ear theorem so let me use
+ 
+
+ align:start position:0%
+and ear theorem so let me use
+uh this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Blackboard now this is really an
+
+ align:start position:0%
+Blackboard now this is really an
+ 
+
+ align:start position:0%
+Blackboard now this is really an
+exciting
+
+ align:start position:0%
+exciting
+ 
+
+ align:start position:0%
+exciting
+theorem and it's a little bit hard to
+
+ align:start position:0%
+theorem and it's a little bit hard to
+ 
+
+ align:start position:0%
+theorem and it's a little bit hard to
+prove that's why we will need uh a
+
+ align:start position:0%
+prove that's why we will need uh a
+ 
+
+ align:start position:0%
+prove that's why we will need uh a
+little bit more time to do
+
+ align:start position:0%
+little bit more time to do
+ 
+
+ align:start position:0%
+little bit more time to do
+this um ear theorem says the following
+
+ align:start position:0%
+this um ear theorem says the following
+ 
+
+ align:start position:0%
+this um ear theorem says the following
+if if the
+
+ align:start position:0%
+if if the
+ 
+
+ align:start position:0%
+if if the
+gcd of N and
+
+ align:start position:0%
+gcd of N and
+ 
+
+ align:start position:0%
+gcd of N and
+K is equal to one uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then K to the
+
+ align:start position:0%
+then K to the
+ 
+
+ align:start position:0%
+then K to the
+power the ear to function evaluated in N
+
+ align:start position:0%
+power the ear to function evaluated in N
+ 
+
+ align:start position:0%
+power the ear to function evaluated in N
+is actually congruent to One
+
+ align:start position:0%
+is actually congruent to One
+ 
+
+ align:start position:0%
+is actually congruent to One
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+n so this is what we're going to prove
+
+ align:start position:0%
+n so this is what we're going to prove
+ 
+
+ align:start position:0%
+n so this is what we're going to prove
+here so why is this so
+
+ align:start position:0%
+here so why is this so
+ 
+
+ align:start position:0%
+here so why is this so
+interesting well we will talk about an
+
+ align:start position:0%
+interesting well we will talk about an
+ 
+
+ align:start position:0%
+interesting well we will talk about an
+application which is a direct
+
+ align:start position:0%
+application which is a direct
+ 
+
+ align:start position:0%
+application which is a direct
+consequence of this theorem which we
+
+ align:start position:0%
+consequence of this theorem which we
+ 
+
+ align:start position:0%
+consequence of this theorem which we
+call Fat's a little theorem and that in
+
+ align:start position:0%
+call Fat's a little theorem and that in
+ 
+
+ align:start position:0%
+call Fat's a little theorem and that in
+turn we will use to explain the RSA
+
+ align:start position:0%
+turn we will use to explain the RSA
+ 
+
+ align:start position:0%
+turn we will use to explain the RSA
+algorithm and show how decryption works
+
+ align:start position:0%
+algorithm and show how decryption works
+ 
+
+ align:start position:0%
+algorithm and show how decryption works
+and so on so how can we prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this um he will start with uh a first
+
+ align:start position:0%
+this um he will start with uh a first
+ 
+
+ align:start position:0%
+this um he will start with uh a first
+LMA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and then we're going to do a few uh
+
+ align:start position:0%
+um and then we're going to do a few uh
+ 
+
+ align:start position:0%
+um and then we're going to do a few uh
+uh tricks mathematical tricks you will
+
+ align:start position:0%
+uh tricks mathematical tricks you will
+ 
+
+ align:start position:0%
+uh tricks mathematical tricks you will
+see it so the first LMA is that um if I
+
+ align:start position:0%
+see it so the first LMA is that um if I
+ 
+
+ align:start position:0%
+see it so the first LMA is that um if I
+know that the gcd which is what we
+
+ align:start position:0%
+know that the gcd which is what we
+ 
+
+ align:start position:0%
+know that the gcd which is what we
+assuming the statement of the theorem if
+
+ align:start position:0%
+assuming the statement of the theorem if
+ 
+
+ align:start position:0%
+assuming the statement of the theorem if
+I know that the gcd of N and k equals 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I know that um a * K if a * K is
+
+ align:start position:0%
+then I know that um a * K if a * K is
+ 
+
+ align:start position:0%
+then I know that um a * K if a * K is
+congruent to B *
+
+ align:start position:0%
+congruent to B *
+ 
+
+ align:start position:0%
+congruent to B *
+k modul
+
+ align:start position:0%
+k modul
+ 
+
+ align:start position:0%
+k modul
+n then this applies that a is congruent
+
+ align:start position:0%
+n then this applies that a is congruent
+ 
+
+ align:start position:0%
+n then this applies that a is congruent
+to b modulo n well this seems to be kind
+
+ align:start position:0%
+to b modulo n well this seems to be kind
+ 
+
+ align:start position:0%
+to b modulo n well this seems to be kind
+of straightforward Lama I will only talk
+
+ align:start position:0%
+of straightforward Lama I will only talk
+ 
+
+ align:start position:0%
+of straightforward Lama I will only talk
+about it proof um so how do we do it
+
+ align:start position:0%
+about it proof um so how do we do it
+ 
+
+ align:start position:0%
+about it proof um so how do we do it
+well first of all I know that the G of N
+
+ align:start position:0%
+well first of all I know that the G of N
+ 
+
+ align:start position:0%
+well first of all I know that the G of N
+and k equals 1 so that means that um I
+
+ align:start position:0%
+and k equals 1 so that means that um I
+ 
+
+ align:start position:0%
+and k equals 1 so that means that um I
+can create a multiplicative inverse
+
+ align:start position:0%
+can create a multiplicative inverse
+ 
+
+ align:start position:0%
+can create a multiplicative inverse
+because I know that there is such a
+
+ align:start position:0%
+because I know that there is such a
+ 
+
+ align:start position:0%
+because I know that there is such a
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+combination that uh that will end up to
+
+ align:start position:0%
+combination that uh that will end up to
+ 
+
+ align:start position:0%
+combination that uh that will end up to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so I have the multiplicative inverse I
+
+ align:start position:0%
+so I have the multiplicative inverse I
+ 
+
+ align:start position:0%
+so I have the multiplicative inverse I
+multiply both sides with this and then I
+
+ align:start position:0%
+multiply both sides with this and then I
+ 
+
+ align:start position:0%
+multiply both sides with this and then I
+will end up to a is congruent to b modul
+
+ align:start position:0%
+will end up to a is congruent to b modul
+ 
+
+ align:start position:0%
+will end up to a is congruent to b modul
+n and actually you can use some of the
+
+ align:start position:0%
+n and actually you can use some of the
+ 
+
+ align:start position:0%
+n and actually you can use some of the
+facts on your sheet to uh to prove this
+
+ align:start position:0%
+facts on your sheet to uh to prove this
+ 
+
+ align:start position:0%
+facts on your sheet to uh to prove this
+and uh in the problem set you probably
+
+ align:start position:0%
+and uh in the problem set you probably
+ 
+
+ align:start position:0%
+and uh in the problem set you probably
+have seen that there are a number of uh
+
+ align:start position:0%
+have seen that there are a number of uh
+ 
+
+ align:start position:0%
+have seen that there are a number of uh
+problems related to this and uh you will
+
+ align:start position:0%
+problems related to this and uh you will
+ 
+
+ align:start position:0%
+problems related to this and uh you will
+also so you will recognize this and
+
+ align:start position:0%
+also so you will recognize this and
+ 
+
+ align:start position:0%
+also so you will recognize this and
+prove a few of these things
+
+ align:start position:0%
+prove a few of these things
+ 
+
+ align:start position:0%
+prove a few of these things
+yourself okay
+
+ align:start position:0%
+yourself okay
+ 
+
+ align:start position:0%
+yourself okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so this is uh so let me see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me see what we have done here
+
+ align:start position:0%
+so let me see what we have done here
+ 
+
+ align:start position:0%
+so let me see what we have done here
+um actually I noticed that I've missed
+
+ align:start position:0%
+um actually I noticed that I've missed
+ 
+
+ align:start position:0%
+um actually I noticed that I've missed
+one statement that I would like to
+
+ align:start position:0%
+one statement that I would like to
+ 
+
+ align:start position:0%
+one statement that I would like to
+explicitly mention I mean I've used it a
+
+ align:start position:0%
+explicitly mention I mean I've used it a
+ 
+
+ align:start position:0%
+explicitly mention I mean I've used it a
+few
+
+ align:start position:0%
+few
+ 
+
+ align:start position:0%
+few
+times let me do that first which is that
+
+ align:start position:0%
+times let me do that first which is that
+ 
+
+ align:start position:0%
+times let me do that first which is that
+um we know that uh if the
+
+ align:start position:0%
+um we know that uh if the
+ 
+
+ align:start position:0%
+um we know that uh if the
+gcd of N and k equals
+
+ align:start position:0%
+gcd of N and k equals
+ 
+
+ align:start position:0%
+gcd of N and k equals
+one uh then
+
+ align:start position:0%
+one uh then
+ 
+
+ align:start position:0%
+one uh then
+if and this is if and only if the case
+
+ align:start position:0%
+if and this is if and only if the case
+ 
+
+ align:start position:0%
+if and this is if and only if the case
+if K has a multiplicative inverse I
+
+ align:start position:0%
+if K has a multiplicative inverse I
+ 
+
+ align:start position:0%
+if K has a multiplicative inverse I
+didn't I've not yet explicitly stated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and we can uh easily see this let
+
+ align:start position:0%
+this and we can uh easily see this let
+ 
+
+ align:start position:0%
+this and we can uh easily see this let
+me just give a quick
+
+ align:start position:0%
+me just give a quick
+ 
+
+ align:start position:0%
+me just give a quick
+proof to show how this
+
+ align:start position:0%
+proof to show how this
+ 
+
+ align:start position:0%
+proof to show how this
+works um well if the gcd is equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we use the statement up
+
+ align:start position:0%
+then we use the statement up
+ 
+
+ align:start position:0%
+then we use the statement up
+there so this is uh if and only if there
+
+ align:start position:0%
+there so this is uh if and only if there
+ 
+
+ align:start position:0%
+there so this is uh if and only if there
+exists a linear combination so an S and
+
+ align:start position:0%
+exists a linear combination so an S and
+ 
+
+ align:start position:0%
+exists a linear combination so an S and
+a t such that n * s + K * T =
+
+ align:start position:0%
+a t such that n * s + K * T =
+ 
+
+ align:start position:0%
+a t such that n * s + K * T =
+1 well then I also know that there
+
+ align:start position:0%
+1 well then I also know that there
+ 
+
+ align:start position:0%
+1 well then I also know that there
+exists uh a t such that um actually the
+
+ align:start position:0%
+exists uh a t such that um actually the
+ 
+
+ align:start position:0%
+exists uh a t such that um actually the
+the difference uh between 1 and K * T is
+
+ align:start position:0%
+the difference uh between 1 and K * T is
+ 
+
+ align:start position:0%
+the difference uh between 1 and K * T is
+divisible by
+
+ align:start position:0%
+divisible by
+ 
+
+ align:start position:0%
+divisible by
+n so n divides the difference of K * T
+
+ align:start position:0%
+n so n divides the difference of K * T
+ 
+
+ align:start position:0%
+n so n divides the difference of K * T
+minus 1 so why is that well if I look at
+
+ align:start position:0%
+minus 1 so why is that well if I look at
+ 
+
+ align:start position:0%
+minus 1 so why is that well if I look at
+the difference between K * T and 1 that
+
+ align:start position:0%
+the difference between K * T and 1 that
+ 
+
+ align:start position:0%
+the difference between K * T and 1 that
+difference is n * s and n * s is
+
+ align:start position:0%
+difference is n * s and n * s is
+ 
+
+ align:start position:0%
+difference is n * s and n * s is
+divisible by n so now by the definition
+
+ align:start position:0%
+divisible by n so now by the definition
+ 
+
+ align:start position:0%
+divisible by n so now by the definition
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+congruence um I just apply the
+
+ align:start position:0%
+congruence um I just apply the
+ 
+
+ align:start position:0%
+congruence um I just apply the
+definition over here you have written it
+
+ align:start position:0%
+definition over here you have written it
+ 
+
+ align:start position:0%
+definition over here you have written it
+out here we can say that uh K * T is
+
+ align:start position:0%
+out here we can say that uh K * T is
+ 
+
+ align:start position:0%
+out here we can say that uh K * T is
+congruent to One
+
+ align:start position:0%
+congruent to One
+ 
+
+ align:start position:0%
+congruent to One
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+n and uh this is the definition of the
+
+ align:start position:0%
+n and uh this is the definition of the
+ 
+
+ align:start position:0%
+n and uh this is the definition of the
+multiplicative inverse so we have
+
+ align:start position:0%
+multiplicative inverse so we have
+ 
+
+ align:start position:0%
+multiplicative inverse so we have
+essentially shown that if the greatest
+
+ align:start position:0%
+essentially shown that if the greatest
+ 
+
+ align:start position:0%
+essentially shown that if the greatest
+common Defence between n and K is equal
+
+ align:start position:0%
+common Defence between n and K is equal
+ 
+
+ align:start position:0%
+common Defence between n and K is equal
+to one then it has a multiplicative
+
+ align:start position:0%
+to one then it has a multiplicative
+ 
+
+ align:start position:0%
+to one then it has a multiplicative
+inverse okay we have been using this uh
+
+ align:start position:0%
+inverse okay we have been using this uh
+ 
+
+ align:start position:0%
+inverse okay we have been using this uh
+property uh
+
+ align:start position:0%
+property uh
+ 
+
+ align:start position:0%
+property uh
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here because we assume that the gra Comm
+
+ align:start position:0%
+here because we assume that the gra Comm
+ 
+
+ align:start position:0%
+here because we assume that the gra Comm
+divisor is equal to one so we now know
+
+ align:start position:0%
+divisor is equal to one so we now know
+ 
+
+ align:start position:0%
+divisor is equal to one so we now know
+that there exists a multiplicative
+
+ align:start position:0%
+that there exists a multiplicative
+ 
+
+ align:start position:0%
+that there exists a multiplicative
+inverse of K we use that one to
+
+ align:start position:0%
+inverse of K we use that one to
+ 
+
+ align:start position:0%
+inverse of K we use that one to
+multiply uh away essentially the K out
+
+ align:start position:0%
+multiply uh away essentially the K out
+ 
+
+ align:start position:0%
+multiply uh away essentially the K out
+of this equation and get a is congruent
+
+ align:start position:0%
+of this equation and get a is congruent
+ 
+
+ align:start position:0%
+of this equation and get a is congruent
+to b modul
+
+ align:start position:0%
+to b modul
+ 
+
+ align:start position:0%
+to b modul
+n also notice that we use that property
+
+ align:start position:0%
+n also notice that we use that property
+ 
+
+ align:start position:0%
+n also notice that we use that property
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here um we said um that we uh
+
+ align:start position:0%
+here um we said um that we uh
+ 
+
+ align:start position:0%
+here um we said um that we uh
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+compute uh what was it again uh oh over
+
+ align:start position:0%
+compute uh what was it again uh oh over
+ 
+
+ align:start position:0%
+compute uh what was it again uh oh over
+here we started off with the gcd of M
+
+ align:start position:0%
+here we started off with the gcd of M
+ 
+
+ align:start position:0%
+here we started off with the gcd of M
+and P to be equal to one and I know p
+
+ align:start position:0%
+and P to be equal to one and I know p
+ 
+
+ align:start position:0%
+and P to be equal to one and I know p
+and now I can compute the multiplicative
+
+ align:start position:0%
+and now I can compute the multiplicative
+ 
+
+ align:start position:0%
+and now I can compute the multiplicative
+inverse of M and I should have said why
+
+ align:start position:0%
+inverse of M and I should have said why
+ 
+
+ align:start position:0%
+inverse of M and I should have said why
+it exists and it exists because of that
+
+ align:start position:0%
+it exists and it exists because of that
+ 
+
+ align:start position:0%
+it exists and it exists because of that
+uh LMA that that I just mentioned up
+
+ align:start position:0%
+uh LMA that that I just mentioned up
+ 
+
+ align:start position:0%
+uh LMA that that I just mentioned up
+here okay so now let's go back to ear's
+
+ align:start position:0%
+here okay so now let's go back to ear's
+ 
+
+ align:start position:0%
+here okay so now let's go back to ear's
+theorem um
+
+ align:start position:0%
+theorem um
+ 
+
+ align:start position:0%
+theorem um
+this first LMA we are going to use to
+
+ align:start position:0%
+this first LMA we are going to use to
+ 
+
+ align:start position:0%
+this first LMA we are going to use to
+prove a second LMA and that second LMA
+
+ align:start position:0%
+prove a second LMA and that second LMA
+ 
+
+ align:start position:0%
+prove a second LMA and that second LMA
+we can finally use to prove the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem all
+
+ align:start position:0%
+theorem all
+ 
+
+ align:start position:0%
+theorem all
+right so this LMA I will put on a
+
+ align:start position:0%
+right so this LMA I will put on a
+ 
+
+ align:start position:0%
+right so this LMA I will put on a
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+board um because it contains quite a
+
+ align:start position:0%
+board um because it contains quite a
+ 
+
+ align:start position:0%
+board um because it contains quite a
+number of steps to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove so the LMA states that um if we
+
+ align:start position:0%
+prove so the LMA states that um if we
+ 
+
+ align:start position:0%
+prove so the LMA states that um if we
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+that um the
+
+ align:start position:0%
+that um the
+ 
+
+ align:start position:0%
+that um the
+gcd of N and k equals 1 so it's the same
+
+ align:start position:0%
+gcd of N and k equals 1 so it's the same
+ 
+
+ align:start position:0%
+gcd of N and k equals 1 so it's the same
+assumption as
+
+ align:start position:0%
+assumption as
+ 
+
+ align:start position:0%
+assumption as
+before um if we let uh
+
+ align:start position:0%
+before um if we let uh
+ 
+
+ align:start position:0%
+before um if we let uh
+K1 all the way up to KR to be those
+
+ align:start position:0%
+K1 all the way up to KR to be those
+ 
+
+ align:start position:0%
+K1 all the way up to KR to be those
+integers in the range one 2 3 and so on
+
+ align:start position:0%
+integers in the range one 2 3 and so on
+ 
+
+ align:start position:0%
+integers in the range one 2 3 and so on
+to n minus one um that are relatively
+
+ align:start position:0%
+to n minus one um that are relatively
+ 
+
+ align:start position:0%
+to n minus one um that are relatively
+prime so these
+
+ align:start position:0%
+prime so these
+ 
+
+ align:start position:0%
+prime so these
+denote the integers relatively prime to
+
+ align:start position:0%
+denote the integers relatively prime to
+ 
+
+ align:start position:0%
+denote the integers relatively prime to
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n then we can uh prove a very
+
+ align:start position:0%
+n then we can uh prove a very
+ 
+
+ align:start position:0%
+n then we can uh prove a very
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+property now notice by the way that uh R
+
+ align:start position:0%
+property now notice by the way that uh R
+ 
+
+ align:start position:0%
+property now notice by the way that uh R
+in here is equal to the value of of the
+
+ align:start position:0%
+in here is equal to the value of of the
+ 
+
+ align:start position:0%
+in here is equal to the value of of the
+ear stent function evaluated in N
+
+ align:start position:0%
+ear stent function evaluated in N
+ 
+
+ align:start position:0%
+ear stent function evaluated in N
+because this counts the total number of
+
+ align:start position:0%
+because this counts the total number of
+ 
+
+ align:start position:0%
+because this counts the total number of
+uh of of numbers that are relatively
+
+ align:start position:0%
+uh of of numbers that are relatively
+ 
+
+ align:start position:0%
+uh of of numbers that are relatively
+primes um Prime with respect to
+
+ align:start position:0%
+primes um Prime with respect to
+ 
+
+ align:start position:0%
+primes um Prime with respect to
+n so now we can prove something really
+
+ align:start position:0%
+n so now we can prove something really
+ 
+
+ align:start position:0%
+n so now we can prove something really
+spectacular um we can show that the set
+
+ align:start position:0%
+spectacular um we can show that the set
+ 
+
+ align:start position:0%
+spectacular um we can show that the set
+that contains all these remainders the
+
+ align:start position:0%
+that contains all these remainders the
+ 
+
+ align:start position:0%
+that contains all these remainders the
+remainder of K1 *
+
+ align:start position:0%
+remainder of K1 *
+ 
+
+ align:start position:0%
+remainder of K1 *
+K after dividing out as many multiples
+
+ align:start position:0%
+K after dividing out as many multiples
+ 
+
+ align:start position:0%
+K after dividing out as many multiples
+of n is
+
+ align:start position:0%
+of n is
+ 
+
+ align:start position:0%
+of n is
+possible all the way to the remainder of
+
+ align:start position:0%
+possible all the way to the remainder of
+ 
+
+ align:start position:0%
+possible all the way to the remainder of
+KR times K after dividing out as many
+
+ align:start position:0%
+KR times K after dividing out as many
+ 
+
+ align:start position:0%
+KR times K after dividing out as many
+multiples of n as
+
+ align:start position:0%
+multiples of n as
+ 
+
+ align:start position:0%
+multiples of n as
+possible this set is actually equal to
+
+ align:start position:0%
+possible this set is actually equal to
+ 
+
+ align:start position:0%
+possible this set is actually equal to
+the set K1 up to
+
+ align:start position:0%
+the set K1 up to
+ 
+
+ align:start position:0%
+the set K1 up to
+KR so this is what we're going to prove
+
+ align:start position:0%
+KR so this is what we're going to prove
+ 
+
+ align:start position:0%
+KR so this is what we're going to prove
+and we'll do it in two steps uh we first
+
+ align:start position:0%
+and we'll do it in two steps uh we first
+ 
+
+ align:start position:0%
+and we'll do it in two steps uh we first
+show that this set
+
+ align:start position:0%
+show that this set
+ 
+
+ align:start position:0%
+show that this set
+uh has exactly R numbers so the
+
+ align:start position:0%
+uh has exactly R numbers so the
+ 
+
+ align:start position:0%
+uh has exactly R numbers so the
+cardinality of that set is equal to R so
+
+ align:start position:0%
+cardinality of that set is equal to R so
+ 
+
+ align:start position:0%
+cardinality of that set is equal to R so
+that will be our first step in the
+
+ align:start position:0%
+that will be our first step in the
+ 
+
+ align:start position:0%
+that will be our first step in the
+proof and over here we will show that
+
+ align:start position:0%
+proof and over here we will show that
+ 
+
+ align:start position:0%
+proof and over here we will show that
+every remainder is actually a relatively
+
+ align:start position:0%
+every remainder is actually a relatively
+ 
+
+ align:start position:0%
+every remainder is actually a relatively
+prime to n so it must be part of this
+
+ align:start position:0%
+prime to n so it must be part of this
+ 
+
+ align:start position:0%
+prime to n so it must be part of this
+set so we will show that this is a
+
+ align:start position:0%
+set so we will show that this is a
+ 
+
+ align:start position:0%
+set so we will show that this is a
+subset of this set in the second part of
+
+ align:start position:0%
+subset of this set in the second part of
+ 
+
+ align:start position:0%
+subset of this set in the second part of
+the proof and combining those two we are
+
+ align:start position:0%
+the proof and combining those two we are
+ 
+
+ align:start position:0%
+the proof and combining those two we are
+able to prove equality why is that well
+
+ align:start position:0%
+able to prove equality why is that well
+ 
+
+ align:start position:0%
+able to prove equality why is that well
+I I have R distinct elements in this set
+
+ align:start position:0%
+I I have R distinct elements in this set
+ 
+
+ align:start position:0%
+I I have R distinct elements in this set
+I have R distinct elements in this set
+
+ align:start position:0%
+I have R distinct elements in this set
+ 
+
+ align:start position:0%
+I have R distinct elements in this set
+this one is a subset of this so that can
+
+ align:start position:0%
+this one is a subset of this so that can
+ 
+
+ align:start position:0%
+this one is a subset of this so that can
+only happen if they are
+
+ align:start position:0%
+only happen if they are
+ 
+
+ align:start position:0%
+only happen if they are
+equal so this is the uh the method for
+
+ align:start position:0%
+equal so this is the uh the method for
+ 
+
+ align:start position:0%
+equal so this is the uh the method for
+uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof oh I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so we will start with the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part and the way to do that is to uh see
+
+ align:start position:0%
+part and the way to do that is to uh see
+ 
+
+ align:start position:0%
+part and the way to do that is to uh see
+whether it is possible that whether it's
+
+ align:start position:0%
+whether it is possible that whether it's
+ 
+
+ align:start position:0%
+whether it is possible that whether it's
+possible that if that any of those two
+
+ align:start position:0%
+possible that if that any of those two
+ 
+
+ align:start position:0%
+possible that if that any of those two
+REM any two remainders in that set can
+
+ align:start position:0%
+REM any two remainders in that set can
+ 
+
+ align:start position:0%
+REM any two remainders in that set can
+they be equal to one another we will
+
+ align:start position:0%
+they be equal to one another we will
+ 
+
+ align:start position:0%
+they be equal to one another we will
+show that that's not possible so if it's
+
+ align:start position:0%
+show that that's not possible so if it's
+ 
+
+ align:start position:0%
+show that that's not possible so if it's
+not possible then all these remainders
+
+ align:start position:0%
+not possible then all these remainders
+ 
+
+ align:start position:0%
+not possible then all these remainders
+must be different and we have exactly R
+
+ align:start position:0%
+must be different and we have exactly R
+ 
+
+ align:start position:0%
+must be different and we have exactly R
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+so let's do this so the proof for uh
+
+ align:start position:0%
+so let's do this so the proof for uh
+ 
+
+ align:start position:0%
+so let's do this so the proof for uh
+one is as follows let's assume that we
+
+ align:start position:0%
+one is as follows let's assume that we
+ 
+
+ align:start position:0%
+one is as follows let's assume that we
+have two remainders say k i *
+
+ align:start position:0%
+have two remainders say k i *
+ 
+
+ align:start position:0%
+have two remainders say k i *
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+um and uh a
+
+ align:start position:0%
+um and uh a
+ 
+
+ align:start position:0%
+um and uh a
+remainder k j * K after dividing out as
+
+ align:start position:0%
+remainder k j * K after dividing out as
+ 
+
+ align:start position:0%
+remainder k j * K after dividing out as
+many multiples of n supposed that they
+
+ align:start position:0%
+many multiples of n supposed that they
+ 
+
+ align:start position:0%
+many multiples of n supposed that they
+are equal to one another you're going to
+
+ align:start position:0%
+are equal to one another you're going to
+ 
+
+ align:start position:0%
+are equal to one another you're going to
+show that this can only happen if Ki is
+
+ align:start position:0%
+show that this can only happen if Ki is
+ 
+
+ align:start position:0%
+show that this can only happen if Ki is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+KJ and if you uh can see that well then
+
+ align:start position:0%
+KJ and if you uh can see that well then
+ 
+
+ align:start position:0%
+KJ and if you uh can see that well then
+we know that all these different
+
+ align:start position:0%
+we know that all these different
+ 
+
+ align:start position:0%
+we know that all these different
+remainders are actually different from
+
+ align:start position:0%
+remainders are actually different from
+ 
+
+ align:start position:0%
+remainders are actually different from
+one another and if they're all different
+
+ align:start position:0%
+one another and if they're all different
+ 
+
+ align:start position:0%
+one another and if they're all different
+from one another then we must have
+
+ align:start position:0%
+from one another then we must have
+ 
+
+ align:start position:0%
+from one another then we must have
+exactly R because we have K1 up to KR in
+
+ align:start position:0%
+exactly R because we have K1 up to KR in
+ 
+
+ align:start position:0%
+exactly R because we have K1 up to KR in
+here okay let's uh let's see where we
+
+ align:start position:0%
+here okay let's uh let's see where we
+ 
+
+ align:start position:0%
+here okay let's uh let's see where we
+can do this um
+
+ align:start position:0%
+can do this um
+ 
+
+ align:start position:0%
+can do this um
+well if we know that these two
+
+ align:start position:0%
+well if we know that these two
+ 
+
+ align:start position:0%
+well if we know that these two
+remainders are equal to one another we
+
+ align:start position:0%
+remainders are equal to one another we
+ 
+
+ align:start position:0%
+remainders are equal to one another we
+can look at them uh with respect to uh
+
+ align:start position:0%
+can look at them uh with respect to uh
+ 
+
+ align:start position:0%
+can look at them uh with respect to uh
+these definitions over here and we can
+
+ align:start position:0%
+these definitions over here and we can
+ 
+
+ align:start position:0%
+these definitions over here and we can
+uh show that k i * K is actually
+
+ align:start position:0%
+uh show that k i * K is actually
+ 
+
+ align:start position:0%
+uh show that k i * K is actually
+congruent to K J * k modul n so why is
+
+ align:start position:0%
+congruent to K J * k modul n so why is
+ 
+
+ align:start position:0%
+congruent to K J * k modul n so why is
+this well these two remainders are the
+
+ align:start position:0%
+this well these two remainders are the
+ 
+
+ align:start position:0%
+this well these two remainders are the
+same and Ki * K is equal to this
+
+ align:start position:0%
+same and Ki * K is equal to this
+ 
+
+ align:start position:0%
+same and Ki * K is equal to this
+remainder plus a multiple of n this KJ *
+
+ align:start position:0%
+remainder plus a multiple of n this KJ *
+ 
+
+ align:start position:0%
+remainder plus a multiple of n this KJ *
+K is equal to this remainder plus a
+
+ align:start position:0%
+K is equal to this remainder plus a
+ 
+
+ align:start position:0%
+K is equal to this remainder plus a
+multiple of n
+
+ align:start position:0%
+multiple of n
+ 
+
+ align:start position:0%
+multiple of n
+so the difference between those two are
+
+ align:start position:0%
+so the difference between those two are
+ 
+
+ align:start position:0%
+so the difference between those two are
+also is is also a multiple of N and
+
+ align:start position:0%
+also is is also a multiple of N and
+ 
+
+ align:start position:0%
+also is is also a multiple of N and
+that's the definition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+congruence so now uh we can uh use our
+
+ align:start position:0%
+congruence so now uh we can uh use our
+ 
+
+ align:start position:0%
+congruence so now uh we can uh use our
+uh first LMA that is which is stated
+
+ align:start position:0%
+uh first LMA that is which is stated
+ 
+
+ align:start position:0%
+uh first LMA that is which is stated
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here we know that we assumed in ear
+
+ align:start position:0%
+here we know that we assumed in ear
+ 
+
+ align:start position:0%
+here we know that we assumed in ear
+theorem that the gcd of N and K is equal
+
+ align:start position:0%
+theorem that the gcd of N and K is equal
+ 
+
+ align:start position:0%
+theorem that the gcd of N and K is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one um if a * K is congruent to B * k
+
+ align:start position:0%
+one um if a * K is congruent to B * k
+ 
+
+ align:start position:0%
+one um if a * K is congruent to B * k
+modul n then we know that a is congruent
+
+ align:start position:0%
+modul n then we know that a is congruent
+ 
+
+ align:start position:0%
+modul n then we know that a is congruent
+to b modulo n so let's apply it over
+
+ align:start position:0%
+to b modulo n so let's apply it over
+ 
+
+ align:start position:0%
+to b modulo n so let's apply it over
+here and take for a Ki and for B we can
+
+ align:start position:0%
+here and take for a Ki and for B we can
+ 
+
+ align:start position:0%
+here and take for a Ki and for B we can
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+KJ so now we see that key Ki is
+
+ align:start position:0%
+KJ so now we see that key Ki is
+ 
+
+ align:start position:0%
+KJ so now we see that key Ki is
+congruent to k j modulo
+
+ align:start position:0%
+congruent to k j modulo
+ 
+
+ align:start position:0%
+congruent to k j modulo
+n and from this we will
+
+ align:start position:0%
+n and from this we will
+ 
+
+ align:start position:0%
+n and from this we will
+conclude and that takes an extra
+
+ align:start position:0%
+conclude and that takes an extra
+ 
+
+ align:start position:0%
+conclude and that takes an extra
+step that Ki is actually equal to KJ so
+
+ align:start position:0%
+step that Ki is actually equal to KJ so
+ 
+
+ align:start position:0%
+step that Ki is actually equal to KJ so
+how can we do this well we know that uh
+
+ align:start position:0%
+how can we do this well we know that uh
+ 
+
+ align:start position:0%
+how can we do this well we know that uh
+Ki and KJ are both in the range from one
+
+ align:start position:0%
+Ki and KJ are both in the range from one
+ 
+
+ align:start position:0%
+Ki and KJ are both in the range from one
+all the way up to n minus
+
+ align:start position:0%
+all the way up to n minus
+ 
+
+ align:start position:0%
+all the way up to n minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so if I look at the difference between
+
+ align:start position:0%
+so if I look at the difference between
+ 
+
+ align:start position:0%
+so if I look at the difference between
+those two so by definition of congruence
+
+ align:start position:0%
+those two so by definition of congruence
+ 
+
+ align:start position:0%
+those two so by definition of congruence
+I know um that n
+
+ align:start position:0%
+I know um that n
+ 
+
+ align:start position:0%
+I know um that n
+divides k i minus
+
+ align:start position:0%
+divides k i minus
+ 
+
+ align:start position:0%
+divides k i minus
+KJ I know that this one is in the range
+
+ align:start position:0%
+KJ I know that this one is in the range
+ 
+
+ align:start position:0%
+KJ I know that this one is in the range
+from uh 0 up to n minus one this one is
+
+ align:start position:0%
+from uh 0 up to n minus one this one is
+ 
+
+ align:start position:0%
+from uh 0 up to n minus one this one is
+in the range of 0 up to n minus one the
+
+ align:start position:0%
+in the range of 0 up to n minus one the
+ 
+
+ align:start position:0%
+in the range of 0 up to n minus one the
+only way
+
+ align:start position:0%
+only way
+ 
+
+ align:start position:0%
+only way
+how the how a difference of two numbers
+
+ align:start position:0%
+how the how a difference of two numbers
+ 
+
+ align:start position:0%
+how the how a difference of two numbers
+in this range can be divisible by n if
+
+ align:start position:0%
+in this range can be divisible by n if
+ 
+
+ align:start position:0%
+in this range can be divisible by n if
+this thing is equal to
+
+ align:start position:0%
+this thing is equal to
+ 
+
+ align:start position:0%
+this thing is equal to
+zero and that means that Ki equals KJ so
+
+ align:start position:0%
+zero and that means that Ki equals KJ so
+ 
+
+ align:start position:0%
+zero and that means that Ki equals KJ so
+now we are done with the first part
+
+ align:start position:0%
+now we are done with the first part
+ 
+
+ align:start position:0%
+now we are done with the first part
+because we have shown that if I take any
+
+ align:start position:0%
+because we have shown that if I take any
+ 
+
+ align:start position:0%
+because we have shown that if I take any
+two remainders over here it must be that
+
+ align:start position:0%
+two remainders over here it must be that
+ 
+
+ align:start position:0%
+two remainders over here it must be that
+they can only be equal to one another if
+
+ align:start position:0%
+they can only be equal to one another if
+ 
+
+ align:start position:0%
+they can only be equal to one another if
+actually the Ki is equal to the KJ so we
+
+ align:start position:0%
+actually the Ki is equal to the KJ so we
+ 
+
+ align:start position:0%
+actually the Ki is equal to the KJ so we
+actually we're looking at the same
+
+ align:start position:0%
+actually we're looking at the same
+ 
+
+ align:start position:0%
+actually we're looking at the same
+remainder so the remainders in this set
+
+ align:start position:0%
+remainder so the remainders in this set
+ 
+
+ align:start position:0%
+remainder so the remainders in this set
+are all different and there are exactly
+
+ align:start position:0%
+are all different and there are exactly
+ 
+
+ align:start position:0%
+are all different and there are exactly
+R of those so now we go to the second
+
+ align:start position:0%
+R of those so now we go to the second
+ 
+
+ align:start position:0%
+R of those so now we go to the second
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and notice that we are so far we've
+
+ align:start position:0%
+um and notice that we are so far we've
+ 
+
+ align:start position:0%
+um and notice that we are so far we've
+only been proving this second LMA and we
+
+ align:start position:0%
+only been proving this second LMA and we
+ 
+
+ align:start position:0%
+only been proving this second LMA and we
+still need to go to ear theorem as as
+
+ align:start position:0%
+still need to go to ear theorem as as
+ 
+
+ align:start position:0%
+still need to go to ear theorem as as
+well so it still takes a few
+
+ align:start position:0%
+well so it still takes a few
+ 
+
+ align:start position:0%
+well so it still takes a few
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+um so how do we do the second
+
+ align:start position:0%
+um so how do we do the second
+ 
+
+ align:start position:0%
+um so how do we do the second
+part well we saw in last lecture that uh
+
+ align:start position:0%
+part well we saw in last lecture that uh
+ 
+
+ align:start position:0%
+part well we saw in last lecture that uh
+we were explaining uh uh ukids uh
+
+ align:start position:0%
+we were explaining uh uh ukids uh
+ 
+
+ align:start position:0%
+we were explaining uh uh ukids uh
+algorithm and we used essentially this
+
+ align:start position:0%
+algorithm and we used essentially this
+ 
+
+ align:start position:0%
+algorithm and we used essentially this
+property we said that the greatest
+
+ align:start position:0%
+property we said that the greatest
+ 
+
+ align:start position:0%
+property we said that the greatest
+comice between n and the remainder of uh
+
+ align:start position:0%
+comice between n and the remainder of uh
+ 
+
+ align:start position:0%
+comice between n and the remainder of uh
+say k i * K and N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is actually equal to the greatest common
+
+ align:start position:0%
+is actually equal to the greatest common
+ 
+
+ align:start position:0%
+is actually equal to the greatest common
+divisor of N and k i *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K so why is this again well the
+
+ align:start position:0%
+K so why is this again well the
+ 
+
+ align:start position:0%
+K so why is this again well the
+remainder is actually um equal to k i *
+
+ align:start position:0%
+remainder is actually um equal to k i *
+ 
+
+ align:start position:0%
+remainder is actually um equal to k i *
+K minus a multiple of n right so the
+
+ align:start position:0%
+K minus a multiple of n right so the
+ 
+
+ align:start position:0%
+K minus a multiple of n right so the
+greatest common divisor is therefore
+
+ align:start position:0%
+greatest common divisor is therefore
+ 
+
+ align:start position:0%
+greatest common divisor is therefore
+between n and this is the same as the
+
+ align:start position:0%
+between n and this is the same as the
+ 
+
+ align:start position:0%
+between n and this is the same as the
+greatest common devisor between n and K
+
+ align:start position:0%
+greatest common devisor between n and K
+ 
+
+ align:start position:0%
+greatest common devisor between n and K
+k i * K so you should have a look at
+
+ align:start position:0%
+k i * K so you should have a look at
+ 
+
+ align:start position:0%
+k i * K so you should have a look at
+last lecture and uh now we are pretty
+
+ align:start position:0%
+last lecture and uh now we are pretty
+ 
+
+ align:start position:0%
+last lecture and uh now we are pretty
+much done why is this because we have
+
+ align:start position:0%
+much done why is this because we have
+ 
+
+ align:start position:0%
+much done why is this because we have
+assumed that the greatest common divisor
+
+ align:start position:0%
+assumed that the greatest common divisor
+ 
+
+ align:start position:0%
+assumed that the greatest common divisor
+between n and K is equal to one and k i
+
+ align:start position:0%
+between n and K is equal to one and k i
+ 
+
+ align:start position:0%
+between n and K is equal to one and k i
+in the statement of the LMA is
+
+ align:start position:0%
+in the statement of the LMA is
+ 
+
+ align:start position:0%
+in the statement of the LMA is
+relatively prime to n and that means
+
+ align:start position:0%
+relatively prime to n and that means
+ 
+
+ align:start position:0%
+relatively prime to n and that means
+according to the definition over there
+
+ align:start position:0%
+according to the definition over there
+ 
+
+ align:start position:0%
+according to the definition over there
+that the greatest common devisor between
+
+ align:start position:0%
+that the greatest common devisor between
+ 
+
+ align:start position:0%
+that the greatest common devisor between
+k i and N is also equal to one so we
+
+ align:start position:0%
+k i and N is also equal to one so we
+ 
+
+ align:start position:0%
+k i and N is also equal to one so we
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these greatest common devisers are equal
+
+ align:start position:0%
+these greatest common devisers are equal
+ 
+
+ align:start position:0%
+these greatest common devisers are equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one so that means that there is no
+
+ align:start position:0%
+one so that means that there is no
+ 
+
+ align:start position:0%
+one so that means that there is no
+common divisor between n and and this
+
+ align:start position:0%
+common divisor between n and and this
+ 
+
+ align:start position:0%
+common divisor between n and and this
+except for one of
+
+ align:start position:0%
+except for one of
+ 
+
+ align:start position:0%
+except for one of
+course so what does this say well this
+
+ align:start position:0%
+course so what does this say well this
+ 
+
+ align:start position:0%
+course so what does this say well this
+means that this remainder according to
+
+ align:start position:0%
+means that this remainder according to
+ 
+
+ align:start position:0%
+means that this remainder according to
+our definition is relatively prime to n
+
+ align:start position:0%
+our definition is relatively prime to n
+ 
+
+ align:start position:0%
+our definition is relatively prime to n
+because this greatest common devisor is
+
+ align:start position:0%
+because this greatest common devisor is
+ 
+
+ align:start position:0%
+because this greatest common devisor is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+one so if it is a uh um integer
+
+ align:start position:0%
+one so if it is a uh um integer
+ 
+
+ align:start position:0%
+one so if it is a uh um integer
+relatively prime to n then it must be
+
+ align:start position:0%
+relatively prime to n then it must be
+ 
+
+ align:start position:0%
+relatively prime to n then it must be
+one of those k i KJS in this set that is
+
+ align:start position:0%
+one of those k i KJS in this set that is
+ 
+
+ align:start position:0%
+one of those k i KJS in this set that is
+stated in the
+
+ align:start position:0%
+stated in the
+ 
+
+ align:start position:0%
+stated in the
+LMA so this
+
+ align:start position:0%
+LMA so this
+ 
+
+ align:start position:0%
+LMA so this
+shows that it must be part of this set
+
+ align:start position:0%
+shows that it must be part of this set
+ 
+
+ align:start position:0%
+shows that it must be part of this set
+over here so we have Pro proven the the
+
+ align:start position:0%
+over here so we have Pro proven the the
+ 
+
+ align:start position:0%
+over here so we have Pro proven the the
+fact that the set of all the remainers
+
+ align:start position:0%
+fact that the set of all the remainers
+ 
+
+ align:start position:0%
+fact that the set of all the remainers
+is a subset of the set K1 up to KR so
+
+ align:start position:0%
+is a subset of the set K1 up to KR so
+ 
+
+ align:start position:0%
+is a subset of the set K1 up to KR so
+now we're done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now that we have shown this
+
+ align:start position:0%
+so now that we have shown this
+ 
+
+ align:start position:0%
+so now that we have shown this
+particular um uh
+
+ align:start position:0%
+particular um uh
+ 
+
+ align:start position:0%
+particular um uh
+LMA we can continue and um prove O's
+
+ align:start position:0%
+LMA we can continue and um prove O's
+ 
+
+ align:start position:0%
+LMA we can continue and um prove O's
+theorem and I will probably need to wipe
+
+ align:start position:0%
+theorem and I will probably need to wipe
+ 
+
+ align:start position:0%
+theorem and I will probably need to wipe
+out some of this uh
+
+ align:start position:0%
+out some of this uh
+ 
+
+ align:start position:0%
+out some of this uh
+yep so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's so let's use this LMA to prove
+
+ align:start position:0%
+let's so let's use this LMA to prove
+ 
+
+ align:start position:0%
+let's so let's use this LMA to prove
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+theorem so this is really a neat trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so the proof of 's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem is as follows we're going to
+
+ align:start position:0%
+theorem is as follows we're going to
+ 
+
+ align:start position:0%
+theorem is as follows we're going to
+take the product of all those k i over
+
+ align:start position:0%
+take the product of all those k i over
+ 
+
+ align:start position:0%
+take the product of all those k i over
+there and see whether we can find a nice
+
+ align:start position:0%
+there and see whether we can find a nice
+ 
+
+ align:start position:0%
+there and see whether we can find a nice
+relationship so we take K1 * K2 all the
+
+ align:start position:0%
+relationship so we take K1 * K2 all the
+ 
+
+ align:start position:0%
+relationship so we take K1 * K2 all the
+way times
+
+ align:start position:0%
+way times
+ 
+
+ align:start position:0%
+way times
+KR and we know because those two sets
+
+ align:start position:0%
+KR and we know because those two sets
+ 
+
+ align:start position:0%
+KR and we know because those two sets
+are actually the same
+
+ align:start position:0%
+are actually the same
+ 
+
+ align:start position:0%
+are actually the same
+that this is equal to the remainder the
+
+ align:start position:0%
+that this is equal to the remainder the
+ 
+
+ align:start position:0%
+that this is equal to the remainder the
+first remainder K * um K1 *
+
+ align:start position:0%
+first remainder K * um K1 *
+ 
+
+ align:start position:0%
+first remainder K * um K1 *
+k um after dividing out as many
+
+ align:start position:0%
+k um after dividing out as many
+ 
+
+ align:start position:0%
+k um after dividing out as many
+multiples of N and we go all the way up
+
+ align:start position:0%
+multiples of N and we go all the way up
+ 
+
+ align:start position:0%
+multiples of N and we go all the way up
+to the final one the remainder of
+
+ align:start position:0%
+to the final one the remainder of
+ 
+
+ align:start position:0%
+to the final one the remainder of
+KR time K dividing out as many multiples
+
+ align:start position:0%
+KR time K dividing out as many multiples
+ 
+
+ align:start position:0%
+KR time K dividing out as many multiples
+of n so
+
+ align:start position:0%
+of n so
+ 
+
+ align:start position:0%
+of n so
+now we can see that uh well we have
+
+ align:start position:0%
+now we can see that uh well we have
+ 
+
+ align:start position:0%
+now we can see that uh well we have
+already shown that that um each of those
+
+ align:start position:0%
+already shown that that um each of those
+ 
+
+ align:start position:0%
+already shown that that um each of those
+remainders right is congruent to in this
+
+ align:start position:0%
+remainders right is congruent to in this
+ 
+
+ align:start position:0%
+remainders right is congruent to in this
+case this one is congruent to K1 * k
+
+ align:start position:0%
+case this one is congruent to K1 * k
+ 
+
+ align:start position:0%
+case this one is congruent to K1 * k
+modulo n and this one is congruent to KR
+
+ align:start position:0%
+modulo n and this one is congruent to KR
+ 
+
+ align:start position:0%
+modulo n and this one is congruent to KR
+* k modulo n so let's write this out so
+
+ align:start position:0%
+* k modulo n so let's write this out so
+ 
+
+ align:start position:0%
+* k modulo n so let's write this out so
+it's K1 * K and then we have K2 *
+
+ align:start position:0%
+it's K1 * K and then we have K2 *
+ 
+
+ align:start position:0%
+it's K1 * K and then we have K2 *
+K and finally we have k r *
+
+ align:start position:0%
+K and finally we have k r *
+ 
+
+ align:start position:0%
+K and finally we have k r *
+k modulo
+
+ align:start position:0%
+k modulo
+ 
+
+ align:start position:0%
+k modulo
+n so let's uh regroup those
+
+ align:start position:0%
+n so let's uh regroup those
+ 
+
+ align:start position:0%
+n so let's uh regroup those
+we see K1 K2 all the way up to KR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reappearing and we have a k here A K
+
+ align:start position:0%
+reappearing and we have a k here A K
+ 
+
+ align:start position:0%
+reappearing and we have a k here A K
+here and we have that R times so we have
+
+ align:start position:0%
+here and we have that R times so we have
+ 
+
+ align:start position:0%
+here and we have that R times so we have
+times K to the power
+
+ align:start position:0%
+times K to the power
+ 
+
+ align:start position:0%
+times K to the power
+r modulo
+
+ align:start position:0%
+r modulo
+ 
+
+ align:start position:0%
+r modulo
+n so now we are able to again use this
+
+ align:start position:0%
+n so now we are able to again use this
+ 
+
+ align:start position:0%
+n so now we are able to again use this
+particular LMA over here so what do we
+
+ align:start position:0%
+particular LMA over here so what do we
+ 
+
+ align:start position:0%
+particular LMA over here so what do we
+do well um we know that K1 is relatively
+
+ align:start position:0%
+do well um we know that K1 is relatively
+ 
+
+ align:start position:0%
+do well um we know that K1 is relatively
+prime to n and K2 is as well all the way
+
+ align:start position:0%
+prime to n and K2 is as well all the way
+ 
+
+ align:start position:0%
+prime to n and K2 is as well all the way
+up to KR so this whole product is also
+
+ align:start position:0%
+up to KR so this whole product is also
+ 
+
+ align:start position:0%
+up to KR so this whole product is also
+relatively prime with respect to n that
+
+ align:start position:0%
+relatively prime with respect to n that
+ 
+
+ align:start position:0%
+relatively prime with respect to n that
+means that the greatest common divisor
+
+ align:start position:0%
+means that the greatest common divisor
+ 
+
+ align:start position:0%
+means that the greatest common divisor
+of this whole product with n is equal to
+
+ align:start position:0%
+of this whole product with n is equal to
+ 
+
+ align:start position:0%
+of this whole product with n is equal to
+one so that means that I can divide out
+
+ align:start position:0%
+one so that means that I can divide out
+ 
+
+ align:start position:0%
+one so that means that I can divide out
+this whole
+
+ align:start position:0%
+this whole
+ 
+
+ align:start position:0%
+this whole
+product right we have uh so let's do do
+
+ align:start position:0%
+product right we have uh so let's do do
+ 
+
+ align:start position:0%
+product right we have uh so let's do do
+this we have say
+
+ align:start position:0%
+this we have say
+ 
+
+ align:start position:0%
+this we have say
+one times this product we take this for
+
+ align:start position:0%
+one times this product we take this for
+ 
+
+ align:start position:0%
+one times this product we take this for
+a and we take this for B and then we can
+
+ align:start position:0%
+a and we take this for B and then we can
+ 
+
+ align:start position:0%
+a and we take this for B and then we can
+divide this whole thing
+
+ align:start position:0%
+divide this whole thing
+ 
+
+ align:start position:0%
+divide this whole thing
+out uh according to this particular LMA
+
+ align:start position:0%
+out uh according to this particular LMA
+ 
+
+ align:start position:0%
+out uh according to this particular LMA
+by using the multiplicative inverse of
+
+ align:start position:0%
+by using the multiplicative inverse of
+ 
+
+ align:start position:0%
+by using the multiplicative inverse of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+product so now we see that 1 is equal to
+
+ align:start position:0%
+product so now we see that 1 is equal to
+ 
+
+ align:start position:0%
+product so now we see that 1 is equal to
+K to ^ r modul n and remember in our
+
+ align:start position:0%
+K to ^ r modul n and remember in our
+ 
+
+ align:start position:0%
+K to ^ r modul n and remember in our
+theorem uh R over here in this LMA R is
+
+ align:start position:0%
+theorem uh R over here in this LMA R is
+ 
+
+ align:start position:0%
+theorem uh R over here in this LMA R is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+equal uh to
+
+ align:start position:0%
+equal uh to
+ 
+
+ align:start position:0%
+equal uh to
+the oion function in N so now this
+
+ align:start position:0%
+the oion function in N so now this
+ 
+
+ align:start position:0%
+the oion function in N so now this
+equation proves the whole
+
+ align:start position:0%
+equation proves the whole
+ 
+
+ align:start position:0%
+equation proves the whole
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+okay so um now I'm going to talk about
+
+ align:start position:0%
+okay so um now I'm going to talk about
+ 
+
+ align:start position:0%
+okay so um now I'm going to talk about
+RSA which is the last part here so maybe
+
+ align:start position:0%
+RSA which is the last part here so maybe
+ 
+
+ align:start position:0%
+RSA which is the last part here so maybe
+you all would like to have a little
+
+ align:start position:0%
+you all would like to have a little
+ 
+
+ align:start position:0%
+you all would like to have a little
+break of a couple of minutes just to
+
+ align:start position:0%
+break of a couple of minutes just to
+ 
+
+ align:start position:0%
+break of a couple of minutes just to
+relax a bit and then and shake hands
+
+ align:start position:0%
+relax a bit and then and shake hands
+ 
+
+ align:start position:0%
+relax a bit and then and shake hands
+with your neighbor
+
+ align:start position:0%
+with your neighbor
+ 
+
+ align:start position:0%
+with your neighbor
+and jump up in the air if you like to
+
+ align:start position:0%
+and jump up in the air if you like to
+ 
+
+ align:start position:0%
+and jump up in the air if you like to
+all right let's start with the RSA
+
+ align:start position:0%
+all right let's start with the RSA
+ 
+
+ align:start position:0%
+all right let's start with the RSA
+algorithm so we have done uh everything
+
+ align:start position:0%
+algorithm so we have done uh everything
+ 
+
+ align:start position:0%
+algorithm so we have done uh everything
+up to this point and we're actually uh
+
+ align:start position:0%
+up to this point and we're actually uh
+ 
+
+ align:start position:0%
+up to this point and we're actually uh
+we have done these two over here we
+
+ align:start position:0%
+we have done these two over here we
+ 
+
+ align:start position:0%
+we have done these two over here we
+still have to talk about F's little
+
+ align:start position:0%
+still have to talk about F's little
+ 
+
+ align:start position:0%
+still have to talk about F's little
+theorem but then we can go for RSA and
+
+ align:start position:0%
+theorem but then we can go for RSA and
+ 
+
+ align:start position:0%
+theorem but then we can go for RSA and
+that uses this consequence of uh Oilers
+
+ align:start position:0%
+that uses this consequence of uh Oilers
+ 
+
+ align:start position:0%
+that uses this consequence of uh Oilers
+theorem so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fma's a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem is actually talking about what
+
+ align:start position:0%
+theorem is actually talking about what
+ 
+
+ align:start position:0%
+theorem is actually talking about what
+happens if N is a prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number it says well suppose p is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime then uh and if you have
+
+ align:start position:0%
+prime then uh and if you have
+ 
+
+ align:start position:0%
+prime then uh and if you have
+K in the range 1 2 all the way up to P
+
+ align:start position:0%
+K in the range 1 2 all the way up to P
+ 
+
+ align:start position:0%
+K in the range 1 2 all the way up to P
+minus 1
+
+ align:start position:0%
+minus 1
+ 
+
+ align:start position:0%
+minus 1
+then we can then we can conclude that K
+
+ align:start position:0%
+then we can then we can conclude that K
+ 
+
+ align:start position:0%
+then we can then we can conclude that K
+to ^ P minus one is congruent to One
+
+ align:start position:0%
+to ^ P minus one is congruent to One
+ 
+
+ align:start position:0%
+to ^ P minus one is congruent to One
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+n and we can directly prove this uh by
+
+ align:start position:0%
+n and we can directly prove this uh by
+ 
+
+ align:start position:0%
+n and we can directly prove this uh by
+using uh ear theorem so how do we do
+
+ align:start position:0%
+using uh ear theorem so how do we do
+ 
+
+ align:start position:0%
+using uh ear theorem so how do we do
+this well we know that P is
+
+ align:start position:0%
+this well we know that P is
+ 
+
+ align:start position:0%
+this well we know that P is
+prime so the numers
+
+ align:start position:0%
+prime so the numers
+ 
+
+ align:start position:0%
+prime so the numers
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um one two all the way up to p - one are
+
+ align:start position:0%
+um one two all the way up to p - one are
+ 
+
+ align:start position:0%
+um one two all the way up to p - one are
+actually relatively
+
+ align:start position:0%
+actually relatively
+ 
+
+ align:start position:0%
+actually relatively
+prime to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P so why is that well p is prime right
+
+ align:start position:0%
+P so why is that well p is prime right
+ 
+
+ align:start position:0%
+P so why is that well p is prime right
+so the greatest common divisor between
+
+ align:start position:0%
+so the greatest common divisor between
+ 
+
+ align:start position:0%
+so the greatest common divisor between
+any of those with p is equal to one
+
+ align:start position:0%
+any of those with p is equal to one
+ 
+
+ align:start position:0%
+any of those with p is equal to one
+that's a definition of relatively prime
+
+ align:start position:0%
+that's a definition of relatively prime
+ 
+
+ align:start position:0%
+that's a definition of relatively prime
+and we know uh that um we can now uh
+
+ align:start position:0%
+and we know uh that um we can now uh
+ 
+
+ align:start position:0%
+and we know uh that um we can now uh
+apply uh ear theorem over here and see
+
+ align:start position:0%
+apply uh ear theorem over here and see
+ 
+
+ align:start position:0%
+apply uh ear theorem over here and see
+that uh K to the power
+
+ align:start position:0%
+that uh K to the power
+ 
+
+ align:start position:0%
+that uh K to the power
+F of
+
+ align:start position:0%
+F of
+ 
+
+ align:start position:0%
+F of
+p is is of course congruent to one
+
+ align:start position:0%
+p is is of course congruent to one
+ 
+
+ align:start position:0%
+p is is of course congruent to one
+modulo uh P that's ear theorem but now
+
+ align:start position:0%
+modulo uh P that's ear theorem but now
+ 
+
+ align:start position:0%
+modulo uh P that's ear theorem but now
+since we know that these are the exact
+
+ align:start position:0%
+since we know that these are the exact
+ 
+
+ align:start position:0%
+since we know that these are the exact
+ones that are relatively prime we can
+
+ align:start position:0%
+ones that are relatively prime we can
+ 
+
+ align:start position:0%
+ones that are relatively prime we can
+explicitly compute the aoan function of
+
+ align:start position:0%
+explicitly compute the aoan function of
+ 
+
+ align:start position:0%
+explicitly compute the aoan function of
+P because there are P minus one numbers
+
+ align:start position:0%
+P because there are P minus one numbers
+ 
+
+ align:start position:0%
+P because there are P minus one numbers
+that are relatively prime to P so that's
+
+ align:start position:0%
+that are relatively prime to P so that's
+ 
+
+ align:start position:0%
+that are relatively prime to P so that's
+the definition over here so the number
+
+ align:start position:0%
+the definition over here so the number
+ 
+
+ align:start position:0%
+the definition over here so the number
+of integers in the range one up to P
+
+ align:start position:0%
+of integers in the range one up to P
+ 
+
+ align:start position:0%
+of integers in the range one up to P
+minus one they're all relatively prime
+
+ align:start position:0%
+minus one they're all relatively prime
+ 
+
+ align:start position:0%
+minus one they're all relatively prime
+so we know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um 5 of p is equal to P minus
+
+ align:start position:0%
+um 5 of p is equal to P minus
+ 
+
+ align:start position:0%
+um 5 of p is equal to P minus
+one so now we have shown that uh K to ^
+
+ align:start position:0%
+one so now we have shown that uh K to ^
+ 
+
+ align:start position:0%
+one so now we have shown that uh K to ^
+P minus 1 is congruent to one modulo
+
+ align:start position:0%
+P minus 1 is congruent to one modulo
+ 
+
+ align:start position:0%
+P minus 1 is congruent to one modulo
+K now this is kind of interesting
+
+ align:start position:0%
+K now this is kind of interesting
+ 
+
+ align:start position:0%
+K now this is kind of interesting
+because we can use this theorem also to
+
+ align:start position:0%
+because we can use this theorem also to
+ 
+
+ align:start position:0%
+because we can use this theorem also to
+compute the multiplicative inverse of K
+
+ align:start position:0%
+compute the multiplicative inverse of K
+ 
+
+ align:start position:0%
+compute the multiplicative inverse of K
+in this particular case so how how do we
+
+ align:start position:0%
+in this particular case so how how do we
+ 
+
+ align:start position:0%
+in this particular case so how how do we
+do this um we just take uh K and we look
+
+ align:start position:0%
+do this um we just take uh K and we look
+ 
+
+ align:start position:0%
+do this um we just take uh K and we look
+at what happens if you multiply K with K
+
+ align:start position:0%
+at what happens if you multiply K with K
+ 
+
+ align:start position:0%
+at what happens if you multiply K with K
+to ^ P minus
+
+ align:start position:0%
+to ^ P minus
+ 
+
+ align:start position:0%
+to ^ P minus
+2 well this is equal to K to ^ P minus
+
+ align:start position:0%
+2 well this is equal to K to ^ P minus
+ 
+
+ align:start position:0%
+2 well this is equal to K to ^ P minus
+one which is congruent to one
+
+ align:start position:0%
+one which is congruent to one
+ 
+
+ align:start position:0%
+one which is congruent to one
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+p according to our uh according to from
+
+ align:start position:0%
+p according to our uh according to from
+ 
+
+ align:start position:0%
+p according to our uh according to from
+us theorem so now when we look at the
+
+ align:start position:0%
+us theorem so now when we look at the
+ 
+
+ align:start position:0%
+us theorem so now when we look at the
+definition of multiplicative
+
+ align:start position:0%
+definition of multiplicative
+ 
+
+ align:start position:0%
+definition of multiplicative
+inverse over here we see that uh K to ^
+
+ align:start position:0%
+inverse over here we see that uh K to ^
+ 
+
+ align:start position:0%
+inverse over here we see that uh K to ^
+P minus 2 is actually the multiplicative
+
+ align:start position:0%
+P minus 2 is actually the multiplicative
+ 
+
+ align:start position:0%
+P minus 2 is actually the multiplicative
+inverse of
+
+ align:start position:0%
+inverse of
+ 
+
+ align:start position:0%
+inverse of
+K so K inverse is actually equal to k^ P
+
+ align:start position:0%
+K so K inverse is actually equal to k^ P
+ 
+
+ align:start position:0%
+K so K inverse is actually equal to k^ P
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+K all right so this theorem we're going
+
+ align:start position:0%
+K all right so this theorem we're going
+ 
+
+ align:start position:0%
+K all right so this theorem we're going
+to use now in the description of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RSA as I said it was uh um only decades
+
+ align:start position:0%
+RSA as I said it was uh um only decades
+ 
+
+ align:start position:0%
+RSA as I said it was uh um only decades
+later after touring um reest Shamir and
+
+ align:start position:0%
+later after touring um reest Shamir and
+ 
+
+ align:start position:0%
+later after touring um reest Shamir and
+adaman were the first to really show how
+
+ align:start position:0%
+adaman were the first to really show how
+ 
+
+ align:start position:0%
+adaman were the first to really show how
+number Theory could be applied so
+
+ align:start position:0%
+number Theory could be applied so
+ 
+
+ align:start position:0%
+number Theory could be applied so
+successfully in cryptography and they
+
+ align:start position:0%
+successfully in cryptography and they
+ 
+
+ align:start position:0%
+successfully in cryptography and they
+essentially showed the first public key
+
+ align:start position:0%
+essentially showed the first public key
+ 
+
+ align:start position:0%
+essentially showed the first public key
+encryption scheme in which a sender and
+
+ align:start position:0%
+encryption scheme in which a sender and
+ 
+
+ align:start position:0%
+encryption scheme in which a sender and
+receiver do not necessarily have to
+
+ align:start position:0%
+receiver do not necessarily have to
+ 
+
+ align:start position:0%
+receiver do not necessarily have to
+exchange a secret key that's not
+
+ align:start position:0%
+exchange a secret key that's not
+ 
+
+ align:start position:0%
+exchange a secret key that's not
+necessary so they had a public key
+
+ align:start position:0%
+necessary so they had a public key
+ 
+
+ align:start position:0%
+necessary so they had a public key
+method and that's still used today and
+
+ align:start position:0%
+method and that's still used today and
+ 
+
+ align:start position:0%
+method and that's still used today and
+it's uh yeah it's a great invention so
+
+ align:start position:0%
+it's uh yeah it's a great invention so
+ 
+
+ align:start position:0%
+it's uh yeah it's a great invention so
+how does RSA
+
+ align:start position:0%
+how does RSA
+ 
+
+ align:start position:0%
+how does RSA
+work uh again we have to talk within an
+
+ align:start position:0%
+work uh again we have to talk within an
+ 
+
+ align:start position:0%
+work uh again we have to talk within an
+encryption scheme about what happens
+
+ align:start position:0%
+encryption scheme about what happens
+ 
+
+ align:start position:0%
+encryption scheme about what happens
+beforehand so
+
+ align:start position:0%
+beforehand so
+ 
+
+ align:start position:0%
+beforehand so
+beforehand we need to generate this
+
+ align:start position:0%
+beforehand we need to generate this
+ 
+
+ align:start position:0%
+beforehand we need to generate this
+public key in the secret
+
+ align:start position:0%
+public key in the secret
+ 
+
+ align:start position:0%
+public key in the secret
+key so the idea is that the
+
+ align:start position:0%
+key so the idea is that the
+ 
+
+ align:start position:0%
+key so the idea is that the
+receiver uh creates
+
+ align:start position:0%
+receiver uh creates
+ 
+
+ align:start position:0%
+receiver uh creates
+a public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key and also a secret
+
+ align:start position:0%
+key and also a secret
+ 
+
+ align:start position:0%
+key and also a secret
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+um he will publish the public key and he
+
+ align:start position:0%
+um he will publish the public key and he
+ 
+
+ align:start position:0%
+um he will publish the public key and he
+will keep the secret key for himself and
+
+ align:start position:0%
+will keep the secret key for himself and
+ 
+
+ align:start position:0%
+will keep the secret key for himself and
+now anybody can uses the public key to
+
+ align:start position:0%
+now anybody can uses the public key to
+ 
+
+ align:start position:0%
+now anybody can uses the public key to
+encrypt a
+
+ align:start position:0%
+encrypt a
+ 
+
+ align:start position:0%
+encrypt a
+message the encrypted message message is
+
+ align:start position:0%
+message the encrypted message message is
+ 
+
+ align:start position:0%
+message the encrypted message message is
+sent to the receiver and he is going to
+
+ align:start position:0%
+sent to the receiver and he is going to
+ 
+
+ align:start position:0%
+sent to the receiver and he is going to
+use his secret key to get back to the
+
+ align:start position:0%
+use his secret key to get back to the
+ 
+
+ align:start position:0%
+use his secret key to get back to the
+plane message
+
+ align:start position:0%
+plane message
+ 
+
+ align:start position:0%
+plane message
+so how is he going to do this well in
+
+ align:start position:0%
+so how is he going to do this well in
+ 
+
+ align:start position:0%
+so how is he going to do this well in
+the first step um the idea is to
+
+ align:start position:0%
+the first step um the idea is to
+ 
+
+ align:start position:0%
+the first step um the idea is to
+generate uh two distinct
+
+ align:start position:0%
+generate uh two distinct
+ 
+
+ align:start position:0%
+generate uh two distinct
+primes turns out that this can be done
+
+ align:start position:0%
+primes turns out that this can be done
+ 
+
+ align:start position:0%
+primes turns out that this can be done
+in a very efficient
+
+ align:start position:0%
+in a very efficient
+ 
+
+ align:start position:0%
+in a very efficient
+way uh there are lots of primes among
+
+ align:start position:0%
+way uh there are lots of primes among
+ 
+
+ align:start position:0%
+way uh there are lots of primes among
+the integers so it just sample and it
+
+ align:start position:0%
+the integers so it just sample and it
+ 
+
+ align:start position:0%
+the integers so it just sample and it
+turns out that you can test
+
+ align:start position:0%
+turns out that you can test
+ 
+
+ align:start position:0%
+turns out that you can test
+primality
+
+ align:start position:0%
+primality
+ 
+
+ align:start position:0%
+primality
+um with a pretty high probability very
+
+ align:start position:0%
+um with a pretty high probability very
+ 
+
+ align:start position:0%
+um with a pretty high probability very
+efficiently and recently actually there
+
+ align:start position:0%
+efficiently and recently actually there
+ 
+
+ align:start position:0%
+efficiently and recently actually there
+has been a deter istic algorithm uh that
+
+ align:start position:0%
+has been a deter istic algorithm uh that
+ 
+
+ align:start position:0%
+has been a deter istic algorithm uh that
+is polinomial in a number of bits of the
+
+ align:start position:0%
+is polinomial in a number of bits of the
+ 
+
+ align:start position:0%
+is polinomial in a number of bits of the
+primes that can actually tell you
+
+ align:start position:0%
+primes that can actually tell you
+ 
+
+ align:start position:0%
+primes that can actually tell you
+whether you have a prime or not so you
+
+ align:start position:0%
+whether you have a prime or not so you
+ 
+
+ align:start position:0%
+whether you have a prime or not so you
+can do
+
+ align:start position:0%
+can do
+ 
+
+ align:start position:0%
+can do
+this two we are going to create a
+
+ align:start position:0%
+this two we are going to create a
+ 
+
+ align:start position:0%
+this two we are going to create a
+product of these two distinct primes and
+
+ align:start position:0%
+product of these two distinct primes and
+ 
+
+ align:start position:0%
+product of these two distinct primes and
+that's where our assumption is going to
+
+ align:start position:0%
+that's where our assumption is going to
+ 
+
+ align:start position:0%
+that's where our assumption is going to
+help us uh that it is hard to factor a
+
+ align:start position:0%
+help us uh that it is hard to factor a
+ 
+
+ align:start position:0%
+help us uh that it is hard to factor a
+product of two large primes that's going
+
+ align:start position:0%
+product of two large primes that's going
+ 
+
+ align:start position:0%
+product of two large primes that's going
+to be the underlying hardness Assumption
+
+ align:start position:0%
+to be the underlying hardness Assumption
+ 
+
+ align:start position:0%
+to be the underlying hardness Assumption
+of the r RSA encryption
+
+ align:start position:0%
+of the r RSA encryption
+ 
+
+ align:start position:0%
+of the r RSA encryption
+scheme so let N be
+
+ align:start position:0%
+scheme so let N be
+ 
+
+ align:start position:0%
+scheme so let N be
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+three uh we're going to
+
+ align:start position:0%
+three uh we're going to
+ 
+
+ align:start position:0%
+three uh we're going to
+select an uh integer e such that the
+
+ align:start position:0%
+select an uh integer e such that the
+ 
+
+ align:start position:0%
+select an uh integer e such that the
+greatest common divisor of e with the
+
+ align:start position:0%
+greatest common divisor of e with the
+ 
+
+ align:start position:0%
+greatest common divisor of e with the
+product P minus1 * Q -
+
+ align:start position:0%
+product P minus1 * Q -
+ 
+
+ align:start position:0%
+product P minus1 * Q -
+one is actually equal to one
+
+ align:start position:0%
+one is actually equal to one
+ 
+
+ align:start position:0%
+one is actually equal to one
+and the public and and once we have
+
+ align:start position:0%
+and the public and and once we have
+ 
+
+ align:start position:0%
+and the public and and once we have
+created
+
+ align:start position:0%
+created
+ 
+
+ align:start position:0%
+created
+this the public key is going to be a
+
+ align:start position:0%
+this the public key is going to be a
+ 
+
+ align:start position:0%
+this the public key is going to be a
+pair um so is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pair that consists of e itself together
+
+ align:start position:0%
+pair that consists of e itself together
+ 
+
+ align:start position:0%
+pair that consists of e itself together
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+n so that's a public key and the secret
+
+ align:start position:0%
+n so that's a public key and the secret
+ 
+
+ align:start position:0%
+n so that's a public key and the secret
+key is going to be uh computed as
+
+ align:start position:0%
+key is going to be uh computed as
+ 
+
+ align:start position:0%
+key is going to be uh computed as
+follows in step
+
+ align:start position:0%
+follows in step
+ 
+
+ align:start position:0%
+follows in step
+four we going to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+D such that D * e is congruent to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modulo uh that product of P minus one *
+
+ align:start position:0%
+modulo uh that product of P minus one *
+ 
+
+ align:start position:0%
+modulo uh that product of P minus one *
+Q minus
+
+ align:start position:0%
+Q minus
+ 
+
+ align:start position:0%
+Q minus
+one uh can we do this yeah because the
+
+ align:start position:0%
+one uh can we do this yeah because the
+ 
+
+ align:start position:0%
+one uh can we do this yeah because the
+greatest common divisor between e and
+
+ align:start position:0%
+greatest common divisor between e and
+ 
+
+ align:start position:0%
+greatest common divisor between e and
+that product is equal to
+
+ align:start position:0%
+that product is equal to
+ 
+
+ align:start position:0%
+that product is equal to
+one and we have shown over here that
+
+ align:start position:0%
+one and we have shown over here that
+ 
+
+ align:start position:0%
+one and we have shown over here that
+therefore it has a multiplicative
+
+ align:start position:0%
+therefore it has a multiplicative
+ 
+
+ align:start position:0%
+therefore it has a multiplicative
+inverse so first of all we know that the
+
+ align:start position:0%
+inverse so first of all we know that the
+ 
+
+ align:start position:0%
+inverse so first of all we know that the
+solution D exists and we can also
+
+ align:start position:0%
+solution D exists and we can also
+ 
+
+ align:start position:0%
+solution D exists and we can also
+efficiently
+
+ align:start position:0%
+efficiently
+ 
+
+ align:start position:0%
+efficiently
+computed so um the secret key is going
+
+ align:start position:0%
+computed so um the secret key is going
+ 
+
+ align:start position:0%
+computed so um the secret key is going
+to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pair that consists of D and also n so
+
+ align:start position:0%
+pair that consists of D and also n so
+ 
+
+ align:start position:0%
+pair that consists of D and also n so
+how does it work the uh sender is knows
+
+ align:start position:0%
+how does it work the uh sender is knows
+ 
+
+ align:start position:0%
+how does it work the uh sender is knows
+the public key e and n and uses those to
+
+ align:start position:0%
+the public key e and n and uses those to
+ 
+
+ align:start position:0%
+the public key e and n and uses those to
+encrypt a message I will explain it in a
+
+ align:start position:0%
+encrypt a message I will explain it in a
+ 
+
+ align:start position:0%
+encrypt a message I will explain it in a
+moment and then uh the uh receiver knows
+
+ align:start position:0%
+moment and then uh the uh receiver knows
+ 
+
+ align:start position:0%
+moment and then uh the uh receiver knows
+the secret key d and n and then is able
+
+ align:start position:0%
+the secret key d and n and then is able
+ 
+
+ align:start position:0%
+the secret key d and n and then is able
+to decrypt it okay so let's see how
+
+ align:start position:0%
+to decrypt it okay so let's see how
+ 
+
+ align:start position:0%
+to decrypt it okay so let's see how
+encryption
+
+ align:start position:0%
+encryption
+ 
+
+ align:start position:0%
+encryption
+works and then we will have to do a lot
+
+ align:start position:0%
+works and then we will have to do a lot
+ 
+
+ align:start position:0%
+works and then we will have to do a lot
+of mathematics to get the decryption
+
+ align:start position:0%
+of mathematics to get the decryption
+ 
+
+ align:start position:0%
+of mathematics to get the decryption
+going so M Prime which is uh is computed
+
+ align:start position:0%
+going so M Prime which is uh is computed
+ 
+
+ align:start position:0%
+going so M Prime which is uh is computed
+so the encrypted plain text is computed
+
+ align:start position:0%
+so the encrypted plain text is computed
+ 
+
+ align:start position:0%
+so the encrypted plain text is computed
+as the remainder of n to the power e
+
+ align:start position:0%
+as the remainder of n to the power e
+ 
+
+ align:start position:0%
+as the remainder of n to the power e
+which is part of the public key and then
+
+ align:start position:0%
+which is part of the public key and then
+ 
+
+ align:start position:0%
+which is part of the public key and then
+the finding out as many multiples of n
+
+ align:start position:0%
+the finding out as many multiples of n
+ 
+
+ align:start position:0%
+the finding out as many multiples of n
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+possible it turns out and we're going to
+
+ align:start position:0%
+possible it turns out and we're going to
+ 
+
+ align:start position:0%
+possible it turns out and we're going to
+prove this that decryption works as
+
+ align:start position:0%
+prove this that decryption works as
+ 
+
+ align:start position:0%
+prove this that decryption works as
+follows uh we can compute M by using M
+
+ align:start position:0%
+follows uh we can compute M by using M
+ 
+
+ align:start position:0%
+follows uh we can compute M by using M
+Prime so we receive M Prime what do we
+
+ align:start position:0%
+Prime so we receive M Prime what do we
+ 
+
+ align:start position:0%
+Prime so we receive M Prime what do we
+do we're going to take mime Prime raise
+
+ align:start position:0%
+do we're going to take mime Prime raise
+ 
+
+ align:start position:0%
+do we're going to take mime Prime raise
+it to the power D which is uh part of
+
+ align:start position:0%
+it to the power D which is uh part of
+ 
+
+ align:start position:0%
+it to the power D which is uh part of
+the secret key and then dividing out as
+
+ align:start position:0%
+the secret key and then dividing out as
+ 
+
+ align:start position:0%
+the secret key and then dividing out as
+many multiples of
+
+ align:start position:0%
+many multiples of
+ 
+
+ align:start position:0%
+many multiples of
+n now why would that
+
+ align:start position:0%
+n now why would that
+ 
+
+ align:start position:0%
+n now why would that
+work why would uh why would this work so
+
+ align:start position:0%
+work why would uh why would this work so
+ 
+
+ align:start position:0%
+work why would uh why would this work so
+let's prove uh this step over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here well it turns out that we can apply
+
+ align:start position:0%
+here well it turns out that we can apply
+ 
+
+ align:start position:0%
+here well it turns out that we can apply
+fmat
+
+ align:start position:0%
+fmat
+ 
+
+ align:start position:0%
+fmat
+theorem and the IDE is as follows so
+
+ align:start position:0%
+theorem and the IDE is as follows so
+ 
+
+ align:start position:0%
+theorem and the IDE is as follows so
+let's have a look we know that M Prime
+
+ align:start position:0%
+let's have a look we know that M Prime
+ 
+
+ align:start position:0%
+let's have a look we know that M Prime
+is equal to the remainder of M ra to
+
+ align:start position:0%
+is equal to the remainder of M ra to
+ 
+
+ align:start position:0%
+is equal to the remainder of M ra to
+the^
+
+ align:start position:0%
+the^
+ 
+
+ align:start position:0%
+the^
+e uh which is congruent to M the power e
+
+ align:start position:0%
+e uh which is congruent to M the power e
+ 
+
+ align:start position:0%
+e uh which is congruent to M the power e
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+n we have seen this now a number of
+
+ align:start position:0%
+n we have seen this now a number of
+ 
+
+ align:start position:0%
+n we have seen this now a number of
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+right so what does this imply this
+
+ align:start position:0%
+right so what does this imply this
+ 
+
+ align:start position:0%
+right so what does this imply this
+implies that M
+
+ align:start position:0%
+implies that M
+ 
+
+ align:start position:0%
+implies that M
+Prime to the power D is actually equal
+
+ align:start position:0%
+Prime to the power D is actually equal
+ 
+
+ align:start position:0%
+Prime to the power D is actually equal
+is congruent to m to the power e
+
+ align:start position:0%
+is congruent to m to the power e
+ 
+
+ align:start position:0%
+is congruent to m to the power e
+to the power D so I just raise this side
+
+ align:start position:0%
+to the power D so I just raise this side
+ 
+
+ align:start position:0%
+to the power D so I just raise this side
+to the power D and I raise this side to
+
+ align:start position:0%
+to the power D and I raise this side to
+ 
+
+ align:start position:0%
+to the power D and I raise this side to
+the power D and I
+
+ align:start position:0%
+the power D and I
+ 
+
+ align:start position:0%
+the power D and I
+still um and I know now that M Prime to
+
+ align:start position:0%
+still um and I know now that M Prime to
+ 
+
+ align:start position:0%
+still um and I know now that M Prime to
+the^ D is equal to M the power e d
+
+ align:start position:0%
+the^ D is equal to M the power e d
+ 
+
+ align:start position:0%
+the^ D is equal to M the power e d
+congruent to M the^ Ed modul
+
+ align:start position:0%
+congruent to M the^ Ed modul
+ 
+
+ align:start position:0%
+congruent to M the^ Ed modul
+n so now we know that there exists an
+
+ align:start position:0%
+n so now we know that there exists an
+ 
+
+ align:start position:0%
+n so now we know that there exists an
+integer R uh we are going to use the
+
+ align:start position:0%
+integer R uh we are going to use the
+ 
+
+ align:start position:0%
+integer R uh we are going to use the
+fact that we have that e and P minus1 *
+
+ align:start position:0%
+fact that we have that e and P minus1 *
+ 
+
+ align:start position:0%
+fact that we have that e and P minus1 *
+Q -1 have a greatest common divisor of
+
+ align:start position:0%
+Q -1 have a greatest common divisor of
+ 
+
+ align:start position:0%
+Q -1 have a greatest common divisor of
+one so we know that e *
+
+ align:start position:0%
+one so we know that e *
+ 
+
+ align:start position:0%
+one so we know that e *
+D is actually equal to uh 1 + r
+
+ align:start position:0%
+D is actually equal to uh 1 + r
+ 
+
+ align:start position:0%
+D is actually equal to uh 1 + r
+* P - 1 * Q - 1 actually what I use here
+
+ align:start position:0%
+* P - 1 * Q - 1 actually what I use here
+ 
+
+ align:start position:0%
+* P - 1 * Q - 1 actually what I use here
+is uh the fact is this over here by the
+
+ align:start position:0%
+is uh the fact is this over here by the
+ 
+
+ align:start position:0%
+is uh the fact is this over here by the
+definition of congruency I know that the
+
+ align:start position:0%
+definition of congruency I know that the
+ 
+
+ align:start position:0%
+definition of congruency I know that the
+difference between those two D * e and
+
+ align:start position:0%
+difference between those two D * e and
+ 
+
+ align:start position:0%
+difference between those two D * e and
+one is divisible by this product so I
+
+ align:start position:0%
+one is divisible by this product so I
+ 
+
+ align:start position:0%
+one is divisible by this product so I
+know that there exists an integer such
+
+ align:start position:0%
+know that there exists an integer such
+ 
+
+ align:start position:0%
+know that there exists an integer such
+that e * D equals 1 plus a multiple of
+
+ align:start position:0%
+that e * D equals 1 plus a multiple of
+ 
+
+ align:start position:0%
+that e * D equals 1 plus a multiple of
+that product that's how it
+
+ align:start position:0%
+that product that's how it
+ 
+
+ align:start position:0%
+that product that's how it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+so we know that M Prime to the power D
+
+ align:start position:0%
+so we know that M Prime to the power D
+ 
+
+ align:start position:0%
+so we know that M Prime to the power D
+we already saw that it is equal to m to
+
+ align:start position:0%
+we already saw that it is equal to m to
+ 
+
+ align:start position:0%
+we already saw that it is equal to m to
+the power
+
+ align:start position:0%
+the power
+ 
+
+ align:start position:0%
+the power
+Ed um which is congruent to well we just
+
+ align:start position:0%
+Ed um which is congruent to well we just
+ 
+
+ align:start position:0%
+Ed um which is congruent to well we just
+replace Ed by 1 + r * this multiple so
+
+ align:start position:0%
+replace Ed by 1 + r * this multiple so
+ 
+
+ align:start position:0%
+replace Ed by 1 + r * this multiple so
+we have m ^
+
+ align:start position:0%
+we have m ^
+ 
+
+ align:start position:0%
+we have m ^
+1 * m to the power this part are p min-1
+
+ align:start position:0%
+1 * m to the power this part are p min-1
+ 
+
+ align:start position:0%
+1 * m to the power this part are p min-1
+q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-1
+
+ align:start position:0%
+-1
+ 
+
+ align:start position:0%
+-1
+okay so now we're finally uh going to uh
+
+ align:start position:0%
+okay so now we're finally uh going to uh
+ 
+
+ align:start position:0%
+okay so now we're finally uh going to uh
+get to fma's theorem we know that n is
+
+ align:start position:0%
+get to fma's theorem we know that n is
+ 
+
+ align:start position:0%
+get to fma's theorem we know that n is
+the product of p and
+
+ align:start position:0%
+the product of p and
+ 
+
+ align:start position:0%
+the product of p and
+Q and um I'm not actually sure why I do
+
+ align:start position:0%
+Q and um I'm not actually sure why I do
+ 
+
+ align:start position:0%
+Q and um I'm not actually sure why I do
+this here
+
+ align:start position:0%
+this here
+ 
+
+ align:start position:0%
+this here
+but okay so
+
+ align:start position:0%
+but okay so
+ 
+
+ align:start position:0%
+but okay so
+so let's apply FMA theorem and see how
+
+ align:start position:0%
+so let's apply FMA theorem and see how
+ 
+
+ align:start position:0%
+so let's apply FMA theorem and see how
+we can use this so if m is not equal is
+
+ align:start position:0%
+we can use this so if m is not equal is
+ 
+
+ align:start position:0%
+we can use this so if m is not equal is
+not congruent to zero modul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P well then we can apply for a theorem
+
+ align:start position:0%
+P well then we can apply for a theorem
+ 
+
+ align:start position:0%
+P well then we can apply for a theorem
+um where is it it's it's over here uh we
+
+ align:start position:0%
+um where is it it's it's over here uh we
+ 
+
+ align:start position:0%
+um where is it it's it's over here uh we
+can only apply this if K is in the range
+
+ align:start position:0%
+can only apply this if K is in the range
+ 
+
+ align:start position:0%
+can only apply this if K is in the range
+from 1 to P Min - one is not equal to
+
+ align:start position:0%
+from 1 to P Min - one is not equal to
+ 
+
+ align:start position:0%
+from 1 to P Min - one is not equal to
+zero so if m is not equal to zero not
+
+ align:start position:0%
+zero so if m is not equal to zero not
+ 
+
+ align:start position:0%
+zero so if m is not equal to zero not
+congruent to Z modul P then we can apply
+
+ align:start position:0%
+congruent to Z modul P then we can apply
+ 
+
+ align:start position:0%
+congruent to Z modul P then we can apply
+the theorem and state that m ^ p minus1
+
+ align:start position:0%
+the theorem and state that m ^ p minus1
+ 
+
+ align:start position:0%
+the theorem and state that m ^ p minus1
+is congruent to one modulo
+
+ align:start position:0%
+is congruent to one modulo
+ 
+
+ align:start position:0%
+is congruent to one modulo
+p and in the same
+
+ align:start position:0%
+p and in the same
+ 
+
+ align:start position:0%
+p and in the same
+way we can do this for Q so if this is
+
+ align:start position:0%
+way we can do this for Q so if this is
+ 
+
+ align:start position:0%
+way we can do this for Q so if this is
+not true
+
+ align:start position:0%
+not true
+ 
+
+ align:start position:0%
+not true
+modulo
+
+ align:start position:0%
+modulo
+ 
+
+ align:start position:0%
+modulo
+Q then m to the power Q minus one is
+
+ align:start position:0%
+Q then m to the power Q minus one is
+ 
+
+ align:start position:0%
+Q then m to the power Q minus one is
+congruent to one
+
+ align:start position:0%
+congruent to one
+ 
+
+ align:start position:0%
+congruent to one
+modulo Q so here we have used forat
+
+ align:start position:0%
+modulo Q so here we have used forat
+ 
+
+ align:start position:0%
+modulo Q so here we have used forat
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twice now we can apply uh what we have
+
+ align:start position:0%
+twice now we can apply uh what we have
+ 
+
+ align:start position:0%
+twice now we can apply uh what we have
+learned before uh which is uh what we
+
+ align:start position:0%
+learned before uh which is uh what we
+ 
+
+ align:start position:0%
+learned before uh which is uh what we
+wrote down over here M Prime to the
+
+ align:start position:0%
+wrote down over here M Prime to the
+ 
+
+ align:start position:0%
+wrote down over here M Prime to the
+power D is congruent to This modulo n
+
+ align:start position:0%
+power D is congruent to This modulo n
+ 
+
+ align:start position:0%
+power D is congruent to This modulo n
+now n is p * Q so let's have a look what
+
+ align:start position:0%
+now n is p * Q so let's have a look what
+ 
+
+ align:start position:0%
+now n is p * Q so let's have a look what
+that means it means
+
+ align:start position:0%
+that means it means
+ 
+
+ align:start position:0%
+that means it means
+that since N is a product of p and Q we
+
+ align:start position:0%
+that since N is a product of p and Q we
+ 
+
+ align:start position:0%
+that since N is a product of p and Q we
+can also look at this
+
+ align:start position:0%
+can also look at this
+ 
+
+ align:start position:0%
+can also look at this
+congruent modul P so in
+
+ align:start position:0%
+congruent modul P so in
+ 
+
+ align:start position:0%
+congruent modul P so in
+particular we know that M Prime to the
+
+ align:start position:0%
+particular we know that M Prime to the
+ 
+
+ align:start position:0%
+particular we know that M Prime to the
+power D is congruent to M * m r p -1 * Q
+
+ align:start position:0%
+power D is congruent to M * m r p -1 * Q
+ 
+
+ align:start position:0%
+power D is congruent to M * m r p -1 * Q
+-1
+
+ align:start position:0%
+-1
+ 
+
+ align:start position:0%
+-1
+modulo P why is that well we know that n
+
+ align:start position:0%
+modulo P why is that well we know that n
+ 
+
+ align:start position:0%
+modulo P why is that well we know that n
+divides this Difference by the
+
+ align:start position:0%
+divides this Difference by the
+ 
+
+ align:start position:0%
+divides this Difference by the
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+congruency n is equal to P * Q so if n
+
+ align:start position:0%
+congruency n is equal to P * Q so if n
+ 
+
+ align:start position:0%
+congruency n is equal to P * Q so if n
+divides is is is dividing this
+
+ align:start position:0%
+divides is is is dividing this
+ 
+
+ align:start position:0%
+divides is is is dividing this
+difference also p is dividing this
+
+ align:start position:0%
+difference also p is dividing this
+ 
+
+ align:start position:0%
+difference also p is dividing this
+difference so that's why we can write it
+
+ align:start position:0%
+difference so that's why we can write it
+ 
+
+ align:start position:0%
+difference so that's why we can write it
+m Prime to the^ D is congruent to this
+
+ align:start position:0%
+m Prime to the^ D is congruent to this
+ 
+
+ align:start position:0%
+m Prime to the^ D is congruent to this
+thing modul
+
+ align:start position:0%
+thing modul
+ 
+
+ align:start position:0%
+thing modul
+p and of course we can uh repeat this
+
+ align:start position:0%
+p and of course we can uh repeat this
+ 
+
+ align:start position:0%
+p and of course we can uh repeat this
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+Q so let me write this out as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so there it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so now we can um uh use what we have
+
+ align:start position:0%
+is so now we can um uh use what we have
+ 
+
+ align:start position:0%
+is so now we can um uh use what we have
+figured out over here so we know that if
+
+ align:start position:0%
+figured out over here so we know that if
+ 
+
+ align:start position:0%
+figured out over here so we know that if
+m is not equal to
+
+ align:start position:0%
+m is not equal to
+ 
+
+ align:start position:0%
+m is not equal to
+zero then this thing over
+
+ align:start position:0%
+zero then this thing over
+ 
+
+ align:start position:0%
+zero then this thing over
+here cancels out because m ^ P minus one
+
+ align:start position:0%
+here cancels out because m ^ P minus one
+ 
+
+ align:start position:0%
+here cancels out because m ^ P minus one
+is congruent to
+
+ align:start position:0%
+is congruent to
+ 
+
+ align:start position:0%
+is congruent to
+one so we have that M Prime to the power
+
+ align:start position:0%
+one so we have that M Prime to the power
+ 
+
+ align:start position:0%
+one so we have that M Prime to the power
+D is congruent to
+
+ align:start position:0%
+D is congruent to
+ 
+
+ align:start position:0%
+D is congruent to
+m modulo
+
+ align:start position:0%
+m modulo
+ 
+
+ align:start position:0%
+m modulo
+p if m is not congruent to zero modul P
+
+ align:start position:0%
+p if m is not congruent to zero modul P
+ 
+
+ align:start position:0%
+p if m is not congruent to zero modul P
+right because if m is not congruent to
+
+ align:start position:0%
+right because if m is not congruent to
+ 
+
+ align:start position:0%
+right because if m is not congruent to
+zero we have this particular equation we
+
+ align:start position:0%
+zero we have this particular equation we
+ 
+
+ align:start position:0%
+zero we have this particular equation we
+plug it in over here this all cancels
+
+ align:start position:0%
+plug it in over here this all cancels
+ 
+
+ align:start position:0%
+plug it in over here this all cancels
+and we just leave or left with M now if
+
+ align:start position:0%
+and we just leave or left with M now if
+ 
+
+ align:start position:0%
+and we just leave or left with M now if
+m is equal is congruent to zero modulo P
+
+ align:start position:0%
+m is equal is congruent to zero modulo P
+ 
+
+ align:start position:0%
+m is equal is congruent to zero modulo P
+well then we can see that it is equal to
+
+ align:start position:0%
+well then we can see that it is equal to
+ 
+
+ align:start position:0%
+well then we can see that it is equal to
+zero so it's equal to zero so this
+
+ align:start position:0%
+zero so it's equal to zero so this
+ 
+
+ align:start position:0%
+zero so it's equal to zero so this
+actually holds for any
+
+ align:start position:0%
+actually holds for any
+ 
+
+ align:start position:0%
+actually holds for any
+case now we can do the same for a q
+
+ align:start position:0%
+case now we can do the same for a q
+ 
+
+ align:start position:0%
+case now we can do the same for a q
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+argument and show that this must
+
+ align:start position:0%
+argument and show that this must
+ 
+
+ align:start position:0%
+argument and show that this must
+hold so now we know that P divides the
+
+ align:start position:0%
+hold so now we know that P divides the
+ 
+
+ align:start position:0%
+hold so now we know that P divides the
+difference of M Prime D minus m q is
+
+ align:start position:0%
+difference of M Prime D minus m q is
+ 
+
+ align:start position:0%
+difference of M Prime D minus m q is
+another Prime that divides this
+
+ align:start position:0%
+another Prime that divides this
+ 
+
+ align:start position:0%
+another Prime that divides this
+difference and the only way that that is
+
+ align:start position:0%
+difference and the only way that that is
+ 
+
+ align:start position:0%
+difference and the only way that that is
+possible is If the product of p and Q is
+
+ align:start position:0%
+possible is If the product of p and Q is
+ 
+
+ align:start position:0%
+possible is If the product of p and Q is
+dividing both is dividing this
+
+ align:start position:0%
+dividing both is dividing this
+ 
+
+ align:start position:0%
+dividing both is dividing this
+particular number this difference and we
+
+ align:start position:0%
+particular number this difference and we
+ 
+
+ align:start position:0%
+particular number this difference and we
+have two different primes that dividing
+
+ align:start position:0%
+have two different primes that dividing
+ 
+
+ align:start position:0%
+have two different primes that dividing
+the same number so the product must
+
+ align:start position:0%
+the same number so the product must
+ 
+
+ align:start position:0%
+the same number so the product must
+divide it so P * Q divides M Prime
+
+ align:start position:0%
+divide it so P * Q divides M Prime
+ 
+
+ align:start position:0%
+divide it so P * Q divides M Prime
+D minus
+
+ align:start position:0%
+D minus
+ 
+
+ align:start position:0%
+D minus
+M oh but P * Q is equal to
+
+ align:start position:0%
+M oh but P * Q is equal to
+ 
+
+ align:start position:0%
+M oh but P * Q is equal to
+n so now we're almost done because now
+
+ align:start position:0%
+n so now we're almost done because now
+ 
+
+ align:start position:0%
+n so now we're almost done because now
+we can state by the definition of
+
+ align:start position:0%
+we can state by the definition of
+ 
+
+ align:start position:0%
+we can state by the definition of
+congruency that M Prime to the power D
+
+ align:start position:0%
+congruency that M Prime to the power D
+ 
+
+ align:start position:0%
+congruency that M Prime to the power D
+is congruent to m modulo
+
+ align:start position:0%
+is congruent to m modulo
+ 
+
+ align:start position:0%
+is congruent to m modulo
+n now since m is a message that is in
+
+ align:start position:0%
+n now since m is a message that is in
+ 
+
+ align:start position:0%
+n now since m is a message that is in
+the range of uh of of of so I did not
+
+ align:start position:0%
+the range of uh of of of so I did not
+ 
+
+ align:start position:0%
+the range of uh of of of so I did not
+write it down here so m is a message
+
+ align:start position:0%
+write it down here so m is a message
+ 
+
+ align:start position:0%
+write it down here so m is a message
+which is in the range of zero all the
+
+ align:start position:0%
+which is in the range of zero all the
+ 
+
+ align:start position:0%
+which is in the range of zero all the
+way up to n minus one we knowe and we
+
+ align:start position:0%
+way up to n minus one we knowe and we
+ 
+
+ align:start position:0%
+way up to n minus one we knowe and we
+have seen that before with Ching's code
+
+ align:start position:0%
+have seen that before with Ching's code
+ 
+
+ align:start position:0%
+have seen that before with Ching's code
+that we can rewrite this and stay and
+
+ align:start position:0%
+that we can rewrite this and stay and
+ 
+
+ align:start position:0%
+that we can rewrite this and stay and
+say that m equals the
+
+ align:start position:0%
+say that m equals the
+ 
+
+ align:start position:0%
+say that m equals the
+remainder of M Prime to the power D
+
+ align:start position:0%
+remainder of M Prime to the power D
+ 
+
+ align:start position:0%
+remainder of M Prime to the power D
+after multiplying out as many multiples
+
+ align:start position:0%
+after multiplying out as many multiples
+ 
+
+ align:start position:0%
+after multiplying out as many multiples
+of n as
+
+ align:start position:0%
+of n as
+ 
+
+ align:start position:0%
+of n as
+possible so here you go so this is the
+
+ align:start position:0%
+possible so here you go so this is the
+ 
+
+ align:start position:0%
+possible so here you go so this is the
+decryption uh Rule and it works we have
+
+ align:start position:0%
+decryption uh Rule and it works we have
+ 
+
+ align:start position:0%
+decryption uh Rule and it works we have
+shown that this equation truly
+
+ align:start position:0%
+shown that this equation truly
+ 
+
+ align:start position:0%
+shown that this equation truly
+holds so RSA has really withstood the
+
+ align:start position:0%
+holds so RSA has really withstood the
+ 
+
+ align:start position:0%
+holds so RSA has really withstood the
+test of time it's already out there for
+
+ align:start position:0%
+test of time it's already out there for
+ 
+
+ align:start position:0%
+test of time it's already out there for
+many decades and it's still widely used
+
+ align:start position:0%
+many decades and it's still widely used
+ 
+
+ align:start position:0%
+many decades and it's still widely used
+I wanted to talk a little bit about this
+
+ align:start position:0%
+I wanted to talk a little bit about this
+ 
+
+ align:start position:0%
+I wanted to talk a little bit about this
+but there seemed not to be enough time
+
+ align:start position:0%
+but there seemed not to be enough time
+ 
+
+ align:start position:0%
+but there seemed not to be enough time
+but I just like to mention that uh that
+
+ align:start position:0%
+but I just like to mention that uh that
+ 
+
+ align:start position:0%
+but I just like to mention that uh that
+only in 2009
+
+ align:start position:0%
+only in 2009
+ 
+
+ align:start position:0%
+only in 2009
+uh Greg Gentry proved a beautiful
+
+ align:start position:0%
+uh Greg Gentry proved a beautiful
+ 
+
+ align:start position:0%
+uh Greg Gentry proved a beautiful
+theorem and was able to evaluate uh
+
+ align:start position:0%
+theorem and was able to evaluate uh
+ 
+
+ align:start position:0%
+theorem and was able to evaluate uh
+Boolean cirqus or or say a certain type
+
+ align:start position:0%
+Boolean cirqus or or say a certain type
+ 
+
+ align:start position:0%
+Boolean cirqus or or say a certain type
+of programs under encryption so you can
+
+ align:start position:0%
+of programs under encryption so you can
+ 
+
+ align:start position:0%
+of programs under encryption so you can
+sort of add and multiply cyer text
+
+ align:start position:0%
+sort of add and multiply cyer text
+ 
+
+ align:start position:0%
+sort of add and multiply cyer text
+encryptions together and it is as if you
+
+ align:start position:0%
+encryptions together and it is as if you
+ 
+
+ align:start position:0%
+encryptions together and it is as if you
+multiply them at the plain text level
+
+ align:start position:0%
+multiply them at the plain text level
+ 
+
+ align:start position:0%
+multiply them at the plain text level
+that was a fantastic uh that was an
+
+ align:start position:0%
+that was a fantastic uh that was an
+ 
+
+ align:start position:0%
+that was a fantastic uh that was an
+enormous open problem and he solved it
+
+ align:start position:0%
+enormous open problem and he solved it
+ 
+
+ align:start position:0%
+enormous open problem and he solved it
+and only a few months earlier in 20 10
+
+ align:start position:0%
+and only a few months earlier in 20 10
+ 
+
+ align:start position:0%
+and only a few months earlier in 20 10
+in joint work with Greg and some other
+
+ align:start position:0%
+in joint work with Greg and some other
+ 
+
+ align:start position:0%
+in joint work with Greg and some other
+colleagues at IBM we showed it with very
+
+ align:start position:0%
+colleagues at IBM we showed it with very
+ 
+
+ align:start position:0%
+colleagues at IBM we showed it with very
+simple arithmetic that just uses modulo
+
+ align:start position:0%
+simple arithmetic that just uses modulo
+ 
+
+ align:start position:0%
+simple arithmetic that just uses modulo
+p and modulo 2 kind of things we could
+
+ align:start position:0%
+p and modulo 2 kind of things we could
+ 
+
+ align:start position:0%
+p and modulo 2 kind of things we could
+show a construction that uses uh such
+
+ align:start position:0%
+show a construction that uses uh such
+ 
+
+ align:start position:0%
+show a construction that uses uh such
+that has such a property such an
+
+ align:start position:0%
+that has such a property such an
+ 
+
+ align:start position:0%
+that has such a property such an
+encryption scheme over the integers so
+
+ align:start position:0%
+encryption scheme over the integers so
+ 
+
+ align:start position:0%
+encryption scheme over the integers so
+there's still a lot of stuff going on in
+
+ align:start position:0%
+there's still a lot of stuff going on in
+ 
+
+ align:start position:0%
+there's still a lot of stuff going on in
+this area and really we use this type of
+
+ align:start position:0%
+this area and really we use this type of
+ 
+
+ align:start position:0%
+this area and really we use this type of
+very basic stuff the problem in
+
+ align:start position:0%
+very basic stuff the problem in
+ 
+
+ align:start position:0%
+very basic stuff the problem in
+cryptography is to show that is secure
+
+ align:start position:0%
+cryptography is to show that is secure
+ 
+
+ align:start position:0%
+cryptography is to show that is secure
+so we have to show that uh breaking the
+
+ align:start position:0%
+so we have to show that uh breaking the
+ 
+
+ align:start position:0%
+so we have to show that uh breaking the
+scheme needs to be reduced to some
+
+ align:start position:0%
+scheme needs to be reduced to some
+ 
+
+ align:start position:0%
+scheme needs to be reduced to some
+really hard problem and that is us and
+
+ align:start position:0%
+really hard problem and that is us and
+ 
+
+ align:start position:0%
+really hard problem and that is us and
+that's always the really difficult part
+
+ align:start position:0%
+that's always the really difficult part
+ 
+
+ align:start position:0%
+that's always the really difficult part
+of such type of research okay well have
+
+ align:start position:0%
+of such type of research okay well have
+ 
+
+ align:start position:0%
+of such type of research okay well have
+lots of fun with the recitation
\ No newline at end of file
diff --git a/ZWdDKll8qZc.txt b/ZWdDKll8qZc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d620f7941361a850f02c5d5268b30c29d5ac5ff8
--- /dev/null
+++ b/ZWdDKll8qZc.txt
@@ -0,0 +1,234 @@
+LORNA GIBSON: So I think
+one of the special things
+
+about this course
+and about my kind
+
+of research on
+cellular materials
+
+is that I spend a fair
+amount of time talking
+
+about materials in nature.
+
+So I talk about wood,
+for instance, and what
+
+it is about the cellular
+structure that gives rise
+
+to the density dependence
+of wood properties
+
+and the anisotropy
+in wood properties.
+
+I talk about
+trabecular bone, and I
+
+talk about the structure
+and properties of the bone,
+
+but also we do a
+little bit of modeling
+
+on how you might look at
+bone loss and osteoporosis.
+
+So if you lose a certain
+fraction of the bone
+
+density, what residual
+strength would
+
+you expect the bone to have.
+
+We have a project
+on bamboo right now.
+
+We talk about the
+structure of bamboo.
+
+Bamboo is actually a grass.
+
+And this is a Chinese species
+of bamboo called moso bamboo,
+
+and you can see how
+big this one is.
+
+They even get bigger, maybe
+six or eight inches across.
+
+And what we're
+interested in doing
+
+is making something called
+structural bamboo products.
+
+And this is an example of a
+bamboo oriented strand board.
+
+So the same way
+people take wood,
+
+and they chop wood
+up into strands
+
+and make oriented strand boards
+for housing construction,
+
+you could, in principal, do
+the same thing with bamboo.
+
+And we have a project
+that's in collaboration
+
+with some colleagues at the
+University of British Columbia.
+
+They're the ones
+who are actually
+
+making the bamboo
+oriented strand board.
+
+And with some architects in
+England, in Cambridge, England,
+
+we're looking at things like how
+you might modify wood building
+
+codes that talk about
+wood structural products,
+
+how you would modify that for
+bamboo structural products.
+
+And what we're
+doing here at MIT is
+
+we're looking at the
+structure of the bamboo
+
+and doing some modeling of
+the mechanical properties
+
+of the bamboo itself.
+
+So that's one example.
+
+Here's another example.
+
+This is a bamboo laminate.
+
+So this is a little bit like
+a glue laminated wood member,
+
+but in fact, this
+one is made out
+
+of bamboo instead
+of out of wood.
+
+So it's the same kind of idea.
+
+Let's see.
+
+We've also had a project
+in the past on cork.
+
+So this is a cork
+from a wine bottle,
+
+and we've looked at that.
+
+Cork has an unusual
+mechanical property.
+
+You know, if you take a rubber
+band and you pull on it,
+
+if you can make it longer this
+way, it gets narrower that way.
+
+Well, if you load cork
+in one direction, if you,
+
+say, pull on it
+or compress it, it
+
+doesn't get any
+wider or narrower
+
+in the other direction.
+
+It just stays the
+same kind of size.
+
+And you can show
+that that's related
+
+to the structure of the cells.
+
+The cells are like
+little bellows,
+
+or like a little concertina.
+
+So you can imagine if you
+have a little concertina,
+
+and you push on it this
+way, it doesn't really
+
+get any bigger that way
+or smaller that way.
+
+It just stays the
+same dimension.
+
+And the cork cells look
+a little bit like that,
+
+and that's why they do that.
+
+So we have all these
+natural materials.
+
+We talk a little about
+the hierarchical structure
+
+in plants.
+
+The cell walls are
+fiber composites,
+
+and then there's a
+cellular structure.
+
+And plant materials have a
+sort of hierarchical structure,
+
+with several different
+levels of hierarchy,
+
+and we talk about that
+in the class as well.
+
+And we talk a
+little bit about why
+
+that makes these materials
+mechanically efficient
+
+and how you might look
+at designing engineering
+
+materials based on that.
+
+So there's a little bit of
+biomimicking in the class
+
+as well.
\ No newline at end of file
diff --git a/ZYf0tz9oVz8.txt b/ZYf0tz9oVz8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fe519e9b24b6ed5eaaefe2b746eb1fe7c67227dc
--- /dev/null
+++ b/ZYf0tz9oVz8.txt
@@ -0,0 +1,6203 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi Welcome to our final lecture in part
+
+ align:start position:0%
+hi Welcome to our final lecture in part
+ 
+
+ align:start position:0%
+hi Welcome to our final lecture in part
+three of calculus and I suppose it would
+
+ align:start position:0%
+three of calculus and I suppose it would
+ 
+
+ align:start position:0%
+three of calculus and I suppose it would
+be nice to have an appropriate story to
+
+ align:start position:0%
+be nice to have an appropriate story to
+ 
+
+ align:start position:0%
+be nice to have an appropriate story to
+tell and the only story I can think of
+
+ align:start position:0%
+tell and the only story I can think of
+ 
+
+ align:start position:0%
+tell and the only story I can think of
+is on the transatlantic flight the
+
+ align:start position:0%
+is on the transatlantic flight the
+ 
+
+ align:start position:0%
+is on the transatlantic flight the
+steward is coming in to the passengers
+
+ align:start position:0%
+steward is coming in to the passengers
+ 
+
+ align:start position:0%
+steward is coming in to the passengers
+cabin Midway over the Atlantic Ocean and
+
+ align:start position:0%
+cabin Midway over the Atlantic Ocean and
+ 
+
+ align:start position:0%
+cabin Midway over the Atlantic Ocean and
+saying to the passengers well I have
+
+ align:start position:0%
+saying to the passengers well I have
+ 
+
+ align:start position:0%
+saying to the passengers well I have
+some good news and some bad news for you
+
+ align:start position:0%
+some good news and some bad news for you
+ 
+
+ align:start position:0%
+some good news and some bad news for you
+the bad news is that we're almost out of
+
+ align:start position:0%
+the bad news is that we're almost out of
+ 
+
+ align:start position:0%
+the bad news is that we're almost out of
+gas and the good news is that we're
+
+ align:start position:0%
+gas and the good news is that we're
+ 
+
+ align:start position:0%
+gas and the good news is that we're
+making wonderful time and the reason I
+
+ align:start position:0%
+making wonderful time and the reason I
+ 
+
+ align:start position:0%
+making wonderful time and the reason I
+thought of this particular story is that
+
+ align:start position:0%
+thought of this particular story is that
+ 
+
+ align:start position:0%
+thought of this particular story is that
+in a sense we are not almost out of gas
+
+ align:start position:0%
+in a sense we are not almost out of gas
+ 
+
+ align:start position:0%
+in a sense we are not almost out of gas
+but in terms of this being a
+
+ align:start position:0%
+but in terms of this being a
+ 
+
+ align:start position:0%
+but in terms of this being a
+fundamentalist type of course in which
+
+ align:start position:0%
+fundamentalist type of course in which
+ 
+
+ align:start position:0%
+fundamentalist type of course in which
+we're trying to give the ingredients of
+
+ align:start position:0%
+we're trying to give the ingredients of
+ 
+
+ align:start position:0%
+we're trying to give the ingredients of
+what goes into all advanced mathematics
+
+ align:start position:0%
+what goes into all advanced mathematics
+ 
+
+ align:start position:0%
+what goes into all advanced mathematics
+courses we have sort of come to the end
+
+ align:start position:0%
+courses we have sort of come to the end
+ 
+
+ align:start position:0%
+courses we have sort of come to the end
+of the road that we have finished the
+
+ align:start position:0%
+of the road that we have finished the
+ 
+
+ align:start position:0%
+of the road that we have finished the
+so-called ABCs of mathematics as far as
+
+ align:start position:0%
+so-called ABCs of mathematics as far as
+ 
+
+ align:start position:0%
+so-called ABCs of mathematics as far as
+making wonderful time is concerned I
+
+ align:start position:0%
+making wonderful time is concerned I
+ 
+
+ align:start position:0%
+making wonderful time is concerned I
+would say we've done deliberately just
+
+ align:start position:0%
+would say we've done deliberately just
+ 
+
+ align:start position:0%
+would say we've done deliberately just
+the opposite that we have essentially
+
+ align:start position:0%
+the opposite that we have essentially
+ 
+
+ align:start position:0%
+the opposite that we have essentially
+taken one or two Central themes and try
+
+ align:start position:0%
+taken one or two Central themes and try
+ 
+
+ align:start position:0%
+taken one or two Central themes and try
+to unify all of Elementary calculus in
+
+ align:start position:0%
+to unify all of Elementary calculus in
+ 
+
+ align:start position:0%
+to unify all of Elementary calculus in
+terms of these Central themes and when
+
+ align:start position:0%
+terms of these Central themes and when
+ 
+
+ align:start position:0%
+terms of these Central themes and when
+you do something like this it's very
+
+ align:start position:0%
+you do something like this it's very
+ 
+
+ align:start position:0%
+you do something like this it's very
+difficult to come to the end of a course
+
+ align:start position:0%
+difficult to come to the end of a course
+ 
+
+ align:start position:0%
+difficult to come to the end of a course
+you sort of don't know where to stop so
+
+ align:start position:0%
+you sort of don't know where to stop so
+ 
+
+ align:start position:0%
+you sort of don't know where to stop so
+you go back to a little trick that you
+
+ align:start position:0%
+you go back to a little trick that you
+ 
+
+ align:start position:0%
+you go back to a little trick that you
+learned in about the third grade when
+
+ align:start position:0%
+learned in about the third grade when
+ 
+
+ align:start position:0%
+learned in about the third grade when
+you wrote compositions where you learned
+
+ align:start position:0%
+you wrote compositions where you learned
+ 
+
+ align:start position:0%
+you wrote compositions where you learned
+that you could write anything that you
+
+ align:start position:0%
+that you could write anything that you
+ 
+
+ align:start position:0%
+that you could write anything that you
+wanted as long as the last line was we
+
+ align:start position:0%
+wanted as long as the last line was we
+ 
+
+ align:start position:0%
+wanted as long as the last line was we
+all had a very nice time so we now must
+
+ align:start position:0%
+all had a very nice time so we now must
+ 
+
+ align:start position:0%
+all had a very nice time so we now must
+look for a line along those particular
+
+ align:start position:0%
+look for a line along those particular
+ 
+
+ align:start position:0%
+look for a line along those particular
+thoughts and if we recall that we began
+
+ align:start position:0%
+thoughts and if we recall that we began
+ 
+
+ align:start position:0%
+thoughts and if we recall that we began
+as our major theme in this course the
+
+ align:start position:0%
+as our major theme in this course the
+ 
+
+ align:start position:0%
+as our major theme in this course the
+idea of mathematical structure the idea
+
+ align:start position:0%
+idea of mathematical structure the idea
+ 
+
+ align:start position:0%
+idea of mathematical structure the idea
+of what new math really meant not new
+
+ align:start position:0%
+of what new math really meant not new
+ 
+
+ align:start position:0%
+of what new math really meant not new
+meaning brand new but new meaning the
+
+ align:start position:0%
+meaning brand new but new meaning the
+ 
+
+ align:start position:0%
+meaning brand new but new meaning the
+opposite of P new meaning meaningful I
+
+ align:start position:0%
+opposite of P new meaning meaningful I
+ 
+
+ align:start position:0%
+opposite of P new meaning meaningful I
+can think of no nicer way of ending the
+
+ align:start position:0%
+can think of no nicer way of ending the
+ 
+
+ align:start position:0%
+can think of no nicer way of ending the
+course than by picking as an application
+
+ align:start position:0%
+course than by picking as an application
+ 
+
+ align:start position:0%
+course than by picking as an application
+a topic that
+
+ align:start position:0%
+a topic that
+ 
+
+ align:start position:0%
+a topic that
+existed long before the so-called new
+
+ align:start position:0%
+existed long before the so-called new
+ 
+
+ align:start position:0%
+existed long before the so-called new
+math was born and which exists an in an
+
+ align:start position:0%
+math was born and which exists an in an
+ 
+
+ align:start position:0%
+math was born and which exists an in an
+even more enlightened way in the spirit
+
+ align:start position:0%
+even more enlightened way in the spirit
+ 
+
+ align:start position:0%
+even more enlightened way in the spirit
+of the new mathematics and the topic
+
+ align:start position:0%
+of the new mathematics and the topic
+ 
+
+ align:start position:0%
+of the new mathematics and the topic
+that I have in mind to conclude with and
+
+ align:start position:0%
+that I have in mind to conclude with and
+ 
+
+ align:start position:0%
+that I have in mind to conclude with and
+it also ties in with our lecture of last
+
+ align:start position:0%
+it also ties in with our lecture of last
+ 
+
+ align:start position:0%
+it also ties in with our lecture of last
+time on the dot product is the subject
+
+ align:start position:0%
+time on the dot product is the subject
+ 
+
+ align:start position:0%
+time on the dot product is the subject
+called orthogonal functions which has as
+
+ align:start position:0%
+called orthogonal functions which has as
+ 
+
+ align:start position:0%
+called orthogonal functions which has as
+a special subtopic Fier
+
+ align:start position:0%
+a special subtopic Fier
+ 
+
+ align:start position:0%
+a special subtopic Fier
+series now the way this comes about
+
+ align:start position:0%
+series now the way this comes about
+ 
+
+ align:start position:0%
+series now the way this comes about
+is the following and you you have to
+
+ align:start position:0%
+is the following and you you have to
+ 
+
+ align:start position:0%
+is the following and you you have to
+know nothing about Vector spaces to
+
+ align:start position:0%
+know nothing about Vector spaces to
+ 
+
+ align:start position:0%
+know nothing about Vector spaces to
+appreciate what we're going to do now
+
+ align:start position:0%
+appreciate what we're going to do now
+ 
+
+ align:start position:0%
+appreciate what we're going to do now
+that in a sense we imitate what Fier
+
+ align:start position:0%
+that in a sense we imitate what Fier
+ 
+
+ align:start position:0%
+that in a sense we imitate what Fier
+actually did in trying to solve a
+
+ align:start position:0%
+actually did in trying to solve a
+ 
+
+ align:start position:0%
+actually did in trying to solve a
+particular type of problem we suppose
+
+ align:start position:0%
+particular type of problem we suppose
+ 
+
+ align:start position:0%
+particular type of problem we suppose
+that we have an infinite sequence of
+
+ align:start position:0%
+that we have an infinite sequence of
+ 
+
+ align:start position:0%
+that we have an infinite sequence of
+functions which I'll denote by the
+
+ align:start position:0%
+functions which I'll denote by the
+ 
+
+ align:start position:0%
+functions which I'll denote by the
+family F subn ofx and a particular
+
+ align:start position:0%
+family F subn ofx and a particular
+ 
+
+ align:start position:0%
+family F subn ofx and a particular
+closed interval from A to B such that
+
+ align:start position:0%
+closed interval from A to B such that
+ 
+
+ align:start position:0%
+closed interval from A to B such that
+each member of my family f benx is
+
+ align:start position:0%
+each member of my family f benx is
+ 
+
+ align:start position:0%
+each member of my family f benx is
+integral on the interval from A to B and
+
+ align:start position:0%
+integral on the interval from A to B and
+ 
+
+ align:start position:0%
+integral on the interval from A to B and
+we ALS Al assume that the integral from
+
+ align:start position:0%
+we ALS Al assume that the integral from
+ 
+
+ align:start position:0%
+we ALS Al assume that the integral from
+A to B of the product of any two of
+
+ align:start position:0%
+A to B of the product of any two of
+ 
+
+ align:start position:0%
+A to B of the product of any two of
+these functions two different members of
+
+ align:start position:0%
+these functions two different members of
+ 
+
+ align:start position:0%
+these functions two different members of
+this set that that integral is zero in
+
+ align:start position:0%
+this set that that integral is zero in
+ 
+
+ align:start position:0%
+this set that that integral is zero in
+other words the integral from A to B V
+
+ align:start position:0%
+other words the integral from A to B V
+ 
+
+ align:start position:0%
+other words the integral from A to B V
+sub I ofx * V subj ofx DX is zero
+
+ align:start position:0%
+sub I ofx * V subj ofx DX is zero
+ 
+
+ align:start position:0%
+sub I ofx * V subj ofx DX is zero
+provided I is unequal to J okay so we're
+
+ align:start position:0%
+provided I is unequal to J okay so we're
+ 
+
+ align:start position:0%
+provided I is unequal to J okay so we're
+assuming this particular property
+
+ align:start position:0%
+assuming this particular property
+ 
+
+ align:start position:0%
+assuming this particular property
+remembering of course that the product
+
+ align:start position:0%
+remembering of course that the product
+ 
+
+ align:start position:0%
+remembering of course that the product
+of two integraal functions is again
+
+ align:start position:0%
+of two integraal functions is again
+ 
+
+ align:start position:0%
+of two integraal functions is again
+integrable so that this thing makes
+
+ align:start position:0%
+integrable so that this thing makes
+ 
+
+ align:start position:0%
+integrable so that this thing makes
+sense now traditionally
+
+ align:start position:0%
+sense now traditionally
+ 
+
+ align:start position:0%
+sense now traditionally
+when a family of functions had this
+
+ align:start position:0%
+when a family of functions had this
+ 
+
+ align:start position:0%
+when a family of functions had this
+particular property that family was said
+
+ align:start position:0%
+particular property that family was said
+ 
+
+ align:start position:0%
+particular property that family was said
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+orthogonal on the interval from A to B
+
+ align:start position:0%
+orthogonal on the interval from A to B
+ 
+
+ align:start position:0%
+orthogonal on the interval from A to B
+and I will leave it for a little bit
+
+ align:start position:0%
+and I will leave it for a little bit
+ 
+
+ align:start position:0%
+and I will leave it for a little bit
+later to show you how this jibes with
+
+ align:start position:0%
+later to show you how this jibes with
+ 
+
+ align:start position:0%
+later to show you how this jibes with
+the meaning of orthogonal as we defined
+
+ align:start position:0%
+the meaning of orthogonal as we defined
+ 
+
+ align:start position:0%
+the meaning of orthogonal as we defined
+it in terms of dot products last time
+
+ align:start position:0%
+it in terms of dot products last time
+ 
+
+ align:start position:0%
+it in terms of dot products last time
+but let me show you how for example Fier
+
+ align:start position:0%
+but let me show you how for example Fier
+ 
+
+ align:start position:0%
+but let me show you how for example Fier
+decided to use this type of information
+
+ align:start position:0%
+decided to use this type of information
+ 
+
+ align:start position:0%
+decided to use this type of information
+suppose we had a given function f ofx
+
+ align:start position:0%
+suppose we had a given function f ofx
+ 
+
+ align:start position:0%
+suppose we had a given function f ofx
+that also happened to be integrable on
+
+ align:start position:0%
+that also happened to be integrable on
+ 
+
+ align:start position:0%
+that also happened to be integrable on
+the interval from A to B or written more
+
+ align:start position:0%
+the interval from A to B or written more
+ 
+
+ align:start position:0%
+the interval from A to B or written more
+succinctly we assume that the integral
+
+ align:start position:0%
+succinctly we assume that the integral
+ 
+
+ align:start position:0%
+succinctly we assume that the integral
+from A to B F ofx DX exists let's also
+
+ align:start position:0%
+from A to B F ofx DX exists let's also
+ 
+
+ align:start position:0%
+from A to B F ofx DX exists let's also
+suppose that F ofx happens to be a
+
+ align:start position:0%
+suppose that F ofx happens to be a
+ 
+
+ align:start position:0%
+suppose that F ofx happens to be a
+linear combination of the members of the
+
+ align:start position:0%
+linear combination of the members of the
+ 
+
+ align:start position:0%
+linear combination of the members of the
+orthogonal family Fe sub Ben effect
+
+ align:start position:0%
+orthogonal family Fe sub Ben effect
+ 
+
+ align:start position:0%
+orthogonal family Fe sub Ben effect
+effects in other words that for the
+
+ align:start position:0%
+effects in other words that for the
+ 
+
+ align:start position:0%
+effects in other words that for the
+given orthogonal family f ofx is
+
+ align:start position:0%
+given orthogonal family f ofx is
+ 
+
+ align:start position:0%
+given orthogonal family f ofx is
+summation CN FN of X as n goes from one
+
+ align:start position:0%
+summation CN FN of X as n goes from one
+ 
+
+ align:start position:0%
+summation CN FN of X as n goes from one
+to infinity and the question is
+
+ align:start position:0%
+to infinity and the question is
+ 
+
+ align:start position:0%
+to infinity and the question is
+under or with the knowledge that this is
+
+ align:start position:0%
+under or with the knowledge that this is
+ 
+
+ align:start position:0%
+under or with the knowledge that this is
+an orthogonal family how can we
+
+ align:start position:0%
+an orthogonal family how can we
+ 
+
+ align:start position:0%
+an orthogonal family how can we
+determine each coefficient C subn if
+
+ align:start position:0%
+determine each coefficient C subn if
+ 
+
+ align:start position:0%
+determine each coefficient C subn if
+this condition here is to hold or to
+
+ align:start position:0%
+this condition here is to hold or to
+ 
+
+ align:start position:0%
+this condition here is to hold or to
+make this more concrete and and keep it
+
+ align:start position:0%
+make this more concrete and and keep it
+ 
+
+ align:start position:0%
+make this more concrete and and keep it
+as non symbolic as possible let's
+
+ align:start position:0%
+as non symbolic as possible let's
+ 
+
+ align:start position:0%
+as non symbolic as possible let's
+suppose I wanted to figure out here what
+
+ align:start position:0%
+suppose I wanted to figure out here what
+ 
+
+ align:start position:0%
+suppose I wanted to figure out here what
+C sub3 happened to be the trick is this
+
+ align:start position:0%
+C sub3 happened to be the trick is this
+ 
+
+ align:start position:0%
+C sub3 happened to be the trick is this
+I recognize that from this basic
+
+ align:start position:0%
+I recognize that from this basic
+ 
+
+ align:start position:0%
+I recognize that from this basic
+definition If I multiply f sub3 of x by
+
+ align:start position:0%
+definition If I multiply f sub3 of x by
+ 
+
+ align:start position:0%
+definition If I multiply f sub3 of x by
+any other member of this family other
+
+ align:start position:0%
+any other member of this family other
+ 
+
+ align:start position:0%
+any other member of this family other
+than F sub3 itself and integrate from A
+
+ align:start position:0%
+than F sub3 itself and integrate from A
+ 
+
+ align:start position:0%
+than F sub3 itself and integrate from A
+to B that term will be Z
+
+ align:start position:0%
+to B that term will be Z
+ 
+
+ align:start position:0%
+to B that term will be Z
+so what I do is I come back to this
+
+ align:start position:0%
+so what I do is I come back to this
+ 
+
+ align:start position:0%
+so what I do is I come back to this
+relationship and I multiply both sides
+
+ align:start position:0%
+relationship and I multiply both sides
+ 
+
+ align:start position:0%
+relationship and I multiply both sides
+of this equation by F sub3 ofx keeping
+
+ align:start position:0%
+of this equation by F sub3 ofx keeping
+ 
+
+ align:start position:0%
+of this equation by F sub3 ofx keeping
+in mind if I wanted to find C sub K I
+
+ align:start position:0%
+in mind if I wanted to find C sub K I
+ 
+
+ align:start position:0%
+in mind if I wanted to find C sub K I
+would have multiplied both sides by F
+
+ align:start position:0%
+would have multiplied both sides by F
+ 
+
+ align:start position:0%
+would have multiplied both sides by F
+sub K of X I'm just picking k equal 3
+
+ align:start position:0%
+sub K of X I'm just picking k equal 3
+ 
+
+ align:start position:0%
+sub K of X I'm just picking k equal 3
+here I multiply both sides by F sub3 ofx
+
+ align:start position:0%
+here I multiply both sides by F sub3 ofx
+ 
+
+ align:start position:0%
+here I multiply both sides by F sub3 ofx
+and because f sub3 ofx is
+
+ align:start position:0%
+and because f sub3 ofx is
+ 
+
+ align:start position:0%
+and because f sub3 ofx is
+a constant subscript meaning it doesn't
+
+ align:start position:0%
+a constant subscript meaning it doesn't
+ 
+
+ align:start position:0%
+a constant subscript meaning it doesn't
+depend on the summation n which only
+
+ align:start position:0%
+depend on the summation n which only
+ 
+
+ align:start position:0%
+depend on the summation n which only
+affects the subscript here I I can bring
+
+ align:start position:0%
+affects the subscript here I I can bring
+ 
+
+ align:start position:0%
+affects the subscript here I I can bring
+f sub3 of x inside the summation sign
+
+ align:start position:0%
+f sub3 of x inside the summation sign
+ 
+
+ align:start position:0%
+f sub3 of x inside the summation sign
+now the trick is I integrate both sides
+
+ align:start position:0%
+now the trick is I integrate both sides
+ 
+
+ align:start position:0%
+now the trick is I integrate both sides
+of this equality from A to B in other
+
+ align:start position:0%
+of this equality from A to B in other
+ 
+
+ align:start position:0%
+of this equality from A to B in other
+words I put an integral from A to B on
+
+ align:start position:0%
+words I put an integral from A to B on
+ 
+
+ align:start position:0%
+words I put an integral from A to B on
+both sides here augment this with a DX
+
+ align:start position:0%
+both sides here augment this with a DX
+ 
+
+ align:start position:0%
+both sides here augment this with a DX
+and I now know that this is the case my
+
+ align:start position:0%
+and I now know that this is the case my
+ 
+
+ align:start position:0%
+and I now know that this is the case my
+next gimmick if you want to call it that
+
+ align:start position:0%
+next gimmick if you want to call it that
+ 
+
+ align:start position:0%
+next gimmick if you want to call it that
+and if you don't want to call it that
+
+ align:start position:0%
+and if you don't want to call it that
+ 
+
+ align:start position:0%
+and if you don't want to call it that
+you should because it is a gimmick as
+
+ align:start position:0%
+you should because it is a gimmick as
+ 
+
+ align:start position:0%
+you should because it is a gimmick as
+we'll explain in a moment I simply
+
+ align:start position:0%
+we'll explain in a moment I simply
+ 
+
+ align:start position:0%
+we'll explain in a moment I simply
+interchange the order of summation and
+
+ align:start position:0%
+interchange the order of summation and
+ 
+
+ align:start position:0%
+interchange the order of summation and
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+remembering that the integral of a sum
+
+ align:start position:0%
+remembering that the integral of a sum
+ 
+
+ align:start position:0%
+remembering that the integral of a sum
+is the sum of the integrals I
+
+ align:start position:0%
+is the sum of the integrals I
+ 
+
+ align:start position:0%
+is the sum of the integrals I
+interchange this order and I now have
+
+ align:start position:0%
+interchange this order and I now have
+ 
+
+ align:start position:0%
+interchange this order and I now have
+the summation n goes from 1 to Infinity
+
+ align:start position:0%
+the summation n goes from 1 to Infinity
+ 
+
+ align:start position:0%
+the summation n goes from 1 to Infinity
+integral from A to B CN FN of X F3 of X
+
+ align:start position:0%
+integral from A to B CN FN of X F3 of X
+ 
+
+ align:start position:0%
+integral from A to B CN FN of X F3 of X
+DX and now remembering that F sub that
+
+ align:start position:0%
+DX and now remembering that F sub that
+ 
+
+ align:start position:0%
+DX and now remembering that F sub that
+the integral from a to b f subn of x
+
+ align:start position:0%
+the integral from a to b f subn of x
+ 
+
+ align:start position:0%
+the integral from a to b f subn of x
+time V sub3 ofx DX by definition of
+
+ align:start position:0%
+time V sub3 ofx DX by definition of
+ 
+
+ align:start position:0%
+time V sub3 ofx DX by definition of
+orthogonality is zero unless n equals 3
+
+ align:start position:0%
+orthogonality is zero unless n equals 3
+ 
+
+ align:start position:0%
+orthogonality is zero unless n equals 3
+all of these terms drop out except when
+
+ align:start position:0%
+all of these terms drop out except when
+ 
+
+ align:start position:0%
+all of these terms drop out except when
+n equal 3 now what happens here when n
+
+ align:start position:0%
+n equal 3 now what happens here when n
+ 
+
+ align:start position:0%
+n equal 3 now what happens here when n
+equal 3 this term here is C sub3 this is
+
+ align:start position:0%
+equal 3 this term here is C sub3 this is
+ 
+
+ align:start position:0%
+equal 3 this term here is C sub3 this is
+f sub 3^ 2 x DX integrated from A to B
+
+ align:start position:0%
+f sub 3^ 2 x DX integrated from A to B
+ 
+
+ align:start position:0%
+f sub 3^ 2 x DX integrated from A to B
+and all the remaining terms are zero
+
+ align:start position:0%
+and all the remaining terms are zero
+ 
+
+ align:start position:0%
+and all the remaining terms are zero
+because the integrant is zero in other
+
+ align:start position:0%
+because the integrant is zero in other
+ 
+
+ align:start position:0%
+because the integrant is zero in other
+words the right hand side simply becomes
+
+ align:start position:0%
+words the right hand side simply becomes
+ 
+
+ align:start position:0%
+words the right hand side simply becomes
+well since C3 is a constant I can take
+
+ align:start position:0%
+well since C3 is a constant I can take
+ 
+
+ align:start position:0%
+well since C3 is a constant I can take
+it outside the integral sign it's C3
+
+ align:start position:0%
+it outside the integral sign it's C3
+ 
+
+ align:start position:0%
+it outside the integral sign it's C3
+integral from a Tob F sub 3^ 2 of X DX
+
+ align:start position:0%
+integral from a Tob F sub 3^ 2 of X DX
+ 
+
+ align:start position:0%
+integral from a Tob F sub 3^ 2 of X DX
+and now you see from this relationship
+
+ align:start position:0%
+and now you see from this relationship
+ 
+
+ align:start position:0%
+and now you see from this relationship
+ship here I can solve for C sub3 namely
+
+ align:start position:0%
+ship here I can solve for C sub3 namely
+ 
+
+ align:start position:0%
+ship here I can solve for C sub3 namely
+I simply divide both sides of this
+
+ align:start position:0%
+I simply divide both sides of this
+ 
+
+ align:start position:0%
+I simply divide both sides of this
+equation by this number here now what I
+
+ align:start position:0%
+equation by this number here now what I
+ 
+
+ align:start position:0%
+equation by this number here now what I
+said by gimmick is simply this when we
+
+ align:start position:0%
+said by gimmick is simply this when we
+ 
+
+ align:start position:0%
+said by gimmick is simply this when we
+said that the integral of a sum is a sum
+
+ align:start position:0%
+said that the integral of a sum is a sum
+ 
+
+ align:start position:0%
+said that the integral of a sum is a sum
+of the integrals that was only for a
+
+ align:start position:0%
+of the integrals that was only for a
+ 
+
+ align:start position:0%
+of the integrals that was only for a
+finite sum you may remember in part one
+
+ align:start position:0%
+finite sum you may remember in part one
+ 
+
+ align:start position:0%
+finite sum you may remember in part one
+of our course when we talked about
+
+ align:start position:0%
+of our course when we talked about
+ 
+
+ align:start position:0%
+of our course when we talked about
+uniform convergence one of the things
+
+ align:start position:0%
+uniform convergence one of the things
+ 
+
+ align:start position:0%
+uniform convergence one of the things
+that we pointed out was that for
+
+ align:start position:0%
+that we pointed out was that for
+ 
+
+ align:start position:0%
+that we pointed out was that for
+infinite sums you weren't always
+
+ align:start position:0%
+infinite sums you weren't always
+ 
+
+ align:start position:0%
+infinite sums you weren't always
+guaranteed that you could interchange
+
+ align:start position:0%
+guaranteed that you could interchange
+ 
+
+ align:start position:0%
+guaranteed that you could interchange
+the order of summation and integration
+
+ align:start position:0%
+the order of summation and integration
+ 
+
+ align:start position:0%
+the order of summation and integration
+or as I usually put it you could always
+
+ align:start position:0%
+or as I usually put it you could always
+ 
+
+ align:start position:0%
+or as I usually put it you could always
+interchange them but you may not get the
+
+ align:start position:0%
+interchange them but you may not get the
+ 
+
+ align:start position:0%
+interchange them but you may not get the
+same answer so the first question that
+
+ align:start position:0%
+same answer so the first question that
+ 
+
+ align:start position:0%
+same answer so the first question that
+comes up is how do I know that I am
+
+ align:start position:0%
+comes up is how do I know that I am
+ 
+
+ align:start position:0%
+comes up is how do I know that I am
+allowed to Interchange this order by the
+
+ align:start position:0%
+allowed to Interchange this order by the
+ 
+
+ align:start position:0%
+allowed to Interchange this order by the
+way the second question that comes up is
+
+ align:start position:0%
+way the second question that comes up is
+ 
+
+ align:start position:0%
+way the second question that comes up is
+and this is a more subtle question but
+
+ align:start position:0%
+and this is a more subtle question but
+ 
+
+ align:start position:0%
+and this is a more subtle question but
+going back to what we were talking about
+
+ align:start position:0%
+going back to what we were talking about
+ 
+
+ align:start position:0%
+going back to what we were talking about
+before how do I even know that there is
+
+ align:start position:0%
+before how do I even know that there is
+ 
+
+ align:start position:0%
+before how do I even know that there is
+a linear combination of the fens that
+
+ align:start position:0%
+a linear combination of the fens that
+ 
+
+ align:start position:0%
+a linear combination of the fens that
+comes out to be the given F ofx you see
+
+ align:start position:0%
+comes out to be the given F ofx you see
+ 
+
+ align:start position:0%
+comes out to be the given F ofx you see
+notice that demonstration here
+
+ align:start position:0%
+notice that demonstration here
+ 
+
+ align:start position:0%
+notice that demonstration here
+presupposes that F ofx can be written
+
+ align:start position:0%
+presupposes that F ofx can be written
+ 
+
+ align:start position:0%
+presupposes that F ofx can be written
+this way you see the two questions that
+
+ align:start position:0%
+this way you see the two questions that
+ 
+
+ align:start position:0%
+this way you see the two questions that
+come up is given an F ofx first of all
+
+ align:start position:0%
+come up is given an F ofx first of all
+ 
+
+ align:start position:0%
+come up is given an F ofx first of all
+can it be written this way and secondly
+
+ align:start position:0%
+can it be written this way and secondly
+ 
+
+ align:start position:0%
+can it be written this way and secondly
+even if it can do we have the right to
+
+ align:start position:0%
+even if it can do we have the right to
+ 
+
+ align:start position:0%
+even if it can do we have the right to
+Interchange the order of integration and
+
+ align:start position:0%
+Interchange the order of integration and
+ 
+
+ align:start position:0%
+Interchange the order of integration and
+summation by the way assuming for the
+
+ align:start position:0%
+summation by the way assuming for the
+ 
+
+ align:start position:0%
+summation by the way assuming for the
+moment that we can do this mechanically
+
+ align:start position:0%
+moment that we can do this mechanically
+ 
+
+ align:start position:0%
+moment that we can do this mechanically
+at least notice that what C3 turns out
+
+ align:start position:0%
+at least notice that what C3 turns out
+ 
+
+ align:start position:0%
+at least notice that what C3 turns out
+to be is the integral from a to b f ofx
+
+ align:start position:0%
+to be is the integral from a to b f ofx
+ 
+
+ align:start position:0%
+to be is the integral from a to b f ofx
+f sub3 ofx DX divided by the integral
+
+ align:start position:0%
+f sub3 ofx DX divided by the integral
+ 
+
+ align:start position:0%
+f sub3 ofx DX divided by the integral
+from a to be F sub3 of x^2 * DX and
+
+ align:start position:0%
+from a to be F sub3 of x^2 * DX and
+ 
+
+ align:start position:0%
+from a to be F sub3 of x^2 * DX and
+again replacing the 3 by a k this is how
+
+ align:start position:0%
+again replacing the 3 by a k this is how
+ 
+
+ align:start position:0%
+again replacing the 3 by a k this is how
+every one of these coefficients could
+
+ align:start position:0%
+every one of these coefficients could
+ 
+
+ align:start position:0%
+every one of these coefficients could
+have been determined and now you see as
+
+ align:start position:0%
+have been determined and now you see as
+ 
+
+ align:start position:0%
+have been determined and now you see as
+a very very brief aside which I will go
+
+ align:start position:0%
+a very very brief aside which I will go
+ 
+
+ align:start position:0%
+a very very brief aside which I will go
+into much more detail in the study guide
+
+ align:start position:0%
+into much more detail in the study guide
+ 
+
+ align:start position:0%
+into much more detail in the study guide
+when we talk about the exercises and the
+
+ align:start position:0%
+when we talk about the exercises and the
+ 
+
+ align:start position:0%
+when we talk about the exercises and the
+various discussion of the
+
+ align:start position:0%
+various discussion of the
+ 
+
+ align:start position:0%
+various discussion of the
+exercises given a series of functions
+
+ align:start position:0%
+exercises given a series of functions
+ 
+
+ align:start position:0%
+exercises given a series of functions
+which is integrable on a a sequence of
+
+ align:start position:0%
+which is integrable on a a sequence of
+ 
+
+ align:start position:0%
+which is integrable on a a sequence of
+functions integ bable on a given
+
+ align:start position:0%
+functions integ bable on a given
+ 
+
+ align:start position:0%
+functions integ bable on a given
+interval from A to B one usually def
+
+ align:start position:0%
+interval from A to B one usually def
+ 
+
+ align:start position:0%
+interval from A to B one usually def
+finds the dotproduct of these two
+
+ align:start position:0%
+finds the dotproduct of these two
+ 
+
+ align:start position:0%
+finds the dotproduct of these two
+functions to be the integral from A to B
+
+ align:start position:0%
+functions to be the integral from A to B
+ 
+
+ align:start position:0%
+functions to be the integral from A to B
+the product of the two functions times
+
+ align:start position:0%
+the product of the two functions times
+ 
+
+ align:start position:0%
+the product of the two functions times
+DX you see remember last time we showed
+
+ align:start position:0%
+DX you see remember last time we showed
+ 
+
+ align:start position:0%
+DX you see remember last time we showed
+that all you needed to have a DOT
+
+ align:start position:0%
+that all you needed to have a DOT
+ 
+
+ align:start position:0%
+that all you needed to have a DOT
+product was a rule that showed you how
+
+ align:start position:0%
+product was a rule that showed you how
+ 
+
+ align:start position:0%
+product was a rule that showed you how
+to combine two members of your set to
+
+ align:start position:0%
+to combine two members of your set to
+ 
+
+ align:start position:0%
+to combine two members of your set to
+give you a number and certainly this
+
+ align:start position:0%
+give you a number and certainly this
+ 
+
+ align:start position:0%
+give you a number and certainly this
+thing here is a number and it also had
+
+ align:start position:0%
+thing here is a number and it also had
+ 
+
+ align:start position:0%
+thing here is a number and it also had
+to have three or four basic properties
+
+ align:start position:0%
+to have three or four basic properties
+ 
+
+ align:start position:0%
+to have three or four basic properties
+and as one of the exercises we will show
+
+ align:start position:0%
+and as one of the exercises we will show
+ 
+
+ align:start position:0%
+and as one of the exercises we will show
+that those properties for a DOT product
+
+ align:start position:0%
+that those properties for a DOT product
+ 
+
+ align:start position:0%
+that those properties for a DOT product
+are obeyed here but this is where the
+
+ align:start position:0%
+are obeyed here but this is where the
+ 
+
+ align:start position:0%
+are obeyed here but this is where the
+word orthogonal functions come from
+
+ align:start position:0%
+word orthogonal functions come from
+ 
+
+ align:start position:0%
+word orthogonal functions come from
+notice that in terms of this definition
+
+ align:start position:0%
+notice that in terms of this definition
+ 
+
+ align:start position:0%
+notice that in terms of this definition
+of a DOT product two vectors are
+
+ align:start position:0%
+of a DOT product two vectors are
+ 
+
+ align:start position:0%
+of a DOT product two vectors are
+orthogonal if their dot product is zero
+
+ align:start position:0%
+orthogonal if their dot product is zero
+ 
+
+ align:start position:0%
+orthogonal if their dot product is zero
+and notice saying that this equals zero
+
+ align:start position:0%
+and notice saying that this equals zero
+ 
+
+ align:start position:0%
+and notice saying that this equals zero
+is the same as saying that this integral
+
+ align:start position:0%
+is the same as saying that this integral
+ 
+
+ align:start position:0%
+is the same as saying that this integral
+is zero and that's precisely what the
+
+ align:start position:0%
+is zero and that's precisely what the
+ 
+
+ align:start position:0%
+is zero and that's precisely what the
+definition of orthogonal was so you see
+
+ align:start position:0%
+definition of orthogonal was so you see
+ 
+
+ align:start position:0%
+definition of orthogonal was so you see
+this is the connection between the
+
+ align:start position:0%
+this is the connection between the
+ 
+
+ align:start position:0%
+this is the connection between the
+vector space interpretation of
+
+ align:start position:0%
+vector space interpretation of
+ 
+
+ align:start position:0%
+vector space interpretation of
+orthogonal and the traditional uh
+
+ align:start position:0%
+orthogonal and the traditional uh
+ 
+
+ align:start position:0%
+orthogonal and the traditional uh
+interpretation of orthogonal and as I
+
+ align:start position:0%
+interpretation of orthogonal and as I
+ 
+
+ align:start position:0%
+interpretation of orthogonal and as I
+say I'll leave further discussion of
+
+ align:start position:0%
+say I'll leave further discussion of
+ 
+
+ align:start position:0%
+say I'll leave further discussion of
+that for the the notes but the important
+
+ align:start position:0%
+that for the the notes but the important
+ 
+
+ align:start position:0%
+that for the the notes but the important
+point is this if I mechanically solve
+
+ align:start position:0%
+point is this if I mechanically solve
+ 
+
+ align:start position:0%
+point is this if I mechanically solve
+for these coefficients in other words
+
+ align:start position:0%
+for these coefficients in other words
+ 
+
+ align:start position:0%
+for these coefficients in other words
+suppose I'm given F ofx and without and
+
+ align:start position:0%
+suppose I'm given F ofx and without and
+ 
+
+ align:start position:0%
+suppose I'm given F ofx and without and
+I'm given a family of functions Fe subn
+
+ align:start position:0%
+I'm given a family of functions Fe subn
+ 
+
+ align:start position:0%
+I'm given a family of functions Fe subn
+ofx which is orthogonal on the interval
+
+ align:start position:0%
+ofx which is orthogonal on the interval
+ 
+
+ align:start position:0%
+ofx which is orthogonal on the interval
+from A to B suppose that without even
+
+ align:start position:0%
+from A to B suppose that without even
+ 
+
+ align:start position:0%
+from A to B suppose that without even
+knowing whether F ofx can be represented
+
+ align:start position:0%
+knowing whether F ofx can be represented
+ 
+
+ align:start position:0%
+knowing whether F ofx can be represented
+as a linear combination of the fees and
+
+ align:start position:0%
+as a linear combination of the fees and
+ 
+
+ align:start position:0%
+as a linear combination of the fees and
+that without even knowing whether I can
+
+ align:start position:0%
+that without even knowing whether I can
+ 
+
+ align:start position:0%
+that without even knowing whether I can
+interchange these two operations the
+
+ align:start position:0%
+interchange these two operations the
+ 
+
+ align:start position:0%
+interchange these two operations the
+order in which I perform these two
+
+ align:start position:0%
+order in which I perform these two
+ 
+
+ align:start position:0%
+order in which I perform these two
+operations let's suppose that I
+
+ align:start position:0%
+operations let's suppose that I
+ 
+
+ align:start position:0%
+operations let's suppose that I
+mechanically in
+
+ align:start position:0%
+mechanically in
+ 
+
+ align:start position:0%
+mechanically in
+as my coefficients the C's in this
+
+ align:start position:0%
+as my coefficients the C's in this
+ 
+
+ align:start position:0%
+as my coefficients the C's in this
+particular way in other words regardless
+
+ align:start position:0%
+particular way in other words regardless
+ 
+
+ align:start position:0%
+particular way in other words regardless
+of whether it's it means anything or not
+
+ align:start position:0%
+of whether it's it means anything or not
+ 
+
+ align:start position:0%
+of whether it's it means anything or not
+I can always multiply F ofx by F sub K
+
+ align:start position:0%
+I can always multiply F ofx by F sub K
+ 
+
+ align:start position:0%
+I can always multiply F ofx by F sub K
+of X integrate from A to B you see the
+
+ align:start position:0%
+of X integrate from A to B you see the
+ 
+
+ align:start position:0%
+of X integrate from A to B you see the
+product of two integral functions is
+
+ align:start position:0%
+product of two integral functions is
+ 
+
+ align:start position:0%
+product of two integral functions is
+always integral I can always divide that
+
+ align:start position:0%
+always integral I can always divide that
+ 
+
+ align:start position:0%
+always integral I can always divide that
+by the square of the function f subk of
+
+ align:start position:0%
+by the square of the function f subk of
+ 
+
+ align:start position:0%
+by the square of the function f subk of
+x from A to B keeping in mind by the way
+
+ align:start position:0%
+x from A to B keeping in mind by the way
+ 
+
+ align:start position:0%
+x from A to B keeping in mind by the way
+that as long as f sub3 is not
+
+ align:start position:0%
+that as long as f sub3 is not
+ 
+
+ align:start position:0%
+that as long as f sub3 is not
+identically zero or if it's
+
+ align:start position:0%
+identically zero or if it's
+ 
+
+ align:start position:0%
+identically zero or if it's
+not uh zero other than on a uh set of uh
+
+ align:start position:0%
+not uh zero other than on a uh set of uh
+ 
+
+ align:start position:0%
+not uh zero other than on a uh set of uh
+points of measure zero or what have you
+
+ align:start position:0%
+points of measure zero or what have you
+ 
+
+ align:start position:0%
+points of measure zero or what have you
+notice that the square of a number can't
+
+ align:start position:0%
+notice that the square of a number can't
+ 
+
+ align:start position:0%
+notice that the square of a number can't
+be negative so if f sub3 of x is
+
+ align:start position:0%
+be negative so if f sub3 of x is
+ 
+
+ align:start position:0%
+be negative so if f sub3 of x is
+different from zero in enough places by
+
+ align:start position:0%
+different from zero in enough places by
+ 
+
+ align:start position:0%
+different from zero in enough places by
+squaring it I have a positive integrant
+
+ align:start position:0%
+squaring it I have a positive integrant
+ 
+
+ align:start position:0%
+squaring it I have a positive integrant
+and when I integrate a positive
+
+ align:start position:0%
+and when I integrate a positive
+ 
+
+ align:start position:0%
+and when I integrate a positive
+integrant I can't get zero for an answer
+
+ align:start position:0%
+integrant I can't get zero for an answer
+ 
+
+ align:start position:0%
+integrant I can't get zero for an answer
+so I don't have a zero denominator here
+
+ align:start position:0%
+so I don't have a zero denominator here
+ 
+
+ align:start position:0%
+so I don't have a zero denominator here
+but the point is this if I choose the
+
+ align:start position:0%
+but the point is this if I choose the
+ 
+
+ align:start position:0%
+but the point is this if I choose the
+C's as as I did here see with the C's as
+
+ align:start position:0%
+C's as as I did here see with the C's as
+ 
+
+ align:start position:0%
+C's as as I did here see with the C's as
+just defined we write that F ofx and
+
+ align:start position:0%
+just defined we write that F ofx and
+ 
+
+ align:start position:0%
+just defined we write that F ofx and
+then we put a little squiggle here see
+
+ align:start position:0%
+then we put a little squiggle here see
+ 
+
+ align:start position:0%
+then we put a little squiggle here see
+we don't know if we had the right to
+
+ align:start position:0%
+we don't know if we had the right to
+ 
+
+ align:start position:0%
+we don't know if we had the right to
+assume that this series here is equal to
+
+ align:start position:0%
+assume that this series here is equal to
+ 
+
+ align:start position:0%
+assume that this series here is equal to
+F ofx but we write this little squiggle
+
+ align:start position:0%
+F ofx but we write this little squiggle
+ 
+
+ align:start position:0%
+F ofx but we write this little squiggle
+Mark here we call the resulting infinite
+
+ align:start position:0%
+Mark here we call the resulting infinite
+ 
+
+ align:start position:0%
+Mark here we call the resulting infinite
+series capital F ofx and what we say is
+
+ align:start position:0%
+series capital F ofx and what we say is
+ 
+
+ align:start position:0%
+series capital F ofx and what we say is
+that capital F ofx is the fuer
+
+ align:start position:0%
+that capital F ofx is the fuer
+ 
+
+ align:start position:0%
+that capital F ofx is the fuer
+representation of little f ofx with
+
+ align:start position:0%
+representation of little f ofx with
+ 
+
+ align:start position:0%
+representation of little f ofx with
+respect to the family f subn of x you
+
+ align:start position:0%
+respect to the family f subn of x you
+ 
+
+ align:start position:0%
+respect to the family f subn of x you
+see we don't say that these two are
+
+ align:start position:0%
+see we don't say that these two are
+ 
+
+ align:start position:0%
+see we don't say that these two are
+equal but when we choose these
+
+ align:start position:0%
+equal but when we choose these
+ 
+
+ align:start position:0%
+equal but when we choose these
+coefficients the way I just mentioned
+
+ align:start position:0%
+coefficients the way I just mentioned
+ 
+
+ align:start position:0%
+coefficients the way I just mentioned
+this is in any event called the Fier
+
+ align:start position:0%
+this is in any event called the Fier
+ 
+
+ align:start position:0%
+this is in any event called the Fier
+representation of the function little F
+
+ align:start position:0%
+representation of the function little F
+ 
+
+ align:start position:0%
+representation of the function little F
+ofx now you see there are many questions
+
+ align:start position:0%
+ofx now you see there are many questions
+ 
+
+ align:start position:0%
+ofx now you see there are many questions
+that come up and in the form of an
+
+ align:start position:0%
+that come up and in the form of an
+ 
+
+ align:start position:0%
+that come up and in the form of an
+overview let me just State them first of
+
+ align:start position:0%
+overview let me just State them first of
+ 
+
+ align:start position:0%
+overview let me just State them first of
+all how do we know that capital F ofx is
+
+ align:start position:0%
+all how do we know that capital F ofx is
+ 
+
+ align:start position:0%
+all how do we know that capital F ofx is
+even a convergence series after all this
+
+ align:start position:0%
+even a convergence series after all this
+ 
+
+ align:start position:0%
+even a convergence series after all this
+is an infinite series how do we know it
+
+ align:start position:0%
+is an infinite series how do we know it
+ 
+
+ align:start position:0%
+is an infinite series how do we know it
+even converges secondly if it does
+
+ align:start position:0%
+even converges secondly if it does
+ 
+
+ align:start position:0%
+even converges secondly if it does
+converge how do we know that it
+
+ align:start position:0%
+converge how do we know that it
+ 
+
+ align:start position:0%
+converge how do we know that it
+converges to f ofx the answer is we
+
+ align:start position:0%
+converges to f ofx the answer is we
+ 
+
+ align:start position:0%
+converges to f ofx the answer is we
+don't know we really don't know but
+
+ align:start position:0%
+don't know we really don't know but
+ 
+
+ align:start position:0%
+don't know we really don't know but
+there is a rather remarkable result and
+
+ align:start position:0%
+there is a rather remarkable result and
+ 
+
+ align:start position:0%
+there is a rather remarkable result and
+the result is not that difficult to
+
+ align:start position:0%
+the result is not that difficult to
+ 
+
+ align:start position:0%
+the result is not that difficult to
+prove but in the form of an overview I
+
+ align:start position:0%
+prove but in the form of an overview I
+ 
+
+ align:start position:0%
+prove but in the form of an overview I
+prefer to omit the proof here it will be
+
+ align:start position:0%
+prefer to omit the proof here it will be
+ 
+
+ align:start position:0%
+prefer to omit the proof here it will be
+an exercise in the study guide but I
+
+ align:start position:0%
+an exercise in the study guide but I
+ 
+
+ align:start position:0%
+an exercise in the study guide but I
+think it's important to see what the
+
+ align:start position:0%
+think it's important to see what the
+ 
+
+ align:start position:0%
+think it's important to see what the
+statement of the result is and then we
+
+ align:start position:0%
+statement of the result is and then we
+ 
+
+ align:start position:0%
+statement of the result is and then we
+can talk about the ramifications of that
+
+ align:start position:0%
+can talk about the ramifications of that
+ 
+
+ align:start position:0%
+can talk about the ramifications of that
+but the proof would actually obscure the
+
+ align:start position:0%
+but the proof would actually obscure the
+ 
+
+ align:start position:0%
+but the proof would actually obscure the
+beauty of the result and the aside which
+
+ align:start position:0%
+beauty of the result and the aside which
+ 
+
+ align:start position:0%
+beauty of the result and the aside which
+I leave as an exercise is simply there
+
+ align:start position:0%
+I leave as an exercise is simply there
+ 
+
+ align:start position:0%
+I leave as an exercise is simply there
+this suppose you took a linear
+
+ align:start position:0%
+this suppose you took a linear
+ 
+
+ align:start position:0%
+this suppose you took a linear
+combination of the first n of the terms
+
+ align:start position:0%
+combination of the first n of the terms
+ 
+
+ align:start position:0%
+combination of the first n of the terms
+F1 ofx up to FN
+
+ align:start position:0%
+F1 ofx up to FN
+ 
+
+ align:start position:0%
+F1 ofx up to FN
+ofx okay if you choose the C subk to be
+
+ align:start position:0%
+ofx okay if you choose the C subk to be
+ 
+
+ align:start position:0%
+ofx okay if you choose the C subk to be
+the so-called fuer coefficients the way
+
+ align:start position:0%
+the so-called fuer coefficients the way
+ 
+
+ align:start position:0%
+the so-called fuer coefficients the way
+I just mentioned what is interesting is
+
+ align:start position:0%
+I just mentioned what is interesting is
+ 
+
+ align:start position:0%
+I just mentioned what is interesting is
+this that even if the Fier
+
+ align:start position:0%
+this that even if the Fier
+ 
+
+ align:start position:0%
+this that even if the Fier
+representation doesn't converge to F ofx
+
+ align:start position:0%
+representation doesn't converge to F ofx
+ 
+
+ align:start position:0%
+representation doesn't converge to F ofx
+it has the property that it gives you
+
+ align:start position:0%
+it has the property that it gives you
+ 
+
+ align:start position:0%
+it has the property that it gives you
+the best least square of approximation
+
+ align:start position:0%
+the best least square of approximation
+ 
+
+ align:start position:0%
+the best least square of approximation
+in other words if I were to to compute
+
+ align:start position:0%
+in other words if I were to to compute
+ 
+
+ align:start position:0%
+in other words if I were to to compute
+the difference between F ofx and the sum
+
+ align:start position:0%
+the difference between F ofx and the sum
+ 
+
+ align:start position:0%
+the difference between F ofx and the sum
+of the first n terms in the Fier
+
+ align:start position:0%
+of the first n terms in the Fier
+ 
+
+ align:start position:0%
+of the first n terms in the Fier
+representation where the C's were chosen
+
+ align:start position:0%
+representation where the C's were chosen
+ 
+
+ align:start position:0%
+representation where the C's were chosen
+according to the method I just mentioned
+
+ align:start position:0%
+according to the method I just mentioned
+ 
+
+ align:start position:0%
+according to the method I just mentioned
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+before and square that difference you
+
+ align:start position:0%
+before and square that difference you
+ 
+
+ align:start position:0%
+before and square that difference you
+see this is why it's called the mean
+
+ align:start position:0%
+see this is why it's called the mean
+ 
+
+ align:start position:0%
+see this is why it's called the mean
+Square idea you see large errors and
+
+ align:start position:0%
+Square idea you see large errors and
+ 
+
+ align:start position:0%
+Square idea you see large errors and
+small number errors in other words a
+
+ align:start position:0%
+small number errors in other words a
+ 
+
+ align:start position:0%
+small number errors in other words a
+large negative error can cancel a large
+
+ align:start position:0%
+large negative error can cancel a large
+ 
+
+ align:start position:0%
+large negative error can cancel a large
+positive error because the algebraic
+
+ align:start position:0%
+positive error because the algebraic
+ 
+
+ align:start position:0%
+positive error because the algebraic
+signs tend to cancel one another but by
+
+ align:start position:0%
+signs tend to cancel one another but by
+ 
+
+ align:start position:0%
+signs tend to cancel one another but by
+squaring large errors all of these
+
+ align:start position:0%
+squaring large errors all of these
+ 
+
+ align:start position:0%
+squaring large errors all of these
+become what squares of large magnitudes
+
+ align:start position:0%
+become what squares of large magnitudes
+ 
+
+ align:start position:0%
+become what squares of large magnitudes
+are large positive magnitudes by
+
+ align:start position:0%
+are large positive magnitudes by
+ 
+
+ align:start position:0%
+are large positive magnitudes by
+squaring I really magnify the errors the
+
+ align:start position:0%
+squaring I really magnify the errors the
+ 
+
+ align:start position:0%
+squaring I really magnify the errors the
+positives can't cancel the negatives and
+
+ align:start position:0%
+positives can't cancel the negatives and
+ 
+
+ align:start position:0%
+positives can't cancel the negatives and
+what this says is that if I use this
+
+ align:start position:0%
+what this says is that if I use this
+ 
+
+ align:start position:0%
+what this says is that if I use this
+linear combination of the Fe sub NS that
+
+ align:start position:0%
+linear combination of the Fe sub NS that
+ 
+
+ align:start position:0%
+linear combination of the Fe sub NS that
+the least Square approximate the square
+
+ align:start position:0%
+the least Square approximate the square
+ 
+
+ align:start position:0%
+the least Square approximate the square
+approximation error is less using the
+
+ align:start position:0%
+approximation error is less using the
+ 
+
+ align:start position:0%
+approximation error is less using the
+these coefficients than if I had used
+
+ align:start position:0%
+these coefficients than if I had used
+ 
+
+ align:start position:0%
+these coefficients than if I had used
+any other possible coefficients that if
+
+ align:start position:0%
+any other possible coefficients that if
+ 
+
+ align:start position:0%
+any other possible coefficients that if
+I picked any other coefficients in the
+
+ align:start position:0%
+I picked any other coefficients in the
+ 
+
+ align:start position:0%
+I picked any other coefficients in the
+whole world other than the ones that I
+
+ align:start position:0%
+whole world other than the ones that I
+ 
+
+ align:start position:0%
+whole world other than the ones that I
+found by the method indicat just a
+
+ align:start position:0%
+found by the method indicat just a
+ 
+
+ align:start position:0%
+found by the method indicat just a
+little while ago if I summed these terms
+
+ align:start position:0%
+little while ago if I summed these terms
+ 
+
+ align:start position:0%
+little while ago if I summed these terms
+subtracted that from F ofx squared and
+
+ align:start position:0%
+subtracted that from F ofx squared and
+ 
+
+ align:start position:0%
+subtracted that from F ofx squared and
+integrated the result from A to B I
+
+ align:start position:0%
+integrated the result from A to B I
+ 
+
+ align:start position:0%
+integrated the result from A to B I
+would get a number which was at least as
+
+ align:start position:0%
+would get a number which was at least as
+ 
+
+ align:start position:0%
+would get a number which was at least as
+large and in most cases in fact unless
+
+ align:start position:0%
+large and in most cases in fact unless
+ 
+
+ align:start position:0%
+large and in most cases in fact unless
+the D subk were chosen to equal the C
+
+ align:start position:0%
+the D subk were chosen to equal the C
+ 
+
+ align:start position:0%
+the D subk were chosen to equal the C
+subk I would get a number which was
+
+ align:start position:0%
+subk I would get a number which was
+ 
+
+ align:start position:0%
+subk I would get a number which was
+larger than this now you see what this
+
+ align:start position:0%
+larger than this now you see what this
+ 
+
+ align:start position:0%
+larger than this now you see what this
+thing says what this says is that there
+
+ align:start position:0%
+thing says what this says is that there
+ 
+
+ align:start position:0%
+thing says what this says is that there
+can't be any real interval where this
+
+ align:start position:0%
+can't be any real interval where this
+ 
+
+ align:start position:0%
+can't be any real interval where this
+gets very very far away from F ofx
+
+ align:start position:0%
+gets very very far away from F ofx
+ 
+
+ align:start position:0%
+gets very very far away from F ofx
+because you see if it did if it did get
+
+ align:start position:0%
+because you see if it did if it did get
+ 
+
+ align:start position:0%
+because you see if it did if it did get
+very very far away this would be a large
+
+ align:start position:0%
+very very far away this would be a large
+ 
+
+ align:start position:0%
+very very far away this would be a large
+magnitude squaring it would give me a
+
+ align:start position:0%
+magnitude squaring it would give me a
+ 
+
+ align:start position:0%
+magnitude squaring it would give me a
+positive large magnitude integrating
+
+ align:start position:0%
+positive large magnitude integrating
+ 
+
+ align:start position:0%
+positive large magnitude integrating
+that from A to B would make this thing
+
+ align:start position:0%
+that from A to B would make this thing
+ 
+
+ align:start position:0%
+that from A to B would make this thing
+still very very large and why should it
+
+ align:start position:0%
+still very very large and why should it
+ 
+
+ align:start position:0%
+still very very large and why should it
+stay smaller than any other linear
+
+ align:start position:0%
+stay smaller than any other linear
+ 
+
+ align:start position:0%
+stay smaller than any other linear
+combination I can get
+
+ align:start position:0%
+combination I can get
+ 
+
+ align:start position:0%
+combination I can get
+and I'll emphasize this more from a
+
+ align:start position:0%
+and I'll emphasize this more from a
+ 
+
+ align:start position:0%
+and I'll emphasize this more from a
+concrete point of view in a few moments
+
+ align:start position:0%
+concrete point of view in a few moments
+ 
+
+ align:start position:0%
+concrete point of view in a few moments
+but for the time being what the impact
+
+ align:start position:0%
+but for the time being what the impact
+ 
+
+ align:start position:0%
+but for the time being what the impact
+of this beautiful result is and notice
+
+ align:start position:0%
+of this beautiful result is and notice
+ 
+
+ align:start position:0%
+of this beautiful result is and notice
+it doesn't look like much when you look
+
+ align:start position:0%
+it doesn't look like much when you look
+ 
+
+ align:start position:0%
+it doesn't look like much when you look
+at it like this it just looks like some
+
+ align:start position:0%
+at it like this it just looks like some
+ 
+
+ align:start position:0%
+at it like this it just looks like some
+abstract remark but the beauty of this
+
+ align:start position:0%
+abstract remark but the beauty of this
+ 
+
+ align:start position:0%
+abstract remark but the beauty of this
+remark the impact of it is that when you
+
+ align:start position:0%
+remark the impact of it is that when you
+ 
+
+ align:start position:0%
+remark the impact of it is that when you
+write the so-called Fier representation
+
+ align:start position:0%
+write the so-called Fier representation
+ 
+
+ align:start position:0%
+write the so-called Fier representation
+as opposed to power series which I'll
+
+ align:start position:0%
+as opposed to power series which I'll
+ 
+
+ align:start position:0%
+as opposed to power series which I'll
+also mention at the end of the lecture
+
+ align:start position:0%
+also mention at the end of the lecture
+ 
+
+ align:start position:0%
+also mention at the end of the lecture
+what the contrast really is the
+
+ align:start position:0%
+what the contrast really is the
+ 
+
+ align:start position:0%
+what the contrast really is the
+fura representation if it does converge
+
+ align:start position:0%
+fura representation if it does converge
+ 
+
+ align:start position:0%
+fura representation if it does converge
+at all converges to the function what we
+
+ align:start position:0%
+at all converges to the function what we
+ 
+
+ align:start position:0%
+at all converges to the function what we
+call in the lodge that over the whole
+
+ align:start position:0%
+call in the lodge that over the whole
+ 
+
+ align:start position:0%
+call in the lodge that over the whole
+interval it starts to fit the function
+
+ align:start position:0%
+interval it starts to fit the function
+ 
+
+ align:start position:0%
+interval it starts to fit the function
+very nicely now I'll come back to that
+
+ align:start position:0%
+very nicely now I'll come back to that
+ 
+
+ align:start position:0%
+very nicely now I'll come back to that
+in terms of a more specific example in a
+
+ align:start position:0%
+in terms of a more specific example in a
+ 
+
+ align:start position:0%
+in terms of a more specific example in a
+few moments let me point out that fora
+
+ align:start position:0%
+few moments let me point out that fora
+ 
+
+ align:start position:0%
+few moments let me point out that fora
+being basically an engineer and a
+
+ align:start position:0%
+being basically an engineer and a
+ 
+
+ align:start position:0%
+being basically an engineer and a
+scientist work with one particular set
+
+ align:start position:0%
+scientist work with one particular set
+ 
+
+ align:start position:0%
+scientist work with one particular set
+of orthogonal
+
+ align:start position:0%
+of orthogonal
+ 
+
+ align:start position:0%
+of orthogonal
+functions a set of orthogonal functions
+
+ align:start position:0%
+functions a set of orthogonal functions
+ 
+
+ align:start position:0%
+functions a set of orthogonal functions
+that were very very natural to anybody
+
+ align:start position:0%
+that were very very natural to anybody
+ 
+
+ align:start position:0%
+that were very very natural to anybody
+working with wave motion or uh things of
+
+ align:start position:0%
+working with wave motion or uh things of
+ 
+
+ align:start position:0%
+working with wave motion or uh things of
+this type as you'll see in a moment the
+
+ align:start position:0%
+this type as you'll see in a moment the
+ 
+
+ align:start position:0%
+this type as you'll see in a moment the
+special case that I have in mind is this
+
+ align:start position:0%
+special case that I have in mind is this
+ 
+
+ align:start position:0%
+special case that I have in mind is this
+consider the family of functions well I
+
+ align:start position:0%
+consider the family of functions well I
+ 
+
+ align:start position:0%
+consider the family of functions well I
+can call this cosine 0x which is just
+
+ align:start position:0%
+can call this cosine 0x which is just
+ 
+
+ align:start position:0%
+can call this cosine 0x which is just
+another way of writing one but I have 1
+
+ align:start position:0%
+another way of writing one but I have 1
+ 
+
+ align:start position:0%
+another way of writing one but I have 1
+cosine x cosine 2X cosine 3x cosine 4X
+
+ align:start position:0%
+cosine x cosine 2X cosine 3x cosine 4X
+ 
+
+ align:start position:0%
+cosine x cosine 2X cosine 3x cosine 4X
+Etc and also included in this family
+
+ align:start position:0%
+Etc and also included in this family
+ 
+
+ align:start position:0%
+Etc and also included in this family
+sinx sin 2x sin 3x Etc I claim that this
+
+ align:start position:0%
+sinx sin 2x sin 3x Etc I claim that this
+ 
+
+ align:start position:0%
+sinx sin 2x sin 3x Etc I claim that this
+family of functions is orthogonal on the
+
+ align:start position:0%
+family of functions is orthogonal on the
+ 
+
+ align:start position:0%
+family of functions is orthogonal on the
+interval from PI to Pi
+
+ align:start position:0%
+interval from PI to Pi
+ 
+
+ align:start position:0%
+interval from PI to Pi
+what I mean by that is what that if I
+
+ align:start position:0%
+what I mean by that is what that if I
+ 
+
+ align:start position:0%
+what I mean by that is what that if I
+take any two different members of this
+
+ align:start position:0%
+take any two different members of this
+ 
+
+ align:start position:0%
+take any two different members of this
+family multiply them together integrate
+
+ align:start position:0%
+family multiply them together integrate
+ 
+
+ align:start position:0%
+family multiply them together integrate
+from minus pi to Pi the result will
+
+ align:start position:0%
+from minus pi to Pi the result will
+ 
+
+ align:start position:0%
+from minus pi to Pi the result will
+always be zero now the I won't go
+
+ align:start position:0%
+always be zero now the I won't go
+ 
+
+ align:start position:0%
+always be zero now the I won't go
+through this whole thing that will also
+
+ align:start position:0%
+through this whole thing that will also
+ 
+
+ align:start position:0%
+through this whole thing that will also
+be one of the exercises in the study
+
+ align:start position:0%
+be one of the exercises in the study
+ 
+
+ align:start position:0%
+be one of the exercises in the study
+guide would be to verify this but let me
+
+ align:start position:0%
+guide would be to verify this but let me
+ 
+
+ align:start position:0%
+guide would be to verify this but let me
+give you a head start in doing this let
+
+ align:start position:0%
+give you a head start in doing this let
+ 
+
+ align:start position:0%
+give you a head start in doing this let
+me pick two members of the coine two
+
+ align:start position:0%
+me pick two members of the coine two
+ 
+
+ align:start position:0%
+me pick two members of the coine two
+different members of the cosine family
+
+ align:start position:0%
+different members of the cosine family
+ 
+
+ align:start position:0%
+different members of the cosine family
+here and multiply them together and
+
+ align:start position:0%
+here and multiply them together and
+ 
+
+ align:start position:0%
+here and multiply them together and
+integrate from minus pi to Pi in other
+
+ align:start position:0%
+integrate from minus pi to Pi in other
+ 
+
+ align:start position:0%
+integrate from minus pi to Pi in other
+words let me take integral fromus piun
+
+ align:start position:0%
+words let me take integral fromus piun
+ 
+
+ align:start position:0%
+words let me take integral fromus piun
+to Pi cosine MX cosine NX DX where m is
+
+ align:start position:0%
+to Pi cosine MX cosine NX DX where m is
+ 
+
+ align:start position:0%
+to Pi cosine MX cosine NX DX where m is
+unequal to n now again without
+
+ align:start position:0%
+unequal to n now again without
+ 
+
+ align:start position:0%
+unequal to n now again without
+belaboring this point remember that the
+
+ align:start position:0%
+belaboring this point remember that the
+ 
+
+ align:start position:0%
+belaboring this point remember that the
+formula for cosine a cosine B comes from
+
+ align:start position:0%
+formula for cosine a cosine B comes from
+ 
+
+ align:start position:0%
+formula for cosine a cosine B comes from
+looking at the formulas for cosine a
+
+ align:start position:0%
+looking at the formulas for cosine a
+ 
+
+ align:start position:0%
+looking at the formulas for cosine a
+plus b cosine of a minus B and adding
+
+ align:start position:0%
+plus b cosine of a minus B and adding
+ 
+
+ align:start position:0%
+plus b cosine of a minus B and adding
+these two results and the sin a sin B
+
+ align:start position:0%
+these two results and the sin a sin B
+ 
+
+ align:start position:0%
+these two results and the sin a sin B
+terms drop out to make a long story
+
+ align:start position:0%
+terms drop out to make a long story
+ 
+
+ align:start position:0%
+terms drop out to make a long story
+short or somewhat shorter cosine MX *
+
+ align:start position:0%
+short or somewhat shorter cosine MX *
+ 
+
+ align:start position:0%
+short or somewhat shorter cosine MX *
+cosine NX is another way of writing 12
+
+ align:start position:0%
+cosine NX is another way of writing 12
+ 
+
+ align:start position:0%
+cosine NX is another way of writing 12
+the sum of cosine m + NX plus cosine M
+
+ align:start position:0%
+the sum of cosine m + NX plus cosine M
+ 
+
+ align:start position:0%
+the sum of cosine m + NX plus cosine M
+minus n x now you see to integrate this
+
+ align:start position:0%
+minus n x now you see to integrate this
+ 
+
+ align:start position:0%
+minus n x now you see to integrate this
+very simply this just gives me what a
+
+ align:start position:0%
+very simply this just gives me what a
+ 
+
+ align:start position:0%
+very simply this just gives me what a
+1/2 here this is sin m + NX over m + n
+
+ align:start position:0%
+1/2 here this is sin m + NX over m + n
+ 
+
+ align:start position:0%
+1/2 here this is sin m + NX over m + n
+this is sin m- x m minus n * X over M
+
+ align:start position:0%
+this is sin m- x m minus n * X over M
+ 
+
+ align:start position:0%
+this is sin m- x m minus n * X over M
+minus n and notice by the way the fact
+
+ align:start position:0%
+minus n and notice by the way the fact
+ 
+
+ align:start position:0%
+minus n and notice by the way the fact
+that m is une equal to n guarantees me
+
+ align:start position:0%
+that m is une equal to n guarantees me
+ 
+
+ align:start position:0%
+that m is une equal to n guarantees me
+my denominator here can't be zero and at
+
+ align:start position:0%
+my denominator here can't be zero and at
+ 
+
+ align:start position:0%
+my denominator here can't be zero and at
+any rate noticing that when I evaluate
+
+ align:start position:0%
+any rate noticing that when I evaluate
+ 
+
+ align:start position:0%
+any rate noticing that when I evaluate
+this from xal minus pi to Pi that these
+
+ align:start position:0%
+this from xal minus pi to Pi that these
+ 
+
+ align:start position:0%
+this from xal minus pi to Pi that these
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+integral integral meaning whole number
+
+ align:start position:0%
+integral integral meaning whole number
+ 
+
+ align:start position:0%
+integral integral meaning whole number
+multiples of Pi both these terms are
+
+ align:start position:0%
+multiples of Pi both these terms are
+ 
+
+ align:start position:0%
+multiples of Pi both these terms are
+zero and we've established the fact that
+
+ align:start position:0%
+zero and we've established the fact that
+ 
+
+ align:start position:0%
+zero and we've established the fact that
+this is zero so at least the members of
+
+ align:start position:0%
+this is zero so at least the members of
+ 
+
+ align:start position:0%
+this is zero so at least the members of
+the cosine family are orthogonal one can
+
+ align:start position:0%
+the cosine family are orthogonal one can
+ 
+
+ align:start position:0%
+the cosine family are orthogonal one can
+also show the members of the sign family
+
+ align:start position:0%
+also show the members of the sign family
+ 
+
+ align:start position:0%
+also show the members of the sign family
+are orthogonal and one can also show
+
+ align:start position:0%
+are orthogonal and one can also show
+ 
+
+ align:start position:0%
+are orthogonal and one can also show
+that any member of the cosine family
+
+ align:start position:0%
+that any member of the cosine family
+ 
+
+ align:start position:0%
+that any member of the cosine family
+taken uh multiplied by any member of the
+
+ align:start position:0%
+taken uh multiplied by any member of the
+ 
+
+ align:start position:0%
+taken uh multiplied by any member of the
+S family integrated from minus pi to Pi
+
+ align:start position:0%
+S family integrated from minus pi to Pi
+ 
+
+ align:start position:0%
+S family integrated from minus pi to Pi
+also gives zero so the point then is
+
+ align:start position:0%
+also gives zero so the point then is
+ 
+
+ align:start position:0%
+also gives zero so the point then is
+that an that this family here is an
+
+ align:start position:0%
+that an that this family here is an
+ 
+
+ align:start position:0%
+that an that this family here is an
+orthogonal F family on the interval from
+
+ align:start position:0%
+orthogonal F family on the interval from
+ 
+
+ align:start position:0%
+orthogonal F family on the interval from
+minus pi to Pi and the beauty of this
+
+ align:start position:0%
+minus pi to Pi and the beauty of this
+ 
+
+ align:start position:0%
+minus pi to Pi and the beauty of this
+result and let me point out that in
+
+ align:start position:0%
+result and let me point out that in
+ 
+
+ align:start position:0%
+result and let me point out that in
+textbooks on advanced mathematics the
+
+ align:start position:0%
+textbooks on advanced mathematics the
+ 
+
+ align:start position:0%
+textbooks on advanced mathematics the
+multitude of pages are used to prove the
+
+ align:start position:0%
+multitude of pages are used to prove the
+ 
+
+ align:start position:0%
+multitude of pages are used to prove the
+results but the state ments that of the
+
+ align:start position:0%
+results but the state ments that of the
+ 
+
+ align:start position:0%
+results but the state ments that of the
+theorems that you prove are not that
+
+ align:start position:0%
+theorems that you prove are not that
+ 
+
+ align:start position:0%
+theorems that you prove are not that
+difficult to keep track of let me just
+
+ align:start position:0%
+difficult to keep track of let me just
+ 
+
+ align:start position:0%
+difficult to keep track of let me just
+give one major result a result that is
+
+ align:start position:0%
+give one major result a result that is
+ 
+
+ align:start position:0%
+give one major result a result that is
+very very crucial and one that I will
+
+ align:start position:0%
+very very crucial and one that I will
+ 
+
+ align:start position:0%
+very very crucial and one that I will
+emphasize in the study guide and that is
+
+ align:start position:0%
+emphasize in the study guide and that is
+ 
+
+ align:start position:0%
+emphasize in the study guide and that is
+this suppose that I'm given a particular
+
+ align:start position:0%
+this suppose that I'm given a particular
+ 
+
+ align:start position:0%
+this suppose that I'm given a particular
+function little F ofx which is peace
+
+ align:start position:0%
+function little F ofx which is peace
+ 
+
+ align:start position:0%
+function little F ofx which is peace
+wise smooth on the interval from minus
+
+ align:start position:0%
+wise smooth on the interval from minus
+ 
+
+ align:start position:0%
+wise smooth on the interval from minus
+pi to Pi and remember what I mean by pie
+
+ align:start position:0%
+pi to Pi and remember what I mean by pie
+ 
+
+ align:start position:0%
+pi to Pi and remember what I mean by pie
+y smooth I mean it's a differentiable
+
+ align:start position:0%
+y smooth I mean it's a differentiable
+ 
+
+ align:start position:0%
+y smooth I mean it's a differentiable
+function except that it may have a
+
+ align:start position:0%
+function except that it may have a
+ 
+
+ align:start position:0%
+function except that it may have a
+finite number of jump discontinuities
+
+ align:start position:0%
+finite number of jump discontinuities
+ 
+
+ align:start position:0%
+finite number of jump discontinuities
+that if I plot the graph yal F ofx I get
+
+ align:start position:0%
+that if I plot the graph yal F ofx I get
+ 
+
+ align:start position:0%
+that if I plot the graph yal F ofx I get
+a smooth curve with the possible
+
+ align:start position:0%
+a smooth curve with the possible
+ 
+
+ align:start position:0%
+a smooth curve with the possible
+exception that there may be a few jumps
+
+ align:start position:0%
+exception that there may be a few jumps
+ 
+
+ align:start position:0%
+exception that there may be a few jumps
+in it by few meaning what a not too
+
+ align:start position:0%
+in it by few meaning what a not too
+ 
+
+ align:start position:0%
+in it by few meaning what a not too
+great infinite number a set of measures
+
+ align:start position:0%
+great infinite number a set of measures
+ 
+
+ align:start position:0%
+great infinite number a set of measures
+zero type thing but we won't be label
+
+ align:start position:0%
+zero type thing but we won't be label
+ 
+
+ align:start position:0%
+zero type thing but we won't be label
+that point right now but the idea is
+
+ align:start position:0%
+that point right now but the idea is
+ 
+
+ align:start position:0%
+that point right now but the idea is
+this suppose that I have this piece y
+
+ align:start position:0%
+this suppose that I have this piece y
+ 
+
+ align:start position:0%
+this suppose that I have this piece y
+smooth function little F ofx and suppose
+
+ align:start position:0%
+smooth function little F ofx and suppose
+ 
+
+ align:start position:0%
+smooth function little F ofx and suppose
+capital F ofx is the Fier representation
+
+ align:start position:0%
+capital F ofx is the Fier representation
+ 
+
+ align:start position:0%
+capital F ofx is the Fier representation
+of little f F ofx relative to my SS and
+
+ align:start position:0%
+of little f F ofx relative to my SS and
+ 
+
+ align:start position:0%
+of little f F ofx relative to my SS and
+cosiness in other words capital F ofx is
+
+ align:start position:0%
+cosiness in other words capital F ofx is
+ 
+
+ align:start position:0%
+cosiness in other words capital F ofx is
+the linear combinations of the cosine
+
+ align:start position:0%
+the linear combinations of the cosine
+ 
+
+ align:start position:0%
+the linear combinations of the cosine
+terms and the sign terms where the
+
+ align:start position:0%
+terms and the sign terms where the
+ 
+
+ align:start position:0%
+terms and the sign terms where the
+coefficients are chosen by that little
+
+ align:start position:0%
+coefficients are chosen by that little
+ 
+
+ align:start position:0%
+coefficients are chosen by that little
+recipe that I showed you at the
+
+ align:start position:0%
+recipe that I showed you at the
+ 
+
+ align:start position:0%
+recipe that I showed you at the
+beginning of the lecture and which as I
+
+ align:start position:0%
+beginning of the lecture and which as I
+ 
+
+ align:start position:0%
+beginning of the lecture and which as I
+say I'll reinforce as we do the
+
+ align:start position:0%
+say I'll reinforce as we do the
+ 
+
+ align:start position:0%
+say I'll reinforce as we do the
+exercises okay at any rate let's call
+
+ align:start position:0%
+exercises okay at any rate let's call
+ 
+
+ align:start position:0%
+exercises okay at any rate let's call
+this capital F ofx and in this
+
+ align:start position:0%
+this capital F ofx and in this
+ 
+
+ align:start position:0%
+this capital F ofx and in this
+particular case another words what
+
+ align:start position:0%
+particular case another words what
+ 
+
+ align:start position:0%
+particular case another words what
+particular case if little f ofx is pie y
+
+ align:start position:0%
+particular case if little f ofx is pie y
+ 
+
+ align:start position:0%
+particular case if little f ofx is pie y
+smooth and the orthogonal function are
+
+ align:start position:0%
+smooth and the orthogonal function are
+ 
+
+ align:start position:0%
+smooth and the orthogonal function are
+the SS and cosin on the interval fromus
+
+ align:start position:0%
+the SS and cosin on the interval fromus
+ 
+
+ align:start position:0%
+the SS and cosin on the interval fromus
+pi to Pi then the Fier representation of
+
+ align:start position:0%
+pi to Pi then the Fier representation of
+ 
+
+ align:start position:0%
+pi to Pi then the Fier representation of
+f ofx capital F ofx is given by the
+
+ align:start position:0%
+f ofx capital F ofx is given by the
+ 
+
+ align:start position:0%
+f ofx capital F ofx is given by the
+following and this is a remarkable
+
+ align:start position:0%
+following and this is a remarkable
+ 
+
+ align:start position:0%
+following and this is a remarkable
+result it says that capital F ofx at any
+
+ align:start position:0%
+result it says that capital F ofx at any
+ 
+
+ align:start position:0%
+result it says that capital F ofx at any
+value of x in the interval from minus pi
+
+ align:start position:0%
+value of x in the interval from minus pi
+ 
+
+ align:start position:0%
+value of x in the interval from minus pi
+to Pi is little F of X+ plus little F of
+
+ align:start position:0%
+to Pi is little F of X+ plus little F of
+ 
+
+ align:start position:0%
+to Pi is little F of X+ plus little F of
+xus over 2 now what does f ofx plus mean
+
+ align:start position:0%
+xus over 2 now what does f ofx plus mean
+ 
+
+ align:start position:0%
+xus over 2 now what does f ofx plus mean
+that means the limit of f ofx as you
+
+ align:start position:0%
+that means the limit of f ofx as you
+ 
+
+ align:start position:0%
+that means the limit of f ofx as you
+approach the given value of x from the
+
+ align:start position:0%
+approach the given value of x from the
+ 
+
+ align:start position:0%
+approach the given value of x from the
+positive side and this F ofx minus is
+
+ align:start position:0%
+positive side and this F ofx minus is
+ 
+
+ align:start position:0%
+positive side and this F ofx minus is
+the limit of f ofx as you approach the
+
+ align:start position:0%
+the limit of f ofx as you approach the
+ 
+
+ align:start position:0%
+the limit of f ofx as you approach the
+given value of x from the negative side
+
+ align:start position:0%
+given value of x from the negative side
+ 
+
+ align:start position:0%
+given value of x from the negative side
+in fact to keep this easier to
+
+ align:start position:0%
+in fact to keep this easier to
+ 
+
+ align:start position:0%
+in fact to keep this easier to
+understand so I don't use x in two
+
+ align:start position:0%
+understand so I don't use x in two
+ 
+
+ align:start position:0%
+understand so I don't use x in two
+different ways what I'm saying is
+
+ align:start position:0%
+different ways what I'm saying is
+ 
+
+ align:start position:0%
+different ways what I'm saying is
+capital F ofx Sub 0 is computed as
+
+ align:start position:0%
+capital F ofx Sub 0 is computed as
+ 
+
+ align:start position:0%
+capital F ofx Sub 0 is computed as
+follows see what little F ofx Sub 0 is
+
+ align:start position:0%
+follows see what little F ofx Sub 0 is
+ 
+
+ align:start position:0%
+follows see what little F ofx Sub 0 is
+as X approaches x0 from the left see
+
+ align:start position:0%
+as X approaches x0 from the left see
+ 
+
+ align:start position:0%
+as X approaches x0 from the left see
+what F of x0 of f of x approaches as X
+
+ align:start position:0%
+what F of x0 of f of x approaches as X
+ 
+
+ align:start position:0%
+what F of x0 of f of x approaches as X
+approaches x0 from the right
+
+ align:start position:0%
+approaches x0 from the right
+ 
+
+ align:start position:0%
+approaches x0 from the right
+Okay add these two results and divide by
+
+ align:start position:0%
+Okay add these two results and divide by
+ 
+
+ align:start position:0%
+Okay add these two results and divide by
+two I hope that you can see that what
+
+ align:start position:0%
+two I hope that you can see that what
+ 
+
+ align:start position:0%
+two I hope that you can see that what
+I'm doing here is taking the average of
+
+ align:start position:0%
+I'm doing here is taking the average of
+ 
+
+ align:start position:0%
+I'm doing here is taking the average of
+these two results half the sum is the
+
+ align:start position:0%
+these two results half the sum is the
+ 
+
+ align:start position:0%
+these two results half the sum is the
+average also observe that if F happens
+
+ align:start position:0%
+average also observe that if F happens
+ 
+
+ align:start position:0%
+average also observe that if F happens
+to be continuous at x0 F of x0 plus is
+
+ align:start position:0%
+to be continuous at x0 F of x0 plus is
+ 
+
+ align:start position:0%
+to be continuous at x0 F of x0 plus is
+the same as F of x0 minus you see the
+
+ align:start position:0%
+the same as F of x0 minus you see the
+ 
+
+ align:start position:0%
+the same as F of x0 minus you see the
+only time that these two things can be
+
+ align:start position:0%
+only time that these two things can be
+ 
+
+ align:start position:0%
+only time that these two things can be
+different is if there's a jump in the
+
+ align:start position:0%
+different is if there's a jump in the
+ 
+
+ align:start position:0%
+different is if there's a jump in the
+function at X Z because if there's no
+
+ align:start position:0%
+function at X Z because if there's no
+ 
+
+ align:start position:0%
+function at X Z because if there's no
+jump as I approach x0 from the left and
+
+ align:start position:0%
+jump as I approach x0 from the left and
+ 
+
+ align:start position:0%
+jump as I approach x0 from the left and
+approach x0 from the right the two
+
+ align:start position:0%
+approach x0 from the right the two
+ 
+
+ align:start position:0%
+approach x0 from the right the two
+values that I get must be the same in
+
+ align:start position:0%
+values that I get must be the same in
+ 
+
+ align:start position:0%
+values that I get must be the same in
+other words notice that at the points
+
+ align:start position:0%
+other words notice that at the points
+ 
+
+ align:start position:0%
+other words notice that at the points
+where f is continuous this is nothing
+
+ align:start position:0%
+where f is continuous this is nothing
+ 
+
+ align:start position:0%
+where f is continuous this is nothing
+more than f ofx z itself and what this
+
+ align:start position:0%
+more than f ofx z itself and what this
+ 
+
+ align:start position:0%
+more than f ofx z itself and what this
+famous result says is that except at the
+
+ align:start position:0%
+famous result says is that except at the
+ 
+
+ align:start position:0%
+famous result says is that except at the
+points at which cap little f ofx are
+
+ align:start position:0%
+points at which cap little f ofx are
+ 
+
+ align:start position:0%
+points at which cap little f ofx are
+disc is discontinuous capital F the fuer
+
+ align:start position:0%
+disc is discontinuous capital F the fuer
+ 
+
+ align:start position:0%
+disc is discontinuous capital F the fuer
+representation is little F at itself
+
+ align:start position:0%
+representation is little F at itself
+ 
+
+ align:start position:0%
+representation is little F at itself
+that the Fier representation converges
+
+ align:start position:0%
+that the Fier representation converges
+ 
+
+ align:start position:0%
+that the Fier representation converges
+to the function itself and what it does
+
+ align:start position:0%
+to the function itself and what it does
+ 
+
+ align:start position:0%
+to the function itself and what it does
+that's remarkable is that where there's
+
+ align:start position:0%
+that's remarkable is that where there's
+ 
+
+ align:start position:0%
+that's remarkable is that where there's
+a jump in the
+
+ align:start position:0%
+a jump in the
+ 
+
+ align:start position:0%
+a jump in the
+function it equals the average of the
+
+ align:start position:0%
+function it equals the average of the
+ 
+
+ align:start position:0%
+function it equals the average of the
+jump well let me show you that in terms
+
+ align:start position:0%
+jump well let me show you that in terms
+ 
+
+ align:start position:0%
+jump well let me show you that in terms
+of an example let me pick a very simple
+
+ align:start position:0%
+of an example let me pick a very simple
+ 
+
+ align:start position:0%
+of an example let me pick a very simple
+function to begin with let me Define the
+
+ align:start position:0%
+function to begin with let me Define the
+ 
+
+ align:start position:0%
+function to begin with let me Define the
+function little F ofx to be negative 1
+
+ align:start position:0%
+function little F ofx to be negative 1
+ 
+
+ align:start position:0%
+function little F ofx to be negative 1
+when X is from when X is in the interval
+
+ align:start position:0%
+when X is from when X is in the interval
+ 
+
+ align:start position:0%
+when X is from when X is in the interval
+from minus pi to 0 and let it be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say positive 1 when X is in the interval
+
+ align:start position:0%
+say positive 1 when X is in the interval
+ 
+
+ align:start position:0%
+say positive 1 when X is in the interval
+from 0 to Pi so graphically you see how
+
+ align:start position:0%
+from 0 to Pi so graphically you see how
+ 
+
+ align:start position:0%
+from 0 to Pi so graphically you see how
+this thing is going to look it goes like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this by the way notice that this is what
+
+ align:start position:0%
+this by the way notice that this is what
+ 
+
+ align:start position:0%
+this by the way notice that this is what
+mathematically we call an odd function
+
+ align:start position:0%
+mathematically we call an odd function
+ 
+
+ align:start position:0%
+mathematically we call an odd function
+right f ofx is the negative of f of
+
+ align:start position:0%
+right f ofx is the negative of f of
+ 
+
+ align:start position:0%
+right f ofx is the negative of f of
+minus X notice that the sign terms are
+
+ align:start position:0%
+minus X notice that the sign terms are
+ 
+
+ align:start position:0%
+minus X notice that the sign terms are
+odd the cosine terms are even you see
+
+ align:start position:0%
+odd the cosine terms are even you see
+ 
+
+ align:start position:0%
+odd the cosine terms are even you see
+cosine of x is the same as cosine of
+
+ align:start position:0%
+cosine of x is the same as cosine of
+ 
+
+ align:start position:0%
+cosine of x is the same as cosine of
+minus X but s of X is minus sin - x so
+
+ align:start position:0%
+minus X but s of X is minus sin - x so
+ 
+
+ align:start position:0%
+minus X but s of X is minus sin - x so
+the S terms are odd the cosine terms are
+
+ align:start position:0%
+the S terms are odd the cosine terms are
+ 
+
+ align:start position:0%
+the S terms are odd the cosine terms are
+even so the first hint or the first nice
+
+ align:start position:0%
+even so the first hint or the first nice
+ 
+
+ align:start position:0%
+even so the first hint or the first nice
+simplification that takes place by
+
+ align:start position:0%
+simplification that takes place by
+ 
+
+ align:start position:0%
+simplification that takes place by
+choosing this example is that because
+
+ align:start position:0%
+choosing this example is that because
+ 
+
+ align:start position:0%
+choosing this example is that because
+this is an odd function the cosine terms
+
+ align:start position:0%
+this is an odd function the cosine terms
+ 
+
+ align:start position:0%
+this is an odd function the cosine terms
+will all be absent that it turns out
+
+ align:start position:0%
+will all be absent that it turns out
+ 
+
+ align:start position:0%
+will all be absent that it turns out
+that if I use the procedure indicated
+
+ align:start position:0%
+that if I use the procedure indicated
+ 
+
+ align:start position:0%
+that if I use the procedure indicated
+earlier in the lecture and again that
+
+ align:start position:0%
+earlier in the lecture and again that
+ 
+
+ align:start position:0%
+earlier in the lecture and again that
+will be one of the exercises so that you
+
+ align:start position:0%
+will be one of the exercises so that you
+ 
+
+ align:start position:0%
+will be one of the exercises so that you
+get the drill that's necessary here
+
+ align:start position:0%
+get the drill that's necessary here
+ 
+
+ align:start position:0%
+get the drill that's necessary here
+again I only want to give you the
+
+ align:start position:0%
+again I only want to give you the
+ 
+
+ align:start position:0%
+again I only want to give you the
+overview it turns out that the forier
+
+ align:start position:0%
+overview it turns out that the forier
+ 
+
+ align:start position:0%
+overview it turns out that the forier
+series representation of this particular
+
+ align:start position:0%
+series representation of this particular
+ 
+
+ align:start position:0%
+series representation of this particular
+function capital F ofx turns out to be 4
+
+ align:start position:0%
+function capital F ofx turns out to be 4
+ 
+
+ align:start position:0%
+function capital F ofx turns out to be 4
+over pi times the summation sin NX Over
+
+ align:start position:0%
+over pi times the summation sin NX Over
+ 
+
+ align:start position:0%
+over pi times the summation sin NX Over
+N for n odd and what that means is it's
+
+ align:start position:0%
+N for n odd and what that means is it's
+ 
+
+ align:start position:0%
+N for n odd and what that means is it's
+4 over Pi time sin x + sin 3x over 3 +
+
+ align:start position:0%
+4 over Pi time sin x + sin 3x over 3 +
+ 
+
+ align:start position:0%
+4 over Pi time sin x + sin 3x over 3 +
+sin 5x over 5
+
+ align:start position:0%
+sin 5x over 5
+ 
+
+ align:start position:0%
+sin 5x over 5
+Etc by the way these are very difficult
+
+ align:start position:0%
+Etc by the way these are very difficult
+ 
+
+ align:start position:0%
+Etc by the way these are very difficult
+things to draw you're not used to
+
+ align:start position:0%
+things to draw you're not used to
+ 
+
+ align:start position:0%
+things to draw you're not used to
+working with these uh I should point out
+
+ align:start position:0%
+working with these uh I should point out
+ 
+
+ align:start position:0%
+working with these uh I should point out
+this that if there's anything that works
+
+ align:start position:0%
+this that if there's anything that works
+ 
+
+ align:start position:0%
+this that if there's anything that works
+nicely in the laboratory It's s and
+
+ align:start position:0%
+nicely in the laboratory It's s and
+ 
+
+ align:start position:0%
+nicely in the laboratory It's s and
+cosine terms because those are things
+
+ align:start position:0%
+cosine terms because those are things
+ 
+
+ align:start position:0%
+cosine terms because those are things
+that you can produce very nicely on an
+
+ align:start position:0%
+that you can produce very nicely on an
+ 
+
+ align:start position:0%
+that you can produce very nicely on an
+oscilloscope analytically these are very
+
+ align:start position:0%
+oscilloscope analytically these are very
+ 
+
+ align:start position:0%
+oscilloscope analytically these are very
+nasty terms to handle but electronically
+
+ align:start position:0%
+nasty terms to handle but electronically
+ 
+
+ align:start position:0%
+nasty terms to handle but electronically
+uh it's a very nice way of getting a
+
+ align:start position:0%
+uh it's a very nice way of getting a
+ 
+
+ align:start position:0%
+uh it's a very nice way of getting a
+feeling for Fier series but I don't have
+
+ align:start position:0%
+feeling for Fier series but I don't have
+ 
+
+ align:start position:0%
+feeling for Fier series but I don't have
+uh electronic chalk here so I just talk
+
+ align:start position:0%
+uh electronic chalk here so I just talk
+ 
+
+ align:start position:0%
+uh electronic chalk here so I just talk
+about it and draw these things for you
+
+ align:start position:0%
+about it and draw these things for you
+ 
+
+ align:start position:0%
+about it and draw these things for you
+but for example to show you what I mean
+
+ align:start position:0%
+but for example to show you what I mean
+ 
+
+ align:start position:0%
+but for example to show you what I mean
+here let me just take the first two
+
+ align:start position:0%
+here let me just take the first two
+ 
+
+ align:start position:0%
+here let me just take the first two
+terms let me plot the curve y = 4 piun *
+
+ align:start position:0%
+terms let me plot the curve y = 4 piun *
+ 
+
+ align:start position:0%
+terms let me plot the curve y = 4 piun *
+the quantity sin x + sin 3x over 3 and
+
+ align:start position:0%
+the quantity sin x + sin 3x over 3 and
+ 
+
+ align:start position:0%
+the quantity sin x + sin 3x over 3 and
+if I plot that curve which I've done
+
+ align:start position:0%
+if I plot that curve which I've done
+ 
+
+ align:start position:0%
+if I plot that curve which I've done
+here in the accentuated chalk look at
+
+ align:start position:0%
+here in the accentuated chalk look at
+ 
+
+ align:start position:0%
+here in the accentuated chalk look at
+how nicely that curve starts already to
+
+ align:start position:0%
+how nicely that curve starts already to
+ 
+
+ align:start position:0%
+how nicely that curve starts already to
+fit the graph yal F ofx you see how it
+
+ align:start position:0%
+fit the graph yal F ofx you see how it
+ 
+
+ align:start position:0%
+fit the graph yal F ofx you see how it
+fits over here no perfect fit any place
+
+ align:start position:0%
+fits over here no perfect fit any place
+ 
+
+ align:start position:0%
+fits over here no perfect fit any place
+but notice that uh by and large it fits
+
+ align:start position:0%
+but notice that uh by and large it fits
+ 
+
+ align:start position:0%
+but notice that uh by and large it fits
+the curve very nicely without too big an
+
+ align:start position:0%
+the curve very nicely without too big an
+ 
+
+ align:start position:0%
+the curve very nicely without too big an
+error all the way along here it has
+
+ align:start position:0%
+error all the way along here it has
+ 
+
+ align:start position:0%
+error all the way along here it has
+roughly the right shape and notice also
+
+ align:start position:0%
+roughly the right shape and notice also
+ 
+
+ align:start position:0%
+roughly the right shape and notice also
+it goes through the
+
+ align:start position:0%
+it goes through the
+ 
+
+ align:start position:0%
+it goes through the
+origin see because when X is Zer capital
+
+ align:start position:0%
+origin see because when X is Zer capital
+ 
+
+ align:start position:0%
+origin see because when X is Zer capital
+f of x is zero and that's exactly the
+
+ align:start position:0%
+f of x is zero and that's exactly the
+ 
+
+ align:start position:0%
+f of x is zero and that's exactly the
+average of the jump over here see you
+
+ align:start position:0%
+average of the jump over here see you
+ 
+
+ align:start position:0%
+average of the jump over here see you
+jump from minus one to one so the origin
+
+ align:start position:0%
+jump from minus one to one so the origin
+ 
+
+ align:start position:0%
+jump from minus one to one so the origin
+is the average over here by the way even
+
+ align:start position:0%
+is the average over here by the way even
+ 
+
+ align:start position:0%
+is the average over here by the way even
+though I don't draw very well what I
+
+ align:start position:0%
+though I don't draw very well what I
+ 
+
+ align:start position:0%
+though I don't draw very well what I
+have tried to do here is show what
+
+ align:start position:0%
+have tried to do here is show what
+ 
+
+ align:start position:0%
+have tried to do here is show what
+happens if I tack on just a couple of
+
+ align:start position:0%
+happens if I tack on just a couple of
+ 
+
+ align:start position:0%
+happens if I tack on just a couple of
+more terms I've tacked on to this the
+
+ align:start position:0%
+more terms I've tacked on to this the
+ 
+
+ align:start position:0%
+more terms I've tacked on to this the
+term sin 5X X over 5 and sin 7x over 7
+
+ align:start position:0%
+term sin 5X X over 5 and sin 7x over 7
+ 
+
+ align:start position:0%
+term sin 5X X over 5 and sin 7x over 7
+and then the graph would look something
+
+ align:start position:0%
+and then the graph would look something
+ 
+
+ align:start position:0%
+and then the graph would look something
+like this you see how nicely this starts
+
+ align:start position:0%
+like this you see how nicely this starts
+ 
+
+ align:start position:0%
+like this you see how nicely this starts
+to fit it fits very nicely along here
+
+ align:start position:0%
+to fit it fits very nicely along here
+ 
+
+ align:start position:0%
+to fit it fits very nicely along here
+but wherever there's a jump it jumps to
+
+ align:start position:0%
+but wherever there's a jump it jumps to
+ 
+
+ align:start position:0%
+but wherever there's a jump it jumps to
+the it averages out this way by the way
+
+ align:start position:0%
+the it averages out this way by the way
+ 
+
+ align:start position:0%
+the it averages out this way by the way
+one other observation obviously the
+
+ align:start position:0%
+one other observation obviously the
+ 
+
+ align:start position:0%
+one other observation obviously the
+function that I'm constructing here is
+
+ align:start position:0%
+function that I'm constructing here is
+ 
+
+ align:start position:0%
+function that I'm constructing here is
+periodic with Period 2 pi if I replace X
+
+ align:start position:0%
+periodic with Period 2 pi if I replace X
+ 
+
+ align:start position:0%
+periodic with Period 2 pi if I replace X
+by x + 2 pi I don't change the sign any
+
+ align:start position:0%
+by x + 2 pi I don't change the sign any
+ 
+
+ align:start position:0%
+by x + 2 pi I don't change the sign any
+and so obvious the function which I'm
+
+ align:start position:0%
+and so obvious the function which I'm
+ 
+
+ align:start position:0%
+and so obvious the function which I'm
+calling capital F ofx represents More
+
+ align:start position:0%
+calling capital F ofx represents More
+ 
+
+ align:start position:0%
+calling capital F ofx represents More
+Than This given function rather it
+
+ align:start position:0%
+Than This given function rather it
+ 
+
+ align:start position:0%
+Than This given function rather it
+represents the given function reproduced
+
+ align:start position:0%
+represents the given function reproduced
+ 
+
+ align:start position:0%
+represents the given function reproduced
+infinitely in both directions with
+
+ align:start position:0%
+infinitely in both directions with
+ 
+
+ align:start position:0%
+infinitely in both directions with
+Period 2 pi but again I'll leave that
+
+ align:start position:0%
+Period 2 pi but again I'll leave that
+ 
+
+ align:start position:0%
+Period 2 pi but again I'll leave that
+for the exercises to summarize what's
+
+ align:start position:0%
+for the exercises to summarize what's
+ 
+
+ align:start position:0%
+for the exercises to summarize what's
+happened over here you see how nicely
+
+ align:start position:0%
+happened over here you see how nicely
+ 
+
+ align:start position:0%
+happened over here you see how nicely
+this thing fits if I actually took
+
+ align:start position:0%
+this thing fits if I actually took
+ 
+
+ align:start position:0%
+this thing fits if I actually took
+capital F ofx and computed this limit
+
+ align:start position:0%
+capital F ofx and computed this limit
+ 
+
+ align:start position:0%
+capital F ofx and computed this limit
+for each value of x what the graph would
+
+ align:start position:0%
+for each value of x what the graph would
+ 
+
+ align:start position:0%
+for each value of x what the graph would
+look like now obviously I can't get this
+
+ align:start position:0%
+look like now obviously I can't get this
+ 
+
+ align:start position:0%
+look like now obviously I can't get this
+on an oscilloscope because no matter how
+
+ align:start position:0%
+on an oscilloscope because no matter how
+ 
+
+ align:start position:0%
+on an oscilloscope because no matter how
+many terms I use no matter how large a
+
+ align:start position:0%
+many terms I use no matter how large a
+ 
+
+ align:start position:0%
+many terms I use no matter how large a
+number n is still finite but if I
+
+ align:start position:0%
+number n is still finite but if I
+ 
+
+ align:start position:0%
+number n is still finite but if I
+actually took the infinite sum the graph
+
+ align:start position:0%
+actually took the infinite sum the graph
+ 
+
+ align:start position:0%
+actually took the infinite sum the graph
+that I would get mathematically is I
+
+ align:start position:0%
+that I would get mathematically is I
+ 
+
+ align:start position:0%
+that I would get mathematically is I
+would actually get the straight line x
+
+ align:start position:0%
+would actually get the straight line x
+ 
+
+ align:start position:0%
+would actually get the straight line x
+equals I'm sorry
+
+ align:start position:0%
+equals I'm sorry
+ 
+
+ align:start position:0%
+equals I'm sorry
+yal-1 from minus pi to 0 it would be X Y
+
+ align:start position:0%
+yal-1 from minus pi to 0 it would be X Y
+ 
+
+ align:start position:0%
+yal-1 from minus pi to 0 it would be X Y
+= positive 1 from 0 to Pi and at zero at
+
+ align:start position:0%
+= positive 1 from 0 to Pi and at zero at
+ 
+
+ align:start position:0%
+= positive 1 from 0 to Pi and at zero at
+zero itself the function would be zero
+
+ align:start position:0%
+zero itself the function would be zero
+ 
+
+ align:start position:0%
+zero itself the function would be zero
+you see it split
+
+ align:start position:0%
+you see it split
+ 
+
+ align:start position:0%
+you see it split
+the Gap it splits the jump and then of
+
+ align:start position:0%
+the Gap it splits the jump and then of
+ 
+
+ align:start position:0%
+the Gap it splits the jump and then of
+course the function would repeat itself
+
+ align:start position:0%
+course the function would repeat itself
+ 
+
+ align:start position:0%
+course the function would repeat itself
+at a regular interval of uh regular
+
+ align:start position:0%
+at a regular interval of uh regular
+ 
+
+ align:start position:0%
+at a regular interval of uh regular
+period of 2 pi that this is what capital
+
+ align:start position:0%
+period of 2 pi that this is what capital
+ 
+
+ align:start position:0%
+period of 2 pi that this is what capital
+F ofx would look like if we graphed it
+
+ align:start position:0%
+F ofx would look like if we graphed it
+ 
+
+ align:start position:0%
+F ofx would look like if we graphed it
+by the way to give you an example of an
+
+ align:start position:0%
+by the way to give you an example of an
+ 
+
+ align:start position:0%
+by the way to give you an example of an
+even function if we were to use the same
+
+ align:start position:0%
+even function if we were to use the same
+ 
+
+ align:start position:0%
+even function if we were to use the same
+technique for getting the Fier series
+
+ align:start position:0%
+technique for getting the Fier series
+ 
+
+ align:start position:0%
+technique for getting the Fier series
+for f ofx equals the absolute value of x
+
+ align:start position:0%
+for f ofx equals the absolute value of x
+ 
+
+ align:start position:0%
+for f ofx equals the absolute value of x
+on the interval from minus pi to Pi it
+
+ align:start position:0%
+on the interval from minus pi to Pi it
+ 
+
+ align:start position:0%
+on the interval from minus pi to Pi it
+turns out that capital f ofx
+
+ align:start position:0%
+turns out that capital f ofx
+ 
+
+ align:start position:0%
+turns out that capital f ofx
+would be Pi / 2 minus 4 over Pi s
+
+ align:start position:0%
+would be Pi / 2 minus 4 over Pi s
+ 
+
+ align:start position:0%
+would be Pi / 2 minus 4 over Pi s
+summation Over N OD cine NX over n^2 by
+
+ align:start position:0%
+summation Over N OD cine NX over n^2 by
+ 
+
+ align:start position:0%
+summation Over N OD cine NX over n^2 by
+the way if this looks a little bit like
+
+ align:start position:0%
+the way if this looks a little bit like
+ 
+
+ align:start position:0%
+the way if this looks a little bit like
+the previous problem notice that this is
+
+ align:start position:0%
+the previous problem notice that this is
+ 
+
+ align:start position:0%
+the previous problem notice that this is
+more than just coincidence if you
+
+ align:start position:0%
+more than just coincidence if you
+ 
+
+ align:start position:0%
+more than just coincidence if you
+differentiate the square root of x I'm
+
+ align:start position:0%
+differentiate the square root of x I'm
+ 
+
+ align:start position:0%
+differentiate the square root of x I'm
+sorry if you differentiate the absolute
+
+ align:start position:0%
+sorry if you differentiate the absolute
+ 
+
+ align:start position:0%
+sorry if you differentiate the absolute
+value of x what is the derivative it's
+
+ align:start position:0%
+value of x what is the derivative it's
+ 
+
+ align:start position:0%
+value of x what is the derivative it's
+minus1 for x negative and positive 1 for
+
+ align:start position:0%
+minus1 for x negative and positive 1 for
+ 
+
+ align:start position:0%
+minus1 for x negative and positive 1 for
+X positive it's the function that we
+
+ align:start position:0%
+X positive it's the function that we
+ 
+
+ align:start position:0%
+X positive it's the function that we
+were just talking about before only it
+
+ align:start position:0%
+were just talking about before only it
+ 
+
+ align:start position:0%
+were just talking about before only it
+doesn't exist at x equals 0 you see uh
+
+ align:start position:0%
+doesn't exist at x equals 0 you see uh
+ 
+
+ align:start position:0%
+doesn't exist at x equals 0 you see uh
+what I'm driving at over here is that
+
+ align:start position:0%
+what I'm driving at over here is that
+ 
+
+ align:start position:0%
+what I'm driving at over here is that
+it's not surprising that
+
+ align:start position:0%
+it's not surprising that
+ 
+
+ align:start position:0%
+it's not surprising that
+the terms in here are the integrals of
+
+ align:start position:0%
+the terms in here are the integrals of
+ 
+
+ align:start position:0%
+the terms in here are the integrals of
+the terms that were in our previous
+
+ align:start position:0%
+the terms that were in our previous
+ 
+
+ align:start position:0%
+the terms that were in our previous
+summation but notice that the absolute
+
+ align:start position:0%
+summation but notice that the absolute
+ 
+
+ align:start position:0%
+summation but notice that the absolute
+value of x is an even function
+
+ align:start position:0%
+value of x is an even function
+ 
+
+ align:start position:0%
+value of x is an even function
+consequently it's the cosine terms which
+
+ align:start position:0%
+consequently it's the cosine terms which
+ 
+
+ align:start position:0%
+consequently it's the cosine terms which
+appear here rather than the S terms and
+
+ align:start position:0%
+appear here rather than the S terms and
+ 
+
+ align:start position:0%
+appear here rather than the S terms and
+again I've run the risk of drawing my
+
+ align:start position:0%
+again I've run the risk of drawing my
+ 
+
+ align:start position:0%
+again I've run the risk of drawing my
+own diagrams here I have plotted this
+
+ align:start position:0%
+own diagrams here I have plotted this
+ 
+
+ align:start position:0%
+own diagrams here I have plotted this
+for n = 3 meaning I've plotted y = < / 2
+
+ align:start position:0%
+for n = 3 meaning I've plotted y = < / 2
+ 
+
+ align:start position:0%
+for n = 3 meaning I've plotted y = < / 2
+- 4 piun * the quantity cine X plus
+
+ align:start position:0%
+- 4 piun * the quantity cine X plus
+ 
+
+ align:start position:0%
+- 4 piun * the quantity cine X plus
+cosine 3x over 9 and that's represented
+
+ align:start position:0%
+cosine 3x over 9 and that's represented
+ 
+
+ align:start position:0%
+cosine 3x over 9 and that's represented
+by this curve drawn in the accentuated
+
+ align:start position:0%
+by this curve drawn in the accentuated
+ 
+
+ align:start position:0%
+by this curve drawn in the accentuated
+shock over here and again notice how
+
+ align:start position:0%
+shock over here and again notice how
+ 
+
+ align:start position:0%
+shock over here and again notice how
+even for just a small number of terms we
+
+ align:start position:0%
+even for just a small number of terms we
+ 
+
+ align:start position:0%
+even for just a small number of terms we
+have already captured in the lodge the
+
+ align:start position:0%
+have already captured in the lodge the
+ 
+
+ align:start position:0%
+have already captured in the lodge the
+shape of the curve y equals the absolute
+
+ align:start position:0%
+shape of the curve y equals the absolute
+ 
+
+ align:start position:0%
+shape of the curve y equals the absolute
+value of x which by the way contrast
+
+ align:start position:0%
+value of x which by the way contrast
+ 
+
+ align:start position:0%
+value of x which by the way contrast
+very sharply with power series remember
+
+ align:start position:0%
+very sharply with power series remember
+ 
+
+ align:start position:0%
+very sharply with power series remember
+how power series worked first of all you
+
+ align:start position:0%
+how power series worked first of all you
+ 
+
+ align:start position:0%
+how power series worked first of all you
+had to require that the function that
+
+ align:start position:0%
+had to require that the function that
+ 
+
+ align:start position:0%
+had to require that the function that
+you were talking about possess
+
+ align:start position:0%
+you were talking about possess
+ 
+
+ align:start position:0%
+you were talking about possess
+derivatives of all orders secondly when
+
+ align:start position:0%
+derivatives of all orders secondly when
+ 
+
+ align:start position:0%
+derivatives of all orders secondly when
+you wanted to fit the function by its
+
+ align:start position:0%
+you wanted to fit the function by its
+ 
+
+ align:start position:0%
+you wanted to fit the function by its
+power series you picked a particular
+
+ align:start position:0%
+power series you picked a particular
+ 
+
+ align:start position:0%
+power series you picked a particular
+Point remember what you got you first
+
+ align:start position:0%
+Point remember what you got you first
+ 
+
+ align:start position:0%
+Point remember what you got you first
+got a tangent line approximation then
+
+ align:start position:0%
+got a tangent line approximation then
+ 
+
+ align:start position:0%
+got a tangent line approximation then
+you got a quadratic approximation that
+
+ align:start position:0%
+you got a quadratic approximation that
+ 
+
+ align:start position:0%
+you got a quadratic approximation that
+fit the curve in a neighborhood of this
+
+ align:start position:0%
+fit the curve in a neighborhood of this
+ 
+
+ align:start position:0%
+fit the curve in a neighborhood of this
+point better than the straight line did
+
+ align:start position:0%
+point better than the straight line did
+ 
+
+ align:start position:0%
+point better than the straight line did
+but after a while the thing would sag
+
+ align:start position:0%
+but after a while the thing would sag
+ 
+
+ align:start position:0%
+but after a while the thing would sag
+off then you added a cubic
+
+ align:start position:0%
+off then you added a cubic
+ 
+
+ align:start position:0%
+off then you added a cubic
+term and that fit even better for a
+
+ align:start position:0%
+term and that fit even better for a
+ 
+
+ align:start position:0%
+term and that fit even better for a
+while and then again something weird
+
+ align:start position:0%
+while and then again something weird
+ 
+
+ align:start position:0%
+while and then again something weird
+might happen and you kept on going like
+
+ align:start position:0%
+might happen and you kept on going like
+ 
+
+ align:start position:0%
+might happen and you kept on going like
+this so that ultimately even though you
+
+ align:start position:0%
+this so that ultimately even though you
+ 
+
+ align:start position:0%
+this so that ultimately even though you
+had uniform convergence what you were
+
+ align:start position:0%
+had uniform convergence what you were
+ 
+
+ align:start position:0%
+had uniform convergence what you were
+doing was you were getting a splendid
+
+ align:start position:0%
+doing was you were getting a splendid
+ 
+
+ align:start position:0%
+doing was you were getting a splendid
+Fit near one particular point and slowly
+
+ align:start position:0%
+Fit near one particular point and slowly
+ 
+
+ align:start position:0%
+Fit near one particular point and slowly
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+surely and actually very very slowly and
+
+ align:start position:0%
+surely and actually very very slowly and
+ 
+
+ align:start position:0%
+surely and actually very very slowly and
+and also actually very surely but you
+
+ align:start position:0%
+and also actually very surely but you
+ 
+
+ align:start position:0%
+and also actually very surely but you
+may not have noticed it these
+
+ align:start position:0%
+may not have noticed it these
+ 
+
+ align:start position:0%
+may not have noticed it these
+approximations were starting to fit
+
+ align:start position:0%
+approximations were starting to fit
+ 
+
+ align:start position:0%
+approximations were starting to fit
+better and better as you went out
+
+ align:start position:0%
+better and better as you went out
+ 
+
+ align:start position:0%
+better and better as you went out
+here but the least Square approximations
+
+ align:start position:0%
+here but the least Square approximations
+ 
+
+ align:start position:0%
+here but the least Square approximations
+would not be too good in other words out
+
+ align:start position:0%
+would not be too good in other words out
+ 
+
+ align:start position:0%
+would not be too good in other words out
+here someplace there were starting to
+
+ align:start position:0%
+here someplace there were starting to
+ 
+
+ align:start position:0%
+here someplace there were starting to
+become some drastically large errors on
+
+ align:start position:0%
+become some drastically large errors on
+ 
+
+ align:start position:0%
+become some drastically large errors on
+the other hand the Fier representation
+
+ align:start position:0%
+the other hand the Fier representation
+ 
+
+ align:start position:0%
+the other hand the Fier representation
+does what it fits the curve that you're
+
+ align:start position:0%
+does what it fits the curve that you're
+ 
+
+ align:start position:0%
+does what it fits the curve that you're
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about very very nicely very very quickly
+
+ align:start position:0%
+about very very nicely very very quickly
+ 
+
+ align:start position:0%
+about very very nicely very very quickly
+and this is why one reason why Fier
+
+ align:start position:0%
+and this is why one reason why Fier
+ 
+
+ align:start position:0%
+and this is why one reason why Fier
+series are as powerful as they are and
+
+ align:start position:0%
+series are as powerful as they are and
+ 
+
+ align:start position:0%
+series are as powerful as they are and
+by the way again to end on a nice theme
+
+ align:start position:0%
+by the way again to end on a nice theme
+ 
+
+ align:start position:0%
+by the way again to end on a nice theme
+Fier series probably have as much space
+
+ align:start position:0%
+Fier series probably have as much space
+ 
+
+ align:start position:0%
+Fier series probably have as much space
+devoted to them in pure mathematics as
+
+ align:start position:0%
+devoted to them in pure mathematics as
+ 
+
+ align:start position:0%
+devoted to them in pure mathematics as
+they do in Applied Mathematics it's a
+
+ align:start position:0%
+they do in Applied Mathematics it's a
+ 
+
+ align:start position:0%
+they do in Applied Mathematics it's a
+beautiful topic from both points of view
+
+ align:start position:0%
+beautiful topic from both points of view
+ 
+
+ align:start position:0%
+beautiful topic from both points of view
+but I felt that for our lesson today
+
+ align:start position:0%
+but I felt that for our lesson today
+ 
+
+ align:start position:0%
+but I felt that for our lesson today
+since it is a Finishing Touch to
+
+ align:start position:0%
+since it is a Finishing Touch to
+ 
+
+ align:start position:0%
+since it is a Finishing Touch to
+essentially the equivalent of three plus
+
+ align:start position:0%
+essentially the equivalent of three plus
+ 
+
+ align:start position:0%
+essentially the equivalent of three plus
+semesters of calculus that we suj the
+
+ align:start position:0%
+semesters of calculus that we suj the
+ 
+
+ align:start position:0%
+semesters of calculus that we suj the
+position the old and the new and show
+
+ align:start position:0%
+position the old and the new and show
+ 
+
+ align:start position:0%
+position the old and the new and show
+the peaceful coexistence versus this
+
+ align:start position:0%
+the peaceful coexistence versus this
+ 
+
+ align:start position:0%
+the peaceful coexistence versus this
+idea of polarization where you either
+
+ align:start position:0%
+idea of polarization where you either
+ 
+
+ align:start position:0%
+idea of polarization where you either
+have to be a traditionalist or a
+
+ align:start position:0%
+have to be a traditionalist or a
+ 
+
+ align:start position:0%
+have to be a traditionalist or a
+modernist where you either have to be an
+
+ align:start position:0%
+modernist where you either have to be an
+ 
+
+ align:start position:0%
+modernist where you either have to be an
+applied man or a purist that all of
+
+ align:start position:0%
+applied man or a purist that all of
+ 
+
+ align:start position:0%
+applied man or a purist that all of
+these ideas mingle side by side and
+
+ align:start position:0%
+these ideas mingle side by side and
+ 
+
+ align:start position:0%
+these ideas mingle side by side and
+about the only choice you have is a
+
+ align:start position:0%
+about the only choice you have is a
+ 
+
+ align:start position:0%
+about the only choice you have is a
+human being depending on what your
+
+ align:start position:0%
+human being depending on what your
+ 
+
+ align:start position:0%
+human being depending on what your
+interests are is What proportion you're
+
+ align:start position:0%
+interests are is What proportion you're
+ 
+
+ align:start position:0%
+interests are is What proportion you're
+going to mix them in well at any rate
+
+ align:start position:0%
+going to mix them in well at any rate
+ 
+
+ align:start position:0%
+going to mix them in well at any rate
+this brings us to the part of the course
+
+ align:start position:0%
+this brings us to the part of the course
+ 
+
+ align:start position:0%
+this brings us to the part of the course
+that always gives me a little bit of
+
+ align:start position:0%
+that always gives me a little bit of
+ 
+
+ align:start position:0%
+that always gives me a little bit of
+remorse and that is I hate to let my
+
+ align:start position:0%
+remorse and that is I hate to let my
+ 
+
+ align:start position:0%
+remorse and that is I hate to let my
+captive audience go we have now been
+
+ align:start position:0%
+captive audience go we have now been
+ 
+
+ align:start position:0%
+captive audience go we have now been
+through as I say the equivalent of a
+
+ align:start position:0%
+through as I say the equivalent of a
+ 
+
+ align:start position:0%
+through as I say the equivalent of a
+couple of years of mathematics together
+
+ align:start position:0%
+couple of years of mathematics together
+ 
+
+ align:start position:0%
+couple of years of mathematics together
+it has been a great pleasure for me I
+
+ align:start position:0%
+it has been a great pleasure for me I
+ 
+
+ align:start position:0%
+it has been a great pleasure for me I
+hope it has been for you and once again
+
+ align:start position:0%
+hope it has been for you and once again
+ 
+
+ align:start position:0%
+hope it has been for you and once again
+I would like to thank the everybody who
+
+ align:start position:0%
+I would like to thank the everybody who
+ 
+
+ align:start position:0%
+I would like to thank the everybody who
+has worked with me on this but in
+
+ align:start position:0%
+has worked with me on this but in
+ 
+
+ align:start position:0%
+has worked with me on this but in
+particular the usual three people who
+
+ align:start position:0%
+particular the usual three people who
+ 
+
+ align:start position:0%
+particular the usual three people who
+have been with me through thick and thin
+
+ align:start position:0%
+have been with me through thick and thin
+ 
+
+ align:start position:0%
+have been with me through thick and thin
+on this John Fitch our project
+
+ align:start position:0%
+on this John Fitch our project
+ 
+
+ align:start position:0%
+on this John Fitch our project
+self-study
+
+ align:start position:0%
+self-study
+ 
+
+ align:start position:0%
+self-study
+manager who has also done a lot of work
+
+ align:start position:0%
+manager who has also done a lot of work
+ 
+
+ align:start position:0%
+manager who has also done a lot of work
+with me and helping me write the study
+
+ align:start position:0%
+with me and helping me write the study
+ 
+
+ align:start position:0%
+with me and helping me write the study
+guide who has given me a lot of advice
+
+ align:start position:0%
+guide who has given me a lot of advice
+ 
+
+ align:start position:0%
+guide who has given me a lot of advice
+on how to give these lectures and how to
+
+ align:start position:0%
+on how to give these lectures and how to
+ 
+
+ align:start position:0%
+on how to give these lectures and how to
+prepare them for the taping and has also
+
+ align:start position:0%
+prepare them for the taping and has also
+ 
+
+ align:start position:0%
+prepare them for the taping and has also
+been our director for the taping to miss
+
+ align:start position:0%
+been our director for the taping to miss
+ 
+
+ align:start position:0%
+been our director for the taping to miss
+Alise peler who in addition to her usual
+
+ align:start position:0%
+Alise peler who in addition to her usual
+ 
+
+ align:start position:0%
+Alise peler who in addition to her usual
+secretarial work has typed much of our
+
+ align:start position:0%
+secretarial work has typed much of our
+ 
+
+ align:start position:0%
+secretarial work has typed much of our
+study guide and has worked with the uh
+
+ align:start position:0%
+study guide and has worked with the uh
+ 
+
+ align:start position:0%
+study guide and has worked with the uh
+as a video technician for us and to our
+
+ align:start position:0%
+as a video technician for us and to our
+ 
+
+ align:start position:0%
+as a video technician for us and to our
+chief uh I just call him chief of Audi
+
+ align:start position:0%
+chief uh I just call him chief of Audi
+ 
+
+ align:start position:0%
+chief uh I just call him chief of Audi
+visual uh effects at the center here
+
+ align:start position:0%
+visual uh effects at the center here
+ 
+
+ align:start position:0%
+visual uh effects at the center here
+Charles patteron I am particularly
+
+ align:start position:0%
+Charles patteron I am particularly
+ 
+
+ align:start position:0%
+Charles patteron I am particularly
+indebted to these three people indebted
+
+ align:start position:0%
+indebted to these three people indebted
+ 
+
+ align:start position:0%
+indebted to these three people indebted
+to a lot of other people I thank you all
+
+ align:start position:0%
+to a lot of other people I thank you all
+ 
+
+ align:start position:0%
+to a lot of other people I thank you all
+for bearing with me this long and I hope
+
+ align:start position:0%
+for bearing with me this long and I hope
+ 
+
+ align:start position:0%
+for bearing with me this long and I hope
+that our paths will cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again funding for the publication of
+
+ align:start position:0%
+again funding for the publication of
+ 
+
+ align:start position:0%
+again funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/_ZZ6jwuBJxc.txt b/_ZZ6jwuBJxc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b72bad341fa4e0bd88f067371a917ab40c15f116
--- /dev/null
+++ b/_ZZ6jwuBJxc.txt
@@ -0,0 +1,371 @@
+align:start position:0%
+ 
+the first thing I do that when I'm
+
+ align:start position:0%
+the first thing I do that when I'm
+ 
+
+ align:start position:0%
+the first thing I do that when I'm
+getting ready for the class is to go
+
+ align:start position:0%
+getting ready for the class is to go
+ 
+
+ align:start position:0%
+getting ready for the class is to go
+over the handouts and make sure they're
+
+ align:start position:0%
+over the handouts and make sure they're
+ 
+
+ align:start position:0%
+over the handouts and make sure they're
+really what I want update them um and
+
+ align:start position:0%
+really what I want update them um and
+ 
+
+ align:start position:0%
+really what I want update them um and
+and go over that then I usually have um
+
+ align:start position:0%
+and go over that then I usually have um
+ 
+
+ align:start position:0%
+and go over that then I usually have um
+sort of uh back to my theater days I
+
+ align:start position:0%
+sort of uh back to my theater days I
+ 
+
+ align:start position:0%
+sort of uh back to my theater days I
+guess a plan for the lecture that you
+
+ align:start position:0%
+guess a plan for the lecture that you
+ 
+
+ align:start position:0%
+guess a plan for the lecture that you
+know when the clicker questions are
+
+ align:start position:0%
+know when the clicker questions are
+ 
+
+ align:start position:0%
+know when the clicker questions are
+going to be what I'm showing on a
+
+ align:start position:0%
+going to be what I'm showing on a
+ 
+
+ align:start position:0%
+going to be what I'm showing on a
+PowerPoint presentation what I'm going
+
+ align:start position:0%
+PowerPoint presentation what I'm going
+ 
+
+ align:start position:0%
+PowerPoint presentation what I'm going
+to be writing on the board and so have
+
+ align:start position:0%
+to be writing on the board and so have
+ 
+
+ align:start position:0%
+to be writing on the board and so have
+it all organized there's times when I
+
+ align:start position:0%
+it all organized there's times when I
+ 
+
+ align:start position:0%
+it all organized there's times when I
+want to ask them a question and how I'm
+
+ align:start position:0%
+want to ask them a question and how I'm
+ 
+
+ align:start position:0%
+want to ask them a question and how I'm
+going to do that if we're going to have
+
+ align:start position:0%
+going to do that if we're going to have
+ 
+
+ align:start position:0%
+going to do that if we're going to have
+a demo in that particular class where
+
+ align:start position:0%
+a demo in that particular class where
+ 
+
+ align:start position:0%
+a demo in that particular class where
+it's going to fit in how it's going to
+
+ align:start position:0%
+it's going to fit in how it's going to
+ 
+
+ align:start position:0%
+it's going to fit in how it's going to
+be set up um and I like to bring I I
+
+ align:start position:0%
+be set up um and I like to bring I I
+ 
+
+ align:start position:0%
+be set up um and I like to bring I I
+love three-dimensional things so if
+
+ align:start position:0%
+love three-dimensional things so if
+ 
+
+ align:start position:0%
+love three-dimensional things so if
+we're talking about bonding I want giant
+
+ align:start position:0%
+we're talking about bonding I want giant
+ 
+
+ align:start position:0%
+we're talking about bonding I want giant
+atoms um and I'm always trying to think
+
+ align:start position:0%
+atoms um and I'm always trying to think
+ 
+
+ align:start position:0%
+atoms um and I'm always trying to think
+of things that I can bring in to use to
+
+ align:start position:0%
+of things that I can bring in to use to
+ 
+
+ align:start position:0%
+of things that I can bring in to use to
+show someone some kind of concept um and
+
+ align:start position:0%
+show someone some kind of concept um and
+ 
+
+ align:start position:0%
+show someone some kind of concept um and
+uh so I want at least once a a week to
+
+ align:start position:0%
+uh so I want at least once a a week to
+ 
+
+ align:start position:0%
+uh so I want at least once a a week to
+have some kind of demo in the class it's
+
+ align:start position:0%
+have some kind of demo in the class it's
+ 
+
+ align:start position:0%
+have some kind of demo in the class it's
+nice I also like some you know geeky
+
+ align:start position:0%
+nice I also like some you know geeky
+ 
+
+ align:start position:0%
+nice I also like some you know geeky
+Science music and other things um and
+
+ align:start position:0%
+Science music and other things um and
+ 
+
+ align:start position:0%
+Science music and other things um and
+then in the last year where I taught I
+
+ align:start position:0%
+then in the last year where I taught I
+ 
+
+ align:start position:0%
+then in the last year where I taught I
+upped the uh the bar for myself so if
+
+ align:start position:0%
+upped the uh the bar for myself so if
+ 
+
+ align:start position:0%
+upped the uh the bar for myself so if
+people are watching the most current
+
+ align:start position:0%
+people are watching the most current
+ 
+
+ align:start position:0%
+people are watching the most current
+open course whereare they will see my
+
+ align:start position:0%
+open course whereare they will see my
+ 
+
+ align:start position:0%
+open course whereare they will see my
+t-shirt collection um so I decided that
+
+ align:start position:0%
+t-shirt collection um so I decided that
+ 
+
+ align:start position:0%
+t-shirt collection um so I decided that
+in addition to thinking about the demos
+
+ align:start position:0%
+in addition to thinking about the demos
+ 
+
+ align:start position:0%
+in addition to thinking about the demos
+and the songs and what I'm writing on
+
+ align:start position:0%
+and the songs and what I'm writing on
+ 
+
+ align:start position:0%
+and the songs and what I'm writing on
+the board and and when I'm going to ask
+
+ align:start position:0%
+the board and and when I'm going to ask
+ 
+
+ align:start position:0%
+the board and and when I'm going to ask
+questions and all of these things that I
+
+ align:start position:0%
+questions and all of these things that I
+ 
+
+ align:start position:0%
+questions and all of these things that I
+needed to coordinate it with my word R
+
+ align:start position:0%
+needed to coordinate it with my word R
+ 
+
+ align:start position:0%
+needed to coordinate it with my word R
+so that was the high bar that I set for
+
+ align:start position:0%
+so that was the high bar that I set for
+ 
+
+ align:start position:0%
+so that was the high bar that I set for
+myself and that somehow the T-shirt not
+
+ align:start position:0%
+myself and that somehow the T-shirt not
+ 
+
+ align:start position:0%
+myself and that somehow the T-shirt not
+only had to be some kind of geeky
+
+ align:start position:0%
+only had to be some kind of geeky
+ 
+
+ align:start position:0%
+only had to be some kind of geeky
+chemistry thing but related somehow to
+
+ align:start position:0%
+chemistry thing but related somehow to
+ 
+
+ align:start position:0%
+chemistry thing but related somehow to
+the topic at hand so that was one of um
+
+ align:start position:0%
+the topic at hand so that was one of um
+ 
+
+ align:start position:0%
+the topic at hand so that was one of um
+that took a lot of preparation I had to
+
+ align:start position:0%
+that took a lot of preparation I had to
+ 
+
+ align:start position:0%
+that took a lot of preparation I had to
+plan so if I had to order t-shirts I had
+
+ align:start position:0%
+plan so if I had to order t-shirts I had
+ 
+
+ align:start position:0%
+plan so if I had to order t-shirts I had
+to order ahead of time so they arrived
+
+ align:start position:0%
+to order ahead of time so they arrived
+ 
+
+ align:start position:0%
+to order ahead of time so they arrived
+um and figuring out a different t-shirt
+
+ align:start position:0%
+um and figuring out a different t-shirt
+ 
+
+ align:start position:0%
+um and figuring out a different t-shirt
+per lecture that was one of the harder
+
+ align:start position:0%
+per lecture that was one of the harder
+ 
+
+ align:start position:0%
+per lecture that was one of the harder
+challenges
\ No newline at end of file
diff --git a/_gsDTzOpiKo.txt b/_gsDTzOpiKo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..73146d0ad9450164820eaeb492a3e4512b141d22
--- /dev/null
+++ b/_gsDTzOpiKo.txt
@@ -0,0 +1,8731 @@
+align:start position:0%
+ 
+and here in front
+
+ align:start position:0%
+and here in front
+ 
+
+ align:start position:0%
+and here in front
+you asked me whether bird song would
+
+ align:start position:0%
+you asked me whether bird song would
+ 
+
+ align:start position:0%
+you asked me whether bird song would
+count as a fixed action pattern it
+
+ align:start position:0%
+count as a fixed action pattern it
+ 
+
+ align:start position:0%
+count as a fixed action pattern it
+doesn't sound fixed this is because they
+
+ align:start position:0%
+doesn't sound fixed this is because they
+ 
+
+ align:start position:0%
+doesn't sound fixed this is because they
+learn a lot but you know that's true for
+
+ align:start position:0%
+learn a lot but you know that's true for
+ 
+
+ align:start position:0%
+learn a lot but you know that's true for
+every fixation better every instinctive
+
+ align:start position:0%
+every fixation better every instinctive
+ 
+
+ align:start position:0%
+every fixation better every instinctive
+behavior there's always some learning
+
+ align:start position:0%
+behavior there's always some learning
+ 
+
+ align:start position:0%
+behavior there's always some learning
+involved
+
+ align:start position:0%
+involved
+ 
+
+ align:start position:0%
+involved
+it's never fully formed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+walking is a fixed action pattern in us
+
+ align:start position:0%
+walking is a fixed action pattern in us
+ 
+
+ align:start position:0%
+walking is a fixed action pattern in us
+but in fact we do learn things and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we it develops a little bit over time
+
+ align:start position:0%
+we it develops a little bit over time
+ 
+
+ align:start position:0%
+we it develops a little bit over time
+some fixed action patterns have a lot of
+
+ align:start position:0%
+some fixed action patterns have a lot of
+ 
+
+ align:start position:0%
+some fixed action patterns have a lot of
+learning and some very little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an action like sneezing would have
+
+ align:start position:0%
+an action like sneezing would have
+ 
+
+ align:start position:0%
+an action like sneezing would have
+almost none but in fact if i look at
+
+ align:start position:0%
+almost none but in fact if i look at
+ 
+
+ align:start position:0%
+almost none but in fact if i look at
+various people even in the same family
+
+ align:start position:0%
+various people even in the same family
+ 
+
+ align:start position:0%
+various people even in the same family
+sneezing they'll all do it a little
+
+ align:start position:0%
+sneezing they'll all do it a little
+ 
+
+ align:start position:0%
+sneezing they'll all do it a little
+differently because
+
+ align:start position:0%
+differently because
+ 
+
+ align:start position:0%
+differently because
+they've learned they've added some
+
+ align:start position:0%
+they've learned they've added some
+ 
+
+ align:start position:0%
+they've learned they've added some
+learning on top of it
+
+ align:start position:0%
+learning on top of it
+ 
+
+ align:start position:0%
+learning on top of it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we have a few things left from last time
+
+ align:start position:0%
+we have a few things left from last time
+ 
+
+ align:start position:0%
+we have a few things left from last time
+i want to go over a few things
+
+ align:start position:0%
+i want to go over a few things
+ 
+
+ align:start position:0%
+i want to go over a few things
+examples of competition
+
+ align:start position:0%
+examples of competition
+ 
+
+ align:start position:0%
+examples of competition
+among axons during development
+
+ align:start position:0%
+among axons during development
+ 
+
+ align:start position:0%
+among axons during development
+where exons will compete for terminal
+
+ align:start position:0%
+where exons will compete for terminal
+ 
+
+ align:start position:0%
+where exons will compete for terminal
+space they're either competing for
+
+ align:start position:0%
+space they're either competing for
+ 
+
+ align:start position:0%
+space they're either competing for
+growth factors or for occupancy of
+
+ align:start position:0%
+growth factors or for occupancy of
+ 
+
+ align:start position:0%
+growth factors or for occupancy of
+synaptic sites
+
+ align:start position:0%
+synaptic sites
+ 
+
+ align:start position:0%
+synaptic sites
+but they're also contact interactions
+
+ align:start position:0%
+but they're also contact interactions
+ 
+
+ align:start position:0%
+but they're also contact interactions
+between json accents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i changed the heading slightly but these
+
+ align:start position:0%
+i changed the heading slightly but these
+ 
+
+ align:start position:0%
+i changed the heading slightly but these
+are the same pictures you have on the
+
+ align:start position:0%
+are the same pictures you have on the
+ 
+
+ align:start position:0%
+are the same pictures you have on the
+printout
+
+ align:start position:0%
+printout
+ 
+
+ align:start position:0%
+printout
+for the last class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to go through a series of
+
+ align:start position:0%
+we're going to go through a series of
+ 
+
+ align:start position:0%
+we're going to go through a series of
+simple examples in every case there's
+
+ align:start position:0%
+simple examples in every case there's
+ 
+
+ align:start position:0%
+simple examples in every case there's
+some competition among adjacent or
+
+ align:start position:0%
+some competition among adjacent or
+ 
+
+ align:start position:0%
+some competition among adjacent or
+overlapping populations of growing axons
+
+ align:start position:0%
+overlapping populations of growing axons
+ 
+
+ align:start position:0%
+overlapping populations of growing axons
+in the developing brain
+
+ align:start position:0%
+in the developing brain
+ 
+
+ align:start position:0%
+in the developing brain
+so for example in the visual system
+
+ align:start position:0%
+so for example in the visual system
+ 
+
+ align:start position:0%
+so for example in the visual system
+the two eyes project to the geniculate
+
+ align:start position:0%
+the two eyes project to the geniculate
+ 
+
+ align:start position:0%
+the two eyes project to the geniculate
+body okay
+
+ align:start position:0%
+body okay
+ 
+
+ align:start position:0%
+body okay
+the box there indicates the geniculate
+
+ align:start position:0%
+the box there indicates the geniculate
+ 
+
+ align:start position:0%
+the box there indicates the geniculate
+body and then you see the two eyes
+
+ align:start position:0%
+body and then you see the two eyes
+ 
+
+ align:start position:0%
+body and then you see the two eyes
+and axons from the two eyes just mix
+
+ align:start position:0%
+and axons from the two eyes just mix
+ 
+
+ align:start position:0%
+and axons from the two eyes just mix
+with each other if you look with
+
+ align:start position:0%
+with each other if you look with
+ 
+
+ align:start position:0%
+with each other if you look with
+anatomical methods you see that they're
+
+ align:start position:0%
+anatomical methods you see that they're
+ 
+
+ align:start position:0%
+anatomical methods you see that they're
+overlapping okay
+
+ align:start position:0%
+overlapping okay
+ 
+
+ align:start position:0%
+overlapping okay
+but then there's a sorting out they
+
+ align:start position:0%
+but then there's a sorting out they
+ 
+
+ align:start position:0%
+but then there's a sorting out they
+appear to compete in some way
+
+ align:start position:0%
+appear to compete in some way
+ 
+
+ align:start position:0%
+appear to compete in some way
+with each other
+
+ align:start position:0%
+with each other
+ 
+
+ align:start position:0%
+with each other
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+those from the ipsilateral eye end up in
+
+ align:start position:0%
+those from the ipsilateral eye end up in
+ 
+
+ align:start position:0%
+those from the ipsilateral eye end up in
+one part of the geniculate from the
+
+ align:start position:0%
+one part of the geniculate from the
+ 
+
+ align:start position:0%
+one part of the geniculate from the
+contralateral line on the other part of
+
+ align:start position:0%
+contralateral line on the other part of
+ 
+
+ align:start position:0%
+contralateral line on the other part of
+the january so they sort out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that also happens in the spirit
+
+ align:start position:0%
+that also happens in the spirit
+ 
+
+ align:start position:0%
+that also happens in the spirit
+colliculus
+
+ align:start position:0%
+colliculus
+ 
+
+ align:start position:0%
+colliculus
+in abnormal situations where you create
+
+ align:start position:0%
+in abnormal situations where you create
+ 
+
+ align:start position:0%
+in abnormal situations where you create
+a colliculus with
+
+ align:start position:0%
+a colliculus with
+ 
+
+ align:start position:0%
+a colliculus with
+both eyes coming in
+
+ align:start position:0%
+both eyes coming in
+ 
+
+ align:start position:0%
+both eyes coming in
+to the superficial layers
+
+ align:start position:0%
+to the superficial layers
+ 
+
+ align:start position:0%
+to the superficial layers
+now here's another example here you have
+
+ align:start position:0%
+now here's another example here you have
+ 
+
+ align:start position:0%
+now here's another example here you have
+competition between again two
+
+ align:start position:0%
+competition between again two
+ 
+
+ align:start position:0%
+competition between again two
+overlapping populations in this case as
+
+ align:start position:0%
+overlapping populations in this case as
+ 
+
+ align:start position:0%
+overlapping populations in this case as
+in the geniculate body they sort out in
+
+ align:start position:0%
+in the geniculate body they sort out in
+ 
+
+ align:start position:0%
+in the geniculate body they sort out in
+somewhat different way there's two types
+
+ align:start position:0%
+somewhat different way there's two types
+ 
+
+ align:start position:0%
+somewhat different way there's two types
+of axons
+
+ align:start position:0%
+of axons
+ 
+
+ align:start position:0%
+of axons
+and although they're initially
+
+ align:start position:0%
+and although they're initially
+ 
+
+ align:start position:0%
+and although they're initially
+overlapping
+
+ align:start position:0%
+overlapping
+ 
+
+ align:start position:0%
+overlapping
+in fact i've drawn them as if they're
+
+ align:start position:0%
+in fact i've drawn them as if they're
+ 
+
+ align:start position:0%
+in fact i've drawn them as if they're
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+separate they probably the terminal
+
+ align:start position:0%
+separate they probably the terminal
+ 
+
+ align:start position:0%
+separate they probably the terminal
+arbors would actually overlap
+
+ align:start position:0%
+arbors would actually overlap
+ 
+
+ align:start position:0%
+arbors would actually overlap
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+as they mature
+
+ align:start position:0%
+as they mature
+ 
+
+ align:start position:0%
+as they mature
+one population ends up occupying the
+
+ align:start position:0%
+one population ends up occupying the
+ 
+
+ align:start position:0%
+one population ends up occupying the
+upper two-thirds of the layer and
+
+ align:start position:0%
+upper two-thirds of the layer and
+ 
+
+ align:start position:0%
+upper two-thirds of the layer and
+another population
+
+ align:start position:0%
+another population
+ 
+
+ align:start position:0%
+another population
+ends up occupying the lower third
+
+ align:start position:0%
+ends up occupying the lower third
+ 
+
+ align:start position:0%
+ends up occupying the lower third
+there is a little bit of overlap between
+
+ align:start position:0%
+there is a little bit of overlap between
+ 
+
+ align:start position:0%
+there is a little bit of overlap between
+them still
+
+ align:start position:0%
+them still
+ 
+
+ align:start position:0%
+them still
+but basically they
+
+ align:start position:0%
+but basically they
+ 
+
+ align:start position:0%
+but basically they
+they segregate into layers
+
+ align:start position:0%
+they segregate into layers
+ 
+
+ align:start position:0%
+they segregate into layers
+so not so different from the what
+
+ align:start position:0%
+so not so different from the what
+ 
+
+ align:start position:0%
+so not so different from the what
+happens in the geneculate body except in
+
+ align:start position:0%
+happens in the geneculate body except in
+ 
+
+ align:start position:0%
+happens in the geneculate body except in
+this case they're not accidents from the
+
+ align:start position:0%
+this case they're not accidents from the
+ 
+
+ align:start position:0%
+this case they're not accidents from the
+two eyes
+
+ align:start position:0%
+two eyes
+ 
+
+ align:start position:0%
+two eyes
+now they're from the same eye but
+
+ align:start position:0%
+now they're from the same eye but
+ 
+
+ align:start position:0%
+now they're from the same eye but
+they're from different types of exon
+
+ align:start position:0%
+they're from different types of exon
+ 
+
+ align:start position:0%
+they're from different types of exon
+in the same eye one is a larger axon
+
+ align:start position:0%
+in the same eye one is a larger axon
+ 
+
+ align:start position:0%
+in the same eye one is a larger axon
+okay another one is a smaller coming
+
+ align:start position:0%
+okay another one is a smaller coming
+ 
+
+ align:start position:0%
+okay another one is a smaller coming
+from smaller cells
+
+ align:start position:0%
+from smaller cells
+ 
+
+ align:start position:0%
+from smaller cells
+and they end up terminating in these
+
+ align:start position:0%
+and they end up terminating in these
+ 
+
+ align:start position:0%
+and they end up terminating in these
+different layers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's other
+
+ align:start position:0%
+there's other
+ 
+
+ align:start position:0%
+there's other
+cases where two populations are in the
+
+ align:start position:0%
+cases where two populations are in the
+ 
+
+ align:start position:0%
+cases where two populations are in the
+same eye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the because they're coming from
+
+ align:start position:0%
+where the because they're coming from
+ 
+
+ align:start position:0%
+where the because they're coming from
+different cells one axon type might grow
+
+ align:start position:0%
+different cells one axon type might grow
+ 
+
+ align:start position:0%
+different cells one axon type might grow
+bigger than the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and end up occupying more of the space
+
+ align:start position:0%
+and end up occupying more of the space
+ 
+
+ align:start position:0%
+and end up occupying more of the space
+than the smaller axon okay in many cases
+
+ align:start position:0%
+than the smaller axon okay in many cases
+ 
+
+ align:start position:0%
+than the smaller axon okay in many cases
+of that initially they might be very
+
+ align:start position:0%
+of that initially they might be very
+ 
+
+ align:start position:0%
+of that initially they might be very
+similar but they may end up occupying
+
+ align:start position:0%
+similar but they may end up occupying
+ 
+
+ align:start position:0%
+similar but they may end up occupying
+different amounts of space though they
+
+ align:start position:0%
+different amounts of space though they
+ 
+
+ align:start position:0%
+different amounts of space though they
+might still overlap
+
+ align:start position:0%
+might still overlap
+ 
+
+ align:start position:0%
+might still overlap
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we know that
+
+ align:start position:0%
+now we know that
+ 
+
+ align:start position:0%
+now we know that
+these axons form topographic maps
+
+ align:start position:0%
+these axons form topographic maps
+ 
+
+ align:start position:0%
+these axons form topographic maps
+initially we have one axon that might be
+
+ align:start position:0%
+initially we have one axon that might be
+ 
+
+ align:start position:0%
+initially we have one axon that might be
+terminating over a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a span of the collicular space
+
+ align:start position:0%
+a span of the collicular space
+ 
+
+ align:start position:0%
+a span of the collicular space
+but then they segregate because each
+
+ align:start position:0%
+but then they segregate because each
+ 
+
+ align:start position:0%
+but then they segregate because each
+axon seems to compete best in one part
+
+ align:start position:0%
+axon seems to compete best in one part
+ 
+
+ align:start position:0%
+axon seems to compete best in one part
+of the tectum depending on the chemical
+
+ align:start position:0%
+of the tectum depending on the chemical
+ 
+
+ align:start position:0%
+of the tectum depending on the chemical
+environment okay
+
+ align:start position:0%
+environment okay
+ 
+
+ align:start position:0%
+environment okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the chemical factors interact with these
+
+ align:start position:0%
+the chemical factors interact with these
+ 
+
+ align:start position:0%
+the chemical factors interact with these
+competitive interactions in sorting the
+
+ align:start position:0%
+competitive interactions in sorting the
+ 
+
+ align:start position:0%
+competitive interactions in sorting the
+axons into their proper places
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just think of it in every case as
+
+ align:start position:0%
+just think of it in every case as
+ 
+
+ align:start position:0%
+just think of it in every case as
+a kind of competition between adjacent
+
+ align:start position:0%
+a kind of competition between adjacent
+ 
+
+ align:start position:0%
+a kind of competition between adjacent
+or overlapping populations of accents
+
+ align:start position:0%
+or overlapping populations of accents
+ 
+
+ align:start position:0%
+or overlapping populations of accents
+okay very common in development
+
+ align:start position:0%
+okay very common in development
+ 
+
+ align:start position:0%
+okay very common in development
+now let's talk about this intrinsic
+
+ align:start position:0%
+now let's talk about this intrinsic
+ 
+
+ align:start position:0%
+now let's talk about this intrinsic
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+that in a cell
+
+ align:start position:0%
+that in a cell
+ 
+
+ align:start position:0%
+that in a cell
+when it's growing an axon
+
+ align:start position:0%
+when it's growing an axon
+ 
+
+ align:start position:0%
+when it's growing an axon
+can vary in its ability to compete
+
+ align:start position:0%
+can vary in its ability to compete
+ 
+
+ align:start position:0%
+can vary in its ability to compete
+okay and we call this competitive growth
+
+ align:start position:0%
+okay and we call this competitive growth
+ 
+
+ align:start position:0%
+okay and we call this competitive growth
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+the more growth figure an axon has
+
+ align:start position:0%
+the more growth figure an axon has
+ 
+
+ align:start position:0%
+the more growth figure an axon has
+the more it grows and the better it
+
+ align:start position:0%
+the more it grows and the better it
+ 
+
+ align:start position:0%
+the more it grows and the better it
+competes for terminal space but this can
+
+ align:start position:0%
+competes for terminal space but this can
+ 
+
+ align:start position:0%
+competes for terminal space but this can
+be modulated it can be modulated by
+
+ align:start position:0%
+be modulated it can be modulated by
+ 
+
+ align:start position:0%
+be modulated it can be modulated by
+chemical factors for example
+
+ align:start position:0%
+chemical factors for example
+ 
+
+ align:start position:0%
+chemical factors for example
+in gf
+
+ align:start position:0%
+in gf
+ 
+
+ align:start position:0%
+in gf
+in the case of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tissue culture you can see that
+
+ align:start position:0%
+tissue culture you can see that
+ 
+
+ align:start position:0%
+tissue culture you can see that
+the cells here had a lot more growth
+
+ align:start position:0%
+the cells here had a lot more growth
+ 
+
+ align:start position:0%
+the cells here had a lot more growth
+figure in the cells here here they're
+
+ align:start position:0%
+figure in the cells here here they're
+ 
+
+ align:start position:0%
+figure in the cells here here they're
+growing short little stubby axons and
+
+ align:start position:0%
+growing short little stubby axons and
+ 
+
+ align:start position:0%
+growing short little stubby axons and
+not growing very far
+
+ align:start position:0%
+not growing very far
+ 
+
+ align:start position:0%
+not growing very far
+some of them are not growing much at all
+
+ align:start position:0%
+some of them are not growing much at all
+ 
+
+ align:start position:0%
+some of them are not growing much at all
+but if you add little growth factor
+
+ align:start position:0%
+but if you add little growth factor
+ 
+
+ align:start position:0%
+but if you add little growth factor
+they grow much more vigorously so it's
+
+ align:start position:0%
+they grow much more vigorously so it's
+ 
+
+ align:start position:0%
+they grow much more vigorously so it's
+possible then to modulate the growth
+
+ align:start position:0%
+possible then to modulate the growth
+ 
+
+ align:start position:0%
+possible then to modulate the growth
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+with these chemical factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's also factors intrinsic to the
+
+ align:start position:0%
+there's also factors intrinsic to the
+ 
+
+ align:start position:0%
+there's also factors intrinsic to the
+cells and in fact something like ngf is
+
+ align:start position:0%
+cells and in fact something like ngf is
+ 
+
+ align:start position:0%
+cells and in fact something like ngf is
+synthesized by some neurons also so
+
+ align:start position:0%
+synthesized by some neurons also so
+ 
+
+ align:start position:0%
+synthesized by some neurons also so
+sometimes they make their own growth
+
+ align:start position:0%
+sometimes they make their own growth
+ 
+
+ align:start position:0%
+sometimes they make their own growth
+factor and then how much they make will
+
+ align:start position:0%
+factor and then how much they make will
+ 
+
+ align:start position:0%
+factor and then how much they make will
+determine how they grow
+
+ align:start position:0%
+determine how they grow
+ 
+
+ align:start position:0%
+determine how they grow
+they might respond separately to other
+
+ align:start position:0%
+they might respond separately to other
+ 
+
+ align:start position:0%
+they might respond separately to other
+growth factors in the environment
+
+ align:start position:0%
+growth factors in the environment
+ 
+
+ align:start position:0%
+growth factors in the environment
+okay but now there's a couple of other
+
+ align:start position:0%
+okay but now there's a couple of other
+ 
+
+ align:start position:0%
+okay but now there's a couple of other
+things i want to consider briefly one is
+
+ align:start position:0%
+things i want to consider briefly one is
+ 
+
+ align:start position:0%
+things i want to consider briefly one is
+later in development
+
+ align:start position:0%
+later in development
+ 
+
+ align:start position:0%
+later in development
+activity can affect
+
+ align:start position:0%
+activity can affect
+ 
+
+ align:start position:0%
+activity can affect
+the growth figure of the axon
+
+ align:start position:0%
+the growth figure of the axon
+ 
+
+ align:start position:0%
+the growth figure of the axon
+so for example axons representing the
+
+ align:start position:0%
+so for example axons representing the
+ 
+
+ align:start position:0%
+so for example axons representing the
+two eyes
+
+ align:start position:0%
+two eyes
+ 
+
+ align:start position:0%
+two eyes
+grow into the geniculite geniculi by
+
+ align:start position:0%
+grow into the geniculite geniculi by
+ 
+
+ align:start position:0%
+grow into the geniculite geniculi by
+segregate into different laminae
+
+ align:start position:0%
+segregate into different laminae
+ 
+
+ align:start position:0%
+segregate into different laminae
+so you have different laminae all
+
+ align:start position:0%
+so you have different laminae all
+ 
+
+ align:start position:0%
+so you have different laminae all
+but all representing the same place in
+
+ align:start position:0%
+but all representing the same place in
+ 
+
+ align:start position:0%
+but all representing the same place in
+the visual field
+
+ align:start position:0%
+the visual field
+ 
+
+ align:start position:0%
+the visual field
+so the corresponding areas of the two
+
+ align:start position:0%
+so the corresponding areas of the two
+ 
+
+ align:start position:0%
+so the corresponding areas of the two
+retinas okay now all the cells in that
+
+ align:start position:0%
+retinas okay now all the cells in that
+ 
+
+ align:start position:0%
+retinas okay now all the cells in that
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+representing the contralateral and the
+
+ align:start position:0%
+representing the contralateral and the
+ 
+
+ align:start position:0%
+representing the contralateral and the
+ipsilateral eye will project to the same
+
+ align:start position:0%
+ipsilateral eye will project to the same
+ 
+
+ align:start position:0%
+ipsilateral eye will project to the same
+region of the cortex
+
+ align:start position:0%
+region of the cortex
+ 
+
+ align:start position:0%
+region of the cortex
+where we know there's another
+
+ align:start position:0%
+where we know there's another
+ 
+
+ align:start position:0%
+where we know there's another
+topographic map of the visual world but
+
+ align:start position:0%
+topographic map of the visual world but
+ 
+
+ align:start position:0%
+topographic map of the visual world but
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+and again they grow in and they overlap
+
+ align:start position:0%
+and again they grow in and they overlap
+ 
+
+ align:start position:0%
+and again they grow in and they overlap
+with each other
+
+ align:start position:0%
+with each other
+ 
+
+ align:start position:0%
+with each other
+early in development
+
+ align:start position:0%
+early in development
+ 
+
+ align:start position:0%
+early in development
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+just like in the geniculate body they
+
+ align:start position:0%
+just like in the geniculate body they
+ 
+
+ align:start position:0%
+just like in the geniculate body they
+segregate but now they segregate into
+
+ align:start position:0%
+segregate but now they segregate into
+ 
+
+ align:start position:0%
+segregate but now they segregate into
+adjacent slabs of tissue we call them
+
+ align:start position:0%
+adjacent slabs of tissue we call them
+ 
+
+ align:start position:0%
+adjacent slabs of tissue we call them
+cortical columns they're really sort of
+
+ align:start position:0%
+cortical columns they're really sort of
+ 
+
+ align:start position:0%
+cortical columns they're really sort of
+like slabs and if you look at it from
+
+ align:start position:0%
+like slabs and if you look at it from
+ 
+
+ align:start position:0%
+like slabs and if you look at it from
+the surface they're like zebra stripes
+
+ align:start position:0%
+the surface they're like zebra stripes
+ 
+
+ align:start position:0%
+the surface they're like zebra stripes
+many of you have seen those pictures
+
+ align:start position:0%
+many of you have seen those pictures
+ 
+
+ align:start position:0%
+many of you have seen those pictures
+of representation of the two eyes in the
+
+ align:start position:0%
+of representation of the two eyes in the
+ 
+
+ align:start position:0%
+of representation of the two eyes in the
+visual cortex but what i want to bring
+
+ align:start position:0%
+visual cortex but what i want to bring
+ 
+
+ align:start position:0%
+visual cortex but what i want to bring
+out here is that
+
+ align:start position:0%
+out here is that
+ 
+
+ align:start position:0%
+out here is that
+if the activity of the two eyes is
+
+ align:start position:0%
+if the activity of the two eyes is
+ 
+
+ align:start position:0%
+if the activity of the two eyes is
+abnormally different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for some reason perhaps the person
+
+ align:start position:0%
+so for some reason perhaps the person
+ 
+
+ align:start position:0%
+so for some reason perhaps the person
+asked your business and he starts
+
+ align:start position:0%
+asked your business and he starts
+ 
+
+ align:start position:0%
+asked your business and he starts
+suppressing vision then why
+
+ align:start position:0%
+suppressing vision then why
+ 
+
+ align:start position:0%
+suppressing vision then why
+or one eye is patched
+
+ align:start position:0%
+or one eye is patched
+ 
+
+ align:start position:0%
+or one eye is patched
+or because of an injury or something
+
+ align:start position:0%
+or because of an injury or something
+ 
+
+ align:start position:0%
+or because of an injury or something
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the eye with the activity with the more
+
+ align:start position:0%
+the eye with the activity with the more
+ 
+
+ align:start position:0%
+the eye with the activity with the more
+activity will end up occupying more
+
+ align:start position:0%
+activity will end up occupying more
+ 
+
+ align:start position:0%
+activity will end up occupying more
+space in the eye with less activity will
+
+ align:start position:0%
+space in the eye with less activity will
+ 
+
+ align:start position:0%
+space in the eye with less activity will
+occupy less space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+children with strabismus
+
+ align:start position:0%
+children with strabismus
+ 
+
+ align:start position:0%
+children with strabismus
+will often suppress
+
+ align:start position:0%
+will often suppress
+ 
+
+ align:start position:0%
+will often suppress
+cortical vision in one eye at least
+
+ align:start position:0%
+cortical vision in one eye at least
+ 
+
+ align:start position:0%
+cortical vision in one eye at least
+foveal vision
+
+ align:start position:0%
+foveal vision
+ 
+
+ align:start position:0%
+foveal vision
+and one eye loses acuity
+
+ align:start position:0%
+and one eye loses acuity
+ 
+
+ align:start position:0%
+and one eye loses acuity
+the other eye will actually have
+
+ align:start position:0%
+the other eye will actually have
+ 
+
+ align:start position:0%
+the other eye will actually have
+somewhat increased acuity
+
+ align:start position:0%
+somewhat increased acuity
+ 
+
+ align:start position:0%
+somewhat increased acuity
+so if you test the child with the two
+
+ align:start position:0%
+so if you test the child with the two
+ 
+
+ align:start position:0%
+so if you test the child with the two
+eyes he comes in for an eye test when he
+
+ align:start position:0%
+eyes he comes in for an eye test when he
+ 
+
+ align:start position:0%
+eyes he comes in for an eye test when he
+starts school they see very different
+
+ align:start position:0%
+starts school they see very different
+ 
+
+ align:start position:0%
+starts school they see very different
+acuity in the two eyes it's because he's
+
+ align:start position:0%
+acuity in the two eyes it's because he's
+ 
+
+ align:start position:0%
+acuity in the two eyes it's because he's
+normally suppressing vision in one eye i
+
+ align:start position:0%
+normally suppressing vision in one eye i
+ 
+
+ align:start position:0%
+normally suppressing vision in one eye i
+had that when i entered school
+
+ align:start position:0%
+had that when i entered school
+ 
+
+ align:start position:0%
+had that when i entered school
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+so what do they do
+
+ align:start position:0%
+so what do they do
+ 
+
+ align:start position:0%
+so what do they do
+they patch the good eye
+
+ align:start position:0%
+they patch the good eye
+ 
+
+ align:start position:0%
+they patch the good eye
+they in to increase activity
+
+ align:start position:0%
+they in to increase activity
+ 
+
+ align:start position:0%
+they in to increase activity
+now if i had any strabismus it wasn't
+
+ align:start position:0%
+now if i had any strabismus it wasn't
+ 
+
+ align:start position:0%
+now if i had any strabismus it wasn't
+noticeable
+
+ align:start position:0%
+noticeable
+ 
+
+ align:start position:0%
+noticeable
+and i could have coordinated the two
+
+ align:start position:0%
+and i could have coordinated the two
+ 
+
+ align:start position:0%
+and i could have coordinated the two
+eyes are coordinated
+
+ align:start position:0%
+eyes are coordinated
+ 
+
+ align:start position:0%
+eyes are coordinated
+but with that patching over time the
+
+ align:start position:0%
+but with that patching over time the
+ 
+
+ align:start position:0%
+but with that patching over time the
+acuity got better and better
+
+ align:start position:0%
+acuity got better and better
+ 
+
+ align:start position:0%
+acuity got better and better
+in the eye that it was so bad in
+
+ align:start position:0%
+in the eye that it was so bad in
+ 
+
+ align:start position:0%
+in the eye that it was so bad in
+the other i stayed about the same and i
+
+ align:start position:0%
+the other i stayed about the same and i
+ 
+
+ align:start position:0%
+the other i stayed about the same and i
+ended up with about
+
+ align:start position:0%
+ended up with about
+ 
+
+ align:start position:0%
+ended up with about
+instead of 2020 i had 2015 in the left
+
+ align:start position:0%
+instead of 2020 i had 2015 in the left
+ 
+
+ align:start position:0%
+instead of 2020 i had 2015 in the left
+eye better than normal
+
+ align:start position:0%
+eye better than normal
+ 
+
+ align:start position:0%
+eye better than normal
+and 20 30 in the other eye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so apparently the columns representing
+
+ align:start position:0%
+so apparently the columns representing
+ 
+
+ align:start position:0%
+so apparently the columns representing
+the two eyes are still a little bit
+
+ align:start position:0%
+the two eyes are still a little bit
+ 
+
+ align:start position:0%
+the two eyes are still a little bit
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that shows how activity and there's
+
+ align:start position:0%
+that shows how activity and there's
+ 
+
+ align:start position:0%
+that shows how activity and there's
+other examples of how activity can
+
+ align:start position:0%
+other examples of how activity can
+ 
+
+ align:start position:0%
+other examples of how activity can
+influence accidental growth that tends
+
+ align:start position:0%
+influence accidental growth that tends
+ 
+
+ align:start position:0%
+influence accidental growth that tends
+to happen of course later in development
+
+ align:start position:0%
+to happen of course later in development
+ 
+
+ align:start position:0%
+to happen of course later in development
+when the axons are more mature but
+
+ align:start position:0%
+when the axons are more mature but
+ 
+
+ align:start position:0%
+when the axons are more mature but
+they're still growing still competing
+
+ align:start position:0%
+they're still growing still competing
+ 
+
+ align:start position:0%
+they're still growing still competing
+okay you can also vary
+
+ align:start position:0%
+okay you can also vary
+ 
+
+ align:start position:0%
+okay you can also vary
+competitive growth figure with a lesion
+
+ align:start position:0%
+competitive growth figure with a lesion
+ 
+
+ align:start position:0%
+competitive growth figure with a lesion
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to
+
+ align:start position:0%
+i'm going to
+ 
+
+ align:start position:0%
+i'm going to
+illustrate that by showing you what we
+
+ align:start position:0%
+illustrate that by showing you what we
+ 
+
+ align:start position:0%
+illustrate that by showing you what we
+call the pruning effect in axons
+
+ align:start position:0%
+call the pruning effect in axons
+ 
+
+ align:start position:0%
+call the pruning effect in axons
+let's take the top and first
+
+ align:start position:0%
+let's take the top and first
+ 
+
+ align:start position:0%
+let's take the top and first
+this just illustrates how we
+
+ align:start position:0%
+this just illustrates how we
+ 
+
+ align:start position:0%
+this just illustrates how we
+conceptualize it
+
+ align:start position:0%
+conceptualize it
+ 
+
+ align:start position:0%
+conceptualize it
+that early in development the axon is
+
+ align:start position:0%
+that early in development the axon is
+ 
+
+ align:start position:0%
+that early in development the axon is
+just starting to grow terminals it
+
+ align:start position:0%
+just starting to grow terminals it
+ 
+
+ align:start position:0%
+just starting to grow terminals it
+hasn't formed very many yet its growth
+
+ align:start position:0%
+hasn't formed very many yet its growth
+ 
+
+ align:start position:0%
+hasn't formed very many yet its growth
+figure is very high it's growing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in all the local sorry all the local
+
+ align:start position:0%
+in all the local sorry all the local
+ 
+
+ align:start position:0%
+in all the local sorry all the local
+directions from this terminal
+
+ align:start position:0%
+directions from this terminal
+ 
+
+ align:start position:0%
+directions from this terminal
+until finally
+
+ align:start position:0%
+until finally
+ 
+
+ align:start position:0%
+until finally
+once it reaches a certain quantity of
+
+ align:start position:0%
+once it reaches a certain quantity of
+ 
+
+ align:start position:0%
+once it reaches a certain quantity of
+its terminal arbor the growth figure now
+
+ align:start position:0%
+its terminal arbor the growth figure now
+ 
+
+ align:start position:0%
+its terminal arbor the growth figure now
+is very low
+
+ align:start position:0%
+is very low
+ 
+
+ align:start position:0%
+is very low
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it appears that the ac these axons or
+
+ align:start position:0%
+so it appears that the ac these axons or
+ 
+
+ align:start position:0%
+so it appears that the ac these axons or
+cells are programmed to form a certain
+
+ align:start position:0%
+cells are programmed to form a certain
+ 
+
+ align:start position:0%
+cells are programmed to form a certain
+size of terminal arbor and we have a
+
+ align:start position:0%
+size of terminal arbor and we have a
+ 
+
+ align:start position:0%
+size of terminal arbor and we have a
+number of experiments that indicate that
+
+ align:start position:0%
+number of experiments that indicate that
+ 
+
+ align:start position:0%
+number of experiments that indicate that
+so to test that
+
+ align:start position:0%
+so to test that
+ 
+
+ align:start position:0%
+so to test that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we can take an animal that's formed the
+
+ align:start position:0%
+we can take an animal that's formed the
+ 
+
+ align:start position:0%
+we can take an animal that's formed the
+terminal arbors
+
+ align:start position:0%
+terminal arbors
+ 
+
+ align:start position:0%
+terminal arbors
+but now we'll create a lesion we'll make
+
+ align:start position:0%
+but now we'll create a lesion we'll make
+ 
+
+ align:start position:0%
+but now we'll create a lesion we'll make
+a lesion in part of the brain
+
+ align:start position:0%
+a lesion in part of the brain
+ 
+
+ align:start position:0%
+a lesion in part of the brain
+that will
+
+ align:start position:0%
+that will
+ 
+
+ align:start position:0%
+that will
+kill some of the ann arbor
+
+ align:start position:0%
+kill some of the ann arbor
+ 
+
+ align:start position:0%
+kill some of the ann arbor
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i've done this for conceptual
+
+ align:start position:0%
+now i've done this for conceptual
+ 
+
+ align:start position:0%
+now i've done this for conceptual
+purposes
+
+ align:start position:0%
+purposes
+ 
+
+ align:start position:0%
+purposes
+but i'm not going to go over all the
+
+ align:start position:0%
+but i'm not going to go over all the
+ 
+
+ align:start position:0%
+but i'm not going to go over all the
+experiments right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what that does is it increases the
+
+ align:start position:0%
+what that does is it increases the
+ 
+
+ align:start position:0%
+what that does is it increases the
+growth figure
+
+ align:start position:0%
+growth figure
+ 
+
+ align:start position:0%
+growth figure
+in the remaining branches so if it has a
+
+ align:start position:0%
+in the remaining branches so if it has a
+ 
+
+ align:start position:0%
+in the remaining branches so if it has a
+collateral branch here for example this
+
+ align:start position:0%
+collateral branch here for example this
+ 
+
+ align:start position:0%
+collateral branch here for example this
+could be in the thalamus and this could
+
+ align:start position:0%
+could be in the thalamus and this could
+ 
+
+ align:start position:0%
+could be in the thalamus and this could
+be in the tectum it will now increase
+
+ align:start position:0%
+be in the tectum it will now increase
+ 
+
+ align:start position:0%
+be in the tectum it will now increase
+its projections
+
+ align:start position:0%
+its projections
+ 
+
+ align:start position:0%
+its projections
+and those collaterals they'll grow
+
+ align:start position:0%
+and those collaterals they'll grow
+ 
+
+ align:start position:0%
+and those collaterals they'll grow
+bigger than normal
+
+ align:start position:0%
+bigger than normal
+ 
+
+ align:start position:0%
+bigger than normal
+as if in compensation for the loss of
+
+ align:start position:0%
+as if in compensation for the loss of
+ 
+
+ align:start position:0%
+as if in compensation for the loss of
+the arbors here
+
+ align:start position:0%
+the arbors here
+ 
+
+ align:start position:0%
+the arbors here
+and these will grow more also so you'll
+
+ align:start position:0%
+and these will grow more also so you'll
+ 
+
+ align:start position:0%
+and these will grow more also so you'll
+end up with an arbor a total arbor size
+
+ align:start position:0%
+end up with an arbor a total arbor size
+ 
+
+ align:start position:0%
+end up with an arbor a total arbor size
+about the same as it would have been
+
+ align:start position:0%
+about the same as it would have been
+ 
+
+ align:start position:0%
+about the same as it would have been
+normally
+
+ align:start position:0%
+normally
+ 
+
+ align:start position:0%
+normally
+okay but now it's growing them in a
+
+ align:start position:0%
+okay but now it's growing them in a
+ 
+
+ align:start position:0%
+okay but now it's growing them in a
+different pattern because of the damage
+
+ align:start position:0%
+different pattern because of the damage
+ 
+
+ align:start position:0%
+different pattern because of the damage
+so it's not that different from pruning
+
+ align:start position:0%
+so it's not that different from pruning
+ 
+
+ align:start position:0%
+so it's not that different from pruning
+a tree
+
+ align:start position:0%
+a tree
+ 
+
+ align:start position:0%
+a tree
+if you have certain trees show pruning
+
+ align:start position:0%
+if you have certain trees show pruning
+ 
+
+ align:start position:0%
+if you have certain trees show pruning
+effects some do not
+
+ align:start position:0%
+effects some do not
+ 
+
+ align:start position:0%
+effects some do not
+okay a maple tree for example if you
+
+ align:start position:0%
+okay a maple tree for example if you
+ 
+
+ align:start position:0%
+okay a maple tree for example if you
+prune the top of it when it's young
+
+ align:start position:0%
+prune the top of it when it's young
+ 
+
+ align:start position:0%
+prune the top of it when it's young
+you can create a better shade tree
+
+ align:start position:0%
+you can create a better shade tree
+ 
+
+ align:start position:0%
+you can create a better shade tree
+because the lower branches will sprout
+
+ align:start position:0%
+because the lower branches will sprout
+ 
+
+ align:start position:0%
+because the lower branches will sprout
+more it'll become a wider tree
+
+ align:start position:0%
+more it'll become a wider tree
+ 
+
+ align:start position:0%
+more it'll become a wider tree
+and won't just grow like a a tall
+
+ align:start position:0%
+and won't just grow like a a tall
+ 
+
+ align:start position:0%
+and won't just grow like a a tall
+slender maple tree it'll be a broad
+
+ align:start position:0%
+slender maple tree it'll be a broad
+ 
+
+ align:start position:0%
+slender maple tree it'll be a broad
+maple tree in your front lawn
+
+ align:start position:0%
+maple tree in your front lawn
+ 
+
+ align:start position:0%
+maple tree in your front lawn
+it's a pruning of it and many people
+
+ align:start position:0%
+it's a pruning of it and many people
+ 
+
+ align:start position:0%
+it's a pruning of it and many people
+that keep house plants know this azaleas
+
+ align:start position:0%
+that keep house plants know this azaleas
+ 
+
+ align:start position:0%
+that keep house plants know this azaleas
+for example respond very vigorously to
+
+ align:start position:0%
+for example respond very vigorously to
+ 
+
+ align:start position:0%
+for example respond very vigorously to
+pruning
+
+ align:start position:0%
+pruning
+ 
+
+ align:start position:0%
+pruning
+so these cells that not only look like
+
+ align:start position:0%
+so these cells that not only look like
+ 
+
+ align:start position:0%
+so these cells that not only look like
+trees they also act in some ways like
+
+ align:start position:0%
+trees they also act in some ways like
+ 
+
+ align:start position:0%
+trees they also act in some ways like
+growing trees
+
+ align:start position:0%
+growing trees
+ 
+
+ align:start position:0%
+growing trees
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do people have the hand out yet for
+
+ align:start position:0%
+do people have the hand out yet for
+ 
+
+ align:start position:0%
+do people have the hand out yet for
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+you don't well it'll be coming in a
+
+ align:start position:0%
+you don't well it'll be coming in a
+ 
+
+ align:start position:0%
+you don't well it'll be coming in a
+minute
+
+ align:start position:0%
+minute
+ 
+
+ align:start position:0%
+minute
+i can i thought they would have it by
+
+ align:start position:0%
+i can i thought they would have it by
+ 
+
+ align:start position:0%
+i can i thought they would have it by
+about this time
+
+ align:start position:0%
+about this time
+ 
+
+ align:start position:0%
+about this time
+they didn't realize where i had put it
+
+ align:start position:0%
+they didn't realize where i had put it
+ 
+
+ align:start position:0%
+they didn't realize where i had put it
+on the table upstairs so they were
+
+ align:start position:0%
+on the table upstairs so they were
+ 
+
+ align:start position:0%
+on the table upstairs so they were
+looking for me instead of the handout
+
+ align:start position:0%
+looking for me instead of the handout
+ 
+
+ align:start position:0%
+looking for me instead of the handout
+and i was off doing something else
+
+ align:start position:0%
+and i was off doing something else
+ 
+
+ align:start position:0%
+and i was off doing something else
+anyway they will be in here momentarily
+
+ align:start position:0%
+anyway they will be in here momentarily
+ 
+
+ align:start position:0%
+anyway they will be in here momentarily
+we're going to start talking now about
+
+ align:start position:0%
+we're going to start talking now about
+ 
+
+ align:start position:0%
+we're going to start talking now about
+the motor system we'll do that all week
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to start talking with about
+
+ align:start position:0%
+we're going to start talking with about
+ 
+
+ align:start position:0%
+we're going to start talking with about
+spinal reflexes withdrawal reflexes or
+
+ align:start position:0%
+spinal reflexes withdrawal reflexes or
+ 
+
+ align:start position:0%
+spinal reflexes withdrawal reflexes or
+the opposite
+
+ align:start position:0%
+the opposite
+ 
+
+ align:start position:0%
+the opposite
+uh of withdrawal the magnet reflex and
+
+ align:start position:0%
+uh of withdrawal the magnet reflex and
+ 
+
+ align:start position:0%
+uh of withdrawal the magnet reflex and
+the stretch reflex
+
+ align:start position:0%
+the stretch reflex
+ 
+
+ align:start position:0%
+the stretch reflex
+we'll talk a little bit during the talk
+
+ align:start position:0%
+we'll talk a little bit during the talk
+ 
+
+ align:start position:0%
+we'll talk a little bit during the talk
+of these reflexes about
+
+ align:start position:0%
+of these reflexes about
+ 
+
+ align:start position:0%
+of these reflexes about
+inter-segmental spinal organization
+
+ align:start position:0%
+inter-segmental spinal organization
+ 
+
+ align:start position:0%
+inter-segmental spinal organization
+good timing i've just started to talk
+
+ align:start position:0%
+good timing i've just started to talk
+ 
+
+ align:start position:0%
+good timing i've just started to talk
+about the motor system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll say a little bit about plasticity
+
+ align:start position:0%
+we'll say a little bit about plasticity
+ 
+
+ align:start position:0%
+we'll say a little bit about plasticity
+in the spinal cord and then
+
+ align:start position:0%
+in the spinal cord and then
+ 
+
+ align:start position:0%
+in the spinal cord and then
+we're going to talk about
+
+ align:start position:0%
+we're going to talk about
+ 
+
+ align:start position:0%
+we're going to talk about
+higher systems of motor control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because in the last on friday i would
+
+ align:start position:0%
+because in the last on friday i would
+ 
+
+ align:start position:0%
+because in the last on friday i would
+like to show you a
+
+ align:start position:0%
+like to show you a
+ 
+
+ align:start position:0%
+like to show you a
+film
+
+ align:start position:0%
+film
+ 
+
+ align:start position:0%
+film
+of a classic experiment about
+
+ align:start position:0%
+of a classic experiment about
+ 
+
+ align:start position:0%
+of a classic experiment about
+the role of descending pathways
+
+ align:start position:0%
+the role of descending pathways
+ 
+
+ align:start position:0%
+the role of descending pathways
+in primates
+
+ align:start position:0%
+in primates
+ 
+
+ align:start position:0%
+in primates
+experiments are on racist monkeys
+
+ align:start position:0%
+experiments are on racist monkeys
+ 
+
+ align:start position:0%
+experiments are on racist monkeys
+and to understand that film we have to
+
+ align:start position:0%
+and to understand that film we have to
+ 
+
+ align:start position:0%
+and to understand that film we have to
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+in a little more detail the descending
+
+ align:start position:0%
+in a little more detail the descending
+ 
+
+ align:start position:0%
+in a little more detail the descending
+pathways coming from
+
+ align:start position:0%
+pathways coming from
+ 
+
+ align:start position:0%
+pathways coming from
+behind brain midbrain and forebrain to
+
+ align:start position:0%
+behind brain midbrain and forebrain to
+ 
+
+ align:start position:0%
+behind brain midbrain and forebrain to
+the spinal cord
+
+ align:start position:0%
+the spinal cord
+ 
+
+ align:start position:0%
+the spinal cord
+and then if we have time we'll talk a
+
+ align:start position:0%
+and then if we have time we'll talk a
+ 
+
+ align:start position:0%
+and then if we have time we'll talk a
+little bit about corpus triatum and
+
+ align:start position:0%
+little bit about corpus triatum and
+ 
+
+ align:start position:0%
+little bit about corpus triatum and
+cerebellum
+
+ align:start position:0%
+cerebellum
+ 
+
+ align:start position:0%
+cerebellum
+some of the pathologies of
+
+ align:start position:0%
+some of the pathologies of
+ 
+
+ align:start position:0%
+some of the pathologies of
+striatal dysfunction and the role of the
+
+ align:start position:0%
+striatal dysfunction and the role of the
+ 
+
+ align:start position:0%
+striatal dysfunction and the role of the
+striatum and implicit learning if we
+
+ align:start position:0%
+striatum and implicit learning if we
+ 
+
+ align:start position:0%
+striatum and implicit learning if we
+don't get to that we'll do it
+
+ align:start position:0%
+don't get to that we'll do it
+ 
+
+ align:start position:0%
+don't get to that we'll do it
+after the midterm
+
+ align:start position:0%
+after the midterm
+ 
+
+ align:start position:0%
+after the midterm
+we'll just see how far we get this week
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a good place to start
+
+ align:start position:0%
+a good place to start
+ 
+
+ align:start position:0%
+a good place to start
+when you're talking about motor control
+
+ align:start position:0%
+when you're talking about motor control
+ 
+
+ align:start position:0%
+when you're talking about motor control
+is on the output side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we could be reflexologists and assume
+
+ align:start position:0%
+we could be reflexologists and assume
+ 
+
+ align:start position:0%
+we could be reflexologists and assume
+that we should start with the sensations
+
+ align:start position:0%
+that we should start with the sensations
+ 
+
+ align:start position:0%
+that we should start with the sensations
+triggering the responses
+
+ align:start position:0%
+triggering the responses
+ 
+
+ align:start position:0%
+triggering the responses
+but i like to start with the motor
+
+ align:start position:0%
+but i like to start with the motor
+ 
+
+ align:start position:0%
+but i like to start with the motor
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+and then go backward into the cns
+
+ align:start position:0%
+and then go backward into the cns
+ 
+
+ align:start position:0%
+and then go backward into the cns
+so we're going to look at muscle
+
+ align:start position:0%
+so we're going to look at muscle
+ 
+
+ align:start position:0%
+so we're going to look at muscle
+where we find we
+
+ align:start position:0%
+where we find we
+ 
+
+ align:start position:0%
+where we find we
+magnify a little bit we'll see these
+
+ align:start position:0%
+magnify a little bit we'll see these
+ 
+
+ align:start position:0%
+magnify a little bit we'll see these
+myelinated axons of the alpha motor
+
+ align:start position:0%
+myelinated axons of the alpha motor
+ 
+
+ align:start position:0%
+myelinated axons of the alpha motor
+neurons the large motor neurons and the
+
+ align:start position:0%
+neurons the large motor neurons and the
+ 
+
+ align:start position:0%
+neurons the large motor neurons and the
+ventral horn of the spinal cord
+
+ align:start position:0%
+ventral horn of the spinal cord
+ 
+
+ align:start position:0%
+ventral horn of the spinal cord
+terminating
+
+ align:start position:0%
+terminating
+ 
+
+ align:start position:0%
+terminating
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the muscle cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multinucleate cells long cells with
+
+ align:start position:0%
+multinucleate cells long cells with
+ 
+
+ align:start position:0%
+multinucleate cells long cells with
+contractile proteins
+
+ align:start position:0%
+contractile proteins
+ 
+
+ align:start position:0%
+contractile proteins
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then if we do a blow up of the
+
+ align:start position:0%
+and then if we do a blow up of the
+ 
+
+ align:start position:0%
+and then if we do a blow up of the
+muscle end plate
+
+ align:start position:0%
+muscle end plate
+ 
+
+ align:start position:0%
+muscle end plate
+we'll see that
+
+ align:start position:0%
+we'll see that
+ 
+
+ align:start position:0%
+we'll see that
+synaptic connections are made with a
+
+ align:start position:0%
+synaptic connections are made with a
+ 
+
+ align:start position:0%
+synaptic connections are made with a
+muscle
+
+ align:start position:0%
+muscle
+ 
+
+ align:start position:0%
+muscle
+okay at multiple points
+
+ align:start position:0%
+okay at multiple points
+ 
+
+ align:start position:0%
+okay at multiple points
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+trigger basically an action potential in
+
+ align:start position:0%
+trigger basically an action potential in
+ 
+
+ align:start position:0%
+trigger basically an action potential in
+the muscle when that is triggered in the
+
+ align:start position:0%
+the muscle when that is triggered in the
+ 
+
+ align:start position:0%
+the muscle when that is triggered in the
+muscle the muscle contracts
+
+ align:start position:0%
+muscle the muscle contracts
+ 
+
+ align:start position:0%
+muscle the muscle contracts
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's similar to a neuron in some
+
+ align:start position:0%
+so it's similar to a neuron in some
+ 
+
+ align:start position:0%
+so it's similar to a neuron in some
+electrical properties but its response
+
+ align:start position:0%
+electrical properties but its response
+ 
+
+ align:start position:0%
+electrical properties but its response
+is that of contraction okay
+
+ align:start position:0%
+is that of contraction okay
+ 
+
+ align:start position:0%
+is that of contraction okay
+it doesn't communicate
+
+ align:start position:0%
+it doesn't communicate
+ 
+
+ align:start position:0%
+it doesn't communicate
+we don't have
+
+ align:start position:0%
+we don't have
+ 
+
+ align:start position:0%
+we don't have
+miod conduction that i know of there
+
+ align:start position:0%
+miod conduction that i know of there
+ 
+
+ align:start position:0%
+miod conduction that i know of there
+might be a little in smooth muscle but
+
+ align:start position:0%
+might be a little in smooth muscle but
+ 
+
+ align:start position:0%
+might be a little in smooth muscle but
+i'm not aware of it
+
+ align:start position:0%
+i'm not aware of it
+ 
+
+ align:start position:0%
+i'm not aware of it
+where muscles communicate with each
+
+ align:start position:0%
+where muscles communicate with each
+ 
+
+ align:start position:0%
+where muscles communicate with each
+other almost all the
+
+ align:start position:0%
+other almost all the
+ 
+
+ align:start position:0%
+other almost all the
+triggering of contraction is through
+
+ align:start position:0%
+triggering of contraction is through
+ 
+
+ align:start position:0%
+triggering of contraction is through
+neuronal activity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we start with the reflex model
+
+ align:start position:0%
+so if we start with the reflex model
+ 
+
+ align:start position:0%
+so if we start with the reflex model
+remember reflexology was the idea that
+
+ align:start position:0%
+remember reflexology was the idea that
+ 
+
+ align:start position:0%
+remember reflexology was the idea that
+all behavior can be explained in terms
+
+ align:start position:0%
+all behavior can be explained in terms
+ 
+
+ align:start position:0%
+all behavior can be explained in terms
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+s2r processing
+
+ align:start position:0%
+s2r processing
+ 
+
+ align:start position:0%
+s2r processing
+everything was a reflex a simple reflex
+
+ align:start position:0%
+everything was a reflex a simple reflex
+ 
+
+ align:start position:0%
+everything was a reflex a simple reflex
+or more complex reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost everything that pavlov wrote
+
+ align:start position:0%
+almost everything that pavlov wrote
+ 
+
+ align:start position:0%
+almost everything that pavlov wrote
+about motor control was put in those
+
+ align:start position:0%
+about motor control was put in those
+ 
+
+ align:start position:0%
+about motor control was put in those
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+and uh both pavlov and then laters
+
+ align:start position:0%
+and uh both pavlov and then laters
+ 
+
+ align:start position:0%
+and uh both pavlov and then laters
+skinner and others thorndike preceding
+
+ align:start position:0%
+skinner and others thorndike preceding
+ 
+
+ align:start position:0%
+skinner and others thorndike preceding
+him
+
+ align:start position:0%
+him
+ 
+
+ align:start position:0%
+him
+realized that
+
+ align:start position:0%
+realized that
+ 
+
+ align:start position:0%
+realized that
+sr pathways could be plastic you can get
+
+ align:start position:0%
+sr pathways could be plastic you can get
+ 
+
+ align:start position:0%
+sr pathways could be plastic you can get
+conditioning learning pavlov talked
+
+ align:start position:0%
+conditioning learning pavlov talked
+ 
+
+ align:start position:0%
+conditioning learning pavlov talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+classical conditioning or pavlovian
+
+ align:start position:0%
+classical conditioning or pavlovian
+ 
+
+ align:start position:0%
+classical conditioning or pavlovian
+conditioning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skinner talked about instrumental
+
+ align:start position:0%
+skinner talked about instrumental
+ 
+
+ align:start position:0%
+skinner talked about instrumental
+conditioning like an animal solving a
+
+ align:start position:0%
+conditioning like an animal solving a
+ 
+
+ align:start position:0%
+conditioning like an animal solving a
+problem box when he solves it randomly
+
+ align:start position:0%
+problem box when he solves it randomly
+ 
+
+ align:start position:0%
+problem box when he solves it randomly
+at first he will then learn and
+
+ align:start position:0%
+at first he will then learn and
+ 
+
+ align:start position:0%
+at first he will then learn and
+repeat the moves that were rewarding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but they still stuck to the sr model
+
+ align:start position:0%
+but they still stuck to the sr model
+ 
+
+ align:start position:0%
+but they still stuck to the sr model
+now we know and i've mentioned in the
+
+ align:start position:0%
+now we know and i've mentioned in the
+ 
+
+ align:start position:0%
+now we know and i've mentioned in the
+introductory lectures that the circuitry
+
+ align:start position:0%
+introductory lectures that the circuitry
+ 
+
+ align:start position:0%
+introductory lectures that the circuitry
+and individual cells are more complex
+
+ align:start position:0%
+and individual cells are more complex
+ 
+
+ align:start position:0%
+and individual cells are more complex
+they have feedback they have endogenous
+
+ align:start position:0%
+they have feedback they have endogenous
+ 
+
+ align:start position:0%
+they have feedback they have endogenous
+activity they have modulation whether
+
+ align:start position:0%
+activity they have modulation whether
+ 
+
+ align:start position:0%
+activity they have modulation whether
+by other pathways
+
+ align:start position:0%
+by other pathways
+ 
+
+ align:start position:0%
+by other pathways
+that makes the sr model a little bit
+
+ align:start position:0%
+that makes the sr model a little bit
+ 
+
+ align:start position:0%
+that makes the sr model a little bit
+difficult to stick to but
+
+ align:start position:0%
+difficult to stick to but
+ 
+
+ align:start position:0%
+difficult to stick to but
+if you're dealing with an a sim animal
+
+ align:start position:0%
+if you're dealing with an a sim animal
+ 
+
+ align:start position:0%
+if you're dealing with an a sim animal
+like a spinal animal you've removed the
+
+ align:start position:0%
+like a spinal animal you've removed the
+ 
+
+ align:start position:0%
+like a spinal animal you've removed the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+as it was done by sharington in his
+
+ align:start position:0%
+as it was done by sharington in his
+ 
+
+ align:start position:0%
+as it was done by sharington in his
+early studies
+
+ align:start position:0%
+early studies
+ 
+
+ align:start position:0%
+early studies
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+around 1900
+
+ align:start position:0%
+around 1900
+ 
+
+ align:start position:0%
+around 1900
+it works very well and you can explain
+
+ align:start position:0%
+it works very well and you can explain
+ 
+
+ align:start position:0%
+it works very well and you can explain
+most of the behavior that you can get
+
+ align:start position:0%
+most of the behavior that you can get
+ 
+
+ align:start position:0%
+most of the behavior that you can get
+and you'd say well what behavior can you
+
+ align:start position:0%
+and you'd say well what behavior can you
+ 
+
+ align:start position:0%
+and you'd say well what behavior can you
+get out of the spinal animal well quite
+
+ align:start position:0%
+get out of the spinal animal well quite
+ 
+
+ align:start position:0%
+get out of the spinal animal well quite
+a bit actually
+
+ align:start position:0%
+a bit actually
+ 
+
+ align:start position:0%
+a bit actually
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the spinal cord can do a lot by itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why can't we see that in humans with
+
+ align:start position:0%
+why can't we see that in humans with
+ 
+
+ align:start position:0%
+why can't we see that in humans with
+spinal transaction why don't we see more
+
+ align:start position:0%
+spinal transaction why don't we see more
+ 
+
+ align:start position:0%
+spinal transaction why don't we see more
+behavior why do they seem so incredibly
+
+ align:start position:0%
+behavior why do they seem so incredibly
+ 
+
+ align:start position:0%
+behavior why do they seem so incredibly
+paralyzed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember spinal shock
+
+ align:start position:0%
+remember spinal shock
+ 
+
+ align:start position:0%
+remember spinal shock
+and diastasis when you have a huge
+
+ align:start position:0%
+and diastasis when you have a huge
+ 
+
+ align:start position:0%
+and diastasis when you have a huge
+number of excitatory connections removed
+
+ align:start position:0%
+number of excitatory connections removed
+ 
+
+ align:start position:0%
+number of excitatory connections removed
+as in humans with a very large forebrain
+
+ align:start position:0%
+as in humans with a very large forebrain
+ 
+
+ align:start position:0%
+as in humans with a very large forebrain
+it's very difficult to get normal spinal
+
+ align:start position:0%
+it's very difficult to get normal spinal
+ 
+
+ align:start position:0%
+it's very difficult to get normal spinal
+function it's easier in animals with a
+
+ align:start position:0%
+function it's easier in animals with a
+ 
+
+ align:start position:0%
+function it's easier in animals with a
+smaller forebrain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but still even with
+
+ align:start position:0%
+but still even with
+ 
+
+ align:start position:0%
+but still even with
+humans with spinal transection
+
+ align:start position:0%
+humans with spinal transection
+ 
+
+ align:start position:0%
+humans with spinal transection
+they can learn to use spinal reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a number of functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to now talk about two
+
+ align:start position:0%
+so we're going to now talk about two
+ 
+
+ align:start position:0%
+so we're going to now talk about two
+basic responses simple escape or
+
+ align:start position:0%
+basic responses simple escape or
+ 
+
+ align:start position:0%
+basic responses simple escape or
+avoidance responses and approach or
+
+ align:start position:0%
+avoidance responses and approach or
+ 
+
+ align:start position:0%
+avoidance responses and approach or
+grasping responses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll start with the withdrawal reflex
+
+ align:start position:0%
+we'll start with the withdrawal reflex
+ 
+
+ align:start position:0%
+we'll start with the withdrawal reflex
+it's a cutaneous reflex
+
+ align:start position:0%
+it's a cutaneous reflex
+ 
+
+ align:start position:0%
+it's a cutaneous reflex
+it's a flexion reflex always involving
+
+ align:start position:0%
+it's a flexion reflex always involving
+ 
+
+ align:start position:0%
+it's a flexion reflex always involving
+at least two synapses
+
+ align:start position:0%
+at least two synapses
+ 
+
+ align:start position:0%
+at least two synapses
+and i want to ask here at the beginning
+
+ align:start position:0%
+and i want to ask here at the beginning
+ 
+
+ align:start position:0%
+and i want to ask here at the beginning
+well how do you know
+
+ align:start position:0%
+well how do you know
+ 
+
+ align:start position:0%
+well how do you know
+it's not monosynaptic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll go through
+
+ align:start position:0%
+we'll go through
+ 
+
+ align:start position:0%
+we'll go through
+some early studies that demonstrated
+
+ align:start position:0%
+some early studies that demonstrated
+ 
+
+ align:start position:0%
+some early studies that demonstrated
+that it involved more than one synapse
+
+ align:start position:0%
+that it involved more than one synapse
+ 
+
+ align:start position:0%
+that it involved more than one synapse
+and these were studies
+
+ align:start position:0%
+and these were studies
+ 
+
+ align:start position:0%
+and these were studies
+that were done by physiological means
+
+ align:start position:0%
+that were done by physiological means
+ 
+
+ align:start position:0%
+that were done by physiological means
+with some knowledge of the anatomy
+
+ align:start position:0%
+with some knowledge of the anatomy
+ 
+
+ align:start position:0%
+with some knowledge of the anatomy
+they had the knowledge of kahal to do
+
+ align:start position:0%
+they had the knowledge of kahal to do
+ 
+
+ align:start position:0%
+they had the knowledge of kahal to do
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+but after we do that then we'll talk
+
+ align:start position:0%
+but after we do that then we'll talk
+ 
+
+ align:start position:0%
+but after we do that then we'll talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+we'll mention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+responses and other modalities
+
+ align:start position:0%
+responses and other modalities
+ 
+
+ align:start position:0%
+responses and other modalities
+i'll talk about the magnet reflex which
+
+ align:start position:0%
+i'll talk about the magnet reflex which
+ 
+
+ align:start position:0%
+i'll talk about the magnet reflex which
+is the opposite
+
+ align:start position:0%
+is the opposite
+ 
+
+ align:start position:0%
+is the opposite
+something you see more in babies than
+
+ align:start position:0%
+something you see more in babies than
+ 
+
+ align:start position:0%
+something you see more in babies than
+adults
+
+ align:start position:0%
+adults
+ 
+
+ align:start position:0%
+adults
+will mention examples of higher
+
+ align:start position:0%
+will mention examples of higher
+ 
+
+ align:start position:0%
+will mention examples of higher
+influences on the spinal mechanisms and
+
+ align:start position:0%
+influences on the spinal mechanisms and
+ 
+
+ align:start position:0%
+influences on the spinal mechanisms and
+effects of novelty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so first of all cutaneous reflex called
+
+ align:start position:0%
+so first of all cutaneous reflex called
+ 
+
+ align:start position:0%
+so first of all cutaneous reflex called
+the withdrawal reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you trigger it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well a painful stimulus is the best way
+
+ align:start position:0%
+well a painful stimulus is the best way
+ 
+
+ align:start position:0%
+well a painful stimulus is the best way
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we're operating on an animal and we
+
+ align:start position:0%
+if we're operating on an animal and we
+ 
+
+ align:start position:0%
+if we're operating on an animal and we
+want to be sure he's fully anesthetized
+
+ align:start position:0%
+want to be sure he's fully anesthetized
+ 
+
+ align:start position:0%
+want to be sure he's fully anesthetized
+we test it by pinching usually between
+
+ align:start position:0%
+we test it by pinching usually between
+ 
+
+ align:start position:0%
+we test it by pinching usually between
+the digits
+
+ align:start position:0%
+the digits
+ 
+
+ align:start position:0%
+the digits
+if you pinch yourself you'll feel pain
+
+ align:start position:0%
+if you pinch yourself you'll feel pain
+ 
+
+ align:start position:0%
+if you pinch yourself you'll feel pain
+but you probably won't withdraw because
+
+ align:start position:0%
+but you probably won't withdraw because
+ 
+
+ align:start position:0%
+but you probably won't withdraw because
+you're voluntarily
+
+ align:start position:0%
+you're voluntarily
+ 
+
+ align:start position:0%
+you're voluntarily
+you know reducing that but if you do it
+
+ align:start position:0%
+you know reducing that but if you do it
+ 
+
+ align:start position:0%
+you know reducing that but if you do it
+to your friend
+
+ align:start position:0%
+to your friend
+ 
+
+ align:start position:0%
+to your friend
+you know he's much more likely if you
+
+ align:start position:0%
+you know he's much more likely if you
+ 
+
+ align:start position:0%
+you know he's much more likely if you
+suddenly pinch him to pull back
+
+ align:start position:0%
+suddenly pinch him to pull back
+ 
+
+ align:start position:0%
+suddenly pinch him to pull back
+involuntarily
+
+ align:start position:0%
+involuntarily
+ 
+
+ align:start position:0%
+involuntarily
+he thinks he's doing it on purpose but
+
+ align:start position:0%
+he thinks he's doing it on purpose but
+ 
+
+ align:start position:0%
+he thinks he's doing it on purpose but
+in fact it's an involuntary reaction
+
+ align:start position:0%
+in fact it's an involuntary reaction
+ 
+
+ align:start position:0%
+in fact it's an involuntary reaction
+you remember the picture from
+
+ align:start position:0%
+you remember the picture from
+ 
+
+ align:start position:0%
+you remember the picture from
+descartes of the naked boy sticking his
+
+ align:start position:0%
+descartes of the naked boy sticking his
+ 
+
+ align:start position:0%
+descartes of the naked boy sticking his
+foot in the fire okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triggering the withdrawal reflex because
+
+ align:start position:0%
+triggering the withdrawal reflex because
+ 
+
+ align:start position:0%
+triggering the withdrawal reflex because
+that's a reflex that descartes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spurred descartes to start thinking in
+
+ align:start position:0%
+spurred descartes to start thinking in
+ 
+
+ align:start position:0%
+spurred descartes to start thinking in
+terms of nervous pathways and
+
+ align:start position:0%
+terms of nervous pathways and
+ 
+
+ align:start position:0%
+terms of nervous pathways and
+connections through the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's first talk about the
+
+ align:start position:0%
+let's first talk about the
+ 
+
+ align:start position:0%
+let's first talk about the
+effects of the intensity stimulation and
+
+ align:start position:0%
+effects of the intensity stimulation and
+ 
+
+ align:start position:0%
+effects of the intensity stimulation and
+how the effect spreads within the cord
+
+ align:start position:0%
+how the effect spreads within the cord
+ 
+
+ align:start position:0%
+how the effect spreads within the cord
+i'm going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a spinal cord and look at a
+
+ align:start position:0%
+let's take a spinal cord and look at a
+ 
+
+ align:start position:0%
+let's take a spinal cord and look at a
+top view like that
+
+ align:start position:0%
+top view like that
+ 
+
+ align:start position:0%
+top view like that
+and take
+
+ align:start position:0%
+and take
+ 
+
+ align:start position:0%
+and take
+one dorsal root okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here would be the dorsal root
+
+ align:start position:0%
+and here would be the dorsal root
+ 
+
+ align:start position:0%
+and here would be the dorsal root
+ganglion there would be many cell bodies
+
+ align:start position:0%
+ganglion there would be many cell bodies
+ 
+
+ align:start position:0%
+ganglion there would be many cell bodies
+there we're going to let that represent
+
+ align:start position:0%
+there we're going to let that represent
+ 
+
+ align:start position:0%
+there we're going to let that represent
+a series of axons okay
+
+ align:start position:0%
+a series of axons okay
+ 
+
+ align:start position:0%
+a series of axons okay
+sensory accidents coming into the cord
+
+ align:start position:0%
+sensory accidents coming into the cord
+ 
+
+ align:start position:0%
+sensory accidents coming into the cord
+beginning say in the foot
+
+ align:start position:0%
+beginning say in the foot
+ 
+
+ align:start position:0%
+beginning say in the foot
+okay now that comes in the accents
+
+ align:start position:0%
+okay now that comes in the accents
+ 
+
+ align:start position:0%
+okay now that comes in the accents
+actually spread up and down the cord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we let
+
+ align:start position:0%
+and if we let
+ 
+
+ align:start position:0%
+and if we let
+it will show that termination
+
+ align:start position:0%
+it will show that termination
+ 
+
+ align:start position:0%
+it will show that termination
+what i want to show here is that the
+
+ align:start position:0%
+what i want to show here is that the
+ 
+
+ align:start position:0%
+what i want to show here is that the
+termination is most dense
+
+ align:start position:0%
+termination is most dense
+ 
+
+ align:start position:0%
+termination is most dense
+right in the area of entry
+
+ align:start position:0%
+right in the area of entry
+ 
+
+ align:start position:0%
+right in the area of entry
+and it becomes less and less dense when
+
+ align:start position:0%
+and it becomes less and less dense when
+ 
+
+ align:start position:0%
+and it becomes less and less dense when
+you get further from it
+
+ align:start position:0%
+you get further from it
+ 
+
+ align:start position:0%
+you get further from it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now the result of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+with a stimulus that's not very intense
+
+ align:start position:0%
+with a stimulus that's not very intense
+ 
+
+ align:start position:0%
+with a stimulus that's not very intense
+we might activate cells bring them above
+
+ align:start position:0%
+we might activate cells bring them above
+ 
+
+ align:start position:0%
+we might activate cells bring them above
+threshold only in that region
+
+ align:start position:0%
+threshold only in that region
+ 
+
+ align:start position:0%
+threshold only in that region
+okay because there's not enough spatial
+
+ align:start position:0%
+okay because there's not enough spatial
+ 
+
+ align:start position:0%
+okay because there's not enough spatial
+summation
+
+ align:start position:0%
+summation
+ 
+
+ align:start position:0%
+summation
+when we get further from the point of
+
+ align:start position:0%
+when we get further from the point of
+ 
+
+ align:start position:0%
+when we get further from the point of
+entry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what could happen then is that cells
+
+ align:start position:0%
+so what could happen then is that cells
+ 
+
+ align:start position:0%
+so what could happen then is that cells
+in this region
+
+ align:start position:0%
+in this region
+ 
+
+ align:start position:0%
+in this region
+could result
+
+ align:start position:0%
+could result
+ 
+
+ align:start position:0%
+could result
+could conduct action potentials
+
+ align:start position:0%
+could conduct action potentials
+ 
+
+ align:start position:0%
+could conduct action potentials
+and reach motor neurons
+
+ align:start position:0%
+and reach motor neurons
+ 
+
+ align:start position:0%
+and reach motor neurons
+which then could go out and give the
+
+ align:start position:0%
+which then could go out and give the
+ 
+
+ align:start position:0%
+which then could go out and give the
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+with more intense stimulation
+
+ align:start position:0%
+with more intense stimulation
+ 
+
+ align:start position:0%
+with more intense stimulation
+what will happen is it will spread over
+
+ align:start position:0%
+what will happen is it will spread over
+ 
+
+ align:start position:0%
+what will happen is it will spread over
+a wider region
+
+ align:start position:0%
+a wider region
+ 
+
+ align:start position:0%
+a wider region
+you will reach threshold over wider
+
+ align:start position:0%
+you will reach threshold over wider
+ 
+
+ align:start position:0%
+you will reach threshold over wider
+region because with more intense
+
+ align:start position:0%
+region because with more intense
+ 
+
+ align:start position:0%
+region because with more intense
+stimulation you
+
+ align:start position:0%
+stimulation you
+ 
+
+ align:start position:0%
+stimulation you
+now you have more temporal summation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll activate cells over
+
+ align:start position:0%
+you'll activate cells over
+ 
+
+ align:start position:0%
+you'll activate cells over
+this entire region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you get a spread
+
+ align:start position:0%
+so you get a spread
+ 
+
+ align:start position:0%
+so you get a spread
+of effect
+
+ align:start position:0%
+of effect
+ 
+
+ align:start position:0%
+of effect
+but in every case even with the low
+
+ align:start position:0%
+but in every case even with the low
+ 
+
+ align:start position:0%
+but in every case even with the low
+intensity stimulation
+
+ align:start position:0%
+intensity stimulation
+ 
+
+ align:start position:0%
+intensity stimulation
+you are still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you are still activating this entire
+
+ align:start position:0%
+you are still activating this entire
+ 
+
+ align:start position:0%
+you are still activating this entire
+axonal tree
+
+ align:start position:0%
+axonal tree
+ 
+
+ align:start position:0%
+axonal tree
+so what about
+
+ align:start position:0%
+so what about
+ 
+
+ align:start position:0%
+so what about
+out here with the low intensities of
+
+ align:start position:0%
+out here with the low intensities of
+ 
+
+ align:start position:0%
+out here with the low intensities of
+stimulation
+
+ align:start position:0%
+stimulation
+ 
+
+ align:start position:0%
+stimulation
+it's only the most intense stimulation
+
+ align:start position:0%
+it's only the most intense stimulation
+ 
+
+ align:start position:0%
+it's only the most intense stimulation
+that was going to activate that fringe
+
+ align:start position:0%
+that was going to activate that fringe
+ 
+
+ align:start position:0%
+that was going to activate that fringe
+of the distribution pattern of the axons
+
+ align:start position:0%
+of the distribution pattern of the axons
+ 
+
+ align:start position:0%
+of the distribution pattern of the axons
+so the physiologist called that the
+
+ align:start position:0%
+so the physiologist called that the
+ 
+
+ align:start position:0%
+so the physiologist called that the
+subliminal fringe
+
+ align:start position:0%
+subliminal fringe
+ 
+
+ align:start position:0%
+subliminal fringe
+because the stimulation there was
+
+ align:start position:0%
+because the stimulation there was
+ 
+
+ align:start position:0%
+because the stimulation there was
+usually
+
+ align:start position:0%
+usually
+ 
+
+ align:start position:0%
+usually
+below the lehman lehman means threshold
+
+ align:start position:0%
+below the lehman lehman means threshold
+ 
+
+ align:start position:0%
+below the lehman lehman means threshold
+so subliminal
+
+ align:start position:0%
+so subliminal
+ 
+
+ align:start position:0%
+so subliminal
+means below the threshold
+
+ align:start position:0%
+means below the threshold
+ 
+
+ align:start position:0%
+means below the threshold
+you've probably heard about studies of
+
+ align:start position:0%
+you've probably heard about studies of
+ 
+
+ align:start position:0%
+you've probably heard about studies of
+subliminal perception things you don't
+
+ align:start position:0%
+subliminal perception things you don't
+ 
+
+ align:start position:0%
+subliminal perception things you don't
+notice but are still getting into your
+
+ align:start position:0%
+notice but are still getting into your
+ 
+
+ align:start position:0%
+notice but are still getting into your
+nervous system
+
+ align:start position:0%
+nervous system
+ 
+
+ align:start position:0%
+nervous system
+okay but that was
+
+ align:start position:0%
+okay but that was
+ 
+
+ align:start position:0%
+okay but that was
+taken from this idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is that important
+
+ align:start position:0%
+why is that important
+ 
+
+ align:start position:0%
+why is that important
+why is the subliminal fringe important
+
+ align:start position:0%
+why is the subliminal fringe important
+ 
+
+ align:start position:0%
+why is the subliminal fringe important
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+let's put in blue here
+
+ align:start position:0%
+let's put in blue here
+ 
+
+ align:start position:0%
+let's put in blue here
+descending pathways coming from the
+
+ align:start position:0%
+descending pathways coming from the
+ 
+
+ align:start position:0%
+descending pathways coming from the
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and have whoops supposed to be blue here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the axons coming in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say its main distribution is
+
+ align:start position:0%
+and let's say its main distribution is
+ 
+
+ align:start position:0%
+and let's say its main distribution is
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+many terminations up here
+
+ align:start position:0%
+many terminations up here
+ 
+
+ align:start position:0%
+many terminations up here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now the descending input
+
+ align:start position:0%
+now the descending input
+ 
+
+ align:start position:0%
+now the descending input
+might not be intense enough to trigger
+
+ align:start position:0%
+might not be intense enough to trigger
+ 
+
+ align:start position:0%
+might not be intense enough to trigger
+the cells there
+
+ align:start position:0%
+the cells there
+ 
+
+ align:start position:0%
+the cells there
+and the sensory input coming from the
+
+ align:start position:0%
+and the sensory input coming from the
+ 
+
+ align:start position:0%
+and the sensory input coming from the
+stimulus here might also not be intense
+
+ align:start position:0%
+stimulus here might also not be intense
+ 
+
+ align:start position:0%
+stimulus here might also not be intense
+enough but the two together
+
+ align:start position:0%
+enough but the two together
+ 
+
+ align:start position:0%
+enough but the two together
+might be enough
+
+ align:start position:0%
+might be enough
+ 
+
+ align:start position:0%
+might be enough
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you might activate
+
+ align:start position:0%
+so you might activate
+ 
+
+ align:start position:0%
+so you might activate
+okay this region of the cord
+
+ align:start position:0%
+okay this region of the cord
+ 
+
+ align:start position:0%
+okay this region of the cord
+only with converging input from coming
+
+ align:start position:0%
+only with converging input from coming
+ 
+
+ align:start position:0%
+only with converging input from coming
+from the brain and coming from the
+
+ align:start position:0%
+from the brain and coming from the
+ 
+
+ align:start position:0%
+from the brain and coming from the
+sensory input
+
+ align:start position:0%
+sensory input
+ 
+
+ align:start position:0%
+sensory input
+coming into the cord
+
+ align:start position:0%
+coming into the cord
+ 
+
+ align:start position:0%
+coming into the cord
+that's why this limbo area is so
+
+ align:start position:0%
+that's why this limbo area is so
+ 
+
+ align:start position:0%
+that's why this limbo area is so
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's go to this question of
+
+ align:start position:0%
+okay now let's go to this question of
+ 
+
+ align:start position:0%
+okay now let's go to this question of
+how what it was shown by the early
+
+ align:start position:0%
+how what it was shown by the early
+ 
+
+ align:start position:0%
+how what it was shown by the early
+physiologists that the reflex is not
+
+ align:start position:0%
+physiologists that the reflex is not
+ 
+
+ align:start position:0%
+physiologists that the reflex is not
+monosynaptic
+
+ align:start position:0%
+monosynaptic
+ 
+
+ align:start position:0%
+monosynaptic
+and their experiments also gave the
+
+ align:start position:0%
+and their experiments also gave the
+ 
+
+ align:start position:0%
+and their experiments also gave the
+first measure
+
+ align:start position:0%
+first measure
+ 
+
+ align:start position:0%
+first measure
+of synaptic delay
+
+ align:start position:0%
+of synaptic delay
+ 
+
+ align:start position:0%
+of synaptic delay
+synaptic delay means the time it takes
+
+ align:start position:0%
+synaptic delay means the time it takes
+ 
+
+ align:start position:0%
+synaptic delay means the time it takes
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+activation on the presynaptic side
+
+ align:start position:0%
+activation on the presynaptic side
+ 
+
+ align:start position:0%
+activation on the presynaptic side
+to reach the postsynaptic side
+
+ align:start position:0%
+to reach the postsynaptic side
+ 
+
+ align:start position:0%
+to reach the postsynaptic side
+why does it take time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it doesn't take any time if the stimulus
+
+ align:start position:0%
+it doesn't take any time if the stimulus
+ 
+
+ align:start position:0%
+it doesn't take any time if the stimulus
+is electrical but in almost all synapses
+
+ align:start position:0%
+is electrical but in almost all synapses
+ 
+
+ align:start position:0%
+is electrical but in almost all synapses
+in the cns are chemical and it takes
+
+ align:start position:0%
+in the cns are chemical and it takes
+ 
+
+ align:start position:0%
+in the cns are chemical and it takes
+time for molecules to diffuse across the
+
+ align:start position:0%
+time for molecules to diffuse across the
+ 
+
+ align:start position:0%
+time for molecules to diffuse across the
+synaptic clef bind to the
+
+ align:start position:0%
+synaptic clef bind to the
+ 
+
+ align:start position:0%
+synaptic clef bind to the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+receptor molecules there and activate
+
+ align:start position:0%
+receptor molecules there and activate
+ 
+
+ align:start position:0%
+receptor molecules there and activate
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's go through the steps
+
+ align:start position:0%
+so let's go through the steps
+ 
+
+ align:start position:0%
+so let's go through the steps
+they begin
+
+ align:start position:0%
+they begin
+ 
+
+ align:start position:0%
+they begin
+by recording from a ventral root so look
+
+ align:start position:0%
+by recording from a ventral root so look
+ 
+
+ align:start position:0%
+by recording from a ventral root so look
+at this picture first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and here's
+
+ align:start position:0%
+okay and here's
+ 
+
+ align:start position:0%
+okay and here's
+a recording device attached to the
+
+ align:start position:0%
+a recording device attached to the
+ 
+
+ align:start position:0%
+a recording device attached to the
+ventral root and notice this is the way
+
+ align:start position:0%
+ventral root and notice this is the way
+ 
+
+ align:start position:0%
+ventral root and notice this is the way
+the experiment was done
+
+ align:start position:0%
+the experiment was done
+ 
+
+ align:start position:0%
+the experiment was done
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i need my pointer so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they generally crush the nerve here
+
+ align:start position:0%
+they generally crush the nerve here
+ 
+
+ align:start position:0%
+they generally crush the nerve here
+because they didn't want to activate
+
+ align:start position:0%
+because they didn't want to activate
+ 
+
+ align:start position:0%
+because they didn't want to activate
+anything in the periphery here
+
+ align:start position:0%
+anything in the periphery here
+ 
+
+ align:start position:0%
+anything in the periphery here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so they're recording there
+
+ align:start position:0%
+so they're recording there
+ 
+
+ align:start position:0%
+so they're recording there
+and the first place they stimulated
+
+ align:start position:0%
+and the first place they stimulated
+ 
+
+ align:start position:0%
+and the first place they stimulated
+is labeled two here the little pipette
+
+ align:start position:0%
+is labeled two here the little pipette
+ 
+
+ align:start position:0%
+is labeled two here the little pipette
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+going right into
+
+ align:start position:0%
+going right into
+ 
+
+ align:start position:0%
+going right into
+the region of motor neurons
+
+ align:start position:0%
+the region of motor neurons
+ 
+
+ align:start position:0%
+the region of motor neurons
+in the ventral horn okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's described here you record from
+
+ align:start position:0%
+so that's described here you record from
+ 
+
+ align:start position:0%
+so that's described here you record from
+the ventral root you stimulate the motor
+
+ align:start position:0%
+the ventral root you stimulate the motor
+ 
+
+ align:start position:0%
+the ventral root you stimulate the motor
+neurons and of course you then record a
+
+ align:start position:0%
+neurons and of course you then record a
+ 
+
+ align:start position:0%
+neurons and of course you then record a
+valley of action potentials after a
+
+ align:start position:0%
+valley of action potentials after a
+ 
+
+ align:start position:0%
+valley of action potentials after a
+brief conduction delay and i show that
+
+ align:start position:0%
+brief conduction delay and i show that
+ 
+
+ align:start position:0%
+brief conduction delay and i show that
+in the graph here okay
+
+ align:start position:0%
+in the graph here okay
+ 
+
+ align:start position:0%
+in the graph here okay
+you stimulate
+
+ align:start position:0%
+you stimulate
+ 
+
+ align:start position:0%
+you stimulate
+and after a brief delay
+
+ align:start position:0%
+and after a brief delay
+ 
+
+ align:start position:0%
+and after a brief delay
+shown by the
+
+ align:start position:0%
+shown by the
+ 
+
+ align:start position:0%
+shown by the
+two lines there
+
+ align:start position:0%
+two lines there
+ 
+
+ align:start position:0%
+two lines there
+you can record a volume of action
+
+ align:start position:0%
+you can record a volume of action
+ 
+
+ align:start position:0%
+you can record a volume of action
+potential or you could if you had it
+
+ align:start position:0%
+potential or you could if you had it
+ 
+
+ align:start position:0%
+potential or you could if you had it
+connected to the muscles you could
+
+ align:start position:0%
+connected to the muscles you could
+ 
+
+ align:start position:0%
+connected to the muscles you could
+record the muscle twitch but we don't
+
+ align:start position:0%
+record the muscle twitch but we don't
+ 
+
+ align:start position:0%
+record the muscle twitch but we don't
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+the muscle twitch because we don't want
+
+ align:start position:0%
+the muscle twitch because we don't want
+ 
+
+ align:start position:0%
+the muscle twitch because we don't want
+to affect sensory inputs here at all so
+
+ align:start position:0%
+to affect sensory inputs here at all so
+ 
+
+ align:start position:0%
+to affect sensory inputs here at all so
+we're that's why we crush the root okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was the first
+
+ align:start position:0%
+so that was the first
+ 
+
+ align:start position:0%
+so that was the first
+experiment now
+
+ align:start position:0%
+experiment now
+ 
+
+ align:start position:0%
+experiment now
+this is what renshaw did
+
+ align:start position:0%
+this is what renshaw did
+ 
+
+ align:start position:0%
+this is what renshaw did
+he pulled that electrode back
+
+ align:start position:0%
+he pulled that electrode back
+ 
+
+ align:start position:0%
+he pulled that electrode back
+until he was no longer stimulating motor
+
+ align:start position:0%
+until he was no longer stimulating motor
+ 
+
+ align:start position:0%
+until he was no longer stimulating motor
+neurons directly
+
+ align:start position:0%
+neurons directly
+ 
+
+ align:start position:0%
+neurons directly
+he was stimulating interneuron
+
+ align:start position:0%
+he was stimulating interneuron
+ 
+
+ align:start position:0%
+he was stimulating interneuron
+interneurons though that contacted motor
+
+ align:start position:0%
+interneurons though that contacted motor
+ 
+
+ align:start position:0%
+interneurons though that contacted motor
+neurons and he knew all this you could
+
+ align:start position:0%
+neurons and he knew all this you could
+ 
+
+ align:start position:0%
+neurons and he knew all this you could
+guess that from the work of kahal
+
+ align:start position:0%
+guess that from the work of kahal
+ 
+
+ align:start position:0%
+guess that from the work of kahal
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in his recordings he could see that
+
+ align:start position:0%
+but in his recordings he could see that
+ 
+
+ align:start position:0%
+but in his recordings he could see that
+that initial volley suddenly went away
+
+ align:start position:0%
+that initial volley suddenly went away
+ 
+
+ align:start position:0%
+that initial volley suddenly went away
+when he pulled the electrode back a
+
+ align:start position:0%
+when he pulled the electrode back a
+ 
+
+ align:start position:0%
+when he pulled the electrode back a
+certain distance okay and then if he's
+
+ align:start position:0%
+certain distance okay and then if he's
+ 
+
+ align:start position:0%
+certain distance okay and then if he's
+stimulated with the lower intensities
+
+ align:start position:0%
+stimulated with the lower intensities
+ 
+
+ align:start position:0%
+stimulated with the lower intensities
+shown in the solid line there
+
+ align:start position:0%
+shown in the solid line there
+ 
+
+ align:start position:0%
+shown in the solid line there
+he got a volley
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it was after a delay the delay was
+
+ align:start position:0%
+but it was after a delay the delay was
+ 
+
+ align:start position:0%
+but it was after a delay the delay was
+0.5 to 0.7 milliseconds
+
+ align:start position:0%
+0.5 to 0.7 milliseconds
+ 
+
+ align:start position:0%
+0.5 to 0.7 milliseconds
+and if you raise the intensity
+
+ align:start position:0%
+and if you raise the intensity
+ 
+
+ align:start position:0%
+and if you raise the intensity
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it would become larger
+
+ align:start position:0%
+it would become larger
+ 
+
+ align:start position:0%
+it would become larger
+if you raised it enough you would start
+
+ align:start position:0%
+if you raised it enough you would start
+ 
+
+ align:start position:0%
+if you raised it enough you would start
+getting something like this initial one
+
+ align:start position:0%
+getting something like this initial one
+ 
+
+ align:start position:0%
+getting something like this initial one
+followed by the later one
+
+ align:start position:0%
+followed by the later one
+ 
+
+ align:start position:0%
+followed by the later one
+indicating to him that he was the
+
+ align:start position:0%
+indicating to him that he was the
+ 
+
+ align:start position:0%
+indicating to him that he was the
+current head spread with the higher
+
+ align:start position:0%
+current head spread with the higher
+ 
+
+ align:start position:0%
+current head spread with the higher
+intensities to directly stimulate motor
+
+ align:start position:0%
+intensities to directly stimulate motor
+ 
+
+ align:start position:0%
+intensities to directly stimulate motor
+neurons but was still stimulating
+
+ align:start position:0%
+neurons but was still stimulating
+ 
+
+ align:start position:0%
+neurons but was still stimulating
+interneurons
+
+ align:start position:0%
+interneurons
+ 
+
+ align:start position:0%
+interneurons
+which required one synapse to reach the
+
+ align:start position:0%
+which required one synapse to reach the
+ 
+
+ align:start position:0%
+which required one synapse to reach the
+motor
+
+ align:start position:0%
+motor
+ 
+
+ align:start position:0%
+motor
+neuron so this was the first measure of
+
+ align:start position:0%
+neuron so this was the first measure of
+ 
+
+ align:start position:0%
+neuron so this was the first measure of
+synaptic delay
+
+ align:start position:0%
+synaptic delay
+ 
+
+ align:start position:0%
+synaptic delay
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lloyd then did
+
+ align:start position:0%
+lloyd then did
+ 
+
+ align:start position:0%
+lloyd then did
+a further experiment using the same
+
+ align:start position:0%
+a further experiment using the same
+ 
+
+ align:start position:0%
+a further experiment using the same
+paradigm
+
+ align:start position:0%
+paradigm
+ 
+
+ align:start position:0%
+paradigm
+he moved his electrodes with the same
+
+ align:start position:0%
+he moved his electrodes with the same
+ 
+
+ align:start position:0%
+he moved his electrodes with the same
+set up here to the dorsal root
+
+ align:start position:0%
+set up here to the dorsal root
+ 
+
+ align:start position:0%
+set up here to the dorsal root
+and if he stimulates
+
+ align:start position:0%
+and if he stimulates
+ 
+
+ align:start position:0%
+and if he stimulates
+with a intense enough stimulation he's
+
+ align:start position:0%
+with a intense enough stimulation he's
+ 
+
+ align:start position:0%
+with a intense enough stimulation he's
+going to activate all the fibers if he
+
+ align:start position:0%
+going to activate all the fibers if he
+ 
+
+ align:start position:0%
+going to activate all the fibers if he
+stimulates with a milder stimulation he
+
+ align:start position:0%
+stimulates with a milder stimulation he
+ 
+
+ align:start position:0%
+stimulates with a milder stimulation he
+will activate only the large fibers
+
+ align:start position:0%
+will activate only the large fibers
+ 
+
+ align:start position:0%
+will activate only the large fibers
+okay the largest fibers in the dorsal
+
+ align:start position:0%
+okay the largest fibers in the dorsal
+ 
+
+ align:start position:0%
+okay the largest fibers in the dorsal
+root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and again the intensity was varied
+
+ align:start position:0%
+and again the intensity was varied
+ 
+
+ align:start position:0%
+and again the intensity was varied
+and what he found was he got something
+
+ align:start position:0%
+and what he found was he got something
+ 
+
+ align:start position:0%
+and what he found was he got something
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+to what rancho had gotten stimulating
+
+ align:start position:0%
+to what rancho had gotten stimulating
+ 
+
+ align:start position:0%
+to what rancho had gotten stimulating
+the internal pool on the cord he got our
+
+ align:start position:0%
+the internal pool on the cord he got our
+ 
+
+ align:start position:0%
+the internal pool on the cord he got our
+first volley
+
+ align:start position:0%
+first volley
+ 
+
+ align:start position:0%
+first volley
+but then he also got later
+
+ align:start position:0%
+but then he also got later
+ 
+
+ align:start position:0%
+but then he also got later
+volleys and as he raised the intensity
+
+ align:start position:0%
+volleys and as he raised the intensity
+ 
+
+ align:start position:0%
+volleys and as he raised the intensity
+he got
+
+ align:start position:0%
+he got
+ 
+
+ align:start position:0%
+he got
+additional he got greater
+
+ align:start position:0%
+additional he got greater
+ 
+
+ align:start position:0%
+additional he got greater
+amount of number of action potentials
+
+ align:start position:0%
+amount of number of action potentials
+ 
+
+ align:start position:0%
+amount of number of action potentials
+more action potentials appearing in the
+
+ align:start position:0%
+more action potentials appearing in the
+ 
+
+ align:start position:0%
+more action potentials appearing in the
+ventral root
+
+ align:start position:0%
+ventral root
+ 
+
+ align:start position:0%
+ventral root
+and they appeared to be sort of harmonic
+
+ align:start position:0%
+and they appeared to be sort of harmonic
+ 
+
+ align:start position:0%
+and they appeared to be sort of harmonic
+spaced
+
+ align:start position:0%
+spaced
+ 
+
+ align:start position:0%
+spaced
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+distances that indicated that it was
+
+ align:start position:0%
+distances that indicated that it was
+ 
+
+ align:start position:0%
+distances that indicated that it was
+simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one synapse two synapses three synapses
+
+ align:start position:0%
+one synapse two synapses three synapses
+ 
+
+ align:start position:0%
+one synapse two synapses three synapses
+and so forth
+
+ align:start position:0%
+and so forth
+ 
+
+ align:start position:0%
+and so forth
+okay he never got the artifact here
+
+ align:start position:0%
+okay he never got the artifact here
+ 
+
+ align:start position:0%
+okay he never got the artifact here
+because now his electorate was outside
+
+ align:start position:0%
+because now his electorate was outside
+ 
+
+ align:start position:0%
+because now his electorate was outside
+the spinal cord so it wasn't spreading
+
+ align:start position:0%
+the spinal cord so it wasn't spreading
+ 
+
+ align:start position:0%
+the spinal cord so it wasn't spreading
+to motor neurons now
+
+ align:start position:0%
+to motor neurons now
+ 
+
+ align:start position:0%
+to motor neurons now
+that's why he didn't get that artifact
+
+ align:start position:0%
+that's why he didn't get that artifact
+ 
+
+ align:start position:0%
+that's why he didn't get that artifact
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+rancho got here
+
+ align:start position:0%
+rancho got here
+ 
+
+ align:start position:0%
+rancho got here
+is that clear what's happening
+
+ align:start position:0%
+is that clear what's happening
+ 
+
+ align:start position:0%
+is that clear what's happening
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the final experiment was to stimulate
+
+ align:start position:0%
+the final experiment was to stimulate
+ 
+
+ align:start position:0%
+the final experiment was to stimulate
+the cutaneous nerve
+
+ align:start position:0%
+the cutaneous nerve
+ 
+
+ align:start position:0%
+the cutaneous nerve
+now if you go
+
+ align:start position:0%
+now if you go
+ 
+
+ align:start position:0%
+now if you go
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you can after the
+
+ align:start position:0%
+you can after the
+ 
+
+ align:start position:0%
+you can after the
+dorsal and ventral roots come together
+
+ align:start position:0%
+dorsal and ventral roots come together
+ 
+
+ align:start position:0%
+dorsal and ventral roots come together
+you get into the peripheral nerve
+
+ align:start position:0%
+you get into the peripheral nerve
+ 
+
+ align:start position:0%
+you get into the peripheral nerve
+and there are nerves out here that go
+
+ align:start position:0%
+and there are nerves out here that go
+ 
+
+ align:start position:0%
+and there are nerves out here that go
+only to the skin
+
+ align:start position:0%
+only to the skin
+ 
+
+ align:start position:0%
+only to the skin
+other nerves are mixed they go to skin
+
+ align:start position:0%
+other nerves are mixed they go to skin
+ 
+
+ align:start position:0%
+other nerves are mixed they go to skin
+and muscle and there's some that go on
+
+ align:start position:0%
+and muscle and there's some that go on
+ 
+
+ align:start position:0%
+and muscle and there's some that go on
+into muscle just depends on where you
+
+ align:start position:0%
+into muscle just depends on where you
+ 
+
+ align:start position:0%
+into muscle just depends on where you
+are okay
+
+ align:start position:0%
+are okay
+ 
+
+ align:start position:0%
+are okay
+so they found the cutaneous nerve
+
+ align:start position:0%
+so they found the cutaneous nerve
+ 
+
+ align:start position:0%
+so they found the cutaneous nerve
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+stimulated there with a
+
+ align:start position:0%
+stimulated there with a
+ 
+
+ align:start position:0%
+stimulated there with a
+sudden pulse of electricity
+
+ align:start position:0%
+sudden pulse of electricity
+ 
+
+ align:start position:0%
+sudden pulse of electricity
+they corrected for the conduction time
+
+ align:start position:0%
+they corrected for the conduction time
+ 
+
+ align:start position:0%
+they corrected for the conduction time
+okay and they found that with the
+
+ align:start position:0%
+okay and they found that with the
+ 
+
+ align:start position:0%
+okay and they found that with the
+cutaneous nerve they never got this
+
+ align:start position:0%
+cutaneous nerve they never got this
+ 
+
+ align:start position:0%
+cutaneous nerve they never got this
+first volley
+
+ align:start position:0%
+first volley
+ 
+
+ align:start position:0%
+first volley
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+there always seemed to be at least two
+
+ align:start position:0%
+there always seemed to be at least two
+ 
+
+ align:start position:0%
+there always seemed to be at least two
+or more synapses
+
+ align:start position:0%
+or more synapses
+ 
+
+ align:start position:0%
+or more synapses
+between the cutaneous nerve and the
+
+ align:start position:0%
+between the cutaneous nerve and the
+ 
+
+ align:start position:0%
+between the cutaneous nerve and the
+motor neurons the activation of the
+
+ align:start position:0%
+motor neurons the activation of the
+ 
+
+ align:start position:0%
+motor neurons the activation of the
+motor neurons and the actual potentials
+
+ align:start position:0%
+motor neurons and the actual potentials
+ 
+
+ align:start position:0%
+motor neurons and the actual potentials
+that actually appear in the ventral root
+
+ align:start position:0%
+that actually appear in the ventral root
+ 
+
+ align:start position:0%
+that actually appear in the ventral root
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that was how it was demonstrated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cutaneous reflexes
+
+ align:start position:0%
+cutaneous reflexes
+ 
+
+ align:start position:0%
+cutaneous reflexes
+are never monosynaptic
+
+ align:start position:0%
+are never monosynaptic
+ 
+
+ align:start position:0%
+are never monosynaptic
+they always involve at least two
+
+ align:start position:0%
+they always involve at least two
+ 
+
+ align:start position:0%
+they always involve at least two
+synapses
+
+ align:start position:0%
+synapses
+ 
+
+ align:start position:0%
+synapses
+and it was also the way they
+
+ align:start position:0%
+and it was also the way they
+ 
+
+ align:start position:0%
+and it was also the way they
+demonstrated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first evidence for a clear synaptic
+
+ align:start position:0%
+the first evidence for a clear synaptic
+ 
+
+ align:start position:0%
+the first evidence for a clear synaptic
+delay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when they trigger that reflex the
+
+ align:start position:0%
+now when they trigger that reflex the
+ 
+
+ align:start position:0%
+now when they trigger that reflex the
+other things happen too
+
+ align:start position:0%
+other things happen too
+ 
+
+ align:start position:0%
+other things happen too
+when you trigger at a flexion reflex
+
+ align:start position:0%
+when you trigger at a flexion reflex
+ 
+
+ align:start position:0%
+when you trigger at a flexion reflex
+let's say you trigger withdrawal of the
+
+ align:start position:0%
+let's say you trigger withdrawal of the
+ 
+
+ align:start position:0%
+let's say you trigger withdrawal of the
+arm
+
+ align:start position:0%
+arm
+ 
+
+ align:start position:0%
+arm
+not only do you activate flexure muscles
+
+ align:start position:0%
+not only do you activate flexure muscles
+ 
+
+ align:start position:0%
+not only do you activate flexure muscles
+but you also relax extensor muscles
+
+ align:start position:0%
+but you also relax extensor muscles
+ 
+
+ align:start position:0%
+but you also relax extensor muscles
+that's called reciprocal inhibition
+
+ align:start position:0%
+that's called reciprocal inhibition
+ 
+
+ align:start position:0%
+that's called reciprocal inhibition
+okay it's a pretty general principle
+
+ align:start position:0%
+okay it's a pretty general principle
+ 
+
+ align:start position:0%
+okay it's a pretty general principle
+to avoid conflict
+
+ align:start position:0%
+to avoid conflict
+ 
+
+ align:start position:0%
+to avoid conflict
+you get rid of the competing you reduce
+
+ align:start position:0%
+you get rid of the competing you reduce
+ 
+
+ align:start position:0%
+you get rid of the competing you reduce
+activity in the competing response
+
+ align:start position:0%
+activity in the competing response
+ 
+
+ align:start position:0%
+activity in the competing response
+systems it happens in brain mechanisms
+
+ align:start position:0%
+systems it happens in brain mechanisms
+ 
+
+ align:start position:0%
+systems it happens in brain mechanisms
+too it happens during fixed action
+
+ align:start position:0%
+too it happens during fixed action
+ 
+
+ align:start position:0%
+too it happens during fixed action
+patterns okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think of conflict in an animal now if he
+
+ align:start position:0%
+think of conflict in an animal now if he
+ 
+
+ align:start position:0%
+think of conflict in an animal now if he
+gets stimuli
+
+ align:start position:0%
+gets stimuli
+ 
+
+ align:start position:0%
+gets stimuli
+that can trigger approach to food and
+
+ align:start position:0%
+that can trigger approach to food and
+ 
+
+ align:start position:0%
+that can trigger approach to food and
+escape from a predator
+
+ align:start position:0%
+escape from a predator
+ 
+
+ align:start position:0%
+escape from a predator
+which which would you want to
+
+ align:start position:0%
+which which would you want to
+ 
+
+ align:start position:0%
+which which would you want to
+inhibit the other response
+
+ align:start position:0%
+inhibit the other response
+ 
+
+ align:start position:0%
+inhibit the other response
+well of course the escape response
+
+ align:start position:0%
+well of course the escape response
+ 
+
+ align:start position:0%
+well of course the escape response
+should inhibit the feeding
+
+ align:start position:0%
+should inhibit the feeding
+ 
+
+ align:start position:0%
+should inhibit the feeding
+and it generally does
+
+ align:start position:0%
+and it generally does
+ 
+
+ align:start position:0%
+and it generally does
+the animal drops what he's doing and
+
+ align:start position:0%
+the animal drops what he's doing and
+ 
+
+ align:start position:0%
+the animal drops what he's doing and
+freezes or runs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it happens at this very low level in
+
+ align:start position:0%
+but it happens at this very low level in
+ 
+
+ align:start position:0%
+but it happens at this very low level in
+the spinal cord
+
+ align:start position:0%
+the spinal cord
+ 
+
+ align:start position:0%
+the spinal cord
+with reciprocal inhibition of extensors
+
+ align:start position:0%
+with reciprocal inhibition of extensors
+ 
+
+ align:start position:0%
+with reciprocal inhibition of extensors
+i just point out here that it doesn't
+
+ align:start position:0%
+i just point out here that it doesn't
+ 
+
+ align:start position:0%
+i just point out here that it doesn't
+always work with higher systems should i
+
+ align:start position:0%
+always work with higher systems should i
+ 
+
+ align:start position:0%
+always work with higher systems should i
+watch tv or should i study
+
+ align:start position:0%
+watch tv or should i study
+ 
+
+ align:start position:0%
+watch tv or should i study
+sometimes you just experience the
+
+ align:start position:0%
+sometimes you just experience the
+ 
+
+ align:start position:0%
+sometimes you just experience the
+conflict and as we grow older we hope
+
+ align:start position:0%
+conflict and as we grow older we hope
+ 
+
+ align:start position:0%
+conflict and as we grow older we hope
+some of us anyway get better and better
+
+ align:start position:0%
+some of us anyway get better and better
+ 
+
+ align:start position:0%
+some of us anyway get better and better
+at resolving conflicts
+
+ align:start position:0%
+at resolving conflicts
+ 
+
+ align:start position:0%
+at resolving conflicts
+but we never get rid of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other things happen too
+
+ align:start position:0%
+other things happen too
+ 
+
+ align:start position:0%
+other things happen too
+when we trigger this let's say we
+
+ align:start position:0%
+when we trigger this let's say we
+ 
+
+ align:start position:0%
+when we trigger this let's say we
+trigger withdrawal of the leg
+
+ align:start position:0%
+trigger withdrawal of the leg
+ 
+
+ align:start position:0%
+trigger withdrawal of the leg
+it would be a tendency for the
+
+ align:start position:0%
+it would be a tendency for the
+ 
+
+ align:start position:0%
+it would be a tendency for the
+animal to fall over
+
+ align:start position:0%
+animal to fall over
+ 
+
+ align:start position:0%
+animal to fall over
+lose this balance very easily there's
+
+ align:start position:0%
+lose this balance very easily there's
+ 
+
+ align:start position:0%
+lose this balance very easily there's
+usually a cross extension reflex so
+
+ align:start position:0%
+usually a cross extension reflex so
+ 
+
+ align:start position:0%
+usually a cross extension reflex so
+there will be fibers coming from
+
+ align:start position:0%
+there will be fibers coming from
+ 
+
+ align:start position:0%
+there will be fibers coming from
+interneurons that are triggered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the cutaneous activity
+
+ align:start position:0%
+by the cutaneous activity
+ 
+
+ align:start position:0%
+by the cutaneous activity
+okay we'll cross over to the other side
+
+ align:start position:0%
+okay we'll cross over to the other side
+ 
+
+ align:start position:0%
+okay we'll cross over to the other side
+but instead of activating flexion
+
+ align:start position:0%
+but instead of activating flexion
+ 
+
+ align:start position:0%
+but instead of activating flexion
+they'll activate extension
+
+ align:start position:0%
+they'll activate extension
+ 
+
+ align:start position:0%
+they'll activate extension
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so often if you see that happen a person
+
+ align:start position:0%
+so often if you see that happen a person
+ 
+
+ align:start position:0%
+so often if you see that happen a person
+will go like that
+
+ align:start position:0%
+will go like that
+ 
+
+ align:start position:0%
+will go like that
+because he's extending
+
+ align:start position:0%
+because he's extending
+ 
+
+ align:start position:0%
+because he's extending
+the leg and the initial movement is
+
+ align:start position:0%
+the leg and the initial movement is
+ 
+
+ align:start position:0%
+the leg and the initial movement is
+automatic
+
+ align:start position:0%
+automatic
+ 
+
+ align:start position:0%
+automatic
+and then of course the stimulator
+
+ align:start position:0%
+and then of course the stimulator
+ 
+
+ align:start position:0%
+and then of course the stimulator
+reflexes will come into play and tend to
+
+ align:start position:0%
+reflexes will come into play and tend to
+ 
+
+ align:start position:0%
+reflexes will come into play and tend to
+keep him on his feet
+
+ align:start position:0%
+keep him on his feet
+ 
+
+ align:start position:0%
+keep him on his feet
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now if it's very intense
+
+ align:start position:0%
+now if it's very intense
+ 
+
+ align:start position:0%
+now if it's very intense
+it won't just be his foot but withdraws
+
+ align:start position:0%
+it won't just be his foot but withdraws
+ 
+
+ align:start position:0%
+it won't just be his foot but withdraws
+or just his leg he might get more
+
+ align:start position:0%
+or just his leg he might get more
+ 
+
+ align:start position:0%
+or just his leg he might get more
+general flexion of his body
+
+ align:start position:0%
+general flexion of his body
+ 
+
+ align:start position:0%
+general flexion of his body
+in some cases it's difficult to maintain
+
+ align:start position:0%
+in some cases it's difficult to maintain
+ 
+
+ align:start position:0%
+in some cases it's difficult to maintain
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+but generally the crossed extension
+
+ align:start position:0%
+but generally the crossed extension
+ 
+
+ align:start position:0%
+but generally the crossed extension
+reflex will aid that maintaining of
+
+ align:start position:0%
+reflex will aid that maintaining of
+ 
+
+ align:start position:0%
+reflex will aid that maintaining of
+posture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's just think briefly about other
+
+ align:start position:0%
+let's just think briefly about other
+ 
+
+ align:start position:0%
+let's just think briefly about other
+modalities
+
+ align:start position:0%
+modalities
+ 
+
+ align:start position:0%
+modalities
+what happens with intense light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if light is very bright you get
+
+ align:start position:0%
+if light is very bright you get
+ 
+
+ align:start position:0%
+if light is very bright you get
+something like a withdrawal from the
+
+ align:start position:0%
+something like a withdrawal from the
+ 
+
+ align:start position:0%
+something like a withdrawal from the
+stimulus anyway because you get
+
+ align:start position:0%
+stimulus anyway because you get
+ 
+
+ align:start position:0%
+stimulus anyway because you get
+constriction of the pupils
+
+ align:start position:0%
+constriction of the pupils
+ 
+
+ align:start position:0%
+constriction of the pupils
+okay to protect the retina from too much
+
+ align:start position:0%
+okay to protect the retina from too much
+ 
+
+ align:start position:0%
+okay to protect the retina from too much
+light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pupillary
+
+ align:start position:0%
+pupillary
+ 
+
+ align:start position:0%
+pupillary
+contraction does other things too it
+
+ align:start position:0%
+contraction does other things too it
+ 
+
+ align:start position:0%
+contraction does other things too it
+increases
+
+ align:start position:0%
+increases
+ 
+
+ align:start position:0%
+increases
+the resolution possible resolution of
+
+ align:start position:0%
+the resolution possible resolution of
+ 
+
+ align:start position:0%
+the resolution possible resolution of
+the image
+
+ align:start position:0%
+the image
+ 
+
+ align:start position:0%
+the image
+even with poor
+
+ align:start position:0%
+even with poor
+ 
+
+ align:start position:0%
+even with poor
+focus on the retina
+
+ align:start position:0%
+focus on the retina
+ 
+
+ align:start position:0%
+focus on the retina
+if the pupils are very small you will
+
+ align:start position:0%
+if the pupils are very small you will
+ 
+
+ align:start position:0%
+if the pupils are very small you will
+still have an image that's in focus
+
+ align:start position:0%
+still have an image that's in focus
+ 
+
+ align:start position:0%
+still have an image that's in focus
+that's the principle of the pinhole
+
+ align:start position:0%
+that's the principle of the pinhole
+ 
+
+ align:start position:0%
+that's the principle of the pinhole
+camera
+
+ align:start position:0%
+camera
+ 
+
+ align:start position:0%
+camera
+okay but the main thing here is with
+
+ align:start position:0%
+okay but the main thing here is with
+ 
+
+ align:start position:0%
+okay but the main thing here is with
+intense light
+
+ align:start position:0%
+intense light
+ 
+
+ align:start position:0%
+intense light
+the pupils will constrict protect with
+
+ align:start position:0%
+the pupils will constrict protect with
+ 
+
+ align:start position:0%
+the pupils will constrict protect with
+intense sound there's something very
+
+ align:start position:0%
+intense sound there's something very
+ 
+
+ align:start position:0%
+intense sound there's something very
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+there are actually little muscles in the
+
+ align:start position:0%
+there are actually little muscles in the
+ 
+
+ align:start position:0%
+there are actually little muscles in the
+inner ear that will tense up and reduce
+
+ align:start position:0%
+inner ear that will tense up and reduce
+ 
+
+ align:start position:0%
+inner ear that will tense up and reduce
+the oscillations of the middle ear bones
+
+ align:start position:0%
+the oscillations of the middle ear bones
+ 
+
+ align:start position:0%
+the oscillations of the middle ear bones
+and protect
+
+ align:start position:0%
+and protect
+ 
+
+ align:start position:0%
+and protect
+that system from damage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+novel input
+
+ align:start position:0%
+novel input
+ 
+
+ align:start position:0%
+novel input
+does something very different
+
+ align:start position:0%
+does something very different
+ 
+
+ align:start position:0%
+does something very different
+when input is very novel we also respond
+
+ align:start position:0%
+when input is very novel we also respond
+ 
+
+ align:start position:0%
+when input is very novel we also respond
+now this generally to detect the novelty
+
+ align:start position:0%
+now this generally to detect the novelty
+ 
+
+ align:start position:0%
+now this generally to detect the novelty
+we need
+
+ align:start position:0%
+we need
+ 
+
+ align:start position:0%
+we need
+brain mechanisms of midbrain or
+
+ align:start position:0%
+brain mechanisms of midbrain or
+ 
+
+ align:start position:0%
+brain mechanisms of midbrain or
+forebrain
+
+ align:start position:0%
+forebrain
+ 
+
+ align:start position:0%
+forebrain
+it tends to
+
+ align:start position:0%
+it tends to
+ 
+
+ align:start position:0%
+it tends to
+result in an increased sensitivity to
+
+ align:start position:0%
+result in an increased sensitivity to
+ 
+
+ align:start position:0%
+result in an increased sensitivity to
+stimuli
+
+ align:start position:0%
+stimuli
+ 
+
+ align:start position:0%
+stimuli
+that happens in some other sensory
+
+ align:start position:0%
+that happens in some other sensory
+ 
+
+ align:start position:0%
+that happens in some other sensory
+visual auditory systems
+
+ align:start position:0%
+visual auditory systems
+ 
+
+ align:start position:0%
+visual auditory systems
+very different from the effects of
+
+ align:start position:0%
+very different from the effects of
+ 
+
+ align:start position:0%
+very different from the effects of
+intense activity that could
+
+ align:start position:0%
+intense activity that could
+ 
+
+ align:start position:0%
+intense activity that could
+are threatening potentially threatening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i mentioned that there's an opposite
+
+ align:start position:0%
+now i mentioned that there's an opposite
+ 
+
+ align:start position:0%
+now i mentioned that there's an opposite
+kind of reflex you tend to see it in
+
+ align:start position:0%
+kind of reflex you tend to see it in
+ 
+
+ align:start position:0%
+kind of reflex you tend to see it in
+babies
+
+ align:start position:0%
+babies
+ 
+
+ align:start position:0%
+babies
+if you take
+
+ align:start position:0%
+if you take
+ 
+
+ align:start position:0%
+if you take
+if you take a baby even a newborn okay
+
+ align:start position:0%
+if you take a baby even a newborn okay
+ 
+
+ align:start position:0%
+if you take a baby even a newborn okay
+and stroke the back of its hand gently
+
+ align:start position:0%
+and stroke the back of its hand gently
+ 
+
+ align:start position:0%
+and stroke the back of its hand gently
+often it will extend the hand even turn
+
+ align:start position:0%
+often it will extend the hand even turn
+ 
+
+ align:start position:0%
+often it will extend the hand even turn
+and is often followed by a grasp
+
+ align:start position:0%
+and is often followed by a grasp
+ 
+
+ align:start position:0%
+and is often followed by a grasp
+and of course we think
+
+ align:start position:0%
+and of course we think
+ 
+
+ align:start position:0%
+and of course we think
+what an intelligent little child he
+
+ align:start position:0%
+what an intelligent little child he
+ 
+
+ align:start position:0%
+what an intelligent little child he
+likes to grab my hand but actually it's
+
+ align:start position:0%
+likes to grab my hand but actually it's
+ 
+
+ align:start position:0%
+likes to grab my hand but actually it's
+a reflex spinal reflex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same is true of early smiling reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we normally don't see that in adults
+
+ align:start position:0%
+and we normally don't see that in adults
+ 
+
+ align:start position:0%
+and we normally don't see that in adults
+but there are situations where we do see
+
+ align:start position:0%
+but there are situations where we do see
+ 
+
+ align:start position:0%
+but there are situations where we do see
+magnet reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example just take the second one
+
+ align:start position:0%
+for example just take the second one
+ 
+
+ align:start position:0%
+for example just take the second one
+here and brain damage patients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with large frontal lobe lesions you can
+
+ align:start position:0%
+with large frontal lobe lesions you can
+ 
+
+ align:start position:0%
+with large frontal lobe lesions you can
+get enhancement of magnet and glass
+
+ align:start position:0%
+get enhancement of magnet and glass
+ 
+
+ align:start position:0%
+get enhancement of magnet and glass
+reflexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you have a frontal lobe patient
+
+ align:start position:0%
+so if you have a frontal lobe patient
+ 
+
+ align:start position:0%
+so if you have a frontal lobe patient
+lying in a bed and the nurse walks by
+
+ align:start position:0%
+lying in a bed and the nurse walks by
+ 
+
+ align:start position:0%
+lying in a bed and the nurse walks by
+and she brushes his hand you know he can
+
+ align:start position:0%
+and she brushes his hand you know he can
+ 
+
+ align:start position:0%
+and she brushes his hand you know he can
+turn out and grab her and you think what
+
+ align:start position:0%
+turn out and grab her and you think what
+ 
+
+ align:start position:0%
+turn out and grab her and you think what
+a fresh fellow
+
+ align:start position:0%
+a fresh fellow
+ 
+
+ align:start position:0%
+a fresh fellow
+but actually it could be a reflex it
+
+ align:start position:0%
+but actually it could be a reflex it
+ 
+
+ align:start position:0%
+but actually it could be a reflex it
+could be a magnet reflex and he might
+
+ align:start position:0%
+could be a magnet reflex and he might
+ 
+
+ align:start position:0%
+could be a magnet reflex and he might
+not actually know until after it's
+
+ align:start position:0%
+not actually know until after it's
+ 
+
+ align:start position:0%
+not actually know until after it's
+happened what's going on
+
+ align:start position:0%
+happened what's going on
+ 
+
+ align:start position:0%
+happened what's going on
+you can also get enhancement of the
+
+ align:start position:0%
+you can also get enhancement of the
+ 
+
+ align:start position:0%
+you can also get enhancement of the
+withdrawal reflexes with large parietal
+
+ align:start position:0%
+withdrawal reflexes with large parietal
+ 
+
+ align:start position:0%
+withdrawal reflexes with large parietal
+lobe lesions and the other types of
+
+ align:start position:0%
+lobe lesions and the other types of
+ 
+
+ align:start position:0%
+lobe lesions and the other types of
+withdrawal reflexes i've seen it in
+
+ align:start position:0%
+withdrawal reflexes i've seen it in
+ 
+
+ align:start position:0%
+withdrawal reflexes i've seen it in
+animals with large
+
+ align:start position:0%
+animals with large
+ 
+
+ align:start position:0%
+animals with large
+posterior neocortical lesions that
+
+ align:start position:0%
+posterior neocortical lesions that
+ 
+
+ align:start position:0%
+posterior neocortical lesions that
+damage parietal areas
+
+ align:start position:0%
+damage parietal areas
+ 
+
+ align:start position:0%
+damage parietal areas
+so we call those automatisms
+
+ align:start position:0%
+so we call those automatisms
+ 
+
+ align:start position:0%
+so we call those automatisms
+they can occur in spite of conscious
+
+ align:start position:0%
+they can occur in spite of conscious
+ 
+
+ align:start position:0%
+they can occur in spite of conscious
+efforts to control them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about normally
+
+ align:start position:0%
+what about normally
+ 
+
+ align:start position:0%
+what about normally
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+we can certainly get enhancement of
+
+ align:start position:0%
+we can certainly get enhancement of
+ 
+
+ align:start position:0%
+we can certainly get enhancement of
+withdrawal reflexes
+
+ align:start position:0%
+withdrawal reflexes
+ 
+
+ align:start position:0%
+withdrawal reflexes
+let's look at this example
+
+ align:start position:0%
+let's look at this example
+ 
+
+ align:start position:0%
+let's look at this example
+say you've gone down into a dark
+
+ align:start position:0%
+say you've gone down into a dark
+ 
+
+ align:start position:0%
+say you've gone down into a dark
+basement and you're looking for a tool
+
+ align:start position:0%
+basement and you're looking for a tool
+ 
+
+ align:start position:0%
+basement and you're looking for a tool
+there and you can't find the light
+
+ align:start position:0%
+there and you can't find the light
+ 
+
+ align:start position:0%
+there and you can't find the light
+and everything's fine until
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your apartment mate yells down the
+
+ align:start position:0%
+your apartment mate yells down the
+ 
+
+ align:start position:0%
+your apartment mate yells down the
+stairs and says oh by the way i i saw
+
+ align:start position:0%
+stairs and says oh by the way i i saw
+ 
+
+ align:start position:0%
+stairs and says oh by the way i i saw
+rats down there today what happens
+
+ align:start position:0%
+rats down there today what happens
+ 
+
+ align:start position:0%
+rats down there today what happens
+you touch almost anything and you pull
+
+ align:start position:0%
+you touch almost anything and you pull
+ 
+
+ align:start position:0%
+you touch almost anything and you pull
+your hand back involuntarily because the
+
+ align:start position:0%
+your hand back involuntarily because the
+ 
+
+ align:start position:0%
+your hand back involuntarily because the
+threshold for the withdrawal reflexes
+
+ align:start position:0%
+threshold for the withdrawal reflexes
+ 
+
+ align:start position:0%
+threshold for the withdrawal reflexes
+has gone way down
+
+ align:start position:0%
+has gone way down
+ 
+
+ align:start position:0%
+has gone way down
+similarly if you're
+
+ align:start position:0%
+similarly if you're
+ 
+
+ align:start position:0%
+similarly if you're
+the other example i like is the
+
+ align:start position:0%
+the other example i like is the
+ 
+
+ align:start position:0%
+the other example i like is the
+in broad daylight you're looking in tall
+
+ align:start position:0%
+in broad daylight you're looking in tall
+ 
+
+ align:start position:0%
+in broad daylight you're looking in tall
+grass say for a golf ball or a baseball
+
+ align:start position:0%
+grass say for a golf ball or a baseball
+ 
+
+ align:start position:0%
+grass say for a golf ball or a baseball
+and you can't see so you're groping with
+
+ align:start position:0%
+and you can't see so you're groping with
+ 
+
+ align:start position:0%
+and you can't see so you're groping with
+your hand if somebody tells you you know
+
+ align:start position:0%
+your hand if somebody tells you you know
+ 
+
+ align:start position:0%
+your hand if somebody tells you you know
+oh there's snakes there be careful
+
+ align:start position:0%
+oh there's snakes there be careful
+ 
+
+ align:start position:0%
+oh there's snakes there be careful
+the same thing will happen you'll
+
+ align:start position:0%
+the same thing will happen you'll
+ 
+
+ align:start position:0%
+the same thing will happen you'll
+enhance by descending activity to the
+
+ align:start position:0%
+enhance by descending activity to the
+ 
+
+ align:start position:0%
+enhance by descending activity to the
+cord you'll enhance
+
+ align:start position:0%
+cord you'll enhance
+ 
+
+ align:start position:0%
+cord you'll enhance
+withdrawal reflexes okay so you will now
+
+ align:start position:0%
+withdrawal reflexes okay so you will now
+ 
+
+ align:start position:0%
+withdrawal reflexes okay so you will now
+trigger them with much less input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i mentioned the effects of stimulus
+
+ align:start position:0%
+so i mentioned the effects of stimulus
+ 
+
+ align:start position:0%
+so i mentioned the effects of stimulus
+novelty
+
+ align:start position:0%
+novelty
+ 
+
+ align:start position:0%
+novelty
+how they increase sensitivity
+
+ align:start position:0%
+how they increase sensitivity
+ 
+
+ align:start position:0%
+how they increase sensitivity
+why would we want to be more sensitive
+
+ align:start position:0%
+why would we want to be more sensitive
+ 
+
+ align:start position:0%
+why would we want to be more sensitive
+partly because
+
+ align:start position:0%
+partly because
+ 
+
+ align:start position:0%
+partly because
+novelty can indicate problems possible
+
+ align:start position:0%
+novelty can indicate problems possible
+ 
+
+ align:start position:0%
+novelty can indicate problems possible
+problems it's something unknown will
+
+ align:start position:0%
+problems it's something unknown will
+ 
+
+ align:start position:0%
+problems it's something unknown will
+become more hesitant we'll show more
+
+ align:start position:0%
+become more hesitant we'll show more
+ 
+
+ align:start position:0%
+become more hesitant we'll show more
+fear and avoidance
+
+ align:start position:0%
+fear and avoidance
+ 
+
+ align:start position:0%
+fear and avoidance
+that happens with increased novelty
+
+ align:start position:0%
+that happens with increased novelty
+ 
+
+ align:start position:0%
+that happens with increased novelty
+with milder novelty we tend to show the
+
+ align:start position:0%
+with milder novelty we tend to show the
+ 
+
+ align:start position:0%
+with milder novelty we tend to show the
+opposite we show curiosity approach and
+
+ align:start position:0%
+opposite we show curiosity approach and
+ 
+
+ align:start position:0%
+opposite we show curiosity approach and
+avoidance and these are very general
+
+ align:start position:0%
+avoidance and these are very general
+ 
+
+ align:start position:0%
+avoidance and these are very general
+things that happen you can study this in
+
+ align:start position:0%
+things that happen you can study this in
+ 
+
+ align:start position:0%
+things that happen you can study this in
+in many different animals
+
+ align:start position:0%
+in many different animals
+ 
+
+ align:start position:0%
+in many different animals
+but especially the mammals i think all
+
+ align:start position:0%
+but especially the mammals i think all
+ 
+
+ align:start position:0%
+but especially the mammals i think all
+the mammals show a lot of curiosity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we deal with something like
+
+ align:start position:0%
+when we deal with something like
+ 
+
+ align:start position:0%
+when we deal with something like
+obtaining food or water we have
+
+ align:start position:0%
+obtaining food or water we have
+ 
+
+ align:start position:0%
+obtaining food or water we have
+additional influences other than novelty
+
+ align:start position:0%
+additional influences other than novelty
+ 
+
+ align:start position:0%
+additional influences other than novelty
+we have a special role of olfaction
+
+ align:start position:0%
+we have a special role of olfaction
+ 
+
+ align:start position:0%
+we have a special role of olfaction
+which we know happened very early in
+
+ align:start position:0%
+which we know happened very early in
+ 
+
+ align:start position:0%
+which we know happened very early in
+evolution
+
+ align:start position:0%
+evolution
+ 
+
+ align:start position:0%
+evolution
+and then with the other distance
+
+ align:start position:0%
+and then with the other distance
+ 
+
+ align:start position:0%
+and then with the other distance
+receptors we got other effects important
+
+ align:start position:0%
+receptors we got other effects important
+ 
+
+ align:start position:0%
+receptors we got other effects important
+for approach
+
+ align:start position:0%
+for approach
+ 
+
+ align:start position:0%
+for approach
+and avoidance in this case mostly
+
+ align:start position:0%
+and avoidance in this case mostly
+ 
+
+ align:start position:0%
+and avoidance in this case mostly
+approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and limbic forebrain mechanisms became
+
+ align:start position:0%
+and limbic forebrain mechanisms became
+ 
+
+ align:start position:0%
+and limbic forebrain mechanisms became
+more and more important and i'm just
+
+ align:start position:0%
+more and more important and i'm just
+ 
+
+ align:start position:0%
+more and more important and i'm just
+asking this for you to think about
+
+ align:start position:0%
+asking this for you to think about
+ 
+
+ align:start position:0%
+asking this for you to think about
+what's the major additional influence of
+
+ align:start position:0%
+what's the major additional influence of
+ 
+
+ align:start position:0%
+what's the major additional influence of
+the limbic forebrain mechanisms
+
+ align:start position:0%
+the limbic forebrain mechanisms
+ 
+
+ align:start position:0%
+the limbic forebrain mechanisms
+olympic forebrain we say are the
+
+ align:start position:0%
+olympic forebrain we say are the
+ 
+
+ align:start position:0%
+olympic forebrain we say are the
+mechanisms that control our emotions and
+
+ align:start position:0%
+mechanisms that control our emotions and
+ 
+
+ align:start position:0%
+mechanisms that control our emotions and
+our motivations
+
+ align:start position:0%
+our motivations
+ 
+
+ align:start position:0%
+our motivations
+but we had that
+
+ align:start position:0%
+but we had that
+ 
+
+ align:start position:0%
+but we had that
+animals even without much of a forebrain
+
+ align:start position:0%
+animals even without much of a forebrain
+ 
+
+ align:start position:0%
+animals even without much of a forebrain
+certainly still
+
+ align:start position:0%
+certainly still
+ 
+
+ align:start position:0%
+certainly still
+approached food and water they could
+
+ align:start position:0%
+approached food and water they could
+ 
+
+ align:start position:0%
+approached food and water they could
+still forage with
+
+ align:start position:0%
+still forage with
+ 
+
+ align:start position:0%
+still forage with
+midbrain and between brain mechanisms
+
+ align:start position:0%
+midbrain and between brain mechanisms
+ 
+
+ align:start position:0%
+midbrain and between brain mechanisms
+so what is the limbic forebrain adding
+
+ align:start position:0%
+so what is the limbic forebrain adding
+ 
+
+ align:start position:0%
+so what is the limbic forebrain adding
+one thing it does is
+
+ align:start position:0%
+one thing it does is
+ 
+
+ align:start position:0%
+one thing it does is
+it gives
+
+ align:start position:0%
+it gives
+ 
+
+ align:start position:0%
+it gives
+objects in the environment that are
+
+ align:start position:0%
+objects in the environment that are
+ 
+
+ align:start position:0%
+objects in the environment that are
+originally neutral
+
+ align:start position:0%
+originally neutral
+ 
+
+ align:start position:0%
+originally neutral
+it gives them what we call an effective
+
+ align:start position:0%
+it gives them what we call an effective
+ 
+
+ align:start position:0%
+it gives them what we call an effective
+tag we tag things we give them a
+
+ align:start position:0%
+tag we tag things we give them a
+ 
+
+ align:start position:0%
+tag we tag things we give them a
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+okay about how good they are bad they
+
+ align:start position:0%
+okay about how good they are bad they
+ 
+
+ align:start position:0%
+okay about how good they are bad they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+okay we do that to people too
+
+ align:start position:0%
+okay we do that to people too
+ 
+
+ align:start position:0%
+okay we do that to people too
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+because of limbic system activity and
+
+ align:start position:0%
+because of limbic system activity and
+ 
+
+ align:start position:0%
+because of limbic system activity and
+limbic connections
+
+ align:start position:0%
+limbic connections
+ 
+
+ align:start position:0%
+limbic connections
+to the structure to the hypothalamus and
+
+ align:start position:0%
+to the structure to the hypothalamus and
+ 
+
+ align:start position:0%
+to the structure to the hypothalamus and
+other structures involved
+
+ align:start position:0%
+other structures involved
+ 
+
+ align:start position:0%
+other structures involved
+in foraging
+
+ align:start position:0%
+in foraging
+ 
+
+ align:start position:0%
+in foraging
+basically motivation modulation of our
+
+ align:start position:0%
+basically motivation modulation of our
+ 
+
+ align:start position:0%
+basically motivation modulation of our
+motive the motivational effects of
+
+ align:start position:0%
+motive the motivational effects of
+ 
+
+ align:start position:0%
+motive the motivational effects of
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in addition it allows us
+
+ align:start position:0%
+and in addition it allows us
+ 
+
+ align:start position:0%
+and in addition it allows us
+because of learning to be rewarded
+
+ align:start position:0%
+because of learning to be rewarded
+ 
+
+ align:start position:0%
+because of learning to be rewarded
+by things that might not initially we
+
+ align:start position:0%
+by things that might not initially we
+ 
+
+ align:start position:0%
+by things that might not initially we
+might initially be rewarded by taste
+
+ align:start position:0%
+might initially be rewarded by taste
+ 
+
+ align:start position:0%
+might initially be rewarded by taste
+primarily for a
+
+ align:start position:0%
+primarily for a
+ 
+
+ align:start position:0%
+primarily for a
+taste of food but then later we learn
+
+ align:start position:0%
+taste of food but then later we learn
+ 
+
+ align:start position:0%
+taste of food but then later we learn
+certain foods stays good certain food
+
+ align:start position:0%
+certain foods stays good certain food
+ 
+
+ align:start position:0%
+certain foods stays good certain food
+stays bad and we learn by their
+
+ align:start position:0%
+stays bad and we learn by their
+ 
+
+ align:start position:0%
+stays bad and we learn by their
+appearance we don't have to taste them
+
+ align:start position:0%
+appearance we don't have to taste them
+ 
+
+ align:start position:0%
+appearance we don't have to taste them
+every time
+
+ align:start position:0%
+every time
+ 
+
+ align:start position:0%
+every time
+okay we learn
+
+ align:start position:0%
+okay we learn
+ 
+
+ align:start position:0%
+okay we learn
+to associate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tastes with certain visual objects or
+
+ align:start position:0%
+tastes with certain visual objects or
+ 
+
+ align:start position:0%
+tastes with certain visual objects or
+even auditory or semi-sensory okay
+
+ align:start position:0%
+even auditory or semi-sensory okay
+ 
+
+ align:start position:0%
+even auditory or semi-sensory okay
+that always involves the limbic
+
+ align:start position:0%
+that always involves the limbic
+ 
+
+ align:start position:0%
+that always involves the limbic
+forebrain
+
+ align:start position:0%
+forebrain
+ 
+
+ align:start position:0%
+forebrain
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't have much more time this is
+
+ align:start position:0%
+we don't have much more time this is
+ 
+
+ align:start position:0%
+we don't have much more time this is
+what we're gonna do next time we're
+
+ align:start position:0%
+what we're gonna do next time we're
+ 
+
+ align:start position:0%
+what we're gonna do next time we're
+going to talk about the muscle spindle
+
+ align:start position:0%
+going to talk about the muscle spindle
+ 
+
+ align:start position:0%
+going to talk about the muscle spindle
+organs detection of muscle stretch
+
+ align:start position:0%
+organs detection of muscle stretch
+ 
+
+ align:start position:0%
+organs detection of muscle stretch
+and go through these topics and talking
+
+ align:start position:0%
+and go through these topics and talking
+ 
+
+ align:start position:0%
+and go through these topics and talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the monosynaptic reflexes of the spinal
+
+ align:start position:0%
+the monosynaptic reflexes of the spinal
+ 
+
+ align:start position:0%
+the monosynaptic reflexes of the spinal
+cord
\ No newline at end of file
diff --git a/avQ2XUzbsgk.txt b/avQ2XUzbsgk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..06d357c4a6f8cd292ec04facaafaa6d001065731
--- /dev/null
+++ b/avQ2XUzbsgk.txt
@@ -0,0 +1,2955 @@
+align:start position:0%
+ 
+what is a red Berg Adam well it's a an
+
+ align:start position:0%
+what is a red Berg Adam well it's a an
+ 
+
+ align:start position:0%
+what is a red Berg Adam well it's a an
+atom can be a red Berg atom if the
+
+ align:start position:0%
+atom can be a red Berg atom if the
+ 
+
+ align:start position:0%
+atom can be a red Berg atom if the
+outermost electron is in a very high
+
+ align:start position:0%
+outermost electron is in a very high
+ 
+
+ align:start position:0%
+outermost electron is in a very high
+principal quantum number that's the
+
+ align:start position:0%
+principal quantum number that's the
+ 
+
+ align:start position:0%
+principal quantum number that's the
+definition of a red Berg atom the last
+
+ align:start position:0%
+definition of a red Berg atom the last
+ 
+
+ align:start position:0%
+definition of a red Berg atom the last
+electron is in n little and very large
+
+ align:start position:0%
+electron is in n little and very large
+ 
+
+ align:start position:0%
+electron is in n little and very large
+now that is very interesting because
+
+ align:start position:0%
+now that is very interesting because
+ 
+
+ align:start position:0%
+now that is very interesting because
+when that happens with Berg atoms when
+
+ align:start position:0%
+when that happens with Berg atoms when
+ 
+
+ align:start position:0%
+when that happens with Berg atoms when
+that happens you have a nucleus with
+
+ align:start position:0%
+that happens you have a nucleus with
+ 
+
+ align:start position:0%
+that happens you have a nucleus with
+charge ze
+
+ align:start position:0%
+charge ze
+ 
+
+ align:start position:0%
+charge ze
+and you have lots of electrons and the
+
+ align:start position:0%
+and you have lots of electrons and the
+ 
+
+ align:start position:0%
+and you have lots of electrons and the
+last electron suppose the last electrode
+
+ align:start position:0%
+last electron suppose the last electrode
+ 
+
+ align:start position:0%
+last electron suppose the last electrode
+is in an orbit further out you see the
+
+ align:start position:0%
+is in an orbit further out you see the
+ 
+
+ align:start position:0%
+is in an orbit further out you see the
+orbits of do become further out in
+
+ align:start position:0%
+orbits of do become further out in
+ 
+
+ align:start position:0%
+orbits of do become further out in
+general and the suppose the last
+
+ align:start position:0%
+general and the suppose the last
+ 
+
+ align:start position:0%
+general and the suppose the last
+electrode is in some large value of
+
+ align:start position:0%
+electrode is in some large value of
+ 
+
+ align:start position:0%
+electrode is in some large value of
+little n so it's somewhat out so here is
+
+ align:start position:0%
+little n so it's somewhat out so here is
+ 
+
+ align:start position:0%
+little n so it's somewhat out so here is
+the last electron this electron sees a
+
+ align:start position:0%
+the last electron this electron sees a
+ 
+
+ align:start position:0%
+the last electron this electron sees a
+nucleus with charge Z but it also sees Z
+
+ align:start position:0%
+nucleus with charge Z but it also sees Z
+ 
+
+ align:start position:0%
+nucleus with charge Z but it also sees Z
+minus one electrons all the other
+
+ align:start position:0%
+minus one electrons all the other
+ 
+
+ align:start position:0%
+minus one electrons all the other
+electrons see the last electrode is
+
+ align:start position:0%
+electrons see the last electrode is
+ 
+
+ align:start position:0%
+electrons see the last electrode is
+outside the nucleus and the cloud of the
+
+ align:start position:0%
+outside the nucleus and the cloud of the
+ 
+
+ align:start position:0%
+outside the nucleus and the cloud of the
+other electrons so the last electrode
+
+ align:start position:0%
+other electrons so the last electrode
+ 
+
+ align:start position:0%
+other electrons so the last electrode
+sees a charge plus 1 Z from here and Z
+
+ align:start position:0%
+sees a charge plus 1 Z from here and Z
+ 
+
+ align:start position:0%
+sees a charge plus 1 Z from here and Z
+minus 1 of the electrons so the last
+
+ align:start position:0%
+minus 1 of the electrons so the last
+ 
+
+ align:start position:0%
+minus 1 of the electrons so the last
+electrode sees charge 1 so in some sense
+
+ align:start position:0%
+electrode sees charge 1 so in some sense
+ 
+
+ align:start position:0%
+electrode sees charge 1 so in some sense
+to a good approximation the last
+
+ align:start position:0%
+to a good approximation the last
+ 
+
+ align:start position:0%
+to a good approximation the last
+electron says oh there's a hydrogen atom
+
+ align:start position:0%
+electron says oh there's a hydrogen atom
+ 
+
+ align:start position:0%
+electron says oh there's a hydrogen atom
+here I'm part of a hydrogen atom I don't
+
+ align:start position:0%
+here I'm part of a hydrogen atom I don't
+ 
+
+ align:start position:0%
+here I'm part of a hydrogen atom I don't
+see my friends the other electrons are
+
+ align:start position:0%
+see my friends the other electrons are
+ 
+
+ align:start position:0%
+see my friends the other electrons are
+too close to the Duke
+
+ align:start position:0%
+too close to the Duke
+ 
+
+ align:start position:0%
+too close to the Duke
+and I'm out there going around as if I
+
+ align:start position:0%
+and I'm out there going around as if I
+ 
+
+ align:start position:0%
+and I'm out there going around as if I
+were hydrogen so that's a very nice
+
+ align:start position:0%
+were hydrogen so that's a very nice
+ 
+
+ align:start position:0%
+were hydrogen so that's a very nice
+application of hydrogen atoms so the
+
+ align:start position:0%
+application of hydrogen atoms so the
+ 
+
+ align:start position:0%
+application of hydrogen atoms so the
+first question that we want to
+
+ align:start position:0%
+first question that we want to
+ 
+
+ align:start position:0%
+first question that we want to
+understand and it's again conceptually
+
+ align:start position:0%
+understand and it's again conceptually
+ 
+
+ align:start position:0%
+understand and it's again conceptually
+is what is the size if M is large what
+
+ align:start position:0%
+is what is the size if M is large what
+ 
+
+ align:start position:0%
+is what is the size if M is large what
+is the size of the atom now I must say I
+
+ align:start position:0%
+is the size of the atom now I must say I
+ 
+
+ align:start position:0%
+is the size of the atom now I must say I
+myself when I look at these things after
+
+ align:start position:0%
+myself when I look at these things after
+ 
+
+ align:start position:0%
+myself when I look at these things after
+a few years that I don't eat raw
+
+ align:start position:0%
+a few years that I don't eat raw
+ 
+
+ align:start position:0%
+a few years that I don't eat raw
+mechanics I look at here and say okay
+
+ align:start position:0%
+mechanics I look at here and say okay
+ 
+
+ align:start position:0%
+mechanics I look at here and say okay
+this is the solution maybe the size is
+
+ align:start position:0%
+this is the solution maybe the size is
+ 
+
+ align:start position:0%
+this is the solution maybe the size is
+an a0 and fortunately that's completely
+
+ align:start position:0%
+an a0 and fortunately that's completely
+ 
+
+ align:start position:0%
+an a0 and fortunately that's completely
+wrong and we're going to try to explain
+
+ align:start position:0%
+wrong and we're going to try to explain
+ 
+
+ align:start position:0%
+wrong and we're going to try to explain
+what was wrong in looking there you know
+
+ align:start position:0%
+what was wrong in looking there you know
+ 
+
+ align:start position:0%
+what was wrong in looking there you know
+you see your hydrogen atom wave function
+
+ align:start position:0%
+you see your hydrogen atom wave function
+ 
+
+ align:start position:0%
+you see your hydrogen atom wave function
+there's nothing like really the size
+
+ align:start position:0%
+there's nothing like really the size
+ 
+
+ align:start position:0%
+there's nothing like really the size
+there's no such precise definition as
+
+ align:start position:0%
+there's no such precise definition as
+ 
+
+ align:start position:0%
+there's no such precise definition as
+the size but you could say what's the
+
+ align:start position:0%
+the size but you could say what's the
+ 
+
+ align:start position:0%
+the size but you could say what's the
+expected value of the radius that's a
+
+ align:start position:0%
+expected value of the radius that's a
+ 
+
+ align:start position:0%
+expected value of the radius that's a
+reasonable definition of size and you
+
+ align:start position:0%
+reasonable definition of size and you
+ 
+
+ align:start position:0%
+reasonable definition of size and you
+know from this wave function is going to
+
+ align:start position:0%
+know from this wave function is going to
+ 
+
+ align:start position:0%
+know from this wave function is going to
+come out to a 0 a 0 over 2 to a 0
+
+ align:start position:0%
+come out to a 0 a 0 over 2 to a 0
+ 
+
+ align:start position:0%
+come out to a 0 a 0 over 2 to a 0
+maybe PI over 2 a 0 something like that
+
+ align:start position:0%
+maybe PI over 2 a 0 something like that
+ 
+
+ align:start position:0%
+maybe PI over 2 a 0 something like that
+so from here you would say well it's
+
+ align:start position:0%
+so from here you would say well it's
+ 
+
+ align:start position:0%
+so from here you would say well it's
+going to come out to PI and a 0 or
+
+ align:start position:0%
+going to come out to PI and a 0 or
+ 
+
+ align:start position:0%
+going to come out to PI and a 0 or
+something like that but it's not true so
+
+ align:start position:0%
+something like that but it's not true so
+ 
+
+ align:start position:0%
+something like that but it's not true so
+how do we see that it's not true we'll
+
+ align:start position:0%
+how do we see that it's not true we'll
+ 
+
+ align:start position:0%
+how do we see that it's not true we'll
+take a little time in a few minutes but
+
+ align:start position:0%
+take a little time in a few minutes but
+ 
+
+ align:start position:0%
+take a little time in a few minutes but
+how can we get the size of that atom
+
+ align:start position:0%
+how can we get the size of that atom
+ 
+
+ align:start position:0%
+how can we get the size of that atom
+correctly in an intuitive way again want
+
+ align:start position:0%
+correctly in an intuitive way again want
+ 
+
+ align:start position:0%
+correctly in an intuitive way again want
+to just understand a few results about
+
+ align:start position:0%
+to just understand a few results about
+ 
+
+ align:start position:0%
+to just understand a few results about
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+them that become part of your intuition
+
+ align:start position:0%
+them that become part of your intuition
+ 
+
+ align:start position:0%
+them that become part of your intuition
+so the important result here is the
+
+ align:start position:0%
+so the important result here is the
+ 
+
+ align:start position:0%
+so the important result here is the
+virial theorem theorem now whenever I
+
+ align:start position:0%
+virial theorem theorem now whenever I
+ 
+
+ align:start position:0%
+virial theorem theorem now whenever I
+think of the virial theorem I said oh
+
+ align:start position:0%
+think of the virial theorem I said oh
+ 
+
+ align:start position:0%
+think of the virial theorem I said oh
+there was a factor of 2 or 1/2 there how
+
+ align:start position:0%
+there was a factor of 2 or 1/2 there how
+ 
+
+ align:start position:0%
+there was a factor of 2 or 1/2 there how
+did it go
+
+ align:start position:0%
+did it go
+ 
+
+ align:start position:0%
+did it go
+takes me a few seconds to try to
+
+ align:start position:0%
+takes me a few seconds to try to
+ 
+
+ align:start position:0%
+takes me a few seconds to try to
+reconstruct that it's this for the
+
+ align:start position:0%
+reconstruct that it's this for the
+ 
+
+ align:start position:0%
+reconstruct that it's this for the
+hydrogen system for any 1 over R
+
+ align:start position:0%
+hydrogen system for any 1 over R
+ 
+
+ align:start position:0%
+hydrogen system for any 1 over R
+potential there is this relation within
+
+ align:start position:0%
+potential there is this relation within
+ 
+
+ align:start position:0%
+potential there is this relation within
+the expectation value of the kinetic
+
+ align:start position:0%
+the expectation value of the kinetic
+ 
+
+ align:start position:0%
+the expectation value of the kinetic
+energy the potential energy you've seen
+
+ align:start position:0%
+energy the potential energy you've seen
+ 
+
+ align:start position:0%
+energy the potential energy you've seen
+that result probably a couple of times
+
+ align:start position:0%
+that result probably a couple of times
+ 
+
+ align:start position:0%
+that result probably a couple of times
+already in this course because it's a
+
+ align:start position:0%
+already in this course because it's a
+ 
+
+ align:start position:0%
+already in this course because it's a
+really important result it looks like ok
+
+ align:start position:0%
+really important result it looks like ok
+ 
+
+ align:start position:0%
+really important result it looks like ok
+just a theorem about these things but
+
+ align:start position:0%
+just a theorem about these things but
+ 
+
+ align:start position:0%
+just a theorem about these things but
+the intuition is really important so how
+
+ align:start position:0%
+the intuition is really important so how
+ 
+
+ align:start position:0%
+the intuition is really important so how
+does one remember picture that one way
+
+ align:start position:0%
+does one remember picture that one way
+ 
+
+ align:start position:0%
+does one remember picture that one way
+is the following and that's the way I
+
+ align:start position:0%
+is the following and that's the way I
+ 
+
+ align:start position:0%
+is the following and that's the way I
+like it
+
+ align:start position:0%
+like it
+ 
+
+ align:start position:0%
+like it
+oh I imagine the energy line here and
+
+ align:start position:0%
+oh I imagine the energy line here and
+ 
+
+ align:start position:0%
+oh I imagine the energy line here and
+here is zero and the one thing I
+
+ align:start position:0%
+here is zero and the one thing I
+ 
+
+ align:start position:0%
+here is zero and the one thing I
+remember is that yes there is a kinetic
+
+ align:start position:0%
+remember is that yes there is a kinetic
+ 
+
+ align:start position:0%
+remember is that yes there is a kinetic
+energy here and actually the bound state
+
+ align:start position:0%
+energy here and actually the bound state
+ 
+
+ align:start position:0%
+energy here and actually the bound state
+energy is exactly the same but opposite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a way to remember that that's
+
+ align:start position:0%
+that's a way to remember that that's
+ 
+
+ align:start position:0%
+that's a way to remember that that's
+really what is going on that's the key
+
+ align:start position:0%
+really what is going on that's the key
+ 
+
+ align:start position:0%
+really what is going on that's the key
+thing the kinetic energy and the bound
+
+ align:start position:0%
+thing the kinetic energy and the bound
+ 
+
+ align:start position:0%
+thing the kinetic energy and the bound
+state energy are just of opposite signs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why do we see that because then we have
+
+ align:start position:0%
+why do we see that because then we have
+ 
+
+ align:start position:0%
+why do we see that because then we have
+that V from this equation is minus 2t
+
+ align:start position:0%
+that V from this equation is minus 2t
+ 
+
+ align:start position:0%
+that V from this equation is minus 2t
+and if V is minus 2t means that T plus V
+
+ align:start position:0%
+and if V is minus 2t means that T plus V
+ 
+
+ align:start position:0%
+and if V is minus 2t means that T plus V
+is t minus 2 T and T plus V is a total
+
+ align:start position:0%
+is t minus 2 T and T plus V is a total
+ 
+
+ align:start position:0%
+is t minus 2 T and T plus V is a total
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+so P plus V is equal to the total energy
+
+ align:start position:0%
+so P plus V is equal to the total energy
+ 
+
+ align:start position:0%
+so P plus V is equal to the total energy
+of the bound state for any stationary
+
+ align:start position:0%
+of the bound state for any stationary
+ 
+
+ align:start position:0%
+of the bound state for any stationary
+state this is true and this thing given
+
+ align:start position:0%
+state this is true and this thing given
+ 
+
+ align:start position:0%
+state this is true and this thing given
+this condition is minus T so that's
+
+ align:start position:0%
+this condition is minus T so that's
+ 
+
+ align:start position:0%
+this condition is minus T so that's
+that's the way we think of it so we then
+
+ align:start position:0%
+that's the way we think of it so we then
+ 
+
+ align:start position:0%
+that's the way we think of it so we then
+have a nice result because the
+
+ align:start position:0%
+have a nice result because the
+ 
+
+ align:start position:0%
+have a nice result because the
+expectation value of the potential would
+
+ align:start position:0%
+expectation value of the potential would
+ 
+
+ align:start position:0%
+expectation value of the potential would
+then be minus two times the expectation
+
+ align:start position:0%
+then be minus two times the expectation
+ 
+
+ align:start position:0%
+then be minus two times the expectation
+value of T which is itself - are the
+
+ align:start position:0%
+value of T which is itself - are the
+ 
+
+ align:start position:0%
+value of T which is itself - are the
+energy so you have a minus 2 times minus
+
+ align:start position:0%
+energy so you have a minus 2 times minus
+ 
+
+ align:start position:0%
+energy so you have a minus 2 times minus
+the energy and it's equal to the energy
+
+ align:start position:0%
+the energy and it's equal to the energy
+ 
+
+ align:start position:0%
+the energy and it's equal to the energy
+and this is correct the expectation
+
+ align:start position:0%
+and this is correct the expectation
+ 
+
+ align:start position:0%
+and this is correct the expectation
+value of V is the energy and expectation
+
+ align:start position:0%
+value of V is the energy and expectation
+ 
+
+ align:start position:0%
+value of V is the energy and expectation
+value of e V is negative and the energy
+
+ align:start position:0%
+value of e V is negative and the energy
+ 
+
+ align:start position:0%
+value of e V is negative and the energy
+is negative so what is this this is the
+
+ align:start position:0%
+is negative so what is this this is the
+ 
+
+ align:start position:0%
+is negative so what is this this is the
+expectation value of minus e squared
+
+ align:start position:0%
+expectation value of minus e squared
+ 
+
+ align:start position:0%
+expectation value of minus e squared
+over R in fact
+
+ align:start position:0%
+over R in fact
+ 
+
+ align:start position:0%
+over R in fact
+oh yeah I'll leave it like that so I'm
+
+ align:start position:0%
+oh yeah I'll leave it like that so I'm
+ 
+
+ align:start position:0%
+oh yeah I'll leave it like that so I'm
+back to Z equal 1 because we're talking
+
+ align:start position:0%
+back to Z equal 1 because we're talking
+ 
+
+ align:start position:0%
+back to Z equal 1 because we're talking
+about red Burke atoms Oh 2 EB I'm sorry
+
+ align:start position:0%
+about red Burke atoms Oh 2 EB I'm sorry
+ 
+
+ align:start position:0%
+about red Burke atoms Oh 2 EB I'm sorry
+here thank you
+
+ align:start position:0%
+here thank you
+ 
+
+ align:start position:0%
+here thank you
+okay so expectation value of the
+
+ align:start position:0%
+okay so expectation value of the
+ 
+
+ align:start position:0%
+okay so expectation value of the
+potential we have here and 2 times their
+
+ align:start position:0%
+potential we have here and 2 times their
+ 
+
+ align:start position:0%
+potential we have here and 2 times their
+energy yeah I would have gotten this
+
+ align:start position:0%
+energy yeah I would have gotten this
+ 
+
+ align:start position:0%
+energy yeah I would have gotten this
+wrong thanks for correcting it before it
+
+ align:start position:0%
+wrong thanks for correcting it before it
+ 
+
+ align:start position:0%
+wrong thanks for correcting it before it
+did damage to the derivation we have it
+
+ align:start position:0%
+did damage to the derivation we have it
+ 
+
+ align:start position:0%
+did damage to the derivation we have it
+there a squared over 2a not 1 over N
+
+ align:start position:0%
+there a squared over 2a not 1 over N
+ 
+
+ align:start position:0%
+there a squared over 2a not 1 over N
+squared so what can we cancel well the
+
+ align:start position:0%
+squared so what can we cancel well the
+ 
+
+ align:start position:0%
+squared so what can we cancel well the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so the e squares cancel the sines cancel
+
+ align:start position:0%
+so the e squares cancel the sines cancel
+ 
+
+ align:start position:0%
+so the e squares cancel the sines cancel
+and we get expectation value of one over
+
+ align:start position:0%
+and we get expectation value of one over
+ 
+
+ align:start position:0%
+and we get expectation value of one over
+R is equal to one over N squared a
+
+ align:start position:0%
+R is equal to one over N squared a
+ 
+
+ align:start position:0%
+R is equal to one over N squared a
+naught which is suggesting very clearly
+
+ align:start position:0%
+naught which is suggesting very clearly
+ 
+
+ align:start position:0%
+naught which is suggesting very clearly
+that the typical radius is not M a
+
+ align:start position:0%
+that the typical radius is not M a
+ 
+
+ align:start position:0%
+that the typical radius is not M a
+naught is N squared a naught so this is
+
+ align:start position:0%
+naught is N squared a naught so this is
+ 
+
+ align:start position:0%
+naught is N squared a naught so this is
+this is exact the virial theorem is
+
+ align:start position:0%
+this is exact the virial theorem is
+ 
+
+ align:start position:0%
+this is exact the virial theorem is
+exact the energies exact this is exact
+
+ align:start position:0%
+exact the energies exact this is exact
+ 
+
+ align:start position:0%
+exact the energies exact this is exact
+that's not quite the expectation value
+
+ align:start position:0%
+that's not quite the expectation value
+ 
+
+ align:start position:0%
+that's not quite the expectation value
+of r the expectation value of r is not
+
+ align:start position:0%
+of r the expectation value of r is not
+ 
+
+ align:start position:0%
+of r the expectation value of r is not
+the inverse of the expectation value of
+
+ align:start position:0%
+the inverse of the expectation value of
+ 
+
+ align:start position:0%
+the inverse of the expectation value of
+1 over r it's somewhat related but it's
+
+ align:start position:0%
+1 over r it's somewhat related but it's
+ 
+
+ align:start position:0%
+1 over r it's somewhat related but it's
+there's no theorem because it would be
+
+ align:start position:0%
+there's no theorem because it would be
+ 
+
+ align:start position:0%
+there's no theorem because it would be
+false that the expectation value of one
+
+ align:start position:0%
+false that the expectation value of one
+ 
+
+ align:start position:0%
+false that the expectation value of one
+of a random variable is the expectation
+
+ align:start position:0%
+of a random variable is the expectation
+ 
+
+ align:start position:0%
+of a random variable is the expectation
+value of its 1 over the expectation
+
+ align:start position:0%
+value of its 1 over the expectation
+ 
+
+ align:start position:0%
+value of its 1 over the expectation
+value of the random variable it's just
+
+ align:start position:0%
+value of the random variable it's just
+ 
+
+ align:start position:0%
+value of the random variable it's just
+not true this nice we solve for 1 over R
+
+ align:start position:0%
+not true this nice we solve for 1 over R
+ 
+
+ align:start position:0%
+not true this nice we solve for 1 over R
+is exactly true and it's L independent
+
+ align:start position:0%
+is exactly true and it's L independent
+ 
+
+ align:start position:0%
+is exactly true and it's L independent
+on the other hand the expectation value
+
+ align:start position:0%
+on the other hand the expectation value
+ 
+
+ align:start position:0%
+on the other hand the expectation value
+of R can be calculated with a bit more
+
+ align:start position:0%
+of R can be calculated with a bit more
+ 
+
+ align:start position:0%
+of R can be calculated with a bit more
+effort a lot more effort and is equal to
+
+ align:start position:0%
+effort a lot more effort and is equal to
+ 
+
+ align:start position:0%
+effort a lot more effort and is equal to
+this it's just the same thing and one
+
+ align:start position:0%
+this it's just the same thing and one
+ 
+
+ align:start position:0%
+this it's just the same thing and one
+with a little correction which is 1/2 1
+
+ align:start position:0%
+with a little correction which is 1/2 1
+ 
+
+ align:start position:0%
+with a little correction which is 1/2 1
+minus L times L plus 1 over N squared so
+
+ align:start position:0%
+minus L times L plus 1 over N squared so
+ 
+
+ align:start position:0%
+minus L times L plus 1 over N squared so
+actually the expectation value of R in
+
+ align:start position:0%
+actually the expectation value of R in
+ 
+
+ align:start position:0%
+actually the expectation value of R in
+the hydrogen atom is L dependent not
+
+ align:start position:0%
+the hydrogen atom is L dependent not
+ 
+
+ align:start position:0%
+the hydrogen atom is L dependent not
+terribly strongly L dependent but
+
+ align:start position:0%
+terribly strongly L dependent but
+ 
+
+ align:start position:0%
+terribly strongly L dependent but
+somewhat L dependent to get an idea this
+
+ align:start position:0%
+somewhat L dependent to get an idea this
+ 
+
+ align:start position:0%
+somewhat L dependent to get an idea this
+is equal to N squared a
+
+ align:start position:0%
+is equal to N squared a
+ 
+
+ align:start position:0%
+is equal to N squared a
+now times three-halves for l equals zero
+
+ align:start position:0%
+now times three-halves for l equals zero
+ 
+
+ align:start position:0%
+now times three-halves for l equals zero
+when L is equal to zero you see this
+
+ align:start position:0%
+when L is equal to zero you see this
+ 
+
+ align:start position:0%
+when L is equal to zero you see this
+whole bracket becomes three-halves and
+
+ align:start position:0%
+whole bracket becomes three-halves and
+ 
+
+ align:start position:0%
+whole bracket becomes three-halves and
+for the maximum l l equals n minus 1
+
+ align:start position:0%
+for the maximum l l equals n minus 1
+ 
+
+ align:start position:0%
+for the maximum l l equals n minus 1
+this is roughly 1 this is roughly 0 to a
+
+ align:start position:0%
+this is roughly 1 this is roughly 0 to a
+ 
+
+ align:start position:0%
+this is roughly 1 this is roughly 0 to a
+good approximation but not exactly
+
+ align:start position:0%
+good approximation but not exactly
+ 
+
+ align:start position:0%
+good approximation but not exactly
+becomes N squared a not with Corrections
+
+ align:start position:0%
+becomes N squared a not with Corrections
+ 
+
+ align:start position:0%
+becomes N squared a not with Corrections
+that are very very small it's pretty
+
+ align:start position:0%
+that are very very small it's pretty
+ 
+
+ align:start position:0%
+that are very very small it's pretty
+accurate all right so first thing we've
+
+ align:start position:0%
+accurate all right so first thing we've
+ 
+
+ align:start position:0%
+accurate all right so first thing we've
+learned is that we got a radius expected
+
+ align:start position:0%
+learned is that we got a radius expected
+ 
+
+ align:start position:0%
+learned is that we got a radius expected
+radius that goes like N squared a knot
+
+ align:start position:0%
+radius that goes like N squared a knot
+ 
+
+ align:start position:0%
+radius that goes like N squared a knot
+so it's kind of interesting to see what
+
+ align:start position:0%
+so it's kind of interesting to see what
+ 
+
+ align:start position:0%
+so it's kind of interesting to see what
+went wrong if you would have thought
+
+ align:start position:0%
+went wrong if you would have thought
+ 
+
+ align:start position:0%
+went wrong if you would have thought
+with this with the form of the solution
+
+ align:start position:0%
+with this with the form of the solution
+ 
+
+ align:start position:0%
+with this with the form of the solution
+so sy n L m equal a R to the L W and L a
+
+ align:start position:0%
+so sy n L m equal a R to the L W and L a
+ 
+
+ align:start position:0%
+so sy n L m equal a R to the L W and L a
+polynomial e to the minus R over N a not
+
+ align:start position:0%
+polynomial e to the minus R over N a not
+ 
+
+ align:start position:0%
+polynomial e to the minus R over N a not
+ylm of theta and Phi or F n L of our x y
+
+ align:start position:0%
+ylm of theta and Phi or F n L of our x y
+ 
+
+ align:start position:0%
+ylm of theta and Phi or F n L of our x y
+L M of the solid angle and what do we
+
+ align:start position:0%
+L M of the solid angle and what do we
+ 
+
+ align:start position:0%
+L M of the solid angle and what do we
+know about this polynomial
+
+ align:start position:0%
+know about this polynomial
+ 
+
+ align:start position:0%
+know about this polynomial
+it's of degree n minus L plus 1 that's
+
+ align:start position:0%
+it's of degree n minus L plus 1 that's
+ 
+
+ align:start position:0%
+it's of degree n minus L plus 1 that's
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+I need depends on R so so what we're
+
+ align:start position:0%
+I need depends on R so so what we're
+ 
+
+ align:start position:0%
+I need depends on R so so what we're
+looking at is what was the error in
+
+ align:start position:0%
+looking at is what was the error in
+ 
+
+ align:start position:0%
+looking at is what was the error in
+thinking that the typical r was an a
+
+ align:start position:0%
+thinking that the typical r was an a
+ 
+
+ align:start position:0%
+thinking that the typical r was an a
+naught and you see when you make a
+
+ align:start position:0%
+naught and you see when you make a
+ 
+
+ align:start position:0%
+naught and you see when you make a
+mistake like this the mistake i made of
+
+ align:start position:0%
+mistake like this the mistake i made of
+ 
+
+ align:start position:0%
+mistake like this the mistake i made of
+saying oh na naught must be right and
+
+ align:start position:0%
+saying oh na naught must be right and
+ 
+
+ align:start position:0%
+saying oh na naught must be right and
+you find that it's wrong it's very
+
+ align:start position:0%
+you find that it's wrong it's very
+ 
+
+ align:start position:0%
+you find that it's wrong it's very
+important to go back and learn why did
+
+ align:start position:0%
+important to go back and learn why did
+ 
+
+ align:start position:0%
+important to go back and learn why did
+you get the wrong hands
+
+ align:start position:0%
+you get the wrong hands
+ 
+
+ align:start position:0%
+you get the wrong hands
+that's what we're doing now so the one
+
+ align:start position:0%
+that's what we're doing now so the one
+ 
+
+ align:start position:0%
+that's what we're doing now so the one
+question I can ask to begin with is what
+
+ align:start position:0%
+question I can ask to begin with is what
+ 
+
+ align:start position:0%
+question I can ask to begin with is what
+is a probability density to find the
+
+ align:start position:0%
+is a probability density to find the
+ 
+
+ align:start position:0%
+is a probability density to find the
+electron between some radius R and a
+
+ align:start position:0%
+electron between some radius R and a
+ 
+
+ align:start position:0%
+electron between some radius R and a
+radius R Plus D R so you know this is a
+
+ align:start position:0%
+radius R Plus D R so you know this is a
+ 
+
+ align:start position:0%
+radius R Plus D R so you know this is a
+probability and it depends on theta and
+
+ align:start position:0%
+probability and it depends on theta and
+ 
+
+ align:start position:0%
+probability and it depends on theta and
+Phi and it's very complicated how about
+
+ align:start position:0%
+Phi and it's very complicated how about
+ 
+
+ align:start position:0%
+Phi and it's very complicated how about
+giving me a probability along R that I
+
+ align:start position:0%
+giving me a probability along R that I
+ 
+
+ align:start position:0%
+giving me a probability along R that I
+can integrate along R and visualize how
+
+ align:start position:0%
+can integrate along R and visualize how
+ 
+
+ align:start position:0%
+can integrate along R and visualize how
+does it depend on R so the probability
+
+ align:start position:0%
+does it depend on R so the probability
+ 
+
+ align:start position:0%
+does it depend on R so the probability
+to find the electron in this shell must
+
+ align:start position:0%
+to find the electron in this shell must
+ 
+
+ align:start position:0%
+to find the electron in this shell must
+be equal to the value of the wave
+
+ align:start position:0%
+be equal to the value of the wave
+ 
+
+ align:start position:0%
+be equal to the value of the wave
+function squared times the volume
+
+ align:start position:0%
+function squared times the volume
+ 
+
+ align:start position:0%
+function squared times the volume
+element and the volume element here is
+
+ align:start position:0%
+element and the volume element here is
+ 
+
+ align:start position:0%
+element and the volume element here is
+PI squared R squared the R times you
+
+ align:start position:0%
+PI squared R squared the R times you
+ 
+
+ align:start position:0%
+PI squared R squared the R times you
+would say 4 pi but it's not spherically
+
+ align:start position:0%
+would say 4 pi but it's not spherically
+ 
+
+ align:start position:0%
+would say 4 pi but it's not spherically
+symmetric so you have to integrate oops
+
+ align:start position:0%
+symmetric so you have to integrate oops
+ 
+
+ align:start position:0%
+symmetric so you have to integrate oops
+you have to integrate over solid angle
+
+ align:start position:0%
+you have to integrate over solid angle
+ 
+
+ align:start position:0%
+you have to integrate over solid angle
+that is the volume elements and since
+
+ align:start position:0%
+that is the volume elements and since
+ 
+
+ align:start position:0%
+that is the volume elements and since
+they have to integrate over solid angle
+
+ align:start position:0%
+they have to integrate over solid angle
+ 
+
+ align:start position:0%
+they have to integrate over solid angle
+I must have size squared here so that's
+
+ align:start position:0%
+I must have size squared here so that's
+ 
+
+ align:start position:0%
+I must have size squared here so that's
+the right equation they if you want to
+
+ align:start position:0%
+the right equation they if you want to
+ 
+
+ align:start position:0%
+the right equation they if you want to
+make things look perfect put the D cube
+
+ align:start position:0%
+make things look perfect put the D cube
+ 
+
+ align:start position:0%
+make things look perfect put the D cube
+X before at the size squared here and
+
+ align:start position:0%
+X before at the size squared here and
+ 
+
+ align:start position:0%
+X before at the size squared here and
+the problem is that the d cube x is big
+
+ align:start position:0%
+the problem is that the d cube x is big
+ 
+
+ align:start position:0%
+the problem is that the d cube x is big
+enough that it some sense has a partial
+
+ align:start position:0%
+enough that it some sense has a partial
+ 
+
+ align:start position:0%
+enough that it some sense has a partial
+integral so notation is not perfect but
+
+ align:start position:0%
+integral so notation is not perfect but
+ 
+
+ align:start position:0%
+integral so notation is not perfect but
+somehow you must imagine this whole
+
+ align:start position:0%
+somehow you must imagine this whole
+ 
+
+ align:start position:0%
+somehow you must imagine this whole
+volume element that is still
+
+ align:start position:0%
+volume element that is still
+ 
+
+ align:start position:0%
+volume element that is still
+infinitesimally involves some integral
+
+ align:start position:0%
+infinitesimally involves some integral
+ 
+
+ align:start position:0%
+infinitesimally involves some integral
+already so you have this and you get
+
+ align:start position:0%
+already so you have this and you get
+ 
+
+ align:start position:0%
+already so you have this and you get
+that r squared d r f n l squared
+
+ align:start position:0%
+that r squared d r f n l squared
+ 
+
+ align:start position:0%
+that r squared d r f n l squared
+and you have the integral the Omega of
+
+ align:start position:0%
+and you have the integral the Omega of
+ 
+
+ align:start position:0%
+and you have the integral the Omega of
+this Y star LM y LM ad that integral is
+
+ align:start position:0%
+this Y star LM y LM ad that integral is
+ 
+
+ align:start position:0%
+this Y star LM y LM ad that integral is
+exactly one spherical harmonics are
+
+ align:start position:0%
+exactly one spherical harmonics are
+ 
+
+ align:start position:0%
+exactly one spherical harmonics are
+normalized so now I can cancel the dr
+
+ align:start position:0%
+normalized so now I can cancel the dr
+ 
+
+ align:start position:0%
+normalized so now I can cancel the dr
+and i get that the radial probability
+
+ align:start position:0%
+and i get that the radial probability
+ 
+
+ align:start position:0%
+and i get that the radial probability
+distribution which is a nice concept is
+
+ align:start position:0%
+distribution which is a nice concept is
+ 
+
+ align:start position:0%
+distribution which is a nice concept is
+really R squared f NL of R squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radial probability so our mistake my
+
+ align:start position:0%
+radial probability so our mistake my
+ 
+
+ align:start position:0%
+radial probability so our mistake my
+mistake must have been that I didn't
+
+ align:start position:0%
+mistake must have been that I didn't
+ 
+
+ align:start position:0%
+mistake must have been that I didn't
+include all that was relevant the
+
+ align:start position:0%
+include all that was relevant the
+ 
+
+ align:start position:0%
+include all that was relevant the
+exponential is one part but there is the
+
+ align:start position:0%
+exponential is one part but there is the
+ 
+
+ align:start position:0%
+exponential is one part but there is the
+polynomial and the polynomial must be
+
+ align:start position:0%
+polynomial and the polynomial must be
+ 
+
+ align:start position:0%
+polynomial and the polynomial must be
+causing the trouble indeed that's what
+
+ align:start position:0%
+causing the trouble indeed that's what
+ 
+
+ align:start position:0%
+causing the trouble indeed that's what
+is happening let's look at FML from the
+
+ align:start position:0%
+is happening let's look at FML from the
+ 
+
+ align:start position:0%
+is happening let's look at FML from the
+top blackboard that includes R to the L
+
+ align:start position:0%
+top blackboard that includes R to the L
+ 
+
+ align:start position:0%
+top blackboard that includes R to the L
+times at polynomial and it's a
+
+ align:start position:0%
+times at polynomial and it's a
+ 
+
+ align:start position:0%
+times at polynomial and it's a
+polynomial of that degree so it begins
+
+ align:start position:0%
+polynomial of that degree so it begins
+ 
+
+ align:start position:0%
+polynomial of that degree so it begins
+like a not plus up to coefficient a
+
+ align:start position:0%
+like a not plus up to coefficient a
+ 
+
+ align:start position:0%
+like a not plus up to coefficient a
+prime R to the n minus L plus L minus L
+
+ align:start position:0%
+prime R to the n minus L plus L minus L
+ 
+
+ align:start position:0%
+prime R to the n minus L plus L minus L
+minus one and then I have exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now I cannot do this I don't want to do
+
+ align:start position:0%
+now I cannot do this I don't want to do
+ 
+
+ align:start position:0%
+now I cannot do this I don't want to do
+this calculation exactly it's too
+
+ align:start position:0%
+this calculation exactly it's too
+ 
+
+ align:start position:0%
+this calculation exactly it's too
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+so let's ignore the lower parts of the
+
+ align:start position:0%
+so let's ignore the lower parts of the
+ 
+
+ align:start position:0%
+so let's ignore the lower parts of the
+polynomial and we're thinking the radius
+
+ align:start position:0%
+polynomial and we're thinking the radius
+ 
+
+ align:start position:0%
+polynomial and we're thinking the radius
+is going to be reasonably big so it's a
+
+ align:start position:0%
+is going to be reasonably big so it's a
+ 
+
+ align:start position:0%
+is going to be reasonably big so it's a
+reasonable idea to keep the power of the
+
+ align:start position:0%
+reasonable idea to keep the power of the
+ 
+
+ align:start position:0%
+reasonable idea to keep the power of the
+polynomial that is the largest so what
+
+ align:start position:0%
+polynomial that is the largest so what
+ 
+
+ align:start position:0%
+polynomial that is the largest so what
+is the largest and here you see a nice
+
+ align:start position:0%
+is the largest and here you see a nice
+ 
+
+ align:start position:0%
+is the largest and here you see a nice
+thing actually R to the L times this
+
+ align:start position:0%
+thing actually R to the L times this
+ 
+
+ align:start position:0%
+thing actually R to the L times this
+polynomial is a polynomial that begins
+
+ align:start position:0%
+polynomial is a polynomial that begins
+ 
+
+ align:start position:0%
+polynomial is a polynomial that begins
+with R to the L and finishes with R to
+
+ align:start position:0%
+with R to the L and finishes with R to
+ 
+
+ align:start position:0%
+with R to the L and finishes with R to
+the N minus 1 so it has like equal
+
+ align:start position:0%
+the N minus 1 so it has like equal
+ 
+
+ align:start position:0%
+the N minus 1 so it has like equal
+number of terms as reaches a value of n
+
+ align:start position:0%
+number of terms as reaches a value of n
+ 
+
+ align:start position:0%
+number of terms as reaches a value of n
+minus 1 the last term in the polynomial
+
+ align:start position:0%
+minus 1 the last term in the polynomial
+ 
+
+ align:start position:0%
+minus 1 the last term in the polynomial
+when you multiply it in this begins like
+
+ align:start position:0%
+when you multiply it in this begins like
+ 
+
+ align:start position:0%
+when you multiply it in this begins like
+R to the L and the last term is R to the
+
+ align:start position:0%
+R to the L and the last term is R to the
+ 
+
+ align:start position:0%
+R to the L and the last term is R to the
+N minus 1 so let's take this to be
+
+ align:start position:0%
+N minus 1 so let's take this to be
+ 
+
+ align:start position:0%
+N minus 1 so let's take this to be
+proportional to R to the N minus 1 equal
+
+ align:start position:0%
+proportional to R to the N minus 1 equal
+ 
+
+ align:start position:0%
+proportional to R to the N minus 1 equal
+to minus R and a 0 and here is the fight
+
+ align:start position:0%
+to minus R and a 0 and here is the fight
+ 
+
+ align:start position:0%
+to minus R and a 0 and here is the fight
+that actually changes the answer because
+
+ align:start position:0%
+that actually changes the answer because
+ 
+
+ align:start position:0%
+that actually changes the answer because
+this is FNL so actually I can write P of
+
+ align:start position:0%
+this is FNL so actually I can write P of
+ 
+
+ align:start position:0%
+this is FNL so actually I can write P of
+R is proportional up to a constant of
+
+ align:start position:0%
+R is proportional up to a constant of
+ 
+
+ align:start position:0%
+R is proportional up to a constant of
+normalization and and the approximations
+
+ align:start position:0%
+normalization and and the approximations
+ 
+
+ align:start position:0%
+normalization and and the approximations
+they have done R squared times this
+
+ align:start position:0%
+they have done R squared times this
+ 
+
+ align:start position:0%
+they have done R squared times this
+polynomial squared but I'm taking the
+
+ align:start position:0%
+polynomial squared but I'm taking the
+ 
+
+ align:start position:0%
+polynomial squared but I'm taking the
+last term of the polynomial so we get R
+
+ align:start position:0%
+last term of the polynomial so we get R
+ 
+
+ align:start position:0%
+last term of the polynomial so we get R
+to the 2n e to the minus 2 R over m a
+
+ align:start position:0%
+to the 2n e to the minus 2 R over m a
+ 
+
+ align:start position:0%
+to the 2n e to the minus 2 R over m a
+naught that's a probability distribution
+
+ align:start position:0%
+naught that's a probability distribution
+ 
+
+ align:start position:0%
+naught that's a probability distribution
+and with this probability distribution
+
+ align:start position:0%
+and with this probability distribution
+ 
+
+ align:start position:0%
+and with this probability distribution
+then you see what's happening is that
+
+ align:start position:0%
+then you see what's happening is that
+ 
+
+ align:start position:0%
+then you see what's happening is that
+there is a fight between an exponential
+
+ align:start position:0%
+there is a fight between an exponential
+ 
+
+ align:start position:0%
+there is a fight between an exponential
+that has a typical length where it
+
+ align:start position:0%
+that has a typical length where it
+ 
+
+ align:start position:0%
+that has a typical length where it
+decays to half its value that is related
+
+ align:start position:0%
+decays to half its value that is related
+ 
+
+ align:start position:0%
+decays to half its value that is related
+to n
+
+ align:start position:0%
+to n
+ 
+
+ align:start position:0%
+to n
+but the maximum is delay because it's
+
+ align:start position:0%
+but the maximum is delay because it's
+ 
+
+ align:start position:0%
+but the maximum is delay because it's
+multiplied by a function that they've
+
+ align:start position:0%
+multiplied by a function that they've
+ 
+
+ align:start position:0%
+multiplied by a function that they've
+higher the value of n the slower it is
+
+ align:start position:0%
+higher the value of n the slower it is
+ 
+
+ align:start position:0%
+higher the value of n the slower it is
+to take off x squared or R squared takes
+
+ align:start position:0%
+to take off x squared or R squared takes
+ 
+
+ align:start position:0%
+to take off x squared or R squared takes
+off slower than R takes off slower than
+
+ align:start position:0%
+off slower than R takes off slower than
+ 
+
+ align:start position:0%
+off slower than R takes off slower than
+R to the fourth so the pro so here you
+
+ align:start position:0%
+R to the fourth so the pro so here you
+ 
+
+ align:start position:0%
+R to the fourth so the pro so here you
+have a thing that just grows like that
+
+ align:start position:0%
+have a thing that just grows like that
+ 
+
+ align:start position:0%
+have a thing that just grows like that
+but it takes forever to take off and the
+
+ align:start position:0%
+but it takes forever to take off and the
+ 
+
+ align:start position:0%
+but it takes forever to take off and the
+result of this is a function that just
+
+ align:start position:0%
+result of this is a function that just
+ 
+
+ align:start position:0%
+result of this is a function that just
+picks up at some point over here and we
+
+ align:start position:0%
+picks up at some point over here and we
+ 
+
+ align:start position:0%
+picks up at some point over here and we
+want to find the maximum so the maximum
+
+ align:start position:0%
+want to find the maximum so the maximum
+ 
+
+ align:start position:0%
+want to find the maximum so the maximum
+comes from taking a derivative so the
+
+ align:start position:0%
+comes from taking a derivative so the
+ 
+
+ align:start position:0%
+comes from taking a derivative so the
+maximum of P of R is determined by
+
+ align:start position:0%
+maximum of P of R is determined by
+ 
+
+ align:start position:0%
+maximum of P of R is determined by
+setting the derivative of this equal to
+
+ align:start position:0%
+setting the derivative of this equal to
+ 
+
+ align:start position:0%
+setting the derivative of this equal to
+zero so you get 2 n over R times the
+
+ align:start position:0%
+zero so you get 2 n over R times the
+ 
+
+ align:start position:0%
+zero so you get 2 n over R times the
+same R to the 2n e to the minus 2 R over
+
+ align:start position:0%
+same R to the 2n e to the minus 2 R over
+ 
+
+ align:start position:0%
+same R to the 2n e to the minus 2 R over
+m a naught so the first term the
+
+ align:start position:0%
+m a naught so the first term the
+ 
+
+ align:start position:0%
+m a naught so the first term the
+derivative is 2 R and R to the 2n minus
+
+ align:start position:0%
+derivative is 2 R and R to the 2n minus
+ 
+
+ align:start position:0%
+derivative is 2 R and R to the 2n minus
+1 which is divided by R and the same
+
+ align:start position:0%
+1 which is divided by R and the same
+ 
+
+ align:start position:0%
+1 which is divided by R and the same
+thing the second derivative gives you
+
+ align:start position:0%
+thing the second derivative gives you
+ 
+
+ align:start position:0%
+thing the second derivative gives you
+minus 2 over n a naught and that's it
+
+ align:start position:0%
+minus 2 over n a naught and that's it
+ 
+
+ align:start position:0%
+minus 2 over n a naught and that's it
+so from this two you get that M over R
+
+ align:start position:0%
+so from this two you get that M over R
+ 
+
+ align:start position:0%
+so from this two you get that M over R
+is equal to 1 over M naught so R equals
+
+ align:start position:0%
+is equal to 1 over M naught so R equals
+ 
+
+ align:start position:0%
+is equal to 1 over M naught so R equals
+N squared a naught as we had predicted
+
+ align:start position:0%
+N squared a naught as we had predicted
+ 
+
+ align:start position:0%
+N squared a naught as we had predicted
+so it's the interplay of the polynomial
+
+ align:start position:0%
+so it's the interplay of the polynomial
+ 
+
+ align:start position:0%
+so it's the interplay of the polynomial
+with the other thing that makes the
+
+ align:start position:0%
+with the other thing that makes the
+ 
+
+ align:start position:0%
+with the other thing that makes the
+radius
+
+ align:start position:0%
+radius
+ 
+
+ align:start position:0%
+radius
+go very high so what about this red burg
+
+ align:start position:0%
+go very high so what about this red burg
+ 
+
+ align:start position:0%
+go very high so what about this red burg
+atoms in nature well they've been
+
+ align:start position:0%
+atoms in nature well they've been
+ 
+
+ align:start position:0%
+atoms in nature well they've been
+observed in
+
+ align:start position:0%
+observed in
+ 
+
+ align:start position:0%
+observed in
+interstellar gaseous if you see there
+
+ align:start position:0%
+interstellar gaseous if you see there
+ 
+
+ align:start position:0%
+interstellar gaseous if you see there
+was this phenomenon of recombination
+
+ align:start position:0%
+was this phenomenon of recombination
+ 
+
+ align:start position:0%
+was this phenomenon of recombination
+when protons captured electrons as the
+
+ align:start position:0%
+when protons captured electrons as the
+ 
+
+ align:start position:0%
+when protons captured electrons as the
+universe cooled off and form hydrogen
+
+ align:start position:0%
+universe cooled off and form hydrogen
+ 
+
+ align:start position:0%
+universe cooled off and form hydrogen
+atoms and that recombination sometimes
+
+ align:start position:0%
+atoms and that recombination sometimes
+ 
+
+ align:start position:0%
+atoms and that recombination sometimes
+works in such a way that the proton can
+
+ align:start position:0%
+works in such a way that the proton can
+ 
+
+ align:start position:0%
+works in such a way that the proton can
+capture an electron and it captures it
+
+ align:start position:0%
+capture an electron and it captures it
+ 
+
+ align:start position:0%
+capture an electron and it captures it
+in a very high quantum number and it
+
+ align:start position:0%
+in a very high quantum number and it
+ 
+
+ align:start position:0%
+in a very high quantum number and it
+keeps happening as we observe this
+
+ align:start position:0%
+keeps happening as we observe this
+ 
+
+ align:start position:0%
+keeps happening as we observe this
+electron so so people have observed in
+
+ align:start position:0%
+electron so so people have observed in
+ 
+
+ align:start position:0%
+electron so so people have observed in
+astrophysics n equal 350 and proto here
+
+ align:start position:0%
+astrophysics n equal 350 and proto here
+ 
+
+ align:start position:0%
+astrophysics n equal 350 and proto here
+the electron beam captured just not in
+
+ align:start position:0%
+the electron beam captured just not in
+ 
+
+ align:start position:0%
+the electron beam captured just not in
+the usual size but almost a million
+
+ align:start position:0%
+the usual size but almost a million
+ 
+
+ align:start position:0%
+the usual size but almost a million
+times bigger so what happens for this
+
+ align:start position:0%
+times bigger so what happens for this
+ 
+
+ align:start position:0%
+times bigger so what happens for this
+thing R is equal 0.53 times 10 to the
+
+ align:start position:0%
+thing R is equal 0.53 times 10 to the
+ 
+
+ align:start position:0%
+thing R is equal 0.53 times 10 to the
+minus 10 meters that's a zero and then
+
+ align:start position:0%
+minus 10 meters that's a zero and then
+ 
+
+ align:start position:0%
+minus 10 meters that's a zero and then
+you have 350 squared and that gives you
+
+ align:start position:0%
+you have 350 squared and that gives you
+ 
+
+ align:start position:0%
+you have 350 squared and that gives you
+six point five microns that's actually
+
+ align:start position:0%
+six point five microns that's actually
+ 
+
+ align:start position:0%
+six point five microns that's actually
+pretty big a blood cell is eight microns
+
+ align:start position:0%
+pretty big a blood cell is eight microns
+ 
+
+ align:start position:0%
+pretty big a blood cell is eight microns
+red blood cell is eighth microns they
+
+ align:start position:0%
+red blood cell is eighth microns they
+ 
+
+ align:start position:0%
+red blood cell is eighth microns they
+are not stable because eventually they
+
+ align:start position:0%
+are not stable because eventually they
+ 
+
+ align:start position:0%
+are not stable because eventually they
+spiral in but if you had a if you have
+
+ align:start position:0%
+spiral in but if you had a if you have
+ 
+
+ align:start position:0%
+spiral in but if you had a if you have
+an atom that for example has an N equal
+
+ align:start position:0%
+an atom that for example has an N equal
+ 
+
+ align:start position:0%
+an atom that for example has an N equal
+to five it jumps to N equals to one in
+
+ align:start position:0%
+to five it jumps to N equals to one in
+ 
+
+ align:start position:0%
+to five it jumps to N equals to one in
+ten to the minus seven seconds these
+
+ align:start position:0%
+ten to the minus seven seconds these
+ 
+
+ align:start position:0%
+ten to the minus seven seconds these
+atoms are rather stable instead of
+
+ align:start position:0%
+atoms are rather stable instead of
+ 
+
+ align:start position:0%
+atoms are rather stable instead of
+lasting one tenth of a million of a
+
+ align:start position:0%
+lasting one tenth of a million of a
+ 
+
+ align:start position:0%
+lasting one tenth of a million of a
+second they can last a millisecond a
+
+ align:start position:0%
+second they can last a millisecond a
+ 
+
+ align:start position:0%
+second they can last a millisecond a
+tenth of a second sometimes even one
+
+ align:start position:0%
+tenth of a second sometimes even one
+ 
+
+ align:start position:0%
+tenth of a second sometimes even one
+second if it takes a long time to go
+
+ align:start position:0%
+second if it takes a long time to go
+ 
+
+ align:start position:0%
+second if it takes a long time to go
+down that spiral the energy levels if
+
+ align:start position:0%
+down that spiral the energy levels if
+ 
+
+ align:start position:0%
+down that spiral the energy levels if
+you have energies that go like 1 over N
+
+ align:start position:0%
+you have energies that go like 1 over N
+ 
+
+ align:start position:0%
+you have energies that go like 1 over N
+squared the energy levels the separation
+
+ align:start position:0%
+squared the energy levels the separation
+ 
+
+ align:start position:0%
+squared the energy levels the separation
+between them goes like 1 over n cubed so
+
+ align:start position:0%
+between them goes like 1 over n cubed so
+ 
+
+ align:start position:0%
+between them goes like 1 over n cubed so
+lots and lots of states there and it
+
+ align:start position:0%
+lots and lots of states there and it
+ 
+
+ align:start position:0%
+lots and lots of states there and it
+takes a long time for it to decay from
+
+ align:start position:0%
+takes a long time for it to decay from
+ 
+
+ align:start position:0%
+takes a long time for it to decay from
+one to another
+
+ align:start position:0%
+one to another
+ 
+
+ align:start position:0%
+one to another
+oh so they observe them in the lab in
+
+ align:start position:0%
+oh so they observe them in the lab in
+ 
+
+ align:start position:0%
+oh so they observe them in the lab in
+different ways they create them with
+
+ align:start position:0%
+different ways they create them with
+ 
+
+ align:start position:0%
+different ways they create them with
+lasers now you have the Elector busted
+
+ align:start position:0%
+lasers now you have the Elector busted
+ 
+
+ align:start position:0%
+lasers now you have the Elector busted
+later you kick it to another orbit with
+
+ align:start position:0%
+later you kick it to another orbit with
+ 
+
+ align:start position:0%
+later you kick it to another orbit with
+one we use three lasers in the lab at
+
+ align:start position:0%
+one we use three lasers in the lab at
+ 
+
+ align:start position:0%
+one we use three lasers in the lab at
+MIT three lasers
+
+ align:start position:0%
+MIT three lasers
+ 
+
+ align:start position:0%
+MIT three lasers
+one and two to kick it to an N equal ten
+
+ align:start position:0%
+one and two to kick it to an N equal ten
+ 
+
+ align:start position:0%
+one and two to kick it to an N equal ten
+and then the third one to kick it to n
+
+ align:start position:0%
+and then the third one to kick it to n
+ 
+
+ align:start position:0%
+and then the third one to kick it to n
+equal 60 and they detect those atoms by
+
+ align:start position:0%
+equal 60 and they detect those atoms by
+ 
+
+ align:start position:0%
+equal 60 and they detect those atoms by
+ionization a normal atom
+
+ align:start position:0%
+ionization a normal atom
+ 
+
+ align:start position:0%
+ionization a normal atom
+you can't ionize you within millions of
+
+ align:start position:0%
+you can't ionize you within millions of
+ 
+
+ align:start position:0%
+you can't ionize you within millions of
+volts per centimeter to ionize it with
+
+ align:start position:0%
+volts per centimeter to ionize it with
+ 
+
+ align:start position:0%
+volts per centimeter to ionize it with
+an electric field these atoms you can
+
+ align:start position:0%
+an electric field these atoms you can
+ 
+
+ align:start position:0%
+an electric field these atoms you can
+ionize very easily so they can see that
+
+ align:start position:0%
+ionize very easily so they can see that
+ 
+
+ align:start position:0%
+ionize very easily so they can see that
+they've been created that way so also in
+
+ align:start position:0%
+they've been created that way so also in
+ 
+
+ align:start position:0%
+they've been created that way so also in
+terms of sizes the diameter of hair of
+
+ align:start position:0%
+terms of sizes the diameter of hair of
+ 
+
+ align:start position:0%
+terms of sizes the diameter of hair of
+hair is about 50 microns if their hair
+
+ align:start position:0%
+hair is about 50 microns if their hair
+ 
+
+ align:start position:0%
+hair is about 50 microns if their hair
+is very thin but you see it so you're
+
+ align:start position:0%
+is very thin but you see it so you're
+ 
+
+ align:start position:0%
+is very thin but you see it so you're
+about a factor of five or ten to being
+
+ align:start position:0%
+about a factor of five or ten to being
+ 
+
+ align:start position:0%
+about a factor of five or ten to being
+able to see that atom with your naked
+
+ align:start position:0%
+able to see that atom with your naked
+ 
+
+ align:start position:0%
+able to see that atom with your naked
+eye it's pretty impressive incredible in
+
+ align:start position:0%
+eye it's pretty impressive incredible in
+ 
+
+ align:start position:0%
+eye it's pretty impressive incredible in
+fact so a nice laboratory those are
+
+ align:start position:0%
+fact so a nice laboratory those are
+ 
+
+ align:start position:0%
+fact so a nice laboratory those are
+almost semi-classical atoms all what
+
+ align:start position:0%
+almost semi-classical atoms all what
+ 
+
+ align:start position:0%
+almost semi-classical atoms all what
+Bohr was doing of calculated you can
+
+ align:start position:0%
+Bohr was doing of calculated you can
+ 
+
+ align:start position:0%
+Bohr was doing of calculated you can
+derive this law by assuming that the
+
+ align:start position:0%
+derive this law by assuming that the
+ 
+
+ align:start position:0%
+derive this law by assuming that the
+transitions between orbits in the
+
+ align:start position:0%
+transitions between orbits in the
+ 
+
+ align:start position:0%
+transitions between orbits in the
+hydrogen atom and MIT photos of the
+
+ align:start position:0%
+hydrogen atom and MIT photos of the
+ 
+
+ align:start position:0%
+hydrogen atom and MIT photos of the
+right frequency it's all kinds of fun
+
+ align:start position:0%
+right frequency it's all kinds of fun
+ 
+
+ align:start position:0%
+right frequency it's all kinds of fun
+things
\ No newline at end of file
diff --git a/b3szQPSRfjY.txt b/b3szQPSRfjY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61087cea6aaaa81d79c060870625429151ce4999
--- /dev/null
+++ b/b3szQPSRfjY.txt
@@ -0,0 +1,2763 @@
+align:start position:0%
+ 
+the person who sort of invents a new
+
+ align:start position:0%
+the person who sort of invents a new
+ 
+
+ align:start position:0%
+the person who sort of invents a new
+sustainable
+
+ align:start position:0%
+sustainable
+ 
+
+ align:start position:0%
+sustainable
+energy source or figures out how to
+
+ align:start position:0%
+energy source or figures out how to
+ 
+
+ align:start position:0%
+energy source or figures out how to
+remove plastics from the ocean
+
+ align:start position:0%
+remove plastics from the ocean
+ 
+
+ align:start position:0%
+remove plastics from the ocean
+it doesn't matter whether they have a
+
+ align:start position:0%
+it doesn't matter whether they have a
+ 
+
+ align:start position:0%
+it doesn't matter whether they have a
+degree or a certificate what matters is
+
+ align:start position:0%
+degree or a certificate what matters is
+ 
+
+ align:start position:0%
+degree or a certificate what matters is
+can they actually achieve it
+
+ align:start position:0%
+can they actually achieve it
+ 
+
+ align:start position:0%
+can they actually achieve it
+that i think is what we need to keep our
+
+ align:start position:0%
+that i think is what we need to keep our
+ 
+
+ align:start position:0%
+that i think is what we need to keep our
+eye on which is can they solve the
+
+ align:start position:0%
+eye on which is can they solve the
+ 
+
+ align:start position:0%
+eye on which is can they solve the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+today on chalk radio we're sitting down
+
+ align:start position:0%
+today on chalk radio we're sitting down
+ 
+
+ align:start position:0%
+today on chalk radio we're sitting down
+with sanjay sarma the vice president for
+
+ align:start position:0%
+with sanjay sarma the vice president for
+ 
+
+ align:start position:0%
+with sanjay sarma the vice president for
+open learning at mit
+
+ align:start position:0%
+open learning at mit
+ 
+
+ align:start position:0%
+open learning at mit
+sanjay wears many hats he's a professor
+
+ align:start position:0%
+sanjay wears many hats he's a professor
+ 
+
+ align:start position:0%
+sanjay wears many hats he's a professor
+of mechanical engineering a developer
+
+ align:start position:0%
+of mechanical engineering a developer
+ 
+
+ align:start position:0%
+of mechanical engineering a developer
+writer a parent and perhaps most salient
+
+ align:start position:0%
+writer a parent and perhaps most salient
+ 
+
+ align:start position:0%
+writer a parent and perhaps most salient
+for us at mit open courseware
+
+ align:start position:0%
+for us at mit open courseware
+ 
+
+ align:start position:0%
+for us at mit open courseware
+sanjay is a learner
+
+ align:start position:0%
+sanjay is a learner
+ 
+
+ align:start position:0%
+sanjay is a learner
+in today's episode sanji talks to us
+
+ align:start position:0%
+in today's episode sanji talks to us
+ 
+
+ align:start position:0%
+in today's episode sanji talks to us
+about learning from the social systems
+
+ align:start position:0%
+about learning from the social systems
+ 
+
+ align:start position:0%
+about learning from the social systems
+behind how we learn to the biology of
+
+ align:start position:0%
+behind how we learn to the biology of
+ 
+
+ align:start position:0%
+behind how we learn to the biology of
+how we're wired to make sense of the
+
+ align:start position:0%
+how we're wired to make sense of the
+ 
+
+ align:start position:0%
+how we're wired to make sense of the
+world around us
+
+ align:start position:0%
+world around us
+ 
+
+ align:start position:0%
+world around us
+i'm your host sarah hansen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in august of 2020 sanji released his
+
+ align:start position:0%
+in august of 2020 sanji released his
+ 
+
+ align:start position:0%
+in august of 2020 sanji released his
+book grasp the science transforming how
+
+ align:start position:0%
+book grasp the science transforming how
+ 
+
+ align:start position:0%
+book grasp the science transforming how
+we learn
+
+ align:start position:0%
+we learn
+ 
+
+ align:start position:0%
+we learn
+which he co-authored with luke yokinto
+
+ align:start position:0%
+which he co-authored with luke yokinto
+ 
+
+ align:start position:0%
+which he co-authored with luke yokinto
+it's about how we learn it's an attempt
+
+ align:start position:0%
+it's about how we learn it's an attempt
+ 
+
+ align:start position:0%
+it's about how we learn it's an attempt
+to describe how we learn with sort of a
+
+ align:start position:0%
+to describe how we learn with sort of a
+ 
+
+ align:start position:0%
+to describe how we learn with sort of a
+biographical aspect to it
+
+ align:start position:0%
+biographical aspect to it
+ 
+
+ align:start position:0%
+biographical aspect to it
+you know some ask me why is it called
+
+ align:start position:0%
+you know some ask me why is it called
+ 
+
+ align:start position:0%
+you know some ask me why is it called
+grasp
+
+ align:start position:0%
+grasp
+ 
+
+ align:start position:0%
+grasp
+right why grasp think about in english
+
+ align:start position:0%
+right why grasp think about in english
+ 
+
+ align:start position:0%
+right why grasp think about in english
+when you really get something called
+
+ align:start position:0%
+when you really get something called
+ 
+
+ align:start position:0%
+when you really get something called
+grasping something
+
+ align:start position:0%
+grasping something
+ 
+
+ align:start position:0%
+grasping something
+i think the german word is similar
+
+ align:start position:0%
+i think the german word is similar
+ 
+
+ align:start position:0%
+i think the german word is similar
+comprehension it has the word apprehend
+
+ align:start position:0%
+comprehension it has the word apprehend
+ 
+
+ align:start position:0%
+comprehension it has the word apprehend
+you know you apprehend someone right
+
+ align:start position:0%
+you know you apprehend someone right
+ 
+
+ align:start position:0%
+you know you apprehend someone right
+it's grabbing
+
+ align:start position:0%
+it's grabbing
+ 
+
+ align:start position:0%
+it's grabbing
+in hindi which is one of the languages i
+
+ align:start position:0%
+in hindi which is one of the languages i
+ 
+
+ align:start position:0%
+in hindi which is one of the languages i
+grew up with
+
+ align:start position:0%
+grew up with
+ 
+
+ align:start position:0%
+grew up with
+you also use a similar word which is i
+
+ align:start position:0%
+you also use a similar word which is i
+ 
+
+ align:start position:0%
+you also use a similar word which is i
+really got the concept you grab it right
+
+ align:start position:0%
+really got the concept you grab it right
+ 
+
+ align:start position:0%
+really got the concept you grab it right
+so what does it really mean to learn
+
+ align:start position:0%
+so what does it really mean to learn
+ 
+
+ align:start position:0%
+so what does it really mean to learn
+that's what this book is about and what
+
+ align:start position:0%
+that's what this book is about and what
+ 
+
+ align:start position:0%
+that's what this book is about and what
+is the science behind it how does
+
+ align:start position:0%
+is the science behind it how does
+ 
+
+ align:start position:0%
+is the science behind it how does
+curiosity drive it what does it mean to
+
+ align:start position:0%
+curiosity drive it what does it mean to
+ 
+
+ align:start position:0%
+curiosity drive it what does it mean to
+memorize something what does it mean to
+
+ align:start position:0%
+memorize something what does it mean to
+ 
+
+ align:start position:0%
+memorize something what does it mean to
+forget something
+
+ align:start position:0%
+forget something
+ 
+
+ align:start position:0%
+forget something
+what does it mean when you actually
+
+ align:start position:0%
+what does it mean when you actually
+ 
+
+ align:start position:0%
+what does it mean when you actually
+remember something but you can't access
+
+ align:start position:0%
+remember something but you can't access
+ 
+
+ align:start position:0%
+remember something but you can't access
+it but when you get it once you access
+
+ align:start position:0%
+it but when you get it once you access
+ 
+
+ align:start position:0%
+it but when you get it once you access
+it it also comes flowing out so that's
+
+ align:start position:0%
+it it also comes flowing out so that's
+ 
+
+ align:start position:0%
+it it also comes flowing out so that's
+what this book is about and it tries to
+
+ align:start position:0%
+what this book is about and it tries to
+ 
+
+ align:start position:0%
+what this book is about and it tries to
+map it from neurons all the way to
+
+ align:start position:0%
+map it from neurons all the way to
+ 
+
+ align:start position:0%
+map it from neurons all the way to
+societal level
+
+ align:start position:0%
+societal level
+ 
+
+ align:start position:0%
+societal level
+so what prompted him to write the book
+
+ align:start position:0%
+so what prompted him to write the book
+ 
+
+ align:start position:0%
+so what prompted him to write the book
+for sanjay it was about uncovering the
+
+ align:start position:0%
+for sanjay it was about uncovering the
+ 
+
+ align:start position:0%
+for sanjay it was about uncovering the
+history of schooling and rethinking the
+
+ align:start position:0%
+history of schooling and rethinking the
+ 
+
+ align:start position:0%
+history of schooling and rethinking the
+methods we used to teach
+
+ align:start position:0%
+methods we used to teach
+ 
+
+ align:start position:0%
+methods we used to teach
+i always wondered why we ended up doing
+
+ align:start position:0%
+i always wondered why we ended up doing
+ 
+
+ align:start position:0%
+i always wondered why we ended up doing
+things the way we do and it turns out
+
+ align:start position:0%
+things the way we do and it turns out
+ 
+
+ align:start position:0%
+things the way we do and it turns out
+that a lot of it is happenstance
+
+ align:start position:0%
+that a lot of it is happenstance
+ 
+
+ align:start position:0%
+that a lot of it is happenstance
+and perhaps a historical accident the
+
+ align:start position:0%
+and perhaps a historical accident the
+ 
+
+ align:start position:0%
+and perhaps a historical accident the
+impact of
+
+ align:start position:0%
+impact of
+ 
+
+ align:start position:0%
+impact of
+what we were trying to educate people
+
+ align:start position:0%
+what we were trying to educate people
+ 
+
+ align:start position:0%
+what we were trying to educate people
+about which initially was religious
+
+ align:start position:0%
+about which initially was religious
+ 
+
+ align:start position:0%
+about which initially was religious
+books right and eventually it was
+
+ align:start position:0%
+books right and eventually it was
+ 
+
+ align:start position:0%
+books right and eventually it was
+memorizing aspects of the book and there
+
+ align:start position:0%
+memorizing aspects of the book and there
+ 
+
+ align:start position:0%
+memorizing aspects of the book and there
+was the greek thread that sort of wove
+
+ align:start position:0%
+was the greek thread that sort of wove
+ 
+
+ align:start position:0%
+was the greek thread that sort of wove
+into that and then the industrial
+
+ align:start position:0%
+into that and then the industrial
+ 
+
+ align:start position:0%
+into that and then the industrial
+revolution and so on
+
+ align:start position:0%
+revolution and so on
+ 
+
+ align:start position:0%
+revolution and so on
+and so the question was if you went back
+
+ align:start position:0%
+and so the question was if you went back
+ 
+
+ align:start position:0%
+and so the question was if you went back
+to the basics how would you teach and
+
+ align:start position:0%
+to the basics how would you teach and
+ 
+
+ align:start position:0%
+to the basics how would you teach and
+what would you teach
+
+ align:start position:0%
+what would you teach
+ 
+
+ align:start position:0%
+what would you teach
+i too am a product of western education
+
+ align:start position:0%
+i too am a product of western education
+ 
+
+ align:start position:0%
+i too am a product of western education
+principles and i did well but i also
+
+ align:start position:0%
+principles and i did well but i also
+ 
+
+ align:start position:0%
+principles and i did well but i also
+struggled
+
+ align:start position:0%
+struggled
+ 
+
+ align:start position:0%
+struggled
+and so i started wondering what the
+
+ align:start position:0%
+and so i started wondering what the
+ 
+
+ align:start position:0%
+and so i started wondering what the
+science tells us about how educational
+
+ align:start position:0%
+science tells us about how educational
+ 
+
+ align:start position:0%
+science tells us about how educational
+systems should be designed
+
+ align:start position:0%
+systems should be designed
+ 
+
+ align:start position:0%
+systems should be designed
+so once i started researching it i
+
+ align:start position:0%
+so once i started researching it i
+ 
+
+ align:start position:0%
+so once i started researching it i
+thought oh my god the story needs to be
+
+ align:start position:0%
+thought oh my god the story needs to be
+ 
+
+ align:start position:0%
+thought oh my god the story needs to be
+told so the book sort of started writing
+
+ align:start position:0%
+told so the book sort of started writing
+ 
+
+ align:start position:0%
+told so the book sort of started writing
+itself and then i found luke and he
+
+ align:start position:0%
+itself and then i found luke and he
+ 
+
+ align:start position:0%
+itself and then i found luke and he
+shaped it with me and that's what i like
+
+ align:start position:0%
+shaped it with me and that's what i like
+ 
+
+ align:start position:0%
+shaped it with me and that's what i like
+to grasp
+
+ align:start position:0%
+to grasp
+ 
+
+ align:start position:0%
+to grasp
+so what's the difference between simply
+
+ align:start position:0%
+so what's the difference between simply
+ 
+
+ align:start position:0%
+so what's the difference between simply
+picking up concepts and actually
+
+ align:start position:0%
+picking up concepts and actually
+ 
+
+ align:start position:0%
+picking up concepts and actually
+grasping them
+
+ align:start position:0%
+grasping them
+ 
+
+ align:start position:0%
+grasping them
+according to sanjay what it often comes
+
+ align:start position:0%
+according to sanjay what it often comes
+ 
+
+ align:start position:0%
+according to sanjay what it often comes
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+is having an actionable component to
+
+ align:start position:0%
+is having an actionable component to
+ 
+
+ align:start position:0%
+is having an actionable component to
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+not just hearing and regurgitating
+
+ align:start position:0%
+not just hearing and regurgitating
+ 
+
+ align:start position:0%
+not just hearing and regurgitating
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+but locking it in place by physically
+
+ align:start position:0%
+but locking it in place by physically
+ 
+
+ align:start position:0%
+but locking it in place by physically
+applying it
+
+ align:start position:0%
+applying it
+ 
+
+ align:start position:0%
+applying it
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have this assumption that the learner's
+
+ align:start position:0%
+have this assumption that the learner's
+ 
+
+ align:start position:0%
+have this assumption that the learner's
+mind is a sheet of
+
+ align:start position:0%
+mind is a sheet of
+ 
+
+ align:start position:0%
+mind is a sheet of
+paper and the professor has a pen
+
+ align:start position:0%
+paper and the professor has a pen
+ 
+
+ align:start position:0%
+paper and the professor has a pen
+and all the professor has to do is write
+
+ align:start position:0%
+and all the professor has to do is write
+ 
+
+ align:start position:0%
+and all the professor has to do is write
+on the sheet of paper and declare
+
+ align:start position:0%
+on the sheet of paper and declare
+ 
+
+ align:start position:0%
+on the sheet of paper and declare
+victory
+
+ align:start position:0%
+victory
+ 
+
+ align:start position:0%
+victory
+and after 10 minutes 15 minutes 20
+
+ align:start position:0%
+and after 10 minutes 15 minutes 20
+ 
+
+ align:start position:0%
+and after 10 minutes 15 minutes 20
+minutes
+
+ align:start position:0%
+minutes
+ 
+
+ align:start position:0%
+minutes
+if the learner isn't paying attention
+
+ align:start position:0%
+if the learner isn't paying attention
+ 
+
+ align:start position:0%
+if the learner isn't paying attention
+that's the learner's fault not a
+
+ align:start position:0%
+that's the learner's fault not a
+ 
+
+ align:start position:0%
+that's the learner's fault not a
+teacher's fault
+
+ align:start position:0%
+teacher's fault
+ 
+
+ align:start position:0%
+teacher's fault
+and that is just fundamentally wrong
+
+ align:start position:0%
+and that is just fundamentally wrong
+ 
+
+ align:start position:0%
+and that is just fundamentally wrong
+and every parent knows this by the way
+
+ align:start position:0%
+and every parent knows this by the way
+ 
+
+ align:start position:0%
+and every parent knows this by the way
+when we go to the classroom we just
+
+ align:start position:0%
+when we go to the classroom we just
+ 
+
+ align:start position:0%
+when we go to the classroom we just
+ignore that truth
+
+ align:start position:0%
+ignore that truth
+ 
+
+ align:start position:0%
+ignore that truth
+the fact is the learner is forming a
+
+ align:start position:0%
+the fact is the learner is forming a
+ 
+
+ align:start position:0%
+the fact is the learner is forming a
+model of the world
+
+ align:start position:0%
+model of the world
+ 
+
+ align:start position:0%
+model of the world
+it's like a plant growing
+
+ align:start position:0%
+it's like a plant growing
+ 
+
+ align:start position:0%
+it's like a plant growing
+you can give the plant
+
+ align:start position:0%
+you can give the plant
+ 
+
+ align:start position:0%
+you can give the plant
+a lifetime's worth of water on the first
+
+ align:start position:0%
+a lifetime's worth of water on the first
+ 
+
+ align:start position:0%
+a lifetime's worth of water on the first
+day and say you're done
+
+ align:start position:0%
+day and say you're done
+ 
+
+ align:start position:0%
+day and say you're done
+and all the potassium on day two
+
+ align:start position:0%
+and all the potassium on day two
+ 
+
+ align:start position:0%
+and all the potassium on day two
+and all the nitrogen and day three you
+
+ align:start position:0%
+and all the nitrogen and day three you
+ 
+
+ align:start position:0%
+and all the nitrogen and day three you
+can't do that
+
+ align:start position:0%
+can't do that
+ 
+
+ align:start position:0%
+can't do that
+the plant pots water or sunlight or
+
+ align:start position:0%
+the plant pots water or sunlight or
+ 
+
+ align:start position:0%
+the plant pots water or sunlight or
+a particular type of fertilizer when the
+
+ align:start position:0%
+a particular type of fertilizer when the
+ 
+
+ align:start position:0%
+a particular type of fertilizer when the
+plant wants it by the way that's called
+
+ align:start position:0%
+plant wants it by the way that's called
+ 
+
+ align:start position:0%
+plant wants it by the way that's called
+precision agriculture
+
+ align:start position:0%
+precision agriculture
+ 
+
+ align:start position:0%
+precision agriculture
+it's a field right but yet we do that
+
+ align:start position:0%
+it's a field right but yet we do that
+ 
+
+ align:start position:0%
+it's a field right but yet we do that
+human beings
+
+ align:start position:0%
+human beings
+ 
+
+ align:start position:0%
+human beings
+i'm going to teach you all the math you
+
+ align:start position:0%
+i'm going to teach you all the math you
+ 
+
+ align:start position:0%
+i'm going to teach you all the math you
+need in the first
+
+ align:start position:0%
+need in the first
+ 
+
+ align:start position:0%
+need in the first
+four months
+
+ align:start position:0%
+four months
+ 
+
+ align:start position:0%
+four months
+you should be done that's not how it
+
+ align:start position:0%
+you should be done that's not how it
+ 
+
+ align:start position:0%
+you should be done that's not how it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+it's when you use the math that it
+
+ align:start position:0%
+it's when you use the math that it
+ 
+
+ align:start position:0%
+it's when you use the math that it
+becomes valuable
+
+ align:start position:0%
+becomes valuable
+ 
+
+ align:start position:0%
+becomes valuable
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+and every classroom
+
+ align:start position:0%
+and every classroom
+ 
+
+ align:start position:0%
+and every classroom
+violates it every class violence that
+
+ align:start position:0%
+violates it every class violence that
+ 
+
+ align:start position:0%
+violates it every class violence that
+curricula violate that principle
+
+ align:start position:0%
+curricula violate that principle
+ 
+
+ align:start position:0%
+curricula violate that principle
+what marks something as something that
+
+ align:start position:0%
+what marks something as something that
+ 
+
+ align:start position:0%
+what marks something as something that
+needs to be remembered or is valuable
+
+ align:start position:0%
+needs to be remembered or is valuable
+ 
+
+ align:start position:0%
+needs to be remembered or is valuable
+well when you process it
+
+ align:start position:0%
+well when you process it
+ 
+
+ align:start position:0%
+well when you process it
+right so if you have a nice conversation
+
+ align:start position:0%
+right so if you have a nice conversation
+ 
+
+ align:start position:0%
+right so if you have a nice conversation
+with your child or your spouse you
+
+ align:start position:0%
+with your child or your spouse you
+ 
+
+ align:start position:0%
+with your child or your spouse you
+remember that
+
+ align:start position:0%
+remember that
+ 
+
+ align:start position:0%
+remember that
+right but the
+
+ align:start position:0%
+right but the
+ 
+
+ align:start position:0%
+right but the
+conversation you had uh you know sort of
+
+ align:start position:0%
+conversation you had uh you know sort of
+ 
+
+ align:start position:0%
+conversation you had uh you know sort of
+quotidian conversation about uh
+
+ align:start position:0%
+quotidian conversation about uh
+ 
+
+ align:start position:0%
+quotidian conversation about uh
+you know something you know don't forget
+
+ align:start position:0%
+you know something you know don't forget
+ 
+
+ align:start position:0%
+you know something you know don't forget
+to pay the bill or something yeah you'll
+
+ align:start position:0%
+to pay the bill or something yeah you'll
+ 
+
+ align:start position:0%
+to pay the bill or something yeah you'll
+remember that but the conversation
+
+ align:start position:0%
+remember that but the conversation
+ 
+
+ align:start position:0%
+remember that but the conversation
+itself isn't memorable
+
+ align:start position:0%
+itself isn't memorable
+ 
+
+ align:start position:0%
+itself isn't memorable
+so engagement and purpose
+
+ align:start position:0%
+so engagement and purpose
+ 
+
+ align:start position:0%
+so engagement and purpose
+flag learning
+
+ align:start position:0%
+flag learning
+ 
+
+ align:start position:0%
+flag learning
+for the brain as being valuable and they
+
+ align:start position:0%
+for the brain as being valuable and they
+ 
+
+ align:start position:0%
+for the brain as being valuable and they
+put it in a sequence that makes it
+
+ align:start position:0%
+put it in a sequence that makes it
+ 
+
+ align:start position:0%
+put it in a sequence that makes it
+actionable
+
+ align:start position:0%
+actionable
+ 
+
+ align:start position:0%
+actionable
+i've been working with sanjay for many
+
+ align:start position:0%
+i've been working with sanjay for many
+ 
+
+ align:start position:0%
+i've been working with sanjay for many
+years at mit open learning and the
+
+ align:start position:0%
+years at mit open learning and the
+ 
+
+ align:start position:0%
+years at mit open learning and the
+phrase that i hear him utter most is
+
+ align:start position:0%
+phrase that i hear him utter most is
+ 
+
+ align:start position:0%
+phrase that i hear him utter most is
+how does your idea scale
+
+ align:start position:0%
+how does your idea scale
+ 
+
+ align:start position:0%
+how does your idea scale
+i wanted to take this opportunity to ask
+
+ align:start position:0%
+i wanted to take this opportunity to ask
+ 
+
+ align:start position:0%
+i wanted to take this opportunity to ask
+him about his focus on scaling
+
+ align:start position:0%
+him about his focus on scaling
+ 
+
+ align:start position:0%
+him about his focus on scaling
+innovations and learning
+
+ align:start position:0%
+innovations and learning
+ 
+
+ align:start position:0%
+innovations and learning
+there's something about learning that is
+
+ align:start position:0%
+there's something about learning that is
+ 
+
+ align:start position:0%
+there's something about learning that is
+a human evolutionary
+
+ align:start position:0%
+a human evolutionary
+ 
+
+ align:start position:0%
+a human evolutionary
+aspect of our existence which is
+
+ align:start position:0%
+aspect of our existence which is
+ 
+
+ align:start position:0%
+aspect of our existence which is
+children learn parents teach and we keep
+
+ align:start position:0%
+children learn parents teach and we keep
+ 
+
+ align:start position:0%
+children learn parents teach and we keep
+that so as an adult i learn
+
+ align:start position:0%
+that so as an adult i learn
+ 
+
+ align:start position:0%
+that so as an adult i learn
+in similar ways to
+
+ align:start position:0%
+in similar ways to
+ 
+
+ align:start position:0%
+in similar ways to
+how i learned as a baby from my parents
+
+ align:start position:0%
+how i learned as a baby from my parents
+ 
+
+ align:start position:0%
+how i learned as a baby from my parents
+right as a child as a young person
+
+ align:start position:0%
+right as a child as a young person
+ 
+
+ align:start position:0%
+right as a child as a young person
+parenting is not scalable
+
+ align:start position:0%
+parenting is not scalable
+ 
+
+ align:start position:0%
+parenting is not scalable
+there's a reason we have
+
+ align:start position:0%
+there's a reason we have
+ 
+
+ align:start position:0%
+there's a reason we have
+few children but we give them full
+
+ align:start position:0%
+few children but we give them full
+ 
+
+ align:start position:0%
+few children but we give them full
+attention so i think our biggest
+
+ align:start position:0%
+attention so i think our biggest
+ 
+
+ align:start position:0%
+attention so i think our biggest
+challenge is
+
+ align:start position:0%
+challenge is
+ 
+
+ align:start position:0%
+challenge is
+there are lots of people lots of young
+
+ align:start position:0%
+there are lots of people lots of young
+ 
+
+ align:start position:0%
+there are lots of people lots of young
+people lots of adults in the world that
+
+ align:start position:0%
+people lots of adults in the world that
+ 
+
+ align:start position:0%
+people lots of adults in the world that
+need to learn
+
+ align:start position:0%
+need to learn
+ 
+
+ align:start position:0%
+need to learn
+and the challenge is
+
+ align:start position:0%
+and the challenge is
+ 
+
+ align:start position:0%
+and the challenge is
+can we scale what is
+
+ align:start position:0%
+can we scale what is
+ 
+
+ align:start position:0%
+can we scale what is
+very hard to scale it's sort of the most
+
+ align:start position:0%
+very hard to scale it's sort of the most
+ 
+
+ align:start position:0%
+very hard to scale it's sort of the most
+important question
+
+ align:start position:0%
+important question
+ 
+
+ align:start position:0%
+important question
+and we can only do it if we understand
+
+ align:start position:0%
+and we can only do it if we understand
+ 
+
+ align:start position:0%
+and we can only do it if we understand
+how people learn
+
+ align:start position:0%
+how people learn
+ 
+
+ align:start position:0%
+how people learn
+and understand how technology could help
+
+ align:start position:0%
+and understand how technology could help
+ 
+
+ align:start position:0%
+and understand how technology could help
+and how humans could help and how
+
+ align:start position:0%
+and how humans could help and how
+ 
+
+ align:start position:0%
+and how humans could help and how
+coaching could help
+
+ align:start position:0%
+coaching could help
+ 
+
+ align:start position:0%
+coaching could help
+but the scale of demand is so vast if we
+
+ align:start position:0%
+but the scale of demand is so vast if we
+ 
+
+ align:start position:0%
+but the scale of demand is so vast if we
+want to make an impact we got to figure
+
+ align:start position:0%
+want to make an impact we got to figure
+ 
+
+ align:start position:0%
+want to make an impact we got to figure
+out how do we scale this thing that is
+
+ align:start position:0%
+out how do we scale this thing that is
+ 
+
+ align:start position:0%
+out how do we scale this thing that is
+so difficult to scale so to me that's
+
+ align:start position:0%
+so difficult to scale so to me that's
+ 
+
+ align:start position:0%
+so difficult to scale so to me that's
+the existential question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the interesting things about
+
+ align:start position:0%
+one of the interesting things about
+ 
+
+ align:start position:0%
+one of the interesting things about
+sanjay is that he's helping solve this
+
+ align:start position:0%
+sanjay is that he's helping solve this
+ 
+
+ align:start position:0%
+sanjay is that he's helping solve this
+question of scalability through online
+
+ align:start position:0%
+question of scalability through online
+ 
+
+ align:start position:0%
+question of scalability through online
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+as sanji will explain in a moment
+
+ align:start position:0%
+as sanji will explain in a moment
+ 
+
+ align:start position:0%
+as sanji will explain in a moment
+online learning cuts out many of the
+
+ align:start position:0%
+online learning cuts out many of the
+ 
+
+ align:start position:0%
+online learning cuts out many of the
+characteristics of traditional classroom
+
+ align:start position:0%
+characteristics of traditional classroom
+ 
+
+ align:start position:0%
+characteristics of traditional classroom
+models such as one-way lectures and an
+
+ align:start position:0%
+models such as one-way lectures and an
+ 
+
+ align:start position:0%
+models such as one-way lectures and an
+emphasis on memorization
+
+ align:start position:0%
+emphasis on memorization
+ 
+
+ align:start position:0%
+emphasis on memorization
+so imagine you're in the desert and
+
+ align:start position:0%
+so imagine you're in the desert and
+ 
+
+ align:start position:0%
+so imagine you're in the desert and
+you're thirsty
+
+ align:start position:0%
+you're thirsty
+ 
+
+ align:start position:0%
+you're thirsty
+if i give you a glass of water which is
+
+ align:start position:0%
+if i give you a glass of water which is
+ 
+
+ align:start position:0%
+if i give you a glass of water which is
+only half full
+
+ align:start position:0%
+only half full
+ 
+
+ align:start position:0%
+only half full
+you're not gonna say oh my god it's half
+
+ align:start position:0%
+you're not gonna say oh my god it's half
+ 
+
+ align:start position:0%
+you're not gonna say oh my god it's half
+empty you're gonna say it's half full
+
+ align:start position:0%
+empty you're gonna say it's half full
+ 
+
+ align:start position:0%
+empty you're gonna say it's half full
+so for those who don't have access to
+
+ align:start position:0%
+so for those who don't have access to
+ 
+
+ align:start position:0%
+so for those who don't have access to
+learning online education
+
+ align:start position:0%
+learning online education
+ 
+
+ align:start position:0%
+learning online education
+is a glass half full
+
+ align:start position:0%
+is a glass half full
+ 
+
+ align:start position:0%
+is a glass half full
+but it's still water
+
+ align:start position:0%
+but it's still water
+ 
+
+ align:start position:0%
+but it's still water
+for those who can have residential
+
+ align:start position:0%
+for those who can have residential
+ 
+
+ align:start position:0%
+for those who can have residential
+education online learning is quite
+
+ align:start position:0%
+education online learning is quite
+ 
+
+ align:start position:0%
+education online learning is quite
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+it displaces lecture time and creates a
+
+ align:start position:0%
+it displaces lecture time and creates a
+ 
+
+ align:start position:0%
+it displaces lecture time and creates a
+room for doing all the hands-on stuff
+
+ align:start position:0%
+room for doing all the hands-on stuff
+ 
+
+ align:start position:0%
+room for doing all the hands-on stuff
+that makes education
+
+ align:start position:0%
+that makes education
+ 
+
+ align:start position:0%
+that makes education
+doubly wonderful
+
+ align:start position:0%
+doubly wonderful
+ 
+
+ align:start position:0%
+doubly wonderful
+the curiosity the coaching the field
+
+ align:start position:0%
+the curiosity the coaching the field
+ 
+
+ align:start position:0%
+the curiosity the coaching the field
+trips and discussions the disputation
+
+ align:start position:0%
+trips and discussions the disputation
+ 
+
+ align:start position:0%
+trips and discussions the disputation
+the fun the joy of learning the what i
+
+ align:start position:0%
+the fun the joy of learning the what i
+ 
+
+ align:start position:0%
+the fun the joy of learning the what i
+call the magic of mit
+
+ align:start position:0%
+call the magic of mit
+ 
+
+ align:start position:0%
+call the magic of mit
+and online learning gets rid of the
+
+ align:start position:0%
+and online learning gets rid of the
+ 
+
+ align:start position:0%
+and online learning gets rid of the
+thing we waste a lot of time on which is
+
+ align:start position:0%
+thing we waste a lot of time on which is
+ 
+
+ align:start position:0%
+thing we waste a lot of time on which is
+one-way lectures
+
+ align:start position:0%
+one-way lectures
+ 
+
+ align:start position:0%
+one-way lectures
+so to me online learning has two very
+
+ align:start position:0%
+so to me online learning has two very
+ 
+
+ align:start position:0%
+so to me online learning has two very
+different purposes it's a glass
+
+ align:start position:0%
+different purposes it's a glass
+ 
+
+ align:start position:0%
+different purposes it's a glass
+half-full
+
+ align:start position:0%
+half-full
+ 
+
+ align:start position:0%
+half-full
+for those who are
+
+ align:start position:0%
+for those who are
+ 
+
+ align:start position:0%
+for those who are
+parched
+
+ align:start position:0%
+parched
+ 
+
+ align:start position:0%
+parched
+for water it's still great water
+
+ align:start position:0%
+for water it's still great water
+ 
+
+ align:start position:0%
+for water it's still great water
+so online learning it is
+
+ align:start position:0%
+so online learning it is
+ 
+
+ align:start position:0%
+so online learning it is
+something that makes in-person education
+
+ align:start position:0%
+something that makes in-person education
+ 
+
+ align:start position:0%
+something that makes in-person education
+much richer as well
+
+ align:start position:0%
+much richer as well
+ 
+
+ align:start position:0%
+much richer as well
+by leaving time to do the hands-on stuff
+
+ align:start position:0%
+by leaving time to do the hands-on stuff
+ 
+
+ align:start position:0%
+by leaving time to do the hands-on stuff
+that today is occupied by lectures so
+
+ align:start position:0%
+that today is occupied by lectures so
+ 
+
+ align:start position:0%
+that today is occupied by lectures so
+that's the flipped classroom
+
+ align:start position:0%
+that's the flipped classroom
+ 
+
+ align:start position:0%
+that's the flipped classroom
+something sanjay has helped develop at
+
+ align:start position:0%
+something sanjay has helped develop at
+ 
+
+ align:start position:0%
+something sanjay has helped develop at
+mit is the micro masters program
+
+ align:start position:0%
+mit is the micro masters program
+ 
+
+ align:start position:0%
+mit is the micro masters program
+which makes it possible for people from
+
+ align:start position:0%
+which makes it possible for people from
+ 
+
+ align:start position:0%
+which makes it possible for people from
+all over the world to earn professional
+
+ align:start position:0%
+all over the world to earn professional
+ 
+
+ align:start position:0%
+all over the world to earn professional
+and academic credentials for mit courses
+
+ align:start position:0%
+and academic credentials for mit courses
+ 
+
+ align:start position:0%
+and academic credentials for mit courses
+they take online
+
+ align:start position:0%
+they take online
+ 
+
+ align:start position:0%
+they take online
+credentials that can be applied toward
+
+ align:start position:0%
+credentials that can be applied toward
+ 
+
+ align:start position:0%
+credentials that can be applied toward
+degrees at mit and other institutions of
+
+ align:start position:0%
+degrees at mit and other institutions of
+ 
+
+ align:start position:0%
+degrees at mit and other institutions of
+higher learning
+
+ align:start position:0%
+higher learning
+ 
+
+ align:start position:0%
+higher learning
+the micromasters gets rid of the
+
+ align:start position:0%
+the micromasters gets rid of the
+ 
+
+ align:start position:0%
+the micromasters gets rid of the
+winnowing function
+
+ align:start position:0%
+winnowing function
+ 
+
+ align:start position:0%
+winnowing function
+so let me explain so how does a master's
+
+ align:start position:0%
+so let me explain so how does a master's
+ 
+
+ align:start position:0%
+so let me explain so how does a master's
+program work
+
+ align:start position:0%
+program work
+ 
+
+ align:start position:0%
+program work
+you admit someone based on
+
+ align:start position:0%
+you admit someone based on
+ 
+
+ align:start position:0%
+you admit someone based on
+letters or recommendations and scores
+
+ align:start position:0%
+letters or recommendations and scores
+ 
+
+ align:start position:0%
+letters or recommendations and scores
+letters from people you probably have
+
+ align:start position:0%
+letters from people you probably have
+ 
+
+ align:start position:0%
+letters from people you probably have
+never met schools from universities you
+
+ align:start position:0%
+never met schools from universities you
+ 
+
+ align:start position:0%
+never met schools from universities you
+haven't visited or you don't know
+
+ align:start position:0%
+haven't visited or you don't know
+ 
+
+ align:start position:0%
+haven't visited or you don't know
+admissions it's a venuing function it's
+
+ align:start position:0%
+admissions it's a venuing function it's
+ 
+
+ align:start position:0%
+admissions it's a venuing function it's
+based on such sparse information
+
+ align:start position:0%
+based on such sparse information
+ 
+
+ align:start position:0%
+based on such sparse information
+what we do with the micromasters is
+
+ align:start position:0%
+what we do with the micromasters is
+ 
+
+ align:start position:0%
+what we do with the micromasters is
+there is no admissions
+
+ align:start position:0%
+there is no admissions
+ 
+
+ align:start position:0%
+there is no admissions
+all comers are welcome it's online the
+
+ align:start position:0%
+all comers are welcome it's online the
+ 
+
+ align:start position:0%
+all comers are welcome it's online the
+incremental cost of adding a student is
+
+ align:start position:0%
+incremental cost of adding a student is
+ 
+
+ align:start position:0%
+incremental cost of adding a student is
+very low come on in take the courses
+
+ align:start position:0%
+very low come on in take the courses
+ 
+
+ align:start position:0%
+very low come on in take the courses
+finish up
+
+ align:start position:0%
+finish up
+ 
+
+ align:start position:0%
+finish up
+take the proctored exam it's not easy
+
+ align:start position:0%
+take the proctored exam it's not easy
+ 
+
+ align:start position:0%
+take the proctored exam it's not easy
+it's difficult
+
+ align:start position:0%
+it's difficult
+ 
+
+ align:start position:0%
+it's difficult
+when you finish you have a micromasters
+
+ align:start position:0%
+when you finish you have a micromasters
+ 
+
+ align:start position:0%
+when you finish you have a micromasters
+and by the way
+
+ align:start position:0%
+and by the way
+ 
+
+ align:start position:0%
+and by the way
+if you did really well
+
+ align:start position:0%
+if you did really well
+ 
+
+ align:start position:0%
+if you did really well
+when you get into school we'll give you
+
+ align:start position:0%
+when you get into school we'll give you
+ 
+
+ align:start position:0%
+when you get into school we'll give you
+credit for it so we reverse the funnel
+
+ align:start position:0%
+credit for it so we reverse the funnel
+ 
+
+ align:start position:0%
+credit for it so we reverse the funnel
+so that's what the micro master says
+
+ align:start position:0%
+so that's what the micro master says
+ 
+
+ align:start position:0%
+so that's what the micro master says
+sanji has been on this path of making
+
+ align:start position:0%
+sanji has been on this path of making
+ 
+
+ align:start position:0%
+sanji has been on this path of making
+educational materials more accessible on
+
+ align:start position:0%
+educational materials more accessible on
+ 
+
+ align:start position:0%
+educational materials more accessible on
+a large scale for over 20 years
+
+ align:start position:0%
+a large scale for over 20 years
+ 
+
+ align:start position:0%
+a large scale for over 20 years
+so i asked him what advice he has for
+
+ align:start position:0%
+so i asked him what advice he has for
+ 
+
+ align:start position:0%
+so i asked him what advice he has for
+other educators about how to engage with
+
+ align:start position:0%
+other educators about how to engage with
+ 
+
+ align:start position:0%
+other educators about how to engage with
+grasp and how to get involved with
+
+ align:start position:0%
+grasp and how to get involved with
+ 
+
+ align:start position:0%
+grasp and how to get involved with
+scaling education
+
+ align:start position:0%
+scaling education
+ 
+
+ align:start position:0%
+scaling education
+what i suggest educators do is
+
+ align:start position:0%
+what i suggest educators do is
+ 
+
+ align:start position:0%
+what i suggest educators do is
+first of all write down a wish list
+
+ align:start position:0%
+first of all write down a wish list
+ 
+
+ align:start position:0%
+first of all write down a wish list
+of what
+
+ align:start position:0%
+of what
+ 
+
+ align:start position:0%
+of what
+they would like to do what they would
+
+ align:start position:0%
+they would like to do what they would
+ 
+
+ align:start position:0%
+they would like to do what they would
+like to see in the education system how
+
+ align:start position:0%
+like to see in the education system how
+ 
+
+ align:start position:0%
+like to see in the education system how
+they do it differently and how it maps
+
+ align:start position:0%
+they do it differently and how it maps
+ 
+
+ align:start position:0%
+they do it differently and how it maps
+to how they taught their own kids or how
+
+ align:start position:0%
+to how they taught their own kids or how
+ 
+
+ align:start position:0%
+to how they taught their own kids or how
+they learned and how a good teacher
+
+ align:start position:0%
+they learned and how a good teacher
+ 
+
+ align:start position:0%
+they learned and how a good teacher
+inspired them
+
+ align:start position:0%
+inspired them
+ 
+
+ align:start position:0%
+inspired them
+you know i was involved a little bit in
+
+ align:start position:0%
+you know i was involved a little bit in
+ 
+
+ align:start position:0%
+you know i was involved a little bit in
+the creation of open courseware 20 years
+
+ align:start position:0%
+the creation of open courseware 20 years
+ 
+
+ align:start position:0%
+the creation of open courseware 20 years
+ago and when i was doing my dynamics
+
+ align:start position:0%
+ago and when i was doing my dynamics
+ 
+
+ align:start position:0%
+ago and when i was doing my dynamics
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+a colleague said hey can i make
+
+ align:start position:0%
+a colleague said hey can i make
+ 
+
+ align:start position:0%
+a colleague said hey can i make
+recordings because i'm picking up your
+
+ align:start position:0%
+recordings because i'm picking up your
+ 
+
+ align:start position:0%
+recordings because i'm picking up your
+course i want to see how you know the
+
+ align:start position:0%
+course i want to see how you know the
+ 
+
+ align:start position:0%
+course i want to see how you know the
+approach you take to teach it
+
+ align:start position:0%
+approach you take to teach it
+ 
+
+ align:start position:0%
+approach you take to teach it
+and so when i made the recordings i
+
+ align:start position:0%
+and so when i made the recordings i
+ 
+
+ align:start position:0%
+and so when i made the recordings i
+called up open courseway and i said look
+
+ align:start position:0%
+called up open courseway and i said look
+ 
+
+ align:start position:0%
+called up open courseway and i said look
+if it's useful to you i'd like to put
+
+ align:start position:0%
+if it's useful to you i'd like to put
+ 
+
+ align:start position:0%
+if it's useful to you i'd like to put
+them up for what it's worth you know
+
+ align:start position:0%
+them up for what it's worth you know
+ 
+
+ align:start position:0%
+them up for what it's worth you know
+because i teach dynamics differently
+
+ align:start position:0%
+because i teach dynamics differently
+ 
+
+ align:start position:0%
+because i teach dynamics differently
+and one thing led to another and just
+
+ align:start position:0%
+and one thing led to another and just
+ 
+
+ align:start position:0%
+and one thing led to another and just
+went up there and i actually think that
+
+ align:start position:0%
+went up there and i actually think that
+ 
+
+ align:start position:0%
+went up there and i actually think that
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+unself-consciously just share
+
+ align:start position:0%
+unself-consciously just share
+ 
+
+ align:start position:0%
+unself-consciously just share
+yourself is something there's something
+
+ align:start position:0%
+yourself is something there's something
+ 
+
+ align:start position:0%
+yourself is something there's something
+liberating about it frankly
+
+ align:start position:0%
+liberating about it frankly
+ 
+
+ align:start position:0%
+liberating about it frankly
+and i recommend that others try just
+
+ align:start position:0%
+and i recommend that others try just
+ 
+
+ align:start position:0%
+and i recommend that others try just
+make a youtube video of yourself doing
+
+ align:start position:0%
+make a youtube video of yourself doing
+ 
+
+ align:start position:0%
+make a youtube video of yourself doing
+something you love put it up
+
+ align:start position:0%
+something you love put it up
+ 
+
+ align:start position:0%
+something you love put it up
+and i'm sure it'll be of value to others
+
+ align:start position:0%
+and i'm sure it'll be of value to others
+ 
+
+ align:start position:0%
+and i'm sure it'll be of value to others
+making ourselves vulnerable can lead to
+
+ align:start position:0%
+making ourselves vulnerable can lead to
+ 
+
+ align:start position:0%
+making ourselves vulnerable can lead to
+something of great value for others
+
+ align:start position:0%
+something of great value for others
+ 
+
+ align:start position:0%
+something of great value for others
+it's something we see every day here at
+
+ align:start position:0%
+it's something we see every day here at
+ 
+
+ align:start position:0%
+it's something we see every day here at
+mit open courseware
+
+ align:start position:0%
+mit open courseware
+ 
+
+ align:start position:0%
+mit open courseware
+so we'd like to say a huge thank you to
+
+ align:start position:0%
+so we'd like to say a huge thank you to
+ 
+
+ align:start position:0%
+so we'd like to say a huge thank you to
+sanjay sarma and all of the mit faculty
+
+ align:start position:0%
+sanjay sarma and all of the mit faculty
+ 
+
+ align:start position:0%
+sanjay sarma and all of the mit faculty
+who not only share their teaching
+
+ align:start position:0%
+who not only share their teaching
+ 
+
+ align:start position:0%
+who not only share their teaching
+materials but also share how they teach
+
+ align:start position:0%
+materials but also share how they teach
+ 
+
+ align:start position:0%
+materials but also share how they teach
+through interviews on our website and
+
+ align:start position:0%
+through interviews on our website and
+ 
+
+ align:start position:0%
+through interviews on our website and
+through podcast episodes like this one
+
+ align:start position:0%
+through podcast episodes like this one
+ 
+
+ align:start position:0%
+through podcast episodes like this one
+you can find sanjay sarma's teaching
+
+ align:start position:0%
+you can find sanjay sarma's teaching
+ 
+
+ align:start position:0%
+you can find sanjay sarma's teaching
+materials on our mit open courseware
+
+ align:start position:0%
+materials on our mit open courseware
+ 
+
+ align:start position:0%
+materials on our mit open courseware
+website
+
+ align:start position:0%
+website
+ 
+
+ align:start position:0%
+website
+you can also pick up a copy of grasp at
+
+ align:start position:0%
+you can also pick up a copy of grasp at
+ 
+
+ align:start position:0%
+you can also pick up a copy of grasp at
+your local library or bookshop
+
+ align:start position:0%
+your local library or bookshop
+ 
+
+ align:start position:0%
+your local library or bookshop
+some other books he suggests educators
+
+ align:start position:0%
+some other books he suggests educators
+ 
+
+ align:start position:0%
+some other books he suggests educators
+pair with grasp our make it stick and
+
+ align:start position:0%
+pair with grasp our make it stick and
+ 
+
+ align:start position:0%
+pair with grasp our make it stick and
+peak the science of expertise
+
+ align:start position:0%
+peak the science of expertise
+ 
+
+ align:start position:0%
+peak the science of expertise
+and be sure to check out sanjay's latest
+
+ align:start position:0%
+and be sure to check out sanjay's latest
+ 
+
+ align:start position:0%
+and be sure to check out sanjay's latest
+book workforce education a new roadmap
+
+ align:start position:0%
+book workforce education a new roadmap
+ 
+
+ align:start position:0%
+book workforce education a new roadmap
+from mit press
+
+ align:start position:0%
+from mit press
+ 
+
+ align:start position:0%
+from mit press
+thank you so much for listening until
+
+ align:start position:0%
+thank you so much for listening until
+ 
+
+ align:start position:0%
+thank you so much for listening until
+next time signing off from cambridge
+
+ align:start position:0%
+next time signing off from cambridge
+ 
+
+ align:start position:0%
+next time signing off from cambridge
+massachusetts i'm your host sarah hansen
+
+ align:start position:0%
+massachusetts i'm your host sarah hansen
+ 
+
+ align:start position:0%
+massachusetts i'm your host sarah hansen
+from mit open courseware
+
+ align:start position:0%
+from mit open courseware
+ 
+
+ align:start position:0%
+from mit open courseware
+chalk radio's producers include myself
+
+ align:start position:0%
+chalk radio's producers include myself
+ 
+
+ align:start position:0%
+chalk radio's producers include myself
+brett pachi and dave lashansky
+
+ align:start position:0%
+brett pachi and dave lashansky
+ 
+
+ align:start position:0%
+brett pachi and dave lashansky
+scriptwriting assistants from nidhi
+
+ align:start position:0%
+scriptwriting assistants from nidhi
+ 
+
+ align:start position:0%
+scriptwriting assistants from nidhi
+shastri show notes for this episode were
+
+ align:start position:0%
+shastri show notes for this episode were
+ 
+
+ align:start position:0%
+shastri show notes for this episode were
+written by peter chipman
+
+ align:start position:0%
+written by peter chipman
+ 
+
+ align:start position:0%
+written by peter chipman
+we're funded by mit open learning and
+
+ align:start position:0%
+we're funded by mit open learning and
+ 
+
+ align:start position:0%
+we're funded by mit open learning and
+supporters like you
\ No newline at end of file
diff --git a/cHgbCAHQgbU.txt b/cHgbCAHQgbU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..262358fb70505bb28f6f5b770796f4f83bc55eb1
--- /dev/null
+++ b/cHgbCAHQgbU.txt
@@ -0,0 +1,363 @@
+align:start position:0%
+ 
+we have a whole series of things that we
+
+ align:start position:0%
+we have a whole series of things that we
+ 
+
+ align:start position:0%
+we have a whole series of things that we
+drill down and look at the example that
+
+ align:start position:0%
+drill down and look at the example that
+ 
+
+ align:start position:0%
+drill down and look at the example that
+you're going to see is one that worked
+
+ align:start position:0%
+you're going to see is one that worked
+ 
+
+ align:start position:0%
+you're going to see is one that worked
+well for us but yours might be different
+
+ align:start position:0%
+well for us but yours might be different
+ 
+
+ align:start position:0%
+well for us but yours might be different
+but these types of things are what
+
+ align:start position:0%
+but these types of things are what
+ 
+
+ align:start position:0%
+but these types of things are what
+you're going to see so but we as we laid
+
+ align:start position:0%
+you're going to see so but we as we laid
+ 
+
+ align:start position:0%
+you're going to see so but we as we laid
+it out we had entertainment we had uh we
+
+ align:start position:0%
+it out we had entertainment we had uh we
+ 
+
+ align:start position:0%
+it out we had entertainment we had uh we
+had the industrial designer industrial
+
+ align:start position:0%
+had the industrial designer industrial
+ 
+
+ align:start position:0%
+had the industrial designer industrial
+designer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+design I apologize for the uh hardto
+
+ align:start position:0%
+design I apologize for the uh hardto
+ 
+
+ align:start position:0%
+design I apologize for the uh hardto
+read uh writing here and so you can see
+
+ align:start position:0%
+read uh writing here and so you can see
+ 
+
+ align:start position:0%
+read uh writing here and so you can see
+um what they were doing as well
+
+ align:start position:0%
+um what they were doing as well
+ 
+
+ align:start position:0%
+um what they were doing as well
+industrial design you would have medical
+
+ align:start position:0%
+industrial design you would have medical
+ 
+
+ align:start position:0%
+industrial design you would have medical
+visualization um companies like GE had
+
+ align:start position:0%
+visualization um companies like GE had
+ 
+
+ align:start position:0%
+visualization um companies like GE had
+3D data sets that they were getting
+
+ align:start position:0%
+3D data sets that they were getting
+ 
+
+ align:start position:0%
+3D data sets that they were getting
+through CAT scans MRI or and they wanted
+
+ align:start position:0%
+through CAT scans MRI or and they wanted
+ 
+
+ align:start position:0%
+through CAT scans MRI or and they wanted
+to look at them interact with those data
+
+ align:start position:0%
+to look at them interact with those data
+ 
+
+ align:start position:0%
+to look at them interact with those data
+sets we had surgical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulation we also had um Computing for
+
+ align:start position:0%
+simulation we also had um Computing for
+ 
+
+ align:start position:0%
+simulation we also had um Computing for
+the blind human computer interface for
+
+ align:start position:0%
+the blind human computer interface for
+ 
+
+ align:start position:0%
+the blind human computer interface for
+nonvisual nonvisual
+
+ align:start position:0%
+nonvisual nonvisual
+ 
+
+ align:start position:0%
+nonvisual nonvisual
+comp human computer interface and for
+
+ align:start position:0%
+comp human computer interface and for
+ 
+
+ align:start position:0%
+comp human computer interface and for
+each one of these we had molecular
+
+ align:start position:0%
+each one of these we had molecular
+ 
+
+ align:start position:0%
+each one of these we had molecular
+modeling and you go we and uh assembly
+
+ align:start position:0%
+modeling and you go we and uh assembly
+ 
+
+ align:start position:0%
+modeling and you go we and uh assembly
+path planning and we even had Geo uh
+
+ align:start position:0%
+path planning and we even had Geo uh
+ 
+
+ align:start position:0%
+path planning and we even had Geo uh
+seismic analyzing seismic data all of
+
+ align:start position:0%
+seismic analyzing seismic data all of
+ 
+
+ align:start position:0%
+seismic analyzing seismic data all of
+these different ones we laid out and
+
+ align:start position:0%
+these different ones we laid out and
+ 
+
+ align:start position:0%
+these different ones we laid out and
+then we Dug Dug down in here for a
+
+ align:start position:0%
+then we Dug Dug down in here for a
+ 
+
+ align:start position:0%
+then we Dug Dug down in here for a
+matter of a week or two to understand
+
+ align:start position:0%
+matter of a week or two to understand
+ 
+
+ align:start position:0%
+matter of a week or two to understand
+what each of them were and then at that
+
+ align:start position:0%
+what each of them were and then at that
+ 
+
+ align:start position:0%
+what each of them were and then at that
+point we had a nice Market segmentation
+
+ align:start position:0%
+point we had a nice Market segmentation
+ 
+
+ align:start position:0%
+point we had a nice Market segmentation
+that we could then take a step back and
+
+ align:start position:0%
+that we could then take a step back and
+ 
+
+ align:start position:0%
+that we could then take a step back and
+take a look at and say wow those are the
+
+ align:start position:0%
+take a look at and say wow those are the
+ 
+
+ align:start position:0%
+take a look at and say wow those are the
+top opportunities which one should we go
+
+ align:start position:0%
+top opportunities which one should we go
+ 
+
+ align:start position:0%
+top opportunities which one should we go
+after this takes a lot of work I mean
+
+ align:start position:0%
+after this takes a lot of work I mean
+ 
+
+ align:start position:0%
+after this takes a lot of work I mean
+this but the work that we're going to
+
+ align:start position:0%
+this but the work that we're going to
+ 
+
+ align:start position:0%
+this but the work that we're going to
+put in up front is going to pay
+
+ align:start position:0%
+put in up front is going to pay
+ 
+
+ align:start position:0%
+put in up front is going to pay
+dividends because our team will now have
+
+ align:start position:0%
+dividends because our team will now have
+ 
+
+ align:start position:0%
+dividends because our team will now have
+had a chance to look at all the
+
+ align:start position:0%
+had a chance to look at all the
+ 
+
+ align:start position:0%
+had a chance to look at all the
+different opportunities and when we
+
+ align:start position:0%
+different opportunities and when we
+ 
+
+ align:start position:0%
+different opportunities and when we
+choose one we're going to have the
+
+ align:start position:0%
+choose one we're going to have the
+ 
+
+ align:start position:0%
+choose one we're going to have the
+highest level of confidence possible so
+
+ align:start position:0%
+highest level of confidence possible so
+ 
+
+ align:start position:0%
+highest level of confidence possible so
+that is Market segmentation with a very
+
+ align:start position:0%
+that is Market segmentation with a very
+ 
+
+ align:start position:0%
+that is Market segmentation with a very
+specific real example at sensible
+
+ align:start position:0%
+specific real example at sensible
+ 
+
+ align:start position:0%
+specific real example at sensible
+Technologies which ended up working out
+
+ align:start position:0%
+Technologies which ended up working out
+ 
+
+ align:start position:0%
+Technologies which ended up working out
+quite well for us
\ No newline at end of file
diff --git a/cLfyjIlu9Uw.txt b/cLfyjIlu9Uw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c2e4ff3f55696eaa9b507172a2c0df4f44e05fd4
--- /dev/null
+++ b/cLfyjIlu9Uw.txt
@@ -0,0 +1,627 @@
+align:start position:0%
+ 
+we can't think of a more interesting and
+
+ align:start position:0%
+we can't think of a more interesting and
+ 
+
+ align:start position:0%
+we can't think of a more interesting and
+exciting time to launch this course yes
+
+ align:start position:0%
+exciting time to launch this course yes
+ 
+
+ align:start position:0%
+exciting time to launch this course yes
+there are challenges that you and your
+
+ align:start position:0%
+there are challenges that you and your
+ 
+
+ align:start position:0%
+there are challenges that you and your
+peers will face because my baby boom
+
+ align:start position:0%
+peers will face because my baby boom
+ 
+
+ align:start position:0%
+peers will face because my baby boom
+generation didn't do a great job of
+
+ align:start position:0%
+generation didn't do a great job of
+ 
+
+ align:start position:0%
+generation didn't do a great job of
+keeping our policies and practices up to
+
+ align:start position:0%
+keeping our policies and practices up to
+ 
+
+ align:start position:0%
+keeping our policies and practices up to
+date with the changing economy and the
+
+ align:start position:0%
+date with the changing economy and the
+ 
+
+ align:start position:0%
+date with the changing economy and the
+changing Workforce but at the same time
+
+ align:start position:0%
+changing Workforce but at the same time
+ 
+
+ align:start position:0%
+changing Workforce but at the same time
+we're we're in an extremely interesting
+
+ align:start position:0%
+we're we're in an extremely interesting
+ 
+
+ align:start position:0%
+we're we're in an extremely interesting
+era of innovation around the world we're
+
+ align:start position:0%
+era of innovation around the world we're
+ 
+
+ align:start position:0%
+era of innovation around the world we're
+seeing new organizations getting formed
+
+ align:start position:0%
+seeing new organizations getting formed
+ 
+
+ align:start position:0%
+seeing new organizations getting formed
+using crowdsourcing and other modern
+
+ align:start position:0%
+using crowdsourcing and other modern
+ 
+
+ align:start position:0%
+using crowdsourcing and other modern
+techniques organizations we couldn't
+
+ align:start position:0%
+techniques organizations we couldn't
+ 
+
+ align:start position:0%
+techniques organizations we couldn't
+even have imagined several years ago
+
+ align:start position:0%
+even have imagined several years ago
+ 
+
+ align:start position:0%
+even have imagined several years ago
+there are new worker advocacy
+
+ align:start position:0%
+there are new worker advocacy
+ 
+
+ align:start position:0%
+there are new worker advocacy
+organizations coming along that will
+
+ align:start position:0%
+organizations coming along that will
+ 
+
+ align:start position:0%
+organizations coming along that will
+help Empower you to find your way in the
+
+ align:start position:0%
+help Empower you to find your way in the
+ 
+
+ align:start position:0%
+help Empower you to find your way in the
+labor market there are new apps that
+
+ align:start position:0%
+labor market there are new apps that
+ 
+
+ align:start position:0%
+labor market there are new apps that
+allow you to navigate this labor market
+
+ align:start position:0%
+allow you to navigate this labor market
+ 
+
+ align:start position:0%
+allow you to navigate this labor market
+and to figure out where the good jobs
+
+ align:start position:0%
+and to figure out where the good jobs
+ 
+
+ align:start position:0%
+and to figure out where the good jobs
+are and distinguish between good and bad
+
+ align:start position:0%
+are and distinguish between good and bad
+ 
+
+ align:start position:0%
+are and distinguish between good and bad
+employers and then there are courses
+
+ align:start position:0%
+employers and then there are courses
+ 
+
+ align:start position:0%
+employers and then there are courses
+like this exploding all around our
+
+ align:start position:0%
+like this exploding all around our
+ 
+
+ align:start position:0%
+like this exploding all around our
+universities here in the United States
+
+ align:start position:0%
+universities here in the United States
+ 
+
+ align:start position:0%
+universities here in the United States
+and in other countries We rise and fall
+
+ align:start position:0%
+and in other countries We rise and fall
+ 
+
+ align:start position:0%
+and in other countries We rise and fall
+on the strength of our middle class
+
+ align:start position:0%
+on the strength of our middle class
+ 
+
+ align:start position:0%
+on the strength of our middle class
+these online courses allow you to gain
+
+ align:start position:0%
+these online courses allow you to gain
+ 
+
+ align:start position:0%
+these online courses allow you to gain
+access to some of the world's leading
+
+ align:start position:0%
+access to some of the world's leading
+ 
+
+ align:start position:0%
+access to some of the world's leading
+experts in your particular field the
+
+ align:start position:0%
+experts in your particular field the
+ 
+
+ align:start position:0%
+experts in your particular field the
+role of the corporation in the US has
+
+ align:start position:0%
+role of the corporation in the US has
+ 
+
+ align:start position:0%
+role of the corporation in the US has
+changed quite a bit so it's time to
+
+ align:start position:0%
+changed quite a bit so it's time to
+ 
+
+ align:start position:0%
+changed quite a bit so it's time to
+really bring all of this together and
+
+ align:start position:0%
+really bring all of this together and
+ 
+
+ align:start position:0%
+really bring all of this together and
+see if we can't help really shape the
+
+ align:start position:0%
+see if we can't help really shape the
+ 
+
+ align:start position:0%
+see if we can't help really shape the
+future of work we're going to introduce
+
+ align:start position:0%
+future of work we're going to introduce
+ 
+
+ align:start position:0%
+future of work we're going to introduce
+rce you to lots of companies that are
+
+ align:start position:0%
+rce you to lots of companies that are
+ 
+
+ align:start position:0%
+rce you to lots of companies that are
+breaking new ground in every industry we
+
+ align:start position:0%
+breaking new ground in every industry we
+ 
+
+ align:start position:0%
+breaking new ground in every industry we
+can find great companies that are doing
+
+ align:start position:0%
+can find great companies that are doing
+ 
+
+ align:start position:0%
+can find great companies that are doing
+well financially serving their customers
+
+ align:start position:0%
+well financially serving their customers
+ 
+
+ align:start position:0%
+well financially serving their customers
+well focused on a mission that is really
+
+ align:start position:0%
+well focused on a mission that is really
+ 
+
+ align:start position:0%
+well focused on a mission that is really
+important for society and providing good
+
+ align:start position:0%
+important for society and providing good
+ 
+
+ align:start position:0%
+important for society and providing good
+jobs one of the things we want to do is
+
+ align:start position:0%
+jobs one of the things we want to do is
+ 
+
+ align:start position:0%
+jobs one of the things we want to do is
+to highlight those and to learn more
+
+ align:start position:0%
+to highlight those and to learn more
+ 
+
+ align:start position:0%
+to highlight those and to learn more
+about your own experiences with
+
+ align:start position:0%
+about your own experiences with
+ 
+
+ align:start position:0%
+about your own experiences with
+companies and organizations like this
+
+ align:start position:0%
+companies and organizations like this
+ 
+
+ align:start position:0%
+companies and organizations like this
+and so as we go along we're going to
+
+ align:start position:0%
+and so as we go along we're going to
+ 
+
+ align:start position:0%
+and so as we go along we're going to
+learn from your experiences and you're
+
+ align:start position:0%
+learn from your experiences and you're
+ 
+
+ align:start position:0%
+learn from your experiences and you're
+going to meet a whole set of peers who
+
+ align:start position:0%
+going to meet a whole set of peers who
+ 
+
+ align:start position:0%
+going to meet a whole set of peers who
+have good jobs and maybe not such good
+
+ align:start position:0%
+have good jobs and maybe not such good
+ 
+
+ align:start position:0%
+have good jobs and maybe not such good
+jobs some mentors who are ready to work
+
+ align:start position:0%
+jobs some mentors who are ready to work
+ 
+
+ align:start position:0%
+jobs some mentors who are ready to work
+with you to provide advice and all of
+
+ align:start position:0%
+with you to provide advice and all of
+ 
+
+ align:start position:0%
+with you to provide advice and all of
+that will be a learning process together
+
+ align:start position:0%
+that will be a learning process together
+ 
+
+ align:start position:0%
+that will be a learning process together
+and let me say a word about another
+
+ align:start position:0%
+and let me say a word about another
+ 
+
+ align:start position:0%
+and let me say a word about another
+piece of this course that I'm especially
+
+ align:start position:0%
+piece of this course that I'm especially
+ 
+
+ align:start position:0%
+piece of this course that I'm especially
+excited about in every week we're going
+
+ align:start position:0%
+excited about in every week we're going
+ 
+
+ align:start position:0%
+excited about in every week we're going
+to have something called the personal
+
+ align:start position:0%
+to have something called the personal
+ 
+
+ align:start position:0%
+to have something called the personal
+development Corner this is designed to
+
+ align:start position:0%
+development Corner this is designed to
+ 
+
+ align:start position:0%
+development Corner this is designed to
+provide you with a path forward so that
+
+ align:start position:0%
+provide you with a path forward so that
+ 
+
+ align:start position:0%
+provide you with a path forward so that
+you can be empowered to take control of
+
+ align:start position:0%
+you can be empowered to take control of
+ 
+
+ align:start position:0%
+you can be empowered to take control of
+your own career so they'll be readings
+
+ align:start position:0%
+your own career so they'll be readings
+ 
+
+ align:start position:0%
+your own career so they'll be readings
+and videos and exercises and assignments
+
+ align:start position:0%
+and videos and exercises and assignments
+ 
+
+ align:start position:0%
+and videos and exercises and assignments
+that allow you to understand what are
+
+ align:start position:0%
+that allow you to understand what are
+ 
+
+ align:start position:0%
+that allow you to understand what are
+some of your capabilities what are some
+
+ align:start position:0%
+some of your capabilities what are some
+ 
+
+ align:start position:0%
+some of your capabilities what are some
+of your interests what jobs might fit
+
+ align:start position:0%
+of your interests what jobs might fit
+ 
+
+ align:start position:0%
+of your interests what jobs might fit
+well with your background and where you
+
+ align:start position:0%
+well with your background and where you
+ 
+
+ align:start position:0%
+well with your background and where you
+would like to go with your own career
+
+ align:start position:0%
+would like to go with your own career
+ 
+
+ align:start position:0%
+would like to go with your own career
+and how will you develop your own
+
+ align:start position:0%
+and how will you develop your own
+ 
+
+ align:start position:0%
+and how will you develop your own
+personal career plan to make sure that
+
+ align:start position:0%
+personal career plan to make sure that
+ 
+
+ align:start position:0%
+personal career plan to make sure that
+you are ready to take advantage of the
+
+ align:start position:0%
+you are ready to take advantage of the
+ 
+
+ align:start position:0%
+you are ready to take advantage of the
+opportunities that are out
+
+ align:start position:0%
+opportunities that are out
+ 
+
+ align:start position:0%
+opportunities that are out
+there so let's start exploring this
+
+ align:start position:0%
+there so let's start exploring this
+ 
+
+ align:start position:0%
+there so let's start exploring this
+evolving and interesting world of work
+
+ align:start position:0%
+evolving and interesting world of work
+ 
+
+ align:start position:0%
+evolving and interesting world of work
+let's do it with our eyes open let's
+
+ align:start position:0%
+let's do it with our eyes open let's
+ 
+
+ align:start position:0%
+let's do it with our eyes open let's
+understand and learn from our history
+
+ align:start position:0%
+understand and learn from our history
+ 
+
+ align:start position:0%
+understand and learn from our history
+about what worked in the past what's
+
+ align:start position:0%
+about what worked in the past what's
+ 
+
+ align:start position:0%
+about what worked in the past what's
+broken what needs to be fixed and why
+
+ align:start position:0%
+broken what needs to be fixed and why
+ 
+
+ align:start position:0%
+broken what needs to be fixed and why
+and then let's see if together we can't
+
+ align:start position:0%
+and then let's see if together we can't
+ 
+
+ align:start position:0%
+and then let's see if together we can't
+shape the future of work for your
+
+ align:start position:0%
+shape the future of work for your
+ 
+
+ align:start position:0%
+shape the future of work for your
+generation so let's get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started for
\ No newline at end of file
diff --git a/dLeI7A7VezQ.txt b/dLeI7A7VezQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ef1c95800b9c2d6b29fdaced9d778907729d711
--- /dev/null
+++ b/dLeI7A7VezQ.txt
@@ -0,0 +1,207 @@
+Suppose we have a real-time system supporting
+three devices:
+
+a keyboard whose interrupt handler has a service
+time of 800 us,
+
+a disk with a service time of 500 us,
+and a printer with a service time of 400 us.
+
+What is the worst-case latency seen by each
+device?
+
+For now we'll assume that requests are infrequent,
+i.e., that each request only happens once
+
+in each scenario.
+
+Requests can arrive at any time and in any
+order.
+
+If we serve the requests in first-come-first-served
+order, each device might be delayed by the
+
+service of all other devices.
+
+So the start of the keyboard handler might
+be delayed by the execution of the disk and
+
+printer handlers, a worst-case latency of
+900 us.
+
+The start of the disk handler might be delayed
+by the keyboard and printer handlers, a worst-case
+
+latency of 1200 us.
+
+And the printer handler might be delayed by
+the keyboard and disk handlers, a worst-case
+
+latency of 1300 us.
+
+In this scenario we see that long-running
+handlers have a huge impact on the worst-case
+
+latency seen by the other devices.
+
+What are the possibilities for reducing the
+worst-case latencies?
+
+Is there a better scheduling algorithm than
+first-come-first-served?
+
+One strategy is to assign priorities to the
+pending requests and to serve the requests
+
+in priority order.
+
+If the handlers are uninterruptible, the priorities
+will be used to select the *next* task to
+
+be run at the completion of the current task.
+
+Note that under this strategy, the current
+task always runs to completion even if a higher-priority
+
+request arrives while it's executing.
+
+This is called a "nonpreemptive" or "weak"
+priority system.
+
+Using a weak priority system, the worst-case
+latency seen by each device is the worst-case
+
+service time of all the other devices
+(since that handler may have just started
+
+running when the new request arrives),
+plus the service time of all higher-priority
+
+devices (since they'll be run first).
+
+In our example, suppose we assigned the highest
+priority to the disk, the next priority to
+
+the printer, and the lowest priority to the
+keyboard.
+
+The worst-case latency of the keyboard is
+unchanged since it has the lowest priority
+
+and hence can be delayed by the higher-priority
+disk and printer handlers.
+
+The disk handler has the highest priority
+and so will always be selected for execution
+
+after the current handler completes.
+
+So its worst-case latency is the worst-case
+service time for the currently-running handler,
+
+which in this case is the keyboard.
+
+So the worst-case latency for the disk is
+800 us.
+
+This is a considerable improvement over the
+first-come-first-served scenario.
+
+Finally the worst-case scenario for the printer
+is 1300 us since it may have to wait for the
+
+keyboard handler to finish (which can take
+up to 800 us)
+
+and then for a higher-priority disk request
+to be serviced (which takes 500 us).
+
+How should priorities be assigned given hard
+real-time constraints?
+
+We'll assume each device has a service deadline
+D after the arrival of its service request.
+
+If not otherwise specified, assume D is the
+time until the *next* request for the same
+
+device.
+
+This is a reasonably conservative assumption
+that prevents the system from falling further
+
+and further behind.
+
+For example, it makes sense that the keyboard
+handler should finish processing one character
+
+before the next arrives.
+
+"Earliest Deadline" is a strategy for assigning
+priorities that is guaranteed to meet the
+
+deadlines if any priority assignment can meet
+the deadlines.
+
+It's very simple: Sort the requests by their
+deadlines.
+
+Assign the highest priority to the earliest
+deadline, second priority to the next deadline,
+
+and so on.
+
+A weak priority system will choose the pending
+request with the highest priority, i.e., the
+
+request that has the earliest deadline.
+
+Earliest Deadline has an intuitive appeal.
+
+Imagine standing in a long security line at
+the airport.
+
+It would make sense to prioritize the processing
+of passengers who have the earliest flights
+
+assuming that there's enough time to process
+everyone before their flight leaves.
+
+Processing 10 people whose flights leave in
+30 minutes before someone whose flight leaves
+
+in 5 min will cause that last person to miss
+their flight.
+
+But if that person is processed first, the
+other passengers may be slightly delayed but
+
+everyone will make their flight.
+
+This is the sort of scheduling problem that
+Earliest Deadline and a weak priority system
+
+can solve.
+
+It's outside the scope of our discussion,
+but it's interesting to think about what should
+
+happen if some flights are going to be missed.
+
+If the system is overloaded, prioritizing
+by earliest deadline may mean that everyone
+
+will miss their flights!
+
+In this scenario it might be better to assign
+priorities to the minimize the total number
+
+of missed flights.
+
+This gets complicated in a hurry since the
+assignment of priorities now depends on exactly
+
+what requests are pending and how long it
+will take them to be serviced.
+
+An intriguing problem to think about!
\ No newline at end of file
diff --git a/dbSKZx9sfsg.txt b/dbSKZx9sfsg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..237b76f2a2993d82ff7e969aaf8962ec2f47f7ed
--- /dev/null
+++ b/dbSKZx9sfsg.txt
@@ -0,0 +1,924 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+Hi.
+
+I'm Jocelyn, and we're going to
+go over fall 2009, exam 1,
+
+problem number 3.
+
+With every question, we want to
+make sure we read the full
+
+problem first. So answer the
+following questions about the
+
+difluoro-iodate ion.
+
+Draw a three-dimensional
+representation of the
+
+molecular geometry around the
+central atom, not simply the
+
+Lewis structure.
+
+Show all atoms and bonds
+between them.
+
+Because this part seems pretty
+separate from the rest of
+
+them, we're going to
+start with that.
+
+So we have a difluoro-iodate
+ion.
+
+It has a positive charge.
+
+And it asks us to draw the
+molecular geometry in a 3D
+
+representation, and not
+just Lewis structure.
+
+However, to do the molecular
+geometry in 3D, we need to
+
+know the Lewis structure.
+
+So we're going to
+start with that.
+
+To draw the Lewis structure,
+we first need to figure out
+
+which atom is the
+central atom.
+
+And it's always a good idea to
+do that by looking at the
+
+relative electronegativities.
+
+As we know, fluorine is the most
+electronegative element
+
+in the periodic table, and so
+that's probably not going to
+
+be in the middle.
+
+Therefore, iodine, being the
+less electronegative, is going
+
+to be in the middle,
+and it will have
+
+fluorines on either side.
+
+This is our rough sketch of
+the molecular geometry.
+
+Not too important right now.
+
+Next we need to know how many
+electrons we have. Iodine has
+
+seven valence electrons,
+fluoride has seven valence
+
+electrons, and we have a
+positive charge, so we know
+
+that we're missing one.
+
+And that gives us
+20 electrons.
+
+Now that we know how many
+electrons we have to work
+
+with, we need start
+filling them in.
+
+I always start with the
+outer electrons.
+
+Those are usually, hopefully,
+the most electronegative, and
+
+therefore, the most likely to
+have the octet rule satisfied.
+
+Also, if you remember, fluorine
+is in the second row,
+
+and therefore needs to have
+the octet rule satisfied.
+
+Iodine is a little bit lower in
+the periodic table, so the
+
+octet rule isn't as important.
+
+It can have an extended octet
+if we need it to.
+
+So we will work with
+iodine second.
+
+Let's start out with satisfying
+the octet rule for
+
+the fluorine, putting first the
+seven valence electrons
+
+that the fluorines brought
+themselves, and then noticing
+
+that each needs to share one
+from iodine, so that we have a
+
+full octet.
+
+So each has one bond
+with iodine.
+
+We've used 8 electrons,
+or 8 per fluorine.
+
+So we have a total of 16.
+
+We have 4 left, and
+we're going to put
+
+those on the iodine.
+
+Counting up how many electronics
+are around iodine,
+
+1, 2, 3, 4, 5, 6, 7, 8, we see
+that the octet rule is also
+
+satisfied for iodine.
+
+This is looking like a pretty
+good Lewis structure.
+
+Now, just to make sure it's
+really good, we're going to
+
+look at the formal charge.
+
+So if you recall, the formal
+charge is the number of
+
+valence electrons that the
+element usually has, and minus
+
+the number of unshared
+electrons, and
+
+the number of dots.
+
+So this sum subtracted from
+the valence electrons will
+
+give us the formal charge.
+
+Looking at the fluorine, we have
+seven valence electrons.
+
+We have 1, 2, 3, 4,
+5, 6 unpaired, and
+
+one bond to the fluorine.
+
+So that gives us a formal
+charge of 0.
+
+The same goes for the
+other fluorine.
+
+So I guess its formal
+charge is 0.
+
+Now for the iodine, we have--
+
+I'm going to do the formal
+charge down here--
+
+it again has 7 valence
+electrons, usually.
+
+We have 4 unshared electrons,
+and 2 bonds.
+
+That gives us a formal
+charge of plus 1.
+
+Because we have a charged
+species here, the full
+
+molecule has a plus 1 charge.
+
+There's no way we cannot have
+a net formal charge.
+
+Right?
+
+We need to have a net formal
+charge of plus 1.
+
+And it makes sense that that
+formal charge is on the least
+
+electronegative atom.
+
+So this looks like
+the right Lewis
+
+structure for our purposes.
+
+One more thing that you might
+want to write down.
+
+I'm not sure if points were
+taken off from this.
+
+But technically, if you have a
+charged species, put brackets
+
+around your Lewis structure,
+and put the net
+
+charge on the outside.
+
+This is not, however, our
+final answer, right?
+
+This is the Lewis structure.
+
+But the question asks for the
+molecular geometry to be
+
+represented.
+
+So if we remember how we
+determine molecular geometry,
+
+we need to look at the number of
+electron domains around the
+
+essential atom.
+
+So we're going to move over
+here, and I'll redraw our
+
+Lewis structure.
+
+And remember, an electron
+domain can be either an
+
+electron pair, or a bond.
+
+So we see that iodine has
+4 electron domains.
+
+And if we remember our skeletal
+geometry, we know
+
+that that's tetrahedral.
+
+Thus, to draw this in a more 3D
+fashion, we might want to
+
+say that one of the electron
+pairs is here, one of the
+
+electron pairs is over here,
+and then we have a fluorine
+
+coming out of the board, and a
+fluorine going into the board.
+
+We didn't really go
+over how to do
+
+three-dimensional drawings.
+
+So as long as you show something
+like, you know the
+
+fluorines will be an angle, not
+straight from the iodine,
+
+and that the electrons be on the
+other side, something to
+
+that effect.
+
+A little bit more detailed than
+just a Lewis structure,
+
+was what Professor Sadoway was
+looking for in this problem.
+
+And that would be your answer.
+
+And for this one especially, I'd
+say it's important to box
+
+your final answer.
+
+Because you hopefully would
+have figured out the Lewis
+
+structure, but this is not
+the correct answer.
+
+So you always want to
+signify what answer
+
+you want to be graded.
+
+Part B says, name the type of
+hybrid orbitals that the
+
+central atom forms. So we are
+almost all the way to
+
+answering this question, so
+I'll put it down here.
+
+Remember, hybrid
+orbitals are--
+
+we have hybrid orbitals, because
+we can't really say
+
+what orbitals exactly are
+bonding to which atoms. We
+
+want to have 4 equivalent
+orbitals for
+
+this system, right?
+
+We have 4 electron domains,
+so we want 4
+
+equivalent bonding orbitals.
+
+And from our talks earlier
+in the lectures about
+
+hybridization, we know that if
+we want 4, we take 1S and 3P,
+
+and that gives us the
+hybridization of the SP3.
+
+if we only had 3 electron
+domains, it would be SP2,
+
+because we only use
+3 orbitals.
+
+And the number of orbitals that
+go into the hybrid is the
+
+number of orbitals
+you will get out.
+
+So we know that our
+hybridization is SP3.
+
+And that goes along with the
+fact that our shape is
+
+tetrahedral.
+
+Now we need to name
+the molecular
+
+geometry of this molecule.
+
+so we already have the molecular
+shape and the kind
+
+of spacial arrangement
+is tetrahedral.
+
+However, when we're naming the
+molecular geometry, electron
+
+pairs no longer matter.
+
+So for part C, tetrahedral is
+our skeletal geometry, right?
+
+It shows us our special
+arrangement.
+
+The molecular geometry is
+ignoring those electron pairs.
+
+So it is called bent when
+we only have 2 bonds.
+
+And I think about that because
+in spectroscopy and ways that
+
+are used to study molecules,
+you can't see the electron
+
+clouds very well.
+
+So they could only see the
+iodine and the two fluorines,
+
+thus looking like a
+bent structure.
+
+So hopefully you're sticking
+with me here, because this
+
+problem has a lot of parts.
+
+And we're going to move
+on to part D now.
+
+Part D asks, is difluoro-iodate
+polar or
+
+nonpolar, and explain.
+
+If you put down polar or
+nonpolar and did not explain,
+
+we assume you guessed, and you
+didn't get any points.
+
+Explaining shows that you know
+why, and you understand the
+
+concepts behind this,
+and thus deserved
+
+points on this problem.
+
+So there's two different
+parts of this problem.
+
+First, to have a polar molecule,
+you need to have
+
+polar bonds.
+
+So I would first ask myself,
+are the bonds polar?
+
+We have a difference of
+electronegativity that you can
+
+look up on your periodic table
+and know is not negligible.
+
+And so yes.
+
+A difference in
+electronegativity signifies
+
+that our bonds are polar.
+
+However, not all molecules
+that have polar bonds are
+
+themselves polar, right?
+
+if we have spacial symmetry,
+those polar bonds
+
+could cancel out.
+
+So now we need to make sure,
+is the molecule polar?
+
+And for that, we need
+to have answered the
+
+first questions correctly.
+
+Right?
+
+We need to know that this is
+not a linear structure.
+
+If this was a linear structure,
+those polar bonds
+
+would be geometrically
+symmetric, and
+
+cancel each other out.
+
+But we all are very smart, and
+we got this part C right.
+
+We know that we have
+a bent structure.
+
+Thus, I'll rewrite
+this over here.
+
+We know that if we draw in our
+polarity vectors, we can
+
+realize that we'll have a net
+dipole pointing down.
+
+So the answer to this is yes,
+because of the difference in
+
+the electronegativity,
+and because
+
+of the spacial asymmetry.
+
+If you said both of
+those things, you
+
+would get full credit.
+
+If you said one or
+the other, you'd
+
+probably get part credit.
+
+But knowing to look at these
+two things shows that you
+
+fully understand what it means
+to have molecular polarity.
+
+All right.
+
+So now we're going to
+move to part E.
+
+This part is changing gears a
+little bit, so if you didn't
+
+quite understand the
+first part, you can
+
+still try this one.
+
+Part E, again, what is the
+question asking us?
+
+Determine the maximum wavelength
+of electromagnetic
+
+radiation capable of breaking
+the IS bond.
+
+So we need to find the maximum
+wavelengths which corresponds
+
+to the minimum energy.
+
+Right?
+
+Because we have e equals
+hc over over lambda for
+
+electromagnetic radiation.
+
+We're trying to figure out the
+lowest energy of photon that
+
+will break the IF bond.
+
+Now, what are we given to
+answer this question?
+
+We're given the energy of the
+homogeneous fluorine-fluorine
+
+bond, is 160 kilojoules
+per mole.
+
+And the energy of the
+homogeneous iodine-iodine bond
+
+is 150 kilojoules per mole.
+
+And in order to find the
+wavelength that will break the
+
+IS bond, we need to know the
+energy of the IS bond.
+
+Right?
+
+That's what we're working
+towards in this problem.
+
+So given the homogeneous
+energies, do we have a
+
+relationship that will
+help us determine the
+
+energy of the IS bond?
+
+If you recall, in lecture 9,
+Professor Sadoway went over
+
+the Pauling formula for
+determining a heterogeneous
+
+bond energy from the homogeneous
+bond energies, and
+
+the electronegativity.
+
+So I'll just write
+that up here.
+
+The Pauling formula is, in a
+generic form, the energy of an
+
+AB bond equals the square root
+of the product of the
+
+homogeneous bond energies plus
+a constant times the
+
+difference between the
+electronegativities squared.
+
+And I just said what all
+of these terms mean.
+
+Because even if you had this on
+your equation sheet in the
+
+test or something, a lot of
+people wrote this down, and
+
+then used it incorrectly.
+
+So it's really important to know
+not only what equations
+
+you have, but especially what
+each of the terms in the
+
+equations mean.
+
+So we're given the homogeneous
+bond energies, and we have a
+
+periodic table, or some other
+resource, that has the
+
+elecronegativities.
+
+Next step is to plug in the
+numbers and find the energy of
+
+the IF bond.
+
+So we have the square root
+of 150 kilojoules plus.
+
+And the exact values you get for
+the electronegativity may
+
+vary, depending on the source.
+
+But they'll be close
+enough, and
+
+relatively, probably very--
+
+the difference between them
+will be very similar.
+
+So don't worry if your
+numbers were a little
+
+different than mine.
+
+So we wrote all that out,
+and plugging it into the
+
+calculator, you get that the IF
+bond has an energy of 323
+
+kilojoules per mole.
+
+Now that we've found the energy
+of the IS bond, are we
+
+done with the problem?
+
+You have an answer.
+
+You might be ready to move
+on to the next question.
+
+However, this isn't what the
+question is asking us, right?
+
+We are asked for the maximum
+wavelength that can break a
+
+bond of that energy.
+
+So we need to go back to our
+energy relation to our
+
+wavelengths.
+
+And we know that the wavelength
+
+equals hc over the energy.
+
+Now here's where some people
+tripped up a little bit.
+
+You have a value
+for the energy.
+
+h and c are constants.
+
+And you find the lambda.
+
+However, if you plugged that all
+in, your answer would be
+
+6.15 times 10 to the
+negative 31 meters.
+
+Some people, that was the
+answer that they found.
+
+And it makes sense.
+
+You have an energy, you have
+some constants, and you can
+
+get your lambda.
+
+However, if you think about
+it, does this wavelength
+
+actually make sense?
+
+The gamma ray radiation has a
+wavelength of about 10 to the
+
+negative 17.
+
+That's very, very,
+very energetic
+
+electromagnetic radiation.
+
+So this is 14 magnitudes
+smaller than gamma ray
+
+radiation, and it just doesn't
+make sense for a bond energy
+
+of this much.
+
+Plus it doesn't--
+
+it just-- you should look at the
+answer you get, and try to
+
+be comfortable with if it
+makes sense or not.
+
+So where people got tripped
+up, is in the units.
+
+We found Pauling's formula gives
+you the bond energy in
+
+kilojoules per mole.
+
+However, if you look at Planck's
+constant, it has
+
+units of joules time seconds.
+
+The speed of light is in
+meters per second.
+
+And you want lambda in meters.
+
+To make everything or cancel
+out, that means we want the
+
+energy to be in joules.
+
+Not joules per mole, because
+we're looking at the
+
+wavelength of one
+photon, right?
+
+We're looking at the energy of
+one photon to break this bond.
+
+So we want the energy of the
+bond, not per mole of bonds,
+
+but just of one bond.
+
+So instead of just having this
+equation, we want to have put
+
+in h times c over 323, change
+it to joules, and then
+
+multiply by--
+
+sorry, moles are on
+the bottom, 1 mole
+
+and Avogadro's number.
+
+And Planck's constant of the
+speed of light, you should
+
+have on your equation sheet, or
+somewhere else, some other
+
+resource that you have. You
+don't need to memorize those
+
+in most cases.
+
+If you remembered to divide by
+Avogadro's number, you got 3.7
+
+times 10 to the negative 7
+meters, which equals 370
+
+nanometers.
+
+And if we recall, the light we
+can see is in the 400 to 700
+
+nanometer range.
+
+So this puts us in ultraviolet
+radiation, which makes sense
+
+that it would take that much
+energy to break a bond.
+
+The other problem some people
+had was forgetting to convert
+
+from kilojoules to joules.
+
+That would still give you
+a physical answer.
+
+But again, I can't stress
+unit cancel out enough.
+
+So make sure you know that since
+your Planck's constant
+
+is in joules, you want
+to make sure you have
+
+joules on the bottom.
\ No newline at end of file
diff --git a/f1pxiNDTyHc.txt b/f1pxiNDTyHc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..32028043aec6573eb5dec66343cc29af0cf68590
--- /dev/null
+++ b/f1pxiNDTyHc.txt
@@ -0,0 +1,9403 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today we're going to talk about
+
+ align:start position:0%
+today we're going to talk about
+ 
+
+ align:start position:0%
+today we're going to talk about
+vibrations topic of vibration isolation
+
+ align:start position:0%
+vibrations topic of vibration isolation
+ 
+
+ align:start position:0%
+vibrations topic of vibration isolation
+which is a very practical use of knowing
+
+ align:start position:0%
+which is a very practical use of knowing
+ 
+
+ align:start position:0%
+which is a very practical use of knowing
+a little bit about vibration so imagine
+
+ align:start position:0%
+a little bit about vibration so imagine
+ 
+
+ align:start position:0%
+a little bit about vibration so imagine
+you've probably been in a situation
+
+ align:start position:0%
+you've probably been in a situation
+ 
+
+ align:start position:0%
+you've probably been in a situation
+you've been in where there's an air
+
+ align:start position:0%
+you've been in where there's an air
+ 
+
+ align:start position:0%
+you've been in where there's an air
+conditioner in a window and it's causing
+
+ align:start position:0%
+conditioner in a window and it's causing
+ 
+
+ align:start position:0%
+conditioner in a window and it's causing
+your table to shake or where you're
+
+ align:start position:0%
+your table to shake or where you're
+ 
+
+ align:start position:0%
+your table to shake or where you're
+trying to work or your bed rattles or
+
+ align:start position:0%
+trying to work or your bed rattles or
+ 
+
+ align:start position:0%
+trying to work or your bed rattles or
+something like that how many of you have
+
+ align:start position:0%
+something like that how many of you have
+ 
+
+ align:start position:0%
+something like that how many of you have
+ever had an experience like that
+
+ align:start position:0%
+ever had an experience like that
+ 
+
+ align:start position:0%
+ever had an experience like that
+something's kind of annoying messing up
+
+ align:start position:0%
+something's kind of annoying messing up
+ 
+
+ align:start position:0%
+something's kind of annoying messing up
+a lab experiment or whatever yeah you've
+
+ align:start position:0%
+a lab experiment or whatever yeah you've
+ 
+
+ align:start position:0%
+a lab experiment or whatever yeah you've
+all experienced these things right so
+
+ align:start position:0%
+all experienced these things right so
+ 
+
+ align:start position:0%
+all experienced these things right so
+what can you know can we as as clever
+
+ align:start position:0%
+what can you know can we as as clever
+ 
+
+ align:start position:0%
+what can you know can we as as clever
+engineers are there simple solutions
+
+ align:start position:0%
+engineers are there simple solutions
+ 
+
+ align:start position:0%
+engineers are there simple solutions
+sometimes to fixing these problems and
+
+ align:start position:0%
+sometimes to fixing these problems and
+ 
+
+ align:start position:0%
+sometimes to fixing these problems and
+that's what we're going to that's we're
+
+ align:start position:0%
+that's what we're going to that's we're
+ 
+
+ align:start position:0%
+that's what we're going to that's we're
+going to talk about today I have a
+
+ align:start position:0%
+going to talk about today I have a
+ 
+
+ align:start position:0%
+going to talk about today I have a
+little quick demo that I'm going to show
+
+ align:start position:0%
+little quick demo that I'm going to show
+ 
+
+ align:start position:0%
+little quick demo that I'm going to show
+you you saw this the other the other day
+
+ align:start position:0%
+you you saw this the other the other day
+ 
+
+ align:start position:0%
+you you saw this the other the other day
+or this is my little squiggle pen and
+
+ align:start position:0%
+or this is my little squiggle pen and
+ 
+
+ align:start position:0%
+or this is my little squiggle pen and
+it's got a rotating mass inside and
+
+ align:start position:0%
+it's got a rotating mass inside and
+ 
+
+ align:start position:0%
+it's got a rotating mass inside and
+we've looked at rotating masses a lot so
+
+ align:start position:0%
+we've looked at rotating masses a lot so
+ 
+
+ align:start position:0%
+we've looked at rotating masses a lot so
+it has some unbalanced statically
+
+ align:start position:0%
+it has some unbalanced statically
+ 
+
+ align:start position:0%
+it has some unbalanced statically
+unbalanced rotating mass could be a fan
+
+ align:start position:0%
+unbalanced rotating mass could be a fan
+ 
+
+ align:start position:0%
+unbalanced rotating mass could be a fan
+blade with a hunk of chewing gum or
+
+ align:start position:0%
+blade with a hunk of chewing gum or
+ 
+
+ align:start position:0%
+blade with a hunk of chewing gum or
+something stuck on a blade or broken
+
+ align:start position:0%
+something stuck on a blade or broken
+ 
+
+ align:start position:0%
+something stuck on a blade or broken
+piece out of it puts in a four semi
+
+ align:start position:0%
+piece out of it puts in a four semi
+ 
+
+ align:start position:0%
+piece out of it puts in a four semi
+Omega squared cosine Omega T basically
+
+ align:start position:0%
+Omega squared cosine Omega T basically
+ 
+
+ align:start position:0%
+Omega squared cosine Omega T basically
+an F naught cosine Omega T kind of
+
+ align:start position:0%
+an F naught cosine Omega T kind of
+ 
+
+ align:start position:0%
+an F naught cosine Omega T kind of
+excitation and if it happens to be a
+
+ align:start position:0%
+excitation and if it happens to be a
+ 
+
+ align:start position:0%
+excitation and if it happens to be a
+flexibly mounted mass spring dashpot
+
+ align:start position:0%
+flexibly mounted mass spring dashpot
+ 
+
+ align:start position:0%
+flexibly mounted mass spring dashpot
+system it'll vibrate so I showed you
+
+ align:start position:0%
+system it'll vibrate so I showed you
+ 
+
+ align:start position:0%
+system it'll vibrate so I showed you
+that the other day we'll do this and
+
+ align:start position:0%
+that the other day we'll do this and
+ 
+
+ align:start position:0%
+that the other day we'll do this and
+we'll need to lower the lights a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but today I have set your bed here this
+
+ align:start position:0%
+but today I have set your bed here this
+ 
+
+ align:start position:0%
+but today I have set your bed here this
+is your microscope here a little one you
+
+ align:start position:0%
+is your microscope here a little one you
+ 
+
+ align:start position:0%
+is your microscope here a little one you
+can see it in foreground and this is
+
+ align:start position:0%
+can see it in foreground and this is
+ 
+
+ align:start position:0%
+can see it in foreground and this is
+your air conditioner or the water pump
+
+ align:start position:0%
+your air conditioner or the water pump
+ 
+
+ align:start position:0%
+your air conditioner or the water pump
+or whatever it's causing the trouble so
+
+ align:start position:0%
+or whatever it's causing the trouble so
+ 
+
+ align:start position:0%
+or whatever it's causing the trouble so
+this is running about 28 Hertz is what
+
+ align:start position:0%
+this is running about 28 Hertz is what
+ 
+
+ align:start position:0%
+this is running about 28 Hertz is what
+if I set this strobe just right I can
+
+ align:start position:0%
+if I set this strobe just right I can
+ 
+
+ align:start position:0%
+if I set this strobe just right I can
+absolutely stop the motion it doesn't
+
+ align:start position:0%
+absolutely stop the motion it doesn't
+ 
+
+ align:start position:0%
+absolutely stop the motion it doesn't
+look like it's moving at all that's
+
+ align:start position:0%
+look like it's moving at all that's
+ 
+
+ align:start position:0%
+look like it's moving at all that's
+because the strobe is at exactly the
+
+ align:start position:0%
+because the strobe is at exactly the
+ 
+
+ align:start position:0%
+because the strobe is at exactly the
+same rate as the squiggle pen now I'm
+
+ align:start position:0%
+same rate as the squiggle pen now I'm
+ 
+
+ align:start position:0%
+same rate as the squiggle pen now I'm
+going to detune the strobe a little bit
+
+ align:start position:0%
+going to detune the strobe a little bit
+ 
+
+ align:start position:0%
+going to detune the strobe a little bit
+so you can see the motion there's the
+
+ align:start position:0%
+so you can see the motion there's the
+ 
+
+ align:start position:0%
+so you can see the motion there's the
+motion of this main system that's the
+
+ align:start position:0%
+motion of this main system that's the
+ 
+
+ align:start position:0%
+motion of this main system that's the
+process causing the problem but it
+
+ align:start position:0%
+process causing the problem but it
+ 
+
+ align:start position:0%
+process causing the problem but it
+actually puts the vibration into the
+
+ align:start position:0%
+actually puts the vibration into the
+ 
+
+ align:start position:0%
+actually puts the vibration into the
+tabletop a next door over here I have a
+
+ align:start position:0%
+tabletop a next door over here I have a
+ 
+
+ align:start position:0%
+tabletop a next door over here I have a
+little beam and you can just see that
+
+ align:start position:0%
+little beam and you can just see that
+ 
+
+ align:start position:0%
+little beam and you can just see that
+little piece of white moving up and down
+
+ align:start position:0%
+little piece of white moving up and down
+ 
+
+ align:start position:0%
+little piece of white moving up and down
+it's just a little flat piece of spring
+
+ align:start position:0%
+it's just a little flat piece of spring
+ 
+
+ align:start position:0%
+it's just a little flat piece of spring
+steel with a magnet on the end as a mass
+
+ align:start position:0%
+steel with a magnet on the end as a mass
+ 
+
+ align:start position:0%
+steel with a magnet on the end as a mass
+and a piece of white tape so you can see
+
+ align:start position:0%
+and a piece of white tape so you can see
+ 
+
+ align:start position:0%
+and a piece of white tape so you can see
+it but notice it's going up and down in
+
+ align:start position:0%
+it but notice it's going up and down in
+ 
+
+ align:start position:0%
+it but notice it's going up and down in
+synchrony with the other one so this is
+
+ align:start position:0%
+synchrony with the other one so this is
+ 
+
+ align:start position:0%
+synchrony with the other one so this is
+some this is your microscope sitting on
+
+ align:start position:0%
+some this is your microscope sitting on
+ 
+
+ align:start position:0%
+some this is your microscope sitting on
+a lab bench some distance away the
+
+ align:start position:0%
+a lab bench some distance away the
+ 
+
+ align:start position:0%
+a lab bench some distance away the
+problem vibrations being created by the
+
+ align:start position:0%
+problem vibrations being created by the
+ 
+
+ align:start position:0%
+problem vibrations being created by the
+original imbalance in something travels
+
+ align:start position:0%
+original imbalance in something travels
+ 
+
+ align:start position:0%
+original imbalance in something travels
+through the floor gets to your table
+
+ align:start position:0%
+through the floor gets to your table
+ 
+
+ align:start position:0%
+through the floor gets to your table
+with the microscope on it now your
+
+ align:start position:0%
+with the microscope on it now your
+ 
+
+ align:start position:0%
+with the microscope on it now your
+microscope shakes so what can we the
+
+ align:start position:0%
+microscope shakes so what can we the
+ 
+
+ align:start position:0%
+microscope shakes so what can we the
+issue is what can we do about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh I do yeah and we'll leave this
+
+ align:start position:0%
+okay oh I do yeah and we'll leave this
+ 
+
+ align:start position:0%
+okay oh I do yeah and we'll leave this
+for a second I'll turn it off and then
+
+ align:start position:0%
+for a second I'll turn it off and then
+ 
+
+ align:start position:0%
+for a second I'll turn it off and then
+I'm going to have you consider so I want
+
+ align:start position:0%
+I'm going to have you consider so I want
+ 
+
+ align:start position:0%
+I'm going to have you consider so I want
+you to you know get in pairs and talk
+
+ align:start position:0%
+you to you know get in pairs and talk
+ 
+
+ align:start position:0%
+you to you know get in pairs and talk
+about this I want as a group we're going
+
+ align:start position:0%
+about this I want as a group we're going
+ 
+
+ align:start position:0%
+about this I want as a group we're going
+to come up with at least three ways to
+
+ align:start position:0%
+to come up with at least three ways to
+ 
+
+ align:start position:0%
+to come up with at least three ways to
+reduce the vibration of your microscope
+
+ align:start position:0%
+reduce the vibration of your microscope
+ 
+
+ align:start position:0%
+reduce the vibration of your microscope
+relatively simple ways to fix it how
+
+ align:start position:0%
+relatively simple ways to fix it how
+ 
+
+ align:start position:0%
+relatively simple ways to fix it how
+would you do it
+
+ align:start position:0%
+would you do it
+ 
+
+ align:start position:0%
+would you do it
+figure give me so think about it talk
+
+ align:start position:0%
+figure give me so think about it talk
+ 
+
+ align:start position:0%
+figure give me so think about it talk
+about it and come up with three ways of
+
+ align:start position:0%
+about it and come up with three ways of
+ 
+
+ align:start position:0%
+about it and come up with three ways of
+fixing this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to do one more demo on this in
+
+ align:start position:0%
+I'm going to do one more demo on this in
+ 
+
+ align:start position:0%
+I'm going to do one more demo on this in
+a minute and then put up the transfer
+
+ align:start position:0%
+a minute and then put up the transfer
+ 
+
+ align:start position:0%
+a minute and then put up the transfer
+function for the force the one we had
+
+ align:start position:0%
+function for the force the one we had
+ 
+
+ align:start position:0%
+function for the force the one we had
+the other day okay a picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's have some suggestions
+
+ align:start position:0%
+all right let's have some suggestions
+ 
+
+ align:start position:0%
+all right let's have some suggestions
+how would you go about fixing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so put it put some Springs on
+
+ align:start position:0%
+all right so put it put some Springs on
+ 
+
+ align:start position:0%
+all right so put it put some Springs on
+what the spring support the microscope
+
+ align:start position:0%
+what the spring support the microscope
+ 
+
+ align:start position:0%
+what the spring support the microscope
+all right so I have this blue this
+
+ align:start position:0%
+all right so I have this blue this
+ 
+
+ align:start position:0%
+all right so I have this blue this
+little magnet here sitting on this beam
+
+ align:start position:0%
+little magnet here sitting on this beam
+ 
+
+ align:start position:0%
+little magnet here sitting on this beam
+this is that spring supported microscope
+
+ align:start position:0%
+this is that spring supported microscope
+ 
+
+ align:start position:0%
+this is that spring supported microscope
+but I've done a heck of a lousy job this
+
+ align:start position:0%
+but I've done a heck of a lousy job this
+ 
+
+ align:start position:0%
+but I've done a heck of a lousy job this
+thing shakes like crazy so what do you
+
+ align:start position:0%
+thing shakes like crazy so what do you
+ 
+
+ align:start position:0%
+thing shakes like crazy so what do you
+mean not like that how am i okay so if
+
+ align:start position:0%
+mean not like that how am i okay so if
+ 
+
+ align:start position:0%
+mean not like that how am i okay so if
+you think that you could change the
+
+ align:start position:0%
+you think that you could change the
+ 
+
+ align:start position:0%
+you think that you could change the
+properties of this system so that it
+
+ align:start position:0%
+properties of this system so that it
+ 
+
+ align:start position:0%
+properties of this system so that it
+might do better let's think about that
+
+ align:start position:0%
+might do better let's think about that
+ 
+
+ align:start position:0%
+might do better let's think about that
+okay what's another idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if you change the length are you
+
+ align:start position:0%
+yeah if you change the length are you
+ 
+
+ align:start position:0%
+yeah if you change the length are you
+talking about the microscope one the
+
+ align:start position:0%
+talking about the microscope one the
+ 
+
+ align:start position:0%
+talking about the microscope one the
+receiving one if you change the length
+
+ align:start position:0%
+receiving one if you change the length
+ 
+
+ align:start position:0%
+receiving one if you change the length
+of it it change it make it longer it
+
+ align:start position:0%
+of it it change it make it longer it
+ 
+
+ align:start position:0%
+of it it change it make it longer it
+makes it softer actually make it shorter
+
+ align:start position:0%
+makes it softer actually make it shorter
+ 
+
+ align:start position:0%
+makes it softer actually make it shorter
+it makes it stiffer so you would change
+
+ align:start position:0%
+it makes it stiffer so you would change
+ 
+
+ align:start position:0%
+it makes it stiffer so you would change
+its natural frequency that's that now
+
+ align:start position:0%
+its natural frequency that's that now
+ 
+
+ align:start position:0%
+its natural frequency that's that now
+the two ideas together you if you set
+
+ align:start position:0%
+the two ideas together you if you set
+ 
+
+ align:start position:0%
+the two ideas together you if you set
+the natural frequency correctly you can
+
+ align:start position:0%
+the natural frequency correctly you can
+ 
+
+ align:start position:0%
+the natural frequency correctly you can
+actually make that says the second the
+
+ align:start position:0%
+actually make that says the second the
+ 
+
+ align:start position:0%
+actually make that says the second the
+system on the receiving end you can
+
+ align:start position:0%
+system on the receiving end you can
+ 
+
+ align:start position:0%
+system on the receiving end you can
+reduce its vibration and I will
+
+ align:start position:0%
+reduce its vibration and I will
+ 
+
+ align:start position:0%
+reduce its vibration and I will
+demonstrate that in a second what's
+
+ align:start position:0%
+demonstrate that in a second what's
+ 
+
+ align:start position:0%
+demonstrate that in a second what's
+another idea after damping okay well
+
+ align:start position:0%
+another idea after damping okay well
+ 
+
+ align:start position:0%
+another idea after damping okay well
+that's a very interesting suggestion
+
+ align:start position:0%
+that's a very interesting suggestion
+ 
+
+ align:start position:0%
+that's a very interesting suggestion
+damping it helped under one circumstance
+
+ align:start position:0%
+damping it helped under one circumstance
+ 
+
+ align:start position:0%
+damping it helped under one circumstance
+but not under some others we're going to
+
+ align:start position:0%
+but not under some others we're going to
+ 
+
+ align:start position:0%
+but not under some others we're going to
+explore that today what so but we
+
+ align:start position:0%
+explore that today what so but we
+ 
+
+ align:start position:0%
+explore that today what so but we
+Stella's is all basically we've come up
+
+ align:start position:0%
+Stella's is all basically we've come up
+ 
+
+ align:start position:0%
+Stella's is all basically we've come up
+with one of the three ideas what else oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's interesting that's the fourth one
+
+ align:start position:0%
+that's interesting that's the fourth one
+ 
+
+ align:start position:0%
+that's interesting that's the fourth one
+I mean that that can be a little
+
+ align:start position:0%
+I mean that that can be a little
+ 
+
+ align:start position:0%
+I mean that that can be a little
+expensive but these are like noise
+
+ align:start position:0%
+expensive but these are like noise
+ 
+
+ align:start position:0%
+expensive but these are like noise
+cancelling mic headsets right could we
+
+ align:start position:0%
+cancelling mic headsets right could we
+ 
+
+ align:start position:0%
+cancelling mic headsets right could we
+put in something else somewhere else on
+
+ align:start position:0%
+put in something else somewhere else on
+ 
+
+ align:start position:0%
+put in something else somewhere else on
+the table that cancels the vibration at
+
+ align:start position:0%
+the table that cancels the vibration at
+ 
+
+ align:start position:0%
+the table that cancels the vibration at
+where you're trying to wear your
+
+ align:start position:0%
+where you're trying to wear your
+ 
+
+ align:start position:0%
+where you're trying to wear your
+microscope is yeah you could do that a
+
+ align:start position:0%
+microscope is yeah you could do that a
+ 
+
+ align:start position:0%
+microscope is yeah you could do that a
+little expensive what else yeah where
+
+ align:start position:0%
+little expensive what else yeah where
+ 
+
+ align:start position:0%
+little expensive what else yeah where
+would you put that yeah and so that's
+
+ align:start position:0%
+would you put that yeah and so that's
+ 
+
+ align:start position:0%
+would you put that yeah and so that's
+generally the same idea so you're all
+
+ align:start position:0%
+generally the same idea so you're all
+ 
+
+ align:start position:0%
+generally the same idea so you're all
+treating the microscope it can you treat
+
+ align:start position:0%
+treating the microscope it can you treat
+ 
+
+ align:start position:0%
+treating the microscope it can you treat
+something else in the system so yeah
+
+ align:start position:0%
+something else in the system so yeah
+ 
+
+ align:start position:0%
+something else in the system so yeah
+we'll fix the microscope end but that
+
+ align:start position:0%
+we'll fix the microscope end but that
+ 
+
+ align:start position:0%
+we'll fix the microscope end but that
+might knock it down by a factor of 10 I
+
+ align:start position:0%
+might knock it down by a factor of 10 I
+ 
+
+ align:start position:0%
+might knock it down by a factor of 10 I
+want to knock it bound by at least a
+
+ align:start position:0%
+want to knock it bound by at least a
+ 
+
+ align:start position:0%
+want to knock it bound by at least a
+factor of 100 if not a factor of a
+
+ align:start position:0%
+factor of 100 if not a factor of a
+ 
+
+ align:start position:0%
+factor of 100 if not a factor of a
+thousand ah you know put another piece
+
+ align:start position:0%
+thousand ah you know put another piece
+ 
+
+ align:start position:0%
+thousand ah you know put another piece
+of gum on the other blade or tail or
+
+ align:start position:0%
+of gum on the other blade or tail or
+ 
+
+ align:start position:0%
+of gum on the other blade or tail or
+clean it up or balance the rotor in
+
+ align:start position:0%
+clean it up or balance the rotor in
+ 
+
+ align:start position:0%
+clean it up or balance the rotor in
+effect rotors are not manufactured
+
+ align:start position:0%
+effect rotors are not manufactured
+ 
+
+ align:start position:0%
+effect rotors are not manufactured
+defective usually they get rejected at
+
+ align:start position:0%
+defective usually they get rejected at
+ 
+
+ align:start position:0%
+defective usually they get rejected at
+the under at the quote QC before it goes
+
+ align:start position:0%
+the under at the quote QC before it goes
+ 
+
+ align:start position:0%
+the under at the quote QC before it goes
+out the door so fix the rotor can be a
+
+ align:start position:0%
+out the door so fix the rotor can be a
+ 
+
+ align:start position:0%
+out the door so fix the rotor can be a
+little expensive sometimes but worth it
+
+ align:start position:0%
+little expensive sometimes but worth it
+ 
+
+ align:start position:0%
+little expensive sometimes but worth it
+you know they do maintenance checks
+
+ align:start position:0%
+you know they do maintenance checks
+ 
+
+ align:start position:0%
+you know they do maintenance checks
+actually they have accelerometers
+
+ align:start position:0%
+actually they have accelerometers
+ 
+
+ align:start position:0%
+actually they have accelerometers
+built-in to all expensive rotating
+
+ align:start position:0%
+built-in to all expensive rotating
+ 
+
+ align:start position:0%
+built-in to all expensive rotating
+equipment these days it's called
+
+ align:start position:0%
+equipment these days it's called
+ 
+
+ align:start position:0%
+equipment these days it's called
+condition monitoring and when they get
+
+ align:start position:0%
+condition monitoring and when they get
+ 
+
+ align:start position:0%
+condition monitoring and when they get
+outside of certain limits
+
+ align:start position:0%
+outside of certain limits
+ 
+
+ align:start position:0%
+outside of certain limits
+shut the thing down and rebuild it
+
+ align:start position:0%
+shut the thing down and rebuild it
+ 
+
+ align:start position:0%
+shut the thing down and rebuild it
+electric generator sets gas turbines jet
+
+ align:start position:0%
+electric generator sets gas turbines jet
+ 
+
+ align:start position:0%
+electric generator sets gas turbines jet
+engines on all aircraft are all
+
+ align:start position:0%
+engines on all aircraft are all
+ 
+
+ align:start position:0%
+engines on all aircraft are all
+incredibly carefully balancing they
+
+ align:start position:0%
+incredibly carefully balancing they
+ 
+
+ align:start position:0%
+incredibly carefully balancing they
+start getting out of balance they stop
+
+ align:start position:0%
+start getting out of balance they stop
+ 
+
+ align:start position:0%
+start getting out of balance they stop
+and fix them before the things blow up
+
+ align:start position:0%
+and fix them before the things blow up
+ 
+
+ align:start position:0%
+and fix them before the things blow up
+on them and you have a 20 million dollar
+
+ align:start position:0%
+on them and you have a 20 million dollar
+ 
+
+ align:start position:0%
+on them and you have a 20 million dollar
+problem instead of maybe if $20,000
+
+ align:start position:0%
+problem instead of maybe if $20,000
+ 
+
+ align:start position:0%
+problem instead of maybe if $20,000
+teardown alright so yeah if you fix the
+
+ align:start position:0%
+teardown alright so yeah if you fix the
+ 
+
+ align:start position:0%
+teardown alright so yeah if you fix the
+rotor third idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well could you this thing shaking like
+
+ align:start position:0%
+well could you this thing shaking like
+ 
+
+ align:start position:0%
+well could you this thing shaking like
+crazy what if you put it what if you
+
+ align:start position:0%
+crazy what if you put it what if you
+ 
+
+ align:start position:0%
+crazy what if you put it what if you
+change the length of this beam would it
+
+ align:start position:0%
+change the length of this beam would it
+ 
+
+ align:start position:0%
+change the length of this beam would it
+could you stop this thing from shaking
+
+ align:start position:0%
+could you stop this thing from shaking
+ 
+
+ align:start position:0%
+could you stop this thing from shaking
+so much if you stop this I'm shaking so
+
+ align:start position:0%
+so much if you stop this I'm shaking so
+ 
+
+ align:start position:0%
+so much if you stop this I'm shaking so
+much what it puts so much excitation
+
+ align:start position:0%
+much what it puts so much excitation
+ 
+
+ align:start position:0%
+much what it puts so much excitation
+into the table no so treat fix the rotor
+
+ align:start position:0%
+into the table no so treat fix the rotor
+ 
+
+ align:start position:0%
+into the table no so treat fix the rotor
+isolate the source isolate the receiver
+
+ align:start position:0%
+isolate the source isolate the receiver
+ 
+
+ align:start position:0%
+isolate the source isolate the receiver
+now you get at least three ways and the
+
+ align:start position:0%
+now you get at least three ways and the
+ 
+
+ align:start position:0%
+now you get at least three ways and the
+gentleman up here came up with a fourth
+
+ align:start position:0%
+gentleman up here came up with a fourth
+ 
+
+ align:start position:0%
+gentleman up here came up with a fourth
+way active cancellation okay great so
+
+ align:start position:0%
+way active cancellation okay great so
+ 
+
+ align:start position:0%
+way active cancellation okay great so
+let's I have a demo of one of these
+
+ align:start position:0%
+let's I have a demo of one of these
+ 
+
+ align:start position:0%
+let's I have a demo of one of these
+sometimes if you're desperate you're
+
+ align:start position:0%
+sometimes if you're desperate you're
+ 
+
+ align:start position:0%
+sometimes if you're desperate you're
+trying to get some sleep in onto your
+
+ align:start position:0%
+trying to get some sleep in onto your
+ 
+
+ align:start position:0%
+trying to get some sleep in onto your
+bed that's rattling or something you
+
+ align:start position:0%
+bed that's rattling or something you
+ 
+
+ align:start position:0%
+bed that's rattling or something you
+might want to try the following that you
+
+ align:start position:0%
+might want to try the following that you
+ 
+
+ align:start position:0%
+might want to try the following that you
+can do very quickly so we'll dim the
+
+ align:start position:0%
+can do very quickly so we'll dim the
+ 
+
+ align:start position:0%
+can do very quickly so we'll dim the
+lights again we'll turn it back on both
+
+ align:start position:0%
+lights again we'll turn it back on both
+ 
+
+ align:start position:0%
+lights again we'll turn it back on both
+of these things are both are vibrating
+
+ align:start position:0%
+of these things are both are vibrating
+ 
+
+ align:start position:0%
+of these things are both are vibrating
+like crazy alright so one way to detune
+
+ align:start position:0%
+like crazy alright so one way to detune
+ 
+
+ align:start position:0%
+like crazy alright so one way to detune
+the receiver is to put a big weight on
+
+ align:start position:0%
+the receiver is to put a big weight on
+ 
+
+ align:start position:0%
+the receiver is to put a big weight on
+it and change its natural frequency by
+
+ align:start position:0%
+it and change its natural frequency by
+ 
+
+ align:start position:0%
+it and change its natural frequency by
+changing the mass and now the little
+
+ align:start position:0%
+changing the mass and now the little
+ 
+
+ align:start position:0%
+changing the mass and now the little
+thing is hardly shaking at all because
+
+ align:start position:0%
+thing is hardly shaking at all because
+ 
+
+ align:start position:0%
+thing is hardly shaking at all because
+I've detuned it just by switch it's
+
+ align:start position:0%
+I've detuned it just by switch it's
+ 
+
+ align:start position:0%
+I've detuned it just by switch it's
+changing the mass accomplish the same
+
+ align:start position:0%
+changing the mass accomplish the same
+ 
+
+ align:start position:0%
+changing the mass accomplish the same
+thing as change switching the length
+
+ align:start position:0%
+thing as change switching the length
+ 
+
+ align:start position:0%
+thing as change switching the length
+instead of messing with the stiffness
+
+ align:start position:0%
+instead of messing with the stiffness
+ 
+
+ align:start position:0%
+instead of messing with the stiffness
+I've changed the massive system this is
+
+ align:start position:0%
+I've changed the massive system this is
+ 
+
+ align:start position:0%
+I've changed the massive system this is
+still shaking like crazy okay so now
+
+ align:start position:0%
+still shaking like crazy okay so now
+ 
+
+ align:start position:0%
+still shaking like crazy okay so now
+it's back to vibrating again but over
+
+ align:start position:0%
+it's back to vibrating again but over
+ 
+
+ align:start position:0%
+it's back to vibrating again but over
+here is my source I don't know if it'll
+
+ align:start position:0%
+here is my source I don't know if it'll
+ 
+
+ align:start position:0%
+here is my source I don't know if it'll
+work so well in this one because this is
+
+ align:start position:0%
+work so well in this one because this is
+ 
+
+ align:start position:0%
+work so well in this one because this is
+that the source is a lot more massive
+
+ align:start position:0%
+that the source is a lot more massive
+ 
+
+ align:start position:0%
+that the source is a lot more massive
+but I need to put the same mass on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but made it worse
+
+ align:start position:0%
+but made it worse
+ 
+
+ align:start position:0%
+but made it worse
+ah and that's another good demonstration
+
+ align:start position:0%
+ah and that's another good demonstration
+ 
+
+ align:start position:0%
+ah and that's another good demonstration
+excellent so we could come up back up
+
+ align:start position:0%
+excellent so we could come up back up
+ 
+
+ align:start position:0%
+excellent so we could come up back up
+with the lights you got to be careful of
+
+ align:start position:0%
+with the lights you got to be careful of
+ 
+
+ align:start position:0%
+with the lights you got to be careful of
+that you go to mess with one of these
+
+ align:start position:0%
+that you go to mess with one of these
+ 
+
+ align:start position:0%
+that you go to mess with one of these
+systems if you do it wrong you make the
+
+ align:start position:0%
+systems if you do it wrong you make the
+ 
+
+ align:start position:0%
+systems if you do it wrong you make the
+matter worse first consulting job ever
+
+ align:start position:0%
+matter worse first consulting job ever
+ 
+
+ align:start position:0%
+matter worse first consulting job ever
+had back in 1977 or something like that
+
+ align:start position:0%
+had back in 1977 or something like that
+ 
+
+ align:start position:0%
+had back in 1977 or something like that
+they had a vibration problem on a ship
+
+ align:start position:0%
+they had a vibration problem on a ship
+ 
+
+ align:start position:0%
+they had a vibration problem on a ship
+and the first consultant in said stiffen
+
+ align:start position:0%
+and the first consultant in said stiffen
+ 
+
+ align:start position:0%
+and the first consultant in said stiffen
+up it was actually the exhaust stacks on
+
+ align:start position:0%
+up it was actually the exhaust stacks on
+ 
+
+ align:start position:0%
+up it was actually the exhaust stacks on
+these 5,000 horsepower diesel engines
+
+ align:start position:0%
+these 5,000 horsepower diesel engines
+ 
+
+ align:start position:0%
+these 5,000 horsepower diesel engines
+and they were 30 feet tall and shaking
+
+ align:start position:0%
+and they were 30 feet tall and shaking
+ 
+
+ align:start position:0%
+and they were 30 feet tall and shaking
+like crazy and the first guy said
+
+ align:start position:0%
+like crazy and the first guy said
+ 
+
+ align:start position:0%
+like crazy and the first guy said
+stiffen up those exhaust stacks and he
+
+ align:start position:0%
+stiffen up those exhaust stacks and he
+ 
+
+ align:start position:0%
+stiffen up those exhaust stacks and he
+did exactly the wrong thing and it just
+
+ align:start position:0%
+did exactly the wrong thing and it just
+ 
+
+ align:start position:0%
+did exactly the wrong thing and it just
+shook like worse than ever
+
+ align:start position:0%
+shook like worse than ever
+ 
+
+ align:start position:0%
+shook like worse than ever
+okay so now what what I'm going to show
+
+ align:start position:0%
+okay so now what what I'm going to show
+ 
+
+ align:start position:0%
+okay so now what what I'm going to show
+you will put on the board today is a
+
+ align:start position:0%
+you will put on the board today is a
+ 
+
+ align:start position:0%
+you will put on the board today is a
+little bit of mathematics to back up how
+
+ align:start position:0%
+little bit of mathematics to back up how
+ 
+
+ align:start position:0%
+little bit of mathematics to back up how
+you go about doing the two things one is
+
+ align:start position:0%
+you go about doing the two things one is
+ 
+
+ align:start position:0%
+you go about doing the two things one is
+isolating the receiver or the other ones
+
+ align:start position:0%
+isolating the receiver or the other ones
+ 
+
+ align:start position:0%
+isolating the receiver or the other ones
+isolating the source it will start going
+
+ align:start position:0%
+isolating the source it will start going
+ 
+
+ align:start position:0%
+isolating the source it will start going
+to start with isolating the receiver but
+
+ align:start position:0%
+to start with isolating the receiver but
+ 
+
+ align:start position:0%
+to start with isolating the receiver but
+we're going to start with a little bit
+
+ align:start position:0%
+we're going to start with a little bit
+ 
+
+ align:start position:0%
+we're going to start with a little bit
+of math a little math tool that we need
+
+ align:start position:0%
+of math a little math tool that we need
+ 
+
+ align:start position:0%
+of math a little math tool that we need
+that'll make life a lot easier for us
+
+ align:start position:0%
+that'll make life a lot easier for us
+ 
+
+ align:start position:0%
+that'll make life a lot easier for us
+maybe I'll work here if you recall last
+
+ align:start position:0%
+maybe I'll work here if you recall last
+ 
+
+ align:start position:0%
+maybe I'll work here if you recall last
+time that would be the time to do it we
+
+ align:start position:0%
+time that would be the time to do it we
+ 
+
+ align:start position:0%
+time that would be the time to do it we
+derived the transfer function for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially this system where we had an
+
+ align:start position:0%
+essentially this system where we had an
+ 
+
+ align:start position:0%
+essentially this system where we had an
+F naught cosine Omega T and we computed
+
+ align:start position:0%
+F naught cosine Omega T and we computed
+ 
+
+ align:start position:0%
+F naught cosine Omega T and we computed
+the response X of T at some X naught
+
+ align:start position:0%
+the response X of T at some X naught
+ 
+
+ align:start position:0%
+the response X of T at some X naught
+cosine Omega T - a phase angle and we
+
+ align:start position:0%
+cosine Omega T - a phase angle and we
+ 
+
+ align:start position:0%
+cosine Omega T - a phase angle and we
+worked it all down to where we could
+
+ align:start position:0%
+worked it all down to where we could
+ 
+
+ align:start position:0%
+worked it all down to where we could
+plot it like that but you know quite
+
+ align:start position:0%
+plot it like that but you know quite
+ 
+
+ align:start position:0%
+plot it like that but you know quite
+frankly I mean I'd it was kind of a lot
+
+ align:start position:0%
+frankly I mean I'd it was kind of a lot
+ 
+
+ align:start position:0%
+frankly I mean I'd it was kind of a lot
+of lines of math and it was sort of
+
+ align:start position:0%
+of lines of math and it was sort of
+ 
+
+ align:start position:0%
+of lines of math and it was sort of
+painful I actually hated doing it on the
+
+ align:start position:0%
+painful I actually hated doing it on the
+ 
+
+ align:start position:0%
+painful I actually hated doing it on the
+board but it was easy because it was
+
+ align:start position:0%
+board but it was easy because it was
+ 
+
+ align:start position:0%
+board but it was easy because it was
+familiar it's just trig stuff it was all
+
+ align:start position:0%
+familiar it's just trig stuff it was all
+ 
+
+ align:start position:0%
+familiar it's just trig stuff it was all
+trig and a little bit of calculus and so
+
+ align:start position:0%
+trig and a little bit of calculus and so
+ 
+
+ align:start position:0%
+trig and a little bit of calculus and so
+we do that first because it all makes
+
+ align:start position:0%
+we do that first because it all makes
+ 
+
+ align:start position:0%
+we do that first because it all makes
+sense to you mathematically but there's
+
+ align:start position:0%
+sense to you mathematically but there's
+ 
+
+ align:start position:0%
+sense to you mathematically but there's
+a vastly easier and quicker way to do
+
+ align:start position:0%
+a vastly easier and quicker way to do
+ 
+
+ align:start position:0%
+a vastly easier and quicker way to do
+this which we'll address right now and
+
+ align:start position:0%
+this which we'll address right now and
+ 
+
+ align:start position:0%
+this which we'll address right now and
+that's using complex numbers and the so
+
+ align:start position:0%
+that's using complex numbers and the so
+ 
+
+ align:start position:0%
+that's using complex numbers and the so
+we'll we need a couple of bits of
+
+ align:start position:0%
+we'll we need a couple of bits of
+ 
+
+ align:start position:0%
+we'll we need a couple of bits of
+information here one is Euler's formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you have e raised to the power I
+
+ align:start position:0%
+so if you have e raised to the power I
+ 
+
+ align:start position:0%
+so if you have e raised to the power I
+theta you can show that that is the same
+
+ align:start position:0%
+theta you can show that that is the same
+ 
+
+ align:start position:0%
+theta you can show that that is the same
+thing as cosine theta plus I sine of
+
+ align:start position:0%
+thing as cosine theta plus I sine of
+ 
+
+ align:start position:0%
+thing as cosine theta plus I sine of
+theta that breaks into a real part and
+
+ align:start position:0%
+theta that breaks into a real part and
+ 
+
+ align:start position:0%
+theta that breaks into a real part and
+an imaginary part okay so we wanted to
+
+ align:start position:0%
+an imaginary part okay so we wanted to
+ 
+
+ align:start position:0%
+an imaginary part okay so we wanted to
+express this excitation F naught cosine
+
+ align:start position:0%
+express this excitation F naught cosine
+ 
+
+ align:start position:0%
+express this excitation F naught cosine
+Omega T in complex notation we would say
+
+ align:start position:0%
+Omega T in complex notation we would say
+ 
+
+ align:start position:0%
+Omega T in complex notation we would say
+it is the real part which I denote as re
+
+ align:start position:0%
+it is the real part which I denote as re
+ 
+
+ align:start position:0%
+it is the real part which I denote as re
+the real part of F naught e to the I
+
+ align:start position:0%
+the real part of F naught e to the I
+ 
+
+ align:start position:0%
+the real part of F naught e to the I
+Omega T and I'm going to dispense Phi
+
+ align:start position:0%
+Omega T and I'm going to dispense Phi
+ 
+
+ align:start position:0%
+Omega T and I'm going to dispense Phi
+that F naught itself here this is real
+
+ align:start position:0%
+that F naught itself here this is real
+ 
+
+ align:start position:0%
+that F naught itself here this is real
+and positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this this is real and positive so the
+
+ align:start position:0%
+so this this is real and positive so the
+ 
+
+ align:start position:0%
+so this this is real and positive so the
+real part is going to be f naught x and
+
+ align:start position:0%
+real part is going to be f naught x and
+ 
+
+ align:start position:0%
+real part is going to be f naught x and
+if you break down code e to the I Omega
+
+ align:start position:0%
+if you break down code e to the I Omega
+ 
+
+ align:start position:0%
+if you break down code e to the I Omega
+T into its by Euler's formula it gives
+
+ align:start position:0%
+T into its by Euler's formula it gives
+ 
+
+ align:start position:0%
+T into its by Euler's formula it gives
+you cosine Omega T plus I sine Omega T
+
+ align:start position:0%
+you cosine Omega T plus I sine Omega T
+ 
+
+ align:start position:0%
+you cosine Omega T plus I sine Omega T
+and the real part is the cosine part
+
+ align:start position:0%
+and the real part is the cosine part
+ 
+
+ align:start position:0%
+and the real part is the cosine part
+just according to this okay now another
+
+ align:start position:0%
+just according to this okay now another
+ 
+
+ align:start position:0%
+just according to this okay now another
+little fact that I want to show you is
+
+ align:start position:0%
+little fact that I want to show you is
+ 
+
+ align:start position:0%
+little fact that I want to show you is
+if you have a complex number A plus bi I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want to express it as sum c e to the I
+
+ align:start position:0%
+want to express it as sum c e to the I
+ 
+
+ align:start position:0%
+want to express it as sum c e to the I
+theta you want to use Euler's formula to
+
+ align:start position:0%
+theta you want to use Euler's formula to
+ 
+
+ align:start position:0%
+theta you want to use Euler's formula to
+express a complex number and if we draw
+
+ align:start position:0%
+express a complex number and if we draw
+ 
+
+ align:start position:0%
+express a complex number and if we draw
+it the answer becomes pretty obvious
+
+ align:start position:0%
+it the answer becomes pretty obvious
+ 
+
+ align:start position:0%
+it the answer becomes pretty obvious
+this is a point up here a bi this is
+
+ align:start position:0%
+this is a point up here a bi this is
+ 
+
+ align:start position:0%
+this is a point up here a bi this is
+imaginary axis here and the real and
+
+ align:start position:0%
+imaginary axis here and the real and
+ 
+
+ align:start position:0%
+imaginary axis here and the real and
+this point this side is a and this side
+
+ align:start position:0%
+this point this side is a and this side
+ 
+
+ align:start position:0%
+this point this side is a and this side
+here is B and this side here the length
+
+ align:start position:0%
+here is B and this side here the length
+ 
+
+ align:start position:0%
+here is B and this side here the length
+of this triangle is C and the angle in
+
+ align:start position:0%
+of this triangle is C and the angle in
+ 
+
+ align:start position:0%
+of this triangle is C and the angle in
+here is Theta so now if I ask you what's
+
+ align:start position:0%
+here is Theta so now if I ask you what's
+ 
+
+ align:start position:0%
+here is Theta so now if I ask you what's
+C we say oh well C is obviously the
+
+ align:start position:0%
+C we say oh well C is obviously the
+ 
+
+ align:start position:0%
+C we say oh well C is obviously the
+square root of a squared plus B squared
+
+ align:start position:0%
+square root of a squared plus B squared
+ 
+
+ align:start position:0%
+square root of a squared plus B squared
+and theta is a tangent inverse of B over
+
+ align:start position:0%
+and theta is a tangent inverse of B over
+ 
+
+ align:start position:0%
+and theta is a tangent inverse of B over
+a which is the imaginary part over the
+
+ align:start position:0%
+a which is the imaginary part over the
+ 
+
+ align:start position:0%
+a which is the imaginary part over the
+real part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now you can set if you want to
+
+ align:start position:0%
+okay so now you can set if you want to
+ 
+
+ align:start position:0%
+okay so now you can set if you want to
+express a complex number this way well
+
+ align:start position:0%
+express a complex number this way well
+ 
+
+ align:start position:0%
+express a complex number this way well
+the magnitude is square root of a
+
+ align:start position:0%
+the magnitude is square root of a
+ 
+
+ align:start position:0%
+the magnitude is square root of a
+squared plus B squared and the phase
+
+ align:start position:0%
+squared plus B squared and the phase
+ 
+
+ align:start position:0%
+squared plus B squared and the phase
+angle that you put up here is tangent
+
+ align:start position:0%
+angle that you put up here is tangent
+ 
+
+ align:start position:0%
+angle that you put up here is tangent
+inverse of the imaginary part over the
+
+ align:start position:0%
+inverse of the imaginary part over the
+ 
+
+ align:start position:0%
+inverse of the imaginary part over the
+real okay so now we have the basic tools
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we need to take on the vibration problem
+
+ align:start position:0%
+we need to take on the vibration problem
+ 
+
+ align:start position:0%
+we need to take on the vibration problem
+and so we have that system up there and
+
+ align:start position:0%
+and so we have that system up there and
+ 
+
+ align:start position:0%
+and so we have that system up there and
+our output from the way we derived it
+
+ align:start position:0%
+our output from the way we derived it
+ 
+
+ align:start position:0%
+our output from the way we derived it
+last time the output is some X naught
+
+ align:start position:0%
+last time the output is some X naught
+ 
+
+ align:start position:0%
+last time the output is some X naught
+cosine Omega t minus fee
+
+ align:start position:0%
+cosine Omega t minus fee
+ 
+
+ align:start position:0%
+cosine Omega t minus fee
+one of the reasons it was so painful
+
+ align:start position:0%
+one of the reasons it was so painful
+ 
+
+ align:start position:0%
+one of the reasons it was so painful
+doing it this way last time is you have
+
+ align:start position:0%
+doing it this way last time is you have
+ 
+
+ align:start position:0%
+doing it this way last time is you have
+to this is cosine as a functionable time
+
+ align:start position:0%
+to this is cosine as a functionable time
+ 
+
+ align:start position:0%
+to this is cosine as a functionable time
+and phase and to break it apart takes a
+
+ align:start position:0%
+and phase and to break it apart takes a
+ 
+
+ align:start position:0%
+and phase and to break it apart takes a
+lot of work so we want to do the same
+
+ align:start position:0%
+lot of work so we want to do the same
+ 
+
+ align:start position:0%
+lot of work so we want to do the same
+thing but with complex variables this
+
+ align:start position:0%
+thing but with complex variables this
+ 
+
+ align:start position:0%
+thing but with complex variables this
+time so I want to express this then as
+
+ align:start position:0%
+time so I want to express this then as
+ 
+
+ align:start position:0%
+time so I want to express this then as
+the real part of I could say it's the
+
+ align:start position:0%
+the real part of I could say it's the
+ 
+
+ align:start position:0%
+the real part of I could say it's the
+real part of X naught e to the I Omega t
+
+ align:start position:0%
+real part of X naught e to the I Omega t
+ 
+
+ align:start position:0%
+real part of X naught e to the I Omega t
+minus V and just by Euler's formula if
+
+ align:start position:0%
+minus V and just by Euler's formula if
+ 
+
+ align:start position:0%
+minus V and just by Euler's formula if
+this is real just a number then this
+
+ align:start position:0%
+this is real just a number then this
+ 
+
+ align:start position:0%
+this is real just a number then this
+breaks down into cosine Omega t minus V
+
+ align:start position:0%
+breaks down into cosine Omega t minus V
+ 
+
+ align:start position:0%
+breaks down into cosine Omega t minus V
+and I sine Omega T mine
+
+ align:start position:0%
+and I sine Omega T mine
+ 
+
+ align:start position:0%
+and I sine Omega T mine
+minus V but here's the beauty of using
+
+ align:start position:0%
+minus V but here's the beauty of using
+ 
+
+ align:start position:0%
+minus V but here's the beauty of using
+complex notation and Exponential's this
+
+ align:start position:0%
+complex notation and Exponential's this
+ 
+
+ align:start position:0%
+complex notation and Exponential's this
+now becomes the real part of X naught e
+
+ align:start position:0%
+now becomes the real part of X naught e
+ 
+
+ align:start position:0%
+now becomes the real part of X naught e
+to the minus I P times e to the I Omega
+
+ align:start position:0%
+to the minus I P times e to the I Omega
+ 
+
+ align:start position:0%
+to the minus I P times e to the I Omega
+T I can separate these two and this is
+
+ align:start position:0%
+T I can separate these two and this is
+ 
+
+ align:start position:0%
+T I can separate these two and this is
+what makes it so much easier to use this
+
+ align:start position:0%
+what makes it so much easier to use this
+ 
+
+ align:start position:0%
+what makes it so much easier to use this
+approach and I'm going to call
+
+ align:start position:0%
+approach and I'm going to call
+ 
+
+ align:start position:0%
+approach and I'm going to call
+this part of it just some capital X and
+
+ align:start position:0%
+this part of it just some capital X and
+ 
+
+ align:start position:0%
+this part of it just some capital X and
+it is a complex number for sure I break
+
+ align:start position:0%
+it is a complex number for sure I break
+ 
+
+ align:start position:0%
+it is a complex number for sure I break
+this up into cosine V cosine of minus V
+
+ align:start position:0%
+this up into cosine V cosine of minus V
+ 
+
+ align:start position:0%
+this up into cosine V cosine of minus V
+and minus I sine V it's got an IEEE sign
+
+ align:start position:0%
+and minus I sine V it's got an IEEE sign
+ 
+
+ align:start position:0%
+and minus I sine V it's got an IEEE sign
+fees this got this is a complex number a
+
+ align:start position:0%
+fees this got this is a complex number a
+ 
+
+ align:start position:0%
+fees this got this is a complex number a
++ bi kind of form so in general this
+
+ align:start position:0%
++ bi kind of form so in general this
+ 
+
+ align:start position:0%
++ bi kind of form so in general this
+thing is complex so this whole thing is
+
+ align:start position:0%
+thing is complex so this whole thing is
+ 
+
+ align:start position:0%
+thing is complex so this whole thing is
+the real part of some X which I don't
+
+ align:start position:0%
+the real part of some X which I don't
+ 
+
+ align:start position:0%
+the real part of some X which I don't
+know now e to the I Omega T so now we
+
+ align:start position:0%
+know now e to the I Omega T so now we
+ 
+
+ align:start position:0%
+know now e to the I Omega T so now we
+can quickly quite quickly do this the
+
+ align:start position:0%
+can quickly quite quickly do this the
+ 
+
+ align:start position:0%
+can quickly quite quickly do this the
+derivation we did last time we're
+
+ align:start position:0%
+derivation we did last time we're
+ 
+
+ align:start position:0%
+derivation we did last time we're
+talking about representing linear
+
+ align:start position:0%
+talking about representing linear
+ 
+
+ align:start position:0%
+talking about representing linear
+systems by some kind of black box as a
+
+ align:start position:0%
+systems by some kind of black box as a
+ 
+
+ align:start position:0%
+systems by some kind of black box as a
+transfer function in it which we call H
+
+ align:start position:0%
+transfer function in it which we call H
+ 
+
+ align:start position:0%
+transfer function in it which we call H
+in this case X F response X per unit
+
+ align:start position:0%
+in this case X F response X per unit
+ 
+
+ align:start position:0%
+in this case X F response X per unit
+input F remember we're talking about
+
+ align:start position:0%
+input F remember we're talking about
+ 
+
+ align:start position:0%
+input F remember we're talking about
+steady state response only and we have
+
+ align:start position:0%
+steady state response only and we have
+ 
+
+ align:start position:0%
+steady state response only and we have
+as our input here some F naught e to the
+
+ align:start position:0%
+as our input here some F naught e to the
+ 
+
+ align:start position:0%
+as our input here some F naught e to the
+I Omega T and we have as an output some
+
+ align:start position:0%
+I Omega T and we have as an output some
+ 
+
+ align:start position:0%
+I Omega T and we have as an output some
+X e to the I Omega T we know that we're
+
+ align:start position:0%
+X e to the I Omega T we know that we're
+ 
+
+ align:start position:0%
+X e to the I Omega T we know that we're
+going to use the convention that we care
+
+ align:start position:0%
+going to use the convention that we care
+ 
+
+ align:start position:0%
+going to use the convention that we care
+about this is we have to have real
+
+ align:start position:0%
+about this is we have to have real
+ 
+
+ align:start position:0%
+about this is we have to have real
+answers real number answers so we'll be
+
+ align:start position:0%
+answers real number answers so we'll be
+ 
+
+ align:start position:0%
+answers real number answers so we'll be
+using eventually to be actually using
+
+ align:start position:0%
+using eventually to be actually using
+ 
+
+ align:start position:0%
+using eventually to be actually using
+the real part of the input and the real
+
+ align:start position:0%
+the real part of the input and the real
+ 
+
+ align:start position:0%
+the real part of the input and the real
+part of the output but to get there
+
+ align:start position:0%
+part of the output but to get there
+ 
+
+ align:start position:0%
+part of the output but to get there
+we're going to use complex notation
+
+ align:start position:0%
+we're going to use complex notation
+ 
+
+ align:start position:0%
+we're going to use complex notation
+first and separate out the real and
+
+ align:start position:0%
+first and separate out the real and
+ 
+
+ align:start position:0%
+first and separate out the real and
+imaginary parts at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for our system it we know the
+
+ align:start position:0%
+so for our system it we know the
+ 
+
+ align:start position:0%
+so for our system it we know the
+equation of motion so now it's some F
+
+ align:start position:0%
+equation of motion so now it's some F
+ 
+
+ align:start position:0%
+equation of motion so now it's some F
+naught e to the I Omega T there's our
+
+ align:start position:0%
+naught e to the I Omega T there's our
+ 
+
+ align:start position:0%
+naught e to the I Omega T there's our
+equation of motion and I'm going to let
+
+ align:start position:0%
+equation of motion and I'm going to let
+ 
+
+ align:start position:0%
+equation of motion and I'm going to let
+X here be this unknown capital X e to
+
+ align:start position:0%
+X here be this unknown capital X e to
+ 
+
+ align:start position:0%
+X here be this unknown capital X e to
+the I Omega T and I'm going to plug it
+
+ align:start position:0%
+the I Omega T and I'm going to plug it
+ 
+
+ align:start position:0%
+the I Omega T and I'm going to plug it
+in and the Exponential's are
+
+ align:start position:0%
+in and the Exponential's are
+ 
+
+ align:start position:0%
+in and the Exponential's are
+particularly easy to deal with when
+
+ align:start position:0%
+particularly easy to deal with when
+ 
+
+ align:start position:0%
+particularly easy to deal with when
+you're taking derivatives so upon doing
+
+ align:start position:0%
+you're taking derivatives so upon doing
+ 
+
+ align:start position:0%
+you're taking derivatives so upon doing
+that we immediately get minus Omega
+
+ align:start position:0%
+that we immediately get minus Omega
+ 
+
+ align:start position:0%
+that we immediately get minus Omega
+squared M plus I Omega C plus K all of
+
+ align:start position:0%
+squared M plus I Omega C plus K all of
+ 
+
+ align:start position:0%
+squared M plus I Omega C plus K all of
+that times X e to the I Omega T equals F
+
+ align:start position:0%
+that times X e to the I Omega T equals F
+ 
+
+ align:start position:0%
+that times X e to the I Omega T equals F
+naught e to the I Omega T and right
+
+ align:start position:0%
+naught e to the I Omega T and right
+ 
+
+ align:start position:0%
+naught e to the I Omega T and right
+immediately I can get rid of the
+
+ align:start position:0%
+immediately I can get rid of the
+ 
+
+ align:start position:0%
+immediately I can get rid of the
+time-dependent parts and I can solve for
+
+ align:start position:0%
+time-dependent parts and I can solve for
+ 
+
+ align:start position:0%
+time-dependent parts and I can solve for
+x over F which is what we went out we'll
+
+ align:start position:0%
+x over F which is what we went out we'll
+ 
+
+ align:start position:0%
+x over F which is what we went out we'll
+set out to do the other day to find this
+
+ align:start position:0%
+set out to do the other day to find this
+ 
+
+ align:start position:0%
+set out to do the other day to find this
+transfer function between input and
+
+ align:start position:0%
+transfer function between input and
+ 
+
+ align:start position:0%
+transfer function between input and
+output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm if I solve for X divided by F I'm
+
+ align:start position:0%
+so I'm if I solve for X divided by F I'm
+ 
+
+ align:start position:0%
+so I'm if I solve for X divided by F I'm
+going to get all this stuff in the
+
+ align:start position:0%
+going to get all this stuff in the
+ 
+
+ align:start position:0%
+going to get all this stuff in the
+denominator on one side and I'll write
+
+ align:start position:0%
+denominator on one side and I'll write
+ 
+
+ align:start position:0%
+denominator on one side and I'll write
+it out here simply looks like that and
+
+ align:start position:0%
+it out here simply looks like that and
+ 
+
+ align:start position:0%
+it out here simply looks like that and
+now remember I can substitute in some
+
+ align:start position:0%
+now remember I can substitute in some
+ 
+
+ align:start position:0%
+now remember I can substitute in some
+things remember K over m is Omega N
+
+ align:start position:0%
+things remember K over m is Omega N
+ 
+
+ align:start position:0%
+things remember K over m is Omega N
+squared and Zeta is C over 2 Omega n M I
+
+ align:start position:0%
+squared and Zeta is C over 2 Omega n M I
+ 
+
+ align:start position:0%
+squared and Zeta is C over 2 Omega n M I
+plug those things in and just rearrange
+
+ align:start position:0%
+plug those things in and just rearrange
+ 
+
+ align:start position:0%
+plug those things in and just rearrange
+it a little tiny bit well we come up we
+
+ align:start position:0%
+it a little tiny bit well we come up we
+ 
+
+ align:start position:0%
+it a little tiny bit well we come up we
+should come up with something like we
+
+ align:start position:0%
+should come up with something like we
+ 
+
+ align:start position:0%
+should come up with something like we
+found before so that x over F 1 over K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denominator 1 minus Omega squared over
+
+ align:start position:0%
+denominator 1 minus Omega squared over
+ 
+
+ align:start position:0%
+denominator 1 minus Omega squared over
+Omega N squared
+
+ align:start position:0%
+Omega N squared
+ 
+
+ align:start position:0%
+Omega N squared
+not quite yet here plus 2i Zeta Omega
+
+ align:start position:0%
+not quite yet here plus 2i Zeta Omega
+ 
+
+ align:start position:0%
+not quite yet here plus 2i Zeta Omega
+over Omega n that's what it looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you still have a complex denominator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this basically looks like a number 1
+
+ align:start position:0%
+and this basically looks like a number 1
+ 
+
+ align:start position:0%
+and this basically looks like a number 1
+over K times 1 over some a plus bi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a term it should be i-10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I multiply and the way you deal with
+
+ align:start position:0%
+if I multiply and the way you deal with
+ 
+
+ align:start position:0%
+if I multiply and the way you deal with
+something like this you have an A plus
+
+ align:start position:0%
+something like this you have an A plus
+ 
+
+ align:start position:0%
+something like this you have an A plus
+bi in the denominator you multiply the
+
+ align:start position:0%
+bi in the denominator you multiply the
+ 
+
+ align:start position:0%
+bi in the denominator you multiply the
+numerator and denominator by the complex
+
+ align:start position:0%
+numerator and denominator by the complex
+ 
+
+ align:start position:0%
+numerator and denominator by the complex
+conjugate I want to get this into
+
+ align:start position:0%
+conjugate I want to get this into
+ 
+
+ align:start position:0%
+conjugate I want to get this into
+actually standard a plus bi form
+
+ align:start position:0%
+actually standard a plus bi form
+ 
+
+ align:start position:0%
+actually standard a plus bi form
+so I can if I do that symbolically here
+
+ align:start position:0%
+so I can if I do that symbolically here
+ 
+
+ align:start position:0%
+so I can if I do that symbolically here
+it comes out looking like a minus bi
+
+ align:start position:0%
+it comes out looking like a minus bi
+ 
+
+ align:start position:0%
+it comes out looking like a minus bi
+over a squared plus B squared that's 1
+
+ align:start position:0%
+over a squared plus B squared that's 1
+ 
+
+ align:start position:0%
+over a squared plus B squared that's 1
+over K e to the minus I fee over a
+
+ align:start position:0%
+over K e to the minus I fee over a
+ 
+
+ align:start position:0%
+over K e to the minus I fee over a
+square root of a squared plus B squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because now see this is just a real
+
+ align:start position:0%
+because now see this is just a real
+ 
+
+ align:start position:0%
+because now see this is just a real
+denominator is just a real number so
+
+ align:start position:0%
+denominator is just a real number so
+ 
+
+ align:start position:0%
+denominator is just a real number so
+this whole thing is in some form c plus
+
+ align:start position:0%
+this whole thing is in some form c plus
+ 
+
+ align:start position:0%
+this whole thing is in some form c plus
+a di account you could break this into a
+
+ align:start position:0%
+a di account you could break this into a
+ 
+
+ align:start position:0%
+a di account you could break this into a
+real part complex part we could say
+
+ align:start position:0%
+real part complex part we could say
+ 
+
+ align:start position:0%
+real part complex part we could say
+that's equal to some magnitude times a
+
+ align:start position:0%
+that's equal to some magnitude times a
+ 
+
+ align:start position:0%
+that's equal to some magnitude times a
+eetu the I fee and the magnitude to get
+
+ align:start position:0%
+eetu the I fee and the magnitude to get
+ 
+
+ align:start position:0%
+eetu the I fee and the magnitude to get
+the magnitude you multiply they you take
+
+ align:start position:0%
+the magnitude you multiply they you take
+ 
+
+ align:start position:0%
+the magnitude you multiply they you take
+a squared plus b squared square root it
+
+ align:start position:0%
+a squared plus b squared square root it
+ 
+
+ align:start position:0%
+a squared plus b squared square root it
+cancels this is this is squared the
+
+ align:start position:0%
+cancels this is this is squared the
+ 
+
+ align:start position:0%
+cancels this is this is squared the
+denominator to end up with this part
+
+ align:start position:0%
+denominator to end up with this part
+ 
+
+ align:start position:0%
+denominator to end up with this part
+square root in the denominator this is
+
+ align:start position:0%
+square root in the denominator this is
+ 
+
+ align:start position:0%
+square root in the denominator this is
+what the we need to know what fee looks
+
+ align:start position:0%
+what the we need to know what fee looks
+ 
+
+ align:start position:0%
+what the we need to know what fee looks
+like well feed better come out like
+
+ align:start position:0%
+like well feed better come out like
+ 
+
+ align:start position:0%
+like well feed better come out like
+before we're now fee is minus tangent
+
+ align:start position:0%
+before we're now fee is minus tangent
+ 
+
+ align:start position:0%
+before we're now fee is minus tangent
+inverse of the imaginary part over the
+
+ align:start position:0%
+inverse of the imaginary part over the
+ 
+
+ align:start position:0%
+inverse of the imaginary part over the
+real part and the imaginary part has a
+
+ align:start position:0%
+real part and the imaginary part has a
+ 
+
+ align:start position:0%
+real part and the imaginary part has a
+minus here that's why I minus pops up
+
+ align:start position:0%
+minus here that's why I minus pops up
+ 
+
+ align:start position:0%
+minus here that's why I minus pops up
+here imaginary part comes from this the
+
+ align:start position:0%
+here imaginary part comes from this the
+ 
+
+ align:start position:0%
+here imaginary part comes from this the
+real part comes from there
+
+ align:start position:0%
+real part comes from there
+ 
+
+ align:start position:0%
+real part comes from there
+the common denominator stuff all cancels
+
+ align:start position:0%
+the common denominator stuff all cancels
+ 
+
+ align:start position:0%
+the common denominator stuff all cancels
+out when you take the ratio
+
+ align:start position:0%
+out when you take the ratio
+ 
+
+ align:start position:0%
+out when you take the ratio
+this is tangent inverse of 2 Zeta Omega
+
+ align:start position:0%
+this is tangent inverse of 2 Zeta Omega
+ 
+
+ align:start position:0%
+this is tangent inverse of 2 Zeta Omega
+over Omega n all over 1 minus Omega
+
+ align:start position:0%
+over Omega n all over 1 minus Omega
+ 
+
+ align:start position:0%
+over Omega n all over 1 minus Omega
+squared over Omega N squared as before
+
+ align:start position:0%
+squared over Omega N squared as before
+ 
+
+ align:start position:0%
+squared over Omega N squared as before
+I've skipped a couple steps but we crank
+
+ align:start position:0%
+I've skipped a couple steps but we crank
+ 
+
+ align:start position:0%
+I've skipped a couple steps but we crank
+this whole thing out before this is just
+
+ align:start position:0%
+this whole thing out before this is just
+ 
+
+ align:start position:0%
+this whole thing out before this is just
+this is the same trap steps that you
+
+ align:start position:0%
+this is the same trap steps that you
+ 
+
+ align:start position:0%
+this is the same trap steps that you
+would go through to do that we're just
+
+ align:start position:0%
+would go through to do that we're just
+ 
+
+ align:start position:0%
+would go through to do that we're just
+doing this to get to the phase angle but
+
+ align:start position:0%
+doing this to get to the phase angle but
+ 
+
+ align:start position:0%
+doing this to get to the phase angle but
+this now is exactly the same thing we
+
+ align:start position:0%
+this now is exactly the same thing we
+ 
+
+ align:start position:0%
+this now is exactly the same thing we
+got before which we have plotted up
+
+ align:start position:0%
+got before which we have plotted up
+ 
+
+ align:start position:0%
+got before which we have plotted up
+there we tend to work with the magnitude
+
+ align:start position:0%
+there we tend to work with the magnitude
+ 
+
+ align:start position:0%
+there we tend to work with the magnitude
+we work with magnitude and phase angle
+
+ align:start position:0%
+we work with magnitude and phase angle
+ 
+
+ align:start position:0%
+we work with magnitude and phase angle
+so the magnitude of X over F is the same
+
+ align:start position:0%
+so the magnitude of X over F is the same
+ 
+
+ align:start position:0%
+so the magnitude of X over F is the same
+thing as saying the magnitude of the
+
+ align:start position:0%
+thing as saying the magnitude of the
+ 
+
+ align:start position:0%
+thing as saying the magnitude of the
+transfer function and that transfer
+
+ align:start position:0%
+transfer function and that transfer
+ 
+
+ align:start position:0%
+transfer function and that transfer
+function looks like 1 over K the
+
+ align:start position:0%
+function looks like 1 over K the
+ 
+
+ align:start position:0%
+function looks like 1 over K the
+magnitude all divided by 1 minus Omega
+
+ align:start position:0%
+magnitude all divided by 1 minus Omega
+ 
+
+ align:start position:0%
+magnitude all divided by 1 minus Omega
+squared over Omega N squared squared
+
+ align:start position:0%
+squared over Omega N squared squared
+ 
+
+ align:start position:0%
+squared over Omega N squared squared
+plus 2 Zeta Omega over Omega N squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square root that is the same transfer
+
+ align:start position:0%
+square root that is the same transfer
+ 
+
+ align:start position:0%
+square root that is the same transfer
+function magnitude that we derived last
+
+ align:start position:0%
+function magnitude that we derived last
+ 
+
+ align:start position:0%
+function magnitude that we derived last
+time with a lot more work and this
+
+ align:start position:0%
+time with a lot more work and this
+ 
+
+ align:start position:0%
+time with a lot more work and this
+approach using complex variables you can
+
+ align:start position:0%
+approach using complex variables you can
+ 
+
+ align:start position:0%
+approach using complex variables you can
+use for any input/output single-input
+
+ align:start position:0%
+use for any input/output single-input
+ 
+
+ align:start position:0%
+use for any input/output single-input
+single-output linear system and we're
+
+ align:start position:0%
+single-output linear system and we're
+ 
+
+ align:start position:0%
+single-output linear system and we're
+going to do it to derive right away the
+
+ align:start position:0%
+going to do it to derive right away the
+ 
+
+ align:start position:0%
+going to do it to derive right away the
+transfer function for the response of
+
+ align:start position:0%
+transfer function for the response of
+ 
+
+ align:start position:0%
+transfer function for the response of
+this to motion of the base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you follow how we use this complex
+
+ align:start position:0%
+so if you follow how we use this complex
+ 
+
+ align:start position:0%
+so if you follow how we use this complex
+variables and e to the I Omega T's to
+
+ align:start position:0%
+variables and e to the I Omega T's to
+ 
+
+ align:start position:0%
+variables and e to the I Omega T's to
+get here we can now apply the same tools
+
+ align:start position:0%
+get here we can now apply the same tools
+ 
+
+ align:start position:0%
+get here we can now apply the same tools
+to do other transfer functions to be a
+
+ align:start position:0%
+to do other transfer functions to be a
+ 
+
+ align:start position:0%
+to do other transfer functions to be a
+lot more efficient about it before I
+
+ align:start position:0%
+lot more efficient about it before I
+ 
+
+ align:start position:0%
+lot more efficient about it before I
+jump to this one remind you how in
+
+ align:start position:0%
+jump to this one remind you how in
+ 
+
+ align:start position:0%
+jump to this one remind you how in
+practice we use this so if the statement
+
+ align:start position:0%
+practice we use this so if the statement
+ 
+
+ align:start position:0%
+practice we use this so if the statement
+magnitude of X over F equals everything
+
+ align:start position:0%
+magnitude of X over F equals everything
+ 
+
+ align:start position:0%
+magnitude of X over F equals everything
+on the right there then in the way we
+
+ align:start position:0%
+on the right there then in the way we
+ 
+
+ align:start position:0%
+on the right there then in the way we
+would normally use this is to say well
+
+ align:start position:0%
+would normally use this is to say well
+ 
+
+ align:start position:0%
+would normally use this is to say well
+if you want the magnitude of the
+
+ align:start position:0%
+if you want the magnitude of the
+ 
+
+ align:start position:0%
+if you want the magnitude of the
+response you take the magnitude of the
+
+ align:start position:0%
+response you take the magnitude of the
+ 
+
+ align:start position:0%
+response you take the magnitude of the
+input force multiply it by the magnitude
+
+ align:start position:0%
+input force multiply it by the magnitude
+ 
+
+ align:start position:0%
+input force multiply it by the magnitude
+of the transfer function evaluated at
+
+ align:start position:0%
+of the transfer function evaluated at
+ 
+
+ align:start position:0%
+of the transfer function evaluated at
+the correct frequency that would give
+
+ align:start position:0%
+the correct frequency that would give
+ 
+
+ align:start position:0%
+the correct frequency that would give
+you the magnitude if you want the time
+
+ align:start position:0%
+you the magnitude if you want the time
+ 
+
+ align:start position:0%
+you the magnitude if you want the time
+dependence X of T well it's the
+
+ align:start position:0%
+dependence X of T well it's the
+ 
+
+ align:start position:0%
+dependence X of T well it's the
+magnitude of the force magnitude of the
+
+ align:start position:0%
+magnitude of the force magnitude of the
+ 
+
+ align:start position:0%
+magnitude of the force magnitude of the
+transfer function times the real part of
+
+ align:start position:0%
+transfer function times the real part of
+ 
+
+ align:start position:0%
+transfer function times the real part of
+e to the I Omega t minus V and this gets
+
+ align:start position:0%
+e to the I Omega t minus V and this gets
+ 
+
+ align:start position:0%
+e to the I Omega t minus V and this gets
+us back to when you work this out this
+
+ align:start position:0%
+us back to when you work this out this
+ 
+
+ align:start position:0%
+us back to when you work this out this
+is your X naught and this is your cosine
+
+ align:start position:0%
+is your X naught and this is your cosine
+ 
+
+ align:start position:0%
+is your X naught and this is your cosine
+Omega t minus V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so once you know what the excitation
+
+ align:start position:0%
+so once you know what the excitation
+ 
+
+ align:start position:0%
+so once you know what the excitation
+force is and its frequency
+
+ align:start position:0%
+force is and its frequency
+ 
+
+ align:start position:0%
+force is and its frequency
+put the force in here you valuate that
+
+ align:start position:0%
+put the force in here you valuate that
+ 
+
+ align:start position:0%
+put the force in here you valuate that
+thing on the left at the correct
+
+ align:start position:0%
+thing on the left at the correct
+ 
+
+ align:start position:0%
+thing on the left at the correct
+frequency write out the answer directly
+
+ align:start position:0%
+frequency write out the answer directly
+ 
+
+ align:start position:0%
+frequency write out the answer directly
+and one of the homeworks for today we
+
+ align:start position:0%
+and one of the homeworks for today we
+ 
+
+ align:start position:0%
+and one of the homeworks for today we
+just had just the question just had you
+
+ align:start position:0%
+just had just the question just had you
+ 
+
+ align:start position:0%
+just had just the question just had you
+go through the exercise of figuring this
+
+ align:start position:0%
+go through the exercise of figuring this
+ 
+
+ align:start position:0%
+go through the exercise of figuring this
+out at three different frequency ratios
+
+ align:start position:0%
+out at three different frequency ratios
+ 
+
+ align:start position:0%
+out at three different frequency ratios
+like 1/2 1 & 3 or something like that
+
+ align:start position:0%
+like 1/2 1 & 3 or something like that
+ 
+
+ align:start position:0%
+like 1/2 1 & 3 or something like that
+would put you to the left of the peak at
+
+ align:start position:0%
+would put you to the left of the peak at
+ 
+
+ align:start position:0%
+would put you to the left of the peak at
+1/2 on the peak at 1 and way off to the
+
+ align:start position:0%
+1/2 on the peak at 1 and way off to the
+ 
+
+ align:start position:0%
+1/2 on the peak at 1 and way off to the
+right out at the right edge at 3 and
+
+ align:start position:0%
+right out at the right edge at 3 and
+ 
+
+ align:start position:0%
+right out at the right edge at 3 and
+you'll get three different response
+
+ align:start position:0%
+you'll get three different response
+ 
+
+ align:start position:0%
+you'll get three different response
+amplitudes and three different phase
+
+ align:start position:0%
+amplitudes and three different phase
+ 
+
+ align:start position:0%
+amplitudes and three different phase
+angles that go with it all right so
+
+ align:start position:0%
+angles that go with it all right so
+ 
+
+ align:start position:0%
+angles that go with it all right so
+that's the review did the same thing a
+
+ align:start position:0%
+that's the review did the same thing a
+ 
+
+ align:start position:0%
+that's the review did the same thing a
+different way and I'm going to move on
+
+ align:start position:0%
+different way and I'm going to move on
+ 
+
+ align:start position:0%
+different way and I'm going to move on
+to base motion but any questions about
+
+ align:start position:0%
+to base motion but any questions about
+ 
+
+ align:start position:0%
+to base motion but any questions about
+this now yeah yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the very top expression up there we want
+
+ align:start position:0%
+the very top expression up there we want
+ 
+
+ align:start position:0%
+the very top expression up there we want
+it says x over F and says we're trying
+
+ align:start position:0%
+it says x over F and says we're trying
+ 
+
+ align:start position:0%
+it says x over F and says we're trying
+to cast it in e to the minus IP form
+
+ align:start position:0%
+to cast it in e to the minus IP form
+ 
+
+ align:start position:0%
+to cast it in e to the minus IP form
+that's my goal and I did that because we
+
+ align:start position:0%
+that's my goal and I did that because we
+ 
+
+ align:start position:0%
+that's my goal and I did that because we
+started over here with the problem that
+
+ align:start position:0%
+started over here with the problem that
+ 
+
+ align:start position:0%
+started over here with the problem that
+we had done before where that's the way
+
+ align:start position:0%
+we had done before where that's the way
+ 
+
+ align:start position:0%
+we had done before where that's the way
+we decided to write the answer and it
+
+ align:start position:0%
+we decided to write the answer and it
+ 
+
+ align:start position:0%
+we decided to write the answer and it
+turns out that it's just a convention in
+
+ align:start position:0%
+turns out that it's just a convention in
+ 
+
+ align:start position:0%
+turns out that it's just a convention in
+vibration and vibration engineering that
+
+ align:start position:0%
+vibration and vibration engineering that
+ 
+
+ align:start position:0%
+vibration and vibration engineering that
+authors and people have adopted to
+
+ align:start position:0%
+authors and people have adopted to
+ 
+
+ align:start position:0%
+authors and people have adopted to
+express the phase angle as minus fee it
+
+ align:start position:0%
+express the phase angle as minus fee it
+ 
+
+ align:start position:0%
+express the phase angle as minus fee it
+could have done it as plus fee but so
+
+ align:start position:0%
+could have done it as plus fee but so
+ 
+
+ align:start position:0%
+could have done it as plus fee but so
+when you and you plot the plots like
+
+ align:start position:0%
+when you and you plot the plots like
+ 
+
+ align:start position:0%
+when you and you plot the plots like
+this our fee oh I see you mean it is
+
+ align:start position:0%
+this our fee oh I see you mean it is
+ 
+
+ align:start position:0%
+this our fee oh I see you mean it is
+it's in it's in there before you take
+
+ align:start position:0%
+it's in it's in there before you take
+ 
+
+ align:start position:0%
+it's in it's in there before you take
+its magnitude so the hxf when it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here is left in complex notation
+
+ align:start position:0%
+this here is left in complex notation
+ 
+
+ align:start position:0%
+this here is left in complex notation
+and this is this is H X F of Omega and
+
+ align:start position:0%
+and this is this is H X F of Omega and
+ 
+
+ align:start position:0%
+and this is this is H X F of Omega and
+it is it's complex we take its magnitude
+
+ align:start position:0%
+it is it's complex we take its magnitude
+ 
+
+ align:start position:0%
+it is it's complex we take its magnitude
+in it be then the magnitude is not
+
+ align:start position:0%
+in it be then the magnitude is not
+ 
+
+ align:start position:0%
+in it be then the magnitude is not
+complex right and so we take its
+
+ align:start position:0%
+complex right and so we take its
+ 
+
+ align:start position:0%
+complex right and so we take its
+magnitude we get that expression but
+
+ align:start position:0%
+magnitude we get that expression but
+ 
+
+ align:start position:0%
+magnitude we get that expression but
+when we take its magnitude we've thrown
+
+ align:start position:0%
+when we take its magnitude we've thrown
+ 
+
+ align:start position:0%
+when we take its magnitude we've thrown
+away the phase information so we have to
+
+ align:start position:0%
+away the phase information so we have to
+ 
+
+ align:start position:0%
+away the phase information so we have to
+keep it and put it somewhere and so we
+
+ align:start position:0%
+keep it and put it somewhere and so we
+ 
+
+ align:start position:0%
+keep it and put it somewhere and so we
+put it in a the e to the I fee form and
+
+ align:start position:0%
+put it in a the e to the I fee form and
+ 
+
+ align:start position:0%
+put it in a the e to the I fee form and
+I guess I what I could have done here is
+
+ align:start position:0%
+I guess I what I could have done here is
+ 
+
+ align:start position:0%
+I guess I what I could have done here is
+now this is I've taken this is H X F
+
+ align:start position:0%
+now this is I've taken this is H X F
+ 
+
+ align:start position:0%
+now this is I've taken this is H X F
+same thing as x over F in complex form
+
+ align:start position:0%
+same thing as x over F in complex form
+ 
+
+ align:start position:0%
+same thing as x over F in complex form
+and I've chose said ok if I write it
+
+ align:start position:0%
+and I've chose said ok if I write it
+ 
+
+ align:start position:0%
+and I've chose said ok if I write it
+this way I have just said it is a
+
+ align:start position:0%
+this way I have just said it is a
+ 
+
+ align:start position:0%
+this way I have just said it is a
+magnitude times its phase information
+
+ align:start position:0%
+magnitude times its phase information
+ 
+
+ align:start position:0%
+magnitude times its phase information
+I've separated its phase information
+
+ align:start position:0%
+I've separated its phase information
+ 
+
+ align:start position:0%
+I've separated its phase information
+from its magnitude by writing it this
+
+ align:start position:0%
+from its magnitude by writing it this
+ 
+
+ align:start position:0%
+from its magnitude by writing it this
+way okay and the phase then is that and
+
+ align:start position:0%
+way okay and the phase then is that and
+ 
+
+ align:start position:0%
+way okay and the phase then is that and
+its magnitude is that good question all
+
+ align:start position:0%
+its magnitude is that good question all
+ 
+
+ align:start position:0%
+its magnitude is that good question all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's see if we can kind of
+
+ align:start position:0%
+so now let's see if we can kind of
+ 
+
+ align:start position:0%
+so now let's see if we can kind of
+pretty quickly do the same problem for
+
+ align:start position:0%
+pretty quickly do the same problem for
+ 
+
+ align:start position:0%
+pretty quickly do the same problem for
+base motion so this is our microscope
+
+ align:start position:0%
+base motion so this is our microscope
+ 
+
+ align:start position:0%
+base motion so this is our microscope
+now idealizes a mass spring system
+
+ align:start position:0%
+now idealizes a mass spring system
+ 
+
+ align:start position:0%
+now idealizes a mass spring system
+so this is our microscope has some mass
+
+ align:start position:0%
+so this is our microscope has some mass
+ 
+
+ align:start position:0%
+so this is our microscope has some mass
+stiffness damping motion X of T and how
+
+ align:start position:0%
+stiffness damping motion X of T and how
+ 
+
+ align:start position:0%
+stiffness damping motion X of T and how
+do you suppose that and where do you
+
+ align:start position:0%
+do you suppose that and where do you
+ 
+
+ align:start position:0%
+do you suppose that and where do you
+where would you measure that motion X of
+
+ align:start position:0%
+where would you measure that motion X of
+ 
+
+ align:start position:0%
+where would you measure that motion X of
+T from have to define your coordinate
+
+ align:start position:0%
+T from have to define your coordinate
+ 
+
+ align:start position:0%
+T from have to define your coordinate
+here just there's a major point in the
+
+ align:start position:0%
+here just there's a major point in the
+ 
+
+ align:start position:0%
+here just there's a major point in the
+last known work it's gravity involved
+
+ align:start position:0%
+last known work it's gravity involved
+ 
+
+ align:start position:0%
+last known work it's gravity involved
+but only as a constant term mg and the
+
+ align:start position:0%
+but only as a constant term mg and the
+ 
+
+ align:start position:0%
+but only as a constant term mg and the
+equation of motion it's only there if
+
+ align:start position:0%
+equation of motion it's only there if
+ 
+
+ align:start position:0%
+equation of motion it's only there if
+you depending on how you if you write
+
+ align:start position:0%
+you depending on how you if you write
+ 
+
+ align:start position:0%
+you depending on how you if you write
+the equation of motion in the less
+
+ align:start position:0%
+the equation of motion in the less
+ 
+
+ align:start position:0%
+the equation of motion in the less
+desirable way where is this measured
+
+ align:start position:0%
+desirable way where is this measured
+ 
+
+ align:start position:0%
+desirable way where is this measured
+from do you guess equilibrium position
+
+ align:start position:0%
+from do you guess equilibrium position
+ 
+
+ align:start position:0%
+from do you guess equilibrium position
+static equilibrium position or zero
+
+ align:start position:0%
+static equilibrium position or zero
+ 
+
+ align:start position:0%
+static equilibrium position or zero
+spring force position how many suggest
+
+ align:start position:0%
+spring force position how many suggest
+ 
+
+ align:start position:0%
+spring force position how many suggest
+zero spring force position how many
+
+ align:start position:0%
+zero spring force position how many
+ 
+
+ align:start position:0%
+zero spring force position how many
+suggests static equilibrium okay you got
+
+ align:start position:0%
+suggests static equilibrium okay you got
+ 
+
+ align:start position:0%
+suggests static equilibrium okay you got
+the message this is static this is from
+
+ align:start position:0%
+the message this is static this is from
+ 
+
+ align:start position:0%
+the message this is static this is from
+equilibrium because you know you don't
+
+ align:start position:0%
+equilibrium because you know you don't
+ 
+
+ align:start position:0%
+equilibrium because you know you don't
+deal with the mg term so this is from
+
+ align:start position:0%
+deal with the mg term so this is from
+ 
+
+ align:start position:0%
+deal with the mg term so this is from
+measured from equilibrium
+
+ align:start position:0%
+measured from equilibrium
+ 
+
+ align:start position:0%
+measured from equilibrium
+that's the deflection of the microscope
+
+ align:start position:0%
+that's the deflection of the microscope
+ 
+
+ align:start position:0%
+that's the deflection of the microscope
+support this is the deflection of the
+
+ align:start position:0%
+support this is the deflection of the
+ 
+
+ align:start position:0%
+support this is the deflection of the
+floor that's driving it we know we've
+
+ align:start position:0%
+floor that's driving it we know we've
+ 
+
+ align:start position:0%
+floor that's driving it we know we've
+got that table shaking like crazy that's
+
+ align:start position:0%
+got that table shaking like crazy that's
+ 
+
+ align:start position:0%
+got that table shaking like crazy that's
+what's causing this to vibrate and we
+
+ align:start position:0%
+what's causing this to vibrate and we
+ 
+
+ align:start position:0%
+what's causing this to vibrate and we
+need a Freebody diagram and we approach
+
+ align:start position:0%
+need a Freebody diagram and we approach
+ 
+
+ align:start position:0%
+need a Freebody diagram and we approach
+Freebody diagrams just like before you
+
+ align:start position:0%
+Freebody diagrams just like before you
+ 
+
+ align:start position:0%
+Freebody diagrams just like before you
+imagine positive motions of X and X dot
+
+ align:start position:0%
+imagine positive motions of X and X dot
+ 
+
+ align:start position:0%
+imagine positive motions of X and X dot
+positive motions of Y and y dot and
+
+ align:start position:0%
+positive motions of Y and y dot and
+ 
+
+ align:start position:0%
+positive motions of Y and y dot and
+deduce their forces so a positive x
+
+ align:start position:0%
+deduce their forces so a positive x
+ 
+
+ align:start position:0%
+deduce their forces so a positive x
+gives you a KX opposing a positive X dot
+
+ align:start position:0%
+gives you a KX opposing a positive X dot
+ 
+
+ align:start position:0%
+gives you a KX opposing a positive X dot
+gives you a CX dot opposing a positive Y
+
+ align:start position:0%
+gives you a CX dot opposing a positive Y
+ 
+
+ align:start position:0%
+gives you a CX dot opposing a positive Y
+gives you what the force the results on
+
+ align:start position:0%
+gives you what the force the results on
+ 
+
+ align:start position:0%
+gives you what the force the results on
+this positive motion of the floor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive or negative force how many
+
+ align:start position:0%
+positive or negative force how many
+ 
+
+ align:start position:0%
+positive or negative force how many
+think positive how many think negative
+
+ align:start position:0%
+think positive how many think negative
+ 
+
+ align:start position:0%
+think positive how many think negative
+we aren't sure how many aren't awake
+
+ align:start position:0%
+we aren't sure how many aren't awake
+ 
+
+ align:start position:0%
+we aren't sure how many aren't awake
+okay look if I push up on this and now
+
+ align:start position:0%
+okay look if I push up on this and now
+ 
+
+ align:start position:0%
+okay look if I push up on this and now
+this is fixed when you do this mental
+
+ align:start position:0%
+this is fixed when you do this mental
+ 
+
+ align:start position:0%
+this is fixed when you do this mental
+experiment you fix this momentarily you
+
+ align:start position:0%
+experiment you fix this momentarily you
+ 
+
+ align:start position:0%
+experiment you fix this momentarily you
+cause a positive deflection here it
+
+ align:start position:0%
+cause a positive deflection here it
+ 
+
+ align:start position:0%
+cause a positive deflection here it
+compresses the spring there's a spring
+
+ align:start position:0%
+compresses the spring there's a spring
+ 
+
+ align:start position:0%
+compresses the spring there's a spring
+push back or not so if I'm moving
+
+ align:start position:0%
+push back or not so if I'm moving
+ 
+
+ align:start position:0%
+push back or not so if I'm moving
+upwards which way is a spring pushing
+
+ align:start position:0%
+upwards which way is a spring pushing
+ 
+
+ align:start position:0%
+upwards which way is a spring pushing
+all right so the but if I'm pushing
+
+ align:start position:0%
+all right so the but if I'm pushing
+ 
+
+ align:start position:0%
+all right so the but if I'm pushing
+upwards which way is the spring pushing
+
+ align:start position:0%
+upwards which way is the spring pushing
+ 
+
+ align:start position:0%
+upwards which way is the spring pushing
+on the mass up so this one gives me a KY
+
+ align:start position:0%
+on the mass up so this one gives me a KY
+ 
+
+ align:start position:0%
+on the mass up so this one gives me a KY
+up and the dashpot does a similar thing
+
+ align:start position:0%
+up and the dashpot does a similar thing
+ 
+
+ align:start position:0%
+up and the dashpot does a similar thing
+see y dot up and there's also an mg here
+
+ align:start position:0%
+see y dot up and there's also an mg here
+ 
+
+ align:start position:0%
+see y dot up and there's also an mg here
+but there's also a K X static if you
+
+ align:start position:0%
+but there's also a K X static if you
+ 
+
+ align:start position:0%
+but there's also a K X static if you
+will up and they cancel we know that so
+
+ align:start position:0%
+will up and they cancel we know that so
+ 
+
+ align:start position:0%
+will up and they cancel we know that so
+we don't have to deal with the mg terms
+
+ align:start position:0%
+we don't have to deal with the mg terms
+ 
+
+ align:start position:0%
+we don't have to deal with the mg terms
+so now we can write our equation of
+
+ align:start position:0%
+so now we can write our equation of
+ 
+
+ align:start position:0%
+so now we can write our equation of
+motion in the equation of motion for
+
+ align:start position:0%
+motion in the equation of motion for
+ 
+
+ align:start position:0%
+motion in the equation of motion for
+this system is the mass times the
+
+ align:start position:0%
+this system is the mass times the
+ 
+
+ align:start position:0%
+this system is the mass times the
+acceleration has got to equal to the sum
+
+ align:start position:0%
+acceleration has got to equal to the sum
+ 
+
+ align:start position:0%
+acceleration has got to equal to the sum
+of all the external forces one two three
+
+ align:start position:0%
+of all the external forces one two three
+ 
+
+ align:start position:0%
+of all the external forces one two three
+four of them and I'll just to save a
+
+ align:start position:0%
+four of them and I'll just to save a
+ 
+
+ align:start position:0%
+four of them and I'll just to save a
+little time and board space I'll put
+
+ align:start position:0%
+little time and board space I'll put
+ 
+
+ align:start position:0%
+little time and board space I'll put
+them in the on the correct sides of the
+
+ align:start position:0%
+them in the on the correct sides of the
+ 
+
+ align:start position:0%
+them in the on the correct sides of the
+equation so this these are the X put the
+
+ align:start position:0%
+equation so this these are the X put the
+ 
+
+ align:start position:0%
+equation so this these are the X put the
+X terms on the left side CX dot plus KX
+
+ align:start position:0%
+X terms on the left side CX dot plus KX
+ 
+
+ align:start position:0%
+X terms on the left side CX dot plus KX
+and on the right hand side I get KY plus
+
+ align:start position:0%
+and on the right hand side I get KY plus
+ 
+
+ align:start position:0%
+and on the right hand side I get KY plus
+CY dot
+
+ align:start position:0%
+CY dot
+ 
+
+ align:start position:0%
+CY dot
+this is my excitation that's the floor
+
+ align:start position:0%
+this is my excitation that's the floor
+ 
+
+ align:start position:0%
+this is my excitation that's the floor
+motion and this is my response on the
+
+ align:start position:0%
+motion and this is my response on the
+ 
+
+ align:start position:0%
+motion and this is my response on the
+left-hand side so I'm going to let Y of
+
+ align:start position:0%
+left-hand side so I'm going to let Y of
+ 
+
+ align:start position:0%
+left-hand side so I'm going to let Y of
+T the input be some Y not real positive
+
+ align:start position:0%
+T the input be some Y not real positive
+ 
+
+ align:start position:0%
+T the input be some Y not real positive
+times e to the I Omega T and I'm going
+
+ align:start position:0%
+times e to the I Omega T and I'm going
+ 
+
+ align:start position:0%
+times e to the I Omega T and I'm going
+to assume that the response is some X
+
+ align:start position:0%
+to assume that the response is some X
+ 
+
+ align:start position:0%
+to assume that the response is some X
+probably complex e to the I Omega T so
+
+ align:start position:0%
+probably complex e to the I Omega T so
+ 
+
+ align:start position:0%
+probably complex e to the I Omega T so
+this is X of T here equals some X I
+
+ align:start position:0%
+this is X of T here equals some X I
+ 
+
+ align:start position:0%
+this is X of T here equals some X I
+don't know e to the I Omega T and I'm
+
+ align:start position:0%
+don't know e to the I Omega T and I'm
+ 
+
+ align:start position:0%
+don't know e to the I Omega T and I'm
+going to plug those two into this
+
+ align:start position:0%
+going to plug those two into this
+ 
+
+ align:start position:0%
+going to plug those two into this
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just do that directly X is on the left
+
+ align:start position:0%
+I just do that directly X is on the left
+ 
+
+ align:start position:0%
+I just do that directly X is on the left
+side y is on the right side then I find
+
+ align:start position:0%
+side y is on the right side then I find
+ 
+
+ align:start position:0%
+side y is on the right side then I find
+minus Omega squared M plus I Omega C
+
+ align:start position:0%
+minus Omega squared M plus I Omega C
+ 
+
+ align:start position:0%
+minus Omega squared M plus I Omega C
+plus K like before X e to the I Omega T
+
+ align:start position:0%
+plus K like before X e to the I Omega T
+ 
+
+ align:start position:0%
+plus K like before X e to the I Omega T
+equals K plus I Omega C why not e to the
+
+ align:start position:0%
+equals K plus I Omega C why not e to the
+ 
+
+ align:start position:0%
+equals K plus I Omega C why not e to the
+I Omega T and nicely I can for now throw
+
+ align:start position:0%
+I Omega T and nicely I can for now throw
+ 
+
+ align:start position:0%
+I Omega T and nicely I can for now throw
+away get rid of the time dependent part
+
+ align:start position:0%
+away get rid of the time dependent part
+ 
+
+ align:start position:0%
+away get rid of the time dependent part
+and I can solve for response that I'm
+
+ align:start position:0%
+and I can solve for response that I'm
+ 
+
+ align:start position:0%
+and I can solve for response that I'm
+looking for x over the input its real
+
+ align:start position:0%
+looking for x over the input its real
+ 
+
+ align:start position:0%
+looking for x over the input its real
+and positive amplitude of vibration of
+
+ align:start position:0%
+and positive amplitude of vibration of
+ 
+
+ align:start position:0%
+and positive amplitude of vibration of
+the floor and that I will call H x over
+
+ align:start position:0%
+the floor and that I will call H x over
+ 
+
+ align:start position:0%
+the floor and that I will call H x over
+Y of Omega a transfer function probably
+
+ align:start position:0%
+Y of Omega a transfer function probably
+ 
+
+ align:start position:0%
+Y of Omega a transfer function probably
+complex that I can then deal with like I
+
+ align:start position:0%
+complex that I can then deal with like I
+ 
+
+ align:start position:0%
+complex that I can then deal with like I
+did above and when I finish manipulating
+
+ align:start position:0%
+did above and when I finish manipulating
+ 
+
+ align:start position:0%
+did above and when I finish manipulating
+things putting in substituting in Zetas
+
+ align:start position:0%
+things putting in substituting in Zetas
+ 
+
+ align:start position:0%
+things putting in substituting in Zetas
+and Omega n squares and that kind of
+
+ align:start position:0%
+and Omega n squares and that kind of
+ 
+
+ align:start position:0%
+and Omega n squares and that kind of
+thing this becomes well first of all
+
+ align:start position:0%
+thing this becomes well first of all
+ 
+
+ align:start position:0%
+thing this becomes well first of all
+write it this way I can write this as a
+
+ align:start position:0%
+write it this way I can write this as a
+ 
+
+ align:start position:0%
+write it this way I can write this as a
+magnitude times an e to the minus I fee
+
+ align:start position:0%
+magnitude times an e to the minus I fee
+ 
+
+ align:start position:0%
+magnitude times an e to the minus I fee
+again that's what I'm trying that's
+
+ align:start position:0%
+again that's what I'm trying that's
+ 
+
+ align:start position:0%
+again that's what I'm trying that's
+where I want to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when I do that one plus little
+
+ align:start position:0%
+and when I do that one plus little
+ 
+
+ align:start position:0%
+and when I do that one plus little
+Messier to Zeta Omega over Omega N
+
+ align:start position:0%
+Messier to Zeta Omega over Omega N
+ 
+
+ align:start position:0%
+Messier to Zeta Omega over Omega N
+squared square root this is just the
+
+ align:start position:0%
+squared square root this is just the
+ 
+
+ align:start position:0%
+squared square root this is just the
+numerator and the denominator
+
+ align:start position:0%
+numerator and the denominator
+ 
+
+ align:start position:0%
+numerator and the denominator
+denominator is just the same as the
+
+ align:start position:0%
+denominator is just the same as the
+ 
+
+ align:start position:0%
+denominator is just the same as the
+other single degree freedom things 1
+
+ align:start position:0%
+other single degree freedom things 1
+ 
+
+ align:start position:0%
+other single degree freedom things 1
+minus Omega squared over Omega N squared
+
+ align:start position:0%
+minus Omega squared over Omega N squared
+ 
+
+ align:start position:0%
+minus Omega squared over Omega N squared
+squared plus 2 Zeta Omega over Omega N
+
+ align:start position:0%
+squared plus 2 Zeta Omega over Omega N
+ 
+
+ align:start position:0%
+squared plus 2 Zeta Omega over Omega N
+squared square root of e to the minus i
+
+ align:start position:0%
+squared square root of e to the minus i
+ 
+
+ align:start position:0%
+squared square root of e to the minus i
+fee so now it's the same it's the same
+
+ align:start position:0%
+fee so now it's the same it's the same
+ 
+
+ align:start position:0%
+fee so now it's the same it's the same
+transfer function as before except the
+
+ align:start position:0%
+transfer function as before except the
+ 
+
+ align:start position:0%
+transfer function as before except the
+denominator is a little little messy and
+
+ align:start position:0%
+denominator is a little little messy and
+ 
+
+ align:start position:0%
+denominator is a little little messy and
+there's no 1 over K and I am going to
+
+ align:start position:0%
+there's no 1 over K and I am going to
+ 
+
+ align:start position:0%
+there's no 1 over K and I am going to
+have a Messier expression for feet here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there is something wrong with one of
+
+ align:start position:0%
+so there is something wrong with one of
+ 
+
+ align:start position:0%
+so there is something wrong with one of
+the boards this morning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind of messy complicated do I ever use
+
+ align:start position:0%
+kind of messy complicated do I ever use
+ 
+
+ align:start position:0%
+kind of messy complicated do I ever use
+it rarely provide some of what's
+
+ align:start position:0%
+it rarely provide some of what's
+ 
+
+ align:start position:0%
+it rarely provide some of what's
+important in these things and what isn't
+
+ align:start position:0%
+important in these things and what isn't
+ 
+
+ align:start position:0%
+important in these things and what isn't
+really what's important when you're just
+
+ align:start position:0%
+really what's important when you're just
+ 
+
+ align:start position:0%
+really what's important when you're just
+trying to get a quick solution to
+
+ align:start position:0%
+trying to get a quick solution to
+ 
+
+ align:start position:0%
+trying to get a quick solution to
+vibration isolate something you really
+
+ align:start position:0%
+vibration isolate something you really
+ 
+
+ align:start position:0%
+vibration isolate something you really
+want to know what this going to come out
+
+ align:start position:0%
+want to know what this going to come out
+ 
+
+ align:start position:0%
+want to know what this going to come out
+looking like you're trying to make the
+
+ align:start position:0%
+looking like you're trying to make the
+ 
+
+ align:start position:0%
+looking like you're trying to make the
+response X small compared to the input
+
+ align:start position:0%
+response X small compared to the input
+ 
+
+ align:start position:0%
+response X small compared to the input
+that's the whole objective right now you
+
+ align:start position:0%
+that's the whole objective right now you
+ 
+
+ align:start position:0%
+that's the whole objective right now you
+know the table might be moving a half a
+
+ align:start position:0%
+know the table might be moving a half a
+ 
+
+ align:start position:0%
+know the table might be moving a half a
+millimeter or something like that but
+
+ align:start position:0%
+millimeter or something like that but
+ 
+
+ align:start position:0%
+millimeter or something like that but
+this thing's moving out here you know
+
+ align:start position:0%
+this thing's moving out here you know
+ 
+
+ align:start position:0%
+this thing's moving out here you know
+five or six or seven millimeters so IRA
+
+ align:start position:0%
+five or six or seven millimeters so IRA
+ 
+
+ align:start position:0%
+five or six or seven millimeters so IRA
+ten times that what we'd really like is
+
+ align:start position:0%
+ten times that what we'd really like is
+ 
+
+ align:start position:0%
+ten times that what we'd really like is
+if the tables move in a millimeter you'd
+
+ align:start position:0%
+if the tables move in a millimeter you'd
+ 
+
+ align:start position:0%
+if the tables move in a millimeter you'd
+like this thing out here move in a tenth
+
+ align:start position:0%
+like this thing out here move in a tenth
+ 
+
+ align:start position:0%
+like this thing out here move in a tenth
+of a millimeter and so the real
+
+ align:start position:0%
+of a millimeter and so the real
+ 
+
+ align:start position:0%
+of a millimeter and so the real
+objective here is to make this small
+
+ align:start position:0%
+objective here is to make this small
+ 
+
+ align:start position:0%
+objective here is to make this small
+it's the magnitude you care about phase
+
+ align:start position:0%
+it's the magnitude you care about phase
+ 
+
+ align:start position:0%
+it's the magnitude you care about phase
+you rarely even it really even need to
+
+ align:start position:0%
+you rarely even it really even need to
+ 
+
+ align:start position:0%
+you rarely even it really even need to
+know you want to know or need to know so
+
+ align:start position:0%
+know you want to know or need to know so
+ 
+
+ align:start position:0%
+know you want to know or need to know so
+we're going to do a sample calculation
+
+ align:start position:0%
+we're going to do a sample calculation
+ 
+
+ align:start position:0%
+we're going to do a sample calculation
+into an example here so the source is at
+
+ align:start position:0%
+into an example here so the source is at
+ 
+
+ align:start position:0%
+into an example here so the source is at
+20 Hertz so you're unbalanced pump and
+
+ align:start position:0%
+20 Hertz so you're unbalanced pump and
+ 
+
+ align:start position:0%
+20 Hertz so you're unbalanced pump and
+balanced rotor yeah the same like ah
+
+ align:start position:0%
+balanced rotor yeah the same like ah
+ 
+
+ align:start position:0%
+balanced rotor yeah the same like ah
+what's like why wouldn't it be like
+
+ align:start position:0%
+what's like why wouldn't it be like
+ 
+
+ align:start position:0%
+what's like why wouldn't it be like
+twice that okay that's a great question
+
+ align:start position:0%
+twice that okay that's a great question
+ 
+
+ align:start position:0%
+twice that okay that's a great question
+I haven't mentioned this before and I
+
+ align:start position:0%
+I haven't mentioned this before and I
+ 
+
+ align:start position:0%
+I haven't mentioned this before and I
+and intended to these systems that we're
+
+ align:start position:0%
+and intended to these systems that we're
+ 
+
+ align:start position:0%
+and intended to these systems that we're
+looking at our linear systems what's the
+
+ align:start position:0%
+looking at our linear systems what's the
+ 
+
+ align:start position:0%
+looking at our linear systems what's the
+where we started the other day linear
+
+ align:start position:0%
+where we started the other day linear
+ 
+
+ align:start position:0%
+where we started the other day linear
+systems have some interesting property
+
+ align:start position:0%
+systems have some interesting property
+ 
+
+ align:start position:0%
+systems have some interesting property
+and very useful properties that we
+
+ align:start position:0%
+and very useful properties that we
+ 
+
+ align:start position:0%
+and very useful properties that we
+depend upon one was I said you know one
+
+ align:start position:0%
+depend upon one was I said you know one
+ 
+
+ align:start position:0%
+depend upon one was I said you know one
+force gives you force one gives you
+
+ align:start position:0%
+force gives you force one gives you
+ 
+
+ align:start position:0%
+force gives you force one gives you
+output one force two gives you output to
+
+ align:start position:0%
+output one force two gives you output to
+ 
+
+ align:start position:0%
+output one force two gives you output to
+force one plus two gives you up to some
+
+ align:start position:0%
+force one plus two gives you up to some
+ 
+
+ align:start position:0%
+force one plus two gives you up to some
+of the outputs the other feature of a
+
+ align:start position:0%
+of the outputs the other feature of a
+ 
+
+ align:start position:0%
+of the outputs the other feature of a
+linear system is steady state
+
+ align:start position:0%
+linear system is steady state
+ 
+
+ align:start position:0%
+linear system is steady state
+response after the transience of died
+
+ align:start position:0%
+response after the transience of died
+ 
+
+ align:start position:0%
+response after the transience of died
+away if the frequency of the input is at
+
+ align:start position:0%
+away if the frequency of the input is at
+ 
+
+ align:start position:0%
+away if the frequency of the input is at
+21.5 Hertz the frequency the output is
+
+ align:start position:0%
+21.5 Hertz the frequency the output is
+ 
+
+ align:start position:0%
+21.5 Hertz the frequency the output is
+at 21.5 Hertz period linear systems the
+
+ align:start position:0%
+at 21.5 Hertz period linear systems the
+ 
+
+ align:start position:0%
+at 21.5 Hertz period linear systems the
+frequency of the input is equal to the
+
+ align:start position:0%
+frequency of the input is equal to the
+ 
+
+ align:start position:0%
+frequency of the input is equal to the
+frequency the output that's a really
+
+ align:start position:0%
+frequency the output that's a really
+ 
+
+ align:start position:0%
+frequency the output that's a really
+important little factoid to remember so
+
+ align:start position:0%
+important little factoid to remember so
+ 
+
+ align:start position:0%
+important little factoid to remember so
+I turn on the pump the pumps running at
+
+ align:start position:0%
+I turn on the pump the pumps running at
+ 
+
+ align:start position:0%
+I turn on the pump the pumps running at
+20 Hertz 20 Hertz times 60 is 1200 1200
+
+ align:start position:0%
+20 Hertz 20 Hertz times 60 is 1200 1200
+ 
+
+ align:start position:0%
+20 Hertz 20 Hertz times 60 is 1200 1200
+rpm very common motor speed so the pumps
+
+ align:start position:0%
+rpm very common motor speed so the pumps
+ 
+
+ align:start position:0%
+rpm very common motor speed so the pumps
+mounted at 20 Hertz so that fan it's got
+
+ align:start position:0%
+mounted at 20 Hertz so that fan it's got
+ 
+
+ align:start position:0%
+mounted at 20 Hertz so that fan it's got
+an imbalance so that means you're
+
+ align:start position:0%
+an imbalance so that means you're
+ 
+
+ align:start position:0%
+an imbalance so that means you're
+putting excitation into the floor at 20
+
+ align:start position:0%
+putting excitation into the floor at 20
+ 
+
+ align:start position:0%
+putting excitation into the floor at 20
+Hertz and I want to reduce the vibration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the microscope by 90% what that
+
+ align:start position:0%
+at the microscope by 90% what that
+ 
+
+ align:start position:0%
+at the microscope by 90% what that
+really means is I my goal is that the
+
+ align:start position:0%
+really means is I my goal is that the
+ 
+
+ align:start position:0%
+really means is I my goal is that the
+magnitude of x over Y is 0.1 that's the
+
+ align:start position:0%
+magnitude of x over Y is 0.1 that's the
+ 
+
+ align:start position:0%
+magnitude of x over Y is 0.1 that's the
+magnitude of this transfer function H Oh
+
+ align:start position:0%
+magnitude of this transfer function H Oh
+ 
+
+ align:start position:0%
+magnitude of this transfer function H Oh
+x over y so I want this transfer
+
+ align:start position:0%
+x over y so I want this transfer
+ 
+
+ align:start position:0%
+x over y so I want this transfer
+function to be 0.1 so just look at the
+
+ align:start position:0%
+function to be 0.1 so just look at the
+ 
+
+ align:start position:0%
+function to be 0.1 so just look at the
+picture can I get that answer to the
+
+ align:start position:0%
+picture can I get that answer to the
+ 
+
+ align:start position:0%
+picture can I get that answer to the
+left of the peak now what this plot
+
+ align:start position:0%
+left of the peak now what this plot
+ 
+
+ align:start position:0%
+left of the peak now what this plot
+shows you is this magnitude of the
+
+ align:start position:0%
+shows you is this magnitude of the
+ 
+
+ align:start position:0%
+shows you is this magnitude of the
+transfer function for a variety of
+
+ align:start position:0%
+transfer function for a variety of
+ 
+
+ align:start position:0%
+transfer function for a variety of
+values of damping of course the lower
+
+ align:start position:0%
+values of damping of course the lower
+ 
+
+ align:start position:0%
+values of damping of course the lower
+the damping the higher the peak gets at
+
+ align:start position:0%
+the damping the higher the peak gets at
+ 
+
+ align:start position:0%
+the damping the higher the peak gets at
+resonance right so no matter what the
+
+ align:start position:0%
+resonance right so no matter what the
+ 
+
+ align:start position:0%
+resonance right so no matter what the
+damping is what is the curves all go to
+
+ align:start position:0%
+damping is what is the curves all go to
+ 
+
+ align:start position:0%
+damping is what is the curves all go to
+on the left-hand side they go to 1 and
+
+ align:start position:0%
+on the left-hand side they go to 1 and
+ 
+
+ align:start position:0%
+on the left-hand side they go to 1 and
+that's really saying the static response
+
+ align:start position:0%
+that's really saying the static response
+ 
+
+ align:start position:0%
+that's really saying the static response
+of this system is if you deflect the
+
+ align:start position:0%
+of this system is if you deflect the
+ 
+
+ align:start position:0%
+of this system is if you deflect the
+floor an inch the table moves with it
+
+ align:start position:0%
+floor an inch the table moves with it
+ 
+
+ align:start position:0%
+floor an inch the table moves with it
+everything goes everything has to move
+
+ align:start position:0%
+everything goes everything has to move
+ 
+
+ align:start position:0%
+everything goes everything has to move
+together when you get down
+
+ align:start position:0%
+together when you get down
+ 
+
+ align:start position:0%
+together when you get down
+to zero frequency input so everything
+
+ align:start position:0%
+to zero frequency input so everything
+ 
+
+ align:start position:0%
+to zero frequency input so everything
+goes to one on the left you go through
+
+ align:start position:0%
+goes to one on the left you go through
+ 
+
+ align:start position:0%
+goes to one on the left you go through
+resonance at natural mega equals the
+
+ align:start position:0%
+resonance at natural mega equals the
+ 
+
+ align:start position:0%
+resonance at natural mega equals the
+natural frequency but on out to the
+
+ align:start position:0%
+natural frequency but on out to the
+ 
+
+ align:start position:0%
+natural frequency but on out to the
+right as the excitation frequency gets
+
+ align:start position:0%
+right as the excitation frequency gets
+ 
+
+ align:start position:0%
+right as the excitation frequency gets
+higher than the natural frequency the
+
+ align:start position:0%
+higher than the natural frequency the
+ 
+
+ align:start position:0%
+higher than the natural frequency the
+response drops off below one which one
+
+ align:start position:0%
+response drops off below one which one
+ 
+
+ align:start position:0%
+response drops off below one which one
+drops the fastest which as you increase
+
+ align:start position:0%
+drops the fastest which as you increase
+ 
+
+ align:start position:0%
+drops the fastest which as you increase
+Omega over mega and beyond one which
+
+ align:start position:0%
+Omega over mega and beyond one which
+ 
+
+ align:start position:0%
+Omega over mega and beyond one which
+Kurt which each of those the whole mess
+
+ align:start position:0%
+Kurt which each of those the whole mess
+ 
+
+ align:start position:0%
+Kurt which each of those the whole mess
+occurs to the right that blend together
+
+ align:start position:0%
+occurs to the right that blend together
+ 
+
+ align:start position:0%
+occurs to the right that blend together
+then they differ only in damping can you
+
+ align:start position:0%
+then they differ only in damping can you
+ 
+
+ align:start position:0%
+then they differ only in damping can you
+tell which one is the let's say if you
+
+ align:start position:0%
+tell which one is the let's say if you
+ 
+
+ align:start position:0%
+tell which one is the let's say if you
+go to at three there the response is at
+
+ align:start position:0%
+go to at three there the response is at
+ 
+
+ align:start position:0%
+go to at three there the response is at
+about 0.14 the lowest curve on that
+
+ align:start position:0%
+about 0.14 the lowest curve on that
+ 
+
+ align:start position:0%
+about 0.14 the lowest curve on that
+curve right and that's the one with no
+
+ align:start position:0%
+curve right and that's the one with no
+ 
+
+ align:start position:0%
+curve right and that's the one with no
+damping little counterintuitive right
+
+ align:start position:0%
+damping little counterintuitive right
+ 
+
+ align:start position:0%
+damping little counterintuitive right
+all right well come back damping does
+
+ align:start position:0%
+all right well come back damping does
+ 
+
+ align:start position:0%
+all right well come back damping does
+help but not heat not at this point so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we we need to find a value of Omega over
+
+ align:start position:0%
+we we need to find a value of Omega over
+ 
+
+ align:start position:0%
+we we need to find a value of Omega over
+Omega n which is greater than one that
+
+ align:start position:0%
+Omega n which is greater than one that
+ 
+
+ align:start position:0%
+Omega n which is greater than one that
+satisfies this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what we're after and this is kind
+
+ align:start position:0%
+that's what we're after and this is kind
+ 
+
+ align:start position:0%
+that's what we're after and this is kind
+of messy to work with the easy and I
+
+ align:start position:0%
+of messy to work with the easy and I
+ 
+
+ align:start position:0%
+of messy to work with the easy and I
+sense I know the one that works the best
+
+ align:start position:0%
+sense I know the one that works the best
+ 
+
+ align:start position:0%
+sense I know the one that works the best
+is the one with no damping
+
+ align:start position:0%
+is the one with no damping
+ 
+
+ align:start position:0%
+is the one with no damping
+we'll just so we'll solve the no damping
+
+ align:start position:0%
+we'll just so we'll solve the no damping
+ 
+
+ align:start position:0%
+we'll just so we'll solve the no damping
+one first which makes the algebra really
+
+ align:start position:0%
+one first which makes the algebra really
+ 
+
+ align:start position:0%
+one first which makes the algebra really
+easy and then we can go back and say now
+
+ align:start position:0%
+easy and then we can go back and say now
+ 
+
+ align:start position:0%
+easy and then we can go back and say now
+what happens if you add some damping so
+
+ align:start position:0%
+what happens if you add some damping so
+ 
+
+ align:start position:0%
+what happens if you add some damping so
+for the case there's no damping the
+
+ align:start position:0%
+for the case there's no damping the
+ 
+
+ align:start position:0%
+for the case there's no damping the
+numerator goes to one the denominator
+
+ align:start position:0%
+numerator goes to one the denominator
+ 
+
+ align:start position:0%
+numerator goes to one the denominator
+goes to just 1 over 1 minus Omega
+
+ align:start position:0%
+goes to just 1 over 1 minus Omega
+ 
+
+ align:start position:0%
+goes to just 1 over 1 minus Omega
+squared over Omega N squared so it
+
+ align:start position:0%
+squared over Omega N squared so it
+ 
+
+ align:start position:0%
+squared over Omega N squared so it
+becomes that that's simple and because I
+
+ align:start position:0%
+becomes that that's simple and because I
+ 
+
+ align:start position:0%
+becomes that that's simple and because I
+want to work with number this is ratio
+
+ align:start position:0%
+want to work with number this is ratio
+ 
+
+ align:start position:0%
+want to work with number this is ratio
+bigger than 1 I don't want this to be
+
+ align:start position:0%
+bigger than 1 I don't want this to be
+ 
+
+ align:start position:0%
+bigger than 1 I don't want this to be
+negative and I want to mess with keep
+
+ align:start position:0%
+negative and I want to mess with keep
+ 
+
+ align:start position:0%
+negative and I want to mess with keep
+carrying along absolute value signs this
+
+ align:start position:0%
+carrying along absolute value signs this
+ 
+
+ align:start position:0%
+carrying along absolute value signs this
+is the same thing as 1 over Omega
+
+ align:start position:0%
+is the same thing as 1 over Omega
+ 
+
+ align:start position:0%
+is the same thing as 1 over Omega
+squared over Omega N squared minus 1
+
+ align:start position:0%
+squared over Omega N squared minus 1
+ 
+
+ align:start position:0%
+squared over Omega N squared minus 1
+I just reverse this because I know we're
+
+ align:start position:0%
+I just reverse this because I know we're
+ 
+
+ align:start position:0%
+I just reverse this because I know we're
+going to deal only with ones greater
+
+ align:start position:0%
+going to deal only with ones greater
+ 
+
+ align:start position:0%
+going to deal only with ones greater
+than 1 here and I need this to be equal
+
+ align:start position:0%
+than 1 here and I need this to be equal
+ 
+
+ align:start position:0%
+than 1 here and I need this to be equal
+to 0.1 and that's just algebra you can
+
+ align:start position:0%
+to 0.1 and that's just algebra you can
+ 
+
+ align:start position:0%
+to 0.1 and that's just algebra you can
+solve that this implies that Omega over
+
+ align:start position:0%
+solve that this implies that Omega over
+ 
+
+ align:start position:0%
+solve that this implies that Omega over
+Omega N equals root 11 I recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is 3.31
+
+ align:start position:0%
+and that is 3.31
+ 
+
+ align:start position:0%
+and that is 3.31
+so this is saying on that curve if you
+
+ align:start position:0%
+so this is saying on that curve if you
+ 
+
+ align:start position:0%
+so this is saying on that curve if you
+go out to Omega over Omega N equals
+
+ align:start position:0%
+go out to Omega over Omega N equals
+ 
+
+ align:start position:0%
+go out to Omega over Omega N equals
+three point three one right about where
+
+ align:start position:0%
+three point three one right about where
+ 
+
+ align:start position:0%
+three point three one right about where
+that arrow is that the curve for zero
+
+ align:start position:0%
+that arrow is that the curve for zero
+ 
+
+ align:start position:0%
+that arrow is that the curve for zero
+damping drops down to zero point one and
+
+ align:start position:0%
+damping drops down to zero point one and
+ 
+
+ align:start position:0%
+damping drops down to zero point one and
+now if at that frequency so we need that
+
+ align:start position:0%
+now if at that frequency so we need that
+ 
+
+ align:start position:0%
+now if at that frequency so we need that
+means we have to design the spring
+
+ align:start position:0%
+means we have to design the spring
+ 
+
+ align:start position:0%
+means we have to design the spring
+support such that Omega n is equal to
+
+ align:start position:0%
+support such that Omega n is equal to
+ 
+
+ align:start position:0%
+support such that Omega n is equal to
+Omega over three point three one but
+
+ align:start position:0%
+Omega over three point three one but
+ 
+
+ align:start position:0%
+Omega over three point three one but
+Omega where do we start
+
+ align:start position:0%
+Omega where do we start
+ 
+
+ align:start position:0%
+Omega where do we start
+so F equals 20 Hertz Omega equals two pi
+
+ align:start position:0%
+so F equals 20 Hertz Omega equals two pi
+ 
+
+ align:start position:0%
+so F equals 20 Hertz Omega equals two pi
+F do I have that number here no but so
+
+ align:start position:0%
+F do I have that number here no but so
+ 
+
+ align:start position:0%
+F do I have that number here no but so
+this tells me that I need a natural
+
+ align:start position:0%
+this tells me that I need a natural
+ 
+
+ align:start position:0%
+this tells me that I need a natural
+frequency that is omega over three point
+
+ align:start position:0%
+frequency that is omega over three point
+ 
+
+ align:start position:0%
+frequency that is omega over three point
+three one or I need an F and that is F
+
+ align:start position:0%
+three one or I need an F and that is F
+ 
+
+ align:start position:0%
+three one or I need an F and that is F
+over three point three one is twenty
+
+ align:start position:0%
+over three point three one is twenty
+ 
+
+ align:start position:0%
+over three point three one is twenty
+Hertz
+
+ align:start position:0%
+Hertz
+ 
+
+ align:start position:0%
+Hertz
+over three point three one and that
+
+ align:start position:0%
+over three point three one and that
+ 
+
+ align:start position:0%
+over three point three one and that
+number I do have six point zero four
+
+ align:start position:0%
+number I do have six point zero four
+ 
+
+ align:start position:0%
+number I do have six point zero four
+Hertz so I need a support whose natural
+
+ align:start position:0%
+Hertz so I need a support whose natural
+ 
+
+ align:start position:0%
+Hertz so I need a support whose natural
+frequency is twenty Hertz divided by
+
+ align:start position:0%
+frequency is twenty Hertz divided by
+ 
+
+ align:start position:0%
+frequency is twenty Hertz divided by
+this ratio by three point three one and
+
+ align:start position:0%
+this ratio by three point three one and
+ 
+
+ align:start position:0%
+this ratio by three point three one and
+that's I need a support is natural
+
+ align:start position:0%
+that's I need a support is natural
+ 
+
+ align:start position:0%
+that's I need a support is natural
+frequency is six point zero four Hertz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's how you go about designing a
+
+ align:start position:0%
+and that's how you go about designing a
+ 
+
+ align:start position:0%
+and that's how you go about designing a
+flexible base to isolate something from
+
+ align:start position:0%
+flexible base to isolate something from
+ 
+
+ align:start position:0%
+flexible base to isolate something from
+vibration of whatever it's sitting on
+
+ align:start position:0%
+vibration of whatever it's sitting on
+ 
+
+ align:start position:0%
+vibration of whatever it's sitting on
+alright let's so my F here twenty Hertz
+
+ align:start position:0%
+alright let's so my F here twenty Hertz
+ 
+
+ align:start position:0%
+alright let's so my F here twenty Hertz
+well my F n needs to be six point zero
+
+ align:start position:0%
+well my F n needs to be six point zero
+ 
+
+ align:start position:0%
+well my F n needs to be six point zero
+four Hertz that implies x to pi
+
+ align:start position:0%
+four Hertz that implies x to pi
+ 
+
+ align:start position:0%
+four Hertz that implies x to pi
+I'm looking for 37 point ninety six
+
+ align:start position:0%
+I'm looking for 37 point ninety six
+ 
+
+ align:start position:0%
+I'm looking for 37 point ninety six
+radians per second and that's equal to
+
+ align:start position:0%
+radians per second and that's equal to
+ 
+
+ align:start position:0%
+radians per second and that's equal to
+square root of K over m so now what's
+
+ align:start position:0%
+square root of K over m so now what's
+ 
+
+ align:start position:0%
+square root of K over m so now what's
+the M well it's whatever the mass of the
+
+ align:start position:0%
+the M well it's whatever the mass of the
+ 
+
+ align:start position:0%
+the M well it's whatever the mass of the
+microscope plus its base
+
+ align:start position:0%
+microscope plus its base
+ 
+
+ align:start position:0%
+microscope plus its base
+whatever your whatever is being
+
+ align:start position:0%
+whatever your whatever is being
+ 
+
+ align:start position:0%
+whatever your whatever is being
+supported by the springs the will have
+
+ align:start position:0%
+supported by the springs the will have
+ 
+
+ align:start position:0%
+supported by the springs the will have
+that mass you have to choose the K so
+
+ align:start position:0%
+that mass you have to choose the K so
+ 
+
+ align:start position:0%
+that mass you have to choose the K so
+let's say let say the M total for this
+
+ align:start position:0%
+let's say let say the M total for this
+ 
+
+ align:start position:0%
+let's say let say the M total for this
+system is 20 kilograms solve this
+
+ align:start position:0%
+system is 20 kilograms solve this
+ 
+
+ align:start position:0%
+system is 20 kilograms solve this
+equation for K and that implies that K
+
+ align:start position:0%
+equation for K and that implies that K
+ 
+
+ align:start position:0%
+equation for K and that implies that K
+is twenty eight thousand eight hundred
+
+ align:start position:0%
+is twenty eight thousand eight hundred
+ 
+
+ align:start position:0%
+is twenty eight thousand eight hundred
+and twenty-seven Newton's per meter so
+
+ align:start position:0%
+and twenty-seven Newton's per meter so
+ 
+
+ align:start position:0%
+and twenty-seven Newton's per meter so
+if we were designed this system and it
+
+ align:start position:0%
+if we were designed this system and it
+ 
+
+ align:start position:0%
+if we were designed this system and it
+really mounts up to in the case of this
+
+ align:start position:0%
+really mounts up to in the case of this
+ 
+
+ align:start position:0%
+really mounts up to in the case of this
+let's see beams is this stiffness of a
+
+ align:start position:0%
+let's see beams is this stiffness of a
+ 
+
+ align:start position:0%
+let's see beams is this stiffness of a
+beam wow that's a good we'll do this we
+
+ align:start position:0%
+beam wow that's a good we'll do this we
+ 
+
+ align:start position:0%
+beam wow that's a good we'll do this we
+have a little we have a cantilever here
+
+ align:start position:0%
+have a little we have a cantilever here
+ 
+
+ align:start position:0%
+have a little we have a cantilever here
+and we've got a mass on the end but you
+
+ align:start position:0%
+and we've got a mass on the end but you
+ 
+
+ align:start position:0%
+and we've got a mass on the end but you
+most of you have been taken to double O
+
+ align:start position:0%
+most of you have been taken to double O
+ 
+
+ align:start position:0%
+most of you have been taken to double O
+one if you put a force out here P what's
+
+ align:start position:0%
+one if you put a force out here P what's
+ 
+
+ align:start position:0%
+one if you put a force out here P what's
+the deflection at the end of a
+
+ align:start position:0%
+the deflection at the end of a
+ 
+
+ align:start position:0%
+the deflection at the end of a
+cantilever okay so Delta PL cubed over
+
+ align:start position:0%
+cantilever okay so Delta PL cubed over
+ 
+
+ align:start position:0%
+cantilever okay so Delta PL cubed over
+three e I and the load this force is
+
+ align:start position:0%
+three e I and the load this force is
+ 
+
+ align:start position:0%
+three e I and the load this force is
+equal to some K equivalent times Delta
+
+ align:start position:0%
+equal to some K equivalent times Delta
+ 
+
+ align:start position:0%
+equal to some K equivalent times Delta
+right this is just a spring and K times
+
+ align:start position:0%
+right this is just a spring and K times
+ 
+
+ align:start position:0%
+right this is just a spring and K times
+the displacement is the force it takes
+
+ align:start position:0%
+the displacement is the force it takes
+ 
+
+ align:start position:0%
+the displacement is the force it takes
+to do it
+
+ align:start position:0%
+to do it
+ 
+
+ align:start position:0%
+to do it
+so P is my force the Pring constant is
+
+ align:start position:0%
+so P is my force the Pring constant is
+ 
+
+ align:start position:0%
+so P is my force the Pring constant is
+somehow associated with the rest of this
+
+ align:start position:0%
+somehow associated with the rest of this
+ 
+
+ align:start position:0%
+somehow associated with the rest of this
+stuff so if I solve for P over Delta I
+
+ align:start position:0%
+stuff so if I solve for P over Delta I
+ 
+
+ align:start position:0%
+stuff so if I solve for P over Delta I
+get three
+
+ align:start position:0%
+get three
+ 
+
+ align:start position:0%
+get three
+I over L cubed okay so if if my if I'm
+
+ align:start position:0%
+I over L cubed okay so if if my if I'm
+ 
+
+ align:start position:0%
+I over L cubed okay so if if my if I'm
+running right at the natural frequency
+
+ align:start position:0%
+running right at the natural frequency
+ 
+
+ align:start position:0%
+running right at the natural frequency
+here and I want to reduce this to a
+
+ align:start position:0%
+here and I want to reduce this to a
+ 
+
+ align:start position:0%
+here and I want to reduce this to a
+tenth of its motion I need to change the
+
+ align:start position:0%
+tenth of its motion I need to change the
+ 
+
+ align:start position:0%
+tenth of its motion I need to change the
+spring constant of the cantilever by
+
+ align:start position:0%
+spring constant of the cantilever by
+ 
+
+ align:start position:0%
+spring constant of the cantilever by
+factor of what I need to change the
+
+ align:start position:0%
+factor of what I need to change the
+ 
+
+ align:start position:0%
+factor of what I need to change the
+natural frequency by a factor of three
+
+ align:start position:0%
+natural frequency by a factor of three
+ 
+
+ align:start position:0%
+natural frequency by a factor of three
+point three one so my K equivalent here
+
+ align:start position:0%
+point three one so my K equivalent here
+ 
+
+ align:start position:0%
+point three one so my K equivalent here
+is 3e I over L cubed and that's what
+
+ align:start position:0%
+is 3e I over L cubed and that's what
+ 
+
+ align:start position:0%
+is 3e I over L cubed and that's what
+would go into this equation but I know
+
+ align:start position:0%
+would go into this equation but I know
+ 
+
+ align:start position:0%
+would go into this equation but I know
+that I have a I have a natural frequency
+
+ align:start position:0%
+that I have a I have a natural frequency
+ 
+
+ align:start position:0%
+that I have a I have a natural frequency
+right now I want it to go down by a
+
+ align:start position:0%
+right now I want it to go down by a
+ 
+
+ align:start position:0%
+right now I want it to go down by a
+factor of three point three one so that
+
+ align:start position:0%
+factor of three point three one so that
+ 
+
+ align:start position:0%
+factor of three point three one so that
+means I need to decrease K by the such
+
+ align:start position:0%
+means I need to decrease K by the such
+ 
+
+ align:start position:0%
+means I need to decrease K by the such
+that the square root of K goes down by
+
+ align:start position:0%
+that the square root of K goes down by
+ 
+
+ align:start position:0%
+that the square root of K goes down by
+the factor three point three one so how
+
+ align:start position:0%
+the factor three point three one so how
+ 
+
+ align:start position:0%
+the factor three point three one so how
+do how much do I have to change the
+
+ align:start position:0%
+do how much do I have to change the
+ 
+
+ align:start position:0%
+do how much do I have to change the
+length probably something like the
+
+ align:start position:0%
+length probably something like the
+ 
+
+ align:start position:0%
+length probably something like the
+square root of three point three one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly two if I double the length of
+
+ align:start position:0%
+roughly two if I double the length of
+ 
+
+ align:start position:0%
+roughly two if I double the length of
+this thing you think it's going to work
+
+ align:start position:0%
+this thing you think it's going to work
+ 
+
+ align:start position:0%
+this thing you think it's going to work
+I double the length of this thing and
+
+ align:start position:0%
+I double the length of this thing and
+ 
+
+ align:start position:0%
+I double the length of this thing and
+turn it back on we shouldn't see much
+
+ align:start position:0%
+turn it back on we shouldn't see much
+ 
+
+ align:start position:0%
+turn it back on we shouldn't see much
+motion out of this that's moving a lot
+
+ align:start position:0%
+motion out of this that's moving a lot
+ 
+
+ align:start position:0%
+motion out of this that's moving a lot
+Oh a tiny tiny bit it works so that's
+
+ align:start position:0%
+Oh a tiny tiny bit it works so that's
+ 
+
+ align:start position:0%
+Oh a tiny tiny bit it works so that's
+one step of vibration isolation now I'm
+
+ align:start position:0%
+one step of vibration isolation now I'm
+ 
+
+ align:start position:0%
+one step of vibration isolation now I'm
+going to show you a vibration engineer
+
+ align:start position:0%
+going to show you a vibration engineer
+ 
+
+ align:start position:0%
+going to show you a vibration engineer
+trick which is very handy thing to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where's my strong magnet here so I've
+
+ align:start position:0%
+where's my strong magnet here so I've
+ 
+
+ align:start position:0%
+where's my strong magnet here so I've
+got another beam just like this one and
+
+ align:start position:0%
+got another beam just like this one and
+ 
+
+ align:start position:0%
+got another beam just like this one and
+a pretty pretty massive magnet on it so
+
+ align:start position:0%
+a pretty pretty massive magnet on it so
+ 
+
+ align:start position:0%
+a pretty pretty massive magnet on it so
+it makes another cantilever beam just
+
+ align:start position:0%
+it makes another cantilever beam just
+ 
+
+ align:start position:0%
+it makes another cantilever beam just
+like I got over there okay so I claim
+
+ align:start position:0%
+like I got over there okay so I claim
+ 
+
+ align:start position:0%
+like I got over there okay so I claim
+that with just a ruler if I clamp this
+
+ align:start position:0%
+that with just a ruler if I clamp this
+ 
+
+ align:start position:0%
+that with just a ruler if I clamp this
+down and at some length I claim with
+
+ align:start position:0%
+down and at some length I claim with
+ 
+
+ align:start position:0%
+down and at some length I claim with
+just a ruler I can predict the natural
+
+ align:start position:0%
+just a ruler I can predict the natural
+ 
+
+ align:start position:0%
+just a ruler I can predict the natural
+frequency of that take a couple minutes
+
+ align:start position:0%
+frequency of that take a couple minutes
+ 
+
+ align:start position:0%
+frequency of that take a couple minutes
+and see if you figure out how to do it
+
+ align:start position:0%
+and see if you figure out how to do it
+ 
+
+ align:start position:0%
+and see if you figure out how to do it
+think about that just a ruler
+
+ align:start position:0%
+think about that just a ruler
+ 
+
+ align:start position:0%
+think about that just a ruler
+measurements that I can make I don't
+
+ align:start position:0%
+measurements that I can make I don't
+ 
+
+ align:start position:0%
+measurements that I can make I don't
+just I don't know how long it don't know
+
+ align:start position:0%
+just I don't know how long it don't know
+ 
+
+ align:start position:0%
+just I don't know how long it don't know
+how long it actually is I don't know I
+
+ align:start position:0%
+how long it actually is I don't know I
+ 
+
+ align:start position:0%
+how long it actually is I don't know I
+think it is it's I know it's steel but
+
+ align:start position:0%
+think it is it's I know it's steel but
+ 
+
+ align:start position:0%
+think it is it's I know it's steel but
+you just don't have enough information
+
+ align:start position:0%
+you just don't have enough information
+ 
+
+ align:start position:0%
+you just don't have enough information
+to compute L q 3i over L cubed but with
+
+ align:start position:0%
+to compute L q 3i over L cubed but with
+ 
+
+ align:start position:0%
+to compute L q 3i over L cubed but with
+simply with a ruler I'm going to be able
+
+ align:start position:0%
+simply with a ruler I'm going to be able
+ 
+
+ align:start position:0%
+simply with a ruler I'm going to be able
+to do this talk about it think about
+
+ align:start position:0%
+to do this talk about it think about
+ 
+
+ align:start position:0%
+to do this talk about it think about
+that well I set up D set up the
+
+ align:start position:0%
+that well I set up D set up the
+ 
+
+ align:start position:0%
+that well I set up D set up the
+experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay who's got it figured out we want to
+
+ align:start position:0%
+okay who's got it figured out we want to
+ 
+
+ align:start position:0%
+okay who's got it figured out we want to
+take a shot at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's my beam I put the weight on
+
+ align:start position:0%
+so there's my beam I put the weight on
+ 
+
+ align:start position:0%
+so there's my beam I put the weight on
+it what does the beam do statically
+
+ align:start position:0%
+it what does the beam do statically
+ 
+
+ align:start position:0%
+it what does the beam do statically
+bends a little right K X static equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mg right has two so X static is when I
+
+ align:start position:0%
+mg right has two so X static is when I
+ 
+
+ align:start position:0%
+mg right has two so X static is when I
+call it Delta here so K Delta equals mg
+
+ align:start position:0%
+call it Delta here so K Delta equals mg
+ 
+
+ align:start position:0%
+call it Delta here so K Delta equals mg
+K equals mg over Delta natural frequency
+
+ align:start position:0%
+K equals mg over Delta natural frequency
+ 
+
+ align:start position:0%
+K equals mg over Delta natural frequency
+equals square root K over m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+credibly simple huh so what's the
+
+ align:start position:0%
+credibly simple huh so what's the
+ 
+
+ align:start position:0%
+credibly simple huh so what's the
+experiment that I would what what
+
+ align:start position:0%
+experiment that I would what what
+ 
+
+ align:start position:0%
+experiment that I would what what
+measurement would I make Delta right put
+
+ align:start position:0%
+measurement would I make Delta right put
+ 
+
+ align:start position:0%
+measurement would I make Delta right put
+my ruler up there I measure its static
+
+ align:start position:0%
+my ruler up there I measure its static
+ 
+
+ align:start position:0%
+my ruler up there I measure its static
+position like that and I put my mass on
+
+ align:start position:0%
+position like that and I put my mass on
+ 
+
+ align:start position:0%
+position like that and I put my mass on
+it and I measure the static position
+
+ align:start position:0%
+it and I measure the static position
+ 
+
+ align:start position:0%
+it and I measure the static position
+again I measure the Delta and I get a
+
+ align:start position:0%
+again I measure the Delta and I get a
+ 
+
+ align:start position:0%
+again I measure the Delta and I get a
+prediction and I did this in my in my
+
+ align:start position:0%
+prediction and I did this in my in my
+ 
+
+ align:start position:0%
+prediction and I did this in my in my
+office
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the Delta that I measured so the
+
+ align:start position:0%
+and the Delta that I measured so the
+ 
+
+ align:start position:0%
+and the Delta that I measured so the
+length is actually set it at a
+
+ align:start position:0%
+length is actually set it at a
+ 
+
+ align:start position:0%
+length is actually set it at a
+particular length it was 18 centimeters
+
+ align:start position:0%
+particular length it was 18 centimeters
+ 
+
+ align:start position:0%
+particular length it was 18 centimeters
+Delta measured thick 0.5 centimeters or
+
+ align:start position:0%
+Delta measured thick 0.5 centimeters or
+ 
+
+ align:start position:0%
+Delta measured thick 0.5 centimeters or
+0.0 0.0 5 meters and if you compute
+
+ align:start position:0%
+0.0 0.0 5 meters and if you compute
+ 
+
+ align:start position:0%
+0.0 0.0 5 meters and if you compute
+Omega n then equals the square root of
+
+ align:start position:0%
+Omega n then equals the square root of
+ 
+
+ align:start position:0%
+Omega n then equals the square root of
+nine point eight one over 0.05
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want this in Hertz I am divided by
+
+ align:start position:0%
+and I want this in Hertz I am divided by
+ 
+
+ align:start position:0%
+and I want this in Hertz I am divided by
+2pi this comes out as 7.0 five Hertz and
+
+ align:start position:0%
+2pi this comes out as 7.0 five Hertz and
+ 
+
+ align:start position:0%
+2pi this comes out as 7.0 five Hertz and
+FN measured was six point five seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty good but not perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what and it's because it made an
+
+ align:start position:0%
+what and it's because it made an
+ 
+
+ align:start position:0%
+what and it's because it made an
+approximation I glossed over pretty
+
+ align:start position:0%
+approximation I glossed over pretty
+ 
+
+ align:start position:0%
+approximation I glossed over pretty
+quickly what has been left out of this
+
+ align:start position:0%
+quickly what has been left out of this
+ 
+
+ align:start position:0%
+quickly what has been left out of this
+system that would cause the measured
+
+ align:start position:0%
+system that would cause the measured
+ 
+
+ align:start position:0%
+system that would cause the measured
+natural frequency to be lower than the
+
+ align:start position:0%
+natural frequency to be lower than the
+ 
+
+ align:start position:0%
+natural frequency to be lower than the
+predicted what's been ignored yes
+
+ align:start position:0%
+predicted what's been ignored yes
+ 
+
+ align:start position:0%
+predicted what's been ignored yes
+damping ah maybe how much damping do we
+
+ align:start position:0%
+damping ah maybe how much damping do we
+ 
+
+ align:start position:0%
+damping ah maybe how much damping do we
+have in this system probably at least
+
+ align:start position:0%
+have in this system probably at least
+ 
+
+ align:start position:0%
+have in this system probably at least
+ten cycles the decay halfway right
+
+ align:start position:0%
+ten cycles the decay halfway right
+ 
+
+ align:start position:0%
+ten cycles the decay halfway right
+certainly less than one percent so
+
+ align:start position:0%
+certainly less than one percent so
+ 
+
+ align:start position:0%
+certainly less than one percent so
+natural is the damped natural frequency
+
+ align:start position:0%
+natural is the damped natural frequency
+ 
+
+ align:start position:0%
+natural is the damped natural frequency
+is equal to the natural frequency the
+
+ align:start position:0%
+is equal to the natural frequency the
+ 
+
+ align:start position:0%
+is equal to the natural frequency the
+square root of 1 minus Zeta squared so
+
+ align:start position:0%
+square root of 1 minus Zeta squared so
+ 
+
+ align:start position:0%
+square root of 1 minus Zeta squared so
+this is something like way less than
+
+ align:start position:0%
+this is something like way less than
+ 
+
+ align:start position:0%
+this is something like way less than
+half a percent difference so that
+
+ align:start position:0%
+half a percent difference so that
+ 
+
+ align:start position:0%
+half a percent difference so that
+wouldn't account for it that's
+
+ align:start position:0%
+wouldn't account for it that's
+ 
+
+ align:start position:0%
+wouldn't account for it that's
+considerably more than half a percent so
+
+ align:start position:0%
+considerably more than half a percent so
+ 
+
+ align:start position:0%
+considerably more than half a percent so
+damping couldn't do it yeah ah the mass
+
+ align:start position:0%
+damping couldn't do it yeah ah the mass
+ 
+
+ align:start position:0%
+damping couldn't do it yeah ah the mass
+of the bar does this flexure have mass
+
+ align:start position:0%
+of the bar does this flexure have mass
+ 
+
+ align:start position:0%
+of the bar does this flexure have mass
+yeah it's probably the order of you've
+
+ align:start position:0%
+yeah it's probably the order of you've
+ 
+
+ align:start position:0%
+yeah it's probably the order of you've
+stack them all up and compared to that
+
+ align:start position:0%
+stack them all up and compared to that
+ 
+
+ align:start position:0%
+stack them all up and compared to that
+it's probably you I might even be as
+
+ align:start position:0%
+it's probably you I might even be as
+ 
+
+ align:start position:0%
+it's probably you I might even be as
+much as half the mass at the end and as
+
+ align:start position:0%
+much as half the mass at the end and as
+ 
+
+ align:start position:0%
+much as half the mass at the end and as
+it vibrates back and forth does it have
+
+ align:start position:0%
+it vibrates back and forth does it have
+ 
+
+ align:start position:0%
+it vibrates back and forth does it have
+kinetic energy yeah we've ignored the
+
+ align:start position:0%
+kinetic energy yeah we've ignored the
+ 
+
+ align:start position:0%
+kinetic energy yeah we've ignored the
+kinetic energy of the mass and in fact
+
+ align:start position:0%
+kinetic energy of the mass and in fact
+ 
+
+ align:start position:0%
+kinetic energy of the mass and in fact
+that's the principle error here we've
+
+ align:start position:0%
+that's the principle error here we've
+ 
+
+ align:start position:0%
+that's the principle error here we've
+left out the mass it's actually pretty
+
+ align:start position:0%
+left out the mass it's actually pretty
+ 
+
+ align:start position:0%
+left out the mass it's actually pretty
+simple way to account using energy just
+
+ align:start position:0%
+simple way to account using energy just
+ 
+
+ align:start position:0%
+simple way to account using energy just
+thinking in launch terms you can account
+
+ align:start position:0%
+thinking in launch terms you can account
+ 
+
+ align:start position:0%
+thinking in launch terms you can account
+for the energy of the mass in this
+
+ align:start position:0%
+for the energy of the mass in this
+ 
+
+ align:start position:0%
+for the energy of the mass in this
+single degree freedom system and get a
+
+ align:start position:0%
+single degree freedom system and get a
+ 
+
+ align:start position:0%
+single degree freedom system and get a
+very accurate position of a prediction
+
+ align:start position:0%
+very accurate position of a prediction
+ 
+
+ align:start position:0%
+very accurate position of a prediction
+we won't do that today but it will do
+
+ align:start position:0%
+we won't do that today but it will do
+ 
+
+ align:start position:0%
+we won't do that today but it will do
+that before the terms out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this applies to any simple
+
+ align:start position:0%
+okay this applies to any simple
+ 
+
+ align:start position:0%
+okay this applies to any simple
+mass-spring system in the presence of
+
+ align:start position:0%
+mass-spring system in the presence of
+ 
+
+ align:start position:0%
+mass-spring system in the presence of
+gravity so here's a mass and actually
+
+ align:start position:0%
+gravity so here's a mass and actually
+ 
+
+ align:start position:0%
+gravity so here's a mass and actually
+I'm we're doing the problem today where
+
+ align:start position:0%
+I'm we're doing the problem today where
+ 
+
+ align:start position:0%
+I'm we're doing the problem today where
+I'm moving the base here so here's its
+
+ align:start position:0%
+I'm moving the base here so here's its
+ 
+
+ align:start position:0%
+I'm moving the base here so here's its
+base so hisses this is the table moving
+
+ align:start position:0%
+base so hisses this is the table moving
+ 
+
+ align:start position:0%
+base so hisses this is the table moving
+and if I do this it clearly makes that
+
+ align:start position:0%
+and if I do this it clearly makes that
+ 
+
+ align:start position:0%
+and if I do this it clearly makes that
+move if I do this really fast it doesn't
+
+ align:start position:0%
+move if I do this really fast it doesn't
+ 
+
+ align:start position:0%
+move if I do this really fast it doesn't
+know very much if I do a close-up
+
+ align:start position:0%
+know very much if I do a close-up
+ 
+
+ align:start position:0%
+know very much if I do a close-up
+natural frequency it moves a lot if I
+
+ align:start position:0%
+natural frequency it moves a lot if I
+ 
+
+ align:start position:0%
+natural frequency it moves a lot if I
+move it very slowly as I go up one unit
+
+ align:start position:0%
+move it very slowly as I go up one unit
+ 
+
+ align:start position:0%
+move it very slowly as I go up one unit
+this it follows me exactly that's why
+
+ align:start position:0%
+this it follows me exactly that's why
+ 
+
+ align:start position:0%
+this it follows me exactly that's why
+that plot goes to one at very very low
+
+ align:start position:0%
+that plot goes to one at very very low
+ 
+
+ align:start position:0%
+that plot goes to one at very very low
+frequency the support and the mass move
+
+ align:start position:0%
+frequency the support and the mass move
+ 
+
+ align:start position:0%
+frequency the support and the mass move
+exactly together at high very high
+
+ align:start position:0%
+exactly together at high very high
+ 
+
+ align:start position:0%
+exactly together at high very high
+frequency if I can stop the transient
+
+ align:start position:0%
+frequency if I can stop the transient
+ 
+
+ align:start position:0%
+frequency if I can stop the transient
+can't do it very well the mass doesn't
+
+ align:start position:0%
+can't do it very well the mass doesn't
+ 
+
+ align:start position:0%
+can't do it very well the mass doesn't
+move much the basement lives a lot and
+
+ align:start position:0%
+move much the basement lives a lot and
+ 
+
+ align:start position:0%
+move much the basement lives a lot and
+at resonance it goes nuts
+
+ align:start position:0%
+at resonance it goes nuts
+ 
+
+ align:start position:0%
+at resonance it goes nuts
+okay the unstretched length of this
+
+ align:start position:0%
+okay the unstretched length of this
+ 
+
+ align:start position:0%
+okay the unstretched length of this
+spring is about seven inches the square
+
+ align:start position:0%
+spring is about seven inches the square
+ 
+
+ align:start position:0%
+spring is about seven inches the square
+root of G over Delta I ought to be able
+
+ align:start position:0%
+root of G over Delta I ought to be able
+ 
+
+ align:start position:0%
+root of G over Delta I ought to be able
+to predict this so I did a quick
+
+ align:start position:0%
+to predict this so I did a quick
+ 
+
+ align:start position:0%
+to predict this so I did a quick
+calculation on that and I came I had we
+
+ align:start position:0%
+calculation on that and I came I had we
+ 
+
+ align:start position:0%
+calculation on that and I came I had we
+did it it was like one percent error I
+
+ align:start position:0%
+did it it was like one percent error I
+ 
+
+ align:start position:0%
+did it it was like one percent error I
+measured it it's seven point three six
+
+ align:start position:0%
+measured it it's seven point three six
+ 
+
+ align:start position:0%
+measured it it's seven point three six
+radians a second and I'm predicted at
+
+ align:start position:0%
+radians a second and I'm predicted at
+ 
+
+ align:start position:0%
+radians a second and I'm predicted at
+four point seven four seven point four
+
+ align:start position:0%
+four point seven four seven point four
+ 
+
+ align:start position:0%
+four point seven four seven point four
+three measured seven point three six
+
+ align:start position:0%
+three measured seven point three six
+ 
+
+ align:start position:0%
+three measured seven point three six
+same kind of thing ignoring the mass of
+
+ align:start position:0%
+same kind of thing ignoring the mass of
+ 
+
+ align:start position:0%
+same kind of thing ignoring the mass of
+the spring a little bit so G over Delta
+
+ align:start position:0%
+the spring a little bit so G over Delta
+ 
+
+ align:start position:0%
+the spring a little bit so G over Delta
+is a great little thing to remember okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have done all but one everything
+
+ align:start position:0%
+so we have done all but one everything
+ 
+
+ align:start position:0%
+so we have done all but one everything
+we started out with today we said
+
+ align:start position:0%
+we started out with today we said
+ 
+
+ align:start position:0%
+we started out with today we said
+there's three ways to fix this and came
+
+ align:start position:0%
+there's three ways to fix this and came
+ 
+
+ align:start position:0%
+there's three ways to fix this and came
+up with the fourth way so in this case
+
+ align:start position:0%
+up with the fourth way so in this case
+ 
+
+ align:start position:0%
+up with the fourth way so in this case
+soften the spring support a lot so that
+
+ align:start position:0%
+soften the spring support a lot so that
+ 
+
+ align:start position:0%
+soften the spring support a lot so that
+the natural frequency is way less than
+
+ align:start position:0%
+the natural frequency is way less than
+ 
+
+ align:start position:0%
+the natural frequency is way less than
+the excitation we said we could what
+
+ align:start position:0%
+the excitation we said we could what
+ 
+
+ align:start position:0%
+the excitation we said we could what
+about spring supporting softening
+
+ align:start position:0%
+about spring supporting softening
+ 
+
+ align:start position:0%
+about spring supporting softening
+flexibly mounting this source so that it
+
+ align:start position:0%
+flexibly mounting this source so that it
+ 
+
+ align:start position:0%
+flexibly mounting this source so that it
+doesn't put vibration to the table
+
+ align:start position:0%
+doesn't put vibration to the table
+ 
+
+ align:start position:0%
+doesn't put vibration to the table
+that's the piece we haven't addressed so
+
+ align:start position:0%
+that's the piece we haven't addressed so
+ 
+
+ align:start position:0%
+that's the piece we haven't addressed so
+let's look into that problem now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's our source some rotating mass
+
+ align:start position:0%
+so here's our source some rotating mass
+ 
+
+ align:start position:0%
+so here's our source some rotating mass
+eccentricity causing an excitation so
+
+ align:start position:0%
+eccentricity causing an excitation so
+ 
+
+ align:start position:0%
+eccentricity causing an excitation so
+this has a force F naught e to the I
+
+ align:start position:0%
+this has a force F naught e to the I
+ 
+
+ align:start position:0%
+this has a force F naught e to the I
+Omega T which is coming from the
+
+ align:start position:0%
+Omega T which is coming from the
+ 
+
+ align:start position:0%
+Omega T which is coming from the
+rotating mass and it applies to the
+
+ align:start position:0%
+rotating mass and it applies to the
+ 
+
+ align:start position:0%
+rotating mass and it applies to the
+floor through the dashpot in the springs
+
+ align:start position:0%
+floor through the dashpot in the springs
+ 
+
+ align:start position:0%
+floor through the dashpot in the springs
+some ft I'll call it F transmitted to
+
+ align:start position:0%
+some ft I'll call it F transmitted to
+ 
+
+ align:start position:0%
+some ft I'll call it F transmitted to
+the floor e to the I Omega T and I want
+
+ align:start position:0%
+the floor e to the I Omega T and I want
+ 
+
+ align:start position:0%
+the floor e to the I Omega T and I want
+to know I need the H force transmitted
+
+ align:start position:0%
+to know I need the H force transmitted
+ 
+
+ align:start position:0%
+to know I need the H force transmitted
+per unit force input transfer function
+
+ align:start position:0%
+per unit force input transfer function
+ 
+
+ align:start position:0%
+per unit force input transfer function
+that's what I'm looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now Freebody diagram now we're going
+
+ align:start position:0%
+so now Freebody diagram now we're going
+ 
+
+ align:start position:0%
+so now Freebody diagram now we're going
+to make an assumption we're going to
+
+ align:start position:0%
+to make an assumption we're going to
+ 
+
+ align:start position:0%
+to make an assumption we're going to
+assume that the motion of the floor
+
+ align:start position:0%
+assume that the motion of the floor
+ 
+
+ align:start position:0%
+assume that the motion of the floor
+which we'll call Y of T assume that Y is
+
+ align:start position:0%
+which we'll call Y of T assume that Y is
+ 
+
+ align:start position:0%
+which we'll call Y of T assume that Y is
+much much less than X it's generally
+
+ align:start position:0%
+much much less than X it's generally
+ 
+
+ align:start position:0%
+much much less than X it's generally
+true whatever is doing is shaking like
+
+ align:start position:0%
+true whatever is doing is shaking like
+ 
+
+ align:start position:0%
+true whatever is doing is shaking like
+crazy before the tables not moving much
+
+ align:start position:0%
+crazy before the tables not moving much
+ 
+
+ align:start position:0%
+crazy before the tables not moving much
+underneath it so I would assume for the
+
+ align:start position:0%
+underneath it so I would assume for the
+ 
+
+ align:start position:0%
+underneath it so I would assume for the
+purposes of calculating forces that this
+
+ align:start position:0%
+purposes of calculating forces that this
+ 
+
+ align:start position:0%
+purposes of calculating forces that this
+is zero so for the motion X what is the
+
+ align:start position:0%
+is zero so for the motion X what is the
+ 
+
+ align:start position:0%
+is zero so for the motion X what is the
+force applied to the floor so f of T if
+
+ align:start position:0%
+force applied to the floor so f of T if
+ 
+
+ align:start position:0%
+force applied to the floor so f of T if
+you have a positive displacement X the
+
+ align:start position:0%
+you have a positive displacement X the
+ 
+
+ align:start position:0%
+you have a positive displacement X the
+force is KX you have a positive velocity
+
+ align:start position:0%
+force is KX you have a positive velocity
+ 
+
+ align:start position:0%
+force is KX you have a positive velocity
+X the force pulling up on the floor
+
+ align:start position:0%
+X the force pulling up on the floor
+ 
+
+ align:start position:0%
+X the force pulling up on the floor
+through the dashpot is CX dot so the
+
+ align:start position:0%
+through the dashpot is CX dot so the
+ 
+
+ align:start position:0%
+through the dashpot is CX dot so the
+other way of saying that is here's our
+
+ align:start position:0%
+other way of saying that is here's our
+ 
+
+ align:start position:0%
+other way of saying that is here's our
+free body diagram here's our F naught e
+
+ align:start position:0%
+free body diagram here's our F naught e
+ 
+
+ align:start position:0%
+free body diagram here's our F naught e
+to the I Omega T pulling up it responds
+
+ align:start position:0%
+to the I Omega T pulling up it responds
+ 
+
+ align:start position:0%
+to the I Omega T pulling up it responds
+at some X and the resulting forces
+
+ align:start position:0%
+at some X and the resulting forces
+ 
+
+ align:start position:0%
+at some X and the resulting forces
+through the spring of the dashpot we
+
+ align:start position:0%
+through the spring of the dashpot we
+ 
+
+ align:start position:0%
+through the spring of the dashpot we
+know are KX and CX dot opposing the
+
+ align:start position:0%
+know are KX and CX dot opposing the
+ 
+
+ align:start position:0%
+know are KX and CX dot opposing the
+motion acts well by third law if these
+
+ align:start position:0%
+motion acts well by third law if these
+ 
+
+ align:start position:0%
+motion acts well by third law if these
+are the forces on the spring and the
+
+ align:start position:0%
+are the forces on the spring and the
+ 
+
+ align:start position:0%
+are the forces on the spring and the
+dashpot then down here on the floor you
+
+ align:start position:0%
+dashpot then down here on the floor you
+ 
+
+ align:start position:0%
+dashpot then down here on the floor you
+better have some equal and opposite
+
+ align:start position:0%
+better have some equal and opposite
+ 
+
+ align:start position:0%
+better have some equal and opposite
+forces KX and CX dot so motion this
+
+ align:start position:0%
+forces KX and CX dot so motion this
+ 
+
+ align:start position:0%
+forces KX and CX dot so motion this
+force produces a motion X the motion X
+
+ align:start position:0%
+force produces a motion X the motion X
+ 
+
+ align:start position:0%
+force produces a motion X the motion X
+produces forces in the mass in the
+
+ align:start position:0%
+produces forces in the mass in the
+ 
+
+ align:start position:0%
+produces forces in the mass in the
+spring which make this the floor the
+
+ align:start position:0%
+spring which make this the floor the
+ 
+
+ align:start position:0%
+spring which make this the floor the
+force on the floor the spring force and
+
+ align:start position:0%
+force on the floor the spring force and
+ 
+
+ align:start position:0%
+force on the floor the spring force and
+the dashpot force okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this ft is right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's all that is positive and I'm
+
+ align:start position:0%
+that's all that is positive and I'm
+ 
+
+ align:start position:0%
+that's all that is positive and I'm
+going to assume a solution we know to
+
+ align:start position:0%
+going to assume a solution we know to
+ 
+
+ align:start position:0%
+going to assume a solution we know to
+work for X which is X e to the I Omega
+
+ align:start position:0%
+work for X which is X e to the I Omega
+ 
+
+ align:start position:0%
+work for X which is X e to the I Omega
+key we plugged it in before so if I plug
+
+ align:start position:0%
+key we plugged it in before so if I plug
+ 
+
+ align:start position:0%
+key we plugged it in before so if I plug
+that in here I get a ke plus I Omega C X
+
+ align:start position:0%
+that in here I get a ke plus I Omega C X
+ 
+
+ align:start position:0%
+that in here I get a ke plus I Omega C X
+e to the I Omega T so I can just express
+
+ align:start position:0%
+e to the I Omega T so I can just express
+ 
+
+ align:start position:0%
+e to the I Omega T so I can just express
+my force on the floor in terms of the
+
+ align:start position:0%
+my force on the floor in terms of the
+ 
+
+ align:start position:0%
+my force on the floor in terms of the
+motion X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm looking for a transfer function
+
+ align:start position:0%
+and I'm looking for a transfer function
+ 
+
+ align:start position:0%
+and I'm looking for a transfer function
+for force transmitted over force in but
+
+ align:start position:0%
+for force transmitted over force in but
+ 
+
+ align:start position:0%
+for force transmitted over force in but
+force transmitted is my ka plus I Omega
+
+ align:start position:0%
+force transmitted is my ka plus I Omega
+ 
+
+ align:start position:0%
+force transmitted is my ka plus I Omega
+C X e to the I Omega T and the force in
+
+ align:start position:0%
+C X e to the I Omega T and the force in
+ 
+
+ align:start position:0%
+C X e to the I Omega T and the force in
+is F naught e to the I Omega T cancel
+
+ align:start position:0%
+is F naught e to the I Omega T cancel
+ 
+
+ align:start position:0%
+is F naught e to the I Omega T cancel
+out the time dependent part and it says
+
+ align:start position:0%
+out the time dependent part and it says
+ 
+
+ align:start position:0%
+out the time dependent part and it says
+the transmitted force over the input
+
+ align:start position:0%
+the transmitted force over the input
+ 
+
+ align:start position:0%
+the transmitted force over the input
+force is this little complex expression
+
+ align:start position:0%
+force is this little complex expression
+ 
+
+ align:start position:0%
+force is this little complex expression
+times the response x over F but we know
+
+ align:start position:0%
+times the response x over F but we know
+ 
+
+ align:start position:0%
+times the response x over F but we know
+what that is that's the transfer
+
+ align:start position:0%
+what that is that's the transfer
+ 
+
+ align:start position:0%
+what that is that's the transfer
+function HX F so this is K plus I Omega
+
+ align:start position:0%
+function HX F so this is K plus I Omega
+ 
+
+ align:start position:0%
+function HX F so this is K plus I Omega
+C times H X F of Omega so this gives us
+
+ align:start position:0%
+C times H X F of Omega so this gives us
+ 
+
+ align:start position:0%
+C times H X F of Omega so this gives us
+a slightly different transfer function
+
+ align:start position:0%
+a slightly different transfer function
+ 
+
+ align:start position:0%
+a slightly different transfer function
+and have I proved look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before when we did x over Y we ended up
+
+ align:start position:0%
+before when we did x over Y we ended up
+ 
+
+ align:start position:0%
+before when we did x over Y we ended up
+with K plus I Omega C Y e to the I Omega
+
+ align:start position:0%
+with K plus I Omega C Y e to the I Omega
+ 
+
+ align:start position:0%
+with K plus I Omega C Y e to the I Omega
+T and we did when we did then X over Y
+
+ align:start position:0%
+T and we did when we did then X over Y
+ 
+
+ align:start position:0%
+T and we did when we did then X over Y
+we got the same same ratio as this
+
+ align:start position:0%
+we got the same same ratio as this
+ 
+
+ align:start position:0%
+we got the same same ratio as this
+exactly the same thing so I could write
+
+ align:start position:0%
+exactly the same thing so I could write
+ 
+
+ align:start position:0%
+exactly the same thing so I could write
+all this out but and let's say I'll do
+
+ align:start position:0%
+all this out but and let's say I'll do
+ 
+
+ align:start position:0%
+all this out but and let's say I'll do
+this H X over Y no I don't do that well
+
+ align:start position:0%
+this H X over Y no I don't do that well
+ 
+
+ align:start position:0%
+this H X over Y no I don't do that well
+it turns out what I'm going to tell you
+
+ align:start position:0%
+it turns out what I'm going to tell you
+ 
+
+ align:start position:0%
+it turns out what I'm going to tell you
+if you just work through this now you
+
+ align:start position:0%
+if you just work through this now you
+ 
+
+ align:start position:0%
+if you just work through this now you
+will find that H force transmitted over
+
+ align:start position:0%
+will find that H force transmitted over
+ 
+
+ align:start position:0%
+will find that H force transmitted over
+force in is exactly the same as H X over
+
+ align:start position:0%
+force in is exactly the same as H X over
+ 
+
+ align:start position:0%
+force in is exactly the same as H X over
+Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that what we really care about is
+
+ align:start position:0%
+and that what we really care about is
+ 
+
+ align:start position:0%
+and that what we really care about is
+what the magnitude is so the magnitude
+
+ align:start position:0%
+what the magnitude is so the magnitude
+ 
+
+ align:start position:0%
+what the magnitude is so the magnitude
+of these two things are the same and in
+
+ align:start position:0%
+of these two things are the same and in
+ 
+
+ align:start position:0%
+of these two things are the same and in
+fact just work out to that same
+
+ align:start position:0%
+fact just work out to that same
+ 
+
+ align:start position:0%
+fact just work out to that same
+expression as before the 1 plus 2 Zeta
+
+ align:start position:0%
+expression as before the 1 plus 2 Zeta
+ 
+
+ align:start position:0%
+expression as before the 1 plus 2 Zeta
+Omega over Omega N squared square root
+
+ align:start position:0%
+Omega over Omega N squared square root
+ 
+
+ align:start position:0%
+Omega over Omega N squared square root
+all over the usual but denominator so
+
+ align:start position:0%
+all over the usual but denominator so
+ 
+
+ align:start position:0%
+all over the usual but denominator so
+conveniently for vibration isolation the
+
+ align:start position:0%
+conveniently for vibration isolation the
+ 
+
+ align:start position:0%
+conveniently for vibration isolation the
+two the solution to the two problems are
+
+ align:start position:0%
+two the solution to the two problems are
+ 
+
+ align:start position:0%
+two the solution to the two problems are
+exactly the same so if you have that one
+
+ align:start position:0%
+exactly the same so if you have that one
+ 
+
+ align:start position:0%
+exactly the same so if you have that one
+you have the transfer function XY that
+
+ align:start position:0%
+you have the transfer function XY that
+ 
+
+ align:start position:0%
+you have the transfer function XY that
+was projected on the screen a minute ago
+
+ align:start position:0%
+was projected on the screen a minute ago
+ 
+
+ align:start position:0%
+was projected on the screen a minute ago
+it is also the force transmitted to
+
+ align:start position:0%
+it is also the force transmitted to
+ 
+
+ align:start position:0%
+it is also the force transmitted to
+force in transfer function so you just
+
+ align:start position:0%
+force in transfer function so you just
+ 
+
+ align:start position:0%
+force in transfer function so you just
+have to get you have to remember one and
+
+ align:start position:0%
+have to get you have to remember one and
+ 
+
+ align:start position:0%
+have to get you have to remember one and
+if you will now want to we said let's
+
+ align:start position:0%
+if you will now want to we said let's
+ 
+
+ align:start position:0%
+if you will now want to we said let's
+say doubling the length of this just
+
+ align:start position:0%
+say doubling the length of this just
+ 
+
+ align:start position:0%
+say doubling the length of this just
+about accomplish the reducing the
+
+ align:start position:0%
+about accomplish the reducing the
+ 
+
+ align:start position:0%
+about accomplish the reducing the
+vibration of the microscope by this
+
+ align:start position:0%
+vibration of the microscope by this
+ 
+
+ align:start position:0%
+vibration of the microscope by this
+factor of ten so if I doubled the length
+
+ align:start position:0%
+factor of ten so if I doubled the length
+ 
+
+ align:start position:0%
+factor of ten so if I doubled the length
+of this one I would have come I would
+
+ align:start position:0%
+of this one I would have come I would
+ 
+
+ align:start position:0%
+of this one I would have come I would
+roughly do the same thing I would change
+
+ align:start position:0%
+roughly do the same thing I would change
+ 
+
+ align:start position:0%
+roughly do the same thing I would change
+that I would make the change in natural
+
+ align:start position:0%
+that I would make the change in natural
+ 
+
+ align:start position:0%
+that I would make the change in natural
+this thing is right on the natural
+
+ align:start position:0%
+this thing is right on the natural
+ 
+
+ align:start position:0%
+this thing is right on the natural
+frequency this beam that's why it shakes
+
+ align:start position:0%
+frequency this beam that's why it shakes
+ 
+
+ align:start position:0%
+frequency this beam that's why it shakes
+so much and it's Trent it's so it is
+
+ align:start position:0%
+so much and it's Trent it's so it is
+ 
+
+ align:start position:0%
+so much and it's Trent it's so it is
+this system it's shaking like crazy
+
+ align:start position:0%
+this system it's shaking like crazy
+ 
+
+ align:start position:0%
+this system it's shaking like crazy
+putting force into the table the table
+
+ align:start position:0%
+putting force into the table the table
+ 
+
+ align:start position:0%
+putting force into the table the table
+is vibrating putting causing the other
+
+ align:start position:0%
+is vibrating putting causing the other
+ 
+
+ align:start position:0%
+is vibrating putting causing the other
+one to move so now if I change this one
+
+ align:start position:0%
+one to move so now if I change this one
+ 
+
+ align:start position:0%
+one to move so now if I change this one
+and the same kind of idea maybe roughly
+
+ align:start position:0%
+and the same kind of idea maybe roughly
+ 
+
+ align:start position:0%
+and the same kind of idea maybe roughly
+double its length natural frequency
+
+ align:start position:0%
+double its length natural frequency
+ 
+
+ align:start position:0%
+double its length natural frequency
+diminishes by a factor of three or so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the vibration of this ought to go way
+
+ align:start position:0%
+the vibration of this ought to go way
+ 
+
+ align:start position:0%
+the vibration of this ought to go way
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and actually a little beam out here is
+
+ align:start position:0%
+and actually a little beam out here is
+ 
+
+ align:start position:0%
+and actually a little beam out here is
+picking up more than the other one so
+
+ align:start position:0%
+picking up more than the other one so
+ 
+
+ align:start position:0%
+picking up more than the other one so
+this is hardly moving at all in so by
+
+ align:start position:0%
+this is hardly moving at all in so by
+ 
+
+ align:start position:0%
+this is hardly moving at all in so by
+doing that we've essentially detuned it
+
+ align:start position:0%
+doing that we've essentially detuned it
+ 
+
+ align:start position:0%
+doing that we've essentially detuned it
+this is no longer running at the natural
+
+ align:start position:0%
+this is no longer running at the natural
+ 
+
+ align:start position:0%
+this is no longer running at the natural
+frequency of this base so it's no longer
+
+ align:start position:0%
+frequency of this base so it's no longer
+ 
+
+ align:start position:0%
+frequency of this base so it's no longer
+resonant you're way out on the curve to
+
+ align:start position:0%
+resonant you're way out on the curve to
+ 
+
+ align:start position:0%
+resonant you're way out on the curve to
+the right so the response of this isn't
+
+ align:start position:0%
+the right so the response of this isn't
+ 
+
+ align:start position:0%
+the right so the response of this isn't
+very much that means it doesn't transmit
+
+ align:start position:0%
+very much that means it doesn't transmit
+ 
+
+ align:start position:0%
+very much that means it doesn't transmit
+much force to the base maybe down by a
+
+ align:start position:0%
+much force to the base maybe down by a
+ 
+
+ align:start position:0%
+much force to the base maybe down by a
+factor of eight or ten it means the
+
+ align:start position:0%
+factor of eight or ten it means the
+ 
+
+ align:start position:0%
+factor of eight or ten it means the
+table vibration amplitude drops by that
+
+ align:start position:0%
+table vibration amplitude drops by that
+ 
+
+ align:start position:0%
+table vibration amplitude drops by that
+factor means that the base motion over
+
+ align:start position:0%
+factor means that the base motion over
+ 
+
+ align:start position:0%
+factor means that the base motion over
+here is now a factor of ten smaller than
+
+ align:start position:0%
+here is now a factor of ten smaller than
+ 
+
+ align:start position:0%
+here is now a factor of ten smaller than
+was to begin with so that we get a
+
+ align:start position:0%
+was to begin with so that we get a
+ 
+
+ align:start position:0%
+was to begin with so that we get a
+reduction of ten here and we get another
+
+ align:start position:0%
+reduction of ten here and we get another
+ 
+
+ align:start position:0%
+reduction of ten here and we get another
+reduction of ten here because we detuned
+
+ align:start position:0%
+reduction of ten here because we detuned
+ 
+
+ align:start position:0%
+reduction of ten here because we detuned
+it so you might get a factor of a
+
+ align:start position:0%
+it so you might get a factor of a
+ 
+
+ align:start position:0%
+it so you might get a factor of a
+hundred reduction by working on both you
+
+ align:start position:0%
+hundred reduction by working on both you
+ 
+
+ align:start position:0%
+hundred reduction by working on both you
+so you've treated the source and you've
+
+ align:start position:0%
+so you've treated the source and you've
+ 
+
+ align:start position:0%
+so you've treated the source and you've
+treated the receiver but fortunately
+
+ align:start position:0%
+treated the receiver but fortunately
+ 
+
+ align:start position:0%
+treated the receiver but fortunately
+they use the same curve now so damping
+
+ align:start position:0%
+they use the same curve now so damping
+ 
+
+ align:start position:0%
+they use the same curve now so damping
+when you do vibration isolation you're
+
+ align:start position:0%
+when you do vibration isolation you're
+ 
+
+ align:start position:0%
+when you do vibration isolation you're
+trying to get well out on this curve to
+
+ align:start position:0%
+trying to get well out on this curve to
+ 
+
+ align:start position:0%
+trying to get well out on this curve to
+the right so there's a couple of
+
+ align:start position:0%
+the right so there's a couple of
+ 
+
+ align:start position:0%
+the right so there's a couple of
+practical engineering things that limit
+
+ align:start position:0%
+practical engineering things that limit
+ 
+
+ align:start position:0%
+practical engineering things that limit
+how far you can go to get further out in
+
+ align:start position:0%
+how far you can go to get further out in
+ 
+
+ align:start position:0%
+how far you can go to get further out in
+the curve to the right what do you have
+
+ align:start position:0%
+the curve to the right what do you have
+ 
+
+ align:start position:0%
+the curve to the right what do you have
+to do to this spring of in the system to
+
+ align:start position:0%
+to do to this spring of in the system to
+ 
+
+ align:start position:0%
+to do to this spring of in the system to
+get stronger or softer you're trying to
+
+ align:start position:0%
+get stronger or softer you're trying to
+ 
+
+ align:start position:0%
+get stronger or softer you're trying to
+make the natural frequency the
+
+ align:start position:0%
+make the natural frequency the
+ 
+
+ align:start position:0%
+make the natural frequency the
+excitation frequency doesn't change in
+
+ align:start position:0%
+excitation frequency doesn't change in
+ 
+
+ align:start position:0%
+excitation frequency doesn't change in
+order to get omega over Omega n to go
+
+ align:start position:0%
+order to get omega over Omega n to go
+ 
+
+ align:start position:0%
+order to get omega over Omega n to go
+bigger and bigger the excitation staying
+
+ align:start position:0%
+bigger and bigger the excitation staying
+ 
+
+ align:start position:0%
+bigger and bigger the excitation staying
+the same every to reduce the natural
+
+ align:start position:0%
+the same every to reduce the natural
+ 
+
+ align:start position:0%
+the same every to reduce the natural
+frequency and so what do you have to do
+
+ align:start position:0%
+frequency and so what do you have to do
+ 
+
+ align:start position:0%
+frequency and so what do you have to do
+to spring constant decrease it what is
+
+ align:start position:0%
+to spring constant decrease it what is
+ 
+
+ align:start position:0%
+to spring constant decrease it what is
+the practical limit of decreasing the
+
+ align:start position:0%
+the practical limit of decreasing the
+ 
+
+ align:start position:0%
+the practical limit of decreasing the
+spring that supports your pump or your
+
+ align:start position:0%
+spring that supports your pump or your
+ 
+
+ align:start position:0%
+spring that supports your pump or your
+washing machine or your air conditioner
+
+ align:start position:0%
+washing machine or your air conditioner
+ 
+
+ align:start position:0%
+washing machine or your air conditioner
+pretty soon it's just going to if it's
+
+ align:start position:0%
+pretty soon it's just going to if it's
+ 
+
+ align:start position:0%
+pretty soon it's just going to if it's
+to hit put it on they're just going to
+
+ align:start position:0%
+to hit put it on they're just going to
+ 
+
+ align:start position:0%
+to hit put it on they're just going to
+squash the springs right so you can't
+
+ align:start position:0%
+squash the springs right so you can't
+ 
+
+ align:start position:0%
+squash the springs right so you can't
+there's limits to how soft you can make
+
+ align:start position:0%
+there's limits to how soft you can make
+ 
+
+ align:start position:0%
+there's limits to how soft you can make
+Springs just support heavy machines so
+
+ align:start position:0%
+Springs just support heavy machines so
+ 
+
+ align:start position:0%
+Springs just support heavy machines so
+there is a practical limit to how far to
+
+ align:start position:0%
+there is a practical limit to how far to
+ 
+
+ align:start position:0%
+there is a practical limit to how far to
+the right you can go but you normally
+
+ align:start position:0%
+the right you can go but you normally
+ 
+
+ align:start position:0%
+the right you can go but you normally
+you get out there as far as you can
+
+ align:start position:0%
+you get out there as far as you can
+ 
+
+ align:start position:0%
+you get out there as far as you can
+and then if you the real system has
+
+ align:start position:0%
+and then if you the real system has
+ 
+
+ align:start position:0%
+and then if you the real system has
+damping does it improve or degrade the
+
+ align:start position:0%
+damping does it improve or degrade the
+ 
+
+ align:start position:0%
+damping does it improve or degrade the
+performance of your vibration isolation
+
+ align:start position:0%
+performance of your vibration isolation
+ 
+
+ align:start position:0%
+performance of your vibration isolation
+system well the more the damping you
+
+ align:start position:0%
+system well the more the damping you
+ 
+
+ align:start position:0%
+system well the more the damping you
+have the higher up you are on those
+
+ align:start position:0%
+have the higher up you are on those
+ 
+
+ align:start position:0%
+have the higher up you are on those
+curves so the damping decreases the
+
+ align:start position:0%
+curves so the damping decreases the
+ 
+
+ align:start position:0%
+curves so the damping decreases the
+performance but every system has to when
+
+ align:start position:0%
+performance but every system has to when
+ 
+
+ align:start position:0%
+performance but every system has to when
+you first turn on that motor the system
+
+ align:start position:0%
+you first turn on that motor the system
+ 
+
+ align:start position:0%
+you first turn on that motor the system
+has to spin up and you're going to have
+
+ align:start position:0%
+has to spin up and you're going to have
+ 
+
+ align:start position:0%
+has to spin up and you're going to have
+to go through that residence so you want
+
+ align:start position:0%
+to go through that residence so you want
+ 
+
+ align:start position:0%
+to go through that residence so you want
+some damping because if you this is if
+
+ align:start position:0%
+some damping because if you this is if
+ 
+
+ align:start position:0%
+some damping because if you this is if
+you've got your scanning electron
+
+ align:start position:0%
+you've got your scanning electron
+ 
+
+ align:start position:0%
+you've got your scanning electron
+microscope or your laser interferometry
+
+ align:start position:0%
+microscope or your laser interferometry
+ 
+
+ align:start position:0%
+microscope or your laser interferometry
+system set up on a on a spring supported
+
+ align:start position:0%
+system set up on a on a spring supported
+ 
+
+ align:start position:0%
+system set up on a on a spring supported
+table if that table has no damping and
+
+ align:start position:0%
+table if that table has no damping and
+ 
+
+ align:start position:0%
+table if that table has no damping and
+you walk in the door and bump it it is
+
+ align:start position:0%
+you walk in the door and bump it it is
+ 
+
+ align:start position:0%
+you walk in the door and bump it it is
+going to sit there and vibrate all
+
+ align:start position:0%
+going to sit there and vibrate all
+ 
+
+ align:start position:0%
+going to sit there and vibrate all
+afternoon at its natural frequency due
+
+ align:start position:0%
+afternoon at its natural frequency due
+ 
+
+ align:start position:0%
+afternoon at its natural frequency due
+to the initial condition so you need
+
+ align:start position:0%
+to the initial condition so you need
+ 
+
+ align:start position:0%
+to the initial condition so you need
+some damping to prevent problems either
+
+ align:start position:0%
+some damping to prevent problems either
+ 
+
+ align:start position:0%
+some damping to prevent problems either
+response to initial conditions or
+
+ align:start position:0%
+response to initial conditions or
+ 
+
+ align:start position:0%
+response to initial conditions or
+bumping it or whatever or even as the
+
+ align:start position:0%
+bumping it or whatever or even as the
+ 
+
+ align:start position:0%
+bumping it or whatever or even as the
+system turns on and speeds up it'll have
+
+ align:start position:0%
+system turns on and speeds up it'll have
+ 
+
+ align:start position:0%
+system turns on and speeds up it'll have
+to go through that resonance and it'll
+
+ align:start position:0%
+to go through that resonance and it'll
+ 
+
+ align:start position:0%
+to go through that resonance and it'll
+vibrate like crazy as it does and then
+
+ align:start position:0%
+vibrate like crazy as it does and then
+ 
+
+ align:start position:0%
+vibrate like crazy as it does and then
+finally settle down at it's at the
+
+ align:start position:0%
+finally settle down at it's at the
+ 
+
+ align:start position:0%
+finally settle down at it's at the
+higher frequency so you need some
+
+ align:start position:0%
+higher frequency so you need some
+ 
+
+ align:start position:0%
+higher frequency so you need some
+damping but damping does degrade the
+
+ align:start position:0%
+damping but damping does degrade the
+ 
+
+ align:start position:0%
+damping but damping does degrade the
+steady-state performance and I'm out of
+
+ align:start position:0%
+steady-state performance and I'm out of
+ 
+
+ align:start position:0%
+steady-state performance and I'm out of
+time and we'll see you in recitation
+
+ align:start position:0%
+time and we'll see you in recitation
+ 
+
+ align:start position:0%
+time and we'll see you in recitation
+thanks
\ No newline at end of file
diff --git a/f7oXhDatwtY.txt b/f7oXhDatwtY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5439d913dbfe602344914028f0138adc179c44ed
--- /dev/null
+++ b/f7oXhDatwtY.txt
@@ -0,0 +1,7971 @@
+align:start position:0%
+ 
+so I will just go through the
+
+ align:start position:0%
+so I will just go through the
+ 
+
+ align:start position:0%
+so I will just go through the
+oldfashioned paper uh syllabus so the
+
+ align:start position:0%
+oldfashioned paper uh syllabus so the
+ 
+
+ align:start position:0%
+oldfashioned paper uh syllabus so the
+course is going to be taught on canvas
+
+ align:start position:0%
+course is going to be taught on canvas
+ 
+
+ align:start position:0%
+course is going to be taught on canvas
+so the canvas site has been published uh
+
+ align:start position:0%
+so the canvas site has been published uh
+ 
+
+ align:start position:0%
+so the canvas site has been published uh
+we will for for uh homeworks and things
+
+ align:start position:0%
+we will for for uh homeworks and things
+ 
+
+ align:start position:0%
+we will for for uh homeworks and things
+like that they'll be handed out and
+
+ align:start position:0%
+like that they'll be handed out and
+ 
+
+ align:start position:0%
+like that they'll be handed out and
+turned in on paper but you can download
+
+ align:start position:0%
+turned in on paper but you can download
+ 
+
+ align:start position:0%
+turned in on paper but you can download
+them from canvas as
+
+ align:start position:0%
+them from canvas as
+ 
+
+ align:start position:0%
+them from canvas as
+well um the classes are going to be here
+
+ align:start position:0%
+well um the classes are going to be here
+ 
+
+ align:start position:0%
+well um the classes are going to be here
+Mondays Wednesdays and Thursdays so on
+
+ align:start position:0%
+Mondays Wednesdays and Thursdays so on
+ 
+
+ align:start position:0%
+Mondays Wednesdays and Thursdays so on
+usual class schedules 1
+
+ align:start position:0%
+usual class schedules 1
+ 
+
+ align:start position:0%
+usual class schedules 1
+pm uh I've mentioned the textbook there
+
+ align:start position:0%
+pm uh I've mentioned the textbook there
+ 
+
+ align:start position:0%
+pm uh I've mentioned the textbook there
+are some other textbooks that you might
+
+ align:start position:0%
+are some other textbooks that you might
+ 
+
+ align:start position:0%
+are some other textbooks that you might
+find Handy and I've listed those in the
+
+ align:start position:0%
+find Handy and I've listed those in the
+ 
+
+ align:start position:0%
+find Handy and I've listed those in the
+course handout those are completely
+
+ align:start position:0%
+course handout those are completely
+ 
+
+ align:start position:0%
+course handout those are completely
+optional you don't have to buy them the
+
+ align:start position:0%
+optional you don't have to buy them the
+ 
+
+ align:start position:0%
+optional you don't have to buy them the
+libraries also have
+
+ align:start position:0%
+libraries also have
+ 
+
+ align:start position:0%
+libraries also have
+copies um the way homeworks will work in
+
+ align:start position:0%
+copies um the way homeworks will work in
+ 
+
+ align:start position:0%
+copies um the way homeworks will work in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+class is that will typically be issued
+
+ align:start position:0%
+class is that will typically be issued
+ 
+
+ align:start position:0%
+class is that will typically be issued
+on a Monday and do the following Monday
+
+ align:start position:0%
+on a Monday and do the following Monday
+ 
+
+ align:start position:0%
+on a Monday and do the following Monday
+okay and uh for the most part you are
+
+ align:start position:0%
+okay and uh for the most part you are
+ 
+
+ align:start position:0%
+okay and uh for the most part you are
+allowed to collaborate and talk about
+
+ align:start position:0%
+allowed to collaborate and talk about
+ 
+
+ align:start position:0%
+allowed to collaborate and talk about
+the homework problems so you feel free
+
+ align:start position:0%
+the homework problems so you feel free
+ 
+
+ align:start position:0%
+the homework problems so you feel free
+to get together and discuss the problems
+
+ align:start position:0%
+to get together and discuss the problems
+ 
+
+ align:start position:0%
+to get together and discuss the problems
+that there it's intended that you do so
+
+ align:start position:0%
+that there it's intended that you do so
+ 
+
+ align:start position:0%
+that there it's intended that you do so
+the only constraint we have is that you
+
+ align:start position:0%
+the only constraint we have is that you
+ 
+
+ align:start position:0%
+the only constraint we have is that you
+must hand in your own solution right so
+
+ align:start position:0%
+must hand in your own solution right so
+ 
+
+ align:start position:0%
+must hand in your own solution right so
+so you can trade ideas but in the end
+
+ align:start position:0%
+so you can trade ideas but in the end
+ 
+
+ align:start position:0%
+so you can trade ideas but in the end
+the thing you write up it can't be a
+
+ align:start position:0%
+the thing you write up it can't be a
+ 
+
+ align:start position:0%
+the thing you write up it can't be a
+copy your neighbors it has to be your
+
+ align:start position:0%
+copy your neighbors it has to be your
+ 
+
+ align:start position:0%
+copy your neighbors it has to be your
+solution but you can base it on uh you
+
+ align:start position:0%
+solution but you can base it on uh you
+ 
+
+ align:start position:0%
+solution but you can base it on uh you
+know ideas you've exchanged with others
+
+ align:start position:0%
+know ideas you've exchanged with others
+ 
+
+ align:start position:0%
+know ideas you've exchanged with others
+okay for those who don't know
+
+ align:start position:0%
+okay for those who don't know
+ 
+
+ align:start position:0%
+okay for those who don't know
+anybody or or don't have access to study
+
+ align:start position:0%
+anybody or or don't have access to study
+ 
+
+ align:start position:0%
+anybody or or don't have access to study
+partners and may have questions first of
+
+ align:start position:0%
+partners and may have questions first of
+ 
+
+ align:start position:0%
+partners and may have questions first of
+all there will be office hours uh Mon's
+
+ align:start position:0%
+all there will be office hours uh Mon's
+ 
+
+ align:start position:0%
+all there will be office hours uh Mon's
+office hours will be Thursdays 4: to 5:
+
+ align:start position:0%
+office hours will be Thursdays 4: to 5:
+ 
+
+ align:start position:0%
+office hours will be Thursdays 4: to 5:
+p.m. and Fridays 4 to 5:00 P p.m. in
+
+ align:start position:0%
+p.m. and Fridays 4 to 5:00 P p.m. in
+ 
+
+ align:start position:0%
+p.m. and Fridays 4 to 5:00 P p.m. in
+10178 in building 10 okay but there are
+
+ align:start position:0%
+10178 in building 10 okay but there are
+ 
+
+ align:start position:0%
+10178 in building 10 okay but there are
+also a number of students students in
+
+ align:start position:0%
+also a number of students students in
+ 
+
+ align:start position:0%
+also a number of students students in
+the Le laboratory 1050 who have had this
+
+ align:start position:0%
+the Le laboratory 1050 who have had this
+ 
+
+ align:start position:0%
+the Le laboratory 1050 who have had this
+class before will be happy to answer any
+
+ align:start position:0%
+class before will be happy to answer any
+ 
+
+ align:start position:0%
+class before will be happy to answer any
+questions and a few of those students
+
+ align:start position:0%
+questions and a few of those students
+ 
+
+ align:start position:0%
+questions and a few of those students
+are listed in the uh course
+
+ align:start position:0%
+are listed in the uh course
+ 
+
+ align:start position:0%
+are listed in the uh course
+description we've also decided not to
+
+ align:start position:0%
+description we've also decided not to
+ 
+
+ align:start position:0%
+description we've also decided not to
+have exams this term or in-class exams
+
+ align:start position:0%
+have exams this term or in-class exams
+ 
+
+ align:start position:0%
+have exams this term or in-class exams
+rather we're going to have assessments
+
+ align:start position:0%
+rather we're going to have assessments
+ 
+
+ align:start position:0%
+rather we're going to have assessments
+which are essentially take-home mini
+
+ align:start position:0%
+which are essentially take-home mini
+ 
+
+ align:start position:0%
+which are essentially take-home mini
+quizzes uh they will generally be uh um
+
+ align:start position:0%
+quizzes uh they will generally be uh um
+ 
+
+ align:start position:0%
+quizzes uh they will generally be uh um
+they'll be generally issued weekly and
+
+ align:start position:0%
+they'll be generally issued weekly and
+ 
+
+ align:start position:0%
+they'll be generally issued weekly and
+this says they're going to be issued
+
+ align:start position:0%
+this says they're going to be issued
+ 
+
+ align:start position:0%
+this says they're going to be issued
+starting on March 1st I should check if
+
+ align:start position:0%
+starting on March 1st I should check if
+ 
+
+ align:start position:0%
+starting on March 1st I should check if
+that yeah starting on March 1st they'll
+
+ align:start position:0%
+that yeah starting on March 1st they'll
+ 
+
+ align:start position:0%
+that yeah starting on March 1st they'll
+be issued weekly they'll be issued on a
+
+ align:start position:0%
+be issued weekly they'll be issued on a
+ 
+
+ align:start position:0%
+be issued weekly they'll be issued on a
+Wednesday that will be due the next day
+
+ align:start position:0%
+Wednesday that will be due the next day
+ 
+
+ align:start position:0%
+Wednesday that will be due the next day
+Thursday and those will be submitted
+
+ align:start position:0%
+Thursday and those will be submitted
+ 
+
+ align:start position:0%
+Thursday and those will be submitted
+through canvas through grade
+
+ align:start position:0%
+through canvas through grade
+ 
+
+ align:start position:0%
+through canvas through grade
+scope
+
+ align:start position:0%
+scope
+ 
+
+ align:start position:0%
+scope
+um as for homeworks we can take late
+
+ align:start position:0%
+um as for homeworks we can take late
+ 
+
+ align:start position:0%
+um as for homeworks we can take late
+homeworks if you arrange it ahead of
+
+ align:start position:0%
+homeworks if you arrange it ahead of
+ 
+
+ align:start position:0%
+homeworks if you arrange it ahead of
+time and there's some compelling reason
+
+ align:start position:0%
+time and there's some compelling reason
+ 
+
+ align:start position:0%
+time and there's some compelling reason
+why they're late assessments are a
+
+ align:start position:0%
+why they're late assessments are a
+ 
+
+ align:start position:0%
+why they're late assessments are a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+story also the collaboration policy for
+
+ align:start position:0%
+story also the collaboration policy for
+ 
+
+ align:start position:0%
+story also the collaboration policy for
+assessments is different you cannot
+
+ align:start position:0%
+assessments is different you cannot
+ 
+
+ align:start position:0%
+assessments is different you cannot
+collaborate or discuss the problems at
+
+ align:start position:0%
+collaborate or discuss the problems at
+ 
+
+ align:start position:0%
+collaborate or discuss the problems at
+all for assessments and and you know we
+
+ align:start position:0%
+all for assessments and and you know we
+ 
+
+ align:start position:0%
+all for assessments and and you know we
+can't prove or not prove that you're
+
+ align:start position:0%
+can't prove or not prove that you're
+ 
+
+ align:start position:0%
+can't prove or not prove that you're
+doing so but this is you know this is an
+
+ align:start position:0%
+doing so but this is you know this is an
+ 
+
+ align:start position:0%
+doing so but this is you know this is an
+exam effectively so don't discuss it
+
+ align:start position:0%
+exam effectively so don't discuss it
+ 
+
+ align:start position:0%
+exam effectively so don't discuss it
+with your neighbors and don't discuss
+
+ align:start position:0%
+with your neighbors and don't discuss
+ 
+
+ align:start position:0%
+with your neighbors and don't discuss
+anything until the solutions are out
+
+ align:start position:0%
+anything until the solutions are out
+ 
+
+ align:start position:0%
+anything until the solutions are out
+because there may be people who have
+
+ align:start position:0%
+because there may be people who have
+ 
+
+ align:start position:0%
+because there may be people who have
+made some special arrangement for
+
+ align:start position:0%
+made some special arrangement for
+ 
+
+ align:start position:0%
+made some special arrangement for
+because they're traveling or or for
+
+ align:start position:0%
+because they're traveling or or for
+ 
+
+ align:start position:0%
+because they're traveling or or for
+whatever reason to hand it in late okay
+
+ align:start position:0%
+whatever reason to hand it in late okay
+ 
+
+ align:start position:0%
+whatever reason to hand it in late okay
+so we're going to have homework and
+
+ align:start position:0%
+so we're going to have homework and
+ 
+
+ align:start position:0%
+so we're going to have homework and
+assessments and the goal of the
+
+ align:start position:0%
+assessments and the goal of the
+ 
+
+ align:start position:0%
+assessments and the goal of the
+assessments really is instead of a you
+
+ align:start position:0%
+assessments really is instead of a you
+ 
+
+ align:start position:0%
+assessments really is instead of a you
+sort of very few high stakes
+
+ align:start position:0%
+sort of very few high stakes
+ 
+
+ align:start position:0%
+sort of very few high stakes
+opportunities to show your abilities the
+
+ align:start position:0%
+opportunities to show your abilities the
+ 
+
+ align:start position:0%
+opportunities to show your abilities the
+assessments are sort of distributed in
+
+ align:start position:0%
+assessments are sort of distributed in
+ 
+
+ align:start position:0%
+assessments are sort of distributed in
+low stakes and focused and gives you a
+
+ align:start position:0%
+low stakes and focused and gives you a
+ 
+
+ align:start position:0%
+low stakes and focused and gives you a
+better opportunity to show you what you
+
+ align:start position:0%
+better opportunity to show you what you
+ 
+
+ align:start position:0%
+better opportunity to show you what you
+really know okay so please complete them
+
+ align:start position:0%
+really know okay so please complete them
+ 
+
+ align:start position:0%
+really know okay so please complete them
+entirely on your own no consultation the
+
+ align:start position:0%
+entirely on your own no consultation the
+ 
+
+ align:start position:0%
+entirely on your own no consultation the
+only thing you're allowed to do is ask
+
+ align:start position:0%
+only thing you're allowed to do is ask
+ 
+
+ align:start position:0%
+only thing you're allowed to do is ask
+the core staff clarifying questions just
+
+ align:start position:0%
+the core staff clarifying questions just
+ 
+
+ align:start position:0%
+the core staff clarifying questions just
+the way you might in an exam okay
+
+ align:start position:0%
+the way you might in an exam okay
+ 
+
+ align:start position:0%
+the way you might in an exam okay
+and uh as for the assessments you can
+
+ align:start position:0%
+and uh as for the assessments you can
+ 
+
+ align:start position:0%
+and uh as for the assessments you can
+use any of the course materials you know
+
+ align:start position:0%
+use any of the course materials you know
+ 
+
+ align:start position:0%
+use any of the course materials you know
+read the book whatever you want
+
+ align:start position:0%
+read the book whatever you want
+ 
+
+ align:start position:0%
+read the book whatever you want
+uh do
+
+ align:start position:0%
+uh do
+ 
+
+ align:start position:0%
+uh do
+not go outside and try to use the
+
+ align:start position:0%
+not go outside and try to use the
+ 
+
+ align:start position:0%
+not go outside and try to use the
+worldwide web and for that matter the
+
+ align:start position:0%
+worldwide web and for that matter the
+ 
+
+ align:start position:0%
+worldwide web and for that matter the
+use of Bibles is also prohibited I know
+
+ align:start position:0%
+use of Bibles is also prohibited I know
+ 
+
+ align:start position:0%
+use of Bibles is also prohibited I know
+that there's collections of old 6334
+
+ align:start position:0%
+that there's collections of old 6334
+ 
+
+ align:start position:0%
+that there's collections of old 6334
+materials floating around you're not
+
+ align:start position:0%
+materials floating around you're not
+ 
+
+ align:start position:0%
+materials floating around you're not
+supposed to be Consulting those okay
+
+ align:start position:0%
+supposed to be Consulting those okay
+ 
+
+ align:start position:0%
+supposed to be Consulting those okay
+this just supposed to be a measure of
+
+ align:start position:0%
+this just supposed to be a measure of
+ 
+
+ align:start position:0%
+this just supposed to be a measure of
+what you've learned okay okay so the
+
+ align:start position:0%
+what you've learned okay okay so the
+ 
+
+ align:start position:0%
+what you've learned okay okay so the
+grading will be based on three
+
+ align:start position:0%
+grading will be based on three
+ 
+
+ align:start position:0%
+grading will be based on three
+components homeworks are going to be
+
+ align:start position:0%
+components homeworks are going to be
+ 
+
+ align:start position:0%
+components homeworks are going to be
+40% these assessments will be
+
+ align:start position:0%
+40% these assessments will be
+ 
+
+ align:start position:0%
+40% these assessments will be
+50% and there's also a final project
+
+ align:start position:0%
+50% and there's also a final project
+ 
+
+ align:start position:0%
+50% and there's also a final project
+which is 10% and the final project
+
+ align:start position:0%
+which is 10% and the final project
+ 
+
+ align:start position:0%
+which is 10% and the final project
+sounds like it's only 10% but it's the
+
+ align:start position:0%
+sounds like it's only 10% but it's the
+ 
+
+ align:start position:0%
+sounds like it's only 10% but it's the
+last thing we look at when we're going
+
+ align:start position:0%
+last thing we look at when we're going
+ 
+
+ align:start position:0%
+last thing we look at when we're going
+to assign a grade to everybody and it
+
+ align:start position:0%
+to assign a grade to everybody and it
+ 
+
+ align:start position:0%
+to assign a grade to everybody and it
+really is your opportunity to put
+
+ align:start position:0%
+really is your opportunity to put
+ 
+
+ align:start position:0%
+really is your opportunity to put
+together knowledge that you've learned
+
+ align:start position:0%
+together knowledge that you've learned
+ 
+
+ align:start position:0%
+together knowledge that you've learned
+throughout the class into a real it's on
+
+ align:start position:0%
+throughout the class into a real it's on
+ 
+
+ align:start position:0%
+throughout the class into a real it's on
+paper it's not a it's not a phys phical
+
+ align:start position:0%
+paper it's not a it's not a phys phical
+ 
+
+ align:start position:0%
+paper it's not a it's not a phys phical
+converter you will construct but it's a
+
+ align:start position:0%
+converter you will construct but it's a
+ 
+
+ align:start position:0%
+converter you will construct but it's a
+paper design but it's really your
+
+ align:start position:0%
+paper design but it's really your
+ 
+
+ align:start position:0%
+paper design but it's really your
+opportunity to show us how you've
+
+ align:start position:0%
+opportunity to show us how you've
+ 
+
+ align:start position:0%
+opportunity to show us how you've
+synthesized all this knowledge to be
+
+ align:start position:0%
+synthesized all this knowledge to be
+ 
+
+ align:start position:0%
+synthesized all this knowledge to be
+able to really design Power Electronics
+
+ align:start position:0%
+able to really design Power Electronics
+ 
+
+ align:start position:0%
+able to really design Power Electronics
+and I should say just as an aside in
+
+ align:start position:0%
+and I should say just as an aside in
+ 
+
+ align:start position:0%
+and I should say just as an aside in
+this class we only have a paper design
+
+ align:start position:0%
+this class we only have a paper design
+ 
+
+ align:start position:0%
+this class we only have a paper design
+or or but this complements nicely the
+
+ align:start position:0%
+or or but this complements nicely the
+ 
+
+ align:start position:0%
+or or but this complements nicely the
+undergraduate Power Electronics class
+
+ align:start position:0%
+undergraduate Power Electronics class
+ 
+
+ align:start position:0%
+undergraduate Power Electronics class
+which has a lot of really nice lab
+
+ align:start position:0%
+which has a lot of really nice lab
+ 
+
+ align:start position:0%
+which has a lot of really nice lab
+activities and design activities there
+
+ align:start position:0%
+activities and design activities there
+ 
+
+ align:start position:0%
+activities and design activities there
+so even if you're a graduate student
+
+ align:start position:0%
+so even if you're a graduate student
+ 
+
+ align:start position:0%
+so even if you're a graduate student
+it's it can be a pretty good thing to
+
+ align:start position:0%
+it's it can be a pretty good thing to
+ 
+
+ align:start position:0%
+it's it can be a pretty good thing to
+take in terms of of uh rounding out the
+
+ align:start position:0%
+take in terms of of uh rounding out the
+ 
+
+ align:start position:0%
+take in terms of of uh rounding out the
+LA your lab skill set in this area
+
+ align:start position:0%
+LA your lab skill set in this area
+ 
+
+ align:start position:0%
+LA your lab skill set in this area
+Okay um if you have any necessary
+
+ align:start position:0%
+Okay um if you have any necessary
+ 
+
+ align:start position:0%
+Okay um if you have any necessary
+technical accommodations don't have
+
+ align:start position:0%
+technical accommodations don't have
+ 
+
+ align:start position:0%
+technical accommodations don't have
+access to uh iPads or whatever else you
+
+ align:start position:0%
+access to uh iPads or whatever else you
+ 
+
+ align:start position:0%
+access to uh iPads or whatever else you
+need for grade scope please let us know
+
+ align:start position:0%
+need for grade scope please let us know
+ 
+
+ align:start position:0%
+need for grade scope please let us know
+we'll try to assist uh assist with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so with that are there any
+
+ align:start position:0%
+okay so with that are there any
+ 
+
+ align:start position:0%
+okay so with that are there any
+questions about anything like associated
+
+ align:start position:0%
+questions about anything like associated
+ 
+
+ align:start position:0%
+questions about anything like associated
+with the course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanics okay so let me um give you a
+
+ align:start position:0%
+mechanics okay so let me um give you a
+ 
+
+ align:start position:0%
+mechanics okay so let me um give you a
+sense of what this course is going to be
+
+ align:start position:0%
+sense of what this course is going to be
+ 
+
+ align:start position:0%
+sense of what this course is going to be
+about and uh this is one of my favorite
+
+ align:start position:0%
+about and uh this is one of my favorite
+ 
+
+ align:start position:0%
+about and uh this is one of my favorite
+photos is actually one that uh Nicola
+
+ align:start position:0%
+photos is actually one that uh Nicola
+ 
+
+ align:start position:0%
+photos is actually one that uh Nicola
+Tesla mocked up he wasn't really sitting
+
+ align:start position:0%
+Tesla mocked up he wasn't really sitting
+ 
+
+ align:start position:0%
+Tesla mocked up he wasn't really sitting
+next to his Tesla coil when he did this
+
+ align:start position:0%
+next to his Tesla coil when he did this
+ 
+
+ align:start position:0%
+next to his Tesla coil when he did this
+or he might have gotten killed um he
+
+ align:start position:0%
+or he might have gotten killed um he
+ 
+
+ align:start position:0%
+or he might have gotten killed um he
+kind of double exposed this but more to
+
+ align:start position:0%
+kind of double exposed this but more to
+ 
+
+ align:start position:0%
+kind of double exposed this but more to
+the point
+
+ align:start position:0%
+the point
+ 
+
+ align:start position:0%
+the point
+uh the quote from him is if we could
+
+ align:start position:0%
+uh the quote from him is if we could
+ 
+
+ align:start position:0%
+uh the quote from him is if we could
+produce electrical effects of the
+
+ align:start position:0%
+produce electrical effects of the
+ 
+
+ align:start position:0%
+produce electrical effects of the
+required quality this whole planet and
+
+ align:start position:0%
+required quality this whole planet and
+ 
+
+ align:start position:0%
+required quality this whole planet and
+the conditions of existence on it could
+
+ align:start position:0%
+the conditions of existence on it could
+ 
+
+ align:start position:0%
+the conditions of existence on it could
+be transformed and I think the sort of
+
+ align:start position:0%
+be transformed and I think the sort of
+ 
+
+ align:start position:0%
+be transformed and I think the sort of
+the more than a hundred years since he
+
+ align:start position:0%
+the more than a hundred years since he
+ 
+
+ align:start position:0%
+the more than a hundred years since he
+he said that or well more than 100 years
+
+ align:start position:0%
+he said that or well more than 100 years
+ 
+
+ align:start position:0%
+he said that or well more than 100 years
+since he said that uh have borne that
+
+ align:start position:0%
+since he said that uh have borne that
+ 
+
+ align:start position:0%
+since he said that uh have borne that
+out but it's also true that even
+
+ align:start position:0%
+out but it's also true that even
+ 
+
+ align:start position:0%
+out but it's also true that even
+today uh there's really revolutions
+
+ align:start position:0%
+today uh there's really revolutions
+ 
+
+ align:start position:0%
+today uh there's really revolutions
+happening in the way we use energy
+
+ align:start position:0%
+happening in the way we use energy
+ 
+
+ align:start position:0%
+happening in the way we use energy
+everything's being electrified from
+
+ align:start position:0%
+everything's being electrified from
+ 
+
+ align:start position:0%
+everything's being electrified from
+vehicles to transportation to power
+
+ align:start position:0%
+vehicles to transportation to power
+ 
+
+ align:start position:0%
+vehicles to transportation to power
+generation from renewable
+
+ align:start position:0%
+generation from renewable
+ 
+
+ align:start position:0%
+generation from renewable
+resources and um handling all that
+
+ align:start position:0%
+resources and um handling all that
+ 
+
+ align:start position:0%
+resources and um handling all that
+requires some means of processing
+
+ align:start position:0%
+requires some means of processing
+ 
+
+ align:start position:0%
+requires some means of processing
+controlling and converting energy and
+
+ align:start position:0%
+controlling and converting energy and
+ 
+
+ align:start position:0%
+controlling and converting energy and
+that's really what we're about
+
+ align:start position:0%
+that's really what we're about
+ 
+
+ align:start position:0%
+that's really what we're about
+processing controlling converting
+
+ align:start position:0%
+processing controlling converting
+ 
+
+ align:start position:0%
+processing controlling converting
+electrical
+
+ align:start position:0%
+electrical
+ 
+
+ align:start position:0%
+electrical
+energy if you look at what the uh itle e
+
+ align:start position:0%
+energy if you look at what the uh itle e
+ 
+
+ align:start position:0%
+energy if you look at what the uh itle e
+the which is sort of the governing body
+
+ align:start position:0%
+the which is sort of the governing body
+ 
+
+ align:start position:0%
+the which is sort of the governing body
+of electrical engineering says about
+
+ align:start position:0%
+of electrical engineering says about
+ 
+
+ align:start position:0%
+of electrical engineering says about
+Power Electronics it says this
+
+ align:start position:0%
+Power Electronics it says this
+ 
+
+ align:start position:0%
+Power Electronics it says this
+technology encompasses the use of
+
+ align:start position:0%
+technology encompasses the use of
+ 
+
+ align:start position:0%
+technology encompasses the use of
+electronic components
+
+ align:start position:0%
+electronic components
+ 
+
+ align:start position:0%
+electronic components
+the application of circuit Theory and
+
+ align:start position:0%
+the application of circuit Theory and
+ 
+
+ align:start position:0%
+the application of circuit Theory and
+design techniques and the development of
+
+ align:start position:0%
+design techniques and the development of
+ 
+
+ align:start position:0%
+design techniques and the development of
+analytical tools towards efficient
+
+ align:start position:0%
+analytical tools towards efficient
+ 
+
+ align:start position:0%
+analytical tools towards efficient
+electronic conversion control and
+
+ align:start position:0%
+electronic conversion control and
+ 
+
+ align:start position:0%
+electronic conversion control and
+conditioning of electric power and
+
+ align:start position:0%
+conditioning of electric power and
+ 
+
+ align:start position:0%
+conditioning of electric power and
+that's what we're really about here so
+
+ align:start position:0%
+that's what we're really about here so
+ 
+
+ align:start position:0%
+that's what we're really about here so
+we're going to do circuit Theory we're
+
+ align:start position:0%
+we're going to do circuit Theory we're
+ 
+
+ align:start position:0%
+we're going to do circuit Theory we're
+going to learn design techniques we're
+
+ align:start position:0%
+going to learn design techniques we're
+ 
+
+ align:start position:0%
+going to learn design techniques we're
+going to learn about all the components
+
+ align:start position:0%
+going to learn about all the components
+ 
+
+ align:start position:0%
+going to learn about all the components
+you need to do this we're going to learn
+
+ align:start position:0%
+you need to do this we're going to learn
+ 
+
+ align:start position:0%
+you need to do this we're going to learn
+about controls how do you put it all
+
+ align:start position:0%
+about controls how do you put it all
+ 
+
+ align:start position:0%
+about controls how do you put it all
+together to make energy conversion
+
+ align:start position:0%
+together to make energy conversion
+ 
+
+ align:start position:0%
+together to make energy conversion
+systems okay so as I mentioned the
+
+ align:start position:0%
+systems okay so as I mentioned the
+ 
+
+ align:start position:0%
+systems okay so as I mentioned the
+primary function of Power Electronics is
+
+ align:start position:0%
+primary function of Power Electronics is
+ 
+
+ align:start position:0%
+primary function of Power Electronics is
+to take sort of electrical energy in one
+
+ align:start position:0%
+to take sort of electrical energy in one
+ 
+
+ align:start position:0%
+to take sort of electrical energy in one
+form and convert it into some other form
+
+ align:start position:0%
+form and convert it into some other form
+ 
+
+ align:start position:0%
+form and convert it into some other form
+you need uh it's really a core
+
+ align:start position:0%
+you need uh it's really a core
+ 
+
+ align:start position:0%
+you need uh it's really a core
+technology in the electrical
+
+ align:start position:0%
+technology in the electrical
+ 
+
+ align:start position:0%
+technology in the electrical
+infrastructure it used to be that the AC
+
+ align:start position:0%
+infrastructure it used to be that the AC
+ 
+
+ align:start position:0%
+infrastructure it used to be that the AC
+grid was generators and you'd connect it
+
+ align:start position:0%
+grid was generators and you'd connect it
+ 
+
+ align:start position:0%
+grid was generators and you'd connect it
+up to things like directly things like
+
+ align:start position:0%
+up to things like directly things like
+ 
+
+ align:start position:0%
+up to things like directly things like
+Motors or lighting or whatever but
+
+ align:start position:0%
+Motors or lighting or whatever but
+ 
+
+ align:start position:0%
+Motors or lighting or whatever but
+that's pretty much changed at this point
+
+ align:start position:0%
+that's pretty much changed at this point
+ 
+
+ align:start position:0%
+that's pretty much changed at this point
+right lighting is LED lighting you need
+
+ align:start position:0%
+right lighting is LED lighting you need
+ 
+
+ align:start position:0%
+right lighting is LED lighting you need
+power supplies to go between the grid
+
+ align:start position:0%
+power supplies to go between the grid
+ 
+
+ align:start position:0%
+power supplies to go between the grid
+and the lighting same thing heavily
+
+ align:start position:0%
+and the lighting same thing heavily
+ 
+
+ align:start position:0%
+and the lighting same thing heavily
+loads computers Motors everything else
+
+ align:start position:0%
+loads computers Motors everything else
+ 
+
+ align:start position:0%
+loads computers Motors everything else
+you need energy tends to flow through
+
+ align:start position:0%
+you need energy tends to flow through
+ 
+
+ align:start position:0%
+you need energy tends to flow through
+one or even several layers of power
+
+ align:start position:0%
+one or even several layers of power
+ 
+
+ align:start position:0%
+one or even several layers of power
+conversion circuitry from the principal
+
+ align:start position:0%
+conversion circuitry from the principal
+ 
+
+ align:start position:0%
+conversion circuitry from the principal
+source to the final usage okay and so
+
+ align:start position:0%
+source to the final usage okay and so
+ 
+
+ align:start position:0%
+source to the final usage okay and so
+the Power Electronics first of all you
+
+ align:start position:0%
+the Power Electronics first of all you
+ 
+
+ align:start position:0%
+the Power Electronics first of all you
+know the efficiency of that is very
+
+ align:start position:0%
+know the efficiency of that is very
+ 
+
+ align:start position:0%
+know the efficiency of that is very
+important but also how you do it impacts
+
+ align:start position:0%
+important but also how you do it impacts
+ 
+
+ align:start position:0%
+important but also how you do it impacts
+the quality of the final system so the
+
+ align:start position:0%
+the quality of the final system so the
+ 
+
+ align:start position:0%
+the quality of the final system so the
+Power Electronics can really be a major
+
+ align:start position:0%
+Power Electronics can really be a major
+ 
+
+ align:start position:0%
+Power Electronics can really be a major
+factor impacting what you can and can't
+
+ align:start position:0%
+factor impacting what you can and can't
+ 
+
+ align:start position:0%
+factor impacting what you can and can't
+do and how well it works
+
+ align:start position:0%
+do and how well it works
+ 
+
+ align:start position:0%
+do and how well it works
+okay so if you showed up you know
+
+ align:start position:0%
+okay so if you showed up you know
+ 
+
+ align:start position:0%
+okay so if you showed up you know
+hundred years
+
+ align:start position:0%
+hundred years
+ 
+
+ align:start position:0%
+hundred years
+ago this is what Power Electronics would
+
+ align:start position:0%
+ago this is what Power Electronics would
+ 
+
+ align:start position:0%
+ago this is what Power Electronics would
+look like right some vacuum tubes and
+
+ align:start position:0%
+look like right some vacuum tubes and
+ 
+
+ align:start position:0%
+look like right some vacuum tubes and
+some Transformers and that kind of thing
+
+ align:start position:0%
+some Transformers and that kind of thing
+ 
+
+ align:start position:0%
+some Transformers and that kind of thing
+interestingly of course it's nothing
+
+ align:start position:0%
+interestingly of course it's nothing
+ 
+
+ align:start position:0%
+interestingly of course it's nothing
+like that today but with the techniques
+
+ align:start position:0%
+like that today but with the techniques
+ 
+
+ align:start position:0%
+like that today but with the techniques
+you're going to learn in this course you
+
+ align:start position:0%
+you're going to learn in this course you
+ 
+
+ align:start position:0%
+you're going to learn in this course you
+could actually go back and analyze this
+
+ align:start position:0%
+could actually go back and analyze this
+ 
+
+ align:start position:0%
+could actually go back and analyze this
+thing and figure out what it did right
+
+ align:start position:0%
+thing and figure out what it did right
+ 
+
+ align:start position:0%
+thing and figure out what it did right
+so some foundational ideas that we're
+
+ align:start position:0%
+so some foundational ideas that we're
+ 
+
+ align:start position:0%
+so some foundational ideas that we're
+going to come back to which can be 100
+
+ align:start position:0%
+going to come back to which can be 100
+ 
+
+ align:start position:0%
+going to come back to which can be 100
+years old but there's also elements that
+
+ align:start position:0%
+years old but there's also elements that
+ 
+
+ align:start position:0%
+years old but there's also elements that
+are extremely new okay and today you
+
+ align:start position:0%
+are extremely new okay and today you
+ 
+
+ align:start position:0%
+are extremely new okay and today you
+know this this was fancy 100 years ago
+
+ align:start position:0%
+know this this was fancy 100 years ago
+ 
+
+ align:start position:0%
+know this this was fancy 100 years ago
+today Power Electronics is everywhere
+
+ align:start position:0%
+today Power Electronics is everywhere
+ 
+
+ align:start position:0%
+today Power Electronics is everywhere
+from I say from mowatt to gigawatts and
+
+ align:start position:0%
+from I say from mowatt to gigawatts and
+ 
+
+ align:start position:0%
+from I say from mowatt to gigawatts and
+and it does actually use switch mode
+
+ align:start position:0%
+and it does actually use switch mode
+ 
+
+ align:start position:0%
+and it does actually use switch mode
+power conversion down at those power
+
+ align:start position:0%
+power conversion down at those power
+ 
+
+ align:start position:0%
+power conversion down at those power
+levels this is actually a a multi-watt
+
+ align:start position:0%
+levels this is actually a a multi-watt
+ 
+
+ align:start position:0%
+levels this is actually a a multi-watt
+power supply and this is literally at
+
+ align:start position:0%
+power supply and this is literally at
+ 
+
+ align:start position:0%
+power supply and this is literally at
+the gigawatt scale so if you if you go
+
+ align:start position:0%
+the gigawatt scale so if you if you go
+ 
+
+ align:start position:0%
+the gigawatt scale so if you if you go
+out to S the Sandy Pond terminal there
+
+ align:start position:0%
+out to S the Sandy Pond terminal there
+ 
+
+ align:start position:0%
+out to S the Sandy Pond terminal there
+is a power converter that takes two gws
+
+ align:start position:0%
+is a power converter that takes two gws
+ 
+
+ align:start position:0%
+is a power converter that takes two gws
+coming down from Canada hydro and
+
+ align:start position:0%
+coming down from Canada hydro and
+ 
+
+ align:start position:0%
+coming down from Canada hydro and
+converts it to AC to power homes and
+
+ align:start position:0%
+converts it to AC to power homes and
+ 
+
+ align:start position:0%
+converts it to AC to power homes and
+everything else around here right so and
+
+ align:start position:0%
+everything else around here right so and
+ 
+
+ align:start position:0%
+everything else around here right so and
+the techniques that we're going to learn
+
+ align:start position:0%
+the techniques that we're going to learn
+ 
+
+ align:start position:0%
+the techniques that we're going to learn
+in this class really span the entire
+
+ align:start position:0%
+in this class really span the entire
+ 
+
+ align:start position:0%
+in this class really span the entire
+range right so some of the details
+
+ align:start position:0%
+range right so some of the details
+ 
+
+ align:start position:0%
+range right so some of the details
+change and we'll learn about that but
+
+ align:start position:0%
+change and we'll learn about that but
+ 
+
+ align:start position:0%
+change and we'll learn about that but
+there's underlying principles that that
+
+ align:start position:0%
+there's underlying principles that that
+ 
+
+ align:start position:0%
+there's underlying principles that that
+cut across all kinds of electrical
+
+ align:start position:0%
+cut across all kinds of electrical
+ 
+
+ align:start position:0%
+cut across all kinds of electrical
+energy conversion systems
+
+ align:start position:0%
+energy conversion systems
+ 
+
+ align:start position:0%
+energy conversion systems
+okay what kind of applications well
+
+ align:start position:0%
+okay what kind of applications well
+ 
+
+ align:start position:0%
+okay what kind of applications well
+portable Electronics this slightly older
+
+ align:start position:0%
+portable Electronics this slightly older
+ 
+
+ align:start position:0%
+portable Electronics this slightly older
+an iPhone 5 and you think okay iPhones
+
+ align:start position:0%
+an iPhone 5 and you think okay iPhones
+ 
+
+ align:start position:0%
+an iPhone 5 and you think okay iPhones
+got radio transmitters and displays and
+
+ align:start position:0%
+got radio transmitters and displays and
+ 
+
+ align:start position:0%
+got radio transmitters and displays and
+other stuff in it but it turns out that
+
+ align:start position:0%
+other stuff in it but it turns out that
+ 
+
+ align:start position:0%
+other stuff in it but it turns out that
+a large fraction of the volume and board
+
+ align:start position:0%
+a large fraction of the volume and board
+ 
+
+ align:start position:0%
+a large fraction of the volume and board
+area is actually associated with energy
+
+ align:start position:0%
+area is actually associated with energy
+ 
+
+ align:start position:0%
+area is actually associated with energy
+conversion in the thing because no
+
+ align:start position:0%
+conversion in the thing because no
+ 
+
+ align:start position:0%
+conversion in the thing because no
+matter what you're doing you're
+
+ align:start position:0%
+matter what you're doing you're
+ 
+
+ align:start position:0%
+matter what you're doing you're
+processing energy to process information
+
+ align:start position:0%
+processing energy to process information
+ 
+
+ align:start position:0%
+processing energy to process information
+right so something like 40% in this of
+
+ align:start position:0%
+right so something like 40% in this of
+ 
+
+ align:start position:0%
+right so something like 40% in this of
+the motherboard in this example was
+
+ align:start position:0%
+the motherboard in this example was
+ 
+
+ align:start position:0%
+the motherboard in this example was
+associated with power
+
+ align:start position:0%
+associated with power
+ 
+
+ align:start position:0%
+associated with power
+conversion likewise you know at some
+
+ align:start position:0%
+conversion likewise you know at some
+ 
+
+ align:start position:0%
+conversion likewise you know at some
+point you're going to charge your phone
+
+ align:start position:0%
+point you're going to charge your phone
+ 
+
+ align:start position:0%
+point you're going to charge your phone
+or your or your iPad or your computer
+
+ align:start position:0%
+or your or your iPad or your computer
+ 
+
+ align:start position:0%
+or your or your iPad or your computer
+into the wall that's mostly Power
+
+ align:start position:0%
+into the wall that's mostly Power
+ 
+
+ align:start position:0%
+into the wall that's mostly Power
+Electronics too all kinds of computers
+
+ align:start position:0%
+Electronics too all kinds of computers
+ 
+
+ align:start position:0%
+Electronics too all kinds of computers
+if you're in a data center there's
+
+ align:start position:0%
+if you're in a data center there's
+ 
+
+ align:start position:0%
+if you're in a data center there's
+several layers of power conversion
+
+ align:start position:0%
+several layers of power conversion
+ 
+
+ align:start position:0%
+several layers of power conversion
+between the AC group GD and the final
+
+ align:start position:0%
+between the AC group GD and the final
+ 
+
+ align:start position:0%
+between the AC group GD and the final
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+processors okay this is more of what it
+
+ align:start position:0%
+processors okay this is more of what it
+ 
+
+ align:start position:0%
+processors okay this is more of what it
+looks like inside your home computer
+
+ align:start position:0%
+looks like inside your home computer
+ 
+
+ align:start position:0%
+looks like inside your home computer
+we'll actually learn exactly about those
+
+ align:start position:0%
+we'll actually learn exactly about those
+ 
+
+ align:start position:0%
+we'll actually learn exactly about those
+kind of converters and about all the
+
+ align:start position:0%
+kind of converters and about all the
+ 
+
+ align:start position:0%
+kind of converters and about all the
+components that are in them if you're
+
+ align:start position:0%
+components that are in them if you're
+ 
+
+ align:start position:0%
+components that are in them if you're
+going to communicate right the
+
+ align:start position:0%
+going to communicate right the
+ 
+
+ align:start position:0%
+going to communicate right the
+transmitters we tend to think of this as
+
+ align:start position:0%
+transmitters we tend to think of this as
+ 
+
+ align:start position:0%
+transmitters we tend to think of this as
+analog circuits to to make RF
+
+ align:start position:0%
+analog circuits to to make RF
+ 
+
+ align:start position:0%
+analog circuits to to make RF
+transmitters but in fact Power
+
+ align:start position:0%
+transmitters but in fact Power
+ 
+
+ align:start position:0%
+transmitters but in fact Power
+Electronics are heavily embedded in any
+
+ align:start position:0%
+Electronics are heavily embedded in any
+ 
+
+ align:start position:0%
+Electronics are heavily embedded in any
+real communication systems to increase
+
+ align:start position:0%
+real communication systems to increase
+ 
+
+ align:start position:0%
+real communication systems to increase
+the efficiency of transmission
+
+ align:start position:0%
+the efficiency of transmission
+ 
+
+ align:start position:0%
+the efficiency of transmission
+all kinds of commercial applications
+
+ align:start position:0%
+all kinds of commercial applications
+ 
+
+ align:start position:0%
+all kinds of commercial applications
+whether you're you know doing LED
+
+ align:start position:0%
+whether you're you know doing LED
+ 
+
+ align:start position:0%
+whether you're you know doing LED
+lighting or this is actually from some
+
+ align:start position:0%
+lighting or this is actually from some
+ 
+
+ align:start position:0%
+lighting or this is actually from some
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+Purity device but of course it requires
+
+ align:start position:0%
+Purity device but of course it requires
+ 
+
+ align:start position:0%
+Purity device but of course it requires
+a power supply right
+
+ align:start position:0%
+a power supply right
+ 
+
+ align:start position:0%
+a power supply right
+so almost any use of energy these days
+
+ align:start position:0%
+so almost any use of energy these days
+ 
+
+ align:start position:0%
+so almost any use of energy these days
+requires a power
+
+ align:start position:0%
+requires a power
+ 
+
+ align:start position:0%
+requires a power
+supply even in your home I mentioned
+
+ align:start position:0%
+supply even in your home I mentioned
+ 
+
+ align:start position:0%
+supply even in your home I mentioned
+that it used to be that you'd connect
+
+ align:start position:0%
+that it used to be that you'd connect
+ 
+
+ align:start position:0%
+that it used to be that you'd connect
+Motors up to the grid and they'd run and
+
+ align:start position:0%
+Motors up to the grid and they'd run and
+ 
+
+ align:start position:0%
+Motors up to the grid and they'd run and
+maybe You' turn them on and off
+
+ align:start position:0%
+maybe You' turn them on and off
+ 
+
+ align:start position:0%
+maybe You' turn them on and off
+something like that but no longer right
+
+ align:start position:0%
+something like that but no longer right
+ 
+
+ align:start position:0%
+something like that but no longer right
+if you want high performance you need to
+
+ align:start position:0%
+if you want high performance you need to
+ 
+
+ align:start position:0%
+if you want high performance you need to
+be able to modulate that energy so two
+
+ align:start position:0%
+be able to modulate that energy so two
+ 
+
+ align:start position:0%
+be able to modulate that energy so two
+examples here this is for an air
+
+ align:start position:0%
+examples here this is for an air
+ 
+
+ align:start position:0%
+examples here this is for an air
+conditioning unit and it uses an
+
+ align:start position:0%
+conditioning unit and it uses an
+ 
+
+ align:start position:0%
+conditioning unit and it uses an
+inverter a DC to AC converter inside it
+
+ align:start position:0%
+inverter a DC to AC converter inside it
+ 
+
+ align:start position:0%
+inverter a DC to AC converter inside it
+to drive the motor much more quietly and
+
+ align:start position:0%
+to drive the motor much more quietly and
+ 
+
+ align:start position:0%
+to drive the motor much more quietly and
+much more modulated for higher overall
+
+ align:start position:0%
+much more modulated for higher overall
+ 
+
+ align:start position:0%
+much more modulated for higher overall
+system efficiency even your dishwasher
+
+ align:start position:0%
+system efficiency even your dishwasher
+ 
+
+ align:start position:0%
+system efficiency even your dishwasher
+these days has power converters in it
+
+ align:start position:0%
+these days has power converters in it
+ 
+
+ align:start position:0%
+these days has power converters in it
+because it's more efficient in this case
+
+ align:start position:0%
+because it's more efficient in this case
+ 
+
+ align:start position:0%
+because it's more efficient in this case
+quieter to do it that way okay IDE is
+
+ align:start position:0%
+quieter to do it that way okay IDE is
+ 
+
+ align:start position:0%
+quieter to do it that way okay IDE is
+that you might not think of as power
+
+ align:start position:0%
+that you might not think of as power
+ 
+
+ align:start position:0%
+that you might not think of as power
+converters medical applications this is
+
+ align:start position:0%
+converters medical applications this is
+ 
+
+ align:start position:0%
+converters medical applications this is
+this is actually a uh magnetic
+
+ align:start position:0%
+this is actually a uh magnetic
+ 
+
+ align:start position:0%
+this is actually a uh magnetic
+stimulator generates 5,000 amps pulse
+
+ align:start position:0%
+stimulator generates 5,000 amps pulse
+ 
+
+ align:start position:0%
+stimulator generates 5,000 amps pulse
+trains in a transducer coil to throw up
+
+ align:start position:0%
+trains in a transducer coil to throw up
+ 
+
+ align:start position:0%
+trains in a transducer coil to throw up
+magnetic fields that can trigger nerves
+
+ align:start position:0%
+magnetic fields that can trigger nerves
+ 
+
+ align:start position:0%
+magnetic fields that can trigger nerves
+this is an interesting one it's actually
+
+ align:start position:0%
+this is an interesting one it's actually
+ 
+
+ align:start position:0%
+this is an interesting one it's actually
+homework zero so the thing you're
+
+ align:start position:0%
+homework zero so the thing you're
+ 
+
+ align:start position:0%
+homework zero so the thing you're
+analyzing in the first homework just to
+
+ align:start position:0%
+analyzing in the first homework just to
+ 
+
+ align:start position:0%
+analyzing in the first homework just to
+break the rust off is actually this box
+
+ align:start position:0%
+break the rust off is actually this box
+ 
+
+ align:start position:0%
+break the rust off is actually this box
+right here okay scientific applications
+
+ align:start position:0%
+right here okay scientific applications
+ 
+
+ align:start position:0%
+right here okay scientific applications
+you may not be processing energy but
+
+ align:start position:0%
+you may not be processing energy but
+ 
+
+ align:start position:0%
+you may not be processing energy but
+even if you just need to generate
+
+ align:start position:0%
+even if you just need to generate
+ 
+
+ align:start position:0%
+even if you just need to generate
+electric High electrical fields for
+
+ align:start position:0%
+electric High electrical fields for
+ 
+
+ align:start position:0%
+electric High electrical fields for
+whatever reason or magnetic fields as in
+
+ align:start position:0%
+whatever reason or magnetic fields as in
+ 
+
+ align:start position:0%
+whatever reason or magnetic fields as in
+the magnetic stimulator you need energy
+
+ align:start position:0%
+the magnetic stimulator you need energy
+ 
+
+ align:start position:0%
+the magnetic stimulator you need energy
+conversion circuits to do it then
+
+ align:start position:0%
+conversion circuits to do it then
+ 
+
+ align:start position:0%
+conversion circuits to do it then
+there's the sort of the more maybe the
+
+ align:start position:0%
+there's the sort of the more maybe the
+ 
+
+ align:start position:0%
+there's the sort of the more maybe the
+applications you might think of
+
+ align:start position:0%
+applications you might think of
+ 
+
+ align:start position:0%
+applications you might think of
+Transportation right let say that
+
+ align:start position:0%
+Transportation right let say that
+ 
+
+ align:start position:0%
+Transportation right let say that
+electric vehicle or a hybrid vehicle
+
+ align:start position:0%
+electric vehicle or a hybrid vehicle
+ 
+
+ align:start position:0%
+electric vehicle or a hybrid vehicle
+right you
+
+ align:start position:0%
+right you
+ 
+
+ align:start position:0%
+right you
+need Power Electronics to drive the
+
+ align:start position:0%
+need Power Electronics to drive the
+ 
+
+ align:start position:0%
+need Power Electronics to drive the
+energy conversion and this is not a
+
+ align:start position:0%
+energy conversion and this is not a
+ 
+
+ align:start position:0%
+energy conversion and this is not a
+small thing first of all you need the
+
+ align:start position:0%
+small thing first of all you need the
+ 
+
+ align:start position:0%
+small thing first of all you need the
+Power Electronics to drive these things
+
+ align:start position:0%
+Power Electronics to drive these things
+ 
+
+ align:start position:0%
+Power Electronics to drive these things
+right secondly in fact as in one
+
+ align:start position:0%
+right secondly in fact as in one
+ 
+
+ align:start position:0%
+right secondly in fact as in one
+example they redes they
+
+ align:start position:0%
+example they redes they
+ 
+
+ align:start position:0%
+example they redes they
+redesigned the power converter for a
+
+ align:start position:0%
+redesigned the power converter for a
+ 
+
+ align:start position:0%
+redesigned the power converter for a
+Prius the the power train for the Prius
+
+ align:start position:0%
+Prius the the power train for the Prius
+ 
+
+ align:start position:0%
+Prius the the power train for the Prius
+the fuel economy went up by 5% just by
+
+ align:start position:0%
+the fuel economy went up by 5% just by
+ 
+
+ align:start position:0%
+the fuel economy went up by 5% just by
+redesigning the Power Electronics to be
+
+ align:start position:0%
+redesigning the Power Electronics to be
+ 
+
+ align:start position:0%
+redesigning the Power Electronics to be
+better so it has a huge impact on the
+
+ align:start position:0%
+better so it has a huge impact on the
+ 
+
+ align:start position:0%
+better so it has a huge impact on the
+overall application and of course that's
+
+ align:start position:0%
+overall application and of course that's
+ 
+
+ align:start position:0%
+overall application and of course that's
+um electric vehicles but traction right
+
+ align:start position:0%
+um electric vehicles but traction right
+ 
+
+ align:start position:0%
+um electric vehicles but traction right
+trains that's higher power but the same
+
+ align:start position:0%
+trains that's higher power but the same
+ 
+
+ align:start position:0%
+trains that's higher power but the same
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+actually even future trains this it's a
+
+ align:start position:0%
+actually even future trains this it's a
+ 
+
+ align:start position:0%
+actually even future trains this it's a
+little hard to see behind this railing
+
+ align:start position:0%
+little hard to see behind this railing
+ 
+
+ align:start position:0%
+little hard to see behind this railing
+that's a maglev magnetically levitated
+
+ align:start position:0%
+that's a maglev magnetically levitated
+ 
+
+ align:start position:0%
+that's a maglev magnetically levitated
+train along the Wayside over in the back
+
+ align:start position:0%
+train along the Wayside over in the back
+ 
+
+ align:start position:0%
+train along the Wayside over in the back
+corner you see this big building here
+
+ align:start position:0%
+corner you see this big building here
+ 
+
+ align:start position:0%
+corner you see this big building here
+inside that big building as these racks
+
+ align:start position:0%
+inside that big building as these racks
+ 
+
+ align:start position:0%
+inside that big building as these racks
+of Power Electronics now you better have
+
+ align:start position:0%
+of Power Electronics now you better have
+ 
+
+ align:start position:0%
+of Power Electronics now you better have
+pretty reliable Power Electronics if
+
+ align:start position:0%
+pretty reliable Power Electronics if
+ 
+
+ align:start position:0%
+pretty reliable Power Electronics if
+your vehicle's flying along at 400 kmers
+
+ align:start position:0%
+your vehicle's flying along at 400 kmers
+ 
+
+ align:start position:0%
+your vehicle's flying along at 400 kmers
+an hour floating on you know that far
+
+ align:start position:0%
+an hour floating on you know that far
+ 
+
+ align:start position:0%
+an hour floating on you know that far
+off the ground right so not only do you
+
+ align:start position:0%
+off the ground right so not only do you
+ 
+
+ align:start position:0%
+off the ground right so not only do you
+need efficiency but you need reliability
+
+ align:start position:0%
+need efficiency but you need reliability
+ 
+
+ align:start position:0%
+need efficiency but you need reliability
+and precision okay even Strang
+
+ align:start position:0%
+and precision okay even Strang
+ 
+
+ align:start position:0%
+and precision okay even Strang
+things uh this is this is an example of
+
+ align:start position:0%
+things uh this is this is an example of
+ 
+
+ align:start position:0%
+things uh this is this is an example of
+a drone just by powered by high voltage
+
+ align:start position:0%
+a drone just by powered by high voltage
+ 
+
+ align:start position:0%
+a drone just by powered by high voltage
+right you just apply high voltage it
+
+ align:start position:0%
+right you just apply high voltage it
+ 
+
+ align:start position:0%
+right you just apply high voltage it
+breaks down the air accelerates ions and
+
+ align:start position:0%
+breaks down the air accelerates ions and
+ 
+
+ align:start position:0%
+breaks down the air accelerates ions and
+you can use that for propulsion that's
+
+ align:start position:0%
+you can use that for propulsion that's
+ 
+
+ align:start position:0%
+you can use that for propulsion that's
+the first demonstration of it but it
+
+ align:start position:0%
+the first demonstration of it but it
+ 
+
+ align:start position:0%
+the first demonstration of it but it
+actually it's very similar in some
+
+ align:start position:0%
+actually it's very similar in some
+ 
+
+ align:start position:0%
+actually it's very similar in some
+regards to what people use for space
+
+ align:start position:0%
+regards to what people use for space
+ 
+
+ align:start position:0%
+regards to what people use for space
+propulsion you've heard of ion engines
+
+ align:start position:0%
+propulsion you've heard of ion engines
+ 
+
+ align:start position:0%
+propulsion you've heard of ion engines
+right the twin ion engine TIE fighter or
+
+ align:start position:0%
+right the twin ion engine TIE fighter or
+ 
+
+ align:start position:0%
+right the twin ion engine TIE fighter or
+what more practically they use to uh to
+
+ align:start position:0%
+what more practically they use to uh to
+ 
+
+ align:start position:0%
+what more practically they use to uh to
+reposition satellites those require
+
+ align:start position:0%
+reposition satellites those require
+ 
+
+ align:start position:0%
+reposition satellites those require
+Power Electronics to generate high
+
+ align:start position:0%
+Power Electronics to generate high
+ 
+
+ align:start position:0%
+Power Electronics to generate high
+voltages and accelerate ions okay Power
+
+ align:start position:0%
+voltages and accelerate ions okay Power
+ 
+
+ align:start position:0%
+voltages and accelerate ions okay Power
+transmission and generation right that's
+
+ align:start position:0%
+transmission and generation right that's
+ 
+
+ align:start position:0%
+transmission and generation right that's
+so you're getting your energy from
+
+ align:start position:0%
+so you're getting your energy from
+ 
+
+ align:start position:0%
+so you're getting your energy from
+somewhere and increasingly we're getting
+
+ align:start position:0%
+somewhere and increasingly we're getting
+ 
+
+ align:start position:0%
+somewhere and increasingly we're getting
+it from renewable resources well
+
+ align:start position:0%
+it from renewable resources well
+ 
+
+ align:start position:0%
+it from renewable resources well
+generally the way things are trending
+
+ align:start position:0%
+generally the way things are trending
+ 
+
+ align:start position:0%
+generally the way things are trending
+you take some mechanical or solar or
+
+ align:start position:0%
+you take some mechanical or solar or
+ 
+
+ align:start position:0%
+you take some mechanical or solar or
+other source of energy and you
+
+ align:start position:0%
+other source of energy and you
+ 
+
+ align:start position:0%
+other source of energy and you
+transition it not only through a
+
+ align:start position:0%
+transition it not only through a
+ 
+
+ align:start position:0%
+transition it not only through a
+generator but through Power Electronics
+
+ align:start position:0%
+generator but through Power Electronics
+ 
+
+ align:start position:0%
+generator but through Power Electronics
+to get there and that's true for
+
+ align:start position:0%
+to get there and that's true for
+ 
+
+ align:start position:0%
+to get there and that's true for
+terrestrial things things like this is a
+
+ align:start position:0%
+terrestrial things things like this is a
+ 
+
+ align:start position:0%
+terrestrial things things like this is a
+house rooftop PV system this is a micro
+
+ align:start position:0%
+house rooftop PV system this is a micro
+ 
+
+ align:start position:0%
+house rooftop PV system this is a micro
+inverter
+
+ align:start position:0%
+inverter
+ 
+
+ align:start position:0%
+inverter
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Automotive Systems or even much smaller
+
+ align:start position:0%
+Automotive Systems or even much smaller
+ 
+
+ align:start position:0%
+Automotive Systems or even much smaller
+things like uh
+
+ align:start position:0%
+things like uh
+ 
+
+ align:start position:0%
+things like uh
+uh Power harvesting energy harvesting
+
+ align:start position:0%
+uh Power harvesting energy harvesting
+ 
+
+ align:start position:0%
+uh Power harvesting energy harvesting
+techniques you need Power Electronics in
+
+ align:start position:0%
+techniques you need Power Electronics in
+ 
+
+ align:start position:0%
+techniques you need Power Electronics in
+it also all kinds of industrial
+
+ align:start position:0%
+it also all kinds of industrial
+ 
+
+ align:start position:0%
+it also all kinds of industrial
+applications whether you're doing uh
+
+ align:start position:0%
+applications whether you're doing uh
+ 
+
+ align:start position:0%
+applications whether you're doing uh
+plasma processing for Semiconductor
+
+ align:start position:0%
+plasma processing for Semiconductor
+ 
+
+ align:start position:0%
+plasma processing for Semiconductor
+processing or you know you want to
+
+ align:start position:0%
+processing or you know you want to
+ 
+
+ align:start position:0%
+processing or you know you want to
+refine metals like a DC Arc furnace you
+
+ align:start position:0%
+refine metals like a DC Arc furnace you
+ 
+
+ align:start position:0%
+refine metals like a DC Arc furnace you
+need Power Electronics there too okay so
+
+ align:start position:0%
+need Power Electronics there too okay so
+ 
+
+ align:start position:0%
+need Power Electronics there too okay so
+that's just sort of a way long way of
+
+ align:start position:0%
+that's just sort of a way long way of
+ 
+
+ align:start position:0%
+that's just sort of a way long way of
+saying power electronics are in almost
+
+ align:start position:0%
+saying power electronics are in almost
+ 
+
+ align:start position:0%
+saying power electronics are in almost
+everything you care about these days and
+
+ align:start position:0%
+everything you care about these days and
+ 
+
+ align:start position:0%
+everything you care about these days and
+it's only getting more so because we
+
+ align:start position:0%
+it's only getting more so because we
+ 
+
+ align:start position:0%
+it's only getting more so because we
+have to be better about how we use
+
+ align:start position:0%
+have to be better about how we use
+ 
+
+ align:start position:0%
+have to be better about how we use
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what's inside a power converter
+
+ align:start position:0%
+okay so what's inside a power converter
+ 
+
+ align:start position:0%
+okay so what's inside a power converter
+and we're going to talk about this in
+
+ align:start position:0%
+and we're going to talk about this in
+ 
+
+ align:start position:0%
+and we're going to talk about this in
+much greater detail but if you want to
+
+ align:start position:0%
+much greater detail but if you want to
+ 
+
+ align:start position:0%
+much greater detail but if you want to
+think about it what we have
+
+ align:start position:0%
+think about it what we have
+ 
+
+ align:start position:0%
+think about it what we have
+is typically some kind of energy storage
+
+ align:start position:0%
+is typically some kind of energy storage
+ 
+
+ align:start position:0%
+is typically some kind of energy storage
+elements these could be inductors or
+
+ align:start position:0%
+elements these could be inductors or
+ 
+
+ align:start position:0%
+elements these could be inductors or
+capacitors or sometimes other things and
+
+ align:start position:0%
+capacitors or sometimes other things and
+ 
+
+ align:start position:0%
+capacitors or sometimes other things and
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+use semiconductor switches and we're
+
+ align:start position:0%
+use semiconductor switches and we're
+ 
+
+ align:start position:0%
+use semiconductor switches and we're
+going to draw energy from some Source
+
+ align:start position:0%
+going to draw energy from some Source
+ 
+
+ align:start position:0%
+going to draw energy from some Source
+we're going to manipulate it somehow so
+
+ align:start position:0%
+we're going to manipulate it somehow so
+ 
+
+ align:start position:0%
+we're going to manipulate it somehow so
+we store it in these energy storage
+
+ align:start position:0%
+we store it in these energy storage
+ 
+
+ align:start position:0%
+we store it in these energy storage
+elements and then we're going to put it
+
+ align:start position:0%
+elements and then we're going to put it
+ 
+
+ align:start position:0%
+elements and then we're going to put it
+to the output and we're going to repeat
+
+ align:start position:0%
+to the output and we're going to repeat
+ 
+
+ align:start position:0%
+to the output and we're going to repeat
+that right so draw transform put it to
+
+ align:start position:0%
+that right so draw transform put it to
+ 
+
+ align:start position:0%
+that right so draw transform put it to
+the output okay because we do this on a
+
+ align:start position:0%
+the output okay because we do this on a
+ 
+
+ align:start position:0%
+the output okay because we do this on a
+cyclic
+
+ align:start position:0%
+cyclic
+ 
+
+ align:start position:0%
+cyclic
+basis we generate sort of Ripple and
+
+ align:start position:0%
+basis we generate sort of Ripple and
+ 
+
+ align:start position:0%
+basis we generate sort of Ripple and
+potentially noise that could interfere
+
+ align:start position:0%
+potentially noise that could interfere
+ 
+
+ align:start position:0%
+potentially noise that could interfere
+with things like television or
+
+ align:start position:0%
+with things like television or
+ 
+
+ align:start position:0%
+with things like television or
+Electronics so you generally need
+
+ align:start position:0%
+Electronics so you generally need
+ 
+
+ align:start position:0%
+Electronics so you generally need
+filters to do that too we also of course
+
+ align:start position:0%
+filters to do that too we also of course
+ 
+
+ align:start position:0%
+filters to do that too we also of course
+need to control that flow of energy
+
+ align:start position:0%
+need to control that flow of energy
+ 
+
+ align:start position:0%
+need to control that flow of energy
+right we can't be stupid about it we
+
+ align:start position:0%
+right we can't be stupid about it we
+ 
+
+ align:start position:0%
+right we can't be stupid about it we
+have especially for something high
+
+ align:start position:0%
+have especially for something high
+ 
+
+ align:start position:0%
+have especially for something high
+performance like a microprocessor which
+
+ align:start position:0%
+performance like a microprocessor which
+ 
+
+ align:start position:0%
+performance like a microprocessor which
+might be changing its operation very
+
+ align:start position:0%
+might be changing its operation very
+ 
+
+ align:start position:0%
+might be changing its operation very
+very fast we need to control that flow
+
+ align:start position:0%
+very fast we need to control that flow
+ 
+
+ align:start position:0%
+very fast we need to control that flow
+so there's control circuitry we're going
+
+ align:start position:0%
+so there's control circuitry we're going
+ 
+
+ align:start position:0%
+so there's control circuitry we're going
+to be learning about all of the aspects
+
+ align:start position:0%
+to be learning about all of the aspects
+ 
+
+ align:start position:0%
+to be learning about all of the aspects
+of Designing
+
+ align:start position:0%
+of Designing
+ 
+
+ align:start position:0%
+of Designing
+all of these kinds of elements
+
+ align:start position:0%
+all of these kinds of elements
+ 
+
+ align:start position:0%
+all of these kinds of elements
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we're leveraging sort of everything
+
+ align:start position:0%
+so we're leveraging sort of everything
+ 
+
+ align:start position:0%
+so we're leveraging sort of everything
+from circuit design semiconductor
+
+ align:start position:0%
+from circuit design semiconductor
+ 
+
+ align:start position:0%
+from circuit design semiconductor
+devices passive components and materials
+
+ align:start position:0%
+devices passive components and materials
+ 
+
+ align:start position:0%
+devices passive components and materials
+increasingly packaging and Cooling and
+
+ align:start position:0%
+increasingly packaging and Cooling and
+ 
+
+ align:start position:0%
+increasingly packaging and Cooling and
+controls also matter and things have
+
+ align:start position:0%
+controls also matter and things have
+ 
+
+ align:start position:0%
+controls also matter and things have
+been getting better and better and
+
+ align:start position:0%
+been getting better and better and
+ 
+
+ align:start position:0%
+been getting better and better and
+better both because the um ways we can
+
+ align:start position:0%
+better both because the um ways we can
+ 
+
+ align:start position:0%
+better both because the um ways we can
+manufacture things get better and
+
+ align:start position:0%
+manufacture things get better and
+ 
+
+ align:start position:0%
+manufacture things get better and
+because the devices which we have
+
+ align:start position:0%
+because the devices which we have
+ 
+
+ align:start position:0%
+because the devices which we have
+our access to in order to implement
+
+ align:start position:0%
+our access to in order to implement
+ 
+
+ align:start position:0%
+our access to in order to implement
+these things get better okay and so
+
+ align:start position:0%
+these things get better okay and so
+ 
+
+ align:start position:0%
+these things get better okay and so
+we're going to look at some of the
+
+ align:start position:0%
+we're going to look at some of the
+ 
+
+ align:start position:0%
+we're going to look at some of the
+different ways you can do that I'll just
+
+ align:start position:0%
+different ways you can do that I'll just
+ 
+
+ align:start position:0%
+different ways you can do that I'll just
+give you
+
+ align:start position:0%
+give you
+ 
+
+ align:start position:0%
+give you
+uh one example this is what you would
+
+ align:start position:0%
+uh one example this is what you would
+ 
+
+ align:start position:0%
+uh one example this is what you would
+find something like in a data center
+
+ align:start position:0%
+find something like in a data center
+ 
+
+ align:start position:0%
+find something like in a data center
+right so they come in they rectify the
+
+ align:start position:0%
+right so they come in they rectify the
+ 
+
+ align:start position:0%
+right so they come in they rectify the
+voltage they get it to sort of 400 Volts
+
+ align:start position:0%
+voltage they get it to sort of 400 Volts
+ 
+
+ align:start position:0%
+voltage they get it to sort of 400 Volts
+for reasons we'll go into this converter
+
+ align:start position:0%
+for reasons we'll go into this converter
+ 
+
+ align:start position:0%
+for reasons we'll go into this converter
+here was designed to take that 400 volts
+
+ align:start position:0%
+here was designed to take that 400 volts
+ 
+
+ align:start position:0%
+here was designed to take that 400 volts
+and bring it down to 12 volts okay
+
+ align:start position:0%
+and bring it down to 12 volts okay
+ 
+
+ align:start position:0%
+and bring it down to 12 volts okay
+that that tiny little thing a little bit
+
+ align:start position:0%
+that that tiny little thing a little bit
+ 
+
+ align:start position:0%
+that that tiny little thing a little bit
+bigger than a penny there actually can
+
+ align:start position:0%
+bigger than a penny there actually can
+ 
+
+ align:start position:0%
+bigger than a penny there actually can
+handle a kilowatt then you need more
+
+ align:start position:0%
+handle a kilowatt then you need more
+ 
+
+ align:start position:0%
+handle a kilowatt then you need more
+converters to take it down from there to
+
+ align:start position:0%
+converters to take it down from there to
+ 
+
+ align:start position:0%
+converters to take it down from there to
+the one VT that the processor uses okay
+
+ align:start position:0%
+the one VT that the processor uses okay
+ 
+
+ align:start position:0%
+the one VT that the processor uses okay
+so the sort of a long way of saying all
+
+ align:start position:0%
+so the sort of a long way of saying all
+ 
+
+ align:start position:0%
+so the sort of a long way of saying all
+kinds of things are limited by energy
+
+ align:start position:0%
+kinds of things are limited by energy
+ 
+
+ align:start position:0%
+kinds of things are limited by energy
+and how we can control it right across
+
+ align:start position:0%
+and how we can control it right across
+ 
+
+ align:start position:0%
+and how we can control it right across
+all these applications and what we're
+
+ align:start position:0%
+all these applications and what we're
+ 
+
+ align:start position:0%
+all these applications and what we're
+usually trying to do is how figure out
+
+ align:start position:0%
+usually trying to do is how figure out
+ 
+
+ align:start position:0%
+usually trying to do is how figure out
+how to make them smaller and lighter
+
+ align:start position:0%
+how to make them smaller and lighter
+ 
+
+ align:start position:0%
+how to make them smaller and lighter
+right if you're taking up 40% of your
+
+ align:start position:0%
+right if you're taking up 40% of your
+ 
+
+ align:start position:0%
+right if you're taking up 40% of your
+iPhone you want
+
+ align:start position:0%
+iPhone you want
+ 
+
+ align:start position:0%
+iPhone you want
+make that thing smaller so it doesn't
+
+ align:start position:0%
+make that thing smaller so it doesn't
+ 
+
+ align:start position:0%
+make that thing smaller so it doesn't
+take that up and you can replace that
+
+ align:start position:0%
+take that up and you can replace that
+ 
+
+ align:start position:0%
+take that up and you can replace that
+volume either with nothing or with
+
+ align:start position:0%
+volume either with nothing or with
+ 
+
+ align:start position:0%
+volume either with nothing or with
+things that are more interesting to you
+
+ align:start position:0%
+things that are more interesting to you
+ 
+
+ align:start position:0%
+things that are more interesting to you
+we need higher efficiency both for the
+
+ align:start position:0%
+we need higher efficiency both for the
+ 
+
+ align:start position:0%
+we need higher efficiency both for the
+converters and the systems how we
+
+ align:start position:0%
+converters and the systems how we
+ 
+
+ align:start position:0%
+converters and the systems how we
+process energy can matter to the not
+
+ align:start position:0%
+process energy can matter to the not
+ 
+
+ align:start position:0%
+process energy can matter to the not
+only the ultimate efficiency of the
+
+ align:start position:0%
+only the ultimate efficiency of the
+ 
+
+ align:start position:0%
+only the ultimate efficiency of the
+converter but the efficiency of the
+
+ align:start position:0%
+converter but the efficiency of the
+ 
+
+ align:start position:0%
+converter but the efficiency of the
+system how it uses energy can be
+
+ align:start position:0%
+system how it uses energy can be
+ 
+
+ align:start position:0%
+system how it uses energy can be
+determined by the Power Electronics we
+
+ align:start position:0%
+determined by the Power Electronics we
+ 
+
+ align:start position:0%
+determined by the Power Electronics we
+want higher performance that could mean
+
+ align:start position:0%
+want higher performance that could mean
+ 
+
+ align:start position:0%
+want higher performance that could mean
+higher bandwidth or other aspects and
+
+ align:start position:0%
+higher bandwidth or other aspects and
+ 
+
+ align:start position:0%
+higher bandwidth or other aspects and
+then there's all kinds of means that we
+
+ align:start position:0%
+then there's all kinds of means that we
+ 
+
+ align:start position:0%
+then there's all kinds of means that we
+we can use better electrical processing
+
+ align:start position:0%
+we can use better electrical processing
+ 
+
+ align:start position:0%
+we can use better electrical processing
+to enable new applications so these are
+
+ align:start position:0%
+to enable new applications so these are
+ 
+
+ align:start position:0%
+to enable new applications so these are
+the kind of things that we're going to
+
+ align:start position:0%
+the kind of things that we're going to
+ 
+
+ align:start position:0%
+the kind of things that we're going to
+learn about this term I'll pause there
+
+ align:start position:0%
+learn about this term I'll pause there
+ 
+
+ align:start position:0%
+learn about this term I'll pause there
+i' I've been going on a while are there
+
+ align:start position:0%
+i' I've been going on a while are there
+ 
+
+ align:start position:0%
+i' I've been going on a while are there
+any questions about any of this before
+
+ align:start position:0%
+any questions about any of this before
+ 
+
+ align:start position:0%
+any questions about any of this before
+we get going this is just to sort of
+
+ align:start position:0%
+we get going this is just to sort of
+ 
+
+ align:start position:0%
+we get going this is just to sort of
+Orient you as to what we're going to
+
+ align:start position:0%
+Orient you as to what we're going to
+ 
+
+ align:start position:0%
+Orient you as to what we're going to
+focus the term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on I can put the slides on canvas
+
+ align:start position:0%
+on I can put the slides on canvas
+ 
+
+ align:start position:0%
+on I can put the slides on canvas
+sure any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I will just give
+
+ align:start position:0%
+okay I will just give
+ 
+
+ align:start position:0%
+okay I will just give
+you a slight
+
+ align:start position:0%
+you a slight
+ 
+
+ align:start position:0%
+you a slight
+notion okay just and this is a
+
+ align:start position:0%
+notion okay just and this is a
+ 
+
+ align:start position:0%
+notion okay just and this is a
+favorite thing I like to bring in just
+
+ align:start position:0%
+favorite thing I like to bring in just
+ 
+
+ align:start position:0%
+favorite thing I like to bring in just
+to show you the kind of things we're
+
+ align:start position:0%
+to show you the kind of things we're
+ 
+
+ align:start position:0%
+to show you the kind of things we're
+going to look at this
+
+ align:start position:0%
+going to look at this
+ 
+
+ align:start position:0%
+going to look at this
+term this is a piece of commercial
+
+ align:start position:0%
+term this is a piece of commercial
+ 
+
+ align:start position:0%
+term this is a piece of commercial
+Hardware from a company called MKS
+
+ align:start position:0%
+Hardware from a company called MKS
+ 
+
+ align:start position:0%
+Hardware from a company called MKS
+instruments that I just happen to have
+
+ align:start position:0%
+instruments that I just happen to have
+ 
+
+ align:start position:0%
+instruments that I just happen to have
+in my
+
+ align:start position:0%
+in my
+ 
+
+ align:start position:0%
+in my
+office this input piece is a filter so
+
+ align:start position:0%
+office this input piece is a filter so
+ 
+
+ align:start position:0%
+office this input piece is a filter so
+you don't create electrom magnetic
+
+ align:start position:0%
+you don't create electrom magnetic
+ 
+
+ align:start position:0%
+you don't create electrom magnetic
+interference and you don't generate
+
+ align:start position:0%
+interference and you don't generate
+ 
+
+ align:start position:0%
+interference and you don't generate
+noise you don't
+
+ align:start position:0%
+noise you don't
+ 
+
+ align:start position:0%
+noise you don't
+want then this piece here takes energy
+
+ align:start position:0%
+want then this piece here takes energy
+ 
+
+ align:start position:0%
+want then this piece here takes energy
+from the 60 HZ grid and generates DC
+
+ align:start position:0%
+from the 60 HZ grid and generates DC
+ 
+
+ align:start position:0%
+from the 60 HZ grid and generates DC
+from it and it has to do it while making
+
+ align:start position:0%
+from it and it has to do it while making
+ 
+
+ align:start position:0%
+from it and it has to do it while making
+the whole thing look like a resistor to
+
+ align:start position:0%
+the whole thing look like a resistor to
+ 
+
+ align:start position:0%
+the whole thing look like a resistor to
+the grid so you don't mess up the grid
+
+ align:start position:0%
+the grid so you don't mess up the grid
+ 
+
+ align:start position:0%
+the grid so you don't mess up the grid
+okay that's what this part does then it
+
+ align:start position:0%
+okay that's what this part does then it
+ 
+
+ align:start position:0%
+okay that's what this part does then it
+has these isolated dcdc converters that
+
+ align:start position:0%
+has these isolated dcdc converters that
+ 
+
+ align:start position:0%
+has these isolated dcdc converters that
+can take that DC voltage and generate
+
+ align:start position:0%
+can take that DC voltage and generate
+ 
+
+ align:start position:0%
+can take that DC voltage and generate
+other DC voltages referenced in other
+
+ align:start position:0%
+other DC voltages referenced in other
+ 
+
+ align:start position:0%
+other DC voltages referenced in other
+ways and without worrying about uh sort
+
+ align:start position:0%
+ways and without worrying about uh sort
+ 
+
+ align:start position:0%
+ways and without worrying about uh sort
+of currents going back to ground okay
+
+ align:start position:0%
+of currents going back to ground okay
+ 
+
+ align:start position:0%
+of currents going back to ground okay
+it's galvanically isolated and then it
+
+ align:start position:0%
+it's galvanically isolated and then it
+ 
+
+ align:start position:0%
+it's galvanically isolated and then it
+takes that energy and goes back DC to AC
+
+ align:start position:0%
+takes that energy and goes back DC to AC
+ 
+
+ align:start position:0%
+takes that energy and goes back DC to AC
+okay now in some systems you might go DC
+
+ align:start position:0%
+okay now in some systems you might go DC
+ 
+
+ align:start position:0%
+okay now in some systems you might go DC
+to AC for 60 hertz to to generate into
+
+ align:start position:0%
+to AC for 60 hertz to to generate into
+ 
+
+ align:start position:0%
+to AC for 60 hertz to to generate into
+the Grid or for a motor or something
+
+ align:start position:0%
+the Grid or for a motor or something
+ 
+
+ align:start position:0%
+the Grid or for a motor or something
+else this particular one has these
+
+ align:start position:0%
+else this particular one has these
+ 
+
+ align:start position:0%
+else this particular one has these
+outputs that are at 13 megahertz for
+
+ align:start position:0%
+outputs that are at 13 megahertz for
+ 
+
+ align:start position:0%
+outputs that are at 13 megahertz for
+driving plasmas to process
+
+ align:start position:0%
+driving plasmas to process
+ 
+
+ align:start position:0%
+driving plasmas to process
+semiconductors okay but you get all
+
+ align:start position:0%
+semiconductors okay but you get all
+ 
+
+ align:start position:0%
+semiconductors okay but you get all
+these kind of functions AC to DC DC to
+
+ align:start position:0%
+these kind of functions AC to DC DC to
+ 
+
+ align:start position:0%
+these kind of functions AC to DC DC to
+DC DC to AC and we're going to learn the
+
+ align:start position:0%
+DC DC to AC and we're going to learn the
+ 
+
+ align:start position:0%
+DC DC to AC and we're going to learn the
+first of all the
+
+ align:start position:0%
+first of all the
+ 
+
+ align:start position:0%
+first of all the
+underlying uh principles of doing all
+
+ align:start position:0%
+underlying uh principles of doing all
+ 
+
+ align:start position:0%
+underlying uh principles of doing all
+these things and how to design them okay
+
+ align:start position:0%
+these things and how to design them okay
+ 
+
+ align:start position:0%
+these things and how to design them okay
+so the the the real goal
+
+ align:start position:0%
+so the the the real goal
+ 
+
+ align:start position:0%
+so the the the real goal
+is by the time you walk out of here you
+
+ align:start position:0%
+is by the time you walk out of here you
+ 
+
+ align:start position:0%
+is by the time you walk out of here you
+should have all the tools to go off and
+
+ align:start position:0%
+should have all the tools to go off and
+ 
+
+ align:start position:0%
+should have all the tools to go off and
+design Power
+
+ align:start position:0%
+design Power
+ 
+
+ align:start position:0%
+design Power
+Electronics for all kinds of
+
+ align:start position:0%
+Electronics for all kinds of
+ 
+
+ align:start position:0%
+Electronics for all kinds of
+applications and and in fact graduates
+
+ align:start position:0%
+applications and and in fact graduates
+ 
+
+ align:start position:0%
+applications and and in fact graduates
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+class have worked on electric vehicles
+
+ align:start position:0%
+class have worked on electric vehicles
+ 
+
+ align:start position:0%
+class have worked on electric vehicles
+Char battery charger
+
+ align:start position:0%
+Char battery charger
+ 
+
+ align:start position:0%
+Char battery charger
+solar
+
+ align:start position:0%
+solar
+ 
+
+ align:start position:0%
+solar
+uh communication
+
+ align:start position:0%
+uh communication
+ 
+
+ align:start position:0%
+uh communication
+systems data
+
+ align:start position:0%
+systems data
+ 
+
+ align:start position:0%
+systems data
+centers the in fact the the power supply
+
+ align:start position:0%
+centers the in fact the the power supply
+ 
+
+ align:start position:0%
+centers the in fact the the power supply
+I usually use for my laptop and the in
+
+ align:start position:0%
+I usually use for my laptop and the in
+ 
+
+ align:start position:0%
+I usually use for my laptop and the in
+fact the wireless charger for my
+
+ align:start position:0%
+fact the wireless charger for my
+ 
+
+ align:start position:0%
+fact the wireless charger for my
+eyewatch were all designed or the teams
+
+ align:start position:0%
+eyewatch were all designed or the teams
+ 
+
+ align:start position:0%
+eyewatch were all designed or the teams
+were led by graduates of this class
+
+ align:start position:0%
+were led by graduates of this class
+ 
+
+ align:start position:0%
+were led by graduates of this class
+right so this the goal is to give you
+
+ align:start position:0%
+right so this the goal is to give you
+ 
+
+ align:start position:0%
+right so this the goal is to give you
+the tools you need to go do these things
+
+ align:start position:0%
+the tools you need to go do these things
+ 
+
+ align:start position:0%
+the tools you need to go do these things
+okay so with
+
+ align:start position:0%
+okay so with
+ 
+
+ align:start position:0%
+okay so with
+that um let me
+
+ align:start position:0%
+that um let me
+ 
+
+ align:start position:0%
+that um let me
+start by just giving you a sense
+
+ align:start position:0%
+start by just giving you a sense
+ 
+
+ align:start position:0%
+start by just giving you a sense
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um what goes on inside Power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Electronics so let's think of the
+
+ align:start position:0%
+Electronics so let's think of the
+ 
+
+ align:start position:0%
+Electronics so let's think of the
+simplest case I have some DC input
+
+ align:start position:0%
+simplest case I have some DC input
+ 
+
+ align:start position:0%
+simplest case I have some DC input
+voltage and I'd like some other DC
+
+ align:start position:0%
+voltage and I'd like some other DC
+ 
+
+ align:start position:0%
+voltage and I'd like some other DC
+voltage so suppose I have some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input that's you know maybe it's 9 volts
+
+ align:start position:0%
+input that's you know maybe it's 9 volts
+ 
+
+ align:start position:0%
+input that's you know maybe it's 9 volts
+to 6 16
+
+ align:start position:0%
+to 6 16
+ 
+
+ align:start position:0%
+to 6 16
+Vols I'm making that up arbitrarily but
+
+ align:start position:0%
+Vols I'm making that up arbitrarily but
+ 
+
+ align:start position:0%
+Vols I'm making that up arbitrarily but
+that's roughly what you might get in a
+
+ align:start position:0%
+that's roughly what you might get in a
+ 
+
+ align:start position:0%
+that's roughly what you might get in a
+typical vehicle right out of the
+
+ align:start position:0%
+typical vehicle right out of the
+ 
+
+ align:start position:0%
+typical vehicle right out of the
+cigarette lighter
+
+ align:start position:0%
+cigarette lighter
+ 
+
+ align:start position:0%
+cigarette lighter
+okay and suppose I want and I'll call
+
+ align:start position:0%
+okay and suppose I want and I'll call
+ 
+
+ align:start position:0%
+okay and suppose I want and I'll call
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+VN and suppose I want here's some load
+
+ align:start position:0%
+VN and suppose I want here's some load
+ 
+
+ align:start position:0%
+VN and suppose I want here's some load
+that I'm going to represent with a
+
+ align:start position:0%
+that I'm going to represent with a
+ 
+
+ align:start position:0%
+that I'm going to represent with a
+resistor I'm going to call that V out
+
+ align:start position:0%
+resistor I'm going to call that V out
+ 
+
+ align:start position:0%
+resistor I'm going to call that V out
+okay and suppose I want EG 5
+
+ align:start position:0%
+okay and suppose I want EG 5
+ 
+
+ align:start position:0%
+okay and suppose I want EG 5
+volts right to power something that
+
+ align:start position:0%
+volts right to power something that
+ 
+
+ align:start position:0%
+volts right to power something that
+takes five volts
+
+ align:start position:0%
+takes five volts
+ 
+
+ align:start position:0%
+takes five volts
+right what's the most obvious and simple
+
+ align:start position:0%
+right what's the most obvious and simple
+ 
+
+ align:start position:0%
+right what's the most obvious and simple
+way to get 5 volts at my output from
+
+ align:start position:0%
+way to get 5 volts at my output from
+ 
+
+ align:start position:0%
+way to get 5 volts at my output from
+some higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage voltage divider precisely right
+
+ align:start position:0%
+voltage voltage divider precisely right
+ 
+
+ align:start position:0%
+voltage voltage divider precisely right
+I could come up here I could say okay
+
+ align:start position:0%
+I could come up here I could say okay
+ 
+
+ align:start position:0%
+I could come up here I could say okay
+let me put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some volt variable
+
+ align:start position:0%
+in some volt variable
+ 
+
+ align:start position:0%
+in some volt variable
+resistor and I'll drop down this voltage
+
+ align:start position:0%
+resistor and I'll drop down this voltage
+ 
+
+ align:start position:0%
+resistor and I'll drop down this voltage
+to give me the voltage I want and I'm
+
+ align:start position:0%
+to give me the voltage I want and I'm
+ 
+
+ align:start position:0%
+to give me the voltage I want and I'm
+done and in fact a lot of systems that's
+
+ align:start position:0%
+done and in fact a lot of systems that's
+ 
+
+ align:start position:0%
+done and in fact a lot of systems that's
+exactly more or less what they have
+
+ align:start position:0%
+exactly more or less what they have
+ 
+
+ align:start position:0%
+exactly more or less what they have
+inside them in fact inside most
+
+ align:start position:0%
+inside them in fact inside most
+ 
+
+ align:start position:0%
+inside them in fact inside most
+integrated circuits there's lots of
+
+ align:start position:0%
+integrated circuits there's lots of
+ 
+
+ align:start position:0%
+integrated circuits there's lots of
+these things going on okay well okay
+
+ align:start position:0%
+these things going on okay well okay
+ 
+
+ align:start position:0%
+these things going on okay well okay
+they don't do it quite this way what do
+
+ align:start position:0%
+they don't do it quite this way what do
+ 
+
+ align:start position:0%
+they don't do it quite this way what do
+they really do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they will take VN and what they will do
+
+ align:start position:0%
+they will take VN and what they will do
+ 
+
+ align:start position:0%
+they will take VN and what they will do
+is they'll use some kind of transistor a
+
+ align:start position:0%
+is they'll use some kind of transistor a
+ 
+
+ align:start position:0%
+is they'll use some kind of transistor a
+mosfet or a bipolar
+
+ align:start position:0%
+mosfet or a bipolar
+ 
+
+ align:start position:0%
+mosfet or a bipolar
+transistor and they will treat that
+
+ align:start position:0%
+transistor and they will treat that
+ 
+
+ align:start position:0%
+transistor and they will treat that
+essentially as a variable resistor right
+
+ align:start position:0%
+essentially as a variable resistor right
+ 
+
+ align:start position:0%
+essentially as a variable resistor right
+so I implement the variable resistor
+
+ align:start position:0%
+so I implement the variable resistor
+ 
+
+ align:start position:0%
+so I implement the variable resistor
+with a controlled transistor and I will
+
+ align:start position:0%
+with a controlled transistor and I will
+ 
+
+ align:start position:0%
+with a controlled transistor and I will
+come and I'll have some feedback loop
+
+ align:start position:0%
+come and I'll have some feedback loop
+ 
+
+ align:start position:0%
+come and I'll have some feedback loop
+I'll Fe feed in a reference
+
+ align:start position:0%
+I'll Fe feed in a reference
+ 
+
+ align:start position:0%
+I'll Fe feed in a reference
+voltage and I'll measure the output
+
+ align:start position:0%
+voltage and I'll measure the output
+ 
+
+ align:start position:0%
+voltage and I'll measure the output
+voltage and I'll control the Gate of
+
+ align:start position:0%
+voltage and I'll control the Gate of
+ 
+
+ align:start position:0%
+voltage and I'll control the Gate of
+this transistor and essentially make
+
+ align:start position:0%
+this transistor and essentially make
+ 
+
+ align:start position:0%
+this transistor and essentially make
+that transistor look like a variable
+
+ align:start position:0%
+that transistor look like a variable
+ 
+
+ align:start position:0%
+that transistor look like a variable
+resistor and control the voltage
+
+ align:start position:0%
+resistor and control the voltage
+ 
+
+ align:start position:0%
+resistor and control the voltage
+division so that even if this voltage
+
+ align:start position:0%
+division so that even if this voltage
+ 
+
+ align:start position:0%
+division so that even if this voltage
+varies between 9 and 16 volts I always
+
+ align:start position:0%
+varies between 9 and 16 volts I always
+ 
+
+ align:start position:0%
+varies between 9 and 16 volts I always
+get my 5 Vols output
+
+ align:start position:0%
+get my 5 Vols output
+ 
+
+ align:start position:0%
+get my 5 Vols output
+Okay and like I said that's very
+
+ align:start position:0%
+Okay and like I said that's very
+ 
+
+ align:start position:0%
+Okay and like I said that's very
+common but what's the problem with this
+
+ align:start position:0%
+common but what's the problem with this
+ 
+
+ align:start position:0%
+common but what's the problem with this
+well there's a whole lot of problems
+
+ align:start position:0%
+well there's a whole lot of problems
+ 
+
+ align:start position:0%
+well there's a whole lot of problems
+with this right why why wouldn't you
+
+ align:start position:0%
+with this right why why wouldn't you
+ 
+
+ align:start position:0%
+with this right why why wouldn't you
+want to do this uh
+
+ align:start position:0%
+want to do this uh
+ 
+
+ align:start position:0%
+want to do this uh
+in typical
+
+ align:start position:0%
+in typical
+ 
+
+ align:start position:0%
+in typical
+operation efficiency terrible efficiency
+
+ align:start position:0%
+operation efficiency terrible efficiency
+ 
+
+ align:start position:0%
+operation efficiency terrible efficiency
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+exactly so let's think about this if I
+
+ align:start position:0%
+exactly so let's think about this if I
+ 
+
+ align:start position:0%
+exactly so let's think about this if I
+accept the fact let me call this current
+
+ align:start position:0%
+accept the fact let me call this current
+ 
+
+ align:start position:0%
+accept the fact let me call this current
+I in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this current I
+
+ align:start position:0%
+okay and this current I
+ 
+
+ align:start position:0%
+okay and this current I
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay if this thing does act exactly like
+
+ align:start position:0%
+okay if this thing does act exactly like
+ 
+
+ align:start position:0%
+okay if this thing does act exactly like
+a variable resistor the input currents
+
+ align:start position:0%
+a variable resistor the input currents
+ 
+
+ align:start position:0%
+a variable resistor the input currents
+equal to the output current now this
+
+ align:start position:0%
+equal to the output current now this
+ 
+
+ align:start position:0%
+equal to the output current now this
+actually a real system might have some
+
+ align:start position:0%
+actually a real system might have some
+ 
+
+ align:start position:0%
+actually a real system might have some
+current that actually also goes to
+
+ align:start position:0%
+current that actually also goes to
+ 
+
+ align:start position:0%
+current that actually also goes to
+ground let's take the best case where
+
+ align:start position:0%
+ground let's take the best case where
+ 
+
+ align:start position:0%
+ground let's take the best case where
+the output current is equal to the input
+
+ align:start position:0%
+the output current is equal to the input
+ 
+
+ align:start position:0%
+the output current is equal to the input
+current okay what would be the
+
+ align:start position:0%
+current okay what would be the
+ 
+
+ align:start position:0%
+current okay what would be the
+efficiency of this Beast well the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+efficiency the efficiency is equal to
+
+ align:start position:0%
+efficiency the efficiency is equal to
+ 
+
+ align:start position:0%
+efficiency the efficiency is equal to
+the output power over the input power
+
+ align:start position:0%
+the output power over the input power
+ 
+
+ align:start position:0%
+the output power over the input power
+right I'm drawing energy maybe from my
+
+ align:start position:0%
+right I'm drawing energy maybe from my
+ 
+
+ align:start position:0%
+right I'm drawing energy maybe from my
+car battery or whatever my battery
+
+ align:start position:0%
+car battery or whatever my battery
+ 
+
+ align:start position:0%
+car battery or whatever my battery
+source is and I'm delivering it to the
+
+ align:start position:0%
+source is and I'm delivering it to the
+ 
+
+ align:start position:0%
+source is and I'm delivering it to the
+output but not all of it's getting to
+
+ align:start position:0%
+output but not all of it's getting to
+ 
+
+ align:start position:0%
+output but not all of it's getting to
+the output so the output power is V out
+
+ align:start position:0%
+the output so the output power is V out
+ 
+
+ align:start position:0%
+the output so the output power is V out
+time I
+
+ align:start position:0%
+time I
+ 
+
+ align:start position:0%
+time I
+out and my input power is VN time I in
+
+ align:start position:0%
+out and my input power is VN time I in
+ 
+
+ align:start position:0%
+out and my input power is VN time I in
+and I just told you that I out was equal
+
+ align:start position:0%
+and I just told you that I out was equal
+ 
+
+ align:start position:0%
+and I just told you that I out was equal
+to I in in the best case so that's V out
+
+ align:start position:0%
+to I in in the best case so that's V out
+ 
+
+ align:start position:0%
+to I in in the best case so that's V out
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+VN right so if I'm coming in from 15
+
+ align:start position:0%
+VN right so if I'm coming in from 15
+ 
+
+ align:start position:0%
+VN right so if I'm coming in from 15
+volts and I'm getting five
+
+ align:start position:0%
+volts and I'm getting five
+ 
+
+ align:start position:0%
+volts and I'm getting five
+volts that's 33% efficiency right I've
+
+ align:start position:0%
+volts that's 33% efficiency right I've
+ 
+
+ align:start position:0%
+volts that's 33% efficiency right I've
+taken 2/3 of my energy and thrown it
+
+ align:start position:0%
+taken 2/3 of my energy and thrown it
+ 
+
+ align:start position:0%
+taken 2/3 of my energy and thrown it
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+now if I got lots of energy floating
+
+ align:start position:0%
+now if I got lots of energy floating
+ 
+
+ align:start position:0%
+now if I got lots of energy floating
+around and I'm processing a microwatt
+
+ align:start position:0%
+around and I'm processing a microwatt
+ 
+
+ align:start position:0%
+around and I'm processing a microwatt
+maybe maybe I don't care maybe I'll live
+
+ align:start position:0%
+maybe maybe I don't care maybe I'll live
+ 
+
+ align:start position:0%
+maybe maybe I don't care maybe I'll live
+with that because this thing's pretty
+
+ align:start position:0%
+with that because this thing's pretty
+ 
+
+ align:start position:0%
+with that because this thing's pretty
+simple right it's a transistor it's a
+
+ align:start position:0%
+simple right it's a transistor it's a
+ 
+
+ align:start position:0%
+simple right it's a transistor it's a
+power transistor and some controls and
+
+ align:start position:0%
+power transistor and some controls and
+ 
+
+ align:start position:0%
+power transistor and some controls and
+they can often put all that on one
+
+ align:start position:0%
+they can often put all that on one
+ 
+
+ align:start position:0%
+they can often put all that on one
+integrated circuit or even as a subblock
+
+ align:start position:0%
+integrated circuit or even as a subblock
+ 
+
+ align:start position:0%
+integrated circuit or even as a subblock
+on an integrated circuit I might still
+
+ align:start position:0%
+on an integrated circuit I might still
+ 
+
+ align:start position:0%
+on an integrated circuit I might still
+need some filtering it's not it's not
+
+ align:start position:0%
+need some filtering it's not it's not
+ 
+
+ align:start position:0%
+need some filtering it's not it's not
+quite as easy as it sounds but um pretty
+
+ align:start position:0%
+quite as easy as it sounds but um pretty
+ 
+
+ align:start position:0%
+quite as easy as it sounds but um pretty
+much it's relatively simple but my
+
+ align:start position:0%
+much it's relatively simple but my
+ 
+
+ align:start position:0%
+much it's relatively simple but my
+efficiency is miserable now if I thought
+
+ align:start position:0%
+efficiency is miserable now if I thought
+ 
+
+ align:start position:0%
+efficiency is miserable now if I thought
+about in your in your
+
+ align:start position:0%
+about in your in your
+ 
+
+ align:start position:0%
+about in your in your
+computer right your desktop computer
+
+ align:start position:0%
+computer right your desktop computer
+ 
+
+ align:start position:0%
+computer right your desktop computer
+typically the intermediate Supply that
+
+ align:start position:0%
+typically the intermediate Supply that
+ 
+
+ align:start position:0%
+typically the intermediate Supply that
+you're getting after it's sort of come
+
+ align:start position:0%
+you're getting after it's sort of come
+ 
+
+ align:start position:0%
+you're getting after it's sort of come
+in from the grid and been transformed
+
+ align:start position:0%
+in from the grid and been transformed
+ 
+
+ align:start position:0%
+in from the grid and been transformed
+down you get 12 volts right and let's
+
+ align:start position:0%
+down you get 12 volts right and let's
+ 
+
+ align:start position:0%
+down you get 12 volts right and let's
+say your computer is it sort of it
+
+ align:start position:0%
+say your computer is it sort of it
+ 
+
+ align:start position:0%
+say your computer is it sort of it
+depends on what it's doing but say it's
+
+ align:start position:0%
+depends on what it's doing but say it's
+ 
+
+ align:start position:0%
+depends on what it's doing but say it's
+operating at a volt right so then you're
+
+ align:start position:0%
+operating at a volt right so then you're
+ 
+
+ align:start position:0%
+operating at a volt right so then you're
+less than 10% efficient right and if you
+
+ align:start position:0%
+less than 10% efficient right and if you
+ 
+
+ align:start position:0%
+less than 10% efficient right and if you
+think that you know you can have a
+
+ align:start position:0%
+think that you know you can have a
+ 
+
+ align:start position:0%
+think that you know you can have a
+microprocessor that's taking 200 amps at
+
+ align:start position:0%
+microprocessor that's taking 200 amps at
+ 
+
+ align:start position:0%
+microprocessor that's taking 200 amps at
+a volt or few hundred Watts suddenly if
+
+ align:start position:0%
+a volt or few hundred Watts suddenly if
+ 
+
+ align:start position:0%
+a volt or few hundred Watts suddenly if
+I've got less than 10% efficiency on 200
+
+ align:start position:0%
+I've got less than 10% efficiency on 200
+ 
+
+ align:start position:0%
+I've got less than 10% efficiency on 200
+Watts that means I need to put in a few
+
+ align:start position:0%
+Watts that means I need to put in a few
+ 
+
+ align:start position:0%
+Watts that means I need to put in a few
+kilowatts well you can't even plug that
+
+ align:start position:0%
+kilowatts well you can't even plug that
+ 
+
+ align:start position:0%
+kilowatts well you can't even plug that
+into the wall never mind the fact you've
+
+ align:start position:0%
+into the wall never mind the fact you've
+ 
+
+ align:start position:0%
+into the wall never mind the fact you've
+just made a massive room heater right
+
+ align:start position:0%
+just made a massive room heater right
+ 
+
+ align:start position:0%
+just made a massive room heater right
+that's that's like that'd be great for
+
+ align:start position:0%
+that's that's like that'd be great for
+ 
+
+ align:start position:0%
+that's that's like that'd be great for
+heating your dorm room um but pretty
+
+ align:start position:0%
+heating your dorm room um but pretty
+ 
+
+ align:start position:0%
+heating your dorm room um but pretty
+terrible for the overall system okay so
+
+ align:start position:0%
+terrible for the overall system okay so
+ 
+
+ align:start position:0%
+terrible for the overall system okay so
+the number one reason we don't like this
+
+ align:start position:0%
+the number one reason we don't like this
+ 
+
+ align:start position:0%
+the number one reason we don't like this
+solution is
+
+ align:start position:0%
+solution is
+ 
+
+ align:start position:0%
+solution is
+efficiency good thing it's simple bad
+
+ align:start position:0%
+efficiency good thing it's simple bad
+ 
+
+ align:start position:0%
+efficiency good thing it's simple bad
+thing it's terrible efficiency this
+
+ align:start position:0%
+thing it's terrible efficiency this
+ 
+
+ align:start position:0%
+thing it's terrible efficiency this
+technique I should have noted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is what's known for historical reasons
+
+ align:start position:0%
+is what's known for historical reasons
+ 
+
+ align:start position:0%
+is what's known for historical reasons
+as a quote unquote
+
+ align:start position:0%
+as a quote unquote
+ 
+
+ align:start position:0%
+as a quote unquote
+linear power
+
+ align:start position:0%
+linear power
+ 
+
+ align:start position:0%
+linear power
+supply why linear I think only because
+
+ align:start position:0%
+supply why linear I think only because
+ 
+
+ align:start position:0%
+supply why linear I think only because
+analog circuits kind of a category of
+
+ align:start position:0%
+analog circuits kind of a category of
+ 
+
+ align:start position:0%
+analog circuits kind of a category of
+them became known as quote unquote
+
+ align:start position:0%
+them became known as quote unquote
+ 
+
+ align:start position:0%
+them became known as quote unquote
+linear circuits there's nothing really
+
+ align:start position:0%
+linear circuits there's nothing really
+ 
+
+ align:start position:0%
+linear circuits there's nothing really
+that linear about it but this would be
+
+ align:start position:0%
+that linear about it but this would be
+ 
+
+ align:start position:0%
+that linear about it but this would be
+called a linear power converter or or
+
+ align:start position:0%
+called a linear power converter or or
+ 
+
+ align:start position:0%
+called a linear power converter or or
+some sometimes a linear regulator is
+
+ align:start position:0%
+some sometimes a linear regulator is
+ 
+
+ align:start position:0%
+some sometimes a linear regulator is
+what it would be called
+
+ align:start position:0%
+what it would be called
+ 
+
+ align:start position:0%
+what it would be called
+okay for obvious reasons I hate throwing
+
+ align:start position:0%
+okay for obvious reasons I hate throwing
+ 
+
+ align:start position:0%
+okay for obvious reasons I hate throwing
+away energy we're not going to talk
+
+ align:start position:0%
+away energy we're not going to talk
+ 
+
+ align:start position:0%
+away energy we're not going to talk
+about linear Regulators at all in this
+
+ align:start position:0%
+about linear Regulators at all in this
+ 
+
+ align:start position:0%
+about linear Regulators at all in this
+class and there's plenty of classes
+
+ align:start position:0%
+class and there's plenty of classes
+ 
+
+ align:start position:0%
+class and there's plenty of classes
+where you can learn about that we want
+
+ align:start position:0%
+where you can learn about that we want
+ 
+
+ align:start position:0%
+where you can learn about that we want
+to do things some better way that's not
+
+ align:start position:0%
+to do things some better way that's not
+ 
+
+ align:start position:0%
+to do things some better way that's not
+going to burn lots of energy okay so
+
+ align:start position:0%
+going to burn lots of energy okay so
+ 
+
+ align:start position:0%
+going to burn lots of energy okay so
+ideally you know in my world the goal is
+
+ align:start position:0%
+ideally you know in my world the goal is
+ 
+
+ align:start position:0%
+ideally you know in my world the goal is
+to take as much of the input energy in
+
+ align:start position:0%
+to take as much of the input energy in
+ 
+
+ align:start position:0%
+to take as much of the input energy in
+and put it to the output right and
+
+ align:start position:0%
+and put it to the output right and
+ 
+
+ align:start position:0%
+and put it to the output right and
+that's important because think about it
+
+ align:start position:0%
+that's important because think about it
+ 
+
+ align:start position:0%
+that's important because think about it
+this way I I showed you a photo graph of
+
+ align:start position:0%
+this way I I showed you a photo graph of
+ 
+
+ align:start position:0%
+this way I I showed you a photo graph of
+something that was you know really tiny
+
+ align:start position:0%
+something that was you know really tiny
+ 
+
+ align:start position:0%
+something that was you know really tiny
+maybe that big right and that thick and
+
+ align:start position:0%
+maybe that big right and that thick and
+ 
+
+ align:start position:0%
+maybe that big right and that thick and
+was processing a kilowatt right if I
+
+ align:start position:0%
+was processing a kilowatt right if I
+ 
+
+ align:start position:0%
+was processing a kilowatt right if I
+don't do that at really high efficiency
+
+ align:start position:0%
+don't do that at really high efficiency
+ 
+
+ align:start position:0%
+don't do that at really high efficiency
+that thing will burn up right so in
+
+ align:start position:0%
+that thing will burn up right so in
+ 
+
+ align:start position:0%
+that thing will burn up right so in
+order to make something small I need to
+
+ align:start position:0%
+order to make something small I need to
+ 
+
+ align:start position:0%
+order to make something small I need to
+make it efficient all right so we want
+
+ align:start position:0%
+make it efficient all right so we want
+ 
+
+ align:start position:0%
+make it efficient all right so we want
+almost all of the energy at the input to
+
+ align:start position:0%
+almost all of the energy at the input to
+ 
+
+ align:start position:0%
+almost all of the energy at the input to
+get to the output well how can we do
+
+ align:start position:0%
+get to the output well how can we do
+ 
+
+ align:start position:0%
+get to the output well how can we do
+that let's think of a completely
+
+ align:start position:0%
+that let's think of a completely
+ 
+
+ align:start position:0%
+that let's think of a completely
+different way we might achieve this same
+
+ align:start position:0%
+different way we might achieve this same
+ 
+
+ align:start position:0%
+different way we might achieve this same
+function function all right and here's
+
+ align:start position:0%
+function function all right and here's
+ 
+
+ align:start position:0%
+function function all right and here's
+the idea here's my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input I'm going to create a switch here
+
+ align:start position:0%
+input I'm going to create a switch here
+ 
+
+ align:start position:0%
+input I'm going to create a switch here
+single pole double throw switch now
+
+ align:start position:0%
+single pole double throw switch now
+ 
+
+ align:start position:0%
+single pole double throw switch now
+we're not going to go get physical
+
+ align:start position:0%
+we're not going to go get physical
+ 
+
+ align:start position:0%
+we're not going to go get physical
+switches we're probably going to get
+
+ align:start position:0%
+switches we're probably going to get
+ 
+
+ align:start position:0%
+switches we're probably going to get
+semiconductor devices and make it do
+
+ align:start position:0%
+semiconductor devices and make it do
+ 
+
+ align:start position:0%
+semiconductor devices and make it do
+something like this but we could use
+
+ align:start position:0%
+something like this but we could use
+ 
+
+ align:start position:0%
+something like this but we could use
+anything any technology that was
+
+ align:start position:0%
+anything any technology that was
+ 
+
+ align:start position:0%
+anything any technology that was
+practical as a switch okay and let me
+
+ align:start position:0%
+practical as a switch okay and let me
+ 
+
+ align:start position:0%
+practical as a switch okay and let me
+just Define if I'm going to define a
+
+ align:start position:0%
+just Define if I'm going to define a
+ 
+
+ align:start position:0%
+just Define if I'm going to define a
+switching function that I'm going to
+
+ align:start position:0%
+switching function that I'm going to
+ 
+
+ align:start position:0%
+switching function that I'm going to
+call Q of T if Q of T is
+
+ align:start position:0%
+call Q of T if Q of T is
+ 
+
+ align:start position:0%
+call Q of T if Q of T is
+one I'll connect the switch to the input
+
+ align:start position:0%
+one I'll connect the switch to the input
+ 
+
+ align:start position:0%
+one I'll connect the switch to the input
+if Q of T is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero I'll connect the switch to the
+
+ align:start position:0%
+zero I'll connect the switch to the
+ 
+
+ align:start position:0%
+zero I'll connect the switch to the
+ground okay so this notion this voltage
+
+ align:start position:0%
+ground okay so this notion this voltage
+ 
+
+ align:start position:0%
+ground okay so this notion this voltage
+okay maybe I'll call this voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VX all right so one thing I could do is
+
+ align:start position:0%
+VX all right so one thing I could do is
+ 
+
+ align:start position:0%
+VX all right so one thing I could do is
+I could say okay let me just hook this
+
+ align:start position:0%
+I could say okay let me just hook this
+ 
+
+ align:start position:0%
+I could say okay let me just hook this
+up to my load here's my resistive
+
+ align:start position:0%
+up to my load here's my resistive
+ 
+
+ align:start position:0%
+up to my load here's my resistive
+load whatever it is and I'll call this V
+
+ align:start position:0%
+load whatever it is and I'll call this V
+ 
+
+ align:start position:0%
+load whatever it is and I'll call this V
+out all right well all right what would
+
+ align:start position:0%
+out all right well all right what would
+ 
+
+ align:start position:0%
+out all right well all right what would
+that look like well let me Define my
+
+ align:start position:0%
+that look like well let me Define my
+ 
+
+ align:start position:0%
+that look like well let me Define my
+switching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function I'm going to put the switch in
+
+ align:start position:0%
+function I'm going to put the switch in
+ 
+
+ align:start position:0%
+function I'm going to put the switch in
+the up position for a little while then
+
+ align:start position:0%
+the up position for a little while then
+ 
+
+ align:start position:0%
+the up position for a little while then
+I'll put it in the down
+
+ align:start position:0%
+I'll put it in the down
+ 
+
+ align:start position:0%
+I'll put it in the down
+position by setting the switching
+
+ align:start position:0%
+position by setting the switching
+ 
+
+ align:start position:0%
+position by setting the switching
+function to zero and then I'll just
+
+ align:start position:0%
+function to zero and then I'll just
+ 
+
+ align:start position:0%
+function to zero and then I'll just
+repeat that so I said we're going to
+
+ align:start position:0%
+repeat that so I said we're going to
+ 
+
+ align:start position:0%
+repeat that so I said we're going to
+operate in some kind of repetitive
+
+ align:start position:0%
+operate in some kind of repetitive
+ 
+
+ align:start position:0%
+operate in some kind of repetitive
+fashion here and so
+
+ align:start position:0%
+fashion here and so
+ 
+
+ align:start position:0%
+fashion here and so
+forth let me operate with some period
+
+ align:start position:0%
+forth let me operate with some period
+ 
+
+ align:start position:0%
+forth let me operate with some period
+T okay that's mean my switching period
+
+ align:start position:0%
+T okay that's mean my switching period
+ 
+
+ align:start position:0%
+T okay that's mean my switching period
+in this example I'm showing you is a
+
+ align:start position:0%
+in this example I'm showing you is a
+ 
+
+ align:start position:0%
+in this example I'm showing you is a
+fixed switching period okay and I will
+
+ align:start position:0%
+fixed switching period okay and I will
+ 
+
+ align:start position:0%
+fixed switching period okay and I will
+keep the switch in the up position some
+
+ align:start position:0%
+keep the switch in the up position some
+ 
+
+ align:start position:0%
+keep the switch in the up position some
+fraction of the time that I'll call DT
+
+ align:start position:0%
+fraction of the time that I'll call DT
+ 
+
+ align:start position:0%
+fraction of the time that I'll call DT
+so D is a fraction zero is less than D
+
+ align:start position:0%
+so D is a fraction zero is less than D
+ 
+
+ align:start position:0%
+so D is a fraction zero is less than D
+is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay so if I do that then what do I get
+
+ align:start position:0%
+okay so if I do that then what do I get
+ 
+
+ align:start position:0%
+okay so if I do that then what do I get
+for VX VX is going to look something
+
+ align:start position:0%
+for VX VX is going to look something
+ 
+
+ align:start position:0%
+for VX VX is going to look something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this okay um when the switch is in the
+
+ align:start position:0%
+this okay um when the switch is in the
+ 
+
+ align:start position:0%
+this okay um when the switch is in the
+up position VX equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VN so this is VX when the switch is in
+
+ align:start position:0%
+VN so this is VX when the switch is in
+ 
+
+ align:start position:0%
+VN so this is VX when the switch is in
+the down position VX is equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I rinse and repeat and I get
+
+ align:start position:0%
+okay and I rinse and repeat and I get
+ 
+
+ align:start position:0%
+okay and I rinse and repeat and I get
+this now now I have this pulsating
+
+ align:start position:0%
+this now now I have this pulsating
+ 
+
+ align:start position:0%
+this now now I have this pulsating
+voltage VX okay what's the average value
+
+ align:start position:0%
+voltage VX okay what's the average value
+ 
+
+ align:start position:0%
+voltage VX okay what's the average value
+of that voltage
+
+ align:start position:0%
+of that voltage
+ 
+
+ align:start position:0%
+of that voltage
+VX right I can take you know simple
+
+ align:start position:0%
+VX right I can take you know simple
+ 
+
+ align:start position:0%
+VX right I can take you know simple
+integration right one over T the
+
+ align:start position:0%
+integration right one over T the
+ 
+
+ align:start position:0%
+integration right one over T the
+integral of VX of T over a period
+
+ align:start position:0%
+integral of VX of T over a period
+ 
+
+ align:start position:0%
+integral of VX of T over a period
+T okay and what I would
+
+ align:start position:0%
+T okay and what I would
+ 
+
+ align:start position:0%
+T okay and what I would
+find is the average voltage of VX
+
+ align:start position:0%
+find is the average voltage of VX
+ 
+
+ align:start position:0%
+find is the average voltage of VX
+is equal to D *
+
+ align:start position:0%
+is equal to D *
+ 
+
+ align:start position:0%
+is equal to D *
+VN all right so I can create a waveform
+
+ align:start position:0%
+VN all right so I can create a waveform
+ 
+
+ align:start position:0%
+VN all right so I can create a waveform
+here whose average value is something
+
+ align:start position:0%
+here whose average value is something
+ 
+
+ align:start position:0%
+here whose average value is something
+different than VN just by controlling
+
+ align:start position:0%
+different than VN just by controlling
+ 
+
+ align:start position:0%
+different than VN just by controlling
+this timing
+
+ align:start position:0%
+this timing
+ 
+
+ align:start position:0%
+this timing
+D all right so now if my load resistor
+
+ align:start position:0%
+D all right so now if my load resistor
+ 
+
+ align:start position:0%
+D all right so now if my load resistor
+here was a space heater you know maybe
+
+ align:start position:0%
+here was a space heater you know maybe
+ 
+
+ align:start position:0%
+here was a space heater you know maybe
+this is some load resistance RL and I
+
+ align:start position:0%
+this is some load resistance RL and I
+ 
+
+ align:start position:0%
+this is some load resistance RL and I
+wanted to modulate the power to that
+
+ align:start position:0%
+wanted to modulate the power to that
+ 
+
+ align:start position:0%
+wanted to modulate the power to that
+load resistance by controlling the
+
+ align:start position:0%
+load resistance by controlling the
+ 
+
+ align:start position:0%
+load resistance by controlling the
+average voltage on the load resistance
+
+ align:start position:0%
+average voltage on the load resistance
+ 
+
+ align:start position:0%
+average voltage on the load resistance
+then this technique would work
+
+ align:start position:0%
+then this technique would work
+ 
+
+ align:start position:0%
+then this technique would work
+great if on the other hand my load was a
+
+ align:start position:0%
+great if on the other hand my load was a
+ 
+
+ align:start position:0%
+great if on the other hand my load was a
+microprocessor and I start you know
+
+ align:start position:0%
+microprocessor and I start you know
+ 
+
+ align:start position:0%
+microprocessor and I start you know
+pulsing 12 volts between 12 volts and
+
+ align:start position:0%
+pulsing 12 volts between 12 volts and
+ 
+
+ align:start position:0%
+pulsing 12 volts between 12 volts and
+zero on it I'm probably going to blow it
+
+ align:start position:0%
+zero on it I'm probably going to blow it
+ 
+
+ align:start position:0%
+zero on it I'm probably going to blow it
+up right so that's no good all right but
+
+ align:start position:0%
+up right so that's no good all right but
+ 
+
+ align:start position:0%
+up right so that's no good all right but
+this notion is at least that I can
+
+ align:start position:0%
+this notion is at least that I can
+ 
+
+ align:start position:0%
+this notion is at least that I can
+control an average voltage by pulsing a
+
+ align:start position:0%
+control an average voltage by pulsing a
+ 
+
+ align:start position:0%
+control an average voltage by pulsing a
+set a switch okay and this would be
+
+ align:start position:0%
+set a switch okay and this would be
+ 
+
+ align:start position:0%
+set a switch okay and this would be
+known as pwm or pulse width modulation
+
+ align:start position:0%
+known as pwm or pulse width modulation
+ 
+
+ align:start position:0%
+known as pwm or pulse width modulation
+because I control the average volage by
+
+ align:start position:0%
+because I control the average volage by
+ 
+
+ align:start position:0%
+because I control the average volage by
+the fraction of the time the switch is
+
+ align:start position:0%
+the fraction of the time the switch is
+ 
+
+ align:start position:0%
+the fraction of the time the switch is
+in one position versus the
+
+ align:start position:0%
+in one position versus the
+ 
+
+ align:start position:0%
+in one position versus the
+other okay so that's that's the basic
+
+ align:start position:0%
+other okay so that's that's the basic
+ 
+
+ align:start position:0%
+other okay so that's that's the basic
+concept we're going to be using how do I
+
+ align:start position:0%
+concept we're going to be using how do I
+ 
+
+ align:start position:0%
+concept we're going to be using how do I
+fix this
+
+ align:start position:0%
+fix this
+ 
+
+ align:start position:0%
+fix this
+little problem of in practice right what
+
+ align:start position:0%
+little problem of in practice right what
+ 
+
+ align:start position:0%
+little problem of in practice right what
+I wanted was a DC voltage what I got was
+
+ align:start position:0%
+I wanted was a DC voltage what I got was
+ 
+
+ align:start position:0%
+I wanted was a DC voltage what I got was
+a pulsating voltage that just happened
+
+ align:start position:0%
+a pulsating voltage that just happened
+ 
+
+ align:start position:0%
+a pulsating voltage that just happened
+to have the right average value well I
+
+ align:start position:0%
+to have the right average value well I
+ 
+
+ align:start position:0%
+to have the right average value well I
+could go do something like this maybe
+
+ align:start position:0%
+could go do something like this maybe
+ 
+
+ align:start position:0%
+could go do something like this maybe
+I'll go back and say okay let me throw
+
+ align:start position:0%
+I'll go back and say okay let me throw
+ 
+
+ align:start position:0%
+I'll go back and say okay let me throw
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+filter and extract out the component I
+
+ align:start position:0%
+filter and extract out the component I
+ 
+
+ align:start position:0%
+filter and extract out the component I
+want right I want the average value of
+
+ align:start position:0%
+want right I want the average value of
+ 
+
+ align:start position:0%
+want right I want the average value of
+VX so maybe I'll come back here and say
+
+ align:start position:0%
+VX so maybe I'll come back here and say
+ 
+
+ align:start position:0%
+VX so maybe I'll come back here and say
+okay let me throw in a filter and I'll
+
+ align:start position:0%
+okay let me throw in a filter and I'll
+ 
+
+ align:start position:0%
+okay let me throw in a filter and I'll
+use an inductor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here an l and if I want optionally I can
+
+ align:start position:0%
+here an l and if I want optionally I can
+ 
+
+ align:start position:0%
+here an l and if I want optionally I can
+put a capacitor here
+
+ align:start position:0%
+put a capacitor here
+ 
+
+ align:start position:0%
+put a capacitor here
+C okay and you know I think people can
+
+ align:start position:0%
+C okay and you know I think people can
+ 
+
+ align:start position:0%
+C okay and you know I think people can
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+this filter block and recognize that as
+
+ align:start position:0%
+this filter block and recognize that as
+ 
+
+ align:start position:0%
+this filter block and recognize that as
+a low pass filter the DC component of VX
+
+ align:start position:0%
+a low pass filter the DC component of VX
+ 
+
+ align:start position:0%
+a low pass filter the DC component of VX
+passes through the filter to the
+
+ align:start position:0%
+passes through the filter to the
+ 
+
+ align:start position:0%
+passes through the filter to the
+output and the AC component of VX gets
+
+ align:start position:0%
+output and the AC component of VX gets
+ 
+
+ align:start position:0%
+output and the AC component of VX gets
+rejected by the filter and doesn't get
+
+ align:start position:0%
+rejected by the filter and doesn't get
+ 
+
+ align:start position:0%
+rejected by the filter and doesn't get
+to the output so in this case I might
+
+ align:start position:0%
+to the output so in this case I might
+ 
+
+ align:start position:0%
+to the output so in this case I might
+get an output voltage V out that looks
+
+ align:start position:0%
+get an output voltage V out that looks
+ 
+
+ align:start position:0%
+get an output voltage V out that looks
+something like this I'm going to sort of
+
+ align:start position:0%
+something like this I'm going to sort of
+ 
+
+ align:start position:0%
+something like this I'm going to sort of
+make this up but you know I'm amplifying
+
+ align:start position:0%
+make this up but you know I'm amplifying
+ 
+
+ align:start position:0%
+make this up but you know I'm amplifying
+the Ripple but eventually it's going to
+
+ align:start position:0%
+the Ripple but eventually it's going to
+ 
+
+ align:start position:0%
+the Ripple but eventually it's going to
+filter
+
+ align:start position:0%
+filter
+ 
+
+ align:start position:0%
+filter
+the energy content of that and the
+
+ align:start position:0%
+the energy content of that and the
+ 
+
+ align:start position:0%
+the energy content of that and the
+fundamental and higher harmonic terms of
+
+ align:start position:0%
+fundamental and higher harmonic terms of
+ 
+
+ align:start position:0%
+fundamental and higher harmonic terms of
+VX are going to go away and the DC terms
+
+ align:start position:0%
+VX are going to go away and the DC terms
+ 
+
+ align:start position:0%
+VX are going to go away and the DC terms
+going to go through and I get an output
+
+ align:start position:0%
+going to go through and I get an output
+ 
+
+ align:start position:0%
+going to go through and I get an output
+voltage V out that's very close to
+
+ align:start position:0%
+voltage V out that's very close to
+ 
+
+ align:start position:0%
+voltage V out that's very close to
+whatever value I want and if I'm
+
+ align:start position:0%
+whatever value I want and if I'm
+ 
+
+ align:start position:0%
+whatever value I want and if I'm
+basically make the filter cut off hard
+
+ align:start position:0%
+basically make the filter cut off hard
+ 
+
+ align:start position:0%
+basically make the filter cut off hard
+enough I can't distinguish between V out
+
+ align:start position:0%
+enough I can't distinguish between V out
+ 
+
+ align:start position:0%
+enough I can't distinguish between V out
+and the average value of VX and I get
+
+ align:start position:0%
+and the average value of VX and I get
+ 
+
+ align:start position:0%
+and the average value of VX and I get
+exactly what I wanted Okay so we've
+
+ align:start position:0%
+exactly what I wanted Okay so we've
+ 
+
+ align:start position:0%
+exactly what I wanted Okay so we've
+essentially now created
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converter that lets me use this
+
+ align:start position:0%
+converter that lets me use this
+ 
+
+ align:start position:0%
+converter that lets me use this
+pulsewidth modulation by controlling
+
+ align:start position:0%
+pulsewidth modulation by controlling
+ 
+
+ align:start position:0%
+pulsewidth modulation by controlling
+this duty cycle D to regulate the output
+
+ align:start position:0%
+this duty cycle D to regulate the output
+ 
+
+ align:start position:0%
+this duty cycle D to regulate the output
+just the way I wanted so instead of you
+
+ align:start position:0%
+just the way I wanted so instead of you
+ 
+
+ align:start position:0%
+just the way I wanted so instead of you
+know here I'm just changing the gate
+
+ align:start position:0%
+know here I'm just changing the gate
+ 
+
+ align:start position:0%
+know here I'm just changing the gate
+voltage on my transistor to control the
+
+ align:start position:0%
+voltage on my transistor to control the
+ 
+
+ align:start position:0%
+voltage on my transistor to control the
+output here I'm changing timing I'm
+
+ align:start position:0%
+output here I'm changing timing I'm
+ 
+
+ align:start position:0%
+output here I'm changing timing I'm
+going to control
+
+ align:start position:0%
+going to control
+ 
+
+ align:start position:0%
+going to control
+timing okay and by controlling timing I
+
+ align:start position:0%
+timing okay and by controlling timing I
+ 
+
+ align:start position:0%
+timing okay and by controlling timing I
+control average value and then I get
+
+ align:start position:0%
+control average value and then I get
+ 
+
+ align:start position:0%
+control average value and then I get
+what I want right any questions about
+
+ align:start position:0%
+what I want right any questions about
+ 
+
+ align:start position:0%
+what I want right any questions about
+that what's what's the
+
+ align:start position:0%
+that what's what's the
+ 
+
+ align:start position:0%
+that what's what's the
+efficiency that is an excellent question
+
+ align:start position:0%
+efficiency that is an excellent question
+ 
+
+ align:start position:0%
+efficiency that is an excellent question
+the answer is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um ideally theoretically the efficiency
+
+ align:start position:0%
+um ideally theoretically the efficiency
+ 
+
+ align:start position:0%
+um ideally theoretically the efficiency
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+100% in reality it can't be why do I say
+
+ align:start position:0%
+100% in reality it can't be why do I say
+ 
+
+ align:start position:0%
+100% in reality it can't be why do I say
+the efficiency can ideally be
+
+ align:start position:0%
+the efficiency can ideally be
+ 
+
+ align:start position:0%
+the efficiency can ideally be
+100% well how would I implement
+
+ align:start position:0%
+100% well how would I implement
+ 
+
+ align:start position:0%
+100% well how would I implement
+this box in the real world usually I I
+
+ align:start position:0%
+this box in the real world usually I I
+ 
+
+ align:start position:0%
+this box in the real world usually I I
+don't get semiconductor single pole
+
+ align:start position:0%
+don't get semiconductor single pole
+ 
+
+ align:start position:0%
+don't get semiconductor single pole
+double throw switches the way I would
+
+ align:start position:0%
+double throw switches the way I would
+ 
+
+ align:start position:0%
+double throw switches the way I would
+usually build this Beast is like
+
+ align:start position:0%
+usually build this Beast is like
+ 
+
+ align:start position:0%
+usually build this Beast is like
+this okay I would usually have a first
+
+ align:start position:0%
+this okay I would usually have a first
+ 
+
+ align:start position:0%
+this okay I would usually have a first
+switch and a second switch implemented
+
+ align:start position:0%
+switch and a second switch implemented
+ 
+
+ align:start position:0%
+switch and a second switch implemented
+like this so I close this when Q of T is
+
+ align:start position:0%
+like this so I close this when Q of T is
+ 
+
+ align:start position:0%
+like this so I close this when Q of T is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+one and I close this one when Q of T is
+
+ align:start position:0%
+one and I close this one when Q of T is
+ 
+
+ align:start position:0%
+one and I close this one when Q of T is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero okay and then I build my filter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I put my load on here okay
+
+ align:start position:0%
+and then I put my load on here okay
+ 
+
+ align:start position:0%
+and then I put my load on here okay
+so what would be the efficiency of this
+
+ align:start position:0%
+so what would be the efficiency of this
+ 
+
+ align:start position:0%
+so what would be the efficiency of this
+thing well let's think about
+
+ align:start position:0%
+thing well let's think about
+ 
+
+ align:start position:0%
+thing well let's think about
+this um this is voltage Vex and this is
+
+ align:start position:0%
+this um this is voltage Vex and this is
+ 
+
+ align:start position:0%
+this um this is voltage Vex and this is
+voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vout all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what power is theoretically
+
+ align:start position:0%
+right what power is theoretically
+ 
+
+ align:start position:0%
+right what power is theoretically
+dissipated in my switch if I have an
+
+ align:start position:0%
+dissipated in my switch if I have an
+ 
+
+ align:start position:0%
+dissipated in my switch if I have an
+ideal switch has zero resistance when
+
+ align:start position:0%
+ideal switch has zero resistance when
+ 
+
+ align:start position:0%
+ideal switch has zero resistance when
+it's on and has infinite resistance when
+
+ align:start position:0%
+it's on and has infinite resistance when
+ 
+
+ align:start position:0%
+it's on and has infinite resistance when
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+off what's that zero power why because
+
+ align:start position:0%
+off what's that zero power why because
+ 
+
+ align:start position:0%
+off what's that zero power why because
+the power dissipated the power that goes
+
+ align:start position:0%
+the power dissipated the power that goes
+ 
+
+ align:start position:0%
+the power dissipated the power that goes
+into this box let me call this V
+
+ align:start position:0%
+into this box let me call this V
+ 
+
+ align:start position:0%
+into this box let me call this V
+switch let me call this I switch okay
+
+ align:start position:0%
+switch let me call this I switch okay
+ 
+
+ align:start position:0%
+switch let me call this I switch okay
+well P switch the power going into the
+
+ align:start position:0%
+well P switch the power going into the
+ 
+
+ align:start position:0%
+well P switch the power going into the
+switch the power being dissipated in the
+
+ align:start position:0%
+switch the power being dissipated in the
+ 
+
+ align:start position:0%
+switch the power being dissipated in the
+switch is going to be V switch time I
+
+ align:start position:0%
+switch is going to be V switch time I
+ 
+
+ align:start position:0%
+switch is going to be V switch time I
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+okay well if it's an ideal switch then
+
+ align:start position:0%
+okay well if it's an ideal switch then
+ 
+
+ align:start position:0%
+okay well if it's an ideal switch then
+if the switch is on V switch is
+
+ align:start position:0%
+if the switch is on V switch is
+ 
+
+ align:start position:0%
+if the switch is on V switch is
+zero right it's ideal so it has no
+
+ align:start position:0%
+zero right it's ideal so it has no
+ 
+
+ align:start position:0%
+zero right it's ideal so it has no
+voltage drop when it's on so the power
+
+ align:start position:0%
+voltage drop when it's on so the power
+ 
+
+ align:start position:0%
+voltage drop when it's on so the power
+when it's on is
+
+ align:start position:0%
+when it's on is
+ 
+
+ align:start position:0%
+when it's on is
+zero when the switch is off it has
+
+ align:start position:0%
+zero when the switch is off it has
+ 
+
+ align:start position:0%
+zero when the switch is off it has
+infinite resistance so the switch is
+
+ align:start position:0%
+infinite resistance so the switch is
+ 
+
+ align:start position:0%
+infinite resistance so the switch is
+current zero so basically the power
+
+ align:start position:0%
+current zero so basically the power
+ 
+
+ align:start position:0%
+current zero so basically the power
+going into the switch if it's an ideal
+
+ align:start position:0%
+going into the switch if it's an ideal
+ 
+
+ align:start position:0%
+going into the switch if it's an ideal
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+um is ideally zero so these these
+
+ align:start position:0%
+um is ideally zero so these these
+ 
+
+ align:start position:0%
+um is ideally zero so these these
+elements this ideal switch is a lossless
+
+ align:start position:0%
+elements this ideal switch is a lossless
+ 
+
+ align:start position:0%
+elements this ideal switch is a lossless
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+likewise I wasn't I didn't just randomly
+
+ align:start position:0%
+likewise I wasn't I didn't just randomly
+ 
+
+ align:start position:0%
+likewise I wasn't I didn't just randomly
+choose any filter here right I chose an
+
+ align:start position:0%
+choose any filter here right I chose an
+ 
+
+ align:start position:0%
+choose any filter here right I chose an
+LC filter why did I choose an LC filter
+
+ align:start position:0%
+LC filter why did I choose an LC filter
+ 
+
+ align:start position:0%
+LC filter why did I choose an LC filter
+I choose an LC filter because inductors
+
+ align:start position:0%
+I choose an LC filter because inductors
+ 
+
+ align:start position:0%
+I choose an LC filter because inductors
+and capacitors are energy storage
+
+ align:start position:0%
+and capacitors are energy storage
+ 
+
+ align:start position:0%
+and capacitors are energy storage
+elements if they're ideal then they
+
+ align:start position:0%
+elements if they're ideal then they
+ 
+
+ align:start position:0%
+elements if they're ideal then they
+store energy but they don't dissipate
+
+ align:start position:0%
+store energy but they don't dissipate
+ 
+
+ align:start position:0%
+store energy but they don't dissipate
+energy right so basically
+
+ align:start position:0%
+energy right so basically
+ 
+
+ align:start position:0%
+energy right so basically
+everything in the box here everything
+
+ align:start position:0%
+everything in the box here everything
+ 
+
+ align:start position:0%
+everything in the box here everything
+between the input and the output is a
+
+ align:start position:0%
+between the input and the output is a
+ 
+
+ align:start position:0%
+between the input and the output is a
+lossless element so then one would
+
+ align:start position:0%
+lossless element so then one would
+ 
+
+ align:start position:0%
+lossless element so then one would
+assume that if every element's lossless
+
+ align:start position:0%
+assume that if every element's lossless
+ 
+
+ align:start position:0%
+assume that if every element's lossless
+any energy walking in to the left comes
+
+ align:start position:0%
+any energy walking in to the left comes
+ 
+
+ align:start position:0%
+any energy walking in to the left comes
+out to the right right and that's how
+
+ align:start position:0%
+out to the right right and that's how
+ 
+
+ align:start position:0%
+out to the right right and that's how
+that that kilowatt little 400 volt to
+
+ align:start position:0%
+that that kilowatt little 400 volt to
+ 
+
+ align:start position:0%
+that that kilowatt little 400 volt to
+12vt converter I showed you um in the
+
+ align:start position:0%
+12vt converter I showed you um in the
+ 
+
+ align:start position:0%
+12vt converter I showed you um in the
+photo is about 97% efficient it's not
+
+ align:start position:0%
+photo is about 97% efficient it's not
+ 
+
+ align:start position:0%
+photo is about 97% efficient it's not
+100% because you know the wires have
+
+ align:start position:0%
+100% because you know the wires have
+ 
+
+ align:start position:0%
+100% because you know the wires have
+some resistance and the switches have
+
+ align:start position:0%
+some resistance and the switches have
+ 
+
+ align:start position:0%
+some resistance and the switches have
+some on-state resistance a whole bunch
+
+ align:start position:0%
+some on-state resistance a whole bunch
+ 
+
+ align:start position:0%
+some on-state resistance a whole bunch
+of things that contribute to loss and
+
+ align:start position:0%
+of things that contribute to loss and
+ 
+
+ align:start position:0%
+of things that contribute to loss and
+we'll talk about that um but I can make
+
+ align:start position:0%
+we'll talk about that um but I can make
+ 
+
+ align:start position:0%
+we'll talk about that um but I can make
+it really close to 100% even though I
+
+ align:start position:0%
+it really close to 100% even though I
+ 
+
+ align:start position:0%
+it really close to 100% even though I
+might be doing a huge step down right so
+
+ align:start position:0%
+might be doing a huge step down right so
+ 
+
+ align:start position:0%
+might be doing a huge step down right so
+if I tried to build a linear regulator
+
+ align:start position:0%
+if I tried to build a linear regulator
+ 
+
+ align:start position:0%
+if I tried to build a linear regulator
+that was going from 400 to 12 volts
+
+ align:start position:0%
+that was going from 400 to 12 volts
+ 
+
+ align:start position:0%
+that was going from 400 to 12 volts
+that' be about 2 and a half% efficient
+
+ align:start position:0%
+that' be about 2 and a half% efficient
+ 
+
+ align:start position:0%
+that' be about 2 and a half% efficient
+right so if I want to generate a
+
+ align:start position:0%
+right so if I want to generate a
+ 
+
+ align:start position:0%
+right so if I want to generate a
+kilowatt at 2 and a half% efficiency
+
+ align:start position:0%
+kilowatt at 2 and a half% efficiency
+ 
+
+ align:start position:0%
+kilowatt at 2 and a half% efficiency
+what is that 40 kilowatt input and
+
+ align:start position:0%
+what is that 40 kilowatt input and
+ 
+
+ align:start position:0%
+what is that 40 kilowatt input and
+instead what I get is sort of like 1.03
+
+ align:start position:0%
+instead what I get is sort of like 1.03
+ 
+
+ align:start position:0%
+instead what I get is sort of like 1.03
+kilowatt input to generate a kilowatt
+
+ align:start position:0%
+kilowatt input to generate a kilowatt
+ 
+
+ align:start position:0%
+kilowatt input to generate a kilowatt
+output right
+
+ align:start position:0%
+output right
+ 
+
+ align:start position:0%
+output right
+so the whole Magic that we're going to
+
+ align:start position:0%
+so the whole Magic that we're going to
+ 
+
+ align:start position:0%
+so the whole Magic that we're going to
+talk about this term is how can I use
+
+ align:start position:0%
+talk about this term is how can I use
+ 
+
+ align:start position:0%
+talk about this term is how can I use
+sort of perfectly lossless elements draw
+
+ align:start position:0%
+sort of perfectly lossless elements draw
+ 
+
+ align:start position:0%
+sort of perfectly lossless elements draw
+energy in process it and put it out the
+
+ align:start position:0%
+energy in process it and put it out the
+ 
+
+ align:start position:0%
+energy in process it and put it out the
+other side okay and by the way I should
+
+ align:start position:0%
+other side okay and by the way I should
+ 
+
+ align:start position:0%
+other side okay and by the way I should
+say not only did I say oh inductors and
+
+ align:start position:0%
+say not only did I say oh inductors and
+ 
+
+ align:start position:0%
+say not only did I say oh inductors and
+capacitors are lossless in principle
+
+ align:start position:0%
+capacitors are lossless in principle
+ 
+
+ align:start position:0%
+capacitors are lossless in principle
+lossless elements uh it wasn't an
+
+ align:start position:0%
+lossless elements uh it wasn't an
+ 
+
+ align:start position:0%
+lossless elements uh it wasn't an
+accident that we put an inductor
+
+ align:start position:0%
+accident that we put an inductor
+ 
+
+ align:start position:0%
+accident that we put an inductor
+here right because think about it when
+
+ align:start position:0%
+here right because think about it when
+ 
+
+ align:start position:0%
+here right because think about it when
+this switch is
+
+ align:start position:0%
+this switch is
+ 
+
+ align:start position:0%
+this switch is
+closed right I have V in on this side of
+
+ align:start position:0%
+closed right I have V in on this side of
+ 
+
+ align:start position:0%
+closed right I have V in on this side of
+the inductor and V out on this side of
+
+ align:start position:0%
+the inductor and V out on this side of
+ 
+
+ align:start position:0%
+the inductor and V out on this side of
+the inductor and I have current flowing
+
+ align:start position:0%
+the inductor and I have current flowing
+ 
+
+ align:start position:0%
+the inductor and I have current flowing
+this way right well what's happening
+
+ align:start position:0%
+this way right well what's happening
+ 
+
+ align:start position:0%
+this way right well what's happening
+when this switch is closed basically
+
+ align:start position:0%
+when this switch is closed basically
+ 
+
+ align:start position:0%
+when this switch is closed basically
+there's voltage across this inductor and
+
+ align:start position:0%
+there's voltage across this inductor and
+ 
+
+ align:start position:0%
+there's voltage across this inductor and
+current going through it we are storing
+
+ align:start position:0%
+current going through it we are storing
+ 
+
+ align:start position:0%
+current going through it we are storing
+energy in that inductor so the
+
+ align:start position:0%
+energy in that inductor so the
+ 
+
+ align:start position:0%
+energy in that inductor so the
+difference in voltage between the input
+
+ align:start position:0%
+difference in voltage between the input
+ 
+
+ align:start position:0%
+difference in voltage between the input
+and the output is basically putting
+
+ align:start position:0%
+and the output is basically putting
+ 
+
+ align:start position:0%
+and the output is basically putting
+energy in the
+
+ align:start position:0%
+energy in the
+ 
+
+ align:start position:0%
+energy in the
+inductor in this the other part of the
+
+ align:start position:0%
+inductor in this the other part of the
+ 
+
+ align:start position:0%
+inductor in this the other part of the
+cycle
+
+ align:start position:0%
+cycle
+ 
+
+ align:start position:0%
+cycle
+when I turn this switch off and this
+
+ align:start position:0%
+when I turn this switch off and this
+ 
+
+ align:start position:0%
+when I turn this switch off and this
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+on basically I'm taking now I have a
+
+ align:start position:0%
+on basically I'm taking now I have a
+ 
+
+ align:start position:0%
+on basically I'm taking now I have a
+negative voltage across the inductor I'm
+
+ align:start position:0%
+negative voltage across the inductor I'm
+ 
+
+ align:start position:0%
+negative voltage across the inductor I'm
+taking energy out of the inductor and
+
+ align:start position:0%
+taking energy out of the inductor and
+ 
+
+ align:start position:0%
+taking energy out of the inductor and
+put it in the output so essentially I'm
+
+ align:start position:0%
+put it in the output so essentially I'm
+ 
+
+ align:start position:0%
+put it in the output so essentially I'm
+using this inductor as a filter but it's
+
+ align:start position:0%
+using this inductor as a filter but it's
+ 
+
+ align:start position:0%
+using this inductor as a filter but it's
+also an intermediate store of energy
+
+ align:start position:0%
+also an intermediate store of energy
+ 
+
+ align:start position:0%
+also an intermediate store of energy
+that lets me kind of take energy from
+
+ align:start position:0%
+that lets me kind of take energy from
+ 
+
+ align:start position:0%
+that lets me kind of take energy from
+the input and transfer to the output
+
+ align:start position:0%
+the input and transfer to the output
+ 
+
+ align:start position:0%
+the input and transfer to the output
+with a voltage conversion without losing
+
+ align:start position:0%
+with a voltage conversion without losing
+ 
+
+ align:start position:0%
+with a voltage conversion without losing
+any of the
+
+ align:start position:0%
+any of the
+ 
+
+ align:start position:0%
+any of the
+energy excellent question long answer to
+
+ align:start position:0%
+energy excellent question long answer to
+ 
+
+ align:start position:0%
+energy excellent question long answer to
+a short question any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so as I said um my goal
+
+ align:start position:0%
+questions okay so as I said um my goal
+ 
+
+ align:start position:0%
+questions okay so as I said um my goal
+is to sort of first of all teach you a
+
+ align:start position:0%
+is to sort of first of all teach you a
+ 
+
+ align:start position:0%
+is to sort of first of all teach you a
+lot of the underlying principles this is
+
+ align:start position:0%
+lot of the underlying principles this is
+ 
+
+ align:start position:0%
+lot of the underlying principles this is
+the this is the world's if you will
+
+ align:start position:0%
+the this is the world's if you will
+ 
+
+ align:start position:0%
+the this is the world's if you will
+simplest switching power converter so
+
+ align:start position:0%
+simplest switching power converter so
+ 
+
+ align:start position:0%
+simplest switching power converter so
+the when we use this technique we also
+
+ align:start position:0%
+the when we use this technique we also
+ 
+
+ align:start position:0%
+the when we use this technique we also
+often say we're switched
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mode all right with the notion that
+
+ align:start position:0%
+mode all right with the notion that
+ 
+
+ align:start position:0%
+mode all right with the notion that
+we're going to use
+
+ align:start position:0%
+we're going to use
+ 
+
+ align:start position:0%
+we're going to use
+switches and energy storage elements to
+
+ align:start position:0%
+switches and energy storage elements to
+ 
+
+ align:start position:0%
+switches and energy storage elements to
+process energy and that's sort of what
+
+ align:start position:0%
+process energy and that's sort of what
+ 
+
+ align:start position:0%
+process energy and that's sort of what
+sits at the core of Power
+
+ align:start position:0%
+sits at the core of Power
+ 
+
+ align:start position:0%
+sits at the core of Power
+Electronics okay and as I said we're
+
+ align:start position:0%
+Electronics okay and as I said we're
+ 
+
+ align:start position:0%
+Electronics okay and as I said we're
+going to look at all of the aspects how
+
+ align:start position:0%
+going to look at all of the aspects how
+ 
+
+ align:start position:0%
+going to look at all of the aspects how
+do you design these things how do you
+
+ align:start position:0%
+do you design these things how do you
+ 
+
+ align:start position:0%
+do you design these things how do you
+control them how do you design the
+
+ align:start position:0%
+control them how do you design the
+ 
+
+ align:start position:0%
+control them how do you design the
+components and by the time we're done
+
+ align:start position:0%
+components and by the time we're done
+ 
+
+ align:start position:0%
+components and by the time we're done
+you should be able to put it all
+
+ align:start position:0%
+you should be able to put it all
+ 
+
+ align:start position:0%
+you should be able to put it all
+together and and start designing Power
+
+ align:start position:0%
+together and and start designing Power
+ 
+
+ align:start position:0%
+together and and start designing Power
+Electronics of your own and you will for
+
+ align:start position:0%
+Electronics of your own and you will for
+ 
+
+ align:start position:0%
+Electronics of your own and you will for
+the final project
+
+ align:start position:0%
+the final project
+ 
+
+ align:start position:0%
+the final project
+okay so any final questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we'll wrap up today and I will see
+
+ align:start position:0%
+okay we'll wrap up today and I will see
+ 
+
+ align:start position:0%
+okay we'll wrap up today and I will see
+everybody on Wednesday
\ No newline at end of file
diff --git a/fsF79kN9G28.txt b/fsF79kN9G28.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0bcaea632a8325be25fea722d2334165ce30e360
--- /dev/null
+++ b/fsF79kN9G28.txt
@@ -0,0 +1,232 @@
+Let us discuss the performance
+of a benchmark algorithm.
+
+The Random Forest
+algorithm is known
+
+for its attractive property of
+detecting variable interactions
+
+and excellent performance
+as a learning algorithm.
+
+For the decision, we're
+selecting the Random Forest
+
+algorithm as a
+benchmark-- initially,
+
+we randomly partitioned
+the full data
+
+set into two separate parts,
+where the split was 50-50,
+
+and the partitioning was done
+evenly within each cost bin.
+
+The first part,
+the training set,
+
+was used to develop the method.
+
+The second part,
+the test set, was
+
+used to evaluate the
+model's performance.
+
+The table in this slide
+reports the accuracy
+
+of the Random Forest algorithm
+on each of the three buckets.
+
+Let us now introduce
+the idea of clustering.
+
+Patients in each bucket may
+have different characteristics.
+
+For this reason, we create
+clusters for each cost bucket
+
+and make predictions for each
+cluster using the Random Forest
+
+algorithm.
+
+Clustering is mostly used in
+the absence of a target variable
+
+to search for relationships
+among input variables
+
+or to organize data
+into meaningful groups.
+
+In this study, although
+the target variable
+
+is well-defined as a heart
+attack or not a heart attack,
+
+there are many
+different trajectories
+
+that are associated
+with the target.
+
+There's not one set
+pattern of health
+
+or diagnostic combination that
+leads a person to heart attack.
+
+Instead, we'll
+show that there are
+
+many different dynamic health
+patterns and time series
+
+diagnostic relations
+preceding a heart attack.
+
+The clustering
+methods were used were
+
+spectral clustering
+and k-means clustering.
+
+We focus, in the lecture,
+on the k-means clustering.
+
+The broad description of
+the algorithm is as follows.
+
+We first specify the
+number of clusters k.
+
+Then we randomly assign each
+data point to a cluster.
+
+We then compute the
+cluster centroids.
+
+We re-assign each point to
+the closest cluster centroid.
+
+We then re-compute
+the cluster centroids,
+
+and we repeat steps 4 and 5
+until no improvement is made.
+
+Let us illustrate the
+k-means algorithm in action.
+
+We specify the desired
+number of clusters k.
+
+In this case, we use k=2.
+
+We then randomly assign each
+data point to a cluster.
+
+In this case, we have
+the three points in red,
+
+and the two points in black.
+
+We then compute the
+cluster centroids,
+
+indicated by the red
+x and the grey x.
+
+We re-assign each point to
+the closest cluster centroid,
+
+and now you observe that
+this point changes from a red
+
+to a grey.
+
+We re-compute the
+cluster centroids,
+
+and we repeat the
+previous steps, 4 and 5
+
+until no improvement is made.
+
+We observe that, in this case,
+the k-means clustering is done,
+
+and this is our
+final clustering.
+
+Let us discuss some
+practical considerations.
+
+The number of clusters
+k can be selected
+
+from previous knowledge or
+by simply experimenting.
+
+We can strategically select
+initial partition of points
+
+into clusters if we have
+some knowledge of the data.
+
+We can also run the
+algorithm several times
+
+with different random
+starting points.
+
+In the recitations,
+we'll learn how
+
+to run the k-means
+algorithm in R.
+
+So how do we
+measure performance?
+
+After we construct the
+clusters in the training set,
+
+we assign new observations
+to clusters by proximity
+
+to the centroid of each cluster.
+
+We measure performance
+by recording
+
+the average performance
+rate in each cluster.
+
+Let us now discuss the
+performance of the clustering
+
+methods.
+
+We perform clustering on each
+bucket using k=10 clusters.
+
+In the table we record
+the average prediction
+
+rate of each cost bucket.
+
+We observe a very
+visible improvement
+
+when we use clustering-- from
+49% to 64%, from 56% to 73%,
+
+from 58% to 78%.
\ No newline at end of file
diff --git a/fv5QB3eK7jA.txt b/fv5QB3eK7jA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1b7e64ae40780e8c2f21371c9e7b7565aeac7ae7
--- /dev/null
+++ b/fv5QB3eK7jA.txt
@@ -0,0 +1,2635 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why does going to the airport seem to
+
+ align:start position:0%
+why does going to the airport seem to
+ 
+
+ align:start position:0%
+why does going to the airport seem to
+require extra time compared with coming
+
+ align:start position:0%
+require extra time compared with coming
+ 
+
+ align:start position:0%
+require extra time compared with coming
+back from the airport even if the
+
+ align:start position:0%
+back from the airport even if the
+ 
+
+ align:start position:0%
+back from the airport even if the
+traffic is the same in both directions
+
+ align:start position:0%
+traffic is the same in both directions
+ 
+
+ align:start position:0%
+traffic is the same in both directions
+the answer must somehow depend on more
+
+ align:start position:0%
+the answer must somehow depend on more
+ 
+
+ align:start position:0%
+the answer must somehow depend on more
+than just the average travel time which
+
+ align:start position:0%
+than just the average travel time which
+ 
+
+ align:start position:0%
+than just the average travel time which
+we're assuming is the same and often is
+
+ align:start position:0%
+we're assuming is the same and often is
+ 
+
+ align:start position:0%
+we're assuming is the same and often is
+in fact it often depends on the
+
+ align:start position:0%
+in fact it often depends on the
+ 
+
+ align:start position:0%
+in fact it often depends on the
+distribution of travel times probability
+
+ align:start position:0%
+distribution of travel times probability
+ 
+
+ align:start position:0%
+distribution of travel times probability
+distributions are fully described by
+
+ align:start position:0%
+distributions are fully described by
+ 
+
+ align:start position:0%
+distributions are fully described by
+listing or graphing every probability
+
+ align:start position:0%
+listing or graphing every probability
+ 
+
+ align:start position:0%
+listing or graphing every probability
+for example How likely is a journey to
+
+ align:start position:0%
+for example How likely is a journey to
+ 
+
+ align:start position:0%
+for example How likely is a journey to
+the airport to be between 10 and 20
+
+ align:start position:0%
+the airport to be between 10 and 20
+ 
+
+ align:start position:0%
+the airport to be between 10 and 20
+minutes How likely is a 20 to 30-minute
+
+ align:start position:0%
+minutes How likely is a 20 to 30-minute
+ 
+
+ align:start position:0%
+minutes How likely is a 20 to 30-minute
+Journey a 30 to 40 minute journey and so
+
+ align:start position:0%
+Journey a 30 to 40 minute journey and so
+ 
+
+ align:start position:0%
+Journey a 30 to 40 minute journey and so
+on we'll answer the airport question at
+
+ align:start position:0%
+on we'll answer the airport question at
+ 
+
+ align:start position:0%
+on we'll answer the airport question at
+the end of the video this video is part
+
+ align:start position:0%
+the end of the video this video is part
+ 
+
+ align:start position:0%
+the end of the video this video is part
+of the probability and statistics video
+
+ align:start position:0%
+of the probability and statistics video
+ 
+
+ align:start position:0%
+of the probability and statistics video
+series many natural and social phenomena
+
+ align:start position:0%
+series many natural and social phenomena
+ 
+
+ align:start position:0%
+series many natural and social phenomena
+are probabilistic in nature Engineers
+
+ align:start position:0%
+are probabilistic in nature Engineers
+ 
+
+ align:start position:0%
+are probabilistic in nature Engineers
+scientists and policy makers often use
+
+ align:start position:0%
+scientists and policy makers often use
+ 
+
+ align:start position:0%
+scientists and policy makers often use
+probability to model and predict system
+
+ align:start position:0%
+probability to model and predict system
+ 
+
+ align:start position:0%
+probability to model and predict system
+Behavior hi my name is sanjoy Mahajan
+
+ align:start position:0%
+Behavior hi my name is sanjoy Mahajan
+ 
+
+ align:start position:0%
+Behavior hi my name is sanjoy Mahajan
+and I'm a professor of applied science
+
+ align:start position:0%
+and I'm a professor of applied science
+ 
+
+ align:start position:0%
+and I'm a professor of applied science
+and engineering at ol College before
+
+ align:start position:0%
+and engineering at ol College before
+ 
+
+ align:start position:0%
+and engineering at ol College before
+watching this video you should be
+
+ align:start position:0%
+watching this video you should be
+ 
+
+ align:start position:0%
+watching this video you should be
+proficient with integration and have
+
+ align:start position:0%
+proficient with integration and have
+ 
+
+ align:start position:0%
+proficient with integration and have
+some familiarity with probabilities
+
+ align:start position:0%
+some familiarity with probabilities
+ 
+
+ align:start position:0%
+some familiarity with probabilities
+after watching this video you will be
+
+ align:start position:0%
+after watching this video you will be
+ 
+
+ align:start position:0%
+after watching this video you will be
+able to explain what moments of
+
+ align:start position:0%
+able to explain what moments of
+ 
+
+ align:start position:0%
+able to explain what moments of
+distributions are and compute moments
+
+ align:start position:0%
+distributions are and compute moments
+ 
+
+ align:start position:0%
+distributions are and compute moments
+and understand what they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean to illustrate what a probability
+
+ align:start position:0%
+mean to illustrate what a probability
+ 
+
+ align:start position:0%
+mean to illustrate what a probability
+distribution is is let's consider
+
+ align:start position:0%
+distribution is is let's consider
+ 
+
+ align:start position:0%
+distribution is is let's consider
+rolling two Fair dice the probability
+
+ align:start position:0%
+rolling two Fair dice the probability
+ 
+
+ align:start position:0%
+rolling two Fair dice the probability
+distribution of their sum is this table
+
+ align:start position:0%
+distribution of their sum is this table
+ 
+
+ align:start position:0%
+distribution of their sum is this table
+for example the only way to get a sum of
+
+ align:start position:0%
+for example the only way to get a sum of
+ 
+
+ align:start position:0%
+for example the only way to get a sum of
+two is to roll a one on each die and
+
+ align:start position:0%
+two is to roll a one on each die and
+ 
+
+ align:start position:0%
+two is to roll a one on each die and
+there are 36 possible rolls for a pair
+
+ align:start position:0%
+there are 36 possible rolls for a pair
+ 
+
+ align:start position:0%
+there are 36 possible rolls for a pair
+of dice so getting a sum of two has a
+
+ align:start position:0%
+of dice so getting a sum of two has a
+ 
+
+ align:start position:0%
+of dice so getting a sum of two has a
+probability of 1 over
+
+ align:start position:0%
+probability of 1 over
+ 
+
+ align:start position:0%
+probability of 1 over
+36 the probability of rolling a sum of
+
+ align:start position:0%
+36 the probability of rolling a sum of
+ 
+
+ align:start position:0%
+36 the probability of rolling a sum of
+three is 2 over 36 and so on and so
+
+ align:start position:0%
+three is 2 over 36 and so on and so
+ 
+
+ align:start position:0%
+three is 2 over 36 and so on and so
+forth you can fill in a table like this
+
+ align:start position:0%
+forth you can fill in a table like this
+ 
+
+ align:start position:0%
+forth you can fill in a table like this
+your but the whole distribution even for
+
+ align:start position:0%
+your but the whole distribution even for
+ 
+
+ align:start position:0%
+your but the whole distribution even for
+something as simple as two dice is
+
+ align:start position:0%
+something as simple as two dice is
+ 
+
+ align:start position:0%
+something as simple as two dice is
+usually too much
+
+ align:start position:0%
+usually too much
+ 
+
+ align:start position:0%
+usually too much
+information we often want to
+
+ align:start position:0%
+information we often want to
+ 
+
+ align:start position:0%
+information we often want to
+characterize the shape of the
+
+ align:start position:0%
+characterize the shape of the
+ 
+
+ align:start position:0%
+characterize the shape of the
+distribution using only a few
+
+ align:start position:0%
+distribution using only a few
+ 
+
+ align:start position:0%
+distribution using only a few
+numbers of course that throws away
+
+ align:start position:0%
+numbers of course that throws away
+ 
+
+ align:start position:0%
+numbers of course that throws away
+information but throwing away
+
+ align:start position:0%
+information but throwing away
+ 
+
+ align:start position:0%
+information but throwing away
+information is the only way to fit the
+
+ align:start position:0%
+information is the only way to fit the
+ 
+
+ align:start position:0%
+information is the only way to fit the
+complexity of the world into our brains
+
+ align:start position:0%
+complexity of the world into our brains
+ 
+
+ align:start position:0%
+complexity of the world into our brains
+the art comes in keeping the most
+
+ align:start position:0%
+the art comes in keeping the most
+ 
+
+ align:start position:0%
+the art comes in keeping the most
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+information finding the moments of a
+
+ align:start position:0%
+information finding the moments of a
+ 
+
+ align:start position:0%
+information finding the moments of a
+distribution can help us reach our
+
+ align:start position:0%
+distribution can help us reach our
+ 
+
+ align:start position:0%
+distribution can help us reach our
+goal two moments that you are probably
+
+ align:start position:0%
+goal two moments that you are probably
+ 
+
+ align:start position:0%
+goal two moments that you are probably
+already familiar with are mean and
+
+ align:start position:0%
+already familiar with are mean and
+ 
+
+ align:start position:0%
+already familiar with are mean and
+variance they are the two most important
+
+ align:start position:0%
+variance they are the two most important
+ 
+
+ align:start position:0%
+variance they are the two most important
+moments of
+
+ align:start position:0%
+moments of
+ 
+
+ align:start position:0%
+moments of
+distributions let's define these moments
+
+ align:start position:0%
+distributions let's define these moments
+ 
+
+ align:start position:0%
+distributions let's define these moments
+more formally the mean is the first
+
+ align:start position:0%
+more formally the mean is the first
+ 
+
+ align:start position:0%
+more formally the mean is the first
+moment of a
+
+ align:start position:0%
+moment of a
+ 
+
+ align:start position:0%
+moment of a
+distribution it is also called the
+
+ align:start position:0%
+distribution it is also called the
+ 
+
+ align:start position:0%
+distribution it is also called the
+expected value and is computed as
+
+ align:start position:0%
+expected value and is computed as
+ 
+
+ align:start position:0%
+expected value and is computed as
+shown expected value of x that's x with
+
+ align:start position:0%
+shown expected value of x that's x with
+ 
+
+ align:start position:0%
+shown expected value of x that's x with
+angled brackets around it is equal to
+
+ align:start position:0%
+angled brackets around it is equal to
+ 
+
+ align:start position:0%
+angled brackets around it is equal to
+this sum it's the weighted sum of all
+
+ align:start position:0%
+this sum it's the weighted sum of all
+ 
+
+ align:start position:0%
+this sum it's the weighted sum of all
+the X's weighted by their
+
+ align:start position:0%
+the X's weighted by their
+ 
+
+ align:start position:0%
+the X's weighted by their
+probabilities let the x of I be the
+
+ align:start position:0%
+probabilities let the x of I be the
+ 
+
+ align:start position:0%
+probabilities let the x of I be the
+possible values of X for example for the
+
+ align:start position:0%
+possible values of X for example for the
+ 
+
+ align:start position:0%
+possible values of X for example for the
+rolling of two dice the possible values
+
+ align:start position:0%
+rolling of two dice the possible values
+ 
+
+ align:start position:0%
+rolling of two dice the possible values
+for X of I would be 2 3 4 all the way up
+
+ align:start position:0%
+for X of I would be 2 3 4 all the way up
+ 
+
+ align:start position:0%
+for X of I would be 2 3 4 all the way up
+through 12 and P ofi would be the
+
+ align:start position:0%
+through 12 and P ofi would be the
+ 
+
+ align:start position:0%
+through 12 and P ofi would be the
+corresponding probabilities of rolling
+
+ align:start position:0%
+corresponding probabilities of rolling
+ 
+
+ align:start position:0%
+corresponding probabilities of rolling
+those sums so that was 1 over 36 2 over
+
+ align:start position:0%
+those sums so that was 1 over 36 2 over
+ 
+
+ align:start position:0%
+those sums so that was 1 over 36 2 over
+36 and so on so the first moment gives
+
+ align:start position:0%
+36 and so on so the first moment gives
+ 
+
+ align:start position:0%
+36 and so on so the first moment gives
+us some idea of what our distribution
+
+ align:start position:0%
+us some idea of what our distribution
+ 
+
+ align:start position:0%
+us some idea of what our distribution
+might look like but not much
+
+ align:start position:0%
+might look like but not much
+ 
+
+ align:start position:0%
+might look like but not much
+think about it like this the center of
+
+ align:start position:0%
+think about it like this the center of
+ 
+
+ align:start position:0%
+think about it like this the center of
+mass in these two images is in the same
+
+ align:start position:0%
+mass in these two images is in the same
+ 
+
+ align:start position:0%
+mass in these two images is in the same
+place but the mass is actually
+
+ align:start position:0%
+place but the mass is actually
+ 
+
+ align:start position:0%
+place but the mass is actually
+distributed very differently in the two
+
+ align:start position:0%
+distributed very differently in the two
+ 
+
+ align:start position:0%
+distributed very differently in the two
+cases we need more information the
+
+ align:start position:0%
+cases we need more information the
+ 
+
+ align:start position:0%
+cases we need more information the
+second moment can help us the second
+
+ align:start position:0%
+second moment can help us the second
+ 
+
+ align:start position:0%
+second moment can help us the second
+moment is very similar in structure to
+
+ align:start position:0%
+moment is very similar in structure to
+ 
+
+ align:start position:0%
+moment is very similar in structure to
+the first moment we write it the same
+
+ align:start position:0%
+the first moment we write it the same
+ 
+
+ align:start position:0%
+the first moment we write it the same
+way with angled brackets but now we're
+
+ align:start position:0%
+way with angled brackets but now we're
+ 
+
+ align:start position:0%
+way with angled brackets but now we're
+talking about the expected value of x
+
+ align:start position:0%
+talking about the expected value of x
+ 
+
+ align:start position:0%
+talking about the expected value of x
+squared so it's still a sum and it's
+
+ align:start position:0%
+squared so it's still a sum and it's
+ 
+
+ align:start position:0%
+squared so it's still a sum and it's
+still weighted by the probabilities pie
+
+ align:start position:0%
+still weighted by the probabilities pie
+ 
+
+ align:start position:0%
+still weighted by the probabilities pie
+of I but now we Square each possible x
+
+ align:start position:0%
+of I but now we Square each possible x
+ 
+
+ align:start position:0%
+of I but now we Square each possible x
+value for the dice example that was the
+
+ align:start position:0%
+value for the dice example that was the
+ 
+
+ align:start position:0%
+value for the dice example that was the
+values from 2 through 12 this is also
+
+ align:start position:0%
+values from 2 through 12 this is also
+ 
+
+ align:start position:0%
+values from 2 through 12 this is also
+called the mean
+
+ align:start position:0%
+called the mean
+ 
+
+ align:start position:0%
+called the mean
+Square first you square the X values
+
+ align:start position:0%
+Square first you square the X values
+ 
+
+ align:start position:0%
+Square first you square the X values
+then you take the mean waiting each xabi
+
+ align:start position:0%
+then you take the mean waiting each xabi
+ 
+
+ align:start position:0%
+then you take the mean waiting each xabi
+by its probability pie of by in general
+
+ align:start position:0%
+by its probability pie of by in general
+ 
+
+ align:start position:0%
+by its probability pie of by in general
+the nth moment is defined as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows so how does the second moment
+
+ align:start position:0%
+follows so how does the second moment
+ 
+
+ align:start position:0%
+follows so how does the second moment
+help us get a better picture of our
+
+ align:start position:0%
+help us get a better picture of our
+ 
+
+ align:start position:0%
+help us get a better picture of our
+distribution because it can help us
+
+ align:start position:0%
+distribution because it can help us
+ 
+
+ align:start position:0%
+distribution because it can help us
+calculate something called the
+
+ align:start position:0%
+calculate something called the
+ 
+
+ align:start position:0%
+calculate something called the
+variance the variance measures how
+
+ align:start position:0%
+variance the variance measures how
+ 
+
+ align:start position:0%
+variance the variance measures how
+spread out the distribution is around
+
+ align:start position:0%
+spread out the distribution is around
+ 
+
+ align:start position:0%
+spread out the distribution is around
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mean to calculate the variance you first
+
+ align:start position:0%
+mean to calculate the variance you first
+ 
+
+ align:start position:0%
+mean to calculate the variance you first
+subtract the mean from each X
+
+ align:start position:0%
+subtract the mean from each X
+ 
+
+ align:start position:0%
+subtract the mean from each X
+ofi this is like finding the distance of
+
+ align:start position:0%
+ofi this is like finding the distance of
+ 
+
+ align:start position:0%
+ofi this is like finding the distance of
+each x sub I from the mean and then you
+
+ align:start position:0%
+each x sub I from the mean and then you
+ 
+
+ align:start position:0%
+each x sub I from the mean and then you
+square the result and multiply by P sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I what is the dimensions of the variance
+
+ align:start position:0%
+I what is the dimensions of the variance
+ 
+
+ align:start position:0%
+I what is the dimensions of the variance
+the square of the dimensions of X for
+
+ align:start position:0%
+the square of the dimensions of X for
+ 
+
+ align:start position:0%
+the square of the dimensions of X for
+example if the dimension is a length
+
+ align:start position:0%
+example if the dimension is a length
+ 
+
+ align:start position:0%
+example if the dimension is a length
+then the variance is a length
+
+ align:start position:0%
+then the variance is a length
+ 
+
+ align:start position:0%
+then the variance is a length
+squared but we often want to measure of
+
+ align:start position:0%
+squared but we often want to measure of
+ 
+
+ align:start position:0%
+squared but we often want to measure of
+dispersion like the variance but one
+
+ align:start position:0%
+dispersion like the variance but one
+ 
+
+ align:start position:0%
+dispersion like the variance but one
+that has the same dimensions as X
+
+ align:start position:0%
+that has the same dimensions as X
+ 
+
+ align:start position:0%
+that has the same dimensions as X
+itself that measure is the standard
+
+ align:start position:0%
+itself that measure is the standard
+ 
+
+ align:start position:0%
+itself that measure is the standard
+deviation
+
+ align:start position:0%
+deviation
+ 
+
+ align:start position:0%
+deviation
+Sigma Sigma is defined as the square
+
+ align:start position:0%
+Sigma Sigma is defined as the square
+ 
+
+ align:start position:0%
+Sigma Sigma is defined as the square
+root of the variance so if the variable
+
+ align:start position:0%
+root of the variance so if the variable
+ 
+
+ align:start position:0%
+root of the variance so if the variable
+X has dimensions of length then the
+
+ align:start position:0%
+X has dimensions of length then the
+ 
+
+ align:start position:0%
+X has dimensions of length then the
+variance will have dimensions of length
+
+ align:start position:0%
+variance will have dimensions of length
+ 
+
+ align:start position:0%
+variance will have dimensions of length
+squared but the standard deviation Sigma
+
+ align:start position:0%
+squared but the standard deviation Sigma
+ 
+
+ align:start position:0%
+squared but the standard deviation Sigma
+will have dimensions of length so it's
+
+ align:start position:0%
+will have dimensions of length so it's
+ 
+
+ align:start position:0%
+will have dimensions of length so it's
+comparable to X directly this expression
+
+ align:start position:0%
+comparable to X directly this expression
+ 
+
+ align:start position:0%
+comparable to X directly this expression
+for the variance looks like a pain to
+
+ align:start position:0%
+for the variance looks like a pain to
+ 
+
+ align:start position:0%
+for the variance looks like a pain to
+compute but it has an alternative
+
+ align:start position:0%
+compute but it has an alternative
+ 
+
+ align:start position:0%
+compute but it has an alternative
+expression that is much simpler and you
+
+ align:start position:0%
+expression that is much simpler and you
+ 
+
+ align:start position:0%
+expression that is much simpler and you
+get to show that as one of the exercises
+
+ align:start position:0%
+get to show that as one of the exercises
+ 
+
+ align:start position:0%
+get to show that as one of the exercises
+after the
+
+ align:start position:0%
+after the
+ 
+
+ align:start position:0%
+after the
+video the alternative expression the
+
+ align:start position:0%
+video the alternative expression the
+ 
+
+ align:start position:0%
+video the alternative expression the
+much simpler one is that the variance is
+
+ align:start position:0%
+much simpler one is that the variance is
+ 
+
+ align:start position:0%
+much simpler one is that the variance is
+equal to the second moment our old
+
+ align:start position:0%
+equal to the second moment our old
+ 
+
+ align:start position:0%
+equal to the second moment our old
+friend minus the square of the first
+
+ align:start position:0%
+friend minus the square of the first
+ 
+
+ align:start position:0%
+friend minus the square of the first
+moment or the mean pause the video here
+
+ align:start position:0%
+moment or the mean pause the video here
+ 
+
+ align:start position:0%
+moment or the mean pause the video here
+to convince Vince yourself that this
+
+ align:start position:0%
+to convince Vince yourself that this
+ 
+
+ align:start position:0%
+to convince Vince yourself that this
+difference is always non-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative this alternative expression for
+
+ align:start position:0%
+negative this alternative expression for
+ 
+
+ align:start position:0%
+negative this alternative expression for
+the variance this much more useful one
+
+ align:start position:0%
+the variance this much more useful one
+ 
+
+ align:start position:0%
+the variance this much more useful one
+is also the parallel axis theorem in
+
+ align:start position:0%
+is also the parallel axis theorem in
+ 
+
+ align:start position:0%
+is also the parallel axis theorem in
+mechanics which says that the moment of
+
+ align:start position:0%
+mechanics which says that the moment of
+ 
+
+ align:start position:0%
+mechanics which says that the moment of
+inertia of an object about the center of
+
+ align:start position:0%
+inertia of an object about the center of
+ 
+
+ align:start position:0%
+inertia of an object about the center of
+mass is equal to the moment of inertia
+
+ align:start position:0%
+mass is equal to the moment of inertia
+ 
+
+ align:start position:0%
+mass is equal to the moment of inertia
+about an axis shifted by H from the
+
+ align:start position:0%
+about an axis shifted by H from the
+ 
+
+ align:start position:0%
+about an axis shifted by H from the
+center of mass a parallel shift minus
+
+ align:start position:0%
+center of mass a parallel shift minus
+ 
+
+ align:start position:0%
+center of mass a parallel shift minus
+mh^ 2 so how does this analogy
+
+ align:start position:0%
+mh^ 2 so how does this analogy
+ 
+
+ align:start position:0%
+mh^ 2 so how does this analogy
+work this the dispersion around the mean
+
+ align:start position:0%
+work this the dispersion around the mean
+ 
+
+ align:start position:0%
+work this the dispersion around the mean
+which is here at the center of Mass is
+
+ align:start position:0%
+which is here at the center of Mass is
+ 
+
+ align:start position:0%
+which is here at the center of Mass is
+like the variance this is like the
+
+ align:start position:0%
+like the variance this is like the
+ 
+
+ align:start position:0%
+like the variance this is like the
+second moment if we make H equal to the
+
+ align:start position:0%
+second moment if we make H equal to the
+ 
+
+ align:start position:0%
+second moment if we make H equal to the
+mean so this is the dispersion around
+
+ align:start position:0%
+mean so this is the dispersion around
+ 
+
+ align:start position:0%
+mean so this is the dispersion around
+zero or at second moment so this is like
+
+ align:start position:0%
+zero or at second moment so this is like
+ 
+
+ align:start position:0%
+zero or at second moment so this is like
+x^2 the expected value the mass is the
+
+ align:start position:0%
+x^2 the expected value the mass is the
+ 
+
+ align:start position:0%
+x^2 the expected value the mass is the
+sum total of all the weights here for
+
+ align:start position:0%
+sum total of all the weights here for
+ 
+
+ align:start position:0%
+sum total of all the weights here for
+each of the XI which all add up to one
+
+ align:start position:0%
+each of the XI which all add up to one
+ 
+
+ align:start position:0%
+each of the XI which all add up to one
+so this is just like one in this problem
+
+ align:start position:0%
+so this is just like one in this problem
+ 
+
+ align:start position:0%
+so this is just like one in this problem
+and then the h s well H is the mean so
+
+ align:start position:0%
+and then the h s well H is the mean so
+ 
+
+ align:start position:0%
+and then the h s well H is the mean so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+x^2 so you can see the exact same
+
+ align:start position:0%
+x^2 so you can see the exact same
+ 
+
+ align:start position:0%
+x^2 so you can see the exact same
+structure repeated with h the shift of
+
+ align:start position:0%
+structure repeated with h the shift of
+ 
+
+ align:start position:0%
+structure repeated with h the shift of
+axis as the mean and M the mass as the
+
+ align:start position:0%
+axis as the mean and M the mass as the
+ 
+
+ align:start position:0%
+axis as the mean and M the mass as the
+sum of all probabilities which is one so
+
+ align:start position:0%
+sum of all probabilities which is one so
+ 
+
+ align:start position:0%
+sum of all probabilities which is one so
+this formula for the variance is also
+
+ align:start position:0%
+this formula for the variance is also
+ 
+
+ align:start position:0%
+this formula for the variance is also
+the parallel axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem let's use the definitions of the
+
+ align:start position:0%
+theorem let's use the definitions of the
+ 
+
+ align:start position:0%
+theorem let's use the definitions of the
+moments and also of the related quantity
+
+ align:start position:0%
+moments and also of the related quantity
+ 
+
+ align:start position:0%
+moments and also of the related quantity
+the variance and practice on a few
+
+ align:start position:0%
+the variance and practice on a few
+ 
+
+ align:start position:0%
+the variance and practice on a few
+distributions a simple discrete
+
+ align:start position:0%
+distributions a simple discrete
+ 
+
+ align:start position:0%
+distributions a simple discrete
+distribution is a single coin flip
+
+ align:start position:0%
+distribution is a single coin flip
+ 
+
+ align:start position:0%
+distribution is a single coin flip
+instead of thinking of the coin flip as
+
+ align:start position:0%
+instead of thinking of the coin flip as
+ 
+
+ align:start position:0%
+instead of thinking of the coin flip as
+resulting in heads or tails let's think
+
+ align:start position:0%
+resulting in heads or tails let's think
+ 
+
+ align:start position:0%
+resulting in heads or tails let's think
+about the coin as turning up a zero or
+
+ align:start position:0%
+about the coin as turning up a zero or
+ 
+
+ align:start position:0%
+about the coin as turning up a zero or
+one let P be the probability of a one so
+
+ align:start position:0%
+one let P be the probability of a one so
+ 
+
+ align:start position:0%
+one let P be the probability of a one so
+the mean is the weighted sum of the X
+
+ align:start position:0%
+the mean is the weighted sum of the X
+ 
+
+ align:start position:0%
+the mean is the weighted sum of the X
+ofis weighted by the
+
+ align:start position:0%
+ofis weighted by the
+ 
+
+ align:start position:0%
+ofis weighted by the
+probabilities so the mean X is the sum p
+
+ align:start position:0%
+probabilities so the mean X is the sum p
+ 
+
+ align:start position:0%
+probabilities so the mean X is the sum p
+subi x subi which is equal to 1 - P * 0
+
+ align:start position:0%
+subi x subi which is equal to 1 - P * 0
+ 
+
+ align:start position:0%
+subi x subi which is equal to 1 - P * 0
++ P * 1 which is equal to P what about
+
+ align:start position:0%
++ P * 1 which is equal to P what about
+ 
+
+ align:start position:0%
++ P * 1 which is equal to P what about
+the second moment the expected value of
+
+ align:start position:0%
+the second moment the expected value of
+ 
+
+ align:start position:0%
+the second moment the expected value of
+x^2 it's equal to the weighted sum of
+
+ align:start position:0%
+x^2 it's equal to the weighted sum of
+ 
+
+ align:start position:0%
+x^2 it's equal to the weighted sum of
+the xub by^ squ so the weights are the
+
+ align:start position:0%
+the xub by^ squ so the weights are the
+ 
+
+ align:start position:0%
+the xub by^ squ so the weights are the
+same as
+
+ align:start position:0%
+same as
+ 
+
+ align:start position:0%
+same as
+before we then Square each value here
+
+ align:start position:0%
+before we then Square each value here
+ 
+
+ align:start position:0%
+before we then Square each value here
+each X of I but since they're all zero
+
+ align:start position:0%
+each X of I but since they're all zero
+ 
+
+ align:start position:0%
+each X of I but since they're all zero
+or one squaring doesn't change them so
+
+ align:start position:0%
+or one squaring doesn't change them so
+ 
+
+ align:start position:0%
+or one squaring doesn't change them so
+the second moment and the third moment
+
+ align:start position:0%
+the second moment and the third moment
+ 
+
+ align:start position:0%
+the second moment and the third moment
+and every higher moment are all also
+
+ align:start position:0%
+and every higher moment are all also
+ 
+
+ align:start position:0%
+and every higher moment are all also
+P pause the video here and compute the
+
+ align:start position:0%
+P pause the video here and compute the
+ 
+
+ align:start position:0%
+P pause the video here and compute the
+variance and sketch it as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P the variance from our old convenient
+
+ align:start position:0%
+P the variance from our old convenient
+ 
+
+ align:start position:0%
+P the variance from our old convenient
+form of the formula is the mean squar
+
+ align:start position:0%
+form of the formula is the mean squar
+ 
+
+ align:start position:0%
+form of the formula is the mean squar
+minus the squ mean and all the moments
+
+ align:start position:0%
+minus the squ mean and all the moments
+ 
+
+ align:start position:0%
+minus the squ mean and all the moments
+themselves were just P so that's P minus
+
+ align:start position:0%
+themselves were just P so that's P minus
+ 
+
+ align:start position:0%
+themselves were just P so that's P minus
+p^ 2 which is equal to P * 1us P what
+
+ align:start position:0%
+p^ 2 which is equal to P * 1us P what
+ 
+
+ align:start position:0%
+p^ 2 which is equal to P * 1us P what
+does that look like we'll sketch it p on
+
+ align:start position:0%
+does that look like we'll sketch it p on
+ 
+
+ align:start position:0%
+does that look like we'll sketch it p on
+this axis variance on that axis the
+
+ align:start position:0%
+this axis variance on that axis the
+ 
+
+ align:start position:0%
+this axis variance on that axis the
+curve starts at zero Rises to a peak in
+
+ align:start position:0%
+curve starts at zero Rises to a peak in
+ 
+
+ align:start position:0%
+curve starts at zero Rises to a peak in
+the middle and then goes back to zero
+
+ align:start position:0%
+the middle and then goes back to zero
+ 
+
+ align:start position:0%
+the middle and then goes back to zero
+this is a p equal 1 and that's P equal
+
+ align:start position:0%
+this is a p equal 1 and that's P equal
+ 
+
+ align:start position:0%
+this is a p equal 1 and that's P equal
+0 does that make
+
+ align:start position:0%
+0 does that make
+ 
+
+ align:start position:0%
+0 does that make
+sense yeah it does from the meaning of
+
+ align:start position:0%
+sense yeah it does from the meaning of
+ 
+
+ align:start position:0%
+sense yeah it does from the meaning of
+variance as dispersion around the
+
+ align:start position:0%
+variance as dispersion around the
+ 
+
+ align:start position:0%
+variance as dispersion around the
+mean so take the first extreme case of P
+
+ align:start position:0%
+mean so take the first extreme case of P
+ 
+
+ align:start position:0%
+mean so take the first extreme case of P
+equals 0 in other words the coin has no
+
+ align:start position:0%
+equals 0 in other words the coin has no
+ 
+
+ align:start position:0%
+equals 0 in other words the coin has no
+chance of producing a one always
+
+ align:start position:0%
+chance of producing a one always
+ 
+
+ align:start position:0%
+chance of producing a one always
+produces a zero every time there the
+
+ align:start position:0%
+produces a zero every time there the
+ 
+
+ align:start position:0%
+produces a zero every time there the
+mean is zero and there's no dispersion
+
+ align:start position:0%
+mean is zero and there's no dispersion
+ 
+
+ align:start position:0%
+mean is zero and there's no dispersion
+because it always produces zero the same
+
+ align:start position:0%
+because it always produces zero the same
+ 
+
+ align:start position:0%
+because it always produces zero the same
+applies when P equals one here at this
+
+ align:start position:0%
+applies when P equals one here at this
+ 
+
+ align:start position:0%
+applies when P equals one here at this
+extreme the coin always produces a one
+
+ align:start position:0%
+extreme the coin always produces a one
+ 
+
+ align:start position:0%
+extreme the coin always produces a one
+with no dispersion there is no variation
+
+ align:start position:0%
+with no dispersion there is no variation
+ 
+
+ align:start position:0%
+with no dispersion there is no variation
+there is no
+
+ align:start position:0%
+there is no
+ 
+
+ align:start position:0%
+there is no
+variance it's also plausible that the
+
+ align:start position:0%
+variance it's also plausible that the
+ 
+
+ align:start position:0%
+variance it's also plausible that the
+variance should be a maximum right in
+
+ align:start position:0%
+variance should be a maximum right in
+ 
+
+ align:start position:0%
+variance should be a maximum right in
+between here at P equal 12 which it is
+
+ align:start position:0%
+between here at P equal 12 which it is
+ 
+
+ align:start position:0%
+between here at P equal 12 which it is
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+curve so everything looks good our
+
+ align:start position:0%
+curve so everything looks good our
+ 
+
+ align:start position:0%
+curve so everything looks good our
+calculation seems reasonable and checks
+
+ align:start position:0%
+calculation seems reasonable and checks
+ 
+
+ align:start position:0%
+calculation seems reasonable and checks
+out in the extreme
+
+ align:start position:0%
+out in the extreme
+ 
+
+ align:start position:0%
+out in the extreme
+cases before we go back to the airport
+
+ align:start position:0%
+cases before we go back to the airport
+ 
+
+ align:start position:0%
+cases before we go back to the airport
+problem let's extend the idea of moments
+
+ align:start position:0%
+problem let's extend the idea of moments
+ 
+
+ align:start position:0%
+problem let's extend the idea of moments
+to continuous
+
+ align:start position:0%
+to continuous
+ 
+
+ align:start position:0%
+to continuous
+distributions here instead of a list of
+
+ align:start position:0%
+distributions here instead of a list of
+ 
+
+ align:start position:0%
+distributions here instead of a list of
+probabilities for each possible X we
+
+ align:start position:0%
+probabilities for each possible X we
+ 
+
+ align:start position:0%
+probabilities for each possible X we
+have a probability density p as a
+
+ align:start position:0%
+have a probability density p as a
+ 
+
+ align:start position:0%
+have a probability density p as a
+function of X or X is now a continuous
+
+ align:start position:0%
+function of X or X is now a continuous
+ 
+
+ align:start position:0%
+function of X or X is now a continuous
+variable that's the continuous version
+
+ align:start position:0%
+variable that's the continuous version
+ 
+
+ align:start position:0%
+variable that's the continuous version
+of the nth moment as a sum of x ofi to
+
+ align:start position:0%
+of the nth moment as a sum of x ofi to
+ 
+
+ align:start position:0%
+of the nth moment as a sum of x ofi to
+the nth weighted by the
+
+ align:start position:0%
+the nth weighted by the
+ 
+
+ align:start position:0%
+the nth weighted by the
+probabilities here the nth moment is
+
+ align:start position:0%
+probabilities here the nth moment is
+ 
+
+ align:start position:0%
+probabilities here the nth moment is
+equal to instead of a sum an
+
+ align:start position:0%
+equal to instead of a sum an
+ 
+
+ align:start position:0%
+equal to instead of a sum an
+integral weighted again as always by the
+
+ align:start position:0%
+integral weighted again as always by the
+ 
+
+ align:start position:0%
+integral weighted again as always by the
+probability times x to the n as before
+
+ align:start position:0%
+probability times x to the n as before
+ 
+
+ align:start position:0%
+probability times x to the n as before
+and with a DX because P ofx * DX is the
+
+ align:start position:0%
+and with a DX because P ofx * DX is the
+ 
+
+ align:start position:0%
+and with a DX because P ofx * DX is the
+probability and you add them up over all
+
+ align:start position:0%
+probability and you add them up over all
+ 
+
+ align:start position:0%
+probability and you add them up over all
+possible values of
+
+ align:start position:0%
+possible values of
+ 
+
+ align:start position:0%
+possible values of
+X that's the formula for the moments of
+
+ align:start position:0%
+X that's the formula for the moments of
+ 
+
+ align:start position:0%
+X that's the formula for the moments of
+a continuous
+
+ align:start position:0%
+a continuous
+ 
+
+ align:start position:0%
+a continuous
+distribution let's practice on the
+
+ align:start position:0%
+distribution let's practice on the
+ 
+
+ align:start position:0%
+distribution let's practice on the
+simplest continuous distribution the
+
+ align:start position:0%
+simplest continuous distribution the
+ 
+
+ align:start position:0%
+simplest continuous distribution the
+uniform distribution X is equally likely
+
+ align:start position:0%
+uniform distribution X is equally likely
+ 
+
+ align:start position:0%
+uniform distribution X is equally likely
+to be any real number between 0 and 1
+
+ align:start position:0%
+to be any real number between 0 and 1
+ 
+
+ align:start position:0%
+to be any real number between 0 and 1
+that's the distribution and we can
+
+ align:start position:0%
+that's the distribution and we can
+ 
+
+ align:start position:0%
+that's the distribution and we can
+compute the first and second moments and
+
+ align:start position:0%
+compute the first and second moments and
+ 
+
+ align:start position:0%
+compute the first and second moments and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+variance pause the video here use the
+
+ align:start position:0%
+variance pause the video here use the
+ 
+
+ align:start position:0%
+variance pause the video here use the
+definition of moments for a continuous
+
+ align:start position:0%
+definition of moments for a continuous
+ 
+
+ align:start position:0%
+definition of moments for a continuous
+distribution and compute the mean the
+
+ align:start position:0%
+distribution and compute the mean the
+ 
+
+ align:start position:0%
+distribution and compute the mean the
+first moment the second moment and from
+
+ align:start position:0%
+first moment the second moment and from
+ 
+
+ align:start position:0%
+first moment the second moment and from
+those two the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance what you should have found is
+
+ align:start position:0%
+variance what you should have found is
+ 
+
+ align:start position:0%
+variance what you should have found is
+for the mean it's the integral of 1
+
+ align:start position:0%
+for the mean it's the integral of 1
+ 
+
+ align:start position:0%
+for the mean it's the integral of 1
+because P of X is 1 * X between 0 and 1
+
+ align:start position:0%
+because P of X is 1 * X between 0 and 1
+ 
+
+ align:start position:0%
+because P of X is 1 * X between 0 and 1
+DX which is x^2 / 2 evaluated between 0
+
+ align:start position:0%
+DX which is x^2 / 2 evaluated between 0
+ 
+
+ align:start position:0%
+DX which is x^2 / 2 evaluated between 0
+and 1 which equals 12 which makes sense
+
+ align:start position:0%
+and 1 which equals 12 which makes sense
+ 
+
+ align:start position:0%
+and 1 which equals 12 which makes sense
+the mean here the average value is just
+
+ align:start position:0%
+the mean here the average value is just
+ 
+
+ align:start position:0%
+the mean here the average value is just
+1/2 right in the middle of the
+
+ align:start position:0%
+1/2 right in the middle of the
+ 
+
+ align:start position:0%
+1/2 right in the middle of the
+distribution of the possible values of X
+
+ align:start position:0%
+distribution of the possible values of X
+ 
+
+ align:start position:0%
+distribution of the possible values of X
+what about the mean
+
+ align:start position:0%
+what about the mean
+ 
+
+ align:start position:0%
+what about the mean
+Square for that you should have found
+
+ align:start position:0%
+Square for that you should have found
+ 
+
+ align:start position:0%
+Square for that you should have found
+almost the same calculation 1 * x^2 DX
+
+ align:start position:0%
+almost the same calculation 1 * x^2 DX
+ 
+
+ align:start position:0%
+almost the same calculation 1 * x^2 DX
+which = X Cub over 3 between 0 and 1
+
+ align:start position:0%
+which = X Cub over 3 between 0 and 1
+ 
+
+ align:start position:0%
+which = X Cub over 3 between 0 and 1
+which equals 1/3 and thus the variance
+
+ align:start position:0%
+which equals 1/3 and thus the variance
+ 
+
+ align:start position:0%
+which equals 1/3 and thus the variance
+is equal to 1/3 that's the mean Square
+
+ align:start position:0%
+is equal to 1/3 that's the mean Square
+ 
+
+ align:start position:0%
+is equal to 1/3 that's the mean Square
+minus the squared mean which is
+
+ align:start position:0%
+minus the squared mean which is
+ 
+
+ align:start position:0%
+minus the squared mean which is
+112th and that number is familiar that's
+
+ align:start position:0%
+112th and that number is familiar that's
+ 
+
+ align:start position:0%
+112th and that number is familiar that's
+the same 112th that shows up in the
+
+ align:start position:0%
+the same 112th that shows up in the
+ 
+
+ align:start position:0%
+the same 112th that shows up in the
+moment of inertia of a ruler of length L
+
+ align:start position:0%
+moment of inertia of a ruler of length L
+ 
+
+ align:start position:0%
+moment of inertia of a ruler of length L
+and mass m its moment of inertia is 112
+
+ align:start position:0%
+and mass m its moment of inertia is 112
+ 
+
+ align:start position:0%
+and mass m its moment of inertia is 112
+ml squ which illustrates again the
+
+ align:start position:0%
+ml squ which illustrates again the
+ 
+
+ align:start position:0%
+ml squ which illustrates again the
+connection between moments of inertia
+
+ align:start position:0%
+connection between moments of inertia
+ 
+
+ align:start position:0%
+connection between moments of inertia
+and moments of
+
+ align:start position:0%
+and moments of
+ 
+
+ align:start position:0%
+and moments of
+distributions let's apply our knowledge
+
+ align:start position:0%
+distributions let's apply our knowledge
+ 
+
+ align:start position:0%
+distributions let's apply our knowledge
+to understand quantitatively or in a
+
+ align:start position:0%
+to understand quantitatively or in a
+ 
+
+ align:start position:0%
+to understand quantitatively or in a
+formal way what happens with airport
+
+ align:start position:0%
+formal way what happens with airport
+ 
+
+ align:start position:0%
+formal way what happens with airport
+travel why does it seem so much longer
+
+ align:start position:0%
+travel why does it seem so much longer
+ 
+
+ align:start position:0%
+travel why does it seem so much longer
+on the way there than on the way back
+
+ align:start position:0%
+on the way there than on the way back
+ 
+
+ align:start position:0%
+on the way there than on the way back
+here is the ideal travel experience to
+
+ align:start position:0%
+here is the ideal travel experience to
+ 
+
+ align:start position:0%
+here is the ideal travel experience to
+the airport the distribution of travel
+
+ align:start position:0%
+the airport the distribution of travel
+ 
+
+ align:start position:0%
+the airport the distribution of travel
+times T here's the probability of each
+
+ align:start position:0%
+times T here's the probability of each
+ 
+
+ align:start position:0%
+times T here's the probability of each
+particular travel time p of tea in the
+
+ align:start position:0%
+particular travel time p of tea in the
+ 
+
+ align:start position:0%
+particular travel time p of tea in the
+ideal world the travel time would be
+
+ align:start position:0%
+ideal world the travel time would be
+ 
+
+ align:start position:0%
+ideal world the travel time would be
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+predictable let's say it would be almost
+
+ align:start position:0%
+predictable let's say it would be almost
+ 
+
+ align:start position:0%
+predictable let's say it would be almost
+always 20 minutes in that case you would
+
+ align:start position:0%
+always 20 minutes in that case you would
+ 
+
+ align:start position:0%
+always 20 minutes in that case you would
+allow 20 minutes to get to the airport
+
+ align:start position:0%
+allow 20 minutes to get to the airport
+ 
+
+ align:start position:0%
+allow 20 minutes to get to the airport
+and you would allow 20 minutes on the
+
+ align:start position:0%
+and you would allow 20 minutes on the
+ 
+
+ align:start position:0%
+and you would allow 20 minutes on the
+way back going there and coming back
+
+ align:start position:0%
+way back going there and coming back
+ 
+
+ align:start position:0%
+way back going there and coming back
+would seem the same but here's what
+
+ align:start position:0%
+would seem the same but here's what
+ 
+
+ align:start position:0%
+would seem the same but here's what
+travel to the airport actually looks
+
+ align:start position:0%
+travel to the airport actually looks
+ 
+
+ align:start position:0%
+travel to the airport actually looks
+like let's say the mean is still the
+
+ align:start position:0%
+like let's say the mean is still the
+ 
+
+ align:start position:0%
+like let's say the mean is still the
+same but the reality is that there's
+
+ align:start position:0%
+same but the reality is that there's
+ 
+
+ align:start position:0%
+same but the reality is that there's
+lots of dispersion and so so the curve
+
+ align:start position:0%
+lots of dispersion and so so the curve
+ 
+
+ align:start position:0%
+lots of dispersion and so so the curve
+actually looks like that sometimes the
+
+ align:start position:0%
+actually looks like that sometimes the
+ 
+
+ align:start position:0%
+actually looks like that sometimes the
+travel time will be 30 minutes sometimes
+
+ align:start position:0%
+travel time will be 30 minutes sometimes
+ 
+
+ align:start position:0%
+travel time will be 30 minutes sometimes
+40 sometimes
+
+ align:start position:0%
+40 sometimes
+ 
+
+ align:start position:0%
+40 sometimes
+10 so now what do you have to do this is
+
+ align:start position:0%
+10 so now what do you have to do this is
+ 
+
+ align:start position:0%
+10 so now what do you have to do this is
+reality on the way home it's no problem
+
+ align:start position:0%
+reality on the way home it's no problem
+ 
+
+ align:start position:0%
+reality on the way home it's no problem
+on average you get home in 20 minutes
+
+ align:start position:0%
+on average you get home in 20 minutes
+ 
+
+ align:start position:0%
+on average you get home in 20 minutes
+you leave whenever you get out of the
+
+ align:start position:0%
+you leave whenever you get out of the
+ 
+
+ align:start position:0%
+you leave whenever you get out of the
+baggage claim and while it's true that
+
+ align:start position:0%
+baggage claim and while it's true that
+ 
+
+ align:start position:0%
+baggage claim and while it's true that
+the trip to the airport follows the same
+
+ align:start position:0%
+the trip to the airport follows the same
+ 
+
+ align:start position:0%
+the trip to the airport follows the same
+distribution the risk to you of not
+
+ align:start position:0%
+distribution the risk to you of not
+ 
+
+ align:start position:0%
+distribution the risk to you of not
+making it to the airport on time is much
+
+ align:start position:0%
+making it to the airport on time is much
+ 
+
+ align:start position:0%
+making it to the airport on time is much
+greater if if you just allow 20 minutes
+
+ align:start position:0%
+greater if if you just allow 20 minutes
+ 
+
+ align:start position:0%
+greater if if you just allow 20 minutes
+yeah sometimes you'll get lucky but
+
+ align:start position:0%
+yeah sometimes you'll get lucky but
+ 
+
+ align:start position:0%
+yeah sometimes you'll get lucky but
+every once in a while it will take you
+
+ align:start position:0%
+every once in a while it will take you
+ 
+
+ align:start position:0%
+every once in a while it will take you
+25 or 30 minutes so what you have to do
+
+ align:start position:0%
+25 or 30 minutes so what you have to do
+ 
+
+ align:start position:0%
+25 or 30 minutes so what you have to do
+is allow more time on the way there so
+
+ align:start position:0%
+is allow more time on the way there so
+ 
+
+ align:start position:0%
+is allow more time on the way there so
+that you don't miss your flight maybe 30
+
+ align:start position:0%
+that you don't miss your flight maybe 30
+ 
+
+ align:start position:0%
+that you don't miss your flight maybe 30
+minutes maybe even 40 minutes it all
+
+ align:start position:0%
+minutes maybe even 40 minutes it all
+ 
+
+ align:start position:0%
+minutes maybe even 40 minutes it all
+depends on the dispersion or standard
+
+ align:start position:0%
+depends on the dispersion or standard
+ 
+
+ align:start position:0%
+depends on the dispersion or standard
+deviation of the Distribution on the way
+
+ align:start position:0%
+deviation of the Distribution on the way
+ 
+
+ align:start position:0%
+deviation of the Distribution on the way
+to the airport you are much more aware
+
+ align:start position:0%
+to the airport you are much more aware
+ 
+
+ align:start position:0%
+to the airport you are much more aware
+of the distribution if you will than you
+
+ align:start position:0%
+of the distribution if you will than you
+ 
+
+ align:start position:0%
+of the distribution if you will than you
+are on the way back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this video we saw how to calculate
+
+ align:start position:0%
+in this video we saw how to calculate
+ 
+
+ align:start position:0%
+in this video we saw how to calculate
+the moments of a distribution and how
+
+ align:start position:0%
+the moments of a distribution and how
+ 
+
+ align:start position:0%
+the moments of a distribution and how
+these moments can help us quickly
+
+ align:start position:0%
+these moments can help us quickly
+ 
+
+ align:start position:0%
+these moments can help us quickly
+summarize the
+
+ align:start position:0%
+summarize the
+ 
+
+ align:start position:0%
+summarize the
+distribution like life when something is
+
+ align:start position:0%
+distribution like life when something is
+ 
+
+ align:start position:0%
+distribution like life when something is
+complicated simplify it grasp it and
+
+ align:start position:0%
+complicated simplify it grasp it and
+ 
+
+ align:start position:0%
+complicated simplify it grasp it and
+understand it by appreciating its
+
+ align:start position:0%
+understand it by appreciating its
+ 
+
+ align:start position:0%
+understand it by appreciating its
+moments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/gMTiAeE0NCw.txt b/gMTiAeE0NCw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91fe72d53e91c496d4c764a26cad540458b39b71
--- /dev/null
+++ b/gMTiAeE0NCw.txt
@@ -0,0 +1,2455 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So by now you have
+seen pretty much every
+
+possible trick there is in
+basic probability theory,
+
+about how to calculate
+distributions, and so on.
+
+You have the basic tools to
+do pretty much anything.
+
+So what's coming after this?
+
+Well, probability is useful for
+developing the science of
+
+inference, and this is a subject
+to which we're going
+
+to come back at the end
+of the semester.
+
+Another chapter, which is what
+we will be doing over the next
+
+few weeks, is to deal with
+phenomena that evolve in time.
+
+So so-called random processes
+or stochastic processes.
+
+So what is this about?
+
+So in the real world, you don't
+just throw two random
+
+variables and go home.
+
+Rather the world goes on.
+
+So you generate the random
+variable, then you get more
+
+random variables, and things
+evolve in time.
+
+And random processes are
+supposed to be models that
+
+capture the evolution of random
+phenomena over time.
+
+So that's what we
+will be doing.
+
+Now when we have evolution in
+time, mathematically speaking,
+
+you can use discrete time
+or continuous time.
+
+Of course, discrete
+time is easier.
+
+And that's where we're
+going to start from.
+
+And we're going to start from
+the easiest, simplest random
+
+process, which is the so-called
+Bernoulli process,
+
+which is nothing but just a
+sequence of coin flips.
+
+You keep flipping a coin
+and keep going forever.
+
+That's what the Bernoulli
+process is.
+
+So in some sense it's something
+that you have
+
+already seen.
+
+But we're going to introduce a
+few additional ideas here that
+
+will be useful and relevant as
+we go along and we move on to
+
+continuous time processes.
+
+So we're going to define the
+Bernoulli process, talk about
+
+some basic properties that the
+process has, and derive a few
+
+formulas, and exploit the
+special structure that it has
+
+to do a few quite interesting
+things.
+
+By the way, where does the
+word Bernoulli come from?
+
+Well the Bernoulli's were a
+family of mathematicians,
+
+Swiss mathematicians and
+scientists around the 1700s.
+
+There were so many of
+them that actually--
+
+and some of them had the
+same first name--
+
+historians even have difficulty
+of figuring out who
+
+exactly did what.
+
+But in any case, you can imagine
+that at the dinner
+
+table they were probably
+flipping coins and doing
+
+Bernoulli trials.
+
+So maybe that was
+their pass-time.
+
+OK.
+
+So what is the Bernoulli
+process?
+
+The Bernoulli process is nothing
+but a sequence of
+
+independent Bernoulli
+trials that you can
+
+think of as coin flips.
+
+So you can think the result
+of each trial
+
+being heads or tails.
+
+It's a little more convenient
+maybe to talk about successes
+
+and failures instead
+of heads or tails.
+
+Or if you wish numerical values,
+to use a 1 for a
+
+success and 0 for a failure.
+
+So the model is that each one
+of these trials has the same
+
+probability of success, p.
+
+And the other assumption is
+that these trials are
+
+statistically independent
+of each other.
+
+So what could be some examples
+of Bernoulli trials?
+
+You buy a lottery ticket every
+week and you win or lose.
+
+Presumably, these are
+independent of each other.
+
+And if it's the same kind of
+lottery, the probability of
+
+winning should be the same
+during every week.
+
+Maybe you want to model
+the financial markets.
+
+And a crude model could be that
+on any given day the Dow
+
+Jones is going to go up
+or down with a certain
+
+probability.
+
+Well that probability must be
+somewhere around 0.5, or so.
+
+This is a crude model of
+financial markets.
+
+You say, probably there
+is more into them.
+
+Life is not that simple.
+
+But actually it's a pretty
+reasonable model.
+
+It takes quite a bit of work
+to come up with more
+
+sophisticated models that can
+do better predictions than
+
+just pure heads and tails.
+
+Now more interesting, perhaps
+to the examples we will be
+
+dealing with in this class--
+
+a Bernoulli process is a good
+model for streams of arrivals
+
+of any kind to a facility.
+
+So it could be a bank, and
+you are sitting at
+
+the door of the bank.
+
+And at every second, you check
+whether a customer came in
+
+during that second or not.
+
+Or you can think about arrivals
+of jobs to a server.
+
+Or any other kind of requests
+to a service system.
+
+So requests, or jobs, arrive
+at random times.
+
+You split the time
+into time slots.
+
+And during each time slot
+something comes or something
+
+does not come.
+
+And for many applications, it's
+a reasonable assumption
+
+to make that arrivals on any
+given slot are independent of
+
+arrivals in any other
+time slot.
+
+So each time slot can be viewed
+as a trial, where
+
+either something comes
+or doesn't come.
+
+And different trials are
+independent of each other.
+
+Now there's two assumptions
+that we're making here.
+
+One is the independence
+assumption.
+
+The other is that this number,
+p, probability
+
+of success, is constant.
+
+Now if you think about the bank
+example, if you stand
+
+outside the bank at 9:30 in
+the morning, you'll see
+
+arrivals happening at
+a certain rate.
+
+If you stand outside the bank
+at 12:00 noon, probably
+
+arrivals are more frequent.
+
+Which means that the given
+time slot has a higher
+
+probability of seeing an arrival
+around noon time.
+
+This means that the assumption
+of a constant p is probably
+
+not correct in that setting,
+if you're talking
+
+about the whole day.
+
+So the probability of successes
+or arrivals in the
+
+morning is going to be smaller
+than what it would be at noon.
+
+But if you're talking about a
+time period, let's say 10:00
+
+to 10:15, probably all slots
+have the same probability of
+
+seeing an arrival and it's
+a good approximation.
+
+So we're going to stick with
+the assumption that p is
+
+constant, doesn't change
+with time.
+
+Now that we have our model
+what do we do with it?
+
+Well, we start talking about
+the statistical properties
+
+that it has.
+
+And here there's two slightly
+different perspectives of
+
+thinking about what a
+random process is.
+
+The simplest version is to think
+about the random process
+
+as being just a sequence
+of random variables.
+
+We know what random
+variables are.
+
+We know what multiple random
+variables are.
+
+So it's just an experiment that
+has associated with it a
+
+bunch of random variables.
+
+So once you have random
+variables, what do you do
+
+instinctively?
+
+You talk about the
+distribution of
+
+these random variables.
+
+We already specified for the
+Bernoulli process that each Xi
+
+is a Bernoulli random variable,
+with probability of
+
+success equal to p.
+
+That specifies the distribution
+of the random
+
+variable X, or Xt, for
+general time t.
+
+Then you can calculate
+expected values and
+
+variances, and so on.
+
+So the expected value is, with
+probability p, you get a 1.
+
+And with probability
+1 - p, you get a 0.
+
+So the expected value
+is equal to p.
+
+And then we have seen before a
+formula for the variance of
+
+the Bernoulli random variable,
+which is p times 1-p.
+
+So this way we basically now
+have all the statistical
+
+properties of the random
+variable Xt, and we have those
+
+properties for every t.
+
+Is this enough of a
+probabilistic description of a
+
+random process?
+
+Well, no.
+
+You need to know how the
+different random variables
+
+relate to each other.
+
+If you're talking about a
+general random process, you
+
+would like to know things.
+
+For example, the joint
+distribution of X2,
+
+with X5, and X7.
+
+For example, that might be
+something that you're
+
+interested in.
+
+And the way you specify it is
+by giving the joint PMF of
+
+these random variables.
+
+And you have to do that for
+every collection, or any
+
+subset, of the random
+variables you
+
+are interested in.
+
+So to have a complete
+description of a random
+
+processes, you need to specify
+for me all the possible joint
+
+distributions.
+
+And once you have all the
+possible joint distributions,
+
+then you can answer, in
+principle, any questions you
+
+might be interested in.
+
+How did we get around
+this issue for
+
+the Bernoulli process?
+
+I didn't give you the joint
+distributions explicitly.
+
+But I gave them to
+you implicitly.
+
+And this is because I told you
+that the different random
+
+variables are independent
+of each other.
+
+So at least for the Bernoulli
+process, where we make the
+
+independence assumption, we know
+that this is going to be
+
+the product of the PMFs.
+
+And since I have told you what
+the individual PMFs are, this
+
+means that you automatically
+know all the joint PMFs.
+
+And we can go to business
+based on that.
+
+All right.
+
+So this is one view of what a
+random process is, just a
+
+collection of random
+variables.
+
+There's another view that's a
+little more abstract, which is
+
+the following.
+
+The entire process is to be
+thought of as one long
+
+experiment.
+
+So we go back to the
+chapter one view of
+
+probabilistic models.
+
+So there must be a sample
+space involved.
+
+What is the sample space?
+
+If I do my infinite, long
+experiment of flipping an
+
+infinite number of coins,
+a typical outcome of the
+
+experiment would be a sequence
+of 0's and 1's.
+
+So this could be one possible
+outcome of the experiment,
+
+just an infinite sequence
+of 0's and 1's.
+
+My sample space is the
+set of all possible
+
+outcomes of this kind.
+
+Here's another possible
+outcome, and so on.
+
+And essentially we're dealing
+with a sample space, which is
+
+the space of all sequences
+of 0's and 1's.
+
+And we're making some sort of
+probabilistic assumption about
+
+what may happen in
+that experiment.
+
+So one particular sequence that
+we may be interested in
+
+is the sequence of obtaining
+all 1's.
+
+So this is the sequence that
+gives you 1's forever.
+
+Once you take the point of view
+that this is our sample
+
+space-- its the space of all
+infinite sequences--
+
+you can start asking questions
+that have to do
+
+with infinite sequences.
+
+Such as the question, what's the
+probability of obtaining
+
+the infinite sequence that
+consists of all 1's?
+
+So what is this probability?
+
+Let's see how we could
+calculate it.
+
+So the probability of obtaining
+all 1's is certainly
+
+less than or equal to the
+probability of obtaining 1's,
+
+just in the first 10 tosses.
+
+OK.
+
+This is asking for more things
+to happen than this.
+
+If this event is true, then
+this is also true.
+
+Therefore the probability of
+this is smaller than the
+
+probability of that.
+
+This event is contained
+in that event.
+
+This implies this.
+
+So we have this inequality.
+
+Now what's the probability of
+obtaining 1's in 10 trials?
+
+This is just p to the 10th
+because the trials are
+
+independent.
+
+Now of course there's no reason
+why I chose 10 here.
+
+The same argument goes
+through if I use an
+
+arbitrary number, k.
+
+And this has to be
+true for all k.
+
+So this probability is less
+than p to the k, no matter
+
+what k I choose.
+
+Therefore, this must be less
+than or equal to the limit of
+
+this, as k goes to infinity.
+
+This is smaller than
+that for all k's.
+
+Let k go to infinity, take k
+arbitrarily large, this number
+
+is going to become arbitrarily
+small.
+
+It goes to 0.
+
+And that proves that the
+probability of an infinite
+
+sequence of 1's is equal to 0.
+
+So take limits of both sides.
+
+It's going to be less than
+or equal to the limit--
+
+I shouldn't take a limit here.
+
+The probability is less than or
+equal to the limit of p to
+
+the k, as k goes to infinity,
+which is 0.
+
+So this proves in a formal way
+that the sequence of all 1's
+
+has 0 probability.
+
+If you have an infinite number
+of coin flips, what's the
+
+probability that all of the coin
+flips result in heads?
+
+The probability of this
+happening is equal to zero.
+
+So this particular sequence
+has 0 probability.
+
+Of course, I'm assuming here
+that p is less than 1,
+
+strictly less than 1.
+
+Now the interesting thing is
+that if you look at any other
+
+infinite sequence, and you try
+to calculate the probability
+
+of that infinite sequence, you
+would get a product of (1-p)
+
+times 1, 1-p times 1, 1-p,
+times p times p,
+
+times 1-p and so on.
+
+You keep multiplying numbers
+that are less than 1.
+
+Again, I'm making the
+assumption that p is
+
+between 0 and 1.
+
+So 1-p is less than 1,
+p is less than 1.
+
+You keep multiplying numbers
+less than 1.
+
+If you multiply infinitely
+many such numbers, the
+
+infinite product becomes 0.
+
+So any individual sequence in
+this sample space actually has
+
+0 probability.
+
+And that is a little bit
+counter-intuitive perhaps.
+
+But the situation is more like
+the situation where we deal
+
+with continuous random
+variables.
+
+So if you could draw a
+continuous random variable,
+
+every possible outcome
+has 0 probability.
+
+And that's fine.
+
+But all of the outcomes
+collectively still have
+
+positive probability.
+
+So the situation here is
+very much similar.
+
+So the space of infinite
+sequences of 0's and 1's, that
+
+sample space is very much
+like a continuous space.
+
+If you want to push that analogy
+further, you could
+
+think of this as the expansion
+of a real number.
+
+Or the representation of a
+real number in binary.
+
+Take a real number, write it
+down in binary, you are going
+
+to get an infinite sequence
+of 0's and 1's.
+
+So you can think of each
+possible outcome here
+
+essentially as a real number.
+
+So the experiment of doing an
+infinite number of coin flips
+
+is sort of similar to the
+experiment of picking a real
+
+number at random.
+
+When you pick real numbers at
+random, any particular real
+
+number has 0 probability.
+
+So similarly here, any
+particular infinite sequence
+
+has 0 probability.
+
+So if we were to push that
+analogy further, there would
+
+be a few interesting
+things we could do.
+
+But we will not push
+it further.
+
+This is just to give you an
+indication that things can get
+
+pretty subtle and interesting
+once you start talking about
+
+random processes that involve
+forever, over the infinite
+
+time horizon.
+
+So things get interesting even
+in this context of the simple
+
+Bernoulli process.
+
+Just to give you a preview of
+what's coming further, today
+
+we're going to talk just about
+the Bernoulli process.
+
+And you should make sure before
+the next lecture--
+
+I guess between the exam
+and the next lecture--
+
+to understand everything
+we do today.
+
+Because next time we're going
+to do everything once more,
+
+but in continuous time.
+
+And in continuous time, things
+become more subtle and a
+
+little more difficult.
+
+But we are going to build on
+what we understand for the
+
+discrete time case.
+
+Now both the Bernoulli process
+and its continuous time analog
+
+has a property that we call
+memorylessness, whatever
+
+happened in the past does
+not affect the future.
+
+Later on in this class we're
+going to talk about more
+
+general random processes,
+so-called Markov chains, in
+
+which there are certain
+dependences across time.
+
+That is, what has happened in
+the past will have some
+
+bearing on what may happen
+in the future.
+
+So it's like having coin flips
+where the outcome of the next
+
+coin flip has some dependence
+on the previous coin flip.
+
+And that gives us a richer
+class of models.
+
+And once we get there,
+essentially we will have
+
+covered all possible models.
+
+So for random processes that
+are practically useful and
+
+which you can manipulate, Markov
+chains are a pretty
+
+general class of models.
+
+And almost any real world
+phenomenon that evolves in
+
+time can be approximately
+modeled using Markov chains.
+
+So even though this is a first
+class in probability, we will
+
+get pretty far in
+that direction.
+
+All right.
+
+So now let's start doing a few
+calculations and answer some
+
+questions about the
+Bernoulli process.
+
+So again, the best way to think
+in terms of models that
+
+correspond to the Bernoulli
+process is in terms of
+
+arrivals of jobs
+to a facility.
+
+And there's two types of
+questions that you can ask.
+
+In a given amount of time,
+how many jobs arrived?
+
+Or conversely, for a given
+number of jobs, how much time
+
+did it take for them
+to arrive?
+
+So we're going to deal with
+these two questions, starting
+
+with the first.
+
+For a given amount of time--
+
+that is, for a given number
+of time periods--
+
+how many arrivals have we had?
+
+How many of those Xi's
+happen to be 1's?
+
+We fix the number
+of time slots--
+
+let's say n time slots--
+
+and you measure the number
+of successes.
+
+Well this is a very familiar
+random variable.
+
+The number of successes in n
+independent coin flips--
+
+or in n independent trials--
+
+is a binomial random variable.
+
+So we know its distribution is
+given by the binomial PMF, and
+
+it's just this, for k going
+from 0 up to n.
+
+And we know everything by now
+about this random variable.
+
+We know its expected
+value is n times p.
+
+And we know the variance, which
+is n times p, times 1-p.
+
+So there's nothing new here.
+
+That's the easy part.
+
+So now let's look at the
+opposite kind of question.
+
+Instead of fixing the time and
+asking how many arrivals, now
+
+let us fix the number of
+arrivals and ask how much time
+
+did it take.
+
+And let's start with the time
+until the first arrival.
+
+So the process starts.
+
+We got our slots.
+
+And we see, perhaps, a sequence
+of 0's and then at
+
+some point we get a 1.
+
+The number of trials it took
+until we get a 1, we're going
+
+to call it T1.
+
+And it's the time of
+the first arrival.
+
+OK.
+
+What is the probability
+distribution of T1?
+
+What kind of random
+variable is it?
+
+We've gone through
+this before.
+
+The event that the first arrival
+happens at time little
+
+t is the event that the first
+t-1 trials were failures, and
+
+the trial number t happens
+to be a success.
+
+So for the first success to
+happen at time slot number 5,
+
+it means that the first 4 slots
+had failures and the 5th
+
+slot had a success.
+
+So the probability of this
+happening is the probability
+
+of having failures in the first
+t -1 trials, and having
+
+a success at trial number 1.
+
+And this is the formula for
+t equal 1,2, and so on.
+
+So we know what this
+distribution is.
+
+It's the so-called geometric
+distribution.
+
+Let me jump this through
+this for a minute.
+
+In the past, we did calculate
+the expected value of the
+
+geometric distribution,
+and it's 1/p.
+
+Which means that if p is small,
+you expect to take a
+
+long time until the
+first success.
+
+And then there's a formula also
+for the variance of T1,
+
+which we never formally derived
+in class, but it was
+
+in your textbook and it just
+happens to be this.
+
+All right.
+
+So nothing new until
+this point.
+
+Now, let's talk about
+this property, the
+
+memorylessness property.
+
+We kind of touched on this
+property when we discussed--
+
+when we did the derivation
+in class of the
+
+expected value of T1.
+
+Now what is the memoryless
+property?
+
+It's essentially a consequence
+of independence.
+
+If I tell you the results of my
+coin flips up to a certain
+
+time, this, because of
+independence, doesn't give you
+
+any information about the coin
+flips after that time.
+
+So knowing that we had lots of
+0's here does not change what
+
+I believe about the future coin
+flips, because the future
+
+coin flips are going to be just
+independent coin flips
+
+with a given probability,
+p, for obtaining tails.
+
+So this is a statement that I
+made about a specific time.
+
+That is, you do coin flips
+until 12 o'clock.
+
+And then at 12 o'clock,
+you start watching.
+
+No matter what happens before 12
+o'clock, after 12:00, what
+
+you're going to see is just
+a sequence of independent
+
+Bernoulli trials with the
+same probability, p.
+
+Whatever happened in the
+past is irrelevant.
+
+Now instead of talking about
+the fixed time at which you
+
+start watching, let's think
+about a situation where your
+
+sister sits in the next room,
+flips the coins until she
+
+observes the first success,
+and then calls you inside.
+
+And you start watching
+after this time.
+
+What are you're going to see?
+
+Well, you're going to see a coin
+flip with probability p
+
+of success.
+
+You're going to see another
+trial that has probability p
+
+as a success, and these are all
+independent of each other.
+
+So what you're going to see
+starting at that time is going
+
+to be just a sequence of
+independent Bernoulli trials,
+
+as if the process was starting
+at this time.
+
+How long it took for the first
+success to occur doesn't have
+
+any bearing on what is going
+to happen afterwards.
+
+What happens afterwards
+is still a sequence of
+
+independent coin flips.
+
+And this story is actually
+even more general.
+
+So your sister watches the coin
+flips and at some point
+
+tells you, oh, something
+really interesting is
+
+happening here.
+
+I got this string of a
+hundred 1's in a row.
+
+Come and watch.
+
+Now when you go in there and
+you start watching, do you
+
+expect to see something
+unusual?
+
+There were unusual things
+that happened before
+
+you were called in.
+
+Does this means that you're
+going to see unusual things
+
+afterwards?
+
+No.
+
+Afterwards, what you're going
+to see is, again, just a
+
+sequence of independent
+coin flips.
+
+The fact that some strange
+things happened before doesn't
+
+have any bearing as to what is
+going to happen in the future.
+
+So if the roulettes in the
+casino are properly made, the
+
+fact that there were 3 reds in
+a row doesn't affect the odds
+
+of whether in the next
+roll it's going to
+
+be a red or a black.
+
+So whatever happens in
+the past-- no matter
+
+how unusual it is--
+
+at the time when you're called
+in, what's going to happen in
+
+the future is going to be just
+independent Bernoulli trials,
+
+with the same probability, p.
+
+The only case where this story
+changes is if your sister has
+
+a little bit of foresight.
+
+So your sister can look ahead
+into the future and knows that
+
+the next 10 coin flips will be
+heads, and calls you before
+
+those 10 flips will happen.
+
+If she calls you in, then what
+are you going to see?
+
+You're not going to see
+independent Bernoulli trials,
+
+since she has psychic powers
+and she knows that the next
+
+ones would be 1's.
+
+She called you in and you will
+see a sequence of 1's.
+
+So it's no more independent
+Bernoulli trials.
+
+So what's the subtle
+difference here?
+
+The future is independent from
+the past, provided that the
+
+time that you are called and
+asked to start watching is
+
+determined by someone who
+doesn't have any foresight,
+
+who cannot see the future.
+
+If you are called in, just on
+the basis of what has happened
+
+so far, then you don't have any
+
+information about the future.
+
+And one special case is
+the picture here.
+
+You have your coin flips.
+
+Once you see a one that happens,
+once you see a
+
+success, you are called in.
+
+You are called in on the basis
+of what happened in the past,
+
+but without any foresight.
+
+OK.
+
+And this subtle distinction is
+what's going to make our next
+
+example interesting
+and subtle.
+
+So here's the question.
+
+You buy a lottery ticket every
+day, so we have a Bernoulli
+
+process that's running
+in time.
+
+And you're interested in the
+length of the first string of
+
+losing days.
+
+What does that mean?
+
+So suppose that a typical
+sequence of events
+
+could be this one.
+
+So what are we discussing
+here?
+
+We're looking at the first
+string of losing days, where
+
+losing days means 0's.
+
+So the string of losing days
+is this string here.
+
+Let's call the length of that
+string, L. We're interested in
+
+the random variable, which is
+the length of this interval.
+
+What kind of random
+variable is it?
+
+OK.
+
+Here's one possible way you
+might think about the problem.
+
+OK.
+
+Starting from this time, and
+looking until this time here,
+
+what are we looking at?
+
+We're looking at the time,
+starting from here, until the
+
+first success.
+
+So the past doesn't matter.
+
+Starting from here we
+have coin flips
+
+until the first success.
+
+The time until the
+first success
+
+in a Bernoulli process--
+
+we just discussed that it's a
+geometric random variable.
+
+So your first conjecture would
+be that this random variable
+
+here, which is 1 longer than the
+one we are interested in,
+
+that perhaps is a geometric
+random variable.
+
+And if this were so, then you
+could say that the random
+
+variable, L, is a geometric,
+minus 1.
+
+Can that be the correct
+answer?
+
+A geometric random variable,
+what values does it take?
+
+It takes values 1,
+2, 3, and so on.
+
+1 minus a geometric would
+take values from 0,
+
+1, 2, and so on.
+
+Can the random variable
+L be 0?
+
+No.
+
+The random variable L
+is the length of a
+
+string of losing days.
+
+So the shortest that L could
+be, would be just 1.
+
+If you get just one losing day
+and then you start winning, L
+
+would be equal to 1.
+
+So L cannot be 0 by definition,
+which means that L
+
++ 1 cannot be 1,
+by definition.
+
+But if L +1 were geometric,
+it could be equal to 1.
+
+Therefore this random
+variable, L
+
++ 1, is not a geometric.
+
+OK.
+
+Why is it not geometric?
+
+I started watching
+at this time.
+
+From this time until the first
+success, that should be a
+
+geometric random variable.
+
+Where's the catch?
+
+If I'm asked to start watching
+at this time, it's because my
+
+sister knows that the next
+one was a failure.
+
+This is the time where the
+string of failures starts.
+
+In order to know that they
+should start watching here,
+
+it's the same as if
+I'm told that the
+
+next one is a failure.
+
+So to be asked to start watching
+at this time requires
+
+that someone looked
+in the future.
+
+And in that case, it's no longer
+true that these will be
+
+independent Bernoulli trials.
+
+In fact, they're not.
+
+If you start watching here,
+you're certain that the next
+
+one is a failure.
+
+The next one is not an
+independent Bernoulli trial.
+
+That's why the argument that
+would claim that this L + 1 is
+
+geometric would be incorrect.
+
+So if this is not the correct
+answer, which
+
+is the correct answer?
+
+The correct answer
+goes as follows.
+
+Your sister is watching.
+
+Your sister sees the first
+failure, and then tells you,
+
+OK, the failures--
+
+or losing days--
+
+have started.
+
+Come in and watch.
+
+So you start to watching
+at this time.
+
+And you start watching until
+the first success comes.
+
+This will be a geometric
+random variable.
+
+So from here to here, this
+will be geometric.
+
+So things happen.
+
+You are asked to
+start watching.
+
+After you start watching, the
+future is just a sequence of
+
+independent Bernoulli trials.
+
+And the time until the first
+failure occurs, this is going
+
+to be a geometric random
+variable with parameter p.
+
+And then you notice that the
+interval of interest is
+
+exactly the same as the length
+of this interval.
+
+This starts one time step
+later, and ends
+
+one time step later.
+
+So conclusion is that L is
+actually geometric, with
+
+parameter p.
+
+OK, it looks like I'm
+missing one slide.
+
+Can I cheat a little
+from here?
+
+OK.
+
+So now that we dealt with the
+time until the first arrival,
+
+we can start talking about
+the time until the second
+
+arrival, and so on.
+
+How do we define these?
+
+After the first arrival happens,
+we're going to have a
+
+sequence of time slots with no
+arrivals, and then the next
+
+arrival is going to happen.
+
+So we call this time
+that elapses--
+
+or number of time slots after
+the first arrival
+
+until the next one--
+
+we call it T2.
+
+This is the second inter-arrival
+time, that is,
+
+time between arrivals.
+
+Once this arrival has happened,
+then we wait and see
+
+how many more it takes until
+the third arrival.
+
+And we call this
+time here, T3.
+
+We're interested in the time of
+the k-th arrival, which is
+
+going to be just the
+sum of the first k
+
+inter-arrival times.
+
+So for example, let's say Y3
+is the time that the third
+
+arrival comes.
+
+Y3 is just the sum of T1,
+plus T2, plus T3.
+
+So we're interested in this
+random variable, Y3, and it's
+
+the sum of inter-arrival
+times.
+
+To understand what kind of
+random variable it is, I guess
+
+we should understand what kind
+of random variables these are
+
+going to be.
+
+So what kind of random
+variable is T2?
+
+Your sister is doing her coin
+flips until a success is
+
+observed for the first time.
+
+Based on that information about
+what has happened so
+
+far, you are called
+into the room.
+
+And you start watching until a
+success is observed again.
+
+So after you start watching,
+what you have is just a
+
+sequence of independent
+Bernoulli trials.
+
+So each one of these
+has probability
+
+p of being a success.
+
+The time it's going to take
+until the first success, this
+
+number, T2, is going to be again
+just another geometric
+
+random variable.
+
+It's as if the process
+just started.
+
+After you are called into the
+room, you have no foresight,
+
+you don't have any information
+about the future, other than
+
+the fact that these
+are going to be
+
+independent Bernoulli trials.
+
+So T2 itself is going to be
+geometric with the same
+
+parameter p.
+
+And then you can continue the
+arguments and argue that T3 is
+
+also geometric with the
+same parameter p.
+
+Furthermore, whatever happened,
+how long it took
+
+until you were called in, it
+doesn't change the statistics
+
+about what's going to happen
+in the future.
+
+So whatever happens
+in the future is
+
+independent from the past.
+
+So T1, T2, and T3 are
+independent random variables.
+
+So conclusion is that the time
+until the third arrival is the
+
+sum of 3 independent geometric
+random variables, with the
+
+same parameter.
+
+And this is true
+more generally.
+
+The time until the k-th arrival
+is going to be the sum
+
+of k independent random
+variables.
+
+So in general, Yk is going to be
+T1 plus Tk, where the Ti's
+
+are geometric, with the same
+parameter p, and independent.
+
+So now what's more natural
+than trying to find the
+
+distribution of the random
+variable Yk?
+
+How can we find it?
+
+So I fixed k for you.
+
+Let's say k is 100.
+
+I'm interested in how
+long it takes until
+
+100 customers arrive.
+
+How can we find the distribution
+of Yk?
+
+Well one way of doing
+it is to use this
+
+lovely convolution formula.
+
+Take a geometric, convolve it
+with another geometric, you
+
+get something.
+
+Take that something that you
+got, convolve it with a
+
+geometric once more, do this 99
+times, and this gives you
+
+the distribution of Yk.
+
+So that's definitely doable,
+and it's extremely tedious.
+
+Let's try to find
+the distribution
+
+of Yk using a shortcut.
+
+So the probability that
+Yk is equal to t.
+
+So we're trying to find
+the PMF of Yk.
+
+k has been fixed for us.
+
+And we want to calculate this
+probability for the various
+
+values of t, because this
+is going to give
+
+us the PMF of Yk.
+
+OK.
+
+What is this event?
+
+What does it take for the k-th
+arrival to be at time t?
+
+For that to happen, we
+need two things.
+
+In the first t -1 slots,
+how many arrivals
+
+should we have gotten?
+
+k - 1.
+
+And then in the last slot, we
+get one more arrival, and
+
+that's the k-th one.
+
+So this is the probability that
+we have k - 1 arrivals in
+
+the time interval
+from 1 up to t.
+
+And then, an arrival
+at time t.
+
+That's the only way that it
+can happen, that the k-th
+
+arrival happens at time t.
+
+We need to have an arrival
+at time t.
+
+And before that time,
+we need to have
+
+exactly k - 1 arrivals.
+
+Now this is an event
+that refers--
+
+t-1.
+
+In the previous time slots we
+had exactly k -1 arrivals.
+
+And then at the last time slot
+we get one more arrival.
+
+Now the interesting thing is
+that this event here has to do
+
+with what happened from time
+1 up to time t -1.
+
+This event has to do with
+what happened at time t.
+
+Different time slots are
+independent of each other.
+
+So this event and that event
+are independent.
+
+So this means that we can
+multiply their probabilities.
+
+So take the probability
+of this.
+
+What is that?
+
+Well probability of having a
+certain number of arrivals in
+
+a certain number of time slots,
+these are just the
+
+binomial probabilities.
+
+So this is, out of t - 1 slots,
+to get exactly k - 1
+
+arrivals, p to the k-1, (1-p)
+to the t-1 - (k-1),
+
+this gives us t-k.
+
+And then we multiply with this
+probability, the probability
+
+of an arrival, at time
+t is equal to p.
+
+And so this is the formula for
+the PMF of the number--
+
+of the time it takes until
+the k-th arrival happens.
+
+Does it agree with the formula
+in your handout?
+
+Or its not there?
+
+It's not there.
+
+OK.
+
+Yeah.
+
+OK.
+
+So that's the formula and it is
+true for what values of t?
+
+[INAUDIBLE].
+
+It takes at least k time slots
+in order to get k arrivals, so
+
+this formula should be
+true for k larger
+
+than or equal to t.
+
+For t larger than
+or equal to k.
+
+All right.
+
+So this gives us the PMF of
+the random variable Yk.
+
+Of course, we may also be
+interested in the mean and
+
+variance of Yk.
+
+But this is a lot easier.
+
+Since Yk is the sum of
+independent random variables,
+
+the expected value of Yk is
+going to be just k times the
+
+expected value of
+your typical t.
+
+So the expected value of Yk is
+going to be just k times 1/p,
+
+which is the mean of
+the geometric.
+
+And similarly for the variance,
+it's going to be k
+
+times the variance
+of a geometric.
+
+So we have everything there is
+to know about the distribution
+
+of how long it takes until
+the first arrival comes.
+
+OK.
+
+Finally, let's do a few
+more things about
+
+the Bernoulli process.
+
+It's interesting to talk about
+several processes at the time.
+
+So in the situation here of
+splitting a Bernoulli process
+
+is where you have arrivals
+that come to a server.
+
+And that's a picture of which
+slots get arrivals.
+
+But actually maybe you
+have two servers.
+
+And whenever an arrival comes to
+the system, you flip a coin
+
+and with some probability, q,
+you send it to one server.
+
+And with probability 1-q, you
+send it to another server.
+
+So there is a single
+arrival stream, but
+
+two possible servers.
+
+And whenever there's an arrival,
+you either send it
+
+here or you send it there.
+
+And each time you decide where
+you send it by flipping an
+
+independent coin that
+has its own bias q.
+
+The coin flips that decide
+where do you send it are
+
+assumed to be independent from
+the arrival process itself.
+
+So there's two coin flips
+that are happening.
+
+At each time slot, there's a
+coin flip that decides whether
+
+you have an arrival in this
+process here, and that coin
+
+flip is with parameter p.
+
+And if you have something that
+arrives, you flip another coin
+
+with probabilities q, and 1-q,
+that decides whether you send
+
+it up there or you send
+it down there.
+
+So what kind of arrival process
+does this server see?
+
+At any given time slot, there's
+probability p that
+
+there's an arrival here.
+
+And there's a further
+probability q that this
+
+arrival gets sent up there.
+
+So the probability that this
+server sees an arrival at any
+
+given time is p times q.
+
+So this process here is going to
+be a Bernoulli process, but
+
+with a different parameter,
+p times q.
+
+And this one down here, with the
+same argument, is going to
+
+be Bernoulli with parameter
+p times (1-q).
+
+So by taking a Bernoulli
+stream of arrivals and
+
+splitting it into
+two, you get two
+
+separate Bernoulli processes.
+
+This is going to be a Bernoulli
+process, that's
+
+going to be a Bernoulli
+process.
+
+Well actually, I'm running
+a little too fast.
+
+What does it take to verify that
+it's a Bernoulli process?
+
+At each time slot,
+it's a 0 or 1.
+
+And it's going to be a 1, you're
+going to see an arrival
+
+with probability p times q.
+
+What else do we need to verify,
+to be able to tell--
+
+to say that it's a Bernoulli
+process?
+
+We need to make sure that
+whatever happens in this
+
+process, in different time
+slots, are statistically
+
+independent from each other.
+
+Is that property true?
+
+For example, what happens in
+this time slot whether you got
+
+an arrival or not, is it
+independent from what happened
+
+at that time slot?
+
+The answer is yes for the
+following reason.
+
+What happens in this time slot
+has to do with the coin flip
+
+associated with the original
+process at this time, and the
+
+coin flip that decides
+where to send things.
+
+What happens at that time slot
+has to do with the coin flip
+
+here, and the additional coin
+flip that decides where to
+
+send it if something came.
+
+Now all these coin flips are
+independent of each other.
+
+The coin flips that determine
+whether we have an arrival
+
+here is independent from the
+coin flips that determined
+
+whether we had an
+arrival there.
+
+And you can generalize this
+argument and conclude that,
+
+indeed, every time slot here
+is independent from
+
+any other time slot.
+
+And this does make it
+a Bernoulli process.
+
+And the reason is that, in the
+original process, every time
+
+slot is independent from
+every other time slot.
+
+And the additional assumption
+that the coin flips that we're
+
+using to decide where to send
+things, these are also
+
+independent of each other.
+
+So we're using here the basic
+property that functions of
+
+independent things remain
+independent.
+
+There's a converse
+picture of this.
+
+Instead of taking one stream
+and splitting it into two
+
+streams, you can do
+the opposite.
+
+You could start from two
+streams of arrivals.
+
+Let's say you have arrivals of
+men and you have arrivals of
+
+women, but you don't
+care about gender.
+
+And the only thing you record
+is whether, in a given time
+
+slot, you had an
+arrival or not.
+
+Notice that here we may have
+an arrival of a man and the
+
+arrival of a woman.
+
+We just record it with a 1, by
+saying there was an arrival.
+
+So in the merged process, we're
+not keeping track of how
+
+many arrivals we had total.
+
+We just record whether
+there was an
+
+arrival or not an arrival.
+
+So an arrival gets recorded here
+if, and only if, one or
+
+both of these streams
+had an arrival.
+
+So that we call a merging
+of two Bernoull-- of two
+
+processes, of two arrival
+processes.
+
+So let's make the assumption
+that this arrival process is
+
+independent from that
+arrival process.
+
+So what happens at the
+typical slot here?
+
+I'm going to see an arrival,
+unless none of
+
+these had an arrival.
+
+So the probability of an arrival
+in a typical time slot
+
+is going to be 1 minus the
+probability of no arrival.
+
+And the event of no arrival
+corresponds to the first
+
+process having no arrival,
+and the second
+
+process having no arrival.
+
+So there's no arrival in the
+merged process if, and only
+
+if, there's no arrival in the
+first process and no arrival
+
+in the second process.
+
+We're assuming that the two
+processes are independent and
+
+that's why we can multiply
+probabilities here.
+
+And then you can take this
+formula and it simplifies to p
+
++ q, minus p times q.
+
+So each time slot of the merged
+process has a certain
+
+probability of seeing
+an arrival.
+
+Is the merged process
+a Bernoulli process?
+
+Yes, it is after you verify the
+additional property that
+
+different slots are independent
+of each other.
+
+Why are they independent?
+
+What happens in this slot has to
+do with that slot, and that
+
+slot down here.
+
+These two slots--
+
+so what happens here,
+has to do with what
+
+happens here and there.
+
+What happens in this slot has
+to do with whatever happened
+
+here and there.
+
+Now, whatever happens here and
+there is independent from
+
+whatever happens
+here and there.
+
+Therefore, what happens here
+is independent from what
+
+happens there.
+
+So the independence property
+is preserved.
+
+The different slots of this
+merged process are independent
+
+of each other.
+
+So the merged process is itself
+a Bernoulli process.
+
+So please digest these two
+pictures of merging and
+
+splitting, because we're going
+to revisit them in continuous
+
+time where things are little
+subtler than that.
+
+OK.
+
+Good luck on the exam and
+see you in a week.
\ No newline at end of file
diff --git a/hSRcHTafkjE.txt b/hSRcHTafkjE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4124013c155b841d232de0dd790d80a29632848a
--- /dev/null
+++ b/hSRcHTafkjE.txt
@@ -0,0 +1,1747 @@
+align:start position:0%
+ 
+hi everyone welcome back so today I'd
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+ 
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+like to tackle a problem on pseudo
+
+ align:start position:0%
+like to tackle a problem on pseudo
+ 
+
+ align:start position:0%
+like to tackle a problem on pseudo
+inverses so given a matrix a which is
+
+ align:start position:0%
+inverses so given a matrix a which is
+ 
+
+ align:start position:0%
+inverses so given a matrix a which is
+not square so it's just 1 & 2
+
+ align:start position:0%
+not square so it's just 1 & 2
+ 
+
+ align:start position:0%
+not square so it's just 1 & 2
+first what is it pseudo inverse so a
+
+ align:start position:0%
+first what is it pseudo inverse so a
+ 
+
+ align:start position:0%
+first what is it pseudo inverse so a
+plus I'm using to denote the pseudo
+
+ align:start position:0%
+plus I'm using to denote the pseudo
+ 
+
+ align:start position:0%
+plus I'm using to denote the pseudo
+inverse then secondly compute a plus a
+
+ align:start position:0%
+inverse then secondly compute a plus a
+ 
+
+ align:start position:0%
+inverse then secondly compute a plus a
+and a a plus and then thirdly if X is in
+
+ align:start position:0%
+and a a plus and then thirdly if X is in
+ 
+
+ align:start position:0%
+and a a plus and then thirdly if X is in
+the null space of a what is a plus a
+
+ align:start position:0%
+the null space of a what is a plus a
+ 
+
+ align:start position:0%
+the null space of a what is a plus a
+acting on X and lastly if X is in the
+
+ align:start position:0%
+acting on X and lastly if X is in the
+ 
+
+ align:start position:0%
+acting on X and lastly if X is in the
+column space of a transpose what is a
+
+ align:start position:0%
+column space of a transpose what is a
+ 
+
+ align:start position:0%
+column space of a transpose what is a
+plus ax so I'll let you think about this
+
+ align:start position:0%
+plus ax so I'll let you think about this
+ 
+
+ align:start position:0%
+plus ax so I'll let you think about this
+problem for a bit and I'll be back in a
+
+ align:start position:0%
+problem for a bit and I'll be back in a
+ 
+
+ align:start position:0%
+problem for a bit and I'll be back in a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi everyone welcome back okay so let's
+
+ align:start position:0%
+hi everyone welcome back okay so let's
+ 
+
+ align:start position:0%
+hi everyone welcome back okay so let's
+take a look at this problem now first
+
+ align:start position:0%
+take a look at this problem now first
+ 
+
+ align:start position:0%
+take a look at this problem now first
+off what is the pseudo inverse well
+
+ align:start position:0%
+off what is the pseudo inverse well
+ 
+
+ align:start position:0%
+off what is the pseudo inverse well
+we define the pseudo inverse using the
+
+ align:start position:0%
+we define the pseudo inverse using the
+ 
+
+ align:start position:0%
+we define the pseudo inverse using the
+SVD so in actuality this is nothing new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we note that because a is not square
+
+ align:start position:0%
+now we note that because a is not square
+ 
+
+ align:start position:0%
+now we note that because a is not square
+the regular inverse of a doesn't
+
+ align:start position:0%
+the regular inverse of a doesn't
+ 
+
+ align:start position:0%
+the regular inverse of a doesn't
+necessarily exist however we do know
+
+ align:start position:0%
+necessarily exist however we do know
+ 
+
+ align:start position:0%
+necessarily exist however we do know
+that the SVD exists for every matrix a
+
+ align:start position:0%
+that the SVD exists for every matrix a
+ 
+
+ align:start position:0%
+that the SVD exists for every matrix a
+whether it's rectangular or not or sorry
+
+ align:start position:0%
+whether it's rectangular or not or sorry
+ 
+
+ align:start position:0%
+whether it's rectangular or not or sorry
+whether it's square or not so how do we
+
+ align:start position:0%
+whether it's square or not so how do we
+ 
+
+ align:start position:0%
+whether it's square or not so how do we
+compute the SVD of a matrix well let's
+
+ align:start position:0%
+compute the SVD of a matrix well let's
+ 
+
+ align:start position:0%
+compute the SVD of a matrix well let's
+just recall that the SVD of a matrix has
+
+ align:start position:0%
+just recall that the SVD of a matrix has
+ 
+
+ align:start position:0%
+just recall that the SVD of a matrix has
+the form of u Sigma V transpose where u
+
+ align:start position:0%
+the form of u Sigma V transpose where u
+ 
+
+ align:start position:0%
+the form of u Sigma V transpose where u
+and V are orthogonal matrices and Sigma
+
+ align:start position:0%
+and V are orthogonal matrices and Sigma
+ 
+
+ align:start position:0%
+and V are orthogonal matrices and Sigma
+is a matrix with positive values along
+
+ align:start position:0%
+is a matrix with positive values along
+ 
+
+ align:start position:0%
+is a matrix with positive values along
+the diagonal or a zeroes along the
+
+ align:start position:0%
+the diagonal or a zeroes along the
+ 
+
+ align:start position:0%
+the diagonal or a zeroes along the
+diagonal and let's just take a look at
+
+ align:start position:0%
+diagonal and let's just take a look at
+ 
+
+ align:start position:0%
+diagonal and let's just take a look at
+the dimensions of these matrices for a
+
+ align:start position:0%
+the dimensions of these matrices for a
+ 
+
+ align:start position:0%
+the dimensions of these matrices for a
+second so we know that a is a 1 by 2
+
+ align:start position:0%
+second so we know that a is a 1 by 2
+ 
+
+ align:start position:0%
+second so we know that a is a 1 by 2
+matrix and the way to figure out what
+
+ align:start position:0%
+matrix and the way to figure out what
+ 
+
+ align:start position:0%
+matrix and the way to figure out what
+the dimensions of these matrices are I
+
+ align:start position:0%
+the dimensions of these matrices are I
+ 
+
+ align:start position:0%
+the dimensions of these matrices are I
+usually always start with the center
+
+ align:start position:0%
+usually always start with the center
+ 
+
+ align:start position:0%
+usually always start with the center
+matrix Sigma and Sigma is always going
+
+ align:start position:0%
+matrix Sigma and Sigma is always going
+ 
+
+ align:start position:0%
+matrix Sigma and Sigma is always going
+to have the same dimensions as a so it's
+
+ align:start position:0%
+to have the same dimensions as a so it's
+ 
+
+ align:start position:0%
+to have the same dimensions as a so it's
+going to be a 1 by 2 matrix U and V are
+
+ align:start position:0%
+going to be a 1 by 2 matrix U and V are
+ 
+
+ align:start position:0%
+going to be a 1 by 2 matrix U and V are
+always square matrices so to make this
+
+ align:start position:0%
+always square matrices so to make this
+ 
+
+ align:start position:0%
+always square matrices so to make this
+multiplication work out
+
+ align:start position:0%
+multiplication work out
+ 
+
+ align:start position:0%
+multiplication work out
+we need V to have 2 and because it's
+
+ align:start position:0%
+we need V to have 2 and because it's
+ 
+
+ align:start position:0%
+we need V to have 2 and because it's
+square it has to be 2 by 2 and likewise
+
+ align:start position:0%
+square it has to be 2 by 2 and likewise
+ 
+
+ align:start position:0%
+square it has to be 2 by 2 and likewise
+u has to be 1 by 1 so we now have the
+
+ align:start position:0%
+u has to be 1 by 1 so we now have the
+ 
+
+ align:start position:0%
+u has to be 1 by 1 so we now have the
+dimensions of u Sigma and V and note
+
+ align:start position:0%
+dimensions of u Sigma and V and note
+ 
+
+ align:start position:0%
+dimensions of u Sigma and V and note
+because Sigma herb because use a 1 by 1
+
+ align:start position:0%
+because Sigma herb because use a 1 by 1
+ 
+
+ align:start position:0%
+because Sigma herb because use a 1 by 1
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+the only orthogonal 1 by 1 matrix is
+
+ align:start position:0%
+the only orthogonal 1 by 1 matrix is
+ 
+
+ align:start position:0%
+the only orthogonal 1 by 1 matrix is
+just 1 so u we already know is just
+
+ align:start position:0%
+just 1 so u we already know is just
+ 
+
+ align:start position:0%
+just 1 so u we already know is just
+going to be the matrix the identity
+
+ align:start position:0%
+going to be the matrix the identity
+ 
+
+ align:start position:0%
+going to be the matrix the identity
+matrix which is a 1 by 1 matrix ok now
+
+ align:start position:0%
+matrix which is a 1 by 1 matrix ok now
+ 
+
+ align:start position:0%
+matrix which is a 1 by 1 matrix ok now
+how do we compute V and Sigma well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can take a transpose an a and if we
+
+ align:start position:0%
+we can take a transpose an a and if we
+ 
+
+ align:start position:0%
+we can take a transpose an a and if we
+do that we end up getting the matrix V
+
+ align:start position:0%
+do that we end up getting the matrix V
+ 
+
+ align:start position:0%
+do that we end up getting the matrix V
+Sigma AI transpose Sigma V transpose and
+
+ align:start position:0%
+Sigma AI transpose Sigma V transpose and
+ 
+
+ align:start position:0%
+Sigma AI transpose Sigma V transpose and
+this matrix is going to be a square
+
+ align:start position:0%
+this matrix is going to be a square
+ 
+
+ align:start position:0%
+this matrix is going to be a square
+matrix where the diagonal elements are
+
+ align:start position:0%
+matrix where the diagonal elements are
+ 
+
+ align:start position:0%
+matrix where the diagonal elements are
+squares of the singular values so
+
+ align:start position:0%
+squares of the singular values so
+ 
+
+ align:start position:0%
+squares of the singular values so
+computing V and the values along Sigma
+
+ align:start position:0%
+computing V and the values along Sigma
+ 
+
+ align:start position:0%
+computing V and the values along Sigma
+just boil down to diagonalizing a
+
+ align:start position:0%
+just boil down to diagonalizing a
+ 
+
+ align:start position:0%
+just boil down to diagonalizing a
+transpose a so what is a transpose a
+
+ align:start position:0%
+transpose a so what is a transpose a
+ 
+
+ align:start position:0%
+transpose a so what is a transpose a
+well in our case it's 1/2 times 1/2
+
+ align:start position:0%
+well in our case it's 1/2 times 1/2
+ 
+
+ align:start position:0%
+well in our case it's 1/2 times 1/2
+which gives us 1/2 to 4 and note that
+
+ align:start position:0%
+which gives us 1/2 to 4 and note that
+ 
+
+ align:start position:0%
+which gives us 1/2 to 4 and note that
+the second row is just a constant
+
+ align:start position:0%
+the second row is just a constant
+ 
+
+ align:start position:0%
+the second row is just a constant
+multiple times the first row now what
+
+ align:start position:0%
+multiple times the first row now what
+ 
+
+ align:start position:0%
+multiple times the first row now what
+this means is we have a zero eigen value
+
+ align:start position:0%
+this means is we have a zero eigen value
+ 
+
+ align:start position:0%
+this means is we have a zero eigen value
+so we already know that lambda one is
+
+ align:start position:0%
+so we already know that lambda one is
+ 
+
+ align:start position:0%
+so we already know that lambda one is
+going to be zero so one of the
+
+ align:start position:0%
+going to be zero so one of the
+ 
+
+ align:start position:0%
+going to be zero so one of the
+eigenvalues of this matrix is zero and
+
+ align:start position:0%
+eigenvalues of this matrix is zero and
+ 
+
+ align:start position:0%
+eigenvalues of this matrix is zero and
+of course when we square root it this is
+
+ align:start position:0%
+of course when we square root it this is
+ 
+
+ align:start position:0%
+of course when we square root it this is
+going to give us a singular value Sigma
+
+ align:start position:0%
+going to give us a singular value Sigma
+ 
+
+ align:start position:0%
+going to give us a singular value Sigma
+which is also zero and this this is
+
+ align:start position:0%
+which is also zero and this this is
+ 
+
+ align:start position:0%
+which is also zero and this this is
+generally a case when we have a sigma
+
+ align:start position:0%
+generally a case when we have a sigma
+ 
+
+ align:start position:0%
+generally a case when we have a sigma
+which is not square we typically always
+
+ align:start position:0%
+which is not square we typically always
+ 
+
+ align:start position:0%
+which is not square we typically always
+have zero singular values now to compute
+
+ align:start position:0%
+have zero singular values now to compute
+ 
+
+ align:start position:0%
+have zero singular values now to compute
+the second eigen value well we already
+
+ align:start position:0%
+the second eigen value well we already
+ 
+
+ align:start position:0%
+the second eigen value well we already
+know how to compute the eigenvalues of a
+
+ align:start position:0%
+know how to compute the eigenvalues of a
+ 
+
+ align:start position:0%
+know how to compute the eigenvalues of a
+matrix so I'm just going to tell you
+
+ align:start position:0%
+matrix so I'm just going to tell you
+ 
+
+ align:start position:0%
+matrix so I'm just going to tell you
+what it is the second one is lambdas 5
+
+ align:start position:0%
+what it is the second one is lambdas 5
+ 
+
+ align:start position:0%
+what it is the second one is lambdas 5
+and if we just take a quick look what
+
+ align:start position:0%
+and if we just take a quick look what
+ 
+
+ align:start position:0%
+and if we just take a quick look what
+the corresponding eigenvector is going
+
+ align:start position:0%
+the corresponding eigenvector is going
+ 
+
+ align:start position:0%
+the corresponding eigenvector is going
+to be two lambdas 5 it's going to
+
+ align:start position:0%
+to be two lambdas 5 it's going to
+ 
+
+ align:start position:0%
+to be two lambdas 5 it's going to
+satisfy this equation so we can take the
+
+ align:start position:0%
+satisfy this equation so we can take the
+ 
+
+ align:start position:0%
+satisfy this equation so we can take the
+eigen vector U to be 1 and 2 however
+
+ align:start position:0%
+eigen vector U to be 1 and 2 however
+ 
+
+ align:start position:0%
+eigen vector U to be 1 and 2 however
+remember that when we compute the eigen
+
+ align:start position:0%
+remember that when we compute the eigen
+ 
+
+ align:start position:0%
+remember that when we compute the eigen
+vectors for this orthogonal matrix V
+
+ align:start position:0%
+vectors for this orthogonal matrix V
+ 
+
+ align:start position:0%
+vectors for this orthogonal matrix V
+they always have to have a unit length
+
+ align:start position:0%
+they always have to have a unit length
+ 
+
+ align:start position:0%
+they always have to have a unit length
+and this vector right now it doesn't
+
+ align:start position:0%
+and this vector right now it doesn't
+ 
+
+ align:start position:0%
+and this vector right now it doesn't
+have a unit length we have to divide by
+
+ align:start position:0%
+have a unit length we have to divide by
+ 
+
+ align:start position:0%
+have a unit length we have to divide by
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+length of this vector which in our case
+
+ align:start position:0%
+length of this vector which in our case
+ 
+
+ align:start position:0%
+length of this vector which in our case
+is 1 over root 5 and if I go back to the
+
+ align:start position:0%
+is 1 over root 5 and if I go back to the
+ 
+
+ align:start position:0%
+is 1 over root 5 and if I go back to the
+land equals 0 case but we also have
+
+ align:start position:0%
+land equals 0 case but we also have
+ 
+
+ align:start position:0%
+land equals 0 case but we also have
+another eigenvector which I'll just
+
+ align:start position:0%
+another eigenvector which I'll just
+ 
+
+ align:start position:0%
+another eigenvector which I'll just
+state you can actually compute it quite
+
+ align:start position:0%
+state you can actually compute it quite
+ 
+
+ align:start position:0%
+state you can actually compute it quite
+quickly just by noting that it has to be
+
+ align:start position:0%
+quickly just by noting that it has to be
+ 
+
+ align:start position:0%
+quickly just by noting that it has to be
+orthogonal to this eigenvector 2 and 1
+
+ align:start position:0%
+orthogonal to this eigenvector 2 and 1
+ 
+
+ align:start position:0%
+orthogonal to this eigenvector 2 and 1
+ok so what this means is a has a
+
+ align:start position:0%
+ok so what this means is a has a
+ 
+
+ align:start position:0%
+ok so what this means is a has a
+singular value decomposition which looks
+
+ align:start position:0%
+singular value decomposition which looks
+ 
+
+ align:start position:0%
+singular value decomposition which looks
+like 1 so this is U times Sigma which is
+
+ align:start position:0%
+like 1 so this is U times Sigma which is
+ 
+
+ align:start position:0%
+like 1 so this is U times Sigma which is
+going to be root 5 0 remember that the
+
+ align:start position:0%
+going to be root 5 0 remember that the
+ 
+
+ align:start position:0%
+going to be root 5 0 remember that the
+first Sigma is actually the square root
+
+ align:start position:0%
+first Sigma is actually the square root
+ 
+
+ align:start position:0%
+first Sigma is actually the square root
+of the eigenvalue times a matrix which
+
+ align:start position:0%
+of the eigenvalue times a matrix which
+ 
+
+ align:start position:0%
+of the eigenvalue times a matrix which
+looks like now we have to order the
+
+ align:start position:0%
+looks like now we have to order the
+ 
+
+ align:start position:0%
+looks like now we have to order the
+eigenvalues up in the correct order
+
+ align:start position:0%
+eigenvalues up in the correct order
+ 
+
+ align:start position:0%
+eigenvalues up in the correct order
+because 5 appears in the first column we
+
+ align:start position:0%
+because 5 appears in the first column we
+ 
+
+ align:start position:0%
+because 5 appears in the first column we
+have to take this vector to be in the
+
+ align:start position:0%
+have to take this vector to be in the
+ 
+
+ align:start position:0%
+have to take this vector to be in the
+first column as well so this is 1 over
+
+ align:start position:0%
+first column as well so this is 1 over
+ 
+
+ align:start position:0%
+first column as well so this is 1 over
+root 5 this is 2 over root 5 negative 2
+
+ align:start position:0%
+root 5 this is 2 over root 5 negative 2
+ 
+
+ align:start position:0%
+root 5 this is 2 over root 5 negative 2
+over root 5 and 1 over root 5 and now
+
+ align:start position:0%
+over root 5 and 1 over root 5 and now
+ 
+
+ align:start position:0%
+over root 5 and 1 over root 5 and now
+this is V but the singular value is
+
+ align:start position:0%
+this is V but the singular value is
+ 
+
+ align:start position:0%
+this is V but the singular value is
+featured the singular value
+
+ align:start position:0%
+featured the singular value
+ 
+
+ align:start position:0%
+featured the singular value
+decomposition is defined by a V
+
+ align:start position:0%
+decomposition is defined by a V
+ 
+
+ align:start position:0%
+decomposition is defined by a V
+transpose okay so this gives us a
+
+ align:start position:0%
+transpose okay so this gives us a
+ 
+
+ align:start position:0%
+transpose okay so this gives us a
+representation for a and now once we
+
+ align:start position:0%
+representation for a and now once we
+ 
+
+ align:start position:0%
+representation for a and now once we
+have the SVD of a how do we actually
+
+ align:start position:0%
+have the SVD of a how do we actually
+ 
+
+ align:start position:0%
+have the SVD of a how do we actually
+compute a plus or the pseudo inverse of
+
+ align:start position:0%
+compute a plus or the pseudo inverse of
+ 
+
+ align:start position:0%
+compute a plus or the pseudo inverse of
+a well just note if a was invertible
+
+ align:start position:0%
+a well just note if a was invertible
+ 
+
+ align:start position:0%
+a well just note if a was invertible
+then the inverse of a in terms of the
+
+ align:start position:0%
+then the inverse of a in terms of the
+ 
+
+ align:start position:0%
+then the inverse of a in terms of the
+SVD would be the transpose times the
+
+ align:start position:0%
+SVD would be the transpose times the
+ 
+
+ align:start position:0%
+SVD would be the transpose times the
+inverse of Sigma
+
+ align:start position:0%
+inverse of Sigma
+ 
+
+ align:start position:0%
+inverse of Sigma
+oh sorry this is not V transpose this is
+
+ align:start position:0%
+oh sorry this is not V transpose this is
+ 
+
+ align:start position:0%
+oh sorry this is not V transpose this is
+just V so it'd be V Sigma inverse u
+
+ align:start position:0%
+just V so it'd be V Sigma inverse u
+ 
+
+ align:start position:0%
+just V so it'd be V Sigma inverse u
+transpose and when when a is invertible
+
+ align:start position:0%
+transpose and when when a is invertible
+ 
+
+ align:start position:0%
+transpose and when when a is invertible
+Sigma inverse exists so in our case a
+
+ align:start position:0%
+Sigma inverse exists so in our case a
+ 
+
+ align:start position:0%
+Sigma inverse exists so in our case a
+Sigma inverse doesn't necessarily exist
+
+ align:start position:0%
+Sigma inverse doesn't necessarily exist
+ 
+
+ align:start position:0%
+Sigma inverse doesn't necessarily exist
+because Sigma note this is Sigma Sigma
+
+ align:start position:0%
+because Sigma note this is Sigma Sigma
+ 
+
+ align:start position:0%
+because Sigma note this is Sigma Sigma
+is root 5 and 0 so we have to construct
+
+ align:start position:0%
+is root 5 and 0 so we have to construct
+ 
+
+ align:start position:0%
+is root 5 and 0 so we have to construct
+an a pseudo inverse for Sigma so the way
+
+ align:start position:0%
+an a pseudo inverse for Sigma so the way
+ 
+
+ align:start position:0%
+an a pseudo inverse for Sigma so the way
+that we do that is we take one over each
+
+ align:start position:0%
+that we do that is we take one over each
+ 
+
+ align:start position:0%
+that we do that is we take one over each
+singular value and we take the transpose
+
+ align:start position:0%
+singular value and we take the transpose
+ 
+
+ align:start position:0%
+singular value and we take the transpose
+of Sigma so when a is not invertible we
+
+ align:start position:0%
+of Sigma so when a is not invertible we
+ 
+
+ align:start position:0%
+of Sigma so when a is not invertible we
+can still construct a pseudo inverse by
+
+ align:start position:0%
+can still construct a pseudo inverse by
+ 
+
+ align:start position:0%
+can still construct a pseudo inverse by
+taking V Sigma and approximation for
+
+ align:start position:0%
+taking V Sigma and approximation for
+ 
+
+ align:start position:0%
+taking V Sigma and approximation for
+Sigma inverse which in our case is going
+
+ align:start position:0%
+Sigma inverse which in our case is going
+ 
+
+ align:start position:0%
+Sigma inverse which in our case is going
+to be 1 over the singular value and 0 so
+
+ align:start position:0%
+to be 1 over the singular value and 0 so
+ 
+
+ align:start position:0%
+to be 1 over the singular value and 0 so
+note how where Sigma is invertible we
+
+ align:start position:0%
+note how where Sigma is invertible we
+ 
+
+ align:start position:0%
+note how where Sigma is invertible we
+take the inverse and then we fill in
+
+ align:start position:0%
+take the inverse and then we fill in
+ 
+
+ align:start position:0%
+take the inverse and then we fill in
+zeros in the other areas
+
+ align:start position:0%
+zeros in the other areas
+ 
+
+ align:start position:0%
+zeros in the other areas
+times u transpose and we can work this
+
+ align:start position:0%
+times u transpose and we can work this
+ 
+
+ align:start position:0%
+times u transpose and we can work this
+out we get 1 over root 5 1 minus 2 2 1 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over root 5 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if I multiply things out
+
+ align:start position:0%
+and if I multiply things out
+ 
+
+ align:start position:0%
+and if I multiply things out
+I get 1/5 1 2 okay so this is an
+
+ align:start position:0%
+I get 1/5 1 2 okay so this is an
+ 
+
+ align:start position:0%
+I get 1/5 1 2 okay so this is an
+approximation for a inverse which is the
+
+ align:start position:0%
+approximation for a inverse which is the
+ 
+
+ align:start position:0%
+approximation for a inverse which is the
+pseudo inverse okay so this finishes up
+
+ align:start position:0%
+pseudo inverse okay so this finishes up
+ 
+
+ align:start position:0%
+pseudo inverse okay so this finishes up
+part 1 and I'll start on part 2 in a
+
+ align:start position:0%
+part 1 and I'll start on part 2 in a
+ 
+
+ align:start position:0%
+part 1 and I'll start on part 2 in a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now that we've just computed a
+
+ align:start position:0%
+okay so now that we've just computed a
+ 
+
+ align:start position:0%
+okay so now that we've just computed a
+plus the pseudo inverse of a we're gonna
+
+ align:start position:0%
+plus the pseudo inverse of a we're gonna
+ 
+
+ align:start position:0%
+plus the pseudo inverse of a we're gonna
+investigate some properties of the
+
+ align:start position:0%
+investigate some properties of the
+ 
+
+ align:start position:0%
+investigate some properties of the
+pseudo inverse okay so for part two we
+
+ align:start position:0%
+pseudo inverse okay so for part two we
+ 
+
+ align:start position:0%
+pseudo inverse okay so for part two we
+need to compute a times a plus and a
+
+ align:start position:0%
+need to compute a times a plus and a
+ 
+
+ align:start position:0%
+need to compute a times a plus and a
+plus times a okay so we can just go
+
+ align:start position:0%
+plus times a okay so we can just go
+ 
+
+ align:start position:0%
+plus times a okay so we can just go
+ahead and do this so a a plus can do
+
+ align:start position:0%
+ahead and do this so a a plus can do
+ 
+
+ align:start position:0%
+ahead and do this so a a plus can do
+fairly quickly fifth one two and when we
+
+ align:start position:0%
+fairly quickly fifth one two and when we
+ 
+
+ align:start position:0%
+fairly quickly fifth one two and when we
+multiply it out we get one plus four
+
+ align:start position:0%
+multiply it out we get one plus four
+ 
+
+ align:start position:0%
+multiply it out we get one plus four
+divided by 5 is 1 so we just get the one
+
+ align:start position:0%
+divided by 5 is 1 so we just get the one
+ 
+
+ align:start position:0%
+divided by 5 is 1 so we just get the one
+by one matrix which is 1 the identity
+
+ align:start position:0%
+by one matrix which is 1 the identity
+ 
+
+ align:start position:0%
+by one matrix which is 1 the identity
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+and secondly if we take a plus times a
+
+ align:start position:0%
+and secondly if we take a plus times a
+ 
+
+ align:start position:0%
+and secondly if we take a plus times a
+we're going to get 1/5 1/2 times 1/2 and
+
+ align:start position:0%
+we're going to get 1/5 1/2 times 1/2 and
+ 
+
+ align:start position:0%
+we're going to get 1/5 1/2 times 1/2 and
+we can just fill in this matrix just 1/5
+
+ align:start position:0%
+we can just fill in this matrix just 1/5
+ 
+
+ align:start position:0%
+we can just fill in this matrix just 1/5
+1 2 2 1 ok and this concludes part two
+
+ align:start position:0%
+1 2 2 1 ok and this concludes part two
+ 
+
+ align:start position:0%
+1 2 2 1 ok and this concludes part two
+so now let's take a look at what happens
+
+ align:start position:0%
+so now let's take a look at what happens
+ 
+
+ align:start position:0%
+so now let's take a look at what happens
+when a vector X is in the null space of
+
+ align:start position:0%
+when a vector X is in the null space of
+ 
+
+ align:start position:0%
+when a vector X is in the null space of
+a and then secondly what happens that
+
+ align:start position:0%
+a and then secondly what happens that
+ 
+
+ align:start position:0%
+a and then secondly what happens that
+when X is in the column space of a
+
+ align:start position:0%
+when X is in the column space of a
+ 
+
+ align:start position:0%
+when X is in the column space of a
+transpose so for part three let's assume
+
+ align:start position:0%
+transpose so for part three let's assume
+ 
+
+ align:start position:0%
+transpose so for part three let's assume
+X is in the null space of a well what's
+
+ align:start position:0%
+X is in the null space of a well what's
+ 
+
+ align:start position:0%
+X is in the null space of a well what's
+the null space of a we can quickly check
+
+ align:start position:0%
+the null space of a we can quickly check
+ 
+
+ align:start position:0%
+the null space of a we can quickly check
+that the null space of a is a constant
+
+ align:start position:0%
+that the null space of a is a constant
+ 
+
+ align:start position:0%
+that the null space of a is a constant
+times any vector minus 2 1 okay so
+
+ align:start position:0%
+times any vector minus 2 1 okay so
+ 
+
+ align:start position:0%
+times any vector minus 2 1 okay so
+that's the null space so if X is for
+
+ align:start position:0%
+that's the null space so if X is for
+ 
+
+ align:start position:0%
+that's the null space so if X is for
+example ie if we take X is equal to
+
+ align:start position:0%
+example ie if we take X is equal to
+ 
+
+ align:start position:0%
+example ie if we take X is equal to
+minus 2 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we were to say multiply it by a plus
+
+ align:start position:0%
+and we were to say multiply it by a plus
+ 
+
+ align:start position:0%
+and we were to say multiply it by a plus
+a acting on X we see that we get zero
+
+ align:start position:0%
+a acting on X we see that we get zero
+ 
+
+ align:start position:0%
+a acting on X we see that we get zero
+and this isn't very surprising because
+
+ align:start position:0%
+and this isn't very surprising because
+ 
+
+ align:start position:0%
+and this isn't very surprising because
+well if X is in the null space of a we
+
+ align:start position:0%
+well if X is in the null space of a we
+ 
+
+ align:start position:0%
+well if X is in the null space of a we
+know that a acting on X is going to be
+
+ align:start position:0%
+know that a acting on X is going to be
+ 
+
+ align:start position:0%
+know that a acting on X is going to be
+zero so that no matter what matrix a
+
+ align:start position:0%
+zero so that no matter what matrix a
+ 
+
+ align:start position:0%
+zero so that no matter what matrix a
+plus is when we multiply by zero we'll
+
+ align:start position:0%
+plus is when we multiply by zero we'll
+ 
+
+ align:start position:0%
+plus is when we multiply by zero we'll
+always end up with zero okay and then
+
+ align:start position:0%
+always end up with zero okay and then
+ 
+
+ align:start position:0%
+always end up with zero okay and then
+lastly let's take a look at the column
+
+ align:start position:0%
+lastly let's take a look at the column
+ 
+
+ align:start position:0%
+lastly let's take a look at the column
+space of a transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well a transpose is one two so it's any
+
+ align:start position:0%
+well a transpose is one two so it's any
+ 
+
+ align:start position:0%
+well a transpose is one two so it's any
+constant times the vector one two and
+
+ align:start position:0%
+constant times the vector one two and
+ 
+
+ align:start position:0%
+constant times the vector one two and
+specifically if we were to take say X is
+
+ align:start position:0%
+specifically if we were to take say X is
+ 
+
+ align:start position:0%
+specifically if we were to take say X is
+equal to one two we can work out a plus
+
+ align:start position:0%
+equal to one two we can work out a plus
+ 
+
+ align:start position:0%
+equal to one two we can work out a plus
+a acting on the vector 1 2 so we have
+
+ align:start position:0%
+a acting on the vector 1 2 so we have
+ 
+
+ align:start position:0%
+a acting on the vector 1 2 so we have
+1/5 1 2 2 1
+
+ align:start position:0%
+1/5 1 2 2 1
+ 
+
+ align:start position:0%
+1/5 1 2 2 1
+so recall this is a plus a and if we
+
+ align:start position:0%
+so recall this is a plus a and if we
+ 
+
+ align:start position:0%
+so recall this is a plus a and if we
+multiply it on the vector 1 2 we get 1
+
+ align:start position:0%
+multiply it on the vector 1 2 we get 1
+ 
+
+ align:start position:0%
+multiply it on the vector 1 2 we get 1
+plus 4 is 5 divided by 5 so we get 1 2
+
+ align:start position:0%
+plus 4 is 5 divided by 5 so we get 1 2
+ 
+
+ align:start position:0%
+plus 4 is 5 divided by 5 so we get 1 2
+plus 2 is 4
+
+ align:start position:0%
+plus 2 is 4
+ 
+
+ align:start position:0%
+ 
+oh sorry I copied the matrix down so
+
+ align:start position:0%
+oh sorry I copied the matrix down so
+ 
+
+ align:start position:0%
+oh sorry I copied the matrix down so
+it's 2 plus 8 which is 10 divided by 5
+
+ align:start position:0%
+it's 2 plus 8 which is 10 divided by 5
+ 
+
+ align:start position:0%
+it's 2 plus 8 which is 10 divided by 5
+is 2 and we see that at the end we
+
+ align:start position:0%
+is 2 and we see that at the end we
+ 
+
+ align:start position:0%
+is 2 and we see that at the end we
+recover the vector X so in general if we
+
+ align:start position:0%
+recover the vector X so in general if we
+ 
+
+ align:start position:0%
+recover the vector X so in general if we
+take a plus a acting on X where X is in
+
+ align:start position:0%
+take a plus a acting on X where X is in
+ 
+
+ align:start position:0%
+take a plus a acting on X where X is in
+the column space of a transpose
+
+ align:start position:0%
+the column space of a transpose
+ 
+
+ align:start position:0%
+the column space of a transpose
+we always recover X
+
+ align:start position:0%
+we always recover X
+ 
+
+ align:start position:0%
+we always recover X
+the end of the day so intuitively what
+
+ align:start position:0%
+the end of the day so intuitively what
+ 
+
+ align:start position:0%
+the end of the day so intuitively what
+is this matrix a plus a do well if X is
+
+ align:start position:0%
+is this matrix a plus a do well if X is
+ 
+
+ align:start position:0%
+is this matrix a plus a do well if X is
+in the null space of a it just kills it
+
+ align:start position:0%
+in the null space of a it just kills it
+ 
+
+ align:start position:0%
+in the null space of a it just kills it
+we just get 0 if X is not in the null
+
+ align:start position:0%
+we just get 0 if X is not in the null
+ 
+
+ align:start position:0%
+we just get 0 if X is not in the null
+space of a then we just get X back so
+
+ align:start position:0%
+space of a then we just get X back so
+ 
+
+ align:start position:0%
+space of a then we just get X back so
+it's essentially the identity matrix
+
+ align:start position:0%
+it's essentially the identity matrix
+ 
+
+ align:start position:0%
+it's essentially the identity matrix
+acting on X whenever X is in the column
+
+ align:start position:0%
+acting on X whenever X is in the column
+ 
+
+ align:start position:0%
+acting on X whenever X is in the column
+space of a transpose now specifically if
+
+ align:start position:0%
+space of a transpose now specifically if
+ 
+
+ align:start position:0%
+space of a transpose now specifically if
+a is invertible then a doesn't have a
+
+ align:start position:0%
+a is invertible then a doesn't have a
+ 
+
+ align:start position:0%
+a is invertible then a doesn't have a
+null space so what that means is when a
+
+ align:start position:0%
+null space so what that means is when a
+ 
+
+ align:start position:0%
+null space so what that means is when a
+is invertible a plus a recovers the
+
+ align:start position:0%
+is invertible a plus a recovers the
+ 
+
+ align:start position:0%
+is invertible a plus a recovers the
+identity because when we multiply it on
+
+ align:start position:0%
+identity because when we multiply it on
+ 
+
+ align:start position:0%
+identity because when we multiply it on
+any vector we get that vector back ok so
+
+ align:start position:0%
+any vector we get that vector back ok so
+ 
+
+ align:start position:0%
+any vector we get that vector back ok so
+I'd like to conclude here and I'll see
+
+ align:start position:0%
+I'd like to conclude here and I'll see
+ 
+
+ align:start position:0%
+I'd like to conclude here and I'll see
+you next time
\ No newline at end of file
diff --git a/iTgy87R9yRE.txt b/iTgy87R9yRE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c9aa02f08540122f537f2d7bc5fe0dd002e785d4
--- /dev/null
+++ b/iTgy87R9yRE.txt
@@ -0,0 +1,8896 @@
+align:start position:0%
+ 
+okay what is a bet cell
+
+ align:start position:0%
+okay what is a bet cell
+ 
+
+ align:start position:0%
+okay what is a bet cell
+and where is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a few of you were asking questions about
+
+ align:start position:0%
+a few of you were asking questions about
+ 
+
+ align:start position:0%
+a few of you were asking questions about
+that at the end of the last lecture
+
+ align:start position:0%
+that at the end of the last lecture
+ 
+
+ align:start position:0%
+that at the end of the last lecture
+so i thought i would start with that
+
+ align:start position:0%
+so i thought i would start with that
+ 
+
+ align:start position:0%
+so i thought i would start with that
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what kind of a cell is it
+
+ align:start position:0%
+what kind of a cell is it
+ 
+
+ align:start position:0%
+what kind of a cell is it
+that kind of question in neuroscience
+
+ align:start position:0%
+that kind of question in neuroscience
+ 
+
+ align:start position:0%
+that kind of question in neuroscience
+has several different types of answers
+
+ align:start position:0%
+has several different types of answers
+ 
+
+ align:start position:0%
+has several different types of answers
+first of all it's a neuron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the main cell that communicates in the
+
+ align:start position:0%
+the main cell that communicates in the
+ 
+
+ align:start position:0%
+the main cell that communicates in the
+central nervous system or in the
+
+ align:start position:0%
+central nervous system or in the
+ 
+
+ align:start position:0%
+central nervous system or in the
+peripheral nervous system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+another answer would be it's a
+
+ align:start position:0%
+another answer would be it's a
+ 
+
+ align:start position:0%
+another answer would be it's a
+certain type of neuron it's a pyramidal
+
+ align:start position:0%
+certain type of neuron it's a pyramidal
+ 
+
+ align:start position:0%
+certain type of neuron it's a pyramidal
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+in the neocortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that cells are in the
+
+ align:start position:0%
+that cells are in the
+ 
+
+ align:start position:0%
+that cells are in the
+the major output layer
+
+ align:start position:0%
+the major output layer
+ 
+
+ align:start position:0%
+the major output layer
+that is output
+
+ align:start position:0%
+that is output
+ 
+
+ align:start position:0%
+that is output
+to non-cortical sources so
+
+ align:start position:0%
+to non-cortical sources so
+ 
+
+ align:start position:0%
+to non-cortical sources so
+now you don't i don't know how much you
+
+ align:start position:0%
+now you don't i don't know how much you
+ 
+
+ align:start position:0%
+now you don't i don't know how much you
+know even what neocortex is and what
+
+ align:start position:0%
+know even what neocortex is and what
+ 
+
+ align:start position:0%
+know even what neocortex is and what
+subcortical sources means
+
+ align:start position:0%
+subcortical sources means
+ 
+
+ align:start position:0%
+subcortical sources means
+but you will be learning
+
+ align:start position:0%
+but you will be learning
+ 
+
+ align:start position:0%
+but you will be learning
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+don't worry about it if you don't
+
+ align:start position:0%
+don't worry about it if you don't
+ 
+
+ align:start position:0%
+don't worry about it if you don't
+understand something when i first
+
+ align:start position:0%
+understand something when i first
+ 
+
+ align:start position:0%
+understand something when i first
+mention it
+
+ align:start position:0%
+mention it
+ 
+
+ align:start position:0%
+mention it
+anything i expect especially in anything
+
+ align:start position:0%
+anything i expect especially in anything
+ 
+
+ align:start position:0%
+anything i expect especially in anything
+or anatomical that i expect you to know
+
+ align:start position:0%
+or anatomical that i expect you to know
+ 
+
+ align:start position:0%
+or anatomical that i expect you to know
+i will repeat
+
+ align:start position:0%
+i will repeat
+ 
+
+ align:start position:0%
+i will repeat
+and add
+
+ align:start position:0%
+and add
+ 
+
+ align:start position:0%
+and add
+to the information a number of times
+
+ align:start position:0%
+to the information a number of times
+ 
+
+ align:start position:0%
+to the information a number of times
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it won't be something i just mentioned
+
+ align:start position:0%
+it won't be something i just mentioned
+ 
+
+ align:start position:0%
+it won't be something i just mentioned
+once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so be patient with yourself
+
+ align:start position:0%
+so be patient with yourself
+ 
+
+ align:start position:0%
+so be patient with yourself
+i'm going to do something else this year
+
+ align:start position:0%
+i'm going to do something else this year
+ 
+
+ align:start position:0%
+i'm going to do something else this year
+that's different from what i've done in
+
+ align:start position:0%
+that's different from what i've done in
+ 
+
+ align:start position:0%
+that's different from what i've done in
+the past i realized that
+
+ align:start position:0%
+the past i realized that
+ 
+
+ align:start position:0%
+the past i realized that
+these two classes that i teach
+
+ align:start position:0%
+these two classes that i teach
+ 
+
+ align:start position:0%
+these two classes that i teach
+undergraduates
+
+ align:start position:0%
+undergraduates
+ 
+
+ align:start position:0%
+undergraduates
+require you to
+
+ align:start position:0%
+require you to
+ 
+
+ align:start position:0%
+require you to
+basically acquire a language you learn
+
+ align:start position:0%
+basically acquire a language you learn
+ 
+
+ align:start position:0%
+basically acquire a language you learn
+many many new terms
+
+ align:start position:0%
+many many new terms
+ 
+
+ align:start position:0%
+many many new terms
+so we're going to make available to all
+
+ align:start position:0%
+so we're going to make available to all
+ 
+
+ align:start position:0%
+so we're going to make available to all
+of you a program basically a flash card
+
+ align:start position:0%
+of you a program basically a flash card
+ 
+
+ align:start position:0%
+of you a program basically a flash card
+program but it's probably the best of
+
+ align:start position:0%
+program but it's probably the best of
+ 
+
+ align:start position:0%
+program but it's probably the best of
+its type written here at mit
+
+ align:start position:0%
+its type written here at mit
+ 
+
+ align:start position:0%
+its type written here at mit
+by a student of mine in course 6
+
+ align:start position:0%
+by a student of mine in course 6
+ 
+
+ align:start position:0%
+by a student of mine in course 6
+jordan gilliland he will come to the
+
+ align:start position:0%
+jordan gilliland he will come to the
+ 
+
+ align:start position:0%
+jordan gilliland he will come to the
+class probably
+
+ align:start position:0%
+class probably
+ 
+
+ align:start position:0%
+class probably
+next time
+
+ align:start position:0%
+next time
+ 
+
+ align:start position:0%
+next time
+either next time or friday
+
+ align:start position:0%
+either next time or friday
+ 
+
+ align:start position:0%
+either next time or friday
+and describe the program he can
+
+ align:start position:0%
+and describe the program he can
+ 
+
+ align:start position:0%
+and describe the program he can
+demonstrate it to you on my computer
+
+ align:start position:0%
+demonstrate it to you on my computer
+ 
+
+ align:start position:0%
+demonstrate it to you on my computer
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can download it
+
+ align:start position:0%
+you can download it
+ 
+
+ align:start position:0%
+you can download it
+what i will do
+
+ align:start position:0%
+what i will do
+ 
+
+ align:start position:0%
+what i will do
+i will try to remember to do this today
+
+ align:start position:0%
+i will try to remember to do this today
+ 
+
+ align:start position:0%
+i will try to remember to do this today
+is i will
+
+ align:start position:0%
+is i will
+ 
+
+ align:start position:0%
+is i will
+put on the web
+
+ align:start position:0%
+put on the web
+ 
+
+ align:start position:0%
+put on the web
+some text files for the first lectures
+
+ align:start position:0%
+some text files for the first lectures
+ 
+
+ align:start position:0%
+some text files for the first lectures
+that will give you terms and definitions
+
+ align:start position:0%
+that will give you terms and definitions
+ 
+
+ align:start position:0%
+that will give you terms and definitions
+that will help you in your study but
+
+ align:start position:0%
+that will help you in your study but
+ 
+
+ align:start position:0%
+that will help you in your study but
+those will be the files that are used in
+
+ align:start position:0%
+those will be the files that are used in
+ 
+
+ align:start position:0%
+those will be the files that are used in
+his program very useful for learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitions learning languages it's used
+
+ align:start position:0%
+definitions learning languages it's used
+ 
+
+ align:start position:0%
+definitions learning languages it's used
+in the mandarin and japanese classes
+
+ align:start position:0%
+in the mandarin and japanese classes
+ 
+
+ align:start position:0%
+in the mandarin and japanese classes
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i said a bet cell is a
+
+ align:start position:0%
+i said a bet cell is a
+ 
+
+ align:start position:0%
+i said a bet cell is a
+cell in the neocortex in the layer that
+
+ align:start position:0%
+cell in the neocortex in the layer that
+ 
+
+ align:start position:0%
+cell in the neocortex in the layer that
+provides output to non-cortical
+
+ align:start position:0%
+provides output to non-cortical
+ 
+
+ align:start position:0%
+provides output to non-cortical
+structures that means it must have a
+
+ align:start position:0%
+structures that means it must have a
+ 
+
+ align:start position:0%
+structures that means it must have a
+very long process
+
+ align:start position:0%
+very long process
+ 
+
+ align:start position:0%
+very long process
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right there it says a and this is a
+
+ align:start position:0%
+right there it says a and this is a
+ 
+
+ align:start position:0%
+right there it says a and this is a
+picture from monica hall
+
+ align:start position:0%
+picture from monica hall
+ 
+
+ align:start position:0%
+picture from monica hall
+that's the axon
+
+ align:start position:0%
+that's the axon
+ 
+
+ align:start position:0%
+that's the axon
+it shows two branches the accent starts
+
+ align:start position:0%
+it shows two branches the accent starts
+ 
+
+ align:start position:0%
+it shows two branches the accent starts
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and then he has it going like that
+
+ align:start position:0%
+and then he has it going like that
+ 
+
+ align:start position:0%
+and then he has it going like that
+and then like that
+
+ align:start position:0%
+and then like that
+ 
+
+ align:start position:0%
+and then like that
+that's because on the section he was
+
+ align:start position:0%
+that's because on the section he was
+ 
+
+ align:start position:0%
+that's because on the section he was
+studying it was cut off
+
+ align:start position:0%
+studying it was cut off
+ 
+
+ align:start position:0%
+studying it was cut off
+now one of those branches would probably
+
+ align:start position:0%
+now one of those branches would probably
+ 
+
+ align:start position:0%
+now one of those branches would probably
+go up into the cortex and terminate on
+
+ align:start position:0%
+go up into the cortex and terminate on
+ 
+
+ align:start position:0%
+go up into the cortex and terminate on
+adjacent cells the other would go
+
+ align:start position:0%
+adjacent cells the other would go
+ 
+
+ align:start position:0%
+adjacent cells the other would go
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+leave the neocortex and the bet cells
+
+ align:start position:0%
+leave the neocortex and the bet cells
+ 
+
+ align:start position:0%
+leave the neocortex and the bet cells
+are large because they support a very
+
+ align:start position:0%
+are large because they support a very
+ 
+
+ align:start position:0%
+are large because they support a very
+long axon it goes all the way down to
+
+ align:start position:0%
+long axon it goes all the way down to
+ 
+
+ align:start position:0%
+long axon it goes all the way down to
+the spinal cord the longest ones would
+
+ align:start position:0%
+the spinal cord the longest ones would
+ 
+
+ align:start position:0%
+the spinal cord the longest ones would
+end at the bottom the spinal cord or
+
+ align:start position:0%
+end at the bottom the spinal cord or
+ 
+
+ align:start position:0%
+end at the bottom the spinal cord or
+near the bottom of the spinal cord like
+
+ align:start position:0%
+near the bottom of the spinal cord like
+ 
+
+ align:start position:0%
+near the bottom of the spinal cord like
+what we call the caudal enlargement that
+
+ align:start position:0%
+what we call the caudal enlargement that
+ 
+
+ align:start position:0%
+what we call the caudal enlargement that
+innervates the legs and feet
+
+ align:start position:0%
+innervates the legs and feet
+ 
+
+ align:start position:0%
+innervates the legs and feet
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we discussed
+
+ align:start position:0%
+okay we discussed
+ 
+
+ align:start position:0%
+okay we discussed
+car wernicke last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in discussing localizational function we
+
+ align:start position:0%
+in discussing localizational function we
+ 
+
+ align:start position:0%
+in discussing localizational function we
+mentioned the kleist localization map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you look
+
+ align:start position:0%
+and if you look
+ 
+
+ align:start position:0%
+and if you look
+i don't know if you can read it there
+
+ align:start position:0%
+i don't know if you can read it there
+ 
+
+ align:start position:0%
+i don't know if you can read it there
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+on your printout but these are basically
+
+ align:start position:0%
+on your printout but these are basically
+ 
+
+ align:start position:0%
+on your printout but these are basically
+psychological functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that raised many questions and led to uh
+
+ align:start position:0%
+that raised many questions and led to uh
+ 
+
+ align:start position:0%
+that raised many questions and led to uh
+criticism and pointing out of many
+
+ align:start position:0%
+criticism and pointing out of many
+ 
+
+ align:start position:0%
+criticism and pointing out of many
+contradictions in the neurological
+
+ align:start position:0%
+contradictions in the neurological
+ 
+
+ align:start position:0%
+contradictions in the neurological
+literature so people
+
+ align:start position:0%
+literature so people
+ 
+
+ align:start position:0%
+literature so people
+started to simplify these maps the
+
+ align:start position:0%
+started to simplify these maps the
+ 
+
+ align:start position:0%
+started to simplify these maps the
+morgan and stellar map and the first
+
+ align:start position:0%
+morgan and stellar map and the first
+ 
+
+ align:start position:0%
+morgan and stellar map and the first
+text of physiological psychology took
+
+ align:start position:0%
+text of physiological psychology took
+ 
+
+ align:start position:0%
+text of physiological psychology took
+that to an extreme and only mentioned a
+
+ align:start position:0%
+that to an extreme and only mentioned a
+ 
+
+ align:start position:0%
+that to an extreme and only mentioned a
+few places like motor cortex visual
+
+ align:start position:0%
+few places like motor cortex visual
+ 
+
+ align:start position:0%
+few places like motor cortex visual
+visual cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what about this localization of
+
+ align:start position:0%
+so what about this localization of
+ 
+
+ align:start position:0%
+so what about this localization of
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+there's been argument about it since
+
+ align:start position:0%
+there's been argument about it since
+ 
+
+ align:start position:0%
+there's been argument about it since
+very early on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this should go back to your printout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i hope you have those we have a few more
+
+ align:start position:0%
+i hope you have those we have a few more
+ 
+
+ align:start position:0%
+i hope you have those we have a few more
+today if you don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the early objections were of the
+
+ align:start position:0%
+but the early objections were of the
+ 
+
+ align:start position:0%
+but the early objections were of the
+sort that you see
+
+ align:start position:0%
+sort that you see
+ 
+
+ align:start position:0%
+sort that you see
+at the top there
+
+ align:start position:0%
+at the top there
+ 
+
+ align:start position:0%
+at the top there
+isn't the human soul unitary how can you
+
+ align:start position:0%
+isn't the human soul unitary how can you
+ 
+
+ align:start position:0%
+isn't the human soul unitary how can you
+carve it up like that how can you say
+
+ align:start position:0%
+carve it up like that how can you say
+ 
+
+ align:start position:0%
+carve it up like that how can you say
+that one thing's here another thing's
+
+ align:start position:0%
+that one thing's here another thing's
+ 
+
+ align:start position:0%
+that one thing's here another thing's
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+is if people were a bunch of little
+
+ align:start position:0%
+is if people were a bunch of little
+ 
+
+ align:start position:0%
+is if people were a bunch of little
+people in the head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of it was because they would mix
+
+ align:start position:0%
+a lot of it was because they would mix
+ 
+
+ align:start position:0%
+a lot of it was because they would mix
+up arguments about mind
+
+ align:start position:0%
+up arguments about mind
+ 
+
+ align:start position:0%
+up arguments about mind
+and soul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because many people assume they're the
+
+ align:start position:0%
+because many people assume they're the
+ 
+
+ align:start position:0%
+because many people assume they're the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+and to a psychologist
+
+ align:start position:0%
+and to a psychologist
+ 
+
+ align:start position:0%
+and to a psychologist
+the mind is the organizer of behavior
+
+ align:start position:0%
+the mind is the organizer of behavior
+ 
+
+ align:start position:0%
+the mind is the organizer of behavior
+neuroscientist says behavior is
+
+ align:start position:0%
+neuroscientist says behavior is
+ 
+
+ align:start position:0%
+neuroscientist says behavior is
+organized by the brain that would mean
+
+ align:start position:0%
+organized by the brain that would mean
+ 
+
+ align:start position:0%
+organized by the brain that would mean
+the soul is the mind
+
+ align:start position:0%
+the soul is the mind
+ 
+
+ align:start position:0%
+the soul is the mind
+but in fact you don't have to assume
+
+ align:start position:0%
+but in fact you don't have to assume
+ 
+
+ align:start position:0%
+but in fact you don't have to assume
+that and it gets you into lots of
+
+ align:start position:0%
+that and it gets you into lots of
+ 
+
+ align:start position:0%
+that and it gets you into lots of
+problems if you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but let's talk about
+
+ align:start position:0%
+but let's talk about
+ 
+
+ align:start position:0%
+but let's talk about
+then another tradition that arose very
+
+ align:start position:0%
+then another tradition that arose very
+ 
+
+ align:start position:0%
+then another tradition that arose very
+early is sometimes referred to as
+
+ align:start position:0%
+early is sometimes referred to as
+ 
+
+ align:start position:0%
+early is sometimes referred to as
+anti-localization tradition
+
+ align:start position:0%
+anti-localization tradition
+ 
+
+ align:start position:0%
+anti-localization tradition
+but in fact they did believe in a kind
+
+ align:start position:0%
+but in fact they did believe in a kind
+ 
+
+ align:start position:0%
+but in fact they did believe in a kind
+of general
+
+ align:start position:0%
+of general
+ 
+
+ align:start position:0%
+of general
+localization of function
+
+ align:start position:0%
+localization of function
+ 
+
+ align:start position:0%
+localization of function
+and we can begin that with
+
+ align:start position:0%
+and we can begin that with
+ 
+
+ align:start position:0%
+and we can begin that with
+pierre florell
+
+ align:start position:0%
+pierre florell
+ 
+
+ align:start position:0%
+pierre florell
+who studied pigeons and other animals
+
+ align:start position:0%
+who studied pigeons and other animals
+ 
+
+ align:start position:0%
+who studied pigeons and other animals
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+published first in 1824
+
+ align:start position:0%
+published first in 1824
+ 
+
+ align:start position:0%
+published first in 1824
+okay so this was at the time when
+
+ align:start position:0%
+okay so this was at the time when
+ 
+
+ align:start position:0%
+okay so this was at the time when
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phrenology was becoming popular
+
+ align:start position:0%
+phrenology was becoming popular
+ 
+
+ align:start position:0%
+phrenology was becoming popular
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it was before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the minute continued with other
+
+ align:start position:0%
+and the minute continued with other
+ 
+
+ align:start position:0%
+and the minute continued with other
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+after brocco
+
+ align:start position:0%
+after brocco
+ 
+
+ align:start position:0%
+after brocco
+let's talk a little bit about
+
+ align:start position:0%
+let's talk a little bit about
+ 
+
+ align:start position:0%
+let's talk a little bit about
+floral
+
+ align:start position:0%
+floral
+ 
+
+ align:start position:0%
+floral
+i've sketched here
+
+ align:start position:0%
+i've sketched here
+ 
+
+ align:start position:0%
+i've sketched here
+a picture of a pigeon brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when floral studied this brain he
+
+ align:start position:0%
+when floral studied this brain he
+ 
+
+ align:start position:0%
+when floral studied this brain he
+he did it by making lesions and he would
+
+ align:start position:0%
+he did it by making lesions and he would
+ 
+
+ align:start position:0%
+he did it by making lesions and he would
+make lesions in
+
+ align:start position:0%
+make lesions in
+ 
+
+ align:start position:0%
+make lesions in
+one of these four regions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lowest will start with the hindbrain
+
+ align:start position:0%
+the lowest will start with the hindbrain
+ 
+
+ align:start position:0%
+the lowest will start with the hindbrain
+cerebellum
+
+ align:start position:0%
+cerebellum
+ 
+
+ align:start position:0%
+cerebellum
+optic lobe
+
+ align:start position:0%
+optic lobe
+ 
+
+ align:start position:0%
+optic lobe
+and the cerebral hemispheres
+
+ align:start position:0%
+and the cerebral hemispheres
+ 
+
+ align:start position:0%
+and the cerebral hemispheres
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say he made a lesion in the
+
+ align:start position:0%
+so let's say he made a lesion in the
+ 
+
+ align:start position:0%
+so let's say he made a lesion in the
+hind brain
+
+ align:start position:0%
+hind brain
+ 
+
+ align:start position:0%
+hind brain
+he found that if he made a big enough
+
+ align:start position:0%
+he found that if he made a big enough
+ 
+
+ align:start position:0%
+he found that if he made a big enough
+lesion in the hind brain the animal just
+
+ align:start position:0%
+lesion in the hind brain the animal just
+ 
+
+ align:start position:0%
+lesion in the hind brain the animal just
+died
+
+ align:start position:0%
+died
+ 
+
+ align:start position:0%
+died
+he was disturbing
+
+ align:start position:0%
+he was disturbing
+ 
+
+ align:start position:0%
+he was disturbing
+vital functions
+
+ align:start position:0%
+vital functions
+ 
+
+ align:start position:0%
+vital functions
+we know that to be true now
+
+ align:start position:0%
+we know that to be true now
+ 
+
+ align:start position:0%
+we know that to be true now
+but he claimed that in fact the amount
+
+ align:start position:0%
+but he claimed that in fact the amount
+ 
+
+ align:start position:0%
+but he claimed that in fact the amount
+of disturbance depended on the size of
+
+ align:start position:0%
+of disturbance depended on the size of
+ 
+
+ align:start position:0%
+of disturbance depended on the size of
+the lesion but it didn't really seem to
+
+ align:start position:0%
+the lesion but it didn't really seem to
+ 
+
+ align:start position:0%
+the lesion but it didn't really seem to
+make it
+
+ align:start position:0%
+make it
+ 
+
+ align:start position:0%
+make it
+matter where in the hind brain he made
+
+ align:start position:0%
+matter where in the hind brain he made
+ 
+
+ align:start position:0%
+matter where in the hind brain he made
+the lesion
+
+ align:start position:0%
+the lesion
+ 
+
+ align:start position:0%
+the lesion
+so he claimed there wasn't any very
+
+ align:start position:0%
+so he claimed there wasn't any very
+ 
+
+ align:start position:0%
+so he claimed there wasn't any very
+specific localization but there was
+
+ align:start position:0%
+specific localization but there was
+ 
+
+ align:start position:0%
+specific localization but there was
+vital functions were localized in the
+
+ align:start position:0%
+vital functions were localized in the
+ 
+
+ align:start position:0%
+vital functions were localized in the
+hindbrain because when he made lesions
+
+ align:start position:0%
+hindbrain because when he made lesions
+ 
+
+ align:start position:0%
+hindbrain because when he made lesions
+in these other areas the animal didn't
+
+ align:start position:0%
+in these other areas the animal didn't
+ 
+
+ align:start position:0%
+in these other areas the animal didn't
+he didn't deserve vital functions the
+
+ align:start position:0%
+he didn't deserve vital functions the
+ 
+
+ align:start position:0%
+he didn't deserve vital functions the
+animal usually lived
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at least for a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if he made lesions
+
+ align:start position:0%
+okay if he made lesions
+ 
+
+ align:start position:0%
+okay if he made lesions
+in the second area here
+
+ align:start position:0%
+in the second area here
+ 
+
+ align:start position:0%
+in the second area here
+i've abbreviated cb
+
+ align:start position:0%
+i've abbreviated cb
+ 
+
+ align:start position:0%
+i've abbreviated cb
+that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cerebellum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a structure present in mammals as well
+
+ align:start position:0%
+a structure present in mammals as well
+ 
+
+ align:start position:0%
+a structure present in mammals as well
+all the vertebrates
+
+ align:start position:0%
+all the vertebrates
+ 
+
+ align:start position:0%
+all the vertebrates
+i claimed if he made a lesion there
+
+ align:start position:0%
+i claimed if he made a lesion there
+ 
+
+ align:start position:0%
+i claimed if he made a lesion there
+again the disturbance depended on
+
+ align:start position:0%
+again the disturbance depended on
+ 
+
+ align:start position:0%
+again the disturbance depended on
+the size of the lesion and not exact not
+
+ align:start position:0%
+the size of the lesion and not exact not
+ 
+
+ align:start position:0%
+the size of the lesion and not exact not
+the exact location
+
+ align:start position:0%
+the exact location
+ 
+
+ align:start position:0%
+the exact location
+he said it disturbed motor coordination
+
+ align:start position:0%
+he said it disturbed motor coordination
+ 
+
+ align:start position:0%
+he said it disturbed motor coordination
+so if he was doing it in his pigeons
+
+ align:start position:0%
+so if he was doing it in his pigeons
+ 
+
+ align:start position:0%
+so if he was doing it in his pigeons
+they became more and more clumsy
+
+ align:start position:0%
+they became more and more clumsy
+ 
+
+ align:start position:0%
+they became more and more clumsy
+depending on how big a lesion he made in
+
+ align:start position:0%
+depending on how big a lesion he made in
+ 
+
+ align:start position:0%
+depending on how big a lesion he made in
+the cerebellum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if he made a lesion in region 3 there
+
+ align:start position:0%
+if he made a lesion in region 3 there
+ 
+
+ align:start position:0%
+if he made a lesion in region 3 there
+the optic lobe was called the optic
+
+ align:start position:0%
+the optic lobe was called the optic
+ 
+
+ align:start position:0%
+the optic lobe was called the optic
+globe because
+
+ align:start position:0%
+globe because
+ 
+
+ align:start position:0%
+globe because
+even with
+
+ align:start position:0%
+even with
+ 
+
+ align:start position:0%
+even with
+just gross anatomical dissection without
+
+ align:start position:0%
+just gross anatomical dissection without
+ 
+
+ align:start position:0%
+just gross anatomical dissection without
+doing any
+
+ align:start position:0%
+doing any
+ 
+
+ align:start position:0%
+doing any
+sectioning of the brain
+
+ align:start position:0%
+sectioning of the brain
+ 
+
+ align:start position:0%
+sectioning of the brain
+you could see that it was connected to
+
+ align:start position:0%
+you could see that it was connected to
+ 
+
+ align:start position:0%
+you could see that it was connected to
+the eyes
+
+ align:start position:0%
+the eyes
+ 
+
+ align:start position:0%
+the eyes
+okay through the optic nerve and tract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he surprisingly actually considering
+
+ align:start position:0%
+and he surprisingly actually considering
+ 
+
+ align:start position:0%
+and he surprisingly actually considering
+what we know about it today he claimed
+
+ align:start position:0%
+what we know about it today he claimed
+ 
+
+ align:start position:0%
+what we know about it today he claimed
+that vision was disturbed but it didn't
+
+ align:start position:0%
+that vision was disturbed but it didn't
+ 
+
+ align:start position:0%
+that vision was disturbed but it didn't
+make a difference where he put the
+
+ align:start position:0%
+make a difference where he put the
+ 
+
+ align:start position:0%
+make a difference where he put the
+lesion
+
+ align:start position:0%
+lesion
+ 
+
+ align:start position:0%
+lesion
+but if he made a big lesion and disturb
+
+ align:start position:0%
+but if he made a big lesion and disturb
+ 
+
+ align:start position:0%
+but if he made a big lesion and disturb
+vision a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i say it's surprising because we know
+
+ align:start position:0%
+i say it's surprising because we know
+ 
+
+ align:start position:0%
+i say it's surprising because we know
+that the left eye is connected to the
+
+ align:start position:0%
+that the left eye is connected to the
+ 
+
+ align:start position:0%
+that the left eye is connected to the
+right optic lobe in the pigeon right eye
+
+ align:start position:0%
+right optic lobe in the pigeon right eye
+ 
+
+ align:start position:0%
+right optic lobe in the pigeon right eye
+to the left optic lobe so you should
+
+ align:start position:0%
+to the left optic lobe so you should
+ 
+
+ align:start position:0%
+to the left optic lobe so you should
+have been able to tell the difference
+
+ align:start position:0%
+have been able to tell the difference
+ 
+
+ align:start position:0%
+have been able to tell the difference
+between visual fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally if he made lesions in the
+
+ align:start position:0%
+finally if he made lesions in the
+ 
+
+ align:start position:0%
+finally if he made lesions in the
+cerebral hemisphere he claimed disturbed
+
+ align:start position:0%
+cerebral hemisphere he claimed disturbed
+ 
+
+ align:start position:0%
+cerebral hemisphere he claimed disturbed
+functions like
+
+ align:start position:0%
+functions like
+ 
+
+ align:start position:0%
+functions like
+ability to initiate action he didn't use
+
+ align:start position:0%
+ability to initiate action he didn't use
+ 
+
+ align:start position:0%
+ability to initiate action he didn't use
+those terms he called it volition and
+
+ align:start position:0%
+those terms he called it volition and
+ 
+
+ align:start position:0%
+those terms he called it volition and
+will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again it just depended on how big
+
+ align:start position:0%
+and again it just depended on how big
+ 
+
+ align:start position:0%
+and again it just depended on how big
+the lesion
+
+ align:start position:0%
+the lesion
+ 
+
+ align:start position:0%
+the lesion
+so in other words he
+
+ align:start position:0%
+so in other words he
+ 
+
+ align:start position:0%
+so in other words he
+didn't agree with the localization of
+
+ align:start position:0%
+didn't agree with the localization of
+ 
+
+ align:start position:0%
+didn't agree with the localization of
+function people but remember he was
+
+ align:start position:0%
+function people but remember he was
+ 
+
+ align:start position:0%
+function people but remember he was
+using these small animals
+
+ align:start position:0%
+using these small animals
+ 
+
+ align:start position:0%
+using these small animals
+he wasn't using
+
+ align:start position:0%
+he wasn't using
+ 
+
+ align:start position:0%
+he wasn't using
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+very close to
+
+ align:start position:0%
+very close to
+ 
+
+ align:start position:0%
+very close to
+the human brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+other scientists later on
+
+ align:start position:0%
+other scientists later on
+ 
+
+ align:start position:0%
+other scientists later on
+continued that with that same kind of
+
+ align:start position:0%
+continued that with that same kind of
+ 
+
+ align:start position:0%
+continued that with that same kind of
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+golds and published in 1876 studies of
+
+ align:start position:0%
+golds and published in 1876 studies of
+ 
+
+ align:start position:0%
+golds and published in 1876 studies of
+dogs now dogs are a mammal they have a
+
+ align:start position:0%
+dogs now dogs are a mammal they have a
+ 
+
+ align:start position:0%
+dogs now dogs are a mammal they have a
+very a pretty large brain
+
+ align:start position:0%
+very a pretty large brain
+ 
+
+ align:start position:0%
+very a pretty large brain
+much closer to our brains
+
+ align:start position:0%
+much closer to our brains
+ 
+
+ align:start position:0%
+much closer to our brains
+and yet he came to conclusions pretty
+
+ align:start position:0%
+and yet he came to conclusions pretty
+ 
+
+ align:start position:0%
+and yet he came to conclusions pretty
+similar to fluron he studied mainly the
+
+ align:start position:0%
+similar to fluron he studied mainly the
+ 
+
+ align:start position:0%
+similar to fluron he studied mainly the
+cerebral hemispheres he was making
+
+ align:start position:0%
+cerebral hemispheres he was making
+ 
+
+ align:start position:0%
+cerebral hemispheres he was making
+lesions in the neocortex
+
+ align:start position:0%
+lesions in the neocortex
+ 
+
+ align:start position:0%
+lesions in the neocortex
+and he claimed he was disturbing higher
+
+ align:start position:0%
+and he claimed he was disturbing higher
+ 
+
+ align:start position:0%
+and he claimed he was disturbing higher
+higher functions just like
+
+ align:start position:0%
+higher functions just like
+ 
+
+ align:start position:0%
+higher functions just like
+the sort of functions that floral had
+
+ align:start position:0%
+the sort of functions that floral had
+ 
+
+ align:start position:0%
+the sort of functions that floral had
+claimed for his small animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but he the problem was
+
+ align:start position:0%
+but he the problem was
+ 
+
+ align:start position:0%
+but he the problem was
+as i see it with gold is he he was using
+
+ align:start position:0%
+as i see it with gold is he he was using
+ 
+
+ align:start position:0%
+as i see it with gold is he he was using
+very general terms to describe behavior
+
+ align:start position:0%
+very general terms to describe behavior
+ 
+
+ align:start position:0%
+very general terms to describe behavior
+he didn't have any he didn't do
+
+ align:start position:0%
+he didn't have any he didn't do
+ 
+
+ align:start position:0%
+he didn't have any he didn't do
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+he didn't analyze behavior in any very
+
+ align:start position:0%
+he didn't analyze behavior in any very
+ 
+
+ align:start position:0%
+he didn't analyze behavior in any very
+specific way this was before
+
+ align:start position:0%
+specific way this was before
+ 
+
+ align:start position:0%
+specific way this was before
+the development of ethology the study of
+
+ align:start position:0%
+the development of ethology the study of
+ 
+
+ align:start position:0%
+the development of ethology the study of
+natural behaviors and animals
+
+ align:start position:0%
+natural behaviors and animals
+ 
+
+ align:start position:0%
+natural behaviors and animals
+it was before the development
+
+ align:start position:0%
+it was before the development
+ 
+
+ align:start position:0%
+it was before the development
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+experimental psychology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so his problem was really a lack of
+
+ align:start position:0%
+so his problem was really a lack of
+ 
+
+ align:start position:0%
+so his problem was really a lack of
+analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he wasn't look it just depends on how he
+
+ align:start position:0%
+he wasn't look it just depends on how he
+ 
+
+ align:start position:0%
+he wasn't look it just depends on how he
+was looking at the animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher functions he claimed things like
+
+ align:start position:0%
+higher functions he claimed things like
+ 
+
+ align:start position:0%
+higher functions he claimed things like
+volition
+
+ align:start position:0%
+volition
+ 
+
+ align:start position:0%
+volition
+will initiation
+
+ align:start position:0%
+will initiation
+ 
+
+ align:start position:0%
+will initiation
+of action
+
+ align:start position:0%
+of action
+ 
+
+ align:start position:0%
+of action
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there were other people around that
+
+ align:start position:0%
+now there were other people around that
+ 
+
+ align:start position:0%
+now there were other people around that
+same time that were discovering
+
+ align:start position:0%
+same time that were discovering
+ 
+
+ align:start position:0%
+same time that were discovering
+greater localization
+
+ align:start position:0%
+greater localization
+ 
+
+ align:start position:0%
+greater localization
+it was around that time that people
+
+ align:start position:0%
+it was around that time that people
+ 
+
+ align:start position:0%
+it was around that time that people
+began to see that vision was disturbed
+
+ align:start position:0%
+began to see that vision was disturbed
+ 
+
+ align:start position:0%
+began to see that vision was disturbed
+with more posterior lesions in the
+
+ align:start position:0%
+with more posterior lesions in the
+ 
+
+ align:start position:0%
+with more posterior lesions in the
+hemispheres okay
+
+ align:start position:0%
+hemispheres okay
+ 
+
+ align:start position:0%
+hemispheres okay
+and lashley was one of those people
+
+ align:start position:0%
+and lashley was one of those people
+ 
+
+ align:start position:0%
+and lashley was one of those people
+later on who did localize the visual
+
+ align:start position:0%
+later on who did localize the visual
+ 
+
+ align:start position:0%
+later on who did localize the visual
+cortex but in his early work
+
+ align:start position:0%
+cortex but in his early work
+ 
+
+ align:start position:0%
+cortex but in his early work
+he did a large lesion study trying to
+
+ align:start position:0%
+he did a large lesion study trying to
+ 
+
+ align:start position:0%
+he did a large lesion study trying to
+locate the engram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's talk about lashley studies
+
+ align:start position:0%
+okay so let's talk about lashley studies
+ 
+
+ align:start position:0%
+okay so let's talk about lashley studies
+lashley's an important figure in brain
+
+ align:start position:0%
+lashley's an important figure in brain
+ 
+
+ align:start position:0%
+lashley's an important figure in brain
+behavior studies because
+
+ align:start position:0%
+behavior studies because
+ 
+
+ align:start position:0%
+behavior studies because
+unlike the clinical neurologists
+
+ align:start position:0%
+unlike the clinical neurologists
+ 
+
+ align:start position:0%
+unlike the clinical neurologists
+he did experiments he wasn't just
+
+ align:start position:0%
+he did experiments he wasn't just
+ 
+
+ align:start position:0%
+he did experiments he wasn't just
+informally making informal descriptions
+
+ align:start position:0%
+informally making informal descriptions
+ 
+
+ align:start position:0%
+informally making informal descriptions
+of case single cases okay he was using
+
+ align:start position:0%
+of case single cases okay he was using
+ 
+
+ align:start position:0%
+of case single cases okay he was using
+quite a few animals in each experiment
+
+ align:start position:0%
+quite a few animals in each experiment
+ 
+
+ align:start position:0%
+quite a few animals in each experiment
+so he was basically repeating the
+
+ align:start position:0%
+so he was basically repeating the
+ 
+
+ align:start position:0%
+so he was basically repeating the
+experiment many times in different
+
+ align:start position:0%
+experiment many times in different
+ 
+
+ align:start position:0%
+experiment many times in different
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+he was using quantitative methods
+
+ align:start position:0%
+he was using quantitative methods
+ 
+
+ align:start position:0%
+he was using quantitative methods
+applied to both behavior
+
+ align:start position:0%
+applied to both behavior
+ 
+
+ align:start position:0%
+applied to both behavior
+and anatomy
+
+ align:start position:0%
+and anatomy
+ 
+
+ align:start position:0%
+and anatomy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and he was the first one really to do
+
+ align:start position:0%
+and he was the first one really to do
+ 
+
+ align:start position:0%
+and he was the first one really to do
+that systematically
+
+ align:start position:0%
+that systematically
+ 
+
+ align:start position:0%
+that systematically
+and that's why we consider him important
+
+ align:start position:0%
+and that's why we consider him important
+ 
+
+ align:start position:0%
+and that's why we consider him important
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+this particular study he was his
+
+ align:start position:0%
+this particular study he was his
+ 
+
+ align:start position:0%
+this particular study he was his
+conclusions were probably wrong so let's
+
+ align:start position:0%
+conclusions were probably wrong so let's
+ 
+
+ align:start position:0%
+conclusions were probably wrong so let's
+look at that
+
+ align:start position:0%
+look at that
+ 
+
+ align:start position:0%
+look at that
+first i'll show you this picture
+
+ align:start position:0%
+first i'll show you this picture
+ 
+
+ align:start position:0%
+first i'll show you this picture
+taken
+
+ align:start position:0%
+taken
+ 
+
+ align:start position:0%
+taken
+by myself showing hamster brains because
+
+ align:start position:0%
+by myself showing hamster brains because
+ 
+
+ align:start position:0%
+by myself showing hamster brains because
+they're pretty similar to rap
+
+ align:start position:0%
+they're pretty similar to rap
+ 
+
+ align:start position:0%
+they're pretty similar to rap
+i'm showing an adult in a newborn brain
+
+ align:start position:0%
+i'm showing an adult in a newborn brain
+ 
+
+ align:start position:0%
+i'm showing an adult in a newborn brain
+and you'll note there that in the adult
+
+ align:start position:0%
+and you'll note there that in the adult
+ 
+
+ align:start position:0%
+and you'll note there that in the adult
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you appear
+
+ align:start position:0%
+then you appear
+ 
+
+ align:start position:0%
+then you appear
+neocortex okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll note that it's a smooth brain
+
+ align:start position:0%
+you'll note that it's a smooth brain
+ 
+
+ align:start position:0%
+you'll note that it's a smooth brain
+animal
+
+ align:start position:0%
+animal
+ 
+
+ align:start position:0%
+animal
+it doesn't seem to be divided up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the kinds of
+
+ align:start position:0%
+by the kinds of
+ 
+
+ align:start position:0%
+by the kinds of
+fissures that you see
+
+ align:start position:0%
+fissures that you see
+ 
+
+ align:start position:0%
+fissures that you see
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+larger brained animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but anatomical studies do indicate some
+
+ align:start position:0%
+but anatomical studies do indicate some
+ 
+
+ align:start position:0%
+but anatomical studies do indicate some
+subdivisions in that cortex
+
+ align:start position:0%
+subdivisions in that cortex
+ 
+
+ align:start position:0%
+subdivisions in that cortex
+you can also see their subcortical
+
+ align:start position:0%
+you can also see their subcortical
+ 
+
+ align:start position:0%
+you can also see their subcortical
+regions
+
+ align:start position:0%
+regions
+ 
+
+ align:start position:0%
+regions
+if you think of the neocortex it's the
+
+ align:start position:0%
+if you think of the neocortex it's the
+ 
+
+ align:start position:0%
+if you think of the neocortex it's the
+highest part of the brain
+
+ align:start position:0%
+highest part of the brain
+ 
+
+ align:start position:0%
+highest part of the brain
+all these other structures are below it
+
+ align:start position:0%
+all these other structures are below it
+ 
+
+ align:start position:0%
+all these other structures are below it
+in between the spinal cord which you see
+
+ align:start position:0%
+in between the spinal cord which you see
+ 
+
+ align:start position:0%
+in between the spinal cord which you see
+beginning right here
+
+ align:start position:0%
+beginning right here
+ 
+
+ align:start position:0%
+beginning right here
+and then here
+
+ align:start position:0%
+and then here
+ 
+
+ align:start position:0%
+and then here
+behind brain begins the hind brain is
+
+ align:start position:0%
+behind brain begins the hind brain is
+ 
+
+ align:start position:0%
+behind brain begins the hind brain is
+partly covered here by the cerebellum
+
+ align:start position:0%
+partly covered here by the cerebellum
+ 
+
+ align:start position:0%
+partly covered here by the cerebellum
+and then you also see a little bit of
+
+ align:start position:0%
+and then you also see a little bit of
+ 
+
+ align:start position:0%
+and then you also see a little bit of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+superior colliculus which is the
+
+ align:start position:0%
+superior colliculus which is the
+ 
+
+ align:start position:0%
+superior colliculus which is the
+mammalian equivalent of the optic lobe
+
+ align:start position:0%
+mammalian equivalent of the optic lobe
+ 
+
+ align:start position:0%
+mammalian equivalent of the optic lobe
+in the pigeon
+
+ align:start position:0%
+in the pigeon
+ 
+
+ align:start position:0%
+in the pigeon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well here's lashley's way of depicting
+
+ align:start position:0%
+well here's lashley's way of depicting
+ 
+
+ align:start position:0%
+well here's lashley's way of depicting
+his lesions
+
+ align:start position:0%
+his lesions
+ 
+
+ align:start position:0%
+his lesions
+here's
+
+ align:start position:0%
+here's
+ 
+
+ align:start position:0%
+here's
+here's was
+
+ align:start position:0%
+here's was
+ 
+
+ align:start position:0%
+here's was
+here here was his approach his idea was
+
+ align:start position:0%
+here here was his approach his idea was
+ 
+
+ align:start position:0%
+here here was his approach his idea was
+we will train the rats
+
+ align:start position:0%
+we will train the rats
+ 
+
+ align:start position:0%
+we will train the rats
+in problems we'll get them to solve
+
+ align:start position:0%
+in problems we'll get them to solve
+ 
+
+ align:start position:0%
+in problems we'll get them to solve
+mazes
+
+ align:start position:0%
+mazes
+ 
+
+ align:start position:0%
+mazes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we'll teach throughout the maze and then
+
+ align:start position:0%
+we'll teach throughout the maze and then
+ 
+
+ align:start position:0%
+we'll teach throughout the maze and then
+we'll make a lesion
+
+ align:start position:0%
+we'll make a lesion
+ 
+
+ align:start position:0%
+we'll make a lesion
+to see if this memory for the maze that
+
+ align:start position:0%
+to see if this memory for the maze that
+ 
+
+ align:start position:0%
+to see if this memory for the maze that
+he's learned
+
+ align:start position:0%
+he's learned
+ 
+
+ align:start position:0%
+he's learned
+disappears okay so then we'll
+
+ align:start position:0%
+disappears okay so then we'll
+ 
+
+ align:start position:0%
+disappears okay so then we'll
+we'll train him in the maze and we'll
+
+ align:start position:0%
+we'll train him in the maze and we'll
+ 
+
+ align:start position:0%
+we'll train him in the maze and we'll
+make the lesion
+
+ align:start position:0%
+make the lesion
+ 
+
+ align:start position:0%
+make the lesion
+and now after he recovers from lesion
+
+ align:start position:0%
+and now after he recovers from lesion
+ 
+
+ align:start position:0%
+and now after he recovers from lesion
+we'll retrain him
+
+ align:start position:0%
+we'll retrain him
+ 
+
+ align:start position:0%
+we'll retrain him
+and find out now does he
+
+ align:start position:0%
+and find out now does he
+ 
+
+ align:start position:0%
+and find out now does he
+have to learn all over again
+
+ align:start position:0%
+have to learn all over again
+ 
+
+ align:start position:0%
+have to learn all over again
+or does he still remember
+
+ align:start position:0%
+or does he still remember
+ 
+
+ align:start position:0%
+or does he still remember
+and he made a great variety of lesions
+
+ align:start position:0%
+and he made a great variety of lesions
+ 
+
+ align:start position:0%
+and he made a great variety of lesions
+this is an example of his lesion
+
+ align:start position:0%
+this is an example of his lesion
+ 
+
+ align:start position:0%
+this is an example of his lesion
+reconstructions
+
+ align:start position:0%
+reconstructions
+ 
+
+ align:start position:0%
+reconstructions
+of a rat with a
+
+ align:start position:0%
+of a rat with a
+ 
+
+ align:start position:0%
+of a rat with a
+smaller lesion and a larger lesion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he tried to make these lesions
+
+ align:start position:0%
+he tried to make these lesions
+ 
+
+ align:start position:0%
+he tried to make these lesions
+symmetrically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can see
+
+ align:start position:0%
+and you can see
+ 
+
+ align:start position:0%
+and you can see
+the symmetry of the lesion is not
+
+ align:start position:0%
+the symmetry of the lesion is not
+ 
+
+ align:start position:0%
+the symmetry of the lesion is not
+perfect but it's not easy in
+
+ align:start position:0%
+perfect but it's not easy in
+ 
+
+ align:start position:0%
+perfect but it's not easy in
+neurosurgery to make completely
+
+ align:start position:0%
+neurosurgery to make completely
+ 
+
+ align:start position:0%
+neurosurgery to make completely
+symmetric lesions but he
+
+ align:start position:0%
+symmetric lesions but he
+ 
+
+ align:start position:0%
+symmetric lesions but he
+attempted to do that but then he didn't
+
+ align:start position:0%
+attempted to do that but then he didn't
+ 
+
+ align:start position:0%
+attempted to do that but then he didn't
+depend on his
+
+ align:start position:0%
+depend on his
+ 
+
+ align:start position:0%
+depend on his
+surgical notes
+
+ align:start position:0%
+surgical notes
+ 
+
+ align:start position:0%
+surgical notes
+he did histology on the brain afterwards
+
+ align:start position:0%
+he did histology on the brain afterwards
+ 
+
+ align:start position:0%
+he did histology on the brain afterwards
+and reconstructed the lesion
+
+ align:start position:0%
+and reconstructed the lesion
+ 
+
+ align:start position:0%
+and reconstructed the lesion
+that's very important because you can do
+
+ align:start position:0%
+that's very important because you can do
+ 
+
+ align:start position:0%
+that's very important because you can do
+extra damage you can damage blood
+
+ align:start position:0%
+extra damage you can damage blood
+ 
+
+ align:start position:0%
+extra damage you can damage blood
+vessels and produce damage you weren't
+
+ align:start position:0%
+vessels and produce damage you weren't
+ 
+
+ align:start position:0%
+vessels and produce damage you weren't
+intending
+
+ align:start position:0%
+intending
+ 
+
+ align:start position:0%
+intending
+or you might have missed some structures
+
+ align:start position:0%
+or you might have missed some structures
+ 
+
+ align:start position:0%
+or you might have missed some structures
+that you were intending to remove so
+
+ align:start position:0%
+that you were intending to remove so
+ 
+
+ align:start position:0%
+that you were intending to remove so
+it's very important to
+
+ align:start position:0%
+it's very important to
+ 
+
+ align:start position:0%
+it's very important to
+follow up any lesion study like this
+
+ align:start position:0%
+follow up any lesion study like this
+ 
+
+ align:start position:0%
+follow up any lesion study like this
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+at least this kind of anatomy
+
+ align:start position:0%
+at least this kind of anatomy
+ 
+
+ align:start position:0%
+at least this kind of anatomy
+reconstructing the
+
+ align:start position:0%
+reconstructing the
+ 
+
+ align:start position:0%
+reconstructing the
+tissue
+
+ align:start position:0%
+tissue
+ 
+
+ align:start position:0%
+tissue
+the only problem with it is sometimes
+
+ align:start position:0%
+the only problem with it is sometimes
+ 
+
+ align:start position:0%
+the only problem with it is sometimes
+the brains become a little distorted
+
+ align:start position:0%
+the brains become a little distorted
+ 
+
+ align:start position:0%
+the brains become a little distorted
+after a lesion and then you have
+
+ align:start position:0%
+after a lesion and then you have
+ 
+
+ align:start position:0%
+after a lesion and then you have
+difficulty
+
+ align:start position:0%
+difficulty
+ 
+
+ align:start position:0%
+difficulty
+putting
+
+ align:start position:0%
+putting
+ 
+
+ align:start position:0%
+putting
+the lesion in this kind of picture this
+
+ align:start position:0%
+the lesion in this kind of picture this
+ 
+
+ align:start position:0%
+the lesion in this kind of picture this
+is a standard diagram
+
+ align:start position:0%
+is a standard diagram
+ 
+
+ align:start position:0%
+is a standard diagram
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good question you know this is not
+
+ align:start position:0%
+good question you know this is not
+ 
+
+ align:start position:0%
+good question you know this is not
+showing the depth of the lesion
+
+ align:start position:0%
+showing the depth of the lesion
+ 
+
+ align:start position:0%
+showing the depth of the lesion
+he tried to make to remove only cell
+
+ align:start position:0%
+he tried to make to remove only cell
+ 
+
+ align:start position:0%
+he tried to make to remove only cell
+layers of the neocortex and avoid going
+
+ align:start position:0%
+layers of the neocortex and avoid going
+ 
+
+ align:start position:0%
+layers of the neocortex and avoid going
+deep
+
+ align:start position:0%
+deep
+ 
+
+ align:start position:0%
+deep
+but of course that's a question that
+
+ align:start position:0%
+but of course that's a question that
+ 
+
+ align:start position:0%
+but of course that's a question that
+this picture isn't showing you well
+
+ align:start position:0%
+this picture isn't showing you well
+ 
+
+ align:start position:0%
+this picture isn't showing you well
+where did he go deeper because if he
+
+ align:start position:0%
+where did he go deeper because if he
+ 
+
+ align:start position:0%
+where did he go deeper because if he
+went deeper he's going to disturb fibers
+
+ align:start position:0%
+went deeper he's going to disturb fibers
+ 
+
+ align:start position:0%
+went deeper he's going to disturb fibers
+he might even disturb underlying
+
+ align:start position:0%
+he might even disturb underlying
+ 
+
+ align:start position:0%
+he might even disturb underlying
+non-neocortical structures
+
+ align:start position:0%
+non-neocortical structures
+ 
+
+ align:start position:0%
+non-neocortical structures
+but for the most part his lesions were
+
+ align:start position:0%
+but for the most part his lesions were
+ 
+
+ align:start position:0%
+but for the most part his lesions were
+done pretty well
+
+ align:start position:0%
+done pretty well
+ 
+
+ align:start position:0%
+done pretty well
+using aspiration of the superficial
+
+ align:start position:0%
+using aspiration of the superficial
+ 
+
+ align:start position:0%
+using aspiration of the superficial
+cells in the cortex the upper
+
+ align:start position:0%
+cells in the cortex the upper
+ 
+
+ align:start position:0%
+cells in the cortex the upper
+what we call the
+
+ align:start position:0%
+what we call the
+ 
+
+ align:start position:0%
+what we call the
+bark of the brain the neocortex and
+
+ align:start position:0%
+bark of the brain the neocortex and
+ 
+
+ align:start position:0%
+bark of the brain the neocortex and
+avoiding the fibers underneath
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here
+
+ align:start position:0%
+okay so here
+ 
+
+ align:start position:0%
+okay so here
+were the mazes he used he had three
+
+ align:start position:0%
+were the mazes he used he had three
+ 
+
+ align:start position:0%
+were the mazes he used he had three
+different mazes
+
+ align:start position:0%
+different mazes
+ 
+
+ align:start position:0%
+different mazes
+the one at the bottom there very simple
+
+ align:start position:0%
+the one at the bottom there very simple
+ 
+
+ align:start position:0%
+the one at the bottom there very simple
+maze
+
+ align:start position:0%
+maze
+ 
+
+ align:start position:0%
+maze
+it just requires the animal to turn left
+
+ align:start position:0%
+it just requires the animal to turn left
+ 
+
+ align:start position:0%
+it just requires the animal to turn left
+the animals put here
+
+ align:start position:0%
+the animals put here
+ 
+
+ align:start position:0%
+the animals put here
+which says s that's the start box
+
+ align:start position:0%
+which says s that's the start box
+ 
+
+ align:start position:0%
+which says s that's the start box
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+food is placed on one side and not the
+
+ align:start position:0%
+food is placed on one side and not the
+ 
+
+ align:start position:0%
+food is placed on one side and not the
+other the f indicates food
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+he trains him for a number of trials
+
+ align:start position:0%
+he trains him for a number of trials
+ 
+
+ align:start position:0%
+he trains him for a number of trials
+until the rat now is always turning left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maze 2 is a little more complex and mace
+
+ align:start position:0%
+maze 2 is a little more complex and mace
+ 
+
+ align:start position:0%
+maze 2 is a little more complex and mace
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+is the most complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this method again is to train on one
+
+ align:start position:0%
+so this method again is to train on one
+ 
+
+ align:start position:0%
+so this method again is to train on one
+of the mazes only one of them
+
+ align:start position:0%
+of the mazes only one of them
+ 
+
+ align:start position:0%
+of the mazes only one of them
+then make the lesion bilateral lesion
+
+ align:start position:0%
+then make the lesion bilateral lesion
+ 
+
+ align:start position:0%
+then make the lesion bilateral lesion
+then he waited so
+
+ align:start position:0%
+then he waited so
+ 
+
+ align:start position:0%
+then he waited so
+the animal is no longer affected by the
+
+ align:start position:0%
+the animal is no longer affected by the
+ 
+
+ align:start position:0%
+the animal is no longer affected by the
+anesthetic and he recovers for a while
+
+ align:start position:0%
+anesthetic and he recovers for a while
+ 
+
+ align:start position:0%
+anesthetic and he recovers for a while
+from the lesion i don't remember how
+
+ align:start position:0%
+from the lesion i don't remember how
+ 
+
+ align:start position:0%
+from the lesion i don't remember how
+long he recovered
+
+ align:start position:0%
+long he recovered
+ 
+
+ align:start position:0%
+long he recovered
+he let the animals recover probably at
+
+ align:start position:0%
+he let the animals recover probably at
+ 
+
+ align:start position:0%
+he let the animals recover probably at
+least two weeks
+
+ align:start position:0%
+least two weeks
+ 
+
+ align:start position:0%
+least two weeks
+and then he tested for retention
+
+ align:start position:0%
+and then he tested for retention
+ 
+
+ align:start position:0%
+and then he tested for retention
+the question was is the memory still
+
+ align:start position:0%
+the question was is the memory still
+ 
+
+ align:start position:0%
+the question was is the memory still
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this is
+
+ align:start position:0%
+now this is
+ 
+
+ align:start position:0%
+now this is
+a diagram of his findings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well on the abscissa very showing the
+
+ align:start position:0%
+well on the abscissa very showing the
+ 
+
+ align:start position:0%
+well on the abscissa very showing the
+percentage destruction of the neocortex
+
+ align:start position:0%
+percentage destruction of the neocortex
+ 
+
+ align:start position:0%
+percentage destruction of the neocortex
+now notice there's nothing about
+
+ align:start position:0%
+now notice there's nothing about
+ 
+
+ align:start position:0%
+now notice there's nothing about
+localization there just percentage of
+
+ align:start position:0%
+localization there just percentage of
+ 
+
+ align:start position:0%
+localization there just percentage of
+destruction
+
+ align:start position:0%
+destruction
+ 
+
+ align:start position:0%
+destruction
+and on the ordinate he's plotting the
+
+ align:start position:0%
+and on the ordinate he's plotting the
+ 
+
+ align:start position:0%
+and on the ordinate he's plotting the
+errors
+
+ align:start position:0%
+errors
+ 
+
+ align:start position:0%
+errors
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and at least for maze 3 where it's very
+
+ align:start position:0%
+and at least for maze 3 where it's very
+ 
+
+ align:start position:0%
+and at least for maze 3 where it's very
+clear that's the most complex maze
+
+ align:start position:0%
+clear that's the most complex maze
+ 
+
+ align:start position:0%
+clear that's the most complex maze
+okay it's very clear that
+
+ align:start position:0%
+okay it's very clear that
+ 
+
+ align:start position:0%
+okay it's very clear that
+if he makes larger lesions he's
+
+ align:start position:0%
+if he makes larger lesions he's
+ 
+
+ align:start position:0%
+if he makes larger lesions he's
+disturbing the learning a lot they make
+
+ align:start position:0%
+disturbing the learning a lot they make
+ 
+
+ align:start position:0%
+disturbing the learning a lot they make
+many more errors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he claimed
+
+ align:start position:0%
+he claimed
+ 
+
+ align:start position:0%
+he claimed
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it didn't make any difference
+
+ align:start position:0%
+it didn't make any difference
+ 
+
+ align:start position:0%
+it didn't make any difference
+where the lesion was
+
+ align:start position:0%
+where the lesion was
+ 
+
+ align:start position:0%
+where the lesion was
+that anterior lesions
+
+ align:start position:0%
+that anterior lesions
+ 
+
+ align:start position:0%
+that anterior lesions
+if they were of a certain size produced
+
+ align:start position:0%
+if they were of a certain size produced
+ 
+
+ align:start position:0%
+if they were of a certain size produced
+about the same disturbance
+
+ align:start position:0%
+about the same disturbance
+ 
+
+ align:start position:0%
+about the same disturbance
+of the memory of the animal as the
+
+ align:start position:0%
+of the memory of the animal as the
+ 
+
+ align:start position:0%
+of the memory of the animal as the
+posteriorly
+
+ align:start position:0%
+posteriorly
+ 
+
+ align:start position:0%
+posteriorly
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and similarly for other localizations
+
+ align:start position:0%
+and similarly for other localizations
+ 
+
+ align:start position:0%
+and similarly for other localizations
+he said that in that respect the
+
+ align:start position:0%
+he said that in that respect the
+ 
+
+ align:start position:0%
+he said that in that respect the
+neocortex was equi-potential for
+
+ align:start position:0%
+neocortex was equi-potential for
+ 
+
+ align:start position:0%
+neocortex was equi-potential for
+may's learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's his principle of equipotentiality
+
+ align:start position:0%
+that's his principle of equipotentiality
+ 
+
+ align:start position:0%
+that's his principle of equipotentiality
+and he said it
+
+ align:start position:0%
+and he said it
+ 
+
+ align:start position:0%
+and he said it
+to learn the maze the animal what the
+
+ align:start position:0%
+to learn the maze the animal what the
+ 
+
+ align:start position:0%
+to learn the maze the animal what the
+rat needed was a certain quantity of
+
+ align:start position:0%
+rat needed was a certain quantity of
+ 
+
+ align:start position:0%
+rat needed was a certain quantity of
+cortex and the more he had the better
+
+ align:start position:0%
+cortex and the more he had the better
+ 
+
+ align:start position:0%
+cortex and the more he had the better
+okay that was his principle of mass
+
+ align:start position:0%
+okay that was his principle of mass
+ 
+
+ align:start position:0%
+okay that was his principle of mass
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+they mean almost the same thing
+
+ align:start position:0%
+they mean almost the same thing
+ 
+
+ align:start position:0%
+they mean almost the same thing
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was his conclusion and he wrote
+
+ align:start position:0%
+so that was his conclusion and he wrote
+ 
+
+ align:start position:0%
+so that was his conclusion and he wrote
+a book about it
+
+ align:start position:0%
+a book about it
+ 
+
+ align:start position:0%
+a book about it
+published in the late 20s
+
+ align:start position:0%
+published in the late 20s
+ 
+
+ align:start position:0%
+published in the late 20s
+and that remained
+
+ align:start position:0%
+and that remained
+ 
+
+ align:start position:0%
+and that remained
+and it was often cited because of its
+
+ align:start position:0%
+and it was often cited because of its
+ 
+
+ align:start position:0%
+and it was often cited because of its
+beautiful methodology
+
+ align:start position:0%
+beautiful methodology
+ 
+
+ align:start position:0%
+beautiful methodology
+until
+
+ align:start position:0%
+until
+ 
+
+ align:start position:0%
+until
+these irreverent people at mit
+
+ align:start position:0%
+these irreverent people at mit
+ 
+
+ align:start position:0%
+these irreverent people at mit
+in 1965 decided to re-analyze lashley's
+
+ align:start position:0%
+in 1965 decided to re-analyze lashley's
+ 
+
+ align:start position:0%
+in 1965 decided to re-analyze lashley's
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+charlie gross the first author
+
+ align:start position:0%
+charlie gross the first author
+ 
+
+ align:start position:0%
+charlie gross the first author
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+moved to princeton after that and
+
+ align:start position:0%
+moved to princeton after that and
+ 
+
+ align:start position:0%
+moved to princeton after that and
+actually moved to harvard first then
+
+ align:start position:0%
+actually moved to harvard first then
+ 
+
+ align:start position:0%
+actually moved to harvard first then
+princeton
+
+ align:start position:0%
+princeton
+ 
+
+ align:start position:0%
+princeton
+steve sharper is retired
+
+ align:start position:0%
+steve sharper is retired
+ 
+
+ align:start position:0%
+steve sharper is retired
+from our faculty not too long ago and
+
+ align:start position:0%
+from our faculty not too long ago and
+ 
+
+ align:start position:0%
+from our faculty not too long ago and
+cohen was one of their
+
+ align:start position:0%
+cohen was one of their
+ 
+
+ align:start position:0%
+cohen was one of their
+graduate students
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they thought that
+
+ align:start position:0%
+they thought that
+ 
+
+ align:start position:0%
+they thought that
+he was probably what they looked at his
+
+ align:start position:0%
+he was probably what they looked at his
+ 
+
+ align:start position:0%
+he was probably what they looked at his
+lesions they said he was probably
+
+ align:start position:0%
+lesions they said he was probably
+ 
+
+ align:start position:0%
+lesions they said he was probably
+disturbing two distinct functions that
+
+ align:start position:0%
+disturbing two distinct functions that
+ 
+
+ align:start position:0%
+disturbing two distinct functions that
+were both needed for solving his mazes
+
+ align:start position:0%
+were both needed for solving his mazes
+ 
+
+ align:start position:0%
+were both needed for solving his mazes
+one was visual abilities
+
+ align:start position:0%
+one was visual abilities
+ 
+
+ align:start position:0%
+one was visual abilities
+which depend on this area
+
+ align:start position:0%
+which depend on this area
+ 
+
+ align:start position:0%
+which depend on this area
+back here this is the visual cortex
+
+ align:start position:0%
+back here this is the visual cortex
+ 
+
+ align:start position:0%
+back here this is the visual cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it's often called area 17
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or striat cortex
+
+ align:start position:0%
+or striat cortex
+ 
+
+ align:start position:0%
+or striat cortex
+and the other area
+
+ align:start position:0%
+and the other area
+ 
+
+ align:start position:0%
+and the other area
+they felt he was disturbing was this
+
+ align:start position:0%
+they felt he was disturbing was this
+ 
+
+ align:start position:0%
+they felt he was disturbing was this
+region anterior to the motor cortex
+
+ align:start position:0%
+region anterior to the motor cortex
+ 
+
+ align:start position:0%
+region anterior to the motor cortex
+again bilaterally
+
+ align:start position:0%
+again bilaterally
+ 
+
+ align:start position:0%
+again bilaterally
+prefrontal cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why
+
+ align:start position:0%
+now why
+ 
+
+ align:start position:0%
+now why
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+was known in in studies done shortly
+
+ align:start position:0%
+was known in in studies done shortly
+ 
+
+ align:start position:0%
+was known in in studies done shortly
+before this to be important for
+
+ align:start position:0%
+before this to be important for
+ 
+
+ align:start position:0%
+before this to be important for
+learning to alternate left
+
+ align:start position:0%
+learning to alternate left
+ 
+
+ align:start position:0%
+learning to alternate left
+turns and right turns
+
+ align:start position:0%
+turns and right turns
+ 
+
+ align:start position:0%
+turns and right turns
+and if you look at this maze
+
+ align:start position:0%
+and if you look at this maze
+ 
+
+ align:start position:0%
+and if you look at this maze
+you can see that
+
+ align:start position:0%
+you can see that
+ 
+
+ align:start position:0%
+you can see that
+these mazes depend on the rats being
+
+ align:start position:0%
+these mazes depend on the rats being
+ 
+
+ align:start position:0%
+these mazes depend on the rats being
+able to learn to turn one way and then
+
+ align:start position:0%
+able to learn to turn one way and then
+ 
+
+ align:start position:0%
+able to learn to turn one way and then
+the other you see the top maze there is
+
+ align:start position:0%
+the other you see the top maze there is
+ 
+
+ align:start position:0%
+the other you see the top maze there is
+to turn right then left and right and
+
+ align:start position:0%
+to turn right then left and right and
+ 
+
+ align:start position:0%
+to turn right then left and right and
+left then right to get into the food box
+
+ align:start position:0%
+left then right to get into the food box
+ 
+
+ align:start position:0%
+left then right to get into the food box
+so maybe and they did separate tests of
+
+ align:start position:0%
+so maybe and they did separate tests of
+ 
+
+ align:start position:0%
+so maybe and they did separate tests of
+that themselves
+
+ align:start position:0%
+that themselves
+ 
+
+ align:start position:0%
+that themselves
+and they showed that
+
+ align:start position:0%
+and they showed that
+ 
+
+ align:start position:0%
+and they showed that
+if they made lesions
+
+ align:start position:0%
+if they made lesions
+ 
+
+ align:start position:0%
+if they made lesions
+of that anterior area
+
+ align:start position:0%
+of that anterior area
+ 
+
+ align:start position:0%
+of that anterior area
+and compared it with lesions the posture
+
+ align:start position:0%
+and compared it with lesions the posture
+ 
+
+ align:start position:0%
+and compared it with lesions the posture
+area it disturbed only the ability to
+
+ align:start position:0%
+area it disturbed only the ability to
+ 
+
+ align:start position:0%
+area it disturbed only the ability to
+alternate it didn't disturb visual
+
+ align:start position:0%
+alternate it didn't disturb visual
+ 
+
+ align:start position:0%
+alternate it didn't disturb visual
+discrimination abilities they had
+
+ align:start position:0%
+discrimination abilities they had
+ 
+
+ align:start position:0%
+discrimination abilities they had
+separate tests
+
+ align:start position:0%
+separate tests
+ 
+
+ align:start position:0%
+separate tests
+for visual discrimination discrimination
+
+ align:start position:0%
+for visual discrimination discrimination
+ 
+
+ align:start position:0%
+for visual discrimination discrimination
+of patterns
+
+ align:start position:0%
+of patterns
+ 
+
+ align:start position:0%
+of patterns
+that depends on the visual cortex but
+
+ align:start position:0%
+that depends on the visual cortex but
+ 
+
+ align:start position:0%
+that depends on the visual cortex but
+not on that anterior area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so and they demonstrated this also
+
+ align:start position:0%
+okay so and they demonstrated this also
+ 
+
+ align:start position:0%
+okay so and they demonstrated this also
+with they had a series of mazes
+
+ align:start position:0%
+with they had a series of mazes
+ 
+
+ align:start position:0%
+with they had a series of mazes
+that they found to be quite dependent on
+
+ align:start position:0%
+that they found to be quite dependent on
+ 
+
+ align:start position:0%
+that they found to be quite dependent on
+the visual cortex
+
+ align:start position:0%
+the visual cortex
+ 
+
+ align:start position:0%
+the visual cortex
+and they had a separate test of
+
+ align:start position:0%
+and they had a separate test of
+ 
+
+ align:start position:0%
+and they had a separate test of
+alternation and didn't involve mazes at
+
+ align:start position:0%
+alternation and didn't involve mazes at
+ 
+
+ align:start position:0%
+alternation and didn't involve mazes at
+all but involved pressing a bar the left
+
+ align:start position:0%
+all but involved pressing a bar the left
+ 
+
+ align:start position:0%
+all but involved pressing a bar the left
+bar then the right bar and the left bar
+
+ align:start position:0%
+bar then the right bar and the left bar
+ 
+
+ align:start position:0%
+bar then the right bar and the left bar
+on the right bar and so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they showed that these two functions
+
+ align:start position:0%
+so they showed that these two functions
+ 
+
+ align:start position:0%
+so they showed that these two functions
+were disturbed separately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they can these two functions can be
+
+ align:start position:0%
+and they can these two functions can be
+ 
+
+ align:start position:0%
+and they can these two functions can be
+dissociated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by these lesions
+
+ align:start position:0%
+by these lesions
+ 
+
+ align:start position:0%
+by these lesions
+so they concluded that last week's
+
+ align:start position:0%
+so they concluded that last week's
+ 
+
+ align:start position:0%
+so they concluded that last week's
+interpretation was incorrect and in fact
+
+ align:start position:0%
+interpretation was incorrect and in fact
+ 
+
+ align:start position:0%
+interpretation was incorrect and in fact
+after lashley's work
+
+ align:start position:0%
+after lashley's work
+ 
+
+ align:start position:0%
+after lashley's work
+a man named hunter argued
+
+ align:start position:0%
+a man named hunter argued
+ 
+
+ align:start position:0%
+a man named hunter argued
+fairly in a fairly similar way he said
+
+ align:start position:0%
+fairly in a fairly similar way he said
+ 
+
+ align:start position:0%
+fairly in a fairly similar way he said
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+may's learning is such a complex
+
+ align:start position:0%
+may's learning is such a complex
+ 
+
+ align:start position:0%
+may's learning is such a complex
+function the rat is using
+
+ align:start position:0%
+function the rat is using
+ 
+
+ align:start position:0%
+function the rat is using
+many different senses
+
+ align:start position:0%
+many different senses
+ 
+
+ align:start position:0%
+many different senses
+he's probably using olfaction somatic
+
+ align:start position:0%
+he's probably using olfaction somatic
+ 
+
+ align:start position:0%
+he's probably using olfaction somatic
+sensation so forth
+
+ align:start position:0%
+sensation so forth
+ 
+
+ align:start position:0%
+sensation so forth
+he didn't know about this dependence of
+
+ align:start position:0%
+he didn't know about this dependence of
+ 
+
+ align:start position:0%
+he didn't know about this dependence of
+alternation on the frontal cortex he
+
+ align:start position:0%
+alternation on the frontal cortex he
+ 
+
+ align:start position:0%
+alternation on the frontal cortex he
+probably did know about the visual
+
+ align:start position:0%
+probably did know about the visual
+ 
+
+ align:start position:0%
+probably did know about the visual
+cortex and vision
+
+ align:start position:0%
+cortex and vision
+ 
+
+ align:start position:0%
+cortex and vision
+and hunter argued that ashley was
+
+ align:start position:0%
+and hunter argued that ashley was
+ 
+
+ align:start position:0%
+and hunter argued that ashley was
+probably with his lesions just
+
+ align:start position:0%
+probably with his lesions just
+ 
+
+ align:start position:0%
+probably with his lesions just
+disturbing to varying degrees
+
+ align:start position:0%
+disturbing to varying degrees
+ 
+
+ align:start position:0%
+disturbing to varying degrees
+different senses
+
+ align:start position:0%
+different senses
+ 
+
+ align:start position:0%
+different senses
+all which
+
+ align:start position:0%
+all which
+ 
+
+ align:start position:0%
+all which
+were used in maze learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but together the hunter arguments
+
+ align:start position:0%
+but together the hunter arguments
+ 
+
+ align:start position:0%
+but together the hunter arguments
+who and what under always lost the
+
+ align:start position:0%
+who and what under always lost the
+ 
+
+ align:start position:0%
+who and what under always lost the
+debates to lashley lashley was a very
+
+ align:start position:0%
+debates to lashley lashley was a very
+ 
+
+ align:start position:0%
+debates to lashley lashley was a very
+good debater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's why this
+
+ align:start position:0%
+so that's why this
+ 
+
+ align:start position:0%
+so that's why this
+study was needed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we still recognize lashley for
+
+ align:start position:0%
+so now we still recognize lashley for
+ 
+
+ align:start position:0%
+so now we still recognize lashley for
+his methodology but not for
+
+ align:start position:0%
+his methodology but not for
+ 
+
+ align:start position:0%
+his methodology but not for
+his analysis of that particular
+
+ align:start position:0%
+his analysis of that particular
+ 
+
+ align:start position:0%
+his analysis of that particular
+experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the keys to that kind of problem are
+
+ align:start position:0%
+the keys to that kind of problem are
+ 
+
+ align:start position:0%
+the keys to that kind of problem are
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+you need both near anatomical knowledge
+
+ align:start position:0%
+you need both near anatomical knowledge
+ 
+
+ align:start position:0%
+you need both near anatomical knowledge
+and behavioral knowledge
+
+ align:start position:0%
+and behavioral knowledge
+ 
+
+ align:start position:0%
+and behavioral knowledge
+lashley didn't have adequate behavioral
+
+ align:start position:0%
+lashley didn't have adequate behavioral
+ 
+
+ align:start position:0%
+lashley didn't have adequate behavioral
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+about the functions he was
+
+ align:start position:0%
+about the functions he was
+ 
+
+ align:start position:0%
+about the functions he was
+the rat might be using to solve those
+
+ align:start position:0%
+the rat might be using to solve those
+ 
+
+ align:start position:0%
+the rat might be using to solve those
+mazes
+
+ align:start position:0%
+mazes
+ 
+
+ align:start position:0%
+mazes
+did later do
+
+ align:start position:0%
+did later do
+ 
+
+ align:start position:0%
+did later do
+more neuroanatomy and came to
+
+ align:start position:0%
+more neuroanatomy and came to
+ 
+
+ align:start position:0%
+more neuroanatomy and came to
+he actually studied the localization of
+
+ align:start position:0%
+he actually studied the localization of
+ 
+
+ align:start position:0%
+he actually studied the localization of
+the visual cortex in the rat
+
+ align:start position:0%
+the visual cortex in the rat
+ 
+
+ align:start position:0%
+the visual cortex in the rat
+and so he did come to understand
+
+ align:start position:0%
+and so he did come to understand
+ 
+
+ align:start position:0%
+and so he did come to understand
+that posterior localization
+
+ align:start position:0%
+that posterior localization
+ 
+
+ align:start position:0%
+that posterior localization
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+area that
+
+ align:start position:0%
+area that
+ 
+
+ align:start position:0%
+area that
+is most closely connected
+
+ align:start position:0%
+is most closely connected
+ 
+
+ align:start position:0%
+is most closely connected
+to the to the retina
+
+ align:start position:0%
+to the to the retina
+ 
+
+ align:start position:0%
+to the to the retina
+through a pathway that's become well
+
+ align:start position:0%
+through a pathway that's become well
+ 
+
+ align:start position:0%
+through a pathway that's become well
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+was only becoming well known at the time
+
+ align:start position:0%
+was only becoming well known at the time
+ 
+
+ align:start position:0%
+was only becoming well known at the time
+of lashley
+
+ align:start position:0%
+of lashley
+ 
+
+ align:start position:0%
+of lashley
+last year's experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you need both kinds of knowledge to
+
+ align:start position:0%
+so you need both kinds of knowledge to
+ 
+
+ align:start position:0%
+so you need both kinds of knowledge to
+do that and
+
+ align:start position:0%
+do that and
+ 
+
+ align:start position:0%
+do that and
+even when i was in graduate school
+
+ align:start position:0%
+even when i was in graduate school
+ 
+
+ align:start position:0%
+even when i was in graduate school
+which is a long time ago
+
+ align:start position:0%
+which is a long time ago
+ 
+
+ align:start position:0%
+which is a long time ago
+1960s
+
+ align:start position:0%
+1960s
+ 
+
+ align:start position:0%
+1960s
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+many people were still doing this kind
+
+ align:start position:0%
+many people were still doing this kind
+ 
+
+ align:start position:0%
+many people were still doing this kind
+of lesion study with
+
+ align:start position:0%
+of lesion study with
+ 
+
+ align:start position:0%
+of lesion study with
+very little neuroanatomy
+
+ align:start position:0%
+very little neuroanatomy
+ 
+
+ align:start position:0%
+very little neuroanatomy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and they they didn't worry much about
+
+ align:start position:0%
+and they they didn't worry much about
+ 
+
+ align:start position:0%
+and they they didn't worry much about
+connections in the brain they weren't
+
+ align:start position:0%
+connections in the brain they weren't
+ 
+
+ align:start position:0%
+connections in the brain they weren't
+interpreting they were thinking of
+
+ align:start position:0%
+interpreting they were thinking of
+ 
+
+ align:start position:0%
+interpreting they were thinking of
+localization of function without
+
+ align:start position:0%
+localization of function without
+ 
+
+ align:start position:0%
+localization of function without
+thinking about the connections involved
+
+ align:start position:0%
+thinking about the connections involved
+ 
+
+ align:start position:0%
+thinking about the connections involved
+and that was a major problem
+
+ align:start position:0%
+and that was a major problem
+ 
+
+ align:start position:0%
+and that was a major problem
+i'll give you one other example there
+
+ align:start position:0%
+i'll give you one other example there
+ 
+
+ align:start position:0%
+i'll give you one other example there
+we'll show you this kind of problem
+
+ align:start position:0%
+we'll show you this kind of problem
+ 
+
+ align:start position:0%
+we'll show you this kind of problem
+especially with
+
+ align:start position:0%
+especially with
+ 
+
+ align:start position:0%
+especially with
+knowing the behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because neuroscience is studying
+
+ align:start position:0%
+because neuroscience is studying
+ 
+
+ align:start position:0%
+because neuroscience is studying
+branding behavior
+
+ align:start position:0%
+branding behavior
+ 
+
+ align:start position:0%
+branding behavior
+i would say that
+
+ align:start position:0%
+i would say that
+ 
+
+ align:start position:0%
+i would say that
+with all the advances in
+
+ align:start position:0%
+with all the advances in
+ 
+
+ align:start position:0%
+with all the advances in
+anatomy and physiology
+
+ align:start position:0%
+anatomy and physiology
+ 
+
+ align:start position:0%
+anatomy and physiology
+behavioral knowledge is still often legs
+
+ align:start position:0%
+behavioral knowledge is still often legs
+ 
+
+ align:start position:0%
+behavioral knowledge is still often legs
+behind a little bit let me give you one
+
+ align:start position:0%
+behind a little bit let me give you one
+ 
+
+ align:start position:0%
+behind a little bit let me give you one
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+a claim developed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+findings that were done in the
+
+ align:start position:0%
+findings that were done in the
+ 
+
+ align:start position:0%
+findings that were done in the
+experiments at rutgers mainly where the
+
+ align:start position:0%
+experiments at rutgers mainly where the
+ 
+
+ align:start position:0%
+experiments at rutgers mainly where the
+claim was made that sexual ability
+
+ align:start position:0%
+claim was made that sexual ability
+ 
+
+ align:start position:0%
+claim was made that sexual ability
+is located in the neocortex
+
+ align:start position:0%
+is located in the neocortex
+ 
+
+ align:start position:0%
+is located in the neocortex
+in the male rat but not the female
+
+ align:start position:0%
+in the male rat but not the female
+ 
+
+ align:start position:0%
+in the male rat but not the female
+how did they come to that conclusion
+
+ align:start position:0%
+how did they come to that conclusion
+ 
+
+ align:start position:0%
+how did they come to that conclusion
+well very simple
+
+ align:start position:0%
+well very simple
+ 
+
+ align:start position:0%
+well very simple
+they they did lesions like lashley
+
+ align:start position:0%
+they they did lesions like lashley
+ 
+
+ align:start position:0%
+they they did lesions like lashley
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+lesions of varying size in the neocortex
+
+ align:start position:0%
+lesions of varying size in the neocortex
+ 
+
+ align:start position:0%
+lesions of varying size in the neocortex
+and they did it in both male rats and
+
+ align:start position:0%
+and they did it in both male rats and
+ 
+
+ align:start position:0%
+and they did it in both male rats and
+female rats
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then they had a very simple test of
+
+ align:start position:0%
+and then they had a very simple test of
+ 
+
+ align:start position:0%
+and then they had a very simple test of
+sexual behavior they simply observed
+
+ align:start position:0%
+sexual behavior they simply observed
+ 
+
+ align:start position:0%
+sexual behavior they simply observed
+whether the animals would copulate or
+
+ align:start position:0%
+whether the animals would copulate or
+ 
+
+ align:start position:0%
+whether the animals would copulate or
+not and they found that the females
+
+ align:start position:0%
+not and they found that the females
+ 
+
+ align:start position:0%
+not and they found that the females
+would still go into the lordosis posture
+
+ align:start position:0%
+would still go into the lordosis posture
+ 
+
+ align:start position:0%
+would still go into the lordosis posture
+and accept the male rat
+
+ align:start position:0%
+and accept the male rat
+ 
+
+ align:start position:0%
+and accept the male rat
+and the rat the male rats if they had
+
+ align:start position:0%
+and the rat the male rats if they had
+ 
+
+ align:start position:0%
+and the rat the male rats if they had
+much neocortex missing failed to
+
+ align:start position:0%
+much neocortex missing failed to
+ 
+
+ align:start position:0%
+much neocortex missing failed to
+copulate
+
+ align:start position:0%
+copulate
+ 
+
+ align:start position:0%
+copulate
+so very simple they said neocortex
+
+ align:start position:0%
+so very simple they said neocortex
+ 
+
+ align:start position:0%
+so very simple they said neocortex
+is needed for sexual behavior in the
+
+ align:start position:0%
+is needed for sexual behavior in the
+ 
+
+ align:start position:0%
+is needed for sexual behavior in the
+male and not the female
+
+ align:start position:0%
+male and not the female
+ 
+
+ align:start position:0%
+male and not the female
+of course everybody thought well let's
+
+ align:start position:0%
+of course everybody thought well let's
+ 
+
+ align:start position:0%
+of course everybody thought well let's
+see it's a higher function in the male
+
+ align:start position:0%
+see it's a higher function in the male
+ 
+
+ align:start position:0%
+see it's a higher function in the male
+not the female
+
+ align:start position:0%
+not the female
+ 
+
+ align:start position:0%
+not the female
+what was wrong with that
+
+ align:start position:0%
+what was wrong with that
+ 
+
+ align:start position:0%
+what was wrong with that
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+you've got to think about the behavior
+
+ align:start position:0%
+you've got to think about the behavior
+ 
+
+ align:start position:0%
+you've got to think about the behavior
+they didn't understand
+
+ align:start position:0%
+they didn't understand
+ 
+
+ align:start position:0%
+they didn't understand
+sexual behavior in the female at all
+
+ align:start position:0%
+sexual behavior in the female at all
+ 
+
+ align:start position:0%
+sexual behavior in the female at all
+all they understood was this posture
+
+ align:start position:0%
+all they understood was this posture
+ 
+
+ align:start position:0%
+all they understood was this posture
+that the animal entered
+
+ align:start position:0%
+that the animal entered
+ 
+
+ align:start position:0%
+that the animal entered
+the equivalent in the male would be say
+
+ align:start position:0%
+the equivalent in the male would be say
+ 
+
+ align:start position:0%
+the equivalent in the male would be say
+the ejaculation reflex
+
+ align:start position:0%
+the ejaculation reflex
+ 
+
+ align:start position:0%
+the ejaculation reflex
+that wasn't disturbed after the
+
+ align:start position:0%
+that wasn't disturbed after the
+ 
+
+ align:start position:0%
+that wasn't disturbed after the
+neocortical lesions
+
+ align:start position:0%
+neocortical lesions
+ 
+
+ align:start position:0%
+neocortical lesions
+what they were disturbing was the
+
+ align:start position:0%
+what they were disturbing was the
+ 
+
+ align:start position:0%
+what they were disturbing was the
+ability of the rat the male rat to
+
+ align:start position:0%
+ability of the rat the male rat to
+ 
+
+ align:start position:0%
+ability of the rat the male rat to
+orient to the females to find her to
+
+ align:start position:0%
+orient to the females to find her to
+ 
+
+ align:start position:0%
+orient to the females to find her to
+position himself properly and so forth
+
+ align:start position:0%
+position himself properly and so forth
+ 
+
+ align:start position:0%
+position himself properly and so forth
+that involves a lot of
+
+ align:start position:0%
+that involves a lot of
+ 
+
+ align:start position:0%
+that involves a lot of
+sensory motor control they were
+
+ align:start position:0%
+sensory motor control they were
+ 
+
+ align:start position:0%
+sensory motor control they were
+disturbing the senses
+
+ align:start position:0%
+disturbing the senses
+ 
+
+ align:start position:0%
+disturbing the senses
+and motor control by making those
+
+ align:start position:0%
+and motor control by making those
+ 
+
+ align:start position:0%
+and motor control by making those
+lesions but what about the female
+
+ align:start position:0%
+lesions but what about the female
+ 
+
+ align:start position:0%
+lesions but what about the female
+well if they only look at the end point
+
+ align:start position:0%
+well if they only look at the end point
+ 
+
+ align:start position:0%
+well if they only look at the end point
+they're missing solicitation behavior
+
+ align:start position:0%
+they're missing solicitation behavior
+ 
+
+ align:start position:0%
+they're missing solicitation behavior
+mate choice a lot of
+
+ align:start position:0%
+mate choice a lot of
+ 
+
+ align:start position:0%
+mate choice a lot of
+things we know about sexual behavior of
+
+ align:start position:0%
+things we know about sexual behavior of
+ 
+
+ align:start position:0%
+things we know about sexual behavior of
+female
+
+ align:start position:0%
+female
+ 
+
+ align:start position:0%
+female
+rodents and many other animals almost
+
+ align:start position:0%
+rodents and many other animals almost
+ 
+
+ align:start position:0%
+rodents and many other animals almost
+all animals okay because they weren't
+
+ align:start position:0%
+all animals okay because they weren't
+ 
+
+ align:start position:0%
+all animals okay because they weren't
+good ethologists
+
+ align:start position:0%
+good ethologists
+ 
+
+ align:start position:0%
+good ethologists
+they didn't
+
+ align:start position:0%
+they didn't
+ 
+
+ align:start position:0%
+they didn't
+look at the behavior in any
+
+ align:start position:0%
+look at the behavior in any
+ 
+
+ align:start position:0%
+look at the behavior in any
+comprehensive way
+
+ align:start position:0%
+comprehensive way
+ 
+
+ align:start position:0%
+comprehensive way
+so they made the same kind of mistake
+
+ align:start position:0%
+so they made the same kind of mistake
+ 
+
+ align:start position:0%
+so they made the same kind of mistake
+well a somewhat different kind of
+
+ align:start position:0%
+well a somewhat different kind of
+ 
+
+ align:start position:0%
+well a somewhat different kind of
+mistake from what i actually made
+
+ align:start position:0%
+mistake from what i actually made
+ 
+
+ align:start position:0%
+mistake from what i actually made
+i just want to point out that when you
+
+ align:start position:0%
+i just want to point out that when you
+ 
+
+ align:start position:0%
+i just want to point out that when you
+read these kinds of claims in the
+
+ align:start position:0%
+read these kinds of claims in the
+ 
+
+ align:start position:0%
+read these kinds of claims in the
+literature
+
+ align:start position:0%
+literature
+ 
+
+ align:start position:0%
+literature
+you've got to think about
+
+ align:start position:0%
+you've got to think about
+ 
+
+ align:start position:0%
+you've got to think about
+whether they adequately dealt with
+
+ align:start position:0%
+whether they adequately dealt with
+ 
+
+ align:start position:0%
+whether they adequately dealt with
+both anatomical knowledge and behavioral
+
+ align:start position:0%
+both anatomical knowledge and behavioral
+ 
+
+ align:start position:0%
+both anatomical knowledge and behavioral
+knowledge before you just believe it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concerning the memory problem
+
+ align:start position:0%
+concerning the memory problem
+ 
+
+ align:start position:0%
+concerning the memory problem
+i like to tell this story
+
+ align:start position:0%
+i like to tell this story
+ 
+
+ align:start position:0%
+i like to tell this story
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+my first visit to a telephone switching
+
+ align:start position:0%
+my first visit to a telephone switching
+ 
+
+ align:start position:0%
+my first visit to a telephone switching
+station
+
+ align:start position:0%
+station
+ 
+
+ align:start position:0%
+station
+in the middle of the
+
+ align:start position:0%
+in the middle of the
+ 
+
+ align:start position:0%
+in the middle of the
+well it was probably about 40 years ago
+
+ align:start position:0%
+well it was probably about 40 years ago
+ 
+
+ align:start position:0%
+well it was probably about 40 years ago
+my brother was running one of these
+
+ align:start position:0%
+my brother was running one of these
+ 
+
+ align:start position:0%
+my brother was running one of these
+stations for
+
+ align:start position:0%
+stations for
+ 
+
+ align:start position:0%
+stations for
+the telephone a large the large
+
+ align:start position:0%
+the telephone a large the large
+ 
+
+ align:start position:0%
+the telephone a large the large
+telephone company was the only one at
+
+ align:start position:0%
+telephone company was the only one at
+ 
+
+ align:start position:0%
+telephone company was the only one at
+the time bell telephone and
+
+ align:start position:0%
+the time bell telephone and
+ 
+
+ align:start position:0%
+the time bell telephone and
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+inside the station you saw this enormous
+
+ align:start position:0%
+inside the station you saw this enormous
+ 
+
+ align:start position:0%
+inside the station you saw this enormous
+amount of machinery they were basically
+
+ align:start position:0%
+amount of machinery they were basically
+ 
+
+ align:start position:0%
+amount of machinery they were basically
+relays
+
+ align:start position:0%
+relays
+ 
+
+ align:start position:0%
+relays
+connected with wires coming from these
+
+ align:start position:0%
+connected with wires coming from these
+ 
+
+ align:start position:0%
+connected with wires coming from these
+large cables from outside enormous
+
+ align:start position:0%
+large cables from outside enormous
+ 
+
+ align:start position:0%
+large cables from outside enormous
+numbers of wires
+
+ align:start position:0%
+numbers of wires
+ 
+
+ align:start position:0%
+numbers of wires
+and i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i wasn't
+
+ align:start position:0%
+i wasn't
+ 
+
+ align:start position:0%
+i wasn't
+an electrical engineer
+
+ align:start position:0%
+an electrical engineer
+ 
+
+ align:start position:0%
+an electrical engineer
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i understood something about circuits
+
+ align:start position:0%
+i understood something about circuits
+ 
+
+ align:start position:0%
+i understood something about circuits
+and i was learning about the brain so i
+
+ align:start position:0%
+and i was learning about the brain so i
+ 
+
+ align:start position:0%
+and i was learning about the brain so i
+asked him where's the
+
+ align:start position:0%
+asked him where's the
+ 
+
+ align:start position:0%
+asked him where's the
+input and he showed me the input cables
+
+ align:start position:0%
+input and he showed me the input cables
+ 
+
+ align:start position:0%
+input and he showed me the input cables
+coming in where's the output
+
+ align:start position:0%
+coming in where's the output
+ 
+
+ align:start position:0%
+coming in where's the output
+he showed me that enormous amounts of
+
+ align:start position:0%
+he showed me that enormous amounts of
+ 
+
+ align:start position:0%
+he showed me that enormous amounts of
+machinery involved in this i said but
+
+ align:start position:0%
+machinery involved in this i said but
+ 
+
+ align:start position:0%
+machinery involved in this i said but
+there's another problem how do you
+
+ align:start position:0%
+there's another problem how do you
+ 
+
+ align:start position:0%
+there's another problem how do you
+remember who's calling who so you can
+
+ align:start position:0%
+remember who's calling who so you can
+ 
+
+ align:start position:0%
+remember who's calling who so you can
+build them
+
+ align:start position:0%
+build them
+ 
+
+ align:start position:0%
+build them
+and he said oh that's over there it was
+
+ align:start position:0%
+and he said oh that's over there it was
+ 
+
+ align:start position:0%
+and he said oh that's over there it was
+this little device
+
+ align:start position:0%
+this little device
+ 
+
+ align:start position:0%
+this little device
+you know obviously using a different
+
+ align:start position:0%
+you know obviously using a different
+ 
+
+ align:start position:0%
+you know obviously using a different
+kind of circuitry a little tiny thing
+
+ align:start position:0%
+kind of circuitry a little tiny thing
+ 
+
+ align:start position:0%
+kind of circuitry a little tiny thing
+in one part of the room that he said did
+
+ align:start position:0%
+in one part of the room that he said did
+ 
+
+ align:start position:0%
+in one part of the room that he said did
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+all the memory functions
+
+ align:start position:0%
+all the memory functions
+ 
+
+ align:start position:0%
+all the memory functions
+and it made me realize that probably in
+
+ align:start position:0%
+and it made me realize that probably in
+ 
+
+ align:start position:0%
+and it made me realize that probably in
+the brain it's something similar in the
+
+ align:start position:0%
+the brain it's something similar in the
+ 
+
+ align:start position:0%
+the brain it's something similar in the
+neocortex a lot of the cortical
+
+ align:start position:0%
+neocortex a lot of the cortical
+ 
+
+ align:start position:0%
+neocortex a lot of the cortical
+apparatus is involved in sensory
+
+ align:start position:0%
+apparatus is involved in sensory
+ 
+
+ align:start position:0%
+apparatus is involved in sensory
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+and motor coordination
+
+ align:start position:0%
+and motor coordination
+ 
+
+ align:start position:0%
+and motor coordination
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+memory could be distributed or it could
+
+ align:start position:0%
+memory could be distributed or it could
+ 
+
+ align:start position:0%
+memory could be distributed or it could
+be localized but it could be much more
+
+ align:start position:0%
+be localized but it could be much more
+ 
+
+ align:start position:0%
+be localized but it could be much more
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+to deal with and of course that proved
+
+ align:start position:0%
+to deal with and of course that proved
+ 
+
+ align:start position:0%
+to deal with and of course that proved
+to be true with the ensuing years
+
+ align:start position:0%
+to be true with the ensuing years
+ 
+
+ align:start position:0%
+to be true with the ensuing years
+but now we're beginning to get a much
+
+ align:start position:0%
+but now we're beginning to get a much
+ 
+
+ align:start position:0%
+but now we're beginning to get a much
+better handle on that as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we deal with this problem of
+
+ align:start position:0%
+when we deal with this problem of
+ 
+
+ align:start position:0%
+when we deal with this problem of
+localization of function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have to think about the question
+
+ align:start position:0%
+you have to think about the question
+ 
+
+ align:start position:0%
+you have to think about the question
+what is localized
+
+ align:start position:0%
+what is localized
+ 
+
+ align:start position:0%
+what is localized
+what are we trying to localize is it a
+
+ align:start position:0%
+what are we trying to localize is it a
+ 
+
+ align:start position:0%
+what are we trying to localize is it a
+conscious entity is it
+
+ align:start position:0%
+conscious entity is it
+ 
+
+ align:start position:0%
+conscious entity is it
+a psychological ability is it memory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my answer is that no those are
+
+ align:start position:0%
+my answer is that no those are
+ 
+
+ align:start position:0%
+my answer is that no those are
+not brain words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have to be very wary when you read
+
+ align:start position:0%
+you have to be very wary when you read
+ 
+
+ align:start position:0%
+you have to be very wary when you read
+about centers for pleasure the pleasure
+
+ align:start position:0%
+about centers for pleasure the pleasure
+ 
+
+ align:start position:0%
+about centers for pleasure the pleasure
+center the sex center the hunger center
+
+ align:start position:0%
+center the sex center the hunger center
+ 
+
+ align:start position:0%
+center the sex center the hunger center
+the center for mental arithmetic or
+
+ align:start position:0%
+the center for mental arithmetic or
+ 
+
+ align:start position:0%
+the center for mental arithmetic or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+because those are
+
+ align:start position:0%
+because those are
+ 
+
+ align:start position:0%
+because those are
+psychological functions
+
+ align:start position:0%
+psychological functions
+ 
+
+ align:start position:0%
+psychological functions
+that's not what's localized
+
+ align:start position:0%
+that's not what's localized
+ 
+
+ align:start position:0%
+that's not what's localized
+what's localized is
+
+ align:start position:0%
+what's localized is
+ 
+
+ align:start position:0%
+what's localized is
+physical or physiological processes in a
+
+ align:start position:0%
+physical or physiological processes in a
+ 
+
+ align:start position:0%
+physical or physiological processes in a
+structural substrate
+
+ align:start position:0%
+structural substrate
+ 
+
+ align:start position:0%
+structural substrate
+we're never going to find the ghost in
+
+ align:start position:0%
+we're never going to find the ghost in
+ 
+
+ align:start position:0%
+we're never going to find the ghost in
+the machine
+
+ align:start position:0%
+the machine
+ 
+
+ align:start position:0%
+the machine
+it's not there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to find the input pathways
+
+ align:start position:0%
+you're going to find the input pathways
+ 
+
+ align:start position:0%
+you're going to find the input pathways
+you're going to find output pathways
+
+ align:start position:0%
+you're going to find output pathways
+ 
+
+ align:start position:0%
+you're going to find output pathways
+you're going to find
+
+ align:start position:0%
+you're going to find
+ 
+
+ align:start position:0%
+you're going to find
+processing
+
+ align:start position:0%
+processing
+ 
+
+ align:start position:0%
+processing
+connections in the intermediate network
+
+ align:start position:0%
+connections in the intermediate network
+ 
+
+ align:start position:0%
+connections in the intermediate network
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+luria the russian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neuropsychologist the great
+
+ align:start position:0%
+neuropsychologist the great
+ 
+
+ align:start position:0%
+neuropsychologist the great
+neuropsychologist in the
+
+ align:start position:0%
+neuropsychologist in the
+ 
+
+ align:start position:0%
+neuropsychologist in the
+last century
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had this state has this statement in one
+
+ align:start position:0%
+had this state has this statement in one
+ 
+
+ align:start position:0%
+had this state has this statement in one
+of his works on neuropsychology he said
+
+ align:start position:0%
+of his works on neuropsychology he said
+ 
+
+ align:start position:0%
+of his works on neuropsychology he said
+that mental functions is complex
+
+ align:start position:0%
+that mental functions is complex
+ 
+
+ align:start position:0%
+that mental functions is complex
+functional systems cannot be localized
+
+ align:start position:0%
+functional systems cannot be localized
+ 
+
+ align:start position:0%
+functional systems cannot be localized
+in narrow zones of cortex or in isolated
+
+ align:start position:0%
+in narrow zones of cortex or in isolated
+ 
+
+ align:start position:0%
+in narrow zones of cortex or in isolated
+cell groups
+
+ align:start position:0%
+cell groups
+ 
+
+ align:start position:0%
+cell groups
+you see they involve a lot of apparatus
+
+ align:start position:0%
+you see they involve a lot of apparatus
+ 
+
+ align:start position:0%
+you see they involve a lot of apparatus
+you might disturb a function more with
+
+ align:start position:0%
+you might disturb a function more with
+ 
+
+ align:start position:0%
+you might disturb a function more with
+lesions in one place than another
+
+ align:start position:0%
+lesions in one place than another
+ 
+
+ align:start position:0%
+lesions in one place than another
+but the function as a whole you depend
+
+ align:start position:0%
+but the function as a whole you depend
+ 
+
+ align:start position:0%
+but the function as a whole you depend
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a greater complexity of connections and
+
+ align:start position:0%
+a greater complexity of connections and
+ 
+
+ align:start position:0%
+a greater complexity of connections and
+that certainly
+
+ align:start position:0%
+that certainly
+ 
+
+ align:start position:0%
+that certainly
+remains true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if we go to the extreme we can say
+
+ align:start position:0%
+but if we go to the extreme we can say
+ 
+
+ align:start position:0%
+but if we go to the extreme we can say
+well don't brains think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can't we say that thinking's localized
+
+ align:start position:0%
+can't we say that thinking's localized
+ 
+
+ align:start position:0%
+can't we say that thinking's localized
+in the brain
+
+ align:start position:0%
+in the brain
+ 
+
+ align:start position:0%
+in the brain
+makai who we met before
+
+ align:start position:0%
+makai who we met before
+ 
+
+ align:start position:0%
+makai who we met before
+said that this is a poor question
+
+ align:start position:0%
+said that this is a poor question
+ 
+
+ align:start position:0%
+said that this is a poor question
+because it mixes different conceptual
+
+ align:start position:0%
+because it mixes different conceptual
+ 
+
+ align:start position:0%
+because it mixes different conceptual
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+and this is a statement from his paper a
+
+ align:start position:0%
+and this is a statement from his paper a
+ 
+
+ align:start position:0%
+and this is a statement from his paper a
+mind's eye view of the brain
+
+ align:start position:0%
+mind's eye view of the brain
+ 
+
+ align:start position:0%
+mind's eye view of the brain
+he says if we want to use language
+
+ align:start position:0%
+he says if we want to use language
+ 
+
+ align:start position:0%
+he says if we want to use language
+consistently we cannot say that brains
+
+ align:start position:0%
+consistently we cannot say that brains
+ 
+
+ align:start position:0%
+consistently we cannot say that brains
+think or decide
+
+ align:start position:0%
+think or decide
+ 
+
+ align:start position:0%
+think or decide
+brains do those physical things
+
+ align:start position:0%
+brains do those physical things
+ 
+
+ align:start position:0%
+brains do those physical things
+appropriate in their own logical
+
+ align:start position:0%
+appropriate in their own logical
+ 
+
+ align:start position:0%
+appropriate in their own logical
+dimensions as correlates of what people
+
+ align:start position:0%
+dimensions as correlates of what people
+ 
+
+ align:start position:0%
+dimensions as correlates of what people
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+like i say or animals when deciding
+
+ align:start position:0%
+like i say or animals when deciding
+ 
+
+ align:start position:0%
+like i say or animals when deciding
+thinking feeling hoping fearing bleeding
+
+ align:start position:0%
+thinking feeling hoping fearing bleeding
+ 
+
+ align:start position:0%
+thinking feeling hoping fearing bleeding
+so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's just talk briefly about the third
+
+ align:start position:0%
+let's just talk briefly about the third
+ 
+
+ align:start position:0%
+let's just talk briefly about the third
+type of goal
+
+ align:start position:0%
+type of goal
+ 
+
+ align:start position:0%
+type of goal
+of people
+
+ align:start position:0%
+of people
+ 
+
+ align:start position:0%
+of people
+that weren't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessarily concerned with reducing
+
+ align:start position:0%
+necessarily concerned with reducing
+ 
+
+ align:start position:0%
+necessarily concerned with reducing
+behavior to a specific circuit and they
+
+ align:start position:0%
+behavior to a specific circuit and they
+ 
+
+ align:start position:0%
+behavior to a specific circuit and they
+weren't necessarily concerned with
+
+ align:start position:0%
+weren't necessarily concerned with
+ 
+
+ align:start position:0%
+weren't necessarily concerned with
+localizing function but they're
+
+ align:start position:0%
+localizing function but they're
+ 
+
+ align:start position:0%
+localizing function but they're
+interested in correlating
+
+ align:start position:0%
+interested in correlating
+ 
+
+ align:start position:0%
+interested in correlating
+events of
+
+ align:start position:0%
+events of
+ 
+
+ align:start position:0%
+events of
+in the brain with behavioral events
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i find this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these attempts to correlate brand
+
+ align:start position:0%
+these attempts to correlate brand
+ 
+
+ align:start position:0%
+these attempts to correlate brand
+behavior to just be
+
+ align:start position:0%
+behavior to just be
+ 
+
+ align:start position:0%
+behavior to just be
+a never-ending fascination for people
+
+ align:start position:0%
+a never-ending fascination for people
+ 
+
+ align:start position:0%
+a never-ending fascination for people
+in fact they often forget that finding
+
+ align:start position:0%
+in fact they often forget that finding
+ 
+
+ align:start position:0%
+in fact they often forget that finding
+the correlation doesn't
+
+ align:start position:0%
+the correlation doesn't
+ 
+
+ align:start position:0%
+the correlation doesn't
+really prove causation at all
+
+ align:start position:0%
+really prove causation at all
+ 
+
+ align:start position:0%
+really prove causation at all
+and let's just give a few examples
+
+ align:start position:0%
+and let's just give a few examples
+ 
+
+ align:start position:0%
+and let's just give a few examples
+if we record with little electrodes
+
+ align:start position:0%
+if we record with little electrodes
+ 
+
+ align:start position:0%
+if we record with little electrodes
+placed on the scalp we can record very
+
+ align:start position:0%
+placed on the scalp we can record very
+ 
+
+ align:start position:0%
+placed on the scalp we can record very
+small potentials there that are changing
+
+ align:start position:0%
+small potentials there that are changing
+ 
+
+ align:start position:0%
+small potentials there that are changing
+okay because they're picking up
+
+ align:start position:0%
+okay because they're picking up
+ 
+
+ align:start position:0%
+okay because they're picking up
+currents are being induced by electrical
+
+ align:start position:0%
+currents are being induced by electrical
+ 
+
+ align:start position:0%
+currents are being induced by electrical
+changes in the underlying brain at least
+
+ align:start position:0%
+changes in the underlying brain at least
+ 
+
+ align:start position:0%
+changes in the underlying brain at least
+part just below the skull
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we call those recordings the
+
+ align:start position:0%
+and we call those recordings the
+ 
+
+ align:start position:0%
+and we call those recordings the
+electron cephalograph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's usually put on a graph
+
+ align:start position:0%
+it's usually put on a graph
+ 
+
+ align:start position:0%
+it's usually put on a graph
+showing the amplitude of these waves
+
+ align:start position:0%
+showing the amplitude of these waves
+ 
+
+ align:start position:0%
+showing the amplitude of these waves
+picked up by different leads attached to
+
+ align:start position:0%
+picked up by different leads attached to
+ 
+
+ align:start position:0%
+picked up by different leads attached to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cortex the recording is pretty much the
+
+ align:start position:0%
+cortex the recording is pretty much the
+ 
+
+ align:start position:0%
+cortex the recording is pretty much the
+same as with electrocardiogram
+
+ align:start position:0%
+same as with electrocardiogram
+ 
+
+ align:start position:0%
+same as with electrocardiogram
+okay you're looking at electrolyte
+
+ align:start position:0%
+okay you're looking at electrolyte
+ 
+
+ align:start position:0%
+okay you're looking at electrolyte
+tissue the heart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we find that the pattern of what we
+
+ align:start position:0%
+and we find that the pattern of what we
+ 
+
+ align:start position:0%
+and we find that the pattern of what we
+we call those brain waves the pattern of
+
+ align:start position:0%
+we call those brain waves the pattern of
+ 
+
+ align:start position:0%
+we call those brain waves the pattern of
+those currents changes
+
+ align:start position:0%
+those currents changes
+ 
+
+ align:start position:0%
+those currents changes
+it's correlated with states of arousal
+
+ align:start position:0%
+it's correlated with states of arousal
+ 
+
+ align:start position:0%
+it's correlated with states of arousal
+or of sleep
+
+ align:start position:0%
+or of sleep
+ 
+
+ align:start position:0%
+or of sleep
+and that they're not localized functions
+
+ align:start position:0%
+and that they're not localized functions
+ 
+
+ align:start position:0%
+and that they're not localized functions
+but they appear to be they might be a
+
+ align:start position:0%
+but they appear to be they might be a
+ 
+
+ align:start position:0%
+but they appear to be they might be a
+little different and different than
+
+ align:start position:0%
+little different and different than
+ 
+
+ align:start position:0%
+little different and different than
+different leads but
+
+ align:start position:0%
+different leads but
+ 
+
+ align:start position:0%
+different leads but
+basically we're looking at
+
+ align:start position:0%
+basically we're looking at
+ 
+
+ align:start position:0%
+basically we're looking at
+states of the brain
+
+ align:start position:0%
+states of the brain
+ 
+
+ align:start position:0%
+states of the brain
+not at localized functions
+
+ align:start position:0%
+not at localized functions
+ 
+
+ align:start position:0%
+not at localized functions
+and that's fascinated people because
+
+ align:start position:0%
+and that's fascinated people because
+ 
+
+ align:start position:0%
+and that's fascinated people because
+when that was discovered now they had a
+
+ align:start position:0%
+when that was discovered now they had a
+ 
+
+ align:start position:0%
+when that was discovered now they had a
+way of looking at different stages of
+
+ align:start position:0%
+way of looking at different stages of
+ 
+
+ align:start position:0%
+way of looking at different stages of
+sleep and exploring you know what are
+
+ align:start position:0%
+sleep and exploring you know what are
+ 
+
+ align:start position:0%
+sleep and exploring you know what are
+the differences in different stages of
+
+ align:start position:0%
+the differences in different stages of
+ 
+
+ align:start position:0%
+the differences in different stages of
+sleep or in different states of arousal
+
+ align:start position:0%
+sleep or in different states of arousal
+ 
+
+ align:start position:0%
+sleep or in different states of arousal
+in the waking state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this kind of
+
+ align:start position:0%
+so this kind of
+ 
+
+ align:start position:0%
+so this kind of
+these attempts to correlate random
+
+ align:start position:0%
+these attempts to correlate random
+ 
+
+ align:start position:0%
+these attempts to correlate random
+behavior have led to some very different
+
+ align:start position:0%
+behavior have led to some very different
+ 
+
+ align:start position:0%
+behavior have led to some very different
+kinds of information
+
+ align:start position:0%
+kinds of information
+ 
+
+ align:start position:0%
+kinds of information
+about brain and behavior
+
+ align:start position:0%
+about brain and behavior
+ 
+
+ align:start position:0%
+about brain and behavior
+they led to the idea of states of the
+
+ align:start position:0%
+they led to the idea of states of the
+ 
+
+ align:start position:0%
+they led to the idea of states of the
+brain a hole where the brain can change
+
+ align:start position:0%
+brain a hole where the brain can change
+ 
+
+ align:start position:0%
+brain a hole where the brain can change
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+large areas of tissue can change its
+
+ align:start position:0%
+large areas of tissue can change its
+ 
+
+ align:start position:0%
+large areas of tissue can change its
+state behave differently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the other kind of correlation
+
+ align:start position:0%
+but the other kind of correlation
+ 
+
+ align:start position:0%
+but the other kind of correlation
+that you see much more often is to
+
+ align:start position:0%
+that you see much more often is to
+ 
+
+ align:start position:0%
+that you see much more often is to
+correlate the activity of neurons in
+
+ align:start position:0%
+correlate the activity of neurons in
+ 
+
+ align:start position:0%
+correlate the activity of neurons in
+specific areas of the brain with
+
+ align:start position:0%
+specific areas of the brain with
+ 
+
+ align:start position:0%
+specific areas of the brain with
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+so for example if you're looking at the
+
+ align:start position:0%
+so for example if you're looking at the
+ 
+
+ align:start position:0%
+so for example if you're looking at the
+movement of the wrist and you record
+
+ align:start position:0%
+movement of the wrist and you record
+ 
+
+ align:start position:0%
+movement of the wrist and you record
+you've say train the monkey to make
+
+ align:start position:0%
+you've say train the monkey to make
+ 
+
+ align:start position:0%
+you've say train the monkey to make
+simple wrist flexion and extension
+
+ align:start position:0%
+simple wrist flexion and extension
+ 
+
+ align:start position:0%
+simple wrist flexion and extension
+you can find neurons for example in the
+
+ align:start position:0%
+you can find neurons for example in the
+ 
+
+ align:start position:0%
+you can find neurons for example in the
+motor cortex
+
+ align:start position:0%
+motor cortex
+ 
+
+ align:start position:0%
+motor cortex
+that specifically fire with precise in a
+
+ align:start position:0%
+that specifically fire with precise in a
+ 
+
+ align:start position:0%
+that specifically fire with precise in a
+precise temporal correlation
+
+ align:start position:0%
+precise temporal correlation
+ 
+
+ align:start position:0%
+precise temporal correlation
+with that movement
+
+ align:start position:0%
+with that movement
+ 
+
+ align:start position:0%
+with that movement
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+certain neurons will fire when the
+
+ align:start position:0%
+certain neurons will fire when the
+ 
+
+ align:start position:0%
+certain neurons will fire when the
+animal is flexing certain neurons will
+
+ align:start position:0%
+animal is flexing certain neurons will
+ 
+
+ align:start position:0%
+animal is flexing certain neurons will
+fire when he's extending
+
+ align:start position:0%
+fire when he's extending
+ 
+
+ align:start position:0%
+fire when he's extending
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and in fact they find neurons that will
+
+ align:start position:0%
+and in fact they find neurons that will
+ 
+
+ align:start position:0%
+and in fact they find neurons that will
+start to fire before the movement
+
+ align:start position:0%
+start to fire before the movement
+ 
+
+ align:start position:0%
+start to fire before the movement
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+always seem to precede the movement
+
+ align:start position:0%
+always seem to precede the movement
+ 
+
+ align:start position:0%
+always seem to precede the movement
+by a rather precise time interval
+
+ align:start position:0%
+by a rather precise time interval
+ 
+
+ align:start position:0%
+by a rather precise time interval
+there are other neurons especially in
+
+ align:start position:0%
+there are other neurons especially in
+ 
+
+ align:start position:0%
+there are other neurons especially in
+the sensory cortex which will follow the
+
+ align:start position:0%
+the sensory cortex which will follow the
+ 
+
+ align:start position:0%
+the sensory cortex which will follow the
+movement but will fire after the
+
+ align:start position:0%
+movement but will fire after the
+ 
+
+ align:start position:0%
+movement but will fire after the
+movement occurs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that kind of correlation has also
+
+ align:start position:0%
+so that kind of correlation has also
+ 
+
+ align:start position:0%
+so that kind of correlation has also
+been fascinating to people
+
+ align:start position:0%
+been fascinating to people
+ 
+
+ align:start position:0%
+been fascinating to people
+it never
+
+ align:start position:0%
+it never
+ 
+
+ align:start position:0%
+it never
+looking at the limitations here it never
+
+ align:start position:0%
+looking at the limitations here it never
+ 
+
+ align:start position:0%
+looking at the limitations here it never
+tells you exactly what causes what
+
+ align:start position:0%
+tells you exactly what causes what
+ 
+
+ align:start position:0%
+tells you exactly what causes what
+without other experiments to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modern imaging techniques are of a
+
+ align:start position:0%
+modern imaging techniques are of a
+ 
+
+ align:start position:0%
+modern imaging techniques are of a
+similar thing we're looking at
+
+ align:start position:0%
+similar thing we're looking at
+ 
+
+ align:start position:0%
+similar thing we're looking at
+correlations
+
+ align:start position:0%
+correlations
+ 
+
+ align:start position:0%
+correlations
+of what's happening
+
+ align:start position:0%
+of what's happening
+ 
+
+ align:start position:0%
+of what's happening
+not telling us about cause and effect
+
+ align:start position:0%
+not telling us about cause and effect
+ 
+
+ align:start position:0%
+not telling us about cause and effect
+but we do find consistent
+
+ align:start position:0%
+but we do find consistent
+ 
+
+ align:start position:0%
+but we do find consistent
+areas of the brain
+
+ align:start position:0%
+areas of the brain
+ 
+
+ align:start position:0%
+areas of the brain
+that where the tissue oxygenation is
+
+ align:start position:0%
+that where the tissue oxygenation is
+ 
+
+ align:start position:0%
+that where the tissue oxygenation is
+greater the blood flow is greater when
+
+ align:start position:0%
+greater the blood flow is greater when
+ 
+
+ align:start position:0%
+greater the blood flow is greater when
+the person is doing a certain thing or
+
+ align:start position:0%
+the person is doing a certain thing or
+ 
+
+ align:start position:0%
+the person is doing a certain thing or
+sensing a certain thing or
+
+ align:start position:0%
+sensing a certain thing or
+ 
+
+ align:start position:0%
+sensing a certain thing or
+making certain movements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's that third goal that we see
+
+ align:start position:0%
+so it's that third goal that we see
+ 
+
+ align:start position:0%
+so it's that third goal that we see
+pursued
+
+ align:start position:0%
+pursued
+ 
+
+ align:start position:0%
+pursued
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+modern imaging techniques
+
+ align:start position:0%
+modern imaging techniques
+ 
+
+ align:start position:0%
+modern imaging techniques
+but it does make of course many
+
+ align:start position:0%
+but it does make of course many
+ 
+
+ align:start position:0%
+but it does make of course many
+suggestions about behavior if you can
+
+ align:start position:0%
+suggestions about behavior if you can
+ 
+
+ align:start position:0%
+suggestions about behavior if you can
+localize
+
+ align:start position:0%
+localize
+ 
+
+ align:start position:0%
+localize
+consistently areas that are
+
+ align:start position:0%
+consistently areas that are
+ 
+
+ align:start position:0%
+consistently areas that are
+have this kind of activation and a
+
+ align:start position:0%
+have this kind of activation and a
+ 
+
+ align:start position:0%
+have this kind of activation and a
+certain behavior then we know we can go
+
+ align:start position:0%
+certain behavior then we know we can go
+ 
+
+ align:start position:0%
+certain behavior then we know we can go
+from there and thinking about how
+
+ align:start position:0%
+from there and thinking about how
+ 
+
+ align:start position:0%
+from there and thinking about how
+different regions are
+
+ align:start position:0%
+different regions are
+ 
+
+ align:start position:0%
+different regions are
+dividing up the task of
+
+ align:start position:0%
+dividing up the task of
+ 
+
+ align:start position:0%
+dividing up the task of
+controlling a certain function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what we're going i'll let i'm going to
+
+ align:start position:0%
+what we're going i'll let i'm going to
+ 
+
+ align:start position:0%
+what we're going i'll let i'm going to
+go through a little bit about the modern
+
+ align:start position:0%
+go through a little bit about the modern
+ 
+
+ align:start position:0%
+go through a little bit about the modern
+subsystems approach i think that's was
+
+ align:start position:0%
+subsystems approach i think that's was
+ 
+
+ align:start position:0%
+subsystems approach i think that's was
+the last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the modern synthesis has to take into
+
+ align:start position:0%
+the modern synthesis has to take into
+ 
+
+ align:start position:0%
+the modern synthesis has to take into
+account a number of things for one thing
+
+ align:start position:0%
+account a number of things for one thing
+ 
+
+ align:start position:0%
+account a number of things for one thing
+we know that central nervous system
+
+ align:start position:0%
+we know that central nervous system
+ 
+
+ align:start position:0%
+we know that central nervous system
+ingredients the neurons and the other
+
+ align:start position:0%
+ingredients the neurons and the other
+ 
+
+ align:start position:0%
+ingredients the neurons and the other
+cells involved in the nervous system are
+
+ align:start position:0%
+cells involved in the nervous system are
+ 
+
+ align:start position:0%
+cells involved in the nervous system are
+a lot more complex than
+
+ align:start position:0%
+a lot more complex than
+ 
+
+ align:start position:0%
+a lot more complex than
+reflex notions would indicate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our circuits the way we draw circuits
+
+ align:start position:0%
+so our circuits the way we draw circuits
+ 
+
+ align:start position:0%
+so our circuits the way we draw circuits
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+pretty limited and what they mean
+
+ align:start position:0%
+pretty limited and what they mean
+ 
+
+ align:start position:0%
+pretty limited and what they mean
+because they don't take into account
+
+ align:start position:0%
+because they don't take into account
+ 
+
+ align:start position:0%
+because they don't take into account
+some of the complexity of neurons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know that we can localize subsystems
+
+ align:start position:0%
+we know that we can localize subsystems
+ 
+
+ align:start position:0%
+we know that we can localize subsystems
+and we saw that with carl wernicke
+
+ align:start position:0%
+and we saw that with carl wernicke
+ 
+
+ align:start position:0%
+and we saw that with carl wernicke
+localizing areas that were consistently
+
+ align:start position:0%
+localizing areas that were consistently
+ 
+
+ align:start position:0%
+localizing areas that were consistently
+involved in understanding speech and in
+
+ align:start position:0%
+involved in understanding speech and in
+ 
+
+ align:start position:0%
+involved in understanding speech and in
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+so we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+draw information flow diagrams making
+
+ align:start position:0%
+draw information flow diagrams making
+ 
+
+ align:start position:0%
+draw information flow diagrams making
+use of
+
+ align:start position:0%
+use of
+ 
+
+ align:start position:0%
+use of
+their anatomical knowledge
+
+ align:start position:0%
+their anatomical knowledge
+ 
+
+ align:start position:0%
+their anatomical knowledge
+localization of functional knowledge
+
+ align:start position:0%
+localization of functional knowledge
+ 
+
+ align:start position:0%
+localization of functional knowledge
+and what we know about neurons
+
+ align:start position:0%
+and what we know about neurons
+ 
+
+ align:start position:0%
+and what we know about neurons
+we also have to realize that the
+
+ align:start position:0%
+we also have to realize that the
+ 
+
+ align:start position:0%
+we also have to realize that the
+connections aren't always the way the
+
+ align:start position:0%
+connections aren't always the way the
+ 
+
+ align:start position:0%
+connections aren't always the way the
+reflexologists would had depicted them
+
+ align:start position:0%
+reflexologists would had depicted them
+ 
+
+ align:start position:0%
+reflexologists would had depicted them
+from sensory to
+
+ align:start position:0%
+from sensory to
+ 
+
+ align:start position:0%
+from sensory to
+sensation to response
+
+ align:start position:0%
+sensation to response
+ 
+
+ align:start position:0%
+sensation to response
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+feedback from motor to the sensory side
+
+ align:start position:0%
+feedback from motor to the sensory side
+ 
+
+ align:start position:0%
+feedback from motor to the sensory side
+also in fact one of the major
+
+ align:start position:0%
+also in fact one of the major
+ 
+
+ align:start position:0%
+also in fact one of the major
+connections of some these the sensory
+
+ align:start position:0%
+connections of some these the sensory
+ 
+
+ align:start position:0%
+connections of some these the sensory
+cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+responding to somatic sensation
+
+ align:start position:0%
+responding to somatic sensation
+ 
+
+ align:start position:0%
+responding to somatic sensation
+is to the sensory side of the spinal
+
+ align:start position:0%
+is to the sensory side of the spinal
+ 
+
+ align:start position:0%
+is to the sensory side of the spinal
+cord
+
+ align:start position:0%
+cord
+ 
+
+ align:start position:0%
+cord
+that's a connection that in fact
+
+ align:start position:0%
+that's a connection that in fact
+ 
+
+ align:start position:0%
+that's a connection that in fact
+physiologists haven't even now paid a
+
+ align:start position:0%
+physiologists haven't even now paid a
+ 
+
+ align:start position:0%
+physiologists haven't even now paid a
+whole lot of attention to
+
+ align:start position:0%
+whole lot of attention to
+ 
+
+ align:start position:0%
+whole lot of attention to
+but it's one that professor beatsy in
+
+ align:start position:0%
+but it's one that professor beatsy in
+ 
+
+ align:start position:0%
+but it's one that professor beatsy in
+our department is becoming much more
+
+ align:start position:0%
+our department is becoming much more
+ 
+
+ align:start position:0%
+our department is becoming much more
+interested in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we also have to remember that our
+
+ align:start position:0%
+we also have to remember that our
+ 
+
+ align:start position:0%
+we also have to remember that our
+connections can be excitatory and
+
+ align:start position:0%
+connections can be excitatory and
+ 
+
+ align:start position:0%
+connections can be excitatory and
+inhibitory and there are different types
+
+ align:start position:0%
+inhibitory and there are different types
+ 
+
+ align:start position:0%
+inhibitory and there are different types
+of connections which we'll be talking
+
+ align:start position:0%
+of connections which we'll be talking
+ 
+
+ align:start position:0%
+of connections which we'll be talking
+about in the next lectures
+
+ align:start position:0%
+about in the next lectures
+ 
+
+ align:start position:0%
+about in the next lectures
+we also know that our modulating
+
+ align:start position:0%
+we also know that our modulating
+ 
+
+ align:start position:0%
+we also know that our modulating
+influence
+
+ align:start position:0%
+influence
+ 
+
+ align:start position:0%
+influence
+that are more system-wide
+
+ align:start position:0%
+that are more system-wide
+ 
+
+ align:start position:0%
+that are more system-wide
+their diffuse connections of certain
+
+ align:start position:0%
+their diffuse connections of certain
+ 
+
+ align:start position:0%
+their diffuse connections of certain
+systems in the brain
+
+ align:start position:0%
+systems in the brain
+ 
+
+ align:start position:0%
+systems in the brain
+there's also changes in the chemical
+
+ align:start position:0%
+there's also changes in the chemical
+ 
+
+ align:start position:0%
+there's also changes in the chemical
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+that we know less about
+
+ align:start position:0%
+that we know less about
+ 
+
+ align:start position:0%
+that we know less about
+but the anatomists have told us quite a
+
+ align:start position:0%
+but the anatomists have told us quite a
+ 
+
+ align:start position:0%
+but the anatomists have told us quite a
+bit about some of these diffuse
+
+ align:start position:0%
+bit about some of these diffuse
+ 
+
+ align:start position:0%
+bit about some of these diffuse
+connections connections
+
+ align:start position:0%
+connections connections
+ 
+
+ align:start position:0%
+connections connections
+and finally we have to remember that
+
+ align:start position:0%
+and finally we have to remember that
+ 
+
+ align:start position:0%
+and finally we have to remember that
+nerve cells
+
+ align:start position:0%
+nerve cells
+ 
+
+ align:start position:0%
+nerve cells
+can generate their own activity
+
+ align:start position:0%
+can generate their own activity
+ 
+
+ align:start position:0%
+can generate their own activity
+but that varies a lot depending on the
+
+ align:start position:0%
+but that varies a lot depending on the
+ 
+
+ align:start position:0%
+but that varies a lot depending on the
+type of neuron okay
+
+ align:start position:0%
+type of neuron okay
+ 
+
+ align:start position:0%
+type of neuron okay
+they can be spontaneously active
+
+ align:start position:0%
+they can be spontaneously active
+ 
+
+ align:start position:0%
+they can be spontaneously active
+so what i'm going to do and i'll only do
+
+ align:start position:0%
+so what i'm going to do and i'll only do
+ 
+
+ align:start position:0%
+so what i'm going to do and i'll only do
+a case of reflexes and we'll stop this
+
+ align:start position:0%
+a case of reflexes and we'll stop this
+ 
+
+ align:start position:0%
+a case of reflexes and we'll stop this
+lecture and we'll go back we'll do this
+
+ align:start position:0%
+lecture and we'll go back we'll do this
+ 
+
+ align:start position:0%
+lecture and we'll go back we'll do this
+next time and then we'll start talking
+
+ align:start position:0%
+next time and then we'll start talking
+ 
+
+ align:start position:0%
+next time and then we'll start talking
+about single neurons
+
+ align:start position:0%
+about single neurons
+ 
+
+ align:start position:0%
+about single neurons
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+talk about information flow in the case
+
+ align:start position:0%
+talk about information flow in the case
+ 
+
+ align:start position:0%
+talk about information flow in the case
+of reflexes
+
+ align:start position:0%
+of reflexes
+ 
+
+ align:start position:0%
+of reflexes
+then i'll use simple gating mechanisms
+
+ align:start position:0%
+then i'll use simple gating mechanisms
+ 
+
+ align:start position:0%
+then i'll use simple gating mechanisms
+to explain motivation and intention
+
+ align:start position:0%
+to explain motivation and intention
+ 
+
+ align:start position:0%
+to explain motivation and intention
+and talk a little bit about evolution of
+
+ align:start position:0%
+and talk a little bit about evolution of
+ 
+
+ align:start position:0%
+and talk a little bit about evolution of
+higher control
+
+ align:start position:0%
+higher control
+ 
+
+ align:start position:0%
+higher control
+this would be an information flow
+
+ align:start position:0%
+this would be an information flow
+ 
+
+ align:start position:0%
+this would be an information flow
+diagram of the reflex you draw the input
+
+ align:start position:0%
+diagram of the reflex you draw the input
+ 
+
+ align:start position:0%
+diagram of the reflex you draw the input
+the sensory side
+
+ align:start position:0%
+the sensory side
+ 
+
+ align:start position:0%
+the sensory side
+it comes into
+
+ align:start position:0%
+it comes into
+ 
+
+ align:start position:0%
+it comes into
+a box
+
+ align:start position:0%
+a box
+ 
+
+ align:start position:0%
+a box
+which corresponds to the central nervous
+
+ align:start position:0%
+which corresponds to the central nervous
+ 
+
+ align:start position:0%
+which corresponds to the central nervous
+system and then goes out that would
+
+ align:start position:0%
+system and then goes out that would
+ 
+
+ align:start position:0%
+system and then goes out that would
+correspond to the connections that go
+
+ align:start position:0%
+correspond to the connections that go
+ 
+
+ align:start position:0%
+correspond to the connections that go
+out through motor neurons muscles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can draw such diagrams
+
+ align:start position:0%
+we can draw such diagrams
+ 
+
+ align:start position:0%
+we can draw such diagrams
+without referring to the anatomy we can
+
+ align:start position:0%
+without referring to the anatomy we can
+ 
+
+ align:start position:0%
+without referring to the anatomy we can
+base it simply on behavioral studies
+
+ align:start position:0%
+base it simply on behavioral studies
+ 
+
+ align:start position:0%
+base it simply on behavioral studies
+and in fact
+
+ align:start position:0%
+and in fact
+ 
+
+ align:start position:0%
+and in fact
+skinner at harvard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very well known behaviorist said
+
+ align:start position:0%
+very well known behaviorist said
+ 
+
+ align:start position:0%
+very well known behaviorist said
+we don't ever really have to open that
+
+ align:start position:0%
+we don't ever really have to open that
+ 
+
+ align:start position:0%
+we don't ever really have to open that
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+because we can study the laws that
+
+ align:start position:0%
+because we can study the laws that
+ 
+
+ align:start position:0%
+because we can study the laws that
+relate the input and the output
+
+ align:start position:0%
+relate the input and the output
+ 
+
+ align:start position:0%
+relate the input and the output
+we can study this sensory conditions we
+
+ align:start position:0%
+we can study this sensory conditions we
+ 
+
+ align:start position:0%
+we can study this sensory conditions we
+can study behavior of the animal and we
+
+ align:start position:0%
+can study behavior of the animal and we
+ 
+
+ align:start position:0%
+can study behavior of the animal and we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+find the lawful relationships between
+
+ align:start position:0%
+find the lawful relationships between
+ 
+
+ align:start position:0%
+find the lawful relationships between
+these so we don't need the nervous
+
+ align:start position:0%
+these so we don't need the nervous
+ 
+
+ align:start position:0%
+these so we don't need the nervous
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's some famous debates for people
+
+ align:start position:0%
+there's some famous debates for people
+ 
+
+ align:start position:0%
+there's some famous debates for people
+argued with him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and some of those people were here at
+
+ align:start position:0%
+and some of those people were here at
+ 
+
+ align:start position:0%
+and some of those people were here at
+mit
+
+ align:start position:0%
+mit
+ 
+
+ align:start position:0%
+mit
+where the belief was
+
+ align:start position:0%
+where the belief was
+ 
+
+ align:start position:0%
+where the belief was
+no you can't get far enough just the
+
+ align:start position:0%
+no you can't get far enough just the
+ 
+
+ align:start position:0%
+no you can't get far enough just the
+behavioral studies you need to open the
+
+ align:start position:0%
+behavioral studies you need to open the
+ 
+
+ align:start position:0%
+behavioral studies you need to open the
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+and we know that that approach is the
+
+ align:start position:0%
+and we know that that approach is the
+ 
+
+ align:start position:0%
+and we know that that approach is the
+approach that we saw first in
+
+ align:start position:0%
+approach that we saw first in
+ 
+
+ align:start position:0%
+approach that we saw first in
+reflexology and handling with kahal who
+
+ align:start position:0%
+reflexology and handling with kahal who
+ 
+
+ align:start position:0%
+reflexology and handling with kahal who
+finally was able to specify the circuit
+
+ align:start position:0%
+finally was able to specify the circuit
+ 
+
+ align:start position:0%
+finally was able to specify the circuit
+an entire reflex and helped us
+
+ align:start position:0%
+an entire reflex and helped us
+ 
+
+ align:start position:0%
+an entire reflex and helped us
+understand more what's going on and its
+
+ align:start position:0%
+understand more what's going on and its
+ 
+
+ align:start position:0%
+understand more what's going on and its
+complexity
+
+ align:start position:0%
+complexity
+ 
+
+ align:start position:0%
+complexity
+okay so we'll go from there next time
\ No newline at end of file
diff --git a/jBNVKat3GoQ.txt b/jBNVKat3GoQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69081f1f0c2626532b6f4f15d45488e3464c585a
--- /dev/null
+++ b/jBNVKat3GoQ.txt
@@ -0,0 +1,371 @@
+align:start position:0%
+ 
+here in MIT we usually require students
+
+ align:start position:0%
+here in MIT we usually require students
+ 
+
+ align:start position:0%
+here in MIT we usually require students
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+prepare for one hour class for about
+
+ align:start position:0%
+prepare for one hour class for about
+ 
+
+ align:start position:0%
+prepare for one hour class for about
+like an hour and a half so that's the
+
+ align:start position:0%
+like an hour and a half so that's the
+ 
+
+ align:start position:0%
+like an hour and a half so that's the
+time that we expect students to to give
+
+ align:start position:0%
+time that we expect students to to give
+ 
+
+ align:start position:0%
+time that we expect students to to give
+to this course because it's a 12 uni
+
+ align:start position:0%
+to this course because it's a 12 uni
+ 
+
+ align:start position:0%
+to this course because it's a 12 uni
+course so that's a pretty reasonable
+
+ align:start position:0%
+course so that's a pretty reasonable
+ 
+
+ align:start position:0%
+course so that's a pretty reasonable
+time for them expected and students they
+
+ align:start position:0%
+time for them expected and students they
+ 
+
+ align:start position:0%
+time for them expected and students they
+can usually do it but how can students
+
+ align:start position:0%
+can usually do it but how can students
+ 
+
+ align:start position:0%
+can usually do it but how can students
+they make the best out of those 90
+
+ align:start position:0%
+they make the best out of those 90
+ 
+
+ align:start position:0%
+they make the best out of those 90
+minutes it's it's a a totally different
+
+ align:start position:0%
+minutes it's it's a a totally different
+ 
+
+ align:start position:0%
+minutes it's it's a a totally different
+it's a totally different field that so
+
+ align:start position:0%
+it's a totally different field that so
+ 
+
+ align:start position:0%
+it's a totally different field that so
+far we don't have enough we don't have
+
+ align:start position:0%
+far we don't have enough we don't have
+ 
+
+ align:start position:0%
+far we don't have enough we don't have
+enough resources to know what they're
+
+ align:start position:0%
+enough resources to know what they're
+ 
+
+ align:start position:0%
+enough resources to know what they're
+what what do they exactly do during this
+
+ align:start position:0%
+what what do they exactly do during this
+ 
+
+ align:start position:0%
+what what do they exactly do during this
+90 minutes so I think because too often
+
+ align:start position:0%
+90 minutes so I think because too often
+ 
+
+ align:start position:0%
+90 minutes so I think because too often
+students that would say they would say
+
+ align:start position:0%
+students that would say they would say
+ 
+
+ align:start position:0%
+students that would say they would say
+that I follow every procedures that you
+
+ align:start position:0%
+that I follow every procedures that you
+ 
+
+ align:start position:0%
+that I follow every procedures that you
+recommended but I feel the result is not
+
+ align:start position:0%
+recommended but I feel the result is not
+ 
+
+ align:start position:0%
+recommended but I feel the result is not
+that satisfactory what am I supposed to
+
+ align:start position:0%
+that satisfactory what am I supposed to
+ 
+
+ align:start position:0%
+that satisfactory what am I supposed to
+do more and
+
+ align:start position:0%
+do more and
+ 
+
+ align:start position:0%
+do more and
+in this case we usually provide
+
+ align:start position:0%
+in this case we usually provide
+ 
+
+ align:start position:0%
+in this case we usually provide
+individual sessions so we have the
+
+ align:start position:0%
+individual sessions so we have the
+ 
+
+ align:start position:0%
+individual sessions so we have the
+students come into our our office and
+
+ align:start position:0%
+students come into our our office and
+ 
+
+ align:start position:0%
+students come into our our office and
+kind of tell them that show me how you
+
+ align:start position:0%
+kind of tell them that show me how you
+ 
+
+ align:start position:0%
+kind of tell them that show me how you
+prepare for class and kind observe so I
+
+ align:start position:0%
+prepare for class and kind observe so I
+ 
+
+ align:start position:0%
+prepare for class and kind observe so I
+give you 10 minutes so you do your
+
+ align:start position:0%
+give you 10 minutes so you do your
+ 
+
+ align:start position:0%
+give you 10 minutes so you do your
+preparation here in my office and I
+
+ align:start position:0%
+preparation here in my office and I
+ 
+
+ align:start position:0%
+preparation here in my office and I
+observe and based on those 10 minutes to
+
+ align:start position:0%
+observe and based on those 10 minutes to
+ 
+
+ align:start position:0%
+observe and based on those 10 minutes to
+15 minutes students I give you my
+
+ align:start position:0%
+15 minutes students I give you my
+ 
+
+ align:start position:0%
+15 minutes students I give you my
+feedback what I observe is hey you spend
+
+ align:start position:0%
+feedback what I observe is hey you spend
+ 
+
+ align:start position:0%
+feedback what I observe is hey you spend
+too much on on this and this and you're
+
+ align:start position:0%
+too much on on this and this and you're
+ 
+
+ align:start position:0%
+too much on on this and this and you're
+too silence you you cannot be too silent
+
+ align:start position:0%
+too silence you you cannot be too silent
+ 
+
+ align:start position:0%
+too silence you you cannot be too silent
+when you prepare for classes because in
+
+ align:start position:0%
+when you prepare for classes because in
+ 
+
+ align:start position:0%
+when you prepare for classes because in
+class it's about production production
+
+ align:start position:0%
+class it's about production production
+ 
+
+ align:start position:0%
+class it's about production production
+is very loud so this kind of loudness or
+
+ align:start position:0%
+is very loud so this kind of loudness or
+ 
+
+ align:start position:0%
+is very loud so this kind of loudness or
+or the loud part should be reflected
+
+ align:start position:0%
+or the loud part should be reflected
+ 
+
+ align:start position:0%
+or the loud part should be reflected
+from your
+
+ align:start position:0%
+from your
+ 
+
+ align:start position:0%
+from your
+preparation and from the 10 minutes or
+
+ align:start position:0%
+preparation and from the 10 minutes or
+ 
+
+ align:start position:0%
+preparation and from the 10 minutes or
+15 minutes you're solent for 12
+
+ align:start position:0%
+15 minutes you're solent for 12
+ 
+
+ align:start position:0%
+15 minutes you're solent for 12
+minutes which is not the case in class
+
+ align:start position:0%
+minutes which is not the case in class
+ 
+
+ align:start position:0%
+minutes which is not the case in class
+whenever student is say I do this this
+
+ align:start position:0%
+whenever student is say I do this this
+ 
+
+ align:start position:0%
+whenever student is say I do this this
+this and this you really don't know how
+
+ align:start position:0%
+this and this you really don't know how
+ 
+
+ align:start position:0%
+this and this you really don't know how
+much you can trust them in no way so the
+
+ align:start position:0%
+much you can trust them in no way so the
+ 
+
+ align:start position:0%
+much you can trust them in no way so the
+best way to check is to have them here
+
+ align:start position:0%
+best way to check is to have them here
+ 
+
+ align:start position:0%
+best way to check is to have them here
+and show you how to prepare for the
+
+ align:start position:0%
+and show you how to prepare for the
+ 
+
+ align:start position:0%
+and show you how to prepare for the
+class
\ No newline at end of file
diff --git a/kEoJ-teErzM.txt b/kEoJ-teErzM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..32c516b912fd6ff36264335601412870720ed06d
--- /dev/null
+++ b/kEoJ-teErzM.txt
@@ -0,0 +1,1251 @@
+align:start position:0%
+ 
+in this section of the course I'm going
+
+ align:start position:0%
+in this section of the course I'm going
+ 
+
+ align:start position:0%
+in this section of the course I'm going
+to go directly jump to GIS so geographic
+
+ align:start position:0%
+to go directly jump to GIS so geographic
+ 
+
+ align:start position:0%
+to go directly jump to GIS so geographic
+information systems and before going
+
+ align:start position:0%
+information systems and before going
+ 
+
+ align:start position:0%
+information systems and before going
+directly to the code I just wanted to
+
+ align:start position:0%
+directly to the code I just wanted to
+ 
+
+ align:start position:0%
+directly to the code I just wanted to
+make sure that everybody's in the same
+
+ align:start position:0%
+make sure that everybody's in the same
+ 
+
+ align:start position:0%
+make sure that everybody's in the same
+page in some key Concepts so that's why
+
+ align:start position:0%
+page in some key Concepts so that's why
+ 
+
+ align:start position:0%
+page in some key Concepts so that's why
+I'm just going to clarify some of them
+
+ align:start position:0%
+I'm just going to clarify some of them
+ 
+
+ align:start position:0%
+I'm just going to clarify some of them
+um so what you're going going to learn
+
+ align:start position:0%
+um so what you're going going to learn
+ 
+
+ align:start position:0%
+um so what you're going going to learn
+in in this video is to be familiarized
+
+ align:start position:0%
+in in this video is to be familiarized
+ 
+
+ align:start position:0%
+in in this video is to be familiarized
+with Concepts such as uh what are
+
+ align:start position:0%
+with Concepts such as uh what are
+ 
+
+ align:start position:0%
+with Concepts such as uh what are
+victorial maps and what are raster Maps
+
+ align:start position:0%
+victorial maps and what are raster Maps
+ 
+
+ align:start position:0%
+victorial maps and what are raster Maps
+so what are the differences among them
+
+ align:start position:0%
+so what are the differences among them
+ 
+
+ align:start position:0%
+so what are the differences among them
+and where should we use one or the other
+
+ align:start position:0%
+and where should we use one or the other
+ 
+
+ align:start position:0%
+and where should we use one or the other
+uh what is the projection so why do we
+
+ align:start position:0%
+uh what is the projection so why do we
+ 
+
+ align:start position:0%
+uh what is the projection so why do we
+need different projections also what's
+
+ align:start position:0%
+need different projections also what's
+ 
+
+ align:start position:0%
+need different projections also what's
+the concept of resolution and why should
+
+ align:start position:0%
+the concept of resolution and why should
+ 
+
+ align:start position:0%
+the concept of resolution and why should
+we take into account resolution when
+
+ align:start position:0%
+we take into account resolution when
+ 
+
+ align:start position:0%
+we take into account resolution when
+working with maps and also different
+
+ align:start position:0%
+working with maps and also different
+ 
+
+ align:start position:0%
+working with maps and also different
+ways to create Maps so there are mostly
+
+ align:start position:0%
+ways to create Maps so there are mostly
+ 
+
+ align:start position:0%
+ways to create Maps so there are mostly
+two different approaches to create Maps
+
+ align:start position:0%
+two different approaches to create Maps
+ 
+
+ align:start position:0%
+two different approaches to create Maps
+which the first one would be the
+
+ align:start position:0%
+which the first one would be the
+ 
+
+ align:start position:0%
+which the first one would be the
+satellite maps that are created top to
+
+ align:start position:0%
+satellite maps that are created top to
+ 
+
+ align:start position:0%
+satellite maps that are created top to
+bottom and then we have the maps that
+
+ align:start position:0%
+bottom and then we have the maps that
+ 
+
+ align:start position:0%
+bottom and then we have the maps that
+are upscale that they are the other way
+
+ align:start position:0%
+are upscale that they are the other way
+ 
+
+ align:start position:0%
+are upscale that they are the other way
+around so they are created bottom to top
+
+ align:start position:0%
+around so they are created bottom to top
+ 
+
+ align:start position:0%
+around so they are created bottom to top
+so my goal is that then you would be
+
+ align:start position:0%
+so my goal is that then you would be
+ 
+
+ align:start position:0%
+so my goal is that then you would be
+able to apply all these Concepts and
+
+ align:start position:0%
+able to apply all these Concepts and
+ 
+
+ align:start position:0%
+able to apply all these Concepts and
+manage all these Concepts in your R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code okay so here we have the same image
+
+ align:start position:0%
+code okay so here we have the same image
+ 
+
+ align:start position:0%
+code okay so here we have the same image
+represented in the two different Maps so
+
+ align:start position:0%
+represented in the two different Maps so
+ 
+
+ align:start position:0%
+represented in the two different Maps so
+the first one is represented using a
+
+ align:start position:0%
+the first one is represented using a
+ 
+
+ align:start position:0%
+the first one is represented using a
+vectorial map and the second one is
+
+ align:start position:0%
+vectorial map and the second one is
+ 
+
+ align:start position:0%
+vectorial map and the second one is
+represented using raster the main
+
+ align:start position:0%
+represented using raster the main
+ 
+
+ align:start position:0%
+represented using raster the main
+differences is that in vectorial maps we
+
+ align:start position:0%
+differences is that in vectorial maps we
+ 
+
+ align:start position:0%
+differences is that in vectorial maps we
+can have irregular uh polygons but in
+
+ align:start position:0%
+can have irregular uh polygons but in
+ 
+
+ align:start position:0%
+can have irregular uh polygons but in
+the raster Maps we have a grid where all
+
+ align:start position:0%
+the raster Maps we have a grid where all
+ 
+
+ align:start position:0%
+the raster Maps we have a grid where all
+the cells are equally distributed they
+
+ align:start position:0%
+the cells are equally distributed they
+ 
+
+ align:start position:0%
+the cells are equally distributed they
+have the same size and they are in the
+
+ align:start position:0%
+have the same size and they are in the
+ 
+
+ align:start position:0%
+have the same size and they are in the
+same disposition so that might affect
+
+ align:start position:0%
+same disposition so that might affect
+ 
+
+ align:start position:0%
+same disposition so that might affect
+how the different forms are represented
+
+ align:start position:0%
+how the different forms are represented
+ 
+
+ align:start position:0%
+how the different forms are represented
+so in case we are interested in the the
+
+ align:start position:0%
+so in case we are interested in the the
+ 
+
+ align:start position:0%
+so in case we are interested in the the
+shape of the objects maybe we would go
+
+ align:start position:0%
+shape of the objects maybe we would go
+ 
+
+ align:start position:0%
+shape of the objects maybe we would go
+to a vectorial map but if we are
+
+ align:start position:0%
+to a vectorial map but if we are
+ 
+
+ align:start position:0%
+to a vectorial map but if we are
+interested in the content of the map we
+
+ align:start position:0%
+interested in the content of the map we
+ 
+
+ align:start position:0%
+interested in the content of the map we
+would go to raster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representations also there is the
+
+ align:start position:0%
+representations also there is the
+ 
+
+ align:start position:0%
+representations also there is the
+concept of projection uh as we all know
+
+ align:start position:0%
+concept of projection uh as we all know
+ 
+
+ align:start position:0%
+concept of projection uh as we all know
+the Earth is not a flat surface so to
+
+ align:start position:0%
+the Earth is not a flat surface so to
+ 
+
+ align:start position:0%
+the Earth is not a flat surface so to
+overcome this representation in like to
+
+ align:start position:0%
+overcome this representation in like to
+ 
+
+ align:start position:0%
+overcome this representation in like to
+convert this round shape into something
+
+ align:start position:0%
+convert this round shape into something
+ 
+
+ align:start position:0%
+convert this round shape into something
+that's flat uh we have encountered
+
+ align:start position:0%
+that's flat uh we have encountered
+ 
+
+ align:start position:0%
+that's flat uh we have encountered
+several problems so that's why we have
+
+ align:start position:0%
+several problems so that's why we have
+ 
+
+ align:start position:0%
+several problems so that's why we have
+different projections depending on
+
+ align:start position:0%
+different projections depending on
+ 
+
+ align:start position:0%
+different projections depending on
+where we want to focus better on so each
+
+ align:start position:0%
+where we want to focus better on so each
+ 
+
+ align:start position:0%
+where we want to focus better on so each
+representation has its pros and Cones so
+
+ align:start position:0%
+representation has its pros and Cones so
+ 
+
+ align:start position:0%
+representation has its pros and Cones so
+for example if we are more interested in
+
+ align:start position:0%
+for example if we are more interested in
+ 
+
+ align:start position:0%
+for example if we are more interested in
+having accurate shapes in the poles we
+
+ align:start position:0%
+having accurate shapes in the poles we
+ 
+
+ align:start position:0%
+having accurate shapes in the poles we
+would use one projection but if we want
+
+ align:start position:0%
+would use one projection but if we want
+ 
+
+ align:start position:0%
+would use one projection but if we want
+to see kind of accurately the whole glob
+
+ align:start position:0%
+to see kind of accurately the whole glob
+ 
+
+ align:start position:0%
+to see kind of accurately the whole glob
+maybe we choose something else but that
+
+ align:start position:0%
+maybe we choose something else but that
+ 
+
+ align:start position:0%
+maybe we choose something else but that
+has implications in how the shapes look
+
+ align:start position:0%
+has implications in how the shapes look
+ 
+
+ align:start position:0%
+has implications in how the shapes look
+like for example this is the same phase
+
+ align:start position:0%
+like for example this is the same phase
+ 
+
+ align:start position:0%
+like for example this is the same phase
+but how this can be transformed or
+
+ align:start position:0%
+but how this can be transformed or
+ 
+
+ align:start position:0%
+but how this can be transformed or
+deformed depending on how we are
+
+ align:start position:0%
+deformed depending on how we are
+ 
+
+ align:start position:0%
+deformed depending on how we are
+representing it so this is something we
+
+ align:start position:0%
+representing it so this is something we
+ 
+
+ align:start position:0%
+representing it so this is something we
+have to take into account because if we
+
+ align:start position:0%
+have to take into account because if we
+ 
+
+ align:start position:0%
+have to take into account because if we
+want to merge to extract information
+
+ align:start position:0%
+want to merge to extract information
+ 
+
+ align:start position:0%
+want to merge to extract information
+from different Maps they may be in
+
+ align:start position:0%
+from different Maps they may be in
+ 
+
+ align:start position:0%
+from different Maps they may be in
+different projections and how is this
+
+ align:start position:0%
+different projections and how is this
+ 
+
+ align:start position:0%
+different projections and how is this
+affecting us
+
+ align:start position:0%
+affecting us
+ 
+
+ align:start position:0%
+affecting us
+well here you see South America and how
+
+ align:start position:0%
+well here you see South America and how
+ 
+
+ align:start position:0%
+well here you see South America and how
+this South America can be represented on
+
+ align:start position:0%
+this South America can be represented on
+ 
+
+ align:start position:0%
+this South America can be represented on
+how it shape can change depending on the
+
+ align:start position:0%
+how it shape can change depending on the
+ 
+
+ align:start position:0%
+how it shape can change depending on the
+projection we are using so before moving
+
+ align:start position:0%
+projection we are using so before moving
+ 
+
+ align:start position:0%
+projection we are using so before moving
+on in in maps we have to make sure that
+
+ align:start position:0%
+on in in maps we have to make sure that
+ 
+
+ align:start position:0%
+on in in maps we have to make sure that
+the projection we are using is accurate
+
+ align:start position:0%
+the projection we are using is accurate
+ 
+
+ align:start position:0%
+the projection we are using is accurate
+to the piece of the earth that we want
+
+ align:start position:0%
+to the piece of the earth that we want
+ 
+
+ align:start position:0%
+to the piece of the earth that we want
+to represent or that we want to work on
+
+ align:start position:0%
+to represent or that we want to work on
+ 
+
+ align:start position:0%
+to represent or that we want to work on
+what's the scale we are going to work on
+
+ align:start position:0%
+what's the scale we are going to work on
+ 
+
+ align:start position:0%
+what's the scale we are going to work on
+if we're going to work in a regional
+
+ align:start position:0%
+if we're going to work in a regional
+ 
+
+ align:start position:0%
+if we're going to work in a regional
+part or if we're going to work in a
+
+ align:start position:0%
+part or if we're going to work in a
+ 
+
+ align:start position:0%
+part or if we're going to work in a
+global scale and also make sure that all
+
+ align:start position:0%
+global scale and also make sure that all
+ 
+
+ align:start position:0%
+global scale and also make sure that all
+the maps are in the same projection so
+
+ align:start position:0%
+the maps are in the same projection so
+ 
+
+ align:start position:0%
+the maps are in the same projection so
+we don't have problems as in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+image then we have the resolution
+
+ align:start position:0%
+image then we have the resolution
+ 
+
+ align:start position:0%
+image then we have the resolution
+concept this is a a picture but a
+
+ align:start position:0%
+concept this is a a picture but a
+ 
+
+ align:start position:0%
+concept this is a a picture but a
+picture would be a good proxy of a a
+
+ align:start position:0%
+picture would be a good proxy of a a
+ 
+
+ align:start position:0%
+picture would be a good proxy of a a
+raster map the end they are built the
+
+ align:start position:0%
+raster map the end they are built the
+ 
+
+ align:start position:0%
+raster map the end they are built the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+um so here we have the same image um and
+
+ align:start position:0%
+um so here we have the same image um and
+ 
+
+ align:start position:0%
+um so here we have the same image um and
+and the main difference is that the
+
+ align:start position:0%
+and the main difference is that the
+ 
+
+ align:start position:0%
+and the main difference is that the
+square size is completely different so
+
+ align:start position:0%
+square size is completely different so
+ 
+
+ align:start position:0%
+square size is completely different so
+the first one the one is more in the
+
+ align:start position:0%
+the first one the one is more in the
+ 
+
+ align:start position:0%
+the first one the one is more in the
+left um it doesn't have that much of a
+
+ align:start position:0%
+left um it doesn't have that much of a
+ 
+
+ align:start position:0%
+left um it doesn't have that much of a
+detail and the second one is very
+
+ align:start position:0%
+detail and the second one is very
+ 
+
+ align:start position:0%
+detail and the second one is very
+detailed one would think that is always
+
+ align:start position:0%
+detailed one would think that is always
+ 
+
+ align:start position:0%
+detailed one would think that is always
+better to go to more detailed resolution
+
+ align:start position:0%
+better to go to more detailed resolution
+ 
+
+ align:start position:0%
+better to go to more detailed resolution
+but this has some drawbacks which is
+
+ align:start position:0%
+but this has some drawbacks which is
+ 
+
+ align:start position:0%
+but this has some drawbacks which is
+that they are way more heavy so
+
+ align:start position:0%
+that they are way more heavy so
+ 
+
+ align:start position:0%
+that they are way more heavy so
+depending on the capacity your computer
+
+ align:start position:0%
+depending on the capacity your computer
+ 
+
+ align:start position:0%
+depending on the capacity your computer
+has or depending on how good is your
+
+ align:start position:0%
+has or depending on how good is your
+ 
+
+ align:start position:0%
+has or depending on how good is your
+internet connection you might go to one
+
+ align:start position:0%
+internet connection you might go to one
+ 
+
+ align:start position:0%
+internet connection you might go to one
+or the other um just as a um as a
+
+ align:start position:0%
+or the other um just as a um as a
+ 
+
+ align:start position:0%
+or the other um just as a um as a
+reminder that it sometimes even if you
+
+ align:start position:0%
+reminder that it sometimes even if you
+ 
+
+ align:start position:0%
+reminder that it sometimes even if you
+are increasing the resolution maybe
+
+ align:start position:0%
+are increasing the resolution maybe
+ 
+
+ align:start position:0%
+are increasing the resolution maybe
+that's not going to help us to have more
+
+ align:start position:0%
+that's not going to help us to have more
+ 
+
+ align:start position:0%
+that's not going to help us to have more
+accurate calculations just because the
+
+ align:start position:0%
+accurate calculations just because the
+ 
+
+ align:start position:0%
+accurate calculations just because the
+quality of the map uh was initially not
+
+ align:start position:0%
+quality of the map uh was initially not
+ 
+
+ align:start position:0%
+quality of the map uh was initially not
+the the purest and was created in a
+
+ align:start position:0%
+the the purest and was created in a
+ 
+
+ align:start position:0%
+the the purest and was created in a
+corser resolution so even if we come to
+
+ align:start position:0%
+corser resolution so even if we come to
+ 
+
+ align:start position:0%
+corser resolution so even if we come to
+if we can transform a corser resolution
+
+ align:start position:0%
+if we can transform a corser resolution
+ 
+
+ align:start position:0%
+if we can transform a corser resolution
+to a more fine scale um we are not
+
+ align:start position:0%
+to a more fine scale um we are not
+ 
+
+ align:start position:0%
+to a more fine scale um we are not
+creating new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information so this is the top bottom
+
+ align:start position:0%
+information so this is the top bottom
+ 
+
+ align:start position:0%
+information so this is the top bottom
+approach of creating Maps um we know
+
+ align:start position:0%
+approach of creating Maps um we know
+ 
+
+ align:start position:0%
+approach of creating Maps um we know
+that we have satellites going around
+
+ align:start position:0%
+that we have satellites going around
+ 
+
+ align:start position:0%
+that we have satellites going around
+above our heads so they use as a big
+
+ align:start position:0%
+above our heads so they use as a big
+ 
+
+ align:start position:0%
+above our heads so they use as a big
+camera let's say so they have different
+
+ align:start position:0%
+camera let's say so they have different
+ 
+
+ align:start position:0%
+camera let's say so they have different
+sensors they have different lenses so
+
+ align:start position:0%
+sensors they have different lenses so
+ 
+
+ align:start position:0%
+sensors they have different lenses so
+they are taking kind of pictures or
+
+ align:start position:0%
+they are taking kind of pictures or
+ 
+
+ align:start position:0%
+they are taking kind of pictures or
+representations of the surface of the
+
+ align:start position:0%
+representations of the surface of the
+ 
+
+ align:start position:0%
+representations of the surface of the
+Earth so they send different web lengths
+
+ align:start position:0%
+Earth so they send different web lengths
+ 
+
+ align:start position:0%
+Earth so they send different web lengths
+and then they get some bounced back and
+
+ align:start position:0%
+and then they get some bounced back and
+ 
+
+ align:start position:0%
+and then they get some bounced back and
+then they read the signal of that and
+
+ align:start position:0%
+then they read the signal of that and
+ 
+
+ align:start position:0%
+then they read the signal of that and
+based on those signals they apply some
+
+ align:start position:0%
+based on those signals they apply some
+ 
+
+ align:start position:0%
+based on those signals they apply some
+corrections sometimes and that's how
+
+ align:start position:0%
+corrections sometimes and that's how
+ 
+
+ align:start position:0%
+corrections sometimes and that's how
+they create satellite images but then
+
+ align:start position:0%
+they create satellite images but then
+ 
+
+ align:start position:0%
+they create satellite images but then
+another way to create Maps sometimes
+
+ align:start position:0%
+another way to create Maps sometimes
+ 
+
+ align:start position:0%
+another way to create Maps sometimes
+when we don't have a signal from a
+
+ align:start position:0%
+when we don't have a signal from a
+ 
+
+ align:start position:0%
+when we don't have a signal from a
+satellite would be the upscaling
+
+ align:start position:0%
+satellite would be the upscaling
+ 
+
+ align:start position:0%
+satellite would be the upscaling
+approach here in the first map uh we
+
+ align:start position:0%
+approach here in the first map uh we
+ 
+
+ align:start position:0%
+approach here in the first map uh we
+have different dots uh this is taken
+
+ align:start position:0%
+have different dots uh this is taken
+ 
+
+ align:start position:0%
+have different dots uh this is taken
+from a paper uh do it all um
+
+ align:start position:0%
+from a paper uh do it all um
+ 
+
+ align:start position:0%
+from a paper uh do it all um
+2020 um it's just an example of an
+
+ align:start position:0%
+2020 um it's just an example of an
+ 
+
+ align:start position:0%
+2020 um it's just an example of an
+upscaled map where they had real data so
+
+ align:start position:0%
+upscaled map where they had real data so
+ 
+
+ align:start position:0%
+upscaled map where they had real data so
+each point is representing a real point
+
+ align:start position:0%
+each point is representing a real point
+ 
+
+ align:start position:0%
+each point is representing a real point
+where some field data has been taken
+
+ align:start position:0%
+where some field data has been taken
+ 
+
+ align:start position:0%
+where some field data has been taken
+then based on this real information um a
+
+ align:start position:0%
+then based on this real information um a
+ 
+
+ align:start position:0%
+then based on this real information um a
+model is created using some
+
+ align:start position:0%
+model is created using some
+ 
+
+ align:start position:0%
+model is created using some
+environmental drivers so drivers and a
+
+ align:start position:0%
+environmental drivers so drivers and a
+ 
+
+ align:start position:0%
+environmental drivers so drivers and a
+model is created and with this model
+
+ align:start position:0%
+model is created and with this model
+ 
+
+ align:start position:0%
+model is created and with this model
+then we can empty the spaces that are in
+
+ align:start position:0%
+then we can empty the spaces that are in
+ 
+
+ align:start position:0%
+then we can empty the spaces that are in
+between different the different points
+
+ align:start position:0%
+between different the different points
+ 
+
+ align:start position:0%
+between different the different points
+based on an upscaling using that map so
+
+ align:start position:0%
+based on an upscaling using that map so
+ 
+
+ align:start position:0%
+based on an upscaling using that map so
+this is how we can obtain maps from a
+
+ align:start position:0%
+this is how we can obtain maps from a
+ 
+
+ align:start position:0%
+this is how we can obtain maps from a
+bottom top approach
+
+ align:start position:0%
+bottom top approach
+ 
+
+ align:start position:0%
+bottom top approach
+and also here just some resources you
+
+ align:start position:0%
+and also here just some resources you
+ 
+
+ align:start position:0%
+and also here just some resources you
+can find um raster Maps uh the first one
+
+ align:start position:0%
+can find um raster Maps uh the first one
+ 
+
+ align:start position:0%
+can find um raster Maps uh the first one
+is the world cream world caim where you
+
+ align:start position:0%
+is the world cream world caim where you
+ 
+
+ align:start position:0%
+is the world cream world caim where you
+can find environmental uh variables such
+
+ align:start position:0%
+can find environmental uh variables such
+ 
+
+ align:start position:0%
+can find environmental uh variables such
+as what related to climate precipitation
+
+ align:start position:0%
+as what related to climate precipitation
+ 
+
+ align:start position:0%
+as what related to climate precipitation
+temperature and so forth and then if you
+
+ align:start position:0%
+temperature and so forth and then if you
+ 
+
+ align:start position:0%
+temperature and so forth and then if you
+are interested in obtaining information
+
+ align:start position:0%
+are interested in obtaining information
+ 
+
+ align:start position:0%
+are interested in obtaining information
+from soils you might go to soil GDs
+
+ align:start position:0%
+from soils you might go to soil GDs
+ 
+
+ align:start position:0%
+from soils you might go to soil GDs
+where they have a lot of physical and
+
+ align:start position:0%
+where they have a lot of physical and
+ 
+
+ align:start position:0%
+where they have a lot of physical and
+chemical properties uh of different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soils e
\ No newline at end of file
diff --git a/kigLhcTm_gg.txt b/kigLhcTm_gg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df18478d088db3092e41a686b6202af0ab2bce2c
--- /dev/null
+++ b/kigLhcTm_gg.txt
@@ -0,0 +1,16355 @@
+align:start position:0%
+ 
+uh we're talking about
+
+ align:start position:0%
+uh we're talking about
+ 
+
+ align:start position:0%
+uh we're talking about
+photogrammetry and in particular
+
+ align:start position:0%
+photogrammetry and in particular
+ 
+
+ align:start position:0%
+photogrammetry and in particular
+absolute orientation and we're drilling
+
+ align:start position:0%
+absolute orientation and we're drilling
+ 
+
+ align:start position:0%
+absolute orientation and we're drilling
+down into uh details
+
+ align:start position:0%
+down into uh details
+ 
+
+ align:start position:0%
+down into uh details
+uh more details for this one than we
+
+ align:start position:0%
+uh more details for this one than we
+ 
+
+ align:start position:0%
+uh more details for this one than we
+will for the other aspects of
+
+ align:start position:0%
+will for the other aspects of
+ 
+
+ align:start position:0%
+will for the other aspects of
+photogrammetry
+
+ align:start position:0%
+photogrammetry
+ 
+
+ align:start position:0%
+photogrammetry
+because a lot of it's
+
+ align:start position:0%
+because a lot of it's
+ 
+
+ align:start position:0%
+because a lot of it's
+going to be based on what we're doing
+
+ align:start position:0%
+going to be based on what we're doing
+ 
+
+ align:start position:0%
+going to be based on what we're doing
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and we found that rotation is the part
+
+ align:start position:0%
+and we found that rotation is the part
+ 
+
+ align:start position:0%
+and we found that rotation is the part
+that's awkward to handle so we talked
+
+ align:start position:0%
+that's awkward to handle so we talked
+ 
+
+ align:start position:0%
+that's awkward to handle so we talked
+about different ways of representing
+
+ align:start position:0%
+about different ways of representing
+ 
+
+ align:start position:0%
+about different ways of representing
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+and we picked uh unit quaternions
+
+ align:start position:0%
+and we picked uh unit quaternions
+ 
+
+ align:start position:0%
+and we picked uh unit quaternions
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+major reason for that is that um
+
+ align:start position:0%
+major reason for that is that um
+ 
+
+ align:start position:0%
+major reason for that is that um
+given all of the advantages we discussed
+
+ align:start position:0%
+given all of the advantages we discussed
+ 
+
+ align:start position:0%
+given all of the advantages we discussed
+before the the big thing for us is we
+
+ align:start position:0%
+before the the big thing for us is we
+ 
+
+ align:start position:0%
+before the the big thing for us is we
+can get a closed form solution to the
+
+ align:start position:0%
+can get a closed form solution to the
+ 
+
+ align:start position:0%
+can get a closed form solution to the
+least worse problem so in some sense we
+
+ align:start position:0%
+least worse problem so in some sense we
+ 
+
+ align:start position:0%
+least worse problem so in some sense we
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+objective way of getting a quote best
+
+ align:start position:0%
+objective way of getting a quote best
+ 
+
+ align:start position:0%
+objective way of getting a quote best
+fit answer
+
+ align:start position:0%
+fit answer
+ 
+
+ align:start position:0%
+fit answer
+which is more difficult with the other
+
+ align:start position:0%
+which is more difficult with the other
+ 
+
+ align:start position:0%
+which is more difficult with the other
+notations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we talked about
+
+ align:start position:0%
+then we talked about
+ 
+
+ align:start position:0%
+then we talked about
+how to manipulate these things there are
+
+ align:start position:0%
+how to manipulate these things there are
+ 
+
+ align:start position:0%
+how to manipulate these things there are
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+operations we're particularly interested
+
+ align:start position:0%
+operations we're particularly interested
+ 
+
+ align:start position:0%
+operations we're particularly interested
+in the one is
+
+ align:start position:0%
+in the one is
+ 
+
+ align:start position:0%
+in the one is
+composition of rotations if you do
+
+ align:start position:0%
+composition of rotations if you do
+ 
+
+ align:start position:0%
+composition of rotations if you do
+successive rotations what happens
+
+ align:start position:0%
+successive rotations what happens
+ 
+
+ align:start position:0%
+successive rotations what happens
+and the other one is
+
+ align:start position:0%
+and the other one is
+ 
+
+ align:start position:0%
+and the other one is
+rotating a vector so composition of
+
+ align:start position:0%
+rotating a vector so composition of
+ 
+
+ align:start position:0%
+rotating a vector so composition of
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+is just multiplication
+
+ align:start position:0%
+is just multiplication
+ 
+
+ align:start position:0%
+is just multiplication
+and we can represent it in various ways
+
+ align:start position:0%
+and we can represent it in various ways
+ 
+
+ align:start position:0%
+and we can represent it in various ways
+uh for those of us who grew up with
+
+ align:start position:0%
+uh for those of us who grew up with
+ 
+
+ align:start position:0%
+uh for those of us who grew up with
+vectors maybe
+
+ align:start position:0%
+vectors maybe
+ 
+
+ align:start position:0%
+vectors maybe
+mapping it into scalars and vectors is
+
+ align:start position:0%
+mapping it into scalars and vectors is
+ 
+
+ align:start position:0%
+mapping it into scalars and vectors is
+the most intuitive
+
+ align:start position:0%
+the most intuitive
+ 
+
+ align:start position:0%
+the most intuitive
+so we have this formula
+
+ align:start position:0%
+so we have this formula
+ 
+
+ align:start position:0%
+so we have this formula
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+actually quite efficient in terms of
+
+ align:start position:0%
+actually quite efficient in terms of
+ 
+
+ align:start position:0%
+actually quite efficient in terms of
+composition of rotations
+
+ align:start position:0%
+composition of rotations
+ 
+
+ align:start position:0%
+composition of rotations
+a lot in terms of computation it's a lot
+
+ align:start position:0%
+a lot in terms of computation it's a lot
+ 
+
+ align:start position:0%
+a lot in terms of computation it's a lot
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+work than multiplying two orthonormal
+
+ align:start position:0%
+work than multiplying two orthonormal
+ 
+
+ align:start position:0%
+work than multiplying two orthonormal
+three by three matrices
+
+ align:start position:0%
+three by three matrices
+ 
+
+ align:start position:0%
+three by three matrices
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+for much of what we do what's more
+
+ align:start position:0%
+for much of what we do what's more
+ 
+
+ align:start position:0%
+for much of what we do what's more
+important is the other operation which
+
+ align:start position:0%
+important is the other operation which
+ 
+
+ align:start position:0%
+important is the other operation which
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a rotation of a vector and so
+
+ align:start position:0%
+a rotation of a vector and so
+ 
+
+ align:start position:0%
+a rotation of a vector and so
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+uh we have that uh formula where we're
+
+ align:start position:0%
+uh we have that uh formula where we're
+ 
+
+ align:start position:0%
+uh we have that uh formula where we're
+you know rotating in four space using q
+
+ align:start position:0%
+you know rotating in four space using q
+ 
+
+ align:start position:0%
+you know rotating in four space using q
+and then we're kind of unrotating using
+
+ align:start position:0%
+and then we're kind of unrotating using
+ 
+
+ align:start position:0%
+and then we're kind of unrotating using
+q conjugate and somehow we end up back
+
+ align:start position:0%
+q conjugate and somehow we end up back
+ 
+
+ align:start position:0%
+q conjugate and somehow we end up back
+in a real three-dimensional world
+
+ align:start position:0%
+in a real three-dimensional world
+ 
+
+ align:start position:0%
+in a real three-dimensional world
+and for that again if we want to just
+
+ align:start position:0%
+and for that again if we want to just
+ 
+
+ align:start position:0%
+and for that again if we want to just
+think about vectors
+
+ align:start position:0%
+think about vectors
+ 
+
+ align:start position:0%
+think about vectors
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+one way we can write it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we don't you know if we don't want to
+
+ align:start position:0%
+so we don't you know if we don't want to
+ 
+
+ align:start position:0%
+so we don't you know if we don't want to
+think too much about operations in the
+
+ align:start position:0%
+think too much about operations in the
+ 
+
+ align:start position:0%
+think too much about operations in the
+quaternion world world we can just do
+
+ align:start position:0%
+quaternion world world we can just do
+ 
+
+ align:start position:0%
+quaternion world world we can just do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+operation directly using vectors and
+
+ align:start position:0%
+operation directly using vectors and
+ 
+
+ align:start position:0%
+operation directly using vectors and
+scalars and
+
+ align:start position:0%
+scalars and
+ 
+
+ align:start position:0%
+scalars and
+this one we have a disadvantage it takes
+
+ align:start position:0%
+this one we have a disadvantage it takes
+ 
+
+ align:start position:0%
+this one we have a disadvantage it takes
+somewhat more arithmetic operations than
+
+ align:start position:0%
+somewhat more arithmetic operations than
+ 
+
+ align:start position:0%
+somewhat more arithmetic operations than
+multiplying a three by three matrix by a
+
+ align:start position:0%
+multiplying a three by three matrix by a
+ 
+
+ align:start position:0%
+multiplying a three by three matrix by a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+although we saw that the ways of
+
+ align:start position:0%
+although we saw that the ways of
+ 
+
+ align:start position:0%
+although we saw that the ways of
+rewriting this where we reuse the q
+
+ align:start position:0%
+rewriting this where we reuse the q
+ 
+
+ align:start position:0%
+rewriting this where we reuse the q
+cross r
+
+ align:start position:0%
+cross r
+ 
+
+ align:start position:0%
+cross r
+that reduces the number of operations
+
+ align:start position:0%
+that reduces the number of operations
+ 
+
+ align:start position:0%
+that reduces the number of operations
+somewhat
+
+ align:start position:0%
+somewhat
+ 
+
+ align:start position:0%
+somewhat
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+we need to connect this to other
+
+ align:start position:0%
+we need to connect this to other
+ 
+
+ align:start position:0%
+we need to connect this to other
+notations so
+
+ align:start position:0%
+notations so
+ 
+
+ align:start position:0%
+notations so
+we for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want to relate it to
+
+ align:start position:0%
+want to relate it to
+ 
+
+ align:start position:0%
+want to relate it to
+axes and angle notation
+
+ align:start position:0%
+axes and angle notation
+ 
+
+ align:start position:0%
+axes and angle notation
+and there we have the formula of
+
+ align:start position:0%
+and there we have the formula of
+ 
+
+ align:start position:0%
+and there we have the formula of
+rodriguez
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where omega hat is the unit vector in
+
+ align:start position:0%
+where omega hat is the unit vector in
+ 
+
+ align:start position:0%
+where omega hat is the unit vector in
+the direction of the axis
+
+ align:start position:0%
+the direction of the axis
+ 
+
+ align:start position:0%
+the direction of the axis
+and so that gives us
+
+ align:start position:0%
+and so that gives us
+ 
+
+ align:start position:0%
+and so that gives us
+one conversion that we want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so uh we can use that to
+
+ align:start position:0%
+uh so uh we can use that to
+ 
+
+ align:start position:0%
+uh so uh we can use that to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+q dot uh
+
+ align:start position:0%
+q dot uh
+ 
+
+ align:start position:0%
+q dot uh
+sorry about the handwriting yeah
+
+ align:start position:0%
+sorry about the handwriting yeah
+ 
+
+ align:start position:0%
+sorry about the handwriting yeah
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+and when we identify these two formulas
+
+ align:start position:0%
+and when we identify these two formulas
+ 
+
+ align:start position:0%
+and when we identify these two formulas
+uh we find that actually q is cos omega
+
+ align:start position:0%
+uh we find that actually q is cos omega
+ 
+
+ align:start position:0%
+uh we find that actually q is cos omega
+over two
+
+ align:start position:0%
+over two
+ 
+
+ align:start position:0%
+over two
+and omega hat is um
+
+ align:start position:0%
+and omega hat is um
+ 
+
+ align:start position:0%
+and omega hat is um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+well let's see other way around q
+
+ align:start position:0%
+well let's see other way around q
+ 
+
+ align:start position:0%
+well let's see other way around q
+vector is uh omega hat
+
+ align:start position:0%
+vector is uh omega hat
+ 
+
+ align:start position:0%
+vector is uh omega hat
+sine theta over two oh let me make that
+
+ align:start position:0%
+sine theta over two oh let me make that
+ 
+
+ align:start position:0%
+sine theta over two oh let me make that
+theta sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quaternion for rotation looks like that
+
+ align:start position:0%
+quaternion for rotation looks like that
+ 
+
+ align:start position:0%
+quaternion for rotation looks like that
+and so we can right away read off the
+
+ align:start position:0%
+and so we can right away read off the
+ 
+
+ align:start position:0%
+and so we can right away read off the
+axis it's going to be parallel to the
+
+ align:start position:0%
+axis it's going to be parallel to the
+ 
+
+ align:start position:0%
+axis it's going to be parallel to the
+vector part
+
+ align:start position:0%
+vector part
+ 
+
+ align:start position:0%
+vector part
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we want to we can read off the angle
+
+ align:start position:0%
+if we want to we can read off the angle
+ 
+
+ align:start position:0%
+if we want to we can read off the angle
+by using a tan on the ratio of the
+
+ align:start position:0%
+by using a tan on the ratio of the
+ 
+
+ align:start position:0%
+by using a tan on the ratio of the
+real part and the magnitude of the
+
+ align:start position:0%
+real part and the magnitude of the
+ 
+
+ align:start position:0%
+real part and the magnitude of the
+imaginary part so that
+
+ align:start position:0%
+imaginary part so that
+ 
+
+ align:start position:0%
+imaginary part so that
+is one way of converting between two of
+
+ align:start position:0%
+is one way of converting between two of
+ 
+
+ align:start position:0%
+is one way of converting between two of
+these different forms now we had eight
+
+ align:start position:0%
+these different forms now we had eight
+ 
+
+ align:start position:0%
+these different forms now we had eight
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we don't want to go through all uh eight
+
+ align:start position:0%
+we don't want to go through all uh eight
+ 
+
+ align:start position:0%
+we don't want to go through all uh eight
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+but the other one that's important for
+
+ align:start position:0%
+but the other one that's important for
+ 
+
+ align:start position:0%
+but the other one that's important for
+us since we live in a world where
+
+ align:start position:0%
+us since we live in a world where
+ 
+
+ align:start position:0%
+us since we live in a world where
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+orthonormal matrices rule we need to be
+
+ align:start position:0%
+orthonormal matrices rule we need to be
+ 
+
+ align:start position:0%
+orthonormal matrices rule we need to be
+able to convert back and forth between
+
+ align:start position:0%
+able to convert back and forth between
+ 
+
+ align:start position:0%
+able to convert back and forth between
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+if we expand
+
+ align:start position:0%
+if we expand
+ 
+
+ align:start position:0%
+if we expand
+that formula using that isomorphism with
+
+ align:start position:0%
+that formula using that isomorphism with
+ 
+
+ align:start position:0%
+that formula using that isomorphism with
+four by four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we got that and we expanded that
+
+ align:start position:0%
+then we got that and we expanded that
+ 
+
+ align:start position:0%
+then we got that and we expanded that
+out and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when we look at that matrix
+
+ align:start position:0%
+and when we look at that matrix
+ 
+
+ align:start position:0%
+and when we look at that matrix
+we find that
+
+ align:start position:0%
+we find that
+ 
+
+ align:start position:0%
+we find that
+it has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skew symmetric parts and symmetric parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can use that
+
+ align:start position:0%
+and we can use that
+ 
+
+ align:start position:0%
+and we can use that
+to help us in the conversion from one
+
+ align:start position:0%
+to help us in the conversion from one
+ 
+
+ align:start position:0%
+to help us in the conversion from one
+form to the other so first of all if
+
+ align:start position:0%
+form to the other so first of all if
+ 
+
+ align:start position:0%
+form to the other so first of all if
+we're given the quaternion
+
+ align:start position:0%
+we're given the quaternion
+ 
+
+ align:start position:0%
+we're given the quaternion
+this allows us to compute the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal matrix very easily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this transformation it's four by
+
+ align:start position:0%
+so in this transformation it's four by
+ 
+
+ align:start position:0%
+so in this transformation it's four by
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+but we don't care about the first row in
+
+ align:start position:0%
+but we don't care about the first row in
+ 
+
+ align:start position:0%
+but we don't care about the first row in
+the first column because that is a
+
+ align:start position:0%
+the first column because that is a
+ 
+
+ align:start position:0%
+the first column because that is a
+special quaternion that represents a
+
+ align:start position:0%
+special quaternion that represents a
+ 
+
+ align:start position:0%
+special quaternion that represents a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+where the first uh with scalar part is
+
+ align:start position:0%
+where the first uh with scalar part is
+ 
+
+ align:start position:0%
+where the first uh with scalar part is
+zero so all this uh that all the first
+
+ align:start position:0%
+zero so all this uh that all the first
+ 
+
+ align:start position:0%
+zero so all this uh that all the first
+column and the first row tell us
+
+ align:start position:0%
+column and the first row tell us
+ 
+
+ align:start position:0%
+column and the first row tell us
+is that if we have a special
+
+ align:start position:0%
+is that if we have a special
+ 
+
+ align:start position:0%
+is that if we have a special
+a real quaternion no a completely
+
+ align:start position:0%
+a real quaternion no a completely
+ 
+
+ align:start position:0%
+a real quaternion no a completely
+imaginary quaternion then when we
+
+ align:start position:0%
+imaginary quaternion then when we
+ 
+
+ align:start position:0%
+imaginary quaternion then when we
+perform this transformation we get back
+
+ align:start position:0%
+perform this transformation we get back
+ 
+
+ align:start position:0%
+perform this transformation we get back
+one of those so we're back in in the
+
+ align:start position:0%
+one of those so we're back in in the
+ 
+
+ align:start position:0%
+one of those so we're back in in the
+world of vectors
+
+ align:start position:0%
+world of vectors
+ 
+
+ align:start position:0%
+world of vectors
+um so that's the one-way conversion the
+
+ align:start position:0%
+um so that's the one-way conversion the
+ 
+
+ align:start position:0%
+um so that's the one-way conversion the
+other way
+
+ align:start position:0%
+other way
+ 
+
+ align:start position:0%
+other way
+is a little bit less obvious
+
+ align:start position:0%
+is a little bit less obvious
+ 
+
+ align:start position:0%
+is a little bit less obvious
+partly because
+
+ align:start position:0%
+partly because
+ 
+
+ align:start position:0%
+partly because
+we're going to have a three by three
+
+ align:start position:0%
+we're going to have a three by three
+ 
+
+ align:start position:0%
+we're going to have a three by three
+matrix so we have nine numbers
+
+ align:start position:0%
+matrix so we have nine numbers
+ 
+
+ align:start position:0%
+matrix so we have nine numbers
+and our answer only has three degrees of
+
+ align:start position:0%
+and our answer only has three degrees of
+ 
+
+ align:start position:0%
+and our answer only has three degrees of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+we only
+
+ align:start position:0%
+we only
+ 
+
+ align:start position:0%
+we only
+want the axis and the angle and so
+
+ align:start position:0%
+want the axis and the angle and so
+ 
+
+ align:start position:0%
+want the axis and the angle and so
+you've done some of this but one part we
+
+ align:start position:0%
+you've done some of this but one part we
+ 
+
+ align:start position:0%
+you've done some of this but one part we
+can do is to look at the trace of of
+
+ align:start position:0%
+can do is to look at the trace of of
+ 
+
+ align:start position:0%
+can do is to look at the trace of of
+that matrix that three by three sub
+
+ align:start position:0%
+that matrix that three by three sub
+ 
+
+ align:start position:0%
+that matrix that three by three sub
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think we end up with something like
+
+ align:start position:0%
+i think we end up with something like
+ 
+
+ align:start position:0%
+i think we end up with something like
+three q squared minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so it's just running down the
+
+ align:start position:0%
+um so it's just running down the
+ 
+
+ align:start position:0%
+um so it's just running down the
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+of course q0
+
+ align:start position:0%
+of course q0
+ 
+
+ align:start position:0%
+of course q0
+we said over there was cosine of half
+
+ align:start position:0%
+we said over there was cosine of half
+ 
+
+ align:start position:0%
+we said over there was cosine of half
+the angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this part each of these is
+
+ align:start position:0%
+and then this part each of these is
+ 
+
+ align:start position:0%
+and then this part each of these is
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+sine of half the angle but n is the unit
+
+ align:start position:0%
+sine of half the angle but n is the unit
+ 
+
+ align:start position:0%
+sine of half the angle but n is the unit
+vector so if we take the square of these
+
+ align:start position:0%
+vector so if we take the square of these
+ 
+
+ align:start position:0%
+vector so if we take the square of these
+we should get sine squared theta over
+
+ align:start position:0%
+we should get sine squared theta over
+ 
+
+ align:start position:0%
+we should get sine squared theta over
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so uh is equal to that
+
+ align:start position:0%
+so uh is equal to that
+ 
+
+ align:start position:0%
+so uh is equal to that
+and um then we can manipulate this
+
+ align:start position:0%
+and um then we can manipulate this
+ 
+
+ align:start position:0%
+and um then we can manipulate this
+various ways like we could add uh cos
+
+ align:start position:0%
+various ways like we could add uh cos
+ 
+
+ align:start position:0%
+various ways like we could add uh cos
+squared theta over two plus sine squared
+
+ align:start position:0%
+squared theta over two plus sine squared
+ 
+
+ align:start position:0%
+squared theta over two plus sine squared
+theta over two equals one
+
+ align:start position:0%
+theta over two equals one
+ 
+
+ align:start position:0%
+theta over two equals one
+in order to get rid of that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that sine squared theta
+
+ align:start position:0%
+that sine squared theta
+ 
+
+ align:start position:0%
+that sine squared theta
+so we can add that in without changing
+
+ align:start position:0%
+so we can add that in without changing
+ 
+
+ align:start position:0%
+so we can add that in without changing
+anything or we can subtract it
+
+ align:start position:0%
+anything or we can subtract it
+ 
+
+ align:start position:0%
+anything or we can subtract it
+so if we subtract it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we get that submit that thing that's
+
+ align:start position:0%
+and we get that submit that thing that's
+ 
+
+ align:start position:0%
+and we get that submit that thing that's
+more symmetrical in cosine and sine and
+
+ align:start position:0%
+more symmetrical in cosine and sine and
+ 
+
+ align:start position:0%
+more symmetrical in cosine and sine and
+of course that's the
+
+ align:start position:0%
+of course that's the
+ 
+
+ align:start position:0%
+of course that's the
+double angle formula so that's two
+
+ align:start position:0%
+double angle formula so that's two
+ 
+
+ align:start position:0%
+double angle formula so that's two
+cosine of theta oh we need the minus 1.
+
+ align:start position:0%
+cosine of theta oh we need the minus 1.
+ 
+
+ align:start position:0%
+cosine of theta oh we need the minus 1.
+and from that we can solve for cosine of
+
+ align:start position:0%
+and from that we can solve for cosine of
+ 
+
+ align:start position:0%
+and from that we can solve for cosine of
+theta is
+
+ align:start position:0%
+theta is
+ 
+
+ align:start position:0%
+theta is
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+trace of r minus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by the way right away that allows you
+
+ align:start position:0%
+so by the way right away that allows you
+ 
+
+ align:start position:0%
+so by the way right away that allows you
+a quick test on whether rotation matrix
+
+ align:start position:0%
+a quick test on whether rotation matrix
+ 
+
+ align:start position:0%
+a quick test on whether rotation matrix
+could even be a rotation matrix because
+
+ align:start position:0%
+could even be a rotation matrix because
+ 
+
+ align:start position:0%
+could even be a rotation matrix because
+if your trace ends up being
+
+ align:start position:0%
+if your trace ends up being
+ 
+
+ align:start position:0%
+if your trace ends up being
+too large uh or too small
+
+ align:start position:0%
+too large uh or too small
+ 
+
+ align:start position:0%
+too large uh or too small
+i.e cosine theta can only be between
+
+ align:start position:0%
+i.e cosine theta can only be between
+ 
+
+ align:start position:0%
+i.e cosine theta can only be between
+plus and minus one so that limits the
+
+ align:start position:0%
+plus and minus one so that limits the
+ 
+
+ align:start position:0%
+plus and minus one so that limits the
+value of the trace
+
+ align:start position:0%
+value of the trace
+ 
+
+ align:start position:0%
+value of the trace
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+that's a lot cheaper than
+
+ align:start position:0%
+that's a lot cheaper than
+ 
+
+ align:start position:0%
+that's a lot cheaper than
+checking whether it's also orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+that's the way to get the angle
+
+ align:start position:0%
+that's the way to get the angle
+ 
+
+ align:start position:0%
+that's the way to get the angle
+it's not a good way
+
+ align:start position:0%
+it's not a good way
+ 
+
+ align:start position:0%
+it's not a good way
+because the problems near theta
+
+ align:start position:0%
+because the problems near theta
+ 
+
+ align:start position:0%
+because the problems near theta
+equals zero right because we we have
+
+ align:start position:0%
+equals zero right because we we have
+ 
+
+ align:start position:0%
+equals zero right because we we have
+that that thing we're up on the curve
+
+ align:start position:0%
+that that thing we're up on the curve
+ 
+
+ align:start position:0%
+that that thing we're up on the curve
+and a tiny change in the height
+
+ align:start position:0%
+and a tiny change in the height
+ 
+
+ align:start position:0%
+and a tiny change in the height
+potentially corresponds to a large
+
+ align:start position:0%
+potentially corresponds to a large
+ 
+
+ align:start position:0%
+potentially corresponds to a large
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+in theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and similarly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yes this is true but that's not the
+
+ align:start position:0%
+so yes this is true but that's not the
+ 
+
+ align:start position:0%
+so yes this is true but that's not the
+way to compute theta so what do we do
+
+ align:start position:0%
+way to compute theta so what do we do
+ 
+
+ align:start position:0%
+way to compute theta so what do we do
+well we use the off-diagonal elements
+
+ align:start position:0%
+well we use the off-diagonal elements
+ 
+
+ align:start position:0%
+well we use the off-diagonal elements
+right because the off-diagonal elements
+
+ align:start position:0%
+right because the off-diagonal elements
+ 
+
+ align:start position:0%
+right because the off-diagonal elements
+all depend on the sine of theta over two
+
+ align:start position:0%
+all depend on the sine of theta over two
+ 
+
+ align:start position:0%
+all depend on the sine of theta over two
+and then it depends on whether we're
+
+ align:start position:0%
+and then it depends on whether we're
+ 
+
+ align:start position:0%
+and then it depends on whether we're
+going to use
+
+ align:start position:0%
+going to use
+ 
+
+ align:start position:0%
+going to use
+the symmetric part like q x q y
+
+ align:start position:0%
+the symmetric part like q x q y
+ 
+
+ align:start position:0%
+the symmetric part like q x q y
+which would then depend on sine squared
+
+ align:start position:0%
+which would then depend on sine squared
+ 
+
+ align:start position:0%
+which would then depend on sine squared
+of theta over two or the asymmetric part
+
+ align:start position:0%
+of theta over two or the asymmetric part
+ 
+
+ align:start position:0%
+of theta over two or the asymmetric part
+which is q zero q z which is going to
+
+ align:start position:0%
+which is q zero q z which is going to
+ 
+
+ align:start position:0%
+which is q zero q z which is going to
+depend on sine theta over two cosine
+
+ align:start position:0%
+depend on sine theta over two cosine
+ 
+
+ align:start position:0%
+depend on sine theta over two cosine
+theta over two which is the double angle
+
+ align:start position:0%
+theta over two which is the double angle
+ 
+
+ align:start position:0%
+theta over two which is the double angle
+formula for sine theta so anyway need to
+
+ align:start position:0%
+formula for sine theta so anyway need to
+ 
+
+ align:start position:0%
+formula for sine theta so anyway need to
+get sine theta
+
+ align:start position:0%
+get sine theta
+ 
+
+ align:start position:0%
+get sine theta
+so that you can then use a tan 2 and
+
+ align:start position:0%
+so that you can then use a tan 2 and
+ 
+
+ align:start position:0%
+so that you can then use a tan 2 and
+avoid that problem because where this
+
+ align:start position:0%
+avoid that problem because where this
+ 
+
+ align:start position:0%
+avoid that problem because where this
+one is bad sine theta is good so
+
+ align:start position:0%
+one is bad sine theta is good so
+ 
+
+ align:start position:0%
+one is bad sine theta is good so
+okay so that's one way to go um
+
+ align:start position:0%
+okay so that's one way to go um
+ 
+
+ align:start position:0%
+okay so that's one way to go um
+but to make it uh
+
+ align:start position:0%
+but to make it uh
+ 
+
+ align:start position:0%
+but to make it uh
+really explicit let's actually
+
+ align:start position:0%
+really explicit let's actually
+ 
+
+ align:start position:0%
+really explicit let's actually
+give a full inversion formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i do this mostly to vaccinate you
+
+ align:start position:0%
+and i do this mostly to vaccinate you
+ 
+
+ align:start position:0%
+and i do this mostly to vaccinate you
+against conversion formulas that have
+
+ align:start position:0%
+against conversion formulas that have
+ 
+
+ align:start position:0%
+against conversion formulas that have
+been published
+
+ align:start position:0%
+been published
+ 
+
+ align:start position:0%
+been published
+because they are not good so
+
+ align:start position:0%
+because they are not good so
+ 
+
+ align:start position:0%
+because they are not good so
+in the sense in this kind of sense well
+
+ align:start position:0%
+in the sense in this kind of sense well
+ 
+
+ align:start position:0%
+in the sense in this kind of sense well
+yeah mathematically you know you're done
+
+ align:start position:0%
+yeah mathematically you know you're done
+ 
+
+ align:start position:0%
+yeah mathematically you know you're done
+you've got this but actually in terms of
+
+ align:start position:0%
+you've got this but actually in terms of
+ 
+
+ align:start position:0%
+you've got this but actually in terms of
+numerical accuracy uh no
+
+ align:start position:0%
+numerical accuracy uh no
+ 
+
+ align:start position:0%
+numerical accuracy uh no
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+given the three by three matrix
+
+ align:start position:0%
+given the three by three matrix
+ 
+
+ align:start position:0%
+given the three by three matrix
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+we can compute various sums
+
+ align:start position:0%
+we can compute various sums
+ 
+
+ align:start position:0%
+we can compute various sums
+and let's start with a diagonal
+
+ align:start position:0%
+and let's start with a diagonal
+ 
+
+ align:start position:0%
+and let's start with a diagonal
+so we've got our three by three matrix
+
+ align:start position:0%
+so we've got our three by three matrix
+ 
+
+ align:start position:0%
+so we've got our three by three matrix
+over there
+
+ align:start position:0%
+over there
+ 
+
+ align:start position:0%
+over there
+and if we end up with uh
+
+ align:start position:0%
+and if we end up with uh
+ 
+
+ align:start position:0%
+and if we end up with uh
+the diagonal we we get that if we add
+
+ align:start position:0%
+the diagonal we we get that if we add
+ 
+
+ align:start position:0%
+the diagonal we we get that if we add
+one right there's that one
+
+ align:start position:0%
+one right there's that one
+ 
+
+ align:start position:0%
+one right there's that one
+then we can combine it in various other
+
+ align:start position:0%
+then we can combine it in various other
+ 
+
+ align:start position:0%
+then we can combine it in various other
+ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is sort of like you know try all
+
+ align:start position:0%
+this is sort of like you know try all
+ 
+
+ align:start position:0%
+this is sort of like you know try all
+possible ways of subtracting and adding
+
+ align:start position:0%
+possible ways of subtracting and adding
+ 
+
+ align:start position:0%
+possible ways of subtracting and adding
+terms on the diagonal
+
+ align:start position:0%
+terms on the diagonal
+ 
+
+ align:start position:0%
+terms on the diagonal
+as if the off diagonals didn't exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ta-da uh now we just take square
+
+ align:start position:0%
+and ta-da uh now we just take square
+ 
+
+ align:start position:0%
+and ta-da uh now we just take square
+roots
+
+ align:start position:0%
+roots
+ 
+
+ align:start position:0%
+roots
+so so that's one approach
+
+ align:start position:0%
+so so that's one approach
+ 
+
+ align:start position:0%
+so so that's one approach
+um of course the problem is
+
+ align:start position:0%
+um of course the problem is
+ 
+
+ align:start position:0%
+um of course the problem is
+there's a sine ambiguity ambiguity
+
+ align:start position:0%
+there's a sine ambiguity ambiguity
+ 
+
+ align:start position:0%
+there's a sine ambiguity ambiguity
+right because in each case we can
+
+ align:start position:0%
+right because in each case we can
+ 
+
+ align:start position:0%
+right because in each case we can
+compute these uh
+
+ align:start position:0%
+compute these uh
+ 
+
+ align:start position:0%
+compute these uh
+sums and differences
+
+ align:start position:0%
+sums and differences
+ 
+
+ align:start position:0%
+sums and differences
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+divide by four and take the square root
+
+ align:start position:0%
+divide by four and take the square root
+ 
+
+ align:start position:0%
+divide by four and take the square root
+and we've got one component of the
+
+ align:start position:0%
+and we've got one component of the
+ 
+
+ align:start position:0%
+and we've got one component of the
+quaternion
+
+ align:start position:0%
+quaternion
+ 
+
+ align:start position:0%
+quaternion
+but we don't know whether it's plus or
+
+ align:start position:0%
+but we don't know whether it's plus or
+ 
+
+ align:start position:0%
+but we don't know whether it's plus or
+minus and yeah we know that
+
+ align:start position:0%
+minus and yeah we know that
+ 
+
+ align:start position:0%
+minus and yeah we know that
+plus q is the same as minus q but this
+
+ align:start position:0%
+plus q is the same as minus q but this
+ 
+
+ align:start position:0%
+plus q is the same as minus q but this
+is more this allows us
+
+ align:start position:0%
+is more this allows us
+ 
+
+ align:start position:0%
+is more this allows us
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+16 different sign choices
+
+ align:start position:0%
+16 different sign choices
+ 
+
+ align:start position:0%
+16 different sign choices
+so even if you allow for the flipping of
+
+ align:start position:0%
+so even if you allow for the flipping of
+ 
+
+ align:start position:0%
+so even if you allow for the flipping of
+the sign of the quaternion that leaves
+
+ align:start position:0%
+the sign of the quaternion that leaves
+ 
+
+ align:start position:0%
+the sign of the quaternion that leaves
+us with eight so that's
+
+ align:start position:0%
+us with eight so that's
+ 
+
+ align:start position:0%
+us with eight so that's
+that means that we shouldn't rely on
+
+ align:start position:0%
+that means that we shouldn't rely on
+ 
+
+ align:start position:0%
+that means that we shouldn't rely on
+this method alone
+
+ align:start position:0%
+this method alone
+ 
+
+ align:start position:0%
+this method alone
+but what we can do is uh
+
+ align:start position:0%
+but what we can do is uh
+ 
+
+ align:start position:0%
+but what we can do is uh
+compute these and then pick the largest
+
+ align:start position:0%
+compute these and then pick the largest
+ 
+
+ align:start position:0%
+compute these and then pick the largest
+for numerical accuracy
+
+ align:start position:0%
+for numerical accuracy
+ 
+
+ align:start position:0%
+for numerical accuracy
+and solve for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know suppose q y is
+
+ align:start position:0%
+so you know suppose q y is
+ 
+
+ align:start position:0%
+so you know suppose q y is
+suppose this sum is the largest
+
+ align:start position:0%
+suppose this sum is the largest
+ 
+
+ align:start position:0%
+suppose this sum is the largest
+then we'll use it and arbitrarily use
+
+ align:start position:0%
+then we'll use it and arbitrarily use
+ 
+
+ align:start position:0%
+then we'll use it and arbitrarily use
+the positive version
+
+ align:start position:0%
+the positive version
+ 
+
+ align:start position:0%
+the positive version
+because uh we have that minus q is the
+
+ align:start position:0%
+because uh we have that minus q is the
+ 
+
+ align:start position:0%
+because uh we have that minus q is the
+same as q
+
+ align:start position:0%
+same as q
+ 
+
+ align:start position:0%
+same as q
+so we can pick we can make one arbitrary
+
+ align:start position:0%
+so we can pick we can make one arbitrary
+ 
+
+ align:start position:0%
+so we can pick we can make one arbitrary
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+solve for that let's call that q i
+
+ align:start position:0%
+solve for that let's call that q i
+ 
+
+ align:start position:0%
+solve for that let's call that q i
+and then we need to go to the off
+
+ align:start position:0%
+and then we need to go to the off
+ 
+
+ align:start position:0%
+and then we need to go to the off
+diagonals and fortunately
+
+ align:start position:0%
+diagonals and fortunately
+ 
+
+ align:start position:0%
+diagonals and fortunately
+they're symmetric and asymmetric parts
+
+ align:start position:0%
+they're symmetric and asymmetric parts
+ 
+
+ align:start position:0%
+they're symmetric and asymmetric parts
+that we can pull out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this is a bit more involved than the
+
+ align:start position:0%
+this is a bit more involved than the
+ 
+
+ align:start position:0%
+this is a bit more involved than the
+published methods
+
+ align:start position:0%
+published methods
+ 
+
+ align:start position:0%
+published methods
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it works
+
+ align:start position:0%
+it works
+ 
+
+ align:start position:0%
+it works
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+resistant it's robust it's resistant to
+
+ align:start position:0%
+resistant it's robust it's resistant to
+ 
+
+ align:start position:0%
+resistant it's robust it's resistant to
+numerical problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by adding and subtracting
+
+ align:start position:0%
+so by adding and subtracting
+ 
+
+ align:start position:0%
+so by adding and subtracting
+corresponding diag off-diagonal parts we
+
+ align:start position:0%
+corresponding diag off-diagonal parts we
+ 
+
+ align:start position:0%
+corresponding diag off-diagonal parts we
+get six relationships you know more than
+
+ align:start position:0%
+get six relationships you know more than
+ 
+
+ align:start position:0%
+get six relationships you know more than
+we need
+
+ align:start position:0%
+we need
+ 
+
+ align:start position:0%
+we need
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the way this works is we've picked one
+
+ align:start position:0%
+the way this works is we've picked one
+ 
+
+ align:start position:0%
+the way this works is we've picked one
+of these and solved from the diagonal
+
+ align:start position:0%
+of these and solved from the diagonal
+ 
+
+ align:start position:0%
+of these and solved from the diagonal
+and then we go into three of these and
+
+ align:start position:0%
+and then we go into three of these and
+ 
+
+ align:start position:0%
+and then we go into three of these and
+solve for the rest right so for example
+
+ align:start position:0%
+solve for the rest right so for example
+ 
+
+ align:start position:0%
+solve for the rest right so for example
+if we solve for q y
+
+ align:start position:0%
+if we solve for q y
+ 
+
+ align:start position:0%
+if we solve for q y
+uh this involves q y
+
+ align:start position:0%
+uh this involves q y
+ 
+
+ align:start position:0%
+uh this involves q y
+this involves q y and this involves q y
+
+ align:start position:0%
+this involves q y and this involves q y
+ 
+
+ align:start position:0%
+this involves q y and this involves q y
+so we pick those three to solve for q
+
+ align:start position:0%
+so we pick those three to solve for q
+ 
+
+ align:start position:0%
+so we pick those three to solve for q
+zero q x and q and q z so
+
+ align:start position:0%
+zero q x and q and q z so
+ 
+
+ align:start position:0%
+zero q x and q and q z so
+then you know correspondingly if we have
+
+ align:start position:0%
+then you know correspondingly if we have
+ 
+
+ align:start position:0%
+then you know correspondingly if we have
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+a direct way of going from quaternion to
+
+ align:start position:0%
+a direct way of going from quaternion to
+ 
+
+ align:start position:0%
+a direct way of going from quaternion to
+rotation matrix i mean we can also go
+
+ align:start position:0%
+rotation matrix i mean we can also go
+ 
+
+ align:start position:0%
+rotation matrix i mean we can also go
+indirectly we can first find axis and
+
+ align:start position:0%
+indirectly we can first find axis and
+ 
+
+ align:start position:0%
+indirectly we can first find axis and
+angle and then
+
+ align:start position:0%
+angle and then
+ 
+
+ align:start position:0%
+angle and then
+write the rotation matrix in terms of
+
+ align:start position:0%
+write the rotation matrix in terms of
+ 
+
+ align:start position:0%
+write the rotation matrix in terms of
+axis and angle so
+
+ align:start position:0%
+axis and angle so
+ 
+
+ align:start position:0%
+axis and angle so
+and it's it's more complicated mostly
+
+ align:start position:0%
+and it's it's more complicated mostly
+ 
+
+ align:start position:0%
+and it's it's more complicated mostly
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+we've got nine numbers and they could be
+
+ align:start position:0%
+we've got nine numbers and they could be
+ 
+
+ align:start position:0%
+we've got nine numbers and they could be
+noisy and we'd like to get the best
+
+ align:start position:0%
+noisy and we'd like to get the best
+ 
+
+ align:start position:0%
+noisy and we'd like to get the best
+possible result
+
+ align:start position:0%
+possible result
+ 
+
+ align:start position:0%
+possible result
+uh out of those nine numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we've uh out of the 56 ways of
+
+ align:start position:0%
+okay so we've uh out of the 56 ways of
+ 
+
+ align:start position:0%
+okay so we've uh out of the 56 ways of
+converting between different
+
+ align:start position:0%
+converting between different
+ 
+
+ align:start position:0%
+converting between different
+representations we've we've done uh four
+
+ align:start position:0%
+representations we've we've done uh four
+ 
+
+ align:start position:0%
+representations we've we've done uh four
+and that that's that should be enough so
+
+ align:start position:0%
+and that that's that should be enough so
+ 
+
+ align:start position:0%
+and that that's that should be enough so
+we can convert back and forth between
+
+ align:start position:0%
+we can convert back and forth between
+ 
+
+ align:start position:0%
+we can convert back and forth between
+the things that we're
+
+ align:start position:0%
+the things that we're
+ 
+
+ align:start position:0%
+the things that we're
+more familiar with
+
+ align:start position:0%
+more familiar with
+ 
+
+ align:start position:0%
+more familiar with
+maybe not between poorly spin matrices
+
+ align:start position:0%
+maybe not between poorly spin matrices
+ 
+
+ align:start position:0%
+maybe not between poorly spin matrices
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we don't use those much
+
+ align:start position:0%
+we don't use those much
+ 
+
+ align:start position:0%
+we don't use those much
+except in quantum mechanics
+
+ align:start position:0%
+except in quantum mechanics
+ 
+
+ align:start position:0%
+except in quantum mechanics
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and you know you did some of this in the
+
+ align:start position:0%
+and you know you did some of this in the
+ 
+
+ align:start position:0%
+and you know you did some of this in the
+homework and i don't want to repeat that
+
+ align:start position:0%
+homework and i don't want to repeat that
+ 
+
+ align:start position:0%
+homework and i don't want to repeat that
+but let me talk about something in
+
+ align:start position:0%
+but let me talk about something in
+ 
+
+ align:start position:0%
+but let me talk about something in
+particular uh scaling
+
+ align:start position:0%
+particular uh scaling
+ 
+
+ align:start position:0%
+particular uh scaling
+so so far
+
+ align:start position:0%
+so so far
+ 
+
+ align:start position:0%
+so so far
+we'd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume that our coordinate system
+
+ align:start position:0%
+assume that our coordinate system
+ 
+
+ align:start position:0%
+assume that our coordinate system
+transformations were rotation and
+
+ align:start position:0%
+transformations were rotation and
+ 
+
+ align:start position:0%
+transformations were rotation and
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+and in many cases that's all there is
+
+ align:start position:0%
+and in many cases that's all there is
+ 
+
+ align:start position:0%
+and in many cases that's all there is
+if we have actual
+
+ align:start position:0%
+if we have actual
+ 
+
+ align:start position:0%
+if we have actual
+time of flight data to measuring
+
+ align:start position:0%
+time of flight data to measuring
+ 
+
+ align:start position:0%
+time of flight data to measuring
+distances
+
+ align:start position:0%
+distances
+ 
+
+ align:start position:0%
+distances
+there's um
+
+ align:start position:0%
+there's um
+ 
+
+ align:start position:0%
+there's um
+usually no question about the scale
+
+ align:start position:0%
+usually no question about the scale
+ 
+
+ align:start position:0%
+usually no question about the scale
+factor because we know
+
+ align:start position:0%
+factor because we know
+ 
+
+ align:start position:0%
+factor because we know
+the speed of light with you know more
+
+ align:start position:0%
+the speed of light with you know more
+ 
+
+ align:start position:0%
+the speed of light with you know more
+precision than
+
+ align:start position:0%
+precision than
+ 
+
+ align:start position:0%
+precision than
+you can throw a stick at um although
+
+ align:start position:0%
+you can throw a stick at um although
+ 
+
+ align:start position:0%
+you can throw a stick at um although
+there's often an error in offset
+
+ align:start position:0%
+there's often an error in offset
+ 
+
+ align:start position:0%
+there's often an error in offset
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+how do we get into scale well it's quite
+
+ align:start position:0%
+how do we get into scale well it's quite
+ 
+
+ align:start position:0%
+how do we get into scale well it's quite
+easy to get into scale for example if we
+
+ align:start position:0%
+easy to get into scale for example if we
+ 
+
+ align:start position:0%
+easy to get into scale for example if we
+get the baseline wrong
+
+ align:start position:0%
+get the baseline wrong
+ 
+
+ align:start position:0%
+get the baseline wrong
+so our plane is flying along taking one
+
+ align:start position:0%
+so our plane is flying along taking one
+ 
+
+ align:start position:0%
+so our plane is flying along taking one
+picture taking another picture and we
+
+ align:start position:0%
+picture taking another picture and we
+ 
+
+ align:start position:0%
+picture taking another picture and we
+know the speed of the plane and we know
+
+ align:start position:0%
+know the speed of the plane and we know
+ 
+
+ align:start position:0%
+know the speed of the plane and we know
+the time so we know how far we know the
+
+ align:start position:0%
+the time so we know how far we know the
+ 
+
+ align:start position:0%
+the time so we know how far we know the
+baseline but how accurately do we really
+
+ align:start position:0%
+baseline but how accurately do we really
+ 
+
+ align:start position:0%
+baseline but how accurately do we really
+know it
+
+ align:start position:0%
+know it
+ 
+
+ align:start position:0%
+know it
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+uh if we are trying to patch together
+
+ align:start position:0%
+uh if we are trying to patch together
+ 
+
+ align:start position:0%
+uh if we are trying to patch together
+pieces of the terrain that were obtained
+
+ align:start position:0%
+pieces of the terrain that were obtained
+ 
+
+ align:start position:0%
+pieces of the terrain that were obtained
+with successive you know two camera
+
+ align:start position:0%
+with successive you know two camera
+ 
+
+ align:start position:0%
+with successive you know two camera
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+then we should allow for some small
+
+ align:start position:0%
+then we should allow for some small
+ 
+
+ align:start position:0%
+then we should allow for some small
+difference in the scaling because we
+
+ align:start position:0%
+difference in the scaling because we
+ 
+
+ align:start position:0%
+difference in the scaling because we
+don't we know the distance pretty
+
+ align:start position:0%
+don't we know the distance pretty
+ 
+
+ align:start position:0%
+don't we know the distance pretty
+accurately but not perfectly and you
+
+ align:start position:0%
+accurately but not perfectly and you
+ 
+
+ align:start position:0%
+accurately but not perfectly and you
+know we're looking for very high
+
+ align:start position:0%
+know we're looking for very high
+ 
+
+ align:start position:0%
+know we're looking for very high
+accuracy in topographic reconstruction
+
+ align:start position:0%
+accuracy in topographic reconstruction
+ 
+
+ align:start position:0%
+accuracy in topographic reconstruction
+so how to deal with that
+
+ align:start position:0%
+so how to deal with that
+ 
+
+ align:start position:0%
+so how to deal with that
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+let's assume we've uh
+
+ align:start position:0%
+let's assume we've uh
+ 
+
+ align:start position:0%
+let's assume we've uh
+and this isn't hard
+
+ align:start position:0%
+and this isn't hard
+ 
+
+ align:start position:0%
+and this isn't hard
+we again find that centroid maps to
+
+ align:start position:0%
+we again find that centroid maps to
+ 
+
+ align:start position:0%
+we again find that centroid maps to
+centroid even with the introduction of
+
+ align:start position:0%
+centroid even with the introduction of
+ 
+
+ align:start position:0%
+centroid even with the introduction of
+scaling uh that's very easy just
+
+ align:start position:0%
+scaling uh that's very easy just
+ 
+
+ align:start position:0%
+scaling uh that's very easy just
+differentiate with respect to
+
+ align:start position:0%
+differentiate with respect to
+ 
+
+ align:start position:0%
+differentiate with respect to
+translation set the result equal to zero
+
+ align:start position:0%
+translation set the result equal to zero
+ 
+
+ align:start position:0%
+translation set the result equal to zero
+and then we move the origin to the
+
+ align:start position:0%
+and then we move the origin to the
+ 
+
+ align:start position:0%
+and then we move the origin to the
+centroid and we get these prime
+
+ align:start position:0%
+centroid and we get these prime
+ 
+
+ align:start position:0%
+centroid and we get these prime
+coordinates so now uh
+
+ align:start position:0%
+coordinates so now uh
+ 
+
+ align:start position:0%
+coordinates so now uh
+let's look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's a possible version of the
+
+ align:start position:0%
+so here's a possible version of the
+ 
+
+ align:start position:0%
+so here's a possible version of the
+problem we're trying to solve that now
+
+ align:start position:0%
+problem we're trying to solve that now
+ 
+
+ align:start position:0%
+problem we're trying to solve that now
+in the we've got rid of translation by
+
+ align:start position:0%
+in the we've got rid of translation by
+ 
+
+ align:start position:0%
+in the we've got rid of translation by
+moving to centroid uh and now we have an
+
+ align:start position:0%
+moving to centroid uh and now we have an
+ 
+
+ align:start position:0%
+moving to centroid uh and now we have an
+unknown rotation and we have an unknown
+
+ align:start position:0%
+unknown rotation and we have an unknown
+ 
+
+ align:start position:0%
+unknown rotation and we have an unknown
+scaling that that's a new part and so we
+
+ align:start position:0%
+scaling that that's a new part and so we
+ 
+
+ align:start position:0%
+scaling that that's a new part and so we
+might want to set up a least squares
+
+ align:start position:0%
+might want to set up a least squares
+ 
+
+ align:start position:0%
+might want to set up a least squares
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course the norm is the dot
+
+ align:start position:0%
+and of course the norm is the dot
+ 
+
+ align:start position:0%
+and of course the norm is the dot
+product of this thing with itself so we
+
+ align:start position:0%
+product of this thing with itself so we
+ 
+
+ align:start position:0%
+product of this thing with itself so we
+can actually multiply it out we get four
+
+ align:start position:0%
+can actually multiply it out we get four
+ 
+
+ align:start position:0%
+can actually multiply it out we get four
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+and then the sum of those four terms is
+
+ align:start position:0%
+and then the sum of those four terms is
+ 
+
+ align:start position:0%
+and then the sum of those four terms is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sum of four sums
+
+ align:start position:0%
+sum of four sums
+ 
+
+ align:start position:0%
+sum of four sums
+and so we end up with
+
+ align:start position:0%
+and so we end up with
+ 
+
+ align:start position:0%
+and so we end up with
+so this is very similar to
+
+ align:start position:0%
+so this is very similar to
+ 
+
+ align:start position:0%
+so this is very similar to
+what we've done before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how do we find the optimum well of
+
+ align:start position:0%
+and how do we find the optimum well of
+ 
+
+ align:start position:0%
+and how do we find the optimum well of
+course we just differentiate with
+
+ align:start position:0%
+course we just differentiate with
+ 
+
+ align:start position:0%
+course we just differentiate with
+respect to s this is particularly easy
+
+ align:start position:0%
+respect to s this is particularly easy
+ 
+
+ align:start position:0%
+respect to s this is particularly easy
+now it's just a scalar and we set the
+
+ align:start position:0%
+now it's just a scalar and we set the
+ 
+
+ align:start position:0%
+now it's just a scalar and we set the
+result equal to zero and the first term
+
+ align:start position:0%
+result equal to zero and the first term
+ 
+
+ align:start position:0%
+result equal to zero and the first term
+drops out and then we get the second
+
+ align:start position:0%
+drops out and then we get the second
+ 
+
+ align:start position:0%
+drops out and then we get the second
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh here of course we use the fact that
+
+ align:start position:0%
+oh here of course we use the fact that
+ 
+
+ align:start position:0%
+oh here of course we use the fact that
+this the size of this vector is the same
+
+ align:start position:0%
+this the size of this vector is the same
+ 
+
+ align:start position:0%
+this the size of this vector is the same
+as the size of the rotated vector so
+
+ align:start position:0%
+as the size of the rotated vector so
+ 
+
+ align:start position:0%
+as the size of the rotated vector so
+rotation doesn't change the size okay
+
+ align:start position:0%
+rotation doesn't change the size okay
+ 
+
+ align:start position:0%
+rotation doesn't change the size okay
+this is equal to 0 and so we can solve
+
+ align:start position:0%
+this is equal to 0 and so we can solve
+ 
+
+ align:start position:0%
+this is equal to 0 and so we can solve
+for s
+
+ align:start position:0%
+for s
+ 
+
+ align:start position:0%
+for s
+well let's give these things names
+
+ align:start position:0%
+well let's give these things names
+ 
+
+ align:start position:0%
+well let's give these things names
+let's call this
+
+ align:start position:0%
+let's call this
+ 
+
+ align:start position:0%
+let's call this
+sr
+
+ align:start position:0%
+sr
+ 
+
+ align:start position:0%
+sr
+so we don't have to write them too many
+
+ align:start position:0%
+so we don't have to write them too many
+ 
+
+ align:start position:0%
+so we don't have to write them too many
+times and let's call this d
+
+ align:start position:0%
+times and let's call this d
+ 
+
+ align:start position:0%
+times and let's call this d
+and call this is l
+
+ align:start position:0%
+and call this is l
+ 
+
+ align:start position:0%
+and call this is l
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+s equals d of s
+
+ align:start position:0%
+s equals d of s
+ 
+
+ align:start position:0%
+s equals d of s
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+right we just solve this for d we can
+
+ align:start position:0%
+right we just solve this for d we can
+ 
+
+ align:start position:0%
+right we just solve this for d we can
+forget the two
+
+ align:start position:0%
+forget the two
+ 
+
+ align:start position:0%
+forget the two
+and and so
+
+ align:start position:0%
+and and so
+ 
+
+ align:start position:0%
+and and so
+we don't at this point know the answer
+
+ align:start position:0%
+we don't at this point know the answer
+ 
+
+ align:start position:0%
+we don't at this point know the answer
+because we haven't got the rotation yet
+
+ align:start position:0%
+because we haven't got the rotation yet
+ 
+
+ align:start position:0%
+because we haven't got the rotation yet
+but with in the same situation as we
+
+ align:start position:0%
+but with in the same situation as we
+ 
+
+ align:start position:0%
+but with in the same situation as we
+with translation where
+
+ align:start position:0%
+with translation where
+ 
+
+ align:start position:0%
+with translation where
+we can remove the scale factor from
+
+ align:start position:0%
+we can remove the scale factor from
+ 
+
+ align:start position:0%
+we can remove the scale factor from
+consideration now
+
+ align:start position:0%
+consideration now
+ 
+
+ align:start position:0%
+consideration now
+and then at the end we go back and use
+
+ align:start position:0%
+and then at the end we go back and use
+ 
+
+ align:start position:0%
+and then at the end we go back and use
+this formula
+
+ align:start position:0%
+this formula
+ 
+
+ align:start position:0%
+this formula
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute the
+
+ align:start position:0%
+compute the
+ 
+
+ align:start position:0%
+compute the
+scale factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that sort of keeps everything coupled
+
+ align:start position:0%
+so that sort of keeps everything coupled
+ 
+
+ align:start position:0%
+so that sort of keeps everything coupled
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+we can't do it independently of rotation
+
+ align:start position:0%
+we can't do it independently of rotation
+ 
+
+ align:start position:0%
+we can't do it independently of rotation
+now uh we talked earlier about um
+
+ align:start position:0%
+now uh we talked earlier about um
+ 
+
+ align:start position:0%
+now uh we talked earlier about um
+symmetry you know why are we rotating
+
+ align:start position:0%
+symmetry you know why are we rotating
+ 
+
+ align:start position:0%
+symmetry you know why are we rotating
+from left coordinate to right coordinate
+
+ align:start position:0%
+from left coordinate to right coordinate
+ 
+
+ align:start position:0%
+from left coordinate to right coordinate
+rather than from right corner to the
+
+ align:start position:0%
+rather than from right corner to the
+ 
+
+ align:start position:0%
+rather than from right corner to the
+left coordinate and
+
+ align:start position:0%
+left coordinate and
+ 
+
+ align:start position:0%
+left coordinate and
+a method should really be symmetrical in
+
+ align:start position:0%
+a method should really be symmetrical in
+ 
+
+ align:start position:0%
+a method should really be symmetrical in
+that if you compute the inverse you
+
+ align:start position:0%
+that if you compute the inverse you
+ 
+
+ align:start position:0%
+that if you compute the inverse you
+should get the inverse of you know so
+
+ align:start position:0%
+should get the inverse of you know so
+ 
+
+ align:start position:0%
+should get the inverse of you know so
+the rotational matrix you get should be
+
+ align:start position:0%
+the rotational matrix you get should be
+ 
+
+ align:start position:0%
+the rotational matrix you get should be
+the transpose of the rotational matrix
+
+ align:start position:0%
+the transpose of the rotational matrix
+ 
+
+ align:start position:0%
+the transpose of the rotational matrix
+and so on so so here if we now go from
+
+ align:start position:0%
+and so on so so here if we now go from
+ 
+
+ align:start position:0%
+and so on so so here if we now go from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the other way around
+
+ align:start position:0%
+the other way around
+ 
+
+ align:start position:0%
+the other way around
+if we look at this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we expect to get a scale factor
+
+ align:start position:0%
+then we expect to get a scale factor
+ 
+
+ align:start position:0%
+then we expect to get a scale factor
+that's the inverse of that scale factor
+
+ align:start position:0%
+that's the inverse of that scale factor
+ 
+
+ align:start position:0%
+that's the inverse of that scale factor
+right because we're going from
+
+ align:start position:0%
+right because we're going from
+ 
+
+ align:start position:0%
+right because we're going from
+right coordinate system to left we're
+
+ align:start position:0%
+right coordinate system to left we're
+ 
+
+ align:start position:0%
+right coordinate system to left we're
+going from left to right before and if
+
+ align:start position:0%
+going from left to right before and if
+ 
+
+ align:start position:0%
+going from left to right before and if
+you actually work it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get that
+
+ align:start position:0%
+you get that
+ 
+
+ align:start position:0%
+you get that
+so again you can do it
+
+ align:start position:0%
+so again you can do it
+ 
+
+ align:start position:0%
+so again you can do it
+but it's not the same answer
+
+ align:start position:0%
+but it's not the same answer
+ 
+
+ align:start position:0%
+but it's not the same answer
+it's not the inverse of that what we
+
+ align:start position:0%
+it's not the inverse of that what we
+ 
+
+ align:start position:0%
+it's not the inverse of that what we
+would expect is that
+
+ align:start position:0%
+would expect is that
+ 
+
+ align:start position:0%
+would expect is that
+s prime is 1 over s
+
+ align:start position:0%
+s prime is 1 over s
+ 
+
+ align:start position:0%
+s prime is 1 over s
+and it's not
+
+ align:start position:0%
+and it's not
+ 
+
+ align:start position:0%
+and it's not
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+so that suggests that this is not a good
+
+ align:start position:0%
+so that suggests that this is not a good
+ 
+
+ align:start position:0%
+so that suggests that this is not a good
+method
+
+ align:start position:0%
+method
+ 
+
+ align:start position:0%
+method
+and what's what's going on well what's
+
+ align:start position:0%
+and what's what's going on well what's
+ 
+
+ align:start position:0%
+and what's what's going on well what's
+going on is that the least squares
+
+ align:start position:0%
+going on is that the least squares
+ 
+
+ align:start position:0%
+going on is that the least squares
+method is trying to make things as the
+
+ align:start position:0%
+method is trying to make things as the
+ 
+
+ align:start position:0%
+method is trying to make things as the
+errors as small as possible and one way
+
+ align:start position:0%
+errors as small as possible and one way
+ 
+
+ align:start position:0%
+errors as small as possible and one way
+to do that is to make
+
+ align:start position:0%
+to do that is to make
+ 
+
+ align:start position:0%
+to do that is to make
+the transform coordinates smaller
+
+ align:start position:0%
+the transform coordinates smaller
+ 
+
+ align:start position:0%
+the transform coordinates smaller
+up to a point so you can kind of cheat
+
+ align:start position:0%
+up to a point so you can kind of cheat
+ 
+
+ align:start position:0%
+up to a point so you can kind of cheat
+by making the
+
+ align:start position:0%
+by making the
+ 
+
+ align:start position:0%
+by making the
+scale factor a little bit smaller than
+
+ align:start position:0%
+scale factor a little bit smaller than
+ 
+
+ align:start position:0%
+scale factor a little bit smaller than
+it it
+
+ align:start position:0%
+it it
+ 
+
+ align:start position:0%
+it it
+really should be
+
+ align:start position:0%
+really should be
+ 
+
+ align:start position:0%
+really should be
+because you're shrinking things down and
+
+ align:start position:0%
+because you're shrinking things down and
+ 
+
+ align:start position:0%
+because you're shrinking things down and
+making things smaller and then
+
+ align:start position:0%
+making things smaller and then
+ 
+
+ align:start position:0%
+making things smaller and then
+conversely if you go in the other
+
+ align:start position:0%
+conversely if you go in the other
+ 
+
+ align:start position:0%
+conversely if you go in the other
+direction you shrink down the other
+
+ align:start position:0%
+direction you shrink down the other
+ 
+
+ align:start position:0%
+direction you shrink down the other
+coordinate system so
+
+ align:start position:0%
+coordinate system so
+ 
+
+ align:start position:0%
+coordinate system so
+neither of these is really uh
+
+ align:start position:0%
+neither of these is really uh
+ 
+
+ align:start position:0%
+neither of these is really uh
+acceptable
+
+ align:start position:0%
+acceptable
+ 
+
+ align:start position:0%
+acceptable
+and so we look at another error term
+
+ align:start position:0%
+and so we look at another error term
+ 
+
+ align:start position:0%
+and so we look at another error term
+the one that you looked at in the
+
+ align:start position:0%
+the one that you looked at in the
+ 
+
+ align:start position:0%
+the one that you looked at in the
+homework problem
+
+ align:start position:0%
+homework problem
+ 
+
+ align:start position:0%
+homework problem
+in the 2d case
+
+ align:start position:0%
+in the 2d case
+ 
+
+ align:start position:0%
+in the 2d case
+and so in this case we're going to end
+
+ align:start position:0%
+and so in this case we're going to end
+ 
+
+ align:start position:0%
+and so in this case we're going to end
+up with an error that looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right where the you know srsl and d are
+
+ align:start position:0%
+right where the you know srsl and d are
+ 
+
+ align:start position:0%
+right where the you know srsl and d are
+as defined over there
+
+ align:start position:0%
+as defined over there
+ 
+
+ align:start position:0%
+as defined over there
+and that's nice because s doesn't show
+
+ align:start position:0%
+and that's nice because s doesn't show
+ 
+
+ align:start position:0%
+and that's nice because s doesn't show
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+term that has the rotation in it and we
+
+ align:start position:0%
+term that has the rotation in it and we
+ 
+
+ align:start position:0%
+term that has the rotation in it and we
+just have these other terms
+
+ align:start position:0%
+just have these other terms
+ 
+
+ align:start position:0%
+just have these other terms
+and so we can just differentiate with
+
+ align:start position:0%
+and so we can just differentiate with
+ 
+
+ align:start position:0%
+and so we can just differentiate with
+respect to s set the result equal to
+
+ align:start position:0%
+respect to s set the result equal to
+ 
+
+ align:start position:0%
+respect to s set the result equal to
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because the derivative of that
+
+ align:start position:0%
+right because the derivative of that
+ 
+
+ align:start position:0%
+right because the derivative of that
+zero with respect to s is zero and and
+
+ align:start position:0%
+zero with respect to s is zero and and
+ 
+
+ align:start position:0%
+zero with respect to s is zero and and
+so that means that s squared is
+
+ align:start position:0%
+so that means that s squared is
+ 
+
+ align:start position:0%
+so that means that s squared is
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+r over s l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if i
+
+ align:start position:0%
+if i
+ 
+
+ align:start position:0%
+if i
+go in the other direction i'm going to
+
+ align:start position:0%
+go in the other direction i'm going to
+ 
+
+ align:start position:0%
+go in the other direction i'm going to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+s bar squared
+
+ align:start position:0%
+s bar squared
+ 
+
+ align:start position:0%
+s bar squared
+is sl over sr
+
+ align:start position:0%
+is sl over sr
+ 
+
+ align:start position:0%
+is sl over sr
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+the inverse
+
+ align:start position:0%
+the inverse
+ 
+
+ align:start position:0%
+the inverse
+so so that method is much to be
+
+ align:start position:0%
+so so that method is much to be
+ 
+
+ align:start position:0%
+so so that method is much to be
+preferred
+
+ align:start position:0%
+preferred
+ 
+
+ align:start position:0%
+preferred
+it also has the property that
+
+ align:start position:0%
+it also has the property that
+ 
+
+ align:start position:0%
+it also has the property that
+we don't need correspondences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's just like a translation
+
+ align:start position:0%
+so it's just like a translation
+ 
+
+ align:start position:0%
+so it's just like a translation
+where we are able to map centroid to
+
+ align:start position:0%
+where we are able to map centroid to
+ 
+
+ align:start position:0%
+where we are able to map centroid to
+centroid we didn't need correspondences
+
+ align:start position:0%
+centroid we didn't need correspondences
+ 
+
+ align:start position:0%
+centroid we didn't need correspondences
+for that uh here it's very convenient
+
+ align:start position:0%
+for that uh here it's very convenient
+ 
+
+ align:start position:0%
+for that uh here it's very convenient
+that we don't need the the only term
+
+ align:start position:0%
+that we don't need the the only term
+ 
+
+ align:start position:0%
+that we don't need the the only term
+that depends on correspondence is that
+
+ align:start position:0%
+that depends on correspondence is that
+ 
+
+ align:start position:0%
+that depends on correspondence is that
+one we only need these others which
+
+ align:start position:0%
+one we only need these others which
+ 
+
+ align:start position:0%
+one we only need these others which
+basically say you know you've got this
+
+ align:start position:0%
+basically say you know you've got this
+ 
+
+ align:start position:0%
+basically say you know you've got this
+cloud of points how big is it and then
+
+ align:start position:0%
+cloud of points how big is it and then
+ 
+
+ align:start position:0%
+cloud of points how big is it and then
+you have the other cloud of points how
+
+ align:start position:0%
+you have the other cloud of points how
+ 
+
+ align:start position:0%
+you have the other cloud of points how
+big is it well uh just
+
+ align:start position:0%
+big is it well uh just
+ 
+
+ align:start position:0%
+big is it well uh just
+the scale factor is the ratio of those
+
+ align:start position:0%
+the scale factor is the ratio of those
+ 
+
+ align:start position:0%
+the scale factor is the ratio of those
+two sizes it's very intuitive so
+
+ align:start position:0%
+two sizes it's very intuitive so
+ 
+
+ align:start position:0%
+two sizes it's very intuitive so
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that leaves us with the
+
+ align:start position:0%
+so that leaves us with the
+ 
+
+ align:start position:0%
+so that leaves us with the
+problem of
+
+ align:start position:0%
+problem of
+ 
+
+ align:start position:0%
+problem of
+so we can deal with translation and
+
+ align:start position:0%
+so we can deal with translation and
+ 
+
+ align:start position:0%
+so we can deal with translation and
+scaling
+
+ align:start position:0%
+scaling
+ 
+
+ align:start position:0%
+scaling
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+correspondence-free way
+
+ align:start position:0%
+correspondence-free way
+ 
+
+ align:start position:0%
+correspondence-free way
+and also free of rotation we don't need
+
+ align:start position:0%
+and also free of rotation we don't need
+ 
+
+ align:start position:0%
+and also free of rotation we don't need
+to take into account rotation
+
+ align:start position:0%
+to take into account rotation
+ 
+
+ align:start position:0%
+to take into account rotation
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+we can separate the problems
+
+ align:start position:0%
+we can separate the problems
+ 
+
+ align:start position:0%
+we can separate the problems
+so that leaves us with
+
+ align:start position:0%
+so that leaves us with
+ 
+
+ align:start position:0%
+so that leaves us with
+you know the rotation part and we spent
+
+ align:start position:0%
+you know the rotation part and we spent
+ 
+
+ align:start position:0%
+you know the rotation part and we spent
+some time uh on that so i won't
+
+ align:start position:0%
+some time uh on that so i won't
+ 
+
+ align:start position:0%
+some time uh on that so i won't
+review that in great detail
+
+ align:start position:0%
+review that in great detail
+ 
+
+ align:start position:0%
+review that in great detail
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note that in the end
+
+ align:start position:0%
+note that in the end
+ 
+
+ align:start position:0%
+note that in the end
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+this to maximize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because this this was a
+
+ align:start position:0%
+right because this this was a
+ 
+
+ align:start position:0%
+right because this this was a
+minimization
+
+ align:start position:0%
+minimization
+ 
+
+ align:start position:0%
+minimization
+but we have the negative sign so this
+
+ align:start position:0%
+but we have the negative sign so this
+ 
+
+ align:start position:0%
+but we have the negative sign so this
+has to be maximized and n of course is a
+
+ align:start position:0%
+has to be maximized and n of course is a
+ 
+
+ align:start position:0%
+has to be maximized and n of course is a
+four by four matrix which we can show is
+
+ align:start position:0%
+four by four matrix which we can show is
+ 
+
+ align:start position:0%
+four by four matrix which we can show is
+symmetric it's not uh obvious that it is
+
+ align:start position:0%
+symmetric it's not uh obvious that it is
+ 
+
+ align:start position:0%
+symmetric it's not uh obvious that it is
+and so now we have a
+
+ align:start position:0%
+and so now we have a
+ 
+
+ align:start position:0%
+and so now we have a
+calculus problem we just differentiate
+
+ align:start position:0%
+calculus problem we just differentiate
+ 
+
+ align:start position:0%
+calculus problem we just differentiate
+with respect to q
+
+ align:start position:0%
+with respect to q
+ 
+
+ align:start position:0%
+with respect to q
+and set the result equal to zero
+
+ align:start position:0%
+and set the result equal to zero
+ 
+
+ align:start position:0%
+and set the result equal to zero
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+not quite
+
+ align:start position:0%
+not quite
+ 
+
+ align:start position:0%
+not quite
+you know we have that constraint
+
+ align:start position:0%
+you know we have that constraint
+ 
+
+ align:start position:0%
+you know we have that constraint
+and it's just as well because otherwise
+
+ align:start position:0%
+and it's just as well because otherwise
+ 
+
+ align:start position:0%
+and it's just as well because otherwise
+the answer is zero
+
+ align:start position:0%
+the answer is zero
+ 
+
+ align:start position:0%
+the answer is zero
+right because that um differentiate that
+
+ align:start position:0%
+right because that um differentiate that
+ 
+
+ align:start position:0%
+right because that um differentiate that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and you get uh two and q
+
+ align:start position:0%
+and you get uh two and q
+ 
+
+ align:start position:0%
+and you get uh two and q
+uh how do you do that well just
+
+ align:start position:0%
+uh how do you do that well just
+ 
+
+ align:start position:0%
+uh how do you do that well just
+i'm sure you remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these formulas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh all in the appendix
+
+ align:start position:0%
+uh all in the appendix
+ 
+
+ align:start position:0%
+uh all in the appendix
+okay so if we set that equal to zero
+
+ align:start position:0%
+okay so if we set that equal to zero
+ 
+
+ align:start position:0%
+okay so if we set that equal to zero
+well there's a very convenient answer uh
+
+ align:start position:0%
+well there's a very convenient answer uh
+ 
+
+ align:start position:0%
+well there's a very convenient answer uh
+which is that uh q is zero or looked at
+
+ align:start position:0%
+which is that uh q is zero or looked at
+ 
+
+ align:start position:0%
+which is that uh q is zero or looked at
+another way
+
+ align:start position:0%
+another way
+ 
+
+ align:start position:0%
+another way
+if we try
+
+ align:start position:0%
+if we try
+ 
+
+ align:start position:0%
+if we try
+that's an extremum
+
+ align:start position:0%
+that's an extremum
+ 
+
+ align:start position:0%
+that's an extremum
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well we're actually trying to maximize
+
+ align:start position:0%
+well we're actually trying to maximize
+ 
+
+ align:start position:0%
+well we're actually trying to maximize
+so we'd go the other way we would just
+
+ align:start position:0%
+so we'd go the other way we would just
+ 
+
+ align:start position:0%
+so we'd go the other way we would just
+make q grow we can make q as large as we
+
+ align:start position:0%
+make q grow we can make q as large as we
+ 
+
+ align:start position:0%
+make q grow we can make q as large as we
+like and so there's no maximum
+
+ align:start position:0%
+like and so there's no maximum
+ 
+
+ align:start position:0%
+like and so there's no maximum
+well infinity so so that's obviously not
+
+ align:start position:0%
+well infinity so so that's obviously not
+ 
+
+ align:start position:0%
+well infinity so so that's obviously not
+satisfactory we need to take into
+
+ align:start position:0%
+satisfactory we need to take into
+ 
+
+ align:start position:0%
+satisfactory we need to take into
+account the uh
+
+ align:start position:0%
+account the uh
+ 
+
+ align:start position:0%
+account the uh
+constraint and as we saw in the slides
+
+ align:start position:0%
+constraint and as we saw in the slides
+ 
+
+ align:start position:0%
+constraint and as we saw in the slides
+last time one way to do that is using
+
+ align:start position:0%
+last time one way to do that is using
+ 
+
+ align:start position:0%
+last time one way to do that is using
+lagrange multipliers
+
+ align:start position:0%
+lagrange multipliers
+ 
+
+ align:start position:0%
+lagrange multipliers
+very elegant method and it's
+
+ align:start position:0%
+very elegant method and it's
+ 
+
+ align:start position:0%
+very elegant method and it's
+described in the appendix but this is a
+
+ align:start position:0%
+described in the appendix but this is a
+ 
+
+ align:start position:0%
+described in the appendix but this is a
+special case where we can get away with
+
+ align:start position:0%
+special case where we can get away with
+ 
+
+ align:start position:0%
+special case where we can get away with
+something simpler
+
+ align:start position:0%
+something simpler
+ 
+
+ align:start position:0%
+something simpler
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+rally quotient
+
+ align:start position:0%
+rally quotient
+ 
+
+ align:start position:0%
+rally quotient
+so rally did all sorts of interesting
+
+ align:start position:0%
+so rally did all sorts of interesting
+ 
+
+ align:start position:0%
+so rally did all sorts of interesting
+things including um work in optics
+
+ align:start position:0%
+things including um work in optics
+ 
+
+ align:start position:0%
+things including um work in optics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he ran into this problem of trying to
+
+ align:start position:0%
+he ran into this problem of trying to
+ 
+
+ align:start position:0%
+he ran into this problem of trying to
+find uh
+
+ align:start position:0%
+find uh
+ 
+
+ align:start position:0%
+find uh
+an extremum and so he came up with the
+
+ align:start position:0%
+an extremum and so he came up with the
+ 
+
+ align:start position:0%
+an extremum and so he came up with the
+idea well
+
+ align:start position:0%
+idea well
+ 
+
+ align:start position:0%
+idea well
+how do i prevent this from running away
+
+ align:start position:0%
+how do i prevent this from running away
+ 
+
+ align:start position:0%
+how do i prevent this from running away
+by being made very large
+
+ align:start position:0%
+by being made very large
+ 
+
+ align:start position:0%
+by being made very large
+sorry this is transpose
+
+ align:start position:0%
+sorry this is transpose
+ 
+
+ align:start position:0%
+sorry this is transpose
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i just divide by the size of q
+
+ align:start position:0%
+i just divide by the size of q
+ 
+
+ align:start position:0%
+i just divide by the size of q
+so there's no advantage to making q very
+
+ align:start position:0%
+so there's no advantage to making q very
+ 
+
+ align:start position:0%
+so there's no advantage to making q very
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+you know if you think about it as
+
+ align:start position:0%
+you know if you think about it as
+ 
+
+ align:start position:0%
+you know if you think about it as
+directions in a space
+
+ align:start position:0%
+directions in a space
+ 
+
+ align:start position:0%
+directions in a space
+this quantity is constant along any
+
+ align:start position:0%
+this quantity is constant along any
+ 
+
+ align:start position:0%
+this quantity is constant along any
+array
+
+ align:start position:0%
+array
+ 
+
+ align:start position:0%
+array
+right because wherever i am
+
+ align:start position:0%
+right because wherever i am
+ 
+
+ align:start position:0%
+right because wherever i am
+i'm going to divide out by the length of
+
+ align:start position:0%
+i'm going to divide out by the length of
+ 
+
+ align:start position:0%
+i'm going to divide out by the length of
+q itself so that creates a different
+
+ align:start position:0%
+q itself so that creates a different
+ 
+
+ align:start position:0%
+q itself so that creates a different
+function the one that doesn't go off to
+
+ align:start position:0%
+function the one that doesn't go off to
+ 
+
+ align:start position:0%
+function the one that doesn't go off to
+infinity but that is constant along any
+
+ align:start position:0%
+infinity but that is constant along any
+ 
+
+ align:start position:0%
+infinity but that is constant along any
+array and and that's exactly what we
+
+ align:start position:0%
+array and and that's exactly what we
+ 
+
+ align:start position:0%
+array and and that's exactly what we
+want we want to find the ray the
+
+ align:start position:0%
+want we want to find the ray the
+ 
+
+ align:start position:0%
+want we want to find the ray the
+direction of the ray that makes that as
+
+ align:start position:0%
+direction of the ray that makes that as
+ 
+
+ align:start position:0%
+direction of the ray that makes that as
+extreme as pos yeah
+
+ align:start position:0%
+extreme as pos yeah
+ 
+
+ align:start position:0%
+extreme as pos yeah
+what is the matrix
+
+ align:start position:0%
+what is the matrix
+ 
+
+ align:start position:0%
+what is the matrix
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+uh so that's the thing that we got out
+
+ align:start position:0%
+uh so that's the thing that we got out
+ 
+
+ align:start position:0%
+uh so that's the thing that we got out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh where it disappeared uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we took the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representation of a quaternion product
+
+ align:start position:0%
+representation of a quaternion product
+ 
+
+ align:start position:0%
+representation of a quaternion product
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+a four by four as a four by four uh
+
+ align:start position:0%
+a four by four as a four by four uh
+ 
+
+ align:start position:0%
+a four by four as a four by four uh
+rotational orthogonal matrix
+
+ align:start position:0%
+rotational orthogonal matrix
+ 
+
+ align:start position:0%
+rotational orthogonal matrix
+so that that's sort of the key
+
+ align:start position:0%
+so that that's sort of the key
+ 
+
+ align:start position:0%
+so that that's sort of the key
+uh no um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where is their space well let's just
+
+ align:start position:0%
+where is their space well let's just
+ 
+
+ align:start position:0%
+where is their space well let's just
+take this
+
+ align:start position:0%
+take this
+ 
+
+ align:start position:0%
+take this
+just quick uh
+
+ align:start position:0%
+just quick uh
+ 
+
+ align:start position:0%
+just quick uh
+review of that
+
+ align:start position:0%
+review of that
+ 
+
+ align:start position:0%
+review of that
+that part
+
+ align:start position:0%
+that part
+ 
+
+ align:start position:0%
+that part
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+we had
+
+ align:start position:0%
+we had
+ 
+
+ align:start position:0%
+we had
+i'm not going to copy it all out just
+
+ align:start position:0%
+i'm not going to copy it all out just
+ 
+
+ align:start position:0%
+i'm not going to copy it all out just
+the beginning so we had this sigma of
+
+ align:start position:0%
+the beginning so we had this sigma of
+ 
+
+ align:start position:0%
+the beginning so we had this sigma of
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this was the thing we were trying
+
+ align:start position:0%
+right this was the thing we were trying
+ 
+
+ align:start position:0%
+right this was the thing we were trying
+to maximize
+
+ align:start position:0%
+to maximize
+ 
+
+ align:start position:0%
+to maximize
+and then we wrote
+
+ align:start position:0%
+and then we wrote
+ 
+
+ align:start position:0%
+and then we wrote
+first we took this over to the other
+
+ align:start position:0%
+first we took this over to the other
+ 
+
+ align:start position:0%
+first we took this over to the other
+side to make it more symmetrical so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we use that notation where we
+
+ align:start position:0%
+and then we use that notation where we
+ 
+
+ align:start position:0%
+and then we use that notation where we
+represented this as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now before we expanded it the other way
+
+ align:start position:0%
+now before we expanded it the other way
+ 
+
+ align:start position:0%
+now before we expanded it the other way
+out we we converted q into a four by
+
+ align:start position:0%
+out we we converted q into a four by
+ 
+
+ align:start position:0%
+out we we converted q into a four by
+four matrix and multiplied by this uh
+
+ align:start position:0%
+four matrix and multiplied by this uh
+ 
+
+ align:start position:0%
+four matrix and multiplied by this uh
+quaternion
+
+ align:start position:0%
+quaternion
+ 
+
+ align:start position:0%
+quaternion
+and now we do it the other way around
+
+ align:start position:0%
+and now we do it the other way around
+ 
+
+ align:start position:0%
+and now we do it the other way around
+and then because this is a dot product
+
+ align:start position:0%
+and then because this is a dot product
+ 
+
+ align:start position:0%
+and then because this is a dot product
+it's that transpose and then we get q
+
+ align:start position:0%
+it's that transpose and then we get q
+ 
+
+ align:start position:0%
+it's that transpose and then we get q
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+transpose l i
+
+ align:start position:0%
+transpose l i
+ 
+
+ align:start position:0%
+transpose l i
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and of course the sum of that
+
+ align:start position:0%
+and and of course the sum of that
+ 
+
+ align:start position:0%
+and and of course the sum of that
+and q doesn't depend on i so we can get
+
+ align:start position:0%
+and q doesn't depend on i so we can get
+ 
+
+ align:start position:0%
+and q doesn't depend on i so we can get
+rid of that
+
+ align:start position:0%
+rid of that
+ 
+
+ align:start position:0%
+rid of that
+so it's it's that matrix
+
+ align:start position:0%
+so it's it's that matrix
+ 
+
+ align:start position:0%
+so it's it's that matrix
+so it's derived from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's derived from the data from the
+
+ align:start position:0%
+it's derived from the data from the
+ 
+
+ align:start position:0%
+it's derived from the data from the
+chorus correspondences right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we find that well now it's pretty
+
+ align:start position:0%
+how do we find that well now it's pretty
+ 
+
+ align:start position:0%
+how do we find that well now it's pretty
+straightforward calculus problem
+
+ align:start position:0%
+straightforward calculus problem
+ 
+
+ align:start position:0%
+straightforward calculus problem
+we just differentiate with respect to q
+
+ align:start position:0%
+we just differentiate with respect to q
+ 
+
+ align:start position:0%
+we just differentiate with respect to q
+and set the result equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know it's a ratio so we use the
+
+ align:start position:0%
+and you know it's a ratio so we use the
+ 
+
+ align:start position:0%
+and you know it's a ratio so we use the
+rule for differentiation of a ratio
+
+ align:start position:0%
+rule for differentiation of a ratio
+ 
+
+ align:start position:0%
+rule for differentiation of a ratio
+and so first differentiate the numerator
+
+ align:start position:0%
+and so first differentiate the numerator
+ 
+
+ align:start position:0%
+and so first differentiate the numerator
+we get 2 and q
+
+ align:start position:0%
+we get 2 and q
+ 
+
+ align:start position:0%
+we get 2 and q
+divided by this
+
+ align:start position:0%
+divided by this
+ 
+
+ align:start position:0%
+divided by this
+and then we need to
+
+ align:start position:0%
+and then we need to
+ 
+
+ align:start position:0%
+and then we need to
+add
+
+ align:start position:0%
+add
+ 
+
+ align:start position:0%
+add
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know the term involving the
+
+ align:start position:0%
+you know the term involving the
+ 
+
+ align:start position:0%
+you know the term involving the
+denominator the denominator so we get
+
+ align:start position:0%
+denominator the denominator so we get
+ 
+
+ align:start position:0%
+denominator the denominator so we get
+minus 1 over
+
+ align:start position:0%
+minus 1 over
+ 
+
+ align:start position:0%
+minus 1 over
+q dot t
+
+ align:start position:0%
+q dot t
+ 
+
+ align:start position:0%
+q dot t
+q 0 squared
+
+ align:start position:0%
+q 0 squared
+ 
+
+ align:start position:0%
+q 0 squared
+2 q
+
+ align:start position:0%
+2 q
+ 
+
+ align:start position:0%
+2 q
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+q 0 and
+
+ align:start position:0%
+q 0 and
+ 
+
+ align:start position:0%
+q 0 and
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+so this is just the formula for taking
+
+ align:start position:0%
+so this is just the formula for taking
+ 
+
+ align:start position:0%
+so this is just the formula for taking
+the derivative of a ratio
+
+ align:start position:0%
+the derivative of a ratio
+ 
+
+ align:start position:0%
+the derivative of a ratio
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+2q here is the derivative of q transpose
+
+ align:start position:0%
+2q here is the derivative of q transpose
+ 
+
+ align:start position:0%
+2q here is the derivative of q transpose
+q with respect to q
+
+ align:start position:0%
+q with respect to q
+ 
+
+ align:start position:0%
+q with respect to q
+and then this is supposed to be zero so
+
+ align:start position:0%
+and then this is supposed to be zero so
+ 
+
+ align:start position:0%
+and then this is supposed to be zero so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that means that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nq is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this of course is a scalar
+
+ align:start position:0%
+and this of course is a scalar
+ 
+
+ align:start position:0%
+and this of course is a scalar
+from constant
+
+ align:start position:0%
+from constant
+ 
+
+ align:start position:0%
+from constant
+and so so what does this tell us about q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we multiply some matrix by q and we
+
+ align:start position:0%
+that we multiply some matrix by q and we
+ 
+
+ align:start position:0%
+that we multiply some matrix by q and we
+get out
+
+ align:start position:0%
+get out
+ 
+
+ align:start position:0%
+get out
+some scaled version of q so
+
+ align:start position:0%
+some scaled version of q so
+ 
+
+ align:start position:0%
+some scaled version of q so
+eigenvector right
+
+ align:start position:0%
+eigenvector right
+ 
+
+ align:start position:0%
+eigenvector right
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so q is an eigenvector
+
+ align:start position:0%
+so q is an eigenvector
+ 
+
+ align:start position:0%
+so q is an eigenvector
+and now we're trying to maximize this so
+
+ align:start position:0%
+and now we're trying to maximize this so
+ 
+
+ align:start position:0%
+and now we're trying to maximize this so
+we need to know which of the
+
+ align:start position:0%
+we need to know which of the
+ 
+
+ align:start position:0%
+we need to know which of the
+eigenvectors to pick
+
+ align:start position:0%
+eigenvectors to pick
+ 
+
+ align:start position:0%
+eigenvectors to pick
+and it's pretty easy to see that if n
+
+ align:start position:0%
+and it's pretty easy to see that if n
+ 
+
+ align:start position:0%
+and it's pretty easy to see that if n
+is lambda q
+
+ align:start position:0%
+is lambda q
+ 
+
+ align:start position:0%
+is lambda q
+then this ratio over here is going to be
+
+ align:start position:0%
+then this ratio over here is going to be
+ 
+
+ align:start position:0%
+then this ratio over here is going to be
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+lambda q transpose q
+
+ align:start position:0%
+lambda q transpose q
+ 
+
+ align:start position:0%
+lambda q transpose q
+over q transpose q is lambda
+
+ align:start position:0%
+over q transpose q is lambda
+ 
+
+ align:start position:0%
+over q transpose q is lambda
+and so to maximize it we take pick the
+
+ align:start position:0%
+and so to maximize it we take pick the
+ 
+
+ align:start position:0%
+and so to maximize it we take pick the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+eigenvalue pick the largest eigenvalue
+
+ align:start position:0%
+eigenvalue pick the largest eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue pick the largest eigenvalue
+right we want to maximize this ratio
+
+ align:start position:0%
+right we want to maximize this ratio
+ 
+
+ align:start position:0%
+right we want to maximize this ratio
+and the way to do it is to pick the pick
+
+ align:start position:0%
+and the way to do it is to pick the pick
+ 
+
+ align:start position:0%
+and the way to do it is to pick the pick
+q to be the
+
+ align:start position:0%
+q to be the
+ 
+
+ align:start position:0%
+q to be the
+eigenvector corresponding to the largest
+
+ align:start position:0%
+eigenvector corresponding to the largest
+ 
+
+ align:start position:0%
+eigenvector corresponding to the largest
+eigenvalue and then this whole thing is
+
+ align:start position:0%
+eigenvalue and then this whole thing is
+ 
+
+ align:start position:0%
+eigenvalue and then this whole thing is
+equal to that eigenvalue
+
+ align:start position:0%
+equal to that eigenvalue
+ 
+
+ align:start position:0%
+equal to that eigenvalue
+so obviously you wouldn't want to pick a
+
+ align:start position:0%
+so obviously you wouldn't want to pick a
+ 
+
+ align:start position:0%
+so obviously you wouldn't want to pick a
+smaller eigenvalue than the maximum one
+
+ align:start position:0%
+smaller eigenvalue than the maximum one
+ 
+
+ align:start position:0%
+smaller eigenvalue than the maximum one
+okay and so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the only slight sort of
+
+ align:start position:0%
+so the only slight sort of
+ 
+
+ align:start position:0%
+so the only slight sort of
+tripping point
+
+ align:start position:0%
+tripping point
+ 
+
+ align:start position:0%
+tripping point
+is the fact that there's this constraint
+
+ align:start position:0%
+is the fact that there's this constraint
+ 
+
+ align:start position:0%
+is the fact that there's this constraint
+but you know the constraint is so much
+
+ align:start position:0%
+but you know the constraint is so much
+ 
+
+ align:start position:0%
+but you know the constraint is so much
+easier to handle than the constraint we
+
+ align:start position:0%
+easier to handle than the constraint we
+ 
+
+ align:start position:0%
+easier to handle than the constraint we
+had for constraints we had for
+
+ align:start position:0%
+had for constraints we had for
+ 
+
+ align:start position:0%
+had for constraints we had for
+orthonormal matrices so we can actually
+
+ align:start position:0%
+orthonormal matrices so we can actually
+ 
+
+ align:start position:0%
+orthonormal matrices so we can actually
+do this in a very straightforward way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rally quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a couple of things that we usually ask
+
+ align:start position:0%
+a couple of things that we usually ask
+ 
+
+ align:start position:0%
+a couple of things that we usually ask
+after we've
+
+ align:start position:0%
+after we've
+ 
+
+ align:start position:0%
+after we've
+quote found the solution one is you know
+
+ align:start position:0%
+quote found the solution one is you know
+ 
+
+ align:start position:0%
+quote found the solution one is you know
+when does it fail
+
+ align:start position:0%
+when does it fail
+ 
+
+ align:start position:0%
+when does it fail
+and the other one is um
+
+ align:start position:0%
+and the other one is um
+ 
+
+ align:start position:0%
+and the other one is um
+uh you know how many how many points do
+
+ align:start position:0%
+uh you know how many how many points do
+ 
+
+ align:start position:0%
+uh you know how many how many points do
+we need how many correspondences
+
+ align:start position:0%
+we need how many correspondences
+ 
+
+ align:start position:0%
+we need how many correspondences
+and so let's start with that so um
+
+ align:start position:0%
+and so let's start with that so um
+ 
+
+ align:start position:0%
+and so let's start with that so um
+in all of these photogrammetric problems
+
+ align:start position:0%
+in all of these photogrammetric problems
+ 
+
+ align:start position:0%
+in all of these photogrammetric problems
+that's an important point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so well we can approach this from
+
+ align:start position:0%
+and so well we can approach this from
+ 
+
+ align:start position:0%
+and so well we can approach this from
+the point of view of the properties of
+
+ align:start position:0%
+the point of view of the properties of
+ 
+
+ align:start position:0%
+the point of view of the properties of
+this matrix n
+
+ align:start position:0%
+this matrix n
+ 
+
+ align:start position:0%
+this matrix n
+but it's uh
+
+ align:start position:0%
+but it's uh
+ 
+
+ align:start position:0%
+but it's uh
+you know a bit of a bear of a problem to
+
+ align:start position:0%
+you know a bit of a bear of a problem to
+ 
+
+ align:start position:0%
+you know a bit of a bear of a problem to
+uh worry about is n singular is you know
+
+ align:start position:0%
+uh worry about is n singular is you know
+ 
+
+ align:start position:0%
+uh worry about is n singular is you know
+how many eigenvalues are non zero and so
+
+ align:start position:0%
+how many eigenvalues are non zero and so
+ 
+
+ align:start position:0%
+how many eigenvalues are non zero and so
+on let's just do it intuitively
+
+ align:start position:0%
+on let's just do it intuitively
+ 
+
+ align:start position:0%
+on let's just do it intuitively
+so first of all we can say well how many
+
+ align:start position:0%
+so first of all we can say well how many
+ 
+
+ align:start position:0%
+so first of all we can say well how many
+things are we looking for we're looking
+
+ align:start position:0%
+things are we looking for we're looking
+ 
+
+ align:start position:0%
+things are we looking for we're looking
+for six if we're looking for
+
+ align:start position:0%
+for six if we're looking for
+ 
+
+ align:start position:0%
+for six if we're looking for
+translational rotation we're looking for
+
+ align:start position:0%
+translational rotation we're looking for
+ 
+
+ align:start position:0%
+translational rotation we're looking for
+six if we add scaling we might be
+
+ align:start position:0%
+six if we add scaling we might be
+ 
+
+ align:start position:0%
+six if we add scaling we might be
+looking for seven
+
+ align:start position:0%
+looking for seven
+ 
+
+ align:start position:0%
+looking for seven
+so each measurement correspondence
+
+ align:start position:0%
+so each measurement correspondence
+ 
+
+ align:start position:0%
+so each measurement correspondence
+there's a point in 3d
+
+ align:start position:0%
+there's a point in 3d
+ 
+
+ align:start position:0%
+there's a point in 3d
+and a point in 3d that we say are the
+
+ align:start position:0%
+and a point in 3d that we say are the
+ 
+
+ align:start position:0%
+and a point in 3d that we say are the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so that's worth three correspondent
+
+ align:start position:0%
+so that's worth three correspondent
+ 
+
+ align:start position:0%
+so that's worth three correspondent
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+constraints right so we're looking for
+
+ align:start position:0%
+constraints right so we're looking for
+ 
+
+ align:start position:0%
+constraints right so we're looking for
+six things so hey we only we only need
+
+ align:start position:0%
+six things so hey we only we only need
+ 
+
+ align:start position:0%
+six things so hey we only we only need
+two correspondences right
+
+ align:start position:0%
+two correspondences right
+ 
+
+ align:start position:0%
+two correspondences right
+that's assuming there's no redundancy in
+
+ align:start position:0%
+that's assuming there's no redundancy in
+ 
+
+ align:start position:0%
+that's assuming there's no redundancy in
+that information well let's start off
+
+ align:start position:0%
+that information well let's start off
+ 
+
+ align:start position:0%
+that information well let's start off
+with one correspondence so here's
+
+ align:start position:0%
+with one correspondence so here's
+ 
+
+ align:start position:0%
+with one correspondence so here's
+here's an object
+
+ align:start position:0%
+here's an object
+ 
+
+ align:start position:0%
+here's an object
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then we have
+
+ align:start position:0%
+then we have
+ 
+
+ align:start position:0%
+then we have
+a second object and we want to know how
+
+ align:start position:0%
+a second object and we want to know how
+ 
+
+ align:start position:0%
+a second object and we want to know how
+one is rotated relative to the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course we know the duality
+
+ align:start position:0%
+and of course we know the duality
+ 
+
+ align:start position:0%
+and of course we know the duality
+between you know two objects one
+
+ align:start position:0%
+between you know two objects one
+ 
+
+ align:start position:0%
+between you know two objects one
+coordinate system or one object two
+
+ align:start position:0%
+coordinate system or one object two
+ 
+
+ align:start position:0%
+coordinate system or one object two
+coordinate systems so let's do the two
+
+ align:start position:0%
+coordinate systems so let's do the two
+ 
+
+ align:start position:0%
+coordinate systems so let's do the two
+two objects one coordinate system um and
+
+ align:start position:0%
+two objects one coordinate system um and
+ 
+
+ align:start position:0%
+two objects one coordinate system um and
+obviously this isn't gonna do it because
+
+ align:start position:0%
+obviously this isn't gonna do it because
+ 
+
+ align:start position:0%
+obviously this isn't gonna do it because
+you know i can move this thing i can
+
+ align:start position:0%
+you know i can move this thing i can
+ 
+
+ align:start position:0%
+you know i can move this thing i can
+rotate it around that point
+
+ align:start position:0%
+rotate it around that point
+ 
+
+ align:start position:0%
+rotate it around that point
+without changing that correspondence and
+
+ align:start position:0%
+without changing that correspondence and
+ 
+
+ align:start position:0%
+without changing that correspondence and
+also i can rotate it about this axis you
+
+ align:start position:0%
+also i can rotate it about this axis you
+ 
+
+ align:start position:0%
+also i can rotate it about this axis you
+know it's just
+
+ align:start position:0%
+know it's just
+ 
+
+ align:start position:0%
+know it's just
+very little constrainted well
+
+ align:start position:0%
+very little constrainted well
+ 
+
+ align:start position:0%
+very little constrainted well
+uh three
+
+ align:start position:0%
+uh three
+ 
+
+ align:start position:0%
+uh three
+three constraints out of a
+
+ align:start position:0%
+three constraints out of a
+ 
+
+ align:start position:0%
+three constraints out of a
+six-dimensional
+
+ align:start position:0%
+six-dimensional
+ 
+
+ align:start position:0%
+six-dimensional
+uh possibility so that's not good enough
+
+ align:start position:0%
+uh possibility so that's not good enough
+ 
+
+ align:start position:0%
+uh possibility so that's not good enough
+so let's uh pick two suppose that
+
+ align:start position:0%
+so let's uh pick two suppose that
+ 
+
+ align:start position:0%
+so let's uh pick two suppose that
+you know our sort of very rough back of
+
+ align:start position:0%
+you know our sort of very rough back of
+ 
+
+ align:start position:0%
+you know our sort of very rough back of
+the envelope calculation suggested that
+
+ align:start position:0%
+the envelope calculation suggested that
+ 
+
+ align:start position:0%
+the envelope calculation suggested that
+two should be enough because
+
+ align:start position:0%
+two should be enough because
+ 
+
+ align:start position:0%
+two should be enough because
+each of those correspondence gives us
+
+ align:start position:0%
+each of those correspondence gives us
+ 
+
+ align:start position:0%
+each of those correspondence gives us
+three constraints it's very powerful to
+
+ align:start position:0%
+three constraints it's very powerful to
+ 
+
+ align:start position:0%
+three constraints it's very powerful to
+say that you know this point is on top
+
+ align:start position:0%
+say that you know this point is on top
+ 
+
+ align:start position:0%
+say that you know this point is on top
+of that point and so
+
+ align:start position:0%
+of that point and so
+ 
+
+ align:start position:0%
+of that point and so
+we get three out of one correspondence
+
+ align:start position:0%
+we get three out of one correspondence
+ 
+
+ align:start position:0%
+we get three out of one correspondence
+three out of the second correspondence
+
+ align:start position:0%
+three out of the second correspondence
+ 
+
+ align:start position:0%
+three out of the second correspondence
+that makes six we're looking for six
+
+ align:start position:0%
+that makes six we're looking for six
+ 
+
+ align:start position:0%
+that makes six we're looking for six
+degrees of freedom uh maybe that'll do
+
+ align:start position:0%
+degrees of freedom uh maybe that'll do
+ 
+
+ align:start position:0%
+degrees of freedom uh maybe that'll do
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+uh what do you think i mean is that if i
+
+ align:start position:0%
+uh what do you think i mean is that if i
+ 
+
+ align:start position:0%
+uh what do you think i mean is that if i
+tie
+
+ align:start position:0%
+tie
+ 
+
+ align:start position:0%
+tie
+two objects together at two points is
+
+ align:start position:0%
+two objects together at two points is
+ 
+
+ align:start position:0%
+two objects together at two points is
+that enough to rigidly combine them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or is there some degree of freedom left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's hard to see because it's in 2d
+
+ align:start position:0%
+so it's hard to see because it's in 2d
+ 
+
+ align:start position:0%
+so it's hard to see because it's in 2d
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+draw that axis and take one of the
+
+ align:start position:0%
+draw that axis and take one of the
+ 
+
+ align:start position:0%
+draw that axis and take one of the
+objects and rotate it about that axis so
+
+ align:start position:0%
+objects and rotate it about that axis so
+ 
+
+ align:start position:0%
+objects and rotate it about that axis so
+so no that that doesn't work and the
+
+ align:start position:0%
+so no that that doesn't work and the
+ 
+
+ align:start position:0%
+so no that that doesn't work and the
+reason is that when we make the second
+
+ align:start position:0%
+reason is that when we make the second
+ 
+
+ align:start position:0%
+reason is that when we make the second
+measurement we don't get three new
+
+ align:start position:0%
+measurement we don't get three new
+ 
+
+ align:start position:0%
+measurement we don't get three new
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+uh the information's redundant why well
+
+ align:start position:0%
+uh the information's redundant why well
+ 
+
+ align:start position:0%
+uh the information's redundant why well
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+there's the distance between the two
+
+ align:start position:0%
+there's the distance between the two
+ 
+
+ align:start position:0%
+there's the distance between the two
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is fixed and so
+
+ align:start position:0%
+is fixed and so
+ 
+
+ align:start position:0%
+is fixed and so
+there's um true we have six numbers
+
+ align:start position:0%
+there's um true we have six numbers
+ 
+
+ align:start position:0%
+there's um true we have six numbers
+but there's also one that's not worth
+
+ align:start position:0%
+but there's also one that's not worth
+ 
+
+ align:start position:0%
+but there's also one that's not worth
+anything new
+
+ align:start position:0%
+anything new
+ 
+
+ align:start position:0%
+anything new
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we only have five constraints so yes
+
+ align:start position:0%
+we only have five constraints so yes
+ 
+
+ align:start position:0%
+we only have five constraints so yes
+we've we've got
+
+ align:start position:0%
+we've we've got
+ 
+
+ align:start position:0%
+we've we've got
+just one left
+
+ align:start position:0%
+just one left
+ 
+
+ align:start position:0%
+just one left
+and it perfectly makes sense
+
+ align:start position:0%
+and it perfectly makes sense
+ 
+
+ align:start position:0%
+and it perfectly makes sense
+we only have one degree of freedom left
+
+ align:start position:0%
+we only have one degree of freedom left
+ 
+
+ align:start position:0%
+we only have one degree of freedom left
+we can rotate about this axis so
+
+ align:start position:0%
+we can rotate about this axis so
+ 
+
+ align:start position:0%
+we can rotate about this axis so
+okay so it takes three
+
+ align:start position:0%
+okay so it takes three
+ 
+
+ align:start position:0%
+okay so it takes three
+it takes three correspondences to work
+
+ align:start position:0%
+it takes three correspondences to work
+ 
+
+ align:start position:0%
+it takes three correspondences to work
+and that and that um
+
+ align:start position:0%
+and that and that um
+ 
+
+ align:start position:0%
+and that and that um
+method that we deprecated at the
+
+ align:start position:0%
+method that we deprecated at the
+ 
+
+ align:start position:0%
+method that we deprecated at the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+use three correspondences so in that
+
+ align:start position:0%
+use three correspondences so in that
+ 
+
+ align:start position:0%
+use three correspondences so in that
+respect we're not any better
+
+ align:start position:0%
+respect we're not any better
+ 
+
+ align:start position:0%
+respect we're not any better
+we need exactly the same number of
+
+ align:start position:0%
+we need exactly the same number of
+ 
+
+ align:start position:0%
+we need exactly the same number of
+correspondences there's that method that
+
+ align:start position:0%
+correspondences there's that method that
+ 
+
+ align:start position:0%
+correspondences there's that method that
+we pooh-poohed and said wasn't very good
+
+ align:start position:0%
+we pooh-poohed and said wasn't very good
+ 
+
+ align:start position:0%
+we pooh-poohed and said wasn't very good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one question is um
+
+ align:start position:0%
+so one question is um
+ 
+
+ align:start position:0%
+so one question is um
+and we've come across this before in the
+
+ align:start position:0%
+and we've come across this before in the
+ 
+
+ align:start position:0%
+and we've come across this before in the
+2d world is there some way of
+
+ align:start position:0%
+2d world is there some way of
+ 
+
+ align:start position:0%
+2d world is there some way of
+generalizing the transformation so that
+
+ align:start position:0%
+generalizing the transformation so that
+ 
+
+ align:start position:0%
+generalizing the transformation so that
+it it matches so you know here we with
+
+ align:start position:0%
+it it matches so you know here we with
+ 
+
+ align:start position:0%
+it it matches so you know here we with
+three points we get nine constraints
+
+ align:start position:0%
+three points we get nine constraints
+ 
+
+ align:start position:0%
+three points we get nine constraints
+and of course they're highly redundant
+
+ align:start position:0%
+and of course they're highly redundant
+ 
+
+ align:start position:0%
+and of course they're highly redundant
+because the distances between the points
+
+ align:start position:0%
+because the distances between the points
+ 
+
+ align:start position:0%
+because the distances between the points
+are the same in
+
+ align:start position:0%
+are the same in
+ 
+
+ align:start position:0%
+are the same in
+uh and so um
+
+ align:start position:0%
+uh and so um
+ 
+
+ align:start position:0%
+uh and so um
+is this well with scaling we're up to
+
+ align:start position:0%
+is this well with scaling we're up to
+ 
+
+ align:start position:0%
+is this well with scaling we're up to
+seven so so that's already going the
+
+ align:start position:0%
+seven so so that's already going the
+ 
+
+ align:start position:0%
+seven so so that's already going the
+right direction if we add scaling we
+
+ align:start position:0%
+right direction if we add scaling we
+ 
+
+ align:start position:0%
+right direction if we add scaling we
+need to add
+
+ align:start position:0%
+need to add
+ 
+
+ align:start position:0%
+need to add
+two more
+
+ align:start position:0%
+two more
+ 
+
+ align:start position:0%
+two more
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+we would fully use
+
+ align:start position:0%
+we would fully use
+ 
+
+ align:start position:0%
+we would fully use
+and need
+
+ align:start position:0%
+and need
+ 
+
+ align:start position:0%
+and need
+three correspondences
+
+ align:start position:0%
+three correspondences
+ 
+
+ align:start position:0%
+three correspondences
+so one idea is well
+
+ align:start position:0%
+so one idea is well
+ 
+
+ align:start position:0%
+so one idea is well
+how about the general linear
+
+ align:start position:0%
+how about the general linear
+ 
+
+ align:start position:0%
+how about the general linear
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+and we did this in 2d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i guess in 2d we ended up with 6
+
+ align:start position:0%
+and i guess in 2d we ended up with 6
+ 
+
+ align:start position:0%
+and i guess in 2d we ended up with 6
+degrees of freedom
+
+ align:start position:0%
+degrees of freedom
+ 
+
+ align:start position:0%
+degrees of freedom
+what is it in 3d
+
+ align:start position:0%
+what is it in 3d
+ 
+
+ align:start position:0%
+what is it in 3d
+so well
+
+ align:start position:0%
+so well
+ 
+
+ align:start position:0%
+so well
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we could have you know no longer
+
+ align:start position:0%
+so we could have you know no longer
+ 
+
+ align:start position:0%
+so we could have you know no longer
+constrained to orthonormal matrices
+
+ align:start position:0%
+constrained to orthonormal matrices
+ 
+
+ align:start position:0%
+constrained to orthonormal matrices
+and and that actually is a great thing
+
+ align:start position:0%
+and and that actually is a great thing
+ 
+
+ align:start position:0%
+and and that actually is a great thing
+because the orthonormal matrices are the
+
+ align:start position:0%
+because the orthonormal matrices are the
+ 
+
+ align:start position:0%
+because the orthonormal matrices are the
+ones that produce these horrendous uh
+
+ align:start position:0%
+ones that produce these horrendous uh
+ 
+
+ align:start position:0%
+ones that produce these horrendous uh
+problems with the constraints
+
+ align:start position:0%
+problems with the constraints
+ 
+
+ align:start position:0%
+problems with the constraints
+that they are orthonormal
+
+ align:start position:0%
+that they are orthonormal
+ 
+
+ align:start position:0%
+that they are orthonormal
+and oh this this looks just right it's
+
+ align:start position:0%
+and oh this this looks just right it's
+ 
+
+ align:start position:0%
+and oh this this looks just right it's
+got nine numbers in it
+
+ align:start position:0%
+got nine numbers in it
+ 
+
+ align:start position:0%
+got nine numbers in it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+nine constraints uh
+
+ align:start position:0%
+nine constraints uh
+ 
+
+ align:start position:0%
+nine constraints uh
+from three correspondences
+
+ align:start position:0%
+from three correspondences
+ 
+
+ align:start position:0%
+from three correspondences
+matches to that so it looks like this is
+
+ align:start position:0%
+matches to that so it looks like this is
+ 
+
+ align:start position:0%
+matches to that so it looks like this is
+perhaps the generalization that that we
+
+ align:start position:0%
+perhaps the generalization that that we
+ 
+
+ align:start position:0%
+perhaps the generalization that that we
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+well unfortunately not quite
+
+ align:start position:0%
+well unfortunately not quite
+ 
+
+ align:start position:0%
+well unfortunately not quite
+because we have translation as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the general linear
+
+ align:start position:0%
+right so the general linear
+ 
+
+ align:start position:0%
+right so the general linear
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+has 12 elements in 3d we've had six in
+
+ align:start position:0%
+has 12 elements in 3d we've had six in
+ 
+
+ align:start position:0%
+has 12 elements in 3d we've had six in
+2d
+
+ align:start position:0%
+2d
+ 
+
+ align:start position:0%
+2d
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we wouldn't
+
+ align:start position:0%
+we wouldn't
+ 
+
+ align:start position:0%
+we wouldn't
+you know there isn't a nice
+
+ align:start position:0%
+you know there isn't a nice
+ 
+
+ align:start position:0%
+you know there isn't a nice
+symmetric argument
+
+ align:start position:0%
+symmetric argument
+ 
+
+ align:start position:0%
+symmetric argument
+that with three correspondences it would
+
+ align:start position:0%
+that with three correspondences it would
+ 
+
+ align:start position:0%
+that with three correspondences it would
+work we would need four correspondences
+
+ align:start position:0%
+work we would need four correspondences
+ 
+
+ align:start position:0%
+work we would need four correspondences
+and that does work and it's very elegant
+
+ align:start position:0%
+and that does work and it's very elegant
+ 
+
+ align:start position:0%
+and that does work and it's very elegant
+and very neat the least squares comes
+
+ align:start position:0%
+and very neat the least squares comes
+ 
+
+ align:start position:0%
+and very neat the least squares comes
+out beautifully because they're none of
+
+ align:start position:0%
+out beautifully because they're none of
+ 
+
+ align:start position:0%
+out beautifully because they're none of
+these annoying constraints like
+
+ align:start position:0%
+these annoying constraints like
+ 
+
+ align:start position:0%
+these annoying constraints like
+determinant of the matrix is one
+
+ align:start position:0%
+determinant of the matrix is one
+ 
+
+ align:start position:0%
+determinant of the matrix is one
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+that's not the transformation that we're
+
+ align:start position:0%
+that's not the transformation that we're
+ 
+
+ align:start position:0%
+that's not the transformation that we're
+dealing with in the real world
+
+ align:start position:0%
+dealing with in the real world
+ 
+
+ align:start position:0%
+dealing with in the real world
+where we have two sensor systems
+
+ align:start position:0%
+where we have two sensor systems
+ 
+
+ align:start position:0%
+where we have two sensor systems
+looking at the world and they're
+
+ align:start position:0%
+looking at the world and they're
+ 
+
+ align:start position:0%
+looking at the world and they're
+typically only dealing with rotation and
+
+ align:start position:0%
+typically only dealing with rotation and
+ 
+
+ align:start position:0%
+typically only dealing with rotation and
+translation maybe scaling but not
+
+ align:start position:0%
+translation maybe scaling but not
+ 
+
+ align:start position:0%
+translation maybe scaling but not
+that full you know this allows skewing
+
+ align:start position:0%
+that full you know this allows skewing
+ 
+
+ align:start position:0%
+that full you know this allows skewing
+of the axes and asymmetric scaling that
+
+ align:start position:0%
+of the axes and asymmetric scaling that
+ 
+
+ align:start position:0%
+of the axes and asymmetric scaling that
+the x-axis is scaled different from the
+
+ align:start position:0%
+the x-axis is scaled different from the
+ 
+
+ align:start position:0%
+the x-axis is scaled different from the
+y-axis
+
+ align:start position:0%
+y-axis
+ 
+
+ align:start position:0%
+y-axis
+and that there's a slant and and so on
+
+ align:start position:0%
+and that there's a slant and and so on
+ 
+
+ align:start position:0%
+and that there's a slant and and so on
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so back to our analysis of this method
+
+ align:start position:0%
+so back to our analysis of this method
+ 
+
+ align:start position:0%
+so back to our analysis of this method
+we've said something about how many
+
+ align:start position:0%
+we've said something about how many
+ 
+
+ align:start position:0%
+we've said something about how many
+correspondences we need we also should
+
+ align:start position:0%
+correspondences we need we also should
+ 
+
+ align:start position:0%
+correspondences we need we also should
+sort of so one one way to fail is to not
+
+ align:start position:0%
+sort of so one one way to fail is to not
+ 
+
+ align:start position:0%
+sort of so one one way to fail is to not
+have enough correspondences and it's
+
+ align:start position:0%
+have enough correspondences and it's
+ 
+
+ align:start position:0%
+have enough correspondences and it's
+if you have only two correspondences
+
+ align:start position:0%
+if you have only two correspondences
+ 
+
+ align:start position:0%
+if you have only two correspondences
+that matrix n will be singular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which isn't enough to make the method
+
+ align:start position:0%
+which isn't enough to make the method
+ 
+
+ align:start position:0%
+which isn't enough to make the method
+not work but uh it will it will have uh
+
+ align:start position:0%
+not work but uh it will it will have uh
+ 
+
+ align:start position:0%
+not work but uh it will it will have uh
+more than one eigenvalue that zero
+
+ align:start position:0%
+more than one eigenvalue that zero
+ 
+
+ align:start position:0%
+more than one eigenvalue that zero
+and and that's
+
+ align:start position:0%
+and and that's
+ 
+
+ align:start position:0%
+and and that's
+a way to formalize our hand waving
+
+ align:start position:0%
+a way to formalize our hand waving
+ 
+
+ align:start position:0%
+a way to formalize our hand waving
+argument but it's
+
+ align:start position:0%
+argument but it's
+ 
+
+ align:start position:0%
+argument but it's
+kind of messy so didn't want to do that
+
+ align:start position:0%
+kind of messy so didn't want to do that
+ 
+
+ align:start position:0%
+kind of messy so didn't want to do that
+but there is another case that we want
+
+ align:start position:0%
+but there is another case that we want
+ 
+
+ align:start position:0%
+but there is another case that we want
+to look at that's actually kind of
+
+ align:start position:0%
+to look at that's actually kind of
+ 
+
+ align:start position:0%
+to look at that's actually kind of
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how do we find the eigenvalues
+
+ align:start position:0%
+how do we find the eigenvalues
+ 
+
+ align:start position:0%
+how do we find the eigenvalues
+well um
+
+ align:start position:0%
+well um
+ 
+
+ align:start position:0%
+well um
+you know we use matlab
+
+ align:start position:0%
+you know we use matlab
+ 
+
+ align:start position:0%
+you know we use matlab
+or more seriously
+
+ align:start position:0%
+or more seriously
+ 
+
+ align:start position:0%
+or more seriously
+uh we need to solve this uh
+
+ align:start position:0%
+uh we need to solve this uh
+ 
+
+ align:start position:0%
+uh we need to solve this uh
+characteristic equation so which is
+
+ align:start position:0%
+characteristic equation so which is
+ 
+
+ align:start position:0%
+characteristic equation so which is
+obtained from that matrix n so that's uh
+
+ align:start position:0%
+obtained from that matrix n so that's uh
+ 
+
+ align:start position:0%
+obtained from that matrix n so that's uh
+that's the equation that says
+
+ align:start position:0%
+that's the equation that says
+ 
+
+ align:start position:0%
+that's the equation that says
+determinant of n
+
+ align:start position:0%
+determinant of n
+ 
+
+ align:start position:0%
+determinant of n
+minus lambda i is zero
+
+ align:start position:0%
+minus lambda i is zero
+ 
+
+ align:start position:0%
+minus lambda i is zero
+so that's the determinant of a four by
+
+ align:start position:0%
+so that's the determinant of a four by
+ 
+
+ align:start position:0%
+so that's the determinant of a four by
+four matrix that has minus lambdas down
+
+ align:start position:0%
+four matrix that has minus lambdas down
+ 
+
+ align:start position:0%
+four matrix that has minus lambdas down
+the diagonal
+
+ align:start position:0%
+the diagonal
+ 
+
+ align:start position:0%
+the diagonal
+subtracted out the diagonal
+
+ align:start position:0%
+subtracted out the diagonal
+ 
+
+ align:start position:0%
+subtracted out the diagonal
+and when we take the determinant we get
+
+ align:start position:0%
+and when we take the determinant we get
+ 
+
+ align:start position:0%
+and when we take the determinant we get
+up to fourth order combinations of
+
+ align:start position:0%
+up to fourth order combinations of
+ 
+
+ align:start position:0%
+up to fourth order combinations of
+lambda so it's going to look like this
+
+ align:start position:0%
+lambda so it's going to look like this
+ 
+
+ align:start position:0%
+lambda so it's going to look like this
+now our matrix n is a particular matrix
+
+ align:start position:0%
+now our matrix n is a particular matrix
+ 
+
+ align:start position:0%
+now our matrix n is a particular matrix
+that was obtained this way
+
+ align:start position:0%
+that was obtained this way
+ 
+
+ align:start position:0%
+that was obtained this way
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+actually we can say more about this
+
+ align:start position:0%
+actually we can say more about this
+ 
+
+ align:start position:0%
+actually we can say more about this
+and i already mentioned this last time
+
+ align:start position:0%
+and i already mentioned this last time
+ 
+
+ align:start position:0%
+and i already mentioned this last time
+it's not easy to show but
+
+ align:start position:0%
+it's not easy to show but
+ 
+
+ align:start position:0%
+it's not easy to show but
+c3 is the trace of the matrix
+
+ align:start position:0%
+c3 is the trace of the matrix
+ 
+
+ align:start position:0%
+c3 is the trace of the matrix
+that happens to be zero well it's easy
+
+ align:start position:0%
+that happens to be zero well it's easy
+ 
+
+ align:start position:0%
+that happens to be zero well it's easy
+to show it's a trace of the matrix it's
+
+ align:start position:0%
+to show it's a trace of the matrix it's
+ 
+
+ align:start position:0%
+to show it's a trace of the matrix it's
+not easy to show that it's zero so
+
+ align:start position:0%
+not easy to show that it's zero so
+ 
+
+ align:start position:0%
+not easy to show that it's zero so
+anyway it's zero which makes this
+
+ align:start position:0%
+anyway it's zero which makes this
+ 
+
+ align:start position:0%
+anyway it's zero which makes this
+equation easier to solve
+
+ align:start position:0%
+equation easier to solve
+ 
+
+ align:start position:0%
+equation easier to solve
+in fact usually the first step in
+
+ align:start position:0%
+in fact usually the first step in
+ 
+
+ align:start position:0%
+in fact usually the first step in
+solving a fourth order equation is to
+
+ align:start position:0%
+solving a fourth order equation is to
+ 
+
+ align:start position:0%
+solving a fourth order equation is to
+eliminate the third order term well it's
+
+ align:start position:0%
+eliminate the third order term well it's
+ 
+
+ align:start position:0%
+eliminate the third order term well it's
+already happened so we're kind of ahead
+
+ align:start position:0%
+already happened so we're kind of ahead
+ 
+
+ align:start position:0%
+already happened so we're kind of ahead
+of the game
+
+ align:start position:0%
+of the game
+ 
+
+ align:start position:0%
+of the game
+what about the others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the trace of another matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these others aren't 0 so that's
+
+ align:start position:0%
+so these others aren't 0 so that's
+ 
+
+ align:start position:0%
+so these others aren't 0 so that's
+so what is this matrix m well the matrix
+
+ align:start position:0%
+so what is this matrix m well the matrix
+ 
+
+ align:start position:0%
+so what is this matrix m well the matrix
+m is where we actually
+
+ align:start position:0%
+m is where we actually
+ 
+
+ align:start position:0%
+m is where we actually
+started with
+
+ align:start position:0%
+started with
+ 
+
+ align:start position:0%
+started with
+this is what you'd compute when you got
+
+ align:start position:0%
+this is what you'd compute when you got
+ 
+
+ align:start position:0%
+this is what you'd compute when you got
+the correspondences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's that that's a dyadic product so
+
+ align:start position:0%
+what's that that's a dyadic product so
+ 
+
+ align:start position:0%
+what's that that's a dyadic product so
+we take the vector in the left-hand
+
+ align:start position:0%
+we take the vector in the left-hand
+ 
+
+ align:start position:0%
+we take the vector in the left-hand
+coordinate system and multiplied by the
+
+ align:start position:0%
+coordinate system and multiplied by the
+ 
+
+ align:start position:0%
+coordinate system and multiplied by the
+vector in the right-hand coordinate
+
+ align:start position:0%
+vector in the right-hand coordinate
+ 
+
+ align:start position:0%
+vector in the right-hand coordinate
+system but rather than
+
+ align:start position:0%
+system but rather than
+ 
+
+ align:start position:0%
+system but rather than
+the transpose of the first times the
+
+ align:start position:0%
+the transpose of the first times the
+ 
+
+ align:start position:0%
+the transpose of the first times the
+second which gives us a dot product
+
+ align:start position:0%
+second which gives us a dot product
+ 
+
+ align:start position:0%
+second which gives us a dot product
+we do this and you've seen that so
+
+ align:start position:0%
+we do this and you've seen that so
+ 
+
+ align:start position:0%
+we do this and you've seen that so
+that's a three by three matrix we just
+
+ align:start position:0%
+that's a three by three matrix we just
+ 
+
+ align:start position:0%
+that's a three by three matrix we just
+step through the data
+
+ align:start position:0%
+step through the data
+ 
+
+ align:start position:0%
+step through the data
+correspondence by correspondence and we
+
+ align:start position:0%
+correspondence by correspondence and we
+ 
+
+ align:start position:0%
+correspondence by correspondence and we
+compute this diatic product and add it
+
+ align:start position:0%
+compute this diatic product and add it
+ 
+
+ align:start position:0%
+compute this diatic product and add it
+into a total and we get that matrix m
+
+ align:start position:0%
+into a total and we get that matrix m
+ 
+
+ align:start position:0%
+into a total and we get that matrix m
+which is of course 3 by 3.
+
+ align:start position:0%
+which is of course 3 by 3.
+ 
+
+ align:start position:0%
+which is of course 3 by 3.
+and it and it turns out that the four by
+
+ align:start position:0%
+and it and it turns out that the four by
+ 
+
+ align:start position:0%
+and it and it turns out that the four by
+four matrix n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+that are com
+
+ align:start position:0%
+that are com
+ 
+
+ align:start position:0%
+that are com
+can be computed
+
+ align:start position:0%
+can be computed
+ 
+
+ align:start position:0%
+can be computed
+from this matrix so that's actually the
+
+ align:start position:0%
+from this matrix so that's actually the
+ 
+
+ align:start position:0%
+from this matrix so that's actually the
+most efficient way of getting n you just
+
+ align:start position:0%
+most efficient way of getting n you just
+ 
+
+ align:start position:0%
+most efficient way of getting n you just
+step through all of your data and
+
+ align:start position:0%
+step through all of your data and
+ 
+
+ align:start position:0%
+step through all of your data and
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+m and then at the end
+
+ align:start position:0%
+m and then at the end
+ 
+
+ align:start position:0%
+m and then at the end
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+compute n from it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+next thing
+
+ align:start position:0%
+next thing
+ 
+
+ align:start position:0%
+next thing
+suppose that the determinant of m is
+
+ align:start position:0%
+suppose that the determinant of m is
+ 
+
+ align:start position:0%
+suppose that the determinant of m is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+suppose that m is singular
+
+ align:start position:0%
+suppose that m is singular
+ 
+
+ align:start position:0%
+suppose that m is singular
+well that's
+
+ align:start position:0%
+well that's
+ 
+
+ align:start position:0%
+well that's
+pretty useful
+
+ align:start position:0%
+pretty useful
+ 
+
+ align:start position:0%
+pretty useful
+because that means that c1 is zero
+
+ align:start position:0%
+because that means that c1 is zero
+ 
+
+ align:start position:0%
+because that means that c1 is zero
+and then we can all solve this equation
+
+ align:start position:0%
+and then we can all solve this equation
+ 
+
+ align:start position:0%
+and then we can all solve this equation
+without needing to go to any special
+
+ align:start position:0%
+without needing to go to any special
+ 
+
+ align:start position:0%
+without needing to go to any special
+textbook or something because then we've
+
+ align:start position:0%
+textbook or something because then we've
+ 
+
+ align:start position:0%
+textbook or something because then we've
+got lambda to the fourth plus
+
+ align:start position:0%
+got lambda to the fourth plus
+ 
+
+ align:start position:0%
+got lambda to the fourth plus
+c2 lambda squared plus c0 is zero
+
+ align:start position:0%
+c2 lambda squared plus c0 is zero
+ 
+
+ align:start position:0%
+c2 lambda squared plus c0 is zero
+right in that case it reduces to that
+
+ align:start position:0%
+right in that case it reduces to that
+ 
+
+ align:start position:0%
+right in that case it reduces to that
+problem and we use what equation to
+
+ align:start position:0%
+problem and we use what equation to
+ 
+
+ align:start position:0%
+problem and we use what equation to
+solve that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it seems to have lambda to the fourth
+
+ align:start position:0%
+so it seems to have lambda to the fourth
+ 
+
+ align:start position:0%
+so it seems to have lambda to the fourth
+in it which means we should use ferrari
+
+ align:start position:0%
+in it which means we should use ferrari
+ 
+
+ align:start position:0%
+in it which means we should use ferrari
+or cardano
+
+ align:start position:0%
+or cardano
+ 
+
+ align:start position:0%
+or cardano
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+of course it's quadratic in lambda
+
+ align:start position:0%
+of course it's quadratic in lambda
+ 
+
+ align:start position:0%
+of course it's quadratic in lambda
+squared right so
+
+ align:start position:0%
+squared right so
+ 
+
+ align:start position:0%
+squared right so
+so we just apply the quadratic so it's
+
+ align:start position:0%
+so we just apply the quadratic so it's
+ 
+
+ align:start position:0%
+so we just apply the quadratic so it's
+particularly easy case
+
+ align:start position:0%
+particularly easy case
+ 
+
+ align:start position:0%
+particularly easy case
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might wonder well who cares that's a
+
+ align:start position:0%
+you might wonder well who cares that's a
+ 
+
+ align:start position:0%
+you might wonder well who cares that's a
+special case well it turns out it's a
+
+ align:start position:0%
+special case well it turns out it's a
+ 
+
+ align:start position:0%
+special case well it turns out it's a
+it's a particular
+
+ align:start position:0%
+it's a particular
+ 
+
+ align:start position:0%
+it's a particular
+case that's interesting from a geometric
+
+ align:start position:0%
+case that's interesting from a geometric
+ 
+
+ align:start position:0%
+case that's interesting from a geometric
+point of view it's a
+
+ align:start position:0%
+point of view it's a
+ 
+
+ align:start position:0%
+point of view it's a
+it has to do with a distribution of the
+
+ align:start position:0%
+it has to do with a distribution of the
+ 
+
+ align:start position:0%
+it has to do with a distribution of the
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um this matrix n
+
+ align:start position:0%
+um this matrix n
+ 
+
+ align:start position:0%
+um this matrix n
+can have some zero eigen values which
+
+ align:start position:0%
+can have some zero eigen values which
+ 
+
+ align:start position:0%
+can have some zero eigen values which
+are potentially problematic
+
+ align:start position:0%
+are potentially problematic
+ 
+
+ align:start position:0%
+are potentially problematic
+and when does that occur well uh one is
+
+ align:start position:0%
+and when does that occur well uh one is
+ 
+
+ align:start position:0%
+and when does that occur well uh one is
+when points are coplanar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so far we've talked about
+
+ align:start position:0%
+right so so far we've talked about
+ 
+
+ align:start position:0%
+right so so far we've talked about
+you know clouds of points
+
+ align:start position:0%
+you know clouds of points
+ 
+
+ align:start position:0%
+you know clouds of points
+like the spikes on a sea urchin
+
+ align:start position:0%
+like the spikes on a sea urchin
+ 
+
+ align:start position:0%
+like the spikes on a sea urchin
+and we're matching two of these we're
+
+ align:start position:0%
+and we're matching two of these we're
+ 
+
+ align:start position:0%
+and we're matching two of these we're
+rotating one in alignment with the other
+
+ align:start position:0%
+rotating one in alignment with the other
+ 
+
+ align:start position:0%
+rotating one in alignment with the other
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this applies equally well if
+
+ align:start position:0%
+this applies equally well if
+ 
+
+ align:start position:0%
+this applies equally well if
+all of those points are
+
+ align:start position:0%
+all of those points are
+ 
+
+ align:start position:0%
+all of those points are
+in a plane and so what what happens then
+
+ align:start position:0%
+in a plane and so what what happens then
+ 
+
+ align:start position:0%
+in a plane and so what what happens then
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if there's a
+
+ align:start position:0%
+if there's a
+ 
+
+ align:start position:0%
+if there's a
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of our points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in that plane and we can draw a
+
+ align:start position:0%
+in that plane and we can draw a
+ 
+
+ align:start position:0%
+in that plane and we can draw a
+unit normal to the plane
+
+ align:start position:0%
+unit normal to the plane
+ 
+
+ align:start position:0%
+unit normal to the plane
+and then the dot product
+
+ align:start position:0%
+and then the dot product
+ 
+
+ align:start position:0%
+and then the dot product
+has to be zero so
+
+ align:start position:0%
+has to be zero so
+ 
+
+ align:start position:0%
+has to be zero so
+let's suppose that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's suppose all the right hand points
+
+ align:start position:0%
+let's suppose all the right hand points
+ 
+
+ align:start position:0%
+let's suppose all the right hand points
+are in a plane now with
+
+ align:start position:0%
+are in a plane now with
+ 
+
+ align:start position:0%
+are in a plane now with
+our measurement error that implies that
+
+ align:start position:0%
+our measurement error that implies that
+ 
+
+ align:start position:0%
+our measurement error that implies that
+the left-hand points also in a plane but
+
+ align:start position:0%
+the left-hand points also in a plane but
+ 
+
+ align:start position:0%
+the left-hand points also in a plane but
+we we may not
+
+ align:start position:0%
+we we may not
+ 
+
+ align:start position:0%
+we we may not
+need to make that restriction there
+
+ align:start position:0%
+need to make that restriction there
+ 
+
+ align:start position:0%
+need to make that restriction there
+might be measurement error and the
+
+ align:start position:0%
+might be measurement error and the
+ 
+
+ align:start position:0%
+might be measurement error and the
+others might not be exactly in the plan
+
+ align:start position:0%
+others might not be exactly in the plan
+ 
+
+ align:start position:0%
+others might not be exactly in the plan
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so what i've done here is
+
+ align:start position:0%
+so what i've done here is
+ 
+
+ align:start position:0%
+so what i've done here is
+i've drawn the centroid so i've already
+
+ align:start position:0%
+i've drawn the centroid so i've already
+ 
+
+ align:start position:0%
+i've drawn the centroid so i've already
+moved everything to the centroid and
+
+ align:start position:0%
+moved everything to the centroid and
+ 
+
+ align:start position:0%
+moved everything to the centroid and
+therefore i can write the equation of
+
+ align:start position:0%
+therefore i can write the equation of
+ 
+
+ align:start position:0%
+therefore i can write the equation of
+the plane in this simple form
+
+ align:start position:0%
+the plane in this simple form
+ 
+
+ align:start position:0%
+the plane in this simple form
+uh the dot product you know the
+
+ align:start position:0%
+uh the dot product you know the
+ 
+
+ align:start position:0%
+uh the dot product you know the
+component of any one of these vectors
+
+ align:start position:0%
+component of any one of these vectors
+ 
+
+ align:start position:0%
+component of any one of these vectors
+in this direction is zero that that's
+
+ align:start position:0%
+in this direction is zero that that's
+ 
+
+ align:start position:0%
+in this direction is zero that that's
+the definition of the plane
+
+ align:start position:0%
+the definition of the plane
+ 
+
+ align:start position:0%
+the definition of the plane
+okay well then
+
+ align:start position:0%
+okay well then
+ 
+
+ align:start position:0%
+okay well then
+that's the same as r i transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i can go to m and
+
+ align:start position:0%
+and then i can go to m and
+ 
+
+ align:start position:0%
+and then i can go to m and
+hat is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+if the points are coplanar then we do
+
+ align:start position:0%
+if the points are coplanar then we do
+ 
+
+ align:start position:0%
+if the points are coplanar then we do
+have the determinant of m is zero and
+
+ align:start position:0%
+have the determinant of m is zero and
+ 
+
+ align:start position:0%
+have the determinant of m is zero and
+then that problem is particularly uh
+
+ align:start position:0%
+then that problem is particularly uh
+ 
+
+ align:start position:0%
+then that problem is particularly uh
+easy to solve
+
+ align:start position:0%
+easy to solve
+ 
+
+ align:start position:0%
+easy to solve
+now i haven't shown it the other way
+
+ align:start position:0%
+now i haven't shown it the other way
+ 
+
+ align:start position:0%
+now i haven't shown it the other way
+around which is which i should which is
+
+ align:start position:0%
+around which is which i should which is
+ 
+
+ align:start position:0%
+around which is which i should which is
+that if determinant of m is zero the
+
+ align:start position:0%
+that if determinant of m is zero the
+ 
+
+ align:start position:0%
+that if determinant of m is zero the
+points are coplanar but i think you can
+
+ align:start position:0%
+points are coplanar but i think you can
+ 
+
+ align:start position:0%
+points are coplanar but i think you can
+see how to do that without too much
+
+ align:start position:0%
+see how to do that without too much
+ 
+
+ align:start position:0%
+see how to do that without too much
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+now in that case actually we can
+
+ align:start position:0%
+now in that case actually we can
+ 
+
+ align:start position:0%
+now in that case actually we can
+solve the problem more simply
+
+ align:start position:0%
+solve the problem more simply
+ 
+
+ align:start position:0%
+solve the problem more simply
+suppose that
+
+ align:start position:0%
+suppose that
+ 
+
+ align:start position:0%
+suppose that
+things are nice and both are
+
+ align:start position:0%
+things are nice and both are
+ 
+
+ align:start position:0%
+things are nice and both are
+coplanar both the left-hand corner
+
+ align:start position:0%
+coplanar both the left-hand corner
+ 
+
+ align:start position:0%
+coplanar both the left-hand corner
+left-hand cloud of points and the
+
+ align:start position:0%
+left-hand cloud of points and the
+ 
+
+ align:start position:0%
+left-hand cloud of points and the
+right-hand cloud of points
+
+ align:start position:0%
+right-hand cloud of points
+ 
+
+ align:start position:0%
+right-hand cloud of points
+so i can draw these two planes so here's
+
+ align:start position:0%
+so i can draw these two planes so here's
+ 
+
+ align:start position:0%
+so i can draw these two planes so here's
+one plane so all of the points on the in
+
+ align:start position:0%
+one plane so all of the points on the in
+ 
+
+ align:start position:0%
+one plane so all of the points on the in
+the left-hand coordinate system of one
+
+ align:start position:0%
+the left-hand coordinate system of one
+ 
+
+ align:start position:0%
+the left-hand coordinate system of one
+plane all of the right-hand ones are in
+
+ align:start position:0%
+plane all of the right-hand ones are in
+ 
+
+ align:start position:0%
+plane all of the right-hand ones are in
+this other plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not not particularly good drawing well
+
+ align:start position:0%
+not not particularly good drawing well
+ 
+
+ align:start position:0%
+not not particularly good drawing well
+two planes so
+
+ align:start position:0%
+two planes so
+ 
+
+ align:start position:0%
+two planes so
+all of uh left
+
+ align:start position:0%
+all of uh left
+ 
+
+ align:start position:0%
+all of uh left
+point cloud
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh right point cloud
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm gonna
+
+ align:start position:0%
+so i'm gonna
+ 
+
+ align:start position:0%
+so i'm gonna
+then then i can decompose the problem
+
+ align:start position:0%
+then then i can decompose the problem
+ 
+
+ align:start position:0%
+then then i can decompose the problem
+into two parts two steps the one step is
+
+ align:start position:0%
+into two parts two steps the one step is
+ 
+
+ align:start position:0%
+into two parts two steps the one step is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+rotate the one plane so it lies on top
+
+ align:start position:0%
+rotate the one plane so it lies on top
+ 
+
+ align:start position:0%
+rotate the one plane so it lies on top
+of the other plane
+
+ align:start position:0%
+of the other plane
+ 
+
+ align:start position:0%
+of the other plane
+and then an in-plane rotation and i'm
+
+ align:start position:0%
+and then an in-plane rotation and i'm
+ 
+
+ align:start position:0%
+and then an in-plane rotation and i'm
+done so the only two things i can
+
+ align:start position:0%
+done so the only two things i can
+ 
+
+ align:start position:0%
+done so the only two things i can
+decompose the
+
+ align:start position:0%
+decompose the
+ 
+
+ align:start position:0%
+decompose the
+full 3d rotation into two very simple
+
+ align:start position:0%
+full 3d rotation into two very simple
+ 
+
+ align:start position:0%
+full 3d rotation into two very simple
+rotations now to do that i'd need to
+
+ align:start position:0%
+rotations now to do that i'd need to
+ 
+
+ align:start position:0%
+rotations now to do that i'd need to
+find this angle
+
+ align:start position:0%
+find this angle
+ 
+
+ align:start position:0%
+find this angle
+and i need to find this axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the axis is parallel to
+
+ align:start position:0%
+and the axis is parallel to
+ 
+
+ align:start position:0%
+and the axis is parallel to
+n1 cross n2
+
+ align:start position:0%
+n1 cross n2
+ 
+
+ align:start position:0%
+n1 cross n2
+right if we have two planes that have
+
+ align:start position:0%
+right if we have two planes that have
+ 
+
+ align:start position:0%
+right if we have two planes that have
+normals in one and n2
+
+ align:start position:0%
+normals in one and n2
+ 
+
+ align:start position:0%
+normals in one and n2
+they intersect in a line which is
+
+ align:start position:0%
+they intersect in a line which is
+ 
+
+ align:start position:0%
+they intersect in a line which is
+parallel to n1 cross n2
+
+ align:start position:0%
+parallel to n1 cross n2
+ 
+
+ align:start position:0%
+parallel to n1 cross n2
+and the angles of course i can get
+
+ align:start position:0%
+and the angles of course i can get
+ 
+
+ align:start position:0%
+and the angles of course i can get
+very easily also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i take the dot product
+
+ align:start position:0%
+i take the dot product
+ 
+
+ align:start position:0%
+i take the dot product
+that gives me the cosine
+
+ align:start position:0%
+that gives me the cosine
+ 
+
+ align:start position:0%
+that gives me the cosine
+i take the cross product
+
+ align:start position:0%
+i take the cross product
+ 
+
+ align:start position:0%
+i take the cross product
+and the magnitude of that gives me
+
+ align:start position:0%
+and the magnitude of that gives me
+ 
+
+ align:start position:0%
+and the magnitude of that gives me
+the sine and then i use a tan too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+i've got the axis i've got the angle so
+
+ align:start position:0%
+i've got the axis i've got the angle so
+ 
+
+ align:start position:0%
+i've got the axis i've got the angle so
+i can construct the quaternion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i rotate all of the points in
+
+ align:start position:0%
+and then i rotate all of the points in
+ 
+
+ align:start position:0%
+and then i rotate all of the points in
+one of the coordinate systems
+
+ align:start position:0%
+one of the coordinate systems
+ 
+
+ align:start position:0%
+one of the coordinate systems
+and now the two planes on top of each
+
+ align:start position:0%
+and now the two planes on top of each
+ 
+
+ align:start position:0%
+and now the two planes on top of each
+other and now i've just got to take the
+
+ align:start position:0%
+other and now i've just got to take the
+ 
+
+ align:start position:0%
+other and now i've just got to take the
+rotation in that plane
+
+ align:start position:0%
+rotation in that plane
+ 
+
+ align:start position:0%
+rotation in that plane
+uh so that um these points align so
+
+ align:start position:0%
+uh so that um these points align so
+ 
+
+ align:start position:0%
+uh so that um these points align so
+that's a least squares 2d problem
+
+ align:start position:0%
+that's a least squares 2d problem
+ 
+
+ align:start position:0%
+that's a least squares 2d problem
+but like you've solved in homework
+
+ align:start position:0%
+but like you've solved in homework
+ 
+
+ align:start position:0%
+but like you've solved in homework
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+of course it's in a plane that's
+
+ align:start position:0%
+of course it's in a plane that's
+ 
+
+ align:start position:0%
+of course it's in a plane that's
+somewhere in 3d but
+
+ align:start position:0%
+somewhere in 3d but
+ 
+
+ align:start position:0%
+somewhere in 3d but
+pre pretty straightforward anyway so so
+
+ align:start position:0%
+pre pretty straightforward anyway so so
+ 
+
+ align:start position:0%
+pre pretty straightforward anyway so so
+that's interesting that you know the
+
+ align:start position:0%
+that's interesting that you know the
+ 
+
+ align:start position:0%
+that's interesting that you know the
+special cases where
+
+ align:start position:0%
+special cases where
+ 
+
+ align:start position:0%
+special cases where
+things change in terms of the difficulty
+
+ align:start position:0%
+things change in terms of the difficulty
+ 
+
+ align:start position:0%
+things change in terms of the difficulty
+of solution also correspond to some
+
+ align:start position:0%
+of solution also correspond to some
+ 
+
+ align:start position:0%
+of solution also correspond to some
+things that are physically
+
+ align:start position:0%
+things that are physically
+ 
+
+ align:start position:0%
+things that are physically
+relevant so
+
+ align:start position:0%
+relevant so
+ 
+
+ align:start position:0%
+relevant so
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um where to go next i don't want to go
+
+ align:start position:0%
+um where to go next i don't want to go
+ 
+
+ align:start position:0%
+um where to go next i don't want to go
+on to relative orientation too quickly i
+
+ align:start position:0%
+on to relative orientation too quickly i
+ 
+
+ align:start position:0%
+on to relative orientation too quickly i
+want this to
+
+ align:start position:0%
+want this to
+ 
+
+ align:start position:0%
+want this to
+sink in
+
+ align:start position:0%
+sink in
+ 
+
+ align:start position:0%
+sink in
+because this is like a triumph we've got
+
+ align:start position:0%
+because this is like a triumph we've got
+ 
+
+ align:start position:0%
+because this is like a triumph we've got
+a close form solution and sadly
+
+ align:start position:0%
+a close form solution and sadly
+ 
+
+ align:start position:0%
+a close form solution and sadly
+so far there isn't one for relative
+
+ align:start position:0%
+so far there isn't one for relative
+ 
+
+ align:start position:0%
+so far there isn't one for relative
+orientation but we use a lot of the same
+
+ align:start position:0%
+orientation but we use a lot of the same
+ 
+
+ align:start position:0%
+orientation but we use a lot of the same
+tools the representation for rotation
+
+ align:start position:0%
+tools the representation for rotation
+ 
+
+ align:start position:0%
+tools the representation for rotation
+and so on but i want to look at some
+
+ align:start position:0%
+and so on but i want to look at some
+ 
+
+ align:start position:0%
+and so on but i want to look at some
+other aspects one of them is you know
+
+ align:start position:0%
+other aspects one of them is you know
+ 
+
+ align:start position:0%
+other aspects one of them is you know
+least squares everything we've done in
+
+ align:start position:0%
+least squares everything we've done in
+ 
+
+ align:start position:0%
+least squares everything we've done in
+this course is least squares and if you
+
+ align:start position:0%
+this course is least squares and if you
+ 
+
+ align:start position:0%
+this course is least squares and if you
+talk to your more sophisticated friends
+
+ align:start position:0%
+talk to your more sophisticated friends
+ 
+
+ align:start position:0%
+talk to your more sophisticated friends
+they'll say oh that's useless because
+
+ align:start position:0%
+they'll say oh that's useless because
+ 
+
+ align:start position:0%
+they'll say oh that's useless because
+not robust
+
+ align:start position:0%
+not robust
+ 
+
+ align:start position:0%
+not robust
+and what does that mean well it means
+
+ align:start position:0%
+and what does that mean well it means
+ 
+
+ align:start position:0%
+and what does that mean well it means
+that if you have a
+
+ align:start position:0%
+that if you have a
+ 
+
+ align:start position:0%
+that if you have a
+nice noise
+
+ align:start position:0%
+nice noise
+ 
+
+ align:start position:0%
+nice noise
+these squares is the way to go
+
+ align:start position:0%
+these squares is the way to go
+ 
+
+ align:start position:0%
+these squares is the way to go
+by nice noise we mean something that has
+
+ align:start position:0%
+by nice noise we mean something that has
+ 
+
+ align:start position:0%
+by nice noise we mean something that has
+a reasonable distribution like gaussian
+
+ align:start position:0%
+a reasonable distribution like gaussian
+ 
+
+ align:start position:0%
+a reasonable distribution like gaussian
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the problem
+
+ align:start position:0%
+the problem
+ 
+
+ align:start position:0%
+the problem
+we face in practice sometimes is that
+
+ align:start position:0%
+we face in practice sometimes is that
+ 
+
+ align:start position:0%
+we face in practice sometimes is that
+a lot of the measurements sort of follow
+
+ align:start position:0%
+a lot of the measurements sort of follow
+ 
+
+ align:start position:0%
+a lot of the measurements sort of follow
+a gaussian
+
+ align:start position:0%
+a gaussian
+ 
+
+ align:start position:0%
+a gaussian
+distribution but every now and then you
+
+ align:start position:0%
+distribution but every now and then you
+ 
+
+ align:start position:0%
+distribution but every now and then you
+get something that's completely wacko
+
+ align:start position:0%
+get something that's completely wacko
+ 
+
+ align:start position:0%
+get something that's completely wacko
+and so what what do you do with that so
+
+ align:start position:0%
+and so what what do you do with that so
+ 
+
+ align:start position:0%
+and so what what do you do with that so
+how do we deal with outliers
+
+ align:start position:0%
+how do we deal with outliers
+ 
+
+ align:start position:0%
+how do we deal with outliers
+now you can formulate
+
+ align:start position:0%
+now you can formulate
+ 
+
+ align:start position:0%
+now you can formulate
+a new optimization problem
+
+ align:start position:0%
+a new optimization problem
+ 
+
+ align:start position:0%
+a new optimization problem
+that uses something other than square of
+
+ align:start position:0%
+that uses something other than square of
+ 
+
+ align:start position:0%
+that uses something other than square of
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+for example absolute value of error but
+
+ align:start position:0%
+for example absolute value of error but
+ 
+
+ align:start position:0%
+for example absolute value of error but
+it no longer has a closed form solution
+
+ align:start position:0%
+it no longer has a closed form solution
+ 
+
+ align:start position:0%
+it no longer has a closed form solution
+and so there's a trade-off obviously if
+
+ align:start position:0%
+and so there's a trade-off obviously if
+ 
+
+ align:start position:0%
+and so there's a trade-off obviously if
+you don't have a closed-form solution it
+
+ align:start position:0%
+you don't have a closed-form solution it
+ 
+
+ align:start position:0%
+you don't have a closed-form solution it
+might be more work to compute that's
+
+ align:start position:0%
+might be more work to compute that's
+ 
+
+ align:start position:0%
+might be more work to compute that's
+often not an issue
+
+ align:start position:0%
+often not an issue
+ 
+
+ align:start position:0%
+often not an issue
+but it also makes it very hard to say
+
+ align:start position:0%
+but it also makes it very hard to say
+ 
+
+ align:start position:0%
+but it also makes it very hard to say
+anything in general about it like how
+
+ align:start position:0%
+anything in general about it like how
+ 
+
+ align:start position:0%
+anything in general about it like how
+does it vary with the parameters and so
+
+ align:start position:0%
+does it vary with the parameters and so
+ 
+
+ align:start position:0%
+does it vary with the parameters and so
+on you know if the only way you get the
+
+ align:start position:0%
+on you know if the only way you get the
+ 
+
+ align:start position:0%
+on you know if the only way you get the
+answer is to crunch the numbers uh then
+
+ align:start position:0%
+answer is to crunch the numbers uh then
+ 
+
+ align:start position:0%
+answer is to crunch the numbers uh then
+you don't have that uh
+
+ align:start position:0%
+you don't have that uh
+ 
+
+ align:start position:0%
+you don't have that uh
+pleasant experience of a general formula
+
+ align:start position:0%
+pleasant experience of a general formula
+ 
+
+ align:start position:0%
+pleasant experience of a general formula
+that says oh it's going to vary with
+
+ align:start position:0%
+that says oh it's going to vary with
+ 
+
+ align:start position:0%
+that says oh it's going to vary with
+linearly with frequency or something
+
+ align:start position:0%
+linearly with frequency or something
+ 
+
+ align:start position:0%
+linearly with frequency or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so that's one disadvantage of
+
+ align:start position:0%
+so that's one disadvantage of
+ 
+
+ align:start position:0%
+so that's one disadvantage of
+departing from this least squares method
+
+ align:start position:0%
+departing from this least squares method
+ 
+
+ align:start position:0%
+departing from this least squares method
+so suppose that we have a 2d problem and
+
+ align:start position:0%
+so suppose that we have a 2d problem and
+ 
+
+ align:start position:0%
+so suppose that we have a 2d problem and
+we're just doing a
+
+ align:start position:0%
+we're just doing a
+ 
+
+ align:start position:0%
+we're just doing a
+line fit
+
+ align:start position:0%
+line fit
+ 
+
+ align:start position:0%
+line fit
+so we have you know
+
+ align:start position:0%
+so we have you know
+ 
+
+ align:start position:0%
+so we have you know
+there's our
+
+ align:start position:0%
+there's our
+ 
+
+ align:start position:0%
+there's our
+least squares line but now suppose that
+
+ align:start position:0%
+least squares line but now suppose that
+ 
+
+ align:start position:0%
+least squares line but now suppose that
+there's some data point that's just
+
+ align:start position:0%
+there's some data point that's just
+ 
+
+ align:start position:0%
+there's some data point that's just
+completely waco well that has a huge
+
+ align:start position:0%
+completely waco well that has a huge
+ 
+
+ align:start position:0%
+completely waco well that has a huge
+square of uh error and so it's going to
+
+ align:start position:0%
+square of uh error and so it's going to
+ 
+
+ align:start position:0%
+square of uh error and so it's going to
+pull your solution dramatically in that
+
+ align:start position:0%
+pull your solution dramatically in that
+ 
+
+ align:start position:0%
+pull your solution dramatically in that
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+so that's kind of the intuition and it'd
+
+ align:start position:0%
+so that's kind of the intuition and it'd
+ 
+
+ align:start position:0%
+so that's kind of the intuition and it'd
+be slightly better if it was absolute
+
+ align:start position:0%
+be slightly better if it was absolute
+ 
+
+ align:start position:0%
+be slightly better if it was absolute
+value of error because then it wouldn't
+
+ align:start position:0%
+value of error because then it wouldn't
+ 
+
+ align:start position:0%
+value of error because then it wouldn't
+pull quite as hard
+
+ align:start position:0%
+pull quite as hard
+ 
+
+ align:start position:0%
+pull quite as hard
+but it would be even better if you said
+
+ align:start position:0%
+but it would be even better if you said
+ 
+
+ align:start position:0%
+but it would be even better if you said
+oh that point's just crazy forget it so
+
+ align:start position:0%
+oh that point's just crazy forget it so
+ 
+
+ align:start position:0%
+oh that point's just crazy forget it so
+so you know and they're different
+
+ align:start position:0%
+so you know and they're different
+ 
+
+ align:start position:0%
+so you know and they're different
+approaches to this so there's there's a
+
+ align:start position:0%
+approaches to this so there's there's a
+ 
+
+ align:start position:0%
+approaches to this so there's there's a
+sort of question of uh
+
+ align:start position:0%
+sort of question of uh
+ 
+
+ align:start position:0%
+sort of question of uh
+robustly dealing with with outliers
+
+ align:start position:0%
+robustly dealing with with outliers
+ 
+
+ align:start position:0%
+robustly dealing with with outliers
+now uh now it actually goes further than
+
+ align:start position:0%
+now uh now it actually goes further than
+ 
+
+ align:start position:0%
+now uh now it actually goes further than
+that that you can show that there are
+
+ align:start position:0%
+that that you can show that there are
+ 
+
+ align:start position:0%
+that that you can show that there are
+certain problems
+
+ align:start position:0%
+certain problems
+ 
+
+ align:start position:0%
+certain problems
+where if the noise is gaussian then
+
+ align:start position:0%
+where if the noise is gaussian then
+ 
+
+ align:start position:0%
+where if the noise is gaussian then
+least squares gives you the best
+
+ align:start position:0%
+least squares gives you the best
+ 
+
+ align:start position:0%
+least squares gives you the best
+possible answer it's it's not just hand
+
+ align:start position:0%
+possible answer it's it's not just hand
+ 
+
+ align:start position:0%
+possible answer it's it's not just hand
+waving but you know maximum likelihood
+
+ align:start position:0%
+waving but you know maximum likelihood
+ 
+
+ align:start position:0%
+waving but you know maximum likelihood
+all those wonderful things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+how do we deal with this problem
+
+ align:start position:0%
+how do we deal with this problem
+ 
+
+ align:start position:0%
+how do we deal with this problem
+well uh the various approaches the one
+
+ align:start position:0%
+well uh the various approaches the one
+ 
+
+ align:start position:0%
+well uh the various approaches the one
+i'm going to talk about is called
+
+ align:start position:0%
+i'm going to talk about is called
+ 
+
+ align:start position:0%
+i'm going to talk about is called
+ransack random sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know agreement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fishler and bowles invented it
+
+ align:start position:0%
+fishler and bowles invented it
+ 
+
+ align:start position:0%
+fishler and bowles invented it
+at sri
+
+ align:start position:0%
+at sri
+ 
+
+ align:start position:0%
+at sri
+stanford research institute which is you
+
+ align:start position:0%
+stanford research institute which is you
+ 
+
+ align:start position:0%
+stanford research institute which is you
+know connected
+
+ align:start position:0%
+know connected
+ 
+
+ align:start position:0%
+know connected
+to stanford in some way
+
+ align:start position:0%
+to stanford in some way
+ 
+
+ align:start position:0%
+to stanford in some way
+although
+
+ align:start position:0%
+although
+ 
+
+ align:start position:0%
+although
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+because they do classified work it's not
+
+ align:start position:0%
+because they do classified work it's not
+ 
+
+ align:start position:0%
+because they do classified work it's not
+as intimately connected as they see cell
+
+ align:start position:0%
+as intimately connected as they see cell
+ 
+
+ align:start position:0%
+as intimately connected as they see cell
+it's more like lincoln labs anyway what
+
+ align:start position:0%
+it's more like lincoln labs anyway what
+ 
+
+ align:start position:0%
+it's more like lincoln labs anyway what
+they they had problems like satellite
+
+ align:start position:0%
+they they had problems like satellite
+ 
+
+ align:start position:0%
+they they had problems like satellite
+navigation
+
+ align:start position:0%
+navigation
+ 
+
+ align:start position:0%
+navigation
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+making measurements of i don't know star
+
+ align:start position:0%
+making measurements of i don't know star
+ 
+
+ align:start position:0%
+making measurements of i don't know star
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+gyroscopes and occasionally they'd have
+
+ align:start position:0%
+gyroscopes and occasionally they'd have
+ 
+
+ align:start position:0%
+gyroscopes and occasionally they'd have
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+massive error which would completely
+
+ align:start position:0%
+massive error which would completely
+ 
+
+ align:start position:0%
+massive error which would completely
+mess up their result
+
+ align:start position:0%
+mess up their result
+ 
+
+ align:start position:0%
+mess up their result
+even though most of the time the errors
+
+ align:start position:0%
+even though most of the time the errors
+ 
+
+ align:start position:0%
+even though most of the time the errors
+were well behaved they followed some
+
+ align:start position:0%
+were well behaved they followed some
+ 
+
+ align:start position:0%
+were well behaved they followed some
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+smooth
+
+ align:start position:0%
+smooth
+ 
+
+ align:start position:0%
+smooth
+distribution with not too much spread
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the idea
+
+ align:start position:0%
+so what's the idea
+ 
+
+ align:start position:0%
+so what's the idea
+step one random sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i take a random sample of these
+
+ align:start position:0%
+so if i take a random sample of these
+ 
+
+ align:start position:0%
+so if i take a random sample of these
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they're not too many outliers
+
+ align:start position:0%
+and they're not too many outliers
+ 
+
+ align:start position:0%
+and they're not too many outliers
+there's a good chance that i won't hit
+
+ align:start position:0%
+there's a good chance that i won't hit
+ 
+
+ align:start position:0%
+there's a good chance that i won't hit
+the outlier and i will get a good result
+
+ align:start position:0%
+the outlier and i will get a good result
+ 
+
+ align:start position:0%
+the outlier and i will get a good result
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know how how do i know that i picked
+
+ align:start position:0%
+you know how how do i know that i picked
+ 
+
+ align:start position:0%
+you know how how do i know that i picked
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+random sample and how large so there are
+
+ align:start position:0%
+random sample and how large so there are
+ 
+
+ align:start position:0%
+random sample and how large so there are
+several sort of questions
+
+ align:start position:0%
+several sort of questions
+ 
+
+ align:start position:0%
+several sort of questions
+how uh how large a random sample well uh
+
+ align:start position:0%
+how uh how large a random sample well uh
+ 
+
+ align:start position:0%
+how uh how large a random sample well uh
+their recommendation was the the minimum
+
+ align:start position:0%
+their recommendation was the the minimum
+ 
+
+ align:start position:0%
+their recommendation was the the minimum
+needed to fix the transformation so in
+
+ align:start position:0%
+needed to fix the transformation so in
+ 
+
+ align:start position:0%
+needed to fix the transformation so in
+our case of absolute orientation it
+
+ align:start position:0%
+our case of absolute orientation it
+ 
+
+ align:start position:0%
+our case of absolute orientation it
+would be three
+
+ align:start position:0%
+would be three
+ 
+
+ align:start position:0%
+would be three
+now we know
+
+ align:start position:0%
+now we know
+ 
+
+ align:start position:0%
+now we know
+if we get you know a thousand
+
+ align:start position:0%
+if we get you know a thousand
+ 
+
+ align:start position:0%
+if we get you know a thousand
+correspondences we're going to get much
+
+ align:start position:0%
+correspondences we're going to get much
+ 
+
+ align:start position:0%
+correspondences we're going to get much
+better results than with three
+
+ align:start position:0%
+better results than with three
+ 
+
+ align:start position:0%
+better results than with three
+it sort of goes as one over the square
+
+ align:start position:0%
+it sort of goes as one over the square
+ 
+
+ align:start position:0%
+it sort of goes as one over the square
+root of n
+
+ align:start position:0%
+root of n
+ 
+
+ align:start position:0%
+root of n
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+so that's sort of limiting uh the
+
+ align:start position:0%
+so that's sort of limiting uh the
+ 
+
+ align:start position:0%
+so that's sort of limiting uh the
+accuracy so some other people recommend
+
+ align:start position:0%
+accuracy so some other people recommend
+ 
+
+ align:start position:0%
+accuracy so some other people recommend
+that you use more but
+
+ align:start position:0%
+that you use more but
+ 
+
+ align:start position:0%
+that you use more but
+and then what do you do so now you take
+
+ align:start position:0%
+and then what do you do so now you take
+ 
+
+ align:start position:0%
+and then what do you do so now you take
+the random sample and you do a best fit
+
+ align:start position:0%
+the random sample and you do a best fit
+ 
+
+ align:start position:0%
+the random sample and you do a best fit
+typically least squares because it's
+
+ align:start position:0%
+typically least squares because it's
+ 
+
+ align:start position:0%
+typically least squares because it's
+efficient and easy to understand so
+
+ align:start position:0%
+efficient and easy to understand so
+ 
+
+ align:start position:0%
+efficient and easy to understand so
+okay and then
+
+ align:start position:0%
+okay and then
+ 
+
+ align:start position:0%
+okay and then
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+check how much of the data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what you do is if that's your fit
+
+ align:start position:0%
+and so what you do is if that's your fit
+ 
+
+ align:start position:0%
+and so what you do is if that's your fit
+then you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have some sort of band
+
+ align:start position:0%
+have some sort of band
+ 
+
+ align:start position:0%
+have some sort of band
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you count how many of them fall inside
+
+ align:start position:0%
+you count how many of them fall inside
+ 
+
+ align:start position:0%
+you count how many of them fall inside
+and notice that this involves some kind
+
+ align:start position:0%
+and notice that this involves some kind
+ 
+
+ align:start position:0%
+and notice that this involves some kind
+of threshold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know in our case here let's say that
+
+ align:start position:0%
+you know in our case here let's say that
+ 
+
+ align:start position:0%
+you know in our case here let's say that
+all but one point fall in that band then
+
+ align:start position:0%
+all but one point fall in that band then
+ 
+
+ align:start position:0%
+all but one point fall in that band then
+we say we're done
+
+ align:start position:0%
+we say we're done
+ 
+
+ align:start position:0%
+we say we're done
+uh if not uh we take another uh random
+
+ align:start position:0%
+uh if not uh we take another uh random
+ 
+
+ align:start position:0%
+uh if not uh we take another uh random
+sample and we do this operation again
+
+ align:start position:0%
+sample and we do this operation again
+ 
+
+ align:start position:0%
+sample and we do this operation again
+and and they're all sorts of interesting
+
+ align:start position:0%
+and and they're all sorts of interesting
+ 
+
+ align:start position:0%
+and and they're all sorts of interesting
+issues you know one of them is you kind
+
+ align:start position:0%
+issues you know one of them is you kind
+ 
+
+ align:start position:0%
+issues you know one of them is you kind
+of have to know
+
+ align:start position:0%
+of have to know
+ 
+
+ align:start position:0%
+of have to know
+uh what the ratio of in in liars to
+
+ align:start position:0%
+uh what the ratio of in in liars to
+ 
+
+ align:start position:0%
+uh what the ratio of in in liars to
+outliers is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have to have some sort of model
+
+ align:start position:0%
+so you have to have some sort of model
+ 
+
+ align:start position:0%
+so you have to have some sort of model
+of your measurement process
+
+ align:start position:0%
+of your measurement process
+ 
+
+ align:start position:0%
+of your measurement process
+right because that's going to control
+
+ align:start position:0%
+right because that's going to control
+ 
+
+ align:start position:0%
+right because that's going to control
+how you set the threshold so you need to
+
+ align:start position:0%
+how you set the threshold so you need to
+ 
+
+ align:start position:0%
+how you set the threshold so you need to
+know something about the noise to set
+
+ align:start position:0%
+know something about the noise to set
+ 
+
+ align:start position:0%
+know something about the noise to set
+that threshold and then you need to know
+
+ align:start position:0%
+that threshold and then you need to know
+ 
+
+ align:start position:0%
+that threshold and then you need to know
+you know how many so there are two
+
+ align:start position:0%
+you know how many so there are two
+ 
+
+ align:start position:0%
+you know how many so there are two
+thresholds there's a threshold here of
+
+ align:start position:0%
+thresholds there's a threshold here of
+ 
+
+ align:start position:0%
+thresholds there's a threshold here of
+the band
+
+ align:start position:0%
+the band
+ 
+
+ align:start position:0%
+the band
+uh that determines whether these are uh
+
+ align:start position:0%
+uh that determines whether these are uh
+ 
+
+ align:start position:0%
+uh that determines whether these are uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+in the in in liars or not and then
+
+ align:start position:0%
+in the in in liars or not and then
+ 
+
+ align:start position:0%
+in the in in liars or not and then
+there's a second threshold here
+
+ align:start position:0%
+there's a second threshold here
+ 
+
+ align:start position:0%
+there's a second threshold here
+that says um
+
+ align:start position:0%
+that says um
+ 
+
+ align:start position:0%
+that says um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+oops scared her with some equations
+
+ align:start position:0%
+oops scared her with some equations
+ 
+
+ align:start position:0%
+oops scared her with some equations
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+if not enough so we got
+
+ align:start position:0%
+if not enough so we got
+ 
+
+ align:start position:0%
+if not enough so we got
+sort of arbitrary numbers in there which
+
+ align:start position:0%
+sort of arbitrary numbers in there which
+ 
+
+ align:start position:0%
+sort of arbitrary numbers in there which
+assume that you know something about the
+
+ align:start position:0%
+assume that you know something about the
+ 
+
+ align:start position:0%
+assume that you know something about the
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+and this works uh pretty well um
+
+ align:start position:0%
+and this works uh pretty well um
+ 
+
+ align:start position:0%
+and this works uh pretty well um
+i mean i guess you have to have some
+
+ align:start position:0%
+i mean i guess you have to have some
+ 
+
+ align:start position:0%
+i mean i guess you have to have some
+limit on not getting
+
+ align:start position:0%
+limit on not getting
+ 
+
+ align:start position:0%
+limit on not getting
+you know not doing this an infinite
+
+ align:start position:0%
+you know not doing this an infinite
+ 
+
+ align:start position:0%
+you know not doing this an infinite
+number of times so you probably have
+
+ align:start position:0%
+number of times so you probably have
+ 
+
+ align:start position:0%
+number of times so you probably have
+another exit clause which says well if
+
+ align:start position:0%
+another exit clause which says well if
+ 
+
+ align:start position:0%
+another exit clause which says well if
+you've tried 100 random samples then
+
+ align:start position:0%
+you've tried 100 random samples then
+ 
+
+ align:start position:0%
+you've tried 100 random samples then
+let's stop
+
+ align:start position:0%
+let's stop
+ 
+
+ align:start position:0%
+let's stop
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then probably your assumptions about the
+
+ align:start position:0%
+then probably your assumptions about the
+ 
+
+ align:start position:0%
+then probably your assumptions about the
+model are wrong and the thresholds
+
+ align:start position:0%
+model are wrong and the thresholds
+ 
+
+ align:start position:0%
+model are wrong and the thresholds
+aren't right so
+
+ align:start position:0%
+aren't right so
+ 
+
+ align:start position:0%
+aren't right so
+uh need to give up
+
+ align:start position:0%
+uh need to give up
+ 
+
+ align:start position:0%
+uh need to give up
+and they're variations of this so that's
+
+ align:start position:0%
+and they're variations of this so that's
+ 
+
+ align:start position:0%
+and they're variations of this so that's
+a good point i i didn't make that point
+
+ align:start position:0%
+a good point i i didn't make that point
+ 
+
+ align:start position:0%
+a good point i i didn't make that point
+yet but you know we're talking
+
+ align:start position:0%
+yet but you know we're talking
+ 
+
+ align:start position:0%
+yet but you know we're talking
+specifically about absolute orientation
+
+ align:start position:0%
+specifically about absolute orientation
+ 
+
+ align:start position:0%
+specifically about absolute orientation
+but this trick is to be applied uh if
+
+ align:start position:0%
+but this trick is to be applied uh if
+ 
+
+ align:start position:0%
+but this trick is to be applied uh if
+necessary if they outliers to any of the
+
+ align:start position:0%
+necessary if they outliers to any of the
+ 
+
+ align:start position:0%
+necessary if they outliers to any of the
+other least squares method so the least
+
+ align:start position:0%
+other least squares method so the least
+ 
+
+ align:start position:0%
+other least squares method so the least
+squares approach is very appealing
+
+ align:start position:0%
+squares approach is very appealing
+ 
+
+ align:start position:0%
+squares approach is very appealing
+because you get a closed form solution
+
+ align:start position:0%
+because you get a closed form solution
+ 
+
+ align:start position:0%
+because you get a closed form solution
+many times and you get a measure of how
+
+ align:start position:0%
+many times and you get a measure of how
+ 
+
+ align:start position:0%
+many times and you get a measure of how
+much the how large the error is you know
+
+ align:start position:0%
+much the how large the error is you know
+ 
+
+ align:start position:0%
+much the how large the error is you know
+standard deviation and all these good
+
+ align:start position:0%
+standard deviation and all these good
+ 
+
+ align:start position:0%
+standard deviation and all these good
+things but it's always subject to the
+
+ align:start position:0%
+things but it's always subject to the
+ 
+
+ align:start position:0%
+things but it's always subject to the
+problem of bad data and so this is
+
+ align:start position:0%
+problem of bad data and so this is
+ 
+
+ align:start position:0%
+problem of bad data and so this is
+definitely a method to consider
+
+ align:start position:0%
+definitely a method to consider
+ 
+
+ align:start position:0%
+definitely a method to consider
+in the presence of real data which
+
+ align:start position:0%
+in the presence of real data which
+ 
+
+ align:start position:0%
+in the presence of real data which
+sometimes has
+
+ align:start position:0%
+sometimes has
+ 
+
+ align:start position:0%
+sometimes has
+outliers
+
+ align:start position:0%
+outliers
+ 
+
+ align:start position:0%
+outliers
+yes okay
+
+ align:start position:0%
+yes okay
+ 
+
+ align:start position:0%
+yes okay
+and the different variations of this in
+
+ align:start position:0%
+and the different variations of this in
+ 
+
+ align:start position:0%
+and the different variations of this in
+fact the the name of it you know
+
+ align:start position:0%
+fact the the name of it you know
+ 
+
+ align:start position:0%
+fact the the name of it you know
+consensus
+
+ align:start position:0%
+consensus
+ 
+
+ align:start position:0%
+consensus
+uh kind of suggests a different approach
+
+ align:start position:0%
+uh kind of suggests a different approach
+ 
+
+ align:start position:0%
+uh kind of suggests a different approach
+more like a half transform so the way
+
+ align:start position:0%
+more like a half transform so the way
+ 
+
+ align:start position:0%
+more like a half transform so the way
+you know before i read the paper what i
+
+ align:start position:0%
+you know before i read the paper what i
+ 
+
+ align:start position:0%
+you know before i read the paper what i
+thought they were doing was the
+
+ align:start position:0%
+thought they were doing was the
+ 
+
+ align:start position:0%
+thought they were doing was the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+you take random subset
+
+ align:start position:0%
+you take random subset
+ 
+
+ align:start position:0%
+you take random subset
+you do a fit
+
+ align:start position:0%
+you do a fit
+ 
+
+ align:start position:0%
+you do a fit
+and that gives you some
+
+ align:start position:0%
+and that gives you some
+ 
+
+ align:start position:0%
+and that gives you some
+answer like you know
+
+ align:start position:0%
+answer like you know
+ 
+
+ align:start position:0%
+answer like you know
+slope and intercept of a straight line
+
+ align:start position:0%
+slope and intercept of a straight line
+ 
+
+ align:start position:0%
+slope and intercept of a straight line
+say in this case and
+
+ align:start position:0%
+say in this case and
+ 
+
+ align:start position:0%
+say in this case and
+and you do it again do it a certain
+
+ align:start position:0%
+and you do it again do it a certain
+ 
+
+ align:start position:0%
+and you do it again do it a certain
+number of times and then you plot them
+
+ align:start position:0%
+number of times and then you plot them
+ 
+
+ align:start position:0%
+number of times and then you plot them
+in some parameter space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and some of them will cluster tightly
+
+ align:start position:0%
+and some of them will cluster tightly
+ 
+
+ align:start position:0%
+and some of them will cluster tightly
+and some of them that included the
+
+ align:start position:0%
+and some of them that included the
+ 
+
+ align:start position:0%
+and some of them that included the
+outlier will be way off and so uh you
+
+ align:start position:0%
+outlier will be way off and so uh you
+ 
+
+ align:start position:0%
+outlier will be way off and so uh you
+know you can imagine a half transform
+
+ align:start position:0%
+know you can imagine a half transform
+ 
+
+ align:start position:0%
+know you can imagine a half transform
+method where you have an accumulator
+
+ align:start position:0%
+method where you have an accumulator
+ 
+
+ align:start position:0%
+method where you have an accumulator
+array
+
+ align:start position:0%
+array
+ 
+
+ align:start position:0%
+array
+in this parameter space
+
+ align:start position:0%
+in this parameter space
+ 
+
+ align:start position:0%
+in this parameter space
+and whenever you get an answer you
+
+ align:start position:0%
+and whenever you get an answer you
+ 
+
+ align:start position:0%
+and whenever you get an answer you
+increment that cell in the parameter
+
+ align:start position:0%
+increment that cell in the parameter
+ 
+
+ align:start position:0%
+increment that cell in the parameter
+space then after you've done it often
+
+ align:start position:0%
+space then after you've done it often
+ 
+
+ align:start position:0%
+space then after you've done it often
+enough you look for the cell that has
+
+ align:start position:0%
+enough you look for the cell that has
+ 
+
+ align:start position:0%
+enough you look for the cell that has
+the most hits
+
+ align:start position:0%
+the most hits
+ 
+
+ align:start position:0%
+the most hits
+and and that's you know kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehow
+
+ align:start position:0%
+somehow
+ 
+
+ align:start position:0%
+somehow
+hybridizing uh
+
+ align:start position:0%
+hybridizing uh
+ 
+
+ align:start position:0%
+hybridizing uh
+fishler and boll's ransack method
+
+ align:start position:0%
+fishler and boll's ransack method
+ 
+
+ align:start position:0%
+fishler and boll's ransack method
+with a half transform method and this
+
+ align:start position:0%
+with a half transform method and this
+ 
+
+ align:start position:0%
+with a half transform method and this
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+you know all of these are kind of ad hoc
+
+ align:start position:0%
+you know all of these are kind of ad hoc
+ 
+
+ align:start position:0%
+you know all of these are kind of ad hoc
+but they're very useful in practice so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+one of the things we're going to do
+
+ align:start position:0%
+one of the things we're going to do
+ 
+
+ align:start position:0%
+one of the things we're going to do
+a little later is to find
+
+ align:start position:0%
+a little later is to find
+ 
+
+ align:start position:0%
+a little later is to find
+representations for
+
+ align:start position:0%
+representations for
+ 
+
+ align:start position:0%
+representations for
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+that particularly objects that are
+
+ align:start position:0%
+that particularly objects that are
+ 
+
+ align:start position:0%
+that particularly objects that are
+not simple polyhedra but more
+
+ align:start position:0%
+not simple polyhedra but more
+ 
+
+ align:start position:0%
+not simple polyhedra but more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+and particularly objects that um
+
+ align:start position:0%
+and particularly objects that um
+ 
+
+ align:start position:0%
+and particularly objects that um
+are near convex that might not have a
+
+ align:start position:0%
+are near convex that might not have a
+ 
+
+ align:start position:0%
+are near convex that might not have a
+lot of holes and that representation
+
+ align:start position:0%
+lot of holes and that representation
+ 
+
+ align:start position:0%
+lot of holes and that representation
+is very useful for detecting things and
+
+ align:start position:0%
+is very useful for detecting things and
+ 
+
+ align:start position:0%
+is very useful for detecting things and
+finding their orientation
+
+ align:start position:0%
+finding their orientation
+ 
+
+ align:start position:0%
+finding their orientation
+and we run into
+
+ align:start position:0%
+and we run into
+ 
+
+ align:start position:0%
+and we run into
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orientation problems as we have over
+
+ align:start position:0%
+orientation problems as we have over
+ 
+
+ align:start position:0%
+orientation problems as we have over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+often there's not a closed form solution
+
+ align:start position:0%
+often there's not a closed form solution
+ 
+
+ align:start position:0%
+often there's not a closed form solution
+so one approach is to sort of sample the
+
+ align:start position:0%
+so one approach is to sort of sample the
+ 
+
+ align:start position:0%
+so one approach is to sort of sample the
+space of rotations
+
+ align:start position:0%
+space of rotations
+ 
+
+ align:start position:0%
+space of rotations
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+how do you do this so since we're
+
+ align:start position:0%
+how do you do this so since we're
+ 
+
+ align:start position:0%
+how do you do this so since we're
+talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me
+
+ align:start position:0%
+so let me
+ 
+
+ align:start position:0%
+so let me
+first look at sampling a sphere
+
+ align:start position:0%
+first look at sampling a sphere
+ 
+
+ align:start position:0%
+first look at sampling a sphere
+in 3d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+one way we can do it is to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some sort of discretization of latitude
+
+ align:start position:0%
+some sort of discretization of latitude
+ 
+
+ align:start position:0%
+some sort of discretization of latitude
+and longitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know i just
+
+ align:start position:0%
+you know i just
+ 
+
+ align:start position:0%
+you know i just
+find there's some
+
+ align:start position:0%
+find there's some
+ 
+
+ align:start position:0%
+find there's some
+people who forget what the terminology
+
+ align:start position:0%
+people who forget what the terminology
+ 
+
+ align:start position:0%
+people who forget what the terminology
+is but where these lines cross that's
+
+ align:start position:0%
+is but where these lines cross that's
+ 
+
+ align:start position:0%
+is but where these lines cross that's
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+point of convergence and if you go there
+
+ align:start position:0%
+point of convergence and if you go there
+ 
+
+ align:start position:0%
+point of convergence and if you go there
+something magical happens to you
+
+ align:start position:0%
+something magical happens to you
+ 
+
+ align:start position:0%
+something magical happens to you
+particularly if you take along crystals
+
+ align:start position:0%
+particularly if you take along crystals
+ 
+
+ align:start position:0%
+particularly if you take along crystals
+and um sometimes these are in hard to
+
+ align:start position:0%
+and um sometimes these are in hard to
+ 
+
+ align:start position:0%
+and um sometimes these are in hard to
+access places like in the middle of a
+
+ align:start position:0%
+access places like in the middle of a
+ 
+
+ align:start position:0%
+access places like in the middle of a
+military reservation
+
+ align:start position:0%
+military reservation
+ 
+
+ align:start position:0%
+military reservation
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+we sample them and what's wrong with
+
+ align:start position:0%
+we sample them and what's wrong with
+ 
+
+ align:start position:0%
+we sample them and what's wrong with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it gives us a way of sampling the whole
+
+ align:start position:0%
+it gives us a way of sampling the whole
+ 
+
+ align:start position:0%
+it gives us a way of sampling the whole
+space but obviously
+
+ align:start position:0%
+space but obviously
+ 
+
+ align:start position:0%
+space but obviously
+it's not a uniform sampling
+
+ align:start position:0%
+it's not a uniform sampling
+ 
+
+ align:start position:0%
+it's not a uniform sampling
+up here near the poles we're sampling
+
+ align:start position:0%
+up here near the poles we're sampling
+ 
+
+ align:start position:0%
+up here near the poles we're sampling
+points that are very close together
+
+ align:start position:0%
+points that are very close together
+ 
+
+ align:start position:0%
+points that are very close together
+and so that means it's inefficient that
+
+ align:start position:0%
+and so that means it's inefficient that
+ 
+
+ align:start position:0%
+and so that means it's inefficient that
+if we had
+
+ align:start position:0%
+if we had
+ 
+
+ align:start position:0%
+if we had
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+some of those points
+
+ align:start position:0%
+some of those points
+ 
+
+ align:start position:0%
+some of those points
+near the equator we could have done a
+
+ align:start position:0%
+near the equator we could have done a
+ 
+
+ align:start position:0%
+near the equator we could have done a
+better job more even job of
+
+ align:start position:0%
+better job more even job of
+ 
+
+ align:start position:0%
+better job more even job of
+sampling
+
+ align:start position:0%
+sampling
+ 
+
+ align:start position:0%
+sampling
+so you know lots of interesting
+
+ align:start position:0%
+so you know lots of interesting
+ 
+
+ align:start position:0%
+so you know lots of interesting
+questions come out of this one of them
+
+ align:start position:0%
+questions come out of this one of them
+ 
+
+ align:start position:0%
+questions come out of this one of them
+is well can we think of a better
+
+ align:start position:0%
+is well can we think of a better
+ 
+
+ align:start position:0%
+is well can we think of a better
+coordinate system so that if you sample
+
+ align:start position:0%
+coordinate system so that if you sample
+ 
+
+ align:start position:0%
+coordinate system so that if you sample
+uniformly in those two coordinates you
+
+ align:start position:0%
+uniformly in those two coordinates you
+ 
+
+ align:start position:0%
+uniformly in those two coordinates you
+will get
+
+ align:start position:0%
+will get
+ 
+
+ align:start position:0%
+will get
+a nice spacing on the sphere well
+
+ align:start position:0%
+a nice spacing on the sphere well
+ 
+
+ align:start position:0%
+a nice spacing on the sphere well
+good luck with that
+
+ align:start position:0%
+good luck with that
+ 
+
+ align:start position:0%
+good luck with that
+you can show that it's not possible
+
+ align:start position:0%
+you can show that it's not possible
+ 
+
+ align:start position:0%
+you can show that it's not possible
+so um what else can we do well um
+
+ align:start position:0%
+so um what else can we do well um
+ 
+
+ align:start position:0%
+so um what else can we do well um
+we could generate random theta and phi
+
+ align:start position:0%
+we could generate random theta and phi
+ 
+
+ align:start position:0%
+we could generate random theta and phi
+using some distribution so that
+
+ align:start position:0%
+using some distribution so that
+ 
+
+ align:start position:0%
+using some distribution so that
+let's see latitude goes from minus pi
+
+ align:start position:0%
+let's see latitude goes from minus pi
+ 
+
+ align:start position:0%
+let's see latitude goes from minus pi
+over 2 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi over 2
+
+ align:start position:0%
+pi over 2
+ 
+
+ align:start position:0%
+pi over 2
+and longitude minus pi
+
+ align:start position:0%
+and longitude minus pi
+ 
+
+ align:start position:0%
+and longitude minus pi
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we could you know divide this up we
+
+ align:start position:0%
+so we could you know divide this up we
+ 
+
+ align:start position:0%
+so we could you know divide this up we
+could have a random number generator
+
+ align:start position:0%
+could have a random number generator
+ 
+
+ align:start position:0%
+could have a random number generator
+that goes between minus pi and plus pi
+
+ align:start position:0%
+that goes between minus pi and plus pi
+ 
+
+ align:start position:0%
+that goes between minus pi and plus pi
+and one that goes between minus pi over
+
+ align:start position:0%
+and one that goes between minus pi over
+ 
+
+ align:start position:0%
+and one that goes between minus pi over
+two and plus pi over two uniform
+
+ align:start position:0%
+two and plus pi over two uniform
+ 
+
+ align:start position:0%
+two and plus pi over two uniform
+and of course we'd have exactly the same
+
+ align:start position:0%
+and of course we'd have exactly the same
+ 
+
+ align:start position:0%
+and of course we'd have exactly the same
+problem right because we're going to
+
+ align:start position:0%
+problem right because we're going to
+ 
+
+ align:start position:0%
+problem right because we're going to
+sample the polar region more strongly
+
+ align:start position:0%
+sample the polar region more strongly
+ 
+
+ align:start position:0%
+sample the polar region more strongly
+than than the other region so that's
+
+ align:start position:0%
+than than the other region so that's
+ 
+
+ align:start position:0%
+than than the other region so that's
+that's not very good so how to solve
+
+ align:start position:0%
+that's not very good so how to solve
+ 
+
+ align:start position:0%
+that's not very good so how to solve
+that well the trouble is we got this
+
+ align:start position:0%
+that well the trouble is we got this
+ 
+
+ align:start position:0%
+that well the trouble is we got this
+curved surface if we had like a
+
+ align:start position:0%
+curved surface if we had like a
+ 
+
+ align:start position:0%
+curved surface if we had like a
+cartesian world
+
+ align:start position:0%
+cartesian world
+ 
+
+ align:start position:0%
+cartesian world
+would be easy to sample you know if i
+
+ align:start position:0%
+would be easy to sample you know if i
+ 
+
+ align:start position:0%
+would be easy to sample you know if i
+have a cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can just
+
+ align:start position:0%
+i can just
+ 
+
+ align:start position:0%
+i can just
+have a uniform distribution in x a
+
+ align:start position:0%
+have a uniform distribution in x a
+ 
+
+ align:start position:0%
+have a uniform distribution in x a
+uniform distribution y uniform
+
+ align:start position:0%
+uniform distribution y uniform
+ 
+
+ align:start position:0%
+uniform distribution y uniform
+distribution in z and i call the random
+
+ align:start position:0%
+distribution in z and i call the random
+ 
+
+ align:start position:0%
+distribution in z and i call the random
+number generator three times i have a
+
+ align:start position:0%
+number generator three times i have a
+ 
+
+ align:start position:0%
+number generator three times i have a
+point in that space and it's uh
+
+ align:start position:0%
+point in that space and it's uh
+ 
+
+ align:start position:0%
+point in that space and it's uh
+if i do this a lot i don't expect there
+
+ align:start position:0%
+if i do this a lot i don't expect there
+ 
+
+ align:start position:0%
+if i do this a lot i don't expect there
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+sort of aggregation systematic
+
+ align:start position:0%
+sort of aggregation systematic
+ 
+
+ align:start position:0%
+sort of aggregation systematic
+uh clumping you know as we as we have in
+
+ align:start position:0%
+uh clumping you know as we as we have in
+ 
+
+ align:start position:0%
+uh clumping you know as we as we have in
+the case of of the sphere
+
+ align:start position:0%
+the case of of the sphere
+ 
+
+ align:start position:0%
+the case of of the sphere
+so how to go from this to that well one
+
+ align:start position:0%
+so how to go from this to that well one
+ 
+
+ align:start position:0%
+so how to go from this to that well one
+thing to do is to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inscribe a sphere in the cube
+
+ align:start position:0%
+inscribe a sphere in the cube
+ 
+
+ align:start position:0%
+inscribe a sphere in the cube
+and then somehow map
+
+ align:start position:0%
+and then somehow map
+ 
+
+ align:start position:0%
+and then somehow map
+the cube
+
+ align:start position:0%
+the cube
+ 
+
+ align:start position:0%
+the cube
+onto the sphere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one way to do that would be to
+
+ align:start position:0%
+so one way to do that would be to
+ 
+
+ align:start position:0%
+so one way to do that would be to
+imagine the origins at the very center
+
+ align:start position:0%
+imagine the origins at the very center
+ 
+
+ align:start position:0%
+imagine the origins at the very center
+of this thing and any point on the
+
+ align:start position:0%
+of this thing and any point on the
+ 
+
+ align:start position:0%
+of this thing and any point on the
+sphere we draw a line and then we find
+
+ align:start position:0%
+sphere we draw a line and then we find
+ 
+
+ align:start position:0%
+sphere we draw a line and then we find
+where it intersects the uh
+
+ align:start position:0%
+where it intersects the uh
+ 
+
+ align:start position:0%
+where it intersects the uh
+the sphere
+
+ align:start position:0%
+the sphere
+ 
+
+ align:start position:0%
+the sphere
+any point in the cube
+
+ align:start position:0%
+any point in the cube
+ 
+
+ align:start position:0%
+any point in the cube
+we sample and and that point could be
+
+ align:start position:0%
+we sample and and that point could be
+ 
+
+ align:start position:0%
+we sample and and that point could be
+inside this sphere so if it's inside the
+
+ align:start position:0%
+inside this sphere so if it's inside the
+ 
+
+ align:start position:0%
+inside this sphere so if it's inside the
+sphere we draw that line
+
+ align:start position:0%
+sphere we draw that line
+ 
+
+ align:start position:0%
+sphere we draw that line
+and we project it out to the sphere
+
+ align:start position:0%
+and we project it out to the sphere
+ 
+
+ align:start position:0%
+and we project it out to the sphere
+in this case we
+
+ align:start position:0%
+in this case we
+ 
+
+ align:start position:0%
+in this case we
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to be clear again we just have uniform
+
+ align:start position:0%
+to be clear again we just have uniform
+ 
+
+ align:start position:0%
+to be clear again we just have uniform
+you know like most languages give you
+
+ align:start position:0%
+you know like most languages give you
+ 
+
+ align:start position:0%
+you know like most languages give you
+the ability to generate
+
+ align:start position:0%
+the ability to generate
+ 
+
+ align:start position:0%
+the ability to generate
+uniform random numbers between zero and
+
+ align:start position:0%
+uniform random numbers between zero and
+ 
+
+ align:start position:0%
+uniform random numbers between zero and
+one you just map them on to that
+
+ align:start position:0%
+one you just map them on to that
+ 
+
+ align:start position:0%
+one you just map them on to that
+interval in x and then another one
+
+ align:start position:0%
+interval in x and then another one
+ 
+
+ align:start position:0%
+interval in x and then another one
+interval and y another one interval and
+
+ align:start position:0%
+interval and y another one interval and
+ 
+
+ align:start position:0%
+interval and y another one interval and
+z there's a point in 3d
+
+ align:start position:0%
+z there's a point in 3d
+ 
+
+ align:start position:0%
+z there's a point in 3d
+and you have to reduce it to the surface
+
+ align:start position:0%
+and you have to reduce it to the surface
+ 
+
+ align:start position:0%
+and you have to reduce it to the surface
+of a sphere well you just normalize it
+
+ align:start position:0%
+of a sphere well you just normalize it
+ 
+
+ align:start position:0%
+of a sphere well you just normalize it
+so you have a three vector you just take
+
+ align:start position:0%
+so you have a three vector you just take
+ 
+
+ align:start position:0%
+so you have a three vector you just take
+the unit vector version of that and
+
+ align:start position:0%
+the unit vector version of that and
+ 
+
+ align:start position:0%
+the unit vector version of that and
+you're done
+
+ align:start position:0%
+you're done
+ 
+
+ align:start position:0%
+you're done
+so does that give me a uniform
+
+ align:start position:0%
+so does that give me a uniform
+ 
+
+ align:start position:0%
+so does that give me a uniform
+distribution on the surface of the
+
+ align:start position:0%
+distribution on the surface of the
+ 
+
+ align:start position:0%
+distribution on the surface of the
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+no okay so we have some head shaking and
+
+ align:start position:0%
+no okay so we have some head shaking and
+ 
+
+ align:start position:0%
+no okay so we have some head shaking and
+that's because well this the uh cube
+
+ align:start position:0%
+that's because well this the uh cube
+ 
+
+ align:start position:0%
+that's because well this the uh cube
+is uh has these corners
+
+ align:start position:0%
+is uh has these corners
+ 
+
+ align:start position:0%
+is uh has these corners
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+there will be a higher density of points
+
+ align:start position:0%
+there will be a higher density of points
+ 
+
+ align:start position:0%
+there will be a higher density of points
+in the directions of the corners than
+
+ align:start position:0%
+in the directions of the corners than
+ 
+
+ align:start position:0%
+in the directions of the corners than
+there will be
+
+ align:start position:0%
+there will be
+ 
+
+ align:start position:0%
+there will be
+where your
+
+ align:start position:0%
+where your
+ 
+
+ align:start position:0%
+where your
+tangent
+
+ align:start position:0%
+tangent
+ 
+
+ align:start position:0%
+tangent
+where the sphere is tangent to the cube
+
+ align:start position:0%
+where the sphere is tangent to the cube
+ 
+
+ align:start position:0%
+where the sphere is tangent to the cube
+it's better though this one's only off
+
+ align:start position:0%
+it's better though this one's only off
+ 
+
+ align:start position:0%
+it's better though this one's only off
+by um
+
+ align:start position:0%
+by um
+ 
+
+ align:start position:0%
+by um
+i forget factor of 4 over pi
+
+ align:start position:0%
+i forget factor of 4 over pi
+ 
+
+ align:start position:0%
+i forget factor of 4 over pi
+4 over pi i think or
+
+ align:start position:0%
+4 over pi i think or
+ 
+
+ align:start position:0%
+4 over pi i think or
+or pi over 3 no 4 over pi
+
+ align:start position:0%
+or pi over 3 no 4 over pi
+ 
+
+ align:start position:0%
+or pi over 3 no 4 over pi
+so so this isn't too bad
+
+ align:start position:0%
+so so this isn't too bad
+ 
+
+ align:start position:0%
+so so this isn't too bad
+so how can you do better how can you
+
+ align:start position:0%
+so how can you do better how can you
+ 
+
+ align:start position:0%
+so how can you do better how can you
+take this idea and fix it so that you
+
+ align:start position:0%
+take this idea and fix it so that you
+ 
+
+ align:start position:0%
+take this idea and fix it so that you
+don't have the corner problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tessellated shapes yeah we could teslate
+
+ align:start position:0%
+tessellated shapes yeah we could teslate
+ 
+
+ align:start position:0%
+tessellated shapes yeah we could teslate
+the surface of the sphere using regular
+
+ align:start position:0%
+the surface of the sphere using regular
+ 
+
+ align:start position:0%
+the surface of the sphere using regular
+solids
+
+ align:start position:0%
+solids
+ 
+
+ align:start position:0%
+solids
+the magic things that plato organized
+
+ align:start position:0%
+the magic things that plato organized
+ 
+
+ align:start position:0%
+the magic things that plato organized
+his society about
+
+ align:start position:0%
+his society about
+ 
+
+ align:start position:0%
+his society about
+that's certainly a good good approach
+
+ align:start position:0%
+that's certainly a good good approach
+ 
+
+ align:start position:0%
+that's certainly a good good approach
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+is there some way of discarding some of
+
+ align:start position:0%
+is there some way of discarding some of
+ 
+
+ align:start position:0%
+is there some way of discarding some of
+these points that we
+
+ align:start position:0%
+these points that we
+ 
+
+ align:start position:0%
+these points that we
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+we're generating here
+
+ align:start position:0%
+we're generating here
+ 
+
+ align:start position:0%
+we're generating here
+okay so contracting this aggregation
+
+ align:start position:0%
+okay so contracting this aggregation
+ 
+
+ align:start position:0%
+okay so contracting this aggregation
+near the corners uh we could introduce
+
+ align:start position:0%
+near the corners uh we could introduce
+ 
+
+ align:start position:0%
+near the corners uh we could introduce
+some sort of weight and for example if
+
+ align:start position:0%
+some sort of weight and for example if
+ 
+
+ align:start position:0%
+some sort of weight and for example if
+we could uh give the points when
+
+ align:start position:0%
+we could uh give the points when
+ 
+
+ align:start position:0%
+we could uh give the points when
+projected a weight we could just make it
+
+ align:start position:0%
+projected a weight we could just make it
+ 
+
+ align:start position:0%
+projected a weight we could just make it
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+inversely proportional to the radius
+
+ align:start position:0%
+inversely proportional to the radius
+ 
+
+ align:start position:0%
+inversely proportional to the radius
+so if we're far out then
+
+ align:start position:0%
+so if we're far out then
+ 
+
+ align:start position:0%
+so if we're far out then
+so uh that that's an uh good idea um
+
+ align:start position:0%
+so uh that that's an uh good idea um
+ 
+
+ align:start position:0%
+so uh that that's an uh good idea um
+another idea is to say well
+
+ align:start position:0%
+another idea is to say well
+ 
+
+ align:start position:0%
+another idea is to say well
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we could just throw away all the points
+
+ align:start position:0%
+we could just throw away all the points
+ 
+
+ align:start position:0%
+we could just throw away all the points
+that are outside the sphere
+
+ align:start position:0%
+that are outside the sphere
+ 
+
+ align:start position:0%
+that are outside the sphere
+and then we have a random distribution
+
+ align:start position:0%
+and then we have a random distribution
+ 
+
+ align:start position:0%
+and then we have a random distribution
+of points in a sphere
+
+ align:start position:0%
+of points in a sphere
+ 
+
+ align:start position:0%
+of points in a sphere
+right so we we again we generate points
+
+ align:start position:0%
+right so we we again we generate points
+ 
+
+ align:start position:0%
+right so we we again we generate points
+in the cube but then we check whether
+
+ align:start position:0%
+in the cube but then we check whether
+ 
+
+ align:start position:0%
+in the cube but then we check whether
+their radius is bigger than one and if
+
+ align:start position:0%
+their radius is bigger than one and if
+ 
+
+ align:start position:0%
+their radius is bigger than one and if
+it's bigger than one we chuck it out and
+
+ align:start position:0%
+it's bigger than one we chuck it out and
+ 
+
+ align:start position:0%
+it's bigger than one we chuck it out and
+it has a disadvantage that you're not
+
+ align:start position:0%
+it has a disadvantage that you're not
+ 
+
+ align:start position:0%
+it has a disadvantage that you're not
+generating points at a fixed rate that
+
+ align:start position:0%
+generating points at a fixed rate that
+ 
+
+ align:start position:0%
+generating points at a fixed rate that
+it costs you more sometimes because you
+
+ align:start position:0%
+it costs you more sometimes because you
+ 
+
+ align:start position:0%
+it costs you more sometimes because you
+have to go back and regenerate it and
+
+ align:start position:0%
+have to go back and regenerate it and
+ 
+
+ align:start position:0%
+have to go back and regenerate it and
+maybe regenerate it again
+
+ align:start position:0%
+maybe regenerate it again
+ 
+
+ align:start position:0%
+maybe regenerate it again
+so there's a
+
+ align:start position:0%
+so there's a
+ 
+
+ align:start position:0%
+so there's a
+disadvantage but uh what happens then
+
+ align:start position:0%
+disadvantage but uh what happens then
+ 
+
+ align:start position:0%
+disadvantage but uh what happens then
+well then we have
+
+ align:start position:0%
+well then we have
+ 
+
+ align:start position:0%
+well then we have
+a uniform sampling of the inside of the
+
+ align:start position:0%
+a uniform sampling of the inside of the
+ 
+
+ align:start position:0%
+a uniform sampling of the inside of the
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+uh and that's
+
+ align:start position:0%
+uh and that's
+ 
+
+ align:start position:0%
+uh and that's
+almost good enough now we just need to
+
+ align:start position:0%
+almost good enough now we just need to
+ 
+
+ align:start position:0%
+almost good enough now we just need to
+project all those points onto the
+
+ align:start position:0%
+project all those points onto the
+ 
+
+ align:start position:0%
+project all those points onto the
+surface of the sphere and if we want to
+
+ align:start position:0%
+surface of the sphere and if we want to
+ 
+
+ align:start position:0%
+surface of the sphere and if we want to
+avoid nasty numerical problems we might
+
+ align:start position:0%
+avoid nasty numerical problems we might
+ 
+
+ align:start position:0%
+avoid nasty numerical problems we might
+want to also throw away
+
+ align:start position:0%
+want to also throw away
+ 
+
+ align:start position:0%
+want to also throw away
+all points that are close to the origin
+
+ align:start position:0%
+all points that are close to the origin
+ 
+
+ align:start position:0%
+all points that are close to the origin
+right because then we might have numbers
+
+ align:start position:0%
+right because then we might have numbers
+ 
+
+ align:start position:0%
+right because then we might have numbers
+you're dividing by by normalizing the
+
+ align:start position:0%
+you're dividing by by normalizing the
+ 
+
+ align:start position:0%
+you're dividing by by normalizing the
+vector to make it a unit vector you
+
+ align:start position:0%
+vector to make it a unit vector you
+ 
+
+ align:start position:0%
+vector to make it a unit vector you
+might be dividing by some small number
+
+ align:start position:0%
+might be dividing by some small number
+ 
+
+ align:start position:0%
+might be dividing by some small number
+which is going to introduce some error
+
+ align:start position:0%
+which is going to introduce some error
+ 
+
+ align:start position:0%
+which is going to introduce some error
+and biases so you you generate
+
+ align:start position:0%
+and biases so you you generate
+ 
+
+ align:start position:0%
+and biases so you you generate
+points uniform in a cube
+
+ align:start position:0%
+points uniform in a cube
+ 
+
+ align:start position:0%
+points uniform in a cube
+you throw away all points above some
+
+ align:start position:0%
+you throw away all points above some
+ 
+
+ align:start position:0%
+you throw away all points above some
+certain radius and you throw away all
+
+ align:start position:0%
+certain radius and you throw away all
+ 
+
+ align:start position:0%
+certain radius and you throw away all
+points that are below a small radius
+
+ align:start position:0%
+points that are below a small radius
+ 
+
+ align:start position:0%
+points that are below a small radius
+i've drawn it a little big there
+
+ align:start position:0%
+i've drawn it a little big there
+ 
+
+ align:start position:0%
+i've drawn it a little big there
+and then normalize them and so there's
+
+ align:start position:0%
+and then normalize them and so there's
+ 
+
+ align:start position:0%
+and then normalize them and so there's
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there's your point uh
+
+ align:start position:0%
+there's your point uh
+ 
+
+ align:start position:0%
+there's your point uh
+sampling of the surface of the sphere
+
+ align:start position:0%
+sampling of the surface of the sphere
+ 
+
+ align:start position:0%
+sampling of the surface of the sphere
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we may not care about the sphere
+
+ align:start position:0%
+we may not care about the sphere
+ 
+
+ align:start position:0%
+we may not care about the sphere
+but i can't draw this in 4d
+
+ align:start position:0%
+but i can't draw this in 4d
+ 
+
+ align:start position:0%
+but i can't draw this in 4d
+but it works exactly the same way right
+
+ align:start position:0%
+but it works exactly the same way right
+ 
+
+ align:start position:0%
+but it works exactly the same way right
+if we want to have a nice uniform
+
+ align:start position:0%
+if we want to have a nice uniform
+ 
+
+ align:start position:0%
+if we want to have a nice uniform
+sampling of 4d space one way
+
+ align:start position:0%
+sampling of 4d space one way
+ 
+
+ align:start position:0%
+sampling of 4d space one way
+a random sampling one way of doing it is
+
+ align:start position:0%
+a random sampling one way of doing it is
+ 
+
+ align:start position:0%
+a random sampling one way of doing it is
+exactly this we do a four dimensional
+
+ align:start position:0%
+exactly this we do a four dimensional
+ 
+
+ align:start position:0%
+exactly this we do a four dimensional
+equivalent of the cube
+
+ align:start position:0%
+equivalent of the cube
+ 
+
+ align:start position:0%
+equivalent of the cube
+so we generate four random numbers
+
+ align:start position:0%
+so we generate four random numbers
+ 
+
+ align:start position:0%
+so we generate four random numbers
+for x y z and say w
+
+ align:start position:0%
+for x y z and say w
+ 
+
+ align:start position:0%
+for x y z and say w
+and then we check whether there are
+
+ align:start position:0%
+and then we check whether there are
+ 
+
+ align:start position:0%
+and then we check whether there are
+sum of squares is larger than one if so
+
+ align:start position:0%
+sum of squares is larger than one if so
+ 
+
+ align:start position:0%
+sum of squares is larger than one if so
+try again
+
+ align:start position:0%
+try again
+ 
+
+ align:start position:0%
+try again
+if not
+
+ align:start position:0%
+if not
+ 
+
+ align:start position:0%
+if not
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+turn them into a unit quaternion
+
+ align:start position:0%
+turn them into a unit quaternion
+ 
+
+ align:start position:0%
+turn them into a unit quaternion
+and that gives us a very simple way of
+
+ align:start position:0%
+and that gives us a very simple way of
+ 
+
+ align:start position:0%
+and that gives us a very simple way of
+getting a uniform
+
+ align:start position:0%
+getting a uniform
+ 
+
+ align:start position:0%
+getting a uniform
+sampling of that space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+there was mention of uh
+
+ align:start position:0%
+there was mention of uh
+ 
+
+ align:start position:0%
+there was mention of uh
+regular polyhedra so that's an important
+
+ align:start position:0%
+regular polyhedra so that's an important
+ 
+
+ align:start position:0%
+regular polyhedra so that's an important
+thing to think about so we could
+
+ align:start position:0%
+thing to think about so we could
+ 
+
+ align:start position:0%
+thing to think about so we could
+so what what are they well they're
+
+ align:start position:0%
+so what what are they well they're
+ 
+
+ align:start position:0%
+so what what are they well they're
+tetrahedra the
+
+ align:start position:0%
+tetrahedra the
+ 
+
+ align:start position:0%
+tetrahedra the
+hexahedra
+
+ align:start position:0%
+hexahedra
+ 
+
+ align:start position:0%
+hexahedra
+octahedra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dodecahedra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ikosa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are the so-called regular
+
+ align:start position:0%
+so these are the so-called regular
+ 
+
+ align:start position:0%
+so these are the so-called regular
+solids
+
+ align:start position:0%
+solids
+ 
+
+ align:start position:0%
+solids
+regular polyhedra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means that
+
+ align:start position:0%
+that means that
+ 
+
+ align:start position:0%
+that means that
+all of their faces are the
+
+ align:start position:0%
+all of their faces are the
+ 
+
+ align:start position:0%
+all of their faces are the
+same and those aren't the only objects
+
+ align:start position:0%
+same and those aren't the only objects
+ 
+
+ align:start position:0%
+same and those aren't the only objects
+of interest but uh let's start with
+
+ align:start position:0%
+of interest but uh let's start with
+ 
+
+ align:start position:0%
+of interest but uh let's start with
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if we uh want to
+
+ align:start position:0%
+if we uh want to
+ 
+
+ align:start position:0%
+if we uh want to
+sample the surface of the sphere
+
+ align:start position:0%
+sample the surface of the sphere
+ 
+
+ align:start position:0%
+sample the surface of the sphere
+one other way is to project out well
+
+ align:start position:0%
+one other way is to project out well
+ 
+
+ align:start position:0%
+one other way is to project out well
+these are obviously on spheres but you
+
+ align:start position:0%
+these are obviously on spheres but you
+ 
+
+ align:start position:0%
+these are obviously on spheres but you
+can imagine them placed at the origin
+
+ align:start position:0%
+can imagine them placed at the origin
+ 
+
+ align:start position:0%
+can imagine them placed at the origin
+and then projected out onto the sphere
+
+ align:start position:0%
+and then projected out onto the sphere
+ 
+
+ align:start position:0%
+and then projected out onto the sphere
+and we get
+
+ align:start position:0%
+and we get
+ 
+
+ align:start position:0%
+and we get
+great circles wherever there's an edge
+
+ align:start position:0%
+great circles wherever there's an edge
+ 
+
+ align:start position:0%
+great circles wherever there's an edge
+on one of these objects
+
+ align:start position:0%
+on one of these objects
+ 
+
+ align:start position:0%
+on one of these objects
+and so that's a way of dividing up the
+
+ align:start position:0%
+and so that's a way of dividing up the
+ 
+
+ align:start position:0%
+and so that's a way of dividing up the
+sphere in a perfectly regular way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's what's the problem well
+
+ align:start position:0%
+what's what's the problem well
+ 
+
+ align:start position:0%
+what's what's the problem well
+the only thing is that there aren't too
+
+ align:start position:0%
+the only thing is that there aren't too
+ 
+
+ align:start position:0%
+the only thing is that there aren't too
+many facets so tetrahedra 4 6 8
+
+ align:start position:0%
+many facets so tetrahedra 4 6 8
+ 
+
+ align:start position:0%
+many facets so tetrahedra 4 6 8
+12 20.
+
+ align:start position:0%
+12 20.
+ 
+
+ align:start position:0%
+12 20.
+so we're not dividing the sphere up very
+
+ align:start position:0%
+so we're not dividing the sphere up very
+ 
+
+ align:start position:0%
+so we're not dividing the sphere up very
+finely and as plato discovered that's it
+
+ align:start position:0%
+finely and as plato discovered that's it
+ 
+
+ align:start position:0%
+finely and as plato discovered that's it
+there aren't any more
+
+ align:start position:0%
+there aren't any more
+ 
+
+ align:start position:0%
+there aren't any more
+so that means we have to subdivide and
+
+ align:start position:0%
+so that means we have to subdivide and
+ 
+
+ align:start position:0%
+so that means we have to subdivide and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you might say well wait what happened to
+
+ align:start position:0%
+you might say well wait what happened to
+ 
+
+ align:start position:0%
+you might say well wait what happened to
+the soccer ball how many faces on the
+
+ align:start position:0%
+the soccer ball how many faces on the
+ 
+
+ align:start position:0%
+the soccer ball how many faces on the
+soccer ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can people play games and not even
+
+ align:start position:0%
+how can people play games and not even
+ 
+
+ align:start position:0%
+how can people play games and not even
+know how many anyway 32
+
+ align:start position:0%
+know how many anyway 32
+ 
+
+ align:start position:0%
+know how many anyway 32
+so it's a mix of the dodecahedron and
+
+ align:start position:0%
+so it's a mix of the dodecahedron and
+ 
+
+ align:start position:0%
+so it's a mix of the dodecahedron and
+the icosahedron and it uh and it's not
+
+ align:start position:0%
+the icosahedron and it uh and it's not
+ 
+
+ align:start position:0%
+the icosahedron and it uh and it's not
+in this group because it's semi-regular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh i guess these are
+
+ align:start position:0%
+so uh i guess these are
+ 
+
+ align:start position:0%
+so uh i guess these are
+plato gets created for these
+
+ align:start position:0%
+plato gets created for these
+ 
+
+ align:start position:0%
+plato gets created for these
+and archimedes gets created for the
+
+ align:start position:0%
+and archimedes gets created for the
+ 
+
+ align:start position:0%
+and archimedes gets created for the
+semi-regular one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a there's a whole bunch uh
+
+ align:start position:0%
+and there's a there's a whole bunch uh
+ 
+
+ align:start position:0%
+and there's a there's a whole bunch uh
+i don't know
+
+ align:start position:0%
+i don't know
+ 
+
+ align:start position:0%
+i don't know
+14 or it depends on how you count
+
+ align:start position:0%
+14 or it depends on how you count
+ 
+
+ align:start position:0%
+14 or it depends on how you count
+so uh these objects are all their own
+
+ align:start position:0%
+so uh these objects are all their own
+ 
+
+ align:start position:0%
+so uh these objects are all their own
+mirror images
+
+ align:start position:0%
+mirror images
+ 
+
+ align:start position:0%
+mirror images
+but when you get to the semi-regular
+
+ align:start position:0%
+but when you get to the semi-regular
+ 
+
+ align:start position:0%
+but when you get to the semi-regular
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+there's one
+
+ align:start position:0%
+there's one
+ 
+
+ align:start position:0%
+there's one
+where the mirror image is actually
+
+ align:start position:0%
+where the mirror image is actually
+ 
+
+ align:start position:0%
+where the mirror image is actually
+different in other words you can't
+
+ align:start position:0%
+different in other words you can't
+ 
+
+ align:start position:0%
+different in other words you can't
+rotate it to bring it into alignment
+
+ align:start position:0%
+rotate it to bring it into alignment
+ 
+
+ align:start position:0%
+rotate it to bring it into alignment
+with itself
+
+ align:start position:0%
+with itself
+ 
+
+ align:start position:0%
+with itself
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+if you count that it's 14 if you don't
+
+ align:start position:0%
+if you count that it's 14 if you don't
+ 
+
+ align:start position:0%
+if you count that it's 14 if you don't
+count that it's 13. and the soccer ball
+
+ align:start position:0%
+count that it's 13. and the soccer ball
+ 
+
+ align:start position:0%
+count that it's 13. and the soccer ball
+somewhere in here the
+
+ align:start position:0%
+somewhere in here the
+ 
+
+ align:start position:0%
+somewhere in here the
+the icosa dodecahedron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the difference well the
+
+ align:start position:0%
+so what's the difference well the
+ 
+
+ align:start position:0%
+so what's the difference well the
+semi-regular ones still have facets that
+
+ align:start position:0%
+semi-regular ones still have facets that
+ 
+
+ align:start position:0%
+semi-regular ones still have facets that
+are regular polygons
+
+ align:start position:0%
+are regular polygons
+ 
+
+ align:start position:0%
+are regular polygons
+so you know triangle squares
+
+ align:start position:0%
+so you know triangle squares
+ 
+
+ align:start position:0%
+so you know triangle squares
+dodecahedrons
+
+ align:start position:0%
+dodecahedrons
+ 
+
+ align:start position:0%
+dodecahedrons
+hexagons et cetera
+
+ align:start position:0%
+hexagons et cetera
+ 
+
+ align:start position:0%
+hexagons et cetera
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you're now allowed
+
+ align:start position:0%
+you're now allowed
+ 
+
+ align:start position:0%
+you're now allowed
+to have more than one type so over here
+
+ align:start position:0%
+to have more than one type so over here
+ 
+
+ align:start position:0%
+to have more than one type so over here
+once you decided on you know triangles
+
+ align:start position:0%
+once you decided on you know triangles
+ 
+
+ align:start position:0%
+once you decided on you know triangles
+for the facets they all have to be
+
+ align:start position:0%
+for the facets they all have to be
+ 
+
+ align:start position:0%
+for the facets they all have to be
+triangles over here you can have a mix
+
+ align:start position:0%
+triangles over here you can have a mix
+ 
+
+ align:start position:0%
+triangles over here you can have a mix
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+the soccer ball is a mix of
+
+ align:start position:0%
+the soccer ball is a mix of
+ 
+
+ align:start position:0%
+the soccer ball is a mix of
+hexagons and dotec
+
+ align:start position:0%
+hexagons and dotec
+ 
+
+ align:start position:0%
+hexagons and dotec
+and five-sided figures
+
+ align:start position:0%
+and five-sided figures
+ 
+
+ align:start position:0%
+and five-sided figures
+so that gives you a
+
+ align:start position:0%
+so that gives you a
+ 
+
+ align:start position:0%
+so that gives you a
+larger variety but
+
+ align:start position:0%
+larger variety but
+ 
+
+ align:start position:0%
+larger variety but
+you know think about the fact that they
+
+ align:start position:0%
+you know think about the fact that they
+ 
+
+ align:start position:0%
+you know think about the fact that they
+all have to have the same edge length
+
+ align:start position:0%
+all have to have the same edge length
+ 
+
+ align:start position:0%
+all have to have the same edge length
+so for example if you had
+
+ align:start position:0%
+so for example if you had
+ 
+
+ align:start position:0%
+so for example if you had
+you know a uh this is if you had an
+
+ align:start position:0%
+you know a uh this is if you had an
+ 
+
+ align:start position:0%
+you know a uh this is if you had an
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+where you're mixing triangles and
+
+ align:start position:0%
+where you're mixing triangles and
+ 
+
+ align:start position:0%
+where you're mixing triangles and
+squares
+
+ align:start position:0%
+squares
+ 
+
+ align:start position:0%
+squares
+since they have edging matrix
+
+ align:start position:0%
+since they have edging matrix
+ 
+
+ align:start position:0%
+since they have edging matrix
+edge length the facet area is different
+
+ align:start position:0%
+edge length the facet area is different
+ 
+
+ align:start position:0%
+edge length the facet area is different
+and you know there's obviously some
+
+ align:start position:0%
+and you know there's obviously some
+ 
+
+ align:start position:0%
+and you know there's obviously some
+formula for
+
+ align:start position:0%
+formula for
+ 
+
+ align:start position:0%
+formula for
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the area of
+
+ align:start position:0%
+the area of
+ 
+
+ align:start position:0%
+the area of
+regular polygon in terms of the number
+
+ align:start position:0%
+regular polygon in terms of the number
+ 
+
+ align:start position:0%
+regular polygon in terms of the number
+of edges and the edge length
+
+ align:start position:0%
+of edges and the edge length
+ 
+
+ align:start position:0%
+of edges and the edge length
+okay so that means that over here we had
+
+ align:start position:0%
+okay so that means that over here we had
+ 
+
+ align:start position:0%
+okay so that means that over here we had
+equal cells and so it made it very easy
+
+ align:start position:0%
+equal cells and so it made it very easy
+ 
+
+ align:start position:0%
+equal cells and so it made it very easy
+to have a uniform sampling over there
+
+ align:start position:0%
+to have a uniform sampling over there
+ 
+
+ align:start position:0%
+to have a uniform sampling over there
+it's a little bit more tricky because
+
+ align:start position:0%
+it's a little bit more tricky because
+ 
+
+ align:start position:0%
+it's a little bit more tricky because
+now we've got to deal with the fact that
+
+ align:start position:0%
+now we've got to deal with the fact that
+ 
+
+ align:start position:0%
+now we've got to deal with the fact that
+the facets are not equal in area the bet
+
+ align:start position:0%
+the facets are not equal in area the bet
+ 
+
+ align:start position:0%
+the facets are not equal in area the bet
+the good part is that there are more of
+
+ align:start position:0%
+the good part is that there are more of
+ 
+
+ align:start position:0%
+the good part is that there are more of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so that's in uh in on the sphere in 3d
+
+ align:start position:0%
+so that's in uh in on the sphere in 3d
+ 
+
+ align:start position:0%
+so that's in uh in on the sphere in 3d
+we're talking about
+
+ align:start position:0%
+we're talking about
+ 
+
+ align:start position:0%
+we're talking about
+a sphere in the 4d and so
+
+ align:start position:0%
+a sphere in the 4d and so
+ 
+
+ align:start position:0%
+a sphere in the 4d and so
+you know plato and archimedes didn't uh
+
+ align:start position:0%
+you know plato and archimedes didn't uh
+ 
+
+ align:start position:0%
+you know plato and archimedes didn't uh
+think too much about those so we can't
+
+ align:start position:0%
+think too much about those so we can't
+ 
+
+ align:start position:0%
+think too much about those so we can't
+resort to them
+
+ align:start position:0%
+resort to them
+ 
+
+ align:start position:0%
+resort to them
+but um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those figures come into play again
+
+ align:start position:0%
+those figures come into play again
+ 
+
+ align:start position:0%
+those figures come into play again
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+in 4d we're talking about rotations
+
+ align:start position:0%
+in 4d we're talking about rotations
+ 
+
+ align:start position:0%
+in 4d we're talking about rotations
+and we we're looking for regular
+
+ align:start position:0%
+and we we're looking for regular
+ 
+
+ align:start position:0%
+and we we're looking for regular
+patterns of
+
+ align:start position:0%
+patterns of
+ 
+
+ align:start position:0%
+patterns of
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+in this space and so
+
+ align:start position:0%
+in this space and so
+ 
+
+ align:start position:0%
+in this space and so
+one way we can think about that is in
+
+ align:start position:0%
+one way we can think about that is in
+ 
+
+ align:start position:0%
+one way we can think about that is in
+in terms of rotations of these objects
+
+ align:start position:0%
+in terms of rotations of these objects
+ 
+
+ align:start position:0%
+in terms of rotations of these objects
+so let's just do one and see see how
+
+ align:start position:0%
+so let's just do one and see see how
+ 
+
+ align:start position:0%
+so let's just do one and see see how
+that goes so the the aim here is again
+
+ align:start position:0%
+that goes so the the aim here is again
+ 
+
+ align:start position:0%
+that goes so the the aim here is again
+to find some methods for uniformly
+
+ align:start position:0%
+to find some methods for uniformly
+ 
+
+ align:start position:0%
+to find some methods for uniformly
+something the space of rotations so that
+
+ align:start position:0%
+something the space of rotations so that
+ 
+
+ align:start position:0%
+something the space of rotations so that
+if say we do a search so we've we've got
+
+ align:start position:0%
+if say we do a search so we've we've got
+ 
+
+ align:start position:0%
+if say we do a search so we've we've got
+this object in a sensor and we have a
+
+ align:start position:0%
+this object in a sensor and we have a
+ 
+
+ align:start position:0%
+this object in a sensor and we have a
+model in the library and we're trying to
+
+ align:start position:0%
+model in the library and we're trying to
+ 
+
+ align:start position:0%
+model in the library and we're trying to
+figure out
+
+ align:start position:0%
+figure out
+ 
+
+ align:start position:0%
+figure out
+is there some way of rotating this to
+
+ align:start position:0%
+is there some way of rotating this to
+ 
+
+ align:start position:0%
+is there some way of rotating this to
+bring it into alignment with that
+
+ align:start position:0%
+bring it into alignment with that
+ 
+
+ align:start position:0%
+bring it into alignment with that
+and that could be part of recognition
+
+ align:start position:0%
+and that could be part of recognition
+ 
+
+ align:start position:0%
+and that could be part of recognition
+that you know we have multiple objects
+
+ align:start position:0%
+that you know we have multiple objects
+ 
+
+ align:start position:0%
+that you know we have multiple objects
+in the library
+
+ align:start position:0%
+in the library
+ 
+
+ align:start position:0%
+in the library
+which of them can we match but of course
+
+ align:start position:0%
+which of them can we match but of course
+ 
+
+ align:start position:0%
+which of them can we match but of course
+we can't match them directly we first
+
+ align:start position:0%
+we can't match them directly we first
+ 
+
+ align:start position:0%
+we can't match them directly we first
+have to get them rotated
+
+ align:start position:0%
+have to get them rotated
+ 
+
+ align:start position:0%
+have to get them rotated
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+how do we pick the rotations
+
+ align:start position:0%
+how do we pick the rotations
+ 
+
+ align:start position:0%
+how do we pick the rotations
+well to be efficient we don't want to be
+
+ align:start position:0%
+well to be efficient we don't want to be
+ 
+
+ align:start position:0%
+well to be efficient we don't want to be
+sampling parts of the rotation space
+
+ align:start position:0%
+sampling parts of the rotation space
+ 
+
+ align:start position:0%
+sampling parts of the rotation space
+more densely than other parts
+
+ align:start position:0%
+more densely than other parts
+ 
+
+ align:start position:0%
+more densely than other parts
+that be you know the equivalent of
+
+ align:start position:0%
+that be you know the equivalent of
+ 
+
+ align:start position:0%
+that be you know the equivalent of
+searching spending all your time
+
+ align:start position:0%
+searching spending all your time
+ 
+
+ align:start position:0%
+searching spending all your time
+searching around the poles
+
+ align:start position:0%
+searching around the poles
+ 
+
+ align:start position:0%
+searching around the poles
+and so we're trying to find a uniform
+
+ align:start position:0%
+and so we're trying to find a uniform
+ 
+
+ align:start position:0%
+and so we're trying to find a uniform
+way of sampling this
+
+ align:start position:0%
+way of sampling this
+ 
+
+ align:start position:0%
+way of sampling this
+slightly hard to imagine the space
+
+ align:start position:0%
+slightly hard to imagine the space
+ 
+
+ align:start position:0%
+slightly hard to imagine the space
+but let's uh
+
+ align:start position:0%
+but let's uh
+ 
+
+ align:start position:0%
+but let's uh
+start simply with the hexahedron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and think about its rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+well first there's the identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i mean by rotations i mean by
+
+ align:start position:0%
+so what i mean by rotations i mean by
+ 
+
+ align:start position:0%
+so what i mean by rotations i mean by
+rotations that you you take the object
+
+ align:start position:0%
+rotations that you you take the object
+ 
+
+ align:start position:0%
+rotations that you you take the object
+then you rotate it and then the
+
+ align:start position:0%
+then you rotate it and then the
+ 
+
+ align:start position:0%
+then you rotate it and then the
+faces line up with the faces and the
+
+ align:start position:0%
+faces line up with the faces and the
+ 
+
+ align:start position:0%
+faces line up with the faces and the
+edges line up with the edges and the
+
+ align:start position:0%
+edges line up with the edges and the
+ 
+
+ align:start position:0%
+edges line up with the edges and the
+vertices line up with the vertices
+
+ align:start position:0%
+vertices line up with the vertices
+ 
+
+ align:start position:0%
+vertices line up with the vertices
+okay so the identity so in terms of
+
+ align:start position:0%
+okay so the identity so in terms of
+ 
+
+ align:start position:0%
+okay so the identity so in terms of
+quaternions
+
+ align:start position:0%
+quaternions
+ 
+
+ align:start position:0%
+quaternions
+that looks like that
+
+ align:start position:0%
+that looks like that
+ 
+
+ align:start position:0%
+that looks like that
+it has a zero vector part and a scalar
+
+ align:start position:0%
+it has a zero vector part and a scalar
+ 
+
+ align:start position:0%
+it has a zero vector part and a scalar
+part of one
+
+ align:start position:0%
+part of one
+ 
+
+ align:start position:0%
+part of one
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we can think about a rotation let's say
+
+ align:start position:0%
+we can think about a rotation let's say
+ 
+
+ align:start position:0%
+we can think about a rotation let's say
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+through let's say pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so that's going to be let's see
+
+ align:start position:0%
+and so that's going to be let's see
+ 
+
+ align:start position:0%
+and so that's going to be let's see
+cosine pi over 2 is zero
+
+ align:start position:0%
+cosine pi over 2 is zero
+ 
+
+ align:start position:0%
+cosine pi over 2 is zero
+sine pi over 2 is one
+
+ align:start position:0%
+sine pi over 2 is one
+ 
+
+ align:start position:0%
+sine pi over 2 is one
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so that's that quaternion
+
+ align:start position:0%
+so that's that quaternion
+ 
+
+ align:start position:0%
+so that's that quaternion
+so that just turns it 180 degrees about
+
+ align:start position:0%
+so that just turns it 180 degrees about
+ 
+
+ align:start position:0%
+so that just turns it 180 degrees about
+the x
+
+ align:start position:0%
+the x
+ 
+
+ align:start position:0%
+the x
+x axis
+
+ align:start position:0%
+x axis
+ 
+
+ align:start position:0%
+x axis
+and naturally i can do the same thing
+
+ align:start position:0%
+and naturally i can do the same thing
+ 
+
+ align:start position:0%
+and naturally i can do the same thing
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i've already got
+
+ align:start position:0%
+so i've already got
+ 
+
+ align:start position:0%
+so i've already got
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+distinct rotations that line that object
+
+ align:start position:0%
+distinct rotations that line that object
+ 
+
+ align:start position:0%
+distinct rotations that line that object
+up with itself
+
+ align:start position:0%
+up with itself
+ 
+
+ align:start position:0%
+up with itself
+well i don't have to rotate 180 degrees
+
+ align:start position:0%
+well i don't have to rotate 180 degrees
+ 
+
+ align:start position:0%
+well i don't have to rotate 180 degrees
+oh how about minus 180 degrees
+
+ align:start position:0%
+oh how about minus 180 degrees
+ 
+
+ align:start position:0%
+oh how about minus 180 degrees
+well of course that's the same right so
+
+ align:start position:0%
+well of course that's the same right so
+ 
+
+ align:start position:0%
+well of course that's the same right so
+that that doesn't add anything but i
+
+ align:start position:0%
+that that doesn't add anything but i
+ 
+
+ align:start position:0%
+that that doesn't add anything but i
+could think about rotating pi over two
+
+ align:start position:0%
+could think about rotating pi over two
+ 
+
+ align:start position:0%
+could think about rotating pi over two
+so let's try that
+
+ align:start position:0%
+so let's try that
+ 
+
+ align:start position:0%
+so let's try that
+so pi over 2 that's going to be cosine
+
+ align:start position:0%
+so pi over 2 that's going to be cosine
+ 
+
+ align:start position:0%
+so pi over 2 that's going to be cosine
+of pi over 4 which is 1 over square root
+
+ align:start position:0%
+of pi over 4 which is 1 over square root
+ 
+
+ align:start position:0%
+of pi over 4 which is 1 over square root
+of 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i get that
+
+ align:start position:0%
+so i get that
+ 
+
+ align:start position:0%
+so i get that
+and now here i could talk about minus pi
+
+ align:start position:0%
+and now here i could talk about minus pi
+ 
+
+ align:start position:0%
+and now here i could talk about minus pi
+over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because these these two aren't the
+
+ align:start position:0%
+right because these these two aren't the
+ 
+
+ align:start position:0%
+right because these these two aren't the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+this one is not the negative of that
+
+ align:start position:0%
+this one is not the negative of that
+ 
+
+ align:start position:0%
+this one is not the negative of that
+because the
+
+ align:start position:0%
+because the
+ 
+
+ align:start position:0%
+because the
+real part hasn't changed sign whereas
+
+ align:start position:0%
+real part hasn't changed sign whereas
+ 
+
+ align:start position:0%
+real part hasn't changed sign whereas
+with these guys if i flip the sign of x
+
+ align:start position:0%
+with these guys if i flip the sign of x
+ 
+
+ align:start position:0%
+with these guys if i flip the sign of x
+i get a different quaternion but
+
+ align:start position:0%
+i get a different quaternion but
+ 
+
+ align:start position:0%
+i get a different quaternion but
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+minus q is the same rotation as plus q
+
+ align:start position:0%
+minus q is the same rotation as plus q
+ 
+
+ align:start position:0%
+minus q is the same rotation as plus q
+so i flip the sign of that to get a
+
+ align:start position:0%
+so i flip the sign of that to get a
+ 
+
+ align:start position:0%
+so i flip the sign of that to get a
+different quaternion but it's the same
+
+ align:start position:0%
+different quaternion but it's the same
+ 
+
+ align:start position:0%
+different quaternion but it's the same
+rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i can do this for
+
+ align:start position:0%
+okay so i can do this for
+ 
+
+ align:start position:0%
+okay so i can do this for
+x y
+
+ align:start position:0%
+x y
+ 
+
+ align:start position:0%
+x y
+and then i can do it for z
+
+ align:start position:0%
+and then i can do it for z
+ 
+
+ align:start position:0%
+and then i can do it for z
+so i get six of those
+
+ align:start position:0%
+so i get six of those
+ 
+
+ align:start position:0%
+so i get six of those
+uh we've got four there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+10 rotations
+
+ align:start position:0%
+10 rotations
+ 
+
+ align:start position:0%
+10 rotations
+10 samples of the space that we're
+
+ align:start position:0%
+10 samples of the space that we're
+ 
+
+ align:start position:0%
+10 samples of the space that we're
+interested in and so question is you
+
+ align:start position:0%
+interested in and so question is you
+ 
+
+ align:start position:0%
+interested in and so question is you
+know are they more
+
+ align:start position:0%
+know are they more
+ 
+
+ align:start position:0%
+know are they more
+and they're kind of two different ways
+
+ align:start position:0%
+and they're kind of two different ways
+ 
+
+ align:start position:0%
+and they're kind of two different ways
+to proceed the one is sort of
+
+ align:start position:0%
+to proceed the one is sort of
+ 
+
+ align:start position:0%
+to proceed the one is sort of
+geometrically you know look at the
+
+ align:start position:0%
+geometrically you know look at the
+ 
+
+ align:start position:0%
+geometrically you know look at the
+diagram how many other ways can i rotate
+
+ align:start position:0%
+diagram how many other ways can i rotate
+ 
+
+ align:start position:0%
+diagram how many other ways can i rotate
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and the other one is to
+
+ align:start position:0%
+and the other one is to
+ 
+
+ align:start position:0%
+and the other one is to
+just think of this as a exercise in
+
+ align:start position:0%
+just think of this as a exercise in
+ 
+
+ align:start position:0%
+just think of this as a exercise in
+quaternion multiplication
+
+ align:start position:0%
+quaternion multiplication
+ 
+
+ align:start position:0%
+quaternion multiplication
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+let's just do one of those
+
+ align:start position:0%
+let's just do one of those
+ 
+
+ align:start position:0%
+let's just do one of those
+so for example i could pull out
+
+ align:start position:0%
+so for example i could pull out
+ 
+
+ align:start position:0%
+so for example i could pull out
+of that table you know i can
+
+ align:start position:0%
+of that table you know i can
+ 
+
+ align:start position:0%
+of that table you know i can
+now i can try and generate the whole
+
+ align:start position:0%
+now i can try and generate the whole
+ 
+
+ align:start position:0%
+now i can try and generate the whole
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+just by
+
+ align:start position:0%
+just by
+ 
+
+ align:start position:0%
+just by
+multiplication take what i've got take
+
+ align:start position:0%
+multiplication take what i've got take
+ 
+
+ align:start position:0%
+multiplication take what i've got take
+two pairs let's take
+
+ align:start position:0%
+two pairs let's take
+ 
+
+ align:start position:0%
+two pairs let's take
+because it's not very interesting taking
+
+ align:start position:0%
+because it's not very interesting taking
+ 
+
+ align:start position:0%
+because it's not very interesting taking
+the identity but so let's take something
+
+ align:start position:0%
+the identity but so let's take something
+ 
+
+ align:start position:0%
+the identity but so let's take something
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+okay according to our rules for
+
+ align:start position:0%
+okay according to our rules for
+ 
+
+ align:start position:0%
+okay according to our rules for
+multiplication i get 0 minus
+
+ align:start position:0%
+multiplication i get 0 minus
+ 
+
+ align:start position:0%
+multiplication i get 0 minus
+x dot y
+
+ align:start position:0%
+x dot y
+ 
+
+ align:start position:0%
+x dot y
+which is zero
+
+ align:start position:0%
+which is zero
+ 
+
+ align:start position:0%
+which is zero
+and then we get zero times x plus zero
+
+ align:start position:0%
+and then we get zero times x plus zero
+ 
+
+ align:start position:0%
+and then we get zero times x plus zero
+times y
+
+ align:start position:0%
+times y
+ 
+
+ align:start position:0%
+times y
+plus x cross y
+
+ align:start position:0%
+plus x cross y
+ 
+
+ align:start position:0%
+plus x cross y
+and so that's
+
+ align:start position:0%
+and so that's
+ 
+
+ align:start position:0%
+and so that's
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+minus z
+
+ align:start position:0%
+minus z
+ 
+
+ align:start position:0%
+minus z
+hmm uh no
+
+ align:start position:0%
+hmm uh no
+ 
+
+ align:start position:0%
+hmm uh no
+well that's already in the table right
+
+ align:start position:0%
+well that's already in the table right
+ 
+
+ align:start position:0%
+well that's already in the table right
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so that doesn't add uh to the table so
+
+ align:start position:0%
+so that doesn't add uh to the table so
+ 
+
+ align:start position:0%
+so that doesn't add uh to the table so
+let's take something else
+
+ align:start position:0%
+let's take something else
+ 
+
+ align:start position:0%
+let's take something else
+let's take uh some of these 1 over
+
+ align:start position:0%
+let's take uh some of these 1 over
+ 
+
+ align:start position:0%
+let's take uh some of these 1 over
+square root of 2
+
+ align:start position:0%
+square root of 2
+ 
+
+ align:start position:0%
+square root of 2
+1 x 1 over square root of 2
+
+ align:start position:0%
+1 x 1 over square root of 2
+ 
+
+ align:start position:0%
+1 x 1 over square root of 2
+1 y
+
+ align:start position:0%
+1 y
+ 
+
+ align:start position:0%
+1 y
+ok that's going to be more interesting 1
+
+ align:start position:0%
+ok that's going to be more interesting 1
+ 
+
+ align:start position:0%
+ok that's going to be more interesting 1
+times 1 is 1
+
+ align:start position:0%
+times 1 is 1
+ 
+
+ align:start position:0%
+times 1 is 1
+minus x dot y is zero
+
+ align:start position:0%
+minus x dot y is zero
+ 
+
+ align:start position:0%
+minus x dot y is zero
+and our the one over square root of two
+
+ align:start position:0%
+and our the one over square root of two
+ 
+
+ align:start position:0%
+and our the one over square root of two
+gives us
+
+ align:start position:0%
+gives us
+ 
+
+ align:start position:0%
+gives us
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+and then the vector part is one times y
+
+ align:start position:0%
+and then the vector part is one times y
+ 
+
+ align:start position:0%
+and then the vector part is one times y
+plus one times x
+
+ align:start position:0%
+plus one times x
+ 
+
+ align:start position:0%
+plus one times x
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x cross y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's one half
+
+ align:start position:0%
+so that's one half
+ 
+
+ align:start position:0%
+so that's one half
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x hat
+
+ align:start position:0%
+x hat
+ 
+
+ align:start position:0%
+x hat
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+plus x hat y hat t hat
+
+ align:start position:0%
+plus x hat y hat t hat
+ 
+
+ align:start position:0%
+plus x hat y hat t hat
+so that's a new one
+
+ align:start position:0%
+so that's a new one
+ 
+
+ align:start position:0%
+so that's a new one
+so the axis of rotation
+
+ align:start position:0%
+so the axis of rotation
+ 
+
+ align:start position:0%
+so the axis of rotation
+is uh 1 1 1
+
+ align:start position:0%
+is uh 1 1 1
+ 
+
+ align:start position:0%
+is uh 1 1 1
+and if you want to make it the unit
+
+ align:start position:0%
+and if you want to make it the unit
+ 
+
+ align:start position:0%
+and if you want to make it the unit
+vector it's 1 over square root of 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's not not in this table
+
+ align:start position:0%
+and that's not not in this table
+ 
+
+ align:start position:0%
+and that's not not in this table
+and the angle is cosine theta over 2 is
+
+ align:start position:0%
+and the angle is cosine theta over 2 is
+ 
+
+ align:start position:0%
+and the angle is cosine theta over 2 is
+a half
+
+ align:start position:0%
+a half
+ 
+
+ align:start position:0%
+a half
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's see that means
+
+ align:start position:0%
+let's see that means
+ 
+
+ align:start position:0%
+let's see that means
+theta over 2 is
+
+ align:start position:0%
+theta over 2 is
+ 
+
+ align:start position:0%
+theta over 2 is
+pi over 3
+
+ align:start position:0%
+pi over 3
+ 
+
+ align:start position:0%
+pi over 3
+so theta is 2 pi over 3.
+
+ align:start position:0%
+so theta is 2 pi over 3.
+ 
+
+ align:start position:0%
+so theta is 2 pi over 3.
+so that's an interesting
+
+ align:start position:0%
+so that's an interesting
+ 
+
+ align:start position:0%
+so that's an interesting
+new rotation
+
+ align:start position:0%
+new rotation
+ 
+
+ align:start position:0%
+new rotation
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you look at the cube
+
+ align:start position:0%
+if you look at the cube
+ 
+
+ align:start position:0%
+if you look at the cube
+that corresponds to one of its corners
+
+ align:start position:0%
+that corresponds to one of its corners
+ 
+
+ align:start position:0%
+that corresponds to one of its corners
+so we're taking this the origin and
+
+ align:start position:0%
+so we're taking this the origin and
+ 
+
+ align:start position:0%
+so we're taking this the origin and
+connecting it to a corner
+
+ align:start position:0%
+connecting it to a corner
+ 
+
+ align:start position:0%
+connecting it to a corner
+so that's the axis
+
+ align:start position:0%
+so that's the axis
+ 
+
+ align:start position:0%
+so that's the axis
+and we're rotating by
+
+ align:start position:0%
+and we're rotating by
+ 
+
+ align:start position:0%
+and we're rotating by
+120 degrees
+
+ align:start position:0%
+120 degrees
+ 
+
+ align:start position:0%
+120 degrees
+and you can see that that's a rotation
+
+ align:start position:0%
+and you can see that that's a rotation
+ 
+
+ align:start position:0%
+and you can see that that's a rotation
+of the cube that does bring us back into
+
+ align:start position:0%
+of the cube that does bring us back into
+ 
+
+ align:start position:0%
+of the cube that does bring us back into
+alignment with ourselves right if you
+
+ align:start position:0%
+alignment with ourselves right if you
+ 
+
+ align:start position:0%
+alignment with ourselves right if you
+rotate 120 degrees about that axis
+
+ align:start position:0%
+rotate 120 degrees about that axis
+ 
+
+ align:start position:0%
+rotate 120 degrees about that axis
+everything falls back into place and so
+
+ align:start position:0%
+everything falls back into place and so
+ 
+
+ align:start position:0%
+everything falls back into place and so
+we're just about out of time but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can proceed two ways the one is you
+
+ align:start position:0%
+we can proceed two ways the one is you
+ 
+
+ align:start position:0%
+we can proceed two ways the one is you
+know look at that example and some
+
+ align:start position:0%
+know look at that example and some
+ 
+
+ align:start position:0%
+know look at that example and some
+others and we get a total of 24
+
+ align:start position:0%
+others and we get a total of 24
+ 
+
+ align:start position:0%
+others and we get a total of 24
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+or we can
+
+ align:start position:0%
+or we can
+ 
+
+ align:start position:0%
+or we can
+if we're more mathematically inclined we
+
+ align:start position:0%
+if we're more mathematically inclined we
+ 
+
+ align:start position:0%
+if we're more mathematically inclined we
+can go this way
+
+ align:start position:0%
+can go this way
+ 
+
+ align:start position:0%
+can go this way
+or you can you know it's fun to write a
+
+ align:start position:0%
+or you can you know it's fun to write a
+ 
+
+ align:start position:0%
+or you can you know it's fun to write a
+little program that just implements
+
+ align:start position:0%
+little program that just implements
+ 
+
+ align:start position:0%
+little program that just implements
+quaternion multiplication and then
+
+ align:start position:0%
+quaternion multiplication and then
+ 
+
+ align:start position:0%
+quaternion multiplication and then
+builds this uh table by taking pairwise
+
+ align:start position:0%
+builds this uh table by taking pairwise
+ 
+
+ align:start position:0%
+builds this uh table by taking pairwise
+products and seeing whether you get
+
+ align:start position:0%
+products and seeing whether you get
+ 
+
+ align:start position:0%
+products and seeing whether you get
+something new
+
+ align:start position:0%
+something new
+ 
+
+ align:start position:0%
+something new
+and eventually you'll run out and you'll
+
+ align:start position:0%
+and eventually you'll run out and you'll
+ 
+
+ align:start position:0%
+and eventually you'll run out and you'll
+have 24 of them at that point
+
+ align:start position:0%
+have 24 of them at that point
+ 
+
+ align:start position:0%
+have 24 of them at that point
+okay next time we'll start talking about
+
+ align:start position:0%
+okay next time we'll start talking about
+ 
+
+ align:start position:0%
+okay next time we'll start talking about
+relative orientation which is more
+
+ align:start position:0%
+relative orientation which is more
+ 
+
+ align:start position:0%
+relative orientation which is more
+relevant to
+
+ align:start position:0%
+relevant to
+ 
+
+ align:start position:0%
+relevant to
+binocular visions
\ No newline at end of file
diff --git a/kwbDWPrPfQI.txt b/kwbDWPrPfQI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b2e0cb080f081ef83ec91fdd465f50638ce0050
--- /dev/null
+++ b/kwbDWPrPfQI.txt
@@ -0,0 +1,291 @@
+align:start position:0%
+ 
+if our objective is to keep the mean
+
+ align:start position:0%
+if our objective is to keep the mean
+ 
+
+ align:start position:0%
+if our objective is to keep the mean
+squared estimation error small then the
+
+ align:start position:0%
+squared estimation error small then the
+ 
+
+ align:start position:0%
+squared estimation error small then the
+best possible estimator is the
+
+ align:start position:0%
+best possible estimator is the
+ 
+
+ align:start position:0%
+best possible estimator is the
+conditional expectation but sometimes
+
+ align:start position:0%
+conditional expectation but sometimes
+ 
+
+ align:start position:0%
+conditional expectation but sometimes
+the conditional expectation is hard to
+
+ align:start position:0%
+the conditional expectation is hard to
+ 
+
+ align:start position:0%
+the conditional expectation is hard to
+calculate maybe we're missing the
+
+ align:start position:0%
+calculate maybe we're missing the
+ 
+
+ align:start position:0%
+calculate maybe we're missing the
+details of the various probability
+
+ align:start position:0%
+details of the various probability
+ 
+
+ align:start position:0%
+details of the various probability
+distributions or maybe we have all the
+
+ align:start position:0%
+distributions or maybe we have all the
+ 
+
+ align:start position:0%
+distributions or maybe we have all the
+distributions that we need but the
+
+ align:start position:0%
+distributions that we need but the
+ 
+
+ align:start position:0%
+distributions that we need but the
+formulas are complicated
+
+ align:start position:0%
+formulas are complicated
+ 
+
+ align:start position:0%
+formulas are complicated
+after all the conditional expectation
+
+ align:start position:0%
+after all the conditional expectation
+ 
+
+ align:start position:0%
+after all the conditional expectation
+can be a complicated nonlinear function
+
+ align:start position:0%
+can be a complicated nonlinear function
+ 
+
+ align:start position:0%
+can be a complicated nonlinear function
+of the observations for this reason we
+
+ align:start position:0%
+of the observations for this reason we
+ 
+
+ align:start position:0%
+of the observations for this reason we
+may want to consider an estimator that
+
+ align:start position:0%
+may want to consider an estimator that
+ 
+
+ align:start position:0%
+may want to consider an estimator that
+has a simpler structure an estimator
+
+ align:start position:0%
+has a simpler structure an estimator
+ 
+
+ align:start position:0%
+has a simpler structure an estimator
+that is a linear function of the data
+
+ align:start position:0%
+that is a linear function of the data
+ 
+
+ align:start position:0%
+that is a linear function of the data
+and then within this class of estimators
+
+ align:start position:0%
+and then within this class of estimators
+ 
+
+ align:start position:0%
+and then within this class of estimators
+find the one that results in the
+
+ align:start position:0%
+find the one that results in the
+ 
+
+ align:start position:0%
+find the one that results in the
+smallest possible mean squared error in
+
+ align:start position:0%
+smallest possible mean squared error in
+ 
+
+ align:start position:0%
+smallest possible mean squared error in
+this lecture we will formulate this
+
+ align:start position:0%
+this lecture we will formulate this
+ 
+
+ align:start position:0%
+this lecture we will formulate this
+linear least squares estimation problem
+
+ align:start position:0%
+linear least squares estimation problem
+ 
+
+ align:start position:0%
+linear least squares estimation problem
+and then solve it we will see that the
+
+ align:start position:0%
+and then solve it we will see that the
+ 
+
+ align:start position:0%
+and then solve it we will see that the
+solution is given by a simple formula
+
+ align:start position:0%
+solution is given by a simple formula
+ 
+
+ align:start position:0%
+solution is given by a simple formula
+that involves only the means variances
+
+ align:start position:0%
+that involves only the means variances
+ 
+
+ align:start position:0%
+that involves only the means variances
+and covariances of the random variables
+
+ align:start position:0%
+and covariances of the random variables
+ 
+
+ align:start position:0%
+and covariances of the random variables
+involved because of the simplicity of
+
+ align:start position:0%
+involved because of the simplicity of
+ 
+
+ align:start position:0%
+involved because of the simplicity of
+the method linear estimators are used
+
+ align:start position:0%
+the method linear estimators are used
+ 
+
+ align:start position:0%
+the method linear estimators are used
+quite often especially in systems where
+
+ align:start position:0%
+quite often especially in systems where
+ 
+
+ align:start position:0%
+quite often especially in systems where
+estimates need to be computed quickly in
+
+ align:start position:0%
+estimates need to be computed quickly in
+ 
+
+ align:start position:0%
+estimates need to be computed quickly in
+real time as observations are obtained
+
+ align:start position:0%
+real time as observations are obtained
+ 
+
+ align:start position:0%
+real time as observations are obtained
+we will look into some of the
+
+ align:start position:0%
+we will look into some of the
+ 
+
+ align:start position:0%
+we will look into some of the
+mathematical properties of the linear
+
+ align:start position:0%
+mathematical properties of the linear
+ 
+
+ align:start position:0%
+mathematical properties of the linear
+least mean squares estimator and The
+
+ align:start position:0%
+least mean squares estimator and The
+ 
+
+ align:start position:0%
+least mean squares estimator and The
+Associated mean squared error revisit an
+
+ align:start position:0%
+Associated mean squared error revisit an
+ 
+
+ align:start position:0%
+Associated mean squared error revisit an
+example from the previous lecture and
+
+ align:start position:0%
+example from the previous lecture and
+ 
+
+ align:start position:0%
+example from the previous lecture and
+finally close with some comments on the
+
+ align:start position:0%
+finally close with some comments on the
+ 
+
+ align:start position:0%
+finally close with some comments on the
+ways that this estimator can be used
\ No newline at end of file
diff --git a/l8GqOCN8M-w.txt b/l8GqOCN8M-w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f4d978e770f4401fcbcc7d08a79e06a6f986e21c
--- /dev/null
+++ b/l8GqOCN8M-w.txt
@@ -0,0 +1,4051 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, so by this time,
+most of you should have
+
+had your meetings with
+your masters.
+
+How many of you had meetings
+with your masters?
+
+Who didn't yet?
+
+AUDIENCE: Today.
+
+PROFESSOR: Today?
+
+And Friday.
+
+Who hasn't scheduled
+a meeting?
+
+So are you talking to them,
+and do you know--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK, make sure you get
+masters meetings scheduled
+
+because this is a very
+important part.
+
+We are getting feedback
+from the masters.
+
+I think they are giving you guys
+a lot of good advice, and
+
+so make sure you schedule, you
+go, you meet, get that result,
+
+use that result.
+
+It's very hard to arrange that
+kind of a senior person
+
+spending a lot of time
+with only two of
+
+you at a given time.
+
+That's a really good ratio
+to have, so take
+
+advantage of that.
+
+OK, so also, I think at this
+point, most of the beta issues
+
+for project one, we have been
+probably worked with, and they
+
+have some issues some people
+looked at that they are
+
+performance code.
+
+They were not happy because
+the thing is this.
+
+You can always run everything
+instantaneously if it doesn't
+
+have to produce a
+correct answer.
+
+You can just return, and so part
+of performance is also it
+
+has to have some correctness.
+
+So certain amount of correctness
+has to be passed
+
+before we can give
+performer grade.
+
+So some people have
+this question.
+
+Why are you giving me a
+correctness grade because it
+
+seemed to run?
+
+But if you haven't done the
+right checks and stuff like
+
+that, then it's unfair for other
+people because there's
+
+no way people who do the correct
+implementation can
+
+match that performance
+because we're using
+
+that as upper bound.
+
+So make sure you do that.
+
+And another issue people had
+was when you go to masters,
+
+you're going to work with one
+or two other students.
+
+And in your group, you're
+going to share all the
+
+material with your group
+member and nobody else.
+
+But between the beta and final,
+you get opportunity to
+
+basically get input from your
+masters, and also see what the
+
+other people who are coming
+to a project in your
+
+discussion have done.
+
+So it's OK for you to
+see those code.
+
+You can't take the code home.
+
+You can't just say give me a
+print-out, I am going to take
+
+home and re-implement.
+
+That doesn't count, but if you
+see some clever things they
+
+have done, it's all
+here to learn.
+
+Class is all the mostly
+about learning.
+
+However we have to grade you, so
+it's not all about grading,
+
+it's about learning.
+
+So we are trying to get a
+balance where we opportunity
+
+for you to learn from
+your peers.
+
+So if you go look at other
+people's code, if you find
+
+something cool they
+have done, learn.
+
+And also if you [UNINTELLIGIBLE]
+
+for you [UNINTELLIGIBLE]
+
+say, look, I did
+something cool.
+
+It's a good learning experience
+in there, so that's
+
+one opportunity you have to talk
+to other people on other
+
+groups, to basically learn
+something or find some
+
+interesting tidbits of how
+to get good performance.
+
+And hopefully, you learn some
+interesting things and able to
+
+implement that in your final.
+
+OK?
+
+So today we are going to talk
+about memory systems and
+
+performance engineering.
+
+So if you look at basic idea
+of what memory systems, you
+
+want to build a computer
+that seemed to have
+
+a really fast memory.
+
+You don't want things
+to be slow.
+
+For example, a long time ago,
+people build these computers
+
+where memory's always slow,
+everything [UNINTELLIGIBLE]
+
+further away.
+
+It doesn't help anybody.
+
+The way we know how to do that
+is to build small amount of
+
+memory very close to
+the processor.
+
+You can't build a huge amount
+of things all close to you.
+
+That doesn't work, doesn't
+scale like that.
+
+And we made a cache just like
+that, and you build larger and
+
+larger memory [UNINTELLIGIBLE]
+going down, and the illusion
+
+is you want to give the illusion
+of you have huge
+
+amount of memory.
+
+Everybody's very close to you.
+
+OK, so it looks like you have
+millions of friends, that you
+
+talk to everybody, and
+that doesn't happen.
+
+But how do you give
+that illusion?
+
+And the way that you give that
+illusion is when you use
+
+normal programming practice,
+when you normally using data,
+
+people have found there
+are two properties.
+
+The first thing is called
+temporal locality.
+
+That means if I use some data
+item, there's a good chance I
+
+use that data item
+again very soon.
+
+There is something I haven't
+used for a long time, probably
+
+has a good chance I will
+not use it for a
+
+very, very long time.
+
+So can I take advantage
+of temporal locality?
+
+So that mean some data will be
+get for use a lot of time, in
+
+a very quick [UNINTELLIGIBLE],
+so those things should be very
+
+near to you because you might.
+
+Other one is spatial locality.
+
+That means if I use some data
+item, there's a good chance
+
+you'll be using data items next
+to that, closer to that.
+
+So can we take advantage
+of that?
+
+So those two properties help you
+help the compiler to fool
+
+the system, fool everybody,
+thinking that it has this huge
+
+amount of memory very close to
+you, but internally doesn't.
+
+Unfortunately, since it's trying
+to fool you, it doesn't
+
+work all the time, and when it
+doesn't work, it's good to
+
+recognize and able to
+fix those things.
+
+So I showed this picture
+sometime ago, too.
+
+Memories in a big hierarchy.
+
+L1, L2, in fact, we have L3
+cache and a memory, disk,
+
+tapes, it can go up and down.
+
+And the key thing is when you go
+here, you're starting from
+
+registers, you have very
+small amount of
+
+things, very fast access.
+
+Here, we have almost
+infinite amount of
+
+things, very slow access.
+
+And the two reasons why this has
+to be smart because first
+
+of all, those things
+are very expensive.
+
+And second of course, you can't
+[UNINTELLIGIBLE] too
+
+much, and when you go down,
+things get somewhat cheaper.
+
+So that was one of the kind of
+economic incentive here.
+
+So I talked about cache issues,
+and I'm going to go
+
+through this again because we
+are really going to dig deep
+
+into these things.
+
+So when you have a cache, that
+means you have a small memory
+
+close to you that's basically
+shadowing something sitting
+
+behind you.
+
+So when you ask for the data in
+the cache, there are many
+
+reasons why it's not there.
+
+First thing is cold miss.
+
+What that means is you're asking
+for something that you
+
+have never asked before.
+
+It's the first time you're
+asking, so the data is
+
+probably sitting way behind
+in your memory where,
+
+[UNINTELLIGIBLE]
+
+in a disk.
+
+We haven't even loaded
+it in there.
+
+And the first time you have to
+get it, so that get pulled in,
+
+and so this seems to be a place
+where there's nothing
+
+you can do.
+
+But another part of locality is
+a thing called prefetching.
+
+These modern processors
+have a crystal ball.
+
+They carry most of the things
+that branch prediction and
+
+stuff is trying to predict
+what you want to do.
+
+You can do the same
+thing in memory.
+
+You can look at what
+you have done.
+
+And Intel has this huge amount
+of circuitry that they don't
+
+tell anybody what they do, but
+they're trying to predict what
+
+you might fetch next, what data
+you might look for next.
+
+And if it is working well,
+something you had never, ever
+
+looked before, it might deduce
+that you might need it and go
+
+get it for you.
+
+So if that works, great.
+
+So then there's thing called
+capacity miss.
+
+What that means is as I said,
+I am trying to keep my best
+
+friends, or the people I will
+be working with a lot--
+
+Oh, nice.
+
+What's going on here?
+
+Please start later.
+
+OK.
+
+--the people I'm going to work
+a lot with, close to me.
+
+The problem is I can have only
+certain number of friends, and
+
+if you have more than that,
+I can't keep everybody.
+
+So hopefully, your program is
+going to use a lot what we
+
+call the working set that
+can fit in the cache.
+
+And at that point, you get all
+of those people, like I said,
+
+get everybody into one room,
+and the problem is if your
+
+party spills over from
+the room, then
+
+there's a lot of issues.
+
+But if everybody fits in the
+room, things are very nice.
+
+You can have a good interaction,
+continuous
+
+interaction, with them.
+
+And what happens is, if not, the
+worst case is the caches
+
+have eviction policy, normally
+is called least recently used.
+
+That means if I don't have room
+in the cache, I figure
+
+out the cache line that I
+haven't touched for longest,
+
+and I get rid of that,
+bring the next one.
+
+So that's a good policy.
+
+It fits in your locality
+thing, but when
+
+will did not work?
+
+[UNINTELLIGIBLE]
+
+going to figure out when least
+recently used will create a
+
+really bad problem
+in capacity.
+
+AUDIENCE: [INAUDIBLE]
+
+just one.
+
+Say you're [INAUDIBLE] set,
+and that set is, by one,
+
+bigger than the [INAUDIBLE]
+
+missing.
+
+PROFESSOR: Very good.
+
+So what you're going through,
+you're going round some data
+
+again and again, and that amount
+of data is one bigger
+
+than your cache line.
+
+You are going to have
+no locality because
+
+[UNINTELLIGIBLE], and when you
+go to, just before you use
+
+that data, they said, oops, I
+need to bring one more data.
+
+I need to evict something, and
+who am I going to evict?
+
+The guy I'm going to use next
+because it was the least
+
+recently used thing.
+
+So it goes, and then you go
+there, and you bring that.
+
+Who's it going to evict?
+
+You're going to evict the
+one I just brought.
+
+You're going to evict the next
+one that I am just about to
+
+use and bring that one.
+
+And you go use that, and then
+to use the next one, you're
+
+going evict the one you're
+just about to use.
+
+So by going and doing that, you
+basically get no locality.
+
+So that's a really bad
+problem in here.
+
+So another interesting thing is
+called a conflict misses.
+
+Conflict misses says normally,
+when you have a cache--
+
+so what we have is you have
+this large storage, which
+
+[UNINTELLIGIBLE]
+
+the memory, you're going to map
+into smaller storage in
+
+here, which is cache.
+
+So one way to say is any of
+this value line can be
+
+anywhere here.
+
+That's called fully
+associative cache.
+
+Implementing that is somewhat
+complicated, so the other
+
+extreme is called direct
+map cache.
+
+What that means is this segment,
+the same size here,
+
+can map into here, and then
+the next segment also
+
+can map into here.
+
+That means if you get this cache
+line here, it can be
+
+only mapped into one
+place in this here.
+
+This cache line can only be
+here, and also this cache line
+
+can also only be here if
+it is the same offset.
+
+So that means for every cache
+line, there's only one
+
+location in the cache.
+
+So here, what would be
+really sad scenario?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah, I mean
+I assume I have a
+
+lot of these slots.
+
+I read something here, and the
+next time I read something
+
+here, next time I read something
+here, and I go round
+
+and round this way.
+
+I might be touching only very
+few number of data items, but
+
+they also mapping into one
+cache line even though my
+
+working set is very small
+than the cache.
+
+I still don't have
+any cache usage
+
+because I am having conflicts.
+
+And then there are two other
+misses when you're going to
+
+multi-process.
+
+We'll go through them
+in later lectures.
+
+One is called true sharing.
+
+That means there are caches
+private to each core, and what
+
+happens is if one core uses some
+data, you've have to get
+
+the cache line there.
+
+If the other core wants to use
+that data, you have to bring
+
+the cache line back there, and
+the cache lines can ping-pong
+
+[UNINTELLIGIBLE] that.
+
+False sharing is even
+a worst way.
+
+So what happens is if the first
+processor here touches
+
+this value of the cache line,
+second processor touches this
+
+value of the cache line.
+
+We're not sharing anything,
+but unfortunately, the two
+
+things I'm using sits next to
+each other, so when I ride
+
+this thing, I get the cache
+line, he doesn't.
+
+When he need to ride this
+thing, he has to
+
+get the cache line.
+
+So I am seemingly using
+independent data, but I am
+
+bouncing cache line in between,
+and if that happened,
+
+that going to have a huge
+big performance impact.
+
+So these other things.
+
+The last two, we'll get
+to a little bit later.
+
+So today I am going to start
+with modeling how caches work
+
+with a very simplistic cache.
+
+So here's, assume, my cache.
+
+I have 32 kilobytes in here.
+
+This is a direct map cache.
+
+That means that in my memory, 32
+kilobyte chucks get mapped
+
+to direct [UNINTELLIGIBLE].
+
+This 32 kilobyte get
+mapped here.
+
+That 32 kilobyte get
+mapped here.
+
+And the cache line inside is 64
+bytes, 64, and that means I
+
+have basically
+[UNINTELLIGIBLE PHRASE].
+
+32 kilobyte in here.
+
+OK?
+
+So just remember this as we go
+on doing this, we will use
+
+this as a formula.
+
+OK?
+
+And we assume if you getting
+the cache, [UNINTELLIGIBLE]
+
+single cycle, if you
+miss 100 cycles.
+
+OK, so it's nice numbers
+to do that.
+
+And so the first thing is we
+have a reference like this.
+
+OK?
+
+You go from [i] equals 0 to
+[i] less than very large
+
+number, A[i].
+
+I just go to accessing memory
+like one after another after
+
+another after another.
+
+So you see how this is
+going on in here?
+
+So also I am accessing integers,
+so that means four
+
+bytes at a time in cache line.
+
+So what happens here?
+
+So I assume size of int is four,
+so you're getting four
+
+bytes in here.
+
+So yeah, you're doing s reads
+to A. I'm accessing
+
+s elements in here.
+
+And you have 16 elements
+of a per cache line.
+
+OK, you see why 16 if there?
+
+Because I have 64 in here,
+64 bytes in here.
+
+Each time axises four bytes,
+so I have 16 of integers in
+
+cache line.
+
+AUDIENCE: [INAUDIBLE]
+
+bits or bytes?
+
+PROFESSOR: Bytes.
+
+Byte.
+
+Did I say bits?
+
+No, bytes.
+
+So what happens is if it axises
+the same element, 15 of
+
+every 16 is in the cache because
+when we are going one
+
+after the first guy, cache miss,
+I had to go bring it,
+
+and the next 15, I have
+brought to it.
+
+It's in the cache.
+
+So what should be my cost?
+
+[UNINTELLIGIBLE]
+
+cost of memory access.
+
+I am accessing s data, and
+1/16th of that is a cache
+
+miss, 15/16th is a cache hit.
+
+So basically total
+[UNINTELLIGIBLE]
+
+is a 15/16th of s is a cache
+hit, and other 1/16th I have
+
+100 times cycles I need because
+it's a cache miss.
+
+Everybody good so far?
+
+OK, so what type of locality
+do we have here?
+
+First of all, do we
+have locality?
+
+Who thinks we have locality?
+
+OK, lot of people thinks
+we have locality.
+
+What type?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Spatial locality
+because what we are doing is
+
+we are accessing the nearby
+elements even though we are
+
+not getting back any of the
+data yet, so we get some
+
+spacial locality axis here.
+
+That's good, so this is our
+very -- most simple
+
+thing we can do.
+
+So what kind of misses are we
+going to have in the cache?
+
+Cold misses.
+
+I'm missing because I have never
+seen that data before,
+
+so it's a cold miss in here.
+
+OK, so that's that.
+
+Let's look at this one.
+
+I'm accessing A[0]
+
+s times.
+
+OK?
+
+What's the total access time?
+
+How many cache misses
+am I going to get?
+
+One, so I basically have 100
+time for the first cache miss,
+
+and s minus 1 for the rest
+basically it's a hit.
+
+OK?
+
+That's good, so what kind
+of locality's this?
+
+Spatial or temporal.
+
+There's not too many choices.
+
+Or none.
+
+How many people think spatial?
+
+How many people think
+temporal?
+
+How many people said there's
+none locality?
+
+OK, that's a lot of temporal.
+
+OK, you want to get
+[UNINTELLIGIBLE].
+
+That's temporal locality here
+because you're accessing to
+
+the same thing again and again
+and again, same data.
+
+So this is--
+
+Oh, OK.
+
+Want to restart, OK.
+
+Wait a little.
+
+So this is only time we
+notice in a hurry.
+
+Every time, I go to do
+something, I get hourglass.
+
+So what kind of misses
+are we getting?
+
+Trick question.
+
+I got one cold miss, and
+that's about it.
+
+And the rest I don't
+have any misses.
+
+So if I have a miss,
+it's a cold miss.
+
+OK, so here I am doing something
+interesting.
+
+So what the heck is
+in this list?
+
+So I'm accessing A[i]
+
+[UNINTELLIGIBLE]
+
+this 2 to the power number,
+one shifted to the entire
+
+miss, 2 to the power N. I
+shifted between 4 and 13.
+
+What this 13?
+
+Why is 13?
+
+Less than 13.
+
+What's 2 the power of 13?
+
+I think I got this right.
+
+AUDIENCE: 8,192.
+
+PROFESSOR: What's 2 to
+the power of 13?
+
+AUDIENCE: 8,192.
+
+PROFESSOR: Yeah, 8K.
+
+And I have 32K.
+
+So 8K of 32 [UNINTELLIGIBLE].
+
+8K of integers, which is each
+as 4 bytes is how much?
+
+32K.
+
+So what this says is everything
+I access should fit
+
+into the cache.
+
+I am accessing data like that.
+
+I'm going back and accessing
+data like that.
+
+I'm going back and accessing
+data like that, and it should
+
+all fit into the cache.
+
+Do you see what I do?
+
+I access up to 2 to the power
+of 18, and I go back and
+
+access that again.
+
+I'm just going back
+and back because
+
+of the model operation.
+
+Everybody see what's going on?
+
+So how many cache misses
+should I have?
+
+AUDIENCE: There are four
+cache [INAUDIBLE].
+
+PROFESSOR: OK, how many cache
+lines I would be accessing if
+
+I am doing i1 2 to
+the power N?
+
+[i]
+
+mod 2 to the power N.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: So one miss
+for each axis line
+
+the first time around.
+
+Afterward, it's only
+in the cache.
+
+So how many axis lines?
+
+2 to the power N.
+
+Is that right?
+
+I think this is wrong.
+
+Oh, yeah, this is right
+because every axis--
+
+So in the cache line,
+how many--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: This is four.
+
+So there are 16 entries here.
+
+16 entries in here.
+
+OK, only one of them basically
+misses that, so that means if
+
+2 to the power N axises--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You are doing 2 to
+the power N axises before you
+
+go back in here.
+
+So what you're doing
+is you are--
+
+you make this many axises before
+you go back again.
+
+OK?
+
+And how many axises assigned to
+be in the same cache line?
+
+You have 64 bytes
+in the cache.
+
+OK each axis is four.
+
+16.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: 16.
+
+So that's true [UNINTELLIGIBLE].
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah, but what I'm
+saying is I might not access
+
+the [UNINTELLIGIBLE]
+
+because if any small.
+
+I only access a certain amount
+of cache line, so I'm
+
+accessing a part of the cache.
+
+I might not go through the--
+can everybody see this, how
+
+this is working?
+
+Because if I'm only accessing,
+we'll say, accessing one, if
+
+this is, we'll say, 2
+to the power of 5.
+
+OK, I am not going to access
+the entire cache line.
+
+[UNINTELLIGIBLE]
+
+cache is I'm going to
+[UNINTELLIGIBLE]
+
+go through the cache.
+
+So this many cache lines
+I'm accessing.
+
+OK, and the first time I access
+that, I get a cache
+
+miss, and after that, it say
+everything is in the cache.
+
+Everybody's following me?
+
+Or are we like lost in here?
+
+How many people are lost?
+
+OK, let's do this.
+
+So what happens is if you have
+a modular 2 to the power N.
+
+What that means is I'm going
+to keep accessing one to
+
+somewhere 2 to the power N, and
+the next one, I am going
+
+back here again.
+
+That's my axises, basically,
+because it goes
+
+[UNINTELLIGIBLE]
+
+accessing to the power of N.
+
+I nicely said n is
+between 4 and 13.
+
+So n is 13 means the maximum
+I can do is 8K.
+
+8K increase.
+
+8K increase equals 32K
+kilobytes of memory.
+
+So that means you don't
+have any option of
+
+overwriting the cache.
+
+So you go to cache,
+[UNINTELLIGIBLE].
+
+You don't wrap around
+in the cache.
+
+Do you see that?
+
+OK, you know wrap arounding is
+so bad, that means all these
+
+things is going to fit in the
+cache, and then when you get
+
+[UNINTELLIGIBLE], this is
+going to be in the cache
+
+because the data you access is
+smaller than the entire cache.
+
+OK, so what that means is only
+the first line has to have
+
+some cache misses.
+
+So how many cache misses
+you are going to have
+
+in the first line?
+
+Or any of the lines going to
+have cache misses because the
+
+first line still fit
+in the cache.
+
+[UNINTELLIGIBLE]
+
+anything.
+
+We don't need everything.
+
+How many cache misses
+have in here?
+
+The interesting thing is because
+these are four bytes,
+
+we have a 64-byte cache line,
+and each is four bytes.
+
+So that means I can do 16 axises
+every time I have a
+
+cache miss.
+
+OK, so up to here to here is 2
+to the N. My cache misses I do
+
+[UNINTELLIGIBLE]
+
+basically.
+
+My cache misses is basically
+this much.
+
+Everything else is in the cache,
+and after the first
+
+line, everything else is
+in the cache again,
+
+[UNINTELLIGIBLE] nicely,
+got my working set
+
+to fit in the cache.
+
+I'm really happy.
+
+Everybody see this?
+
+How many people don't
+see it now?
+
+OK, good.
+
+So let's move to something a
+little bit more complicated.
+
+What kind of locality
+do we have?
+
+AUDIENCE: Temporal
+and spatial.
+
+PROFESSOR: Good.
+
+We have temporal and spatial.
+
+You have spatial because every
+time you go, you only get the
+
+first line of the cache.
+
+Rest is in the cache.
+
+From that, I got a 16x
+improvement because I have
+
+temporal locality.
+
+And since I only access when I
+go back to the data, after
+
+accessing this, since it's
+already in the cache, I get
+
+spatial locality because
+of the 16.
+
+16 things are in the cache,
+I am going through that.
+
+I get spatial locality.
+
+I get temporal locality because
+next time I access,
+
+it's still in the cache.
+
+I haven't taken anything
+out of the cache.
+
+OK, what kind of misses?
+
+Should be cold misses again.
+
+Cold misses because the first
+time I [UNINTELLIGIBLE]
+
+things.
+
+I haven't seen that data.
+
+After I get it, everything
+is in the cache.
+
+So now, here's interesting
+case.
+
+Now, I am doing 2 to the power
+N, where N is great than 14.
+
+Now, what happens?
+
+Now, what happens in our picture
+here is I am going--
+
+So as you might cache
+is somewhere here.
+
+At this point, I fill
+out the cache.
+
+I still keep going, and minute
+I access something
+
+[UNINTELLIGIBLE]
+
+cache, what's going to happen?
+
+So I went through accessing
+34 kilobyte.
+
+If I access the next
+one, what happens?
+
+OK, no, no, no shutting
+down, please.
+
+OK, what happened?
+
+So I am accessing more than
+I can fit into the cache.
+
+Next time access, what's
+going to happen?
+
+Anyone want to take
+a wild guess?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR:
+[UNINTELLIGIBLE PHRASE]
+
+before that.
+
+[UNINTELLIGIBLE]
+
+in there.
+
+So what happens is then am
+I ever going to have any
+
+temporal locality?
+
+No.
+
+OK, so now, first access to
+each line basically misses
+
+forever because by the time
+I get back to the
+
+[UNINTELLIGIBLE],
+it's not there.
+
+So basically, it's gone
+out of the cache.
+
+So what that means is my total
+access time is basically every
+
+16th element, I am getting
+cache miss forever.
+
+So what that means, every 15th
+of 16, I have a hit.
+
+So what I have is 15 out of
+16, I have a cache hit.
+
+1/16th of the time, I have
+a cache miss forever.
+
+So what kind of locality
+do I have now?
+
+I have spatial locality.
+
+I don't have any temporal
+locality.
+
+I don't ever go back to
+something in the cache again.
+
+So what I have is spatial
+locality, so what type of
+
+misses now do I have?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Cold, right.
+
+AUDIENCE: Is it like
+shared misses?
+
+[INAUDIBLE]
+
+PROFESSOR: It's not shared.
+
+When you fill out the cache,
+you go back to
+
+[UNINTELLIGIBLE].
+
+You fill the cache.
+
+So what type of miss is that?
+
+AUDIENCE: Capacity?
+
+PROFESSOR: Capacity miss.
+
+OK, so you have basically
+cold and capacity
+
+misses happening now.
+
+OK?
+
+AUDIENCE: One question.
+
+[INAUDIBLE]
+
+that you multiplied whenever
+you're trying to load from
+
+memory, is that like an
+arbitrary number, or is that
+
+the actual cost of going--
+
+PROFESSOR: Every machine, you
+can get this beautiful table.
+
+I will go off what your
+machines have.
+
+We still have a number saying
+this is your miss
+
+[UNINTELLIGIBLE], this
+is the thing--
+
+I mean, so some of these things
+you realize because of
+
+all of the complexity.
+
+It's not that nice and simple,
+but this, I just pull out of
+
+hat, and it's kind of normal.
+
+So what do I do, now?
+
+I am doing the mod, but I am
+multiplying [i] by 16.
+
+So now, I am accessing this
+value, this value, this value,
+
+this value in here.
+
+I'm accessing this value, this
+value, this value, this value.
+
+One value in each cache line.
+
+OK?
+
+How much cache misses do you
+think I'm going to get?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: 100 for every access
+is basically beginning
+
+a cache line, you're taking one
+value and if I go back to
+
+that value, I have already
+filled up the cache.
+
+So basically, I have first
+access in the cache.
+
+And what's your total
+access time?
+
+Anyone will take a guess?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yep, 100 times
+x because I have no--
+
+OK, so this is a
+[UNINTELLIGIBLE]
+
+locality.
+
+That was clear.
+
+What kind of misses
+am I getting now?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Now, I'm getting
+conflict misses.
+
+I get a cold miss at the
+beginning, first time around,
+
+and then every time I do
+something, I'm getting
+
+conflict miss because the thing
+is, now, this N, I am
+
+only accessing small
+amount of data.
+
+It doesn't fit in the cache, but
+I'm not still getting any
+
+kind of sharing, so I'm having
+conflict misses.
+
+[UNINTELLIGIBLE] second
+time, I guess I will
+
+probably jump over this.
+
+I just did OK, if I go random
+access, what happens?
+
+So let me jump over that.
+
+Actually can do a calculation
+to figure out how many,
+
+probabilistically, how
+much you might have
+
+and stuff like that.
+
+OK.
+
+So now, if you look at what's
+going on, when you have no
+
+locality, you'd have
+no locality.
+
+That's a pretty obvious
+statement.
+
+And then if you have spatial
+locality and no temporal
+
+locality, we are
+streaming data.
+
+That means you are going through
+the data, but you're
+
+not getting back to it
+fast enough, so I
+
+have temporal locality.
+
+So I stream through data, so
+that means I go through data
+
+in a streaming fashion.
+
+OK?
+
+So what we have is if working
+set fits in cache, you have
+
+InCache mode.
+
+If working set is too big for
+cache, you can get some
+
+streaming mode and still get
+some locality because we are
+
+bringing the lines in here.
+
+And you can do other things
+like optimizers like
+
+prefetching we'll get to.
+
+And other issues
+[UNINTELLIGIBLE]
+
+this last one, but to deal
+with cache axises.
+
+So if you have more than one
+axis-- so here what I have is
+
+too nice arrays.
+
+[UNINTELLIGIBLE] is 2 to the
+power size array 2 to the 19
+
+power arrays.
+
+OK, so now what happens when
+I put this in the cache?
+
+Look what happens in here.
+
+So what happens is this array
+get mapped in this one.
+
+This array get maps this
+nicely in here.
+
+So what happens is this line
+can only be in this cache
+
+line, and this line also
+only can be in
+
+this line of the cache.
+
+Do you see what's
+going on, now?
+
+So if you do this one, basically
+every time you
+
+access something--
+
+See, assume I'm accessing this
+data item, so I'm doing A, B.
+
+I access A, I get this line.
+
+I access B, what happens?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: So this
+[UNINTELLIGIBLE] is gone.
+
+It is gone.
+
+Now, I am accessing the
+next one in that
+
+cache line we made.
+
+AUDIENCE: How do you know
+what cache line-- or how
+
+[INAUDIBLE]
+
+cache?
+
+[INAUDIBLE]
+
+PROFESSOR: Normally, in language
+like C, if people two
+
+arrays next to each other, they
+should be mapped next to
+
+each other in memory.
+
+And if you want to be more
+adventurous, you can go to the
+
+assembly and then see what
+their locations is.
+
+So if you put A, A next to each
+other, you normally kind
+
+of get it next to each other.
+
+So what this one is this
+is pretty bad.
+
+I should have gotten at least
+some spatial locality.
+
+I'm getting nothing.
+
+Do you see what's
+going on here?
+
+Do you know what's
+going on here?
+
+Know why I'm not getting
+any spatial locality?
+
+Because I am bouncing.
+
+When I access this one, this one
+is gone even though I have
+
+more data in the same cache
+line, so I'm kind of bouncing
+
+two cache lines because
+of that.
+
+What's a good solution
+for this?
+
+Back there.
+
+AUDIENCE: [INAUDIBLE]
+
+A and B could be mapped to
+the same cache line.
+
+PROFESSOR: The thing A is
+a nice 2 to the power.
+
+A size is a multiple
+of the cache size.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: The size of A is a
+multiple of the cache size.
+
+So what happens is if you have
+memory in here, you map
+
+something like A, C here.
+
+If this is a multiple of cache
+line, so assume this is 32K
+
+times some number, and you map
+B here, and then this is
+
+normally what happens in C.
+You put all adjacent map
+
+allocations next to each
+other in memory.
+
+Do you got A here, and
+you start having B in
+
+here, next to it.
+
+OK, so what happens is now if
+A starts to assume address,
+
+we'll say 100, this is 100 plus
+32K times N, basically.
+
+And you do this mod 32K, this
+mod 32K, this same number.
+
+It maps into the same line.
+
+OK, so I kind of gave
+you the problem.
+
+What can be the solution?
+
+AUDIENCE: [INAUDIBLE]
+
+allocate one line.
+
+PROFESSOR: Yes, it's
+called padding.
+
+OK, so I have no locality in
+here, let me go to the next
+
+slide, what kind of misses?
+
+I have cold and conflict.
+
+What I can do is just
+basically add a
+
+little bit of padding.
+
+I did 16 here.
+
+Normally, you do a prime number
+so it will not clash
+
+with anything.
+
+Add a little bit of padding at
+the end of array, and that
+
+means the next array
+will not be
+
+conflicted most of the time.
+
+So a lot of times when you
+declare things next to each
+
+other, it's always good
+to add a little bit of
+
+a padding in between.
+
+Normally, a smaller prime number
+would be a good thing
+
+to add a padding.
+
+Now, I start getting back my
+nice locality because the two
+
+things are mapping the
+two cache lines.
+
+What type of locality
+do I get here?
+
+Anybody want to take any
+guess what type of
+
+locality I have here?
+
+AUDIENCE: Question, sorry.
+
+[INAUDIBLE]
+
+you actually added
+just an extra 16.
+
+PROFESSOR: Yes.
+
+AUDIENCE: Why would that just
+make the A and B [INAUDIBLE]?
+
+PROFESSOR: Because what happens
+is normally it doesn't
+
+make A and B into leaving the
+cache, but it makes A[0]
+
+not exactly matching to B[0].
+
+A[0]
+
+will interleave with something
+like B[16]
+
+or something.
+
+This thing might map into
+the same place.
+
+AUDIENCE: I mean, but
+I [INAUDIBLE].
+
+PROFESSOR: Yes, normally
+in a computation,
+
+people do that, A[i]
+
+equals B[i]
+
+plus something.
+
+AUDIENCE: Oh, OK,
+so [INAUDIBLE].
+
+Like I understand what you're
+saying, but I don't understand
+
+how that [INAUDIBLE]
+
+because they're both accessing
+[i] at the same time.
+
+Why would they [INAUDIBLE]?
+
+PROFESSOR: So here's
+the problem.
+
+Assume I have [UNINTELLIGIBLE]
+
+32K.
+
+I'm assuming [UNINTELLIGIBLE].
+
+OK, so first one is, we'll say,
+you start with 100, 100
+
+plus [i], and the other one
+is 100 plus 32K plus [i].
+
+OK, then you take a mod
+32K, and this end up
+
+being 100 plus [i]
+
+with another 100 plus [i].
+
+So this is basically
+[UNINTELLIGIBLE].
+
+You still have one or one
+element in the cache it's all
+
+going to map into.
+
+You see that?
+
+But now, if I add 16 more to
+this one, then this map into
+
+116 plus [i].
+
+AUDIENCE: I don't see that
+reflected in the code.
+
+You just [INAUDIBLE], so
+how is B different
+
+from A in your code?
+
+PROFESSOR: Because
+[UNINTELLIGIBLE] my S. I added
+
+16 to S, so my A is a little
+bit bigger, now.
+
+AUDIENCE: But isn't B
+also [INAUDIBLE]?
+
+PROFESSOR: Yeah, B's
+also bigger here.
+
+I don't care.
+
+B goes down here.
+
+B, I add a little bit more to
+the B. It doesn't matter.
+
+I padded B, too.
+
+So what that means
+is the first A[i]
+
+and B[i] are not in the
+same cache line.
+
+AUDIENCE: How do we allocate
+A and B right
+
+next to each other?
+
+PROFESSOR: So normally in C, if
+you declare something like
+
+int A [100], int B [100], more
+or less, they will be
+
+allocated next to each other.
+
+If you look at the assembly
+listing, it'll say code
+
+allocated next to each
+other in memory.
+
+Even in the stack, if you do
+that, if you allocate things,
+
+compiler has no incentive to
+go and move things around.
+
+AUDIENCE: This is only for
+global and [INAUDIBLE]?
+
+PROFESSOR: Global variable,
+local variables.
+
+AUDIENCE: Does any of it still
+apply if you use malloc?
+
+PROFESSOR: The thing
+about malloc is--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It might do something
+[UNINTELLIGIBLE],
+
+but on the other hand, if it is
+fitting on the same page,
+
+it might also do something
+like that, too.
+
+So it depends on
+how we do that.
+
+At the beginning, if you keep
+mallocing things, it might be
+
+[UNINTELLIGIBLE].
+
+They might be a little bit off
+because malloc put some
+
+metadata with each status.
+
+If you ask for [UNINTELLIGIBLE],
+you're not
+
+getting exactly 100.
+
+You're getting a little
+bit of a bigger size.
+
+But you might have some
+configuring to do, but after
+
+some time, when you have done a
+lot of [UNINTELLIGIBLE], we
+
+have no idea where
+it's going to go.
+
+It's random.
+
+Anymore questions?
+
+OK, good, that is
+a good question.
+
+So what kind of locality
+do I have here?
+
+[UNINTELLIGIBLE]
+
+two lines, I am accessing each,
+and I got 16 times 15
+
+out of 16 hits.
+
+What's that?
+
+AUDIENCE: Spatial?
+
+PROFESSOR: Spatial locality.
+
+And of course, if you have
+spatial locality, you get cold
+
+misses, basically.
+
+And I think [UNINTELLIGIBLE],
+you get what
+
+other type of misses?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: [UNINTELLIGIBLE]
+conflict here.
+
+Basically, capacity.
+
+Capacity miss, exactly.
+
+So in order to avoid this, what
+we have done is we make
+
+cache-- instead of mapping into
+one place before, and
+
+what we said was we had
+this memory, and
+
+assume we have 32 sets.
+
+And if you have a cache like
+this, we make this entire map
+
+into this one, and this
+map into this one.
+
+What people have done is instead
+of doing that, what
+
+you can make is make the cache,
+instead of one big
+
+block, two small blocks.
+
+So what that means is this
+can happen to this one.
+
+My drawings are not
+that great, but I
+
+hope you get the picture.
+
+This map into this one, so
+what that means is each
+
+reference here, so maps
+here, and these
+
+two basically conflicts.
+
+But now with that
+[UNINTELLIGIBLE]
+
+too, I can put this
+one here or here.
+
+I have two places to put the
+value, basically, and that
+
+[UNINTELLIGIBLE].
+
+OK, so that means if I access
+something conflicting,
+
+[UNINTELLIGIBLE], you cannot
+just two things.
+
+Still, there are places in
+the cache for them to go.
+
+And one way to do people is
+fully associative cache.
+
+It can go anywhere, but that's
+very hard to do in hardware,
+
+but you can do some small
+number of ways.
+
+So in here, if you do two basic
+associative cache, in
+
+the first axis in here, even
+though these are conflicted,
+
+on can go to one
+[UNINTELLIGIBLE] set, another
+
+one can go to the other set.
+
+OK, so two associative cache
+[UNINTELLIGIBLE].
+
+So total access time, again, I
+have nice locality in here,
+
+spatial locality, and I have
+both cold and, I guess,
+
+capacity misses.
+
+But if you have two associative
+cache, what's the
+
+next problem?
+
+How about if you have three
+different things?
+
+So we have two different
+things like that.
+
+OK, now that I only have two
+associated [UNINTELLIGIBLE],
+
+it doesn't work because, in
+a [UNINTELLIGIBLE], I will
+
+replace the last thing, and you
+might still end up with
+
+nothing in here because you are
+replacing nothing, and the
+
+next thing replaced
+the other thing.
+
+And basically after you
+gave B, C, then you go
+
+to A. A Is not there.
+
+When you go to B, B is not
+there, C is not there.
+
+You kind of go back to the same
+problem in here, and then
+
+basically have to access
+everything again.
+
+There is some spatial locality
+but cache can't use it.
+
+Basically, you have
+conflict misses.
+
+OK, so you see that?
+
+So associative is good because
+normally people assume you
+
+don't need that much
+
+associativity, but it's limited.
+
+So if you have too many things,
+you might run into
+
+this problem again.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You mean capacity?
+
+AUDIENCE: Yeah, [INAUDIBLE]
+capacity.
+
+PROFESSOR: Less.
+
+AUDIENCE: [INAUDIBLE]
+
+elements in a cache before you
+pick [INAUDIBLE] because it
+
+looks as though the matrix
+is is using half
+
+the cache by itself.
+
+PROFESSOR: Because it's
+associated, you mean?
+
+You have multiple there?
+
+I mean, the thing is since it's
+associated, no, because
+
+you have enough room.
+
+I mean, if you're going
+[UNINTELLIGIBLE]
+
+everything, you have two
+places to put the
+
+name because it maps.
+
+That's a good question.
+
+So what happens is now, assume
+this many things fit into the
+
+cache before.
+
+Now, cache has two banks, and
+in each bank, only this many
+
+things fit in, but the
+next thing can go
+
+to the other bank.
+
+So if you go through
+[UNINTELLIGIBLE], you have the
+
+same behavior even if you
+have associativity.
+
+OK, you can go and--
+
+because if the cache is the same
+size, the size is what
+
+matters for if you are going
+through [UNINTELLIGIBLE] axis.
+
+AUDIENCE: So far, [INAUDIBLE]
+machines that we're working
+
+on, do they have a fixed
+kind of cache, or
+
+can we decide like--
+
+PROFESSOR: The fixed
+kind of cache.
+
+It's built into the hardware.
+
+I will show the table
+to say what type of
+
+associativity is in there.
+
+AUDIENCE: Is there not a
+way to say [INAUDIBLE]
+
+three-way associative?
+
+Can you have something on top
+of it so that it looks like
+
+it's two-way associative
+or something?
+
+PROFESSOR: I mean, you can do
+things like that in software,
+
+but they're very expensive.
+
+I mean, think about cache is
+trying to fool the cache in
+
+that direction cannot be that
+easy because they are like
+
+really hard-baked into hardware.
+that's a good
+
+question, but there are things
+you can do, not exactly
+
+modeling something, but kind of
+putting offsets and stuff
+
+like that so it doesn't get into
+these kind of conflicts.
+
+So yeah, I will answer
+this thing.
+
+Why don't you have more?
+
+Because if you go back to
+your [UNINTELLIGIBLE]
+
+lectures.
+
+Perhaps it might have
+explanation in it's hardware
+
+why it's much harder to build.
+
+And if you have the
+linked lists now--
+
+so assume I have linked lists we
+are going through in here.
+
+And what's my [UNINTELLIGIBLE]?
+
+Basically, depending on
+allocation and using some
+
+things, so best case is
+everything is in cache, so I
+
+have a small list.
+
+And I go through again and
+again, round and around my
+
+list, everything's in cache
+and [UNINTELLIGIBLE]
+
+S. That's really great.
+
+Next best is everything
+is adjacent.
+
+OK, everything might not be in
+the cache, but everything at
+
+least in adjacent memory.
+
+So basically, first time I
+allocate my malloc did a nice
+
+thing for me, and at that time,
+I basically get a nice
+
+basic spatial locality since
+my size is 16 in here.
+
+So I get this much.
+
+And the worst case is random.
+
+Malloc puts it all
+over the place.
+
+Question?
+
+AUDIENCE: [INAUDIBLE]
+
+cache, does the thing behind it
+[UNINTELLIGIBLE] in front
+
+of it [UNINTELLIGIBLE]
+also going to?
+
+Do those both have a
+spatial locality?
+
+PROFESSOR: What happens is
+normally, we assume 64 element
+
+cache, so it's at that boundary,
+so basically 2 to
+
+the 8 boundaries is
+what happens.
+
+So what happens is cache line
+begins at 0 address, 64
+
+address here.
+
+So if you get 63, that means
+this value is not in the
+
+cache, so you get
+this cache line.
+
+So the cache line
+doesn't shift.
+
+It's fixed chunks in here, so
+that if you get address 0, you
+
+get this one, and all
+these things.
+
+If you get something in the
+middle, you'll get the left
+
+and right [UNINTELLIGIBLE], but
+if you get here, you only
+
+get the right.
+
+So this basically 0 and 64,
+they are boundaries
+
+[INAUDIBLE].
+
+If you like 65, that's it.
+
+But that said, if you're
+accessing [UNINTELLIGIBLE],
+
+that's this thing called
+prefetcher that say you are
+
+going through linear pattern,
+and you might need that next,
+
+and it'll bring this
+up for you.
+
+And what you find, I'll show
+later, that in fact, the
+
+machine you're using has a
+really powerful prefetcher, so
+
+it can hide a lot
+of these things.
+
+So we'll get to that.
+
+So this is my total access
+time in here.
+
+Random case.
+
+Random case is basically, every
+time I access something,
+
+it's not in the cache.
+
+And then if you have a bigger
+struct in here--
+
+but assume I have this big
+struct in here, but I am only
+
+accessing one element of
+this struct in here.
+
+I do a lot.
+
+I created this large struct,
+and I am [UNINTELLIGIBLE]
+
+things in the struct,
+and I just basically
+
+looking at my data.
+
+Only one element.
+
+What's the problem here?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Exactly, so I bring
+the entire cache line, but I'm
+
+only using a little bit of it.
+
+Because I bring all these things
+into the cache, it
+
+comes with axis and that,
+but I'm only using data.
+
+So basically, what happens is,
+if everything in the cache, I
+
+have access time S.
+That's great.
+
+That's not a problem,
+[UNINTELLIGIBLE]
+
+streaming.
+
+Even though I'm getting spatial
+locality, I only get
+
+half of it because even though
+I'm bringing the cache line,
+
+only two have datas because
+this is 32 bytes long.
+
+It's in my cache.
+
+Even though I am bringing all
+this data, I only two of them
+
+in the cache because rest of
+this other data is kind of
+
+hanging in there with me,
+and so I don't get that.
+
+And random, of course,
+you have no locality.
+
+So how can I basically
+make this better?
+
+How can I make this better?
+
+OK, I just showed
+it very fast.
+
+OK.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: So instead, if I
+ask you, I have this large
+
+data structure, but most of
+time, I'm only accessing a
+
+small part of it, this is kind
+of a little bit of a hack.
+
+I mean, this is kind of going
+against, I guess 6005 kind of
+
+building, but this
+actually works.
+
+What you can do is, you can go
+back and instead of doing
+
+structs, what you can do
+is you can do arrays
+
+of each data item.
+
+And now what happens is that I
+am basically bringing these,
+
+and then the data I am accessing
+is basically right
+
+now next to each other.
+
+So you might have this very
+large data structure
+
+representing something you
+have a lot of, then.
+
+But most of the time, you're
+only using few of them, so you
+
+don't have to be structs
+of arrays.
+
+You might have couple of
+different data structures.
+
+One is the one that you access
+regularly hopefully you get
+
+them next to each other.
+
+And the nice thing about arrays
+is it guarantees things
+
+are next to each other.
+
+Of course, was managing
+it is harder.
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: You can do both.
+
+So that means instead of doing
+the structs, you use arrays of
+
+each field.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Instead of.
+
+So instead of doing this one,
+you just do this one.
+
+AUDIENCE: [INAUDIBLE]
+
+instead of being able
+to pass stuff over.
+
+Now you have to kind of be able
+to know [UNINTELLIGIBLE],
+
+so what that is where because
+you cannot just pass the
+
+struct [UNINTELLIGIBLE].
+
+PROFESSOR: No, you can't
+pass the struct.
+
+You basically have to pad the
+index in here for this
+
+structure, basically.
+
+So you have to know something
+in there.
+
+So this is a lot messier, but
+it can actually give you a
+
+performance if you do this type
+of access, so it's not
+
+something you want everywhere.
+
+That's why you still want to
+use structures and nice
+
+classes and stuff.
+
+But this, if you're doing very
+large data, but most of the
+
+you're accessing only small
+amount, this kind of
+
+representation can help.
+
+So I want to get a little bit
+into matrix multiplying.
+
+So what we're looking at is this
+four by four matrix, and
+
+you can represent it using
+this representation.
+
+But to make it clear, what I'm
+going to do is I'm just going
+
+to allocate this entire thing
+as a single array, and I'm
+
+going to do that
+[UNINTELLIGIBLE] calculation
+
+myself because if you go a
+little bit down, you realize
+
+this is allocated in a little
+bit of a weird way.
+
+And so this is what we call
+row-major because all rows are
+
+next to each other, and you
+can access allocated
+
+column-major.
+
+Basically that means now A001,
+instead of that, 1, 0 is next
+
+to 0, 0, 1, 0, 2, 0.
+
+And then basically saying same
+thing, [UNINTELLIGIBLE]
+
+instead of saying 4i plus
+j, it's just 4j plus i.
+
+You can do both.
+
+So this is my nice matrix
+multiply function, because the
+
+reason I did it this way, it's
+just very clear how many axis
+
+I'm going to use.
+
+So if you look at C, let's look
+at only the inner loop.
+
+Most of the mapping matters
+in the inner loop.
+
+I go for k in 0 to size.
+
+Only first axis on C is going to
+miss because it's going up
+
+[UNINTELLIGIBLE]
+
+same K, da-da-da-da-da, so
+C is very nice in here.
+
+Only get one miss in here.
+
+You have a question?
+
+OK.
+
+A has a streaming pattern
+because every time I update K,
+
+I go to the next element,
+next element, next
+
+element, next element.
+
+[INAUDIBLE].
+
+What type of a pattern
+do I have in B?
+
+AUDIENCE: Looks like
+[INAUDIBLE].
+
+PROFESSOR: Yeah, exactly.
+
+I have jumping on memory.
+
+I'm jumping one to another.
+
+So if you look at that, I am
+going through A like that, and
+
+B, and going through C element
+at a time, basically.
+
+So if you look at doing this
+in order to calculate one
+
+element of A, [INAUDIBLE]
+calculating these, what you
+
+have to do is I am getting
+B and C this way.
+
+I'm going through row here
+and column, and this row
+
+[UNINTELLIGIBLE]
+
+fit into the cache line through
+that because this is
+
+the memory.
+
+But C is just jumping all over
+the memory, and I have no
+
+locality in here.
+
+So what can we do here?
+
+What's the simplest
+thing in here?
+
+How do we get some locality
+into the C?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: So yeah, you're
+coming, you're getting it.
+
+That's the next thing that's
+most important.
+
+That's the more advanced
+thing you can do.
+
+We'll get there.
+
+What was a simple thing
+you can do for C?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: [UNINTELLIGIBLE]
+
+So here's the [UNINTELLIGIBLE]
+
+execution time, original, and
+voila, when you transpose
+
+that, you can actually get a
+huge benefit in here because,
+
+now, I get spatial locality
+in both sides in here.
+
+And so now when you're
+transposed, I am going
+
+through like this.
+
+So now what I did was I am
+giving this CPI, and what
+
+happens is when you transpose,
+I have a 5x
+
+improvement in sync CPI.
+
+That means instructions actually
+not waiting, not
+
+doing nothing.
+
+I have a pretty good reduce
+of cache misread.
+
+because, now, I'm
+actually going
+
+through cache very nicely.
+
+So the next thing we can
+do is, what she just
+
+pointed out, blocking.
+
+So instead of matrix multiply,
+just multiplying this matrix
+
+at a time, you can multiply
+submatrices and calculate
+
+small submatrices.
+
+And if you do that, the
+submatrix can nicely fit in
+
+the memory, so let
+me show you that.
+
+This is the blocking code.
+
+Let me show you what
+that means.
+
+So what we are doing is you are
+multiplying this matrix by
+
+this matrix in there and
+getting this matrix.
+
+So what that means is, normally,
+what you do is, to
+
+get one element, you have to
+multiply a row and a column.
+
+Normally, we are calculating
+a row of A at a time.
+
+In order to get a row of A,
+I had to get a row of B
+
+[UNINTELLIGIBLE]
+
+entire C has to participate into
+calculate A. So by the
+
+time I have calculated 1024
+elements, I have gone through
+
+this many axises to new elements
+basically because I
+
+am getting B again and again,
+but I had to go through the
+
+entire C in here.
+
+So if this much data is bigger
+than the cache, I have no
+
+locality in here.
+
+But if, instead of calculating
+a row, if I calculate a 32 by
+
+32 block, which is again 1024
+elements I am calculating.
+
+If I do that, I need a block
+here and a block here, and I
+
+only type this much data.
+
+OK, I'm getting the same amount
+of output, but because
+
+of reuse, I touch a lot
+less inputting here.
+
+And just by doing this
+transformation, I can really
+
+reduce the amount of data.
+
+Basically, I can create a
+smaller working set, go
+
+through that much more, and
+reduce the amount of cache
+
+misses you get.
+
+So by doing that, I basically go
+out another 3x improvement
+
+in my CPI, really brought down
+my L1 cache misses, and
+
+basically eliminated
+L2 cache misses.
+
+OK, so I got a really good
+speed up in here.
+
+So you can block multiple
+levels, L1, L2, L3, because
+
+every time you figure out the
+workings and size, you block
+
+so the data in that will be
+safe in the cache in here.
+
+And this is kind of nasty
+to do by hand.
+
+We'll see.
+
+So the other interesting thing
+is call stack locality.
+
+So if you do something like fib
+in here, traditional fib,
+
+if you do fib(4), you calculate
+a fib(4), fib(3),
+
+fib(2), you kind of build
+a stack, go up
+
+back again in here.
+
+So if you keep doing that,
+the nice thing is you're
+
+going up, but its--
+
+Hopefully, one of these days,
+I am going to hit the wrong
+
+button, and--
+
+What kind of locality do we have
+if we are accessing data
+
+like this in my call stack?
+
+What kind of locality
+do we have?
+
+I mean, I access here, fib(4),
+and I get back to fib(4) here.
+
+So within each frame, I am
+accessing data next to each
+
+other, so I can have a little
+bit of a spatial locality
+
+because, each frame, all the
+data is next to each other.
+
+But across frames, normally,
+I will have some temporal
+
+because I will get back to
+that data some time.
+
+OK?
+
+OK, before I summarize,
+this one.
+
+If you are reading a lot of
+data, processing through stage
+
+one, [UNINTELLIGIBLE]
+
+and producing [UNINTELLIGIBLE],
+that means
+
+you're reading a huge amount
+of data through stage one,
+
+save, save data again, do stage
+two, you have really bad
+
+cache locality.
+
+One thing you can do is read a
+small chunk, do all the stages
+
+on that small chunk, save it,
+and go to another chunk.
+
+So instead of doing the entire
+data, doing something
+
+[UNINTELLIGIBLE]
+
+producing, you can do this
+chunk-ifying, and by doing
+
+that, you can get a
+lot of locality.
+
+So once you bring in data, you
+like to do as many things as
+
+possible to that data before
+it gets out of the cache.
+
+That's the entire thing about
+locality, and you can
+
+restructure code through that.
+
+So if you look at that, what
+we have done today, we have
+
+looked at things like
+associativity, cache lines,
+
+cache sets in here, and how to
+address and map to a cache, we
+
+kind of did this thing, and we
+look at [UNINTELLIGIBLE]
+
+streamings versus InCache
+versus no
+
+locality type patterns.
+
+And then when you look at data
+structure transformation, we
+
+look at how to basically replace
+structured arrays and
+
+split data structures to make
+sure that you get a lot of
+
+nice locality if you access a
+certain amount of data, and
+
+pack data to get smaller cache
+footprints kind of things.
+
+And we also look at computer
+transformations, things like
+
+transpose copying, compute copy,
+outtype things you can
+
+do, so you can actually get nice
+locality, so you can do
+
+both data and compute
+transformations.
+
+And [UNINTELLIGIBLE]
+
+axises and [? re-cast ?]
+
+calculation stages, so this
+is kind of summary.
+
+Next thing I want go is
+look at what machines
+
+you guys are using.
+
+So this is the machines
+we used last year.
+
+These are quad cores, and it
+had L1 cache, so these
+
+[UNINTELLIGIBLE].
+
+So this has 32 kilobyte
+L1 cache, data cache
+
+[UNINTELLIGIBLE]
+
+two caches in here for data and
+instructions, each core,
+
+and then the cache line size
+is normally 64 bytes
+
+[UNINTELLIGIBLE].
+
+And here, latency
+[UNINTELLIGIBLE], you get
+
+three cycles.
+
+If not, you get 14 cycles to
+go to to L2 in here if data
+
+doesn't meet there.
+
+And associated with this
+[UNINTELLIGIBLE PHRASE].
+
+So that was what we
+did last year.
+
+This year, we have a bigger
+machine that has multiple
+
+levels of caches.
+
+So each core has L1 instruction
+and data cache.
+
+It's kind of the same, 32
+kilobyte cache, four
+
+nanosecond latency in here.
+
+Eight, three and four
+[UNINTELLIGIBLE], they kind of
+
+reduced that, but they added a
+256-kilobyte L2 cache in here,
+
+and then a pretty large humongo
+
+12-megabyte L3 cache in here.
+
+The interesting thing is here,
+this pretty fast access to
+
+these ones.
+
+If you miss in here, this is
+about 2 and 1/2 times cost
+
+from going from here to here.
+
+From here to [UNINTELLIGIBLE],
+about a five times cost, so
+
+here to here is a
+five times cost.
+
+The interesting thing that
+actually surprises a lot us
+
+was here to here, it's cost
+is not that different.
+
+[UNINTELLIGIBLE PHRASE]
+
+So actually memory, even though
+it's sitting out in
+
+there, they have managed to get
+it pretty cheap access.
+
+Normally, my intuition say this
+should be much higher
+
+because you're going off-chip,
+so this is the structure here.
+
+It's a lot more complicated.
+
+So here's something I
+produced last year.
+
+So what I did was I
+ran this program.
+
+And in these machines, there's a
+way to turn off the prefetch
+
+of the previous
+[UNINTELLIGIBLE].
+
+So when you've turned on the
+prefetch and then you run,
+
+what you are doing is I am
+accessing data with a working
+
+set, small working set, little
+bit bigger working set.
+
+So this is basically when you
+consider working set size.
+
+So you get a graph like this.
+
+I am hitting my L1 cache, and
+if it is more than that, I
+
+[UNINTELLIGIBLE]
+
+L1 cache, I go to my L2 cache.
+
+And if L2 misses, I have
+to go to main memory.
+
+Very traditional kind
+of a graph in here.
+
+Another a little bit of an
+interesting thing, which is
+
+instead of accessing
+next item, I kind
+
+of skipped in here.
+
+So this trying to force how
+to get conflict misses.
+
+And so if you line up things
+like this exactly, what
+
+happens is you get these
+conflict misses, and you get
+
+this number.
+
+So I have interesting
+story to tell.
+
+When I was a graduate student,
+we were running this bunch of
+
+benchmarks, and normally when
+you run a benchmark, you try
+
+it for an equal
+
+[UNINTELLIGIBLE], stuff like that.
+
+And we got this graph
+like this.
+
+I mean, we expect a graph
+going like this.
+
+OK, that how a benchmark
+[UNINTELLIGIBLE].
+
+Then at one point, by accident,
+instead of typing an
+
+equal 64-something, I typed an
+equal 63, and suddenly, I got
+
+a performance like this.
+
+Wait a minute, what's
+going on?
+
+So in here, what I got
+was not a line.
+
+I got 16, 32, 64, 128,
+nice graph like that.
+
+And then I just did 63,
+like down to here.
+
+I'm like, geeze, that
+can't be right.
+
+And then I start looking
+at 62, which is here.
+
+61 is here.
+
+So I realize if I enumerate
+all those things, I got a
+
+graph like this, basically.
+
+Kind of something like this.
+
+And the thing is, if I had never
+tried the 63, I would
+
+have basically thought my
+performance was like
+
+this, so far worse.
+
+Never realized because it was
+all having conflicts in memory
+
+because I'm [UNINTELLIGIBLE]
+
+2 to the power numbers.
+
+So this is what happens if you
+just look at 2 to the power
+
+numbers, you'll think, yeah,
+this is the performance you're
+
+getting, without realizing
+that, in fact, you
+
+can get this far.
+
+So this is good.
+
+So I ran it on the
+new machine.
+
+The problem with our new machine
+is there's no way to
+
+turn off prefetching.
+
+OK, so this is what
+you're getting.
+
+Everything, because I am
+accessing this nice linear,
+
+looks same.
+
+This is exactly what
+you want to happen.
+
+What it's doing is, minute you
+go to access, it realizes you
+
+accessing linearly.
+
+It start fetching, fetching,
+fetching data in front you,
+
+it's going to catch up.
+
+It's not feeding you data, so
+you're not going to have any
+
+cache missed because you're
+going through this nice,
+
+linear pattern, and you just
+basic end up with this
+
+beautiful graph, which gives the
+feeling your working set
+
+could be, now, gigabytes long.
+
+At this point, I am fitting into
+the entire L3 cache, and
+
+still look like this works
+beautiful because this is what
+
+you want for it to figure out.
+
+So now I'm like, geeze,
+this is great.
+
+This means my cache works, it's
+very nice, but I want to
+
+show you guys what's going
+on, so that doesn't help.
+
+So I came up with
+this program.
+
+So this program, what I did was
+I created a working set,
+
+but I'm accessing randomly
+within that working set.
+
+I calculated this address.
+
+This is my poor man's random
+number generator, so basically
+
+I'm adding number in here and
+multiplying this, and then the
+
+masking these to get the
+right [UNINTELLIGIBLE]
+
+so I get within that
+set in here.
+
+And then I just access
+data, so I'm getting
+
+[UNINTELLIGIBLE].
+
+So I get a number like this,
+and this jump up here, and
+
+then I had this kind
+of behavior.
+
+This is a lot more
+complicated.
+
+I need to figure out what the
+hell is going on in here, so I
+
+said, OK, let's now look at
+performance counters.
+
+I look at L1 cache miss.
+
+OK, up to 32K, I have
+no cache misses.
+
+Boom, cache misses jump up.
+
+Perfect.
+
+And I have this little bit of a
+kink in here, this beautiful
+
+describes because I have 32K
+L1 cache, and until then, I
+
+have no things, and then when
+the cache start missing, I'm
+
+jumping up.
+
+Perfect.
+
+I got that description here.
+
+Then I look at my
+L2 cache misses.
+
+This is, I think, the L2 cache
+in this machine might have a
+
+little bit more complex
+[UNINTELLIGIBLE]
+
+telling us because this
+is not going like
+
+here had jumping up.
+
+That's a 256K [UNINTELLIGIBLE]
+
+get.
+
+Is this 256?
+
+Yeah.
+
+[INAUDIBLE]
+
+250 is [UNINTELLIGIBLE]
+
+these things.
+
+OK, so we have 32 256 2L
+megabytes in here.
+
+Even if you have 256 in here--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Hm?
+
+AUDIENCE: Should it
+be 256 or 32--
+
+PROFESSOR: [UNINTELLIGIBLE]
+
+because everything's backed
+up, it's hierarchy
+
+[UNINTELLIGIBLE], so it's not
+added to, it's not next to
+
+each other, because at this
+point, L1 is now useless.
+
+It'll run everything is just
+going to L2, so L2 is the one
+
+who was serving it.
+
+Come on.
+
+So what happens in here, this
+normally should start jumping
+
+here, 256, but it start jumping
+earlier, so there
+
+might be some other interesting
+
+thing going on here.
+
+It might be interesting
+to investigate.
+
+So this is OK, so still
+I am pretty close.
+
+I realized this jump is
+basically because of L2
+
+happen, this jump in here.
+
+L2 start missing.
+
+Then I look at L3.
+
+It's here.
+
+What's happening here?
+
+So this was a big mystery the
+two of us were trying to debug
+
+what one hour ago.
+
+Not one hour.
+
+Class is going.
+
+Like two hours ago.
+
+We was trying to figure out,
+OK, wait a minute, this
+
+doesn't make sense.
+
+My performance is here.
+
+L3 should be just basically a
+nice flattening out here, and
+
+just jumping.
+
+It's not doing that, and we are
+like what's going on here.
+
+So then we were scratching our
+heads, and we start looking.
+
+I say, ha, there were other
+things going on.
+
+We looked at this thing
+called TLB.
+
+Let me tell you what TLB is.
+
+What we realize is at this
+point, we are [? seeing ?]
+
+TLB misses.
+
+How many people know
+what a TLB is?
+
+OK, good, so let me spend the
+last couple of minutes
+
+explaining what a TLB this,
+and that kind of explain
+
+what's going on in this graph.
+
+So TLB means--
+
+Normally, data is stored in
+memory using real addresses.
+
+That means there's a memory
+size in here, there's an
+
+address format, there's certain
+[UNINTELLIGIBLE].
+
+And then the program for
+it use virtual memory.
+
+That means programs want to feel
+like they have a lot more
+
+memory than actual, physical
+memory available.
+
+So what happens is you have
+virtual memory address, but
+
+somebody has to map virtual
+memory to physical memory.
+
+So the way it work is there's
+a thing called translation
+
+lookaside buffer, TLB, that says
+if you give this virtual
+
+address, here's the right
+physical address.
+
+So of course you can't do it for
+each address by address.
+
+What you have is you have 4K
+pages, so the address space is
+
+broken down into 4K pages.
+
+Each page will have an entry in
+this TLB, saying if you get
+
+this virtual address, here's
+the right physical address.
+
+So normally what happens is when
+the operating system they
+
+created this large table, for
+every place in memory, you use
+
+this table, and it loads
+into memory.
+
+Then the hardware will fetch
+and cache some of those
+
+entries in this TLB
+cache in there.
+
+So normally what happens is in
+here, it caches 52L entries.
+
+It can keep 52L entries
+to 52L pages,
+
+saying here's the mapping.
+
+The problem with 52L pages is
+in a 4K byte page size, 52L
+
+pages can only hold two
+megabytes of data.
+
+If you're accessing more than
+two megabytes of data, you
+
+have to go more than 52L pages,
+and at that point, that
+
+mapping is not in the TLB, and
+that means that you have to go
+
+do a mapping translation.
+
+The problem for this is
+these 4K pages is a
+
+very ancient artifact.
+
+There's the new machines, you
+can I ask for what we call
+
+large-pages or super, but you
+can ask for 2-megabyte or
+
+4-megabyte pages.
+
+If you ask for super-pages, then
+of course, 52L entry's
+
+good enough.
+
+It can hold enough things not
+to have TLB miss, at least
+
+while you're in the cache.
+
+But since Linux, without doing
+anything, only asks for 4K
+
+pages, before you run out of
+your L3 cache, you run out of
+
+the TLB table.
+
+And it has to start fetching
+and [UNINTELLIGIBLE]
+
+data table, that means you had
+to actually fetch the table
+
+entries, and so you have
+to do more fetchings.
+
+So that is why this is even
+running higher, because it's
+
+trying to fetch this TLB entry
+and stuff like that.
+
+Question?
+
+AUDIENCE: Is there a way to then
+actually fiddle with the
+
+TLB so that you have to fit
+your pages rather than--
+
+PROFESSOR: So in allocation, you
+can ask for super-pages or
+
+large-pages.
+
+But in Linux, normally just ask
+for 4K pages, so that the
+
+operating systems haven't
+kind of caught up
+
+to the current hardware.
+
+And this is was built
+[UNINTELLIGIBLE]
+
+doesn't make sense TLB
+to run out before
+
+you run out the cache.
+
+I mean, that's kind of
+mismatch in here.
+
+But it's built assuming you'll
+get large-pages, but if you
+
+don't, you're going to run
+out of the TLB in there.
+
+So this is why sometimes
+performance engineering is
+
+interesting, exciting, and
+frustrating, because you
+
+assume you know where the
+hell this is going.
+
+You assume this is going to go
+here and that, and suddenly,
+
+this miss shows up, and so we
+have to scratch our heads.
+
+And luckily, we found what's
+going on, but we could have
+
+spent hours or days trying to
+figure out what's going on
+
+here because this is one
+[UNINTELLIGIBLE]
+
+say OK, let's try TLB,
+and it worked.
+
+That was really good, but I
+have, many cases, spent days
+
+trying to figure out why
+something is going on because
+
+performance is kind of
+a [UNINTELLIGIBLE]
+
+of everything.
+
+There's no nice abstractions
+and stuff like that.
+
+If you think abstraction wise,
+somewhere outside the
+
+abstraction, that's
+going to kill you.
+
+So that is why it can be
+interesting, because you have
+
+to know everything.
+
+And the fun thing is, once you
+understand performance, you
+
+basically understand end-to-end,
+soup to nuts,
+
+what's going on.
+
+OK, with that encouraging
+thought, let's see how you
+
+guys do in the next part
+of project two.
\ No newline at end of file
diff --git a/lA8-N_ARHTw.txt b/lA8-N_ARHTw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..43c0814a91fa74b548f12c64dd212adc7db2a1d2
--- /dev/null
+++ b/lA8-N_ARHTw.txt
@@ -0,0 +1,883 @@
+align:start position:0%
+ 
+we have found in this solution with some
+
+ align:start position:0%
+we have found in this solution with some
+ 
+
+ align:start position:0%
+we have found in this solution with some
+energy like this that there's a decaying
+
+ align:start position:0%
+energy like this that there's a decaying
+ 
+
+ align:start position:0%
+energy like this that there's a decaying
+exponential over this side and the
+
+ align:start position:0%
+exponential over this side and the
+ 
+
+ align:start position:0%
+exponential over this side and the
+question is often asked well what
+
+ align:start position:0%
+question is often asked well what
+ 
+
+ align:start position:0%
+question is often asked well what
+happens if you try to measure the
+
+ align:start position:0%
+happens if you try to measure the
+ 
+
+ align:start position:0%
+happens if you try to measure the
+particle in the forbidden region must be
+
+ align:start position:0%
+particle in the forbidden region must be
+ 
+
+ align:start position:0%
+particle in the forbidden region must be
+a problem if you find the particle in
+
+ align:start position:0%
+a problem if you find the particle in
+ 
+
+ align:start position:0%
+a problem if you find the particle in
+the forbidden region it has energy that
+
+ align:start position:0%
+the forbidden region it has energy that
+ 
+
+ align:start position:0%
+the forbidden region it has energy that
+is less than V naught so you you have
+
+ align:start position:0%
+is less than V naught so you you have
+ 
+
+ align:start position:0%
+is less than V naught so you you have
+found a particle with negative kinetic
+
+ align:start position:0%
+found a particle with negative kinetic
+ 
+
+ align:start position:0%
+found a particle with negative kinetic
+energy how does it look how can it
+
+ align:start position:0%
+energy how does it look how can it
+ 
+
+ align:start position:0%
+energy how does it look how can it
+happen what's going on can you really
+
+ align:start position:0%
+happen what's going on can you really
+ 
+
+ align:start position:0%
+happen what's going on can you really
+find the particle in the forbidden
+
+ align:start position:0%
+find the particle in the forbidden
+ 
+
+ align:start position:0%
+find the particle in the forbidden
+region and then how does this negative
+
+ align:start position:0%
+region and then how does this negative
+ 
+
+ align:start position:0%
+region and then how does this negative
+kinetic energy look like and the answer
+
+ align:start position:0%
+kinetic energy look like and the answer
+ 
+
+ align:start position:0%
+kinetic energy look like and the answer
+is that it's kind of funny what happens
+
+ align:start position:0%
+is that it's kind of funny what happens
+ 
+
+ align:start position:0%
+is that it's kind of funny what happens
+here you can make two statements it
+
+ align:start position:0%
+here you can make two statements it
+ 
+
+ align:start position:0%
+here you can make two statements it
+would be contradictory contradictory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory if you could make could say the
+
+ align:start position:0%
+theory if you could make could say the
+ 
+
+ align:start position:0%
+theory if you could make could say the
+following things one that the particle
+
+ align:start position:0%
+following things one that the particle
+ 
+
+ align:start position:0%
+following things one that the particle
+is in the forbidden region forbidden
+
+ align:start position:0%
+is in the forbidden region forbidden
+ 
+
+ align:start position:0%
+is in the forbidden region forbidden
+region until that the particle has
+
+ align:start position:0%
+region until that the particle has
+ 
+
+ align:start position:0%
+region until that the particle has
+energy less than V naught because then
+
+ align:start position:0%
+energy less than V naught because then
+ 
+
+ align:start position:0%
+energy less than V naught because then
+it would mean negative kinetic energy so
+
+ align:start position:0%
+it would mean negative kinetic energy so
+ 
+
+ align:start position:0%
+it would mean negative kinetic energy so
+if you can say these two things it seems
+
+ align:start position:0%
+if you can say these two things it seems
+ 
+
+ align:start position:0%
+if you can say these two things it seems
+a contradictory so quantum mechanics
+
+ align:start position:0%
+a contradictory so quantum mechanics
+ 
+
+ align:start position:0%
+a contradictory so quantum mechanics
+evades this problem now this is not
+
+ align:start position:0%
+evades this problem now this is not
+ 
+
+ align:start position:0%
+evades this problem now this is not
+discussed as far I can see except in
+
+ align:start position:0%
+discussed as far I can see except in
+ 
+
+ align:start position:0%
+discussed as far I can see except in
+some lecture loads of Gordon beam and
+
+ align:start position:0%
+some lecture loads of Gordon beam and
+ 
+
+ align:start position:0%
+some lecture loads of Gordon beam and
+and because the argument is not a
+
+ align:start position:0%
+and because the argument is not a
+ 
+
+ align:start position:0%
+and because the argument is not a
+hundred percent precise but I think the
+
+ align:start position:0%
+hundred percent precise but I think the
+ 
+
+ align:start position:0%
+hundred percent precise but I think the
+spirit of the argument is clear so I
+
+ align:start position:0%
+spirit of the argument is clear so I
+ 
+
+ align:start position:0%
+spirit of the argument is clear so I
+want to share it with you so here is the
+
+ align:start position:0%
+want to share it with you so here is the
+ 
+
+ align:start position:0%
+want to share it with you so here is the
+catch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this particle remember it's governed by
+
+ align:start position:0%
+this particle remember it's governed by
+ 
+
+ align:start position:0%
+this particle remember it's governed by
+e to the minus Kappa X in the forbidden
+
+ align:start position:0%
+e to the minus Kappa X in the forbidden
+ 
+
+ align:start position:0%
+e to the minus Kappa X in the forbidden
+region so the length scale here where
+
+ align:start position:0%
+region so the length scale here where
+ 
+
+ align:start position:0%
+region so the length scale here where
+you can find it the particle the length
+
+ align:start position:0%
+you can find it the particle the length
+ 
+
+ align:start position:0%
+you can find it the particle the length
+scale is this forbidden region stretches
+
+ align:start position:0%
+scale is this forbidden region stretches
+ 
+
+ align:start position:0%
+scale is this forbidden region stretches
+to about X of the order 1 over Kappa you
+
+ align:start position:0%
+to about X of the order 1 over Kappa you
+ 
+
+ align:start position:0%
+to about X of the order 1 over Kappa you
+know if you are going to find it in the
+
+ align:start position:0%
+know if you are going to find it in the
+ 
+
+ align:start position:0%
+know if you are going to find it in the
+region of a distance 1 over Kappa at N 1
+
+ align:start position:0%
+region of a distance 1 over Kappa at N 1
+ 
+
+ align:start position:0%
+region of a distance 1 over Kappa at N 1
+over Kappa you're not going to find it
+
+ align:start position:0%
+over Kappa you're not going to find it
+ 
+
+ align:start position:0%
+over Kappa you're not going to find it
+exponential is too small but remember
+
+ align:start position:0%
+exponential is too small but remember
+ 
+
+ align:start position:0%
+exponential is too small but remember
+what was Kappa Kappa squared was 2m V
+
+ align:start position:0%
+what was Kappa Kappa squared was 2m V
+ 
+
+ align:start position:0%
+what was Kappa Kappa squared was 2m V
+naught minus e over H squared that's
+
+ align:start position:0%
+naught minus e over H squared that's
+ 
+
+ align:start position:0%
+naught minus e over H squared that's
+what it was now if you want to look to
+
+ align:start position:0%
+what it was now if you want to look to
+ 
+
+ align:start position:0%
+what it was now if you want to look to
+see and declare that you have this
+
+ align:start position:0%
+see and declare that you have this
+ 
+
+ align:start position:0%
+see and declare that you have this
+particle you would have to be able to
+
+ align:start position:0%
+particle you would have to be able to
+ 
+
+ align:start position:0%
+particle you would have to be able to
+measure position with some precision
+
+ align:start position:0%
+measure position with some precision
+ 
+
+ align:start position:0%
+measure position with some precision
+with a precision small a little smaller
+
+ align:start position:0%
+with a precision small a little smaller
+ 
+
+ align:start position:0%
+with a precision small a little smaller
+than this otherwise if you measure with
+
+ align:start position:0%
+than this otherwise if you measure with
+ 
+
+ align:start position:0%
+than this otherwise if you measure with
+precision ten times that well maybe to
+
+ align:start position:0%
+precision ten times that well maybe to
+ 
+
+ align:start position:0%
+precision ten times that well maybe to
+the left maybe it's somewhere else so
+
+ align:start position:0%
+the left maybe it's somewhere else so
+ 
+
+ align:start position:0%
+the left maybe it's somewhere else so
+you need to measure position with Delta
+
+ align:start position:0%
+you need to measure position with Delta
+ 
+
+ align:start position:0%
+you need to measure position with Delta
+X a little smaller than one over Kappa
+
+ align:start position:0%
+X a little smaller than one over Kappa
+ 
+
+ align:start position:0%
+X a little smaller than one over Kappa
+otherwise you cannot really tell it's
+
+ align:start position:0%
+otherwise you cannot really tell it's
+ 
+
+ align:start position:0%
+otherwise you cannot really tell it's
+inside the forbidden region but now the
+
+ align:start position:0%
+inside the forbidden region but now the
+ 
+
+ align:start position:0%
+inside the forbidden region but now the
+problem is that if you do a position
+
+ align:start position:0%
+problem is that if you do a position
+ 
+
+ align:start position:0%
+problem is that if you do a position
+measurement there's gonna and you
+
+ align:start position:0%
+measurement there's gonna and you
+ 
+
+ align:start position:0%
+measurement there's gonna and you
+localize the wave function there's a
+
+ align:start position:0%
+localize the wave function there's a
+ 
+
+ align:start position:0%
+localize the wave function there's a
+momentum uncertainty the particle that
+
+ align:start position:0%
+momentum uncertainty the particle that
+ 
+
+ align:start position:0%
+momentum uncertainty the particle that
+you're looking at as opposed to the
+
+ align:start position:0%
+you're looking at as opposed to the
+ 
+
+ align:start position:0%
+you're looking at as opposed to the
+particle to the left has no momentum
+
+ align:start position:0%
+particle to the left has no momentum
+ 
+
+ align:start position:0%
+particle to the left has no momentum
+it's it's a different kind of wave
+
+ align:start position:0%
+it's it's a different kind of wave
+ 
+
+ align:start position:0%
+it's it's a different kind of wave
+function there's no momentum really
+
+ align:start position:0%
+function there's no momentum really
+ 
+
+ align:start position:0%
+function there's no momentum really
+associated or well-defined momentum to
+
+ align:start position:0%
+associated or well-defined momentum to
+ 
+
+ align:start position:0%
+associated or well-defined momentum to
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so because you make a position you
+
+ align:start position:0%
+so because you make a position you
+ 
+
+ align:start position:0%
+so because you make a position you
+localize in X whatever wave function you
+
+ align:start position:0%
+localize in X whatever wave function you
+ 
+
+ align:start position:0%
+localize in X whatever wave function you
+have you're going to have some
+
+ align:start position:0%
+have you're going to have some
+ 
+
+ align:start position:0%
+have you're going to have some
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+20 and some momentum that is going to be
+
+ align:start position:0%
+20 and some momentum that is going to be
+ 
+
+ align:start position:0%
+20 and some momentum that is going to be
+of kind of bigger than h-bar over Delta
+
+ align:start position:0%
+of kind of bigger than h-bar over Delta
+ 
+
+ align:start position:0%
+of kind of bigger than h-bar over Delta
+X so a momentum that is bigger than of
+
+ align:start position:0%
+X so a momentum that is bigger than of
+ 
+
+ align:start position:0%
+X so a momentum that is bigger than of
+or a little bigger than h-bar Kappa you
+
+ align:start position:0%
+or a little bigger than h-bar Kappa you
+ 
+
+ align:start position:0%
+or a little bigger than h-bar Kappa you
+know if Delta X is less than that the
+
+ align:start position:0%
+know if Delta X is less than that the
+ 
+
+ align:start position:0%
+know if Delta X is less than that the
+inequality goes in the same direction so
+
+ align:start position:0%
+inequality goes in the same direction so
+ 
+
+ align:start position:0%
+inequality goes in the same direction so
+there's going to be an uncertainty P and
+
+ align:start position:0%
+there's going to be an uncertainty P and
+ 
+
+ align:start position:0%
+there's going to be an uncertainty P and
+therefore this particle has now some
+
+ align:start position:0%
+therefore this particle has now some
+ 
+
+ align:start position:0%
+therefore this particle has now some
+kinetic energy due to this uncertain
+
+ align:start position:0%
+kinetic energy due to this uncertain
+ 
+
+ align:start position:0%
+kinetic energy due to this uncertain
+momentum so our uncertainty in the
+
+ align:start position:0%
+momentum so our uncertainty in the
+ 
+
+ align:start position:0%
+momentum so our uncertainty in the
+kinetic energy is how much is P squared
+
+ align:start position:0%
+kinetic energy is how much is P squared
+ 
+
+ align:start position:0%
+kinetic energy is how much is P squared
+over 2m where P is this uncertain
+
+ align:start position:0%
+over 2m where P is this uncertain
+ 
+
+ align:start position:0%
+over 2m where P is this uncertain
+momentum so this is equal to H bar Kappa
+
+ align:start position:0%
+momentum so this is equal to H bar Kappa
+ 
+
+ align:start position:0%
+momentum so this is equal to H bar Kappa
+squared over 2m which is equal to V
+
+ align:start position:0%
+squared over 2m which is equal to V
+ 
+
+ align:start position:0%
+squared over 2m which is equal to V
+naught minus e so actually if you think
+
+ align:start position:0%
+naught minus e so actually if you think
+ 
+
+ align:start position:0%
+naught minus e so actually if you think
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+here is V naught this difference is V
+
+ align:start position:0%
+here is V naught this difference is V
+ 
+
+ align:start position:0%
+here is V naught this difference is V
+naught minus E and you are going to say
+
+ align:start position:0%
+naught minus E and you are going to say
+ 
+
+ align:start position:0%
+naught minus E and you are going to say
+oh I found the particle it has negative
+
+ align:start position:0%
+oh I found the particle it has negative
+ 
+
+ align:start position:0%
+oh I found the particle it has negative
+kinetic energy but not answer to the
+
+ align:start position:0%
+kinetic energy but not answer to the
+ 
+
+ align:start position:0%
+kinetic energy but not answer to the
+principles that you found it localized
+
+ align:start position:0%
+principles that you found it localized
+ 
+
+ align:start position:0%
+principles that you found it localized
+okay your kinetic energy I'm sorry now
+
+ align:start position:0%
+okay your kinetic energy I'm sorry now
+ 
+
+ align:start position:0%
+okay your kinetic energy I'm sorry now
+has an uncertainty how much V not minus
+
+ align:start position:0%
+has an uncertainty how much V not minus
+ 
+
+ align:start position:0%
+has an uncertainty how much V not minus
+E so whatever you wanted to prove it has
+
+ align:start position:0%
+E so whatever you wanted to prove it has
+ 
+
+ align:start position:0%
+E so whatever you wanted to prove it has
+been disproved you can't do it the total
+
+ align:start position:0%
+been disproved you can't do it the total
+ 
+
+ align:start position:0%
+been disproved you can't do it the total
+energy total energy is now e
+
+ align:start position:0%
+energy total energy is now e
+ 
+
+ align:start position:0%
+energy total energy is now e
+plus the uncertainty in the energy which
+
+ align:start position:0%
+plus the uncertainty in the energy which
+ 
+
+ align:start position:0%
+plus the uncertainty in the energy which
+is e plus V naught minus E and it's
+
+ align:start position:0%
+is e plus V naught minus E and it's
+ 
+
+ align:start position:0%
+is e plus V naught minus E and it's
+therefore greater than or equal to V
+
+ align:start position:0%
+therefore greater than or equal to V
+ 
+
+ align:start position:0%
+therefore greater than or equal to V
+naught and no no real contradiction so
+
+ align:start position:0%
+naught and no no real contradiction so
+ 
+
+ align:start position:0%
+naught and no no real contradiction so
+then certainly principle sort of
+
+ align:start position:0%
+then certainly principle sort of
+ 
+
+ align:start position:0%
+then certainly principle sort of
+conspires to prevent you from finding a
+
+ align:start position:0%
+conspires to prevent you from finding a
+ 
+
+ align:start position:0%
+conspires to prevent you from finding a
+particle with negative kinetic energy
+
+ align:start position:0%
+particle with negative kinetic energy
+ 
+
+ align:start position:0%
+particle with negative kinetic energy
+and if you do detect the particle in the
+
+ align:start position:0%
+and if you do detect the particle in the
+ 
+
+ align:start position:0%
+and if you do detect the particle in the
+furby
+
+ align:start position:0%
+furby
+ 
+
+ align:start position:0%
+furby
+originally will have energy total energy
+
+ align:start position:0%
+originally will have energy total energy
+ 
+
+ align:start position:0%
+originally will have energy total energy
+zero or total kinetic energy zero it
+
+ align:start position:0%
+zero or total kinetic energy zero it
+ 
+
+ align:start position:0%
+zero or total kinetic energy zero it
+will be a normal particle nothing
+
+ align:start position:0%
+will be a normal particle nothing
+ 
+
+ align:start position:0%
+will be a normal particle nothing
+strange about
\ No newline at end of file
diff --git a/lkrsGRNsoEU.txt b/lkrsGRNsoEU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a4a2b210fa7bdd75dae1d7a9930e95506dab7b1
--- /dev/null
+++ b/lkrsGRNsoEU.txt
@@ -0,0 +1,1675 @@
+align:start position:0%
+ 
+okay so solving successfully finished
+
+ align:start position:0%
+okay so solving successfully finished
+ 
+
+ align:start position:0%
+okay so solving successfully finished
+and we've got the results if you had any
+
+ align:start position:0%
+and we've got the results if you had any
+ 
+
+ align:start position:0%
+and we've got the results if you had any
+trouble solving this problem then you
+
+ align:start position:0%
+trouble solving this problem then you
+ 
+
+ align:start position:0%
+trouble solving this problem then you
+should go into options in the solver and
+
+ align:start position:0%
+should go into options in the solver and
+ 
+
+ align:start position:0%
+should go into options in the solver and
+select that you want to edit the length
+
+ align:start position:0%
+select that you want to edit the length
+ 
+
+ align:start position:0%
+select that you want to edit the length
+of solution time and increase it past
+
+ align:start position:0%
+of solution time and increase it past
+ 
+
+ align:start position:0%
+of solution time and increase it past
+100 seconds the LibreOffice solver is
+
+ align:start position:0%
+100 seconds the LibreOffice solver is
+ 
+
+ align:start position:0%
+100 seconds the LibreOffice solver is
+not incredibly powerful so it may need
+
+ align:start position:0%
+not incredibly powerful so it may need
+ 
+
+ align:start position:0%
+not incredibly powerful so it may need
+more time to find the solution we do
+
+ align:start position:0%
+more time to find the solution we do
+ 
+
+ align:start position:0%
+more time to find the solution we do
+recommend that if you have access to
+
+ align:start position:0%
+recommend that if you have access to
+ 
+
+ align:start position:0%
+recommend that if you have access to
+Excel that you use Excel instead for
+
+ align:start position:0%
+Excel that you use Excel instead for
+ 
+
+ align:start position:0%
+Excel that you use Excel instead for
+integer optimization problems because
+
+ align:start position:0%
+integer optimization problems because
+ 
+
+ align:start position:0%
+integer optimization problems because
+Excel is a little bit better with
+
+ align:start position:0%
+Excel is a little bit better with
+ 
+
+ align:start position:0%
+Excel is a little bit better with
+integer optimization however you
+
+ align:start position:0%
+integer optimization however you
+ 
+
+ align:start position:0%
+integer optimization however you
+probably got the solution just fine so
+
+ align:start position:0%
+probably got the solution just fine so
+ 
+
+ align:start position:0%
+probably got the solution just fine so
+you'll want to go ahead and click keep
+
+ align:start position:0%
+you'll want to go ahead and click keep
+ 
+
+ align:start position:0%
+you'll want to go ahead and click keep
+results okay so now we can take a look
+
+ align:start position:0%
+results okay so now we can take a look
+ 
+
+ align:start position:0%
+results okay so now we can take a look
+at our solution so we've got the
+
+ align:start position:0%
+at our solution so we've got the
+ 
+
+ align:start position:0%
+at our solution so we've got the
+objective of 4.46 this is not
+
+ align:start position:0%
+objective of 4.46 this is not
+ 
+
+ align:start position:0%
+objective of 4.46 this is not
+particularly interpretable until you
+
+ align:start position:0%
+particularly interpretable until you
+ 
+
+ align:start position:0%
+particularly interpretable until you
+remember that what our objective is is
+
+ align:start position:0%
+remember that what our objective is is
+ 
+
+ align:start position:0%
+remember that what our objective is is
+the total of all departments percent of
+
+ align:start position:0%
+the total of all departments percent of
+ 
+
+ align:start position:0%
+the total of all departments percent of
+target allocation hours reached so the
+
+ align:start position:0%
+target allocation hours reached so the
+ 
+
+ align:start position:0%
+target allocation hours reached so the
+best possible number that we could get
+
+ align:start position:0%
+best possible number that we could get
+ 
+
+ align:start position:0%
+best possible number that we could get
+here would be five if every department
+
+ align:start position:0%
+here would be five if every department
+ 
+
+ align:start position:0%
+here would be five if every department
+had 100 percent of their target
+
+ align:start position:0%
+had 100 percent of their target
+ 
+
+ align:start position:0%
+had 100 percent of their target
+allocation hours reached so we've got
+
+ align:start position:0%
+allocation hours reached so we've got
+ 
+
+ align:start position:0%
+allocation hours reached so we've got
+four point four six so let's go up and
+
+ align:start position:0%
+four point four six so let's go up and
+ 
+
+ align:start position:0%
+four point four six so let's go up and
+take a look at the solution so we're
+
+ align:start position:0%
+take a look at the solution so we're
+ 
+
+ align:start position:0%
+take a look at the solution so we're
+giving ophthalmology a total of four
+
+ align:start position:0%
+giving ophthalmology a total of four
+ 
+
+ align:start position:0%
+giving ophthalmology a total of four
+operating rooms per week which is 32
+
+ align:start position:0%
+operating rooms per week which is 32
+ 
+
+ align:start position:0%
+operating rooms per week which is 32
+weekly hours or 81 percent of their
+
+ align:start position:0%
+weekly hours or 81 percent of their
+ 
+
+ align:start position:0%
+weekly hours or 81 percent of their
+target we're giving gynecology 14 which
+
+ align:start position:0%
+target we're giving gynecology 14 which
+ 
+
+ align:start position:0%
+target we're giving gynecology 14 which
+is 112 weekly hours 95 percent of their
+
+ align:start position:0%
+is 112 weekly hours 95 percent of their
+ 
+
+ align:start position:0%
+is 112 weekly hours 95 percent of their
+target we're giving oral surgery too and
+
+ align:start position:0%
+target we're giving oral surgery too and
+ 
+
+ align:start position:0%
+target we're giving oral surgery too and
+as we see the constraints restricted us
+
+ align:start position:0%
+as we see the constraints restricted us
+ 
+
+ align:start position:0%
+as we see the constraints restricted us
+so that we only gave oral surgery
+
+ align:start position:0%
+so that we only gave oral surgery
+ 
+
+ align:start position:0%
+so that we only gave oral surgery
+operating rooms on Tuesdays and
+
+ align:start position:0%
+operating rooms on Tuesdays and
+ 
+
+ align:start position:0%
+operating rooms on Tuesdays and
+Thursdays
+
+ align:start position:0%
+Thursdays
+ 
+
+ align:start position:0%
+Thursdays
+this is 80% of the target we gave
+
+ align:start position:0%
+this is 80% of the target we gave
+ 
+
+ align:start position:0%
+this is 80% of the target we gave
+general surgery three operating rooms
+
+ align:start position:0%
+general surgery three operating rooms
+ 
+
+ align:start position:0%
+general surgery three operating rooms
+and we gave hope sorry we gave
+
+ align:start position:0%
+and we gave hope sorry we gave
+ 
+
+ align:start position:0%
+and we gave hope sorry we gave
+Otolaryngology three operating rooms and
+
+ align:start position:0%
+Otolaryngology three operating rooms and
+ 
+
+ align:start position:0%
+Otolaryngology three operating rooms and
+general surgery 23 operating rooms
+
+ align:start position:0%
+general surgery 23 operating rooms
+ 
+
+ align:start position:0%
+general surgery 23 operating rooms
+getting 91 and 97 percent of their
+
+ align:start position:0%
+getting 91 and 97 percent of their
+ 
+
+ align:start position:0%
+getting 91 and 97 percent of their
+target allocation hours so suppose that
+
+ align:start position:0%
+target allocation hours so suppose that
+ 
+
+ align:start position:0%
+target allocation hours so suppose that
+you were the operating room manager who
+
+ align:start position:0%
+you were the operating room manager who
+ 
+
+ align:start position:0%
+you were the operating room manager who
+knows integer optimization in practice
+
+ align:start position:0%
+knows integer optimization in practice
+ 
+
+ align:start position:0%
+knows integer optimization in practice
+what would happen is that you would go
+
+ align:start position:0%
+what would happen is that you would go
+ 
+
+ align:start position:0%
+what would happen is that you would go
+off and you would design what we
+
+ align:start position:0%
+off and you would design what we
+ 
+
+ align:start position:0%
+off and you would design what we
+did here in the recitation you would
+
+ align:start position:0%
+did here in the recitation you would
+ 
+
+ align:start position:0%
+did here in the recitation you would
+have this optimization model for
+
+ align:start position:0%
+have this optimization model for
+ 
+
+ align:start position:0%
+have this optimization model for
+operating room scheduling in the
+
+ align:start position:0%
+operating room scheduling in the
+ 
+
+ align:start position:0%
+operating room scheduling in the
+hospital you'd solve it you'd find the
+
+ align:start position:0%
+hospital you'd solve it you'd find the
+ 
+
+ align:start position:0%
+hospital you'd solve it you'd find the
+optimal solution and you'd come back and
+
+ align:start position:0%
+optimal solution and you'd come back and
+ 
+
+ align:start position:0%
+optimal solution and you'd come back and
+present it to the surgical departments
+
+ align:start position:0%
+present it to the surgical departments
+ 
+
+ align:start position:0%
+present it to the surgical departments
+and they'll look at the schedule and all
+
+ align:start position:0%
+and they'll look at the schedule and all
+ 
+
+ align:start position:0%
+and they'll look at the schedule and all
+of a sudden they'll tell you it doesn't
+
+ align:start position:0%
+of a sudden they'll tell you it doesn't
+ 
+
+ align:start position:0%
+of a sudden they'll tell you it doesn't
+work for them and you'll say why not
+
+ align:start position:0%
+work for them and you'll say why not
+ 
+
+ align:start position:0%
+work for them and you'll say why not
+I incorporated everything that you asked
+
+ align:start position:0%
+I incorporated everything that you asked
+ 
+
+ align:start position:0%
+I incorporated everything that you asked
+for and it's true you did but oftentimes
+
+ align:start position:0%
+for and it's true you did but oftentimes
+ 
+
+ align:start position:0%
+for and it's true you did but oftentimes
+there are actually other constraints
+
+ align:start position:0%
+there are actually other constraints
+ 
+
+ align:start position:0%
+there are actually other constraints
+that they forgot to tell you about so
+
+ align:start position:0%
+that they forgot to tell you about so
+ 
+
+ align:start position:0%
+that they forgot to tell you about so
+what would you do in that case well
+
+ align:start position:0%
+what would you do in that case well
+ 
+
+ align:start position:0%
+what would you do in that case well
+you'd listen to their additional
+
+ align:start position:0%
+you'd listen to their additional
+ 
+
+ align:start position:0%
+you'd listen to their additional
+constraints and go back and add them to
+
+ align:start position:0%
+constraints and go back and add them to
+ 
+
+ align:start position:0%
+constraints and go back and add them to
+the model so that's exactly what we'll
+
+ align:start position:0%
+the model so that's exactly what we'll
+ 
+
+ align:start position:0%
+the model so that's exactly what we'll
+do here suppose the general surgery
+
+ align:start position:0%
+do here suppose the general surgery
+ 
+
+ align:start position:0%
+do here suppose the general surgery
+department took a look at the schedule
+
+ align:start position:0%
+department took a look at the schedule
+ 
+
+ align:start position:0%
+department took a look at the schedule
+and said oh great we have 23 operating
+
+ align:start position:0%
+and said oh great we have 23 operating
+ 
+
+ align:start position:0%
+and said oh great we have 23 operating
+rooms per week that's exactly 2 less
+
+ align:start position:0%
+rooms per week that's exactly 2 less
+ 
+
+ align:start position:0%
+rooms per week that's exactly 2 less
+than actually our maximum it's right in
+
+ align:start position:0%
+than actually our maximum it's right in
+ 
+
+ align:start position:0%
+than actually our maximum it's right in
+between our minimum or maximum and we're
+
+ align:start position:0%
+between our minimum or maximum and we're
+ 
+
+ align:start position:0%
+between our minimum or maximum and we're
+getting 97% of our weekly target we
+
+ align:start position:0%
+getting 97% of our weekly target we
+ 
+
+ align:start position:0%
+getting 97% of our weekly target we
+think that's wonderful
+
+ align:start position:0%
+think that's wonderful
+ 
+
+ align:start position:0%
+think that's wonderful
+however it's a little bit uneven you
+
+ align:start position:0%
+however it's a little bit uneven you
+ 
+
+ align:start position:0%
+however it's a little bit uneven you
+know six on Wednesday three on Thursday
+
+ align:start position:0%
+know six on Wednesday three on Thursday
+ 
+
+ align:start position:0%
+know six on Wednesday three on Thursday
+can we just have at least four per day
+
+ align:start position:0%
+can we just have at least four per day
+ 
+
+ align:start position:0%
+can we just have at least four per day
+okay well we can do that so let's go up
+
+ align:start position:0%
+okay well we can do that so let's go up
+ 
+
+ align:start position:0%
+okay well we can do that so let's go up
+to the minimum number of operating rooms
+
+ align:start position:0%
+to the minimum number of operating rooms
+ 
+
+ align:start position:0%
+to the minimum number of operating rooms
+per day and for general surgery let's
+
+ align:start position:0%
+per day and for general surgery let's
+ 
+
+ align:start position:0%
+per day and for general surgery let's
+change this from 0 to 4 this will help
+
+ align:start position:0%
+change this from 0 to 4 this will help
+ 
+
+ align:start position:0%
+change this from 0 to 4 this will help
+them balance throughout the week and
+
+ align:start position:0%
+them balance throughout the week and
+ 
+
+ align:start position:0%
+them balance throughout the week and
+potentially ophthalmology we'll look at
+
+ align:start position:0%
+potentially ophthalmology we'll look at
+ 
+
+ align:start position:0%
+potentially ophthalmology we'll look at
+their schedule and they'll think the
+
+ align:start position:0%
+their schedule and they'll think the
+ 
+
+ align:start position:0%
+their schedule and they'll think the
+same thing and they'll think well we
+
+ align:start position:0%
+same thing and they'll think well we
+ 
+
+ align:start position:0%
+same thing and they'll think well we
+actually would prefer to balance it
+
+ align:start position:0%
+actually would prefer to balance it
+ 
+
+ align:start position:0%
+actually would prefer to balance it
+throughout the week we want at most one
+
+ align:start position:0%
+throughout the week we want at most one
+ 
+
+ align:start position:0%
+throughout the week we want at most one
+operating room per day we don't want to
+
+ align:start position:0%
+operating room per day we don't want to
+ 
+
+ align:start position:0%
+operating room per day we don't want to
+have two on Monday let's put one of
+
+ align:start position:0%
+have two on Monday let's put one of
+ 
+
+ align:start position:0%
+have two on Monday let's put one of
+those on Thursday or Friday so that's ok
+
+ align:start position:0%
+those on Thursday or Friday so that's ok
+ 
+
+ align:start position:0%
+those on Thursday or Friday so that's ok
+we can do that too we just go to the
+
+ align:start position:0%
+we can do that too we just go to the
+ 
+
+ align:start position:0%
+we can do that too we just go to the
+maximum number of operating rooms per
+
+ align:start position:0%
+maximum number of operating rooms per
+ 
+
+ align:start position:0%
+maximum number of operating rooms per
+day and for ophthalmology we change it
+
+ align:start position:0%
+day and for ophthalmology we change it
+ 
+
+ align:start position:0%
+day and for ophthalmology we change it
+to 1 let's resolve the model and see
+
+ align:start position:0%
+to 1 let's resolve the model and see
+ 
+
+ align:start position:0%
+to 1 let's resolve the model and see
+what we get again we select the
+
+ align:start position:0%
+what we get again we select the
+ 
+
+ align:start position:0%
+what we get again we select the
+objective go to tools pull down the
+
+ align:start position:0%
+objective go to tools pull down the
+ 
+
+ align:start position:0%
+objective go to tools pull down the
+solver it should have everything already
+
+ align:start position:0%
+solver it should have everything already
+ 
+
+ align:start position:0%
+solver it should have everything already
+loaded up and we just get to hit solve
+
+ align:start position:0%
+loaded up and we just get to hit solve
+ 
+
+ align:start position:0%
+loaded up and we just get to hit solve
+all right so that was quick solving
+
+ align:start position:0%
+all right so that was quick solving
+ 
+
+ align:start position:0%
+all right so that was quick solving
+successfully finished and it looks like
+
+ align:start position:0%
+successfully finished and it looks like
+ 
+
+ align:start position:0%
+successfully finished and it looks like
+we actually have exactly the same
+
+ align:start position:0%
+we actually have exactly the same
+ 
+
+ align:start position:0%
+we actually have exactly the same
+results as we had before
+
+ align:start position:0%
+results as we had before
+ 
+
+ align:start position:0%
+results as we had before
+let's hit keep result and take a closer
+
+ align:start position:0%
+let's hit keep result and take a closer
+ 
+
+ align:start position:0%
+let's hit keep result and take a closer
+look at this so our objective functions
+
+ align:start position:0%
+look at this so our objective functions
+ 
+
+ align:start position:0%
+look at this so our objective functions
+stayed exactly the same but we were able
+
+ align:start position:0%
+stayed exactly the same but we were able
+ 
+
+ align:start position:0%
+stayed exactly the same but we were able
+to incorporate the new constraints the
+
+ align:start position:0%
+to incorporate the new constraints the
+ 
+
+ align:start position:0%
+to incorporate the new constraints the
+new requirement that the general surgery
+
+ align:start position:0%
+new requirement that the general surgery
+ 
+
+ align:start position:0%
+new requirement that the general surgery
+department have at least four operating
+
+ align:start position:0%
+department have at least four operating
+ 
+
+ align:start position:0%
+department have at least four operating
+rooms per day and that the ophthalmology
+
+ align:start position:0%
+rooms per day and that the ophthalmology
+ 
+
+ align:start position:0%
+rooms per day and that the ophthalmology
+department have at most one operating
+
+ align:start position:0%
+department have at most one operating
+ 
+
+ align:start position:0%
+department have at most one operating
+room per day this means that within the
+
+ align:start position:0%
+room per day this means that within the
+ 
+
+ align:start position:0%
+room per day this means that within the
+solution we had before there's actually
+
+ align:start position:0%
+solution we had before there's actually
+ 
+
+ align:start position:0%
+solution we had before there's actually
+a little bit of wiggle room we could
+
+ align:start position:0%
+a little bit of wiggle room we could
+ 
+
+ align:start position:0%
+a little bit of wiggle room we could
+move some things around without changing
+
+ align:start position:0%
+move some things around without changing
+ 
+
+ align:start position:0%
+move some things around without changing
+the optimality of the solution that is
+
+ align:start position:0%
+the optimality of the solution that is
+ 
+
+ align:start position:0%
+the optimality of the solution that is
+without changing the percent of target
+
+ align:start position:0%
+without changing the percent of target
+ 
+
+ align:start position:0%
+without changing the percent of target
+that each department received and as you
+
+ align:start position:0%
+that each department received and as you
+ 
+
+ align:start position:0%
+that each department received and as you
+see this is a little boring balanced for
+
+ align:start position:0%
+see this is a little boring balanced for
+ 
+
+ align:start position:0%
+see this is a little boring balanced for
+the ophthalmology department and the
+
+ align:start position:0%
+the ophthalmology department and the
+ 
+
+ align:start position:0%
+the ophthalmology department and the
+general surgery department so great so
+
+ align:start position:0%
+general surgery department so great so
+ 
+
+ align:start position:0%
+general surgery department so great so
+so maybe seeing that this was available
+
+ align:start position:0%
+so maybe seeing that this was available
+ 
+
+ align:start position:0%
+so maybe seeing that this was available
+then you'd go back you'd present it and
+
+ align:start position:0%
+then you'd go back you'd present it and
+ 
+
+ align:start position:0%
+then you'd go back you'd present it and
+general surgery would say well maybe
+
+ align:start position:0%
+general surgery would say well maybe
+ 
+
+ align:start position:0%
+general surgery would say well maybe
+could we have at least five per day so
+
+ align:start position:0%
+could we have at least five per day so
+ 
+
+ align:start position:0%
+could we have at least five per day so
+if you went up and changed this made it
+
+ align:start position:0%
+if you went up and changed this made it
+ 
+
+ align:start position:0%
+if you went up and changed this made it
+five all the way across instead of four
+
+ align:start position:0%
+five all the way across instead of four
+ 
+
+ align:start position:0%
+five all the way across instead of four
+and you solved it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would happen you probably have an
+
+ align:start position:0%
+what would happen you probably have an
+ 
+
+ align:start position:0%
+what would happen you probably have an
+idea already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is exactly what you were
+
+ align:start position:0%
+and this is exactly what you were
+ 
+
+ align:start position:0%
+and this is exactly what you were
+thinking no solution was found the model
+
+ align:start position:0%
+thinking no solution was found the model
+ 
+
+ align:start position:0%
+thinking no solution was found the model
+is infeasible check limiting conditions
+
+ align:start position:0%
+is infeasible check limiting conditions
+ 
+
+ align:start position:0%
+is infeasible check limiting conditions
+so why is the model infeasible well
+
+ align:start position:0%
+so why is the model infeasible well
+ 
+
+ align:start position:0%
+so why is the model infeasible well
+let's take a look oops
+
+ align:start position:0%
+let's take a look oops
+ 
+
+ align:start position:0%
+let's take a look oops
+scroll back over the model is infeasible
+
+ align:start position:0%
+scroll back over the model is infeasible
+ 
+
+ align:start position:0%
+scroll back over the model is infeasible
+because let's see so it's not because of
+
+ align:start position:0%
+because let's see so it's not because of
+ 
+
+ align:start position:0%
+because let's see so it's not because of
+the minimum and maximum weekly
+
+ align:start position:0%
+the minimum and maximum weekly
+ 
+
+ align:start position:0%
+the minimum and maximum weekly
+Department requirements because general
+
+ align:start position:0%
+Department requirements because general
+ 
+
+ align:start position:0%
+Department requirements because general
+surgery said that they were willing to
+
+ align:start position:0%
+surgery said that they were willing to
+ 
+
+ align:start position:0%
+surgery said that they were willing to
+have up to 25 operating rooms per week
+
+ align:start position:0%
+have up to 25 operating rooms per week
+ 
+
+ align:start position:0%
+have up to 25 operating rooms per week
+however if you look at the weekly
+
+ align:start position:0%
+however if you look at the weekly
+ 
+
+ align:start position:0%
+however if you look at the weekly
+targets 25 times 8 is 200 so if we were
+
+ align:start position:0%
+targets 25 times 8 is 200 so if we were
+ 
+
+ align:start position:0%
+targets 25 times 8 is 200 so if we were
+to actually assign general surgery 5
+
+ align:start position:0%
+to actually assign general surgery 5
+ 
+
+ align:start position:0%
+to actually assign general surgery 5
+operating rooms per day we would be
+
+ align:start position:0%
+operating rooms per day we would be
+ 
+
+ align:start position:0%
+operating rooms per day we would be
+assigning them 200 hours per week which
+
+ align:start position:0%
+assigning them 200 hours per week which
+ 
+
+ align:start position:0%
+assigning them 200 hours per week which
+exceeds their weekly target and our
+
+ align:start position:0%
+exceeds their weekly target and our
+ 
+
+ align:start position:0%
+exceeds their weekly target and our
+optimization model says we cannot exceed
+
+ align:start position:0%
+optimization model says we cannot exceed
+ 
+
+ align:start position:0%
+optimization model says we cannot exceed
+the weekly targets so just right there
+
+ align:start position:0%
+the weekly targets so just right there
+ 
+
+ align:start position:0%
+the weekly targets so just right there
+we can tell that it's infeasible because
+
+ align:start position:0%
+we can tell that it's infeasible because
+ 
+
+ align:start position:0%
+we can tell that it's infeasible because
+of this constraint so let's change this
+
+ align:start position:0%
+of this constraint so let's change this
+ 
+
+ align:start position:0%
+of this constraint so let's change this
+back to 4 ok so suppose you've you know
+
+ align:start position:0%
+back to 4 ok so suppose you've you know
+ 
+
+ align:start position:0%
+back to 4 ok so suppose you've you know
+you've come up with a solution you've
+
+ align:start position:0%
+you've come up with a solution you've
+ 
+
+ align:start position:0%
+you've come up with a solution you've
+gone back to the surgical departments
+
+ align:start position:0%
+gone back to the surgical departments
+ 
+
+ align:start position:0%
+gone back to the surgical departments
+you've presented your solution they've
+
+ align:start position:0%
+you've presented your solution they've
+ 
+
+ align:start position:0%
+you've presented your solution they've
+maybe requested additional changes and
+
+ align:start position:0%
+maybe requested additional changes and
+ 
+
+ align:start position:0%
+maybe requested additional changes and
+we've made those changes here so does
+
+ align:start position:0%
+we've made those changes here so does
+ 
+
+ align:start position:0%
+we've made those changes here so does
+this mean that your job is done well no
+
+ align:start position:0%
+this mean that your job is done well no
+ 
+
+ align:start position:0%
+this mean that your job is done well no
+not really
+
+ align:start position:0%
+not really
+ 
+
+ align:start position:0%
+not really
+of course you could go back to the
+
+ align:start position:0%
+of course you could go back to the
+ 
+
+ align:start position:0%
+of course you could go back to the
+surgical departments and tell them that
+
+ align:start position:0%
+surgical departments and tell them that
+ 
+
+ align:start position:0%
+surgical departments and tell them that
+this is the schedule they're going to
+
+ align:start position:0%
+this is the schedule they're going to
+ 
+
+ align:start position:0%
+this is the schedule they're going to
+have every week but I bet if you did
+
+ align:start position:0%
+have every week but I bet if you did
+ 
+
+ align:start position:0%
+have every week but I bet if you did
+that you would hear some complaints
+
+ align:start position:0%
+that you would hear some complaints
+ 
+
+ align:start position:0%
+that you would hear some complaints
+let's go into our solution and take a
+
+ align:start position:0%
+let's go into our solution and take a
+ 
+
+ align:start position:0%
+let's go into our solution and take a
+closer look to see why so for example
+
+ align:start position:0%
+closer look to see why so for example
+ 
+
+ align:start position:0%
+closer look to see why so for example
+let's look at the ophthalmology
+
+ align:start position:0%
+let's look at the ophthalmology
+ 
+
+ align:start position:0%
+let's look at the ophthalmology
+department in our solution we're
+
+ align:start position:0%
+department in our solution we're
+ 
+
+ align:start position:0%
+department in our solution we're
+assigning them for operating rooms per
+
+ align:start position:0%
+assigning them for operating rooms per
+ 
+
+ align:start position:0%
+assigning them for operating rooms per
+week that gives them 32 weekly hours
+
+ align:start position:0%
+week that gives them 32 weekly hours
+ 
+
+ align:start position:0%
+week that gives them 32 weekly hours
+which is 81 percent of their target
+
+ align:start position:0%
+which is 81 percent of their target
+ 
+
+ align:start position:0%
+which is 81 percent of their target
+allocation hours
+
+ align:start position:0%
+allocation hours
+ 
+
+ align:start position:0%
+allocation hours
+if you assigned the schedule to off the
+
+ align:start position:0%
+if you assigned the schedule to off the
+ 
+
+ align:start position:0%
+if you assigned the schedule to off the
+malla G every week then they would never
+
+ align:start position:0%
+malla G every week then they would never
+ 
+
+ align:start position:0%
+malla G every week then they would never
+get more than 81 percent of their target
+
+ align:start position:0%
+get more than 81 percent of their target
+ 
+
+ align:start position:0%
+get more than 81 percent of their target
+allocation hours and overtime this would
+
+ align:start position:0%
+allocation hours and overtime this would
+ 
+
+ align:start position:0%
+allocation hours and overtime this would
+lead to a real shortage the reason why
+
+ align:start position:0%
+lead to a real shortage the reason why
+ 
+
+ align:start position:0%
+lead to a real shortage the reason why
+we never assign them more than 4 in our
+
+ align:start position:0%
+we never assign them more than 4 in our
+ 
+
+ align:start position:0%
+we never assign them more than 4 in our
+optimization model
+
+ align:start position:0%
+optimization model
+ 
+
+ align:start position:0%
+optimization model
+is because their weekly target number of
+
+ align:start position:0%
+is because their weekly target number of
+ 
+
+ align:start position:0%
+is because their weekly target number of
+hours was 39.4 if we had assigned them
+
+ align:start position:0%
+hours was 39.4 if we had assigned them
+ 
+
+ align:start position:0%
+hours was 39.4 if we had assigned them
+five operating rooms it would be giving
+
+ align:start position:0%
+five operating rooms it would be giving
+ 
+
+ align:start position:0%
+five operating rooms it would be giving
+them 40 hours per week which exceeds
+
+ align:start position:0%
+them 40 hours per week which exceeds
+ 
+
+ align:start position:0%
+them 40 hours per week which exceeds
+their weekly target so the way our
+
+ align:start position:0%
+their weekly target so the way our
+ 
+
+ align:start position:0%
+their weekly target so the way our
+optimization model is set up we will
+
+ align:start position:0%
+optimization model is set up we will
+ 
+
+ align:start position:0%
+optimization model is set up we will
+never give them more than four operating
+
+ align:start position:0%
+never give them more than four operating
+ 
+
+ align:start position:0%
+never give them more than four operating
+rooms per week but if you were the ORM
+
+ align:start position:0%
+rooms per week but if you were the ORM
+ 
+
+ align:start position:0%
+rooms per week but if you were the ORM
+manager you would realize that this is
+
+ align:start position:0%
+manager you would realize that this is
+ 
+
+ align:start position:0%
+manager you would realize that this is
+actually something that we should be a
+
+ align:start position:0%
+actually something that we should be a
+ 
+
+ align:start position:0%
+actually something that we should be a
+little more flexible about perhaps you
+
+ align:start position:0%
+little more flexible about perhaps you
+ 
+
+ align:start position:0%
+little more flexible about perhaps you
+would consider giving them five
+
+ align:start position:0%
+would consider giving them five
+ 
+
+ align:start position:0%
+would consider giving them five
+operating rooms one week or maybe five
+
+ align:start position:0%
+operating rooms one week or maybe five
+ 
+
+ align:start position:0%
+operating rooms one week or maybe five
+operating rooms you know every two weeks
+
+ align:start position:0%
+operating rooms you know every two weeks
+ 
+
+ align:start position:0%
+operating rooms you know every two weeks
+out of the month this is feasible
+
+ align:start position:0%
+out of the month this is feasible
+ 
+
+ align:start position:0%
+out of the month this is feasible
+because we have extra operating rooms on
+
+ align:start position:0%
+because we have extra operating rooms on
+ 
+
+ align:start position:0%
+because we have extra operating rooms on
+Thursday and Friday as you can see down
+
+ align:start position:0%
+Thursday and Friday as you can see down
+ 
+
+ align:start position:0%
+Thursday and Friday as you can see down
+here plus it seems like it's a more
+
+ align:start position:0%
+here plus it seems like it's a more
+ 
+
+ align:start position:0%
+here plus it seems like it's a more
+efficient and fair solution yes although
+
+ align:start position:0%
+efficient and fair solution yes although
+ 
+
+ align:start position:0%
+efficient and fair solution yes although
+they do exceed their weekly target by
+
+ align:start position:0%
+they do exceed their weekly target by
+ 
+
+ align:start position:0%
+they do exceed their weekly target by
+0.6 hours it means that on the weeks
+
+ align:start position:0%
+0.6 hours it means that on the weeks
+ 
+
+ align:start position:0%
+0.6 hours it means that on the weeks
+when they only get to have 81 percent of
+
+ align:start position:0%
+when they only get to have 81 percent of
+ 
+
+ align:start position:0%
+when they only get to have 81 percent of
+their target allocation they've got they
+
+ align:start position:0%
+their target allocation they've got they
+ 
+
+ align:start position:0%
+their target allocation they've got they
+know that the next week they'll be able
+
+ align:start position:0%
+know that the next week they'll be able
+ 
+
+ align:start position:0%
+know that the next week they'll be able
+to make up for it so it seems like a
+
+ align:start position:0%
+to make up for it so it seems like a
+ 
+
+ align:start position:0%
+to make up for it so it seems like a
+more fair solution as well as a more
+
+ align:start position:0%
+more fair solution as well as a more
+ 
+
+ align:start position:0%
+more fair solution as well as a more
+efficient solution by combining the
+
+ align:start position:0%
+efficient solution by combining the
+ 
+
+ align:start position:0%
+efficient solution by combining the
+power of integer optimization with the
+
+ align:start position:0%
+power of integer optimization with the
+ 
+
+ align:start position:0%
+power of integer optimization with the
+understanding and flexibility of human
+
+ align:start position:0%
+understanding and flexibility of human
+ 
+
+ align:start position:0%
+understanding and flexibility of human
+judgment you really get the best of both
+
+ align:start position:0%
+judgment you really get the best of both
+ 
+
+ align:start position:0%
+judgment you really get the best of both
+worlds
\ No newline at end of file
diff --git a/ocZMDMZwhCY.txt b/ocZMDMZwhCY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..662c73df85195bc42462b0fa496effc590ae9be8
--- /dev/null
+++ b/ocZMDMZwhCY.txt
@@ -0,0 +1,2594 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Today we're going
+to solve three problems,
+
+a problem called
+Parenthesization,
+
+a problem called Edit Distance,
+which is used in practice
+
+a lot, for things like
+comparing two strings of DNA,
+
+and a problem called
+Knapsack, just
+
+about how to pack your bags.
+
+And we're going to get a
+couple of general ideas,
+
+one is about how to deal with
+string problems in general
+
+with dynamic programming.
+
+The first two and
+our previous lecture
+
+are all about strings,
+certain sense or sequences,
+
+and we're going to introduce
+a new concept, kind
+
+of like polynomial time, but
+only kind of, sort of-- pseudo
+
+polynomial time.
+
+Remember, dynamic programming
+in five easy steps.
+
+You define what your sub
+problems are and count
+
+how many there are, to
+solve a sub problem,
+
+you guess some part of the
+solution, where there's not too
+
+many different possibilities
+for that guess.
+
+You count them,
+better be polynomial.
+
+Then you, using that guess--
+this is sort of optional,
+
+but I think it's a useful
+way to think about things.
+
+You write a recurrence relating
+the solution to the subproblem
+
+you want to solve, in terms of
+smaller subproblem, something
+
+that you already
+know how to solve,
+
+but it's got to be
+within this list.
+
+And when you do
+that, you're going
+
+to get a min or a max
+of a bunch of options,
+
+those correspond
+to your guesses.
+
+And you get some
+running time, in order
+
+to compute that recurrence,
+ignoring the recursion, that's
+
+time for subproblem.
+
+Then, to make a dynamic
+program, you either just
+
+make that a recursive algorithm
+and memoize everything,
+
+or you write the bottom
+up version of the DP.
+
+They do exactly the same
+computations, more or less,
+
+and you need to check that
+this recurrence is acyclic,
+
+that you never end up
+depending on yourself,
+
+otherwise these will
+be infinite algorithms
+
+or incorrect algorithms.
+
+Either way is bad.
+
+From the bottom up, you
+really like to explicitly know
+
+a topological order
+on the subproblems,
+
+and that's usually
+pretty easy, but you've
+
+got make sure that it's acyclic.
+
+And then, to compute the
+running time of the algorithm,
+
+you just take the number
+of subproblems from part 1
+
+and you multiply it
+by the time it takes
+
+per subproblem, ignoring
+recursion, in part 3.
+
+That gives you
+your running time.
+
+I've written this formula
+by now three times
+
+are more, remember it.
+
+We use it all the time.
+
+And then you need to double
+check that you can actually
+
+solve the original
+problem you cared about,
+
+either it was one
+of your subproblems
+
+or a combination of them.
+
+So that's what we're going
+to do three times today.
+
+One of the hardest parts
+in dynamic programming
+
+is step 1, defining
+your subproblems.
+
+Usually if you do that right,
+it becomes-- with some practice,
+
+step 2 is pretty easy.
+
+Step 1 is really where most
+of the insight comes in,
+
+and step 3 is usually trivial,
+once you know 1 and 2.
+
+Once you realize 1 and 2 will
+work, the recurrence is clear.
+
+So I want to give you some
+general tips for step 1,
+
+how to choose
+subproblems, and we're
+
+going to start with problems
+that involve strings
+
+or sequences as input,
+where the problem, the input
+
+to the problem is
+string or sequence.
+
+Last class we saw
+text justification,
+
+where the input was
+a sequence of words,
+
+and we saw Blackjack, where the
+input was a sequence of cards.
+
+Both of these are examples,
+and if you look at them,
+
+in both cases we
+used suffixes, what
+
+do I call it, x,
+as our subproblems.
+
+If x was our sequence,
+we did all the suffixes,
+
+I equals zero up to the
+length of the thing.
+
+So they're about n, n
+plus 1, such subproblems.
+
+This is good.
+
+Not very many of them,
+and usually if you're
+
+plucking things off the
+beginning of the string
+
+or of the sequence, then
+you'll be left with the suffix.
+
+If you always are plucking
+from the beginning,
+
+you always have suffixes,
+you'll stay in this class,
+
+and that's good,
+because you always
+
+want a recurrence
+that relates, in terms
+
+of the same subproblems
+that you know.
+
+Sometimes it doesn't work.
+
+Sometimes prefixes
+are more convenient.
+
+These are usually
+pretty much identical,
+
+but if you're plucking
+off from the end instead
+
+of the beginning, you'll end
+up with prefixes, not suffixes.
+
+Both of these have
+linear size, so they're
+
+good news, quite efficient.
+
+Another possibility
+when that doesn't work,
+
+we're going to see an
+example of that today,
+
+is you do all substrings.
+
+So I don't mean
+subsequences, they
+
+have to be consecutive
+substrains, i through j.
+
+And now for all i and j.
+
+How many of these are there?
+
+For a string of length n?
+
+N squared.
+
+So this one is n squared,
+the others are linear.
+
+Out of room here.
+
+Theta n.
+
+So you obviously you prefer
+to use these subproblems
+
+because there's fewer of
+them, but if sometimes they
+
+don't work, then use this
+one, still polynomial, still
+
+pretty good.
+
+This will get you
+through most DP's.
+
+It's pretty simple,
+but very useful.
+
+Let me define the next
+problem we consider.
+
+For each of them we're going
+to go through the five steps.
+
+So the first problem for
+today is parenthesization.
+
+You're given an
+associative expression,
+
+and you want to evaluate
+it in some order.
+
+So I'm going to-- for
+associative expression,
+
+I'm going to think of
+matrix multiplication,
+
+and I probably want
+to start at zero.
+
+So let's say you
+have n matrices,
+
+you want to compute
+their product.
+
+So you remember matrix
+multiplication is not
+
+commutative, I can't
+reorder these things.
+
+All I can do is,
+if I want to do it
+
+by sequence of pairwise
+multiplications,
+
+is I get to choose where
+the parentheses are, and do
+
+whatever I want for
+the parentheses,
+
+because it's associative.
+
+It doesn't matter where they go.
+
+Now it turns out if you
+use straightforward matrix
+
+multiplication, really
+any algorithm for matrix
+
+multiplication, it matters
+how you parenthesize.
+
+Some will be
+cheaper than others,
+
+and we can use
+dynamic programming
+
+to find out which is best.
+
+So let me draw a simple example.
+
+Suppose I have a column
+vector times a row
+
+vector times a column vector.
+
+And there are two ways
+to compute this product.
+
+One is like this, and
+the other is like this.
+
+If I compute the
+product this way,
+
+it's every row
+times every column,
+
+and then every row
+times every column,
+
+and every row
+times every column.
+
+This subresult is a square
+matrix, so if these are-- say
+
+everything here is n, and
+this will be an n by n matrix.
+
+Then we multiply it by a
+vector and this computation
+
+has to take, if
+you do it well, it
+
+will take theta n
+squared time, because I
+
+need to compute n
+squared values here,
+
+and then it's n squared to
+do this final multiplication.
+
+Versus if I do it this way,
+I take all the rows here,
+
+multiply them on all the columns
+here, it's a single number,
+
+and then I multiply
+by this column.
+
+This will take linear time.
+
+So this is better
+parenthesization than this one.
+
+Now, I don't even
+need to define in
+
+general for an x by y matrix,
+times a y by z matrix,
+
+you can think about the running
+time of that multiplication.
+
+Whatever the running time
+is, dynamic programming
+
+can solve this problem,
+as long as it only
+
+depends on the dimensions
+of the matrices
+
+that you're multiplying.
+
+So for this problem,
+there's going
+
+to be the issue of which
+subproblems we use.
+
+Now we have a
+sequence of matrices
+
+here, so we naturally think
+of these as subproblems,
+
+but before we get to the
+subproblems, let me ask you,
+
+what you think you should guess?
+
+Let's just say from the
+outset, if I give you
+
+this entire sequence,
+what feature
+
+of the solution of
+the optimal solution
+
+would you like to guess?
+
+Can't know the whole solution,
+because there's exponentially
+
+many ways to parenthesize.
+
+What's one piece
+of it that you'd
+
+like to guess that
+will make progress?
+
+Any idea?
+
+It's not so easy.
+
+AUDIENCE: Well, wouldn't
+you need the last operation?
+
+PROFESSOR: What's
+the last operation
+
+we're going to do, exactly.
+
+You might call it the
+outermost multiplication
+
+or the last multiplication.
+
+So that's going to look like we
+somehow multiply a 0 through ak
+
+minus 1, and then we somehow
+multiply aK through an minus 1,
+
+and this is the last one.
+
+So now we have two subproblems.
+
+Somehow we want to multiply
+this, somehow-- I mean,
+
+there's got to be some
+last thing you do.
+
+I don't know what it
+is, so just guess it.
+
+Try all possibilities for k,
+it's got to be one of them,
+
+take the best.
+
+If somehow we know the optimal
+way to do a0 to k minus 1
+
+and the optimal way to ak to
+an minus 1, then we're golden.
+
+Now, this looks like a prefix,
+this looks like a suffix.
+
+So do you think we can just
+combine subproblems, suffixes
+
+and prefixes?
+
+How many people think yes?
+
+A few?
+
+How many people
+think no, OK, why?
+
+AUDIENCE: So, for example if
+you split, if you were to split,
+
+like [INAUDIBLE]?
+
+PROFESSOR: Yeah.
+
+The very next thing
+we're going to do
+
+is recurse on this subproblem,
+recurse on this subproblem.
+
+When we recurse
+here, we're going
+
+to split it into a0 to ak prime
+minus 1, and ak prime minus 1,
+
+or ak prime to ak minus 1.
+
+We're going to consider
+all possible partitions,
+
+and this thing, from
+ak prime to ak minus 1,
+
+is not a prefix or a suffix.
+
+What is it?
+
+A substring.
+
+There's only one thing left.
+
+I claim these are usually
+enough, and in this case
+
+substrings will be enough.
+
+But this is how
+you can figure out
+
+that, ah, I'm not staying
+within the family prefixes,
+
+I'm not staying within
+the family suffixes.
+
+In general, you never use
+both of these together.
+
+If you're going to need both,
+you probably need substrings.
+
+So if just suffixes work, fine.
+
+If just prefixes work,
+fine, but otherwise
+
+you're probably going
+to need substrings.
+
+That's just a rule
+of thumb, of course.
+
+Cool.
+
+So, part 1 subproblem is going
+to be the optimal evaluation
+
+parenthesization of
+ai to aj minus 1.
+
+So that's part of
+the problem here.
+
+We want to do a0 to n minus 1.
+
+So in general, let's just
+take some substring in here
+
+and say, well what's the
+best way to multiply that,
+
+and that's the
+sorts of subproblems
+
+we're getting if
+we use this guess.
+
+And if you start with a
+substring and you do this,
+
+you will still remain
+within a substring,
+
+so actually I have to
+revise this slightly.
+
+Now we're going from ai-- to
+solve this subproblem, which
+
+is what we need to do
+in the guessing step,
+
+we start from ai, we go to
+some guest place, ak minus 1,
+
+then from ak up to aj minus 1.
+
+This is the i
+colon j subproblem.
+
+So we guess some point in the
+middle, some choice for k.
+
+The number of choices
+for k is-- number
+
+of possible choices
+for this guess,
+
+so we have to try all of them,
+is like order j minus i plus 1.
+
+I put order in case I'm
+off by 1 or something.
+
+But in particular
+this is [INAUDIBLE].
+
+And that's all we'll need.
+
+So that's the guess.
+
+Now we go to step 3,
+which is the recurrence.
+
+And this-- we're going to
+do this over and over again.
+
+Hopefully by the end,
+it's really obvious
+
+how to do this recurrence.
+
+Let me just fix my notation,
+we're going to use dp,
+
+I believe.
+
+For whatever reason, in my
+notes I often write dp of ij.
+
+This is supposed
+to be the solution
+
+to the subproblem i colon j.
+
+I want to write it recursively,
+in terms of smaller
+
+subproblems, and I want
+to minimize the cost,
+
+so I'm going to
+write a min overall.
+
+And for each choice of k, so
+there's going to be a for loop,
+
+I'm going to use Python
+notation here with iterators.
+
+So k is going to
+be in the range,
+
+I think range ij is correct.
+
+I'm going to double check
+there's no off by 1's here.
+
+Says i plus 1j.
+
+I think that's probably right.
+
+Once I choose where
+k is, where I'm
+
+going to split my
+multiplication,
+
+I do the cost for
+i up to k, that's
+
+the left multiplication,
+plus the cost for k up to j,
+
+plus-- so those are the two
+recursive multiplications.
+
+So then I also have to
+do this outermost one.
+
+So how much does that cost?
+
+Well, it's something,
+so cost of the product
+
+ai colon k times the
+product ak colon j.
+
+So I'm assuming I can
+compute this cost,
+
+not even going to try to
+write down a general formula,
+
+you could do it, it's
+not hard, it's like xyz.
+
+For a standard matrix
+multiplication algorithm.
+
+But whatever algorithm
+you're using,
+
+assuming you could figure out
+the dimensions of this matrix,
+
+it doesn't matter
+how it's computed,
+
+the dimensions will
+always be the same.
+
+You compute the dimensions
+of this matrix that
+
+will result from
+that product, it's
+
+always going to be
+the first dimension
+
+here, with the last
+dimension there.
+
+And it's constant
+time, you know that.
+
+And then if you can figure out
+the cost of a multiplication
+
+in constant time, just
+knowing the dimensions
+
+of these matrices, then
+you could plug this
+
+in to this dynamic
+program, and you
+
+will get the optimal solution.
+
+This is magically considering
+all possible parenthesizations
+
+of these matrices, but magically
+it does it in polynomial time.
+
+Because the time for
+subproblem here--
+
+We're spending constant
+time for each iteration
+
+of this for loop,
+because this is
+
+a constant time just
+computing the cost.
+
+These are free
+recursive calls, so it's
+
+dominated by the length of
+the for loop, which we already
+
+said was order n, so it's
+order n time for subproblem,
+
+ignoring recursions.
+
+And so when we
+put this together,
+
+the total time is
+going to be the number
+
+of some problems,
+which I did not write.
+
+The number of problems
+in step 1 is n squared,
+
+that's what we said over
+here, for substrings.
+
+So running time is number
+of subproblems, which is n
+
+squared, times linear for each,
+and so it's order n cubed,
+
+it's actually theta n cubed.
+
+So polynomial time,
+much better than trying
+
+all possible parenthesizations,
+they're about 4
+
+to the n parenthesizations,
+that's a lot.
+
+Topological order here is
+a little more interesting,
+
+if you think about that.
+
+I can tell you, for
+suffixes, topological order
+
+is almost always right to left.
+
+And for prefixes,
+it's almost always
+
+left to right, for
+increasing i, decreasing i.
+
+For substrings, what
+do you think it is?
+
+Or for this situation
+in particular?
+
+In what order should I
+evaluate these subproblems?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: This is
+the running time
+
+to determine the best way
+to multiply-- that's right.
+
+So yeah, it's worth
+checking, because we also
+
+have to do the multiplication.
+
+But if you imagine
+this n, the number
+
+of matrices you're
+multiplying is probably
+
+much smaller than their sizes.
+
+In that situation,
+this will be tiny,
+
+whereas the time to actually
+do the multiplication, that's
+
+what's being computed by the DP,
+hopefully that's much larger,
+
+otherwise you're kind of
+wasting your time doing the DP.
+
+But hey, at least you
+could tell somebody
+
+that you did it optimally.
+
+But it gets into a
+fun issue of cost
+
+of planning verses execution,
+but we're not really
+
+going to worry about that here.
+
+So, in what order should I
+evaluate this recurrence,
+
+in order to-- I want, when
+I'm evaluating DP of ij,
+
+I've already done DP
+of ik and DP of kj,
+
+and this is what you need
+for bottom up execution.
+
+Yeah.
+
+AUDIENCE: Small to large.
+
+PROFESSOR: Small
+to large, exactly.
+
+We want to do increasing
+substring size.
+
+That's actually
+what we're always
+
+doing for all of those
+subproblems over there.
+
+When I say all suffixes,
+you go right to left.
+
+Well, that's because the
+rightmost suffix is nothing,
+
+and then you build up a larger
+and larger strings, same thing
+
+here.
+
+Exercise, try to draw
+the DAG for this picture.
+
+It's a little harder,
+but if you-- I
+
+mean you could basically
+imagine-- I'll do it for you.
+
+Here is, let's say--
+well, at the top
+
+there's everything, the
+longest substring, that
+
+would be from zero to
+n, that's everything.
+
+Then you're going to
+have n different ways
+
+to have substrings
+of, or actually just
+
+two different ways, to have
+a slightly smaller substring.
+
+At the bottom you have
+a bunch of substrings,
+
+which are the length zero
+ones, and in between,
+
+like in the middle
+here, you're going
+
+to have a much larger number.
+
+And all these edges
+are pointed up,
+
+so you can compute
+all the length
+
+zero ones without any
+dependencies and then just
+
+increasing in length.
+
+It's a little hard to see,
+but in each case-- Yeah,
+
+ah, interesting.
+
+This is a little harder to
+formulate as a regular shortest
+
+paths problem, because if you
+look at one of these nodes,
+
+it depends on two
+different values,
+
+and you have to take
+the sum of both of them.
+
+And then you also add
+the cost of that split.
+
+Cool.
+
+So this is the subproblem
+DAG, you could draw it,
+
+but this DP is not
+shortest paths in that DAG.
+
+So perhaps dynamic programming
+is not just shortest paths
+
+in a DAG, that's a
+new realization for me
+
+as of right now.
+
+OK.
+
+Some other things
+I forgot to do-- I
+
+didn't specify the base case.
+
+The base case for
+that recurrence
+
+is when your string is of
+length 0 or even of length 1,
+
+because when it's length
+1, there's only one matrix,
+
+there's no multiplication to
+do, and so the cost is zero.
+
+So you have something like dp
+of i, i plus 1 equals zero.
+
+That's the base case.
+
+And then step 5,
+step 5 is what's
+
+the overall problem
+I want to solve,
+
+and that's just dp from 0 to
+n, that's the whole string.
+
+Any questions about that DP?
+
+I didn't write down, I didn't
+write down a memoized recursive
+
+algorithm, you all
+know how to do that.
+
+Just do this for loop
+and put this inside,
+
+that would be the
+bottom up one, or just
+
+write this with
+memoization, that
+
+would be the
+recursive algorithm.
+
+It's totally easy once
+you have this recurrence.
+
+All right, good.
+
+How many people is this
+completely clear to?
+
+OK.
+
+How many people does
+it kind of make sense?
+
+And how many people it
+doesn't make sense at all?
+
+OK, good.
+
+Hopefully we're
+going to shift more
+
+towards the first category.
+
+It's a little magical, how
+this guessing works out,
+
+but I think the only way to
+really get it is to see more
+
+examples and write
+code to do it,
+
+that's-- the ladder
+is your problem set,
+
+examples is what we'll do here.
+
+So next problem
+we're going to solve.
+
+Dynamic programming is
+one of these things that's
+
+really easy once you get it,
+but it takes a little while
+
+to get there.
+
+So edit distance, we're going
+to make things a little harder.
+
+Now we're going to be given two
+strings instead of just one.
+
+And I want to know the cheapest
+way to convert x into y.
+
+I'm going to define
+what transform means.
+
+We're going to allow
+character edits.
+
+We want to transform this
+string x into string y,
+
+so what character
+edits are we allowed?
+
+Very simple, we're allowed to
+insert a character anywhere
+
+in the strength, we're allowed
+to delete a character anywhere
+
+in the string, and we're allowed
+to replace a character anywhere
+
+in the string, replace
+c with c prime.
+
+Now, you could do a replacement
+by deleting c and inserting
+
+c that's, one way
+to do it, but I'm
+
+going to imagine that in
+general someone tells me
+
+how much each of these
+operations costs,
+
+and that cost may depend on
+the character you're inserting.
+
+So deleting a character and then
+inserting a different character
+
+will cost one thing.
+
+It will cost the sum of
+those two cost values.
+
+Replacing a character
+with another character
+
+might be cheaper.
+
+It depends.
+
+Someone gives me a little table,
+saying for this character,
+
+for letter a, it costs this
+much to insert, for letter
+
+b it costs this much to
+insert, this much to delete,
+
+and there's a little
+matrix for, if I
+
+want to convert an a into a b
+it costs this much to replace.
+
+Imagine, if you
+will, you're trying
+
+to do a spelling correction,
+someone's typing on a keyboard,
+
+and you have some model
+of, oh, well if I hit a,
+
+I might have meant to
+hit an s, because s
+
+is right next to an a,
+and that's an easy mistake
+
+to make if you're not
+touch typing, because it's
+
+on the same finger, or maybe
+you're shifted over by one.
+
+So you can come up
+with some cost models,
+
+someone could do a lot
+of work and research
+
+and whatnot and see
+what are typical typos,
+
+replacing one
+letter for another,
+
+and then associate some
+cost for each character,
+
+for each pair characters,
+what's the likelihood
+
+that that was the mistake?
+
+I call that the cost,
+that's the unlikeliness.
+
+And then you want to
+minimize the sum of costs,
+
+and so you want to find what
+was the least set of errors that
+
+would end up with this
+word instead of this word.
+
+You do that on all
+words of your dictionary
+
+and then you'll
+find the one that
+
+was most likely what
+you meant to type.
+
+And insertions
+and deletions are,
+
+I didn't hit the
+key hard enough,
+
+or I hit it twice, or
+accidentally hit a key
+
+because it was right next
+to another one, or whatever.
+
+OK, so this is used for
+spelling correction.
+
+It's used for comparing
+DNA sequences,
+
+and DNA sequences, if you
+have one strand of DNA,
+
+there's a lot of mutation--
+some mutations are
+
+more likely than others.
+
+For example, c to
+a g mutation is
+
+more common than c
+to an a mutation,
+
+and so you give this
+replacement a high cost,
+
+you give this one a
+low cost, to represent
+
+this is more likely than this.
+
+And then at a distance
+will give your measure
+
+of how similar two DNA
+strings are evolutionarily.
+
+And you also get extra
+characters randomly inserted
+
+and deleted in mutation.
+
+So, it's a simplified model
+of what happens in mutation,
+
+but still it's used a lot.
+
+So all these are encompassed
+by edit distance.
+
+Another problem encompassed
+by edit distance
+
+is the longest common
+subsequence problem.
+
+And I have a fun example,
+which I spent some hours,
+
+way back when, coming up with.
+
+I can't spell it, though.
+
+It's such a weird word.
+
+Hieroglyphology
+is an English word
+
+and Michelangelo is
+another English word,
+
+if you allow proper
+nouns, unlike Scrabble.
+
+So, think of these as strings.
+
+This is x, this is y.
+
+What is the longest
+common subsequence?
+
+So not substring,
+I get to choose--
+
+I can drop any set of letters
+from x, drop any set of letters
+
+from y, and I want them
+to, in the end, be equal.
+
+It's a puzzle for you.
+
+While you're thinking
+about it, you
+
+can model this as an
+edit distance problem,
+
+you just define the cost of
+an insert or a delete to be 1,
+
+and the cost of a
+replace to be 0.
+
+So this is a c to c
+prime replacement.
+
+It's going to be 0
+if c equals c prime,
+
+and I guess infinity otherwise.
+
+You just don't consider
+it in that situation.
+
+Can anyone find the longest
+common subsequence here?
+
+It's in English
+word, that's a hint.
+
+So if you do this
+you're, basically
+
+trying to minimize number
+of insertions and deletions.
+
+Insertions in x correspond
+to deletions in y,
+
+and deletions in x
+correspond to deletions in x.
+
+So this is the minimum number
+of deletions in both strings,
+
+so you end up with
+a common substring.
+
+Because replacement says,
+I don't pay anything
+
+if the characters match exactly,
+otherwise I pay everything.
+
+I'd never want to do this,
+so if there's a mismatch
+
+I have to delete it.
+
+And so this model
+is the same thing
+
+as long as common subsequence.
+
+I want to solve this
+more general problem,
+
+it's actually easier to solve
+the more general problem,
+
+but in particular,
+you can use it
+
+to solve this tricky problem.
+
+Any answers?
+
+Yeah.
+
+Hello.
+
+Very good.
+
+Hello is the longest
+common subsequence.
+
+You can imagine
+how I found that.
+
+Searching for all
+English words that
+
+have "hello" as the subsequence.
+
+That can also be done
+in polynomial time.
+
+So how are we going to do this?
+
+Well, I'd like to somehow
+use subproblems for strings,
+
+suffixes, prefixes,
+or substrings.
+
+But now I have two strings,
+that's kind of annoying.
+
+But don't worry, we can do
+sort of dynamic programming
+
+simultaneously over x and y.
+
+What we're going to do is look
+at suffixes of x and suffixes
+
+of y, and to make
+our subproblems
+
+we need to combine all of those
+subproblems by multiplication.
+
+We need to think about both
+of them simultaneously.
+
+So subproblem is going to
+be solve edit distance,
+
+edit distance problem on
+two different strings,
+
+a suffix of x and a possibly
+different suffix of y.
+
+Because this is for all
+possible i and j choices.
+
+And so the number
+of subproblems is?
+
+AUDIENCE: N squared.
+
+PROFESSOR: N squared, yes.
+
+If x is of length n
+and y is of length n,
+
+there's n choices for
+this, n choices for that,
+
+and we have to do
+all of them as pairs,
+
+if there's n squared pairs.
+
+In general, if they
+have different lengths,
+
+it's going to be the length
+of x times length of y.
+
+It's quadratic.
+
+Good.
+
+So, next we need to
+guess something, step 2.
+
+This is maybe not so
+obvious, let's see.
+
+You have here's x,
+starting at position i.
+
+You have y starting
+at position j.
+
+Somehow I need to
+convert x into y,
+
+I think it's probably
+better if I line these up,
+
+even though in some sense
+they're not lined up,
+
+that's OK.
+
+I want to convert x into y.
+
+What should I look at here?
+
+Well, I should look at
+the very first characters,
+
+because we're
+looking at suffixes.
+
+We want to cut off first
+characters somehow.
+
+How could it-- what are the
+possible ways to convert, or to
+
+deal with the first
+character of x?
+
+What are the possible
+things I could do?
+
+Given that, ultimately, I
+want the first character
+
+of x to become the
+first character of y.
+
+AUDIENCE: Delete [INAUDIBLE].
+
+PROFESSOR: You could
+delete this character
+
+and then insert this one, yes.
+
+Other things?
+
+There's a few possibilities.
+
+If you look at it right,
+there are three possibilities.
+
+And three possibilities are
+insert, delete, or replace.
+
+So let's figure out
+how that's the case.
+
+I could replace this
+character with that character,
+
+so that's one choice.
+
+That will make progress.
+
+Once I do that, I can cross
+off those first characters
+
+and deal with the rest
+of the substrings.
+
+Let's think about
+insert and delete.
+
+If I wanted to
+insert, presumably, I
+
+need this character
+at some point.
+
+So in order to make
+this character,
+
+if it's not going to come
+from replacing this one,
+
+it's got to be from inserting
+that character right there.
+
+Once I do that, I can cross out
+that newly inserted character
+
+in this one, and then I have
+all of the string x from i
+
+onward still, but then I've
+removed one character from y,
+
+so that's progress.
+
+The other possibility
+is deletion,
+
+so maybe I delete
+this character,
+
+and then maybe I insert
+it in the next step,
+
+but it could be this
+character matches that one,
+
+or maybe I have to delete
+several characters before I
+
+get to one that
+matches, something.
+
+But I don't know that,
+so that's hard to guess,
+
+because that would be
+more time to guess.
+
+But I could say, well, this
+character might get deleted.
+
+If it gets deleted, that's
+it, it gets deleted.
+
+And then somehow the rest
+of the x, from i plus 1 on,
+
+has to match with
+all of y, from j on.
+
+But those are the
+three possibilities,
+
+and in some sense capture
+all possibilities.
+
+So it could be we
+replace xi with yj,
+
+and so that has some
+cost, which we're given.
+
+It could be that we insert
+yj at the beginning,
+
+or it could be
+that we delete xi.
+
+You can see that's
+definitely spanning
+
+all the possible
+operations we can do,
+
+and if you think
+about it long enough,
+
+you will be
+convinced this really
+
+covers every possible
+thing you can do.
+
+If you think about
+the optimal solution,
+
+it's got to do something to
+make this first character.
+
+Either it does it by replacement
+or it does it by an insertion.
+
+But if it inserts
+it later on, it's
+
+got to get this out
+of the way somehow,
+
+and that's the deletion case.
+
+If it inserts it at the
+beginning, that's the insertion
+
+case, if it just
+does a replacement,
+
+that's the replace case.
+
+Those are all possibilities
+for the optimal solution.
+
+Then you can write
+a recurrence, which
+
+is just a max of those
+things, those three options.
+
+So I'm going to write, I
+guess, dp of ij, yes, of i,j,
+
+but now i,j is not a substring.
+
+It's a suffix of x
+and a suffix of y,
+
+so it corresponds
+to this subproblem.
+
+If I want to solve
+that subproblem,
+
+it's going to be the
+min of three options.
+
+We've got the
+replace case, so it's
+
+going to be some cost of
+the replace, from xi to yj.
+
+So that's a quantity
+which we're given.
+
+Plus the cost of the rest.
+
+So after we do this
+replacement, we can cross off
+
+both those characters, and
+so we look at i plus 1 on
+
+for x, and j plus
+1 onwards for y.
+
+So that's option 1.
+
+Then comma for the min.
+
+Option 2 is we have
+the cost of insert yj.
+
+So that's also
+something we're given.
+
+Then we add on what we
+have to do afterwards,
+
+which is we've just
+gotten rid of yj,
+
+so x still has the
+entire string from i on,
+
+and y has a smaller string.
+
+Comma.
+
+Last option is basically the
+same, cost of the delete,
+
+deleting xi, and then we have
+to add on DP of i plus 1j.
+
+Because here we did not
+advance y but we advanced x.
+
+It's crucial that we
+always advance at least one
+
+of the strings, because that
+means we're making progress,
+
+and indeed, if you want to jump
+to step 4, which is topological
+
+ordering-- sorry, I
+reused my symbols here,
+
+some different symbols.
+
+Head back to step 4 of
+DP, topological order.
+
+Well, these are
+suffixes, and so I
+
+know with suffixes I like
+to go from the smaller
+
+suffixes, which is the
+end, to the beginning.
+
+And, indeed, because
+we're always increasing,
+
+we're always looking at later
+substrings, later suffixes,
+
+for one or the other.
+
+It's enough to just
+do-- come over here.
+
+To just do that for
+both of the strings,
+
+it doesn't really
+matter the order.
+
+So you can do for i
+equals x down to zero,
+
+for j equals y down to
+zero, and that will work.
+
+Now this is another
+dynamic programming
+
+you can think of as just
+shortest paths in the DAG.
+
+The DAG is most easily seen as
+a two-dimensional matrix, where
+
+the i index is between zero and
+length of x, and the j index
+
+is between zero and
+length of y, and each
+
+of the cells in this matrix
+is a node in the DAG.
+
+That's one of our
+subproblems, dp of ij.
+
+And it depends on these
+three adjacent cells.
+
+The edges are like this.
+
+If you look at it,
+we have to check i
+
+plus 1, j plus 1,
+that's this guy.
+
+We have to check ij
+plus 1, that's this guy.
+
+We have to check i plus
+1j, that's this guy.
+
+And so, as long as we
+compute the matrix this way,
+
+what I've done here is
+row by row, bottom up.
+
+You could do it
+anti-diagonals, you
+
+could do it column by column
+backwards, all of those
+
+will work because we're making
+progress towards the origin.
+
+And so if you ever-- if
+you look up at a distance,
+
+most descriptions think
+about it in the matrix form,
+
+but I think it's easier to think
+of it in this recursive form,
+
+whatever your poison.
+
+But this is, again,
+shortest paths in a DAG.
+
+The original problem
+we care about
+
+is dp of zero zero,
+the upper left corner.
+
+So to be clear in the
+DAG, what you write here
+
+is like the cost of,
+the weight of that edge
+
+is the cost of, I
+believe, a deletion.
+
+Deletion, oh sorry,
+it's an insertion.
+
+Inserting that character,
+this one's a cost of deletion,
+
+this is a cost to replace, so
+you just put those edge weights
+
+in, and then just do a
+shortest paths in the DAG,
+
+I think, from this
+corner to this corner.
+
+And that will give you this, or
+you could just do this for loop
+
+and do that in the
+for loop, same thing.
+
+OK.
+
+What's the running time?
+
+Well, the number of
+subproblems here is x times y,
+
+the running time
+for subproblem is?
+
+I'm assuming that I know
+these costs in constant time,
+
+so what's the overall running
+time of that, evaluating that?
+
+Constant.
+
+And so the overall running time
+is the number of subproblems
+
+times a constant
+equals x times y.
+
+This is the best known
+algorithm for edit distance,
+
+no one knows how
+to do any better.
+
+It's a big open problem
+whether you can.
+
+You can improve the
+space a little bit,
+
+because we really
+only need to store
+
+the last row or the
+last column, depending
+
+on the order you're
+evaluating things.
+
+To even get down to linear
+space, as far as we know,
+
+we need quadratic time.
+
+One more problem, are you ready?
+
+This one's going to blow
+your minds hopefully.
+
+Because we're going to diverge
+from strings and sequences,
+
+kind of.
+
+So far everything we've
+looked at involves one or two
+
+strings or sequences,
+except for [INAUDIBLE].
+
+That involved a graph, that
+was a little more exciting.
+
+But we'd already seen that,
+so it wasn't that exciting.
+
+OK, our last problem
+for today is knapsack.
+
+It's a practical problem.
+
+You're going camping.
+
+You're going backpacking,
+I should say,
+
+and you can only
+afford to take whatever
+
+you can fit on your back.
+
+You have some limit
+to capacity, let's say
+
+one giant backpack
+is all you can carry.
+
+Let's imagine it's the size
+of the backpack that matters,
+
+not the weight, but
+you could reformulate
+
+this in terms of weight.
+
+And you've got a lot of
+stuff you want to bring.
+
+Ideally you bring
+everything you own,
+
+that would be kind
+of nice, convenient,
+
+but it'd be kind of heavy.
+
+So you're limited, you're
+not able to do that.
+
+So you have a list of items and
+each of them has a size, si,
+
+and has a desire,
+a value to you,
+
+how much you care about it, how
+much you need it on this trip.
+
+OK, each item has two things,
+and the sizes are integers.
+
+This is going to be important.
+
+It won't work without
+that assumption.
+
+And we have a
+knapsack, backpack,
+
+whatever, I guess it's the
+British, but I don't know,
+
+I get confused.
+
+Growing up in Canada, I use
+both, so it's very confusing.
+
+Knapsack of total size, S.
+
+And what you'd like to do is
+choose a subset of the items.
+
+If you're lucky, the sum
+of the si's fit within s,
+
+then you bring everything.
+
+But if you're not lucky,
+that's not possible,
+
+you want to choose a subset of
+the items whose total size is
+
+less than or equal
+to s, in order
+
+to maximize the
+sum of the values.
+
+So you want to maximize
+the sum of values
+
+for a subset of items, of total
+size less than or equal to S.
+
+You can imagine size as
+weights instead of size, not
+
+a big deal, or you could
+have sizes and weights.
+
+All of these things generalize.
+
+But we're going to need that
+the sizes/weights are integers.
+
+And so the items have to
+fit, because you can't cheat,
+
+you can't have more
+things than what fit,
+
+but then you want to
+maximize the value.
+
+How do we do this with
+dynamic programming?
+
+With difficulty.
+
+I don't have a ton
+of time, so I think
+
+I'm going to tell
+you-- well, let's see.
+
+Start with guessing.
+
+This is the easy
+part to this problem.
+
+We should also be thinking about
+subproblems at the same time.
+
+Even though I said we're
+leaving sequences, in fact,
+
+we have a sequence here, we
+have a sequence of items.
+
+We don't actually care about
+the order of the items, but hey,
+
+they're in an order.
+
+If they weren't, we could
+put them in an order,
+
+in an arbitrary order.
+
+We're going to use
+that order, and we're
+
+going to look at
+suffixes of items.
+
+i colon of items.
+
+That's helpful, because
+now it says, oh, well, we
+
+should be plucking off
+items from the beginning.
+
+Starting with the
+i-th item, what
+
+should I decide
+about the i-th item,
+
+relative to the
+optimal solution?
+
+What should I guess?
+
+AUDIENCE: Is i included or not?
+
+PROFESSOR: Is i included
+or not, exactly.
+
+Is item i in the subset or not.
+
+Two choices, easy.
+
+Of course, those
+are the choices.
+
+If I do that for everybody,
+then I know the entire subset.
+
+Somehow I need to
+be able to write
+
+and this is what's
+actually impossible
+
+if I choose this
+as my subproblem.
+
+I want to write DP of i,
+somehow, in terms of, I guess,
+
+DP of i plus 1.
+
+And we'd like to do max, and
+either we don't put it in,
+
+in which case that's our value,
+or we put it in, in which case
+
+we get an additional
+v i in value.
+
+OK, but we consume
+in size, and there's
+
+no way to remember that
+we've consumed the size here.
+
+We just called DP of i plus 1.
+
+In this case, it has
+everything, all this.
+
+In this case, we
+lose si of S, but we
+
+can't represent that here.
+
+That's bad, this would be
+an incorrect algorithm.
+
+I would always choose
+to put everything in,
+
+because it's not keeping
+track of the size bound.
+
+There's no capital S in
+this formula, that's wrong.
+
+So, to fix that, I'm
+going to write that again,
+
+but a subproblem is going
+to have more information,
+
+it's going to have
+an index i, and it's
+
+going to have
+remaining capacity.
+
+I'm going to call it capital
+X, at some integer at most
+
+S. We're assuming that the
+sizes are all integers,
+
+so this is valid.
+
+The number of subproblems
+is equal to n,
+
+the number of items, did
+I say there are n items?
+
+Now there are n items, times
+capital S, really S plus 1,
+
+because I have to
+go down to zero.
+
+But n times S,
+different subproblems.
+
+Now for each of them I
+can write a recurrence,
+
+and that is DP of
+i comma s, is going
+
+to be the max of
+DP of i plus 1s.
+
+This is the case where we
+don't include the items,
+
+so S stays the same.
+
+Actually I should write x
+here, because it's not actually
+
+our original value of s.
+
+x is the general situation.
+
+The other possibility
+is we include item i,
+
+and then we give DP of i plus 1.
+
+We still consume item i.
+
+We now have x minus si
+as our new capacity,
+
+what remains after
+we add in this item.
+
+And then we add on
+vi, because that's
+
+the value we gain from
+putting that item in.
+
+That's it, that's the
+DP, pretty simple.
+
+Let me say a little bit about
+the running time of this thing.
+
+Again, you check there's a
+topological order and all
+
+that, it's in the notes.
+
+The total running time,
+we spend constant time
+
+to evaluate this formula,
+so it's super easy.
+
+The number of subproblems
+is the bottleneck.
+
+So it's n times s.
+
+Is this polynomial time?
+
+You might guess from the outline
+of today that the answer is no.
+
+This is not polynomial time.
+
+What this polynomial time mean?
+
+It's polynomial and n, where
+n is the size of the input.
+
+What's the size
+of the input here?
+
+Well, we're given n items, each
+with a size, each with a value.
+
+If you think of the
+sizes and values
+
+as being single word
+items, then the size is n.
+
+If you think of them as
+being ginormous values,
+
+at most, the size
+of this input is
+
+going to be something
+like n times log s,
+
+because if you write
+it out in binary
+
+you would need log s, bits
+to write down those numbers.
+
+But it is not n times s.
+
+This would be the binary
+encoding of the input,
+
+but the running time is this.
+
+Now s is exponential in
+log s, this is, at best,
+
+an exponential time algorithm.
+
+But it's really not
+that bad if s is small,
+
+and so we call it
+pseudopolynomial time.
+
+What does pseudopolynomial mean?
+
+It just means that
+your polynomial
+
+in n, the input size,
+which might be this,
+
+and in the numbers
+that are in your input.
+
+Numbers here means
+integers, basically,
+
+otherwise it's not
+really well defined.
+
+So in this case we have
+a bunch of integers,
+
+but in particular we have s.
+
+And so there's S and the si's.
+
+This is definitely
+polynomial in n and s.
+
+It is the product
+of n and S. So you
+
+think of this as
+pseudoquadratic time, I guess?
+
+Because it's quadratic, but
+one of the things is pseudo,
+
+meaning it is one of the
+numbers in the input.
+
+So if the number
+is big in k bits,
+
+so I can write down a number
+that's of size 2 to the k.
+
+So it's kind of in between
+polynomial and exponential,
+
+you might say.
+
+Polynomial good,
+exponential bad,
+
+pseudopolynomial,
+it's all right.
+
+That's the lesson.
+
+And for knapsack, this
+is the best we can do,
+
+as we'll talk about later.
+
+Pseudopolynomial is really
+the best you could hope for.
+
+So, sometimes that's
+as good as you can do
+
+and dynamic programming
+lets you do it.
\ No newline at end of file
diff --git a/opMnuRnfaX0.txt b/opMnuRnfaX0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8cf9941dd283081929e16696a4d4d1a48b51230e
--- /dev/null
+++ b/opMnuRnfaX0.txt
@@ -0,0 +1,14411 @@
+align:start position:0%
+ 
+the following content is provided under
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to talk about the statistical physics of
+
+ align:start position:0%
+to talk about the statistical physics of
+ 
+
+ align:start position:0%
+to talk about the statistical physics of
+deep learning essentially so this is
+
+ align:start position:0%
+deep learning essentially so this is
+ 
+
+ align:start position:0%
+deep learning essentially so this is
+some ongoing work in my lab that was
+
+ align:start position:0%
+some ongoing work in my lab that was
+ 
+
+ align:start position:0%
+some ongoing work in my lab that was
+really motivated by trying to understand
+
+ align:start position:0%
+really motivated by trying to understand
+ 
+
+ align:start position:0%
+really motivated by trying to understand
+how neural networks and infants learn
+
+ align:start position:0%
+how neural networks and infants learn
+ 
+
+ align:start position:0%
+how neural networks and infants learn
+categories and then it sort of led to a
+
+ align:start position:0%
+categories and then it sort of led to a
+ 
+
+ align:start position:0%
+categories and then it sort of led to a
+bunch of results in in deep learning
+
+ align:start position:0%
+bunch of results in in deep learning
+ 
+
+ align:start position:0%
+bunch of results in in deep learning
+that involves two Cisco physics so I
+
+ align:start position:0%
+that involves two Cisco physics so I
+ 
+
+ align:start position:0%
+that involves two Cisco physics so I
+wanted to just introduce my my lab a
+
+ align:start position:0%
+wanted to just introduce my my lab a
+ 
+
+ align:start position:0%
+wanted to just introduce my my lab a
+little bit I'm an interloper from the
+
+ align:start position:0%
+little bit I'm an interloper from the
+ 
+
+ align:start position:0%
+little bit I'm an interloper from the
+methods and computational neuroscience
+
+ align:start position:0%
+methods and computational neuroscience
+ 
+
+ align:start position:0%
+methods and computational neuroscience
+summer school where I tend to spend a
+
+ align:start position:0%
+summer school where I tend to spend a
+ 
+
+ align:start position:0%
+summer school where I tend to spend a
+month and so there you know the the the
+
+ align:start position:0%
+month and so there you know the the the
+ 
+
+ align:start position:0%
+month and so there you know the the the
+flavor of research that we do there in
+
+ align:start position:0%
+flavor of research that we do there in
+ 
+
+ align:start position:0%
+flavor of research that we do there in
+the flavor research we do in our lab is
+
+ align:start position:0%
+the flavor research we do in our lab is
+ 
+
+ align:start position:0%
+the flavor research we do in our lab is
+sort of drilling down into neural
+
+ align:start position:0%
+sort of drilling down into neural
+ 
+
+ align:start position:0%
+sort of drilling down into neural
+mechanisms underlying well-defined
+
+ align:start position:0%
+mechanisms underlying well-defined
+ 
+
+ align:start position:0%
+mechanisms underlying well-defined
+computations and we've been working on
+
+ align:start position:0%
+computations and we've been working on
+ 
+
+ align:start position:0%
+computations and we've been working on
+that with you know I spend a lot of time
+
+ align:start position:0%
+that with you know I spend a lot of time
+ 
+
+ align:start position:0%
+that with you know I spend a lot of time
+talking to neurophysiologists especially
+
+ align:start position:0%
+talking to neurophysiologists especially
+ 
+
+ align:start position:0%
+talking to neurophysiologists especially
+at Stanford where I am so we have a
+
+ align:start position:0%
+at Stanford where I am so we have a
+ 
+
+ align:start position:0%
+at Stanford where I am so we have a
+whole bunch of collaborations going on
+
+ align:start position:0%
+whole bunch of collaborations going on
+ 
+
+ align:start position:0%
+whole bunch of collaborations going on
+now involving understanding neural
+
+ align:start position:0%
+now involving understanding neural
+ 
+
+ align:start position:0%
+now involving understanding neural
+computation so for example the retina
+
+ align:start position:0%
+computation so for example the retina
+ 
+
+ align:start position:0%
+computation so for example the retina
+itself is actually a deep neural circuit
+
+ align:start position:0%
+itself is actually a deep neural circuit
+ 
+
+ align:start position:0%
+itself is actually a deep neural circuit
+already because there's interview
+
+ align:start position:0%
+already because there's interview
+ 
+
+ align:start position:0%
+already because there's interview
+there's an intervening layer of neurons
+
+ align:start position:0%
+there's an intervening layer of neurons
+ 
+
+ align:start position:0%
+there's an intervening layer of neurons
+the bipolar cells and a broken cells
+
+ align:start position:0%
+the bipolar cells and a broken cells
+ 
+
+ align:start position:0%
+the bipolar cells and a broken cells
+that intervene between the
+
+ align:start position:0%
+that intervene between the
+ 
+
+ align:start position:0%
+that intervene between the
+photoreceptors and the ganglion cells
+
+ align:start position:0%
+photoreceptors and the ganglion cells
+ 
+
+ align:start position:0%
+photoreceptors and the ganglion cells
+and oftentimes what we do is we we shine
+
+ align:start position:0%
+and oftentimes what we do is we we shine
+ 
+
+ align:start position:0%
+and oftentimes what we do is we we shine
+light on the photoreceptors and we
+
+ align:start position:0%
+light on the photoreceptors and we
+ 
+
+ align:start position:0%
+light on the photoreceptors and we
+measure the ganglion cells but we have
+
+ align:start position:0%
+measure the ganglion cells but we have
+ 
+
+ align:start position:0%
+measure the ganglion cells but we have
+no clue what's going on in the interior
+
+ align:start position:0%
+no clue what's going on in the interior
+ 
+
+ align:start position:0%
+no clue what's going on in the interior
+so we've developed computational methods
+
+ align:start position:0%
+so we've developed computational methods
+ 
+
+ align:start position:0%
+so we've developed computational methods
+that can successfully computationally
+
+ align:start position:0%
+that can successfully computationally
+ 
+
+ align:start position:0%
+that can successfully computationally
+reconstruct what's going on in the
+
+ align:start position:0%
+reconstruct what's going on in the
+ 
+
+ align:start position:0%
+reconstruct what's going on in the
+interior of this putative deep neural
+
+ align:start position:0%
+interior of this putative deep neural
+ 
+
+ align:start position:0%
+interior of this putative deep neural
+network even though we don't have access
+
+ align:start position:0%
+network even though we don't have access
+ 
+
+ align:start position:0%
+network even though we don't have access
+to these things and we can actually
+
+ align:start position:0%
+to these things and we can actually
+ 
+
+ align:start position:0%
+to these things and we can actually
+infer the existence and properties of
+
+ align:start position:0%
+infer the existence and properties of
+ 
+
+ align:start position:0%
+infer the existence and properties of
+intermediate neurons here and those
+
+ align:start position:0%
+intermediate neurons here and those
+ 
+
+ align:start position:0%
+intermediate neurons here and those
+properties are sort of similar to what's
+
+ align:start position:0%
+properties are sort of similar to what's
+ 
+
+ align:start position:0%
+properties are sort of similar to what's
+been previously recorded when people do
+
+ align:start position:0%
+been previously recorded when people do
+ 
+
+ align:start position:0%
+been previously recorded when people do
+directly record from those say the
+
+ align:start position:0%
+directly record from those say the
+ 
+
+ align:start position:0%
+directly record from those say the
+bipolar cells in the cleansing in lab
+
+ align:start position:0%
+bipolar cells in the cleansing in lab
+ 
+
+ align:start position:0%
+bipolar cells in the cleansing in lab
+we've sort of been unraveling the the
+
+ align:start position:0%
+we've sort of been unraveling the the
+ 
+
+ align:start position:0%
+we've sort of been unraveling the the
+motions underlying underlying the
+
+ align:start position:0%
+motions underlying underlying the
+ 
+
+ align:start position:0%
+motions underlying underlying the
+computations the competitions underlying
+
+ align:start position:0%
+computations the competitions underlying
+ 
+
+ align:start position:0%
+computations the competitions underlying
+of motion vision so you know when you
+
+ align:start position:0%
+of motion vision so you know when you
+ 
+
+ align:start position:0%
+of motion vision so you know when you
+swat a fly it's really hard because they
+
+ align:start position:0%
+swat a fly it's really hard because they
+ 
+
+ align:start position:0%
+swat a fly it's really hard because they
+can really quickly detect motion coming
+
+ align:start position:0%
+can really quickly detect motion coming
+ 
+
+ align:start position:0%
+can really quickly detect motion coming
+towards it and they fly away so we've
+
+ align:start position:0%
+towards it and they fly away so we've
+ 
+
+ align:start position:0%
+towards it and they fly away so we've
+been you know there's so there's been
+
+ align:start position:0%
+been you know there's so there's been
+ 
+
+ align:start position:0%
+been you know there's so there's been
+lots of work on what kinds of algorithms
+
+ align:start position:0%
+lots of work on what kinds of algorithms
+ 
+
+ align:start position:0%
+lots of work on what kinds of algorithms
+might underlie motion estimation for
+
+ align:start position:0%
+might underlie motion estimation for
+ 
+
+ align:start position:0%
+might underlie motion estimation for
+example the Rijkaard correlator the
+
+ align:start position:0%
+example the Rijkaard correlator the
+ 
+
+ align:start position:0%
+example the Rijkaard correlator the
+Barlow Levesque model and so forth we've
+
+ align:start position:0%
+Barlow Levesque model and so forth we've
+ 
+
+ align:start position:0%
+Barlow Levesque model and so forth we've
+been applying systems identification
+
+ align:start position:0%
+been applying systems identification
+ 
+
+ align:start position:0%
+been applying systems identification
+techniques to whole grain calcium
+
+ align:start position:0%
+techniques to whole grain calcium
+ 
+
+ align:start position:0%
+techniques to whole grain calcium
+imaging data we'll whole brain meaning
+
+ align:start position:0%
+imaging data we'll whole brain meaning
+ 
+
+ align:start position:0%
+imaging data we'll whole brain meaning
+from the fly visual circuit and you know
+
+ align:start position:0%
+from the fly visual circuit and you know
+ 
+
+ align:start position:0%
+from the fly visual circuit and you know
+we find we just literally identify the
+
+ align:start position:0%
+we find we just literally identify the
+ 
+
+ align:start position:0%
+we find we just literally identify the
+computation and we find that it's sort
+
+ align:start position:0%
+computation and we find that it's sort
+ 
+
+ align:start position:0%
+computation and we find that it's sort
+of none of the above it's a mixture of
+
+ align:start position:0%
+of none of the above it's a mixture of
+ 
+
+ align:start position:0%
+of none of the above it's a mixture of
+all previous approaches so grid cells we
+
+ align:start position:0%
+all previous approaches so grid cells we
+ 
+
+ align:start position:0%
+all previous approaches so grid cells we
+have some results in grid cells so these
+
+ align:start position:0%
+have some results in grid cells so these
+ 
+
+ align:start position:0%
+have some results in grid cells so these
+are these famous cells that
+
+ align:start position:0%
+are these famous cells that
+ 
+
+ align:start position:0%
+are these famous cells that
+resulted in a Nobel Prize recently we
+
+ align:start position:0%
+resulted in a Nobel Prize recently we
+ 
+
+ align:start position:0%
+resulted in a Nobel Prize recently we
+can actually show that these grid cells
+
+ align:start position:0%
+can actually show that these grid cells
+ 
+
+ align:start position:0%
+can actually show that these grid cells
+maintain their spatial coherence because
+
+ align:start position:0%
+maintain their spatial coherence because
+ 
+
+ align:start position:0%
+maintain their spatial coherence because
+the rat and the mouse are always
+
+ align:start position:0%
+the rat and the mouse are always
+ 
+
+ align:start position:0%
+the rat and the mouse are always
+interacting with the boundaries and the
+
+ align:start position:0%
+interacting with the boundaries and the
+ 
+
+ align:start position:0%
+interacting with the boundaries and the
+boundaries actually correct the rats
+
+ align:start position:0%
+boundaries actually correct the rats
+ 
+
+ align:start position:0%
+boundaries actually correct the rats
+internal estimated position and were it
+
+ align:start position:0%
+internal estimated position and were it
+ 
+
+ align:start position:0%
+internal estimated position and were it
+not for these interactions two
+
+ align:start position:0%
+not for these interactions two
+ 
+
+ align:start position:0%
+not for these interactions two
+boundaries the grid cells would rapidly
+
+ align:start position:0%
+boundaries the grid cells would rapidly
+ 
+
+ align:start position:0%
+boundaries the grid cells would rapidly
+Tico hair decohere on the timescale of
+
+ align:start position:0%
+Tico hair decohere on the timescale of
+ 
+
+ align:start position:0%
+Tico hair decohere on the timescale of
+minutes you know like less than a minute
+
+ align:start position:0%
+minutes you know like less than a minute
+ 
+
+ align:start position:0%
+minutes you know like less than a minute
+and so it's actually quite interesting
+
+ align:start position:0%
+and so it's actually quite interesting
+ 
+
+ align:start position:0%
+and so it's actually quite interesting
+we can show that whenever the rat
+
+ align:start position:0%
+we can show that whenever the rat
+ 
+
+ align:start position:0%
+we can show that whenever the rat
+encounters they encounters a boundary it
+
+ align:start position:0%
+encounters they encounters a boundary it
+ 
+
+ align:start position:0%
+encounters they encounters a boundary it
+corrects its internal estimate of
+
+ align:start position:0%
+corrects its internal estimate of
+ 
+
+ align:start position:0%
+corrects its internal estimate of
+position perpendicular to the boundary
+
+ align:start position:0%
+position perpendicular to the boundary
+ 
+
+ align:start position:0%
+position perpendicular to the boundary
+but it doesn't parallel and it doesn't
+
+ align:start position:0%
+but it doesn't parallel and it doesn't
+ 
+
+ align:start position:0%
+but it doesn't parallel and it doesn't
+because it can because when it hits a
+
+ align:start position:0%
+because it can because when it hits a
+ 
+
+ align:start position:0%
+because it can because when it hits a
+boundary it receives no information
+
+ align:start position:0%
+boundary it receives no information
+ 
+
+ align:start position:0%
+boundary it receives no information
+about where it is parallel to the
+
+ align:start position:0%
+about where it is parallel to the
+ 
+
+ align:start position:0%
+about where it is parallel to the
+boundary but it receives information in
+
+ align:start position:0%
+boundary but it receives information in
+ 
+
+ align:start position:0%
+boundary but it receives information in
+this direction and then with the Shenoy
+
+ align:start position:0%
+this direction and then with the Shenoy
+ 
+
+ align:start position:0%
+this direction and then with the Shenoy
+lab we've been looking at I think a
+
+ align:start position:0%
+lab we've been looking at I think a
+ 
+
+ align:start position:0%
+lab we've been looking at I think a
+really major conceptual puzzle in
+
+ align:start position:0%
+really major conceptual puzzle in
+ 
+
+ align:start position:0%
+really major conceptual puzzle in
+neuroscience is why can we record from a
+
+ align:start position:0%
+neuroscience is why can we record from a
+ 
+
+ align:start position:0%
+neuroscience is why can we record from a
+hundred neurons in a circuit containing
+
+ align:start position:0%
+hundred neurons in a circuit containing
+ 
+
+ align:start position:0%
+hundred neurons in a circuit containing
+millions of neurons and do
+
+ align:start position:0%
+millions of neurons and do
+ 
+
+ align:start position:0%
+millions of neurons and do
+dimensionality direction and infer these
+
+ align:start position:0%
+dimensionality direction and infer these
+ 
+
+ align:start position:0%
+dimensionality direction and infer these
+dynamical portraits of how the you know
+
+ align:start position:0%
+dynamical portraits of how the you know
+ 
+
+ align:start position:0%
+dynamical portraits of how the you know
+try to infer the state space dynamics in
+
+ align:start position:0%
+try to infer the state space dynamics in
+ 
+
+ align:start position:0%
+try to infer the state space dynamics in
+the circuit and claim that we've
+
+ align:start position:0%
+the circuit and claim that we've
+ 
+
+ align:start position:0%
+the circuit and claim that we've
+achieved success right we're doing
+
+ align:start position:0%
+achieved success right we're doing
+ 
+
+ align:start position:0%
+achieved success right we're doing
+dramatic undersampling recording a
+
+ align:start position:0%
+dramatic undersampling recording a
+ 
+
+ align:start position:0%
+dramatic undersampling recording a
+hundred neurons out of millions how
+
+ align:start position:0%
+hundred neurons out of millions how
+ 
+
+ align:start position:0%
+hundred neurons out of millions how
+would the how would the state space
+
+ align:start position:0%
+would the how would the state space
+ 
+
+ align:start position:0%
+would the how would the state space
+dynamics that we infer change if we
+
+ align:start position:0%
+dynamics that we infer change if we
+ 
+
+ align:start position:0%
+dynamics that we infer change if we
+recorded more neurons and we can show
+
+ align:start position:0%
+recorded more neurons and we can show
+ 
+
+ align:start position:0%
+recorded more neurons and we can show
+that essentially it will not change
+
+ align:start position:0%
+that essentially it will not change
+ 
+
+ align:start position:0%
+that essentially it will not change
+because we've come up with a novel
+
+ align:start position:0%
+because we've come up with a novel
+ 
+
+ align:start position:0%
+because we've come up with a novel
+connection between the active neural
+
+ align:start position:0%
+connection between the active neural
+ 
+
+ align:start position:0%
+connection between the active neural
+measurement and the act of random
+
+ align:start position:0%
+measurement and the act of random
+ 
+
+ align:start position:0%
+measurement and the act of random
+projections so we can show that the act
+
+ align:start position:0%
+projections so we can show that the act
+ 
+
+ align:start position:0%
+projections so we can show that the act
+of recording from a hundred neurons in
+
+ align:start position:0%
+of recording from a hundred neurons in
+ 
+
+ align:start position:0%
+of recording from a hundred neurons in
+the brain is like the act of measuring a
+
+ align:start position:0%
+the brain is like the act of measuring a
+ 
+
+ align:start position:0%
+the brain is like the act of measuring a
+hundred random linear combinations of
+
+ align:start position:0%
+hundred random linear combinations of
+ 
+
+ align:start position:0%
+hundred random linear combinations of
+all neurons in the relevant brain
+
+ align:start position:0%
+all neurons in the relevant brain
+ 
+
+ align:start position:0%
+all neurons in the relevant brain
+circuit and then we can apply random
+
+ align:start position:0%
+circuit and then we can apply random
+ 
+
+ align:start position:0%
+circuit and then we can apply random
+projection 3 to give us a predictive
+
+ align:start position:0%
+projection 3 to give us a predictive
+ 
+
+ align:start position:0%
+projection 3 to give us a predictive
+theory of experimental design that tells
+
+ align:start position:0%
+theory of experimental design that tells
+ 
+
+ align:start position:0%
+theory of experimental design that tells
+us given the complexity of the task how
+
+ align:start position:0%
+us given the complexity of the task how
+ 
+
+ align:start position:0%
+us given the complexity of the task how
+many neurons would you need to record to
+
+ align:start position:0%
+many neurons would you need to record to
+ 
+
+ align:start position:0%
+many neurons would you need to record to
+correctly recover the state space
+
+ align:start position:0%
+correctly recover the state space
+ 
+
+ align:start position:0%
+correctly recover the state space
+dynamics of the circuit and then in the
+
+ align:start position:0%
+dynamics of the circuit and then in the
+ 
+
+ align:start position:0%
+dynamics of the circuit and then in the
+Raymond lab at Stanford we've been
+
+ align:start position:0%
+Raymond lab at Stanford we've been
+ 
+
+ align:start position:0%
+Raymond lab at Stanford we've been
+looking at houseing synaptic plasticity
+
+ align:start position:0%
+looking at houseing synaptic plasticity
+ 
+
+ align:start position:0%
+looking at houseing synaptic plasticity
+can either enhance or impair learning
+
+ align:start position:0%
+can either enhance or impair learning
+ 
+
+ align:start position:0%
+can either enhance or impair learning
+depending on experience so for example
+
+ align:start position:0%
+depending on experience so for example
+ 
+
+ align:start position:0%
+depending on experience so for example
+we know that we think that synaptic
+
+ align:start position:0%
+we know that we think that synaptic
+ 
+
+ align:start position:0%
+we know that we think that synaptic
+plasticity underlies the very basis of
+
+ align:start position:0%
+plasticity underlies the very basis of
+ 
+
+ align:start position:0%
+plasticity underlies the very basis of
+our ability to learn and remember so you
+
+ align:start position:0%
+our ability to learn and remember so you
+ 
+
+ align:start position:0%
+our ability to learn and remember so you
+might think that enhancing synaptic
+
+ align:start position:0%
+might think that enhancing synaptic
+ 
+
+ align:start position:0%
+might think that enhancing synaptic
+plasticity through various
+
+ align:start position:0%
+plasticity through various
+ 
+
+ align:start position:0%
+plasticity through various
+pharmacological or genetic genetic
+
+ align:start position:0%
+pharmacological or genetic genetic
+ 
+
+ align:start position:0%
+pharmacological or genetic genetic
+modifications might enhance our ability
+
+ align:start position:0%
+modifications might enhance our ability
+ 
+
+ align:start position:0%
+modifications might enhance our ability
+to learn learn and remember but previous
+
+ align:start position:0%
+to learn learn and remember but previous
+ 
+
+ align:start position:0%
+to learn learn and remember but previous
+results have been mixed when you perturb
+
+ align:start position:0%
+results have been mixed when you perturb
+ 
+
+ align:start position:0%
+results have been mixed when you perturb
+synaptic plasticity sometimes you
+
+ align:start position:0%
+synaptic plasticity sometimes you
+ 
+
+ align:start position:0%
+synaptic plasticity sometimes you
+enhance learning
+
+ align:start position:0%
+enhance learning
+ 
+
+ align:start position:0%
+enhance learning
+sometimes you impair learning
+
+ align:start position:0%
+sometimes you impair learning
+ 
+
+ align:start position:0%
+sometimes you impair learning
+so I believe in the Raymond lab they're
+
+ align:start position:0%
+so I believe in the Raymond lab they're
+ 
+
+ align:start position:0%
+so I believe in the Raymond lab they're
+the first to show that in the same
+
+ align:start position:0%
+the first to show that in the same
+ 
+
+ align:start position:0%
+the first to show that in the same
+subject enhancing synaptic plasticity
+
+ align:start position:0%
+subject enhancing synaptic plasticity
+ 
+
+ align:start position:0%
+subject enhancing synaptic plasticity
+for example the cerebellum can either
+
+ align:start position:0%
+for example the cerebellum can either
+ 
+
+ align:start position:0%
+for example the cerebellum can either
+enhance or impair learning depending in
+
+ align:start position:0%
+enhance or impair learning depending in
+ 
+
+ align:start position:0%
+enhance or impair learning depending in
+the history of prior experience and we
+
+ align:start position:0%
+the history of prior experience and we
+ 
+
+ align:start position:0%
+the history of prior experience and we
+can show that in order to explain the
+
+ align:start position:0%
+can show that in order to explain the
+ 
+
+ align:start position:0%
+can show that in order to explain the
+behavioral learning curves you need much
+
+ align:start position:0%
+behavioral learning curves you need much
+ 
+
+ align:start position:0%
+behavioral learning curves you need much
+more complex than optic dynamics than
+
+ align:start position:0%
+more complex than optic dynamics than
+ 
+
+ align:start position:0%
+more complex than optic dynamics than
+people naturally assume we have to
+
+ align:start position:0%
+people naturally assume we have to
+ 
+
+ align:start position:0%
+people naturally assume we have to
+really promote our notion of what a
+
+ align:start position:0%
+really promote our notion of what a
+ 
+
+ align:start position:0%
+really promote our notion of what a
+synapse is from a single scalar like a W
+
+ align:start position:0%
+synapse is from a single scalar like a W
+ 
+
+ align:start position:0%
+synapse is from a single scalar like a W
+IJ in a neural network to an entire
+
+ align:start position:0%
+IJ in a neural network to an entire
+ 
+
+ align:start position:0%
+IJ in a neural network to an entire
+dynamical system in its own right so
+
+ align:start position:0%
+dynamical system in its own right so
+ 
+
+ align:start position:0%
+dynamical system in its own right so
+this relates to view our learning so
+
+ align:start position:0%
+this relates to view our learning so
+ 
+
+ align:start position:0%
+this relates to view our learning so
+this is sort of the low-level stuff that
+
+ align:start position:0%
+this is sort of the low-level stuff that
+ 
+
+ align:start position:0%
+this is sort of the low-level stuff that
+we've been doing I know that in this
+
+ align:start position:0%
+we've been doing I know that in this
+ 
+
+ align:start position:0%
+we've been doing I know that in this
+course you guys study a higher level
+
+ align:start position:0%
+course you guys study a higher level
+ 
+
+ align:start position:0%
+course you guys study a higher level
+stuff so I'm not going to talk about any
+
+ align:start position:0%
+stuff so I'm not going to talk about any
+ 
+
+ align:start position:0%
+stuff so I'm not going to talk about any
+of these that each of them could be like
+
+ align:start position:0%
+of these that each of them could be like
+ 
+
+ align:start position:0%
+of these that each of them could be like
+a one-hour talk but I wanted to discuss
+
+ align:start position:0%
+a one-hour talk but I wanted to discuss
+ 
+
+ align:start position:0%
+a one-hour talk but I wanted to discuss
+some more high level stuff that we've
+
+ align:start position:0%
+some more high level stuff that we've
+ 
+
+ align:start position:0%
+some more high level stuff that we've
+been doing
+
+ align:start position:0%
+been doing
+ 
+
+ align:start position:0%
+been doing
+oh sorry and the other sorry the other
+
+ align:start position:0%
+oh sorry and the other sorry the other
+ 
+
+ align:start position:0%
+oh sorry and the other sorry the other
+sort of direction in our lab that we're
+
+ align:start position:0%
+sort of direction in our lab that we're
+ 
+
+ align:start position:0%
+sort of direction in our lab that we're
+looking at is actually the statistical
+
+ align:start position:0%
+looking at is actually the statistical
+ 
+
+ align:start position:0%
+looking at is actually the statistical
+mechanics of high dimensional data
+
+ align:start position:0%
+mechanics of high dimensional data
+ 
+
+ align:start position:0%
+mechanics of high dimensional data
+analysis so this is of course very
+
+ align:start position:0%
+analysis so this is of course very
+ 
+
+ align:start position:0%
+analysis so this is of course very
+relevant and the age of the brain
+
+ align:start position:0%
+relevant and the age of the brain
+ 
+
+ align:start position:0%
+relevant and the age of the brain
+initiative and so on we're developing
+
+ align:start position:0%
+initiative and so on we're developing
+ 
+
+ align:start position:0%
+initiative and so on we're developing
+very large scale data sets and we'd like
+
+ align:start position:0%
+very large scale data sets and we'd like
+ 
+
+ align:start position:0%
+very large scale data sets and we'd like
+to extract theories from this so-called
+
+ align:start position:0%
+to extract theories from this so-called
+ 
+
+ align:start position:0%
+to extract theories from this so-called
+big data so the entire edifice of
+
+ align:start position:0%
+big data so the entire edifice of
+ 
+
+ align:start position:0%
+big data so the entire edifice of
+classical statistics is predicated on
+
+ align:start position:0%
+classical statistics is predicated on
+ 
+
+ align:start position:0%
+classical statistics is predicated on
+the assumption that you have many many
+
+ align:start position:0%
+the assumption that you have many many
+ 
+
+ align:start position:0%
+the assumption that you have many many
+data points and you have a small number
+
+ align:start position:0%
+data points and you have a small number
+ 
+
+ align:start position:0%
+data points and you have a small number
+of features right so then it's very easy
+
+ align:start position:0%
+of features right so then it's very easy
+ 
+
+ align:start position:0%
+of features right so then it's very easy
+to see patterns in your data but what's
+
+ align:start position:0%
+to see patterns in your data but what's
+ 
+
+ align:start position:0%
+to see patterns in your data but what's
+actually happening nowadays is that we
+
+ align:start position:0%
+actually happening nowadays is that we
+ 
+
+ align:start position:0%
+actually happening nowadays is that we
+have a large number of data points and a
+
+ align:start position:0%
+have a large number of data points and a
+ 
+
+ align:start position:0%
+have a large number of data points and a
+large number of features so for example
+
+ align:start position:0%
+large number of features so for example
+ 
+
+ align:start position:0%
+large number of features so for example
+where you can record from a hundred
+
+ align:start position:0%
+where you can record from a hundred
+ 
+
+ align:start position:0%
+where you can record from a hundred
+neurons using electrophysiology maybe
+
+ align:start position:0%
+neurons using electrophysiology maybe
+ 
+
+ align:start position:0%
+neurons using electrophysiology maybe
+for only a hundred trials of any given
+
+ align:start position:0%
+for only a hundred trials of any given
+ 
+
+ align:start position:0%
+for only a hundred trials of any given
+trial type in a monkey doing some tasks
+
+ align:start position:0%
+trial type in a monkey doing some tasks
+ 
+
+ align:start position:0%
+trial type in a monkey doing some tasks
+so the ratio of the amount of data to
+
+ align:start position:0%
+so the ratio of the amount of data to
+ 
+
+ align:start position:0%
+so the ratio of the amount of data to
+the the number of the number of features
+
+ align:start position:0%
+the the number of the number of features
+ 
+
+ align:start position:0%
+the the number of the number of features
+is something that's order one so you
+
+ align:start position:0%
+is something that's order one so you
+ 
+
+ align:start position:0%
+is something that's order one so you
+know the data sets are like three points
+
+ align:start position:0%
+know the data sets are like three points
+ 
+
+ align:start position:0%
+know the data sets are like three points
+in a three-dimensional space that's the
+
+ align:start position:0%
+in a three-dimensional space that's the
+ 
+
+ align:start position:0%
+in a three-dimensional space that's the
+best we can visualize so it's a
+
+ align:start position:0%
+best we can visualize so it's a
+ 
+
+ align:start position:0%
+best we can visualize so it's a
+significant challenge to do data
+
+ align:start position:0%
+significant challenge to do data
+ 
+
+ align:start position:0%
+significant challenge to do data
+analysis in this scenario so it turns
+
+ align:start position:0%
+analysis in this scenario so it turns
+ 
+
+ align:start position:0%
+analysis in this scenario so it turns
+out there's beautiful connections
+
+ align:start position:0%
+out there's beautiful connections
+ 
+
+ align:start position:0%
+out there's beautiful connections
+between machine learning and data
+
+ align:start position:0%
+between machine learning and data
+ 
+
+ align:start position:0%
+between machine learning and data
+analysis and the statistical physics of
+
+ align:start position:0%
+analysis and the statistical physics of
+ 
+
+ align:start position:0%
+analysis and the statistical physics of
+systems of the quench disorder so so
+
+ align:start position:0%
+systems of the quench disorder so so
+ 
+
+ align:start position:0%
+systems of the quench disorder so so
+what I mean by that is in data analysis
+
+ align:start position:0%
+what I mean by that is in data analysis
+ 
+
+ align:start position:0%
+what I mean by that is in data analysis
+you want to learn statistical parameters
+
+ align:start position:0%
+you want to learn statistical parameters
+ 
+
+ align:start position:0%
+you want to learn statistical parameters
+by maximizing the log likelihood of the
+
+ align:start position:0%
+by maximizing the log likelihood of the
+ 
+
+ align:start position:0%
+by maximizing the log likelihood of the
+data given the parameters and Cisco
+
+ align:start position:0%
+data given the parameters and Cisco
+ 
+
+ align:start position:0%
+data given the parameters and Cisco
+physics you often want to minimize an
+
+ align:start position:0%
+physics you often want to minimize an
+ 
+
+ align:start position:0%
+physics you often want to minimize an
+you know this can be viewed as energy
+
+ align:start position:0%
+you know this can be viewed as energy
+ 
+
+ align:start position:0%
+you know this can be viewed as energy
+minimization and so there's beautiful
+
+ align:start position:0%
+minimization and so there's beautiful
+ 
+
+ align:start position:0%
+minimization and so there's beautiful
+connections between these and so we work
+
+ align:start position:0%
+connections between these and so we work
+ 
+
+ align:start position:0%
+connections between these and so we work
+on that so we've applied this to
+
+ align:start position:0%
+on that so we've applied this to
+ 
+
+ align:start position:0%
+on that so we've applied this to
+compress sensing we've applied this to
+
+ align:start position:0%
+compress sensing we've applied this to
+ 
+
+ align:start position:0%
+compress sensing we've applied this to
+the problem of what's the optimal
+
+ align:start position:0%
+the problem of what's the optimal
+ 
+
+ align:start position:0%
+the problem of what's the optimal
+inference procedure in a written
+
+ align:start position:0%
+inference procedure in a written
+ 
+
+ align:start position:0%
+inference procedure in a written
+in a regime in the high-dimensional
+
+ align:start position:0%
+in a regime in the high-dimensional
+ 
+
+ align:start position:0%
+in a regime in the high-dimensional
+regime we know that maximum likelihood
+
+ align:start position:0%
+regime we know that maximum likelihood
+ 
+
+ align:start position:0%
+regime we know that maximum likelihood
+is optimal in this regime but something
+
+ align:start position:0%
+is optimal in this regime but something
+ 
+
+ align:start position:0%
+is optimal in this regime but something
+else is better in this regime and we
+
+ align:start position:0%
+else is better in this regime and we
+ 
+
+ align:start position:0%
+else is better in this regime and we
+found what's better it turns out to be a
+
+ align:start position:0%
+found what's better it turns out to be a
+ 
+
+ align:start position:0%
+found what's better it turns out to be a
+smooth maximum likelihood and of course
+
+ align:start position:0%
+smooth maximum likelihood and of course
+ 
+
+ align:start position:0%
+smooth maximum likelihood and of course
+we've applied this to a theory of neural
+
+ align:start position:0%
+we've applied this to a theory of neural
+ 
+
+ align:start position:0%
+we've applied this to a theory of neural
+dimensionality and measurement so you
+
+ align:start position:0%
+dimensionality and measurement so you
+ 
+
+ align:start position:0%
+dimensionality and measurement so you
+know there's lots of beautiful
+
+ align:start position:0%
+know there's lots of beautiful
+ 
+
+ align:start position:0%
+know there's lots of beautiful
+interactions between physics machine
+
+ align:start position:0%
+interactions between physics machine
+ 
+
+ align:start position:0%
+interactions between physics machine
+learning and neuroscience and and you
+
+ align:start position:0%
+learning and neuroscience and and you
+ 
+
+ align:start position:0%
+learning and neuroscience and and you
+know this school is a lot about that if
+
+ align:start position:0%
+know this school is a lot about that if
+ 
+
+ align:start position:0%
+know this school is a lot about that if
+you're interested actually we wrote like
+
+ align:start position:0%
+you're interested actually we wrote like
+ 
+
+ align:start position:0%
+you're interested actually we wrote like
+a 70 page review on statistical
+
+ align:start position:0%
+a 70 page review on statistical
+ 
+
+ align:start position:0%
+a 70 page review on statistical
+mechanics of complex neural systems and
+
+ align:start position:0%
+mechanics of complex neural systems and
+ 
+
+ align:start position:0%
+mechanics of complex neural systems and
+high dimensional data we cover a whole
+
+ align:start position:0%
+high dimensional data we cover a whole
+ 
+
+ align:start position:0%
+high dimensional data we cover a whole
+bunch of things like spin glasses the
+
+ align:start position:0%
+bunch of things like spin glasses the
+ 
+
+ align:start position:0%
+bunch of things like spin glasses the
+statistical mechanics of learning random
+
+ align:start position:0%
+statistical mechanics of learning random
+ 
+
+ align:start position:0%
+statistical mechanics of learning random
+matrix theory random dimensional
+
+ align:start position:0%
+matrix theory random dimensional
+ 
+
+ align:start position:0%
+matrix theory random dimensional
+reduction compressed sensing and so on
+
+ align:start position:0%
+reduction compressed sensing and so on
+ 
+
+ align:start position:0%
+reduction compressed sensing and so on
+and so forth it was our attempt to sort
+
+ align:start position:0%
+and so forth it was our attempt to sort
+ 
+
+ align:start position:0%
+and so forth it was our attempt to sort
+of put some systematic order on the
+
+ align:start position:0%
+of put some systematic order on the
+ 
+
+ align:start position:0%
+of put some systematic order on the
+diversity of topics viewed through the
+
+ align:start position:0%
+diversity of topics viewed through the
+ 
+
+ align:start position:0%
+diversity of topics viewed through the
+lens of statistical physics but what do
+
+ align:start position:0%
+lens of statistical physics but what do
+ 
+
+ align:start position:0%
+lens of statistical physics but what do
+I want to talk about today and why did I
+
+ align:start position:0%
+I want to talk about today and why did I
+ 
+
+ align:start position:0%
+I want to talk about today and why did I
+decide to branch out in the direction
+
+ align:start position:0%
+decide to branch out in the direction
+ 
+
+ align:start position:0%
+decide to branch out in the direction
+I'm going to tell you about well I think
+
+ align:start position:0%
+I'm going to tell you about well I think
+ 
+
+ align:start position:0%
+I'm going to tell you about well I think
+there's lots of motivations for an
+
+ align:start position:0%
+there's lots of motivations for an
+ 
+
+ align:start position:0%
+there's lots of motivations for an
+alliance between theoretical
+
+ align:start position:0%
+alliance between theoretical
+ 
+
+ align:start position:0%
+alliance between theoretical
+neuroscience theoretical machine
+
+ align:start position:0%
+neuroscience theoretical machine
+ 
+
+ align:start position:0%
+neuroscience theoretical machine
+learning that lead to opportunities for
+
+ align:start position:0%
+learning that lead to opportunities for
+ 
+
+ align:start position:0%
+learning that lead to opportunities for
+physics and math and so on so and this
+
+ align:start position:0%
+physics and math and so on so and this
+ 
+
+ align:start position:0%
+physics and math and so on so and this
+is the question that should haunt all of
+
+ align:start position:0%
+is the question that should haunt all of
+ 
+
+ align:start position:0%
+is the question that should haunt all of
+us right the question is what does it
+
+ align:start position:0%
+us right the question is what does it
+ 
+
+ align:start position:0%
+us right the question is what does it
+even mean to understand how the brain
+
+ align:start position:0%
+even mean to understand how the brain
+ 
+
+ align:start position:0%
+even mean to understand how the brain
+works or how a neural circuit works okay
+
+ align:start position:0%
+works or how a neural circuit works okay
+ 
+
+ align:start position:0%
+works or how a neural circuit works okay
+you know it that's an open question that
+
+ align:start position:0%
+you know it that's an open question that
+ 
+
+ align:start position:0%
+you know it that's an open question that
+we really have to come to terms with a
+
+ align:start position:0%
+we really have to come to terms with a
+ 
+
+ align:start position:0%
+we really have to come to terms with a
+proximal sort of a specification or a
+
+ align:start position:0%
+proximal sort of a specification or a
+ 
+
+ align:start position:0%
+proximal sort of a specification or a
+more concrete version of this question
+
+ align:start position:0%
+more concrete version of this question
+ 
+
+ align:start position:0%
+more concrete version of this question
+might be or a specification this
+
+ align:start position:0%
+might be or a specification this
+ 
+
+ align:start position:0%
+might be or a specification this
+question might be we will understand
+
+ align:start position:0%
+question might be we will understand
+ 
+
+ align:start position:0%
+question might be we will understand
+this when we understand how the
+
+ align:start position:0%
+this when we understand how the
+ 
+
+ align:start position:0%
+this when we understand how the
+connectivity and dynamics of a neural
+
+ align:start position:0%
+connectivity and dynamics of a neural
+ 
+
+ align:start position:0%
+connectivity and dynamics of a neural
+circuit give rise to behavior and also
+
+ align:start position:0%
+circuit give rise to behavior and also
+ 
+
+ align:start position:0%
+circuit give rise to behavior and also
+how neural activity and synaptic
+
+ align:start position:0%
+how neural activity and synaptic
+ 
+
+ align:start position:0%
+how neural activity and synaptic
+learning rules conspire to self-organize
+
+ align:start position:0%
+learning rules conspire to self-organize
+ 
+
+ align:start position:0%
+learning rules conspire to self-organize
+useful connectivity that's observes
+
+ align:start position:0%
+useful connectivity that's observes
+ 
+
+ align:start position:0%
+useful connectivity that's observes
+behavior okay so so you know the you
+
+ align:start position:0%
+behavior okay so so you know the you
+ 
+
+ align:start position:0%
+behavior okay so so you know the you
+know various brain interests are
+
+ align:start position:0%
+know various brain interests are
+ 
+
+ align:start position:0%
+know various brain interests are
+promising to give us recording some
+
+ align:start position:0%
+promising to give us recording some
+ 
+
+ align:start position:0%
+promising to give us recording some
+large numbers of neurons and even give
+
+ align:start position:0%
+large numbers of neurons and even give
+ 
+
+ align:start position:0%
+large numbers of neurons and even give
+us the connectivity between those
+
+ align:start position:0%
+us the connectivity between those
+ 
+
+ align:start position:0%
+us the connectivity between those
+neurons now what what if theorists own
+
+ align:start position:0%
+neurons now what what if theorists own
+ 
+
+ align:start position:0%
+neurons now what what if theorists own
+often what theorists in competition
+
+ align:start position:0%
+often what theorists in competition
+ 
+
+ align:start position:0%
+often what theorists in competition
+neuroscience do is they they often
+
+ align:start position:0%
+neuroscience do is they they often
+ 
+
+ align:start position:0%
+neuroscience do is they they often
+develop theories of random networks that
+
+ align:start position:0%
+develop theories of random networks that
+ 
+
+ align:start position:0%
+develop theories of random networks that
+have no function but what we would like
+
+ align:start position:0%
+have no function but what we would like
+ 
+
+ align:start position:0%
+have no function but what we would like
+to do is we'd like to understand
+
+ align:start position:0%
+to do is we'd like to understand
+ 
+
+ align:start position:0%
+to do is we'd like to understand
+engineered networks that have function
+
+ align:start position:0%
+engineered networks that have function
+ 
+
+ align:start position:0%
+engineered networks that have function
+so the field of machine learning has
+
+ align:start position:0%
+so the field of machine learning has
+ 
+
+ align:start position:0%
+so the field of machine learning has
+generated a plethora of learn neural
+
+ align:start position:0%
+generated a plethora of learn neural
+ 
+
+ align:start position:0%
+generated a plethora of learn neural
+networks that accomplish interesting
+
+ align:start position:0%
+networks that accomplish interesting
+ 
+
+ align:start position:0%
+networks that accomplish interesting
+functions yet we still don't have a
+
+ align:start position:0%
+functions yet we still don't have a
+ 
+
+ align:start position:0%
+functions yet we still don't have a
+meaningful understanding of how their
+
+ align:start position:0%
+meaningful understanding of how their
+ 
+
+ align:start position:0%
+meaningful understanding of how their
+connectivity dynamics the learning
+
+ align:start position:0%
+connectivity dynamics the learning
+ 
+
+ align:start position:0%
+connectivity dynamics the learning
+the developmental experience okay so
+
+ align:start position:0%
+the developmental experience okay so
+ 
+
+ align:start position:0%
+the developmental experience okay so
+basically we can measure anything we
+
+ align:start position:0%
+basically we can measure anything we
+ 
+
+ align:start position:0%
+basically we can measure anything we
+want in in these artificial neural
+
+ align:start position:0%
+want in in these artificial neural
+ 
+
+ align:start position:0%
+want in in these artificial neural
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+
+ align:start position:0%
+networks right we can measure the
+ 
+
+ align:start position:0%
+networks right we can measure the
+connectivity between all the neurons we
+
+ align:start position:0%
+connectivity between all the neurons we
+ 
+
+ align:start position:0%
+connectivity between all the neurons we
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+
+ align:start position:0%
+know the dynamics of all the neurons we
+ 
+
+ align:start position:0%
+know the dynamics of all the neurons we
+know the learning rule we know the
+
+ align:start position:0%
+know the learning rule we know the
+ 
+
+ align:start position:0%
+know the learning rule we know the
+entire developmental experience the
+
+ align:start position:0%
+entire developmental experience the
+ 
+
+ align:start position:0%
+entire developmental experience the
+network because we know the training
+
+ align:start position:0%
+network because we know the training
+ 
+
+ align:start position:0%
+network because we know the training
+data that was exposed to yet we still do
+
+ align:start position:0%
+data that was exposed to yet we still do
+ 
+
+ align:start position:0%
+data that was exposed to yet we still do
+not have a meaningful understanding of
+
+ align:start position:0%
+not have a meaningful understanding of
+ 
+
+ align:start position:0%
+not have a meaningful understanding of
+how they learn and how they work and if
+
+ align:start position:0%
+how they learn and how they work and if
+ 
+
+ align:start position:0%
+how they learn and how they work and if
+we can't solve that problem how are we
+
+ align:start position:0%
+we can't solve that problem how are we
+ 
+
+ align:start position:0%
+we can't solve that problem how are we
+ever going to understand the brain right
+
+ align:start position:0%
+ever going to understand the brain right
+ 
+
+ align:start position:0%
+ever going to understand the brain right
+in the form of this question okay so
+
+ align:start position:0%
+in the form of this question okay so
+ 
+
+ align:start position:0%
+in the form of this question okay so
+that was sort of what was motivating me
+
+ align:start position:0%
+that was sort of what was motivating me
+ 
+
+ align:start position:0%
+that was sort of what was motivating me
+to look into this so so this is the
+
+ align:start position:0%
+to look into this so so this is the
+ 
+
+ align:start position:0%
+to look into this so so this is the
+outline of the talk the original entry
+
+ align:start position:0%
+outline of the talk the original entry
+ 
+
+ align:start position:0%
+outline of the talk the original entry
+point was trying to understand category
+
+ align:start position:0%
+point was trying to understand category
+ 
+
+ align:start position:0%
+point was trying to understand category
+learning in neural networks and then at
+
+ align:start position:0%
+learning in neural networks and then at
+ 
+
+ align:start position:0%
+learning in neural networks and then at
+the end of the day we made actually
+
+ align:start position:0%
+the end of the day we made actually
+ 
+
+ align:start position:0%
+the end of the day we made actually
+several theoretical advances that led to
+
+ align:start position:0%
+several theoretical advances that led to
+ 
+
+ align:start position:0%
+several theoretical advances that led to
+advances in machine learning and
+
+ align:start position:0%
+advances in machine learning and
+ 
+
+ align:start position:0%
+advances in machine learning and
+applications to engineering so for
+
+ align:start position:0%
+applications to engineering so for
+ 
+
+ align:start position:0%
+applications to engineering so for
+example we find we found random weight
+
+ align:start position:0%
+example we find we found random weight
+ 
+
+ align:start position:0%
+example we find we found random weight
+initializations that make a network
+
+ align:start position:0%
+initializations that make a network
+ 
+
+ align:start position:0%
+initializations that make a network
+dynamically critical and allow very very
+
+ align:start position:0%
+dynamically critical and allow very very
+ 
+
+ align:start position:0%
+dynamically critical and allow very very
+rapid training of deep neural networks
+
+ align:start position:0%
+rapid training of deep neural networks
+ 
+
+ align:start position:0%
+rapid training of deep neural networks
+we were able to understand and exploit
+
+ align:start position:0%
+we were able to understand and exploit
+ 
+
+ align:start position:0%
+we were able to understand and exploit
+the geometry of high dimensional error
+
+ align:start position:0%
+the geometry of high dimensional error
+ 
+
+ align:start position:0%
+the geometry of high dimensional error
+surfaces to again speed up learning like
+
+ align:start position:0%
+surfaces to again speed up learning like
+ 
+
+ align:start position:0%
+surfaces to again speed up learning like
+training deep neural networks and we're
+
+ align:start position:0%
+training deep neural networks and we're
+ 
+
+ align:start position:0%
+training deep neural networks and we're
+also able to exploit sort of recent work
+
+ align:start position:0%
+also able to exploit sort of recent work
+ 
+
+ align:start position:0%
+also able to exploit sort of recent work
+in non-equilibrium thermodynamics to
+
+ align:start position:0%
+in non-equilibrium thermodynamics to
+ 
+
+ align:start position:0%
+in non-equilibrium thermodynamics to
+learn complex probabilistic generative
+
+ align:start position:0%
+learn complex probabilistic generative
+ 
+
+ align:start position:0%
+learn complex probabilistic generative
+models so it's a diversity of topics but
+
+ align:start position:0%
+models so it's a diversity of topics but
+ 
+
+ align:start position:0%
+models so it's a diversity of topics but
+I'll walk you through them and you can
+
+ align:start position:0%
+I'll walk you through them and you can
+ 
+
+ align:start position:0%
+I'll walk you through them and you can
+relax because almost everything I'm
+
+ align:start position:0%
+relax because almost everything I'm
+ 
+
+ align:start position:0%
+relax because almost everything I'm
+going to talk about is is is published
+
+ align:start position:0%
+going to talk about is is is published
+ 
+
+ align:start position:0%
+going to talk about is is is published
+okay so let's start with the motivation
+
+ align:start position:0%
+okay so let's start with the motivation
+ 
+
+ align:start position:0%
+okay so let's start with the motivation
+a mathematical theory of semantic
+
+ align:start position:0%
+a mathematical theory of semantic
+ 
+
+ align:start position:0%
+a mathematical theory of semantic
+development I think this speaks to some
+
+ align:start position:0%
+development I think this speaks to some
+ 
+
+ align:start position:0%
+development I think this speaks to some
+of the high-level stuff that you guys
+
+ align:start position:0%
+of the high-level stuff that you guys
+ 
+
+ align:start position:0%
+of the high-level stuff that you guys
+think about this part could equally be
+
+ align:start position:0%
+think about this part could equally be
+ 
+
+ align:start position:0%
+think about this part could equally be
+talked it could could be called the
+
+ align:start position:0%
+talked it could could be called the
+ 
+
+ align:start position:0%
+talked it could could be called the
+misadventures and implied physicists who
+
+ align:start position:0%
+misadventures and implied physicists who
+ 
+
+ align:start position:0%
+misadventures and implied physicists who
+found himself lost in the psychology
+
+ align:start position:0%
+found himself lost in the psychology
+ 
+
+ align:start position:0%
+found himself lost in the psychology
+department so I sort of showed up at
+
+ align:start position:0%
+department so I sort of showed up at
+ 
+
+ align:start position:0%
+department so I sort of showed up at
+Stanford Jay's a great guy was talking
+
+ align:start position:0%
+Stanford Jay's a great guy was talking
+ 
+
+ align:start position:0%
+Stanford Jay's a great guy was talking
+to him and I learned about his work and
+
+ align:start position:0%
+to him and I learned about his work and
+ 
+
+ align:start position:0%
+to him and I learned about his work and
+I realized I didn't understand it
+
+ align:start position:0%
+I realized I didn't understand it
+ 
+
+ align:start position:0%
+I realized I didn't understand it
+and and this is my attempt to understand
+
+ align:start position:0%
+and and this is my attempt to understand
+ 
+
+ align:start position:0%
+and and this is my attempt to understand
+that work with Andrew and NJ so ok so
+
+ align:start position:0%
+that work with Andrew and NJ so ok so
+ 
+
+ align:start position:0%
+that work with Andrew and NJ so ok so
+what is semantic cognition so human
+
+ align:start position:0%
+what is semantic cognition so human
+ 
+
+ align:start position:0%
+what is semantic cognition so human
+semantic cognition a rough definition of
+
+ align:start position:0%
+semantic cognition a rough definition of
+ 
+
+ align:start position:0%
+semantic cognition a rough definition of
+this field is that we have an ability to
+
+ align:start position:0%
+this field is that we have an ability to
+ 
+
+ align:start position:0%
+this field is that we have an ability to
+learn recognize comprehend and produce
+
+ align:start position:0%
+learn recognize comprehend and produce
+ 
+
+ align:start position:0%
+learn recognize comprehend and produce
+inferences about properties of objects
+
+ align:start position:0%
+inferences about properties of objects
+ 
+
+ align:start position:0%
+inferences about properties of objects
+and events in the world especially
+
+ align:start position:0%
+and events in the world especially
+ 
+
+ align:start position:0%
+and events in the world especially
+properties that are not present in your
+
+ align:start position:0%
+properties that are not present in your
+ 
+
+ align:start position:0%
+properties that are not present in your
+current perceptual stimulus so for
+
+ align:start position:0%
+current perceptual stimulus so for
+ 
+
+ align:start position:0%
+current perceptual stimulus so for
+example I can ask you does a cat have
+
+ align:start position:0%
+example I can ask you does a cat have
+ 
+
+ align:start position:0%
+example I can ask you does a cat have
+fur and do birds fly and you can answer
+
+ align:start position:0%
+fur and do birds fly and you can answer
+ 
+
+ align:start position:0%
+fur and do birds fly and you can answer
+these questions correctly despite the
+
+ align:start position:0%
+these questions correctly despite the
+ 
+
+ align:start position:0%
+these questions correctly despite the
+fact that there's currently no cat or
+
+ align:start position:0%
+fact that there's currently no cat or
+ 
+
+ align:start position:0%
+fact that there's currently no cat or
+bird in the room
+
+ align:start position:0%
+bird in the room
+ 
+
+ align:start position:0%
+bird in the room
+right so you know our ability to do this
+
+ align:start position:0%
+right so you know our ability to do this
+ 
+
+ align:start position:0%
+right so you know our ability to do this
+likely relies on our ability to form
+
+ align:start position:0%
+likely relies on our ability to form
+ 
+
+ align:start position:0%
+likely relies on our ability to form
+internal representations of categories
+
+ align:start position:0%
+internal representations of categories
+ 
+
+ align:start position:0%
+internal representations of categories
+in the external world and associate
+
+ align:start position:0%
+in the external world and associate
+ 
+
+ align:start position:0%
+in the external world and associate
+properties with those categories because
+
+ align:start position:0%
+properties with those categories because
+ 
+
+ align:start position:0%
+properties with those categories because
+we never see the same stimulus twice so
+
+ align:start position:0%
+we never see the same stimulus twice so
+ 
+
+ align:start position:0%
+we never see the same stimulus twice so
+whenever we see a new stimulus or we
+
+ align:start position:0%
+whenever we see a new stimulus or we
+ 
+
+ align:start position:0%
+whenever we see a new stimulus or we
+trying to recall information from our
+
+ align:start position:0%
+trying to recall information from our
+ 
+
+ align:start position:0%
+trying to recall information from our
+brain we rapidly identify the relevant
+
+ align:start position:0%
+brain we rapidly identify the relevant
+ 
+
+ align:start position:0%
+brain we rapidly identify the relevant
+category that contains the information
+
+ align:start position:0%
+category that contains the information
+ 
+
+ align:start position:0%
+category that contains the information
+and we use that categorical
+
+ align:start position:0%
+and we use that categorical
+ 
+
+ align:start position:0%
+and we use that categorical
+representation to guide future actions
+
+ align:start position:0%
+representation to guide future actions
+ 
+
+ align:start position:0%
+representation to guide future actions
+or give answers right so a category
+
+ align:start position:0%
+or give answers right so a category
+ 
+
+ align:start position:0%
+or give answers right so a category
+formation is central to this right so
+
+ align:start position:0%
+formation is central to this right so
+ 
+
+ align:start position:0%
+formation is central to this right so
+what are the kinds of psychophysical
+
+ align:start position:0%
+what are the kinds of psychophysical
+ 
+
+ align:start position:0%
+what are the kinds of psychophysical
+tasks that people use to probe semantic
+
+ align:start position:0%
+tasks that people use to probe semantic
+ 
+
+ align:start position:0%
+tasks that people use to probe semantic
+cognition so this is a very rich field
+
+ align:start position:0%
+cognition so this is a very rich field
+ 
+
+ align:start position:0%
+cognition so this is a very rich field
+psychologists have been working on this
+
+ align:start position:0%
+psychologists have been working on this
+ 
+
+ align:start position:0%
+psychologists have been working on this
+all the time so one example is looking
+
+ align:start position:0%
+all the time so one example is looking
+ 
+
+ align:start position:0%
+all the time so one example is looking
+time studies to ascertain whether or not
+
+ align:start position:0%
+time studies to ascertain whether or not
+ 
+
+ align:start position:0%
+time studies to ascertain whether or not
+an infant can distinguish between two
+
+ align:start position:0%
+an infant can distinguish between two
+ 
+
+ align:start position:0%
+an infant can distinguish between two
+categories of objects at what age so for
+
+ align:start position:0%
+categories of objects at what age so for
+ 
+
+ align:start position:0%
+categories of objects at what age so for
+example they'll show a sequence of
+
+ align:start position:0%
+example they'll show a sequence of
+ 
+
+ align:start position:0%
+example they'll show a sequence of
+objects from category one say horses and
+
+ align:start position:0%
+objects from category one say horses and
+ 
+
+ align:start position:0%
+objects from category one say horses and
+the first time the infant sees a horse
+
+ align:start position:0%
+the first time the infant sees a horse
+ 
+
+ align:start position:0%
+the first time the infant sees a horse
+the looking time will go up and then it
+
+ align:start position:0%
+the looking time will go up and then it
+ 
+
+ align:start position:0%
+the looking time will go up and then it
+goes down over time it gets bored then
+
+ align:start position:0%
+goes down over time it gets bored then
+ 
+
+ align:start position:0%
+goes down over time it gets bored then
+you show a cow and if the infant is old
+
+ align:start position:0%
+you show a cow and if the infant is old
+ 
+
+ align:start position:0%
+you show a cow and if the infant is old
+enough the looking time will go up and
+
+ align:start position:0%
+enough the looking time will go up and
+ 
+
+ align:start position:0%
+enough the looking time will go up and
+then go back down and that's from that
+
+ align:start position:0%
+then go back down and that's from that
+ 
+
+ align:start position:0%
+then go back down and that's from that
+we infer that the infant can distinguish
+
+ align:start position:0%
+we infer that the infant can distinguish
+ 
+
+ align:start position:0%
+we infer that the infant can distinguish
+between horses and cows but if it's not
+
+ align:start position:0%
+between horses and cows but if it's not
+ 
+
+ align:start position:0%
+between horses and cows but if it's not
+old enough the looking time will not go
+
+ align:start position:0%
+old enough the looking time will not go
+ 
+
+ align:start position:0%
+old enough the looking time will not go
+up so it as the infant gets older and
+
+ align:start position:0%
+up so it as the infant gets older and
+ 
+
+ align:start position:0%
+up so it as the infant gets older and
+older it can make more and more fine
+
+ align:start position:0%
+older it can make more and more fine
+ 
+
+ align:start position:0%
+older it can make more and more fine
+scale discriminations between categories
+
+ align:start position:0%
+scale discriminations between categories
+ 
+
+ align:start position:0%
+scale discriminations between categories
+it turns out so property verification
+
+ align:start position:0%
+it turns out so property verification
+ 
+
+ align:start position:0%
+it turns out so property verification
+tasks you can ask can a canary move can
+
+ align:start position:0%
+tasks you can ask can a canary move can
+ 
+
+ align:start position:0%
+tasks you can ask can a canary move can
+it sing and certain questions are
+
+ align:start position:0%
+it sing and certain questions are
+ 
+
+ align:start position:0%
+it sing and certain questions are
+answered quickly certain questions are
+
+ align:start position:0%
+answered quickly certain questions are
+ 
+
+ align:start position:0%
+answered quickly certain questions are
+answered late which speaks to certain
+
+ align:start position:0%
+answered late which speaks to certain
+ 
+
+ align:start position:0%
+answered late which speaks to certain
+properties being central and peripheral
+
+ align:start position:0%
+properties being central and peripheral
+ 
+
+ align:start position:0%
+properties being central and peripheral
+to certain categories a category
+
+ align:start position:0%
+to certain categories a category
+ 
+
+ align:start position:0%
+to certain categories a category
+membership queries is a sparrow a bird
+
+ align:start position:0%
+membership queries is a sparrow a bird
+ 
+
+ align:start position:0%
+membership queries is a sparrow a bird
+or as an ostrich bird again there's
+
+ align:start position:0%
+or as an ostrich bird again there's
+ 
+
+ align:start position:0%
+or as an ostrich bird again there's
+different relate latencies and that's
+
+ align:start position:0%
+different relate latencies and that's
+ 
+
+ align:start position:0%
+different relate latencies and that's
+that suggests that there are typical and
+
+ align:start position:0%
+that suggests that there are typical and
+ 
+
+ align:start position:0%
+that suggests that there are typical and
+atypical category members and also very
+
+ align:start position:0%
+atypical category members and also very
+ 
+
+ align:start position:0%
+atypical category members and also very
+very important to us in is inductive
+
+ align:start position:0%
+very important to us in is inductive
+ 
+
+ align:start position:0%
+very important to us in is inductive
+generalization we can both generalize
+
+ align:start position:0%
+generalization we can both generalize
+ 
+
+ align:start position:0%
+generalization we can both generalize
+familiar properties to novel objects for
+
+ align:start position:0%
+familiar properties to novel objects for
+ 
+
+ align:start position:0%
+familiar properties to novel objects for
+example a blick has feathers does it fly
+
+ align:start position:0%
+example a blick has feathers does it fly
+ 
+
+ align:start position:0%
+example a blick has feathers does it fly
+does it sing and we can generalize novel
+
+ align:start position:0%
+does it sing and we can generalize novel
+ 
+
+ align:start position:0%
+does it sing and we can generalize novel
+properties to familiar objects a bird
+
+ align:start position:0%
+properties to familiar objects a bird
+ 
+
+ align:start position:0%
+properties to familiar objects a bird
+has gene X does a crocodile have gene X
+
+ align:start position:0%
+has gene X does a crocodile have gene X
+ 
+
+ align:start position:0%
+has gene X does a crocodile have gene X
+does a dog have gene X you know so the
+
+ align:start position:0%
+does a dog have gene X you know so the
+ 
+
+ align:start position:0%
+does a dog have gene X you know so the
+so people have measured these patterns
+
+ align:start position:0%
+so people have measured these patterns
+ 
+
+ align:start position:0%
+so people have measured these patterns
+of inductive generalizations and there's
+
+ align:start position:0%
+of inductive generalizations and there's
+ 
+
+ align:start position:0%
+of inductive generalizations and there's
+various theories that try to explain all
+
+ align:start position:0%
+various theories that try to explain all
+ 
+
+ align:start position:0%
+various theories that try to explain all
+of this stuff so jay has been working on
+
+ align:start position:0%
+of this stuff so jay has been working on
+ 
+
+ align:start position:0%
+of this stuff so jay has been working on
+this stuff from a neural network
+
+ align:start position:0%
+this stuff from a neural network
+ 
+
+ align:start position:0%
+this stuff from a neural network
+perspective and he wrote a beautiful
+
+ align:start position:0%
+perspective and he wrote a beautiful
+ 
+
+ align:start position:0%
+perspective and he wrote a beautiful
+book called semantic cognition where he
+
+ align:start position:0%
+book called semantic cognition where he
+ 
+
+ align:start position:0%
+book called semantic cognition where he
+uses neural networks to explain a whole
+
+ align:start position:0%
+uses neural networks to explain a whole
+ 
+
+ align:start position:0%
+uses neural networks to explain a whole
+variety of phenomena especially for
+
+ align:start position:0%
+variety of phenomena especially for
+ 
+
+ align:start position:0%
+variety of phenomena especially for
+example the progressive differential of
+
+ align:start position:0%
+example the progressive differential of
+ 
+
+ align:start position:0%
+example the progressive differential of
+progressive differentiation of concepts
+
+ align:start position:0%
+progressive differentiation of concepts
+ 
+
+ align:start position:0%
+progressive differentiation of concepts
+so let me just walk you through that and
+
+ align:start position:0%
+so let me just walk you through that and
+ 
+
+ align:start position:0%
+so let me just walk you through that and
+so this was you know my you know an
+
+ align:start position:0%
+so this was you know my you know an
+ 
+
+ align:start position:0%
+so this was you know my you know an
+encounter with a you know at first
+
+ align:start position:0%
+encounter with a you know at first
+ 
+
+ align:start position:0%
+encounter with a you know at first
+encounter with a deep neural network so
+
+ align:start position:0%
+encounter with a deep neural network so
+ 
+
+ align:start position:0%
+encounter with a deep neural network so
+they were they were doing deep neural
+
+ align:start position:0%
+they were they were doing deep neural
+ 
+
+ align:start position:0%
+they were they were doing deep neural
+networks before they became popular and
+
+ align:start position:0%
+networks before they became popular and
+ 
+
+ align:start position:0%
+networks before they became popular and
+so what they were doing was they asked
+
+ align:start position:0%
+so what they were doing was they asked
+ 
+
+ align:start position:0%
+so what they were doing was they asked
+can we model infants the development of
+
+ align:start position:0%
+can we model infants the development of
+ 
+
+ align:start position:0%
+can we model infants the development of
+say concepts and infants and so what
+
+ align:start position:0%
+say concepts and infants and so what
+ 
+
+ align:start position:0%
+say concepts and infants and so what
+they did was they had a toy data set
+
+ align:start position:0%
+they did was they had a toy data set
+ 
+
+ align:start position:0%
+they did was they had a toy data set
+where they had a bunch of objects and
+
+ align:start position:0%
+where they had a bunch of objects and
+ 
+
+ align:start position:0%
+where they had a bunch of objects and
+each object had a whole bunch of
+
+ align:start position:0%
+each object had a whole bunch of
+ 
+
+ align:start position:0%
+each object had a whole bunch of
+properties so for example a canary can
+
+ align:start position:0%
+properties so for example a canary can
+ 
+
+ align:start position:0%
+properties so for example a canary can
+grow move fly and swing sing right and
+
+ align:start position:0%
+grow move fly and swing sing right and
+ 
+
+ align:start position:0%
+grow move fly and swing sing right and
+and so what they did was they exposed
+
+ align:start position:0%
+and so what they did was they exposed
+ 
+
+ align:start position:0%
+and so what they did was they exposed
+this deep neural network to training
+
+ align:start position:0%
+this deep neural network to training
+ 
+
+ align:start position:0%
+this deep neural network to training
+data of this form you know they had a
+
+ align:start position:0%
+data of this form you know they had a
+ 
+
+ align:start position:0%
+data of this form you know they had a
+whole bunch of features and questions
+
+ align:start position:0%
+whole bunch of features and questions
+ 
+
+ align:start position:0%
+whole bunch of features and questions
+and objects and they just exposed the
+
+ align:start position:0%
+and objects and they just exposed the
+ 
+
+ align:start position:0%
+and objects and they just exposed the
+network to training data trained it
+
+ align:start position:0%
+network to training data trained it
+ 
+
+ align:start position:0%
+network to training data trained it
+using back propagation and they looked
+
+ align:start position:0%
+using back propagation and they looked
+ 
+
+ align:start position:0%
+using back propagation and they looked
+at the internal representations in the
+
+ align:start position:0%
+at the internal representations in the
+ 
+
+ align:start position:0%
+at the internal representations in the
+network especially their evolution over
+
+ align:start position:0%
+network especially their evolution over
+ 
+
+ align:start position:0%
+network especially their evolution over
+developmental time or training time
+
+ align:start position:0%
+developmental time or training time
+ 
+
+ align:start position:0%
+developmental time or training time
+right and this is what they found
+
+ align:start position:0%
+right and this is what they found
+ 
+
+ align:start position:0%
+right and this is what they found
+so initially the network started with
+
+ align:start position:0%
+so initially the network started with
+ 
+
+ align:start position:0%
+so initially the network started with
+random weights so there was no structure
+
+ align:start position:0%
+random weights so there was no structure
+ 
+
+ align:start position:0%
+random weights so there was no structure
+so these are okay so what what did they
+
+ align:start position:0%
+so these are okay so what what did they
+ 
+
+ align:start position:0%
+so these are okay so what what did they
+do here they looked at the the distances
+
+ align:start position:0%
+do here they looked at the the distances
+ 
+
+ align:start position:0%
+do here they looked at the the distances
+between the internal representations in
+
+ align:start position:0%
+between the internal representations in
+ 
+
+ align:start position:0%
+between the internal representations in
+this space and they did har cocoa
+
+ align:start position:0%
+this space and they did har cocoa
+ 
+
+ align:start position:0%
+this space and they did har cocoa
+clustering or multi-dimensional scaling
+
+ align:start position:0%
+clustering or multi-dimensional scaling
+ 
+
+ align:start position:0%
+clustering or multi-dimensional scaling
+and they found these plots or these
+
+ align:start position:0%
+and they found these plots or these
+ 
+
+ align:start position:0%
+and they found these plots or these
+plots right so so what you see is early
+
+ align:start position:0%
+plots right so so what you see is early
+ 
+
+ align:start position:0%
+plots right so so what you see is early
+in developmental time the network first
+
+ align:start position:0%
+in developmental time the network first
+ 
+
+ align:start position:0%
+in developmental time the network first
+makes a coarse grained discrimination
+
+ align:start position:0%
+makes a coarse grained discrimination
+ 
+
+ align:start position:0%
+makes a coarse grained discrimination
+between animals and and plants right and
+
+ align:start position:0%
+between animals and and plants right and
+ 
+
+ align:start position:0%
+between animals and and plants right and
+then and then later it makes finer scale
+
+ align:start position:0%
+then and then later it makes finer scale
+ 
+
+ align:start position:0%
+then and then later it makes finer scale
+discriminations and then eventually when
+
+ align:start position:0%
+discriminations and then eventually when
+ 
+
+ align:start position:0%
+discriminations and then eventually when
+it's fully learned it has it learns the
+
+ align:start position:0%
+it's fully learned it has it learns the
+ 
+
+ align:start position:0%
+it's fully learned it has it learns the
+hierarchical structure that's implicit
+
+ align:start position:0%
+hierarchical structure that's implicit
+ 
+
+ align:start position:0%
+hierarchical structure that's implicit
+in the training data okay and this is
+
+ align:start position:0%
+in the training data okay and this is
+ 
+
+ align:start position:0%
+in the training data okay and this is
+the multi-dimensional scaling plot where
+
+ align:start position:0%
+the multi-dimensional scaling plot where
+ 
+
+ align:start position:0%
+the multi-dimensional scaling plot where
+initially the animals move away from the
+
+ align:start position:0%
+initially the animals move away from the
+ 
+
+ align:start position:0%
+initially the animals move away from the
+plants and then you know fish move away
+
+ align:start position:0%
+plants and then you know fish move away
+ 
+
+ align:start position:0%
+plants and then you know fish move away
+from birds and and trees move away from
+
+ align:start position:0%
+from birds and and trees move away from
+ 
+
+ align:start position:0%
+from birds and and trees move away from
+flowers and then finally individual
+
+ align:start position:0%
+flowers and then finally individual
+ 
+
+ align:start position:0%
+flowers and then finally individual
+discriminations are learned so when I
+
+ align:start position:0%
+discriminations are learned so when I
+ 
+
+ align:start position:0%
+discriminations are learned so when I
+learned about this I was at once excited
+
+ align:start position:0%
+learned about this I was at once excited
+ 
+
+ align:start position:0%
+learned about this I was at once excited
+and mystify and also mystified because
+
+ align:start position:0%
+and mystify and also mystified because
+ 
+
+ align:start position:0%
+and mystify and also mystified because
+this is sort of qualitatively behaving
+
+ align:start position:0%
+this is sort of qualitatively behaving
+ 
+
+ align:start position:0%
+this is sort of qualitatively behaving
+like the way that an infant behaves yet
+
+ align:start position:0%
+like the way that an infant behaves yet
+ 
+
+ align:start position:0%
+like the way that an infant behaves yet
+it's a really stupid neural network with
+
+ align:start position:0%
+it's a really stupid neural network with
+ 
+
+ align:start position:0%
+it's a really stupid neural network with
+like five layers yet I don't understand
+
+ align:start position:0%
+like five layers yet I don't understand
+ 
+
+ align:start position:0%
+like five layers yet I don't understand
+how it's doing this right it so so I
+
+ align:start position:0%
+how it's doing this right it so so I
+ 
+
+ align:start position:0%
+how it's doing this right it so so I
+wanted a theory of what's going on here
+
+ align:start position:0%
+wanted a theory of what's going on here
+ 
+
+ align:start position:0%
+wanted a theory of what's going on here
+right so and by the way you know there's
+
+ align:start position:0%
+right so and by the way you know there's
+ 
+
+ align:start position:0%
+right so and by the way you know there's
+lots of reasons to believe that semantic
+
+ align:start position:0%
+lots of reasons to believe that semantic
+ 
+
+ align:start position:0%
+lots of reasons to believe that semantic
+relations
+
+ align:start position:0%
+relations
+ 
+
+ align:start position:0%
+relations
+are in cloak are encoded in the brain
+
+ align:start position:0%
+are in cloak are encoded in the brain
+ 
+
+ align:start position:0%
+are in cloak are encoded in the brain
+using relatively simple metrics like
+
+ align:start position:0%
+using relatively simple metrics like
+ 
+
+ align:start position:0%
+using relatively simple metrics like
+Euclidean distance between neural
+
+ align:start position:0%
+Euclidean distance between neural
+ 
+
+ align:start position:0%
+Euclidean distance between neural
+representations for different objects so
+
+ align:start position:0%
+representations for different objects so
+ 
+
+ align:start position:0%
+representations for different objects so
+for example this is a famous study which
+
+ align:start position:0%
+for example this is a famous study which
+ 
+
+ align:start position:0%
+for example this is a famous study which
+I'm sure you've seen what they showed
+
+ align:start position:0%
+I'm sure you've seen what they showed
+ 
+
+ align:start position:0%
+I'm sure you've seen what they showed
+was a whole bunch of objects to both
+
+ align:start position:0%
+was a whole bunch of objects to both
+ 
+
+ align:start position:0%
+was a whole bunch of objects to both
+monkeys and humans and they clustered
+
+ align:start position:0%
+monkeys and humans and they clustered
+ 
+
+ align:start position:0%
+monkeys and humans and they clustered
+the objects or looked at similarity
+
+ align:start position:0%
+the objects or looked at similarity
+ 
+
+ align:start position:0%
+the objects or looked at similarity
+matrix of the objects measured using a
+
+ align:start position:0%
+matrix of the objects measured using a
+ 
+
+ align:start position:0%
+matrix of the objects measured using a
+Euclidean distance in neural NIR
+
+ align:start position:0%
+Euclidean distance in neural NIR
+ 
+
+ align:start position:0%
+Euclidean distance in neural NIR
+electrophysiology space of firing rates
+
+ align:start position:0%
+electrophysiology space of firing rates
+ 
+
+ align:start position:0%
+electrophysiology space of firing rates
+of neurons here and voxel activity
+
+ align:start position:0%
+of neurons here and voxel activity
+ 
+
+ align:start position:0%
+of neurons here and voxel activity
+patterns in the human and they showed
+
+ align:start position:0%
+patterns in the human and they showed
+ 
+
+ align:start position:0%
+patterns in the human and they showed
+the same set of objects the monkey and
+
+ align:start position:0%
+the same set of objects the monkey and
+ 
+
+ align:start position:0%
+the same set of objects the monkey and
+human and and the matrices aligned
+
+ align:start position:0%
+human and and the matrices aligned
+ 
+
+ align:start position:0%
+human and and the matrices aligned
+essentially so basically the similarity
+
+ align:start position:0%
+essentially so basically the similarity
+ 
+
+ align:start position:0%
+essentially so basically the similarity
+structure of internal representations as
+
+ align:start position:0%
+structure of internal representations as
+ 
+
+ align:start position:0%
+structure of internal representations as
+both monkey and human is the same so we
+
+ align:start position:0%
+both monkey and human is the same so we
+ 
+
+ align:start position:0%
+both monkey and human is the same so we
+tend to encode similar we tend to encode
+
+ align:start position:0%
+tend to encode similar we tend to encode
+ 
+
+ align:start position:0%
+tend to encode similar we tend to encode
+semantic information using these
+
+ align:start position:0%
+semantic information using these
+ 
+
+ align:start position:0%
+semantic information using these
+similarity representations so this is
+
+ align:start position:0%
+similarity representations so this is
+ 
+
+ align:start position:0%
+similarity representations so this is
+the hierarchical clustering view so this
+
+ align:start position:0%
+the hierarchical clustering view so this
+ 
+
+ align:start position:0%
+the hierarchical clustering view so this
+sort of you know this sort of seems to
+
+ align:start position:0%
+sort of you know this sort of seems to
+ 
+
+ align:start position:0%
+sort of you know this sort of seems to
+actually happen in in real live animals
+
+ align:start position:0%
+actually happen in in real live animals
+ 
+
+ align:start position:0%
+actually happen in in real live animals
+and humans okay there's actually
+
+ align:start position:0%
+and humans okay there's actually
+ 
+
+ align:start position:0%
+and humans okay there's actually
+something else that happens is that
+
+ align:start position:0%
+something else that happens is that
+ 
+
+ align:start position:0%
+something else that happens is that
+different properties are learned on
+
+ align:start position:0%
+different properties are learned on
+ 
+
+ align:start position:0%
+different properties are learned on
+different time scales so for example the
+
+ align:start position:0%
+different time scales so for example the
+ 
+
+ align:start position:0%
+different time scales so for example the
+network can learn that Canaries can move
+
+ align:start position:0%
+network can learn that Canaries can move
+ 
+
+ align:start position:0%
+network can learn that Canaries can move
+much more quickly than it learns that a
+
+ align:start position:0%
+much more quickly than it learns that a
+ 
+
+ align:start position:0%
+much more quickly than it learns that a
+canary is yellow so it learns these sort
+
+ align:start position:0%
+canary is yellow so it learns these sort
+ 
+
+ align:start position:0%
+canary is yellow so it learns these sort
+of so some properties are much easier to
+
+ align:start position:0%
+of so some properties are much easier to
+ 
+
+ align:start position:0%
+of so some properties are much easier to
+learn than others and the properties
+
+ align:start position:0%
+learn than others and the properties
+ 
+
+ align:start position:0%
+learn than others and the properties
+that are easier to learn it for the
+
+ align:start position:0%
+that are easier to learn it for the
+ 
+
+ align:start position:0%
+that are easier to learn it for the
+network are also easier to learn for the
+
+ align:start position:0%
+network are also easier to learn for the
+ 
+
+ align:start position:0%
+network are also easier to learn for the
+infant ok so these are the theoretical
+
+ align:start position:0%
+infant ok so these are the theoretical
+ 
+
+ align:start position:0%
+infant ok so these are the theoretical
+questions we'd like to answer what are
+
+ align:start position:0%
+questions we'd like to answer what are
+ 
+
+ align:start position:0%
+questions we'd like to answer what are
+the mathematical principles underlying
+
+ align:start position:0%
+the mathematical principles underlying
+ 
+
+ align:start position:0%
+the mathematical principles underlying
+the hierarchical self-organization of
+
+ align:start position:0%
+the hierarchical self-organization of
+ 
+
+ align:start position:0%
+the hierarchical self-organization of
+internal representations in the network
+
+ align:start position:0%
+internal representations in the network
+ 
+
+ align:start position:0%
+internal representations in the network
+you know this is a complex system so
+
+ align:start position:0%
+you know this is a complex system so
+ 
+
+ align:start position:0%
+you know this is a complex system so
+what are the relative roles of the
+
+ align:start position:0%
+what are the relative roles of the
+ 
+
+ align:start position:0%
+what are the relative roles of the
+various ingredients it's and there's a
+
+ align:start position:0%
+various ingredients it's and there's a
+ 
+
+ align:start position:0%
+various ingredients it's and there's a
+nonlinear input-output response there's
+
+ align:start position:0%
+nonlinear input-output response there's
+ 
+
+ align:start position:0%
+nonlinear input-output response there's
+a learning rule which is back
+
+ align:start position:0%
+a learning rule which is back
+ 
+
+ align:start position:0%
+a learning rule which is back
+propagation
+
+ align:start position:0%
+propagation
+ 
+
+ align:start position:0%
+propagation
+there's the input statistics is the
+
+ align:start position:0%
+there's the input statistics is the
+ 
+
+ align:start position:0%
+there's the input statistics is the
+network somehow reaching into complex
+
+ align:start position:0%
+network somehow reaching into complex
+ 
+
+ align:start position:0%
+network somehow reaching into complex
+input statistics in the in the training
+
+ align:start position:0%
+input statistics in the in the training
+ 
+
+ align:start position:0%
+input statistics in the in the training
+set or or can it really rely on just
+
+ align:start position:0%
+set or or can it really rely on just
+ 
+
+ align:start position:0%
+set or or can it really rely on just
+second-order statistics you know there
+
+ align:start position:0%
+second-order statistics you know there
+ 
+
+ align:start position:0%
+second-order statistics you know there
+what is a mathematical definition of
+
+ align:start position:0%
+what is a mathematical definition of
+ 
+
+ align:start position:0%
+what is a mathematical definition of
+something called category currents and
+
+ align:start position:0%
+something called category currents and
+ 
+
+ align:start position:0%
+something called category currents and
+how does it relate to the speed of
+
+ align:start position:0%
+how does it relate to the speed of
+ 
+
+ align:start position:0%
+how does it relate to the speed of
+category learning so what determines the
+
+ align:start position:0%
+category learning so what determines the
+ 
+
+ align:start position:0%
+category learning so what determines the
+speed at which we learn categories why
+
+ align:start position:0%
+speed at which we learn categories why
+ 
+
+ align:start position:0%
+speed at which we learn categories why
+are some properties learn more quickly
+
+ align:start position:0%
+are some properties learn more quickly
+ 
+
+ align:start position:0%
+are some properties learn more quickly
+than others and how can we explain
+
+ align:start position:0%
+than others and how can we explain
+ 
+
+ align:start position:0%
+than others and how can we explain
+changing patterns of inductive
+
+ align:start position:0%
+changing patterns of inductive
+ 
+
+ align:start position:0%
+changing patterns of inductive
+generalization over these developmental
+
+ align:start position:0%
+generalization over these developmental
+ 
+
+ align:start position:0%
+generalization over these developmental
+timescales so ok so how do we get a
+
+ align:start position:0%
+timescales so ok so how do we get a
+ 
+
+ align:start position:0%
+timescales so ok so how do we get a
+theory well it turns out if you look at
+
+ align:start position:0%
+theory well it turns out if you look at
+ 
+
+ align:start position:0%
+theory well it turns out if you look at
+the activations of this network as its
+
+ align:start position:0%
+the activations of this network as its
+ 
+
+ align:start position:0%
+the activations of this network as its
+training over time so these are sigmoid
+
+ align:start position:0%
+training over time so these are sigmoid
+ 
+
+ align:start position:0%
+training over time so these are sigmoid
+units and that the activations don't
+
+ align:start position:0%
+units and that the activations don't
+ 
+
+ align:start position:0%
+units and that the activations don't
+really hit
+
+ align:start position:0%
+really hit
+ 
+
+ align:start position:0%
+really hit
+the saturating regime that much during
+
+ align:start position:0%
+the saturating regime that much during
+ 
+
+ align:start position:0%
+the saturating regime that much during
+training because you start from small
+
+ align:start position:0%
+training because you start from small
+ 
+
+ align:start position:0%
+training because you start from small
+weights so we started with an audacious
+
+ align:start position:0%
+weights so we started with an audacious
+ 
+
+ align:start position:0%
+weights so we started with an audacious
+proposal that maybe even a linear neural
+
+ align:start position:0%
+proposal that maybe even a linear neural
+ 
+
+ align:start position:0%
+proposal that maybe even a linear neural
+network might exhibit this kind of
+
+ align:start position:0%
+network might exhibit this kind of
+ 
+
+ align:start position:0%
+network might exhibit this kind of
+learning dynamics okay now it's not at
+
+ align:start position:0%
+learning dynamics okay now it's not at
+ 
+
+ align:start position:0%
+learning dynamics okay now it's not at
+all obvious that it should because it's
+
+ align:start position:0%
+all obvious that it should because it's
+ 
+
+ align:start position:0%
+all obvious that it should because it's
+a simple linear neural network and this
+
+ align:start position:0%
+a simple linear neural network and this
+ 
+
+ align:start position:0%
+a simple linear neural network and this
+learning dynamics is highly nonlinear
+
+ align:start position:0%
+learning dynamics is highly nonlinear
+ 
+
+ align:start position:0%
+learning dynamics is highly nonlinear
+all right but it turns out that even in
+
+ align:start position:0%
+all right but it turns out that even in
+ 
+
+ align:start position:0%
+all right but it turns out that even in
+a linear neural network the dynamics of
+
+ align:start position:0%
+a linear neural network the dynamics of
+ 
+
+ align:start position:0%
+a linear neural network the dynamics of
+learning on synaptic weight space is
+
+ align:start position:0%
+learning on synaptic weight space is
+ 
+
+ align:start position:0%
+learning on synaptic weight space is
+nonlinear and so there might be a hope
+
+ align:start position:0%
+nonlinear and so there might be a hope
+ 
+
+ align:start position:0%
+nonlinear and so there might be a hope
+that it might work and we might be able
+
+ align:start position:0%
+that it might work and we might be able
+ 
+
+ align:start position:0%
+that it might work and we might be able
+to get a coherent theory okay so what we
+
+ align:start position:0%
+to get a coherent theory okay so what we
+ 
+
+ align:start position:0%
+to get a coherent theory okay so what we
+did was we analyzed just a simple linear
+
+ align:start position:0%
+did was we analyzed just a simple linear
+ 
+
+ align:start position:0%
+did was we analyzed just a simple linear
+neural network that looks like this that
+
+ align:start position:0%
+neural network that looks like this that
+ 
+
+ align:start position:0%
+neural network that looks like this that
+goes from a input layer to hidden layer
+
+ align:start position:0%
+goes from a input layer to hidden layer
+ 
+
+ align:start position:0%
+goes from a input layer to hidden layer
+to output layer so the composite map is
+
+ align:start position:0%
+to output layer so the composite map is
+ 
+
+ align:start position:0%
+to output layer so the composite map is
+linear okay so so we can write down
+
+ align:start position:0%
+linear okay so so we can write down
+ 
+
+ align:start position:0%
+linear okay so so we can write down
+dynamical equations on weight space for
+
+ align:start position:0%
+dynamical equations on weight space for
+ 
+
+ align:start position:0%
+dynamical equations on weight space for
+the learning dynamics so this is the
+
+ align:start position:0%
+the learning dynamics so this is the
+ 
+
+ align:start position:0%
+the learning dynamics so this is the
+training data and we can adjust the
+
+ align:start position:0%
+training data and we can adjust the
+ 
+
+ align:start position:0%
+training data and we can adjust the
+weights using back propagation and these
+
+ align:start position:0%
+weights using back propagation and these
+ 
+
+ align:start position:0%
+weights using back propagation and these
+are the back propagation equations and
+
+ align:start position:0%
+are the back propagation equations and
+ 
+
+ align:start position:0%
+are the back propagation equations and
+if we work in a limit where the learning
+
+ align:start position:0%
+if we work in a limit where the learning
+ 
+
+ align:start position:0%
+if we work in a limit where the learning
+is slow relative to the time it takes to
+
+ align:start position:0%
+is slow relative to the time it takes to
+ 
+
+ align:start position:0%
+is slow relative to the time it takes to
+cycle through the data set you can take
+
+ align:start position:0%
+cycle through the data set you can take
+ 
+
+ align:start position:0%
+cycle through the data set you can take
+a continuous time limit and you
+
+ align:start position:0%
+a continuous time limit and you
+ 
+
+ align:start position:0%
+a continuous time limit and you
+essentially get a nonlinear set of
+
+ align:start position:0%
+essentially get a nonlinear set of
+ 
+
+ align:start position:0%
+essentially get a nonlinear set of
+equations on weight space right and the
+
+ align:start position:0%
+equations on weight space right and the
+ 
+
+ align:start position:0%
+equations on weight space right and the
+equations are cubic in the weights right
+
+ align:start position:0%
+equations are cubic in the weights right
+ 
+
+ align:start position:0%
+equations are cubic in the weights right
+and that's because the error is quartic
+
+ align:start position:0%
+and that's because the error is quartic
+ 
+
+ align:start position:0%
+and that's because the error is quartic
+in the weights right the error is the
+
+ align:start position:0%
+in the weights right the error is the
+ 
+
+ align:start position:0%
+in the weights right the error is the
+output minus W w times the input squared
+
+ align:start position:0%
+output minus W w times the input squared
+ 
+
+ align:start position:0%
+output minus W w times the input squared
+so the errors quartic in the weights and
+
+ align:start position:0%
+so the errors quartic in the weights and
+ 
+
+ align:start position:0%
+so the errors quartic in the weights and
+so if you differentiate we're supposed
+
+ align:start position:0%
+so if you differentiate we're supposed
+ 
+
+ align:start position:0%
+so if you differentiate we're supposed
+to get the weights on the right hand
+
+ align:start position:0%
+to get the weights on the right hand
+ 
+
+ align:start position:0%
+to get the weights on the right hand
+side the gradient descent equations will
+
+ align:start position:0%
+side the gradient descent equations will
+ 
+
+ align:start position:0%
+side the gradient descent equations will
+be cubic in the weights but there is one
+
+ align:start position:0%
+be cubic in the weights but there is one
+ 
+
+ align:start position:0%
+be cubic in the weights but there is one
+simplification that happens because the
+
+ align:start position:0%
+simplification that happens because the
+ 
+
+ align:start position:0%
+simplification that happens because the
+network is linear it's learning dynamics
+
+ align:start position:0%
+network is linear it's learning dynamics
+ 
+
+ align:start position:0%
+network is linear it's learning dynamics
+is sensitive only to the second-order
+
+ align:start position:0%
+is sensitive only to the second-order
+ 
+
+ align:start position:0%
+is sensitive only to the second-order
+statistics of the data right so in
+
+ align:start position:0%
+statistics of the data right so in
+ 
+
+ align:start position:0%
+statistics of the data right so in
+particular the input input covariance
+
+ align:start position:0%
+particular the input input covariance
+ 
+
+ align:start position:0%
+particular the input input covariance
+matrix and the input-output covariance
+
+ align:start position:0%
+matrix and the input-output covariance
+ 
+
+ align:start position:0%
+matrix and the input-output covariance
+matrix okay
+
+ align:start position:0%
+matrix okay
+ 
+
+ align:start position:0%
+matrix okay
+so essentially this network knows only
+
+ align:start position:0%
+so essentially this network knows only
+ 
+
+ align:start position:0%
+so essentially this network knows only
+about second-order statistics in our
+
+ align:start position:0%
+about second-order statistics in our
+ 
+
+ align:start position:0%
+about second-order statistics in our
+work here that the input statistics is
+
+ align:start position:0%
+work here that the input statistics is
+ 
+
+ align:start position:0%
+work here that the input statistics is
+white so it's really only the
+
+ align:start position:0%
+white so it's really only the
+ 
+
+ align:start position:0%
+white so it's really only the
+input-output statistics the drives
+
+ align:start position:0%
+input-output statistics the drives
+ 
+
+ align:start position:0%
+input-output statistics the drives
+learning okay so this is a set of
+
+ align:start position:0%
+learning okay so this is a set of
+ 
+
+ align:start position:0%
+learning okay so this is a set of
+coupled nonlinear differential equations
+
+ align:start position:0%
+coupled nonlinear differential equations
+ 
+
+ align:start position:0%
+coupled nonlinear differential equations
+they're in general hard to solve but we
+
+ align:start position:0%
+they're in general hard to solve but we
+ 
+
+ align:start position:0%
+they're in general hard to solve but we
+found solutions to them so what we we
+
+ align:start position:0%
+found solutions to them so what we we
+ 
+
+ align:start position:0%
+found solutions to them so what we we
+can express the solutions in terms of
+
+ align:start position:0%
+can express the solutions in terms of
+ 
+
+ align:start position:0%
+can express the solutions in terms of
+the singular value decomposition of the
+
+ align:start position:0%
+the singular value decomposition of the
+ 
+
+ align:start position:0%
+the singular value decomposition of the
+input-output covariance matrix so so any
+
+ align:start position:0%
+input-output covariance matrix so so any
+ 
+
+ align:start position:0%
+input-output covariance matrix so so any
+you know any rectangular matrix has a
+
+ align:start position:0%
+you know any rectangular matrix has a
+ 
+
+ align:start position:0%
+you know any rectangular matrix has a
+unique singular value decomposition in
+
+ align:start position:0%
+unique singular value decomposition in
+ 
+
+ align:start position:0%
+unique singular value decomposition in
+this context we can think about the
+
+ align:start position:0%
+this context we can think about the
+ 
+
+ align:start position:0%
+this context we can think about the
+input-output covariance matrix as a
+
+ align:start position:0%
+input-output covariance matrix as a
+ 
+
+ align:start position:0%
+input-output covariance matrix as a
+matrix that map's input objects to
+
+ align:start position:0%
+matrix that map's input objects to
+ 
+
+ align:start position:0%
+matrix that map's input objects to
+feature attributes and the singular
+
+ align:start position:0%
+feature attributes and the singular
+ 
+
+ align:start position:0%
+feature attributes and the singular
+vectors have an interpretation where the
+
+ align:start position:0%
+vectors have an interpretation where the
+ 
+
+ align:start position:0%
+vectors have an interpretation where the
+the these singular vector is essentially
+
+ align:start position:0%
+the these singular vector is essentially
+ 
+
+ align:start position:0%
+the these singular vector is essentially
+map objects into interim representations
+
+ align:start position:0%
+map objects into interim representations
+ 
+
+ align:start position:0%
+map objects into interim representations
+the singular values amplify them and
+
+ align:start position:0%
+the singular values amplify them and
+ 
+
+ align:start position:0%
+the singular values amplify them and
+then the columns of you are sort of
+
+ align:start position:0%
+then the columns of you are sort of
+ 
+
+ align:start position:0%
+then the columns of you are sort of
+feature synthesizers the columns are
+
+ align:start position:0%
+feature synthesizers the columns are
+ 
+
+ align:start position:0%
+feature synthesizers the columns are
+sort of modes in the output feature
+
+ align:start position:0%
+sort of modes in the output feature
+ 
+
+ align:start position:0%
+sort of modes in the output feature
+space okay so this is the SVD but the
+
+ align:start position:0%
+space okay so this is the SVD but the
+ 
+
+ align:start position:0%
+space okay so this is the SVD but the
+question is how does the learning
+
+ align:start position:0%
+question is how does the learning
+ 
+
+ align:start position:0%
+question is how does the learning
+dynamics how does this drive the
+
+ align:start position:0%
+dynamics how does this drive the
+ 
+
+ align:start position:0%
+dynamics how does this drive the
+learning dynamics so what we did was was
+
+ align:start position:0%
+learning dynamics so what we did was was
+ 
+
+ align:start position:0%
+learning dynamics so what we did was was
+we found exact solutions to the learning
+
+ align:start position:0%
+we found exact solutions to the learning
+ 
+
+ align:start position:0%
+we found exact solutions to the learning
+dynamics of this form where the product
+
+ align:start position:0%
+dynamics of this form where the product
+ 
+
+ align:start position:0%
+dynamics of this form where the product
+of the in the layer 1 to layer 2 weights
+
+ align:start position:0%
+of the in the layer 1 to layer 2 weights
+ 
+
+ align:start position:0%
+of the in the layer 1 to layer 2 weights
+in layer 2 to layer 3 weights are of
+
+ align:start position:0%
+in layer 2 to layer 3 weights are of
+ 
+
+ align:start position:0%
+in layer 2 to layer 3 weights are of
+this form where essentially the system
+
+ align:start position:0%
+this form where essentially the system
+ 
+
+ align:start position:0%
+this form where essentially the system
+what it's doing the composite system is
+
+ align:start position:0%
+what it's doing the composite system is
+ 
+
+ align:start position:0%
+what it's doing the composite system is
+building up the singular value
+
+ align:start position:0%
+building up the singular value
+ 
+
+ align:start position:0%
+building up the singular value
+decomposition of the input-output
+
+ align:start position:0%
+decomposition of the input-output
+ 
+
+ align:start position:0%
+decomposition of the input-output
+covariance matrix mode by mode and each
+
+ align:start position:0%
+covariance matrix mode by mode and each
+ 
+
+ align:start position:0%
+covariance matrix mode by mode and each
+mode alpha associated with singular
+
+ align:start position:0%
+mode alpha associated with singular
+ 
+
+ align:start position:0%
+mode alpha associated with singular
+value alpha in the training data is
+
+ align:start position:0%
+value alpha in the training data is
+ 
+
+ align:start position:0%
+value alpha in the training data is
+being learned in the sigmoid illan ok in
+
+ align:start position:0%
+being learned in the sigmoid illan ok in
+ 
+
+ align:start position:0%
+being learned in the sigmoid illan ok in
+a way that so at x 0 a is sort of small
+
+ align:start position:0%
+a way that so at x 0 a is sort of small
+ 
+
+ align:start position:0%
+a way that so at x 0 a is sort of small
+and random you know some initial
+
+ align:start position:0%
+and random you know some initial
+ 
+
+ align:start position:0%
+and random you know some initial
+condition a 0 but over time as as time
+
+ align:start position:0%
+condition a 0 but over time as as time
+ 
+
+ align:start position:0%
+condition a 0 but over time as as time
+goes to infinity training time goes to
+
+ align:start position:0%
+goes to infinity training time goes to
+ 
+
+ align:start position:0%
+goes to infinity training time goes to
+infinity the the a approaches the actual
+
+ align:start position:0%
+infinity the the a approaches the actual
+ 
+
+ align:start position:0%
+infinity the the a approaches the actual
+singular value in the input-output
+
+ align:start position:0%
+singular value in the input-output
+ 
+
+ align:start position:0%
+singular value in the input-output
+covariance matrix so basically this is
+
+ align:start position:0%
+covariance matrix so basically this is
+ 
+
+ align:start position:0%
+covariance matrix so basically this is
+the learning dynamic so nothing happens
+
+ align:start position:0%
+the learning dynamic so nothing happens
+ 
+
+ align:start position:0%
+the learning dynamic so nothing happens
+for a while and then suddenly the
+
+ align:start position:0%
+for a while and then suddenly the
+ 
+
+ align:start position:0%
+for a while and then suddenly the
+strongest singular mode defined by the
+
+ align:start position:0%
+strongest singular mode defined by the
+ 
+
+ align:start position:0%
+strongest singular mode defined by the
+largest single value gets learned and
+
+ align:start position:0%
+largest single value gets learned and
+ 
+
+ align:start position:0%
+largest single value gets learned and
+then later on smaller singular mode gets
+
+ align:start position:0%
+then later on smaller singular mode gets
+ 
+
+ align:start position:0%
+then later on smaller singular mode gets
+learned and later on a even smaller
+
+ align:start position:0%
+learned and later on a even smaller
+ 
+
+ align:start position:0%
+learned and later on a even smaller
+singular mode gets learned and the time
+
+ align:start position:0%
+singular mode gets learned and the time
+ 
+
+ align:start position:0%
+singular mode gets learned and the time
+it takes to learn each mode is governed
+
+ align:start position:0%
+it takes to learn each mode is governed
+ 
+
+ align:start position:0%
+it takes to learn each mode is governed
+by 1 over the singular value so just
+
+ align:start position:0%
+by 1 over the singular value so just
+ 
+
+ align:start position:0%
+by 1 over the singular value so just
+intuitively stronger statistical
+
+ align:start position:0%
+intuitively stronger statistical
+ 
+
+ align:start position:0%
+intuitively stronger statistical
+structure as quantified by singular
+
+ align:start position:0%
+structure as quantified by singular
+ 
+
+ align:start position:0%
+structure as quantified by singular
+value is learned first okay that's the
+
+ align:start position:0%
+value is learned first okay that's the
+ 
+
+ align:start position:0%
+value is learned first okay that's the
+intuition often time when we train
+
+ align:start position:0%
+intuition often time when we train
+ 
+
+ align:start position:0%
+intuition often time when we train
+neural networks we see sort of these
+
+ align:start position:0%
+neural networks we see sort of these
+ 
+
+ align:start position:0%
+neural networks we see sort of these
+plateaus in performance where the
+
+ align:start position:0%
+plateaus in performance where the
+ 
+
+ align:start position:0%
+plateaus in performance where the
+network does nothing and then suddenly
+
+ align:start position:0%
+network does nothing and then suddenly
+ 
+
+ align:start position:0%
+network does nothing and then suddenly
+drops plateaus and drops and this
+
+ align:start position:0%
+drops plateaus and drops and this
+ 
+
+ align:start position:0%
+drops plateaus and drops and this
+actually shows that you can see very
+
+ align:start position:0%
+actually shows that you can see very
+ 
+
+ align:start position:0%
+actually shows that you can see very
+very sharp transitions in learning and
+
+ align:start position:0%
+very sharp transitions in learning and
+ 
+
+ align:start position:0%
+very sharp transitions in learning and
+you can actually show that the ratio of
+
+ align:start position:0%
+you can actually show that the ratio of
+ 
+
+ align:start position:0%
+you can actually show that the ratio of
+the transition period to the the
+
+ align:start position:0%
+the transition period to the the
+ 
+
+ align:start position:0%
+the transition period to the the
+ignorance period can be arbitrarily
+
+ align:start position:0%
+ignorance period can be arbitrarily
+ 
+
+ align:start position:0%
+ignorance period can be arbitrarily
+small infants also seem to show these
+
+ align:start position:0%
+small infants also seem to show these
+ 
+
+ align:start position:0%
+small infants also seem to show these
+developmental transitions but
+
+ align:start position:0%
+developmental transitions but
+ 
+
+ align:start position:0%
+developmental transitions but
+okay yes so that's so yeah you you can
+
+ align:start position:0%
+okay yes so that's so yeah you you can
+ 
+
+ align:start position:0%
+okay yes so that's so yeah you you can
+have arbitrarily sharp transitions in
+
+ align:start position:0%
+have arbitrarily sharp transitions in
+ 
+
+ align:start position:0%
+have arbitrarily sharp transitions in
+the system okay so the take-home
+
+ align:start position:0%
+the system okay so the take-home
+ 
+
+ align:start position:0%
+the system okay so the take-home
+messages so so far that is the network
+
+ align:start position:0%
+messages so so far that is the network
+ 
+
+ align:start position:0%
+messages so so far that is the network
+learns different modes of covariation
+
+ align:start position:0%
+learns different modes of covariation
+ 
+
+ align:start position:0%
+learns different modes of covariation
+between input and output and timescale
+
+ align:start position:0%
+between input and output and timescale
+ 
+
+ align:start position:0%
+between input and output and timescale
+inversely proportional to the
+
+ align:start position:0%
+inversely proportional to the
+ 
+
+ align:start position:0%
+inversely proportional to the
+statistical strength of that covariation
+
+ align:start position:0%
+statistical strength of that covariation
+ 
+
+ align:start position:0%
+statistical strength of that covariation
+and you can get these sudden transitions
+
+ align:start position:0%
+and you can get these sudden transitions
+ 
+
+ align:start position:0%
+and you can get these sudden transitions
+and learning now the question is what
+
+ align:start position:0%
+and learning now the question is what
+ 
+
+ align:start position:0%
+and learning now the question is what
+does this have to do with the
+
+ align:start position:0%
+does this have to do with the
+ 
+
+ align:start position:0%
+does this have to do with the
+hierarchical differentiation of concepts
+
+ align:start position:0%
+hierarchical differentiation of concepts
+ 
+
+ align:start position:0%
+hierarchical differentiation of concepts
+right that's what we'd like to
+
+ align:start position:0%
+right that's what we'd like to
+ 
+
+ align:start position:0%
+right that's what we'd like to
+understand first so now we've come up
+
+ align:start position:0%
+understand first so now we've come up
+ 
+
+ align:start position:0%
+understand first so now we've come up
+with a general theory of learning the
+
+ align:start position:0%
+with a general theory of learning the
+ 
+
+ align:start position:0%
+with a general theory of learning the
+nonlinear dynamics of learning in these
+
+ align:start position:0%
+nonlinear dynamics of learning in these
+ 
+
+ align:start position:0%
+nonlinear dynamics of learning in these
+in these deep circuits now we want to
+
+ align:start position:0%
+in these deep circuits now we want to
+ 
+
+ align:start position:0%
+in these deep circuits now we want to
+connect this back to hierarchical
+
+ align:start position:0%
+connect this back to hierarchical
+ 
+
+ align:start position:0%
+connect this back to hierarchical
+structure so one of the the things with
+
+ align:start position:0%
+structure so one of the the things with
+ 
+
+ align:start position:0%
+structure so one of the the things with
+J's work is they were just working with
+
+ align:start position:0%
+J's work is they were just working with
+ 
+
+ align:start position:0%
+J's work is they were just working with
+toy datasets and we didn't have any
+
+ align:start position:0%
+toy datasets and we didn't have any
+ 
+
+ align:start position:0%
+toy datasets and we didn't have any
+theoretical control over those toy
+
+ align:start position:0%
+theoretical control over those toy
+ 
+
+ align:start position:0%
+theoretical control over those toy
+datasets but we sort of understood
+
+ align:start position:0%
+datasets but we sort of understood
+ 
+
+ align:start position:0%
+datasets but we sort of understood
+implicitly these toy datasets of
+
+ align:start position:0%
+implicitly these toy datasets of
+ 
+
+ align:start position:0%
+implicitly these toy datasets of
+hierarchical structure so we need a
+
+ align:start position:0%
+hierarchical structure so we need a
+ 
+
+ align:start position:0%
+hierarchical structure so we need a
+generative model of data controlled
+
+ align:start position:0%
+generative model of data controlled
+ 
+
+ align:start position:0%
+generative model of data controlled
+mathematically well-defined generative
+
+ align:start position:0%
+mathematically well-defined generative
+ 
+
+ align:start position:0%
+mathematically well-defined generative
+model of data that encodes the notion of
+
+ align:start position:0%
+model of data that encodes the notion of
+ 
+
+ align:start position:0%
+model of data that encodes the notion of
+hierarchy okay so so can we move beyond
+
+ align:start position:0%
+hierarchy okay so so can we move beyond
+ 
+
+ align:start position:0%
+hierarchy okay so so can we move beyond
+specific data sets to general principles
+
+ align:start position:0%
+specific data sets to general principles
+ 
+
+ align:start position:0%
+specific data sets to general principles
+of what happens when a neural network is
+
+ align:start position:0%
+of what happens when a neural network is
+ 
+
+ align:start position:0%
+of what happens when a neural network is
+exposed to hierarchical structure that's
+
+ align:start position:0%
+exposed to hierarchical structure that's
+ 
+
+ align:start position:0%
+exposed to hierarchical structure that's
+what we like to answer so we consider a
+
+ align:start position:0%
+what we like to answer so we consider a
+ 
+
+ align:start position:0%
+what we like to answer so we consider a
+hierarchical generative model and a
+
+ align:start position:0%
+hierarchical generative model and a
+ 
+
+ align:start position:0%
+hierarchical generative model and a
+classic hierarchical generative model is
+
+ align:start position:0%
+classic hierarchical generative model is
+ 
+
+ align:start position:0%
+classic hierarchical generative model is
+is a yeah so essentially what we want to
+
+ align:start position:0%
+is a yeah so essentially what we want to
+ 
+
+ align:start position:0%
+is a yeah so essentially what we want to
+do is we want to connect the world of
+
+ align:start position:0%
+do is we want to connect the world of
+ 
+
+ align:start position:0%
+do is we want to connect the world of
+generative models to the world of neural
+
+ align:start position:0%
+generative models to the world of neural
+ 
+
+ align:start position:0%
+generative models to the world of neural
+networks and that you know that will
+
+ align:start position:0%
+networks and that you know that will
+ 
+
+ align:start position:0%
+networks and that you know that will
+connect the methods in computational
+
+ align:start position:0%
+connect the methods in computational
+ 
+
+ align:start position:0%
+connect the methods in computational
+neuroscience to this course eventually
+
+ align:start position:0%
+neuroscience to this course eventually
+ 
+
+ align:start position:0%
+neuroscience to this course eventually
+right so so so yeah so we have data
+
+ align:start position:0%
+right so so so yeah so we have data
+ 
+
+ align:start position:0%
+right so so so yeah so we have data
+generated by some generative model we
+
+ align:start position:0%
+generated by some generative model we
+ 
+
+ align:start position:0%
+generated by some generative model we
+take that data and we expose it to a
+
+ align:start position:0%
+take that data and we expose it to a
+ 
+
+ align:start position:0%
+take that data and we expose it to a
+neural network and we'd like to
+
+ align:start position:0%
+neural network and we'd like to
+ 
+
+ align:start position:0%
+neural network and we'd like to
+understand how the dynamics of learning
+
+ align:start position:0%
+understand how the dynamics of learning
+ 
+
+ align:start position:0%
+understand how the dynamics of learning
+depends on the parameters of the
+
+ align:start position:0%
+depends on the parameters of the
+ 
+
+ align:start position:0%
+depends on the parameters of the
+generative model okay so a natural
+
+ align:start position:0%
+generative model okay so a natural
+ 
+
+ align:start position:0%
+generative model okay so a natural
+generative model for defining
+
+ align:start position:0%
+generative model for defining
+ 
+
+ align:start position:0%
+generative model for defining
+hierarchical structure is a branching
+
+ align:start position:0%
+hierarchical structure is a branching
+ 
+
+ align:start position:0%
+hierarchical structure is a branching
+diffusion process that essentially makes
+
+ align:start position:0%
+diffusion process that essentially makes
+ 
+
+ align:start position:0%
+diffusion process that essentially makes
+the process of evolution where
+
+ align:start position:0%
+the process of evolution where
+ 
+
+ align:start position:0%
+the process of evolution where
+properties diffuse down a tree and
+
+ align:start position:0%
+properties diffuse down a tree and
+ 
+
+ align:start position:0%
+properties diffuse down a tree and
+instantiate themselves across a set of
+
+ align:start position:0%
+instantiate themselves across a set of
+ 
+
+ align:start position:0%
+instantiate themselves across a set of
+items so what do I mean by that okay
+
+ align:start position:0%
+items so what do I mean by that okay
+ 
+
+ align:start position:0%
+items so what do I mean by that okay
+okay so so so basically imagine for
+
+ align:start position:0%
+okay so so so basically imagine for
+ 
+
+ align:start position:0%
+okay so so so basically imagine for
+example that your items are at the
+
+ align:start position:0%
+example that your items are at the
+ 
+
+ align:start position:0%
+example that your items are at the
+leaves of a tree right and you can
+
+ align:start position:0%
+leaves of a tree right and you can
+ 
+
+ align:start position:0%
+leaves of a tree right and you can
+imagine that this is the process of
+
+ align:start position:0%
+imagine that this is the process of
+ 
+
+ align:start position:0%
+imagine that this is the process of
+evolution where there's some ancestral
+
+ align:start position:0%
+evolution where there's some ancestral
+ 
+
+ align:start position:0%
+evolution where there's some ancestral
+state maybe for one property so we do
+
+ align:start position:0%
+state maybe for one property so we do
+ 
+
+ align:start position:0%
+state maybe for one property so we do
+one property at a time and the
+
+ align:start position:0%
+one property at a time and the
+ 
+
+ align:start position:0%
+one property at a time and the
+properties are independent of each other
+
+ align:start position:0%
+properties are independent of each other
+ 
+
+ align:start position:0%
+properties are independent of each other
+this might be an ancestral state like
+
+ align:start position:0%
+this might be an ancestral state like
+ 
+
+ align:start position:0%
+this might be an ancestral state like
+can move right and then each time it
+
+ align:start position:0%
+can move right and then each time it
+ 
+
+ align:start position:0%
+can move right and then each time it
+that this
+
+ align:start position:0%
+that this
+ 
+
+ align:start position:0%
+that this
+this property diffuses down the tree
+
+ align:start position:0%
+this property diffuses down the tree
+ 
+
+ align:start position:0%
+this property diffuses down the tree
+there's a probability of flipping okay
+
+ align:start position:0%
+there's a probability of flipping okay
+ 
+
+ align:start position:0%
+there's a probability of flipping okay
+so maybe in this lineage which might
+
+ align:start position:0%
+so maybe in this lineage which might
+ 
+
+ align:start position:0%
+so maybe in this lineage which might
+correspond to animals
+
+ align:start position:0%
+correspond to animals
+ 
+
+ align:start position:0%
+correspond to animals
+this doesn't flip right and in these
+
+ align:start position:0%
+this doesn't flip right and in these
+ 
+
+ align:start position:0%
+this doesn't flip right and in these
+lineages corresponding to plants it does
+
+ align:start position:0%
+lineages corresponding to plants it does
+ 
+
+ align:start position:0%
+lineages corresponding to plants it does
+flip so these things cannot move and
+
+ align:start position:0%
+flip so these things cannot move and
+ 
+
+ align:start position:0%
+flip so these things cannot move and
+these things can move and then maybe it
+
+ align:start position:0%
+these things can move and then maybe it
+ 
+
+ align:start position:0%
+these things can move and then maybe it
+doesn't flip so all of these things
+
+ align:start position:0%
+doesn't flip so all of these things
+ 
+
+ align:start position:0%
+doesn't flip so all of these things
+inherit the property of moving so these
+
+ align:start position:0%
+inherit the property of moving so these
+ 
+
+ align:start position:0%
+inherit the property of moving so these
+are the animals and these things cannot
+
+ align:start position:0%
+are the animals and these things cannot
+ 
+
+ align:start position:0%
+are the animals and these things cannot
+move so these are the plants and then we
+
+ align:start position:0%
+move so these are the plants and then we
+ 
+
+ align:start position:0%
+move so these are the plants and then we
+do that for every single property
+
+ align:start position:0%
+do that for every single property
+ 
+
+ align:start position:0%
+do that for every single property
+independently and we generate a set of
+
+ align:start position:0%
+independently and we generate a set of
+ 
+
+ align:start position:0%
+independently and we generate a set of
+feature vectors so that's our generative
+
+ align:start position:0%
+feature vectors so that's our generative
+ 
+
+ align:start position:0%
+feature vectors so that's our generative
+model so what are the statistical
+
+ align:start position:0%
+model so what are the statistical
+ 
+
+ align:start position:0%
+model so what are the statistical
+properties of generative model so
+
+ align:start position:0%
+properties of generative model so
+ 
+
+ align:start position:0%
+properties of generative model so
+essentially because we know that we're
+
+ align:start position:0%
+essentially because we know that we're
+ 
+
+ align:start position:0%
+essentially because we know that we're
+analyzing these deep linear networks and
+
+ align:start position:0%
+analyzing these deep linear networks and
+ 
+
+ align:start position:0%
+analyzing these deep linear networks and
+we know that the learning dynamics of
+
+ align:start position:0%
+we know that the learning dynamics of
+ 
+
+ align:start position:0%
+we know that the learning dynamics of
+such networks is driven only by the
+
+ align:start position:0%
+such networks is driven only by the
+ 
+
+ align:start position:0%
+such networks is driven only by the
+input upper covariance matrix to
+
+ align:start position:0%
+input upper covariance matrix to
+ 
+
+ align:start position:0%
+input upper covariance matrix to
+understand the learning dynamics we just
+
+ align:start position:0%
+understand the learning dynamics we just
+ 
+
+ align:start position:0%
+understand the learning dynamics we just
+have to compute the singular values and
+
+ align:start position:0%
+have to compute the singular values and
+ 
+
+ align:start position:0%
+have to compute the singular values and
+singular vectors of Harken through
+
+ align:start position:0%
+singular vectors of Harken through
+ 
+
+ align:start position:0%
+singular vectors of Harken through
+structured data generated in this
+
+ align:start position:0%
+structured data generated in this
+ 
+
+ align:start position:0%
+structured data generated in this
+fashion and it's actually quite easy and
+
+ align:start position:0%
+fashion and it's actually quite easy and
+ 
+
+ align:start position:0%
+fashion and it's actually quite easy and
+we did it so here's what happens so
+
+ align:start position:0%
+we did it so here's what happens so
+ 
+
+ align:start position:0%
+we did it so here's what happens so
+imagine a nice symmetric tree like this
+
+ align:start position:0%
+imagine a nice symmetric tree like this
+ 
+
+ align:start position:0%
+imagine a nice symmetric tree like this
+so these are objects if we look at the
+
+ align:start position:0%
+so these are objects if we look at the
+ 
+
+ align:start position:0%
+so these are objects if we look at the
+similarity structure of objects measured
+
+ align:start position:0%
+similarity structure of objects measured
+ 
+
+ align:start position:0%
+similarity structure of objects measured
+by dot product in the feature space
+
+ align:start position:0%
+by dot product in the feature space
+ 
+
+ align:start position:0%
+by dot product in the feature space
+generated by the features under this
+
+ align:start position:0%
+generated by the features under this
+ 
+
+ align:start position:0%
+generated by the features under this
+branching diffusion process we get this
+
+ align:start position:0%
+branching diffusion process we get this
+ 
+
+ align:start position:0%
+branching diffusion process we get this
+nice blocks within block similarity
+
+ align:start position:0%
+nice blocks within block similarity
+ 
+
+ align:start position:0%
+nice blocks within block similarity
+structure where all the items on this on
+
+ align:start position:0%
+structure where all the items on this on
+ 
+
+ align:start position:0%
+structure where all the items on this on
+this branch are you know this item this
+
+ align:start position:0%
+this branch are you know this item this
+ 
+
+ align:start position:0%
+this branch are you know this item this
+item are slightly similar this item this
+
+ align:start position:0%
+item are slightly similar this item this
+ 
+
+ align:start position:0%
+item are slightly similar this item this
+item are even more similar and of course
+
+ align:start position:0%
+item are even more similar and of course
+ 
+
+ align:start position:0%
+item are even more similar and of course
+each item is most similar to itself so
+
+ align:start position:0%
+each item is most similar to itself so
+ 
+
+ align:start position:0%
+each item is most similar to itself so
+you have this hierarchical hierarchy of
+
+ align:start position:0%
+you have this hierarchical hierarchy of
+ 
+
+ align:start position:0%
+you have this hierarchical hierarchy of
+clusters that naturally arise because of
+
+ align:start position:0%
+clusters that naturally arise because of
+ 
+
+ align:start position:0%
+clusters that naturally arise because of
+this branching diffusion process so what
+
+ align:start position:0%
+this branching diffusion process so what
+ 
+
+ align:start position:0%
+this branching diffusion process so what
+are the singular values and singular
+
+ align:start position:0%
+are the singular values and singular
+ 
+
+ align:start position:0%
+are the singular values and singular
+vectors of the of the associated
+
+ align:start position:0%
+vectors of the of the associated
+ 
+
+ align:start position:0%
+vectors of the of the associated
+input-output covariance matrix
+
+ align:start position:0%
+input-output covariance matrix
+ 
+
+ align:start position:0%
+input-output covariance matrix
+well they turn out these are the one set
+
+ align:start position:0%
+well they turn out these are the one set
+ 
+
+ align:start position:0%
+well they turn out these are the one set
+of singular vectors the so called object
+
+ align:start position:0%
+of singular vectors the so called object
+ 
+
+ align:start position:0%
+of singular vectors the so called object
+analyzers which are functions across
+
+ align:start position:0%
+analyzers which are functions across
+ 
+
+ align:start position:0%
+analyzers which are functions across
+objects there's another set of singular
+
+ align:start position:0%
+objects there's another set of singular
+ 
+
+ align:start position:0%
+objects there's another set of singular
+vectors that are functions across
+
+ align:start position:0%
+vectors that are functions across
+ 
+
+ align:start position:0%
+vectors that are functions across
+features which I'm not showing you but
+
+ align:start position:0%
+features which I'm not showing you but
+ 
+
+ align:start position:0%
+features which I'm not showing you but
+we can under but but there's of course
+
+ align:start position:0%
+we can under but but there's of course
+ 
+
+ align:start position:0%
+we can under but but there's of course
+the duality right so that you get pairs
+
+ align:start position:0%
+the duality right so that you get pairs
+ 
+
+ align:start position:0%
+the duality right so that you get pairs
+of singular vectors for each singular
+
+ align:start position:0%
+of singular vectors for each singular
+ 
+
+ align:start position:0%
+of singular vectors for each singular
+value okay so what's the singular vector
+
+ align:start position:0%
+value okay so what's the singular vector
+ 
+
+ align:start position:0%
+value okay so what's the singular vector
+associate or the largest singular value
+
+ align:start position:0%
+associate or the largest singular value
+ 
+
+ align:start position:0%
+associate or the largest singular value
+well it's a uniform mode that's constant
+
+ align:start position:0%
+well it's a uniform mode that's constant
+ 
+
+ align:start position:0%
+well it's a uniform mode that's constant
+across all the objects but the next the
+
+ align:start position:0%
+across all the objects but the next the
+ 
+
+ align:start position:0%
+across all the objects but the next the
+most interesting one the next largest
+
+ align:start position:0%
+most interesting one the next largest
+ 
+
+ align:start position:0%
+most interesting one the next largest
+one is the most lowest frequency
+
+ align:start position:0%
+one is the most lowest frequency
+ 
+
+ align:start position:0%
+one is the most lowest frequency
+function essentially it's constant along
+
+ align:start position:0%
+function essentially it's constant along
+ 
+
+ align:start position:0%
+function essentially it's constant along
+all the ancestors of this branch and a
+
+ align:start position:0%
+all the ancestors of this branch and a
+ 
+
+ align:start position:0%
+all the ancestors of this branch and a
+different constant along all the
+
+ align:start position:0%
+different constant along all the
+ 
+
+ align:start position:0%
+different constant along all the
+ancestors of this branch so this
+
+ align:start position:0%
+ancestors of this branch so this
+ 
+
+ align:start position:0%
+ancestors of this branch so this
+singular vector essentially makes the
+
+ align:start position:0%
+singular vector essentially makes the
+ 
+
+ align:start position:0%
+singular vector essentially makes the
+most coarse-grained discrimination in
+
+ align:start position:0%
+most coarse-grained discrimination in
+ 
+
+ align:start position:0%
+most coarse-grained discrimination in
+this heart cookie structure data set the
+
+ align:start position:0%
+this heart cookie structure data set the
+ 
+
+ align:start position:0%
+this heart cookie structure data set the
+next set of seeing
+
+ align:start position:0%
+next set of seeing
+ 
+
+ align:start position:0%
+next set of seeing
+the vectors as a pair of them
+
+ align:start position:0%
+the vectors as a pair of them
+ 
+
+ align:start position:0%
+the vectors as a pair of them
+discriminate between this set of objects
+
+ align:start position:0%
+discriminate between this set of objects
+ 
+
+ align:start position:0%
+discriminate between this set of objects
+in this set of objects and don't know
+
+ align:start position:0%
+in this set of objects and don't know
+ 
+
+ align:start position:0%
+in this set of objects and don't know
+about these ones and the next one
+
+ align:start position:0%
+about these ones and the next one
+ 
+
+ align:start position:0%
+about these ones and the next one
+discriminates between this set of
+
+ align:start position:0%
+discriminates between this set of
+ 
+
+ align:start position:0%
+discriminates between this set of
+objects in this set of objects okay and
+
+ align:start position:0%
+objects in this set of objects okay and
+ 
+
+ align:start position:0%
+objects in this set of objects okay and
+then as you go down to the smaller
+
+ align:start position:0%
+then as you go down to the smaller
+ 
+
+ align:start position:0%
+then as you go down to the smaller
+singular values you get fine scale you
+
+ align:start position:0%
+singular values you get fine scale you
+ 
+
+ align:start position:0%
+singular values you get fine scale you
+get individual object discriminations
+
+ align:start position:0%
+get individual object discriminations
+ 
+
+ align:start position:0%
+get individual object discriminations
+right so this is how the Hart
+
+ align:start position:0%
+right so this is how the Hart
+ 
+
+ align:start position:0%
+right so this is how the Hart
+constructor is reflected in the second
+
+ align:start position:0%
+constructor is reflected in the second
+ 
+
+ align:start position:0%
+constructor is reflected in the second
+order statistics of the data and and
+
+ align:start position:0%
+order statistics of the data and and
+ 
+
+ align:start position:0%
+order statistics of the data and and
+this these are the singular values so
+
+ align:start position:0%
+this these are the singular values so
+ 
+
+ align:start position:0%
+this these are the singular values so
+the this is the theory for the singular
+
+ align:start position:0%
+the this is the theory for the singular
+ 
+
+ align:start position:0%
+the this is the theory for the singular
+values in a tree that has five levels of
+
+ align:start position:0%
+values in a tree that has five levels of
+ 
+
+ align:start position:0%
+values in a tree that has five levels of
+hierarchy and you can see that the
+
+ align:start position:0%
+hierarchy and you can see that the
+ 
+
+ align:start position:0%
+hierarchy and you can see that the
+singular values decay with the hierarchy
+
+ align:start position:0%
+singular values decay with the hierarchy
+ 
+
+ align:start position:0%
+singular values decay with the hierarchy
+level of the singular vectors okay so
+
+ align:start position:0%
+level of the singular vectors okay so
+ 
+
+ align:start position:0%
+level of the singular vectors okay so
+there's a general theory for this in
+
+ align:start position:0%
+there's a general theory for this in
+ 
+
+ align:start position:0%
+there's a general theory for this in
+which singular vectors are associated
+
+ align:start position:0%
+which singular vectors are associated
+ 
+
+ align:start position:0%
+which singular vectors are associated
+with levels of the tree okay so now you
+
+ align:start position:0%
+with levels of the tree okay so now you
+ 
+
+ align:start position:0%
+with levels of the tree okay so now you
+can see the end of the end of the story
+
+ align:start position:0%
+can see the end of the end of the story
+ 
+
+ align:start position:0%
+can see the end of the end of the story
+if you put the two together you
+
+ align:start position:0%
+if you put the two together you
+ 
+
+ align:start position:0%
+if you put the two together you
+automatically get the results that we
+
+ align:start position:0%
+automatically get the results that we
+ 
+
+ align:start position:0%
+automatically get the results that we
+that we were trying to explain right so
+
+ align:start position:0%
+that we were trying to explain right so
+ 
+
+ align:start position:0%
+that we were trying to explain right so
+essentially the general theory of
+
+ align:start position:0%
+essentially the general theory of
+ 
+
+ align:start position:0%
+essentially the general theory of
+learning says that the network learns
+
+ align:start position:0%
+learning says that the network learns
+ 
+
+ align:start position:0%
+learning says that the network learns
+input-output modes in a time scale given
+
+ align:start position:0%
+input-output modes in a time scale given
+ 
+
+ align:start position:0%
+input-output modes in a time scale given
+by 1 over C 1 over the singular value
+
+ align:start position:0%
+by 1 over C 1 over the singular value
+ 
+
+ align:start position:0%
+by 1 over C 1 over the singular value
+when the data is hierarchically
+
+ align:start position:0%
+when the data is hierarchically
+ 
+
+ align:start position:0%
+when the data is hierarchically
+structured singular values of broader
+
+ align:start position:0%
+structured singular values of broader
+ 
+
+ align:start position:0%
+structured singular values of broader
+hierarchical distinctions are larger
+
+ align:start position:0%
+hierarchical distinctions are larger
+ 
+
+ align:start position:0%
+hierarchical distinctions are larger
+than singular values of finer
+
+ align:start position:0%
+than singular values of finer
+ 
+
+ align:start position:0%
+than singular values of finer
+distinctions and the input-output modes
+
+ align:start position:0%
+distinctions and the input-output modes
+ 
+
+ align:start position:0%
+distinctions and the input-output modes
+correspond exactly to heart conditions
+
+ align:start position:0%
+correspond exactly to heart conditions
+ 
+
+ align:start position:0%
+correspond exactly to heart conditions
+in the tree so that essentially says the
+
+ align:start position:0%
+in the tree so that essentially says the
+ 
+
+ align:start position:0%
+in the tree so that essentially says the
+network must learn broad scale
+
+ align:start position:0%
+network must learn broad scale
+ 
+
+ align:start position:0%
+network must learn broad scale
+discriminations before it can learn fine
+
+ align:start position:0%
+discriminations before it can learn fine
+ 
+
+ align:start position:0%
+discriminations before it can learn fine
+scale discriminations so then actually
+
+ align:start position:0%
+scale discriminations so then actually
+ 
+
+ align:start position:0%
+scale discriminations so then actually
+what we did was we just analytically
+
+ align:start position:0%
+what we did was we just analytically
+ 
+
+ align:start position:0%
+what we did was we just analytically
+worked out that the dynamics of learning
+
+ align:start position:0%
+worked out that the dynamics of learning
+ 
+
+ align:start position:0%
+worked out that the dynamics of learning
+for hard Kuki structured data and we
+
+ align:start position:0%
+for hard Kuki structured data and we
+ 
+
+ align:start position:0%
+for hard Kuki structured data and we
+computed the multi-dimensional scaling
+
+ align:start position:0%
+computed the multi-dimensional scaling
+ 
+
+ align:start position:0%
+computed the multi-dimensional scaling
+and this was theory we never did a
+
+ align:start position:0%
+and this was theory we never did a
+ 
+
+ align:start position:0%
+and this was theory we never did a
+single simulation to get this plot we
+
+ align:start position:0%
+single simulation to get this plot we
+ 
+
+ align:start position:0%
+single simulation to get this plot we
+generated we generated a branching
+
+ align:start position:0%
+generated we generated a branching
+ 
+
+ align:start position:0%
+generated we generated a branching
+diffusion process with it was
+
+ align:start position:0%
+diffusion process with it was
+ 
+
+ align:start position:0%
+diffusion process with it was
+essentially this one and we just labeled
+
+ align:start position:0%
+essentially this one and we just labeled
+ 
+
+ align:start position:0%
+essentially this one and we just labeled
+these nodes arbitrarily with these
+
+ align:start position:0%
+these nodes arbitrarily with these
+ 
+
+ align:start position:0%
+these nodes arbitrarily with these
+labels and this is what we get right so
+
+ align:start position:0%
+labels and this is what we get right so
+ 
+
+ align:start position:0%
+labels and this is what we get right so
+we see the multi-dimensional scaling
+
+ align:start position:0%
+we see the multi-dimensional scaling
+ 
+
+ align:start position:0%
+we see the multi-dimensional scaling
+plot that we sort of see here and
+
+ align:start position:0%
+plot that we sort of see here and
+ 
+
+ align:start position:0%
+plot that we sort of see here and
+essentially just to compare this is what
+
+ align:start position:0%
+essentially just to compare this is what
+ 
+
+ align:start position:0%
+essentially just to compare this is what
+was done with a toy dataset over which
+
+ align:start position:0%
+was done with a toy dataset over which
+ 
+
+ align:start position:0%
+was done with a toy dataset over which
+had no theoretical control in a
+
+ align:start position:0%
+had no theoretical control in a
+ 
+
+ align:start position:0%
+had no theoretical control in a
+nonlinear neural network over which we
+
+ align:start position:0%
+nonlinear neural network over which we
+ 
+
+ align:start position:0%
+nonlinear neural network over which we
+had no theoretical control and this is a
+
+ align:start position:0%
+had no theoretical control and this is a
+ 
+
+ align:start position:0%
+had no theoretical control and this is a
+well-defined mathematical generative
+
+ align:start position:0%
+well-defined mathematical generative
+ 
+
+ align:start position:0%
+well-defined mathematical generative
+model under linear neural network and we
+
+ align:start position:0%
+model under linear neural network and we
+ 
+
+ align:start position:0%
+model under linear neural network and we
+see that we qualitatively explain the
+
+ align:start position:0%
+see that we qualitatively explain the
+ 
+
+ align:start position:0%
+see that we qualitatively explain the
+results so this is the difference
+
+ align:start position:0%
+results so this is the difference
+ 
+
+ align:start position:0%
+results so this is the difference
+between simulation and theory right now
+
+ align:start position:0%
+between simulation and theory right now
+ 
+
+ align:start position:0%
+between simulation and theory right now
+we have a conceptual understanding of
+
+ align:start position:0%
+we have a conceptual understanding of
+ 
+
+ align:start position:0%
+we have a conceptual understanding of
+effectively what was going on in the
+
+ align:start position:0%
+effectively what was going on in the
+ 
+
+ align:start position:0%
+effectively what was going on in the
+circuit and we really a sort of now it's
+
+ align:start position:0%
+circuit and we really a sort of now it's
+ 
+
+ align:start position:0%
+circuit and we really a sort of now it's
+no longer a mystery so now I think I
+
+ align:start position:0%
+no longer a mystery so now I think I
+ 
+
+ align:start position:0%
+no longer a mystery so now I think I
+understand what Jay was doing Jay and
+
+ align:start position:0%
+understand what Jay was doing Jay and
+ 
+
+ align:start position:0%
+understand what Jay was doing Jay and
+collaborators were doing
+
+ align:start position:0%
+collaborators were doing
+ 
+
+ align:start position:0%
+collaborators were doing
+it would be lovely if for all of the
+
+ align:start position:0%
+it would be lovely if for all of the
+ 
+
+ align:start position:0%
+it would be lovely if for all of the
+stuff that's going on in this course we
+
+ align:start position:0%
+stuff that's going on in this course we
+ 
+
+ align:start position:0%
+stuff that's going on in this course we
+could obtain such a deep rigorous
+
+ align:start position:0%
+could obtain such a deep rigorous
+ 
+
+ align:start position:0%
+could obtain such a deep rigorous
+understanding it's much more challenging
+
+ align:start position:0%
+understanding it's much more challenging
+ 
+
+ align:start position:0%
+understanding it's much more challenging
+but it's a goal worthy of pursuit I
+
+ align:start position:0%
+but it's a goal worthy of pursuit I
+ 
+
+ align:start position:0%
+but it's a goal worthy of pursuit I
+think ok so conclusions progressive
+
+ align:start position:0%
+think ok so conclusions progressive
+ 
+
+ align:start position:0%
+think ok so conclusions progressive
+differentiation of hierarchical
+
+ align:start position:0%
+differentiation of hierarchical
+ 
+
+ align:start position:0%
+differentiation of hierarchical
+structure is a general feature of
+
+ align:start position:0%
+structure is a general feature of
+ 
+
+ align:start position:0%
+structure is a general feature of
+learning and deep neural networks it
+
+ align:start position:0%
+learning and deep neural networks it
+ 
+
+ align:start position:0%
+learning and deep neural networks it
+cannot be any other way
+
+ align:start position:0%
+cannot be any other way
+ 
+
+ align:start position:0%
+cannot be any other way
+ok interestingly enough deep but not
+
+ align:start position:0%
+ok interestingly enough deep but not
+ 
+
+ align:start position:0%
+ok interestingly enough deep but not
+shallow networks exhibit such stage like
+
+ align:start position:0%
+shallow networks exhibit such stage like
+ 
+
+ align:start position:0%
+shallow networks exhibit such stage like
+transitions during learning so if you
+
+ align:start position:0%
+transitions during learning so if you
+ 
+
+ align:start position:0%
+transitions during learning so if you
+just do no hidden layers you don't get
+
+ align:start position:0%
+just do no hidden layers you don't get
+ 
+
+ align:start position:0%
+just do no hidden layers you don't get
+this actually you need it in and layer
+
+ align:start position:0%
+this actually you need it in and layer
+ 
+
+ align:start position:0%
+this actually you need it in and layer
+to do this and somewhat surprisingly it
+
+ align:start position:0%
+to do this and somewhat surprisingly it
+ 
+
+ align:start position:0%
+to do this and somewhat surprisingly it
+turns out that even only the second
+
+ align:start position:0%
+turns out that even only the second
+ 
+
+ align:start position:0%
+turns out that even only the second
+order statistics of semantic properties
+
+ align:start position:0%
+order statistics of semantic properties
+ 
+
+ align:start position:0%
+order statistics of semantic properties
+provide powerful statistical signals
+
+ align:start position:0%
+provide powerful statistical signals
+ 
+
+ align:start position:0%
+provide powerful statistical signals
+that are sufficient to drive this
+
+ align:start position:0%
+that are sufficient to drive this
+ 
+
+ align:start position:0%
+that are sufficient to drive this
+nonlinear learning dynamics right you
+
+ align:start position:0%
+nonlinear learning dynamics right you
+ 
+
+ align:start position:0%
+nonlinear learning dynamics right you
+don't need to look at the higher order
+
+ align:start position:0%
+don't need to look at the higher order
+ 
+
+ align:start position:0%
+don't need to look at the higher order
+statistics of the data to get this
+
+ align:start position:0%
+statistics of the data to get this
+ 
+
+ align:start position:0%
+statistics of the data to get this
+dynamic second order sisters sick
+
+ align:start position:0%
+dynamic second order sisters sick
+ 
+
+ align:start position:0%
+dynamic second order sisters sick
+suffice which was not obvious before we
+
+ align:start position:0%
+suffice which was not obvious before we
+ 
+
+ align:start position:0%
+suffice which was not obvious before we
+started okay so in ongoing work we can
+
+ align:start position:0%
+started okay so in ongoing work we can
+ 
+
+ align:start position:0%
+started okay so in ongoing work we can
+explain a whole bunch of things like
+
+ align:start position:0%
+explain a whole bunch of things like
+ 
+
+ align:start position:0%
+explain a whole bunch of things like
+illusory correlations early in learning
+
+ align:start position:0%
+illusory correlations early in learning
+ 
+
+ align:start position:0%
+illusory correlations early in learning
+so for example infants will initially
+
+ align:start position:0%
+so for example infants will initially
+ 
+
+ align:start position:0%
+so for example infants will initially
+say that they don't even know that for
+
+ align:start position:0%
+say that they don't even know that for
+ 
+
+ align:start position:0%
+say that they don't even know that for
+example pine trees don't don't have
+
+ align:start position:0%
+example pine trees don't don't have
+ 
+
+ align:start position:0%
+example pine trees don't don't have
+leaves then at an intermediate point
+
+ align:start position:0%
+leaves then at an intermediate point
+ 
+
+ align:start position:0%
+leaves then at an intermediate point
+they think that pine trees have leaves
+
+ align:start position:0%
+they think that pine trees have leaves
+ 
+
+ align:start position:0%
+they think that pine trees have leaves
+and then at a later point they correctly
+
+ align:start position:0%
+and then at a later point they correctly
+ 
+
+ align:start position:0%
+and then at a later point they correctly
+know that pine trees don't have leaves
+
+ align:start position:0%
+know that pine trees don't have leaves
+ 
+
+ align:start position:0%
+know that pine trees don't have leaves
+right so we can explain these non
+
+ align:start position:0%
+right so we can explain these non
+ 
+
+ align:start position:0%
+right so we can explain these non
+monotonic learning curves we can explain
+
+ align:start position:0%
+monotonic learning curves we can explain
+ 
+
+ align:start position:0%
+monotonic learning curves we can explain
+these familiar in typicality effects we
+
+ align:start position:0%
+these familiar in typicality effects we
+ 
+
+ align:start position:0%
+these familiar in typicality effects we
+can explain an inductive property
+
+ align:start position:0%
+can explain an inductive property
+ 
+
+ align:start position:0%
+can explain an inductive property
+judgments analytically we're looking at
+
+ align:start position:0%
+judgments analytically we're looking at
+ 
+
+ align:start position:0%
+judgments analytically we're looking at
+basic level effects we have a theory of
+
+ align:start position:0%
+basic level effects we have a theory of
+ 
+
+ align:start position:0%
+basic level effects we have a theory of
+category coherence and so on but in the
+
+ align:start position:0%
+category coherence and so on but in the
+ 
+
+ align:start position:0%
+category coherence and so on but in the
+interest of moving forward I wanted to
+
+ align:start position:0%
+interest of moving forward I wanted to
+ 
+
+ align:start position:0%
+interest of moving forward I wanted to
+give short shrift to this stuff so we
+
+ align:start position:0%
+give short shrift to this stuff so we
+ 
+
+ align:start position:0%
+give short shrift to this stuff so we
+essentially we can answer why are some
+
+ align:start position:0%
+essentially we can answer why are some
+ 
+
+ align:start position:0%
+essentially we can answer why are some
+properties learned faster basically
+
+ align:start position:0%
+properties learned faster basically
+ 
+
+ align:start position:0%
+properties learned faster basically
+properties that look that are low
+
+ align:start position:0%
+properties that look that are low
+ 
+
+ align:start position:0%
+properties that look that are low
+frequency properties on the leaves of
+
+ align:start position:0%
+frequency properties on the leaves of
+ 
+
+ align:start position:0%
+frequency properties on the leaves of
+the tree get learned faster properties
+
+ align:start position:0%
+the tree get learned faster properties
+ 
+
+ align:start position:0%
+the tree get learned faster properties
+whose inner product with sync with the
+
+ align:start position:0%
+whose inner product with sync with the
+ 
+
+ align:start position:0%
+whose inner product with sync with the
+singular vectors of largest singular
+
+ align:start position:0%
+singular vectors of largest singular
+ 
+
+ align:start position:0%
+singular vectors of largest singular
+value get learned faster that's the
+
+ align:start position:0%
+value get learned faster that's the
+ 
+
+ align:start position:0%
+value get learned faster that's the
+story why are some items more typical we
+
+ align:start position:0%
+story why are some items more typical we
+ 
+
+ align:start position:0%
+story why are some items more typical we
+have a theory for that how is inductive
+
+ align:start position:0%
+have a theory for that how is inductive
+ 
+
+ align:start position:0%
+have a theory for that how is inductive
+generalization achieved by neural
+
+ align:start position:0%
+generalization achieved by neural
+ 
+
+ align:start position:0%
+generalization achieved by neural
+networks we have a theory for that and
+
+ align:start position:0%
+networks we have a theory for that and
+ 
+
+ align:start position:0%
+networks we have a theory for that and
+so on and you know what is a useful
+
+ align:start position:0%
+so on and you know what is a useful
+ 
+
+ align:start position:0%
+so on and you know what is a useful
+mathematical definition of category hair
+
+ align:start position:0%
+mathematical definition of category hair
+ 
+
+ align:start position:0%
+mathematical definition of category hair
+and so for example you know there
+
+ align:start position:0%
+and so for example you know there
+ 
+
+ align:start position:0%
+and so for example you know there
+some things that are just intuitively
+
+ align:start position:0%
+some things that are just intuitively
+ 
+
+ align:start position:0%
+some things that are just intuitively
+called incoherent categories the set of
+
+ align:start position:0%
+called incoherent categories the set of
+ 
+
+ align:start position:0%
+called incoherent categories the set of
+all things are blue is a very incoherent
+
+ align:start position:0%
+all things are blue is a very incoherent
+ 
+
+ align:start position:0%
+all things are blue is a very incoherent
+category in fact it's so incoherent we
+
+ align:start position:0%
+category in fact it's so incoherent we
+ 
+
+ align:start position:0%
+category in fact it's so incoherent we
+don't have a name for such a category
+
+ align:start position:0%
+don't have a name for such a category
+ 
+
+ align:start position:0%
+don't have a name for such a category
+the set of all things that are dogs
+
+ align:start position:0%
+the set of all things that are dogs
+ 
+
+ align:start position:0%
+the set of all things that are dogs
+seems to be a very coherent category and
+
+ align:start position:0%
+seems to be a very coherent category and
+ 
+
+ align:start position:0%
+seems to be a very coherent category and
+so coherent that we have a you know
+
+ align:start position:0%
+so coherent that we have a you know
+ 
+
+ align:start position:0%
+so coherent that we have a you know
+well-known name for it names quite short
+
+ align:start position:0%
+well-known name for it names quite short
+ 
+
+ align:start position:0%
+well-known name for it names quite short
+actually to actually know I wonder if
+
+ align:start position:0%
+actually to actually know I wonder if
+ 
+
+ align:start position:0%
+actually to actually know I wonder if
+there's a theory where shorter words
+
+ align:start position:0%
+there's a theory where shorter words
+ 
+
+ align:start position:0%
+there's a theory where shorter words
+correspond to more coherent categories
+
+ align:start position:0%
+correspond to more coherent categories
+ 
+
+ align:start position:0%
+correspond to more coherent categories
+and that's like a an informative or
+
+ align:start position:0%
+and that's like a an informative or
+ 
+
+ align:start position:0%
+and that's like a an informative or
+efficient representation of category
+
+ align:start position:0%
+efficient representation of category
+ 
+
+ align:start position:0%
+efficient representation of category
+structure of anyways so we have a
+
+ align:start position:0%
+structure of anyways so we have a
+ 
+
+ align:start position:0%
+structure of anyways so we have a
+natural definition of coherent category
+
+ align:start position:0%
+natural definition of coherent category
+ 
+
+ align:start position:0%
+natural definition of coherent category
+that's precise enough to prove a theorem
+
+ align:start position:0%
+that's precise enough to prove a theorem
+ 
+
+ align:start position:0%
+that's precise enough to prove a theorem
+that coherent categories are learned
+
+ align:start position:0%
+that coherent categories are learned
+ 
+
+ align:start position:0%
+that coherent categories are learned
+faster and actually this this also
+
+ align:start position:0%
+faster and actually this this also
+ 
+
+ align:start position:0%
+faster and actually this this also
+relates the size of the categories so
+
+ align:start position:0%
+relates the size of the categories so
+ 
+
+ align:start position:0%
+relates the size of the categories so
+frequency effects show up anyway so
+
+ align:start position:0%
+frequency effects show up anyway so
+ 
+
+ align:start position:0%
+frequency effects show up anyway so
+there's a lot of stuff there but that
+
+ align:start position:0%
+there's a lot of stuff there but that
+ 
+
+ align:start position:0%
+there's a lot of stuff there but that
+was sort of the entry point so now what
+
+ align:start position:0%
+was sort of the entry point so now what
+ 
+
+ align:start position:0%
+was sort of the entry point so now what
+about a theory of learning in much
+
+ align:start position:0%
+about a theory of learning in much
+ 
+
+ align:start position:0%
+about a theory of learning in much
+deeper networks that have many many
+
+ align:start position:0%
+deeper networks that have many many
+ 
+
+ align:start position:0%
+deeper networks that have many many
+layers okay so again I'm gonna make a
+
+ align:start position:0%
+layers okay so again I'm gonna make a
+ 
+
+ align:start position:0%
+layers okay so again I'm gonna make a
+long story short because it's all
+
+ align:start position:0%
+long story short because it's all
+ 
+
+ align:start position:0%
+long story short because it's all
+published you can read all the details
+
+ align:start position:0%
+published you can read all the details
+ 
+
+ align:start position:0%
+published you can read all the details
+but I wanted to give you the the spirit
+
+ align:start position:0%
+but I wanted to give you the the spirit
+ 
+
+ align:start position:0%
+but I wanted to give you the the spirit
+or the essence of the intuition behind
+
+ align:start position:0%
+or the essence of the intuition behind
+ 
+
+ align:start position:0%
+or the essence of the intuition behind
+the work okay so the questions we like
+
+ align:start position:0%
+the work okay so the questions we like
+ 
+
+ align:start position:0%
+the work okay so the questions we like
+to answer are how does training time
+
+ align:start position:0%
+to answer are how does training time
+ 
+
+ align:start position:0%
+to answer are how does training time
+scale with depth how should learning
+
+ align:start position:0%
+scale with depth how should learning
+ 
+
+ align:start position:0%
+scale with depth how should learning
+rate scale with depth how do different
+
+ align:start position:0%
+rate scale with depth how do different
+ 
+
+ align:start position:0%
+rate scale with depth how do different
+weight initialization impact learning
+
+ align:start position:0%
+weight initialization impact learning
+ 
+
+ align:start position:0%
+weight initialization impact learning
+speed and what we'll do is once we
+
+ align:start position:0%
+speed and what we'll do is once we
+ 
+
+ align:start position:0%
+speed and what we'll do is once we
+understand these theoretically we'll
+
+ align:start position:0%
+understand these theoretically we'll
+ 
+
+ align:start position:0%
+understand these theoretically we'll
+find certain weighed initializations
+
+ align:start position:0%
+find certain weighed initializations
+ 
+
+ align:start position:0%
+find certain weighed initializations
+that correspond to critical dynamics
+
+ align:start position:0%
+that correspond to critical dynamics
+ 
+
+ align:start position:0%
+that correspond to critical dynamics
+which I'll define can aid deep learning
+
+ align:start position:0%
+which I'll define can aid deep learning
+ 
+
+ align:start position:0%
+which I'll define can aid deep learning
+and generalization so the basic idea is
+
+ align:start position:0%
+and generalization so the basic idea is
+ 
+
+ align:start position:0%
+and generalization so the basic idea is
+in a very very deep neural network right
+
+ align:start position:0%
+in a very very deep neural network right
+ 
+
+ align:start position:0%
+in a very very deep neural network right
+you have a you you have a vanishing
+
+ align:start position:0%
+you have a you you have a vanishing
+ 
+
+ align:start position:0%
+you have a you you have a vanishing
+exploding or gradient problem and that's
+
+ align:start position:0%
+exploding or gradient problem and that's
+ 
+
+ align:start position:0%
+exploding or gradient problem and that's
+one of the issues that makes deep neural
+
+ align:start position:0%
+one of the issues that makes deep neural
+ 
+
+ align:start position:0%
+one of the issues that makes deep neural
+network learning hard so if you're going
+
+ align:start position:0%
+network learning hard so if you're going
+ 
+
+ align:start position:0%
+network learning hard so if you're going
+to back propagate the error through
+
+ align:start position:0%
+to back propagate the error through
+ 
+
+ align:start position:0%
+to back propagate the error through
+multiple layers the back propagation
+
+ align:start position:0%
+multiple layers the back propagation
+ 
+
+ align:start position:0%
+multiple layers the back propagation
+operation is a product of jacobians from
+
+ align:start position:0%
+operation is a product of jacobians from
+ 
+
+ align:start position:0%
+operation is a product of jacobians from
+layer to layer and that product of
+
+ align:start position:0%
+layer to layer and that product of
+ 
+
+ align:start position:0%
+layer to layer and that product of
+jacobians is fundamentally of linear
+
+ align:start position:0%
+jacobians is fundamentally of linear
+ 
+
+ align:start position:0%
+jacobians is fundamentally of linear
+mapping right so if the singular value
+
+ align:start position:0%
+mapping right so if the singular value
+ 
+
+ align:start position:0%
+mapping right so if the singular value
+is associated with that linear mapping
+
+ align:start position:0%
+is associated with that linear mapping
+ 
+
+ align:start position:0%
+is associated with that linear mapping
+so essentially if the singular values of
+
+ align:start position:0%
+so essentially if the singular values of
+ 
+
+ align:start position:0%
+so essentially if the singular values of
+the Jacobian and each layer are large
+
+ align:start position:0%
+the Jacobian and each layer are large
+ 
+
+ align:start position:0%
+the Jacobian and each layer are large
+bigger than 1 the product of such
+
+ align:start position:0%
+bigger than 1 the product of such
+ 
+
+ align:start position:0%
+bigger than 1 the product of such
+matrices will lead to a product matrix
+
+ align:start position:0%
+matrices will lead to a product matrix
+ 
+
+ align:start position:0%
+matrices will lead to a product matrix
+that has singular values that grow
+
+ align:start position:0%
+that has singular values that grow
+ 
+
+ align:start position:0%
+that has singular values that grow
+exponentially with depth similarly if
+
+ align:start position:0%
+exponentially with depth similarly if
+ 
+
+ align:start position:0%
+exponentially with depth similarly if
+the singular values are less than 1
+
+ align:start position:0%
+the singular values are less than 1
+ 
+
+ align:start position:0%
+the singular values are less than 1
+they'll decay with depth right so that's
+
+ align:start position:0%
+they'll decay with depth right so that's
+ 
+
+ align:start position:0%
+they'll decay with depth right so that's
+that's a vanishing gradient in the
+
+ align:start position:0%
+that's a vanishing gradient in the
+ 
+
+ align:start position:0%
+that's a vanishing gradient in the
+latter case and an exploding gradient in
+
+ align:start position:0%
+latter case and an exploding gradient in
+ 
+
+ align:start position:0%
+latter case and an exploding gradient in
+the former case that seems to be one of
+
+ align:start position:0%
+the former case that seems to be one of
+ 
+
+ align:start position:0%
+the former case that seems to be one of
+the major impediments
+
+ align:start position:0%
+the major impediments
+ 
+
+ align:start position:0%
+the major impediments
+understanding deep learning so what
+
+ align:start position:0%
+understanding deep learning so what
+ 
+
+ align:start position:0%
+understanding deep learning so what
+people often did was they tried to scale
+
+ align:start position:0%
+people often did was they tried to scale
+ 
+
+ align:start position:0%
+people often did was they tried to scale
+the matrices to avoid this question
+
+ align:start position:0%
+the matrices to avoid this question
+ 
+
+ align:start position:0%
+the matrices to avoid this question
+right so what they often do is they they
+
+ align:start position:0%
+right so what they often do is they they
+ 
+
+ align:start position:0%
+right so what they often do is they they
+picked they initialize the weights
+
+ align:start position:0%
+picked they initialize the weights
+ 
+
+ align:start position:0%
+picked they initialize the weights
+randomly so that W is a random matrix
+
+ align:start position:0%
+randomly so that W is a random matrix
+ 
+
+ align:start position:0%
+randomly so that W is a random matrix
+where the elements W IJ are iid and
+
+ align:start position:0%
+where the elements W IJ are iid and
+ 
+
+ align:start position:0%
+where the elements W IJ are iid and
+Gaussian with a scale factor scaled
+
+ align:start position:0%
+Gaussian with a scale factor scaled
+ 
+
+ align:start position:0%
+Gaussian with a scale factor scaled
+precisely so that the largest eigen
+
+ align:start position:0%
+precisely so that the largest eigen
+ 
+
+ align:start position:0%
+precisely so that the largest eigen
+value of the Jacobian or the
+
+ align:start position:0%
+value of the Jacobian or the
+ 
+
+ align:start position:0%
+value of the Jacobian or the
+backpropagation operator is one okay so
+
+ align:start position:0%
+backpropagation operator is one okay so
+ 
+
+ align:start position:0%
+backpropagation operator is one okay so
+it's like scaling the system so that if
+
+ align:start position:0%
+it's like scaling the system so that if
+ 
+
+ align:start position:0%
+it's like scaling the system so that if
+you place a random error vector here
+
+ align:start position:0%
+you place a random error vector here
+ 
+
+ align:start position:0%
+you place a random error vector here
+right the desired output minus the
+
+ align:start position:0%
+right the desired output minus the
+ 
+
+ align:start position:0%
+right the desired output minus the
+actual output and back propagated
+
+ align:start position:0%
+actual output and back propagated
+ 
+
+ align:start position:0%
+actual output and back propagated
+through a random network a random vector
+
+ align:start position:0%
+through a random network a random vector
+ 
+
+ align:start position:0%
+through a random network a random vector
+will preserve a rare vector will
+
+ align:start position:0%
+will preserve a rare vector will
+ 
+
+ align:start position:0%
+will preserve a rare vector will
+preserve its norm as its back propagated
+
+ align:start position:0%
+preserve its norm as its back propagated
+ 
+
+ align:start position:0%
+preserve its norm as its back propagated
+across and so such and this is the
+
+ align:start position:0%
+across and so such and this is the
+ 
+
+ align:start position:0%
+across and so such and this is the
+famous sort of glory and Benjy Oh
+
+ align:start position:0%
+famous sort of glory and Benjy Oh
+ 
+
+ align:start position:0%
+famous sort of glory and Benjy Oh
+initialization and it works pretty well
+
+ align:start position:0%
+initialization and it works pretty well
+ 
+
+ align:start position:0%
+initialization and it works pretty well
+for depth four or five or whatever right
+
+ align:start position:0%
+for depth four or five or whatever right
+ 
+
+ align:start position:0%
+for depth four or five or whatever right
+okay so we would like a theory of that
+
+ align:start position:0%
+okay so we would like a theory of that
+ 
+
+ align:start position:0%
+okay so we would like a theory of that
+for the learning dynamics of that and as
+
+ align:start position:0%
+for the learning dynamics of that and as
+ 
+
+ align:start position:0%
+for the learning dynamics of that and as
+I said there's no hope for a complete
+
+ align:start position:0%
+I said there's no hope for a complete
+ 
+
+ align:start position:0%
+I said there's no hope for a complete
+theory at the moment with arbitrary
+
+ align:start position:0%
+theory at the moment with arbitrary
+ 
+
+ align:start position:0%
+theory at the moment with arbitrary
+nonlinearities okay so what we're going
+
+ align:start position:0%
+nonlinearities okay so what we're going
+ 
+
+ align:start position:0%
+nonlinearities okay so what we're going
+to do is we're to analyze the learning
+
+ align:start position:0%
+to do is we're to analyze the learning
+ 
+
+ align:start position:0%
+to do is we're to analyze the learning
+dynamics just we'll get rid of the
+
+ align:start position:0%
+dynamics just we'll get rid of the
+ 
+
+ align:start position:0%
+dynamics just we'll get rid of the
+nonlinearities right so again it might
+
+ align:start position:0%
+nonlinearities right so again it might
+ 
+
+ align:start position:0%
+nonlinearities right so again it might
+seem like we're throwing the baby out
+
+ align:start position:0%
+seem like we're throwing the baby out
+ 
+
+ align:start position:0%
+seem like we're throwing the baby out
+with the bathwater but we're actually
+
+ align:start position:0%
+with the bathwater but we're actually
+ 
+
+ align:start position:0%
+with the bathwater but we're actually
+going to learn something that helps us
+
+ align:start position:0%
+going to learn something that helps us
+ 
+
+ align:start position:0%
+going to learn something that helps us
+to Train on than your networks okay so
+
+ align:start position:0%
+to Train on than your networks okay so
+ 
+
+ align:start position:0%
+to Train on than your networks okay so
+the basic idea then is that we have a
+
+ align:start position:0%
+the basic idea then is that we have a
+ 
+
+ align:start position:0%
+the basic idea then is that we have a
+network which is linear so why the
+
+ align:start position:0%
+network which is linear so why the
+ 
+
+ align:start position:0%
+network which is linear so why the
+output is a product of waves right so
+
+ align:start position:0%
+output is a product of waves right so
+ 
+
+ align:start position:0%
+output is a product of waves right so
+then the the back propagation okay so so
+
+ align:start position:0%
+then the the back propagation okay so so
+ 
+
+ align:start position:0%
+then the the back propagation okay so so
+then the back propagation is again just
+
+ align:start position:0%
+then the back propagation is again just
+ 
+
+ align:start position:0%
+then the back propagation is again just
+a product of matrices right the gradient
+
+ align:start position:0%
+a product of matrices right the gradient
+ 
+
+ align:start position:0%
+a product of matrices right the gradient
+descent dynamics is long linear and
+
+ align:start position:0%
+descent dynamics is long linear and
+ 
+
+ align:start position:0%
+descent dynamics is long linear and
+coupled and non convex and actually even
+
+ align:start position:0%
+coupled and non convex and actually even
+ 
+
+ align:start position:0%
+coupled and non convex and actually even
+in this linear network you see plateaus
+
+ align:start position:0%
+in this linear network you see plateaus
+ 
+
+ align:start position:0%
+in this linear network you see plateaus
+and sudden transitions right and
+
+ align:start position:0%
+and sudden transitions right and
+ 
+
+ align:start position:0%
+and sudden transitions right and
+actually interestingly enough even in
+
+ align:start position:0%
+actually interestingly enough even in
+ 
+
+ align:start position:0%
+actually interestingly enough even in
+this very deep linear network you see
+
+ align:start position:0%
+this very deep linear network you see
+ 
+
+ align:start position:0%
+this very deep linear network you see
+faster convergence from pre-trained
+
+ align:start position:0%
+faster convergence from pre-trained
+ 
+
+ align:start position:0%
+faster convergence from pre-trained
+initial conditions right so basically if
+
+ align:start position:0%
+initial conditions right so basically if
+ 
+
+ align:start position:0%
+initial conditions right so basically if
+you start from random Gaussian initial
+
+ align:start position:0%
+you start from random Gaussian initial
+ 
+
+ align:start position:0%
+you start from random Gaussian initial
+conditions you get slow learning for a
+
+ align:start position:0%
+conditions you get slow learning for a
+ 
+
+ align:start position:0%
+conditions you get slow learning for a
+while and then sudden sudden learning
+
+ align:start position:0%
+while and then sudden sudden learning
+ 
+
+ align:start position:0%
+while and then sudden sudden learning
+here relatively sudden learning year
+
+ align:start position:0%
+here relatively sudden learning year
+ 
+
+ align:start position:0%
+here relatively sudden learning year
+whereas if you pre train the network
+
+ align:start position:0%
+whereas if you pre train the network
+ 
+
+ align:start position:0%
+whereas if you pre train the network
+using greedy unsupervised learning right
+
+ align:start position:0%
+using greedy unsupervised learning right
+ 
+
+ align:start position:0%
+using greedy unsupervised learning right
+so this is the time it takes to pre
+
+ align:start position:0%
+so this is the time it takes to pre
+ 
+
+ align:start position:0%
+so this is the time it takes to pre
+train you get sudden learning in a drop
+
+ align:start position:0%
+train you get sudden learning in a drop
+ 
+
+ align:start position:0%
+train you get sudden learning in a drop
+here so remember if you go back to
+
+ align:start position:0%
+here so remember if you go back to
+ 
+
+ align:start position:0%
+here so remember if you go back to
+the original Hinton paper this was the
+
+ align:start position:0%
+the original Hinton paper this was the
+ 
+
+ align:start position:0%
+the original Hinton paper this was the
+phenomenon that started deep learning
+
+ align:start position:0%
+phenomenon that started deep learning
+ 
+
+ align:start position:0%
+phenomenon that started deep learning
+greedy unsupervised pre-training allows
+
+ align:start position:0%
+greedy unsupervised pre-training allows
+ 
+
+ align:start position:0%
+greedy unsupervised pre-training allows
+you to rapidly train very very deep
+
+ align:start position:0%
+you to rapidly train very very deep
+ 
+
+ align:start position:0%
+you to rapidly train very very deep
+neural networks so the very empirical
+
+ align:start position:0%
+neural networks so the very empirical
+ 
+
+ align:start position:0%
+neural networks so the very empirical
+phenomenon that led to the genesis of
+
+ align:start position:0%
+phenomenon that led to the genesis of
+ 
+
+ align:start position:0%
+phenomenon that led to the genesis of
+deep learning was present already in
+
+ align:start position:0%
+deep learning was present already in
+ 
+
+ align:start position:0%
+deep learning was present already in
+deep linear neural networks right so
+
+ align:start position:0%
+deep linear neural networks right so
+ 
+
+ align:start position:0%
+deep linear neural networks right so
+deeply linear neural networks in terms
+
+ align:start position:0%
+deeply linear neural networks in terms
+ 
+
+ align:start position:0%
+deeply linear neural networks in terms
+of their expressive power are crappy
+
+ align:start position:0%
+of their expressive power are crappy
+ 
+
+ align:start position:0%
+of their expressive power are crappy
+because the composition of linear
+
+ align:start position:0%
+because the composition of linear
+ 
+
+ align:start position:0%
+because the composition of linear
+operations is linear they're not good
+
+ align:start position:0%
+operations is linear they're not good
+ 
+
+ align:start position:0%
+operations is linear they're not good
+they're not a good model for deep
+
+ align:start position:0%
+they're not a good model for deep
+ 
+
+ align:start position:0%
+they're not a good model for deep
+nonlinear networks in terms of
+
+ align:start position:0%
+nonlinear networks in terms of
+ 
+
+ align:start position:0%
+nonlinear networks in terms of
+input-output mappings but they're a
+
+ align:start position:0%
+input-output mappings but they're a
+ 
+
+ align:start position:0%
+input-output mappings but they're a
+surprisingly good model theoretical toy
+
+ align:start position:0%
+surprisingly good model theoretical toy
+ 
+
+ align:start position:0%
+surprisingly good model theoretical toy
+model for modeling the dynamics of
+
+ align:start position:0%
+model for modeling the dynamics of
+ 
+
+ align:start position:0%
+model for modeling the dynamics of
+learning in nonlinear networks
+
+ align:start position:0%
+learning in nonlinear networks
+ 
+
+ align:start position:0%
+learning in nonlinear networks
+ok because because very important
+
+ align:start position:0%
+ok because because very important
+ 
+
+ align:start position:0%
+ok because because very important
+phenomena also arise in the deep linear
+
+ align:start position:0%
+phenomena also arise in the deep linear
+ 
+
+ align:start position:0%
+phenomena also arise in the deep linear
+networks and we're focusing on learning
+
+ align:start position:0%
+networks and we're focusing on learning
+ 
+
+ align:start position:0%
+networks and we're focusing on learning
+dynamics here ok so we can build
+
+ align:start position:0%
+dynamics here ok so we can build
+ 
+
+ align:start position:0%
+dynamics here ok so we can build
+intuitions for the nonlinear case by
+
+ align:start position:0%
+intuitions for the nonlinear case by
+ 
+
+ align:start position:0%
+intuitions for the nonlinear case by
+analyzing the linear case ok so we went
+
+ align:start position:0%
+analyzing the linear case ok so we went
+ 
+
+ align:start position:0%
+analyzing the linear case ok so we went
+through the three layer dynamics already
+
+ align:start position:0%
+through the three layer dynamics already
+ 
+
+ align:start position:0%
+through the three layer dynamics already
+what about the multiple layer dynamics
+
+ align:start position:0%
+what about the multiple layer dynamics
+ 
+
+ align:start position:0%
+what about the multiple layer dynamics
+so again the Jacobian can back
+
+ align:start position:0%
+so again the Jacobian can back
+ 
+
+ align:start position:0%
+so again the Jacobian can back
+propagator explode
+
+ align:start position:0%
+propagator explode
+ 
+
+ align:start position:0%
+propagator explode
+right so what we okay so again I'm going
+
+ align:start position:0%
+right so what we okay so again I'm going
+ 
+
+ align:start position:0%
+right so what we okay so again I'm going
+to make a long story short but what we
+
+ align:start position:0%
+to make a long story short but what we
+ 
+
+ align:start position:0%
+to make a long story short but what we
+find is that if you take what we tell
+
+ align:start position:0%
+find is that if you take what we tell
+ 
+
+ align:start position:0%
+find is that if you take what we tell
+you the final result what we find is
+
+ align:start position:0%
+you the final result what we find is
+ 
+
+ align:start position:0%
+you the final result what we find is
+that we find a class of weight
+
+ align:start position:0%
+that we find a class of weight
+ 
+
+ align:start position:0%
+that we find a class of weight
+initializations that allow learning time
+
+ align:start position:0%
+initializations that allow learning time
+ 
+
+ align:start position:0%
+initializations that allow learning time
+to remain constant as the depth of the
+
+ align:start position:0%
+to remain constant as the depth of the
+ 
+
+ align:start position:0%
+to remain constant as the depth of the
+network goes to infinity now I'm
+
+ align:start position:0%
+network goes to infinity now I'm
+ 
+
+ align:start position:0%
+network goes to infinity now I'm
+measuring learning time in units of
+
+ align:start position:0%
+measuring learning time in units of
+ 
+
+ align:start position:0%
+measuring learning time in units of
+learning epochs right so obviously to
+
+ align:start position:0%
+learning epochs right so obviously to
+ 
+
+ align:start position:0%
+learning epochs right so obviously to
+train a deep neural network very very
+
+ align:start position:0%
+train a deep neural network very very
+ 
+
+ align:start position:0%
+train a deep neural network very very
+deep neural network it just takes longer
+
+ align:start position:0%
+deep neural network it just takes longer
+ 
+
+ align:start position:0%
+deep neural network it just takes longer
+to compute each gradient right so in
+
+ align:start position:0%
+to compute each gradient right so in
+ 
+
+ align:start position:0%
+to compute each gradient right so in
+cutting in terms of real time of course
+
+ align:start position:0%
+cutting in terms of real time of course
+ 
+
+ align:start position:0%
+cutting in terms of real time of course
+the time will scale with the depth of
+
+ align:start position:0%
+the time will scale with the depth of
+ 
+
+ align:start position:0%
+the time will scale with the depth of
+the network but you might imagine in
+
+ align:start position:0%
+the network but you might imagine in
+ 
+
+ align:start position:0%
+the network but you might imagine in
+terms of number of gradient evaluations
+
+ align:start position:0%
+terms of number of gradient evaluations
+ 
+
+ align:start position:0%
+terms of number of gradient evaluations
+as the network gets deeper and deeper it
+
+ align:start position:0%
+as the network gets deeper and deeper it
+ 
+
+ align:start position:0%
+as the network gets deeper and deeper it
+might take longer and longer to train it
+
+ align:start position:0%
+might take longer and longer to train it
+ 
+
+ align:start position:0%
+might take longer and longer to train it
+and we show a class of initial
+
+ align:start position:0%
+and we show a class of initial
+ 
+
+ align:start position:0%
+and we show a class of initial
+conditions which that's not true as the
+
+ align:start position:0%
+conditions which that's not true as the
+ 
+
+ align:start position:0%
+conditions which that's not true as the
+as the network gets deeper and deeper
+
+ align:start position:0%
+as the network gets deeper and deeper
+ 
+
+ align:start position:0%
+as the network gets deeper and deeper
+the number of gradient evaluations you
+
+ align:start position:0%
+the number of gradient evaluations you
+ 
+
+ align:start position:0%
+the number of gradient evaluations you
+need to train the network can remain
+
+ align:start position:0%
+need to train the network can remain
+ 
+
+ align:start position:0%
+need to train the network can remain
+constant even as the depth goes to
+
+ align:start position:0%
+constant even as the depth goes to
+ 
+
+ align:start position:0%
+constant even as the depth goes to
+infinity okay even in a nonlinear
+
+ align:start position:0%
+infinity okay even in a nonlinear
+ 
+
+ align:start position:0%
+infinity okay even in a nonlinear
+network ok so let me give you the
+
+ align:start position:0%
+network ok so let me give you the
+ 
+
+ align:start position:0%
+network ok so let me give you the
+intuition for why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for example we okay and the
+
+ align:start position:0%
+okay so for example we okay and the
+ 
+
+ align:start position:0%
+okay so for example we okay and the
+classical initialization this the
+
+ align:start position:0%
+classical initialization this the
+ 
+
+ align:start position:0%
+classical initialization this the
+scleral and Benjy initialization doesn't
+
+ align:start position:0%
+scleral and Benjy initialization doesn't
+ 
+
+ align:start position:0%
+scleral and Benjy initialization doesn't
+have that but our initialization does so
+
+ align:start position:0%
+have that but our initialization does so
+ 
+
+ align:start position:0%
+have that but our initialization does so
+basically what we did was we'll start
+
+ align:start position:0%
+basically what we did was we'll start
+ 
+
+ align:start position:0%
+basically what we did was we'll start
+off with the linear networks we trained
+
+ align:start position:0%
+off with the linear networks we trained
+ 
+
+ align:start position:0%
+off with the linear networks we trained
+deep linear networks on M NIST and we
+
+ align:start position:0%
+deep linear networks on M NIST and we
+ 
+
+ align:start position:0%
+deep linear networks on M NIST and we
+scaled the depth like this right and we
+
+ align:start position:0%
+scaled the depth like this right and we
+ 
+
+ align:start position:0%
+scaled the depth like this right and we
+started with random Gaussian initial
+
+ align:start position:0%
+started with random Gaussian initial
+ 
+
+ align:start position:0%
+started with random Gaussian initial
+conditions and then ran back propagation
+
+ align:start position:0%
+conditions and then ran back propagation
+ 
+
+ align:start position:0%
+conditions and then ran back propagation
+but scaled random - the notion was
+
+ align:start position:0%
+but scaled random - the notion was
+ 
+
+ align:start position:0%
+but scaled random - the notion was
+random Gaussian initializations and we
+
+ align:start position:0%
+random Gaussian initializations and we
+ 
+
+ align:start position:0%
+random Gaussian initializations and we
+found that the training time as you
+
+ align:start position:0%
+found that the training time as you
+ 
+
+ align:start position:0%
+found that the training time as you
+might expect grew with depth this is
+
+ align:start position:0%
+might expect grew with depth this is
+ 
+
+ align:start position:0%
+might expect grew with depth this is
+training time measured a number of
+
+ align:start position:0%
+training time measured a number of
+ 
+
+ align:start position:0%
+training time measured a number of
+learning a box or a number of gradient
+
+ align:start position:0%
+learning a box or a number of gradient
+ 
+
+ align:start position:0%
+learning a box or a number of gradient
+evaluations but here what we did was we
+
+ align:start position:0%
+evaluations but here what we did was we
+ 
+
+ align:start position:0%
+evaluations but here what we did was we
+initialize the weights using random
+
+ align:start position:0%
+initialize the weights using random
+ 
+
+ align:start position:0%
+initialize the weights using random
+orthogonal weights right and then we
+
+ align:start position:0%
+orthogonal weights right and then we
+ 
+
+ align:start position:0%
+orthogonal weights right and then we
+found that the learning time didn't grow
+
+ align:start position:0%
+found that the learning time didn't grow
+ 
+
+ align:start position:0%
+found that the learning time didn't grow
+with depth and also if you pre train it
+
+ align:start position:0%
+with depth and also if you pre train it
+ 
+
+ align:start position:0%
+with depth and also if you pre train it
+it doesn't grow with depth okay so
+
+ align:start position:0%
+it doesn't grow with depth okay so
+ 
+
+ align:start position:0%
+it doesn't grow with depth okay so
+there's a dramatically different scaling
+
+ align:start position:0%
+there's a dramatically different scaling
+ 
+
+ align:start position:0%
+there's a dramatically different scaling
+and learning time between random
+
+ align:start position:0%
+and learning time between random
+ 
+
+ align:start position:0%
+and learning time between random
+Gaussian initialization and random
+
+ align:start position:0%
+Gaussian initialization and random
+ 
+
+ align:start position:0%
+Gaussian initialization and random
+orthogonal initialization why okay and
+
+ align:start position:0%
+orthogonal initialization why okay and
+ 
+
+ align:start position:0%
+orthogonal initialization why okay and
+the answer is the following right let's
+
+ align:start position:0%
+the answer is the following right let's
+ 
+
+ align:start position:0%
+the answer is the following right let's
+think about the back propagation
+
+ align:start position:0%
+think about the back propagation
+ 
+
+ align:start position:0%
+think about the back propagation
+operator let's say you want to back
+
+ align:start position:0%
+operator let's say you want to back
+ 
+
+ align:start position:0%
+operator let's say you want to back
+propagate errors from the output to the
+
+ align:start position:0%
+propagate errors from the output to the
+ 
+
+ align:start position:0%
+propagate errors from the output to the
+input right so the the back propagation
+
+ align:start position:0%
+input right so the the back propagation
+ 
+
+ align:start position:0%
+input right so the the back propagation
+operated in a linear network right it's
+
+ align:start position:0%
+operated in a linear network right it's
+ 
+
+ align:start position:0%
+operated in a linear network right it's
+just the product of weights throughout
+
+ align:start position:0%
+just the product of weights throughout
+ 
+
+ align:start position:0%
+just the product of weights throughout
+the entire network okay
+
+ align:start position:0%
+the entire network okay
+ 
+
+ align:start position:0%
+the entire network okay
+so so your your so the back if you do a
+
+ align:start position:0%
+so so your your so the back if you do a
+ 
+
+ align:start position:0%
+so so your your so the back if you do a
+random weight random Gaussian weight
+
+ align:start position:0%
+random weight random Gaussian weight
+ 
+
+ align:start position:0%
+random weight random Gaussian weight
+initialization here then the this is a
+
+ align:start position:0%
+initialization here then the this is a
+ 
+
+ align:start position:0%
+initialization here then the this is a
+product of random Gaussian matrices so
+
+ align:start position:0%
+product of random Gaussian matrices so
+ 
+
+ align:start position:0%
+product of random Gaussian matrices so
+to understand the statistical properties
+
+ align:start position:0%
+to understand the statistical properties
+ 
+
+ align:start position:0%
+to understand the statistical properties
+of back propagation you need to
+
+ align:start position:0%
+of back propagation you need to
+ 
+
+ align:start position:0%
+of back propagation you need to
+understand the statistical properties of
+
+ align:start position:0%
+understand the statistical properties of
+ 
+
+ align:start position:0%
+understand the statistical properties of
+the singular value spectrum of random
+
+ align:start position:0%
+the singular value spectrum of random
+ 
+
+ align:start position:0%
+the singular value spectrum of random
+Gaussian matrices there isn't really a
+
+ align:start position:0%
+Gaussian matrices there isn't really a
+ 
+
+ align:start position:0%
+Gaussian matrices there isn't really a
+general theory for that but we can look
+
+ align:start position:0%
+general theory for that but we can look
+ 
+
+ align:start position:0%
+general theory for that but we can look
+at it numerically and get intuition for
+
+ align:start position:0%
+at it numerically and get intuition for
+ 
+
+ align:start position:0%
+at it numerically and get intuition for
+it so the basic idea is if you have one
+
+ align:start position:0%
+it so the basic idea is if you have one
+ 
+
+ align:start position:0%
+it so the basic idea is if you have one
+random Gaussian matrix right the
+
+ align:start position:0%
+random Gaussian matrix right the
+ 
+
+ align:start position:0%
+random Gaussian matrix right the
+singular values of W are the are the
+
+ align:start position:0%
+singular values of W are the are the
+ 
+
+ align:start position:0%
+singular values of W are the are the
+eigen values of W transpose W that's a
+
+ align:start position:0%
+eigen values of W transpose W that's a
+ 
+
+ align:start position:0%
+eigen values of W transpose W that's a
+famous distribution called the Marcinko
+
+ align:start position:0%
+famous distribution called the Marcinko
+ 
+
+ align:start position:0%
+famous distribution called the Marcinko
+posterior distribution and you know
+
+ align:start position:0%
+posterior distribution and you know
+ 
+
+ align:start position:0%
+posterior distribution and you know
+they're they vary in a range that's
+
+ align:start position:0%
+they're they vary in a range that's
+ 
+
+ align:start position:0%
+they're they vary in a range that's
+order one okay so if you're back
+
+ align:start position:0%
+order one okay so if you're back
+ 
+
+ align:start position:0%
+order one okay so if you're back
+propagate through one layer you're fine
+
+ align:start position:0%
+propagate through one layer you're fine
+ 
+
+ align:start position:0%
+propagate through one layer you're fine
+right you don't get vanishing x1
+
+ align:start position:0%
+right you don't get vanishing x1
+ 
+
+ align:start position:0%
+right you don't get vanishing x1
+ingredients okay but if you if you look
+
+ align:start position:0%
+ingredients okay but if you if you look
+ 
+
+ align:start position:0%
+ingredients okay but if you if you look
+at the singular values of a product of
+
+ align:start position:0%
+at the singular values of a product of
+ 
+
+ align:start position:0%
+at the singular values of a product of
+five random Gaussian matrices the
+
+ align:start position:0%
+five random Gaussian matrices the
+ 
+
+ align:start position:0%
+five random Gaussian matrices the
+singular value per spectrum gets very
+
+ align:start position:0%
+singular value per spectrum gets very
+ 
+
+ align:start position:0%
+singular value per spectrum gets very
+distorted
+
+ align:start position:0%
+distorted
+ 
+
+ align:start position:0%
+distorted
+you get a large number of single values
+
+ align:start position:0%
+you get a large number of single values
+ 
+
+ align:start position:0%
+you get a large number of single values
+that are that are close to zero and a
+
+ align:start position:0%
+that are that are close to zero and a
+ 
+
+ align:start position:0%
+that are that are close to zero and a
+long tail that you know extends up to
+
+ align:start position:0%
+long tail that you know extends up to
+ 
+
+ align:start position:0%
+long tail that you know extends up to
+four okay but if you if you do a hundred
+
+ align:start position:0%
+four okay but if you if you do a hundred
+ 
+
+ align:start position:0%
+four okay but if you if you do a hundred
+layers you get a very very large number
+
+ align:start position:0%
+layers you get a very very large number
+ 
+
+ align:start position:0%
+layers you get a very very large number
+of singular values that are close to
+
+ align:start position:0%
+of singular values that are close to
+ 
+
+ align:start position:0%
+of singular values that are close to
+zero and a very much longer tail okay
+
+ align:start position:0%
+zero and a very much longer tail okay
+ 
+
+ align:start position:0%
+zero and a very much longer tail okay
+now these this is a product of random
+
+ align:start position:0%
+now these this is a product of random
+ 
+
+ align:start position:0%
+now these this is a product of random
+Gaussian matrices so if you feed a
+
+ align:start position:0%
+Gaussian matrices so if you feed a
+ 
+
+ align:start position:0%
+Gaussian matrices so if you feed a
+random vector into this on average its
+
+ align:start position:0%
+random vector into this on average its
+ 
+
+ align:start position:0%
+random vector into this on average its
+norm will be preserved
+
+ align:start position:0%
+norm will be preserved
+ 
+
+ align:start position:0%
+norm will be preserved
+the vectors length will not change but
+
+ align:start position:0%
+the vectors length will not change but
+ 
+
+ align:start position:0%
+the vectors length will not change but
+we know that preserving the length of a
+
+ align:start position:0%
+we know that preserving the length of a
+ 
+
+ align:start position:0%
+we know that preserving the length of a
+vector is not the same as preserving
+
+ align:start position:0%
+vector is not the same as preserving
+ 
+
+ align:start position:0%
+vector is not the same as preserving
+angles between all pairs of vectors okay
+
+ align:start position:0%
+angles between all pairs of vectors okay
+ 
+
+ align:start position:0%
+angles between all pairs of vectors okay
+so actually the way that this network
+
+ align:start position:0%
+so actually the way that this network
+ 
+
+ align:start position:0%
+so actually the way that this network
+that the way that this product of random
+
+ align:start position:0%
+that the way that this product of random
+ 
+
+ align:start position:0%
+that the way that this product of random
+Gaussian matrices preserves the norm of
+
+ align:start position:0%
+Gaussian matrices preserves the norm of
+ 
+
+ align:start position:0%
+Gaussian matrices preserves the norm of
+the gradient is it does it in a very
+
+ align:start position:0%
+the gradient is it does it in a very
+ 
+
+ align:start position:0%
+the gradient is it does it in a very
+anisotropic way it takes an error vector
+
+ align:start position:0%
+anisotropic way it takes an error vector
+ 
+
+ align:start position:0%
+anisotropic way it takes an error vector
+at the output and it projects it into a
+
+ align:start position:0%
+at the output and it projects it into a
+ 
+
+ align:start position:0%
+at the output and it projects it into a
+low dimensional space corresponding to
+
+ align:start position:0%
+low dimensional space corresponding to
+ 
+
+ align:start position:0%
+low dimensional space corresponding to
+the singular values that are large and
+
+ align:start position:0%
+the singular values that are large and
+ 
+
+ align:start position:0%
+the singular values that are large and
+then it amplifies it in that space so
+
+ align:start position:0%
+then it amplifies it in that space so
+ 
+
+ align:start position:0%
+then it amplifies it in that space so
+the length is preserved but all error
+
+ align:start position:0%
+the length is preserved but all error
+ 
+
+ align:start position:0%
+the length is preserved but all error
+vectors get projected onto a low
+
+ align:start position:0%
+vectors get projected onto a low
+ 
+
+ align:start position:0%
+vectors get projected onto a low
+dimensional space and amplified so a lot
+
+ align:start position:0%
+dimensional space and amplified so a lot
+ 
+
+ align:start position:0%
+dimensional space and amplified so a lot
+of error information is lost in a
+
+ align:start position:0%
+of error information is lost in a
+ 
+
+ align:start position:0%
+of error information is lost in a
+product of random Gaussian matrices okay
+
+ align:start position:0%
+product of random Gaussian matrices okay
+ 
+
+ align:start position:0%
+product of random Gaussian matrices okay
+so that's why the Gloria and Benjy
+
+ align:start position:0%
+so that's why the Gloria and Benjy
+ 
+
+ align:start position:0%
+so that's why the Gloria and Benjy
+initial conditions work well up to depth
+
+ align:start position:0%
+initial conditions work well up to depth
+ 
+
+ align:start position:0%
+initial conditions work well up to depth
+five or six or seven but they don't work
+
+ align:start position:0%
+five or six or seven but they don't work
+ 
+
+ align:start position:0%
+five or six or seven but they don't work
+well up to depths say a hundred or in
+
+ align:start position:0%
+well up to depths say a hundred or in
+ 
+
+ align:start position:0%
+well up to depths say a hundred or in
+recurrent neural networks as well okay
+
+ align:start position:0%
+recurrent neural networks as well okay
+ 
+
+ align:start position:0%
+recurrent neural networks as well okay
+so so what can we do well a simple thing
+
+ align:start position:0%
+so so what can we do well a simple thing
+ 
+
+ align:start position:0%
+so so what can we do well a simple thing
+we can do is we can replace the the
+
+ align:start position:0%
+we can do is we can replace the the
+ 
+
+ align:start position:0%
+we can do is we can replace the the
+matrices these random matrices with a
+
+ align:start position:0%
+matrices these random matrices with a
+ 
+
+ align:start position:0%
+matrices these random matrices with a
+fog '''l matrices okay so we know that
+
+ align:start position:0%
+fog '''l matrices okay so we know that
+ 
+
+ align:start position:0%
+fog '''l matrices okay so we know that
+all the singular values of an orthogonal
+
+ align:start position:0%
+all the singular values of an orthogonal
+ 
+
+ align:start position:0%
+all the singular values of an orthogonal
+matrix are one every single one and the
+
+ align:start position:0%
+matrix are one every single one and the
+ 
+
+ align:start position:0%
+matrix are one every single one and the
+product of orthogonal matrices is
+
+ align:start position:0%
+product of orthogonal matrices is
+ 
+
+ align:start position:0%
+product of orthogonal matrices is
+orthogonal so therefore the back
+
+ align:start position:0%
+orthogonal so therefore the back
+ 
+
+ align:start position:0%
+orthogonal so therefore the back
+propagation operator has all of its
+
+ align:start position:0%
+propagation operator has all of its
+ 
+
+ align:start position:0%
+propagation operator has all of its
+singular values equal to 1 and there's
+
+ align:start position:0%
+singular values equal to 1 and there's
+ 
+
+ align:start position:0%
+singular values equal to 1 and there's
+generalizations of orthogonal matrices
+
+ align:start position:0%
+generalizations of orthogonal matrices
+ 
+
+ align:start position:0%
+generalizations of orthogonal matrices
+to two rectangular versions when when
+
+ align:start position:0%
+to two rectangular versions when when
+ 
+
+ align:start position:0%
+to two rectangular versions when when
+the layers don't have the same number of
+
+ align:start position:0%
+the layers don't have the same number of
+ 
+
+ align:start position:0%
+the layers don't have the same number of
+neurons in each layer okay so this is
+
+ align:start position:0%
+neurons in each layer okay so this is
+ 
+
+ align:start position:0%
+neurons in each layer okay so this is
+fantastic so this works really well for
+
+ align:start position:0%
+fantastic so this works really well for
+ 
+
+ align:start position:0%
+fantastic so this works really well for
+linear networks okay but how does this
+
+ align:start position:0%
+linear networks okay but how does this
+ 
+
+ align:start position:0%
+linear networks okay but how does this
+generalize to non linear networks
+
+ align:start position:0%
+generalize to non linear networks
+ 
+
+ align:start position:0%
+generalize to non linear networks
+because then you have a product of
+
+ align:start position:0%
+because then you have a product of
+ 
+
+ align:start position:0%
+because then you have a product of
+jacobians right so what happens here
+
+ align:start position:0%
+jacobians right so what happens here
+ 
+
+ align:start position:0%
+jacobians right so what happens here
+okay so what is that what is the the
+
+ align:start position:0%
+okay so what is that what is the the
+ 
+
+ align:start position:0%
+okay so what is that what is the the
+product of Jacobian so what you have is
+
+ align:start position:0%
+product of Jacobian so what you have is
+ 
+
+ align:start position:0%
+product of Jacobian so what you have is
+you have a so if we imagine how if we
+
+ align:start position:0%
+you have a so if we imagine how if we
+ 
+
+ align:start position:0%
+you have a so if we imagine how if we
+imagine how either errors back propagate
+
+ align:start position:0%
+imagine how either errors back propagate
+ 
+
+ align:start position:0%
+imagine how either errors back propagate
+to the front or how input perturbations
+
+ align:start position:0%
+to the front or how input perturbations
+ 
+
+ align:start position:0%
+to the front or how input perturbations
+back propagate
+
+ align:start position:0%
+back propagate
+ 
+
+ align:start position:0%
+back propagate
+to the to the end right it's the same
+
+ align:start position:0%
+to the to the end right it's the same
+ 
+
+ align:start position:0%
+to the to the end right it's the same
+thing so it's easier to think about
+
+ align:start position:0%
+thing so it's easier to think about
+ 
+
+ align:start position:0%
+thing so it's easier to think about
+forward propagation imagine that you
+
+ align:start position:0%
+forward propagation imagine that you
+ 
+
+ align:start position:0%
+forward propagation imagine that you
+have an input and you perturb it
+
+ align:start position:0%
+have an input and you perturb it
+ 
+
+ align:start position:0%
+have an input and you perturb it
+slightly how does the perturbation grow
+
+ align:start position:0%
+slightly how does the perturbation grow
+ 
+
+ align:start position:0%
+slightly how does the perturbation grow
+or decay well what happens is there's a
+
+ align:start position:0%
+or decay well what happens is there's a
+ 
+
+ align:start position:0%
+or decay well what happens is there's a
+linear expansion or contraction due to W
+
+ align:start position:0%
+linear expansion or contraction due to W
+ 
+
+ align:start position:0%
+linear expansion or contraction due to W
+and then this this nominator is usually
+
+ align:start position:0%
+and then this this nominator is usually
+ 
+
+ align:start position:0%
+and then this this nominator is usually
+compressive so there's a nonlinear
+
+ align:start position:0%
+compressive so there's a nonlinear
+ 
+
+ align:start position:0%
+compressive so there's a nonlinear
+compression due to the Jacobian passes
+
+ align:start position:0%
+compression due to the Jacobian passes
+ 
+
+ align:start position:0%
+compression due to the Jacobian passes
+at the diagonal Jacobian passing through
+
+ align:start position:0%
+at the diagonal Jacobian passing through
+ 
+
+ align:start position:0%
+at the diagonal Jacobian passing through
+the point wise non-linearity and then
+
+ align:start position:0%
+the point wise non-linearity and then
+ 
+
+ align:start position:0%
+the point wise non-linearity and then
+again linear modification and nonlinear
+
+ align:start position:0%
+again linear modification and nonlinear
+ 
+
+ align:start position:0%
+again linear modification and nonlinear
+compression linear modification
+
+ align:start position:0%
+compression linear modification
+ 
+
+ align:start position:0%
+compression linear modification
+nonlinear compression okay so what we
+
+ align:start position:0%
+nonlinear compression okay so what we
+ 
+
+ align:start position:0%
+nonlinear compression okay so what we
+could do is just simply choose these
+
+ align:start position:0%
+could do is just simply choose these
+ 
+
+ align:start position:0%
+could do is just simply choose these
+again to be random orthogonal matrices
+
+ align:start position:0%
+again to be random orthogonal matrices
+ 
+
+ align:start position:0%
+again to be random orthogonal matrices
+and then what happens is the growth or
+
+ align:start position:0%
+and then what happens is the growth or
+ 
+
+ align:start position:0%
+and then what happens is the growth or
+decay of perturbations is and we scale
+
+ align:start position:0%
+decay of perturbations is and we scale
+ 
+
+ align:start position:0%
+decay of perturbations is and we scale
+the we scale the random Gauss image the
+
+ align:start position:0%
+the we scale the random Gauss image the
+ 
+
+ align:start position:0%
+the we scale the random Gauss image the
+random orthogonal matrices by a scale
+
+ align:start position:0%
+random orthogonal matrices by a scale
+ 
+
+ align:start position:0%
+random orthogonal matrices by a scale
+factor to combat the nominee or
+
+ align:start position:0%
+factor to combat the nominee or
+ 
+
+ align:start position:0%
+factor to combat the nominee or
+compression and then the dynamics of
+
+ align:start position:0%
+compression and then the dynamics of
+ 
+
+ align:start position:0%
+compression and then the dynamics of
+perturbations is like this you rotate
+
+ align:start position:0%
+perturbations is like this you rotate
+ 
+
+ align:start position:0%
+perturbations is like this you rotate
+linearly scale non linearly compressed
+
+ align:start position:0%
+linearly scale non linearly compressed
+ 
+
+ align:start position:0%
+linearly scale non linearly compressed
+rotate linearly scale nonlinear compress
+
+ align:start position:0%
+rotate linearly scale nonlinear compress
+ 
+
+ align:start position:0%
+rotate linearly scale nonlinear compress
+and so on that's essentially the type of
+
+ align:start position:0%
+and so on that's essentially the type of
+ 
+
+ align:start position:0%
+and so on that's essentially the type of
+dynamics that occurs in in dynamically
+
+ align:start position:0%
+dynamics that occurs in in dynamically
+ 
+
+ align:start position:0%
+dynamics that occurs in in dynamically
+critical systems that are close to the
+
+ align:start position:0%
+critical systems that are close to the
+ 
+
+ align:start position:0%
+critical systems that are close to the
+edge of chaos you get this alternating
+
+ align:start position:0%
+edge of chaos you get this alternating
+ 
+
+ align:start position:0%
+edge of chaos you get this alternating
+phase space expansion and compression
+
+ align:start position:0%
+phase space expansion and compression
+ 
+
+ align:start position:0%
+phase space expansion and compression
+that's in different dimensions at
+
+ align:start position:0%
+that's in different dimensions at
+ 
+
+ align:start position:0%
+that's in different dimensions at
+different times okay so now you can just
+
+ align:start position:0%
+different times okay so now you can just
+ 
+
+ align:start position:0%
+different times okay so now you can just
+compute numerically under that
+
+ align:start position:0%
+compute numerically under that
+ 
+
+ align:start position:0%
+compute numerically under that
+initialization how does the product of
+
+ align:start position:0%
+initialization how does the product of
+ 
+
+ align:start position:0%
+initialization how does the product of
+Jib how does a singular value spectrum
+
+ align:start position:0%
+Jib how does a singular value spectrum
+ 
+
+ align:start position:0%
+Jib how does a singular value spectrum
+the product of Jacobian scale and it
+
+ align:start position:0%
+the product of Jacobian scale and it
+ 
+
+ align:start position:0%
+the product of Jacobian scale and it
+scales beautifully so this is the scale
+
+ align:start position:0%
+scales beautifully so this is the scale
+ 
+
+ align:start position:0%
+scales beautifully so this is the scale
+factor for the type of non-linearity
+
+ align:start position:0%
+factor for the type of non-linearity
+ 
+
+ align:start position:0%
+factor for the type of non-linearity
+that we used the hyperbolic tangent
+
+ align:start position:0%
+that we used the hyperbolic tangent
+ 
+
+ align:start position:0%
+that we used the hyperbolic tangent
+non-linearity the optimal scale factor
+
+ align:start position:0%
+non-linearity the optimal scale factor
+ 
+
+ align:start position:0%
+non-linearity the optimal scale factor
+in front of the random orthogonal matrix
+
+ align:start position:0%
+in front of the random orthogonal matrix
+ 
+
+ align:start position:0%
+in front of the random orthogonal matrix
+is 1 and you see when you choose that
+
+ align:start position:0%
+is 1 and you see when you choose that
+ 
+
+ align:start position:0%
+is 1 and you see when you choose that
+even for this was a hundred layers I
+
+ align:start position:0%
+even for this was a hundred layers I
+ 
+
+ align:start position:0%
+even for this was a hundred layers I
+believe even for a hundred layers the
+
+ align:start position:0%
+believe even for a hundred layers the
+ 
+
+ align:start position:0%
+believe even for a hundred layers the
+end-to-end Jacobian from the input to
+
+ align:start position:0%
+end-to-end Jacobian from the input to
+ 
+
+ align:start position:0%
+end-to-end Jacobian from the input to
+output has a singular value spectrum
+
+ align:start position:0%
+output has a singular value spectrum
+ 
+
+ align:start position:0%
+output has a singular value spectrum
+that remains within a range of order one
+
+ align:start position:0%
+that remains within a range of order one
+ 
+
+ align:start position:0%
+that remains within a range of order one
+if G is even slightly less than one the
+
+ align:start position:0%
+if G is even slightly less than one the
+ 
+
+ align:start position:0%
+if G is even slightly less than one the
+singular values exponentially vanished
+
+ align:start position:0%
+singular values exponentially vanished
+ 
+
+ align:start position:0%
+singular values exponentially vanished
+with depth if G is larger than one the
+
+ align:start position:0%
+with depth if G is larger than one the
+ 
+
+ align:start position:0%
+with depth if G is larger than one the
+singular values grow but actually not
+
+ align:start position:0%
+singular values grow but actually not
+ 
+
+ align:start position:0%
+singular values grow but actually not
+not as as quickly as you'd think so this
+
+ align:start position:0%
+not as as quickly as you'd think so this
+ 
+
+ align:start position:0%
+not as as quickly as you'd think so this
+is the the critically dynamical regime
+
+ align:start position:0%
+is the the critically dynamical regime
+ 
+
+ align:start position:0%
+is the the critically dynamical regime
+that at least preserves not only the
+
+ align:start position:0%
+that at least preserves not only the
+ 
+
+ align:start position:0%
+that at least preserves not only the
+norm of back propagated gradients but
+
+ align:start position:0%
+norm of back propagated gradients but
+ 
+
+ align:start position:0%
+norm of back propagated gradients but
+all angles between pairs of gradients
+
+ align:start position:0%
+all angles between pairs of gradients
+ 
+
+ align:start position:0%
+all angles between pairs of gradients
+right so it's an isotropic isotropic
+
+ align:start position:0%
+right so it's an isotropic isotropic
+ 
+
+ align:start position:0%
+right so it's an isotropic isotropic
+preservation of error information from
+
+ align:start position:0%
+preservation of error information from
+ 
+
+ align:start position:0%
+preservation of error information from
+the end of the network all the way to
+
+ align:start position:0%
+the end of the network all the way to
+ 
+
+ align:start position:0%
+the end of the network all the way to
+the beginning ok
+
+ align:start position:0%
+the beginning ok
+ 
+
+ align:start position:0%
+the beginning ok
+so does it work and it works better than
+
+ align:start position:0%
+so does it work and it works better than
+ 
+
+ align:start position:0%
+so does it work and it works better than
+other initializations even in nonlinear
+
+ align:start position:0%
+other initializations even in nonlinear
+ 
+
+ align:start position:0%
+other initializations even in nonlinear
+Network so we trained 30 layer nonlinear
+
+ align:start position:0%
+Network so we trained 30 layer nonlinear
+ 
+
+ align:start position:0%
+Network so we trained 30 layer nonlinear
+networks and the initialization works
+
+ align:start position:0%
+networks and the initialization works
+ 
+
+ align:start position:0%
+networks and the initialization works
+better and and so also interestingly
+
+ align:start position:0%
+better and and so also interestingly
+ 
+
+ align:start position:0%
+better and and so also interestingly
+enough at this critical factor you also
+
+ align:start position:0%
+enough at this critical factor you also
+ 
+
+ align:start position:0%
+enough at this critical factor you also
+achieve better generalization error and
+
+ align:start position:0%
+achieve better generalization error and
+ 
+
+ align:start position:0%
+achieve better generalization error and
+we don't have a good theory for that
+
+ align:start position:0%
+we don't have a good theory for that
+ 
+
+ align:start position:0%
+we don't have a good theory for that
+actually the test error and the training
+
+ align:start position:0%
+actually the test error and the training
+ 
+
+ align:start position:0%
+actually the test error and the training
+error of course goes goes down so okay
+
+ align:start position:0%
+error of course goes goes down so okay
+ 
+
+ align:start position:0%
+error of course goes goes down so okay
+so that's an interesting situation where
+
+ align:start position:0%
+so that's an interesting situation where
+ 
+
+ align:start position:0%
+so that's an interesting situation where
+a theory of linear networks led to a
+
+ align:start position:0%
+a theory of linear networks led to a
+ 
+
+ align:start position:0%
+a theory of linear networks led to a
+practical training advantage for
+
+ align:start position:0%
+practical training advantage for
+ 
+
+ align:start position:0%
+practical training advantage for
+nonlinear networks ok so here's another
+
+ align:start position:0%
+nonlinear networks ok so here's another
+ 
+
+ align:start position:0%
+nonlinear networks ok so here's another
+question that we had ok there's a whole
+
+ align:start position:0%
+question that we had ok there's a whole
+ 
+
+ align:start position:0%
+question that we had ok there's a whole
+like world of convex optimization we
+
+ align:start position:0%
+like world of convex optimization we
+ 
+
+ align:start position:0%
+like world of convex optimization we
+want our machine learning algorithms to
+
+ align:start position:0%
+want our machine learning algorithms to
+ 
+
+ align:start position:0%
+want our machine learning algorithms to
+correspond to convex optimization so we
+
+ align:start position:0%
+correspond to convex optimization so we
+ 
+
+ align:start position:0%
+correspond to convex optimization so we
+can find the global minimum and there
+
+ align:start position:0%
+can find the global minimum and there
+ 
+
+ align:start position:0%
+can find the global minimum and there
+are no local minima to impede us from
+
+ align:start position:0%
+are no local minima to impede us from
+ 
+
+ align:start position:0%
+are no local minima to impede us from
+finding the global minimum
+
+ align:start position:0%
+finding the global minimum
+ 
+
+ align:start position:0%
+finding the global minimum
+all right that's a conventional wisdom
+
+ align:start position:0%
+all right that's a conventional wisdom
+ 
+
+ align:start position:0%
+all right that's a conventional wisdom
+yet the deep neural network people
+
+ align:start position:0%
+yet the deep neural network people
+ 
+
+ align:start position:0%
+yet the deep neural network people
+ignore this conventional wisdom and
+
+ align:start position:0%
+ignore this conventional wisdom and
+ 
+
+ align:start position:0%
+ignore this conventional wisdom and
+train very very deep neural networks and
+
+ align:start position:0%
+train very very deep neural networks and
+ 
+
+ align:start position:0%
+train very very deep neural networks and
+don't worry about the potential
+
+ align:start position:0%
+don't worry about the potential
+ 
+
+ align:start position:0%
+don't worry about the potential
+impediments to local minima they seem to
+
+ align:start position:0%
+impediments to local minima they seem to
+ 
+
+ align:start position:0%
+impediments to local minima they seem to
+find pretty good solutions why ok is the
+
+ align:start position:0%
+find pretty good solutions why ok is the
+ 
+
+ align:start position:0%
+find pretty good solutions why ok is the
+intuition that local minima are really
+
+ align:start position:0%
+intuition that local minima are really
+ 
+
+ align:start position:0%
+intuition that local minima are really
+an impediment to nonlinear caught non
+
+ align:start position:0%
+an impediment to nonlinear caught non
+ 
+
+ align:start position:0%
+an impediment to nonlinear caught non
+convex optimization in high dimensional
+
+ align:start position:0%
+convex optimization in high dimensional
+ 
+
+ align:start position:0%
+convex optimization in high dimensional
+spaces really true ok and you might
+
+ align:start position:0%
+spaces really true ok and you might
+ 
+
+ align:start position:0%
+spaces really true ok and you might
+think that it's not true for the
+
+ align:start position:0%
+think that it's not true for the
+ 
+
+ align:start position:0%
+think that it's not true for the
+following intuitive reason right so
+
+ align:start position:0%
+following intuitive reason right so
+ 
+
+ align:start position:0%
+following intuitive reason right so
+again it's often thought the local
+
+ align:start position:0%
+again it's often thought the local
+ 
+
+ align:start position:0%
+again it's often thought the local
+minima at some high level of error in
+
+ align:start position:0%
+minima at some high level of error in
+ 
+
+ align:start position:0%
+minima at some high level of error in
+training error stand is a major
+
+ align:start position:0%
+training error stand is a major
+ 
+
+ align:start position:0%
+training error stand is a major
+impediment to non convex optimization
+
+ align:start position:0%
+impediment to non convex optimization
+ 
+
+ align:start position:0%
+impediment to non convex optimization
+ok and you know this is an example a
+
+ align:start position:0%
+ok and you know this is an example a
+ 
+
+ align:start position:0%
+ok and you know this is an example a
+two-dimensional caricature of a protein
+
+ align:start position:0%
+two-dimensional caricature of a protein
+ 
+
+ align:start position:0%
+two-dimensional caricature of a protein
+folding energy landscape and it's very
+
+ align:start position:0%
+folding energy landscape and it's very
+ 
+
+ align:start position:0%
+folding energy landscape and it's very
+rough so there's many many local minima
+
+ align:start position:0%
+rough so there's many many local minima
+ 
+
+ align:start position:0%
+rough so there's many many local minima
+and and the global minimum might be hard
+
+ align:start position:0%
+and and the global minimum might be hard
+ 
+
+ align:start position:0%
+and and the global minimum might be hard
+to find and that's true if you sort of
+
+ align:start position:0%
+to find and that's true if you sort of
+ 
+
+ align:start position:0%
+to find and that's true if you sort of
+draw a random generic surfaces over low
+
+ align:start position:0%
+draw a random generic surfaces over low
+ 
+
+ align:start position:0%
+draw a random generic surfaces over low
+dimensions those random surfaces will
+
+ align:start position:0%
+dimensions those random surfaces will
+ 
+
+ align:start position:0%
+dimensions those random surfaces will
+have many local minima but of course our
+
+ align:start position:0%
+have many local minima but of course our
+ 
+
+ align:start position:0%
+have many local minima but of course our
+intuition about geometry derived from
+
+ align:start position:0%
+intuition about geometry derived from
+ 
+
+ align:start position:0%
+intuition about geometry derived from
+our experience with a low dimensional
+
+ align:start position:0%
+our experience with a low dimensional
+ 
+
+ align:start position:0%
+our experience with a low dimensional
+world is woefully inadequate for
+
+ align:start position:0%
+world is woefully inadequate for
+ 
+
+ align:start position:0%
+world is woefully inadequate for
+thinking about geometry in high
+
+ align:start position:0%
+thinking about geometry in high
+ 
+
+ align:start position:0%
+thinking about geometry in high
+dimensional spaces ok so it turns out
+
+ align:start position:0%
+dimensional spaces ok so it turns out
+ 
+
+ align:start position:0%
+dimensional spaces ok so it turns out
+that random non convex error functions
+
+ align:start position:0%
+that random non convex error functions
+ 
+
+ align:start position:0%
+that random non convex error functions
+over high dimensional spaces local
+
+ align:start position:0%
+over high dimensional spaces local
+ 
+
+ align:start position:0%
+over high dimensional spaces local
+minima are sort of exponentially rare in
+
+ align:start position:0%
+minima are sort of exponentially rare in
+ 
+
+ align:start position:0%
+minima are sort of exponentially rare in
+the dimensionality relative to saddle
+
+ align:start position:0%
+the dimensionality relative to saddle
+ 
+
+ align:start position:0%
+the dimensionality relative to saddle
+points just intuitively imagine you have
+
+ align:start position:0%
+points just intuitively imagine you have
+ 
+
+ align:start position:0%
+points just intuitively imagine you have
+an error function over a thousand
+
+ align:start position:0%
+an error function over a thousand
+ 
+
+ align:start position:0%
+an error function over a thousand
+variables say a thousand synaptic weight
+
+ align:start position:0%
+variables say a thousand synaptic weight
+ 
+
+ align:start position:0%
+variables say a thousand synaptic weight
+it's a deep network that's a small deep
+
+ align:start position:0%
+it's a deep network that's a small deep
+ 
+
+ align:start position:0%
+it's a deep network that's a small deep
+network but anyways let's say there's a
+
+ align:start position:0%
+network but anyways let's say there's a
+ 
+
+ align:start position:0%
+network but anyways let's say there's a
+point at which the gradient and weight
+
+ align:start position:0%
+point at which the gradient and weight
+ 
+
+ align:start position:0%
+point at which the gradient and weight
+space vanishes so now there's a thousand
+
+ align:start position:0%
+space vanishes so now there's a thousand
+ 
+
+ align:start position:0%
+space vanishes so now there's a thousand
+directions in weight space you could
+
+ align:start position:0%
+directions in weight space you could
+ 
+
+ align:start position:0%
+directions in weight space you could
+move away from that from that extrema
+
+ align:start position:0%
+move away from that from that extrema
+ 
+
+ align:start position:0%
+move away from that from that extrema
+what are the chances that every single
+
+ align:start position:0%
+what are the chances that every single
+ 
+
+ align:start position:0%
+what are the chances that every single
+direction you move has positive
+
+ align:start position:0%
+direction you move has positive
+ 
+
+ align:start position:0%
+direction you move has positive
+curvature right if it's a fairly generic
+
+ align:start position:0%
+curvature right if it's a fairly generic
+ 
+
+ align:start position:0%
+curvature right if it's a fairly generic
+landscape the answer is exponentially
+
+ align:start position:0%
+landscape the answer is exponentially
+ 
+
+ align:start position:0%
+landscape the answer is exponentially
+small in the dimensionality some
+
+ align:start position:0%
+small in the dimensionality some
+ 
+
+ align:start position:0%
+small in the dimensionality some
+directions will have negative curvature
+
+ align:start position:0%
+directions will have negative curvature
+ 
+
+ align:start position:0%
+directions will have negative curvature
+some directions will have positive
+
+ align:start position:0%
+some directions will have positive
+ 
+
+ align:start position:0%
+some directions will have positive
+curvature unless your critical point is
+
+ align:start position:0%
+curvature unless your critical point is
+ 
+
+ align:start position:0%
+curvature unless your critical point is
+already at the bottom in that case most
+
+ align:start position:0%
+already at the bottom in that case most
+ 
+
+ align:start position:0%
+already at the bottom in that case most
+direction will have positive curvature
+
+ align:start position:0%
+direction will have positive curvature
+ 
+
+ align:start position:0%
+direction will have positive curvature
+or unless your critical point is at the
+
+ align:start position:0%
+or unless your critical point is at the
+ 
+
+ align:start position:0%
+or unless your critical point is at the
+top and higher than most directions no
+
+ align:start position:0%
+top and higher than most directions no
+ 
+
+ align:start position:0%
+top and higher than most directions no
+negative curvature right so statistical
+
+ align:start position:0%
+negative curvature right so statistical
+ 
+
+ align:start position:0%
+negative curvature right so statistical
+physicists have made this intuition very
+
+ align:start position:0%
+physicists have made this intuition very
+ 
+
+ align:start position:0%
+physicists have made this intuition very
+precise for random landscapes and
+
+ align:start position:0%
+precise for random landscapes and
+ 
+
+ align:start position:0%
+precise for random landscapes and
+they've developed a theory for it so
+
+ align:start position:0%
+they've developed a theory for it so
+ 
+
+ align:start position:0%
+they've developed a theory for it so
+this is a paper in Physical Review
+
+ align:start position:0%
+this is a paper in Physical Review
+ 
+
+ align:start position:0%
+this is a paper in Physical Review
+Letters by Bray and Dean so what they
+
+ align:start position:0%
+Letters by Bray and Dean so what they
+ 
+
+ align:start position:0%
+Letters by Bray and Dean so what they
+did was they imagined just a random
+
+ align:start position:0%
+did was they imagined just a random
+ 
+
+ align:start position:0%
+did was they imagined just a random
+Gaussian error landscape so what they
+
+ align:start position:0%
+Gaussian error landscape so what they
+ 
+
+ align:start position:0%
+Gaussian error landscape so what they
+did was they looked at an error
+
+ align:start position:0%
+did was they looked at an error
+ 
+
+ align:start position:0%
+did was they looked at an error
+landscape ok that's a continuous
+
+ align:start position:0%
+landscape ok that's a continuous
+ 
+
+ align:start position:0%
+landscape ok that's a continuous
+function over n dimensions but there is
+
+ align:start position:0%
+function over n dimensions but there is
+ 
+
+ align:start position:0%
+function over n dimensions but there is
+correlations it's correlated over some
+
+ align:start position:0%
+correlations it's correlated over some
+ 
+
+ align:start position:0%
+correlations it's correlated over some
+length scale so it's like a rat it's a
+
+ align:start position:0%
+length scale so it's like a rat it's a
+ 
+
+ align:start position:0%
+length scale so it's like a rat it's a
+single draw from a random Gaussian
+
+ align:start position:0%
+single draw from a random Gaussian
+ 
+
+ align:start position:0%
+single draw from a random Gaussian
+process where the kernel of the random
+
+ align:start position:0%
+process where the kernel of the random
+ 
+
+ align:start position:0%
+process where the kernel of the random
+cows of the Gaussian process is falling
+
+ align:start position:0%
+cows of the Gaussian process is falling
+ 
+
+ align:start position:0%
+cows of the Gaussian process is falling
+off with some length scale so the error
+
+ align:start position:0%
+off with some length scale so the error
+ 
+
+ align:start position:0%
+off with some length scale so the error
+at point 1 is correlated with the error
+
+ align:start position:0%
+at point 1 is correlated with the error
+ 
+
+ align:start position:0%
+at point 1 is correlated with the error
+at point 2 over some length scale and
+
+ align:start position:0%
+at point 2 over some length scale and
+ 
+
+ align:start position:0%
+at point 2 over some length scale and
+that that correlation falls off smoothly
+
+ align:start position:0%
+that that correlation falls off smoothly
+ 
+
+ align:start position:0%
+that that correlation falls off smoothly
+so it's a random smooth landscape ok but
+
+ align:start position:0%
+so it's a random smooth landscape ok but
+ 
+
+ align:start position:0%
+so it's a random smooth landscape ok but
+the correlations are local essentially
+
+ align:start position:0%
+the correlations are local essentially
+ 
+
+ align:start position:0%
+the correlations are local essentially
+and then what they did was they asked
+
+ align:start position:0%
+and then what they did was they asked
+ 
+
+ align:start position:0%
+and then what they did was they asked
+the following question Let X be a
+
+ align:start position:0%
+the following question Let X be a
+ 
+
+ align:start position:0%
+the following question Let X be a
+critical point a point where the
+
+ align:start position:0%
+critical point a point where the
+ 
+
+ align:start position:0%
+critical point a point where the
+gradient vanishes ok we can plot every
+
+ align:start position:0%
+gradient vanishes ok we can plot every
+ 
+
+ align:start position:0%
+gradient vanishes ok we can plot every
+single critical point in a two
+
+ align:start position:0%
+single critical point in a two
+ 
+
+ align:start position:0%
+single critical point in a two
+dimensional feature space
+
+ align:start position:0%
+dimensional feature space
+ 
+
+ align:start position:0%
+dimensional feature space
+what is that feature space well the
+
+ align:start position:0%
+what is that feature space well the
+ 
+
+ align:start position:0%
+what is that feature space well the
+horizontal axis is the error level of
+
+ align:start position:0%
+horizontal axis is the error level of
+ 
+
+ align:start position:0%
+horizontal axis is the error level of
+the critical point at how high on the
+
+ align:start position:0%
+the critical point at how high on the
+ 
+
+ align:start position:0%
+the critical point at how high on the
+error axis does this critical point sit
+
+ align:start position:0%
+error axis does this critical point sit
+ 
+
+ align:start position:0%
+error axis does this critical point sit
+and then this F is the fraction of
+
+ align:start position:0%
+and then this F is the fraction of
+ 
+
+ align:start position:0%
+and then this F is the fraction of
+negative eigenvalues of the Hessian at
+
+ align:start position:0%
+negative eigenvalues of the Hessian at
+ 
+
+ align:start position:0%
+negative eigenvalues of the Hessian at
+that critical point so it's the fraction
+
+ align:start position:0%
+that critical point so it's the fraction
+ 
+
+ align:start position:0%
+that critical point so it's the fraction
+of directions that curve downwards and
+
+ align:start position:0%
+of directions that curve downwards and
+ 
+
+ align:start position:0%
+of directions that curve downwards and
+the fraction ok so now a priority
+
+ align:start position:0%
+the fraction ok so now a priority
+ 
+
+ align:start position:0%
+the fraction ok so now a priority
+critical points could potentially sit
+
+ align:start position:0%
+critical points could potentially sit
+ 
+
+ align:start position:0%
+critical points could potentially sit
+anywhere in this 2 dimensional feature
+
+ align:start position:0%
+anywhere in this 2 dimensional feature
+ 
+
+ align:start position:0%
+anywhere in this 2 dimensional feature
+space right it turns out they don't they
+
+ align:start position:0%
+space right it turns out they don't they
+ 
+
+ align:start position:0%
+space right it turns out they don't they
+concentrate on a monotonically
+
+ align:start position:0%
+concentrate on a monotonically
+ 
+
+ align:start position:0%
+concentrate on a monotonically
+increasing curve that looks like this so
+
+ align:start position:0%
+increasing curve that looks like this so
+ 
+
+ align:start position:0%
+increasing curve that looks like this so
+the higher the error level of critical
+
+ align:start position:0%
+the higher the error level of critical
+ 
+
+ align:start position:0%
+the higher the error level of critical
+point the more the negative curvature
+
+ align:start position:0%
+point the more the negative curvature
+ 
+
+ align:start position:0%
+point the more the negative curvature
+directions you have
+
+ align:start position:0%
+directions you have
+ 
+
+ align:start position:0%
+directions you have
+and to be an order one distance away
+
+ align:start position:0%
+and to be an order one distance away
+ 
+
+ align:start position:0%
+and to be an order one distance away
+from this curve the probability of that
+
+ align:start position:0%
+from this curve the probability of that
+ 
+
+ align:start position:0%
+from this curve the probability of that
+happening is exponentially small in the
+
+ align:start position:0%
+happening is exponentially small in the
+ 
+
+ align:start position:0%
+happening is exponentially small in the
+dimensionality of the problem okay
+
+ align:start position:0%
+dimensionality of the problem okay
+ 
+
+ align:start position:0%
+dimensionality of the problem okay
+now what does that mean it automatically
+
+ align:start position:0%
+now what does that mean it automatically
+ 
+
+ align:start position:0%
+now what does that mean it automatically
+implies that there are no local minima
+
+ align:start position:0%
+implies that there are no local minima
+ 
+
+ align:start position:0%
+implies that there are no local minima
+at high error or at least they're
+
+ align:start position:0%
+at high error or at least they're
+ 
+
+ align:start position:0%
+at high error or at least they're
+exponentially rel rare rather to saddle
+
+ align:start position:0%
+exponentially rel rare rather to saddle
+ 
+
+ align:start position:0%
+exponentially rel rare rather to saddle
+points of a given index okay so
+
+ align:start position:0%
+points of a given index okay so
+ 
+
+ align:start position:0%
+points of a given index okay so
+basically you typically never encounter
+
+ align:start position:0%
+basically you typically never encounter
+ 
+
+ align:start position:0%
+basically you typically never encounter
+local minimum at high error right that
+
+ align:start position:0%
+local minimum at high error right that
+ 
+
+ align:start position:0%
+local minimum at high error right that
+would be stuff that sits here and
+
+ align:start position:0%
+would be stuff that sits here and
+ 
+
+ align:start position:0%
+would be stuff that sits here and
+there's nothing here okay second if you
+
+ align:start position:0%
+there's nothing here okay second if you
+ 
+
+ align:start position:0%
+there's nothing here okay second if you
+are a local minimum which means on this
+
+ align:start position:0%
+are a local minimum which means on this
+ 
+
+ align:start position:0%
+are a local minimum which means on this
+axis you're at the bottom then your
+
+ align:start position:0%
+axis you're at the bottom then your
+ 
+
+ align:start position:0%
+axis you're at the bottom then your
+error level must be very very close to
+
+ align:start position:0%
+error level must be very very close to
+ 
+
+ align:start position:0%
+error level must be very very close to
+the global minimum okay so if you're if
+
+ align:start position:0%
+the global minimum okay so if you're if
+ 
+
+ align:start position:0%
+the global minimum okay so if you're if
+you get stuck in a local minimum you're
+
+ align:start position:0%
+you get stuck in a local minimum you're
+ 
+
+ align:start position:0%
+you get stuck in a local minimum you're
+already closed an error to the global
+
+ align:start position:0%
+already closed an error to the global
+ 
+
+ align:start position:0%
+already closed an error to the global
+minimum yeah so if you're a local
+
+ align:start position:0%
+minimum yeah so if you're a local
+ 
+
+ align:start position:0%
+minimum yeah so if you're a local
+minimum your error level will be close
+
+ align:start position:0%
+minimum your error level will be close
+ 
+
+ align:start position:0%
+minimum your error level will be close
+to the error level of the global minima
+
+ align:start position:0%
+to the error level of the global minima
+ 
+
+ align:start position:0%
+to the error level of the global minima
+why because what does it mean to be a
+
+ align:start position:0%
+why because what does it mean to be a
+ 
+
+ align:start position:0%
+why because what does it mean to be a
+local minimum it means that F is zero
+
+ align:start position:0%
+local minimum it means that F is zero
+ 
+
+ align:start position:0%
+local minimum it means that F is zero
+the fraction of negative curvature
+
+ align:start position:0%
+the fraction of negative curvature
+ 
+
+ align:start position:0%
+the fraction of negative curvature
+eigenvalues lasting is zero and this is
+
+ align:start position:0%
+eigenvalues lasting is zero and this is
+ 
+
+ align:start position:0%
+eigenvalues lasting is zero and this is
+the distribution of error levels of such
+
+ align:start position:0%
+the distribution of error levels of such
+ 
+
+ align:start position:0%
+the distribution of error levels of such
+critical points they're strongly peaked
+
+ align:start position:0%
+critical points they're strongly peaked
+ 
+
+ align:start position:0%
+critical points they're strongly peaked
+at this value which is the value of the
+
+ align:start position:0%
+at this value which is the value of the
+ 
+
+ align:start position:0%
+at this value which is the value of the
+global minimum essentially there's
+
+ align:start position:0%
+global minimum essentially there's
+ 
+
+ align:start position:0%
+global minimum essentially there's
+nothing out here okay all right now in
+
+ align:start position:0%
+nothing out here okay all right now in
+ 
+
+ align:start position:0%
+nothing out here okay all right now in
+physics there's this well-known
+
+ align:start position:0%
+physics there's this well-known
+ 
+
+ align:start position:0%
+physics there's this well-known
+principle called universality there are
+
+ align:start position:0%
+principle called universality there are
+ 
+
+ align:start position:0%
+principle called universality there are
+certain questions whose answers don't
+
+ align:start position:0%
+certain questions whose answers don't
+ 
+
+ align:start position:0%
+certain questions whose answers don't
+depend on the details for example
+
+ align:start position:0%
+depend on the details for example
+ 
+
+ align:start position:0%
+depend on the details for example
+certain critical exponents in the liquid
+
+ align:start position:0%
+certain critical exponents in the liquid
+ 
+
+ align:start position:0%
+certain critical exponents in the liquid
+gas phase transition are the exactly the
+
+ align:start position:0%
+gas phase transition are the exactly the
+ 
+
+ align:start position:0%
+gas phase transition are the exactly the
+same as critical exponents in the
+
+ align:start position:0%
+same as critical exponents in the
+ 
+
+ align:start position:0%
+same as critical exponents in the
+ferromagnetic phase transition because
+
+ align:start position:0%
+ferromagnetic phase transition because
+ 
+
+ align:start position:0%
+ferromagnetic phase transition because
+the symmetry and dimensionality the
+
+ align:start position:0%
+the symmetry and dimensionality the
+ 
+
+ align:start position:0%
+the symmetry and dimensionality the
+order parameter density in the case of
+
+ align:start position:0%
+order parameter density in the case of
+ 
+
+ align:start position:0%
+order parameter density in the case of
+liquid and magnetization in the in the
+
+ align:start position:0%
+liquid and magnetization in the in the
+ 
+
+ align:start position:0%
+liquid and magnetization in the in the
+case of ferromagnets are the same so
+
+ align:start position:0%
+case of ferromagnets are the same so
+ 
+
+ align:start position:0%
+case of ferromagnets are the same so
+there's certain questions whose answers
+
+ align:start position:0%
+there's certain questions whose answers
+ 
+
+ align:start position:0%
+there's certain questions whose answers
+don't depend on the detail they only
+
+ align:start position:0%
+don't depend on the detail they only
+ 
+
+ align:start position:0%
+don't depend on the detail they only
+depend on the symmetry and
+
+ align:start position:0%
+depend on the symmetry and
+ 
+
+ align:start position:0%
+depend on the symmetry and
+dimensionality of the problem so one
+
+ align:start position:0%
+dimensionality of the problem so one
+ 
+
+ align:start position:0%
+dimensionality of the problem so one
+might think that this qualitative
+
+ align:start position:0%
+might think that this qualitative
+ 
+
+ align:start position:0%
+might think that this qualitative
+prediction is true in just generic high
+
+ align:start position:0%
+prediction is true in just generic high
+ 
+
+ align:start position:0%
+prediction is true in just generic high
+dimensional error landscapes now the
+
+ align:start position:0%
+dimensional error landscapes now the
+ 
+
+ align:start position:0%
+dimensional error landscapes now the
+computer scientist would say no no no no
+
+ align:start position:0%
+computer scientist would say no no no no
+ 
+
+ align:start position:0%
+computer scientist would say no no no no
+no no no your random landscapes are a
+
+ align:start position:0%
+no no no your random landscapes are a
+ 
+
+ align:start position:0%
+no no no your random landscapes are a
+horrible model for our error landscapes
+
+ align:start position:0%
+horrible model for our error landscapes
+ 
+
+ align:start position:0%
+horrible model for our error landscapes
+of deep neural networks trained on Emma
+
+ align:start position:0%
+of deep neural networks trained on Emma
+ 
+
+ align:start position:0%
+of deep neural networks trained on Emma
+stand in CFR 10 and and so on and so
+
+ align:start position:0%
+stand in CFR 10 and and so on and so
+ 
+
+ align:start position:0%
+stand in CFR 10 and and so on and so
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+you're completely irrelevant to us
+
+ align:start position:0%
+you're completely irrelevant to us
+ 
+
+ align:start position:0%
+you're completely irrelevant to us
+because we're doing something special
+
+ align:start position:0%
+because we're doing something special
+ 
+
+ align:start position:0%
+because we're doing something special
+we're not doing something random we have
+
+ align:start position:0%
+we're not doing something random we have
+ 
+
+ align:start position:0%
+we're not doing something random we have
+a lot of structure okay the physicist
+
+ align:start position:0%
+a lot of structure okay the physicist
+ 
+
+ align:start position:0%
+a lot of structure okay the physicist
+might counter well you know you just
+
+ align:start position:0%
+might counter well you know you just
+ 
+
+ align:start position:0%
+might counter well you know you just
+have a high dimensional problem and just
+
+ align:start position:0%
+have a high dimensional problem and just
+ 
+
+ align:start position:0%
+have a high dimensional problem and just
+the basic intuition that in
+
+ align:start position:0%
+the basic intuition that in
+ 
+
+ align:start position:0%
+the basic intuition that in
+my dimensions it's very hard to have all
+
+ align:start position:0%
+my dimensions it's very hard to have all
+ 
+
+ align:start position:0%
+my dimensions it's very hard to have all
+directions curved up at high at a
+
+ align:start position:0%
+directions curved up at high at a
+ 
+
+ align:start position:0%
+directions curved up at high at a
+critical point high error should also
+
+ align:start position:0%
+critical point high error should also
+ 
+
+ align:start position:0%
+critical point high error should also
+hold true in your problem okay but of
+
+ align:start position:0%
+hold true in your problem okay but of
+ 
+
+ align:start position:0%
+hold true in your problem okay but of
+course we'll never get anywhere if we
+
+ align:start position:0%
+course we'll never get anywhere if we
+ 
+
+ align:start position:0%
+course we'll never get anywhere if we
+stop there right we have to move over
+
+ align:start position:0%
+stop there right we have to move over
+ 
+
+ align:start position:0%
+stop there right we have to move over
+into your lands which is also my land
+
+ align:start position:0%
+into your lands which is also my land
+ 
+
+ align:start position:0%
+into your lands which is also my land
+and and and just simulate the system so
+
+ align:start position:0%
+and and and just simulate the system so
+ 
+
+ align:start position:0%
+and and and just simulate the system so
+oftentimes you know biologists and
+
+ align:start position:0%
+oftentimes you know biologists and
+ 
+
+ align:start position:0%
+oftentimes you know biologists and
+computer scientists don't believe a
+
+ align:start position:0%
+computer scientists don't believe a
+ 
+
+ align:start position:0%
+computer scientists don't believe a
+theory until they see the simulation
+
+ align:start position:0%
+theory until they see the simulation
+ 
+
+ align:start position:0%
+theory until they see the simulation
+okay so what we'll do is we'll search
+
+ align:start position:0%
+okay so what we'll do is we'll search
+ 
+
+ align:start position:0%
+okay so what we'll do is we'll search
+for critical points in the error
+
+ align:start position:0%
+for critical points in the error
+ 
+
+ align:start position:0%
+for critical points in the error
+landscape of deep neural networks and
+
+ align:start position:0%
+landscape of deep neural networks and
+ 
+
+ align:start position:0%
+landscape of deep neural networks and
+that's what we did so what we did was we
+
+ align:start position:0%
+that's what we did so what we did was we
+ 
+
+ align:start position:0%
+that's what we did so what we did was we
+use Newton's method okay to find
+
+ align:start position:0%
+use Newton's method okay to find
+ 
+
+ align:start position:0%
+use Newton's method okay to find
+critical points so it turns out that
+
+ align:start position:0%
+critical points so it turns out that
+ 
+
+ align:start position:0%
+critical points so it turns out that
+Newton's method is attracted to saddles
+
+ align:start position:0%
+Newton's method is attracted to saddles
+ 
+
+ align:start position:0%
+Newton's method is attracted to saddles
+right so Newton's method will descend in
+
+ align:start position:0%
+right so Newton's method will descend in
+ 
+
+ align:start position:0%
+right so Newton's method will descend in
+the positive curvature direction that it
+
+ align:start position:0%
+the positive curvature direction that it
+ 
+
+ align:start position:0%
+the positive curvature direction that it
+will ascend in the negative curvature
+
+ align:start position:0%
+will ascend in the negative curvature
+ 
+
+ align:start position:0%
+will ascend in the negative curvature
+direction because Newton's method is
+
+ align:start position:0%
+direction because Newton's method is
+ 
+
+ align:start position:0%
+direction because Newton's method is
+gradient descent multiplied by the
+
+ align:start position:0%
+gradient descent multiplied by the
+ 
+
+ align:start position:0%
+gradient descent multiplied by the
+inverse of the Hessian so if the Hessian
+
+ align:start position:0%
+inverse of the Hessian so if the Hessian
+ 
+
+ align:start position:0%
+inverse of the Hessian so if the Hessian
+has a negative eigen value you take the
+
+ align:start position:0%
+has a negative eigen value you take the
+ 
+
+ align:start position:0%
+has a negative eigen value you take the
+negative gradient multiply it by the
+
+ align:start position:0%
+negative gradient multiply it by the
+ 
+
+ align:start position:0%
+negative gradient multiply it by the
+negative eigen value to turn back around
+
+ align:start position:0%
+negative eigen value to turn back around
+ 
+
+ align:start position:0%
+negative eigen value to turn back around
+and you go uphill so Newton's method
+
+ align:start position:0%
+and you go uphill so Newton's method
+ 
+
+ align:start position:0%
+and you go uphill so Newton's method
+uncorrect it is attracted to saddle
+
+ align:start position:0%
+uncorrect it is attracted to saddle
+ 
+
+ align:start position:0%
+uncorrect it is attracted to saddle
+points okay so what we did was we looked
+
+ align:start position:0%
+points okay so what we did was we looked
+ 
+
+ align:start position:0%
+points okay so what we did was we looked
+at the error landscape of deep neural
+
+ align:start position:0%
+at the error landscape of deep neural
+ 
+
+ align:start position:0%
+at the error landscape of deep neural
+networks trained on em missed and c510
+
+ align:start position:0%
+networks trained on em missed and c510
+ 
+
+ align:start position:0%
+networks trained on em missed and c510
+and we just plotted the prediction of
+
+ align:start position:0%
+and we just plotted the prediction of
+ 
+
+ align:start position:0%
+and we just plotted the prediction of
+random landscape theory right and what
+
+ align:start position:0%
+random landscape theory right and what
+ 
+
+ align:start position:0%
+random landscape theory right and what
+we found was exactly qualitative either
+
+ align:start position:0%
+we found was exactly qualitative either
+ 
+
+ align:start position:0%
+we found was exactly qualitative either
+prediction we took each critical point
+
+ align:start position:0%
+prediction we took each critical point
+ 
+
+ align:start position:0%
+prediction we took each critical point
+and plotted in this two dimensional
+
+ align:start position:0%
+and plotted in this two dimensional
+ 
+
+ align:start position:0%
+and plotted in this two dimensional
+feature space and we found that the
+
+ align:start position:0%
+feature space and we found that the
+ 
+
+ align:start position:0%
+feature space and we found that the
+critical points concentrated on a
+
+ align:start position:0%
+critical points concentrated on a
+ 
+
+ align:start position:0%
+critical points concentrated on a
+monotonically increasing curve which
+
+ align:start position:0%
+monotonically increasing curve which
+ 
+
+ align:start position:0%
+monotonically increasing curve which
+again shows that there are no local
+
+ align:start position:0%
+again shows that there are no local
+ 
+
+ align:start position:0%
+again shows that there are no local
+minima at high error and if you're a
+
+ align:start position:0%
+minima at high error and if you're a
+ 
+
+ align:start position:0%
+minima at high error and if you're a
+local minimum your error is close to at
+
+ align:start position:0%
+local minimum your error is close to at
+ 
+
+ align:start position:0%
+local minimum your error is close to at
+least the the lowest error minimum that
+
+ align:start position:0%
+least the the lowest error minimum that
+ 
+
+ align:start position:0%
+least the the lowest error minimum that
+we found we can't guarantee that the
+
+ align:start position:0%
+we found we can't guarantee that the
+ 
+
+ align:start position:0%
+we found we can't guarantee that the
+lowest error minimum we found is a
+
+ align:start position:0%
+lowest error minimum we found is a
+ 
+
+ align:start position:0%
+lowest error minimum we found is a
+global minimum but qualitatively the
+
+ align:start position:0%
+global minimum but qualitatively the
+ 
+
+ align:start position:0%
+global minimum but qualitatively the
+structure holds okay now the issue is
+
+ align:start position:0%
+structure holds okay now the issue is
+ 
+
+ align:start position:0%
+structure holds okay now the issue is
+what can we do about it so what this is
+
+ align:start position:0%
+what can we do about it so what this is
+ 
+
+ align:start position:0%
+what can we do about it so what this is
+telling us that even in these problems
+
+ align:start position:0%
+telling us that even in these problems
+ 
+
+ align:start position:0%
+telling us that even in these problems
+of practical interest saddle points
+
+ align:start position:0%
+of practical interest saddle points
+ 
+
+ align:start position:0%
+of practical interest saddle points
+might stand as the major impediment to
+
+ align:start position:0%
+might stand as the major impediment to
+ 
+
+ align:start position:0%
+might stand as the major impediment to
+optimization right because saddle points
+
+ align:start position:0%
+optimization right because saddle points
+ 
+
+ align:start position:0%
+optimization right because saddle points
+can trap you you know you might get you
+
+ align:start position:0%
+can trap you you know you might get you
+ 
+
+ align:start position:0%
+can trap you you know you might get you
+might go down here and then there might
+
+ align:start position:0%
+might go down here and then there might
+ 
+
+ align:start position:0%
+might go down here and then there might
+be a very slowly curving negative
+
+ align:start position:0%
+be a very slowly curving negative
+ 
+
+ align:start position:0%
+be a very slowly curving negative
+curvature direction that might take you
+
+ align:start position:0%
+curvature direction that might take you
+ 
+
+ align:start position:0%
+curvature direction that might take you
+a while to escape in fact in the
+
+ align:start position:0%
+a while to escape in fact in the
+ 
+
+ align:start position:0%
+a while to escape in fact in the
+learning dynamics that I showed in these
+
+ align:start position:0%
+learning dynamics that I showed in these
+ 
+
+ align:start position:0%
+learning dynamics that I showed in these
+transitions in learning hierarchical
+
+ align:start position:0%
+transitions in learning hierarchical
+ 
+
+ align:start position:0%
+transitions in learning hierarchical
+structure the thing controlling the
+
+ align:start position:0%
+structure the thing controlling the
+ 
+
+ align:start position:0%
+structure the thing controlling the
+transitions with the existence of saddle
+
+ align:start position:0%
+transitions with the existence of saddle
+ 
+
+ align:start position:0%
+transitions with the existence of saddle
+points and weight space of the linear
+
+ align:start position:0%
+points and weight space of the linear
+ 
+
+ align:start position:0%
+points and weight space of the linear
+neural
+
+ align:start position:0%
+neural
+ 
+
+ align:start position:0%
+neural
+and so the the part of no learning
+
+ align:start position:0%
+and so the the part of no learning
+ 
+
+ align:start position:0%
+and so the the part of no learning
+correspond to to sort of falling down
+
+ align:start position:0%
+correspond to to sort of falling down
+ 
+
+ align:start position:0%
+correspond to to sort of falling down
+this direction slowly and then the rapid
+
+ align:start position:0%
+this direction slowly and then the rapid
+ 
+
+ align:start position:0%
+this direction slowly and then the rapid
+learning on to eventually coming out
+
+ align:start position:0%
+learning on to eventually coming out
+ 
+
+ align:start position:0%
+learning on to eventually coming out
+this way okay so how do we how do we do
+
+ align:start position:0%
+this way okay so how do we how do we do
+ 
+
+ align:start position:0%
+this way okay so how do we how do we do
+that well what we can do is we can do a
+
+ align:start position:0%
+that well what we can do is we can do a
+ 
+
+ align:start position:0%
+that well what we can do is we can do a
+simple modification to Newton's method
+
+ align:start position:0%
+simple modification to Newton's method
+ 
+
+ align:start position:0%
+simple modification to Newton's method
+which instead of dividing by the Hessian
+
+ align:start position:0%
+which instead of dividing by the Hessian
+ 
+
+ align:start position:0%
+which instead of dividing by the Hessian
+we divide by the absolute value of the
+
+ align:start position:0%
+we divide by the absolute value of the
+ 
+
+ align:start position:0%
+we divide by the absolute value of the
+Hessian and again I should say that this
+
+ align:start position:0%
+Hessian and again I should say that this
+ 
+
+ align:start position:0%
+Hessian and again I should say that this
+was done in collaboration yoshua bengio
+
+ align:start position:0%
+was done in collaboration yoshua bengio
+ 
+
+ align:start position:0%
+was done in collaboration yoshua bengio
+slab and a set of fantastic graduate
+
+ align:start position:0%
+slab and a set of fantastic graduate
+ 
+
+ align:start position:0%
+slab and a set of fantastic graduate
+students in yoshua bengio slab did all
+
+ align:start position:0%
+students in yoshua bengio slab did all
+ 
+
+ align:start position:0%
+students in yoshua bengio slab did all
+of this work on the training and testing
+
+ align:start position:0%
+of this work on the training and testing
+ 
+
+ align:start position:0%
+of this work on the training and testing
+of these predictions okay so what we we
+
+ align:start position:0%
+of these predictions okay so what we we
+ 
+
+ align:start position:0%
+of these predictions okay so what we we
+suggested was you know the offending
+
+ align:start position:0%
+suggested was you know the offending
+ 
+
+ align:start position:0%
+suggested was you know the offending
+thing is dividing by negative
+
+ align:start position:0%
+thing is dividing by negative
+ 
+
+ align:start position:0%
+thing is dividing by negative
+eigenvalues so just take the absolute
+
+ align:start position:0%
+eigenvalues so just take the absolute
+ 
+
+ align:start position:0%
+eigenvalues so just take the absolute
+value of the Hessian which by definition
+
+ align:start position:0%
+value of the Hessian which by definition
+ 
+
+ align:start position:0%
+value of the Hessian which by definition
+I mean take the Hessian compute its
+
+ align:start position:0%
+I mean take the Hessian compute its
+ 
+
+ align:start position:0%
+I mean take the Hessian compute its
+eigenvalues and replace each negative
+
+ align:start position:0%
+eigenvalues and replace each negative
+ 
+
+ align:start position:0%
+eigenvalues and replace each negative
+one with its absolute value okay so that
+
+ align:start position:0%
+one with its absolute value okay so that
+ 
+
+ align:start position:0%
+one with its absolute value okay so that
+will obviously get repelled by saddles
+
+ align:start position:0%
+will obviously get repelled by saddles
+ 
+
+ align:start position:0%
+will obviously get repelled by saddles
+all right and and that actually works
+
+ align:start position:0%
+all right and and that actually works
+ 
+
+ align:start position:0%
+all right and and that actually works
+really really well and there's a way to
+
+ align:start position:0%
+really really well and there's a way to
+ 
+
+ align:start position:0%
+really really well and there's a way to
+derive this algorithm in a way that
+
+ align:start position:0%
+derive this algorithm in a way that
+ 
+
+ align:start position:0%
+derive this algorithm in a way that
+makes sense even far from saddles using
+
+ align:start position:0%
+makes sense even far from saddles using
+ 
+
+ align:start position:0%
+makes sense even far from saddles using
+by minimizing a linear approximation to
+
+ align:start position:0%
+by minimizing a linear approximation to
+ 
+
+ align:start position:0%
+by minimizing a linear approximation to
+F within a trust region in which the
+
+ align:start position:0%
+F within a trust region in which the
+ 
+
+ align:start position:0%
+F within a trust region in which the
+linear and quadratic approximations
+
+ align:start position:0%
+linear and quadratic approximations
+ 
+
+ align:start position:0%
+linear and quadratic approximations
+agree okay so let me just show you first
+
+ align:start position:0%
+agree okay so let me just show you first
+ 
+
+ align:start position:0%
+agree okay so let me just show you first
+that it works so that this is the most
+
+ align:start position:0%
+that it works so that this is the most
+ 
+
+ align:start position:0%
+that it works so that this is the most
+dramatic plot so basically what we did
+
+ align:start position:0%
+dramatic plot so basically what we did
+ 
+
+ align:start position:0%
+dramatic plot so basically what we did
+was we did stochastic gradient descent
+
+ align:start position:0%
+was we did stochastic gradient descent
+ 
+
+ align:start position:0%
+was we did stochastic gradient descent
+right for awhile and then it seemed like
+
+ align:start position:0%
+right for awhile and then it seemed like
+ 
+
+ align:start position:0%
+right for awhile and then it seemed like
+the error as a function of training time
+
+ align:start position:0%
+the error as a function of training time
+ 
+
+ align:start position:0%
+the error as a function of training time
+plateaued both for a deep autoencoder
+
+ align:start position:0%
+plateaued both for a deep autoencoder
+ 
+
+ align:start position:0%
+plateaued both for a deep autoencoder
+and a recurrent neural network problem
+
+ align:start position:0%
+and a recurrent neural network problem
+ 
+
+ align:start position:0%
+and a recurrent neural network problem
+so when the error is a function of
+
+ align:start position:0%
+so when the error is a function of
+ 
+
+ align:start position:0%
+so when the error is a function of
+training time plateaus that sort of
+
+ align:start position:0%
+training time plateaus that sort of
+ 
+
+ align:start position:0%
+training time plateaus that sort of
+interpreted as the fact that you're
+
+ align:start position:0%
+interpreted as the fact that you're
+ 
+
+ align:start position:0%
+interpreted as the fact that you're
+stuck in a local minimum right but
+
+ align:start position:0%
+stuck in a local minimum right but
+ 
+
+ align:start position:0%
+stuck in a local minimum right but
+actually when we switch to this what we
+
+ align:start position:0%
+actually when we switch to this what we
+ 
+
+ align:start position:0%
+actually when we switch to this what we
+call the saddle free Newton method the
+
+ align:start position:0%
+call the saddle free Newton method the
+ 
+
+ align:start position:0%
+call the saddle free Newton method the
+error suddenly drops again so this was
+
+ align:start position:0%
+error suddenly drops again so this was
+ 
+
+ align:start position:0%
+error suddenly drops again so this was
+an illusory signature of a local minimum
+
+ align:start position:0%
+an illusory signature of a local minimum
+ 
+
+ align:start position:0%
+an illusory signature of a local minimum
+it was actually a saddle point with
+
+ align:start position:0%
+it was actually a saddle point with
+ 
+
+ align:start position:0%
+it was actually a saddle point with
+probably a very shallow negative
+
+ align:start position:0%
+probably a very shallow negative
+ 
+
+ align:start position:0%
+probably a very shallow negative
+curvature direction it was hard to
+
+ align:start position:0%
+curvature direction it was hard to
+ 
+
+ align:start position:0%
+curvature direction it was hard to
+escape and then we switched to our
+
+ align:start position:0%
+escape and then we switched to our
+ 
+
+ align:start position:0%
+escape and then we switched to our
+algorithm we could escape it okay and
+
+ align:start position:0%
+algorithm we could escape it okay and
+ 
+
+ align:start position:0%
+algorithm we could escape it okay and
+and and you know that what these curves
+
+ align:start position:0%
+and and you know that what these curves
+ 
+
+ align:start position:0%
+and and you know that what these curves
+show is that we do do better in the
+
+ align:start position:0%
+show is that we do do better in the
+ 
+
+ align:start position:0%
+show is that we do do better in the
+final training error as well so now how
+
+ align:start position:0%
+final training error as well so now how
+ 
+
+ align:start position:0%
+final training error as well so now how
+do we train deep neural networks with
+
+ align:start position:0%
+do we train deep neural networks with
+ 
+
+ align:start position:0%
+do we train deep neural networks with
+thousands of layers and actually how do
+
+ align:start position:0%
+thousands of layers and actually how do
+ 
+
+ align:start position:0%
+thousands of layers and actually how do
+we how do we model complex probability
+
+ align:start position:0%
+we how do we model complex probability
+ 
+
+ align:start position:0%
+we how do we model complex probability
+distributions so we want to we want to
+
+ align:start position:0%
+distributions so we want to we want to
+ 
+
+ align:start position:0%
+distributions so we want to we want to
+sample from very very complex
+
+ align:start position:0%
+sample from very very complex
+ 
+
+ align:start position:0%
+sample from very very complex
+probability distributions and do complex
+
+ align:start position:0%
+probability distributions and do complex
+ 
+
+ align:start position:0%
+probability distributions and do complex
+distributional learning
+
+ align:start position:0%
+distributional learning
+ 
+
+ align:start position:0%
+distributional learning
+right so this was done by a fantastic
+
+ align:start position:0%
+right so this was done by a fantastic
+ 
+
+ align:start position:0%
+right so this was done by a fantastic
+postdoc of mine Joshua Sol Dickstein so
+
+ align:start position:0%
+postdoc of mine Joshua Sol Dickstein so
+ 
+
+ align:start position:0%
+postdoc of mine Joshua Sol Dickstein so
+we were going to Berkeley for this nanak
+
+ align:start position:0%
+we were going to Berkeley for this nanak
+ 
+
+ align:start position:0%
+we were going to Berkeley for this nanak
+Cobra missile mechanics meetings and
+
+ align:start position:0%
+Cobra missile mechanics meetings and
+ 
+
+ align:start position:0%
+Cobra missile mechanics meetings and
+things like that and there's been lots
+
+ align:start position:0%
+things like that and there's been lots
+ 
+
+ align:start position:0%
+things like that and there's been lots
+of advances in our computer system
+
+ align:start position:0%
+of advances in our computer system
+ 
+
+ align:start position:0%
+of advances in our computer system
+mechanics where you can show that
+
+ align:start position:0%
+mechanics where you can show that
+ 
+
+ align:start position:0%
+mechanics where you can show that
+roughly speaking the second law of
+
+ align:start position:0%
+roughly speaking the second law of
+ 
+
+ align:start position:0%
+roughly speaking the second law of
+thermodynamics which says that things
+
+ align:start position:0%
+thermodynamics which says that things
+ 
+
+ align:start position:0%
+thermodynamics which says that things
+get more and more disordered with time
+
+ align:start position:0%
+get more and more disordered with time
+ 
+
+ align:start position:0%
+get more and more disordered with time
+can be transiently violated in small
+
+ align:start position:0%
+can be transiently violated in small
+ 
+
+ align:start position:0%
+can be transiently violated in small
+systems or short periods of time so you
+
+ align:start position:0%
+systems or short periods of time so you
+ 
+
+ align:start position:0%
+systems or short periods of time so you
+can spontaneously generate order
+
+ align:start position:0%
+can spontaneously generate order
+ 
+
+ align:start position:0%
+can spontaneously generate order
+okay so let's so I'll just go through
+
+ align:start position:0%
+okay so let's so I'll just go through
+ 
+
+ align:start position:0%
+okay so let's so I'll just go through
+this again very quickly so so here's the
+
+ align:start position:0%
+this again very quickly so so here's the
+ 
+
+ align:start position:0%
+this again very quickly so so here's the
+basic idea let's say you have a
+
+ align:start position:0%
+basic idea let's say you have a
+ 
+
+ align:start position:0%
+basic idea let's say you have a
+complicated probability distribution
+
+ align:start position:0%
+complicated probability distribution
+ 
+
+ align:start position:0%
+complicated probability distribution
+let's just destroy it let's feed that
+
+ align:start position:0%
+let's just destroy it let's feed that
+ 
+
+ align:start position:0%
+let's just destroy it let's feed that
+probability distribution through
+
+ align:start position:0%
+probability distribution through
+ 
+
+ align:start position:0%
+probability distribution through
+diffusion to turn it into a simple
+
+ align:start position:0%
+diffusion to turn it into a simple
+ 
+
+ align:start position:0%
+diffusion to turn it into a simple
+distribution maybe an isotropic Gaussian
+
+ align:start position:0%
+distribution maybe an isotropic Gaussian
+ 
+
+ align:start position:0%
+distribution maybe an isotropic Gaussian
+and we keep a record of that destruction
+
+ align:start position:0%
+and we keep a record of that destruction
+ 
+
+ align:start position:0%
+and we keep a record of that destruction
+of structure and then we try to reverse
+
+ align:start position:0%
+of structure and then we try to reverse
+ 
+
+ align:start position:0%
+of structure and then we try to reverse
+time in that process by using deep
+
+ align:start position:0%
+time in that process by using deep
+ 
+
+ align:start position:0%
+time in that process by using deep
+neural networks to reverse time and then
+
+ align:start position:0%
+neural networks to reverse time and then
+ 
+
+ align:start position:0%
+neural networks to reverse time and then
+essentially create structure from noise
+
+ align:start position:0%
+essentially create structure from noise
+ 
+
+ align:start position:0%
+essentially create structure from noise
+and then you have a very very simple way
+
+ align:start position:0%
+and then you have a very very simple way
+ 
+
+ align:start position:0%
+and then you have a very very simple way
+to sample from complex distributions if
+
+ align:start position:0%
+to sample from complex distributions if
+ 
+
+ align:start position:0%
+to sample from complex distributions if
+you can train the neural network which
+
+ align:start position:0%
+you can train the neural network which
+ 
+
+ align:start position:0%
+you can train the neural network which
+is you just sample noise and you feed it
+
+ align:start position:0%
+is you just sample noise and you feed it
+ 
+
+ align:start position:0%
+is you just sample noise and you feed it
+through a deterministic neural network
+
+ align:start position:0%
+through a deterministic neural network
+ 
+
+ align:start position:0%
+through a deterministic neural network
+and that constants a sample from a
+
+ align:start position:0%
+and that constants a sample from a
+ 
+
+ align:start position:0%
+and that constants a sample from a
+complex distribution and so this was
+
+ align:start position:0%
+complex distribution and so this was
+ 
+
+ align:start position:0%
+complex distribution and so this was
+inspired by recent results in non
+
+ align:start position:0%
+inspired by recent results in non
+ 
+
+ align:start position:0%
+inspired by recent results in non
+equilibrium static so the basic idea
+
+ align:start position:0%
+equilibrium static so the basic idea
+ 
+
+ align:start position:0%
+equilibrium static so the basic idea
+again is you know let's imagine that you
+
+ align:start position:0%
+again is you know let's imagine that you
+ 
+
+ align:start position:0%
+again is you know let's imagine that you
+have a very complex distribution
+
+ align:start position:0%
+have a very complex distribution
+ 
+
+ align:start position:0%
+have a very complex distribution
+corresponding to this density of dye you
+
+ align:start position:0%
+corresponding to this density of dye you
+ 
+
+ align:start position:0%
+corresponding to this density of dye you
+diffuse for a while it becomes a simpler
+
+ align:start position:0%
+diffuse for a while it becomes a simpler
+ 
+
+ align:start position:0%
+diffuse for a while it becomes a simpler
+distribution eventually become uniform
+
+ align:start position:0%
+distribution eventually become uniform
+ 
+
+ align:start position:0%
+distribution eventually become uniform
+you keep a destruction now you if you if
+
+ align:start position:0%
+you keep a destruction now you if you if
+ 
+
+ align:start position:0%
+you keep a destruction now you if you if
+your reverse process of diffusion you'll
+
+ align:start position:0%
+your reverse process of diffusion you'll
+ 
+
+ align:start position:0%
+your reverse process of diffusion you'll
+never go from this back to this but if
+
+ align:start position:0%
+never go from this back to this but if
+ 
+
+ align:start position:0%
+never go from this back to this but if
+your reverse process is a neural network
+
+ align:start position:0%
+your reverse process is a neural network
+ 
+
+ align:start position:0%
+your reverse process is a neural network
+trained to do it you might be able to do
+
+ align:start position:0%
+trained to do it you might be able to do
+ 
+
+ align:start position:0%
+trained to do it you might be able to do
+it okay so that's the basic idea so
+
+ align:start position:0%
+it okay so that's the basic idea so
+ 
+
+ align:start position:0%
+it okay so that's the basic idea so
+that's what we did and I'll just show
+
+ align:start position:0%
+that's what we did and I'll just show
+ 
+
+ align:start position:0%
+that's what we did and I'll just show
+you some nice movies to show that it
+
+ align:start position:0%
+you some nice movies to show that it
+ 
+
+ align:start position:0%
+you some nice movies to show that it
+works this is the classical toy model
+
+ align:start position:0%
+works this is the classical toy model
+ 
+
+ align:start position:0%
+works this is the classical toy model
+will go to more complex models this is
+
+ align:start position:0%
+will go to more complex models this is
+ 
+
+ align:start position:0%
+will go to more complex models this is
+some distribution in two-dimensional
+
+ align:start position:0%
+some distribution in two-dimensional
+ 
+
+ align:start position:0%
+some distribution in two-dimensional
+space and so what we do is we just
+
+ align:start position:0%
+space and so what we do is we just
+ 
+
+ align:start position:0%
+space and so what we do is we just
+systematically have the points to fuse
+
+ align:start position:0%
+systematically have the points to fuse
+ 
+
+ align:start position:0%
+systematically have the points to fuse
+under Gaussian to fusion with the
+
+ align:start position:0%
+under Gaussian to fusion with the
+ 
+
+ align:start position:0%
+under Gaussian to fusion with the
+restoring force to the origin so the
+
+ align:start position:0%
+restoring force to the origin so the
+ 
+
+ align:start position:0%
+restoring force to the origin so the
+stationary distribution of that of that
+
+ align:start position:0%
+stationary distribution of that of that
+ 
+
+ align:start position:0%
+stationary distribution of that of that
+destructive process is an isotropic
+
+ align:start position:0%
+destructive process is an isotropic
+ 
+
+ align:start position:0%
+destructive process is an isotropic
+Gaussian okay and that and that's that's
+
+ align:start position:0%
+Gaussian okay and that and that's that's
+ 
+
+ align:start position:0%
+Gaussian okay and that and that's that's
+that's what happens so that's our
+
+ align:start position:0%
+that's what happens so that's our
+ 
+
+ align:start position:0%
+that's what happens so that's our
+training data ire movie is the training
+
+ align:start position:0%
+training data ire movie is the training
+ 
+
+ align:start position:0%
+training data ire movie is the training
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+okay then what we do is we train a
+
+ align:start position:0%
+okay then what we do is we train a
+ 
+
+ align:start position:0%
+okay then what we do is we train a
+neural network to reverse time in that
+
+ align:start position:0%
+neural network to reverse time in that
+ 
+
+ align:start position:0%
+neural network to reverse time in that
+movie so it's an it's a neural network
+
+ align:start position:0%
+movie so it's an it's a neural network
+ 
+
+ align:start position:0%
+movie so it's an it's a neural network
+with many many layers hundreds and
+
+ align:start position:0%
+with many many layers hundreds and
+ 
+
+ align:start position:0%
+with many many layers hundreds and
+hundreds of layers right so classically
+
+ align:start position:0%
+hundreds of layers right so classically
+ 
+
+ align:start position:0%
+hundreds of layers right so classically
+training a network of hundreds of layers
+
+ align:start position:0%
+training a network of hundreds of layers
+ 
+
+ align:start position:0%
+training a network of hundreds of layers
+you have the credit assignment problem
+
+ align:start position:0%
+you have the credit assignment problem
+ 
+
+ align:start position:0%
+you have the credit assignment problem
+because you don't know what they the
+
+ align:start position:0%
+because you don't know what they the
+ 
+
+ align:start position:0%
+because you don't know what they the
+intermediate neurons are supposed to do
+
+ align:start position:0%
+intermediate neurons are supposed to do
+ 
+
+ align:start position:0%
+intermediate neurons are supposed to do
+convened the credit assignment problem
+
+ align:start position:0%
+convened the credit assignment problem
+ 
+
+ align:start position:0%
+convened the credit assignment problem
+because each layer going up to the next
+
+ align:start position:0%
+because each layer going up to the next
+ 
+
+ align:start position:0%
+because each layer going up to the next
+layer just has to go from time T to time
+
+ align:start position:0%
+layer just has to go from time T to time
+ 
+
+ align:start position:0%
+layer just has to go from time T to time
+t minus one in the in the training data
+
+ align:start position:0%
+t minus one in the in the training data
+ 
+
+ align:start position:0%
+t minus one in the in the training data
+so you have targets for all the
+
+ align:start position:0%
+so you have targets for all the
+ 
+
+ align:start position:0%
+so you have targets for all the
+intermediate layers therefore you've
+
+ align:start position:0%
+intermediate layers therefore you've
+ 
+
+ align:start position:0%
+intermediate layers therefore you've
+circumvented the credit assignment
+
+ align:start position:0%
+circumvented the credit assignment
+ 
+
+ align:start position:0%
+circumvented the credit assignment
+problem okay so it's it's relatively
+
+ align:start position:0%
+problem okay so it's it's relatively
+ 
+
+ align:start position:0%
+problem okay so it's it's relatively
+easy to train such networks and so once
+
+ align:start position:0%
+easy to train such networks and so once
+ 
+
+ align:start position:0%
+easy to train such networks and so once
+you have such a network what should be
+
+ align:start position:0%
+you have such a network what should be
+ 
+
+ align:start position:0%
+you have such a network what should be
+able to do you should be able to feed
+
+ align:start position:0%
+able to do you should be able to feed
+ 
+
+ align:start position:0%
+able to do you should be able to feed
+that neural network an isotropic
+
+ align:start position:0%
+that neural network an isotropic
+ 
+
+ align:start position:0%
+that neural network an isotropic
+Gaussian and then have that Gaussian be
+
+ align:start position:0%
+Gaussian and then have that Gaussian be
+ 
+
+ align:start position:0%
+Gaussian and then have that Gaussian be
+turned into the data distribution so
+
+ align:start position:0%
+turned into the data distribution so
+ 
+
+ align:start position:0%
+turned into the data distribution so
+that's what happens this on the right is
+
+ align:start position:0%
+that's what happens this on the right is
+ 
+
+ align:start position:0%
+that's what happens this on the right is
+a different Gaussian and we just feed it
+
+ align:start position:0%
+a different Gaussian and we just feed it
+ 
+
+ align:start position:0%
+a different Gaussian and we just feed it
+through the trained deterministic neural
+
+ align:start position:0%
+through the trained deterministic neural
+ 
+
+ align:start position:0%
+through the trained deterministic neural
+network and out pops the it's not
+
+ align:start position:0%
+network and out pops the it's not
+ 
+
+ align:start position:0%
+network and out pops the it's not
+perfect there's some data points that
+
+ align:start position:0%
+perfect there's some data points that
+ 
+
+ align:start position:0%
+perfect there's some data points that
+are over here but this is roughly the
+
+ align:start position:0%
+are over here but this is roughly the
+ 
+
+ align:start position:0%
+are over here but this is roughly the
+distribution that had learned which is
+
+ align:start position:0%
+distribution that had learned which is
+ 
+
+ align:start position:0%
+distribution that had learned which is
+similar to what it was trained on okay
+
+ align:start position:0%
+similar to what it was trained on okay
+ 
+
+ align:start position:0%
+similar to what it was trained on okay
+so now we can look at slightly more
+
+ align:start position:0%
+so now we can look at slightly more
+ 
+
+ align:start position:0%
+so now we can look at slightly more
+complicated distribution so okay so
+
+ align:start position:0%
+complicated distribution so okay so
+ 
+
+ align:start position:0%
+complicated distribution so okay so
+that's that so now we can train it on a
+
+ align:start position:0%
+that's that so now we can train it on a
+ 
+
+ align:start position:0%
+that's that so now we can train it on a
+toy model of natural images right so a
+
+ align:start position:0%
+toy model of natural images right so a
+ 
+
+ align:start position:0%
+toy model of natural images right so a
+classic toy model of natural images is
+
+ align:start position:0%
+classic toy model of natural images is
+ 
+
+ align:start position:0%
+classic toy model of natural images is
+the dead leaves model where the sampling
+
+ align:start position:0%
+the dead leaves model where the sampling
+ 
+
+ align:start position:0%
+the dead leaves model where the sampling
+process is you just throw down circles
+
+ align:start position:0%
+process is you just throw down circles
+ 
+
+ align:start position:0%
+process is you just throw down circles
+of different radii so you get a complex
+
+ align:start position:0%
+of different radii so you get a complex
+ 
+
+ align:start position:0%
+of different radii so you get a complex
+model of natural images that in count
+
+ align:start position:0%
+model of natural images that in count
+ 
+
+ align:start position:0%
+model of natural images that in count
+that has long range edges occlusion
+
+ align:start position:0%
+that has long range edges occlusion
+ 
+
+ align:start position:0%
+that has long range edges occlusion
+coherence over long length scales and so
+
+ align:start position:0%
+coherence over long length scales and so
+ 
+
+ align:start position:0%
+coherence over long length scales and so
+on and so forth so we can train the
+
+ align:start position:0%
+on and so forth so we can train the
+ 
+
+ align:start position:0%
+on and so forth so we can train the
+neural network on such distributions we
+
+ align:start position:0%
+neural network on such distributions we
+ 
+
+ align:start position:0%
+neural network on such distributions we
+train it in a convolutional fashion by
+
+ align:start position:0%
+train it in a convolutional fashion by
+ 
+
+ align:start position:0%
+train it in a convolutional fashion by
+working on local image patches and we
+
+ align:start position:0%
+working on local image patches and we
+ 
+
+ align:start position:0%
+working on local image patches and we
+convolve so information and propagate
+
+ align:start position:0%
+convolve so information and propagate
+ 
+
+ align:start position:0%
+convolve so information and propagate
+over long ranges and so again we take
+
+ align:start position:0%
+over long ranges and so again we take
+ 
+
+ align:start position:0%
+over long ranges and so again we take
+these natural images and turn them into
+
+ align:start position:0%
+these natural images and turn them into
+ 
+
+ align:start position:0%
+these natural images and turn them into
+noise keep a record of that movie and
+
+ align:start position:0%
+noise keep a record of that movie and
+ 
+
+ align:start position:0%
+noise keep a record of that movie and
+then reverse the flow of time using a
+
+ align:start position:0%
+then reverse the flow of time using a
+ 
+
+ align:start position:0%
+then reverse the flow of time using a
+deep neural network and it's okay so
+
+ align:start position:0%
+deep neural network and it's okay so
+ 
+
+ align:start position:0%
+deep neural network and it's okay so
+once we train that right we should be
+
+ align:start position:0%
+once we train that right we should be
+ 
+
+ align:start position:0%
+once we train that right we should be
+able to turn noise into the network's
+
+ align:start position:0%
+able to turn noise into the network's
+ 
+
+ align:start position:0%
+able to turn noise into the network's
+best guess as to what a dead leaves
+
+ align:start position:0%
+best guess as to what a dead leaves
+ 
+
+ align:start position:0%
+best guess as to what a dead leaves
+model would look like so this is what
+
+ align:start position:0%
+model would look like so this is what
+ 
+
+ align:start position:0%
+model would look like so this is what
+happens it's taking noise and it turns
+
+ align:start position:0%
+happens it's taking noise and it turns
+ 
+
+ align:start position:0%
+happens it's taking noise and it turns
+it into a gas
+
+ align:start position:0%
+it into a gas
+ 
+
+ align:start position:0%
+it into a gas
+okay so it's not a perfect model but it
+
+ align:start position:0%
+okay so it's not a perfect model but it
+ 
+
+ align:start position:0%
+okay so it's not a perfect model but it
+turns out log probability of dead leaves
+
+ align:start position:0%
+turns out log probability of dead leaves
+ 
+
+ align:start position:0%
+turns out log probability of dead leaves
+under this generative model that
+
+ align:start position:0%
+under this generative model that
+ 
+
+ align:start position:0%
+under this generative model that
+consists of a thousand layer deep neural
+
+ align:start position:0%
+consists of a thousand layer deep neural
+ 
+
+ align:start position:0%
+consists of a thousand layer deep neural
+network that's higher than any other
+
+ align:start position:0%
+network that's higher than any other
+ 
+
+ align:start position:0%
+network that's higher than any other
+model so far so this is currently state
+
+ align:start position:0%
+model so far so this is currently state
+ 
+
+ align:start position:0%
+model so far so this is currently state
+of the art okay and as you can see it
+
+ align:start position:0%
+of the art okay and as you can see it
+ 
+
+ align:start position:0%
+of the art okay and as you can see it
+gets long-range coherence and sharp
+
+ align:start position:0%
+gets long-range coherence and sharp
+ 
+
+ align:start position:0%
+gets long-range coherence and sharp
+edges and moreover it gets long-range
+
+ align:start position:0%
+edges and moreover it gets long-range
+ 
+
+ align:start position:0%
+edges and moreover it gets long-range
+coherence and the orientation and hard
+
+ align:start position:0%
+coherence and the orientation and hard
+ 
+
+ align:start position:0%
+coherence and the orientation and hard
+to do in in generative models of natural
+
+ align:start position:0%
+to do in in generative models of natural
+ 
+
+ align:start position:0%
+to do in in generative models of natural
+images okay now we can actually do
+
+ align:start position:0%
+images okay now we can actually do
+ 
+
+ align:start position:0%
+images okay now we can actually do
+something somewhat practical with this
+
+ align:start position:0%
+something somewhat practical with this
+ 
+
+ align:start position:0%
+something somewhat practical with this
+is we sample from the conditional so
+
+ align:start position:0%
+is we sample from the conditional so
+ 
+
+ align:start position:0%
+is we sample from the conditional so
+then we also trained it on textures okay
+
+ align:start position:0%
+then we also trained it on textures okay
+ 
+
+ align:start position:0%
+then we also trained it on textures okay
+so so so for example textures of bark
+
+ align:start position:0%
+so so so for example textures of bark
+ 
+
+ align:start position:0%
+so so so for example textures of bark
+right and we can also sample from the
+
+ align:start position:0%
+right and we can also sample from the
+ 
+
+ align:start position:0%
+right and we can also sample from the
+conditional distribution so what we can
+
+ align:start position:0%
+conditional distribution so what we can
+ 
+
+ align:start position:0%
+conditional distribution so what we can
+do is we can clamp the the pixels
+
+ align:start position:0%
+do is we can clamp the the pixels
+ 
+
+ align:start position:0%
+do is we can clamp the the pixels
+outside of a certain range replace the
+
+ align:start position:0%
+outside of a certain range replace the
+ 
+
+ align:start position:0%
+outside of a certain range replace the
+interior wouldn't make it blank and
+
+ align:start position:0%
+interior wouldn't make it blank and
+ 
+
+ align:start position:0%
+interior wouldn't make it blank and
+because the network operates in a
+
+ align:start position:0%
+because the network operates in a
+ 
+
+ align:start position:0%
+because the network operates in a
+convolutional fashion information from
+
+ align:start position:0%
+convolutional fashion information from
+ 
+
+ align:start position:0%
+convolutional fashion information from
+the boundary should propagate into the
+
+ align:start position:0%
+the boundary should propagate into the
+ 
+
+ align:start position:0%
+the boundary should propagate into the
+interior and fill it in right so if we
+
+ align:start position:0%
+interior and fill it in right so if we
+ 
+
+ align:start position:0%
+interior and fill it in right so if we
+look at that
+
+ align:start position:0%
+look at that
+ 
+
+ align:start position:0%
+look at that
+so that's white noise and the network is
+
+ align:start position:0%
+so that's white noise and the network is
+ 
+
+ align:start position:0%
+so that's white noise and the network is
+filling it in and it fills in the it
+
+ align:start position:0%
+filling it in and it fills in the it
+ 
+
+ align:start position:0%
+filling it in and it fills in the it
+fills in the best guess image okay and
+
+ align:start position:0%
+fills in the best guess image okay and
+ 
+
+ align:start position:0%
+fills in the best guess image okay and
+so again it's not identical to the
+
+ align:start position:0%
+so again it's not identical to the
+ 
+
+ align:start position:0%
+so again it's not identical to the
+original image but it does get
+
+ align:start position:0%
+original image but it does get
+ 
+
+ align:start position:0%
+original image but it does get
+long-range edge structure coherence and
+
+ align:start position:0%
+long-range edge structure coherence and
+ 
+
+ align:start position:0%
+long-range edge structure coherence and
+the orientation of the edge and smooth
+
+ align:start position:0%
+the orientation of the edge and smooth
+ 
+
+ align:start position:0%
+the orientation of the edge and smooth
+structure as well and again this is like
+
+ align:start position:0%
+structure as well and again this is like
+ 
+
+ align:start position:0%
+structure as well and again this is like
+a thousand layer neural network now
+
+ align:start position:0%
+a thousand layer neural network now
+ 
+
+ align:start position:0%
+a thousand layer neural network now
+there's some lessons here okay
+
+ align:start position:0%
+there's some lessons here okay
+ 
+
+ align:start position:0%
+there's some lessons here okay
+oftentimes when we model complex data
+
+ align:start position:0%
+oftentimes when we model complex data
+ 
+
+ align:start position:0%
+oftentimes when we model complex data
+distributions what we try to do is we
+
+ align:start position:0%
+distributions what we try to do is we
+ 
+
+ align:start position:0%
+distributions what we try to do is we
+try to create a stochastic process whose
+
+ align:start position:0%
+try to create a stochastic process whose
+ 
+
+ align:start position:0%
+try to create a stochastic process whose
+stationary distribution is the complex
+
+ align:start position:0%
+stationary distribution is the complex
+ 
+
+ align:start position:0%
+stationary distribution is the complex
+distribution right now if your
+
+ align:start position:0%
+distribution right now if your
+ 
+
+ align:start position:0%
+distribution right now if your
+distribution has multiple modes you're
+
+ align:start position:0%
+distribution has multiple modes you're
+ 
+
+ align:start position:0%
+distribution has multiple modes you're
+going to run into a mixing problem
+
+ align:start position:0%
+going to run into a mixing problem
+ 
+
+ align:start position:0%
+going to run into a mixing problem
+because it can take a stochastic process
+
+ align:start position:0%
+because it can take a stochastic process
+ 
+
+ align:start position:0%
+because it can take a stochastic process
+a long time to jump over energy barriers
+
+ align:start position:0%
+a long time to jump over energy barriers
+ 
+
+ align:start position:0%
+a long time to jump over energy barriers
+that separate the multiple modes so you
+
+ align:start position:0%
+that separate the multiple modes so you
+ 
+
+ align:start position:0%
+that separate the multiple modes so you
+always have a mixing problem that often
+
+ align:start position:0%
+always have a mixing problem that often
+ 
+
+ align:start position:0%
+always have a mixing problem that often
+times a new train system train
+
+ align:start position:0%
+times a new train system train
+ 
+
+ align:start position:0%
+times a new train system train
+publishing models you have to sample and
+
+ align:start position:0%
+publishing models you have to sample and
+ 
+
+ align:start position:0%
+publishing models you have to sample and
+then use the train the model so that
+
+ align:start position:0%
+then use the train the model so that
+ 
+
+ align:start position:0%
+then use the train the model so that
+makes training along the long that makes
+
+ align:start position:0%
+makes training along the long that makes
+ 
+
+ align:start position:0%
+makes training along the long that makes
+trailing training take a long time so
+
+ align:start position:0%
+trailing training take a long time so
+ 
+
+ align:start position:0%
+trailing training take a long time so
+what we're also doing in addition to
+
+ align:start position:0%
+what we're also doing in addition to
+ 
+
+ align:start position:0%
+what we're also doing in addition to
+circumventing the credit assignment
+
+ align:start position:0%
+circumventing the credit assignment
+ 
+
+ align:start position:0%
+circumventing the credit assignment
+problem in training very deep neural
+
+ align:start position:0%
+problem in training very deep neural
+ 
+
+ align:start position:0%
+problem in training very deep neural
+networks
+
+ align:start position:0%
+networks
+ 
+
+ align:start position:0%
+networks
+we're circumventing the mixing problem
+
+ align:start position:0%
+we're circumventing the mixing problem
+ 
+
+ align:start position:0%
+we're circumventing the mixing problem
+in training the generative model because
+
+ align:start position:0%
+in training the generative model because
+ 
+
+ align:start position:0%
+in training the generative model because
+we're not trying to model the data
+
+ align:start position:0%
+we're not trying to model the data
+ 
+
+ align:start position:0%
+we're not trying to model the data
+distribution as a stationary
+
+ align:start position:0%
+distribution as a stationary
+ 
+
+ align:start position:0%
+distribution as a stationary
+distribution of us to catch
+
+ align:start position:0%
+distribution of us to catch
+ 
+
+ align:start position:0%
+distribution of us to catch
+there would have to run for a very long
+
+ align:start position:0%
+there would have to run for a very long
+ 
+
+ align:start position:0%
+there would have to run for a very long
+time to get to the station distribution
+
+ align:start position:0%
+time to get to the station distribution
+ 
+
+ align:start position:0%
+time to get to the station distribution
+we're demanding that during training the
+
+ align:start position:0%
+we're demanding that during training the
+ 
+
+ align:start position:0%
+we're demanding that during training the
+process get to the the data distribution
+
+ align:start position:0%
+process get to the the data distribution
+ 
+
+ align:start position:0%
+process get to the the data distribution
+in a finite amount of time right so
+
+ align:start position:0%
+in a finite amount of time right so
+ 
+
+ align:start position:0%
+in a finite amount of time right so
+because during training we demand that
+
+ align:start position:0%
+because during training we demand that
+ 
+
+ align:start position:0%
+because during training we demand that
+we get to the data distribution of fine
+
+ align:start position:0%
+we get to the data distribution of fine
+ 
+
+ align:start position:0%
+we get to the data distribution of fine
+item at a time
+
+ align:start position:0%
+item at a time
+ 
+
+ align:start position:0%
+item at a time
+we're circumventing the mixing problem
+
+ align:start position:0%
+we're circumventing the mixing problem
+ 
+
+ align:start position:0%
+we're circumventing the mixing problem
+during training and that's the idea that
+
+ align:start position:0%
+during training and that's the idea that
+ 
+
+ align:start position:0%
+during training and that's the idea that
+that's idea there's lots of results now
+
+ align:start position:0%
+that's idea there's lots of results now
+ 
+
+ align:start position:0%
+that's idea there's lots of results now
+that show that you can attain
+
+ align:start position:0%
+that show that you can attain
+ 
+
+ align:start position:0%
+that show that you can attain
+information about stationary equilibrium
+
+ align:start position:0%
+information about stationary equilibrium
+ 
+
+ align:start position:0%
+information about stationary equilibrium
+distribution through non equilibrium
+
+ align:start position:0%
+distribution through non equilibrium
+ 
+
+ align:start position:0%
+distribution through non equilibrium
+trajectories okay so that now I'm done
+
+ align:start position:0%
+trajectories okay so that now I'm done
+ 
+
+ align:start position:0%
+trajectories okay so that now I'm done
+so let's see well okay so there's that
+
+ align:start position:0%
+so let's see well okay so there's that
+ 
+
+ align:start position:0%
+so let's see well okay so there's that
+ok so again you can read about all of
+
+ align:start position:0%
+ok so again you can read about all of
+ 
+
+ align:start position:0%
+ok so again you can read about all of
+this stuff in this set of papers again
+
+ align:start position:0%
+this stuff in this set of papers again
+ 
+
+ align:start position:0%
+this stuff in this set of papers again
+I'd like to thank my funding and just
+
+ align:start position:0%
+I'd like to thank my funding and just
+ 
+
+ align:start position:0%
+I'd like to thank my funding and just
+the the key players so Andrew sacks you
+
+ align:start position:0%
+the the key players so Andrew sacks you
+ 
+
+ align:start position:0%
+the the key players so Andrew sacks you
+know did the work with me on nonlinear
+
+ align:start position:0%
+know did the work with me on nonlinear
+ 
+
+ align:start position:0%
+know did the work with me on nonlinear
+learning dynamics and learning how
+
+ align:start position:0%
+learning dynamics and learning how
+ 
+
+ align:start position:0%
+learning dynamics and learning how
+academy structure joshua's addiction did
+
+ align:start position:0%
+academy structure joshua's addiction did
+ 
+
+ align:start position:0%
+academy structure joshua's addiction did
+the work on deep learning using noncom
+
+ align:start position:0%
+the work on deep learning using noncom
+ 
+
+ align:start position:0%
+the work on deep learning using noncom
+thermodynamics and the the the work and
+
+ align:start position:0%
+thermodynamics and the the the work and
+ 
+
+ align:start position:0%
+thermodynamics and the the the work and
+saddle points was a nice collaboration
+
+ align:start position:0%
+saddle points was a nice collaboration
+ 
+
+ align:start position:0%
+saddle points was a nice collaboration
+Yoshi Avengers lab and again fantastic
+
+ align:start position:0%
+Yoshi Avengers lab and again fantastic
+ 
+
+ align:start position:0%
+Yoshi Avengers lab and again fantastic
+graduate students in yoshua bengio
+
+ align:start position:0%
+graduate students in yoshua bengio
+ 
+
+ align:start position:0%
+graduate students in yoshua bengio
+Salaam okay so I think there's a lot
+
+ align:start position:0%
+Salaam okay so I think there's a lot
+ 
+
+ align:start position:0%
+Salaam okay so I think there's a lot
+more to do in terms of unifying
+
+ align:start position:0%
+more to do in terms of unifying
+ 
+
+ align:start position:0%
+more to do in terms of unifying
+neuroscience machine learning physics
+
+ align:start position:0%
+neuroscience machine learning physics
+ 
+
+ align:start position:0%
+neuroscience machine learning physics
+math statistics all of that stuff it'll
+
+ align:start position:0%
+math statistics all of that stuff it'll
+ 
+
+ align:start position:0%
+math statistics all of that stuff it'll
+keep us busy for the next century
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/p2j16ebu14U.txt b/p2j16ebu14U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..40d470005efd05637592d4dadac1e549b8582eff
--- /dev/null
+++ b/p2j16ebu14U.txt
@@ -0,0 +1,73 @@
+So here's the final version of our 5-stage
+pipelined data path.
+
+To deal with data hazards we've added stall
+logic to the IF and RF input registers.
+
+We've also added bypass muxes on the output
+of the register file read ports so we can
+
+route values from later in the data path if
+we need to access a register value that's
+
+been computed but not yet written to the register
+file.
+
+We also made a provision to insert NOPs into
+the pipeline after the RF stage if the IF
+
+and RF stages are stalled.
+
+To deal with control hazards, we speculate
+that the next instruction is at PC+4.
+
+But for JMPs and taken branches, that guess
+is wrong so we added a provision for annulling
+
+the instruction in the IF stage.
+
+To deal with exceptions and interrupts we
+added instruction muxes in all but the final
+
+pipeline stage.
+
+An instruction that causes an exception is
+replaced by our magic BNE instruction to capture
+
+its PC+4 value.
+
+And instructions in earlier stages are annulled.
+
+All this extra circuitry has been added to
+ensure that pipelined execution gives the
+
+same result as unpipelined execution.
+
+The use of bypassing and branch prediction
+ensures that data and control hazards have
+
+only a small negative impact on the effective
+CPI.
+
+This means that the much shorter clock period
+translates to a large increase in instruction
+
+throughput.
+
+It's worth remembering the strategies we used
+to deal with hazards: stalling, bypassing
+
+and speculation.
+
+Most execution issues can be dealt with using
+one of these strategies, so keep these in
+
+mind if you ever need to design a high-performance
+pipelined system.
+
+This completes our discussion of pipelining.
+
+We'll explore other avenues to higher processor
+performance in the last lecture, which discusses
+
+parallel processing.
\ No newline at end of file
diff --git a/ptjKegETGuA.txt b/ptjKegETGuA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..208431fd5761e7121c882dfb9c2c5e6bd5b6427f
--- /dev/null
+++ b/ptjKegETGuA.txt
@@ -0,0 +1,21043 @@
+align:start position:0%
+ 
+The following content is provided by MIT
+
+ align:start position:0%
+The following content is provided by MIT
+ 
+
+ align:start position:0%
+The following content is provided by MIT
+Open Courseware under a creative common
+
+ align:start position:0%
+Open Courseware under a creative common
+ 
+
+ align:start position:0%
+Open Courseware under a creative common
+license. Additional information about
+
+ align:start position:0%
+license. Additional information about
+ 
+
+ align:start position:0%
+license. Additional information about
+our license and MIT Open Courseware in
+
+ align:start position:0%
+our license and MIT Open Courseware in
+ 
+
+ align:start position:0%
+our license and MIT Open Courseware in
+general is available at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Welcome to the CDD forum. Sensing place
+
+ align:start position:0%
+Welcome to the CDD forum. Sensing place
+ 
+
+ align:start position:0%
+Welcome to the CDD forum. Sensing place
+photography is inquiry.
+
+ align:start position:0%
+photography is inquiry.
+ 
+
+ align:start position:0%
+photography is inquiry.
+Uh we have today with us Martin Kger
+
+ align:start position:0%
+Uh we have today with us Martin Kger
+ 
+
+ align:start position:0%
+Uh we have today with us Martin Kger
+who's a professor of urban planning at
+
+ align:start position:0%
+who's a professor of urban planning at
+ 
+
+ align:start position:0%
+who's a professor of urban planning at
+um from California and who interestingly
+
+ align:start position:0%
+um from California and who interestingly
+ 
+
+ align:start position:0%
+um from California and who interestingly
+enough started out in physics and got
+
+ align:start position:0%
+enough started out in physics and got
+ 
+
+ align:start position:0%
+enough started out in physics and got
+his PhD in physics before moving to
+
+ align:start position:0%
+his PhD in physics before moving to
+ 
+
+ align:start position:0%
+his PhD in physics before moving to
+planning uh and ask him how he made that
+
+ align:start position:0%
+planning uh and ask him how he made that
+ 
+
+ align:start position:0%
+planning uh and ask him how he made that
+was an interesting shift to to make that
+
+ align:start position:0%
+was an interesting shift to to make that
+ 
+
+ align:start position:0%
+was an interesting shift to to make that
+uh connection between the understanding
+
+ align:start position:0%
+uh connection between the understanding
+ 
+
+ align:start position:0%
+uh connection between the understanding
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+physics and
+
+ align:start position:0%
+physics and
+ 
+
+ align:start position:0%
+physics and
+issues around the planet. I first
+
+ align:start position:0%
+issues around the planet. I first
+ 
+
+ align:start position:0%
+issues around the planet. I first
+encountered his work in the pages of
+
+ align:start position:0%
+encountered his work in the pages of
+ 
+
+ align:start position:0%
+encountered his work in the pages of
+landscape architecture magazine in a
+
+ align:start position:0%
+landscape architecture magazine in a
+ 
+
+ align:start position:0%
+landscape architecture magazine in a
+wonderful article called What's Wrong
+
+ align:start position:0%
+wonderful article called What's Wrong
+ 
+
+ align:start position:0%
+wonderful article called What's Wrong
+with Plastic Trees? It was quite
+
+ align:start position:0%
+with Plastic Trees? It was quite
+ 
+
+ align:start position:0%
+with Plastic Trees? It was quite
+provocative and is the title of a more
+
+ align:start position:0%
+provocative and is the title of a more
+ 
+
+ align:start position:0%
+provocative and is the title of a more
+recent
+
+ align:start position:0%
+recent
+ 
+
+ align:start position:0%
+recent
+book. So I think uh you'll all be set
+
+ align:start position:0%
+book. So I think uh you'll all be set
+ 
+
+ align:start position:0%
+book. So I think uh you'll all be set
+for quite a ride here of uh presentation
+
+ align:start position:0%
+for quite a ride here of uh presentation
+ 
+
+ align:start position:0%
+for quite a ride here of uh presentation
+of looking at the city uh using
+
+ align:start position:0%
+of looking at the city uh using
+ 
+
+ align:start position:0%
+of looking at the city uh using
+photography and uh as a form of research
+
+ align:start position:0%
+photography and uh as a form of research
+ 
+
+ align:start position:0%
+photography and uh as a form of research
+and Mark Schuster will be giving a few
+
+ align:start position:0%
+and Mark Schuster will be giving a few
+ 
+
+ align:start position:0%
+and Mark Schuster will be giving a few
+comments after Martin Creger's
+
+ align:start position:0%
+comments after Martin Creger's
+ 
+
+ align:start position:0%
+comments after Martin Creger's
+presentation. So welcome. Before um I
+
+ align:start position:0%
+presentation. So welcome. Before um I
+ 
+
+ align:start position:0%
+presentation. So welcome. Before um I
+turn this over to Martin, I'd like to
+
+ align:start position:0%
+turn this over to Martin, I'd like to
+ 
+
+ align:start position:0%
+turn this over to Martin, I'd like to
+announce that Leslie Tuttle will be
+
+ align:start position:0%
+announce that Leslie Tuttle will be
+ 
+
+ align:start position:0%
+announce that Leslie Tuttle will be
+speaking next Monday at 6:00 on uh title
+
+ align:start position:0%
+speaking next Monday at 6:00 on uh title
+ 
+
+ align:start position:0%
+speaking next Monday at 6:00 on uh title
+Leaving Tradition Behind. Leaving
+
+ align:start position:0%
+Leaving Tradition Behind. Leaving
+ 
+
+ align:start position:0%
+Leaving Tradition Behind. Leaving
+tradition behind which is about uh
+
+ align:start position:0%
+tradition behind which is about uh
+ 
+
+ align:start position:0%
+tradition behind which is about uh
+several generations of Muslim Kurdish
+
+ align:start position:0%
+several generations of Muslim Kurdish
+ 
+
+ align:start position:0%
+several generations of Muslim Kurdish
+women in and their families in Turkey
+
+ align:start position:0%
+women in and their families in Turkey
+ 
+
+ align:start position:0%
+women in and their families in Turkey
+and the migration of the children and
+
+ align:start position:0%
+and the migration of the children and
+ 
+
+ align:start position:0%
+and the migration of the children and
+grandchildren uh from the village to
+
+ align:start position:0%
+grandchildren uh from the village to
+ 
+
+ align:start position:0%
+grandchildren uh from the village to
+cities and then onto London. So please
+
+ align:start position:0%
+cities and then onto London. So please
+ 
+
+ align:start position:0%
+cities and then onto London. So please
+join us uh next Monday.
+
+ align:start position:0%
+join us uh next Monday.
+ 
+
+ align:start position:0%
+join us uh next Monday.
+Martin, thank you very much. Um, I'll
+
+ align:start position:0%
+Martin, thank you very much. Um, I'll
+ 
+
+ align:start position:0%
+Martin, thank you very much. Um, I'll
+explain the title which has lots of sort
+
+ align:start position:0%
+explain the title which has lots of sort
+ 
+
+ align:start position:0%
+explain the title which has lots of sort
+of $100 words in it like ambiences and
+
+ align:start position:0%
+of $100 words in it like ambiences and
+ 
+
+ align:start position:0%
+of $100 words in it like ambiences and
+choreographies and sensorium
+
+ align:start position:0%
+choreographies and sensorium
+ 
+
+ align:start position:0%
+choreographies and sensorium
+uh as I go along. Um, first of all, it's
+
+ align:start position:0%
+uh as I go along. Um, first of all, it's
+ 
+
+ align:start position:0%
+uh as I go along. Um, first of all, it's
+really very lovely to be back in 10485
+
+ align:start position:0%
+really very lovely to be back in 10485
+ 
+
+ align:start position:0%
+really very lovely to be back in 10485
+after having uh left it about 20 years
+
+ align:start position:0%
+after having uh left it about 20 years
+ 
+
+ align:start position:0%
+after having uh left it about 20 years
+ago and or 22 years ago and see some of
+
+ align:start position:0%
+ago and or 22 years ago and see some of
+ 
+
+ align:start position:0%
+ago and or 22 years ago and see some of
+my old friends here and new people and
+
+ align:start position:0%
+my old friends here and new people and
+ 
+
+ align:start position:0%
+my old friends here and new people and
+people who were once uh sort of young
+
+ align:start position:0%
+people who were once uh sort of young
+ 
+
+ align:start position:0%
+people who were once uh sort of young
+and now or less young as they say and
+
+ align:start position:0%
+and now or less young as they say and
+ 
+
+ align:start position:0%
+and now or less young as they say and
+some of us who are middle-aged and now
+
+ align:start position:0%
+some of us who are middle-aged and now
+ 
+
+ align:start position:0%
+some of us who are middle-aged and now
+older. Um, so it's really nice and MIT
+
+ align:start position:0%
+older. Um, so it's really nice and MIT
+ 
+
+ align:start position:0%
+older. Um, so it's really nice and MIT
+has really quite a distinguished
+
+ align:start position:0%
+has really quite a distinguished
+ 
+
+ align:start position:0%
+has really quite a distinguished
+tradition in photography as you're
+
+ align:start position:0%
+tradition in photography as you're
+ 
+
+ align:start position:0%
+tradition in photography as you're
+probably aware of. um minor white taught
+
+ align:start position:0%
+probably aware of. um minor white taught
+ 
+
+ align:start position:0%
+probably aware of. um minor white taught
+here in the 60s I believe and uh where
+
+ align:start position:0%
+here in the 60s I believe and uh where
+ 
+
+ align:start position:0%
+here in the 60s I believe and uh where
+Jerry Weezner some thought that somehow
+
+ align:start position:0%
+Jerry Weezner some thought that somehow
+ 
+
+ align:start position:0%
+Jerry Weezner some thought that somehow
+the arts could humanize the engineers.
+
+ align:start position:0%
+the arts could humanize the engineers.
+ 
+
+ align:start position:0%
+the arts could humanize the engineers.
+I'm not sure if that's uh in fact the
+
+ align:start position:0%
+I'm not sure if that's uh in fact the
+ 
+
+ align:start position:0%
+I'm not sure if that's uh in fact the
+way to do it but it certainly was good
+
+ align:start position:0%
+way to do it but it certainly was good
+ 
+
+ align:start position:0%
+way to do it but it certainly was good
+to have uh minor white teaching here. Uh
+
+ align:start position:0%
+to have uh minor white teaching here. Uh
+ 
+
+ align:start position:0%
+to have uh minor white teaching here. Uh
+and if you my favorite thing about MIT
+
+ align:start position:0%
+and if you my favorite thing about MIT
+ 
+
+ align:start position:0%
+and if you my favorite thing about MIT
+is that if you go in E51 and E53 on the
+
+ align:start position:0%
+is that if you go in E51 and E53 on the
+ 
+
+ align:start position:0%
+is that if you go in E51 and E53 on the
+third floor at least 20 years ago there
+
+ align:start position:0%
+third floor at least 20 years ago there
+ 
+
+ align:start position:0%
+third floor at least 20 years ago there
+were photographs by Bernice Abbott of
+
+ align:start position:0%
+were photographs by Bernice Abbott of
+ 
+
+ align:start position:0%
+were photographs by Bernice Abbott of
+various physics experiments. Are they
+
+ align:start position:0%
+various physics experiments. Are they
+ 
+
+ align:start position:0%
+various physics experiments. Are they
+still there? They're in the president's
+
+ align:start position:0%
+still there? They're in the president's
+ 
+
+ align:start position:0%
+still there? They're in the president's
+office. They're spectacular images and I
+
+ align:start position:0%
+office. They're spectacular images and I
+ 
+
+ align:start position:0%
+office. They're spectacular images and I
+recommend them highly to you. Uh they
+
+ align:start position:0%
+recommend them highly to you. Uh they
+ 
+
+ align:start position:0%
+recommend them highly to you. Uh they
+used for the physical sciences study
+
+ align:start position:0%
+used for the physical sciences study
+ 
+
+ align:start position:0%
+used for the physical sciences study
+committee. Uh she was commissioned to do
+
+ align:start position:0%
+committee. Uh she was commissioned to do
+ 
+
+ align:start position:0%
+committee. Uh she was commissioned to do
+that. And if you don't know who Bernie
+
+ align:start position:0%
+that. And if you don't know who Bernie
+ 
+
+ align:start position:0%
+that. And if you don't know who Bernie
+Sabbat is, she'll come up later. Um and
+
+ align:start position:0%
+Sabbat is, she'll come up later. Um and
+ 
+
+ align:start position:0%
+Sabbat is, she'll come up later. Um and
+I'm also grateful in some sense for
+
+ align:start position:0%
+I'm also grateful in some sense for
+ 
+
+ align:start position:0%
+I'm also grateful in some sense for
+having left MIT and gone Hollywood, so
+
+ align:start position:0%
+having left MIT and gone Hollywood, so
+ 
+
+ align:start position:0%
+having left MIT and gone Hollywood, so
+to speak, as you'll see. I teach at the
+
+ align:start position:0%
+to speak, as you'll see. I teach at the
+ 
+
+ align:start position:0%
+to speak, as you'll see. I teach at the
+University of Southern California and as
+
+ align:start position:0%
+University of Southern California and as
+ 
+
+ align:start position:0%
+University of Southern California and as
+I was saying before half our faculty
+
+ align:start position:0%
+I was saying before half our faculty
+ 
+
+ align:start position:0%
+I was saying before half our faculty
+would wish if you ask them what they
+
+ align:start position:0%
+would wish if you ask them what they
+ 
+
+ align:start position:0%
+would wish if you ask them what they
+really want to do they really want to
+
+ align:start position:0%
+really want to do they really want to
+ 
+
+ align:start position:0%
+really want to do they really want to
+direct. Uh in any case uh I thought
+
+ align:start position:0%
+direct. Uh in any case uh I thought
+ 
+
+ align:start position:0%
+direct. Uh in any case uh I thought
+inquiry and sensing is a perfect theme
+
+ align:start position:0%
+inquiry and sensing is a perfect theme
+ 
+
+ align:start position:0%
+inquiry and sensing is a perfect theme
+because in fact that's what I'm up to.
+
+ align:start position:0%
+because in fact that's what I'm up to.
+ 
+
+ align:start position:0%
+because in fact that's what I'm up to.
+Let me give you a preview of what I'll
+
+ align:start position:0%
+Let me give you a preview of what I'll
+ 
+
+ align:start position:0%
+Let me give you a preview of what I'll
+be saying. Uh I gather questions should
+
+ align:start position:0%
+be saying. Uh I gather questions should
+ 
+
+ align:start position:0%
+be saying. Uh I gather questions should
+be deferred to later on so that the
+
+ align:start position:0%
+be deferred to later on so that the
+ 
+
+ align:start position:0%
+be deferred to later on so that the
+recording can go smoothly but uh I'll be
+
+ align:start position:0%
+recording can go smoothly but uh I'll be
+ 
+
+ align:start position:0%
+recording can go smoothly but uh I'll be
+glad to take on any questions. Normally
+
+ align:start position:0%
+glad to take on any questions. Normally
+ 
+
+ align:start position:0%
+glad to take on any questions. Normally
+I take them during
+
+ align:start position:0%
+I take them during
+ 
+
+ align:start position:0%
+I take them during
+um this work on photography I'll argue
+
+ align:start position:0%
+um this work on photography I'll argue
+ 
+
+ align:start position:0%
+um this work on photography I'll argue
+was a natural continuation my other work
+
+ align:start position:0%
+was a natural continuation my other work
+ 
+
+ align:start position:0%
+was a natural continuation my other work
+and what gave me the courage to pursue
+
+ align:start position:0%
+and what gave me the courage to pursue
+ 
+
+ align:start position:0%
+and what gave me the courage to pursue
+it besides getting older was the work of
+
+ align:start position:0%
+it besides getting older was the work of
+ 
+
+ align:start position:0%
+it besides getting older was the work of
+diet in the French encyclopedia of 1760
+
+ align:start position:0%
+diet in the French encyclopedia of 1760
+ 
+
+ align:start position:0%
+diet in the French encyclopedia of 1760
+Charles Marviel's work of 1860 where he
+
+ align:start position:0%
+Charles Marviel's work of 1860 where he
+ 
+
+ align:start position:0%
+Charles Marviel's work of 1860 where he
+photographed Paris before it was
+
+ align:start position:0%
+photographed Paris before it was
+ 
+
+ align:start position:0%
+photographed Paris before it was
+eviscerated by Baron Houseman and Eugene
+
+ align:start position:0%
+eviscerated by Baron Houseman and Eugene
+ 
+
+ align:start position:0%
+eviscerated by Baron Houseman and Eugene
+Ajett's photographs of Paris in around
+
+ align:start position:0%
+Ajett's photographs of Paris in around
+ 
+
+ align:start position:0%
+Ajett's photographs of Paris in around
+1910 1920 uh as it slowly fully but
+
+ align:start position:0%
+1910 1920 uh as it slowly fully but
+ 
+
+ align:start position:0%
+1910 1920 uh as it slowly fully but
+wasn't modernizing yet. Uh my insight
+
+ align:start position:0%
+wasn't modernizing yet. Uh my insight
+ 
+
+ align:start position:0%
+wasn't modernizing yet. Uh my insight
+was that I didn't have to be an artistic
+
+ align:start position:0%
+was that I didn't have to be an artistic
+ 
+
+ align:start position:0%
+was that I didn't have to be an artistic
+photographer to do the work but I could
+
+ align:start position:0%
+photographer to do the work but I could
+ 
+
+ align:start position:0%
+photographer to do the work but I could
+learn an enormous amount from the
+
+ align:start position:0%
+learn an enormous amount from the
+ 
+
+ align:start position:0%
+learn an enormous amount from the
+artists and the craftsman in the field.
+
+ align:start position:0%
+artists and the craftsman in the field.
+ 
+
+ align:start position:0%
+artists and the craftsman in the field.
+Uh in other words, I didn't have to
+
+ align:start position:0%
+Uh in other words, I didn't have to
+ 
+
+ align:start position:0%
+Uh in other words, I didn't have to
+worry about whether I was going to be a
+
+ align:start position:0%
+worry about whether I was going to be a
+ 
+
+ align:start position:0%
+worry about whether I was going to be a
+great photographer, but I could learn
+
+ align:start position:0%
+great photographer, but I could learn
+ 
+
+ align:start position:0%
+great photographer, but I could learn
+tremendous amounts from the techniques
+
+ align:start position:0%
+tremendous amounts from the techniques
+ 
+
+ align:start position:0%
+tremendous amounts from the techniques
+and styles and methods.
+
+ align:start position:0%
+and styles and methods.
+ 
+
+ align:start position:0%
+and styles and methods.
+And if someone said to me, you're
+
+ align:start position:0%
+And if someone said to me, you're
+ 
+
+ align:start position:0%
+And if someone said to me, you're
+imitating uh DRO, I would say, thank
+
+ align:start position:0%
+imitating uh DRO, I would say, thank
+ 
+
+ align:start position:0%
+imitating uh DRO, I would say, thank
+God. In other words, I'm not worried
+
+ align:start position:0%
+God. In other words, I'm not worried
+ 
+
+ align:start position:0%
+God. In other words, I'm not worried
+about being original, which for an
+
+ align:start position:0%
+about being original, which for an
+ 
+
+ align:start position:0%
+about being original, which for an
+artist is crucial. I have other
+
+ align:start position:0%
+artist is crucial. I have other
+ 
+
+ align:start position:0%
+artist is crucial. I have other
+concerns. Uh there are several themes
+
+ align:start position:0%
+concerns. Uh there are several themes
+ 
+
+ align:start position:0%
+concerns. Uh there are several themes
+that come up in my work. One is I'm
+
+ align:start position:0%
+that come up in my work. One is I'm
+ 
+
+ align:start position:0%
+that come up in my work. One is I'm
+interested in repetition. I'm interested
+
+ align:start position:0%
+interested in repetition. I'm interested
+ 
+
+ align:start position:0%
+interested in repetition. I'm interested
+in phenomena that happen lots and lots
+
+ align:start position:0%
+in phenomena that happen lots and lots
+ 
+
+ align:start position:0%
+in phenomena that happen lots and lots
+and lots of times, not unique
+
+ align:start position:0%
+and lots of times, not unique
+ 
+
+ align:start position:0%
+and lots of times, not unique
+events. As you'll see, for example, I've
+
+ align:start position:0%
+events. As you'll see, for example, I've
+ 
+
+ align:start position:0%
+events. As you'll see, for example, I've
+photographed about 800 storefront
+
+ align:start position:0%
+photographed about 800 storefront
+ 
+
+ align:start position:0%
+photographed about 800 storefront
+churches in Los Angeles.
+
+ align:start position:0%
+churches in Los Angeles.
+ 
+
+ align:start position:0%
+churches in Los Angeles.
+Each one of them is special but in their
+
+ align:start position:0%
+Each one of them is special but in their
+ 
+
+ align:start position:0%
+Each one of them is special but in their
+toto there's a story to be told which I
+
+ align:start position:0%
+toto there's a story to be told which I
+ 
+
+ align:start position:0%
+toto there's a story to be told which I
+think is rather interesting. I'm
+
+ align:start position:0%
+think is rather interesting. I'm
+ 
+
+ align:start position:0%
+think is rather interesting. I'm
+interested in ordinary things not
+
+ align:start position:0%
+interested in ordinary things not
+ 
+
+ align:start position:0%
+interested in ordinary things not
+extraordinary things that happen every
+
+ align:start position:0%
+extraordinary things that happen every
+ 
+
+ align:start position:0%
+extraordinary things that happen every
+day. It doesn't mean you pay attention
+
+ align:start position:0%
+day. It doesn't mean you pay attention
+ 
+
+ align:start position:0%
+day. It doesn't mean you pay attention
+to them every day but they're
+
+ align:start position:0%
+to them every day but they're
+ 
+
+ align:start position:0%
+to them every day but they're
+around in when people talk about in
+
+ align:start position:0%
+around in when people talk about in
+ 
+
+ align:start position:0%
+around in when people talk about in
+people who do make motion pictures and
+
+ align:start position:0%
+people who do make motion pictures and
+ 
+
+ align:start position:0%
+people who do make motion pictures and
+they talk about the background town
+
+ align:start position:0%
+they talk about the background town
+ 
+
+ align:start position:0%
+they talk about the background town
+sound of a room because no room is
+
+ align:start position:0%
+sound of a room because no room is
+ 
+
+ align:start position:0%
+sound of a room because no room is
+silent. There's always things going on.
+
+ align:start position:0%
+silent. There's always things going on.
+ 
+
+ align:start position:0%
+silent. There's always things going on.
+The heat, ventilation, air conditioning,
+
+ align:start position:0%
+The heat, ventilation, air conditioning,
+ 
+
+ align:start position:0%
+The heat, ventilation, air conditioning,
+the out outside sound of the traffic.
+
+ align:start position:0%
+the out outside sound of the traffic.
+ 
+
+ align:start position:0%
+the out outside sound of the traffic.
+The word they use is ambience. A m i n
+
+ align:start position:0%
+The word they use is ambience. A m i n
+ 
+
+ align:start position:0%
+The word they use is ambience. A m i n
+ce or room tone. And so I'm interested,
+
+ align:start position:0%
+ce or room tone. And so I'm interested,
+ 
+
+ align:start position:0%
+ce or room tone. And so I'm interested,
+as you'll see, not only in what's
+
+ align:start position:0%
+as you'll see, not only in what's
+ 
+
+ align:start position:0%
+as you'll see, not only in what's
+ordinary visually, but what's ordinary
+
+ align:start position:0%
+ordinary visually, but what's ordinary
+ 
+
+ align:start position:0%
+ordinary visually, but what's ordinary
+sonically or
+
+ align:start position:0%
+sonically or
+ 
+
+ align:start position:0%
+sonically or
+orally. I also use the word
+
+ align:start position:0%
+orally. I also use the word
+ 
+
+ align:start position:0%
+orally. I also use the word
+choreography. And what I mean by that is
+
+ align:start position:0%
+choreography. And what I mean by that is
+ 
+
+ align:start position:0%
+choreography. And what I mean by that is
+the idea that people's motions,
+
+ align:start position:0%
+the idea that people's motions,
+ 
+
+ align:start position:0%
+the idea that people's motions,
+collective motions are coordinated. A
+
+ align:start position:0%
+collective motions are coordinated. A
+ 
+
+ align:start position:0%
+collective motions are coordinated. A
+factory depends on people working
+
+ align:start position:0%
+factory depends on people working
+ 
+
+ align:start position:0%
+factory depends on people working
+together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you don't do your part, the
+
+ align:start position:0%
+because if you don't do your part, the
+ 
+
+ align:start position:0%
+because if you don't do your part, the
+next guy can't do
+
+ align:start position:0%
+next guy can't do
+ 
+
+ align:start position:0%
+next guy can't do
+theirs. And so, one of the things I want
+
+ align:start position:0%
+theirs. And so, one of the things I want
+ 
+
+ align:start position:0%
+theirs. And so, one of the things I want
+to do is figure out how in the world to
+
+ align:start position:0%
+to do is figure out how in the world to
+ 
+
+ align:start position:0%
+to do is figure out how in the world to
+convey that choreography, which by the
+
+ align:start position:0%
+convey that choreography, which by the
+ 
+
+ align:start position:0%
+convey that choreography, which by the
+way is very difficult to do visually.
+
+ align:start position:0%
+way is very difficult to do visually.
+ 
+
+ align:start position:0%
+way is very difficult to do visually.
+And there are whole books devoted to how
+
+ align:start position:0%
+And there are whole books devoted to how
+ 
+
+ align:start position:0%
+And there are whole books devoted to how
+do you make visual representations of
+
+ align:start position:0%
+do you make visual representations of
+ 
+
+ align:start position:0%
+do you make visual representations of
+dance, you know, what are the right kind
+
+ align:start position:0%
+dance, you know, what are the right kind
+ 
+
+ align:start position:0%
+dance, you know, what are the right kind
+of photographs, what's the style to use
+
+ align:start position:0%
+of photographs, what's the style to use
+ 
+
+ align:start position:0%
+of photographs, what's the style to use
+and so forth. And there's people who
+
+ align:start position:0%
+and so forth. And there's people who
+ 
+
+ align:start position:0%
+and so forth. And there's people who
+worry about this a good deal in the
+
+ align:start position:0%
+worry about this a good deal in the
+ 
+
+ align:start position:0%
+worry about this a good deal in the
+dance business. The other theme is what
+
+ align:start position:0%
+dance business. The other theme is what
+ 
+
+ align:start position:0%
+dance business. The other theme is what
+I call the sensorium. What I mean is
+
+ align:start position:0%
+I call the sensorium. What I mean is
+ 
+
+ align:start position:0%
+I call the sensorium. What I mean is
+what is the experience of a place like?
+
+ align:start position:0%
+what is the experience of a place like?
+ 
+
+ align:start position:0%
+what is the experience of a place like?
+How do you record it? How do you record
+
+ align:start position:0%
+How do you record it? How do you record
+ 
+
+ align:start position:0%
+How do you record it? How do you record
+it archally so that 50 or 100 years ago,
+
+ align:start position:0%
+it archally so that 50 or 100 years ago,
+ 
+
+ align:start position:0%
+it archally so that 50 or 100 years ago,
+50 or 100 years from now, you have some
+
+ align:start position:0%
+50 or 100 years from now, you have some
+ 
+
+ align:start position:0%
+50 or 100 years from now, you have some
+idea of what it was, you know, what it
+
+ align:start position:0%
+idea of what it was, you know, what it
+ 
+
+ align:start position:0%
+idea of what it was, you know, what it
+felt like. um are probably we know the
+
+ align:start position:0%
+felt like. um are probably we know the
+ 
+
+ align:start position:0%
+felt like. um are probably we know the
+most about cities and what they were
+
+ align:start position:0%
+most about cities and what they were
+ 
+
+ align:start position:0%
+most about cities and what they were
+like from novels and visual uh I mean
+
+ align:start position:0%
+like from novels and visual uh I mean
+ 
+
+ align:start position:0%
+like from novels and visual uh I mean
+verbal descriptions certainly smells
+
+ align:start position:0%
+verbal descriptions certainly smells
+ 
+
+ align:start position:0%
+verbal descriptions certainly smells
+sounds and so
+
+ align:start position:0%
+sounds and so
+ 
+
+ align:start position:0%
+sounds and so
+forth and can we do and of course you
+
+ align:start position:0%
+forth and can we do and of course you
+ 
+
+ align:start position:0%
+forth and can we do and of course you
+know not everybody can be phobia but can
+
+ align:start position:0%
+know not everybody can be phobia but can
+ 
+
+ align:start position:0%
+know not everybody can be phobia but can
+we do interesting work without being
+
+ align:start position:0%
+we do interesting work without being
+ 
+
+ align:start position:0%
+we do interesting work without being
+great writers and that's an interesting
+
+ align:start position:0%
+great writers and that's an interesting
+ 
+
+ align:start position:0%
+great writers and that's an interesting
+question my second big thing besides the
+
+ align:start position:0%
+question my second big thing besides the
+ 
+
+ align:start position:0%
+question my second big thing besides the
+themes of repetition and the sensorium
+
+ align:start position:0%
+themes of repetition and the sensorium
+ 
+
+ align:start position:0%
+themes of repetition and the sensorium
+is that I take technology ology and I'll
+
+ align:start position:0%
+is that I take technology ology and I'll
+ 
+
+ align:start position:0%
+is that I take technology ology and I'll
+explain what I mean as the
+
+ align:start position:0%
+explain what I mean as the
+ 
+
+ align:start position:0%
+explain what I mean as the
+transcendental condition to use a
+
+ align:start position:0%
+transcendental condition to use a
+ 
+
+ align:start position:0%
+transcendental condition to use a
+content phrase for the work. In other
+
+ align:start position:0%
+content phrase for the work. In other
+ 
+
+ align:start position:0%
+content phrase for the work. In other
+words, it sets up the conditions for
+
+ align:start position:0%
+words, it sets up the conditions for
+ 
+
+ align:start position:0%
+words, it sets up the conditions for
+doing the work. So that if I use a wide
+
+ align:start position:0%
+doing the work. So that if I use a wide
+ 
+
+ align:start position:0%
+doing the work. So that if I use a wide
+angle lens or certain kind of color
+
+ align:start position:0%
+angle lens or certain kind of color
+ 
+
+ align:start position:0%
+angle lens or certain kind of color
+film, some things are possible, some
+
+ align:start position:0%
+film, some things are possible, some
+ 
+
+ align:start position:0%
+film, some things are possible, some
+things are not possible. You can always
+
+ align:start position:0%
+things are not possible. You can always
+ 
+
+ align:start position:0%
+things are not possible. You can always
+push the envelope, but you're always
+
+ align:start position:0%
+push the envelope, but you're always
+ 
+
+ align:start position:0%
+push the envelope, but you're always
+pushing an envelope given what's
+
+ align:start position:0%
+pushing an envelope given what's
+ 
+
+ align:start position:0%
+pushing an envelope given what's
+possible within a range. All right? Um
+
+ align:start position:0%
+possible within a range. All right? Um
+ 
+
+ align:start position:0%
+possible within a range. All right? Um
+and uh and that comes to me now that I'm
+
+ align:start position:0%
+and uh and that comes to me now that I'm
+ 
+
+ align:start position:0%
+and uh and that comes to me now that I'm
+beginning an oral documentation project
+
+ align:start position:0%
+beginning an oral documentation project
+ 
+
+ align:start position:0%
+beginning an oral documentation project
+where my knowledge of uh sound recording
+
+ align:start position:0%
+where my knowledge of uh sound recording
+ 
+
+ align:start position:0%
+where my knowledge of uh sound recording
+is very elementary compared to what I
+
+ align:start position:0%
+is very elementary compared to what I
+ 
+
+ align:start position:0%
+is very elementary compared to what I
+knew about photography when I started
+
+ align:start position:0%
+knew about photography when I started
+ 
+
+ align:start position:0%
+knew about photography when I started
+and I'm just encountering that. And the
+
+ align:start position:0%
+and I'm just encountering that. And the
+ 
+
+ align:start position:0%
+and I'm just encountering that. And the
+third theme in my work is what I call
+
+ align:start position:0%
+third theme in my work is what I call
+ 
+
+ align:start position:0%
+third theme in my work is what I call
+it's being social science informed.
+
+ align:start position:0%
+it's being social science informed.
+ 
+
+ align:start position:0%
+it's being social science informed.
+Uh, one of the problems of visual
+
+ align:start position:0%
+Uh, one of the problems of visual
+ 
+
+ align:start position:0%
+Uh, one of the problems of visual
+materials in the modern university is
+
+ align:start position:0%
+materials in the modern university is
+ 
+
+ align:start position:0%
+materials in the modern university is
+that if it ends up in the humanities
+
+ align:start position:0%
+that if it ends up in the humanities
+ 
+
+ align:start position:0%
+that if it ends up in the humanities
+hands, it can be like what the art
+
+ align:start position:0%
+hands, it can be like what the art
+ 
+
+ align:start position:0%
+hands, it can be like what the art
+historians do, which are careful
+
+ align:start position:0%
+historians do, which are careful
+ 
+
+ align:start position:0%
+historians do, which are careful
+description and and careful using of
+
+ align:start position:0%
+description and and careful using of
+ 
+
+ align:start position:0%
+description and and careful using of
+instances. But the social scientists in
+
+ align:start position:0%
+instances. But the social scientists in
+ 
+
+ align:start position:0%
+instances. But the social scientists in
+general do reductionist bits on it.
+
+ align:start position:0%
+general do reductionist bits on it.
+ 
+
+ align:start position:0%
+general do reductionist bits on it.
+They're always trying to say, well, you
+
+ align:start position:0%
+They're always trying to say, well, you
+ 
+
+ align:start position:0%
+They're always trying to say, well, you
+just how do you code the images? Or you,
+
+ align:start position:0%
+just how do you code the images? Or you,
+ 
+
+ align:start position:0%
+just how do you code the images? Or you,
+you know, if the anthropologists are so
+
+ align:start position:0%
+you know, if the anthropologists are so
+ 
+
+ align:start position:0%
+you know, if the anthropologists are so
+worried about the fact that visual
+
+ align:start position:0%
+worried about the fact that visual
+ 
+
+ align:start position:0%
+worried about the fact that visual
+anthropology is biased and prejudiced in
+
+ align:start position:0%
+anthropology is biased and prejudiced in
+ 
+
+ align:start position:0%
+anthropology is biased and prejudiced in
+various ways, you wonder why they do it
+
+ align:start position:0%
+various ways, you wonder why they do it
+ 
+
+ align:start position:0%
+various ways, you wonder why they do it
+at all. Um, and I want to talk about a
+
+ align:start position:0%
+at all. Um, and I want to talk about a
+ 
+
+ align:start position:0%
+at all. Um, and I want to talk about a
+way of thinking about this that I find
+
+ align:start position:0%
+way of thinking about this that I find
+ 
+
+ align:start position:0%
+way of thinking about this that I find
+valuable that doesn't that allows me to
+
+ align:start position:0%
+valuable that doesn't that allows me to
+ 
+
+ align:start position:0%
+valuable that doesn't that allows me to
+do my work and feel like I am being
+
+ align:start position:0%
+do my work and feel like I am being
+ 
+
+ align:start position:0%
+do my work and feel like I am being
+social scientific without being
+
+ align:start position:0%
+social scientific without being
+ 
+
+ align:start position:0%
+social scientific without being
+reductionist. And what I mean by
+
+ align:start position:0%
+reductionist. And what I mean by
+ 
+
+ align:start position:0%
+reductionist. And what I mean by
+reductionist is taking giving
+
+ align:start position:0%
+reductionist is taking giving
+ 
+
+ align:start position:0%
+reductionist is taking giving
+photographs or images less credence than
+
+ align:start position:0%
+photographs or images less credence than
+ 
+
+ align:start position:0%
+photographs or images less credence than
+verbal summaries thereof. All
+
+ align:start position:0%
+verbal summaries thereof. All
+ 
+
+ align:start position:0%
+verbal summaries thereof. All
+right. And remember we have a tremendous
+
+ align:start position:0%
+right. And remember we have a tremendous
+ 
+
+ align:start position:0%
+right. And remember we have a tremendous
+literature on nowadays of how ver visual
+
+ align:start position:0%
+literature on nowadays of how ver visual
+ 
+
+ align:start position:0%
+literature on nowadays of how ver visual
+images deceive us. And of course
+
+ align:start position:0%
+images deceive us. And of course
+ 
+
+ align:start position:0%
+images deceive us. And of course
+historically uh one of the great fields
+
+ align:start position:0%
+historically uh one of the great fields
+ 
+
+ align:start position:0%
+historically uh one of the great fields
+of intellectual inquiry was rhetoric and
+
+ align:start position:0%
+of intellectual inquiry was rhetoric and
+ 
+
+ align:start position:0%
+of intellectual inquiry was rhetoric and
+was all that was also about how verbal
+
+ align:start position:0%
+was all that was also about how verbal
+ 
+
+ align:start position:0%
+was all that was also about how verbal
+stuff deceive us. So why do people not
+
+ align:start position:0%
+stuff deceive us. So why do people not
+ 
+
+ align:start position:0%
+stuff deceive us. So why do people not
+talk? Why do people still make images?
+
+ align:start position:0%
+talk? Why do people still make images?
+ 
+
+ align:start position:0%
+talk? Why do people still make images?
+There's a reason I think I don't think
+
+ align:start position:0%
+There's a reason I think I don't think
+ 
+
+ align:start position:0%
+There's a reason I think I don't think
+we have to be uh uh
+
+ align:start position:0%
+we have to be uh uh
+ 
+
+ align:start position:0%
+we have to be uh uh
+paralyzed. All right, that's the general
+
+ align:start position:0%
+paralyzed. All right, that's the general
+ 
+
+ align:start position:0%
+paralyzed. All right, that's the general
+themes I'm going to be talking about. Um
+
+ align:start position:0%
+themes I'm going to be talking about. Um
+ 
+
+ align:start position:0%
+themes I'm going to be talking about. Um
+I am almost all my work can be described
+
+ align:start position:0%
+I am almost all my work can be described
+ 
+
+ align:start position:0%
+I am almost all my work can be described
+as by the way I will get to images
+
+ align:start position:0%
+as by the way I will get to images
+ 
+
+ align:start position:0%
+as by the way I will get to images
+shortly. So don't give up hope. Um
+
+ align:start position:0%
+shortly. So don't give up hope. Um
+ 
+
+ align:start position:0%
+shortly. So don't give up hope. Um
+almost all my work can be described as
+
+ align:start position:0%
+almost all my work can be described as
+ 
+
+ align:start position:0%
+almost all my work can be described as
+analytic description whether it be of
+
+ align:start position:0%
+analytic description whether it be of
+ 
+
+ align:start position:0%
+analytic description whether it be of
+math or physics of planning and design.
+
+ align:start position:0%
+math or physics of planning and design.
+ 
+
+ align:start position:0%
+math or physics of planning and design.
+I want to show the world to people who
+
+ align:start position:0%
+I want to show the world to people who
+ 
+
+ align:start position:0%
+I want to show the world to people who
+do it in such a way that it's
+
+ align:start position:0%
+do it in such a way that it's
+ 
+
+ align:start position:0%
+do it in such a way that it's
+recognizable to them but it's
+
+ align:start position:0%
+recognizable to them but it's
+ 
+
+ align:start position:0%
+recognizable to them but it's
+analytically described in a small number
+
+ align:start position:0%
+analytically described in a small number
+ 
+
+ align:start position:0%
+analytically described in a small number
+of categories and a collected leaked set
+
+ align:start position:0%
+of categories and a collected leaked set
+ 
+
+ align:start position:0%
+of categories and a collected leaked set
+of ideas. So that for example I wrote a
+
+ align:start position:0%
+of ideas. So that for example I wrote a
+ 
+
+ align:start position:0%
+of ideas. So that for example I wrote a
+book called uh on the physicist toolkit
+
+ align:start position:0%
+book called uh on the physicist toolkit
+ 
+
+ align:start position:0%
+book called uh on the physicist toolkit
+and the idea was could I set a small
+
+ align:start position:0%
+and the idea was could I set a small
+ 
+
+ align:start position:0%
+and the idea was could I set a small
+number of basic ideas that dominate how
+
+ align:start position:0%
+number of basic ideas that dominate how
+ 
+
+ align:start position:0%
+number of basic ideas that dominate how
+people do analysis or basic models and
+
+ align:start position:0%
+people do analysis or basic models and
+ 
+
+ align:start position:0%
+people do analysis or basic models and
+all I can ask from the scientist is yes
+
+ align:start position:0%
+all I can ask from the scientist is yes
+ 
+
+ align:start position:0%
+all I can ask from the scientist is yes
+that sounds right. Yeah. So what? Then
+
+ align:start position:0%
+that sounds right. Yeah. So what? Then
+ 
+
+ align:start position:0%
+that sounds right. Yeah. So what? Then
+I've won the game. Why? Because I found
+
+ align:start position:0%
+I've won the game. Why? Because I found
+ 
+
+ align:start position:0%
+I've won the game. Why? Because I found
+a representation that they find
+
+ align:start position:0%
+a representation that they find
+ 
+
+ align:start position:0%
+a representation that they find
+believable. Now you could say, well, why
+
+ align:start position:0%
+believable. Now you could say, well, why
+ 
+
+ align:start position:0%
+believable. Now you could say, well, why
+should you give them authority about,
+
+ align:start position:0%
+should you give them authority about,
+ 
+
+ align:start position:0%
+should you give them authority about,
+you know, what physics is? Well, my idea
+
+ align:start position:0%
+you know, what physics is? Well, my idea
+ 
+
+ align:start position:0%
+you know, what physics is? Well, my idea
+is that if I can reproduce the world
+
+ align:start position:0%
+is that if I can reproduce the world
+ 
+
+ align:start position:0%
+is that if I can reproduce the world
+that they know and they recognize it,
+
+ align:start position:0%
+that they know and they recognize it,
+ 
+
+ align:start position:0%
+that they know and they recognize it,
+I've done pretty
+
+ align:start position:0%
+I've done pretty
+ 
+
+ align:start position:0%
+I've done pretty
+well. And the reason I say all these
+
+ align:start position:0%
+well. And the reason I say all these
+ 
+
+ align:start position:0%
+well. And the reason I say all these
+skeptical remarks is because I've
+
+ align:start position:0%
+skeptical remarks is because I've
+ 
+
+ align:start position:0%
+skeptical remarks is because I've
+encountered them over the years. Uh, and
+
+ align:start position:0%
+encountered them over the years. Uh, and
+ 
+
+ align:start position:0%
+encountered them over the years. Uh, and
+it's the bread and butter of social
+
+ align:start position:0%
+it's the bread and butter of social
+ 
+
+ align:start position:0%
+it's the bread and butter of social
+scientists and and academics to be
+
+ align:start position:0%
+scientists and and academics to be
+ 
+
+ align:start position:0%
+scientists and and academics to be
+skeptical. Uh, I could do it, I guess,
+
+ align:start position:0%
+skeptical. Uh, I could do it, I guess,
+ 
+
+ align:start position:0%
+skeptical. Uh, I could do it, I guess,
+as well as anybody, but it's not what my
+
+ align:start position:0%
+as well as anybody, but it's not what my
+ 
+
+ align:start position:0%
+as well as anybody, but it's not what my
+bread and butter is. Um, and what I want
+
+ align:start position:0%
+bread and butter is. Um, and what I want
+ 
+
+ align:start position:0%
+bread and butter is. Um, and what I want
+to do is give analytic description for
+
+ align:start position:0%
+to do is give analytic description for
+ 
+
+ align:start position:0%
+to do is give analytic description for
+the purposes here of what I call the
+
+ align:start position:0%
+the purposes here of what I call the
+ 
+
+ align:start position:0%
+the purposes here of what I call the
+drama of ordinary life, whether it be
+
+ align:start position:0%
+drama of ordinary life, whether it be
+ 
+
+ align:start position:0%
+drama of ordinary life, whether it be
+worship in a Pentecostal church, how
+
+ align:start position:0%
+worship in a Pentecostal church, how
+ 
+
+ align:start position:0%
+worship in a Pentecostal church, how
+factories are organized and how people
+
+ align:start position:0%
+factories are organized and how people
+ 
+
+ align:start position:0%
+factories are organized and how people
+work together.
+
+ align:start position:0%
+work together.
+ 
+
+ align:start position:0%
+work together.
+Uh, and also I want to talk how the
+
+ align:start position:0%
+Uh, and also I want to talk how the
+ 
+
+ align:start position:0%
+Uh, and also I want to talk how the
+built environment is mold mold and is
+
+ align:start position:0%
+built environment is mold mold and is
+ 
+
+ align:start position:0%
+built environment is mold mold and is
+molded by us. So, for example, most
+
+ align:start position:0%
+molded by us. So, for example, most
+ 
+
+ align:start position:0%
+molded by us. So, for example, most
+recently, uh we have uh a general count
+
+ align:start position:0%
+recently, uh we have uh a general count
+ 
+
+ align:start position:0%
+recently, uh we have uh a general count
+LA County General Hospital, which I
+
+ align:start position:0%
+LA County General Hospital, which I
+ 
+
+ align:start position:0%
+LA County General Hospital, which I
+think has been featured on TV shows for
+
+ align:start position:0%
+think has been featured on TV shows for
+ 
+
+ align:start position:0%
+think has been featured on TV shows for
+one of the TV series, but it's county is
+
+ align:start position:0%
+one of the TV series, but it's county is
+ 
+
+ align:start position:0%
+one of the TV series, but it's county is
+famous. It's a place you go to get lots
+
+ align:start position:0%
+famous. It's a place you go to get lots
+ 
+
+ align:start position:0%
+famous. It's a place you go to get lots
+of experience with gunshot wounds and so
+
+ align:start position:0%
+of experience with gunshot wounds and so
+ 
+
+ align:start position:0%
+of experience with gunshot wounds and so
+forth. And it's being closed down and a
+
+ align:start position:0%
+forth. And it's being closed down and a
+ 
+
+ align:start position:0%
+forth. And it's being closed down and a
+new hospital is being built because of
+
+ align:start position:0%
+new hospital is being built because of
+ 
+
+ align:start position:0%
+new hospital is being built because of
+earthquake and politics. And so, I
+
+ align:start position:0%
+earthquake and politics. And so, I
+ 
+
+ align:start position:0%
+earthquake and politics. And so, I
+recently got permission and went top to
+
+ align:start position:0%
+recently got permission and went top to
+ 
+
+ align:start position:0%
+recently got permission and went top to
+bottom photographing the hospital and
+
+ align:start position:0%
+bottom photographing the hospital and
+ 
+
+ align:start position:0%
+bottom photographing the hospital and
+people working there, not any of the
+
+ align:start position:0%
+people working there, not any of the
+ 
+
+ align:start position:0%
+people working there, not any of the
+patients because that would have been
+
+ align:start position:0%
+patients because that would have been
+ 
+
+ align:start position:0%
+patients because that would have been
+impossible.
+
+ align:start position:0%
+impossible.
+ 
+
+ align:start position:0%
+impossible.
+because it'd be interesting to ask how
+
+ align:start position:0%
+because it'd be interesting to ask how
+ 
+
+ align:start position:0%
+because it'd be interesting to ask how
+is the design of the place affect the
+
+ align:start position:0%
+is the design of the place affect the
+ 
+
+ align:start position:0%
+is the design of the place affect the
+coordination of people in it. And of
+
+ align:start position:0%
+coordination of people in it. And of
+ 
+
+ align:start position:0%
+coordination of people in it. And of
+course lot you could do lots of field
+
+ align:start position:0%
+course lot you could do lots of field
+ 
+
+ align:start position:0%
+course lot you could do lots of field
+work but one of the possibilities is
+
+ align:start position:0%
+work but one of the possibilities is
+ 
+
+ align:start position:0%
+work but one of the possibilities is
+just to do the photographs and I spent
+
+ align:start position:0%
+just to do the photographs and I spent
+ 
+
+ align:start position:0%
+just to do the photographs and I spent
+about three or four days literally going
+
+ align:start position:0%
+about three or four days literally going
+ 
+
+ align:start position:0%
+about three or four days literally going
+through the hospital with a
+
+ align:start position:0%
+through the hospital with a
+ 
+
+ align:start position:0%
+through the hospital with a
+guide. Now one question you might ask is
+
+ align:start position:0%
+guide. Now one question you might ask is
+ 
+
+ align:start position:0%
+guide. Now one question you might ask is
+why photographs? Why you are doing
+
+ align:start position:0%
+why photographs? Why you are doing
+ 
+
+ align:start position:0%
+why photographs? Why you are doing
+photographs when most of your career is
+
+ align:start position:0%
+photographs when most of your career is
+ 
+
+ align:start position:0%
+photographs when most of your career is
+writing fairly analytic books? I wrote
+
+ align:start position:0%
+writing fairly analytic books? I wrote
+ 
+
+ align:start position:0%
+writing fairly analytic books? I wrote
+four books on mathematical modeling
+
+ align:start position:0%
+four books on mathematical modeling
+ 
+
+ align:start position:0%
+four books on mathematical modeling
+including quite technical stuff on
+
+ align:start position:0%
+including quite technical stuff on
+ 
+
+ align:start position:0%
+including quite technical stuff on
+mathematics. Three books on planning and
+
+ align:start position:0%
+mathematics. Three books on planning and
+ 
+
+ align:start position:0%
+mathematics. Three books on planning and
+design theory where I use religion and
+
+ align:start position:0%
+design theory where I use religion and
+ 
+
+ align:start position:0%
+design theory where I use religion and
+phenomenology. Where do I get warrant to
+
+ align:start position:0%
+phenomenology. Where do I get warrant to
+ 
+
+ align:start position:0%
+phenomenology. Where do I get warrant to
+do this? Well, there are three reasons.
+
+ align:start position:0%
+do this? Well, there are three reasons.
+ 
+
+ align:start position:0%
+do this? Well, there are three reasons.
+One, I've had a long-standing interest
+
+ align:start position:0%
+One, I've had a long-standing interest
+ 
+
+ align:start position:0%
+One, I've had a long-standing interest
+in this and actually wrote about it. And
+
+ align:start position:0%
+in this and actually wrote about it. And
+ 
+
+ align:start position:0%
+in this and actually wrote about it. And
+in graduate school, for reasons which I
+
+ align:start position:0%
+in graduate school, for reasons which I
+ 
+
+ align:start position:0%
+in graduate school, for reasons which I
+can't recall, I ended up taking a course
+
+ align:start position:0%
+can't recall, I ended up taking a course
+ 
+
+ align:start position:0%
+can't recall, I ended up taking a course
+on social science uses of photography
+
+ align:start position:0%
+on social science uses of photography
+ 
+
+ align:start position:0%
+on social science uses of photography
+from a guy named Paul Buyers who was
+
+ align:start position:0%
+from a guy named Paul Buyers who was
+ 
+
+ align:start position:0%
+from a guy named Paul Buyers who was
+Margaret me's
+
+ align:start position:0%
+Margaret me's
+ 
+
+ align:start position:0%
+Margaret me's
+photographer. And Margaret me was very
+
+ align:start position:0%
+photographer. And Margaret me was very
+ 
+
+ align:start position:0%
+photographer. And Margaret me was very
+big on photographs, visual materials in
+
+ align:start position:0%
+big on photographs, visual materials in
+ 
+
+ align:start position:0%
+big on photographs, visual materials in
+social
+
+ align:start position:0%
+social
+ 
+
+ align:start position:0%
+social
+science. Second, what do you do after
+
+ align:start position:0%
+science. Second, what do you do after
+ 
+
+ align:start position:0%
+science. Second, what do you do after
+you write your big book in your 50s?
+
+ align:start position:0%
+you write your big book in your 50s?
+ 
+
+ align:start position:0%
+you write your big book in your 50s?
+Here I am. I write my big book. All
+
+ align:start position:0%
+Here I am. I write my big book. All
+ 
+
+ align:start position:0%
+Here I am. I write my big book. All
+right? You know, deepest, most
+
+ align:start position:0%
+right? You know, deepest, most
+ 
+
+ align:start position:0%
+right? You know, deepest, most
+difficult, kills you, right? Knocks you
+
+ align:start position:0%
+difficult, kills you, right? Knocks you
+ 
+
+ align:start position:0%
+difficult, kills you, right? Knocks you
+dead. It's not necessarily longest,
+
+ align:start position:0%
+dead. It's not necessarily longest,
+ 
+
+ align:start position:0%
+dead. It's not necessarily longest,
+though I think it was. Uh, it's called
+
+ align:start position:0%
+though I think it was. Uh, it's called
+ 
+
+ align:start position:0%
+though I think it was. Uh, it's called
+doing mathematics. And I barely get away
+
+ align:start position:0%
+doing mathematics. And I barely get away
+ 
+
+ align:start position:0%
+doing mathematics. And I barely get away
+with writing it in the sense that it's
+
+ align:start position:0%
+with writing it in the sense that it's
+ 
+
+ align:start position:0%
+with writing it in the sense that it's
+at the edge of what I understand. And do
+
+ align:start position:0%
+at the edge of what I understand. And do
+ 
+
+ align:start position:0%
+at the edge of what I understand. And do
+I want to write another one? And it's
+
+ align:start position:0%
+I want to write another one? And it's
+ 
+
+ align:start position:0%
+I want to write another one? And it's
+very interesting. I realized that I had
+
+ align:start position:0%
+very interesting. I realized that I had
+ 
+
+ align:start position:0%
+very interesting. I realized that I had
+nothing more to say or I mean I could
+
+ align:start position:0%
+nothing more to say or I mean I could
+ 
+
+ align:start position:0%
+nothing more to say or I mean I could
+have more to say but it wouldn't be much
+
+ align:start position:0%
+have more to say but it wouldn't be much
+ 
+
+ align:start position:0%
+have more to say but it wouldn't be much
+of an improvement. So in some sense I
+
+ align:start position:0%
+of an improvement. So in some sense I
+ 
+
+ align:start position:0%
+of an improvement. So in some sense I
+had room in my research
+
+ align:start position:0%
+had room in my research
+ 
+
+ align:start position:0%
+had room in my research
+portfolio. And thirdly we when I moved
+
+ align:start position:0%
+portfolio. And thirdly we when I moved
+ 
+
+ align:start position:0%
+portfolio. And thirdly we when I moved
+we moved into a new building uh five six
+
+ align:start position:0%
+we moved into a new building uh five six
+ 
+
+ align:start position:0%
+we moved into a new building uh five six
+seven years ago and it had a room called
+
+ align:start position:0%
+seven years ago and it had a room called
+ 
+
+ align:start position:0%
+seven years ago and it had a room called
+a gallery and I was put on the committee
+
+ align:start position:0%
+a gallery and I was put on the committee
+ 
+
+ align:start position:0%
+a gallery and I was put on the committee
+to figure out what to put in the
+
+ align:start position:0%
+to figure out what to put in the
+ 
+
+ align:start position:0%
+to figure out what to put in the
+gallery. Well you know what committees
+
+ align:start position:0%
+gallery. Well you know what committees
+ 
+
+ align:start position:0%
+gallery. Well you know what committees
+do? Nothing. So um I just figured I
+
+ align:start position:0%
+do? Nothing. So um I just figured I
+ 
+
+ align:start position:0%
+do? Nothing. So um I just figured I
+asked him well I can put up a show of
+
+ align:start position:0%
+asked him well I can put up a show of
+ 
+
+ align:start position:0%
+asked him well I can put up a show of
+this stuff and that stuff and so I
+
+ align:start position:0%
+this stuff and that stuff and so I
+ 
+
+ align:start position:0%
+this stuff and that stuff and so I
+became quotes curator though I didn't
+
+ align:start position:0%
+became quotes curator though I didn't
+ 
+
+ align:start position:0%
+became quotes curator though I didn't
+know that I just putting up kept putting
+
+ align:start position:0%
+know that I just putting up kept putting
+ 
+
+ align:start position:0%
+know that I just putting up kept putting
+up shows and my secret was I didn't ask
+
+ align:start position:0%
+up shows and my secret was I didn't ask
+ 
+
+ align:start position:0%
+up shows and my secret was I didn't ask
+for much money from my dean so no one
+
+ align:start position:0%
+for much money from my dean so no one
+ 
+
+ align:start position:0%
+for much money from my dean so no one
+controlled it you know the shows kept
+
+ align:start position:0%
+controlled it you know the shows kept
+ 
+
+ align:start position:0%
+controlled it you know the shows kept
+going up they may have been a little
+
+ align:start position:0%
+going up they may have been a little
+ 
+
+ align:start position:0%
+going up they may have been a little
+cheesy and how they things were stuck on
+
+ align:start position:0%
+cheesy and how they things were stuck on
+ 
+
+ align:start position:0%
+cheesy and how they things were stuck on
+the wall the posters didn't look
+
+ align:start position:0%
+the wall the posters didn't look
+ 
+
+ align:start position:0%
+the wall the posters didn't look
+gorgeous but there was a show three
+
+ align:start position:0%
+gorgeous but there was a show three
+ 
+
+ align:start position:0%
+gorgeous but there was a show three
+shows a year and it's been going on for
+
+ align:start position:0%
+shows a year and it's been going on for
+ 
+
+ align:start position:0%
+shows a year and it's been going on for
+five six years and eventually everybody
+
+ align:start position:0%
+five six years and eventually everybody
+ 
+
+ align:start position:0%
+five six years and eventually everybody
+thinks it's part of the
+
+ align:start position:0%
+thinks it's part of the
+ 
+
+ align:start position:0%
+thinks it's part of the
+furniture which is what I've done. Um,
+
+ align:start position:0%
+furniture which is what I've done. Um,
+ 
+
+ align:start position:0%
+furniture which is what I've done. Um,
+so what I did was about eight nine years
+
+ align:start position:0%
+so what I did was about eight nine years
+ 
+
+ align:start position:0%
+so what I did was about eight nine years
+ago I started gingerly and started
+
+ align:start position:0%
+ago I started gingerly and started
+ 
+
+ align:start position:0%
+ago I started gingerly and started
+taking
+
+ align:start position:0%
+taking
+ 
+
+ align:start position:0%
+taking
+photographs and what made it work was
+
+ align:start position:0%
+photographs and what made it work was
+ 
+
+ align:start position:0%
+photographs and what made it work was
+and this is the thing that seems to me
+
+ align:start position:0%
+and this is the thing that seems to me
+ 
+
+ align:start position:0%
+and this is the thing that seems to me
+the deep insight. A city is an archive
+
+ align:start position:0%
+the deep insight. A city is an archive
+ 
+
+ align:start position:0%
+the deep insight. A city is an archive
+of its
+
+ align:start position:0%
+of its
+ 
+
+ align:start position:0%
+of its
+past. Nothing goes away virtually. The
+
+ align:start position:0%
+past. Nothing goes away virtually. The
+ 
+
+ align:start position:0%
+past. Nothing goes away virtually. The
+physical infra the built infrastructure
+
+ align:start position:0%
+physical infra the built infrastructure
+ 
+
+ align:start position:0%
+physical infra the built infrastructure
+does not go away. You build it for 50
+
+ align:start position:0%
+does not go away. You build it for 50
+ 
+
+ align:start position:0%
+does not go away. You build it for 50
+years it lasts much longer in general.
+
+ align:start position:0%
+years it lasts much longer in general.
+ 
+
+ align:start position:0%
+years it lasts much longer in general.
+Everybody says everything gets knocked
+
+ align:start position:0%
+Everybody says everything gets knocked
+ 
+
+ align:start position:0%
+Everybody says everything gets knocked
+down in Los Angeles. That's not
+
+ align:start position:0%
+down in Los Angeles. That's not
+ 
+
+ align:start position:0%
+down in Los Angeles. That's not
+true. It just isn't true. Everything,
+
+ align:start position:0%
+true. It just isn't true. Everything,
+ 
+
+ align:start position:0%
+true. It just isn't true. Everything,
+you know, essentially, for whatever
+
+ align:start position:0%
+you know, essentially, for whatever
+ 
+
+ align:start position:0%
+you know, essentially, for whatever
+reason, almost nothing gets knocked down
+
+ align:start position:0%
+reason, almost nothing gets knocked down
+ 
+
+ align:start position:0%
+reason, almost nothing gets knocked down
+compared to what gets renovated,
+
+ align:start position:0%
+compared to what gets renovated,
+ 
+
+ align:start position:0%
+compared to what gets renovated,
+repainted, redone.
+
+ align:start position:0%
+repainted, redone.
+ 
+
+ align:start position:0%
+repainted, redone.
+Um, I've been walking around Boston all
+
+ align:start position:0%
+Um, I've been walking around Boston all
+ 
+
+ align:start position:0%
+Um, I've been walking around Boston all
+day today. And what's really impressive
+
+ align:start position:0%
+day today. And what's really impressive
+ 
+
+ align:start position:0%
+day today. And what's really impressive
+is how much that's going on in in in
+
+ align:start position:0%
+is how much that's going on in in in
+ 
+
+ align:start position:0%
+is how much that's going on in in in
+Boston. I mean, much more than in LA,
+
+ align:start position:0%
+Boston. I mean, much more than in LA,
+ 
+
+ align:start position:0%
+Boston. I mean, much more than in LA,
+but you have more old infrastructure and
+
+ align:start position:0%
+but you have more old infrastructure and
+ 
+
+ align:start position:0%
+but you have more old infrastructure and
+old buildings and so forth. And I guess
+
+ align:start position:0%
+old buildings and so forth. And I guess
+ 
+
+ align:start position:0%
+old buildings and so forth. And I guess
+a deep need for condos.
+
+ align:start position:0%
+a deep need for condos.
+ 
+
+ align:start position:0%
+a deep need for condos.
+Uh and so if you go look at a city
+
+ align:start position:0%
+Uh and so if you go look at a city
+ 
+
+ align:start position:0%
+Uh and so if you go look at a city
+visually, you will see the historical
+
+ align:start position:0%
+visually, you will see the historical
+ 
+
+ align:start position:0%
+visually, you will see the historical
+layers right then and there. So it's
+
+ align:start position:0%
+layers right then and there. So it's
+ 
+
+ align:start position:0%
+layers right then and there. So it's
+enormously rich. In other words, it's
+
+ align:start position:0%
+enormously rich. In other words, it's
+ 
+
+ align:start position:0%
+enormously rich. In other words, it's
+sort of like doing um uh archaeology,
+
+ align:start position:0%
+sort of like doing um uh archaeology,
+ 
+
+ align:start position:0%
+sort of like doing um uh archaeology,
+but you don't have to dig very
+
+ align:start position:0%
+but you don't have to dig very
+ 
+
+ align:start position:0%
+but you don't have to dig very
+much. And you know, there's a field
+
+ align:start position:0%
+much. And you know, there's a field
+ 
+
+ align:start position:0%
+much. And you know, there's a field
+called industrial archaeology where
+
+ align:start position:0%
+called industrial archaeology where
+ 
+
+ align:start position:0%
+called industrial archaeology where
+they, you know, they try to figure out
+
+ align:start position:0%
+they, you know, they try to figure out
+ 
+
+ align:start position:0%
+they, you know, they try to figure out
+how a factory worked 100 years ago.
+
+ align:start position:0%
+how a factory worked 100 years ago.
+ 
+
+ align:start position:0%
+how a factory worked 100 years ago.
+Well, this is much like that except lots
+
+ align:start position:0%
+Well, this is much like that except lots
+ 
+
+ align:start position:0%
+Well, this is much like that except lots
+of things are just there on the surface
+
+ align:start position:0%
+of things are just there on the surface
+ 
+
+ align:start position:0%
+of things are just there on the surface
+and it's quite remarkable and I'll get
+
+ align:start position:0%
+and it's quite remarkable and I'll get
+ 
+
+ align:start position:0%
+and it's quite remarkable and I'll get
+to some examples. And also I could get
+
+ align:start position:0%
+to some examples. And also I could get
+ 
+
+ align:start position:0%
+to some examples. And also I could get
+away with doing this photography. For
+
+ align:start position:0%
+away with doing this photography. For
+ 
+
+ align:start position:0%
+away with doing this photography. For
+whatever reason, I was not
+
+ align:start position:0%
+whatever reason, I was not
+ 
+
+ align:start position:0%
+whatever reason, I was not
+obtrusive. I go there and I look like
+
+ align:start position:0%
+obtrusive. I go there and I look like
+ 
+
+ align:start position:0%
+obtrusive. I go there and I look like
+someone said, "Oh, there's that old man
+
+ align:start position:0%
+someone said, "Oh, there's that old man
+ 
+
+ align:start position:0%
+someone said, "Oh, there's that old man
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+camera." And that's wonderful because
+
+ align:start position:0%
+camera." And that's wonderful because
+ 
+
+ align:start position:0%
+camera." And that's wonderful because
+that means they don't care about you.
+
+ align:start position:0%
+that means they don't care about you.
+ 
+
+ align:start position:0%
+that means they don't care about you.
+They don't think you're up to anything
+
+ align:start position:0%
+They don't think you're up to anything
+ 
+
+ align:start position:0%
+They don't think you're up to anything
+harmful for the most part. I would go in
+
+ align:start position:0%
+harmful for the most part. I would go in
+ 
+
+ align:start position:0%
+harmful for the most part. I would go in
+and I'd say to a factory owner, uh,
+
+ align:start position:0%
+and I'd say to a factory owner, uh,
+ 
+
+ align:start position:0%
+and I'd say to a factory owner, uh,
+could I'm professor from USC. I'm
+
+ align:start position:0%
+could I'm professor from USC. I'm
+ 
+
+ align:start position:0%
+could I'm professor from USC. I'm
+interested in developing an archive of
+
+ align:start position:0%
+interested in developing an archive of
+ 
+
+ align:start position:0%
+interested in developing an archive of
+industry in Los Angeles. It's for the
+
+ align:start position:0%
+industry in Los Angeles. It's for the
+ 
+
+ align:start position:0%
+industry in Los Angeles. It's for the
+libraries. At about onethird of the
+
+ align:start position:0%
+libraries. At about onethird of the
+ 
+
+ align:start position:0%
+libraries. At about onethird of the
+time, they say yes. Well, you know, if
+
+ align:start position:0%
+time, they say yes. Well, you know, if
+ 
+
+ align:start position:0%
+time, they say yes. Well, you know, if
+you hit have a hit rate of 1/3 or 1/5,
+
+ align:start position:0%
+you hit have a hit rate of 1/3 or 1/5,
+ 
+
+ align:start position:0%
+you hit have a hit rate of 1/3 or 1/5,
+you're in business because all you have
+
+ align:start position:0%
+you're in business because all you have
+ 
+
+ align:start position:0%
+you're in business because all you have
+to do is ask five people to get one yes.
+
+ align:start position:0%
+to do is ask five people to get one yes.
+ 
+
+ align:start position:0%
+to do is ask five people to get one yes.
+Of course, that's not true
+
+ align:start position:0%
+Of course, that's not true
+ 
+
+ align:start position:0%
+Of course, that's not true
+probabilistically, but there's something
+
+ align:start position:0%
+probabilistically, but there's something
+ 
+
+ align:start position:0%
+probabilistically, but there's something
+else. Uh but the point is that the hit
+
+ align:start position:0%
+else. Uh but the point is that the hit
+ 
+
+ align:start position:0%
+else. Uh but the point is that the hit
+rates are fairly
+
+ align:start position:0%
+rates are fairly
+ 
+
+ align:start position:0%
+rates are fairly
+high that the major thing you have to
+
+ align:start position:0%
+high that the major thing you have to
+ 
+
+ align:start position:0%
+high that the major thing you have to
+realize is most owners are never there
+
+ align:start position:0%
+realize is most owners are never there
+ 
+
+ align:start position:0%
+realize is most owners are never there
+till 11:00 in the morning. The owner is
+
+ align:start position:0%
+till 11:00 in the morning. The owner is
+ 
+
+ align:start position:0%
+till 11:00 in the morning. The owner is
+not here is the usual line if you go
+
+ align:start position:0%
+not here is the usual line if you go
+ 
+
+ align:start position:0%
+not here is the usual line if you go
+early. What owners are doing before 11
+
+ align:start position:0%
+early. What owners are doing before 11
+ 
+
+ align:start position:0%
+early. What owners are doing before 11
+is something else. Um the other thing
+
+ align:start position:0%
+is something else. Um the other thing
+ 
+
+ align:start position:0%
+is something else. Um the other thing
+you have to realize is that because
+
+ align:start position:0%
+you have to realize is that because
+ 
+
+ align:start position:0%
+you have to realize is that because
+someone says no, you just go to the next
+
+ align:start position:0%
+someone says no, you just go to the next
+ 
+
+ align:start position:0%
+someone says no, you just go to the next
+place. You never ever worry about the
+
+ align:start position:0%
+place. You never ever worry about the
+ 
+
+ align:start position:0%
+place. You never ever worry about the
+people who say no. You could say, "Well,
+
+ align:start position:0%
+people who say no. You could say, "Well,
+ 
+
+ align:start position:0%
+people who say no. You could say, "Well,
+isn't aren't you don't you ever buy a
+
+ align:start position:0%
+isn't aren't you don't you ever buy a
+ 
+
+ align:start position:0%
+isn't aren't you don't you ever buy a
+sample?" The answer, I'm sure, is yes.
+
+ align:start position:0%
+sample?" The answer, I'm sure, is yes.
+ 
+
+ align:start position:0%
+sample?" The answer, I'm sure, is yes.
+But if I have enough of them, I figure
+
+ align:start position:0%
+But if I have enough of them, I figure
+ 
+
+ align:start position:0%
+But if I have enough of them, I figure
+the biases will get worked through. I'm
+
+ align:start position:0%
+the biases will get worked through. I'm
+ 
+
+ align:start position:0%
+the biases will get worked through. I'm
+sure the places where they're torturing
+
+ align:start position:0%
+sure the places where they're torturing
+ 
+
+ align:start position:0%
+sure the places where they're torturing
+people to work will not let me
+
+ align:start position:0%
+people to work will not let me
+ 
+
+ align:start position:0%
+people to work will not let me
+photograph. But I do not believe there
+
+ align:start position:0%
+photograph. But I do not believe there
+ 
+
+ align:start position:0%
+photograph. But I do not believe there
+are very many of them
+
+ align:start position:0%
+are very many of them
+ 
+
+ align:start position:0%
+are very many of them
+statistically because the places where
+
+ align:start position:0%
+statistically because the places where
+ 
+
+ align:start position:0%
+statistically because the places where
+they let me photograph do not look like
+
+ align:start position:0%
+they let me photograph do not look like
+ 
+
+ align:start position:0%
+they let me photograph do not look like
+heaven. Um, and the other thing it helps
+
+ align:start position:0%
+heaven. Um, and the other thing it helps
+ 
+
+ align:start position:0%
+heaven. Um, and the other thing it helps
+is that I'm dogged. I recommend it
+
+ align:start position:0%
+is that I'm dogged. I recommend it
+ 
+
+ align:start position:0%
+is that I'm dogged. I recommend it
+highly. I would go out every morning,
+
+ align:start position:0%
+highly. I would go out every morning,
+ 
+
+ align:start position:0%
+highly. I would go out every morning,
+three, four days a week and
+
+ align:start position:0%
+three, four days a week and
+ 
+
+ align:start position:0%
+three, four days a week and
+photograph. When I was photographing
+
+ align:start position:0%
+photograph. When I was photographing
+ 
+
+ align:start position:0%
+photograph. When I was photographing
+churches, I would go up and down the
+
+ align:start position:0%
+churches, I would go up and down the
+ 
+
+ align:start position:0%
+churches, I would go up and down the
+streets of Los Angeles and
+
+ align:start position:0%
+streets of Los Angeles and
+ 
+
+ align:start position:0%
+streets of Los Angeles and
+systematically go up and down the
+
+ align:start position:0%
+systematically go up and down the
+ 
+
+ align:start position:0%
+systematically go up and down the
+streets, you know, and you don't run out
+
+ align:start position:0%
+streets, you know, and you don't run out
+ 
+
+ align:start position:0%
+streets, you know, and you don't run out
+of them. And some days you have you hit
+
+ align:start position:0%
+of them. And some days you have you hit
+ 
+
+ align:start position:0%
+of them. And some days you have you hit
+pay dirt and someday you don't. But your
+
+ align:start position:0%
+pay dirt and someday you don't. But your
+ 
+
+ align:start position:0%
+pay dirt and someday you don't. But your
+secret is you keep doing it. And if you
+
+ align:start position:0%
+secret is you keep doing it. And if you
+ 
+
+ align:start position:0%
+secret is you keep doing it. And if you
+keep doing it, you'll beat
+
+ align:start position:0%
+keep doing it, you'll beat
+ 
+
+ align:start position:0%
+keep doing it, you'll beat
+everybody. And if you don't worry about
+
+ align:start position:0%
+everybody. And if you don't worry about
+ 
+
+ align:start position:0%
+everybody. And if you don't worry about
+your photographs being perfect, but
+
+ align:start position:0%
+your photographs being perfect, but
+ 
+
+ align:start position:0%
+your photographs being perfect, but
+making sure you just get decent images
+
+ align:start position:0%
+making sure you just get decent images
+ 
+
+ align:start position:0%
+making sure you just get decent images
+and you keep doing it so you're not
+
+ align:start position:0%
+and you keep doing it so you're not
+ 
+
+ align:start position:0%
+and you keep doing it so you're not
+sitting there
+
+ align:start position:0%
+sitting there
+ 
+
+ align:start position:0%
+sitting there
+agonizing, you know, and adjusting your
+
+ align:start position:0%
+agonizing, you know, and adjusting your
+ 
+
+ align:start position:0%
+agonizing, you know, and adjusting your
+this and that, you get it done. Um, and
+
+ align:start position:0%
+this and that, you get it done. Um, and
+ 
+
+ align:start position:0%
+this and that, you get it done. Um, and
+there are costs to my technique, but the
+
+ align:start position:0%
+there are costs to my technique, but the
+ 
+
+ align:start position:0%
+there are costs to my technique, but the
+advantage is it gets done and I'm big on
+
+ align:start position:0%
+advantage is it gets done and I'm big on
+ 
+
+ align:start position:0%
+advantage is it gets done and I'm big on
+that. Nothing is worth doing if you're
+
+ align:start position:0%
+that. Nothing is worth doing if you're
+ 
+
+ align:start position:0%
+that. Nothing is worth doing if you're
+not going to do it. At least so I
+
+ align:start position:0%
+not going to do it. At least so I
+ 
+
+ align:start position:0%
+not going to do it. At least so I
+believe. Anyway, let me show you some of
+
+ align:start position:0%
+believe. Anyway, let me show you some of
+ 
+
+ align:start position:0%
+believe. Anyway, let me show you some of
+the work I've worked on. Um, and so what
+
+ align:start position:0%
+the work I've worked on. Um, and so what
+ 
+
+ align:start position:0%
+the work I've worked on. Um, and so what
+happened is that I had the the
+
+ align:start position:0%
+happened is that I had the the
+ 
+
+ align:start position:0%
+happened is that I had the the
+doggginess. I had the fortune of not,
+
+ align:start position:0%
+doggginess. I had the fortune of not,
+ 
+
+ align:start position:0%
+doggginess. I had the fortune of not,
+you know, I mean some people I mean
+
+ align:start position:0%
+you know, I mean some people I mean
+ 
+
+ align:start position:0%
+you know, I mean some people I mean
+there's a guy named Ken Haymon who is 6'
+
+ align:start position:0%
+there's a guy named Ken Haymon who is 6'
+ 
+
+ align:start position:0%
+there's a guy named Ken Haymon who is 6'
+something big guy. He can fit into any
+
+ align:start position:0%
+something big guy. He can fit into any
+ 
+
+ align:start position:0%
+something big guy. He can fit into any
+corner. He does never seems to take up
+
+ align:start position:0%
+corner. He does never seems to take up
+ 
+
+ align:start position:0%
+corner. He does never seems to take up
+space, you know, probably twice my size.
+
+ align:start position:0%
+space, you know, probably twice my size.
+ 
+
+ align:start position:0%
+space, you know, probably twice my size.
+Other people, you know, just don't have
+
+ align:start position:0%
+Other people, you know, just don't have
+ 
+
+ align:start position:0%
+Other people, you know, just don't have
+the style or something. I have no idea
+
+ align:start position:0%
+the style or something. I have no idea
+ 
+
+ align:start position:0%
+the style or something. I have no idea
+why I get away with it. Um, I'm polite
+
+ align:start position:0%
+why I get away with it. Um, I'm polite
+ 
+
+ align:start position:0%
+why I get away with it. Um, I'm polite
+and so forth, but maybe anyone can do
+
+ align:start position:0%
+and so forth, but maybe anyone can do
+ 
+
+ align:start position:0%
+and so forth, but maybe anyone can do
+it. I recommend it highly to try. Uh,
+
+ align:start position:0%
+it. I recommend it highly to try. Uh,
+ 
+
+ align:start position:0%
+it. I recommend it highly to try. Uh,
+anyway, there are several important
+
+ align:start position:0%
+anyway, there are several important
+ 
+
+ align:start position:0%
+anyway, there are several important
+themes in the work I've done. I started
+
+ align:start position:0%
+themes in the work I've done. I started
+ 
+
+ align:start position:0%
+themes in the work I've done. I started
+out actually the first thing I started
+
+ align:start position:0%
+out actually the first thing I started
+ 
+
+ align:start position:0%
+out actually the first thing I started
+doing is in Beverly Hills where I live.
+
+ align:start position:0%
+doing is in Beverly Hills where I live.
+ 
+
+ align:start position:0%
+doing is in Beverly Hills where I live.
+The largest form of urban renewal in
+
+ align:start position:0%
+The largest form of urban renewal in
+ 
+
+ align:start position:0%
+The largest form of urban renewal in
+Beverly Hills is done by Persian
+
+ align:start position:0%
+Beverly Hills is done by Persian
+ 
+
+ align:start position:0%
+Beverly Hills is done by Persian
+immigrants who buy a property, knock it
+
+ align:start position:0%
+immigrants who buy a property, knock it
+ 
+
+ align:start position:0%
+immigrants who buy a property, knock it
+down, and put up what I call a Persian
+
+ align:start position:0%
+down, and put up what I call a Persian
+ 
+
+ align:start position:0%
+down, and put up what I call a Persian
+palace. A Persian palace is
+
+ align:start position:0%
+palace. A Persian palace is
+ 
+
+ align:start position:0%
+palace. A Persian palace is
+a a western design that's that's been
+
+ align:start position:0%
+a a western design that's that's been
+ 
+
+ align:start position:0%
+a a western design that's that's been
+translated to Tehran, modern section,
+
+ align:start position:0%
+translated to Tehran, modern section,
+ 
+
+ align:start position:0%
+translated to Tehran, modern section,
+and then when they come here, they want
+
+ align:start position:0%
+and then when they come here, they want
+ 
+
+ align:start position:0%
+and then when they come here, they want
+to put some version of it up. It always
+
+ align:start position:0%
+to put some version of it up. It always
+ 
+
+ align:start position:0%
+to put some version of it up. It always
+has lots of balconies, lots of columns.
+
+ align:start position:0%
+has lots of balconies, lots of columns.
+ 
+
+ align:start position:0%
+has lots of balconies, lots of columns.
+It has a window over the front which is
+
+ align:start position:0%
+It has a window over the front which is
+ 
+
+ align:start position:0%
+It has a window over the front which is
+sometimes with, you know, fancy glass.
+
+ align:start position:0%
+sometimes with, you know, fancy glass.
+ 
+
+ align:start position:0%
+sometimes with, you know, fancy glass.
+It's fills up the envelope. It's a a
+
+ align:start position:0%
+It's fills up the envelope. It's a a
+ 
+
+ align:start position:0%
+It's fills up the envelope. It's a a
+mansionette and there are lots of them.
+
+ align:start position:0%
+mansionette and there are lots of them.
+ 
+
+ align:start position:0%
+mansionette and there are lots of them.
+Now, Beverly Hills has is
+
+ align:start position:0%
+Now, Beverly Hills has is
+ 
+
+ align:start position:0%
+Now, Beverly Hills has is
+undistinguished architecture. So, people
+
+ align:start position:0%
+undistinguished architecture. So, people
+ 
+
+ align:start position:0%
+undistinguished architecture. So, people
+say, "Oh, it's destroying our our the
+
+ align:start position:0%
+say, "Oh, it's destroying our our the
+ 
+
+ align:start position:0%
+say, "Oh, it's destroying our our the
+quality of our architecture." And I
+
+ align:start position:0%
+quality of our architecture." And I
+ 
+
+ align:start position:0%
+quality of our architecture." And I
+consider that one of the uh canards of
+
+ align:start position:0%
+consider that one of the uh canards of
+ 
+
+ align:start position:0%
+consider that one of the uh canards of
+the lowest sort. Um the quality of
+
+ align:start position:0%
+the lowest sort. Um the quality of
+ 
+
+ align:start position:0%
+the lowest sort. Um the quality of
+architecture for the price of the house
+
+ align:start position:0%
+architecture for the price of the house
+ 
+
+ align:start position:0%
+architecture for the price of the house
+is probably lower than any place in the
+
+ align:start position:0%
+is probably lower than any place in the
+ 
+
+ align:start position:0%
+is probably lower than any place in the
+world.
+
+ align:start position:0%
+world.
+ 
+
+ align:start position:0%
+world.
+Um, it's not that it's bad. It's just
+
+ align:start position:0%
+Um, it's not that it's bad. It's just
+ 
+
+ align:start position:0%
+Um, it's not that it's bad. It's just
+undistinguished. It's not architecture.
+
+ align:start position:0%
+undistinguished. It's not architecture.
+ 
+
+ align:start position:0%
+undistinguished. It's not architecture.
+It's some sort of, you know, you wanted
+
+ align:start position:0%
+It's some sort of, you know, you wanted
+ 
+
+ align:start position:0%
+It's some sort of, you know, you wanted
+a some years Georgian was popular. All
+
+ align:start position:0%
+a some years Georgian was popular. All
+ 
+
+ align:start position:0%
+a some years Georgian was popular. All
+right. So, I started photographing the
+
+ align:start position:0%
+right. So, I started photographing the
+ 
+
+ align:start position:0%
+right. So, I started photographing the
+Persian palaces, as I called them, and I
+
+ align:start position:0%
+Persian palaces, as I called them, and I
+ 
+
+ align:start position:0%
+Persian palaces, as I called them, and I
+didn't like doing it after a while. I
+
+ align:start position:0%
+didn't like doing it after a while. I
+ 
+
+ align:start position:0%
+didn't like doing it after a while. I
+realized this is just too funny. I was
+
+ align:start position:0%
+realized this is just too funny. I was
+ 
+
+ align:start position:0%
+realized this is just too funny. I was
+making fun of people at some level, and
+
+ align:start position:0%
+making fun of people at some level, and
+ 
+
+ align:start position:0%
+making fun of people at some level, and
+I didn't like that. Um, and then I
+
+ align:start position:0%
+I didn't like that. Um, and then I
+ 
+
+ align:start position:0%
+I didn't like that. Um, and then I
+noticed I did some other things. And let
+
+ align:start position:0%
+noticed I did some other things. And let
+ 
+
+ align:start position:0%
+noticed I did some other things. And let
+me give you some examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see. Yes, this is nail
+
+ align:start position:0%
+see. Yes, this is nail
+ 
+
+ align:start position:0%
+see. Yes, this is nail
+parlors. Um, I'm convinced that in
+
+ align:start position:0%
+parlors. Um, I'm convinced that in
+ 
+
+ align:start position:0%
+parlors. Um, I'm convinced that in
+California and Los Angeles, more money
+
+ align:start position:0%
+California and Los Angeles, more money
+ 
+
+ align:start position:0%
+California and Los Angeles, more money
+is spent on keeping uh women's nails in
+
+ align:start position:0%
+is spent on keeping uh women's nails in
+ 
+
+ align:start position:0%
+is spent on keeping uh women's nails in
+shape than the budgets of most small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+countries. The nail polars are
+
+ align:start position:0%
+countries. The nail polars are
+ 
+
+ align:start position:0%
+countries. The nail polars are
+ubiquitous. They reflect the fact that
+
+ align:start position:0%
+ubiquitous. They reflect the fact that
+ 
+
+ align:start position:0%
+ubiquitous. They reflect the fact that
+and but it's not just that there's
+
+ align:start position:0%
+and but it's not just that there's
+ 
+
+ align:start position:0%
+and but it's not just that there's
+demand. There's a supply. You know who
+
+ align:start position:0%
+demand. There's a supply. You know who
+ 
+
+ align:start position:0%
+demand. There's a supply. You know who
+the the nail pol people who do the nail
+
+ align:start position:0%
+the the nail pol people who do the nail
+ 
+
+ align:start position:0%
+the the nail pol people who do the nail
+polish. They're mostly Vietnamese
+
+ align:start position:0%
+polish. They're mostly Vietnamese
+ 
+
+ align:start position:0%
+polish. They're mostly Vietnamese
+immigrants historic of late. I mean, I'm
+
+ align:start position:0%
+immigrants historic of late. I mean, I'm
+ 
+
+ align:start position:0%
+immigrants historic of late. I mean, I'm
+sure it's changing who could get into
+
+ align:start position:0%
+sure it's changing who could get into
+ 
+
+ align:start position:0%
+sure it's changing who could get into
+this field for some reason. They started
+
+ align:start position:0%
+this field for some reason. They started
+ 
+
+ align:start position:0%
+this field for some reason. They started
+and they get into it. And nail pol are
+
+ align:start position:0%
+and they get into it. And nail pol are
+ 
+
+ align:start position:0%
+and they get into it. And nail pol are
+everywhere. I don't know if that's true
+
+ align:start position:0%
+everywhere. I don't know if that's true
+ 
+
+ align:start position:0%
+everywhere. I don't know if that's true
+here, but where I am, they're
+
+ align:start position:0%
+here, but where I am, they're
+ 
+
+ align:start position:0%
+here, but where I am, they're
+everywhere. And so I started noticing
+
+ align:start position:0%
+everywhere. And so I started noticing
+ 
+
+ align:start position:0%
+everywhere. And so I started noticing
+them. And once you start noticing a few,
+
+ align:start position:0%
+them. And once you start noticing a few,
+ 
+
+ align:start position:0%
+them. And once you start noticing a few,
+you start seeing them everywhere.
+
+ align:start position:0%
+you start seeing them everywhere.
+ 
+
+ align:start position:0%
+you start seeing them everywhere.
+And that's the basic phenomenon in most
+
+ align:start position:0%
+And that's the basic phenomenon in most
+ 
+
+ align:start position:0%
+And that's the basic phenomenon in most
+of my work. I notice something and then
+
+ align:start position:0%
+of my work. I notice something and then
+ 
+
+ align:start position:0%
+of my work. I notice something and then
+when I open up my eyes, I just don't
+
+ align:start position:0%
+when I open up my eyes, I just don't
+ 
+
+ align:start position:0%
+when I open up my eyes, I just don't
+notice one. I notice hundreds. That's
+
+ align:start position:0%
+notice one. I notice hundreds. That's
+ 
+
+ align:start position:0%
+notice one. I notice hundreds. That's
+the deepest thing. So for example,
+
+ align:start position:0%
+the deepest thing. So for example,
+ 
+
+ align:start position:0%
+the deepest thing. So for example,
+um yes, these are houses, storefront
+
+ align:start position:0%
+um yes, these are houses, storefront
+ 
+
+ align:start position:0%
+um yes, these are houses, storefront
+houses of worship. Not all of them are
+
+ align:start position:0%
+houses of worship. Not all of them are
+ 
+
+ align:start position:0%
+houses of worship. Not all of them are
+storefront houses of worship. This is a
+
+ align:start position:0%
+storefront houses of worship. This is a
+ 
+
+ align:start position:0%
+storefront houses of worship. This is a
+first church of the Rasta for example
+
+ align:start position:0%
+first church of the Rasta for example
+ 
+
+ align:start position:0%
+first church of the Rasta for example
+here. Uh all right. And this is not
+
+ align:start position:0%
+here. Uh all right. And this is not
+ 
+
+ align:start position:0%
+here. Uh all right. And this is not
+really a a a church. I mean it's a
+
+ align:start position:0%
+really a a a church. I mean it's a
+ 
+
+ align:start position:0%
+really a a a church. I mean it's a
+market actually. Uh but the Jefferson
+
+ align:start position:0%
+market actually. Uh but the Jefferson
+ 
+
+ align:start position:0%
+market actually. Uh but the Jefferson
+Boulevard in fact once had plastic trees
+
+ align:start position:0%
+Boulevard in fact once had plastic trees
+ 
+
+ align:start position:0%
+Boulevard in fact once had plastic trees
+on it. Uh it's on the it's and let me
+
+ align:start position:0%
+on it. Uh it's on the it's and let me
+ 
+
+ align:start position:0%
+on it. Uh it's on the it's and let me
+just show you a typical these are not
+
+ align:start position:0%
+just show you a typical these are not
+ 
+
+ align:start position:0%
+just show you a typical these are not
+the most standard of the ones. Let me
+
+ align:start position:0%
+the most standard of the ones. Let me
+ 
+
+ align:start position:0%
+the most standard of the ones. Let me
+just see if I can find one. Yeah, this
+
+ align:start position:0%
+just see if I can find one. Yeah, this
+ 
+
+ align:start position:0%
+just see if I can find one. Yeah, this
+is you know a converted um movie theater
+
+ align:start position:0%
+is you know a converted um movie theater
+ 
+
+ align:start position:0%
+is you know a converted um movie theater
+and so forth. There are loads of them.
+
+ align:start position:0%
+and so forth. There are loads of them.
+ 
+
+ align:start position:0%
+and so forth. There are loads of them.
+And then I can show you some more um in
+
+ align:start position:0%
+And then I can show you some more um in
+ 
+
+ align:start position:0%
+And then I can show you some more um in
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment. Yes. Another thing is I started
+
+ align:start position:0%
+moment. Yes. Another thing is I started
+ 
+
+ align:start position:0%
+moment. Yes. Another thing is I started
+noticing uh Los Angeles, as you probably
+
+ align:start position:0%
+noticing uh Los Angeles, as you probably
+ 
+
+ align:start position:0%
+noticing uh Los Angeles, as you probably
+know, has one of the largest um
+
+ align:start position:0%
+know, has one of the largest um
+ 
+
+ align:start position:0%
+know, has one of the largest um
+municipal utilities in the United
+
+ align:start position:0%
+municipal utilities in the United
+ 
+
+ align:start position:0%
+municipal utilities in the United
+States, if not the largest, the
+
+ align:start position:0%
+States, if not the largest, the
+ 
+
+ align:start position:0%
+States, if not the largest, the
+Department of Water and Power of
+
+ align:start position:0%
+Department of Water and Power of
+ 
+
+ align:start position:0%
+Department of Water and Power of
+Chinatown fame. And it has everywhere,
+
+ align:start position:0%
+Chinatown fame. And it has everywhere,
+ 
+
+ align:start position:0%
+Chinatown fame. And it has everywhere,
+it's a monopoly. It was meant as a
+
+ align:start position:0%
+it's a monopoly. It was meant as a
+ 
+
+ align:start position:0%
+it's a monopoly. It was meant as a
+monopoly. Um it essentially scared out
+
+ align:start position:0%
+monopoly. Um it essentially scared out
+ 
+
+ align:start position:0%
+monopoly. Um it essentially scared out
+and bought out all the competitors in
+
+ align:start position:0%
+and bought out all the competitors in
+ 
+
+ align:start position:0%
+and bought out all the competitors in
+Los Angeles, uh so it could run the grid
+
+ align:start position:0%
+Los Angeles, uh so it could run the grid
+ 
+
+ align:start position:0%
+Los Angeles, uh so it could run the grid
+itself. and and so it has these
+
+ align:start position:0%
+itself. and and so it has these
+ 
+
+ align:start position:0%
+itself. and and so it has these
+electrical distribution stations which
+
+ align:start position:0%
+electrical distribution stations which
+ 
+
+ align:start position:0%
+electrical distribution stations which
+are places which take the voltage from a
+
+ align:start position:0%
+are places which take the voltage from a
+ 
+
+ align:start position:0%
+are places which take the voltage from a
+high voltage to say 4500 volts and then
+
+ align:start position:0%
+high voltage to say 4500 volts and then
+ 
+
+ align:start position:0%
+high voltage to say 4500 volts and then
+it's distributed around and lowered for
+
+ align:start position:0%
+it's distributed around and lowered for
+ 
+
+ align:start position:0%
+it's distributed around and lowered for
+your home use. All right and uh so it
+
+ align:start position:0%
+your home use. All right and uh so it
+ 
+
+ align:start position:0%
+your home use. All right and uh so it
+turns out there areund about 135 to 150
+
+ align:start position:0%
+turns out there areund about 135 to 150
+ 
+
+ align:start position:0%
+turns out there areund about 135 to 150
+of these stations and so I visited them
+
+ align:start position:0%
+of these stations and so I visited them
+ 
+
+ align:start position:0%
+of these stations and so I visited them
+all. All right. Once I started noticing
+
+ align:start position:0%
+all. All right. Once I started noticing
+ 
+
+ align:start position:0%
+all. All right. Once I started noticing
+them, you see, and these are these are
+
+ align:start position:0%
+them, you see, and these are these are
+ 
+
+ align:start position:0%
+them, you see, and these are these are
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+20. All right. And you know, like this
+
+ align:start position:0%
+20. All right. And you know, like this
+ 
+
+ align:start position:0%
+20. All right. And you know, like this
+one's a palace here. Can you see my If I
+
+ align:start position:0%
+one's a palace here. Can you see my If I
+ 
+
+ align:start position:0%
+one's a palace here. Can you see my If I
+do that, you see? Yes. All right. Some
+
+ align:start position:0%
+do that, you see? Yes. All right. Some
+ 
+
+ align:start position:0%
+do that, you see? Yes. All right. Some
+of them are undistinguished. Some of
+
+ align:start position:0%
+of them are undistinguished. Some of
+ 
+
+ align:start position:0%
+of them are undistinguished. Some of
+them are This one looks different
+
+ align:start position:0%
+them are This one looks different
+ 
+
+ align:start position:0%
+them are This one looks different
+because it was a different company that
+
+ align:start position:0%
+because it was a different company that
+ 
+
+ align:start position:0%
+because it was a different company that
+built
+
+ align:start position:0%
+built
+ 
+
+ align:start position:0%
+built
+it and it was LA Gas and Electric. And
+
+ align:start position:0%
+it and it was LA Gas and Electric. And
+ 
+
+ align:start position:0%
+it and it was LA Gas and Electric. And
+uh in 1937, they were forced to sell
+
+ align:start position:0%
+uh in 1937, they were forced to sell
+ 
+
+ align:start position:0%
+uh in 1937, they were forced to sell
+out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, but many of them look like these
+
+ align:start position:0%
+Um, but many of them look like these
+ 
+
+ align:start position:0%
+Um, but many of them look like these
+monument. They're monumental structures.
+
+ align:start position:0%
+monument. They're monumental structures.
+ 
+
+ align:start position:0%
+monument. They're monumental structures.
+Okay. And what happened is I started
+
+ align:start position:0%
+Okay. And what happened is I started
+ 
+
+ align:start position:0%
+Okay. And what happened is I started
+noticing them and I was fortunate, this
+
+ align:start position:0%
+noticing them and I was fortunate, this
+ 
+
+ align:start position:0%
+noticing them and I was fortunate, this
+was before 9/11, I could get a list of
+
+ align:start position:0%
+was before 9/11, I could get a list of
+ 
+
+ align:start position:0%
+was before 9/11, I could get a list of
+them all from the Department of Water
+
+ align:start position:0%
+them all from the Department of Water
+ 
+
+ align:start position:0%
+them all from the Department of Water
+and Power. I'm sure after 9/11 I could
+
+ align:start position:0%
+and Power. I'm sure after 9/11 I could
+ 
+
+ align:start position:0%
+and Power. I'm sure after 9/11 I could
+not have gotten it. And but I was
+
+ align:start position:0%
+not have gotten it. And but I was
+ 
+
+ align:start position:0%
+not have gotten it. And but I was
+fortunate the guy liked me so he was
+
+ align:start position:0%
+fortunate the guy liked me so he was
+ 
+
+ align:start position:0%
+fortunate the guy liked me so he was
+willing to let me see it informally the
+
+ align:start position:0%
+willing to let me see it informally the
+ 
+
+ align:start position:0%
+willing to let me see it informally the
+list. Um, and so I could they're all on
+
+ align:start position:0%
+list. Um, and so I could they're all on
+ 
+
+ align:start position:0%
+list. Um, and so I could they're all on
+the street. they're not hidden, but to
+
+ align:start position:0%
+the street. they're not hidden, but to
+ 
+
+ align:start position:0%
+the street. they're not hidden, but to
+have a nice convenient list. And so that
+
+ align:start position:0%
+have a nice convenient list. And so that
+ 
+
+ align:start position:0%
+have a nice convenient list. And so that
+involved literally visiting all over Los
+
+ align:start position:0%
+involved literally visiting all over Los
+ 
+
+ align:start position:0%
+involved literally visiting all over Los
+Angeles because they have to be in every
+
+ align:start position:0%
+Angeles because they have to be in every
+ 
+
+ align:start position:0%
+Angeles because they have to be in every
+neighborhood cuz their job is to apply
+
+ align:start position:0%
+neighborhood cuz their job is to apply
+ 
+
+ align:start position:0%
+neighborhood cuz their job is to apply
+power. So in some sense, if you visit
+
+ align:start position:0%
+power. So in some sense, if you visit
+ 
+
+ align:start position:0%
+power. So in some sense, if you visit
+every one of these, you visited almost
+
+ align:start position:0%
+every one of these, you visited almost
+ 
+
+ align:start position:0%
+every one of these, you visited almost
+every section of the city of
+
+ align:start position:0%
+every section of the city of
+ 
+
+ align:start position:0%
+every section of the city of
+necessity, which is sort of nice.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um I also did things like for example um
+
+ align:start position:0%
+Um I also did things like for example um
+ 
+
+ align:start position:0%
+Um I also did things like for example um
+let's see where is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it? Yes. Uh this is not very clear
+
+ align:start position:0%
+it? Yes. Uh this is not very clear
+ 
+
+ align:start position:0%
+it? Yes. Uh this is not very clear
+unfortunately but what I did was I I
+
+ align:start position:0%
+unfortunately but what I did was I I
+ 
+
+ align:start position:0%
+unfortunately but what I did was I I
+started photographing industrial
+
+ align:start position:0%
+started photographing industrial
+ 
+
+ align:start position:0%
+started photographing industrial
+streetscapes. In other words, I would
+
+ align:start position:0%
+streetscapes. In other words, I would
+ 
+
+ align:start position:0%
+streetscapes. In other words, I would
+find industrial streets in Los Angeles
+
+ align:start position:0%
+find industrial streets in Los Angeles
+ 
+
+ align:start position:0%
+find industrial streets in Los Angeles
+and literally photograph every building
+
+ align:start position:0%
+and literally photograph every building
+ 
+
+ align:start position:0%
+and literally photograph every building
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+street. Okay. And this is one street in
+
+ align:start position:0%
+street. Okay. And this is one street in
+ 
+
+ align:start position:0%
+street. Okay. And this is one street in
+um on uh Clarence Street actually, which
+
+ align:start position:0%
+um on uh Clarence Street actually, which
+ 
+
+ align:start position:0%
+um on uh Clarence Street actually, which
+is on the east side of the river in the
+
+ align:start position:0%
+is on the east side of the river in the
+ 
+
+ align:start position:0%
+is on the east side of the river in the
+flats. And over here, this market is
+
+ align:start position:0%
+flats. And over here, this market is
+ 
+
+ align:start position:0%
+flats. And over here, this market is
+where some guys got killed uh soon
+
+ align:start position:0%
+where some guys got killed uh soon
+ 
+
+ align:start position:0%
+where some guys got killed uh soon
+before. And people are always worried
+
+ align:start position:0%
+before. And people are always worried
+ 
+
+ align:start position:0%
+before. And people are always worried
+about my well-being, but I tell them, no
+
+ align:start position:0%
+about my well-being, but I tell them, no
+ 
+
+ align:start position:0%
+about my well-being, but I tell them, no
+one no one commits murder at 9:00 in the
+
+ align:start position:0%
+one no one commits murder at 9:00 in the
+ 
+
+ align:start position:0%
+one no one commits murder at 9:00 in the
+morning on a weekday. you know, there's
+
+ align:start position:0%
+morning on a weekday. you know, there's
+ 
+
+ align:start position:0%
+morning on a weekday. you know, there's
+no one out to do it. You know, the
+
+ align:start position:0%
+no one out to do it. You know, the
+ 
+
+ align:start position:0%
+no one out to do it. You know, the
+crooks are not there. But, uh, so this
+
+ align:start position:0%
+crooks are not there. But, uh, so this
+ 
+
+ align:start position:0%
+crooks are not there. But, uh, so this
+is one area where I went, you know, it
+
+ align:start position:0%
+is one area where I went, you know, it
+ 
+
+ align:start position:0%
+is one area where I went, you know, it
+it's a industrial area and I and the
+
+ align:start position:0%
+it's a industrial area and I and the
+ 
+
+ align:start position:0%
+it's a industrial area and I and the
+idea was to somehow capture that
+
+ align:start position:0%
+idea was to somehow capture that
+ 
+
+ align:start position:0%
+idea was to somehow capture that
+industrial streetscape for future
+
+ align:start position:0%
+industrial streetscape for future
+ 
+
+ align:start position:0%
+industrial streetscape for future
+use.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, now what what informs all this work?
+
+ align:start position:0%
+Um, now what what informs all this work?
+ 
+
+ align:start position:0%
+Um, now what what informs all this work?
+the ideas of repetition that there's not
+
+ align:start position:0%
+the ideas of repetition that there's not
+ 
+
+ align:start position:0%
+the ideas of repetition that there's not
+just one of them but there are multiple
+
+ align:start position:0%
+just one of them but there are multiple
+ 
+
+ align:start position:0%
+just one of them but there are multiple
+and there are multiple for good reasons.
+
+ align:start position:0%
+and there are multiple for good reasons.
+ 
+
+ align:start position:0%
+and there are multiple for good reasons.
+There are multiple of these departments
+
+ align:start position:0%
+There are multiple of these departments
+ 
+
+ align:start position:0%
+There are multiple of these departments
+of water and power electrical
+
+ align:start position:0%
+of water and power electrical
+ 
+
+ align:start position:0%
+of water and power electrical
+distribution stations because they have
+
+ align:start position:0%
+distribution stations because they have
+ 
+
+ align:start position:0%
+distribution stations because they have
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+sizes roughly. You can't make you know
+
+ align:start position:0%
+sizes roughly. You can't make you know
+ 
+
+ align:start position:0%
+sizes roughly. You can't make you know
+you you don't want to it's sort of the
+
+ align:start position:0%
+you you don't want to it's sort of the
+ 
+
+ align:start position:0%
+you you don't want to it's sort of the
+solving a networking problem where you
+
+ align:start position:0%
+solving a networking problem where you
+ 
+
+ align:start position:0%
+solving a networking problem where you
+want to break it down to smaller units
+
+ align:start position:0%
+want to break it down to smaller units
+ 
+
+ align:start position:0%
+want to break it down to smaller units
+but you don't want too much
+
+ align:start position:0%
+but you don't want too much
+ 
+
+ align:start position:0%
+but you don't want too much
+centralization. you have the right level
+
+ align:start position:0%
+centralization. you have the right level
+ 
+
+ align:start position:0%
+centralization. you have the right level
+of centralization and for the powered
+
+ align:start position:0%
+of centralization and for the powered
+ 
+
+ align:start position:0%
+of centralization and for the powered
+needs. Uh you have too many at the edges
+
+ align:start position:0%
+needs. Uh you have too many at the edges
+ 
+
+ align:start position:0%
+needs. Uh you have too many at the edges
+of Los Angeles at the edges of Los
+
+ align:start position:0%
+of Los Angeles at the edges of Los
+ 
+
+ align:start position:0%
+of Los Angeles at the edges of Los
+Angeles's uh boundaries. Why? Because
+
+ align:start position:0%
+Angeles's uh boundaries. Why? Because
+ 
+
+ align:start position:0%
+Angeles's uh boundaries. Why? Because
+they Los Angeles is a place that's been
+
+ align:start position:0%
+they Los Angeles is a place that's been
+ 
+
+ align:start position:0%
+they Los Angeles is a place that's been
+in the business of annexation for 100
+
+ align:start position:0%
+in the business of annexation for 100
+ 
+
+ align:start position:0%
+in the business of annexation for 100
+years. And so people from Department of
+
+ align:start position:0%
+years. And so people from Department of
+ 
+
+ align:start position:0%
+years. And so people from Department of
+Water Power figure well we might annex
+
+ align:start position:0%
+Water Power figure well we might annex
+ 
+
+ align:start position:0%
+Water Power figure well we might annex
+there so we may as well put it closer to
+
+ align:start position:0%
+there so we may as well put it closer to
+ 
+
+ align:start position:0%
+there so we may as well put it closer to
+the edge. They stopped annexing at some
+
+ align:start position:0%
+the edge. They stopped annexing at some
+ 
+
+ align:start position:0%
+the edge. They stopped annexing at some
+point but that's why they're there. Um
+
+ align:start position:0%
+point but that's why they're there. Um
+ 
+
+ align:start position:0%
+point but that's why they're there. Um
+and for example the um the store houses
+
+ align:start position:0%
+and for example the um the store houses
+ 
+
+ align:start position:0%
+and for example the um the store houses
+of worship which I visited and I have
+
+ align:start position:0%
+of worship which I visited and I have
+ 
+
+ align:start position:0%
+of worship which I visited and I have
+about 800 of them. And the secret of
+
+ align:start position:0%
+about 800 of them. And the secret of
+ 
+
+ align:start position:0%
+about 800 of them. And the secret of
+that how do you get so many? You just go
+
+ align:start position:0%
+that how do you get so many? You just go
+ 
+
+ align:start position:0%
+that how do you get so many? You just go
+up and down streets and you keep doing
+
+ align:start position:0%
+up and down streets and you keep doing
+ 
+
+ align:start position:0%
+up and down streets and you keep doing
+it until you get sick of it. And you
+
+ align:start position:0%
+it until you get sick of it. And you
+ 
+
+ align:start position:0%
+it until you get sick of it. And you
+know if your stomach is good you keep
+
+ align:start position:0%
+know if your stomach is good you keep
+ 
+
+ align:start position:0%
+know if your stomach is good you keep
+doing it for a few months. And the trick
+
+ align:start position:0%
+doing it for a few months. And the trick
+ 
+
+ align:start position:0%
+doing it for a few months. And the trick
+there is the following. By the way
+
+ align:start position:0%
+there is the following. By the way
+ 
+
+ align:start position:0%
+there is the following. By the way
+everybody know today this month is the
+
+ align:start position:0%
+everybody know today this month is the
+ 
+
+ align:start position:0%
+everybody know today this month is the
+100th anniversary of Pentecostalism.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh here's what happens. In 1906 in Los
+
+ align:start position:0%
+Uh here's what happens. In 1906 in Los
+ 
+
+ align:start position:0%
+Uh here's what happens. In 1906 in Los
+Angeles at the Isuza Street Mission,
+
+ align:start position:0%
+Angeles at the Isuza Street Mission,
+ 
+
+ align:start position:0%
+Angeles at the Isuza Street Mission,
+which is now in what we little
+
+ align:start position:0%
+which is now in what we little
+ 
+
+ align:start position:0%
+which is now in what we little
+Tokyo, there was a people started
+
+ align:start position:0%
+Tokyo, there was a people started
+ 
+
+ align:start position:0%
+Tokyo, there was a people started
+speaking in
+
+ align:start position:0%
+speaking in
+ 
+
+ align:start position:0%
+speaking in
+tongues. Now it turns out people have
+
+ align:start position:0%
+tongues. Now it turns out people have
+ 
+
+ align:start position:0%
+tongues. Now it turns out people have
+been speaking in tongues before this,
+
+ align:start position:0%
+been speaking in tongues before this,
+ 
+
+ align:start position:0%
+been speaking in tongues before this,
+well before this in other parts of the
+
+ align:start position:0%
+well before this in other parts of the
+ 
+
+ align:start position:0%
+well before this in other parts of the
+United States and the world. But this
+
+ align:start position:0%
+United States and the world. But this
+ 
+
+ align:start position:0%
+United States and the world. But this
+turns out to be the archetypal moment
+
+ align:start position:0%
+turns out to be the archetypal moment
+ 
+
+ align:start position:0%
+turns out to be the archetypal moment
+from which it
+
+ align:start position:0%
+from which it
+ 
+
+ align:start position:0%
+from which it
+spreads in April
+
+ align:start position:0%
+spreads in April
+ 
+
+ align:start position:0%
+spreads in April
+1906. and it's a source for what we call
+
+ align:start position:0%
+1906. and it's a source for what we call
+ 
+
+ align:start position:0%
+1906. and it's a source for what we call
+modern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pentecostalism. So, Los Angeles is the
+
+ align:start position:0%
+Pentecostalism. So, Los Angeles is the
+ 
+
+ align:start position:0%
+Pentecostalism. So, Los Angeles is the
+Jerusalem of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pentecostalism. And this and then the
+
+ align:start position:0%
+Pentecostalism. And this and then the
+ 
+
+ align:start position:0%
+Pentecostalism. And this and then the
+other thing that's very important is the
+
+ align:start position:0%
+other thing that's very important is the
+ 
+
+ align:start position:0%
+other thing that's very important is the
+great migrations up north from the south
+
+ align:start position:0%
+great migrations up north from the south
+ 
+
+ align:start position:0%
+great migrations up north from the south
+to the north which brings
+
+ align:start position:0%
+to the north which brings
+ 
+
+ align:start position:0%
+to the north which brings
+African-Americans and c on certain
+
+ align:start position:0%
+African-Americans and c on certain
+ 
+
+ align:start position:0%
+African-Americans and c on certain
+routes and so forth. The other thing
+
+ align:start position:0%
+routes and so forth. The other thing
+ 
+
+ align:start position:0%
+routes and so forth. The other thing
+that's crucial about the um storefront
+
+ align:start position:0%
+that's crucial about the um storefront
+ 
+
+ align:start position:0%
+that's crucial about the um storefront
+churches which is important to
+
+ align:start position:0%
+churches which is important to
+ 
+
+ align:start position:0%
+churches which is important to
+understand is where are they located?
+
+ align:start position:0%
+understand is where are they located?
+ 
+
+ align:start position:0%
+understand is where are they located?
+They're always located in storefronts,
+
+ align:start position:0%
+They're always located in storefronts,
+ 
+
+ align:start position:0%
+They're always located in storefronts,
+right? Well, people don't build
+
+ align:start position:0%
+right? Well, people don't build
+ 
+
+ align:start position:0%
+right? Well, people don't build
+storefronts for churches. They don't pay
+
+ align:start position:0%
+storefronts for churches. They don't pay
+ 
+
+ align:start position:0%
+storefronts for churches. They don't pay
+enough rent. They built them because if
+
+ align:start position:0%
+enough rent. They built them because if
+ 
+
+ align:start position:0%
+enough rent. They built them because if
+you had um trolley lines, people would
+
+ align:start position:0%
+you had um trolley lines, people would
+ 
+
+ align:start position:0%
+you had um trolley lines, people would
+get off the trolley lines and do some
+
+ align:start position:0%
+get off the trolley lines and do some
+ 
+
+ align:start position:0%
+get off the trolley lines and do some
+shopping on their way home or to and
+
+ align:start position:0%
+shopping on their way home or to and
+ 
+
+ align:start position:0%
+shopping on their way home or to and
+from. Well, the trolley lines eventually
+
+ align:start position:0%
+from. Well, the trolley lines eventually
+ 
+
+ align:start position:0%
+from. Well, the trolley lines eventually
+go. The storefronts are still
+
+ align:start position:0%
+go. The storefronts are still
+ 
+
+ align:start position:0%
+go. The storefronts are still
+there. Turns out, and then the
+
+ align:start position:0%
+there. Turns out, and then the
+ 
+
+ align:start position:0%
+there. Turns out, and then the
+neighborhood doesn't do too well. So the
+
+ align:start position:0%
+neighborhood doesn't do too well. So the
+ 
+
+ align:start position:0%
+neighborhood doesn't do too well. So the
+these the people who can afford you know
+
+ align:start position:0%
+these the people who can afford you know
+ 
+
+ align:start position:0%
+these the people who can afford you know
+who can rent them and there's obviously
+
+ align:start position:0%
+who can rent them and there's obviously
+ 
+
+ align:start position:0%
+who can rent them and there's obviously
+nothing better you can do with them. So
+
+ align:start position:0%
+nothing better you can do with them. So
+ 
+
+ align:start position:0%
+nothing better you can do with them. So
+you have large numbers of storefront
+
+ align:start position:0%
+you have large numbers of storefront
+ 
+
+ align:start position:0%
+you have large numbers of storefront
+churches. Uh most storefront churches
+
+ align:start position:0%
+churches. Uh most storefront churches
+ 
+
+ align:start position:0%
+churches. Uh most storefront churches
+are small you know 50 to 100 at most
+
+ align:start position:0%
+are small you know 50 to 100 at most
+ 
+
+ align:start position:0%
+are small you know 50 to 100 at most
+members. The mega churches are entirely
+
+ align:start position:0%
+members. The mega churches are entirely
+ 
+
+ align:start position:0%
+members. The mega churches are entirely
+different business. Uh I don't know what
+
+ align:start position:0%
+different business. Uh I don't know what
+ 
+
+ align:start position:0%
+different business. Uh I don't know what
+happens here but mega churches nowadays
+
+ align:start position:0%
+happens here but mega churches nowadays
+ 
+
+ align:start position:0%
+happens here but mega churches nowadays
+are occupying in you find them in
+
+ align:start position:0%
+are occupying in you find them in
+ 
+
+ align:start position:0%
+are occupying in you find them in
+industrial parks in Los Angeles.
+
+ align:start position:0%
+industrial parks in Los Angeles.
+ 
+
+ align:start position:0%
+industrial parks in Los Angeles.
+you know, they take over a building and
+
+ align:start position:0%
+you know, they take over a building and
+ 
+
+ align:start position:0%
+you know, they take over a building and
+suitably, you know, uh, relig relig
+
+ align:start position:0%
+suitably, you know, uh, relig relig
+ 
+
+ align:start position:0%
+suitably, you know, uh, relig relig
+sacralize it, but remember it's still a
+
+ align:start position:0%
+sacralize it, but remember it's still a
+ 
+
+ align:start position:0%
+sacralize it, but remember it's still a
+tiltup, right? And so there's an there's
+
+ align:start position:0%
+tiltup, right? And so there's an there's
+ 
+
+ align:start position:0%
+tiltup, right? And so there's an there's
+a long story and what I've done with
+
+ align:start position:0%
+a long story and what I've done with
+ 
+
+ align:start position:0%
+a long story and what I've done with
+that, for example, uh, is I try to look
+
+ align:start position:0%
+that, for example, uh, is I try to look
+ 
+
+ align:start position:0%
+that, for example, uh, is I try to look
+at the symbolic content. I look at the
+
+ align:start position:0%
+at the symbolic content. I look at the
+ 
+
+ align:start position:0%
+at the symbolic content. I look at the
+quotes from scripture that they all put
+
+ align:start position:0%
+quotes from scripture that they all put
+ 
+
+ align:start position:0%
+quotes from scripture that they all put
+on their thing. It's connected. Do you
+
+ align:start position:0%
+on their thing. It's connected. Do you
+ 
+
+ align:start position:0%
+on their thing. It's connected. Do you
+know why it's Pentecostalism? Because on
+
+ align:start position:0%
+know why it's Pentecostalism? Because on
+ 
+
+ align:start position:0%
+know why it's Pentecostalism? Because on
+Pentecost the apostles uh it's if you
+
+ align:start position:0%
+Pentecost the apostles uh it's if you
+ 
+
+ align:start position:0%
+Pentecost the apostles uh it's if you
+look in Acts there's a the apostles are
+
+ align:start position:0%
+look in Acts there's a the apostles are
+ 
+
+ align:start position:0%
+look in Acts there's a the apostles are
+start speaking in in uh in
+
+ align:start position:0%
+start speaking in in uh in
+ 
+
+ align:start position:0%
+start speaking in in uh in
+tongues and so these are the return of
+
+ align:start position:0%
+tongues and so these are the return of
+ 
+
+ align:start position:0%
+tongues and so these are the return of
+so the so Pentecostals think of
+
+ align:start position:0%
+so the so Pentecostals think of
+ 
+
+ align:start position:0%
+so the so Pentecostals think of
+themselves as essentially
+
+ align:start position:0%
+themselves as essentially
+ 
+
+ align:start position:0%
+themselves as essentially
+um as recurrences of the
+
+ align:start position:0%
+um as recurrences of the
+ 
+
+ align:start position:0%
+um as recurrences of the
+apostles and that's what's so
+
+ align:start position:0%
+apostles and that's what's so
+ 
+
+ align:start position:0%
+apostles and that's what's so
+interesting about
+
+ align:start position:0%
+interesting about
+ 
+
+ align:start position:0%
+interesting about
+it. Um, and so you can connect the
+
+ align:start position:0%
+it. Um, and so you can connect the
+ 
+
+ align:start position:0%
+it. Um, and so you can connect the
+locations of the places, how they're
+
+ align:start position:0%
+locations of the places, how they're
+ 
+
+ align:start position:0%
+locations of the places, how they're
+marked, what are the structures look
+
+ align:start position:0%
+marked, what are the structures look
+ 
+
+ align:start position:0%
+marked, what are the structures look
+like, what kinds of symbolic contents,
+
+ align:start position:0%
+like, what kinds of symbolic contents,
+ 
+
+ align:start position:0%
+like, what kinds of symbolic contents,
+why they're where they are, and who's
+
+ align:start position:0%
+why they're where they are, and who's
+ 
+
+ align:start position:0%
+why they're where they are, and who's
+going to them in a systematic way. And
+
+ align:start position:0%
+going to them in a systematic way. And
+ 
+
+ align:start position:0%
+going to them in a systematic way. And
+so what you see is not just hundreds of
+
+ align:start position:0%
+so what you see is not just hundreds of
+ 
+
+ align:start position:0%
+so what you see is not just hundreds of
+storefront churches, but storefront
+
+ align:start position:0%
+storefront churches, but storefront
+ 
+
+ align:start position:0%
+storefront churches, but storefront
+churches in certain parts of
+
+ align:start position:0%
+churches in certain parts of
+ 
+
+ align:start position:0%
+churches in certain parts of
+town. And they have reasons why the
+
+ align:start position:0%
+town. And they have reasons why the
+ 
+
+ align:start position:0%
+town. And they have reasons why the
+storefronts are now occupied by the
+
+ align:start position:0%
+storefronts are now occupied by the
+ 
+
+ align:start position:0%
+storefronts are now occupied by the
+churches rather than by
+
+ align:start position:0%
+churches rather than by
+ 
+
+ align:start position:0%
+churches rather than by
+bakeries or something else.
+
+ align:start position:0%
+bakeries or something else.
+ 
+
+ align:start position:0%
+bakeries or something else.
+So that's so that's the kind of thing
+
+ align:start position:0%
+So that's so that's the kind of thing
+ 
+
+ align:start position:0%
+So that's so that's the kind of thing
+you want to do. The same thing with the
+
+ align:start position:0%
+you want to do. The same thing with the
+ 
+
+ align:start position:0%
+you want to do. The same thing with the
+department of water power. You can start
+
+ align:start position:0%
+department of water power. You can start
+ 
+
+ align:start position:0%
+department of water power. You can start
+telling a whole story about the history
+
+ align:start position:0%
+telling a whole story about the history
+ 
+
+ align:start position:0%
+telling a whole story about the history
+of the architecture because at one times
+
+ align:start position:0%
+of the architecture because at one times
+ 
+
+ align:start position:0%
+of the architecture because at one times
+it looks monumental eventually it sort
+
+ align:start position:0%
+it looks monumental eventually it sort
+ 
+
+ align:start position:0%
+it looks monumental eventually it sort
+of becomes boring and dull and of late
+
+ align:start position:0%
+of becomes boring and dull and of late
+ 
+
+ align:start position:0%
+of becomes boring and dull and of late
+it's become
+
+ align:start position:0%
+it's become
+ 
+
+ align:start position:0%
+it's become
+handsome and it all to do with the
+
+ align:start position:0%
+handsome and it all to do with the
+ 
+
+ align:start position:0%
+handsome and it all to do with the
+nature of relationship of uh the city to
+
+ align:start position:0%
+nature of relationship of uh the city to
+ 
+
+ align:start position:0%
+nature of relationship of uh the city to
+the people who live there.
+
+ align:start position:0%
+the people who live there.
+ 
+
+ align:start position:0%
+the people who live there.
+Um, in other words, these photographs
+
+ align:start position:0%
+Um, in other words, these photographs
+ 
+
+ align:start position:0%
+Um, in other words, these photographs
+gives you a handle on much larger
+
+ align:start position:0%
+gives you a handle on much larger
+ 
+
+ align:start position:0%
+gives you a handle on much larger
+systemic factors once you start learning
+
+ align:start position:0%
+systemic factors once you start learning
+ 
+
+ align:start position:0%
+systemic factors once you start learning
+more about it. But of course, you have
+
+ align:start position:0%
+more about it. But of course, you have
+ 
+
+ align:start position:0%
+more about it. But of course, you have
+to start reading the history of
+
+ align:start position:0%
+to start reading the history of
+ 
+
+ align:start position:0%
+to start reading the history of
+Pentecostalism or start understanding uh
+
+ align:start position:0%
+Pentecostalism or start understanding uh
+ 
+
+ align:start position:0%
+Pentecostalism or start understanding uh
+the kind of stuff that your students at
+
+ align:start position:0%
+the kind of stuff that your students at
+ 
+
+ align:start position:0%
+the kind of stuff that your students at
+MIT would know. Well, actually, they
+
+ align:start position:0%
+MIT would know. Well, actually, they
+ 
+
+ align:start position:0%
+MIT would know. Well, actually, they
+don't know usually because they learn
+
+ align:start position:0%
+don't know usually because they learn
+ 
+
+ align:start position:0%
+don't know usually because they learn
+about micro electronics, not about power
+
+ align:start position:0%
+about micro electronics, not about power
+ 
+
+ align:start position:0%
+about micro electronics, not about power
+systems in general, but you know, would
+
+ align:start position:0%
+systems in general, but you know, would
+ 
+
+ align:start position:0%
+systems in general, but you know, would
+learn about how electrical systems might
+
+ align:start position:0%
+learn about how electrical systems might
+ 
+
+ align:start position:0%
+learn about how electrical systems might
+work. Um, and so forth.
+
+ align:start position:0%
+work. Um, and so forth.
+ 
+
+ align:start position:0%
+work. Um, and so forth.
+Uh, and so that's what makes it really
+
+ align:start position:0%
+Uh, and so that's what makes it really
+ 
+
+ align:start position:0%
+Uh, and so that's what makes it really
+worth doing is that you're not just
+
+ align:start position:0%
+worth doing is that you're not just
+ 
+
+ align:start position:0%
+worth doing is that you're not just
+finding casual images. You're also
+
+ align:start position:0%
+finding casual images. You're also
+ 
+
+ align:start position:0%
+finding casual images. You're also
+really getting a chance to uh plug into
+
+ align:start position:0%
+really getting a chance to uh plug into
+ 
+
+ align:start position:0%
+really getting a chance to uh plug into
+much larger
+
+ align:start position:0%
+much larger
+ 
+
+ align:start position:0%
+much larger
+stories. Now, you can say, do you need
+
+ align:start position:0%
+stories. Now, you can say, do you need
+ 
+
+ align:start position:0%
+stories. Now, you can say, do you need
+800? Wouldn't 600 be enough of the
+
+ align:start position:0%
+800? Wouldn't 600 be enough of the
+ 
+
+ align:start position:0%
+800? Wouldn't 600 be enough of the
+storefront churches? I don't know how
+
+ align:start position:0%
+storefront churches? I don't know how
+ 
+
+ align:start position:0%
+storefront churches? I don't know how
+many you need. Um, Leo Steinberg in a
+
+ align:start position:0%
+many you need. Um, Leo Steinberg in a
+ 
+
+ align:start position:0%
+many you need. Um, Leo Steinberg in a
+very different context, he's a very
+
+ align:start position:0%
+very different context, he's a very
+ 
+
+ align:start position:0%
+very different context, he's a very
+distinguished art historian said, for
+
+ align:start position:0%
+distinguished art historian said, for
+ 
+
+ align:start position:0%
+distinguished art historian said, for
+phenomena which people don't want to
+
+ align:start position:0%
+phenomena which people don't want to
+ 
+
+ align:start position:0%
+phenomena which people don't want to
+believe, no number is too few. Once they
+
+ align:start position:0%
+believe, no number is too few. Once they
+ 
+
+ align:start position:0%
+believe, no number is too few. Once they
+think they agree with you that this is
+
+ align:start position:0%
+think they agree with you that this is
+ 
+
+ align:start position:0%
+think they agree with you that this is
+re a real phenomenon, two or three is
+
+ align:start position:0%
+re a real phenomenon, two or three is
+ 
+
+ align:start position:0%
+re a real phenomenon, two or three is
+enough. So you owe because their
+
+ align:start position:0%
+enough. So you owe because their
+ 
+
+ align:start position:0%
+enough. So you owe because their
+skepticism says, "Oh, this can't be real
+
+ align:start position:0%
+skepticism says, "Oh, this can't be real
+ 
+
+ align:start position:0%
+skepticism says, "Oh, this can't be real
+what you're
+
+ align:start position:0%
+what you're
+ 
+
+ align:start position:0%
+what you're
+saying." You know, to take P treat
+
+ align:start position:0%
+saying." You know, to take P treat
+ 
+
+ align:start position:0%
+saying." You know, to take P treat
+Pentecostal church, these storefront
+
+ align:start position:0%
+Pentecostal church, these storefront
+ 
+
+ align:start position:0%
+Pentecostal church, these storefront
+churches like you would
+
+ align:start position:0%
+churches like you would
+ 
+
+ align:start position:0%
+churches like you would
+treat interpreting its content and so
+
+ align:start position:0%
+treat interpreting its content and so
+ 
+
+ align:start position:0%
+treat interpreting its content and so
+forth. Oh, come on. So, you have to keep
+
+ align:start position:0%
+forth. Oh, come on. So, you have to keep
+ 
+
+ align:start position:0%
+forth. Oh, come on. So, you have to keep
+doing it. When they finally get it, they
+
+ align:start position:0%
+doing it. When they finally get it, they
+ 
+
+ align:start position:0%
+doing it. When they finally get it, they
+don't want to see anymore. So, the
+
+ align:start position:0%
+don't want to see anymore. So, the
+ 
+
+ align:start position:0%
+don't want to see anymore. So, the
+numbers are
+
+ align:start position:0%
+numbers are
+ 
+
+ align:start position:0%
+numbers are
+partially just sheer persistence and
+
+ align:start position:0%
+partially just sheer persistence and
+ 
+
+ align:start position:0%
+partially just sheer persistence and
+survey. partially if you had to bury
+
+ align:start position:0%
+survey. partially if you had to bury
+ 
+
+ align:start position:0%
+survey. partially if you had to bury
+people in the data so they can't that
+
+ align:start position:0%
+people in the data so they can't that
+ 
+
+ align:start position:0%
+people in the data so they can't that
+their ordinary skepticism has to be put
+
+ align:start position:0%
+their ordinary skepticism has to be put
+ 
+
+ align:start position:0%
+their ordinary skepticism has to be put
+aside. Uh they still can challenge you
+
+ align:start position:0%
+aside. Uh they still can challenge you
+ 
+
+ align:start position:0%
+aside. Uh they still can challenge you
+but they can't just say this is
+
+ align:start position:0%
+but they can't just say this is
+ 
+
+ align:start position:0%
+but they can't just say this is
+nonsense.
+
+ align:start position:0%
+nonsense.
+ 
+
+ align:start position:0%
+nonsense.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and so it depends to do this kind of
+
+ align:start position:0%
+and so it depends to do this kind of
+ 
+
+ align:start position:0%
+and so it depends to do this kind of
+work you have to have a a wide range of
+
+ align:start position:0%
+work you have to have a a wide range of
+ 
+
+ align:start position:0%
+work you have to have a a wide range of
+knowledge which you have to pick up. I
+
+ align:start position:0%
+knowledge which you have to pick up. I
+ 
+
+ align:start position:0%
+knowledge which you have to pick up. I
+mean I did not uh come to this subject
+
+ align:start position:0%
+mean I did not uh come to this subject
+ 
+
+ align:start position:0%
+mean I did not uh come to this subject
+with a vast knowledge of Pentecostalism.
+
+ align:start position:0%
+with a vast knowledge of Pentecostalism.
+ 
+
+ align:start position:0%
+with a vast knowledge of Pentecostalism.
+uh but thank god there are very few
+
+ align:start position:0%
+uh but thank god there are very few
+ 
+
+ align:start position:0%
+uh but thank god there are very few
+books written on it compared to some
+
+ align:start position:0%
+books written on it compared to some
+ 
+
+ align:start position:0%
+books written on it compared to some
+other uh aspects of Christianity and so
+
+ align:start position:0%
+other uh aspects of Christianity and so
+ 
+
+ align:start position:0%
+other uh aspects of Christianity and so
+actually one can master the literature
+
+ align:start position:0%
+actually one can master the literature
+ 
+
+ align:start position:0%
+actually one can master the literature
+fairly quickly
+
+ align:start position:0%
+fairly quickly
+ 
+
+ align:start position:0%
+fairly quickly
+uh that's changing slowly but not as
+
+ align:start position:0%
+uh that's changing slowly but not as
+ 
+
+ align:start position:0%
+uh that's changing slowly but not as
+fast as you can keep up with it the
+
+ align:start position:0%
+fast as you can keep up with it the
+ 
+
+ align:start position:0%
+fast as you can keep up with it the
+second uh idea besides repetition is
+
+ align:start position:0%
+second uh idea besides repetition is
+ 
+
+ align:start position:0%
+second uh idea besides repetition is
+choreography what I want to do there is
+
+ align:start position:0%
+choreography what I want to do there is
+ 
+
+ align:start position:0%
+choreography what I want to do there is
+try to understand how complex systems of
+
+ align:start position:0%
+try to understand how complex systems of
+ 
+
+ align:start position:0%
+try to understand how complex systems of
+people and machinery and processes work
+
+ align:start position:0%
+people and machinery and processes work
+ 
+
+ align:start position:0%
+people and machinery and processes work
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+And that could be the flows of people
+
+ align:start position:0%
+And that could be the flows of people
+ 
+
+ align:start position:0%
+And that could be the flows of people
+and machinery and goods in a
+
+ align:start position:0%
+and machinery and goods in a
+ 
+
+ align:start position:0%
+and machinery and goods in a
+factory or uh the worship process in a
+
+ align:start position:0%
+factory or uh the worship process in a
+ 
+
+ align:start position:0%
+factory or uh the worship process in a
+church. In other words, it's different.
+
+ align:start position:0%
+church. In other words, it's different.
+ 
+
+ align:start position:0%
+church. In other words, it's different.
+It's one thing to take pictures of 800
+
+ align:start position:0%
+It's one thing to take pictures of 800
+ 
+
+ align:start position:0%
+It's one thing to take pictures of 800
+churches facads. It's another to go into
+
+ align:start position:0%
+churches facads. It's another to go into
+ 
+
+ align:start position:0%
+churches facads. It's another to go into
+them and start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+photographing or making videos. And with
+
+ align:start position:0%
+photographing or making videos. And with
+ 
+
+ align:start position:0%
+photographing or making videos. And with
+the one thing you want to do when you go
+
+ align:start position:0%
+the one thing you want to do when you go
+ 
+
+ align:start position:0%
+the one thing you want to do when you go
+to these churches, you stop take
+
+ align:start position:0%
+to these churches, you stop take
+ 
+
+ align:start position:0%
+to these churches, you stop take
+pictures of people having transcendent
+
+ align:start position:0%
+pictures of people having transcendent
+ 
+
+ align:start position:0%
+pictures of people having transcendent
+experiences. you know, the eyes rolling
+
+ align:start position:0%
+experiences. you know, the eyes rolling
+ 
+
+ align:start position:0%
+experiences. you know, the eyes rolling
+back, all that stuff. You know, that's
+
+ align:start position:0%
+back, all that stuff. You know, that's
+ 
+
+ align:start position:0%
+back, all that stuff. You know, that's
+that's a sensationalism. Tom Roman
+
+ align:start position:0%
+that's a sensationalism. Tom Roman
+ 
+
+ align:start position:0%
+that's a sensationalism. Tom Roman
+specializes in that. Um, and other
+
+ align:start position:0%
+specializes in that. Um, and other
+ 
+
+ align:start position:0%
+specializes in that. Um, and other
+people do. What's really interesting is
+
+ align:start position:0%
+people do. What's really interesting is
+ 
+
+ align:start position:0%
+people do. What's really interesting is
+their ordinary sets of behaviors, how
+
+ align:start position:0%
+their ordinary sets of behaviors, how
+ 
+
+ align:start position:0%
+their ordinary sets of behaviors, how
+they're coordinated, how they work
+
+ align:start position:0%
+they're coordinated, how they work
+ 
+
+ align:start position:0%
+they're coordinated, how they work
+together. How in Pentecostalism in
+
+ align:start position:0%
+together. How in Pentecostalism in
+ 
+
+ align:start position:0%
+together. How in Pentecostalism in
+particular, which is supposed to not
+
+ align:start position:0%
+particular, which is supposed to not
+ 
+
+ align:start position:0%
+particular, which is supposed to not
+have an order of worship and everybody
+
+ align:start position:0%
+have an order of worship and everybody
+ 
+
+ align:start position:0%
+have an order of worship and everybody
+is to just feel it, everybody actually
+
+ align:start position:0%
+is to just feel it, everybody actually
+ 
+
+ align:start position:0%
+is to just feel it, everybody actually
+feels it, but they they're highly
+
+ align:start position:0%
+feels it, but they they're highly
+ 
+
+ align:start position:0%
+feels it, but they they're highly
+disciplined by the pastor and by the
+
+ align:start position:0%
+disciplined by the pastor and by the
+ 
+
+ align:start position:0%
+disciplined by the pastor and by the
+rules. In other words, even though it's
+
+ align:start position:0%
+rules. In other words, even though it's
+ 
+
+ align:start position:0%
+rules. In other words, even though it's
+supposed to be spontaneous, the
+
+ align:start position:0%
+supposed to be spontaneous, the
+ 
+
+ align:start position:0%
+supposed to be spontaneous, the
+spontaneity is highly disciplined and
+
+ align:start position:0%
+spontaneity is highly disciplined and
+ 
+
+ align:start position:0%
+spontaneity is highly disciplined and
+controlled,
+
+ align:start position:0%
+controlled,
+ 
+
+ align:start position:0%
+controlled,
+right? And so that choreography is what
+
+ align:start position:0%
+right? And so that choreography is what
+ 
+
+ align:start position:0%
+right? And so that choreography is what
+interests me. And how do you photograph
+
+ align:start position:0%
+interests me. And how do you photograph
+ 
+
+ align:start position:0%
+interests me. And how do you photograph
+that? And how do you get documentation
+
+ align:start position:0%
+that? And how do you get documentation
+ 
+
+ align:start position:0%
+that? And how do you get documentation
+that is very difficult and I've been
+
+ align:start position:0%
+that is very difficult and I've been
+ 
+
+ align:start position:0%
+that is very difficult and I've been
+trying to do it and I make no great
+
+ align:start position:0%
+trying to do it and I make no great
+ 
+
+ align:start position:0%
+trying to do it and I make no great
+claim there.
+
+ align:start position:0%
+claim there.
+ 
+
+ align:start position:0%
+claim there.
+My most wonderful thing that happened to
+
+ align:start position:0%
+My most wonderful thing that happened to
+ 
+
+ align:start position:0%
+My most wonderful thing that happened to
+me last week is I was down photographing
+
+ align:start position:0%
+me last week is I was down photographing
+ 
+
+ align:start position:0%
+me last week is I was down photographing
+I was going to photograph the moss in
+
+ align:start position:0%
+I was going to photograph the moss in
+ 
+
+ align:start position:0%
+I was going to photograph the moss in
+the cracks in the concrete because I was
+
+ align:start position:0%
+the cracks in the concrete because I was
+ 
+
+ align:start position:0%
+the cracks in the concrete because I was
+interested in in what kind of plants
+
+ align:start position:0%
+interested in in what kind of plants
+ 
+
+ align:start position:0%
+interested in in what kind of plants
+grow in a city that are
+
+ align:start position:0%
+grow in a city that are
+ 
+
+ align:start position:0%
+grow in a city that are
+inadvertent and there's I haven't been
+
+ align:start position:0%
+inadvertent and there's I haven't been
+ 
+
+ align:start position:0%
+inadvertent and there's I haven't been
+able to find the literature on this but
+
+ align:start position:0%
+able to find the literature on this but
+ 
+
+ align:start position:0%
+able to find the literature on this but
+I'm looking and I was down in in uh
+
+ align:start position:0%
+I'm looking and I was down in in uh
+ 
+
+ align:start position:0%
+I'm looking and I was down in in uh
+downtown Los Angeles in the industrial
+
+ align:start position:0%
+downtown Los Angeles in the industrial
+ 
+
+ align:start position:0%
+downtown Los Angeles in the industrial
+area which is sort of on the east side
+
+ align:start position:0%
+area which is sort of on the east side
+ 
+
+ align:start position:0%
+area which is sort of on the east side
+and um I didn't find that much
+
+ align:start position:0%
+and um I didn't find that much
+ 
+
+ align:start position:0%
+and um I didn't find that much
+interesting in a plant life but there
+
+ align:start position:0%
+interesting in a plant life but there
+ 
+
+ align:start position:0%
+interesting in a plant life but there
+was a there's a firm there called Brook
+
+ align:start position:0%
+was a there's a firm there called Brook
+ 
+
+ align:start position:0%
+was a there's a firm there called Brook
+Braid which I've been to once before,
+
+ align:start position:0%
+Braid which I've been to once before,
+ 
+
+ align:start position:0%
+Braid which I've been to once before,
+but the guy said, "We can't let you
+
+ align:start position:0%
+but the guy said, "We can't let you
+ 
+
+ align:start position:0%
+but the guy said, "We can't let you
+photograph now cuz we're having some
+
+ align:start position:0%
+photograph now cuz we're having some
+ 
+
+ align:start position:0%
+photograph now cuz we're having some
+legal problems." Um, and it's it's if
+
+ align:start position:0%
+legal problems." Um, and it's it's if
+ 
+
+ align:start position:0%
+legal problems." Um, and it's it's if
+you drive along the freeways in Los
+
+ align:start position:0%
+you drive along the freeways in Los
+ 
+
+ align:start position:0%
+you drive along the freeways in Los
+Angeles, their building stands out. You
+
+ align:start position:0%
+Angeles, their building stands out. You
+ 
+
+ align:start position:0%
+Angeles, their building stands out. You
+know, it's Brook and Hollywood narrow
+
+ align:start position:0%
+know, it's Brook and Hollywood narrow
+ 
+
+ align:start position:0%
+know, it's Brook and Hollywood narrow
+fabrics. Hollywood Hollywood brand
+
+ align:start position:0%
+fabrics. Hollywood Hollywood brand
+ 
+
+ align:start position:0%
+fabrics. Hollywood Hollywood brand
+fabrics are less fancy than Brookid
+
+ align:start position:0%
+fabrics are less fancy than Brookid
+ 
+
+ align:start position:0%
+fabrics are less fancy than Brookid
+fabrics. The same company, but it's two
+
+ align:start position:0%
+fabrics. The same company, but it's two
+ 
+
+ align:start position:0%
+fabrics. The same company, but it's two
+lines. So, anyway, I go in this time and
+
+ align:start position:0%
+lines. So, anyway, I go in this time and
+ 
+
+ align:start position:0%
+lines. So, anyway, I go in this time and
+the guy says, "Sure, we're selling, you
+
+ align:start position:0%
+the guy says, "Sure, we're selling, you
+ 
+
+ align:start position:0%
+the guy says, "Sure, we're selling, you
+know, I'll let you this time." So his
+
+ align:start position:0%
+know, I'll let you this time." So his
+ 
+
+ align:start position:0%
+know, I'll let you this time." So his
+son uh takes me around and it's filled
+
+ align:start position:0%
+son uh takes me around and it's filled
+ 
+
+ align:start position:0%
+son uh takes me around and it's filled
+with all these weaving
+
+ align:start position:0%
+with all these weaving
+ 
+
+ align:start position:0%
+with all these weaving
+machines with wood frames. They're all
+
+ align:start position:0%
+machines with wood frames. They're all
+ 
+
+ align:start position:0%
+machines with wood frames. They're all
+60 70 years old, 50 years old, often
+
+ align:start position:0%
+60 70 years old, 50 years old, often
+ 
+
+ align:start position:0%
+60 70 years old, 50 years old, often
+with power that comes from uh a rotating
+
+ align:start position:0%
+with power that comes from uh a rotating
+ 
+
+ align:start position:0%
+with power that comes from uh a rotating
+uh armature with with le with with
+
+ align:start position:0%
+uh armature with with le with with
+ 
+
+ align:start position:0%
+uh armature with with le with with
+leather
+
+ align:start position:0%
+leather
+ 
+
+ align:start position:0%
+leather
+belts. It was like and you see all these
+
+ align:start position:0%
+belts. It was like and you see all these
+ 
+
+ align:start position:0%
+belts. It was like and you see all these
+weaving machines. Anyway, that was my
+
+ align:start position:0%
+weaving machines. Anyway, that was my
+ 
+
+ align:start position:0%
+weaving machines. Anyway, that was my
+favorite thing of the last two weeks.
+
+ align:start position:0%
+favorite thing of the last two weeks.
+ 
+
+ align:start position:0%
+favorite thing of the last two weeks.
+And what you're trying to understand is
+
+ align:start position:0%
+And what you're trying to understand is
+ 
+
+ align:start position:0%
+And what you're trying to understand is
+the flows of people. And the big thing,
+
+ align:start position:0%
+the flows of people. And the big thing,
+ 
+
+ align:start position:0%
+the flows of people. And the big thing,
+by the way, of getting my chance to go
+
+ align:start position:0%
+by the way, of getting my chance to go
+ 
+
+ align:start position:0%
+by the way, of getting my chance to go
+inside industry is I never used a flash.
+
+ align:start position:0%
+inside industry is I never used a flash.
+ 
+
+ align:start position:0%
+inside industry is I never used a flash.
+I never used a
+
+ align:start position:0%
+I never used a
+ 
+
+ align:start position:0%
+I never used a
+tripod. In other words, I didn't
+
+ align:start position:0%
+tripod. In other words, I didn't
+ 
+
+ align:start position:0%
+tripod. In other words, I didn't
+interrupt
+
+ align:start position:0%
+interrupt
+ 
+
+ align:start position:0%
+interrupt
+them. I didn't tell people to pose for
+
+ align:start position:0%
+them. I didn't tell people to pose for
+ 
+
+ align:start position:0%
+them. I didn't tell people to pose for
+me. You might be able to do much
+
+ align:start position:0%
+me. You might be able to do much
+ 
+
+ align:start position:0%
+me. You might be able to do much
+more. All right. Lee Freedellander's
+
+ align:start position:0%
+more. All right. Lee Freedellander's
+ 
+
+ align:start position:0%
+more. All right. Lee Freedellander's
+omage book of at work is all images
+
+ align:start position:0%
+omage book of at work is all images
+ 
+
+ align:start position:0%
+omage book of at work is all images
+which were if not posed, you know, with
+
+ align:start position:0%
+which were if not posed, you know, with
+ 
+
+ align:start position:0%
+which were if not posed, you know, with
+flash and all that. But I wasn't invited
+
+ align:start position:0%
+flash and all that. But I wasn't invited
+ 
+
+ align:start position:0%
+flash and all that. But I wasn't invited
+in as a great photographer. And I
+
+ align:start position:0%
+in as a great photographer. And I
+ 
+
+ align:start position:0%
+in as a great photographer. And I
+figured that my whole idea was to get
+
+ align:start position:0%
+figured that my whole idea was to get
+ 
+
+ align:start position:0%
+figured that my whole idea was to get
+all my images before they decided to
+
+ align:start position:0%
+all my images before they decided to
+ 
+
+ align:start position:0%
+all my images before they decided to
+kick me
+
+ align:start position:0%
+kick me
+ 
+
+ align:start position:0%
+kick me
+out.
+
+ align:start position:0%
+out.
+ 
+
+ align:start position:0%
+out.
+Uh, and in the church thing, it's very
+
+ align:start position:0%
+Uh, and in the church thing, it's very
+ 
+
+ align:start position:0%
+Uh, and in the church thing, it's very
+interesting. I'm a Jew from Brooklyn, so
+
+ align:start position:0%
+interesting. I'm a Jew from Brooklyn, so
+ 
+
+ align:start position:0%
+interesting. I'm a Jew from Brooklyn, so
+you can imagine uh, you know, I'm not
+
+ align:start position:0%
+you can imagine uh, you know, I'm not
+ 
+
+ align:start position:0%
+you can imagine uh, you know, I'm not
+exactly about to be converted. And, uh,
+
+ align:start position:0%
+exactly about to be converted. And, uh,
+ 
+
+ align:start position:0%
+exactly about to be converted. And, uh,
+but it turns out uh, they're usually not
+
+ align:start position:0%
+but it turns out uh, they're usually not
+ 
+
+ align:start position:0%
+but it turns out uh, they're usually not
+interested. They'd like to know if
+
+ align:start position:0%
+interested. They'd like to know if
+ 
+
+ align:start position:0%
+interested. They'd like to know if
+you're religious a little bit, but they
+
+ align:start position:0%
+you're religious a little bit, but they
+ 
+
+ align:start position:0%
+you're religious a little bit, but they
+but I could go. Most of these places are
+
+ align:start position:0%
+but I could go. Most of these places are
+ 
+
+ align:start position:0%
+but I could go. Most of these places are
+quite willing to let me uh, photograph
+
+ align:start position:0%
+quite willing to let me uh, photograph
+ 
+
+ align:start position:0%
+quite willing to let me uh, photograph
+their service.
+
+ align:start position:0%
+their service.
+ 
+
+ align:start position:0%
+their service.
+Now, you know that many churches make
+
+ align:start position:0%
+Now, you know that many churches make
+ 
+
+ align:start position:0%
+Now, you know that many churches make
+DVDs uh and CDs of the uh minister's
+
+ align:start position:0%
+DVDs uh and CDs of the uh minister's
+ 
+
+ align:start position:0%
+DVDs uh and CDs of the uh minister's
+uh sermon so you can buy it on the way
+
+ align:start position:0%
+uh sermon so you can buy it on the way
+ 
+
+ align:start position:0%
+uh sermon so you can buy it on the way
+out.
+
+ align:start position:0%
+out.
+ 
+
+ align:start position:0%
+out.
+In fact, one of the big consumers of
+
+ align:start position:0%
+In fact, one of the big consumers of
+ 
+
+ align:start position:0%
+In fact, one of the big consumers of
+sound equipment are small
+
+ align:start position:0%
+sound equipment are small
+ 
+
+ align:start position:0%
+sound equipment are small
+churches, you know, with B with CD
+
+ align:start position:0%
+churches, you know, with B with CD
+ 
+
+ align:start position:0%
+churches, you know, with B with CD
+burners and the whole shebang because
+
+ align:start position:0%
+burners and the whole shebang because
+ 
+
+ align:start position:0%
+burners and the whole shebang because
+they, you know, you can get the you can
+
+ align:start position:0%
+they, you know, you can get the you can
+ 
+
+ align:start position:0%
+they, you know, you can get the you can
+buy and uh but this is different and
+
+ align:start position:0%
+buy and uh but this is different and
+ 
+
+ align:start position:0%
+buy and uh but this is different and
+they seem to be, you
+
+ align:start position:0%
+they seem to be, you
+ 
+
+ align:start position:0%
+they seem to be, you
+know, they were very they've been very
+
+ align:start position:0%
+know, they were very they've been very
+ 
+
+ align:start position:0%
+know, they were very they've been very
+open to it. Um, one of my students is a
+
+ align:start position:0%
+open to it. Um, one of my students is a
+ 
+
+ align:start position:0%
+open to it. Um, one of my students is a
+is a Pentecostal minister and so he he
+
+ align:start position:0%
+is a Pentecostal minister and so he he
+ 
+
+ align:start position:0%
+is a Pentecostal minister and so he he
+thinks the world of me, bless his soul,
+
+ align:start position:0%
+thinks the world of me, bless his soul,
+ 
+
+ align:start position:0%
+thinks the world of me, bless his soul,
+and so he said, "Sure." introduced me to
+
+ align:start position:0%
+and so he said, "Sure." introduced me to
+ 
+
+ align:start position:0%
+and so he said, "Sure." introduced me to
+the church. I I photographed and uh uh a
+
+ align:start position:0%
+the church. I I photographed and uh uh a
+ 
+
+ align:start position:0%
+the church. I I photographed and uh uh a
+ser his special service which went on
+
+ align:start position:0%
+ser his special service which went on
+ 
+
+ align:start position:0%
+ser his special service which went on
+for too many hours um for everybody. But
+
+ align:start position:0%
+for too many hours um for everybody. But
+ 
+
+ align:start position:0%
+for too many hours um for everybody. But
+it what I'm really telling you about is
+
+ align:start position:0%
+it what I'm really telling you about is
+ 
+
+ align:start position:0%
+it what I'm really telling you about is
+about access about those issues which
+
+ align:start position:0%
+about access about those issues which
+ 
+
+ align:start position:0%
+about access about those issues which
+are terribly terribly important because
+
+ align:start position:0%
+are terribly terribly important because
+ 
+
+ align:start position:0%
+are terribly terribly important because
+you're asking people to let you them
+
+ align:start position:0%
+you're asking people to let you them
+ 
+
+ align:start position:0%
+you're asking people to let you them
+into your most their most sacred places
+
+ align:start position:0%
+into your most their most sacred places
+ 
+
+ align:start position:0%
+into your most their most sacred places
+or their private lives.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um what I'm going to go on for another
+
+ align:start position:0%
+Um what I'm going to go on for another
+ 
+
+ align:start position:0%
+Um what I'm going to go on for another
+about 10 minutes. So I hope that's not
+
+ align:start position:0%
+about 10 minutes. So I hope that's not
+ 
+
+ align:start position:0%
+about 10 minutes. So I hope that's not
+too is that okay? Fine. Uh I want to
+
+ align:start position:0%
+too is that okay? Fine. Uh I want to
+ 
+
+ align:start position:0%
+too is that okay? Fine. Uh I want to
+talk about two other issues. Uh
+
+ align:start position:0%
+talk about two other issues. Uh
+ 
+
+ align:start position:0%
+talk about two other issues. Uh
+technology and finally what I call
+
+ align:start position:0%
+technology and finally what I call
+ 
+
+ align:start position:0%
+technology and finally what I call
+social science informed photo
+
+ align:start position:0%
+social science informed photo
+ 
+
+ align:start position:0%
+social science informed photo
+documentation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm fascinated about how the technology
+
+ align:start position:0%
+I'm fascinated about how the technology
+ 
+
+ align:start position:0%
+I'm fascinated about how the technology
+I use for photographing makes a
+
+ align:start position:0%
+I use for photographing makes a
+ 
+
+ align:start position:0%
+I use for photographing makes a
+difference. I'll admit I use
+
+ align:start position:0%
+difference. I'll admit I use
+ 
+
+ align:start position:0%
+difference. I'll admit I use
+film. I use transparency film. I do not
+
+ align:start position:0%
+film. I use transparency film. I do not
+ 
+
+ align:start position:0%
+film. I use transparency film. I do not
+use digital. If you want to have a long
+
+ align:start position:0%
+use digital. If you want to have a long
+ 
+
+ align:start position:0%
+use digital. If you want to have a long
+discussion about which is more archival.
+
+ align:start position:0%
+discussion about which is more archival.
+ 
+
+ align:start position:0%
+discussion about which is more archival.
+My attitude is film is wonderful because
+
+ align:start position:0%
+My attitude is film is wonderful because
+ 
+
+ align:start position:0%
+My attitude is film is wonderful because
+it sits there in the dark and if you
+
+ align:start position:0%
+it sits there in the dark and if you
+ 
+
+ align:start position:0%
+it sits there in the dark and if you
+don't get it wet and too hot, it'll be
+
+ align:start position:0%
+don't get it wet and too hot, it'll be
+ 
+
+ align:start position:0%
+don't get it wet and too hot, it'll be
+there in 50 years. I don't know what to
+
+ align:start position:0%
+there in 50 years. I don't know what to
+ 
+
+ align:start position:0%
+there in 50 years. I don't know what to
+do about digital right now. five years
+
+ align:start position:0%
+do about digital right now. five years
+ 
+
+ align:start position:0%
+do about digital right now. five years
+from now, maybe there'll be a better way
+
+ align:start position:0%
+from now, maybe there'll be a better way
+ 
+
+ align:start position:0%
+from now, maybe there'll be a better way
+of doing it, but I'm not going to worry.
+
+ align:start position:0%
+of doing it, but I'm not going to worry.
+ 
+
+ align:start position:0%
+of doing it, but I'm not going to worry.
+Um, but depending on the lens you use
+
+ align:start position:0%
+Um, but depending on the lens you use
+ 
+
+ align:start position:0%
+Um, but depending on the lens you use
+and so forth, you it's certain
+
+ align:start position:0%
+and so forth, you it's certain
+ 
+
+ align:start position:0%
+and so forth, you it's certain
+consequences. And I happen I discovered
+
+ align:start position:0%
+consequences. And I happen I discovered
+ 
+
+ align:start position:0%
+consequences. And I happen I discovered
+early on in my work that a wide angle
+
+ align:start position:0%
+early on in my work that a wide angle
+ 
+
+ align:start position:0%
+early on in my work that a wide angle
+lens is what I needed. I needed to stick
+
+ align:start position:0%
+lens is what I needed. I needed to stick
+ 
+
+ align:start position:0%
+lens is what I needed. I needed to stick
+my snout into the world and see it all.
+
+ align:start position:0%
+my snout into the world and see it all.
+ 
+
+ align:start position:0%
+my snout into the world and see it all.
+And that's what a wide angle allows you
+
+ align:start position:0%
+And that's what a wide angle allows you
+ 
+
+ align:start position:0%
+And that's what a wide angle allows you
+to do. You get very close, but you have
+
+ align:start position:0%
+to do. You get very close, but you have
+ 
+
+ align:start position:0%
+to do. You get very close, but you have
+a wide
+
+ align:start position:0%
+a wide
+ 
+
+ align:start position:0%
+a wide
+view so you can see context and detail.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And also I didn't like the idea of using
+
+ align:start position:0%
+And also I didn't like the idea of using
+ 
+
+ align:start position:0%
+And also I didn't like the idea of using
+a telephoto lens because it made me feel
+
+ align:start position:0%
+a telephoto lens because it made me feel
+ 
+
+ align:start position:0%
+a telephoto lens because it made me feel
+like a voyer. I mean I'm a voyer clearly
+
+ align:start position:0%
+like a voyer. I mean I'm a voyer clearly
+ 
+
+ align:start position:0%
+like a voyer. I mean I'm a voyer clearly
+so that's not the point but it made me
+
+ align:start position:0%
+so that's not the point but it made me
+ 
+
+ align:start position:0%
+so that's not the point but it made me
+feel like a a dirty voyer. And um so uh
+
+ align:start position:0%
+feel like a a dirty voyer. And um so uh
+ 
+
+ align:start position:0%
+feel like a a dirty voyer. And um so uh
+I've ended up using you know film which
+
+ align:start position:0%
+I've ended up using you know film which
+ 
+
+ align:start position:0%
+I've ended up using you know film which
+has consequences in terms of its
+
+ align:start position:0%
+has consequences in terms of its
+ 
+
+ align:start position:0%
+has consequences in terms of its
+sensitivity and color faithfulness and
+
+ align:start position:0%
+sensitivity and color faithfulness and
+ 
+
+ align:start position:0%
+sensitivity and color faithfulness and
+so forth and wideangle lenses which have
+
+ align:start position:0%
+so forth and wideangle lenses which have
+ 
+
+ align:start position:0%
+so forth and wideangle lenses which have
+other consequences. And it turns out,
+
+ align:start position:0%
+other consequences. And it turns out,
+ 
+
+ align:start position:0%
+other consequences. And it turns out,
+for example, one of the things you want,
+
+ align:start position:0%
+for example, one of the things you want,
+ 
+
+ align:start position:0%
+for example, one of the things you want,
+which is not obvious, is you want really
+
+ align:start position:0%
+which is not obvious, is you want really
+ 
+
+ align:start position:0%
+which is not obvious, is you want really
+good lenses. Why? Not because it matters
+
+ align:start position:0%
+good lenses. Why? Not because it matters
+ 
+
+ align:start position:0%
+good lenses. Why? Not because it matters
+that much, except it might. Maybe
+
+ align:start position:0%
+that much, except it might. Maybe
+ 
+
+ align:start position:0%
+that much, except it might. Maybe
+there's something interesting in the
+
+ align:start position:0%
+there's something interesting in the
+ 
+
+ align:start position:0%
+there's something interesting in the
+corner of the image that someone in 50
+
+ align:start position:0%
+corner of the image that someone in 50
+ 
+
+ align:start position:0%
+corner of the image that someone in 50
+years wants to un see and
+
+ align:start position:0%
+years wants to un see and
+ 
+
+ align:start position:0%
+years wants to un see and
+read. Only good lenses are good in the
+
+ align:start position:0%
+read. Only good lenses are good in the
+ 
+
+ align:start position:0%
+read. Only good lenses are good in the
+corners. Most lenses are superb in the
+
+ align:start position:0%
+corners. Most lenses are superb in the
+ 
+
+ align:start position:0%
+corners. Most lenses are superb in the
+center, but to get them good in the
+
+ align:start position:0%
+center, but to get them good in the
+ 
+
+ align:start position:0%
+center, but to get them good in the
+corners, you have to pay a lot of money.
+
+ align:start position:0%
+corners, you have to pay a lot of money.
+ 
+
+ align:start position:0%
+corners, you have to pay a lot of money.
+And most so-called consumer quality
+
+ align:start position:0%
+And most so-called consumer quality
+ 
+
+ align:start position:0%
+And most so-called consumer quality
+lenses are in fact not that good once
+
+ align:start position:0%
+lenses are in fact not that good once
+ 
+
+ align:start position:0%
+lenses are in fact not that good once
+they get to the edges. They fall off
+
+ align:start position:0%
+they get to the edges. They fall off
+ 
+
+ align:start position:0%
+they get to the edges. They fall off
+fairly well and no one
+
+ align:start position:0%
+fairly well and no one
+ 
+
+ align:start position:0%
+fairly well and no one
+cares. If you use documentation lenses,
+
+ align:start position:0%
+cares. If you use documentation lenses,
+ 
+
+ align:start position:0%
+cares. If you use documentation lenses,
+that's something else. But documentation
+
+ align:start position:0%
+that's something else. But documentation
+ 
+
+ align:start position:0%
+that's something else. But documentation
+lenses are not fast. There's lots of
+
+ align:start position:0%
+lenses are not fast. There's lots of
+ 
+
+ align:start position:0%
+lenses are not fast. There's lots of
+things wrong with
+
+ align:start position:0%
+things wrong with
+ 
+
+ align:start position:0%
+things wrong with
+them. And I'll give you two other
+
+ align:start position:0%
+them. And I'll give you two other
+ 
+
+ align:start position:0%
+them. And I'll give you two other
+examples. I I thought I would do some
+
+ align:start position:0%
+examples. I I thought I would do some
+ 
+
+ align:start position:0%
+examples. I I thought I would do some
+video work or at least film. And I tried
+
+ align:start position:0%
+video work or at least film. And I tried
+ 
+
+ align:start position:0%
+video work or at least film. And I tried
+first Super 8 and Kodakchrome uh which
+
+ align:start position:0%
+first Super 8 and Kodakchrome uh which
+ 
+
+ align:start position:0%
+first Super 8 and Kodakchrome uh which
+codchrome lasts forever. Uh, and Super 8
+
+ align:start position:0%
+codchrome lasts forever. Uh, and Super 8
+ 
+
+ align:start position:0%
+codchrome lasts forever. Uh, and Super 8
+film is still made and Super Eight
+
+ align:start position:0%
+film is still made and Super Eight
+ 
+
+ align:start position:0%
+film is still made and Super Eight
+cameras can be bought on bought on eBay.
+
+ align:start position:0%
+cameras can be bought on bought on eBay.
+ 
+
+ align:start position:0%
+cameras can be bought on bought on eBay.
+Um, but the problem turned out to be the
+
+ align:start position:0%
+Um, but the problem turned out to be the
+ 
+
+ align:start position:0%
+Um, but the problem turned out to be the
+editing that I wasn't going to do the
+
+ align:start position:0%
+editing that I wasn't going to do the
+ 
+
+ align:start position:0%
+editing that I wasn't going to do the
+editing. It's just too much
+
+ align:start position:0%
+editing. It's just too much
+ 
+
+ align:start position:0%
+editing. It's just too much
+work and it was a bit expensive. So, I
+
+ align:start position:0%
+work and it was a bit expensive. So, I
+ 
+
+ align:start position:0%
+work and it was a bit expensive. So, I
+did go to digital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+video and digital video is easy to edit.
+
+ align:start position:0%
+video and digital video is easy to edit.
+ 
+
+ align:start position:0%
+video and digital video is easy to edit.
+iMovie does a fine job. Uh but of course
+
+ align:start position:0%
+iMovie does a fine job. Uh but of course
+ 
+
+ align:start position:0%
+iMovie does a fine job. Uh but of course
+using video is really hard and I think
+
+ align:start position:0%
+using video is really hard and I think
+ 
+
+ align:start position:0%
+using video is really hard and I think
+it's too hard for me to be honest but
+
+ align:start position:0%
+it's too hard for me to be honest but
+ 
+
+ align:start position:0%
+it's too hard for me to be honest but
+the there technology of digital made it
+
+ align:start position:0%
+the there technology of digital made it
+ 
+
+ align:start position:0%
+the there technology of digital made it
+possible for me to use it. My third
+
+ align:start position:0%
+possible for me to use it. My third
+ 
+
+ align:start position:0%
+possible for me to use it. My third
+example is my current project. About
+
+ align:start position:0%
+example is my current project. About
+ 
+
+ align:start position:0%
+example is my current project. About
+four months ago our provost I don't I
+
+ align:start position:0%
+four months ago our provost I don't I
+ 
+
+ align:start position:0%
+four months ago our provost I don't I
+don't know if MIT has this but our
+
+ align:start position:0%
+don't know if MIT has this but our
+ 
+
+ align:start position:0%
+don't know if MIT has this but our
+provost sends out initiatives for new
+
+ align:start position:0%
+provost sends out initiatives for new
+ 
+
+ align:start position:0%
+provost sends out initiatives for new
+ways of encouraging collaboration
+
+ align:start position:0%
+ways of encouraging collaboration
+ 
+
+ align:start position:0%
+ways of encouraging collaboration
+presumably bringing in more research
+
+ align:start position:0%
+presumably bringing in more research
+ 
+
+ align:start position:0%
+presumably bringing in more research
+grants and making university better. Um,
+
+ align:start position:0%
+grants and making university better. Um,
+ 
+
+ align:start position:0%
+grants and making university better. Um,
+and they come out fairly often and most
+
+ align:start position:0%
+and they come out fairly often and most
+ 
+
+ align:start position:0%
+and they come out fairly often and most
+of the time should be ignored from my
+
+ align:start position:0%
+of the time should be ignored from my
+ 
+
+ align:start position:0%
+of the time should be ignored from my
+point of view because they're just
+
+ align:start position:0%
+point of view because they're just
+ 
+
+ align:start position:0%
+point of view because they're just
+distracting. But there was one about the
+
+ align:start position:0%
+distracting. But there was one about the
+ 
+
+ align:start position:0%
+distracting. But there was one about the
+arts and the humanities and I was
+
+ align:start position:0%
+arts and the humanities and I was
+ 
+
+ align:start position:0%
+arts and the humanities and I was
+invited to the meeting about it and I
+
+ align:start position:0%
+invited to the meeting about it and I
+ 
+
+ align:start position:0%
+invited to the meeting about it and I
+said, "Oh, I this I need like a hole in
+
+ align:start position:0%
+said, "Oh, I this I need like a hole in
+ 
+
+ align:start position:0%
+said, "Oh, I this I need like a hole in
+the head." But somehow getting invited
+
+ align:start position:0%
+the head." But somehow getting invited
+ 
+
+ align:start position:0%
+the head." But somehow getting invited
+means I usually say yes. So it turns out
+
+ align:start position:0%
+means I usually say yes. So it turns out
+ 
+
+ align:start position:0%
+means I usually say yes. So it turns out
+I mention at this meeting that I tried
+
+ align:start position:0%
+I mention at this meeting that I tried
+ 
+
+ align:start position:0%
+I mention at this meeting that I tried
+using audio and I can't make it, you
+
+ align:start position:0%
+using audio and I can't make it, you
+ 
+
+ align:start position:0%
+using audio and I can't make it, you
+know, I don't know what I'm doing. And
+
+ align:start position:0%
+know, I don't know what I'm doing. And
+ 
+
+ align:start position:0%
+know, I don't know what I'm doing. And
+that's because um even using D I just
+
+ align:start position:0%
+that's because um even using D I just
+ 
+
+ align:start position:0%
+that's because um even using D I just
+wasn't it wasn't the audio my recording
+
+ align:start position:0%
+wasn't it wasn't the audio my recording
+ 
+
+ align:start position:0%
+wasn't it wasn't the audio my recording
+was not very good. I was using miniis
+
+ align:start position:0%
+was not very good. I was using miniis
+ 
+
+ align:start position:0%
+was not very good. I was using miniis
+and so forth but it wasn't very good.
+
+ align:start position:0%
+and so forth but it wasn't very good.
+ 
+
+ align:start position:0%
+and so forth but it wasn't very good.
+And it turns out someone comes up to me
+
+ align:start position:0%
+And it turns out someone comes up to me
+ 
+
+ align:start position:0%
+And it turns out someone comes up to me
+at the break. Who is Mr. THX? The guy
+
+ align:start position:0%
+at the break. Who is Mr. THX? The guy
+ 
+
+ align:start position:0%
+at the break. Who is Mr. THX? The guy
+who invented THX Mr. 5.1 sound a guy
+
+ align:start position:0%
+who invented THX Mr. 5.1 sound a guy
+ 
+
+ align:start position:0%
+who invented THX Mr. 5.1 sound a guy
+named Tom Holman who's a a guru of this
+
+ align:start position:0%
+named Tom Holman who's a a guru of this
+ 
+
+ align:start position:0%
+named Tom Holman who's a a guru of this
+sort. He's a professor of film sound at
+
+ align:start position:0%
+sort. He's a professor of film sound at
+ 
+
+ align:start position:0%
+sort. He's a professor of film sound at
+USC. And he says here's I I could help
+
+ align:start position:0%
+USC. And he says here's I I could help
+ 
+
+ align:start position:0%
+USC. And he says here's I I could help
+you. And two few days later he sends me
+
+ align:start position:0%
+you. And two few days later he sends me
+ 
+
+ align:start position:0%
+you. And two few days later he sends me
+a memo. Here's what you need. Here's
+
+ align:start position:0%
+a memo. Here's what you need. Here's
+ 
+
+ align:start position:0%
+a memo. Here's what you need. Here's
+where how to do it. Um, and so that's my
+
+ align:start position:0%
+where how to do it. Um, and so that's my
+ 
+
+ align:start position:0%
+where how to do it. Um, and so that's my
+next big project. And why am I going to
+
+ align:start position:0%
+next big project. And why am I going to
+ 
+
+ align:start position:0%
+next big project. And why am I going to
+do it? Because first of all, I have Tom
+
+ align:start position:0%
+do it? Because first of all, I have Tom
+ 
+
+ align:start position:0%
+do it? Because first of all, I have Tom
+behind me, so he'll tell me what to do
+
+ align:start position:0%
+behind me, so he'll tell me what to do
+ 
+
+ align:start position:0%
+behind me, so he'll tell me what to do
+technically. And that involves things
+
+ align:start position:0%
+technically. And that involves things
+ 
+
+ align:start position:0%
+technically. And that involves things
+like advice, which microphone to buy.
+
+ align:start position:0%
+like advice, which microphone to buy.
+ 
+
+ align:start position:0%
+like advice, which microphone to buy.
+There are many more microphones than
+
+ align:start position:0%
+There are many more microphones than
+ 
+
+ align:start position:0%
+There are many more microphones than
+lenses. And I don't understand it all
+
+ align:start position:0%
+lenses. And I don't understand it all
+ 
+
+ align:start position:0%
+lenses. And I don't understand it all
+very well. So he recommends a $5,000
+
+ align:start position:0%
+very well. So he recommends a $5,000
+ 
+
+ align:start position:0%
+very well. So he recommends a $5,000
+pair. And you know what am I going to
+
+ align:start position:0%
+pair. And you know what am I going to
+ 
+
+ align:start position:0%
+pair. And you know what am I going to
+say? Uh, you know, you go and you get
+
+ align:start position:0%
+say? Uh, you know, you go and you get
+ 
+
+ align:start position:0%
+say? Uh, you know, you go and you get
+that. and then a certain kind of
+
+ align:start position:0%
+that. and then a certain kind of
+ 
+
+ align:start position:0%
+that. and then a certain kind of
+recorder, you know, and you try to get a
+
+ align:start position:0%
+recorder, you know, and you try to get a
+ 
+
+ align:start position:0%
+recorder, you know, and you try to get a
+grant to, as he said, you have to shake
+
+ align:start position:0%
+grant to, as he said, you have to shake
+ 
+
+ align:start position:0%
+grant to, as he said, you have to shake
+the trees to get the money, but I don't
+
+ align:start position:0%
+the trees to get the money, but I don't
+ 
+
+ align:start position:0%
+the trees to get the money, but I don't
+mind shaking trees. And I got some
+
+ align:start position:0%
+mind shaking trees. And I got some
+ 
+
+ align:start position:0%
+mind shaking trees. And I got some
+money. Second of all, what is my goal?
+
+ align:start position:0%
+money. Second of all, what is my goal?
+ 
+
+ align:start position:0%
+money. Second of all, what is my goal?
+My goal is to do accurate and archable
+
+ align:start position:0%
+My goal is to do accurate and archable
+ 
+
+ align:start position:0%
+My goal is to do accurate and archable
+audio. Accurate, which means that people
+
+ align:start position:0%
+audio. Accurate, which means that people
+ 
+
+ align:start position:0%
+audio. Accurate, which means that people
+in 50 years from now can know how to
+
+ align:start position:0%
+in 50 years from now can know how to
+ 
+
+ align:start position:0%
+in 50 years from now can know how to
+reproduce it so it sounds right. The
+
+ align:start position:0%
+reproduce it so it sounds right. The
+ 
+
+ align:start position:0%
+reproduce it so it sounds right. The
+right volume levels, the right spatial
+
+ align:start position:0%
+right volume levels, the right spatial
+ 
+
+ align:start position:0%
+right volume levels, the right spatial
+things. In other words, you have to give
+
+ align:start position:0%
+things. In other words, you have to give
+ 
+
+ align:start position:0%
+things. In other words, you have to give
+it metadata and calibration. And that's
+
+ align:start position:0%
+it metadata and calibration. And that's
+ 
+
+ align:start position:0%
+it metadata and calibration. And that's
+never done in audio
+
+ align:start position:0%
+never done in audio
+ 
+
+ align:start position:0%
+never done in audio
+recording. In the sound recording, the
+
+ align:start position:0%
+recording. In the sound recording, the
+ 
+
+ align:start position:0%
+recording. In the sound recording, the
+sound libraries of the studios often do
+
+ align:start position:0%
+sound libraries of the studios often do
+ 
+
+ align:start position:0%
+sound libraries of the studios often do
+not identify the source of it because
+
+ align:start position:0%
+not identify the source of it because
+ 
+
+ align:start position:0%
+not identify the source of it because
+they want you to think generically. In
+
+ align:start position:0%
+they want you to think generically. In
+ 
+
+ align:start position:0%
+they want you to think generically. In
+other words, if this sound is taken in
+
+ align:start position:0%
+other words, if this sound is taken in
+ 
+
+ align:start position:0%
+other words, if this sound is taken in
+Los Angeles, maybe you can use it in
+
+ align:start position:0%
+Los Angeles, maybe you can use it in
+ 
+
+ align:start position:0%
+Los Angeles, maybe you can use it in
+Hong Kong
+
+ align:start position:0%
+Hong Kong
+ 
+
+ align:start position:0%
+Hong Kong
+anyway for Hong, you know, Hong Kong
+
+ align:start position:0%
+anyway for Hong, you know, Hong Kong
+ 
+
+ align:start position:0%
+anyway for Hong, you know, Hong Kong
+sound. And so, in fact, they hide the
+
+ align:start position:0%
+sound. And so, in fact, they hide the
+ 
+
+ align:start position:0%
+sound. And so, in fact, they hide the
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+deliberately. And most people who do
+
+ align:start position:0%
+deliberately. And most people who do
+ 
+
+ align:start position:0%
+deliberately. And most people who do
+sound art are not concerned about
+
+ align:start position:0%
+sound art are not concerned about
+ 
+
+ align:start position:0%
+sound art are not concerned about
+accuracy because they're using the sound
+
+ align:start position:0%
+accuracy because they're using the sound
+ 
+
+ align:start position:0%
+accuracy because they're using the sound
+to do certain kinds of wonderful things.
+
+ align:start position:0%
+to do certain kinds of wonderful things.
+ 
+
+ align:start position:0%
+to do certain kinds of wonderful things.
+So the idea of accuracy in fact turns
+
+ align:start position:0%
+So the idea of accuracy in fact turns
+ 
+
+ align:start position:0%
+So the idea of accuracy in fact turns
+out according to Tom and what I've been
+
+ align:start position:0%
+out according to Tom and what I've been
+ 
+
+ align:start position:0%
+out according to Tom and what I've been
+able to find not very given much
+
+ align:start position:0%
+able to find not very given much
+ 
+
+ align:start position:0%
+able to find not very given much
+energy. Even the people who worry about
+
+ align:start position:0%
+energy. Even the people who worry about
+ 
+
+ align:start position:0%
+energy. Even the people who worry about
+hi-fi don't really care because they're
+
+ align:start position:0%
+hi-fi don't really care because they're
+ 
+
+ align:start position:0%
+hi-fi don't really care because they're
+caring they're not really concerned
+
+ align:start position:0%
+caring they're not really concerned
+ 
+
+ align:start position:0%
+caring they're not really concerned
+about accuracy. They're interested in a
+
+ align:start position:0%
+about accuracy. They're interested in a
+ 
+
+ align:start position:0%
+about accuracy. They're interested in a
+certain semblance of a certain sort.
+
+ align:start position:0%
+certain semblance of a certain sort.
+ 
+
+ align:start position:0%
+certain semblance of a certain sort.
+Um and the other thing is
+
+ align:start position:0%
+Um and the other thing is
+ 
+
+ align:start position:0%
+Um and the other thing is
+archable. What way of storing it will be
+
+ align:start position:0%
+archable. What way of storing it will be
+ 
+
+ align:start position:0%
+archable. What way of storing it will be
+around for hundred
+
+ align:start position:0%
+around for hundred
+ 
+
+ align:start position:0%
+around for hundred
+years and how do you store it the best
+
+ align:start position:0%
+years and how do you store it the best
+ 
+
+ align:start position:0%
+years and how do you store it the best
+way you know and what's the you know you
+
+ align:start position:0%
+way you know and what's the you know you
+ 
+
+ align:start position:0%
+way you know and what's the you know you
+have and these are technical issues but
+
+ align:start position:0%
+have and these are technical issues but
+ 
+
+ align:start position:0%
+have and these are technical issues but
+they're generally not addressed. It
+
+ align:start position:0%
+they're generally not addressed. It
+ 
+
+ align:start position:0%
+they're generally not addressed. It
+turns
+
+ align:start position:0%
+turns
+ 
+
+ align:start position:0%
+turns
+out it turns out I didn't know it how
+
+ align:start position:0%
+out it turns out I didn't know it how
+ 
+
+ align:start position:0%
+out it turns out I didn't know it how
+much it's not turned out but you know
+
+ align:start position:0%
+much it's not turned out but you know
+ 
+
+ align:start position:0%
+much it's not turned out but you know
+it's required of figuring this out and
+
+ align:start position:0%
+it's required of figuring this out and
+ 
+
+ align:start position:0%
+it's required of figuring this out and
+the idea that we've decided is we want
+
+ align:start position:0%
+the idea that we've decided is we want
+ 
+
+ align:start position:0%
+the idea that we've decided is we want
+to give people a sense of being there
+
+ align:start position:0%
+to give people a sense of being there
+ 
+
+ align:start position:0%
+to give people a sense of being there
+whatever the sounds are but we're not
+
+ align:start position:0%
+whatever the sounds are but we're not
+ 
+
+ align:start position:0%
+whatever the sounds are but we're not
+going to worry about uh Tom has
+
+ align:start position:0%
+going to worry about uh Tom has
+ 
+
+ align:start position:0%
+going to worry about uh Tom has
+something called 10.2 sound which is
+
+ align:start position:0%
+something called 10.2 sound which is
+ 
+
+ align:start position:0%
+something called 10.2 sound which is
+double
+
+ align:start position:0%
+double
+ 
+
+ align:start position:0%
+double
+5.1 and involves don't worry it's DARPA
+
+ align:start position:0%
+5.1 and involves don't worry it's DARPA
+ 
+
+ align:start position:0%
+5.1 and involves don't worry it's DARPA
+pays for it um you know they're
+
+ align:start position:0%
+pays for it um you know they're
+ 
+
+ align:start position:0%
+pays for it um you know they're
+interested in simulating
+
+ align:start position:0%
+interested in simulating
+ 
+
+ align:start position:0%
+interested in simulating
+warfare and whatnot. And so there's
+
+ align:start position:0%
+warfare and whatnot. And so there's
+ 
+
+ align:start position:0%
+warfare and whatnot. And so there's
+people in the engineering school who
+
+ align:start position:0%
+people in the engineering school who
+ 
+
+ align:start position:0%
+people in the engineering school who
+worry about this. Uh and uh and I've
+
+ align:start position:0%
+worry about this. Uh and uh and I've
+ 
+
+ align:start position:0%
+worry about this. Uh and uh and I've
+been in rooms with this 10.2 sound. It's
+
+ align:start position:0%
+been in rooms with this 10.2 sound. It's
+ 
+
+ align:start position:0%
+been in rooms with this 10.2 sound. It's
+really quite
+
+ align:start position:0%
+really quite
+ 
+
+ align:start position:0%
+really quite
+spectacular. Uh and the way I've
+
+ align:start position:0%
+spectacular. Uh and the way I've
+ 
+
+ align:start position:0%
+spectacular. Uh and the way I've
+described this that work I want to
+
+ align:start position:0%
+described this that work I want to
+ 
+
+ align:start position:0%
+described this that work I want to
+record ambience as the technical term in
+
+ align:start position:0%
+record ambience as the technical term in
+ 
+
+ align:start position:0%
+record ambience as the technical term in
+the cinema is called the sounds you
+
+ align:start position:0%
+the cinema is called the sounds you
+ 
+
+ align:start position:0%
+the cinema is called the sounds you
+don't listen
+
+ align:start position:0%
+don't listen
+ 
+
+ align:start position:0%
+don't listen
+to because they're just there. You don't
+
+ align:start position:0%
+to because they're just there. You don't
+ 
+
+ align:start position:0%
+to because they're just there. You don't
+pay attention to them.
+
+ align:start position:0%
+pay attention to them.
+ 
+
+ align:start position:0%
+pay attention to them.
+uh street noise, apartment noise from
+
+ align:start position:0%
+uh street noise, apartment noise from
+ 
+
+ align:start position:0%
+uh street noise, apartment noise from
+your neighbors, uh impure sounds, for
+
+ align:start position:0%
+your neighbors, uh impure sounds, for
+ 
+
+ align:start position:0%
+your neighbors, uh impure sounds, for
+example, people talking over something
+
+ align:start position:0%
+example, people talking over something
+ 
+
+ align:start position:0%
+example, people talking over something
+else, uh boring long passages because
+
+ align:start position:0%
+else, uh boring long passages because
+ 
+
+ align:start position:0%
+else, uh boring long passages because
+life is lots of boring long passages of
+
+ align:start position:0%
+life is lots of boring long passages of
+ 
+
+ align:start position:0%
+life is lots of boring long passages of
+sound. And most people say, "All right,
+
+ align:start position:0%
+sound. And most people say, "All right,
+ 
+
+ align:start position:0%
+sound. And most people say, "All right,
+30 seconds, that's enough." But the
+
+ align:start position:0%
+30 seconds, that's enough." But the
+ 
+
+ align:start position:0%
+30 seconds, that's enough." But the
+whole idea of a boring long passage is
+
+ align:start position:0%
+whole idea of a boring long passage is
+ 
+
+ align:start position:0%
+whole idea of a boring long passage is
+very important as
+
+ align:start position:0%
+very important as
+ 
+
+ align:start position:0%
+very important as
+experienced. So that's the kind of stuff
+
+ align:start position:0%
+experienced. So that's the kind of stuff
+ 
+
+ align:start position:0%
+experienced. So that's the kind of stuff
+I'm up to. And I don't know what I'm
+
+ align:start position:0%
+I'm up to. And I don't know what I'm
+ 
+
+ align:start position:0%
+I'm up to. And I don't know what I'm
+doing, by the way, in since this is my
+
+ align:start position:0%
+doing, by the way, in since this is my
+ 
+
+ align:start position:0%
+doing, by the way, in since this is my
+specs. I've done I've rented equipment
+
+ align:start position:0%
+specs. I've done I've rented equipment
+ 
+
+ align:start position:0%
+specs. I've done I've rented equipment
+and tried it out. So I know I can do it.
+
+ align:start position:0%
+and tried it out. So I know I can do it.
+ 
+
+ align:start position:0%
+and tried it out. So I know I can do it.
+But ask me in a in six months when I've
+
+ align:start position:0%
+But ask me in a in six months when I've
+ 
+
+ align:start position:0%
+But ask me in a in six months when I've
+done it because I don't believe in
+
+ align:start position:0%
+done it because I don't believe in
+ 
+
+ align:start position:0%
+done it because I don't believe in
+promising
+
+ align:start position:0%
+promising
+ 
+
+ align:start position:0%
+promising
+um ex you know other than trying hard.
+
+ align:start position:0%
+um ex you know other than trying hard.
+ 
+
+ align:start position:0%
+um ex you know other than trying hard.
+Uh for those who are interested a
+
+ align:start position:0%
+Uh for those who are interested a
+ 
+
+ align:start position:0%
+Uh for those who are interested a
+fisheye lens has a very similar um
+
+ align:start position:0%
+fisheye lens has a very similar um
+ 
+
+ align:start position:0%
+fisheye lens has a very similar um
+acceptance as a cardioid
+
+ align:start position:0%
+acceptance as a cardioid
+ 
+
+ align:start position:0%
+acceptance as a cardioid
+microphone. In other words the fisheye
+
+ align:start position:0%
+microphone. In other words the fisheye
+ 
+
+ align:start position:0%
+microphone. In other words the fisheye
+lens the way it sees the world is very
+
+ align:start position:0%
+lens the way it sees the world is very
+ 
+
+ align:start position:0%
+lens the way it sees the world is very
+much like the cardio cardioid
+
+ align:start position:0%
+much like the cardio cardioid
+ 
+
+ align:start position:0%
+much like the cardio cardioid
+microphone hears the world. So you might
+
+ align:start position:0%
+microphone hears the world. So you might
+ 
+
+ align:start position:0%
+microphone hears the world. So you might
+even use the image to give some idea of
+
+ align:start position:0%
+even use the image to give some idea of
+ 
+
+ align:start position:0%
+even use the image to give some idea of
+what you're hearing.
+
+ align:start position:0%
+what you're hearing.
+ 
+
+ align:start position:0%
+what you're hearing.
+And what you have to do is you have to
+
+ align:start position:0%
+And what you have to do is you have to
+ 
+
+ align:start position:0%
+And what you have to do is you have to
+be calibrated which mean you have to
+
+ align:start position:0%
+be calibrated which mean you have to
+ 
+
+ align:start position:0%
+be calibrated which mean you have to
+calibrate the process so you know what's
+
+ align:start position:0%
+calibrate the process so you know what's
+ 
+
+ align:start position:0%
+calibrate the process so you know what's
+what those bits on the CD should be
+
+ align:start position:0%
+what those bits on the CD should be
+ 
+
+ align:start position:0%
+what those bits on the CD should be
+correspond to and it has to be slated to
+
+ align:start position:0%
+correspond to and it has to be slated to
+ 
+
+ align:start position:0%
+correspond to and it has to be slated to
+use the term of art from cinema and that
+
+ align:start position:0%
+use the term of art from cinema and that
+ 
+
+ align:start position:0%
+use the term of art from cinema and that
+means that it has to have the metadata
+
+ align:start position:0%
+means that it has to have the metadata
+ 
+
+ align:start position:0%
+means that it has to have the metadata
+built in and what I and finally you have
+
+ align:start position:0%
+built in and what I and finally you have
+ 
+
+ align:start position:0%
+built in and what I and finally you have
+to use the right kind of microphones. If
+
+ align:start position:0%
+to use the right kind of microphones. If
+ 
+
+ align:start position:0%
+to use the right kind of microphones. If
+you go look at a microphone catalog,
+
+ align:start position:0%
+you go look at a microphone catalog,
+ 
+
+ align:start position:0%
+you go look at a microphone catalog,
+microphones are sort of um like getting
+
+ align:start position:0%
+microphones are sort of um like getting
+ 
+
+ align:start position:0%
+microphones are sort of um like getting
+plastic surgery. It's not that you want
+
+ align:start position:0%
+plastic surgery. It's not that you want
+ 
+
+ align:start position:0%
+plastic surgery. It's not that you want
+to get the same look, you want to sound
+
+ align:start position:0%
+to get the same look, you want to sound
+ 
+
+ align:start position:0%
+to get the same look, you want to sound
+look certain way or sound a certain way.
+
+ align:start position:0%
+look certain way or sound a certain way.
+ 
+
+ align:start position:0%
+look certain way or sound a certain way.
+And they have all sorts of interesting
+
+ align:start position:0%
+And they have all sorts of interesting
+ 
+
+ align:start position:0%
+And they have all sorts of interesting
+um nonlinearities in effect. And a truly
+
+ align:start position:0%
+um nonlinearities in effect. And a truly
+ 
+
+ align:start position:0%
+um nonlinearities in effect. And a truly
+linear microphone is not necessarily
+
+ align:start position:0%
+linear microphone is not necessarily
+ 
+
+ align:start position:0%
+linear microphone is not necessarily
+what people want for most recording, it
+
+ align:start position:0%
+what people want for most recording, it
+ 
+
+ align:start position:0%
+what people want for most recording, it
+turns out. So you have to get the right
+
+ align:start position:0%
+turns out. So you have to get the right
+ 
+
+ align:start position:0%
+turns out. So you have to get the right
+kinds of
+
+ align:start position:0%
+kinds of
+ 
+
+ align:start position:0%
+kinds of
+microphones with high degrees of coding
+
+ align:start position:0%
+microphones with high degrees of coding
+ 
+
+ align:start position:0%
+microphones with high degrees of coding
+and skill. And what I call is
+
+ align:start position:0%
+and skill. And what I call is
+ 
+
+ align:start position:0%
+and skill. And what I call is
+anti-velva. Velva is a film which soups
+
+ align:start position:0%
+anti-velva. Velva is a film which soups
+ 
+
+ align:start position:0%
+anti-velva. Velva is a film which soups
+up color and contra um saturation
+
+ align:start position:0%
+up color and contra um saturation
+ 
+
+ align:start position:0%
+up color and contra um saturation
+enormously. And you want the reverse of
+
+ align:start position:0%
+enormously. And you want the reverse of
+ 
+
+ align:start position:0%
+enormously. And you want the reverse of
+that. You want a natural color. And by
+
+ align:start position:0%
+that. You want a natural color. And by
+ 
+
+ align:start position:0%
+that. You want a natural color. And by
+the way, there are very few films that
+
+ align:start position:0%
+the way, there are very few films that
+ 
+
+ align:start position:0%
+the way, there are very few films that
+you can buy which have anything close to
+
+ align:start position:0%
+you can buy which have anything close to
+ 
+
+ align:start position:0%
+you can buy which have anything close to
+natural color. Very few professional
+
+ align:start position:0%
+natural color. Very few professional
+ 
+
+ align:start position:0%
+natural color. Very few professional
+unprofessional almost all of them are
+
+ align:start position:0%
+unprofessional almost all of them are
+ 
+
+ align:start position:0%
+unprofessional almost all of them are
+souped one way or the other for various
+
+ align:start position:0%
+souped one way or the other for various
+ 
+
+ align:start position:0%
+souped one way or the other for various
+purposes. And even then it's very hard
+
+ align:start position:0%
+purposes. And even then it's very hard
+ 
+
+ align:start position:0%
+purposes. And even then it's very hard
+to get anything close to natural color.
+
+ align:start position:0%
+to get anything close to natural color.
+ 
+
+ align:start position:0%
+to get anything close to natural color.
+And I could go on about you know which
+
+ align:start position:0%
+And I could go on about you know which
+ 
+
+ align:start position:0%
+And I could go on about you know which
+kind of recording system for those who
+
+ align:start position:0%
+kind of recording system for those who
+ 
+
+ align:start position:0%
+kind of recording system for those who
+care you use midside technique and I can
+
+ align:start position:0%
+care you use midside technique and I can
+ 
+
+ align:start position:0%
+care you use midside technique and I can
+explain later. All right. So my point is
+
+ align:start position:0%
+explain later. All right. So my point is
+ 
+
+ align:start position:0%
+explain later. All right. So my point is
+that I'm getting involved in a field
+
+ align:start position:0%
+that I'm getting involved in a field
+ 
+
+ align:start position:0%
+that I'm getting involved in a field
+where the technology is much less
+
+ align:start position:0%
+where the technology is much less
+ 
+
+ align:start position:0%
+where the technology is much less
+obvious to me much more apparent about
+
+ align:start position:0%
+obvious to me much more apparent about
+ 
+
+ align:start position:0%
+obvious to me much more apparent about
+the choices I make and much more crucial
+
+ align:start position:0%
+the choices I make and much more crucial
+ 
+
+ align:start position:0%
+the choices I make and much more crucial
+to what I do if I want to get something
+
+ align:start position:0%
+to what I do if I want to get something
+ 
+
+ align:start position:0%
+to what I do if I want to get something
+accurate and
+
+ align:start position:0%
+accurate and
+ 
+
+ align:start position:0%
+accurate and
+archival. And that's a discovery I made.
+
+ align:start position:0%
+archival. And that's a discovery I made.
+ 
+
+ align:start position:0%
+archival. And that's a discovery I made.
+I mean, I knew I if I used really good
+
+ align:start position:0%
+I mean, I knew I if I used really good
+ 
+
+ align:start position:0%
+I mean, I knew I if I used really good
+lenses, I'd be okay. I mean, I didn't,
+
+ align:start position:0%
+lenses, I'd be okay. I mean, I didn't,
+ 
+
+ align:start position:0%
+lenses, I'd be okay. I mean, I didn't,
+you know, I figured that's about all I
+
+ align:start position:0%
+you know, I figured that's about all I
+ 
+
+ align:start position:0%
+you know, I figured that's about all I
+can hope for, but this is much
+
+ align:start position:0%
+can hope for, but this is much
+ 
+
+ align:start position:0%
+can hope for, but this is much
+harder. Finally, I want to say something
+
+ align:start position:0%
+harder. Finally, I want to say something
+ 
+
+ align:start position:0%
+harder. Finally, I want to say something
+about what I call social science
+
+ align:start position:0%
+about what I call social science
+ 
+
+ align:start position:0%
+about what I call social science
+informed photo documentation.
+
+ align:start position:0%
+informed photo documentation.
+ 
+
+ align:start position:0%
+informed photo documentation.
+Um if you read the literature on visual
+
+ align:start position:0%
+Um if you read the literature on visual
+ 
+
+ align:start position:0%
+Um if you read the literature on visual
+documentation for example um what's the
+
+ align:start position:0%
+documentation for example um what's the
+ 
+
+ align:start position:0%
+documentation for example um what's the
+journal uh from the society of visual
+
+ align:start position:0%
+journal uh from the society of visual
+ 
+
+ align:start position:0%
+journal uh from the society of visual
+visual anthropology review or um what's
+
+ align:start position:0%
+visual anthropology review or um what's
+ 
+
+ align:start position:0%
+visual anthropology review or um what's
+the sociological one called I forgot but
+
+ align:start position:0%
+the sociological one called I forgot but
+ 
+
+ align:start position:0%
+the sociological one called I forgot but
+there's one the sociologist run or the
+
+ align:start position:0%
+there's one the sociologist run or the
+ 
+
+ align:start position:0%
+there's one the sociologist run or the
+literature on visual stuff there's as I
+
+ align:start position:0%
+literature on visual stuff there's as I
+ 
+
+ align:start position:0%
+literature on visual stuff there's as I
+said there's all the skepticism and
+
+ align:start position:0%
+said there's all the skepticism and
+ 
+
+ align:start position:0%
+said there's all the skepticism and
+there's all this stuff about methodology
+
+ align:start position:0%
+there's all this stuff about methodology
+ 
+
+ align:start position:0%
+there's all this stuff about methodology
+you know the right qualitative methods
+
+ align:start position:0%
+you know the right qualitative methods
+ 
+
+ align:start position:0%
+you know the right qualitative methods
+and if anyone's had to teach a
+
+ align:start position:0%
+and if anyone's had to teach a
+ 
+
+ align:start position:0%
+and if anyone's had to teach a
+qualitative methods course and try to
+
+ align:start position:0%
+qualitative methods course and try to
+ 
+
+ align:start position:0%
+qualitative methods course and try to
+use visual
+
+ align:start position:0%
+use visual
+ 
+
+ align:start position:0%
+use visual
+I mean after you read the qual articles
+
+ align:start position:0%
+I mean after you read the qual articles
+ 
+
+ align:start position:0%
+I mean after you read the qual articles
+on qualitative methods about visual
+
+ align:start position:0%
+on qualitative methods about visual
+ 
+
+ align:start position:0%
+on qualitative methods about visual
+images I don't know why anybody would
+
+ align:start position:0%
+images I don't know why anybody would
+ 
+
+ align:start position:0%
+images I don't know why anybody would
+use them you know it sort of takes all
+
+ align:start position:0%
+use them you know it sort of takes all
+ 
+
+ align:start position:0%
+use them you know it sort of takes all
+the pleasure out of it and um so what I
+
+ align:start position:0%
+the pleasure out of it and um so what I
+ 
+
+ align:start position:0%
+the pleasure out of it and um so what I
+say is that my topics and understanding
+
+ align:start position:0%
+say is that my topics and understanding
+ 
+
+ align:start position:0%
+say is that my topics and understanding
+of how these systems
+
+ align:start position:0%
+of how these systems
+ 
+
+ align:start position:0%
+of how these systems
+work comes out of my understanding of
+
+ align:start position:0%
+work comes out of my understanding of
+ 
+
+ align:start position:0%
+work comes out of my understanding of
+how cities work or how industrial
+
+ align:start position:0%
+how cities work or how industrial
+ 
+
+ align:start position:0%
+how cities work or how industrial
+processes work. I'm fortunate that I
+
+ align:start position:0%
+processes work. I'm fortunate that I
+ 
+
+ align:start position:0%
+processes work. I'm fortunate that I
+have a historian of uh uh Greg Heis
+
+ align:start position:0%
+have a historian of uh uh Greg Heis
+ 
+
+ align:start position:0%
+have a historian of uh uh Greg Heis
+who's my neighbor my off next to my
+
+ align:start position:0%
+who's my neighbor my off next to my
+ 
+
+ align:start position:0%
+who's my neighbor my off next to my
+office and he's been writing about the
+
+ align:start position:0%
+office and he's been writing about the
+ 
+
+ align:start position:0%
+office and he's been writing about the
+history of industry in Los Angeles and
+
+ align:start position:0%
+history of industry in Los Angeles and
+ 
+
+ align:start position:0%
+history of industry in Los Angeles and
+more general the history of industry in
+
+ align:start position:0%
+more general the history of industry in
+ 
+
+ align:start position:0%
+more general the history of industry in
+cities and so I have this expert to
+
+ align:start position:0%
+cities and so I have this expert to
+ 
+
+ align:start position:0%
+cities and so I have this expert to
+consult with. I you know I walk in and
+
+ align:start position:0%
+consult with. I you know I walk in and
+ 
+
+ align:start position:0%
+consult with. I you know I walk in and
+say look what I found and he'll tell me
+
+ align:start position:0%
+say look what I found and he'll tell me
+ 
+
+ align:start position:0%
+say look what I found and he'll tell me
+what it means. Um and what I say in
+
+ align:start position:0%
+what it means. Um and what I say in
+ 
+
+ align:start position:0%
+what it means. Um and what I say in
+other words is that I'm not I don't have
+
+ align:start position:0%
+other words is that I'm not I don't have
+ 
+
+ align:start position:0%
+other words is that I'm not I don't have
+a methodology but I have a
+
+ align:start position:0%
+a methodology but I have a
+ 
+
+ align:start position:0%
+a methodology but I have a
+well-informed mode of inquiry with lots
+
+ align:start position:0%
+well-informed mode of inquiry with lots
+ 
+
+ align:start position:0%
+well-informed mode of inquiry with lots
+and lots of information. So, if I'm
+
+ align:start position:0%
+and lots of information. So, if I'm
+ 
+
+ align:start position:0%
+and lots of information. So, if I'm
+writing about uh as I told you before
+
+ align:start position:0%
+writing about uh as I told you before
+ 
+
+ align:start position:0%
+writing about uh as I told you before
+about the storefront churches, my secret
+
+ align:start position:0%
+about the storefront churches, my secret
+ 
+
+ align:start position:0%
+about the storefront churches, my secret
+is that I'm not just telling you cute
+
+ align:start position:0%
+is that I'm not just telling you cute
+ 
+
+ align:start position:0%
+is that I'm not just telling you cute
+remarks, but it's based on the scholarly
+
+ align:start position:0%
+remarks, but it's based on the scholarly
+ 
+
+ align:start position:0%
+remarks, but it's based on the scholarly
+literature. And the people who know
+
+ align:start position:0%
+literature. And the people who know
+ 
+
+ align:start position:0%
+literature. And the people who know
+about storefront churches will know that
+
+ align:start position:0%
+about storefront churches will know that
+ 
+
+ align:start position:0%
+about storefront churches will know that
+I'm not that stupid about it, right? I
+
+ align:start position:0%
+I'm not that stupid about it, right? I
+ 
+
+ align:start position:0%
+I'm not that stupid about it, right? I
+know the books. I know what the the main
+
+ align:start position:0%
+know the books. I know what the the main
+ 
+
+ align:start position:0%
+know the books. I know what the the main
+arguments are and so
+
+ align:start position:0%
+arguments are and so
+ 
+
+ align:start position:0%
+arguments are and so
+forth.
+
+ align:start position:0%
+forth.
+ 
+
+ align:start position:0%
+forth.
+Um there are two other things that I
+
+ align:start position:0%
+Um there are two other things that I
+ 
+
+ align:start position:0%
+Um there are two other things that I
+think import that I would like to say. I
+
+ align:start position:0%
+think import that I would like to say. I
+ 
+
+ align:start position:0%
+think import that I would like to say. I
+could not do this work if I didn't think
+
+ align:start position:0%
+could not do this work if I didn't think
+ 
+
+ align:start position:0%
+could not do this work if I didn't think
+there were people who did work like it
+
+ align:start position:0%
+there were people who did work like it
+ 
+
+ align:start position:0%
+there were people who did work like it
+who who are universally acknowledged.
+
+ align:start position:0%
+who who are universally acknowledged.
+ 
+
+ align:start position:0%
+who who are universally acknowledged.
+All right, let me give you some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples. This did go was the French
+
+ align:start position:0%
+examples. This did go was the French
+ 
+
+ align:start position:0%
+examples. This did go was the French
+philosopher or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+philosopher more or less put together
+
+ align:start position:0%
+philosopher more or less put together
+ 
+
+ align:start position:0%
+philosopher more or less put together
+the encyclopedia in 1760, the first
+
+ align:start position:0%
+the encyclopedia in 1760, the first
+ 
+
+ align:start position:0%
+the encyclopedia in 1760, the first
+modern encyclopedia. And you've probably
+
+ align:start position:0%
+modern encyclopedia. And you've probably
+ 
+
+ align:start position:0%
+modern encyclopedia. And you've probably
+seen images like this one or this one
+
+ align:start position:0%
+seen images like this one or this one
+ 
+
+ align:start position:0%
+seen images like this one or this one
+which are wood engravings from the the
+
+ align:start position:0%
+which are wood engravings from the the
+ 
+
+ align:start position:0%
+which are wood engravings from the the
+encyclopedia. Uh you can buy a whole two
+
+ align:start position:0%
+encyclopedia. Uh you can buy a whole two
+ 
+
+ align:start position:0%
+encyclopedia. Uh you can buy a whole two
+volumes of dover volumes of all the
+
+ align:start position:0%
+volumes of dover volumes of all the
+ 
+
+ align:start position:0%
+volumes of dover volumes of all the
+illustrations or many of them of various
+
+ align:start position:0%
+illustrations or many of them of various
+ 
+
+ align:start position:0%
+illustrations or many of them of various
+industrial processes. Uh I gather that
+
+ align:start position:0%
+industrial processes. Uh I gather that
+ 
+
+ align:start position:0%
+industrial processes. Uh I gather that
+uh dedo did a lot of field work himself
+
+ align:start position:0%
+uh dedo did a lot of field work himself
+ 
+
+ align:start position:0%
+uh dedo did a lot of field work himself
+but he also stole the images from Mayo
+
+ align:start position:0%
+but he also stole the images from Mayo
+ 
+
+ align:start position:0%
+but he also stole the images from Mayo
+Mir who was doing similar work. So
+
+ align:start position:0%
+Mir who was doing similar work. So
+ 
+
+ align:start position:0%
+Mir who was doing similar work. So
+there's some questions about who
+
+ align:start position:0%
+there's some questions about who
+ 
+
+ align:start position:0%
+there's some questions about who
+deserves all the credit. But uh the
+
+ align:start position:0%
+deserves all the credit. But uh the
+ 
+
+ align:start position:0%
+deserves all the credit. But uh the
+point is if you go look at this you see
+
+ align:start position:0%
+point is if you go look at this you see
+ 
+
+ align:start position:0%
+point is if you go look at this you see
+the details. I this morning I was in a
+
+ align:start position:0%
+the details. I this morning I was in a
+ 
+
+ align:start position:0%
+the details. I this morning I was in a
+place called Slade Gorton and company
+
+ align:start position:0%
+place called Slade Gorton and company
+ 
+
+ align:start position:0%
+place called Slade Gorton and company
+which is a fish company in um in uh New
+
+ align:start position:0%
+which is a fish company in um in uh New
+ 
+
+ align:start position:0%
+which is a fish company in um in uh New
+Market Square. And if you I was walked
+
+ align:start position:0%
+Market Square. And if you I was walked
+ 
+
+ align:start position:0%
+Market Square. And if you I was walked
+up the stairs and what did I see? I saw
+
+ align:start position:0%
+up the stairs and what did I see? I saw
+ 
+
+ align:start position:0%
+up the stairs and what did I see? I saw
+the engravings from Dro for making
+
+ align:start position:0%
+the engravings from Dro for making
+ 
+
+ align:start position:0%
+the engravings from Dro for making
+fishnetss.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Amazing. Say to me the second person who
+
+ align:start position:0%
+Amazing. Say to me the second person who
+ 
+
+ align:start position:0%
+Amazing. Say to me the second person who
+gives me courage. So DO does all of this
+
+ align:start position:0%
+gives me courage. So DO does all of this
+ 
+
+ align:start position:0%
+gives me courage. So DO does all of this
+stuff about industry. So if I want to
+
+ align:start position:0%
+stuff about industry. So if I want to
+ 
+
+ align:start position:0%
+stuff about industry. So if I want to
+describe how industry is done, I'm not
+
+ align:start position:0%
+describe how industry is done, I'm not
+ 
+
+ align:start position:0%
+describe how industry is done, I'm not
+alone. And DO is the best representative
+
+ align:start position:0%
+alone. And DO is the best representative
+ 
+
+ align:start position:0%
+alone. And DO is the best representative
+I know cuz most industrial photography
+
+ align:start position:0%
+I know cuz most industrial photography
+ 
+
+ align:start position:0%
+I know cuz most industrial photography
+is either about how great the machine is
+
+ align:start position:0%
+is either about how great the machine is
+ 
+
+ align:start position:0%
+is either about how great the machine is
+or how happy or unhappy the worker is.
+
+ align:start position:0%
+or how happy or unhappy the worker is.
+ 
+
+ align:start position:0%
+or how happy or unhappy the worker is.
+They rarely tell you how the m what's
+
+ align:start position:0%
+They rarely tell you how the m what's
+ 
+
+ align:start position:0%
+They rarely tell you how the m what's
+really going on because that's not what
+
+ align:start position:0%
+really going on because that's not what
+ 
+
+ align:start position:0%
+really going on because that's not what
+industrial photography has been about
+
+ align:start position:0%
+industrial photography has been about
+ 
+
+ align:start position:0%
+industrial photography has been about
+for the most part. Uh, I have nothing
+
+ align:start position:0%
+for the most part. Uh, I have nothing
+ 
+
+ align:start position:0%
+for the most part. Uh, I have nothing
+against how great the machine is or how
+
+ align:start position:0%
+against how great the machine is or how
+ 
+
+ align:start position:0%
+against how great the machine is or how
+unhappy or happy the worker is, but I
+
+ align:start position:0%
+unhappy or happy the worker is, but I
+ 
+
+ align:start position:0%
+unhappy or happy the worker is, but I
+was I have a different interest. All
+
+ align:start position:0%
+was I have a different interest. All
+ 
+
+ align:start position:0%
+was I have a different interest. All
+right. The other person is Charles
+
+ align:start position:0%
+right. The other person is Charles
+ 
+
+ align:start position:0%
+right. The other person is Charles
+Marval, who I mentioned
+
+ align:start position:0%
+Marval, who I mentioned
+ 
+
+ align:start position:0%
+Marval, who I mentioned
+before. Uh, I think this is what I want.
+
+ align:start position:0%
+before. Uh, I think this is what I want.
+ 
+
+ align:start position:0%
+before. Uh, I think this is what I want.
+Yes. Uh, who was hired by um um Baron
+
+ align:start position:0%
+Yes. Uh, who was hired by um um Baron
+ 
+
+ align:start position:0%
+Yes. Uh, who was hired by um um Baron
+Houseman to photograph Paris before and
+
+ align:start position:0%
+Houseman to photograph Paris before and
+ 
+
+ align:start position:0%
+Houseman to photograph Paris before and
+after it was eviscerated.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and he so he literally
+
+ align:start position:0%
+and and he so he literally
+ 
+
+ align:start position:0%
+and and he so he literally
+systematically photographed the Paris
+
+ align:start position:0%
+systematically photographed the Paris
+ 
+
+ align:start position:0%
+systematically photographed the Paris
+before and you can buy books with a
+
+ align:start position:0%
+before and you can buy books with a
+ 
+
+ align:start position:0%
+before and you can buy books with a
+thousand illustrations thousand of his
+
+ align:start position:0%
+thousand illustrations thousand of his
+ 
+
+ align:start position:0%
+thousand illustrations thousand of his
+images or 500 of his images and the best
+
+ align:start position:0%
+images or 500 of his images and the best
+ 
+
+ align:start position:0%
+images or 500 of his images and the best
+part the book I have is it shows you
+
+ align:start position:0%
+part the book I have is it shows you
+ 
+
+ align:start position:0%
+part the book I have is it shows you
+where he likely took the images
+
+ align:start position:0%
+where he likely took the images
+ 
+
+ align:start position:0%
+where he likely took the images
+from you know they figured out
+
+ align:start position:0%
+from you know they figured out
+ 
+
+ align:start position:0%
+from you know they figured out
+perspective which and the third person
+
+ align:start position:0%
+perspective which and the third person
+ 
+
+ align:start position:0%
+perspective which and the third person
+uh who sort of gives me courage is um
+
+ align:start position:0%
+uh who sort of gives me courage is um
+ 
+
+ align:start position:0%
+uh who sort of gives me courage is um
+nope Not that I'm
+
+ align:start position:0%
+nope Not that I'm
+ 
+
+ align:start position:0%
+nope Not that I'm
+sorry. Oops. Excuse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me. Is uh Eugene Aette who you probably
+
+ align:start position:0%
+me. Is uh Eugene Aette who you probably
+ 
+
+ align:start position:0%
+me. Is uh Eugene Aette who you probably
+heard about who um John Sharowski u sort
+
+ align:start position:0%
+heard about who um John Sharowski u sort
+ 
+
+ align:start position:0%
+heard about who um John Sharowski u sort
+of idealized the Museum of Modern Art.
+
+ align:start position:0%
+of idealized the Museum of Modern Art.
+ 
+
+ align:start position:0%
+of idealized the Museum of Modern Art.
+And this is one of his photographs of a
+
+ align:start position:0%
+And this is one of his photographs of a
+ 
+
+ align:start position:0%
+And this is one of his photographs of a
+uh I don't think I can make it bigger.
+
+ align:start position:0%
+uh I don't think I can make it bigger.
+ 
+
+ align:start position:0%
+uh I don't think I can make it bigger.
+I'll try, but I don't think Can I? No,
+
+ align:start position:0%
+I'll try, but I don't think Can I? No,
+ 
+
+ align:start position:0%
+I'll try, but I don't think Can I? No,
+it won't matter. All right. Uh this is
+
+ align:start position:0%
+it won't matter. All right. Uh this is
+ 
+
+ align:start position:0%
+it won't matter. All right. Uh this is
+of a of a store
+
+ align:start position:0%
+of a of a store
+ 
+
+ align:start position:0%
+of a of a store
+window in
+
+ align:start position:0%
+window in
+ 
+
+ align:start position:0%
+window in
+Paris and he he does he has seven or
+
+ align:start position:0%
+Paris and he he does he has seven or
+ 
+
+ align:start position:0%
+Paris and he he does he has seven or
+eight different topics from store
+
+ align:start position:0%
+eight different topics from store
+ 
+
+ align:start position:0%
+eight different topics from store
+windows to parks to interiors and so
+
+ align:start position:0%
+windows to parks to interiors and so
+ 
+
+ align:start position:0%
+windows to parks to interiors and so
+forth and he makes these images for
+
+ align:start position:0%
+forth and he makes these images for
+ 
+
+ align:start position:0%
+forth and he makes these images for
+artists to use. Right? He said I'm not
+
+ align:start position:0%
+artists to use. Right? He said I'm not
+ 
+
+ align:start position:0%
+artists to use. Right? He said I'm not
+I'm not a photo an artist. I'm just I
+
+ align:start position:0%
+I'm not a photo an artist. I'm just I
+ 
+
+ align:start position:0%
+I'm not a photo an artist. I'm just I
+just make uh
+
+ align:start position:0%
+just make uh
+ 
+
+ align:start position:0%
+just make uh
+documents. So even though azis really is
+
+ align:start position:0%
+documents. So even though azis really is
+ 
+
+ align:start position:0%
+documents. So even though azis really is
+a great artist I'm delighted to have
+
+ align:start position:0%
+a great artist I'm delighted to have
+ 
+
+ align:start position:0%
+a great artist I'm delighted to have
+someone who said that.
+
+ align:start position:0%
+someone who said that.
+ 
+
+ align:start position:0%
+someone who said that.
+Uh the last reason why I can do this
+
+ align:start position:0%
+Uh the last reason why I can do this
+ 
+
+ align:start position:0%
+Uh the last reason why I can do this
+work is because it's fundable. I've been
+
+ align:start position:0%
+work is because it's fundable. I've been
+ 
+
+ align:start position:0%
+work is because it's fundable. I've been
+able to get some grants to do
+
+ align:start position:0%
+able to get some grants to do
+ 
+
+ align:start position:0%
+able to get some grants to do
+it. Uh that's very important. Not for
+
+ align:start position:0%
+it. Uh that's very important. Not for
+ 
+
+ align:start position:0%
+it. Uh that's very important. Not for
+two reasons. One, because it's a good
+
+ align:start position:0%
+two reasons. One, because it's a good
+ 
+
+ align:start position:0%
+two reasons. One, because it's a good
+way of scaring off the people who tell
+
+ align:start position:0%
+way of scaring off the people who tell
+ 
+
+ align:start position:0%
+way of scaring off the people who tell
+you you shouldn't do it. In a
+
+ align:start position:0%
+you you shouldn't do it. In a
+ 
+
+ align:start position:0%
+you you shouldn't do it. In a
+university, if you can get a grant from
+
+ align:start position:0%
+university, if you can get a grant from
+ 
+
+ align:start position:0%
+university, if you can get a grant from
+a respectable people to let you do
+
+ align:start position:0%
+a respectable people to let you do
+ 
+
+ align:start position:0%
+a respectable people to let you do
+something, they pay attention.
+
+ align:start position:0%
+something, they pay attention.
+ 
+
+ align:start position:0%
+something, they pay attention.
+I mean, you know that it's it's the
+
+ align:start position:0%
+I mean, you know that it's it's the
+ 
+
+ align:start position:0%
+I mean, you know that it's it's the
+it's maybe you don't know it, but if you
+
+ align:start position:0%
+it's maybe you don't know it, but if you
+ 
+
+ align:start position:0%
+it's maybe you don't know it, but if you
+don't, you should. And the other thing
+
+ align:start position:0%
+don't, you should. And the other thing
+ 
+
+ align:start position:0%
+don't, you should. And the other thing
+is that it buys off time that you need.
+
+ align:start position:0%
+is that it buys off time that you need.
+ 
+
+ align:start position:0%
+is that it buys off time that you need.
+You know, if you start going out three
+
+ align:start position:0%
+You know, if you start going out three
+ 
+
+ align:start position:0%
+You know, if you start going out three
+or four days a week to photograph every
+
+ align:start position:0%
+or four days a week to photograph every
+ 
+
+ align:start position:0%
+or four days a week to photograph every
+morning, and remember, every hour you
+
+ align:start position:0%
+morning, and remember, every hour you
+ 
+
+ align:start position:0%
+morning, and remember, every hour you
+spend photographing usually involves two
+
+ align:start position:0%
+spend photographing usually involves two
+ 
+
+ align:start position:0%
+spend photographing usually involves two
+hours of cataloging time in the end.
+
+ align:start position:0%
+hours of cataloging time in the end.
+ 
+
+ align:start position:0%
+hours of cataloging time in the end.
+Remember, I have I've not mentioned
+
+ align:start position:0%
+Remember, I have I've not mentioned
+ 
+
+ align:start position:0%
+Remember, I have I've not mentioned
+this, but I should finally I'll be
+
+ align:start position:0%
+this, but I should finally I'll be
+ 
+
+ align:start position:0%
+this, but I should finally I'll be
+through in two minutes. is I have uh um
+
+ align:start position:0%
+through in two minutes. is I have uh um
+ 
+
+ align:start position:0%
+through in two minutes. is I have uh um
+Excel um spreadsheets listing all my
+
+ align:start position:0%
+Excel um spreadsheets listing all my
+ 
+
+ align:start position:0%
+Excel um spreadsheets listing all my
+images by their
+
+ align:start position:0%
+images by their
+ 
+
+ align:start position:0%
+images by their
+topics. Every factory, every church,
+
+ align:start position:0%
+topics. Every factory, every church,
+ 
+
+ align:start position:0%
+topics. Every factory, every church,
+every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+street. I have maps of
+
+ align:start position:0%
+street. I have maps of
+ 
+
+ align:start position:0%
+street. I have maps of
+them. So there's an enormous amount of
+
+ align:start position:0%
+them. So there's an enormous amount of
+ 
+
+ align:start position:0%
+them. So there's an enormous amount of
+work and to do that so they're
+
+ align:start position:0%
+work and to do that so they're
+ 
+
+ align:start position:0%
+work and to do that so they're
+reasonably accurate. I'm not talking
+
+ align:start position:0%
+reasonably accurate. I'm not talking
+ 
+
+ align:start position:0%
+reasonably accurate. I'm not talking
+about perfect, but reasonably accurate
+
+ align:start position:0%
+about perfect, but reasonably accurate
+ 
+
+ align:start position:0%
+about perfect, but reasonably accurate
+turns out to be a lot of work,
+
+ align:start position:0%
+turns out to be a lot of work,
+ 
+
+ align:start position:0%
+turns out to be a lot of work,
+especially if you're not as perfect as I
+
+ align:start position:0%
+especially if you're not as perfect as I
+ 
+
+ align:start position:0%
+especially if you're not as perfect as I
+am. No, you're as imperfect as I am. You
+
+ align:start position:0%
+am. No, you're as imperfect as I am. You
+ 
+
+ align:start position:0%
+am. No, you're as imperfect as I am. You
+know, you just have to go back and keep
+
+ align:start position:0%
+know, you just have to go back and keep
+ 
+
+ align:start position:0%
+know, you just have to go back and keep
+doing it. Uh, and sometimes you can't
+
+ align:start position:0%
+doing it. Uh, and sometimes you can't
+ 
+
+ align:start position:0%
+doing it. Uh, and sometimes you can't
+remember where you took the photographs.
+
+ align:start position:0%
+remember where you took the photographs.
+ 
+
+ align:start position:0%
+remember where you took the photographs.
+You pay for every sin, by the way. Every
+
+ align:start position:0%
+You pay for every sin, by the way. Every
+ 
+
+ align:start position:0%
+You pay for every sin, by the way. Every
+time you don't take good notes, you pay
+
+ align:start position:0%
+time you don't take good notes, you pay
+ 
+
+ align:start position:0%
+time you don't take good notes, you pay
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+it. All right, let me close. I think
+
+ align:start position:0%
+it. All right, let me close. I think
+ 
+
+ align:start position:0%
+it. All right, let me close. I think
+that the notion of inquiry and sensing
+
+ align:start position:0%
+that the notion of inquiry and sensing
+ 
+
+ align:start position:0%
+that the notion of inquiry and sensing
+place, as you call this thing, is superb
+
+ align:start position:0%
+place, as you call this thing, is superb
+ 
+
+ align:start position:0%
+place, as you call this thing, is superb
+description of what I'm up to.
+
+ align:start position:0%
+description of what I'm up to.
+ 
+
+ align:start position:0%
+description of what I'm up to.
+Um, what I've done is there's an outline
+
+ align:start position:0%
+Um, what I've done is there's an outline
+ 
+
+ align:start position:0%
+Um, what I've done is there's an outline
+over there that a handout for those of
+
+ align:start position:0%
+over there that a handout for those of
+ 
+
+ align:start position:0%
+over there that a handout for those of
+you who want it, which is an outline of
+
+ align:start position:0%
+you who want it, which is an outline of
+ 
+
+ align:start position:0%
+you who want it, which is an outline of
+my talk, but also includes a two-page
+
+ align:start position:0%
+my talk, but also includes a two-page
+ 
+
+ align:start position:0%
+my talk, but also includes a two-page
+essay which I call systematic reflective
+
+ align:start position:0%
+essay which I call systematic reflective
+ 
+
+ align:start position:0%
+essay which I call systematic reflective
+fieldwork because I've been challenged
+
+ align:start position:0%
+fieldwork because I've been challenged
+ 
+
+ align:start position:0%
+fieldwork because I've been challenged
+by people who say, "Well, how can I rely
+
+ align:start position:0%
+by people who say, "Well, how can I rely
+ 
+
+ align:start position:0%
+by people who say, "Well, how can I rely
+on your data and so forth?" I've had to
+
+ align:start position:0%
+on your data and so forth?" I've had to
+ 
+
+ align:start position:0%
+on your data and so forth?" I've had to
+think a lot about how do you justify
+
+ align:start position:0%
+think a lot about how do you justify
+ 
+
+ align:start position:0%
+think a lot about how do you justify
+doing this kind of work to your uh
+
+ align:start position:0%
+doing this kind of work to your uh
+ 
+
+ align:start position:0%
+doing this kind of work to your uh
+skeptical colleagues? And I'm not
+
+ align:start position:0%
+skeptical colleagues? And I'm not
+ 
+
+ align:start position:0%
+skeptical colleagues? And I'm not
+talking about people who just want to
+
+ align:start position:0%
+talking about people who just want to
+ 
+
+ align:start position:0%
+talking about people who just want to
+give you trouble. I'm talking about
+
+ align:start position:0%
+give you trouble. I'm talking about
+ 
+
+ align:start position:0%
+give you trouble. I'm talking about
+people who are honestly
+
+ align:start position:0%
+people who are honestly
+ 
+
+ align:start position:0%
+people who are honestly
+skeptical, you know, who who who uh
+
+ align:start position:0%
+skeptical, you know, who who who uh
+ 
+
+ align:start position:0%
+skeptical, you know, who who who uh
+think it's better to do a statistical
+
+ align:start position:0%
+think it's better to do a statistical
+ 
+
+ align:start position:0%
+think it's better to do a statistical
+analysis or who somehow say, well, what
+
+ align:start position:0%
+analysis or who somehow say, well, what
+ 
+
+ align:start position:0%
+analysis or who somehow say, well, what
+about what you're leaving out? And my
+
+ align:start position:0%
+about what you're leaving out? And my
+ 
+
+ align:start position:0%
+about what you're leaving out? And my
+job in doing this project was to figure
+
+ align:start position:0%
+job in doing this project was to figure
+ 
+
+ align:start position:0%
+job in doing this project was to figure
+out how to justify it. And uh about a
+
+ align:start position:0%
+out how to justify it. And uh about a
+ 
+
+ align:start position:0%
+out how to justify it. And uh about a
+week ago, maybe two weeks ago, I said,
+
+ align:start position:0%
+week ago, maybe two weeks ago, I said,
+ 
+
+ align:start position:0%
+week ago, maybe two weeks ago, I said,
+well, I started looking through my notes
+
+ align:start position:0%
+well, I started looking through my notes
+ 
+
+ align:start position:0%
+well, I started looking through my notes
+and I I I figured out a story I could
+
+ align:start position:0%
+and I I I figured out a story I could
+ 
+
+ align:start position:0%
+and I I I figured out a story I could
+tell, which is what I call the
+
+ align:start position:0%
+tell, which is what I call the
+ 
+
+ align:start position:0%
+tell, which is what I call the
+systematic reflective fieldwork. The
+
+ align:start position:0%
+systematic reflective fieldwork. The
+ 
+
+ align:start position:0%
+systematic reflective fieldwork. The
+systematic as you can get from what I'm
+
+ align:start position:0%
+systematic as you can get from what I'm
+ 
+
+ align:start position:0%
+systematic as you can get from what I'm
+doing is you keep doing lots of it in an
+
+ align:start position:0%
+doing is you keep doing lots of it in an
+ 
+
+ align:start position:0%
+doing is you keep doing lots of it in an
+organized way. Reflective, you try to
+
+ align:start position:0%
+organized way. Reflective, you try to
+ 
+
+ align:start position:0%
+organized way. Reflective, you try to
+understand what you're doing and you do
+
+ align:start position:0%
+understand what you're doing and you do
+ 
+
+ align:start position:0%
+understand what you're doing and you do
+lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fieldwork. Uh is that enough? That's a
+
+ align:start position:0%
+fieldwork. Uh is that enough? That's a
+ 
+
+ align:start position:0%
+fieldwork. Uh is that enough? That's a
+good question. But that's what, you
+
+ align:start position:0%
+good question. But that's what, you
+ 
+
+ align:start position:0%
+good question. But that's what, you
+know, what justifies what I do. Um, I
+
+ align:start position:0%
+know, what justifies what I do. Um, I
+ 
+
+ align:start position:0%
+know, what justifies what I do. Um, I
+have a terrific time doing this. I'm
+
+ align:start position:0%
+have a terrific time doing this. I'm
+ 
+
+ align:start position:0%
+have a terrific time doing this. I'm
+getting away with murder. But, uh, but I
+
+ align:start position:0%
+getting away with murder. But, uh, but I
+ 
+
+ align:start position:0%
+getting away with murder. But, uh, but I
+think it's really valuable. What happens
+
+ align:start position:0%
+think it's really valuable. What happens
+ 
+
+ align:start position:0%
+think it's really valuable. What happens
+with all this work is ends up an archive
+
+ align:start position:0%
+with all this work is ends up an archive
+ 
+
+ align:start position:0%
+with all this work is ends up an archive
+in the university. That's the most
+
+ align:start position:0%
+in the university. That's the most
+ 
+
+ align:start position:0%
+in the university. That's the most
+important thing. We put on shows and so
+
+ align:start position:0%
+important thing. We put on shows and so
+ 
+
+ align:start position:0%
+important thing. We put on shows and so
+forth, but I I'm not worried about
+
+ align:start position:0%
+forth, but I I'm not worried about
+ 
+
+ align:start position:0%
+forth, but I I'm not worried about
+making books of this or anything. That's
+
+ align:start position:0%
+making books of this or anything. That's
+ 
+
+ align:start position:0%
+making books of this or anything. That's
+not my purpose. My purpose is to have an
+
+ align:start position:0%
+not my purpose. My purpose is to have an
+ 
+
+ align:start position:0%
+not my purpose. My purpose is to have an
+archive that 60 to 100 years from now
+
+ align:start position:0%
+archive that 60 to 100 years from now
+ 
+
+ align:start position:0%
+archive that 60 to 100 years from now
+someone can use for work.
+
+ align:start position:0%
+someone can use for work.
+ 
+
+ align:start position:0%
+someone can use for work.
+That means if you want to do a good job
+
+ align:start position:0%
+That means if you want to do a good job
+ 
+
+ align:start position:0%
+That means if you want to do a good job
+on this, you got to give them the kinds
+
+ align:start position:0%
+on this, you got to give them the kinds
+ 
+
+ align:start position:0%
+on this, you got to give them the kinds
+of indexes and information so they don't
+
+ align:start position:0%
+of indexes and information so they don't
+ 
+
+ align:start position:0%
+of indexes and information so they don't
+have to go crazy trying to figure out
+
+ align:start position:0%
+have to go crazy trying to figure out
+ 
+
+ align:start position:0%
+have to go crazy trying to figure out
+what you
+
+ align:start position:0%
+what you
+ 
+
+ align:start position:0%
+what you
+did. Uh my as I said my next big project
+
+ align:start position:0%
+did. Uh my as I said my next big project
+ 
+
+ align:start position:0%
+did. Uh my as I said my next big project
+is going to be on or oral documentation
+
+ align:start position:0%
+is going to be on or oral documentation
+ 
+
+ align:start position:0%
+is going to be on or oral documentation
+and uh I've done a little but I don't
+
+ align:start position:0%
+and uh I've done a little but I don't
+ 
+
+ align:start position:0%
+and uh I've done a little but I don't
+trust my knowledge of that and we'll see
+
+ align:start position:0%
+trust my knowledge of that and we'll see
+ 
+
+ align:start position:0%
+trust my knowledge of that and we'll see
+what happens. Thank you.
+
+ align:start position:0%
+what happens. Thank you.
+ 
+
+ align:start position:0%
+what happens. Thank you.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+We've asked Mark Schuster to give brief
+
+ align:start position:0%
+We've asked Mark Schuster to give brief
+ 
+
+ align:start position:0%
+We've asked Mark Schuster to give brief
+comment. Oh, that's good. You do you
+
+ align:start position:0%
+comment. Oh, that's good. You do you
+ 
+
+ align:start position:0%
+comment. Oh, that's good. You do you
+need this? I guess I do.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's very good to have Marty back here
+
+ align:start position:0%
+It's very good to have Marty back here
+ 
+
+ align:start position:0%
+It's very good to have Marty back here
+in 10485 cuz as you can see, the level
+
+ align:start position:0%
+in 10485 cuz as you can see, the level
+ 
+
+ align:start position:0%
+in 10485 cuz as you can see, the level
+of energy goes up
+
+ align:start position:0%
+of energy goes up
+ 
+
+ align:start position:0%
+of energy goes up
+instantaneously. Uh, and I remember
+
+ align:start position:0%
+instantaneously. Uh, and I remember
+ 
+
+ align:start position:0%
+instantaneously. Uh, and I remember
+those days with great fondness. So,
+
+ align:start position:0%
+those days with great fondness. So,
+ 
+
+ align:start position:0%
+those days with great fondness. So,
+we're glad to have you back. Thank you.
+
+ align:start position:0%
+we're glad to have you back. Thank you.
+ 
+
+ align:start position:0%
+we're glad to have you back. Thank you.
+Um, so much to say uh that was that was
+
+ align:start position:0%
+Um, so much to say uh that was that was
+ 
+
+ align:start position:0%
+Um, so much to say uh that was that was
+raised uh in Marty's presentation and
+
+ align:start position:0%
+raised uh in Marty's presentation and
+ 
+
+ align:start position:0%
+raised uh in Marty's presentation and
+also by the the two-page essay here. Um,
+
+ align:start position:0%
+also by the the two-page essay here. Um,
+ 
+
+ align:start position:0%
+also by the the two-page essay here. Um,
+uh, but I want to start with something
+
+ align:start position:0%
+uh, but I want to start with something
+ 
+
+ align:start position:0%
+uh, but I want to start with something
+that's just been on my mind. The last
+
+ align:start position:0%
+that's just been on my mind. The last
+ 
+
+ align:start position:0%
+that's just been on my mind. The last
+two weeks, I've had guests from France
+
+ align:start position:0%
+two weeks, I've had guests from France
+ 
+
+ align:start position:0%
+two weeks, I've had guests from France
+uh, visiting with me and, uh, friends
+
+ align:start position:0%
+uh, visiting with me and, uh, friends
+ 
+
+ align:start position:0%
+uh, visiting with me and, uh, friends
+from many, many years ago. Uh, this was
+
+ align:start position:0%
+from many, many years ago. Uh, this was
+ 
+
+ align:start position:0%
+from many, many years ago. Uh, this was
+the first time in the United States for
+
+ align:start position:0%
+the first time in the United States for
+ 
+
+ align:start position:0%
+the first time in the United States for
+the husband. Um, the the wife had been
+
+ align:start position:0%
+the husband. Um, the the wife had been
+ 
+
+ align:start position:0%
+the husband. Um, the the wife had been
+here uh, as a youngster. her father
+
+ align:start position:0%
+here uh, as a youngster. her father
+ 
+
+ align:start position:0%
+here uh, as a youngster. her father
+worked in the embassy in in Washington
+
+ align:start position:0%
+worked in the embassy in in Washington
+ 
+
+ align:start position:0%
+worked in the embassy in in Washington
+and their 17-year-old son. And uh they
+
+ align:start position:0%
+and their 17-year-old son. And uh they
+ 
+
+ align:start position:0%
+and their 17-year-old son. And uh they
+did a lot of observing. He's an he's an
+
+ align:start position:0%
+did a lot of observing. He's an he's an
+ 
+
+ align:start position:0%
+did a lot of observing. He's an he's an
+artist, amateur artist. Uh but they did
+
+ align:start position:0%
+artist, amateur artist. Uh but they did
+ 
+
+ align:start position:0%
+artist, amateur artist. Uh but they did
+a lot of observing of the cities that
+
+ align:start position:0%
+a lot of observing of the cities that
+ 
+
+ align:start position:0%
+a lot of observing of the cities that
+they were in. Boston, New York, um
+
+ align:start position:0%
+they were in. Boston, New York, um
+ 
+
+ align:start position:0%
+they were in. Boston, New York, um
+Capean. Uh and I wonder if you might
+
+ align:start position:0%
+Capean. Uh and I wonder if you might
+ 
+
+ align:start position:0%
+Capean. Uh and I wonder if you might
+guess what the things they were most
+
+ align:start position:0%
+guess what the things they were most
+ 
+
+ align:start position:0%
+guess what the things they were most
+impressed
+
+ align:start position:0%
+impressed
+ 
+
+ align:start position:0%
+impressed
+with. Right? I asked them, you know,
+
+ align:start position:0%
+with. Right? I asked them, you know,
+ 
+
+ align:start position:0%
+with. Right? I asked them, you know,
+what did you find most interesting in
+
+ align:start position:0%
+what did you find most interesting in
+ 
+
+ align:start position:0%
+what did you find most interesting in
+walking around?
+
+ align:start position:0%
+walking around?
+ 
+
+ align:start position:0%
+walking around?
+What are you doing to me? The answer is
+
+ align:start position:0%
+What are you doing to me? The answer is
+ 
+
+ align:start position:0%
+What are you doing to me? The answer is
+not going to be on the screen. Um,
+
+ align:start position:0%
+not going to be on the screen. Um,
+ 
+
+ align:start position:0%
+not going to be on the screen. Um,
+uh, what were the most interesting
+
+ align:start position:0%
+uh, what were the most interesting
+ 
+
+ align:start position:0%
+uh, what were the most interesting
+things? And, uh, they said, first,
+
+ align:start position:0%
+things? And, uh, they said, first,
+ 
+
+ align:start position:0%
+things? And, uh, they said, first,
+everyone goes around carrying a beverage
+
+ align:start position:0%
+everyone goes around carrying a beverage
+ 
+
+ align:start position:0%
+everyone goes around carrying a beverage
+in their
+
+ align:start position:0%
+in their
+ 
+
+ align:start position:0%
+in their
+hand, right? Everyone goes around
+
+ align:start position:0%
+hand, right? Everyone goes around
+ 
+
+ align:start position:0%
+hand, right? Everyone goes around
+carrying a beverage in their hand. It's
+
+ align:start position:0%
+carrying a beverage in their hand. It's
+ 
+
+ align:start position:0%
+carrying a beverage in their hand. It's
+absolutely true and it's something that
+
+ align:start position:0%
+absolutely true and it's something that
+ 
+
+ align:start position:0%
+absolutely true and it's something that
+we don't notice.
+
+ align:start position:0%
+we don't notice.
+ 
+
+ align:start position:0%
+we don't notice.
+Um, second thing, in the United States,
+
+ align:start position:0%
+Um, second thing, in the United States,
+ 
+
+ align:start position:0%
+Um, second thing, in the United States,
+Q's
+
+ align:start position:0%
+Q's
+ 
+
+ align:start position:0%
+Q's
+work. And they were astonished. When we
+
+ align:start position:0%
+work. And they were astonished. When we
+ 
+
+ align:start position:0%
+work. And they were astonished. When we
+went into a restaurant, we put our name
+
+ align:start position:0%
+went into a restaurant, we put our name
+ 
+
+ align:start position:0%
+went into a restaurant, we put our name
+on a list. They said, "Come back in a
+
+ align:start position:0%
+on a list. They said, "Come back in a
+ 
+
+ align:start position:0%
+on a list. They said, "Come back in a
+half an hour." We walked around Newbury
+
+ align:start position:0%
+half an hour." We walked around Newbury
+ 
+
+ align:start position:0%
+half an hour." We walked around Newbury
+Port half an hour. We came back. They
+
+ align:start position:0%
+Port half an hour. We came back. They
+ 
+
+ align:start position:0%
+Port half an hour. We came back. They
+said, "Your table's ready." You know,
+
+ align:start position:0%
+said, "Your table's ready." You know,
+ 
+
+ align:start position:0%
+said, "Your table's ready." You know,
+and that everybody who was in front of
+
+ align:start position:0%
+and that everybody who was in front of
+ 
+
+ align:start position:0%
+and that everybody who was in front of
+us had been seated. And everybody who
+
+ align:start position:0%
+us had been seated. And everybody who
+ 
+
+ align:start position:0%
+us had been seated. And everybody who
+was behind us hadn't yet been seated.
+
+ align:start position:0%
+was behind us hadn't yet been seated.
+ 
+
+ align:start position:0%
+was behind us hadn't yet been seated.
+They couldn't believe it. Um, and the
+
+ align:start position:0%
+They couldn't believe it. Um, and the
+ 
+
+ align:start position:0%
+They couldn't believe it. Um, and the
+third one was uh was something that is a
+
+ align:start position:0%
+third one was uh was something that is a
+ 
+
+ align:start position:0%
+third one was uh was something that is a
+little harder to believe. They said,
+
+ align:start position:0%
+little harder to believe. They said,
+ 
+
+ align:start position:0%
+little harder to believe. They said,
+"It's so clean here." you know, when we
+
+ align:start position:0%
+"It's so clean here." you know, when we
+ 
+
+ align:start position:0%
+"It's so clean here." you know, when we
+go traveling other places and we say we
+
+ align:start position:0%
+go traveling other places and we say we
+ 
+
+ align:start position:0%
+go traveling other places and we say we
+go to Toronto and we say it's so clean
+
+ align:start position:0%
+go to Toronto and we say it's so clean
+ 
+
+ align:start position:0%
+go to Toronto and we say it's so clean
+or we go to Disneyland and say it's so
+
+ align:start position:0%
+or we go to Disneyland and say it's so
+ 
+
+ align:start position:0%
+or we go to Disneyland and say it's so
+clean. Uh well, here are French folks
+
+ align:start position:0%
+clean. Uh well, here are French folks
+ 
+
+ align:start position:0%
+clean. Uh well, here are French folks
+who came to Boston and
+
+ align:start position:0%
+who came to Boston and
+ 
+
+ align:start position:0%
+who came to Boston and
+um New York and said it's so clean.
+
+ align:start position:0%
+um New York and said it's so clean.
+ 
+
+ align:start position:0%
+um New York and said it's so clean.
+Now I was astonished at their power of
+
+ align:start position:0%
+Now I was astonished at their power of
+ 
+
+ align:start position:0%
+Now I was astonished at their power of
+observation and uh uh it's not a power
+
+ align:start position:0%
+observation and uh uh it's not a power
+ 
+
+ align:start position:0%
+observation and uh uh it's not a power
+of observation that I have and I think
+
+ align:start position:0%
+of observation that I have and I think
+ 
+
+ align:start position:0%
+of observation that I have and I think
+there's a clue in what uh Marty has said
+
+ align:start position:0%
+there's a clue in what uh Marty has said
+ 
+
+ align:start position:0%
+there's a clue in what uh Marty has said
+about this repetition to work at it and
+
+ align:start position:0%
+about this repetition to work at it and
+ 
+
+ align:start position:0%
+about this repetition to work at it and
+do it over and over again um that really
+
+ align:start position:0%
+do it over and over again um that really
+ 
+
+ align:start position:0%
+do it over and over again um that really
+um that really reminds us that it's hard
+
+ align:start position:0%
+um that really reminds us that it's hard
+ 
+
+ align:start position:0%
+um that really reminds us that it's hard
+work but it's work that's worth doing.
+
+ align:start position:0%
+work but it's work that's worth doing.
+ 
+
+ align:start position:0%
+work but it's work that's worth doing.
+Um Marty said toward the end, I don't
+
+ align:start position:0%
+Um Marty said toward the end, I don't
+ 
+
+ align:start position:0%
+Um Marty said toward the end, I don't
+have a methodology. I don't buy that for
+
+ align:start position:0%
+have a methodology. I don't buy that for
+ 
+
+ align:start position:0%
+have a methodology. I don't buy that for
+a second. You know, I think that he does
+
+ align:start position:0%
+a second. You know, I think that he does
+ 
+
+ align:start position:0%
+a second. You know, I think that he does
+have a methodology. It's an
+
+ align:start position:0%
+have a methodology. It's an
+ 
+
+ align:start position:0%
+have a methodology. It's an
+unconventional methodology perhaps. Um,
+
+ align:start position:0%
+unconventional methodology perhaps. Um,
+ 
+
+ align:start position:0%
+unconventional methodology perhaps. Um,
+but there are echoes of this methodology
+
+ align:start position:0%
+but there are echoes of this methodology
+ 
+
+ align:start position:0%
+but there are echoes of this methodology
+in things that many of us have read. Um,
+
+ align:start position:0%
+in things that many of us have read. Um,
+ 
+
+ align:start position:0%
+in things that many of us have read. Um,
+I I just grabbed a couple things off my
+
+ align:start position:0%
+I I just grabbed a couple things off my
+ 
+
+ align:start position:0%
+I I just grabbed a couple things off my
+shelf. For example,
+
+ align:start position:0%
+shelf. For example,
+ 
+
+ align:start position:0%
+shelf. For example,
+um, I didn't bring the book down because
+
+ align:start position:0%
+um, I didn't bring the book down because
+ 
+
+ align:start position:0%
+um, I didn't bring the book down because
+it's too big, but uh, um, I remembered
+
+ align:start position:0%
+it's too big, but uh, um, I remembered
+ 
+
+ align:start position:0%
+it's too big, but uh, um, I remembered
+when Larry Vale and I taught
+
+ align:start position:0%
+when Larry Vale and I taught
+ 
+
+ align:start position:0%
+when Larry Vale and I taught
+quantitative qualit excuse me,
+
+ align:start position:0%
+quantitative qualit excuse me,
+ 
+
+ align:start position:0%
+quantitative qualit excuse me,
+qualitative methods. Uh, and I want to
+
+ align:start position:0%
+qualitative methods. Uh, and I want to
+ 
+
+ align:start position:0%
+qualitative methods. Uh, and I want to
+disagree about that in a second. Uh we
+
+ align:start position:0%
+disagree about that in a second. Uh we
+ 
+
+ align:start position:0%
+disagree about that in a second. Uh we
+used an essay that Kevin Lynch wrote
+
+ align:start position:0%
+used an essay that Kevin Lynch wrote
+ 
+
+ align:start position:0%
+used an essay that Kevin Lynch wrote
+which was called A Walk Around the Block
+
+ align:start position:0%
+which was called A Walk Around the Block
+ 
+
+ align:start position:0%
+which was called A Walk Around the Block
+published in 1959. Uh it's reproduced in
+
+ align:start position:0%
+published in 1959. Uh it's reproduced in
+ 
+
+ align:start position:0%
+published in 1959. Uh it's reproduced in
+Michael Southworth's collection of the
+
+ align:start position:0%
+Michael Southworth's collection of the
+ 
+
+ align:start position:0%
+Michael Southworth's collection of the
+published articles of Kevin Lynch. Um
+
+ align:start position:0%
+published articles of Kevin Lynch. Um
+ 
+
+ align:start position:0%
+published articles of Kevin Lynch. Um
+and uh it uses a methodology that's a
+
+ align:start position:0%
+and uh it uses a methodology that's a
+ 
+
+ align:start position:0%
+and uh it uses a methodology that's a
+first cousin to what Marty was talking
+
+ align:start position:0%
+first cousin to what Marty was talking
+ 
+
+ align:start position:0%
+first cousin to what Marty was talking
+about. Um he would take people downtown
+
+ align:start position:0%
+about. Um he would take people downtown
+ 
+
+ align:start position:0%
+about. Um he would take people downtown
+and they would walk Newbury Street,
+
+ align:start position:0%
+and they would walk Newbury Street,
+ 
+
+ align:start position:0%
+and they would walk Newbury Street,
+Arlington Street, the alley between
+
+ align:start position:0%
+Arlington Street, the alley between
+ 
+
+ align:start position:0%
+Arlington Street, the alley between
+Newbury Street and uh and and uh Boilson
+
+ align:start position:0%
+Newbury Street and uh and and uh Boilson
+ 
+
+ align:start position:0%
+Newbury Street and uh and and uh Boilson
+Street, Berkeley Street, and he would
+
+ align:start position:0%
+Street, Berkeley Street, and he would
+ 
+
+ align:start position:0%
+Street, Berkeley Street, and he would
+ask people, you know, we are about to
+
+ align:start position:0%
+ask people, you know, we are about to
+ 
+
+ align:start position:0%
+ask people, you know, we are about to
+take a short walk. Don't look for
+
+ align:start position:0%
+take a short walk. Don't look for
+ 
+
+ align:start position:0%
+take a short walk. Don't look for
+anything in particular, but tell me
+
+ align:start position:0%
+anything in particular, but tell me
+ 
+
+ align:start position:0%
+anything in particular, but tell me
+about the things you see, hear or smell,
+
+ align:start position:0%
+about the things you see, hear or smell,
+ 
+
+ align:start position:0%
+about the things you see, hear or smell,
+everything and anything you notice. Um
+
+ align:start position:0%
+everything and anything you notice. Um
+ 
+
+ align:start position:0%
+everything and anything you notice. Um
+and he tries to capture um in an essay
+
+ align:start position:0%
+and he tries to capture um in an essay
+ 
+
+ align:start position:0%
+and he tries to capture um in an essay
+then what people have told him about
+
+ align:start position:0%
+then what people have told him about
+ 
+
+ align:start position:0%
+then what people have told him about
+this little voyage around one small
+
+ align:start position:0%
+this little voyage around one small
+ 
+
+ align:start position:0%
+this little voyage around one small
+simple ordinary block uh in Boston. It
+
+ align:start position:0%
+simple ordinary block uh in Boston. It
+ 
+
+ align:start position:0%
+simple ordinary block uh in Boston. It
+was probably more ordinary then than it
+
+ align:start position:0%
+was probably more ordinary then than it
+ 
+
+ align:start position:0%
+was probably more ordinary then than it
+is today. Um or uh 1980 Grady Clay
+
+ align:start position:0%
+is today. Um or uh 1980 Grady Clay
+ 
+
+ align:start position:0%
+is today. Um or uh 1980 Grady Clay
+closeup how to read the American city.
+
+ align:start position:0%
+closeup how to read the American city.
+ 
+
+ align:start position:0%
+closeup how to read the American city.
+Uh 1985 Alan Jacobs looking at cities. U
+
+ align:start position:0%
+Uh 1985 Alan Jacobs looking at cities. U
+ 
+
+ align:start position:0%
+Uh 1985 Alan Jacobs looking at cities. U
+John Stillgo 1998 outside lies magic. um
+
+ align:start position:0%
+John Stillgo 1998 outside lies magic. um
+ 
+
+ align:start position:0%
+John Stillgo 1998 outside lies magic. um
+or Grady Clay again in 1998. Uh Real
+
+ align:start position:0%
+or Grady Clay again in 1998. Uh Real
+ 
+
+ align:start position:0%
+or Grady Clay again in 1998. Uh Real
+Places um an unconventional guide to the
+
+ align:start position:0%
+Places um an unconventional guide to the
+ 
+
+ align:start position:0%
+Places um an unconventional guide to the
+American landscape. Um all of these you
+
+ align:start position:0%
+American landscape. Um all of these you
+ 
+
+ align:start position:0%
+American landscape. Um all of these you
+are using similar methodologies to what
+
+ align:start position:0%
+are using similar methodologies to what
+ 
+
+ align:start position:0%
+are using similar methodologies to what
+Marty is up to. Um but uh and all of
+
+ align:start position:0%
+Marty is up to. Um but uh and all of
+ 
+
+ align:start position:0%
+Marty is up to. Um but uh and all of
+them are dealing with the same
+
+ align:start position:0%
+them are dealing with the same
+ 
+
+ align:start position:0%
+them are dealing with the same
+fundamental problem which I think is is
+
+ align:start position:0%
+fundamental problem which I think is is
+ 
+
+ align:start position:0%
+fundamental problem which I think is is
+Marty's problem although he hasn't quite
+
+ align:start position:0%
+Marty's problem although he hasn't quite
+ 
+
+ align:start position:0%
+Marty's problem although he hasn't quite
+named it and that is how do I take it
+
+ align:start position:0%
+named it and that is how do I take it
+ 
+
+ align:start position:0%
+named it and that is how do I take it
+home with
+
+ align:start position:0%
+home with
+ 
+
+ align:start position:0%
+home with
+me? Right? Because there's two things
+
+ align:start position:0%
+me? Right? Because there's two things
+ 
+
+ align:start position:0%
+me? Right? Because there's two things
+going on here. One thing is his
+
+ align:start position:0%
+going on here. One thing is his
+ 
+
+ align:start position:0%
+going on here. One thing is his
+experience of being out in the field
+
+ align:start position:0%
+experience of being out in the field
+ 
+
+ align:start position:0%
+experience of being out in the field
+looking at these things and and
+
+ align:start position:0%
+looking at these things and and
+ 
+
+ align:start position:0%
+looking at these things and and
+reflecting upon them and the other is
+
+ align:start position:0%
+reflecting upon them and the other is
+ 
+
+ align:start position:0%
+reflecting upon them and the other is
+how do I capture that and take it home
+
+ align:start position:0%
+how do I capture that and take it home
+ 
+
+ align:start position:0%
+how do I capture that and take it home
+and save it so that someone else can
+
+ align:start position:0%
+and save it so that someone else can
+ 
+
+ align:start position:0%
+and save it so that someone else can
+have something of the same experience.
+
+ align:start position:0%
+have something of the same experience.
+ 
+
+ align:start position:0%
+have something of the same experience.
+Okay? And and I think Marty would be the
+
+ align:start position:0%
+Okay? And and I think Marty would be the
+ 
+
+ align:start position:0%
+Okay? And and I think Marty would be the
+first to admit that that person 50 or 60
+
+ align:start position:0%
+first to admit that that person 50 or 60
+ 
+
+ align:start position:0%
+first to admit that that person 50 or 60
+years from now will not have the same
+
+ align:start position:0%
+years from now will not have the same
+ 
+
+ align:start position:0%
+years from now will not have the same
+experience. Right? It'll be a different
+
+ align:start position:0%
+experience. Right? It'll be a different
+ 
+
+ align:start position:0%
+experience. Right? It'll be a different
+experience. Um although you can u you
+
+ align:start position:0%
+experience. Um although you can u you
+ 
+
+ align:start position:0%
+experience. Um although you can u you
+can work as hard as you possibly can to
+
+ align:start position:0%
+can work as hard as you possibly can to
+ 
+
+ align:start position:0%
+can work as hard as you possibly can to
+make it an uh as equivalent experience
+
+ align:start position:0%
+make it an uh as equivalent experience
+ 
+
+ align:start position:0%
+make it an uh as equivalent experience
+as you possibly uh can. Now um you you
+
+ align:start position:0%
+as you possibly uh can. Now um you you
+ 
+
+ align:start position:0%
+as you possibly uh can. Now um you you
+you spoke about qualitative methods and
+
+ align:start position:0%
+you spoke about qualitative methods and
+ 
+
+ align:start position:0%
+you spoke about qualitative methods and
+I just uh up until that moment in your
+
+ align:start position:0%
+I just uh up until that moment in your
+ 
+
+ align:start position:0%
+I just uh up until that moment in your
+talk um I was having very fond memories
+
+ align:start position:0%
+talk um I was having very fond memories
+ 
+
+ align:start position:0%
+talk um I was having very fond memories
+of this course that we used to offer in
+
+ align:start position:0%
+of this course that we used to offer in
+ 
+
+ align:start position:0%
+of this course that we used to offer in
+the group called qualitative methods.
+
+ align:start position:0%
+the group called qualitative methods.
+ 
+
+ align:start position:0%
+the group called qualitative methods.
+Larry and I taught it once or twice. Uh
+
+ align:start position:0%
+Larry and I taught it once or twice. Uh
+ 
+
+ align:start position:0%
+Larry and I taught it once or twice. Uh
+Larry taught it with Sam another time or
+
+ align:start position:0%
+Larry taught it with Sam another time or
+ 
+
+ align:start position:0%
+Larry taught it with Sam another time or
+two. Um, and it's been a long while
+
+ align:start position:0%
+two. Um, and it's been a long while
+ 
+
+ align:start position:0%
+two. Um, and it's been a long while
+since we've actually uh actually taught
+
+ align:start position:0%
+since we've actually uh actually taught
+ 
+
+ align:start position:0%
+since we've actually uh actually taught
+it. Um, and perhaps the way in which we
+
+ align:start position:0%
+it. Um, and perhaps the way in which we
+ 
+
+ align:start position:0%
+it. Um, and perhaps the way in which we
+went about that is not a way that you
+
+ align:start position:0%
+went about that is not a way that you
+ 
+
+ align:start position:0%
+went about that is not a way that you
+would today accept after your
+
+ align:start position:0%
+would today accept after your
+ 
+
+ align:start position:0%
+would today accept after your
+experiences in the field. Um, um, but I
+
+ align:start position:0%
+experiences in the field. Um, um, but I
+ 
+
+ align:start position:0%
+experiences in the field. Um, um, but I
+think it's a mistake. Um, and I think
+
+ align:start position:0%
+think it's a mistake. Um, and I think
+ 
+
+ align:start position:0%
+think it's a mistake. Um, and I think
+many of the students think it's a
+
+ align:start position:0%
+many of the students think it's a
+ 
+
+ align:start position:0%
+many of the students think it's a
+mistake that we don't offer such a
+
+ align:start position:0%
+mistake that we don't offer such a
+ 
+
+ align:start position:0%
+mistake that we don't offer such a
+course. Uh, and that we really ought to
+
+ align:start position:0%
+course. Uh, and that we really ought to
+ 
+
+ align:start position:0%
+course. Uh, and that we really ought to
+um, and maybe um, you suggest, uh, to
+
+ align:start position:0%
+um, and maybe um, you suggest, uh, to
+ 
+
+ align:start position:0%
+um, and maybe um, you suggest, uh, to
+us, uh, Marty a way to do that. Stillgo
+
+ align:start position:0%
+us, uh, Marty a way to do that. Stillgo
+ 
+
+ align:start position:0%
+us, uh, Marty a way to do that. Stillgo
+in the in the beginning of Stillgo's
+
+ align:start position:0%
+in the in the beginning of Stillgo's
+ 
+
+ align:start position:0%
+in the in the beginning of Stillgo's
+book he talks in the very first few
+
+ align:start position:0%
+book he talks in the very first few
+ 
+
+ align:start position:0%
+book he talks in the very first few
+pages about how he started
+
+ align:start position:0%
+pages about how he started
+ 
+
+ align:start position:0%
+pages about how he started
+conventionally for for many years with a
+
+ align:start position:0%
+conventionally for for many years with a
+ 
+
+ align:start position:0%
+conventionally for for many years with a
+syllabus and eventually he sort of threw
+
+ align:start position:0%
+syllabus and eventually he sort of threw
+ 
+
+ align:start position:0%
+syllabus and eventually he sort of threw
+the syllabus away and he said what my
+
+ align:start position:0%
+the syllabus away and he said what my
+ 
+
+ align:start position:0%
+the syllabus away and he said what my
+course is about is about exploring and
+
+ align:start position:0%
+course is about is about exploring and
+ 
+
+ align:start position:0%
+course is about is about exploring and
+so as we explore what we're going to
+
+ align:start position:0%
+so as we explore what we're going to
+ 
+
+ align:start position:0%
+so as we explore what we're going to
+explore is going to change from year to
+
+ align:start position:0%
+explore is going to change from year to
+ 
+
+ align:start position:0%
+explore is going to change from year to
+year as uh I get reactions from students
+
+ align:start position:0%
+year as uh I get reactions from students
+ 
+
+ align:start position:0%
+year as uh I get reactions from students
+as they come back from their experiences
+
+ align:start position:0%
+as they come back from their experiences
+ 
+
+ align:start position:0%
+as they come back from their experiences
+in in the field. Um now I want to say
+
+ align:start position:0%
+in in the field. Um now I want to say
+ 
+
+ align:start position:0%
+in in the field. Um now I want to say
+something about photography I suppose uh
+
+ align:start position:0%
+something about photography I suppose uh
+ 
+
+ align:start position:0%
+something about photography I suppose uh
+because that's what this is about. Um
+
+ align:start position:0%
+because that's what this is about. Um
+ 
+
+ align:start position:0%
+because that's what this is about. Um
+and and maybe uh speak about it a little
+
+ align:start position:0%
+and and maybe uh speak about it a little
+ 
+
+ align:start position:0%
+and and maybe uh speak about it a little
+bit more personally. I have found as I
+
+ align:start position:0%
+bit more personally. I have found as I
+ 
+
+ align:start position:0%
+bit more personally. I have found as I
+have traveled of late I have often left
+
+ align:start position:0%
+have traveled of late I have often left
+ 
+
+ align:start position:0%
+have traveled of late I have often left
+my camera at home. Uh and the reason is
+
+ align:start position:0%
+my camera at home. Uh and the reason is
+ 
+
+ align:start position:0%
+my camera at home. Uh and the reason is
+because I got really tired of looking uh
+
+ align:start position:0%
+because I got really tired of looking uh
+ 
+
+ align:start position:0%
+because I got really tired of looking uh
+at the world through a rectangular uh
+
+ align:start position:0%
+at the world through a rectangular uh
+ 
+
+ align:start position:0%
+at the world through a rectangular uh
+frame um and spending all my time
+
+ align:start position:0%
+frame um and spending all my time
+ 
+
+ align:start position:0%
+frame um and spending all my time
+viewing it this way rather than viewing
+
+ align:start position:0%
+viewing it this way rather than viewing
+ 
+
+ align:start position:0%
+viewing it this way rather than viewing
+it this way. Maybe the key is the wide
+
+ align:start position:0%
+it this way. Maybe the key is the wide
+ 
+
+ align:start position:0%
+it this way. Maybe the key is the wide
+angle lens. Um uh and maybe that's what
+
+ align:start position:0%
+angle lens. Um uh and maybe that's what
+ 
+
+ align:start position:0%
+angle lens. Um uh and maybe that's what
+would make a difference. I do take the
+
+ align:start position:0%
+would make a difference. I do take the
+ 
+
+ align:start position:0%
+would make a difference. I do take the
+camera along when when um uh uh I'm I'm
+
+ align:start position:0%
+camera along when when um uh uh I'm I'm
+ 
+
+ align:start position:0%
+camera along when when um uh uh I'm I'm
+on a project and need uh you know visual
+
+ align:start position:0%
+on a project and need uh you know visual
+ 
+
+ align:start position:0%
+on a project and need uh you know visual
+evidence of one sort or another to
+
+ align:start position:0%
+evidence of one sort or another to
+ 
+
+ align:start position:0%
+evidence of one sort or another to
+illustrate the project. But I have found
+
+ align:start position:0%
+illustrate the project. But I have found
+ 
+
+ align:start position:0%
+illustrate the project. But I have found
+personally that it has been more
+
+ align:start position:0%
+personally that it has been more
+ 
+
+ align:start position:0%
+personally that it has been more
+restrictive for me. That makes the trick
+
+ align:start position:0%
+restrictive for me. That makes the trick
+ 
+
+ align:start position:0%
+restrictive for me. That makes the trick
+of bringing it home much more difficult.
+
+ align:start position:0%
+of bringing it home much more difficult.
+ 
+
+ align:start position:0%
+of bringing it home much more difficult.
+Right? Is it a journal? Is it just your
+
+ align:start position:0%
+Right? Is it a journal? Is it just your
+ 
+
+ align:start position:0%
+Right? Is it a journal? Is it just your
+memory? Is it is it some other form of
+
+ align:start position:0%
+memory? Is it is it some other form of
+ 
+
+ align:start position:0%
+memory? Is it is it some other form of
+recording? um that uh allows you to
+
+ align:start position:0%
+recording? um that uh allows you to
+ 
+
+ align:start position:0%
+recording? um that uh allows you to
+bring some of this home to catalog it to
+
+ align:start position:0%
+bring some of this home to catalog it to
+ 
+
+ align:start position:0%
+bring some of this home to catalog it to
+categorize it to uh you know you're
+
+ align:start position:0%
+categorize it to uh you know you're
+ 
+
+ align:start position:0%
+categorize it to uh you know you're
+doing a lot of very traditional social
+
+ align:start position:0%
+doing a lot of very traditional social
+ 
+
+ align:start position:0%
+doing a lot of very traditional social
+science things. You're categorizing and
+
+ align:start position:0%
+science things. You're categorizing and
+ 
+
+ align:start position:0%
+science things. You're categorizing and
+you're sorting and you're organizing and
+
+ align:start position:0%
+you're sorting and you're organizing and
+ 
+
+ align:start position:0%
+you're sorting and you're organizing and
+I I bet that Excel spreadsheet is
+
+ align:start position:0%
+I I bet that Excel spreadsheet is
+ 
+
+ align:start position:0%
+I I bet that Excel spreadsheet is
+organized by uh you could sort it by uh
+
+ align:start position:0%
+organized by uh you could sort it by uh
+ 
+
+ align:start position:0%
+organized by uh you could sort it by uh
+the various columns which helps you sort
+
+ align:start position:0%
+the various columns which helps you sort
+ 
+
+ align:start position:0%
+the various columns which helps you sort
+it into different categories. That's not
+
+ align:start position:0%
+it into different categories. That's not
+ 
+
+ align:start position:0%
+it into different categories. That's not
+very far away from uh the traditional
+
+ align:start position:0%
+very far away from uh the traditional
+ 
+
+ align:start position:0%
+very far away from uh the traditional
+social social science methodology. Um uh
+
+ align:start position:0%
+social social science methodology. Um uh
+ 
+
+ align:start position:0%
+social social science methodology. Um uh
+and and and finally I end with a with a
+
+ align:start position:0%
+and and and finally I end with a with a
+ 
+
+ align:start position:0%
+and and and finally I end with a with a
+with a question. I mentioned the name
+
+ align:start position:0%
+with a question. I mentioned the name
+ 
+
+ align:start position:0%
+with a question. I mentioned the name
+Tim Samuelson to you once before and I
+
+ align:start position:0%
+Tim Samuelson to you once before and I
+ 
+
+ align:start position:0%
+Tim Samuelson to you once before and I
+you haven't you haven't contacted Tim.
+
+ align:start position:0%
+you haven't you haven't contacted Tim.
+ 
+
+ align:start position:0%
+you haven't you haven't contacted Tim.
+Tim is uh Tim has worked with um uh one
+
+ align:start position:0%
+Tim is uh Tim has worked with um uh one
+ 
+
+ align:start position:0%
+Tim is uh Tim has worked with um uh one
+of the photographers who came early and
+
+ align:start position:0%
+of the photographers who came early and
+ 
+
+ align:start position:0%
+of the photographers who came early and
+help me remember did did a book called
+
+ align:start position:0%
+help me remember did did a book called
+ 
+
+ align:start position:0%
+help me remember did did a book called
+Unexpected Chicago
+
+ align:start position:0%
+Unexpected Chicago
+ 
+
+ align:start position:0%
+Unexpected Chicago
+with Camille right um and they're
+
+ align:start position:0%
+with Camille right um and they're
+ 
+
+ align:start position:0%
+with Camille right um and they're
+they're they've been working on
+
+ align:start position:0%
+they're they've been working on
+ 
+
+ align:start position:0%
+they're they've been working on
+storefront churches in Chicago. Yes. Um,
+
+ align:start position:0%
+storefront churches in Chicago. Yes. Um,
+ 
+
+ align:start position:0%
+storefront churches in Chicago. Yes. Um,
+and Tim is the cultural historian for
+
+ align:start position:0%
+and Tim is the cultural historian for
+ 
+
+ align:start position:0%
+and Tim is the cultural historian for
+the city of Chicago and would be an
+
+ align:start position:0%
+the city of Chicago and would be an
+ 
+
+ align:start position:0%
+the city of Chicago and would be an
+interesting person to to to talk to
+
+ align:start position:0%
+interesting person to to to talk to
+ 
+
+ align:start position:0%
+interesting person to to to talk to
+about their experiences going out and
+
+ align:start position:0%
+about their experiences going out and
+ 
+
+ align:start position:0%
+about their experiences going out and
+photographing uh and documenting the
+
+ align:start position:0%
+photographing uh and documenting the
+ 
+
+ align:start position:0%
+photographing uh and documenting the
+storefront um churches. So, there are
+
+ align:start position:0%
+storefront um churches. So, there are
+ 
+
+ align:start position:0%
+storefront um churches. So, there are
+some thoughts that I'd like to put on
+
+ align:start position:0%
+some thoughts that I'd like to put on
+ 
+
+ align:start position:0%
+some thoughts that I'd like to put on
+the table. Uh, we need to give you a
+
+ align:start position:0%
+the table. Uh, we need to give you a
+ 
+
+ align:start position:0%
+the table. Uh, we need to give you a
+chance to to ask questions. So, let's uh
+
+ align:start position:0%
+chance to to ask questions. So, let's uh
+ 
+
+ align:start position:0%
+chance to to ask questions. So, let's uh
+let's turn to that and maybe I'll give
+
+ align:start position:0%
+let's turn to that and maybe I'll give
+ 
+
+ align:start position:0%
+let's turn to that and maybe I'll give
+this back to you, Marty, and you can
+
+ align:start position:0%
+this back to you, Marty, and you can
+ 
+
+ align:start position:0%
+this back to you, Marty, and you can
+Well, I think it's better to let Oh, let
+
+ align:start position:0%
+Well, I think it's better to let Oh, let
+ 
+
+ align:start position:0%
+Well, I think it's better to let Oh, let
+them ask us questions, but they're going
+
+ align:start position:0%
+them ask us questions, but they're going
+ 
+
+ align:start position:0%
+them ask us questions, but they're going
+to be of you. So, Right. Yeah.
+
+ align:start position:0%
+to be of you. So, Right. Yeah.
+ 
+
+ align:start position:0%
+to be of you. So, Right. Yeah.
+questions.
+
+ align:start position:0%
+questions.
+ 
+
+ align:start position:0%
+questions.
+Well, I just have to add one question in
+
+ align:start position:0%
+Well, I just have to add one question in
+ 
+
+ align:start position:0%
+Well, I just have to add one question in
+relationship to Mark's comment about
+
+ align:start position:0%
+relationship to Mark's comment about
+ 
+
+ align:start position:0%
+relationship to Mark's comment about
+about the work. Is it categorized? In
+
+ align:start position:0%
+about the work. Is it categorized? In
+ 
+
+ align:start position:0%
+about the work. Is it categorized? In
+other words, if I look at the 800
+
+ align:start position:0%
+other words, if I look at the 800
+ 
+
+ align:start position:0%
+other words, if I look at the 800
+uh pictures of Pentecostal
+
+ align:start position:0%
+uh pictures of Pentecostal
+ 
+
+ align:start position:0%
+uh pictures of Pentecostal
+churches, are they categorized or are
+
+ align:start position:0%
+churches, are they categorized or are
+ 
+
+ align:start position:0%
+churches, are they categorized or are
+they just categorized by dress and so
+
+ align:start position:0%
+they just categorized by dress and so
+ 
+
+ align:start position:0%
+they just categorized by dress and so
+forth?
+
+ align:start position:0%
+forth?
+ 
+
+ align:start position:0%
+forth?
+There's information, for example, about
+
+ align:start position:0%
+There's information, for example, about
+ 
+
+ align:start position:0%
+There's information, for example, about
+what their uh what their uh biblical
+
+ align:start position:0%
+what their uh what their uh biblical
+ 
+
+ align:start position:0%
+what their uh what their uh biblical
+pass passages are. That's one thing. It
+
+ align:start position:0%
+pass passages are. That's one thing. It
+ 
+
+ align:start position:0%
+pass passages are. That's one thing. It
+lists the biblical passages in each and
+
+ align:start position:0%
+lists the biblical passages in each and
+ 
+
+ align:start position:0%
+lists the biblical passages in each and
+another column lists the the symbols
+
+ align:start position:0%
+another column lists the the symbols
+ 
+
+ align:start position:0%
+another column lists the the symbols
+that are on the church. Another column
+
+ align:start position:0%
+that are on the church. Another column
+ 
+
+ align:start position:0%
+that are on the church. Another column
+uh what else is there? Those are the two
+
+ align:start position:0%
+uh what else is there? Those are the two
+ 
+
+ align:start position:0%
+uh what else is there? Those are the two
+things I can think of immediately. If I
+
+ align:start position:0%
+things I can think of immediately. If I
+ 
+
+ align:start position:0%
+things I can think of immediately. If I
+were an architect, by the way, and the
+
+ align:start position:0%
+were an architect, by the way, and the
+ 
+
+ align:start position:0%
+were an architect, by the way, and the
+architects think differently, they would
+
+ align:start position:0%
+architects think differently, they would
+ 
+
+ align:start position:0%
+architects think differently, they would
+start saying how has the building been
+
+ align:start position:0%
+start saying how has the building been
+ 
+
+ align:start position:0%
+start saying how has the building been
+modified or color or color. Yeah. Well,
+
+ align:start position:0%
+modified or color or color. Yeah. Well,
+ 
+
+ align:start position:0%
+modified or color or color. Yeah. Well,
+no, I didn't do that. Um and obviously
+
+ align:start position:0%
+no, I didn't do that. Um and obviously
+ 
+
+ align:start position:0%
+no, I didn't do that. Um and obviously
+one could do much more of that work. But
+
+ align:start position:0%
+one could do much more of that work. But
+ 
+
+ align:start position:0%
+one could do much more of that work. But
+the architects for example uh there was
+
+ align:start position:0%
+the architects for example uh there was
+ 
+
+ align:start position:0%
+the architects for example uh there was
+a woman in Houston who was concerned
+
+ align:start position:0%
+a woman in Houston who was concerned
+ 
+
+ align:start position:0%
+a woman in Houston who was concerned
+about the modifications of the buildings
+
+ align:start position:0%
+about the modifications of the buildings
+ 
+
+ align:start position:0%
+about the modifications of the buildings
+which was interesting but nothing I
+
+ align:start position:0%
+which was interesting but nothing I
+ 
+
+ align:start position:0%
+which was interesting but nothing I
+spent much time on frankly. So but the
+
+ align:start position:0%
+spent much time on frankly. So but the
+ 
+
+ align:start position:0%
+spent much time on frankly. So but the
+categorizations are not very deep I must
+
+ align:start position:0%
+categorizations are not very deep I must
+ 
+
+ align:start position:0%
+categorizations are not very deep I must
+admit. Um someone else would have to go
+
+ align:start position:0%
+admit. Um someone else would have to go
+ 
+
+ align:start position:0%
+admit. Um someone else would have to go
+through it all and start thinking much
+
+ align:start position:0%
+through it all and start thinking much
+ 
+
+ align:start position:0%
+through it all and start thinking much
+more deeply about what they were looking
+
+ align:start position:0%
+more deeply about what they were looking
+ 
+
+ align:start position:0%
+more deeply about what they were looking
+for. For example, what are your
+
+ align:start position:0%
+for. For example, what are your
+ 
+
+ align:start position:0%
+for. For example, what are your
+neighbors? My favorite one was next to a
+
+ align:start position:0%
+neighbors? My favorite one was next to a
+ 
+
+ align:start position:0%
+neighbors? My favorite one was next to a
+to a uh you know a hot bed
+
+ align:start position:0%
+to a uh you know a hot bed
+ 
+
+ align:start position:0%
+to a uh you know a hot bed
+motel you know for prostitutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on Western Avenue. I had just a couple
+
+ align:start position:0%
+on Western Avenue. I had just a couple
+ 
+
+ align:start position:0%
+on Western Avenue. I had just a couple
+of other uh comments about this. For one
+
+ align:start position:0%
+of other uh comments about this. For one
+ 
+
+ align:start position:0%
+of other uh comments about this. For one
+one thing, I'm sitting here with
+
+ align:start position:0%
+one thing, I'm sitting here with
+ 
+
+ align:start position:0%
+one thing, I'm sitting here with
+tremendous regret because uh at one
+
+ align:start position:0%
+tremendous regret because uh at one
+ 
+
+ align:start position:0%
+tremendous regret because uh at one
+point in my career, I was documenting
+
+ align:start position:0%
+point in my career, I was documenting
+ 
+
+ align:start position:0%
+point in my career, I was documenting
+bridges in Boston and came across an
+
+ align:start position:0%
+bridges in Boston and came across an
+ 
+
+ align:start position:0%
+bridges in Boston and came across an
+archive
+
+ align:start position:0%
+archive
+ 
+
+ align:start position:0%
+archive
+uh in a bridge house in South Boston,
+
+ align:start position:0%
+uh in a bridge house in South Boston,
+ 
+
+ align:start position:0%
+uh in a bridge house in South Boston,
+which were the engineering records,
+
+ align:start position:0%
+which were the engineering records,
+ 
+
+ align:start position:0%
+which were the engineering records,
+photographs of every bridge in Boston,
+
+ align:start position:0%
+photographs of every bridge in Boston,
+ 
+
+ align:start position:0%
+photographs of every bridge in Boston,
+taken every year for about 50 years. Oh
+
+ align:start position:0%
+taken every year for about 50 years. Oh
+ 
+
+ align:start position:0%
+taken every year for about 50 years. Oh
+my god. And somebody had rescued them.
+
+ align:start position:0%
+my god. And somebody had rescued them.
+ 
+
+ align:start position:0%
+my god. And somebody had rescued them.
+And I took a bunch of photos for what I
+
+ align:start position:0%
+And I took a bunch of photos for what I
+ 
+
+ align:start position:0%
+And I took a bunch of photos for what I
+was working on at the time. I probably
+
+ align:start position:0%
+was working on at the time. I probably
+ 
+
+ align:start position:0%
+was working on at the time. I probably
+still have those photographs, but I'm
+
+ align:start position:0%
+still have those photographs, but I'm
+ 
+
+ align:start position:0%
+still have those photographs, but I'm
+sure the rest of it along with the
+
+ align:start position:0%
+sure the rest of it along with the
+ 
+
+ align:start position:0%
+sure the rest of it along with the
+bridge house and one of the last
+
+ align:start position:0%
+bridge house and one of the last
+ 
+
+ align:start position:0%
+bridge house and one of the last
+remaining bridges of this type were
+
+ align:start position:0%
+remaining bridges of this type were
+ 
+
+ align:start position:0%
+remaining bridges of this type were
+swept away. And when you were showing
+
+ align:start position:0%
+swept away. And when you were showing
+ 
+
+ align:start position:0%
+swept away. And when you were showing
+this, I said to myself, goodness, there
+
+ align:start position:0%
+this, I said to myself, goodness, there
+ 
+
+ align:start position:0%
+this, I said to myself, goodness, there
+are lots of archives actually like this
+
+ align:start position:0%
+are lots of archives actually like this
+ 
+
+ align:start position:0%
+are lots of archives actually like this
+out there that people have done based
+
+ align:start position:0%
+out there that people have done based
+ 
+
+ align:start position:0%
+out there that people have done based
+upon their particular cut at the world.
+
+ align:start position:0%
+upon their particular cut at the world.
+ 
+
+ align:start position:0%
+upon their particular cut at the world.
+Uh engineering for example, all these
+
+ align:start position:0%
+Uh engineering for example, all these
+ 
+
+ align:start position:0%
+Uh engineering for example, all these
+bridges are documented for other
+
+ align:start position:0%
+bridges are documented for other
+ 
+
+ align:start position:0%
+bridges are documented for other
+reasons. uh and it might be quite
+
+ align:start position:0%
+reasons. uh and it might be quite
+ 
+
+ align:start position:0%
+reasons. uh and it might be quite
+extraordinary to begin to collect those
+
+ align:start position:0%
+extraordinary to begin to collect those
+ 
+
+ align:start position:0%
+extraordinary to begin to collect those
+archives into a meta. No, that's exactly
+
+ align:start position:0%
+archives into a meta. No, that's exactly
+ 
+
+ align:start position:0%
+archives into a meta. No, that's exactly
+what's valuable about a university. The
+
+ align:start position:0%
+what's valuable about a university. The
+ 
+
+ align:start position:0%
+what's valuable about a university. The
+thing about universities is they don't
+
+ align:start position:0%
+thing about universities is they don't
+ 
+
+ align:start position:0%
+thing about universities is they don't
+disappear too soon, too rapidly and they
+
+ align:start position:0%
+disappear too soon, too rapidly and they
+ 
+
+ align:start position:0%
+disappear too soon, too rapidly and they
+don't throw out archives too often and
+
+ align:start position:0%
+don't throw out archives too often and
+ 
+
+ align:start position:0%
+don't throw out archives too often and
+that's what their big advantage is. You
+
+ align:start position:0%
+that's what their big advantage is. You
+ 
+
+ align:start position:0%
+that's what their big advantage is. You
+know, they're long-standing
+
+ align:start position:0%
+know, they're long-standing
+ 
+
+ align:start position:0%
+know, they're long-standing
+institutions and uh you know, libraries
+
+ align:start position:0%
+institutions and uh you know, libraries
+ 
+
+ align:start position:0%
+institutions and uh you know, libraries
+are like that too, but there are very
+
+ align:start position:0%
+are like that too, but there are very
+ 
+
+ align:start position:0%
+are like that too, but there are very
+few places that would do that. You know,
+
+ align:start position:0%
+few places that would do that. You know,
+ 
+
+ align:start position:0%
+few places that would do that. You know,
+most corporations eventually with their
+
+ align:start position:0%
+most corporations eventually with their
+ 
+
+ align:start position:0%
+most corporations eventually with their
+corporate uh what's
+
+ align:start position:0%
+corporate uh what's
+ 
+
+ align:start position:0%
+corporate uh what's
+um the Huntington Library just got the
+
+ align:start position:0%
+um the Huntington Library just got the
+ 
+
+ align:start position:0%
+um the Huntington Library just got the
+corporate archives of got something of
+
+ align:start position:0%
+corporate archives of got something of
+ 
+
+ align:start position:0%
+corporate archives of got something of
+the Southern California
+
+ align:start position:0%
+the Southern California
+ 
+
+ align:start position:0%
+the Southern California
+Edison with photographs just infinite
+
+ align:start position:0%
+Edison with photographs just infinite
+ 
+
+ align:start position:0%
+Edison with photographs just infinite
+amounts of photographs that were taken
+
+ align:start position:0%
+amounts of photographs that were taken
+ 
+
+ align:start position:0%
+amounts of photographs that were taken
+for technical reasons typicized way what
+
+ align:start position:0%
+for technical reasons typicized way what
+ 
+
+ align:start position:0%
+for technical reasons typicized way what
+a lot of them were done in a very
+
+ align:start position:0%
+a lot of them were done in a very
+ 
+
+ align:start position:0%
+a lot of them were done in a very
+regularized way. Yes. first grade
+
+ align:start position:0%
+regularized way. Yes. first grade
+ 
+
+ align:start position:0%
+regularized way. Yes. first grade
+quality. And the major problem is at
+
+ align:start position:0%
+quality. And the major problem is at
+ 
+
+ align:start position:0%
+quality. And the major problem is at
+some point it's too expensive to keep
+
+ align:start position:0%
+some point it's too expensive to keep
+ 
+
+ align:start position:0%
+some point it's too expensive to keep
+them. So they shred them or you know and
+
+ align:start position:0%
+them. So they shred them or you know and
+ 
+
+ align:start position:0%
+them. So they shred them or you know and
+so you know anybody here who's historian
+
+ align:start position:0%
+so you know anybody here who's historian
+ 
+
+ align:start position:0%
+so you know anybody here who's historian
+has worked in archives knows that the
+
+ align:start position:0%
+has worked in archives knows that the
+ 
+
+ align:start position:0%
+has worked in archives knows that the
+miracle is if you could only get them to
+
+ align:start position:0%
+miracle is if you could only get them to
+ 
+
+ align:start position:0%
+miracle is if you could only get them to
+forget about their what they own for 100
+
+ align:start position:0%
+forget about their what they own for 100
+ 
+
+ align:start position:0%
+forget about their what they own for 100
+years. I just had two other sorry random
+
+ align:start position:0%
+years. I just had two other sorry random
+ 
+
+ align:start position:0%
+years. I just had two other sorry random
+comments. The other comment I had was
+
+ align:start position:0%
+comments. The other comment I had was
+ 
+
+ align:start position:0%
+comments. The other comment I had was
+that if you didn't do Pentecostal
+
+ align:start position:0%
+that if you didn't do Pentecostal
+ 
+
+ align:start position:0%
+that if you didn't do Pentecostal
+churches,
+
+ align:start position:0%
+churches,
+ 
+
+ align:start position:0%
+churches,
+just pick anything, move to the building
+
+ align:start position:0%
+just pick anything, move to the building
+ 
+
+ align:start position:0%
+just pick anything, move to the building
+next door. Yeah. And then go out and
+
+ align:start position:0%
+next door. Yeah. And then go out and
+ 
+
+ align:start position:0%
+next door. Yeah. And then go out and
+record all buildings like that building.
+
+ align:start position:0%
+record all buildings like that building.
+ 
+
+ align:start position:0%
+record all buildings like that building.
+You would come up with a similar and
+
+ align:start position:0%
+You would come up with a similar and
+ 
+
+ align:start position:0%
+You would come up with a similar and
+equally provocative. No, I think not. I
+
+ align:start position:0%
+equally provocative. No, I think not. I
+ 
+
+ align:start position:0%
+equally provocative. No, I think not. I
+think actually taste matters. I think
+
+ align:start position:0%
+think actually taste matters. I think
+ 
+
+ align:start position:0%
+think actually taste matters. I think
+that I have pretty good taste. Uh maybe
+
+ align:start position:0%
+that I have pretty good taste. Uh maybe
+ 
+
+ align:start position:0%
+that I have pretty good taste. Uh maybe
+not superb, but not bad. I mean my trick
+
+ align:start position:0%
+not superb, but not bad. I mean my trick
+ 
+
+ align:start position:0%
+not superb, but not bad. I mean my trick
+was most people who I mean including
+
+ align:start position:0%
+was most people who I mean including
+ 
+
+ align:start position:0%
+was most people who I mean including
+Vgara do not worry about Pentecostal
+
+ align:start position:0%
+Vgara do not worry about Pentecostal
+ 
+
+ align:start position:0%
+Vgara do not worry about Pentecostal
+theology. They just like the pictures.
+
+ align:start position:0%
+theology. They just like the pictures.
+ 
+
+ align:start position:0%
+theology. They just like the pictures.
+They just think it's they get off on the
+
+ align:start position:0%
+They just think it's they get off on the
+ 
+
+ align:start position:0%
+They just think it's they get off on the
+religiosity. But do they know anything
+
+ align:start position:0%
+religiosity. But do they know anything
+ 
+
+ align:start position:0%
+religiosity. But do they know anything
+about the history of Pentecostalism?
+
+ align:start position:0%
+about the history of Pentecostalism?
+ 
+
+ align:start position:0%
+about the history of Pentecostalism?
+Very little. Do they care about the
+
+ align:start position:0%
+Very little. Do they care about the
+ 
+
+ align:start position:0%
+Very little. Do they care about the
+theology? Very
+
+ align:start position:0%
+theology? Very
+ 
+
+ align:start position:0%
+theology? Very
+little. I think I mean that's why I find
+
+ align:start position:0%
+little. I think I mean that's why I find
+ 
+
+ align:start position:0%
+little. I think I mean that's why I find
+Tom Roman's pictures a little bit too
+
+ align:start position:0%
+Tom Roman's pictures a little bit too
+ 
+
+ align:start position:0%
+Tom Roman's pictures a little bit too
+much. you know, yes, it's nice that
+
+ align:start position:0%
+much. you know, yes, it's nice that
+ 
+
+ align:start position:0%
+much. you know, yes, it's nice that
+they're rolling their eyes back and
+
+ align:start position:0%
+they're rolling their eyes back and
+ 
+
+ align:start position:0%
+they're rolling their eyes back and
+they're getting the feeling the spirit,
+
+ align:start position:0%
+they're getting the feeling the spirit,
+ 
+
+ align:start position:0%
+they're getting the feeling the spirit,
+but I think it that we owe those people
+
+ align:start position:0%
+but I think it that we owe those people
+ 
+
+ align:start position:0%
+but I think it that we owe those people
+more than that. Um, and it may turn out
+
+ align:start position:0%
+more than that. Um, and it may turn out
+ 
+
+ align:start position:0%
+more than that. Um, and it may turn out
+that the stores next to the buildings
+
+ align:start position:0%
+that the stores next to the buildings
+ 
+
+ align:start position:0%
+that the stores next to the buildings
+next to the churches have an interesting
+
+ align:start position:0%
+next to the churches have an interesting
+ 
+
+ align:start position:0%
+next to the churches have an interesting
+story and maybe it's better, but my
+
+ align:start position:0%
+story and maybe it's better, but my
+ 
+
+ align:start position:0%
+story and maybe it's better, but my
+intuitions are no, but you might be
+
+ align:start position:0%
+intuitions are no, but you might be
+ 
+
+ align:start position:0%
+intuitions are no, but you might be
+right. Well, I think my thought was
+
+ align:start position:0%
+right. Well, I think my thought was
+ 
+
+ align:start position:0%
+right. Well, I think my thought was
+slightly just slightly different and I
+
+ align:start position:0%
+slightly just slightly different and I
+ 
+
+ align:start position:0%
+slightly just slightly different and I
+not meaning this to be skeptical any
+
+ align:start position:0%
+not meaning this to be skeptical any
+ 
+
+ align:start position:0%
+not meaning this to be skeptical any
+way. I'm just saying that one of the
+
+ align:start position:0%
+way. I'm just saying that one of the
+ 
+
+ align:start position:0%
+way. I'm just saying that one of the
+beauties of this is I could go to Greek
+
+ align:start position:0%
+beauties of this is I could go to Greek
+ 
+
+ align:start position:0%
+beauties of this is I could go to Greek
+revival homes and all the Greek revival
+
+ align:start position:0%
+revival homes and all the Greek revival
+ 
+
+ align:start position:0%
+revival homes and all the Greek revival
+homes. I could go to homes made with a
+
+ align:start position:0%
+homes. I could go to homes made with a
+ 
+
+ align:start position:0%
+homes. I could go to homes made with a
+certain kind of pattern of brick or made
+
+ align:start position:0%
+certain kind of pattern of brick or made
+ 
+
+ align:start position:0%
+certain kind of pattern of brick or made
+by and the environment is filled with an
+
+ align:start position:0%
+by and the environment is filled with an
+ 
+
+ align:start position:0%
+by and the environment is filled with an
+infinite number of these patterns and
+
+ align:start position:0%
+infinite number of these patterns and
+ 
+
+ align:start position:0%
+infinite number of these patterns and
+the problem is to choose examples that
+
+ align:start position:0%
+the problem is to choose examples that
+ 
+
+ align:start position:0%
+the problem is to choose examples that
+allow for rich
+
+ align:start position:0%
+allow for rich
+ 
+
+ align:start position:0%
+allow for rich
+elaboration and it depends on your own
+
+ align:start position:0%
+elaboration and it depends on your own
+ 
+
+ align:start position:0%
+elaboration and it depends on your own
+skills. You mean I cannot do what an
+
+ align:start position:0%
+skills. You mean I cannot do what an
+ 
+
+ align:start position:0%
+skills. You mean I cannot do what an
+architect will do you know who sees the
+
+ align:start position:0%
+architect will do you know who sees the
+ 
+
+ align:start position:0%
+architect will do you know who sees the
+world entirely
+
+ align:start position:0%
+world entirely
+ 
+
+ align:start position:0%
+world entirely
+differently you know I mean acutely
+
+ align:start position:0%
+differently you know I mean acutely
+ 
+
+ align:start position:0%
+differently you know I mean acutely
+aware of when they have foam columns
+
+ align:start position:0%
+aware of when they have foam columns
+ 
+
+ align:start position:0%
+aware of when they have foam columns
+rather than you know real columns all
+
+ align:start position:0%
+rather than you know real columns all
+ 
+
+ align:start position:0%
+rather than you know real columns all
+right and all that stuff but so but I
+
+ align:start position:0%
+right and all that stuff but so but I
+ 
+
+ align:start position:0%
+right and all that stuff but so but I
+think that so it's a question and why in
+
+ align:start position:0%
+think that so it's a question and why in
+ 
+
+ align:start position:0%
+think that so it's a question and why in
+the world was I interested in that
+
+ align:start position:0%
+the world was I interested in that
+ 
+
+ align:start position:0%
+the world was I interested in that
+religious stuff I've written a book on
+
+ align:start position:0%
+religious stuff I've written a book on
+ 
+
+ align:start position:0%
+religious stuff I've written a book on
+um religious figures as model
+
+ align:start position:0%
+um religious figures as model
+ 
+
+ align:start position:0%
+um religious figures as model
+entrepreneurs the first chapter was on
+
+ align:start position:0%
+entrepreneurs the first chapter was on
+ 
+
+ align:start position:0%
+entrepreneurs the first chapter was on
+Augustine the second chapter was on
+
+ align:start position:0%
+Augustine the second chapter was on
+ 
+
+ align:start position:0%
+Augustine the second chapter was on
+Moses all right I got a And for that
+
+ align:start position:0%
+Moses all right I got a And for that
+ 
+
+ align:start position:0%
+Moses all right I got a And for that
+too, which is why I
+
+ align:start position:0%
+too, which is why I
+ 
+
+ align:start position:0%
+too, which is why I
+mean the point is that I was acutely
+
+ align:start position:0%
+mean the point is that I was acutely
+ 
+
+ align:start position:0%
+mean the point is that I was acutely
+aware there that if you take the
+
+ align:start position:0%
+aware there that if you take the
+ 
+
+ align:start position:0%
+aware there that if you take the
+theology seriously as such, you learn a
+
+ align:start position:0%
+theology seriously as such, you learn a
+ 
+
+ align:start position:0%
+theology seriously as such, you learn a
+lot. Not that you have to believe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything. But if you take it seriously,
+
+ align:start position:0%
+anything. But if you take it seriously,
+ 
+
+ align:start position:0%
+anything. But if you take it seriously,
+you go very far. And that was my that
+
+ align:start position:0%
+you go very far. And that was my that
+ 
+
+ align:start position:0%
+you go very far. And that was my that
+was my discovery. In other words, if I
+
+ align:start position:0%
+was my discovery. In other words, if I
+ 
+
+ align:start position:0%
+was my discovery. In other words, if I
+understood why Augustine did what he
+
+ align:start position:0%
+understood why Augustine did what he
+ 
+
+ align:start position:0%
+understood why Augustine did what he
+did, I could understand things about
+
+ align:start position:0%
+did, I could understand things about
+ 
+
+ align:start position:0%
+did, I could understand things about
+decision-m that were
+
+ align:start position:0%
+decision-m that were
+ 
+
+ align:start position:0%
+decision-m that were
+illuminating. Now, do I do I think he
+
+ align:start position:0%
+illuminating. Now, do I do I think he
+ 
+
+ align:start position:0%
+illuminating. Now, do I do I think he
+really had heard some tree talking to
+
+ align:start position:0%
+really had heard some tree talking to
+ 
+
+ align:start position:0%
+really had heard some tree talking to
+him, you know, in the backyard when he
+
+ align:start position:0%
+him, you know, in the backyard when he
+ 
+
+ align:start position:0%
+him, you know, in the backyard when he
+said, you know, tree said, "Take it and
+
+ align:start position:0%
+said, you know, tree said, "Take it and
+ 
+
+ align:start position:0%
+said, you know, tree said, "Take it and
+read." And opened up the book and
+
+ align:start position:0%
+read." And opened up the book and
+ 
+
+ align:start position:0%
+read." And opened up the book and
+pointed or that that what's his name? U
+
+ align:start position:0%
+pointed or that that what's his name? U
+ 
+
+ align:start position:0%
+pointed or that that what's his name? U
+had a flash of life and fell off the
+
+ align:start position:0%
+had a flash of life and fell off the
+ 
+
+ align:start position:0%
+had a flash of life and fell off the
+donkey.
+
+ align:start position:0%
+donkey.
+ 
+
+ align:start position:0%
+donkey.
+Paul, who cares?
+
+ align:start position:0%
+Paul, who cares?
+ 
+
+ align:start position:0%
+Paul, who cares?
+But you know I'm a Jew from
+
+ align:start position:0%
+But you know I'm a Jew from
+ 
+
+ align:start position:0%
+But you know I'm a Jew from
+Brooklyn so it doesn't matter to me. But
+
+ align:start position:0%
+Brooklyn so it doesn't matter to me. But
+ 
+
+ align:start position:0%
+Brooklyn so it doesn't matter to me. But
+I mean you know for Christians it's
+
+ align:start position:0%
+I mean you know for Christians it's
+ 
+
+ align:start position:0%
+I mean you know for Christians it's
+obvious for certain kinds of Christians
+
+ align:start position:0%
+obvious for certain kinds of Christians
+ 
+
+ align:start position:0%
+obvious for certain kinds of Christians
+it's very important issue but as a
+
+ align:start position:0%
+it's very important issue but as a
+ 
+
+ align:start position:0%
+it's very important issue but as a
+scholar what matters is to take those
+
+ align:start position:0%
+scholar what matters is to take those
+ 
+
+ align:start position:0%
+scholar what matters is to take those
+events as serious accounts which then
+
+ align:start position:0%
+events as serious accounts which then
+ 
+
+ align:start position:0%
+events as serious accounts which then
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+illuminating and that's what really is
+
+ align:start position:0%
+illuminating and that's what really is
+ 
+
+ align:start position:0%
+illuminating and that's what really is
+wonderful. Um but I think your point is
+
+ align:start position:0%
+wonderful. Um but I think your point is
+ 
+
+ align:start position:0%
+wonderful. Um but I think your point is
+very well taken. I mean I don't think
+
+ align:start position:0%
+very well taken. I mean I don't think
+ 
+
+ align:start position:0%
+very well taken. I mean I don't think
+that I know what's interesting. I don't
+
+ align:start position:0%
+that I know what's interesting. I don't
+ 
+
+ align:start position:0%
+that I know what's interesting. I don't
+know, you know, I mean, you know, a good
+
+ align:start position:0%
+know, you know, I mean, you know, a good
+ 
+
+ align:start position:0%
+know, you know, I mean, you know, a good
+Marxist probably could take the uh, you
+
+ align:start position:0%
+Marxist probably could take the uh, you
+ 
+
+ align:start position:0%
+Marxist probably could take the uh, you
+know, the garbage on the street and
+
+ align:start position:0%
+know, the garbage on the street and
+ 
+
+ align:start position:0%
+know, the garbage on the street and
+convert it to a good
+
+ align:start position:0%
+convert it to a good
+ 
+
+ align:start position:0%
+convert it to a good
+story, but probably the good Marxist is
+
+ align:start position:0%
+story, but probably the good Marxist is
+ 
+
+ align:start position:0%
+story, but probably the good Marxist is
+Carl and you know, the rest don't do as
+
+ align:start position:0%
+Carl and you know, the rest don't do as
+ 
+
+ align:start position:0%
+Carl and you know, the rest don't do as
+well.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes, sir. Uh well first of all thank you
+
+ align:start position:0%
+Yes, sir. Uh well first of all thank you
+ 
+
+ align:start position:0%
+Yes, sir. Uh well first of all thank you
+for your for your presentation which was
+
+ align:start position:0%
+for your for your presentation which was
+ 
+
+ align:start position:0%
+for your for your presentation which was
+very impressive especially as as a
+
+ align:start position:0%
+very impressive especially as as a
+ 
+
+ align:start position:0%
+very impressive especially as as a
+various recordings and uh pictures also
+
+ align:start position:0%
+various recordings and uh pictures also
+ 
+
+ align:start position:0%
+various recordings and uh pictures also
+offer a window on the on the
+
+ align:start position:0%
+offer a window on the on the
+ 
+
+ align:start position:0%
+offer a window on the on the
+organizations of the space that you're
+
+ align:start position:0%
+organizations of the space that you're
+ 
+
+ align:start position:0%
+organizations of the space that you're
+looking into like you know the
+
+ align:start position:0%
+looking into like you know the
+ 
+
+ align:start position:0%
+looking into like you know the
+organization of the of
+
+ align:start position:0%
+organization of the of
+ 
+
+ align:start position:0%
+organization of the of
+the of the Pentecostalist meeting. Yeah.
+
+ align:start position:0%
+the of the Pentecostalist meeting. Yeah.
+ 
+
+ align:start position:0%
+the of the Pentecostalist meeting. Yeah.
+Uh but my question is
+
+ align:start position:0%
+Uh but my question is
+ 
+
+ align:start position:0%
+Uh but my question is
+uh the great 19th century surveys of
+
+ align:start position:0%
+uh the great 19th century surveys of
+ 
+
+ align:start position:0%
+uh the great 19th century surveys of
+cities which this makes me in a way
+
+ align:start position:0%
+cities which this makes me in a way
+ 
+
+ align:start position:0%
+cities which this makes me in a way
+think of also uh had a very particular
+
+ align:start position:0%
+think of also uh had a very particular
+ 
+
+ align:start position:0%
+think of also uh had a very particular
+motivation very particular purpose which
+
+ align:start position:0%
+motivation very particular purpose which
+ 
+
+ align:start position:0%
+motivation very particular purpose which
+is to map you know the proletarian and
+
+ align:start position:0%
+is to map you know the proletarian and
+ 
+
+ align:start position:0%
+is to map you know the proletarian and
+understand how how it could be how to
+
+ align:start position:0%
+understand how how it could be how to
+ 
+
+ align:start position:0%
+understand how how it could be how to
+control the disease the source of
+
+ align:start position:0%
+control the disease the source of
+ 
+
+ align:start position:0%
+control the disease the source of
+disease exactly how would be normalized
+
+ align:start position:0%
+disease exactly how would be normalized
+ 
+
+ align:start position:0%
+disease exactly how would be normalized
+afterwards etc. So I was wondering if
+
+ align:start position:0%
+afterwards etc. So I was wondering if
+ 
+
+ align:start position:0%
+afterwards etc. So I was wondering if
+what your particular motivations from
+
+ align:start position:0%
+what your particular motivations from
+ 
+
+ align:start position:0%
+what your particular motivations from
+from an outsider perspective. It seems
+
+ align:start position:0%
+from an outsider perspective. It seems
+ 
+
+ align:start position:0%
+from an outsider perspective. It seems
+that it's it is motivated by the the
+
+ align:start position:0%
+that it's it is motivated by the the
+ 
+
+ align:start position:0%
+that it's it is motivated by the the
+freakiness of of Los Angeles is sort of
+
+ align:start position:0%
+freakiness of of Los Angeles is sort of
+ 
+
+ align:start position:0%
+freakiness of of Los Angeles is sort of
+urban. Los Angeles is the least freaky
+
+ align:start position:0%
+urban. Los Angeles is the least freaky
+ 
+
+ align:start position:0%
+urban. Los Angeles is the least freaky
+places. It's very ordinary. I mean
+
+ align:start position:0%
+places. It's very ordinary. I mean
+ 
+
+ align:start position:0%
+places. It's very ordinary. I mean
+Boston seems weird to me. Uh but you
+
+ align:start position:0%
+Boston seems weird to me. Uh but you
+ 
+
+ align:start position:0%
+Boston seems weird to me. Uh but you
+know uh the whole thing of Los Angeles
+
+ align:start position:0%
+know uh the whole thing of Los Angeles
+ 
+
+ align:start position:0%
+know uh the whole thing of Los Angeles
+exceptionalism strikes me as unlikely to
+
+ align:start position:0%
+exceptionalism strikes me as unlikely to
+ 
+
+ align:start position:0%
+exceptionalism strikes me as unlikely to
+get you very far. But let me go back
+
+ align:start position:0%
+get you very far. But let me go back
+ 
+
+ align:start position:0%
+get you very far. But let me go back
+more seriously to your remark. Well the
+
+ align:start position:0%
+more seriously to your remark. Well the
+ 
+
+ align:start position:0%
+more seriously to your remark. Well the
+question is what what is what is driving
+
+ align:start position:0%
+question is what what is what is driving
+ 
+
+ align:start position:0%
+question is what what is what is driving
+you? was propelling you forward. What
+
+ align:start position:0%
+you? was propelling you forward. What
+ 
+
+ align:start position:0%
+you? was propelling you forward. What
+propels me forward? It's a good
+
+ align:start position:0%
+propels me forward? It's a good
+ 
+
+ align:start position:0%
+propels me forward? It's a good
+question. Why in the world will I get
+
+ align:start position:0%
+question. Why in the world will I get
+ 
+
+ align:start position:0%
+question. Why in the world will I get
+interested in such a thing?
+
+ align:start position:0%
+interested in such a thing?
+ 
+
+ align:start position:0%
+interested in such a thing?
+Um I one of the things is it was so
+
+ align:start position:0%
+Um I one of the things is it was so
+ 
+
+ align:start position:0%
+Um I one of the things is it was so
+interesting visually. Second of all,
+
+ align:start position:0%
+interesting visually. Second of all,
+ 
+
+ align:start position:0%
+interesting visually. Second of all,
+there were so many of them. And third, I
+
+ align:start position:0%
+there were so many of them. And third, I
+ 
+
+ align:start position:0%
+there were so many of them. And third, I
+had a feeling I knew I could do
+
+ align:start position:0%
+had a feeling I knew I could do
+ 
+
+ align:start position:0%
+had a feeling I knew I could do
+something with
+
+ align:start position:0%
+something with
+ 
+
+ align:start position:0%
+something with
+it. And those don't sound like like
+
+ align:start position:0%
+it. And those don't sound like like
+ 
+
+ align:start position:0%
+it. And those don't sound like like
+cleaning up the idiots in the world or,
+
+ align:start position:0%
+cleaning up the idiots in the world or,
+ 
+
+ align:start position:0%
+cleaning up the idiots in the world or,
+you know, solving problems. And maybe I
+
+ align:start position:0%
+you know, solving problems. And maybe I
+ 
+
+ align:start position:0%
+you know, solving problems. And maybe I
+do have some nefarious purposes, but I
+
+ align:start position:0%
+do have some nefarious purposes, but I
+ 
+
+ align:start position:0%
+do have some nefarious purposes, but I
+suspect a lot of it has to do with um
+
+ align:start position:0%
+suspect a lot of it has to do with um
+ 
+
+ align:start position:0%
+suspect a lot of it has to do with um
+and also it was distant from me.
+
+ align:start position:0%
+and also it was distant from me.
+ 
+
+ align:start position:0%
+and also it was distant from me.
+I mean I've gone for example where I
+
+ align:start position:0%
+I mean I've gone for example where I
+ 
+
+ align:start position:0%
+I mean I've gone for example where I
+live in Los Angeles there's lots of
+
+ align:start position:0%
+live in Los Angeles there's lots of
+ 
+
+ align:start position:0%
+live in Los Angeles there's lots of
+synagogues which are not storefront
+
+ align:start position:0%
+synagogues which are not storefront
+ 
+
+ align:start position:0%
+synagogues which are not storefront
+synagogues but there are you know and
+
+ align:start position:0%
+synagogues but there are you know and
+ 
+
+ align:start position:0%
+synagogues but there are you know and
+you know essentially four four Jews have
+
+ align:start position:0%
+you know essentially four four Jews have
+ 
+
+ align:start position:0%
+you know essentially four four Jews have
+five synagogues because you know they
+
+ align:start position:0%
+five synagogues because you know they
+ 
+
+ align:start position:0%
+five synagogues because you know they
+have one they wouldn't go to but the
+
+ align:start position:0%
+have one they wouldn't go to but the
+ 
+
+ align:start position:0%
+have one they wouldn't go to but the
+point is that uh the the the basic the
+
+ align:start position:0%
+point is that uh the the the basic the
+ 
+
+ align:start position:0%
+point is that uh the the the basic the
+point is that there is sectarianism
+
+ align:start position:0%
+point is that there is sectarianism
+ 
+
+ align:start position:0%
+point is that there is sectarianism
+there but they don't wear it in the same
+
+ align:start position:0%
+there but they don't wear it in the same
+ 
+
+ align:start position:0%
+there but they don't wear it in the same
+way. They don't it doesn't quite uh
+
+ align:start position:0%
+way. They don't it doesn't quite uh
+ 
+
+ align:start position:0%
+way. They don't it doesn't quite uh
+evidence it in the same way. All right.
+
+ align:start position:0%
+evidence it in the same way. All right.
+ 
+
+ align:start position:0%
+evidence it in the same way. All right.
+Uh but there is stuff like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and by the way, it wasn't only
+
+ align:start position:0%
+Uh and by the way, it wasn't only
+ 
+
+ align:start position:0%
+Uh and by the way, it wasn't only
+Pentecostal churches. Storefront
+
+ align:start position:0%
+Pentecostal churches. Storefront
+ 
+
+ align:start position:0%
+Pentecostal churches. Storefront
+churches include lots that are not
+
+ align:start position:0%
+churches include lots that are not
+ 
+
+ align:start position:0%
+churches include lots that are not
+Pentecostal. Uh and I I they're part of
+
+ align:start position:0%
+Pentecostal. Uh and I I they're part of
+ 
+
+ align:start position:0%
+Pentecostal. Uh and I I they're part of
+my large sample. Uh you know, but
+
+ align:start position:0%
+my large sample. Uh you know, but
+ 
+
+ align:start position:0%
+my large sample. Uh you know, but
+Pentecostalism is just very rich with
+
+ align:start position:0%
+Pentecostalism is just very rich with
+ 
+
+ align:start position:0%
+Pentecostalism is just very rich with
+sectarianism. That's what makes it so
+
+ align:start position:0%
+sectarianism. That's what makes it so
+ 
+
+ align:start position:0%
+sectarianism. That's what makes it so
+wonderful. Uh it starts out as one
+
+ align:start position:0%
+wonderful. Uh it starts out as one
+ 
+
+ align:start position:0%
+wonderful. Uh it starts out as one
+movement and then it gets racially sec
+
+ align:start position:0%
+movement and then it gets racially sec
+ 
+
+ align:start position:0%
+movement and then it gets racially sec
+and then it has arguments about whether
+
+ align:start position:0%
+and then it has arguments about whether
+ 
+
+ align:start position:0%
+and then it has arguments about whether
+it's the first or the the second or
+
+ align:start position:0%
+it's the first or the the second or
+ 
+
+ align:start position:0%
+it's the first or the the second or
+third um uh what is it you know um
+
+ align:start position:0%
+third um uh what is it you know um
+ 
+
+ align:start position:0%
+third um uh what is it you know um
+salvation I mean the whole bunch of
+
+ align:start position:0%
+salvation I mean the whole bunch of
+ 
+
+ align:start position:0%
+salvation I mean the whole bunch of
+interesting issues would split them
+
+ align:start position:0%
+interesting issues would split them
+ 
+
+ align:start position:0%
+interesting issues would split them
+up and uh and and therefore it says for
+
+ align:start position:0%
+up and uh and and therefore it says for
+ 
+
+ align:start position:0%
+up and uh and and therefore it says for
+example when it says read the Bible all
+
+ align:start position:0%
+example when it says read the Bible all
+ 
+
+ align:start position:0%
+example when it says read the Bible all
+right you know you'll see all that why
+
+ align:start position:0%
+right you know you'll see all that why
+ 
+
+ align:start position:0%
+right you know you'll see all that why
+do they say read the Bible because
+
+ align:start position:0%
+do they say read the Bible because
+ 
+
+ align:start position:0%
+do they say read the Bible because
+you're not supposed to listen to the
+
+ align:start position:0%
+you're not supposed to listen to the
+ 
+
+ align:start position:0%
+you're not supposed to listen to the
+church supposed to read the Bible. But
+
+ align:start position:0%
+church supposed to read the Bible. But
+ 
+
+ align:start position:0%
+church supposed to read the Bible. But
+it's more than that. If they have they
+
+ align:start position:0%
+it's more than that. If they have they
+ 
+
+ align:start position:0%
+it's more than that. If they have they
+say something in Spanish or English,
+
+ align:start position:0%
+say something in Spanish or English,
+ 
+
+ align:start position:0%
+say something in Spanish or English,
+there's always some argument that
+
+ align:start position:0%
+there's always some argument that
+ 
+
+ align:start position:0%
+there's always some argument that
+they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+having. And I think I've always been
+
+ align:start position:0%
+having. And I think I've always been
+ 
+
+ align:start position:0%
+having. And I think I've always been
+fascinated by Protestant sectarianism.
+
+ align:start position:0%
+fascinated by Protestant sectarianism.
+ 
+
+ align:start position:0%
+fascinated by Protestant sectarianism.
+But why? Because I never understood it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+you see can I make just a comment? Yes.
+
+ align:start position:0%
+you see can I make just a comment? Yes.
+ 
+
+ align:start position:0%
+you see can I make just a comment? Yes.
+On what you shared with us tonight which
+
+ align:start position:0%
+On what you shared with us tonight which
+ 
+
+ align:start position:0%
+On what you shared with us tonight which
+I enjoy very very much.
+
+ align:start position:0%
+I enjoy very very much.
+ 
+
+ align:start position:0%
+I enjoy very very much.
+When and I saw you
+
+ align:start position:0%
+When and I saw you
+ 
+
+ align:start position:0%
+When and I saw you
+here, you were concerned with
+
+ align:start position:0%
+here, you were concerned with
+ 
+
+ align:start position:0%
+here, you were concerned with
+possibility of falls
+
+ align:start position:0%
+possibility of falls
+ 
+
+ align:start position:0%
+possibility of falls
+where and the great
+
+ align:start position:0%
+where and the great
+ 
+
+ align:start position:0%
+where and the great
+difficulties operating those in any way
+
+ align:start position:0%
+difficulties operating those in any way
+ 
+
+ align:start position:0%
+difficulties operating those in any way
+that give you a predictive description
+
+ align:start position:0%
+that give you a predictive description
+ 
+
+ align:start position:0%
+that give you a predictive description
+the conditions that need to meet in
+
+ align:start position:0%
+the conditions that need to meet in
+ 
+
+ align:start position:0%
+the conditions that need to meet in
+order to perform
+
+ align:start position:0%
+order to perform
+ 
+
+ align:start position:0%
+order to perform
+well. And seems to be that you're
+
+ align:start position:0%
+well. And seems to be that you're
+ 
+
+ align:start position:0%
+well. And seems to be that you're
+exactly on that same track. wanted to
+
+ align:start position:0%
+exactly on that same track. wanted to
+ 
+
+ align:start position:0%
+exactly on that same track. wanted to
+move in the other direction. We said I
+
+ align:start position:0%
+move in the other direction. We said I
+ 
+
+ align:start position:0%
+move in the other direction. We said I
+want to enable those who would follow
+
+ align:start position:0%
+want to enable those who would follow
+ 
+
+ align:start position:0%
+want to enable those who would follow
+how the late 20th century city
+
+ align:start position:0%
+how the late 20th century city
+ 
+
+ align:start position:0%
+how the late 20th century city
+work to give causal accounts day by year
+
+ align:start position:0%
+work to give causal accounts day by year
+ 
+
+ align:start position:0%
+work to give causal accounts day by year
+of what the city was doing well but not
+
+ align:start position:0%
+of what the city was doing well but not
+ 
+
+ align:start position:0%
+of what the city was doing well but not
+let me see if I understand the change in
+
+ align:start position:0%
+let me see if I understand the change in
+ 
+
+ align:start position:0%
+let me see if I understand the change in
+my work is when I'm doing field work and
+
+ align:start position:0%
+my work is when I'm doing field work and
+ 
+
+ align:start position:0%
+my work is when I'm doing field work and
+remember I didn't always do field work
+
+ align:start position:0%
+remember I didn't always do field work
+ 
+
+ align:start position:0%
+remember I didn't always do field work
+most of my life all right most of my I
+
+ align:start position:0%
+most of my life all right most of my I
+ 
+
+ align:start position:0%
+most of my life all right most of my I
+sat in my office field work in the
+
+ align:start position:0%
+sat in my office field work in the
+ 
+
+ align:start position:0%
+sat in my office field work in the
+Yeah, at
+
+ align:start position:0%
+Yeah, at
+ 
+
+ align:start position:0%
+Yeah, at
+best mostly up here, but you know, and
+
+ align:start position:0%
+best mostly up here, but you know, and
+ 
+
+ align:start position:0%
+best mostly up here, but you know, and
+then I would go to the library to
+
+ align:start position:0%
+then I would go to the library to
+ 
+
+ align:start position:0%
+then I would go to the library to
+confirm it. But the point is this is a
+
+ align:start position:0%
+confirm it. But the point is this is a
+ 
+
+ align:start position:0%
+confirm it. But the point is this is a
+very different life I lead now. I mean,
+
+ align:start position:0%
+very different life I lead now. I mean,
+ 
+
+ align:start position:0%
+very different life I lead now. I mean,
+I don't feel like reading most of the
+
+ align:start position:0%
+I don't feel like reading most of the
+ 
+
+ align:start position:0%
+I don't feel like reading most of the
+time. What I want to do is go out and
+
+ align:start position:0%
+time. What I want to do is go out and
+ 
+
+ align:start position:0%
+time. What I want to do is go out and
+look. I go read because I want to
+
+ align:start position:0%
+look. I go read because I want to
+ 
+
+ align:start position:0%
+look. I go read because I want to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+something, you know, but it's a very
+
+ align:start position:0%
+something, you know, but it's a very
+ 
+
+ align:start position:0%
+something, you know, but it's a very
+you're right. It's it's it's a very big
+
+ align:start position:0%
+you're right. It's it's it's a very big
+ 
+
+ align:start position:0%
+you're right. It's it's it's a very big
+change. Uh it's not that my previous
+
+ align:start position:0%
+change. Uh it's not that my previous
+ 
+
+ align:start position:0%
+change. Uh it's not that my previous
+work wasn't empirical. It was very
+
+ align:start position:0%
+work wasn't empirical. It was very
+ 
+
+ align:start position:0%
+work wasn't empirical. It was very
+empirical to my mind. But this is driven
+
+ align:start position:0%
+empirical to my mind. But this is driven
+ 
+
+ align:start position:0%
+empirical to my mind. But this is driven
+by the
+
+ align:start position:0%
+by the
+ 
+
+ align:start position:0%
+by the
+world, you know. It's what the world
+
+ align:start position:0%
+world, you know. It's what the world
+ 
+
+ align:start position:0%
+world, you know. It's what the world
+takes hold of
+
+ align:start position:0%
+takes hold of
+ 
+
+ align:start position:0%
+takes hold of
+me. Does that say and it's very
+
+ align:start position:0%
+me. Does that say and it's very
+ 
+
+ align:start position:0%
+me. Does that say and it's very
+powerful. I mean, the example is my
+
+ align:start position:0%
+powerful. I mean, the example is my
+ 
+
+ align:start position:0%
+powerful. I mean, the example is my
+walking around Boston this morning since
+
+ align:start position:0%
+walking around Boston this morning since
+ 
+
+ align:start position:0%
+walking around Boston this morning since
+I got off the plane. Uh, and I used to
+
+ align:start position:0%
+I got off the plane. Uh, and I used to
+ 
+
+ align:start position:0%
+I got off the plane. Uh, and I used to
+live here, but I never walked around. I
+
+ align:start position:0%
+live here, but I never walked around. I
+ 
+
+ align:start position:0%
+live here, but I never walked around. I
+never saw
+
+ align:start position:0%
+never saw
+ 
+
+ align:start position:0%
+never saw
+anything. And no one else I did knew
+
+ align:start position:0%
+anything. And no one else I did knew
+ 
+
+ align:start position:0%
+anything. And no one else I did knew
+either did much of it as far as I know.
+
+ align:start position:0%
+either did much of it as far as I know.
+ 
+
+ align:start position:0%
+either did much of it as far as I know.
+They must have maybe they were closet uh
+
+ align:start position:0%
+They must have maybe they were closet uh
+ 
+
+ align:start position:0%
+They must have maybe they were closet uh
+viewers but they never mentioned it. But
+
+ align:start position:0%
+viewers but they never mentioned it. But
+ 
+
+ align:start position:0%
+viewers but they never mentioned it. But
+the point was that it was so interesting
+
+ align:start position:0%
+the point was that it was so interesting
+ 
+
+ align:start position:0%
+the point was that it was so interesting
+to look at. First of all I had new eyes
+
+ align:start position:0%
+to look at. First of all I had new eyes
+ 
+
+ align:start position:0%
+to look at. First of all I had new eyes
+right because you know I've seen other
+
+ align:start position:0%
+right because you know I've seen other
+ 
+
+ align:start position:0%
+right because you know I've seen other
+places and you
+
+ align:start position:0%
+places and you
+ 
+
+ align:start position:0%
+places and you
+know it was just it the world hit me and
+
+ align:start position:0%
+know it was just it the world hit me and
+ 
+
+ align:start position:0%
+know it was just it the world hit me and
+I I don't know what to do with it now.
+
+ align:start position:0%
+I I don't know what to do with it now.
+ 
+
+ align:start position:0%
+I I don't know what to do with it now.
+And you can say come on this is just
+
+ align:start position:0%
+And you can say come on this is just
+ 
+
+ align:start position:0%
+And you can say come on this is just
+Boston probably the most studied
+
+ align:start position:0%
+Boston probably the most studied
+ 
+
+ align:start position:0%
+Boston probably the most studied
+academically studied city in America.
+
+ align:start position:0%
+academically studied city in America.
+ 
+
+ align:start position:0%
+academically studied city in America.
+All
+
+ align:start position:0%
+All
+ 
+
+ align:start position:0%
+All
+right. But maybe other than Chicago and
+
+ align:start position:0%
+right. But maybe other than Chicago and
+ 
+
+ align:start position:0%
+right. But maybe other than Chicago and
+but it was remarkable what I saw and it
+
+ align:start position:0%
+but it was remarkable what I saw and it
+ 
+
+ align:start position:0%
+but it was remarkable what I saw and it
+will force me to think again and I
+
+ align:start position:0%
+will force me to think again and I
+ 
+
+ align:start position:0%
+will force me to think again and I
+probably will have to come back and do a
+
+ align:start position:0%
+probably will have to come back and do a
+ 
+
+ align:start position:0%
+probably will have to come back and do a
+whole bunch of photographing and
+
+ align:start position:0%
+whole bunch of photographing and
+ 
+
+ align:start position:0%
+whole bunch of photographing and
+thinking and probably write things on
+
+ align:start position:0%
+thinking and probably write things on
+ 
+
+ align:start position:0%
+thinking and probably write things on
+brick and some other things. And also
+
+ align:start position:0%
+brick and some other things. And also
+ 
+
+ align:start position:0%
+brick and some other things. And also
+the most interesting phenomena is the
+
+ align:start position:0%
+the most interesting phenomena is the
+ 
+
+ align:start position:0%
+the most interesting phenomena is the
+cheek by jouness of it. It's also in Los
+
+ align:start position:0%
+cheek by jouness of it. It's also in Los
+ 
+
+ align:start position:0%
+cheek by jouness of it. It's also in Los
+Angeles. The most interesting is how
+
+ align:start position:0%
+Angeles. The most interesting is how
+ 
+
+ align:start position:0%
+Angeles. The most interesting is how
+housing and industry are cheap by jou
+
+ align:start position:0%
+housing and industry are cheap by jou
+ 
+
+ align:start position:0%
+housing and industry are cheap by jou
+all over.
+
+ align:start position:0%
+all over.
+ 
+
+ align:start position:0%
+all over.
+If your big companies know, but if
+
+ align:start position:0%
+If your big companies know, but if
+ 
+
+ align:start position:0%
+If your big companies know, but if
+smaller factories and so forth,
+
+ align:start position:0%
+smaller factories and so forth,
+ 
+
+ align:start position:0%
+smaller factories and so forth,
+historically, you have an enormous
+
+ align:start position:0%
+historically, you have an enormous
+ 
+
+ align:start position:0%
+historically, you have an enormous
+amount of housing and factories across
+
+ align:start position:0%
+amount of housing and factories across
+ 
+
+ align:start position:0%
+amount of housing and factories across
+the street from each
+
+ align:start position:0%
+the street from each
+ 
+
+ align:start position:0%
+the street from each
+other and around each
+
+ align:start position:0%
+other and around each
+ 
+
+ align:start position:0%
+other and around each
+other. And I don't know if everybody
+
+ align:start position:0%
+other. And I don't know if everybody
+ 
+
+ align:start position:0%
+other. And I don't know if everybody
+notices that here, but it was really
+
+ align:start position:0%
+notices that here, but it was really
+ 
+
+ align:start position:0%
+notices that here, but it was really
+striking to me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today. And so, yes, you're right. You're
+
+ align:start position:0%
+today. And so, yes, you're right. You're
+ 
+
+ align:start position:0%
+today. And so, yes, you're right. You're
+deeply right. I mean, I just I the best
+
+ align:start position:0%
+deeply right. I mean, I just I the best
+ 
+
+ align:start position:0%
+deeply right. I mean, I just I the best
+thing in my life is to go out and do
+
+ align:start position:0%
+thing in my life is to go out and do
+ 
+
+ align:start position:0%
+thing in my life is to go out and do
+field work.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Why don't you take that one more step,
+
+ align:start position:0%
+Why don't you take that one more step,
+ 
+
+ align:start position:0%
+Why don't you take that one more step,
+right? And say, how can the
+
+ align:start position:0%
+right? And say, how can the
+ 
+
+ align:start position:0%
+right? And say, how can the
+designer take advantage of your insights
+
+ align:start position:0%
+designer take advantage of your insights
+ 
+
+ align:start position:0%
+designer take advantage of your insights
+and your taxonomies?
+
+ align:start position:0%
+and your taxonomies?
+ 
+
+ align:start position:0%
+and your taxonomies?
+Two points. One, I think it really does
+
+ align:start position:0%
+Two points. One, I think it really does
+ 
+
+ align:start position:0%
+Two points. One, I think it really does
+say that it's worth going to look. You
+
+ align:start position:0%
+say that it's worth going to look. You
+ 
+
+ align:start position:0%
+say that it's worth going to look. You
+know, the usual line about architects is
+
+ align:start position:0%
+know, the usual line about architects is
+ 
+
+ align:start position:0%
+know, the usual line about architects is
+they go traveling with their cameras and
+
+ align:start position:0%
+they go traveling with their cameras and
+ 
+
+ align:start position:0%
+they go traveling with their cameras and
+bring home
+
+ align:start position:0%
+bring home
+ 
+
+ align:start position:0%
+bring home
+slides, you know, and um and they look,
+
+ align:start position:0%
+slides, you know, and um and they look,
+ 
+
+ align:start position:0%
+slides, you know, and um and they look,
+you know, they're looking all the time
+
+ align:start position:0%
+you know, they're looking all the time
+ 
+
+ align:start position:0%
+you know, they're looking all the time
+and you know, at least, you know, at
+
+ align:start position:0%
+and you know, at least, you know, at
+ 
+
+ align:start position:0%
+and you know, at least, you know, at
+least the architects I used to know. Um
+
+ align:start position:0%
+least the architects I used to know. Um
+ 
+
+ align:start position:0%
+least the architects I used to know. Um
+and but I think it so there's one
+
+ align:start position:0%
+and but I think it so there's one
+ 
+
+ align:start position:0%
+and but I think it so there's one
+important thing that you really need to
+
+ align:start position:0%
+important thing that you really need to
+ 
+
+ align:start position:0%
+important thing that you really need to
+go look. You can't read books. Books and
+
+ align:start position:0%
+go look. You can't read books. Books and
+ 
+
+ align:start position:0%
+go look. You can't read books. Books and
+pictures will teach you nothing unless
+
+ align:start position:0%
+pictures will teach you nothing unless
+ 
+
+ align:start position:0%
+pictures will teach you nothing unless
+you get hit in the face. I would
+
+ align:start position:0%
+you get hit in the face. I would
+ 
+
+ align:start position:0%
+you get hit in the face. I would
+maintain they teach you a lot but they
+
+ align:start position:0%
+maintain they teach you a lot but they
+ 
+
+ align:start position:0%
+maintain they teach you a lot but they
+don't teach you the deep things. All
+
+ align:start position:0%
+don't teach you the deep things. All
+ 
+
+ align:start position:0%
+don't teach you the deep things. All
+right. So that's one remark which is not
+
+ align:start position:0%
+right. So that's one remark which is not
+ 
+
+ align:start position:0%
+right. So that's one remark which is not
+the not what you asked but I mean to say
+
+ align:start position:0%
+the not what you asked but I mean to say
+ 
+
+ align:start position:0%
+the not what you asked but I mean to say
+that is probably not surprising to
+
+ align:start position:0%
+that is probably not surprising to
+ 
+
+ align:start position:0%
+that is probably not surprising to
+professors of design. You know the
+
+ align:start position:0%
+professors of design. You know the
+ 
+
+ align:start position:0%
+professors of design. You know the
+students that's what you you tell them
+
+ align:start position:0%
+students that's what you you tell them
+ 
+
+ align:start position:0%
+students that's what you you tell them
+go do fieldwork.
+
+ align:start position:0%
+go do fieldwork.
+ 
+
+ align:start position:0%
+go do fieldwork.
+Um the other point is that if I'm lucky
+
+ align:start position:0%
+Um the other point is that if I'm lucky
+ 
+
+ align:start position:0%
+Um the other point is that if I'm lucky
+what I do is make it impossible people
+
+ align:start position:0%
+what I do is make it impossible people
+ 
+
+ align:start position:0%
+what I do is make it impossible people
+not to see things. Usually after I've
+
+ align:start position:0%
+not to see things. Usually after I've
+ 
+
+ align:start position:0%
+not to see things. Usually after I've
+shown them, I put up an exhibit of
+
+ align:start position:0%
+shown them, I put up an exhibit of
+ 
+
+ align:start position:0%
+shown them, I put up an exhibit of
+something like the storefront churches,
+
+ align:start position:0%
+something like the storefront churches,
+ 
+
+ align:start position:0%
+something like the storefront churches,
+the typical remark I get is my they
+
+ align:start position:0%
+the typical remark I get is my they
+ 
+
+ align:start position:0%
+the typical remark I get is my they
+said, "My god, now they're
+
+ align:start position:0%
+said, "My god, now they're
+ 
+
+ align:start position:0%
+said, "My god, now they're
+everywhere." Because you've
+
+ align:start position:0%
+everywhere." Because you've
+ 
+
+ align:start position:0%
+everywhere." Because you've
+systematically learned not to see things
+
+ align:start position:0%
+systematically learned not to see things
+ 
+
+ align:start position:0%
+systematically learned not to see things
+and once you are sort of they become
+
+ align:start position:0%
+and once you are sort of they become
+ 
+
+ align:start position:0%
+and once you are sort of they become
+topical, what's the word? There's a word
+
+ align:start position:0%
+topical, what's the word? There's a word
+ 
+
+ align:start position:0%
+topical, what's the word? There's a word
+that they use topic
+
+ align:start position:0%
+that they use topic
+ 
+
+ align:start position:0%
+that they use topic
+um salient, but there's a nicer word
+
+ align:start position:0%
+um salient, but there's a nicer word
+ 
+
+ align:start position:0%
+um salient, but there's a nicer word
+than that. essentially when they become
+
+ align:start position:0%
+than that. essentially when they become
+ 
+
+ align:start position:0%
+than that. essentially when they become
+topics for discussion, people then start
+
+ align:start position:0%
+topics for discussion, people then start
+ 
+
+ align:start position:0%
+topics for discussion, people then start
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+things. And one of the major purposes of
+
+ align:start position:0%
+things. And one of the major purposes of
+ 
+
+ align:start position:0%
+things. And one of the major purposes of
+the work I do is to make people see
+
+ align:start position:0%
+the work I do is to make people see
+ 
+
+ align:start position:0%
+the work I do is to make people see
+things that are I mean, I told you I'm
+
+ align:start position:0%
+things that are I mean, I told you I'm
+ 
+
+ align:start position:0%
+things that are I mean, I told you I'm
+photo photographing
+
+ align:start position:0%
+photo photographing
+ 
+
+ align:start position:0%
+photo photographing
+mosses, you know, you know, in the
+
+ align:start position:0%
+mosses, you know, you know, in the
+ 
+
+ align:start position:0%
+mosses, you know, you know, in the
+cracks. And I I have a feeling it might
+
+ align:start position:0%
+cracks. And I I have a feeling it might
+ 
+
+ align:start position:0%
+cracks. And I I have a feeling it might
+be interesting, but it might not be. I
+
+ align:start position:0%
+be interesting, but it might not be. I
+ 
+
+ align:start position:0%
+be interesting, but it might not be. I
+haven't found a useful botist yet. Uh
+
+ align:start position:0%
+haven't found a useful botist yet. Uh
+ 
+
+ align:start position:0%
+haven't found a useful botist yet. Uh
+there's lots of people by the way if you
+
+ align:start position:0%
+there's lots of people by the way if you
+ 
+
+ align:start position:0%
+there's lots of people by the way if you
+care about something called roadside
+
+ align:start position:0%
+care about something called roadside
+ 
+
+ align:start position:0%
+care about something called roadside
+ecology where people worry about um you
+
+ align:start position:0%
+ecology where people worry about um you
+ 
+
+ align:start position:0%
+ecology where people worry about um you
+know what happens on roads and there's
+
+ align:start position:0%
+know what happens on roads and there's
+ 
+
+ align:start position:0%
+know what happens on roads and there's
+lots of money for it but this is in
+
+ align:start position:0%
+lots of money for it but this is in
+ 
+
+ align:start position:0%
+lots of money for it but this is in
+cities you know and there I found one
+
+ align:start position:0%
+cities you know and there I found one
+ 
+
+ align:start position:0%
+cities you know and there I found one
+essay on mosses in cities but once
+
+ align:start position:0%
+essay on mosses in cities but once
+ 
+
+ align:start position:0%
+essay on mosses in cities but once
+people hear about this they can't help
+
+ align:start position:0%
+people hear about this they can't help
+ 
+
+ align:start position:0%
+people hear about this they can't help
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+see especially if I have something
+
+ align:start position:0%
+see especially if I have something
+ 
+
+ align:start position:0%
+see especially if I have something
+interesting to say which at the moment I
+
+ align:start position:0%
+interesting to say which at the moment I
+ 
+
+ align:start position:0%
+interesting to say which at the moment I
+don't. Does that answer a little bit? I
+
+ align:start position:0%
+don't. Does that answer a little bit? I
+ 
+
+ align:start position:0%
+don't. Does that answer a little bit? I
+mean I don't in other words I don't know
+
+ align:start position:0%
+mean I don't in other words I don't know
+ 
+
+ align:start position:0%
+mean I don't in other words I don't know
+if anything I say is so important as the
+
+ align:start position:0%
+if anything I say is so important as the
+ 
+
+ align:start position:0%
+if anything I say is so important as the
+fact that it's there that's
+
+ align:start position:0%
+fact that it's there that's
+ 
+
+ align:start position:0%
+fact that it's there that's
+unavoidable you know it's just
+
+ align:start position:0%
+unavoidable you know it's just
+ 
+
+ align:start position:0%
+unavoidable you know it's just
+unavoidable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um or when I talk about stuff um worship
+
+ align:start position:0%
+um or when I talk about stuff um worship
+ 
+
+ align:start position:0%
+um or when I talk about stuff um worship
+uh it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doesn't there's nothing profound there
+
+ align:start position:0%
+doesn't there's nothing profound there
+ 
+
+ align:start position:0%
+doesn't there's nothing profound there
+it's just that people don't take it
+
+ align:start position:0%
+it's just that people don't take it
+ 
+
+ align:start position:0%
+it's just that people don't take it
+seriously if that's what I mean you know
+
+ align:start position:0%
+seriously if that's what I mean you know
+ 
+
+ align:start position:0%
+seriously if that's what I mean you know
+they sort dismiss it unless they're
+
+ align:start position:0%
+they sort dismiss it unless they're
+ 
+
+ align:start position:0%
+they sort dismiss it unless they're
+professor of religion or a believer. But
+
+ align:start position:0%
+professor of religion or a believer. But
+ 
+
+ align:start position:0%
+professor of religion or a believer. But
+there's other places ways to take it
+
+ align:start position:0%
+there's other places ways to take it
+ 
+
+ align:start position:0%
+there's other places ways to take it
+seriously.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um I think that's the most useful thing
+
+ align:start position:0%
+Um I think that's the most useful thing
+ 
+
+ align:start position:0%
+Um I think that's the most useful thing
+or that you see the other way to put
+
+ align:start position:0%
+or that you see the other way to put
+ 
+
+ align:start position:0%
+or that you see the other way to put
+this is that what you have to learn as a
+
+ align:start position:0%
+this is that what you have to learn as a
+ 
+
+ align:start position:0%
+this is that what you have to learn as a
+designer is that things just don't
+
+ align:start position:0%
+designer is that things just don't
+ 
+
+ align:start position:0%
+designer is that things just don't
+happen. They're happening for a set of
+
+ align:start position:0%
+happen. They're happening for a set of
+ 
+
+ align:start position:0%
+happen. They're happening for a set of
+usually political, sociological,
+
+ align:start position:0%
+usually political, sociological,
+ 
+
+ align:start position:0%
+usually political, sociological,
+economic reasons. And there there's a
+
+ align:start position:0%
+economic reasons. And there there's a
+ 
+
+ align:start position:0%
+economic reasons. And there there's a
+reason why the storefront churches are
+
+ align:start position:0%
+reason why the storefront churches are
+ 
+
+ align:start position:0%
+reason why the storefront churches are
+where they are. And there's a story
+
+ align:start position:0%
+where they are. And there's a story
+ 
+
+ align:start position:0%
+where they are. And there's a story
+behind that. And so it's not just things
+
+ align:start position:0%
+behind that. And so it's not just things
+ 
+
+ align:start position:0%
+behind that. And so it's not just things
+happen, they happen in a coherent way,
+
+ align:start position:0%
+happen, they happen in a coherent way,
+ 
+
+ align:start position:0%
+happen, they happen in a coherent way,
+in a meaningful
+
+ align:start position:0%
+in a meaningful
+ 
+
+ align:start position:0%
+in a meaningful
+way. And that changes things because
+
+ align:start position:0%
+way. And that changes things because
+ 
+
+ align:start position:0%
+way. And that changes things because
+then it becomes a linked set of motives.
+
+ align:start position:0%
+then it becomes a linked set of motives.
+ 
+
+ align:start position:0%
+then it becomes a linked set of motives.
+And what you see and how it works are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+related. And that seems to be a deeply
+
+ align:start position:0%
+related. And that seems to be a deeply
+ 
+
+ align:start position:0%
+related. And that seems to be a deeply
+important thing for people who do do
+
+ align:start position:0%
+important thing for people who do do
+ 
+
+ align:start position:0%
+important thing for people who do do
+design. They know this sort of. They're
+
+ align:start position:0%
+design. They know this sort of. They're
+ 
+
+ align:start position:0%
+design. They know this sort of. They're
+not stupid. It's just not part of
+
+ align:start position:0%
+not stupid. It's just not part of
+ 
+
+ align:start position:0%
+not stupid. It's just not part of
+their breadandbut way of thinking in
+
+ align:start position:0%
+their breadandbut way of thinking in
+ 
+
+ align:start position:0%
+their breadandbut way of thinking in
+general. That's why city planners and
+
+ align:start position:0%
+general. That's why city planners and
+ 
+
+ align:start position:0%
+general. That's why city planners and
+designers are often so very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+anything one final thought in that
+
+ align:start position:0%
+anything one final thought in that
+ 
+
+ align:start position:0%
+anything one final thought in that
+respect what you're doing for us is
+
+ align:start position:0%
+respect what you're doing for us is
+ 
+
+ align:start position:0%
+respect what you're doing for us is
+saying you must attend to greater number
+
+ align:start position:0%
+saying you must attend to greater number
+ 
+
+ align:start position:0%
+saying you must attend to greater number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+conditions and
+
+ align:start position:0%
+conditions and
+ 
+
+ align:start position:0%
+conditions and
+everything you've got to be reasonably
+
+ align:start position:0%
+everything you've got to be reasonably
+ 
+
+ align:start position:0%
+everything you've got to be reasonably
+flat your
+
+ align:start position:0%
+flat your
+ 
+
+ align:start position:0%
+flat your
+priorities with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deceased. So
+
+ align:start position:0%
+deceased. So
+ 
+
+ align:start position:0%
+deceased. So
+it's number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the gentleman over there was saying to
+
+ align:start position:0%
+the gentleman over there was saying to
+ 
+
+ align:start position:0%
+the gentleman over there was saying to
+me well could you do it with everything?
+
+ align:start position:0%
+me well could you do it with everything?
+ 
+
+ align:start position:0%
+me well could you do it with everything?
+I think it's not true that everything
+
+ align:start position:0%
+I think it's not true that everything
+ 
+
+ align:start position:0%
+I think it's not true that everything
+counts but the idea is to learn a few
+
+ align:start position:0%
+counts but the idea is to learn a few
+ 
+
+ align:start position:0%
+counts but the idea is to learn a few
+more things. I mean, you can't tell
+
+ align:start position:0%
+more things. I mean, you can't tell
+ 
+
+ align:start position:0%
+more things. I mean, you can't tell
+people everything counts because that's
+
+ align:start position:0%
+people everything counts because that's
+ 
+
+ align:start position:0%
+people everything counts because that's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+disastrous. You know, that's that's the
+
+ align:start position:0%
+disastrous. You know, that's that's the
+ 
+
+ align:start position:0%
+disastrous. You know, that's that's the
+kind of advice that that's paralyzing.
+
+ align:start position:0%
+kind of advice that that's paralyzing.
+ 
+
+ align:start position:0%
+kind of advice that that's paralyzing.
+But to give them more things that
+
+ align:start position:0%
+But to give them more things that
+ 
+
+ align:start position:0%
+But to give them more things that
+count is just
+
+ align:start position:0%
+count is just
+ 
+
+ align:start position:0%
+count is just
+amazing. And if you choose the things
+
+ align:start position:0%
+amazing. And if you choose the things
+ 
+
+ align:start position:0%
+amazing. And if you choose the things
+with some
+
+ align:start position:0%
+with some
+ 
+
+ align:start position:0%
+with some
+care, you know, it could be this Morse
+
+ align:start position:0%
+care, you know, it could be this Morse
+ 
+
+ align:start position:0%
+care, you know, it could be this Morse
+idea is ridiculous and stupid, you know,
+
+ align:start position:0%
+idea is ridiculous and stupid, you know,
+ 
+
+ align:start position:0%
+idea is ridiculous and stupid, you know,
+that I really can't go any place with
+
+ align:start position:0%
+that I really can't go any place with
+ 
+
+ align:start position:0%
+that I really can't go any place with
+it. Uh, but we'll see. And the sound
+
+ align:start position:0%
+it. Uh, but we'll see. And the sound
+ 
+
+ align:start position:0%
+it. Uh, but we'll see. And the sound
+stuff I don't think will be stupid but
+
+ align:start position:0%
+stuff I don't think will be stupid but
+ 
+
+ align:start position:0%
+stuff I don't think will be stupid but
+you know it might turn out not to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+productive. It's an empirical it's
+
+ align:start position:0%
+productive. It's an empirical it's
+ 
+
+ align:start position:0%
+productive. It's an empirical it's
+a intellectual question. Can you make
+
+ align:start position:0%
+a intellectual question. Can you make
+ 
+
+ align:start position:0%
+a intellectual question. Can you make
+something of it?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. I mean you know it it my thing I'm
+
+ align:start position:0%
+Yeah. I mean you know it it my thing I'm
+ 
+
+ align:start position:0%
+Yeah. I mean you know it it my thing I'm
+right now thinking about is what does it
+
+ align:start position:0%
+right now thinking about is what does it
+ 
+
+ align:start position:0%
+right now thinking about is what does it
+sound like to be in your apartment with
+
+ align:start position:0%
+sound like to be in your apartment with
+ 
+
+ align:start position:0%
+sound like to be in your apartment with
+traffic
+
+ align:start position:0%
+traffic
+ 
+
+ align:start position:0%
+traffic
+outside and how you don't hear it. Where
+
+ align:start position:0%
+outside and how you don't hear it. Where
+ 
+
+ align:start position:0%
+outside and how you don't hear it. Where
+I live, there's always accidents and
+
+ align:start position:0%
+I live, there's always accidents and
+ 
+
+ align:start position:0%
+I live, there's always accidents and
+most of the time you hear a crash, you
+
+ align:start position:0%
+most of the time you hear a crash, you
+ 
+
+ align:start position:0%
+most of the time you hear a crash, you
+don't do anything. You go on, you know,
+
+ align:start position:0%
+don't do anything. You go on, you know,
+ 
+
+ align:start position:0%
+don't do anything. You go on, you know,
+after a while. It's
+
+ align:start position:0%
+after a while. It's
+ 
+
+ align:start position:0%
+after a while. It's
+interesting.
+
+ align:start position:0%
+interesting.
+ 
+
+ align:start position:0%
+interesting.
+Um, I don't know what I'm talking about
+
+ align:start position:0%
+Um, I don't know what I'm talking about
+ 
+
+ align:start position:0%
+Um, I don't know what I'm talking about
+here, but hopefully in a year I will. My
+
+ align:start position:0%
+here, but hopefully in a year I will. My
+ 
+
+ align:start position:0%
+here, but hopefully in a year I will. My
+friends who do sound design and sound
+
+ align:start position:0%
+friends who do sound design and sound
+ 
+
+ align:start position:0%
+friends who do sound design and sound
+editing for films, they're very
+
+ align:start position:0%
+editing for films, they're very
+ 
+
+ align:start position:0%
+editing for films, they're very
+articulate about using
+
+ align:start position:0%
+articulate about using
+ 
+
+ align:start position:0%
+articulate about using
+sound. They know exactly what they want.
+
+ align:start position:0%
+sound. They know exactly what they want.
+ 
+
+ align:start position:0%
+sound. They know exactly what they want.
+Not exactly, but you know, for them it's
+
+ align:start position:0%
+Not exactly, but you know, for them it's
+ 
+
+ align:start position:0%
+Not exactly, but you know, for them it's
+it's a it's a vocabulary rich laden
+
+ align:start position:0%
+it's a it's a vocabulary rich laden
+ 
+
+ align:start position:0%
+it's a it's a vocabulary rich laden
+thing, but and their thing is to create
+
+ align:start position:0%
+thing, but and their thing is to create
+ 
+
+ align:start position:0%
+thing, but and their thing is to create
+an ordinary feeling. You know what I
+
+ align:start position:0%
+an ordinary feeling. You know what I
+ 
+
+ align:start position:0%
+an ordinary feeling. You know what I
+mean? They're trying remember their
+
+ align:start position:0%
+mean? They're trying remember their
+ 
+
+ align:start position:0%
+mean? They're trying remember their
+problem is there is no good ordinary
+
+ align:start position:0%
+problem is there is no good ordinary
+ 
+
+ align:start position:0%
+problem is there is no good ordinary
+sound to be recorded. They have to put
+
+ align:start position:0%
+sound to be recorded. They have to put
+ 
+
+ align:start position:0%
+sound to be recorded. They have to put
+it all in because the background sound
+
+ align:start position:0%
+it all in because the background sound
+ 
+
+ align:start position:0%
+it all in because the background sound
+is never
+
+ align:start position:0%
+is never
+ 
+
+ align:start position:0%
+is never
+right. you know, the background sound in
+
+ align:start position:0%
+right. you know, the background sound in
+ 
+
+ align:start position:0%
+right. you know, the background sound in
+the in the in the in the uh studio or
+
+ align:start position:0%
+the in the in the in the uh studio or
+ 
+
+ align:start position:0%
+the in the in the in the uh studio or
+even on on uh on stage, they're always
+
+ align:start position:0%
+even on on uh on stage, they're always
+ 
+
+ align:start position:0%
+even on on uh on stage, they're always
+they're completely artificial about
+
+ align:start position:0%
+they're completely artificial about
+ 
+
+ align:start position:0%
+they're completely artificial about
+it. And uh and think of lighting in
+
+ align:start position:0%
+it. And uh and think of lighting in
+ 
+
+ align:start position:0%
+it. And uh and think of lighting in
+theater,
+
+ align:start position:0%
+theater,
+ 
+
+ align:start position:0%
+theater,
+right? Where it's all, you know, let
+
+ align:start position:0%
+right? Where it's all, you know, let
+ 
+
+ align:start position:0%
+right? Where it's all, you know, let
+there be light. Each each lighting
+
+ align:start position:0%
+there be light. Each each lighting
+ 
+
+ align:start position:0%
+there be light. Each each lighting
+designer is like God.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There were some questions that did you
+
+ align:start position:0%
+There were some questions that did you
+ 
+
+ align:start position:0%
+There were some questions that did you
+have a question before? Yeah. Yeah.
+
+ align:start position:0%
+have a question before? Yeah. Yeah.
+ 
+
+ align:start position:0%
+have a question before? Yeah. Yeah.
+Well, I was I was going to ask I think
+
+ align:start position:0%
+Well, I was I was going to ask I think
+ 
+
+ align:start position:0%
+Well, I was I was going to ask I think
+you sort of revealed the answer, but I
+
+ align:start position:0%
+you sort of revealed the answer, but I
+ 
+
+ align:start position:0%
+you sort of revealed the answer, but I
+was I was going to ask about your
+
+ align:start position:0%
+was I was going to ask about your
+ 
+
+ align:start position:0%
+was I was going to ask about your
+comment when you said, you know, perhaps
+
+ align:start position:0%
+comment when you said, you know, perhaps
+ 
+
+ align:start position:0%
+comment when you said, you know, perhaps
+800 makes a better argument than 600.
+
+ align:start position:0%
+800 makes a better argument than 600.
+ 
+
+ align:start position:0%
+800 makes a better argument than 600.
+But what is your argument? But it sounds
+
+ align:start position:0%
+But what is your argument? But it sounds
+ 
+
+ align:start position:0%
+But what is your argument? But it sounds
+like your argument is this exists. Um
+
+ align:start position:0%
+like your argument is this exists. Um
+ 
+
+ align:start position:0%
+like your argument is this exists. Um
+you give us the future. Well, no. That
+
+ align:start position:0%
+you give us the future. Well, no. That
+ 
+
+ align:start position:0%
+you give us the future. Well, no. That
+was a joke partially. Probably I could
+
+ align:start position:0%
+was a joke partially. Probably I could
+ 
+
+ align:start position:0%
+was a joke partially. Probably I could
+have stopped at 600. All right. Uh I
+
+ align:start position:0%
+have stopped at 600. All right. Uh I
+ 
+
+ align:start position:0%
+have stopped at 600. All right. Uh I
+couldn't have stopped at 100. I know
+
+ align:start position:0%
+couldn't have stopped at 100. I know
+ 
+
+ align:start position:0%
+couldn't have stopped at 100. I know
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+And I could have could I have stopped at
+
+ align:start position:0%
+And I could have could I have stopped at
+ 
+
+ align:start position:0%
+And I could have could I have stopped at
+400? Probably. All right. But there were
+
+ align:start position:0%
+400? Probably. All right. But there were
+ 
+
+ align:start position:0%
+400? Probably. All right. But there were
+questions of represent
+
+ align:start position:0%
+questions of represent
+ 
+
+ align:start position:0%
+questions of represent
+representativeness. I had it wasn't on
+
+ align:start position:0%
+representativeness. I had it wasn't on
+ 
+
+ align:start position:0%
+representativeness. I had it wasn't on
+400, but I needed some other parts of
+
+ align:start position:0%
+400, but I needed some other parts of
+ 
+
+ align:start position:0%
+400, but I needed some other parts of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+city. I had a feel like I was running
+
+ align:start position:0%
+city. I had a feel like I was running
+ 
+
+ align:start position:0%
+city. I had a feel like I was running
+out of interesting cases.
+
+ align:start position:0%
+out of interesting cases.
+ 
+
+ align:start position:0%
+out of interesting cases.
+I mean, I've gone to about 40 um clothes
+
+ align:start position:0%
+I mean, I've gone to about 40 um clothes
+ 
+
+ align:start position:0%
+I mean, I've gone to about 40 um clothes
+manufacturers in Los Angeles, you know,
+
+ align:start position:0%
+manufacturers in Los Angeles, you know,
+ 
+
+ align:start position:0%
+manufacturers in Los Angeles, you know,
+where they do sewing or cutting, maybe
+
+ align:start position:0%
+where they do sewing or cutting, maybe
+ 
+
+ align:start position:0%
+where they do sewing or cutting, maybe
+more. All right. At some point, it
+
+ align:start position:0%
+more. All right. At some point, it
+ 
+
+ align:start position:0%
+more. All right. At some point, it
+doesn't seem like I'm going to learn
+
+ align:start position:0%
+doesn't seem like I'm going to learn
+ 
+
+ align:start position:0%
+doesn't seem like I'm going to learn
+anymore. I went to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe, let me give you another example.
+
+ align:start position:0%
+maybe, let me give you another example.
+ 
+
+ align:start position:0%
+maybe, let me give you another example.
+I went to one very large foundry where
+
+ align:start position:0%
+I went to one very large foundry where
+ 
+
+ align:start position:0%
+I went to one very large foundry where
+they make things like for Saturn rockets
+
+ align:start position:0%
+they make things like for Saturn rockets
+ 
+
+ align:start position:0%
+they make things like for Saturn rockets
+the the round parts the thing that holds
+
+ align:start position:0%
+the the round parts the thing that holds
+ 
+
+ align:start position:0%
+the the round parts the thing that holds
+it the bands and so forth and that's
+
+ align:start position:0%
+it the bands and so forth and that's
+ 
+
+ align:start position:0%
+it the bands and so forth and that's
+very high purity metal you know you can
+
+ align:start position:0%
+very high purity metal you know you can
+ 
+
+ align:start position:0%
+very high purity metal you know you can
+imagine and it has the biggest you know
+
+ align:start position:0%
+imagine and it has the biggest you know
+ 
+
+ align:start position:0%
+imagine and it has the biggest you know
+forge in the west coast or maybe in the
+
+ align:start position:0%
+forge in the west coast or maybe in the
+ 
+
+ align:start position:0%
+forge in the west coast or maybe in the
+world whatnot and it might be nice to go
+
+ align:start position:0%
+world whatnot and it might be nice to go
+ 
+
+ align:start position:0%
+world whatnot and it might be nice to go
+to another one but one's enough probably
+
+ align:start position:0%
+to another one but one's enough probably
+ 
+
+ align:start position:0%
+to another one but one's enough probably
+of that on the other hand there is a
+
+ align:start position:0%
+of that on the other hand there is a
+ 
+
+ align:start position:0%
+of that on the other hand there is a
+foundry in downtown Los Angeles, which
+
+ align:start position:0%
+foundry in downtown Los Angeles, which
+ 
+
+ align:start position:0%
+foundry in downtown Los Angeles, which
+my favorite one called Alphacast. And
+
+ align:start position:0%
+my favorite one called Alphacast. And
+ 
+
+ align:start position:0%
+my favorite one called Alphacast. And
+what do they make? They make things like
+
+ align:start position:0%
+what do they make? They make things like
+ 
+
+ align:start position:0%
+what do they make? They make things like
+light poles, you know, and those
+
+ align:start position:0%
+light poles, you know, and those
+ 
+
+ align:start position:0%
+light poles, you know, and those
+decorated things out of cast aluminum
+
+ align:start position:0%
+decorated things out of cast aluminum
+ 
+
+ align:start position:0%
+decorated things out of cast aluminum
+and all right. And I'm convinced that
+
+ align:start position:0%
+and all right. And I'm convinced that
+ 
+
+ align:start position:0%
+and all right. And I'm convinced that
+what I need to do there is not go to
+
+ align:start position:0%
+what I need to do there is not go to
+ 
+
+ align:start position:0%
+what I need to do there is not go to
+other foundaries, but study this one
+
+ align:start position:0%
+other foundaries, but study this one
+ 
+
+ align:start position:0%
+other foundaries, but study this one
+better, more because the men there,
+
+ align:start position:0%
+better, more because the men there,
+ 
+
+ align:start position:0%
+better, more because the men there,
+first of all, they know me finally. You
+
+ align:start position:0%
+first of all, they know me finally. You
+ 
+
+ align:start position:0%
+first of all, they know me finally. You
+know, they're used to this guy who keeps
+
+ align:start position:0%
+know, they're used to this guy who keeps
+ 
+
+ align:start position:0%
+know, they're used to this guy who keeps
+showing up. But they they're friendly
+
+ align:start position:0%
+showing up. But they they're friendly
+ 
+
+ align:start position:0%
+showing up. But they they're friendly
+and they work together and they, you
+
+ align:start position:0%
+and they work together and they, you
+ 
+
+ align:start position:0%
+and they work together and they, you
+know, it's a very coordinated business.
+
+ align:start position:0%
+know, it's a very coordinated business.
+ 
+
+ align:start position:0%
+know, it's a very coordinated business.
+You know, I don't know if you know that
+
+ align:start position:0%
+You know, I don't know if you know that
+ 
+
+ align:start position:0%
+You know, I don't know if you know that
+many kinds of work are are really quite
+
+ align:start position:0%
+many kinds of work are are really quite
+ 
+
+ align:start position:0%
+many kinds of work are are really quite
+dangerous. For example, working at the
+
+ align:start position:0%
+dangerous. For example, working at the
+ 
+
+ align:start position:0%
+dangerous. For example, working at the
+ports is extremely dangerous because all
+
+ align:start position:0%
+ports is extremely dangerous because all
+ 
+
+ align:start position:0%
+ports is extremely dangerous because all
+you need to do is have a uh a um
+
+ align:start position:0%
+you need to do is have a uh a um
+ 
+
+ align:start position:0%
+you need to do is have a uh a um
+container fall on
+
+ align:start position:0%
+container fall on
+ 
+
+ align:start position:0%
+container fall on
+you splat. All right? And this
+
+ align:start position:0%
+you splat. All right? And this
+ 
+
+ align:start position:0%
+you splat. All right? And this
+happens. So, um it's um so let me give
+
+ align:start position:0%
+happens. So, um it's um so let me give
+ 
+
+ align:start position:0%
+happens. So, um it's um so let me give
+an example of that. And I I had a guy
+
+ align:start position:0%
+an example of that. And I I had a guy
+ 
+
+ align:start position:0%
+an example of that. And I I had a guy
+who took me to the ports. He was a high
+
+ align:start position:0%
+who took me to the ports. He was a high
+ 
+
+ align:start position:0%
+who took me to the ports. He was a high
+guy in the ILW, International Longshore
+
+ align:start position:0%
+guy in the ILW, International Longshore
+ 
+
+ align:start position:0%
+guy in the ILW, International Longshore
+Workers, Longshore and Warehouse Workers
+
+ align:start position:0%
+Workers, Longshore and Warehouse Workers
+ 
+
+ align:start position:0%
+Workers, Longshore and Warehouse Workers
+Union, which is the West Coast Union.
+
+ align:start position:0%
+Union, which is the West Coast Union.
+ 
+
+ align:start position:0%
+Union, which is the West Coast Union.
+It's much less corrupt than the East
+
+ align:start position:0%
+It's much less corrupt than the East
+ 
+
+ align:start position:0%
+It's much less corrupt than the East
+Coast one. All right. Harry Bridges, you
+
+ align:start position:0%
+Coast one. All right. Harry Bridges, you
+ 
+
+ align:start position:0%
+Coast one. All right. Harry Bridges, you
+ever hear of him? He was he he was an
+
+ align:start position:0%
+ever hear of him? He was he he was an
+ 
+
+ align:start position:0%
+ever hear of him? He was he he was an
+Australian guy. He was a communist. You
+
+ align:start position:0%
+Australian guy. He was a communist. You
+ 
+
+ align:start position:0%
+Australian guy. He was a communist. You
+can imagine how popular he was at a
+
+ align:start position:0%
+can imagine how popular he was at a
+ 
+
+ align:start position:0%
+can imagine how popular he was at a
+certain time. He was the leader. All
+
+ align:start position:0%
+certain time. He was the leader. All
+ 
+
+ align:start position:0%
+certain time. He was the leader. All
+right. And worth knowing about. And so
+
+ align:start position:0%
+right. And worth knowing about. And so
+ 
+
+ align:start position:0%
+right. And worth knowing about. And so
+so um Dominic took me around. Dominic's
+
+ align:start position:0%
+so um Dominic took me around. Dominic's
+ 
+
+ align:start position:0%
+so um Dominic took me around. Dominic's
+father was the founder, one of the
+
+ align:start position:0%
+father was the founder, one of the
+ 
+
+ align:start position:0%
+father was the founder, one of the
+founders of the union, I'm told. And
+
+ align:start position:0%
+founders of the union, I'm told. And
+ 
+
+ align:start position:0%
+founders of the union, I'm told. And
+Dominic is about
+
+ align:start position:0%
+Dominic is about
+ 
+
+ align:start position:0%
+Dominic is about
+72. He still works at the port. He's
+
+ align:start position:0%
+72. He still works at the port. He's
+ 
+
+ align:start position:0%
+72. He still works at the port. He's
+also a professor at a local community
+
+ align:start position:0%
+also a professor at a local community
+ 
+
+ align:start position:0%
+also a professor at a local community
+college. And so we went to uh about
+
+ align:start position:0%
+college. And so we went to uh about
+ 
+
+ align:start position:0%
+college. And so we went to uh about
+seven different kinds of ships, roll on,
+
+ align:start position:0%
+seven different kinds of ships, roll on,
+ 
+
+ align:start position:0%
+seven different kinds of ships, roll on,
+roll off, uh so-called bulk loaders. I
+
+ align:start position:0%
+roll off, uh so-called bulk loaders. I
+ 
+
+ align:start position:0%
+roll off, uh so-called bulk loaders. I
+could give you the names of all these.
+
+ align:start position:0%
+could give you the names of all these.
+ 
+
+ align:start position:0%
+could give you the names of all these.
+All right? And he wanted me to see it.
+
+ align:start position:0%
+All right? And he wanted me to see it.
+ 
+
+ align:start position:0%
+All right? And he wanted me to see it.
+Now, you know, he had his own agenda. He
+
+ align:start position:0%
+Now, you know, he had his own agenda. He
+ 
+
+ align:start position:0%
+Now, you know, he had his own agenda. He
+wanted me to show the men at work and be
+
+ align:start position:0%
+wanted me to show the men at work and be
+ 
+
+ align:start position:0%
+wanted me to show the men at work and be
+sympathetic to them, but I come from the
+
+ align:start position:0%
+sympathetic to them, but I come from the
+ 
+
+ align:start position:0%
+sympathetic to them, but I come from the
+background where that's free. So that
+
+ align:start position:0%
+background where that's free. So that
+ 
+
+ align:start position:0%
+background where that's free. So that
+wasn't he didn't have to work on me. But
+
+ align:start position:0%
+wasn't he didn't have to work on me. But
+ 
+
+ align:start position:0%
+wasn't he didn't have to work on me. But
+um and so I was able to go to, you know,
+
+ align:start position:0%
+um and so I was able to go to, you know,
+ 
+
+ align:start position:0%
+um and so I was able to go to, you know,
+seven or eight
+
+ align:start position:0%
+seven or eight
+ 
+
+ align:start position:0%
+seven or eight
+sites. Um should I go to more is a
+
+ align:start position:0%
+sites. Um should I go to more is a
+ 
+
+ align:start position:0%
+sites. Um should I go to more is a
+question. I don't think so. All right.
+
+ align:start position:0%
+question. I don't think so. All right.
+ 
+
+ align:start position:0%
+question. I don't think so. All right.
+But it might be interesting, but I'm not
+
+ align:start position:0%
+But it might be interesting, but I'm not
+ 
+
+ align:start position:0%
+But it might be interesting, but I'm not
+going to cuz it was hard to gain access.
+
+ align:start position:0%
+going to cuz it was hard to gain access.
+ 
+
+ align:start position:0%
+going to cuz it was hard to gain access.
+But I went to every main kind of ship,
+
+ align:start position:0%
+But I went to every main kind of ship,
+ 
+
+ align:start position:0%
+But I went to every main kind of ship,
+you know, freight ship from container
+
+ align:start position:0%
+you know, freight ship from container
+ 
+
+ align:start position:0%
+you know, freight ship from container
+ships. Oh, I let me show you this with
+
+ align:start position:0%
+ships. Oh, I let me show you this with
+ 
+
+ align:start position:0%
+ships. Oh, I let me show you this with
+just for the f just to
+
+ align:start position:0%
+just for the f just to
+ 
+
+ align:start position:0%
+just for the f just to
+brag. Um, oh god, these problem with all
+
+ align:start position:0%
+brag. Um, oh god, these problem with all
+ 
+
+ align:start position:0%
+brag. Um, oh god, these problem with all
+this stuff is that we've worked so hard
+
+ align:start position:0%
+this stuff is that we've worked so hard
+ 
+
+ align:start position:0%
+this stuff is that we've worked so hard
+at producing this that I can't find it.
+
+ align:start position:0%
+at producing this that I can't find it.
+ 
+
+ align:start position:0%
+at producing this that I can't find it.
+Let me get rid of some of these. I want
+
+ align:start position:0%
+Let me get rid of some of these. I want
+ 
+
+ align:start position:0%
+Let me get rid of some of these. I want
+to show you uh one other
+
+ align:start position:0%
+to show you uh one other
+ 
+
+ align:start position:0%
+to show you uh one other
+thing. Yeah, these are photographs I
+
+ align:start position:0%
+thing. Yeah, these are photographs I
+ 
+
+ align:start position:0%
+thing. Yeah, these are photographs I
+took. Where are they? Oh god. Come on.
+
+ align:start position:0%
+took. Where are they? Oh god. Come on.
+ 
+
+ align:start position:0%
+took. Where are they? Oh god. Come on.
+Are they here? No. Here. These
+
+ align:start position:0%
+Are they here? No. Here. These
+ 
+
+ align:start position:0%
+Are they here? No. Here. These
+photographs here are you see them in the
+
+ align:start position:0%
+photographs here are you see them in the
+ 
+
+ align:start position:0%
+photographs here are you see them in the
+poster. This is a couple actually. They
+
+ align:start position:0%
+poster. This is a couple actually. They
+ 
+
+ align:start position:0%
+poster. This is a couple actually. They
+met in the union hiring call. All right.
+
+ align:start position:0%
+met in the union hiring call. All right.
+ 
+
+ align:start position:0%
+met in the union hiring call. All right.
+And they are called frontmen. The things
+
+ align:start position:0%
+And they are called frontmen. The things
+ 
+
+ align:start position:0%
+And they are called frontmen. The things
+coming off the ship. This is looking
+
+ align:start position:0%
+coming off the ship. This is looking
+ 
+
+ align:start position:0%
+coming off the ship. This is looking
+into the hold of a ship. This is uh some
+
+ align:start position:0%
+into the hold of a ship. This is uh some
+ 
+
+ align:start position:0%
+into the hold of a ship. This is uh some
+of the documents that go on. This is I
+
+ align:start position:0%
+of the documents that go on. This is I
+ 
+
+ align:start position:0%
+of the documents that go on. This is I
+was I was up at 10tory high in a
+
+ align:start position:0%
+was I was up at 10tory high in a
+ 
+
+ align:start position:0%
+was I was up at 10tory high in a
+crane. That's my bragging. And it's a
+
+ align:start position:0%
+crane. That's my bragging. And it's a
+ 
+
+ align:start position:0%
+crane. That's my bragging. And it's a
+woman doing it. She's she's a crane
+
+ align:start position:0%
+woman doing it. She's she's a crane
+ 
+
+ align:start position:0%
+woman doing it. She's she's a crane
+operator. And then you ask, "How'd she
+
+ align:start position:0%
+operator. And then you ask, "How'd she
+ 
+
+ align:start position:0%
+operator. And then you ask, "How'd she
+get to be a crane operator?" There's a
+
+ align:start position:0%
+get to be a crane operator?" There's a
+ 
+
+ align:start position:0%
+get to be a crane operator?" There's a
+story. Um, these guys love their work.
+
+ align:start position:0%
+story. Um, these guys love their work.
+ 
+
+ align:start position:0%
+story. Um, these guys love their work.
+They're really terrific at stowing and
+
+ align:start position:0%
+They're really terrific at stowing and
+ 
+
+ align:start position:0%
+They're really terrific at stowing and
+untowing things. They really like doing
+
+ align:start position:0%
+untowing things. They really like doing
+ 
+
+ align:start position:0%
+untowing things. They really like doing
+their work. I mean, I met them and
+
+ align:start position:0%
+their work. I mean, I met them and
+ 
+
+ align:start position:0%
+their work. I mean, I met them and
+talked to them.
+
+ align:start position:0%
+talked to them.
+ 
+
+ align:start position:0%
+talked to them.
+Um, yeah. What's his name? Oh, I forgot
+
+ align:start position:0%
+Um, yeah. What's his name? Oh, I forgot
+ 
+
+ align:start position:0%
+Um, yeah. What's his name? Oh, I forgot
+his name. I met him see him. I kept
+
+ align:start position:0%
+his name. I met him see him. I kept
+ 
+
+ align:start position:0%
+his name. I met him see him. I kept
+meeting him at various different having
+
+ align:start position:0%
+meeting him at various different having
+ 
+
+ align:start position:0%
+meeting him at various different having
+different jobs. when they load up a
+
+ align:start position:0%
+different jobs. when they load up a
+ 
+
+ align:start position:0%
+different jobs. when they load up a
+ship, the idea is you have to make it
+
+ align:start position:0%
+ship, the idea is you have to make it
+ 
+
+ align:start position:0%
+ship, the idea is you have to make it
+sort of uniform otherwise the ship will
+
+ align:start position:0%
+sort of uniform otherwise the ship will
+ 
+
+ align:start position:0%
+sort of uniform otherwise the ship will
+tilt and which is not what you want. Uh
+
+ align:start position:0%
+tilt and which is not what you want. Uh
+ 
+
+ align:start position:0%
+tilt and which is not what you want. Uh
+this is uh the set of uh assignments at
+
+ align:start position:0%
+this is uh the set of uh assignments at
+ 
+
+ align:start position:0%
+this is uh the set of uh assignments at
+uh Disney at a Disney crew boat you know
+
+ align:start position:0%
+uh Disney at a Disney crew boat you know
+ 
+
+ align:start position:0%
+uh Disney at a Disney crew boat you know
+at a Disney cruise boat and each of the
+
+ align:start position:0%
+at a Disney cruise boat and each of the
+ 
+
+ align:start position:0%
+at a Disney cruise boat and each of the
+each of the uh different
+
+ align:start position:0%
+each of the uh different
+ 
+
+ align:start position:0%
+each of the uh different
+um kinds of uh luggage different groups
+
+ align:start position:0%
+um kinds of uh luggage different groups
+ 
+
+ align:start position:0%
+um kinds of uh luggage different groups
+of luggage has a different Disney figure
+
+ align:start position:0%
+of luggage has a different Disney figure
+ 
+
+ align:start position:0%
+of luggage has a different Disney figure
+associated with it.
+
+ align:start position:0%
+associated with it.
+ 
+
+ align:start position:0%
+associated with it.
+Um this is another one. This is guy has
+
+ align:start position:0%
+Um this is another one. This is guy has
+ 
+
+ align:start position:0%
+Um this is another one. This is guy has
+an ILWU um you know
+
+ align:start position:0%
+an ILWU um you know
+ 
+
+ align:start position:0%
+an ILWU um you know
+um tattoo and this is people waiting to
+
+ align:start position:0%
+um tattoo and this is people waiting to
+ 
+
+ align:start position:0%
+um tattoo and this is people waiting to
+find jobs. All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I don't think I would learn more by
+
+ align:start position:0%
+So I don't think I would learn more by
+ 
+
+ align:start position:0%
+So I don't think I would learn more by
+doing many more photographs but I could
+
+ align:start position:0%
+doing many more photographs but I could
+ 
+
+ align:start position:0%
+doing many more photographs but I could
+have a lot I could you know do much
+
+ align:start position:0%
+have a lot I could you know do much
+ 
+
+ align:start position:0%
+have a lot I could you know do much
+more. Have you ever read a book by Alan
+
+ align:start position:0%
+more. Have you ever read a book by Alan
+ 
+
+ align:start position:0%
+more. Have you ever read a book by Alan
+Sakula called Fish Story? Um, Sakula is
+
+ align:start position:0%
+Sakula called Fish Story? Um, Sakula is
+ 
+
+ align:start position:0%
+Sakula called Fish Story? Um, Sakula is
+something of a, let's call him a Marxist
+
+ align:start position:0%
+something of a, let's call him a Marxist
+ 
+
+ align:start position:0%
+something of a, let's call him a Marxist
+and a and a terrific photographer. And
+
+ align:start position:0%
+and a and a terrific photographer. And
+ 
+
+ align:start position:0%
+and a and a terrific photographer. And
+you ought to read it. It's all about
+
+ align:start position:0%
+you ought to read it. It's all about
+ 
+
+ align:start position:0%
+you ought to read it. It's all about
+essentially how the destruction of the
+
+ align:start position:0%
+essentially how the destruction of the
+ 
+
+ align:start position:0%
+essentially how the destruction of the
+of essentially the the ordinary the old
+
+ align:start position:0%
+of essentially the the ordinary the old
+ 
+
+ align:start position:0%
+of essentially the the ordinary the old
+labor ways destroys a certain
+
+ align:start position:0%
+labor ways destroys a certain
+ 
+
+ align:start position:0%
+labor ways destroys a certain
+society. Very smart man. A little bit
+
+ align:start position:0%
+society. Very smart man. A little bit
+ 
+
+ align:start position:0%
+society. Very smart man. A little bit
+too much for me, but that doesn't
+
+ align:start position:0%
+too much for me, but that doesn't
+ 
+
+ align:start position:0%
+too much for me, but that doesn't
+matter, you know. But the photographs
+
+ align:start position:0%
+matter, you know. But the photographs
+ 
+
+ align:start position:0%
+matter, you know. But the photographs
+are so gorgeous it gets in the way. You
+
+ align:start position:0%
+are so gorgeous it gets in the way. You
+ 
+
+ align:start position:0%
+are so gorgeous it gets in the way. You
+know, it's someone who's you if the
+
+ align:start position:0%
+know, it's someone who's you if the
+ 
+
+ align:start position:0%
+know, it's someone who's you if the
+photographs are too gorgeous, it's hard
+
+ align:start position:0%
+photographs are too gorgeous, it's hard
+ 
+
+ align:start position:0%
+photographs are too gorgeous, it's hard
+to think of people as being victimized.
+
+ align:start position:0%
+to think of people as being victimized.
+ 
+
+ align:start position:0%
+to think of people as being victimized.
+But that's another problem. But I do
+
+ align:start position:0%
+But that's another problem. But I do
+ 
+
+ align:start position:0%
+But that's another problem. But I do
+recommend it if you want to see
+
+ align:start position:0%
+recommend it if you want to see
+ 
+
+ align:start position:0%
+recommend it if you want to see
+something like that. But my purpose was
+
+ align:start position:0%
+something like that. But my purpose was
+ 
+
+ align:start position:0%
+something like that. But my purpose was
+not to do the fish story. My picture
+
+ align:start position:0%
+not to do the fish story. My picture
+ 
+
+ align:start position:0%
+not to do the fish story. My picture
+purpose was to show the context in which
+
+ align:start position:0%
+purpose was to show the context in which
+ 
+
+ align:start position:0%
+purpose was to show the context in which
+people did their work. Um I was less
+
+ align:start position:0%
+people did their work. Um I was less
+ 
+
+ align:start position:0%
+people did their work. Um I was less
+concerned about worrying about whether
+
+ align:start position:0%
+concerned about worrying about whether
+ 
+
+ align:start position:0%
+concerned about worrying about whether
+they're they're victimized or not.
+
+ align:start position:0%
+they're they're victimized or not.
+ 
+
+ align:start position:0%
+they're they're victimized or not.
+Um I don't know why I just that doesn't
+
+ align:start position:0%
+Um I don't know why I just that doesn't
+ 
+
+ align:start position:0%
+Um I don't know why I just that doesn't
+seem to me where I can do any good. I
+
+ align:start position:0%
+seem to me where I can do any good. I
+ 
+
+ align:start position:0%
+seem to me where I can do any good. I
+just don't have the kind of personality
+
+ align:start position:0%
+just don't have the kind of personality
+ 
+
+ align:start position:0%
+just don't have the kind of personality
+the right you need a certain kind of
+
+ align:start position:0%
+the right you need a certain kind of
+ 
+
+ align:start position:0%
+the right you need a certain kind of
+righteousness when you start doing that
+
+ align:start position:0%
+righteousness when you start doing that
+ 
+
+ align:start position:0%
+righteousness when you start doing that
+you know I'm on the right side of the
+
+ align:start position:0%
+you know I'm on the right side of the
+ 
+
+ align:start position:0%
+you know I'm on the right side of the
+good I tend not that I think that uh you
+
+ align:start position:0%
+good I tend not that I think that uh you
+ 
+
+ align:start position:0%
+good I tend not that I think that uh you
+know that Hitler there's a good thing to
+
+ align:start position:0%
+know that Hitler there's a good thing to
+ 
+
+ align:start position:0%
+know that Hitler there's a good thing to
+be said for Hitler or for uh you know
+
+ align:start position:0%
+be said for Hitler or for uh you know
+ 
+
+ align:start position:0%
+be said for Hitler or for uh you know
+for the head of GM but um but I I just
+
+ align:start position:0%
+for the head of GM but um but I I just
+ 
+
+ align:start position:0%
+for the head of GM but um but I I just
+don't have that kind of personality.
+
+ align:start position:0%
+don't have that kind of personality.
+ 
+
+ align:start position:0%
+don't have that kind of personality.
+Other people do and they're much better
+
+ align:start position:0%
+Other people do and they're much better
+ 
+
+ align:start position:0%
+Other people do and they're much better
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. More questions please. Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, I have a bioconical demand for an
+
+ align:start position:0%
+Yeah, I have a bioconical demand for an
+ 
+
+ align:start position:0%
+Yeah, I have a bioconical demand for an
+education as a scientist, right? M and
+
+ align:start position:0%
+education as a scientist, right? M and
+ 
+
+ align:start position:0%
+education as a scientist, right? M and
+this a different sort of empiricism
+
+ align:start position:0%
+this a different sort of empiricism
+ 
+
+ align:start position:0%
+this a different sort of empiricism
+shows you I don't mean the indexing but
+
+ align:start position:0%
+shows you I don't mean the indexing but
+ 
+
+ align:start position:0%
+shows you I don't mean the indexing but
+it's it's really specific when you say
+
+ align:start position:0%
+it's it's really specific when you say
+ 
+
+ align:start position:0%
+it's it's really specific when you say
+you know these places exist at the
+
+ align:start position:0%
+you know these places exist at the
+ 
+
+ align:start position:0%
+you know these places exist at the
+periphery and you know when talking
+
+ align:start position:0%
+periphery and you know when talking
+ 
+
+ align:start position:0%
+periphery and you know when talking
+about the power station and you sort of
+
+ align:start position:0%
+about the power station and you sort of
+ 
+
+ align:start position:0%
+about the power station and you sort of
+if you were to map them in a certain
+
+ align:start position:0%
+if you were to map them in a certain
+ 
+
+ align:start position:0%
+if you were to map them in a certain
+pattern would emerge of
+
+ align:start position:0%
+pattern would emerge of
+ 
+
+ align:start position:0%
+pattern would emerge of
+how and things like that that's an
+
+ align:start position:0%
+how and things like that that's an
+ 
+
+ align:start position:0%
+how and things like that that's an
+empiricism that's embedded in your work
+
+ align:start position:0%
+empiricism that's embedded in your work
+ 
+
+ align:start position:0%
+empiricism that's embedded in your work
+and you mentioned leader and Yeah, Mar
+
+ align:start position:0%
+and you mentioned leader and Yeah, Mar
+ 
+
+ align:start position:0%
+and you mentioned leader and Yeah, Mar
+and I I'm curious about what you think
+
+ align:start position:0%
+and I I'm curious about what you think
+ 
+
+ align:start position:0%
+and I I'm curious about what you think
+of some other Frenchmen who write about
+
+ align:start position:0%
+of some other Frenchmen who write about
+ 
+
+ align:start position:0%
+of some other Frenchmen who write about
+critical theory and everyday urbanism in
+
+ align:start position:0%
+critical theory and everyday urbanism in
+ 
+
+ align:start position:0%
+critical theory and everyday urbanism in
+critical theory. And I wonder what your
+
+ align:start position:0%
+critical theory. And I wonder what your
+ 
+
+ align:start position:0%
+critical theory. And I wonder what your
+views are on that because that's
+
+ align:start position:0%
+views are on that because that's
+ 
+
+ align:start position:0%
+views are on that because that's
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+non-empirical. It's I mean, no, it's
+
+ align:start position:0%
+non-empirical. It's I mean, no, it's
+ 
+
+ align:start position:0%
+non-empirical. It's I mean, no, it's
+critical and it's theoretical. It's
+
+ align:start position:0%
+critical and it's theoretical. It's
+ 
+
+ align:start position:0%
+critical and it's theoretical. It's
+meant to be empirical. It's meant to
+
+ align:start position:0%
+meant to be empirical. It's meant to
+ 
+
+ align:start position:0%
+meant to be empirical. It's meant to
+draw from examples and so forth, but
+
+ align:start position:0%
+draw from examples and so forth, but
+ 
+
+ align:start position:0%
+draw from examples and so forth, but
+it's it's I um do you think they draw
+
+ align:start position:0%
+it's it's I um do you think they draw
+ 
+
+ align:start position:0%
+it's it's I um do you think they draw
+from examples? I'm not. Let me put it
+
+ align:start position:0%
+from examples? I'm not. Let me put it
+ 
+
+ align:start position:0%
+from examples? I'm not. Let me put it
+this way. Here's your problem with me. I
+
+ align:start position:0%
+this way. Here's your problem with me. I
+ 
+
+ align:start position:0%
+this way. Here's your problem with me. I
+mean, this is this is just being honest.
+
+ align:start position:0%
+mean, this is this is just being honest.
+ 
+
+ align:start position:0%
+mean, this is this is just being honest.
+It's really terrible to admit. I was
+
+ align:start position:0%
+It's really terrible to admit. I was
+ 
+
+ align:start position:0%
+It's really terrible to admit. I was
+reading Dered Da and all those people
+
+ align:start position:0%
+reading Dered Da and all those people
+ 
+
+ align:start position:0%
+reading Dered Da and all those people
+when they were in French and only a
+
+ align:start position:0%
+when they were in French and only a
+ 
+
+ align:start position:0%
+when they were in French and only a
+little bit in English because my friends
+
+ align:start position:0%
+little bit in English because my friends
+ 
+
+ align:start position:0%
+little bit in English because my friends
+I had friends in French departments who
+
+ align:start position:0%
+I had friends in French departments who
+ 
+
+ align:start position:0%
+I had friends in French departments who
+told me, "Oh, go read this guy." And I
+
+ align:start position:0%
+told me, "Oh, go read this guy." And I
+ 
+
+ align:start position:0%
+told me, "Oh, go read this guy." And I
+was reading and I was teaching and
+
+ align:start position:0%
+was reading and I was teaching and
+ 
+
+ align:start position:0%
+was reading and I was teaching and
+reading um Haidiger before it became as
+
+ align:start position:0%
+reading um Haidiger before it became as
+ 
+
+ align:start position:0%
+reading um Haidiger before it became as
+popular as it is. Once it became
+
+ align:start position:0%
+popular as it is. Once it became
+ 
+
+ align:start position:0%
+popular as it is. Once it became
+popular, you know, in the sort of the
+
+ align:start position:0%
+popular, you know, in the sort of the
+ 
+
+ align:start position:0%
+popular, you know, in the sort of the
+the post-modernist line, I couldn't read
+
+ align:start position:0%
+the post-modernist line, I couldn't read
+ 
+
+ align:start position:0%
+the post-modernist line, I couldn't read
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+stuff, which doesn't mean I just don't
+
+ align:start position:0%
+stuff, which doesn't mean I just don't
+ 
+
+ align:start position:0%
+stuff, which doesn't mean I just don't
+have the stomach for it. Um, I don't
+
+ align:start position:0%
+have the stomach for it. Um, I don't
+ 
+
+ align:start position:0%
+have the stomach for it. Um, I don't
+have the style that's
+
+ align:start position:0%
+have the style that's
+ 
+
+ align:start position:0%
+have the style that's
+required. I mean, I just don't have I'm
+
+ align:start position:0%
+required. I mean, I just don't have I'm
+ 
+
+ align:start position:0%
+required. I mean, I just don't have I'm
+not built that way. Um, when I read
+
+ align:start position:0%
+not built that way. Um, when I read
+ 
+
+ align:start position:0%
+not built that way. Um, when I read
+Haidiger, I read him in a very
+
+ align:start position:0%
+Haidiger, I read him in a very
+ 
+
+ align:start position:0%
+Haidiger, I read him in a very
+unromanticized way, uh, in a fairly
+
+ align:start position:0%
+unromanticized way, uh, in a fairly
+ 
+
+ align:start position:0%
+unromanticized way, uh, in a fairly
+technical way. um what I learned from
+
+ align:start position:0%
+technical way. um what I learned from
+ 
+
+ align:start position:0%
+technical way. um what I learned from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um I mean I've learned something from
+
+ align:start position:0%
+um I mean I've learned something from
+ 
+
+ align:start position:0%
+um I mean I've learned something from
+Der Da but not very much compared to
+
+ align:start position:0%
+Der Da but not very much compared to
+ 
+
+ align:start position:0%
+Der Da but not very much compared to
+what most people seem to have learned.
+
+ align:start position:0%
+what most people seem to have learned.
+ 
+
+ align:start position:0%
+what most people seem to have learned.
+So, but you I think you have a deep
+
+ align:start position:0%
+So, but you I think you have a deep
+ 
+
+ align:start position:0%
+So, but you I think you have a deep
+question that's that's been on my mind.
+
+ align:start position:0%
+question that's that's been on my mind.
+ 
+
+ align:start position:0%
+question that's that's been on my mind.
+And anybody who has an answer, you know,
+
+ align:start position:0%
+And anybody who has an answer, you know,
+ 
+
+ align:start position:0%
+And anybody who has an answer, you know,
+be grateful for why in the world these
+
+ align:start position:0%
+be grateful for why in the world these
+ 
+
+ align:start position:0%
+be grateful for why in the world these
+three Frenchmen I keep mentioning. It's
+
+ align:start position:0%
+three Frenchmen I keep mentioning. It's
+ 
+
+ align:start position:0%
+three Frenchmen I keep mentioning. It's
+not like I spend my life, you know,
+
+ align:start position:0%
+not like I spend my life, you know,
+ 
+
+ align:start position:0%
+not like I spend my life, you know,
+where I care only for French people, but
+
+ align:start position:0%
+where I care only for French people, but
+ 
+
+ align:start position:0%
+where I care only for French people, but
+why did Marvil and Ache, right? And I
+
+ align:start position:0%
+why did Marvil and Ache, right? And I
+ 
+
+ align:start position:0%
+why did Marvil and Ache, right? And I
+asked a friend of mine um who who's the
+
+ align:start position:0%
+asked a friend of mine um who who's the
+ 
+
+ align:start position:0%
+asked a friend of mine um who who's the
+one who got me to read Dared? This is in
+
+ align:start position:0%
+one who got me to read Dared? This is in
+ 
+
+ align:start position:0%
+one who got me to read Dared? This is in
+the 70 in the he got me to read Derid
+
+ align:start position:0%
+the 70 in the he got me to read Derid
+ 
+
+ align:start position:0%
+the 70 in the he got me to read Derid
+Don in like the mid70s. All right.
+
+ align:start position:0%
+Don in like the mid70s. All right.
+ 
+
+ align:start position:0%
+Don in like the mid70s. All right.
+Before it was, you know, it was popular
+
+ align:start position:0%
+Before it was, you know, it was popular
+ 
+
+ align:start position:0%
+Before it was, you know, it was popular
+in literature, but it wasn't Gatri
+
+ align:start position:0%
+in literature, but it wasn't Gatri
+ 
+
+ align:start position:0%
+in literature, but it wasn't Gatri
+Spac's book hadn't come out and things
+
+ align:start position:0%
+Spac's book hadn't come out and things
+ 
+
+ align:start position:0%
+Spac's book hadn't come out and things
+like that. And um he said, well, it's
+
+ align:start position:0%
+like that. And um he said, well, it's
+ 
+
+ align:start position:0%
+like that. And um he said, well, it's
+partially the the the the Frenchmen are
+
+ align:start position:0%
+partially the the the the Frenchmen are
+ 
+
+ align:start position:0%
+partially the the the the Frenchmen are
+the great
+
+ align:start position:0%
+the great
+ 
+
+ align:start position:0%
+the great
+systematizers, you know, and very the
+
+ align:start position:0%
+systematizers, you know, and very the
+ 
+
+ align:start position:0%
+systematizers, you know, and very the
+rationality of it, you know, the
+
+ align:start position:0%
+rationality of it, you know, the
+ 
+
+ align:start position:0%
+rationality of it, you know, the
+systematic organization. And maybe
+
+ align:start position:0%
+systematic organization. And maybe
+ 
+
+ align:start position:0%
+systematic organization. And maybe
+that's true. All right. Now, how that
+
+ align:start position:0%
+that's true. All right. Now, how that
+ 
+
+ align:start position:0%
+that's true. All right. Now, how that
+connects with this other thread is an
+
+ align:start position:0%
+connects with this other thread is an
+ 
+
+ align:start position:0%
+connects with this other thread is an
+interesting question. And of course
+
+ align:start position:0%
+interesting question. And of course
+ 
+
+ align:start position:0%
+interesting question. And of course
+there could be several threads. I mean
+
+ align:start position:0%
+there could be several threads. I mean
+ 
+
+ align:start position:0%
+there could be several threads. I mean
+there's also a tradition in France of uh
+
+ align:start position:0%
+there's also a tradition in France of uh
+ 
+
+ align:start position:0%
+there's also a tradition in France of uh
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um fantastic
+
+ align:start position:0%
+um fantastic
+ 
+
+ align:start position:0%
+um fantastic
+thinking but I've chosen these
+
+ align:start position:0%
+thinking but I've chosen these
+ 
+
+ align:start position:0%
+thinking but I've chosen these
+particular you know figures. So maybe
+
+ align:start position:0%
+particular you know figures. So maybe
+ 
+
+ align:start position:0%
+particular you know figures. So maybe
+I've chosen one thread in French thought
+
+ align:start position:0%
+I've chosen one thread in French thought
+ 
+
+ align:start position:0%
+I've chosen one thread in French thought
+but I don't uh but I'm not answering a
+
+ align:start position:0%
+but I don't uh but I'm not answering a
+ 
+
+ align:start position:0%
+but I don't uh but I'm not answering a
+question. I know that but I don't have
+
+ align:start position:0%
+question. I know that but I don't have
+ 
+
+ align:start position:0%
+question. I know that but I don't have
+anything smart to say about it. Um but I
+
+ align:start position:0%
+anything smart to say about it. Um but I
+ 
+
+ align:start position:0%
+anything smart to say about it. Um but I
+was but I was sort of struck one day. I
+
+ align:start position:0%
+was but I was sort of struck one day. I
+ 
+
+ align:start position:0%
+was but I was sort of struck one day. I
+said, "What am I doing with these French
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys?" You know, and it's because they
+
+ align:start position:0%
+guys?" You know, and it's because they
+ 
+
+ align:start position:0%
+guys?" You know, and it's because they
+serve my
+
+ align:start position:0%
+serve my
+ 
+
+ align:start position:0%
+serve my
+purpose. But then you say, "Well, you
+
+ align:start position:0%
+purpose. But then you say, "Well, you
+ 
+
+ align:start position:0%
+purpose. But then you say, "Well, you
+know, this is not exactly an abstract
+
+ align:start position:0%
+know, this is not exactly an abstract
+ 
+
+ align:start position:0%
+know, this is not exactly an abstract
+tradition. These are people who know
+
+ align:start position:0%
+tradition. These are people who know
+ 
+
+ align:start position:0%
+tradition. These are people who know
+about each other
+
+ align:start position:0%
+about each other
+ 
+
+ align:start position:0%
+about each other
+historically." And so it's an
+
+ align:start position:0%
+historically." And so it's an
+ 
+
+ align:start position:0%
+historically." And so it's an
+interesting question. Yes, it seems that
+
+ align:start position:0%
+interesting question. Yes, it seems that
+ 
+
+ align:start position:0%
+interesting question. Yes, it seems that
+the branches sort
+
+ align:start position:0%
+the branches sort
+ 
+
+ align:start position:0%
+the branches sort
+of I'm not sure of this, but if in the
+
+ align:start position:0%
+of I'm not sure of this, but if in the
+ 
+
+ align:start position:0%
+of I'm not sure of this, but if in the
+past they they knew each other and maybe
+
+ align:start position:0%
+past they they knew each other and maybe
+ 
+
+ align:start position:0%
+past they they knew each other and maybe
+sort of the sensibility spread more into
+
+ align:start position:0%
+sort of the sensibility spread more into
+ 
+
+ align:start position:0%
+sort of the sensibility spread more into
+different streams of thought, it doesn't
+
+ align:start position:0%
+different streams of thought, it doesn't
+ 
+
+ align:start position:0%
+different streams of thought, it doesn't
+seem to sort of happen now where this
+
+ align:start position:0%
+seem to sort of happen now where this
+ 
+
+ align:start position:0%
+seem to sort of happen now where this
+sort of empirical work and sort of other
+
+ align:start position:0%
+sort of empirical work and sort of other
+ 
+
+ align:start position:0%
+sort of empirical work and sort of other
+presentation we've seen in this series
+
+ align:start position:0%
+presentation we've seen in this series
+ 
+
+ align:start position:0%
+presentation we've seen in this series
+that are empirical don't seem to borrow
+
+ align:start position:0%
+that are empirical don't seem to borrow
+ 
+
+ align:start position:0%
+that are empirical don't seem to borrow
+from there and um from where from from
+
+ align:start position:0%
+from there and um from where from from
+ 
+
+ align:start position:0%
+from there and um from where from from
+say critical theory and I I I don't I'm
+
+ align:start position:0%
+say critical theory and I I I don't I'm
+ 
+
+ align:start position:0%
+say critical theory and I I I don't I'm
+not suggesting that they should. What
+
+ align:start position:0%
+not suggesting that they should. What
+ 
+
+ align:start position:0%
+not suggesting that they should. What
+I'm interested in knowing is what what
+
+ align:start position:0%
+I'm interested in knowing is what what
+ 
+
+ align:start position:0%
+I'm interested in knowing is what what
+your view on on the intelligence of of
+
+ align:start position:0%
+your view on on the intelligence of of
+ 
+
+ align:start position:0%
+your view on on the intelligence of of
+those theories are. Well, can they feed
+
+ align:start position:0%
+those theories are. Well, can they feed
+ 
+
+ align:start position:0%
+those theories are. Well, can they feed
+into into sort of Oh, sure. No, first of
+
+ align:start position:0%
+into into sort of Oh, sure. No, first of
+ 
+
+ align:start position:0%
+into into sort of Oh, sure. No, first of
+all, there's there's a whole bunch of
+
+ align:start position:0%
+all, there's there's a whole bunch of
+ 
+
+ align:start position:0%
+all, there's there's a whole bunch of
+people who um um who you know, there's a
+
+ align:start position:0%
+people who um um who you know, there's a
+ 
+
+ align:start position:0%
+people who um um who you know, there's a
+book called uh by um Oh, God.
+
+ align:start position:0%
+book called uh by um Oh, God.
+ 
+
+ align:start position:0%
+book called uh by um Oh, God.
+She's married to a photographer. She's a
+
+ align:start position:0%
+She's married to a photographer. She's a
+ 
+
+ align:start position:0%
+She's married to a photographer. She's a
+literary critic. Um, the cover has a
+
+ align:start position:0%
+literary critic. Um, the cover has a
+ 
+
+ align:start position:0%
+literary critic. Um, the cover has a
+picture of her naked um taken by her
+
+ align:start position:0%
+picture of her naked um taken by her
+ 
+
+ align:start position:0%
+picture of her naked um taken by her
+husband.
+
+ align:start position:0%
+husband.
+ 
+
+ align:start position:0%
+husband.
+Uh, oh god, I can't think of her name.
+
+ align:start position:0%
+Uh, oh god, I can't think of her name.
+ 
+
+ align:start position:0%
+Uh, oh god, I can't think of her name.
+She's I think she's at Iowa or
+
+ align:start position:0%
+She's I think she's at Iowa or
+ 
+
+ align:start position:0%
+She's I think she's at Iowa or
+something. She's a well-known feminist
+
+ align:start position:0%
+something. She's a well-known feminist
+ 
+
+ align:start position:0%
+something. She's a well-known feminist
+critic. All right. And there are people
+
+ align:start position:0%
+critic. All right. And there are people
+ 
+
+ align:start position:0%
+critic. All right. And there are people
+who do worry about this. Remember,
+
+ align:start position:0%
+who do worry about this. Remember,
+ 
+
+ align:start position:0%
+who do worry about this. Remember,
+there's there's Look, here's what here's
+
+ align:start position:0%
+there's there's Look, here's what here's
+ 
+
+ align:start position:0%
+there's there's Look, here's what here's
+the answer to you, which is sort of the
+
+ align:start position:0%
+the answer to you, which is sort of the
+ 
+
+ align:start position:0%
+the answer to you, which is sort of the
+blunt thing. There's Susan Zontag.
+
+ align:start position:0%
+blunt thing. There's Susan Zontag.
+ 
+
+ align:start position:0%
+blunt thing. There's Susan Zontag.
+There's uh Bach who writes about you
+
+ align:start position:0%
+There's uh Bach who writes about you
+ 
+
+ align:start position:0%
+There's uh Bach who writes about you
+know photography. There's um what's his
+
+ align:start position:0%
+know photography. There's um what's his
+ 
+
+ align:start position:0%
+know photography. There's um what's his
+name? Um has a whole book on
+
+ align:start position:0%
+name? Um has a whole book on
+ 
+
+ align:start position:0%
+name? Um has a whole book on
+photography. The sociologist
+
+ align:start position:0%
+photography. The sociologist
+ 
+
+ align:start position:0%
+photography. The sociologist
+Bourju there's a whole if you want the
+
+ align:start position:0%
+Bourju there's a whole if you want the
+ 
+
+ align:start position:0%
+Bourju there's a whole if you want the
+French there's a whole bunch of these
+
+ align:start position:0%
+French there's a whole bunch of these
+ 
+
+ align:start position:0%
+French there's a whole bunch of these
+Frenchmen who do this. Why don't I quote
+
+ align:start position:0%
+Frenchmen who do this. Why don't I quote
+ 
+
+ align:start position:0%
+Frenchmen who do this. Why don't I quote
+from them you might ask right? It
+
+ align:start position:0%
+from them you might ask right? It
+ 
+
+ align:start position:0%
+from them you might ask right? It
+doesn't help me
+
+ align:start position:0%
+doesn't help me
+ 
+
+ align:start position:0%
+doesn't help me
+think. All right now and you could say
+
+ align:start position:0%
+think. All right now and you could say
+ 
+
+ align:start position:0%
+think. All right now and you could say
+well uh maybe you're you're you should
+
+ align:start position:0%
+well uh maybe you're you're you should
+ 
+
+ align:start position:0%
+well uh maybe you're you're you should
+No, my my question is not why don't you
+
+ align:start position:0%
+No, my my question is not why don't you
+ 
+
+ align:start position:0%
+No, my my question is not why don't you
+quote from them but what is your
+
+ align:start position:0%
+quote from them but what is your
+ 
+
+ align:start position:0%
+quote from them but what is your
+they don't help me do my work right
+
+ align:start position:0%
+they don't help me do my work right
+ 
+
+ align:start position:0%
+they don't help me do my work right
+right but then what is behind that
+
+ align:start position:0%
+right but then what is behind that
+ 
+
+ align:start position:0%
+right but then what is behind that
+rejection or well I don't know I mean
+
+ align:start position:0%
+rejection or well I don't know I mean
+ 
+
+ align:start position:0%
+rejection or well I don't know I mean
+sort of like asking a lady who's
+
+ align:start position:0%
+sort of like asking a lady who's
+ 
+
+ align:start position:0%
+sort of like asking a lady who's
+crossing the street why doesn't she want
+
+ align:start position:0%
+crossing the street why doesn't she want
+ 
+
+ align:start position:0%
+crossing the street why doesn't she want
+someone to help him help her um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no because it's obviously I think no no
+
+ align:start position:0%
+no because it's obviously I think no no
+ 
+
+ align:start position:0%
+no because it's obviously I think no no
+I think it's it's aund it's a good $100
+
+ align:start position:0%
+I think it's it's aund it's a good $100
+ 
+
+ align:start position:0%
+I think it's it's aund it's a good $100
+question um and Maybe not everybody is
+
+ align:start position:0%
+question um and Maybe not everybody is
+ 
+
+ align:start position:0%
+question um and Maybe not everybody is
+concerned, but you know, we know what's
+
+ align:start position:0%
+concerned, but you know, we know what's
+ 
+
+ align:start position:0%
+concerned, but you know, we know what's
+going on intellectually. There's a whole
+
+ align:start position:0%
+going on intellectually. There's a whole
+ 
+
+ align:start position:0%
+going on intellectually. There's a whole
+bunch of people who concerned about
+
+ align:start position:0%
+bunch of people who concerned about
+ 
+
+ align:start position:0%
+bunch of people who concerned about
+postmodern photography. There's a whole
+
+ align:start position:0%
+postmodern photography. There's a whole
+ 
+
+ align:start position:0%
+postmodern photography. There's a whole
+bunch of people who do read those
+
+ align:start position:0%
+bunch of people who do read those
+ 
+
+ align:start position:0%
+bunch of people who do read those
+people. All right. And you know,
+
+ align:start position:0%
+people. All right. And you know,
+ 
+
+ align:start position:0%
+people. All right. And you know,
+photographer, I mean, photographic
+
+ align:start position:0%
+photographer, I mean, photographic
+ 
+
+ align:start position:0%
+photographer, I mean, photographic
+criticism is imbued with discussions of
+
+ align:start position:0%
+criticism is imbued with discussions of
+ 
+
+ align:start position:0%
+criticism is imbued with discussions of
+about and and Susan Zantag and um and
+
+ align:start position:0%
+about and and Susan Zantag and um and
+ 
+
+ align:start position:0%
+about and and Susan Zantag and um and
+and and uh and in fact, this book, which
+
+ align:start position:0%
+and and uh and in fact, this book, which
+ 
+
+ align:start position:0%
+and and uh and in fact, this book, which
+I can't remember the title of
+
+ align:start position:0%
+I can't remember the title of
+ 
+
+ align:start position:0%
+I can't remember the title of
+is is is amusing on these kinds of
+
+ align:start position:0%
+is is is amusing on these kinds of
+ 
+
+ align:start position:0%
+is is is amusing on these kinds of
+things. Um and there must be people who
+
+ align:start position:0%
+things. Um and there must be people who
+ 
+
+ align:start position:0%
+things. Um and there must be people who
+are very much influenced by it. Um
+
+ align:start position:0%
+are very much influenced by it. Um
+ 
+
+ align:start position:0%
+are very much influenced by it. Um
+because I'm not a real photographer.
+
+ align:start position:0%
+because I'm not a real photographer.
+ 
+
+ align:start position:0%
+because I'm not a real photographer.
+That's the point. I just take pictures.
+
+ align:start position:0%
+That's the point. I just take pictures.
+ 
+
+ align:start position:0%
+That's the point. I just take pictures.
+Real
+
+ align:start position:0%
+Real
+ 
+
+ align:start position:0%
+Real
+photographers look the what I mean by
+
+ align:start position:0%
+photographers look the what I mean by
+ 
+
+ align:start position:0%
+photographers look the what I mean by
+photographer is someone who is either
+
+ align:start position:0%
+photographer is someone who is either
+ 
+
+ align:start position:0%
+photographer is someone who is either
+part of an art
+
+ align:start position:0%
+part of an art
+ 
+
+ align:start position:0%
+part of an art
+tradition or a photojournalistic
+
+ align:start position:0%
+tradition or a photojournalistic
+ 
+
+ align:start position:0%
+tradition or a photojournalistic
+tradition or maybe a commercial
+
+ align:start position:0%
+tradition or maybe a commercial
+ 
+
+ align:start position:0%
+tradition or maybe a commercial
+tradition. At best I'm part of a
+
+ align:start position:0%
+tradition. At best I'm part of a
+ 
+
+ align:start position:0%
+tradition. At best I'm part of a
+documentation
+
+ align:start position:0%
+documentation
+ 
+
+ align:start position:0%
+documentation
+tradition. All right. But most of we
+
+ align:start position:0%
+tradition. All right. But most of we
+ 
+
+ align:start position:0%
+tradition. All right. But most of we
+call the documentation
+
+ align:start position:0%
+call the documentation
+ 
+
+ align:start position:0%
+call the documentation
+photographers have been elevated to
+
+ align:start position:0%
+photographers have been elevated to
+ 
+
+ align:start position:0%
+photographers have been elevated to
+artists. Etch is an artist. Marvel is an
+
+ align:start position:0%
+artists. Etch is an artist. Marvel is an
+ 
+
+ align:start position:0%
+artists. Etch is an artist. Marvel is an
+artist. You know, I mean, there no there
+
+ align:start position:0%
+artist. You know, I mean, there no there
+ 
+
+ align:start position:0%
+artist. You know, I mean, there no there
+no second rate documentary photographers
+
+ align:start position:0%
+no second rate documentary photographers
+ 
+
+ align:start position:0%
+no second rate documentary photographers
+as far as one can tell. The ones that
+
+ align:start position:0%
+as far as one can tell. The ones that
+ 
+
+ align:start position:0%
+as far as one can tell. The ones that
+written about to do documentation are
+
+ align:start position:0%
+written about to do documentation are
+ 
+
+ align:start position:0%
+written about to do documentation are
+great artists. I mean, you know, buy
+
+ align:start position:0%
+great artists. I mean, you know, buy
+ 
+
+ align:start position:0%
+great artists. I mean, you know, buy
+this thing. I can't I'm not smart enough
+
+ align:start position:0%
+this thing. I can't I'm not smart enough
+ 
+
+ align:start position:0%
+this thing. I can't I'm not smart enough
+to handle that stuff. I don't know what
+
+ align:start position:0%
+to handle that stuff. I don't know what
+ 
+
+ align:start position:0%
+to handle that stuff. I don't know what
+to do with it. All right. I mean, I can
+
+ align:start position:0%
+to do with it. All right. I mean, I can
+ 
+
+ align:start position:0%
+to do with it. All right. I mean, I can
+like the photographs, but I'm not smart
+
+ align:start position:0%
+like the photographs, but I'm not smart
+ 
+
+ align:start position:0%
+like the photographs, but I'm not smart
+about what's a great artist. I mean,
+
+ align:start position:0%
+about what's a great artist. I mean,
+ 
+
+ align:start position:0%
+about what's a great artist. I mean,
+yes, I know that, you know, Shelley Co
+
+ align:start position:0%
+yes, I know that, you know, Shelley Co
+ 
+
+ align:start position:0%
+yes, I know that, you know, Shelley Co
+is a great artist, but I don't need
+
+ align:start position:0%
+is a great artist, but I don't need
+ 
+
+ align:start position:0%
+is a great artist, but I don't need
+we're not talking about that. And you
+
+ align:start position:0%
+we're not talking about that. And you
+ 
+
+ align:start position:0%
+we're not talking about that. And you
+know, but I mean it's a fair question to
+
+ align:start position:0%
+know, but I mean it's a fair question to
+ 
+
+ align:start position:0%
+know, but I mean it's a fair question to
+ask, but in so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the these you have to go, who would I
+
+ align:start position:0%
+as the these you have to go, who would I
+ 
+
+ align:start position:0%
+as the these you have to go, who would I
+look at?
+
+ align:start position:0%
+look at?
+ 
+
+ align:start position:0%
+look at?
+Um, let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see. Well, I mean, Sakula is a perfect
+
+ align:start position:0%
+see. Well, I mean, Sakula is a perfect
+ 
+
+ align:start position:0%
+see. Well, I mean, Sakula is a perfect
+example of writing with a Marxist tone.
+
+ align:start position:0%
+example of writing with a Marxist tone.
+ 
+
+ align:start position:0%
+example of writing with a Marxist tone.
+And there must be a whole bunch of
+
+ align:start position:0%
+And there must be a whole bunch of
+ 
+
+ align:start position:0%
+And there must be a whole bunch of
+people, photographers, who now write
+
+ align:start position:0%
+people, photographers, who now write
+ 
+
+ align:start position:0%
+people, photographers, who now write
+with uh, you know, with a postmodernist
+
+ align:start position:0%
+with uh, you know, with a postmodernist
+ 
+
+ align:start position:0%
+with uh, you know, with a postmodernist
+uh, Frenchy tone. I just don't keep up
+
+ align:start position:0%
+uh, Frenchy tone. I just don't keep up
+ 
+
+ align:start position:0%
+uh, Frenchy tone. I just don't keep up
+with it because I can't read it. I don't
+
+ align:start position:0%
+with it because I can't read it. I don't
+ 
+
+ align:start position:0%
+with it because I can't read it. I don't
+have the brain for
+
+ align:start position:0%
+have the brain for
+ 
+
+ align:start position:0%
+have the brain for
+it. Um, it the the words go right before
+
+ align:start position:0%
+it. Um, it the the words go right before
+ 
+
+ align:start position:0%
+it. Um, it the the words go right before
+my eyes. I mean, now maybe I'm becoming
+
+ align:start position:0%
+my eyes. I mean, now maybe I'm becoming
+ 
+
+ align:start position:0%
+my eyes. I mean, now maybe I'm becoming
+an old man, you know, that's always a
+
+ align:start position:0%
+an old man, you know, that's always a
+ 
+
+ align:start position:0%
+an old man, you know, that's always a
+possibility. I am becoming an old man,
+
+ align:start position:0%
+possibility. I am becoming an old man,
+ 
+
+ align:start position:0%
+possibility. I am becoming an old man,
+but I mean, maybe I'm, you know, losing
+
+ align:start position:0%
+but I mean, maybe I'm, you know, losing
+ 
+
+ align:start position:0%
+but I mean, maybe I'm, you know, losing
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Um but I think what John deo asked me
+
+ align:start position:0%
+Um but I think what John deo asked me
+ 
+
+ align:start position:0%
+Um but I think what John deo asked me
+was a serious remark when I said I get
+
+ align:start position:0%
+was a serious remark when I said I get
+ 
+
+ align:start position:0%
+was a serious remark when I said I get
+happy you know going out in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field somewhere along the line I lost my
+
+ align:start position:0%
+field somewhere along the line I lost my
+ 
+
+ align:start position:0%
+field somewhere along the line I lost my
+interest in that stuff. I mean I I was
+
+ align:start position:0%
+interest in that stuff. I mean I I was
+ 
+
+ align:start position:0%
+interest in that stuff. I mean I I was
+reading an article in in technology and
+
+ align:start position:0%
+reading an article in in technology and
+ 
+
+ align:start position:0%
+reading an article in in technology and
+culture which is the society of history
+
+ align:start position:0%
+culture which is the society of history
+ 
+
+ align:start position:0%
+culture which is the society of history
+of technology magazine a marvelous
+
+ align:start position:0%
+of technology magazine a marvelous
+ 
+
+ align:start position:0%
+of technology magazine a marvelous
+article about um scanning tunning tunnel
+
+ align:start position:0%
+article about um scanning tunning tunnel
+ 
+
+ align:start position:0%
+article about um scanning tunning tunnel
+microscopy and as an instrumental
+
+ align:start position:0%
+microscopy and as an instrumental
+ 
+
+ align:start position:0%
+microscopy and as an instrumental
+community and all I could think of as
+
+ align:start position:0%
+community and all I could think of as
+ 
+
+ align:start position:0%
+community and all I could think of as
+which was wonderful stuff but I said oh
+
+ align:start position:0%
+which was wonderful stuff but I said oh
+ 
+
+ align:start position:0%
+which was wonderful stuff but I said oh
+my god they're having this argument
+
+ align:start position:0%
+my god they're having this argument
+ 
+
+ align:start position:0%
+my god they're having this argument
+internal to the discipline about what
+
+ align:start position:0%
+internal to the discipline about what
+ 
+
+ align:start position:0%
+internal to the discipline about what
+instrumental community is and who's
+
+ align:start position:0%
+instrumental community is and who's
+ 
+
+ align:start position:0%
+instrumental community is and who's
+going to get points and will it be Peter
+
+ align:start position:0%
+going to get points and will it be Peter
+ 
+
+ align:start position:0%
+going to get points and will it be Peter
+Gallison or will it be Jed Buckwald you
+
+ align:start position:0%
+Gallison or will it be Jed Buckwald you
+ 
+
+ align:start position:0%
+Gallison or will it be Jed Buckwald you
+know all people I know all of whom are
+
+ align:start position:0%
+know all people I know all of whom are
+ 
+
+ align:start position:0%
+know all people I know all of whom are
+very well thought of, but each one of
+
+ align:start position:0%
+very well thought of, but each one of
+ 
+
+ align:start position:0%
+very well thought of, but each one of
+them wants to be on top, right? You
+
+ align:start position:0%
+them wants to be on top, right? You
+ 
+
+ align:start position:0%
+them wants to be on top, right? You
+know, the m major rule is the more
+
+ align:start position:0%
+know, the m major rule is the more
+ 
+
+ align:start position:0%
+know, the m major rule is the more
+famous they are, the the more they feel
+
+ align:start position:0%
+famous they are, the the more they feel
+ 
+
+ align:start position:0%
+famous they are, the the more they feel
+like they're
+
+ align:start position:0%
+like they're
+ 
+
+ align:start position:0%
+like they're
+underrecognized. If you don't know that,
+
+ align:start position:0%
+underrecognized. If you don't know that,
+ 
+
+ align:start position:0%
+underrecognized. If you don't know that,
+that's an important
+
+ align:start position:0%
+that's an important
+ 
+
+ align:start position:0%
+that's an important
+principle. And I don't
+
+ align:start position:0%
+principle. And I don't
+ 
+
+ align:start position:0%
+principle. And I don't
+care. I mean, I'll be honest with you. I
+
+ align:start position:0%
+care. I mean, I'll be honest with you. I
+ 
+
+ align:start position:0%
+care. I mean, I'll be honest with you. I
+just think of this is all this doesn't
+
+ align:start position:0%
+just think of this is all this doesn't
+ 
+
+ align:start position:0%
+just think of this is all this doesn't
+do me any good.
+
+ align:start position:0%
+do me any good.
+ 
+
+ align:start position:0%
+do me any good.
+Now that is to admit that as an
+
+ align:start position:0%
+Now that is to admit that as an
+ 
+
+ align:start position:0%
+Now that is to admit that as an
+professor is really sinful is you know
+
+ align:start position:0%
+professor is really sinful is you know
+ 
+
+ align:start position:0%
+professor is really sinful is you know
+but I don't I mean it won't help me
+
+ align:start position:0%
+but I don't I mean it won't help me
+ 
+
+ align:start position:0%
+but I don't I mean it won't help me
+where I want to know is how did industry
+
+ align:start position:0%
+where I want to know is how did industry
+ 
+
+ align:start position:0%
+where I want to know is how did industry
+works. I want to I'll read Phil Scranton
+
+ align:start position:0%
+works. I want to I'll read Phil Scranton
+ 
+
+ align:start position:0%
+works. I want to I'll read Phil Scranton
+who writes about industrial industry and
+
+ align:start position:0%
+who writes about industrial industry and
+ 
+
+ align:start position:0%
+who writes about industrial industry and
+cities or I'll read my colleague um uh
+
+ align:start position:0%
+cities or I'll read my colleague um uh
+ 
+
+ align:start position:0%
+cities or I'll read my colleague um uh
+Greg Heis. I mean, I read his stuff
+
+ align:start position:0%
+Greg Heis. I mean, I read his stuff
+ 
+
+ align:start position:0%
+Greg Heis. I mean, I read his stuff
+religiously even though he's a friend
+
+ align:start position:0%
+religiously even though he's a friend
+ 
+
+ align:start position:0%
+religiously even though he's a friend
+because or that's a joke, but you know,
+
+ align:start position:0%
+because or that's a joke, but you know,
+ 
+
+ align:start position:0%
+because or that's a joke, but you know,
+because I learn how to think about
+
+ align:start position:0%
+because I learn how to think about
+ 
+
+ align:start position:0%
+because I learn how to think about
+things.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I think that's a good place. Fine.
+
+ align:start position:0%
+So, I think that's a good place. Fine.
+ 
+
+ align:start position:0%
+So, I think that's a good place. Fine.
+All right. I mean, all good. Is that
+
+ align:start position:0%
+All right. I mean, all good. Is that
+ 
+
+ align:start position:0%
+All right. I mean, all good. Is that
+okay? Yeah. Good. All right. Thank you
+
+ align:start position:0%
+okay? Yeah. Good. All right. Thank you
+ 
+
+ align:start position:0%
+okay? Yeah. Good. All right. Thank you
+all. Thank you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/qmCbc9dbwXU.txt b/qmCbc9dbwXU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..941bd1c83f1667d6f814ea1f8c1a3e3c73cd7a84
--- /dev/null
+++ b/qmCbc9dbwXU.txt
@@ -0,0 +1,531 @@
+align:start position:0%
+ 
+let's consider a very simple example of
+
+ align:start position:0%
+let's consider a very simple example of
+ 
+
+ align:start position:0%
+let's consider a very simple example of
+a runner in which our position function
+
+ align:start position:0%
+a runner in which our position function
+ 
+
+ align:start position:0%
+a runner in which our position function
+X of T is given as a quadratic function
+
+ align:start position:0%
+X of T is given as a quadratic function
+ 
+
+ align:start position:0%
+X of T is given as a quadratic function
+in time it will be a constant B times T
+
+ align:start position:0%
+in time it will be a constant B times T
+ 
+
+ align:start position:0%
+in time it will be a constant B times T
+squared here B is a constant now it's
+
+ align:start position:0%
+squared here B is a constant now it's
+ 
+
+ align:start position:0%
+squared here B is a constant now it's
+always important in SI units to consider
+
+ align:start position:0%
+always important in SI units to consider
+ 
+
+ align:start position:0%
+always important in SI units to consider
+what the units of this constant is
+
+ align:start position:0%
+what the units of this constant is
+ 
+
+ align:start position:0%
+what the units of this constant is
+because the position function is
+
+ align:start position:0%
+because the position function is
+ 
+
+ align:start position:0%
+because the position function is
+measured in meters and time is measured
+
+ align:start position:0%
+measured in meters and time is measured
+ 
+
+ align:start position:0%
+measured in meters and time is measured
+in seconds B is a constant and it has
+
+ align:start position:0%
+in seconds B is a constant and it has
+ 
+
+ align:start position:0%
+in seconds B is a constant and it has
+units of meters per second squared and
+
+ align:start position:0%
+units of meters per second squared and
+ 
+
+ align:start position:0%
+units of meters per second squared and
+there's an example of a runner and let's
+
+ align:start position:0%
+there's an example of a runner and let's
+ 
+
+ align:start position:0%
+there's an example of a runner and let's
+make a plot of that position function so
+
+ align:start position:0%
+make a plot of that position function so
+ 
+
+ align:start position:0%
+make a plot of that position function so
+we're going to plot X of T as a function
+
+ align:start position:0%
+we're going to plot X of T as a function
+ 
+
+ align:start position:0%
+we're going to plot X of T as a function
+of time B here let's make be a positive
+
+ align:start position:0%
+of time B here let's make be a positive
+ 
+
+ align:start position:0%
+of time B here let's make be a positive
+constant and so our function looks
+
+ align:start position:0%
+constant and so our function looks
+ 
+
+ align:start position:0%
+constant and so our function looks
+something like that now the velocity
+
+ align:start position:0%
+something like that now the velocity
+ 
+
+ align:start position:0%
+something like that now the velocity
+component of the velocity remember D of
+
+ align:start position:0%
+component of the velocity remember D of
+ 
+
+ align:start position:0%
+component of the velocity remember D of
+T is given by DX DT of this function and
+
+ align:start position:0%
+T is given by DX DT of this function and
+ 
+
+ align:start position:0%
+T is given by DX DT of this function and
+the derivative of a polynomial T squared
+
+ align:start position:0%
+the derivative of a polynomial T squared
+ 
+
+ align:start position:0%
+the derivative of a polynomial T squared
+is very simple that's just simply 2 B
+
+ align:start position:0%
+is very simple that's just simply 2 B
+ 
+
+ align:start position:0%
+is very simple that's just simply 2 B
+times T again let's look at our units
+
+ align:start position:0%
+times T again let's look at our units
+ 
+
+ align:start position:0%
+times T again let's look at our units
+because B has the units of meters per
+
+ align:start position:0%
+because B has the units of meters per
+ 
+
+ align:start position:0%
+because B has the units of meters per
+second squared and we're multiplying
+
+ align:start position:0%
+second squared and we're multiplying
+ 
+
+ align:start position:0%
+second squared and we're multiplying
+that by second we have the units of
+
+ align:start position:0%
+that by second we have the units of
+ 
+
+ align:start position:0%
+that by second we have the units of
+velocity in SI units as meters per
+
+ align:start position:0%
+velocity in SI units as meters per
+ 
+
+ align:start position:0%
+velocity in SI units as meters per
+second now 2 let's plot that function
+
+ align:start position:0%
+second now 2 let's plot that function
+ 
+
+ align:start position:0%
+second now 2 let's plot that function
+notice this is a linear function and so
+
+ align:start position:0%
+notice this is a linear function and so
+ 
+
+ align:start position:0%
+notice this is a linear function and so
+if I plotted underneath here the
+
+ align:start position:0%
+if I plotted underneath here the
+ 
+
+ align:start position:0%
+if I plotted underneath here the
+velocity as a function of time its
+
+ align:start position:0%
+velocity as a function of time its
+ 
+
+ align:start position:0%
+velocity as a function of time its
+starts off with a 0 slope remember we're
+
+ align:start position:0%
+starts off with a 0 slope remember we're
+ 
+
+ align:start position:0%
+starts off with a 0 slope remember we're
+looking our velocity at any given time
+
+ align:start position:0%
+looking our velocity at any given time
+ 
+
+ align:start position:0%
+looking our velocity at any given time
+corresponds to the slope of the tangent
+
+ align:start position:0%
+corresponds to the slope of the tangent
+ 
+
+ align:start position:0%
+corresponds to the slope of the tangent
+line to the position function and you
+
+ align:start position:0%
+line to the position function and you
+ 
+
+ align:start position:0%
+line to the position function and you
+can see that slope is increasing now you
+
+ align:start position:0%
+can see that slope is increasing now you
+ 
+
+ align:start position:0%
+can see that slope is increasing now you
+wouldn't know from this graph but if you
+
+ align:start position:0%
+wouldn't know from this graph but if you
+ 
+
+ align:start position:0%
+wouldn't know from this graph but if you
+did plot T squared it's increasing
+
+ align:start position:0%
+did plot T squared it's increasing
+ 
+
+ align:start position:0%
+did plot T squared it's increasing
+linearly and so our velocity function
+
+ align:start position:0%
+linearly and so our velocity function
+ 
+
+ align:start position:0%
+linearly and so our velocity function
+the initial slope is zero at T equals
+
+ align:start position:0%
+the initial slope is zero at T equals
+ 
+
+ align:start position:0%
+the initial slope is zero at T equals
+zero and it's increasing linearly in
+
+ align:start position:0%
+zero and it's increasing linearly in
+ 
+
+ align:start position:0%
+zero and it's increasing linearly in
+time so we'll just draw that as some
+
+ align:start position:0%
+time so we'll just draw that as some
+ 
+
+ align:start position:0%
+time so we'll just draw that as some
+linear function and the slope here
+
+ align:start position:0%
+linear function and the slope here
+ 
+
+ align:start position:0%
+linear function and the slope here
+of this function will be now the
+
+ align:start position:0%
+of this function will be now the
+ 
+
+ align:start position:0%
+of this function will be now the
+acceleration so a of T is the derivative
+
+ align:start position:0%
+acceleration so a of T is the derivative
+ 
+
+ align:start position:0%
+acceleration so a of T is the derivative
+of the component of the velocity
+
+ align:start position:0%
+of the component of the velocity
+ 
+
+ align:start position:0%
+of the component of the velocity
+function as a function of time and this
+
+ align:start position:0%
+function as a function of time and this
+ 
+
+ align:start position:0%
+function as a function of time and this
+derivative is quite easy it's just
+
+ align:start position:0%
+derivative is quite easy it's just
+ 
+
+ align:start position:0%
+derivative is quite easy it's just
+simply to be now notice those have the
+
+ align:start position:0%
+simply to be now notice those have the
+ 
+
+ align:start position:0%
+simply to be now notice those have the
+units of meters per second squared we
+
+ align:start position:0%
+units of meters per second squared we
+ 
+
+ align:start position:0%
+units of meters per second squared we
+saw our units for acceleration when we
+
+ align:start position:0%
+saw our units for acceleration when we
+ 
+
+ align:start position:0%
+saw our units for acceleration when we
+again look at the slope notice that at
+
+ align:start position:0%
+again look at the slope notice that at
+ 
+
+ align:start position:0%
+again look at the slope notice that at
+every single point the slope of the
+
+ align:start position:0%
+every single point the slope of the
+ 
+
+ align:start position:0%
+every single point the slope of the
+velocity as a function of time is a
+
+ align:start position:0%
+velocity as a function of time is a
+ 
+
+ align:start position:0%
+velocity as a function of time is a
+constant the slope here is just equal to
+
+ align:start position:0%
+constant the slope here is just equal to
+ 
+
+ align:start position:0%
+constant the slope here is just equal to
+2b and so now if we plotted our
+
+ align:start position:0%
+2b and so now if we plotted our
+ 
+
+ align:start position:0%
+2b and so now if we plotted our
+acceleration function we have this point
+
+ align:start position:0%
+acceleration function we have this point
+ 
+
+ align:start position:0%
+acceleration function we have this point
+to be and every single point has the
+
+ align:start position:0%
+to be and every single point has the
+ 
+
+ align:start position:0%
+to be and every single point has the
+same value of acceleration so here the
+
+ align:start position:0%
+same value of acceleration so here the
+ 
+
+ align:start position:0%
+same value of acceleration so here the
+acceleration is an example of constant
+
+ align:start position:0%
+acceleration is an example of constant
+ 
+
+ align:start position:0%
+acceleration is an example of constant
+acceleration and this is our simplest
+
+ align:start position:0%
+acceleration and this is our simplest
+ 
+
+ align:start position:0%
+acceleration and this is our simplest
+case notice we started with a position
+
+ align:start position:0%
+case notice we started with a position
+ 
+
+ align:start position:0%
+case notice we started with a position
+function we differentiate to get the
+
+ align:start position:0%
+function we differentiate to get the
+ 
+
+ align:start position:0%
+function we differentiate to get the
+component of the velocity and to get the
+
+ align:start position:0%
+component of the velocity and to get the
+ 
+
+ align:start position:0%
+component of the velocity and to get the
+component of the acceleration so this is
+
+ align:start position:0%
+component of the acceleration so this is
+ 
+
+ align:start position:0%
+component of the acceleration so this is
+a very simple model for a runner whose
+
+ align:start position:0%
+a very simple model for a runner whose
+ 
+
+ align:start position:0%
+a very simple model for a runner whose
+increasing speed linearly accelerating
+
+ align:start position:0%
+increasing speed linearly accelerating
+ 
+
+ align:start position:0%
+increasing speed linearly accelerating
+at a constant rate
\ No newline at end of file
diff --git a/rCG6r6gotZQ.txt b/rCG6r6gotZQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d3046e9b0cf629b5c08ca3af7db876d7f3221c89
--- /dev/null
+++ b/rCG6r6gotZQ.txt
@@ -0,0 +1,7003 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hey guys.
+
+ align:start position:0%
+Hey guys.
+ 
+
+ align:start position:0%
+Hey guys.
+So these are our special guest lectures
+
+ align:start position:0%
+So these are our special guest lectures
+ 
+
+ align:start position:0%
+So these are our special guest lectures
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+today. These are sixth graders from the
+
+ align:start position:0%
+today. These are sixth graders from the
+ 
+
+ align:start position:0%
+today. These are sixth graders from the
+RT. You guys want to go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And everyone rotate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hi. Music matters. It really does. Are
+
+ align:start position:0%
+Hi. Music matters. It really does. Are
+ 
+
+ align:start position:0%
+Hi. Music matters. It really does. Are
+you a musician? Yep. Where you play? I
+
+ align:start position:0%
+you a musician? Yep. Where you play? I
+ 
+
+ align:start position:0%
+you a musician? Yep. Where you play? I
+play the snare drum, the bass drum, tan,
+
+ align:start position:0%
+play the snare drum, the bass drum, tan,
+ 
+
+ align:start position:0%
+play the snare drum, the bass drum, tan,
+marine, pretty much all
+
+ align:start position:0%
+marine, pretty much all
+ 
+
+ align:start position:0%
+marine, pretty much all
+the guys trying.
+
+ align:start position:0%
+the guys trying.
+ 
+
+ align:start position:0%
+the guys trying.
+That's really cool. All
+
+ align:start position:0%
+That's really cool. All
+ 
+
+ align:start position:0%
+That's really cool. All
+right, you guys. So, before we get
+
+ align:start position:0%
+right, you guys. So, before we get
+ 
+
+ align:start position:0%
+right, you guys. So, before we get
+started, um the way this is going to
+
+ align:start position:0%
+started, um the way this is going to
+ 
+
+ align:start position:0%
+started, um the way this is going to
+work is give you um five minutes at each
+
+ align:start position:0%
+work is give you um five minutes at each
+ 
+
+ align:start position:0%
+work is give you um five minutes at each
+station with your consultants. Um and
+
+ align:start position:0%
+station with your consultants. Um and
+ 
+
+ align:start position:0%
+station with your consultants. Um and
+during this five minutes, go ahead and
+
+ align:start position:0%
+during this five minutes, go ahead and
+ 
+
+ align:start position:0%
+during this five minutes, go ahead and
+uh this is for the MIT students. Go
+
+ align:start position:0%
+uh this is for the MIT students. Go
+ 
+
+ align:start position:0%
+uh this is for the MIT students. Go
+ahead and introduce yourselves. Uh tell
+
+ align:start position:0%
+ahead and introduce yourselves. Uh tell
+ 
+
+ align:start position:0%
+ahead and introduce yourselves. Uh tell
+them what you study, maybe what year you
+
+ align:start position:0%
+them what you study, maybe what year you
+ 
+
+ align:start position:0%
+them what you study, maybe what year you
+are, what you're interested in. And then
+
+ align:start position:0%
+are, what you're interested in. And then
+ 
+
+ align:start position:0%
+are, what you're interested in. And then
+if you feel comfortable showing them the
+
+ align:start position:0%
+if you feel comfortable showing them the
+ 
+
+ align:start position:0%
+if you feel comfortable showing them the
+video pitch that you made last night, we
+
+ align:start position:0%
+video pitch that you made last night, we
+ 
+
+ align:start position:0%
+video pitch that you made last night, we
+we have this to deal with. So, just just
+
+ align:start position:0%
+we have this to deal with. So, just just
+ 
+
+ align:start position:0%
+we have this to deal with. So, just just
+know that that's out of our control and
+
+ align:start position:0%
+know that that's out of our control and
+ 
+
+ align:start position:0%
+know that that's out of our control and
+we're really sorry that they're doing
+
+ align:start position:0%
+we're really sorry that they're doing
+ 
+
+ align:start position:0%
+we're really sorry that they're doing
+some construction over there and it's
+
+ align:start position:0%
+some construction over there and it's
+ 
+
+ align:start position:0%
+some construction over there and it's
+going to be a little noisy. Sorry.
+
+ align:start position:0%
+going to be a little noisy. Sorry.
+ 
+
+ align:start position:0%
+going to be a little noisy. Sorry.
+So, go ahead and show them your pitch if
+
+ align:start position:0%
+So, go ahead and show them your pitch if
+ 
+
+ align:start position:0%
+So, go ahead and show them your pitch if
+you're comfortable with it. If not, you
+
+ align:start position:0%
+you're comfortable with it. If not, you
+ 
+
+ align:start position:0%
+you're comfortable with it. If not, you
+can just tell them your idea and then
+
+ align:start position:0%
+can just tell them your idea and then
+ 
+
+ align:start position:0%
+can just tell them your idea and then
+workshop some of the backup ideas that
+
+ align:start position:0%
+workshop some of the backup ideas that
+ 
+
+ align:start position:0%
+workshop some of the backup ideas that
+you thought about last night and the
+
+ align:start position:0%
+you thought about last night and the
+ 
+
+ align:start position:0%
+you thought about last night and the
+Cummings Middle School students know
+
+ align:start position:0%
+Cummings Middle School students know
+ 
+
+ align:start position:0%
+Cummings Middle School students know
+exactly what criteria you're looking
+
+ align:start position:0%
+exactly what criteria you're looking
+ 
+
+ align:start position:0%
+exactly what criteria you're looking
+for, right? So, you can use the rubrics
+
+ align:start position:0%
+for, right? So, you can use the rubrics
+ 
+
+ align:start position:0%
+for, right? So, you can use the rubrics
+that that we gave you. Um, and at the
+
+ align:start position:0%
+that that we gave you. Um, and at the
+ 
+
+ align:start position:0%
+that that we gave you. Um, and at the
+end of the five minutes, we're we're
+
+ align:start position:0%
+end of the five minutes, we're we're
+ 
+
+ align:start position:0%
+end of the five minutes, we're we're
+gonna have the MIT students rotate. So,
+
+ align:start position:0%
+gonna have the MIT students rotate. So,
+ 
+
+ align:start position:0%
+gonna have the MIT students rotate. So,
+um, Nathan, you'll go to the back. Paul,
+
+ align:start position:0%
+um, Nathan, you'll go to the back. Paul,
+ 
+
+ align:start position:0%
+um, Nathan, you'll go to the back. Paul,
+you'll scoot here. Everyone will just
+
+ align:start position:0%
+you'll scoot here. Everyone will just
+ 
+
+ align:start position:0%
+you'll scoot here. Everyone will just
+shift that way. Does that make sense to
+
+ align:start position:0%
+shift that way. Does that make sense to
+ 
+
+ align:start position:0%
+shift that way. Does that make sense to
+everyone? We'll try it out for the first
+
+ align:start position:0%
+everyone? We'll try it out for the first
+ 
+
+ align:start position:0%
+everyone? We'll try it out for the first
+time. Um, and if anyone has any
+
+ align:start position:0%
+time. Um, and if anyone has any
+ 
+
+ align:start position:0%
+time. Um, and if anyone has any
+questions, you can always come talk to
+
+ align:start position:0%
+questions, you can always come talk to
+ 
+
+ align:start position:0%
+questions, you can always come talk to
+one of the instructors. Okay. So, does
+
+ align:start position:0%
+one of the instructors. Okay. So, does
+ 
+
+ align:start position:0%
+one of the instructors. Okay. So, does
+anyone have any questions about how this
+
+ align:start position:0%
+anyone have any questions about how this
+ 
+
+ align:start position:0%
+anyone have any questions about how this
+is going to work before we get started
+
+ align:start position:0%
+is going to work before we get started
+ 
+
+ align:start position:0%
+is going to work before we get started
+or what your job is? Does anyone have a
+
+ align:start position:0%
+or what your job is? Does anyone have a
+ 
+
+ align:start position:0%
+or what your job is? Does anyone have a
+question about that either?
+
+ align:start position:0%
+question about that either?
+ 
+
+ align:start position:0%
+question about that either?
+Good job. Your job. It's a very
+
+ align:start position:0%
+Good job. Your job. It's a very
+ 
+
+ align:start position:0%
+Good job. Your job. It's a very
+important job. Your critics,
+
+ align:start position:0%
+important job. Your critics,
+ 
+
+ align:start position:0%
+important job. Your critics,
+right? All right, then. It looks like
+
+ align:start position:0%
+right? All right, then. It looks like
+ 
+
+ align:start position:0%
+right? All right, then. It looks like
+everyone knows what to do. So, I will go
+
+ align:start position:0%
+everyone knows what to do. So, I will go
+ 
+
+ align:start position:0%
+everyone knows what to do. So, I will go
+ahead and start the timer for the first
+
+ align:start position:0%
+ahead and start the timer for the first
+ 
+
+ align:start position:0%
+ahead and start the timer for the first
+five minutes. Um, and if at any point
+
+ align:start position:0%
+five minutes. Um, and if at any point
+ 
+
+ align:start position:0%
+five minutes. Um, and if at any point
+you have a question about what you're
+
+ align:start position:0%
+you have a question about what you're
+ 
+
+ align:start position:0%
+you have a question about what you're
+doing or just a clarification, then you
+
+ align:start position:0%
+doing or just a clarification, then you
+ 
+
+ align:start position:0%
+doing or just a clarification, then you
+can come find one of us. Yeah.
+
+ align:start position:0%
+can come find one of us. Yeah.
+ 
+
+ align:start position:0%
+can come find one of us. Yeah.
+Have fun.
+
+ align:start position:0%
+Have fun.
+ 
+
+ align:start position:0%
+Have fun.
+Right. Yeah. Just a short introduction.
+
+ align:start position:0%
+Right. Yeah. Just a short introduction.
+ 
+
+ align:start position:0%
+Right. Yeah. Just a short introduction.
+I study computer science. Anyone know
+
+ align:start position:0%
+I study computer science. Anyone know
+ 
+
+ align:start position:0%
+I study computer science. Anyone know
+what that is? Kind of like programming
+
+ align:start position:0%
+what that is? Kind of like programming
+ 
+
+ align:start position:0%
+what that is? Kind of like programming
+kind of stuff like Oh, and so the kind
+
+ align:start position:0%
+kind of stuff like Oh, and so the kind
+ 
+
+ align:start position:0%
+kind of stuff like Oh, and so the kind
+of stuff I like to do is like I make
+
+ align:start position:0%
+of stuff I like to do is like I make
+ 
+
+ align:start position:0%
+of stuff I like to do is like I make
+computer games. So this kind of like
+
+ align:start position:0%
+computer games. So this kind of like
+ 
+
+ align:start position:0%
+computer games. So this kind of like
+slash snowflake, you know? So you you
+
+ align:start position:0%
+slash snowflake, you know? So you you
+ 
+
+ align:start position:0%
+slash snowflake, you know? So you you
+it's kind of like Fruit Ninja. Ever
+
+ align:start position:0%
+it's kind of like Fruit Ninja. Ever
+ 
+
+ align:start position:0%
+it's kind of like Fruit Ninja. Ever
+heard of Fruit Ninja? But except cuz
+
+ align:start position:0%
+heard of Fruit Ninja? But except cuz
+ 
+
+ align:start position:0%
+heard of Fruit Ninja? But except cuz
+it's snowing today, you slash the
+
+ align:start position:0%
+it's snowing today, you slash the
+ 
+
+ align:start position:0%
+it's snowing today, you slash the
+snowflake. It's kind of like the same,
+
+ align:start position:0%
+snowflake. It's kind of like the same,
+ 
+
+ align:start position:0%
+snowflake. It's kind of like the same,
+but this time you get a lot of combos.
+
+ align:start position:0%
+but this time you get a lot of combos.
+ 
+
+ align:start position:0%
+but this time you get a lot of combos.
+Oh, if you slash the red one, you kind
+
+ align:start position:0%
+Oh, if you slash the red one, you kind
+ 
+
+ align:start position:0%
+Oh, if you slash the red one, you kind
+of lose time. You lose points and you
+
+ align:start position:0%
+of lose time. You lose points and you
+ 
+
+ align:start position:0%
+of lose time. You lose points and you
+eventually lose the game. It's kind of
+
+ align:start position:0%
+eventually lose the game. It's kind of
+ 
+
+ align:start position:0%
+eventually lose the game. It's kind of
+like the kind of things I do. Did you
+
+ align:start position:0%
+like the kind of things I do. Did you
+ 
+
+ align:start position:0%
+like the kind of things I do. Did you
+make that? Yeah, I made that. Oh, I
+
+ align:start position:0%
+make that? Yeah, I made that. Oh, I
+ 
+
+ align:start position:0%
+make that? Yeah, I made that. Oh, I
+didn't. Yeah, you can. You can. I got
+
+ align:start position:0%
+didn't. Yeah, you can. You can. I got
+ 
+
+ align:start position:0%
+didn't. Yeah, you can. You can. I got
+Fruit Ninja. It's kind of like Fruit
+
+ align:start position:0%
+Fruit Ninja. It's kind of like Fruit
+ 
+
+ align:start position:0%
+Fruit Ninja. It's kind of like Fruit
+Ninja, but except that don't slash the
+
+ align:start position:0%
+Ninja, but except that don't slash the
+ 
+
+ align:start position:0%
+Ninja, but except that don't slash the
+red snowflakes and it's okay if the
+
+ align:start position:0%
+red snowflakes and it's okay if the
+ 
+
+ align:start position:0%
+red snowflakes and it's okay if the
+snowflakes fall off. Oh, the blue ones
+
+ align:start position:0%
+snowflakes fall off. Oh, the blue ones
+ 
+
+ align:start position:0%
+snowflakes fall off. Oh, the blue ones
+give you these mega explosions and they
+
+ align:start position:0%
+give you these mega explosions and they
+ 
+
+ align:start position:0%
+give you these mega explosions and they
+can layer. Yeah. So, I have this idea
+
+ align:start position:0%
+can layer. Yeah. So, I have this idea
+ 
+
+ align:start position:0%
+can layer. Yeah. So, I have this idea
+like it's just without programming. How
+
+ align:start position:0%
+like it's just without programming. How
+ 
+
+ align:start position:0%
+like it's just without programming. How
+can you make computer games? That's kind
+
+ align:start position:0%
+can you make computer games? That's kind
+ 
+
+ align:start position:0%
+can you make computer games? That's kind
+of like what I was thinking of off my
+
+ align:start position:0%
+of like what I was thinking of off my
+ 
+
+ align:start position:0%
+of like what I was thinking of off my
+head. What do you think of that? Like um
+
+ align:start position:0%
+head. What do you think of that? Like um
+ 
+
+ align:start position:0%
+head. What do you think of that? Like um
+Do you have like things you like when
+
+ align:start position:0%
+Do you have like things you like when
+ 
+
+ align:start position:0%
+Do you have like things you like when
+you playing your phone? Do do you play
+
+ align:start position:0%
+you playing your phone? Do do you play
+ 
+
+ align:start position:0%
+you playing your phone? Do do you play
+games a lot on your phone? Yeah,
+
+ align:start position:0%
+games a lot on your phone? Yeah,
+ 
+
+ align:start position:0%
+games a lot on your phone? Yeah,
+definitely. Right. What's your favorite?
+
+ align:start position:0%
+definitely. Right. What's your favorite?
+ 
+
+ align:start position:0%
+definitely. Right. What's your favorite?
+Oh,
+
+ align:start position:0%
+Oh,
+ 
+
+ align:start position:0%
+Oh,
+um I like a lot of them. I love social
+
+ align:start position:0%
+um I like a lot of them. I love social
+ 
+
+ align:start position:0%
+um I like a lot of them. I love social
+media. Ah, social media. That kind of
+
+ align:start position:0%
+media. Ah, social media. That kind of
+ 
+
+ align:start position:0%
+media. Ah, social media. That kind of
+Yeah, that kind of thing. I don't really
+
+ align:start position:0%
+Yeah, that kind of thing. I don't really
+ 
+
+ align:start position:0%
+Yeah, that kind of thing. I don't really
+have a favorite. Oh, I see. I play
+
+ align:start position:0%
+have a favorite. Oh, I see. I play
+ 
+
+ align:start position:0%
+have a favorite. Oh, I see. I play
+Madden Mobile in Clash of Clans. Ah,
+
+ align:start position:0%
+Madden Mobile in Clash of Clans. Ah,
+ 
+
+ align:start position:0%
+Madden Mobile in Clash of Clans. Ah,
+Clash of Clans was thoroughly
+
+ align:start position:0%
+Clash of Clans was thoroughly
+ 
+
+ align:start position:0%
+Clash of Clans was thoroughly
+addictive. Yeah. So it'll probably be
+
+ align:start position:0%
+addictive. Yeah. So it'll probably be
+ 
+
+ align:start position:0%
+addictive. Yeah. So it'll probably be
+about like how can you come up ideas to
+
+ align:start position:0%
+about like how can you come up ideas to
+ 
+
+ align:start position:0%
+about like how can you come up ideas to
+make games because honestly the people
+
+ align:start position:0%
+make games because honestly the people
+ 
+
+ align:start position:0%
+make games because honestly the people
+who is trying to make games are probably
+
+ align:start position:0%
+who is trying to make games are probably
+ 
+
+ align:start position:0%
+who is trying to make games are probably
+not as smart as anyone out there cuz you
+
+ align:start position:0%
+not as smart as anyone out there cuz you
+ 
+
+ align:start position:0%
+not as smart as anyone out there cuz you
+play the games. You know what people
+
+ align:start position:0%
+play the games. You know what people
+ 
+
+ align:start position:0%
+play the games. You know what people
+like to play and it's not it's not me
+
+ align:start position:0%
+like to play and it's not it's not me
+ 
+
+ align:start position:0%
+like to play and it's not it's not me
+it's it's you you know what likes to
+
+ align:start position:0%
+it's it's you you know what likes to
+ 
+
+ align:start position:0%
+it's it's you you know what likes to
+play. So if people like you could make
+
+ align:start position:0%
+play. So if people like you could make
+ 
+
+ align:start position:0%
+play. So if people like you could make
+the games that people that of all ages
+
+ align:start position:0%
+the games that people that of all ages
+ 
+
+ align:start position:0%
+the games that people that of all ages
+could play then that would be great,
+
+ align:start position:0%
+could play then that would be great,
+ 
+
+ align:start position:0%
+could play then that would be great,
+right? Yeah. Okay. Well, just just
+
+ align:start position:0%
+right? Yeah. Okay. Well, just just
+ 
+
+ align:start position:0%
+right? Yeah. Okay. Well, just just
+another curious cat question. Do you
+
+ align:start position:0%
+another curious cat question. Do you
+ 
+
+ align:start position:0%
+another curious cat question. Do you
+know what a hacker is?
+
+ align:start position:0%
+know what a hacker is?
+ 
+
+ align:start position:0%
+know what a hacker is?
+What? No. Hacker. Oh, a hacker. Yeah, a
+
+ align:start position:0%
+What? No. Hacker. Oh, a hacker. Yeah, a
+ 
+
+ align:start position:0%
+What? No. Hacker. Oh, a hacker. Yeah, a
+hacker. Oh, yeah. Someone tries to like
+
+ align:start position:0%
+hacker. Oh, yeah. Someone tries to like
+ 
+
+ align:start position:0%
+hacker. Oh, yeah. Someone tries to like
+invade the
+
+ align:start position:0%
+invade the
+ 
+
+ align:start position:0%
+invade the
+firewall thingy or Uhhuh. security get
+
+ align:start position:0%
+firewall thingy or Uhhuh. security get
+ 
+
+ align:start position:0%
+firewall thingy or Uhhuh. security get
+through the security bar. Yeah. Yeah.
+
+ align:start position:0%
+through the security bar. Yeah. Yeah.
+ 
+
+ align:start position:0%
+through the security bar. Yeah. Yeah.
+Would you like would you want to know
+
+ align:start position:0%
+Would you like would you want to know
+ 
+
+ align:start position:0%
+Would you like would you want to know
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+what they do? No, I don't. No. Okay,
+
+ align:start position:0%
+what they do? No, I don't. No. Okay,
+ 
+
+ align:start position:0%
+what they do? No, I don't. No. Okay,
+then let's just script it. How about a
+
+ align:start position:0%
+then let's just script it. How about a
+ 
+
+ align:start position:0%
+then let's just script it. How about a
+curious question? Everyone knows Google,
+
+ align:start position:0%
+curious question? Everyone knows Google,
+ 
+
+ align:start position:0%
+curious question? Everyone knows Google,
+right? Yeah. But what do they do?
+
+ align:start position:0%
+right? Yeah. But what do they do?
+ 
+
+ align:start position:0%
+right? Yeah. But what do they do?
+search engine. Okay. Yeah. So, um and
+
+ align:start position:0%
+search engine. Okay. Yeah. So, um and
+ 
+
+ align:start position:0%
+search engine. Okay. Yeah. So, um and
+then what what does that what does that
+
+ align:start position:0%
+then what what does that what does that
+ 
+
+ align:start position:0%
+then what what does that what does that
+make them like? How are they like so
+
+ align:start position:0%
+make them like? How are they like so
+ 
+
+ align:start position:0%
+make them like? How are they like so
+important in our lives? Oh, cuz we like
+
+ align:start position:0%
+important in our lives? Oh, cuz we like
+ 
+
+ align:start position:0%
+important in our lives? Oh, cuz we like
+when we do our homework like kind of
+
+ align:start position:0%
+when we do our homework like kind of
+ 
+
+ align:start position:0%
+when we do our homework like kind of
+look up on Google that stuff. Okay.
+
+ align:start position:0%
+look up on Google that stuff. Okay.
+ 
+
+ align:start position:0%
+look up on Google that stuff. Okay.
+History is helpful.
+
+ align:start position:0%
+History is helpful.
+ 
+
+ align:start position:0%
+History is helpful.
+Yeah. Okay. You can also ask Siri on
+
+ align:start position:0%
+Yeah. Okay. You can also ask Siri on
+ 
+
+ align:start position:0%
+Yeah. Okay. You can also ask Siri on
+like your phone or something like a
+
+ align:start position:0%
+like your phone or something like a
+ 
+
+ align:start position:0%
+like your phone or something like a
+button. Okay. Just curious. Do you do
+
+ align:start position:0%
+button. Okay. Just curious. Do you do
+ 
+
+ align:start position:0%
+button. Okay. Just curious. Do you do
+you cuz I'm I'm actually not from US.
+
+ align:start position:0%
+you cuz I'm I'm actually not from US.
+ 
+
+ align:start position:0%
+you cuz I'm I'm actually not from US.
+I'm actually from a little country in
+
+ align:start position:0%
+I'm actually from a little country in
+ 
+
+ align:start position:0%
+I'm actually from a little country in
+Asia called Singapore. Yeah. So I'm just
+
+ align:start position:0%
+Asia called Singapore. Yeah. So I'm just
+ 
+
+ align:start position:0%
+Asia called Singapore. Yeah. So I'm just
+curious. Do you study programming at
+
+ align:start position:0%
+curious. Do you study programming at
+ 
+
+ align:start position:0%
+curious. Do you study programming at
+your age? No. Like any kind. So Okay. Me
+
+ align:start position:0%
+your age? No. Like any kind. So Okay. Me
+ 
+
+ align:start position:0%
+your age? No. Like any kind. So Okay. Me
+neither. I've never studied programming
+
+ align:start position:0%
+neither. I've never studied programming
+ 
+
+ align:start position:0%
+neither. I've never studied programming
+until I came to university. Yes. Yeah.
+
+ align:start position:0%
+until I came to university. Yes. Yeah.
+ 
+
+ align:start position:0%
+until I came to university. Yes. Yeah.
+So yeah. So what do you think program
+
+ align:start position:0%
+So yeah. So what do you think program
+ 
+
+ align:start position:0%
+So yeah. So what do you think program
+like? What do you think programmers do?
+
+ align:start position:0%
+like? What do you think programmers do?
+ 
+
+ align:start position:0%
+like? What do you think programmers do?
+Um, they create, they help build games
+
+ align:start position:0%
+Um, they create, they help build games
+ 
+
+ align:start position:0%
+Um, they create, they help build games
+and code and stuff. If you were to be
+
+ align:start position:0%
+and code and stuff. If you were to be
+ 
+
+ align:start position:0%
+and code and stuff. If you were to be
+like curious about what a programmer or
+
+ align:start position:0%
+like curious about what a programmer or
+ 
+
+ align:start position:0%
+like curious about what a programmer or
+or what can he do, what what would
+
+ align:start position:0%
+or what can he do, what what would
+ 
+
+ align:start position:0%
+or what can he do, what what would
+interest you games perhaps? Yeah.
+
+ align:start position:0%
+interest you games perhaps? Yeah.
+ 
+
+ align:start position:0%
+interest you games perhaps? Yeah.
+Anything else?
+
+ align:start position:0%
+Anything else?
+ 
+
+ align:start position:0%
+Anything else?
+I pretty much just play games.
+
+ align:start position:0%
+I pretty much just play games.
+ 
+
+ align:start position:0%
+I pretty much just play games.
+Yeah. I can't call online cuz it's an
+
+ align:start position:0%
+Yeah. I can't call online cuz it's an
+ 
+
+ align:start position:0%
+Yeah. I can't call online cuz it's an
+iPod. I don't have an iPhone. I only
+
+ align:start position:0%
+iPod. I don't have an iPhone. I only
+ 
+
+ align:start position:0%
+iPod. I don't have an iPhone. I only
+have an iPod. So, yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, out of the like random ideas to um
+
+ align:start position:0%
+So, out of the like random ideas to um
+ 
+
+ align:start position:0%
+So, out of the like random ideas to um
+which one like would would you be
+
+ align:start position:0%
+which one like would would you be
+ 
+
+ align:start position:0%
+which one like would would you be
+interested in in like a possible video?
+
+ align:start position:0%
+interested in in like a possible video?
+ 
+
+ align:start position:0%
+interested in in like a possible video?
+Um football games like football games.
+
+ align:start position:0%
+Um football games like football games.
+ 
+
+ align:start position:0%
+Um football games like football games.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Um I don't know.
+
+ align:start position:0%
+Um I don't know.
+ 
+
+ align:start position:0%
+Um I don't know.
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+something has to do with What's the like
+
+ align:start position:0%
+something has to do with What's the like
+ 
+
+ align:start position:0%
+something has to do with What's the like
+the weirdest thing you have in your
+
+ align:start position:0%
+the weirdest thing you have in your
+ 
+
+ align:start position:0%
+the weirdest thing you have in your
+mind? Like it always nags you about
+
+ align:start position:0%
+mind? Like it always nags you about
+ 
+
+ align:start position:0%
+mind? Like it always nags you about
+computers. I guess it's too slow
+
+ align:start position:0%
+computers. I guess it's too slow
+ 
+
+ align:start position:0%
+computers. I guess it's too slow
+sometimes. It's too slow. Yeah, too
+
+ align:start position:0%
+sometimes. It's too slow. Yeah, too
+ 
+
+ align:start position:0%
+sometimes. It's too slow. Yeah, too
+slow. Like even when you have Wi-Fi in
+
+ align:start position:0%
+slow. Like even when you have Wi-Fi in
+ 
+
+ align:start position:0%
+slow. Like even when you have Wi-Fi in
+range and you're like near the router or
+
+ align:start position:0%
+range and you're like near the router or
+ 
+
+ align:start position:0%
+range and you're like near the router or
+something, it's always really slow. Oh,
+
+ align:start position:0%
+something, it's always really slow. Oh,
+ 
+
+ align:start position:0%
+something, it's always really slow. Oh,
+okay. Oh, yeah. And Wi-Fi. You can't get
+
+ align:start position:0%
+okay. Oh, yeah. And Wi-Fi. You can't get
+ 
+
+ align:start position:0%
+okay. Oh, yeah. And Wi-Fi. You can't get
+like when I'm in my car, I can't play on
+
+ align:start position:0%
+like when I'm in my car, I can't play on
+ 
+
+ align:start position:0%
+like when I'm in my car, I can't play on
+like the internet and stuff. Ah, okay. I
+
+ align:start position:0%
+like the internet and stuff. Ah, okay. I
+ 
+
+ align:start position:0%
+like the internet and stuff. Ah, okay. I
+can play games that don't need internet.
+
+ align:start position:0%
+can play games that don't need internet.
+ 
+
+ align:start position:0%
+can play games that don't need internet.
+Yeah. Okay. So, like I don't like Wi-Fi
+
+ align:start position:0%
+Yeah. Okay. So, like I don't like Wi-Fi
+ 
+
+ align:start position:0%
+Yeah. Okay. So, like I don't like Wi-Fi
+cuz I would We should have builtin Wi-Fi
+
+ align:start position:0%
+cuz I would We should have builtin Wi-Fi
+ 
+
+ align:start position:0%
+cuz I would We should have builtin Wi-Fi
+and everything. So, that would be cool.
+
+ align:start position:0%
+and everything. So, that would be cool.
+ 
+
+ align:start position:0%
+and everything. So, that would be cool.
+Okay. What about um maybe um you know
+
+ align:start position:0%
+Okay. What about um maybe um you know
+ 
+
+ align:start position:0%
+Okay. What about um maybe um you know
+Pixar? You like the movies? Yeah. Oh, I
+
+ align:start position:0%
+Pixar? You like the movies? Yeah. Oh, I
+ 
+
+ align:start position:0%
+Pixar? You like the movies? Yeah. Oh, I
+I love The Incredibles, but that was
+
+ align:start position:0%
+I love The Incredibles, but that was
+ 
+
+ align:start position:0%
+I love The Incredibles, but that was
+really old, but I still love it here
+
+ align:start position:0%
+really old, but I still love it here
+ 
+
+ align:start position:0%
+really old, but I still love it here
+today. Like Yeah. And have you ever
+
+ align:start position:0%
+today. Like Yeah. And have you ever
+ 
+
+ align:start position:0%
+today. Like Yeah. And have you ever
+wondered like how they do it? It kind of
+
+ align:start position:0%
+wondered like how they do it? It kind of
+ 
+
+ align:start position:0%
+wondered like how they do it? It kind of
+looks different from like the normal
+
+ align:start position:0%
+looks different from like the normal
+ 
+
+ align:start position:0%
+looks different from like the normal
+Yeah. So, they actually use some
+
+ align:start position:0%
+Yeah. So, they actually use some
+ 
+
+ align:start position:0%
+Yeah. So, they actually use some
+computer software to do it. It's called
+
+ align:start position:0%
+computer software to do it. It's called
+ 
+
+ align:start position:0%
+computer software to do it. It's called
+3D animation like threedimensional. Is
+
+ align:start position:0%
+3D animation like threedimensional. Is
+ 
+
+ align:start position:0%
+3D animation like threedimensional. Is
+that like interesting or Yeah, I would
+
+ align:start position:0%
+that like interesting or Yeah, I would
+ 
+
+ align:start position:0%
+that like interesting or Yeah, I would
+be interested in that. Yeah. Like how do
+
+ align:start position:0%
+be interested in that. Yeah. Like how do
+ 
+
+ align:start position:0%
+be interested in that. Yeah. Like how do
+you draw but on the computer? Like do
+
+ align:start position:0%
+you draw but on the computer? Like do
+ 
+
+ align:start position:0%
+you draw but on the computer? Like do
+they have to draw all little pictures
+
+ align:start position:0%
+they have to draw all little pictures
+ 
+
+ align:start position:0%
+they have to draw all little pictures
+like of every movement like ah that's
+
+ align:start position:0%
+like of every movement like ah that's
+ 
+
+ align:start position:0%
+like of every movement like ah that's
+the key. It's no. It's actually the
+
+ align:start position:0%
+the key. It's no. It's actually the
+ 
+
+ align:start position:0%
+the key. It's no. It's actually the
+answer is no. Oh yeah they did. It's
+
+ align:start position:0%
+answer is no. Oh yeah they did. It's
+ 
+
+ align:start position:0%
+answer is no. Oh yeah they did. It's
+pretty cool right? What they do is like
+
+ align:start position:0%
+pretty cool right? What they do is like
+ 
+
+ align:start position:0%
+pretty cool right? What they do is like
+kind of like they make a teddy bear in
+
+ align:start position:0%
+kind of like they make a teddy bear in
+ 
+
+ align:start position:0%
+kind of like they make a teddy bear in
+in the computer like some kind of like
+
+ align:start position:0%
+in the computer like some kind of like
+ 
+
+ align:start position:0%
+in the computer like some kind of like
+3D image of it and they put bones in
+
+ align:start position:0%
+3D image of it and they put bones in
+ 
+
+ align:start position:0%
+3D image of it and they put bones in
+like like just like how you put bones in
+
+ align:start position:0%
+like like just like how you put bones in
+ 
+
+ align:start position:0%
+like like just like how you put bones in
+humans but you programming you put like
+
+ align:start position:0%
+humans but you programming you put like
+ 
+
+ align:start position:0%
+humans but you programming you put like
+logical bones and then you can shift the
+
+ align:start position:0%
+logical bones and then you can shift the
+ 
+
+ align:start position:0%
+logical bones and then you can shift the
+bones and you're like puppets you know.
+
+ align:start position:0%
+bones and you're like puppets you know.
+ 
+
+ align:start position:0%
+bones and you're like puppets you know.
+Yeah. Yeah. That's kind of like what
+
+ align:start position:0%
+Yeah. Yeah. That's kind of like what
+ 
+
+ align:start position:0%
+Yeah. Yeah. That's kind of like what
+they're doing all the time.
+
+ align:start position:0%
+they're doing all the time.
+ 
+
+ align:start position:0%
+they're doing all the time.
+Okay. So which one of the ideas was like
+
+ align:start position:0%
+Okay. So which one of the ideas was like
+ 
+
+ align:start position:0%
+Okay. So which one of the ideas was like
+I like the last one. Last one. Yeah. The
+
+ align:start position:0%
+I like the last one. Last one. Yeah. The
+ 
+
+ align:start position:0%
+I like the last one. Last one. Yeah. The
+last one the most. All right. Thank you
+
+ align:start position:0%
+last one the most. All right. Thank you
+ 
+
+ align:start position:0%
+last one the most. All right. Thank you
+guys. You're so amazing.
+
+ align:start position:0%
+guys. You're so amazing.
+ 
+
+ align:start position:0%
+guys. You're so amazing.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I'm Michael. I'm going to sit down with
+
+ align:start position:0%
+I'm Michael. I'm going to sit down with
+ 
+
+ align:start position:0%
+I'm Michael. I'm going to sit down with
+you guys, too. My name is Sarah.
+
+ align:start position:0%
+you guys, too. My name is Sarah.
+ 
+
+ align:start position:0%
+you guys, too. My name is Sarah.
+Um I'm
+
+ align:start position:0%
+Um I'm
+ 
+
+ align:start position:0%
+Um I'm
+Nathan. Um I
+
+ align:start position:0%
+Nathan. Um I
+ 
+
+ align:start position:0%
+Nathan. Um I
+study something that's a mix of
+
+ align:start position:0%
+study something that's a mix of
+ 
+
+ align:start position:0%
+study something that's a mix of
+mechanical today and geology.
+
+ align:start position:0%
+mechanical today and geology.
+ 
+
+ align:start position:0%
+mechanical today and geology.
+Geology. Mhm.
+
+ align:start position:0%
+Geology. Mhm.
+ 
+
+ align:start position:0%
+Geology. Mhm.
+Um sorry. Yeah. I'm a second year.
+
+ align:start position:0%
+Um sorry. Yeah. I'm a second year.
+ 
+
+ align:start position:0%
+Um sorry. Yeah. I'm a second year.
+I have two ideas. It looks like my main
+
+ align:start position:0%
+I have two ideas. It looks like my main
+ 
+
+ align:start position:0%
+I have two ideas. It looks like my main
+idea has been scrapped at this point.
+
+ align:start position:0%
+idea has been scrapped at this point.
+ 
+
+ align:start position:0%
+idea has been scrapped at this point.
+Um, but I'll still mention it to you in
+
+ align:start position:0%
+Um, but I'll still mention it to you in
+ 
+
+ align:start position:0%
+Um, but I'll still mention it to you in
+case one of you is fervently interested
+
+ align:start position:0%
+case one of you is fervently interested
+ 
+
+ align:start position:0%
+case one of you is fervently interested
+in it, which is I was interested in
+
+ align:start position:0%
+in it, which is I was interested in
+ 
+
+ align:start position:0%
+in it, which is I was interested in
+possibly doing something on how and why
+
+ align:start position:0%
+possibly doing something on how and why
+ 
+
+ align:start position:0%
+possibly doing something on how and why
+food
+
+ align:start position:0%
+food
+ 
+
+ align:start position:0%
+food
+decomposes. Um, but I guess my backup
+
+ align:start position:0%
+decomposes. Um, but I guess my backup
+ 
+
+ align:start position:0%
+decomposes. Um, but I guess my backup
+idea was is a bit more interesting to
+
+ align:start position:0%
+idea was is a bit more interesting to
+ 
+
+ align:start position:0%
+idea was is a bit more interesting to
+most people. Uh, which
+
+ align:start position:0%
+most people. Uh, which
+ 
+
+ align:start position:0%
+most people. Uh, which
+is how you can tell if there's like
+
+ align:start position:0%
+is how you can tell if there's like
+ 
+
+ align:start position:0%
+is how you can tell if there's like
+magma or lava under a surface like and
+
+ align:start position:0%
+magma or lava under a surface like and
+ 
+
+ align:start position:0%
+magma or lava under a surface like and
+how you can detect and map it and then
+
+ align:start position:0%
+how you can detect and map it and then
+ 
+
+ align:start position:0%
+how you can detect and map it and then
+you might be able to say, "Oh, is this
+
+ align:start position:0%
+you might be able to say, "Oh, is this
+ 
+
+ align:start position:0%
+you might be able to say, "Oh, is this
+place in risk of having some sort of
+
+ align:start position:0%
+place in risk of having some sort of
+ 
+
+ align:start position:0%
+place in risk of having some sort of
+eruption at some point
+
+ align:start position:0%
+eruption at some point
+ 
+
+ align:start position:0%
+eruption at some point
+um or not?" Still have to work on the
+
+ align:start position:0%
+um or not?" Still have to work on the
+ 
+
+ align:start position:0%
+um or not?" Still have to work on the
+hook.
+
+ align:start position:0%
+hook.
+ 
+
+ align:start position:0%
+hook.
+Um I don't
+
+ align:start position:0%
+Um I don't
+ 
+
+ align:start position:0%
+Um I don't
+know. I'm
+
+ align:start position:0%
+know. I'm
+ 
+
+ align:start position:0%
+know. I'm
+here do you think is more interesting?
+
+ align:start position:0%
+here do you think is more interesting?
+ 
+
+ align:start position:0%
+here do you think is more interesting?
+What was the first one? Uh um how and
+
+ align:start position:0%
+What was the first one? Uh um how and
+ 
+
+ align:start position:0%
+What was the first one? Uh um how and
+why food rots and decomposes.
+
+ align:start position:0%
+why food rots and decomposes.
+ 
+
+ align:start position:0%
+why food rots and decomposes.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+I would probably do the lava stuff.
+
+ align:start position:0%
+I would probably do the lava stuff.
+ 
+
+ align:start position:0%
+I would probably do the lava stuff.
+Yeah, it's like
+
+ align:start position:0%
+Yeah, it's like
+ 
+
+ align:start position:0%
+Yeah, it's like
+Yeah, save lives.
+
+ align:start position:0%
+Yeah, save lives.
+ 
+
+ align:start position:0%
+Yeah, save lives.
+Yeah. Um, so I know
+
+ align:start position:0%
+Yeah. Um, so I know
+ 
+
+ align:start position:0%
+Yeah. Um, so I know
+exactly what to say about that. Um,
+
+ align:start position:0%
+exactly what to say about that. Um,
+ 
+
+ align:start position:0%
+exactly what to say about that. Um,
+what would you be like expecting if you
+
+ align:start position:0%
+what would you be like expecting if you
+ 
+
+ align:start position:0%
+what would you be like expecting if you
+wanted to watch a video about lava? Like
+
+ align:start position:0%
+wanted to watch a video about lava? Like
+ 
+
+ align:start position:0%
+wanted to watch a video about lava? Like
+what would you want to be?
+
+ align:start position:0%
+what would you want to be?
+ 
+
+ align:start position:0%
+what would you want to be?
+A diagram of the Earth. Okay. probably
+
+ align:start position:0%
+A diagram of the Earth. Okay. probably
+ 
+
+ align:start position:0%
+A diagram of the Earth. Okay. probably
+having the lithosphere and a cenosphere
+
+ align:start position:0%
+having the lithosphere and a cenosphere
+ 
+
+ align:start position:0%
+having the lithosphere and a cenosphere
+and like the layers and then having like
+
+ align:start position:0%
+and like the layers and then having like
+ 
+
+ align:start position:0%
+and like the layers and then having like
+problems like you said how you can
+
+ align:start position:0%
+problems like you said how you can
+ 
+
+ align:start position:0%
+problems like you said how you can
+detect if there's lava under a surface
+
+ align:start position:0%
+detect if there's lava under a surface
+ 
+
+ align:start position:0%
+detect if there's lava under a surface
+probably having like a place that
+
+ align:start position:0%
+probably having like a place that
+ 
+
+ align:start position:0%
+probably having like a place that
+already does have lava under the surface
+
+ align:start position:0%
+already does have lava under the surface
+ 
+
+ align:start position:0%
+already does have lava under the surface
+and like showing the magma chamber
+
+ align:start position:0%
+and like showing the magma chamber
+ 
+
+ align:start position:0%
+and like showing the magma chamber
+stuff.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do you have It sounds like you guys have
+
+ align:start position:0%
+Do you have It sounds like you guys have
+ 
+
+ align:start position:0%
+Do you have It sounds like you guys have
+already done a unit on volcanoes like
+
+ align:start position:0%
+already done a unit on volcanoes like
+ 
+
+ align:start position:0%
+already done a unit on volcanoes like
+um is there any like any questions that
+
+ align:start position:0%
+um is there any like any questions that
+ 
+
+ align:start position:0%
+um is there any like any questions that
+you still have after that that you might
+
+ align:start position:0%
+you still have after that that you might
+ 
+
+ align:start position:0%
+you still have after that that you might
+want to have answered like really
+
+ align:start position:0%
+want to have answered like really
+ 
+
+ align:start position:0%
+want to have answered like really
+volcanoes or things like
+
+ align:start position:0%
+volcanoes or things like
+ 
+
+ align:start position:0%
+volcanoes or things like
+that? I know it's kind of a hard
+
+ align:start position:0%
+that? I know it's kind of a hard
+ 
+
+ align:start position:0%
+that? I know it's kind of a hard
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or like the coolest part of the unit
+
+ align:start position:0%
+or like the coolest part of the unit
+ 
+
+ align:start position:0%
+or like the coolest part of the unit
+that you
+
+ align:start position:0%
+that you
+ 
+
+ align:start position:0%
+that you
+remember how it looks. I've seen videos
+
+ align:start position:0%
+remember how it looks. I've seen videos
+ 
+
+ align:start position:0%
+remember how it looks. I've seen videos
+of volcanoes erupting at night.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd probably probably question I
+
+ align:start position:0%
+I'd probably probably question I
+ 
+
+ align:start position:0%
+I'd probably probably question I
+have there's some volcanoes that do like
+
+ align:start position:0%
+have there's some volcanoes that do like
+ 
+
+ align:start position:0%
+have there's some volcanoes that do like
+they're big but they have small
+
+ align:start position:0%
+they're big but they have small
+ 
+
+ align:start position:0%
+they're big but they have small
+eruptions and then they do like a big
+
+ align:start position:0%
+eruptions and then they do like a big
+ 
+
+ align:start position:0%
+eruptions and then they do like a big
+one and then there's other volcanoes
+
+ align:start position:0%
+one and then there's other volcanoes
+ 
+
+ align:start position:0%
+one and then there's other volcanoes
+that just like have huge eruptions every
+
+ align:start position:0%
+that just like have huge eruptions every
+ 
+
+ align:start position:0%
+that just like have huge eruptions every
+time they go.
+
+ align:start position:0%
+time they go.
+ 
+
+ align:start position:0%
+time they go.
+Why would some volcanoes have big
+
+ align:start position:0%
+Why would some volcanoes have big
+ 
+
+ align:start position:0%
+Why would some volcanoes have big
+eruptions and some have small small and
+
+ align:start position:0%
+eruptions and some have small small and
+ 
+
+ align:start position:0%
+eruptions and some have small small and
+then a big eruption? All right,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's what I would say. Um, of
+
+ align:start position:0%
+so here's what I would say. Um, of
+ 
+
+ align:start position:0%
+so here's what I would say. Um, of
+volcanoes that tend to have small
+
+ align:start position:0%
+volcanoes that tend to have small
+ 
+
+ align:start position:0%
+volcanoes that tend to have small
+eruptions. It's actually based a lot on
+
+ align:start position:0%
+eruptions. It's actually based a lot on
+ 
+
+ align:start position:0%
+eruptions. It's actually based a lot on
+what the makeup of the reef the lava
+
+ align:start position:0%
+what the makeup of the reef the lava
+ 
+
+ align:start position:0%
+what the makeup of the reef the lava
+from the volcano is.
+
+ align:start position:0%
+from the volcano is.
+ 
+
+ align:start position:0%
+from the volcano is.
+Um I don't know if you did you cover um
+
+ align:start position:0%
+Um I don't know if you did you cover um
+ 
+
+ align:start position:0%
+Um I don't know if you did you cover um
+the difference between andic
+
+ align:start position:0%
+the difference between andic
+ 
+
+ align:start position:0%
+the difference between andic
+um and amocidic um
+
+ align:start position:0%
+um and amocidic um
+ 
+
+ align:start position:0%
+um and amocidic um
+volcanoes um basically
+
+ align:start position:0%
+volcanoes um basically
+ 
+
+ align:start position:0%
+volcanoes um basically
+um glass is made of something called sil
+
+ align:start position:0%
+um glass is made of something called sil
+ 
+
+ align:start position:0%
+um glass is made of something called sil
+um silicon silicate
+
+ align:start position:0%
+um silicon silicate
+ 
+
+ align:start position:0%
+um silicon silicate
+uh um it's an element and volcanoes that
+
+ align:start position:0%
+uh um it's an element and volcanoes that
+ 
+
+ align:start position:0%
+uh um it's an element and volcanoes that
+have a lot more silica in it um they
+
+ align:start position:0%
+have a lot more silica in it um they
+ 
+
+ align:start position:0%
+have a lot more silica in it um they
+tend to be a little less dense and once
+
+ align:start position:0%
+tend to be a little less dense and once
+ 
+
+ align:start position:0%
+tend to be a little less dense and once
+ones that have lower content are a lot
+
+ align:start position:0%
+ones that have lower content are a lot
+ 
+
+ align:start position:0%
+ones that have lower content are a lot
+heavier than magma. And so, as you might
+
+ align:start position:0%
+heavier than magma. And so, as you might
+ 
+
+ align:start position:0%
+heavier than magma. And so, as you might
+expect, the ones that are heavier when
+
+ align:start position:0%
+expect, the ones that are heavier when
+ 
+
+ align:start position:0%
+expect, the ones that are heavier when
+they erupt, it doesn't just shoot out
+
+ align:start position:0%
+they erupt, it doesn't just shoot out
+ 
+
+ align:start position:0%
+they erupt, it doesn't just shoot out
+everywhere. It just kind of like bubbles
+
+ align:start position:0%
+everywhere. It just kind of like bubbles
+ 
+
+ align:start position:0%
+everywhere. It just kind of like bubbles
+over the side and it's like more viscous
+
+ align:start position:0%
+over the side and it's like more viscous
+ 
+
+ align:start position:0%
+over the side and it's like more viscous
+and it flows slowly. And so those ones
+
+ align:start position:0%
+and it flows slowly. And so those ones
+ 
+
+ align:start position:0%
+and it flows slowly. And so those ones
+often will be the ones like the big
+
+ align:start position:0%
+often will be the ones like the big
+ 
+
+ align:start position:0%
+often will be the ones like the big
+mountains that
+
+ align:start position:0%
+mountains that
+ 
+
+ align:start position:0%
+mountains that
+like kind of like spread out this way a
+
+ align:start position:0%
+like kind of like spread out this way a
+ 
+
+ align:start position:0%
+like kind of like spread out this way a
+lot. Sort of like a shield volcano.
+
+ align:start position:0%
+lot. Sort of like a shield volcano.
+ 
+
+ align:start position:0%
+lot. Sort of like a shield volcano.
+Yeah, those are the shield volcanoes.
+
+ align:start position:0%
+Yeah, those are the shield volcanoes.
+ 
+
+ align:start position:0%
+Yeah, those are the shield volcanoes.
+And so the lava type causes it to have a
+
+ align:start position:0%
+And so the lava type causes it to have a
+ 
+
+ align:start position:0%
+And so the lava type causes it to have a
+lot more smaller eruptions because it
+
+ align:start position:0%
+lot more smaller eruptions because it
+ 
+
+ align:start position:0%
+lot more smaller eruptions because it
+takes a lot of buildup of pressure if
+
+ align:start position:0%
+takes a lot of buildup of pressure if
+ 
+
+ align:start position:0%
+takes a lot of buildup of pressure if
+you want to have a big eruption than
+
+ align:start position:0%
+you want to have a big eruption than
+ 
+
+ align:start position:0%
+you want to have a big eruption than
+that. Whereas when you have a higher
+
+ align:start position:0%
+that. Whereas when you have a higher
+ 
+
+ align:start position:0%
+that. Whereas when you have a higher
+silica content, which means it weighs
+
+ align:start position:0%
+silica content, which means it weighs
+ 
+
+ align:start position:0%
+silica content, which means it weighs
+less, it's going to explode more and
+
+ align:start position:0%
+less, it's going to explode more and
+ 
+
+ align:start position:0%
+less, it's going to explode more and
+it's going to have more violent
+
+ align:start position:0%
+it's going to have more violent
+ 
+
+ align:start position:0%
+it's going to have more violent
+eruptions. Um, and there's other factors
+
+ align:start position:0%
+eruptions. Um, and there's other factors
+ 
+
+ align:start position:0%
+eruptions. Um, and there's other factors
+as well, um, like water content,
+
+ align:start position:0%
+as well, um, like water content,
+ 
+
+ align:start position:0%
+as well, um, like water content,
+um, and at what depth the magma chamber
+
+ align:start position:0%
+um, and at what depth the magma chamber
+ 
+
+ align:start position:0%
+um, and at what depth the magma chamber
+underneath the volcano is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Um, another question. Let me see.
+
+ align:start position:0%
+Yeah. Um, another question. Let me see.
+ 
+
+ align:start position:0%
+Yeah. Um, another question. Let me see.
+If you don't have one, I have one. All
+
+ align:start position:0%
+If you don't have one, I have one. All
+ 
+
+ align:start position:0%
+If you don't have one, I have one. All
+right. You um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Which was a long time and then blew
+
+ align:start position:0%
+the Which was a long time and then blew
+ 
+
+ align:start position:0%
+the Which was a long time and then blew
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+crazy. Yes.
+
+ align:start position:0%
+crazy. Yes.
+ 
+
+ align:start position:0%
+crazy. Yes.
+That's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+what if volcanoes are doormat for a
+
+ align:start position:0%
+what if volcanoes are doormat for a
+ 
+
+ align:start position:0%
+what if volcanoes are doormat for a
+longer period when they erupt would they
+
+ align:start position:0%
+longer period when they erupt would they
+ 
+
+ align:start position:0%
+longer period when they erupt would they
+have a violent eruption than ones that a
+
+ align:start position:0%
+have a violent eruption than ones that a
+ 
+
+ align:start position:0%
+have a violent eruption than ones that a
+doormat shorter? Um I can't actually
+
+ align:start position:0%
+doormat shorter? Um I can't actually
+ 
+
+ align:start position:0%
+doormat shorter? Um I can't actually
+answer that question. Um,
+
+ align:start position:0%
+answer that question. Um,
+ 
+
+ align:start position:0%
+answer that question. Um,
+I know like what causes our parents to
+
+ align:start position:0%
+I know like what causes our parents to
+ 
+
+ align:start position:0%
+I know like what causes our parents to
+go in more dormant what make them might
+
+ align:start position:0%
+go in more dormant what make them might
+ 
+
+ align:start position:0%
+go in more dormant what make them might
+make them not dormant, but I can't
+
+ align:start position:0%
+make them not dormant, but I can't
+ 
+
+ align:start position:0%
+make them not dormant, but I can't
+really say if that would affect it.
+
+ align:start position:0%
+really say if that would affect it.
+ 
+
+ align:start position:0%
+really say if that would affect it.
+Okay. One thing about Matt that you have
+
+ align:start position:0%
+Okay. One thing about Matt that you have
+ 
+
+ align:start position:0%
+Okay. One thing about Matt that you have
+really enjoyed or really hated or two
+
+ align:start position:0%
+really enjoyed or really hated or two
+ 
+
+ align:start position:0%
+really enjoyed or really hated or two
+things. So, we'll start from left to
+
+ align:start position:0%
+things. So, we'll start from left to
+ 
+
+ align:start position:0%
+things. So, we'll start from left to
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+So, name um favorite subject and things
+
+ align:start position:0%
+So, name um favorite subject and things
+ 
+
+ align:start position:0%
+So, name um favorite subject and things
+about math that you have really loved or
+
+ align:start position:0%
+about math that you have really loved or
+ 
+
+ align:start position:0%
+about math that you have really loved or
+really hated. Okay, my name is
+
+ align:start position:0%
+really hated. Okay, my name is
+ 
+
+ align:start position:0%
+really hated. Okay, my name is
+Brian. My favorite subject is gym and I
+
+ align:start position:0%
+Brian. My favorite subject is gym and I
+ 
+
+ align:start position:0%
+Brian. My favorite subject is gym and I
+hate
+
+ align:start position:0%
+hate
+ 
+
+ align:start position:0%
+hate
+math. Kind of
+
+ align:start position:0%
+math. Kind of
+ 
+
+ align:start position:0%
+math. Kind of
+boring. Okay. Um, actually there is I
+
+ align:start position:0%
+boring. Okay. Um, actually there is I
+ 
+
+ align:start position:0%
+boring. Okay. Um, actually there is I
+guess it's a kind of new direction, but
+
+ align:start position:0%
+guess it's a kind of new direction, but
+ 
+
+ align:start position:0%
+guess it's a kind of new direction, but
+a lot of people are actually studying
+
+ align:start position:0%
+a lot of people are actually studying
+ 
+
+ align:start position:0%
+a lot of people are actually studying
+the math of sports. So they go out and
+
+ align:start position:0%
+the math of sports. So they go out and
+ 
+
+ align:start position:0%
+the math of sports. So they go out and
+do really weird things with sports like
+
+ align:start position:0%
+do really weird things with sports like
+ 
+
+ align:start position:0%
+do really weird things with sports like
+throwing basketballs at
+
+ align:start position:0%
+throwing basketballs at
+ 
+
+ align:start position:0%
+throwing basketballs at
+like places where you should shoot an
+
+ align:start position:0%
+like places where you should shoot an
+ 
+
+ align:start position:0%
+like places where you should shoot an
+arrow kind of thing and they do math
+
+ align:start position:0%
+arrow kind of thing and they do math
+ 
+
+ align:start position:0%
+arrow kind of thing and they do math
+with it. So that's kind of a connection
+
+ align:start position:0%
+with it. So that's kind of a connection
+ 
+
+ align:start position:0%
+with it. So that's kind of a connection
+gym and
+
+ align:start position:0%
+gym and
+ 
+
+ align:start position:0%
+gym and
+math getting closer together.
+
+ align:start position:0%
+math getting closer together.
+ 
+
+ align:start position:0%
+math getting closer together.
+My name is Matt. I like math.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You hear that,
+
+ align:start position:0%
+You hear that,
+ 
+
+ align:start position:0%
+You hear that,
+Brian? And what was the third thing that
+
+ align:start position:0%
+Brian? And what was the third thing that
+ 
+
+ align:start position:0%
+Brian? And what was the third thing that
+I have to say? Um, some things that you
+
+ align:start position:0%
+I have to say? Um, some things that you
+ 
+
+ align:start position:0%
+I have to say? Um, some things that you
+really enjoyed or hated about math. Um,
+
+ align:start position:0%
+really enjoyed or hated about math. Um,
+ 
+
+ align:start position:0%
+really enjoyed or hated about math. Um,
+I enjoy solving variables and equations
+
+ align:start position:0%
+I enjoy solving variables and equations
+ 
+
+ align:start position:0%
+I enjoy solving variables and equations
+and graphing things.
+
+ align:start position:0%
+and graphing things.
+ 
+
+ align:start position:0%
+and graphing things.
+That's good. You're ready for high
+
+ align:start position:0%
+That's good. You're ready for high
+ 
+
+ align:start position:0%
+That's good. You're ready for high
+school. burn. My name
+
+ align:start position:0%
+school. burn. My name
+ 
+
+ align:start position:0%
+school. burn. My name
+is My name is John and um my favorite
+
+ align:start position:0%
+is My name is John and um my favorite
+ 
+
+ align:start position:0%
+is My name is John and um my favorite
+subject is
+
+ align:start position:0%
+subject is
+ 
+
+ align:start position:0%
+subject is
+history and
+
+ align:start position:0%
+history and
+ 
+
+ align:start position:0%
+history and
+uh I personally do not like
+
+ align:start position:0%
+uh I personally do not like
+ 
+
+ align:start position:0%
+uh I personally do not like
+math. Um hi guys.
+
+ align:start position:0%
+math. Um hi guys.
+ 
+
+ align:start position:0%
+math. Um hi guys.
+Um, if I had to like say what I like
+
+ align:start position:0%
+Um, if I had to like say what I like
+ 
+
+ align:start position:0%
+Um, if I had to like say what I like
+about it, it would be
+
+ align:start position:0%
+about it, it would be
+ 
+
+ align:start position:0%
+about it, it would be
+like I'm really into like fractions kind
+
+ align:start position:0%
+like I'm really into like fractions kind
+ 
+
+ align:start position:0%
+like I'm really into like fractions kind
+of. Okay. I just like the idea.
+
+ align:start position:0%
+of. Okay. I just like the idea.
+ 
+
+ align:start position:0%
+of. Okay. I just like the idea.
+Okay. What do you know what about the
+
+ align:start position:0%
+Okay. What do you know what about the
+ 
+
+ align:start position:0%
+Okay. What do you know what about the
+idea? I've never heard anybody say I
+
+ align:start position:0%
+idea? I've never heard anybody say I
+ 
+
+ align:start position:0%
+idea? I've never heard anybody say I
+like the idea of fractions. So that's
+
+ align:start position:0%
+like the idea of fractions. So that's
+ 
+
+ align:start position:0%
+like the idea of fractions. So that's
+really interesting to me.
+
+ align:start position:0%
+really interesting to me.
+ 
+
+ align:start position:0%
+really interesting to me.
+think of like this table being like
+
+ align:start position:0%
+think of like this table being like
+ 
+
+ align:start position:0%
+think of like this table being like
+broken up into like a thousand.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now really wacky things that
+
+ align:start position:0%
+Now really wacky things that
+ 
+
+ align:start position:0%
+Now really wacky things that
+mathematicians do later on is that they
+
+ align:start position:0%
+mathematicians do later on is that they
+ 
+
+ align:start position:0%
+mathematicians do later on is that they
+don't just break the table into a
+
+ align:start position:0%
+don't just break the table into a
+ 
+
+ align:start position:0%
+don't just break the table into a
+thousand pieces. That's like too easy.
+
+ align:start position:0%
+thousand pieces. That's like too easy.
+ 
+
+ align:start position:0%
+thousand pieces. That's like too easy.
+They break it into an infinite number of
+
+ align:start position:0%
+They break it into an infinite number of
+ 
+
+ align:start position:0%
+They break it into an infinite number of
+pieces and then they see what they can
+
+ align:start position:0%
+pieces and then they see what they can
+ 
+
+ align:start position:0%
+pieces and then they see what they can
+do with that.
+
+ align:start position:0%
+do with that.
+ 
+
+ align:start position:0%
+do with that.
+Um and kind of related to that um math
+
+ align:start position:0%
+Um and kind of related to that um math
+ 
+
+ align:start position:0%
+Um and kind of related to that um math
+mathematicians have proved that you can
+
+ align:start position:0%
+mathematicians have proved that you can
+ 
+
+ align:start position:0%
+mathematicians have proved that you can
+take a ball of you know just volume one
+
+ align:start position:0%
+take a ball of you know just volume one
+ 
+
+ align:start position:0%
+take a ball of you know just volume one
+one gallon ball and you can cut it in
+
+ align:start position:0%
+one gallon ball and you can cut it in
+ 
+
+ align:start position:0%
+one gallon ball and you can cut it in
+such a way that you can make two onegon
+
+ align:start position:0%
+such a way that you can make two onegon
+ 
+
+ align:start position:0%
+such a way that you can make two onegon
+balls. So you can make two out of one
+
+ align:start position:0%
+balls. So you can make two out of one
+ 
+
+ align:start position:0%
+balls. So you can make two out of one
+using math. Um it's cool. So that's uh
+
+ align:start position:0%
+using math. Um it's cool. So that's uh
+ 
+
+ align:start position:0%
+using math. Um it's cool. So that's uh
+semi relative. You like math now boys? I
+
+ align:start position:0%
+semi relative. You like math now boys? I
+ 
+
+ align:start position:0%
+semi relative. You like math now boys? I
+still don't know.
+
+ align:start position:0%
+still don't know.
+ 
+
+ align:start position:0%
+still don't know.
+I mean, if you think about it, math
+
+ align:start position:0%
+I mean, if you think about it, math
+ 
+
+ align:start position:0%
+I mean, if you think about it, math
+people do really cool things. Like, um,
+
+ align:start position:0%
+people do really cool things. Like, um,
+ 
+
+ align:start position:0%
+people do really cool things. Like, um,
+there was a study once where they
+
+ align:start position:0%
+there was a study once where they
+ 
+
+ align:start position:0%
+there was a study once where they
+analyzed the language of King George and
+
+ align:start position:0%
+analyzed the language of King George and
+ 
+
+ align:start position:0%
+analyzed the language of King George and
+Kanye West and they compared them. And
+
+ align:start position:0%
+Kanye West and they compared them. And
+ 
+
+ align:start position:0%
+Kanye West and they compared them. And
+this is like an actual study, like they
+
+ align:start position:0%
+this is like an actual study, like they
+ 
+
+ align:start position:0%
+this is like an actual study, like they
+put time into it. So, I thought that was
+
+ align:start position:0%
+put time into it. So, I thought that was
+ 
+
+ align:start position:0%
+put time into it. So, I thought that was
+pretty cool. But, um,
+
+ align:start position:0%
+pretty cool. But, um,
+ 
+
+ align:start position:0%
+pretty cool. But, um,
+anyway, that's not what my pitch is
+
+ align:start position:0%
+anyway, that's not what my pitch is
+ 
+
+ align:start position:0%
+anyway, that's not what my pitch is
+about. Um, and I'll just kind of say
+
+ align:start position:0%
+about. Um, and I'll just kind of say
+ 
+
+ align:start position:0%
+about. Um, and I'll just kind of say
+real quick, not going to show the video
+
+ align:start position:0%
+real quick, not going to show the video
+ 
+
+ align:start position:0%
+real quick, not going to show the video
+because the sound is terrible.
+
+ align:start position:0%
+because the sound is terrible.
+ 
+
+ align:start position:0%
+because the sound is terrible.
+Um what I want to talk about in my video
+
+ align:start position:0%
+Um what I want to talk about in my video
+ 
+
+ align:start position:0%
+Um what I want to talk about in my video
+is just the question of is math real and
+
+ align:start position:0%
+is just the question of is math real and
+ 
+
+ align:start position:0%
+is just the question of is math real and
+true because what uh mathematicians
+
+ align:start position:0%
+true because what uh mathematicians
+ 
+
+ align:start position:0%
+true because what uh mathematicians
+learned in the 20th century um there was
+
+ align:start position:0%
+learned in the 20th century um there was
+ 
+
+ align:start position:0%
+learned in the 20th century um there was
+a young man named Kurt Girdle who proved
+
+ align:start position:0%
+a young man named Kurt Girdle who proved
+ 
+
+ align:start position:0%
+a young man named Kurt Girdle who proved
+that you can never prove if math is true
+
+ align:start position:0%
+that you can never prove if math is true
+ 
+
+ align:start position:0%
+that you can never prove if math is true
+or not. So the arithmetic we learned in
+
+ align:start position:0%
+or not. So the arithmetic we learned in
+ 
+
+ align:start position:0%
+or not. So the arithmetic we learned in
+school like we think it's true because
+
+ align:start position:0%
+school like we think it's true because
+ 
+
+ align:start position:0%
+school like we think it's true because
+it's worked but it may not be. There's
+
+ align:start position:0%
+it's worked but it may not be. There's
+ 
+
+ align:start position:0%
+it's worked but it may not be. There's
+no way to say for sure. Wait, is Kurt
+
+ align:start position:0%
+no way to say for sure. Wait, is Kurt
+ 
+
+ align:start position:0%
+no way to say for sure. Wait, is Kurt
+Kernel the guy who made Kentucky Fried
+
+ align:start position:0%
+Kernel the guy who made Kentucky Fried
+ 
+
+ align:start position:0%
+Kernel the guy who made Kentucky Fried
+Chicken? No, it's Kurt Girdle.
+
+ align:start position:0%
+Chicken? No, it's Kurt Girdle.
+ 
+
+ align:start position:0%
+Chicken? No, it's Kurt Girdle.
+Oh, I mean, I think it would be really
+
+ align:start position:0%
+Oh, I mean, I think it would be really
+ 
+
+ align:start position:0%
+Oh, I mean, I think it would be really
+cool if he did math and Kentucky Fried
+
+ align:start position:0%
+cool if he did math and Kentucky Fried
+ 
+
+ align:start position:0%
+cool if he did math and Kentucky Fried
+Chicken. Like, that would be the best.
+
+ align:start position:0%
+Chicken. Like, that would be the best.
+ 
+
+ align:start position:0%
+Chicken. Like, that would be the best.
+Our family guy. And he was like, he went
+
+ align:start position:0%
+Our family guy. And he was like, he went
+ 
+
+ align:start position:0%
+Our family guy. And he was like, he went
+to Kentucky to get chicken. He's like,
+
+ align:start position:0%
+to Kentucky to get chicken. He's like,
+ 
+
+ align:start position:0%
+to Kentucky to get chicken. He's like,
+is like whatever his name is sounding
+
+ align:start position:0%
+is like whatever his name is sounding
+ 
+
+ align:start position:0%
+is like whatever his name is sounding
+like what he said. And he's like, and
+
+ align:start position:0%
+like what he said. And he's like, and
+ 
+
+ align:start position:0%
+like what he said. And he's like, and
+he's like, no, he's dead. And he's like
+
+ align:start position:0%
+he's like, no, he's dead. And he's like
+ 
+
+ align:start position:0%
+he's like, no, he's dead. And he's like
+the something. That was so fun. Have to
+
+ align:start position:0%
+the something. That was so fun. Have to
+ 
+
+ align:start position:0%
+the something. That was so fun. Have to
+look into, you know, did any
+
+ align:start position:0%
+look into, you know, did any
+ 
+
+ align:start position:0%
+look into, you know, did any
+mathematicians open fast food chains?
+
+ align:start position:0%
+mathematicians open fast food chains?
+ 
+
+ align:start position:0%
+mathematicians open fast food chains?
+It's probably an interesting question. I
+
+ align:start position:0%
+It's probably an interesting question. I
+ 
+
+ align:start position:0%
+It's probably an interesting question. I
+don't think anyone's asked it before,
+
+ align:start position:0%
+don't think anyone's asked it before,
+ 
+
+ align:start position:0%
+don't think anyone's asked it before,
+but um that said, um any thoughts on the
+
+ align:start position:0%
+but um that said, um any thoughts on the
+ 
+
+ align:start position:0%
+but um that said, um any thoughts on the
+idea? Just I'll get a thumbs up, thumbs
+
+ align:start position:0%
+idea? Just I'll get a thumbs up, thumbs
+ 
+
+ align:start position:0%
+idea? Just I'll get a thumbs up, thumbs
+down, or thumbs middle.
+
+ align:start position:0%
+down, or thumbs middle.
+ 
+
+ align:start position:0%
+down, or thumbs middle.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Thanks, guys. Uh it was nice
+
+ align:start position:0%
+All right. Thanks, guys. Uh it was nice
+ 
+
+ align:start position:0%
+All right. Thanks, guys. Uh it was nice
+meeting you and enjoy playing or not.
+
+ align:start position:0%
+meeting you and enjoy playing or not.
+ 
+
+ align:start position:0%
+meeting you and enjoy playing or not.
+So you want like a aha moment in Euro
+
+ align:start position:0%
+So you want like a aha moment in Euro
+ 
+
+ align:start position:0%
+So you want like a aha moment in Euro
+kind of I think I think you want to get
+
+ align:start position:0%
+kind of I think I think you want to get
+ 
+
+ align:start position:0%
+kind of I think I think you want to get
+away from instruction and more of like
+
+ align:start position:0%
+away from instruction and more of like
+ 
+
+ align:start position:0%
+away from instruction and more of like
+concept, right? So see if you can think
+
+ align:start position:0%
+concept, right? So see if you can think
+ 
+
+ align:start position:0%
+concept, right? So see if you can think
+of a little narrower focus than these
+
+ align:start position:0%
+of a little narrower focus than these
+ 
+
+ align:start position:0%
+of a little narrower focus than these
+big big big concepts and that might help
+
+ align:start position:0%
+big big big concepts and that might help
+ 
+
+ align:start position:0%
+big big big concepts and that might help
+you with your next group. So like you
+
+ align:start position:0%
+you with your next group. So like you
+ 
+
+ align:start position:0%
+you with your next group. So like you
+guys like like some of them are like
+
+ align:start position:0%
+guys like like some of them are like
+ 
+
+ align:start position:0%
+guys like like some of them are like
+like the robots. Yeah. Yeah. So what
+
+ align:start position:0%
+like the robots. Yeah. Yeah. So what
+ 
+
+ align:start position:0%
+like the robots. Yeah. Yeah. So what
+they're doing so we're teaching them Do
+
+ align:start position:0%
+they're doing so we're teaching them Do
+ 
+
+ align:start position:0%
+they're doing so we're teaching them Do
+you need to rotate? No, you're okay.
+
+ align:start position:0%
+you need to rotate? No, you're okay.
+ 
+
+ align:start position:0%
+you need to rotate? No, you're okay.
+What we're doing is we're they're
+
+ align:start position:0%
+What we're doing is we're they're
+ 
+
+ align:start position:0%
+What we're doing is we're they're
+scientists and we're teaching them how
+
+ align:start position:0%
+scientists and we're teaching them how
+ 
+
+ align:start position:0%
+scientists and we're teaching them how
+to make Have you ever looked on cool
+
+ align:start position:0%
+to make Have you ever looked on cool
+ 
+
+ align:start position:0%
+to make Have you ever looked on cool
+videos? was like, "Have you seen um
+
+ align:start position:0%
+videos? was like, "Have you seen um
+ 
+
+ align:start position:0%
+videos? was like, "Have you seen um
+Charlie the Unicorn or you've seen
+
+ align:start position:0%
+Charlie the Unicorn or you've seen
+ 
+
+ align:start position:0%
+Charlie the Unicorn or you've seen
+Charlie?" Charlie or maybe you've seen
+
+ align:start position:0%
+Charlie?" Charlie or maybe you've seen
+ 
+
+ align:start position:0%
+Charlie?" Charlie or maybe you've seen
+um the was it my I used to work with
+
+ align:start position:0%
+um the was it my I used to work with
+ 
+
+ align:start position:0%
+um the was it my I used to work with
+kids your age and they loved that one.
+
+ align:start position:0%
+kids your age and they loved that one.
+ 
+
+ align:start position:0%
+kids your age and they loved that one.
+Um it was about this little snail Marcel
+
+ align:start position:0%
+Um it was about this little snail Marcel
+ 
+
+ align:start position:0%
+Um it was about this little snail Marcel
+the shell. Have you seen that one? No.
+
+ align:start position:0%
+the shell. Have you seen that one? No.
+ 
+
+ align:start position:0%
+the shell. Have you seen that one? No.
+Well, you see these little YouTube
+
+ align:start position:0%
+Well, you see these little YouTube
+ 
+
+ align:start position:0%
+Well, you see these little YouTube
+videos and everyone's like, "Oh, that's
+
+ align:start position:0%
+videos and everyone's like, "Oh, that's
+ 
+
+ align:start position:0%
+videos and everyone's like, "Oh, that's
+cool. You got to watch that, too."
+
+ align:start position:0%
+cool. You got to watch that, too."
+ 
+
+ align:start position:0%
+cool. You got to watch that, too."
+Right. The 21 kid. Which one? The 21 kid
+
+ align:start position:0%
+Right. The 21 kid. Which one? The 21 kid
+ 
+
+ align:start position:0%
+Right. The 21 kid. Which one? The 21 kid
+that says 21. Every everybody in America
+
+ align:start position:0%
+that says 21. Every everybody in America
+ 
+
+ align:start position:0%
+that says 21. Every everybody in America
+says 21 now. Oh, really? Is that Is that
+
+ align:start position:0%
+says 21 now. Oh, really? Is that Is that
+ 
+
+ align:start position:0%
+says 21 now. Oh, really? Is that Is that
+the one you have to watch? 21. It's like
+
+ align:start position:0%
+the one you have to watch? 21. It's like
+ 
+
+ align:start position:0%
+the one you have to watch? 21. It's like
+it's like a vine
+
+ align:start position:0%
+it's like a vine
+ 
+
+ align:start position:0%
+it's like a vine
+and then they make them into a video or
+
+ align:start position:0%
+and then they make them into a video or
+ 
+
+ align:start position:0%
+and then they make them into a video or
+there's um a series of shows in YouTube
+
+ align:start position:0%
+there's um a series of shows in YouTube
+ 
+
+ align:start position:0%
+there's um a series of shows in YouTube
+called ASDF. It's about this little like
+
+ align:start position:0%
+called ASDF. It's about this little like
+ 
+
+ align:start position:0%
+called ASDF. It's about this little like
+stick figures, right? So So you guys see
+
+ align:start position:0%
+stick figures, right? So So you guys see
+ 
+
+ align:start position:0%
+stick figures, right? So So you guys see
+them and then you're like, "Hey friend,
+
+ align:start position:0%
+them and then you're like, "Hey friend,
+ 
+
+ align:start position:0%
+them and then you're like, "Hey friend,
+you've got to see this too." And then
+
+ align:start position:0%
+you've got to see this too." And then
+ 
+
+ align:start position:0%
+you've got to see this too." And then
+you're like, you get everyone to watch
+
+ align:start position:0%
+you're like, you get everyone to watch
+ 
+
+ align:start position:0%
+you're like, you get everyone to watch
+it, right? We're trying to make those
+
+ align:start position:0%
+it, right? We're trying to make those
+ 
+
+ align:start position:0%
+it, right? We're trying to make those
+really cool short videos about science
+
+ align:start position:0%
+really cool short videos about science
+ 
+
+ align:start position:0%
+really cool short videos about science
+topics, right? And so we're going to
+
+ align:start position:0%
+topics, right? And so we're going to
+ 
+
+ align:start position:0%
+topics, right? And so we're going to
+make them free so that anyone so that it
+
+ align:start position:0%
+make them free so that anyone so that it
+ 
+
+ align:start position:0%
+make them free so that anyone so that it
+also teaches people something while it's
+
+ align:start position:0%
+also teaches people something while it's
+ 
+
+ align:start position:0%
+also teaches people something while it's
+also cool and fun, right? Okay. And so
+
+ align:start position:0%
+also cool and fun, right? Okay. And so
+ 
+
+ align:start position:0%
+also cool and fun, right? Okay. And so
+what he's trying to figure out is like
+
+ align:start position:0%
+what he's trying to figure out is like
+ 
+
+ align:start position:0%
+what he's trying to figure out is like
+what in his world of computer science
+
+ align:start position:0%
+what in his world of computer science
+ 
+
+ align:start position:0%
+what in his world of computer science
+would be like cool enough that you'd be
+
+ align:start position:0%
+would be like cool enough that you'd be
+ 
+
+ align:start position:0%
+would be like cool enough that you'd be
+like, "Hey friend, you got to check this
+
+ align:start position:0%
+like, "Hey friend, you got to check this
+ 
+
+ align:start position:0%
+like, "Hey friend, you got to check this
+out. It's really awesome." I think the
+
+ align:start position:0%
+out. It's really awesome." I think the
+ 
+
+ align:start position:0%
+out. It's really awesome." I think the
+hacker one would be good for people our
+
+ align:start position:0%
+hacker one would be good for people our
+ 
+
+ align:start position:0%
+hacker one would be good for people our
+age to understand like how someone
+
+ align:start position:0%
+age to understand like how someone
+ 
+
+ align:start position:0%
+age to understand like how someone
+hacked your account. Yeah. But then you
+
+ align:start position:0%
+hacked your account. Yeah. But then you
+ 
+
+ align:start position:0%
+hacked your account. Yeah. But then you
+don't want then you want kids to hack
+
+ align:start position:0%
+don't want then you want kids to hack
+ 
+
+ align:start position:0%
+don't want then you want kids to hack
+people. Well, that's the fear, right?
+
+ align:start position:0%
+people. Well, that's the fear, right?
+ 
+
+ align:start position:0%
+people. Well, that's the fear, right?
+You don't want to end up giving kids
+
+ align:start position:0%
+You don't want to end up giving kids
+ 
+
+ align:start position:0%
+You don't want to end up giving kids
+instructions on how to hack cuz I don't
+
+ align:start position:0%
+instructions on how to hack cuz I don't
+ 
+
+ align:start position:0%
+instructions on how to hack cuz I don't
+think the government or anyone else
+
+ align:start position:0%
+think the government or anyone else
+ 
+
+ align:start position:0%
+think the government or anyone else
+would probably like that. But but that's
+
+ align:start position:0%
+would probably like that. But but that's
+ 
+
+ align:start position:0%
+would probably like that. But but that's
+a fear, right? is just making sure that
+
+ align:start position:0%
+a fear, right? is just making sure that
+ 
+
+ align:start position:0%
+a fear, right? is just making sure that
+we're not actually giving instructional
+
+ align:start position:0%
+we're not actually giving instructional
+ 
+
+ align:start position:0%
+we're not actually giving instructional
+videos on how to destroy other people's
+
+ align:start position:0%
+videos on how to destroy other people's
+ 
+
+ align:start position:0%
+videos on how to destroy other people's
+credit cards. Google might feel
+
+ align:start position:0%
+credit cards. Google might feel
+ 
+
+ align:start position:0%
+credit cards. Google might feel
+good ATM.
+
+ align:start position:0%
+good ATM.
+ 
+
+ align:start position:0%
+good ATM.
+Yeah. Of make protecting your how to
+
+ align:start position:0%
+Yeah. Of make protecting your how to
+ 
+
+ align:start position:0%
+Yeah. Of make protecting your how to
+protect your like yourself like make
+
+ align:start position:0%
+protect your like yourself like make
+ 
+
+ align:start position:0%
+protect your like yourself like make
+sure your money's safe or something like
+
+ align:start position:0%
+sure your money's safe or something like
+ 
+
+ align:start position:0%
+sure your money's safe or something like
+that would be like how to protect
+
+ align:start position:0%
+that would be like how to protect
+ 
+
+ align:start position:0%
+that would be like how to protect
+yourself from hackers. How to protect
+
+ align:start position:0%
+yourself from hackers. How to protect
+ 
+
+ align:start position:0%
+yourself from hackers. How to protect
+how to protect yourself is instead of
+
+ align:start position:0%
+how to protect yourself is instead of
+ 
+
+ align:start position:0%
+how to protect yourself is instead of
+like destroying someone else's
+
+ align:start position:0%
+like destroying someone else's
+ 
+
+ align:start position:0%
+like destroying someone else's
+something. It was a nice way of
+
+ align:start position:0%
+something. It was a nice way of
+ 
+
+ align:start position:0%
+something. It was a nice way of
+learning. So say if someone lost their
+
+ align:start position:0%
+learning. So say if someone lost their
+ 
+
+ align:start position:0%
+learning. So say if someone lost their
+um wallet and they had their credit card
+
+ align:start position:0%
+um wallet and they had their credit card
+ 
+
+ align:start position:0%
+um wallet and they had their credit card
+in there and they can access to the bank
+
+ align:start position:0%
+in there and they can access to the bank
+ 
+
+ align:start position:0%
+in there and they can access to the bank
+is that the person if someone found it
+
+ align:start position:0%
+is that the person if someone found it
+ 
+
+ align:start position:0%
+is that the person if someone found it
+and the person access do do they end up
+
+ align:start position:0%
+and the person access do do they end up
+ 
+
+ align:start position:0%
+and the person access do do they end up
+giving them the money sometimes and
+
+ align:start position:0%
+giving them the money sometimes and
+ 
+
+ align:start position:0%
+giving them the money sometimes and
+that's why credit cards are really good
+
+ align:start position:0%
+that's why credit cards are really good
+ 
+
+ align:start position:0%
+that's why credit cards are really good
+at being do you know anything about this
+
+ align:start position:0%
+at being do you know anything about this
+ 
+
+ align:start position:0%
+at being do you know anything about this
+in your work or no? um credit cards,
+
+ align:start position:0%
+in your work or no? um credit cards,
+ 
+
+ align:start position:0%
+in your work or no? um credit cards,
+credit card like protecting credit card
+
+ align:start position:0%
+credit card like protecting credit card
+ 
+
+ align:start position:0%
+credit card like protecting credit card
+identity and all that, but don't they
+
+ align:start position:0%
+identity and all that, but don't they
+ 
+
+ align:start position:0%
+identity and all that, but don't they
+have like your picture or something so
+
+ align:start position:0%
+have like your picture or something so
+ 
+
+ align:start position:0%
+have like your picture or something so
+they know? It's like But online you it's
+
+ align:start position:0%
+they know? It's like But online you it's
+ 
+
+ align:start position:0%
+they know? It's like But online you it's
+really easy to like use another person's
+
+ align:start position:0%
+really easy to like use another person's
+ 
+
+ align:start position:0%
+really easy to like use another person's
+credit card if you know all the
+
+ align:start position:0%
+credit card if you know all the
+ 
+
+ align:start position:0%
+credit card if you know all the
+information. Yeah, it's kind of like I
+
+ align:start position:0%
+information. Yeah, it's kind of like I
+ 
+
+ align:start position:0%
+information. Yeah, it's kind of like I
+get called often from my bank saying did
+
+ align:start position:0%
+get called often from my bank saying did
+ 
+
+ align:start position:0%
+get called often from my bank saying did
+you make this purchase or did someone
+
+ align:start position:0%
+you make this purchase or did someone
+ 
+
+ align:start position:0%
+you make this purchase or did someone
+else? Um but that's an interesting thing
+
+ align:start position:0%
+else? Um but that's an interesting thing
+ 
+
+ align:start position:0%
+else? Um but that's an interesting thing
+for people who who do a lot of shopping
+
+ align:start position:0%
+for people who who do a lot of shopping
+ 
+
+ align:start position:0%
+for people who who do a lot of shopping
+online. How do you protect yourself? If
+
+ align:start position:0%
+online. How do you protect yourself? If
+ 
+
+ align:start position:0%
+online. How do you protect yourself? If
+somebody else took your money, would you
+
+ align:start position:0%
+somebody else took your money, would you
+ 
+
+ align:start position:0%
+somebody else took your money, would you
+get that back or no?
+
+ align:start position:0%
+get that back or no?
+ 
+
+ align:start position:0%
+get that back or no?
+That's why if you catch it quickly with
+
+ align:start position:0%
+That's why if you catch it quickly with
+ 
+
+ align:start position:0%
+That's why if you catch it quickly with
+your bank, sometimes they can they can
+
+ align:start position:0%
+your bank, sometimes they can they can
+ 
+
+ align:start position:0%
+your bank, sometimes they can they can
+quickly stop it before it ends up
+
+ align:start position:0%
+quickly stop it before it ends up
+ 
+
+ align:start position:0%
+quickly stop it before it ends up
+getting charged to you. But that's an
+
+ align:start position:0%
+getting charged to you. But that's an
+ 
+
+ align:start position:0%
+getting charged to you. But that's an
+interesting idea is how do you how do
+
+ align:start position:0%
+interesting idea is how do you how do
+ 
+
+ align:start position:0%
+interesting idea is how do you how do
+you if you're buying stuff on this on
+
+ align:start position:0%
+you if you're buying stuff on this on
+ 
+
+ align:start position:0%
+you if you're buying stuff on this on
+the internet like what's actually
+
+ align:start position:0%
+the internet like what's actually
+ 
+
+ align:start position:0%
+the internet like what's actually
+happening to protect yourself? What if
+
+ align:start position:0%
+happening to protect yourself? What if
+ 
+
+ align:start position:0%
+happening to protect yourself? What if
+um like someone like um um like if they
+
+ align:start position:0%
+um like someone like um um like if they
+ 
+
+ align:start position:0%
+um like someone like um um like if they
+did if they did like catch the person
+
+ align:start position:0%
+did if they did like catch the person
+ 
+
+ align:start position:0%
+did if they did like catch the person
+and the person already used all the
+
+ align:start position:0%
+and the person already used all the
+ 
+
+ align:start position:0%
+and the person already used all the
+money and that you can't like return it
+
+ align:start position:0%
+money and that you can't like return it
+ 
+
+ align:start position:0%
+money and that you can't like return it
+after that? Did the bank end up giving
+
+ align:start position:0%
+after that? Did the bank end up giving
+ 
+
+ align:start position:0%
+after that? Did the bank end up giving
+like their money to Do you ever wonder
+
+ align:start position:0%
+like their money to Do you ever wonder
+ 
+
+ align:start position:0%
+like their money to Do you ever wonder
+what happens when you type in the credit
+
+ align:start position:0%
+what happens when you type in the credit
+ 
+
+ align:start position:0%
+what happens when you type in the credit
+card number and like how the money
+
+ align:start position:0%
+card number and like how the money
+ 
+
+ align:start position:0%
+card number and like how the money
+actually gets where it needs to go? Oh,
+
+ align:start position:0%
+actually gets where it needs to go? Oh,
+ 
+
+ align:start position:0%
+actually gets where it needs to go? Oh,
+they um track them down. Like have you
+
+ align:start position:0%
+they um track them down. Like have you
+ 
+
+ align:start position:0%
+they um track them down. Like have you
+ever wondered about how that happens?
+
+ align:start position:0%
+ever wondered about how that happens?
+ 
+
+ align:start position:0%
+ever wondered about how that happens?
+No, not really. You just care about
+
+ align:start position:0%
+No, not really. You just care about
+ 
+
+ align:start position:0%
+No, not really. You just care about
+getting your package. Um do
+
+ align:start position:0%
+getting your package. Um do
+ 
+
+ align:start position:0%
+getting your package. Um do
+they ATM make the money or do they put
+
+ align:start position:0%
+they ATM make the money or do they put
+ 
+
+ align:start position:0%
+they ATM make the money or do they put
+it in?
+
+ align:start position:0%
+it in?
+ 
+
+ align:start position:0%
+it in?
+Do they just put the money in there?
+
+ align:start position:0%
+Do they just put the money in there?
+ 
+
+ align:start position:0%
+Do they just put the money in there?
+There's a whole every country is
+
+ align:start position:0%
+There's a whole every country is
+ 
+
+ align:start position:0%
+There's a whole every country is
+different but at least here um there's a
+
+ align:start position:0%
+different but at least here um there's a
+ 
+
+ align:start position:0%
+different but at least here um there's a
+central office that makes money and then
+
+ align:start position:0%
+central office that makes money and then
+ 
+
+ align:start position:0%
+central office that makes money and then
+they just distribute it into different
+
+ align:start position:0%
+they just distribute it into different
+ 
+
+ align:start position:0%
+they just distribute it into different
+places. Them doesn't make the money.
+
+ align:start position:0%
+places. Them doesn't make the money.
+ 
+
+ align:start position:0%
+places. Them doesn't make the money.
+It's a good question. But interesting
+
+ align:start position:0%
+It's a good question. But interesting
+ 
+
+ align:start position:0%
+It's a good question. But interesting
+thing for you to think about is sort of
+
+ align:start position:0%
+thing for you to think about is sort of
+ 
+
+ align:start position:0%
+thing for you to think about is sort of
+what within these topics more
+
+ align:start position:0%
+what within these topics more
+ 
+
+ align:start position:0%
+what within these topics more
+specifically because the hacking is a
+
+ align:start position:0%
+specifically because the hacking is a
+ 
+
+ align:start position:0%
+specifically because the hacking is a
+cool topic, but you're right, it's a
+
+ align:start position:0%
+cool topic, but you're right, it's a
+ 
+
+ align:start position:0%
+cool topic, but you're right, it's a
+dangerous one and we'd want to make sure
+
+ align:start position:0%
+dangerous one and we'd want to make sure
+ 
+
+ align:start position:0%
+dangerous one and we'd want to make sure
+we had the right angle so that we're not
+
+ align:start position:0%
+we had the right angle so that we're not
+ 
+
+ align:start position:0%
+we had the right angle so that we're not
+accidentally giving sixth graders the
+
+ align:start position:0%
+accidentally giving sixth graders the
+ 
+
+ align:start position:0%
+accidentally giving sixth graders the
+tools to be able to hack into whatever
+
+ align:start position:0%
+tools to be able to hack into whatever
+ 
+
+ align:start position:0%
+tools to be able to hack into whatever
+account, right? That would be scary.
+
+ align:start position:0%
+account, right? That would be scary.
+ 
+
+ align:start position:0%
+account, right? That would be scary.
+Google might be a good one. Could be,
+
+ align:start position:0%
+Google might be a good one. Could be,
+ 
+
+ align:start position:0%
+Google might be a good one. Could be,
+right? How does Google actually work?
+
+ align:start position:0%
+right? How does Google actually work?
+ 
+
+ align:start position:0%
+right? How does Google actually work?
+How does it find your result? Like if
+
+ align:start position:0%
+How does it find your result? Like if
+ 
+
+ align:start position:0%
+How does it find your result? Like if
+you want to learn how zebras have
+
+ align:start position:0%
+you want to learn how zebras have
+ 
+
+ align:start position:0%
+you want to learn how zebras have
+stripes, how does it actually give you
+
+ align:start position:0%
+stripes, how does it actually give you
+ 
+
+ align:start position:0%
+stripes, how does it actually give you
+an answer? Like how does
+
+ align:start position:0%
+an answer? Like how does
+ 
+
+ align:start position:0%
+an answer? Like how does
+like spread like a virus? Like
+
+ align:start position:0%
+like spread like a virus? Like
+ 
+
+ align:start position:0%
+like spread like a virus? Like
+that's a cool idea, too. Something to
+
+ align:start position:0%
+that's a cool idea, too. Something to
+ 
+
+ align:start position:0%
+that's a cool idea, too. Something to
+think about. Keep thinking. You're on
+
+ align:start position:0%
+think about. Keep thinking. You're on
+ 
+
+ align:start position:0%
+think about. Keep thinking. You're on
+it. Good, good, good.
+
+ align:start position:0%
+it. Good, good, good.
+ 
+
+ align:start position:0%
+it. Good, good, good.
+And you are Anama. Anemma. Anama. Nema.
+
+ align:start position:0%
+And you are Anama. Anemma. Anama. Nema.
+ 
+
+ align:start position:0%
+And you are Anama. Anemma. Anama. Nema.
+Okay. Two really cool names. Yeah. Thank
+
+ align:start position:0%
+Okay. Two really cool names. Yeah. Thank
+ 
+
+ align:start position:0%
+Okay. Two really cool names. Yeah. Thank
+you. And Giana. Giana. So, we're going
+
+ align:start position:0%
+you. And Giana. Giana. So, we're going
+ 
+
+ align:start position:0%
+you. And Giana. Giana. So, we're going
+to have to move a little quick because
+
+ align:start position:0%
+to have to move a little quick because
+ 
+
+ align:start position:0%
+to have to move a little quick because
+we got two teams to talk about. So, you
+
+ align:start position:0%
+we got two teams to talk about. So, you
+ 
+
+ align:start position:0%
+we got two teams to talk about. So, you
+go first. Um, okay. Introduction first.
+
+ align:start position:0%
+go first. Um, okay. Introduction first.
+ 
+
+ align:start position:0%
+go first. Um, okay. Introduction first.
+Um, I'm a first year here at MIT. I like
+
+ align:start position:0%
+Um, I'm a first year here at MIT. I like
+ 
+
+ align:start position:0%
+Um, I'm a first year here at MIT. I like
+to study math, uh, physics and
+
+ align:start position:0%
+to study math, uh, physics and
+ 
+
+ align:start position:0%
+to study math, uh, physics and
+education. I said it's too much. Um,
+
+ align:start position:0%
+education. I said it's too much. Um,
+ 
+
+ align:start position:0%
+education. I said it's too much. Um,
+and, um, I'm going to just pitch the
+
+ align:start position:0%
+and, um, I'm going to just pitch the
+ 
+
+ align:start position:0%
+and, um, I'm going to just pitch the
+idea right away. Normally, I would ask
+
+ align:start position:0%
+idea right away. Normally, I would ask
+ 
+
+ align:start position:0%
+idea right away. Normally, I would ask
+you guys what you like. Um, but the
+
+ align:start position:0%
+you guys what you like. Um, but the
+ 
+
+ align:start position:0%
+you guys what you like. Um, but the
+question that I would like to discuss in
+
+ align:start position:0%
+question that I would like to discuss in
+ 
+
+ align:start position:0%
+question that I would like to discuss in
+a video
+
+ align:start position:0%
+a video
+ 
+
+ align:start position:0%
+a video
+is whether math is actually real and
+
+ align:start position:0%
+is whether math is actually real and
+ 
+
+ align:start position:0%
+is whether math is actually real and
+true. And the thing is that
+
+ align:start position:0%
+true. And the thing is that
+ 
+
+ align:start position:0%
+true. And the thing is that
+mathematicians have proved that they can
+
+ align:start position:0%
+mathematicians have proved that they can
+ 
+
+ align:start position:0%
+mathematicians have proved that they can
+never prove that. So we can never know
+
+ align:start position:0%
+never prove that. So we can never know
+ 
+
+ align:start position:0%
+never prove that. So we can never know
+for sure if math is true. Even
+
+ align:start position:0%
+for sure if math is true. Even
+ 
+
+ align:start position:0%
+for sure if math is true. Even
+arithmetic, you know, it's worked for us
+
+ align:start position:0%
+arithmetic, you know, it's worked for us
+ 
+
+ align:start position:0%
+arithmetic, you know, it's worked for us
+so well. You know, t plus 2 is always
+
+ align:start position:0%
+so well. You know, t plus 2 is always
+ 
+
+ align:start position:0%
+so well. You know, t plus 2 is always
+four, it seems,
+
+ align:start position:0%
+four, it seems,
+ 
+
+ align:start position:0%
+four, it seems,
+but that may not be true. Um, so I guess
+
+ align:start position:0%
+but that may not be true. Um, so I guess
+ 
+
+ align:start position:0%
+but that may not be true. Um, so I guess
+that's kind of the question I wanted to
+
+ align:start position:0%
+that's kind of the question I wanted to
+ 
+
+ align:start position:0%
+that's kind of the question I wanted to
+address. And out of that, it also comes,
+
+ align:start position:0%
+address. And out of that, it also comes,
+ 
+
+ align:start position:0%
+address. And out of that, it also comes,
+you know, can machines be smarter than
+
+ align:start position:0%
+you know, can machines be smarter than
+ 
+
+ align:start position:0%
+you know, can machines be smarter than
+humans? And, you know, can robots
+
+ align:start position:0%
+humans? And, you know, can robots
+ 
+
+ align:start position:0%
+humans? And, you know, can robots
+overtake the world. So just things like
+
+ align:start position:0%
+overtake the world. So just things like
+ 
+
+ align:start position:0%
+overtake the world. So just things like
+that. Um, so any thoughts? Which one? So
+
+ align:start position:0%
+that. Um, so any thoughts? Which one? So
+ 
+
+ align:start position:0%
+that. Um, so any thoughts? Which one? So
+those were three topics, right? Um, so
+
+ align:start position:0%
+those were three topics, right? Um, so
+ 
+
+ align:start position:0%
+those were three topics, right? Um, so
+that was one topic. one topic like just
+
+ align:start position:0%
+that was one topic. one topic like just
+ 
+
+ align:start position:0%
+that was one topic. one topic like just
+like all those questions kind of come
+
+ align:start position:0%
+like all those questions kind of come
+ 
+
+ align:start position:0%
+like all those questions kind of come
+out of that.
+
+ align:start position:0%
+out of that.
+ 
+
+ align:start position:0%
+out of that.
+Those are big questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do you guys respond? Do you think
+
+ align:start position:0%
+What do you guys respond? Do you think
+ 
+
+ align:start position:0%
+What do you guys respond? Do you think
+any of those ideas that she mentioned
+
+ align:start position:0%
+any of those ideas that she mentioned
+ 
+
+ align:start position:0%
+any of those ideas that she mentioned
+are things that you would be like, "Hey,
+
+ align:start position:0%
+are things that you would be like, "Hey,
+ 
+
+ align:start position:0%
+are things that you would be like, "Hey,
+friend. This is really cool. You got to
+
+ align:start position:0%
+friend. This is really cool. You got to
+ 
+
+ align:start position:0%
+friend. This is really cool. You got to
+check out this video." Mhm. Yeah. Which
+
+ align:start position:0%
+check out this video." Mhm. Yeah. Which
+ 
+
+ align:start position:0%
+check out this video." Mhm. Yeah. Which
+one? The robot thing. The robot. Would
+
+ align:start position:0%
+one? The robot thing. The robot. Would
+ 
+
+ align:start position:0%
+one? The robot thing. The robot. Would
+robots take over the world? They're all
+
+ align:start position:0%
+robots take over the world? They're all
+ 
+
+ align:start position:0%
+robots take over the world? They're all
+related, you know. I like the one that
+
+ align:start position:0%
+related, you know. I like the one that
+ 
+
+ align:start position:0%
+related, you know. I like the one that
+is like Is it like true is like for It's
+
+ align:start position:0%
+is like Is it like true is like for It's
+ 
+
+ align:start position:0%
+is like Is it like true is like for It's
+like like for like eight. Is that true?
+
+ align:start position:0%
+like like for like eight. Is that true?
+ 
+
+ align:start position:0%
+like like for like eight. Is that true?
+Okay. So, I'll I'll tell you a secret.
+
+ align:start position:0%
+Okay. So, I'll I'll tell you a secret.
+ 
+
+ align:start position:0%
+Okay. So, I'll I'll tell you a secret.
+Even though we cannot tell that math is
+
+ align:start position:0%
+Even though we cannot tell that math is
+ 
+
+ align:start position:0%
+Even though we cannot tell that math is
+true, that's sad. That also means that
+
+ align:start position:0%
+true, that's sad. That also means that
+ 
+
+ align:start position:0%
+true, that's sad. That also means that
+robots cannot overtake the world. In
+
+ align:start position:0%
+robots cannot overtake the world. In
+ 
+
+ align:start position:0%
+robots cannot overtake the world. In
+case possible, it's not answer. Changing
+
+ align:start position:0%
+case possible, it's not answer. Changing
+ 
+
+ align:start position:0%
+case possible, it's not answer. Changing
+it to math. The math one, but you'll get
+
+ align:start position:0%
+it to math. The math one, but you'll get
+ 
+
+ align:start position:0%
+it to math. The math one, but you'll get
+to the math one through the robots one,
+
+ align:start position:0%
+to the math one through the robots one,
+ 
+
+ align:start position:0%
+to the math one through the robots one,
+right? So, you could Did you have any
+
+ align:start position:0%
+right? So, you could Did you have any
+ 
+
+ align:start position:0%
+right? So, you could Did you have any
+other ideas or was this like the big
+
+ align:start position:0%
+other ideas or was this like the big
+ 
+
+ align:start position:0%
+other ideas or was this like the big
+idea? Uh, that was the that was the big
+
+ align:start position:0%
+idea? Uh, that was the that was the big
+ 
+
+ align:start position:0%
+idea? Uh, that was the that was the big
+one. So, you think that if she talks
+
+ align:start position:0%
+one. So, you think that if she talks
+ 
+
+ align:start position:0%
+one. So, you think that if she talks
+about the idea of could robots overtake
+
+ align:start position:0%
+about the idea of could robots overtake
+ 
+
+ align:start position:0%
+about the idea of could robots overtake
+the world and through that she answers
+
+ align:start position:0%
+the world and through that she answers
+ 
+
+ align:start position:0%
+the world and through that she answers
+some of the questions about math being
+
+ align:start position:0%
+some of the questions about math being
+ 
+
+ align:start position:0%
+some of the questions about math being
+true or not true, that would be really
+
+ align:start position:0%
+true or not true, that would be really
+ 
+
+ align:start position:0%
+true or not true, that would be really
+cool? Yes. I don't think robots can take
+
+ align:start position:0%
+cool? Yes. I don't think robots can take
+ 
+
+ align:start position:0%
+cool? Yes. I don't think robots can take
+over the world. You don't think so? They
+
+ align:start position:0%
+over the world. You don't think so? They
+ 
+
+ align:start position:0%
+over the world. You don't think so? They
+because Wait, what about that weird
+
+ align:start position:0%
+because Wait, what about that weird
+ 
+
+ align:start position:0%
+because Wait, what about that weird
+robot the face of that thing? I mean,
+
+ align:start position:0%
+robot the face of that thing? I mean,
+ 
+
+ align:start position:0%
+robot the face of that thing? I mean,
+you can smash them and they break. But
+
+ align:start position:0%
+you can smash them and they break. But
+ 
+
+ align:start position:0%
+you can smash them and they break. But
+what if they try to smash you?
+
+ align:start position:0%
+what if they try to smash you?
+ 
+
+ align:start position:0%
+what if they try to smash you?
+So eventually we'll be smarter because
+
+ align:start position:0%
+So eventually we'll be smarter because
+ 
+
+ align:start position:0%
+So eventually we'll be smarter because
+that's kind of what a mathematician
+
+ align:start position:0%
+that's kind of what a mathematician
+ 
+
+ align:start position:0%
+that's kind of what a mathematician
+proved is that a machine can never be as
+
+ align:start position:0%
+proved is that a machine can never be as
+ 
+
+ align:start position:0%
+proved is that a machine can never be as
+smart as a human or do as many things
+
+ align:start position:0%
+smart as a human or do as many things
+ 
+
+ align:start position:0%
+smart as a human or do as many things
+that we can do. So you guys said could
+
+ align:start position:0%
+that we can do. So you guys said could
+ 
+
+ align:start position:0%
+that we can do. So you guys said could
+robots take over the world idea with all
+
+ align:start position:0%
+robots take over the world idea with all
+ 
+
+ align:start position:0%
+robots take over the world idea with all
+this other stuff connected to it. I
+
+ align:start position:0%
+this other stuff connected to it. I
+ 
+
+ align:start position:0%
+this other stuff connected to it. I
+think that's a cool idea. Do you know
+
+ align:start position:0%
+think that's a cool idea. Do you know
+ 
+
+ align:start position:0%
+think that's a cool idea. Do you know
+the um show Lab Rats? No, I don't. Well,
+
+ align:start position:0%
+the um show Lab Rats? No, I don't. Well,
+ 
+
+ align:start position:0%
+the um show Lab Rats? No, I don't. Well,
+there was like these three humans who
+
+ align:start position:0%
+there was like these three humans who
+ 
+
+ align:start position:0%
+there was like these three humans who
+are like also like um a robot thing and
+
+ align:start position:0%
+are like also like um a robot thing and
+ 
+
+ align:start position:0%
+are like also like um a robot thing and
+they have like all kinds of powers and
+
+ align:start position:0%
+they have like all kinds of powers and
+ 
+
+ align:start position:0%
+they have like all kinds of powers and
+and because there's this guy that wanted
+
+ align:start position:0%
+and because there's this guy that wanted
+ 
+
+ align:start position:0%
+and because there's this guy that wanted
+to make them evil and like take over the
+
+ align:start position:0%
+to make them evil and like take over the
+ 
+
+ align:start position:0%
+to make them evil and like take over the
+world. Not Disney Channel
+
+ align:start position:0%
+world. Not Disney Channel
+ 
+
+ align:start position:0%
+world. Not Disney Channel
+and and then like this person stole them
+
+ align:start position:0%
+and and then like this person stole them
+ 
+
+ align:start position:0%
+and and then like this person stole them
+and make them became heroes. But can
+
+ align:start position:0%
+and make them became heroes. But can
+ 
+
+ align:start position:0%
+and make them became heroes. But can
+what if like someone that invents a
+
+ align:start position:0%
+what if like someone that invents a
+ 
+
+ align:start position:0%
+what if like someone that invents a
+robot gives them all kinds of like Yeah,
+
+ align:start position:0%
+robot gives them all kinds of like Yeah,
+ 
+
+ align:start position:0%
+robot gives them all kinds of like Yeah,
+that's what she was saying that robots
+
+ align:start position:0%
+that's what she was saying that robots
+ 
+
+ align:start position:0%
+that's what she was saying that robots
+can be really really smart but not as
+
+ align:start position:0%
+can be really really smart but not as
+ 
+
+ align:start position:0%
+can be really really smart but not as
+smart as us. So, I guess eventually
+
+ align:start position:0%
+smart as us. So, I guess eventually
+ 
+
+ align:start position:0%
+smart as us. So, I guess eventually
+we'll win if robots do decide to break
+
+ align:start position:0%
+we'll win if robots do decide to break
+ 
+
+ align:start position:0%
+we'll win if robots do decide to break
+down on us. I want to make sure Andrea
+
+ align:start position:0%
+down on us. I want to make sure Andrea
+ 
+
+ align:start position:0%
+down on us. I want to make sure Andrea
+gets some time. So, let's hear your
+
+ align:start position:0%
+gets some time. So, let's hear your
+ 
+
+ align:start position:0%
+gets some time. So, let's hear your
+ideas. So, you guys have an I'll go get
+
+ align:start position:0%
+ideas. So, you guys have an I'll go get
+ 
+
+ align:start position:0%
+ideas. So, you guys have an I'll go get
+you some. You keep going. Okay. I'm
+
+ align:start position:0%
+you some. You keep going. Okay. I'm
+ 
+
+ align:start position:0%
+you some. You keep going. Okay. I'm
+sorry about that. It's okay.
+
+ align:start position:0%
+sorry about that. It's okay.
+ 
+
+ align:start position:0%
+sorry about that. It's okay.
+So, um I already know the answer for
+
+ align:start position:0%
+So, um I already know the answer for
+ 
+
+ align:start position:0%
+So, um I already know the answer for
+you. Are you going to have to have
+
+ align:start position:0%
+you. Are you going to have to have
+ 
+
+ align:start position:0%
+you. Are you going to have to have
+braces someday? Do you know? No. No. I
+
+ align:start position:0%
+braces someday? Do you know? No. No. I
+ 
+
+ align:start position:0%
+braces someday? Do you know? No. No. I
+want They're cool. They look cool. You
+
+ align:start position:0%
+want They're cool. They look cool. You
+ 
+
+ align:start position:0%
+want They're cool. They look cool. You
+want them? No. Kind of. No, I don't. No,
+
+ align:start position:0%
+want them? No. Kind of. No, I don't. No,
+ 
+
+ align:start position:0%
+want them? No. Kind of. No, I don't. No,
+you don't.
+
+ align:start position:0%
+you don't.
+ 
+
+ align:start position:0%
+you don't.
+So, what how long have you had your
+
+ align:start position:0%
+So, what how long have you had your
+ 
+
+ align:start position:0%
+So, what how long have you had your
+braces?
+
+ align:start position:0%
+braces?
+ 
+
+ align:start position:0%
+braces?
+Beginning of fifth grade. So, you've had
+
+ align:start position:0%
+Beginning of fifth grade. So, you've had
+ 
+
+ align:start position:0%
+Beginning of fifth grade. So, you've had
+them a while. Yeah. I don't even know if
+
+ align:start position:0%
+them a while. Yeah. I don't even know if
+ 
+
+ align:start position:0%
+them a while. Yeah. I don't even know if
+I want braces cuz you can't eat gum or
+
+ align:start position:0%
+I want braces cuz you can't eat gum or
+ 
+
+ align:start position:0%
+I want braces cuz you can't eat gum or
+anything.
+
+ align:start position:0%
+anything.
+ 
+
+ align:start position:0%
+anything.
+No, I don't. I do.
+
+ align:start position:0%
+No, I don't. I do.
+ 
+
+ align:start position:0%
+No, I don't. I do.
+So, are you curious about like what they
+
+ align:start position:0%
+So, are you curious about like what they
+ 
+
+ align:start position:0%
+So, are you curious about like what they
+do to your teeth? Make them straight, I
+
+ align:start position:0%
+do to your teeth? Make them straight, I
+ 
+
+ align:start position:0%
+do to your teeth? Make them straight, I
+guess. Do you know how do you know how
+
+ align:start position:0%
+guess. Do you know how do you know how
+ 
+
+ align:start position:0%
+guess. Do you know how do you know how
+they do that? Yeah, they put them They
+
+ align:start position:0%
+they do that? Yeah, they put them They
+ 
+
+ align:start position:0%
+they do that? Yeah, they put them They
+put them together.
+
+ align:start position:0%
+put them together.
+ 
+
+ align:start position:0%
+put them together.
+That made them straighten. I had like
+
+ align:start position:0%
+That made them straighten. I had like
+ 
+
+ align:start position:0%
+That made them straighten. I had like
+two teeth up here. Hold them down,
+
+ align:start position:0%
+two teeth up here. Hold them down,
+ 
+
+ align:start position:0%
+two teeth up here. Hold them down,
+right? Yeah. You have two teeth that
+
+ align:start position:0%
+right? Yeah. You have two teeth that
+ 
+
+ align:start position:0%
+right? Yeah. You have two teeth that
+flipped out. I had a pallet expander,
+
+ align:start position:0%
+flipped out. I had a pallet expander,
+ 
+
+ align:start position:0%
+flipped out. I had a pallet expander,
+too, that they took out a couple months
+
+ align:start position:0%
+too, that they took out a couple months
+ 
+
+ align:start position:0%
+too, that they took out a couple months
+ago. Tissue. You're going to make me
+
+ align:start position:0%
+ago. Tissue. You're going to make me
+ 
+
+ align:start position:0%
+ago. Tissue. You're going to make me
+talk like like like that. I couldn't
+
+ align:start position:0%
+talk like like like that. I couldn't
+ 
+
+ align:start position:0%
+talk like like like that. I couldn't
+talk for a while. It's like widening my
+
+ align:start position:0%
+talk for a while. It's like widening my
+ 
+
+ align:start position:0%
+talk for a while. It's like widening my
+jaw.
+
+ align:start position:0%
+jaw.
+ 
+
+ align:start position:0%
+jaw.
+I had to key it everywhere. It kind of
+
+ align:start position:0%
+I had to key it everywhere. It kind of
+ 
+
+ align:start position:0%
+I had to key it everywhere. It kind of
+hurt. You don't want braces.
+
+ align:start position:0%
+hurt. You don't want braces.
+ 
+
+ align:start position:0%
+hurt. You don't want braces.
+What was it? I'm sorry I missed it. What
+
+ align:start position:0%
+What was it? I'm sorry I missed it. What
+ 
+
+ align:start position:0%
+What was it? I'm sorry I missed it. What
+was your idea? um to talk about braces.
+
+ align:start position:0%
+was your idea? um to talk about braces.
+ 
+
+ align:start position:0%
+was your idea? um to talk about braces.
+Basically, what they're doing to your
+
+ align:start position:0%
+Basically, what they're doing to your
+ 
+
+ align:start position:0%
+Basically, what they're doing to your
+teeth. Oh, that's cool. Are they bad for
+
+ align:start position:0%
+teeth. Oh, that's cool. Are they bad for
+ 
+
+ align:start position:0%
+teeth. Oh, that's cool. Are they bad for
+your teeth also? Are they bad for your
+
+ align:start position:0%
+your teeth also? Are they bad for your
+ 
+
+ align:start position:0%
+your teeth also? Are they bad for your
+teeth? That's a good question. Why did
+
+ align:start position:0%
+teeth? That's a good question. Why did
+ 
+
+ align:start position:0%
+teeth? That's a good question. Why did
+my teeth move back? Why did my gum like
+
+ align:start position:0%
+my teeth move back? Why did my gum like
+ 
+
+ align:start position:0%
+my teeth move back? Why did my gum like
+scratches everything? What happens when
+
+ align:start position:0%
+scratches everything? What happens when
+ 
+
+ align:start position:0%
+scratches everything? What happens when
+stuff gets Oh, I just I just got my
+
+ align:start position:0%
+stuff gets Oh, I just I just got my
+ 
+
+ align:start position:0%
+stuff gets Oh, I just I just got my
+braces off in October. Good for you. My
+
+ align:start position:0%
+braces off in October. Good for you. My
+ 
+
+ align:start position:0%
+braces off in October. Good for you. My
+dad hasn't hooked me to get them changed
+
+ align:start position:0%
+dad hasn't hooked me to get them changed
+ 
+
+ align:start position:0%
+dad hasn't hooked me to get them changed
+every month, but it's been like 3
+
+ align:start position:0%
+every month, but it's been like 3
+ 
+
+ align:start position:0%
+every month, but it's been like 3
+months. Yeah. So, what's actually going
+
+ align:start position:0%
+months. Yeah. So, what's actually going
+ 
+
+ align:start position:0%
+months. Yeah. So, what's actually going
+on with your braces? That's a cool, very
+
+ align:start position:0%
+on with your braces? That's a cool, very
+ 
+
+ align:start position:0%
+on with your braces? That's a cool, very
+age relevant topic. Wait, instead of
+
+ align:start position:0%
+age relevant topic. Wait, instead of
+ 
+
+ align:start position:0%
+age relevant topic. Wait, instead of
+getting braces, can't you get that like
+
+ align:start position:0%
+getting braces, can't you get that like
+ 
+
+ align:start position:0%
+getting braces, can't you get that like
+plastic thing? Yeah, the the aligners.
+
+ align:start position:0%
+plastic thing? Yeah, the the aligners.
+ 
+
+ align:start position:0%
+plastic thing? Yeah, the the aligners.
+Yeah, I have. Do you know if I have to
+
+ align:start position:0%
+Yeah, I have. Do you know if I have to
+ 
+
+ align:start position:0%
+Yeah, I have. Do you know if I have to
+get a retainer? I have to wear a
+
+ align:start position:0%
+get a retainer? I have to wear a
+ 
+
+ align:start position:0%
+get a retainer? I have to wear a
+retainer.
+
+ align:start position:0%
+retainer.
+ 
+
+ align:start position:0%
+retainer.
+I know one of my friends who had them
+
+ align:start position:0%
+I know one of my friends who had them
+ 
+
+ align:start position:0%
+I know one of my friends who had them
+who like still wears this retainer. Do
+
+ align:start position:0%
+who like still wears this retainer. Do
+ 
+
+ align:start position:0%
+who like still wears this retainer. Do
+you have to like wear it every day or if
+
+ align:start position:0%
+you have to like wear it every day or if
+ 
+
+ align:start position:0%
+you have to like wear it every day or if
+you don't wear every night? Every night
+
+ align:start position:0%
+you don't wear every night? Every night
+ 
+
+ align:start position:0%
+you don't wear every night? Every night
+of that actually for the rest of your
+
+ align:start position:0%
+of that actually for the rest of your
+ 
+
+ align:start position:0%
+of that actually for the rest of your
+life that if you don't wear your
+
+ align:start position:0%
+life that if you don't wear your
+ 
+
+ align:start position:0%
+life that if you don't wear your
+retainer, your teeth wear it from
+
+ align:start position:0%
+retainer, your teeth wear it from
+ 
+
+ align:start position:0%
+retainer, your teeth wear it from
+school. I just hear stuff about you have
+
+ align:start position:0%
+school. I just hear stuff about you have
+ 
+
+ align:start position:0%
+school. I just hear stuff about you have
+to wear the rest of your life.
+
+ align:start position:0%
+to wear the rest of your life.
+ 
+
+ align:start position:0%
+to wear the rest of your life.
+See, I still wear retainers at night.
+
+ align:start position:0%
+See, I still wear retainers at night.
+ 
+
+ align:start position:0%
+See, I still wear retainers at night.
+And I don't understand they give kids
+
+ align:start position:0%
+And I don't understand they give kids
+ 
+
+ align:start position:0%
+And I don't understand they give kids
+braces so young now. Like you can be in
+
+ align:start position:0%
+braces so young now. Like you can be in
+ 
+
+ align:start position:0%
+braces so young now. Like you can be in
+third grade and have braces, whereas
+
+ align:start position:0%
+third grade and have braces, whereas
+ 
+
+ align:start position:0%
+third grade and have braces, whereas
+when I was a kid, you didn't get them
+
+ align:start position:0%
+when I was a kid, you didn't get them
+ 
+
+ align:start position:0%
+when I was a kid, you didn't get them
+until like high school. Third grade?
+
+ align:start position:0%
+until like high school. Third grade?
+ 
+
+ align:start position:0%
+until like high school. Third grade?
+Yeah. I mean, do they I I've seen lots
+
+ align:start position:0%
+Yeah. I mean, do they I I've seen lots
+ 
+
+ align:start position:0%
+Yeah. I mean, do they I I've seen lots
+of little kids with braces and you're
+
+ align:start position:0%
+of little kids with braces and you're
+ 
+
+ align:start position:0%
+of little kids with braces and you're
+like, "Your teeth are so little." Yeah.
+
+ align:start position:0%
+like, "Your teeth are so little." Yeah.
+ 
+
+ align:start position:0%
+like, "Your teeth are so little." Yeah.
+You have to wear um retainers every for
+
+ align:start position:0%
+You have to wear um retainers every for
+ 
+
+ align:start position:0%
+You have to wear um retainers every for
+the rest of your life. For a while. What
+
+ align:start position:0%
+the rest of your life. For a while. What
+ 
+
+ align:start position:0%
+the rest of your life. For a while. What
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the head gear? The head gear. Oh, I like
+
+ align:start position:0%
+the head gear? The head gear. Oh, I like
+ 
+
+ align:start position:0%
+the head gear? The head gear. Oh, I like
+that. That's so gross.
+
+ align:start position:0%
+that. That's so gross.
+ 
+
+ align:start position:0%
+that. That's so gross.
+It looks weird. Charlie. Yeah. Yeah.
+
+ align:start position:0%
+It looks weird. Charlie. Yeah. Yeah.
+ 
+
+ align:start position:0%
+It looks weird. Charlie. Yeah. Yeah.
+Where wears.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It makes you talk weird, too. We're
+
+ align:start position:0%
+It makes you talk weird, too. We're
+ 
+
+ align:start position:0%
+It makes you talk weird, too. We're
+actually really good on Would you do
+
+ align:start position:0%
+actually really good on Would you do
+ 
+
+ align:start position:0%
+actually really good on Would you do
+Would you If you like
+
+ align:start position:0%
+Would you If you like
+ 
+
+ align:start position:0%
+Would you If you like
+everybody, what are you doing?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I heard some amazing conversations and
+
+ align:start position:0%
+I heard some amazing conversations and
+ 
+
+ align:start position:0%
+I heard some amazing conversations and
+you sixth graders asked fantastic
+
+ align:start position:0%
+you sixth graders asked fantastic
+ 
+
+ align:start position:0%
+you sixth graders asked fantastic
+questions. As we're just wrapping up,
+
+ align:start position:0%
+questions. As we're just wrapping up,
+ 
+
+ align:start position:0%
+questions. As we're just wrapping up,
+I'd love to hear from a couple groups of
+
+ align:start position:0%
+I'd love to hear from a couple groups of
+ 
+
+ align:start position:0%
+I'd love to hear from a couple groups of
+the students, the sixth graders. What
+
+ align:start position:0%
+the students, the sixth graders. What
+ 
+
+ align:start position:0%
+the students, the sixth graders. What
+were some of the best ideas that you
+
+ align:start position:0%
+were some of the best ideas that you
+ 
+
+ align:start position:0%
+were some of the best ideas that you
+heard all day that you're like, I can't
+
+ align:start position:0%
+heard all day that you're like, I can't
+ 
+
+ align:start position:0%
+heard all day that you're like, I can't
+wait for this video to come out. I
+
+ align:start position:0%
+wait for this video to come out. I
+ 
+
+ align:start position:0%
+wait for this video to come out. I
+really want to watch it. Any of you hear
+
+ align:start position:0%
+really want to watch it. Any of you hear
+ 
+
+ align:start position:0%
+really want to watch it. Any of you hear
+any like ideas that you're really
+
+ align:start position:0%
+any like ideas that you're really
+ 
+
+ align:start position:0%
+any like ideas that you're really
+excited about? Yeah. Navy one. The Navy
+
+ align:start position:0%
+excited about? Yeah. Navy one. The Navy
+ 
+
+ align:start position:0%
+excited about? Yeah. Navy one. The Navy
+one. What about it? Which what what did
+
+ align:start position:0%
+one. What about it? Which what what did
+ 
+
+ align:start position:0%
+one. What about it? Which what what did
+he Torpedoes?
+
+ align:start position:0%
+he Torpedoes?
+ 
+
+ align:start position:0%
+he Torpedoes?
+Torpedoes. Interesting. The idea of
+
+ align:start position:0%
+Torpedoes. Interesting. The idea of
+ 
+
+ align:start position:0%
+Torpedoes. Interesting. The idea of
+watching things blow up is exciting to
+
+ align:start position:0%
+watching things blow up is exciting to
+ 
+
+ align:start position:0%
+watching things blow up is exciting to
+you. Yes. What else? I like the idea
+
+ align:start position:0%
+you. Yes. What else? I like the idea
+ 
+
+ align:start position:0%
+you. Yes. What else? I like the idea
+with the robot and like we would talk
+
+ align:start position:0%
+with the robot and like we would talk
+ 
+
+ align:start position:0%
+with the robot and like we would talk
+and like we could with Wi-Fi and stuff
+
+ align:start position:0%
+and like we could with Wi-Fi and stuff
+ 
+
+ align:start position:0%
+and like we could with Wi-Fi and stuff
+and you can play with it, run around
+
+ align:start position:0%
+and you can play with it, run around
+ 
+
+ align:start position:0%
+and you can play with it, run around
+with it. I like to see it. So, you're
+
+ align:start position:0%
+with it. I like to see it. So, you're
+ 
+
+ align:start position:0%
+with it. I like to see it. So, you're
+excited about learning more about robots
+
+ align:start position:0%
+excited about learning more about robots
+ 
+
+ align:start position:0%
+excited about learning more about robots
+and how they work? Yeah. Awesome. Anyone
+
+ align:start position:0%
+and how they work? Yeah. Awesome. Anyone
+ 
+
+ align:start position:0%
+and how they work? Yeah. Awesome. Anyone
+else have one? Tiana? Yeah, I have
+
+ align:start position:0%
+else have one? Tiana? Yeah, I have
+ 
+
+ align:start position:0%
+else have one? Tiana? Yeah, I have
+three. Pick one. Pick your best.
+
+ align:start position:0%
+three. Pick one. Pick your best.
+ 
+
+ align:start position:0%
+three. Pick one. Pick your best.
+I like the braces. Yeah, braces.
+
+ align:start position:0%
+I like the braces. Yeah, braces.
+ 
+
+ align:start position:0%
+I like the braces. Yeah, braces.
+Understanding what braces do your teeth
+
+ align:start position:0%
+Understanding what braces do your teeth
+ 
+
+ align:start position:0%
+Understanding what braces do your teeth
+and how they work. That's cool because
+
+ align:start position:0%
+and how they work. That's cool because
+ 
+
+ align:start position:0%
+and how they work. That's cool because
+you've got braces. So that that would be
+
+ align:start position:0%
+you've got braces. So that that would be
+ 
+
+ align:start position:0%
+you've got braces. So that that would be
+interesting. Um, someone said like
+
+ align:start position:0%
+interesting. Um, someone said like
+ 
+
+ align:start position:0%
+interesting. Um, someone said like
+something about volcanoes. The
+
+ align:start position:0%
+something about volcanoes. The
+ 
+
+ align:start position:0%
+something about volcanoes. The
+volcanoes, understanding if there's a
+
+ align:start position:0%
+volcanoes, understanding if there's a
+ 
+
+ align:start position:0%
+volcanoes, understanding if there's a
+volcano underneath your house. That was
+
+ align:start position:0%
+volcano underneath your house. That was
+ 
+
+ align:start position:0%
+volcano underneath your house. That was
+a cool idea. Is there lava under my
+
+ align:start position:0%
+a cool idea. Is there lava under my
+ 
+
+ align:start position:0%
+a cool idea. Is there lava under my
+house? Right. Yikes. Any sixth graders,
+
+ align:start position:0%
+house? Right. Yikes. Any sixth graders,
+ 
+
+ align:start position:0%
+house? Right. Yikes. Any sixth graders,
+any advice to our MIT students before
+
+ align:start position:0%
+any advice to our MIT students before
+ 
+
+ align:start position:0%
+any advice to our MIT students before
+they take your good feedback and turn
+
+ align:start position:0%
+they take your good feedback and turn
+ 
+
+ align:start position:0%
+they take your good feedback and turn
+them into videos? Anything you want to
+
+ align:start position:0%
+them into videos? Anything you want to
+ 
+
+ align:start position:0%
+them into videos? Anything you want to
+make sure that they know to do or not to
+
+ align:start position:0%
+make sure that they know to do or not to
+ 
+
+ align:start position:0%
+make sure that they know to do or not to
+do as they take your good ideas and over
+
+ align:start position:0%
+do as they take your good ideas and over
+ 
+
+ align:start position:0%
+do as they take your good ideas and over
+the next month develop them into actual
+
+ align:start position:0%
+the next month develop them into actual
+ 
+
+ align:start position:0%
+the next month develop them into actual
+movies?
+
+ align:start position:0%
+movies?
+ 
+
+ align:start position:0%
+movies?
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+like picture ideas instead of talking to
+
+ align:start position:0%
+like picture ideas instead of talking to
+ 
+
+ align:start position:0%
+like picture ideas instead of talking to
+them like show examples so they can
+
+ align:start position:0%
+them like show examples so they can
+ 
+
+ align:start position:0%
+them like show examples so they can
+memorize it. That's what So we talked
+
+ align:start position:0%
+memorize it. That's what So we talked
+ 
+
+ align:start position:0%
+memorize it. That's what So we talked
+about that MIT students yesterday the
+
+ align:start position:0%
+about that MIT students yesterday the
+ 
+
+ align:start position:0%
+about that MIT students yesterday the
+idea of showing don't telling which I'm
+
+ align:start position:0%
+idea of showing don't telling which I'm
+ 
+
+ align:start position:0%
+idea of showing don't telling which I'm
+sure you guys talk about in your writing
+
+ align:start position:0%
+sure you guys talk about in your writing
+ 
+
+ align:start position:0%
+sure you guys talk about in your writing
+a lot right showing don't telling. Cool.
+
+ align:start position:0%
+a lot right showing don't telling. Cool.
+ 
+
+ align:start position:0%
+a lot right showing don't telling. Cool.
+Don't ask too many questions like cuz we
+
+ align:start position:0%
+Don't ask too many questions like cuz we
+ 
+
+ align:start position:0%
+Don't ask too many questions like cuz we
+watched one video and it asked a ton of
+
+ align:start position:0%
+watched one video and it asked a ton of
+ 
+
+ align:start position:0%
+watched one video and it asked a ton of
+questions and we didn't really
+
+ align:start position:0%
+questions and we didn't really
+ 
+
+ align:start position:0%
+questions and we didn't really
+understand it. Do you mean asking the
+
+ align:start position:0%
+understand it. Do you mean asking the
+ 
+
+ align:start position:0%
+understand it. Do you mean asking the
+audience questions? Like saying like
+
+ align:start position:0%
+audience questions? Like saying like
+ 
+
+ align:start position:0%
+audience questions? Like saying like
+what does this do? What does this do? It
+
+ align:start position:0%
+what does this do? What does this do? It
+ 
+
+ align:start position:0%
+what does this do? What does this do? It
+could just say one thing and then show
+
+ align:start position:0%
+could just say one thing and then show
+ 
+
+ align:start position:0%
+could just say one thing and then show
+it. So asking your audience too many
+
+ align:start position:0%
+it. So asking your audience too many
+ 
+
+ align:start position:0%
+it. So asking your audience too many
+questions is annoying. Yeah.
+
+ align:start position:0%
+questions is annoying. Yeah.
+ 
+
+ align:start position:0%
+questions is annoying. Yeah.
+You first and then you. The original.
+
+ align:start position:0%
+You first and then you. The original.
+ 
+
+ align:start position:0%
+You first and then you. The original.
+The original. So try to have a new idea.
+
+ align:start position:0%
+The original. So try to have a new idea.
+ 
+
+ align:start position:0%
+The original. So try to have a new idea.
+And what else? Um while you explain how
+
+ align:start position:0%
+And what else? Um while you explain how
+ 
+
+ align:start position:0%
+And what else? Um while you explain how
+things work, try and make some jokes
+
+ align:start position:0%
+things work, try and make some jokes
+ 
+
+ align:start position:0%
+things work, try and make some jokes
+while you do it so your audience laughs
+
+ align:start position:0%
+while you do it so your audience laughs
+ 
+
+ align:start position:0%
+while you do it so your audience laughs
+at it and like they understand what
+
+ align:start position:0%
+at it and like they understand what
+ 
+
+ align:start position:0%
+at it and like they understand what
+you're talking about. Awesome. Last one.
+
+ align:start position:0%
+you're talking about. Awesome. Last one.
+ 
+
+ align:start position:0%
+you're talking about. Awesome. Last one.
+Um, don't use like a monotonous pitch.
+
+ align:start position:0%
+Um, don't use like a monotonous pitch.
+ 
+
+ align:start position:0%
+Um, don't use like a monotonous pitch.
+Awesome. To change your voice around and
+
+ align:start position:0%
+Awesome. To change your voice around and
+ 
+
+ align:start position:0%
+Awesome. To change your voice around and
+make it more interesting. MIT students,
+
+ align:start position:0%
+make it more interesting. MIT students,
+ 
+
+ align:start position:0%
+make it more interesting. MIT students,
+I'm curious from you. What was valuable
+
+ align:start position:0%
+I'm curious from you. What was valuable
+ 
+
+ align:start position:0%
+I'm curious from you. What was valuable
+that you got from the sixth graders
+
+ align:start position:0%
+that you got from the sixth graders
+ 
+
+ align:start position:0%
+that you got from the sixth graders
+today to give them some feedback about
+
+ align:start position:0%
+today to give them some feedback about
+ 
+
+ align:start position:0%
+today to give them some feedback about
+this experience? Did anyone get some
+
+ align:start position:0%
+this experience? Did anyone get some
+ 
+
+ align:start position:0%
+this experience? Did anyone get some
+good feedback? Yeah. Uh, well, I found
+
+ align:start position:0%
+good feedback? Yeah. Uh, well, I found
+ 
+
+ align:start position:0%
+good feedback? Yeah. Uh, well, I found
+that um, and I should have realized this
+
+ align:start position:0%
+that um, and I should have realized this
+ 
+
+ align:start position:0%
+that um, and I should have realized this
+is that having robots stomping around
+
+ align:start position:0%
+is that having robots stomping around
+ 
+
+ align:start position:0%
+is that having robots stomping around
+and destroying cities is way more fun
+
+ align:start position:0%
+and destroying cities is way more fun
+ 
+
+ align:start position:0%
+and destroying cities is way more fun
+than showing old people doing math.
+
+ align:start position:0%
+than showing old people doing math.
+ 
+
+ align:start position:0%
+than showing old people doing math.
+Robots are more than old people doing
+
+ align:start position:0%
+Robots are more than old people doing
+ 
+
+ align:start position:0%
+Robots are more than old people doing
+math. H.
+
+ align:start position:0%
+math. H.
+ 
+
+ align:start position:0%
+math. H.
+Uh I too learned that my tastes are
+
+ align:start position:0%
+Uh I too learned that my tastes are
+ 
+
+ align:start position:0%
+Uh I too learned that my tastes are
+different. Uh that uh lava and volcanoes
+
+ align:start position:0%
+different. Uh that uh lava and volcanoes
+ 
+
+ align:start position:0%
+different. Uh that uh lava and volcanoes
+are a lot more interesting than food
+
+ align:start position:0%
+are a lot more interesting than food
+ 
+
+ align:start position:0%
+are a lot more interesting than food
+decomposing.
+
+ align:start position:0%
+decomposing.
+ 
+
+ align:start position:0%
+decomposing.
+He wanted to show food rotting and
+
+ align:start position:0%
+He wanted to show food rotting and
+ 
+
+ align:start position:0%
+He wanted to show food rotting and
+everyone thought that was not as fun as
+
+ align:start position:0%
+everyone thought that was not as fun as
+ 
+
+ align:start position:0%
+everyone thought that was not as fun as
+volcanoes exploding. Um any other thing
+
+ align:start position:0%
+volcanoes exploding. Um any other thing
+ 
+
+ align:start position:0%
+volcanoes exploding. Um any other thing
+from the MIT students that you found was
+
+ align:start position:0%
+from the MIT students that you found was
+ 
+
+ align:start position:0%
+from the MIT students that you found was
+helpful? Yeah, I was kind of like I
+
+ align:start position:0%
+helpful? Yeah, I was kind of like I
+ 
+
+ align:start position:0%
+helpful? Yeah, I was kind of like I
+don't know. It was humbling to know how
+
+ align:start position:0%
+don't know. It was humbling to know how
+ 
+
+ align:start position:0%
+don't know. It was humbling to know how
+much people like even sixth graders know
+
+ align:start position:0%
+much people like even sixth graders know
+ 
+
+ align:start position:0%
+much people like even sixth graders know
+about some of the really complicated
+
+ align:start position:0%
+about some of the really complicated
+ 
+
+ align:start position:0%
+about some of the really complicated
+subjects that we're even learning here.
+
+ align:start position:0%
+subjects that we're even learning here.
+ 
+
+ align:start position:0%
+subjects that we're even learning here.
+So awesome. A lot. We had some good
+
+ align:start position:0%
+So awesome. A lot. We had some good
+ 
+
+ align:start position:0%
+So awesome. A lot. We had some good
+conversation about sticking and floating
+
+ align:start position:0%
+conversation about sticking and floating
+ 
+
+ align:start position:0%
+conversation about sticking and floating
+and how do boats even work. It was
+
+ align:start position:0%
+and how do boats even work. It was
+ 
+
+ align:start position:0%
+and how do boats even work. It was
+awesome how much you guys do. Well, we
+
+ align:start position:0%
+awesome how much you guys do. Well, we
+ 
+
+ align:start position:0%
+awesome how much you guys do. Well, we
+can't thank you six readers enough for
+
+ align:start position:0%
+can't thank you six readers enough for
+ 
+
+ align:start position:0%
+can't thank you six readers enough for
+coming here today. It was so helpful.
+
+ align:start position:0%
+coming here today. It was so helpful.
+ 
+
+ align:start position:0%
+coming here today. It was so helpful.
+Thank
+
+ align:start position:0%
+Thank
+ 
+
+ align:start position:0%
+Thank
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+you. And I'm sure Elizabeth will be in
+
+ align:start position:0%
+you. And I'm sure Elizabeth will be in
+ 
+
+ align:start position:0%
+you. And I'm sure Elizabeth will be in
+touch with you guys to let you know how
+
+ align:start position:0%
+touch with you guys to let you know how
+ 
+
+ align:start position:0%
+touch with you guys to let you know how
+we our ideas and the videos that you
+
+ align:start position:0%
+we our ideas and the videos that you
+ 
+
+ align:start position:0%
+we our ideas and the videos that you
+guys made with me last month. They're
+
+ align:start position:0%
+guys made with me last month. They're
+ 
+
+ align:start position:0%
+guys made with me last month. They're
+almost finished. Carrie is almost
+
+ align:start position:0%
+almost finished. Carrie is almost
+ 
+
+ align:start position:0%
+almost finished. Carrie is almost
+finished with them today. So I will send
+
+ align:start position:0%
+finished with them today. So I will send
+ 
+
+ align:start position:0%
+finished with them today. So I will send
+those over to your teacher and you can
+
+ align:start position:0%
+those over to your teacher and you can
+ 
+
+ align:start position:0%
+those over to your teacher and you can
+watch them sometimes.
+
+ align:start position:0%
+watch them sometimes.
+ 
+
+ align:start position:0%
+watch them sometimes.
+Any directions from teachers before they
+
+ align:start position:0%
+Any directions from teachers before they
+ 
+
+ align:start position:0%
+Any directions from teachers before they
+leave the room on what's coming up next?
+
+ align:start position:0%
+leave the room on what's coming up next?
+ 
+
+ align:start position:0%
+leave the room on what's coming up next?
+Nope. Just um make one long single line
+
+ align:start position:0%
+Nope. Just um make one long single line
+ 
+
+ align:start position:0%
+Nope. Just um make one long single line
+so I can count you before you leave the
+
+ align:start position:0%
+so I can count you before you leave the
+ 
+
+ align:start position:0%
+so I can count you before you leave the
+building and then I'll count you on the
+
+ align:start position:0%
+building and then I'll count you on the
+ 
+
+ align:start position:0%
+building and then I'll count you on the
+bus again. check for jackets and all
+
+ align:start position:0%
+bus again. check for jackets and all
+ 
+
+ align:start position:0%
+bus again. check for jackets and all
+those things, but have a safe trip back
+
+ align:start position:0%
+those things, but have a safe trip back
+ 
+
+ align:start position:0%
+those things, but have a safe trip back
+home. Did you say thank you? Thank you.
+
+ align:start position:0%
+home. Did you say thank you? Thank you.
+ 
+
+ align:start position:0%
+home. Did you say thank you? Thank you.
+Thank you so much.
\ No newline at end of file
diff --git a/rWnyP-iZGu4.txt b/rWnyP-iZGu4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b9a185398280a8c0760c2a79802a8c3b3429790
--- /dev/null
+++ b/rWnyP-iZGu4.txt
@@ -0,0 +1,12187 @@
+align:start position:0%
+ 
+okay greetings everyone
+
+ align:start position:0%
+okay greetings everyone
+ 
+
+ align:start position:0%
+okay greetings everyone
+thank you for coming today
+
+ align:start position:0%
+thank you for coming today
+ 
+
+ align:start position:0%
+thank you for coming today
+i'll say a few things so in terms of the
+
+ align:start position:0%
+i'll say a few things so in terms of the
+ 
+
+ align:start position:0%
+i'll say a few things so in terms of the
+calendar
+
+ align:start position:0%
+calendar
+ 
+
+ align:start position:0%
+calendar
+and we're finishing off this section
+
+ align:start position:0%
+and we're finishing off this section
+ 
+
+ align:start position:0%
+and we're finishing off this section
+right before thanksgiving break when i
+
+ align:start position:0%
+right before thanksgiving break when i
+ 
+
+ align:start position:0%
+right before thanksgiving break when i
+get excuse me on identification today
+
+ align:start position:0%
+get excuse me on identification today
+ 
+
+ align:start position:0%
+get excuse me on identification today
+we're on that momentarily
+
+ align:start position:0%
+we're on that momentarily
+ 
+
+ align:start position:0%
+we're on that momentarily
+and we have two
+
+ align:start position:0%
+and we have two
+ 
+
+ align:start position:0%
+and we have two
+formal lectures after the break
+
+ align:start position:0%
+formal lectures after the break
+ 
+
+ align:start position:0%
+formal lectures after the break
+on tuesday thursday so that's the
+
+ align:start position:0%
+on tuesday thursday so that's the
+ 
+
+ align:start position:0%
+on tuesday thursday so that's the
+calendar
+
+ align:start position:0%
+calendar
+ 
+
+ align:start position:0%
+calendar
+then in terms of the readings today is
+
+ align:start position:0%
+then in terms of the readings today is
+ 
+
+ align:start position:0%
+then in terms of the readings today is
+kind of important to point out
+
+ align:start position:0%
+kind of important to point out
+ 
+
+ align:start position:0%
+kind of important to point out
+the section on identification and
+
+ align:start position:0%
+the section on identification and
+ 
+
+ align:start position:0%
+the section on identification and
+falsification we're about to do
+
+ align:start position:0%
+falsification we're about to do
+ 
+
+ align:start position:0%
+falsification we're about to do
+uh there are three starred readings and
+
+ align:start position:0%
+uh there are three starred readings and
+ 
+
+ align:start position:0%
+uh there are three starred readings and
+they all come from varian
+
+ align:start position:0%
+they all come from varian
+ 
+
+ align:start position:0%
+they all come from varian
+and they're all really really good in
+
+ align:start position:0%
+and they're all really really good in
+ 
+
+ align:start position:0%
+and they're all really really good in
+fact i had to abbreviate in spots in
+
+ align:start position:0%
+fact i had to abbreviate in spots in
+ 
+
+ align:start position:0%
+fact i had to abbreviate in spots in
+order to cover all the topics so we were
+
+ align:start position:0%
+order to cover all the topics so we were
+ 
+
+ align:start position:0%
+order to cover all the topics so we were
+drawing on this material in part and
+
+ align:start position:0%
+drawing on this material in part and
+ 
+
+ align:start position:0%
+drawing on this material in part and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you you will find it useful
+
+ align:start position:0%
+you you will find it useful
+ 
+
+ align:start position:0%
+you you will find it useful
+again it's not the whole book it's just
+
+ align:start position:0%
+again it's not the whole book it's just
+ 
+
+ align:start position:0%
+again it's not the whole book it's just
+very in these sections 8.1 through 8.3
+
+ align:start position:0%
+very in these sections 8.1 through 8.3
+ 
+
+ align:start position:0%
+very in these sections 8.1 through 8.3
+8.5 and 8.7
+
+ align:start position:0%
+8.5 and 8.7
+ 
+
+ align:start position:0%
+8.5 and 8.7
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+from last time let's have a little bit
+
+ align:start position:0%
+from last time let's have a little bit
+ 
+
+ align:start position:0%
+from last time let's have a little bit
+of a discussion
+
+ align:start position:0%
+of a discussion
+ 
+
+ align:start position:0%
+of a discussion
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+daniel
+
+ align:start position:0%
+daniel
+ 
+
+ align:start position:0%
+daniel
+can you tell me as best you can
+
+ align:start position:0%
+can you tell me as best you can
+ 
+
+ align:start position:0%
+can you tell me as best you can
+what the definition of is the positive
+
+ align:start position:0%
+what the definition of is the positive
+ 
+
+ align:start position:0%
+what the definition of is the positive
+representative consumer and
+
+ align:start position:0%
+representative consumer and
+ 
+
+ align:start position:0%
+representative consumer and
+the normal
+
+ align:start position:0%
+the normal
+ 
+
+ align:start position:0%
+the normal
+normative representative consumer
+
+ align:start position:0%
+normative representative consumer
+ 
+
+ align:start position:0%
+normative representative consumer
+sort of explaining what they are
+
+ align:start position:0%
+sort of explaining what they are
+ 
+
+ align:start position:0%
+sort of explaining what they are
+intuitively so like the idea is you're
+
+ align:start position:0%
+intuitively so like the idea is you're
+ 
+
+ align:start position:0%
+intuitively so like the idea is you're
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+treat the entire economy as a single
+
+ align:start position:0%
+treat the entire economy as a single
+ 
+
+ align:start position:0%
+treat the entire economy as a single
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+so um a positive representative consumer
+
+ align:start position:0%
+so um a positive representative consumer
+ 
+
+ align:start position:0%
+so um a positive representative consumer
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the um at any given like level of wealth
+
+ align:start position:0%
+the um at any given like level of wealth
+ 
+
+ align:start position:0%
+the um at any given like level of wealth
+and input the
+
+ align:start position:0%
+and input the
+ 
+
+ align:start position:0%
+and input the
+the way to maximize um utility
+
+ align:start position:0%
+the way to maximize um utility
+ 
+
+ align:start position:0%
+the way to maximize um utility
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+um spend your
+
+ align:start position:0%
+um spend your
+ 
+
+ align:start position:0%
+um spend your
+your wealth the way that customer would
+
+ align:start position:0%
+your wealth the way that customer would
+ 
+
+ align:start position:0%
+your wealth the way that customer would
+and then um
+
+ align:start position:0%
+and then um
+ 
+
+ align:start position:0%
+and then um
+and then uh distribute that to the
+
+ align:start position:0%
+and then uh distribute that to the
+ 
+
+ align:start position:0%
+and then uh distribute that to the
+people like
+
+ align:start position:0%
+people like
+ 
+
+ align:start position:0%
+people like
+in some way uh
+
+ align:start position:0%
+in some way uh
+ 
+
+ align:start position:0%
+in some way uh
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+we don't really know which way from the
+
+ align:start position:0%
+we don't really know which way from the
+ 
+
+ align:start position:0%
+we don't really know which way from the
+consumer but like it'll just be like the
+
+ align:start position:0%
+consumer but like it'll just be like the
+ 
+
+ align:start position:0%
+consumer but like it'll just be like the
+best distribution and then the
+
+ align:start position:0%
+best distribution and then the
+ 
+
+ align:start position:0%
+best distribution and then the
+um normative is very similar except for
+
+ align:start position:0%
+um normative is very similar except for
+ 
+
+ align:start position:0%
+um normative is very similar except for
+instead of the
+
+ align:start position:0%
+instead of the
+ 
+
+ align:start position:0%
+instead of the
+utility maximizing it's the pareto
+
+ align:start position:0%
+utility maximizing it's the pareto
+ 
+
+ align:start position:0%
+utility maximizing it's the pareto
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+way to distribute the wealth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess i would sharpen up a little bit
+
+ align:start position:0%
+i guess i would sharpen up a little bit
+ 
+
+ align:start position:0%
+i guess i would sharpen up a little bit
+the positive one the idea is to get the
+
+ align:start position:0%
+the positive one the idea is to get the
+ 
+
+ align:start position:0%
+the positive one the idea is to get the
+the excess demand curve for the economy
+
+ align:start position:0%
+the excess demand curve for the economy
+ 
+
+ align:start position:0%
+the excess demand curve for the economy
+as if it were coming from this
+
+ align:start position:0%
+as if it were coming from this
+ 
+
+ align:start position:0%
+as if it were coming from this
+representative consumer maximizing
+
+ align:start position:0%
+representative consumer maximizing
+ 
+
+ align:start position:0%
+representative consumer maximizing
+utilities subject to
+
+ align:start position:0%
+utilities subject to
+ 
+
+ align:start position:0%
+utilities subject to
+resource constraints and the and that
+
+ align:start position:0%
+resource constraints and the and that
+ 
+
+ align:start position:0%
+resource constraints and the and that
+can representative consumer has
+
+ align:start position:0%
+can representative consumer has
+ 
+
+ align:start position:0%
+can representative consumer has
+all the resource constraints in the
+
+ align:start position:0%
+all the resource constraints in the
+ 
+
+ align:start position:0%
+all the resource constraints in the
+entire economy in particular
+
+ align:start position:0%
+entire economy in particular
+ 
+
+ align:start position:0%
+entire economy in particular
+the budget just says don't spend more
+
+ align:start position:0%
+the budget just says don't spend more
+ 
+
+ align:start position:0%
+the budget just says don't spend more
+than the economy wide wealth
+
+ align:start position:0%
+than the economy wide wealth
+ 
+
+ align:start position:0%
+than the economy wide wealth
+and you kind of said that but
+
+ align:start position:0%
+and you kind of said that but
+ 
+
+ align:start position:0%
+and you kind of said that but
+maybe better for me to
+
+ align:start position:0%
+maybe better for me to
+ 
+
+ align:start position:0%
+maybe better for me to
+repeat it a little bit
+
+ align:start position:0%
+repeat it a little bit
+ 
+
+ align:start position:0%
+repeat it a little bit
+yeah and then the normative one is a way
+
+ align:start position:0%
+yeah and then the normative one is a way
+ 
+
+ align:start position:0%
+yeah and then the normative one is a way
+to rank order allocations
+
+ align:start position:0%
+to rank order allocations
+ 
+
+ align:start position:0%
+to rank order allocations
+according to the
+
+ align:start position:0%
+according to the
+ 
+
+ align:start position:0%
+according to the
+pareto principle but ironically rather
+
+ align:start position:0%
+pareto principle but ironically rather
+ 
+
+ align:start position:0%
+pareto principle but ironically rather
+than keeping track of all the
+
+ align:start position:0%
+than keeping track of all the
+ 
+
+ align:start position:0%
+than keeping track of all the
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+and whether they're made better off or
+
+ align:start position:0%
+and whether they're made better off or
+ 
+
+ align:start position:0%
+and whether they're made better off or
+worse off we can collapse it to
+
+ align:start position:0%
+worse off we can collapse it to
+ 
+
+ align:start position:0%
+worse off we can collapse it to
+as if we were maximizing utility for the
+
+ align:start position:0%
+as if we were maximizing utility for the
+ 
+
+ align:start position:0%
+as if we were maximizing utility for the
+whole economy
+
+ align:start position:0%
+whole economy
+ 
+
+ align:start position:0%
+whole economy
+through the lens of this representative
+
+ align:start position:0%
+through the lens of this representative
+ 
+
+ align:start position:0%
+through the lens of this representative
+consumer
+
+ align:start position:0%
+consumer
+ 
+
+ align:start position:0%
+consumer
+and as you said
+
+ align:start position:0%
+and as you said
+ 
+
+ align:start position:0%
+and as you said
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that that kind of determines the overall
+
+ align:start position:0%
+that that kind of determines the overall
+ 
+
+ align:start position:0%
+that that kind of determines the overall
+allocation it doesn't
+
+ align:start position:0%
+allocation it doesn't
+ 
+
+ align:start position:0%
+allocation it doesn't
+pin down the
+
+ align:start position:0%
+pin down the
+ 
+
+ align:start position:0%
+pin down the
+potential reallocation of wealth
+
+ align:start position:0%
+potential reallocation of wealth
+ 
+
+ align:start position:0%
+potential reallocation of wealth
+that is uh necessary if you go from
+
+ align:start position:0%
+that is uh necessary if you go from
+ 
+
+ align:start position:0%
+that is uh necessary if you go from
+something pareto fury inferior to
+
+ align:start position:0%
+something pareto fury inferior to
+ 
+
+ align:start position:0%
+something pareto fury inferior to
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+credo superior or pareto optimal
+
+ align:start position:0%
+credo superior or pareto optimal
+ 
+
+ align:start position:0%
+credo superior or pareto optimal
+you may have to
+
+ align:start position:0%
+you may have to
+ 
+
+ align:start position:0%
+you may have to
+compensate
+
+ align:start position:0%
+compensate
+ 
+
+ align:start position:0%
+compensate
+the losers and
+
+ align:start position:0%
+the losers and
+ 
+
+ align:start position:0%
+the losers and
+by taxing the winners
+
+ align:start position:0%
+by taxing the winners
+ 
+
+ align:start position:0%
+by taxing the winners
+okay great
+
+ align:start position:0%
+okay great
+ 
+
+ align:start position:0%
+okay great
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we made a lot of use of this gorman
+
+ align:start position:0%
+so we made a lot of use of this gorman
+ 
+
+ align:start position:0%
+so we made a lot of use of this gorman
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+caleb can you tell me
+
+ align:start position:0%
+caleb can you tell me
+ 
+
+ align:start position:0%
+caleb can you tell me
+what in words what is this gorman
+
+ align:start position:0%
+what in words what is this gorman
+ 
+
+ align:start position:0%
+what in words what is this gorman
+polar form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah so it
+
+ align:start position:0%
+uh yeah so it
+ 
+
+ align:start position:0%
+uh yeah so it
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+actually like it breaks down the uh
+
+ align:start position:0%
+actually like it breaks down the uh
+ 
+
+ align:start position:0%
+actually like it breaks down the uh
+the the like equilibrium into like a
+
+ align:start position:0%
+the the like equilibrium into like a
+ 
+
+ align:start position:0%
+the the like equilibrium into like a
+linear form i guess i don't know exactly
+
+ align:start position:0%
+linear form i guess i don't know exactly
+ 
+
+ align:start position:0%
+linear form i guess i don't know exactly
+how to explain it um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+do you remember any of the notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it breaking down exactly
+
+ align:start position:0%
+what is it breaking down exactly
+ 
+
+ align:start position:0%
+what is it breaking down exactly
+um like like the equilibrium in the
+
+ align:start position:0%
+um like like the equilibrium in the
+ 
+
+ align:start position:0%
+um like like the equilibrium in the
+economy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does the word indirect utility come to
+
+ align:start position:0%
+does the word indirect utility come to
+ 
+
+ align:start position:0%
+does the word indirect utility come to
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's the
+
+ align:start position:0%
+okay it's the
+ 
+
+ align:start position:0%
+okay it's the
+it's the indirect utility function
+
+ align:start position:0%
+it's the indirect utility function
+ 
+
+ align:start position:0%
+it's the indirect utility function
+which is the maximized utility
+
+ align:start position:0%
+which is the maximized utility
+ 
+
+ align:start position:0%
+which is the maximized utility
+subject to the given vector of prices
+
+ align:start position:0%
+subject to the given vector of prices
+ 
+
+ align:start position:0%
+subject to the given vector of prices
+and wealth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the statement about gorman forum is this
+
+ align:start position:0%
+the statement about gorman forum is this
+ 
+
+ align:start position:0%
+the statement about gorman forum is this
+form in which
+
+ align:start position:0%
+form in which
+ 
+
+ align:start position:0%
+form in which
+uh that that
+
+ align:start position:0%
+uh that that
+ 
+
+ align:start position:0%
+uh that that
+indirect utility function must take
+
+ align:start position:0%
+indirect utility function must take
+ 
+
+ align:start position:0%
+indirect utility function must take
+in order to do this positive and
+
+ align:start position:0%
+in order to do this positive and
+ 
+
+ align:start position:0%
+in order to do this positive and
+normative thing just can someone
+
+ align:start position:0%
+normative thing just can someone
+ 
+
+ align:start position:0%
+normative thing just can someone
+volunteer to tell me what
+
+ align:start position:0%
+volunteer to tell me what
+ 
+
+ align:start position:0%
+volunteer to tell me what
+in words if you can what the gorman form
+
+ align:start position:0%
+in words if you can what the gorman form
+ 
+
+ align:start position:0%
+in words if you can what the gorman form
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+uh sure i can take this one
+
+ align:start position:0%
+uh sure i can take this one
+ 
+
+ align:start position:0%
+uh sure i can take this one
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+um so the garmin form is basically
+
+ align:start position:0%
+um so the garmin form is basically
+ 
+
+ align:start position:0%
+um so the garmin form is basically
+um an indirect utility function that is
+
+ align:start position:0%
+um an indirect utility function that is
+ 
+
+ align:start position:0%
+um an indirect utility function that is
+linear in w uh the overall like wealth
+
+ align:start position:0%
+linear in w uh the overall like wealth
+ 
+
+ align:start position:0%
+linear in w uh the overall like wealth
+of the economy so it's some function a
+
+ align:start position:0%
+of the economy so it's some function a
+ 
+
+ align:start position:0%
+of the economy so it's some function a
+which depends on prices plus some
+
+ align:start position:0%
+which depends on prices plus some
+ 
+
+ align:start position:0%
+which depends on prices plus some
+function b which depends on prices plus
+
+ align:start position:0%
+function b which depends on prices plus
+ 
+
+ align:start position:0%
+function b which depends on prices plus
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+that's exactly right
+
+ align:start position:0%
+that's exactly right
+ 
+
+ align:start position:0%
+that's exactly right
+well it's at the level of the
+
+ align:start position:0%
+well it's at the level of the
+ 
+
+ align:start position:0%
+well it's at the level of the
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if we had an individual i where do we
+
+ align:start position:0%
+if we had an individual i where do we
+ 
+
+ align:start position:0%
+if we had an individual i where do we
+put the i in that equation
+
+ align:start position:0%
+put the i in that equation
+ 
+
+ align:start position:0%
+put the i in that equation
+um so it is the
+
+ align:start position:0%
+um so it is the
+ 
+
+ align:start position:0%
+um so it is the
+um it is on both the wealth that an
+
+ align:start position:0%
+um it is on both the wealth that an
+ 
+
+ align:start position:0%
+um it is on both the wealth that an
+individual person faces and i think as
+
+ align:start position:0%
+individual person faces and i think as
+ 
+
+ align:start position:0%
+individual person faces and i think as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on the functions a and b they can have
+
+ align:start position:0%
+on the functions a and b they can have
+ 
+
+ align:start position:0%
+on the functions a and b they can have
+each individual can have their own
+
+ align:start position:0%
+each individual can have their own
+ 
+
+ align:start position:0%
+each individual can have their own
+specific form for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two out of three so it's on the wealth
+
+ align:start position:0%
+two out of three so it's on the wealth
+ 
+
+ align:start position:0%
+two out of three so it's on the wealth
+because at the individual level it's the
+
+ align:start position:0%
+because at the individual level it's the
+ 
+
+ align:start position:0%
+because at the individual level it's the
+indirect utility is a function of the
+
+ align:start position:0%
+indirect utility is a function of the
+ 
+
+ align:start position:0%
+indirect utility is a function of the
+individual's wealth say w sub i
+
+ align:start position:0%
+individual's wealth say w sub i
+ 
+
+ align:start position:0%
+individual's wealth say w sub i
+the intercept term the a of p is the a i
+
+ align:start position:0%
+the intercept term the a of p is the a i
+ 
+
+ align:start position:0%
+the intercept term the a of p is the a i
+of p
+
+ align:start position:0%
+of p
+ 
+
+ align:start position:0%
+of p
+so that's where the heterogeneity is
+
+ align:start position:0%
+so that's where the heterogeneity is
+ 
+
+ align:start position:0%
+so that's where the heterogeneity is
+loaded
+
+ align:start position:0%
+loaded
+ 
+
+ align:start position:0%
+loaded
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but it's not on the b and maybe
+
+ align:start position:0%
+but it's not on the b and maybe
+ 
+
+ align:start position:0%
+but it's not on the b and maybe
+you can remember y what did we say about
+
+ align:start position:0%
+you can remember y what did we say about
+ 
+
+ align:start position:0%
+you can remember y what did we say about
+those linear expansion paths oh those
+
+ align:start position:0%
+those linear expansion paths oh those
+ 
+
+ align:start position:0%
+those linear expansion paths oh those
+need to be parallel linear expansion
+
+ align:start position:0%
+need to be parallel linear expansion
+ 
+
+ align:start position:0%
+need to be parallel linear expansion
+paths and so they need to be identical
+
+ align:start position:0%
+paths and so they need to be identical
+ 
+
+ align:start position:0%
+paths and so they need to be identical
+for each consumer exactly so that's
+
+ align:start position:0%
+for each consumer exactly so that's
+ 
+
+ align:start position:0%
+for each consumer exactly so that's
+perfect so there's no i
+
+ align:start position:0%
+perfect so there's no i
+ 
+
+ align:start position:0%
+perfect so there's no i
+for the b part
+
+ align:start position:0%
+for the b part
+ 
+
+ align:start position:0%
+for the b part
+uh okay and then finally
+
+ align:start position:0%
+uh okay and then finally
+ 
+
+ align:start position:0%
+uh okay and then finally
+oh i
+
+ align:start position:0%
+oh i
+ 
+
+ align:start position:0%
+oh i
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+answered this already
+
+ align:start position:0%
+answered this already
+ 
+
+ align:start position:0%
+answered this already
+but we can discuss it some more how
+
+ align:start position:0%
+but we can discuss it some more how
+ 
+
+ align:start position:0%
+but we can discuss it some more how
+realistic are the necessary and
+
+ align:start position:0%
+realistic are the necessary and
+ 
+
+ align:start position:0%
+realistic are the necessary and
+sufficient conditions
+
+ align:start position:0%
+sufficient conditions
+ 
+
+ align:start position:0%
+sufficient conditions
+for gorman aggregation based on what
+
+ align:start position:0%
+for gorman aggregation based on what
+ 
+
+ align:start position:0%
+for gorman aggregation based on what
+you've learned in previous lectures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words do you believe it or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah i think one i believe one of the
+
+ align:start position:0%
+yeah i think one i believe one of the
+ 
+
+ align:start position:0%
+yeah i think one i believe one of the
+necessary conditions was that like the
+
+ align:start position:0%
+necessary conditions was that like the
+ 
+
+ align:start position:0%
+necessary conditions was that like the
+the aggregate the aggregate demand
+
+ align:start position:0%
+the aggregate the aggregate demand
+ 
+
+ align:start position:0%
+the aggregate the aggregate demand
+doesn't depend on the sort of the
+
+ align:start position:0%
+doesn't depend on the sort of the
+ 
+
+ align:start position:0%
+doesn't depend on the sort of the
+distribution of the wealth it has to
+
+ align:start position:0%
+distribution of the wealth it has to
+ 
+
+ align:start position:0%
+distribution of the wealth it has to
+demand like only on the total wealth
+
+ align:start position:0%
+demand like only on the total wealth
+ 
+
+ align:start position:0%
+demand like only on the total wealth
+that's true and then what does that
+
+ align:start position:0%
+that's true and then what does that
+ 
+
+ align:start position:0%
+that's true and then what does that
+imply about the underlying
+
+ align:start position:0%
+imply about the underlying
+ 
+
+ align:start position:0%
+imply about the underlying
+households in the economy
+
+ align:start position:0%
+households in the economy
+ 
+
+ align:start position:0%
+households in the economy
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+i think i believe it i believe it i
+
+ align:start position:0%
+i think i believe it i believe it i
+ 
+
+ align:start position:0%
+i think i believe it i believe it i
+believe there's some sort of like
+
+ align:start position:0%
+believe there's some sort of like
+ 
+
+ align:start position:0%
+believe there's some sort of like
+implies some sort of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniformity
+
+ align:start position:0%
+uniformity
+ 
+
+ align:start position:0%
+uniformity
+yeah it's uniform
+
+ align:start position:0%
+yeah it's uniform
+ 
+
+ align:start position:0%
+yeah it's uniform
+in the way that wealth
+
+ align:start position:0%
+in the way that wealth
+ 
+
+ align:start position:0%
+in the way that wealth
+impacts marginal changes
+
+ align:start position:0%
+impacts marginal changes
+ 
+
+ align:start position:0%
+impacts marginal changes
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah those linear expansion paths are a
+
+ align:start position:0%
+yeah those linear expansion paths are a
+ 
+
+ align:start position:0%
+yeah those linear expansion paths are a
+shorthand way of saying
+
+ align:start position:0%
+shorthand way of saying
+ 
+
+ align:start position:0%
+shorthand way of saying
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+different people can consume different
+
+ align:start position:0%
+different people can consume different
+ 
+
+ align:start position:0%
+different people can consume different
+amounts because they have different
+
+ align:start position:0%
+amounts because they have different
+ 
+
+ align:start position:0%
+amounts because they have different
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+but if you start changing wealth
+
+ align:start position:0%
+but if you start changing wealth
+ 
+
+ align:start position:0%
+but if you start changing wealth
+distribution by definition holding the
+
+ align:start position:0%
+distribution by definition holding the
+ 
+
+ align:start position:0%
+distribution by definition holding the
+aggregate fixed if you're going to
+
+ align:start position:0%
+aggregate fixed if you're going to
+ 
+
+ align:start position:0%
+aggregate fixed if you're going to
+change the distribution
+
+ align:start position:0%
+change the distribution
+ 
+
+ align:start position:0%
+change the distribution
+you're increasing wealth for some
+
+ align:start position:0%
+you're increasing wealth for some
+ 
+
+ align:start position:0%
+you're increasing wealth for some
+households and decreasing it for others
+
+ align:start position:0%
+households and decreasing it for others
+ 
+
+ align:start position:0%
+households and decreasing it for others
+and those marginal changes and not just
+
+ align:start position:0%
+and those marginal changes and not just
+ 
+
+ align:start position:0%
+and those marginal changes and not just
+local changes global changes these could
+
+ align:start position:0%
+local changes global changes these could
+ 
+
+ align:start position:0%
+local changes global changes these could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+big redistributions
+
+ align:start position:0%
+big redistributions
+ 
+
+ align:start position:0%
+big redistributions
+sort of offset each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the aggregate the amount that
+
+ align:start position:0%
+in the aggregate the amount that
+ 
+
+ align:start position:0%
+in the aggregate the amount that
+consumption of a given good is going
+
+ align:start position:0%
+consumption of a given good is going
+ 
+
+ align:start position:0%
+consumption of a given good is going
+down for the people who are taxed is
+
+ align:start position:0%
+down for the people who are taxed is
+ 
+
+ align:start position:0%
+down for the people who are taxed is
+exactly equal to
+
+ align:start position:0%
+exactly equal to
+ 
+
+ align:start position:0%
+exactly equal to
+the amount that
+
+ align:start position:0%
+the amount that
+ 
+
+ align:start position:0%
+the amount that
+consumption of that good is going up for
+
+ align:start position:0%
+consumption of that good is going up for
+ 
+
+ align:start position:0%
+consumption of that good is going up for
+the people who get the subsidies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's why the redistribution
+
+ align:start position:0%
+and that's why the redistribution
+ 
+
+ align:start position:0%
+and that's why the redistribution
+doesn't matter for the aggregate that's
+
+ align:start position:0%
+doesn't matter for the aggregate that's
+ 
+
+ align:start position:0%
+doesn't matter for the aggregate that's
+why we can do this representative
+
+ align:start position:0%
+why we can do this representative
+ 
+
+ align:start position:0%
+why we can do this representative
+consumer thing
+
+ align:start position:0%
+consumer thing
+ 
+
+ align:start position:0%
+consumer thing
+to get the aggregates
+
+ align:start position:0%
+to get the aggregates
+ 
+
+ align:start position:0%
+to get the aggregates
+because only aggregate wealth matters
+
+ align:start position:0%
+because only aggregate wealth matters
+ 
+
+ align:start position:0%
+because only aggregate wealth matters
+for aggregate demand as you said
+
+ align:start position:0%
+for aggregate demand as you said
+ 
+
+ align:start position:0%
+for aggregate demand as you said
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+it matters a whole lot for the
+
+ align:start position:0%
+it matters a whole lot for the
+ 
+
+ align:start position:0%
+it matters a whole lot for the
+individuals i mean if you're paying
+
+ align:start position:0%
+individuals i mean if you're paying
+ 
+
+ align:start position:0%
+individuals i mean if you're paying
+taxes lump sum
+
+ align:start position:0%
+taxes lump sum
+ 
+
+ align:start position:0%
+taxes lump sum
+to the government for it to be
+
+ align:start position:0%
+to the government for it to be
+ 
+
+ align:start position:0%
+to the government for it to be
+redistributed you know you get hurt
+
+ align:start position:0%
+redistributed you know you get hurt
+ 
+
+ align:start position:0%
+redistributed you know you get hurt
+so it's not a welfare statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and and i'll just repeat that's why
+
+ align:start position:0%
+and and i'll just repeat that's why
+ 
+
+ align:start position:0%
+and and i'll just repeat that's why
+depending on what we're doing with free
+
+ align:start position:0%
+depending on what we're doing with free
+ 
+
+ align:start position:0%
+depending on what we're doing with free
+trade or something else
+
+ align:start position:0%
+trade or something else
+ 
+
+ align:start position:0%
+trade or something else
+in principle we may be able to make
+
+ align:start position:0%
+in principle we may be able to make
+ 
+
+ align:start position:0%
+in principle we may be able to make
+everyone better off
+
+ align:start position:0%
+everyone better off
+ 
+
+ align:start position:0%
+everyone better off
+as we are told by
+
+ align:start position:0%
+as we are told by
+ 
+
+ align:start position:0%
+as we are told by
+situations where
+
+ align:start position:0%
+situations where
+ 
+
+ align:start position:0%
+situations where
+there is a representative indifference
+
+ align:start position:0%
+there is a representative indifference
+ 
+
+ align:start position:0%
+there is a representative indifference
+curve and we're using implicitly
+
+ align:start position:0%
+curve and we're using implicitly
+ 
+
+ align:start position:0%
+curve and we're using implicitly
+gorman's
+
+ align:start position:0%
+gorman's
+ 
+
+ align:start position:0%
+gorman's
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+for the indirect utilities but that
+
+ align:start position:0%
+for the indirect utilities but that
+ 
+
+ align:start position:0%
+for the indirect utilities but that
+doesn't mean everyone is actually better
+
+ align:start position:0%
+doesn't mean everyone is actually better
+ 
+
+ align:start position:0%
+doesn't mean everyone is actually better
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+without the intervention because the
+
+ align:start position:0%
+without the intervention because the
+ 
+
+ align:start position:0%
+without the intervention because the
+factor prices are moving and
+
+ align:start position:0%
+factor prices are moving and
+ 
+
+ align:start position:0%
+factor prices are moving and
+some people own more labor than capital
+
+ align:start position:0%
+some people own more labor than capital
+ 
+
+ align:start position:0%
+some people own more labor than capital
+and vice versa so we really do
+
+ align:start position:0%
+and vice versa so we really do
+ 
+
+ align:start position:0%
+and vice versa so we really do
+need to be actively redistributing
+
+ align:start position:0%
+need to be actively redistributing
+ 
+
+ align:start position:0%
+need to be actively redistributing
+wealth in order to reap the gains
+
+ align:start position:0%
+wealth in order to reap the gains
+ 
+
+ align:start position:0%
+wealth in order to reap the gains
+from uh
+
+ align:start position:0%
+from uh
+ 
+
+ align:start position:0%
+from uh
+for everyone to benefit from the gains
+
+ align:start position:0%
+for everyone to benefit from the gains
+ 
+
+ align:start position:0%
+for everyone to benefit from the gains
+to trade
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this lecture
+
+ align:start position:0%
+so so this lecture
+ 
+
+ align:start position:0%
+so so this lecture
+from 18
+
+ align:start position:0%
+from 18
+ 
+
+ align:start position:0%
+from 18
+was about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a tool namely gorman aggregation which
+
+ align:start position:0%
+a tool namely gorman aggregation which
+ 
+
+ align:start position:0%
+a tool namely gorman aggregation which
+you kind of
+
+ align:start position:0%
+you kind of
+ 
+
+ align:start position:0%
+you kind of
+saw in the form of the earlier lectures
+
+ align:start position:0%
+saw in the form of the earlier lectures
+ 
+
+ align:start position:0%
+saw in the form of the earlier lectures
+without me elaborating on it
+
+ align:start position:0%
+without me elaborating on it
+ 
+
+ align:start position:0%
+without me elaborating on it
+so this was an opportunity to do that
+
+ align:start position:0%
+so this was an opportunity to do that
+ 
+
+ align:start position:0%
+so this was an opportunity to do that
+but it does take underlying assumptions
+
+ align:start position:0%
+but it does take underlying assumptions
+ 
+
+ align:start position:0%
+but it does take underlying assumptions
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in part the micro data seem to
+
+ align:start position:0%
+in part the micro data seem to
+ 
+
+ align:start position:0%
+in part the micro data seem to
+contradict
+
+ align:start position:0%
+contradict
+ 
+
+ align:start position:0%
+contradict
+yeah i didn't push you guys very hard
+
+ align:start position:0%
+yeah i didn't push you guys very hard
+ 
+
+ align:start position:0%
+yeah i didn't push you guys very hard
+but do you believe it or not you know
+
+ align:start position:0%
+but do you believe it or not you know
+ 
+
+ align:start position:0%
+but do you believe it or not you know
+then it's
+
+ align:start position:0%
+then it's
+ 
+
+ align:start position:0%
+then it's
+do we see these differential wealth
+
+ align:start position:0%
+do we see these differential wealth
+ 
+
+ align:start position:0%
+do we see these differential wealth
+effects in practice we have
+
+ align:start position:0%
+effects in practice we have
+ 
+
+ align:start position:0%
+effects in practice we have
+normal goods and you know
+
+ align:start position:0%
+normal goods and you know
+ 
+
+ align:start position:0%
+normal goods and you know
+necessary goods and so on and even
+
+ align:start position:0%
+necessary goods and so on and even
+ 
+
+ align:start position:0%
+necessary goods and so on and even
+giffen goods as i said so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to know if it's a bad approximation we'd
+
+ align:start position:0%
+to know if it's a bad approximation we'd
+ 
+
+ align:start position:0%
+to know if it's a bad approximation we'd
+have to take a stand on the underlying
+
+ align:start position:0%
+have to take a stand on the underlying
+ 
+
+ align:start position:0%
+have to take a stand on the underlying
+non-gorman
+
+ align:start position:0%
+non-gorman
+ 
+
+ align:start position:0%
+non-gorman
+indirect utility functions and simulate
+
+ align:start position:0%
+indirect utility functions and simulate
+ 
+
+ align:start position:0%
+indirect utility functions and simulate
+the economy and see if it looks almost
+
+ align:start position:0%
+the economy and see if it looks almost
+ 
+
+ align:start position:0%
+the economy and see if it looks almost
+linear even though
+
+ align:start position:0%
+linear even though
+ 
+
+ align:start position:0%
+linear even though
+it's not in which case the
+
+ align:start position:0%
+it's not in which case the
+ 
+
+ align:start position:0%
+it's not in which case the
+redistribution might be small
+
+ align:start position:0%
+redistribution might be small
+ 
+
+ align:start position:0%
+redistribution might be small
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+sorry the
+
+ align:start position:0%
+sorry the
+ 
+
+ align:start position:0%
+sorry the
+i said that wrong the
+
+ align:start position:0%
+i said that wrong the
+ 
+
+ align:start position:0%
+i said that wrong the
+the uh literal form of gorman
+
+ align:start position:0%
+the uh literal form of gorman
+ 
+
+ align:start position:0%
+the uh literal form of gorman
+aggregation
+
+ align:start position:0%
+aggregation
+ 
+
+ align:start position:0%
+aggregation
+as an analytic technique might get us
+
+ align:start position:0%
+as an analytic technique might get us
+ 
+
+ align:start position:0%
+as an analytic technique might get us
+close to what we want as a benchmark
+
+ align:start position:0%
+close to what we want as a benchmark
+ 
+
+ align:start position:0%
+close to what we want as a benchmark
+and since it's so tractable it's very
+
+ align:start position:0%
+and since it's so tractable it's very
+ 
+
+ align:start position:0%
+and since it's so tractable it's very
+tempted to use it but then again for
+
+ align:start position:0%
+tempted to use it but then again for
+ 
+
+ align:start position:0%
+tempted to use it but then again for
+other utility functions we could be
+
+ align:start position:0%
+other utility functions we could be
+ 
+
+ align:start position:0%
+other utility functions we could be
+really really far off and be misleading
+
+ align:start position:0%
+really really far off and be misleading
+ 
+
+ align:start position:0%
+really really far off and be misleading
+policy makers
+
+ align:start position:0%
+policy makers
+ 
+
+ align:start position:0%
+policy makers
+hence the micro data
+
+ align:start position:0%
+hence the micro data
+ 
+
+ align:start position:0%
+hence the micro data
+or my pitch is if you're going to do
+
+ align:start position:0%
+or my pitch is if you're going to do
+ 
+
+ align:start position:0%
+or my pitch is if you're going to do
+macro policy you have to have micro data
+
+ align:start position:0%
+macro policy you have to have micro data
+ 
+
+ align:start position:0%
+macro policy you have to have micro data
+period
+
+ align:start position:0%
+period
+ 
+
+ align:start position:0%
+period
+but that's partly a belief that i've
+
+ align:start position:0%
+but that's partly a belief that i've
+ 
+
+ align:start position:0%
+but that's partly a belief that i've
+acquired over time it's a matter of
+
+ align:start position:0%
+acquired over time it's a matter of
+ 
+
+ align:start position:0%
+acquired over time it's a matter of
+of experience
+
+ align:start position:0%
+of experience
+ 
+
+ align:start position:0%
+of experience
+although it's not always true that's the
+
+ align:start position:0%
+although it's not always true that's the
+ 
+
+ align:start position:0%
+although it's not always true that's the
+approximations can be very helpful
+
+ align:start position:0%
+approximations can be very helpful
+ 
+
+ align:start position:0%
+approximations can be very helpful
+uh okay so
+
+ align:start position:0%
+uh okay so
+ 
+
+ align:start position:0%
+uh okay so
+this the lecture today is kind of the
+
+ align:start position:0%
+this the lecture today is kind of the
+ 
+
+ align:start position:0%
+this the lecture today is kind of the
+reverse of that instead of putting
+
+ align:start position:0%
+reverse of that instead of putting
+ 
+
+ align:start position:0%
+reverse of that instead of putting
+structure on indirect utility functions
+
+ align:start position:0%
+structure on indirect utility functions
+ 
+
+ align:start position:0%
+structure on indirect utility functions
+we're going to see
+
+ align:start position:0%
+we're going to see
+ 
+
+ align:start position:0%
+we're going to see
+if we can get by with almost no
+
+ align:start position:0%
+if we can get by with almost no
+ 
+
+ align:start position:0%
+if we can get by with almost no
+structure at all
+
+ align:start position:0%
+structure at all
+ 
+
+ align:start position:0%
+structure at all
+on preferences and still be able to make
+
+ align:start position:0%
+on preferences and still be able to make
+ 
+
+ align:start position:0%
+on preferences and still be able to make
+predictions which are
+
+ align:start position:0%
+predictions which are
+ 
+
+ align:start position:0%
+predictions which are
+testable or rejectable
+
+ align:start position:0%
+testable or rejectable
+ 
+
+ align:start position:0%
+testable or rejectable
+so this part this lecture is all about
+
+ align:start position:0%
+so this part this lecture is all about
+ 
+
+ align:start position:0%
+so this part this lecture is all about
+economic science i kind of featured the
+
+ align:start position:0%
+economic science i kind of featured the
+ 
+
+ align:start position:0%
+economic science i kind of featured the
+science of experiments in lecture one
+
+ align:start position:0%
+science of experiments in lecture one
+ 
+
+ align:start position:0%
+science of experiments in lecture one
+as a motivation for the class we went
+
+ align:start position:0%
+as a motivation for the class we went
+ 
+
+ align:start position:0%
+as a motivation for the class we went
+through coupons and
+
+ align:start position:0%
+through coupons and
+ 
+
+ align:start position:0%
+through coupons and
+lucas and josh and
+
+ align:start position:0%
+lucas and josh and
+ 
+
+ align:start position:0%
+lucas and josh and
+and maskin and so on so
+
+ align:start position:0%
+and maskin and so on so
+ 
+
+ align:start position:0%
+and maskin and so on so
+so this is very much the science of
+
+ align:start position:0%
+so this is very much the science of
+ 
+
+ align:start position:0%
+so this is very much the science of
+doing experiments and i'll tell you
+
+ align:start position:0%
+doing experiments and i'll tell you
+ 
+
+ align:start position:0%
+doing experiments and i'll tell you
+exactly what we're going to do with
+
+ align:start position:0%
+exactly what we're going to do with
+ 
+
+ align:start position:0%
+exactly what we're going to do with
+micro data depending on the amount of
+
+ align:start position:0%
+micro data depending on the amount of
+ 
+
+ align:start position:0%
+micro data depending on the amount of
+data available and also sort of macro
+
+ align:start position:0%
+data available and also sort of macro
+ 
+
+ align:start position:0%
+data available and also sort of macro
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+trying to put as little structure as
+
+ align:start position:0%
+trying to put as little structure as
+ 
+
+ align:start position:0%
+trying to put as little structure as
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+and still get rejectable restrictions
+
+ align:start position:0%
+and still get rejectable restrictions
+ 
+
+ align:start position:0%
+and still get rejectable restrictions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+said that
+
+ align:start position:0%
+said that
+ 
+
+ align:start position:0%
+said that
+so we're going to go through consumer
+
+ align:start position:0%
+so we're going to go through consumer
+ 
+
+ align:start position:0%
+so we're going to go through consumer
+optimization again which is as always a
+
+ align:start position:0%
+optimization again which is as always a
+ 
+
+ align:start position:0%
+optimization again which is as always a
+bit of a review
+
+ align:start position:0%
+bit of a review
+ 
+
+ align:start position:0%
+bit of a review
+we're going to approach that as if we
+
+ align:start position:0%
+we're going to approach that as if we
+ 
+
+ align:start position:0%
+we're going to approach that as if we
+had an infinite amount of data
+
+ align:start position:0%
+had an infinite amount of data
+ 
+
+ align:start position:0%
+had an infinite amount of data
+and that will take us back to the
+
+ align:start position:0%
+and that will take us back to the
+ 
+
+ align:start position:0%
+and that will take us back to the
+slutsky matrix which you may have
+
+ align:start position:0%
+slutsky matrix which you may have
+ 
+
+ align:start position:0%
+slutsky matrix which you may have
+forgotten by now but i'll try to remind
+
+ align:start position:0%
+forgotten by now but i'll try to remind
+ 
+
+ align:start position:0%
+forgotten by now but i'll try to remind
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+that's with an infinite amount of data
+
+ align:start position:0%
+that's with an infinite amount of data
+ 
+
+ align:start position:0%
+that's with an infinite amount of data
+we get restrictions that we can reject
+
+ align:start position:0%
+we get restrictions that we can reject
+ 
+
+ align:start position:0%
+we get restrictions that we can reject
+consumer rationality in principle
+
+ align:start position:0%
+consumer rationality in principle
+ 
+
+ align:start position:0%
+consumer rationality in principle
+and then we'll do the same thing with
+
+ align:start position:0%
+and then we'll do the same thing with
+ 
+
+ align:start position:0%
+and then we'll do the same thing with
+finite data and still derive algorithms
+
+ align:start position:0%
+finite data and still derive algorithms
+ 
+
+ align:start position:0%
+finite data and still derive algorithms
+running on finite data sets that would
+
+ align:start position:0%
+running on finite data sets that would
+ 
+
+ align:start position:0%
+running on finite data sets that would
+allow us to
+
+ align:start position:0%
+allow us to
+ 
+
+ align:start position:0%
+allow us to
+not reject or alternatively reject the
+
+ align:start position:0%
+not reject or alternatively reject the
+ 
+
+ align:start position:0%
+not reject or alternatively reject the
+rationality of the household generating
+
+ align:start position:0%
+rationality of the household generating
+ 
+
+ align:start position:0%
+rationality of the household generating
+the data then we'll come back to lucas a
+
+ align:start position:0%
+the data then we'll come back to lucas a
+ 
+
+ align:start position:0%
+the data then we'll come back to lucas a
+bit and computational considerations
+
+ align:start position:0%
+bit and computational considerations
+ 
+
+ align:start position:0%
+bit and computational considerations
+which i think has been clear throughout
+
+ align:start position:0%
+which i think has been clear throughout
+ 
+
+ align:start position:0%
+which i think has been clear throughout
+the lectures that we visit from time to
+
+ align:start position:0%
+the lectures that we visit from time to
+ 
+
+ align:start position:0%
+the lectures that we visit from time to
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and i have some dug up some really
+
+ align:start position:0%
+and i have some dug up some really
+ 
+
+ align:start position:0%
+and i have some dug up some really
+interesting computer science material to
+
+ align:start position:0%
+interesting computer science material to
+ 
+
+ align:start position:0%
+interesting computer science material to
+share with you about how hard or easy it
+
+ align:start position:0%
+share with you about how hard or easy it
+ 
+
+ align:start position:0%
+share with you about how hard or easy it
+is to solve certain problems and whether
+
+ align:start position:0%
+is to solve certain problems and whether
+ 
+
+ align:start position:0%
+is to solve certain problems and whether
+it matters be provocative
+
+ align:start position:0%
+it matters be provocative
+ 
+
+ align:start position:0%
+it matters be provocative
+and then we'll go to general equilibrium
+
+ align:start position:0%
+and then we'll go to general equilibrium
+ 
+
+ align:start position:0%
+and then we'll go to general equilibrium
+theory and kind of do the same thing all
+
+ align:start position:0%
+theory and kind of do the same thing all
+ 
+
+ align:start position:0%
+theory and kind of do the same thing all
+over again
+
+ align:start position:0%
+over again
+ 
+
+ align:start position:0%
+over again
+and that's going to again come back to
+
+ align:start position:0%
+and that's going to again come back to
+ 
+
+ align:start position:0%
+and that's going to again come back to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you need micro to do macro statement
+
+ align:start position:0%
+you need micro to do macro statement
+ 
+
+ align:start position:0%
+you need micro to do macro statement
+that i
+
+ align:start position:0%
+that i
+ 
+
+ align:start position:0%
+that i
+just mentioned
+
+ align:start position:0%
+just mentioned
+ 
+
+ align:start position:0%
+just mentioned
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+to get in the content of it
+
+ align:start position:0%
+to get in the content of it
+ 
+
+ align:start position:0%
+to get in the content of it
+this slide appears to come out of
+
+ align:start position:0%
+this slide appears to come out of
+ 
+
+ align:start position:0%
+this slide appears to come out of
+nowhere
+
+ align:start position:0%
+nowhere
+ 
+
+ align:start position:0%
+nowhere
+uh it was actually
+
+ align:start position:0%
+uh it was actually
+ 
+
+ align:start position:0%
+uh it was actually
+almost part of the lecture we had on
+
+ align:start position:0%
+almost part of the lecture we had on
+ 
+
+ align:start position:0%
+almost part of the lecture we had on
+income and substitution effects and i'll
+
+ align:start position:0%
+income and substitution effects and i'll
+ 
+
+ align:start position:0%
+income and substitution effects and i'll
+remind you of that in a minute in
+
+ align:start position:0%
+remind you of that in a minute in
+ 
+
+ align:start position:0%
+remind you of that in a minute in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+it has to do with the hixion demand
+
+ align:start position:0%
+it has to do with the hixion demand
+ 
+
+ align:start position:0%
+it has to do with the hixion demand
+and the expenditure function well i'll
+
+ align:start position:0%
+and the expenditure function well i'll
+ 
+
+ align:start position:0%
+and the expenditure function well i'll
+remind you now
+
+ align:start position:0%
+remind you now
+ 
+
+ align:start position:0%
+remind you now
+we did utility maximization subject to
+
+ align:start position:0%
+we did utility maximization subject to
+ 
+
+ align:start position:0%
+we did utility maximization subject to
+the budget and we got the falrazian or
+
+ align:start position:0%
+the budget and we got the falrazian or
+ 
+
+ align:start position:0%
+the budget and we got the falrazian or
+marshallian demand we also decomposed
+
+ align:start position:0%
+marshallian demand we also decomposed
+ 
+
+ align:start position:0%
+marshallian demand we also decomposed
+that into income and substitution
+
+ align:start position:0%
+that into income and substitution
+ 
+
+ align:start position:0%
+that into income and substitution
+effects and the way we got the
+
+ align:start position:0%
+effects and the way we got the
+ 
+
+ align:start position:0%
+effects and the way we got the
+substitution effects was to do
+
+ align:start position:0%
+substitution effects was to do
+ 
+
+ align:start position:0%
+substitution effects was to do
+compensation prices say if they decrease
+
+ align:start position:0%
+compensation prices say if they decrease
+ 
+
+ align:start position:0%
+compensation prices say if they decrease
+or associated with increases in income
+
+ align:start position:0%
+or associated with increases in income
+ 
+
+ align:start position:0%
+or associated with increases in income
+we take the income effects away and just
+
+ align:start position:0%
+we take the income effects away and just
+ 
+
+ align:start position:0%
+we take the income effects away and just
+look at how demands change as we change
+
+ align:start position:0%
+look at how demands change as we change
+ 
+
+ align:start position:0%
+look at how demands change as we change
+prices in other words we
+
+ align:start position:0%
+prices in other words we
+ 
+
+ align:start position:0%
+prices in other words we
+minimize the expenditure necessary to
+
+ align:start position:0%
+minimize the expenditure necessary to
+ 
+
+ align:start position:0%
+minimize the expenditure necessary to
+achieve a certain level of utility and
+
+ align:start position:0%
+achieve a certain level of utility and
+ 
+
+ align:start position:0%
+achieve a certain level of utility and
+we got the hicksian demand
+
+ align:start position:0%
+we got the hicksian demand
+ 
+
+ align:start position:0%
+we got the hicksian demand
+so with the hicks in demand and the
+
+ align:start position:0%
+so with the hicks in demand and the
+ 
+
+ align:start position:0%
+so with the hicks in demand and the
+expenditure function i checked we didn't
+
+ align:start position:0%
+expenditure function i checked we didn't
+ 
+
+ align:start position:0%
+expenditure function i checked we didn't
+actually go through these properties in
+
+ align:start position:0%
+actually go through these properties in
+ 
+
+ align:start position:0%
+actually go through these properties in
+lecture three but they are
+
+ align:start position:0%
+lecture three but they are
+ 
+
+ align:start position:0%
+lecture three but they are
+intuitive
+
+ align:start position:0%
+intuitive
+ 
+
+ align:start position:0%
+intuitive
+if the utility function is continuous
+
+ align:start position:0%
+if the utility function is continuous
+ 
+
+ align:start position:0%
+if the utility function is continuous
+represents locally non-satiated
+
+ align:start position:0%
+represents locally non-satiated
+ 
+
+ align:start position:0%
+represents locally non-satiated
+preferences we might as well define the
+
+ align:start position:0%
+preferences we might as well define the
+ 
+
+ align:start position:0%
+preferences we might as well define the
+consumption set to be the non-negative l
+
+ align:start position:0%
+consumption set to be the non-negative l
+ 
+
+ align:start position:0%
+consumption set to be the non-negative l
+dimensional orthot then we have the
+
+ align:start position:0%
+dimensional orthot then we have the
+ 
+
+ align:start position:0%
+dimensional orthot then we have the
+following four properties
+
+ align:start position:0%
+following four properties
+ 
+
+ align:start position:0%
+following four properties
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+expenditure function this minimized
+
+ align:start position:0%
+expenditure function this minimized
+ 
+
+ align:start position:0%
+expenditure function this minimized
+expenditure at prices p to achieve a
+
+ align:start position:0%
+expenditure at prices p to achieve a
+ 
+
+ align:start position:0%
+expenditure at prices p to achieve a
+certain utility level u is homogeneous
+
+ align:start position:0%
+certain utility level u is homogeneous
+ 
+
+ align:start position:0%
+certain utility level u is homogeneous
+of degree what
+
+ align:start position:0%
+of degree what
+ 
+
+ align:start position:0%
+of degree what
+one in
+
+ align:start position:0%
+one in
+ 
+
+ align:start position:0%
+one in
+those prices p
+
+ align:start position:0%
+those prices p
+ 
+
+ align:start position:0%
+those prices p
+i think i slipped up the other day when
+
+ align:start position:0%
+i think i slipped up the other day when
+ 
+
+ align:start position:0%
+i think i slipped up the other day when
+i said zero and then i switched back to
+
+ align:start position:0%
+i said zero and then i switched back to
+ 
+
+ align:start position:0%
+i said zero and then i switched back to
+one it depends on what object
+
+ align:start position:0%
+one it depends on what object
+ 
+
+ align:start position:0%
+one it depends on what object
+when we do utility maximization to
+
+ align:start position:0%
+when we do utility maximization to
+ 
+
+ align:start position:0%
+when we do utility maximization to
+budgets if we increase income and prices
+
+ align:start position:0%
+budgets if we increase income and prices
+ 
+
+ align:start position:0%
+budgets if we increase income and prices
+things are homogeneous of degrees zero
+
+ align:start position:0%
+things are homogeneous of degrees zero
+ 
+
+ align:start position:0%
+things are homogeneous of degrees zero
+because nothing changes
+
+ align:start position:0%
+because nothing changes
+ 
+
+ align:start position:0%
+because nothing changes
+but this is a property of the
+
+ align:start position:0%
+but this is a property of the
+ 
+
+ align:start position:0%
+but this is a property of the
+expenditure function so logically if
+
+ align:start position:0%
+expenditure function so logically if
+ 
+
+ align:start position:0%
+expenditure function so logically if
+prices go up and you're hitting the same
+
+ align:start position:0%
+prices go up and you're hitting the same
+ 
+
+ align:start position:0%
+prices go up and you're hitting the same
+level of utility it's going to cost you
+
+ align:start position:0%
+level of utility it's going to cost you
+ 
+
+ align:start position:0%
+level of utility it's going to cost you
+more so the expenditures just double if
+
+ align:start position:0%
+more so the expenditures just double if
+ 
+
+ align:start position:0%
+more so the expenditures just double if
+you're doubling prices
+
+ align:start position:0%
+you're doubling prices
+ 
+
+ align:start position:0%
+you're doubling prices
+it's homogeneous of degree one
+
+ align:start position:0%
+it's homogeneous of degree one
+ 
+
+ align:start position:0%
+it's homogeneous of degree one
+expenditure function
+
+ align:start position:0%
+expenditure function
+ 
+
+ align:start position:0%
+expenditure function
+for any given price vector p
+
+ align:start position:0%
+for any given price vector p
+ 
+
+ align:start position:0%
+for any given price vector p
+is increasing in utility that kind of
+
+ align:start position:0%
+is increasing in utility that kind of
+ 
+
+ align:start position:0%
+is increasing in utility that kind of
+makes sense when you think about having
+
+ align:start position:0%
+makes sense when you think about having
+ 
+
+ align:start position:0%
+makes sense when you think about having
+nice concave indifference curves or even
+
+ align:start position:0%
+nice concave indifference curves or even
+ 
+
+ align:start position:0%
+nice concave indifference curves or even
+linear indifference curves if you do
+
+ align:start position:0%
+linear indifference curves if you do
+ 
+
+ align:start position:0%
+linear indifference curves if you do
+increase u by moving further and further
+
+ align:start position:0%
+increase u by moving further and further
+ 
+
+ align:start position:0%
+increase u by moving further and further
+north out hitting higher and higher
+
+ align:start position:0%
+north out hitting higher and higher
+ 
+
+ align:start position:0%
+north out hitting higher and higher
+indifference curves than to minimize the
+
+ align:start position:0%
+indifference curves than to minimize the
+ 
+
+ align:start position:0%
+indifference curves than to minimize the
+expenditure of achieving those points
+
+ align:start position:0%
+expenditure of achieving those points
+ 
+
+ align:start position:0%
+expenditure of achieving those points
+the expenditure
+
+ align:start position:0%
+the expenditure
+ 
+
+ align:start position:0%
+the expenditure
+has to go up likewise as prices go up
+
+ align:start position:0%
+has to go up likewise as prices go up
+ 
+
+ align:start position:0%
+has to go up likewise as prices go up
+expenditures go up which i kind of
+
+ align:start position:0%
+expenditures go up which i kind of
+ 
+
+ align:start position:0%
+expenditures go up which i kind of
+already said
+
+ align:start position:0%
+already said
+ 
+
+ align:start position:0%
+already said
+and this is a key property
+
+ align:start position:0%
+and this is a key property
+ 
+
+ align:start position:0%
+and this is a key property
+in addition the expenditure function is
+
+ align:start position:0%
+in addition the expenditure function is
+ 
+
+ align:start position:0%
+in addition the expenditure function is
+concave in the prices so
+
+ align:start position:0%
+concave in the prices so
+ 
+
+ align:start position:0%
+concave in the prices so
+we're given that the utility function
+
+ align:start position:0%
+we're given that the utility function
+ 
+
+ align:start position:0%
+we're given that the utility function
+represents local non-satiated
+
+ align:start position:0%
+represents local non-satiated
+ 
+
+ align:start position:0%
+represents local non-satiated
+preferences we're not given much else so
+
+ align:start position:0%
+preferences we're not given much else so
+ 
+
+ align:start position:0%
+preferences we're not given much else so
+this this might be a bit surprising this
+
+ align:start position:0%
+this this might be a bit surprising this
+ 
+
+ align:start position:0%
+this this might be a bit surprising this
+allows for it to be linear however and
+
+ align:start position:0%
+allows for it to be linear however and
+ 
+
+ align:start position:0%
+allows for it to be linear however and
+in a minute we'll make it strictly
+
+ align:start position:0%
+in a minute we'll make it strictly
+ 
+
+ align:start position:0%
+in a minute we'll make it strictly
+concave
+
+ align:start position:0%
+concave
+ 
+
+ align:start position:0%
+concave
+anyway you remember how these proofs go
+
+ align:start position:0%
+anyway you remember how these proofs go
+ 
+
+ align:start position:0%
+anyway you remember how these proofs go
+pick two prices take pick a linear
+
+ align:start position:0%
+pick two prices take pick a linear
+ 
+
+ align:start position:0%
+pick two prices take pick a linear
+combination kind of prove that that
+
+ align:start position:0%
+combination kind of prove that that
+ 
+
+ align:start position:0%
+combination kind of prove that that
+intermediate combination is also
+
+ align:start position:0%
+intermediate combination is also
+ 
+
+ align:start position:0%
+intermediate combination is also
+minimizing expenditure etc
+
+ align:start position:0%
+minimizing expenditure etc
+ 
+
+ align:start position:0%
+minimizing expenditure etc
+and then the utility expenditure
+
+ align:start position:0%
+and then the utility expenditure
+ 
+
+ align:start position:0%
+and then the utility expenditure
+function is continuous in both objects
+
+ align:start position:0%
+function is continuous in both objects
+ 
+
+ align:start position:0%
+function is continuous in both objects
+the one i want to focus on is number
+
+ align:start position:0%
+the one i want to focus on is number
+ 
+
+ align:start position:0%
+the one i want to focus on is number
+three that the expenditure function is
+
+ align:start position:0%
+three that the expenditure function is
+ 
+
+ align:start position:0%
+three that the expenditure function is
+concave in prices for fixed utility
+
+ align:start position:0%
+concave in prices for fixed utility
+ 
+
+ align:start position:0%
+concave in prices for fixed utility
+okay relatedly
+
+ align:start position:0%
+okay relatedly
+ 
+
+ align:start position:0%
+okay relatedly
+the hixing demand
+
+ align:start position:0%
+the hixing demand
+ 
+
+ align:start position:0%
+the hixing demand
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+if you're going to achieve a target
+
+ align:start position:0%
+if you're going to achieve a target
+ 
+
+ align:start position:0%
+if you're going to achieve a target
+utility u
+
+ align:start position:0%
+utility u
+ 
+
+ align:start position:0%
+utility u
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you will achieve it exactly essentially
+
+ align:start position:0%
+you will achieve it exactly essentially
+ 
+
+ align:start position:0%
+you will achieve it exactly essentially
+that is to say the x's which are part of
+
+ align:start position:0%
+that is to say the x's which are part of
+ 
+
+ align:start position:0%
+that is to say the x's which are part of
+the solution to the minimizing
+
+ align:start position:0%
+the solution to the minimizing
+ 
+
+ align:start position:0%
+the solution to the minimizing
+expenditure problem when substituted
+
+ align:start position:0%
+expenditure problem when substituted
+ 
+
+ align:start position:0%
+expenditure problem when substituted
+into the utility function generate u
+
+ align:start position:0%
+into the utility function generate u
+ 
+
+ align:start position:0%
+into the utility function generate u
+exactly if preferences are number two
+
+ align:start position:0%
+exactly if preferences are number two
+ 
+
+ align:start position:0%
+exactly if preferences are number two
+convex then these minimize expension
+
+ align:start position:0%
+convex then these minimize expension
+ 
+
+ align:start position:0%
+convex then these minimize expension
+demands are convex valued entertaining
+
+ align:start position:0%
+demands are convex valued entertaining
+ 
+
+ align:start position:0%
+demands are convex valued entertaining
+multiple solutions
+
+ align:start position:0%
+multiple solutions
+ 
+
+ align:start position:0%
+multiple solutions
+that minimize expenditure for given p
+
+ align:start position:0%
+that minimize expenditure for given p
+ 
+
+ align:start position:0%
+that minimize expenditure for given p
+and u
+
+ align:start position:0%
+and u
+ 
+
+ align:start position:0%
+and u
+but if preferences are strictly convex
+
+ align:start position:0%
+but if preferences are strictly convex
+ 
+
+ align:start position:0%
+but if preferences are strictly convex
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this h function is single valued and
+
+ align:start position:0%
+this h function is single valued and
+ 
+
+ align:start position:0%
+this h function is single valued and
+continuous so here is where the strict
+
+ align:start position:0%
+continuous so here is where the strict
+ 
+
+ align:start position:0%
+continuous so here is where the strict
+convexity of the preferences comes in
+
+ align:start position:0%
+convexity of the preferences comes in
+ 
+
+ align:start position:0%
+convexity of the preferences comes in
+okay which we're going to get again to
+
+ align:start position:0%
+okay which we're going to get again to
+ 
+
+ align:start position:0%
+okay which we're going to get again to
+in four
+
+ align:start position:0%
+in four
+ 
+
+ align:start position:0%
+in four
+three says this pixie and demand is
+
+ align:start position:0%
+three says this pixie and demand is
+ 
+
+ align:start position:0%
+three says this pixie and demand is
+single value if it's single valued which
+
+ align:start position:0%
+single value if it's single valued which
+ 
+
+ align:start position:0%
+single value if it's single valued which
+it would be with strictly convex
+
+ align:start position:0%
+it would be with strictly convex
+ 
+
+ align:start position:0%
+it would be with strictly convex
+preferences then it's differentiable and
+
+ align:start position:0%
+preferences then it's differentiable and
+ 
+
+ align:start position:0%
+preferences then it's differentiable and
+moreover when you take the derivative of
+
+ align:start position:0%
+moreover when you take the derivative of
+ 
+
+ align:start position:0%
+moreover when you take the derivative of
+it with respect to say a price p sub l
+
+ align:start position:0%
+it with respect to say a price p sub l
+ 
+
+ align:start position:0%
+it with respect to say a price p sub l
+for the health good you get the
+
+ align:start position:0%
+for the health good you get the
+ 
+
+ align:start position:0%
+for the health good you get the
+minimize you get the quantities back
+
+ align:start position:0%
+minimize you get the quantities back
+ 
+
+ align:start position:0%
+minimize you get the quantities back
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the intuition for this is
+
+ align:start position:0%
+the intuition for this is
+ 
+
+ align:start position:0%
+the intuition for this is
+expenditure is just p1 x1 p2 x2 dot dot
+
+ align:start position:0%
+expenditure is just p1 x1 p2 x2 dot dot
+ 
+
+ align:start position:0%
+expenditure is just p1 x1 p2 x2 dot dot
+pl xl uh you take the derivative with
+
+ align:start position:0%
+pl xl uh you take the derivative with
+ 
+
+ align:start position:0%
+pl xl uh you take the derivative with
+respect to p you're going to get the x
+
+ align:start position:0%
+respect to p you're going to get the x
+ 
+
+ align:start position:0%
+respect to p you're going to get the x
+that's a bit sloppy and we did the
+
+ align:start position:0%
+that's a bit sloppy and we did the
+ 
+
+ align:start position:0%
+that's a bit sloppy and we did the
+envelope theorem earlier and reviewed it
+
+ align:start position:0%
+envelope theorem earlier and reviewed it
+ 
+
+ align:start position:0%
+envelope theorem earlier and reviewed it
+last time but basically the derivative
+
+ align:start position:0%
+last time but basically the derivative
+ 
+
+ align:start position:0%
+last time but basically the derivative
+at the optimizing minimize expenditures
+
+ align:start position:0%
+at the optimizing minimize expenditures
+ 
+
+ align:start position:0%
+at the optimizing minimize expenditures
+at parametric price p sub l is
+
+ align:start position:0%
+at parametric price p sub l is
+ 
+
+ align:start position:0%
+at parametric price p sub l is
+you get the solution back the uh
+
+ align:start position:0%
+you get the solution back the uh
+ 
+
+ align:start position:0%
+you get the solution back the uh
+hixing demand
+
+ align:start position:0%
+hixing demand
+ 
+
+ align:start position:0%
+hixing demand
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so these two pieces
+
+ align:start position:0%
+so these two pieces
+ 
+
+ align:start position:0%
+so these two pieces
+three and
+
+ align:start position:0%
+three and
+ 
+
+ align:start position:0%
+three and
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+on each of the two slides
+
+ align:start position:0%
+on each of the two slides
+ 
+
+ align:start position:0%
+on each of the two slides
+generate this statement that if you take
+
+ align:start position:0%
+generate this statement that if you take
+ 
+
+ align:start position:0%
+generate this statement that if you take
+the hixing demands and differentiate
+
+ align:start position:0%
+the hixing demands and differentiate
+ 
+
+ align:start position:0%
+the hixing demands and differentiate
+with respect to prices then because
+
+ align:start position:0%
+with respect to prices then because
+ 
+
+ align:start position:0%
+with respect to prices then because
+level h is on the right hand side in
+
+ align:start position:0%
+level h is on the right hand side in
+ 
+
+ align:start position:0%
+level h is on the right hand side in
+eight but the derivative is already on
+
+ align:start position:0%
+eight but the derivative is already on
+ 
+
+ align:start position:0%
+eight but the derivative is already on
+the left hand side so if you're
+
+ align:start position:0%
+the left hand side so if you're
+ 
+
+ align:start position:0%
+the left hand side so if you're
+differentiating the right all over again
+
+ align:start position:0%
+differentiating the right all over again
+ 
+
+ align:start position:0%
+differentiating the right all over again
+with respect to p you're double
+
+ align:start position:0%
+with respect to p you're double
+ 
+
+ align:start position:0%
+with respect to p you're double
+differentiating so to speak the left
+
+ align:start position:0%
+differentiating so to speak the left
+ 
+
+ align:start position:0%
+differentiating so to speak the left
+hand side so we get these second order
+
+ align:start position:0%
+hand side so we get these second order
+ 
+
+ align:start position:0%
+hand side so we get these second order
+partial derivatives bone and cross
+
+ align:start position:0%
+partial derivatives bone and cross
+ 
+
+ align:start position:0%
+partial derivatives bone and cross
+partial derivatives of the expenditure
+
+ align:start position:0%
+partial derivatives of the expenditure
+ 
+
+ align:start position:0%
+partial derivatives of the expenditure
+function when we differentiate the
+
+ align:start position:0%
+function when we differentiate the
+ 
+
+ align:start position:0%
+function when we differentiate the
+hixing demands
+
+ align:start position:0%
+hixing demands
+ 
+
+ align:start position:0%
+hixing demands
+this is really compact notation
+
+ align:start position:0%
+this is really compact notation
+ 
+
+ align:start position:0%
+this is really compact notation
+obviously there's a whole vector of
+
+ align:start position:0%
+obviously there's a whole vector of
+ 
+
+ align:start position:0%
+obviously there's a whole vector of
+prices p1 through pl
+
+ align:start position:0%
+prices p1 through pl
+ 
+
+ align:start position:0%
+prices p1 through pl
+etc or writing it down almost as if it
+
+ align:start position:0%
+etc or writing it down almost as if it
+ 
+
+ align:start position:0%
+etc or writing it down almost as if it
+were single dimension but it's meant to
+
+ align:start position:0%
+were single dimension but it's meant to
+ 
+
+ align:start position:0%
+were single dimension but it's meant to
+capture the entire l by l matrix that is
+
+ align:start position:0%
+capture the entire l by l matrix that is
+ 
+
+ align:start position:0%
+capture the entire l by l matrix that is
+to say the derivative of the first
+
+ align:start position:0%
+to say the derivative of the first
+ 
+
+ align:start position:0%
+to say the derivative of the first
+fixing demand with respect to the first
+
+ align:start position:0%
+fixing demand with respect to the first
+ 
+
+ align:start position:0%
+fixing demand with respect to the first
+price the first 60 in demand could with
+
+ align:start position:0%
+price the first 60 in demand could with
+ 
+
+ align:start position:0%
+price the first 60 in demand could with
+respect to the second price and so on
+
+ align:start position:0%
+respect to the second price and so on
+ 
+
+ align:start position:0%
+respect to the second price and so on
+going across the row
+
+ align:start position:0%
+going across the row
+ 
+
+ align:start position:0%
+going across the row
+fill out all the rows so it has all the
+
+ align:start position:0%
+fill out all the rows so it has all the
+ 
+
+ align:start position:0%
+fill out all the rows so it has all the
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+ii h i p i derivatives as well as h i j
+
+ align:start position:0%
+ii h i p i derivatives as well as h i j
+ 
+
+ align:start position:0%
+ii h i p i derivatives as well as h i j
+i good was with respect to the chafe
+
+ align:start position:0%
+i good was with respect to the chafe
+ 
+
+ align:start position:0%
+i good was with respect to the chafe
+price it's all loaded into this compact
+
+ align:start position:0%
+price it's all loaded into this compact
+ 
+
+ align:start position:0%
+price it's all loaded into this compact
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+now i'm saving the best for last which
+
+ align:start position:0%
+now i'm saving the best for last which
+ 
+
+ align:start position:0%
+now i'm saving the best for last which
+is this guy here is the matrix of second
+
+ align:start position:0%
+is this guy here is the matrix of second
+ 
+
+ align:start position:0%
+is this guy here is the matrix of second
+order derivatives of the expenditure
+
+ align:start position:0%
+order derivatives of the expenditure
+ 
+
+ align:start position:0%
+order derivatives of the expenditure
+function and three
+
+ align:start position:0%
+function and three
+ 
+
+ align:start position:0%
+function and three
+already told us the expenditure function
+
+ align:start position:0%
+already told us the expenditure function
+ 
+
+ align:start position:0%
+already told us the expenditure function
+is concave
+
+ align:start position:0%
+is concave
+ 
+
+ align:start position:0%
+is concave
+so that means you know if you think
+
+ align:start position:0%
+so that means you know if you think
+ 
+
+ align:start position:0%
+so that means you know if you think
+about first order conditions and second
+
+ align:start position:0%
+about first order conditions and second
+ 
+
+ align:start position:0%
+about first order conditions and second
+order conditions that second order
+
+ align:start position:0%
+order conditions that second order
+ 
+
+ align:start position:0%
+order conditions that second order
+conditions are going to be satisfied
+
+ align:start position:0%
+conditions are going to be satisfied
+ 
+
+ align:start position:0%
+conditions are going to be satisfied
+for a concave function and in fact if
+
+ align:start position:0%
+for a concave function and in fact if
+ 
+
+ align:start position:0%
+for a concave function and in fact if
+you look it up stuff does slip memory a
+
+ align:start position:0%
+you look it up stuff does slip memory a
+ 
+
+ align:start position:0%
+you look it up stuff does slip memory a
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+it means that this matrix of own and
+
+ align:start position:0%
+it means that this matrix of own and
+ 
+
+ align:start position:0%
+it means that this matrix of own and
+cross partial derivatives is symmetric
+
+ align:start position:0%
+cross partial derivatives is symmetric
+ 
+
+ align:start position:0%
+cross partial derivatives is symmetric
+and negative semi-definite
+
+ align:start position:0%
+and negative semi-definite
+ 
+
+ align:start position:0%
+and negative semi-definite
+you you may not remember that
+
+ align:start position:0%
+you you may not remember that
+ 
+
+ align:start position:0%
+you you may not remember that
+you think about one good then you just
+
+ align:start position:0%
+you think about one good then you just
+ 
+
+ align:start position:0%
+you think about one good then you just
+have first the ii derivative you think
+
+ align:start position:0%
+have first the ii derivative you think
+ 
+
+ align:start position:0%
+have first the ii derivative you think
+about 2 then you're going to have a
+
+ align:start position:0%
+about 2 then you're going to have a
+ 
+
+ align:start position:0%
+about 2 then you're going to have a
+2 by 2 matrix and you have the
+
+ align:start position:0%
+2 by 2 matrix and you have the
+ 
+
+ align:start position:0%
+2 by 2 matrix and you have the
+determinant of that matrix if you have
+
+ align:start position:0%
+determinant of that matrix if you have
+ 
+
+ align:start position:0%
+determinant of that matrix if you have
+three goods and it's a bit tricky you
+
+ align:start position:0%
+three goods and it's a bit tricky you
+ 
+
+ align:start position:0%
+three goods and it's a bit tricky you
+have to to factor the matrix you got to
+
+ align:start position:0%
+have to to factor the matrix you got to
+ 
+
+ align:start position:0%
+have to to factor the matrix you got to
+figure out the determinant of each of
+
+ align:start position:0%
+figure out the determinant of each of
+ 
+
+ align:start position:0%
+figure out the determinant of each of
+the sub components and so on but
+
+ align:start position:0%
+the sub components and so on but
+ 
+
+ align:start position:0%
+the sub components and so on but
+an equivalent way to check and see
+
+ align:start position:0%
+an equivalent way to check and see
+ 
+
+ align:start position:0%
+an equivalent way to check and see
+whether all the conditions are satisfied
+
+ align:start position:0%
+whether all the conditions are satisfied
+ 
+
+ align:start position:0%
+whether all the conditions are satisfied
+for concavity is just to pre-multiply
+
+ align:start position:0%
+for concavity is just to pre-multiply
+ 
+
+ align:start position:0%
+for concavity is just to pre-multiply
+and post multiply the matrix
+
+ align:start position:0%
+and post multiply the matrix
+ 
+
+ align:start position:0%
+and post multiply the matrix
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+a prime and a as
+
+ align:start position:0%
+a prime and a as
+ 
+
+ align:start position:0%
+a prime and a as
+as arbitrary vectors and make sure the
+
+ align:start position:0%
+as arbitrary vectors and make sure the
+ 
+
+ align:start position:0%
+as arbitrary vectors and make sure the
+result is
+
+ align:start position:0%
+result is
+ 
+
+ align:start position:0%
+result is
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+so that's a little bit of a review don't
+
+ align:start position:0%
+so that's a little bit of a review don't
+ 
+
+ align:start position:0%
+so that's a little bit of a review don't
+worry about it if you never learned it
+
+ align:start position:0%
+worry about it if you never learned it
+ 
+
+ align:start position:0%
+worry about it if you never learned it
+it's the same thing as getting
+
+ align:start position:0%
+it's the same thing as getting
+ 
+
+ align:start position:0%
+it's the same thing as getting
+concavity of the
+
+ align:start position:0%
+concavity of the
+ 
+
+ align:start position:0%
+concavity of the
+expenditure function
+
+ align:start position:0%
+expenditure function
+ 
+
+ align:start position:0%
+expenditure function
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well it's a bit problematic
+
+ align:start position:0%
+well it's a bit problematic
+ 
+
+ align:start position:0%
+well it's a bit problematic
+i said the motive today was to get
+
+ align:start position:0%
+i said the motive today was to get
+ 
+
+ align:start position:0%
+i said the motive today was to get
+restrictions on observables but we don't
+
+ align:start position:0%
+restrictions on observables but we don't
+ 
+
+ align:start position:0%
+restrictions on observables but we don't
+see this guy we don't see the hixing
+
+ align:start position:0%
+see this guy we don't see the hixing
+ 
+
+ align:start position:0%
+see this guy we don't see the hixing
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+we just see the marshallian demand so
+
+ align:start position:0%
+we just see the marshallian demand so
+ 
+
+ align:start position:0%
+we just see the marshallian demand so
+we're kind of in trouble
+
+ align:start position:0%
+we're kind of in trouble
+ 
+
+ align:start position:0%
+we're kind of in trouble
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this is a statement about the slutsky
+
+ align:start position:0%
+this is a statement about the slutsky
+ 
+
+ align:start position:0%
+this is a statement about the slutsky
+matrix what we want to find which is the
+
+ align:start position:0%
+matrix what we want to find which is the
+ 
+
+ align:start position:0%
+matrix what we want to find which is the
+derivative of that thing we just looked
+
+ align:start position:0%
+derivative of that thing we just looked
+ 
+
+ align:start position:0%
+derivative of that thing we just looked
+at turns out it is associated with
+
+ align:start position:0%
+at turns out it is associated with
+ 
+
+ align:start position:0%
+at turns out it is associated with
+observables this is the elf good
+
+ align:start position:0%
+observables this is the elf good
+ 
+
+ align:start position:0%
+observables this is the elf good
+changing with respect to the k price is
+
+ align:start position:0%
+changing with respect to the k price is
+ 
+
+ align:start position:0%
+changing with respect to the k price is
+equal to the way the whole demand is
+
+ align:start position:0%
+equal to the way the whole demand is
+ 
+
+ align:start position:0%
+equal to the way the whole demand is
+changing of the health good as we change
+
+ align:start position:0%
+changing of the health good as we change
+ 
+
+ align:start position:0%
+changing of the health good as we change
+the price p k but we adjust for the
+
+ align:start position:0%
+the price p k but we adjust for the
+ 
+
+ align:start position:0%
+the price p k but we adjust for the
+income effect which is how the health
+
+ align:start position:0%
+income effect which is how the health
+ 
+
+ align:start position:0%
+income effect which is how the health
+grid is changing as we change income or
+
+ align:start position:0%
+grid is changing as we change income or
+ 
+
+ align:start position:0%
+grid is changing as we change income or
+wealth post multiplied by the quantity
+
+ align:start position:0%
+wealth post multiplied by the quantity
+ 
+
+ align:start position:0%
+wealth post multiplied by the quantity
+of the good price of which is changing
+
+ align:start position:0%
+of the good price of which is changing
+ 
+
+ align:start position:0%
+of the good price of which is changing
+namely pxk for pk okay
+
+ align:start position:0%
+namely pxk for pk okay
+ 
+
+ align:start position:0%
+namely pxk for pk okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and you're probably still struggling i
+
+ align:start position:0%
+and you're probably still struggling i
+ 
+
+ align:start position:0%
+and you're probably still struggling i
+went back to check
+
+ align:start position:0%
+went back to check
+ 
+
+ align:start position:0%
+went back to check
+you may remember this remember these
+
+ align:start position:0%
+you may remember this remember these
+ 
+
+ align:start position:0%
+you may remember this remember these
+this lecture where we did the income and
+
+ align:start position:0%
+this lecture where we did the income and
+ 
+
+ align:start position:0%
+this lecture where we did the income and
+substitution effects
+
+ align:start position:0%
+substitution effects
+ 
+
+ align:start position:0%
+substitution effects
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+and then we decomposed
+
+ align:start position:0%
+and then we decomposed
+ 
+
+ align:start position:0%
+and then we decomposed
+the total demand change
+
+ align:start position:0%
+the total demand change
+ 
+
+ align:start position:0%
+the total demand change
+as a consequence of the price change
+
+ align:start position:0%
+as a consequence of the price change
+ 
+
+ align:start position:0%
+as a consequence of the price change
+into the substitution effect
+
+ align:start position:0%
+into the substitution effect
+ 
+
+ align:start position:0%
+into the substitution effect
+and the income effect
+
+ align:start position:0%
+and the income effect
+ 
+
+ align:start position:0%
+and the income effect
+and we had to clarify that the income
+
+ align:start position:0%
+and we had to clarify that the income
+ 
+
+ align:start position:0%
+and we had to clarify that the income
+effect was negative because in that
+
+ align:start position:0%
+effect was negative because in that
+ 
+
+ align:start position:0%
+effect was negative because in that
+diagram we had p on the wrong axis
+
+ align:start position:0%
+diagram we had p on the wrong axis
+ 
+
+ align:start position:0%
+diagram we had p on the wrong axis
+given the strange way economists
+
+ align:start position:0%
+given the strange way economists
+ 
+
+ align:start position:0%
+given the strange way economists
+invented demand curves okay so then
+
+ align:start position:0%
+invented demand curves okay so then
+ 
+
+ align:start position:0%
+invented demand curves okay so then
+what we're trying to do today is to get
+
+ align:start position:0%
+what we're trying to do today is to get
+ 
+
+ align:start position:0%
+what we're trying to do today is to get
+this substitution effect matrix and
+
+ align:start position:0%
+this substitution effect matrix and
+ 
+
+ align:start position:0%
+this substitution effect matrix and
+we're getting it from observables
+
+ align:start position:0%
+we're getting it from observables
+ 
+
+ align:start position:0%
+we're getting it from observables
+how demand is changing as price changes
+
+ align:start position:0%
+how demand is changing as price changes
+ 
+
+ align:start position:0%
+how demand is changing as price changes
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+how demand is changing as income is
+
+ align:start position:0%
+how demand is changing as income is
+ 
+
+ align:start position:0%
+how demand is changing as income is
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+so this simple example equation is
+
+ align:start position:0%
+so this simple example equation is
+ 
+
+ align:start position:0%
+so this simple example equation is
+elaborated in this slutsky matrix the
+
+ align:start position:0%
+elaborated in this slutsky matrix the
+ 
+
+ align:start position:0%
+elaborated in this slutsky matrix the
+sign changes only because we change
+
+ align:start position:0%
+sign changes only because we change
+ 
+
+ align:start position:0%
+sign changes only because we change
+what's on the left-hand side from the
+
+ align:start position:0%
+what's on the left-hand side from the
+ 
+
+ align:start position:0%
+what's on the left-hand side from the
+total demand to the substitution effect
+
+ align:start position:0%
+total demand to the substitution effect
+ 
+
+ align:start position:0%
+total demand to the substitution effect
+substitute fact equals total demand plus
+
+ align:start position:0%
+substitute fact equals total demand plus
+ 
+
+ align:start position:0%
+substitute fact equals total demand plus
+income changes substitution effect
+
+ align:start position:0%
+income changes substitution effect
+ 
+
+ align:start position:0%
+income changes substitution effect
+equals the change in total demand plus
+
+ align:start position:0%
+equals the change in total demand plus
+ 
+
+ align:start position:0%
+equals the change in total demand plus
+income changes so in fact the slutsky
+
+ align:start position:0%
+income changes so in fact the slutsky
+ 
+
+ align:start position:0%
+income changes so in fact the slutsky
+thing is really familiar to you
+
+ align:start position:0%
+thing is really familiar to you
+ 
+
+ align:start position:0%
+thing is really familiar to you
+from that entire lecture that we did on
+
+ align:start position:0%
+from that entire lecture that we did on
+ 
+
+ align:start position:0%
+from that entire lecture that we did on
+income and substitution effects
+
+ align:start position:0%
+income and substitution effects
+ 
+
+ align:start position:0%
+income and substitution effects
+and now back to the point to reiterate
+
+ align:start position:0%
+and now back to the point to reiterate
+ 
+
+ align:start position:0%
+and now back to the point to reiterate
+this thing
+
+ align:start position:0%
+this thing
+ 
+
+ align:start position:0%
+this thing
+under the assumptions on the previous
+
+ align:start position:0%
+under the assumptions on the previous
+ 
+
+ align:start position:0%
+under the assumptions on the previous
+slide has to be if we enumerated it out
+
+ align:start position:0%
+slide has to be if we enumerated it out
+ 
+
+ align:start position:0%
+slide has to be if we enumerated it out
+for all l and k
+
+ align:start position:0%
+for all l and k
+ 
+
+ align:start position:0%
+for all l and k
+a symmetric negative semi-definite
+
+ align:start position:0%
+a symmetric negative semi-definite
+ 
+
+ align:start position:0%
+a symmetric negative semi-definite
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+so we can fill in the i the row com
+
+ align:start position:0%
+so we can fill in the i the row com
+ 
+
+ align:start position:0%
+so we can fill in the i the row com
+column elements
+
+ align:start position:0%
+column elements
+ 
+
+ align:start position:0%
+column elements
+from all these observables and just
+
+ align:start position:0%
+from all these observables and just
+ 
+
+ align:start position:0%
+from all these observables and just
+check and see whether it's true
+
+ align:start position:0%
+check and see whether it's true
+ 
+
+ align:start position:0%
+check and see whether it's true
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+i should have said
+
+ align:start position:0%
+i should have said
+ 
+
+ align:start position:0%
+i should have said
+this is with infinite data because you
+
+ align:start position:0%
+this is with infinite data because you
+ 
+
+ align:start position:0%
+this is with infinite data because you
+know we're talking about having
+
+ align:start position:0%
+know we're talking about having
+ 
+
+ align:start position:0%
+know we're talking about having
+derivatives which is infinitesimally
+
+ align:start position:0%
+derivatives which is infinitesimally
+ 
+
+ align:start position:0%
+derivatives which is infinitesimally
+small data but it's still good to know
+
+ align:start position:0%
+small data but it's still good to know
+ 
+
+ align:start position:0%
+small data but it's still good to know
+that in principle there's a way to do it
+
+ align:start position:0%
+that in principle there's a way to do it
+ 
+
+ align:start position:0%
+that in principle there's a way to do it
+if you can't identify something with
+
+ align:start position:0%
+if you can't identify something with
+ 
+
+ align:start position:0%
+if you can't identify something with
+infinite data you're not going to
+
+ align:start position:0%
+infinite data you're not going to
+ 
+
+ align:start position:0%
+infinite data you're not going to
+identify something with finite data
+
+ align:start position:0%
+identify something with finite data
+ 
+
+ align:start position:0%
+identify something with finite data
+so let's review where we are
+
+ align:start position:0%
+so let's review where we are
+ 
+
+ align:start position:0%
+so let's review where we are
+the goal here is see whether we have
+
+ align:start position:0%
+the goal here is see whether we have
+ 
+
+ align:start position:0%
+the goal here is see whether we have
+testable restrictions
+
+ align:start position:0%
+testable restrictions
+ 
+
+ align:start position:0%
+testable restrictions
+in particular ask the question whether
+
+ align:start position:0%
+in particular ask the question whether
+ 
+
+ align:start position:0%
+in particular ask the question whether
+what we see in terms of the demand
+
+ align:start position:0%
+what we see in terms of the demand
+ 
+
+ align:start position:0%
+what we see in terms of the demand
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+came from a utility maximizing rational
+
+ align:start position:0%
+came from a utility maximizing rational
+ 
+
+ align:start position:0%
+came from a utility maximizing rational
+consumer or not so i'm just going to
+
+ align:start position:0%
+consumer or not so i'm just going to
+ 
+
+ align:start position:0%
+consumer or not so i'm just going to
+stick you with a big database in this
+
+ align:start position:0%
+stick you with a big database in this
+ 
+
+ align:start position:0%
+stick you with a big database in this
+case an infinite dimensional database
+
+ align:start position:0%
+case an infinite dimensional database
+ 
+
+ align:start position:0%
+case an infinite dimensional database
+and have you check and see whether it
+
+ align:start position:0%
+and have you check and see whether it
+ 
+
+ align:start position:0%
+and have you check and see whether it
+could have come from a rational
+
+ align:start position:0%
+could have come from a rational
+ 
+
+ align:start position:0%
+could have come from a rational
+maximizing maximizing some utility
+
+ align:start position:0%
+maximizing maximizing some utility
+ 
+
+ align:start position:0%
+maximizing maximizing some utility
+function consumer okay
+
+ align:start position:0%
+function consumer okay
+ 
+
+ align:start position:0%
+function consumer okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what are the three properties
+
+ align:start position:0%
+what are the three properties
+ 
+
+ align:start position:0%
+what are the three properties
+homogeneity of degree zero
+
+ align:start position:0%
+homogeneity of degree zero
+ 
+
+ align:start position:0%
+homogeneity of degree zero
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+multiplying income and prices by a
+
+ align:start position:0%
+multiplying income and prices by a
+ 
+
+ align:start position:0%
+multiplying income and prices by a
+scalar you just get nothing changes
+
+ align:start position:0%
+scalar you just get nothing changes
+ 
+
+ align:start position:0%
+scalar you just get nothing changes
+that's a statement about you know not
+
+ align:start position:0%
+that's a statement about you know not
+ 
+
+ align:start position:0%
+that's a statement about you know not
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+naive about inflation for example
+
+ align:start position:0%
+naive about inflation for example
+ 
+
+ align:start position:0%
+naive about inflation for example
+although i guess arguably
+
+ align:start position:0%
+although i guess arguably
+ 
+
+ align:start position:0%
+although i guess arguably
+it could be violated but it seems
+
+ align:start position:0%
+it could be violated but it seems
+ 
+
+ align:start position:0%
+it could be violated but it seems
+pretty reasonable for a thoughtful
+
+ align:start position:0%
+pretty reasonable for a thoughtful
+ 
+
+ align:start position:0%
+pretty reasonable for a thoughtful
+consumer
+
+ align:start position:0%
+consumer
+ 
+
+ align:start position:0%
+consumer
+in two different situations with prices
+
+ align:start position:0%
+in two different situations with prices
+ 
+
+ align:start position:0%
+in two different situations with prices
+and income just being multiples of one
+
+ align:start position:0%
+and income just being multiples of one
+ 
+
+ align:start position:0%
+and income just being multiples of one
+another they shouldn't change what they
+
+ align:start position:0%
+another they shouldn't change what they
+ 
+
+ align:start position:0%
+another they shouldn't change what they
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+the second property is called vol ross
+
+ align:start position:0%
+the second property is called vol ross
+ 
+
+ align:start position:0%
+the second property is called vol ross
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+which is a fancy name for spending all
+
+ align:start position:0%
+which is a fancy name for spending all
+ 
+
+ align:start position:0%
+which is a fancy name for spending all
+your money
+
+ align:start position:0%
+your money
+ 
+
+ align:start position:0%
+your money
+namely if you have wealth w
+
+ align:start position:0%
+namely if you have wealth w
+ 
+
+ align:start position:0%
+namely if you have wealth w
+and you add up all the expenses observed
+
+ align:start position:0%
+and you add up all the expenses observed
+ 
+
+ align:start position:0%
+and you add up all the expenses observed
+to take place at prices p
+
+ align:start position:0%
+to take place at prices p
+ 
+
+ align:start position:0%
+to take place at prices p
+that's also equal to your wealth so you
+
+ align:start position:0%
+that's also equal to your wealth so you
+ 
+
+ align:start position:0%
+that's also equal to your wealth so you
+don't underspend you can't overspend
+
+ align:start position:0%
+don't underspend you can't overspend
+ 
+
+ align:start position:0%
+don't underspend you can't overspend
+because that would violate the budget
+
+ align:start position:0%
+because that would violate the budget
+ 
+
+ align:start position:0%
+because that would violate the budget
+you don't have the money
+
+ align:start position:0%
+you don't have the money
+ 
+
+ align:start position:0%
+you don't have the money
+but you could in principle under spend
+
+ align:start position:0%
+but you could in principle under spend
+ 
+
+ align:start position:0%
+but you could in principle under spend
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+a rational consumer with local
+
+ align:start position:0%
+a rational consumer with local
+ 
+
+ align:start position:0%
+a rational consumer with local
+non-satiated preferences would never do
+
+ align:start position:0%
+non-satiated preferences would never do
+ 
+
+ align:start position:0%
+non-satiated preferences would never do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+they'd go right out to the budget
+
+ align:start position:0%
+they'd go right out to the budget
+ 
+
+ align:start position:0%
+they'd go right out to the budget
+technically
+
+ align:start position:0%
+technically
+ 
+
+ align:start position:0%
+technically
+vol ross law is used to mean you only
+
+ align:start position:0%
+vol ross law is used to mean you only
+ 
+
+ align:start position:0%
+vol ross law is used to mean you only
+need to solve for the equilibrium if
+
+ align:start position:0%
+need to solve for the equilibrium if
+ 
+
+ align:start position:0%
+need to solve for the equilibrium if
+there are capital l goods you only need
+
+ align:start position:0%
+there are capital l goods you only need
+ 
+
+ align:start position:0%
+there are capital l goods you only need
+to solve for the equilibrium in l minus
+
+ align:start position:0%
+to solve for the equilibrium in l minus
+ 
+
+ align:start position:0%
+to solve for the equilibrium in l minus
+one of them because the elf one
+
+ align:start position:0%
+one of them because the elf one
+ 
+
+ align:start position:0%
+one of them because the elf one
+is pinned down
+
+ align:start position:0%
+is pinned down
+ 
+
+ align:start position:0%
+is pinned down
+by this budget equation
+
+ align:start position:0%
+by this budget equation
+ 
+
+ align:start position:0%
+by this budget equation
+so there's kind of like no extra
+
+ align:start position:0%
+so there's kind of like no extra
+ 
+
+ align:start position:0%
+so there's kind of like no extra
+restrictions
+
+ align:start position:0%
+restrictions
+ 
+
+ align:start position:0%
+restrictions
+okay and finally the slutsky matrix if
+
+ align:start position:0%
+okay and finally the slutsky matrix if
+ 
+
+ align:start position:0%
+okay and finally the slutsky matrix if
+the demand function is differentiable
+
+ align:start position:0%
+the demand function is differentiable
+ 
+
+ align:start position:0%
+the demand function is differentiable
+and single valued
+
+ align:start position:0%
+and single valued
+ 
+
+ align:start position:0%
+and single valued
+then that
+
+ align:start position:0%
+then that
+ 
+
+ align:start position:0%
+then that
+matrix s of p and w is symmetric and
+
+ align:start position:0%
+matrix s of p and w is symmetric and
+ 
+
+ align:start position:0%
+matrix s of p and w is symmetric and
+negative semi-definite
+
+ align:start position:0%
+negative semi-definite
+ 
+
+ align:start position:0%
+negative semi-definite
+okay who cares
+
+ align:start position:0%
+okay who cares
+ 
+
+ align:start position:0%
+okay who cares
+here's the content
+
+ align:start position:0%
+here's the content
+ 
+
+ align:start position:0%
+here's the content
+if the other two things are true
+
+ align:start position:0%
+if the other two things are true
+ 
+
+ align:start position:0%
+if the other two things are true
+and which one would argue is likely to
+
+ align:start position:0%
+and which one would argue is likely to
+ 
+
+ align:start position:0%
+and which one would argue is likely to
+be true in any generated data set
+
+ align:start position:0%
+be true in any generated data set
+ 
+
+ align:start position:0%
+be true in any generated data set
+if you can find anything that's not
+
+ align:start position:0%
+if you can find anything that's not
+ 
+
+ align:start position:0%
+if you can find anything that's not
+symmetric or not negative semi-definite
+
+ align:start position:0%
+symmetric or not negative semi-definite
+ 
+
+ align:start position:0%
+symmetric or not negative semi-definite
+then preferences could not have come
+
+ align:start position:0%
+then preferences could not have come
+ 
+
+ align:start position:0%
+then preferences could not have come
+from a locally not from locally
+
+ align:start position:0%
+from a locally not from locally
+ 
+
+ align:start position:0%
+from a locally not from locally
+non-satiated preference as a solution to
+
+ align:start position:0%
+non-satiated preference as a solution to
+ 
+
+ align:start position:0%
+non-satiated preference as a solution to
+the max problem
+
+ align:start position:0%
+the max problem
+ 
+
+ align:start position:0%
+the max problem
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is sort of the necessity part if
+
+ align:start position:0%
+this is sort of the necessity part if
+ 
+
+ align:start position:0%
+this is sort of the necessity part if
+we have utility max then all three
+
+ align:start position:0%
+we have utility max then all three
+ 
+
+ align:start position:0%
+we have utility max then all three
+properties have to hold
+
+ align:start position:0%
+properties have to hold
+ 
+
+ align:start position:0%
+properties have to hold
+otherwise can't be true that it came
+
+ align:start position:0%
+otherwise can't be true that it came
+ 
+
+ align:start position:0%
+otherwise can't be true that it came
+from utility max problem
+
+ align:start position:0%
+from utility max problem
+ 
+
+ align:start position:0%
+from utility max problem
+now one thing we'll get to convexity in
+
+ align:start position:0%
+now one thing we'll get to convexity in
+ 
+
+ align:start position:0%
+now one thing we'll get to convexity in
+a minute
+
+ align:start position:0%
+a minute
+ 
+
+ align:start position:0%
+a minute
+but i'll just earmark that
+
+ align:start position:0%
+but i'll just earmark that
+ 
+
+ align:start position:0%
+but i'll just earmark that
+that there's no statement here about
+
+ align:start position:0%
+that there's no statement here about
+ 
+
+ align:start position:0%
+that there's no statement here about
+convexity it's just locally non-satiated
+
+ align:start position:0%
+convexity it's just locally non-satiated
+ 
+
+ align:start position:0%
+convexity it's just locally non-satiated
+preferences
+
+ align:start position:0%
+preferences
+ 
+
+ align:start position:0%
+preferences
+it's not quite fair
+
+ align:start position:0%
+it's not quite fair
+ 
+
+ align:start position:0%
+it's not quite fair
+the slutsky thing we derived did rely on
+
+ align:start position:0%
+the slutsky thing we derived did rely on
+ 
+
+ align:start position:0%
+the slutsky thing we derived did rely on
+at least the way i presented it it
+
+ align:start position:0%
+at least the way i presented it it
+ 
+
+ align:start position:0%
+at least the way i presented it it
+relied on convex preferences
+
+ align:start position:0%
+relied on convex preferences
+ 
+
+ align:start position:0%
+relied on convex preferences
+the question here
+
+ align:start position:0%
+the question here
+ 
+
+ align:start position:0%
+the question here
+is whether one can test for non-convex
+
+ align:start position:0%
+is whether one can test for non-convex
+ 
+
+ align:start position:0%
+is whether one can test for non-convex
+preferences
+
+ align:start position:0%
+preferences
+ 
+
+ align:start position:0%
+preferences
+with the data which is a bit of a
+
+ align:start position:0%
+with the data which is a bit of a
+ 
+
+ align:start position:0%
+with the data which is a bit of a
+different question and and i'll come
+
+ align:start position:0%
+different question and and i'll come
+ 
+
+ align:start position:0%
+different question and and i'll come
+back to that
+
+ align:start position:0%
+back to that
+ 
+
+ align:start position:0%
+back to that
+so those three properties are
+
+ align:start position:0%
+so those three properties are
+ 
+
+ align:start position:0%
+so those three properties are
+not only have to be true if we maximize
+
+ align:start position:0%
+not only have to be true if we maximize
+ 
+
+ align:start position:0%
+not only have to be true if we maximize
+utility
+
+ align:start position:0%
+utility
+ 
+
+ align:start position:0%
+utility
+but if they're true in the data then we
+
+ align:start position:0%
+but if they're true in the data then we
+ 
+
+ align:start position:0%
+but if they're true in the data then we
+can always find a utility function that
+
+ align:start position:0%
+can always find a utility function that
+ 
+
+ align:start position:0%
+can always find a utility function that
+generated the observations and that's
+
+ align:start position:0%
+generated the observations and that's
+ 
+
+ align:start position:0%
+generated the observations and that's
+called integrability let me give you the
+
+ align:start position:0%
+called integrability let me give you the
+ 
+
+ align:start position:0%
+called integrability let me give you the
+formal statement of it
+
+ align:start position:0%
+formal statement of it
+ 
+
+ align:start position:0%
+formal statement of it
+so this is like the sufficient part
+
+ align:start position:0%
+so this is like the sufficient part
+ 
+
+ align:start position:0%
+so this is like the sufficient part
+if preferences are of a household
+
+ align:start position:0%
+if preferences are of a household
+ 
+
+ align:start position:0%
+if preferences are of a household
+are strictly increasing strictly
+
+ align:start position:0%
+are strictly increasing strictly
+ 
+
+ align:start position:0%
+are strictly increasing strictly
+quasi-concave
+
+ align:start position:0%
+quasi-concave
+ 
+
+ align:start position:0%
+quasi-concave
+then the voracion demand function
+
+ align:start position:0%
+then the voracion demand function
+ 
+
+ align:start position:0%
+then the voracion demand function
+is homogeneous of degree zero
+
+ align:start position:0%
+is homogeneous of degree zero
+ 
+
+ align:start position:0%
+is homogeneous of degree zero
+satisfies vol ross law
+
+ align:start position:0%
+satisfies vol ross law
+ 
+
+ align:start position:0%
+satisfies vol ross law
+and and its slotsky matrix is symmetric
+
+ align:start position:0%
+and and its slotsky matrix is symmetric
+ 
+
+ align:start position:0%
+and and its slotsky matrix is symmetric
+and negative semi-definite
+
+ align:start position:0%
+and negative semi-definite
+ 
+
+ align:start position:0%
+and negative semi-definite
+that's the first part
+
+ align:start position:0%
+that's the first part
+ 
+
+ align:start position:0%
+that's the first part
+the second part is if the demand
+
+ align:start position:0%
+the second part is if the demand
+ 
+
+ align:start position:0%
+the second part is if the demand
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is homogeneous of degree zero
+
+ align:start position:0%
+is homogeneous of degree zero
+ 
+
+ align:start position:0%
+is homogeneous of degree zero
+satisfies volara's law
+
+ align:start position:0%
+satisfies volara's law
+ 
+
+ align:start position:0%
+satisfies volara's law
+and the slutsky matrix is symmetric and
+
+ align:start position:0%
+and the slutsky matrix is symmetric and
+ 
+
+ align:start position:0%
+and the slutsky matrix is symmetric and
+negative semi-definite then
+
+ align:start position:0%
+negative semi-definite then
+ 
+
+ align:start position:0%
+negative semi-definite then
+there exists a utility function that is
+
+ align:start position:0%
+there exists a utility function that is
+ 
+
+ align:start position:0%
+there exists a utility function that is
+increasing
+
+ align:start position:0%
+increasing
+ 
+
+ align:start position:0%
+increasing
+quasi-concave that would generate
+
+ align:start position:0%
+quasi-concave that would generate
+ 
+
+ align:start position:0%
+quasi-concave that would generate
+the observed data
+
+ align:start position:0%
+the observed data
+ 
+
+ align:start position:0%
+the observed data
+so let me backtrack this first part a is
+
+ align:start position:0%
+so let me backtrack this first part a is
+ 
+
+ align:start position:0%
+so let me backtrack this first part a is
+what we did initially the second part b
+
+ align:start position:0%
+what we did initially the second part b
+ 
+
+ align:start position:0%
+what we did initially the second part b
+is the integrability theorem that says
+
+ align:start position:0%
+is the integrability theorem that says
+ 
+
+ align:start position:0%
+is the integrability theorem that says
+we can work backwards from the data set
+
+ align:start position:0%
+we can work backwards from the data set
+ 
+
+ align:start position:0%
+we can work backwards from the data set
+to an underlying utility function which
+
+ align:start position:0%
+to an underlying utility function which
+ 
+
+ align:start position:0%
+to an underlying utility function which
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+has to be increasing quasi concave
+
+ align:start position:0%
+has to be increasing quasi concave
+ 
+
+ align:start position:0%
+has to be increasing quasi concave
+and would generate the data as if a
+
+ align:start position:0%
+and would generate the data as if a
+ 
+
+ align:start position:0%
+and would generate the data as if a
+solution to the max problem so
+
+ align:start position:0%
+solution to the max problem so
+ 
+
+ align:start position:0%
+solution to the max problem so
+this is the bit about not testability of
+
+ align:start position:0%
+this is the bit about not testability of
+ 
+
+ align:start position:0%
+this is the bit about not testability of
+convex preferences
+
+ align:start position:0%
+convex preferences
+ 
+
+ align:start position:0%
+convex preferences
+and the idea is we've deliberately drawn
+
+ align:start position:0%
+and the idea is we've deliberately drawn
+ 
+
+ align:start position:0%
+and the idea is we've deliberately drawn
+an underlying utility function
+
+ align:start position:0%
+an underlying utility function
+ 
+
+ align:start position:0%
+an underlying utility function
+which is not concave or these upper
+
+ align:start position:0%
+which is not concave or these upper
+ 
+
+ align:start position:0%
+which is not concave or these upper
+contour sets are not strictly convex you
+
+ align:start position:0%
+contour sets are not strictly convex you
+ 
+
+ align:start position:0%
+contour sets are not strictly convex you
+see the the wiggle here
+
+ align:start position:0%
+see the the wiggle here
+ 
+
+ align:start position:0%
+see the the wiggle here
+but if we start rotating a budget line
+
+ align:start position:0%
+but if we start rotating a budget line
+ 
+
+ align:start position:0%
+but if we start rotating a budget line
+or along the indifference curve and
+
+ align:start position:0%
+or along the indifference curve and
+ 
+
+ align:start position:0%
+or along the indifference curve and
+picking out the tangencies
+
+ align:start position:0%
+picking out the tangencies
+ 
+
+ align:start position:0%
+picking out the tangencies
+we would generate like the hixing demand
+
+ align:start position:0%
+we would generate like the hixing demand
+ 
+
+ align:start position:0%
+we would generate like the hixing demand
+etc then we get to this particular
+
+ align:start position:0%
+etc then we get to this particular
+ 
+
+ align:start position:0%
+etc then we get to this particular
+budget line
+
+ align:start position:0%
+budget line
+ 
+
+ align:start position:0%
+budget line
+where we no longer pivoting
+
+ align:start position:0%
+where we no longer pivoting
+ 
+
+ align:start position:0%
+where we no longer pivoting
+we jump or for a moment we would be
+
+ align:start position:0%
+we jump or for a moment we would be
+ 
+
+ align:start position:0%
+we jump or for a moment we would be
+indifferent between this point and this
+
+ align:start position:0%
+indifferent between this point and this
+ 
+
+ align:start position:0%
+indifferent between this point and this
+point and as we keep rotating the line
+
+ align:start position:0%
+point and as we keep rotating the line
+ 
+
+ align:start position:0%
+point and as we keep rotating the line
+and making it have less and less slope
+
+ align:start position:0%
+and making it have less and less slope
+ 
+
+ align:start position:0%
+and making it have less and less slope
+we will start finding you know pivoting
+
+ align:start position:0%
+we will start finding you know pivoting
+ 
+
+ align:start position:0%
+we will start finding you know pivoting
+along this curved indifference curve
+
+ align:start position:0%
+along this curved indifference curve
+ 
+
+ align:start position:0%
+along this curved indifference curve
+that shouldn't be bending back up again
+
+ align:start position:0%
+that shouldn't be bending back up again
+ 
+
+ align:start position:0%
+that shouldn't be bending back up again
+but anyway so the point is we never end
+
+ align:start position:0%
+but anyway so the point is we never end
+ 
+
+ align:start position:0%
+but anyway so the point is we never end
+up in this non-concave portion so we
+
+ align:start position:0%
+up in this non-concave portion so we
+ 
+
+ align:start position:0%
+up in this non-concave portion so we
+don't generate observables in there what
+
+ align:start position:0%
+don't generate observables in there what
+ 
+
+ align:start position:0%
+don't generate observables in there what
+we would infer
+
+ align:start position:0%
+we would infer
+ 
+
+ align:start position:0%
+we would infer
+is they have strictly concave or weekly
+
+ align:start position:0%
+is they have strictly concave or weekly
+ 
+
+ align:start position:0%
+is they have strictly concave or weekly
+linear preferences over certain ranges
+
+ align:start position:0%
+linear preferences over certain ranges
+ 
+
+ align:start position:0%
+linear preferences over certain ranges
+of prices
+
+ align:start position:0%
+of prices
+ 
+
+ align:start position:0%
+of prices
+which is consistent with underlying
+
+ align:start position:0%
+which is consistent with underlying
+ 
+
+ align:start position:0%
+which is consistent with underlying
+quasi-weekly quasi-concave utility
+
+ align:start position:0%
+quasi-weekly quasi-concave utility
+ 
+
+ align:start position:0%
+quasi-weekly quasi-concave utility
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+now this doesn't mean that we can't test
+
+ align:start position:0%
+now this doesn't mean that we can't test
+ 
+
+ align:start position:0%
+now this doesn't mean that we can't test
+for convexity of preferences in other
+
+ align:start position:0%
+for convexity of preferences in other
+ 
+
+ align:start position:0%
+for convexity of preferences in other
+ways but this whole lecture is about
+
+ align:start position:0%
+ways but this whole lecture is about
+ 
+
+ align:start position:0%
+ways but this whole lecture is about
+restrictions on data that come from
+
+ align:start position:0%
+restrictions on data that come from
+ 
+
+ align:start position:0%
+restrictions on data that come from
+market behavior maximizing utilities
+
+ align:start position:0%
+market behavior maximizing utilities
+ 
+
+ align:start position:0%
+market behavior maximizing utilities
+subject to budgets and if that's all we
+
+ align:start position:0%
+subject to budgets and if that's all we
+ 
+
+ align:start position:0%
+subject to budgets and if that's all we
+have in the data we cannot test for
+
+ align:start position:0%
+have in the data we cannot test for
+ 
+
+ align:start position:0%
+have in the data we cannot test for
+convexity
+
+ align:start position:0%
+convexity
+ 
+
+ align:start position:0%
+convexity
+again the statement there exists a
+
+ align:start position:0%
+again the statement there exists a
+ 
+
+ align:start position:0%
+again the statement there exists a
+utility function that is increasing in
+
+ align:start position:0%
+utility function that is increasing in
+ 
+
+ align:start position:0%
+utility function that is increasing in
+quasi-concave
+
+ align:start position:0%
+quasi-concave
+ 
+
+ align:start position:0%
+quasi-concave
+that's probably confusing because it
+
+ align:start position:0%
+that's probably confusing because it
+ 
+
+ align:start position:0%
+that's probably confusing because it
+looks like we just said the utility
+
+ align:start position:0%
+looks like we just said the utility
+ 
+
+ align:start position:0%
+looks like we just said the utility
+function is quasi-concave
+
+ align:start position:0%
+function is quasi-concave
+ 
+
+ align:start position:0%
+function is quasi-concave
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+this one is not
+
+ align:start position:0%
+this one is not
+ 
+
+ align:start position:0%
+this one is not
+that's the true underlying function but
+
+ align:start position:0%
+that's the true underlying function but
+ 
+
+ align:start position:0%
+that's the true underlying function but
+we can't test for that
+
+ align:start position:0%
+we can't test for that
+ 
+
+ align:start position:0%
+we can't test for that
+all we see in the observables are you
+
+ align:start position:0%
+all we see in the observables are you
+ 
+
+ align:start position:0%
+all we see in the observables are you
+know the one that as if generated the
+
+ align:start position:0%
+know the one that as if generated the
+ 
+
+ align:start position:0%
+know the one that as if generated the
+dashed line
+
+ align:start position:0%
+dashed line
+ 
+
+ align:start position:0%
+dashed line
+and that utility function is quasi
+
+ align:start position:0%
+and that utility function is quasi
+ 
+
+ align:start position:0%
+and that utility function is quasi
+concave so that's the content of
+
+ align:start position:0%
+concave so that's the content of
+ 
+
+ align:start position:0%
+concave so that's the content of
+of this statement it's as if there were
+
+ align:start position:0%
+of this statement it's as if there were
+ 
+
+ align:start position:0%
+of this statement it's as if there were
+a utility function which is quasi
+
+ align:start position:0%
+a utility function which is quasi
+ 
+
+ align:start position:0%
+a utility function which is quasi
+concave
+
+ align:start position:0%
+concave
+ 
+
+ align:start position:0%
+concave
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so operationally we might as well assume
+
+ align:start position:0%
+so operationally we might as well assume
+ 
+
+ align:start position:0%
+so operationally we might as well assume
+convex preferences because we're not
+
+ align:start position:0%
+convex preferences because we're not
+ 
+
+ align:start position:0%
+convex preferences because we're not
+going to be able to reject it anyway
+
+ align:start position:0%
+going to be able to reject it anyway
+ 
+
+ align:start position:0%
+going to be able to reject it anyway
+that's kind of a odd sounding corollary
+
+ align:start position:0%
+that's kind of a odd sounding corollary
+ 
+
+ align:start position:0%
+that's kind of a odd sounding corollary
+to this whole first part of the lecture
+
+ align:start position:0%
+to this whole first part of the lecture
+ 
+
+ align:start position:0%
+to this whole first part of the lecture
+which is the goal of placing
+
+ align:start position:0%
+which is the goal of placing
+ 
+
+ align:start position:0%
+which is the goal of placing
+restrictions on data whether data place
+
+ align:start position:0%
+restrictions on data whether data place
+ 
+
+ align:start position:0%
+restrictions on data whether data place
+restrictions on theory or not and
+
+ align:start position:0%
+restrictions on theory or not and
+ 
+
+ align:start position:0%
+restrictions on theory or not and
+finally let me say again
+
+ align:start position:0%
+finally let me say again
+ 
+
+ align:start position:0%
+finally let me say again
+why are we trying so hard to see what we
+
+ align:start position:0%
+why are we trying so hard to see what we
+ 
+
+ align:start position:0%
+why are we trying so hard to see what we
+could potentially reject i mean the
+
+ align:start position:0%
+could potentially reject i mean the
+ 
+
+ align:start position:0%
+could potentially reject i mean the
+answer is if say it's not slitsky then
+
+ align:start position:0%
+answer is if say it's not slitsky then
+ 
+
+ align:start position:0%
+answer is if say it's not slitsky then
+it could not have come from you know a
+
+ align:start position:0%
+it could not have come from you know a
+ 
+
+ align:start position:0%
+it could not have come from you know a
+rational consumer maximizing utility and
+
+ align:start position:0%
+rational consumer maximizing utility and
+ 
+
+ align:start position:0%
+rational consumer maximizing utility and
+that's kind of good news
+
+ align:start position:0%
+that's kind of good news
+ 
+
+ align:start position:0%
+that's kind of good news
+if for any data set we can always find a
+
+ align:start position:0%
+if for any data set we can always find a
+ 
+
+ align:start position:0%
+if for any data set we can always find a
+consumer maximizing utility that could
+
+ align:start position:0%
+consumer maximizing utility that could
+ 
+
+ align:start position:0%
+consumer maximizing utility that could
+have generated the data then there's no
+
+ align:start position:0%
+have generated the data then there's no
+ 
+
+ align:start position:0%
+have generated the data then there's no
+content to the theory
+
+ align:start position:0%
+content to the theory
+ 
+
+ align:start position:0%
+content to the theory
+it might be fun to do the theory
+
+ align:start position:0%
+it might be fun to do the theory
+ 
+
+ align:start position:0%
+it might be fun to do the theory
+but it's a vacuous empirical exercise it
+
+ align:start position:0%
+but it's a vacuous empirical exercise it
+ 
+
+ align:start position:0%
+but it's a vacuous empirical exercise it
+has no content if it's always true
+
+ align:start position:0%
+has no content if it's always true
+ 
+
+ align:start position:0%
+has no content if it's always true
+fortunately it's not always true and
+
+ align:start position:0%
+fortunately it's not always true and
+ 
+
+ align:start position:0%
+fortunately it's not always true and
+these are the conditions we can check
+
+ align:start position:0%
+these are the conditions we can check
+ 
+
+ align:start position:0%
+these are the conditions we can check
+it's an odd thing because then you could
+
+ align:start position:0%
+it's an odd thing because then you could
+ 
+
+ align:start position:0%
+it's an odd thing because then you could
+end up with oh my god where did this
+
+ align:start position:0%
+end up with oh my god where did this
+ 
+
+ align:start position:0%
+end up with oh my god where did this
+data come from it couldn't be coming
+
+ align:start position:0%
+data come from it couldn't be coming
+ 
+
+ align:start position:0%
+data come from it couldn't be coming
+from a rational consumer but anyway
+
+ align:start position:0%
+from a rational consumer but anyway
+ 
+
+ align:start position:0%
+from a rational consumer but anyway
+we actually like it if we can reject
+
+ align:start position:0%
+we actually like it if we can reject
+ 
+
+ align:start position:0%
+we actually like it if we can reject
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+strange science
+
+ align:start position:0%
+strange science
+ 
+
+ align:start position:0%
+strange science
+so now let's go to finite data
+
+ align:start position:0%
+so now let's go to finite data
+ 
+
+ align:start position:0%
+so now let's go to finite data
+we had observed a minute ago we had the
+
+ align:start position:0%
+we had observed a minute ago we had the
+ 
+
+ align:start position:0%
+we had observed a minute ago we had the
+entire vol raising demand function for
+
+ align:start position:0%
+entire vol raising demand function for
+ 
+
+ align:start position:0%
+entire vol raising demand function for
+arbitrarily small changes in prices and
+
+ align:start position:0%
+arbitrarily small changes in prices and
+ 
+
+ align:start position:0%
+arbitrarily small changes in prices and
+wealth and so on but typically we don't
+
+ align:start position:0%
+wealth and so on but typically we don't
+ 
+
+ align:start position:0%
+wealth and so on but typically we don't
+see that we don't have an infinite data
+
+ align:start position:0%
+see that we don't have an infinite data
+ 
+
+ align:start position:0%
+see that we don't have an infinite data
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+we may have a household and if we're
+
+ align:start position:0%
+we may have a household and if we're
+ 
+
+ align:start position:0%
+we may have a household and if we're
+lucky we can observe that household over
+
+ align:start position:0%
+lucky we can observe that household over
+ 
+
+ align:start position:0%
+lucky we can observe that household over
+long periods of time and see you know
+
+ align:start position:0%
+long periods of time and see you know
+ 
+
+ align:start position:0%
+long periods of time and see you know
+what decisions are being made
+
+ align:start position:0%
+what decisions are being made
+ 
+
+ align:start position:0%
+what decisions are being made
+if those things are recorded on alipay
+
+ align:start position:0%
+if those things are recorded on alipay
+ 
+
+ align:start position:0%
+if those things are recorded on alipay
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+and if it were true that everything that
+
+ align:start position:0%
+and if it were true that everything that
+ 
+
+ align:start position:0%
+and if it were true that everything that
+was bought where it's acquired on alipay
+
+ align:start position:0%
+was bought where it's acquired on alipay
+ 
+
+ align:start position:0%
+was bought where it's acquired on alipay
+then we would see
+
+ align:start position:0%
+then we would see
+ 
+
+ align:start position:0%
+then we would see
+and if we also saw the wealth because
+
+ align:start position:0%
+and if we also saw the wealth because
+ 
+
+ align:start position:0%
+and if we also saw the wealth because
+they're spending everything on alipay
+
+ align:start position:0%
+they're spending everything on alipay
+ 
+
+ align:start position:0%
+they're spending everything on alipay
+then we would actually potentially have
+
+ align:start position:0%
+then we would actually potentially have
+ 
+
+ align:start position:0%
+then we would actually potentially have
+a very long data set but not infinite so
+
+ align:start position:0%
+a very long data set but not infinite so
+ 
+
+ align:start position:0%
+a very long data set but not infinite so
+we want to see whether we can
+
+ align:start position:0%
+we want to see whether we can
+ 
+
+ align:start position:0%
+we want to see whether we can
+nevertheless test the hypothesis of
+
+ align:start position:0%
+nevertheless test the hypothesis of
+ 
+
+ align:start position:0%
+nevertheless test the hypothesis of
+rationality and the answer is going to
+
+ align:start position:0%
+rationality and the answer is going to
+ 
+
+ align:start position:0%
+rationality and the answer is going to
+be positive there is a way to take the
+
+ align:start position:0%
+be positive there is a way to take the
+ 
+
+ align:start position:0%
+be positive there is a way to take the
+data and run an algorithm
+
+ align:start position:0%
+data and run an algorithm
+ 
+
+ align:start position:0%
+data and run an algorithm
+and uh see whether the results are
+
+ align:start position:0%
+and uh see whether the results are
+ 
+
+ align:start position:0%
+and uh see whether the results are
+consistent but potentially inconsistent
+
+ align:start position:0%
+consistent but potentially inconsistent
+ 
+
+ align:start position:0%
+consistent but potentially inconsistent
+and in the latter case we can reject
+
+ align:start position:0%
+and in the latter case we can reject
+ 
+
+ align:start position:0%
+and in the latter case we can reject
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this is the definition of the weak axiom
+
+ align:start position:0%
+this is the definition of the weak axiom
+ 
+
+ align:start position:0%
+this is the definition of the weak axiom
+of revealed preference
+
+ align:start position:0%
+of revealed preference
+ 
+
+ align:start position:0%
+of revealed preference
+let's start with just having
+
+ align:start position:0%
+let's start with just having
+ 
+
+ align:start position:0%
+let's start with just having
+two observations with different prices
+
+ align:start position:0%
+two observations with different prices
+ 
+
+ align:start position:0%
+two observations with different prices
+and different choices okay p1 x1 p2 x2
+
+ align:start position:0%
+and different choices okay p1 x1 p2 x2
+ 
+
+ align:start position:0%
+and different choices okay p1 x1 p2 x2
+is a pair of observations on prices and
+
+ align:start position:0%
+is a pair of observations on prices and
+ 
+
+ align:start position:0%
+is a pair of observations on prices and
+consumption bundles
+
+ align:start position:0%
+consumption bundles
+ 
+
+ align:start position:0%
+consumption bundles
+implicitly for a given household
+
+ align:start position:0%
+implicitly for a given household
+ 
+
+ align:start position:0%
+implicitly for a given household
+p t
+
+ align:start position:0%
+p t
+ 
+
+ align:start position:0%
+p t
+doesn't mean necessarily t over time
+
+ align:start position:0%
+doesn't mean necessarily t over time
+ 
+
+ align:start position:0%
+doesn't mean necessarily t over time
+although you could imagine
+
+ align:start position:0%
+although you could imagine
+ 
+
+ align:start position:0%
+although you could imagine
+we observed at t equal one the first
+
+ align:start position:0%
+we observed at t equal one the first
+ 
+
+ align:start position:0%
+we observed at t equal one the first
+choice and at t equal to the second
+
+ align:start position:0%
+choice and at t equal to the second
+ 
+
+ align:start position:0%
+choice and at t equal to the second
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+but that's confusing because it raises
+
+ align:start position:0%
+but that's confusing because it raises
+ 
+
+ align:start position:0%
+but that's confusing because it raises
+the dynamic issues and everything else
+
+ align:start position:0%
+the dynamic issues and everything else
+ 
+
+ align:start position:0%
+the dynamic issues and everything else
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+t is really only meant here to index the
+
+ align:start position:0%
+t is really only meant here to index the
+ 
+
+ align:start position:0%
+t is really only meant here to index the
+data point
+
+ align:start position:0%
+data point
+ 
+
+ align:start position:0%
+data point
+and there's two data points and hence
+
+ align:start position:0%
+and there's two data points and hence
+ 
+
+ align:start position:0%
+and there's two data points and hence
+two values for t
+
+ align:start position:0%
+two values for t
+ 
+
+ align:start position:0%
+two values for t
+and let's suppose
+
+ align:start position:0%
+and let's suppose
+ 
+
+ align:start position:0%
+and let's suppose
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+not trivial
+
+ align:start position:0%
+not trivial
+ 
+
+ align:start position:0%
+not trivial
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+these choices are different
+
+ align:start position:0%
+these choices are different
+ 
+
+ align:start position:0%
+these choices are different
+and we say the individual choices these
+
+ align:start position:0%
+and we say the individual choices these
+ 
+
+ align:start position:0%
+and we say the individual choices these
+choices satisfy the weak axiom of real
+
+ align:start position:0%
+choices satisfy the weak axiom of real
+ 
+
+ align:start position:0%
+choices satisfy the weak axiom of real
+preference if whenever at the second
+
+ align:start position:0%
+preference if whenever at the second
+ 
+
+ align:start position:0%
+preference if whenever at the second
+price is p2
+
+ align:start position:0%
+price is p2
+ 
+
+ align:start position:0%
+price is p2
+with x2 chosen
+
+ align:start position:0%
+with x2 chosen
+ 
+
+ align:start position:0%
+with x2 chosen
+and x1 in the interior of the budget we
+
+ align:start position:0%
+and x1 in the interior of the budget we
+ 
+
+ align:start position:0%
+and x1 in the interior of the budget we
+must then have at prices p1 spending p1
+
+ align:start position:0%
+must then have at prices p1 spending p1
+ 
+
+ align:start position:0%
+must then have at prices p1 spending p1
+x1 that x2 is not attainable so let me
+
+ align:start position:0%
+x1 that x2 is not attainable so let me
+ 
+
+ align:start position:0%
+x1 that x2 is not attainable so let me
+say it again
+
+ align:start position:0%
+say it again
+ 
+
+ align:start position:0%
+say it again
+it's an if then thing
+
+ align:start position:0%
+it's an if then thing
+ 
+
+ align:start position:0%
+it's an if then thing
+if this is true in the data
+
+ align:start position:0%
+if this is true in the data
+ 
+
+ align:start position:0%
+if this is true in the data
+that if they had chosen x1 they would
+
+ align:start position:0%
+that if they had chosen x1 they would
+ 
+
+ align:start position:0%
+that if they had chosen x1 they would
+not have been
+
+ align:start position:0%
+not have been
+ 
+
+ align:start position:0%
+not have been
+spending all their money
+
+ align:start position:0%
+spending all their money
+ 
+
+ align:start position:0%
+spending all their money
+if that configuration is true in the
+
+ align:start position:0%
+if that configuration is true in the
+ 
+
+ align:start position:0%
+if that configuration is true in the
+data then we better find that at prices
+
+ align:start position:0%
+data then we better find that at prices
+ 
+
+ align:start position:0%
+data then we better find that at prices
+p1 the valuation of expenditures on x2
+
+ align:start position:0%
+p1 the valuation of expenditures on x2
+ 
+
+ align:start position:0%
+p1 the valuation of expenditures on x2
+is strictly greater than x1
+
+ align:start position:0%
+is strictly greater than x1
+ 
+
+ align:start position:0%
+is strictly greater than x1
+and again the ideas revealed preference
+
+ align:start position:0%
+and again the ideas revealed preference
+ 
+
+ align:start position:0%
+and again the ideas revealed preference
+so at prices p2 they are revealed to
+
+ align:start position:0%
+so at prices p2 they are revealed to
+ 
+
+ align:start position:0%
+so at prices p2 they are revealed to
+prefer x2 over x1
+
+ align:start position:0%
+prefer x2 over x1
+ 
+
+ align:start position:0%
+prefer x2 over x1
+because x1 is available and they didn't
+
+ align:start position:0%
+because x1 is available and they didn't
+ 
+
+ align:start position:0%
+because x1 is available and they didn't
+choose it so it better not be the case
+
+ align:start position:0%
+choose it so it better not be the case
+ 
+
+ align:start position:0%
+choose it so it better not be the case
+that in some other way of looking at the
+
+ align:start position:0%
+that in some other way of looking at the
+ 
+
+ align:start position:0%
+that in some other way of looking at the
+data this inequality is violated because
+
+ align:start position:0%
+data this inequality is violated because
+ 
+
+ align:start position:0%
+data this inequality is violated because
+if at prices p1
+
+ align:start position:0%
+if at prices p1
+ 
+
+ align:start position:0%
+if at prices p1
+x2 were available
+
+ align:start position:0%
+x2 were available
+ 
+
+ align:start position:0%
+x2 were available
+because it's interior to the budget at
+
+ align:start position:0%
+because it's interior to the budget at
+ 
+
+ align:start position:0%
+because it's interior to the budget at
+prices p1 then to be consistent they
+
+ align:start position:0%
+prices p1 then to be consistent they
+ 
+
+ align:start position:0%
+prices p1 then to be consistent they
+should have chosen it because it's
+
+ align:start position:0%
+should have chosen it because it's
+ 
+
+ align:start position:0%
+should have chosen it because it's
+already shown to be weekly preferred x1
+
+ align:start position:0%
+already shown to be weekly preferred x1
+ 
+
+ align:start position:0%
+already shown to be weekly preferred x1
+okay so that's the idea
+
+ align:start position:0%
+okay so that's the idea
+ 
+
+ align:start position:0%
+okay so that's the idea
+if this is true then this is true so
+
+ align:start position:0%
+if this is true then this is true so
+ 
+
+ align:start position:0%
+if this is true then this is true so
+it's like a statement of of an algorithm
+
+ align:start position:0%
+it's like a statement of of an algorithm
+ 
+
+ align:start position:0%
+it's like a statement of of an algorithm
+running over the data
+
+ align:start position:0%
+running over the data
+ 
+
+ align:start position:0%
+running over the data
+and we're going to generalize that
+
+ align:start position:0%
+and we're going to generalize that
+ 
+
+ align:start position:0%
+and we're going to generalize that
+so what happens if this isn't true
+
+ align:start position:0%
+so what happens if this isn't true
+ 
+
+ align:start position:0%
+so what happens if this isn't true
+this is true but this is not so let's
+
+ align:start position:0%
+this is true but this is not so let's
+ 
+
+ align:start position:0%
+this is true but this is not so let's
+look at a picture
+
+ align:start position:0%
+look at a picture
+ 
+
+ align:start position:0%
+look at a picture
+at prices p2
+
+ align:start position:0%
+at prices p2
+ 
+
+ align:start position:0%
+at prices p2
+they choose x2
+
+ align:start position:0%
+they choose x2
+ 
+
+ align:start position:0%
+they choose x2
+which on the budget
+
+ align:start position:0%
+which on the budget
+ 
+
+ align:start position:0%
+which on the budget
+and x1 is interior
+
+ align:start position:0%
+and x1 is interior
+ 
+
+ align:start position:0%
+and x1 is interior
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's this condition
+
+ align:start position:0%
+that's this condition
+ 
+
+ align:start position:0%
+that's this condition
+x1 is interior to the budget at prices
+
+ align:start position:0%
+x1 is interior to the budget at prices
+ 
+
+ align:start position:0%
+x1 is interior to the budget at prices
+p2
+
+ align:start position:0%
+p2
+ 
+
+ align:start position:0%
+p2
+then we look at prices p2 p1
+
+ align:start position:0%
+then we look at prices p2 p1
+ 
+
+ align:start position:0%
+then we look at prices p2 p1
+are they
+
+ align:start position:0%
+are they
+ 
+
+ align:start position:0%
+are they
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so here's x1 it's on the budget at price
+
+ align:start position:0%
+so here's x1 it's on the budget at price
+ 
+
+ align:start position:0%
+so here's x1 it's on the budget at price
+p1
+
+ align:start position:0%
+p1
+ 
+
+ align:start position:0%
+p1
+the question is where is x2
+
+ align:start position:0%
+the question is where is x2
+ 
+
+ align:start position:0%
+the question is where is x2
+in this case x2 is interior
+
+ align:start position:0%
+in this case x2 is interior
+ 
+
+ align:start position:0%
+in this case x2 is interior
+to the p1 budget line
+
+ align:start position:0%
+to the p1 budget line
+ 
+
+ align:start position:0%
+to the p1 budget line
+that violates
+
+ align:start position:0%
+that violates
+ 
+
+ align:start position:0%
+that violates
+we didn't want to find that that
+
+ align:start position:0%
+we didn't want to find that that
+ 
+
+ align:start position:0%
+we didn't want to find that that
+violates
+
+ align:start position:0%
+violates
+ 
+
+ align:start position:0%
+violates
+what ought to be true
+
+ align:start position:0%
+what ought to be true
+ 
+
+ align:start position:0%
+what ought to be true
+and it so it violates the weak axiom
+
+ align:start position:0%
+and it so it violates the weak axiom
+ 
+
+ align:start position:0%
+and it so it violates the weak axiom
+not only that try to draw indifference
+
+ align:start position:0%
+not only that try to draw indifference
+ 
+
+ align:start position:0%
+not only that try to draw indifference
+curves
+
+ align:start position:0%
+curves
+ 
+
+ align:start position:0%
+curves
+from a quasi-concave or you know linear
+
+ align:start position:0%
+from a quasi-concave or you know linear
+ 
+
+ align:start position:0%
+from a quasi-concave or you know linear
+or strictly convex
+
+ align:start position:0%
+or strictly convex
+ 
+
+ align:start position:0%
+or strictly convex
+you can't do it
+
+ align:start position:0%
+you can't do it
+ 
+
+ align:start position:0%
+you can't do it
+you get a tangency here you'd get a
+
+ align:start position:0%
+you get a tangency here you'd get a
+ 
+
+ align:start position:0%
+you get a tangency here you'd get a
+tangency here
+
+ align:start position:0%
+tangency here
+ 
+
+ align:start position:0%
+tangency here
+or you know looking at the bottom
+
+ align:start position:0%
+or you know looking at the bottom
+ 
+
+ align:start position:0%
+or you know looking at the bottom
+the indifference curves would cross
+
+ align:start position:0%
+the indifference curves would cross
+ 
+
+ align:start position:0%
+the indifference curves would cross
+there's no way you can draw this picture
+
+ align:start position:0%
+there's no way you can draw this picture
+ 
+
+ align:start position:0%
+there's no way you can draw this picture
+without crossing the indifference curves
+
+ align:start position:0%
+without crossing the indifference curves
+ 
+
+ align:start position:0%
+without crossing the indifference curves
+and have a tangent at the two choices
+
+ align:start position:0%
+and have a tangent at the two choices
+ 
+
+ align:start position:0%
+and have a tangent at the two choices
+well we learned right in lecture two
+
+ align:start position:0%
+well we learned right in lecture two
+ 
+
+ align:start position:0%
+well we learned right in lecture two
+that indifference curves can't cross for
+
+ align:start position:0%
+that indifference curves can't cross for
+ 
+
+ align:start position:0%
+that indifference curves can't cross for
+rational consumers
+
+ align:start position:0%
+rational consumers
+ 
+
+ align:start position:0%
+rational consumers
+if a is preferred to b b is preferred to
+
+ align:start position:0%
+if a is preferred to b b is preferred to
+ 
+
+ align:start position:0%
+if a is preferred to b b is preferred to
+z a is preferred to c you may remember
+
+ align:start position:0%
+z a is preferred to c you may remember
+ 
+
+ align:start position:0%
+z a is preferred to c you may remember
+that diagram
+
+ align:start position:0%
+that diagram
+ 
+
+ align:start position:0%
+that diagram
+so that's meant to be an intuitive proof
+
+ align:start position:0%
+so that's meant to be an intuitive proof
+ 
+
+ align:start position:0%
+so that's meant to be an intuitive proof
+of the picture
+
+ align:start position:0%
+of the picture
+ 
+
+ align:start position:0%
+of the picture
+of the proposition
+
+ align:start position:0%
+of the proposition
+ 
+
+ align:start position:0%
+of the proposition
+so in conclusion for the weak axiom
+
+ align:start position:0%
+so in conclusion for the weak axiom
+ 
+
+ align:start position:0%
+so in conclusion for the weak axiom
+if the agent has preferences which are
+
+ align:start position:0%
+if the agent has preferences which are
+ 
+
+ align:start position:0%
+if the agent has preferences which are
+locally non-satiated and rational then
+
+ align:start position:0%
+locally non-satiated and rational then
+ 
+
+ align:start position:0%
+locally non-satiated and rational then
+given you know observations on prices
+
+ align:start position:0%
+given you know observations on prices
+ 
+
+ align:start position:0%
+given you know observations on prices
+expenditures and wealth you must have
+
+ align:start position:0%
+expenditures and wealth you must have
+ 
+
+ align:start position:0%
+expenditures and wealth you must have
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+pairs of data points satisfy this weak
+
+ align:start position:0%
+pairs of data points satisfy this weak
+ 
+
+ align:start position:0%
+pairs of data points satisfy this weak
+axiom of revealed preference warp
+
+ align:start position:0%
+axiom of revealed preference warp
+ 
+
+ align:start position:0%
+axiom of revealed preference warp
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so now we want to generalize
+
+ align:start position:0%
+all right so now we want to generalize
+ 
+
+ align:start position:0%
+all right so now we want to generalize
+we have here still two data points just
+
+ align:start position:0%
+we have here still two data points just
+ 
+
+ align:start position:0%
+we have here still two data points just
+slightly different notation
+
+ align:start position:0%
+slightly different notation
+ 
+
+ align:start position:0%
+slightly different notation
+the data points are indexed by t and s
+
+ align:start position:0%
+the data points are indexed by t and s
+ 
+
+ align:start position:0%
+the data points are indexed by t and s
+and we write
+
+ align:start position:0%
+and we write
+ 
+
+ align:start position:0%
+and we write
+that the t data point of x is revealed
+
+ align:start position:0%
+that the t data point of x is revealed
+ 
+
+ align:start position:0%
+that the t data point of x is revealed
+directly preferred to the data point
+
+ align:start position:0%
+directly preferred to the data point
+ 
+
+ align:start position:0%
+directly preferred to the data point
+indexed by s
+
+ align:start position:0%
+indexed by s
+ 
+
+ align:start position:0%
+indexed by s
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+x is available and price is p t
+
+ align:start position:0%
+x is available and price is p t
+ 
+
+ align:start position:0%
+x is available and price is p t
+so again at prices pt they chose xt
+
+ align:start position:0%
+so again at prices pt they chose xt
+ 
+
+ align:start position:0%
+so again at prices pt they chose xt
+that's the way the data are organized
+
+ align:start position:0%
+that's the way the data are organized
+ 
+
+ align:start position:0%
+that's the way the data are organized
+they could have chosen xs because it's
+
+ align:start position:0%
+they could have chosen xs because it's
+ 
+
+ align:start position:0%
+they could have chosen xs because it's
+in the budget but they didn't do it
+
+ align:start position:0%
+in the budget but they didn't do it
+ 
+
+ align:start position:0%
+in the budget but they didn't do it
+so we say you know directly revealed
+
+ align:start position:0%
+so we say you know directly revealed
+ 
+
+ align:start position:0%
+so we say you know directly revealed
+preferred
+
+ align:start position:0%
+preferred
+ 
+
+ align:start position:0%
+preferred
+this might imply strict preference but
+
+ align:start position:0%
+this might imply strict preference but
+ 
+
+ align:start position:0%
+this might imply strict preference but
+you know it doesn't really mean that it
+
+ align:start position:0%
+you know it doesn't really mean that it
+ 
+
+ align:start position:0%
+you know it doesn't really mean that it
+just means as with the axioms of
+
+ align:start position:0%
+just means as with the axioms of
+ 
+
+ align:start position:0%
+just means as with the axioms of
+revealed preference
+
+ align:start position:0%
+revealed preference
+ 
+
+ align:start position:0%
+revealed preference
+what we see is what they want that's all
+
+ align:start position:0%
+what we see is what they want that's all
+ 
+
+ align:start position:0%
+what we see is what they want that's all
+we're saying
+
+ align:start position:0%
+we're saying
+ 
+
+ align:start position:0%
+we're saying
+they're revealed to prefer it then you
+
+ align:start position:0%
+they're revealed to prefer it then you
+ 
+
+ align:start position:0%
+they're revealed to prefer it then you
+know they continue to prefer it
+
+ align:start position:0%
+know they continue to prefer it
+ 
+
+ align:start position:0%
+know they continue to prefer it
+in this case they prefer it over other
+
+ align:start position:0%
+in this case they prefer it over other
+ 
+
+ align:start position:0%
+in this case they prefer it over other
+things they could have chosen and didn't
+
+ align:start position:0%
+things they could have chosen and didn't
+ 
+
+ align:start position:0%
+things they could have chosen and didn't
+pretty simple-minded
+
+ align:start position:0%
+pretty simple-minded
+ 
+
+ align:start position:0%
+pretty simple-minded
+then we come to
+
+ align:start position:0%
+then we come to
+ 
+
+ align:start position:0%
+then we come to
+i almost want to say indirectly revealed
+
+ align:start position:0%
+i almost want to say indirectly revealed
+ 
+
+ align:start position:0%
+i almost want to say indirectly revealed
+preferred actually it's in parentheses
+
+ align:start position:0%
+preferred actually it's in parentheses
+ 
+
+ align:start position:0%
+preferred actually it's in parentheses
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+to contrast with the directly revealed
+
+ align:start position:0%
+to contrast with the directly revealed
+ 
+
+ align:start position:0%
+to contrast with the directly revealed
+preferred so now we're going to have a
+
+ align:start position:0%
+preferred so now we're going to have a
+ 
+
+ align:start position:0%
+preferred so now we're going to have a
+bigger data set we're going to have a
+
+ align:start position:0%
+bigger data set we're going to have a
+ 
+
+ align:start position:0%
+bigger data set we're going to have a
+whole sequence and we say that x t with
+
+ align:start position:0%
+whole sequence and we say that x t with
+ 
+
+ align:start position:0%
+whole sequence and we say that x t with
+r without the d
+
+ align:start position:0%
+r without the d
+ 
+
+ align:start position:0%
+r without the d
+just revealed preferred not directly
+
+ align:start position:0%
+just revealed preferred not directly
+ 
+
+ align:start position:0%
+just revealed preferred not directly
+preferred or if you like i for
+
+ align:start position:0%
+preferred or if you like i for
+ 
+
+ align:start position:0%
+preferred or if you like i for
+indirectly preferred
+
+ align:start position:0%
+indirectly preferred
+ 
+
+ align:start position:0%
+indirectly preferred
+xt is revealed prefer to access if
+
+ align:start position:0%
+xt is revealed prefer to access if
+ 
+
+ align:start position:0%
+xt is revealed prefer to access if
+we have a sequence of data points such
+
+ align:start position:0%
+we have a sequence of data points such
+ 
+
+ align:start position:0%
+we have a sequence of data points such
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+pairwise we have direct revelation
+
+ align:start position:0%
+pairwise we have direct revelation
+ 
+
+ align:start position:0%
+pairwise we have direct revelation
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we want xt to at the beginning to can be
+
+ align:start position:0%
+we want xt to at the beginning to can be
+ 
+
+ align:start position:0%
+we want xt to at the beginning to can be
+compared to xs at the end
+
+ align:start position:0%
+compared to xs at the end
+ 
+
+ align:start position:0%
+compared to xs at the end
+but we do that we never see say in the
+
+ align:start position:0%
+but we do that we never see say in the
+ 
+
+ align:start position:0%
+but we do that we never see say in the
+data that they're
+
+ align:start position:0%
+data that they're
+ 
+
+ align:start position:0%
+data that they're
+directly comparable
+
+ align:start position:0%
+directly comparable
+ 
+
+ align:start position:0%
+directly comparable
+instead we see xt
+
+ align:start position:0%
+instead we see xt
+ 
+
+ align:start position:0%
+instead we see xt
+in a situation where
+
+ align:start position:0%
+in a situation where
+ 
+
+ align:start position:0%
+in a situation where
+within the budget xt is revealed
+
+ align:start position:0%
+within the budget xt is revealed
+ 
+
+ align:start position:0%
+within the budget xt is revealed
+directly preferred to xr1 in another
+
+ align:start position:0%
+directly preferred to xr1 in another
+ 
+
+ align:start position:0%
+directly preferred to xr1 in another
+piece of the data we see xr1 is revealed
+
+ align:start position:0%
+piece of the data we see xr1 is revealed
+ 
+
+ align:start position:0%
+piece of the data we see xr1 is revealed
+directly preferred to xr2 and so on down
+
+ align:start position:0%
+directly preferred to xr2 and so on down
+ 
+
+ align:start position:0%
+directly preferred to xr2 and so on down
+the chain
+
+ align:start position:0%
+the chain
+ 
+
+ align:start position:0%
+the chain
+with xrk being revealed directly
+
+ align:start position:0%
+with xrk being revealed directly
+ 
+
+ align:start position:0%
+with xrk being revealed directly
+preferred to xs
+
+ align:start position:0%
+preferred to xs
+ 
+
+ align:start position:0%
+preferred to xs
+this is like the transitivity axiom
+
+ align:start position:0%
+this is like the transitivity axiom
+ 
+
+ align:start position:0%
+this is like the transitivity axiom
+which is part of the axioms of a
+
+ align:start position:0%
+which is part of the axioms of a
+ 
+
+ align:start position:0%
+which is part of the axioms of a
+rational consumer
+
+ align:start position:0%
+rational consumer
+ 
+
+ align:start position:0%
+rational consumer
+right we have a chain in which we have
+
+ align:start position:0%
+right we have a chain in which we have
+ 
+
+ align:start position:0%
+right we have a chain in which we have
+directly revealed preference hence the
+
+ align:start position:0%
+directly revealed preference hence the
+ 
+
+ align:start position:0%
+directly revealed preference hence the
+one at the beginning ought to be
+
+ align:start position:0%
+one at the beginning ought to be
+ 
+
+ align:start position:0%
+one at the beginning ought to be
+indirectly revealed preferred to the one
+
+ align:start position:0%
+indirectly revealed preferred to the one
+ 
+
+ align:start position:0%
+indirectly revealed preferred to the one
+at the end xt access
+
+ align:start position:0%
+at the end xt access
+ 
+
+ align:start position:0%
+at the end xt access
+okay so then we come to the
+
+ align:start position:0%
+okay so then we come to the
+ 
+
+ align:start position:0%
+okay so then we come to the
+generalized axiom of revealed preference
+
+ align:start position:0%
+generalized axiom of revealed preference
+ 
+
+ align:start position:0%
+generalized axiom of revealed preference
+called garp so i don't know there was a
+
+ align:start position:0%
+called garp so i don't know there was a
+ 
+
+ align:start position:0%
+called garp so i don't know there was a
+famous movie the world according to garp
+
+ align:start position:0%
+famous movie the world according to garp
+ 
+
+ align:start position:0%
+famous movie the world according to garp
+i don't know if you was a robin williams
+
+ align:start position:0%
+i don't know if you was a robin williams
+ 
+
+ align:start position:0%
+i don't know if you was a robin williams
+movie they didn't mean this so
+
+ align:start position:0%
+movie they didn't mean this so
+ 
+
+ align:start position:0%
+movie they didn't mean this so
+generalized revealed preference
+
+ align:start position:0%
+generalized revealed preference
+ 
+
+ align:start position:0%
+generalized revealed preference
+is building on this notion of indirectly
+
+ align:start position:0%
+is building on this notion of indirectly
+ 
+
+ align:start position:0%
+is building on this notion of indirectly
+revealed preference
+
+ align:start position:0%
+revealed preference
+ 
+
+ align:start position:0%
+revealed preference
+if we have the data point so the
+
+ align:start position:0%
+if we have the data point so the
+ 
+
+ align:start position:0%
+if we have the data point so the
+dimensionality of the data set is
+
+ align:start position:0%
+dimensionality of the data set is
+ 
+
+ align:start position:0%
+dimensionality of the data set is
+capital t
+
+ align:start position:0%
+capital t
+ 
+
+ align:start position:0%
+capital t
+and we have prices and demands for each
+
+ align:start position:0%
+and we have prices and demands for each
+ 
+
+ align:start position:0%
+and we have prices and demands for each
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+then the general axiom of real
+
+ align:start position:0%
+then the general axiom of real
+ 
+
+ align:start position:0%
+then the general axiom of real
+preference
+
+ align:start position:0%
+preference
+ 
+
+ align:start position:0%
+preference
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+if x t is indirectly revealed to x s
+
+ align:start position:0%
+if x t is indirectly revealed to x s
+ 
+
+ align:start position:0%
+if x t is indirectly revealed to x s
+then if we're able to make the
+
+ align:start position:0%
+then if we're able to make the
+ 
+
+ align:start position:0%
+then if we're able to make the
+comparison we have the strict inequality
+
+ align:start position:0%
+comparison we have the strict inequality
+ 
+
+ align:start position:0%
+comparison we have the strict inequality
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+x t is preferred to access it better be
+
+ align:start position:0%
+x t is preferred to access it better be
+ 
+
+ align:start position:0%
+x t is preferred to access it better be
+the case that at price's ps xt is
+
+ align:start position:0%
+the case that at price's ps xt is
+ 
+
+ align:start position:0%
+the case that at price's ps xt is
+outside the budget relative to the
+
+ align:start position:0%
+outside the budget relative to the
+ 
+
+ align:start position:0%
+outside the budget relative to the
+expenditures on xs and the intuition as
+
+ align:start position:0%
+expenditures on xs and the intuition as
+ 
+
+ align:start position:0%
+expenditures on xs and the intuition as
+i wrote in red at the bottom of the
+
+ align:start position:0%
+i wrote in red at the bottom of the
+ 
+
+ align:start position:0%
+i wrote in red at the bottom of the
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+is simply imagine this inequality is
+
+ align:start position:0%
+is simply imagine this inequality is
+ 
+
+ align:start position:0%
+is simply imagine this inequality is
+reversed then we would have at prices ps
+
+ align:start position:0%
+reversed then we would have at prices ps
+ 
+
+ align:start position:0%
+reversed then we would have at prices ps
+xt is within the budget and xs ought to
+
+ align:start position:0%
+xt is within the budget and xs ought to
+ 
+
+ align:start position:0%
+xt is within the budget and xs ought to
+be at least weekly if not strictly
+
+ align:start position:0%
+be at least weekly if not strictly
+ 
+
+ align:start position:0%
+be at least weekly if not strictly
+preferred
+
+ align:start position:0%
+preferred
+ 
+
+ align:start position:0%
+preferred
+because xs was chosen and xt was
+
+ align:start position:0%
+because xs was chosen and xt was
+ 
+
+ align:start position:0%
+because xs was chosen and xt was
+available so xs would be
+
+ align:start position:0%
+available so xs would be
+ 
+
+ align:start position:0%
+available so xs would be
+directly revealed to be preferred to x t
+
+ align:start position:0%
+directly revealed to be preferred to x t
+ 
+
+ align:start position:0%
+directly revealed to be preferred to x t
+according to this definition but it goes
+
+ align:start position:0%
+according to this definition but it goes
+ 
+
+ align:start position:0%
+according to this definition but it goes
+the other way here where
+
+ align:start position:0%
+the other way here where
+ 
+
+ align:start position:0%
+the other way here where
+x t is revealed granted indirectly to be
+
+ align:start position:0%
+x t is revealed granted indirectly to be
+ 
+
+ align:start position:0%
+x t is revealed granted indirectly to be
+preferred to excess so that if this were
+
+ align:start position:0%
+preferred to excess so that if this were
+ 
+
+ align:start position:0%
+preferred to excess so that if this were
+a weak inequality a strict inequality
+
+ align:start position:0%
+a weak inequality a strict inequality
+ 
+
+ align:start position:0%
+a weak inequality a strict inequality
+going the other way we would intuitively
+
+ align:start position:0%
+going the other way we would intuitively
+ 
+
+ align:start position:0%
+going the other way we would intuitively
+violate these two pieces of information
+
+ align:start position:0%
+violate these two pieces of information
+ 
+
+ align:start position:0%
+violate these two pieces of information
+would not be consistent with each other
+
+ align:start position:0%
+would not be consistent with each other
+ 
+
+ align:start position:0%
+would not be consistent with each other
+now again you should think about this as
+
+ align:start position:0%
+now again you should think about this as
+ 
+
+ align:start position:0%
+now again you should think about this as
+an algorithm you know i just some
+
+ align:start position:0%
+an algorithm you know i just some
+ 
+
+ align:start position:0%
+an algorithm you know i just some
+classes do this i found one on the web
+
+ align:start position:0%
+classes do this i found one on the web
+ 
+
+ align:start position:0%
+classes do this i found one on the web
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+they give students a very large data set
+
+ align:start position:0%
+they give students a very large data set
+ 
+
+ align:start position:0%
+they give students a very large data set
+of prices and quantities and that's to
+
+ align:start position:0%
+of prices and quantities and that's to
+ 
+
+ align:start position:0%
+of prices and quantities and that's to
+ask them is this consistent with a
+
+ align:start position:0%
+ask them is this consistent with a
+ 
+
+ align:start position:0%
+ask them is this consistent with a
+rational household
+
+ align:start position:0%
+rational household
+ 
+
+ align:start position:0%
+rational household
+and how do you approach that well you
+
+ align:start position:0%
+and how do you approach that well you
+ 
+
+ align:start position:0%
+and how do you approach that well you
+start looking for these chains you have
+
+ align:start position:0%
+start looking for these chains you have
+ 
+
+ align:start position:0%
+start looking for these chains you have
+to construct them algorithmically
+
+ align:start position:0%
+to construct them algorithmically
+ 
+
+ align:start position:0%
+to construct them algorithmically
+and get you know as a result when it's
+
+ align:start position:0%
+and get you know as a result when it's
+ 
+
+ align:start position:0%
+and get you know as a result when it's
+true a statement about x and t
+
+ align:start position:0%
+true a statement about x and t
+ 
+
+ align:start position:0%
+true a statement about x and t
+indirectly revealed preferred and then
+
+ align:start position:0%
+indirectly revealed preferred and then
+ 
+
+ align:start position:0%
+indirectly revealed preferred and then
+in the same data set go looking for an
+
+ align:start position:0%
+in the same data set go looking for an
+ 
+
+ align:start position:0%
+in the same data set go looking for an
+instance where there was a direct
+
+ align:start position:0%
+instance where there was a direct
+ 
+
+ align:start position:0%
+instance where there was a direct
+comparison and it better be that the
+
+ align:start position:0%
+comparison and it better be that the
+ 
+
+ align:start position:0%
+comparison and it better be that the
+inequality is weakly going this
+
+ align:start position:0%
+inequality is weakly going this
+ 
+
+ align:start position:0%
+inequality is weakly going this
+direction so it's an algorithm i'm
+
+ align:start position:0%
+direction so it's an algorithm i'm
+ 
+
+ align:start position:0%
+direction so it's an algorithm i'm
+trying to say
+
+ align:start position:0%
+trying to say
+ 
+
+ align:start position:0%
+trying to say
+because again if it doesn't go in this
+
+ align:start position:0%
+because again if it doesn't go in this
+ 
+
+ align:start position:0%
+because again if it doesn't go in this
+direction then it kind of contradicts
+
+ align:start position:0%
+direction then it kind of contradicts
+ 
+
+ align:start position:0%
+direction then it kind of contradicts
+the whole notion of revealed preference
+
+ align:start position:0%
+the whole notion of revealed preference
+ 
+
+ align:start position:0%
+the whole notion of revealed preference
+and transitivity
+
+ align:start position:0%
+and transitivity
+ 
+
+ align:start position:0%
+and transitivity
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again good news ironically
+
+ align:start position:0%
+again good news ironically
+ 
+
+ align:start position:0%
+again good news ironically
+we are potentially able to reject there
+
+ align:start position:0%
+we are potentially able to reject there
+ 
+
+ align:start position:0%
+we are potentially able to reject there
+are comparisons in the data which if if
+
+ align:start position:0%
+are comparisons in the data which if if
+ 
+
+ align:start position:0%
+are comparisons in the data which if if
+this inequality goes the other way would
+
+ align:start position:0%
+this inequality goes the other way would
+ 
+
+ align:start position:0%
+this inequality goes the other way would
+tell us there's no way that this data
+
+ align:start position:0%
+tell us there's no way that this data
+ 
+
+ align:start position:0%
+tell us there's no way that this data
+came from a rational maximizing consumer
+
+ align:start position:0%
+came from a rational maximizing consumer
+ 
+
+ align:start position:0%
+came from a rational maximizing consumer
+and that's good for us now it doesn't
+
+ align:start position:0%
+and that's good for us now it doesn't
+ 
+
+ align:start position:0%
+and that's good for us now it doesn't
+mean that in any given data set you will
+
+ align:start position:0%
+mean that in any given data set you will
+ 
+
+ align:start position:0%
+mean that in any given data set you will
+necessarily find a violation but you and
+
+ align:start position:0%
+necessarily find a violation but you and
+ 
+
+ align:start position:0%
+necessarily find a violation but you and
+you end up with a weak statement that
+
+ align:start position:0%
+you end up with a weak statement that
+ 
+
+ align:start position:0%
+you end up with a weak statement that
+the data set look as if there was
+
+ align:start position:0%
+the data set look as if there was
+ 
+
+ align:start position:0%
+the data set look as if there was
+nothing inconsistent in this data with
+
+ align:start position:0%
+nothing inconsistent in this data with
+ 
+
+ align:start position:0%
+nothing inconsistent in this data with
+respect to the statement that they came
+
+ align:start position:0%
+respect to the statement that they came
+ 
+
+ align:start position:0%
+respect to the statement that they came
+from a rational maximizing consumer
+
+ align:start position:0%
+from a rational maximizing consumer
+ 
+
+ align:start position:0%
+from a rational maximizing consumer
+so we should check and make sure that
+
+ align:start position:0%
+so we should check and make sure that
+ 
+
+ align:start position:0%
+so we should check and make sure that
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+so that's the spirit of it
+
+ align:start position:0%
+so that's the spirit of it
+ 
+
+ align:start position:0%
+so that's the spirit of it
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let me get to the computational part
+
+ align:start position:0%
+so let me get to the computational part
+ 
+
+ align:start position:0%
+so let me get to the computational part
+these guys at caltech consumer theory
+
+ align:start position:0%
+these guys at caltech consumer theory
+ 
+
+ align:start position:0%
+these guys at caltech consumer theory
+assumes consumers possess infinite
+
+ align:start position:0%
+assumes consumers possess infinite
+ 
+
+ align:start position:0%
+assumes consumers possess infinite
+computational abilities like they can
+
+ align:start position:0%
+computational abilities like they can
+ 
+
+ align:start position:0%
+computational abilities like they can
+solve max problems and potentially hard
+
+ align:start position:0%
+solve max problems and potentially hard
+ 
+
+ align:start position:0%
+solve max problems and potentially hard
+problems proponents of bounded
+
+ align:start position:0%
+problems proponents of bounded
+ 
+
+ align:start position:0%
+problems proponents of bounded
+rationality want to require that any
+
+ align:start position:0%
+rationality want to require that any
+ 
+
+ align:start position:0%
+rationality want to require that any
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+model of consumer behavior incorporate
+
+ align:start position:0%
+model of consumer behavior incorporate
+ 
+
+ align:start position:0%
+model of consumer behavior incorporate
+computational constraints
+
+ align:start position:0%
+computational constraints
+ 
+
+ align:start position:0%
+computational constraints
+in other words they may not be able to
+
+ align:start position:0%
+in other words they may not be able to
+ 
+
+ align:start position:0%
+in other words they may not be able to
+solve a hard problem
+
+ align:start position:0%
+solve a hard problem
+ 
+
+ align:start position:0%
+solve a hard problem
+they may choose something but it
+
+ align:start position:0%
+they may choose something but it
+ 
+
+ align:start position:0%
+they may choose something but it
+wouldn't be the full solution because
+
+ align:start position:0%
+wouldn't be the full solution because
+ 
+
+ align:start position:0%
+wouldn't be the full solution because
+they're not able to compute it
+
+ align:start position:0%
+they're not able to compute it
+ 
+
+ align:start position:0%
+they're not able to compute it
+and nichinike and his co-authors are
+
+ align:start position:0%
+and nichinike and his co-authors are
+ 
+
+ align:start position:0%
+and nichinike and his co-authors are
+saying that's false
+
+ align:start position:0%
+saying that's false
+ 
+
+ align:start position:0%
+saying that's false
+very much in the spirit of revealed
+
+ align:start position:0%
+very much in the spirit of revealed
+ 
+
+ align:start position:0%
+very much in the spirit of revealed
+preference any consumption data set that
+
+ align:start position:0%
+preference any consumption data set that
+ 
+
+ align:start position:0%
+preference any consumption data set that
+is compatible with a rational consumer
+
+ align:start position:0%
+is compatible with a rational consumer
+ 
+
+ align:start position:0%
+is compatible with a rational consumer
+excuse me it is also compatible with a
+
+ align:start position:0%
+excuse me it is also compatible with a
+ 
+
+ align:start position:0%
+excuse me it is also compatible with a
+rational and computationally bounded
+
+ align:start position:0%
+rational and computationally bounded
+ 
+
+ align:start position:0%
+rational and computationally bounded
+consumer that is to say the data set in
+
+ align:start position:0%
+consumer that is to say the data set in
+ 
+
+ align:start position:0%
+consumer that is to say the data set in
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+can always be rationalized by a utility
+
+ align:start position:0%
+can always be rationalized by a utility
+ 
+
+ align:start position:0%
+can always be rationalized by a utility
+function that's pretty easy to solve
+
+ align:start position:0%
+function that's pretty easy to solve
+ 
+
+ align:start position:0%
+function that's pretty easy to solve
+meaning solved in polynomial time
+
+ align:start position:0%
+meaning solved in polynomial time
+ 
+
+ align:start position:0%
+meaning solved in polynomial time
+so this is very much like not being able
+
+ align:start position:0%
+so this is very much like not being able
+ 
+
+ align:start position:0%
+so this is very much like not being able
+to test the convexity of preferences
+
+ align:start position:0%
+to test the convexity of preferences
+ 
+
+ align:start position:0%
+to test the convexity of preferences
+you start with something non-convex but
+
+ align:start position:0%
+you start with something non-convex but
+ 
+
+ align:start position:0%
+you start with something non-convex but
+it generates a data set that could also
+
+ align:start position:0%
+it generates a data set that could also
+ 
+
+ align:start position:0%
+it generates a data set that could also
+be generated by something convex
+
+ align:start position:0%
+be generated by something convex
+ 
+
+ align:start position:0%
+be generated by something convex
+we start with something that could have
+
+ align:start position:0%
+we start with something that could have
+ 
+
+ align:start position:0%
+we start with something that could have
+come from
+
+ align:start position:0%
+come from
+ 
+
+ align:start position:0%
+come from
+the household solving a hard problem
+
+ align:start position:0%
+the household solving a hard problem
+ 
+
+ align:start position:0%
+the household solving a hard problem
+but it could also have come from a
+
+ align:start position:0%
+but it could also have come from a
+ 
+
+ align:start position:0%
+but it could also have come from a
+household solving a simpler problem
+
+ align:start position:0%
+household solving a simpler problem
+ 
+
+ align:start position:0%
+household solving a simpler problem
+i'm not giving you any intuition on this
+
+ align:start position:0%
+i'm not giving you any intuition on this
+ 
+
+ align:start position:0%
+i'm not giving you any intuition on this
+right now i'm telling you what these
+
+ align:start position:0%
+right now i'm telling you what these
+ 
+
+ align:start position:0%
+right now i'm telling you what these
+computer scientists have figured out and
+
+ align:start position:0%
+computer scientists have figured out and
+ 
+
+ align:start position:0%
+computer scientists have figured out and
+again their matrix
+
+ align:start position:0%
+again their matrix
+ 
+
+ align:start position:0%
+again their matrix
+their metric is how hard is it to solve
+
+ align:start position:0%
+their metric is how hard is it to solve
+ 
+
+ align:start position:0%
+their metric is how hard is it to solve
+the problem you know it's sort of
+
+ align:start position:0%
+the problem you know it's sort of
+ 
+
+ align:start position:0%
+the problem you know it's sort of
+looking at derivatives and so on how
+
+ align:start position:0%
+looking at derivatives and so on how
+ 
+
+ align:start position:0%
+looking at derivatives and so on how
+long does it take as we say increase the
+
+ align:start position:0%
+long does it take as we say increase the
+ 
+
+ align:start position:0%
+long does it take as we say increase the
+number of goods
+
+ align:start position:0%
+number of goods
+ 
+
+ align:start position:0%
+number of goods
+if it's exponential it's bad if it's
+
+ align:start position:0%
+if it's exponential it's bad if it's
+ 
+
+ align:start position:0%
+if it's exponential it's bad if it's
+polynomial it's good all right another
+
+ align:start position:0%
+polynomial it's good all right another
+ 
+
+ align:start position:0%
+polynomial it's good all right another
+version of this instead of having a
+
+ align:start position:0%
+version of this instead of having a
+ 
+
+ align:start position:0%
+version of this instead of having a
+single household maximizing or otherwise
+
+ align:start position:0%
+single household maximizing or otherwise
+ 
+
+ align:start position:0%
+single household maximizing or otherwise
+we have multiple agents interacting in a
+
+ align:start position:0%
+we have multiple agents interacting in a
+ 
+
+ align:start position:0%
+we have multiple agents interacting in a
+market economy we want to say
+
+ align:start position:0%
+market economy we want to say
+ 
+
+ align:start position:0%
+market economy we want to say
+if possible that the observed market
+
+ align:start position:0%
+if possible that the observed market
+ 
+
+ align:start position:0%
+if possible that the observed market
+outcomes are consistent not only with
+
+ align:start position:0%
+outcomes are consistent not only with
+ 
+
+ align:start position:0%
+outcomes are consistent not only with
+individual maximization but with a
+
+ align:start position:0%
+individual maximization but with a
+ 
+
+ align:start position:0%
+individual maximization but with a
+volrazian equilibrium
+
+ align:start position:0%
+volrazian equilibrium
+ 
+
+ align:start position:0%
+volrazian equilibrium
+so what is the empirical content is it
+
+ align:start position:0%
+so what is the empirical content is it
+ 
+
+ align:start position:0%
+so what is the empirical content is it
+really hard to solve the general
+
+ align:start position:0%
+really hard to solve the general
+ 
+
+ align:start position:0%
+really hard to solve the general
+equilibrium computationally in which
+
+ align:start position:0%
+equilibrium computationally in which
+ 
+
+ align:start position:0%
+equilibrium computationally in which
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+it's not likely we're going to be able
+
+ align:start position:0%
+it's not likely we're going to be able
+ 
+
+ align:start position:0%
+it's not likely we're going to be able
+to accept in the data that it came from
+
+ align:start position:0%
+to accept in the data that it came from
+ 
+
+ align:start position:0%
+to accept in the data that it came from
+the underlying economy or it's a version
+
+ align:start position:0%
+the underlying economy or it's a version
+ 
+
+ align:start position:0%
+the underlying economy or it's a version
+of the individual maximization problem
+
+ align:start position:0%
+of the individual maximization problem
+ 
+
+ align:start position:0%
+of the individual maximization problem
+that there's another economy which is
+
+ align:start position:0%
+that there's another economy which is
+ 
+
+ align:start position:0%
+that there's another economy which is
+actually easy easier to solve that could
+
+ align:start position:0%
+actually easy easier to solve that could
+ 
+
+ align:start position:0%
+actually easy easier to solve that could
+have generated the same data
+
+ align:start position:0%
+have generated the same data
+ 
+
+ align:start position:0%
+have generated the same data
+this is totally remarkable stuff
+
+ align:start position:0%
+this is totally remarkable stuff
+ 
+
+ align:start position:0%
+this is totally remarkable stuff
+because it goes against the grain of the
+
+ align:start position:0%
+because it goes against the grain of the
+ 
+
+ align:start position:0%
+because it goes against the grain of the
+way one would like to think about it a
+
+ align:start position:0%
+way one would like to think about it a
+ 
+
+ align:start position:0%
+way one would like to think about it a
+rational as rational as consumers can
+
+ align:start position:0%
+rational as rational as consumers can
+ 
+
+ align:start position:0%
+rational as rational as consumers can
+possibly be
+
+ align:start position:0%
+possibly be
+ 
+
+ align:start position:0%
+possibly be
+it's unlikely they can solve in their
+
+ align:start position:0%
+it's unlikely they can solve in their
+ 
+
+ align:start position:0%
+it's unlikely they can solve in their
+minds problems that prove intractable
+
+ align:start position:0%
+minds problems that prove intractable
+ 
+
+ align:start position:0%
+minds problems that prove intractable
+for computer scientists equipped with
+
+ align:start position:0%
+for computer scientists equipped with
+ 
+
+ align:start position:0%
+for computer scientists equipped with
+the latest technology it's a cool
+
+ align:start position:0%
+the latest technology it's a cool
+ 
+
+ align:start position:0%
+the latest technology it's a cool
+statement these are really famous
+
+ align:start position:0%
+statement these are really famous
+ 
+
+ align:start position:0%
+statement these are really famous
+theorists by the way
+
+ align:start position:0%
+theorists by the way
+ 
+
+ align:start position:0%
+theorists by the way
+gilboa schmeidler and possibly
+
+ align:start position:0%
+gilboa schmeidler and possibly
+ 
+
+ align:start position:0%
+gilboa schmeidler and possibly
+solve in their minds get it
+
+ align:start position:0%
+solve in their minds get it
+ 
+
+ align:start position:0%
+solve in their minds get it
+the way what you would need for a you
+
+ align:start position:0%
+the way what you would need for a you
+ 
+
+ align:start position:0%
+the way what you would need for a you
+know a supercomputer
+
+ align:start position:0%
+know a supercomputer
+ 
+
+ align:start position:0%
+know a supercomputer
+if an equilibrium is not efficiently
+
+ align:start position:0%
+if an equilibrium is not efficiently
+ 
+
+ align:start position:0%
+if an equilibrium is not efficiently
+computed this is the market version
+
+ align:start position:0%
+computed this is the market version
+ 
+
+ align:start position:0%
+computed this is the market version
+much of the credibility of using the
+
+ align:start position:0%
+much of the credibility of using the
+ 
+
+ align:start position:0%
+much of the credibility of using the
+predicate that we have rational agents
+
+ align:start position:0%
+predicate that we have rational agents
+ 
+
+ align:start position:0%
+predicate that we have rational agents
+is lost and a shorthand version of that
+
+ align:start position:0%
+is lost and a shorthand version of that
+ 
+
+ align:start position:0%
+is lost and a shorthand version of that
+if your laptop can't find it neither can
+
+ align:start position:0%
+if your laptop can't find it neither can
+ 
+
+ align:start position:0%
+if your laptop can't find it neither can
+the market but these guys are saying
+
+ align:start position:0%
+the market but these guys are saying
+ 
+
+ align:start position:0%
+the market but these guys are saying
+that's just wrong it's just completely
+
+ align:start position:0%
+that's just wrong it's just completely
+ 
+
+ align:start position:0%
+that's just wrong it's just completely
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+because they misunderstand the role of
+
+ align:start position:0%
+because they misunderstand the role of
+ 
+
+ align:start position:0%
+because they misunderstand the role of
+models in economics which is as if the
+
+ align:start position:0%
+models in economics which is as if the
+ 
+
+ align:start position:0%
+models in economics which is as if the
+model were a reality
+
+ align:start position:0%
+model were a reality
+ 
+
+ align:start position:0%
+model were a reality
+then there are restrictions on data it
+
+ align:start position:0%
+then there are restrictions on data it
+ 
+
+ align:start position:0%
+then there are restrictions on data it
+is not a statement that we have all of
+
+ align:start position:0%
+is not a statement that we have all of
+ 
+
+ align:start position:0%
+is not a statement that we have all of
+the reality captured in the model
+
+ align:start position:0%
+the reality captured in the model
+ 
+
+ align:start position:0%
+the reality captured in the model
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+reality behaves as if the theory were
+
+ align:start position:0%
+reality behaves as if the theory were
+ 
+
+ align:start position:0%
+reality behaves as if the theory were
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+a consumption data set
+
+ align:start position:0%
+a consumption data set
+ 
+
+ align:start position:0%
+a consumption data set
+is either not rationalizable at all so
+
+ align:start position:0%
+is either not rationalizable at all so
+ 
+
+ align:start position:0%
+is either not rationalizable at all so
+that's the rejection part they're not
+
+ align:start position:0%
+that's the rejection part they're not
+ 
+
+ align:start position:0%
+that's the rejection part they're not
+going to overturn that there's still
+
+ align:start position:0%
+going to overturn that there's still
+ 
+
+ align:start position:0%
+going to overturn that there's still
+content it's either not rationalizable
+
+ align:start position:0%
+content it's either not rationalizable
+ 
+
+ align:start position:0%
+content it's either not rationalizable
+at all or
+
+ align:start position:0%
+at all or
+ 
+
+ align:start position:0%
+at all or
+it's rationalizable by a utility
+
+ align:start position:0%
+it's rationalizable by a utility
+ 
+
+ align:start position:0%
+it's rationalizable by a utility
+function that's fairly easy to maximize
+
+ align:start position:0%
+function that's fairly easy to maximize
+ 
+
+ align:start position:0%
+function that's fairly easy to maximize
+when i show you these slides i kind of
+
+ align:start position:0%
+when i show you these slides i kind of
+ 
+
+ align:start position:0%
+when i show you these slides i kind of
+want to show you more but i guess we
+
+ align:start position:0%
+want to show you more but i guess we
+ 
+
+ align:start position:0%
+want to show you more but i guess we
+have limited time so i probably should
+
+ align:start position:0%
+have limited time so i probably should
+ 
+
+ align:start position:0%
+have limited time so i probably should
+have put this paper on the reading list
+
+ align:start position:0%
+have put this paper on the reading list
+ 
+
+ align:start position:0%
+have put this paper on the reading list
+as optional
+
+ align:start position:0%
+as optional
+ 
+
+ align:start position:0%
+as optional
+okay so let's go to general equilibrium
+
+ align:start position:0%
+okay so let's go to general equilibrium
+ 
+
+ align:start position:0%
+okay so let's go to general equilibrium
+in a paper of brown and matskin which
+
+ align:start position:0%
+in a paper of brown and matskin which
+ 
+
+ align:start position:0%
+in a paper of brown and matskin which
+all things considered relatively recent
+
+ align:start position:0%
+all things considered relatively recent
+ 
+
+ align:start position:0%
+all things considered relatively recent
+suppose we're given data set on a number
+
+ align:start position:0%
+suppose we're given data set on a number
+ 
+
+ align:start position:0%
+suppose we're given data set on a number
+of households capital i in the economy
+
+ align:start position:0%
+of households capital i in the economy
+ 
+
+ align:start position:0%
+of households capital i in the economy
+and we see their individual endowments
+
+ align:start position:0%
+and we see their individual endowments
+ 
+
+ align:start position:0%
+and we see their individual endowments
+private ownership economy
+
+ align:start position:0%
+private ownership economy
+ 
+
+ align:start position:0%
+private ownership economy
+omega i across households capital i
+
+ align:start position:0%
+omega i across households capital i
+ 
+
+ align:start position:0%
+omega i across households capital i
+then there's something
+
+ align:start position:0%
+then there's something
+ 
+
+ align:start position:0%
+then there's something
+that i'll elaborate in words now called
+
+ align:start position:0%
+that i'll elaborate in words now called
+ 
+
+ align:start position:0%
+that i'll elaborate in words now called
+anything goes
+
+ align:start position:0%
+anything goes
+ 
+
+ align:start position:0%
+anything goes
+general equilibrium theory does not put
+
+ align:start position:0%
+general equilibrium theory does not put
+ 
+
+ align:start position:0%
+general equilibrium theory does not put
+restrictions on data anything goes now
+
+ align:start position:0%
+restrictions on data anything goes now
+ 
+
+ align:start position:0%
+restrictions on data anything goes now
+and that was a killer that kind of
+
+ align:start position:0%
+and that was a killer that kind of
+ 
+
+ align:start position:0%
+and that was a killer that kind of
+killed the whole subject for a long time
+
+ align:start position:0%
+killed the whole subject for a long time
+ 
+
+ align:start position:0%
+killed the whole subject for a long time
+because of what i'm saying
+
+ align:start position:0%
+because of what i'm saying
+ 
+
+ align:start position:0%
+because of what i'm saying
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the object in question was the our
+
+ align:start position:0%
+the object in question was the our
+ 
+
+ align:start position:0%
+the object in question was the our
+famous excess demand function that we
+
+ align:start position:0%
+famous excess demand function that we
+ 
+
+ align:start position:0%
+famous excess demand function that we
+have used before the aggregate demand
+
+ align:start position:0%
+have used before the aggregate demand
+ 
+
+ align:start position:0%
+have used before the aggregate demand
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+that we've been focusing on with
+
+ align:start position:0%
+that we've been focusing on with
+ 
+
+ align:start position:0%
+that we've been focusing on with
+aggregation and so on
+
+ align:start position:0%
+aggregation and so on
+ 
+
+ align:start position:0%
+aggregation and so on
+what shape does that aggregate demand
+
+ align:start position:0%
+what shape does that aggregate demand
+ 
+
+ align:start position:0%
+what shape does that aggregate demand
+function have as we vary prices
+
+ align:start position:0%
+function have as we vary prices
+ 
+
+ align:start position:0%
+function have as we vary prices
+and the answer was whatever wiggle and
+
+ align:start position:0%
+and the answer was whatever wiggle and
+ 
+
+ align:start position:0%
+and the answer was whatever wiggle and
+turn it has including upsloping forces
+
+ align:start position:0%
+turn it has including upsloping forces
+ 
+
+ align:start position:0%
+turn it has including upsloping forces
+and portions and so on you can always
+
+ align:start position:0%
+and portions and so on you can always
+ 
+
+ align:start position:0%
+and portions and so on you can always
+find an underlying economy that would
+
+ align:start position:0%
+find an underlying economy that would
+ 
+
+ align:start position:0%
+find an underlying economy that would
+have generated that excess demand
+
+ align:start position:0%
+have generated that excess demand
+ 
+
+ align:start position:0%
+have generated that excess demand
+so this part of it is the seeming answer
+
+ align:start position:0%
+so this part of it is the seeming answer
+ 
+
+ align:start position:0%
+so this part of it is the seeming answer
+to the question what happens if we don't
+
+ align:start position:0%
+to the question what happens if we don't
+ 
+
+ align:start position:0%
+to the question what happens if we don't
+put any restrictions on utility
+
+ align:start position:0%
+put any restrictions on utility
+ 
+
+ align:start position:0%
+put any restrictions on utility
+functions other than you know things
+
+ align:start position:0%
+functions other than you know things
+ 
+
+ align:start position:0%
+functions other than you know things
+like rationality and the answer is
+
+ align:start position:0%
+like rationality and the answer is
+ 
+
+ align:start position:0%
+like rationality and the answer is
+anything could happen
+
+ align:start position:0%
+anything could happen
+ 
+
+ align:start position:0%
+anything could happen
+that aggregate demand function could
+
+ align:start position:0%
+that aggregate demand function could
+ 
+
+ align:start position:0%
+that aggregate demand function could
+look any way you want it to for any
+
+ align:start position:0%
+look any way you want it to for any
+ 
+
+ align:start position:0%
+look any way you want it to for any
+aggregate demand function we can
+
+ align:start position:0%
+aggregate demand function we can
+ 
+
+ align:start position:0%
+aggregate demand function we can
+populate an economy with a finite number
+
+ align:start position:0%
+populate an economy with a finite number
+ 
+
+ align:start position:0%
+populate an economy with a finite number
+of households give them certain
+
+ align:start position:0%
+of households give them certain
+ 
+
+ align:start position:0%
+of households give them certain
+preferences
+
+ align:start position:0%
+preferences
+ 
+
+ align:start position:0%
+preferences
+and ownership of resources in such a way
+
+ align:start position:0%
+and ownership of resources in such a way
+ 
+
+ align:start position:0%
+and ownership of resources in such a way
+we can get that aggregate demand to
+
+ align:start position:0%
+we can get that aggregate demand to
+ 
+
+ align:start position:0%
+we can get that aggregate demand to
+shift and turn and and do whatever we
+
+ align:start position:0%
+shift and turn and and do whatever we
+ 
+
+ align:start position:0%
+shift and turn and and do whatever we
+want so again
+
+ align:start position:0%
+want so again
+ 
+
+ align:start position:0%
+want so again
+the shorthand is anything goes and
+
+ align:start position:0%
+the shorthand is anything goes and
+ 
+
+ align:start position:0%
+the shorthand is anything goes and
+because we could never reject the model
+
+ align:start position:0%
+because we could never reject the model
+ 
+
+ align:start position:0%
+because we could never reject the model
+people thought that general equilibrium
+
+ align:start position:0%
+people thought that general equilibrium
+ 
+
+ align:start position:0%
+people thought that general equilibrium
+had no content and they stopped doing it
+
+ align:start position:0%
+had no content and they stopped doing it
+ 
+
+ align:start position:0%
+had no content and they stopped doing it
+it's kind of discredited
+
+ align:start position:0%
+it's kind of discredited
+ 
+
+ align:start position:0%
+it's kind of discredited
+this was not just one person it was hugo
+
+ align:start position:0%
+this was not just one person it was hugo
+ 
+
+ align:start position:0%
+this was not just one person it was hugo
+sun and sean debrew and montel
+
+ align:start position:0%
+sun and sean debrew and montel
+ 
+
+ align:start position:0%
+sun and sean debrew and montel
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but let's just change this a bit
+
+ align:start position:0%
+but let's just change this a bit
+ 
+
+ align:start position:0%
+but let's just change this a bit
+first what is this seemingly reasonable
+
+ align:start position:0%
+first what is this seemingly reasonable
+ 
+
+ align:start position:0%
+first what is this seemingly reasonable
+but actually crazy thing that we
+
+ align:start position:0%
+but actually crazy thing that we
+ 
+
+ align:start position:0%
+but actually crazy thing that we
+actually see the excess demand we never
+
+ align:start position:0%
+actually see the excess demand we never
+ 
+
+ align:start position:0%
+actually see the excess demand we never
+see that
+
+ align:start position:0%
+see that
+ 
+
+ align:start position:0%
+see that
+if we see market economy we only see
+
+ align:start position:0%
+if we see market economy we only see
+ 
+
+ align:start position:0%
+if we see market economy we only see
+market clearing prices we don't see what
+
+ align:start position:0%
+market clearing prices we don't see what
+ 
+
+ align:start position:0%
+market clearing prices we don't see what
+happens out of out of equilibrium
+
+ align:start position:0%
+happens out of out of equilibrium
+ 
+
+ align:start position:0%
+happens out of out of equilibrium
+so we only see where it crosses we see
+
+ align:start position:0%
+so we only see where it crosses we see
+ 
+
+ align:start position:0%
+so we only see where it crosses we see
+the fixed points
+
+ align:start position:0%
+the fixed points
+ 
+
+ align:start position:0%
+the fixed points
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well let's give us a little more data
+
+ align:start position:0%
+well let's give us a little more data
+ 
+
+ align:start position:0%
+well let's give us a little more data
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+given a set of observations on prices
+
+ align:start position:0%
+given a set of observations on prices
+ 
+
+ align:start position:0%
+given a set of observations on prices
+and individual endowments does there
+
+ align:start position:0%
+and individual endowments does there
+ 
+
+ align:start position:0%
+and individual endowments does there
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+okay so t now indicates the economy
+
+ align:start position:0%
+okay so t now indicates the economy
+ 
+
+ align:start position:0%
+okay so t now indicates the economy
+it's as if we're going to go in the
+
+ align:start position:0%
+it's as if we're going to go in the
+ 
+
+ align:start position:0%
+it's as if we're going to go in the
+cross section across several or many
+
+ align:start position:0%
+cross section across several or many
+ 
+
+ align:start position:0%
+cross section across several or many
+economies that vary in the individual
+
+ align:start position:0%
+economies that vary in the individual
+ 
+
+ align:start position:0%
+economies that vary in the individual
+ownership of endowments so it's omega i
+
+ align:start position:0%
+ownership of endowments so it's omega i
+ 
+
+ align:start position:0%
+ownership of endowments so it's omega i
+t for the teeth economy observation for
+
+ align:start position:0%
+t for the teeth economy observation for
+ 
+
+ align:start position:0%
+t for the teeth economy observation for
+any t it varies over i we have a finite
+
+ align:start position:0%
+any t it varies over i we have a finite
+ 
+
+ align:start position:0%
+any t it varies over i we have a finite
+number of households but t is varying in
+
+ align:start position:0%
+number of households but t is varying in
+ 
+
+ align:start position:0%
+number of households but t is varying in
+the sample that's the number of
+
+ align:start position:0%
+the sample that's the number of
+ 
+
+ align:start position:0%
+the sample that's the number of
+economies in the sample those economies
+
+ align:start position:0%
+economies in the sample those economies
+ 
+
+ align:start position:0%
+economies in the sample those economies
+are all alike for preferences that's
+
+ align:start position:0%
+are all alike for preferences that's
+ 
+
+ align:start position:0%
+are all alike for preferences that's
+assumed
+
+ align:start position:0%
+assumed
+ 
+
+ align:start position:0%
+assumed
+but they differ in the ownership
+
+ align:start position:0%
+but they differ in the ownership
+ 
+
+ align:start position:0%
+but they differ in the ownership
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+the omega it's
+
+ align:start position:0%
+the omega it's
+ 
+
+ align:start position:0%
+the omega it's
+so then does there exist a
+
+ align:start position:0%
+so then does there exist a
+ 
+
+ align:start position:0%
+so then does there exist a
+sequence of these economies with
+
+ align:start position:0%
+sequence of these economies with
+ 
+
+ align:start position:0%
+sequence of these economies with
+each with its associated aggregate
+
+ align:start position:0%
+each with its associated aggregate
+ 
+
+ align:start position:0%
+each with its associated aggregate
+excess demand
+
+ align:start position:0%
+excess demand
+ 
+
+ align:start position:0%
+excess demand
+but such that those prices that we see
+
+ align:start position:0%
+but such that those prices that we see
+ 
+
+ align:start position:0%
+but such that those prices that we see
+stuck into the aggregated excess demand
+
+ align:start position:0%
+stuck into the aggregated excess demand
+ 
+
+ align:start position:0%
+stuck into the aggregated excess demand
+equals zero this last statement is just
+
+ align:start position:0%
+equals zero this last statement is just
+ 
+
+ align:start position:0%
+equals zero this last statement is just
+a statement that
+
+ align:start position:0%
+a statement that
+ 
+
+ align:start position:0%
+a statement that
+that the prices come from the market in
+
+ align:start position:0%
+that the prices come from the market in
+ 
+
+ align:start position:0%
+that the prices come from the market in
+other words the data set we're going to
+
+ align:start position:0%
+other words the data set we're going to
+ 
+
+ align:start position:0%
+other words the data set we're going to
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+would be the prices
+
+ align:start position:0%
+would be the prices
+ 
+
+ align:start position:0%
+would be the prices
+that because it's a market are
+
+ align:start position:0%
+that because it's a market are
+ 
+
+ align:start position:0%
+that because it's a market are
+associated with with zero excess demand
+
+ align:start position:0%
+associated with with zero excess demand
+ 
+
+ align:start position:0%
+associated with with zero excess demand
+equilibrium prices
+
+ align:start position:0%
+equilibrium prices
+ 
+
+ align:start position:0%
+equilibrium prices
+so we're going to see equilibrium prices
+
+ align:start position:0%
+so we're going to see equilibrium prices
+ 
+
+ align:start position:0%
+so we're going to see equilibrium prices
+and we're also going to
+
+ align:start position:0%
+and we're also going to
+ 
+
+ align:start position:0%
+and we're also going to
+see individual endowments
+
+ align:start position:0%
+see individual endowments
+ 
+
+ align:start position:0%
+see individual endowments
+assuming preferences are all the same
+
+ align:start position:0%
+assuming preferences are all the same
+ 
+
+ align:start position:0%
+assuming preferences are all the same
+okay so i'll give you the the punch line
+
+ align:start position:0%
+okay so i'll give you the the punch line
+ 
+
+ align:start position:0%
+okay so i'll give you the the punch line
+that's brown and mask and
+
+ align:start position:0%
+that's brown and mask and
+ 
+
+ align:start position:0%
+that's brown and mask and
+the punch line is going to be
+
+ align:start position:0%
+the punch line is going to be
+ 
+
+ align:start position:0%
+the punch line is going to be
+what we've been saying throughout the
+
+ align:start position:0%
+what we've been saying throughout the
+ 
+
+ align:start position:0%
+what we've been saying throughout the
+lecture today
+
+ align:start position:0%
+lecture today
+ 
+
+ align:start position:0%
+lecture today
+namely if we're given data like this we
+
+ align:start position:0%
+namely if we're given data like this we
+ 
+
+ align:start position:0%
+namely if we're given data like this we
+can actually reject that the data could
+
+ align:start position:0%
+can actually reject that the data could
+ 
+
+ align:start position:0%
+can actually reject that the data could
+have come
+
+ align:start position:0%
+have come
+ 
+
+ align:start position:0%
+have come
+as a market equilibrium that is to say
+
+ align:start position:0%
+as a market equilibrium that is to say
+ 
+
+ align:start position:0%
+as a market equilibrium that is to say
+that the market the data couldn't
+
+ align:start position:0%
+that the market the data couldn't
+ 
+
+ align:start position:0%
+that the market the data couldn't
+potentially never have come from
+
+ align:start position:0%
+potentially never have come from
+ 
+
+ align:start position:0%
+potentially never have come from
+individual household maximization
+
+ align:start position:0%
+individual household maximization
+ 
+
+ align:start position:0%
+individual household maximization
+and market clearing so it has content
+
+ align:start position:0%
+and market clearing so it has content
+ 
+
+ align:start position:0%
+and market clearing so it has content
+here's the differentiable version of it
+
+ align:start position:0%
+here's the differentiable version of it
+ 
+
+ align:start position:0%
+here's the differentiable version of it
+as abstract as general equilibrium
+
+ align:start position:0%
+as abstract as general equilibrium
+ 
+
+ align:start position:0%
+as abstract as general equilibrium
+theory is the sononshine debrew montel
+
+ align:start position:0%
+theory is the sononshine debrew montel
+ 
+
+ align:start position:0%
+theory is the sononshine debrew montel
+is overturned they're applying it to an
+
+ align:start position:0%
+is overturned they're applying it to an
+ 
+
+ align:start position:0%
+is overturned they're applying it to an
+exchange economy where we see prices and
+
+ align:start position:0%
+exchange economy where we see prices and
+ 
+
+ align:start position:0%
+exchange economy where we see prices and
+endowments they derive necessary and
+
+ align:start position:0%
+endowments they derive necessary and
+ 
+
+ align:start position:0%
+endowments they derive necessary and
+sufficient conditions for the
+
+ align:start position:0%
+sufficient conditions for the
+ 
+
+ align:start position:0%
+sufficient conditions for the
+equilibrium prices as a function of
+
+ align:start position:0%
+equilibrium prices as a function of
+ 
+
+ align:start position:0%
+equilibrium prices as a function of
+initial endowments and in their language
+
+ align:start position:0%
+initial endowments and in their language
+ 
+
+ align:start position:0%
+initial endowments and in their language
+they show that the economy can be
+
+ align:start position:0%
+they show that the economy can be
+ 
+
+ align:start position:0%
+they show that the economy can be
+generically
+
+ align:start position:0%
+generically
+ 
+
+ align:start position:0%
+generically
+identified what they mean by that is
+
+ align:start position:0%
+identified what they mean by that is
+ 
+
+ align:start position:0%
+identified what they mean by that is
+there is an underlying economy that
+
+ align:start position:0%
+there is an underlying economy that
+ 
+
+ align:start position:0%
+there is an underlying economy that
+would have generated the data
+
+ align:start position:0%
+would have generated the data
+ 
+
+ align:start position:0%
+would have generated the data
+but also
+
+ align:start position:0%
+but also
+ 
+
+ align:start position:0%
+but also
+that in principle one could have not
+
+ align:start position:0%
+that in principle one could have not
+ 
+
+ align:start position:0%
+that in principle one could have not
+been able to find such an economy and
+
+ align:start position:0%
+been able to find such an economy and
+ 
+
+ align:start position:0%
+been able to find such an economy and
+then sort of summarize where we are
+
+ align:start position:0%
+then sort of summarize where we are
+ 
+
+ align:start position:0%
+then sort of summarize where we are
+if you only had aggregate data you're
+
+ align:start position:0%
+if you only had aggregate data you're
+ 
+
+ align:start position:0%
+if you only had aggregate data you're
+sunk you're never going to get
+
+ align:start position:0%
+sunk you're never going to get
+ 
+
+ align:start position:0%
+sunk you're never going to get
+sufficients that allow you conditions
+
+ align:start position:0%
+sufficients that allow you conditions
+ 
+
+ align:start position:0%
+sufficients that allow you conditions
+that allow you to reject
+
+ align:start position:0%
+that allow you to reject
+ 
+
+ align:start position:0%
+that allow you to reject
+but when you have individual data
+
+ align:start position:0%
+but when you have individual data
+ 
+
+ align:start position:0%
+but when you have individual data
+you can get testable restrictions
+
+ align:start position:0%
+you can get testable restrictions
+ 
+
+ align:start position:0%
+you can get testable restrictions
+and bring back the content of general
+
+ align:start position:0%
+and bring back the content of general
+ 
+
+ align:start position:0%
+and bring back the content of general
+equilibrium theory
+
+ align:start position:0%
+equilibrium theory
+ 
+
+ align:start position:0%
+equilibrium theory
+so again this kind of summarizes my
+
+ align:start position:0%
+so again this kind of summarizes my
+ 
+
+ align:start position:0%
+so again this kind of summarizes my
+deliberately provocative statement that
+
+ align:start position:0%
+deliberately provocative statement that
+ 
+
+ align:start position:0%
+deliberately provocative statement that
+you need microdata to do macro
+
+ align:start position:0%
+you need microdata to do macro
+ 
+
+ align:start position:0%
+you need microdata to do macro
+and then they go on to talk about
+
+ align:start position:0%
+and then they go on to talk about
+ 
+
+ align:start position:0%
+and then they go on to talk about
+something you're familiar with because
+
+ align:start position:0%
+something you're familiar with because
+ 
+
+ align:start position:0%
+something you're familiar with because
+we did it in the class
+
+ align:start position:0%
+we did it in the class
+ 
+
+ align:start position:0%
+we did it in the class
+we're sharing in indian villages
+
+ align:start position:0%
+we're sharing in indian villages
+ 
+
+ align:start position:0%
+we're sharing in indian villages
+it's not uncommon to observe endowments
+
+ align:start position:0%
+it's not uncommon to observe endowments
+ 
+
+ align:start position:0%
+it's not uncommon to observe endowments
+like crops and prices we did a little
+
+ align:start position:0%
+like crops and prices we did a little
+ 
+
+ align:start position:0%
+like crops and prices we did a little
+bit of that and less so with the risk
+
+ align:start position:0%
+bit of that and less so with the risk
+ 
+
+ align:start position:0%
+bit of that and less so with the risk
+sharing in which case their
+
+ align:start position:0%
+sharing in which case their
+ 
+
+ align:start position:0%
+sharing in which case their
+content works directly
+
+ align:start position:0%
+content works directly
+ 
+
+ align:start position:0%
+content works directly
+if you really believed you were going
+
+ align:start position:0%
+if you really believed you were going
+ 
+
+ align:start position:0%
+if you really believed you were going
+from one village to another each were
+
+ align:start position:0%
+from one village to another each were
+ 
+
+ align:start position:0%
+from one village to another each were
+self-contained they had the same
+
+ align:start position:0%
+self-contained they had the same
+ 
+
+ align:start position:0%
+self-contained they had the same
+preferences and the premise would be
+
+ align:start position:0%
+preferences and the premise would be
+ 
+
+ align:start position:0%
+preferences and the premise would be
+we're seeing market outcomes then their
+
+ align:start position:0%
+we're seeing market outcomes then their
+ 
+
+ align:start position:0%
+we're seeing market outcomes then their
+theory applies directly you can even go
+
+ align:start position:0%
+theory applies directly you can even go
+ 
+
+ align:start position:0%
+theory applies directly you can even go
+to large economies not villages and
+
+ align:start position:0%
+to large economies not villages and
+ 
+
+ align:start position:0%
+to large economies not villages and
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+types of individuals finite number of
+
+ align:start position:0%
+types of individuals finite number of
+ 
+
+ align:start position:0%
+types of individuals finite number of
+types but a large number of individuals
+
+ align:start position:0%
+types but a large number of individuals
+ 
+
+ align:start position:0%
+types but a large number of individuals
+of a given type
+
+ align:start position:0%
+of a given type
+ 
+
+ align:start position:0%
+of a given type
+and again you can use their artillery
+
+ align:start position:0%
+and again you can use their artillery
+ 
+
+ align:start position:0%
+and again you can use their artillery
+now interestingly lest you think
+
+ align:start position:0%
+now interestingly lest you think
+ 
+
+ align:start position:0%
+now interestingly lest you think
+economists have this all figured out
+
+ align:start position:0%
+economists have this all figured out
+ 
+
+ align:start position:0%
+economists have this all figured out
+an interesting question is how to extend
+
+ align:start position:0%
+an interesting question is how to extend
+ 
+
+ align:start position:0%
+an interesting question is how to extend
+this to production
+
+ align:start position:0%
+this to production
+ 
+
+ align:start position:0%
+this to production
+they refer to
+
+ align:start position:0%
+they refer to
+ 
+
+ align:start position:0%
+they refer to
+changes in factor endowments which have
+
+ align:start position:0%
+changes in factor endowments which have
+ 
+
+ align:start position:0%
+changes in factor endowments which have
+observable impact on factor prices so
+
+ align:start position:0%
+observable impact on factor prices so
+ 
+
+ align:start position:0%
+observable impact on factor prices so
+that's an allusion to the trade lectures
+
+ align:start position:0%
+that's an allusion to the trade lectures
+ 
+
+ align:start position:0%
+that's an allusion to the trade lectures
+we did
+
+ align:start position:0%
+we did
+ 
+
+ align:start position:0%
+we did
+and they haven't figured it out yet they
+
+ align:start position:0%
+and they haven't figured it out yet they
+ 
+
+ align:start position:0%
+and they haven't figured it out yet they
+haven't figured out
+
+ align:start position:0%
+haven't figured out
+ 
+
+ align:start position:0%
+haven't figured out
+whether you know there are rejectable
+
+ align:start position:0%
+whether you know there are rejectable
+ 
+
+ align:start position:0%
+whether you know there are rejectable
+restrictions remember when we did the
+
+ align:start position:0%
+restrictions remember when we did the
+ 
+
+ align:start position:0%
+restrictions remember when we did the
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+the two by two case we had constant
+
+ align:start position:0%
+the two by two case we had constant
+ 
+
+ align:start position:0%
+the two by two case we had constant
+returns to scale and a few other
+
+ align:start position:0%
+returns to scale and a few other
+ 
+
+ align:start position:0%
+returns to scale and a few other
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+so they're saying like drop all
+
+ align:start position:0%
+so they're saying like drop all
+ 
+
+ align:start position:0%
+so they're saying like drop all
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+can we could we put restrictions on data
+
+ align:start position:0%
+can we could we put restrictions on data
+ 
+
+ align:start position:0%
+can we could we put restrictions on data
+and say we'd never
+
+ align:start position:0%
+and say we'd never
+ 
+
+ align:start position:0%
+and say we'd never
+see in the co you know
+
+ align:start position:0%
+see in the co you know
+ 
+
+ align:start position:0%
+see in the co you know
+violations of some kind and they haven't
+
+ align:start position:0%
+violations of some kind and they haven't
+ 
+
+ align:start position:0%
+violations of some kind and they haven't
+figured it out
+
+ align:start position:0%
+figured it out
+ 
+
+ align:start position:0%
+figured it out
+so we're on the research frontier at
+
+ align:start position:0%
+so we're on the research frontier at
+ 
+
+ align:start position:0%
+so we're on the research frontier at
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+what i have for today
+
+ align:start position:0%
+what i have for today
+ 
+
+ align:start position:0%
+what i have for today
+again very much part and parcel of the
+
+ align:start position:0%
+again very much part and parcel of the
+ 
+
+ align:start position:0%
+again very much part and parcel of the
+whole spirit of the class which is to
+
+ align:start position:0%
+whole spirit of the class which is to
+ 
+
+ align:start position:0%
+whole spirit of the class which is to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+economists as running experiments
+
+ align:start position:0%
+economists as running experiments
+ 
+
+ align:start position:0%
+economists as running experiments
+and you saw three of them today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/s-QcRrGppsk.txt b/s-QcRrGppsk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..971e8a4d162240381fdef26ea95158a687048c7b
--- /dev/null
+++ b/s-QcRrGppsk.txt
@@ -0,0 +1,2163 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+so the name of this class is called
+
+ align:start position:0%
+so the name of this class is called
+ 
+
+ align:start position:0%
+so the name of this class is called
+cardiomystic but what we're actually
+
+ align:start position:0%
+cardiomystic but what we're actually
+ 
+
+ align:start position:0%
+cardiomystic but what we're actually
+going to do
+
+ align:start position:0%
+going to do
+ 
+
+ align:start position:0%
+going to do
+is we're going to evaluate or learn how
+
+ align:start position:0%
+is we're going to evaluate or learn how
+ 
+
+ align:start position:0%
+is we're going to evaluate or learn how
+to deal with spin information
+
+ align:start position:0%
+to deal with spin information
+ 
+
+ align:start position:0%
+to deal with spin information
+in the calculation of our matrix
+
+ align:start position:0%
+in the calculation of our matrix
+ 
+
+ align:start position:0%
+in the calculation of our matrix
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+so now what what is it what we're trying
+
+ align:start position:0%
+so now what what is it what we're trying
+ 
+
+ align:start position:0%
+so now what what is it what we're trying
+to do so the first
+
+ align:start position:0%
+to do so the first
+ 
+
+ align:start position:0%
+to do so the first
+problem we might have is that we have
+
+ align:start position:0%
+problem we might have is that we have
+ 
+
+ align:start position:0%
+problem we might have is that we have
+polarized particles
+
+ align:start position:0%
+polarized particles
+ 
+
+ align:start position:0%
+polarized particles
+so we have here again our example of
+
+ align:start position:0%
+so we have here again our example of
+ 
+
+ align:start position:0%
+so we have here again our example of
+electron neuron scattering
+
+ align:start position:0%
+electron neuron scattering
+ 
+
+ align:start position:0%
+electron neuron scattering
+and if you assume that the electron and
+
+ align:start position:0%
+and if you assume that the electron and
+ 
+
+ align:start position:0%
+and if you assume that the electron and
+the neurons are polarized
+
+ align:start position:0%
+the neurons are polarized
+ 
+
+ align:start position:0%
+the neurons are polarized
+you you will find as we discussed in the
+
+ align:start position:0%
+you you will find as we discussed in the
+ 
+
+ align:start position:0%
+you you will find as we discussed in the
+previous lecture
+
+ align:start position:0%
+previous lecture
+ 
+
+ align:start position:0%
+previous lecture
+that our matrix element is proportional
+
+ align:start position:0%
+that our matrix element is proportional
+ 
+
+ align:start position:0%
+that our matrix element is proportional
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the joint vector of u1 times
+
+ align:start position:0%
+the joint vector of u1 times
+ 
+
+ align:start position:0%
+the joint vector of u1 times
+some sort of gamma matrix times the
+
+ align:start position:0%
+some sort of gamma matrix times the
+ 
+
+ align:start position:0%
+some sort of gamma matrix times the
+sphenoid and we probably have a
+
+ align:start position:0%
+sphenoid and we probably have a
+ 
+
+ align:start position:0%
+sphenoid and we probably have a
+polarization vector as well included
+
+ align:start position:0%
+polarization vector as well included
+ 
+
+ align:start position:0%
+polarization vector as well included
+here to give the polarization of the
+
+ align:start position:0%
+here to give the polarization of the
+ 
+
+ align:start position:0%
+here to give the polarization of the
+photon involved in
+
+ align:start position:0%
+photon involved in
+ 
+
+ align:start position:0%
+photon involved in
+in the um as a propagation good
+
+ align:start position:0%
+in the um as a propagation good
+ 
+
+ align:start position:0%
+in the um as a propagation good
+now in order to now get a number for m
+
+ align:start position:0%
+now in order to now get a number for m
+ 
+
+ align:start position:0%
+now in order to now get a number for m
+we actually have to be explicit
+
+ align:start position:0%
+we actually have to be explicit
+ 
+
+ align:start position:0%
+we actually have to be explicit
+about um the wave function of the
+
+ align:start position:0%
+about um the wave function of the
+ 
+
+ align:start position:0%
+about um the wave function of the
+external particles and you can do this
+
+ align:start position:0%
+external particles and you can do this
+ 
+
+ align:start position:0%
+external particles and you can do this
+you can just write this down
+
+ align:start position:0%
+you can just write this down
+ 
+
+ align:start position:0%
+you can just write this down
+however in experiments we are often
+
+ align:start position:0%
+however in experiments we are often
+ 
+
+ align:start position:0%
+however in experiments we are often
+interested in the scattering of
+
+ align:start position:0%
+interested in the scattering of
+ 
+
+ align:start position:0%
+interested in the scattering of
+unpolarized particles
+
+ align:start position:0%
+unpolarized particles
+ 
+
+ align:start position:0%
+unpolarized particles
+um you know even if you have a way to
+
+ align:start position:0%
+um you know even if you have a way to
+ 
+
+ align:start position:0%
+um you know even if you have a way to
+polarize a beam
+
+ align:start position:0%
+polarize a beam
+ 
+
+ align:start position:0%
+polarize a beam
+your polarization is not going to be
+
+ align:start position:0%
+your polarization is not going to be
+ 
+
+ align:start position:0%
+your polarization is not going to be
+perfect so in your calculation you might
+
+ align:start position:0%
+perfect so in your calculation you might
+ 
+
+ align:start position:0%
+perfect so in your calculation you might
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+you know average or
+
+ align:start position:0%
+you know average or
+ 
+
+ align:start position:0%
+you know average or
+thumb over the available spins of your
+
+ align:start position:0%
+thumb over the available spins of your
+ 
+
+ align:start position:0%
+thumb over the available spins of your
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+so now how how are we going to do this
+
+ align:start position:0%
+so now how how are we going to do this
+ 
+
+ align:start position:0%
+so now how how are we going to do this
+um so we're trying to calculate the spin
+
+ align:start position:0%
+um so we're trying to calculate the spin
+ 
+
+ align:start position:0%
+um so we're trying to calculate the spin
+averaged amplitude why averaging
+
+ align:start position:0%
+averaged amplitude why averaging
+ 
+
+ align:start position:0%
+averaged amplitude why averaging
+um we want to average over the
+
+ align:start position:0%
+um we want to average over the
+ 
+
+ align:start position:0%
+um we want to average over the
+polarization of the incoming particles
+
+ align:start position:0%
+polarization of the incoming particles
+ 
+
+ align:start position:0%
+polarization of the incoming particles
+again because we don't know what the
+
+ align:start position:0%
+again because we don't know what the
+ 
+
+ align:start position:0%
+again because we don't know what the
+polarization states
+
+ align:start position:0%
+polarization states
+ 
+
+ align:start position:0%
+polarization states
+are and we want to sum over the
+
+ align:start position:0%
+are and we want to sum over the
+ 
+
+ align:start position:0%
+are and we want to sum over the
+polarization of all final state
+
+ align:start position:0%
+polarization of all final state
+ 
+
+ align:start position:0%
+polarization of all final state
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+simply because you know each
+
+ align:start position:0%
+simply because you know each
+ 
+
+ align:start position:0%
+simply because you know each
+polarization state is a possible outcome
+
+ align:start position:0%
+polarization state is a possible outcome
+ 
+
+ align:start position:0%
+polarization state is a possible outcome
+of the interaction and we have to sum
+
+ align:start position:0%
+of the interaction and we have to sum
+ 
+
+ align:start position:0%
+of the interaction and we have to sum
+over all possible outcomes good
+
+ align:start position:0%
+over all possible outcomes good
+ 
+
+ align:start position:0%
+over all possible outcomes good
+um so how do we calculate the spin
+
+ align:start position:0%
+um so how do we calculate the spin
+ 
+
+ align:start position:0%
+um so how do we calculate the spin
+average amplitude
+
+ align:start position:0%
+average amplitude
+ 
+
+ align:start position:0%
+average amplitude
+so again we start from our matrix
+
+ align:start position:0%
+so again we start from our matrix
+ 
+
+ align:start position:0%
+so again we start from our matrix
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+where we have the joint vector some
+
+ align:start position:0%
+where we have the joint vector some
+ 
+
+ align:start position:0%
+where we have the joint vector some
+gamma matrix and
+
+ align:start position:0%
+gamma matrix and
+ 
+
+ align:start position:0%
+gamma matrix and
+our sphenoid um if we then calculate the
+
+ align:start position:0%
+our sphenoid um if we then calculate the
+ 
+
+ align:start position:0%
+our sphenoid um if we then calculate the
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+of this matrix we find this solution
+
+ align:start position:0%
+of this matrix we find this solution
+ 
+
+ align:start position:0%
+of this matrix we find this solution
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+great and now we're just doing a few
+
+ align:start position:0%
+great and now we're just doing a few
+ 
+
+ align:start position:0%
+great and now we're just doing a few
+tricks um
+
+ align:start position:0%
+tricks um
+ 
+
+ align:start position:0%
+tricks um
+so first of all we can write our joint
+
+ align:start position:0%
+so first of all we can write our joint
+ 
+
+ align:start position:0%
+so first of all we can write our joint
+vector u1
+
+ align:start position:0%
+vector u1
+ 
+
+ align:start position:0%
+vector u1
+equal to u dagger 1
+
+ align:start position:0%
+equal to u dagger 1
+ 
+
+ align:start position:0%
+equal to u dagger 1
+gamma not and then just continue this
+
+ align:start position:0%
+gamma not and then just continue this
+ 
+
+ align:start position:0%
+gamma not and then just continue this
+rewriting
+
+ align:start position:0%
+rewriting
+ 
+
+ align:start position:0%
+rewriting
+until we find this part here the
+
+ align:start position:0%
+until we find this part here the
+ 
+
+ align:start position:0%
+until we find this part here the
+solution which looks a little bit
+
+ align:start position:0%
+solution which looks a little bit
+ 
+
+ align:start position:0%
+solution which looks a little bit
+simpler
+
+ align:start position:0%
+simpler
+ 
+
+ align:start position:0%
+simpler
+where we have um now their joint matrix
+
+ align:start position:0%
+where we have um now their joint matrix
+ 
+
+ align:start position:0%
+where we have um now their joint matrix
+instead of their joint
+
+ align:start position:0%
+instead of their joint
+ 
+
+ align:start position:0%
+instead of their joint
+joint matrix given here so we want to
+
+ align:start position:0%
+joint matrix given here so we want to
+ 
+
+ align:start position:0%
+joint matrix given here so we want to
+evaluate
+
+ align:start position:0%
+evaluate
+ 
+
+ align:start position:0%
+evaluate
+what this a joint q1 gamma
+
+ align:start position:0%
+what this a joint q1 gamma
+ 
+
+ align:start position:0%
+what this a joint q1 gamma
+u2 is times the joint u2 gamma
+
+ align:start position:0%
+u2 is times the joint u2 gamma
+ 
+
+ align:start position:0%
+u2 is times the joint u2 gamma
+the joint u1 okay good so this was just
+
+ align:start position:0%
+the joint u1 okay good so this was just
+ 
+
+ align:start position:0%
+the joint u1 okay good so this was just
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+algebra and working with camera matrix
+
+ align:start position:0%
+algebra and working with camera matrix
+ 
+
+ align:start position:0%
+algebra and working with camera matrix
+so far
+
+ align:start position:0%
+so far
+ 
+
+ align:start position:0%
+so far
+now we're using this completion relation
+
+ align:start position:0%
+now we're using this completion relation
+ 
+
+ align:start position:0%
+now we're using this completion relation
+um where i probably haven't told you yet
+
+ align:start position:0%
+um where i probably haven't told you yet
+ 
+
+ align:start position:0%
+um where i probably haven't told you yet
+what this
+
+ align:start position:0%
+what this
+ 
+
+ align:start position:0%
+what this
+um what this syntax here is
+
+ align:start position:0%
+um what this syntax here is
+ 
+
+ align:start position:0%
+um what this syntax here is
+so gamma flash is equal to gamma mu
+
+ align:start position:0%
+so gamma flash is equal to gamma mu
+ 
+
+ align:start position:0%
+so gamma flash is equal to gamma mu
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and that's just the way to simplify
+
+ align:start position:0%
+and that's just the way to simplify
+ 
+
+ align:start position:0%
+and that's just the way to simplify
+writing multiply the equation so if
+
+ align:start position:0%
+writing multiply the equation so if
+ 
+
+ align:start position:0%
+writing multiply the equation so if
+if you use this so-called find slash
+
+ align:start position:0%
+if you use this so-called find slash
+ 
+
+ align:start position:0%
+if you use this so-called find slash
+you can also rewrite the dirac equation
+
+ align:start position:0%
+you can also rewrite the dirac equation
+ 
+
+ align:start position:0%
+you can also rewrite the dirac equation
+in a simple form
+
+ align:start position:0%
+in a simple form
+ 
+
+ align:start position:0%
+in a simple form
+i del slash minus m
+
+ align:start position:0%
+i del slash minus m
+ 
+
+ align:start position:0%
+i del slash minus m
+y equal to zero that's now our directive
+
+ align:start position:0%
+y equal to zero that's now our directive
+ 
+
+ align:start position:0%
+y equal to zero that's now our directive
+remember there was a
+
+ align:start position:0%
+remember there was a
+ 
+
+ align:start position:0%
+remember there was a
+um gamma mu uh
+
+ align:start position:0%
+um gamma mu uh
+ 
+
+ align:start position:0%
+um gamma mu uh
+dnu here all right um that's just the
+
+ align:start position:0%
+dnu here all right um that's just the
+ 
+
+ align:start position:0%
+dnu here all right um that's just the
+cycle mark and we have to
+
+ align:start position:0%
+cycle mark and we have to
+ 
+
+ align:start position:0%
+cycle mark and we have to
+sum over all spin states uh or the spin
+
+ align:start position:0%
+sum over all spin states uh or the spin
+ 
+
+ align:start position:0%
+sum over all spin states uh or the spin
+states of all
+
+ align:start position:0%
+states of all
+ 
+
+ align:start position:0%
+states of all
+of all both particles now if we start
+
+ align:start position:0%
+of all both particles now if we start
+ 
+
+ align:start position:0%
+of all both particles now if we start
+with summing over particle two
+
+ align:start position:0%
+with summing over particle two
+ 
+
+ align:start position:0%
+with summing over particle two
+we can rewrite this here we use this
+
+ align:start position:0%
+we can rewrite this here we use this
+ 
+
+ align:start position:0%
+we can rewrite this here we use this
+equation this
+
+ align:start position:0%
+equation this
+ 
+
+ align:start position:0%
+equation this
+completely relation and just redefine
+
+ align:start position:0%
+completely relation and just redefine
+ 
+
+ align:start position:0%
+completely relation and just redefine
+this q as equal to this part here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have this equation here
+
+ align:start position:0%
+okay so now we have this equation here
+ 
+
+ align:start position:0%
+okay so now we have this equation here
+which looks a little bit simpler because
+
+ align:start position:0%
+which looks a little bit simpler because
+ 
+
+ align:start position:0%
+which looks a little bit simpler because
+we just have
+
+ align:start position:0%
+we just have
+ 
+
+ align:start position:0%
+we just have
+our um incoming and outgoing spinos
+
+ align:start position:0%
+our um incoming and outgoing spinos
+ 
+
+ align:start position:0%
+our um incoming and outgoing spinos
+for particle one given here
+
+ align:start position:0%
+for particle one given here
+ 
+
+ align:start position:0%
+for particle one given here
+all right now we're looking at this part
+
+ align:start position:0%
+all right now we're looking at this part
+ 
+
+ align:start position:0%
+all right now we're looking at this part
+of the equation now
+
+ align:start position:0%
+of the equation now
+ 
+
+ align:start position:0%
+of the equation now
+and again we're just doing a little bit
+
+ align:start position:0%
+and again we're just doing a little bit
+ 
+
+ align:start position:0%
+and again we're just doing a little bit
+of matrix
+
+ align:start position:0%
+of matrix
+ 
+
+ align:start position:0%
+of matrix
+algebra here we find that this is equal
+
+ align:start position:0%
+algebra here we find that this is equal
+ 
+
+ align:start position:0%
+algebra here we find that this is equal
+to uh qu1 u1
+
+ align:start position:0%
+to uh qu1 u1
+ 
+
+ align:start position:0%
+to uh qu1 u1
+ii which is just simply summing over the
+
+ align:start position:0%
+ii which is just simply summing over the
+ 
+
+ align:start position:0%
+ii which is just simply summing over the
+same indices
+
+ align:start position:0%
+same indices
+ 
+
+ align:start position:0%
+same indices
+which is the same as building the trace
+
+ align:start position:0%
+which is the same as building the trace
+ 
+
+ align:start position:0%
+which is the same as building the trace
+of this matrix
+
+ align:start position:0%
+of this matrix
+ 
+
+ align:start position:0%
+of this matrix
+all right so if you just put all of
+
+ align:start position:0%
+all right so if you just put all of
+ 
+
+ align:start position:0%
+all right so if you just put all of
+those together he finds that
+
+ align:start position:0%
+those together he finds that
+ 
+
+ align:start position:0%
+those together he finds that
+calculating the sum of matrix elements
+
+ align:start position:0%
+calculating the sum of matrix elements
+ 
+
+ align:start position:0%
+calculating the sum of matrix elements
+is similar to building the trace of a
+
+ align:start position:0%
+is similar to building the trace of a
+ 
+
+ align:start position:0%
+is similar to building the trace of a
+matrix and then
+
+ align:start position:0%
+matrix and then
+ 
+
+ align:start position:0%
+matrix and then
+our final results think even though this
+
+ align:start position:0%
+our final results think even though this
+ 
+
+ align:start position:0%
+our final results think even though this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+all right so summarizing this part
+
+ align:start position:0%
+all right so summarizing this part
+ 
+
+ align:start position:0%
+all right so summarizing this part
+we have a matrix element and we saw that
+
+ align:start position:0%
+we have a matrix element and we saw that
+ 
+
+ align:start position:0%
+we have a matrix element and we saw that
+the matrix elements of this form is
+
+ align:start position:0%
+the matrix elements of this form is
+ 
+
+ align:start position:0%
+the matrix elements of this form is
+proportional to this form
+
+ align:start position:0%
+proportional to this form
+ 
+
+ align:start position:0%
+proportional to this form
+and then when we try to calculate the
+
+ align:start position:0%
+and then when we try to calculate the
+ 
+
+ align:start position:0%
+and then when we try to calculate the
+spin average matrix element squared
+
+ align:start position:0%
+spin average matrix element squared
+ 
+
+ align:start position:0%
+spin average matrix element squared
+that's equal to the traces of the
+
+ align:start position:0%
+that's equal to the traces of the
+ 
+
+ align:start position:0%
+that's equal to the traces of the
+particles involved using the completion
+
+ align:start position:0%
+particles involved using the completion
+ 
+
+ align:start position:0%
+particles involved using the completion
+function there's an additional part one
+
+ align:start position:0%
+function there's an additional part one
+ 
+
+ align:start position:0%
+function there's an additional part one
+additional factor one half here which
+
+ align:start position:0%
+additional factor one half here which
+ 
+
+ align:start position:0%
+additional factor one half here which
+comes from the averaging over the
+
+ align:start position:0%
+comes from the averaging over the
+ 
+
+ align:start position:0%
+comes from the averaging over the
+initial spins
+
+ align:start position:0%
+initial spins
+ 
+
+ align:start position:0%
+initial spins
+so assuming exactly one of u1 and q2
+
+ align:start position:0%
+so assuming exactly one of u1 and q2
+ 
+
+ align:start position:0%
+so assuming exactly one of u1 and q2
+corresponds to the initial to the
+
+ align:start position:0%
+corresponds to the initial to the
+ 
+
+ align:start position:0%
+corresponds to the initial to the
+initial particles we find this factor
+
+ align:start position:0%
+initial particles we find this factor
+ 
+
+ align:start position:0%
+initial particles we find this factor
+one half if both initial particles
+
+ align:start position:0%
+one half if both initial particles
+ 
+
+ align:start position:0%
+one half if both initial particles
+are the same like in perineulation
+
+ align:start position:0%
+are the same like in perineulation
+ 
+
+ align:start position:0%
+are the same like in perineulation
+then factor is one quarter and if
+
+ align:start position:0%
+then factor is one quarter and if
+ 
+
+ align:start position:0%
+then factor is one quarter and if
+neither is
+
+ align:start position:0%
+neither is
+ 
+
+ align:start position:0%
+neither is
+in the initial state then the factor is
+
+ align:start position:0%
+in the initial state then the factor is
+ 
+
+ align:start position:0%
+in the initial state then the factor is
+one one
+
+ align:start position:0%
+one one
+ 
+
+ align:start position:0%
+one one
+which you would have for a pair
+
+ align:start position:0%
+which you would have for a pair
+ 
+
+ align:start position:0%
+which you would have for a pair
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+okay good so now we simplified the
+
+ align:start position:0%
+okay good so now we simplified the
+ 
+
+ align:start position:0%
+okay good so now we simplified the
+calculation of
+
+ align:start position:0%
+calculation of
+ 
+
+ align:start position:0%
+calculation of
+our matrix elements putting the specific
+
+ align:start position:0%
+our matrix elements putting the specific
+ 
+
+ align:start position:0%
+our matrix elements putting the specific
+spin states in there in the specific
+
+ align:start position:0%
+spin states in there in the specific
+ 
+
+ align:start position:0%
+spin states in there in the specific
+polarization
+
+ align:start position:0%
+polarization
+ 
+
+ align:start position:0%
+polarization
+um vectors towards the calculation of
+
+ align:start position:0%
+um vectors towards the calculation of
+ 
+
+ align:start position:0%
+um vectors towards the calculation of
+traces of matrices so now we can look in
+
+ align:start position:0%
+traces of matrices so now we can look in
+ 
+
+ align:start position:0%
+traces of matrices so now we can look in
+what does it mean so what is that
+
+ align:start position:0%
+what does it mean so what is that
+ 
+
+ align:start position:0%
+what does it mean so what is that
+this is this is what carbonyl's trick
+
+ align:start position:0%
+this is this is what carbonyl's trick
+ 
+
+ align:start position:0%
+this is this is what carbonyl's trick
+really is about
+
+ align:start position:0%
+really is about
+ 
+
+ align:start position:0%
+really is about
+so summing over all spins reduces to
+
+ align:start position:0%
+so summing over all spins reduces to
+ 
+
+ align:start position:0%
+so summing over all spins reduces to
+coming over mattresses if you have
+
+ align:start position:0%
+coming over mattresses if you have
+ 
+
+ align:start position:0%
+coming over mattresses if you have
+anti-particles
+
+ align:start position:0%
+anti-particles
+ 
+
+ align:start position:0%
+anti-particles
+the completeness relation reduces to
+
+ align:start position:0%
+the completeness relation reduces to
+ 
+
+ align:start position:0%
+the completeness relation reduces to
+p slash minus m um
+
+ align:start position:0%
+p slash minus m um
+ 
+
+ align:start position:0%
+p slash minus m um
+and then we can go ahead so all you need
+
+ align:start position:0%
+and then we can go ahead so all you need
+ 
+
+ align:start position:0%
+and then we can go ahead so all you need
+to know now is how to do these traces
+
+ align:start position:0%
+to know now is how to do these traces
+ 
+
+ align:start position:0%
+to know now is how to do these traces
+so first some general remarks and traces
+
+ align:start position:0%
+so first some general remarks and traces
+ 
+
+ align:start position:0%
+so first some general remarks and traces
+if you have two matrices a and b
+
+ align:start position:0%
+if you have two matrices a and b
+ 
+
+ align:start position:0%
+if you have two matrices a and b
+you want to calculate the trace of a
+
+ align:start position:0%
+you want to calculate the trace of a
+ 
+
+ align:start position:0%
+you want to calculate the trace of a
+plus b
+
+ align:start position:0%
+plus b
+ 
+
+ align:start position:0%
+plus b
+that's equal to the trace of a plus
+
+ align:start position:0%
+that's equal to the trace of a plus
+ 
+
+ align:start position:0%
+that's equal to the trace of a plus
+trade of b
+
+ align:start position:0%
+trade of b
+ 
+
+ align:start position:0%
+trade of b
+if you have a multiplicator here a
+
+ align:start position:0%
+if you have a multiplicator here a
+ 
+
+ align:start position:0%
+if you have a multiplicator here a
+vector alpha you can just take this out
+
+ align:start position:0%
+vector alpha you can just take this out
+ 
+
+ align:start position:0%
+vector alpha you can just take this out
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+of the calculation of the trace
+
+ align:start position:0%
+of the calculation of the trace
+ 
+
+ align:start position:0%
+of the calculation of the trace
+um thus in those traces
+
+ align:start position:0%
+um thus in those traces
+ 
+
+ align:start position:0%
+um thus in those traces
+two matrices commit communicate the
+
+ align:start position:0%
+two matrices commit communicate the
+ 
+
+ align:start position:0%
+two matrices commit communicate the
+trace of a times b
+
+ align:start position:0%
+trace of a times b
+ 
+
+ align:start position:0%
+trace of a times b
+is equal to the trace of b times a and
+
+ align:start position:0%
+is equal to the trace of b times a and
+ 
+
+ align:start position:0%
+is equal to the trace of b times a and
+then you can use this in order to show
+
+ align:start position:0%
+then you can use this in order to show
+ 
+
+ align:start position:0%
+then you can use this in order to show
+more complicated relations like this
+
+ align:start position:0%
+more complicated relations like this
+ 
+
+ align:start position:0%
+more complicated relations like this
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good um we have already started playing
+
+ align:start position:0%
+good um we have already started playing
+ 
+
+ align:start position:0%
+good um we have already started playing
+around with the gamma matrices here are
+
+ align:start position:0%
+around with the gamma matrices here are
+ 
+
+ align:start position:0%
+around with the gamma matrices here are
+a few more identities which might be of
+
+ align:start position:0%
+a few more identities which might be of
+ 
+
+ align:start position:0%
+a few more identities which might be of
+use when you calculate
+
+ align:start position:0%
+use when you calculate
+ 
+
+ align:start position:0%
+use when you calculate
+traces and you calculate matrix elements
+
+ align:start position:0%
+traces and you calculate matrix elements
+ 
+
+ align:start position:0%
+traces and you calculate matrix elements
+overall the first one is this
+
+ align:start position:0%
+overall the first one is this
+ 
+
+ align:start position:0%
+overall the first one is this
+g minou times g minou is equal to four
+
+ align:start position:0%
+g minou times g minou is equal to four
+ 
+
+ align:start position:0%
+g minou times g minou is equal to four
+um the anti-community commutator
+
+ align:start position:0%
+um the anti-community commutator
+ 
+
+ align:start position:0%
+um the anti-community commutator
+relation we already discussed and have
+
+ align:start position:0%
+relation we already discussed and have
+ 
+
+ align:start position:0%
+relation we already discussed and have
+shown
+
+ align:start position:0%
+shown
+ 
+
+ align:start position:0%
+shown
+in our one of our presentation and if
+
+ align:start position:0%
+in our one of our presentation and if
+ 
+
+ align:start position:0%
+in our one of our presentation and if
+you have three matrices you can rewrite
+
+ align:start position:0%
+you have three matrices you can rewrite
+ 
+
+ align:start position:0%
+you have three matrices you can rewrite
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+as minus two times the metric
+
+ align:start position:0%
+as minus two times the metric
+ 
+
+ align:start position:0%
+as minus two times the metric
+which is in the middle here okay
+
+ align:start position:0%
+which is in the middle here okay
+ 
+
+ align:start position:0%
+which is in the middle here okay
+so i'm not going through this in much
+
+ align:start position:0%
+so i'm not going through this in much
+ 
+
+ align:start position:0%
+so i'm not going through this in much
+detail here but i encourage you
+
+ align:start position:0%
+detail here but i encourage you
+ 
+
+ align:start position:0%
+detail here but i encourage you
+to just follow those additional exercise
+
+ align:start position:0%
+to just follow those additional exercise
+ 
+
+ align:start position:0%
+to just follow those additional exercise
+if you didn't have the opportunity yet
+
+ align:start position:0%
+if you didn't have the opportunity yet
+ 
+
+ align:start position:0%
+if you didn't have the opportunity yet
+to play with those mattresses
+
+ align:start position:0%
+to play with those mattresses
+ 
+
+ align:start position:0%
+to play with those mattresses
+and then you can use those those tricks
+
+ align:start position:0%
+and then you can use those those tricks
+ 
+
+ align:start position:0%
+and then you can use those those tricks
+for example the anti-communic commutator
+
+ align:start position:0%
+for example the anti-communic commutator
+ 
+
+ align:start position:0%
+for example the anti-communic commutator
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+to calculate the traces of
+
+ align:start position:0%
+to calculate the traces of
+ 
+
+ align:start position:0%
+to calculate the traces of
+uh for example gamma mu which is four
+
+ align:start position:0%
+uh for example gamma mu which is four
+ 
+
+ align:start position:0%
+uh for example gamma mu which is four
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+g minus okay so what you see here is i
+
+ align:start position:0%
+g minus okay so what you see here is i
+ 
+
+ align:start position:0%
+g minus okay so what you see here is i
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+used this anti-community commutator
+
+ align:start position:0%
+used this anti-community commutator
+ 
+
+ align:start position:0%
+used this anti-community commutator
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+put it in here use this part here
+
+ align:start position:0%
+put it in here use this part here
+ 
+
+ align:start position:0%
+put it in here use this part here
+this is basically one straight of one is
+
+ align:start position:0%
+this is basically one straight of one is
+ 
+
+ align:start position:0%
+this is basically one straight of one is
+four so
+
+ align:start position:0%
+four so
+ 
+
+ align:start position:0%
+four so
+we get gb mu times the trailer one
+
+ align:start position:0%
+we get gb mu times the trailer one
+ 
+
+ align:start position:0%
+we get gb mu times the trailer one
+over four times four matrix is four and
+
+ align:start position:0%
+over four times four matrix is four and
+ 
+
+ align:start position:0%
+over four times four matrix is four and
+so you get
+
+ align:start position:0%
+so you get
+ 
+
+ align:start position:0%
+so you get
+the trace of gamma mu common is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so on um later on um we haven't
+
+ align:start position:0%
+okay and so on um later on um we haven't
+ 
+
+ align:start position:0%
+okay and so on um later on um we haven't
+discussed gamma 5 yet so much
+
+ align:start position:0%
+discussed gamma 5 yet so much
+ 
+
+ align:start position:0%
+discussed gamma 5 yet so much
+gamma 5 is defined as i times gamma 0
+
+ align:start position:0%
+gamma 5 is defined as i times gamma 0
+ 
+
+ align:start position:0%
+gamma 5 is defined as i times gamma 0
+comma 1 gamma 2 gamma 3.
+
+ align:start position:0%
+comma 1 gamma 2 gamma 3.
+ 
+
+ align:start position:0%
+comma 1 gamma 2 gamma 3.
+you will see when we discuss the weak
+
+ align:start position:0%
+you will see when we discuss the weak
+ 
+
+ align:start position:0%
+you will see when we discuss the weak
+interaction that there is a prominent
+
+ align:start position:0%
+interaction that there is a prominent
+ 
+
+ align:start position:0%
+interaction that there is a prominent
+role for gamma 5 this
+
+ align:start position:0%
+role for gamma 5 this
+ 
+
+ align:start position:0%
+role for gamma 5 this
+is very special common matrix and here
+
+ align:start position:0%
+is very special common matrix and here
+ 
+
+ align:start position:0%
+is very special common matrix and here
+are just some
+
+ align:start position:0%
+are just some
+ 
+
+ align:start position:0%
+are just some
+um pieces of information for traces for
+
+ align:start position:0%
+um pieces of information for traces for
+ 
+
+ align:start position:0%
+um pieces of information for traces for
+number five the trace of comma 5 is
+
+ align:start position:0%
+number five the trace of comma 5 is
+ 
+
+ align:start position:0%
+number five the trace of comma 5 is
+zero the j gamma five times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a different gamma matrix is zero and
+
+ align:start position:0%
+a different gamma matrix is zero and
+ 
+
+ align:start position:0%
+a different gamma matrix is zero and
+that's also true for the products of
+
+ align:start position:0%
+that's also true for the products of
+ 
+
+ align:start position:0%
+that's also true for the products of
+additional gamma matrices which you can
+
+ align:start position:0%
+additional gamma matrices which you can
+ 
+
+ align:start position:0%
+additional gamma matrices which you can
+find when you
+
+ align:start position:0%
+find when you
+ 
+
+ align:start position:0%
+find when you
+just try to calculate this relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um one last piece of the
+
+ align:start position:0%
+okay um one last piece of the
+ 
+
+ align:start position:0%
+okay um one last piece of the
+uh traces with gamma matrices is shown
+
+ align:start position:0%
+uh traces with gamma matrices is shown
+ 
+
+ align:start position:0%
+uh traces with gamma matrices is shown
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um only with four or more gamma matrices
+
+ align:start position:0%
+um only with four or more gamma matrices
+ 
+
+ align:start position:0%
+um only with four or more gamma matrices
+can you define
+
+ align:start position:0%
+can you define
+ 
+
+ align:start position:0%
+can you define
+or find a non-zero trace involving gamma
+
+ align:start position:0%
+or find a non-zero trace involving gamma
+ 
+
+ align:start position:0%
+or find a non-zero trace involving gamma
+matrices and here's one example
+
+ align:start position:0%
+matrices and here's one example
+ 
+
+ align:start position:0%
+matrices and here's one example
+where you have the product of five or
+
+ align:start position:0%
+where you have the product of five or
+ 
+
+ align:start position:0%
+where you have the product of five or
+four gamma matrices with gamma five
+
+ align:start position:0%
+four gamma matrices with gamma five
+ 
+
+ align:start position:0%
+four gamma matrices with gamma five
+and that's equal in this case 4 times i
+
+ align:start position:0%
+and that's equal in this case 4 times i
+ 
+
+ align:start position:0%
+and that's equal in this case 4 times i
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+the total asymmetric tensor the total
+
+ align:start position:0%
+the total asymmetric tensor the total
+ 
+
+ align:start position:0%
+the total asymmetric tensor the total
+asymmetry tender is defined as -1
+
+ align:start position:0%
+asymmetry tender is defined as -1
+ 
+
+ align:start position:0%
+asymmetry tender is defined as -1
+for even permutations of those numbers
+
+ align:start position:0%
+for even permutations of those numbers
+ 
+
+ align:start position:0%
+for even permutations of those numbers
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+plus 1 for odd permutations and zero
+
+ align:start position:0%
+plus 1 for odd permutations and zero
+ 
+
+ align:start position:0%
+plus 1 for odd permutations and zero
+if there's two indexes all right
+
+ align:start position:0%
+if there's two indexes all right
+ 
+
+ align:start position:0%
+if there's two indexes all right
+again i'm not showing you this um
+
+ align:start position:0%
+again i'm not showing you this um
+ 
+
+ align:start position:0%
+again i'm not showing you this um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in too much detail but i encourage you
+
+ align:start position:0%
+in too much detail but i encourage you
+ 
+
+ align:start position:0%
+in too much detail but i encourage you
+to you know play around and you will be
+
+ align:start position:0%
+to you know play around and you will be
+ 
+
+ align:start position:0%
+to you know play around and you will be
+asked in the homework in the next
+
+ align:start position:0%
+asked in the homework in the next
+ 
+
+ align:start position:0%
+asked in the homework in the next
+homework
+
+ align:start position:0%
+homework
+ 
+
+ align:start position:0%
+homework
+to play around with some of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculations
\ No newline at end of file
diff --git a/sNLB6_ZIfX0.txt b/sNLB6_ZIfX0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ec82f2a60c10164b90912505d51c7278de522df
--- /dev/null
+++ b/sNLB6_ZIfX0.txt
@@ -0,0 +1,387 @@
+PROFESSOR: Hi.
+
+Last time we talked about NVCC
+method and how to reduce the
+
+number of equations we had
+to deal with to solve a
+
+particular circuit.
+
+At this point, we're pretty
+well equipped to solve
+
+circuits in the general sense,
+but we really haven't talked
+
+about how to use that
+information or possibly use
+
+circuits in a particular way.
+
+Before we jump into both that
+and abstraction of circuits,
+
+we need to talk about op-amps.
+
+Op-amps is short for Operational
+Amplifier.
+
+And it's a tool that we can
+use in order to sample
+
+particular voltages from a
+subsection of the circuit
+
+without affecting it.
+
+Another thing we can
+use op-amps to do
+
+is modify our signal.
+
+Or if we're going to sample a
+voltage from a particular
+
+subsection of the circuit, we
+can then do stuff to that
+
+voltage without affecting the
+circuit, all within the op-amp
+
+or within the op-amp's special
+subset of circuitry.
+
+So first of all what is an
+operational amplifier?
+
+Well, an operational amplifier
+is a giant web of transistors.
+
+But what an operational
+amplifier does is act as a
+
+voltage-dependent
+voltage source.
+
+It can effectively sample
+voltages from an existing
+
+circuit and then use them to
+power some other object, for
+
+instance a light bulb.
+
+If you set up this kind of
+circuit, you will not actually
+
+be powering this light bulb
+with 5 Volts, because the
+
+light bulb itself acts
+as a resistor.
+
+And so the voltage drop across
+this part of the circuit is
+
+going to be different
+from just 5 Volts.
+
+If you want to enable a voltage
+drop of 5 Volts across
+
+this light bulb, then you have
+to stick up an op-amp.
+
+You have to use an op-amp to
+sample the voltage drop at
+
+this component and put it in
+between the light bulb and the
+
+rest of the circuit.
+
+When you see an op-amp on a
+schematic diagram, it'll
+
+frequently look like this.
+
+You'll have a positive input
+voltage, a negative input
+
+voltage, power rails, which are
+actually the thing that
+
+determine the range of
+expressivity that the op-amp
+
+has, and an output voltage.
+
+In reality, the relationship
+between the output voltage and
+
+then input voltages is something
+like this, where K
+
+is a very large number.
+
+The effect that this has is
+that Vout is going to be
+
+whatever Vout needs
+to be, such that
+
+Vplus is equal to Vminus.
+
+That's the basic rule you want
+to use when you're interacting
+
+with op-amps.
+
+So in this case, if we wanted to
+power this light bulb with
+
+5 Volts, we would do something
+like this.
+
+Excuse the sloppiness of
+the second diagram.
+
+We still have our 10 Volt
+voltage source.
+
+We still have our
+voltage divider.
+
+This point samples 5 Volts
+from this sub-circuit --
+
+and isolates this part of the
+circuit from the light bulb.
+
+Vout has to be whatever value
+is necessary such that this
+
+sample point and this sample
+point are equal.
+
+Since this value is 5 Volts,
+this value will also be driven
+
+to 5 Volts by the op-amp,
+which means that
+
+this value is 5 Volts.
+
+And we've successfully
+managed to power a
+
+light bulb with 5 Volts.
+
+The other thing you might be
+asked to do is to take an
+
+existing schematic, an existing
+circuit diagram and
+
+figure out what the operational
+amplifier does to
+
+a given signal or possibly what
+Vout is or possibly what
+
+Vout is in terms of
+the input signal.
+
+So let's practice using
+this diagram.
+
+Here's what we're after.
+
+I'm going to figure out where
+Vplus is going to be.
+
+This is another voltage
+divider.
+
+I'm now interested in Vminus,
+in terms of Vout, which is
+
+another voltage divider.
+
+I can set these two equations
+equal to one another
+
+and solve for Vout.
+
+I found a new expression for
+Vout in the particular case
+
+where V is 10 Volts.
+
+If my input voltage were
+previously unspecified, or if
+
+this voltage source were not
+specified or just Vin, then I
+
+would be after this
+expression.
+
+Some things I'd like to mention,
+while we're talking
+
+about op-amps, all the
+operational amplifiers we've
+
+been working with so far deal
+with Vout in terms of Vin,
+
+where Vin is driven through the
+positive terminal, and the
+
+negative terminal is typically
+connected to ground.
+
+You can do the opposite
+and end up with
+
+some interesting effects.
+
+But it comes at a cost.
+
+It is entirely possible that you
+will end up driving your
+
+op-amp to an unstable
+equilibrium.
+
+What you need to look at
+is this relationship.
+
+There may be a particular point,
+in which case your
+
+system is stable.
+
+But if you get any sort of minor
+perturbations, you'll
+
+actually end up with
+divergence.
+
+If this is the case, then
+you'll probably
+
+burn out your op-amp.
+
+You can do this by hooking
+it up in this way.
+
+This is expensive and could
+possibly burn you.
+
+The other thing to note is that
+the power rails on your
+
+op-amp limit its range
+of expressivity.
+
+And I think I've said this
+before, but it's worth
+
+mentioning again.
+
+If your op-amp is only powered
+by 10 Volts, it cannot amplify
+
+your input signal to a final
+value greater than 10 Volts.
+
+Likewise, if your input value
+is a negative voltage, and
+
+you're working with a
+non-inverting amplifier, if
+
+your ground is truly ground or
+if your ground is higher
+
+relative than your input
+voltage, you cannot actually
+
+express a negative voltage.
+
+The third thing I'd like to
+quickly mention is that there
+
+are some terms associated with
+op-amps that you might hear
+
+used by the staff or online,
+that sort of thing.
+
+A buffer and a voltage follower
+are the same thing.
+
+And that's explicitly when you
+want to sample a signal or you
+
+want to sample a particular
+voltage, and you don't want to
+
+multiply it or add it to
+something or do any kind of
+
+LTI operations that we might be
+able to do using op-amps in
+
+this course.
+
+You can work with amplifiers.
+
+And the thing we worked with
+earlier was an amplifier for a
+
+value less than 1.
+
+You can also use op-amps
+to some signals.
+
+And if you look for a voltage
+summer amplifier on the
+
+internet, you should be able
+to find some information.
+
+In any case, op-amps are
+really powerful.
+
+They allow us to both isolate
+a particular section of a
+
+circuit and sample a particular
+voltage value from
+
+that circuit without affecting
+that circuit, and also allow
+
+us to modify that particular
+voltage value before using it
+
+in another part of our
+overall circuit.
+
+Therefore, we're enabled to
+design more complicated and
+
+powerful things.
+
+Next time, I'll talk about
+superposition and Thevenin
+
+Norton equivalence, which will
+further enable modularity and
+
+abstraction in our
+circuit design.
\ No newline at end of file
diff --git a/w4uxYDPsjbw.txt b/w4uxYDPsjbw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7cba160c54cf075bbe82b115daf955d3cf827a77
--- /dev/null
+++ b/w4uxYDPsjbw.txt
@@ -0,0 +1,147 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I have this variable name once which
+
+ align:start position:0%
+So I have this variable name once which
+ 
+
+ align:start position:0%
+So I have this variable name once which
+is um um MBR. Looks like people are
+
+ align:start position:0%
+is um um MBR. Looks like people are
+ 
+
+ align:start position:0%
+is um um MBR. Looks like people are
+getting it. We have a variable called
+
+ align:start position:0%
+getting it. We have a variable called
+ 
+
+ align:start position:0%
+getting it. We have a variable called
+repeat which is E L A and I'm creating a
+
+ align:start position:0%
+repeat which is E L A and I'm creating a
+ 
+
+ align:start position:0%
+repeat which is E L A and I'm creating a
+variable U which is the concatenation of
+
+ align:start position:0%
+variable U which is the concatenation of
+ 
+
+ align:start position:0%
+variable U which is the concatenation of
+that with the repeat
+
+ align:start position:0%
+that with the repeat
+ 
+
+ align:start position:0%
+that with the repeat
+U multiplied by four. So I think people
+
+ align:start position:0%
+U multiplied by four. So I think people
+ 
+
+ align:start position:0%
+U multiplied by four. So I think people
+are on the right track. Seeing by the
+
+ align:start position:0%
+are on the right track. Seeing by the
+ 
+
+ align:start position:0%
+are on the right track. Seeing by the
+90% here it's going to give me u this
+
+ align:start position:0%
+90% here it's going to give me u this
+ 
+
+ align:start position:0%
+90% here it's going to give me u this
+result right here.
+
+ align:start position:0%
+result right here.
+ 
+
+ align:start position:0%
+result right here.
+Great.
\ No newline at end of file
diff --git a/y4EcXTVqFb4.txt b/y4EcXTVqFb4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..96fc4014ca3515a1dc5de1ce627416fbe29c36f2
--- /dev/null
+++ b/y4EcXTVqFb4.txt
@@ -0,0 +1,1228 @@
+NARRATOR: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Hi.
+
+Our lecture today actually has
+us backtrack a little bit to a
+
+concept which is actually more
+fundamental than that of
+
+differentiability.
+
+It's a topic which is called
+'continuous functions'.
+
+In other words, our lecture
+today is concerned with a
+
+topic called Continuity.
+
+And actually, the topic of
+continuity had its roots way
+
+back at the beginning of our
+course when we first raised
+
+the question: does the limit of
+'f of x' as 'x' approaches
+
+'a' equal 'f of a'?
+
+Remember, when we first started
+talking about the
+
+limit concept, our intuitive
+approach was to say, look-it,
+
+as 'x' gets arbitrarily close
+to 'a', 'f of x' gets
+
+arbitrarily close to 'f of a'.
+
+And we saw that this particular
+definition had a
+
+few loopholes in it, even though
+intuitively this is
+
+what we would have liked.
+
+And so what I want to do today
+is to see what happens if we
+
+can be sure that the limit of 'f
+of x' as 'x' approaches 'a'
+
+equals 'f of a'.
+
+What is implied if this happens
+
+to be a true statement?
+
+And my first claim is that it is
+implicitly implied that 'f
+
+of a' must at least
+make sense.
+
+Otherwise, we wouldn't have
+written it over here.
+
+In other words, 'f' must be
+defined when 'x' equals 'a'.
+
+'f of a' must be defined.
+
+Now to correlate that with
+material that we've had
+
+previously, let's go back
+to an example that we've
+
+discussed before, or at least
+an example which is close to
+
+something we've studied
+before.
+
+Let's define 'f of x' to be 'x
+squared minus 1' over 'x - 1'.
+
+Now you see as long as 'x' is
+not equal to 1, we can cancel
+
+'x - 1' from both numerator and
+denominator, leaving this
+
+equal to 'x + 1'.
+
+And we then see what?
+
+That the limit of 'f of
+x' as 'x' approaches
+
+1 is equal to 2.
+
+On the other hand, notice that
+'f of 1' turns out to be 0/0
+
+in this case, which
+is undefined.
+
+In other words, in this
+particular case, the limit of
+
+'f of x' as 'x' approaches 1
+is not equal to 'f of 1' if
+
+only because 'f of 1'
+isn't even defined.
+
+And again, by way of a review,
+let's look at this thing
+
+pictorially.
+
+Remember, 'x squared minus 1'
+over 'x - 1' is 'x + 1' except
+
+when 'x' equals 1.
+
+Consequently, to graph 'y'
+equals 'x squared minus 1'
+
+over 'x - 1', we simply graph
+'y' equals 'x + 1' with the
+
+point corresponding to 'x'
+equals 1, meaning the point 1
+
+comma 2 deleted.
+
+In other words, this point
+deleted is the graph 'y'
+
+equals 'x squared minus
+1' over 'x - 1'.
+
+You see again there is no
+definition at 'x' equals 1
+
+because this point is missing.
+
+It would be the 0/0 form.
+
+Now, to be sure, we can clean
+this up in the sense that we
+
+could define a new function 'g
+of x' to be 'x squared minus
+
+1' over 'x - 1' as long as 'x'
+is not equal to 1 and define
+
+it to be 2 when 'x' equals
+1, which, by the way,
+
+geometrically is just a fancy
+way of writing the equation of
+
+the line 'y' equals 'x + 1'.
+
+In other words, all we're saying
+is that letting 'g of
+
+x' be 2 when 'x' equals 1 plugs
+the little hole to the
+
+periods over here.
+
+Now again, I hope that this
+seems fairly familiar from our
+
+discussion on limits, but for
+the time being, all I want us
+
+to see is that as soon as you
+write down that the limit of
+
+'f of x' as 'x' approaches 'a'
+equals 'f of a', you at least
+
+imply that 'f of a'
+must be defined.
+
+Let's see another property
+that's implied by our
+
+definition.
+
+I claim, as you might expect,
+that if the limit of 'f of x'
+
+as 'x' approaches 'a' is 'f of
+a', that means that 'f of x'
+
+is near 'f of a' when
+'x' is near 'a'.
+
+In other words, my claim is that
+the curve 'y' equals 'f
+
+of x' is unbroken in
+a neighborhood
+
+of 'x' equals 'a'.
+
+And to see what I mean by
+that, let's look at this
+
+picture over here.
+
+Suppose, for example, that our
+curve 'y' equals 'f of x'--
+
+let me darken this up so that we
+can see it a little better.
+
+Suppose that curve had a break
+at 'x' equals 'a', OK?
+
+Now, let's say 'f of
+a' is over here.
+
+What I could do is now pick an
+interval surrounding 'f of a',
+
+if there was a break over here,
+such that this band
+
+never touched or included
+the top curve here.
+
+Now notice, from this point of
+view, that no matter how close
+
+'x' gets to 'a', as long as 'x'
+is greater than 'a', 'f of
+
+x', which is up here on this
+dark curve, can never be
+
+within epsilon of 'f of a'.
+
+In other words, if there's a
+break in the curve I could
+
+always fix it up so that the
+limit of 'f of x' as 'x'
+
+approaches 'a' is not
+equal to 'f of a'.
+
+At any rate, with these two
+properties as motivation, let
+
+us now give our basic
+definition.
+
+And the basic definition is
+simply this: a function 'f' is
+
+called continuous that 'x'
+equals 'a' precisely if the
+
+property that we were discussing
+is present, namely,
+
+if the limit of 'f of x' as
+'x' approaches 'a' is
+
+equal to 'f of a'.
+
+We generalize this definition
+and say 'f' is called
+
+continuous on the entire
+interval 'I', or on the
+
+interval 'I', if the limit of 'f
+of x' as 'x' approaches 'a'
+
+is equal to 'f of a' for
+each 'a' in 'I'.
+
+In other words, notice that
+our first definition is a
+
+local property.
+
+Namely, we define continuous or
+
+continuity at a given value.
+
+And then if the function happens
+to be continuous at
+
+every point, then we call the
+function itself continuous.
+
+What the thing means pictorially
+is that if the
+
+function is continuous at 'x'
+equals 'a', it means that in
+
+terms of the graph of the
+function, that in a
+
+neighborhood of the point 'a'
+comma 'f' of a on the graph,
+
+in a neighborhood of that point,
+in other words, in a
+
+sufficiently small interval
+surrounding that point, the
+
+curve itself must be unbroken.
+
+Now, you see, this may
+sound trivial.
+
+Remember, when we first started
+talking about limits,
+
+we had the feeling that limit of
+'f of x' as 'x' approaches
+
+a should always equal
+'f of a'.
+
+And the reason for this was that
+instinctively we seem to
+
+always think of continuous
+functions.
+
+We think of what?
+
+Things changing in such a way
+the graph of the change is
+
+unbroken even though, of course,
+there are places where
+
+discontinuities occur.
+
+At any rate, what I'm saying
+is that many of the results
+
+that I now want to discuss
+with you, which are very
+
+important properties of
+continuous functions, may seem
+
+self-evident because we keep
+thinking about any function as
+
+being continuous.
+
+But I will try to emphasize the
+fact that these properties
+
+are not true if the function
+is not continuous.
+
+I also would like to show a
+balance between geometric
+
+ideas and analytic ideas.
+
+In other words, let me start off
+by seeing what things seem
+
+to follow about continuous
+functions based primarily on
+
+the graph idea.
+
+For example, I claimed that
+continuous functions assume
+
+their maximum and minimum values
+on any closed interval.
+
+Now, this sounds like a big
+mouthful, and it also sounds
+
+kind of trivial.
+
+You say doesn't any function
+have a maximum and minimum
+
+value on a closed interval?
+
+And the answer is no.
+
+For example, take the
+curve 'y' equals '1
+
+over ''x - 1' squared''.
+
+Notice that when 'x' is 1, 'y'
+is infinite, which means that
+
+if we graph this particular
+function, we find that the
+
+graph does something
+like this.
+
+In other words, it goes--
+
+it jumps up here, comes
+back, et cetera.
+
+Now, what is the highest value
+or what is the highest point
+
+on our graph here?
+
+Well, notice that the graph
+is broken here.
+
+It's discontinuous when
+'x' equals 1.
+
+Notice that the curve
+rises to infinity.
+
+In other words, the maximum
+value is undefined on this
+
+particular closed interval.
+
+You see there's a
+jump over here.
+
+Of course, the fact that this
+is an infinite jump may make
+
+you feel uneasy if
+you don't feel
+
+comfortable with infinity.
+
+So let me paraphrase this just
+a little bit in terms of a
+
+finite jump.
+
+Let me write down the
+following function.
+
+Let's think of the function 'f
+of x' equals 'x' if 'x' is
+
+less than 1.
+
+Then as soon as 'x' is at
+least as big as 1, the
+
+function becomes 'minus x'.
+
+In other words, graphically,
+we have the line 'y' equals
+
+'x' from 0 up to 1, but
+not including 1.
+
+And then at 1, the function
+jumps down to minus 1 and
+
+becomes the line 'y'
+equals 'minus x'.
+
+Let's look, for example,
+at the closed interval
+
+again from 0 to 2.
+
+What is the biggest value?
+
+What is the maximum that the
+function can have if 'x' is
+
+between 0 and 2?
+
+Well, notice that as 'x' gets
+closer and closer to 1, 'f of
+
+x' gets closer and closer to 1,
+But 'f of x' never equals
+
+exactly 1, because when
+'x' is 1, the curve
+
+jumps down to here.
+
+In other words, notice that as
+'x' gets arbitrarily close to
+
+1, 'f of x' increases and gets
+arbitrarily close to but
+
+never equals 1.
+
+In other words, notice that by
+picking 'x' to be less than 1,
+
+we can make 'f of x' as close
+to 1 as we want, but we can
+
+never make it exactly equal to
+1 because of this jump which
+
+takes place over here.
+
+You see, this discontinuity
+causes us a little bit of
+
+difficulty.
+
+By the way, we can use
+this example from
+
+another point of view.
+
+If we just look at the part
+where it says 'f of x' is
+
+equal to 'x' where 'x' is less
+than 1, that means that we'll
+
+just look at this part
+of the curve.
+
+Notice that this part of
+the curve is unbroken.
+
+And yet as 'x' approaches 1, 'f
+of x' approaches but never
+
+equals 1, which means that to
+get the maximum value in here,
+
+I would have to include the
+end point 'x' equals 1.
+
+In other words, notice that
+even if the function is
+
+continuous, if the interval is
+open, it may not assume the
+
+maximum value.
+
+In other words, you may not be
+able to find the value of 'x'
+
+in that interval such as the
+function will be maximum at
+
+that particular value.
+
+Now again, this is making a
+mountain out of a mole hill in
+
+terms of your intuition because
+these are result which
+
+I'm sure you believe
+are true anyway.
+
+In other words, it
+seems to be true.
+
+But all I hope is that these
+little examples here show you
+
+what the importance of
+continuity is, because as we
+
+progress later in our work,
+these so called fine points
+
+are going to become crucial
+in many of our proofs.
+
+And by the way, I think it's a
+truism to say that if you make
+
+fine points seem very, very
+important before you get to
+
+use them and don't emphasize
+them, people tend to think
+
+that you overestimated
+your case.
+
+So I prefer not to beat this to
+death and wait until such
+
+times in our course that we need
+these results before I
+
+emphasize them more.
+
+So these are results which are
+in the textbook, which I'll
+
+test you on in the exercises and
+the like, but just want to
+
+go through with you now so that
+you get an overall idea.
+
+Another result that's rather
+clear geometrically is
+
+something called the
+intermediate value theorem.
+
+Suppose that 'f' is continuous
+on the closed interval from
+
+'a' to 'b'.
+
+And without loss of generality,
+let's suppose 'f
+
+of a' is less than 'f of b'.
+
+The same kind of an argument
+would hold if 'f of b' were
+
+less than 'f of a', but I just
+need some sort of an
+
+orientation.
+
+Now I say let 'm' be any number
+such that m is what?
+
+Between 'f of a' and 'f of b'.
+
+In other words, 'm' is greater
+than 'f of a' but
+
+less than 'f of b'.
+
+You see, if 'f of b' were less
+than 'f of a', I would just
+
+reverse the inequality
+signs here.
+
+At any rate, what my claim is
+that we can find the number
+
+'c' in the open interval from
+'a' to 'b' such that 'f of c'
+
+equals 'm'.
+
+Again, this may sound
+kind of complicated.
+
+All it says in terms of
+a picture is this.
+
+If our curve goes from point 1
+to point 2 where the height of
+
+'p1' is 'f of a' and the height
+of 'p2' is 'f of b',
+
+then it must assume every
+intermediary height between 'f
+
+of a' and 'f of b' on that
+particular interval.
+
+Again, you can think of
+that in terms of an
+
+automobile, if you want.
+
+If an automobile goes from a
+speed of 20 miles an hour to a
+
+speed of 30 miles per hour in
+what we think of as being
+
+continuous motion, then at some
+time in that interval, it
+
+must've had any particular
+speed you want to mention
+
+between 20 and 30 miles.
+
+In other words, we don't
+visualize a car going from 20
+
+miles an hour to 30 miles an
+hour, say, without at one time
+
+having passed the speed
+of 27 miles per hour
+
+or some such thing.
+
+And geometrically, you see,
+this proof is very simple,
+
+namely, draw the line
+'y' equals 'm'.
+
+And now what you're saying is
+you want to get from this
+
+point to this point.
+
+And the idea is that the only
+way you can get from this
+
+point to this point without
+crossing this line is if
+
+someplace along the way, you
+jump over this line.
+
+In other words, geometrically,
+all you're saying is lookit,
+
+if I have to join 'p1' and 'p2'
+with an unbroken line,
+
+then I must cross the line
+'y' equals 'm' someplace.
+
+By the way, notice I say that at
+least one place, the curve
+
+could have done something
+like this, for example.
+
+But the important
+point is what?
+
+There's at least one number
+'c' such that 'f
+
+of c' equals 'm'.
+
+Again, somebody might think in
+terms of an end run and say
+
+couldn't we have done something
+like this and not
+
+cross this line?
+
+That brings us back again
+to our concept of
+
+single-valuedness.
+
+In other words, notice, if we
+remove the restriction that 'f
+
+be a' single-valued function,
+in other words, if 'f' can
+
+double back, notice that if we
+think of the line 'y' equals
+
+'m' as being endless, the
+point remains what?
+
+That you must someplace cross
+this line in going
+
+from 'p1' to 'p2'.
+
+But if we remove the
+single-valued restriction,
+
+then the point at which
+you cross this line
+
+would not have to be--
+
+see, in this case, 'c' would
+not be in the open interval
+
+from 'a' to 'b' since 'f'
+is not single- valued.
+
+And what I'm hoping this
+discussion does for us is
+
+gives us a good geometric
+feeling as to what is
+
+happening in terms of a
+continuous function.
+
+By the same token, remember
+our basic definition of
+
+continuity goes back to
+our concept of limit.
+
+And our concept of limit has
+been cemented down fairly
+
+firmly from an analytical point
+of view, and that means
+
+that we can also see these
+things theoretically as well
+
+as pictorially.
+
+And hopefully what we will do
+is combine pictorial and
+
+analytic aspects to
+the best possible
+
+advantage for solving problems.
+
+But to show you what I mean by
+this, let's look at a few
+
+analytical properties of
+continuous functions.
+
+For example, suppose 'f' and 'g'
+are both continuous at 'x'
+
+equals 'a'.
+
+And suppose we define 'h' to
+be the sum of 'f' and 'g'.
+
+In other words, 'h of x' is 'f
+of x' plus 'g of x', OK?
+
+Let's compute the limit of 'h
+of x' as 'x' approaches 'a'.
+
+By definition, the limit of 'h
+of x' as 'x' approaches 'a' is
+
+the limit of the quantity 'f
+of x' plus 'g of x' as 'x'
+
+approaches 'a'.
+
+Now, if we look at this
+particular expression, notice
+
+that because of our theorems on
+limits, we can do an awful
+
+lot with this without having
+to make any recourse to our
+
+picture at all.
+
+For example, notice that we can
+say right away that since
+
+the limit of a sum is the sum
+of the limits, this is the
+
+limit of 'f of x' as 'x'
+approaches 'a' plus the limit
+
+of 'g of x' as 'x'
+approaches 'a'.
+
+Secondly, since 'f' and 'g' are
+continuous at 'x' equals
+
+'a', by definition of continuous
+that 'x' equals
+
+'a', this says that the limit of
+'f of x' as 'x' approaches
+
+'a' is 'f of a'.
+
+The limit of 'g of x' as 'x'
+approaches 'a' is 'g of a'.
+
+Therefore, this expression is
+'f of a' plus 'g of a'.
+
+But by the definition of 'h',
+this is just 'h of a'.
+
+And if we now look at
+this, we see what?
+
+That the limit of 'h of x'
+as 'x' approaches 'a'
+
+equals 'h of a'.
+
+Notice that this result came
+about under the assumption
+
+that 'f' and 'g' were both
+continuous that 'x' equals
+
+'a', and what have we
+proven over here?
+
+This is precisely the statement
+that 'h' is
+
+continuous at 'x' equals 'a'.
+
+In other words, what we've now
+proven analytically is that a
+
+sum of two continuous
+functions is
+
+a continuous function.
+
+By induction, we could prove
+this for the sum
+
+of more than two.
+
+We can in a similar way by using
+limit theorems prove
+
+things like the product of two
+continuous functions is
+
+continuous, et cetera.
+
+We also were on the verge of a
+topic like this when we talked
+
+about differentiability
+sometime back.
+
+Namely, I claim that there is
+an interesting connection
+
+between differentiable and
+continuous, and that the
+
+connection is that any
+differentiable function is
+
+continuous.
+
+And by the way, the proofs
+utilizes that which we used in
+
+our first lecture on derivatives
+in this block.
+
+Namely, we take the expression
+'f' of--
+
+we want to show that if 'f prime
+of a' exists, that 'f'
+
+must be continuous at
+'x' equals 'a'.
+
+That means we want to show that
+the limit of 'f of x' as
+
+'x' approaches 'a' is 'f of
+a', and that's the same as
+
+saying we want to show that this
+difference approaches 0
+
+and the limit.
+
+And the trick is we take 'f of
+x' minus 'f of a' and write it
+
+as ''f of x' minus 'f of a'
+divided by 'x - a'' times 'x -
+
+a', the idea being that we'll
+now take the limit as 'x'
+
+approaches 'a'.
+
+The limit of a product is the
+product of the limits.
+
+The limit of this as 'x'
+approaches 'a' is just going
+
+to be 'f prime of a'.
+
+That's our definition
+of derivative.
+
+And the limit of 'x - a' as 'x'
+approaches 'a' is just 0.
+
+In other words, putting
+these steps together,
+
+look what we get.
+
+The limit as 'x' approaches 'a',
+'f of x' minus 'f of a',
+
+is the limit as 'x' approaches
+'a' of this bracketed
+
+expression ''f of x' minus 'f of
+a' over 'x - a'' times the
+
+limit of 'x - a' as 'x'
+approaches 'a'.
+
+By definition, 'f' being
+differentiable at 'a' means
+
+that this limit exists and is,
+in fact, 'f prime of a'.
+
+But any finite number
+times 0 is still 0.
+
+And therefore, it follows that
+the limit of 'f of x' as 'x'
+
+approaches 'a' is 'f of a'.
+
+There's a legitimate analytic
+proof that differentiability
+
+implies continuity.
+
+Now, it's not necessarily true
+that continuity implies
+
+differentiability.
+
+And you see even though you
+can prove these things
+
+analytically, if you don't
+form some picture in your
+
+mind, you frequently will my
+wind up memorizing results
+
+rather than having a
+feeling for them.
+
+What I mean by having pictures
+and proofs coexist is this.
+
+Instead of saying to yourself,
+let's see, continuity is a
+
+weaker condition than
+differentiability, it's a
+
+strong-- which one is it?
+
+You say look-it.
+
+We identified continuity
+with unbroken.
+
+Remember, continuous
+means unbroken.
+
+What did differentiable mean?
+
+Differentiable meant that the
+curve had a tangent line, and
+
+that, in turn, meant that
+the curve was smooth.
+
+In other words, we may think
+of differentiable as the
+
+geometric analog of smoothness,
+continuity as the
+
+geometric analog of
+unbrokenness.
+
+And now I think it's very easy
+to see pictorially that a
+
+smooth curve must be unbroken,
+but an unbroken curve doesn't
+
+have to be smooth.
+
+And in fact, a very trivial
+illustration of this is the
+
+graph 'y' equals the absolute
+value of 'x'.
+
+You see, well, what
+happens here?
+
+At the origin, notice that we
+have a sharp corner, but that
+
+the curve itself is
+unbroken there.
+
+You see, I can draw the curve
+without taking the pencil off
+
+the paper, the chalk
+off the board.
+
+That's what continuity
+means from an
+
+intuitive point of view.
+
+Yet I have a sharp corner.
+
+It's not smooth here.
+
+That's why I write smooth
+in quotation marks.
+
+Hopefully, the textbook,
+together with our exercises,
+
+will make this much
+clear to you.
+
+But notice again in terms of
+the picture how an unbroken
+
+curve doesn't have to be smooth,
+but a smooth curve has
+
+to be unbroken.
+
+Now, the point is we
+could say much more
+
+about continuous functions.
+
+I think that all we have
+to say, though, has
+
+already been said.
+
+It'll be reinforced
+in the text.
+
+We'll have exercises on this.
+
+But the important thing for now
+is to understand what we
+
+mean by continuous, how we will
+use it in the future, and
+
+at any rate, we'll be talking
+about that more later.
+
+And so until next
+time, goodbye.
+
+NARRATOR: Funding for the
+publication of this video was
+
+provided by the Gabriella and
+Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/z79v39lMR3k.txt b/z79v39lMR3k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17d6d8165f7226d9a181b70fbdafe8ba1dbcfe25
--- /dev/null
+++ b/z79v39lMR3k.txt
@@ -0,0 +1,1827 @@
+align:start position:0%
+ 
+I've put on the blackboard here the
+
+ align:start position:0%
+I've put on the blackboard here the
+ 
+
+ align:start position:0%
+I've put on the blackboard here the
+things we were doing last time we began
+
+ align:start position:0%
+things we were doing last time we began
+ 
+
+ align:start position:0%
+things we were doing last time we began
+our study of stationary states that are
+
+ align:start position:0%
+our study of stationary states that are
+ 
+
+ align:start position:0%
+our study of stationary states that are
+not normalizable these are scattering
+
+ align:start position:0%
+not normalizable these are scattering
+ 
+
+ align:start position:0%
+not normalizable these are scattering
+states momentum eigenstates were not
+
+ align:start position:0%
+states momentum eigenstates were not
+ 
+
+ align:start position:0%
+states momentum eigenstates were not
+normalizable but now we have more
+
+ align:start position:0%
+normalizable but now we have more
+ 
+
+ align:start position:0%
+normalizable but now we have more
+interesting states that represent the
+
+ align:start position:0%
+interesting states that represent the
+ 
+
+ align:start position:0%
+interesting states that represent the
+solutions of the Schrodinger equation
+
+ align:start position:0%
+solutions of the Schrodinger equation
+ 
+
+ align:start position:0%
+solutions of the Schrodinger equation
+that are stationary States with some
+
+ align:start position:0%
+that are stationary States with some
+ 
+
+ align:start position:0%
+that are stationary States with some
+energy e because they are not
+
+ align:start position:0%
+energy e because they are not
+ 
+
+ align:start position:0%
+energy e because they are not
+normalizable we cannot directly
+
+ align:start position:0%
+normalizable we cannot directly
+ 
+
+ align:start position:0%
+normalizable we cannot directly
+interpret any of these solutions as the
+
+ align:start position:0%
+interpret any of these solutions as the
+ 
+
+ align:start position:0%
+interpret any of these solutions as the
+behavior of a particle I cannot tell you
+
+ align:start position:0%
+behavior of a particle I cannot tell you
+ 
+
+ align:start position:0%
+behavior of a particle I cannot tell you
+story okay so this is a particle is
+
+ align:start position:0%
+story okay so this is a particle is
+ 
+
+ align:start position:0%
+story okay so this is a particle is
+coming colliding doing something these
+
+ align:start position:0%
+coming colliding doing something these
+ 
+
+ align:start position:0%
+coming colliding doing something these
+are not normalizable states so part of
+
+ align:start position:0%
+are not normalizable states so part of
+ 
+
+ align:start position:0%
+are not normalizable states so part of
+what we're going to be trying to do
+
+ align:start position:0%
+what we're going to be trying to do
+ 
+
+ align:start position:0%
+what we're going to be trying to do
+today is connect to the picture of wave
+
+ align:start position:0%
+today is connect to the picture of wave
+ 
+
+ align:start position:0%
+today is connect to the picture of wave
+packets and see how this is used to
+
+ align:start position:0%
+packets and see how this is used to
+ 
+
+ align:start position:0%
+packets and see how this is used to
+really calculate what would happen if
+
+ align:start position:0%
+really calculate what would happen if
+ 
+
+ align:start position:0%
+really calculate what would happen if
+you send in a particle into potential
+
+ align:start position:0%
+you send in a particle into potential
+ 
+
+ align:start position:0%
+you send in a particle into potential
+nevertheless we wrote a solution that
+
+ align:start position:0%
+nevertheless we wrote a solution that
+ 
+
+ align:start position:0%
+nevertheless we wrote a solution that
+has roughly that interpretation at least
+
+ align:start position:0%
+has roughly that interpretation at least
+ 
+
+ align:start position:0%
+has roughly that interpretation at least
+they're morally speaking we think of a
+
+ align:start position:0%
+they're morally speaking we think of a
+ 
+
+ align:start position:0%
+they're morally speaking we think of a
+wave that is coming from the left
+
+ align:start position:0%
+wave that is coming from the left
+ 
+
+ align:start position:0%
+wave that is coming from the left
+that's a e to the ikx T now in order to
+
+ align:start position:0%
+that's a e to the ikx T now in order to
+ 
+
+ align:start position:0%
+that's a e to the ikx T now in order to
+have a wave you would have to have time
+
+ align:start position:0%
+have a wave you would have to have time
+ 
+
+ align:start position:0%
+have a wave you would have to have time
+dependence and this is a stationary
+
+ align:start position:0%
+dependence and this is a stationary
+ 
+
+ align:start position:0%
+dependence and this is a stationary
+solution and there is some time
+
+ align:start position:0%
+solution and there is some time
+ 
+
+ align:start position:0%
+solution and there is some time
+dependence there is exponential of e to
+
+ align:start position:0%
+dependence there is exponential of e to
+ 
+
+ align:start position:0%
+dependence there is exponential of e to
+the minus i e t over H bar or e is the
+
+ align:start position:0%
+the minus i e t over H bar or e is the
+ 
+
+ align:start position:0%
+the minus i e t over H bar or e is the
+energy so this could be out of here to
+
+ align:start position:0%
+energy so this could be out of here to
+ 
+
+ align:start position:0%
+energy so this could be out of here to
+produce the full stationary state sy of
+
+ align:start position:0%
+produce the full stationary state sy of
+ 
+
+ align:start position:0%
+produce the full stationary state sy of
+X and T but we'll leave it understood
+
+ align:start position:0%
+X and T but we'll leave it understood
+ 
+
+ align:start position:0%
+X and T but we'll leave it understood
+it's a common phase factor for both the
+
+ align:start position:0%
+it's a common phase factor for both the
+ 
+
+ align:start position:0%
+it's a common phase factor for both the
+solutions at X less than 0 and X greater
+
+ align:start position:0%
+solutions at X less than 0 and X greater
+ 
+
+ align:start position:0%
+solutions at X less than 0 and X greater
+than 0 because the whole solution
+
+ align:start position:0%
+than 0 because the whole solution
+ 
+
+ align:start position:0%
+than 0 because the whole solution
+represents a single solution it's not
+
+ align:start position:0%
+represents a single solution it's not
+ 
+
+ align:start position:0%
+represents a single solution it's not
+like a solution on the left and a
+
+ align:start position:0%
+like a solution on the left and a
+ 
+
+ align:start position:0%
+like a solution on the left and a
+solution on the right is a single
+
+ align:start position:0%
+solution on the right is a single
+ 
+
+ align:start position:0%
+solution on the right is a single
+solution over all of X for up sy that
+
+ align:start position:0%
+solution over all of X for up sy that
+ 
+
+ align:start position:0%
+solution over all of X for up sy that
+has some definite energy so
+
+ align:start position:0%
+has some definite energy so
+ 
+
+ align:start position:0%
+has some definite energy so
+we looked at the conditions of
+
+ align:start position:0%
+we looked at the conditions of
+ 
+
+ align:start position:0%
+we looked at the conditions of
+continuity of the wave function and
+
+ align:start position:0%
+continuity of the wave function and
+ 
+
+ align:start position:0%
+continuity of the wave function and
+continuty of the derivative of the wave
+
+ align:start position:0%
+continuty of the derivative of the wave
+ 
+
+ align:start position:0%
+continuty of the derivative of the wave
+function at x equals zero those were two
+
+ align:start position:0%
+function at x equals zero those were two
+ 
+
+ align:start position:0%
+function at x equals zero those were two
+conditions and they gave you this
+
+ align:start position:0%
+conditions and they gave you this
+ 
+
+ align:start position:0%
+conditions and they gave you this
+expressions for the ratios of C over a
+
+ align:start position:0%
+expressions for the ratios of C over a
+ 
+
+ align:start position:0%
+expressions for the ratios of C over a
+and B over a we could even imagine since
+
+ align:start position:0%
+and B over a we could even imagine since
+ 
+
+ align:start position:0%
+and B over a we could even imagine since
+we can't normalize this setting a equal
+
+ align:start position:0%
+we can't normalize this setting a equal
+ 
+
+ align:start position:0%
+we can't normalize this setting a equal
+to 1 and then calculating B and C from
+
+ align:start position:0%
+to 1 and then calculating B and C from
+ 
+
+ align:start position:0%
+to 1 and then calculating B and C from
+those numbers we have to Kasich a in a K
+
+ align:start position:0%
+those numbers we have to Kasich a in a K
+ 
+
+ align:start position:0%
+those numbers we have to Kasich a in a K
+bar the K is relevant to the wave
+
+ align:start position:0%
+bar the K is relevant to the wave
+ 
+
+ align:start position:0%
+bar the K is relevant to the wave
+function for X less than 0 the k bar is
+
+ align:start position:0%
+function for X less than 0 the k bar is
+ 
+
+ align:start position:0%
+function for X less than 0 the k bar is
+relevant for X greater than 0 they have
+
+ align:start position:0%
+relevant for X greater than 0 they have
+ 
+
+ align:start position:0%
+relevant for X greater than 0 they have
+to be different because this represents
+
+ align:start position:0%
+to be different because this represents
+ 
+
+ align:start position:0%
+to be different because this represents
+a de Broglie wavelength and the de
+
+ align:start position:0%
+a de Broglie wavelength and the de
+ 
+
+ align:start position:0%
+a de Broglie wavelength and the de
+Broglie wavelength encodes the momentum
+
+ align:start position:0%
+Broglie wavelength encodes the momentum
+ 
+
+ align:start position:0%
+Broglie wavelength encodes the momentum
+of the particle and the momentum of the
+
+ align:start position:0%
+of the particle and the momentum of the
+ 
+
+ align:start position:0%
+of the particle and the momentum of the
+particle that we imagined here
+
+ align:start position:0%
+particle that we imagined here
+ 
+
+ align:start position:0%
+particle that we imagined here
+classically is different here where this
+
+ align:start position:0%
+classically is different here where this
+ 
+
+ align:start position:0%
+classically is different here where this
+has this much kinetic energy and in the
+
+ align:start position:0%
+has this much kinetic energy and in the
+ 
+
+ align:start position:0%
+has this much kinetic energy and in the
+region on the right where the particle
+
+ align:start position:0%
+region on the right where the particle
+ 
+
+ align:start position:0%
+region on the right where the particle
+only has a much smaller kinetic energy
+
+ align:start position:0%
+only has a much smaller kinetic energy
+ 
+
+ align:start position:0%
+only has a much smaller kinetic energy
+so that's represented by K bar and K bar
+
+ align:start position:0%
+so that's represented by K bar and K bar
+ 
+
+ align:start position:0%
+so that's represented by K bar and K bar
+being the energy proportional to the
+
+ align:start position:0%
+being the energy proportional to the
+ 
+
+ align:start position:0%
+being the energy proportional to the
+energy minus V naught well K squared has
+
+ align:start position:0%
+energy minus V naught well K squared has
+ 
+
+ align:start position:0%
+energy minus V naught well K squared has
+just the energy is smaller than K so
+
+ align:start position:0%
+just the energy is smaller than K so
+ 
+
+ align:start position:0%
+just the energy is smaller than K so
+this is what with it we essentially
+
+ align:start position:0%
+this is what with it we essentially
+ 
+
+ align:start position:0%
+this is what with it we essentially
+solve the problem and this qualifies as
+
+ align:start position:0%
+solve the problem and this qualifies as
+ 
+
+ align:start position:0%
+solve the problem and this qualifies as
+a solution but we still haven't learned
+
+ align:start position:0%
+a solution but we still haven't learned
+ 
+
+ align:start position:0%
+a solution but we still haven't learned
+anything very interesting from it we
+
+ align:start position:0%
+anything very interesting from it we
+ 
+
+ align:start position:0%
+anything very interesting from it we
+have to understand more what's going on
+
+ align:start position:0%
+have to understand more what's going on
+ 
+
+ align:start position:0%
+have to understand more what's going on
+and one thing we can do is a think of a
+
+ align:start position:0%
+and one thing we can do is a think of a
+ 
+
+ align:start position:0%
+and one thing we can do is a think of a
+particular limit the limit or the case
+
+ align:start position:0%
+particular limit the limit or the case
+ 
+
+ align:start position:0%
+particular limit the limit or the case
+when e is equal to V not exactly equal
+
+ align:start position:0%
+when e is equal to V not exactly equal
+ 
+
+ align:start position:0%
+when e is equal to V not exactly equal
+to V naught what happens well K bar
+
+ align:start position:0%
+to V naught what happens well K bar
+ 
+
+ align:start position:0%
+to V naught what happens well K bar
+would be equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if K bar is equal to zero you're
+
+ align:start position:0%
+and if K bar is equal to zero you're
+ 
+
+ align:start position:0%
+and if K bar is equal to zero you're
+going to have just the constant scene
+
+ align:start position:0%
+going to have just the constant scene
+ 
+
+ align:start position:0%
+going to have just the constant scene
+here but now if K bar is equal to zero
+
+ align:start position:0%
+here but now if K bar is equal to zero
+ 
+
+ align:start position:0%
+here but now if K bar is equal to zero
+first B is equal to a because then it's
+
+ align:start position:0%
+first B is equal to a because then it's
+ 
+
+ align:start position:0%
+first B is equal to a because then it's
+K over K so B is equal to a and C is
+
+ align:start position:0%
+K over K so B is equal to a and C is
+ 
+
+ align:start position:0%
+K over K so B is equal to a and C is
+equal to 2a and the solution would
+
+ align:start position:0%
+equal to 2a and the solution would
+ 
+
+ align:start position:0%
+equal to 2a and the solution would
+become Phi of x equals well a is equal
+
+ align:start position:0%
+become Phi of x equals well a is equal
+ 
+
+ align:start position:0%
+become Phi of x equals well a is equal
+to B so this is twice a times the cosine
+
+ align:start position:0%
+to B so this is twice a times the cosine
+ 
+
+ align:start position:0%
+to B so this is twice a times the cosine
+of K X when a is equal to B is a common
+
+ align:start position:0%
+of K X when a is equal to B is a common
+ 
+
+ align:start position:0%
+of K X when a is equal to B is a common
+factor call it a and this thing is the
+
+ align:start position:0%
+factor call it a and this thing is the
+ 
+
+ align:start position:0%
+factor call it a and this thing is the
+sum of two Exponential's with opposite
+
+ align:start position:0%
+sum of two Exponential's with opposite
+ 
+
+ align:start position:0%
+sum of two Exponential's with opposite
+signs that gives you the cosine and for
+
+ align:start position:0%
+signs that gives you the cosine and for
+ 
+
+ align:start position:0%
+signs that gives you the cosine and for
+C you have to a and since K bar is equal
+
+ align:start position:0%
+C you have to a and since K bar is equal
+ 
+
+ align:start position:0%
+C you have to a and since K bar is equal
+to zero well it's just a it's a number
+
+ align:start position:0%
+to zero well it's just a it's a number
+ 
+
+ align:start position:0%
+to zero well it's just a it's a number
+this is a normalizable but even the
+
+ align:start position:0%
+this is a normalizable but even the
+ 
+
+ align:start position:0%
+this is a normalizable but even the
+original solution isn't normalizable so
+
+ align:start position:0%
+original solution isn't normalizable so
+ 
+
+ align:start position:0%
+original solution isn't normalizable so
+we wouldn't worry too much about it so
+
+ align:start position:0%
+we wouldn't worry too much about it so
+ 
+
+ align:start position:0%
+we wouldn't worry too much about it so
+how does that look for x over here you
+
+ align:start position:0%
+how does that look for x over here you
+ 
+
+ align:start position:0%
+how does that look for x over here you
+have a cosine of KX so it's going to be
+
+ align:start position:0%
+have a cosine of KX so it's going to be
+ 
+
+ align:start position:0%
+have a cosine of KX so it's going to be
+doing this to the left that for X less
+
+ align:start position:0%
+doing this to the left that for X less
+ 
+
+ align:start position:0%
+doing this to the left that for X less
+than 0 and at this point in those like
+
+ align:start position:0%
+than 0 and at this point in those like
+ 
+
+ align:start position:0%
+than 0 and at this point in those like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+just flat sigh of X and here is 2 a so
+
+ align:start position:0%
+just flat sigh of X and here is 2 a so
+ 
+
+ align:start position:0%
+just flat sigh of X and here is 2 a so
+there's nothing wrong with a solution in
+
+ align:start position:0%
+there's nothing wrong with a solution in
+ 
+
+ align:start position:0%
+there's nothing wrong with a solution in
+this case it's kind of a little strange
+
+ align:start position:0%
+this case it's kind of a little strange
+ 
+
+ align:start position:0%
+this case it's kind of a little strange
+that it becomes a constant but but
+
+ align:start position:0%
+that it becomes a constant but but
+ 
+
+ align:start position:0%
+that it becomes a constant but but
+perfectly okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what really helps you here is to find
+
+ align:start position:0%
+what really helps you here is to find
+ 
+
+ align:start position:0%
+what really helps you here is to find
+some conditions that Express the
+
+ align:start position:0%
+some conditions that Express the
+ 
+
+ align:start position:0%
+some conditions that Express the
+conservation of probability you see you
+
+ align:start position:0%
+conservation of probability you see you
+ 
+
+ align:start position:0%
+conservation of probability you see you
+have a stationary state solution now
+
+ align:start position:0%
+have a stationary state solution now
+ 
+
+ align:start position:0%
+have a stationary state solution now
+stationary states are our finest state
+
+ align:start position:0%
+stationary states are our finest state
+ 
+
+ align:start position:0%
+stationary states are our finest state
+they're not static States completely
+
+ align:start position:0%
+they're not static States completely
+ 
+
+ align:start position:0%
+they're not static States completely
+static state now for example if you have
+
+ align:start position:0%
+static state now for example if you have
+ 
+
+ align:start position:0%
+static state now for example if you have
+a loop and you have a current that never
+
+ align:start position:0%
+a loop and you have a current that never
+ 
+
+ align:start position:0%
+a loop and you have a current that never
+changes in time this is a stationary
+
+ align:start position:0%
+changes in time this is a stationary
+ 
+
+ align:start position:0%
+changes in time this is a stationary
+condition even in electromagnetism so
+
+ align:start position:0%
+condition even in electromagnetism so
+ 
+
+ align:start position:0%
+condition even in electromagnetism so
+what we imagine here is that we're going
+
+ align:start position:0%
+what we imagine here is that we're going
+ 
+
+ align:start position:0%
+what we imagine here is that we're going
+to have some current probability current
+
+ align:start position:0%
+to have some current probability current
+ 
+
+ align:start position:0%
+to have some current probability current
+that is coming from the left and some of
+
+ align:start position:0%
+that is coming from the left and some of
+ 
+
+ align:start position:0%
+that is coming from the left and some of
+it maybe bounces back and some of it
+
+ align:start position:0%
+it maybe bounces back and some of it
+ 
+
+ align:start position:0%
+it maybe bounces back and some of it
+goes forward but essentially if you
+
+ align:start position:0%
+goes forward but essentially if you
+ 
+
+ align:start position:0%
+goes forward but essentially if you
+think of the barrier whatever you look a
+
+ align:start position:0%
+think of the barrier whatever you look a
+ 
+
+ align:start position:0%
+think of the barrier whatever you look a
+little to the left of the barrier and a
+
+ align:start position:0%
+little to the left of the barrier and a
+ 
+
+ align:start position:0%
+little to the left of the barrier and a
+little to the right of the barrier
+
+ align:start position:0%
+little to the right of the barrier
+ 
+
+ align:start position:0%
+little to the right of the barrier
+whatever is coming in say must be going
+
+ align:start position:0%
+whatever is coming in say must be going
+ 
+
+ align:start position:0%
+whatever is coming in say must be going
+out there because probability cannot
+
+ align:start position:0%
+out there because probability cannot
+ 
+
+ align:start position:0%
+out there because probability cannot
+increase in this region it would be like
+
+ align:start position:0%
+increase in this region it would be like
+ 
+
+ align:start position:0%
+increase in this region it would be like
+saying that the particle son requires
+
+ align:start position:0%
+saying that the particle son requires
+ 
+
+ align:start position:0%
+saying that the particle son requires
+larger and larger probability to be in
+
+ align:start position:0%
+larger and larger probability to be in
+ 
+
+ align:start position:0%
+larger and larger probability to be in
+this this portion of the graph and that
+
+ align:start position:0%
+this this portion of the graph and that
+ 
+
+ align:start position:0%
+this this portion of the graph and that
+can't happen so probability current
+
+ align:start position:0%
+can't happen so probability current
+ 
+
+ align:start position:0%
+can't happen so probability current
+gives you a way to quantify some of the
+
+ align:start position:0%
+gives you a way to quantify some of the
+ 
+
+ align:start position:0%
+gives you a way to quantify some of the
+things that are happening here so
+
+ align:start position:0%
+things that are happening here so
+ 
+
+ align:start position:0%
+things that are happening here so
+probability current was J of X which was
+
+ align:start position:0%
+probability current was J of X which was
+ 
+
+ align:start position:0%
+probability current was J of X which was
+H bar over m imaginary part of size star
+
+ align:start position:0%
+H bar over m imaginary part of size star
+ 
+
+ align:start position:0%
+H bar over m imaginary part of size star
+D psi DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's compute the probability current
+
+ align:start position:0%
+so let's compute the probability current
+ 
+
+ align:start position:0%
+so let's compute the probability current
+let's compute for X less than 0 what is
+
+ align:start position:0%
+let's compute for X less than 0 what is
+ 
+
+ align:start position:0%
+let's compute for X less than 0 what is
+the probability current J of X we can
+
+ align:start position:0%
+the probability current J of X we can
+ 
+
+ align:start position:0%
+the probability current J of X we can
+call it the parabola curl on the left
+
+ align:start position:0%
+call it the parabola curl on the left
+ 
+
+ align:start position:0%
+call it the parabola curl on the left
+side I would have to substitute the
+
+ align:start position:0%
+side I would have to substitute the
+ 
+
+ align:start position:0%
+side I would have to substitute the
+value of the wave function for a for X
+
+ align:start position:0%
+value of the wave function for a for X
+ 
+
+ align:start position:0%
+value of the wave function for a for X
+less than 0 which is the top line there
+
+ align:start position:0%
+less than 0 which is the top line there
+ 
+
+ align:start position:0%
+less than 0 which is the top line there
+into this formula and see what is the
+
+ align:start position:0%
+into this formula and see what is the
+ 
+
+ align:start position:0%
+into this formula and see what is the
+current in fact I believe you've done
+
+ align:start position:0%
+current in fact I believe you've done
+ 
+
+ align:start position:0%
+current in fact I believe you've done
+that in an exercise some time ago and as
+
+ align:start position:0%
+that in an exercise some time ago and as
+ 
+
+ align:start position:0%
+that in an exercise some time ago and as
+you can imagine the current is
+
+ align:start position:0%
+you can imagine the current is
+ 
+
+ align:start position:0%
+you can imagine the current is
+proportional to the modulus of a squared
+
+ align:start position:0%
+proportional to the modulus of a squared
+ 
+
+ align:start position:0%
+proportional to the modulus of a squared
+the length of a squared the length of B
+
+ align:start position:0%
+the length of a squared the length of B
+ 
+
+ align:start position:0%
+the length of a squared the length of B
+squared also enters and the funny thing
+
+ align:start position:0%
+squared also enters and the funny thing
+ 
+
+ align:start position:0%
+squared also enters and the funny thing
+is between those two waves one that is
+
+ align:start position:0%
+is between those two waves one that is
+ 
+
+ align:start position:0%
+is between those two waves one that is
+going to the right and one that is going
+
+ align:start position:0%
+going to the right and one that is going
+ 
+
+ align:start position:0%
+going to the right and one that is going
+to the left that that's very visible in
+
+ align:start position:0%
+to the left that that's very visible in
+ 
+
+ align:start position:0%
+to the left that that's very visible in
+the current this is h-bar K over m a
+
+ align:start position:0%
+the current this is h-bar K over m a
+ 
+
+ align:start position:0%
+the current this is h-bar K over m a
+squared minus B squared it's a short
+
+ align:start position:0%
+squared minus B squared it's a short
+ 
+
+ align:start position:0%
+squared minus B squared it's a short
+computation might be okay when a good
+
+ align:start position:0%
+computation might be okay when a good
+ 
+
+ align:start position:0%
+computation might be okay when a good
+idea to do it again was done in the
+
+ align:start position:0%
+idea to do it again was done in the
+ 
+
+ align:start position:0%
+idea to do it again was done in the
+homework and X greater than 0 J right of
+
+ align:start position:0%
+homework and X greater than 0 J right of
+ 
+
+ align:start position:0%
+homework and X greater than 0 J right of
+X would be equal to H Bar K bar now that
+
+ align:start position:0%
+X would be equal to H Bar K bar now that
+ 
+
+ align:start position:0%
+X would be equal to H Bar K bar now that
+you know you can almost do it in your
+
+ align:start position:0%
+you know you can almost do it in your
+ 
+
+ align:start position:0%
+you know you can almost do it in your
+head the SI e to the I K bar X look
+
+ align:start position:0%
+head the SI e to the I K bar X look
+ 
+
+ align:start position:0%
+head the SI e to the I K bar X look
+what's happening from pi star you get
+
+ align:start position:0%
+what's happening from pi star you get
+ 
+
+ align:start position:0%
+what's happening from pi star you get
+the C star from sorry you get the C so
+
+ align:start position:0%
+the C star from sorry you get the C so
+ 
+
+ align:start position:0%
+the C star from sorry you get the C so
+that's going to be a C squared the face
+
+ align:start position:0%
+that's going to be a C squared the face
+ 
+
+ align:start position:0%
+that's going to be a C squared the face
+is going to cancel between the one here
+
+ align:start position:0%
+is going to cancel between the one here
+ 
+
+ align:start position:0%
+is going to cancel between the one here
+and the one on sy but the derivative
+
+ align:start position:0%
+and the one on sy but the derivative
+ 
+
+ align:start position:0%
+and the one on sy but the derivative
+will bring down an I K bar and the
+
+ align:start position:0%
+will bring down an I K bar and the
+ 
+
+ align:start position:0%
+will bring down an I K bar and the
+imaginary part of that is just K bar so
+
+ align:start position:0%
+imaginary part of that is just K bar so
+ 
+
+ align:start position:0%
+imaginary part of that is just K bar so
+the answer is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these are the two currents now if we
+
+ align:start position:0%
+and these are the two currents now if we
+ 
+
+ align:start position:0%
+and these are the two currents now if we
+are doing things correctly the two
+
+ align:start position:0%
+are doing things correctly the two
+ 
+
+ align:start position:0%
+are doing things correctly the two
+currents should be the same whatever
+
+ align:start position:0%
+currents should be the same whatever
+ 
+
+ align:start position:0%
+currents should be the same whatever
+current exists to the left say a
+
+ align:start position:0%
+current exists to the left say a
+ 
+
+ align:start position:0%
+current exists to the left say a
+positive current that is coming in to
+
+ align:start position:0%
+positive current that is coming in to
+ 
+
+ align:start position:0%
+positive current that is coming in to
+the right must be the same another
+
+ align:start position:0%
+the right must be the same another
+ 
+
+ align:start position:0%
+the right must be the same another
+pleasant thing is that this current
+
+ align:start position:0%
+pleasant thing is that this current
+ 
+
+ align:start position:0%
+pleasant thing is that this current
+doesn't depend on the value of X as X is
+
+ align:start position:0%
+doesn't depend on the value of X as X is
+ 
+
+ align:start position:0%
+doesn't depend on the value of X as X is
+less than zero nor on the value of X
+
+ align:start position:0%
+less than zero nor on the value of X
+ 
+
+ align:start position:0%
+less than zero nor on the value of X
+when X is greater than zero and that's
+
+ align:start position:0%
+when X is greater than zero and that's
+ 
+
+ align:start position:0%
+when X is greater than zero and that's
+good for conservation it would be pretty
+
+ align:start position:0%
+good for conservation it would be pretty
+ 
+
+ align:start position:0%
+good for conservation it would be pretty
+bad as well if you look at two places
+
+ align:start position:0%
+bad as well if you look at two places
+ 
+
+ align:start position:0%
+bad as well if you look at two places
+for X less than zero and you find that
+
+ align:start position:0%
+for X less than zero and you find that
+ 
+
+ align:start position:0%
+for X less than zero and you find that
+the current is not the same so where is
+
+ align:start position:0%
+the current is not the same so where is
+ 
+
+ align:start position:0%
+the current is not the same so where is
+it accumulating what what's going on
+
+ align:start position:0%
+it accumulating what what's going on
+ 
+
+ align:start position:0%
+it accumulating what what's going on
+so the independence of these things from
+
+ align:start position:0%
+so the independence of these things from
+ 
+
+ align:start position:0%
+so the independence of these things from
+X this is constant and a constant is
+
+ align:start position:0%
+X this is constant and a constant is
+ 
+
+ align:start position:0%
+X this is constant and a constant is
+very important because this causes
+
+ align:start position:0%
+very important because this causes
+ 
+
+ align:start position:0%
+very important because this causes
+should be the same now whether or not
+
+ align:start position:0%
+should be the same now whether or not
+ 
+
+ align:start position:0%
+should be the same now whether or not
+you know about current conservation it's
+
+ align:start position:0%
+you know about current conservation it's
+ 
+
+ align:start position:0%
+you know about current conservation it's
+encoded in Schrodinger's equation and we
+
+ align:start position:0%
+encoded in Schrodinger's equation and we
+ 
+
+ align:start position:0%
+encoded in Schrodinger's equation and we
+solve showing our equation that's how we
+
+ align:start position:0%
+solve showing our equation that's how we
+ 
+
+ align:start position:0%
+solve showing our equation that's how we
+got this relations between B a and C so
+
+ align:start position:0%
+got this relations between B a and C so
+ 
+
+ align:start position:0%
+got this relations between B a and C so
+it better be that these two things are
+
+ align:start position:0%
+it better be that these two things are
+ 
+
+ align:start position:0%
+it better be that these two things are
+the same so J l squared J L for example
+
+ align:start position:0%
+the same so J l squared J L for example
+ 
+
+ align:start position:0%
+the same so J l squared J L for example
+I want put of X because it's just clear
+
+ align:start position:0%
+I want put of X because it's just clear
+ 
+
+ align:start position:0%
+I want put of X because it's just clear
+it doesn't depend on X 1 minus B over a
+
+ align:start position:0%
+it doesn't depend on X 1 minus B over a
+ 
+
+ align:start position:0%
+it doesn't depend on X 1 minus B over a
+squared a squared I'm starting to
+
+ align:start position:0%
+squared a squared I'm starting to
+ 
+
+ align:start position:0%
+squared a squared I'm starting to
+manipulate the left one and see if
+
+ align:start position:0%
+manipulate the left one and see if
+ 
+
+ align:start position:0%
+manipulate the left one and see if
+indeed the currents are the same and now
+
+ align:start position:0%
+indeed the currents are the same and now
+ 
+
+ align:start position:0%
+indeed the currents are the same and now
+I get h-bar K over m 1 minus B over a
+
+ align:start position:0%
+I get h-bar K over m 1 minus B over a
+ 
+
+ align:start position:0%
+I get h-bar K over m 1 minus B over a
+squared you know I put the modulus
+
+ align:start position:0%
+squared you know I put the modulus
+ 
+
+ align:start position:0%
+squared you know I put the modulus
+square but so far everything is real in
+
+ align:start position:0%
+square but so far everything is real in
+ 
+
+ align:start position:0%
+square but so far everything is real in
+this KK bar b AC all real that right no
+
+ align:start position:0%
+this KK bar b AC all real that right no
+ 
+
+ align:start position:0%
+this KK bar b AC all real that right no
+now complex numbers
+
+ align:start position:0%
+now complex numbers
+ 
+
+ align:start position:0%
+now complex numbers
+I'll have to be that careful B over a
+
+ align:start position:0%
+I'll have to be that careful B over a
+ 
+
+ align:start position:0%
+I'll have to be that careful B over a
+squared is K minus K bar over k plus K
+
+ align:start position:0%
+squared is K minus K bar over k plus K
+ 
+
+ align:start position:0%
+squared is K minus K bar over k plus K
+bar squared a squared and I fit that
+
+ align:start position:0%
+bar squared a squared and I fit that
+ 
+
+ align:start position:0%
+bar squared a squared and I fit that
+here maybe h-bar K over m now what up
+
+ align:start position:0%
+here maybe h-bar K over m now what up
+ 
+
+ align:start position:0%
+here maybe h-bar K over m now what up
+this is square so the sum squared passes
+
+ align:start position:0%
+this is square so the sum squared passes
+ 
+
+ align:start position:0%
+this is square so the sum squared passes
+here to the numerator minus the
+
+ align:start position:0%
+here to the numerator minus the
+ 
+
+ align:start position:0%
+here to the numerator minus the
+difference squared that's going to be a
+
+ align:start position:0%
+difference squared that's going to be a
+ 
+
+ align:start position:0%
+difference squared that's going to be a
+4k k bar over k plus k bar squared a
+
+ align:start position:0%
+4k k bar over k plus k bar squared a
+ 
+
+ align:start position:0%
+4k k bar over k plus k bar squared a
+squared and yes this seems to be working
+
+ align:start position:0%
+squared and yes this seems to be working
+ 
+
+ align:start position:0%
+squared and yes this seems to be working
+quite well flip this case these two case
+
+ align:start position:0%
+quite well flip this case these two case
+ 
+
+ align:start position:0%
+quite well flip this case these two case
+flip them around so the answer for JL so
+
+ align:start position:0%
+flip them around so the answer for JL so
+ 
+
+ align:start position:0%
+flip them around so the answer for JL so
+far is H bar now k bar because they flip
+
+ align:start position:0%
+far is H bar now k bar because they flip
+ 
+
+ align:start position:0%
+far is H bar now k bar because they flip
+that M and now I would have for K
+
+ align:start position:0%
+that M and now I would have for K
+ 
+
+ align:start position:0%
+that M and now I would have for K
+squared over this thing which is 2 K
+
+ align:start position:0%
+squared over this thing which is 2 K
+ 
+
+ align:start position:0%
+squared over this thing which is 2 K
+over k plus K bar squared on a squared
+
+ align:start position:0%
+over k plus K bar squared on a squared
+ 
+
+ align:start position:0%
+over k plus K bar squared on a squared
+and this quantity if I remember right is
+
+ align:start position:0%
+and this quantity if I remember right is
+ 
+
+ align:start position:0%
+and this quantity if I remember right is
+just C squared as you can see from there
+
+ align:start position:0%
+just C squared as you can see from there
+ 
+
+ align:start position:0%
+just C squared as you can see from there
+so indeed this is J right and it worked
+
+ align:start position:0%
+so indeed this is J right and it worked
+ 
+
+ align:start position:0%
+so indeed this is J right and it worked
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+this is J right so J left is equal to J
+
+ align:start position:0%
+this is J right so J left is equal to J
+ 
+
+ align:start position:0%
+this is J right so J left is equal to J
+right by current conservation so that's
+
+ align:start position:0%
+right by current conservation so that's
+ 
+
+ align:start position:0%
+right by current conservation so that's
+nice that's another way of getting
+
+ align:start position:0%
+nice that's another way of getting
+ 
+
+ align:start position:0%
+nice that's another way of getting
+insight into these coefficients and the
+
+ align:start position:0%
+insight into these coefficients and the
+ 
+
+ align:start position:0%
+insight into these coefficients and the
+kind of thing that makes you feel
+
+ align:start position:0%
+kind of thing that makes you feel
+ 
+
+ align:start position:0%
+kind of thing that makes you feel
+there's no chance you got this wrong
+
+ align:start position:0%
+there's no chance you got this wrong
+ 
+
+ align:start position:0%
+there's no chance you got this wrong
+it it all works well
\ No newline at end of file
diff --git a/zU1x6UK64gs.txt b/zU1x6UK64gs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f2709ca2118c56b4b3d2024aabbb14706f0ca25
--- /dev/null
+++ b/zU1x6UK64gs.txt
@@ -0,0 +1,2467 @@
+align:start position:0%
+ 
+let us look at an application of the
+
+ align:start position:0%
+let us look at an application of the
+ 
+
+ align:start position:0%
+let us look at an application of the
+probabilistic method to extremal set
+
+ align:start position:0%
+probabilistic method to extremal set
+ 
+
+ align:start position:0%
+probabilistic method to extremal set
+theory the extremal set theory concerns
+
+ align:start position:0%
+theory the extremal set theory concerns
+ 
+
+ align:start position:0%
+theory the extremal set theory concerns
+the study of families of sets that have
+
+ align:start position:0%
+the study of families of sets that have
+ 
+
+ align:start position:0%
+the study of families of sets that have
+certain desirable properties and asking
+
+ align:start position:0%
+certain desirable properties and asking
+ 
+
+ align:start position:0%
+certain desirable properties and asking
+questions such as what is the largest
+
+ align:start position:0%
+questions such as what is the largest
+ 
+
+ align:start position:0%
+questions such as what is the largest
+set family that you can have with such
+
+ align:start position:0%
+set family that you can have with such
+ 
+
+ align:start position:0%
+set family that you can have with such
+with such properties and in this video
+
+ align:start position:0%
+with such properties and in this video
+ 
+
+ align:start position:0%
+with such properties and in this video
+we'll focus on the following property of
+
+ align:start position:0%
+we'll focus on the following property of
+ 
+
+ align:start position:0%
+we'll focus on the following property of
+being an intersecting family this means
+
+ align:start position:0%
+being an intersecting family this means
+ 
+
+ align:start position:0%
+being an intersecting family this means
+a collection of sets A1 through a l such
+
+ align:start position:0%
+a collection of sets A1 through a l such
+ 
+
+ align:start position:0%
+a collection of sets A1 through a l such
+that these sets pairwise intersect in a
+
+ align:start position:0%
+that these sets pairwise intersect in a
+ 
+
+ align:start position:0%
+that these sets pairwise intersect in a
+non-empty intersection okay so we want
+
+ align:start position:0%
+non-empty intersection okay so we want
+ 
+
+ align:start position:0%
+non-empty intersection okay so we want
+sets A1 through a l such that whenever
+
+ align:start position:0%
+sets A1 through a l such that whenever
+ 
+
+ align:start position:0%
+sets A1 through a l such that whenever
+you take any two of these sets and take
+
+ align:start position:0%
+you take any two of these sets and take
+ 
+
+ align:start position:0%
+you take any two of these sets and take
+their intersection it is never the empty
+
+ align:start position:0%
+their intersection it is never the empty
+ 
+
+ align:start position:0%
+their intersection it is never the empty
+set so here are two basic questions that
+
+ align:start position:0%
+set so here are two basic questions that
+ 
+
+ align:start position:0%
+set so here are two basic questions that
+one can ask the first one which will
+
+ align:start position:0%
+one can ask the first one which will
+ 
+
+ align:start position:0%
+one can ask the first one which will
+turn out to be an easy warmup is what is
+
+ align:start position:0%
+turn out to be an easy warmup is what is
+ 
+
+ align:start position:0%
+turn out to be an easy warmup is what is
+the largest intersecting family of
+
+ align:start position:0%
+the largest intersecting family of
+ 
+
+ align:start position:0%
+the largest intersecting family of
+subsets of 1 through n so here there are
+
+ align:start position:0%
+subsets of 1 through n so here there are
+ 
+
+ align:start position:0%
+subsets of 1 through n so here there are
+in total two to the N subsets of 1
+
+ align:start position:0%
+in total two to the N subsets of 1
+ 
+
+ align:start position:0%
+in total two to the N subsets of 1
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+n but if I want to only keep a
+
+ align:start position:0%
+n but if I want to only keep a
+ 
+
+ align:start position:0%
+n but if I want to only keep a
+collection of sets that's an
+
+ align:start position:0%
+collection of sets that's an
+ 
+
+ align:start position:0%
+collection of sets that's an
+intersecting family what is the largest
+
+ align:start position:0%
+intersecting family what is the largest
+ 
+
+ align:start position:0%
+intersecting family what is the largest
+family I can get and the second question
+
+ align:start position:0%
+family I can get and the second question
+ 
+
+ align:start position:0%
+family I can get and the second question
+which will turn out to be far more
+
+ align:start position:0%
+which will turn out to be far more
+ 
+
+ align:start position:0%
+which will turn out to be far more
+interesting and will involve an
+
+ align:start position:0%
+interesting and will involve an
+ 
+
+ align:start position:0%
+interesting and will involve an
+application of the probabilist method is
+
+ align:start position:0%
+application of the probabilist method is
+ 
+
+ align:start position:0%
+application of the probabilist method is
+a question what is the largest
+
+ align:start position:0%
+a question what is the largest
+ 
+
+ align:start position:0%
+a question what is the largest
+intersecting family of K element subsets
+
+ align:start position:0%
+intersecting family of K element subsets
+ 
+
+ align:start position:0%
+intersecting family of K element subsets
+of 1 through n so here n and K are
+
+ align:start position:0%
+of 1 through n so here n and K are
+ 
+
+ align:start position:0%
+of 1 through n so here n and K are
+inputs to the question so they are given
+
+ align:start position:0%
+inputs to the question so they are given
+ 
+
+ align:start position:0%
+inputs to the question so they are given
+and we're asked to find what is the
+
+ align:start position:0%
+and we're asked to find what is the
+ 
+
+ align:start position:0%
+and we're asked to find what is the
+largest intersecting family of K element
+
+ align:start position:0%
+largest intersecting family of K element
+ 
+
+ align:start position:0%
+largest intersecting family of K element
+subsets of 1 through
+
+ align:start position:0%
+subsets of 1 through
+ 
+
+ align:start position:0%
+subsets of 1 through
+n all right so the first question as I
+
+ align:start position:0%
+n all right so the first question as I
+ 
+
+ align:start position:0%
+n all right so the first question as I
+mentioned earlier turns out to be a
+
+ align:start position:0%
+mentioned earlier turns out to be a
+ 
+
+ align:start position:0%
+mentioned earlier turns out to be a
+fairly easy one and we'll solve it as a
+
+ align:start position:0%
+fairly easy one and we'll solve it as a
+ 
+
+ align:start position:0%
+fairly easy one and we'll solve it as a
+warmup so as an example just to
+
+ align:start position:0%
+warmup so as an example just to
+ 
+
+ align:start position:0%
+warmup so as an example just to
+illustrate what we're talking about if
+
+ align:start position:0%
+illustrate what we're talking about if
+ 
+
+ align:start position:0%
+illustrate what we're talking about if
+we look at all
+
+ align:start position:0%
+we look at all
+ 
+
+ align:start position:0%
+we look at all
+sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing the element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one well this collection of sets is
+
+ align:start position:0%
+one well this collection of sets is
+ 
+
+ align:start position:0%
+one well this collection of sets is
+intersecting because they all have the
+
+ align:start position:0%
+intersecting because they all have the
+ 
+
+ align:start position:0%
+intersecting because they all have the
+element one so every pair intersects in
+
+ align:start position:0%
+element one so every pair intersects in
+ 
+
+ align:start position:0%
+element one so every pair intersects in
+some set that contains the element one
+
+ align:start position:0%
+some set that contains the element one
+ 
+
+ align:start position:0%
+some set that contains the element one
+in particular non
+
+ align:start position:0%
+in particular non
+ 
+
+ align:start position:0%
+in particular non
+empty this collection of sets has size 2
+
+ align:start position:0%
+empty this collection of sets has size 2
+ 
+
+ align:start position:0%
+empty this collection of sets has size 2
+to the n minus one because once you fix
+
+ align:start position:0%
+to the n minus one because once you fix
+ 
+
+ align:start position:0%
+to the n minus one because once you fix
+the element one the other elements can
+
+ align:start position:0%
+the element one the other elements can
+ 
+
+ align:start position:0%
+the element one the other elements can
+be in or not in the sets and they're two
+
+ align:start position:0%
+be in or not in the sets and they're two
+ 
+
+ align:start position:0%
+be in or not in the sets and they're two
+to the N minus one such possibilities
+
+ align:start position:0%
+to the N minus one such possibilities
+ 
+
+ align:start position:0%
+to the N minus one such possibilities
+right so a binary choice for each the
+
+ align:start position:0%
+right so a binary choice for each the
+ 
+
+ align:start position:0%
+right so a binary choice for each the
+elements outside
+
+ align:start position:0%
+elements outside
+ 
+
+ align:start position:0%
+elements outside
+one okay now this is just an example but
+
+ align:start position:0%
+one okay now this is just an example but
+ 
+
+ align:start position:0%
+one okay now this is just an example but
+it turns out this is the best that we
+
+ align:start position:0%
+it turns out this is the best that we
+ 
+
+ align:start position:0%
+it turns out this is the best that we
+can do
+
+ align:start position:0%
+can do
+ 
+
+ align:start position:0%
+can do
+because okay so the claims that we
+
+ align:start position:0%
+because okay so the claims that we
+ 
+
+ align:start position:0%
+because okay so the claims that we
+cannot do better or we cannot get an
+
+ align:start position:0%
+cannot do better or we cannot get an
+ 
+
+ align:start position:0%
+cannot do better or we cannot get an
+even larger set
+
+ align:start position:0%
+even larger set
+ 
+
+ align:start position:0%
+even larger set
+and this is because for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every subset a of 1 through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most one of
+
+ align:start position:0%
+most one of
+ 
+
+ align:start position:0%
+most one of
+a and the complement of
+
+ align:start position:0%
+a and the complement of
+ 
+
+ align:start position:0%
+a and the complement of
+a so the elements 1 through n subtract a
+
+ align:start position:0%
+a so the elements 1 through n subtract a
+ 
+
+ align:start position:0%
+a so the elements 1 through n subtract a
+so the complement of a and most one of
+
+ align:start position:0%
+so the complement of a and most one of
+ 
+
+ align:start position:0%
+so the complement of a and most one of
+these can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the intersecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+family so what we're doing here is
+
+ align:start position:0%
+family so what we're doing here is
+ 
+
+ align:start position:0%
+family so what we're doing here is
+pairing up the sets with their
+
+ align:start position:0%
+pairing up the sets with their
+ 
+
+ align:start position:0%
+pairing up the sets with their
+complement and because it's an
+
+ align:start position:0%
+complement and because it's an
+ 
+
+ align:start position:0%
+complement and because it's an
+intersecting family you cannot
+
+ align:start position:0%
+intersecting family you cannot
+ 
+
+ align:start position:0%
+intersecting family you cannot
+simultaneously have a set and its
+
+ align:start position:0%
+simultaneously have a set and its
+ 
+
+ align:start position:0%
+simultaneously have a set and its
+complement in this intersecting family
+
+ align:start position:0%
+complement in this intersecting family
+ 
+
+ align:start position:0%
+complement in this intersecting family
+and so this
+
+ align:start position:0%
+and so this
+ 
+
+ align:start position:0%
+and so this
+eliminates so this means that you can
+
+ align:start position:0%
+eliminates so this means that you can
+ 
+
+ align:start position:0%
+eliminates so this means that you can
+have at most half of all the two to the
+
+ align:start position:0%
+have at most half of all the two to the
+ 
+
+ align:start position:0%
+have at most half of all the two to the
+N sets thereby showing that this 2 to
+
+ align:start position:0%
+N sets thereby showing that this 2 to
+ 
+
+ align:start position:0%
+N sets thereby showing that this 2 to
+the N minus one is indeed the best that
+
+ align:start position:0%
+the N minus one is indeed the best that
+ 
+
+ align:start position:0%
+the N minus one is indeed the best that
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+do okay so this
+
+ align:start position:0%
+do okay so this
+ 
+
+ align:start position:0%
+do okay so this
+finishes part one question one and now
+
+ align:start position:0%
+finishes part one question one and now
+ 
+
+ align:start position:0%
+finishes part one question one and now
+let's move on to the more interesting
+
+ align:start position:0%
+let's move on to the more interesting
+ 
+
+ align:start position:0%
+let's move on to the more interesting
+and harder question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two again let's start with some
+
+ align:start position:0%
+two again let's start with some
+ 
+
+ align:start position:0%
+two again let's start with some
+examples first here's
+
+ align:start position:0%
+examples first here's
+ 
+
+ align:start position:0%
+examples first here's
+a easy case if n is less than
+
+ align:start position:0%
+a easy case if n is less than
+ 
+
+ align:start position:0%
+a easy case if n is less than
+2K
+
+ align:start position:0%
+2K
+ 
+
+ align:start position:0%
+2K
+then okay so this is the easy setting if
+
+ align:start position:0%
+then okay so this is the easy setting if
+ 
+
+ align:start position:0%
+then okay so this is the easy setting if
+n is less than 2K then by pitching hole
+
+ align:start position:0%
+n is less than 2K then by pitching hole
+ 
+
+ align:start position:0%
+n is less than 2K then by pitching hole
+principle any pair of K element subsets
+
+ align:start position:0%
+principle any pair of K element subsets
+ 
+
+ align:start position:0%
+principle any pair of K element subsets
+of 1 through n intersect so we can take
+
+ align:start position:0%
+of 1 through n intersect so we can take
+ 
+
+ align:start position:0%
+of 1 through n intersect so we can take
+all n choose K
+
+ align:start position:0%
+all n choose K
+ 
+
+ align:start position:0%
+all n choose K
+sets and they form an
+
+ align:start position:0%
+sets and they form an
+ 
+
+ align:start position:0%
+sets and they form an
+intersecting family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's nothing really to do
+
+ align:start position:0%
+okay so there's nothing really to do
+ 
+
+ align:start position:0%
+okay so there's nothing really to do
+here because we can just take all the K
+
+ align:start position:0%
+here because we can just take all the K
+ 
+
+ align:start position:0%
+here because we can just take all the K
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+sets so the harder part of the question
+
+ align:start position:0%
+sets so the harder part of the question
+ 
+
+ align:start position:0%
+sets so the harder part of the question
+the more interesting part is what
+
+ align:start position:0%
+the more interesting part is what
+ 
+
+ align:start position:0%
+the more interesting part is what
+happens when n is at least
+
+ align:start position:0%
+happens when n is at least
+ 
+
+ align:start position:0%
+happens when n is at least
+2K here as an
+
+ align:start position:0%
+2K here as an
+ 
+
+ align:start position:0%
+2K here as an
+example we can take as earlier all sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing the element one
+
+ align:start position:0%
+containing the element one
+ 
+
+ align:start position:0%
+containing the element one
+and this gives us n minus one choose K
+
+ align:start position:0%
+and this gives us n minus one choose K
+ 
+
+ align:start position:0%
+and this gives us n minus one choose K
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+sets Okay and as before these sets they
+
+ align:start position:0%
+sets Okay and as before these sets they
+ 
+
+ align:start position:0%
+sets Okay and as before these sets they
+all this set form set this collection of
+
+ align:start position:0%
+all this set form set this collection of
+ 
+
+ align:start position:0%
+all this set form set this collection of
+sets form an intersecting family because
+
+ align:start position:0%
+sets form an intersecting family because
+ 
+
+ align:start position:0%
+sets form an intersecting family because
+any pair their intersection contains the
+
+ align:start position:0%
+any pair their intersection contains the
+ 
+
+ align:start position:0%
+any pair their intersection contains the
+element one and is thus
+
+ align:start position:0%
+element one and is thus
+ 
+
+ align:start position:0%
+element one and is thus
+nonempty right so this is a construction
+
+ align:start position:0%
+nonempty right so this is a construction
+ 
+
+ align:start position:0%
+nonempty right so this is a construction
+it gives you n minus1 choose K minus one
+
+ align:start position:0%
+it gives you n minus1 choose K minus one
+ 
+
+ align:start position:0%
+it gives you n minus1 choose K minus one
+sets but is this the best you can do
+
+ align:start position:0%
+sets but is this the best you can do
+ 
+
+ align:start position:0%
+sets but is this the best you can do
+right perhaps through some other methods
+
+ align:start position:0%
+right perhaps through some other methods
+ 
+
+ align:start position:0%
+right perhaps through some other methods
+of construction through other examples
+
+ align:start position:0%
+of construction through other examples
+ 
+
+ align:start position:0%
+of construction through other examples
+maybe there are even larger intersecting
+
+ align:start position:0%
+maybe there are even larger intersecting
+ 
+
+ align:start position:0%
+maybe there are even larger intersecting
+families of K element
+
+ align:start position:0%
+families of K element
+ 
+
+ align:start position:0%
+families of K element
+subsets that turns out not to be the
+
+ align:start position:0%
+subsets that turns out not to be the
+ 
+
+ align:start position:0%
+subsets that turns out not to be the
+case and that is the main theorem that
+
+ align:start position:0%
+case and that is the main theorem that
+ 
+
+ align:start position:0%
+case and that is the main theorem that
+we'll prove in this video and this
+
+ align:start position:0%
+we'll prove in this video and this
+ 
+
+ align:start position:0%
+we'll prove in this video and this
+result is known as the aish C rle
+
+ align:start position:0%
+result is known as the aish C rle
+ 
+
+ align:start position:0%
+result is known as the aish C rle
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a seminal and a beautiful
+
+ align:start position:0%
+so this is a seminal and a beautiful
+ 
+
+ align:start position:0%
+so this is a seminal and a beautiful
+result in extremal set
+
+ align:start position:0%
+result in extremal set
+ 
+
+ align:start position:0%
+result in extremal set
+theory and the ERS cor theorem says that
+
+ align:start position:0%
+theory and the ERS cor theorem says that
+ 
+
+ align:start position:0%
+theory and the ERS cor theorem says that
+if n is at least
+
+ align:start position:0%
+if n is at least
+ 
+
+ align:start position:0%
+if n is at least
+2K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+intersecting
+
+ align:start position:0%
+intersecting
+ 
+
+ align:start position:0%
+intersecting
+family and we give this family a name
+
+ align:start position:0%
+family and we give this family a name
+ 
+
+ align:start position:0%
+family and we give this family a name
+curly
+
+ align:start position:0%
+curly
+ 
+
+ align:start position:0%
+curly
+F of sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets of 1 through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay subsets um
+
+ align:start position:0%
+n okay subsets um
+ 
+
+ align:start position:0%
+n okay subsets um
+and any intersecting family of K element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsets of 1 through n
+
+ align:start position:0%
+subsets of 1 through n
+ 
+
+ align:start position:0%
+subsets of 1 through n
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+size at most n minus1 choose K minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one in other words the construction that
+
+ align:start position:0%
+one in other words the construction that
+ 
+
+ align:start position:0%
+one in other words the construction that
+we gave just now is indeed optimal you
+
+ align:start position:0%
+we gave just now is indeed optimal you
+ 
+
+ align:start position:0%
+we gave just now is indeed optimal you
+cannot get a bigger intersecting family
+
+ align:start position:0%
+cannot get a bigger intersecting family
+ 
+
+ align:start position:0%
+cannot get a bigger intersecting family
+of K element subsets of 1 through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n let us now prove the erors corado
+
+ align:start position:0%
+n let us now prove the erors corado
+ 
+
+ align:start position:0%
+n let us now prove the erors corado
+theorem and we'll introduce Randomness
+
+ align:start position:0%
+theorem and we'll introduce Randomness
+ 
+
+ align:start position:0%
+theorem and we'll introduce Randomness
+into to the problem and use the uh use
+
+ align:start position:0%
+into to the problem and use the uh use
+ 
+
+ align:start position:0%
+into to the problem and use the uh use
+some beautiful ideas from the
+
+ align:start position:0%
+some beautiful ideas from the
+ 
+
+ align:start position:0%
+some beautiful ideas from the
+probabilistic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method so here's how we start the
+
+ align:start position:0%
+method so here's how we start the
+ 
+
+ align:start position:0%
+method so here's how we start the
+proof let us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order the numbers 1 2 3 and so on
+
+ align:start position:0%
+order the numbers 1 2 3 and so on
+ 
+
+ align:start position:0%
+order the numbers 1 2 3 and so on
+through n
+
+ align:start position:0%
+through n
+ 
+
+ align:start position:0%
+through n
+randomly around a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle okay so what do I mean by this
+
+ align:start position:0%
+circle okay so what do I mean by this
+ 
+
+ align:start position:0%
+circle okay so what do I mean by this
+take a
+
+ align:start position:0%
+take a
+ 
+
+ align:start position:0%
+take a
+circle and then basically take a uniform
+
+ align:start position:0%
+circle and then basically take a uniform
+ 
+
+ align:start position:0%
+circle and then basically take a uniform
+the random permutation of 1 through n
+
+ align:start position:0%
+the random permutation of 1 through n
+ 
+
+ align:start position:0%
+the random permutation of 1 through n
+and then place the
+
+ align:start position:0%
+and then place the
+ 
+
+ align:start position:0%
+and then place the
+numbers around the circle in the order
+
+ align:start position:0%
+numbers around the circle in the order
+ 
+
+ align:start position:0%
+numbers around the circle in the order
+of that permutation so for example I'm
+
+ align:start position:0%
+of that permutation so for example I'm
+ 
+
+ align:start position:0%
+of that permutation so for example I'm
+putting down nine numbers here n equal
+
+ align:start position:0%
+putting down nine numbers here n equal
+ 
+
+ align:start position:0%
+putting down nine numbers here n equal
+to 9 in some circular order chosen
+
+ align:start position:0%
+to 9 in some circular order chosen
+ 
+
+ align:start position:0%
+to 9 in some circular order chosen
+uniformly at random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missing a number here six right so here
+
+ align:start position:0%
+missing a number here six right so here
+ 
+
+ align:start position:0%
+missing a number here six right so here
+nine numbers okay uniformly around the
+
+ align:start position:0%
+nine numbers okay uniformly around the
+ 
+
+ align:start position:0%
+nine numbers okay uniformly around the
+circle and let us
+
+ align:start position:0%
+circle and let us
+ 
+
+ align:start position:0%
+circle and let us
+call a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set subset of 1 through
+
+ align:start position:0%
+set subset of 1 through
+ 
+
+ align:start position:0%
+set subset of 1 through
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+contiguous I'm here I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defining term
+
+ align:start position:0%
+defining term
+ 
+
+ align:start position:0%
+defining term
+contiguous call this subset contigous us
+
+ align:start position:0%
+contiguous call this subset contigous us
+ 
+
+ align:start position:0%
+contiguous call this subset contigous us
+if its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements the way they're ordered around
+
+ align:start position:0%
+elements the way they're ordered around
+ 
+
+ align:start position:0%
+elements the way they're ordered around
+the circle form an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arc in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ordering so for
+
+ align:start position:0%
+ordering so for
+ 
+
+ align:start position:0%
+ordering so for
+example the set of numbers 4 3 9 5 this
+
+ align:start position:0%
+example the set of numbers 4 3 9 5 this
+ 
+
+ align:start position:0%
+example the set of numbers 4 3 9 5 this
+Four Element set is
+
+ align:start position:0%
+Four Element set is
+ 
+
+ align:start position:0%
+Four Element set is
+contiguous so 3 4 5 9 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contiguous because the orders they're
+
+ align:start position:0%
+contiguous because the orders they're
+ 
+
+ align:start position:0%
+contiguous because the orders they're
+according to the circular ordering these
+
+ align:start position:0%
+according to the circular ordering these
+ 
+
+ align:start position:0%
+according to the circular ordering these
+four numbers form a contiguous block on
+
+ align:start position:0%
+four numbers form a contiguous block on
+ 
+
+ align:start position:0%
+four numbers form a contiguous block on
+the other hand the set 1 three is not
+
+ align:start position:0%
+the other hand the set 1 three is not
+ 
+
+ align:start position:0%
+the other hand the set 1 three is not
+contiguous because they do not form a
+
+ align:start position:0%
+contiguous because they do not form a
+ 
+
+ align:start position:0%
+contiguous because they do not form a
+contiguous
+
+ align:start position:0%
+contiguous
+ 
+
+ align:start position:0%
+contiguous
+block okay so that's just a
+
+ align:start position:0%
+block okay so that's just a
+ 
+
+ align:start position:0%
+block okay so that's just a
+definition and now for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given set sub a a subset of 1 through
+
+ align:start position:0%
+given set sub a a subset of 1 through
+ 
+
+ align:start position:0%
+given set sub a a subset of 1 through
+M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with K
+
+ align:start position:0%
+with K
+ 
+
+ align:start position:0%
+with K
+elements so for a given K element subset
+
+ align:start position:0%
+elements so for a given K element subset
+ 
+
+ align:start position:0%
+elements so for a given K element subset
+of 1 through n what is the probability
+
+ align:start position:0%
+of 1 through n what is the probability
+ 
+
+ align:start position:0%
+of 1 through n what is the probability
+so here a is fixed a is not random so we
+
+ align:start position:0%
+so here a is fixed a is not random so we
+ 
+
+ align:start position:0%
+so here a is fixed a is not random so we
+given this a what is the probability
+
+ align:start position:0%
+given this a what is the probability
+ 
+
+ align:start position:0%
+given this a what is the probability
+that a is contiguous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the ordering Is Random so given
+
+ align:start position:0%
+okay so the ordering Is Random so given
+ 
+
+ align:start position:0%
+okay so the ordering Is Random so given
+a set what is the probability that under
+
+ align:start position:0%
+a set what is the probability that under
+ 
+
+ align:start position:0%
+a set what is the probability that under
+this random ordering is
+
+ align:start position:0%
+this random ordering is
+ 
+
+ align:start position:0%
+this random ordering is
+contiguous well let's think about
+
+ align:start position:0%
+contiguous well let's think about
+ 
+
+ align:start position:0%
+contiguous well let's think about
+that so the ordering is random but here
+
+ align:start position:0%
+that so the ordering is random but here
+ 
+
+ align:start position:0%
+that so the ordering is random but here
+if a has K elements can think about how
+
+ align:start position:0%
+if a has K elements can think about how
+ 
+
+ align:start position:0%
+if a has K elements can think about how
+many different ways these K elements can
+
+ align:start position:0%
+many different ways these K elements can
+ 
+
+ align:start position:0%
+many different ways these K elements can
+be placed around the circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are n different
+
+ align:start position:0%
+there are n different
+ 
+
+ align:start position:0%
+there are n different
+positions from where geometrically this
+
+ align:start position:0%
+positions from where geometrically this
+ 
+
+ align:start position:0%
+positions from where geometrically this
+K length K Arc lies and once you fix
+
+ align:start position:0%
+K length K Arc lies and once you fix
+ 
+
+ align:start position:0%
+K length K Arc lies and once you fix
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+position the
+
+ align:start position:0%
+position the
+ 
+
+ align:start position:0%
+position the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+that the elements the K elements of a
+
+ align:start position:0%
+that the elements the K elements of a
+ 
+
+ align:start position:0%
+that the elements the K elements of a
+actually falls into the desired
+
+ align:start position:0%
+actually falls into the desired
+ 
+
+ align:start position:0%
+actually falls into the desired
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+is 1/ K one over and choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K okay so this is the probability that a
+
+ align:start position:0%
+K okay so this is the probability that a
+ 
+
+ align:start position:0%
+K okay so this is the probability that a
+is a contiguous set under this random
+
+ align:start position:0%
+is a contiguous set under this random
+ 
+
+ align:start position:0%
+is a contiguous set under this random
+ordering and
+
+ align:start position:0%
+ordering and
+ 
+
+ align:start position:0%
+ordering and
+now by the linearity of
+
+ align:start position:0%
+now by the linearity of
+ 
+
+ align:start position:0%
+now by the linearity of
+expectations the expected number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contiguous sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this collection
+
+ align:start position:0%
+in this collection
+ 
+
+ align:start position:0%
+in this collection
+f is equal to the size of f times the
+
+ align:start position:0%
+f is equal to the size of f times the
+ 
+
+ align:start position:0%
+f is equal to the size of f times the
+probability that each individual set is
+
+ align:start position:0%
+probability that each individual set is
+ 
+
+ align:start position:0%
+probability that each individual set is
+contiguous and that was calculated
+
+ align:start position:0%
+contiguous and that was calculated
+ 
+
+ align:start position:0%
+contiguous and that was calculated
+earlier to be this quantity so n / n
+
+ align:start position:0%
+earlier to be this quantity so n / n
+ 
+
+ align:start position:0%
+earlier to be this quantity so n / n
+choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K on the other hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the property of f being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersecting a claim implies that in any
+
+ align:start position:0%
+intersecting a claim implies that in any
+ 
+
+ align:start position:0%
+intersecting a claim implies that in any
+given circular ordering there are at
+
+ align:start position:0%
+given circular ordering there are at
+ 
+
+ align:start position:0%
+given circular ordering there are at
+most K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contiguous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+for so in a
+
+ align:start position:0%
+for so in a
+ 
+
+ align:start position:0%
+for so in a
+given circular ordering okay so let's
+
+ align:start position:0%
+given circular ordering okay so let's
+ 
+
+ align:start position:0%
+given circular ordering okay so let's
+pause and think about why this claim is
+
+ align:start position:0%
+pause and think about why this claim is
+ 
+
+ align:start position:0%
+pause and think about why this claim is
+true if I give you an
+
+ align:start position:0%
+true if I give you an
+ 
+
+ align:start position:0%
+true if I give you an
+ordering and ask well how many
+
+ align:start position:0%
+ordering and ask well how many
+ 
+
+ align:start position:0%
+ordering and ask well how many
+contiguous sets can there be and now
+
+ align:start position:0%
+contiguous sets can there be and now
+ 
+
+ align:start position:0%
+contiguous sets can there be and now
+this sets these contiguous sets they
+
+ align:start position:0%
+this sets these contiguous sets they
+ 
+
+ align:start position:0%
+this sets these contiguous sets they
+have to be intersecting right so if we
+
+ align:start position:0%
+have to be intersecting right so if we
+ 
+
+ align:start position:0%
+have to be intersecting right so if we
+have one set so here let me denote the
+
+ align:start position:0%
+have one set so here let me denote the
+ 
+
+ align:start position:0%
+have one set so here let me denote the
+elements these circles as think about
+
+ align:start position:0%
+elements these circles as think about
+ 
+
+ align:start position:0%
+elements these circles as think about
+them as positions on the circle so these
+
+ align:start position:0%
+them as positions on the circle so these
+ 
+
+ align:start position:0%
+them as positions on the circle so these
+dots as positions on the circle so if
+
+ align:start position:0%
+dots as positions on the circle so if
+ 
+
+ align:start position:0%
+dots as positions on the circle so if
+that's one set well where can the other
+
+ align:start position:0%
+that's one set well where can the other
+ 
+
+ align:start position:0%
+that's one set well where can the other
+sets be well they have to intersect this
+
+ align:start position:0%
+sets be well they have to intersect this
+ 
+
+ align:start position:0%
+sets be well they have to intersect this
+block so maybe another set is like this
+
+ align:start position:0%
+block so maybe another set is like this
+ 
+
+ align:start position:0%
+block so maybe another set is like this
+one but if that set is in then it
+
+ align:start position:0%
+one but if that set is in then it
+ 
+
+ align:start position:0%
+one but if that set is in then it
+excludes if this blue set is in then
+
+ align:start position:0%
+excludes if this blue set is in then
+ 
+
+ align:start position:0%
+excludes if this blue set is in then
+excludes this green set from a
+
+ align:start position:0%
+excludes this green set from a
+ 
+
+ align:start position:0%
+excludes this green set from a
+possibility and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay so you see that given that this
+
+ align:start position:0%
+and okay so you see that given that this
+ 
+
+ align:start position:0%
+and okay so you see that given that this
+red set is
+
+ align:start position:0%
+red set is
+ 
+
+ align:start position:0%
+red set is
+in well at most one of the blue and
+
+ align:start position:0%
+in well at most one of the blue and
+ 
+
+ align:start position:0%
+in well at most one of the blue and
+green on the second line can be in and
+
+ align:start position:0%
+green on the second line can be in and
+ 
+
+ align:start position:0%
+green on the second line can be in and
+the most one of the blue and green on
+
+ align:start position:0%
+the most one of the blue and green on
+ 
+
+ align:start position:0%
+the most one of the blue and green on
+the third line can be in and the most
+
+ align:start position:0%
+the third line can be in and the most
+ 
+
+ align:start position:0%
+the third line can be in and the most
+one of blue and green on the fourth line
+
+ align:start position:0%
+one of blue and green on the fourth line
+ 
+
+ align:start position:0%
+one of blue and green on the fourth line
+can be in and these are the all the
+
+ align:start position:0%
+can be in and these are the all the
+ 
+
+ align:start position:0%
+can be in and these are the all the
+possibilities of how another contiguous
+
+ align:start position:0%
+possibilities of how another contiguous
+ 
+
+ align:start position:0%
+possibilities of how another contiguous
+set can intersect the the red set so
+
+ align:start position:0%
+set can intersect the the red set so
+ 
+
+ align:start position:0%
+set can intersect the the red set so
+that's an argument that can translate
+
+ align:start position:0%
+that's an argument that can translate
+ 
+
+ align:start position:0%
+that's an argument that can translate
+into this claim that F being
+
+ align:start position:0%
+into this claim that F being
+ 
+
+ align:start position:0%
+into this claim that F being
+intersecting implies that most K
+
+ align:start position:0%
+intersecting implies that most K
+ 
+
+ align:start position:0%
+intersecting implies that most K
+contiguous sets in any given
+
+ align:start position:0%
+contiguous sets in any given
+ 
+
+ align:start position:0%
+contiguous sets in any given
+order okay so this argument is very
+
+ align:start position:0%
+order okay so this argument is very
+ 
+
+ align:start position:0%
+order okay so this argument is very
+analog to the argument that we did at
+
+ align:start position:0%
+analog to the argument that we did at
+ 
+
+ align:start position:0%
+analog to the argument that we did at
+the beginning where we pair up
+
+ align:start position:0%
+the beginning where we pair up
+ 
+
+ align:start position:0%
+the beginning where we pair up
+complimentary sets but this time we're
+
+ align:start position:0%
+complimentary sets but this time we're
+ 
+
+ align:start position:0%
+complimentary sets but this time we're
+only looking at contiguous sets that
+
+ align:start position:0%
+only looking at contiguous sets that
+ 
+
+ align:start position:0%
+only looking at contiguous sets that
+intersect a given
+
+ align:start position:0%
+intersect a given
+ 
+
+ align:start position:0%
+intersect a given
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+okay well if you can only get at most K
+
+ align:start position:0%
+okay well if you can only get at most K
+ 
+
+ align:start position:0%
+okay well if you can only get at most K
+contiguous sets in any given order then
+
+ align:start position:0%
+contiguous sets in any given order then
+ 
+
+ align:start position:0%
+contiguous sets in any given order then
+this quantity which is a random variable
+
+ align:start position:0%
+this quantity which is a random variable
+ 
+
+ align:start position:0%
+this quantity which is a random variable
+it is always at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K so in it's expectation then this
+
+ align:start position:0%
+K so in it's expectation then this
+ 
+
+ align:start position:0%
+K so in it's expectation then this
+quantity that we got at the end is also
+
+ align:start position:0%
+quantity that we got at the end is also
+ 
+
+ align:start position:0%
+quantity that we got at the end is also
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+thus the size of f is at most K Over N
+
+ align:start position:0%
+thus the size of f is at most K Over N
+ 
+
+ align:start position:0%
+thus the size of f is at most K Over N
+time n chose
+
+ align:start position:0%
+time n chose
+ 
+
+ align:start position:0%
+time n chose
+K which one can then expand the binomial
+
+ align:start position:0%
+K which one can then expand the binomial
+ 
+
+ align:start position:0%
+K which one can then expand the binomial
+coefficient to see that the final
+
+ align:start position:0%
+coefficient to see that the final
+ 
+
+ align:start position:0%
+coefficient to see that the final
+quantity is equal to nus1 choose K -1
+
+ align:start position:0%
+quantity is equal to nus1 choose K -1
+ 
+
+ align:start position:0%
+quantity is equal to nus1 choose K -1
+one and that's exactly what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claimed all right so this finishes the
+
+ align:start position:0%
+claimed all right so this finishes the
+ 
+
+ align:start position:0%
+claimed all right so this finishes the
+proof of the ERS corado theorem which is
+
+ align:start position:0%
+proof of the ERS corado theorem which is
+ 
+
+ align:start position:0%
+proof of the ERS corado theorem which is
+a foundational result in extremal set
+
+ align:start position:0%
+a foundational result in extremal set
+ 
+
+ align:start position:0%
+a foundational result in extremal set
+theory and it's a beautiful application
+
+ align:start position:0%
+theory and it's a beautiful application
+ 
+
+ align:start position:0%
+theory and it's a beautiful application
+of the probabilistic method to extremal
+
+ align:start position:0%
+of the probabilistic method to extremal
+ 
+
+ align:start position:0%
+of the probabilistic method to extremal
+set theory and to combinatorics in
+
+ align:start position:0%
+set theory and to combinatorics in
+ 
+
+ align:start position:0%
+set theory and to combinatorics in
+general where we start with a claim a
+
+ align:start position:0%
+general where we start with a claim a
+ 
+
+ align:start position:0%
+general where we start with a claim a
+theorem that is not random at all it is
+
+ align:start position:0%
+theorem that is not random at all it is
+ 
+
+ align:start position:0%
+theorem that is not random at all it is
+completely deterministic it's about
+
+ align:start position:0%
+completely deterministic it's about
+ 
+
+ align:start position:0%
+completely deterministic it's about
+finding the maximum possible set size
+
+ align:start position:0%
+finding the maximum possible set size
+ 
+
+ align:start position:0%
+finding the maximum possible set size
+the size of something that satisfies
+
+ align:start position:0%
+the size of something that satisfies
+ 
+
+ align:start position:0%
+the size of something that satisfies
+some constraints and yet the proof goes
+
+ align:start position:0%
+some constraints and yet the proof goes
+ 
+
+ align:start position:0%
+some constraints and yet the proof goes
+by introducing new Randomness into the
+
+ align:start position:0%
+by introducing new Randomness into the
+ 
+
+ align:start position:0%
+by introducing new Randomness into the
+setup that allows us then to derive this
+
+ align:start position:0%
+setup that allows us then to derive this
+ 
+
+ align:start position:0%
+setup that allows us then to derive this
+beautiful conclusion
\ No newline at end of file
diff --git a/ziViLYrf1Ak.txt b/ziViLYrf1Ak.txt
new file mode 100644
index 0000000000000000000000000000000000000000..387bc649ad7acfe7400d95ddb933f0c15c60630c
--- /dev/null
+++ b/ziViLYrf1Ak.txt
@@ -0,0 +1,15075 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, welcome back to 6890. Uh
+
+ align:start position:0%
+All right, welcome back to 6890. Uh
+ 
+
+ align:start position:0%
+All right, welcome back to 6890. Uh
+today will be our last lecture about
+
+ align:start position:0%
+today will be our last lecture about
+ 
+
+ align:start position:0%
+today will be our last lecture about
+pure thresat so to speak and we'll be
+
+ align:start position:0%
+pure thresat so to speak and we'll be
+ 
+
+ align:start position:0%
+pure thresat so to speak and we'll be
+focusing in particular on circuit sat
+
+ align:start position:0%
+focusing in particular on circuit sat
+ 
+
+ align:start position:0%
+focusing in particular on circuit sat
+today. Um but before we get started with
+
+ align:start position:0%
+today. Um but before we get started with
+ 
+
+ align:start position:0%
+today. Um but before we get started with
+more reductions I want to highlight uh
+
+ align:start position:0%
+more reductions I want to highlight uh
+ 
+
+ align:start position:0%
+more reductions I want to highlight uh
+two styles of threes proofs that we've
+
+ align:start position:0%
+two styles of threes proofs that we've
+ 
+
+ align:start position:0%
+two styles of threes proofs that we've
+seen. Um this sort of this is orthogonal
+
+ align:start position:0%
+seen. Um this sort of this is orthogonal
+ 
+
+ align:start position:0%
+seen. Um this sort of this is orthogonal
+to the circuit perspective versus uh
+
+ align:start position:0%
+to the circuit perspective versus uh
+ 
+
+ align:start position:0%
+to the circuit perspective versus uh
+logic perspective. Um, so I think and I
+
+ align:start position:0%
+logic perspective. Um, so I think and I
+ 
+
+ align:start position:0%
+logic perspective. Um, so I think and I
+think it's interesting to highlight the
+
+ align:start position:0%
+think it's interesting to highlight the
+ 
+
+ align:start position:0%
+think it's interesting to highlight the
+two different approaches.
+
+ align:start position:0%
+two different approaches.
+ 
+
+ align:start position:0%
+two different approaches.
+So approach one I'm going to call dual
+
+ align:start position:0%
+So approach one I'm going to call dual
+ 
+
+ align:start position:0%
+So approach one I'm going to call dual
+rail logic.
+
+ align:start position:0%
+rail logic.
+ 
+
+ align:start position:0%
+rail logic.
+These are not the usual names. We're
+
+ align:start position:0%
+These are not the usual names. We're
+ 
+
+ align:start position:0%
+These are not the usual names. We're
+making up names here. There aren't
+
+ align:start position:0%
+making up names here. There aren't
+ 
+
+ align:start position:0%
+making up names here. There aren't
+really names for these types of
+
+ align:start position:0%
+really names for these types of
+ 
+
+ align:start position:0%
+really names for these types of
+reductions. And the other type I'm going
+
+ align:start position:0%
+reductions. And the other type I'm going
+ 
+
+ align:start position:0%
+reductions. And the other type I'm going
+to call binary logic.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+These names come from uh actual circuit
+
+ align:start position:0%
+These names come from uh actual circuit
+ 
+
+ align:start position:0%
+These names come from uh actual circuit
+stuff, real hardware. Um so for example,
+
+ align:start position:0%
+stuff, real hardware. Um so for example,
+ 
+
+ align:start position:0%
+stuff, real hardware. Um so for example,
+the all the Nintendo proofs we saw are
+
+ align:start position:0%
+the all the Nintendo proofs we saw are
+ 
+
+ align:start position:0%
+the all the Nintendo proofs we saw are
+in the style of what I would call dual
+
+ align:start position:0%
+in the style of what I would call dual
+ 
+
+ align:start position:0%
+in the style of what I would call dual
+rail logic because the variables have
+
+ align:start position:0%
+rail logic because the variables have
+ 
+
+ align:start position:0%
+rail logic because the variables have
+two outputs. The idea is that this one
+
+ align:start position:0%
+two outputs. The idea is that this one
+ 
+
+ align:start position:0%
+two outputs. The idea is that this one
+is activated when X is set to true. This
+
+ align:start position:0%
+is activated when X is set to true. This
+ 
+
+ align:start position:0%
+is activated when X is set to true. This
+one is activated when not X is set to
+
+ align:start position:0%
+one is activated when not X is set to
+ 
+
+ align:start position:0%
+one is activated when not X is set to
+true or X is set to false. Uh never
+
+ align:start position:0%
+true or X is set to false. Uh never
+ 
+
+ align:start position:0%
+true or X is set to false. Uh never
+should both of them be activated. So you
+
+ align:start position:0%
+should both of them be activated. So you
+ 
+
+ align:start position:0%
+should both of them be activated. So you
+have a separate rail, a separate line
+
+ align:start position:0%
+have a separate rail, a separate line
+ 
+
+ align:start position:0%
+have a separate rail, a separate line
+for the true case and a separate line
+
+ align:start position:0%
+for the true case and a separate line
+ 
+
+ align:start position:0%
+for the true case and a separate line
+for the false case. So and this is
+
+ align:start position:0%
+for the false case. So and this is
+ 
+
+ align:start position:0%
+for the false case. So and this is
+usually called the variable gadget that
+
+ align:start position:0%
+usually called the variable gadget that
+ 
+
+ align:start position:0%
+usually called the variable gadget that
+does that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I'm going to make up some more
+
+ align:start position:0%
+And I'm going to make up some more
+ 
+
+ align:start position:0%
+And I'm going to make up some more
+terminology. I'll call these semiwires.
+
+ align:start position:0%
+terminology. I'll call these semiwires.
+ 
+
+ align:start position:0%
+terminology. I'll call these semiwires.
+to distinguish from wires.
+
+ align:start position:0%
+to distinguish from wires.
+ 
+
+ align:start position:0%
+to distinguish from wires.
+Um so over here in the binary logic case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is sort of a half of a distinction.
+
+ align:start position:0%
+this is sort of a half of a distinction.
+ 
+
+ align:start position:0%
+this is sort of a half of a distinction.
+It's a semi- distinction. So um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is my attempt to unify things
+
+ align:start position:0%
+but this is my attempt to unify things
+ 
+
+ align:start position:0%
+but this is my attempt to unify things
+slightly. Uh so we have um
+
+ align:start position:0%
+slightly. Uh so we have um
+ 
+
+ align:start position:0%
+slightly. Uh so we have um
+yeah so so the idea is that these
+
+ align:start position:0%
+yeah so so the idea is that these
+ 
+
+ align:start position:0%
+yeah so so the idea is that these
+semiwires either they get activated or
+
+ align:start position:0%
+semiwires either they get activated or
+ 
+
+ align:start position:0%
+semiwires either they get activated or
+they don't get activated at all. Um in
+
+ align:start position:0%
+they don't get activated at all. Um in
+ 
+
+ align:start position:0%
+they don't get activated at all. Um in
+the unactivated case they're I mean
+
+ align:start position:0%
+the unactivated case they're I mean
+ 
+
+ align:start position:0%
+the unactivated case they're I mean
+there nothing happens to them. So uh
+
+ align:start position:0%
+there nothing happens to them. So uh
+ 
+
+ align:start position:0%
+there nothing happens to them. So uh
+they're not really interesting in the
+
+ align:start position:0%
+they're not really interesting in the
+ 
+
+ align:start position:0%
+they're not really interesting in the
+binary logic case. The idea is that the
+
+ align:start position:0%
+binary logic case. The idea is that the
+ 
+
+ align:start position:0%
+binary logic case. The idea is that the
+wire gadget is active in all situations
+
+ align:start position:0%
+wire gadget is active in all situations
+ 
+
+ align:start position:0%
+wire gadget is active in all situations
+but it can be active in two different
+
+ align:start position:0%
+but it can be active in two different
+ 
+
+ align:start position:0%
+but it can be active in two different
+ways. You can either set it to the true
+
+ align:start position:0%
+ways. You can either set it to the true
+ 
+
+ align:start position:0%
+ways. You can either set it to the true
+state or you can set it to the false
+
+ align:start position:0%
+state or you can set it to the false
+ 
+
+ align:start position:0%
+state or you can set it to the false
+state and it represents both sort of in
+
+ align:start position:0%
+state and it represents both sort of in
+ 
+
+ align:start position:0%
+state and it represents both sort of in
+one wire. Now this distinction is going
+
+ align:start position:0%
+one wire. Now this distinction is going
+ 
+
+ align:start position:0%
+one wire. Now this distinction is going
+to get a little bit vague but we saw an
+
+ align:start position:0%
+to get a little bit vague but we saw an
+ 
+
+ align:start position:0%
+to get a little bit vague but we saw an
+example of this kind of proof uh when we
+
+ align:start position:0%
+example of this kind of proof uh when we
+ 
+
+ align:start position:0%
+example of this kind of proof uh when we
+were talking about crease pattern flat
+
+ align:start position:0%
+were talking about crease pattern flat
+ 
+
+ align:start position:0%
+were talking about crease pattern flat
+foldability and P hardness. Uh the wire
+
+ align:start position:0%
+foldability and P hardness. Uh the wire
+ 
+
+ align:start position:0%
+foldability and P hardness. Uh the wire
+was the pleat and the pleat could be
+
+ align:start position:0%
+was the pleat and the pleat could be
+ 
+
+ align:start position:0%
+was the pleat and the pleat could be
+folded one way or the other. Uh but
+
+ align:start position:0%
+folded one way or the other. Uh but
+ 
+
+ align:start position:0%
+folded one way or the other. Uh but
+either way the the information is right
+
+ align:start position:0%
+either way the the information is right
+ 
+
+ align:start position:0%
+either way the the information is right
+here and it this the same wire gets put
+
+ align:start position:0%
+here and it this the same wire gets put
+ 
+
+ align:start position:0%
+here and it this the same wire gets put
+into this gadget whether you're true or
+
+ align:start position:0%
+into this gadget whether you're true or
+ 
+
+ align:start position:0%
+into this gadget whether you're true or
+false. Okay. Whereas over here
+
+ align:start position:0%
+false. Okay. Whereas over here
+ 
+
+ align:start position:0%
+false. Okay. Whereas over here
+uh you're connecting to this clause only
+
+ align:start position:0%
+uh you're connecting to this clause only
+ 
+
+ align:start position:0%
+uh you're connecting to this clause only
+the true uh half wire or semiwire goes
+
+ align:start position:0%
+the true uh half wire or semiwire goes
+ 
+
+ align:start position:0%
+the true uh half wire or semiwire goes
+to this clause. Uh the false one goes to
+
+ align:start position:0%
+to this clause. Uh the false one goes to
+ 
+
+ align:start position:0%
+to this clause. Uh the false one goes to
+this clause and to this clause. Okay. So
+
+ align:start position:0%
+this clause and to this clause. Okay. So
+ 
+
+ align:start position:0%
+this clause and to this clause. Okay. So
+there's a distinction between here where
+
+ align:start position:0%
+there's a distinction between here where
+ 
+
+ align:start position:0%
+there's a distinction between here where
+the wire has been split in half and here
+
+ align:start position:0%
+the wire has been split in half and here
+ 
+
+ align:start position:0%
+the wire has been split in half and here
+where it's all in one place and the wire
+
+ align:start position:0%
+where it's all in one place and the wire
+ 
+
+ align:start position:0%
+where it's all in one place and the wire
+goes to the gadget whether it said true
+
+ align:start position:0%
+goes to the gadget whether it said true
+ 
+
+ align:start position:0%
+goes to the gadget whether it said true
+or false. Um I think that's sort of what
+
+ align:start position:0%
+or false. Um I think that's sort of what
+ 
+
+ align:start position:0%
+or false. Um I think that's sort of what
+I wanted to say. My main intent here is
+
+ align:start position:0%
+I wanted to say. My main intent here is
+ 
+
+ align:start position:0%
+I wanted to say. My main intent here is
+to highlight what kind of gadgets you
+
+ align:start position:0%
+to highlight what kind of gadgets you
+ 
+
+ align:start position:0%
+to highlight what kind of gadgets you
+need. So
+
+ align:start position:0%
+need. So
+ 
+
+ align:start position:0%
+need. So
+uh we have a wire gadget on this side, a
+
+ align:start position:0%
+uh we have a wire gadget on this side, a
+ 
+
+ align:start position:0%
+uh we have a wire gadget on this side, a
+variable gadget on this side. Uh for
+
+ align:start position:0%
+variable gadget on this side. Uh for
+ 
+
+ align:start position:0%
+variable gadget on this side. Uh for
+binary logic, you also need a splitter
+
+ align:start position:0%
+binary logic, you also need a splitter
+ 
+
+ align:start position:0%
+binary logic, you also need a splitter
+or split gadget
+
+ align:start position:0%
+or split gadget
+ 
+
+ align:start position:0%
+or split gadget
+to make copies of the wire.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the idea is you have one wire coming
+
+ align:start position:0%
+So the idea is you have one wire coming
+ 
+
+ align:start position:0%
+So the idea is you have one wire coming
+in. There's some magic split gadget
+
+ align:start position:0%
+in. There's some magic split gadget
+ 
+
+ align:start position:0%
+in. There's some magic split gadget
+which makes two wires or three wires
+
+ align:start position:0%
+which makes two wires or three wires
+ 
+
+ align:start position:0%
+which makes two wires or three wires
+whatever uh coming out. So then you can
+
+ align:start position:0%
+whatever uh coming out. So then you can
+ 
+
+ align:start position:0%
+whatever uh coming out. So then you can
+repeat split however many times that
+
+ align:start position:0%
+repeat split however many times that
+ 
+
+ align:start position:0%
+repeat split however many times that
+variable occurs. um you can uh make a
+
+ align:start position:0%
+variable occurs. um you can uh make a
+ 
+
+ align:start position:0%
+variable occurs. um you can uh make a
+copy in the non-monotone versions of
+
+ align:start position:0%
+copy in the non-monotone versions of
+ 
+
+ align:start position:0%
+copy in the non-monotone versions of
+threes. You may also need uh a negation
+
+ align:start position:0%
+threes. You may also need uh a negation
+ 
+
+ align:start position:0%
+threes. You may also need uh a negation
+or not gadget.
+
+ align:start position:0%
+or not gadget.
+ 
+
+ align:start position:0%
+or not gadget.
+If you need negation, then you'll need a
+
+ align:start position:0%
+If you need negation, then you'll need a
+ 
+
+ align:start position:0%
+If you need negation, then you'll need a
+negation gadget. Um in some cases, you
+
+ align:start position:0%
+negation gadget. Um in some cases, you
+ 
+
+ align:start position:0%
+negation gadget. Um in some cases, you
+also need uh a terminator gadget.
+
+ align:start position:0%
+also need uh a terminator gadget.
+ 
+
+ align:start position:0%
+also need uh a terminator gadget.
+In this perspective,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminator gadget uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just uh the end of a wire, you might
+
+ align:start position:0%
+is just uh the end of a wire, you might
+ 
+
+ align:start position:0%
+is just uh the end of a wire, you might
+say. So if you want to just not use a
+
+ align:start position:0%
+say. So if you want to just not use a
+ 
+
+ align:start position:0%
+say. So if you want to just not use a
+wire, then that's uh you would put a
+
+ align:start position:0%
+wire, then that's uh you would put a
+ 
+
+ align:start position:0%
+wire, then that's uh you would put a
+terminator gadget. And the idea of the
+
+ align:start position:0%
+terminator gadget. And the idea of the
+ 
+
+ align:start position:0%
+terminator gadget. And the idea of the
+terminator gadget is it leaves it free.
+
+ align:start position:0%
+terminator gadget is it leaves it free.
+ 
+
+ align:start position:0%
+terminator gadget is it leaves it free.
+Leaves the wire free to choose true or
+
+ align:start position:0%
+Leaves the wire free to choose true or
+ 
+
+ align:start position:0%
+Leaves the wire free to choose true or
+false. Uh now sometimes you can get away
+
+ align:start position:0%
+false. Uh now sometimes you can get away
+ 
+
+ align:start position:0%
+false. Uh now sometimes you can get away
+without a terminator gadget if uh you
+
+ align:start position:0%
+without a terminator gadget if uh you
+ 
+
+ align:start position:0%
+without a terminator gadget if uh you
+can for example if each of your
+
+ align:start position:0%
+can for example if each of your
+ 
+
+ align:start position:0%
+can for example if each of your
+variables occurs exactly four times uh
+
+ align:start position:0%
+variables occurs exactly four times uh
+ 
+
+ align:start position:0%
+variables occurs exactly four times uh
+then you can just use two splitters make
+
+ align:start position:0%
+then you can just use two splitters make
+ 
+
+ align:start position:0%
+then you can just use two splitters make
+four copies and then connect those
+
+ align:start position:0%
+four copies and then connect those
+ 
+
+ align:start position:0%
+four copies and then connect those
+directly to the clauses. So maybe with
+
+ align:start position:0%
+directly to the clauses. So maybe with
+ 
+
+ align:start position:0%
+directly to the clauses. So maybe with
+some negations. So in that case you
+
+ align:start position:0%
+some negations. So in that case you
+ 
+
+ align:start position:0%
+some negations. So in that case you
+wouldn't need a terminator. Uh over here
+
+ align:start position:0%
+wouldn't need a terminator. Uh over here
+ 
+
+ align:start position:0%
+wouldn't need a terminator. Uh over here
+we're using a terminator in a certain
+
+ align:start position:0%
+we're using a terminator in a certain
+ 
+
+ align:start position:0%
+we're using a terminator in a certain
+sense which is the edge of the paper. If
+
+ align:start position:0%
+sense which is the edge of the paper. If
+ 
+
+ align:start position:0%
+sense which is the edge of the paper. If
+a wire goes to the edge of the paper it
+
+ align:start position:0%
+a wire goes to the edge of the paper it
+ 
+
+ align:start position:0%
+a wire goes to the edge of the paper it
+becomes free. Uh so that sort of the
+
+ align:start position:0%
+becomes free. Uh so that sort of the
+ 
+
+ align:start position:0%
+becomes free. Uh so that sort of the
+terminator gadget here although we
+
+ align:start position:0%
+terminator gadget here although we
+ 
+
+ align:start position:0%
+terminator gadget here although we
+didn't make it explicit it was part of
+
+ align:start position:0%
+didn't make it explicit it was part of
+ 
+
+ align:start position:0%
+didn't make it explicit it was part of
+this uh overall plan.
+
+ align:start position:0%
+this uh overall plan.
+ 
+
+ align:start position:0%
+this uh overall plan.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+in both cases
+
+ align:start position:0%
+in both cases
+ 
+
+ align:start position:0%
+in both cases
+in one and two
+
+ align:start position:0%
+in one and two
+ 
+
+ align:start position:0%
+in one and two
+you probably need something like a turn
+
+ align:start position:0%
+you probably need something like a turn
+ 
+
+ align:start position:0%
+you probably need something like a turn
+gadget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and maybe a crossover gadget.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we've seen we've seen these in
+
+ align:start position:0%
+And we've seen we've seen these in
+ 
+
+ align:start position:0%
+And we've seen we've seen these in
+various forms. In this case, the turn
+
+ align:start position:0%
+various forms. In this case, the turn
+ 
+
+ align:start position:0%
+various forms. In this case, the turn
+gadget was very explicit. Uh I mean it
+
+ align:start position:0%
+gadget was very explicit. Uh I mean it
+ 
+
+ align:start position:0%
+gadget was very explicit. Uh I mean it
+was also a splitter and also a negator,
+
+ align:start position:0%
+was also a splitter and also a negator,
+ 
+
+ align:start position:0%
+was also a splitter and also a negator,
+but in particular it changed the angle.
+
+ align:start position:0%
+but in particular it changed the angle.
+ 
+
+ align:start position:0%
+but in particular it changed the angle.
+And we needed that in order to take this
+
+ align:start position:0%
+And we needed that in order to take this
+ 
+
+ align:start position:0%
+And we needed that in order to take this
+truth value and send it up to the clause
+
+ align:start position:0%
+truth value and send it up to the clause
+ 
+
+ align:start position:0%
+truth value and send it up to the clause
+and aim everything, right?
+
+ align:start position:0%
+and aim everything, right?
+ 
+
+ align:start position:0%
+and aim everything, right?
+Uh, and in general, if you're doing any
+
+ align:start position:0%
+Uh, and in general, if you're doing any
+ 
+
+ align:start position:0%
+Uh, and in general, if you're doing any
+kind of embedding into two dimensions,
+
+ align:start position:0%
+kind of embedding into two dimensions,
+ 
+
+ align:start position:0%
+kind of embedding into two dimensions,
+you're probably going to need a turn
+
+ align:start position:0%
+you're probably going to need a turn
+ 
+
+ align:start position:0%
+you're probably going to need a turn
+gadget so you can move your wires or
+
+ align:start position:0%
+gadget so you can move your wires or
+ 
+
+ align:start position:0%
+gadget so you can move your wires or
+semi-wires around. Um, most a lot of the
+
+ align:start position:0%
+semi-wires around. Um, most a lot of the
+ 
+
+ align:start position:0%
+semi-wires around. Um, most a lot of the
+time people might call this also a wire.
+
+ align:start position:0%
+time people might call this also a wire.
+ 
+
+ align:start position:0%
+time people might call this also a wire.
+So, that's why uh, but I think it's
+
+ align:start position:0%
+So, that's why uh, but I think it's
+ 
+
+ align:start position:0%
+So, that's why uh, but I think it's
+useful to have a word to distinguish
+
+ align:start position:0%
+useful to have a word to distinguish
+ 
+
+ align:start position:0%
+useful to have a word to distinguish
+these kinds of wires which are only
+
+ align:start position:0%
+these kinds of wires which are only
+ 
+
+ align:start position:0%
+these kinds of wires which are only
+active or inactive versus the wires
+
+ align:start position:0%
+active or inactive versus the wires
+ 
+
+ align:start position:0%
+active or inactive versus the wires
+which are always active but in two
+
+ align:start position:0%
+which are always active but in two
+ 
+
+ align:start position:0%
+which are always active but in two
+possible states.
+
+ align:start position:0%
+possible states.
+ 
+
+ align:start position:0%
+possible states.
+Hopefully that's that clarifies or makes
+
+ align:start position:0%
+Hopefully that's that clarifies or makes
+ 
+
+ align:start position:0%
+Hopefully that's that clarifies or makes
+more explicit the types of proofs we've
+
+ align:start position:0%
+more explicit the types of proofs we've
+ 
+
+ align:start position:0%
+more explicit the types of proofs we've
+seen so far. Um now today we're going to
+
+ align:start position:0%
+seen so far. Um now today we're going to
+ 
+
+ align:start position:0%
+seen so far. Um now today we're going to
+do a couple of circuit sat proofs which
+
+ align:start position:0%
+do a couple of circuit sat proofs which
+ 
+
+ align:start position:0%
+do a couple of circuit sat proofs which
+all of this applies to circuit SAT
+
+ align:start position:0%
+all of this applies to circuit SAT
+ 
+
+ align:start position:0%
+all of this applies to circuit SAT
+proofs as well as SAT and one and three
+
+ align:start position:0%
+proofs as well as SAT and one and three
+ 
+
+ align:start position:0%
+proofs as well as SAT and one and three
+sat and not all equals SAT not all equal
+
+ align:start position:0%
+sat and not all equals SAT not all equal
+ 
+
+ align:start position:0%
+sat and not all equals SAT not all equal
+threes. um circuit set you're going to
+
+ align:start position:0%
+threes. um circuit set you're going to
+ 
+
+ align:start position:0%
+threes. um circuit set you're going to
+have I guess in principle you could do
+
+ align:start position:0%
+have I guess in principle you could do
+ 
+
+ align:start position:0%
+have I guess in principle you could do
+it uh dual rail logic or binary logic
+
+ align:start position:0%
+it uh dual rail logic or binary logic
+ 
+
+ align:start position:0%
+it uh dual rail logic or binary logic
+although usually we probably think of
+
+ align:start position:0%
+although usually we probably think of
+ 
+
+ align:start position:0%
+although usually we probably think of
+them in this capacity um in binary logic
+
+ align:start position:0%
+them in this capacity um in binary logic
+ 
+
+ align:start position:0%
+them in this capacity um in binary logic
+and you're going to have wires you still
+
+ align:start position:0%
+and you're going to have wires you still
+ 
+
+ align:start position:0%
+and you're going to have wires you still
+need splits because you need to be able
+
+ align:start position:0%
+need splits because you need to be able
+ 
+
+ align:start position:0%
+need splits because you need to be able
+to take the output of a gate and send it
+
+ align:start position:0%
+to take the output of a gate and send it
+ 
+
+ align:start position:0%
+to take the output of a gate and send it
+to multiple other gates um in addition
+
+ align:start position:0%
+to multiple other gates um in addition
+ 
+
+ align:start position:0%
+to multiple other gates um in addition
+to a not gadget you're going to want
+
+ align:start position:0%
+to a not gadget you're going to want
+ 
+
+ align:start position:0%
+to a not gadget you're going to want
+some other universal uh logic gate
+
+ align:start position:0%
+some other universal uh logic gate
+ 
+
+ align:start position:0%
+some other universal uh logic gate
+So we're going to talk about that in a
+
+ align:start position:0%
+So we're going to talk about that in a
+ 
+
+ align:start position:0%
+So we're going to talk about that in a
+bit after we see some examples.
+
+ align:start position:0%
+bit after we see some examples.
+ 
+
+ align:start position:0%
+bit after we see some examples.
+So our first example
+
+ align:start position:0%
+So our first example
+ 
+
+ align:start position:0%
+So our first example
+is called Akari or light up. Uh this is
+
+ align:start position:0%
+is called Akari or light up. Uh this is
+ 
+
+ align:start position:0%
+is called Akari or light up. Uh this is
+another nicoli puzzle like Sudoku and uh
+
+ align:start position:0%
+another nicoli puzzle like Sudoku and uh
+ 
+
+ align:start position:0%
+another nicoli puzzle like Sudoku and uh
+uh number link we saw last time. Uh so
+
+ align:start position:0%
+uh number link we saw last time. Uh so
+ 
+
+ align:start position:0%
+uh number link we saw last time. Uh so
+here's the sample input and a sample
+
+ align:start position:0%
+here's the sample input and a sample
+ 
+
+ align:start position:0%
+here's the sample input and a sample
+output. Uh ignore the black dots there.
+
+ align:start position:0%
+output. Uh ignore the black dots there.
+ 
+
+ align:start position:0%
+output. Uh ignore the black dots there.
+So, uh, you're given a grid. Uh, there's
+
+ align:start position:0%
+So, uh, you're given a grid. Uh, there's
+ 
+
+ align:start position:0%
+So, uh, you're given a grid. Uh, there's
+blank squares and there's obstacle
+
+ align:start position:0%
+blank squares and there's obstacle
+ 
+
+ align:start position:0%
+blank squares and there's obstacle
+squares where you're not allowed to put
+
+ align:start position:0%
+squares where you're not allowed to put
+ 
+
+ align:start position:0%
+squares where you're not allowed to put
+anything. Some of the obstacle squares
+
+ align:start position:0%
+anything. Some of the obstacle squares
+ 
+
+ align:start position:0%
+anything. Some of the obstacle squares
+may have a number between zero and four
+
+ align:start position:0%
+may have a number between zero and four
+ 
+
+ align:start position:0%
+may have a number between zero and four
+on them. And that number represents how
+
+ align:start position:0%
+on them. And that number represents how
+ 
+
+ align:start position:0%
+on them. And that number represents how
+many among the four neighbors, edge
+
+ align:start position:0%
+many among the four neighbors, edge
+ 
+
+ align:start position:0%
+many among the four neighbors, edge
+neighbors of that square, how many of
+
+ align:start position:0%
+neighbors of that square, how many of
+ 
+
+ align:start position:0%
+neighbors of that square, how many of
+them should have a light. These blue
+
+ align:start position:0%
+them should have a light. These blue
+ 
+
+ align:start position:0%
+them should have a light. These blue
+circles are lights. Okay? So, like this
+
+ align:start position:0%
+circles are lights. Okay? So, like this
+ 
+
+ align:start position:0%
+circles are lights. Okay? So, like this
+one has zero lights in those four
+
+ align:start position:0%
+one has zero lights in those four
+ 
+
+ align:start position:0%
+one has zero lights in those four
+positions. This one has two. This one
+
+ align:start position:0%
+positions. This one has two. This one
+ 
+
+ align:start position:0%
+positions. This one has two. This one
+has four. That's forced. and so on. A
+
+ align:start position:0%
+has four. That's forced. and so on. A
+ 
+
+ align:start position:0%
+has four. That's forced. and so on. A
+lot of the cells are free, but whether
+
+ align:start position:0%
+lot of the cells are free, but whether
+ 
+
+ align:start position:0%
+lot of the cells are free, but whether
+you're lit or not. And then the rules
+
+ align:start position:0%
+you're lit or not. And then the rules
+ 
+
+ align:start position:0%
+you're lit or not. And then the rules
+are uh so you can think of a light as a
+
+ align:start position:0%
+are uh so you can think of a light as a
+ 
+
+ align:start position:0%
+are uh so you can think of a light as a
+rook in chess. So it can see everything
+
+ align:start position:0%
+rook in chess. So it can see everything
+ 
+
+ align:start position:0%
+rook in chess. So it can see everything
+horizontally in the same row up to
+
+ align:start position:0%
+horizontally in the same row up to
+ 
+
+ align:start position:0%
+horizontally in the same row up to
+obstacles and in the same column up to
+
+ align:start position:0%
+obstacles and in the same column up to
+ 
+
+ align:start position:0%
+obstacles and in the same column up to
+obstacles. So this guy for example
+
+ align:start position:0%
+obstacles. So this guy for example
+ 
+
+ align:start position:0%
+obstacles. So this guy for example
+lights these this portion and this
+
+ align:start position:0%
+lights these this portion and this
+ 
+
+ align:start position:0%
+lights these this portion and this
+portion. This guy lights that portion
+
+ align:start position:0%
+portion. This guy lights that portion
+ 
+
+ align:start position:0%
+portion. This guy lights that portion
+and nothing here and so on. Uh and the
+
+ align:start position:0%
+and nothing here and so on. Uh and the
+ 
+
+ align:start position:0%
+and nothing here and so on. Uh and the
+goal is first of all to light the entire
+
+ align:start position:0%
+goal is first of all to light the entire
+ 
+
+ align:start position:0%
+goal is first of all to light the entire
+board. So that's why it's all green.
+
+ align:start position:0%
+board. So that's why it's all green.
+ 
+
+ align:start position:0%
+board. So that's why it's all green.
+It's all lit um in such in that way. And
+
+ align:start position:0%
+It's all lit um in such in that way. And
+ 
+
+ align:start position:0%
+It's all lit um in such in that way. And
+no two lights should light each other
+
+ align:start position:0%
+no two lights should light each other
+ 
+
+ align:start position:0%
+no two lights should light each other
+because then it's too bright, I guess. I
+
+ align:start position:0%
+because then it's too bright, I guess. I
+ 
+
+ align:start position:0%
+because then it's too bright, I guess. I
+don't know. So uh uh no two rooks can
+
+ align:start position:0%
+don't know. So uh uh no two rooks can
+ 
+
+ align:start position:0%
+don't know. So uh uh no two rooks can
+attack each other would be another
+
+ align:start position:0%
+attack each other would be another
+ 
+
+ align:start position:0%
+attack each other would be another
+perspective. Um and I think those are
+
+ align:start position:0%
+perspective. Um and I think those are
+ 
+
+ align:start position:0%
+perspective. Um and I think those are
+the rules. So you've got to have you've
+
+ align:start position:0%
+the rules. So you've got to have you've
+ 
+
+ align:start position:0%
+the rules. So you've got to have you've
+got to satisfy the number constraint.
+
+ align:start position:0%
+got to satisfy the number constraint.
+ 
+
+ align:start position:0%
+got to satisfy the number constraint.
+You can only place lights in the blank
+
+ align:start position:0%
+You can only place lights in the blank
+ 
+
+ align:start position:0%
+You can only place lights in the blank
+squares. Uh you have to light everything
+
+ align:start position:0%
+squares. Uh you have to light everything
+ 
+
+ align:start position:0%
+squares. Uh you have to light everything
+and they can't see each other. So, this
+
+ align:start position:0%
+and they can't see each other. So, this
+ 
+
+ align:start position:0%
+and they can't see each other. So, this
+is a valid solution. This is puzzle one
+
+ align:start position:0%
+is a valid solution. This is puzzle one
+ 
+
+ align:start position:0%
+is a valid solution. This is puzzle one
+on the Nickel website, and there's a ton
+
+ align:start position:0%
+on the Nickel website, and there's a ton
+ 
+
+ align:start position:0%
+on the Nickel website, and there's a ton
+more if you want to to play.
+
+ align:start position:0%
+more if you want to to play.
+ 
+
+ align:start position:0%
+more if you want to to play.
+But you're saying they can't be in the
+
+ align:start position:0%
+But you're saying they can't be in the
+ 
+
+ align:start position:0%
+But you're saying they can't be in the
+same row or column.
+
+ align:start position:0%
+same row or column.
+ 
+
+ align:start position:0%
+same row or column.
+Uh, I mean, they can be in the same
+
+ align:start position:0%
+Uh, I mean, they can be in the same
+ 
+
+ align:start position:0%
+Uh, I mean, they can be in the same
+column, but they have to be separated by
+
+ align:start position:0%
+column, but they have to be separated by
+ 
+
+ align:start position:0%
+column, but they have to be separated by
+an obstacle. Yeah. So, they can't see
+
+ align:start position:0%
+an obstacle. Yeah. So, they can't see
+ 
+
+ align:start position:0%
+an obstacle. Yeah. So, they can't see
+each other within a sort of sub column
+
+ align:start position:0%
+each other within a sort of sub column
+ 
+
+ align:start position:0%
+each other within a sort of sub column
+or within a sub row
+
+ align:start position:0%
+or within a sub row
+ 
+
+ align:start position:0%
+or within a sub row
+as given by the obstacles. Cool. So,
+
+ align:start position:0%
+as given by the obstacles. Cool. So,
+ 
+
+ align:start position:0%
+as given by the obstacles. Cool. So,
+that's the problem. And now we're going
+
+ align:start position:0%
+that's the problem. And now we're going
+ 
+
+ align:start position:0%
+that's the problem. And now we're going
+to prove that it's empty. Um this is a
+
+ align:start position:0%
+to prove that it's empty. Um this is a
+ 
+
+ align:start position:0%
+to prove that it's empty. Um this is a
+nice proof because it's relatively
+
+ align:start position:0%
+nice proof because it's relatively
+ 
+
+ align:start position:0%
+nice proof because it's relatively
+simple and it illustrates a kind of
+
+ align:start position:0%
+simple and it illustrates a kind of
+ 
+
+ align:start position:0%
+simple and it illustrates a kind of
+circuit SAT style reduction.
+
+ align:start position:0%
+circuit SAT style reduction.
+ 
+
+ align:start position:0%
+circuit SAT style reduction.
+Uh so for starters and most I would say
+
+ align:start position:0%
+Uh so for starters and most I would say
+ 
+
+ align:start position:0%
+Uh so for starters and most I would say
+most SAT proofs a good starting point is
+
+ align:start position:0%
+most SAT proofs a good starting point is
+ 
+
+ align:start position:0%
+most SAT proofs a good starting point is
+a wire gadget. You want to think about
+
+ align:start position:0%
+a wire gadget. You want to think about
+ 
+
+ align:start position:0%
+a wire gadget. You want to think about
+can I make some construction that has
+
+ align:start position:0%
+can I make some construction that has
+ 
+
+ align:start position:0%
+can I make some construction that has
+ideally exactly two solutions one to
+
+ align:start position:0%
+ideally exactly two solutions one to
+ 
+
+ align:start position:0%
+ideally exactly two solutions one to
+represent true one to represent false.
+
+ align:start position:0%
+represent true one to represent false.
+ 
+
+ align:start position:0%
+represent true one to represent false.
+So here are a very variety of ways to do
+
+ align:start position:0%
+So here are a very variety of ways to do
+ 
+
+ align:start position:0%
+So here are a very variety of ways to do
+wires and this is a fairly flexible kind
+
+ align:start position:0%
+wires and this is a fairly flexible kind
+ 
+
+ align:start position:0%
+wires and this is a fairly flexible kind
+of game. The basic one looks like this.
+
+ align:start position:0%
+of game. The basic one looks like this.
+ 
+
+ align:start position:0%
+of game. The basic one looks like this.
+So most of the things are going to be
+
+ align:start position:0%
+So most of the things are going to be
+ 
+
+ align:start position:0%
+So most of the things are going to be
+obstacles to make to tie it down, make
+
+ align:start position:0%
+obstacles to make to tie it down, make
+ 
+
+ align:start position:0%
+obstacles to make to tie it down, make
+it easy to separate gadgets. Uh but here
+
+ align:start position:0%
+it easy to separate gadgets. Uh but here
+ 
+
+ align:start position:0%
+it easy to separate gadgets. Uh but here
+we have two blank squares, a one, two
+
+ align:start position:0%
+we have two blank squares, a one, two
+ 
+
+ align:start position:0%
+we have two blank squares, a one, two
+blank squares, a one, two blank squares.
+
+ align:start position:0%
+blank squares, a one, two blank squares.
+ 
+
+ align:start position:0%
+blank squares, a one, two blank squares.
+That's sort of a simple kind of wire
+
+ align:start position:0%
+That's sort of a simple kind of wire
+ 
+
+ align:start position:0%
+That's sort of a simple kind of wire
+because you know from this one either x
+
+ align:start position:0%
+because you know from this one either x
+ 
+
+ align:start position:0%
+because you know from this one either x
+or x prime is a light. Exactly one of
+
+ align:start position:0%
+or x prime is a light. Exactly one of
+ 
+
+ align:start position:0%
+or x prime is a light. Exactly one of
+them is. So uh that forces alternation.
+
+ align:start position:0%
+them is. So uh that forces alternation.
+ 
+
+ align:start position:0%
+them is. So uh that forces alternation.
+Done. Uh why? uh because if we choose X,
+
+ align:start position:0%
+Done. Uh why? uh because if we choose X,
+ 
+
+ align:start position:0%
+Done. Uh why? uh because if we choose X,
+we can't choose X prime because then
+
+ align:start position:0%
+we can't choose X prime because then
+ 
+
+ align:start position:0%
+we can't choose X prime because then
+they're in the same sub row and all the
+
+ align:start position:0%
+they're in the same sub row and all the
+ 
+
+ align:start position:0%
+they're in the same sub row and all the
+way down the chain. So in general, uh if
+
+ align:start position:0%
+way down the chain. So in general, uh if
+ 
+
+ align:start position:0%
+way down the chain. So in general, uh if
+X is true, the idea is that the X's are
+
+ align:start position:0%
+X is true, the idea is that the X's are
+ 
+
+ align:start position:0%
+X is true, the idea is that the X's are
+the lights. If X is false, then the X
+
+ align:start position:0%
+the lights. If X is false, then the X
+ 
+
+ align:start position:0%
+the lights. If X is false, then the X
+primes are the lights. Okay, now uh
+
+ align:start position:0%
+primes are the lights. Okay, now uh
+ 
+
+ align:start position:0%
+primes are the lights. Okay, now uh
+that's a basic wire, but sort of part of
+
+ align:start position:0%
+that's a basic wire, but sort of part of
+ 
+
+ align:start position:0%
+that's a basic wire, but sort of part of
+the wire is we need a turn gadget. So
+
+ align:start position:0%
+the wire is we need a turn gadget. So
+ 
+
+ align:start position:0%
+the wire is we need a turn gadget. So
+this is a 90° turn. Um just check that
+
+ align:start position:0%
+this is a 90° turn. Um just check that
+ 
+
+ align:start position:0%
+this is a 90° turn. Um just check that
+this is still lit. Uh if these guys
+
+ align:start position:0%
+this is still lit. Uh if these guys
+ 
+
+ align:start position:0%
+this is still lit. Uh if these guys
+could not see each other, I think this
+
+ align:start position:0%
+could not see each other, I think this
+ 
+
+ align:start position:0%
+could not see each other, I think this
+is black. It's also okay. The
+
+ align:start position:0%
+is black. It's also okay. The
+ 
+
+ align:start position:0%
+is black. It's also okay. The
+alternation is forced by the one, but
+
+ align:start position:0%
+alternation is forced by the one, but
+ 
+
+ align:start position:0%
+alternation is forced by the one, but
+some flexibility.
+
+ align:start position:0%
+some flexibility.
+ 
+
+ align:start position:0%
+some flexibility.
+Uh, and let's see. Uh, the other fun
+
+ align:start position:0%
+Uh, and let's see. Uh, the other fun
+ 
+
+ align:start position:0%
+Uh, and let's see. Uh, the other fun
+thing you can do is spread out the x and
+
+ align:start position:0%
+thing you can do is spread out the x and
+ 
+
+ align:start position:0%
+thing you can do is spread out the x and
+x prime. If you put a bunch of zeros
+
+ align:start position:0%
+x prime. If you put a bunch of zeros
+ 
+
+ align:start position:0%
+x prime. If you put a bunch of zeros
+here to force that there's no lights
+
+ align:start position:0%
+here to force that there's no lights
+ 
+
+ align:start position:0%
+here to force that there's no lights
+here, uh, because this has to be lit.
+
+ align:start position:0%
+here, uh, because this has to be lit.
+ 
+
+ align:start position:0%
+here, uh, because this has to be lit.
+Again, one of these has to be active and
+
+ align:start position:0%
+Again, one of these has to be active and
+ 
+
+ align:start position:0%
+Again, one of these has to be active and
+the ones force an alternation. So, this
+
+ align:start position:0%
+the ones force an alternation. So, this
+ 
+
+ align:start position:0%
+the ones force an alternation. So, this
+is helpful uh because if our wires just
+
+ align:start position:0%
+is helpful uh because if our wires just
+ 
+
+ align:start position:0%
+is helpful uh because if our wires just
+look like this, and we'll we this will
+
+ align:start position:0%
+look like this, and we'll we this will
+ 
+
+ align:start position:0%
+look like this, and we'll we this will
+come up again today. uh then you're
+
+ align:start position:0%
+come up again today. uh then you're
+ 
+
+ align:start position:0%
+come up again today. uh then you're
+forced to be congruent to zero mod 3.
+
+ align:start position:0%
+forced to be congruent to zero mod 3.
+ 
+
+ align:start position:0%
+forced to be congruent to zero mod 3.
+You have first of your width has to be a
+
+ align:start position:0%
+You have first of your width has to be a
+ 
+
+ align:start position:0%
+You have first of your width has to be a
+multiple of three. Uh and this can be an
+
+ align:start position:0%
+multiple of three. Uh and this can be an
+ 
+
+ align:start position:0%
+multiple of three. Uh and this can be an
+issue if you have a bunch of gadgets
+
+ align:start position:0%
+issue if you have a bunch of gadgets
+ 
+
+ align:start position:0%
+issue if you have a bunch of gadgets
+each of different sizes. Maybe one is
+
+ align:start position:0%
+each of different sizes. Maybe one is
+ 
+
+ align:start position:0%
+each of different sizes. Maybe one is
+5x5, another's 3x3 and other fun prime
+
+ align:start position:0%
+5x5, another's 3x3 and other fun prime
+ 
+
+ align:start position:0%
+5x5, another's 3x3 and other fun prime
+numbers, then you might have trouble
+
+ align:start position:0%
+numbers, then you might have trouble
+ 
+
+ align:start position:0%
+numbers, then you might have trouble
+actually getting gadgets to meet edge
+
+ align:start position:0%
+actually getting gadgets to meet edge
+ 
+
+ align:start position:0%
+actually getting gadgets to meet edge
+on. Uh maybe there's a gap of one or two
+
+ align:start position:0%
+on. Uh maybe there's a gap of one or two
+ 
+
+ align:start position:0%
+on. Uh maybe there's a gap of one or two
+or something between the gadgets. Uh but
+
+ align:start position:0%
+or something between the gadgets. Uh but
+ 
+
+ align:start position:0%
+or something between the gadgets. Uh but
+once you if you have a setup where you
+
+ align:start position:0%
+once you if you have a setup where you
+ 
+
+ align:start position:0%
+once you if you have a setup where you
+can make wires you can adjust the wire
+
+ align:start position:0%
+can make wires you can adjust the wire
+ 
+
+ align:start position:0%
+can make wires you can adjust the wire
+lengths to be any integer that's good
+
+ align:start position:0%
+lengths to be any integer that's good
+ 
+
+ align:start position:0%
+lengths to be any integer that's good
+because then you can go do this most of
+
+ align:start position:0%
+because then you can go do this most of
+ 
+
+ align:start position:0%
+because then you can go do this most of
+the time but then when you're getting
+
+ align:start position:0%
+the time but then when you're getting
+ 
+
+ align:start position:0%
+the time but then when you're getting
+close to the gate uh if you're off by
+
+ align:start position:0%
+close to the gate uh if you're off by
+ 
+
+ align:start position:0%
+close to the gate uh if you're off by
+one or two or three you just uh make it
+
+ align:start position:0%
+one or two or three you just uh make it
+ 
+
+ align:start position:0%
+one or two or three you just uh make it
+a little bit longer and you're all set.
+
+ align:start position:0%
+a little bit longer and you're all set.
+ 
+
+ align:start position:0%
+a little bit longer and you're all set.
+The unfilled one can also just have a
+
+ align:start position:0%
+The unfilled one can also just have a
+ 
+
+ align:start position:0%
+The unfilled one can also just have a
+crossover gadget. Then
+
+ align:start position:0%
+crossover gadget. Then
+ 
+
+ align:start position:0%
+crossover gadget. Then
+uh sorry
+
+ align:start position:0%
+uh sorry
+ 
+
+ align:start position:0%
+uh sorry
+since you have nothing it's very natural
+
+ align:start position:0%
+since you have nothing it's very natural
+ 
+
+ align:start position:0%
+since you have nothing it's very natural
+to have a crossover gadget by putting
+
+ align:start position:0%
+to have a crossover gadget by putting
+ 
+
+ align:start position:0%
+to have a crossover gadget by putting
+two of them orthogonal.
+
+ align:start position:0%
+two of them orthogonal.
+ 
+
+ align:start position:0%
+two of them orthogonal.
+Oh yeah, you can make a crossover gadget
+
+ align:start position:0%
+Oh yeah, you can make a crossover gadget
+ 
+
+ align:start position:0%
+Oh yeah, you can make a crossover gadget
+easy in this setup. I think that is a
+
+ align:start position:0%
+easy in this setup. I think that is a
+ 
+
+ align:start position:0%
+easy in this setup. I think that is a
+future slide.
+
+ align:start position:0%
+future slide.
+ 
+
+ align:start position:0%
+future slide.
+Um let's so we'll do crossover in a bit.
+
+ align:start position:0%
+Um let's so we'll do crossover in a bit.
+ 
+
+ align:start position:0%
+Um let's so we'll do crossover in a bit.
+Let's start with uh yeah you can very
+
+ align:start position:0%
+Let's start with uh yeah you can very
+ 
+
+ align:start position:0%
+Let's start with uh yeah you can very
+easily do a crossover. Uh we won't need
+
+ align:start position:0%
+easily do a crossover. Uh we won't need
+ 
+
+ align:start position:0%
+easily do a crossover. Uh we won't need
+a crossover here. That's what I mean.
+
+ align:start position:0%
+a crossover here. That's what I mean.
+ 
+
+ align:start position:0%
+a crossover here. That's what I mean.
+Uh so we definitely need splitting
+
+ align:start position:0%
+Uh so we definitely need splitting
+ 
+
+ align:start position:0%
+Uh so we definitely need splitting
+though in general whenever you have
+
+ align:start position:0%
+though in general whenever you have
+ 
+
+ align:start position:0%
+though in general whenever you have
+wires you've got to be able to make
+
+ align:start position:0%
+wires you've got to be able to make
+ 
+
+ align:start position:0%
+wires you've got to be able to make
+copies because if your variable only
+
+ align:start position:0%
+copies because if your variable only
+ 
+
+ align:start position:0%
+copies because if your variable only
+appears in two places uh threes is easy
+
+ align:start position:0%
+appears in two places uh threes is easy
+ 
+
+ align:start position:0%
+appears in two places uh threes is easy
+or circuit set is probably easy. Uh so
+
+ align:start position:0%
+or circuit set is probably easy. Uh so
+ 
+
+ align:start position:0%
+or circuit set is probably easy. Uh so
+uh here is a splitter. Uh this is the
+
+ align:start position:0%
+uh here is a splitter. Uh this is the
+ 
+
+ align:start position:0%
+uh here is a splitter. Uh this is the
+the main mechanism. Uh I guess these
+
+ align:start position:0%
+the main mechanism. Uh I guess these
+ 
+
+ align:start position:0%
+the main mechanism. Uh I guess these
+ones and this two. So these ones force
+
+ align:start position:0%
+ones and this two. So these ones force
+ 
+
+ align:start position:0%
+ones and this two. So these ones force
+an alternation uh between here and here.
+
+ align:start position:0%
+an alternation uh between here and here.
+ 
+
+ align:start position:0%
+an alternation uh between here and here.
+These have to be opposites of each
+
+ align:start position:0%
+These have to be opposites of each
+ 
+
+ align:start position:0%
+These have to be opposites of each
+other. and then the two. So if both of
+
+ align:start position:0%
+other. and then the two. So if both of
+ 
+
+ align:start position:0%
+other. and then the two. So if both of
+the x's are present, if this is absent,
+
+ align:start position:0%
+the x's are present, if this is absent,
+ 
+
+ align:start position:0%
+the x's are present, if this is absent,
+then these two have to be present by the
+
+ align:start position:0%
+then these two have to be present by the
+ 
+
+ align:start position:0%
+then these two have to be present by the
+ones. And so by this two, that's all
+
+ align:start position:0%
+ones. And so by this two, that's all
+ 
+
+ align:start position:0%
+ones. And so by this two, that's all
+there is. And therefore, this is absent.
+
+ align:start position:0%
+there is. And therefore, this is absent.
+ 
+
+ align:start position:0%
+there is. And therefore, this is absent.
+So these guys have to be the same. These
+
+ align:start position:0%
+So these guys have to be the same. These
+ 
+
+ align:start position:0%
+So these guys have to be the same. These
+guys have to be opposite. Uh and
+
+ align:start position:0%
+guys have to be opposite. Uh and
+ 
+
+ align:start position:0%
+guys have to be opposite. Uh and
+conversely, if this is present by these
+
+ align:start position:0%
+conversely, if this is present by these
+ 
+
+ align:start position:0%
+conversely, if this is present by these
+ones, these have to be absent. And by
+
+ align:start position:0%
+ones, these have to be absent. And by
+ 
+
+ align:start position:0%
+ones, these have to be absent. And by
+this two, this has to be present. So
+
+ align:start position:0%
+this two, this has to be present. So
+ 
+
+ align:start position:0%
+this two, this has to be present. So
+this is this is almost sort of a well,
+
+ align:start position:0%
+this is this is almost sort of a well,
+ 
+
+ align:start position:0%
+this is this is almost sort of a well,
+you could also put some ones here, I
+
+ align:start position:0%
+you could also put some ones here, I
+ 
+
+ align:start position:0%
+you could also put some ones here, I
+guess, uh if you felt like it. Anyway,
+
+ align:start position:0%
+guess, uh if you felt like it. Anyway,
+ 
+
+ align:start position:0%
+guess, uh if you felt like it. Anyway,
+if you think about the parity here, what
+
+ align:start position:0%
+if you think about the parity here, what
+ 
+
+ align:start position:0%
+if you think about the parity here, what
+we we have for an when we're
+
+ align:start position:0%
+we we have for an when we're
+ 
+
+ align:start position:0%
+we we have for an when we're
+representing a signal coming into a
+
+ align:start position:0%
+representing a signal coming into a
+ 
+
+ align:start position:0%
+representing a signal coming into a
+gadget, there's X on the left and X
+
+ align:start position:0%
+gadget, there's X on the left and X
+ 
+
+ align:start position:0%
+gadget, there's X on the left and X
+prime on the right. Uh so that means
+
+ align:start position:0%
+prime on the right. Uh so that means
+ 
+
+ align:start position:0%
+prime on the right. Uh so that means
+coming out here, there's now X prime on
+
+ align:start position:0%
+coming out here, there's now X prime on
+ 
+
+ align:start position:0%
+coming out here, there's now X prime on
+the left and X on the right. So this is
+
+ align:start position:0%
+the left and X on the right. So this is
+ 
+
+ align:start position:0%
+the left and X on the right. So this is
+actually a negated copy of X. Um and up
+
+ align:start position:0%
+actually a negated copy of X. Um and up
+ 
+
+ align:start position:0%
+actually a negated copy of X. Um and up
+here with some turns, uh we have a
+
+ align:start position:0%
+here with some turns, uh we have a
+ 
+
+ align:start position:0%
+here with some turns, uh we have a
+regular copy of X and a regular copy of
+
+ align:start position:0%
+regular copy of X and a regular copy of
+ 
+
+ align:start position:0%
+regular copy of X and a regular copy of
+X. This is actually a fairly common
+
+ align:start position:0%
+X. This is actually a fairly common
+ 
+
+ align:start position:0%
+X. This is actually a fairly common
+thing that happens when you try to
+
+ align:start position:0%
+thing that happens when you try to
+ 
+
+ align:start position:0%
+thing that happens when you try to
+split. Maybe you also get a negated copy
+
+ align:start position:0%
+split. Maybe you also get a negated copy
+ 
+
+ align:start position:0%
+split. Maybe you also get a negated copy
+or instead you get a negated copy. Uh
+
+ align:start position:0%
+or instead you get a negated copy. Uh
+ 
+
+ align:start position:0%
+or instead you get a negated copy. Uh
+this is actually great because it kills
+
+ align:start position:0%
+this is actually great because it kills
+ 
+
+ align:start position:0%
+this is actually great because it kills
+two birds with one stone. You can use
+
+ align:start position:0%
+two birds with one stone. You can use
+ 
+
+ align:start position:0%
+two birds with one stone. You can use
+this as a splitter. It kind of makes
+
+ align:start position:0%
+this as a splitter. It kind of makes
+ 
+
+ align:start position:0%
+this as a splitter. It kind of makes
+three copies of your signal. Uh but you
+
+ align:start position:0%
+three copies of your signal. Uh but you
+ 
+
+ align:start position:0%
+three copies of your signal. Uh but you
+can also use it just as a negation
+
+ align:start position:0%
+can also use it just as a negation
+ 
+
+ align:start position:0%
+can also use it just as a negation
+gadget as a not gate. I think I have a
+
+ align:start position:0%
+gadget as a not gate. I think I have a
+ 
+
+ align:start position:0%
+gadget as a not gate. I think I have a
+slide of those done explicitly.
+
+ align:start position:0%
+slide of those done explicitly.
+ 
+
+ align:start position:0%
+slide of those done explicitly.
+Uh yeah. So uh here we're effectively
+
+ align:start position:0%
+Uh yeah. So uh here we're effectively
+ 
+
+ align:start position:0%
+Uh yeah. So uh here we're effectively
+using a terminator gadget. We're saying,
+
+ align:start position:0%
+using a terminator gadget. We're saying,
+ 
+
+ align:start position:0%
+using a terminator gadget. We're saying,
+well, we could throw away this negated
+
+ align:start position:0%
+well, we could throw away this negated
+ 
+
+ align:start position:0%
+well, we could throw away this negated
+copy because we already have two
+
+ align:start position:0%
+copy because we already have two
+ 
+
+ align:start position:0%
+copy because we already have two
+positive copies and that's enough for a
+
+ align:start position:0%
+positive copies and that's enough for a
+ 
+
+ align:start position:0%
+positive copies and that's enough for a
+splitter. So, if we just end the the
+
+ align:start position:0%
+splitter. So, if we just end the the
+ 
+
+ align:start position:0%
+splitter. So, if we just end the the
+this wire here, great, we've got a
+
+ align:start position:0%
+this wire here, great, we've got a
+ 
+
+ align:start position:0%
+this wire here, great, we've got a
+split. Um, or if we throw away the two
+
+ align:start position:0%
+split. Um, or if we throw away the two
+ 
+
+ align:start position:0%
+split. Um, or if we throw away the two
+copies of X and we just want the negated
+
+ align:start position:0%
+copies of X and we just want the negated
+ 
+
+ align:start position:0%
+copies of X and we just want the negated
+copy of X, then ends up looking like
+
+ align:start position:0%
+copy of X, then ends up looking like
+ 
+
+ align:start position:0%
+copy of X, then ends up looking like
+this. So, we get uh a split gadget and a
+
+ align:start position:0%
+this. So, we get uh a split gadget and a
+ 
+
+ align:start position:0%
+this. So, we get uh a split gadget and a
+notgate essentially for free out of
+
+ align:start position:0%
+notgate essentially for free out of
+ 
+
+ align:start position:0%
+notgate essentially for free out of
+this. You could just present this gadget
+
+ align:start position:0%
+this. You could just present this gadget
+ 
+
+ align:start position:0%
+this. You could just present this gadget
+and say, "Oh, I also have terminators."
+
+ align:start position:0%
+and say, "Oh, I also have terminators."
+ 
+
+ align:start position:0%
+and say, "Oh, I also have terminators."
+And then you know that you get these uh
+
+ align:start position:0%
+And then you know that you get these uh
+ 
+
+ align:start position:0%
+And then you know that you get these uh
+but for fun he drew them and I'll show
+
+ align:start position:0%
+but for fun he drew them and I'll show
+ 
+
+ align:start position:0%
+but for fun he drew them and I'll show
+you them. I won't show you them in
+
+ align:start position:0%
+you them. I won't show you them in
+ 
+
+ align:start position:0%
+you them. I won't show you them in
+future proofs but
+
+ align:start position:0%
+future proofs but
+ 
+
+ align:start position:0%
+future proofs but
+uh cool. So let's see what do we have.
+
+ align:start position:0%
+uh cool. So let's see what do we have.
+ 
+
+ align:start position:0%
+uh cool. So let's see what do we have.
+We've got a wire.
+
+ align:start position:0%
+We've got a wire.
+ 
+
+ align:start position:0%
+We've got a wire.
+We've got a split. We've got a knot.
+
+ align:start position:0%
+We've got a split. We've got a knot.
+ 
+
+ align:start position:0%
+We've got a split. We've got a knot.
+We've got a terminator. Uh we need some
+
+ align:start position:0%
+We've got a terminator. Uh we need some
+ 
+
+ align:start position:0%
+We've got a terminator. Uh we need some
+kind of clause or some kind of logic
+
+ align:start position:0%
+kind of clause or some kind of logic
+ 
+
+ align:start position:0%
+kind of clause or some kind of logic
+gate. Uh and then possibly we also need
+
+ align:start position:0%
+gate. Uh and then possibly we also need
+ 
+
+ align:start position:0%
+gate. Uh and then possibly we also need
+a crossover. We have turns.
+
+ align:start position:0%
+a crossover. We have turns.
+ 
+
+ align:start position:0%
+a crossover. We have turns.
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+uh, next up is a, uh, gate. It's sort of
+
+ align:start position:0%
+uh, next up is a, uh, gate. It's sort of
+ 
+
+ align:start position:0%
+uh, next up is a, uh, gate. It's sort of
+a a mega gate. I'm guessing, uh, McFale
+
+ align:start position:0%
+a a mega gate. I'm guessing, uh, McFale
+ 
+
+ align:start position:0%
+a a mega gate. I'm guessing, uh, McFale
+tried various little configurations and
+
+ align:start position:0%
+tried various little configurations and
+ 
+
+ align:start position:0%
+tried various little configurations and
+then found one that did interesting
+
+ align:start position:0%
+then found one that did interesting
+ 
+
+ align:start position:0%
+then found one that did interesting
+things. It actually does, uh, two
+
+ align:start position:0%
+things. It actually does, uh, two
+ 
+
+ align:start position:0%
+things. It actually does, uh, two
+interesting things at once. So, we have
+
+ align:start position:0%
+interesting things at once. So, we have
+ 
+
+ align:start position:0%
+interesting things at once. So, we have
+X coming in on the left and Y coming in
+
+ align:start position:0%
+X coming in on the left and Y coming in
+ 
+
+ align:start position:0%
+X coming in on the left and Y coming in
+on the right. So, both of them have this
+
+ align:start position:0%
+on the right. So, both of them have this
+ 
+
+ align:start position:0%
+on the right. So, both of them have this
+X- prime and Y prime, the negated
+
+ align:start position:0%
+X- prime and Y prime, the negated
+ 
+
+ align:start position:0%
+X- prime and Y prime, the negated
+copies. And then we've got some fun
+
+ align:start position:0%
+copies. And then we've got some fun
+ 
+
+ align:start position:0%
+copies. And then we've got some fun
+stuff in here. So, uh, let's start with
+
+ align:start position:0%
+stuff in here. So, uh, let's start with
+ 
+
+ align:start position:0%
+stuff in here. So, uh, let's start with
+maybe the bottom, which is supposed to
+
+ align:start position:0%
+maybe the bottom, which is supposed to
+ 
+
+ align:start position:0%
+maybe the bottom, which is supposed to
+be an ore of X and Y. So, um, let's say
+
+ align:start position:0%
+be an ore of X and Y. So, um, let's say
+ 
+
+ align:start position:0%
+be an ore of X and Y. So, um, let's say
+that they are both false, for example.
+
+ align:start position:0%
+that they are both false, for example.
+ 
+
+ align:start position:0%
+that they are both false, for example.
+And general, we're going to have to
+
+ align:start position:0%
+And general, we're going to have to
+ 
+
+ align:start position:0%
+And general, we're going to have to
+check all the cases, but I won't do all
+
+ align:start position:0%
+check all the cases, but I won't do all
+ 
+
+ align:start position:0%
+check all the cases, but I won't do all
+of them. So, let's say this is absent.
+
+ align:start position:0%
+of them. So, let's say this is absent.
+ 
+
+ align:start position:0%
+of them. So, let's say this is absent.
+This is absent, meaning the other it's
+
+ align:start position:0%
+This is absent, meaning the other it's
+ 
+
+ align:start position:0%
+This is absent, meaning the other it's
+lit from the other end.
+
+ align:start position:0%
+lit from the other end.
+ 
+
+ align:start position:0%
+lit from the other end.
+If it's false, it means X prime is
+
+ align:start position:0%
+If it's false, it means X prime is
+ 
+
+ align:start position:0%
+If it's false, it means X prime is
+present.
+
+ align:start position:0%
+present.
+ 
+
+ align:start position:0%
+present.
+Oh, right. Sorry. Right. If they're both
+
+ align:start position:0%
+Oh, right. Sorry. Right. If they're both
+ 
+
+ align:start position:0%
+Oh, right. Sorry. Right. If they're both
+false, good. uh then both of these are
+
+ align:start position:0%
+false, good. uh then both of these are
+ 
+
+ align:start position:0%
+false, good. uh then both of these are
+present and therefore uh we're gonna get
+
+ align:start position:0%
+present and therefore uh we're gonna get
+ 
+
+ align:start position:0%
+present and therefore uh we're gonna get
+hopefully that this one is absent
+
+ align:start position:0%
+hopefully that this one is absent
+ 
+
+ align:start position:0%
+hopefully that this one is absent
+because the ore of false and false is
+
+ align:start position:0%
+because the ore of false and false is
+ 
+
+ align:start position:0%
+because the ore of false and false is
+false. Uh so the claim would be that a
+
+ align:start position:0%
+false. Uh so the claim would be that a
+ 
+
+ align:start position:0%
+false. Uh so the claim would be that a
+prime and b prime must be activated.
+
+ align:start position:0%
+prime and b prime must be activated.
+ 
+
+ align:start position:0%
+prime and b prime must be activated.
+If they weren't then you couldn't light
+
+ align:start position:0%
+If they weren't then you couldn't light
+ 
+
+ align:start position:0%
+If they weren't then you couldn't light
+both A and B.
+
+ align:start position:0%
+both A and B.
+ 
+
+ align:start position:0%
+both A and B.
+Uh right these are at best ored
+
+ align:start position:0%
+Uh right these are at best ored
+ 
+
+ align:start position:0%
+Uh right these are at best ored
+together. At most one of these is
+
+ align:start position:0%
+together. At most one of these is
+ 
+
+ align:start position:0%
+together. At most one of these is
+present. These regions both need to be
+
+ align:start position:0%
+present. These regions both need to be
+ 
+
+ align:start position:0%
+present. These regions both need to be
+lit. Uh, so we're going to need uh at
+
+ align:start position:0%
+lit. Uh, so we're going to need uh at
+ 
+
+ align:start position:0%
+lit. Uh, so we're going to need uh at
+least one of them to be on, but once one
+
+ align:start position:0%
+least one of them to be on, but once one
+ 
+
+ align:start position:0%
+least one of them to be on, but once one
+of them is on, we know that Z is absent.
+
+ align:start position:0%
+of them is on, we know that Z is absent.
+ 
+
+ align:start position:0%
+of them is on, we know that Z is absent.
+And then the other one must be on. Try
+
+ align:start position:0%
+And then the other one must be on. Try
+ 
+
+ align:start position:0%
+And then the other one must be on. Try
+this two. Good.
+
+ align:start position:0%
+this two. Good.
+ 
+
+ align:start position:0%
+this two. Good.
+Okay. And then we should up here get
+
+ align:start position:0%
+Okay. And then we should up here get
+ 
+
+ align:start position:0%
+Okay. And then we should up here get
+Xnor
+
+ align:start position:0%
+Xnor
+ 
+
+ align:start position:0%
+Xnor
+uh because so when these were both false
+
+ align:start position:0%
+uh because so when these were both false
+ 
+
+ align:start position:0%
+uh because so when these were both false
+and present, these were present. Uh
+
+ align:start position:0%
+and present, these were present. Uh
+ 
+
+ align:start position:0%
+and present, these were present. Uh
+these are absent and therefore this is
+
+ align:start position:0%
+these are absent and therefore this is
+ 
+
+ align:start position:0%
+these are absent and therefore this is
+present. and the xor of 0 and 0 is zero.
+
+ align:start position:0%
+present. and the xor of 0 and 0 is zero.
+ 
+
+ align:start position:0%
+present. and the xor of 0 and 0 is zero.
+The x nor is one. So that's good. So in
+
+ align:start position:0%
+The x nor is one. So that's good. So in
+ 
+
+ align:start position:0%
+The x nor is one. So that's good. So in
+general, you check all the cases and
+
+ align:start position:0%
+general, you check all the cases and
+ 
+
+ align:start position:0%
+general, you check all the cases and
+confirm this is the case. Again, by
+
+ align:start position:0%
+confirm this is the case. Again, by
+ 
+
+ align:start position:0%
+confirm this is the case. Again, by
+putting terminators on here, we can get
+
+ align:start position:0%
+putting terminators on here, we can get
+ 
+
+ align:start position:0%
+putting terminators on here, we can get
+either x or y or x nor x x nor y sounds
+
+ align:start position:0%
+either x or y or x nor x x nor y sounds
+ 
+
+ align:start position:0%
+either x or y or x nor x x nor y sounds
+funny. Um that's great. Uh we actually
+
+ align:start position:0%
+funny. Um that's great. Uh we actually
+ 
+
+ align:start position:0%
+funny. Um that's great. Uh we actually
+uh this is the one that we really care
+
+ align:start position:0%
+uh this is the one that we really care
+ 
+
+ align:start position:0%
+uh this is the one that we really care
+about. Uh the or gate. Well, so
+
+ align:start position:0%
+about. Uh the or gate. Well, so
+ 
+
+ align:start position:0%
+about. Uh the or gate. Well, so
+different answers to this, but uh you
+
+ align:start position:0%
+different answers to this, but uh you
+ 
+
+ align:start position:0%
+different answers to this, but uh you
+should know and we'll talk more about
+
+ align:start position:0%
+should know and we'll talk more about
+ 
+
+ align:start position:0%
+should know and we'll talk more about
+this later. NAND and or let's say
+
+ align:start position:0%
+this later. NAND and or let's say
+ 
+
+ align:start position:0%
+this later. NAND and or let's say
+the NANDgate is universal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a NOR gate by itself is universal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+These are just good things you should
+
+ align:start position:0%
+These are just good things you should
+ 
+
+ align:start position:0%
+These are just good things you should
+know. Uh they go back at least 50 years.
+
+ align:start position:0%
+know. Uh they go back at least 50 years.
+ 
+
+ align:start position:0%
+know. Uh they go back at least 50 years.
+And uh
+
+ align:start position:0%
+And uh
+ 
+
+ align:start position:0%
+And uh
+what does universal mean?
+
+ align:start position:0%
+what does universal mean?
+ 
+
+ align:start position:0%
+what does universal mean?
+Uh so universal means that from that
+
+ align:start position:0%
+Uh so universal means that from that
+ 
+
+ align:start position:0%
+Uh so universal means that from that
+those from if you're just given a bunch
+
+ align:start position:0%
+those from if you're just given a bunch
+ 
+
+ align:start position:0%
+those from if you're just given a bunch
+of nans then you can construct any
+
+ align:start position:0%
+of nans then you can construct any
+ 
+
+ align:start position:0%
+of nans then you can construct any
+logical gate you want. Uh I will talk
+
+ align:start position:0%
+logical gate you want. Uh I will talk
+ 
+
+ align:start position:0%
+logical gate you want. Uh I will talk
+about that more in a moment. So this ore
+
+ align:start position:0%
+about that more in a moment. So this ore
+ 
+
+ align:start position:0%
+about that more in a moment. So this ore
+is particularly interesting because we
+
+ align:start position:0%
+is particularly interesting because we
+ 
+
+ align:start position:0%
+is particularly interesting because we
+already have not. And so from from or
+
+ align:start position:0%
+already have not. And so from from or
+ 
+
+ align:start position:0%
+already have not. And so from from or
+and not we can make nor it's just the
+
+ align:start position:0%
+and not we can make nor it's just the
+ 
+
+ align:start position:0%
+and not we can make nor it's just the
+knot of the ore. And so from that we
+
+ align:start position:0%
+knot of the ore. And so from that we
+ 
+
+ align:start position:0%
+knot of the ore. And so from that we
+should be able to make anything
+
+ align:start position:0%
+should be able to make anything
+ 
+
+ align:start position:0%
+should be able to make anything
+which is great except uh for one thing
+
+ align:start position:0%
+which is great except uh for one thing
+ 
+
+ align:start position:0%
+which is great except uh for one thing
+which is the crossover gadget. So in the
+
+ align:start position:0%
+which is the crossover gadget. So in the
+ 
+
+ align:start position:0%
+which is the crossover gadget. So in the
+case of lightup uh crossover gadget is
+
+ align:start position:0%
+case of lightup uh crossover gadget is
+ 
+
+ align:start position:0%
+case of lightup uh crossover gadget is
+easy to construct but uh because we have
+
+ align:start position:0%
+easy to construct but uh because we have
+ 
+
+ align:start position:0%
+easy to construct but uh because we have
+exor anyway we can use this fun fact
+
+ align:start position:0%
+exor anyway we can use this fun fact
+ 
+
+ align:start position:0%
+exor anyway we can use this fun fact
+that if you this is a symbol for exor.
+
+ align:start position:0%
+that if you this is a symbol for exor.
+ 
+
+ align:start position:0%
+that if you this is a symbol for exor.
+If you have exor gadgets, you can make
+
+ align:start position:0%
+If you have exor gadgets, you can make
+ 
+
+ align:start position:0%
+If you have exor gadgets, you can make
+uh a crossover gadget for free. So this
+
+ align:start position:0%
+uh a crossover gadget for free. So this
+ 
+
+ align:start position:0%
+uh a crossover gadget for free. So this
+communicates x to x y to y. Again,
+
+ align:start position:0%
+communicates x to x y to y. Again,
+ 
+
+ align:start position:0%
+communicates x to x y to y. Again,
+there's four cases. I won't check all of
+
+ align:start position:0%
+there's four cases. I won't check all of
+ 
+
+ align:start position:0%
+there's four cases. I won't check all of
+them. Uh but that's cool because we have
+
+ align:start position:0%
+them. Uh but that's cool because we have
+ 
+
+ align:start position:0%
+them. Uh but that's cool because we have
+x nor. We can negate it and get xor. And
+
+ align:start position:0%
+x nor. We can negate it and get xor. And
+ 
+
+ align:start position:0%
+x nor. We can negate it and get xor. And
+then we can take three of them, plug
+
+ align:start position:0%
+then we can take three of them, plug
+ 
+
+ align:start position:0%
+then we can take three of them, plug
+them together, and we get a rather
+
+ align:start position:0%
+them together, and we get a rather
+ 
+
+ align:start position:0%
+them together, and we get a rather
+complicated crossover gadget. If I
+
+ align:start position:0%
+complicated crossover gadget. If I
+ 
+
+ align:start position:0%
+complicated crossover gadget. If I
+expanded it out, there is a simpler one,
+
+ align:start position:0%
+expanded it out, there is a simpler one,
+ 
+
+ align:start position:0%
+expanded it out, there is a simpler one,
+but we don't care about simplicity here.
+
+ align:start position:0%
+but we don't care about simplicity here.
+ 
+
+ align:start position:0%
+but we don't care about simplicity here.
+These are just constants. uh and we just
+
+ align:start position:0%
+These are just constants. uh and we just
+ 
+
+ align:start position:0%
+These are just constants. uh and we just
+care about polomial. So uh that's light
+
+ align:start position:0%
+care about polomial. So uh that's light
+ 
+
+ align:start position:0%
+care about polomial. So uh that's light
+up is MP MP hard. Yeah.
+
+ align:start position:0%
+up is MP MP hard. Yeah.
+ 
+
+ align:start position:0%
+up is MP MP hard. Yeah.
+Do we need crossover gadgets in general
+
+ align:start position:0%
+Do we need crossover gadgets in general
+ 
+
+ align:start position:0%
+Do we need crossover gadgets in general
+for circuit set? Is planner circuit set
+
+ align:start position:0%
+for circuit set? Is planner circuit set
+ 
+
+ align:start position:0%
+for circuit set? Is planner circuit set
+hard?
+
+ align:start position:0%
+hard?
+ 
+
+ align:start position:0%
+hard?
+Please wait.
+
+ align:start position:0%
+Please wait.
+ 
+
+ align:start position:0%
+Please wait.
+Yeah. Uh this is a something well yeah I
+
+ align:start position:0%
+Yeah. Uh this is a something well yeah I
+ 
+
+ align:start position:0%
+Yeah. Uh this is a something well yeah I
+want to talk about that after the next
+
+ align:start position:0%
+want to talk about that after the next
+ 
+
+ align:start position:0%
+want to talk about that after the next
+example.
+
+ align:start position:0%
+example.
+ 
+
+ align:start position:0%
+example.
+Okay. uh which we'll get to an answer to
+
+ align:start position:0%
+Okay. uh which we'll get to an answer to
+ 
+
+ align:start position:0%
+Okay. uh which we'll get to an answer to
+that question which as far as I know
+
+ align:start position:0%
+that question which as far as I know
+ 
+
+ align:start position:0%
+that question which as far as I know
+haven't hasn't been explicitly raised
+
+ align:start position:0%
+haven't hasn't been explicitly raised
+ 
+
+ align:start position:0%
+haven't hasn't been explicitly raised
+before but uh it's pretty the answer is
+
+ align:start position:0%
+before but uh it's pretty the answer is
+ 
+
+ align:start position:0%
+before but uh it's pretty the answer is
+basically you don't need crossover
+
+ align:start position:0%
+basically you don't need crossover
+ 
+
+ align:start position:0%
+basically you don't need crossover
+gadgets and for all the cases I can
+
+ align:start position:0%
+gadgets and for all the cases I can
+ 
+
+ align:start position:0%
+gadgets and for all the cases I can
+think of so uh that was lightup is np
+
+ align:start position:0%
+think of so uh that was lightup is np
+ 
+
+ align:start position:0%
+think of so uh that was lightup is np
+hard it's also innp because certificate
+
+ align:start position:0%
+hard it's also innp because certificate
+ 
+
+ align:start position:0%
+hard it's also innp because certificate
+is just where do you put the lights
+
+ align:start position:0%
+is just where do you put the lights
+ 
+
+ align:start position:0%
+is just where do you put the lights
+there's only polinomial number of places
+
+ align:start position:0%
+there's only polinomial number of places
+ 
+
+ align:start position:0%
+there's only polinomial number of places
+to put them and checking it is easy cool
+
+ align:start position:0%
+to put them and checking it is easy cool
+ 
+
+ align:start position:0%
+to put them and checking it is easy cool
+so nplete
+
+ align:start position:0%
+so nplete
+ 
+
+ align:start position:0%
+so nplete
+oh here's uh for on an overall
+
+ align:start position:0%
+oh here's uh for on an overall
+ 
+
+ align:start position:0%
+oh here's uh for on an overall
+construction which uh McFale worked out.
+
+ align:start position:0%
+construction which uh McFale worked out.
+ 
+
+ align:start position:0%
+construction which uh McFale worked out.
+So putting all the pieces together and
+
+ align:start position:0%
+So putting all the pieces together and
+ 
+
+ align:start position:0%
+So putting all the pieces together and
+possibly using I think here there's
+
+ align:start position:0%
+possibly using I think here there's
+ 
+
+ align:start position:0%
+possibly using I think here there's
+maybe no crossovers.
+
+ align:start position:0%
+maybe no crossovers.
+ 
+
+ align:start position:0%
+maybe no crossovers.
+Uh but so so in general with circuit set
+
+ align:start position:0%
+Uh but so so in general with circuit set
+ 
+
+ align:start position:0%
+Uh but so so in general with circuit set
+you can construct sort of any boolean
+
+ align:start position:0%
+you can construct sort of any boolean
+ 
+
+ align:start position:0%
+you can construct sort of any boolean
+formula you want once you have a
+
+ align:start position:0%
+formula you want once you have a
+ 
+
+ align:start position:0%
+formula you want once you have a
+universal uh set of gates. Um but yeah
+
+ align:start position:0%
+universal uh set of gates. Um but yeah
+ 
+
+ align:start position:0%
+universal uh set of gates. Um but yeah
+you can work through details here once
+
+ align:start position:0%
+you can work through details here once
+ 
+
+ align:start position:0%
+you can work through details here once
+you have it's easy to convert between
+
+ align:start position:0%
+you have it's easy to convert between
+ 
+
+ align:start position:0%
+you have it's easy to convert between
+and and or uh just by negating the
+
+ align:start position:0%
+and and or uh just by negating the
+ 
+
+ align:start position:0%
+and and or uh just by negating the
+inputs by deorggan right so you've got
+
+ align:start position:0%
+inputs by deorggan right so you've got
+ 
+
+ align:start position:0%
+inputs by deorggan right so you've got
+uh not x or y is not x and not y or vice
+
+ align:start position:0%
+uh not x or y is not x and not y or vice
+ 
+
+ align:start position:0%
+uh not x or y is not x and not y or vice
+versa. So as long as you've got not and
+
+ align:start position:0%
+versa. So as long as you've got not and
+ 
+
+ align:start position:0%
+versa. So as long as you've got not and
+or you can construct and and vice versa
+
+ align:start position:0%
+or you can construct and and vice versa
+ 
+
+ align:start position:0%
+or you can construct and and vice versa
+by negating things appropriately.
+
+ align:start position:0%
+by negating things appropriately.
+ 
+
+ align:start position:0%
+by negating things appropriately.
+So that's what he's doing here for
+
+ align:start position:0%
+So that's what he's doing here for
+ 
+
+ align:start position:0%
+So that's what he's doing here for
+getting some ores and and so on.
+
+ align:start position:0%
+getting some ores and and so on.
+ 
+
+ align:start position:0%
+getting some ores and and so on.
+And because there's two copies of X uh
+
+ align:start position:0%
+And because there's two copies of X uh
+ 
+
+ align:start position:0%
+And because there's two copies of X uh
+while X is sort of getting split here. I
+
+ align:start position:0%
+while X is sort of getting split here. I
+ 
+
+ align:start position:0%
+while X is sort of getting split here. I
+guess you didn't have to split X. You
+
+ align:start position:0%
+guess you didn't have to split X. You
+ 
+
+ align:start position:0%
+guess you didn't have to split X. You
+could just connect directly. But
+
+ align:start position:0%
+could just connect directly. But
+ 
+
+ align:start position:0%
+could just connect directly. But
+this is a pretty nice clean
+
+ align:start position:0%
+this is a pretty nice clean
+ 
+
+ align:start position:0%
+this is a pretty nice clean
+construction. You could actually make
+
+ align:start position:0%
+construction. You could actually make
+ 
+
+ align:start position:0%
+construction. You could actually make
+decently sized puzzles with it.
+
+ align:start position:0%
+decently sized puzzles with it.
+ 
+
+ align:start position:0%
+decently sized puzzles with it.
+So you end up with the wire carrying the
+
+ align:start position:0%
+So you end up with the wire carrying the
+ 
+
+ align:start position:0%
+So you end up with the wire carrying the
+formula just by doing all these
+
+ align:start position:0%
+formula just by doing all these
+ 
+
+ align:start position:0%
+formula just by doing all these
+combinations, right?
+
+ align:start position:0%
+combinations, right?
+ 
+
+ align:start position:0%
+combinations, right?
+And then what you do?
+
+ align:start position:0%
+And then what you do?
+ 
+
+ align:start position:0%
+And then what you do?
+Ah, good point. Thank you. There's there
+
+ align:start position:0%
+Ah, good point. Thank you. There's there
+ 
+
+ align:start position:0%
+Ah, good point. Thank you. There's there
+was one more point to to this picture
+
+ align:start position:0%
+was one more point to to this picture
+ 
+
+ align:start position:0%
+was one more point to to this picture
+which is this zero. This should be an or
+
+ align:start position:0%
+which is this zero. This should be an or
+ 
+
+ align:start position:0%
+which is this zero. This should be an or
+of x false and this ore of this and of
+
+ align:start position:0%
+of x false and this ore of this and of
+ 
+
+ align:start position:0%
+of x false and this ore of this and of
+blah blah blah which is this thing. Uh
+
+ align:start position:0%
+blah blah blah which is this thing. Uh
+ 
+
+ align:start position:0%
+blah blah blah which is this thing. Uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so if that wire is carrying true then
+
+ align:start position:0%
+so if that wire is carrying true then
+ 
+
+ align:start position:0%
+so if that wire is carrying true then
+you don't need to put a light next to
+
+ align:start position:0%
+you don't need to put a light next to
+ 
+
+ align:start position:0%
+you don't need to put a light next to
+the zero otherwise you would have to but
+
+ align:start position:0%
+the zero otherwise you would have to but
+ 
+
+ align:start position:0%
+the zero otherwise you would have to but
+then that means the puzzle can't be
+
+ align:start position:0%
+then that means the puzzle can't be
+ 
+
+ align:start position:0%
+then that means the puzzle can't be
+solved
+
+ align:start position:0%
+solved
+ 
+
+ align:start position:0%
+solved
+right so for this puzzle to be solvable
+
+ align:start position:0%
+right so for this puzzle to be solvable
+ 
+
+ align:start position:0%
+right so for this puzzle to be solvable
+uh we better not put a light here which
+
+ align:start position:0%
+uh we better not put a light here which
+ 
+
+ align:start position:0%
+uh we better not put a light here which
+means it has to be here which
+
+ align:start position:0%
+means it has to be here which
+ 
+
+ align:start position:0%
+means it has to be here which
+corresponds to this formula being true I
+
+ align:start position:0%
+corresponds to this formula being true I
+ 
+
+ align:start position:0%
+corresponds to this formula being true I
+think if I got the par right so or
+
+ align:start position:0%
+think if I got the par right so or
+ 
+
+ align:start position:0%
+think if I got the par right so or
+either way you could put a one there and
+
+ align:start position:0%
+either way you could put a one there and
+ 
+
+ align:start position:0%
+either way you could put a one there and
+force there to be a light
+
+ align:start position:0%
+force there to be a light
+ 
+
+ align:start position:0%
+force there to be a light
+uh so this makes the puzzle feasible if
+
+ align:start position:0%
+uh so this makes the puzzle feasible if
+ 
+
+ align:start position:0%
+uh so this makes the puzzle feasible if
+and only if this formula is feasible
+
+ align:start position:0%
+and only if this formula is feasible
+ 
+
+ align:start position:0%
+and only if this formula is feasible
+because the wires are unconstrained
+
+ align:start position:0%
+because the wires are unconstrained
+ 
+
+ align:start position:0%
+because the wires are unconstrained
+except by setting this thing equal to
+
+ align:start position:0%
+except by setting this thing equal to
+ 
+
+ align:start position:0%
+except by setting this thing equal to
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+Yeah. So, this is a special kind of
+
+ align:start position:0%
+Yeah. So, this is a special kind of
+ 
+
+ align:start position:0%
+Yeah. So, this is a special kind of
+terminator, you might say, uh, a true
+
+ align:start position:0%
+terminator, you might say, uh, a true
+ 
+
+ align:start position:0%
+terminator, you might say, uh, a true
+terminator if you want to force the
+
+ align:start position:0%
+terminator if you want to force the
+ 
+
+ align:start position:0%
+terminator if you want to force the
+thing to be true in the end. That's
+
+ align:start position:0%
+thing to be true in the end. That's
+ 
+
+ align:start position:0%
+thing to be true in the end. That's
+usually pretty easy to do. Terminators
+
+ align:start position:0%
+usually pretty easy to do. Terminators
+ 
+
+ align:start position:0%
+usually pretty easy to do. Terminators
+are usually one of the simplest gadgets
+
+ align:start position:0%
+are usually one of the simplest gadgets
+ 
+
+ align:start position:0%
+are usually one of the simplest gadgets
+to worry about. But yeah, you do need
+
+ align:start position:0%
+to worry about. But yeah, you do need
+ 
+
+ align:start position:0%
+to worry about. But yeah, you do need
+it. For circuit set, you need let's add
+
+ align:start position:0%
+it. For circuit set, you need let's add
+ 
+
+ align:start position:0%
+it. For circuit set, you need let's add
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Circuit set. you need to uh let's say a
+
+ align:start position:0%
+Circuit set. you need to uh let's say a
+ 
+
+ align:start position:0%
+Circuit set. you need to uh let's say a
+true terminator.
+
+ align:start position:0%
+true terminator.
+ 
+
+ align:start position:0%
+true terminator.
+There are other ways you could do it,
+
+ align:start position:0%
+There are other ways you could do it,
+ 
+
+ align:start position:0%
+There are other ways you could do it,
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool. Other questions about Aotti?
+
+ align:start position:0%
+cool. Other questions about Aotti?
+ 
+
+ align:start position:0%
+cool. Other questions about Aotti?
+All right, so uh next topic is
+
+ align:start position:0%
+All right, so uh next topic is
+ 
+
+ align:start position:0%
+All right, so uh next topic is
+Mindeeper. This is from our poster. We
+
+ align:start position:0%
+Mindeeper. This is from our poster. We
+ 
+
+ align:start position:0%
+Mindeeper. This is from our poster. We
+did Super Mario Brothers and briefly did
+
+ align:start position:0%
+did Super Mario Brothers and briefly did
+ 
+
+ align:start position:0%
+did Super Mario Brothers and briefly did
+Rush Hour, so Mind Sweeper is the last
+
+ align:start position:0%
+Rush Hour, so Mind Sweeper is the last
+ 
+
+ align:start position:0%
+Rush Hour, so Mind Sweeper is the last
+one on the poster. Um let's prove it
+
+ align:start position:0%
+one on the poster. Um let's prove it
+ 
+
+ align:start position:0%
+one on the poster. Um let's prove it
+hard.
+
+ align:start position:0%
+hard.
+ 
+
+ align:start position:0%
+hard.
+Uh we're actually going to cover two
+
+ align:start position:0%
+Uh we're actually going to cover two
+ 
+
+ align:start position:0%
+Uh we're actually going to cover two
+proofs about mind sweeper uh because
+
+ align:start position:0%
+proofs about mind sweeper uh because
+ 
+
+ align:start position:0%
+proofs about mind sweeper uh because
+there are sort of two natural problems
+
+ align:start position:0%
+there are sort of two natural problems
+ 
+
+ align:start position:0%
+there are sort of two natural problems
+you might ask about it. The first
+
+ align:start position:0%
+you might ask about it. The first
+ 
+
+ align:start position:0%
+you might ask about it. The first
+problem is uh consistency. So this is I
+
+ align:start position:0%
+problem is uh consistency. So this is I
+ 
+
+ align:start position:0%
+problem is uh consistency. So this is I
+give you uh a setup. I'm going to give
+
+ align:start position:0%
+give you uh a setup. I'm going to give
+ 
+
+ align:start position:0%
+give you uh a setup. I'm going to give
+you a partially solved board that you're
+
+ align:start position:0%
+you a partially solved board that you're
+ 
+
+ align:start position:0%
+you a partially solved board that you're
+not given the x levels. Uh so just a
+
+ align:start position:0%
+not given the x levels. Uh so just a
+ 
+
+ align:start position:0%
+not given the x levels. Uh so just a
+regular instance of mind sweeper. Uh
+
+ align:start position:0%
+regular instance of mind sweeper. Uh
+ 
+
+ align:start position:0%
+regular instance of mind sweeper. Uh
+maybe you're told where some of the
+
+ align:start position:0%
+maybe you're told where some of the
+ 
+
+ align:start position:0%
+maybe you're told where some of the
+bombs are. Uh it won't actually matter
+
+ align:start position:0%
+bombs are. Uh it won't actually matter
+ 
+
+ align:start position:0%
+bombs are. Uh it won't actually matter
+because all the bombs that I'll draw
+
+ align:start position:0%
+because all the bombs that I'll draw
+ 
+
+ align:start position:0%
+because all the bombs that I'll draw
+here are derable. you know from this I
+
+ align:start position:0%
+here are derable. you know from this I
+ 
+
+ align:start position:0%
+here are derable. you know from this I
+should mention the rules of mind sweeper
+
+ align:start position:0%
+should mention the rules of mind sweeper
+ 
+
+ align:start position:0%
+should mention the rules of mind sweeper
+just in case you haven't played anyone
+
+ align:start position:0%
+just in case you haven't played anyone
+ 
+
+ align:start position:0%
+just in case you haven't played anyone
+not played mind sweeper
+
+ align:start position:0%
+not played mind sweeper
+ 
+
+ align:start position:0%
+not played mind sweeper
+not willing to admit it so the numbers
+
+ align:start position:0%
+not willing to admit it so the numbers
+ 
+
+ align:start position:0%
+not willing to admit it so the numbers
+here representing among all your vertex
+
+ align:start position:0%
+here representing among all your vertex
+ 
+
+ align:start position:0%
+here representing among all your vertex
+neighbors all eight neighbors how many
+
+ align:start position:0%
+neighbors all eight neighbors how many
+ 
+
+ align:start position:0%
+neighbors all eight neighbors how many
+of them are bombs uh you don't want to
+
+ align:start position:0%
+of them are bombs uh you don't want to
+ 
+
+ align:start position:0%
+of them are bombs uh you don't want to
+click on the bombs because then you die
+
+ align:start position:0%
+click on the bombs because then you die
+ 
+
+ align:start position:0%
+click on the bombs because then you die
+so your goal is to from this partial
+
+ align:start position:0%
+so your goal is to from this partial
+ 
+
+ align:start position:0%
+so your goal is to from this partial
+information these blank squares
+
+ align:start position:0%
+information these blank squares
+ 
+
+ align:start position:0%
+information these blank squares
+represent zeros from this partial
+
+ align:start position:0%
+represent zeros from this partial
+ 
+
+ align:start position:0%
+represent zeros from this partial
+information you want to figure out where
+
+ align:start position:0%
+information you want to figure out where
+ 
+
+ align:start position:0%
+information you want to figure out where
+the bombs must be
+
+ align:start position:0%
+the bombs must be
+ 
+
+ align:start position:0%
+the bombs must be
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+here's a very familiar looking wire. Uh
+
+ align:start position:0%
+here's a very familiar looking wire. Uh
+ 
+
+ align:start position:0%
+here's a very familiar looking wire. Uh
+here, um we're we can't just have
+
+ align:start position:0%
+here, um we're we can't just have
+ 
+
+ align:start position:0%
+here, um we're we can't just have
+obstacles that are wild cards. So, we
+
+ align:start position:0%
+obstacles that are wild cards. So, we
+ 
+
+ align:start position:0%
+obstacles that are wild cards. So, we
+have to put it numbers if we don't want
+
+ align:start position:0%
+have to put it numbers if we don't want
+ 
+
+ align:start position:0%
+have to put it numbers if we don't want
+there to be bombs there. That makes the
+
+ align:start position:0%
+there to be bombs there. That makes the
+ 
+
+ align:start position:0%
+there to be bombs there. That makes the
+gadgets quite a bit trickier to work
+
+ align:start position:0%
+gadgets quite a bit trickier to work
+ 
+
+ align:start position:0%
+gadgets quite a bit trickier to work
+with. But, uh this looks pretty similar.
+
+ align:start position:0%
+with. But, uh this looks pretty similar.
+ 
+
+ align:start position:0%
+with. But, uh this looks pretty similar.
+We've got these ones which force an
+
+ align:start position:0%
+We've got these ones which force an
+ 
+
+ align:start position:0%
+We've got these ones which force an
+alternation. Exactly one of these two is
+
+ align:start position:0%
+alternation. Exactly one of these two is
+ 
+
+ align:start position:0%
+alternation. Exactly one of these two is
+a bomb. So, if x is present, x prime is
+
+ align:start position:0%
+a bomb. So, if x is present, x prime is
+ 
+
+ align:start position:0%
+a bomb. So, if x is present, x prime is
+absent. Vice versa. Um and then this one
+
+ align:start position:0%
+absent. Vice versa. Um and then this one
+ 
+
+ align:start position:0%
+absent. Vice versa. Um and then this one
+forces I guess actually this one forces
+
+ align:start position:0%
+forces I guess actually this one forces
+ 
+
+ align:start position:0%
+forces I guess actually this one forces
+these to be opposite.
+
+ align:start position:0%
+these to be opposite.
+ 
+
+ align:start position:0%
+these to be opposite.
+So uh that forces the alternation down
+
+ align:start position:0%
+So uh that forces the alternation down
+ 
+
+ align:start position:0%
+So uh that forces the alternation down
+the line. So again there are exactly two
+
+ align:start position:0%
+the line. So again there are exactly two
+ 
+
+ align:start position:0%
+the line. So again there are exactly two
+solutions to this wire gadget uh for
+
+ align:start position:0%
+solutions to this wire gadget uh for
+ 
+
+ align:start position:0%
+solutions to this wire gadget uh for
+where the bombs could be. And so the
+
+ align:start position:0%
+where the bombs could be. And so the
+ 
+
+ align:start position:0%
+where the bombs could be. And so the
+mind sweeper consistency problem is I
+
+ align:start position:0%
+mind sweeper consistency problem is I
+ 
+
+ align:start position:0%
+mind sweeper consistency problem is I
+give you some picture involving these
+
+ align:start position:0%
+give you some picture involving these
+ 
+
+ align:start position:0%
+give you some picture involving these
+things. Uh and I want to know is there a
+
+ align:start position:0%
+things. Uh and I want to know is there a
+ 
+
+ align:start position:0%
+things. Uh and I want to know is there a
+solution to uh is there a placement of
+
+ align:start position:0%
+solution to uh is there a placement of
+ 
+
+ align:start position:0%
+solution to uh is there a placement of
+the bombs that satisfies all of these
+
+ align:start position:0%
+the bombs that satisfies all of these
+ 
+
+ align:start position:0%
+the bombs that satisfies all of these
+constraints. Okay. Now uh you might ask
+
+ align:start position:0%
+constraints. Okay. Now uh you might ask
+ 
+
+ align:start position:0%
+constraints. Okay. Now uh you might ask
+why is that the problem we care about?
+
+ align:start position:0%
+why is that the problem we care about?
+ 
+
+ align:start position:0%
+why is that the problem we care about?
+Um, and one reason if you're playing
+
+ align:start position:0%
+Um, and one reason if you're playing
+ 
+
+ align:start position:0%
+Um, and one reason if you're playing
+Mind Sweeper, you'd like to know, for
+
+ align:start position:0%
+Mind Sweeper, you'd like to know, for
+ 
+
+ align:start position:0%
+Mind Sweeper, you'd like to know, for
+example, could there be a bomb at this
+
+ align:start position:0%
+example, could there be a bomb at this
+ 
+
+ align:start position:0%
+example, could there be a bomb at this
+position? Uh, so could there be a bomb
+
+ align:start position:0%
+position? Uh, so could there be a bomb
+ 
+
+ align:start position:0%
+position? Uh, so could there be a bomb
+at this position? I could solve that
+
+ align:start position:0%
+at this position? I could solve that
+ 
+
+ align:start position:0%
+at this position? I could solve that
+problem potentially if I could solve
+
+ align:start position:0%
+problem potentially if I could solve
+ 
+
+ align:start position:0%
+problem potentially if I could solve
+mind sweeper consistency by saying, uh,
+
+ align:start position:0%
+mind sweeper consistency by saying, uh,
+ 
+
+ align:start position:0%
+mind sweeper consistency by saying, uh,
+let's put a bomb there as part of the
+
+ align:start position:0%
+let's put a bomb there as part of the
+ 
+
+ align:start position:0%
+let's put a bomb there as part of the
+partial information. Is that consistent
+
+ align:start position:0%
+partial information. Is that consistent
+ 
+
+ align:start position:0%
+partial information. Is that consistent
+with everything else? So add a bomb to
+
+ align:start position:0%
+with everything else? So add a bomb to
+ 
+
+ align:start position:0%
+with everything else? So add a bomb to
+the partial information. Is that a
+
+ align:start position:0%
+the partial information. Is that a
+ 
+
+ align:start position:0%
+the partial information. Is that a
+consistent configuration?
+
+ align:start position:0%
+consistent configuration?
+ 
+
+ align:start position:0%
+consistent configuration?
+Uh, so if I could solve mind sweeper
+
+ align:start position:0%
+Uh, so if I could solve mind sweeper
+ 
+
+ align:start position:0%
+Uh, so if I could solve mind sweeper
+consistency, I could play a mind sweeper
+
+ align:start position:0%
+consistency, I could play a mind sweeper
+ 
+
+ align:start position:0%
+consistency, I could play a mind sweeper
+very well by just testing which are
+
+ align:start position:0%
+very well by just testing which are
+ 
+
+ align:start position:0%
+very well by just testing which are
+bombable positions. If they're not
+
+ align:start position:0%
+bombable positions. If they're not
+ 
+
+ align:start position:0%
+bombable positions. If they're not
+possible to be a bomb there, I should
+
+ align:start position:0%
+possible to be a bomb there, I should
+ 
+
+ align:start position:0%
+possible to be a bomb there, I should
+click there and get more information and
+
+ align:start position:0%
+click there and get more information and
+ 
+
+ align:start position:0%
+click there and get more information and
+cook until done. Now maybe you could
+
+ align:start position:0%
+cook until done. Now maybe you could
+ 
+
+ align:start position:0%
+cook until done. Now maybe you could
+solve mind sweeper in a different way
+
+ align:start position:0%
+solve mind sweeper in a different way
+ 
+
+ align:start position:0%
+solve mind sweeper in a different way
+than using consistency. But one way to
+
+ align:start position:0%
+than using consistency. But one way to
+ 
+
+ align:start position:0%
+than using consistency. But one way to
+solve it would be consistency. Question.
+
+ align:start position:0%
+solve it would be consistency. Question.
+ 
+
+ align:start position:0%
+solve it would be consistency. Question.
+By consistency, you don't mean unique
+
+ align:start position:0%
+By consistency, you don't mean unique
+ 
+
+ align:start position:0%
+By consistency, you don't mean unique
+solution.
+
+ align:start position:0%
+solution.
+ 
+
+ align:start position:0%
+solution.
+I do not mean unique solution, right?
+
+ align:start position:0%
+I do not mean unique solution, right?
+ 
+
+ align:start position:0%
+I do not mean unique solution, right?
+Yeah. So when you actually want to solve
+
+ align:start position:0%
+Yeah. So when you actually want to solve
+ 
+
+ align:start position:0%
+Yeah. So when you actually want to solve
+the game, you'd like there to be unique
+
+ align:start position:0%
+the game, you'd like there to be unique
+ 
+
+ align:start position:0%
+the game, you'd like there to be unique
+solution. That's a problem we will get
+
+ align:start position:0%
+solution. That's a problem we will get
+ 
+
+ align:start position:0%
+solution. That's a problem we will get
+to in a moment.
+
+ align:start position:0%
+to in a moment.
+ 
+
+ align:start position:0%
+to in a moment.
+So, a blank board, unfilled information
+
+ align:start position:0%
+So, a blank board, unfilled information
+ 
+
+ align:start position:0%
+So, a blank board, unfilled information
+is consistent.
+
+ align:start position:0%
+is consistent.
+ 
+
+ align:start position:0%
+is consistent.
+Yes. Completely blank board is
+
+ align:start position:0%
+Yes. Completely blank board is
+ 
+
+ align:start position:0%
+Yes. Completely blank board is
+consistent. And wouldn't it be
+
+ align:start position:0%
+consistent. And wouldn't it be
+ 
+
+ align:start position:0%
+consistent. And wouldn't it be
+interesting if as you're playing you
+
+ align:start position:0%
+interesting if as you're playing you
+ 
+
+ align:start position:0%
+interesting if as you're playing you
+imagine you've got you've gathered some
+
+ align:start position:0%
+imagine you've got you've gathered some
+ 
+
+ align:start position:0%
+imagine you've got you've gathered some
+information, you add a bomb, you want to
+
+ align:start position:0%
+information, you add a bomb, you want to
+ 
+
+ align:start position:0%
+information, you add a bomb, you want to
+say, is this consistent? If it says yes,
+
+ align:start position:0%
+say, is this consistent? If it says yes,
+ 
+
+ align:start position:0%
+say, is this consistent? If it says yes,
+like you have a blank board, like could
+
+ align:start position:0%
+like you have a blank board, like could
+ 
+
+ align:start position:0%
+like you have a blank board, like could
+there be a bomb here? Of course there
+
+ align:start position:0%
+there be a bomb here? Of course there
+ 
+
+ align:start position:0%
+there be a bomb here? Of course there
+could be. Uh then that's not a safe
+
+ align:start position:0%
+could be. Uh then that's not a safe
+ 
+
+ align:start position:0%
+could be. Uh then that's not a safe
+move. So, this will help you. If you
+
+ align:start position:0%
+move. So, this will help you. If you
+ 
+
+ align:start position:0%
+move. So, this will help you. If you
+could solve this, uh you could identify
+
+ align:start position:0%
+could solve this, uh you could identify
+ 
+
+ align:start position:0%
+could solve this, uh you could identify
+safe moves. Turns out you can't solve
+
+ align:start position:0%
+safe moves. Turns out you can't solve
+ 
+
+ align:start position:0%
+safe moves. Turns out you can't solve
+it. So, uh it doesn't directly help you.
+
+ align:start position:0%
+it. So, uh it doesn't directly help you.
+ 
+
+ align:start position:0%
+it. So, uh it doesn't directly help you.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+So, um there doesn't always exist a safe
+
+ align:start position:0%
+So, um there doesn't always exist a safe
+ 
+
+ align:start position:0%
+So, um there doesn't always exist a safe
+move.
+
+ align:start position:0%
+move.
+ 
+
+ align:start position:0%
+move.
+There doesn't always exist a safe move,
+
+ align:start position:0%
+There doesn't always exist a safe move,
+ 
+
+ align:start position:0%
+There doesn't always exist a safe move,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+What good is it kind of
+
+ align:start position:0%
+What good is it kind of
+ 
+
+ align:start position:0%
+What good is it kind of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to know whether you see what I mean?
+
+ align:start position:0%
+to know whether you see what I mean?
+ 
+
+ align:start position:0%
+to know whether you see what I mean?
+Like
+
+ align:start position:0%
+Like
+ 
+
+ align:start position:0%
+Like
+I would say consistency is the wrong
+
+ align:start position:0%
+I would say consistency is the wrong
+ 
+
+ align:start position:0%
+I would say consistency is the wrong
+problem to solve for mind sweeper. Uh we
+
+ align:start position:0%
+problem to solve for mind sweeper. Uh we
+ 
+
+ align:start position:0%
+problem to solve for mind sweeper. Uh we
+will get but it was the first problem
+
+ align:start position:0%
+will get but it was the first problem
+ 
+
+ align:start position:0%
+will get but it was the first problem
+solved. It the gadgets are relatively
+
+ align:start position:0%
+solved. It the gadgets are relatively
+ 
+
+ align:start position:0%
+solved. It the gadgets are relatively
+easy which is going to be fairly
+
+ align:start position:0%
+easy which is going to be fairly
+ 
+
+ align:start position:0%
+easy which is going to be fairly
+complicated. uh and then we'll get to
+
+ align:start position:0%
+complicated. uh and then we'll get to
+ 
+
+ align:start position:0%
+complicated. uh and then we'll get to
+the right problem for if you wanted to
+
+ align:start position:0%
+the right problem for if you wanted to
+ 
+
+ align:start position:0%
+the right problem for if you wanted to
+solve the puzzle. It's just at this
+
+ align:start position:0%
+solve the puzzle. It's just at this
+ 
+
+ align:start position:0%
+solve the puzzle. It's just at this
+point it's an interesting question. You
+
+ align:start position:0%
+point it's an interesting question. You
+ 
+
+ align:start position:0%
+point it's an interesting question. You
+just want to know is it consistent? Did
+
+ align:start position:0%
+just want to know is it consistent? Did
+ 
+
+ align:start position:0%
+just want to know is it consistent? Did
+the computer cheat would be one other
+
+ align:start position:0%
+the computer cheat would be one other
+ 
+
+ align:start position:0%
+the computer cheat would be one other
+perspective or you could imagine some
+
+ align:start position:0%
+perspective or you could imagine some
+ 
+
+ align:start position:0%
+perspective or you could imagine some
+adversarial mind sweeper where you only
+
+ align:start position:0%
+adversarial mind sweeper where you only
+ 
+
+ align:start position:0%
+adversarial mind sweeper where you only
+decide the bombs as the person is
+
+ align:start position:0%
+decide the bombs as the person is
+ 
+
+ align:start position:0%
+decide the bombs as the person is
+playing.
+
+ align:start position:0%
+playing.
+ 
+
+ align:start position:0%
+playing.
+So this would so here just even telling
+
+ align:start position:0%
+So this would so here just even telling
+ 
+
+ align:start position:0%
+So this would so here just even telling
+whether your opponent is cheating is
+
+ align:start position:0%
+whether your opponent is cheating is
+ 
+
+ align:start position:0%
+whether your opponent is cheating is
+hard. Okay. So that's that's another
+
+ align:start position:0%
+hard. Okay. So that's that's another
+ 
+
+ align:start position:0%
+hard. Okay. So that's that's another
+perspective. So okay let's finish this
+
+ align:start position:0%
+perspective. So okay let's finish this
+ 
+
+ align:start position:0%
+perspective. So okay let's finish this
+proof. Uh we have a terminator uh which
+
+ align:start position:0%
+proof. Uh we have a terminator uh which
+ 
+
+ align:start position:0%
+proof. Uh we have a terminator uh which
+is actually a little bit tricky here.
+
+ align:start position:0%
+is actually a little bit tricky here.
+ 
+
+ align:start position:0%
+is actually a little bit tricky here.
+You can't just end with ones because
+
+ align:start position:0%
+You can't just end with ones because
+ 
+
+ align:start position:0%
+You can't just end with ones because
+that would force this guy to be a bomb.
+
+ align:start position:0%
+that would force this guy to be a bomb.
+ 
+
+ align:start position:0%
+that would force this guy to be a bomb.
+So you end with these threes which force
+
+ align:start position:0%
+So you end with these threes which force
+ 
+
+ align:start position:0%
+So you end with these threes which force
+uh these guys are already bombs because
+
+ align:start position:0%
+uh these guys are already bombs because
+ 
+
+ align:start position:0%
+uh these guys are already bombs because
+of this picture. Uh and then exactly one
+
+ align:start position:0%
+of this picture. Uh and then exactly one
+ 
+
+ align:start position:0%
+of this picture. Uh and then exactly one
+of those will still have to be a bomb.
+
+ align:start position:0%
+of those will still have to be a bomb.
+ 
+
+ align:start position:0%
+of those will still have to be a bomb.
+Okay. And then we have a splitter. Uh
+
+ align:start position:0%
+Okay. And then we have a splitter. Uh
+ 
+
+ align:start position:0%
+Okay. And then we have a splitter. Uh
+this is similar picture to Aari. Uh we
+
+ align:start position:0%
+this is similar picture to Aari. Uh we
+ 
+
+ align:start position:0%
+this is similar picture to Aari. Uh we
+have this two which forces exactly two
+
+ align:start position:0%
+have this two which forces exactly two
+ 
+
+ align:start position:0%
+have this two which forces exactly two
+of these to be present and these ones
+
+ align:start position:0%
+of these to be present and these ones
+ 
+
+ align:start position:0%
+of these to be present and these ones
+force alternation. So that makes uh now
+
+ align:start position:0%
+force alternation. So that makes uh now
+ 
+
+ align:start position:0%
+force alternation. So that makes uh now
+I'm orienting things I'm orienting these
+
+ align:start position:0%
+I'm orienting things I'm orienting these
+ 
+
+ align:start position:0%
+I'm orienting things I'm orienting these
+arrows for the splitter and defining
+
+ align:start position:0%
+arrows for the splitter and defining
+ 
+
+ align:start position:0%
+arrows for the splitter and defining
+true to be when the the pointy the
+
+ align:start position:0%
+true to be when the the pointy the
+ 
+
+ align:start position:0%
+true to be when the the pointy the
+pointy end of the arrow is present. Um
+
+ align:start position:0%
+pointy end of the arrow is present. Um
+ 
+
+ align:start position:0%
+pointy end of the arrow is present. Um
+so that means this is actually a negated
+
+ align:start position:0%
+so that means this is actually a negated
+ 
+
+ align:start position:0%
+so that means this is actually a negated
+copy and these are unnegated copies. Uh
+
+ align:start position:0%
+copy and these are unnegated copies. Uh
+ 
+
+ align:start position:0%
+copy and these are unnegated copies. Uh
+but that's only from the orientation.
+
+ align:start position:0%
+but that's only from the orientation.
+ 
+
+ align:start position:0%
+but that's only from the orientation.
+This gadget is actually symmetric
+
+ align:start position:0%
+This gadget is actually symmetric
+ 
+
+ align:start position:0%
+This gadget is actually symmetric
+four-fold but uh but if you put these
+
+ align:start position:0%
+four-fold but uh but if you put these
+ 
+
+ align:start position:0%
+four-fold but uh but if you put these
+arrows in which you would do if you're
+
+ align:start position:0%
+arrows in which you would do if you're
+ 
+
+ align:start position:0%
+arrows in which you would do if you're
+actually following a circuit it's a
+
+ align:start position:0%
+actually following a circuit it's a
+ 
+
+ align:start position:0%
+actually following a circuit it's a
+directed our circuits are directed a
+
+ align:start position:0%
+directed our circuits are directed a
+ 
+
+ align:start position:0%
+directed our circuits are directed a
+cyclic graphs remember so uh this is
+
+ align:start position:0%
+cyclic graphs remember so uh this is
+ 
+
+ align:start position:0%
+cyclic graphs remember so uh this is
+negation which is good because it gives
+
+ align:start position:0%
+negation which is good because it gives
+ 
+
+ align:start position:0%
+negation which is good because it gives
+us a knot also gives us a split you can
+
+ align:start position:0%
+us a knot also gives us a split you can
+ 
+
+ align:start position:0%
+us a knot also gives us a split you can
+also uh end these two things and get a
+
+ align:start position:0%
+also uh end these two things and get a
+ 
+
+ align:start position:0%
+also uh end these two things and get a
+turn so great three gadgets in one
+
+ align:start position:0%
+turn so great three gadgets in one
+ 
+
+ align:start position:0%
+turn so great three gadgets in one
+uh so uh we already have not this is
+
+ align:start position:0%
+uh so uh we already have not this is
+ 
+
+ align:start position:0%
+uh so uh we already have not this is
+another way to do not and it's
+
+ align:start position:0%
+another way to do not and it's
+ 
+
+ align:start position:0%
+another way to do not and it's
+interesting here because uh with Aari we
+
+ align:start position:0%
+interesting here because uh with Aari we
+ 
+
+ align:start position:0%
+interesting here because uh with Aari we
+could stretch wires to any length uh any
+
+ align:start position:0%
+could stretch wires to any length uh any
+ 
+
+ align:start position:0%
+could stretch wires to any length uh any
+integer length that is long sufficiently
+
+ align:start position:0%
+integer length that is long sufficiently
+ 
+
+ align:start position:0%
+integer length that is long sufficiently
+long. Uh here we're forced in this u
+
+ align:start position:0%
+long. Uh here we're forced in this u
+ 
+
+ align:start position:0%
+long. Uh here we're forced in this u
+modulo 3 picture normally. But when we
+
+ align:start position:0%
+modulo 3 picture normally. But when we
+ 
+
+ align:start position:0%
+modulo 3 picture normally. But when we
+do something like a negation here we we
+
+ align:start position:0%
+do something like a negation here we we
+ 
+
+ align:start position:0%
+do something like a negation here we we
+get kind of messed up. We're no longer
+
+ align:start position:0%
+get kind of messed up. We're no longer
+ 
+
+ align:start position:0%
+get kind of messed up. We're no longer
+in the same position modulo 3.
+
+ align:start position:0%
+in the same position modulo 3.
+ 
+
+ align:start position:0%
+in the same position modulo 3.
+Uh we should be uh off by one I believe.
+
+ align:start position:0%
+Uh we should be uh off by one I believe.
+ 
+
+ align:start position:0%
+Uh we should be uh off by one I believe.
+So the idea is if you do two negations
+
+ align:start position:0%
+So the idea is if you do two negations
+ 
+
+ align:start position:0%
+So the idea is if you do two negations
+in a row uh then you can end up shifting
+
+ align:start position:0%
+in a row uh then you can end up shifting
+ 
+
+ align:start position:0%
+in a row uh then you can end up shifting
+by exactly two um and still have the
+
+ align:start position:0%
+by exactly two um and still have the
+ 
+
+ align:start position:0%
+by exactly two um and still have the
+same signal. Uh so you can see here we
+
+ align:start position:0%
+same signal. Uh so you can see here we
+ 
+
+ align:start position:0%
+same signal. Uh so you can see here we
+have xxar
+
+ align:start position:0%
+have xxar
+ 
+
+ align:start position:0%
+have xxar
+but uh down here we have it shifted uh
+
+ align:start position:0%
+but uh down here we have it shifted uh
+ 
+
+ align:start position:0%
+but uh down here we have it shifted uh
+two positions over uh yeah or I guess
+
+ align:start position:0%
+two positions over uh yeah or I guess
+ 
+
+ align:start position:0%
+two positions over uh yeah or I guess
+it's more impressive over here. So xarx
+
+ align:start position:0%
+it's more impressive over here. So xarx
+ 
+
+ align:start position:0%
+it's more impressive over here. So xarx
+um and normally this would repeat in
+
+ align:start position:0%
+um and normally this would repeat in
+ 
+
+ align:start position:0%
+um and normally this would repeat in
+this kind of pattern.
+
+ align:start position:0%
+this kind of pattern.
+ 
+
+ align:start position:0%
+this kind of pattern.
+Ah, so it actually shifted by one
+
+ align:start position:0%
+Ah, so it actually shifted by one
+ 
+
+ align:start position:0%
+Ah, so it actually shifted by one
+position. Good. That's that's actually
+
+ align:start position:0%
+position. Good. That's that's actually
+ 
+
+ align:start position:0%
+position. Good. That's that's actually
+what I want. So see the pattern here,
+
+ align:start position:0%
+what I want. So see the pattern here,
+ 
+
+ align:start position:0%
+what I want. So see the pattern here,
+here, here, here, and shift by one.
+
+ align:start position:0%
+here, here, here, and shift by one.
+ 
+
+ align:start position:0%
+here, here, here, and shift by one.
+Yeah. Or to the other direction.
+
+ align:start position:0%
+Yeah. Or to the other direction.
+ 
+
+ align:start position:0%
+Yeah. Or to the other direction.
+Okay. So that's good. That that lets me
+
+ align:start position:0%
+Okay. So that's good. That that lets me
+ 
+
+ align:start position:0%
+Okay. So that's good. That that lets me
+adjust my wire lengths. Uh these are
+
+ align:start position:0%
+adjust my wire lengths. Uh these are
+ 
+
+ align:start position:0%
+adjust my wire lengths. Uh these are
+also often called shift gadgets. Uh they
+
+ align:start position:0%
+also often called shift gadgets. Uh they
+ 
+
+ align:start position:0%
+also often called shift gadgets. Uh they
+just sort of let you shift by one. And
+
+ align:start position:0%
+just sort of let you shift by one. And
+ 
+
+ align:start position:0%
+just sort of let you shift by one. And
+whenever you have gadgets that force
+
+ align:start position:0%
+whenever you have gadgets that force
+ 
+
+ align:start position:0%
+whenever you have gadgets that force
+certain modulo constraints, just having
+
+ align:start position:0%
+certain modulo constraints, just having
+ 
+
+ align:start position:0%
+certain modulo constraints, just having
+the ability to add one is great because
+
+ align:start position:0%
+the ability to add one is great because
+ 
+
+ align:start position:0%
+the ability to add one is great because
+then you can break all such constraints.
+
+ align:start position:0%
+then you can break all such constraints.
+ 
+
+ align:start position:0%
+then you can break all such constraints.
+You no longer have to live in a mod 3
+
+ align:start position:0%
+You no longer have to live in a mod 3
+ 
+
+ align:start position:0%
+You no longer have to live in a mod 3
+grid or whatever if you don't want to.
+
+ align:start position:0%
+grid or whatever if you don't want to.
+ 
+
+ align:start position:0%
+grid or whatever if you don't want to.
+So this is important in general. Uh
+
+ align:start position:0%
+So this is important in general. Uh
+ 
+
+ align:start position:0%
+So this is important in general. Uh
+maybe I'll add it to the list here. Um,
+
+ align:start position:0%
+maybe I'll add it to the list here. Um,
+ 
+
+ align:start position:0%
+maybe I'll add it to the list here. Um,
+when you're dealing with wires, uh, you
+
+ align:start position:0%
+when you're dealing with wires, uh, you
+ 
+
+ align:start position:0%
+when you're dealing with wires, uh, you
+may need some kind of shift gadget that
+
+ align:start position:0%
+may need some kind of shift gadget that
+ 
+
+ align:start position:0%
+may need some kind of shift gadget that
+lets you, uh, fix par issues, or in this
+
+ align:start position:0%
+lets you, uh, fix par issues, or in this
+ 
+
+ align:start position:0%
+lets you, uh, fix par issues, or in this
+case, a mod 3 par.
+
+ align:start position:0%
+case, a mod 3 par.
+ 
+
+ align:start position:0%
+case, a mod 3 par.
+Okay. Uh, here's a more complicated
+
+ align:start position:0%
+Okay. Uh, here's a more complicated
+ 
+
+ align:start position:0%
+Okay. Uh, here's a more complicated
+gadget, which I will not go through. It
+
+ align:start position:0%
+gadget, which I will not go through. It
+ 
+
+ align:start position:0%
+gadget, which I will not go through. It
+looks scary. It's not actually a ton
+
+ align:start position:0%
+looks scary. It's not actually a ton
+ 
+
+ align:start position:0%
+looks scary. It's not actually a ton
+going on. It's a lot of gadgets we've
+
+ align:start position:0%
+going on. It's a lot of gadgets we've
+ 
+
+ align:start position:0%
+going on. It's a lot of gadgets we've
+already seen. Um, it uses a slight I've
+
+ align:start position:0%
+already seen. Um, it uses a slight I've
+ 
+
+ align:start position:0%
+already seen. Um, it uses a slight I've
+mentioned a turn gadget. This is another
+
+ align:start position:0%
+mentioned a turn gadget. This is another
+ 
+
+ align:start position:0%
+mentioned a turn gadget. This is another
+way to do a turn. Uh there's a few
+
+ align:start position:0%
+way to do a turn. Uh there's a few
+ 
+
+ align:start position:0%
+way to do a turn. Uh there's a few
+redundant gadgets in this paper because
+
+ align:start position:0%
+redundant gadgets in this paper because
+ 
+
+ align:start position:0%
+redundant gadgets in this paper because
+it's fun to make gadgets. So why not
+
+ align:start position:0%
+it's fun to make gadgets. So why not
+ 
+
+ align:start position:0%
+it's fun to make gadgets. So why not
+have more? Um and uh so there's for
+
+ align:start position:0%
+have more? Um and uh so there's for
+ 
+
+ align:start position:0%
+have more? Um and uh so there's for
+example just a turn gadget here. There's
+
+ align:start position:0%
+example just a turn gadget here. There's
+ 
+
+ align:start position:0%
+example just a turn gadget here. There's
+a splitter here. Another turn gadget.
+
+ align:start position:0%
+a splitter here. Another turn gadget.
+ 
+
+ align:start position:0%
+a splitter here. Another turn gadget.
+This is uh reflectionally symmetric
+
+ align:start position:0%
+This is uh reflectionally symmetric
+ 
+
+ align:start position:0%
+This is uh reflectionally symmetric
+around the x-axis. Uh there's basically
+
+ align:start position:0%
+around the x-axis. Uh there's basically
+ 
+
+ align:start position:0%
+around the x-axis. Uh there's basically
+just a turn here. So x is just getting
+
+ align:start position:0%
+just a turn here. So x is just getting
+ 
+
+ align:start position:0%
+just a turn here. So x is just getting
+copied or and negated into here. Uh z is
+
+ align:start position:0%
+copied or and negated into here. Uh z is
+ 
+
+ align:start position:0%
+copied or and negated into here. Uh z is
+getting copied and negated into here. Um
+
+ align:start position:0%
+getting copied and negated into here. Um
+ 
+
+ align:start position:0%
+getting copied and negated into here. Um
+this is the output value which is
+
+ align:start position:0%
+this is the output value which is
+ 
+
+ align:start position:0%
+this is the output value which is
+getting copied around into here. And
+
+ align:start position:0%
+getting copied around into here. And
+ 
+
+ align:start position:0%
+getting copied around into here. And
+then a little bit of magic happens here
+
+ align:start position:0%
+then a little bit of magic happens here
+ 
+
+ align:start position:0%
+then a little bit of magic happens here
+and here to get these to interact in the
+
+ align:start position:0%
+and here to get these to interact in the
+ 
+
+ align:start position:0%
+and here to get these to interact in the
+right way. And it's essentially just
+
+ align:start position:0%
+right way. And it's essentially just
+ 
+
+ align:start position:0%
+right way. And it's essentially just
+checking uh cases to see that this
+
+ align:start position:0%
+checking uh cases to see that this
+ 
+
+ align:start position:0%
+checking uh cases to see that this
+computes an of these two inputs.
+
+ align:start position:0%
+computes an of these two inputs.
+ 
+
+ align:start position:0%
+computes an of these two inputs.
+Okay. Uh but you know a little bit
+
+ align:start position:0%
+Okay. Uh but you know a little bit
+ 
+
+ align:start position:0%
+Okay. Uh but you know a little bit
+complicated.
+
+ align:start position:0%
+complicated.
+ 
+
+ align:start position:0%
+complicated.
+Is coming up with these gadgets harder
+
+ align:start position:0%
+Is coming up with these gadgets harder
+ 
+
+ align:start position:0%
+Is coming up with these gadgets harder
+than checking them? Uh,
+
+ align:start position:0%
+than checking them? Uh,
+ 
+
+ align:start position:0%
+than checking them? Uh,
+good question. It's unclear. Often when
+
+ align:start position:0%
+good question. It's unclear. Often when
+ 
+
+ align:start position:0%
+good question. It's unclear. Often when
+you're designing things, you have a lot
+
+ align:start position:0%
+you're designing things, you have a lot
+ 
+
+ align:start position:0%
+you're designing things, you have a lot
+more control and it could potentially be
+
+ align:start position:0%
+more control and it could potentially be
+ 
+
+ align:start position:0%
+more control and it could potentially be
+easier to design hard problems than to
+
+ align:start position:0%
+easier to design hard problems than to
+ 
+
+ align:start position:0%
+easier to design hard problems than to
+check them. Uh, because we know it's
+
+ align:start position:0%
+check them. Uh, because we know it's
+ 
+
+ align:start position:0%
+check them. Uh, because we know it's
+MPcomplete to check this. So, in in a
+
+ align:start position:0%
+MPcomplete to check this. So, in in a
+ 
+
+ align:start position:0%
+MPcomplete to check this. So, in in a
+certain sense, uh, yeah, I mean, of
+
+ align:start position:0%
+certain sense, uh, yeah, I mean, of
+ 
+
+ align:start position:0%
+certain sense, uh, yeah, I mean, of
+course, in this case, there's only four
+
+ align:start position:0%
+course, in this case, there's only four
+ 
+
+ align:start position:0%
+course, in this case, there's only four
+cases, so it's not really that hard. Uh
+
+ align:start position:0%
+cases, so it's not really that hard. Uh
+ 
+
+ align:start position:0%
+cases, so it's not really that hard. Uh
+but yeah, when you're designing things,
+
+ align:start position:0%
+but yeah, when you're designing things,
+ 
+
+ align:start position:0%
+but yeah, when you're designing things,
+you you have in mind a certain
+
+ align:start position:0%
+you you have in mind a certain
+ 
+
+ align:start position:0%
+you you have in mind a certain
+connectivity structure and then it's a
+
+ align:start position:0%
+connectivity structure and then it's a
+ 
+
+ align:start position:0%
+connectivity structure and then it's a
+matter of getting things to resolve in
+
+ align:start position:0%
+matter of getting things to resolve in
+ 
+
+ align:start position:0%
+matter of getting things to resolve in
+the grid and not have cross things
+
+ align:start position:0%
+the grid and not have cross things
+ 
+
+ align:start position:0%
+the grid and not have cross things
+overlapping and so on, which is a
+
+ align:start position:0%
+overlapping and so on, which is a
+ 
+
+ align:start position:0%
+overlapping and so on, which is a
+different kind of constraint. It's
+
+ align:start position:0%
+different kind of constraint. It's
+ 
+
+ align:start position:0%
+different kind of constraint. It's
+usually a I might say it's a more fun
+
+ align:start position:0%
+usually a I might say it's a more fun
+ 
+
+ align:start position:0%
+usually a I might say it's a more fun
+one. I would call designing these
+
+ align:start position:0%
+one. I would call designing these
+ 
+
+ align:start position:0%
+one. I would call designing these
+puzzles metapuzzles and to me that's
+
+ align:start position:0%
+puzzles metapuzzles and to me that's
+ 
+
+ align:start position:0%
+puzzles metapuzzles and to me that's
+more fun, but of course I'm a
+
+ align:start position:0%
+more fun, but of course I'm a
+ 
+
+ align:start position:0%
+more fun, but of course I'm a
+theoretical computer scientist, so
+
+ align:start position:0%
+theoretical computer scientist, so
+ 
+
+ align:start position:0%
+theoretical computer scientist, so
+that's uh that's why we're here. Um
+
+ align:start position:0%
+that's uh that's why we're here. Um
+ 
+
+ align:start position:0%
+that's uh that's why we're here. Um
+anyway, yeah, fun abstract question.
+
+ align:start position:0%
+anyway, yeah, fun abstract question.
+ 
+
+ align:start position:0%
+anyway, yeah, fun abstract question.
+Uh so here's a fun thing. I hadn't seen
+
+ align:start position:0%
+Uh so here's a fun thing. I hadn't seen
+ 
+
+ align:start position:0%
+Uh so here's a fun thing. I hadn't seen
+this paper before uh by uh Goldlogger in
+
+ align:start position:0%
+this paper before uh by uh Goldlogger in
+ 
+
+ align:start position:0%
+this paper before uh by uh Goldlogger in
+1977. Uh they were worried about
+
+ align:start position:0%
+1977. Uh they were worried about
+ 
+
+ align:start position:0%
+1977. Uh they were worried about
+Pmpleteness, which we haven't talked
+
+ align:start position:0%
+Pmpleteness, which we haven't talked
+ 
+
+ align:start position:0%
+Pmpleteness, which we haven't talked
+about yet, but uh in particular, they
+
+ align:start position:0%
+about yet, but uh in particular, they
+ 
+
+ align:start position:0%
+about yet, but uh in particular, they
+give these two pictures. This one we've
+
+ align:start position:0%
+give these two pictures. This one we've
+ 
+
+ align:start position:0%
+give these two pictures. This one we've
+seen uh from if you have an exor gadget,
+
+ align:start position:0%
+seen uh from if you have an exor gadget,
+ 
+
+ align:start position:0%
+seen uh from if you have an exor gadget,
+you can construct a crossover. Now, we
+
+ align:start position:0%
+you can construct a crossover. Now, we
+ 
+
+ align:start position:0%
+you can construct a crossover. Now, we
+don't have an exor gadget in this case,
+
+ align:start position:0%
+don't have an exor gadget in this case,
+ 
+
+ align:start position:0%
+don't have an exor gadget in this case,
+but we have an AND gadget or a NAND
+
+ align:start position:0%
+but we have an AND gadget or a NAND
+ 
+
+ align:start position:0%
+but we have an AND gadget or a NAND
+gadget. This is a funny way of writing
+
+ align:start position:0%
+gadget. This is a funny way of writing
+ 
+
+ align:start position:0%
+gadget. This is a funny way of writing
+NAND, not of an and. And if you have
+
+ align:start position:0%
+NAND, not of an and. And if you have
+ 
+
+ align:start position:0%
+NAND, not of an and. And if you have
+NAND gadgets, you can construct an exor.
+
+ align:start position:0%
+NAND gadgets, you can construct an exor.
+ 
+
+ align:start position:0%
+NAND gadgets, you can construct an exor.
+So if you plug this picture into each of
+
+ align:start position:0%
+So if you plug this picture into each of
+ 
+
+ align:start position:0%
+So if you plug this picture into each of
+these three pictures, you get a kind of
+
+ align:start position:0%
+these three pictures, you get a kind of
+ 
+
+ align:start position:0%
+these three pictures, you get a kind of
+ugly thing, but it's planer and it
+
+ align:start position:0%
+ugly thing, but it's planer and it
+ 
+
+ align:start position:0%
+ugly thing, but it's planer and it
+implements a crossover, which means if
+
+ align:start position:0%
+implements a crossover, which means if
+ 
+
+ align:start position:0%
+implements a crossover, which means if
+you have NAND, you get planerity for
+
+ align:start position:0%
+you have NAND, you get planerity for
+ 
+
+ align:start position:0%
+you have NAND, you get planerity for
+free. Okay. So, I'm going to call this
+
+ align:start position:0%
+free. Okay. So, I'm going to call this
+ 
+
+ align:start position:0%
+free. Okay. So, I'm going to call this
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planer circuit set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Slight catch is that this I think is
+
+ align:start position:0%
+Slight catch is that this I think is
+ 
+
+ align:start position:0%
+Slight catch is that this I think is
+also a madeup term. I haven't seen it in
+
+ align:start position:0%
+also a madeup term. I haven't seen it in
+ 
+
+ align:start position:0%
+also a madeup term. I haven't seen it in
+the literature because it's a little bit
+
+ align:start position:0%
+the literature because it's a little bit
+ 
+
+ align:start position:0%
+the literature because it's a little bit
+vague what it could mean. Uh but let's
+
+ align:start position:0%
+vague what it could mean. Uh but let's
+ 
+
+ align:start position:0%
+vague what it could mean. Uh but let's
+say we're given a planer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh directed as cyclic circuit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say all gates
+
+ align:start position:0%
+and let's say all gates
+ 
+
+ align:start position:0%
+and let's say all gates
+are NAND
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this is MP complete.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in checking whether a particular
+
+ align:start position:0%
+in checking whether a particular
+ 
+
+ align:start position:0%
+in checking whether a particular
+ah right sorry um and at the end you
+
+ align:start position:0%
+ah right sorry um and at the end you
+ 
+
+ align:start position:0%
+ah right sorry um and at the end you
+want it to be true thank you so you have
+
+ align:start position:0%
+want it to be true thank you so you have
+ 
+
+ align:start position:0%
+want it to be true thank you so you have
+the let's say the sources are
+
+ align:start position:0%
+the let's say the sources are
+ 
+
+ align:start position:0%
+the let's say the sources are
+unconstrained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those represent the variables and
+
+ align:start position:0%
+so those represent the variables and
+ 
+
+ align:start position:0%
+so those represent the variables and
+there's a sync
+
+ align:start position:0%
+there's a sync
+ 
+
+ align:start position:0%
+there's a sync
+which is set to one and we can say
+
+ align:start position:0%
+which is set to one and we can say
+ 
+
+ align:start position:0%
+which is set to one and we can say
+there's just one sync. So you have some
+
+ align:start position:0%
+there's just one sync. So you have some
+ 
+
+ align:start position:0%
+there's just one sync. So you have some
+starting points. Those are completely
+
+ align:start position:0%
+starting points. Those are completely
+ 
+
+ align:start position:0%
+starting points. Those are completely
+free to choose true or false. And then
+
+ align:start position:0%
+free to choose true or false. And then
+ 
+
+ align:start position:0%
+free to choose true or false. And then
+at the end you have a sync. Uh I guess
+
+ align:start position:0%
+at the end you have a sync. Uh I guess
+ 
+
+ align:start position:0%
+at the end you have a sync. Uh I guess
+it just has one thing probably coming
+
+ align:start position:0%
+it just has one thing probably coming
+ 
+
+ align:start position:0%
+it just has one thing probably coming
+into it. Wouldn't make sense otherwise.
+
+ align:start position:0%
+into it. Wouldn't make sense otherwise.
+ 
+
+ align:start position:0%
+into it. Wouldn't make sense otherwise.
+And we set this to be one. So that's
+
+ align:start position:0%
+And we set this to be one. So that's
+ 
+
+ align:start position:0%
+And we set this to be one. So that's
+just like satisfying a formula but drawn
+
+ align:start position:0%
+just like satisfying a formula but drawn
+ 
+
+ align:start position:0%
+just like satisfying a formula but drawn
+as a boolean circuit. And it's planer.
+
+ align:start position:0%
+as a boolean circuit. And it's planer.
+ 
+
+ align:start position:0%
+as a boolean circuit. And it's planer.
+Okay. Now we're going to see more
+
+ align:start position:0%
+Okay. Now we're going to see more
+ 
+
+ align:start position:0%
+Okay. Now we're going to see more
+versions of planer sat next class. Uh
+
+ align:start position:0%
+versions of planer sat next class. Uh
+ 
+
+ align:start position:0%
+versions of planer sat next class. Uh
+but this one as far as I know is newish.
+
+ align:start position:0%
+but this one as far as I know is newish.
+ 
+
+ align:start position:0%
+but this one as far as I know is newish.
+I mean it's obvious it's essentially
+
+ align:start position:0%
+I mean it's obvious it's essentially
+ 
+
+ align:start position:0%
+I mean it's obvious it's essentially
+argued in this paper say hey look um
+
+ align:start position:0%
+argued in this paper say hey look um
+ 
+
+ align:start position:0%
+argued in this paper say hey look um
+this paper was not talking about NP
+
+ align:start position:0%
+this paper was not talking about NP
+ 
+
+ align:start position:0%
+this paper was not talking about NP
+completeness but uh the K paper uh says
+
+ align:start position:0%
+completeness but uh the K paper uh says
+ 
+
+ align:start position:0%
+completeness but uh the K paper uh says
+hey we've got these two things so as
+
+ align:start position:0%
+hey we've got these two things so as
+ 
+
+ align:start position:0%
+hey we've got these two things so as
+long as you have NAND you've got
+
+ align:start position:0%
+long as you have NAND you've got
+ 
+
+ align:start position:0%
+long as you have NAND you've got
+crossovers for free so you don't have to
+
+ align:start position:0%
+crossovers for free so you don't have to
+ 
+
+ align:start position:0%
+crossovers for free so you don't have to
+worry about planerity which is good
+
+ align:start position:0%
+worry about planerity which is good
+ 
+
+ align:start position:0%
+worry about planerity which is good
+news. So no crossover gadget needed
+
+ align:start position:0%
+news. So no crossover gadget needed
+ 
+
+ align:start position:0%
+news. So no crossover gadget needed
+there is one. It's actually not that
+
+ align:start position:0%
+there is one. It's actually not that
+ 
+
+ align:start position:0%
+there is one. It's actually not that
+hard in mind sweeper but it's nicer when
+
+ align:start position:0%
+hard in mind sweeper but it's nicer when
+ 
+
+ align:start position:0%
+hard in mind sweeper but it's nicer when
+you don't have to do it.
+
+ align:start position:0%
+you don't have to do it.
+ 
+
+ align:start position:0%
+you don't have to do it.
+questions.
+
+ align:start position:0%
+questions.
+ 
+
+ align:start position:0%
+questions.
+I guess I did talk about termination.
+
+ align:start position:0%
+I guess I did talk about termination.
+ 
+
+ align:start position:0%
+I guess I did talk about termination.
+Uh but if you we do need a true
+
+ align:start position:0%
+Uh but if you we do need a true
+ 
+
+ align:start position:0%
+Uh but if you we do need a true
+terminator here because we're doing
+
+ align:start position:0%
+terminator here because we're doing
+ 
+
+ align:start position:0%
+terminator here because we're doing
+circuit set that's really easy. Um in
+
+ align:start position:0%
+circuit set that's really easy. Um in
+ 
+
+ align:start position:0%
+circuit set that's really easy. Um in
+fact this would do it. Just ending with
+
+ align:start position:0%
+fact this would do it. Just ending with
+ 
+
+ align:start position:0%
+fact this would do it. Just ending with
+all ones means in fact you have if
+
+ align:start position:0%
+all ones means in fact you have if
+ 
+
+ align:start position:0%
+all ones means in fact you have if
+there's zeros out here that means this
+
+ align:start position:0%
+there's zeros out here that means this
+ 
+
+ align:start position:0%
+there's zeros out here that means this
+has to be a bomb and so that sets it to
+
+ align:start position:0%
+has to be a bomb and so that sets it to
+ 
+
+ align:start position:0%
+has to be a bomb and so that sets it to
+one. So there's a true terminator for
+
+ align:start position:0%
+one. So there's a true terminator for
+ 
+
+ align:start position:0%
+one. So there's a true terminator for
+mind sweeper consistency. But as we've
+
+ align:start position:0%
+mind sweeper consistency. But as we've
+ 
+
+ align:start position:0%
+mind sweeper consistency. But as we've
+seen in various ways mind Mind sweeper
+
+ align:start position:0%
+seen in various ways mind Mind sweeper
+ 
+
+ align:start position:0%
+seen in various ways mind Mind sweeper
+consistency is probably not what we want
+
+ align:start position:0%
+consistency is probably not what we want
+ 
+
+ align:start position:0%
+consistency is probably not what we want
+uh to actually play the game. Um the
+
+ align:start position:0%
+uh to actually play the game. Um the
+ 
+
+ align:start position:0%
+uh to actually play the game. Um the
+algorithm I gave you is maybe is one way
+
+ align:start position:0%
+algorithm I gave you is maybe is one way
+ 
+
+ align:start position:0%
+algorithm I gave you is maybe is one way
+to think about playing the game where
+
+ align:start position:0%
+to think about playing the game where
+ 
+
+ align:start position:0%
+to think about playing the game where
+you're you add a thing and you check for
+
+ align:start position:0%
+you're you add a thing and you check for
+ 
+
+ align:start position:0%
+you're you add a thing and you check for
+consistency. U that's also a little bit
+
+ align:start position:0%
+consistency. U that's also a little bit
+ 
+
+ align:start position:0%
+consistency. U that's also a little bit
+weird where you're just where you're
+
+ align:start position:0%
+weird where you're just where you're
+ 
+
+ align:start position:0%
+weird where you're just where you're
+assuming that the input is consistent
+
+ align:start position:0%
+assuming that the input is consistent
+ 
+
+ align:start position:0%
+assuming that the input is consistent
+and then you add one bomb and you want
+
+ align:start position:0%
+and then you add one bomb and you want
+ 
+
+ align:start position:0%
+and then you add one bomb and you want
+to see whether that makes it
+
+ align:start position:0%
+to see whether that makes it
+ 
+
+ align:start position:0%
+to see whether that makes it
+inconsistent. That's a special case of
+
+ align:start position:0%
+inconsistent. That's a special case of
+ 
+
+ align:start position:0%
+inconsistent. That's a special case of
+this instance. Maybe not as hard as the
+
+ align:start position:0%
+this instance. Maybe not as hard as the
+ 
+
+ align:start position:0%
+this instance. Maybe not as hard as the
+general picture. everything was
+
+ align:start position:0%
+general picture. everything was
+ 
+
+ align:start position:0%
+general picture. everything was
+consistent up until the moment you added
+
+ align:start position:0%
+consistent up until the moment you added
+ 
+
+ align:start position:0%
+consistent up until the moment you added
+one new bomb information. These pictures
+
+ align:start position:0%
+one new bomb information. These pictures
+ 
+
+ align:start position:0%
+one new bomb information. These pictures
+don't look exactly like that. Uh,
+
+ align:start position:0%
+don't look exactly like that. Uh,
+ 
+
+ align:start position:0%
+don't look exactly like that. Uh,
+another thing I want to point out in
+
+ align:start position:0%
+another thing I want to point out in
+ 
+
+ align:start position:0%
+another thing I want to point out in
+these uh, gadgets
+
+ align:start position:0%
+these uh, gadgets
+ 
+
+ align:start position:0%
+these uh, gadgets
+is that the let's say the number of x
+
+ align:start position:0%
+is that the let's say the number of x
+ 
+
+ align:start position:0%
+is that the let's say the number of x
+and x bars is not the same. Maybe this
+
+ align:start position:0%
+and x bars is not the same. Maybe this
+ 
+
+ align:start position:0%
+and x bars is not the same. Maybe this
+negation uh, there's equal numbers of x
+
+ align:start position:0%
+negation uh, there's equal numbers of x
+ 
+
+ align:start position:0%
+negation uh, there's equal numbers of x
+and x bars over here, but there's one
+
+ align:start position:0%
+and x bars over here, but there's one
+ 
+
+ align:start position:0%
+and x bars over here, but there's one
+extra xar. What that means is local to
+
+ align:start position:0%
+extra xar. What that means is local to
+ 
+
+ align:start position:0%
+extra xar. What that means is local to
+this picture, uh, the number of bombs
+
+ align:start position:0%
+this picture, uh, the number of bombs
+ 
+
+ align:start position:0%
+this picture, uh, the number of bombs
+that get used varies, right? There's
+
+ align:start position:0%
+that get used varies, right? There's
+ 
+
+ align:start position:0%
+that get used varies, right? There's
+either one, two, three, four bombs if
+
+ align:start position:0%
+either one, two, three, four bombs if
+ 
+
+ align:start position:0%
+either one, two, three, four bombs if
+you choose X or there's five bombs if
+
+ align:start position:0%
+you choose X or there's five bombs if
+ 
+
+ align:start position:0%
+you choose X or there's five bombs if
+you choose XAR. And one of the minor
+
+ align:start position:0%
+you choose XAR. And one of the minor
+ 
+
+ align:start position:0%
+you choose XAR. And one of the minor
+things in mind sweeper is that the
+
+ align:start position:0%
+things in mind sweeper is that the
+ 
+
+ align:start position:0%
+things in mind sweeper is that the
+number of total number of bombs is given
+
+ align:start position:0%
+number of total number of bombs is given
+ 
+
+ align:start position:0%
+number of total number of bombs is given
+to you as input. Uh, so that actually
+
+ align:start position:0%
+to you as input. Uh, so that actually
+ 
+
+ align:start position:0%
+to you as input. Uh, so that actually
+also kind of messes things up. Um,
+
+ align:start position:0%
+also kind of messes things up. Um,
+ 
+
+ align:start position:0%
+also kind of messes things up. Um,
+anyway, luckily this problem is solved.
+
+ align:start position:0%
+anyway, luckily this problem is solved.
+ 
+
+ align:start position:0%
+anyway, luckily this problem is solved.
+uh is actually independently solved by
+
+ align:start position:0%
+uh is actually independently solved by
+ 
+
+ align:start position:0%
+uh is actually independently solved by
+multiple people. Uh it's claimed in um
+
+ align:start position:0%
+multiple people. Uh it's claimed in um
+ 
+
+ align:start position:0%
+multiple people. Uh it's claimed in um
+in Bob Hearn's PhD thesis, though it
+
+ align:start position:0%
+in Bob Hearn's PhD thesis, though it
+ 
+
+ align:start position:0%
+in Bob Hearn's PhD thesis, though it
+never got fully written up. Uh and then
+
+ align:start position:0%
+never got fully written up. Uh and then
+ 
+
+ align:start position:0%
+never got fully written up. Uh and then
+it got published, so there's no reason
+
+ align:start position:0%
+it got published, so there's no reason
+ 
+
+ align:start position:0%
+it got published, so there's no reason
+to write it up anymore. Uh so here is
+
+ align:start position:0%
+to write it up anymore. Uh so here is
+ 
+
+ align:start position:0%
+to write it up anymore. Uh so here is
+their proof. Uh both this proof and the
+
+ align:start position:0%
+their proof. Uh both this proof and the
+ 
+
+ align:start position:0%
+their proof. Uh both this proof and the
+previous one appeared in mathematical
+
+ align:start position:0%
+previous one appeared in mathematical
+ 
+
+ align:start position:0%
+previous one appeared in mathematical
+intelligencer. Um so they draw the
+
+ align:start position:0%
+intelligencer. Um so they draw the
+ 
+
+ align:start position:0%
+intelligencer. Um so they draw the
+gadget slightly differently and so far
+
+ align:start position:0%
+gadget slightly differently and so far
+ 
+
+ align:start position:0%
+gadget slightly differently and so far
+everything looks about the same. They're
+
+ align:start position:0%
+everything looks about the same. They're
+ 
+
+ align:start position:0%
+everything looks about the same. They're
+not going to use a phase changer in this
+
+ align:start position:0%
+not going to use a phase changer in this
+ 
+
+ align:start position:0%
+not going to use a phase changer in this
+form at least. Uh so they're going to
+
+ align:start position:0%
+form at least. Uh so they're going to
+ 
+
+ align:start position:0%
+form at least. Uh so they're going to
+draw the wire gadget like this and the
+
+ align:start position:0%
+draw the wire gadget like this and the
+ 
+
+ align:start position:0%
+draw the wire gadget like this and the
+idea is that you would copy it. You get
+
+ align:start position:0%
+idea is that you would copy it. You get
+ 
+
+ align:start position:0%
+idea is that you would copy it. You get
+things mod 3. Uh that will turn out to
+
+ align:start position:0%
+things mod 3. Uh that will turn out to
+ 
+
+ align:start position:0%
+things mod 3. Uh that will turn out to
+be okay for them. But what they really
+
+ align:start position:0%
+be okay for them. But what they really
+ 
+
+ align:start position:0%
+be okay for them. But what they really
+want is that in each diagram there an
+
+ align:start position:0%
+want is that in each diagram there an
+ 
+
+ align:start position:0%
+want is that in each diagram there an
+equal number of x and x bars. Why? And
+
+ align:start position:0%
+equal number of x and x bars. Why? And
+ 
+
+ align:start position:0%
+equal number of x and x bars. Why? And
+also what are they proving? So this is
+
+ align:start position:0%
+also what are they proving? So this is
+ 
+
+ align:start position:0%
+also what are they proving? So this is
+uh what they call the
+
+ align:start position:0%
+uh what they call the
+ 
+
+ align:start position:0%
+uh what they call the
+mind sweeper inference problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But it's also what you might just call
+
+ align:start position:0%
+But it's also what you might just call
+ 
+
+ align:start position:0%
+But it's also what you might just call
+mind sweeper.
+
+ align:start position:0%
+mind sweeper.
+ 
+
+ align:start position:0%
+mind sweeper.
+I want to solve this puzzle. What does
+
+ align:start position:0%
+I want to solve this puzzle. What does
+ 
+
+ align:start position:0%
+I want to solve this puzzle. What does
+it mean to solve the puzzle? Well, it
+
+ align:start position:0%
+it mean to solve the puzzle? Well, it
+ 
+
+ align:start position:0%
+it mean to solve the puzzle? Well, it
+means you're given this partial
+
+ align:start position:0%
+means you're given this partial
+ 
+
+ align:start position:0%
+means you're given this partial
+information. You want to know, am I
+
+ align:start position:0%
+information. You want to know, am I
+ 
+
+ align:start position:0%
+information. You want to know, am I
+done? Did I solve it? Can I solve it?
+
+ align:start position:0%
+done? Did I solve it? Can I solve it?
+ 
+
+ align:start position:0%
+done? Did I solve it? Can I solve it?
+Can I figure out where all the bombs
+
+ align:start position:0%
+Can I figure out where all the bombs
+ 
+
+ align:start position:0%
+Can I figure out where all the bombs
+are? This is like there being a unique
+
+ align:start position:0%
+are? This is like there being a unique
+ 
+
+ align:start position:0%
+are? This is like there being a unique
+solution. Um, so I want to conclude that
+
+ align:start position:0%
+solution. Um, so I want to conclude that
+ 
+
+ align:start position:0%
+solution. Um, so I want to conclude that
+okay, I can figure out where all the
+
+ align:start position:0%
+okay, I can figure out where all the
+ 
+
+ align:start position:0%
+okay, I can figure out where all the
+bombs are.
+
+ align:start position:0%
+bombs are.
+ 
+
+ align:start position:0%
+bombs are.
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you figure everything out?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So again, uh the reduction is from
+
+ align:start position:0%
+Okay. So again, uh the reduction is from
+ 
+
+ align:start position:0%
+Okay. So again, uh the reduction is from
+something like circuit SAT. Uh it's
+
+ align:start position:0%
+something like circuit SAT. Uh it's
+ 
+
+ align:start position:0%
+something like circuit SAT. Uh it's
+going to be a reduction from circuit
+
+ align:start position:0%
+going to be a reduction from circuit
+ 
+
+ align:start position:0%
+going to be a reduction from circuit
+unsat.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unsatisfiability.
+
+ align:start position:0%
+unsatisfiability.
+ 
+
+ align:start position:0%
+unsatisfiability.
+So satisfiability, you want to set the
+
+ align:start position:0%
+So satisfiability, you want to set the
+ 
+
+ align:start position:0%
+So satisfiability, you want to set the
+variable so that the outcome is true.
+
+ align:start position:0%
+variable so that the outcome is true.
+ 
+
+ align:start position:0%
+variable so that the outcome is true.
+You might say, well, I could try to set
+
+ align:start position:0%
+You might say, well, I could try to set
+ 
+
+ align:start position:0%
+You might say, well, I could try to set
+the variable so the outcome is false.
+
+ align:start position:0%
+the variable so the outcome is false.
+ 
+
+ align:start position:0%
+the variable so the outcome is false.
+That's the same problem. Uh that won't
+
+ align:start position:0%
+That's the same problem. Uh that won't
+ 
+
+ align:start position:0%
+That's the same problem. Uh that won't
+change anything. You just put a knot at
+
+ align:start position:0%
+change anything. You just put a knot at
+ 
+
+ align:start position:0%
+change anything. You just put a knot at
+the end. Okay. Unsatisfiability means
+
+ align:start position:0%
+the end. Okay. Unsatisfiability means
+ 
+
+ align:start position:0%
+the end. Okay. Unsatisfiability means
+that you cannot satisfy this formula.
+
+ align:start position:0%
+that you cannot satisfy this formula.
+ 
+
+ align:start position:0%
+that you cannot satisfy this formula.
+There's no way to set the variables to
+
+ align:start position:0%
+There's no way to set the variables to
+ 
+
+ align:start position:0%
+There's no way to set the variables to
+make the output true.
+
+ align:start position:0%
+make the output true.
+ 
+
+ align:start position:0%
+make the output true.
+There is no
+
+ align:start position:0%
+There is no
+ 
+
+ align:start position:0%
+There is no
+there does not exist uh choices for the
+
+ align:start position:0%
+there does not exist uh choices for the
+ 
+
+ align:start position:0%
+there does not exist uh choices for the
+xns
+
+ align:start position:0%
+xns
+ 
+
+ align:start position:0%
+xns
+such that sum f of
+
+ align:start position:0%
+such that sum f of
+ 
+
+ align:start position:0%
+such that sum f of
+x i's uh equals 1.
+
+ align:start position:0%
+x i's uh equals 1.
+ 
+
+ align:start position:0%
+x i's uh equals 1.
+If we do some sort of I don't know if
+
+ align:start position:0%
+If we do some sort of I don't know if
+ 
+
+ align:start position:0%
+If we do some sort of I don't know if
+this is called deorggan probably not uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another fun fact is uh not there exists
+
+ align:start position:0%
+another fun fact is uh not there exists
+ 
+
+ align:start position:0%
+another fun fact is uh not there exists
+not is the same thing as for all or
+
+ align:start position:0%
+not is the same thing as for all or
+ 
+
+ align:start position:0%
+not is the same thing as for all or
+however you want to write it. Um so if
+
+ align:start position:0%
+however you want to write it. Um so if
+ 
+
+ align:start position:0%
+however you want to write it. Um so if
+we put this negation over to here uh
+
+ align:start position:0%
+we put this negation over to here uh
+ 
+
+ align:start position:0%
+we put this negation over to here uh
+this turns into uni universal
+
+ align:start position:0%
+this turns into uni universal
+ 
+
+ align:start position:0%
+this turns into uni universal
+quantifiers. These are existential
+
+ align:start position:0%
+quantifiers. These are existential
+ 
+
+ align:start position:0%
+quantifiers. These are existential
+quantifiers to for alls. Uh so this is
+
+ align:start position:0%
+quantifiers to for alls. Uh so this is
+ 
+
+ align:start position:0%
+quantifiers to for alls. Uh so this is
+quite a different problem right is about
+
+ align:start position:0%
+quite a different problem right is about
+ 
+
+ align:start position:0%
+quite a different problem right is about
+do there exist the settings for these n
+
+ align:start position:0%
+do there exist the settings for these n
+ 
+
+ align:start position:0%
+do there exist the settings for these n
+variables such that this comes out to be
+
+ align:start position:0%
+variables such that this comes out to be
+ 
+
+ align:start position:0%
+variables such that this comes out to be
+true. Uh now we're saying for no matter
+
+ align:start position:0%
+true. Uh now we're saying for no matter
+ 
+
+ align:start position:0%
+true. Uh now we're saying for no matter
+how you set the variables this comes out
+
+ align:start position:0%
+how you set the variables this comes out
+ 
+
+ align:start position:0%
+how you set the variables this comes out
+to be true or false I guess. But again
+
+ align:start position:0%
+to be true or false I guess. But again
+ 
+
+ align:start position:0%
+to be true or false I guess. But again
+that doesn't matter. You can just put
+
+ align:start position:0%
+that doesn't matter. You can just put
+ 
+
+ align:start position:0%
+that doesn't matter. You can just put
+the negation inside f if you wanted to.
+
+ align:start position:0%
+the negation inside f if you wanted to.
+ 
+
+ align:start position:0%
+the negation inside f if you wanted to.
+So the key difference here is we switch
+
+ align:start position:0%
+So the key difference here is we switch
+ 
+
+ align:start position:0%
+So the key difference here is we switch
+the quantifier direction. This is such a
+
+ align:start position:0%
+the quantifier direction. This is such a
+ 
+
+ align:start position:0%
+the quantifier direction. This is such a
+big difference that this problem is not
+
+ align:start position:0%
+big difference that this problem is not
+ 
+
+ align:start position:0%
+big difference that this problem is not
+nplete unless np equals cop. Uh this
+
+ align:start position:0%
+nplete unless np equals cop. Uh this
+ 
+
+ align:start position:0%
+nplete unless np equals cop. Uh this
+problem is co-enpe.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh recall co-enp are the problems
+
+ align:start position:0%
+Okay. Uh recall co-enp are the problems
+ 
+
+ align:start position:0%
+Okay. Uh recall co-enp are the problems
+where uh it's easy you can always give a
+
+ align:start position:0%
+where uh it's easy you can always give a
+ 
+
+ align:start position:0%
+where uh it's easy you can always give a
+no certificate. Whenever the answer is
+
+ align:start position:0%
+no certificate. Whenever the answer is
+ 
+
+ align:start position:0%
+no certificate. Whenever the answer is
+no, I can give you a short proof that
+
+ align:start position:0%
+no, I can give you a short proof that
+ 
+
+ align:start position:0%
+no, I can give you a short proof that
+the answer is no. How would I tell you
+
+ align:start position:0%
+the answer is no. How would I tell you
+ 
+
+ align:start position:0%
+the answer is no. How would I tell you
+that the answer to this question is no,
+
+ align:start position:0%
+that the answer to this question is no,
+ 
+
+ align:start position:0%
+that the answer to this question is no,
+I would give you a satisfying assignment
+
+ align:start position:0%
+I would give you a satisfying assignment
+ 
+
+ align:start position:0%
+I would give you a satisfying assignment
+and give you x1 through xn where f ends
+
+ align:start position:0%
+and give you x1 through xn where f ends
+ 
+
+ align:start position:0%
+and give you x1 through xn where f ends
+up being one. Then you know this is not
+
+ align:start position:0%
+up being one. Then you know this is not
+ 
+
+ align:start position:0%
+up being one. Then you know this is not
+true. It's very hard to prove yes here.
+
+ align:start position:0%
+true. It's very hard to prove yes here.
+ 
+
+ align:start position:0%
+true. It's very hard to prove yes here.
+You'd have I mean you might have to
+
+ align:start position:0%
+You'd have I mean you might have to
+ 
+
+ align:start position:0%
+You'd have I mean you might have to
+check all possible exponentially many
+
+ align:start position:0%
+check all possible exponentially many
+ 
+
+ align:start position:0%
+check all possible exponentially many
+assignments to the xis. Of course, we
+
+ align:start position:0%
+assignments to the xis. Of course, we
+ 
+
+ align:start position:0%
+assignments to the xis. Of course, we
+don't know whether that's possible.
+
+ align:start position:0%
+don't know whether that's possible.
+ 
+
+ align:start position:0%
+don't know whether that's possible.
+That's compp completeness. It's the same
+
+ align:start position:0%
+That's compp completeness. It's the same
+ 
+
+ align:start position:0%
+That's compp completeness. It's the same
+NP versus uh P problem but negated.
+
+ align:start position:0%
+NP versus uh P problem but negated.
+ 
+
+ align:start position:0%
+NP versus uh P problem but negated.
+Cool. Uh so claim is mind sweeper
+
+ align:start position:0%
+Cool. Uh so claim is mind sweeper
+ 
+
+ align:start position:0%
+Cool. Uh so claim is mind sweeper
+inference is compplete and in general
+
+ align:start position:0%
+inference is compplete and in general
+ 
+
+ align:start position:0%
+inference is compplete and in general
+the proper statement is mind sweeper is
+
+ align:start position:0%
+the proper statement is mind sweeper is
+ 
+
+ align:start position:0%
+the proper statement is mind sweeper is
+compp complete. Uh it's mind sweeper
+
+ align:start position:0%
+compp complete. Uh it's mind sweeper
+ 
+
+ align:start position:0%
+compp complete. Uh it's mind sweeper
+uh consistency is npmplete but mind
+
+ align:start position:0%
+uh consistency is npmplete but mind
+ 
+
+ align:start position:0%
+uh consistency is npmplete but mind
+sweeper the game I want to solve the
+
+ align:start position:0%
+sweeper the game I want to solve the
+ 
+
+ align:start position:0%
+sweeper the game I want to solve the
+game is compp complete. Cool. Uh this
+
+ align:start position:0%
+game is compp complete. Cool. Uh this
+ 
+
+ align:start position:0%
+game is compp complete. Cool. Uh this
+will be one of the few cases where co
+
+ align:start position:0%
+will be one of the few cases where co
+ 
+
+ align:start position:0%
+will be one of the few cases where co
+arises for us.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Where does co lie on? We don't know
+
+ align:start position:0%
+Where does co lie on? We don't know
+ 
+
+ align:start position:0%
+Where does co lie on? We don't know
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+uh in my one-dimensional diagram you can
+
+ align:start position:0%
+uh in my one-dimensional diagram you can
+ 
+
+ align:start position:0%
+uh in my one-dimensional diagram you can
+think of NP and comp lying in the same
+
+ align:start position:0%
+think of NP and comp lying in the same
+ 
+
+ align:start position:0%
+think of NP and comp lying in the same
+space but maybe like in a parallel
+
+ align:start position:0%
+space but maybe like in a parallel
+ 
+
+ align:start position:0%
+space but maybe like in a parallel
+universe.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think uh people always draw this
+
+ align:start position:0%
+I think uh people always draw this
+ 
+
+ align:start position:0%
+I think uh people always draw this
+picture of uh
+
+ align:start position:0%
+picture of uh
+ 
+
+ align:start position:0%
+picture of uh
+NP co-enp
+
+ align:start position:0%
+NP co-enp
+ 
+
+ align:start position:0%
+NP co-enp
+uh P is here and this is NP intersect
+
+ align:start position:0%
+uh P is here and this is NP intersect
+ 
+
+ align:start position:0%
+uh P is here and this is NP intersect
+co-enp
+
+ align:start position:0%
+co-enp
+ 
+
+ align:start position:0%
+co-enp
+who knows um so it's it's really off
+
+ align:start position:0%
+who knows um so it's it's really off
+ 
+
+ align:start position:0%
+who knows um so it's it's really off
+it's there are parallel universes one
+
+ align:start position:0%
+it's there are parallel universes one
+ 
+
+ align:start position:0%
+it's there are parallel universes one
+about positive problems one about
+
+ align:start position:0%
+about positive problems one about
+ 
+
+ align:start position:0%
+about positive problems one about
+negative problems
+
+ align:start position:0%
+negative problems
+ 
+
+ align:start position:0%
+negative problems
+uh but in some sense equal complexity if
+
+ align:start position:0%
+uh but in some sense equal complexity if
+ 
+
+ align:start position:0%
+uh but in some sense equal complexity if
+you Think about when we in this class we
+
+ align:start position:0%
+you Think about when we in this class we
+ 
+
+ align:start position:0%
+you Think about when we in this class we
+think about reductions as being one call
+
+ align:start position:0%
+think about reductions as being one call
+ 
+
+ align:start position:0%
+think about reductions as being one call
+reductions. You take your problem you
+
+ align:start position:0%
+reductions. You take your problem you
+ 
+
+ align:start position:0%
+reductions. You take your problem you
+map it so that the output uh when you
+
+ align:start position:0%
+map it so that the output uh when you
+ 
+
+ align:start position:0%
+map it so that the output uh when you
+solve this new problem it has exactly
+
+ align:start position:0%
+solve this new problem it has exactly
+ 
+
+ align:start position:0%
+solve this new problem it has exactly
+the same solution to your original
+
+ align:start position:0%
+the same solution to your original
+ 
+
+ align:start position:0%
+the same solution to your original
+problem. If you instead think about
+
+ align:start position:0%
+problem. If you instead think about
+ 
+
+ align:start position:0%
+problem. If you instead think about
+multiol reductions where you can make
+
+ align:start position:0%
+multiol reductions where you can make
+ 
+
+ align:start position:0%
+multiol reductions where you can make
+calls to an oracle that solve the target
+
+ align:start position:0%
+calls to an oracle that solve the target
+ 
+
+ align:start position:0%
+calls to an oracle that solve the target
+problem multiple times and then do stuff
+
+ align:start position:0%
+problem multiple times and then do stuff
+ 
+
+ align:start position:0%
+problem multiple times and then do stuff
+with it. You could for example call that
+
+ align:start position:0%
+with it. You could for example call that
+ 
+
+ align:start position:0%
+with it. You could for example call that
+thing then negate the answer and return
+
+ align:start position:0%
+thing then negate the answer and return
+ 
+
+ align:start position:0%
+thing then negate the answer and return
+that. In that universe, NP and Comp
+
+ align:start position:0%
+that. In that universe, NP and Comp
+ 
+
+ align:start position:0%
+that. In that universe, NP and Comp
+become the same thing or NP completeness
+
+ align:start position:0%
+become the same thing or NP completeness
+ 
+
+ align:start position:0%
+become the same thing or NP completeness
+and co-enpesseness which are about
+
+ align:start position:0%
+and co-enpesseness which are about
+ 
+
+ align:start position:0%
+and co-enpesseness which are about
+reductions become the same thing. So
+
+ align:start position:0%
+reductions become the same thing. So
+ 
+
+ align:start position:0%
+reductions become the same thing. So
+that's the only thing holding them apart
+
+ align:start position:0%
+that's the only thing holding them apart
+ 
+
+ align:start position:0%
+that's the only thing holding them apart
+is that we're not allowed to negate the
+
+ align:start position:0%
+is that we're not allowed to negate the
+ 
+
+ align:start position:0%
+is that we're not allowed to negate the
+answer. So I view them as almost the
+
+ align:start position:0%
+answer. So I view them as almost the
+ 
+
+ align:start position:0%
+answer. So I view them as almost the
+same but obviously they're different and
+
+ align:start position:0%
+same but obviously they're different and
+ 
+
+ align:start position:0%
+same but obviously they're different and
+you have to distinguish one from the
+
+ align:start position:0%
+you have to distinguish one from the
+ 
+
+ align:start position:0%
+you have to distinguish one from the
+other. But in terms of difficulty
+
+ align:start position:0%
+other. But in terms of difficulty
+ 
+
+ align:start position:0%
+other. But in terms of difficulty
+they're about the same like difference
+
+ align:start position:0%
+they're about the same like difference
+ 
+
+ align:start position:0%
+they're about the same like difference
+between NP and co-enpace is totally
+
+ align:start position:0%
+between NP and co-enpace is totally
+ 
+
+ align:start position:0%
+between NP and co-enpace is totally
+different or X time or you know other
+
+ align:start position:0%
+different or X time or you know other
+ 
+
+ align:start position:0%
+different or X time or you know other
+things in my onedimensional diagram.
+
+ align:start position:0%
+things in my onedimensional diagram.
+ 
+
+ align:start position:0%
+things in my onedimensional diagram.
+Yeah. Would P equals NP imply P equals
+
+ align:start position:0%
+Yeah. Would P equals NP imply P equals
+ 
+
+ align:start position:0%
+Yeah. Would P equals NP imply P equals
+Coen NP? If p equals np then I'm pretty
+
+ align:start position:0%
+Coen NP? If p equals np then I'm pretty
+ 
+
+ align:start position:0%
+Coen NP? If p equals np then I'm pretty
+sure co uh np equals co p uh because
+
+ align:start position:0%
+sure co uh np equals co p uh because
+ 
+
+ align:start position:0%
+sure co uh np equals co p uh because
+under in polinomial time you can do yeah
+
+ align:start position:0%
+under in polinomial time you can do yeah
+ 
+
+ align:start position:0%
+under in polinomial time you can do yeah
+p is closed under complement because you
+
+ align:start position:0%
+p is closed under complement because you
+ 
+
+ align:start position:0%
+p is closed under complement because you
+can just solve the problem that negate
+
+ align:start position:0%
+can just solve the problem that negate
+ 
+
+ align:start position:0%
+can just solve the problem that negate
+so I should say np and compp are
+
+ align:start position:0%
+so I should say np and compp are
+ 
+
+ align:start position:0%
+so I should say np and compp are
+different but nplete and comp complete
+
+ align:start position:0%
+different but nplete and comp complete
+ 
+
+ align:start position:0%
+different but nplete and comp complete
+are very close let's say they're you
+
+ align:start position:0%
+are very close let's say they're you
+ 
+
+ align:start position:0%
+are very close let's say they're you
+know this they're sort of dual for every
+
+ align:start position:0%
+know this they're sort of dual for every
+ 
+
+ align:start position:0%
+know this they're sort of dual for every
+problem over here is a corresponding
+
+ align:start position:0%
+problem over here is a corresponding
+ 
+
+ align:start position:0%
+problem over here is a corresponding
+problem over here is like the hardest
+
+ align:start position:0%
+problem over here is like the hardest
+ 
+
+ align:start position:0%
+problem over here is like the hardest
+and they're sort of symmetric or
+
+ align:start position:0%
+and they're sort of symmetric or
+ 
+
+ align:start position:0%
+and they're sort of symmetric or
+something.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right,
+
+ align:start position:0%
+All right,
+ 
+
+ align:start position:0%
+All right,
+back to mind sweeper. So, uh here is the
+
+ align:start position:0%
+back to mind sweeper. So, uh here is the
+ 
+
+ align:start position:0%
+back to mind sweeper. So, uh here is the
+compp completeness. We have wires just
+
+ align:start position:0%
+compp completeness. We have wires just
+ 
+
+ align:start position:0%
+compp completeness. We have wires just
+like before, but I'm drawing them
+
+ align:start position:0%
+like before, but I'm drawing them
+ 
+
+ align:start position:0%
+like before, but I'm drawing them
+differently because uh part of the issue
+
+ align:start position:0%
+differently because uh part of the issue
+ 
+
+ align:start position:0%
+differently because uh part of the issue
+here is we are told how many bombs there
+
+ align:start position:0%
+here is we are told how many bombs there
+ 
+
+ align:start position:0%
+here is we are told how many bombs there
+are and we don't want that information
+
+ align:start position:0%
+are and we don't want that information
+ 
+
+ align:start position:0%
+are and we don't want that information
+to help us. So, we want every diagram to
+
+ align:start position:0%
+to help us. So, we want every diagram to
+ 
+
+ align:start position:0%
+to help us. So, we want every diagram to
+have an equal number of say x and x
+
+ align:start position:0%
+have an equal number of say x and x
+ 
+
+ align:start position:0%
+have an equal number of say x and x
+bars. So if we set it with X or set it
+
+ align:start position:0%
+bars. So if we set it with X or set it
+ 
+
+ align:start position:0%
+bars. So if we set it with X or set it
+with XAR, we use exactly the same number
+
+ align:start position:0%
+with XAR, we use exactly the same number
+ 
+
+ align:start position:0%
+with XAR, we use exactly the same number
+of bombs, which means just knowing what
+
+ align:start position:0%
+of bombs, which means just knowing what
+ 
+
+ align:start position:0%
+of bombs, which means just knowing what
+gadgets are glued together, we can just
+
+ align:start position:0%
+gadgets are glued together, we can just
+ 
+
+ align:start position:0%
+gadgets are glued together, we can just
+add up how many bombs each one has, that
+
+ align:start position:0%
+add up how many bombs each one has, that
+ 
+
+ align:start position:0%
+add up how many bombs each one has, that
+will be the total number of bombs given
+
+ align:start position:0%
+will be the total number of bombs given
+ 
+
+ align:start position:0%
+will be the total number of bombs given
+to the puzzle. Um, and that shouldn't
+
+ align:start position:0%
+to the puzzle. Um, and that shouldn't
+ 
+
+ align:start position:0%
+to the puzzle. Um, and that shouldn't
+give you any extra information because
+
+ align:start position:0%
+give you any extra information because
+ 
+
+ align:start position:0%
+give you any extra information because
+all of these pictures will have equal
+
+ align:start position:0%
+all of these pictures will have equal
+ 
+
+ align:start position:0%
+all of these pictures will have equal
+number of X's and X bars. So here we
+
+ align:start position:0%
+number of X's and X bars. So here we
+ 
+
+ align:start position:0%
+number of X's and X bars. So here we
+have wire, terminator, and turn. pretty
+
+ align:start position:0%
+have wire, terminator, and turn. pretty
+ 
+
+ align:start position:0%
+have wire, terminator, and turn. pretty
+similar to before but now checking that
+
+ align:start position:0%
+similar to before but now checking that
+ 
+
+ align:start position:0%
+similar to before but now checking that
+everything has equal number of x's and x
+
+ align:start position:0%
+everything has equal number of x's and x
+ 
+
+ align:start position:0%
+everything has equal number of x's and x
+bars. I think this turn for example that
+
+ align:start position:0%
+bars. I think this turn for example that
+ 
+
+ align:start position:0%
+bars. I think this turn for example that
+one happens to be balanced but some of
+
+ align:start position:0%
+one happens to be balanced but some of
+ 
+
+ align:start position:0%
+one happens to be balanced but some of
+these gadgets are not balanced. This one
+
+ align:start position:0%
+these gadgets are not balanced. This one
+ 
+
+ align:start position:0%
+these gadgets are not balanced. This one
+almost certainly.
+
+ align:start position:0%
+almost certainly.
+ 
+
+ align:start position:0%
+almost certainly.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So um in this case they construct
+
+ align:start position:0%
+So um in this case they construct
+ 
+
+ align:start position:0%
+So um in this case they construct
+a notgate and an orgate and then uh they
+
+ align:start position:0%
+a notgate and an orgate and then uh they
+ 
+
+ align:start position:0%
+a notgate and an orgate and then uh they
+also build a shifter. This is a
+
+ align:start position:0%
+also build a shifter. This is a
+ 
+
+ align:start position:0%
+also build a shifter. This is a
+different kind of shifter. um it's
+
+ align:start position:0%
+different kind of shifter. um it's
+ 
+
+ align:start position:0%
+different kind of shifter. um it's
+actually it still has you know width a
+
+ align:start position:0%
+actually it still has you know width a
+ 
+
+ align:start position:0%
+actually it still has you know width a
+multiple of three but we're taking the
+
+ align:start position:0%
+multiple of three but we're taking the
+ 
+
+ align:start position:0%
+multiple of three but we're taking the
+wire and shifting it perpendicular by
+
+ align:start position:0%
+wire and shifting it perpendicular by
+ 
+
+ align:start position:0%
+wire and shifting it perpendicular by
+one unit with turns you can simulate the
+
+ align:start position:0%
+one unit with turns you can simulate the
+ 
+
+ align:start position:0%
+one unit with turns you can simulate the
+other type of shifter but this turns out
+
+ align:start position:0%
+other type of shifter but this turns out
+ 
+
+ align:start position:0%
+other type of shifter but this turns out
+to be the only one that they need uh so
+
+ align:start position:0%
+to be the only one that they need uh so
+ 
+
+ align:start position:0%
+to be the only one that they need uh so
+it's let's let's talk about that first
+
+ align:start position:0%
+it's let's let's talk about that first
+ 
+
+ align:start position:0%
+it's let's let's talk about that first
+let's say so if x is set by this two uh
+
+ align:start position:0%
+let's say so if x is set by this two uh
+ 
+
+ align:start position:0%
+let's say so if x is set by this two uh
+and this bomb this one is not set okay
+
+ align:start position:0%
+and this bomb this one is not set okay
+ 
+
+ align:start position:0%
+and this bomb this one is not set okay
+this four already has three of them so
+
+ align:start position:0%
+this four already has three of them so
+ 
+
+ align:start position:0%
+this four already has three of them so
+it effectively becomes a one so then
+
+ align:start position:0%
+it effectively becomes a one so then
+ 
+
+ align:start position:0%
+it effectively becomes a one so then
+these two have to be opposites from each
+
+ align:start position:0%
+these two have to be opposites from each
+ 
+
+ align:start position:0%
+these two have to be opposites from each
+other. This is sort of where the shift
+
+ align:start position:0%
+other. This is sort of where the shift
+ 
+
+ align:start position:0%
+other. This is sort of where the shift
+happens. Uh and then uh because we have
+
+ align:start position:0%
+happens. Uh and then uh because we have
+ 
+
+ align:start position:0%
+happens. Uh and then uh because we have
+to deal with these bombs that are left
+
+ align:start position:0%
+to deal with these bombs that are left
+ 
+
+ align:start position:0%
+to deal with these bombs that are left
+over, let's put some more in. And then
+
+ align:start position:0%
+over, let's put some more in. And then
+ 
+
+ align:start position:0%
+over, let's put some more in. And then
+this is five. So there's already four
+
+ align:start position:0%
+this is five. So there's already four
+ 
+
+ align:start position:0%
+this is five. So there's already four
+here. And so that forces an alternation
+
+ align:start position:0%
+here. And so that forces an alternation
+ 
+
+ align:start position:0%
+here. And so that forces an alternation
+there. So same idea, but with some bombs
+
+ align:start position:0%
+there. So same idea, but with some bombs
+ 
+
+ align:start position:0%
+there. So same idea, but with some bombs
+added in to uh fill the space. Let's
+
+ align:start position:0%
+added in to uh fill the space. Let's
+ 
+
+ align:start position:0%
+added in to uh fill the space. Let's
+say, could I do a one here and a one
+
+ align:start position:0%
+say, could I do a one here and a one
+ 
+
+ align:start position:0%
+say, could I do a one here and a one
+here? A one there. Uh this is a problem.
+
+ align:start position:0%
+here? A one there. Uh this is a problem.
+ 
+
+ align:start position:0%
+here? A one there. Uh this is a problem.
+I couldn't can't put a one here. That
+
+ align:start position:0%
+I couldn't can't put a one here. That
+ 
+
+ align:start position:0%
+I couldn't can't put a one here. That
+would force this guy to be present. So
+
+ align:start position:0%
+would force this guy to be present. So
+ 
+
+ align:start position:0%
+would force this guy to be present. So
+that's probably why that bomb is there
+
+ align:start position:0%
+that's probably why that bomb is there
+ 
+
+ align:start position:0%
+that's probably why that bomb is there
+because we don't want to have to say how
+
+ align:start position:0%
+because we don't want to have to say how
+ 
+
+ align:start position:0%
+because we don't want to have to say how
+many bombs are adjacent to this corner.
+
+ align:start position:0%
+many bombs are adjacent to this corner.
+ 
+
+ align:start position:0%
+many bombs are adjacent to this corner.
+With regular wires, you don't have
+
+ align:start position:0%
+With regular wires, you don't have
+ 
+
+ align:start position:0%
+With regular wires, you don't have
+corners. Good. But when you're doing
+
+ align:start position:0%
+corners. Good. But when you're doing
+ 
+
+ align:start position:0%
+corners. Good. But when you're doing
+this shift, you have sort of corner.
+
+ align:start position:0%
+this shift, you have sort of corner.
+ 
+
+ align:start position:0%
+this shift, you have sort of corner.
+Same thing with the turn gadget that we
+
+ align:start position:0%
+Same thing with the turn gadget that we
+ 
+
+ align:start position:0%
+Same thing with the turn gadget that we
+already saw. Okay. Uh I think not is
+
+ align:start position:0%
+already saw. Okay. Uh I think not is
+ 
+
+ align:start position:0%
+already saw. Okay. Uh I think not is
+also pretty intelligible, but it's
+
+ align:start position:0%
+also pretty intelligible, but it's
+ 
+
+ align:start position:0%
+also pretty intelligible, but it's
+fairly complicated. It essentially
+
+ align:start position:0%
+fairly complicated. It essentially
+ 
+
+ align:start position:0%
+fairly complicated. It essentially
+involves making another copy of the
+
+ align:start position:0%
+involves making another copy of the
+ 
+
+ align:start position:0%
+involves making another copy of the
+signal just so we get an equal number of
+
+ align:start position:0%
+signal just so we get an equal number of
+ 
+
+ align:start position:0%
+signal just so we get an equal number of
+X's and X bars because we saw in the in
+
+ align:start position:0%
+X's and X bars because we saw in the in
+ 
+
+ align:start position:0%
+X's and X bars because we saw in the in
+the previous reduction with the notgate
+
+ align:start position:0%
+the previous reduction with the notgate
+ 
+
+ align:start position:0%
+the previous reduction with the notgate
+we had this one isolated guy that would
+
+ align:start position:0%
+we had this one isolated guy that would
+ 
+
+ align:start position:0%
+we had this one isolated guy that would
+be like this one and so if you just have
+
+ align:start position:0%
+be like this one and so if you just have
+ 
+
+ align:start position:0%
+be like this one and so if you just have
+this picture uh yeah it would negate
+
+ align:start position:0%
+this picture uh yeah it would negate
+ 
+
+ align:start position:0%
+this picture uh yeah it would negate
+things and and again this is designed to
+
+ align:start position:0%
+things and and again this is designed to
+ 
+
+ align:start position:0%
+things and and again this is designed to
+be mod 3. So there's three six this is
+
+ align:start position:0%
+be mod 3. So there's three six this is
+ 
+
+ align:start position:0%
+be mod 3. So there's three six this is
+hard to do 9 12 15. Okay. So things are
+
+ align:start position:0%
+hard to do 9 12 15. Okay. So things are
+ 
+
+ align:start position:0%
+hard to do 9 12 15. Okay. So things are
+nicely aligned on the mod 3 boundary but
+
+ align:start position:0%
+nicely aligned on the mod 3 boundary but
+ 
+
+ align:start position:0%
+nicely aligned on the mod 3 boundary but
+they end up with these three dudes. Uh
+
+ align:start position:0%
+they end up with these three dudes. Uh
+ 
+
+ align:start position:0%
+they end up with these three dudes. Uh
+they end up flipping the signal. Here's
+
+ align:start position:0%
+they end up flipping the signal. Here's
+ 
+
+ align:start position:0%
+they end up flipping the signal. Here's
+X. Here it's also X which is like the
+
+ align:start position:0%
+X. Here it's also X which is like the
+ 
+
+ align:start position:0%
+X. Here it's also X which is like the
+reverse because it's on the left. Uh
+
+ align:start position:0%
+reverse because it's on the left. Uh
+ 
+
+ align:start position:0%
+reverse because it's on the left. Uh
+but this would have an unequal number of
+
+ align:start position:0%
+but this would have an unequal number of
+ 
+
+ align:start position:0%
+but this would have an unequal number of
+X's and X bars. There's too many X's in
+
+ align:start position:0%
+X's and X bars. There's too many X's in
+ 
+
+ align:start position:0%
+X's and X bars. There's too many X's in
+this row. So uh we end up splitting off
+
+ align:start position:0%
+this row. So uh we end up splitting off
+ 
+
+ align:start position:0%
+this row. So uh we end up splitting off
+a negated copy here basically to balance
+
+ align:start position:0%
+a negated copy here basically to balance
+ 
+
+ align:start position:0%
+a negated copy here basically to balance
+things out. And now if you count all the
+
+ align:start position:0%
+things out. And now if you count all the
+ 
+
+ align:start position:0%
+things out. And now if you count all the
+x's and x bars they should be equal.
+
+ align:start position:0%
+x's and x bars they should be equal.
+ 
+
+ align:start position:0%
+x's and x bars they should be equal.
+Cool. Uh and then they build an orgate.
+
+ align:start position:0%
+Cool. Uh and then they build an orgate.
+ 
+
+ align:start position:0%
+Cool. Uh and then they build an orgate.
+So uh it's again looks fairly
+
+ align:start position:0%
+So uh it's again looks fairly
+ 
+
+ align:start position:0%
+So uh it's again looks fairly
+complicated probably pretty simple in
+
+ align:start position:0%
+complicated probably pretty simple in
+ 
+
+ align:start position:0%
+complicated probably pretty simple in
+essence but I don't feel like checking
+
+ align:start position:0%
+essence but I don't feel like checking
+ 
+
+ align:start position:0%
+essence but I don't feel like checking
+all those cases. Uh what is annoying is
+
+ align:start position:0%
+all those cases. Uh what is annoying is
+ 
+
+ align:start position:0%
+all those cases. Uh what is annoying is
+that this thing is not mod 3 aligned.
+
+ align:start position:0%
+that this thing is not mod 3 aligned.
+ 
+
+ align:start position:0%
+that this thing is not mod 3 aligned.
+Mod 3 aligned would be here or here with
+
+ align:start position:0%
+Mod 3 aligned would be here or here with
+ 
+
+ align:start position:0%
+Mod 3 aligned would be here or here with
+the output always in the middle finger.
+
+ align:start position:0%
+the output always in the middle finger.
+ 
+
+ align:start position:0%
+the output always in the middle finger.
+But instead it's here. And so they use
+
+ align:start position:0%
+But instead it's here. And so they use
+ 
+
+ align:start position:0%
+But instead it's here. And so they use
+the shift gadget over here to offset
+
+ align:start position:0%
+the shift gadget over here to offset
+ 
+
+ align:start position:0%
+the shift gadget over here to offset
+that by one. And similarly in all three
+
+ align:start position:0%
+that by one. And similarly in all three
+ 
+
+ align:start position:0%
+that by one. And similarly in all three
+pictures. Okay. And then you get an
+
+ align:start position:0%
+pictures. Okay. And then you get an
+ 
+
+ align:start position:0%
+pictures. Okay. And then you get an
+orgate with proper alignment. Everything
+
+ align:start position:0%
+orgate with proper alignment. Everything
+ 
+
+ align:start position:0%
+orgate with proper alignment. Everything
+works out mod 3.
+
+ align:start position:0%
+works out mod 3.
+ 
+
+ align:start position:0%
+works out mod 3.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Cool. Uh so we have not and we have or
+
+ align:start position:0%
+Cool. Uh so we have not and we have or
+ 
+
+ align:start position:0%
+Cool. Uh so we have not and we have or
+therefore we have nor and therefore we
+
+ align:start position:0%
+therefore we have nor and therefore we
+ 
+
+ align:start position:0%
+therefore we have nor and therefore we
+can build any uh logical gate we want.
+
+ align:start position:0%
+can build any uh logical gate we want.
+ 
+
+ align:start position:0%
+can build any uh logical gate we want.
+Uh, and so we have turns,
+
+ align:start position:0%
+Uh, and so we have turns,
+ 
+
+ align:start position:0%
+Uh, and so we have turns,
+we have shifts that we need, we have
+
+ align:start position:0%
+we have shifts that we need, we have
+ 
+
+ align:start position:0%
+we have shifts that we need, we have
+not, we have, do we do split? I think we
+
+ align:start position:0%
+not, we have, do we do split? I think we
+ 
+
+ align:start position:0%
+not, we have, do we do split? I think we
+did split on the previous. No, we didn't
+
+ align:start position:0%
+did split on the previous. No, we didn't
+ 
+
+ align:start position:0%
+did split on the previous. No, we didn't
+do split. Okay, then let's do split. Uh,
+
+ align:start position:0%
+do split. Okay, then let's do split. Uh,
+ 
+
+ align:start position:0%
+do split. Okay, then let's do split. Uh,
+so we need to copy our wires. Uh, this
+
+ align:start position:0%
+so we need to copy our wires. Uh, this
+ 
+
+ align:start position:0%
+so we need to copy our wires. Uh, this
+is a more complicated version of the
+
+ align:start position:0%
+is a more complicated version of the
+ 
+
+ align:start position:0%
+is a more complicated version of the
+previous split again with some extra
+
+ align:start position:0%
+previous split again with some extra
+ 
+
+ align:start position:0%
+previous split again with some extra
+things thrown in. Like this is not
+
+ align:start position:0%
+things thrown in. Like this is not
+ 
+
+ align:start position:0%
+things thrown in. Like this is not
+needed. You don't have to put this here,
+
+ align:start position:0%
+needed. You don't have to put this here,
+ 
+
+ align:start position:0%
+needed. You don't have to put this here,
+but it adds an extra XAR. So uh there's
+
+ align:start position:0%
+but it adds an extra XAR. So uh there's
+ 
+
+ align:start position:0%
+but it adds an extra XAR. So uh there's
+actually two of those things and so
+
+ align:start position:0%
+actually two of those things and so
+ 
+
+ align:start position:0%
+actually two of those things and so
+together that offsets all the extra x
+
+ align:start position:0%
+together that offsets all the extra x
+ 
+
+ align:start position:0%
+together that offsets all the extra x
+copies that are on the inside and so
+
+ align:start position:0%
+copies that are on the inside and so
+ 
+
+ align:start position:0%
+copies that are on the inside and so
+that forces uh again equal number of
+
+ align:start position:0%
+that forces uh again equal number of
+ 
+
+ align:start position:0%
+that forces uh again equal number of
+bombs whether it's x or xar chosen.
+
+ align:start position:0%
+bombs whether it's x or xar chosen.
+ 
+
+ align:start position:0%
+bombs whether it's x or xar chosen.
+So uh we can just count how many bombs
+
+ align:start position:0%
+So uh we can just count how many bombs
+ 
+
+ align:start position:0%
+So uh we can just count how many bombs
+are needed in this picture. Uh cool. Uh
+
+ align:start position:0%
+are needed in this picture. Uh cool. Uh
+ 
+
+ align:start position:0%
+are needed in this picture. Uh cool. Uh
+this is again a symmetric version. So if
+
+ align:start position:0%
+this is again a symmetric version. So if
+ 
+
+ align:start position:0%
+this is again a symmetric version. So if
+you're thinking of of let's say this as
+
+ align:start position:0%
+you're thinking of of let's say this as
+ 
+
+ align:start position:0%
+you're thinking of of let's say this as
+the input and these two as the output uh
+
+ align:start position:0%
+the input and these two as the output uh
+ 
+
+ align:start position:0%
+the input and these two as the output uh
+then negation happened. So if you don't
+
+ align:start position:0%
+then negation happened. So if you don't
+ 
+
+ align:start position:0%
+then negation happened. So if you don't
+want negation to happen just put a big
+
+ align:start position:0%
+want negation to happen just put a big
+ 
+
+ align:start position:0%
+want negation to happen just put a big
+not gate there.
+
+ align:start position:0%
+not gate there.
+ 
+
+ align:start position:0%
+not gate there.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And uh in this case they give a
+
+ align:start position:0%
+And uh in this case they give a
+ 
+
+ align:start position:0%
+And uh in this case they give a
+crossover gadget uh in particular
+
+ align:start position:0%
+crossover gadget uh in particular
+ 
+
+ align:start position:0%
+crossover gadget uh in particular
+because it's not that hard to give a
+
+ align:start position:0%
+because it's not that hard to give a
+ 
+
+ align:start position:0%
+because it's not that hard to give a
+crossover gadget but uh it's also not
+
+ align:start position:0%
+crossover gadget but uh it's also not
+ 
+
+ align:start position:0%
+crossover gadget but uh it's also not
+necessary. So you could do crossover
+
+ align:start position:0%
+necessary. So you could do crossover
+ 
+
+ align:start position:0%
+necessary. So you could do crossover
+explicitly but in fact uh I just looked
+
+ align:start position:0%
+explicitly but in fact uh I just looked
+ 
+
+ align:start position:0%
+explicitly but in fact uh I just looked
+on Wikipedia earlier today uh how do you
+
+ align:start position:0%
+on Wikipedia earlier today uh how do you
+ 
+
+ align:start position:0%
+on Wikipedia earlier today uh how do you
+build we already know that planer
+
+ align:start position:0%
+build we already know that planer
+ 
+
+ align:start position:0%
+build we already know that planer
+circuit sat with NAND gates is hard so
+
+ align:start position:0%
+circuit sat with NAND gates is hard so
+ 
+
+ align:start position:0%
+circuit sat with NAND gates is hard so
+can we build NAND and so I looked up in
+
+ align:start position:0%
+can we build NAND and so I looked up in
+ 
+
+ align:start position:0%
+can we build NAND and so I looked up in
+Wikipedia how do you build NAND out of
+
+ align:start position:0%
+Wikipedia how do you build NAND out of
+ 
+
+ align:start position:0%
+Wikipedia how do you build NAND out of
+NORS and the answer is this and that's
+
+ align:start position:0%
+NORS and the answer is this and that's
+ 
+
+ align:start position:0%
+NORS and the answer is this and that's
+planer so we're done so you take this
+
+ align:start position:0%
+planer so we're done so you take this
+ 
+
+ align:start position:0%
+planer so we're done so you take this
+picture you plug it into each of these
+
+ align:start position:0%
+picture you plug it into each of these
+ 
+
+ align:start position:0%
+picture you plug it into each of these
+guys and you take that picture you plug
+
+ align:start position:0%
+guys and you take that picture you plug
+ 
+
+ align:start position:0%
+guys and you take that picture you plug
+it into each of these guys make sure it
+
+ align:start position:0%
+it into each of these guys make sure it
+ 
+
+ align:start position:0%
+it into each of these guys make sure it
+preserves plainerity all the way
+
+ align:start position:0%
+preserves plainerity all the way
+ 
+
+ align:start position:0%
+preserves plainerity all the way
+through. It does. And then from uh I
+
+ align:start position:0%
+through. It does. And then from uh I
+ 
+
+ align:start position:0%
+through. It does. And then from uh I
+should know that's how you construct
+
+ align:start position:0%
+should know that's how you construct
+ 
+
+ align:start position:0%
+should know that's how you construct
+NAND out of NOR. It's exactly from de
+
+ align:start position:0%
+NAND out of NOR. It's exactly from de
+ 
+
+ align:start position:0%
+NAND out of NOR. It's exactly from de
+Morgan's law. Uh because this is just
+
+ align:start position:0%
+Morgan's law. Uh because this is just
+ 
+
+ align:start position:0%
+Morgan's law. Uh because this is just
+negation. So cool thing is all these
+
+ align:start position:0%
+negation. So cool thing is all these
+ 
+
+ align:start position:0%
+negation. So cool thing is all these
+constructions preserve plarity which
+
+ align:start position:0%
+constructions preserve plarity which
+ 
+
+ align:start position:0%
+constructions preserve plarity which
+means we can add to our definition of
+
+ align:start position:0%
+means we can add to our definition of
+ 
+
+ align:start position:0%
+means we can add to our definition of
+planer circuit set. uh all gates are
+
+ align:start position:0%
+planer circuit set. uh all gates are
+ 
+
+ align:start position:0%
+planer circuit set. uh all gates are
+NAND
+
+ align:start position:0%
+NAND
+ 
+
+ align:start position:0%
+NAND
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or all gates are NOR.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is nice because when you're solving
+
+ align:start position:0%
+This is nice because when you're solving
+ 
+
+ align:start position:0%
+This is nice because when you're solving
+next P set or whatever uh you can uh
+
+ align:start position:0%
+next P set or whatever uh you can uh
+ 
+
+ align:start position:0%
+next P set or whatever uh you can uh
+just take planer circuits and if you
+
+ align:start position:0%
+just take planer circuits and if you
+ 
+
+ align:start position:0%
+just take planer circuits and if you
+happen to construct an ANDgate you're
+
+ align:start position:0%
+happen to construct an ANDgate you're
+ 
+
+ align:start position:0%
+happen to construct an ANDgate you're
+done. If you happen to construct a
+
+ align:start position:0%
+done. If you happen to construct a
+ 
+
+ align:start position:0%
+done. If you happen to construct a
+norate you're done no crossover needed.
+
+ align:start position:0%
+norate you're done no crossover needed.
+ 
+
+ align:start position:0%
+norate you're done no crossover needed.
+You'll still need turns and maybe a
+
+ align:start position:0%
+You'll still need turns and maybe a
+ 
+
+ align:start position:0%
+You'll still need turns and maybe a
+shift and maybe a terminator. Uh you
+
+ align:start position:0%
+shift and maybe a terminator. Uh you
+ 
+
+ align:start position:0%
+shift and maybe a terminator. Uh you
+won't need not if you build NAND or nor
+
+ align:start position:0%
+won't need not if you build NAND or nor
+ 
+
+ align:start position:0%
+won't need not if you build NAND or nor
+uh you'll need a split, but you don't
+
+ align:start position:0%
+uh you'll need a split, but you don't
+ 
+
+ align:start position:0%
+uh you'll need a split, but you don't
+need a crossover anymore. This is cool
+
+ align:start position:0%
+need a crossover anymore. This is cool
+ 
+
+ align:start position:0%
+need a crossover anymore. This is cool
+as far as I know a new result, but I
+
+ align:start position:0%
+as far as I know a new result, but I
+ 
+
+ align:start position:0%
+as far as I know a new result, but I
+mean obviously implicit in all of these
+
+ align:start position:0%
+mean obviously implicit in all of these
+ 
+
+ align:start position:0%
+mean obviously implicit in all of these
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Uh yeah.
+
+ align:start position:0%
+Uh yeah.
+ 
+
+ align:start position:0%
+Uh yeah.
+Do you know if there's any um sub
+
+ align:start position:0%
+Do you know if there's any um sub
+ 
+
+ align:start position:0%
+Do you know if there's any um sub
+problem I guess of SAT where you don't
+
+ align:start position:0%
+problem I guess of SAT where you don't
+ 
+
+ align:start position:0%
+problem I guess of SAT where you don't
+have universal gates and you can't be
+
+ align:start position:0%
+have universal gates and you can't be
+ 
+
+ align:start position:0%
+have universal gates and you can't be
+planer and yet it's still hard.
+
+ align:start position:0%
+planer and yet it's still hard.
+ 
+
+ align:start position:0%
+planer and yet it's still hard.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+so maybe you can you can
+
+ align:start position:0%
+so maybe you can you can
+ 
+
+ align:start position:0%
+so maybe you can you can
+oh interesting
+
+ align:start position:0%
+oh interesting
+ 
+
+ align:start position:0%
+oh interesting
+you can split wires and you have a
+
+ align:start position:0%
+you can split wires and you have a
+ 
+
+ align:start position:0%
+you can split wires and you have a
+variable that has you know the negation
+
+ align:start position:0%
+variable that has you know the negation
+ 
+
+ align:start position:0%
+variable that has you know the negation
+of it coming out but that's all you can
+
+ align:start position:0%
+of it coming out but that's all you can
+ 
+
+ align:start position:0%
+of it coming out but that's all you can
+do no other gates.
+
+ align:start position:0%
+do no other gates.
+ 
+
+ align:start position:0%
+do no other gates.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+my guess is that all such problems are
+
+ align:start position:0%
+my guess is that all such problems are
+ 
+
+ align:start position:0%
+my guess is that all such problems are
+polomally solvable but maybe that's
+
+ align:start position:0%
+polomally solvable but maybe that's
+ 
+
+ align:start position:0%
+polomally solvable but maybe that's
+something we could think about. Um
+
+ align:start position:0%
+something we could think about. Um
+ 
+
+ align:start position:0%
+something we could think about. Um
+certainly plausible that you don't need
+
+ align:start position:0%
+certainly plausible that you don't need
+ 
+
+ align:start position:0%
+certainly plausible that you don't need
+to be able to construct all boolean
+
+ align:start position:0%
+to be able to construct all boolean
+ 
+
+ align:start position:0%
+to be able to construct all boolean
+formulas in order to be hard but my
+
+ align:start position:0%
+formulas in order to be hard but my
+ 
+
+ align:start position:0%
+formulas in order to be hard but my
+vague sense slash experience playing
+
+ align:start position:0%
+vague sense slash experience playing
+ 
+
+ align:start position:0%
+vague sense slash experience playing
+around with uh other weird other gates
+
+ align:start position:0%
+around with uh other weird other gates
+ 
+
+ align:start position:0%
+around with uh other weird other gates
+most of them are all equivalent to
+
+ align:start position:0%
+most of them are all equivalent to
+ 
+
+ align:start position:0%
+most of them are all equivalent to
+splits if they're not universal.
+
+ align:start position:0%
+splits if they're not universal.
+ 
+
+ align:start position:0%
+splits if they're not universal.
+something like a split. Maybe with some
+
+ align:start position:0%
+something like a split. Maybe with some
+ 
+
+ align:start position:0%
+something like a split. Maybe with some
+like five operand operator, you could do
+
+ align:start position:0%
+like five operand operator, you could do
+ 
+
+ align:start position:0%
+like five operand operator, you could do
+something cool. But uh usually they
+
+ align:start position:0%
+something cool. But uh usually they
+ 
+
+ align:start position:0%
+something cool. But uh usually they
+degenerate to either split-like things
+
+ align:start position:0%
+degenerate to either split-like things
+ 
+
+ align:start position:0%
+degenerate to either split-like things
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+uh clauseike things. But if you don't
+
+ align:start position:0%
+uh clauseike things. But if you don't
+ 
+
+ align:start position:0%
+uh clauseike things. But if you don't
+have both, you don't get enough to be
+
+ align:start position:0%
+have both, you don't get enough to be
+ 
+
+ align:start position:0%
+have both, you don't get enough to be
+hard. We should prove a theorem like
+
+ align:start position:0%
+hard. We should prove a theorem like
+ 
+
+ align:start position:0%
+hard. We should prove a theorem like
+that. But I would guess that you need
+
+ align:start position:0%
+that. But I would guess that you need
+ 
+
+ align:start position:0%
+that. But I would guess that you need
+something like this. Now, these are not
+
+ align:start position:0%
+something like this. Now, these are not
+ 
+
+ align:start position:0%
+something like this. Now, these are not
+the only universal gate sets. I think in
+
+ align:start position:0%
+the only universal gate sets. I think in
+ 
+
+ align:start position:0%
+the only universal gate sets. I think in
+a moment I will have a uh I in if you
+
+ align:start position:0%
+a moment I will have a uh I in if you
+ 
+
+ align:start position:0%
+a moment I will have a uh I in if you
+are curious about more of what universal
+
+ align:start position:0%
+are curious about more of what universal
+ 
+
+ align:start position:0%
+are curious about more of what universal
+gate sets are these are usually called
+
+ align:start position:0%
+gate sets are these are usually called
+ 
+
+ align:start position:0%
+gate sets are these are usually called
+functionally complete or functional
+
+ align:start position:0%
+functionally complete or functional
+ 
+
+ align:start position:0%
+functionally complete or functional
+completeness if you look at that
+
+ align:start position:0%
+completeness if you look at that
+ 
+
+ align:start position:0%
+completeness if you look at that
+Wikipedia this is an excerpt from
+
+ align:start position:0%
+Wikipedia this is an excerpt from
+ 
+
+ align:start position:0%
+Wikipedia this is an excerpt from
+Wikipedia you see NAND andor are the
+
+ align:start position:0%
+Wikipedia you see NAND andor are the
+ 
+
+ align:start position:0%
+Wikipedia you see NAND andor are the
+only among uh two operators so you have
+
+ align:start position:0%
+only among uh two operators so you have
+ 
+
+ align:start position:0%
+only among uh two operators so you have
+two inputs one output um NAND andor the
+
+ align:start position:0%
+two inputs one output um NAND andor the
+ 
+
+ align:start position:0%
+two inputs one output um NAND andor the
+only things that by themselves are
+
+ align:start position:0%
+only things that by themselves are
+ 
+
+ align:start position:0%
+only things that by themselves are
+universal but once you allow two
+
+ align:start position:0%
+universal but once you allow two
+ 
+
+ align:start position:0%
+universal but once you allow two
+different gates you can do other things
+
+ align:start position:0%
+different gates you can do other things
+ 
+
+ align:start position:0%
+different gates you can do other things
+so uh these are particularly
+
+ align:start position:0%
+so uh these are particularly
+ 
+
+ align:start position:0%
+so uh these are particularly
+interesting. This is false, I think. Uh
+
+ align:start position:0%
+interesting. This is false, I think. Uh
+ 
+
+ align:start position:0%
+interesting. This is false, I think. Uh
+it's called bot and this is and this is
+
+ align:start position:0%
+it's called bot and this is and this is
+ 
+
+ align:start position:0%
+it's called bot and this is and this is
+called top. That's true. Um and so uh
+
+ align:start position:0%
+called top. That's true. Um and so uh
+ 
+
+ align:start position:0%
+called top. That's true. Um and so uh
+these are slightly unusual ways for me
+
+ align:start position:0%
+these are slightly unusual ways for me
+ 
+
+ align:start position:0%
+these are slightly unusual ways for me
+to think about writing them. Here we
+
+ align:start position:0%
+to think about writing them. Here we
+ 
+
+ align:start position:0%
+to think about writing them. Here we
+have of course and and not. Um but this
+
+ align:start position:0%
+have of course and and not. Um but this
+ 
+
+ align:start position:0%
+have of course and and not. Um but this
+is this is right implication uh which is
+
+ align:start position:0%
+is this is right implication uh which is
+ 
+
+ align:start position:0%
+is this is right implication uh which is
+like not the left thing or the right
+
+ align:start position:0%
+like not the left thing or the right
+ 
+
+ align:start position:0%
+like not the left thing or the right
+thing. We talked about that in the past.
+
+ align:start position:0%
+thing. We talked about that in the past.
+ 
+
+ align:start position:0%
+thing. We talked about that in the past.
+That by itself is not enough because you
+
+ align:start position:0%
+That by itself is not enough because you
+ 
+
+ align:start position:0%
+That by itself is not enough because you
+can just follow implication change. But
+
+ align:start position:0%
+can just follow implication change. But
+ 
+
+ align:start position:0%
+can just follow implication change. But
+if you also have false that is universal
+
+ align:start position:0%
+if you also have false that is universal
+ 
+
+ align:start position:0%
+if you also have false that is universal
+that's kind of funny. Uh and this is
+
+ align:start position:0%
+that's kind of funny. Uh and this is
+ 
+
+ align:start position:0%
+that's kind of funny. Uh and this is
+exor. I think exor is the same as saying
+
+ align:start position:0%
+exor. I think exor is the same as saying
+ 
+
+ align:start position:0%
+exor. I think exor is the same as saying
+that the two things are different. Um
+
+ align:start position:0%
+that the two things are different. Um
+ 
+
+ align:start position:0%
+that the two things are different. Um
+and this is xnor. So those by themselves
+
+ align:start position:0%
+and this is xnor. So those by themselves
+ 
+
+ align:start position:0%
+and this is xnor. So those by themselves
+are not universal. But if you have some
+
+ align:start position:0%
+are not universal. But if you have some
+ 
+
+ align:start position:0%
+are not universal. But if you have some
+other kind of one-way implication then
+
+ align:start position:0%
+other kind of one-way implication then
+ 
+
+ align:start position:0%
+other kind of one-way implication then
+uh that gives you any logical formulas.
+
+ align:start position:0%
+uh that gives you any logical formulas.
+ 
+
+ align:start position:0%
+uh that gives you any logical formulas.
+Now whether these in the planer version
+
+ align:start position:0%
+Now whether these in the planer version
+ 
+
+ align:start position:0%
+Now whether these in the planer version
+are hard I don't know. But I know that
+
+ align:start position:0%
+are hard I don't know. But I know that
+ 
+
+ align:start position:0%
+are hard I don't know. But I know that
+these in the planer version are hard.
+
+ align:start position:0%
+these in the planer version are hard.
+ 
+
+ align:start position:0%
+these in the planer version are hard.
+Okay, back to mind sweeper. Uh they drew
+
+ align:start position:0%
+Okay, back to mind sweeper. Uh they drew
+ 
+
+ align:start position:0%
+Okay, back to mind sweeper. Uh they drew
+a picture of how everything fits
+
+ align:start position:0%
+a picture of how everything fits
+ 
+
+ align:start position:0%
+a picture of how everything fits
+together. So it's maybe nice to have the
+
+ align:start position:0%
+together. So it's maybe nice to have the
+ 
+
+ align:start position:0%
+together. So it's maybe nice to have the
+big picture. Uh but let's in particular
+
+ align:start position:0%
+big picture. Uh but let's in particular
+ 
+
+ align:start position:0%
+big picture. Uh but let's in particular
+think about what the decision question
+
+ align:start position:0%
+think about what the decision question
+ 
+
+ align:start position:0%
+think about what the decision question
+is and make sure what I mean I claim
+
+ align:start position:0%
+is and make sure what I mean I claim
+ 
+
+ align:start position:0%
+is and make sure what I mean I claim
+this is coenp and that we're doing
+
+ align:start position:0%
+this is coenp and that we're doing
+ 
+
+ align:start position:0%
+this is coenp and that we're doing
+unsat, but we should actually check
+
+ align:start position:0%
+unsat, but we should actually check
+ 
+
+ align:start position:0%
+unsat, but we should actually check
+that. At this point, we've just
+
+ align:start position:0%
+that. At this point, we've just
+ 
+
+ align:start position:0%
+that. At this point, we've just
+simulated a circuit. We haven't thought
+
+ align:start position:0%
+simulated a circuit. We haven't thought
+ 
+
+ align:start position:0%
+simulated a circuit. We haven't thought
+about what we're trying to solve
+
+ align:start position:0%
+about what we're trying to solve
+ 
+
+ align:start position:0%
+about what we're trying to solve
+overall. Now we want to know whether we
+
+ align:start position:0%
+overall. Now we want to know whether we
+ 
+
+ align:start position:0%
+overall. Now we want to know whether we
+can derive everything.
+
+ align:start position:0%
+can derive everything.
+ 
+
+ align:start position:0%
+can derive everything.
+So we compute our formula and then the
+
+ align:start position:0%
+So we compute our formula and then the
+ 
+
+ align:start position:0%
+So we compute our formula and then the
+output is here and at this point there's
+
+ align:start position:0%
+output is here and at this point there's
+ 
+
+ align:start position:0%
+output is here and at this point there's
+just a terminal there saying I don't
+
+ align:start position:0%
+just a terminal there saying I don't
+ 
+
+ align:start position:0%
+just a terminal there saying I don't
+know what it is
+
+ align:start position:0%
+know what it is
+ 
+
+ align:start position:0%
+know what it is
+different from the previous proof right
+
+ align:start position:0%
+different from the previous proof right
+ 
+
+ align:start position:0%
+different from the previous proof right
+the previous proof said uh that should
+
+ align:start position:0%
+the previous proof said uh that should
+ 
+
+ align:start position:0%
+the previous proof said uh that should
+be one at the end and then you have to
+
+ align:start position:0%
+be one at the end and then you have to
+ 
+
+ align:start position:0%
+be one at the end and then you have to
+figure out how to fill in the things now
+
+ align:start position:0%
+figure out how to fill in the things now
+ 
+
+ align:start position:0%
+figure out how to fill in the things now
+we're saying I don't know what's there
+
+ align:start position:0%
+we're saying I don't know what's there
+ 
+
+ align:start position:0%
+we're saying I don't know what's there
+can you figure out what's there and if
+
+ align:start position:0%
+can you figure out what's there and if
+ 
+
+ align:start position:0%
+can you figure out what's there and if
+it's the case that no matter how you set
+
+ align:start position:0%
+it's the case that no matter how you set
+ 
+
+ align:start position:0%
+it's the case that no matter how you set
+the variables you always get false
+
+ align:start position:0%
+the variables you always get false
+ 
+
+ align:start position:0%
+the variables you always get false
+then you know uh what this wire looks
+
+ align:start position:0%
+then you know uh what this wire looks
+ 
+
+ align:start position:0%
+then you know uh what this wire looks
+like, you know that it's false. And in
+
+ align:start position:0%
+like, you know that it's false. And in
+ 
+
+ align:start position:0%
+like, you know that it's false. And in
+fact, you can figure out everything. If
+
+ align:start position:0%
+fact, you can figure out everything. If
+ 
+
+ align:start position:0%
+fact, you can figure out everything. If
+you know what all the x i are, you can
+
+ align:start position:0%
+you know what all the x i are, you can
+ 
+
+ align:start position:0%
+you know what all the x i are, you can
+just run through the circuit. Uh so you
+
+ align:start position:0%
+just run through the circuit. Uh so you
+ 
+
+ align:start position:0%
+just run through the circuit. Uh so you
+can figure out the entire diagram. But
+
+ align:start position:0%
+can figure out the entire diagram. But
+ 
+
+ align:start position:0%
+can figure out the entire diagram. But
+in general, just asking the question,
+
+ align:start position:0%
+in general, just asking the question,
+ 
+
+ align:start position:0%
+in general, just asking the question,
+can I figure out this square? Is there a
+
+ align:start position:0%
+can I figure out this square? Is there a
+ 
+
+ align:start position:0%
+can I figure out this square? Is there a
+bomb or not? In order for there not to
+
+ align:start position:0%
+bomb or not? In order for there not to
+ 
+
+ align:start position:0%
+bomb or not? In order for there not to
+be a bomb, uh you would have to solve
+
+ align:start position:0%
+be a bomb, uh you would have to solve
+ 
+
+ align:start position:0%
+be a bomb, uh you would have to solve
+this problem. uh you need to determine
+
+ align:start position:0%
+this problem. uh you need to determine
+ 
+
+ align:start position:0%
+this problem. uh you need to determine
+that no matter how you set the things
+
+ align:start position:0%
+that no matter how you set the things
+ 
+
+ align:start position:0%
+that no matter how you set the things
+you end up with a zero or the adjacent
+
+ align:start position:0%
+you end up with a zero or the adjacent
+ 
+
+ align:start position:0%
+you end up with a zero or the adjacent
+position it would be the opposite. Okay.
+
+ align:start position:0%
+position it would be the opposite. Okay.
+ 
+
+ align:start position:0%
+position it would be the opposite. Okay.
+So conversely what I really care about
+
+ align:start position:0%
+So conversely what I really care about
+ 
+
+ align:start position:0%
+So conversely what I really care about
+that was the wrong direction. I want I'm
+
+ align:start position:0%
+that was the wrong direction. I want I'm
+ 
+
+ align:start position:0%
+that was the wrong direction. I want I'm
+given a circuit unsat instance. I want
+
+ align:start position:0%
+given a circuit unsat instance. I want
+ 
+
+ align:start position:0%
+given a circuit unsat instance. I want
+to turn it into a mind sweeper instance.
+
+ align:start position:0%
+to turn it into a mind sweeper instance.
+ 
+
+ align:start position:0%
+to turn it into a mind sweeper instance.
+So I do that and then the the the
+
+ align:start position:0%
+So I do that and then the the the
+ 
+
+ align:start position:0%
+So I do that and then the the the
+question is you know uh get this right.
+
+ align:start position:0%
+question is you know uh get this right.
+ 
+
+ align:start position:0%
+question is you know uh get this right.
+Can you derive whether there is a bomb
+
+ align:start position:0%
+Can you derive whether there is a bomb
+ 
+
+ align:start position:0%
+Can you derive whether there is a bomb
+in this square? Can you determine that
+
+ align:start position:0%
+in this square? Can you determine that
+ 
+
+ align:start position:0%
+in this square? Can you determine that
+there uh must be a bomb in this square
+
+ align:start position:0%
+there uh must be a bomb in this square
+ 
+
+ align:start position:0%
+there uh must be a bomb in this square
+for example? That would be a slightly
+
+ align:start position:0%
+for example? That would be a slightly
+ 
+
+ align:start position:0%
+for example? That would be a slightly
+cleaner version.
+
+ align:start position:0%
+cleaner version.
+ 
+
+ align:start position:0%
+cleaner version.
+And that will be true if and only if no
+
+ align:start position:0%
+And that will be true if and only if no
+ 
+
+ align:start position:0%
+And that will be true if and only if no
+matter what you do there's a bomb in
+
+ align:start position:0%
+matter what you do there's a bomb in
+ 
+
+ align:start position:0%
+matter what you do there's a bomb in
+that square which is like saying no
+
+ align:start position:0%
+that square which is like saying no
+ 
+
+ align:start position:0%
+that square which is like saying no
+matter what you do uh this formula comes
+
+ align:start position:0%
+matter what you do uh this formula comes
+ 
+
+ align:start position:0%
+matter what you do uh this formula comes
+out to zero. Okay. So any kind of
+
+ align:start position:0%
+out to zero. Okay. So any kind of
+ 
+
+ align:start position:0%
+out to zero. Okay. So any kind of
+inference question like that is going to
+
+ align:start position:0%
+inference question like that is going to
+ 
+
+ align:start position:0%
+inference question like that is going to
+require you uh to solve this problem
+
+ align:start position:0%
+require you uh to solve this problem
+ 
+
+ align:start position:0%
+require you uh to solve this problem
+or rather this problem can be reduced to
+
+ align:start position:0%
+or rather this problem can be reduced to
+ 
+
+ align:start position:0%
+or rather this problem can be reduced to
+any inference problem like that. Clear?
+
+ align:start position:0%
+any inference problem like that. Clear?
+ 
+
+ align:start position:0%
+any inference problem like that. Clear?
+It's easy to get backwards here. So hope
+
+ align:start position:0%
+It's easy to get backwards here. So hope
+ 
+
+ align:start position:0%
+It's easy to get backwards here. So hope
+I got it all right. Uh and that's co-enp
+
+ align:start position:0%
+I got it all right. Uh and that's co-enp
+ 
+
+ align:start position:0%
+I got it all right. Uh and that's co-enp
+completeness. Reductions look the same
+
+ align:start position:0%
+completeness. Reductions look the same
+ 
+
+ align:start position:0%
+completeness. Reductions look the same
+for co-enp uh we just start with
+
+ align:start position:0%
+for co-enp uh we just start with
+ 
+
+ align:start position:0%
+for co-enp uh we just start with
+different problems.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. So that was mind sweeper
+
+ align:start position:0%
+Cool. So that was mind sweeper
+ 
+
+ align:start position:0%
+Cool. So that was mind sweeper
+uh and functional completeness. I have
+
+ align:start position:0%
+uh and functional completeness. I have
+ 
+
+ align:start position:0%
+uh and functional completeness. I have
+one more well sort of two more proofs
+
+ align:start position:0%
+one more well sort of two more proofs
+ 
+
+ align:start position:0%
+one more well sort of two more proofs
+only one that I will talk about in
+
+ align:start position:0%
+only one that I will talk about in
+ 
+
+ align:start position:0%
+only one that I will talk about in
+detail uh for Candy Crush and soon
+
+ align:start position:0%
+detail uh for Candy Crush and soon
+ 
+
+ align:start position:0%
+detail uh for Candy Crush and soon
+enough bejeweled. Um so but let's let's
+
+ align:start position:0%
+enough bejeweled. Um so but let's let's
+ 
+
+ align:start position:0%
+enough bejeweled. Um so but let's let's
+think about Candy Crush. This is the
+
+ align:start position:0%
+think about Candy Crush. This is the
+ 
+
+ align:start position:0%
+think about Candy Crush. This is the
+modern version. I'm guessing you've all
+
+ align:start position:0%
+modern version. I'm guessing you've all
+ 
+
+ align:start position:0%
+modern version. I'm guessing you've all
+played but in case not uh please don't
+
+ align:start position:0%
+played but in case not uh please don't
+ 
+
+ align:start position:0%
+played but in case not uh please don't
+play. It's very addictive.
+
+ align:start position:0%
+play. It's very addictive.
+ 
+
+ align:start position:0%
+play. It's very addictive.
+But on the slides, we're allowed to. So,
+
+ align:start position:0%
+But on the slides, we're allowed to. So,
+ 
+
+ align:start position:0%
+But on the slides, we're allowed to. So,
+um, you have a grid of colors,
+
+ align:start position:0%
+um, you have a grid of colors,
+ 
+
+ align:start position:0%
+um, you have a grid of colors,
+colored candies, and a move in this game
+
+ align:start position:0%
+colored candies, and a move in this game
+ 
+
+ align:start position:0%
+colored candies, and a move in this game
+is to take two candies and switch their
+
+ align:start position:0%
+is to take two candies and switch their
+ 
+
+ align:start position:0%
+is to take two candies and switch their
+order. Uh, I guess in this picture, I
+
+ align:start position:0%
+order. Uh, I guess in this picture, I
+ 
+
+ align:start position:0%
+order. Uh, I guess in this picture, I
+did these two. Okay, if you switch these
+
+ align:start position:0%
+did these two. Okay, if you switch these
+ 
+
+ align:start position:0%
+did these two. Okay, if you switch these
+two, you get this picture. And whenever
+
+ align:start position:0%
+two, you get this picture. And whenever
+ 
+
+ align:start position:0%
+two, you get this picture. And whenever
+and the the mechanics of the game, the
+
+ align:start position:0%
+and the the mechanics of the game, the
+ 
+
+ align:start position:0%
+and the the mechanics of the game, the
+physics or whatever is whenever you have
+
+ align:start position:0%
+physics or whatever is whenever you have
+ 
+
+ align:start position:0%
+physics or whatever is whenever you have
+three or more candies of the same color
+
+ align:start position:0%
+three or more candies of the same color
+ 
+
+ align:start position:0%
+three or more candies of the same color
+in a row or column, right in a row, uh
+
+ align:start position:0%
+in a row or column, right in a row, uh
+ 
+
+ align:start position:0%
+in a row or column, right in a row, uh
+then they disappear and anything above
+
+ align:start position:0%
+then they disappear and anything above
+ 
+
+ align:start position:0%
+then they disappear and anything above
+them falls. So like this red candy ends
+
+ align:start position:0%
+them falls. So like this red candy ends
+ 
+
+ align:start position:0%
+them falls. So like this red candy ends
+up there. In this case, there were no
+
+ align:start position:0%
+up there. In this case, there were no
+ 
+
+ align:start position:0%
+up there. In this case, there were no
+more candies above in the real game.
+
+ align:start position:0%
+more candies above in the real game.
+ 
+
+ align:start position:0%
+more candies above in the real game.
+Usually there's always more candies
+
+ align:start position:0%
+Usually there's always more candies
+ 
+
+ align:start position:0%
+Usually there's always more candies
+above. But if we're in a small game, uh
+
+ align:start position:0%
+above. But if we're in a small game, uh
+ 
+
+ align:start position:0%
+above. But if we're in a small game, uh
+this will if we're in a big game and
+
+ align:start position:0%
+this will if we're in a big game and
+ 
+
+ align:start position:0%
+this will if we're in a big game and
+looking at a small window, uh we know
+
+ align:start position:0%
+looking at a small window, uh we know
+ 
+
+ align:start position:0%
+looking at a small window, uh we know
+everything about what will fall. Do you
+
+ align:start position:0%
+everything about what will fall. Do you
+ 
+
+ align:start position:0%
+everything about what will fall. Do you
+need to move make them fall or do they
+
+ align:start position:0%
+need to move make them fall or do they
+ 
+
+ align:start position:0%
+need to move make them fall or do they
+automatically fall once you get
+
+ align:start position:0%
+automatically fall once you get
+ 
+
+ align:start position:0%
+automatically fall once you get
+they automatically fall? Yeah. So they
+
+ align:start position:0%
+they automatically fall? Yeah. So they
+ 
+
+ align:start position:0%
+they automatically fall? Yeah. So they
+they're forced to fall.
+
+ align:start position:0%
+they're forced to fall.
+ 
+
+ align:start position:0%
+they're forced to fall.
+Uh it's all I get to do is make this
+
+ align:start position:0%
+Uh it's all I get to do is make this
+ 
+
+ align:start position:0%
+Uh it's all I get to do is make this
+move and then stuff happens. So I make
+
+ align:start position:0%
+move and then stuff happens. So I make
+ 
+
+ align:start position:0%
+move and then stuff happens. So I make
+this move and then anything that uh any
+
+ align:start position:0%
+this move and then anything that uh any
+ 
+
+ align:start position:0%
+this move and then anything that uh any
+three in a rows or more disappear and
+
+ align:start position:0%
+three in a rows or more disappear and
+ 
+
+ align:start position:0%
+three in a rows or more disappear and
+then if that makes more three in a rows
+
+ align:start position:0%
+then if that makes more three in a rows
+ 
+
+ align:start position:0%
+then if that makes more three in a rows
+they will disappear and so on and I'm my
+
+ align:start position:0%
+they will disappear and so on and I'm my
+ 
+
+ align:start position:0%
+they will disappear and so on and I'm my
+hands are off at that point. Once that's
+
+ align:start position:0%
+hands are off at that point. Once that's
+ 
+
+ align:start position:0%
+hands are off at that point. Once that's
+once the chain reactions are finished.
+
+ align:start position:0%
+once the chain reactions are finished.
+ 
+
+ align:start position:0%
+once the chain reactions are finished.
+Not all games work this way but Candy
+
+ align:start position:0%
+Not all games work this way but Candy
+ 
+
+ align:start position:0%
+Not all games work this way but Candy
+Crush happens to work this way. Once
+
+ align:start position:0%
+Crush happens to work this way. Once
+ 
+
+ align:start position:0%
+Crush happens to work this way. Once
+these things are finished, then I can do
+
+ align:start position:0%
+these things are finished, then I can do
+ 
+
+ align:start position:0%
+these things are finished, then I can do
+another exchange. And when I do an
+
+ align:start position:0%
+another exchange. And when I do an
+ 
+
+ align:start position:0%
+another exchange. And when I do an
+exchange, I must make three in a row. I
+
+ align:start position:0%
+exchange, I must make three in a row. I
+ 
+
+ align:start position:0%
+exchange, I must make three in a row. I
+can't just swap these two guys because
+
+ align:start position:0%
+can't just swap these two guys because
+ 
+
+ align:start position:0%
+can't just swap these two guys because
+uh it's not interesting.
+
+ align:start position:0%
+uh it's not interesting.
+ 
+
+ align:start position:0%
+uh it's not interesting.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+What if it's like a T pattern or like
+
+ align:start position:0%
+What if it's like a T pattern or like
+ 
+
+ align:start position:0%
+What if it's like a T pattern or like
+nonlinear?
+
+ align:start position:0%
+nonlinear?
+ 
+
+ align:start position:0%
+nonlinear?
+Uh in this uh T Yeah. Okay. In this
+
+ align:start position:0%
+Uh in this uh T Yeah. Okay. In this
+ 
+
+ align:start position:0%
+Uh in this uh T Yeah. Okay. In this
+picture, we'll never have T's. It'll
+
+ align:start position:0%
+picture, we'll never have T's. It'll
+ 
+
+ align:start position:0%
+picture, we'll never have T's. It'll
+always be three in a row. We'll never
+
+ align:start position:0%
+always be three in a row. We'll never
+ 
+
+ align:start position:0%
+always be three in a row. We'll never
+have four in a row. With four in a row,
+
+ align:start position:0%
+have four in a row. With four in a row,
+ 
+
+ align:start position:0%
+have four in a row. With four in a row,
+magical striped candies happen, and you
+
+ align:start position:0%
+magical striped candies happen, and you
+ 
+
+ align:start position:0%
+magical striped candies happen, and you
+don't want to know.
+
+ align:start position:0%
+don't want to know.
+ 
+
+ align:start position:0%
+don't want to know.
+So, uh, potentially you could get up to
+
+ align:start position:0%
+So, uh, potentially you could get up to
+ 
+
+ align:start position:0%
+So, uh, potentially you could get up to
+five in a row with these rules, but that
+
+ align:start position:0%
+five in a row with these rules, but that
+ 
+
+ align:start position:0%
+five in a row with these rules, but that
+that that in these reductions that won't
+
+ align:start position:0%
+that that in these reductions that won't
+ 
+
+ align:start position:0%
+that that in these reductions that won't
+happen. So, we don't care what the rules
+
+ align:start position:0%
+happen. So, we don't care what the rules
+ 
+
+ align:start position:0%
+happen. So, we don't care what the rules
+say there. Um, we're only going to get
+
+ align:start position:0%
+say there. Um, we're only going to get
+ 
+
+ align:start position:0%
+say there. Um, we're only going to get
+three in a rows. There is a weird catch
+
+ align:start position:0%
+three in a rows. There is a weird catch
+ 
+
+ align:start position:0%
+three in a rows. There is a weird catch
+in this proof. These I'm going to cover
+
+ align:start position:0%
+in this proof. These I'm going to cover
+ 
+
+ align:start position:0%
+in this proof. These I'm going to cover
+two mentioned two proofs from 2014. So,
+
+ align:start position:0%
+two mentioned two proofs from 2014. So,
+ 
+
+ align:start position:0%
+two mentioned two proofs from 2014. So,
+all very recent. I guess the game isn't
+
+ align:start position:0%
+all very recent. I guess the game isn't
+ 
+
+ align:start position:0%
+all very recent. I guess the game isn't
+that old. Um, and in this proof, we're
+
+ align:start position:0%
+that old. Um, and in this proof, we're
+ 
+
+ align:start position:0%
+that old. Um, and in this proof, we're
+going to assume if there are in general,
+
+ align:start position:0%
+going to assume if there are in general,
+ 
+
+ align:start position:0%
+going to assume if there are in general,
+there may be multiple three in a rows at
+
+ align:start position:0%
+there may be multiple three in a rows at
+ 
+
+ align:start position:0%
+there may be multiple three in a rows at
+once. And the proof is going to assume
+
+ align:start position:0%
+once. And the proof is going to assume
+ 
+
+ align:start position:0%
+once. And the proof is going to assume
+that they are resolved bottom to top. So
+
+ align:start position:0%
+that they are resolved bottom to top. So
+ 
+
+ align:start position:0%
+that they are resolved bottom to top. So
+you do the bottommost one first,
+
+ align:start position:0%
+you do the bottommost one first,
+ 
+
+ align:start position:0%
+you do the bottommost one first,
+things fall, then you do the next one,
+
+ align:start position:0%
+things fall, then you do the next one,
+ 
+
+ align:start position:0%
+things fall, then you do the next one,
+things fall. Do the next one, things
+
+ align:start position:0%
+things fall. Do the next one, things
+ 
+
+ align:start position:0%
+things fall. Do the next one, things
+fall. That's not how the actual game
+
+ align:start position:0%
+fall. That's not how the actual game
+ 
+
+ align:start position:0%
+fall. That's not how the actual game
+works. The game in the game, they all uh
+
+ align:start position:0%
+works. The game in the game, they all uh
+ 
+
+ align:start position:0%
+works. The game in the game, they all uh
+disappear simultaneously
+
+ align:start position:0%
+disappear simultaneously
+ 
+
+ align:start position:0%
+disappear simultaneously
+and then stuff falls. Okay, but ignore
+
+ align:start position:0%
+and then stuff falls. Okay, but ignore
+ 
+
+ align:start position:0%
+and then stuff falls. Okay, but ignore
+that for the moment. The next proof will
+
+ align:start position:0%
+that for the moment. The next proof will
+ 
+
+ align:start position:0%
+that for the moment. The next proof will
+change the model. Okay, this is a much
+
+ align:start position:0%
+change the model. Okay, this is a much
+ 
+
+ align:start position:0%
+change the model. Okay, this is a much
+easier one to think about and draw the
+
+ align:start position:0%
+easier one to think about and draw the
+ 
+
+ align:start position:0%
+easier one to think about and draw the
+pictures. So uh in that model, here's a
+
+ align:start position:0%
+pictures. So uh in that model, here's a
+ 
+
+ align:start position:0%
+pictures. So uh in that model, here's a
+variable gadget. We have uh this is the
+
+ align:start position:0%
+variable gadget. We have uh this is the
+ 
+
+ align:start position:0%
+variable gadget. We have uh this is the
+starting point. It's the same picture
+
+ align:start position:0%
+starting point. It's the same picture
+ 
+
+ align:start position:0%
+starting point. It's the same picture
+top and bottom. And the idea is either
+
+ align:start position:0%
+top and bottom. And the idea is either
+ 
+
+ align:start position:0%
+top and bottom. And the idea is either
+you exchange these two to make three or
+
+ align:start position:0%
+you exchange these two to make three or
+ 
+
+ align:start position:0%
+you exchange these two to make three or
+you exchange these two to make three.
+
+ align:start position:0%
+you exchange these two to make three.
+ 
+
+ align:start position:0%
+you exchange these two to make three.
+And the consequence is either the right
+
+ align:start position:0%
+And the consequence is either the right
+ 
+
+ align:start position:0%
+And the consequence is either the right
+column falls by three or the middle
+
+ align:start position:0%
+column falls by three or the middle
+ 
+
+ align:start position:0%
+column falls by three or the middle
+column falls by three. And that's all
+
+ align:start position:0%
+column falls by three. And that's all
+ 
+
+ align:start position:0%
+column falls by three. And that's all
+you can do local to this gadget. So
+
+ align:start position:0%
+you can do local to this gadget. So
+ 
+
+ align:start position:0%
+you can do local to this gadget. So
+that's easy. Things are going to get
+
+ align:start position:0%
+that's easy. Things are going to get
+ 
+
+ align:start position:0%
+that's easy. Things are going to get
+messier but um
+
+ align:start position:0%
+messier but um
+ 
+
+ align:start position:0%
+messier but um
+okay. So imag you have this picture
+
+ align:start position:0%
+okay. So imag you have this picture
+ 
+
+ align:start position:0%
+okay. So imag you have this picture
+variable gadget for XI. above it. I'm
+
+ align:start position:0%
+variable gadget for XI. above it. I'm
+ 
+
+ align:start position:0%
+variable gadget for XI. above it. I'm
+going to make one of these two gadgets.
+
+ align:start position:0%
+going to make one of these two gadgets.
+ 
+
+ align:start position:0%
+going to make one of these two gadgets.
+Actually, both of them, but one at a
+
+ align:start position:0%
+Actually, both of them, but one at a
+ 
+
+ align:start position:0%
+Actually, both of them, but one at a
+time. So, in fact, it will actually look
+
+ align:start position:0%
+time. So, in fact, it will actually look
+ 
+
+ align:start position:0%
+time. So, in fact, it will actually look
+kind of like this stacked on top of the
+
+ align:start position:0%
+kind of like this stacked on top of the
+ 
+
+ align:start position:0%
+kind of like this stacked on top of the
+variable, which is down here. So,
+
+ align:start position:0%
+variable, which is down here. So,
+ 
+
+ align:start position:0%
+variable, which is down here. So,
+variables down here. Either the uh
+
+ align:start position:0%
+variables down here. Either the uh
+ 
+
+ align:start position:0%
+variables down here. Either the uh
+center column falls or the right column
+
+ align:start position:0%
+center column falls or the right column
+ 
+
+ align:start position:0%
+center column falls or the right column
+falls. Now, the idea is this is going to
+
+ align:start position:0%
+falls. Now, the idea is this is going to
+ 
+
+ align:start position:0%
+falls. Now, the idea is this is going to
+eventually connect to a clause. And this
+
+ align:start position:0%
+eventually connect to a clause. And this
+ 
+
+ align:start position:0%
+eventually connect to a clause. And this
+variable, I should say this is not from
+
+ align:start position:0%
+variable, I should say this is not from
+ 
+
+ align:start position:0%
+variable, I should say this is not from
+circuit. This is from three set. Regular
+
+ align:start position:0%
+circuit. This is from three set. Regular
+ 
+
+ align:start position:0%
+circuit. This is from three set. Regular
+old 3AT. So that variable appears in the
+
+ align:start position:0%
+old 3AT. So that variable appears in the
+ 
+
+ align:start position:0%
+old 3AT. So that variable appears in the
+clause either in positive form or
+
+ align:start position:0%
+clause either in positive form or
+ 
+
+ align:start position:0%
+clause either in positive form or
+negative form. Positive use this gadget.
+
+ align:start position:0%
+negative form. Positive use this gadget.
+ 
+
+ align:start position:0%
+negative form. Positive use this gadget.
+Negative use this gadget. So in the
+
+ align:start position:0%
+Negative use this gadget. So in the
+ 
+
+ align:start position:0%
+Negative use this gadget. So in the
+positive case if this falls by three we
+
+ align:start position:0%
+positive case if this falls by three we
+ 
+
+ align:start position:0%
+positive case if this falls by three we
+get this picture and then these
+
+ align:start position:0%
+get this picture and then these
+ 
+
+ align:start position:0%
+get this picture and then these
+disappear and so this guy falls one
+
+ align:start position:0%
+disappear and so this guy falls one
+ 
+
+ align:start position:0%
+disappear and so this guy falls one
+more. And the idea is that's going to
+
+ align:start position:0%
+more. And the idea is that's going to
+ 
+
+ align:start position:0%
+more. And the idea is that's going to
+trigger something off to the right. That
+
+ align:start position:0%
+trigger something off to the right. That
+ 
+
+ align:start position:0%
+trigger something off to the right. That
+will be next slide. Okay. Uh that will
+
+ align:start position:0%
+will be next slide. Okay. Uh that will
+ 
+
+ align:start position:0%
+will be next slide. Okay. Uh that will
+be the wire gadget. Uh if the center
+
+ align:start position:0%
+be the wire gadget. Uh if the center
+ 
+
+ align:start position:0%
+be the wire gadget. Uh if the center
+column fell by three, nothing would
+
+ align:start position:0%
+column fell by three, nothing would
+ 
+
+ align:start position:0%
+column fell by three, nothing would
+happen, right? the purples. I should
+
+ align:start position:0%
+happen, right? the purples. I should
+ 
+
+ align:start position:0%
+happen, right? the purples. I should
+mention uh how these gadgets are
+
+ align:start position:0%
+mention uh how these gadgets are
+ 
+
+ align:start position:0%
+mention uh how these gadgets are
+constructed. There's a a fourcolor sort
+
+ align:start position:0%
+constructed. There's a a fourcolor sort
+ 
+
+ align:start position:0%
+constructed. There's a a fourcolor sort
+of checkerboard pattern. Every in odd
+
+ align:start position:0%
+of checkerboard pattern. Every in odd
+ 
+
+ align:start position:0%
+of checkerboard pattern. Every in odd
+rows it's alternating orange, green,
+
+ align:start position:0%
+rows it's alternating orange, green,
+ 
+
+ align:start position:0%
+rows it's alternating orange, green,
+orange, green. In even rows, it's
+
+ align:start position:0%
+orange, green. In even rows, it's
+ 
+
+ align:start position:0%
+orange, green. In even rows, it's
+alternating red, yellow, red, yellow.
+
+ align:start position:0%
+alternating red, yellow, red, yellow.
+ 
+
+ align:start position:0%
+alternating red, yellow, red, yellow.
+And then in a few places, we're going to
+
+ align:start position:0%
+And then in a few places, we're going to
+ 
+
+ align:start position:0%
+And then in a few places, we're going to
+put the purple ones cuz purple's best.
+
+ align:start position:0%
+put the purple ones cuz purple's best.
+ 
+
+ align:start position:0%
+put the purple ones cuz purple's best.
+Uh and all the action is going to be in
+
+ align:start position:0%
+Uh and all the action is going to be in
+ 
+
+ align:start position:0%
+Uh and all the action is going to be in
+the purple candies. Okay, the these guys
+
+ align:start position:0%
+the purple candies. Okay, the these guys
+ 
+
+ align:start position:0%
+the purple candies. Okay, the these guys
+are just uh out there. And the real game
+
+ align:start position:0%
+are just uh out there. And the real game
+ 
+
+ align:start position:0%
+are just uh out there. And the real game
+has six colors. We're only using five of
+
+ align:start position:0%
+has six colors. We're only using five of
+ 
+
+ align:start position:0%
+has six colors. We're only using five of
+them. So cool. Uh these guys are just
+
+ align:start position:0%
+them. So cool. Uh these guys are just
+ 
+
+ align:start position:0%
+them. So cool. Uh these guys are just
+sort of filler to make sure nothing else
+
+ align:start position:0%
+sort of filler to make sure nothing else
+ 
+
+ align:start position:0%
+sort of filler to make sure nothing else
+happens. But still things fall
+
+ align:start position:0%
+happens. But still things fall
+ 
+
+ align:start position:0%
+happens. But still things fall
+vertically in a nice controlled way.
+
+ align:start position:0%
+vertically in a nice controlled way.
+ 
+
+ align:start position:0%
+vertically in a nice controlled way.
+Okay. So if you if these fall by three,
+
+ align:start position:0%
+Okay. So if you if these fall by three,
+ 
+
+ align:start position:0%
+Okay. So if you if these fall by three,
+the purples don't align. So nothing
+
+ align:start position:0%
+the purples don't align. So nothing
+ 
+
+ align:start position:0%
+the purples don't align. So nothing
+happens in this case. Uh if the center
+
+ align:start position:0%
+happens in this case. Uh if the center
+ 
+
+ align:start position:0%
+happens in this case. Uh if the center
+one falls by three, we get alignment and
+
+ align:start position:0%
+one falls by three, we get alignment and
+ 
+
+ align:start position:0%
+one falls by three, we get alignment and
+that falls by one. So great. Uh also
+
+ align:start position:0%
+that falls by one. So great. Uh also
+ 
+
+ align:start position:0%
+that falls by one. So great. Uh also
+note these gadgets stack
+
+ align:start position:0%
+note these gadgets stack
+ 
+
+ align:start position:0%
+note these gadgets stack
+somewhat nicely in that other than these
+
+ align:start position:0%
+somewhat nicely in that other than these
+ 
+
+ align:start position:0%
+somewhat nicely in that other than these
+this three gap uh in in reality more
+
+ align:start position:0%
+this three gap uh in in reality more
+ 
+
+ align:start position:0%
+this three gap uh in in reality more
+candies will fill in here. I drew it
+
+ align:start position:0%
+candies will fill in here. I drew it
+ 
+
+ align:start position:0%
+candies will fill in here. I drew it
+this way so you could see how much the
+
+ align:start position:0%
+this way so you could see how much the
+ 
+
+ align:start position:0%
+this way so you could see how much the
+columns actually fall. Remember this all
+
+ align:start position:0%
+columns actually fall. Remember this all
+ 
+
+ align:start position:0%
+columns actually fall. Remember this all
+sort of happens in one one move. So this
+
+ align:start position:0%
+sort of happens in one one move. So this
+ 
+
+ align:start position:0%
+sort of happens in one one move. So this
+falls, these clear, then this will clear
+
+ align:start position:0%
+falls, these clear, then this will clear
+ 
+
+ align:start position:0%
+falls, these clear, then this will clear
+and stuff happens. Uh it's annoying. So,
+
+ align:start position:0%
+and stuff happens. Uh it's annoying. So,
+ 
+
+ align:start position:0%
+and stuff happens. Uh it's annoying. So,
+so far everything's good because uh
+
+ align:start position:0%
+so far everything's good because uh
+ 
+
+ align:start position:0%
+so far everything's good because uh
+we've each of these is followed by one
+
+ align:start position:0%
+we've each of these is followed by one
+ 
+
+ align:start position:0%
+we've each of these is followed by one
+in addition to the original three.
+
+ align:start position:0%
+in addition to the original three.
+ 
+
+ align:start position:0%
+in addition to the original three.
+Uh but in this case, uh this follows by
+
+ align:start position:0%
+Uh but in this case, uh this follows by
+ 
+
+ align:start position:0%
+Uh but in this case, uh this follows by
+an extra one. I think you need to add an
+
+ align:start position:0%
+an extra one. I think you need to add an
+ 
+
+ align:start position:0%
+an extra one. I think you need to add an
+extra candy here. I'm a little unclear
+
+ align:start position:0%
+extra candy here. I'm a little unclear
+ 
+
+ align:start position:0%
+extra candy here. I'm a little unclear
+in the details of how to do that. It's
+
+ align:start position:0%
+in the details of how to do that. It's
+ 
+
+ align:start position:0%
+in the details of how to do that. It's
+mentioned in the paper, but without
+
+ align:start position:0%
+mentioned in the paper, but without
+ 
+
+ align:start position:0%
+mentioned in the paper, but without
+details. So, uh anyway, in the end, we
+
+ align:start position:0%
+details. So, uh anyway, in the end, we
+ 
+
+ align:start position:0%
+details. So, uh anyway, in the end, we
+will have uh a bunch of these stacked on
+
+ align:start position:0%
+will have uh a bunch of these stacked on
+ 
+
+ align:start position:0%
+will have uh a bunch of these stacked on
+top of each other. Each time the
+
+ align:start position:0%
+top of each other. Each time the
+ 
+
+ align:start position:0%
+top of each other. Each time the
+variable occurs in various clauses,
+
+ align:start position:0%
+variable occurs in various clauses,
+ 
+
+ align:start position:0%
+variable occurs in various clauses,
+we're going to have some positive and
+
+ align:start position:0%
+we're going to have some positive and
+ 
+
+ align:start position:0%
+we're going to have some positive and
+some negative ones. And we want the same
+
+ align:start position:0%
+some negative ones. And we want the same
+ 
+
+ align:start position:0%
+some negative ones. And we want the same
+variable trigger. Ah, that's right. Uh,
+
+ align:start position:0%
+variable trigger. Ah, that's right. Uh,
+ 
+
+ align:start position:0%
+variable trigger. Ah, that's right. Uh,
+there will be well, okay, no, I'm going
+
+ align:start position:0%
+there will be well, okay, no, I'm going
+ 
+
+ align:start position:0%
+there will be well, okay, no, I'm going
+to leave it like that.
+
+ align:start position:0%
+to leave it like that.
+ 
+
+ align:start position:0%
+to leave it like that.
+So, at this point, we have um a purple
+
+ align:start position:0%
+So, at this point, we have um a purple
+ 
+
+ align:start position:0%
+So, at this point, we have um a purple
+thing triggering something to the right.
+
+ align:start position:0%
+thing triggering something to the right.
+ 
+
+ align:start position:0%
+thing triggering something to the right.
+So, now I'm going to show you how that
+
+ align:start position:0%
+So, now I'm going to show you how that
+ 
+
+ align:start position:0%
+So, now I'm going to show you how that
+part works. This is the wire. So, the
+
+ align:start position:0%
+part works. This is the wire. So, the
+ 
+
+ align:start position:0%
+part works. This is the wire. So, the
+wire itself is like this. And the idea
+
+ align:start position:0%
+wire itself is like this. And the idea
+ 
+
+ align:start position:0%
+wire itself is like this. And the idea
+is that when there's a purple one here,
+
+ align:start position:0%
+is that when there's a purple one here,
+ 
+
+ align:start position:0%
+is that when there's a purple one here,
+chain reaction happens. And it happens
+
+ align:start position:0%
+chain reaction happens. And it happens
+ 
+
+ align:start position:0%
+chain reaction happens. And it happens
+in this way. As soon as there's a purple
+
+ align:start position:0%
+in this way. As soon as there's a purple
+ 
+
+ align:start position:0%
+in this way. As soon as there's a purple
+um candy here, this clears, which makes
+
+ align:start position:0%
+um candy here, this clears, which makes
+ 
+
+ align:start position:0%
+um candy here, this clears, which makes
+these two fall by one, which clears that
+
+ align:start position:0%
+these two fall by one, which clears that
+ 
+
+ align:start position:0%
+these two fall by one, which clears that
+which makes this fall by one and
+
+ align:start position:0%
+which makes this fall by one and
+ 
+
+ align:start position:0%
+which makes this fall by one and
+triggers the next thing. Okay, this one
+
+ align:start position:0%
+triggers the next thing. Okay, this one
+ 
+
+ align:start position:0%
+triggers the next thing. Okay, this one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+some stacking happens. Let's see. So
+
+ align:start position:0%
+some stacking happens. Let's see. So
+ 
+
+ align:start position:0%
+some stacking happens. Let's see. So
+overall, uh I think this one is actually
+
+ align:start position:0%
+overall, uh I think this one is actually
+ 
+
+ align:start position:0%
+overall, uh I think this one is actually
+better behaved. Uh this falls by one
+
+ align:start position:0%
+better behaved. Uh this falls by one
+ 
+
+ align:start position:0%
+better behaved. Uh this falls by one
+here and then two. So overall these
+
+ align:start position:0%
+here and then two. So overall these
+ 
+
+ align:start position:0%
+here and then two. So overall these
+columns fell by two. This column has
+
+ align:start position:0%
+columns fell by two. This column has
+ 
+
+ align:start position:0%
+columns fell by two. This column has
+fallen so far by one uh but it's about
+
+ align:start position:0%
+fallen so far by one uh but it's about
+ 
+
+ align:start position:0%
+fallen so far by one uh but it's about
+to fall by a second one because this
+
+ align:start position:0%
+to fall by a second one because this
+ 
+
+ align:start position:0%
+to fall by a second one because this
+will always trigger something. And so
+
+ align:start position:0%
+will always trigger something. And so
+ 
+
+ align:start position:0%
+will always trigger something. And so
+these do stack nicely because you always
+
+ align:start position:0%
+these do stack nicely because you always
+ 
+
+ align:start position:0%
+these do stack nicely because you always
+clear exactly two columns. So the worry
+
+ align:start position:0%
+clear exactly two columns. So the worry
+ 
+
+ align:start position:0%
+clear exactly two columns. So the worry
+is that the gadget above it uh will be
+
+ align:start position:0%
+is that the gadget above it uh will be
+ 
+
+ align:start position:0%
+is that the gadget above it uh will be
+skewed.
+
+ align:start position:0%
+skewed.
+ 
+
+ align:start position:0%
+skewed.
+Okay. Uh
+
+ align:start position:0%
+Okay. Uh
+ 
+
+ align:start position:0%
+Okay. Uh
+let me give you one more gadget then
+
+ align:start position:0%
+let me give you one more gadget then
+ 
+
+ align:start position:0%
+let me give you one more gadget then
+I'll tell you how um no actually I think
+
+ align:start position:0%
+I'll tell you how um no actually I think
+ 
+
+ align:start position:0%
+I'll tell you how um no actually I think
+at this point I should tell you how
+
+ align:start position:0%
+at this point I should tell you how
+ 
+
+ align:start position:0%
+at this point I should tell you how
+things fit together
+
+ align:start position:0%
+things fit together
+ 
+
+ align:start position:0%
+things fit together
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+this picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so we have
+
+ align:start position:0%
+Okay, so we have
+ 
+
+ align:start position:0%
+Okay, so we have
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+down here in the lower left.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then uh let's worry about one thing at a
+
+ align:start position:0%
+Then uh let's worry about one thing at a
+ 
+
+ align:start position:0%
+Then uh let's worry about one thing at a
+time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+These are the uh connection gadgets.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I didn't I don't think I told you their
+
+ align:start position:0%
+I didn't I don't think I told you their
+ 
+
+ align:start position:0%
+I didn't I don't think I told you their
+name, but they're your connector
+
+ align:start position:0%
+name, but they're your connector
+ 
+
+ align:start position:0%
+name, but they're your connector
+gadgets. This is sort of making a 90°
+
+ align:start position:0%
+gadgets. This is sort of making a 90°
+ 
+
+ align:start position:0%
+gadgets. This is sort of making a 90°
+turn. From the falling action, we're
+
+ align:start position:0%
+turn. From the falling action, we're
+ 
+
+ align:start position:0%
+turn. From the falling action, we're
+going to get a purple in a particular
+
+ align:start position:0%
+going to get a purple in a particular
+ 
+
+ align:start position:0%
+going to get a purple in a particular
+position, which causes rightward motion.
+
+ align:start position:0%
+position, which causes rightward motion.
+ 
+
+ align:start position:0%
+position, which causes rightward motion.
+And then, uh, the wires, as you saw,
+
+ align:start position:0%
+And then, uh, the wires, as you saw,
+ 
+
+ align:start position:0%
+And then, uh, the wires, as you saw,
+basically go in some angle off to the
+
+ align:start position:0%
+basically go in some angle off to the
+ 
+
+ align:start position:0%
+basically go in some angle off to the
+right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want these all to be non-intersecting.
+
+ align:start position:0%
+I want these all to be non-intersecting.
+ 
+
+ align:start position:0%
+I want these all to be non-intersecting.
+Uh,
+
+ align:start position:0%
+Uh,
+ 
+
+ align:start position:0%
+Uh,
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's sort of two of them. There's
+
+ align:start position:0%
+there's sort of two of them. There's
+ 
+
+ align:start position:0%
+there's sort of two of them. There's
+going to be the true case and the false
+
+ align:start position:0%
+going to be the true case and the false
+ 
+
+ align:start position:0%
+going to be the true case and the false
+case.
+
+ align:start position:0%
+case.
+ 
+
+ align:start position:0%
+case.
+Okay? And then way over here somewhere,
+
+ align:start position:0%
+Okay? And then way over here somewhere,
+ 
+
+ align:start position:0%
+Okay? And then way over here somewhere,
+we're going to have clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where these wires all attach. And then
+
+ align:start position:0%
+where these wires all attach. And then
+ 
+
+ align:start position:0%
+where these wires all attach. And then
+above it, we're going to have a reward
+
+ align:start position:0%
+above it, we're going to have a reward
+ 
+
+ align:start position:0%
+above it, we're going to have a reward
+where you get tons of points and uh etc.
+
+ align:start position:0%
+where you get tons of points and uh etc.
+ 
+
+ align:start position:0%
+where you get tons of points and uh etc.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+let me tell you what happens next. Uh
+
+ align:start position:0%
+let me tell you what happens next. Uh
+ 
+
+ align:start position:0%
+let me tell you what happens next. Uh
+this is a fun way to draw the picture.
+
+ align:start position:0%
+this is a fun way to draw the picture.
+ 
+
+ align:start position:0%
+this is a fun way to draw the picture.
+So, above these we'll have some other
+
+ align:start position:0%
+So, above these we'll have some other
+ 
+
+ align:start position:0%
+So, above these we'll have some other
+connections.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should not do it in the same pattern.
+
+ align:start position:0%
+I should not do it in the same pattern.
+ 
+
+ align:start position:0%
+I should not do it in the same pattern.
+I should not do it like that. Yeah,
+
+ align:start position:0%
+I should not do it like that. Yeah,
+ 
+
+ align:start position:0%
+I should not do it like that. Yeah,
+sure. Connection.
+
+ align:start position:0%
+sure. Connection.
+ 
+
+ align:start position:0%
+sure. Connection.
+Connection.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Again, diagonal lines.
+
+ align:start position:0%
+Okay. Again, diagonal lines.
+ 
+
+ align:start position:0%
+Okay. Again, diagonal lines.
+Great. Not quite diagonal. They're at
+
+ align:start position:0%
+Great. Not quite diagonal. They're at
+ 
+
+ align:start position:0%
+Great. Not quite diagonal. They're at
+some angle. We have a clause. Everything
+
+ align:start position:0%
+some angle. We have a clause. Everything
+ 
+
+ align:start position:0%
+some angle. We have a clause. Everything
+connects up. Above the claws is a
+
+ align:start position:0%
+connects up. Above the claws is a
+ 
+
+ align:start position:0%
+connects up. Above the claws is a
+reward.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then I move the boards.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that's the picture.
+
+ align:start position:0%
+And that's the picture.
+ 
+
+ align:start position:0%
+And that's the picture.
+Okay. So, and just above the variables,
+
+ align:start position:0%
+Okay. So, and just above the variables,
+ 
+
+ align:start position:0%
+Okay. So, and just above the variables,
+we just keep adding more connections
+
+ align:start position:0%
+we just keep adding more connections
+ 
+
+ align:start position:0%
+we just keep adding more connections
+connected to some clauses. And in this
+
+ align:start position:0%
+connected to some clauses. And in this
+ 
+
+ align:start position:0%
+connected to some clauses. And in this
+way, and it's not just three variables,
+
+ align:start position:0%
+way, and it's not just three variables,
+ 
+
+ align:start position:0%
+way, and it's not just three variables,
+of course, we can have different uh
+
+ align:start position:0%
+of course, we can have different uh
+ 
+
+ align:start position:0%
+of course, we can have different uh
+there's n variables down here, and we
+
+ align:start position:0%
+there's n variables down here, and we
+ 
+
+ align:start position:0%
+there's n variables down here, and we
+use some three of them, and then connect
+
+ align:start position:0%
+use some three of them, and then connect
+ 
+
+ align:start position:0%
+use some three of them, and then connect
+that off to a clause, and they're all
+
+ align:start position:0%
+that off to a clause, and they're all
+ 
+
+ align:start position:0%
+that off to a clause, and they're all
+just stacked. Uh I happen to draw the
+
+ align:start position:0%
+just stacked. Uh I happen to draw the
+ 
+
+ align:start position:0%
+just stacked. Uh I happen to draw the
+clauses one on top of the other. That
+
+ align:start position:0%
+clauses one on top of the other. That
+ 
+
+ align:start position:0%
+clauses one on top of the other. That
+shouldn't happen. Uh so there's some
+
+ align:start position:0%
+shouldn't happen. Uh so there's some
+ 
+
+ align:start position:0%
+shouldn't happen. Uh so there's some
+extra space here. This is more over to
+
+ align:start position:0%
+extra space here. This is more over to
+ 
+
+ align:start position:0%
+extra space here. This is more over to
+the right. So that none of them will
+
+ align:start position:0%
+the right. So that none of them will
+ 
+
+ align:start position:0%
+the right. So that none of them will
+interact with each other. That's the
+
+ align:start position:0%
+interact with each other. That's the
+ 
+
+ align:start position:0%
+interact with each other. That's the
+goal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Except there are some issues like uh
+
+ align:start position:0%
+Except there are some issues like uh
+ 
+
+ align:start position:0%
+Except there are some issues like uh
+notice this wire gadget. Notice uh dual
+
+ align:start position:0%
+notice this wire gadget. Notice uh dual
+ 
+
+ align:start position:0%
+notice this wire gadget. Notice uh dual
+rail logic, right? Either this is active
+
+ align:start position:0%
+rail logic, right? Either this is active
+ 
+
+ align:start position:0%
+rail logic, right? Either this is active
+or this is active. And we hope that not
+
+ align:start position:0%
+or this is active. And we hope that not
+ 
+
+ align:start position:0%
+or this is active. And we hope that not
+both of them are active, although that
+
+ align:start position:0%
+both of them are active, although that
+ 
+
+ align:start position:0%
+both of them are active, although that
+can actually happen here. I'll get to
+
+ align:start position:0%
+can actually happen here. I'll get to
+ 
+
+ align:start position:0%
+can actually happen here. I'll get to
+that. Uh so uh when this activates,
+
+ align:start position:0%
+that. Uh so uh when this activates,
+ 
+
+ align:start position:0%
+that. Uh so uh when this activates,
+notice this might this goes on top of a
+
+ align:start position:0%
+notice this might this goes on top of a
+ 
+
+ align:start position:0%
+notice this might this goes on top of a
+variable gadget. Now wire by itself is
+
+ align:start position:0%
+variable gadget. Now wire by itself is
+ 
+
+ align:start position:0%
+variable gadget. Now wire by itself is
+kind of good. We've seen uh it removes
+
+ align:start position:0%
+kind of good. We've seen uh it removes
+ 
+
+ align:start position:0%
+kind of good. We've seen uh it removes
+two things from every spot. So uh things
+
+ align:start position:0%
+two things from every spot. So uh things
+ 
+
+ align:start position:0%
+two things from every spot. So uh things
+don't shift too much.
+
+ align:start position:0%
+don't shift too much.
+ 
+
+ align:start position:0%
+don't shift too much.
+And furthermore uh we know we hope that
+
+ align:start position:0%
+And furthermore uh we know we hope that
+ 
+
+ align:start position:0%
+And furthermore uh we know we hope that
+either this activates or this activates.
+
+ align:start position:0%
+either this activates or this activates.
+ 
+
+ align:start position:0%
+either this activates or this activates.
+So this will shift by a consistent
+
+ align:start position:0%
+So this will shift by a consistent
+ 
+
+ align:start position:0%
+So this will shift by a consistent
+amount in either case.
+
+ align:start position:0%
+amount in either case.
+ 
+
+ align:start position:0%
+amount in either case.
+But uh
+
+ align:start position:0%
+But uh
+ 
+
+ align:start position:0%
+But uh
+the wire may get messed up because the
+
+ align:start position:0%
+the wire may get messed up because the
+ 
+
+ align:start position:0%
+the wire may get messed up because the
+variable actually removes three things
+
+ align:start position:0%
+variable actually removes three things
+ 
+
+ align:start position:0%
+variable actually removes three things
+from one of the columns. So, we need a
+
+ align:start position:0%
+from one of the columns. So, we need a
+ 
+
+ align:start position:0%
+from one of the columns. So, we need a
+better wire gadget, which looks like
+
+ align:start position:0%
+better wire gadget, which looks like
+ 
+
+ align:start position:0%
+better wire gadget, which looks like
+uh this. This is a super wire gadget.
+
+ align:start position:0%
+uh this. This is a super wire gadget.
+ 
+
+ align:start position:0%
+uh this. This is a super wire gadget.
+It's really cool. It works no matter how
+
+ align:start position:0%
+It's really cool. It works no matter how
+ 
+
+ align:start position:0%
+It's really cool. It works no matter how
+you use it kind of. So, this is what it
+
+ align:start position:0%
+you use it kind of. So, this is what it
+ 
+
+ align:start position:0%
+you use it kind of. So, this is what it
+looks like in general. And this is
+
+ align:start position:0%
+looks like in general. And this is
+ 
+
+ align:start position:0%
+looks like in general. And this is
+regular use. So, this is as before. Uh
+
+ align:start position:0%
+regular use. So, this is as before. Uh
+ 
+
+ align:start position:0%
+regular use. So, this is as before. Uh
+if we trigger this, then this triggers
+
+ align:start position:0%
+if we trigger this, then this triggers
+ 
+
+ align:start position:0%
+if we trigger this, then this triggers
+and this guy falls by one just like
+
+ align:start position:0%
+and this guy falls by one just like
+ 
+
+ align:start position:0%
+and this guy falls by one just like
+before. But now also if there's a
+
+ align:start position:0%
+before. But now also if there's a
+ 
+
+ align:start position:0%
+before. But now also if there's a
+variable down here and this column falls
+
+ align:start position:0%
+variable down here and this column falls
+ 
+
+ align:start position:0%
+variable down here and this column falls
+by three or sorry if this column falls
+
+ align:start position:0%
+by three or sorry if this column falls
+ 
+
+ align:start position:0%
+by three or sorry if this column falls
+by three. So it's same picture but
+
+ align:start position:0%
+by three. So it's same picture but
+ 
+
+ align:start position:0%
+by three. So it's same picture but
+things fell by three still everything
+
+ align:start position:0%
+things fell by three still everything
+ 
+
+ align:start position:0%
+things fell by three still everything
+works out. Uh this these two fall it's a
+
+ align:start position:0%
+works out. Uh this these two fall it's a
+ 
+
+ align:start position:0%
+works out. Uh this these two fall it's a
+different uh these two fall but they
+
+ align:start position:0%
+different uh these two fall but they
+ 
+
+ align:start position:0%
+different uh these two fall but they
+meet a different dude but there were a
+
+ align:start position:0%
+meet a different dude but there were a
+ 
+
+ align:start position:0%
+meet a different dude but there were a
+bunch of guys to meet up with so it's
+
+ align:start position:0%
+bunch of guys to meet up with so it's
+ 
+
+ align:start position:0%
+bunch of guys to meet up with so it's
+fine. Uh and I clearly drew the output
+
+ align:start position:0%
+fine. Uh and I clearly drew the output
+ 
+
+ align:start position:0%
+fine. Uh and I clearly drew the output
+in the wrong place. Uh the output should
+
+ align:start position:0%
+in the wrong place. Uh the output should
+ 
+
+ align:start position:0%
+in the wrong place. Uh the output should
+be here I think. Yeah. So in in this
+
+ align:start position:0%
+be here I think. Yeah. So in in this
+ 
+
+ align:start position:0%
+be here I think. Yeah. So in in this
+picture the output was here also it
+
+ align:start position:0%
+picture the output was here also it
+ 
+
+ align:start position:0%
+picture the output was here also it
+shifted by one. In this picture the
+
+ align:start position:0%
+shifted by one. In this picture the
+ 
+
+ align:start position:0%
+shifted by one. In this picture the
+output is here not up there. Okay. So in
+
+ align:start position:0%
+output is here not up there. Okay. So in
+ 
+
+ align:start position:0%
+output is here not up there. Okay. So in
+both cases it triggers. And finally if
+
+ align:start position:0%
+both cases it triggers. And finally if
+ 
+
+ align:start position:0%
+both cases it triggers. And finally if
+the middle column fell by three before
+
+ align:start position:0%
+the middle column fell by three before
+ 
+
+ align:start position:0%
+the middle column fell by three before
+this gadget activated then uh this again
+
+ align:start position:0%
+this gadget activated then uh this again
+ 
+
+ align:start position:0%
+this gadget activated then uh this again
+triggers uh this time with this guy
+
+ align:start position:0%
+triggers uh this time with this guy
+ 
+
+ align:start position:0%
+triggers uh this time with this guy
+being different. Instead of this one
+
+ align:start position:0%
+being different. Instead of this one
+ 
+
+ align:start position:0%
+being different. Instead of this one
+matching this one's matching. Uh that
+
+ align:start position:0%
+matching this one's matching. Uh that
+ 
+
+ align:start position:0%
+matching this one's matching. Uh that
+still triggers these guys and this is
+
+ align:start position:0%
+still triggers these guys and this is
+ 
+
+ align:start position:0%
+still triggers these guys and this is
+still the output. Okay. So this is a
+
+ align:start position:0%
+still the output. Okay. So this is a
+ 
+
+ align:start position:0%
+still the output. Okay. So this is a
+different wire gadget that works in
+
+ align:start position:0%
+different wire gadget that works in
+ 
+
+ align:start position:0%
+different wire gadget that works in
+three different scenarios depending on
+
+ align:start position:0%
+three different scenarios depending on
+ 
+
+ align:start position:0%
+three different scenarios depending on
+what happened below it. So that's good
+
+ align:start position:0%
+what happened below it. So that's good
+ 
+
+ align:start position:0%
+what happened below it. So that's good
+news that lets us
+
+ align:start position:0%
+news that lets us
+ 
+
+ align:start position:0%
+news that lets us
+do this type of wire. In general, we're
+
+ align:start position:0%
+do this type of wire. In general, we're
+ 
+
+ align:start position:0%
+do this type of wire. In general, we're
+going to have a chain reaction all the
+
+ align:start position:0%
+going to have a chain reaction all the
+ 
+
+ align:start position:0%
+going to have a chain reaction all the
+way down here till we get to the claws
+
+ align:start position:0%
+way down here till we get to the claws
+ 
+
+ align:start position:0%
+way down here till we get to the claws
+uh from bottom to top. These will
+
+ align:start position:0%
+uh from bottom to top. These will
+ 
+
+ align:start position:0%
+uh from bottom to top. These will
+resolve and let me show you the claws.
+
+ align:start position:0%
+resolve and let me show you the claws.
+ 
+
+ align:start position:0%
+resolve and let me show you the claws.
+Uh I think details are a little bit
+
+ align:start position:0%
+Uh I think details are a little bit
+ 
+
+ align:start position:0%
+Uh I think details are a little bit
+messy. Um there's a little locking
+
+ align:start position:0%
+messy. Um there's a little locking
+ 
+
+ align:start position:0%
+messy. Um there's a little locking
+mechanism here, but uh basically the
+
+ align:start position:0%
+mechanism here, but uh basically the
+ 
+
+ align:start position:0%
+mechanism here, but uh basically the
+idea is all of the these things come in
+
+ align:start position:0%
+idea is all of the these things come in
+ 
+
+ align:start position:0%
+idea is all of the these things come in
+X1, X1 bar, X2, X2 bar, all of the half
+
+ align:start position:0%
+X1, X1 bar, X2, X2 bar, all of the half
+ 
+
+ align:start position:0%
+X1, X1 bar, X2, X2 bar, all of the half
+wires or semiwires. Um and so we we
+
+ align:start position:0%
+wires or semiwires. Um and so we we
+ 
+
+ align:start position:0%
+wires or semiwires. Um and so we we
+expect one of these to activate.
+
+ align:start position:0%
+expect one of these to activate.
+ 
+
+ align:start position:0%
+expect one of these to activate.
+Maybe you don't do that, but that would
+
+ align:start position:0%
+Maybe you don't do that, but that would
+ 
+
+ align:start position:0%
+Maybe you don't do that, but that would
+be weird
+
+ align:start position:0%
+be weird
+ 
+
+ align:start position:0%
+be weird
+and you won't end up satisfying the
+
+ align:start position:0%
+and you won't end up satisfying the
+ 
+
+ align:start position:0%
+and you won't end up satisfying the
+clause. So if this one activates uh then
+
+ align:start position:0%
+clause. So if this one activates uh then
+ 
+
+ align:start position:0%
+clause. So if this one activates uh then
+these align and you're happy. If in
+
+ align:start position:0%
+these align and you're happy. If in
+ 
+
+ align:start position:0%
+these align and you're happy. If in
+general if you can get this column to
+
+ align:start position:0%
+general if you can get this column to
+ 
+
+ align:start position:0%
+general if you can get this column to
+fall you're going to be happy because
+
+ align:start position:0%
+fall you're going to be happy because
+ 
+
+ align:start position:0%
+fall you're going to be happy because
+above this thing is this reward gadget.
+
+ align:start position:0%
+above this thing is this reward gadget.
+ 
+
+ align:start position:0%
+above this thing is this reward gadget.
+If this column falls by one you get a
+
+ align:start position:0%
+If this column falls by one you get a
+ 
+
+ align:start position:0%
+If this column falls by one you get a
+million points. Okay. And every clause
+
+ align:start position:0%
+million points. Okay. And every clause
+ 
+
+ align:start position:0%
+million points. Okay. And every clause
+has its own reward of a million points.
+
+ align:start position:0%
+has its own reward of a million points.
+ 
+
+ align:start position:0%
+has its own reward of a million points.
+So and million here is like n squared or
+
+ align:start position:0%
+So and million here is like n squared or
+ 
+
+ align:start position:0%
+So and million here is like n squared or
+something. Uh so you really want to get
+
+ align:start position:0%
+something. Uh so you really want to get
+ 
+
+ align:start position:0%
+something. Uh so you really want to get
+these and the only way to do it is to
+
+ align:start position:0%
+these and the only way to do it is to
+ 
+
+ align:start position:0%
+these and the only way to do it is to
+satisfy the clauses. The only way to get
+
+ align:start position:0%
+satisfy the clauses. The only way to get
+ 
+
+ align:start position:0%
+satisfy the clauses. The only way to get
+all the points is to satisfy all the
+
+ align:start position:0%
+all the points is to satisfy all the
+ 
+
+ align:start position:0%
+all the points is to satisfy all the
+clauses. Okay. Now, uh the goal in this
+
+ align:start position:0%
+clauses. Okay. Now, uh the goal in this
+ 
+
+ align:start position:0%
+clauses. Okay. Now, uh the goal in this
+game, I didn't mention is to maximize
+
+ align:start position:0%
+game, I didn't mention is to maximize
+ 
+
+ align:start position:0%
+game, I didn't mention is to maximize
+the number of points you can get uh for
+
+ align:start position:0%
+the number of points you can get uh for
+ 
+
+ align:start position:0%
+the number of points you can get uh for
+a given number of moves. Usually in uh
+
+ align:start position:0%
+a given number of moves. Usually in uh
+ 
+
+ align:start position:0%
+a given number of moves. Usually in uh
+Candy Crush, you have a limited number
+
+ align:start position:0%
+Candy Crush, you have a limited number
+ 
+
+ align:start position:0%
+Candy Crush, you have a limited number
+of moves. Okay? So, the idea is you're
+
+ align:start position:0%
+of moves. Okay? So, the idea is you're
+ 
+
+ align:start position:0%
+of moves. Okay? So, the idea is you're
+just going to have enough moves to set
+
+ align:start position:0%
+just going to have enough moves to set
+ 
+
+ align:start position:0%
+just going to have enough moves to set
+each of the variables, right? If you end
+
+ align:start position:0%
+each of the variables, right? If you end
+ 
+
+ align:start position:0%
+each of the variables, right? If you end
+up setting one of the wires directly,
+
+ align:start position:0%
+up setting one of the wires directly,
+ 
+
+ align:start position:0%
+up setting one of the wires directly,
+you can trigger any wire by doing a
+
+ align:start position:0%
+you can trigger any wire by doing a
+ 
+
+ align:start position:0%
+you can trigger any wire by doing a
+little flip. You can say, "Oh, trigger
+
+ align:start position:0%
+little flip. You can say, "Oh, trigger
+ 
+
+ align:start position:0%
+little flip. You can say, "Oh, trigger
+this one wire." But that will satisfy at
+
+ align:start position:0%
+this one wire." But that will satisfy at
+ 
+
+ align:start position:0%
+this one wire." But that will satisfy at
+most one clause. Whereas if you do it on
+
+ align:start position:0%
+most one clause. Whereas if you do it on
+ 
+
+ align:start position:0%
+most one clause. Whereas if you do it on
+a variable, you're going to satisfy a
+
+ align:start position:0%
+a variable, you're going to satisfy a
+ 
+
+ align:start position:0%
+a variable, you're going to satisfy a
+bunch of clauses and that's clearly
+
+ align:start position:0%
+bunch of clauses and that's clearly
+ 
+
+ align:start position:0%
+bunch of clauses and that's clearly
+better. Uh so that's a bit of a argument
+
+ align:start position:0%
+better. Uh so that's a bit of a argument
+ 
+
+ align:start position:0%
+better. Uh so that's a bit of a argument
+you need to make. Uh it doesn't help
+
+ align:start position:0%
+you need to make. Uh it doesn't help
+ 
+
+ align:start position:0%
+you need to make. Uh it doesn't help
+enough. You could even set this wire and
+
+ align:start position:0%
+enough. You could even set this wire and
+ 
+
+ align:start position:0%
+enough. You could even set this wire and
+this wire uh you know an x wire and an
+
+ align:start position:0%
+this wire uh you know an x wire and an
+ 
+
+ align:start position:0%
+this wire uh you know an x wire and an
+xar wire. But uh you can show the claim
+
+ align:start position:0%
+xar wire. But uh you can show the claim
+ 
+
+ align:start position:0%
+xar wire. But uh you can show the claim
+is that will never uh buy you more uh
+
+ align:start position:0%
+is that will never uh buy you more uh
+ 
+
+ align:start position:0%
+is that will never uh buy you more uh
+that will never buy you as much as
+
+ align:start position:0%
+that will never buy you as much as
+ 
+
+ align:start position:0%
+that will never buy you as much as
+setting an entire variable. we set uh
+
+ align:start position:0%
+setting an entire variable. we set uh
+ 
+
+ align:start position:0%
+setting an entire variable. we set uh
+and here's the reason why uh I drew this
+
+ align:start position:0%
+and here's the reason why uh I drew this
+ 
+
+ align:start position:0%
+and here's the reason why uh I drew this
+picture simply that say oh for every
+
+ align:start position:0%
+picture simply that say oh for every
+ 
+
+ align:start position:0%
+picture simply that say oh for every
+clause we're going to have this picture
+
+ align:start position:0%
+clause we're going to have this picture
+ 
+
+ align:start position:0%
+clause we're going to have this picture
+connected to some variables in fact
+
+ align:start position:0%
+connected to some variables in fact
+ 
+
+ align:start position:0%
+connected to some variables in fact
+every time you have a clause you make a
+
+ align:start position:0%
+every time you have a clause you make a
+ 
+
+ align:start position:0%
+every time you have a clause you make a
+million copies of the clause a million
+
+ align:start position:0%
+million copies of the clause a million
+ 
+
+ align:start position:0%
+million copies of the clause a million
+is like n uh so that it's really worth
+
+ align:start position:0%
+is like n uh so that it's really worth
+ 
+
+ align:start position:0%
+is like n uh so that it's really worth
+setting the var every variable appears
+
+ align:start position:0%
+setting the var every variable appears
+ 
+
+ align:start position:0%
+setting the var every variable appears
+in in millions of clauses so you really
+
+ align:start position:0%
+in in millions of clauses so you really
+ 
+
+ align:start position:0%
+in in millions of clauses so you really
+want to set the variables if you just
+
+ align:start position:0%
+want to set the variables if you just
+ 
+
+ align:start position:0%
+want to set the variables if you just
+satisfy one measly clause and get one
+
+ align:start position:0%
+satisfy one measly clause and get one
+ 
+
+ align:start position:0%
+satisfy one measly clause and get one
+measly million points it's not worth it
+
+ align:start position:0%
+measly million points it's not worth it
+ 
+
+ align:start position:0%
+measly million points it's not worth it
+but if you You can get a million times a
+
+ align:start position:0%
+but if you You can get a million times a
+ 
+
+ align:start position:0%
+but if you You can get a million times a
+million points. Whoa. Trillion points.
+
+ align:start position:0%
+million points. Whoa. Trillion points.
+ 
+
+ align:start position:0%
+million points. Whoa. Trillion points.
+Okay. So that's why you should only set
+
+ align:start position:0%
+Okay. So that's why you should only set
+ 
+
+ align:start position:0%
+Okay. So that's why you should only set
+variables, not set wires directly.
+
+ align:start position:0%
+variables, not set wires directly.
+ 
+
+ align:start position:0%
+variables, not set wires directly.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+I think I have roughly covered this
+
+ align:start position:0%
+I think I have roughly covered this
+ 
+
+ align:start position:0%
+I think I have roughly covered this
+proof except I didn't go up the chain.
+
+ align:start position:0%
+proof except I didn't go up the chain.
+ 
+
+ align:start position:0%
+proof except I didn't go up the chain.
+Uh here setting X1 bar doesn't do much
+
+ align:start position:0%
+Uh here setting X1 bar doesn't do much
+ 
+
+ align:start position:0%
+Uh here setting X1 bar doesn't do much
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+setting one or the other of these ends
+
+ align:start position:0%
+setting one or the other of these ends
+ 
+
+ align:start position:0%
+setting one or the other of these ends
+up shifting all of these things by one
+
+ align:start position:0%
+up shifting all of these things by one
+ 
+
+ align:start position:0%
+up shifting all of these things by one
+which ends up clearing this which shifts
+
+ align:start position:0%
+which ends up clearing this which shifts
+ 
+
+ align:start position:0%
+which ends up clearing this which shifts
+all of these columns by one. And
+
+ align:start position:0%
+all of these columns by one. And
+ 
+
+ align:start position:0%
+all of these columns by one. And
+basically things look really spread out
+
+ align:start position:0%
+basically things look really spread out
+ 
+
+ align:start position:0%
+basically things look really spread out
+here but as you work your way up they're
+
+ align:start position:0%
+here but as you work your way up they're
+ 
+
+ align:start position:0%
+here but as you work your way up they're
+coming more and more into alignment. So
+
+ align:start position:0%
+coming more and more into alignment. So
+ 
+
+ align:start position:0%
+coming more and more into alignment. So
+the idea is as long as things resolve
+
+ align:start position:0%
+the idea is as long as things resolve
+ 
+
+ align:start position:0%
+the idea is as long as things resolve
+from bottom to top um you fir well it
+
+ align:start position:0%
+from bottom to top um you fir well it
+ 
+
+ align:start position:0%
+from bottom to top um you fir well it
+doesn't yeah
+
+ align:start position:0%
+doesn't yeah
+ 
+
+ align:start position:0%
+doesn't yeah
+uh yeah then first you figure out
+
+ align:start position:0%
+uh yeah then first you figure out
+ 
+
+ align:start position:0%
+uh yeah then first you figure out
+whether x1 satisfy the clause if it
+
+ align:start position:0%
+whether x1 satisfy the clause if it
+ 
+
+ align:start position:0%
+whether x1 satisfy the clause if it
+doesn't it sets things up for x2 and
+
+ align:start position:0%
+doesn't it sets things up for x2 and
+ 
+
+ align:start position:0%
+doesn't it sets things up for x2 and
+then maybe x2 satisfies the clause if it
+
+ align:start position:0%
+then maybe x2 satisfies the clause if it
+ 
+
+ align:start position:0%
+then maybe x2 satisfies the clause if it
+doesn't it sets things up for x3 here
+
+ align:start position:0%
+doesn't it sets things up for x3 here
+ 
+
+ align:start position:0%
+doesn't it sets things up for x3 here
+they're spread out even more but by the
+
+ align:start position:0%
+they're spread out even more but by the
+ 
+
+ align:start position:0%
+they're spread out even more but by the
+time you've done these things below uh
+
+ align:start position:0%
+time you've done these things below uh
+ 
+
+ align:start position:0%
+time you've done these things below uh
+that that thing will be ready
+
+ align:start position:0%
+that that thing will be ready
+ 
+
+ align:start position:0%
+that that thing will be ready
+okay so that was the first proof
+
+ align:start position:0%
+okay so that was the first proof
+ 
+
+ align:start position:0%
+okay so that was the first proof
+The second proof uh uh sorry before
+
+ align:start position:0%
+The second proof uh uh sorry before
+ 
+
+ align:start position:0%
+The second proof uh uh sorry before
+interlude uh Candy Crush is based on a
+
+ align:start position:0%
+interlude uh Candy Crush is based on a
+ 
+
+ align:start position:0%
+interlude uh Candy Crush is based on a
+variety of games. Um most famous is
+
+ align:start position:0%
+variety of games. Um most famous is
+ 
+
+ align:start position:0%
+variety of games. Um most famous is
+Bejeweled but there's a long history of
+
+ align:start position:0%
+Bejeweled but there's a long history of
+ 
+
+ align:start position:0%
+Bejeweled but there's a long history of
+even Tetris is in there but uh there's a
+
+ align:start position:0%
+even Tetris is in there but uh there's a
+ 
+
+ align:start position:0%
+even Tetris is in there but uh there's a
+long history of match three games and
+
+ align:start position:0%
+long history of match three games and
+ 
+
+ align:start position:0%
+long history of match three games and
+pretty much all of these are nplete. I
+
+ align:start position:0%
+pretty much all of these are nplete. I
+ 
+
+ align:start position:0%
+pretty much all of these are nplete. I
+don't know the details of all of them,
+
+ align:start position:0%
+don't know the details of all of them,
+ 
+
+ align:start position:0%
+don't know the details of all of them,
+but there's this paper uh by three
+
+ align:start position:0%
+but there's this paper uh by three
+ 
+
+ align:start position:0%
+but there's this paper uh by three
+authors a little bit later in the year
+
+ align:start position:0%
+authors a little bit later in the year
+ 
+
+ align:start position:0%
+authors a little bit later in the year
+uh that proves basically all of these
+
+ align:start position:0%
+uh that proves basically all of these
+ 
+
+ align:start position:0%
+uh that proves basically all of these
+games are emptying complete even when
+
+ align:start position:0%
+games are emptying complete even when
+ 
+
+ align:start position:0%
+games are emptying complete even when
+you're not given a move limit. So this
+
+ align:start position:0%
+you're not given a move limit. So this
+ 
+
+ align:start position:0%
+you're not given a move limit. So this
+is interesting in Bejeweled the goal is
+
+ align:start position:0%
+is interesting in Bejeweled the goal is
+ 
+
+ align:start position:0%
+is interesting in Bejeweled the goal is
+just to maximize your score. You don't
+
+ align:start position:0%
+just to maximize your score. You don't
+ 
+
+ align:start position:0%
+just to maximize your score. You don't
+necessarily have a limit on the number
+
+ align:start position:0%
+necessarily have a limit on the number
+ 
+
+ align:start position:0%
+necessarily have a limit on the number
+of moves unlike Candy Crush. Uh so or in
+
+ align:start position:0%
+of moves unlike Candy Crush. Uh so or in
+ 
+
+ align:start position:0%
+of moves unlike Candy Crush. Uh so or in
+also in some levels of Candy Crush it's
+
+ align:start position:0%
+also in some levels of Candy Crush it's
+ 
+
+ align:start position:0%
+also in some levels of Candy Crush it's
+like that. So uh here it was very
+
+ align:start position:0%
+like that. So uh here it was very
+ 
+
+ align:start position:0%
+like that. So uh here it was very
+crucial that we only had enough moves to
+
+ align:start position:0%
+crucial that we only had enough moves to
+ 
+
+ align:start position:0%
+crucial that we only had enough moves to
+trigger all the variables. We didn't
+
+ align:start position:0%
+trigger all the variables. We didn't
+ 
+
+ align:start position:0%
+trigger all the variables. We didn't
+want to be able to do other things. Um,
+
+ align:start position:0%
+want to be able to do other things. Um,
+ 
+
+ align:start position:0%
+want to be able to do other things. Um,
+so here's a different proof and I'm just
+
+ align:start position:0%
+so here's a different proof and I'm just
+ 
+
+ align:start position:0%
+so here's a different proof and I'm just
+going to give the highle picture. Uh,
+
+ align:start position:0%
+going to give the highle picture. Uh,
+ 
+
+ align:start position:0%
+going to give the highle picture. Uh,
+basically, uh, this is cool because even
+
+ align:start position:0%
+basically, uh, this is cool because even
+ 
+
+ align:start position:0%
+basically, uh, this is cool because even
+just figuring out whether you can get
+
+ align:start position:0%
+just figuring out whether you can get
+ 
+
+ align:start position:0%
+just figuring out whether you can get
+this one gem, this one, uh, candy is
+
+ align:start position:0%
+this one gem, this one, uh, candy is
+ 
+
+ align:start position:0%
+this one gem, this one, uh, candy is
+hard. Uh, in order to do so, you have to
+
+ align:start position:0%
+hard. Uh, in order to do so, you have to
+ 
+
+ align:start position:0%
+hard. Uh, in order to do so, you have to
+line up all of these things for each
+
+ align:start position:0%
+line up all of these things for each
+ 
+
+ align:start position:0%
+line up all of these things for each
+clause.
+
+ align:start position:0%
+clause.
+ 
+
+ align:start position:0%
+clause.
+And here it's a reduction from exactly
+
+ align:start position:0%
+And here it's a reduction from exactly
+ 
+
+ align:start position:0%
+And here it's a reduction from exactly
+one three set, one and three set. So
+
+ align:start position:0%
+one three set, one and three set. So
+ 
+
+ align:start position:0%
+one three set, one and three set. So
+only if exactly one of the variables
+
+ align:start position:0%
+only if exactly one of the variables
+ 
+
+ align:start position:0%
+only if exactly one of the variables
+gets set correctly does this shift to
+
+ align:start position:0%
+gets set correctly does this shift to
+ 
+
+ align:start position:0%
+gets set correctly does this shift to
+the right level. And only when all of
+
+ align:start position:0%
+the right level. And only when all of
+ 
+
+ align:start position:0%
+the right level. And only when all of
+these are shifted to the right level can
+
+ align:start position:0%
+these are shifted to the right level can
+ 
+
+ align:start position:0%
+these are shifted to the right level can
+you trigger this wire to go all the way
+
+ align:start position:0%
+you trigger this wire to go all the way
+ 
+
+ align:start position:0%
+you trigger this wire to go all the way
+here and get that guy. And it's the only
+
+ align:start position:0%
+here and get that guy. And it's the only
+ 
+
+ align:start position:0%
+here and get that guy. And it's the only
+way to get that guy. You can't do it
+
+ align:start position:0%
+way to get that guy. You can't do it
+ 
+
+ align:start position:0%
+way to get that guy. You can't do it
+directly. You can only be triggered from
+
+ align:start position:0%
+directly. You can only be triggered from
+ 
+
+ align:start position:0%
+directly. You can only be triggered from
+the left hand side. And there's also a
+
+ align:start position:0%
+the left hand side. And there's also a
+ 
+
+ align:start position:0%
+the left hand side. And there's also a
+sequencer over here which forces all of
+
+ align:start position:0%
+sequencer over here which forces all of
+ 
+
+ align:start position:0%
+sequencer over here which forces all of
+the variables to get set before this
+
+ align:start position:0%
+the variables to get set before this
+ 
+
+ align:start position:0%
+the variables to get set before this
+happens. Uh so it's a little tricky
+
+ align:start position:0%
+happens. Uh so it's a little tricky
+ 
+
+ align:start position:0%
+happens. Uh so it's a little tricky
+because you don't want to have to you
+
+ align:start position:0%
+because you don't want to have to you
+ 
+
+ align:start position:0%
+because you don't want to have to you
+don't want it to be you could set half
+
+ align:start position:0%
+don't want it to be you could set half
+ 
+
+ align:start position:0%
+don't want it to be you could set half
+of them and then trigger this and then
+
+ align:start position:0%
+of them and then trigger this and then
+ 
+
+ align:start position:0%
+of them and then trigger this and then
+things happen to align in a cheating
+
+ align:start position:0%
+things happen to align in a cheating
+ 
+
+ align:start position:0%
+things happen to align in a cheating
+way. The details are complicated, but
+
+ align:start position:0%
+way. The details are complicated, but
+ 
+
+ align:start position:0%
+way. The details are complicated, but
+they actually implemented their
+
+ align:start position:0%
+they actually implemented their
+ 
+
+ align:start position:0%
+they actually implemented their
+reduction.
+
+ align:start position:0%
+reduction.
+ 
+
+ align:start position:0%
+reduction.
+Uh, so this is it. Now there, as it says
+
+ align:start position:0%
+Uh, so this is it. Now there, as it says
+ 
+
+ align:start position:0%
+Uh, so this is it. Now there, as it says
+here, there are 4,000 rows above and
+
+ align:start position:0%
+here, there are 4,000 rows above and
+ 
+
+ align:start position:0%
+here, there are 4,000 rows above and
+2,000 rows below. So it's a large
+
+ align:start position:0%
+2,000 rows below. So it's a large
+ 
+
+ align:start position:0%
+2,000 rows below. So it's a large
+construction and this is for this
+
+ align:start position:0%
+construction and this is for this
+ 
+
+ align:start position:0%
+construction and this is for this
+formula.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, I can clean it up a little bit.
+
+ align:start position:0%
+Um, I can clean it up a little bit.
+ 
+
+ align:start position:0%
+Um, I can clean it up a little bit.
+Remove the again there's a background
+
+ align:start position:0%
+Remove the again there's a background
+ 
+
+ align:start position:0%
+Remove the again there's a background
+checkerboard pattern here. So if I
+
+ align:start position:0%
+checkerboard pattern here. So if I
+ 
+
+ align:start position:0%
+checkerboard pattern here. So if I
+generate instance then uh things are a
+
+ align:start position:0%
+generate instance then uh things are a
+ 
+
+ align:start position:0%
+generate instance then uh things are a
+little bit cleaner and I think
+
+ align:start position:0%
+little bit cleaner and I think
+ 
+
+ align:start position:0%
+little bit cleaner and I think
+highlighted in red are the moves you can
+
+ align:start position:0%
+highlighted in red are the moves you can
+ 
+
+ align:start position:0%
+highlighted in red are the moves you can
+make. So here's the first variable. You
+
+ align:start position:0%
+make. So here's the first variable. You
+ 
+
+ align:start position:0%
+make. So here's the first variable. You
+can either uh let's do the simple one
+
+ align:start position:0%
+can either uh let's do the simple one
+ 
+
+ align:start position:0%
+can either uh let's do the simple one
+first. Move this guy with this one and
+
+ align:start position:0%
+first. Move this guy with this one and
+ 
+
+ align:start position:0%
+first. Move this guy with this one and
+then trigger trigger trigger. All this
+
+ align:start position:0%
+then trigger trigger trigger. All this
+ 
+
+ align:start position:0%
+then trigger trigger trigger. All this
+happens without you able to do anything.
+
+ align:start position:0%
+happens without you able to do anything.
+ 
+
+ align:start position:0%
+happens without you able to do anything.
+And that will move some stuff up top. Um
+
+ align:start position:0%
+And that will move some stuff up top. Um
+ 
+
+ align:start position:0%
+And that will move some stuff up top. Um
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+uh we can move this one here and then
+
+ align:start position:0%
+uh we can move this one here and then
+ 
+
+ align:start position:0%
+uh we can move this one here and then
+this is fun. The variable goes down and
+
+ align:start position:0%
+this is fun. The variable goes down and
+ 
+
+ align:start position:0%
+this is fun. The variable goes down and
+it just keeps it goes down basically to
+
+ align:start position:0%
+it just keeps it goes down basically to
+ 
+
+ align:start position:0%
+it just keeps it goes down basically to
+where the x1 bar is down here and then
+
+ align:start position:0%
+where the x1 bar is down here and then
+ 
+
+ align:start position:0%
+where the x1 bar is down here and then
+it triggers that guy and maybe that guy
+
+ align:start position:0%
+it triggers that guy and maybe that guy
+ 
+
+ align:start position:0%
+it triggers that guy and maybe that guy
+also. Okay. And that one and that one.
+
+ align:start position:0%
+also. Okay. And that one and that one.
+ 
+
+ align:start position:0%
+also. Okay. And that one and that one.
+Okay. Uh, lots of stuff happens. Anyway,
+
+ align:start position:0%
+Okay. Uh, lots of stuff happens. Anyway,
+ 
+
+ align:start position:0%
+Okay. Uh, lots of stuff happens. Anyway,
+eventually we'll get down to X2 and
+
+ align:start position:0%
+eventually we'll get down to X2 and
+ 
+
+ align:start position:0%
+eventually we'll get down to X2 and
+we'll be able to set it one way or the
+
+ align:start position:0%
+we'll be able to set it one way or the
+ 
+
+ align:start position:0%
+we'll be able to set it one way or the
+other. Uh, so the details are obviously
+
+ align:start position:0%
+other. Uh, so the details are obviously
+ 
+
+ align:start position:0%
+other. Uh, so the details are obviously
+a little bit complicated, but clearly
+
+ align:start position:0%
+a little bit complicated, but clearly
+ 
+
+ align:start position:0%
+a little bit complicated, but clearly
+they've been explicitly worked out
+
+ align:start position:0%
+they've been explicitly worked out
+ 
+
+ align:start position:0%
+they've been explicitly worked out
+because they can even play the game,
+
+ align:start position:0%
+because they can even play the game,
+ 
+
+ align:start position:0%
+because they can even play the game,
+which is pretty awesome. Uh, anyway, and
+
+ align:start position:0%
+which is pretty awesome. Uh, anyway, and
+ 
+
+ align:start position:0%
+which is pretty awesome. Uh, anyway, and
+they also have the greatest URL, uh,
+
+ align:start position:0%
+they also have the greatest URL, uh,
+ 
+
+ align:start position:0%
+they also have the greatest URL, uh,
+candycrush.ismpnard.com.
+
+ align:start position:0%
+candycrush.ismpnard.com.
+ 
+
+ align:start position:0%
+candycrush.ismpnard.com.
+We should try to get other
+
+ align:start position:0%
+We should try to get other
+ 
+
+ align:start position:0%
+We should try to get other
+things.ismpnard.com.
+
+ align:start position:0%
+things.ismpnard.com.
+ 
+
+ align:start position:0%
+things.ismpnard.com.
+Um, and that is Candy Crush and
+
+ align:start position:0%
+Um, and that is Candy Crush and
+ 
+
+ align:start position:0%
+Um, and that is Candy Crush and
+Bejeweled and all of its friends RNP
+
+ align:start position:0%
+Bejeweled and all of its friends RNP
+ 
+
+ align:start position:0%
+Bejeweled and all of its friends RNP
+hard. Uh, and I think that's it unless
+
+ align:start position:0%
+hard. Uh, and I think that's it unless
+ 
+
+ align:start position:0%
+hard. Uh, and I think that's it unless
+there are questions.
+
+ align:start position:0%
+there are questions.
+ 
+
+ align:start position:0%
+there are questions.
+Uh, so we've just started to scratch the
+
+ align:start position:0%
+Uh, so we've just started to scratch the
+ 
+
+ align:start position:0%
+Uh, so we've just started to scratch the
+surface on the idea that planer graphs
+
+ align:start position:0%
+surface on the idea that planer graphs
+ 
+
+ align:start position:0%
+surface on the idea that planer graphs
+are hard and next class we'll see planer
+
+ align:start position:0%
+are hard and next class we'll see planer
+ 
+
+ align:start position:0%
+are hard and next class we'll see planer
+versions of threes and one and three
+
+ align:start position:0%
+versions of threes and one and three
+ 
+
+ align:start position:0%
+versions of threes and one and three
+setat which we weren't using here. This
+
+ align:start position:0%
+setat which we weren't using here. This
+ 
+
+ align:start position:0%
+setat which we weren't using here. This
+is using a non-pler thing. Uh, so that
+
+ align:start position:0%
+is using a non-pler thing. Uh, so that
+ 
+
+ align:start position:0%
+is using a non-pler thing. Uh, so that
+will that helps with a lot of proofs
+
+ align:start position:0%
+will that helps with a lot of proofs
+ 
+
+ align:start position:0%
+will that helps with a lot of proofs
+especially ones that happen in the
+
+ align:start position:0%
+especially ones that happen in the
+ 
+
+ align:start position:0%
+especially ones that happen in the
+plane.
+
+ align:start position:0%
+plane.
+ 
+
+ align:start position:0%
+plane.
+Um so we've seen it with planer circuit
+
+ align:start position:0%
+Um so we've seen it with planer circuit
+ 
+
+ align:start position:0%
+Um so we've seen it with planer circuit
+set but next we'll do planer three set
+
+ align:start position:0%
+set but next we'll do planer three set
+ 
+
+ align:start position:0%
+set but next we'll do planer three set
+planer one and three setat planer not
+
+ align:start position:0%
+planer one and three setat planer not
+ 
+
+ align:start position:0%
+planer one and three setat planer not
+all equal sat those kinds of things and
+
+ align:start position:0%
+all equal sat those kinds of things and
+ 
+
+ align:start position:0%
+all equal sat those kinds of things and
+again be able to avoid crossovers which
+
+ align:start position:0%
+again be able to avoid crossovers which
+ 
+
+ align:start position:0%
+again be able to avoid crossovers which
+is nice.
+
+ align:start position:0%
+is nice.
+ 
+
+ align:start position:0%
+is nice.
+Cool.
\ No newline at end of file
diff --git a/zvu9SoCyDec.txt b/zvu9SoCyDec.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f01fc3156c059114119f83e6fcbf30110d85c1a8
--- /dev/null
+++ b/zvu9SoCyDec.txt
@@ -0,0 +1,7790 @@
+align:start position:0%
+ 
+okay we'll go through these together
+
+ align:start position:0%
+okay we'll go through these together
+ 
+
+ align:start position:0%
+okay we'll go through these together
+repeat after me civil civil civility
+
+ align:start position:0%
+repeat after me civil civil civility
+ 
+
+ align:start position:0%
+repeat after me civil civil civility
+civility civilized civilized
+
+ align:start position:0%
+civility civilized civilized
+ 
+
+ align:start position:0%
+civility civilized civilized
+civilization civilization equal equal
+
+ align:start position:0%
+civilization civilization equal equal
+ 
+
+ align:start position:0%
+civilization civilization equal equal
+equality equality equalize equalize
+
+ align:start position:0%
+equality equality equalize equalize
+ 
+
+ align:start position:0%
+equality equality equalize equalize
+Equalization Equalization fertile
+
+ align:start position:0%
+Equalization Equalization fertile
+ 
+
+ align:start position:0%
+Equalization Equalization fertile
+fertile fertility fertility fertilize
+
+ align:start position:0%
+fertile fertility fertility fertilize
+ 
+
+ align:start position:0%
+fertile fertility fertility fertilize
+fertilize fertilization fertilization
+
+ align:start position:0%
+fertilize fertilization fertilization
+ 
+
+ align:start position:0%
+fertilize fertilization fertilization
+final final finale
+
+ align:start position:0%
+final final finale
+ 
+
+ align:start position:0%
+final final finale
+finality finalize finalize finalization
+
+ align:start position:0%
+finality finalize finalize finalization
+ 
+
+ align:start position:0%
+finality finalize finalize finalization
+finalization General General generality
+
+ align:start position:0%
+finalization General General generality
+ 
+
+ align:start position:0%
+finalization General General generality
+generality generalize generalize
+
+ align:start position:0%
+generality generalize generalize
+ 
+
+ align:start position:0%
+generality generalize generalize
+generalization generalization hospital
+
+ align:start position:0%
+generalization generalization hospital
+ 
+
+ align:start position:0%
+generalization generalization hospital
+hospital Hospitality Hospitality
+
+ align:start position:0%
+hospital Hospitality Hospitality
+ 
+
+ align:start position:0%
+hospital Hospitality Hospitality
+hospitalized hospitalized
+
+ align:start position:0%
+hospitalized hospitalized
+ 
+
+ align:start position:0%
+hospitalized hospitalized
+hospitalization hospitalization legal
+
+ align:start position:0%
+hospitalization hospitalization legal
+ 
+
+ align:start position:0%
+hospitalization hospitalization legal
+legal legality legality legalize
+
+ align:start position:0%
+legal legality legality legalize
+ 
+
+ align:start position:0%
+legal legality legality legalize
+legalize legalization legalization
+
+ align:start position:0%
+legalize legalization legalization
+ 
+
+ align:start position:0%
+legalize legalization legalization
+mobile mobile Mobility Mobility mobilize
+
+ align:start position:0%
+mobile mobile Mobility Mobility mobilize
+ 
+
+ align:start position:0%
+mobile mobile Mobility Mobility mobilize
+mobilize mobilization mobilization
+
+ align:start position:0%
+mobilize mobilization mobilization
+ 
+
+ align:start position:0%
+mobilize mobilization mobilization
+National National nationality
+
+ align:start position:0%
+National National nationality
+ 
+
+ align:start position:0%
+National National nationality
+nationality nationalize nationalize
+
+ align:start position:0%
+nationality nationalize nationalize
+ 
+
+ align:start position:0%
+nationality nationalize nationalize
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+
+ align:start position:0%
+nationalization nationalization neutral
+ 
+
+ align:start position:0%
+nationalization nationalization neutral
+neutral neutrality neutrality NE
+
+ align:start position:0%
+neutral neutrality neutrality NE
+ 
+
+ align:start position:0%
+neutral neutrality neutrality NE
+neutralize neutralized neutralization
+
+ align:start position:0%
+neutralize neutralized neutralization
+ 
+
+ align:start position:0%
+neutralize neutralized neutralization
+neutralization personal personal
+
+ align:start position:0%
+neutralization personal personal
+ 
+
+ align:start position:0%
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+personality personality personalize
+
+ align:start position:0%
+personality personality personalize
+ 
+
+ align:start position:0%
+personality personality personalize
+personalized personalization personaliz
+
+ align:start position:0%
+personalized personalization personaliz
+ 
+
+ align:start position:0%
+personalized personalization personaliz
+realation real real reality reality
+
+ align:start position:0%
+realation real real reality reality
+ 
+
+ align:start position:0%
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+realize realize realization realization
+
+ align:start position:0%
+realize realize realization realization
+ 
+
+ align:start position:0%
+realize realize realization realization
+stable stable stability stability
+
+ align:start position:0%
+stable stable stability stability
+ 
+
+ align:start position:0%
+stable stable stability stability
+stabilize stabilize stabilization
+
+ align:start position:0%
+stabilize stabilize stabilization
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+stabilization sterile sterile sterility
+ 
+
+ align:start position:0%
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+sterility sterilize sterilize
+
+ align:start position:0%
+sterility sterilize sterilize
+ 
+
+ align:start position:0%
+sterility sterilize sterilize
+sterilization sterilization
+
+ align:start position:0%
+sterilization sterilization
+ 
+
+ align:start position:0%
+sterilization sterilization
+sterilization
+
+ align:start position:0%
+sterilization
+ 
+
+ align:start position:0%
+sterilization
+okay so we're going to go like this
+
+ align:start position:0%
+okay so we're going to go like this
+ 
+
+ align:start position:0%
+okay so we're going to go like this
+like this okay like this each person
+
+ align:start position:0%
+like this okay like this each person
+ 
+
+ align:start position:0%
+like this okay like this each person
+reads each one word starting with Geno
+
+ align:start position:0%
+reads each one word starting with Geno
+ 
+
+ align:start position:0%
+reads each one word starting with Geno
+loud as loudly as possible one word
+
+ align:start position:0%
+loud as loudly as possible one word
+ 
+
+ align:start position:0%
+loud as loudly as possible one word
+cability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+civilized civiliz civilized
+
+ align:start position:0%
+civilized civiliz civilized
+ 
+
+ align:start position:0%
+civilized civiliz civilized
+Cil civilized civiliz next civilization
+
+ align:start position:0%
+Cil civilized civiliz next civilization
+ 
+
+ align:start position:0%
+Cil civilized civiliz next civilization
+equal equality
+
+ align:start position:0%
+equal equality
+ 
+
+ align:start position:0%
+equal equality
+equalize Equalization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F becomes a FL ferle ferle next
+
+ align:start position:0%
+F becomes a FL ferle ferle next
+ 
+
+ align:start position:0%
+F becomes a FL ferle ferle next
+fertility very good next F fer
+
+ align:start position:0%
+fertility very good next F fer
+ 
+
+ align:start position:0%
+fertility very good next F fer
+fation
+
+ align:start position:0%
+fation
+ 
+
+ align:start position:0%
+fation
+fation
+
+ align:start position:0%
+fation
+ 
+
+ align:start position:0%
+fation
+fer
+
+ align:start position:0%
+fer
+ 
+
+ align:start position:0%
+fer
+this is very difficult because you have
+
+ align:start position:0%
+this is very difficult because you have
+ 
+
+ align:start position:0%
+this is very difficult because you have
+the r and the flat fle
+
+ align:start position:0%
+the r and the flat fle
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+ferle
+ 
+
+ align:start position:0%
+ferle
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+I think uh fertile fertile I think
+
+ align:start position:0%
+I think uh fertile fertile I think
+ 
+
+ align:start position:0%
+I think uh fertile fertile I think
+that's uh British English fertile know
+
+ align:start position:0%
+that's uh British English fertile know
+ 
+
+ align:start position:0%
+that's uh British English fertile know
+but here in America we usually say
+
+ align:start position:0%
+but here in America we usually say
+ 
+
+ align:start position:0%
+but here in America we usually say
+fertile ferle
+
+ align:start position:0%
+fertile ferle
+ 
+
+ align:start position:0%
+fertile ferle
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+louder
+
+ align:start position:0%
+louder
+ 
+
+ align:start position:0%
+louder
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+generality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good generaliz very good
+
+ align:start position:0%
+very good generaliz very good
+ 
+
+ align:start position:0%
+very good generaliz very good
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+generalization okay generalization
+
+ align:start position:0%
+generalization okay generalization
+ 
+
+ align:start position:0%
+generalization okay generalization
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+usually General love J and a j and a j
+
+ align:start position:0%
+usually General love J and a j and a j
+ 
+
+ align:start position:0%
+usually General love J and a j and a j
+and z generalization
+
+ align:start position:0%
+and z generalization
+ 
+
+ align:start position:0%
+and z generalization
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+very good next Hospitality huh
+
+ align:start position:0%
+very good next Hospitality huh
+ 
+
+ align:start position:0%
+very good next Hospitality huh
+Hospitality
+
+ align:start position:0%
+Hospitality
+ 
+
+ align:start position:0%
+Hospitality
+hosp okay first one what's the first one
+
+ align:start position:0%
+hosp okay first one what's the first one
+ 
+
+ align:start position:0%
+hosp okay first one what's the first one
+hospital hospital becomes T becomes a
+
+ align:start position:0%
+hospital hospital becomes T becomes a
+ 
+
+ align:start position:0%
+hospital hospital becomes T becomes a
+flat right Hospital what happens to the
+
+ align:start position:0%
+flat right Hospital what happens to the
+ 
+
+ align:start position:0%
+flat right Hospital what happens to the
+next one
+
+ align:start position:0%
+next one
+ 
+
+ align:start position:0%
+next one
+Hospitality
+
+ align:start position:0%
+Hospitality
+ 
+
+ align:start position:0%
+Hospitality
+Hospitality why
+
+ align:start position:0%
+Hospitality why
+ 
+
+ align:start position:0%
+Hospitality why
+stress stress okay one more time
+
+ align:start position:0%
+stress stress okay one more time
+ 
+
+ align:start position:0%
+stress stress okay one more time
+Hospitality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hospitality Hospitality hospitality very
+
+ align:start position:0%
+Hospitality Hospitality hospitality very
+ 
+
+ align:start position:0%
+Hospitality Hospitality hospitality very
+good next uh starting with J again
+
+ align:start position:0%
+good next uh starting with J again
+ 
+
+ align:start position:0%
+good next uh starting with J again
+hospitalize
+
+ align:start position:0%
+hospitalize
+ 
+
+ align:start position:0%
+hospitalize
+hospitalize
+
+ align:start position:0%
+hospitalize
+ 
+
+ align:start position:0%
+hospitalize
+okay give us the flat hospitalize
+
+ align:start position:0%
+okay give us the flat hospitalize
+ 
+
+ align:start position:0%
+okay give us the flat hospitalize
+hospitalize hospitalize hospitalize next
+
+ align:start position:0%
+hospitalize hospitalize hospitalize next
+ 
+
+ align:start position:0%
+hospitalize hospitalize hospitalize next
+hospitalization
+
+ align:start position:0%
+hospitalization
+ 
+
+ align:start position:0%
+hospitalization
+Hospital okay next
+
+ align:start position:0%
+Hospital okay next
+ 
+
+ align:start position:0%
+Hospital okay next
+next legality
+
+ align:start position:0%
+next legality
+ 
+
+ align:start position:0%
+next legality
+legality leg use a legality or legal
+
+ align:start position:0%
+legality leg use a legality or legal
+ 
+
+ align:start position:0%
+legality leg use a legality or legal
+that's fine legality next legalize next
+
+ align:start position:0%
+that's fine legality next legalize next
+ 
+
+ align:start position:0%
+that's fine legality next legalize next
+I'm sorry legalization huh legalization
+
+ align:start position:0%
+I'm sorry legalization huh legalization
+ 
+
+ align:start position:0%
+I'm sorry legalization huh legalization
+very good next mobile perfect mobile
+
+ align:start position:0%
+very good next mobile perfect mobile
+ 
+
+ align:start position:0%
+very good next mobile perfect mobile
+okay mobile stress is a mo so it becomes
+
+ align:start position:0%
+okay mobile stress is a mo so it becomes
+ 
+
+ align:start position:0%
+okay mobile stress is a mo so it becomes
+M mile okay next Mobility perfect next
+
+ align:start position:0%
+M mile okay next Mobility perfect next
+ 
+
+ align:start position:0%
+M mile okay next Mobility perfect next
+mobilize perfect next mobilization good
+
+ align:start position:0%
+mobilize perfect next mobilization good
+ 
+
+ align:start position:0%
+mobilize perfect next mobilization good
+next national good next nationality
+
+ align:start position:0%
+next national good next nationality
+ 
+
+ align:start position:0%
+next national good next nationality
+huh nationality
+
+ align:start position:0%
+huh nationality
+ 
+
+ align:start position:0%
+huh nationality
+give us the flat
+
+ align:start position:0%
+give us the flat
+ 
+
+ align:start position:0%
+give us the flat
+nationality
+
+ align:start position:0%
+nationality
+ 
+
+ align:start position:0%
+nationality
+nationality
+
+ align:start position:0%
+nationality
+ 
+
+ align:start position:0%
+nationality
+a okay nationality next
+
+ align:start position:0%
+a okay nationality next
+ 
+
+ align:start position:0%
+a okay nationality next
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+neutal neutrality neut t r TR R together
+
+ align:start position:0%
+neutal neutrality neut t r TR R together
+ 
+
+ align:start position:0%
+neutal neutrality neut t r TR R together
+TR R whenever you have TR together T
+
+ align:start position:0%
+TR R whenever you have TR together T
+ 
+
+ align:start position:0%
+TR R whenever you have TR together T
+sounds like what two like tree tree tree
+
+ align:start position:0%
+sounds like what two like tree tree tree
+ 
+
+ align:start position:0%
+sounds like what two like tree tree tree
+like church so ne ne liing neutrality
+
+ align:start position:0%
+like church so ne ne liing neutrality
+ 
+
+ align:start position:0%
+like church so ne ne liing neutrality
+many times Neal how many times Neal no
+
+ align:start position:0%
+many times Neal how many times Neal no
+ 
+
+ align:start position:0%
+many times Neal how many times Neal no
+no no
+
+ align:start position:0%
+no no
+ 
+
+ align:start position:0%
+no no
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good neutrality
+
+ align:start position:0%
+very good neutrality
+ 
+
+ align:start position:0%
+very good neutrality
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+next neutralization next personal next
+
+ align:start position:0%
+next neutralization next personal next
+ 
+
+ align:start position:0%
+next neutralization next personal next
+was the flap personality very good
+
+ align:start position:0%
+was the flap personality very good
+ 
+
+ align:start position:0%
+was the flap personality very good
+personality
+
+ align:start position:0%
+personality
+ 
+
+ align:start position:0%
+personality
+next personal next personalization next
+
+ align:start position:0%
+next personal next personalization next
+ 
+
+ align:start position:0%
+next personal next personalization next
+uh you know real next reality next
+
+ align:start position:0%
+uh you know real next reality next
+ 
+
+ align:start position:0%
+uh you know real next reality next
+real realize realize realize realize
+
+ align:start position:0%
+real realize realize realize realize
+ 
+
+ align:start position:0%
+real realize realize realize realize
+next realization next stable next
+
+ align:start position:0%
+next realization next stable next
+ 
+
+ align:start position:0%
+next realization next stable next
+stability stability stability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+stability stability stability
+
+ align:start position:0%
+stability stability stability
+ 
+
+ align:start position:0%
+stability stability stability
+stabilize huh stabilize
+
+ align:start position:0%
+stabilize huh stabilize
+ 
+
+ align:start position:0%
+stabilize huh stabilize
+stabilize
+
+ align:start position:0%
+stabilize
+ 
+
+ align:start position:0%
+stabilize
+St a a stabilize stabilize stabilize
+
+ align:start position:0%
+St a a stabilize stabilize stabilize
+ 
+
+ align:start position:0%
+St a a stabilize stabilize stabilize
+stabilize next stabil stabilization
+
+ align:start position:0%
+stabilize next stabil stabilization
+ 
+
+ align:start position:0%
+stabilize next stabil stabilization
+stabil stable stabilization
+
+ align:start position:0%
+stabil stable stabilization
+ 
+
+ align:start position:0%
+stabil stable stabilization
+stabilization stabilization
+
+ align:start position:0%
+stabilization stabilization
+ 
+
+ align:start position:0%
+stabilization stabilization
+okay next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sterile
+
+ align:start position:0%
+sterile
+ 
+
+ align:start position:0%
+sterile
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+sterile ster okay next sterility very
+
+ align:start position:0%
+sterile ster okay next sterility very
+ 
+
+ align:start position:0%
+sterile ster okay next sterility very
+good give us the flap sterility very
+
+ align:start position:0%
+good give us the flap sterility very
+ 
+
+ align:start position:0%
+good give us the flap sterility very
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+one more time sterility sterility
+
+ align:start position:0%
+one more time sterility sterility
+ 
+
+ align:start position:0%
+one more time sterility sterility
+sterility St steril St sterility okay St
+
+ align:start position:0%
+sterility St steril St sterility okay St
+ 
+
+ align:start position:0%
+sterility St steril St sterility okay St
+plus all St St stay stay stable St
+
+ align:start position:0%
+plus all St St stay stay stable St
+ 
+
+ align:start position:0%
+plus all St St stay stay stable St
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+stability next St huh St sterilize
+
+ align:start position:0%
+stability next St huh St sterilize
+ 
+
+ align:start position:0%
+stability next St huh St sterilize
+steril next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sterilization
+
+ align:start position:0%
+sterilization
+ 
+
+ align:start position:0%
+sterilization
+any questions what's the pronunciation
+
+ align:start position:0%
+any questions what's the pronunciation
+ 
+
+ align:start position:0%
+any questions what's the pronunciation
+of mobile or mobile mobile which one
+
+ align:start position:0%
+of mobile or mobile mobile which one
+ 
+
+ align:start position:0%
+of mobile or mobile mobile which one
+mobile in American English mob is more
+
+ align:start position:0%
+mobile in American English mob is more
+ 
+
+ align:start position:0%
+mobile in American English mob is more
+common whenever you have here the i e i
+
+ align:start position:0%
+common whenever you have here the i e i
+ 
+
+ align:start position:0%
+common whenever you have here the i e i
+e it's usually oh sterile sterile mobile
+
+ align:start position:0%
+e it's usually oh sterile sterile mobile
+ 
+
+ align:start position:0%
+e it's usually oh sterile sterile mobile
+ferle okay in TV people say mobile
+
+ align:start position:0%
+ferle okay in TV people say mobile
+ 
+
+ align:start position:0%
+ferle okay in TV people say mobile
+mobile T-Mobile mob T
+
+ align:start position:0%
+mobile T-Mobile mob T
+ 
+
+ align:start position:0%
+mobile T-Mobile mob T
+T-Mobile mobile T-Mobile T-Mobile me the
+
+ align:start position:0%
+T-Mobile mobile T-Mobile T-Mobile me the
+ 
+
+ align:start position:0%
+T-Mobile mobile T-Mobile T-Mobile me the
+phone
+
+ align:start position:0%
+phone
+ 
+
+ align:start position:0%
+phone
+T-Mobile it's T-Mobile right T-Mobile no
+
+ align:start position:0%
+T-Mobile it's T-Mobile right T-Mobile no
+ 
+
+ align:start position:0%
+T-Mobile it's T-Mobile right T-Mobile no
+it's not mobile people say T-Mobile
+
+ align:start position:0%
+it's not mobile people say T-Mobile
+ 
+
+ align:start position:0%
+it's not mobile people say T-Mobile
+T-Mobile T-Mobile yeah see again your
+
+ align:start position:0%
+T-Mobile T-Mobile yeah see again your
+ 
+
+ align:start position:0%
+T-Mobile T-Mobile yeah see again your
+brain is tricking you mobile people say
+
+ align:start position:0%
+brain is tricking you mobile people say
+ 
+
+ align:start position:0%
+brain is tricking you mobile people say
+mobile but you you look at it and you
+
+ align:start position:0%
+mobile but you you look at it and you
+ 
+
+ align:start position:0%
+mobile but you you look at it and you
+think okay it's m o b i l e it has to be
+
+ align:start position:0%
+think okay it's m o b i l e it has to be
+ 
+
+ align:start position:0%
+think okay it's m o b i l e it has to be
+mobile so people are saying mobile what
+
+ align:start position:0%
+mobile so people are saying mobile what
+ 
+
+ align:start position:0%
+mobile so people are saying mobile what
+you hear is Mo
+
+ align:start position:0%
+you hear is Mo
+ 
+
+ align:start position:0%
+you hear is Mo
+I think I mean mobile is not a wrong
+
+ align:start position:0%
+I think I mean mobile is not a wrong
+ 
+
+ align:start position:0%
+I think I mean mobile is not a wrong
+pronunciation but mobile mobile is more
+
+ align:start position:0%
+pronunciation but mobile mobile is more
+ 
+
+ align:start position:0%
+pronunciation but mobile mobile is more
+common in American English
+
+ align:start position:0%
+common in American English
+ 
+
+ align:start position:0%
+common in American English
+you say fertile fertile is okay it's not
+
+ align:start position:0%
+you say fertile fertile is okay it's not
+ 
+
+ align:start position:0%
+you say fertile fertile is okay it's not
+it's not the wrong pronunciation but
+
+ align:start position:0%
+it's not the wrong pronunciation but
+ 
+
+ align:start position:0%
+it's not the wrong pronunciation but
+it's just not that common in American
+
+ align:start position:0%
+it's just not that common in American
+ 
+
+ align:start position:0%
+it's just not that common in American
+English
+
+ align:start position:0%
+English
+ 
+
+ align:start position:0%
+English
+okay so if you on saying fertile that's
+
+ align:start position:0%
+okay so if you on saying fertile that's
+ 
+
+ align:start position:0%
+okay so if you on saying fertile that's
+okay but if you if people say fertile
+
+ align:start position:0%
+okay but if you if people say fertile
+ 
+
+ align:start position:0%
+okay but if you if people say fertile
+you need to understand it okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+today I have a cartoon
+
+ align:start position:0%
+today I have a cartoon
+ 
+
+ align:start position:0%
+today I have a cartoon
+that is really funny
+
+ align:start position:0%
+that is really funny
+ 
+
+ align:start position:0%
+that is really funny
+trust me this one will be funny if this
+
+ align:start position:0%
+trust me this one will be funny if this
+ 
+
+ align:start position:0%
+trust me this one will be funny if this
+is not funny I don't know what is
+
+ align:start position:0%
+is not funny I don't know what is
+ 
+
+ align:start position:0%
+is not funny I don't know what is
+but in order to make sure that this will
+
+ align:start position:0%
+but in order to make sure that this will
+ 
+
+ align:start position:0%
+but in order to make sure that this will
+be funny
+
+ align:start position:0%
+be funny
+ 
+
+ align:start position:0%
+be funny
+you will laugh
+
+ align:start position:0%
+you will laugh
+ 
+
+ align:start position:0%
+you will laugh
+I decided to do some priming
+
+ align:start position:0%
+I decided to do some priming
+ 
+
+ align:start position:0%
+I decided to do some priming
+uh you know the word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody knows Batman right Batman and
+
+ align:start position:0%
+everybody knows Batman right Batman and
+ 
+
+ align:start position:0%
+everybody knows Batman right Batman and
+Robin
+
+ align:start position:0%
+Robin
+ 
+
+ align:start position:0%
+Robin
+Batman and Robin
+
+ align:start position:0%
+Batman and Robin
+ 
+
+ align:start position:0%
+Batman and Robin
+huh Robin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stress is here ra so it becomes Robin
+
+ align:start position:0%
+stress is here ra so it becomes Robin
+ 
+
+ align:start position:0%
+stress is here ra so it becomes Robin
+Robin Robin or Robin Robin becomes a
+
+ align:start position:0%
+Robin Robin or Robin Robin becomes a
+ 
+
+ align:start position:0%
+Robin Robin or Robin Robin becomes a
+unstressed spell Robin
+
+ align:start position:0%
+unstressed spell Robin
+ 
+
+ align:start position:0%
+unstressed spell Robin
+it's not Rin not Rin Robin Robin okay
+
+ align:start position:0%
+it's not Rin not Rin Robin Robin okay
+ 
+
+ align:start position:0%
+it's not Rin not Rin Robin Robin okay
+Batman and Robin you know where you know
+
+ align:start position:0%
+Batman and Robin you know where you know
+ 
+
+ align:start position:0%
+Batman and Robin you know where you know
+where they live
+
+ align:start position:0%
+where they live
+ 
+
+ align:start position:0%
+where they live
+huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you read thisam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goam
+
+ align:start position:0%
+goam
+ 
+
+ align:start position:0%
+goam
+k no no one's going to understand you
+
+ align:start position:0%
+k no no one's going to understand you
+ 
+
+ align:start position:0%
+k no no one's going to understand you
+it's not K it's not even goam if you say
+
+ align:start position:0%
+it's not K it's not even goam if you say
+ 
+
+ align:start position:0%
+it's not K it's not even goam if you say
+goam maybe you have a chance it's it's
+
+ align:start position:0%
+goam maybe you have a chance it's it's
+ 
+
+ align:start position:0%
+goam maybe you have a chance it's it's
+thumb it's voiceless okay Gotham Gotham
+
+ align:start position:0%
+thumb it's voiceless okay Gotham Gotham
+ 
+
+ align:start position:0%
+thumb it's voiceless okay Gotham Gotham
+you know you know what Gotham is you
+
+ align:start position:0%
+you know you know what Gotham is you
+ 
+
+ align:start position:0%
+you know you know what Gotham is you
+know what that means you know what that
+
+ align:start position:0%
+know what that means you know what that
+ 
+
+ align:start position:0%
+know what that means you know what that
+refers to
+
+ align:start position:0%
+refers to
+ 
+
+ align:start position:0%
+refers to
+it's actually a nickname for New York
+
+ align:start position:0%
+it's actually a nickname for New York
+ 
+
+ align:start position:0%
+it's actually a nickname for New York
+New York City okay so you know Batman
+
+ align:start position:0%
+New York City okay so you know Batman
+ 
+
+ align:start position:0%
+New York City okay so you know Batman
+and Robbie do you know where they live
+
+ align:start position:0%
+and Robbie do you know where they live
+ 
+
+ align:start position:0%
+and Robbie do you know where they live
+they live in New York huh
+
+ align:start position:0%
+they live in New York huh
+ 
+
+ align:start position:0%
+they live in New York huh
+I have no idea
+
+ align:start position:0%
+I have no idea
+ 
+
+ align:start position:0%
+I have no idea
+you know why it's I don't know American
+
+ align:start position:0%
+you know why it's I don't know American
+ 
+
+ align:start position:0%
+you know why it's I don't know American
+writer Washington Irving I think he
+
+ align:start position:0%
+writer Washington Irving I think he
+ 
+
+ align:start position:0%
+writer Washington Irving I think he
+started using this name I I don't know
+
+ align:start position:0%
+started using this name I I don't know
+ 
+
+ align:start position:0%
+started using this name I I don't know
+why so Batman and Robin they they live
+
+ align:start position:0%
+why so Batman and Robin they they live
+ 
+
+ align:start position:0%
+why so Batman and Robin they they live
+in New York
+
+ align:start position:0%
+in New York
+ 
+
+ align:start position:0%
+in New York
+every superhero lives in New York
+
+ align:start position:0%
+every superhero lives in New York
+ 
+
+ align:start position:0%
+every superhero lives in New York
+super man lives in New York you know
+
+ align:start position:0%
+super man lives in New York you know
+ 
+
+ align:start position:0%
+super man lives in New York you know
+Spider-Man
+
+ align:start position:0%
+Spider-Man
+ 
+
+ align:start position:0%
+Spider-Man
+York do you did you see Spider-Man too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he he's really he's really smart you
+
+ align:start position:0%
+he he's really he's really smart you
+ 
+
+ align:start position:0%
+he he's really he's really smart you
+know right he's really into science
+
+ align:start position:0%
+know right he's really into science
+ 
+
+ align:start position:0%
+know right he's really into science
+he's really good at science but he can't
+
+ align:start position:0%
+he's really good at science but he can't
+ 
+
+ align:start position:0%
+he's really good at science but he can't
+I mean if he's really good at science he
+
+ align:start position:0%
+I mean if he's really good at science he
+ 
+
+ align:start position:0%
+I mean if he's really good at science he
+has to come to our school right
+
+ align:start position:0%
+has to come to our school right
+ 
+
+ align:start position:0%
+has to come to our school right
+but he goes to what school
+
+ align:start position:0%
+but he goes to what school
+ 
+
+ align:start position:0%
+but he goes to what school
+he goes to Columbia in New York why
+
+ align:start position:0%
+he goes to Columbia in New York why
+ 
+
+ align:start position:0%
+he goes to Columbia in New York why
+because he has to live in New York
+
+ align:start position:0%
+because he has to live in New York
+ 
+
+ align:start position:0%
+because he has to live in New York
+he can't come to Boston he can't come to
+
+ align:start position:0%
+he can't come to Boston he can't come to
+ 
+
+ align:start position:0%
+he can't come to Boston he can't come to
+MIT he can't go to Harvard why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because super but why did yeah but
+
+ align:start position:0%
+because super but why did yeah but
+ 
+
+ align:start position:0%
+because super but why did yeah but
+Superman and Batman if they wanted to
+
+ align:start position:0%
+Superman and Batman if they wanted to
+ 
+
+ align:start position:0%
+Superman and Batman if they wanted to
+they could move here actually but not
+
+ align:start position:0%
+they could move here actually but not
+ 
+
+ align:start position:0%
+they could move here actually but not
+Spider-Man why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good very good Spider-Man he needs
+
+ align:start position:0%
+very good very good Spider-Man he needs
+ 
+
+ align:start position:0%
+very good very good Spider-Man he needs
+to so
+
+ align:start position:0%
+to so
+ 
+
+ align:start position:0%
+to so
+okay so this is how do you say thisam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now H stresses here becomes sh
+
+ align:start position:0%
+okay so now H stresses here becomes sh
+ 
+
+ align:start position:0%
+okay so now H stresses here becomes sh
+on stretch syllable Gotham Gotham very
+
+ align:start position:0%
+on stretch syllable Gotham Gotham very
+ 
+
+ align:start position:0%
+on stretch syllable Gotham Gotham very
+important if you say go go nobody's
+
+ align:start position:0%
+important if you say go go nobody's
+ 
+
+ align:start position:0%
+important if you say go go nobody's
+going to understand you Gotham Gotham
+
+ align:start position:0%
+going to understand you Gotham Gotham
+ 
+
+ align:start position:0%
+going to understand you Gotham Gotham
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a cartoon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is about when you're supposed to
+
+ align:start position:0%
+this is about when you're supposed to
+ 
+
+ align:start position:0%
+this is about when you're supposed to
+laugh now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come on
+
+ align:start position:0%
+come on
+ 
+
+ align:start position:0%
+come on
+this is not funny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Batman and Robin right holy
+
+ align:start position:0%
+Batman and Robin right holy
+ 
+
+ align:start position:0%
+Batman and Robin right holy
+how how how would you read this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you how do you say this what's
+
+ align:start position:0%
+how do you how do you say this what's
+ 
+
+ align:start position:0%
+how do you how do you say this what's
+the stress syllable right okay we we're
+
+ align:start position:0%
+the stress syllable right okay we we're
+ 
+
+ align:start position:0%
+the stress syllable right okay we we're
+adding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cent the stress is here now okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here read this Batman and Robin are
+
+ align:start position:0%
+now here read this Batman and Robin are
+ 
+
+ align:start position:0%
+now here read this Batman and Robin are
+called in to free a Gotham from the grip
+
+ align:start position:0%
+called in to free a Gotham from the grip
+ 
+
+ align:start position:0%
+called in to free a Gotham from the grip
+of an evil graphic designer
+
+ align:start position:0%
+of an evil graphic designer
+ 
+
+ align:start position:0%
+of an evil graphic designer
+and the graphic designer in know graphic
+
+ align:start position:0%
+and the graphic designer in know graphic
+ 
+
+ align:start position:0%
+and the graphic designer in know graphic
+designer yes
+
+ align:start position:0%
+designer yes
+ 
+
+ align:start position:0%
+designer yes
+he or she made the sign like visit how
+
+ align:start position:0%
+he or she made the sign like visit how
+ 
+
+ align:start position:0%
+he or she made the sign like visit how
+do you read this
+
+ align:start position:0%
+do you read this
+ 
+
+ align:start position:0%
+do you read this
+God Hand God Hand
+
+ align:start position:0%
+God Hand God Hand
+ 
+
+ align:start position:0%
+God Hand God Hand
+it's not Gotham anymore godam
+
+ align:start position:0%
+it's not Gotham anymore godam
+ 
+
+ align:start position:0%
+it's not Gotham anymore godam
+got hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no let's not funny
+
+ align:start position:0%
+no let's not funny
+ 
+
+ align:start position:0%
+no let's not funny
+Gotham godam
+
+ align:start position:0%
+Gotham godam
+ 
+
+ align:start position:0%
+Gotham godam
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now why am I doing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gotam
+
+ align:start position:0%
+gotam
+ 
+
+ align:start position:0%
+gotam
+well it's like got milk you know the
+
+ align:start position:0%
+well it's like got milk you know the
+ 
+
+ align:start position:0%
+well it's like got milk you know the
+commercial got milk got milk do we have
+
+ align:start position:0%
+commercial got milk got milk do we have
+ 
+
+ align:start position:0%
+commercial got milk got milk do we have
+milk got milk okay got hand so we have H
+
+ align:start position:0%
+milk got milk okay got hand so we have H
+ 
+
+ align:start position:0%
+milk got milk okay got hand so we have H
+got ham got ham got ham now here you
+
+ align:start position:0%
+got ham got ham got ham now here you
+ 
+
+ align:start position:0%
+got ham got ham got ham now here you
+can't say got h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+got ham got ham got ham but here you
+
+ align:start position:0%
+got ham got ham got ham but here you
+ 
+
+ align:start position:0%
+got ham got ham got ham but here you
+have to say God thumb
+
+ align:start position:0%
+have to say God thumb
+ 
+
+ align:start position:0%
+have to say God thumb
+okay the Val gets reduced but here the
+
+ align:start position:0%
+okay the Val gets reduced but here the
+ 
+
+ align:start position:0%
+okay the Val gets reduced but here the
+Val is not reduced because this is a
+
+ align:start position:0%
+Val is not reduced because this is a
+ 
+
+ align:start position:0%
+Val is not reduced because this is a
+compound
+
+ align:start position:0%
+compound
+ 
+
+ align:start position:0%
+compound
+compound
+
+ align:start position:0%
+compound
+ 
+
+ align:start position:0%
+compound
+what's a compound
+
+ align:start position:0%
+what's a compound
+ 
+
+ align:start position:0%
+what's a compound
+what's a compound so compound
+
+ align:start position:0%
+what's a compound so compound
+ 
+
+ align:start position:0%
+what's a compound so compound
+if you turn to our textbook B on page
+
+ align:start position:0%
+if you turn to our textbook B on page
+ 
+
+ align:start position:0%
+if you turn to our textbook B on page
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 107 in your textbook
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 107
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 107
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 107 page 107 does anybody want to
+
+ align:start position:0%
+page 107 page 107 does anybody want to
+ 
+
+ align:start position:0%
+page 107 page 107 does anybody want to
+read page 107 for us a compound noun is
+
+ align:start position:0%
+read page 107 for us a compound noun is
+ 
+
+ align:start position:0%
+read page 107 for us a compound noun is
+a compound noun is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the compound noun is the sequence of two
+
+ align:start position:0%
+the compound noun is the sequence of two
+ 
+
+ align:start position:0%
+the compound noun is the sequence of two
+or more was
+
+ align:start position:0%
+or more was
+ 
+
+ align:start position:0%
+or more was
+that that together have a new meaning
+
+ align:start position:0%
+that that together have a new meaning
+ 
+
+ align:start position:0%
+that that together have a new meaning
+and function as a single
+
+ align:start position:0%
+and function as a single
+ 
+
+ align:start position:0%
+and function as a single
+you okay read on the second element of
+
+ align:start position:0%
+you okay read on the second element of
+ 
+
+ align:start position:0%
+you okay read on the second element of
+word of the of the is a n the first
+
+ align:start position:0%
+word of the of the is a n the first
+ 
+
+ align:start position:0%
+word of the of the is a n the first
+element is usually a n but may also be
+
+ align:start position:0%
+element is usually a n but may also be
+ 
+
+ align:start position:0%
+element is usually a n but may also be
+another part of speech a compound may be
+
+ align:start position:0%
+another part of speech a compound may be
+ 
+
+ align:start position:0%
+another part of speech a compound may be
+written as one or two words okay so a
+
+ align:start position:0%
+written as one or two words okay so a
+ 
+
+ align:start position:0%
+written as one or two words okay so a
+compound noun is a sequence of two or
+
+ align:start position:0%
+compound noun is a sequence of two or
+ 
+
+ align:start position:0%
+compound noun is a sequence of two or
+more words that together have a new
+
+ align:start position:0%
+more words that together have a new
+ 
+
+ align:start position:0%
+more words that together have a new
+meaning and function as a single noun
+
+ align:start position:0%
+meaning and function as a single noun
+ 
+
+ align:start position:0%
+meaning and function as a single noun
+function is a single noun okay that's a
+
+ align:start position:0%
+function is a single noun okay that's a
+ 
+
+ align:start position:0%
+function is a single noun okay that's a
+compound we turn to and we have some
+
+ align:start position:0%
+compound we turn to and we have some
+ 
+
+ align:start position:0%
+compound we turn to and we have some
+examples roommate newspaper School Bus
+
+ align:start position:0%
+examples roommate newspaper School Bus
+ 
+
+ align:start position:0%
+examples roommate newspaper School Bus
+Waste Paper basket
+
+ align:start position:0%
+Waste Paper basket
+ 
+
+ align:start position:0%
+Waste Paper basket
+but the important thing about compound
+
+ align:start position:0%
+but the important thing about compound
+ 
+
+ align:start position:0%
+but the important thing about compound
+nouns is that if you turn to page 108
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the word weekends right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a compound this is not a
+
+ align:start position:0%
+this is a compound this is not a
+ 
+
+ align:start position:0%
+this is a compound this is not a
+compound this is a compound this is this
+
+ align:start position:0%
+compound this is a compound this is this
+ 
+
+ align:start position:0%
+compound this is a compound this is this
+is not a compound because we have two
+
+ align:start position:0%
+is not a compound because we have two
+ 
+
+ align:start position:0%
+is not a compound because we have two
+words here we
+
+ align:start position:0%
+words here we
+ 
+
+ align:start position:0%
+words here we
+and and two words that we could actually
+
+ align:start position:0%
+and and two words that we could actually
+ 
+
+ align:start position:0%
+and and two words that we could actually
+recognize right
+
+ align:start position:0%
+recognize right
+ 
+
+ align:start position:0%
+recognize right
+this is one word where is the stress we
+
+ align:start position:0%
+this is one word where is the stress we
+ 
+
+ align:start position:0%
+this is one word where is the stress we
+right so you say we
+
+ align:start position:0%
+right so you say we
+ 
+
+ align:start position:0%
+right so you say we
+we okay in a normal word single word if
+
+ align:start position:0%
+we okay in a normal word single word if
+ 
+
+ align:start position:0%
+we okay in a normal word single word if
+you have a stressed syllable unstressed
+
+ align:start position:0%
+you have a stressed syllable unstressed
+ 
+
+ align:start position:0%
+you have a stressed syllable unstressed
+syllables becomes a right weaken weaken
+
+ align:start position:0%
+syllables becomes a right weaken weaken
+ 
+
+ align:start position:0%
+syllables becomes a right weaken weaken
+but in a compound noun the second in a
+
+ align:start position:0%
+but in a compound noun the second in a
+ 
+
+ align:start position:0%
+but in a compound noun the second in a
+compound noun or noun compounds it's
+
+ align:start position:0%
+compound noun or noun compounds it's
+ 
+
+ align:start position:0%
+compound noun or noun compounds it's
+always the first one that gets stress
+
+ align:start position:0%
+always the first one that gets stress
+ 
+
+ align:start position:0%
+always the first one that gets stress
+the second one has a secondary stress
+
+ align:start position:0%
+the second one has a secondary stress
+ 
+
+ align:start position:0%
+the second one has a secondary stress
+okay so you do not say we weeken you say
+
+ align:start position:0%
+okay so you do not say we weeken you say
+ 
+
+ align:start position:0%
+okay so you do not say we weeken you say
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+we okay weekend weeken we okay so Gotham
+
+ align:start position:0%
+we okay weekend weeken we okay so Gotham
+ 
+
+ align:start position:0%
+we okay weekend weeken we okay so Gotham
+one word becomes goam
+
+ align:start position:0%
+one word becomes goam
+ 
+
+ align:start position:0%
+one word becomes goam
+but God ham God ham God ham okay it's
+
+ align:start position:0%
+but God ham God ham God ham okay it's
+ 
+
+ align:start position:0%
+but God ham God ham God ham okay it's
+God ham
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's very important okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could turn to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 10 uh page 63 in your course pocket
+
+ align:start position:0%
+page 10 uh page 63 in your course pocket
+ 
+
+ align:start position:0%
+page 10 uh page 63 in your course pocket
+compounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we actually have four different
+
+ align:start position:0%
+so we actually have four different
+ 
+
+ align:start position:0%
+so we actually have four different
+compounds one the most common one is the
+
+ align:start position:0%
+compounds one the most common one is the
+ 
+
+ align:start position:0%
+compounds one the most common one is the
+noun compounds we say sometimes noun
+
+ align:start position:0%
+noun compounds we say sometimes noun
+ 
+
+ align:start position:0%
+noun compounds we say sometimes noun
+compounds or compound nouns both are
+
+ align:start position:0%
+compounds or compound nouns both are
+ 
+
+ align:start position:0%
+compounds or compound nouns both are
+interchangeable okay the most common
+
+ align:start position:0%
+interchangeable okay the most common
+ 
+
+ align:start position:0%
+interchangeable okay the most common
+ones are noun compounds we also have
+
+ align:start position:0%
+ones are noun compounds we also have
+ 
+
+ align:start position:0%
+ones are noun compounds we also have
+verb compounds adjective compounds and
+
+ align:start position:0%
+verb compounds adjective compounds and
+ 
+
+ align:start position:0%
+verb compounds adjective compounds and
+adverb compounds okay adverb compounds
+
+ align:start position:0%
+adverb compounds okay adverb compounds
+ 
+
+ align:start position:0%
+adverb compounds okay adverb compounds
+are the least common one and so we're
+
+ align:start position:0%
+are the least common one and so we're
+ 
+
+ align:start position:0%
+are the least common one and so we're
+not really going to talk about uh adverb
+
+ align:start position:0%
+not really going to talk about uh adverb
+ 
+
+ align:start position:0%
+not really going to talk about uh adverb
+compounds
+
+ align:start position:0%
+compounds
+ 
+
+ align:start position:0%
+compounds
+now compounds the most important thing
+
+ align:start position:0%
+now compounds the most important thing
+ 
+
+ align:start position:0%
+now compounds the most important thing
+that you want to remember is
+
+ align:start position:0%
+that you want to remember is
+ 
+
+ align:start position:0%
+that you want to remember is
+the place of stress where is the stress
+
+ align:start position:0%
+the place of stress where is the stress
+ 
+
+ align:start position:0%
+the place of stress where is the stress
+first first one first one that's very
+
+ align:start position:0%
+first first one first one that's very
+ 
+
+ align:start position:0%
+first first one first one that's very
+important okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+noun compounds can actually uh consist
+
+ align:start position:0%
+noun compounds can actually uh consist
+ 
+
+ align:start position:0%
+noun compounds can actually uh consist
+of two nouns like a or adjective and
+
+ align:start position:0%
+of two nouns like a or adjective and
+ 
+
+ align:start position:0%
+of two nouns like a or adjective and
+nouns like B so first first a toothbrush
+
+ align:start position:0%
+nouns like B so first first a toothbrush
+ 
+
+ align:start position:0%
+nouns like B so first first a toothbrush
+repeat after me toothbrush toothbrush
+
+ align:start position:0%
+repeat after me toothbrush toothbrush
+ 
+
+ align:start position:0%
+repeat after me toothbrush toothbrush
+Window Seat Window Seat airplane
+
+ align:start position:0%
+Window Seat Window Seat airplane
+ 
+
+ align:start position:0%
+Window Seat Window Seat airplane
+airplane laundry basket laundry basket
+
+ align:start position:0%
+airplane laundry basket laundry basket
+ 
+
+ align:start position:0%
+airplane laundry basket laundry basket
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's get this B we could also have
+
+ align:start position:0%
+let's get this B we could also have
+ 
+
+ align:start position:0%
+let's get this B we could also have
+adjectives and noun together and they
+
+ align:start position:0%
+adjectives and noun together and they
+ 
+
+ align:start position:0%
+adjectives and noun together and they
+can form a compound okay it could be
+
+ align:start position:0%
+can form a compound okay it could be
+ 
+
+ align:start position:0%
+can form a compound okay it could be
+written as one word or it could be
+
+ align:start position:0%
+written as one word or it could be
+ 
+
+ align:start position:0%
+written as one word or it could be
+written as two different two words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blackb
+
+ align:start position:0%
+blackb
+ 
+
+ align:start position:0%
+blackb
+dark room dark room Chief skates Chief
+
+ align:start position:0%
+dark room dark room Chief skates Chief
+ 
+
+ align:start position:0%
+dark room dark room Chief skates Chief
+Gates White House White House English
+
+ align:start position:0%
+Gates White House White House English
+ 
+
+ align:start position:0%
+Gates White House White House English
+teacher
+
+ align:start position:0%
+teacher
+ 
+
+ align:start position:0%
+teacher
+English teacher head doctor head doctor
+
+ align:start position:0%
+English teacher head doctor head doctor
+ 
+
+ align:start position:0%
+English teacher head doctor head doctor
+now the question is okay so what's
+
+ align:start position:0%
+now the question is okay so what's
+ 
+
+ align:start position:0%
+now the question is okay so what's
+difference if you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have an adjective and noun that
+
+ align:start position:0%
+if you have an adjective and noun that
+ 
+
+ align:start position:0%
+if you have an adjective and noun that
+do not function as a compound noun
+
+ align:start position:0%
+do not function as a compound noun
+ 
+
+ align:start position:0%
+do not function as a compound noun
+compound the stress is where in the noun
+
+ align:start position:0%
+compound the stress is where in the noun
+ 
+
+ align:start position:0%
+compound the stress is where in the noun
+okay uh we haven't really talked about
+
+ align:start position:0%
+okay uh we haven't really talked about
+ 
+
+ align:start position:0%
+okay uh we haven't really talked about
+this yet yet we haven't talked about
+
+ align:start position:0%
+this yet yet we haven't talked about
+ 
+
+ align:start position:0%
+this yet yet we haven't talked about
+this yet but uh usually you put most
+
+ align:start position:0%
+this yet but uh usually you put most
+ 
+
+ align:start position:0%
+this yet but uh usually you put most
+stress on the last content word okay
+
+ align:start position:0%
+stress on the last content word okay
+ 
+
+ align:start position:0%
+stress on the last content word okay
+adjective is a Content word and noun is
+
+ align:start position:0%
+adjective is a Content word and noun is
+ 
+
+ align:start position:0%
+adjective is a Content word and noun is
+a Content word we have adjective and
+
+ align:start position:0%
+a Content word we have adjective and
+ 
+
+ align:start position:0%
+a Content word we have adjective and
+noun okay we put more stress on the last
+
+ align:start position:0%
+noun okay we put more stress on the last
+ 
+
+ align:start position:0%
+noun okay we put more stress on the last
+content One content word usually so
+
+ align:start position:0%
+content One content word usually so
+ 
+
+ align:start position:0%
+content One content word usually so
+that's why the noun gets more stress
+
+ align:start position:0%
+that's why the noun gets more stress
+ 
+
+ align:start position:0%
+that's why the noun gets more stress
+okay so how do you say this black black
+
+ align:start position:0%
+okay so how do you say this black black
+ 
+
+ align:start position:0%
+okay so how do you say this black black
+board black dark room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what house
+
+ align:start position:0%
+what house
+ 
+
+ align:start position:0%
+what house
+Engish teacher
+
+ align:start position:0%
+Engish teacher
+ 
+
+ align:start position:0%
+Engish teacher
+doctor okay so I mean what's what's a
+
+ align:start position:0%
+doctor okay so I mean what's what's a
+ 
+
+ align:start position:0%
+doctor okay so I mean what's what's a
+black board
+
+ align:start position:0%
+black board
+ 
+
+ align:start position:0%
+black board
+that's a black board right
+
+ align:start position:0%
+that's a black board right
+ 
+
+ align:start position:0%
+that's a black board right
+that's not even black is it but we say
+
+ align:start position:0%
+that's not even black is it but we say
+ 
+
+ align:start position:0%
+that's not even black is it but we say
+Blackboard right but Blackport is what's
+
+ align:start position:0%
+Blackboard right but Blackport is what's
+ 
+
+ align:start position:0%
+Blackboard right but Blackport is what's
+a black board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board that is black right what's a dark
+
+ align:start position:0%
+board that is black right what's a dark
+ 
+
+ align:start position:0%
+board that is black right what's a dark
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+Theo
+
+ align:start position:0%
+Theo
+ 
+
+ align:start position:0%
+Theo
+for the photo you
+
+ align:start position:0%
+for the photo you
+ 
+
+ align:start position:0%
+for the photo you
+the develop photos pictures dark room
+
+ align:start position:0%
+the develop photos pictures dark room
+ 
+
+ align:start position:0%
+the develop photos pictures dark room
+you need a dark room to develop photos
+
+ align:start position:0%
+you need a dark room to develop photos
+ 
+
+ align:start position:0%
+you need a dark room to develop photos
+dark room you can't just be
+
+ align:start position:0%
+dark room you can't just be
+ 
+
+ align:start position:0%
+dark room you can't just be
+any room that's dark I think you need
+
+ align:start position:0%
+any room that's dark I think you need
+ 
+
+ align:start position:0%
+any room that's dark I think you need
+more things okay I could make this a
+
+ align:start position:0%
+more things okay I could make this a
+ 
+
+ align:start position:0%
+more things okay I could make this a
+dark room by turning off the lights but
+
+ align:start position:0%
+dark room by turning off the lights but
+ 
+
+ align:start position:0%
+dark room by turning off the lights but
+I can't make it a dark room
+
+ align:start position:0%
+I can't make it a dark room
+ 
+
+ align:start position:0%
+I can't make it a dark room
+okay what's a chip skate
+
+ align:start position:0%
+okay what's a chip skate
+ 
+
+ align:start position:0%
+okay what's a chip skate
+a chip skate or chip skate two chip
+
+ align:start position:0%
+a chip skate or chip skate two chip
+ 
+
+ align:start position:0%
+a chip skate or chip skate two chip
+skates what's a chip skate someone
+
+ align:start position:0%
+skates what's a chip skate someone
+ 
+
+ align:start position:0%
+skates what's a chip skate someone
+do not money okay someone who's cheap
+
+ align:start position:0%
+do not money okay someone who's cheap
+ 
+
+ align:start position:0%
+do not money okay someone who's cheap
+someone who who's stingy someone who's
+
+ align:start position:0%
+someone who who's stingy someone who's
+ 
+
+ align:start position:0%
+someone who who's stingy someone who's
+stingy okay who's not who doesn't want
+
+ align:start position:0%
+stingy okay who's not who doesn't want
+ 
+
+ align:start position:0%
+stingy okay who's not who doesn't want
+to spend his money uh that well
+
+ align:start position:0%
+to spend his money uh that well
+ 
+
+ align:start position:0%
+to spend his money uh that well
+cheap skates it's skates that are cheap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who lives in the White House
+
+ align:start position:0%
+who lives in the White House
+ 
+
+ align:start position:0%
+who lives in the White House
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+George Bush George W bush Okay W bush he
+
+ align:start position:0%
+George Bush George W bush Okay W bush he
+ 
+
+ align:start position:0%
+George Bush George W bush Okay W bush he
+lives in the White House
+
+ align:start position:0%
+lives in the White House
+ 
+
+ align:start position:0%
+lives in the White House
+I live in a white house I live in a I'm
+
+ align:start position:0%
+I live in a white house I live in a I'm
+ 
+
+ align:start position:0%
+I live in a white house I live in a I'm
+serious I live in a white house but
+
+ align:start position:0%
+serious I live in a white house but
+ 
+
+ align:start position:0%
+serious I live in a white house but
+nobody lives in the White House except
+
+ align:start position:0%
+nobody lives in the White House except
+ 
+
+ align:start position:0%
+nobody lives in the White House except
+George Bush right now okay and it'll be
+
+ align:start position:0%
+George Bush right now okay and it'll be
+ 
+
+ align:start position:0%
+George Bush right now okay and it'll be
+that way for the next four years too
+
+ align:start position:0%
+that way for the next four years too
+ 
+
+ align:start position:0%
+that way for the next four years too
+White House White House live in the
+
+ align:start position:0%
+White House White House live in the
+ 
+
+ align:start position:0%
+White House White House live in the
+White House okay George Bush lives in
+
+ align:start position:0%
+White House okay George Bush lives in
+ 
+
+ align:start position:0%
+White House okay George Bush lives in
+the White House
+
+ align:start position:0%
+the White House
+ 
+
+ align:start position:0%
+the White House
+can say the whole sentence George
+
+ align:start position:0%
+can say the whole sentence George
+ 
+
+ align:start position:0%
+can say the whole sentence George
+white house but Isaiah isah lives in a
+
+ align:start position:0%
+white house but Isaiah isah lives in a
+ 
+
+ align:start position:0%
+white house but Isaiah isah lives in a
+White House Liv in house
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Isaiah is an English teacher or English
+
+ align:start position:0%
+Isaiah is an English teacher or English
+ 
+
+ align:start position:0%
+Isaiah is an English teacher or English
+teacher English teacher English teacher
+
+ align:start position:0%
+teacher English teacher English teacher
+ 
+
+ align:start position:0%
+teacher English teacher English teacher
+English teacher Isaiah I'm I'm an
+
+ align:start position:0%
+English teacher Isaiah I'm I'm an
+ 
+
+ align:start position:0%
+English teacher Isaiah I'm I'm an
+English teacher from Korea okay I'm not
+
+ align:start position:0%
+English teacher from Korea okay I'm not
+ 
+
+ align:start position:0%
+English teacher from Korea okay I'm not
+an English teacher what's an English
+
+ align:start position:0%
+an English teacher what's an English
+ 
+
+ align:start position:0%
+an English teacher what's an English
+teacher teer from teacher from England
+
+ align:start position:0%
+teacher teer from teacher from England
+ 
+
+ align:start position:0%
+teacher teer from teacher from England
+teacher from England right English
+
+ align:start position:0%
+teacher from England right English
+ 
+
+ align:start position:0%
+teacher from England right English
+teacher is someone who
+
+ align:start position:0%
+teacher is someone who
+ 
+
+ align:start position:0%
+teacher is someone who
+teaches English Okay
+
+ align:start position:0%
+teaches English Okay
+ 
+
+ align:start position:0%
+teaches English Okay
+rep English teacher English teacher okay
+
+ align:start position:0%
+rep English teacher English teacher okay
+ 
+
+ align:start position:0%
+rep English teacher English teacher okay
+so I'm an English teacher I'm an English
+
+ align:start position:0%
+so I'm an English teacher I'm an English
+ 
+
+ align:start position:0%
+so I'm an English teacher I'm an English
+teacher not I'm not an English teacher
+
+ align:start position:0%
+teacher not I'm not an English teacher
+ 
+
+ align:start position:0%
+teacher not I'm not an English teacher
+I'm a Korean teacher but I'm not a Kore
+
+ align:start position:0%
+I'm a Korean teacher but I'm not a Kore
+ 
+
+ align:start position:0%
+I'm a Korean teacher but I'm not a Kore
+Korean teacher okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well korean-american teacher
+
+ align:start position:0%
+well korean-american teacher
+ 
+
+ align:start position:0%
+well korean-american teacher
+what's up head doctor doctor head doctor
+
+ align:start position:0%
+what's up head doctor doctor head doctor
+ 
+
+ align:start position:0%
+what's up head doctor doctor head doctor
+head doctor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chief
+
+ align:start position:0%
+Chief
+ 
+
+ align:start position:0%
+Chief
+doctor chief chief of staff chief chief
+
+ align:start position:0%
+doctor chief chief of staff chief chief
+ 
+
+ align:start position:0%
+doctor chief chief of staff chief chief
+would be doctor head doctor Chief is
+
+ align:start position:0%
+would be doctor head doctor Chief is
+ 
+
+ align:start position:0%
+would be doctor head doctor Chief is
+head doctor okay you can say my brother
+
+ align:start position:0%
+head doctor okay you can say my brother
+ 
+
+ align:start position:0%
+head doctor okay you can say my brother
+is a head doctor doctor my brother is a
+
+ align:start position:0%
+is a head doctor doctor my brother is a
+ 
+
+ align:start position:0%
+is a head doctor doctor my brother is a
+head doctor my brother is the head my
+
+ align:start position:0%
+head doctor my brother is the head my
+ 
+
+ align:start position:0%
+head doctor my brother is the head my
+brother is a head doctor uh uh at his
+
+ align:start position:0%
+brother is a head doctor uh uh at his
+ 
+
+ align:start position:0%
+brother is a head doctor uh uh at his
+Hospital something like that that but
+
+ align:start position:0%
+Hospital something like that that but
+ 
+
+ align:start position:0%
+Hospital something like that that but
+you could say my my my brother is a head
+
+ align:start position:0%
+you could say my my my brother is a head
+ 
+
+ align:start position:0%
+you could say my my my brother is a head
+doctor head doctor
+
+ align:start position:0%
+doctor head doctor
+ 
+
+ align:start position:0%
+doctor head doctor
+um I mean that's usually for kids you
+
+ align:start position:0%
+um I mean that's usually for kids you
+ 
+
+ align:start position:0%
+um I mean that's usually for kids you
+would you should say instead of head
+
+ align:start position:0%
+would you should say instead of head
+ 
+
+ align:start position:0%
+would you should say instead of head
+doctor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you read this
+
+ align:start position:0%
+how would you read this
+ 
+
+ align:start position:0%
+how would you read this
+where is the stress okay the first thing
+
+ align:start position:0%
+where is the stress okay the first thing
+ 
+
+ align:start position:0%
+where is the stress okay the first thing
+you want to do is what
+
+ align:start position:0%
+you want to do is what
+ 
+
+ align:start position:0%
+you want to do is what
+find out the stress right okay where is
+
+ align:start position:0%
+find out the stress right okay where is
+ 
+
+ align:start position:0%
+find out the stress right okay where is
+the stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K okay Kai so
+
+ align:start position:0%
+K okay Kai so
+ 
+
+ align:start position:0%
+K okay Kai so
+everything else becomes what so we're
+
+ align:start position:0%
+everything else becomes what so we're
+ 
+
+ align:start position:0%
+everything else becomes what so we're
+going to say Kai okay we have this B
+
+ align:start position:0%
+going to say Kai okay we have this B
+ 
+
+ align:start position:0%
+going to say Kai okay we have this B
+this B this B what are you going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens here what happens here
+
+ align:start position:0%
+what happens here what happens here
+ 
+
+ align:start position:0%
+what happens here what happens here
+psychiatrist
+
+ align:start position:0%
+psychiatrist
+ 
+
+ align:start position:0%
+psychiatrist
+psychiatrist Psych psychiatrist
+
+ align:start position:0%
+psychiatrist Psych psychiatrist
+ 
+
+ align:start position:0%
+psychiatrist Psych psychiatrist
+psychiatrist okay but here actuallyy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people say also I actually say
+
+ align:start position:0%
+people say also I actually say
+ 
+
+ align:start position:0%
+people say also I actually say
+psychiatrist I say psychiatrist Psy
+
+ align:start position:0%
+psychiatrist I say psychiatrist Psy
+ 
+
+ align:start position:0%
+psychiatrist I say psychiatrist Psy
+psychiatrist okay so Krist
+
+ align:start position:0%
+psychiatrist okay so Krist
+ 
+
+ align:start position:0%
+psychiatrist okay so Krist
+psychiatrist
+
+ align:start position:0%
+psychiatrist
+ 
+
+ align:start position:0%
+psychiatrist
+so which one is a psychiatrist
+
+ align:start position:0%
+so which one is a psychiatrist
+ 
+
+ align:start position:0%
+so which one is a psychiatrist
+which one doctor head doctor doctor okay
+
+ align:start position:0%
+which one doctor head doctor doctor okay
+ 
+
+ align:start position:0%
+which one doctor head doctor doctor okay
+doctor
+
+ align:start position:0%
+doctor
+ 
+
+ align:start position:0%
+doctor
+head doctor doctor okay now we could
+
+ align:start position:0%
+head doctor doctor okay now we could
+ 
+
+ align:start position:0%
+head doctor doctor okay now we could
+have simple compounds or complex
+
+ align:start position:0%
+have simple compounds or complex
+ 
+
+ align:start position:0%
+have simple compounds or complex
+compounds
+
+ align:start position:0%
+compounds
+ 
+
+ align:start position:0%
+compounds
+airplane airplane wing airplane wing
+
+ align:start position:0%
+airplane airplane wing airplane wing
+ 
+
+ align:start position:0%
+airplane airplane wing airplane wing
+cowboy cowboy hat hot dog hot dog bun
+
+ align:start position:0%
+cowboy cowboy hat hot dog hot dog bun
+ 
+
+ align:start position:0%
+cowboy cowboy hat hot dog hot dog bun
+tap Dan tap School tap School these are
+
+ align:start position:0%
+tap Dan tap School tap School these are
+ 
+
+ align:start position:0%
+tap Dan tap School tap School these are
+complex compounds still
+
+ align:start position:0%
+complex compounds still
+ 
+
+ align:start position:0%
+complex compounds still
+uh the word that gets most stressed is
+
+ align:start position:0%
+uh the word that gets most stressed is
+ 
+
+ align:start position:0%
+uh the word that gets most stressed is
+the first n airplane wing cowboy hat Hot
+
+ align:start position:0%
+the first n airplane wing cowboy hat Hot
+ 
+
+ align:start position:0%
+the first n airplane wing cowboy hat Hot
+Dog tap School okay
+
+ align:start position:0%
+Dog tap School okay
+ 
+
+ align:start position:0%
+Dog tap School okay
+hot a
+
+ align:start position:0%
+hot a
+ 
+
+ align:start position:0%
+hot a
+hot you know you know what a hot dog is
+
+ align:start position:0%
+hot you know you know what a hot dog is
+ 
+
+ align:start position:0%
+hot you know you know what a hot dog is
+Right hot dog hot dog the bread the
+
+ align:start position:0%
+Right hot dog hot dog the bread the
+ 
+
+ align:start position:0%
+Right hot dog hot dog the bread the
+bread Bunny's bread
+
+ align:start position:0%
+bread Bunny's bread
+ 
+
+ align:start position:0%
+bread Bunny's bread
+you like hot dogs yes not hot dogs right
+
+ align:start position:0%
+you like hot dogs yes not hot dogs right
+ 
+
+ align:start position:0%
+you like hot dogs yes not hot dogs right
+hot dogs hot dogs not hot dogs right
+
+ align:start position:0%
+hot dogs hot dogs not hot dogs right
+ 
+
+ align:start position:0%
+hot dogs hot dogs not hot dogs right
+hot dogs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how would you say this the first one
+
+ align:start position:0%
+so how would you say this the first one
+ 
+
+ align:start position:0%
+so how would you say this the first one
+how would you say the
+
+ align:start position:0%
+how would you say the
+ 
+
+ align:start position:0%
+how would you say the
+how you say how' you say the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay Jin can you say the first sentence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good black bird nest okay black
+
+ align:start position:0%
+very good black bird nest okay black
+ 
+
+ align:start position:0%
+very good black bird nest okay black
+bird nest black bird nest okay y can you
+
+ align:start position:0%
+bird nest black bird nest okay y can you
+ 
+
+ align:start position:0%
+bird nest black bird nest okay y can you
+say the second sentence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+black nest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bird nest black bird nest black bird
+
+ align:start position:0%
+bird nest black bird nest black bird
+ 
+
+ align:start position:0%
+bird nest black bird nest black bird
+bird n what kind of nest first okay
+
+ align:start position:0%
+bird n what kind of nest first okay
+ 
+
+ align:start position:0%
+bird n what kind of nest first okay
+compound is actually
+
+ align:start position:0%
+compound is actually
+ 
+
+ align:start position:0%
+compound is actually
+trying to figure out what you you look
+
+ align:start position:0%
+trying to figure out what you you look
+ 
+
+ align:start position:0%
+trying to figure out what you you look
+at a word right or two ad adjective noun
+
+ align:start position:0%
+at a word right or two ad adjective noun
+ 
+
+ align:start position:0%
+at a word right or two ad adjective noun
+it's actually very difficult uh to
+
+ align:start position:0%
+it's actually very difficult uh to
+ 
+
+ align:start position:0%
+it's actually very difficult uh to
+figure out whether this is compound noun
+
+ align:start position:0%
+figure out whether this is compound noun
+ 
+
+ align:start position:0%
+figure out whether this is compound noun
+or adjective and adjective and noun it's
+
+ align:start position:0%
+or adjective and adjective and noun it's
+ 
+
+ align:start position:0%
+or adjective and adjective and noun it's
+actually very difficult one thing you
+
+ align:start position:0%
+actually very difficult one thing you
+ 
+
+ align:start position:0%
+actually very difficult one thing you
+could do is to ask yourself if you could
+
+ align:start position:0%
+could do is to ask yourself if you could
+ 
+
+ align:start position:0%
+could do is to ask yourself if you could
+say what kind of Nest is it you can say
+
+ align:start position:0%
+say what kind of Nest is it you can say
+ 
+
+ align:start position:0%
+say what kind of Nest is it you can say
+it's a birth Nest then it's a compound
+
+ align:start position:0%
+it's a birth Nest then it's a compound
+ 
+
+ align:start position:0%
+it's a birth Nest then it's a compound
+down there that's just one of many ways
+
+ align:start position:0%
+down there that's just one of many ways
+ 
+
+ align:start position:0%
+down there that's just one of many ways
+if you say what kind of brush is it it's
+
+ align:start position:0%
+if you say what kind of brush is it it's
+ 
+
+ align:start position:0%
+if you say what kind of brush is it it's
+a toothbrush what kind of brush is it
+
+ align:start position:0%
+a toothbrush what kind of brush is it
+ 
+
+ align:start position:0%
+a toothbrush what kind of brush is it
+it's a hair brush paintbrush then then
+
+ align:start position:0%
+it's a hair brush paintbrush then then
+ 
+
+ align:start position:0%
+it's a hair brush paintbrush then then
+it's a compound now right you could say
+
+ align:start position:0%
+it's a compound now right you could say
+ 
+
+ align:start position:0%
+it's a compound now right you could say
+what kind of Nest is it right it's a
+
+ align:start position:0%
+what kind of Nest is it right it's a
+ 
+
+ align:start position:0%
+what kind of Nest is it right it's a
+black bird nest birdest so here it's a
+
+ align:start position:0%
+black bird nest birdest so here it's a
+ 
+
+ align:start position:0%
+black bird nest birdest so here it's a
+bird nest that is black but here it's
+
+ align:start position:0%
+bird nest that is black but here it's
+ 
+
+ align:start position:0%
+bird nest that is black but here it's
+black bird is a kind of kind of bird
+
+ align:start position:0%
+black bird is a kind of kind of bird
+ 
+
+ align:start position:0%
+black bird is a kind of kind of bird
+it's a black bird nest so you say black
+
+ align:start position:0%
+it's a black bird nest so you say black
+ 
+
+ align:start position:0%
+it's a black bird nest so you say black
+bird nest
+
+ align:start position:0%
+bird nest
+ 
+
+ align:start position:0%
+bird nest
+only only the Nast is Right which one
+
+ align:start position:0%
+only only the Nast is Right which one
+ 
+
+ align:start position:0%
+only only the Nast is Right which one
+this one the second one
+
+ align:start position:0%
+this one the second one
+ 
+
+ align:start position:0%
+this one the second one
+second one
+
+ align:start position:0%
+second one
+ 
+
+ align:start position:0%
+second one
+a black what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a black
+
+ align:start position:0%
+it's a black
+ 
+
+ align:start position:0%
+it's a black
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+nestest is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a flat bird nest yes Nest is black
+
+ align:start position:0%
+it's a flat bird nest yes Nest is black
+ 
+
+ align:start position:0%
+it's a flat bird nest yes Nest is black
+not a bird it's a flat bird nest the
+
+ align:start position:0%
+not a bird it's a flat bird nest the
+ 
+
+ align:start position:0%
+not a bird it's a flat bird nest the
+black bird nest not not not the bird
+
+ align:start position:0%
+black bird nest not not not the bird
+ 
+
+ align:start position:0%
+black bird nest not not not the bird
+nest is black nest is it's a nest that
+
+ align:start position:0%
+nest is black nest is it's a nest that
+ 
+
+ align:start position:0%
+nest is black nest is it's a nest that
+is black it's a bird nest that is black
+
+ align:start position:0%
+is black it's a bird nest that is black
+ 
+
+ align:start position:0%
+is black it's a bird nest that is black
+yes okay it's a it's a
+
+ align:start position:0%
+yes okay it's a it's a
+ 
+
+ align:start position:0%
+yes okay it's a it's a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+verb compounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verb compounds what you want to remember
+
+ align:start position:0%
+verb compounds what you want to remember
+ 
+
+ align:start position:0%
+verb compounds what you want to remember
+is just like noun compounds what do you
+
+ align:start position:0%
+is just like noun compounds what do you
+ 
+
+ align:start position:0%
+is just like noun compounds what do you
+do with the noun compounds where is the
+
+ align:start position:0%
+do with the noun compounds where is the
+ 
+
+ align:start position:0%
+do with the noun compounds where is the
+stress
+
+ align:start position:0%
+stress
+ 
+
+ align:start position:0%
+stress
+uh the first first one or the second one
+
+ align:start position:0%
+uh the first first one or the second one
+ 
+
+ align:start position:0%
+uh the first first one or the second one
+first one it doesn't matter whether it's
+
+ align:start position:0%
+first one it doesn't matter whether it's
+ 
+
+ align:start position:0%
+first one it doesn't matter whether it's
+adjective or noun the first one is
+
+ align:start position:0%
+adjective or noun the first one is
+ 
+
+ align:start position:0%
+adjective or noun the first one is
+always stressed in a in a verb compound
+
+ align:start position:0%
+always stressed in a in a verb compound
+ 
+
+ align:start position:0%
+always stressed in a in a verb compound
+it's all it's also the same you stress
+
+ align:start position:0%
+it's all it's also the same you stress
+ 
+
+ align:start position:0%
+it's all it's also the same you stress
+the first word okay you stress the first
+
+ align:start position:0%
+the first word okay you stress the first
+ 
+
+ align:start position:0%
+the first word okay you stress the first
+one here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is becoming this becomes
+
+ align:start position:0%
+now this is becoming this becomes
+ 
+
+ align:start position:0%
+now this is becoming this becomes
+important because last week we learned
+
+ align:start position:0%
+important because last week we learned
+ 
+
+ align:start position:0%
+important because last week we learned
+that when you have a prefix in a verb
+
+ align:start position:0%
+that when you have a prefix in a verb
+ 
+
+ align:start position:0%
+that when you have a prefix in a verb
+What Happens prefix usually
+
+ align:start position:0%
+What Happens prefix usually
+ 
+
+ align:start position:0%
+What Happens prefix usually
+no no stress right so you say
+
+ align:start position:0%
+no no stress right so you say
+ 
+
+ align:start position:0%
+no no stress right so you say
+overflow overflow ins insult
+
+ align:start position:0%
+overflow overflow ins insult
+ 
+
+ align:start position:0%
+overflow overflow ins insult
+conduct
+
+ align:start position:0%
+conduct
+ 
+
+ align:start position:0%
+conduct
+protest
+
+ align:start position:0%
+protest
+ 
+
+ align:start position:0%
+protest
+record record okay so you don't want to
+
+ align:start position:0%
+record record okay so you don't want to
+ 
+
+ align:start position:0%
+record record okay so you don't want to
+get those two mixed up okay that's a
+
+ align:start position:0%
+get those two mixed up okay that's a
+ 
+
+ align:start position:0%
+get those two mixed up okay that's a
+very common mistake students learn okay
+
+ align:start position:0%
+very common mistake students learn okay
+ 
+
+ align:start position:0%
+very common mistake students learn okay
+prefix wow in a verb
+
+ align:start position:0%
+prefix wow in a verb
+ 
+
+ align:start position:0%
+prefix wow in a verb
+you you stretch the second one okay oh
+
+ align:start position:0%
+you you stretch the second one okay oh
+ 
+
+ align:start position:0%
+you you stretch the second one okay oh
+that's easy and you you read something
+
+ align:start position:0%
+that's easy and you you read something
+ 
+
+ align:start position:0%
+that's easy and you you read something
+like this how sit and C goes right no
+
+ align:start position:0%
+like this how sit and C goes right no
+ 
+
+ align:start position:0%
+like this how sit and C goes right no
+these are compounds compounds compounds
+
+ align:start position:0%
+these are compounds compounds compounds
+ 
+
+ align:start position:0%
+these are compounds compounds compounds
+and words that has prefixes they are
+
+ align:start position:0%
+and words that has prefixes they are
+ 
+
+ align:start position:0%
+and words that has prefixes they are
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+Fact one compound nouns and verbs are
+
+ align:start position:0%
+Fact one compound nouns and verbs are
+ 
+
+ align:start position:0%
+Fact one compound nouns and verbs are
+always stressed in the first word there
+
+ align:start position:0%
+always stressed in the first word there
+ 
+
+ align:start position:0%
+always stressed in the first word there
+are no exceptions compound nouns and
+
+ align:start position:0%
+are no exceptions compound nouns and
+ 
+
+ align:start position:0%
+are no exceptions compound nouns and
+verbs always stressed in this uh first
+
+ align:start position:0%
+verbs always stressed in this uh first
+ 
+
+ align:start position:0%
+verbs always stressed in this uh first
+word fact two
+
+ align:start position:0%
+word fact two
+ 
+
+ align:start position:0%
+word fact two
+prefixes are not stressed in verbs okay
+
+ align:start position:0%
+prefixes are not stressed in verbs okay
+ 
+
+ align:start position:0%
+prefixes are not stressed in verbs okay
+there are no exceptions prefixes are
+
+ align:start position:0%
+there are no exceptions prefixes are
+ 
+
+ align:start position:0%
+there are no exceptions prefixes are
+never stressed in verbs and adjectives
+
+ align:start position:0%
+never stressed in verbs and adjectives
+ 
+
+ align:start position:0%
+never stressed in verbs and adjectives
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+but are stressed in nouns some nouns
+
+ align:start position:0%
+but are stressed in nouns some nouns
+ 
+
+ align:start position:0%
+but are stressed in nouns some nouns
+some some nouns we uh
+
+ align:start position:0%
+some some nouns we uh
+ 
+
+ align:start position:0%
+some some nouns we uh
+usually with Germanic prefixes okay and
+
+ align:start position:0%
+usually with Germanic prefixes okay and
+ 
+
+ align:start position:0%
+usually with Germanic prefixes okay and
+some latiny prefixes too so we have
+
+ align:start position:0%
+some latiny prefixes too so we have
+ 
+
+ align:start position:0%
+some latiny prefixes too so we have
+those two uh part of speech Al
+
+ align:start position:0%
+those two uh part of speech Al
+ 
+
+ align:start position:0%
+those two uh part of speech Al
+alternations record record right insult
+
+ align:start position:0%
+alternations record record right insult
+ 
+
+ align:start position:0%
+alternations record record right insult
+insult
+
+ align:start position:0%
+insult
+ 
+
+ align:start position:0%
+insult
+permit permit any other
+
+ align:start position:0%
+permit permit any other
+ 
+
+ align:start position:0%
+permit permit any other
+record huh record yeah record record any
+
+ align:start position:0%
+record huh record yeah record record any
+ 
+
+ align:start position:0%
+record huh record yeah record record any
+other words any other huh conduct
+
+ align:start position:0%
+other words any other huh conduct
+ 
+
+ align:start position:0%
+other words any other huh conduct
+conduct
+
+ align:start position:0%
+conduct
+ 
+
+ align:start position:0%
+conduct
+come on give me some give me some
+
+ align:start position:0%
+come on give me some give me some
+ 
+
+ align:start position:0%
+come on give me some give me some
+examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm conducting huh huh
+
+ align:start position:0%
+I'm conducting huh huh
+ 
+
+ align:start position:0%
+I'm conducting huh huh
+present present present present present
+
+ align:start position:0%
+present present present present present
+ 
+
+ align:start position:0%
+present present present present present
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you see did you see the movie
+
+ align:start position:0%
+did you see did you see the movie
+ 
+
+ align:start position:0%
+did you see did you see the movie
+momento
+
+ align:start position:0%
+momento
+ 
+
+ align:start position:0%
+momento
+momento
+
+ align:start position:0%
+momento
+ 
+
+ align:start position:0%
+momento
+m m stress is a men m m m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momento
+
+ align:start position:0%
+momento
+ 
+
+ align:start position:0%
+momento
+Latin yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M stress is meant momento
+
+ align:start position:0%
+M stress is meant momento
+ 
+
+ align:start position:0%
+M stress is meant momento
+in in Latin translation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stress is the second cell but momentum
+
+ align:start position:0%
+stress is the second cell but momentum
+ 
+
+ align:start position:0%
+stress is the second cell but momentum
+that's fine but in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh but it's now it's Engish Eng
+
+ align:start position:0%
+oh but it's now it's Engish Eng
+ 
+
+ align:start position:0%
+oh but it's now it's Engish Eng
+I don't care if it comes from Greek or
+
+ align:start position:0%
+I don't care if it comes from Greek or
+ 
+
+ align:start position:0%
+I don't care if it comes from Greek or
+Latin but we we say it as a as English
+
+ align:start position:0%
+Latin but we we say it as a as English
+ 
+
+ align:start position:0%
+Latin but we we say it as a as English
+word so it becomes momento momentum we
+
+ align:start position:0%
+word so it becomes momento momentum we
+ 
+
+ align:start position:0%
+word so it becomes momento momentum we
+say if you see that movie he writes like
+
+ align:start position:0%
+say if you see that movie he writes like
+ 
+
+ align:start position:0%
+say if you see that movie he writes like
+fact on his body right so I made this
+
+ align:start position:0%
+fact on his body right so I made this
+ 
+
+ align:start position:0%
+fact on his body right so I made this
+lesson after watching that movie so one
+
+ align:start position:0%
+lesson after watching that movie so one
+ 
+
+ align:start position:0%
+lesson after watching that movie so one
+a fact one fact two
+
+ align:start position:0%
+a fact one fact two
+ 
+
+ align:start position:0%
+a fact one fact two
+okay adjective compounds it's a little
+
+ align:start position:0%
+okay adjective compounds it's a little
+ 
+
+ align:start position:0%
+okay adjective compounds it's a little
+bit U more complicated verb compounds
+
+ align:start position:0%
+bit U more complicated verb compounds
+ 
+
+ align:start position:0%
+bit U more complicated verb compounds
+noun compounds always stress in the
+
+ align:start position:0%
+noun compounds always stress in the
+ 
+
+ align:start position:0%
+noun compounds always stress in the
+first syllable Okay add itive compounds
+
+ align:start position:0%
+first syllable Okay add itive compounds
+ 
+
+ align:start position:0%
+first syllable Okay add itive compounds
+usually
+
+ align:start position:0%
+usually
+ 
+
+ align:start position:0%
+usually
+the default is stressing the second one
+
+ align:start position:0%
+the default is stressing the second one
+ 
+
+ align:start position:0%
+the default is stressing the second one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+my dog's well trained my dog's well
+
+ align:start position:0%
+my dog's well trained my dog's well
+ 
+
+ align:start position:0%
+my dog's well trained my dog's well
+trained
+
+ align:start position:0%
+trained
+ 
+
+ align:start position:0%
+trained
+it's second hand
+
+ align:start position:0%
+it's second hand
+ 
+
+ align:start position:0%
+it's second hand
+second hand second
+
+ align:start position:0%
+second hand second
+ 
+
+ align:start position:0%
+second hand second
+he's good looking
+
+ align:start position:0%
+he's good looking
+ 
+
+ align:start position:0%
+he's good looking
+he's good looking
+
+ align:start position:0%
+he's good looking
+ 
+
+ align:start position:0%
+he's good looking
+looking not l l L Luke is Luke I'm your
+
+ align:start position:0%
+looking not l l L Luke is Luke I'm your
+ 
+
+ align:start position:0%
+looking not l l L Luke is Luke I'm your
+father okay look look he's good looking
+
+ align:start position:0%
+father okay look look he's good looking
+ 
+
+ align:start position:0%
+father okay look look he's good looking
+he's good looking okay but if these
+
+ align:start position:0%
+he's good looking okay but if these
+ 
+
+ align:start position:0%
+he's good looking okay but if these
+compound adjectives are followed by
+
+ align:start position:0%
+compound adjectives are followed by
+ 
+
+ align:start position:0%
+compound adjectives are followed by
+nouns then you shift the stress you put
+
+ align:start position:0%
+nouns then you shift the stress you put
+ 
+
+ align:start position:0%
+nouns then you shift the stress you put
+the stress at the the uh on the first
+
+ align:start position:0%
+the stress at the the uh on the first
+ 
+
+ align:start position:0%
+the stress at the the uh on the first
+word so you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well trained dog
+
+ align:start position:0%
+well trained dog
+ 
+
+ align:start position:0%
+well trained dog
+second second in bookstore
+
+ align:start position:0%
+second second in bookstore
+ 
+
+ align:start position:0%
+second second in bookstore
+bookstore
+
+ align:start position:0%
+bookstore
+ 
+
+ align:start position:0%
+bookstore
+secondhand bookstore second book
+
+ align:start position:0%
+secondhand bookstore second book
+ 
+
+ align:start position:0%
+secondhand bookstore second book
+secondhand bookstore second book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good looking
+
+ align:start position:0%
+good looking
+ 
+
+ align:start position:0%
+good looking
+haircut
+
+ align:start position:0%
+haircut
+ 
+
+ align:start position:0%
+haircut
+yes yes
+
+ align:start position:0%
+yes yes
+ 
+
+ align:start position:0%
+yes yes
+$10
+
+ align:start position:0%
+$10
+ 
+
+ align:start position:0%
+$10
+Har Harbor Square $10
+
+ align:start position:0%
+Har Harbor Square $10
+ 
+
+ align:start position:0%
+Har Harbor Square $10
+very cheap so I'm not a chip skate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the te numbers
+
+ align:start position:0%
+okay the te numbers
+ 
+
+ align:start position:0%
+okay the te numbers
+as well as Al hyphenated numbers are
+
+ align:start position:0%
+as well as Al hyphenated numbers are
+ 
+
+ align:start position:0%
+as well as Al hyphenated numbers are
+comp they're compound adjectives okay so
+
+ align:start position:0%
+comp they're compound adjectives okay so
+ 
+
+ align:start position:0%
+comp they're compound adjectives okay so
+for instance Isaiah was 17
+
+ align:start position:0%
+for instance Isaiah was 17
+ 
+
+ align:start position:0%
+for instance Isaiah was 17
+Isaiah was 17 repat after me Isaiah was
+
+ align:start position:0%
+Isaiah was 17 repat after me Isaiah was
+ 
+
+ align:start position:0%
+Isaiah was 17 repat after me Isaiah was
+17 Isaiah 1 Isaiah was 17 when he first
+
+ align:start position:0%
+17 Isaiah 1 Isaiah was 17 when he first
+ 
+
+ align:start position:0%
+17 Isaiah 1 Isaiah was 17 when he first
+came to America Isaiah was 17 is 1 but
+
+ align:start position:0%
+came to America Isaiah was 17 is 1 but
+ 
+
+ align:start position:0%
+came to America Isaiah was 17 is 1 but
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you say 17 years old
+
+ align:start position:0%
+you say 17 years old
+ 
+
+ align:start position:0%
+you say 17 years old
+the stress than seven 17 years old 17
+
+ align:start position:0%
+the stress than seven 17 years old 17
+ 
+
+ align:start position:0%
+the stress than seven 17 years old 17
+years old okay
+
+ align:start position:0%
+years old okay
+ 
+
+ align:start position:0%
+years old okay
+we're 27 years old
+
+ align:start position:0%
+we're 27 years old
+ 
+
+ align:start position:0%
+we're 27 years old
+but here so the stress is here 20 and 7
+
+ align:start position:0%
+but here so the stress is here 20 and 7
+ 
+
+ align:start position:0%
+but here so the stress is here 20 and 7
+here you say Isaiah Isaiah 27 is7
+
+ align:start position:0%
+here you say Isaiah Isaiah 27 is7
+ 
+
+ align:start position:0%
+here you say Isaiah Isaiah 27 is7
+I wish Isaiah 2 s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what no this is true look at the
+
+ align:start position:0%
+uh what no this is true look at the
+ 
+
+ align:start position:0%
+uh what no this is true look at the
+tense Isaiah is 27
+
+ align:start position:0%
+tense Isaiah is 27
+ 
+
+ align:start position:0%
+tense Isaiah is 27
+I kind of sto getting older after a
+
+ align:start position:0%
+I kind of sto getting older after a
+ 
+
+ align:start position:0%
+I kind of sto getting older after a
+certain point okay
+
+ align:start position:0%
+certain point okay
+ 
+
+ align:start position:0%
+certain point okay
+the T Numbers 30 and 70 are always
+
+ align:start position:0%
+the T Numbers 30 and 70 are always
+ 
+
+ align:start position:0%
+the T Numbers 30 and 70 are always
+stressed on the first syllable so you
+
+ align:start position:0%
+stressed on the first syllable so you
+ 
+
+ align:start position:0%
+stressed on the first syllable so you
+say so how do you tell the difference
+
+ align:start position:0%
+say so how do you tell the difference
+ 
+
+ align:start position:0%
+say so how do you tell the difference
+between 30 and 13 30 you put stress 30
+
+ align:start position:0%
+between 30 and 13 30 you put stress 30
+ 
+
+ align:start position:0%
+between 30 and 13 30 you put stress 30
+13 1 13 1 13 13 okay but here
+
+ align:start position:0%
+13 1 13 1 13 13 okay but here
+ 
+
+ align:start position:0%
+13 1 13 1 13 13 okay but here
+if you in cases like these we put stress
+
+ align:start position:0%
+if you in cases like these we put stress
+ 
+
+ align:start position:0%
+if you in cases like these we put stress
+on the third the 13
+
+ align:start position:0%
+on the third the 13
+ 
+
+ align:start position:0%
+on the third the 13
+or 30 so how do you tell the difference
+
+ align:start position:0%
+or 30 so how do you tell the difference
+ 
+
+ align:start position:0%
+or 30 so how do you tell the difference
+if the stress is moves to the first one
+
+ align:start position:0%
+if the stress is moves to the first one
+ 
+
+ align:start position:0%
+if the stress is moves to the first one
+13 very good flap flap you pay attention
+
+ align:start position:0%
+13 very good flap flap you pay attention
+ 
+
+ align:start position:0%
+13 very good flap flap you pay attention
+to the flap 30 if you hear a flap then
+
+ align:start position:0%
+to the flap 30 if you hear a flap then
+ 
+
+ align:start position:0%
+to the flap 30 if you hear a flap then
+it becomes a 10 10 30
+
+ align:start position:0%
+it becomes a 10 10 30
+ 
+
+ align:start position:0%
+it becomes a 10 10 30
+40 50
+
+ align:start position:0%
+40 50
+ 
+
+ align:start position:0%
+40 50
+50 50 60 7 okay 30 40 but 30 13 14 15
+
+ align:start position:0%
+50 50 60 7 okay 30 40 but 30 13 14 15
+ 
+
+ align:start position:0%
+50 50 60 7 okay 30 40 but 30 13 14 15
+okay you pay attention to the flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay reflexives
+
+ align:start position:0%
+okay reflexives
+ 
+
+ align:start position:0%
+okay reflexives
+are actually kind of you can think of it
+
+ align:start position:0%
+are actually kind of you can think of it
+ 
+
+ align:start position:0%
+are actually kind of you can think of it
+as exceptions
+
+ align:start position:0%
+as exceptions
+ 
+
+ align:start position:0%
+as exceptions
+because my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are two words right two words but
+
+ align:start position:0%
+these are two words right two words but
+ 
+
+ align:start position:0%
+these are two words right two words but
+then we always put stress in the second
+
+ align:start position:0%
+then we always put stress in the second
+ 
+
+ align:start position:0%
+then we always put stress in the second
+one myself myself yourself your
+
+ align:start position:0%
+one myself myself yourself your
+ 
+
+ align:start position:0%
+one myself myself yourself your
+himself ourselves ourselves themselves
+
+ align:start position:0%
+himself ourselves ourselves themselves
+ 
+
+ align:start position:0%
+himself ourselves ourselves themselves
+themselves okay
+
+ align:start position:0%
+themselves okay
+ 
+
+ align:start position:0%
+themselves okay
+yourselves
+
+ align:start position:0%
+yourselves
+ 
+
+ align:start position:0%
+yourselves
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to stop here we're going to
+
+ align:start position:0%
+we're going to stop here we're going to
+ 
+
+ align:start position:0%
+we're going to stop here we're going to
+uh take a look at phrasal verbs next
+
+ align:start position:0%
+uh take a look at phrasal verbs next
+ 
+
+ align:start position:0%
+uh take a look at phrasal verbs next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay H is very interesting
+
+ align:start position:0%
+okay H is very interesting
+ 
+
+ align:start position:0%
+okay H is very interesting
+they are playing cards
+
+ align:start position:0%
+they are playing cards
+ 
+
+ align:start position:0%
+they are playing cards
+they're playing cards say they're
+
+ align:start position:0%
+they're playing cards say they're
+ 
+
+ align:start position:0%
+they're playing cards say they're
+playing cards what does that mean
+
+ align:start position:0%
+playing cards what does that mean
+ 
+
+ align:start position:0%
+playing cards what does that mean
+they're playing cards
+
+ align:start position:0%
+they're playing cards
+ 
+
+ align:start position:0%
+they're playing cards
+deck of cards they're playing cards
+
+ align:start position:0%
+deck of cards they're playing cards
+ 
+
+ align:start position:0%
+deck of cards they're playing cards
+okay and they are and they are playing
+
+ align:start position:0%
+okay and they are and they are playing
+ 
+
+ align:start position:0%
+okay and they are and they are playing
+cars if you say they're playing cars
+
+ align:start position:0%
+cars if you say they're playing cars
+ 
+
+ align:start position:0%
+cars if you say they're playing cars
+they're playing cars they're playing
+
+ align:start position:0%
+they're playing cars they're playing
+ 
+
+ align:start position:0%
+they're playing cars they're playing
+playing games with the cards okay
+
+ align:start position:0%
+playing games with the cards okay
+ 
+
+ align:start position:0%
+playing games with the cards okay
+fascinating no just by moving the stress
+
+ align:start position:0%
+fascinating no just by moving the stress
+ 
+
+ align:start position:0%
+fascinating no just by moving the stress
+they're playing cards becomes they are
+
+ align:start position:0%
+they're playing cards becomes they are
+ 
+
+ align:start position:0%
+they're playing cards becomes they are
+NS they're playing cards playing becomes
+
+ align:start position:0%
+NS they're playing cards playing becomes
+ 
+
+ align:start position:0%
+NS they're playing cards playing becomes
+they're playing playing becomes a verb
+
+ align:start position:0%
+they're playing playing becomes a verb
+ 
+
+ align:start position:0%
+they're playing playing becomes a verb
+don't you find that fascinating
+
+ align:start position:0%
+don't you find that fascinating
+ 
+
+ align:start position:0%
+don't you find that fascinating
+the stress makes a huge difference
+
+ align:start position:0%
+the stress makes a huge difference
+ 
+
+ align:start position:0%
+the stress makes a huge difference
+what about K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are they washing machines
+
+ align:start position:0%
+are they washing machines
+ 
+
+ align:start position:0%
+are they washing machines
+this is something that we haven't talked
+
+ align:start position:0%
+this is something that we haven't talked
+ 
+
+ align:start position:0%
+this is something that we haven't talked
+about yet but we're going to talk about
+
+ align:start position:0%
+about yet but we're going to talk about
+ 
+
+ align:start position:0%
+about yet but we're going to talk about
+ination later on uh once you go up you
+
+ align:start position:0%
+ination later on uh once you go up you
+ 
+
+ align:start position:0%
+ination later on uh once you go up you
+don't want to come down are they washing
+
+ align:start position:0%
+don't want to come down are they washing
+ 
+
+ align:start position:0%
+don't want to come down are they washing
+machines
+
+ align:start position:0%
+machines
+ 
+
+ align:start position:0%
+machines
+washing you don't say are they washing
+
+ align:start position:0%
+washing you don't say are they washing
+ 
+
+ align:start position:0%
+washing you don't say are they washing
+machines you don't say are they are they
+
+ align:start position:0%
+machines you don't say are they are they
+ 
+
+ align:start position:0%
+machines you don't say are they are they
+washing machine if you you went up on
+
+ align:start position:0%
+washing machine if you you went up on
+ 
+
+ align:start position:0%
+washing machine if you you went up on
+washing right then you have to stay up
+
+ align:start position:0%
+washing right then you have to stay up
+ 
+
+ align:start position:0%
+washing right then you have to stay up
+are they washing machines
+
+ align:start position:0%
+are they washing machines
+ 
+
+ align:start position:0%
+are they washing machines
+you say are they washing machines
+
+ align:start position:0%
+you say are they washing machines
+ 
+
+ align:start position:0%
+you say are they washing machines
+are they washing machines
+
+ align:start position:0%
+are they washing machines
+ 
+
+ align:start position:0%
+are they washing machines
+and then washing becomes again again
+
+ align:start position:0%
+and then washing becomes again again
+ 
+
+ align:start position:0%
+and then washing becomes again again
+present participle washing a verb okay
+
+ align:start position:0%
+present participle washing a verb okay
+ 
+
+ align:start position:0%
+present participle washing a verb okay
+are there washing machines
+
+ align:start position:0%
+are there washing machines
+ 
+
+ align:start position:0%
+are there washing machines
+are they washing machines
+
+ align:start position:0%
+are they washing machines
+ 
+
+ align:start position:0%
+are they washing machines
+fascinating fascinating amazing
+
+ align:start position:0%
+fascinating fascinating amazing
+ 
+
+ align:start position:0%
+fascinating fascinating amazing
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other questions about this
+
+ align:start position:0%
+any other questions about this
+ 
+
+ align:start position:0%
+any other questions about this
+what about n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have have you ever seen a boardwalk
+
+ align:start position:0%
+have have you ever seen a boardwalk
+ 
+
+ align:start position:0%
+have have you ever seen a boardwalk
+have you ever seen a boardwalk
+
+ align:start position:0%
+have you ever seen a boardwalk
+ 
+
+ align:start position:0%
+have you ever seen a boardwalk
+or what does the second one mean have
+
+ align:start position:0%
+or what does the second one mean have
+ 
+
+ align:start position:0%
+or what does the second one mean have
+you ever seen a board walk have you ever
+
+ align:start position:0%
+you ever seen a board walk have you ever
+ 
+
+ align:start position:0%
+you ever seen a board walk have you ever
+seen a board walk
+
+ align:start position:0%
+seen a board walk
+ 
+
+ align:start position:0%
+seen a board walk
+what does that mean
+
+ align:start position:0%
+what does that mean
+ 
+
+ align:start position:0%
+what does that mean
+cartoon you know cartoon some boards
+
+ align:start position:0%
+cartoon you know cartoon some boards
+ 
+
+ align:start position:0%
+cartoon you know cartoon some boards
+they walk right have you ever seen a
+
+ align:start position:0%
+they walk right have you ever seen a
+ 
+
+ align:start position:0%
+they walk right have you ever seen a
+board walk walk is a verb there
+
+ align:start position:0%
+board walk walk is a verb there
+ 
+
+ align:start position:0%
+board walk walk is a verb there
+okay seen okay have you ever seen
+
+ align:start position:0%
+okay seen okay have you ever seen
+ 
+
+ align:start position:0%
+okay seen okay have you ever seen
+Michael Jordan play okay see something C
+
+ align:start position:0%
+Michael Jordan play okay see something C
+ 
+
+ align:start position:0%
+Michael Jordan play okay see something C
+is an interesting verb it takes a a be
+
+ align:start position:0%
+is an interesting verb it takes a a be
+ 
+
+ align:start position:0%
+is an interesting verb it takes a a be
+infinitive okay see watch him play see
+
+ align:start position:0%
+infinitive okay see watch him play see
+ 
+
+ align:start position:0%
+infinitive okay see watch him play see
+him play okay
+
+ align:start position:0%
+him play okay
+ 
+
+ align:start position:0%
+him play okay
+have you ever seen a board walk okay now
+
+ align:start position:0%
+have you ever seen a board walk okay now
+ 
+
+ align:start position:0%
+have you ever seen a board walk okay now
+let's turn to any other questions about
+
+ align:start position:0%
+let's turn to any other questions about
+ 
+
+ align:start position:0%
+let's turn to any other questions about
+this any other questions about compounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+okay now let's turn to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what where where are we now uh course
+
+ align:start position:0%
+what where where are we now uh course
+ 
+
+ align:start position:0%
+what where where are we now uh course
+packet page 66
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you turn to page 66
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're going to number off one
+
+ align:start position:0%
+okay so we're going to number off one
+ 
+
+ align:start position:0%
+okay so we're going to number off one
+two one two one two one two okay
+
+ align:start position:0%
+two one two one two one two okay
+ 
+
+ align:start position:0%
+two one two one two one two okay
+two two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you're number one you're
+
+ align:start position:0%
+okay so if you're number one you're
+ 
+
+ align:start position:0%
+okay so if you're number one you're
+going to be looking at uh page 66 okay
+
+ align:start position:0%
+going to be looking at uh page 66 okay
+ 
+
+ align:start position:0%
+going to be looking at uh page 66 okay
+your partner number one your friend
+
+ align:start position:0%
+your partner number one your friend
+ 
+
+ align:start position:0%
+your partner number one your friend
+number two
+
+ align:start position:0%
+number two
+ 
+
+ align:start position:0%
+number two
+uh you're going to look at page 67 okay
+
+ align:start position:0%
+uh you're going to look at page 67 okay
+ 
+
+ align:start position:0%
+uh you're going to look at page 67 okay
+so think about the stress think about
+
+ align:start position:0%
+so think about the stress think about
+ 
+
+ align:start position:0%
+so think about the stress think about
+the stress okay partner one for instance
+
+ align:start position:0%
+the stress okay partner one for instance
+ 
+
+ align:start position:0%
+the stress okay partner one for instance
+you say how many people were at your
+
+ align:start position:0%
+you say how many people were at your
+ 
+
+ align:start position:0%
+you say how many people were at your
+party
+
+ align:start position:0%
+party
+ 
+
+ align:start position:0%
+party
+and you just read your answer about 40
+
+ align:start position:0%
+and you just read your answer about 40
+ 
+
+ align:start position:0%
+and you just read your answer about 40
+40 okay get the flap there 40 okay and
+
+ align:start position:0%
+40 okay get the flap there 40 okay and
+ 
+
+ align:start position:0%
+40 okay get the flap there 40 okay and
+so you read eight eight you go through
+
+ align:start position:0%
+so you read eight eight you go through
+ 
+
+ align:start position:0%
+so you read eight eight you go through
+eight questions and then switch roles
+
+ align:start position:0%
+eight questions and then switch roles
+ 
+
+ align:start position:0%
+eight questions and then switch roles
+okay switch roles and partner two asks
+
+ align:start position:0%
+okay switch roles and partner two asks
+ 
+
+ align:start position:0%
+okay switch roles and partner two asks
+from 9 to 16 okay and partner one
+
+ align:start position:0%
+from 9 to 16 okay and partner one
+ 
+
+ align:start position:0%
+from 9 to 16 okay and partner one
+answers the question okay let's do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you answer
+
+ align:start position:0%
+you answer
+ 
+
+ align:start position:0%
+you answer
+how J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how old how old is your friend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manys there Circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looking for a pencil
+
+ align:start position:0%
+looking for a pencil
+ 
+
+ align:start position:0%
+looking for a pencil
+finished
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no not yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he 16 he 16 16 16 16 16 16
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+40 40
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll just do the finished
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+did you finish the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just do the first one now first one you
+
+ align:start position:0%
+just do the first one now first one you
+ 
+
+ align:start position:0%
+just do the first one now first one you
+finished the first one
+
+ align:start position:0%
+finished the first one
+ 
+
+ align:start position:0%
+finished the first one
+any questions
+
+ align:start position:0%
+any questions
+ 
+
+ align:start position:0%
+any questions
+any questions
+
+ align:start position:0%
+any questions
+ 
+
+ align:start position:0%
+any questions
+first one's very easy right okay uh what
+
+ align:start position:0%
+first one's very easy right okay uh what
+ 
+
+ align:start position:0%
+first one's very easy right okay uh what
+about 12
+
+ align:start position:0%
+about 12
+ 
+
+ align:start position:0%
+about 12
+what's the answer for uh 12 okay part
+
+ align:start position:0%
+what's the answer for uh 12 okay part
+ 
+
+ align:start position:0%
+what's the answer for uh 12 okay part
+part the partner partner two everyone
+
+ align:start position:0%
+part the partner partner two everyone
+ 
+
+ align:start position:0%
+part the partner partner two everyone
+partner two read question 12 please
+
+ align:start position:0%
+partner two read question 12 please
+ 
+
+ align:start position:0%
+partner two read question 12 please
+partner two
+
+ align:start position:0%
+partner two
+ 
+
+ align:start position:0%
+partner two
+one more time
+
+ align:start position:0%
+one more time
+ 
+
+ align:start position:0%
+one more time
+one more time
+
+ align:start position:0%
+one more time
+ 
+
+ align:start position:0%
+one more time
+how old is what Tyler Tyler okay and
+
+ align:start position:0%
+how old is what Tyler Tyler okay and
+ 
+
+ align:start position:0%
+how old is what Tyler Tyler okay and
+number one
+
+ align:start position:0%
+number one
+ 
+
+ align:start position:0%
+number one
+he's 16 he's 16 okay he's 16 he's 16 16
+
+ align:start position:0%
+he's 16 he's 16 okay he's 16 he's 16 16
+ 
+
+ align:start position:0%
+he's 16 he's 16 okay he's 16 he's 16 16
+okay okay now let's move on to any
+
+ align:start position:0%
+okay okay now let's move on to any
+ 
+
+ align:start position:0%
+okay okay now let's move on to any
+questions about number one
+
+ align:start position:0%
+questions about number one
+ 
+
+ align:start position:0%
+questions about number one
+okay let's move on to the second one the
+
+ align:start position:0%
+okay let's move on to the second one the
+ 
+
+ align:start position:0%
+okay let's move on to the second one the
+bottom one same thing if you're partner
+
+ align:start position:0%
+bottom one same thing if you're partner
+ 
+
+ align:start position:0%
+bottom one same thing if you're partner
+one you ask the question who drives a
+
+ align:start position:0%
+one you ask the question who drives a
+ 
+
+ align:start position:0%
+one you ask the question who drives a
+cap and you say partner two says what
+
+ align:start position:0%
+cap and you say partner two says what
+ 
+
+ align:start position:0%
+cap and you say partner two says what
+who drives a cap
+
+ align:start position:0%
+who drives a cap
+ 
+
+ align:start position:0%
+who drives a cap
+a cap driver cap driver
+
+ align:start position:0%
+a cap driver cap driver
+ 
+
+ align:start position:0%
+a cap driver cap driver
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+d r i v how say d r i
+
+ align:start position:0%
+d r i v how say d r i
+ 
+
+ align:start position:0%
+d r i v how say d r i
+driver driver grounding driver driver
+
+ align:start position:0%
+driver driver grounding driver driver
+ 
+
+ align:start position:0%
+driver driver grounding driver driver
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dishes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a b truck driver
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plays records on the radio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+news reporter
+
+ align:start position:0%
+news reporter
+ 
+
+ align:start position:0%
+news reporter
+reporter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+French French French teacher French
+
+ align:start position:0%
+French French French teacher French
+ 
+
+ align:start position:0%
+French French French teacher French
+teacher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+painter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the furnace so what kind of painter
+
+ align:start position:0%
+so the furnace so what kind of painter
+ 
+
+ align:start position:0%
+so the furnace so what kind of painter
+is he it's a sign painter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pain
+
+ align:start position:0%
+pain
+ 
+
+ align:start position:0%
+pain
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+no no no no no you put stress on the
+
+ align:start position:0%
+no no no no no you put stress on the
+ 
+
+ align:start position:0%
+no no no no no you put stress on the
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+
+ align:start position:0%
+first one this one p in the first
+ 
+
+ align:start position:0%
+first one this one p in the first
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dishwasher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dishwasher
+
+ align:start position:0%
+dishwasher
+ 
+
+ align:start position:0%
+dishwasher
+no dishwasher
+
+ align:start position:0%
+no dishwasher
+ 
+
+ align:start position:0%
+no dishwasher
+dishwashing machine it's person right
+
+ align:start position:0%
+dishwashing machine it's person right
+ 
+
+ align:start position:0%
+dishwashing machine it's person right
+who washes dishes yes dishwasher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound now it's a compound now right
+
+ align:start position:0%
+compound now it's a compound now right
+ 
+
+ align:start position:0%
+compound now it's a compound now right
+so you put stress in the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dishwasher dish
+
+ align:start position:0%
+dishwasher dish
+ 
+
+ align:start position:0%
+dishwasher dish
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+dishwashing machine dishwashing machine
+
+ align:start position:0%
+dishwashing machine dishwashing machine
+ 
+
+ align:start position:0%
+dishwashing machine dishwashing machine
+dish what do you diswashing yeah F
+
+ align:start position:0%
+dish what do you diswashing yeah F
+ 
+
+ align:start position:0%
+dish what do you diswashing yeah F
+dishwashing FH washing machine FH
+
+ align:start position:0%
+dishwashing FH washing machine FH
+ 
+
+ align:start position:0%
+dishwashing FH washing machine FH
+washing machine
+
+ align:start position:0%
+washing machine
+ 
+
+ align:start position:0%
+washing machine
+put dish washing machine
+
+ align:start position:0%
+put dish washing machine
+ 
+
+ align:start position:0%
+put dish washing machine
+dishwash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got me on that one
+
+ align:start position:0%
+you got me on that one
+ 
+
+ align:start position:0%
+you got me on that one
+I'm confused now dishwasher
+
+ align:start position:0%
+I'm confused now dishwasher
+ 
+
+ align:start position:0%
+I'm confused now dishwasher
+dishwasher
+
+ align:start position:0%
+dishwasher
+ 
+
+ align:start position:0%
+dishwasher
+do you have a dish
+
+ align:start position:0%
+do you have a dish
+ 
+
+ align:start position:0%
+do you have a dish
+I think so too
+
+ align:start position:0%
+I think so too
+ 
+
+ align:start position:0%
+I think so too
+dishwasher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we we'll look it up we'll look it
+
+ align:start position:0%
+yeah we we'll look it up we'll look it
+ 
+
+ align:start position:0%
+yeah we we'll look it up we'll look it
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay partner one number one partner one
+
+ align:start position:0%
+okay partner one number one partner one
+ 
+
+ align:start position:0%
+okay partner one number one partner one
+number one read the question partner one
+
+ align:start position:0%
+number one read the question partner one
+ 
+
+ align:start position:0%
+number one read the question partner one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+partner two answers the question
+
+ align:start position:0%
+partner two answers the question
+ 
+
+ align:start position:0%
+partner two answers the question
+tap driver
+
+ align:start position:0%
+tap driver
+ 
+
+ align:start position:0%
+tap driver
+okay number two
+
+ align:start position:0%
+okay number two
+ 
+
+ align:start position:0%
+okay number two
+okay answer
+
+ align:start position:0%
+okay answer
+ 
+
+ align:start position:0%
+okay answer
+a sign
+
+ align:start position:0%
+a sign
+ 
+
+ align:start position:0%
+a sign
+sign painter
+
+ align:start position:0%
+sign painter
+ 
+
+ align:start position:0%
+sign painter
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more time
+
+ align:start position:0%
+more time
+ 
+
+ align:start position:0%
+more time
+at a bank at a becomes a flap
+
+ align:start position:0%
+at a bank at a becomes a flap
+ 
+
+ align:start position:0%
+at a bank at a becomes a flap
+who counts money at a bank count aank
+
+ align:start position:0%
+who counts money at a bank count aank
+ 
+
+ align:start position:0%
+who counts money at a bank count aank
+okay so you do not want to say at you
+
+ align:start position:0%
+okay so you do not want to say at you
+ 
+
+ align:start position:0%
+okay so you do not want to say at you
+don't want to say at if you say at
+
+ align:start position:0%
+don't want to say at if you say at
+ 
+
+ align:start position:0%
+don't want to say at if you say at
+you're finished say
+
+ align:start position:0%
+you're finished say
+ 
+
+ align:start position:0%
+you're finished say
+a bank at a bank think of linoln at a
+
+ align:start position:0%
+a bank at a bank think of linoln at a
+ 
+
+ align:start position:0%
+a bank at a bank think of linoln at a
+bank okay the answer aank a bank teller
+
+ align:start position:0%
+bank okay the answer aank a bank teller
+ 
+
+ align:start position:0%
+bank okay the answer aank a bank teller
+a bank teller next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n a n doctor n doctor n doctor
+
+ align:start position:0%
+n a n doctor n doctor n doctor
+ 
+
+ align:start position:0%
+n a n doctor n doctor n doctor
+okay next
+
+ align:start position:0%
+okay next
+ 
+
+ align:start position:0%
+okay next
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+who puts out fires
+
+ align:start position:0%
+who puts out fires
+ 
+
+ align:start position:0%
+who puts out fires
+next the answer
+
+ align:start position:0%
+next the answer
+ 
+
+ align:start position:0%
+next the answer
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+fireman
+
+ align:start position:0%
+fireman
+ 
+
+ align:start position:0%
+fireman
+okay next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+louder
+
+ align:start position:0%
+louder
+ 
+
+ align:start position:0%
+louder
+okay next question
+
+ align:start position:0%
+okay next question
+ 
+
+ align:start position:0%
+okay next question
+okay the answer
+
+ align:start position:0%
+okay the answer
+ 
+
+ align:start position:0%
+okay the answer
+uh Milkman or milkman
+
+ align:start position:0%
+uh Milkman or milkman
+ 
+
+ align:start position:0%
+uh Milkman or milkman
+okay next
+
+ align:start position:0%
+okay next
+ 
+
+ align:start position:0%
+okay next
+number nine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a French teacher who teaches French
+
+ align:start position:0%
+a French teacher who teaches French
+ 
+
+ align:start position:0%
+a French teacher who teaches French
+French teacher 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer a carer okay 11
+
+ align:start position:0%
+the answer a carer okay 11
+ 
+
+ align:start position:0%
+the answer a carer okay 11
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the answer
+
+ align:start position:0%
+the answer
+ 
+
+ align:start position:0%
+the answer
+okay 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer truck dri truck driver truck
+
+ align:start position:0%
+answer truck dri truck driver truck
+ 
+
+ align:start position:0%
+answer truck dri truck driver truck
+driver truck driver
+
+ align:start position:0%
+driver truck driver
+ 
+
+ align:start position:0%
+driver truck driver
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+the answer
+
+ align:start position:0%
+the answer
+ 
+
+ align:start position:0%
+the answer
+a mailman
+
+ align:start position:0%
+a mailman
+ 
+
+ align:start position:0%
+a mailman
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh 14
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer Jo disc jockey
+
+ align:start position:0%
+answer Jo disc jockey
+ 
+
+ align:start position:0%
+answer Jo disc jockey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+doorman 16 driv a bus the answer
+
+ align:start position:0%
+doorman 16 driv a bus the answer
+ 
+
+ align:start position:0%
+doorman 16 driv a bus the answer
+okay any questions no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+report you can ready you can get ready
+
+ align:start position:0%
+report you can ready you can get ready
+ 
+
+ align:start position:0%
+report you can ready you can get ready
+to go home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+report reports is verb report is a verb
+
+ align:start position:0%
+report reports is verb report is a verb
+ 
+
+ align:start position:0%
+report reports is verb report is a verb
+and if this word is n you just a report
+
+ align:start position:0%
+and if this word is n you just a report
+ 
+
+ align:start position:0%
+and if this word is n you just a report
+I need to write a report yes report so
+
+ align:start position:0%
+I need to write a report yes report so
+ 
+
+ align:start position:0%
+I need to write a report yes report so
+that's yeah not all words not all pairs
+
+ align:start position:0%
+that's yeah not all words not all pairs
+ 
+
+ align:start position:0%
+that's yeah not all words not all pairs
+follow those part of speech altern
+
+ align:start position:0%
+follow those part of speech altern
+ 
+
+ align:start position:0%
+follow those part of speech altern
+pattern report report control control
+
+ align:start position:0%
+pattern report report control control
+ 
+
+ align:start position:0%
+pattern report report control control
+survey survey you know one thing
+
+ align:start position:0%
+survey survey you know one thing
+ 
+
+ align:start position:0%
+survey survey you know one thing
+actually you can get ready to pack up uh
+
+ align:start position:0%
+actually you can get ready to pack up uh
+ 
+
+ align:start position:0%
+actually you can get ready to pack up uh
+you know firemen
+
+ align:start position:0%
+you know firemen
+ 
+
+ align:start position:0%
+you know firemen
+that's actually supposed to be according
+
+ align:start position:0%
+that's actually supposed to be according
+ 
+
+ align:start position:0%
+that's actually supposed to be according
+to the rule you're not
+
+ align:start position:0%
+to the rule you're not
+ 
+
+ align:start position:0%
+to the rule you're not
+you're supposed to say what fire
+
+ align:start position:0%
+you're supposed to say what fire
+ 
+
+ align:start position:0%
+you're supposed to say what fire
+man
+
+ align:start position:0%
+man
+ 
+
+ align:start position:0%
+man
+because it's it's a compound right so
+
+ align:start position:0%
+because it's it's a compound right so
+ 
+
+ align:start position:0%
+because it's it's a compound right so
+suppos say firen it's not supposed to
+
+ align:start position:0%
+suppos say firen it's not supposed to
+ 
+
+ align:start position:0%
+suppos say firen it's not supposed to
+get reduced to awah but we say firemen
+
+ align:start position:0%
+get reduced to awah but we say firemen
+ 
+
+ align:start position:0%
+get reduced to awah but we say firemen
+but I mean now we don't even say firemen
+
+ align:start position:0%
+but I mean now we don't even say firemen
+ 
+
+ align:start position:0%
+but I mean now we don't even say firemen
+now we say what do we say firefighters
+
+ align:start position:0%
+now we say what do we say firefighters
+ 
+
+ align:start position:0%
+now we say what do we say firefighters
+right instead of policemen we say police
+
+ align:start position:0%
+right instead of policemen we say police
+ 
+
+ align:start position:0%
+right instead of policemen we say police
+officers right off but it's actually it
+
+ align:start position:0%
+officers right off but it's actually it
+ 
+
+ align:start position:0%
+officers right off but it's actually it
+does not follow the rule it's supposed
+
+ align:start position:0%
+does not follow the rule it's supposed
+ 
+
+ align:start position:0%
+does not follow the rule it's supposed
+to be police man but nobody says
+
+ align:start position:0%
+to be police man but nobody says
+ 
+
+ align:start position:0%
+to be police man but nobody says
+policeman polican becomes reduced right
+
+ align:start position:0%
+policeman polican becomes reduced right
+ 
+
+ align:start position:0%
+policeman polican becomes reduced right
+actually uh you you know friends you
+
+ align:start position:0%
+actually uh you you know friends you
+ 
+
+ align:start position:0%
+actually uh you you know friends you
+know Friends TV show Friends you know
+
+ align:start position:0%
+know Friends TV show Friends you know
+ 
+
+ align:start position:0%
+know Friends TV show Friends you know
+Joe not a smart guy in that show one of
+
+ align:start position:0%
+Joe not a smart guy in that show one of
+ 
+
+ align:start position:0%
+Joe not a smart guy in that show one of
+the episodes he goes
+
+ align:start position:0%
+the episodes he goes
+ 
+
+ align:start position:0%
+the episodes he goes
+you know what you know how we say
+
+ align:start position:0%
+you know what you know how we say
+ 
+
+ align:start position:0%
+you know what you know how we say
+policemen and firemen and other people
+
+ align:start position:0%
+policemen and firemen and other people
+ 
+
+ align:start position:0%
+policemen and firemen and other people
+go yeah and and Joe goes don't you think
+
+ align:start position:0%
+go yeah and and Joe goes don't you think
+ 
+
+ align:start position:0%
+go yeah and and Joe goes don't you think
+we should say Superman and Spiderman
+
+ align:start position:0%
+we should say Superman and Spiderman
+ 
+
+ align:start position:0%
+we should say Superman and Spiderman
+Batman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's actually the other way around
+
+ align:start position:0%
+but it's actually the other way around
+ 
+
+ align:start position:0%
+but it's actually the other way around
+right according to a rule we should say
+
+ align:start position:0%
+right according to a rule we should say
+ 
+
+ align:start position:0%
+right according to a rule we should say
+police man
+
+ align:start position:0%
+police man
+ 
+
+ align:start position:0%
+police man
+right not Superman follows the rule
+
+ align:start position:0%
+right not Superman follows the rule
+ 
+
+ align:start position:0%
+right not Superman follows the rule
+because it's a compound Superman Batman
+
+ align:start position:0%
+because it's a compound Superman Batman
+ 
+
+ align:start position:0%
+because it's a compound Superman Batman
+we're not supposed to say Batman okay
+
+ align:start position:0%
+we're not supposed to say Batman okay
+ 
+
+ align:start position:0%
+we're not supposed to say Batman okay
+okay for homework
+
+ align:start position:0%
+okay for homework
+ 
+
+ align:start position:0%
+okay for homework
+on Thursday there's no class on Thursday
+
+ align:start position:0%
+on Thursday there's no class on Thursday
+ 
+
+ align:start position:0%
+on Thursday there's no class on Thursday
+we have a Veterans Day what's on
+
+ align:start position:0%
+we have a Veterans Day what's on
+ 
+
+ align:start position:0%
+we have a Veterans Day what's on
+Thursday what
+
+ align:start position:0%
+Thursday what
+ 
+
+ align:start position:0%
+Thursday what
+get the flap veteran veteran Veteran Day
+
+ align:start position:0%
+get the flap veteran veteran Veteran Day
+ 
+
+ align:start position:0%
+get the flap veteran veteran Veteran Day
+okay on Tuesday please read these
+
+ align:start position:0%
+okay on Tuesday please read these
+ 
+
+ align:start position:0%
+okay on Tuesday please read these
+chapters chapter 13 and 14 for big
+
+ align:start position:0%
+chapters chapter 13 and 14 for big
+ 
+
+ align:start position:0%
+chapters chapter 13 and 14 for big
+picture and accur English chapter 8
\ No newline at end of file